diff --git a/.gitattributes b/.gitattributes
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@@ -2810,3 +2810,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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diff --git a/2023/Fantasia3D_ Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation/5c5d4c5d-3820-44df-916a-bfeef9c352be_content_list.json b/2023/Fantasia3D_ Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation/5c5d4c5d-3820-44df-916a-bfeef9c352be_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2c5eb2106e09b7c4434a547040dda1f2175888a9
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+++ b/2023/Fantasia3D_ Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation/5c5d4c5d-3820-44df-916a-bfeef9c352be_content_list.json	
@@ -0,0 +1,1805 @@
+[
+    {
+        "type": "text",
+        "text": "Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation",
+        "text_level": 1,
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+            127,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Rui Chen,\\* Yongwei Chen,\\* Ningxin Jiao, Kui Jia\\* South China University of Technology",
+        "bbox": [
+            294,
+            202,
+            679,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+            273,
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+            289
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.",
+        "bbox": [
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+        "type": "text",
+        "text": "1. Introduction",
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+    {
+        "type": "text",
+        "text": "Automatic 3D content creation [43, 18, 33, 44] powered by large language models has drawn significant attention recently, due to its convenience to entertaining and gaming industries, virtual/augmented reality, and robotic applications. The traditional process of creating 3D assets typically involves multiple, labor-intensive stages, including geome",
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+        "image_caption": [
+            "generation"
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+        "image_caption": [
+            "soft body simulation"
+        ],
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+        "img_path": "images/81e844df219938fd9a1c280d47899aa8d89aa4fd386b6e849704c8af9889bb14.jpg",
+        "image_caption": [
+            "cloth simulation"
+        ],
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+        "img_path": "images/54615609df4386e2bd48d11e5254e4d2b89e52bda915aa9211934a0fee8d4a9a.jpg",
+        "image_caption": [
+            "material editing",
+            "Figure 1. Provided with a textual description of \"a highly detailed stone bust of Theodoros Kolokotronis\", our method produces high-quality geometry as well as disentangled materials, and enables photorealistic rendering."
+        ],
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+        "image_caption": [
+            "material"
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+        "img_path": "images/be0ba8595891df06b02efd6cc89aa298288081bfb2422bcaa638683f2c9b5141.jpg",
+        "image_caption": [
+            "geometry"
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+    {
+        "type": "text",
+        "text": "try modeling, shape baking, UV mapping, material creation, and texturing, as described in [15], where different software tools and the expertise of skilled artists are often required. Imperfections would also accumulate across these stages, resulting in low-quality 3D assets. It is thus desirable to automate such a process, and ideally to generate high-quality 3D assets that have geometrically fair surfaces, rich materials and textures, and support photorealistic rendering under arbitrary views.",
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+    {
+        "type": "text",
+        "text": "In this work, we focus on automatic 3D content creation given text prompts encoded by large language models, i.e., the text-to-3D tasks [18, 33]. Text-to-3D is inspired by the tremendous success of text-to-image research [34, 36, 30, 35]. To enable 3D generation, most existing methods [33, 23] rely on the implicit scene modeling of Neural Radiance Field (NeRF) [25, 4, 27], and learn the NeRFs by back-propagating the supervision signals from image diffusion models. However, NeRF modeling is less effective for surface recovery [43, 46], since it couples the learning of surface geometry with that of pixel colors via volume rendering. Consequently, 3D creation based on",
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+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "* Equal contribution.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "22246",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "NeRF modeling is less effective for recovery of both the fine surface and its material and texture. In the meanwhile, explicit and hybrid scene representations [43, 46, 38] are proposed to improve over NeRF by modeling the surface explicitly and performing view synthesis via surface rendering.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we are motivated to use 3D scene representations that are more amenable to the generation of high-quality 3D assets given text prompts. We present an automatic text-to-3D method called Fantasia3D. Key to Fantasia3D is a disentangled learning of geometry and appearance models, such that both a fine surface and a rich material/texture can be generated. To enable such a disentangled learning, we use the hybrid scene representation of DMTET [38], which maintains a deformable tetrahedral grid and a differentiable mesh extraction layer; deformation can thus be learned through the layer to explicitly control the shape generation. For geometry learning, we technically propose to encode a rendered normal map, and use shape encoding of the normal as the input of a pre-trained, image diffusion model; this is in contrast different from existing methods that commonly encode rendered color images. For appearance modeling, we introduce, for the first time, the spatially varying Bidirectional Reflectance Distribution Function (BRDF) into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. We implement the geometry model and the BRDF appearance model as simple MLPs. Both models are learned through the pre-trained image diffusion model, using a loss of Score Distillation Sampling (SDS) [33]. We use the pre-trained stable diffusion [35, 40] as the image generation model in this work.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We note that except for text prompts, our method can also be triggered with additional inputs of users' preferences, such as a customized 3D shape or a generic 3D shape of a certain object category; this is flexible for users to better control what content is to be generated. In addition, given the disentangled generation of geometry and appearance, it is convenient for our method to support relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments to verify the efficacy of our proposed methods. Results show that our proposed Fantasia3D outperforms existing methods for high-quality and diverse 3D content creation. We summarize our technical contributions as follows.",
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+    {
+        "type": "text",
+        "text": "- We propose a novel method, termed Fantasia3D, for high-quality text-to-3D content creation. Our method disentangles the modeling and learning of geometry and appearance, and thus enables both a fine recovery of geometry and photorealistic rendering of per-view images.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "- For geometry learning, we use a hybrid representation",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "of DMTET, which supports learning surface deformation via a differentiable mesh extraction; we propose to render and encode the surface normal extracted from DMTET as the input of the pre-trained image diffusion model, which enables more subtle control of shape generation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "- For appearance modeling, to the best of our knowledge, we are the first to introduce the full BRDF learning into text-to-3D content creation, facilitated by our proposed geometry-appearance disentangled framework. BRDF modeling promises high-quality 3D generation via photorealistic rendering.",
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+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Text-to-3D content creation. Motivated by the desire to generate high-quality 3D content from simple semantics such as text prompts, text-to-3D has drawn considerable attention in recent years [33, 13, 18]. Existing methods either use pre-trained 2D text-to-image models [35, 3, 36], together with score distillation sampling [33], to generate 3D geometries [18] or synthesize novel views [33], or train a text-conditioned 3D generative model from scratch [39, 49, 17, 29]. These methods generate 3D geometries with little exploration of generating high-quality lighting and surface materials. On the other hand, TANGO [8] is able to generate high-quality surface materials given text prompts; unfortunately, the method requires as input a 3D surface mesh. Our proposed method addresses the shortcomings of the above methods, and is able to generate both high-quality surface geometries and their corresponding materials, both of which are crucial for photorealistic rendering of the generated 3D content. Our method thus, for the first time, closes the loop of object-level text-to-3D content creation.",
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+    {
+        "type": "text",
+        "text": "Surface material estimation. The estimation of surface materials is a long-standing challenge in computer vision and graphics research. Earlier methods [2, 45] focus on recovering physically based materials under known lighting conditions, whose usefulness is, however, limited in real-world scenarios. Subsequent methods [12, 11, 5, 1] try to estimate materials under natural lighting conditions, assuming the availability of complete geometry information. More recently, the joint reconstruction of geometry and materials is proposed given calibrated multi-view images [6, 7, 19, 48]. Alternative to these methods, we explore the novel creation of surface materials and geometries from trained language models.",
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+        "text": "3. Preliminary",
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+    {
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+        "text": "In this section, we present a few preliminaries that are necessary for presenting our proposed method in Section 4.",
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+        "image_caption": [
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+        "image_caption": [
+            "\"A German Sheperd\""
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+        "image_caption": [
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+        "image_caption": [
+            "Figure 2. Results of our method. The upper portion of this figure showcases the generation results obtained from solely text prompts. The lower portion showcases user-guided generation results given guiding meshes with the corresponding textual descriptions."
+        ],
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+        "text": "3.1. Score distillation sampling",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "DreamFusion [33] presents a method that optimizes 3D scene parameters and synthesizes novel views from tex-",
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+    {
+        "type": "text",
+        "text": "tual descriptions, by employing a pre-trained 2D diffusion model. The scene is represented as a differentiable image parameterization [26], where a differentiable generator  $g$",
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+        "image_caption": [
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+            "(a) Disentangled representation"
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+        "image_caption": [
+            "\" a highly detailed stone bust of Theodoros Kolokotronis \"",
+            "appearance"
+        ],
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+        "image_caption": [
+            "$k_{n}$"
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+        "page_idx": 3
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+        "image_caption": [
+            "(c) Appearance modeling",
+            "Figure 3. Overview of our method. Our method can generate disentangled geometry and appearance given a text prompt (cf. figure (a)), which are produced by (b) geometry modeling and (c) appearance modeling, respectively. (b) We employ DMTET as our 3D geometry representation, which is initialized as a 3D ellipsoid here. To optimize the parameters of DMTET, we render the normal map (and the object mask in the early training phase) of the extracted mesh from DMTet as the shape encoding of stable diffusion [35, 40]. (c) For appearance modeling, we introduce the spatially-varying Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn to predict three components (namely,  $k_d$ ,  $k_{rm}$ , and  $k_n$ ) of the appearance. Both geometry and appearance modeling are supervised by Score Distillation Sampling (SDS) loss [33]."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            573,
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "renders 2D images  $x = g(\\theta)$  from a modified Mip-NeRF [4] parameterized as  $\\theta$ . DreamFusion leverages a diffusion model  $\\phi$  (Imagen [36] in this instance) to provide a score function  $\\hat{\\epsilon}_{\\phi}(x_t; y, t)$ , which predicts the sampled noise  $\\epsilon$  given the noisy image  $x_t$ , text-embedding  $y$ , and noise level  $t$ . This score function guides the direction of the gradient for updating the scene parameters  $\\theta$ , and the gradient is calculated by Score Distillation Sampling (SDS):",
+        "bbox": [
+            75,
+            364,
+            472,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bigtriangledown_ {\\theta} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , x) = \\mathbb {E} _ {t, \\epsilon} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(x _ {t}; y, t\\right) - \\epsilon\\right) \\frac {\\partial x}{\\partial \\theta} \\right], \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            493,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "while  $w(t)$  is a weighting function. Since Imagen is not publicly accessible, in this work, we use the released latent space diffusion model of Stable Diffusion [35, 40] as our guidance model, and revise the SDS loss (1) accordingly. Details are given in Section 4.2.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.DMTET",
+        "text_level": 1,
+        "bbox": [
+            76,
+            618,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Implicit surface representations [25, 31, 22] are popularly used in novel view synthesis and 3D reconstruction, due to their capabilities to represent complex scenes. However, surfaces of lower quality may be obtained [28] by extracting explicit meshes from these implicit representations using marching cubes [20]. Instead, Shen et al. [38] propose a hybrid representation, termed DMTET, that has two key features, i.e., a deformable tetrahedral grid and a differentiable Marching Tetrahedral (MT) layer. The deformable tetrahedral grid  $(V_{T}, T)$  has vertices  $V_{T}$  in the tetrahedral grid  $T$ . For each vertex  $v_{i} \\in V_{T}$ , the proposed method predicts the Signed Distance Function (SDF) value  $s(v_{i})$  and a position offset  $\\triangle v_{i}$  by:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n(s (v _ {i}), \\triangle v _ {i}) = \\Psi (v _ {i}; \\psi), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\psi$  is the parameters of a network  $\\Psi$ , enabling the extraction of explicit meshes through MT layer during each",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "iteration of training. In this work, We use DMTET as our geometry representation and render the mesh extracted from MT layer iteratively by a differentiable renderer[16, 28].",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. The Proposed Method",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present our proposed method of Fantasia3D for high-quality text-to-3D object generation, by disentangling the modeling and learning of geometry and appearance. For geometry modeling, we rely on the hybrid surface representation of DMTET, and parameterize the 3D geometry as an MLP  $\\Psi$  that learns to predict the SDF value and position offset for each vertex in the deformable tetrahedral grid of DMTET; in contrast to previous methods, we propose to use the rendered normal map (and the object mask in the early training phase) of the extracted mesh from DMTET as the input of shape encoding. For appearance modeling, we introduce, for the first time, the full Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn an MLP  $\\Gamma$  that predicts parameters of surface material and supports high-quality 3D generation via photorealistic rendering. Given the disentangled modeling of  $\\Psi$  and  $\\Gamma$ , the whole pipeline is learned with SDS supervision, and the gradients are backpropagated through the pre-trained stable diffusion model. Our pipeline is initialized either as a 3D ellipsoid or as a customized 3D model provided by users. Fig. 3 gives an illustration of our proposed method. In contrast, previous methods couple the geometry and appearance learning, and are suboptimal in terms of leveraging the powerful pretrained 2D image diffusion models via SDS loss. Details of the proposed Fantasia3D are presented as follows.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22249",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. DMTET initialization",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            274,
+            104
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We adopt DMTET as our 3D scene representation, which is parameterized as the MLP network  $\\Psi$ . For each vertex  $v_{i} \\in V_{T}$  of the tetrahedral grid  $(V_{T}, T)$ ,  $\\Psi$  is trained to predict the SDF value  $s(v_{i})$  and the deformation offset  $\\triangle v_{i}$ . A triangular mesh can be extracted from  $(V_{T}, T)$  using the MT layer, whose procedure is also differentiable w.r.t. the parameters of  $\\Psi$ . We initialize DMTET either as a 3D ellipsoid or as a customized 3D model provided by users; the latter choice is useful when the text-to-3D task is to be conditioned on users' preferences. In either case, we initialize  $\\Psi$  by the following fitting procedure. We sample a point set  $\\{p_{i} \\in \\mathbb{R}^{3}\\}$  whose points are in close proximity to the initialized 3D ellipsoid or customized model, and compute their SDF values, resulting in  $\\{SDF(p_{i})\\}$ ; we use the following loss to optimize the parameters  $\\psi$  of  $\\Psi$ :",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S D F}} = \\sum_ {p _ {i} \\in P} \\| s (p _ {i}; \\psi) - S D F (p _ {i}) \\| _ {2} ^ {2}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Geometry modeling",
+        "text_level": 1,
+        "bbox": [
+            76,
+            392,
+            267,
+            407
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Previous text-to-3D methods [33, 13] commonly use NeRF [25, 4] as the implicit scene representation, which couples the geometry with color/appearance and use volume rendering for view synthesis. Since NeRF modeling is less effective for surface reconstruction [43, 46], these methods are consequently less effective to generate high-quality 3D surfaces by back-propagating the supervision of SDS loss through pre-trained text-to-image models. As a remedy, the method [18] uses a second stage of the refined generation that is based on scene modeling of explicit surfaces.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose to decouple the generation of geometry from that of appearance, based on the hybrid scene representation of DMTET, which enables photorealistic surface rendering to make better use of the powerful pre-trained text-to-image models. More specifically, given the current DMTET with MLP parameters  $\\psi$ , we generate a normal map  $n$ , together with an object mask  $o$ , as:",
+        "bbox": [
+            75,
+            580,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n(n, o) = g _ {n} (\\psi , c), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            210,
+            698,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $g_{n}$  is a differentiable render (e.g., nvidiffrast [16]), and  $c$  is a sampled camera pose. We randomly sample the camera poses in the spherical coordinate system to ensure that the camera poses are distributed uniformly on the sphere. We propose to use the generated  $n$  (and  $o$ ) as the input of shape encoding to connect with stable diffusion. To update  $\\psi$ , we again employ SDS loss that computes the gradient w.r.t.  $\\psi$  as:",
+        "bbox": [
+            75,
+            723,
+            468,
+            845
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bigtriangledown_ {\\psi} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , \\tilde {n}) = \\mathbb {E} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(z _ {t} ^ {\\tilde {n}}; y, t\\right) - \\epsilon\\right) \\frac {\\partial \\tilde {n}}{\\partial \\psi} \\frac {\\partial z ^ {\\tilde {n}}}{\\partial \\tilde {n}} \\right], \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            854,
+            468,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/a9292b7196f2979ecd8e71863033957bbc30c2bcbd57e8c1788c7ee7c010a3c1.jpg",
+        "image_caption": [
+            "Figure 4. Three components of the material model, namely the diffuse term  $k_{d}$ , the roughness and metallic term  $k_{rm}$ , and the normal variation term  $k_{n}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            517,
+            90,
+            874,
+            200
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/6f644163abc5fb23b018f1347ed4afa289c4ffc69a52407db83b1811defae0e5.jpg",
+        "image_caption": [
+            "Figure 5. A comparison of UV edge padding (cf. the left column) and original texturing (cf. the right column). UV edge padding removes the white seams that appear in the right rendering."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            513,
+            287,
+            880,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\phi$  parameterizes the pre-trained stable diffusion model,  $\\tilde{n}$  denotes concatenation of the normal  $n$  with the mask  $o$ ,  $z^{\\tilde{n}}$  is the latent code of  $\\tilde{n}$  via shape encoding,  $\\hat{\\epsilon}_{\\phi}(z_t^{\\tilde{n}};y,t)$  is the predicted noise given text embedding  $y$  and noise level  $t$ , and  $\\epsilon$  is the noise added in  $z_t^{\\tilde{n}}$ . In practice, we utilize a coarse-to-fine strategy to model the geometry. During the early phase of training, we use the downsampled  $\\tilde{n}$  as the latent code, which is inspired by [23], to rapidly update  $\\Psi$  and attain a coarse shape. However, a domain gap exists between  $\\tilde{n}$  and the latent space data distribution learned by the VAE encoder in the stable diffusion, which may lead to a mismatch of the generated geometry from the textual description. To mitigate this discrepancy, we implement a data augmentation technique by introducing random rotations to  $\\tilde{n}$ . Our experimental observations reveal that this technique enhances the alignment between the generated geometry and the provided textual description. In the later phase of training, aiming to capture finer geometric details with greater precision, we encode the high-resolution normal  $n$  (without the mask  $o$ ) to derive  $z^n$ , using the pretrained image encoder in stable diffusion.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "22250",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Appearance modeling",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            281,
+            107
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Given a learned DMTET with geometry parameters  $\\psi$ , we aim for photorealistic surface rendering to better leverage the powerful image diffusion model. This is achieved by introducing into text-to-3D generation the Physically-Based Rendering (PBR) material model. As illustrated in Fig. 4, the material model we use [21] comprises three components, namely the diffuse term  $k_{d} \\in \\mathbb{R}^{3}$ , the roughness and metallic term  $k_{rm} \\in \\mathbb{R}^{2}$ , and the normal variation term  $k_{n} \\in \\mathbb{R}^{3}$ . The  $k_{d}$  term denotes the diffuse value, while the  $k_{rm}$  term encompasses the roughness  $r$  and metalness  $m$ ; the roughness  $r$  serves as a metric for measuring the extent of specular reflection and a parameter of the GGX [42] normal distribution function in the rendering equation. The metalness parameter  $m$  and diffuse value  $k_{d}$  can be used to compute the specular term  $k_{s}$  using  $k_{s} = (1 - m) \\cdot 0.04 + m \\cdot k_{d}$ . Furthermore, we use a normal variation  $k_{n}$  in tangent space to enhance the surface lighting effect and introduce additional geometric variations.",
+        "bbox": [
+            75,
+            114,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We use an MLP  $\\Gamma$  as our parameterized material model.  $\\Gamma$  is learned to predict spatially varying material parameters, which are subsequently used to render the surface extracted from DMTET. More specifically, for any point  $p\\in \\mathbb{R}^3$  on the surface, we use hash-grid positional encoding [27], and generate the diffuse term  $k_{d}$ , the specular term  $k_{rm}$ , and the tangent space normal  $k_{n}$  as:",
+        "bbox": [
+            75,
+            387,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(k _ {d}, k _ {r m}, k _ {n}\\right) = \\Gamma (\\beta (p); \\gamma), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            179,
+            507,
+            468,
+            525
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\beta$  is the positional encoding of  $p$ , and  $\\gamma$  parameterizes the MLP  $\\Gamma$ . The basic rendering equation suggests that each image pixel at a specific viewing direction can be rendered as",
+        "bbox": [
+            75,
+            537,
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+            595
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL (p, \\omega) = \\int_ {\\Omega} L _ {i} (p, \\omega_ {i}) f (p, \\omega_ {i}, \\omega) (\\omega_ {i} \\cdot n _ {p}) \\mathrm {d} \\omega_ {i}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            104,
+            608,
+            468,
+            641
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $L$  is the rendered pixel color along the direction  $\\omega$  from the surface point  $p$ ,  $\\Omega = \\{\\omega_i : \\omega_i \\cdot n_p \\geq 0\\}$  denotes a hemisphere with the incident direction  $\\omega_i$  and surface normal  $n_p$  at  $p$ ,  $L_i$  is the incident light that is represented by an off-the-shelf environment map [32], and  $f$  is the BRDF determined by the material parameters  $(k_d, k_{rm}, k_n)$  predicted by (6). We note that  $L$  is the summation of diffuse intensity  $L_d$  and specular intensity  $L_s$ , and the two terms can be computed as follows:",
+        "bbox": [
+            75,
+            652,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L (p, \\omega) = L _ {d} (p) + L _ {s} (p, \\omega), \\\\ L _ {d} (p) = k _ {d} (1 - m) \\int_ {\\Omega} L _ {i} (p, \\omega_ {i}) (\\omega_ {i} \\cdot n _ {p}) \\mathrm {d} \\omega_ {i}, \\\\ L _ {s} (p, \\omega) = \\int_ {\\Omega} \\frac {D F G}{4 (\\omega \\cdot n _ {p}) \\left(\\omega_ {i} \\cdot n _ {p}\\right)} L _ {i} \\left(p, \\omega_ {i}\\right) \\left(\\omega_ {i} \\cdot n _ {p}\\right) \\mathrm {d} \\omega_ {i}, \\tag {8} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            88,
+            803,
+            468,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $F$ ,  $G$ , and  $D$  represent the Fresnel term, the shadowing-mask term, and the GGX distribution of normal, respectively. Following [28], the hemisphere integration can be calculated using the split-sum method.",
+        "bbox": [
+            496,
+            90,
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+            151
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "By aggregating the rendered pixel colors along the direction  $\\omega$  (i.e., camera pose), we have the rendered image  $x = \\{L(p,\\omega)\\}$  that connects with the image encoder of the pre-trained stable diffusion model. We update the parameters  $\\gamma$  by computing the gradient of the SDS loss w.r.t.  $\\gamma$ :",
+        "bbox": [
+            496,
+            151,
+            890,
+            227
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla_ {\\gamma} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , x) = \\mathbb {E} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(z _ {t} ^ {x}; y, t\\right) - \\epsilon\\right) \\frac {\\partial x}{\\partial \\gamma} \\frac {\\partial z ^ {x}}{\\partial x} \\right]. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            508,
+            247,
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+            281
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Notations in (9) are similarly defined as those in (5).",
+        "bbox": [
+            496,
+            289,
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+            303
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Texturing. Given the trained  $\\Gamma$ , we proceed by sampling the generated appearance as 2D texture maps, in accordance with the UV map generated by the xatlas [47]. Note that texture seams would emerge by direct incorporation of the sampled 2D textures into graphics engines (e.g., Blender [10]). We instead employ the UV edge padding technique [9], which involves expanding the boundaries of UV islands and filling empty regions. As illustrated in Fig. 5, this padding technique removes background pixels in the texture map and also removes the seams in the resulting renderings.",
+        "bbox": [
+            496,
+            304,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We implement the network  $\\Psi$  as a three-layer MLP with 32 hidden units, and implement  $\\Gamma$  as a two-layer MLP with 32 hidden units. Our method is optimized on 8 Nvidia RTX 3090 GPUs for about 15 minutes for learning  $\\Psi$  and about 16 minutes for learning  $\\Gamma$ , respectively, where we use AdamW optimizer with the respective learning rates of  $1 \\times 10^{-3}$  and  $1 \\times 10^{-2}$ . For each iteration, we uniformly sample 24 camera poses for the rendering of normal maps and colored images. More details of our implementation are available in the supplemental material. In geometry modeling, we set  $\\omega(t) = \\sigma^2$  during the early phase and then transition to  $w(t) = \\sigma^2 \\sqrt{1 - \\sigma^2}$  as we progress to the later phase. In appearance modeling, we apply  $w(t) = \\sigma^2 \\sqrt{1 - \\sigma^2}$  during the early phase, followed by a shift to  $1 / \\sigma^2$  as we enter the later phase. This approach mitigates the issue related to over-saturated color within the appearance modeling.",
+        "bbox": [
+            496,
+            455,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            724,
+            630,
+            741
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present comprehensive experiments to evaluate the efficacy of our proposed method for text-to-3D content creation. We first conduct ablation studies in Section 5.1 that verify the importance of our key design of disentangling geometry and appearance for text-to-3D generation. In Section 5.2, we show the efficacy of our method for the generation of 3D models with PBR materials from arbitrary text prompts, where we also compare with two recent state-of-the-art methods (namely, Magic3D [18] and DreamFusion [33]). In Section 5.3, we present our results",
+        "bbox": [
+            496,
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+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "22251",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "under the setting of user-guided generation and compare them with Latent-NeRF [23]. We finally demonstrate in Section 5.4 that the 3D assets generated by our method are readily compatible with popular graphics engines such as Blender [10], thus facilitating relighting, editing, and physical simulation of the resulting 3D models.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1. Ablation studies",
+        "text_level": 1,
+        "bbox": [
+            80,
+            195,
+            235,
+            209
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We use an example text prompt of \"a highly detailed stone bust of Theodoros Kolokotronis\" for the ablation studies. Results of alternative settings are given in Fig. 6. As the reference, the first two columns show the geometry and appearance results of our Fantasia3D rendered from the front and back views. To verify the effectiveness of the disentangled design in Fantasia3D, we also conduct experiments as follows: in each iteration, we render shaded images of the mesh extracted from DMTET, and learn to update the parameters of a network responsible for both the geometry and material, using the gradient computed by SDS loss. Results in the second two columns show that such an entangled learning fails to generate plausible results. Previous methods (e.g., DreamFusion [33] and Magic3D [18]) couple the geometry and appearance generation together, following NeRF [25]. Our adoption of the disentangled representation is mainly motivated by the difference of problem nature for generating surface geometry and appearance. In fact, when dealing with finer recovery of surface geometry from multi-view images, methods (e.g., VolSDF [46], ndiffrec [28], etc) that explicitly take the surface modeling into account triumph; our disentangled representation enjoys the benefit similar to these methods. The disentangled representation also enables us to include the BRDF material representation in the appearance modeling, achieving better photo-realistic rendering by the BRDF physical prior.",
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+        "type": "text",
+        "text": "To investigate how shape encoding of the normal map plays role in Fantasia3D, we replace the normal map with an image that is shaded on the mesh extracted from DMTET using fixed material parameters; results in the third two columns become weird with twisted geometries. This is indeed one of the key factors that makes the success of Fantasia3D. Our initial hypothesis is that shape information contained in normal and mask images could be beneficial to geometry learning, and as such, we further observe that the value range of normal maps is normalized in  $(-1, 1)$ , which aligns with the data range required for latent space diffusion; our empirical studies verify our hypothesis. Our hypothesis is further corroborated by observing that the LAION-5B [37] dataset used for training Stable Diffusion contains normals (referring to website for retrieval of normal data in LAION-5B [37]), which allows Stable Diffusion to handle the optimization of normal maps effectively. To deal with rough and coarse geometry in the early stage of learning, we use the concatenated  $64 \\times 64 \\times 4$  (normal,",
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+    {
+        "type": "text",
+        "text": "mask) images for better convergence. As the learning progresses, it becomes essential to render the  $512 \\times 512 \\times 3$  high-resolution normal images for capturing finer geometry details, and we choose to use normal images only in the later stage. This strategy strikes an accuracy-efficiency balance throughout the geometry optimization process.",
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+        "text": "Finally, we replace the full BRDF in Fantasia3D with a simple diffuse color rendering; the results in the last two columns become less realistic and are short of reflection effects when rendered from different views.",
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+        "text": "5.2. Zero-shot generation",
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+        "text": "In this section, we evaluate our method for generating 3D assets from solely natural language descriptions (i.e., the setting of zero-shot generation), by comparing with two state-of-the-art methods, namely DreamFusion [33] and Magic3D [18]. Fig. 7 gives the comparative results given the same text prompts. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. Comparing our method with Magic3D, we observe that our results are more photorealistic with competitive geometries. We consistently outperform DreamFusion in both appearance and geometry generation. Notably, our method also offers the convenience of easy geometry extraction and editing, as demonstrated in 5.4, which are less obvious from DreamFusion or Magic3D. More of our results are given in the top half of Fig. 2 and Fig. 8. Furthermore, we compare our appearance modeling stage with several mesh stylization methods, namely Text2mesh [24], CLIP-Mesh [14] and Latent-NeRF [23]. Fig. 9 shows that our method excels in generating more realistic appearances, outperforming the other competitors. We present additional results and comparisons in the supplemental materials.",
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+        "text": "5.3. User-guided generation",
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+        "type": "text",
+        "text": "In addition to zero-shot generation, our method is flexible to accept a customized 3D model as the initialization, alternative to a 3D ellipsoid, thereby facilitating user-guided asset generation. As shown in the lower half of Fig. 2, our method is able to generate rich details in both the geometry and appearance when provided with low-quality 3D models for initialization. The three meshes used in the experiments are from Text2Mesh [24], Latent-NeRF [23], and the creation of Stable DreamFusion [41], respectively. We also compare with the state-of-the-art approach of Latent-NeRF [23] under this user-guided generation setting; results are given in Fig. 10. Our method outperforms Latent-NeRF [23] in both the geometry and texture generation when given the same input meshes and text prompts.",
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+        "img_path": "images/90fc4edd80a9d14b2ecc57ad26065df184394285f382d351e77384ce0fffec43.jpg",
+        "image_caption": [
+            "Figure 6. Ablation studies of our method. The text prompt is \"a highly detailed stone bust of Theodoros Kolokotronis\". Please refer to Section 5.1 for specific settings of individual columns. Please refer to the video results in the supplemental materials for better comparisons."
+        ],
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+        "image_caption": [
+            "A 3D model of an adorable cottage with a thatched roof"
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+        "image_caption": [
+            "Figure 8. Geometries beyond genus-zero ones. DMTET can deform to any topologies, which enables Fantasia3D to generate complex geometries, including those beyond genus-zero ones."
+        ],
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+    {
+        "type": "text",
+        "text": "5.4. Scene editing and simulation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Given the disentangled design, our method produces high-quality generation of both the surface and appearance, and is compatible with popular graphics engines for scene editing and physical simulation. In Figure 1, we import into",
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+    {
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+        "image_caption": [
+            "Figure 7. Comparison of zero-shot generation. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. More results and comparisons are available in the supplemental materials.",
+            "Figure 9. Comparison of Texturing. We compare the appearance stage of Fantasia3D with three text-driven texturing methods, using the geometry generated by the geometry stage of Fantasia3D."
+        ],
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+    {
+        "type": "text",
+        "text": "Blender a stone statue generated by our method from the text prompt of \"a highly detailed stone bust of Theodoros Kolokotronis\", where soft body and cloth simulations are performed along with material editing. Given the high qual",
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+        "image_caption": [
+            "Latent -NeRF",
+            "Ours",
+            "A robot hand, realistic",
+            "A teddy bear in a tuxedo",
+            "A German Shepherd"
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/513fdc5ce70fe11e9496aa15d0c0f0d58257daca1feb5ce76727407754fcf6b2.jpg",
+        "image_caption": [
+            "Figure 10. Comparison of user-guided generation. The top row shows the input meshes provided by users, the bottom row gives the input text prompts, and the middle two rows show the results from the comparative methods.",
+            "Figure 11. Scene Editing. Three generated objects, namely crown, tiger, and ice cream, are imported into the Cornell Box scene. The scene is then rendered using the Cycles path tracer in Blender, producing natural shadows and reflectance effects."
+        ],
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+        "img_path": "images/865ce3ebe886c160b4d5062fc459c395e17bd01f9eb6eda8e9519790a5ccf4df.jpg",
+        "image_caption": [
+            "Original",
+            "Figure 12. Relighting. Our generated Iron Man model is relit using different lighting setups in Blender, producing diverse reflectance effects on the armor."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/71c6448fe863f12eecc4d8b63406fa896669848e8a5d58691f969869ad572f7f.jpg",
+        "image_caption": [
+            "Factory"
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+        "img_path": "images/c96d51c45b96de43aef0245606b668a1ff4e25e1bf42f95eecee602db3a4a5fe.jpg",
+        "image_caption": [
+            "Night"
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+        "page_idx": 8
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+    {
+        "type": "image",
+        "img_path": "images/7d58f17661be479ef40debeb6fdf66026eb1da9fb8e12a33fff9e2cee3bcf8be.jpg",
+        "image_caption": [
+            "Studio"
+        ],
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+    },
+    {
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+        "img_path": "images/610b8842a83c9c64698a995d209d2817682a8c779cc1878256c466a66e074071.jpg",
+        "image_caption": [
+            "Sunset"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "ity of the generated surface geometry (e.g., no holes on the surface), the simulations are of high-level physical accuracy, as shown in the accompanying supplemental video.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Moreover, we showcase the ability to modify the material of the statue by replacing it with another wood material downloaded from the Internet [32], which poses a challenge for comparative methods such as DreamFusion [33]. Additionally, in Fig. 11, by importing generated ice cream, tiger, and crown into the Cornell Box, we demonstrate the plausible physical interaction between our generated results and the scene, with natural shadows being cast. Finally, Fig. 12 illustrates the replacement of the HDR environment map to produce diverse lighting and corresponding reflectance effects on the generated iron man.",
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+    {
+        "type": "text",
+        "text": "6. Limitations",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "While Fantasia3D demonstrates promising advancements in the realm of generating photorealistic 3D assets from text prompts, several limitations remain. For instance, while our method successfully produces loose visual effects, it remains a significant challenge to generate corresponding loose geometries, such as hair, fur, and grass, solely based on text prompts. Additionally, our method primarily emphasizes object generation, thereby lacking the capacity to generate complete scenes with background from text prompts. Consequently, our future research endeavors will be dedicated to addressing these limitations by focusing on the generation of complete scenes and intricate loose geometries.",
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+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present Fantasia3D, a new method for automatic text-to-3D generation. Fantasia3D uses disentangled modeling and learning of geometry and appearance, and is able to generate both the fine surface and rich material/texture. Fantasia3D is based on the hybrid scene representation of DMTET. For geometry learning, we propose to encode a rendered normal map, and use shape encoding of the normal as the input of the pre-trained, stable diffusion model. For appearance modeling, we introduce the spatially varying BRDF into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. Expect for text prompts, our method can be triggered with a customized 3D shape as well; this is flexible for users to better control what content is to be generated. Our method is also convenient to support relighting, editing, and physical simulation of the generated 3D assets. Our method is based on pre-trained image diffusion models (i.e., the stable diffusion). In future research, we are interested in learning 3D diffusion directly from the large language models.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work is supported in part by Program for Guangdong Introducing Innovative and Entrepreneurial Teams (No.: 2017ZT07X183) and Guangdong R&D key project of China (No.: 2019B010155001).",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            104
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+        "page_idx": 9
+    },
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+            "[34] Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125, 2022.",
+            "[35] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10684-10695, 2022.",
+            "[36] Chitwan Sahara, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily Denton, Seyed Kamyar Seyed Ghasemipour, Burcu Karagol Ayan, S Sara Mahdavi, Rapha Gontijo Lopes, et al. Photorealistic text-to-image diffusion models with deep language understanding. Advances in Neural Information Processing Systems (NeurIPS), 2022.",
+            "[37] Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, et al. Laion-5b: An open large-scale dataset for training next generation image-text models. Advances in Neural Information Processing Systems (NeurIPS), 2022.",
+            "[38] Tianchang Shen, Jun Gao, Kangxue Yin, Ming-Yu Liu, and Sanja Fidler. Deep marching tetrahedra: a hybrid representation for high-resolution 3D shape synthesis. In Advances in Neural Information Processing Systems (NeurIPS), 2021.",
+            "[39] J Ryan Shue, Eric Ryan Chan, Ryan Po, Zachary Ankner, Jiajun Wu, and Gordon Wetzstein. 3D neural field generation using triplane diffusion. arXiv preprint arXiv:2211.16677, 2022.",
+            "[40] Stability.AI. Stable diffusion. https://stability.ai/blog/stable-diffusion-public-release.",
+            "[41] Jiaxiang Tang. Stable dreamfusion. https://github.com/ashawkey/stable-dreamfusion."
+        ],
+        "bbox": [
+            78,
+            90,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[42] Bruce Walter, Stephen R Marschner, Hongsong Li, and Kenneth E Torrance. Microfacet models for refraction through rough surfaces. In Proceedings of the 18th Eurographics conference on Rendering Techniques, pages 195-206, 2007.",
+            "[43] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Advances in Neural Information Processing Systems (NeurIPS), 2021.",
+            "[44] Tengfei Wang, Bo Zhang, Ting Zhang, Shuyang Gu, Jianmin Bao, Tadas Baltrusaitis, Jingjing Shen, Dong Chen, Fang Wen, Qifeng Chen, et al. Rodin: A generative model for sculpting 3d digital avatars using diffusion. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023.",
+            "[45] Hongzhi Wu, Julie Dorsey, and Holly Rushmeier. A sparse parametric mixture model for btf compression, editing and rendering. In Computer Graphics Forum (Comput Graph Forum), volume 30, pages 465-473. Wiley Online Library, 2011.",
+            "[46] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. In Advances in Neural Information Processing Systems (NeurIPS), 2021.",
+            "[47] Jonathan Young. xatlas. https://github.com/jpcy/xatlas.git, 2021.",
+            "[48] Yuxuan Zhang, Wenzheng Chen, Huan Ling, Jun Gao, Yi-nan Zhang, Antonio Torralba, and Sanja Fidler. Image gans meet differentiable rendering for inverse graphics and interpretable 3d neural rendering. International Conference on Learning Representations (ICLR), 2020.",
+            "[49] Linqi Zhou, Yilun Du, and Jiajun Wu. 3d shape generation and completion through point-voxel diffusion. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826-5835, 2021."
+        ],
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+            92,
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diff --git a/2023/Fantasia3D_ Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation/5c5d4c5d-3820-44df-916a-bfeef9c352be_model.json b/2023/Fantasia3D_ Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation/5c5d4c5d-3820-44df-916a-bfeef9c352be_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..f26eca1be951f0f9b9d4967eec0afd1bf2824b36
--- /dev/null
+++ b/2023/Fantasia3D_ Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation/5c5d4c5d-3820-44df-916a-bfeef9c352be_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
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+            "content": "Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation"
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+            "content": "Rui Chen,\\* Yongwei Chen,\\* Ningxin Jiao, Kui Jia\\* South China University of Technology"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
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+            "content": "Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "1. Introduction"
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+            "content": "Automatic 3D content creation [43, 18, 33, 44] powered by large language models has drawn significant attention recently, due to its convenience to entertaining and gaming industries, virtual/augmented reality, and robotic applications. The traditional process of creating 3D assets typically involves multiple, labor-intensive stages, including geome"
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+            "content": "soft body simulation"
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+            "angle": 0,
+            "content": "cloth simulation"
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+            "content": "geometry"
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+            "bbox": [
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+            "content": "Figure 1. Provided with a textual description of \"a highly detailed stone bust of Theodoros Kolokotronis\", our method produces high-quality geometry as well as disentangled materials, and enables photorealistic rendering."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "try modeling, shape baking, UV mapping, material creation, and texturing, as described in [15], where different software tools and the expertise of skilled artists are often required. Imperfections would also accumulate across these stages, resulting in low-quality 3D assets. It is thus desirable to automate such a process, and ideally to generate high-quality 3D assets that have geometrically fair surfaces, rich materials and textures, and support photorealistic rendering under arbitrary views."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "In this work, we focus on automatic 3D content creation given text prompts encoded by large language models, i.e., the text-to-3D tasks [18, 33]. Text-to-3D is inspired by the tremendous success of text-to-image research [34, 36, 30, 35]. To enable 3D generation, most existing methods [33, 23] rely on the implicit scene modeling of Neural Radiance Field (NeRF) [25, 4, 27], and learn the NeRFs by back-propagating the supervision signals from image diffusion models. However, NeRF modeling is less effective for surface recovery [43, 46], since it couples the learning of surface geometry with that of pixel colors via volume rendering. Consequently, 3D creation based on"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "* Equal contribution."
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+            "bbox": [
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+            "angle": 0,
+            "content": "† Corresponding author."
+        },
+        {
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+    [
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "NeRF modeling is less effective for recovery of both the fine surface and its material and texture. In the meanwhile, explicit and hybrid scene representations [43, 46, 38] are proposed to improve over NeRF by modeling the surface explicitly and performing view synthesis via surface rendering."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In this work, we are motivated to use 3D scene representations that are more amenable to the generation of high-quality 3D assets given text prompts. We present an automatic text-to-3D method called Fantasia3D. Key to Fantasia3D is a disentangled learning of geometry and appearance models, such that both a fine surface and a rich material/texture can be generated. To enable such a disentangled learning, we use the hybrid scene representation of DMTET [38], which maintains a deformable tetrahedral grid and a differentiable mesh extraction layer; deformation can thus be learned through the layer to explicitly control the shape generation. For geometry learning, we technically propose to encode a rendered normal map, and use shape encoding of the normal as the input of a pre-trained, image diffusion model; this is in contrast different from existing methods that commonly encode rendered color images. For appearance modeling, we introduce, for the first time, the spatially varying Bidirectional Reflectance Distribution Function (BRDF) into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. We implement the geometry model and the BRDF appearance model as simple MLPs. Both models are learned through the pre-trained image diffusion model, using a loss of Score Distillation Sampling (SDS) [33]. We use the pre-trained stable diffusion [35, 40] as the image generation model in this work."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "We note that except for text prompts, our method can also be triggered with additional inputs of users' preferences, such as a customized 3D shape or a generic 3D shape of a certain object category; this is flexible for users to better control what content is to be generated. In addition, given the disentangled generation of geometry and appearance, it is convenient for our method to support relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments to verify the efficacy of our proposed methods. Results show that our proposed Fantasia3D outperforms existing methods for high-quality and diverse 3D content creation. We summarize our technical contributions as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- We propose a novel method, termed Fantasia3D, for high-quality text-to-3D content creation. Our method disentangles the modeling and learning of geometry and appearance, and thus enables both a fine recovery of geometry and photorealistic rendering of per-view images."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- For geometry learning, we use a hybrid representation"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "of DMTET, which supports learning surface deformation via a differentiable mesh extraction; we propose to render and encode the surface normal extracted from DMTET as the input of the pre-trained image diffusion model, which enables more subtle control of shape generation."
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+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "- For appearance modeling, to the best of our knowledge, we are the first to introduce the full BRDF learning into text-to-3D content creation, facilitated by our proposed geometry-appearance disentangled framework. BRDF modeling promises high-quality 3D generation via photorealistic rendering."
+        },
+        {
+            "type": "title",
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+            "content": "2. Related work"
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+            "angle": 0,
+            "content": "Text-to-3D content creation. Motivated by the desire to generate high-quality 3D content from simple semantics such as text prompts, text-to-3D has drawn considerable attention in recent years [33, 13, 18]. Existing methods either use pre-trained 2D text-to-image models [35, 3, 36], together with score distillation sampling [33], to generate 3D geometries [18] or synthesize novel views [33], or train a text-conditioned 3D generative model from scratch [39, 49, 17, 29]. These methods generate 3D geometries with little exploration of generating high-quality lighting and surface materials. On the other hand, TANGO [8] is able to generate high-quality surface materials given text prompts; unfortunately, the method requires as input a 3D surface mesh. Our proposed method addresses the shortcomings of the above methods, and is able to generate both high-quality surface geometries and their corresponding materials, both of which are crucial for photorealistic rendering of the generated 3D content. Our method thus, for the first time, closes the loop of object-level text-to-3D content creation."
+        },
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+            "content": "Surface material estimation. The estimation of surface materials is a long-standing challenge in computer vision and graphics research. Earlier methods [2, 45] focus on recovering physically based materials under known lighting conditions, whose usefulness is, however, limited in real-world scenarios. Subsequent methods [12, 11, 5, 1] try to estimate materials under natural lighting conditions, assuming the availability of complete geometry information. More recently, the joint reconstruction of geometry and materials is proposed given calibrated multi-view images [6, 7, 19, 48]. Alternative to these methods, we explore the novel creation of surface materials and geometries from trained language models."
+        },
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+            "type": "title",
+            "bbox": [
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+            "content": "3. Preliminary"
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+            "content": "In this section, we present a few preliminaries that are necessary for presenting our proposed method in Section 4."
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+            ],
+            "angle": 0,
+            "content": "A highly detailed sandcastle"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.655,
+                0.385,
+                0.829,
+                0.485
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.66,
+                0.487,
+                0.835,
+                0.501
+            ],
+            "angle": 0,
+            "content": "A car made out of cheese"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.164,
+                0.524,
+                0.221,
+                0.599
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.245,
+                0.547,
+                0.355,
+                0.576
+            ],
+            "angle": 0,
+            "content": "\"A photo of the ironman\""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.408,
+                0.535,
+                0.495,
+                0.589
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.516,
+                0.547,
+                0.597,
+                0.577
+            ],
+            "angle": 0,
+            "content": "\"A German Sheperd\""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.624,
+                0.535,
+                0.725,
+                0.599
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.734,
+                0.548,
+                0.846,
+                0.577
+            ],
+            "angle": 0,
+            "content": "\"A tarantula, highly detailed\""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.164,
+                0.6,
+                0.334,
+                0.785
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.396,
+                0.605,
+                0.59,
+                0.774
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.616,
+                0.648,
+                0.757,
+                0.743
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.756,
+                0.613,
+                0.843,
+                0.675
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.749,
+                0.709,
+                0.837,
+                0.767
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.795,
+                0.893,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Figure 2. Results of our method. The upper portion of this figure showcases the generation results obtained from solely text prompts. The lower portion showcases user-guided generation results given guiding meshes with the corresponding textual descriptions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.318,
+                0.865
+            ],
+            "angle": 0,
+            "content": "3.1. Score distillation sampling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "DreamFusion [33] presents a method that optimizes 3D scene parameters and synthesizes novel views from tex-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.849,
+                0.893,
+                0.894
+            ],
+            "angle": 0,
+            "content": "tual descriptions, by employing a pre-trained 2D diffusion model. The scene is represented as a differentiable image parameterization [26], where a differentiable generator \\( g \\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22248"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.097,
+                0.095,
+                0.244,
+                0.119
+            ],
+            "angle": 0,
+            "content": "\" a highly detailed stone bust of Theodoros Kolokotronis \""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.095,
+                0.128,
+                0.159,
+                0.191
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.1,
+                0.195,
+                0.15,
+                0.206
+            ],
+            "angle": 0,
+            "content": "geometry"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.173,
+                0.118,
+                0.239,
+                0.19
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.175,
+                0.196,
+                0.234,
+                0.206
+            ],
+            "angle": 0,
+            "content": "appearance"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.244,
+                0.116,
+                0.27,
+                0.19
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.244,
+                0.191,
+                0.264,
+                0.2
+            ],
+            "angle": 0,
+            "content": "\\(k_{n}\\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.095,
+                0.217,
+                0.253,
+                0.23
+            ],
+            "angle": 0,
+            "content": "(a) Disentangled representation"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.286,
+                0.09,
+                0.568,
+                0.209
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.367,
+                0.217,
+                0.487,
+                0.23
+            ],
+            "angle": 0,
+            "content": "(b) Geometry modeling"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.575,
+                0.09,
+                0.88,
+                0.21
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.662,
+                0.217,
+                0.79,
+                0.23
+            ],
+            "angle": 0,
+            "content": "(c) Appearance modeling"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.244,
+                0.894,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Figure 3. Overview of our method. Our method can generate disentangled geometry and appearance given a text prompt (cf. figure (a)), which are produced by (b) geometry modeling and (c) appearance modeling, respectively. (b) We employ DMTET as our 3D geometry representation, which is initialized as a 3D ellipsoid here. To optimize the parameters of DMTET, we render the normal map (and the object mask in the early training phase) of the extracted mesh from DMTet as the shape encoding of stable diffusion [35, 40]. (c) For appearance modeling, we introduce the spatially-varying Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn to predict three components (namely, \\( k_d \\), \\( k_{rm} \\), and \\( k_n \\)) of the appearance. Both geometry and appearance modeling are supervised by Score Distillation Sampling (SDS) loss [33]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.366,
+                0.473,
+                0.488
+            ],
+            "angle": 0,
+            "content": "renders 2D images \\( x = g(\\theta) \\) from a modified Mip-NeRF [4] parameterized as \\( \\theta \\). DreamFusion leverages a diffusion model \\( \\phi \\) (Imagen [36] in this instance) to provide a score function \\( \\hat{\\epsilon}_{\\phi}(x_t; y, t) \\), which predicts the sampled noise \\( \\epsilon \\) given the noisy image \\( x_t \\), text-embedding \\( y \\), and noise level \\( t \\). This score function guides the direction of the gradient for updating the scene parameters \\( \\theta \\), and the gradient is calculated by Score Distillation Sampling (SDS):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.494,
+                0.47,
+                0.529
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bigtriangledown_ {\\theta} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , x) = \\mathbb {E} _ {t, \\epsilon} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(x _ {t}; y, t\\right) - \\epsilon\\right) \\frac {\\partial x}{\\partial \\theta} \\right], \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.535,
+                0.47,
+                0.61
+            ],
+            "angle": 0,
+            "content": "while \\( w(t) \\) is a weighting function. Since Imagen is not publicly accessible, in this work, we use the released latent space diffusion model of Stable Diffusion [35, 40] as our guidance model, and revise the SDS loss (1) accordingly. Details are given in Section 4.2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.619,
+                0.174,
+                0.633
+            ],
+            "angle": 0,
+            "content": "3.2.DMTET"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.642,
+                0.47,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Implicit surface representations [25, 31, 22] are popularly used in novel view synthesis and 3D reconstruction, due to their capabilities to represent complex scenes. However, surfaces of lower quality may be obtained [28] by extracting explicit meshes from these implicit representations using marching cubes [20]. Instead, Shen et al. [38] propose a hybrid representation, termed DMTET, that has two key features, i.e., a deformable tetrahedral grid and a differentiable Marching Tetrahedral (MT) layer. The deformable tetrahedral grid \\((V_{T}, T)\\) has vertices \\(V_{T}\\) in the tetrahedral grid \\(T\\). For each vertex \\(v_{i} \\in V_{T}\\), the proposed method predicts the Signed Distance Function (SDF) value \\(s(v_{i})\\) and a position offset \\(\\triangle v_{i}\\) by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.847,
+                0.469,
+                0.864
+            ],
+            "angle": 0,
+            "content": "\\[\n(s (v _ {i}), \\triangle v _ {i}) = \\Psi (v _ {i}; \\psi), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\psi\\) is the parameters of a network \\(\\Psi\\), enabling the extraction of explicit meshes through MT layer during each"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.366,
+                0.893,
+                0.413
+            ],
+            "angle": 0,
+            "content": "iteration of training. In this work, We use DMTET as our geometry representation and render the mesh extracted from MT layer iteratively by a differentiable renderer[16, 28]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.468,
+                0.71,
+                0.485
+            ],
+            "angle": 0,
+            "content": "4. The Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.509,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, we present our proposed method of Fantasia3D for high-quality text-to-3D object generation, by disentangling the modeling and learning of geometry and appearance. For geometry modeling, we rely on the hybrid surface representation of DMTET, and parameterize the 3D geometry as an MLP \\(\\Psi\\) that learns to predict the SDF value and position offset for each vertex in the deformable tetrahedral grid of DMTET; in contrast to previous methods, we propose to use the rendered normal map (and the object mask in the early training phase) of the extracted mesh from DMTET as the input of shape encoding. For appearance modeling, we introduce, for the first time, the full Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn an MLP \\(\\Gamma\\) that predicts parameters of surface material and supports high-quality 3D generation via photorealistic rendering. Given the disentangled modeling of \\(\\Psi\\) and \\(\\Gamma\\), the whole pipeline is learned with SDS supervision, and the gradients are backpropagated through the pre-trained stable diffusion model. Our pipeline is initialized either as a 3D ellipsoid or as a customized 3D model provided by users. Fig. 3 gives an illustration of our proposed method. In contrast, previous methods couple the geometry and appearance learning, and are suboptimal in terms of leveraging the powerful pretrained 2D image diffusion models via SDS loss. Details of the proposed Fantasia3D are presented as follows."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22249"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.091,
+                0.275,
+                0.106
+            ],
+            "angle": 0,
+            "content": "4.1. DMTET initialization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.113,
+                0.474,
+                0.342
+            ],
+            "angle": 0,
+            "content": "We adopt DMTET as our 3D scene representation, which is parameterized as the MLP network \\(\\Psi\\). For each vertex \\(v_{i} \\in V_{T}\\) of the tetrahedral grid \\((V_{T}, T)\\), \\(\\Psi\\) is trained to predict the SDF value \\(s(v_{i})\\) and the deformation offset \\(\\triangle v_{i}\\). A triangular mesh can be extracted from \\((V_{T}, T)\\) using the MT layer, whose procedure is also differentiable w.r.t. the parameters of \\(\\Psi\\). We initialize DMTET either as a 3D ellipsoid or as a customized 3D model provided by users; the latter choice is useful when the text-to-3D task is to be conditioned on users' preferences. In either case, we initialize \\(\\Psi\\) by the following fitting procedure. We sample a point set \\(\\{p_{i} \\in \\mathbb{R}^{3}\\}\\) whose points are in close proximity to the initialized 3D ellipsoid or customized model, and compute their SDF values, resulting in \\(\\{SDF(p_{i})\\}\\); we use the following loss to optimize the parameters \\(\\psi\\) of \\(\\Psi\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.142,
+                0.35,
+                0.47,
+                0.385
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {S D F}} = \\sum_ {p _ {i} \\in P} \\| s (p _ {i}; \\psi) - S D F (p _ {i}) \\| _ {2} ^ {2}. \\tag {3}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.393,
+                0.268,
+                0.409
+            ],
+            "angle": 0,
+            "content": "4.2. Geometry modeling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.416,
+                0.471,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Previous text-to-3D methods [33, 13] commonly use NeRF [25, 4] as the implicit scene representation, which couples the geometry with color/appearance and use volume rendering for view synthesis. Since NeRF modeling is less effective for surface reconstruction [43, 46], these methods are consequently less effective to generate high-quality 3D surfaces by back-propagating the supervision of SDS loss through pre-trained text-to-image models. As a remedy, the method [18] uses a second stage of the refined generation that is based on scene modeling of explicit surfaces."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.582,
+                0.47,
+                0.689
+            ],
+            "angle": 0,
+            "content": "In this work, we propose to decouple the generation of geometry from that of appearance, based on the hybrid scene representation of DMTET, which enables photorealistic surface rendering to make better use of the powerful pre-trained text-to-image models. More specifically, given the current DMTET with MLP parameters \\(\\psi\\), we generate a normal map \\(n\\), together with an object mask \\(o\\), as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.212,
+                0.699,
+                0.47,
+                0.715
+            ],
+            "angle": 0,
+            "content": "\\[\n(n, o) = g _ {n} (\\psi , c), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.724,
+                0.47,
+                0.846
+            ],
+            "angle": 0,
+            "content": "where \\( g_{n} \\) is a differentiable render (e.g., nvidiffrast [16]), and \\( c \\) is a sampled camera pose. We randomly sample the camera poses in the spherical coordinate system to ensure that the camera poses are distributed uniformly on the sphere. We propose to use the generated \\( n \\) (and \\( o \\)) as the input of shape encoding to connect with stable diffusion. To update \\( \\psi \\), we again employ SDS loss that computes the gradient w.r.t. \\( \\psi \\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.092,
+                0.855,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bigtriangledown_ {\\psi} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , \\tilde {n}) = \\mathbb {E} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(z _ {t} ^ {\\tilde {n}}; y, t\\right) - \\epsilon\\right) \\frac {\\partial \\tilde {n}}{\\partial \\psi} \\frac {\\partial z ^ {\\tilde {n}}}{\\partial \\tilde {n}} \\right], \\tag {5}\n\\]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.518,
+                0.091,
+                0.875,
+                0.201
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.208,
+                0.894,
+                0.25
+            ],
+            "angle": 0,
+            "content": "Figure 4. Three components of the material model, namely the diffuse term \\( k_{d} \\), the roughness and metallic term \\( k_{rm} \\), and the normal variation term \\( k_{n} \\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.514,
+                0.289,
+                0.882,
+                0.474
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.488,
+                0.893,
+                0.531
+            ],
+            "angle": 0,
+            "content": "Figure 5. A comparison of UV edge padding (cf. the left column) and original texturing (cf. the right column). UV edge padding removes the white seams that appear in the right rendering."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where \\(\\phi\\) parameterizes the pre-trained stable diffusion model, \\(\\tilde{n}\\) denotes concatenation of the normal \\(n\\) with the mask \\(o\\), \\(z^{\\tilde{n}}\\) is the latent code of \\(\\tilde{n}\\) via shape encoding, \\(\\hat{\\epsilon}_{\\phi}(z_t^{\\tilde{n}};y,t)\\) is the predicted noise given text embedding \\(y\\) and noise level \\(t\\), and \\(\\epsilon\\) is the noise added in \\(z_t^{\\tilde{n}}\\). In practice, we utilize a coarse-to-fine strategy to model the geometry. During the early phase of training, we use the downsampled \\(\\tilde{n}\\) as the latent code, which is inspired by [23], to rapidly update \\(\\Psi\\) and attain a coarse shape. However, a domain gap exists between \\(\\tilde{n}\\) and the latent space data distribution learned by the VAE encoder in the stable diffusion, which may lead to a mismatch of the generated geometry from the textual description. To mitigate this discrepancy, we implement a data augmentation technique by introducing random rotations to \\(\\tilde{n}\\). Our experimental observations reveal that this technique enhances the alignment between the generated geometry and the provided textual description. In the later phase of training, aiming to capture finer geometric details with greater precision, we encode the high-resolution normal \\(n\\) (without the mask \\(o\\)) to derive \\(z^n\\), using the pretrained image encoder in stable diffusion."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22250"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.091,
+                0.282,
+                0.108
+            ],
+            "angle": 0,
+            "content": "4.3. Appearance modeling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.115,
+                0.47,
+                0.386
+            ],
+            "angle": 0,
+            "content": "Given a learned DMTET with geometry parameters \\(\\psi\\), we aim for photorealistic surface rendering to better leverage the powerful image diffusion model. This is achieved by introducing into text-to-3D generation the Physically-Based Rendering (PBR) material model. As illustrated in Fig. 4, the material model we use [21] comprises three components, namely the diffuse term \\(k_{d} \\in \\mathbb{R}^{3}\\), the roughness and metallic term \\(k_{rm} \\in \\mathbb{R}^{2}\\), and the normal variation term \\(k_{n} \\in \\mathbb{R}^{3}\\). The \\(k_{d}\\) term denotes the diffuse value, while the \\(k_{rm}\\) term encompasses the roughness \\(r\\) and metalness \\(m\\); the roughness \\(r\\) serves as a metric for measuring the extent of specular reflection and a parameter of the GGX [42] normal distribution function in the rendering equation. The metalness parameter \\(m\\) and diffuse value \\(k_{d}\\) can be used to compute the specular term \\(k_{s}\\) using \\(k_{s} = (1 - m) \\cdot 0.04 + m \\cdot k_{d}\\). Furthermore, we use a normal variation \\(k_{n}\\) in tangent space to enhance the surface lighting effect and introduce additional geometric variations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.388,
+                0.469,
+                0.493
+            ],
+            "angle": 0,
+            "content": "We use an MLP \\(\\Gamma\\) as our parameterized material model. \\(\\Gamma\\) is learned to predict spatially varying material parameters, which are subsequently used to render the surface extracted from DMTET. More specifically, for any point \\(p\\in \\mathbb{R}^3\\) on the surface, we use hash-grid positional encoding [27], and generate the diffuse term \\(k_{d}\\), the specular term \\(k_{rm}\\), and the tangent space normal \\(k_{n}\\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.508,
+                0.469,
+                0.526
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(k _ {d}, k _ {r m}, k _ {n}\\right) = \\Gamma (\\beta (p); \\gamma), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.539,
+                0.469,
+                0.597
+            ],
+            "angle": 0,
+            "content": "where \\(\\beta\\) is the positional encoding of \\(p\\), and \\(\\gamma\\) parameterizes the MLP \\(\\Gamma\\). The basic rendering equation suggests that each image pixel at a specific viewing direction can be rendered as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.106,
+                0.609,
+                0.469,
+                0.642
+            ],
+            "angle": 0,
+            "content": "\\[\nL (p, \\omega) = \\int_ {\\Omega} L _ {i} (p, \\omega_ {i}) f (p, \\omega_ {i}, \\omega) (\\omega_ {i} \\cdot n _ {p}) \\mathrm {d} \\omega_ {i}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.653,
+                0.469,
+                0.789
+            ],
+            "angle": 0,
+            "content": "where \\( L \\) is the rendered pixel color along the direction \\( \\omega \\) from the surface point \\( p \\), \\( \\Omega = \\{\\omega_i : \\omega_i \\cdot n_p \\geq 0\\} \\) denotes a hemisphere with the incident direction \\( \\omega_i \\) and surface normal \\( n_p \\) at \\( p \\), \\( L_i \\) is the incident light that is represented by an off-the-shelf environment map [32], and \\( f \\) is the BRDF determined by the material parameters \\( (k_d, k_{rm}, k_n) \\) predicted by (6). We note that \\( L \\) is the summation of diffuse intensity \\( L_d \\) and specular intensity \\( L_s \\), and the two terms can be computed as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.089,
+                0.804,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L (p, \\omega) = L _ {d} (p) + L _ {s} (p, \\omega), \\\\ L _ {d} (p) = k _ {d} (1 - m) \\int_ {\\Omega} L _ {i} (p, \\omega_ {i}) (\\omega_ {i} \\cdot n _ {p}) \\mathrm {d} \\omega_ {i}, \\\\ L _ {s} (p, \\omega) = \\int_ {\\Omega} \\frac {D F G}{4 (\\omega \\cdot n _ {p}) \\left(\\omega_ {i} \\cdot n _ {p}\\right)} L _ {i} \\left(p, \\omega_ {i}\\right) \\left(\\omega_ {i} \\cdot n _ {p}\\right) \\mathrm {d} \\omega_ {i}, \\tag {8} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "where \\(F\\), \\(G\\), and \\(D\\) represent the Fresnel term, the shadowing-mask term, and the GGX distribution of normal, respectively. Following [28], the hemisphere integration can be calculated using the split-sum method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.152,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "By aggregating the rendered pixel colors along the direction \\(\\omega\\) (i.e., camera pose), we have the rendered image \\(x = \\{L(p,\\omega)\\}\\) that connects with the image encoder of the pre-trained stable diffusion model. We update the parameters \\(\\gamma\\) by computing the gradient of the SDS loss w.r.t. \\(\\gamma\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.509,
+                0.248,
+                0.892,
+                0.282
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla_ {\\gamma} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , x) = \\mathbb {E} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(z _ {t} ^ {x}; y, t\\right) - \\epsilon\\right) \\frac {\\partial x}{\\partial \\gamma} \\frac {\\partial z ^ {x}}{\\partial x} \\right]. \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.29,
+                0.845,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Notations in (9) are similarly defined as those in (5)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.305,
+                0.892,
+                0.456
+            ],
+            "angle": 0,
+            "content": "Texturing. Given the trained \\(\\Gamma\\), we proceed by sampling the generated appearance as 2D texture maps, in accordance with the UV map generated by the xatlas [47]. Note that texture seams would emerge by direct incorporation of the sampled 2D textures into graphics engines (e.g., Blender [10]). We instead employ the UV edge padding technique [9], which involves expanding the boundaries of UV islands and filling empty regions. As illustrated in Fig. 5, this padding technique removes background pixels in the texture map and also removes the seams in the resulting renderings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.892,
+                0.712
+            ],
+            "angle": 0,
+            "content": "Implementation Details. We implement the network \\(\\Psi\\) as a three-layer MLP with 32 hidden units, and implement \\(\\Gamma\\) as a two-layer MLP with 32 hidden units. Our method is optimized on 8 Nvidia RTX 3090 GPUs for about 15 minutes for learning \\(\\Psi\\) and about 16 minutes for learning \\(\\Gamma\\), respectively, where we use AdamW optimizer with the respective learning rates of \\(1 \\times 10^{-3}\\) and \\(1 \\times 10^{-2}\\). For each iteration, we uniformly sample 24 camera poses for the rendering of normal maps and colored images. More details of our implementation are available in the supplemental material. In geometry modeling, we set \\(\\omega(t) = \\sigma^2\\) during the early phase and then transition to \\(w(t) = \\sigma^2 \\sqrt{1 - \\sigma^2}\\) as we progress to the later phase. In appearance modeling, we apply \\(w(t) = \\sigma^2 \\sqrt{1 - \\sigma^2}\\) during the early phase, followed by a shift to \\(1 / \\sigma^2\\) as we enter the later phase. This approach mitigates the issue related to over-saturated color within the appearance modeling."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.725,
+                0.632,
+                0.742
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we present comprehensive experiments to evaluate the efficacy of our proposed method for text-to-3D content creation. We first conduct ablation studies in Section 5.1 that verify the importance of our key design of disentangling geometry and appearance for text-to-3D generation. In Section 5.2, we show the efficacy of our method for the generation of 3D models with PBR materials from arbitrary text prompts, where we also compare with two recent state-of-the-art methods (namely, Magic3D [18] and DreamFusion [33]). In Section 5.3, we present our results"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22251"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.092,
+                0.468,
+                0.181
+            ],
+            "angle": 0,
+            "content": "under the setting of user-guided generation and compare them with Latent-NeRF [23]. We finally demonstrate in Section 5.4 that the 3D assets generated by our method are readily compatible with popular graphics engines such as Blender [10], thus facilitating relighting, editing, and physical simulation of the resulting 3D models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.081,
+                0.196,
+                0.236,
+                0.21
+            ],
+            "angle": 0,
+            "content": "5.1. Ablation studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.221,
+                0.468,
+                0.612
+            ],
+            "angle": 0,
+            "content": "We use an example text prompt of \"a highly detailed stone bust of Theodoros Kolokotronis\" for the ablation studies. Results of alternative settings are given in Fig. 6. As the reference, the first two columns show the geometry and appearance results of our Fantasia3D rendered from the front and back views. To verify the effectiveness of the disentangled design in Fantasia3D, we also conduct experiments as follows: in each iteration, we render shaded images of the mesh extracted from DMTET, and learn to update the parameters of a network responsible for both the geometry and material, using the gradient computed by SDS loss. Results in the second two columns show that such an entangled learning fails to generate plausible results. Previous methods (e.g., DreamFusion [33] and Magic3D [18]) couple the geometry and appearance generation together, following NeRF [25]. Our adoption of the disentangled representation is mainly motivated by the difference of problem nature for generating surface geometry and appearance. In fact, when dealing with finer recovery of surface geometry from multi-view images, methods (e.g., VolSDF [46], ndiffrec [28], etc) that explicitly take the surface modeling into account triumph; our disentangled representation enjoys the benefit similar to these methods. The disentangled representation also enables us to include the BRDF material representation in the appearance modeling, achieving better photo-realistic rendering by the BRDF physical prior."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.615,
+                0.468,
+                0.899
+            ],
+            "angle": 0,
+            "content": "To investigate how shape encoding of the normal map plays role in Fantasia3D, we replace the normal map with an image that is shaded on the mesh extracted from DMTET using fixed material parameters; results in the third two columns become weird with twisted geometries. This is indeed one of the key factors that makes the success of Fantasia3D. Our initial hypothesis is that shape information contained in normal and mask images could be beneficial to geometry learning, and as such, we further observe that the value range of normal maps is normalized in \\((-1, 1)\\), which aligns with the data range required for latent space diffusion; our empirical studies verify our hypothesis. Our hypothesis is further corroborated by observing that the LAION-5B [37] dataset used for training Stable Diffusion contains normals (referring to website for retrieval of normal data in LAION-5B [37]), which allows Stable Diffusion to handle the optimization of normal maps effectively. To deal with rough and coarse geometry in the early stage of learning, we use the concatenated \\(64 \\times 64 \\times 4\\) (normal,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.89,
+                0.182
+            ],
+            "angle": 0,
+            "content": "mask) images for better convergence. As the learning progresses, it becomes essential to render the \\(512 \\times 512 \\times 3\\) high-resolution normal images for capturing finer geometry details, and we choose to use normal images only in the later stage. This strategy strikes an accuracy-efficiency balance throughout the geometry optimization process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.188,
+                0.89,
+                0.247
+            ],
+            "angle": 0,
+            "content": "Finally, we replace the full BRDF in Fantasia3D with a simple diffuse color rendering; the results in the last two columns become less realistic and are short of reflection effects when rendered from different views."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.274,
+                0.695,
+                0.289
+            ],
+            "angle": 0,
+            "content": "5.2. Zero-shot generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.303,
+                0.89,
+                0.634
+            ],
+            "angle": 0,
+            "content": "In this section, we evaluate our method for generating 3D assets from solely natural language descriptions (i.e., the setting of zero-shot generation), by comparing with two state-of-the-art methods, namely DreamFusion [33] and Magic3D [18]. Fig. 7 gives the comparative results given the same text prompts. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. Comparing our method with Magic3D, we observe that our results are more photorealistic with competitive geometries. We consistently outperform DreamFusion in both appearance and geometry generation. Notably, our method also offers the convenience of easy geometry extraction and editing, as demonstrated in 5.4, which are less obvious from DreamFusion or Magic3D. More of our results are given in the top half of Fig. 2 and Fig. 8. Furthermore, we compare our appearance modeling stage with several mesh stylization methods, namely Text2mesh [24], CLIP-Mesh [14] and Latent-NeRF [23]. Fig. 9 shows that our method excels in generating more realistic appearances, outperforming the other competitors. We present additional results and comparisons in the supplemental materials."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.661,
+                0.714,
+                0.676
+            ],
+            "angle": 0,
+            "content": "5.3. User-guided generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.69,
+                0.89,
+                0.9
+            ],
+            "angle": 0,
+            "content": "In addition to zero-shot generation, our method is flexible to accept a customized 3D model as the initialization, alternative to a 3D ellipsoid, thereby facilitating user-guided asset generation. As shown in the lower half of Fig. 2, our method is able to generate rich details in both the geometry and appearance when provided with low-quality 3D models for initialization. The three meshes used in the experiments are from Text2Mesh [24], Latent-NeRF [23], and the creation of Stable DreamFusion [41], respectively. We also compare with the state-of-the-art approach of Latent-NeRF [23] under this user-guided generation setting; results are given in Fig. 10. Our method outperforms Latent-NeRF [23] in both the geometry and texture generation when given the same input meshes and text prompts."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.947,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22252"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.129,
+                0.09,
+                0.844,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.271,
+                0.893,
+                0.302
+            ],
+            "angle": 0,
+            "content": "Figure 6. Ablation studies of our method. The text prompt is \"a highly detailed stone bust of Theodoros Kolokotronis\". Please refer to Section 5.1 for specific settings of individual columns. Please refer to the video results in the supplemental materials for better comparisons."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.31,
+                0.855,
+                0.584
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.312,
+                0.589,
+                0.655,
+                0.604
+            ],
+            "angle": 0,
+            "content": "A 3D model of an adorable cottage with a thatched roof"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.615,
+                0.893,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Figure 7. Comparison of zero-shot generation. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. More results and comparisons are available in the supplemental materials."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.668,
+                0.472,
+                0.727
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.744,
+                0.47,
+                0.786
+            ],
+            "angle": 0,
+            "content": "Figure 8. Geometries beyond genus-zero ones. DMTET can deform to any topologies, which enables Fantasia3D to generate complex geometries, including those beyond genus-zero ones."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.815,
+                0.334,
+                0.831
+            ],
+            "angle": 0,
+            "content": "5.4. Scene editing and simulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.841,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Given the disentangled design, our method produces high-quality generation of both the surface and appearance, and is compatible with popular graphics engines for scene editing and physical simulation. In Figure 1, we import into"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.667,
+                0.895,
+                0.751
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.763,
+                0.893,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Figure 9. Comparison of Texturing. We compare the appearance stage of Fantasia3D with three text-driven texturing methods, using the geometry generated by the geometry stage of Fantasia3D."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.841,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Blender a stone statue generated by our method from the text prompt of \"a highly detailed stone bust of Theodoros Kolokotronis\", where soft body and cloth simulations are performed along with material editing. Given the high qual"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22253"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.084,
+                0.163,
+                0.122,
+                0.186
+            ],
+            "angle": 0,
+            "content": "Latent -NeRF"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.088,
+                0.223,
+                0.117,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.138,
+                0.099,
+                0.449,
+                0.256
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.126,
+                0.259,
+                0.229,
+                0.269
+            ],
+            "angle": 0,
+            "content": "A robot hand, realistic"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.24,
+                0.258,
+                0.355,
+                0.269
+            ],
+            "angle": 0,
+            "content": "A teddy bear in a tuxedo"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.365,
+                0.099,
+                0.448,
+                0.256
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.366,
+                0.258,
+                0.461,
+                0.269
+            ],
+            "angle": 0,
+            "content": "A German Shepherd"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.284,
+                0.471,
+                0.34
+            ],
+            "angle": 0,
+            "content": "Figure 10. Comparison of user-guided generation. The top row shows the input meshes provided by users, the bottom row gives the input text prompts, and the middle two rows show the results from the comparative methods."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.111,
+                0.357,
+                0.437,
+                0.607
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.614,
+                0.47,
+                0.671
+            ],
+            "angle": 0,
+            "content": "Figure 11. Scene Editing. Three generated objects, namely crown, tiger, and ice cream, are imported into the Cornell Box scene. The scene is then rendered using the Cycles path tracer in Blender, producing natural shadows and reflectance effects."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.683,
+                0.143,
+                0.775
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.084,
+                0.777,
+                0.127,
+                0.787
+            ],
+            "angle": 0,
+            "content": "Original"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.161,
+                0.683,
+                0.224,
+                0.775
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.168,
+                0.777,
+                0.207,
+                0.787
+            ],
+            "angle": 0,
+            "content": "Factory"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.244,
+                0.683,
+                0.306,
+                0.775
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.255,
+                0.777,
+                0.285,
+                0.787
+            ],
+            "angle": 0,
+            "content": "Night"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.325,
+                0.683,
+                0.388,
+                0.775
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.334,
+                0.777,
+                0.367,
+                0.787
+            ],
+            "angle": 0,
+            "content": "Studio"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.407,
+                0.683,
+                0.47,
+                0.775
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.417,
+                0.777,
+                0.451,
+                0.787
+            ],
+            "angle": 0,
+            "content": "Sunset"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.79,
+                0.47,
+                0.83
+            ],
+            "angle": 0,
+            "content": "Figure 12. Relighting. Our generated Iron Man model is relit using different lighting setups in Blender, producing diverse reflectance effects on the armor."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.903
+            ],
+            "angle": 0,
+            "content": "ity of the generated surface geometry (e.g., no holes on the surface), the simulations are of high-level physical accuracy, as shown in the accompanying supplemental video."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.258
+            ],
+            "angle": 0,
+            "content": "Moreover, we showcase the ability to modify the material of the statue by replacing it with another wood material downloaded from the Internet [32], which poses a challenge for comparative methods such as DreamFusion [33]. Additionally, in Fig. 11, by importing generated ice cream, tiger, and crown into the Cornell Box, we demonstrate the plausible physical interaction between our generated results and the scene, with natural shadows being cast. Finally, Fig. 12 illustrates the replacement of the HDR environment map to produce diverse lighting and corresponding reflectance effects on the generated iron man."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.27,
+                0.623,
+                0.285
+            ],
+            "angle": 0,
+            "content": "6. Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.295,
+                0.892,
+                0.491
+            ],
+            "angle": 0,
+            "content": "While Fantasia3D demonstrates promising advancements in the realm of generating photorealistic 3D assets from text prompts, several limitations remain. For instance, while our method successfully produces loose visual effects, it remains a significant challenge to generate corresponding loose geometries, such as hair, fur, and grass, solely based on text prompts. Additionally, our method primarily emphasizes object generation, thereby lacking the capacity to generate complete scenes with background from text prompts. Consequently, our future research endeavors will be dedicated to addressing these limitations by focusing on the generation of complete scenes and intricate loose geometries."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.504,
+                0.619,
+                0.52
+            ],
+            "angle": 0,
+            "content": "7. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.529,
+                0.892,
+                0.832
+            ],
+            "angle": 0,
+            "content": "In this paper, we present Fantasia3D, a new method for automatic text-to-3D generation. Fantasia3D uses disentangled modeling and learning of geometry and appearance, and is able to generate both the fine surface and rich material/texture. Fantasia3D is based on the hybrid scene representation of DMTET. For geometry learning, we propose to encode a rendered normal map, and use shape encoding of the normal as the input of the pre-trained, stable diffusion model. For appearance modeling, we introduce the spatially varying BRDF into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. Expect for text prompts, our method can be triggered with a customized 3D shape as well; this is flexible for users to better control what content is to be generated. Our method is also convenient to support relighting, editing, and physical simulation of the generated 3D assets. Our method is based on pre-trained image diffusion models (i.e., the stable diffusion). In future research, we are interested in learning 3D diffusion directly from the large language models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work is supported in part by Program for Guangdong Introducing Innovative and Entrepreneurial Teams (No.: 2017ZT07X183) and Guangdong R&D key project of China (No.: 2019B010155001)."
+        },
+        {
+            "type": "page_number",
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+            "angle": 0,
+            "content": "22254"
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+            "content": "[45] Hongzhi Wu, Julie Dorsey, and Holly Rushmeier. A sparse parametric mixture model for btf compression, editing and rendering. In Computer Graphics Forum (Comput Graph Forum), volume 30, pages 465-473. Wiley Online Library, 2011."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.375,
+                0.892,
+                0.416
+            ],
+            "angle": 0,
+            "content": "[46] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. In Advances in Neural Information Processing Systems (NeurIPS), 2021."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
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+                0.445
+            ],
+            "angle": 0,
+            "content": "[47] Jonathan Young. xatlas. https://github.com/jpcy/xatlas.git, 2021."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.446,
+                0.892,
+                0.515
+            ],
+            "angle": 0,
+            "content": "[48] Yuxuan Zhang, Wenzheng Chen, Huan Ling, Jun Gao, Yi-nan Zhang, Antonio Torralba, and Sanja Fidler. Image gans meet differentiable rendering for inverse graphics and interpretable 3d neural rendering. International Conference on Learning Representations (ICLR), 2020."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
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+            ],
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+            "content": "[49] Linqi Zhou, Yilun Du, and Jiajun Wu. 3d shape generation and completion through point-voxel diffusion. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5826-5835, 2021."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.503,
+                0.093,
+                0.892,
+                0.573
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.946,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22256"
+        }
+    ]
+]
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+# Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation
+
+Rui Chen,\* Yongwei Chen,\* Ningxin Jiao, Kui Jia\* South China University of Technology
+
+# Abstract
+
+Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.
+
+# 1. Introduction
+
+Automatic 3D content creation [43, 18, 33, 44] powered by large language models has drawn significant attention recently, due to its convenience to entertaining and gaming industries, virtual/augmented reality, and robotic applications. The traditional process of creating 3D assets typically involves multiple, labor-intensive stages, including geome
+
+![](images/96bd34b20c430d182c285af1cf737506089d17e9a8f1432f9d0beaf516feea90.jpg)  
+generation
+
+![](images/5c460cdc38d10888d583404ce2a6d3c9b8d9fdbeab1eadde14427d7b3bf3d0f5.jpg)  
+soft body simulation
+
+![](images/81e844df219938fd9a1c280d47899aa8d89aa4fd386b6e849704c8af9889bb14.jpg)  
+cloth simulation
+
+![](images/54615609df4386e2bd48d11e5254e4d2b89e52bda915aa9211934a0fee8d4a9a.jpg)  
+material editing  
+Figure 1. Provided with a textual description of "a highly detailed stone bust of Theodoros Kolokotronis", our method produces high-quality geometry as well as disentangled materials, and enables photorealistic rendering.
+
+![](images/8b094c93b38ea99503b7da547a637fe2052d8d49bf6179f21364e32256e7b4da.jpg)  
+material
+
+![](images/be0ba8595891df06b02efd6cc89aa298288081bfb2422bcaa638683f2c9b5141.jpg)  
+geometry
+
+try modeling, shape baking, UV mapping, material creation, and texturing, as described in [15], where different software tools and the expertise of skilled artists are often required. Imperfections would also accumulate across these stages, resulting in low-quality 3D assets. It is thus desirable to automate such a process, and ideally to generate high-quality 3D assets that have geometrically fair surfaces, rich materials and textures, and support photorealistic rendering under arbitrary views.
+
+In this work, we focus on automatic 3D content creation given text prompts encoded by large language models, i.e., the text-to-3D tasks [18, 33]. Text-to-3D is inspired by the tremendous success of text-to-image research [34, 36, 30, 35]. To enable 3D generation, most existing methods [33, 23] rely on the implicit scene modeling of Neural Radiance Field (NeRF) [25, 4, 27], and learn the NeRFs by back-propagating the supervision signals from image diffusion models. However, NeRF modeling is less effective for surface recovery [43, 46], since it couples the learning of surface geometry with that of pixel colors via volume rendering. Consequently, 3D creation based on
+
+NeRF modeling is less effective for recovery of both the fine surface and its material and texture. In the meanwhile, explicit and hybrid scene representations [43, 46, 38] are proposed to improve over NeRF by modeling the surface explicitly and performing view synthesis via surface rendering.
+
+In this work, we are motivated to use 3D scene representations that are more amenable to the generation of high-quality 3D assets given text prompts. We present an automatic text-to-3D method called Fantasia3D. Key to Fantasia3D is a disentangled learning of geometry and appearance models, such that both a fine surface and a rich material/texture can be generated. To enable such a disentangled learning, we use the hybrid scene representation of DMTET [38], which maintains a deformable tetrahedral grid and a differentiable mesh extraction layer; deformation can thus be learned through the layer to explicitly control the shape generation. For geometry learning, we technically propose to encode a rendered normal map, and use shape encoding of the normal as the input of a pre-trained, image diffusion model; this is in contrast different from existing methods that commonly encode rendered color images. For appearance modeling, we introduce, for the first time, the spatially varying Bidirectional Reflectance Distribution Function (BRDF) into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. We implement the geometry model and the BRDF appearance model as simple MLPs. Both models are learned through the pre-trained image diffusion model, using a loss of Score Distillation Sampling (SDS) [33]. We use the pre-trained stable diffusion [35, 40] as the image generation model in this work.
+
+We note that except for text prompts, our method can also be triggered with additional inputs of users' preferences, such as a customized 3D shape or a generic 3D shape of a certain object category; this is flexible for users to better control what content is to be generated. In addition, given the disentangled generation of geometry and appearance, it is convenient for our method to support relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments to verify the efficacy of our proposed methods. Results show that our proposed Fantasia3D outperforms existing methods for high-quality and diverse 3D content creation. We summarize our technical contributions as follows.
+
+- We propose a novel method, termed Fantasia3D, for high-quality text-to-3D content creation. Our method disentangles the modeling and learning of geometry and appearance, and thus enables both a fine recovery of geometry and photorealistic rendering of per-view images.
+
+- For geometry learning, we use a hybrid representation
+
+of DMTET, which supports learning surface deformation via a differentiable mesh extraction; we propose to render and encode the surface normal extracted from DMTET as the input of the pre-trained image diffusion model, which enables more subtle control of shape generation.
+
+- For appearance modeling, to the best of our knowledge, we are the first to introduce the full BRDF learning into text-to-3D content creation, facilitated by our proposed geometry-appearance disentangled framework. BRDF modeling promises high-quality 3D generation via photorealistic rendering.
+
+# 2. Related work
+
+Text-to-3D content creation. Motivated by the desire to generate high-quality 3D content from simple semantics such as text prompts, text-to-3D has drawn considerable attention in recent years [33, 13, 18]. Existing methods either use pre-trained 2D text-to-image models [35, 3, 36], together with score distillation sampling [33], to generate 3D geometries [18] or synthesize novel views [33], or train a text-conditioned 3D generative model from scratch [39, 49, 17, 29]. These methods generate 3D geometries with little exploration of generating high-quality lighting and surface materials. On the other hand, TANGO [8] is able to generate high-quality surface materials given text prompts; unfortunately, the method requires as input a 3D surface mesh. Our proposed method addresses the shortcomings of the above methods, and is able to generate both high-quality surface geometries and their corresponding materials, both of which are crucial for photorealistic rendering of the generated 3D content. Our method thus, for the first time, closes the loop of object-level text-to-3D content creation.
+
+Surface material estimation. The estimation of surface materials is a long-standing challenge in computer vision and graphics research. Earlier methods [2, 45] focus on recovering physically based materials under known lighting conditions, whose usefulness is, however, limited in real-world scenarios. Subsequent methods [12, 11, 5, 1] try to estimate materials under natural lighting conditions, assuming the availability of complete geometry information. More recently, the joint reconstruction of geometry and materials is proposed given calibrated multi-view images [6, 7, 19, 48]. Alternative to these methods, we explore the novel creation of surface materials and geometries from trained language models.
+
+# 3. Preliminary
+
+In this section, we present a few preliminaries that are necessary for presenting our proposed method in Section 4.
+
+![](images/efaab1140d7d7f4a549406d3df2f1028a6f1033fa7525bba6a62538effcb4176.jpg)  
+A vintage record player
+
+![](images/3f889ac1671c93b008d312a19598a61610b7addb47c9ce49f911c5aac8555964.jpg)  
+An ice cream sundae
+
+![](images/cfca4ad8b7ef41fadb3d6ad5549e9176b8bc843d0750cfc0c983f7244c7f16fb.jpg)  
+A red rotary telephone
+
+![](images/977880aae93c629c67dcc75f318615a9b246639d3f95e30f9fe08575e5d687f0.jpg)  
+A fresh cinnamon roll covered in glaze, high resolution
+
+![](images/7af8a7efb801773ee139c1360c344b8d25d45c6bb4096c181d435d1c16154f78.jpg)  
+A delicious croissant
+
+![](images/310577bb002178b94ee712d1d777efb063e59e21fdbfbd1199192d36d1efc293.jpg)  
+A golden goblet
+
+![](images/cd68ae1ee09e6f898f35af71ea0dfdd3b0ca618bfd1037c9cd1186d95e935c43.jpg)  
+The leaning tower of Pisa
+
+![](images/1eb0689c79bf1bca25041fbb85d0300a09952c6d63d3e35e85b8ebbfd2466aca.jpg)  
+A highly detailed sandcastle
+
+![](images/5abca5ddc0ed465e757f91032dd28e56402b1e523568177593cd245c62de9c8a.jpg)  
+A car made out of cheese
+
+![](images/d09aaba1c901dcde7f947e7903bbe0cbc20734adf99d9b8d10db3179f1ab3478.jpg)  
+"A photo of the ironman"
+
+![](images/5e1735da28df1709758d6e240912baa9d45a642fe7ef93f7ce74681eb6e89a6f.jpg)  
+"A German Sheperd"
+
+![](images/4fb5d3401db09062591137976c2f8cd89f14a718c1cbaa21227dd4c08b98e1f1.jpg)  
+"A tarantula, highly detailed"
+
+![](images/088851f3e6e8f887a07e1b6e33ecbb56c95e1f0cf0cd08d8f33aa68a57ec7b0c.jpg)  
+Figure 2. Results of our method. The upper portion of this figure showcases the generation results obtained from solely text prompts. The lower portion showcases user-guided generation results given guiding meshes with the corresponding textual descriptions.
+
+![](images/2338b92c54b6d8bd4ccff44292cfd3c790d41827bb693b50d4f9d361cec8a077.jpg)
+
+![](images/167cc07b1c69f662772595ee0b3ac9718c35d761290ae6ff3f616694bcaf65de.jpg)
+
+![](images/c68b5c6e1eb8913bbc3c6a44d382eec2d3a267066c912865c70dbac964f42d87.jpg)
+
+![](images/2affc69c296889b59bb6986e48f8bfaa71b3c05d57faffc770ad0b83b8b65db6.jpg)
+
+# 3.1. Score distillation sampling
+
+DreamFusion [33] presents a method that optimizes 3D scene parameters and synthesizes novel views from tex-
+
+tual descriptions, by employing a pre-trained 2D diffusion model. The scene is represented as a differentiable image parameterization [26], where a differentiable generator  $g$
+
+![](images/5625c428fe0b0a1b3863b553f7e9b35fc62664aa5c343b0e0bfc93e0575054d4.jpg)  
+geometry  
+(a) Disentangled representation
+
+![](images/e20e35b90ad9c479de972d8428518ae7051ac5c2c4e6e4b07a96c85b26c51dfc.jpg)  
+" a highly detailed stone bust of Theodoros Kolokotronis "  
+appearance
+
+![](images/84227980e03bb45164660a3bdc801221765cda8fcba743f6f4ad29c0ed530a19.jpg)  
+$k_{n}$
+
+![](images/b6ace02311bd3129b3d5d532a4b11cc19e4eb0dd146283cd0e4242099d495721.jpg)  
+(b) Geometry modeling
+
+![](images/22deeb2b6fd38fc676c0bc2dac6f5e39cafab9efb4d8db75093505ae48e12505.jpg)  
+(c) Appearance modeling  
+Figure 3. Overview of our method. Our method can generate disentangled geometry and appearance given a text prompt (cf. figure (a)), which are produced by (b) geometry modeling and (c) appearance modeling, respectively. (b) We employ DMTET as our 3D geometry representation, which is initialized as a 3D ellipsoid here. To optimize the parameters of DMTET, we render the normal map (and the object mask in the early training phase) of the extracted mesh from DMTet as the shape encoding of stable diffusion [35, 40]. (c) For appearance modeling, we introduce the spatially-varying Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn to predict three components (namely,  $k_d$ ,  $k_{rm}$ , and  $k_n$ ) of the appearance. Both geometry and appearance modeling are supervised by Score Distillation Sampling (SDS) loss [33].
+
+renders 2D images  $x = g(\theta)$  from a modified Mip-NeRF [4] parameterized as  $\theta$ . DreamFusion leverages a diffusion model  $\phi$  (Imagen [36] in this instance) to provide a score function  $\hat{\epsilon}_{\phi}(x_t; y, t)$ , which predicts the sampled noise  $\epsilon$  given the noisy image  $x_t$ , text-embedding  $y$ , and noise level  $t$ . This score function guides the direction of the gradient for updating the scene parameters  $\theta$ , and the gradient is calculated by Score Distillation Sampling (SDS):
+
+$$
+\bigtriangledown_ {\theta} \mathcal {L} _ {\mathrm {S D S}} (\phi , x) = \mathbb {E} _ {t, \epsilon} \left[ w (t) \left(\hat {\epsilon} _ {\phi} \left(x _ {t}; y, t\right) - \epsilon\right) \frac {\partial x}{\partial \theta} \right], \tag {1}
+$$
+
+while  $w(t)$  is a weighting function. Since Imagen is not publicly accessible, in this work, we use the released latent space diffusion model of Stable Diffusion [35, 40] as our guidance model, and revise the SDS loss (1) accordingly. Details are given in Section 4.2.
+
+# 3.2.DMTET
+
+Implicit surface representations [25, 31, 22] are popularly used in novel view synthesis and 3D reconstruction, due to their capabilities to represent complex scenes. However, surfaces of lower quality may be obtained [28] by extracting explicit meshes from these implicit representations using marching cubes [20]. Instead, Shen et al. [38] propose a hybrid representation, termed DMTET, that has two key features, i.e., a deformable tetrahedral grid and a differentiable Marching Tetrahedral (MT) layer. The deformable tetrahedral grid  $(V_{T}, T)$  has vertices  $V_{T}$  in the tetrahedral grid  $T$ . For each vertex  $v_{i} \in V_{T}$ , the proposed method predicts the Signed Distance Function (SDF) value  $s(v_{i})$  and a position offset  $\triangle v_{i}$  by:
+
+$$
+(s (v _ {i}), \triangle v _ {i}) = \Psi (v _ {i}; \psi), \tag {2}
+$$
+
+where  $\psi$  is the parameters of a network  $\Psi$ , enabling the extraction of explicit meshes through MT layer during each
+
+iteration of training. In this work, We use DMTET as our geometry representation and render the mesh extracted from MT layer iteratively by a differentiable renderer[16, 28].
+
+# 4. The Proposed Method
+
+In this section, we present our proposed method of Fantasia3D for high-quality text-to-3D object generation, by disentangling the modeling and learning of geometry and appearance. For geometry modeling, we rely on the hybrid surface representation of DMTET, and parameterize the 3D geometry as an MLP  $\Psi$  that learns to predict the SDF value and position offset for each vertex in the deformable tetrahedral grid of DMTET; in contrast to previous methods, we propose to use the rendered normal map (and the object mask in the early training phase) of the extracted mesh from DMTET as the input of shape encoding. For appearance modeling, we introduce, for the first time, the full Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn an MLP  $\Gamma$  that predicts parameters of surface material and supports high-quality 3D generation via photorealistic rendering. Given the disentangled modeling of  $\Psi$  and  $\Gamma$ , the whole pipeline is learned with SDS supervision, and the gradients are backpropagated through the pre-trained stable diffusion model. Our pipeline is initialized either as a 3D ellipsoid or as a customized 3D model provided by users. Fig. 3 gives an illustration of our proposed method. In contrast, previous methods couple the geometry and appearance learning, and are suboptimal in terms of leveraging the powerful pretrained 2D image diffusion models via SDS loss. Details of the proposed Fantasia3D are presented as follows.
+
+# 4.1. DMTET initialization
+
+We adopt DMTET as our 3D scene representation, which is parameterized as the MLP network  $\Psi$ . For each vertex  $v_{i} \in V_{T}$  of the tetrahedral grid  $(V_{T}, T)$ ,  $\Psi$  is trained to predict the SDF value  $s(v_{i})$  and the deformation offset  $\triangle v_{i}$ . A triangular mesh can be extracted from  $(V_{T}, T)$  using the MT layer, whose procedure is also differentiable w.r.t. the parameters of  $\Psi$ . We initialize DMTET either as a 3D ellipsoid or as a customized 3D model provided by users; the latter choice is useful when the text-to-3D task is to be conditioned on users' preferences. In either case, we initialize  $\Psi$  by the following fitting procedure. We sample a point set  $\{p_{i} \in \mathbb{R}^{3}\}$  whose points are in close proximity to the initialized 3D ellipsoid or customized model, and compute their SDF values, resulting in  $\{SDF(p_{i})\}$ ; we use the following loss to optimize the parameters  $\psi$  of  $\Psi$ :
+
+$$
+\mathcal {L} _ {\mathrm {S D F}} = \sum_ {p _ {i} \in P} \| s (p _ {i}; \psi) - S D F (p _ {i}) \| _ {2} ^ {2}. \tag {3}
+$$
+
+# 4.2. Geometry modeling
+
+Previous text-to-3D methods [33, 13] commonly use NeRF [25, 4] as the implicit scene representation, which couples the geometry with color/appearance and use volume rendering for view synthesis. Since NeRF modeling is less effective for surface reconstruction [43, 46], these methods are consequently less effective to generate high-quality 3D surfaces by back-propagating the supervision of SDS loss through pre-trained text-to-image models. As a remedy, the method [18] uses a second stage of the refined generation that is based on scene modeling of explicit surfaces.
+
+In this work, we propose to decouple the generation of geometry from that of appearance, based on the hybrid scene representation of DMTET, which enables photorealistic surface rendering to make better use of the powerful pre-trained text-to-image models. More specifically, given the current DMTET with MLP parameters  $\psi$ , we generate a normal map  $n$ , together with an object mask  $o$ , as:
+
+$$
+(n, o) = g _ {n} (\psi , c), \tag {4}
+$$
+
+where  $g_{n}$  is a differentiable render (e.g., nvidiffrast [16]), and  $c$  is a sampled camera pose. We randomly sample the camera poses in the spherical coordinate system to ensure that the camera poses are distributed uniformly on the sphere. We propose to use the generated  $n$  (and  $o$ ) as the input of shape encoding to connect with stable diffusion. To update  $\psi$ , we again employ SDS loss that computes the gradient w.r.t.  $\psi$  as:
+
+$$
+\bigtriangledown_ {\psi} \mathcal {L} _ {\mathrm {S D S}} (\phi , \tilde {n}) = \mathbb {E} \left[ w (t) \left(\hat {\epsilon} _ {\phi} \left(z _ {t} ^ {\tilde {n}}; y, t\right) - \epsilon\right) \frac {\partial \tilde {n}}{\partial \psi} \frac {\partial z ^ {\tilde {n}}}{\partial \tilde {n}} \right], \tag {5}
+$$
+
+![](images/a9292b7196f2979ecd8e71863033957bbc30c2bcbd57e8c1788c7ee7c010a3c1.jpg)  
+Figure 4. Three components of the material model, namely the diffuse term  $k_{d}$ , the roughness and metallic term  $k_{rm}$ , and the normal variation term  $k_{n}$ .
+
+![](images/6f644163abc5fb23b018f1347ed4afa289c4ffc69a52407db83b1811defae0e5.jpg)  
+Figure 5. A comparison of UV edge padding (cf. the left column) and original texturing (cf. the right column). UV edge padding removes the white seams that appear in the right rendering.
+
+where  $\phi$  parameterizes the pre-trained stable diffusion model,  $\tilde{n}$  denotes concatenation of the normal  $n$  with the mask  $o$ ,  $z^{\tilde{n}}$  is the latent code of  $\tilde{n}$  via shape encoding,  $\hat{\epsilon}_{\phi}(z_t^{\tilde{n}};y,t)$  is the predicted noise given text embedding  $y$  and noise level  $t$ , and  $\epsilon$  is the noise added in  $z_t^{\tilde{n}}$ . In practice, we utilize a coarse-to-fine strategy to model the geometry. During the early phase of training, we use the downsampled  $\tilde{n}$  as the latent code, which is inspired by [23], to rapidly update  $\Psi$  and attain a coarse shape. However, a domain gap exists between  $\tilde{n}$  and the latent space data distribution learned by the VAE encoder in the stable diffusion, which may lead to a mismatch of the generated geometry from the textual description. To mitigate this discrepancy, we implement a data augmentation technique by introducing random rotations to  $\tilde{n}$ . Our experimental observations reveal that this technique enhances the alignment between the generated geometry and the provided textual description. In the later phase of training, aiming to capture finer geometric details with greater precision, we encode the high-resolution normal  $n$  (without the mask  $o$ ) to derive  $z^n$ , using the pretrained image encoder in stable diffusion.
+
+# 4.3. Appearance modeling
+
+Given a learned DMTET with geometry parameters  $\psi$ , we aim for photorealistic surface rendering to better leverage the powerful image diffusion model. This is achieved by introducing into text-to-3D generation the Physically-Based Rendering (PBR) material model. As illustrated in Fig. 4, the material model we use [21] comprises three components, namely the diffuse term  $k_{d} \in \mathbb{R}^{3}$ , the roughness and metallic term  $k_{rm} \in \mathbb{R}^{2}$ , and the normal variation term  $k_{n} \in \mathbb{R}^{3}$ . The  $k_{d}$  term denotes the diffuse value, while the  $k_{rm}$  term encompasses the roughness  $r$  and metalness  $m$ ; the roughness  $r$  serves as a metric for measuring the extent of specular reflection and a parameter of the GGX [42] normal distribution function in the rendering equation. The metalness parameter  $m$  and diffuse value  $k_{d}$  can be used to compute the specular term  $k_{s}$  using  $k_{s} = (1 - m) \cdot 0.04 + m \cdot k_{d}$ . Furthermore, we use a normal variation  $k_{n}$  in tangent space to enhance the surface lighting effect and introduce additional geometric variations.
+
+We use an MLP  $\Gamma$  as our parameterized material model.  $\Gamma$  is learned to predict spatially varying material parameters, which are subsequently used to render the surface extracted from DMTET. More specifically, for any point  $p\in \mathbb{R}^3$  on the surface, we use hash-grid positional encoding [27], and generate the diffuse term  $k_{d}$ , the specular term  $k_{rm}$ , and the tangent space normal  $k_{n}$  as:
+
+$$
+\left(k _ {d}, k _ {r m}, k _ {n}\right) = \Gamma (\beta (p); \gamma), \tag {6}
+$$
+
+where  $\beta$  is the positional encoding of  $p$ , and  $\gamma$  parameterizes the MLP  $\Gamma$ . The basic rendering equation suggests that each image pixel at a specific viewing direction can be rendered as
+
+$$
+L (p, \omega) = \int_ {\Omega} L _ {i} (p, \omega_ {i}) f (p, \omega_ {i}, \omega) (\omega_ {i} \cdot n _ {p}) \mathrm {d} \omega_ {i}, \tag {7}
+$$
+
+where  $L$  is the rendered pixel color along the direction  $\omega$  from the surface point  $p$ ,  $\Omega = \{\omega_i : \omega_i \cdot n_p \geq 0\}$  denotes a hemisphere with the incident direction  $\omega_i$  and surface normal  $n_p$  at  $p$ ,  $L_i$  is the incident light that is represented by an off-the-shelf environment map [32], and  $f$  is the BRDF determined by the material parameters  $(k_d, k_{rm}, k_n)$  predicted by (6). We note that  $L$  is the summation of diffuse intensity  $L_d$  and specular intensity  $L_s$ , and the two terms can be computed as follows:
+
+$$
+\begin{array}{l} L (p, \omega) = L _ {d} (p) + L _ {s} (p, \omega), \\ L _ {d} (p) = k _ {d} (1 - m) \int_ {\Omega} L _ {i} (p, \omega_ {i}) (\omega_ {i} \cdot n _ {p}) \mathrm {d} \omega_ {i}, \\ L _ {s} (p, \omega) = \int_ {\Omega} \frac {D F G}{4 (\omega \cdot n _ {p}) \left(\omega_ {i} \cdot n _ {p}\right)} L _ {i} \left(p, \omega_ {i}\right) \left(\omega_ {i} \cdot n _ {p}\right) \mathrm {d} \omega_ {i}, \tag {8} \\ \end{array}
+$$
+
+where  $F$ ,  $G$ , and  $D$  represent the Fresnel term, the shadowing-mask term, and the GGX distribution of normal, respectively. Following [28], the hemisphere integration can be calculated using the split-sum method.
+
+By aggregating the rendered pixel colors along the direction  $\omega$  (i.e., camera pose), we have the rendered image  $x = \{L(p,\omega)\}$  that connects with the image encoder of the pre-trained stable diffusion model. We update the parameters  $\gamma$  by computing the gradient of the SDS loss w.r.t.  $\gamma$ :
+
+$$
+\nabla_ {\gamma} \mathcal {L} _ {\mathrm {S D S}} (\phi , x) = \mathbb {E} \left[ w (t) \left(\hat {\epsilon} _ {\phi} \left(z _ {t} ^ {x}; y, t\right) - \epsilon\right) \frac {\partial x}{\partial \gamma} \frac {\partial z ^ {x}}{\partial x} \right]. \tag {9}
+$$
+
+Notations in (9) are similarly defined as those in (5).
+
+Texturing. Given the trained  $\Gamma$ , we proceed by sampling the generated appearance as 2D texture maps, in accordance with the UV map generated by the xatlas [47]. Note that texture seams would emerge by direct incorporation of the sampled 2D textures into graphics engines (e.g., Blender [10]). We instead employ the UV edge padding technique [9], which involves expanding the boundaries of UV islands and filling empty regions. As illustrated in Fig. 5, this padding technique removes background pixels in the texture map and also removes the seams in the resulting renderings.
+
+Implementation Details. We implement the network  $\Psi$  as a three-layer MLP with 32 hidden units, and implement  $\Gamma$  as a two-layer MLP with 32 hidden units. Our method is optimized on 8 Nvidia RTX 3090 GPUs for about 15 minutes for learning  $\Psi$  and about 16 minutes for learning  $\Gamma$ , respectively, where we use AdamW optimizer with the respective learning rates of  $1 \times 10^{-3}$  and  $1 \times 10^{-2}$ . For each iteration, we uniformly sample 24 camera poses for the rendering of normal maps and colored images. More details of our implementation are available in the supplemental material. In geometry modeling, we set  $\omega(t) = \sigma^2$  during the early phase and then transition to  $w(t) = \sigma^2 \sqrt{1 - \sigma^2}$  as we progress to the later phase. In appearance modeling, we apply  $w(t) = \sigma^2 \sqrt{1 - \sigma^2}$  during the early phase, followed by a shift to  $1 / \sigma^2$  as we enter the later phase. This approach mitigates the issue related to over-saturated color within the appearance modeling.
+
+# 5. Experiments
+
+In this section, we present comprehensive experiments to evaluate the efficacy of our proposed method for text-to-3D content creation. We first conduct ablation studies in Section 5.1 that verify the importance of our key design of disentangling geometry and appearance for text-to-3D generation. In Section 5.2, we show the efficacy of our method for the generation of 3D models with PBR materials from arbitrary text prompts, where we also compare with two recent state-of-the-art methods (namely, Magic3D [18] and DreamFusion [33]). In Section 5.3, we present our results
+
+under the setting of user-guided generation and compare them with Latent-NeRF [23]. We finally demonstrate in Section 5.4 that the 3D assets generated by our method are readily compatible with popular graphics engines such as Blender [10], thus facilitating relighting, editing, and physical simulation of the resulting 3D models.
+
+# 5.1. Ablation studies
+
+We use an example text prompt of "a highly detailed stone bust of Theodoros Kolokotronis" for the ablation studies. Results of alternative settings are given in Fig. 6. As the reference, the first two columns show the geometry and appearance results of our Fantasia3D rendered from the front and back views. To verify the effectiveness of the disentangled design in Fantasia3D, we also conduct experiments as follows: in each iteration, we render shaded images of the mesh extracted from DMTET, and learn to update the parameters of a network responsible for both the geometry and material, using the gradient computed by SDS loss. Results in the second two columns show that such an entangled learning fails to generate plausible results. Previous methods (e.g., DreamFusion [33] and Magic3D [18]) couple the geometry and appearance generation together, following NeRF [25]. Our adoption of the disentangled representation is mainly motivated by the difference of problem nature for generating surface geometry and appearance. In fact, when dealing with finer recovery of surface geometry from multi-view images, methods (e.g., VolSDF [46], ndiffrec [28], etc) that explicitly take the surface modeling into account triumph; our disentangled representation enjoys the benefit similar to these methods. The disentangled representation also enables us to include the BRDF material representation in the appearance modeling, achieving better photo-realistic rendering by the BRDF physical prior.
+
+To investigate how shape encoding of the normal map plays role in Fantasia3D, we replace the normal map with an image that is shaded on the mesh extracted from DMTET using fixed material parameters; results in the third two columns become weird with twisted geometries. This is indeed one of the key factors that makes the success of Fantasia3D. Our initial hypothesis is that shape information contained in normal and mask images could be beneficial to geometry learning, and as such, we further observe that the value range of normal maps is normalized in  $(-1, 1)$ , which aligns with the data range required for latent space diffusion; our empirical studies verify our hypothesis. Our hypothesis is further corroborated by observing that the LAION-5B [37] dataset used for training Stable Diffusion contains normals (referring to website for retrieval of normal data in LAION-5B [37]), which allows Stable Diffusion to handle the optimization of normal maps effectively. To deal with rough and coarse geometry in the early stage of learning, we use the concatenated  $64 \times 64 \times 4$  (normal,
+
+mask) images for better convergence. As the learning progresses, it becomes essential to render the  $512 \times 512 \times 3$  high-resolution normal images for capturing finer geometry details, and we choose to use normal images only in the later stage. This strategy strikes an accuracy-efficiency balance throughout the geometry optimization process.
+
+Finally, we replace the full BRDF in Fantasia3D with a simple diffuse color rendering; the results in the last two columns become less realistic and are short of reflection effects when rendered from different views.
+
+# 5.2. Zero-shot generation
+
+In this section, we evaluate our method for generating 3D assets from solely natural language descriptions (i.e., the setting of zero-shot generation), by comparing with two state-of-the-art methods, namely DreamFusion [33] and Magic3D [18]. Fig. 7 gives the comparative results given the same text prompts. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. Comparing our method with Magic3D, we observe that our results are more photorealistic with competitive geometries. We consistently outperform DreamFusion in both appearance and geometry generation. Notably, our method also offers the convenience of easy geometry extraction and editing, as demonstrated in 5.4, which are less obvious from DreamFusion or Magic3D. More of our results are given in the top half of Fig. 2 and Fig. 8. Furthermore, we compare our appearance modeling stage with several mesh stylization methods, namely Text2mesh [24], CLIP-Mesh [14] and Latent-NeRF [23]. Fig. 9 shows that our method excels in generating more realistic appearances, outperforming the other competitors. We present additional results and comparisons in the supplemental materials.
+
+# 5.3. User-guided generation
+
+In addition to zero-shot generation, our method is flexible to accept a customized 3D model as the initialization, alternative to a 3D ellipsoid, thereby facilitating user-guided asset generation. As shown in the lower half of Fig. 2, our method is able to generate rich details in both the geometry and appearance when provided with low-quality 3D models for initialization. The three meshes used in the experiments are from Text2Mesh [24], Latent-NeRF [23], and the creation of Stable DreamFusion [41], respectively. We also compare with the state-of-the-art approach of Latent-NeRF [23] under this user-guided generation setting; results are given in Fig. 10. Our method outperforms Latent-NeRF [23] in both the geometry and texture generation when given the same input meshes and text prompts.
+
+![](images/90fc4edd80a9d14b2ecc57ad26065df184394285f382d351e77384ce0fffec43.jpg)  
+Figure 6. Ablation studies of our method. The text prompt is "a highly detailed stone bust of Theodoros Kolokotronis". Please refer to Section 5.1 for specific settings of individual columns. Please refer to the video results in the supplemental materials for better comparisons.
+
+![](images/26f31b77563130a7e73b932d38d49e3bed73d3e99e6a89ee6de0cdec610cc77f.jpg)  
+A 3D model of an adorable cottage with a thatched roof
+
+![](images/9c2b524a175e69f80b8cb6910c8cf53e1df5785e7315e4f90669cf3e229aeb87.jpg)  
+Figure 8. Geometries beyond genus-zero ones. DMTET can deform to any topologies, which enables Fantasia3D to generate complex geometries, including those beyond genus-zero ones.
+
+# 5.4. Scene editing and simulation
+
+Given the disentangled design, our method produces high-quality generation of both the surface and appearance, and is compatible with popular graphics engines for scene editing and physical simulation. In Figure 1, we import into
+
+![](images/1bcca3ebbd3a06cd4d488e7d69f1bbaf2d9c320b2f3acf54c4b72a97fb4de7c3.jpg)  
+Figure 7. Comparison of zero-shot generation. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. More results and comparisons are available in the supplemental materials.  
+Figure 9. Comparison of Texturing. We compare the appearance stage of Fantasia3D with three text-driven texturing methods, using the geometry generated by the geometry stage of Fantasia3D.
+
+Blender a stone statue generated by our method from the text prompt of "a highly detailed stone bust of Theodoros Kolokotronis", where soft body and cloth simulations are performed along with material editing. Given the high qual
+
+![](images/2fefd7402f365968e37abfa2fdd69ac05811d5df7ff2c82ee6639f71c540c7a0.jpg)  
+Latent -NeRF  
+Ours  
+A robot hand, realistic  
+A teddy bear in a tuxedo  
+A German Shepherd
+
+![](images/513fdc5ce70fe11e9496aa15d0c0f0d58257daca1feb5ce76727407754fcf6b2.jpg)  
+Figure 10. Comparison of user-guided generation. The top row shows the input meshes provided by users, the bottom row gives the input text prompts, and the middle two rows show the results from the comparative methods.  
+Figure 11. Scene Editing. Three generated objects, namely crown, tiger, and ice cream, are imported into the Cornell Box scene. The scene is then rendered using the Cycles path tracer in Blender, producing natural shadows and reflectance effects.
+
+![](images/865ce3ebe886c160b4d5062fc459c395e17bd01f9eb6eda8e9519790a5ccf4df.jpg)  
+Original  
+Figure 12. Relighting. Our generated Iron Man model is relit using different lighting setups in Blender, producing diverse reflectance effects on the armor.
+
+![](images/71c6448fe863f12eecc4d8b63406fa896669848e8a5d58691f969869ad572f7f.jpg)  
+Factory
+
+![](images/c96d51c45b96de43aef0245606b668a1ff4e25e1bf42f95eecee602db3a4a5fe.jpg)  
+Night
+
+![](images/7d58f17661be479ef40debeb6fdf66026eb1da9fb8e12a33fff9e2cee3bcf8be.jpg)  
+Studio
+
+![](images/610b8842a83c9c64698a995d209d2817682a8c779cc1878256c466a66e074071.jpg)  
+Sunset
+
+ity of the generated surface geometry (e.g., no holes on the surface), the simulations are of high-level physical accuracy, as shown in the accompanying supplemental video.
+
+Moreover, we showcase the ability to modify the material of the statue by replacing it with another wood material downloaded from the Internet [32], which poses a challenge for comparative methods such as DreamFusion [33]. Additionally, in Fig. 11, by importing generated ice cream, tiger, and crown into the Cornell Box, we demonstrate the plausible physical interaction between our generated results and the scene, with natural shadows being cast. Finally, Fig. 12 illustrates the replacement of the HDR environment map to produce diverse lighting and corresponding reflectance effects on the generated iron man.
+
+# 6. Limitations
+
+While Fantasia3D demonstrates promising advancements in the realm of generating photorealistic 3D assets from text prompts, several limitations remain. For instance, while our method successfully produces loose visual effects, it remains a significant challenge to generate corresponding loose geometries, such as hair, fur, and grass, solely based on text prompts. Additionally, our method primarily emphasizes object generation, thereby lacking the capacity to generate complete scenes with background from text prompts. Consequently, our future research endeavors will be dedicated to addressing these limitations by focusing on the generation of complete scenes and intricate loose geometries.
+
+# 7. Conclusion
+
+In this paper, we present Fantasia3D, a new method for automatic text-to-3D generation. Fantasia3D uses disentangled modeling and learning of geometry and appearance, and is able to generate both the fine surface and rich material/texture. Fantasia3D is based on the hybrid scene representation of DMTET. For geometry learning, we propose to encode a rendered normal map, and use shape encoding of the normal as the input of the pre-trained, stable diffusion model. For appearance modeling, we introduce the spatially varying BRDF into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. Expect for text prompts, our method can be triggered with a customized 3D shape as well; this is flexible for users to better control what content is to be generated. Our method is also convenient to support relighting, editing, and physical simulation of the generated 3D assets. Our method is based on pre-trained image diffusion models (i.e., the stable diffusion). In future research, we are interested in learning 3D diffusion directly from the large language models.
+
+Acknowledgements. This work is supported in part by Program for Guangdong Introducing Innovative and Entrepreneurial Teams (No.: 2017ZT07X183) and Guangdong R&D key project of China (No.: 2019B010155001).
+
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+                                    "content": "Rui Chen,\\* Yongwei Chen,\\* Ningxin Jiao, Kui Jia\\* South China University of Technology"
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+                                    "content": "Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/."
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+                                    "content": "In this work, we are motivated to use 3D scene representations that are more amenable to the generation of high-quality 3D assets given text prompts. We present an automatic text-to-3D method called Fantasia3D. Key to Fantasia3D is a disentangled learning of geometry and appearance models, such that both a fine surface and a rich material/texture can be generated. To enable such a disentangled learning, we use the hybrid scene representation of DMTET [38], which maintains a deformable tetrahedral grid and a differentiable mesh extraction layer; deformation can thus be learned through the layer to explicitly control the shape generation. For geometry learning, we technically propose to encode a rendered normal map, and use shape encoding of the normal as the input of a pre-trained, image diffusion model; this is in contrast different from existing methods that commonly encode rendered color images. For appearance modeling, we introduce, for the first time, the spatially varying Bidirectional Reflectance Distribution Function (BRDF) into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. We implement the geometry model and the BRDF appearance model as simple MLPs. Both models are learned through the pre-trained image diffusion model, using a loss of Score Distillation Sampling (SDS) [33]. We use the pre-trained stable diffusion [35, 40] as the image generation model in this work."
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+                                    "content": "We note that except for text prompts, our method can also be triggered with additional inputs of users' preferences, such as a customized 3D shape or a generic 3D shape of a certain object category; this is flexible for users to better control what content is to be generated. In addition, given the disentangled generation of geometry and appearance, it is convenient for our method to support relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments to verify the efficacy of our proposed methods. Results show that our proposed Fantasia3D outperforms existing methods for high-quality and diverse 3D content creation. We summarize our technical contributions as follows."
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+                                    "content": "- We propose a novel method, termed Fantasia3D, for high-quality text-to-3D content creation. Our method disentangles the modeling and learning of geometry and appearance, and thus enables both a fine recovery of geometry and photorealistic rendering of per-view images."
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+                                    "content": "- For geometry learning, we use a hybrid representation"
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+                                    "content": "of DMTET, which supports learning surface deformation via a differentiable mesh extraction; we propose to render and encode the surface normal extracted from DMTET as the input of the pre-trained image diffusion model, which enables more subtle control of shape generation."
+                                }
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+                                    "content": "- For appearance modeling, to the best of our knowledge, we are the first to introduce the full BRDF learning into text-to-3D content creation, facilitated by our proposed geometry-appearance disentangled framework. BRDF modeling promises high-quality 3D generation via photorealistic rendering."
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+                                    "content": "Text-to-3D content creation. Motivated by the desire to generate high-quality 3D content from simple semantics such as text prompts, text-to-3D has drawn considerable attention in recent years [33, 13, 18]. Existing methods either use pre-trained 2D text-to-image models [35, 3, 36], together with score distillation sampling [33], to generate 3D geometries [18] or synthesize novel views [33], or train a text-conditioned 3D generative model from scratch [39, 49, 17, 29]. These methods generate 3D geometries with little exploration of generating high-quality lighting and surface materials. On the other hand, TANGO [8] is able to generate high-quality surface materials given text prompts; unfortunately, the method requires as input a 3D surface mesh. Our proposed method addresses the shortcomings of the above methods, and is able to generate both high-quality surface geometries and their corresponding materials, both of which are crucial for photorealistic rendering of the generated 3D content. Our method thus, for the first time, closes the loop of object-level text-to-3D content creation."
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+                                    "content": "Surface material estimation. The estimation of surface materials is a long-standing challenge in computer vision and graphics research. Earlier methods [2, 45] focus on recovering physically based materials under known lighting conditions, whose usefulness is, however, limited in real-world scenarios. Subsequent methods [12, 11, 5, 1] try to estimate materials under natural lighting conditions, assuming the availability of complete geometry information. More recently, the joint reconstruction of geometry and materials is proposed given calibrated multi-view images [6, 7, 19, 48]. Alternative to these methods, we explore the novel creation of surface materials and geometries from trained language models."
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+                                    "content": "3. Preliminary"
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+                                            "content": "Figure 3. Overview of our method. Our method can generate disentangled geometry and appearance given a text prompt (cf. figure (a)), which are produced by (b) geometry modeling and (c) appearance modeling, respectively. (b) We employ DMTET as our 3D geometry representation, which is initialized as a 3D ellipsoid here. To optimize the parameters of DMTET, we render the normal map (and the object mask in the early training phase) of the extracted mesh from DMTet as the shape encoding of stable diffusion [35, 40]. (c) For appearance modeling, we introduce the spatially-varying Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn to predict three components (namely, "
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+                                            "type": "text",
+                                            "content": ") of the appearance. Both geometry and appearance modeling are supervised by Score Distillation Sampling (SDS) loss [33]."
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+                                    ]
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+                            ],
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+                            "angle": 0,
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+                                    "content": "renders 2D images "
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+                                    "type": "text",
+                                    "content": " from a modified Mip-NeRF [4] parameterized as "
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+                                    "type": "text",
+                                    "content": ". DreamFusion leverages a diffusion model "
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+                                    "type": "text",
+                                    "content": " (Imagen [36] in this instance) to provide a score function "
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+                                    "content": "\\hat{\\epsilon}_{\\phi}(x_t; y, t)"
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+                                    "type": "text",
+                                    "content": ", which predicts the sampled noise "
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+                                    "type": "text",
+                                    "content": " given the noisy image "
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+                                    "content": ". This score function guides the direction of the gradient for updating the scene parameters "
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+                                    "content": ", and the gradient is calculated by Score Distillation Sampling (SDS):"
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+                                    "content": "\\bigtriangledown_ {\\theta} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , x) = \\mathbb {E} _ {t, \\epsilon} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(x _ {t}; y, t\\right) - \\epsilon\\right) \\frac {\\partial x}{\\partial \\theta} \\right], \\tag {1}",
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+                                    "type": "text",
+                                    "content": "while "
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+                                    "content": " is a weighting function. Since Imagen is not publicly accessible, in this work, we use the released latent space diffusion model of Stable Diffusion [35, 40] as our guidance model, and revise the SDS loss (1) accordingly. Details are given in Section 4.2."
+                                }
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+                                    "content": "Implicit surface representations [25, 31, 22] are popularly used in novel view synthesis and 3D reconstruction, due to their capabilities to represent complex scenes. However, surfaces of lower quality may be obtained [28] by extracting explicit meshes from these implicit representations using marching cubes [20]. Instead, Shen et al. [38] propose a hybrid representation, termed DMTET, that has two key features, i.e., a deformable tetrahedral grid and a differentiable Marching Tetrahedral (MT) layer. The deformable tetrahedral grid "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " in the tetrahedral grid "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". For each vertex "
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+                                    "content": "v_{i} \\in V_{T}"
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+                                    "type": "text",
+                                    "content": ", the proposed method predicts the Signed Distance Function (SDF) value "
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+                                    "content": " and a position offset "
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+                                    "type": "text",
+                                    "content": " is the parameters of a network "
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+                                    "type": "text",
+                                    "content": ", enabling the extraction of explicit meshes through MT layer during each"
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+                                    "type": "text",
+                                    "content": "iteration of training. In this work, We use DMTET as our geometry representation and render the mesh extracted from MT layer iteratively by a differentiable renderer[16, 28]."
+                                }
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+                                    "content": "4. The Proposed Method"
+                                }
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+                                    "type": "text",
+                                    "content": "In this section, we present our proposed method of Fantasia3D for high-quality text-to-3D object generation, by disentangling the modeling and learning of geometry and appearance. For geometry modeling, we rely on the hybrid surface representation of DMTET, and parameterize the 3D geometry as an MLP "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " that learns to predict the SDF value and position offset for each vertex in the deformable tetrahedral grid of DMTET; in contrast to previous methods, we propose to use the rendered normal map (and the object mask in the early training phase) of the extracted mesh from DMTET as the input of shape encoding. For appearance modeling, we introduce, for the first time, the full Bidirectional Reflectance Distribution Function (BRDF) modeling into text-to-3D generation, and learn an MLP "
+                                },
+                                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " that predicts parameters of surface material and supports high-quality 3D generation via photorealistic rendering. Given the disentangled modeling of "
+                                },
+                                {
+                                    "bbox": [
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+                                        403,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Psi"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\Gamma"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the whole pipeline is learned with SDS supervision, and the gradients are backpropagated through the pre-trained stable diffusion model. Our pipeline is initialized either as a 3D ellipsoid or as a customized 3D model provided by users. Fig. 3 gives an illustration of our proposed method. In contrast, previous methods couple the geometry and appearance learning, and are suboptimal in terms of leveraging the powerful pretrained 2D image diffusion models via SDS loss. Details of the proposed Fantasia3D are presented as follows."
+                                }
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+                                    "type": "text",
+                                    "content": "4.1. DMTET initialization"
+                                }
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+                                    "content": "We adopt DMTET as our 3D scene representation, which is parameterized as the MLP network "
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+                                    "type": "text",
+                                    "content": ". For each vertex "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "v_{i} \\in V_{T}"
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+                                    "type": "text",
+                                    "content": " of the tetrahedral grid "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(V_{T}, T)"
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+                                    "type": "text",
+                                    "content": ", "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\Psi"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is trained to predict the SDF value "
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+                                    "type": "inline_equation",
+                                    "content": "s(v_{i})"
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+                                {
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+                                    "type": "text",
+                                    "content": " and the deformation offset "
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+                                    "type": "inline_equation",
+                                    "content": "\\triangle v_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                        89,
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+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ". A triangular mesh can be extracted from "
+                                },
+                                {
+                                    "bbox": [
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+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(V_{T}, T)"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " using the MT layer, whose procedure is also differentiable w.r.t. the parameters of "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\Psi"
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+                                {
+                                    "bbox": [
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+                                        89,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We initialize DMTET either as a 3D ellipsoid or as a customized 3D model provided by users; the latter choice is useful when the text-to-3D task is to be conditioned on users' preferences. In either case, we initialize "
+                                },
+                                {
+                                    "bbox": [
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+                                        270
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+                                    "type": "inline_equation",
+                                    "content": "\\Psi"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        89,
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+                                    ],
+                                    "type": "text",
+                                    "content": " by the following fitting procedure. We sample a point set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{p_{i} \\in \\mathbb{R}^{3}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        89,
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+                                    ],
+                                    "type": "text",
+                                    "content": " whose points are in close proximity to the initialized 3D ellipsoid or customized model, and compute their SDF values, resulting in "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\{SDF(p_{i})\\}"
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+                                    "type": "text",
+                                    "content": "; we use the following loss to optimize the parameters "
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+                                    "type": "text",
+                                    "content": " of "
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {S D F}} = \\sum_ {p _ {i} \\in P} \\| s (p _ {i}; \\psi) - S D F (p _ {i}) \\| _ {2} ^ {2}. \\tag {3}",
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+                                    "type": "text",
+                                    "content": "4.2. Geometry modeling"
+                                }
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+                                    "type": "text",
+                                    "content": "Previous text-to-3D methods [33, 13] commonly use NeRF [25, 4] as the implicit scene representation, which couples the geometry with color/appearance and use volume rendering for view synthesis. Since NeRF modeling is less effective for surface reconstruction [43, 46], these methods are consequently less effective to generate high-quality 3D surfaces by back-propagating the supervision of SDS loss through pre-trained text-to-image models. As a remedy, the method [18] uses a second stage of the refined generation that is based on scene modeling of explicit surfaces."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "In this work, we propose to decouple the generation of geometry from that of appearance, based on the hybrid scene representation of DMTET, which enables photorealistic surface rendering to make better use of the powerful pre-trained text-to-image models. More specifically, given the current DMTET with MLP parameters "
+                                },
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+                                    "content": ", we generate a normal map "
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+                                    "type": "text",
+                                    "content": ", together with an object mask "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", as:"
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+                                    "content": "where "
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+                                    "type": "text",
+                                    "content": " is a sampled camera pose. We randomly sample the camera poses in the spherical coordinate system to ensure that the camera poses are distributed uniformly on the sphere. We propose to use the generated "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " (and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ") as the input of shape encoding to connect with stable diffusion. To update "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we again employ SDS loss that computes the gradient w.r.t. "
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+                                    "type": "text",
+                                    "content": " as:"
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+                                    "type": "interline_equation",
+                                    "content": "\\bigtriangledown_ {\\psi} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , \\tilde {n}) = \\mathbb {E} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(z _ {t} ^ {\\tilde {n}}; y, t\\right) - \\epsilon\\right) \\frac {\\partial \\tilde {n}}{\\partial \\psi} \\frac {\\partial z ^ {\\tilde {n}}}{\\partial \\tilde {n}} \\right], \\tag {5}",
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+                                            "content": "Figure 5. A comparison of UV edge padding (cf. the left column) and original texturing (cf. the right column). UV edge padding removes the white seams that appear in the right rendering."
+                                        }
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+                                    "type": "text",
+                                    "content": " parameterizes the pre-trained stable diffusion model, "
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+                                    "type": "text",
+                                    "content": " denotes concatenation of the normal "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "z^{\\tilde{n}}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the latent code of "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " via shape encoding, "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\epsilon}_{\\phi}(z_t^{\\tilde{n}};y,t)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the predicted noise given text embedding "
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+                                    "content": " and noise level "
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " is the noise added in "
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+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". In practice, we utilize a coarse-to-fine strategy to model the geometry. During the early phase of training, we use the downsampled "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " as the latent code, which is inspired by [23], to rapidly update "
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+                                    "type": "inline_equation",
+                                    "content": "\\Psi"
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+                                    "type": "text",
+                                    "content": " and attain a coarse shape. However, a domain gap exists between "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and the latent space data distribution learned by the VAE encoder in the stable diffusion, which may lead to a mismatch of the generated geometry from the textual description. To mitigate this discrepancy, we implement a data augmentation technique by introducing random rotations to "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". Our experimental observations reveal that this technique enhances the alignment between the generated geometry and the provided textual description. In the later phase of training, aiming to capture finer geometric details with greater precision, we encode the high-resolution normal "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " (without the mask "
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+                                    "type": "text",
+                                    "content": ") to derive "
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+                                    "type": "inline_equation",
+                                    "content": "z^n"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", using the pretrained image encoder in stable diffusion."
+                                }
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+                        }
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+            ],
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+                                    "content": "4.3. Appearance modeling"
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+                                    "type": "text",
+                                    "content": "Given a learned DMTET with geometry parameters "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we aim for photorealistic surface rendering to better leverage the powerful image diffusion model. This is achieved by introducing into text-to-3D generation the Physically-Based Rendering (PBR) material model. As illustrated in Fig. 4, the material model we use [21] comprises three components, namely the diffuse term "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "k_{d} \\in \\mathbb{R}^{3}"
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+                                {
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+                                    "type": "text",
+                                    "content": ", the roughness and metallic term "
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+                                    "type": "inline_equation",
+                                    "content": "k_{rm} \\in \\mathbb{R}^{2}"
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+                                    "type": "text",
+                                    "content": ", and the normal variation term "
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+                                    "type": "inline_equation",
+                                    "content": "k_{n} \\in \\mathbb{R}^{3}"
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+                                    "type": "text",
+                                    "content": ". The "
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " term denotes the diffuse value, while the "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "k_{rm}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " term encompasses the roughness "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "r"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and metalness "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "m"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "; the roughness "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        305
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " serves as a metric for measuring the extent of specular reflection and a parameter of the GGX [42] normal distribution function in the rendering equation. The metalness parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "inline_equation",
+                                    "content": "m"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and diffuse value "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "k_{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " can be used to compute the specular term "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{s}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " using "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{s} = (1 - m) \\cdot 0.04 + m \\cdot k_{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        91,
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+                                        305
+                                    ],
+                                    "type": "text",
+                                    "content": ". Furthermore, we use a normal variation "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{n}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in tangent space to enhance the surface lighting effect and introduce additional geometric variations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
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+                                    ],
+                                    "type": "text",
+                                    "content": "We use an MLP "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " as our parameterized material model. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " is learned to predict spatially varying material parameters, which are subsequently used to render the surface extracted from DMTET. More specifically, for any point "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p\\in \\mathbb{R}^3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " on the surface, we use hash-grid positional encoding [27], and generate the diffuse term "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": ", the specular term "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{rm}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the tangent space normal "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        307,
+                                        287,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        110,
+                        402,
+                        287,
+                        416
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\left(k _ {d}, k _ {r m}, k _ {n}\\right) = \\Gamma (\\beta (p); \\gamma), \\tag {6}",
+                                    "image_path": "7666b98533f2263cc2617c829fa06620eb423cc441b7a13036823b99b2082840.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
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+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " is the positional encoding of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " parameterizes the MLP "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        426,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ". The basic rendering equation suggests that each image pixel at a specific viewing direction can be rendered as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        64,
+                        482,
+                        287,
+                        508
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        64,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L (p, \\omega) = \\int_ {\\Omega} L _ {i} (p, \\omega_ {i}) f (p, \\omega_ {i}, \\omega) (\\omega_ {i} \\cdot n _ {p}) \\mathrm {d} \\omega_ {i}, \\tag {7}",
+                                    "image_path": "6ac6dbbbf6f651170208b51cd03605aaf43f20a7905a4513e1d566761ea48a7c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
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+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " is the rendered pixel color along the direction "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\omega"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " from the surface point "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Omega = \\{\\omega_i : \\omega_i \\cdot n_p \\geq 0\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes a hemisphere with the incident direction "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\omega_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " and surface normal "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " is the incident light that is represented by an off-the-shelf environment map [32], and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " is the BRDF determined by the material parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(k_d, k_{rm}, k_n)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " predicted by (6). We note that "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " is the summation of diffuse intensity "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " and specular intensity "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_s"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        517,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the two terms can be computed as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        54,
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+                        714
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        54,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} L (p, \\omega) = L _ {d} (p) + L _ {s} (p, \\omega), \\\\ L _ {d} (p) = k _ {d} (1 - m) \\int_ {\\Omega} L _ {i} (p, \\omega_ {i}) (\\omega_ {i} \\cdot n _ {p}) \\mathrm {d} \\omega_ {i}, \\\\ L _ {s} (p, \\omega) = \\int_ {\\Omega} \\frac {D F G}{4 (\\omega \\cdot n _ {p}) \\left(\\omega_ {i} \\cdot n _ {p}\\right)} L _ {i} \\left(p, \\omega_ {i}\\right) \\left(\\omega_ {i} \\cdot n _ {p}\\right) \\mathrm {d} \\omega_ {i}, \\tag {8} \\\\ \\end{array}",
+                                    "image_path": "43d8bebbdee85a4605fbfbf97fec80185d7f4caf93ddd03c65d94aa0aea0ef1c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
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+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": " represent the Fresnel term, the shadowing-mask term, and the GGX distribution of normal, respectively. Following [28], the hemisphere integration can be calculated using the split-sum method."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
+                        120,
+                        545,
+                        180
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                120,
+                                545,
+                                180
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "text",
+                                    "content": "By aggregating the rendered pixel colors along the direction "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\omega"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "text",
+                                    "content": " (i.e., camera pose), we have the rendered image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x = \\{L(p,\\omega)\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "text",
+                                    "content": " that connects with the image encoder of the pre-trained stable diffusion model. We update the parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "text",
+                                    "content": " by computing the gradient of the SDS loss w.r.t. "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        311,
+                        196,
+                        545,
+                        223
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                311,
+                                196,
+                                545,
+                                223
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        311,
+                                        196,
+                                        545,
+                                        223
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\nabla_ {\\gamma} \\mathcal {L} _ {\\mathrm {S D S}} (\\phi , x) = \\mathbb {E} \\left[ w (t) \\left(\\hat {\\epsilon} _ {\\phi} \\left(z _ {t} ^ {x}; y, t\\right) - \\epsilon\\right) \\frac {\\partial x}{\\partial \\gamma} \\frac {\\partial z ^ {x}}{\\partial x} \\right]. \\tag {9}",
+                                    "image_path": "fdaf2037f33c8e8bf0ac000111e22c77228ace9f6d5e509bcac0dd7771adf0c7.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        229,
+                        517,
+                        240
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        229,
+                                        517,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": "Notations in (9) are similarly defined as those in (5)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                        361
+                                    ],
+                                    "type": "text",
+                                    "content": "Texturing. Given the trained "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        241,
+                                        545,
+                                        361
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        241,
+                                        545,
+                                        361
+                                    ],
+                                    "type": "text",
+                                    "content": ", we proceed by sampling the generated appearance as 2D texture maps, in accordance with the UV map generated by the xatlas [47]. Note that texture seams would emerge by direct incorporation of the sampled 2D textures into graphics engines (e.g., Blender [10]). We instead employ the UV edge padding technique [9], which involves expanding the boundaries of UV islands and filling empty regions. As illustrated in Fig. 5, this padding technique removes background pixels in the texture map and also removes the seams in the resulting renderings."
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+                                    "content": "Implementation Details. We implement the network "
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+                                    "content": " as a three-layer MLP with 32 hidden units, and implement "
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+                                    "content": " as a two-layer MLP with 32 hidden units. Our method is optimized on 8 Nvidia RTX 3090 GPUs for about 15 minutes for learning "
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+                                    "content": ", respectively, where we use AdamW optimizer with the respective learning rates of "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". For each iteration, we uniformly sample 24 camera poses for the rendering of normal maps and colored images. More details of our implementation are available in the supplemental material. In geometry modeling, we set "
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+                                    "content": "\\omega(t) = \\sigma^2"
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+                                    "type": "text",
+                                    "content": " as we progress to the later phase. In appearance modeling, we apply "
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+                                    "content": "w(t) = \\sigma^2 \\sqrt{1 - \\sigma^2}"
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+                                    "type": "text",
+                                    "content": " during the early phase, followed by a shift to "
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+                                    "content": "1 / \\sigma^2"
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+                                    "type": "text",
+                                    "content": " as we enter the later phase. This approach mitigates the issue related to over-saturated color within the appearance modeling."
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+                                    "content": "5. Experiments"
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+                                    "content": "In this section, we present comprehensive experiments to evaluate the efficacy of our proposed method for text-to-3D content creation. We first conduct ablation studies in Section 5.1 that verify the importance of our key design of disentangling geometry and appearance for text-to-3D generation. In Section 5.2, we show the efficacy of our method for the generation of 3D models with PBR materials from arbitrary text prompts, where we also compare with two recent state-of-the-art methods (namely, Magic3D [18] and DreamFusion [33]). In Section 5.3, we present our results"
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+                                    "content": "under the setting of user-guided generation and compare them with Latent-NeRF [23]. We finally demonstrate in Section 5.4 that the 3D assets generated by our method are readily compatible with popular graphics engines such as Blender [10], thus facilitating relighting, editing, and physical simulation of the resulting 3D models."
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+                                    "content": "We use an example text prompt of \"a highly detailed stone bust of Theodoros Kolokotronis\" for the ablation studies. Results of alternative settings are given in Fig. 6. As the reference, the first two columns show the geometry and appearance results of our Fantasia3D rendered from the front and back views. To verify the effectiveness of the disentangled design in Fantasia3D, we also conduct experiments as follows: in each iteration, we render shaded images of the mesh extracted from DMTET, and learn to update the parameters of a network responsible for both the geometry and material, using the gradient computed by SDS loss. Results in the second two columns show that such an entangled learning fails to generate plausible results. Previous methods (e.g., DreamFusion [33] and Magic3D [18]) couple the geometry and appearance generation together, following NeRF [25]. Our adoption of the disentangled representation is mainly motivated by the difference of problem nature for generating surface geometry and appearance. In fact, when dealing with finer recovery of surface geometry from multi-view images, methods (e.g., VolSDF [46], ndiffrec [28], etc) that explicitly take the surface modeling into account triumph; our disentangled representation enjoys the benefit similar to these methods. The disentangled representation also enables us to include the BRDF material representation in the appearance modeling, achieving better photo-realistic rendering by the BRDF physical prior."
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+                                    "content": "To investigate how shape encoding of the normal map plays role in Fantasia3D, we replace the normal map with an image that is shaded on the mesh extracted from DMTET using fixed material parameters; results in the third two columns become weird with twisted geometries. This is indeed one of the key factors that makes the success of Fantasia3D. Our initial hypothesis is that shape information contained in normal and mask images could be beneficial to geometry learning, and as such, we further observe that the value range of normal maps is normalized in "
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+                                    "content": ", which aligns with the data range required for latent space diffusion; our empirical studies verify our hypothesis. Our hypothesis is further corroborated by observing that the LAION-5B [37] dataset used for training Stable Diffusion contains normals (referring to website for retrieval of normal data in LAION-5B [37]), which allows Stable Diffusion to handle the optimization of normal maps effectively. To deal with rough and coarse geometry in the early stage of learning, we use the concatenated "
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+                                    "content": "mask) images for better convergence. As the learning progresses, it becomes essential to render the "
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+                                    "content": " high-resolution normal images for capturing finer geometry details, and we choose to use normal images only in the later stage. This strategy strikes an accuracy-efficiency balance throughout the geometry optimization process."
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+                                    "content": "Finally, we replace the full BRDF in Fantasia3D with a simple diffuse color rendering; the results in the last two columns become less realistic and are short of reflection effects when rendered from different views."
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+                                    "content": "5.2. Zero-shot generation"
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+                                    "content": "In this section, we evaluate our method for generating 3D assets from solely natural language descriptions (i.e., the setting of zero-shot generation), by comparing with two state-of-the-art methods, namely DreamFusion [33] and Magic3D [18]. Fig. 7 gives the comparative results given the same text prompts. Since DreamFusion and Magic3D do not have released codes, their results are obtained by downloading from their project pages. Comparing our method with Magic3D, we observe that our results are more photorealistic with competitive geometries. We consistently outperform DreamFusion in both appearance and geometry generation. Notably, our method also offers the convenience of easy geometry extraction and editing, as demonstrated in 5.4, which are less obvious from DreamFusion or Magic3D. More of our results are given in the top half of Fig. 2 and Fig. 8. Furthermore, we compare our appearance modeling stage with several mesh stylization methods, namely Text2mesh [24], CLIP-Mesh [14] and Latent-NeRF [23]. Fig. 9 shows that our method excels in generating more realistic appearances, outperforming the other competitors. We present additional results and comparisons in the supplemental materials."
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+                                    "content": "In addition to zero-shot generation, our method is flexible to accept a customized 3D model as the initialization, alternative to a 3D ellipsoid, thereby facilitating user-guided asset generation. As shown in the lower half of Fig. 2, our method is able to generate rich details in both the geometry and appearance when provided with low-quality 3D models for initialization. The three meshes used in the experiments are from Text2Mesh [24], Latent-NeRF [23], and the creation of Stable DreamFusion [41], respectively. We also compare with the state-of-the-art approach of Latent-NeRF [23] under this user-guided generation setting; results are given in Fig. 10. Our method outperforms Latent-NeRF [23] in both the geometry and texture generation when given the same input meshes and text prompts."
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+                                            "type": "text",
+                                            "content": "Sunset"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 19,
+                            "angle": 0,
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+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "ity of the generated surface geometry (e.g., no holes on the surface), the simulations are of high-level physical accuracy, as shown in the accompanying supplemental video."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
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+                                    "type": "text",
+                                    "content": "Moreover, we showcase the ability to modify the material of the statue by replacing it with another wood material downloaded from the Internet [32], which poses a challenge for comparative methods such as DreamFusion [33]. Additionally, in Fig. 11, by importing generated ice cream, tiger, and crown into the Cornell Box, we demonstrate the plausible physical interaction between our generated results and the scene, with natural shadows being cast. Finally, Fig. 12 illustrates the replacement of the HDR environment map to produce diverse lighting and corresponding reflectance effects on the generated iron man."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "6. Limitations"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
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+                                    "type": "text",
+                                    "content": "While Fantasia3D demonstrates promising advancements in the realm of generating photorealistic 3D assets from text prompts, several limitations remain. For instance, while our method successfully produces loose visual effects, it remains a significant challenge to generate corresponding loose geometries, such as hair, fur, and grass, solely based on text prompts. Additionally, our method primarily emphasizes object generation, thereby lacking the capacity to generate complete scenes with background from text prompts. Consequently, our future research endeavors will be dedicated to addressing these limitations by focusing on the generation of complete scenes and intricate loose geometries."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
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+                                    "content": "7. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this paper, we present Fantasia3D, a new method for automatic text-to-3D generation. Fantasia3D uses disentangled modeling and learning of geometry and appearance, and is able to generate both the fine surface and rich material/texture. Fantasia3D is based on the hybrid scene representation of DMTET. For geometry learning, we propose to encode a rendered normal map, and use shape encoding of the normal as the input of the pre-trained, stable diffusion model. For appearance modeling, we introduce the spatially varying BRDF into the text-to-3D task, thus enabling material learning that supports photorealistic rendering of the learned surface. Expect for text prompts, our method can be triggered with a customized 3D shape as well; this is flexible for users to better control what content is to be generated. Our method is also convenient to support relighting, editing, and physical simulation of the generated 3D assets. Our method is based on pre-trained image diffusion models (i.e., the stable diffusion). In future research, we are interested in learning 3D diffusion directly from the large language models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work is supported in part by Program for Guangdong Introducing Innovative and Entrepreneurial Teams (No.: 2017ZT07X183) and Guangdong R&D key project of China (No.: 2019B010155001)."
+                                }
+                            ]
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+                                }
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+                                            "bbox": [
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+                                            "type": "text",
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+                                        {
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+                                            "type": "text",
+                                            "content": "[3] Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Jiaming Song, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, Bryan Catanzaro, Tero Karras, and Ming-Yu Liu. ediff-i: Text-to-image diffusion models with ensemble of expert denoisers. arXiv preprint arXiv:2211.01324, 2022."
+                                        }
+                                    ]
+                                }
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+                                        {
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
+                                                53,
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+                                                338
+                                            ],
+                                            "type": "text",
+                                            "content": "[5] Sai Bi, Zexiang Xu, Pratul Srinivasan, Ben Mildenhall, Kalyan Sunkavalli, Miloš Hasan, Yannick Hold-Geoffroy, David Kriegman, and Ravi Ramamoorthi. Neural reflectance fields for appearance acquisition. arXiv preprint arXiv:2008.03824, 2020."
+                                        }
+                                    ]
+                                }
+                            ],
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+                            "angle": 0,
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "[6] Wenzheng Chen, Huan Ling, Jun Gao, Edward Smith, Jaakko Lehtinen, Alec Jacobson, and Sanja Fidler. Learning to predict 3d objects with an interpolation-based differentiable renderer. Advances in Neural Information Processing Systems (NeurIPS), 32, 2019."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "ref_text",
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+                                        {
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                            "bbox": [
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+                                        }
+                                    ]
+                                }
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+                        {
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                                        }
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diff --git a/2023/FashionNTM_ Multi-turn Fashion Image Retrieval via Cascaded Memory/96c19156-eda3-4f76-b877-c0799e40849d_content_list.json b/2023/FashionNTM_ Multi-turn Fashion Image Retrieval via Cascaded Memory/96c19156-eda3-4f76-b877-c0799e40849d_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..4a09ab8cf01ea399c48c62a7a4e69c0f143a4ee8
--- /dev/null
+++ b/2023/FashionNTM_ Multi-turn Fashion Image Retrieval via Cascaded Memory/96c19156-eda3-4f76-b877-c0799e40849d_content_list.json	
@@ -0,0 +1,1528 @@
+[
+    {
+        "type": "text",
+        "text": "FashionNTM: Multi-turn Fashion Image Retrieval via Cascaded Memory",
+        "text_level": 1,
+        "bbox": [
+            114,
+            130,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anwesan Pal\\*, Sahil Wadhwa?, Ayush Jaiswal?, Xu Zhang?, Yue Wu?, Rakesh Chada?, Pradeep Natarajan?, and Henrik I. Christensen",
+        "bbox": [
+            104,
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+            229
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ UC San Diego,  $^{2}$ Amazon Alexa Natural Understanding,",
+        "bbox": [
+            254,
+            239,
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+            258
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{a2pal, hichristensen}@ucsd.edu,{sahilwa, ayujaisw, xzhnamz, wuyue, rakhada, natarap}@amazon.com",
+        "bbox": [
+            101,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            315,
+            313,
+            330
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Multi-turn textual feedback-based fashion image retrieval focuses on a real-world setting, where users can iteratively provide information to refine retrieval results until they find an item that fits all their requirements. In this work, we present a novel memory-based method, called FashionNTM, for such a multi-turn system. Our framework incorporates a new Cascaded Memory Neural Turing Machine (CM-NTM) approach for implicit state management, thereby learning to integrate information across all past turns to retrieve new images, for a given turn. Unlike vanilla Neural Turing Machine (NTM), our CM-NTM operates on multiple inputs, which interact with their respective memories via individual read and write heads, to learn complex relationships. Extensive evaluation results show that our proposed method outperforms the previous state-of-the-art algorithm by  $50.5\\%$ , on Multi-turn FashionIQ [60] – the only existing multi-turn fashion dataset currently, in addition to having a relative improvement of  $12.6\\%$  on Multi-turn Shoes – an extension of the single-turn Shoes dataset [5] that we created in this work. Further analysis of the model in a real-world interactive setting demonstrates two important capabilities of our model – memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, user study results show that images retrieved by FashionNTM were favored by  $83.1\\%$  over other multi-turn models.",
+        "bbox": [
+            76,
+            348,
+            473,
+            741
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            747,
+            209,
+            762
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Image retrieval has been extensively studied in the computer vision community, both using classical approaches [10, 52, 25] and recently, using learning-based techniques [2, 15, 41, 43, 23]. Existing works can be grouped based on input queries considered – from image-only queries, commonly known as Content-Based Image Retrieval (CBIR)",
+        "bbox": [
+            76,
+            773,
+            468,
+            864
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/8ecb308d0ed8fef39963a7d3739c45ca2d5a58f521f5981f8419e3ca53342207.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of multi-turn fashion image retrieval. Initially (Turn 1), the system receives an initial query image, and a textual feedback mentioning the user's desired changes. The model then retrieves a ranked list of closest matching images. Subsequently, the user keeps refining their choice by providing more feedback, while the model retrieves newer images by considering both current and past feedback. This continues until the multi-turn system has successfully obtained the final retrieved image (Turn N) with all the desired properties mentioned across every past turn."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            313,
+            890,
+            512
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "[35, 39, 48], to attributes [18], sketches [44], and natural language [32, 61]. However, most of these methods do not incorporate interactive user feedback, which is necessary for a personalized task such as fashion retrieval.",
+        "bbox": [
+            496,
+            667,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Textual feedback-based fashion image retrieval allows users to refine online shopping search results by providing information about how the results differ from their desired product (e.g., \"a dress like this but darker in color\"). Several approaches for implementing such a system have been proposed recently [14, 7, 31, 56, 17, 60, 63], which involve learning a joint representation via multi-modal information fusion across the query (reference) image and the associated feedback, and using it to retrieve the closest matching image in the database (product catalog) as the target.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Popular methods for fashion retrieval task [14, 31, 7,",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Work primarily done during internship at Amazon. Additional details are available at https://sites.google.com/eng.ucsd.edu/fashionntm.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "11323",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "4, 23] involve single-turn exchange of information, where users provide feedback exactly once to update the search results. However, this is not characteristic of the real-world setting as online shopping customers typically start with a general idea of what they want and iteratively update the requirements until they find something that matches their desired features. This usually involves providing additional attributes, or modifying previously specified features in each turn to refine the search results. The ideal feedback-based fashion image retrieval system is, hence, inherently multi-turn, as illustrated in Figure 1.",
+        "bbox": [
+            75,
+            90,
+            472,
+            257
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There are two major challenges associated with multi-turn image retrieval. First, there is a lack of sufficient training and evaluation datasets - despite the abundance of single-turn fashion retrieval datasets, to the best of our knowledge, there is only one publicly available multi-turn fashion image retrieval dataset [60] currently. This is because labeling a sequence of images while ensuring continuity, consistency, and uni-directional information flow is a difficult problem. Thus, to facilitate research in this domain, we created a new fashion image retrieval dataset to allow for further benchmarking. Second, generalizing performance to real-world dynamic user interactive cases is non-trivial - as this is still a relatively new research domain, most existing algorithms do not generalize beyond the training dataset to consider multiple turns of interactive feedback. In this work, we propose a novel memory-based framework to explicitly consider sequential feedback from users across multiple turns to retrieve desired items, both for the static image datasets, as well as real-world dynamic users.",
+        "bbox": [
+            75,
+            261,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Sequential modeling is a relatively mature field of research. However, a majority of the existing approaches [46, 27, 49, 20, 9] do not maintain an explicit memory, and therefore cannot learn long and complex information. Vanilla memory network-based methods, which explicitly maintain an external memory, could be used for retaining past information, but they do not provide a robust mechanism to iteratively update their memory [55, 51]. In contrast, Neural Turing Machines (NTMs) [16] provide a fully differentiable model with sophisticated read and write operations to extract and update historical information in its explicit memory via an attention mechanism. Therefore, in this work, we build on NTMs to develop a novel framework for the multi-turn retrieval task. We further propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) that allows us to encode multiple relationships from the features of a particular turn and store them over time across multiple memories in a multi-turn setting. This is similar to how multi-head attention (MHA) operates for transformers [53]. To ensure that the individual memories effectively utilize each other's information, we link them together in a cascaded fashion. Evaluation results demonstrate that our proposed approach improves the retrieval performance as com",
+        "bbox": [
+            75,
+            553,
+            472,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "pared to the previous state-of-the-art by  $50.5\\%$  on Multi-turn FashionIQ, and by  $12.6\\%$  on Multi-turn Shoes.",
+        "bbox": [
+            496,
+            90,
+            890,
+            119
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, we make the following contributions. First, we propose a state-of-the-art memory-based framework, called FashionNTM, for multi-turn feedback-based fashion image retrieval, that uses an external memory to learn complex long-term relationships. Second, we develop a novel Cascaded Memory Neural Turing Machine (CM-NTM), that extends NTM to learn relationships across multiple inputs via additional controllers and read/write heads in a cascaded fashion. Third, we conduct experiments to show that the proposed approach outperforms existing state-of-the-art retrieval models by  $50.5\\%$  on Multi-turn FashionIQ [60], and around  $12.6\\%$  on the multi-turn version of Shoes dataset [5] respectively. Additionally, by performing an interactive analysis, we demonstrated two important capabilities of our multi-turn system - memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, a user study result shows that on an average, the images retrieved by our model are preferred  $83.1\\%$  more than those from other multi-turn methods.",
+        "bbox": [
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+            121,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            422,
+            640,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Single turn feedback-based fashion image retrieval - Previous works in feedback-based fashion image retrieval have primarily focused on the single-turn scenario [14, 40, 31, 7, 54, 4, 3, 59, 6, 36, 22], where a model is provided with a reference image along with an associated feedback text highlighting the desired attribute changes. The typical approach is to encode the multi-modal image and text input using pre-trained visual feature extractors [19, 24, 34] and sequential natural language processors [20, 12], respectively. More recently, pre-trained extractors such as Contrastive Language-Image Pre-training (CLIP) [45] have also been used [4, 3]. This is then followed by a transformer-based decoder network [53] for generating information-rich features for image retrieval from the database. Although these methods perform well in single-turn settings, they cannot be directly used for real-world applications that deal with multiple turns of information exchange.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Multi-turn visuo-linguistic methods - A few methods have been proposed recently for fusing visual and textual input across multiple turns of information exchange. A popular application has been the video dialog task [42, 21, 33, 30, 17], where a trained system is asked to answer questions based on an ongoing video dialog. However, these kinds of dialogs are primarily text-based for both the questioner and the answering agent, without any interaction across image and text inputs. In the fashion domain, there have been some early works for the multi-turn retrieval task. Guo et al. [17] proposed a model that uses convolutional neural networks (CNNs) for encoding images and text, followed by a recurrent neural network for aggregating sequences. Then,",
+        "bbox": [
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+        "type": "page_number",
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+        "img_path": "images/c762c27b3c1f5f4a7dbe63b4bc7c1448a76711883d925d4bb33cd25b057f45a7.jpg",
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+            "Single-turn model; fine-tuned on multi-turn data"
+        ],
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+            "Figure 2: The complete FashionNTM framework. During training, the model receives an input query image,  $I_{n}$ , and associated feedback,  $U_{n}$ . From these, query features  $f_{qry}(n)$  are computed using an off-the-shelf single-turn fashion image retrieval model. These features are then fed into the memory network which learns to retain useful information from the current turn, and combine it with information from previous turns by interacting with an external memory bank, via read/write operations. The memory-modified features  $f_{qry}'(n)$  are compared with the target index features  $f_{tar}(n)$ , and other negative samples  $f_{neg}(n)$ , to compute the training loss. At inference, the model receives a series of multi-modal inputs turn-wise and computes the final modified feature  $f_{qry}'(N)$  using the trained memory network. This is compared with features  $f_{cand}$  derived from different candidate images in the database to retrieve the closest matching images."
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+            "Multi-turn dataset"
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+        "image_caption": [
+            " Cascaded Memory Neural Turing Machine"
+        ],
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+        "image_caption": [
+            "Feature vectors"
+        ],
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+        "image_caption": [
+            "Similarity metric"
+        ],
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+        "type": "text",
+        "text": "a  $k$ -Nearest Neighbor search is performed across sampled images to get the closest match. The entire model is trained end-to-end using reinforcement learning (RL). Inspired by this, Zhang et al. [63, 62] proposed two approaches for enhancing the text-image feature fusion by adding constraints, and using offline interactive recommendation. Recently, Yuan et al. [60] released the first multi-turn fashion image retrieval dataset, based on the original single turn FashionIQ [56]. They also proposed a state-of-the-art model, which we directly compare with our approach.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Memory networks for vision and language - Memory networks have been widely used for a number of natural language processing and computer vision applications. Some works [55, 51, 13, 11] utilize it for Sentence Video Questions and Answering (QA) task. Another popular application is video object segmentation [8, 58, 50, 37]. Recently, there have been some works on including memory in transformer architectures [26, 47, 57, 38]. However, these approaches design their memory to be used only for specific tasks, and hence cannot be directly compared with ours. In this work, we propose a memory network based method for the multi-turn fashion image retrieval task.",
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+    {
+        "type": "text",
+        "text": "3. FashionNTM",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The multi-turn feedback-based image retrieval task can be viewed as a series of information exchange transactions. We define a transaction as one session of query context comprising a query image and the associated feedback",
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+    {
+        "type": "text",
+        "text": "text. Notationally, an  $N$ -turn transaction is represented as  $T = [(I_1,U_1),(I_2,U_2),\\dots ,(I_N,U_N)]$ , where  $I_{n}$  and  $U_{n}$  correspond to the query image and feedback utterance respectively, at turn  $n\\in [1,N]$ . Given such a transaction, the aim of a multi-turn model is to iteratively retrieve the final desired target image  $I_{tar}(N)$  by ranking candidates in the fashion image database based on a matching score.",
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+        "type": "text",
+        "text": "The overall pipeline of our approach, called Fashion-NTM, is illustrated in Figure 2. We start with a single-turn feature extraction module to encode the multi-modal image and text inputs of each turn  $n$  in a multi-turn transaction. It comprises two parallel blocks - (i) a query feature extractor (QE), for processing  $I_{n}$  and  $U_{n}$  to generate the joint query representation  $f_{qry}(n)$ , and (ii) a target feature extractor (TE), for encoding all the images in the database into their corresponding index features. For the ground-truth target image  $I_{tar}(n)$ , we call these features  $f_{tar}(n)$ , while for every other sample  $I_{neg}(n)$  in the batch, we name it  $f_{neg}(n)$ . The query feature  $f_{qry}(n)$  is fed turn-wise to the Cascaded Memory Neural Turing Machine (CM-NTM) block. CM-NTM first computes several derived features from the original query feature. Subsequently, the original query feature and each of the derived features interact with their own controllers, read/write heads, and sequentially update the memories in a cascaded manner, i.e. output of one memory goes as input to the next. Ultimately, we get the enhanced feature  $f_{qry}'(n)$  as the final output, which is then compared with the target feature  $f_{tar}(n)$  using a similarity score-based batch",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "11325",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/5d5325cefed9cbf5fae460ef795f671d31d32e65cacf004d4db81605f92a3c41.jpg",
+        "image_caption": [
+            "Figure 3: Cascaded Memory Neural Turing Machine (CM-NTM). It consists of  $C$  controllers; one for the query feature and  $C - 1$  for the derived features. Each controller interacts with its own memory using its own read and write heads. The controllers are linked with each other, forming a cascaded chain. The modified features from the last memory are output as the final embedding."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "loss function. This loss treats  $f_{tar}(n)$  as a positive sample and every other feature in the batch,  $f_{neg}(n)$ , as a negative sample. We use cosine-similarity [54, 31, 14] between feature vectors as the matching score. During inference, the model receives a sequence of multi-modal turn-wise inputs and computes the final modified feature  $f_{qry}'(N)$ . This is compared with feature  $f_{cand}$  derived from different candidate images in the database, and the closest match is retrieved as output. In the following sections, we describe the key components of our framework.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Single-turn feature extractor - We utilize the state-of-the-art single-turn image retrieval model, FashionVLP [14], for extracting multi-modal text and image features. FashionVLP extracts image embeddings at multiple levels of granularity and incorporates a vision-language pre-trained transformer for fusing these encodings with text feedback to obtain multi-modal query features. It adopts a convolutional neural network (CNN) architecture with contextual attention for fusing fashion-contextual image features of target images. Specifically, for each turn of a multi-turn transaction, we obtain query features  $f_{qry}$  and target features  $f_{tar}$ . An  $N$ -turn retrieval transaction is of the form  $T_{retr} = [f_{qry}(1), f_{qry}(2), \\dots, f_{qry}(N)]$ , with the target feature representation given by  $f_{tar}(N)$ .",
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+    {
+        "type": "text",
+        "text": "3.1. Cascaded Memory Neural Turing Machine",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "To learn relationships across transactions, we propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) module. CM-NTM allows multiple inputs to interact with their own memories using individual read and write heads to learn multiple complex relationships in the input data. We achieve this by deriving several features from the original  $n$ -th turn query feature  $f_{qry}(n)$  using a projection function  $\\mathcal{F}$ , which comprises a fully-connected (FC) layer with batch normalization. Specifically, for a  $C$ -stage cascaded CM-NTM, we obtain the derived feature",
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+    },
+    {
+        "type": "text",
+        "text": "$f_{drv}^{c} = \\mathrm{BatchNorm}(\\mathrm{FC}_{\\mathrm{c}}(f_{qry}(n)))$  where  $c \\in [1, C - 1]$ , and  $\\mathrm{FC}_{\\mathrm{c}}(\\cdot)$  is the FC layer for the  $c$ -th stage. Having obtained  $C$  inputs comprising the original query and  $C - 1$  derived features, we pass them sequentially to our memory network. Figure 3 presents our memory network architecture. It consists of three main components: Controller, Read/Write heads, and Memory blocks.",
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+        "type": "text",
+        "text": "Controller - The vanilla NTM has a single controller which takes the query feature at turn  $n$ , along with the previous turn's read vector, and emits an intermediate controller output. This is used by the read and write heads to compute the current turn's attention weights, which are then used to update the memory. In our work, we introduce  $C$  different controllers - one for each of our inputs. Each controller,  $c \\in [1, C]$  can therefore interactively update its memory via individual read and write heads, allowing it to learn multiple complex relationships in each turn.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Read/Write heads - The controller output is fed to these heads. The write head learns to generate erase and add parameters, which are used to update the current memory. Similarly, the read head generates an attention weight vector, which is used to obtain a weighted sum over the memory locations to get the read vector  $\\mathbf{r}_{out}(n)$ . In our work, we have separate read and write heads for each memory.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Memory block - This is represented as a 2-D matrix of the form  $N \\times M$ , where  $N$  corresponds to memory locations and  $M$  to the vector size at each location. The output of each memory block is a fused representation of the controller output and the read vector. In our cascaded multi-memory setup, the controllers are linked in a chain, such that the memory-modified features are sequentially propagated. Specifically, for controller  $c \\in [1, C]$  at turn  $n$ , the input is given by  $\\mathrm{input}^c(n) = [\\mathbf{r}_{out}^{c-1}(n); f_{drv}^c; \\mathbf{r}_{out}^c(n-1)]$ , where  $\\mathbf{r}_{out}^0(n) = \\mathbf{r}_{out}^C(n-1)$ ,  $f_{drv}^C = f_{qry}(n)$ , and ; represents concatenation. The final output,  $f_{qry}'(n)$ , is the fused representation of the last controller output  $\\mathrm{output}_{ctrl}^C$  and final read vector  $\\mathbf{r}_{out}^C$ . We experiment with a different number of memories  $C$  and memory sizes in Section 4.7.",
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+    {
+        "type": "text",
+        "text": "3.2. Loss function",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We adopt a batch cross-entropy loss [14], where each entry in a batch acts as a negative sample for all other entries. In the multi-turn setting, we compute the loss function turnwise. Given a batch size  $B$ , the loss between predicted feature  $\\mathbf{x}_n = [{}^1 f_{qry}'(n), {}^2 f_{qry}'(n), \\ldots, {}^B f_{qry}'(n)]$ , and ground-truth  $\\mathbf{y}_n = [{}^1 f_{tar}(n), {}^2 f_{tar}(n), \\ldots, {}^B f_{tar}(n)]$ , at turn  $n$  is of the form",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} (\\mathbf {x} _ {n}, \\mathbf {y} _ {n}) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} - \\log \\frac {e ^ {\\kappa (^ {i} f _ {q r y} ^ {\\prime} (n) , ^ {i} f _ {t a r} (n))}}{\\sum_ {j = 1} ^ {B} e ^ {\\kappa (^ {i} f _ {q r y} ^ {\\prime} (n) , ^ {j} f _ {t a r} (n))}}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>We mainly discuss our novel changes to the NTM design. For details regarding the vanilla architecture, please refer to the original paper [16].",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "11326",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/1bf8c356c197e52a9b09ae5a2f50c37978a6d2e84276af064db1bd1f744ad94d.jpg",
+        "table_caption": [
+            "Table 1: Statistics of the datasets used in this work. The top 2 rows are for the recently proposed Multi-turn FashionIQ dataset [60]. The bottom two rows are for the Multi-turn version of the Shoes [5] dataset, which we created as part of our work."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Split</td><td colspan=\"3\">Number of transactions with</td><td rowspan=\"2\">Total images</td></tr><tr><td>2-turns</td><td>3-turns</td><td>4-turns</td></tr><tr><td rowspan=\"2\">Multi-turn FashionIQ [60]</td><td>Train</td><td>6,897</td><td>1,733</td><td>475</td><td>10,438</td></tr><tr><td>Test</td><td>1,752</td><td>483</td><td>165</td><td>6,274</td></tr><tr><td rowspan=\"2\">Multi-turn Shoes (ours)</td><td>Train</td><td>1,659</td><td>1,036</td><td>982</td><td>11,030</td></tr><tr><td>Test</td><td>296</td><td>96</td><td>28</td><td>4,631</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\kappa$  is the cosine similarity metric [14]. In this way, each  $f_{tar}(n)$  in the batch,  $\\forall j\\in [1,B]$  and  $j\\neq i$  , serves as a negative sample  $f_{neg}(n)$  for a given  $f_{qry}^{\\prime}(n)$  . The turn-wise retrieval loss function is represented as  $\\mathcal{L}_{retr}^{n} =$ $\\mathcal{L}(\\mathbf{x}_n,\\mathbf{y}_n)$  , with the overall loss function for our proposed multi-turn model given by  $\\mathcal{L} = \\frac{1}{N}\\sum_{n = 1}^{N}\\mathcal{L}_{retr}^{n}$",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experimental Evaluation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Multi-turn FashionIQ [60]: To the best of our knowledge, this is the only existing fashion dataset with multi-turn sessions, where each turn is derived from the original single-turn FashionIQ [56] dataset. It comprises of 11,505 sessions across three clothing types - dress, top-tee, and shirt. The dataset is split into transactions of 2-turns, 3-turns, and 4-turns. In each turn, the data is represented as a pair  $(I_n, U_n)$ , where  $I_n$  and  $U_n$  correspond to the query image and the feedback text for turn  $n$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Multi-turn Shoes: The original Shoes dataset [5] contains images of 10 categories of women's shoes obtained from the web along with automatic labeling of attributes. Guo et al. [17] provide additional natural language descriptions of the images to make them suitable for single-turn feedback-based image retrieval. This resulted in about 10k training pairs and 4.6k test queries. In this work, we create a multi-turn extension of this dataset to further research in this domain. Like the approach described in [60], we concatenated several single-turn transactions by matching the target image of one session to the query of another. To maintain",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "consistency with Multi-turn FashionIQ, we also developed transactions of 2-turns, 3-turns, and 4-turns. Table 1 provides the statistics of both the datasets.",
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+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Single-turn feature extractor pre-training - We use the recently proposed single turn (ST) fashion image retrieval model, FashionVLP [14], to extract the query and target features for both datasets. To ensure a fair comparison with other algorithms, we re-train FashionVLP only on those single-turn queries that are part of the multi-turn dataset. The implementation details and hyperparameters are similar to those mentioned in Goenka et al. [14].",
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+    {
+        "type": "text",
+        "text": "CM-NTM training - We build our CM-NTM model using the open-source implementation [28] of NTM [16]. We implement a separate controller for each memory in our cascaded design using Long Short Term Memory (LSTM) networks [20]. The read and write heads are composed of multi-layer perceptrons (MLPs) and attention networks. We use  $C = 4$  for Shoes, and  $C = 8$  memory stages for FashionIQ, as it is a larger dataset. To ensure equal turn lengths for batch training, we pad the short turn transactions by repeating the last transaction similar to Yuan et al. [60]. We train our models for 100 epochs with a batch size of 80 and a learning rate of 1e-4. We used the PyTorch framework with Adam [29] optimizer for training.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Baselines and Previous State-of-the-art",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We compare the performance of our model with six other single-turn and multi-turn approaches.",
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+    },
+    {
+        "type": "text",
+        "text": "Single-turn methods - In these methods, we aggregate the multi-turn query data into a single feature without iterating over them turn-wise. The first baseline is  $\\mathrm{ST} + \\mathrm{avg}(\\mathrm{all~turns})$ , where we take the mean of all the  $N$  query features in a transaction to get a single mean query  $\\bar{f}_{qry}(N)$ . This is compared with the candidate target features  $f_{tar}(N)$ . Next, we have  $\\mathrm{ST} + \\mathrm{cat}(\\mathrm{all~captions})$ , where all the captions of a multi-turn transaction are concatenated into one long caption, along with initial reference image, to get query features  $\\hat{f}_{qry}(N)$ . This is compared with target features  $f_{tar}(N)$  to retrieve the final images.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/66f68bd13d416788b92343d9503a1e7837205d74db189d4d101da74d88354806.jpg",
+        "table_caption": [
+            "Table 2: Quantitative results on Multi-turn FashionIQ [60]. We compare with multiple single-turn and multi-turn baselines, and state-of-the-art works [17, 60]. Results show the superior performance of our proposed approach on the popularly used recall rate evaluation metric."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Dress</td><td colspan=\"2\">Toptee</td><td colspan=\"2\">Shirt</td><td colspan=\"3\">Overall</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan=\"10\">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>25.6</td><td>32.5</td><td>32.1</td><td>38.1</td><td>27.0</td><td>32.3</td><td>28.2</td><td>34.3</td><td>31.3</td></tr><tr><td>ST + cat(all captions)</td><td>30.2</td><td>36.3</td><td>36.0</td><td>44.1</td><td>35.3</td><td>42.5</td><td>33.8</td><td>41.0</td><td>37.4</td></tr><tr><td colspan=\"10\">Multi-turn</td></tr><tr><td>Dialog Manager [17]</td><td>12.7</td><td>16.7</td><td>11.6</td><td>15.8</td><td>13.9</td><td>17.7</td><td>13.1</td><td>15.2</td><td>14.2</td></tr><tr><td>CFIR [60]</td><td>29.8</td><td>33.5</td><td>29.4</td><td>33.6</td><td>30.5</td><td>34.1</td><td>30.3</td><td>33.4</td><td>31.9</td></tr><tr><td>ST + EWMA (ours)</td><td>42.0</td><td>48.4</td><td>43.8</td><td>50.9</td><td>36.9</td><td>44.2</td><td>40.9</td><td>47.8</td><td>44.4</td></tr><tr><td>ST + LSTM (ours)</td><td>47.8</td><td>52.5</td><td>44.4</td><td>50.5</td><td>41.6</td><td>47.6</td><td>44.6</td><td>50.2</td><td>47.4</td></tr><tr><td>FashionNTM (ours)</td><td>48.3</td><td>52.8</td><td>45.1</td><td>49.8</td><td>43.8</td><td>48.8</td><td>45.7</td><td>50.4</td><td>48.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "11327",
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+    {
+        "type": "text",
+        "text": "Multi-turn methods - In these methods, the multi-turn data is fed turn-wise to the model. The first method is Dialog Manager [17], which employs reinforcement learning (RL) framework to learn relationships between turns. Next, we have the previous state-of-the-art Conversational Fashion Image Retrieval CFIR method [60], which encodes only the text using a transformer network [53], and uses a simple Gated Recurrent Unit (GRU) layer for multi-turn image retrieval. The third baseline is  $\\mathrm{ST} + \\mathrm{EWMA}$ , where we use exponential weighted moving average [1] to heuristically aggregate past turns, with more weights given to recent history. Finally, we have the  $\\mathrm{ST} + \\mathrm{LSTM}$  model that uses a single-layer LSTM [20] with a hidden size of 100 for aggregating past information.",
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics - Following [14, 60, 17], we evaluate models using the standard top-K recall (i.e. R@K) for image retrieval. Overall performance are compared specifically on the average of R@5 and R@8.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Quantitative results on multi-turn datasets - In Table 2, we compare the results of different methods on the multi-turn FashionIQ dataset. We observe that the multi-turn baselines generally perform better than single-turn methods. This is expected as aggregating data by naively averaging/concatenating loses feedback content and turn-order information and hence is likely to miss out on important cues. Our memory-based approach outperforms all the other multi-turn baselines by a large margin. This shows that the memory network can store and retrieve useful information to and from the memory between intermediate turns, which allows it to keep track of past information better than other networks that do not use explicit memory. The  $50.5\\%$  performance gain over the previous state-of-the-art highlights our model's capability to learn meaningful representations over multiple turns of conversational feedback.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Table 3, we provide a similar comparison for the Multi-turn Shoes dataset. Consistent with results for Multi-turn FashionIQ, the multi-turn baselines perform better than",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 3: Comparison with existing single-turn and multi-turn models on the multi-turn version of the Shoes [5] dataset. We compare with multiple single-turn, and multi-turn baselines. Comparative analysis shows the superior performance of our proposed approach using the popular recall rate evaluation metric.",
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+    {
+        "type": "table",
+        "img_path": "images/bc2f8144efc625fca9621db7e46ddeaa6a24bbb1167c3fcbdca6480848fa57ec.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan=\"4\">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>12.4</td><td>17.6</td><td>15.0</td></tr><tr><td>ST + cat(all captions)</td><td>10.7</td><td>13.6</td><td>12.2</td></tr><tr><td colspan=\"4\">Multi-turn</td></tr><tr><td>ST + EWMA (ours)</td><td>18.3</td><td>23.8</td><td>21.1</td></tr><tr><td>ST + LSTM (ours)</td><td>23.3</td><td>32.1</td><td>27.7</td></tr><tr><td>FashionNTM (ours)</td><td>26.7</td><td>35.7</td><td>31.2</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "all the single-turn ones, and our memory network-based approach performs the best with a relative improvement of  $12.6\\%$ . The difference in performance across different models is more pronounced in these results than in Table 2. This is possibly because the annotations are cleaner and more consistent in this dataset as compared to Multi-turn FashionIQ [60]. For instance, multiple images in the FashionIQ dataset can match a particular query, but only one of them is labeled as the ground-truth.",
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+    },
+    {
+        "type": "text",
+        "text": "An important property of a good multi-turn system is that performance should be robust to the length of the historical information (number of past turns). For example, even for a large number of previous turns considered, the model should efficiently retain desirable details, while filtering out unnecessary information. In Table 4, we analyze this property for models with and without memory. A single-turn model that assumes ground-truth information for all past turns, and evaluated only on the final-turn, is taken as reference. This is expected to be the upper-bound on the performance in a single-turn setting, as perfect information about the history is guaranteed. We vary the number of past turns included in the input transaction history (versus treated as ground-truth) for the multi-turn models (with or without memory) in order to evaluate their effectiveness at capturing and utilizing past information. As seen from the table, for a model without memory, the performance depreciates significantly with each additional turn from the",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 4: Importance of aggregating historical data using memory-based vs non-memory approach. In the first row, we show the result of a model using only the final turn information of a multi-turn transaction. This assumes the groundtruth retrieval for all previous turns, and therefore provides the upper-bound on single-turn performance for final retrieval. Subsequently, we include additional information from the history, and compare performance across models with and without memory. As seen from the non-memory case, the performance depreciates a lot ( $\\approx$  64.9% difference compared to the final turn's performance), as we try to aggregate longer historical information. In contrast, for the memory network model, it can be seen that the performance is fairly consistent ( $\\approx$  0.5% difference) across the turn length.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0c73d11e836bd8ed07209ff79930e73a576d31b9d80ceddb47f2c5e628137385.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Memory usage</td><td rowspan=\"2\">Turn configuration</td><td colspan=\"2\">Dress</td><td colspan=\"2\">Toptee</td><td colspan=\"2\">Shirt</td><td colspan=\"3\">Overall</td><td rowspan=\"2\">Difference from final turn</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td>-</td><td>only final turn</td><td>77.9</td><td>77.9</td><td>84.0</td><td>84.0</td><td>74.1</td><td>77.8</td><td>78.7</td><td>79.9</td><td>79.3</td><td>-</td></tr><tr><td colspan=\"12\">Experiments with data aggregated across multiple-turns</td></tr><tr><td rowspan=\"3\">Only single turn (w/o memory)</td><td>last two turns</td><td>51.3</td><td>58.4</td><td>56.0</td><td>76.0</td><td>44.4</td><td>48.1</td><td>50.6</td><td>60.9</td><td>55.8</td><td>-29.6%</td></tr><tr><td>last three turns</td><td>33.6</td><td>43.4</td><td>32.0</td><td>44.0</td><td>29.6</td><td>40.7</td><td>31.8</td><td>42.7</td><td>37.3</td><td>-53.0%</td></tr><tr><td>all turns</td><td>18.6</td><td>28.3</td><td>32.0</td><td>32.0</td><td>25.9</td><td>29.6</td><td>25.5</td><td>30.0</td><td>27.8</td><td>-64.9%</td></tr><tr><td rowspan=\"3\">FashionNTM (with memory)</td><td>last two turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr><tr><td>last three turns</td><td>77.0</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.6</td><td>79.9</td><td>79.8</td><td>+0.6%</td></tr><tr><td>all turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "11328",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/4f2d844c6cd723d0ff98953db67cb4307fcd4ceaf7fa767f0e827d0e310f3ba6.jpg",
+        "image_caption": [
+            "(a) Multi-turn FashionIQ. From left to right, the images belong to the Dress, Shirt, and Toptee categories respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2f7685d81cb666dc03f51972cdba64f2870b305f1d65baa6d982d579c99787d1.jpg",
+        "image_caption": [
+            "(b) Multi-turn Shoes. From left to right, we have three different samples of shoes from the dataset.",
+            "Figure 4: Top-5 final image retrievals on the evaluated multi-turn datasets. The top row illustrates 3 sets of multi-turn query session. We consider three different multi-turn models - EWMA, LSTM, and our proposed FashionNTM. As seen from the retrievals, our proposed model correctly predicts the target image in all 3 cases for the FashionIQ dataset, and in 2 out of 3 cases for the Shoes dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "past treated as input rather than ground-truth. As we go further back in history, the performance consistently reduces. However, for our multi-turn model with memory, the performance does not change appreciably as the number of turns change. This shows that our proposed approach can successfully retain/filter out past data based on their relevance, across various lengths of history.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "An interesting observation is that having only the final turn with memory does not yield a good result. This is possibly due to the initialization method of the memory network, which is random. Hence, in absence of a history (only single turn case), the only past features to be aggregated are the random initialization features.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Qualitative results - In addition to the quantitative experiments described above, we also present some qualitative final image retrieval results of our evaluated models on both the multi-turn datasets. The first set of results are shown in Figures 4a and 4b for the Multi-turn FashionIQ [60] and the",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Multi-turn Shoes datasets, respectively<sup>2</sup>. We compare the top-5 predicted results from our proposed model with two other multi-turn baselines, ST + EWMA and ST + LSTM. As seen in the figures, our approach can correctly predict the desired target image for both datasets with higher ranks as compared to other baselines. More specifically, we see that in Figure 4a, even though all the three multi-turn models can infer the general sense of desired attributes, such as \"is longer\" in the left block and \"has short sleeves\" in the right, only our model can capture complex and detailed properties, e.g., \"gray and not red\" in the left block, and \"red color with center logo\" in the middle block. Furthermore, our model can retrieve multiple desirable products, as seen by the first four images in the middle block, and four out of five images in the right block. Similar results are observed for Shoes in Figure 4b, where our model correctly predicts",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_footnote",
+        "text": "2Please refer to the supplementary material for additional results, along with the differences in annotation quality between the two datasets.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "11329",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f7eb55bc6d7b6c2e082298f5770b585b7874676b8514e0f827e55a0542b77e65.jpg",
+        "image_caption": [
+            "Figure 5: Memory retention capability of our proposed approach. Given an initial query image, we take two interactive user feedbacks in turns. On the left side, we have the single-turn model which only learns to retrieve an image using a single dialog exchange. As a result, none of the retrieved images in turn 2 are \"green in color\", which was desired in turn 1. In contrast, our proposed approach on the right can learn to retain data from both the turns, and therefore retrieves desirable product in 2 out of 3 cases."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "the desired target as rank-1 in two out of three examples, whereas the other models fail to retrieve meaningful results.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5. Model Analysis in Interactive Settings",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In addition to the results above for the static dataset, we also performed some interactive experiments to evaluate whether our model can adapt to real-world dynamic use cases beyond the trained datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Memory retention - In this experiment, we demonstrate the memory retention capability of our proposed model by comparing it with a single-turn network, which does not retain historical information. We start with an initial query image retrieved via a single-turn model. Subsequently, we take user input for the next two turns to retrieve newer sets of images. As seen in Figure 5, for the single-turn model (left side), none of the retrieved images in turn 2 are green in color. This is because the \"green in color\" attribute was a desired property in turn 1, which the model without memory could not recover. In contrast, for our memory network approach (right side) both the top-2 retrieved images for turn 2 are \"green in color\" in addition to having \"a solid color and small image\". Thus, our model can learn to retain information from previous turns.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Agnosticity to turn order - Ideally, a deployed multi-turn image retrieval system should be independent of the order of feedbacks provided, as long as they are non-contradictory. This is demonstrated in the experiment conducted in Figure 6. In the first case, we take two text inputs as feedbacks from a user and present them to the model. In the second case, we reverse the order of the feedbacks. As shown in the figure, for the flipped case, our proposed FashionNTM model retrieves similar looking final products, even though the intermediate retrievals are very different.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "It is to be noted that for both the experiments depicted in Figures 5 and 6, the feedback is taken from a dynamic user, thereby establishing the interactive capability of our",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/9d9d51acf4766157a663d3f12189104f011612f36551dadc14201d924d0e795e.jpg",
+        "image_caption": [
+            "Figure 6: Turn order independence feature of a memory network. In this experiment, we start with an initial query image, and take two non-contradictory user feedbacks. In one case (left), we let the model retrieve images based on the original order of the feedbacks, whilst in the other (right), we flip the order of the feedbacks. Our proposed approach adapts to presented input, and retrieves similar looking final results for both the cases, even though the intermediate outputs are quite different."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "proposed model beyond the training dataset.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.6. User Study",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fashion image retrieval is inherently a subjective task, where the task success heavily relies on the satisfaction of a customer. Thus, we conducted a small human-preference survey among 5 participants (not associated with the paper in any way). To each user, we showed the final top-1 retrieved image by the 3-best multi-turn models on the FashionIQ [60] dataset from Table 2 - EWMA, LSTM, and our proposed FashionNTM. To ensure consistency, we generated 45 queries for this study, whose results are shown in Figure 7. The  $y$ -axis shows the number of preferred retrieval results for each user. Results show that each of the 5 users preferred images retrieved by the proposed FashionNTM model, on an average  $83.1\\%$  more as compared to other multi-turn methods. In the supplementary material, we include some examples of the user interface shown to",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/e66da7637eaa55744a96b737a57f5cae4c4cbed8b312a63d04a3288beda6ebd8.jpg",
+        "image_caption": [
+            "Figure 7: Human preference study of top multi-turn systems."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            517,
+            656,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "11330",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fbb40748c5145270ff5fb3cf0a47bb229d7afc5f072bf68ce478e4d871530e18.jpg",
+        "table_caption": [
+            "Table 5: Different number of memories for the proposed approach by fixing the memory size to  $4 \\times 768$ . We select the mean value for comparison and pick the best one."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Number of memories (C)</td><td>R@5</td><td>R@8</td><td>Mean</td><td>% increase</td></tr><tr><td>ST+v-NTM</td><td>1</td><td>24.5</td><td>30.5</td><td>27.5</td><td>-</td></tr><tr><td rowspan=\"4\">FashionNTM</td><td>2</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr><tr><td>4</td><td>27.6</td><td>35.5</td><td>31.5</td><td>14.5</td></tr><tr><td>8</td><td>26.9</td><td>35.2</td><td>31.1</td><td>13.1</td></tr><tr><td>16</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "the participants during this study.",
+        "bbox": [
+            76,
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+            299,
+            250
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.7. Ablation Studies",
+        "text_level": 1,
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+        "text": "We perform multiple ablation studies to gain insights on how changing different configurations of the memory network affect the overall performance. We perform these ablations on the multi-turn Shoes dataset as it contains more realistic and consistent feedback texts.<sup>3</sup>",
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+        "text": "Number of memories in CM-NTM - This experiment involves varying the number of memories  $C$  in our cascaded memory architecture. In Table 5, we observe that the cascaded memory CM-NTM models perform significantly better than vanilla NTM, which has only one memory. We hypothesize that having inputs from multiple turns interacting with the same memory could eventually lead to saturation as we get additional data which could be alleviated if there are multiple memories in the network to recover the past which might help in capturing multiple complex relationships in multi-turn interactions better. Additionally, multiple memory networks can help in learning diverse representations of the input using derived features, which is not possible with a single memory network. As seen in Table 5 for Shoes dataset, the performance increases with the number of memories, peaking at  $C = 4$ , and then gradually decreases as the model starts to overfit.",
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+        "text": "Inference time with multiple memories - In this experiment, we study the performance of FashionNTM in terms of the mean of R@5 and R@8 recall rates along with the time taken to process one multi-turn transaction. For each  $C$ , we evaluate the performance across four different memory sizes. As seen from Figure 8, the inference time increases with additional memories. Configurations in the green and blue clusters are desirable, as they provide a good trade-off between recall performance and computation time, while the pink and red clusters are undesirable due to poor performance and longer inference time, respectively.",
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+        "text": "In this paper, we presented a novel cascaded Neural Turing Machine-based approach, called FashionNTM, for multi-turn feedback-based fashion image retrieval. Multiple",
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+        "image_caption": [
+            "Figure 8: Scatter plot showing recall versus inference time for multiple memories in our CM-NTM for the Multi-turn Shoes dataset. The configurations belonging to the green cluster give the best recall overall, while having a high inference time. The configurations in the blue cluster provide a suitable alternative with quicker inference at the cost of lower recall. The magenta and red clusters are undesirable configurations due to poor performance and long inference time, respectively."
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+        "text": "memories in our model allow it to effectively retain and recall a number of complex relationships across transactions in the multi-turn setting, and multiple controllers help in assigning relative importance to each feature stored in the memory. This aids in attending to different parts of the input at different levels, thus leading to better performance across datasets. We also performed extensive experiments to compare our performance with baselines and previous state-of-the-art and observed that our multi-memory model significantly outperforms previous works [60], with up to  $50.5\\%$  relative improvement on Multi-turn FashionIQ, and by  $12.6\\%$  on the multi-turn Shoes dataset, which we created in this work. We further demonstrated that our model can generalize beyond the trained setting to dynamically interact with real-world users to retrieve meaningful final product images. Finally, a user preference study reveals that our model is preferred by human participants on an average  $83.1\\%$  more as compared to other multi-turn methods.",
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+        "text": "Despite promising results, there are a few limitations that make multi-turn image retrieval a hard problem to solve. Firstly, there is dearth of high quality and diverse multi-turn image retrieval datasets in the fashion domain which hinders comprehensive studies in this field. Additionally, deploying current approaches to real-world scenarios (e.g., virtual private assistants) becomes a challenge due to computational requirements. Lastly, selecting the right configuration for different components such as memory size, number of memories, etc. in a memory-based network is not a trivial task and depends a lot on the use case. Nevertheless, for future work, our approach could be further extended to non-fashion domains where multi-turn feedback-based information retrieval solutions are required.",
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+        "text": "3For a similar study on the Multi-turn Fashion-IQ dataset, please refer to the supplementary material.",
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+    {
+        "type": "text",
+        "text": "References",
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diff --git a/2023/FashionNTM_ Multi-turn Fashion Image Retrieval via Cascaded Memory/96c19156-eda3-4f76-b877-c0799e40849d_model.json b/2023/FashionNTM_ Multi-turn Fashion Image Retrieval via Cascaded Memory/96c19156-eda3-4f76-b877-c0799e40849d_model.json
new file mode 100644
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--- /dev/null
+++ b/2023/FashionNTM_ Multi-turn Fashion Image Retrieval via Cascaded Memory/96c19156-eda3-4f76-b877-c0799e40849d_model.json	
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+[
+    [
+        {
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
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+            "content": "FashionNTM: Multi-turn Fashion Image Retrieval via Cascaded Memory"
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+            "angle": 0,
+            "content": "Anwesan Pal\\*, Sahil Wadhwa?, Ayush Jaiswal?, Xu Zhang?, Yue Wu?, Rakesh Chada?, Pradeep Natarajan?, and Henrik I. Christensen"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "\\(^{1}\\)UC San Diego, \\(^{2}\\)Amazon Alexa Natural Understanding,"
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+            "content": "{a2pal, hichristensen}@ucsd.edu,{sahilwa, ayujaisw, xzhnamz, wuyue, rakhada, natarap}@amazon.com"
+        },
+        {
+            "type": "title",
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+            "content": "Multi-turn textual feedback-based fashion image retrieval focuses on a real-world setting, where users can iteratively provide information to refine retrieval results until they find an item that fits all their requirements. In this work, we present a novel memory-based method, called FashionNTM, for such a multi-turn system. Our framework incorporates a new Cascaded Memory Neural Turing Machine (CM-NTM) approach for implicit state management, thereby learning to integrate information across all past turns to retrieve new images, for a given turn. Unlike vanilla Neural Turing Machine (NTM), our CM-NTM operates on multiple inputs, which interact with their respective memories via individual read and write heads, to learn complex relationships. Extensive evaluation results show that our proposed method outperforms the previous state-of-the-art algorithm by \\(50.5\\%\\), on Multi-turn FashionIQ [60] – the only existing multi-turn fashion dataset currently, in addition to having a relative improvement of \\(12.6\\%\\) on Multi-turn Shoes – an extension of the single-turn Shoes dataset [5] that we created in this work. Further analysis of the model in a real-world interactive setting demonstrates two important capabilities of our model – memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, user study results show that images retrieved by FashionNTM were favored by \\(83.1\\%\\) over other multi-turn models."
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+            "content": "1. Introduction"
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+            ],
+            "angle": 0,
+            "content": "Image retrieval has been extensively studied in the computer vision community, both using classical approaches [10, 52, 25] and recently, using learning-based techniques [2, 15, 41, 43, 23]. Existing works can be grouped based on input queries considered – from image-only queries, commonly known as Content-Based Image Retrieval (CBIR)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.314,
+                0.891,
+                0.513
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.523,
+                0.895,
+                0.65
+            ],
+            "angle": 0,
+            "content": "Figure 1: Illustration of multi-turn fashion image retrieval. Initially (Turn 1), the system receives an initial query image, and a textual feedback mentioning the user's desired changes. The model then retrieves a ranked list of closest matching images. Subsequently, the user keeps refining their choice by providing more feedback, while the model retrieves newer images by considering both current and past feedback. This continues until the multi-turn system has successfully obtained the final retrieved image (Turn N) with all the desired properties mentioned across every past turn."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.668,
+                0.893,
+                0.729
+            ],
+            "angle": 0,
+            "content": "[35, 39, 48], to attributes [18], sketches [44], and natural language [32, 61]. However, most of these methods do not incorporate interactive user feedback, which is necessary for a personalized task such as fashion retrieval."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.732,
+                0.895,
+                0.883
+            ],
+            "angle": 0,
+            "content": "Textual feedback-based fashion image retrieval allows users to refine online shopping search results by providing information about how the results differ from their desired product (e.g., \"a dress like this but darker in color\"). Several approaches for implementing such a system have been proposed recently [14, 7, 31, 56, 17, 60, 63], which involve learning a joint representation via multi-modal information fusion across the query (reference) image and the associated feedback, and using it to retrieve the closest matching image in the database (product catalog) as the target."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Popular methods for fashion retrieval task [14, 31, 7,"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.878,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Work primarily done during internship at Amazon. Additional details are available at https://sites.google.com/eng.ucsd.edu/fashionntm."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11323"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.258
+            ],
+            "angle": 0,
+            "content": "4, 23] involve single-turn exchange of information, where users provide feedback exactly once to update the search results. However, this is not characteristic of the real-world setting as online shopping customers typically start with a general idea of what they want and iteratively update the requirements until they find something that matches their desired features. This usually involves providing additional attributes, or modifying previously specified features in each turn to refine the search results. The ideal feedback-based fashion image retrieval system is, hence, inherently multi-turn, as illustrated in Figure 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.262,
+                0.473,
+                0.549
+            ],
+            "angle": 0,
+            "content": "There are two major challenges associated with multi-turn image retrieval. First, there is a lack of sufficient training and evaluation datasets - despite the abundance of single-turn fashion retrieval datasets, to the best of our knowledge, there is only one publicly available multi-turn fashion image retrieval dataset [60] currently. This is because labeling a sequence of images while ensuring continuity, consistency, and uni-directional information flow is a difficult problem. Thus, to facilitate research in this domain, we created a new fashion image retrieval dataset to allow for further benchmarking. Second, generalizing performance to real-world dynamic user interactive cases is non-trivial - as this is still a relatively new research domain, most existing algorithms do not generalize beyond the training dataset to consider multiple turns of interactive feedback. In this work, we propose a novel memory-based framework to explicitly consider sequential feedback from users across multiple turns to retrieve desired items, both for the static image datasets, as well as real-world dynamic users."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.554,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Sequential modeling is a relatively mature field of research. However, a majority of the existing approaches [46, 27, 49, 20, 9] do not maintain an explicit memory, and therefore cannot learn long and complex information. Vanilla memory network-based methods, which explicitly maintain an external memory, could be used for retaining past information, but they do not provide a robust mechanism to iteratively update their memory [55, 51]. In contrast, Neural Turing Machines (NTMs) [16] provide a fully differentiable model with sophisticated read and write operations to extract and update historical information in its explicit memory via an attention mechanism. Therefore, in this work, we build on NTMs to develop a novel framework for the multi-turn retrieval task. We further propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) that allows us to encode multiple relationships from the features of a particular turn and store them over time across multiple memories in a multi-turn setting. This is similar to how multi-head attention (MHA) operates for transformers [53]. To ensure that the individual memories effectively utilize each other's information, we link them together in a cascaded fashion. Evaluation results demonstrate that our proposed approach improves the retrieval performance as com"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "pared to the previous state-of-the-art by \\(50.5\\%\\) on Multi-turn FashionIQ, and by \\(12.6\\%\\) on Multi-turn Shoes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.122,
+                0.895,
+                0.409
+            ],
+            "angle": 0,
+            "content": "In summary, we make the following contributions. First, we propose a state-of-the-art memory-based framework, called FashionNTM, for multi-turn feedback-based fashion image retrieval, that uses an external memory to learn complex long-term relationships. Second, we develop a novel Cascaded Memory Neural Turing Machine (CM-NTM), that extends NTM to learn relationships across multiple inputs via additional controllers and read/write heads in a cascaded fashion. Third, we conduct experiments to show that the proposed approach outperforms existing state-of-the-art retrieval models by \\(50.5\\%\\) on Multi-turn FashionIQ [60], and around \\(12.6\\%\\) on the multi-turn version of Shoes dataset [5] respectively. Additionally, by performing an interactive analysis, we demonstrated two important capabilities of our multi-turn system - memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, a user study result shows that on an average, the images retrieved by our model are preferred \\(83.1\\%\\) more than those from other multi-turn methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.448,
+                0.895,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Single turn feedback-based fashion image retrieval - Previous works in feedback-based fashion image retrieval have primarily focused on the single-turn scenario [14, 40, 31, 7, 54, 4, 3, 59, 6, 36, 22], where a model is provided with a reference image along with an associated feedback text highlighting the desired attribute changes. The typical approach is to encode the multi-modal image and text input using pre-trained visual feature extractors [19, 24, 34] and sequential natural language processors [20, 12], respectively. More recently, pre-trained extractors such as Contrastive Language-Image Pre-training (CLIP) [45] have also been used [4, 3]. This is then followed by a transformer-based decoder network [53] for generating information-rich features for image retrieval from the database. Although these methods perform well in single-turn settings, they cannot be directly used for real-world applications that deal with multiple turns of information exchange."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
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+            ],
+            "angle": 0,
+            "content": "Multi-turn visuo-linguistic methods - A few methods have been proposed recently for fusing visual and textual input across multiple turns of information exchange. A popular application has been the video dialog task [42, 21, 33, 30, 17], where a trained system is asked to answer questions based on an ongoing video dialog. However, these kinds of dialogs are primarily text-based for both the questioner and the answering agent, without any interaction across image and text inputs. In the fashion domain, there have been some early works for the multi-turn retrieval task. Guo et al. [17] proposed a model that uses convolutional neural networks (CNNs) for encoding images and text, followed by a recurrent neural network for aggregating sequences. Then,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
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+            ],
+            "angle": 0,
+            "content": "11324"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.089,
+                0.541,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.155,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.16,
+                0.327,
+                0.324,
+                0.335
+            ],
+            "angle": 0,
+            "content": "Single-turn model; fine-tuned on multi-turn data"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.339,
+                0.323,
+                0.361,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.37,
+                0.327,
+                0.433,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Multi-turn dataset"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.451,
+                0.323,
+                0.489,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.327,
+                0.645,
+                0.335
+            ],
+            "angle": 0,
+            "content": " Cascaded Memory Neural Turing Machine"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.545,
+                0.09,
+                0.885,
+                0.319
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.663,
+                0.323,
+                0.688,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.694,
+                0.327,
+                0.75,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Feature vectors"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.774,
+                0.323,
+                0.799,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.808,
+                0.327,
+                0.865,
+                0.335
+            ],
+            "angle": 0,
+            "content": "Similarity metric"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.352,
+                0.892,
+                0.45
+            ],
+            "angle": 0,
+            "content": "Figure 2: The complete FashionNTM framework. During training, the model receives an input query image, \\( I_{n} \\), and associated feedback, \\( U_{n} \\). From these, query features \\( f_{qry}(n) \\) are computed using an off-the-shelf single-turn fashion image retrieval model. These features are then fed into the memory network which learns to retain useful information from the current turn, and combine it with information from previous turns by interacting with an external memory bank, via read/write operations. The memory-modified features \\( f_{qry}'(n) \\) are compared with the target index features \\( f_{tar}(n) \\), and other negative samples \\( f_{neg}(n) \\), to compute the training loss. At inference, the model receives a series of multi-modal inputs turn-wise and computes the final modified feature \\( f_{qry}'(N) \\) using the trained memory network. This is compared with features \\( f_{cand} \\) derived from different candidate images in the database to retrieve the closest matching images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.464,
+                0.469,
+                0.614
+            ],
+            "angle": 0,
+            "content": "a \\(k\\)-Nearest Neighbor search is performed across sampled images to get the closest match. The entire model is trained end-to-end using reinforcement learning (RL). Inspired by this, Zhang et al. [63, 62] proposed two approaches for enhancing the text-image feature fusion by adding constraints, and using offline interactive recommendation. Recently, Yuan et al. [60] released the first multi-turn fashion image retrieval dataset, based on the original single turn FashionIQ [56]. They also proposed a state-of-the-art model, which we directly compare with our approach."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.616,
+                0.469,
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+            ],
+            "angle": 0,
+            "content": "Memory networks for vision and language - Memory networks have been widely used for a number of natural language processing and computer vision applications. Some works [55, 51, 13, 11] utilize it for Sentence Video Questions and Answering (QA) task. Another popular application is video object segmentation [8, 58, 50, 37]. Recently, there have been some works on including memory in transformer architectures [26, 47, 57, 38]. However, these approaches design their memory to be used only for specific tasks, and hence cannot be directly compared with ours. In this work, we propose a memory network based method for the multi-turn fashion image retrieval task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.814,
+                0.214,
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+            ],
+            "angle": 0,
+            "content": "3. FashionNTM"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The multi-turn feedback-based image retrieval task can be viewed as a series of information exchange transactions. We define a transaction as one session of query context comprising a query image and the associated feedback"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.464,
+                0.892,
+                0.57
+            ],
+            "angle": 0,
+            "content": "text. Notationally, an \\(N\\)-turn transaction is represented as \\(T = [(I_1,U_1),(I_2,U_2),\\dots ,(I_N,U_N)]\\), where \\(I_{n}\\) and \\(U_{n}\\) correspond to the query image and feedback utterance respectively, at turn \\(n\\in [1,N]\\). Given such a transaction, the aim of a multi-turn model is to iteratively retrieve the final desired target image \\(I_{tar}(N)\\) by ranking candidates in the fashion image database based on a matching score."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The overall pipeline of our approach, called Fashion-NTM, is illustrated in Figure 2. We start with a single-turn feature extraction module to encode the multi-modal image and text inputs of each turn \\( n \\) in a multi-turn transaction. It comprises two parallel blocks - (i) a query feature extractor (QE), for processing \\( I_{n} \\) and \\( U_{n} \\) to generate the joint query representation \\( f_{qry}(n) \\), and (ii) a target feature extractor (TE), for encoding all the images in the database into their corresponding index features. For the ground-truth target image \\( I_{tar}(n) \\), we call these features \\( f_{tar}(n) \\), while for every other sample \\( I_{neg}(n) \\) in the batch, we name it \\( f_{neg}(n) \\). The query feature \\( f_{qry}(n) \\) is fed turn-wise to the Cascaded Memory Neural Turing Machine (CM-NTM) block. CM-NTM first computes several derived features from the original query feature. Subsequently, the original query feature and each of the derived features interact with their own controllers, read/write heads, and sequentially update the memories in a cascaded manner, i.e. output of one memory goes as input to the next. Ultimately, we get the enhanced feature \\( f_{qry}'(n) \\) as the final output, which is then compared with the target feature \\( f_{tar}(n) \\) using a similarity score-based batch"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11325"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.088,
+                0.473,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.259,
+                0.47,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Figure 3: Cascaded Memory Neural Turing Machine (CM-NTM). It consists of \\( C \\) controllers; one for the query feature and \\( C - 1 \\) for the derived features. Each controller interacts with its own memory using its own read and write heads. The controllers are linked with each other, forming a cascaded chain. The modified features from the last memory are output as the final embedding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.351,
+                0.47,
+                0.501
+            ],
+            "angle": 0,
+            "content": "loss function. This loss treats \\( f_{tar}(n) \\) as a positive sample and every other feature in the batch, \\( f_{neg}(n) \\), as a negative sample. We use cosine-similarity [54, 31, 14] between feature vectors as the matching score. During inference, the model receives a sequence of multi-modal turn-wise inputs and computes the final modified feature \\( f_{qry}'(N) \\). This is compared with feature \\( f_{cand} \\) derived from different candidate images in the database, and the closest match is retrieved as output. In the following sections, we describe the key components of our framework."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.503,
+                0.471,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Single-turn feature extractor - We utilize the state-of-the-art single-turn image retrieval model, FashionVLP [14], for extracting multi-modal text and image features. FashionVLP extracts image embeddings at multiple levels of granularity and incorporates a vision-language pre-trained transformer for fusing these encodings with text feedback to obtain multi-modal query features. It adopts a convolutional neural network (CNN) architecture with contextual attention for fusing fashion-contextual image features of target images. Specifically, for each turn of a multi-turn transaction, we obtain query features \\(f_{qry}\\) and target features \\(f_{tar}\\). An \\(N\\)-turn retrieval transaction is of the form \\(T_{retr} = [f_{qry}(1), f_{qry}(2), \\dots, f_{qry}(N)]\\), with the target feature representation given by \\(f_{tar}(N)\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.726,
+                0.444,
+                0.743
+            ],
+            "angle": 0,
+            "content": "3.1. Cascaded Memory Neural Turing Machine"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To learn relationships across transactions, we propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) module. CM-NTM allows multiple inputs to interact with their own memories using individual read and write heads to learn multiple complex relationships in the input data. We achieve this by deriving several features from the original \\( n \\)-th turn query feature \\( f_{qry}(n) \\) using a projection function \\( \\mathcal{F} \\), which comprises a fully-connected (FC) layer with batch normalization. Specifically, for a \\( C \\)-stage cascaded CM-NTM, we obtain the derived feature"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.091,
+                0.892,
+                0.197
+            ],
+            "angle": 0,
+            "content": "\\(f_{drv}^{c} = \\mathrm{BatchNorm}(\\mathrm{FC}_{\\mathrm{c}}(f_{qry}(n)))\\) where \\(c \\in [1, C - 1]\\), and \\(\\mathrm{FC}_{\\mathrm{c}}(\\cdot)\\) is the FC layer for the \\(c\\)-th stage. Having obtained \\(C\\) inputs comprising the original query and \\(C - 1\\) derived features, we pass them sequentially to our memory network. Figure 3 presents our memory network architecture. It consists of three main components: Controller, Read/Write heads, and Memory blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.197,
+                0.893,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Controller - The vanilla NTM has a single controller which takes the query feature at turn \\( n \\), along with the previous turn's read vector, and emits an intermediate controller output. This is used by the read and write heads to compute the current turn's attention weights, which are then used to update the memory. In our work, we introduce \\( C \\) different controllers - one for each of our inputs. Each controller, \\( c \\in [1, C] \\) can therefore interactively update its memory via individual read and write heads, allowing it to learn multiple complex relationships in each turn."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.348,
+                0.893,
+                0.454
+            ],
+            "angle": 0,
+            "content": "Read/Write heads - The controller output is fed to these heads. The write head learns to generate erase and add parameters, which are used to update the current memory. Similarly, the read head generates an attention weight vector, which is used to obtain a weighted sum over the memory locations to get the read vector \\(\\mathbf{r}_{out}(n)\\). In our work, we have separate read and write heads for each memory."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.454,
+                0.894,
+                0.668
+            ],
+            "angle": 0,
+            "content": "Memory block - This is represented as a 2-D matrix of the form \\( N \\times M \\), where \\( N \\) corresponds to memory locations and \\( M \\) to the vector size at each location. The output of each memory block is a fused representation of the controller output and the read vector. In our cascaded multi-memory setup, the controllers are linked in a chain, such that the memory-modified features are sequentially propagated. Specifically, for controller \\( c \\in [1, C] \\) at turn \\( n \\), the input is given by \\( \\mathrm{input}^c(n) = [\\mathbf{r}_{out}^{c-1}(n); f_{drv}^c; \\mathbf{r}_{out}^c(n-1)] \\), where \\( \\mathbf{r}_{out}^0(n) = \\mathbf{r}_{out}^C(n-1) \\), \\( f_{drv}^C = f_{qry}(n) \\), and ; represents concatenation. The final output, \\( f_{qry}'(n) \\), is the fused representation of the last controller output \\( \\mathrm{output}_{ctrl}^C \\) and final read vector \\( \\mathbf{r}_{out}^C \\). We experiment with a different number of memories \\( C \\) and memory sizes in Section 4.7."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.676,
+                0.64,
+                0.69
+            ],
+            "angle": 0,
+            "content": "3.2. Loss function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.699,
+                0.892,
+                0.806
+            ],
+            "angle": 0,
+            "content": "We adopt a batch cross-entropy loss [14], where each entry in a batch acts as a negative sample for all other entries. In the multi-turn setting, we compute the loss function turnwise. Given a batch size \\( B \\), the loss between predicted feature \\( \\mathbf{x}_n = [{}^1 f_{qry}'(n), {}^2 f_{qry}'(n), \\ldots, {}^B f_{qry}'(n)] \\), and ground-truth \\( \\mathbf{y}_n = [{}^1 f_{tar}(n), {}^2 f_{tar}(n), \\ldots, {}^B f_{tar}(n)] \\), at turn \\( n \\) is of the form"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
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+                0.871,
+                0.856
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} (\\mathbf {x} _ {n}, \\mathbf {y} _ {n}) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} - \\log \\frac {e ^ {\\kappa (^ {i} f _ {q r y} ^ {\\prime} (n) , ^ {i} f _ {t a r} (n))}}{\\sum_ {j = 1} ^ {B} e ^ {\\kappa (^ {i} f _ {q r y} ^ {\\prime} (n) , ^ {j} f _ {t a r} (n))}}\n\\]"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.875,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>We mainly discuss our novel changes to the NTM design. For details regarding the vanilla architecture, please refer to the original paper [16]."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11326"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.089,
+                0.472,
+                0.146
+            ],
+            "angle": 0,
+            "content": "Table 1: Statistics of the datasets used in this work. The top 2 rows are for the recently proposed Multi-turn FashionIQ dataset [60]. The bottom two rows are for the Multi-turn version of the Shoes [5] dataset, which we created as part of our work."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.157,
+                0.472,
+                0.239
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Split</td><td colspan=\"3\">Number of transactions with</td><td rowspan=\"2\">Total images</td></tr><tr><td>2-turns</td><td>3-turns</td><td>4-turns</td></tr><tr><td rowspan=\"2\">Multi-turn FashionIQ [60]</td><td>Train</td><td>6,897</td><td>1,733</td><td>475</td><td>10,438</td></tr><tr><td>Test</td><td>1,752</td><td>483</td><td>165</td><td>6,274</td></tr><tr><td rowspan=\"2\">Multi-turn Shoes (ours)</td><td>Train</td><td>1,659</td><td>1,036</td><td>982</td><td>11,030</td></tr><tr><td>Test</td><td>296</td><td>96</td><td>28</td><td>4,631</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.261,
+                0.47,
+                0.356
+            ],
+            "angle": 0,
+            "content": "where \\(\\kappa\\) is the cosine similarity metric [14]. In this way, each \\(f_{tar}(n)\\) in the batch, \\(\\forall j\\in [1,B]\\) and \\(j\\neq i\\) , serves as a negative sample \\(f_{neg}(n)\\) for a given \\(f_{qry}^{\\prime}(n)\\) . The turn-wise retrieval loss function is represented as \\(\\mathcal{L}_{retr}^{n} =\\) \\(\\mathcal{L}(\\mathbf{x}_n,\\mathbf{y}_n)\\) , with the overall loss function for our proposed multi-turn model given by \\(\\mathcal{L} = \\frac{1}{N}\\sum_{n = 1}^{N}\\mathcal{L}_{retr}^{n}\\)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.371,
+                0.313,
+                0.387
+            ],
+            "angle": 0,
+            "content": "4. Experimental Evaluation"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.396,
+                0.18,
+                0.411
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.42,
+                0.47,
+                0.555
+            ],
+            "angle": 0,
+            "content": "Multi-turn FashionIQ [60]: To the best of our knowledge, this is the only existing fashion dataset with multi-turn sessions, where each turn is derived from the original single-turn FashionIQ [56] dataset. It comprises of 11,505 sessions across three clothing types - dress, top-tee, and shirt. The dataset is split into transactions of 2-turns, 3-turns, and 4-turns. In each turn, the data is represented as a pair \\((I_n, U_n)\\), where \\(I_n\\) and \\(U_n\\) correspond to the query image and the feedback text for turn \\(n\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.557,
+                0.471,
+                0.724
+            ],
+            "angle": 0,
+            "content": "Multi-turn Shoes: The original Shoes dataset [5] contains images of 10 categories of women's shoes obtained from the web along with automatic labeling of attributes. Guo et al. [17] provide additional natural language descriptions of the images to make them suitable for single-turn feedback-based image retrieval. This resulted in about 10k training pairs and 4.6k test queries. In this work, we create a multi-turn extension of this dataset to further research in this domain. Like the approach described in [60], we concatenated several single-turn transactions by matching the target image of one session to the query of another. To maintain"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.136
+            ],
+            "angle": 0,
+            "content": "consistency with Multi-turn FashionIQ, we also developed transactions of 2-turns, 3-turns, and 4-turns. Table 1 provides the statistics of both the datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.149,
+                0.719,
+                0.166
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.172,
+                0.892,
+                0.293
+            ],
+            "angle": 0,
+            "content": "Single-turn feature extractor pre-training - We use the recently proposed single turn (ST) fashion image retrieval model, FashionVLP [14], to extract the query and target features for both datasets. To ensure a fair comparison with other algorithms, we re-train FashionVLP only on those single-turn queries that are part of the multi-turn dataset. The implementation details and hyperparameters are similar to those mentioned in Goenka et al. [14]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.294,
+                0.893,
+                0.491
+            ],
+            "angle": 0,
+            "content": "CM-NTM training - We build our CM-NTM model using the open-source implementation [28] of NTM [16]. We implement a separate controller for each memory in our cascaded design using Long Short Term Memory (LSTM) networks [20]. The read and write heads are composed of multi-layer perceptrons (MLPs) and attention networks. We use \\( C = 4 \\) for Shoes, and \\( C = 8 \\) memory stages for FashionIQ, as it is a larger dataset. To ensure equal turn lengths for batch training, we pad the short turn transactions by repeating the last transaction similar to Yuan et al. [60]. We train our models for 100 epochs with a batch size of 80 and a learning rate of 1e-4. We used the PyTorch framework with Adam [29] optimizer for training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.503,
+                0.836,
+                0.518
+            ],
+            "angle": 0,
+            "content": "4.3. Baselines and Previous State-of-the-art"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.526,
+                0.892,
+                0.556
+            ],
+            "angle": 0,
+            "content": "We compare the performance of our model with six other single-turn and multi-turn approaches."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.557,
+                0.892,
+                0.724
+            ],
+            "angle": 0,
+            "content": "Single-turn methods - In these methods, we aggregate the multi-turn query data into a single feature without iterating over them turn-wise. The first baseline is \\(\\mathrm{ST} + \\mathrm{avg}(\\mathrm{all~turns})\\), where we take the mean of all the \\(N\\) query features in a transaction to get a single mean query \\(\\bar{f}_{qry}(N)\\). This is compared with the candidate target features \\(f_{tar}(N)\\). Next, we have \\(\\mathrm{ST} + \\mathrm{cat}(\\mathrm{all~captions})\\), where all the captions of a multi-turn transaction are concatenated into one long caption, along with initial reference image, to get query features \\(\\hat{f}_{qry}(N)\\). This is compared with target features \\(f_{tar}(N)\\) to retrieve the final images."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.744,
+                0.892,
+                0.773
+            ],
+            "angle": 0,
+            "content": "Table 2: Quantitative results on Multi-turn FashionIQ [60]. We compare with multiple single-turn and multi-turn baselines, and state-of-the-art works [17, 60]. Results show the superior performance of our proposed approach on the popularly used recall rate evaluation metric."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.178,
+                0.783,
+                0.794,
+                0.907
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Dress</td><td colspan=\"2\">Toptee</td><td colspan=\"2\">Shirt</td><td colspan=\"3\">Overall</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan=\"10\">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>25.6</td><td>32.5</td><td>32.1</td><td>38.1</td><td>27.0</td><td>32.3</td><td>28.2</td><td>34.3</td><td>31.3</td></tr><tr><td>ST + cat(all captions)</td><td>30.2</td><td>36.3</td><td>36.0</td><td>44.1</td><td>35.3</td><td>42.5</td><td>33.8</td><td>41.0</td><td>37.4</td></tr><tr><td colspan=\"10\">Multi-turn</td></tr><tr><td>Dialog Manager [17]</td><td>12.7</td><td>16.7</td><td>11.6</td><td>15.8</td><td>13.9</td><td>17.7</td><td>13.1</td><td>15.2</td><td>14.2</td></tr><tr><td>CFIR [60]</td><td>29.8</td><td>33.5</td><td>29.4</td><td>33.6</td><td>30.5</td><td>34.1</td><td>30.3</td><td>33.4</td><td>31.9</td></tr><tr><td>ST + EWMA (ours)</td><td>42.0</td><td>48.4</td><td>43.8</td><td>50.9</td><td>36.9</td><td>44.2</td><td>40.9</td><td>47.8</td><td>44.4</td></tr><tr><td>ST + LSTM (ours)</td><td>47.8</td><td>52.5</td><td>44.4</td><td>50.5</td><td>41.6</td><td>47.6</td><td>44.6</td><td>50.2</td><td>47.4</td></tr><tr><td>FashionNTM (ours)</td><td>48.3</td><td>52.8</td><td>45.1</td><td>49.8</td><td>43.8</td><td>48.8</td><td>45.7</td><td>50.4</td><td>48.1</td></tr></table>"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11327"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Multi-turn methods - In these methods, the multi-turn data is fed turn-wise to the model. The first method is Dialog Manager [17], which employs reinforcement learning (RL) framework to learn relationships between turns. Next, we have the previous state-of-the-art Conversational Fashion Image Retrieval CFIR method [60], which encodes only the text using a transformer network [53], and uses a simple Gated Recurrent Unit (GRU) layer for multi-turn image retrieval. The third baseline is \\(\\mathrm{ST} + \\mathrm{EWMA}\\), where we use exponential weighted moving average [1] to heuristically aggregate past turns, with more weights given to recent history. Finally, we have the \\(\\mathrm{ST} + \\mathrm{LSTM}\\) model that uses a single-layer LSTM [20] with a hidden size of 100 for aggregating past information."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.312,
+                0.172,
+                0.326
+            ],
+            "angle": 0,
+            "content": "4.4. Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.335,
+                0.47,
+                0.395
+            ],
+            "angle": 0,
+            "content": "Evaluation Metrics - Following [14, 60, 17], we evaluate models using the standard top-K recall (i.e. R@K) for image retrieval. Overall performance are compared specifically on the average of R@5 and R@8."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.396,
+                0.471,
+                0.636
+            ],
+            "angle": 0,
+            "content": "Quantitative results on multi-turn datasets - In Table 2, we compare the results of different methods on the multi-turn FashionIQ dataset. We observe that the multi-turn baselines generally perform better than single-turn methods. This is expected as aggregating data by naively averaging/concatenating loses feedback content and turn-order information and hence is likely to miss out on important cues. Our memory-based approach outperforms all the other multi-turn baselines by a large margin. This shows that the memory network can store and retrieve useful information to and from the memory between intermediate turns, which allows it to keep track of past information better than other networks that do not use explicit memory. The \\(50.5\\%\\) performance gain over the previous state-of-the-art highlights our model's capability to learn meaningful representations over multiple turns of conversational feedback."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.637,
+                0.47,
+                0.682
+            ],
+            "angle": 0,
+            "content": "In Table 3, we provide a similar comparison for the Multi-turn Shoes dataset. Consistent with results for Multi-turn FashionIQ, the multi-turn baselines perform better than"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.09,
+                0.892,
+                0.16
+            ],
+            "angle": 0,
+            "content": "Table 3: Comparison with existing single-turn and multi-turn models on the multi-turn version of the Shoes [5] dataset. We compare with multiple single-turn, and multi-turn baselines. Comparative analysis shows the superior performance of our proposed approach using the popular recall rate evaluation metric."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.565,
+                0.17,
+                0.828,
+                0.265
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan=\"4\">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>12.4</td><td>17.6</td><td>15.0</td></tr><tr><td>ST + cat(all captions)</td><td>10.7</td><td>13.6</td><td>12.2</td></tr><tr><td colspan=\"4\">Multi-turn</td></tr><tr><td>ST + EWMA (ours)</td><td>18.3</td><td>23.8</td><td>21.1</td></tr><tr><td>ST + LSTM (ours)</td><td>23.3</td><td>32.1</td><td>27.7</td></tr><tr><td>FashionNTM (ours)</td><td>26.7</td><td>35.7</td><td>31.2</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.274,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "all the single-turn ones, and our memory network-based approach performs the best with a relative improvement of \\(12.6\\%\\). The difference in performance across different models is more pronounced in these results than in Table 2. This is possibly because the annotations are cleaner and more consistent in this dataset as compared to Multi-turn FashionIQ [60]. For instance, multiple images in the FashionIQ dataset can match a particular query, but only one of them is labeled as the ground-truth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.411,
+                0.893,
+                0.683
+            ],
+            "angle": 0,
+            "content": "An important property of a good multi-turn system is that performance should be robust to the length of the historical information (number of past turns). For example, even for a large number of previous turns considered, the model should efficiently retain desirable details, while filtering out unnecessary information. In Table 4, we analyze this property for models with and without memory. A single-turn model that assumes ground-truth information for all past turns, and evaluated only on the final-turn, is taken as reference. This is expected to be the upper-bound on the performance in a single-turn setting, as perfect information about the history is guaranteed. We vary the number of past turns included in the input transaction history (versus treated as ground-truth) for the multi-turn models (with or without memory) in order to evaluate their effectiveness at capturing and utilizing past information. As seen from the table, for a model without memory, the performance depreciates significantly with each additional turn from the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.703,
+                0.892,
+                0.788
+            ],
+            "angle": 0,
+            "content": "Table 4: Importance of aggregating historical data using memory-based vs non-memory approach. In the first row, we show the result of a model using only the final turn information of a multi-turn transaction. This assumes the groundtruth retrieval for all previous turns, and therefore provides the upper-bound on single-turn performance for final retrieval. Subsequently, we include additional information from the history, and compare performance across models with and without memory. As seen from the non-memory case, the performance depreciates a lot (\\(\\approx\\) 64.9% difference compared to the final turn's performance), as we try to aggregate longer historical information. In contrast, for the memory network model, it can be seen that the performance is fairly consistent (\\(\\approx\\) 0.5% difference) across the turn length."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.798,
+                0.887,
+                0.911
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Memory usage</td><td rowspan=\"2\">Turn configuration</td><td colspan=\"2\">Dress</td><td colspan=\"2\">Toptee</td><td colspan=\"2\">Shirt</td><td colspan=\"3\">Overall</td><td rowspan=\"2\">Difference from final turn</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td>-</td><td>only final turn</td><td>77.9</td><td>77.9</td><td>84.0</td><td>84.0</td><td>74.1</td><td>77.8</td><td>78.7</td><td>79.9</td><td>79.3</td><td>-</td></tr><tr><td colspan=\"12\">Experiments with data aggregated across multiple-turns</td></tr><tr><td rowspan=\"3\">Only single turn (w/o memory)</td><td>last two turns</td><td>51.3</td><td>58.4</td><td>56.0</td><td>76.0</td><td>44.4</td><td>48.1</td><td>50.6</td><td>60.9</td><td>55.8</td><td>-29.6%</td></tr><tr><td>last three turns</td><td>33.6</td><td>43.4</td><td>32.0</td><td>44.0</td><td>29.6</td><td>40.7</td><td>31.8</td><td>42.7</td><td>37.3</td><td>-53.0%</td></tr><tr><td>all turns</td><td>18.6</td><td>28.3</td><td>32.0</td><td>32.0</td><td>25.9</td><td>29.6</td><td>25.5</td><td>30.0</td><td>27.8</td><td>-64.9%</td></tr><tr><td rowspan=\"3\">FashionNTM (with memory)</td><td>last two turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr><tr><td>last three turns</td><td>77.0</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.6</td><td>79.9</td><td>79.8</td><td>+0.6%</td></tr><tr><td>all turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr></table>"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11328"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.086,
+                0.895,
+                0.312
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.178,
+                0.315,
+                0.796,
+                0.328
+            ],
+            "angle": 0,
+            "content": "(a) Multi-turn FashionIQ. From left to right, the images belong to the Dress, Shirt, and Toptee categories respectively."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.34,
+                0.892,
+                0.522
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.228,
+                0.526,
+                0.746,
+                0.54
+            ],
+            "angle": 0,
+            "content": "(b) Multi-turn Shoes. From left to right, we have three different samples of shoes from the dataset."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.551,
+                0.893,
+                0.593
+            ],
+            "angle": 0,
+            "content": "Figure 4: Top-5 final image retrievals on the evaluated multi-turn datasets. The top row illustrates 3 sets of multi-turn query session. We consider three different multi-turn models - EWMA, LSTM, and our proposed FashionNTM. As seen from the retrievals, our proposed model correctly predicts the target image in all 3 cases for the FashionIQ dataset, and in 2 out of 3 cases for the Shoes dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.62,
+                0.47,
+                0.727
+            ],
+            "angle": 0,
+            "content": "past treated as input rather than ground-truth. As we go further back in history, the performance consistently reduces. However, for our multi-turn model with memory, the performance does not change appreciably as the number of turns change. This shows that our proposed approach can successfully retain/filter out past data based on their relevance, across various lengths of history."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.73,
+                0.47,
+                0.821
+            ],
+            "angle": 0,
+            "content": "An interesting observation is that having only the final turn with memory does not yield a good result. This is possibly due to the initialization method of the memory network, which is random. Hence, in absence of a history (only single turn case), the only past features to be aggregated are the random initialization features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.826,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Qualitative results - In addition to the quantitative experiments described above, we also present some qualitative final image retrieval results of our evaluated models on both the multi-turn datasets. The first set of results are shown in Figures 4a and 4b for the Multi-turn FashionIQ [60] and the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.619,
+                0.895,
+                0.863
+            ],
+            "angle": 0,
+            "content": "Multi-turn Shoes datasets, respectively<sup>2</sup>. We compare the top-5 predicted results from our proposed model with two other multi-turn baselines, ST + EWMA and ST + LSTM. As seen in the figures, our approach can correctly predict the desired target image for both datasets with higher ranks as compared to other baselines. More specifically, we see that in Figure 4a, even though all the three multi-turn models can infer the general sense of desired attributes, such as \"is longer\" in the left block and \"has short sleeves\" in the right, only our model can capture complex and detailed properties, e.g., \"gray and not red\" in the left block, and \"red color with center logo\" in the middle block. Furthermore, our model can retrieve multiple desirable products, as seen by the first four images in the middle block, and four out of five images in the right block. Similar results are observed for Shoes in Figure 4b, where our model correctly predicts"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.875,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "2Please refer to the supplementary material for additional results, along with the differences in annotation quality between the two datasets."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
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+            "angle": 0,
+            "content": "11329"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.473,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.225,
+                0.47,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Figure 5: Memory retention capability of our proposed approach. Given an initial query image, we take two interactive user feedbacks in turns. On the left side, we have the single-turn model which only learns to retrieve an image using a single dialog exchange. As a result, none of the retrieved images in turn 2 are \"green in color\", which was desired in turn 1. In contrast, our proposed approach on the right can learn to retain data from both the turns, and therefore retrieves desirable product in 2 out of 3 cases."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.346,
+                0.47,
+                0.378
+            ],
+            "angle": 0,
+            "content": "the desired target as rank-1 in two out of three examples, whereas the other models fail to retrieve meaningful results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.39,
+                0.405,
+                0.406
+            ],
+            "angle": 0,
+            "content": "4.5. Model Analysis in Interactive Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.415,
+                0.469,
+                0.474
+            ],
+            "angle": 0,
+            "content": "In addition to the results above for the static dataset, we also performed some interactive experiments to evaluate whether our model can adapt to real-world dynamic use cases beyond the trained datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.476,
+                0.47,
+                0.702
+            ],
+            "angle": 0,
+            "content": "Memory retention - In this experiment, we demonstrate the memory retention capability of our proposed model by comparing it with a single-turn network, which does not retain historical information. We start with an initial query image retrieved via a single-turn model. Subsequently, we take user input for the next two turns to retrieve newer sets of images. As seen in Figure 5, for the single-turn model (left side), none of the retrieved images in turn 2 are green in color. This is because the \"green in color\" attribute was a desired property in turn 1, which the model without memory could not recover. In contrast, for our memory network approach (right side) both the top-2 retrieved images for turn 2 are \"green in color\" in addition to having \"a solid color and small image\". Thus, our model can learn to retain information from previous turns."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.704,
+                0.47,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Agnosticity to turn order - Ideally, a deployed multi-turn image retrieval system should be independent of the order of feedbacks provided, as long as they are non-contradictory. This is demonstrated in the experiment conducted in Figure 6. In the first case, we take two text inputs as feedbacks from a user and present them to the model. In the second case, we reverse the order of the feedbacks. As shown in the figure, for the flipped case, our proposed FashionNTM model retrieves similar looking final products, even though the intermediate retrievals are very different."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "It is to be noted that for both the experiments depicted in Figures 5 and 6, the feedback is taken from a dynamic user, thereby establishing the interactive capability of our"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.089,
+                0.882,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.235,
+                0.892,
+                0.347
+            ],
+            "angle": 0,
+            "content": "Figure 6: Turn order independence feature of a memory network. In this experiment, we start with an initial query image, and take two non-contradictory user feedbacks. In one case (left), we let the model retrieve images based on the original order of the feedbacks, whilst in the other (right), we flip the order of the feedbacks. Our proposed approach adapts to presented input, and retrieves similar looking final results for both the cases, even though the intermediate outputs are quite different."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.36,
+                0.794,
+                0.375
+            ],
+            "angle": 0,
+            "content": "proposed model beyond the training dataset."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.385,
+                0.623,
+                0.401
+            ],
+            "angle": 0,
+            "content": "4.6. User Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.409,
+                0.893,
+                0.635
+            ],
+            "angle": 0,
+            "content": "Fashion image retrieval is inherently a subjective task, where the task success heavily relies on the satisfaction of a customer. Thus, we conducted a small human-preference survey among 5 participants (not associated with the paper in any way). To each user, we showed the final top-1 retrieved image by the 3-best multi-turn models on the FashionIQ [60] dataset from Table 2 - EWMA, LSTM, and our proposed FashionNTM. To ensure consistency, we generated 45 queries for this study, whose results are shown in Figure 7. The \\( y \\)-axis shows the number of preferred retrieval results for each user. Results show that each of the 5 users preferred images retrieved by the proposed FashionNTM model, on an average \\( 83.1\\% \\) more as compared to other multi-turn methods. In the supplementary material, we include some examples of the user interface shown to"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.519,
+                0.657,
+                0.87,
+                0.892
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.515,
+                0.902,
+                0.877,
+                0.916
+            ],
+            "angle": 0,
+            "content": "Figure 7: Human preference study of top multi-turn systems."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11330"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.089,
+                0.472,
+                0.132
+            ],
+            "angle": 0,
+            "content": "Table 5: Different number of memories for the proposed approach by fixing the memory size to \\(4 \\times 768\\). We select the mean value for comparison and pick the best one."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.143,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Number of memories (C)</td><td>R@5</td><td>R@8</td><td>Mean</td><td>% increase</td></tr><tr><td>ST+v-NTM</td><td>1</td><td>24.5</td><td>30.5</td><td>27.5</td><td>-</td></tr><tr><td rowspan=\"4\">FashionNTM</td><td>2</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr><tr><td>4</td><td>27.6</td><td>35.5</td><td>31.5</td><td>14.5</td></tr><tr><td>8</td><td>26.9</td><td>35.2</td><td>31.1</td><td>13.1</td></tr><tr><td>16</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.235,
+                0.3,
+                0.251
+            ],
+            "angle": 0,
+            "content": "the participants during this study."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.26,
+                0.241,
+                0.275
+            ],
+            "angle": 0,
+            "content": "4.7. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.283,
+                0.469,
+                0.357
+            ],
+            "angle": 0,
+            "content": "We perform multiple ablation studies to gain insights on how changing different configurations of the memory network affect the overall performance. We perform these ablations on the multi-turn Shoes dataset as it contains more realistic and consistent feedback texts.<sup>3</sup>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.358,
+                0.47,
+                0.614
+            ],
+            "angle": 0,
+            "content": "Number of memories in CM-NTM - This experiment involves varying the number of memories \\( C \\) in our cascaded memory architecture. In Table 5, we observe that the cascaded memory CM-NTM models perform significantly better than vanilla NTM, which has only one memory. We hypothesize that having inputs from multiple turns interacting with the same memory could eventually lead to saturation as we get additional data which could be alleviated if there are multiple memories in the network to recover the past which might help in capturing multiple complex relationships in multi-turn interactions better. Additionally, multiple memory networks can help in learning diverse representations of the input using derived features, which is not possible with a single memory network. As seen in Table 5 for Shoes dataset, the performance increases with the number of memories, peaking at \\( C = 4 \\), and then gradually decreases as the model starts to overfit."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.616,
+                0.47,
+                0.782
+            ],
+            "angle": 0,
+            "content": "Inference time with multiple memories - In this experiment, we study the performance of FashionNTM in terms of the mean of R@5 and R@8 recall rates along with the time taken to process one multi-turn transaction. For each \\( C \\), we evaluate the performance across four different memory sizes. As seen from Figure 8, the inference time increases with additional memories. Configurations in the green and blue clusters are desirable, as they provide a good trade-off between recall performance and computation time, while the pink and red clusters are undesirable due to poor performance and longer inference time, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.795,
+                0.347,
+                0.811
+            ],
+            "angle": 0,
+            "content": "5. Conclusion and Future Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.821,
+                0.469,
+                0.866
+            ],
+            "angle": 0,
+            "content": "In this paper, we presented a novel cascaded Neural Turing Machine-based approach, called FashionNTM, for multi-turn feedback-based fashion image retrieval. Multiple"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "3For a similar study on the Multi-turn Fashion-IQ dataset, please refer to the supplementary material."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.499,
+                0.088,
+                0.885,
+                0.289
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.299,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Figure 8: Scatter plot showing recall versus inference time for multiple memories in our CM-NTM for the Multi-turn Shoes dataset. The configurations belonging to the green cluster give the best recall overall, while having a high inference time. The configurations in the blue cluster provide a suitable alternative with quicker inference at the cost of lower recall. The magenta and red clusters are undesirable configurations due to poor performance and long inference time, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.417,
+                0.893,
+                0.689
+            ],
+            "angle": 0,
+            "content": "memories in our model allow it to effectively retain and recall a number of complex relationships across transactions in the multi-turn setting, and multiple controllers help in assigning relative importance to each feature stored in the memory. This aids in attending to different parts of the input at different levels, thus leading to better performance across datasets. We also performed extensive experiments to compare our performance with baselines and previous state-of-the-art and observed that our multi-memory model significantly outperforms previous works [60], with up to \\(50.5\\%\\) relative improvement on Multi-turn FashionIQ, and by \\(12.6\\%\\) on the multi-turn Shoes dataset, which we created in this work. We further demonstrated that our model can generalize beyond the trained setting to dynamically interact with real-world users to retrieve meaningful final product images. Finally, a user preference study reveals that our model is preferred by human participants on an average \\(83.1\\%\\) more as compared to other multi-turn methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.69,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Despite promising results, there are a few limitations that make multi-turn image retrieval a hard problem to solve. Firstly, there is dearth of high quality and diverse multi-turn image retrieval datasets in the fashion domain which hinders comprehensive studies in this field. Additionally, deploying current approaches to real-world scenarios (e.g., virtual private assistants) becomes a challenge due to computational requirements. Lastly, selecting the right configuration for different components such as memory size, number of memories, etc. in a memory-based network is not a trivial task and depends a lot on the use case. Nevertheless, for future work, our approach could be further extended to non-fashion domains where multi-turn feedback-based information retrieval solutions are required."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11331"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.105
+            ],
+            "angle": 0,
+            "content": "References"
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+# FashionNTM: Multi-turn Fashion Image Retrieval via Cascaded Memory
+
+Anwesan Pal\*, Sahil Wadhwa?, Ayush Jaiswal?, Xu Zhang?, Yue Wu?, Rakesh Chada?, Pradeep Natarajan?, and Henrik I. Christensen
+
+$^{1}$ UC San Diego,  $^{2}$ Amazon Alexa Natural Understanding,
+
+{a2pal, hichristensen}@ucsd.edu,{sahilwa, ayujaisw, xzhnamz, wuyue, rakhada, natarap}@amazon.com
+
+# Abstract
+
+Multi-turn textual feedback-based fashion image retrieval focuses on a real-world setting, where users can iteratively provide information to refine retrieval results until they find an item that fits all their requirements. In this work, we present a novel memory-based method, called FashionNTM, for such a multi-turn system. Our framework incorporates a new Cascaded Memory Neural Turing Machine (CM-NTM) approach for implicit state management, thereby learning to integrate information across all past turns to retrieve new images, for a given turn. Unlike vanilla Neural Turing Machine (NTM), our CM-NTM operates on multiple inputs, which interact with their respective memories via individual read and write heads, to learn complex relationships. Extensive evaluation results show that our proposed method outperforms the previous state-of-the-art algorithm by  $50.5\%$ , on Multi-turn FashionIQ [60] – the only existing multi-turn fashion dataset currently, in addition to having a relative improvement of  $12.6\%$  on Multi-turn Shoes – an extension of the single-turn Shoes dataset [5] that we created in this work. Further analysis of the model in a real-world interactive setting demonstrates two important capabilities of our model – memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, user study results show that images retrieved by FashionNTM were favored by  $83.1\%$  over other multi-turn models.
+
+# 1. Introduction
+
+Image retrieval has been extensively studied in the computer vision community, both using classical approaches [10, 52, 25] and recently, using learning-based techniques [2, 15, 41, 43, 23]. Existing works can be grouped based on input queries considered – from image-only queries, commonly known as Content-Based Image Retrieval (CBIR)
+
+![](images/8ecb308d0ed8fef39963a7d3739c45ca2d5a58f521f5981f8419e3ca53342207.jpg)  
+Figure 1: Illustration of multi-turn fashion image retrieval. Initially (Turn 1), the system receives an initial query image, and a textual feedback mentioning the user's desired changes. The model then retrieves a ranked list of closest matching images. Subsequently, the user keeps refining their choice by providing more feedback, while the model retrieves newer images by considering both current and past feedback. This continues until the multi-turn system has successfully obtained the final retrieved image (Turn N) with all the desired properties mentioned across every past turn.
+
+[35, 39, 48], to attributes [18], sketches [44], and natural language [32, 61]. However, most of these methods do not incorporate interactive user feedback, which is necessary for a personalized task such as fashion retrieval.
+
+Textual feedback-based fashion image retrieval allows users to refine online shopping search results by providing information about how the results differ from their desired product (e.g., "a dress like this but darker in color"). Several approaches for implementing such a system have been proposed recently [14, 7, 31, 56, 17, 60, 63], which involve learning a joint representation via multi-modal information fusion across the query (reference) image and the associated feedback, and using it to retrieve the closest matching image in the database (product catalog) as the target.
+
+Popular methods for fashion retrieval task [14, 31, 7,
+
+4, 23] involve single-turn exchange of information, where users provide feedback exactly once to update the search results. However, this is not characteristic of the real-world setting as online shopping customers typically start with a general idea of what they want and iteratively update the requirements until they find something that matches their desired features. This usually involves providing additional attributes, or modifying previously specified features in each turn to refine the search results. The ideal feedback-based fashion image retrieval system is, hence, inherently multi-turn, as illustrated in Figure 1.
+
+There are two major challenges associated with multi-turn image retrieval. First, there is a lack of sufficient training and evaluation datasets - despite the abundance of single-turn fashion retrieval datasets, to the best of our knowledge, there is only one publicly available multi-turn fashion image retrieval dataset [60] currently. This is because labeling a sequence of images while ensuring continuity, consistency, and uni-directional information flow is a difficult problem. Thus, to facilitate research in this domain, we created a new fashion image retrieval dataset to allow for further benchmarking. Second, generalizing performance to real-world dynamic user interactive cases is non-trivial - as this is still a relatively new research domain, most existing algorithms do not generalize beyond the training dataset to consider multiple turns of interactive feedback. In this work, we propose a novel memory-based framework to explicitly consider sequential feedback from users across multiple turns to retrieve desired items, both for the static image datasets, as well as real-world dynamic users.
+
+Sequential modeling is a relatively mature field of research. However, a majority of the existing approaches [46, 27, 49, 20, 9] do not maintain an explicit memory, and therefore cannot learn long and complex information. Vanilla memory network-based methods, which explicitly maintain an external memory, could be used for retaining past information, but they do not provide a robust mechanism to iteratively update their memory [55, 51]. In contrast, Neural Turing Machines (NTMs) [16] provide a fully differentiable model with sophisticated read and write operations to extract and update historical information in its explicit memory via an attention mechanism. Therefore, in this work, we build on NTMs to develop a novel framework for the multi-turn retrieval task. We further propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) that allows us to encode multiple relationships from the features of a particular turn and store them over time across multiple memories in a multi-turn setting. This is similar to how multi-head attention (MHA) operates for transformers [53]. To ensure that the individual memories effectively utilize each other's information, we link them together in a cascaded fashion. Evaluation results demonstrate that our proposed approach improves the retrieval performance as com
+
+pared to the previous state-of-the-art by  $50.5\%$  on Multi-turn FashionIQ, and by  $12.6\%$  on Multi-turn Shoes.
+
+In summary, we make the following contributions. First, we propose a state-of-the-art memory-based framework, called FashionNTM, for multi-turn feedback-based fashion image retrieval, that uses an external memory to learn complex long-term relationships. Second, we develop a novel Cascaded Memory Neural Turing Machine (CM-NTM), that extends NTM to learn relationships across multiple inputs via additional controllers and read/write heads in a cascaded fashion. Third, we conduct experiments to show that the proposed approach outperforms existing state-of-the-art retrieval models by  $50.5\%$  on Multi-turn FashionIQ [60], and around  $12.6\%$  on the multi-turn version of Shoes dataset [5] respectively. Additionally, by performing an interactive analysis, we demonstrated two important capabilities of our multi-turn system - memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, a user study result shows that on an average, the images retrieved by our model are preferred  $83.1\%$  more than those from other multi-turn methods.
+
+# 2. Related Work
+
+Single turn feedback-based fashion image retrieval - Previous works in feedback-based fashion image retrieval have primarily focused on the single-turn scenario [14, 40, 31, 7, 54, 4, 3, 59, 6, 36, 22], where a model is provided with a reference image along with an associated feedback text highlighting the desired attribute changes. The typical approach is to encode the multi-modal image and text input using pre-trained visual feature extractors [19, 24, 34] and sequential natural language processors [20, 12], respectively. More recently, pre-trained extractors such as Contrastive Language-Image Pre-training (CLIP) [45] have also been used [4, 3]. This is then followed by a transformer-based decoder network [53] for generating information-rich features for image retrieval from the database. Although these methods perform well in single-turn settings, they cannot be directly used for real-world applications that deal with multiple turns of information exchange.
+
+Multi-turn visuo-linguistic methods - A few methods have been proposed recently for fusing visual and textual input across multiple turns of information exchange. A popular application has been the video dialog task [42, 21, 33, 30, 17], where a trained system is asked to answer questions based on an ongoing video dialog. However, these kinds of dialogs are primarily text-based for both the questioner and the answering agent, without any interaction across image and text inputs. In the fashion domain, there have been some early works for the multi-turn retrieval task. Guo et al. [17] proposed a model that uses convolutional neural networks (CNNs) for encoding images and text, followed by a recurrent neural network for aggregating sequences. Then,
+
+![](images/c762c27b3c1f5f4a7dbe63b4bc7c1448a76711883d925d4bb33cd25b057f45a7.jpg)  
+Single-turn model; fine-tuned on multi-turn data
+
+![](images/b7b27d1364b087b746b6837d63caf9ae1703c7b378da4e6f7aa7e2cdde645c88.jpg)  
+Figure 2: The complete FashionNTM framework. During training, the model receives an input query image,  $I_{n}$ , and associated feedback,  $U_{n}$ . From these, query features  $f_{qry}(n)$  are computed using an off-the-shelf single-turn fashion image retrieval model. These features are then fed into the memory network which learns to retain useful information from the current turn, and combine it with information from previous turns by interacting with an external memory bank, via read/write operations. The memory-modified features  $f_{qry}'(n)$  are compared with the target index features  $f_{tar}(n)$ , and other negative samples  $f_{neg}(n)$ , to compute the training loss. At inference, the model receives a series of multi-modal inputs turn-wise and computes the final modified feature  $f_{qry}'(N)$  using the trained memory network. This is compared with features  $f_{cand}$  derived from different candidate images in the database to retrieve the closest matching images.
+
+![](images/0a93bcd3c48137cf8df02f4721975b3ffd4112d58b27586905fe1bab10ae0a7a.jpg)  
+Multi-turn dataset
+
+![](images/03ed5232c9152ec6d51e339eca8d452d04d34d2a622ff422ec516e29ad11407e.jpg)
+
+![](images/daa67cb922be2029d925d4dfe9531c9a80373c998bf45ca6a8fe118af4323b91.jpg)  
+ Cascaded Memory Neural Turing Machine
+
+![](images/ce2c536c100748bb3484cf9df099bea6109ecb2f6c1d61338fd3af15f74b4023.jpg)  
+Feature vectors
+
+![](images/dd26d56686c72ab14bb528c677466893b7539f0e8b650a492c4ca0d86a1372b9.jpg)  
+Similarity metric
+
+a  $k$ -Nearest Neighbor search is performed across sampled images to get the closest match. The entire model is trained end-to-end using reinforcement learning (RL). Inspired by this, Zhang et al. [63, 62] proposed two approaches for enhancing the text-image feature fusion by adding constraints, and using offline interactive recommendation. Recently, Yuan et al. [60] released the first multi-turn fashion image retrieval dataset, based on the original single turn FashionIQ [56]. They also proposed a state-of-the-art model, which we directly compare with our approach.
+
+Memory networks for vision and language - Memory networks have been widely used for a number of natural language processing and computer vision applications. Some works [55, 51, 13, 11] utilize it for Sentence Video Questions and Answering (QA) task. Another popular application is video object segmentation [8, 58, 50, 37]. Recently, there have been some works on including memory in transformer architectures [26, 47, 57, 38]. However, these approaches design their memory to be used only for specific tasks, and hence cannot be directly compared with ours. In this work, we propose a memory network based method for the multi-turn fashion image retrieval task.
+
+# 3. FashionNTM
+
+The multi-turn feedback-based image retrieval task can be viewed as a series of information exchange transactions. We define a transaction as one session of query context comprising a query image and the associated feedback
+
+text. Notationally, an  $N$ -turn transaction is represented as  $T = [(I_1,U_1),(I_2,U_2),\dots ,(I_N,U_N)]$ , where  $I_{n}$  and  $U_{n}$  correspond to the query image and feedback utterance respectively, at turn  $n\in [1,N]$ . Given such a transaction, the aim of a multi-turn model is to iteratively retrieve the final desired target image  $I_{tar}(N)$  by ranking candidates in the fashion image database based on a matching score.
+
+The overall pipeline of our approach, called Fashion-NTM, is illustrated in Figure 2. We start with a single-turn feature extraction module to encode the multi-modal image and text inputs of each turn  $n$  in a multi-turn transaction. It comprises two parallel blocks - (i) a query feature extractor (QE), for processing  $I_{n}$  and  $U_{n}$  to generate the joint query representation  $f_{qry}(n)$ , and (ii) a target feature extractor (TE), for encoding all the images in the database into their corresponding index features. For the ground-truth target image  $I_{tar}(n)$ , we call these features  $f_{tar}(n)$ , while for every other sample  $I_{neg}(n)$  in the batch, we name it  $f_{neg}(n)$ . The query feature  $f_{qry}(n)$  is fed turn-wise to the Cascaded Memory Neural Turing Machine (CM-NTM) block. CM-NTM first computes several derived features from the original query feature. Subsequently, the original query feature and each of the derived features interact with their own controllers, read/write heads, and sequentially update the memories in a cascaded manner, i.e. output of one memory goes as input to the next. Ultimately, we get the enhanced feature  $f_{qry}'(n)$  as the final output, which is then compared with the target feature  $f_{tar}(n)$  using a similarity score-based batch
+
+![](images/5d5325cefed9cbf5fae460ef795f671d31d32e65cacf004d4db81605f92a3c41.jpg)  
+Figure 3: Cascaded Memory Neural Turing Machine (CM-NTM). It consists of  $C$  controllers; one for the query feature and  $C - 1$  for the derived features. Each controller interacts with its own memory using its own read and write heads. The controllers are linked with each other, forming a cascaded chain. The modified features from the last memory are output as the final embedding.
+
+loss function. This loss treats  $f_{tar}(n)$  as a positive sample and every other feature in the batch,  $f_{neg}(n)$ , as a negative sample. We use cosine-similarity [54, 31, 14] between feature vectors as the matching score. During inference, the model receives a sequence of multi-modal turn-wise inputs and computes the final modified feature  $f_{qry}'(N)$ . This is compared with feature  $f_{cand}$  derived from different candidate images in the database, and the closest match is retrieved as output. In the following sections, we describe the key components of our framework.
+
+Single-turn feature extractor - We utilize the state-of-the-art single-turn image retrieval model, FashionVLP [14], for extracting multi-modal text and image features. FashionVLP extracts image embeddings at multiple levels of granularity and incorporates a vision-language pre-trained transformer for fusing these encodings with text feedback to obtain multi-modal query features. It adopts a convolutional neural network (CNN) architecture with contextual attention for fusing fashion-contextual image features of target images. Specifically, for each turn of a multi-turn transaction, we obtain query features  $f_{qry}$  and target features  $f_{tar}$ . An  $N$ -turn retrieval transaction is of the form  $T_{retr} = [f_{qry}(1), f_{qry}(2), \dots, f_{qry}(N)]$ , with the target feature representation given by  $f_{tar}(N)$ .
+
+# 3.1. Cascaded Memory Neural Turing Machine
+
+To learn relationships across transactions, we propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) module. CM-NTM allows multiple inputs to interact with their own memories using individual read and write heads to learn multiple complex relationships in the input data. We achieve this by deriving several features from the original  $n$ -th turn query feature  $f_{qry}(n)$  using a projection function  $\mathcal{F}$ , which comprises a fully-connected (FC) layer with batch normalization. Specifically, for a  $C$ -stage cascaded CM-NTM, we obtain the derived feature
+
+$f_{drv}^{c} = \mathrm{BatchNorm}(\mathrm{FC}_{\mathrm{c}}(f_{qry}(n)))$  where  $c \in [1, C - 1]$ , and  $\mathrm{FC}_{\mathrm{c}}(\cdot)$  is the FC layer for the  $c$ -th stage. Having obtained  $C$  inputs comprising the original query and  $C - 1$  derived features, we pass them sequentially to our memory network. Figure 3 presents our memory network architecture. It consists of three main components: Controller, Read/Write heads, and Memory blocks.
+
+Controller - The vanilla NTM has a single controller which takes the query feature at turn  $n$ , along with the previous turn's read vector, and emits an intermediate controller output. This is used by the read and write heads to compute the current turn's attention weights, which are then used to update the memory. In our work, we introduce  $C$  different controllers - one for each of our inputs. Each controller,  $c \in [1, C]$  can therefore interactively update its memory via individual read and write heads, allowing it to learn multiple complex relationships in each turn.
+
+Read/Write heads - The controller output is fed to these heads. The write head learns to generate erase and add parameters, which are used to update the current memory. Similarly, the read head generates an attention weight vector, which is used to obtain a weighted sum over the memory locations to get the read vector  $\mathbf{r}_{out}(n)$ . In our work, we have separate read and write heads for each memory.
+
+Memory block - This is represented as a 2-D matrix of the form  $N \times M$ , where  $N$  corresponds to memory locations and  $M$  to the vector size at each location. The output of each memory block is a fused representation of the controller output and the read vector. In our cascaded multi-memory setup, the controllers are linked in a chain, such that the memory-modified features are sequentially propagated. Specifically, for controller  $c \in [1, C]$  at turn  $n$ , the input is given by  $\mathrm{input}^c(n) = [\mathbf{r}_{out}^{c-1}(n); f_{drv}^c; \mathbf{r}_{out}^c(n-1)]$ , where  $\mathbf{r}_{out}^0(n) = \mathbf{r}_{out}^C(n-1)$ ,  $f_{drv}^C = f_{qry}(n)$ , and ; represents concatenation. The final output,  $f_{qry}'(n)$ , is the fused representation of the last controller output  $\mathrm{output}_{ctrl}^C$  and final read vector  $\mathbf{r}_{out}^C$ . We experiment with a different number of memories  $C$  and memory sizes in Section 4.7.
+
+# 3.2. Loss function
+
+We adopt a batch cross-entropy loss [14], where each entry in a batch acts as a negative sample for all other entries. In the multi-turn setting, we compute the loss function turnwise. Given a batch size  $B$ , the loss between predicted feature  $\mathbf{x}_n = [{}^1 f_{qry}'(n), {}^2 f_{qry}'(n), \ldots, {}^B f_{qry}'(n)]$ , and ground-truth  $\mathbf{y}_n = [{}^1 f_{tar}(n), {}^2 f_{tar}(n), \ldots, {}^B f_{tar}(n)]$ , at turn  $n$  is of the form
+
+$$
+\mathcal {L} (\mathbf {x} _ {n}, \mathbf {y} _ {n}) = \frac {1}{B} \sum_ {i = 1} ^ {B} - \log \frac {e ^ {\kappa (^ {i} f _ {q r y} ^ {\prime} (n) , ^ {i} f _ {t a r} (n))}}{\sum_ {j = 1} ^ {B} e ^ {\kappa (^ {i} f _ {q r y} ^ {\prime} (n) , ^ {j} f _ {t a r} (n))}}
+$$
+
+Table 1: Statistics of the datasets used in this work. The top 2 rows are for the recently proposed Multi-turn FashionIQ dataset [60]. The bottom two rows are for the Multi-turn version of the Shoes [5] dataset, which we created as part of our work.  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Split</td><td colspan="3">Number of transactions with</td><td rowspan="2">Total images</td></tr><tr><td>2-turns</td><td>3-turns</td><td>4-turns</td></tr><tr><td rowspan="2">Multi-turn FashionIQ [60]</td><td>Train</td><td>6,897</td><td>1,733</td><td>475</td><td>10,438</td></tr><tr><td>Test</td><td>1,752</td><td>483</td><td>165</td><td>6,274</td></tr><tr><td rowspan="2">Multi-turn Shoes (ours)</td><td>Train</td><td>1,659</td><td>1,036</td><td>982</td><td>11,030</td></tr><tr><td>Test</td><td>296</td><td>96</td><td>28</td><td>4,631</td></tr></table>
+
+where  $\kappa$  is the cosine similarity metric [14]. In this way, each  $f_{tar}(n)$  in the batch,  $\forall j\in [1,B]$  and  $j\neq i$  , serves as a negative sample  $f_{neg}(n)$  for a given  $f_{qry}^{\prime}(n)$  . The turn-wise retrieval loss function is represented as  $\mathcal{L}_{retr}^{n} =$ $\mathcal{L}(\mathbf{x}_n,\mathbf{y}_n)$  , with the overall loss function for our proposed multi-turn model given by  $\mathcal{L} = \frac{1}{N}\sum_{n = 1}^{N}\mathcal{L}_{retr}^{n}$
+
+# 4. Experimental Evaluation
+
+# 4.1. Datasets
+
+Multi-turn FashionIQ [60]: To the best of our knowledge, this is the only existing fashion dataset with multi-turn sessions, where each turn is derived from the original single-turn FashionIQ [56] dataset. It comprises of 11,505 sessions across three clothing types - dress, top-tee, and shirt. The dataset is split into transactions of 2-turns, 3-turns, and 4-turns. In each turn, the data is represented as a pair  $(I_n, U_n)$ , where  $I_n$  and  $U_n$  correspond to the query image and the feedback text for turn  $n$ .
+
+Multi-turn Shoes: The original Shoes dataset [5] contains images of 10 categories of women's shoes obtained from the web along with automatic labeling of attributes. Guo et al. [17] provide additional natural language descriptions of the images to make them suitable for single-turn feedback-based image retrieval. This resulted in about 10k training pairs and 4.6k test queries. In this work, we create a multi-turn extension of this dataset to further research in this domain. Like the approach described in [60], we concatenated several single-turn transactions by matching the target image of one session to the query of another. To maintain
+
+consistency with Multi-turn FashionIQ, we also developed transactions of 2-turns, 3-turns, and 4-turns. Table 1 provides the statistics of both the datasets.
+
+# 4.2. Implementation Details
+
+Single-turn feature extractor pre-training - We use the recently proposed single turn (ST) fashion image retrieval model, FashionVLP [14], to extract the query and target features for both datasets. To ensure a fair comparison with other algorithms, we re-train FashionVLP only on those single-turn queries that are part of the multi-turn dataset. The implementation details and hyperparameters are similar to those mentioned in Goenka et al. [14].
+
+CM-NTM training - We build our CM-NTM model using the open-source implementation [28] of NTM [16]. We implement a separate controller for each memory in our cascaded design using Long Short Term Memory (LSTM) networks [20]. The read and write heads are composed of multi-layer perceptrons (MLPs) and attention networks. We use  $C = 4$  for Shoes, and  $C = 8$  memory stages for FashionIQ, as it is a larger dataset. To ensure equal turn lengths for batch training, we pad the short turn transactions by repeating the last transaction similar to Yuan et al. [60]. We train our models for 100 epochs with a batch size of 80 and a learning rate of 1e-4. We used the PyTorch framework with Adam [29] optimizer for training.
+
+# 4.3. Baselines and Previous State-of-the-art
+
+We compare the performance of our model with six other single-turn and multi-turn approaches.
+
+Single-turn methods - In these methods, we aggregate the multi-turn query data into a single feature without iterating over them turn-wise. The first baseline is  $\mathrm{ST} + \mathrm{avg}(\mathrm{all~turns})$ , where we take the mean of all the  $N$  query features in a transaction to get a single mean query  $\bar{f}_{qry}(N)$ . This is compared with the candidate target features  $f_{tar}(N)$ . Next, we have  $\mathrm{ST} + \mathrm{cat}(\mathrm{all~captions})$ , where all the captions of a multi-turn transaction are concatenated into one long caption, along with initial reference image, to get query features  $\hat{f}_{qry}(N)$ . This is compared with target features  $f_{tar}(N)$  to retrieve the final images.
+
+Table 2: Quantitative results on Multi-turn FashionIQ [60]. We compare with multiple single-turn and multi-turn baselines, and state-of-the-art works [17, 60]. Results show the superior performance of our proposed approach on the popularly used recall rate evaluation metric.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Dress</td><td colspan="2">Toptee</td><td colspan="2">Shirt</td><td colspan="3">Overall</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan="10">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>25.6</td><td>32.5</td><td>32.1</td><td>38.1</td><td>27.0</td><td>32.3</td><td>28.2</td><td>34.3</td><td>31.3</td></tr><tr><td>ST + cat(all captions)</td><td>30.2</td><td>36.3</td><td>36.0</td><td>44.1</td><td>35.3</td><td>42.5</td><td>33.8</td><td>41.0</td><td>37.4</td></tr><tr><td colspan="10">Multi-turn</td></tr><tr><td>Dialog Manager [17]</td><td>12.7</td><td>16.7</td><td>11.6</td><td>15.8</td><td>13.9</td><td>17.7</td><td>13.1</td><td>15.2</td><td>14.2</td></tr><tr><td>CFIR [60]</td><td>29.8</td><td>33.5</td><td>29.4</td><td>33.6</td><td>30.5</td><td>34.1</td><td>30.3</td><td>33.4</td><td>31.9</td></tr><tr><td>ST + EWMA (ours)</td><td>42.0</td><td>48.4</td><td>43.8</td><td>50.9</td><td>36.9</td><td>44.2</td><td>40.9</td><td>47.8</td><td>44.4</td></tr><tr><td>ST + LSTM (ours)</td><td>47.8</td><td>52.5</td><td>44.4</td><td>50.5</td><td>41.6</td><td>47.6</td><td>44.6</td><td>50.2</td><td>47.4</td></tr><tr><td>FashionNTM (ours)</td><td>48.3</td><td>52.8</td><td>45.1</td><td>49.8</td><td>43.8</td><td>48.8</td><td>45.7</td><td>50.4</td><td>48.1</td></tr></table>
+
+Multi-turn methods - In these methods, the multi-turn data is fed turn-wise to the model. The first method is Dialog Manager [17], which employs reinforcement learning (RL) framework to learn relationships between turns. Next, we have the previous state-of-the-art Conversational Fashion Image Retrieval CFIR method [60], which encodes only the text using a transformer network [53], and uses a simple Gated Recurrent Unit (GRU) layer for multi-turn image retrieval. The third baseline is  $\mathrm{ST} + \mathrm{EWMA}$ , where we use exponential weighted moving average [1] to heuristically aggregate past turns, with more weights given to recent history. Finally, we have the  $\mathrm{ST} + \mathrm{LSTM}$  model that uses a single-layer LSTM [20] with a hidden size of 100 for aggregating past information.
+
+# 4.4. Results
+
+Evaluation Metrics - Following [14, 60, 17], we evaluate models using the standard top-K recall (i.e. R@K) for image retrieval. Overall performance are compared specifically on the average of R@5 and R@8.
+
+Quantitative results on multi-turn datasets - In Table 2, we compare the results of different methods on the multi-turn FashionIQ dataset. We observe that the multi-turn baselines generally perform better than single-turn methods. This is expected as aggregating data by naively averaging/concatenating loses feedback content and turn-order information and hence is likely to miss out on important cues. Our memory-based approach outperforms all the other multi-turn baselines by a large margin. This shows that the memory network can store and retrieve useful information to and from the memory between intermediate turns, which allows it to keep track of past information better than other networks that do not use explicit memory. The  $50.5\%$  performance gain over the previous state-of-the-art highlights our model's capability to learn meaningful representations over multiple turns of conversational feedback.
+
+In Table 3, we provide a similar comparison for the Multi-turn Shoes dataset. Consistent with results for Multi-turn FashionIQ, the multi-turn baselines perform better than
+
+Table 3: Comparison with existing single-turn and multi-turn models on the multi-turn version of the Shoes [5] dataset. We compare with multiple single-turn, and multi-turn baselines. Comparative analysis shows the superior performance of our proposed approach using the popular recall rate evaluation metric.
+
+<table><tr><td>Model</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan="4">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>12.4</td><td>17.6</td><td>15.0</td></tr><tr><td>ST + cat(all captions)</td><td>10.7</td><td>13.6</td><td>12.2</td></tr><tr><td colspan="4">Multi-turn</td></tr><tr><td>ST + EWMA (ours)</td><td>18.3</td><td>23.8</td><td>21.1</td></tr><tr><td>ST + LSTM (ours)</td><td>23.3</td><td>32.1</td><td>27.7</td></tr><tr><td>FashionNTM (ours)</td><td>26.7</td><td>35.7</td><td>31.2</td></tr></table>
+
+all the single-turn ones, and our memory network-based approach performs the best with a relative improvement of  $12.6\%$ . The difference in performance across different models is more pronounced in these results than in Table 2. This is possibly because the annotations are cleaner and more consistent in this dataset as compared to Multi-turn FashionIQ [60]. For instance, multiple images in the FashionIQ dataset can match a particular query, but only one of them is labeled as the ground-truth.
+
+An important property of a good multi-turn system is that performance should be robust to the length of the historical information (number of past turns). For example, even for a large number of previous turns considered, the model should efficiently retain desirable details, while filtering out unnecessary information. In Table 4, we analyze this property for models with and without memory. A single-turn model that assumes ground-truth information for all past turns, and evaluated only on the final-turn, is taken as reference. This is expected to be the upper-bound on the performance in a single-turn setting, as perfect information about the history is guaranteed. We vary the number of past turns included in the input transaction history (versus treated as ground-truth) for the multi-turn models (with or without memory) in order to evaluate their effectiveness at capturing and utilizing past information. As seen from the table, for a model without memory, the performance depreciates significantly with each additional turn from the
+
+Table 4: Importance of aggregating historical data using memory-based vs non-memory approach. In the first row, we show the result of a model using only the final turn information of a multi-turn transaction. This assumes the groundtruth retrieval for all previous turns, and therefore provides the upper-bound on single-turn performance for final retrieval. Subsequently, we include additional information from the history, and compare performance across models with and without memory. As seen from the non-memory case, the performance depreciates a lot ( $\approx$  64.9% difference compared to the final turn's performance), as we try to aggregate longer historical information. In contrast, for the memory network model, it can be seen that the performance is fairly consistent ( $\approx$  0.5% difference) across the turn length.
+
+<table><tr><td rowspan="2">Memory usage</td><td rowspan="2">Turn configuration</td><td colspan="2">Dress</td><td colspan="2">Toptee</td><td colspan="2">Shirt</td><td colspan="3">Overall</td><td rowspan="2">Difference from final turn</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td>-</td><td>only final turn</td><td>77.9</td><td>77.9</td><td>84.0</td><td>84.0</td><td>74.1</td><td>77.8</td><td>78.7</td><td>79.9</td><td>79.3</td><td>-</td></tr><tr><td colspan="12">Experiments with data aggregated across multiple-turns</td></tr><tr><td rowspan="3">Only single turn (w/o memory)</td><td>last two turns</td><td>51.3</td><td>58.4</td><td>56.0</td><td>76.0</td><td>44.4</td><td>48.1</td><td>50.6</td><td>60.9</td><td>55.8</td><td>-29.6%</td></tr><tr><td>last three turns</td><td>33.6</td><td>43.4</td><td>32.0</td><td>44.0</td><td>29.6</td><td>40.7</td><td>31.8</td><td>42.7</td><td>37.3</td><td>-53.0%</td></tr><tr><td>all turns</td><td>18.6</td><td>28.3</td><td>32.0</td><td>32.0</td><td>25.9</td><td>29.6</td><td>25.5</td><td>30.0</td><td>27.8</td><td>-64.9%</td></tr><tr><td rowspan="3">FashionNTM (with memory)</td><td>last two turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr><tr><td>last three turns</td><td>77.0</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.6</td><td>79.9</td><td>79.8</td><td>+0.6%</td></tr><tr><td>all turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr></table>
+
+![](images/4f2d844c6cd723d0ff98953db67cb4307fcd4ceaf7fa767f0e827d0e310f3ba6.jpg)  
+(a) Multi-turn FashionIQ. From left to right, the images belong to the Dress, Shirt, and Toptee categories respectively.
+
+![](images/2f7685d81cb666dc03f51972cdba64f2870b305f1d65baa6d982d579c99787d1.jpg)  
+(b) Multi-turn Shoes. From left to right, we have three different samples of shoes from the dataset.  
+Figure 4: Top-5 final image retrievals on the evaluated multi-turn datasets. The top row illustrates 3 sets of multi-turn query session. We consider three different multi-turn models - EWMA, LSTM, and our proposed FashionNTM. As seen from the retrievals, our proposed model correctly predicts the target image in all 3 cases for the FashionIQ dataset, and in 2 out of 3 cases for the Shoes dataset.
+
+past treated as input rather than ground-truth. As we go further back in history, the performance consistently reduces. However, for our multi-turn model with memory, the performance does not change appreciably as the number of turns change. This shows that our proposed approach can successfully retain/filter out past data based on their relevance, across various lengths of history.
+
+An interesting observation is that having only the final turn with memory does not yield a good result. This is possibly due to the initialization method of the memory network, which is random. Hence, in absence of a history (only single turn case), the only past features to be aggregated are the random initialization features.
+
+Qualitative results - In addition to the quantitative experiments described above, we also present some qualitative final image retrieval results of our evaluated models on both the multi-turn datasets. The first set of results are shown in Figures 4a and 4b for the Multi-turn FashionIQ [60] and the
+
+Multi-turn Shoes datasets, respectively<sup>2</sup>. We compare the top-5 predicted results from our proposed model with two other multi-turn baselines, ST + EWMA and ST + LSTM. As seen in the figures, our approach can correctly predict the desired target image for both datasets with higher ranks as compared to other baselines. More specifically, we see that in Figure 4a, even though all the three multi-turn models can infer the general sense of desired attributes, such as "is longer" in the left block and "has short sleeves" in the right, only our model can capture complex and detailed properties, e.g., "gray and not red" in the left block, and "red color with center logo" in the middle block. Furthermore, our model can retrieve multiple desirable products, as seen by the first four images in the middle block, and four out of five images in the right block. Similar results are observed for Shoes in Figure 4b, where our model correctly predicts
+
+![](images/f7eb55bc6d7b6c2e082298f5770b585b7874676b8514e0f827e55a0542b77e65.jpg)  
+Figure 5: Memory retention capability of our proposed approach. Given an initial query image, we take two interactive user feedbacks in turns. On the left side, we have the single-turn model which only learns to retrieve an image using a single dialog exchange. As a result, none of the retrieved images in turn 2 are "green in color", which was desired in turn 1. In contrast, our proposed approach on the right can learn to retain data from both the turns, and therefore retrieves desirable product in 2 out of 3 cases.
+
+the desired target as rank-1 in two out of three examples, whereas the other models fail to retrieve meaningful results.
+
+# 4.5. Model Analysis in Interactive Settings
+
+In addition to the results above for the static dataset, we also performed some interactive experiments to evaluate whether our model can adapt to real-world dynamic use cases beyond the trained datasets.
+
+Memory retention - In this experiment, we demonstrate the memory retention capability of our proposed model by comparing it with a single-turn network, which does not retain historical information. We start with an initial query image retrieved via a single-turn model. Subsequently, we take user input for the next two turns to retrieve newer sets of images. As seen in Figure 5, for the single-turn model (left side), none of the retrieved images in turn 2 are green in color. This is because the "green in color" attribute was a desired property in turn 1, which the model without memory could not recover. In contrast, for our memory network approach (right side) both the top-2 retrieved images for turn 2 are "green in color" in addition to having "a solid color and small image". Thus, our model can learn to retain information from previous turns.
+
+Agnosticity to turn order - Ideally, a deployed multi-turn image retrieval system should be independent of the order of feedbacks provided, as long as they are non-contradictory. This is demonstrated in the experiment conducted in Figure 6. In the first case, we take two text inputs as feedbacks from a user and present them to the model. In the second case, we reverse the order of the feedbacks. As shown in the figure, for the flipped case, our proposed FashionNTM model retrieves similar looking final products, even though the intermediate retrievals are very different.
+
+It is to be noted that for both the experiments depicted in Figures 5 and 6, the feedback is taken from a dynamic user, thereby establishing the interactive capability of our
+
+![](images/9d9d51acf4766157a663d3f12189104f011612f36551dadc14201d924d0e795e.jpg)  
+Figure 6: Turn order independence feature of a memory network. In this experiment, we start with an initial query image, and take two non-contradictory user feedbacks. In one case (left), we let the model retrieve images based on the original order of the feedbacks, whilst in the other (right), we flip the order of the feedbacks. Our proposed approach adapts to presented input, and retrieves similar looking final results for both the cases, even though the intermediate outputs are quite different.
+
+proposed model beyond the training dataset.
+
+# 4.6. User Study
+
+Fashion image retrieval is inherently a subjective task, where the task success heavily relies on the satisfaction of a customer. Thus, we conducted a small human-preference survey among 5 participants (not associated with the paper in any way). To each user, we showed the final top-1 retrieved image by the 3-best multi-turn models on the FashionIQ [60] dataset from Table 2 - EWMA, LSTM, and our proposed FashionNTM. To ensure consistency, we generated 45 queries for this study, whose results are shown in Figure 7. The  $y$ -axis shows the number of preferred retrieval results for each user. Results show that each of the 5 users preferred images retrieved by the proposed FashionNTM model, on an average  $83.1\%$  more as compared to other multi-turn methods. In the supplementary material, we include some examples of the user interface shown to
+
+![](images/e66da7637eaa55744a96b737a57f5cae4c4cbed8b312a63d04a3288beda6ebd8.jpg)  
+Figure 7: Human preference study of top multi-turn systems.
+
+Table 5: Different number of memories for the proposed approach by fixing the memory size to  $4 \times 768$ . We select the mean value for comparison and pick the best one.  
+
+<table><tr><td>Model</td><td>Number of memories (C)</td><td>R@5</td><td>R@8</td><td>Mean</td><td>% increase</td></tr><tr><td>ST+v-NTM</td><td>1</td><td>24.5</td><td>30.5</td><td>27.5</td><td>-</td></tr><tr><td rowspan="4">FashionNTM</td><td>2</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr><tr><td>4</td><td>27.6</td><td>35.5</td><td>31.5</td><td>14.5</td></tr><tr><td>8</td><td>26.9</td><td>35.2</td><td>31.1</td><td>13.1</td></tr><tr><td>16</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr></table>
+
+the participants during this study.
+
+# 4.7. Ablation Studies
+
+We perform multiple ablation studies to gain insights on how changing different configurations of the memory network affect the overall performance. We perform these ablations on the multi-turn Shoes dataset as it contains more realistic and consistent feedback texts.<sup>3</sup>
+
+Number of memories in CM-NTM - This experiment involves varying the number of memories  $C$  in our cascaded memory architecture. In Table 5, we observe that the cascaded memory CM-NTM models perform significantly better than vanilla NTM, which has only one memory. We hypothesize that having inputs from multiple turns interacting with the same memory could eventually lead to saturation as we get additional data which could be alleviated if there are multiple memories in the network to recover the past which might help in capturing multiple complex relationships in multi-turn interactions better. Additionally, multiple memory networks can help in learning diverse representations of the input using derived features, which is not possible with a single memory network. As seen in Table 5 for Shoes dataset, the performance increases with the number of memories, peaking at  $C = 4$ , and then gradually decreases as the model starts to overfit.
+
+Inference time with multiple memories - In this experiment, we study the performance of FashionNTM in terms of the mean of R@5 and R@8 recall rates along with the time taken to process one multi-turn transaction. For each  $C$ , we evaluate the performance across four different memory sizes. As seen from Figure 8, the inference time increases with additional memories. Configurations in the green and blue clusters are desirable, as they provide a good trade-off between recall performance and computation time, while the pink and red clusters are undesirable due to poor performance and longer inference time, respectively.
+
+# 5. Conclusion and Future Work
+
+In this paper, we presented a novel cascaded Neural Turing Machine-based approach, called FashionNTM, for multi-turn feedback-based fashion image retrieval. Multiple
+
+![](images/f18ce485451afd9b388c4009f09403a9674bffd8188731395ffe15d2ab912694.jpg)  
+Figure 8: Scatter plot showing recall versus inference time for multiple memories in our CM-NTM for the Multi-turn Shoes dataset. The configurations belonging to the green cluster give the best recall overall, while having a high inference time. The configurations in the blue cluster provide a suitable alternative with quicker inference at the cost of lower recall. The magenta and red clusters are undesirable configurations due to poor performance and long inference time, respectively.
+
+memories in our model allow it to effectively retain and recall a number of complex relationships across transactions in the multi-turn setting, and multiple controllers help in assigning relative importance to each feature stored in the memory. This aids in attending to different parts of the input at different levels, thus leading to better performance across datasets. We also performed extensive experiments to compare our performance with baselines and previous state-of-the-art and observed that our multi-memory model significantly outperforms previous works [60], with up to  $50.5\%$  relative improvement on Multi-turn FashionIQ, and by  $12.6\%$  on the multi-turn Shoes dataset, which we created in this work. We further demonstrated that our model can generalize beyond the trained setting to dynamically interact with real-world users to retrieve meaningful final product images. Finally, a user preference study reveals that our model is preferred by human participants on an average  $83.1\%$  more as compared to other multi-turn methods.
+
+Despite promising results, there are a few limitations that make multi-turn image retrieval a hard problem to solve. Firstly, there is dearth of high quality and diverse multi-turn image retrieval datasets in the fashion domain which hinders comprehensive studies in this field. Additionally, deploying current approaches to real-world scenarios (e.g., virtual private assistants) becomes a challenge due to computational requirements. Lastly, selecting the right configuration for different components such as memory size, number of memories, etc. in a memory-based network is not a trivial task and depends a lot on the use case. Nevertheless, for future work, our approach could be further extended to non-fashion domains where multi-turn feedback-based information retrieval solutions are required.
+
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+[63] Ruiyi Zhang, Tong Yu, Yilin Shen, Hongxia Jin, and Changyou Chen. Text-based interactive recommendation via constraint-augmented reinforcement learning. Advances in neural information processing systems, 32, 2019. 1, 3
\ No newline at end of file
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+                                    "content": "Multi-turn textual feedback-based fashion image retrieval focuses on a real-world setting, where users can iteratively provide information to refine retrieval results until they find an item that fits all their requirements. In this work, we present a novel memory-based method, called FashionNTM, for such a multi-turn system. Our framework incorporates a new Cascaded Memory Neural Turing Machine (CM-NTM) approach for implicit state management, thereby learning to integrate information across all past turns to retrieve new images, for a given turn. Unlike vanilla Neural Turing Machine (NTM), our CM-NTM operates on multiple inputs, which interact with their respective memories via individual read and write heads, to learn complex relationships. Extensive evaluation results show that our proposed method outperforms the previous state-of-the-art algorithm by "
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+                                    "content": ", on Multi-turn FashionIQ [60] – the only existing multi-turn fashion dataset currently, in addition to having a relative improvement of "
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+                                    "content": " on Multi-turn Shoes – an extension of the single-turn Shoes dataset [5] that we created in this work. Further analysis of the model in a real-world interactive setting demonstrates two important capabilities of our model – memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, user study results show that images retrieved by FashionNTM were favored by "
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+                                            "type": "text",
+                                            "content": "Figure 1: Illustration of multi-turn fashion image retrieval. Initially (Turn 1), the system receives an initial query image, and a textual feedback mentioning the user's desired changes. The model then retrieves a ranked list of closest matching images. Subsequently, the user keeps refining their choice by providing more feedback, while the model retrieves newer images by considering both current and past feedback. This continues until the multi-turn system has successfully obtained the final retrieved image (Turn N) with all the desired properties mentioned across every past turn."
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+                                    "type": "text",
+                                    "content": "[35, 39, 48], to attributes [18], sketches [44], and natural language [32, 61]. However, most of these methods do not incorporate interactive user feedback, which is necessary for a personalized task such as fashion retrieval."
+                                }
+                            ]
+                        }
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+                {
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+                                    "content": "Textual feedback-based fashion image retrieval allows users to refine online shopping search results by providing information about how the results differ from their desired product (e.g., \"a dress like this but darker in color\"). Several approaches for implementing such a system have been proposed recently [14, 7, 31, 56, 17, 60, 63], which involve learning a joint representation via multi-modal information fusion across the query (reference) image and the associated feedback, and using it to retrieve the closest matching image in the database (product catalog) as the target."
+                                }
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+                                    "type": "text",
+                                    "content": "Popular methods for fashion retrieval task [14, 31, 7,"
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+                            ]
+                        }
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+                    "index": 14
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+                                    "type": "text",
+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "*Work primarily done during internship at Amazon. Additional details are available at https://sites.google.com/eng.ucsd.edu/fashionntm."
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+                                    "content": "4, 23] involve single-turn exchange of information, where users provide feedback exactly once to update the search results. However, this is not characteristic of the real-world setting as online shopping customers typically start with a general idea of what they want and iteratively update the requirements until they find something that matches their desired features. This usually involves providing additional attributes, or modifying previously specified features in each turn to refine the search results. The ideal feedback-based fashion image retrieval system is, hence, inherently multi-turn, as illustrated in Figure 1."
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+                                    "content": "Sequential modeling is a relatively mature field of research. However, a majority of the existing approaches [46, 27, 49, 20, 9] do not maintain an explicit memory, and therefore cannot learn long and complex information. Vanilla memory network-based methods, which explicitly maintain an external memory, could be used for retaining past information, but they do not provide a robust mechanism to iteratively update their memory [55, 51]. In contrast, Neural Turing Machines (NTMs) [16] provide a fully differentiable model with sophisticated read and write operations to extract and update historical information in its explicit memory via an attention mechanism. Therefore, in this work, we build on NTMs to develop a novel framework for the multi-turn retrieval task. We further propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) that allows us to encode multiple relationships from the features of a particular turn and store them over time across multiple memories in a multi-turn setting. This is similar to how multi-head attention (MHA) operates for transformers [53]. To ensure that the individual memories effectively utilize each other's information, we link them together in a cascaded fashion. Evaluation results demonstrate that our proposed approach improves the retrieval performance as com"
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+                                    "content": " on the multi-turn version of Shoes dataset [5] respectively. Additionally, by performing an interactive analysis, we demonstrated two important capabilities of our multi-turn system - memory retention across turns, and agnosticity to turn order for non-contradictory feedback. Finally, a user study result shows that on an average, the images retrieved by our model are preferred "
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+                                    "content": "-Nearest Neighbor search is performed across sampled images to get the closest match. The entire model is trained end-to-end using reinforcement learning (RL). Inspired by this, Zhang et al. [63, 62] proposed two approaches for enhancing the text-image feature fusion by adding constraints, and using offline interactive recommendation. Recently, Yuan et al. [60] released the first multi-turn fashion image retrieval dataset, based on the original single turn FashionIQ [56]. They also proposed a state-of-the-art model, which we directly compare with our approach."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Memory networks for vision and language - Memory networks have been widely used for a number of natural language processing and computer vision applications. Some works [55, 51, 13, 11] utilize it for Sentence Video Questions and Answering (QA) task. Another popular application is video object segmentation [8, 58, 50, 37]. Recently, there have been some works on including memory in transformer architectures [26, 47, 57, 38]. However, these approaches design their memory to be used only for specific tasks, and hence cannot be directly compared with ours. In this work, we propose a memory network based method for the multi-turn fashion image retrieval task."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "3. FashionNTM"
+                                }
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+                                    "content": "The multi-turn feedback-based image retrieval task can be viewed as a series of information exchange transactions. We define a transaction as one session of query context comprising a query image and the associated feedback"
+                                }
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+                        }
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+                                    "type": "text",
+                                    "content": "text. Notationally, an "
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+                                    "type": "inline_equation",
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+                                    "content": "-turn transaction is represented as "
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+                                    "type": "inline_equation",
+                                    "content": "T = [(I_1,U_1),(I_2,U_2),\\dots ,(I_N,U_N)]"
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " correspond to the query image and feedback utterance respectively, at turn "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "n\\in [1,N]"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Given such a transaction, the aim of a multi-turn model is to iteratively retrieve the final desired target image "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "I_{tar}(N)"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " by ranking candidates in the fashion image database based on a matching score."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "The overall pipeline of our approach, called Fashion-NTM, is illustrated in Figure 2. We start with a single-turn feature extraction module to encode the multi-modal image and text inputs of each turn "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " in a multi-turn transaction. It comprises two parallel blocks - (i) a query feature extractor (QE), for processing "
+                                },
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to generate the joint query representation "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{qry}(n)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and (ii) a target feature extractor (TE), for encoding all the images in the database into their corresponding index features. For the ground-truth target image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "I_{tar}(n)"
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+                                {
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+                                    "type": "text",
+                                    "content": ", we call these features "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "f_{tar}(n)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", while for every other sample "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "I_{neg}(n)"
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+                                {
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+                                    "type": "text",
+                                    "content": " in the batch, we name it "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f_{neg}(n)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The query feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is fed turn-wise to the Cascaded Memory Neural Turing Machine (CM-NTM) block. CM-NTM first computes several derived features from the original query feature. Subsequently, the original query feature and each of the derived features interact with their own controllers, read/write heads, and sequentially update the memories in a cascaded manner, i.e. output of one memory goes as input to the next. Ultimately, we get the enhanced feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{qry}'(n)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as the final output, which is then compared with the target feature "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " using a similarity score-based batch"
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+                                            "type": "text",
+                                            "content": "Figure 3: Cascaded Memory Neural Turing Machine (CM-NTM). It consists of "
+                                        },
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+                                            "type": "text",
+                                            "content": " controllers; one for the query feature and "
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+                                            "type": "text",
+                                            "content": " for the derived features. Each controller interacts with its own memory using its own read and write heads. The controllers are linked with each other, forming a cascaded chain. The modified features from the last memory are output as the final embedding."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "loss function. This loss treats "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{tar}(n)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as a positive sample and every other feature in the batch, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{neg}(n)"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", as a negative sample. We use cosine-similarity [54, 31, 14] between feature vectors as the matching score. During inference, the model receives a sequence of multi-modal turn-wise inputs and computes the final modified feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{qry}'(N)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This is compared with feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        277,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{cand}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " derived from different candidate images in the database, and the closest match is retrieved as output. In the following sections, we describe the key components of our framework."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Single-turn feature extractor - We utilize the state-of-the-art single-turn image retrieval model, FashionVLP [14], for extracting multi-modal text and image features. FashionVLP extracts image embeddings at multiple levels of granularity and incorporates a vision-language pre-trained transformer for fusing these encodings with text feedback to obtain multi-modal query features. It adopts a convolutional neural network (CNN) architecture with contextual attention for fusing fashion-contextual image features of target images. Specifically, for each turn of a multi-turn transaction, we obtain query features "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f_{qry}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and target features "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f_{tar}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". An "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-turn retrieval transaction is of the form "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{retr} = [f_{qry}(1), f_{qry}(2), \\dots, f_{qry}(N)]"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", with the target feature representation given by "
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+                                    "type": "inline_equation",
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                                        588
+                                    ],
+                                    "type": "text",
+                                    "content": "3.1. Cascaded Memory Neural Turing Machine"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "To learn relationships across transactions, we propose a novel Cascaded Memory Neural Turing Machine (CM-NTM) module. CM-NTM allows multiple inputs to interact with their own memories using individual read and write heads to learn multiple complex relationships in the input data. We achieve this by deriving several features from the original "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    "type": "inline_equation",
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+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    "type": "text",
+                                    "content": "-th turn query feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{qry}(n)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    ],
+                                    "type": "text",
+                                    "content": " using a projection function "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which comprises a fully-connected (FC) layer with batch normalization. Specifically, for a "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": "-stage cascaded CM-NTM, we obtain the derived feature"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{drv}^{c} = \\mathrm{BatchNorm}(\\mathrm{FC}_{\\mathrm{c}}(f_{qry}(n)))"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " where "
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+                                    "type": "inline_equation",
+                                    "content": "c \\in [1, C - 1]"
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{FC}_{\\mathrm{c}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": " is the FC layer for the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th stage. Having obtained "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        156
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": " inputs comprising the original query and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        156
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C - 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": " derived features, we pass them sequentially to our memory network. Figure 3 presents our memory network architecture. It consists of three main components: Controller, Read/Write heads, and Memory blocks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Controller - The vanilla NTM has a single controller which takes the query feature at turn "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        156,
+                                        546,
+                                        275
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", along with the previous turn's read vector, and emits an intermediate controller output. This is used by the read and write heads to compute the current turn's attention weights, which are then used to update the memory. In our work, we introduce "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        156,
+                                        546,
+                                        275
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        156,
+                                        546,
+                                        275
+                                    ],
+                                    "type": "text",
+                                    "content": " different controllers - one for each of our inputs. Each controller, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        156,
+                                        546,
+                                        275
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c \\in [1, C]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        156,
+                                        546,
+                                        275
+                                    ],
+                                    "type": "text",
+                                    "content": " can therefore interactively update its memory via individual read and write heads, allowing it to learn multiple complex relationships in each turn."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                        546,
+                        359
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Read/Write heads - The controller output is fed to these heads. The write head learns to generate erase and add parameters, which are used to update the current memory. Similarly, the read head generates an attention weight vector, which is used to obtain a weighted sum over the memory locations to get the read vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        275,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}_{out}(n)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        275,
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+                                        359
+                                    ],
+                                    "type": "text",
+                                    "content": ". In our work, we have separate read and write heads for each memory."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Memory block - This is represented as a 2-D matrix of the form "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N \\times M"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " corresponds to memory locations and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " to the vector size at each location. The output of each memory block is a fused representation of the controller output and the read vector. In our cascaded multi-memory setup, the controllers are linked in a chain, such that the memory-modified features are sequentially propagated. Specifically, for controller "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c \\in [1, C]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
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+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " at turn "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
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+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", the input is given by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{input}^c(n) = [\\mathbf{r}_{out}^{c-1}(n); f_{drv}^c; \\mathbf{r}_{out}^c(n-1)]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}_{out}^0(n) = \\mathbf{r}_{out}^C(n-1)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{drv}^C = f_{qry}(n)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", and ; represents concatenation. The final output, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{qry}'(n)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", is the fused representation of the last controller output "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{output}_{ctrl}^C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " and final read vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}_{out}^C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ". We experiment with a different number of memories "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        359,
+                                        547,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " and memory sizes in Section 4.7."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Loss function"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We adopt a batch cross-entropy loss [14], where each entry in a batch acts as a negative sample for all other entries. In the multi-turn setting, we compute the loss function turnwise. Given a batch size "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        553,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the loss between predicted feature "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        553,
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+                                        638
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_n = [{}^1 f_{qry}'(n), {}^2 f_{qry}'(n), \\ldots, {}^B f_{qry}'(n)]"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and ground-truth "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y}_n = [{}^1 f_{tar}(n), {}^2 f_{tar}(n), \\ldots, {}^B f_{tar}(n)]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", at turn "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is of the form"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} (\\mathbf {x} _ {n}, \\mathbf {y} _ {n}) = \\frac {1}{B} \\sum_ {i = 1} ^ {B} - \\log \\frac {e ^ {\\kappa (^ {i} f _ {q r y} ^ {\\prime} (n) , ^ {i} f _ {t a r} (n))}}{\\sum_ {j = 1} ^ {B} e ^ {\\kappa (^ {i} f _ {q r y} ^ {\\prime} (n) , ^ {j} f _ {t a r} (n))}}",
+                                    "image_path": "af7661b4aa146e8af4b8224bef94edf9de90fc13bdd62a0976906181f475fe15.jpg"
+                                }
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+                }
+            ],
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+                    "type": "page_footnote",
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+                                    "type": "text",
+                                    "content": "<sup>1</sup>We mainly discuss our novel changes to the NTM design. For details regarding the vanilla architecture, please refer to the original paper [16]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
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+                                            "content": "Table 1: Statistics of the datasets used in this work. The top 2 rows are for the recently proposed Multi-turn FashionIQ dataset [60]. The bottom two rows are for the Multi-turn version of the Shoes [5] dataset, which we created as part of our work."
+                                        }
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+                                            "html": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Split</td><td colspan=\"3\">Number of transactions with</td><td rowspan=\"2\">Total images</td></tr><tr><td>2-turns</td><td>3-turns</td><td>4-turns</td></tr><tr><td rowspan=\"2\">Multi-turn FashionIQ [60]</td><td>Train</td><td>6,897</td><td>1,733</td><td>475</td><td>10,438</td></tr><tr><td>Test</td><td>1,752</td><td>483</td><td>165</td><td>6,274</td></tr><tr><td rowspan=\"2\">Multi-turn Shoes (ours)</td><td>Train</td><td>1,659</td><td>1,036</td><td>982</td><td>11,030</td></tr><tr><td>Test</td><td>296</td><td>96</td><td>28</td><td>4,631</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the cosine similarity metric [14]. In this way, each "
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+                                    "type": "text",
+                                    "content": " in the batch, "
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+                                    "content": "\\forall j\\in [1,B]"
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+                                    "type": "text",
+                                    "content": " , serves as a negative sample "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for a given "
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+                                    "type": "inline_equation",
+                                    "content": "f_{qry}^{\\prime}(n)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " . The turn-wise retrieval loss function is represented as "
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+                                    "content": "\\mathcal{L}_{retr}^{n} ="
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+                                    "content": "\\mathcal{L}(\\mathbf{x}_n,\\mathbf{y}_n)"
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+                                    "type": "text",
+                                    "content": " , with the overall loss function for our proposed multi-turn model given by "
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+                                    "content": "\\mathcal{L} = \\frac{1}{N}\\sum_{n = 1}^{N}\\mathcal{L}_{retr}^{n}"
+                                }
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+                    ],
+                    "index": 2
+                },
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+                                    "type": "text",
+                                    "content": "4. Experimental Evaluation"
+                                }
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+                                    "type": "text",
+                                    "content": "4.1. Datasets"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "Multi-turn FashionIQ [60]: To the best of our knowledge, this is the only existing fashion dataset with multi-turn sessions, where each turn is derived from the original single-turn FashionIQ [56] dataset. It comprises of 11,505 sessions across three clothing types - dress, top-tee, and shirt. The dataset is split into transactions of 2-turns, 3-turns, and 4-turns. In each turn, the data is represented as a pair "
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+                                    "type": "inline_equation",
+                                    "content": "(I_n, U_n)"
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "U_n"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " correspond to the query image and the feedback text for turn "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "n"
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Multi-turn Shoes: The original Shoes dataset [5] contains images of 10 categories of women's shoes obtained from the web along with automatic labeling of attributes. Guo et al. [17] provide additional natural language descriptions of the images to make them suitable for single-turn feedback-based image retrieval. This resulted in about 10k training pairs and 4.6k test queries. In this work, we create a multi-turn extension of this dataset to further research in this domain. Like the approach described in [60], we concatenated several single-turn transactions by matching the target image of one session to the query of another. To maintain"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "consistency with Multi-turn FashionIQ, we also developed transactions of 2-turns, 3-turns, and 4-turns. Table 1 provides the statistics of both the datasets."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
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+                                    "type": "text",
+                                    "content": "4.2. Implementation Details"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "Single-turn feature extractor pre-training - We use the recently proposed single turn (ST) fashion image retrieval model, FashionVLP [14], to extract the query and target features for both datasets. To ensure a fair comparison with other algorithms, we re-train FashionVLP only on those single-turn queries that are part of the multi-turn dataset. The implementation details and hyperparameters are similar to those mentioned in Goenka et al. [14]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
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+                                    "type": "text",
+                                    "content": "CM-NTM training - We build our CM-NTM model using the open-source implementation [28] of NTM [16]. We implement a separate controller for each memory in our cascaded design using Long Short Term Memory (LSTM) networks [20]. The read and write heads are composed of multi-layer perceptrons (MLPs) and attention networks. We use "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "C = 4"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " for Shoes, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "C = 8"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " memory stages for FashionIQ, as it is a larger dataset. To ensure equal turn lengths for batch training, we pad the short turn transactions by repeating the last transaction similar to Yuan et al. [60]. We train our models for 100 epochs with a batch size of 80 and a learning rate of 1e-4. We used the PyTorch framework with Adam [29] optimizer for training."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.3. Baselines and Previous State-of-the-art"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We compare the performance of our model with six other single-turn and multi-turn approaches."
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+                        }
+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "Single-turn methods - In these methods, we aggregate the multi-turn query data into a single feature without iterating over them turn-wise. The first baseline is "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{ST} + \\mathrm{avg}(\\mathrm{all~turns})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where we take the mean of all the "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "N"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " query features in a transaction to get a single mean query "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{f}_{qry}(N)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This is compared with the candidate target features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{tar}(N)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Next, we have "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{ST} + \\mathrm{cat}(\\mathrm{all~captions})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where all the captions of a multi-turn transaction are concatenated into one long caption, along with initial reference image, to get query features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        441,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{f}_{qry}(N)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This is compared with target features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{tar}(N)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to retrieve the final images."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
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+                    "type": "table",
+                    "bbox": [
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+                                            "type": "text",
+                                            "content": "Table 2: Quantitative results on Multi-turn FashionIQ [60]. We compare with multiple single-turn and multi-turn baselines, and state-of-the-art works [17, 60]. Results show the superior performance of our proposed approach on the popularly used recall rate evaluation metric."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14,
+                            "angle": 0,
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+                                            "html": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Dress</td><td colspan=\"2\">Toptee</td><td colspan=\"2\">Shirt</td><td colspan=\"3\">Overall</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan=\"10\">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>25.6</td><td>32.5</td><td>32.1</td><td>38.1</td><td>27.0</td><td>32.3</td><td>28.2</td><td>34.3</td><td>31.3</td></tr><tr><td>ST + cat(all captions)</td><td>30.2</td><td>36.3</td><td>36.0</td><td>44.1</td><td>35.3</td><td>42.5</td><td>33.8</td><td>41.0</td><td>37.4</td></tr><tr><td colspan=\"10\">Multi-turn</td></tr><tr><td>Dialog Manager [17]</td><td>12.7</td><td>16.7</td><td>11.6</td><td>15.8</td><td>13.9</td><td>17.7</td><td>13.1</td><td>15.2</td><td>14.2</td></tr><tr><td>CFIR [60]</td><td>29.8</td><td>33.5</td><td>29.4</td><td>33.6</td><td>30.5</td><td>34.1</td><td>30.3</td><td>33.4</td><td>31.9</td></tr><tr><td>ST + EWMA (ours)</td><td>42.0</td><td>48.4</td><td>43.8</td><td>50.9</td><td>36.9</td><td>44.2</td><td>40.9</td><td>47.8</td><td>44.4</td></tr><tr><td>ST + LSTM (ours)</td><td>47.8</td><td>52.5</td><td>44.4</td><td>50.5</td><td>41.6</td><td>47.6</td><td>44.6</td><td>50.2</td><td>47.4</td></tr><tr><td>FashionNTM (ours)</td><td>48.3</td><td>52.8</td><td>45.1</td><td>49.8</td><td>43.8</td><td>48.8</td><td>45.7</td><td>50.4</td><td>48.1</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Multi-turn methods - In these methods, the multi-turn data is fed turn-wise to the model. The first method is Dialog Manager [17], which employs reinforcement learning (RL) framework to learn relationships between turns. Next, we have the previous state-of-the-art Conversational Fashion Image Retrieval CFIR method [60], which encodes only the text using a transformer network [53], and uses a simple Gated Recurrent Unit (GRU) layer for multi-turn image retrieval. The third baseline is "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{ST} + \\mathrm{EWMA}"
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+                                    "type": "text",
+                                    "content": ", where we use exponential weighted moving average [1] to heuristically aggregate past turns, with more weights given to recent history. Finally, we have the "
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+                                    "type": "text",
+                                    "content": " model that uses a single-layer LSTM [20] with a hidden size of 100 for aggregating past information."
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+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.4. Results"
+                                }
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+                                    "content": "Evaluation Metrics - Following [14, 60, 17], we evaluate models using the standard top-K recall (i.e. R@K) for image retrieval. Overall performance are compared specifically on the average of R@5 and R@8."
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+                                    "content": "Quantitative results on multi-turn datasets - In Table 2, we compare the results of different methods on the multi-turn FashionIQ dataset. We observe that the multi-turn baselines generally perform better than single-turn methods. This is expected as aggregating data by naively averaging/concatenating loses feedback content and turn-order information and hence is likely to miss out on important cues. Our memory-based approach outperforms all the other multi-turn baselines by a large margin. This shows that the memory network can store and retrieve useful information to and from the memory between intermediate turns, which allows it to keep track of past information better than other networks that do not use explicit memory. The "
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+                                    "content": "50.5\\%"
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+                                    "type": "text",
+                                    "content": " performance gain over the previous state-of-the-art highlights our model's capability to learn meaningful representations over multiple turns of conversational feedback."
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+                                    "type": "text",
+                                    "content": "In Table 3, we provide a similar comparison for the Multi-turn Shoes dataset. Consistent with results for Multi-turn FashionIQ, the multi-turn baselines perform better than"
+                                }
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+                                    "content": "Table 3: Comparison with existing single-turn and multi-turn models on the multi-turn version of the Shoes [5] dataset. We compare with multiple single-turn, and multi-turn baselines. Comparative analysis shows the superior performance of our proposed approach using the popular recall rate evaluation metric."
+                                }
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+                                            "html": "<table><tr><td>Model</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td colspan=\"4\">Single-turn</td></tr><tr><td>ST + avg(all turns)</td><td>12.4</td><td>17.6</td><td>15.0</td></tr><tr><td>ST + cat(all captions)</td><td>10.7</td><td>13.6</td><td>12.2</td></tr><tr><td colspan=\"4\">Multi-turn</td></tr><tr><td>ST + EWMA (ours)</td><td>18.3</td><td>23.8</td><td>21.1</td></tr><tr><td>ST + LSTM (ours)</td><td>23.3</td><td>32.1</td><td>27.7</td></tr><tr><td>FashionNTM (ours)</td><td>26.7</td><td>35.7</td><td>31.2</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "all the single-turn ones, and our memory network-based approach performs the best with a relative improvement of "
+                                },
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+                                    "content": "12.6\\%"
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+                                    "type": "text",
+                                    "content": ". The difference in performance across different models is more pronounced in these results than in Table 2. This is possibly because the annotations are cleaner and more consistent in this dataset as compared to Multi-turn FashionIQ [60]. For instance, multiple images in the FashionIQ dataset can match a particular query, but only one of them is labeled as the ground-truth."
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+                                    "content": "An important property of a good multi-turn system is that performance should be robust to the length of the historical information (number of past turns). For example, even for a large number of previous turns considered, the model should efficiently retain desirable details, while filtering out unnecessary information. In Table 4, we analyze this property for models with and without memory. A single-turn model that assumes ground-truth information for all past turns, and evaluated only on the final-turn, is taken as reference. This is expected to be the upper-bound on the performance in a single-turn setting, as perfect information about the history is guaranteed. We vary the number of past turns included in the input transaction history (versus treated as ground-truth) for the multi-turn models (with or without memory) in order to evaluate their effectiveness at capturing and utilizing past information. As seen from the table, for a model without memory, the performance depreciates significantly with each additional turn from the"
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+                                    "type": "text",
+                                    "content": "Table 4: Importance of aggregating historical data using memory-based vs non-memory approach. In the first row, we show the result of a model using only the final turn information of a multi-turn transaction. This assumes the groundtruth retrieval for all previous turns, and therefore provides the upper-bound on single-turn performance for final retrieval. Subsequently, we include additional information from the history, and compare performance across models with and without memory. As seen from the non-memory case, the performance depreciates a lot ("
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+                                    "type": "text",
+                                    "content": " 64.9% difference compared to the final turn's performance), as we try to aggregate longer historical information. In contrast, for the memory network model, it can be seen that the performance is fairly consistent ("
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+                                    "type": "text",
+                                    "content": " 0.5% difference) across the turn length."
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+                                            "html": "<table><tr><td rowspan=\"2\">Memory usage</td><td rowspan=\"2\">Turn configuration</td><td colspan=\"2\">Dress</td><td colspan=\"2\">Toptee</td><td colspan=\"2\">Shirt</td><td colspan=\"3\">Overall</td><td rowspan=\"2\">Difference from final turn</td></tr><tr><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>R@5</td><td>R@8</td><td>Mean</td></tr><tr><td>-</td><td>only final turn</td><td>77.9</td><td>77.9</td><td>84.0</td><td>84.0</td><td>74.1</td><td>77.8</td><td>78.7</td><td>79.9</td><td>79.3</td><td>-</td></tr><tr><td colspan=\"12\">Experiments with data aggregated across multiple-turns</td></tr><tr><td rowspan=\"3\">Only single turn (w/o memory)</td><td>last two turns</td><td>51.3</td><td>58.4</td><td>56.0</td><td>76.0</td><td>44.4</td><td>48.1</td><td>50.6</td><td>60.9</td><td>55.8</td><td>-29.6%</td></tr><tr><td>last three turns</td><td>33.6</td><td>43.4</td><td>32.0</td><td>44.0</td><td>29.6</td><td>40.7</td><td>31.8</td><td>42.7</td><td>37.3</td><td>-53.0%</td></tr><tr><td>all turns</td><td>18.6</td><td>28.3</td><td>32.0</td><td>32.0</td><td>25.9</td><td>29.6</td><td>25.5</td><td>30.0</td><td>27.8</td><td>-64.9%</td></tr><tr><td rowspan=\"3\">FashionNTM (with memory)</td><td>last two turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr><tr><td>last three turns</td><td>77.0</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.6</td><td>79.9</td><td>79.8</td><td>+0.6%</td></tr><tr><td>all turns</td><td>76.1</td><td>77.9</td><td>84.0</td><td>84.0</td><td>77.8</td><td>77.8</td><td>79.3</td><td>79.9</td><td>79.6</td><td>+0.4%</td></tr></table>",
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+                                            "content": "(a) Multi-turn FashionIQ. From left to right, the images belong to the Dress, Shirt, and Toptee categories respectively."
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+                                            "content": "(b) Multi-turn Shoes. From left to right, we have three different samples of shoes from the dataset."
+                                        }
+                                    ]
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 4: Top-5 final image retrievals on the evaluated multi-turn datasets. The top row illustrates 3 sets of multi-turn query session. We consider three different multi-turn models - EWMA, LSTM, and our proposed FashionNTM. As seen from the retrievals, our proposed model correctly predicts the target image in all 3 cases for the FashionIQ dataset, and in 2 out of 3 cases for the Shoes dataset."
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+                                    "type": "text",
+                                    "content": "past treated as input rather than ground-truth. As we go further back in history, the performance consistently reduces. However, for our multi-turn model with memory, the performance does not change appreciably as the number of turns change. This shows that our proposed approach can successfully retain/filter out past data based on their relevance, across various lengths of history."
+                                }
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+                                    "content": "An interesting observation is that having only the final turn with memory does not yield a good result. This is possibly due to the initialization method of the memory network, which is random. Hence, in absence of a history (only single turn case), the only past features to be aggregated are the random initialization features."
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+                                    "type": "text",
+                                    "content": "Qualitative results - In addition to the quantitative experiments described above, we also present some qualitative final image retrieval results of our evaluated models on both the multi-turn datasets. The first set of results are shown in Figures 4a and 4b for the Multi-turn FashionIQ [60] and the"
+                                }
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+                                    "content": "Multi-turn Shoes datasets, respectively<sup>2</sup>. We compare the top-5 predicted results from our proposed model with two other multi-turn baselines, ST + EWMA and ST + LSTM. As seen in the figures, our approach can correctly predict the desired target image for both datasets with higher ranks as compared to other baselines. More specifically, we see that in Figure 4a, even though all the three multi-turn models can infer the general sense of desired attributes, such as \"is longer\" in the left block and \"has short sleeves\" in the right, only our model can capture complex and detailed properties, e.g., \"gray and not red\" in the left block, and \"red color with center logo\" in the middle block. Furthermore, our model can retrieve multiple desirable products, as seen by the first four images in the middle block, and four out of five images in the right block. Similar results are observed for Shoes in Figure 4b, where our model correctly predicts"
+                                }
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+                                    "content": "2Please refer to the supplementary material for additional results, along with the differences in annotation quality between the two datasets."
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+                                            "content": "Figure 5: Memory retention capability of our proposed approach. Given an initial query image, we take two interactive user feedbacks in turns. On the left side, we have the single-turn model which only learns to retrieve an image using a single dialog exchange. As a result, none of the retrieved images in turn 2 are \"green in color\", which was desired in turn 1. In contrast, our proposed approach on the right can learn to retain data from both the turns, and therefore retrieves desirable product in 2 out of 3 cases."
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+                                    "content": "the desired target as rank-1 in two out of three examples, whereas the other models fail to retrieve meaningful results."
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+                                    "content": "In addition to the results above for the static dataset, we also performed some interactive experiments to evaluate whether our model can adapt to real-world dynamic use cases beyond the trained datasets."
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+                                    "content": "Memory retention - In this experiment, we demonstrate the memory retention capability of our proposed model by comparing it with a single-turn network, which does not retain historical information. We start with an initial query image retrieved via a single-turn model. Subsequently, we take user input for the next two turns to retrieve newer sets of images. As seen in Figure 5, for the single-turn model (left side), none of the retrieved images in turn 2 are green in color. This is because the \"green in color\" attribute was a desired property in turn 1, which the model without memory could not recover. In contrast, for our memory network approach (right side) both the top-2 retrieved images for turn 2 are \"green in color\" in addition to having \"a solid color and small image\". Thus, our model can learn to retain information from previous turns."
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+                                    "type": "text",
+                                    "content": "Agnosticity to turn order - Ideally, a deployed multi-turn image retrieval system should be independent of the order of feedbacks provided, as long as they are non-contradictory. This is demonstrated in the experiment conducted in Figure 6. In the first case, we take two text inputs as feedbacks from a user and present them to the model. In the second case, we reverse the order of the feedbacks. As shown in the figure, for the flipped case, our proposed FashionNTM model retrieves similar looking final products, even though the intermediate retrievals are very different."
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+                                    "content": "It is to be noted that for both the experiments depicted in Figures 5 and 6, the feedback is taken from a dynamic user, thereby establishing the interactive capability of our"
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+                                            "content": "Figure 6: Turn order independence feature of a memory network. In this experiment, we start with an initial query image, and take two non-contradictory user feedbacks. In one case (left), we let the model retrieve images based on the original order of the feedbacks, whilst in the other (right), we flip the order of the feedbacks. Our proposed approach adapts to presented input, and retrieves similar looking final results for both the cases, even though the intermediate outputs are quite different."
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+                                    "content": "Fashion image retrieval is inherently a subjective task, where the task success heavily relies on the satisfaction of a customer. Thus, we conducted a small human-preference survey among 5 participants (not associated with the paper in any way). To each user, we showed the final top-1 retrieved image by the 3-best multi-turn models on the FashionIQ [60] dataset from Table 2 - EWMA, LSTM, and our proposed FashionNTM. To ensure consistency, we generated 45 queries for this study, whose results are shown in Figure 7. The "
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+                                    "content": "-axis shows the number of preferred retrieval results for each user. Results show that each of the 5 users preferred images retrieved by the proposed FashionNTM model, on an average "
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+                                    "type": "text",
+                                    "content": " more as compared to other multi-turn methods. In the supplementary material, we include some examples of the user interface shown to"
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+                                            "content": ". We select the mean value for comparison and pick the best one."
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+                                            "html": "<table><tr><td>Model</td><td>Number of memories (C)</td><td>R@5</td><td>R@8</td><td>Mean</td><td>% increase</td></tr><tr><td>ST+v-NTM</td><td>1</td><td>24.5</td><td>30.5</td><td>27.5</td><td>-</td></tr><tr><td rowspan=\"4\">FashionNTM</td><td>2</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr><tr><td>4</td><td>27.6</td><td>35.5</td><td>31.5</td><td>14.5</td></tr><tr><td>8</td><td>26.9</td><td>35.2</td><td>31.1</td><td>13.1</td></tr><tr><td>16</td><td>26.4</td><td>33.8</td><td>30.1</td><td>9.5</td></tr></table>",
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+                                    "content": "the participants during this study."
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+                                    "content": "4.7. Ablation Studies"
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+                                    "content": "We perform multiple ablation studies to gain insights on how changing different configurations of the memory network affect the overall performance. We perform these ablations on the multi-turn Shoes dataset as it contains more realistic and consistent feedback texts.<sup>3</sup>"
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+                                    "content": "Number of memories in CM-NTM - This experiment involves varying the number of memories "
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+                                    "type": "text",
+                                    "content": " in our cascaded memory architecture. In Table 5, we observe that the cascaded memory CM-NTM models perform significantly better than vanilla NTM, which has only one memory. We hypothesize that having inputs from multiple turns interacting with the same memory could eventually lead to saturation as we get additional data which could be alleviated if there are multiple memories in the network to recover the past which might help in capturing multiple complex relationships in multi-turn interactions better. Additionally, multiple memory networks can help in learning diverse representations of the input using derived features, which is not possible with a single memory network. As seen in Table 5 for Shoes dataset, the performance increases with the number of memories, peaking at "
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+                                    "type": "text",
+                                    "content": ", and then gradually decreases as the model starts to overfit."
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+                                    "content": "Inference time with multiple memories - In this experiment, we study the performance of FashionNTM in terms of the mean of R@5 and R@8 recall rates along with the time taken to process one multi-turn transaction. For each "
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+                                    "type": "text",
+                                    "content": ", we evaluate the performance across four different memory sizes. As seen from Figure 8, the inference time increases with additional memories. Configurations in the green and blue clusters are desirable, as they provide a good trade-off between recall performance and computation time, while the pink and red clusters are undesirable due to poor performance and longer inference time, respectively."
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+                                    "content": "5. Conclusion and Future Work"
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+                                    "type": "text",
+                                    "content": "In this paper, we presented a novel cascaded Neural Turing Machine-based approach, called FashionNTM, for multi-turn feedback-based fashion image retrieval. Multiple"
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+                                            "content": "Figure 8: Scatter plot showing recall versus inference time for multiple memories in our CM-NTM for the Multi-turn Shoes dataset. The configurations belonging to the green cluster give the best recall overall, while having a high inference time. The configurations in the blue cluster provide a suitable alternative with quicker inference at the cost of lower recall. The magenta and red clusters are undesirable configurations due to poor performance and long inference time, respectively."
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+                                    "content": "memories in our model allow it to effectively retain and recall a number of complex relationships across transactions in the multi-turn setting, and multiple controllers help in assigning relative importance to each feature stored in the memory. This aids in attending to different parts of the input at different levels, thus leading to better performance across datasets. We also performed extensive experiments to compare our performance with baselines and previous state-of-the-art and observed that our multi-memory model significantly outperforms previous works [60], with up to "
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+                                    "content": " relative improvement on Multi-turn FashionIQ, and by "
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+                                    "type": "text",
+                                    "content": " on the multi-turn Shoes dataset, which we created in this work. We further demonstrated that our model can generalize beyond the trained setting to dynamically interact with real-world users to retrieve meaningful final product images. Finally, a user preference study reveals that our model is preferred by human participants on an average "
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+                                    "content": " more as compared to other multi-turn methods."
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+                                    "content": "Despite promising results, there are a few limitations that make multi-turn image retrieval a hard problem to solve. Firstly, there is dearth of high quality and diverse multi-turn image retrieval datasets in the fashion domain which hinders comprehensive studies in this field. Additionally, deploying current approaches to real-world scenarios (e.g., virtual private assistants) becomes a challenge due to computational requirements. Lastly, selecting the right configuration for different components such as memory size, number of memories, etc. in a memory-based network is not a trivial task and depends a lot on the use case. Nevertheless, for future work, our approach could be further extended to non-fashion domains where multi-turn feedback-based information retrieval solutions are required."
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+                                    "content": "3For a similar study on the Multi-turn Fashion-IQ dataset, please refer to the supplementary material."
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+                                            "type": "text",
+                                            "content": "[1] Moving Average. https://en.wikipedia.org/wiki/Movingaverage.6"
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+                                            "type": "text",
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
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+                                            "type": "text",
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+                                    ]
+                                }
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+                    "sub_type": "ref_text"
+                }
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+                                        }
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+                            ],
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+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
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+                                        }
+                                    ]
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+                            "bbox": [
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+                                        }
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+                            "index": 5
+                        },
+                        {
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+                                407
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                            ],
+                                            "type": "text",
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+                                        }
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+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                                            "bbox": [
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+                                        }
+                                    ]
+                                }
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diff --git a/2023/Fast Adversarial Training with Smooth Convergence/23b31082-56d8-432b-80e3-85fc235c4ff5_content_list.json b/2023/Fast Adversarial Training with Smooth Convergence/23b31082-56d8-432b-80e3-85fc235c4ff5_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2058fd70d9e422ad5dae33fc1e587321461820f3
--- /dev/null
+++ b/2023/Fast Adversarial Training with Smooth Convergence/23b31082-56d8-432b-80e3-85fc235c4ff5_content_list.json	
@@ -0,0 +1,1834 @@
+[
+    {
+        "type": "text",
+        "text": "Fast Adversarial Training with Smooth Convergence",
+        "text_level": 1,
+        "bbox": [
+            218,
+            130,
+            751,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Mengnan Zhao, Lihe Zhang*, Yuqiu Kong and Baocai Yin",
+        "bbox": [
+            256,
+            193,
+            712,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Dalian University of Technology, China",
+        "bbox": [
+            325,
+            223,
+            643,
+            241
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "zmnwelcome@mail.dlut.edu.cn，{zhanglihe，yqkong，ybc}@dlut.edu.cn",
+        "bbox": [
+            196,
+            244,
+            771,
+            258
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            303,
+            313,
+            319
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, i.e. the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth.",
+        "bbox": [
+            76,
+            335,
+            472,
+            698
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            728,
+            209,
+            744
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent breakthroughs in deep learning [21, 32] have aroused researchers' interest in the security of neural networks [45, 48, 39]. In particular, the advanced research proves the vulnerability of deep models to adversarial attacks [8, 11, 27]. For instance, tiny crafted perturbations can fool models in various fields into making wrong decisions [15, 50, 35, 24]. Considering the security risks brought by adversarial attacks [18, 46, 33, 44], there is a quickly grow",
+        "bbox": [
+            76,
+            753,
+            468,
+            877
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ing body of work [43, 46, 18] on improving the adversarial robustness of neural networks. Among them, adversarial training is widely applied by practitioners [31, 12].",
+        "bbox": [
+            500,
+            304,
+            890,
+            349
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In recent years, projected gradient descent based adversarial training (PGD-AT) [25, 34] has been widely employed for its stability and effectiveness. However, this mechanism is computationally expensive. It requires multiple gradient descent steps to generate the adversarial training data [38]. An alternative of PGD-AT is the fast adversarial training (FAT) [28], which only adopts a single-step fast gradient sign method (FGSM) [11] to generate training data. Compared to PGD-AT, FAT can efficiently train models, but easily falls into catastrophic overfitting [40, 29].",
+        "bbox": [
+            496,
+            352,
+            892,
+            503
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A number of FAT methods have been proposed to mitigate catastrophic overfitting. For example, Wong et al. [40] use randomly initialized perturbations to enhance the diversity of adversarial perturbations. Based on it, Andriushchenko et al. [2] raise a complementary regularizer named GradAlign to maximize the gradient alignment between benign and adversarial examples explicitly. Similarly, NuAT [36] and FGSM-MEP [42] adopt nuclear norm or p-norm to regularize the adversarial training, thereby increasing the prediction alignment between benign and adversarial examples. However, the above methods can only resolve catastrophic overfitting within the limited perturbation budget ( $\\xi \\leq 8/255$ ).  $\\xi$  specifies the perturbation degree of adversarial training data generated by various attacks. Besides, models trained by small perturbations are vulnerable to adversarial attacks with a large  $\\xi$ , e.g. the models trained by NuAT and FGSM-MEP at  $\\xi = 8/255$  perform  $53\\%$  and  $54\\%$  robustness against the PGD-50 attack with  $\\xi = 8/255$ , but only  $22\\%$  and  $20\\%$  robustness against the same attack with  $\\xi = 16/255$  respectively. Therefore, we aspire to prevent catastrophic overfitting to improve the adversarial robustness of neural models at larger perturbation budgets.",
+        "bbox": [
+            496,
+            505,
+            893,
+            838
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "By analyzing adversarial training processes of representative work, we observe that catastrophic overfitting is usually accompanied by a slight fluctuation in the classification loss for benign samples and a sharp drop in the classification",
+        "bbox": [
+            498,
+            839,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            805,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author",
+        "bbox": [
+            94,
+            886,
+            220,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "4720",
+        "bbox": [
+            482,
+            944,
+            516,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "loss for adversarial examples. This motivates us to question whether a smooth loss convergence process is also a stable FAT process. Moreover, we find that an oscillating adversarial training phase may restart the FAT process after catastrophic overfitting. Fig. 1 shows the details.",
+        "bbox": [
+            75,
+            90,
+            468,
+            167
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "According to these observations, we introduce an oscillatory constraint that limits the difference in loss between adjacent training epochs, called ConvergeSmooth. A dynamic convergence stride of ConvergeSmooth is designed considering the nonlinear decay rate of loss functions. Inspired by the smoothness of loss convergence, we further verify the effect of the proposed weight centralization on model stability. Weight centralization refers to taking the weights average of the previously trained models as the convergence center of the current model weight. Our proposed methods are attack-agnostic and thus can be combined with existing adversarial strategies in FAT, such as FGSM-RS and FGSM-MEP, to evaluate their performance.",
+        "bbox": [
+            75,
+            167,
+            468,
+            362
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The contributions are summarized in four aspects: (1) We verify that previous FAT works still suffer from catastrophic overfitting at a large  $\\xi$  and then study catastrophic overfitting from the perspective of convergence instability of loss functions; (2) We propose a smooth convergence constraint, ConvergeSmooth, and design a dynamic convergence stride for it, to help various FAT methods avoid catastrophic overfitting on different perturbation budgets; (3) The weight centralization is proposed without introducing extra hyperparameters other than the loss balance coefficient to stabilize FAT; (4) Extensive experiments show that the proposed methods outperform the state-of-the-art FAT techniques in terms of efficiency, robustness, and stability.",
+        "bbox": [
+            75,
+            363,
+            470,
+            559
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            571,
+            218,
+            588
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Adversarial attacks. Adversarial attacks are usually used to deceive deep-learning models. Goodfellow et al. [11] first discuss the adversarial attack (FGSM) within the classification task. They prove that adversarial examples  $x'$  generated by a single-step gradient backward can misclassify the model  $f(\\cdot; \\theta)$  with high confidence.  $\\theta$  denotes the fixed model weights.  $x'$  is generated by",
+        "bbox": [
+            75,
+            597,
+            468,
+            704
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx ^ {\\prime} = x + \\xi \\cdot \\operatorname {s g n} \\left(\\nabla_ {x} \\mathcal {L} (f (x; \\theta), y)\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            712,
+            468,
+            729
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $x$  is an input image,  $\\xi$  represents the perturbation budget,  $\\operatorname{sgn}(\\cdot)$  means the sign function,  $\\mathcal{L}(\\cdot)$  is usually the cross-entropy loss,  $\\nabla_{x}\\mathcal{L}(\\cdot)$  calculates the gradient of loss at  $x$ , and  $y$  denotes the ground truth labels of  $x$ . Following the FGSM [11], researchers propose a series of attack methods based on the iterative gradient backward, e.g. I-FGSM [22], MIM [8], and PGD [25]. Taking the PGD attack as an example, the adversarial example  $x_{t + 1}^{\\prime}$  produced in the iteration  $t + 1$  can be formulated as",
+        "bbox": [
+            75,
+            739,
+            468,
+            875
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t + 1} ^ {\\prime} = \\operatorname {c l i p} _ {\\xi} \\left(x _ {t} ^ {\\prime} + \\epsilon \\cdot \\operatorname {s g n} \\left(\\nabla_ {x _ {t} ^ {\\prime}} \\mathcal {L} \\left(f \\left(x _ {t} ^ {\\prime}; \\theta\\right), y\\right)\\right)\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            104,
+            883,
+            468,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $\\epsilon$  denotes the single-step stride and  $\\mathrm{clip}_{\\xi}$  refers to projecting adversarial perturbations to a  $\\xi$ -ball.",
+        "bbox": [
+            498,
+            90,
+            890,
+            121
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Adversarial training. Madry et al. [25] formalize the adversarial training as a min-max optimization problem,",
+        "bbox": [
+            498,
+            121,
+            890,
+            151
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\theta} \\mathbb {E} _ {(x, y) \\sim D} [ \\max  _ {\\delta \\in [ - \\xi , \\xi ]} \\mathcal {L} (f \\left(x ^ {\\prime}; \\theta\\right), y) ], \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            162,
+            890,
+            186
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $x' = x + \\delta$ ,  $\\delta$  represents the adversarial perturbations generated by various attacks such as PGD and FGSM.  $D$  is the data generator. The internal maximization maximizes the classification loss to generate adversarial perturbations with fixed model weights. The external minimization minimizes the classification loss on the generated adversarial examples when optimizing the model weights.",
+        "bbox": [
+            496,
+            196,
+            890,
+            303
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Actually, there is a trade-off between computational efficiency and adversarial robustness in recent adversarial training methods. Compared to PGD-AT [25], FGSM-based fast adversarial training (FAT) accelerates the training process but damages the robustness of models for the problem of catastrophic overfitting [19, 17]. To mitigate this issue, Wong et.al [40] demonstrate that the FGSM with a random start strategy (FGSM-RS) can achieve comparable performance against the PGD-AT. ZeroGrad [10] zeroes the elements of gradient that are too small to craft the perturbations. enforces the model loss to increase with the increase in perturbation size. Besides, GradAlign [2] prevents catastrophic overfitting by maximizing the alignment between gradients of benign samples and adversarial examples.",
+        "bbox": [
+            496,
+            304,
+            890,
+            513
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Similarly, NuAT [36] introduces a nuclear norm regularization between logits for benign and adversarial examples and uses the Bernoulli noise as the initial perturbation. ATAS [16] learns an instantiated adaptive step size that is inversely proportional to the gradient norm. It applies the adversarial perturbations from the previous epoch as the initialization of FGSM in the current training phase. In addition, Jia et al. [42] propose several prior-guided initialization methods to replace the random start strategy of FGSM-RS. Specifically, FGSM-BP adopts the adversarial perturbations from the previous batch as the attack initialization in the current batch. FGSM-MEP employs a momentum mechanism to combine all adversarial perturbations from the previous epochs to yield adversarial initialization.",
+        "bbox": [
+            496,
+            515,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although these FAT methods have resolved catastrophic overfitting at small perturbation budgets, they still suffer from catastrophic overfitting under larger perturbation budgets (e.g.  $\\xi = 16 / 255$ ). Unlike these methods, we revisit the catastrophic overfitting problem from the perspective of loss convergence instability and prevent this exception by limiting the magnitude of loss fluctuations during training.",
+        "bbox": [
+            496,
+            726,
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+            832
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Proposed Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            844,
+            671,
+            862
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first study the performance of previous FAT methods when subjected to a large perturbation budget",
+        "bbox": [
+            500,
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+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "4721",
+        "bbox": [
+            480,
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+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/cd9ecbc383adc2a12e7ab4b5a3256b22e64a083407a68b7b5fbdf8cacf2a38fa.jpg",
+        "image_caption": [
+            "(a) ResNet18 trained with FGSM-RS"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            103,
+            356,
+            193
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/f2568362360d16210983537fbbc98350642e7fe840781af21c1099d1b6ebfb67.jpg",
+        "image_caption": [
+            "(b) ResNet18 $_2$  trained with FGSM-RS"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            357,
+            103,
+            620,
+            193
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/fdd50d80d63a5e6b09bf7fb39d5738ac55fa6b9d105d1b63edcf06374cb43fd0.jpg",
+        "image_caption": [
+            "(c) ResNet18 trained with FGSM-RS"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            622,
+            103,
+            885,
+            193
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/888d940547966a2de7eeb0aac3b876c80c50ae5fb0cbdda61901363669dbe86b.jpg",
+        "image_caption": [
+            "(d) ResNet18 trained with GradAlign"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            205,
+            356,
+            296
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6b673903b39c5fb94588140a51c32a46441f9a527c1e7d9af4534d7a47470ae1.jpg",
+        "image_caption": [
+            "(e) ResNet18 $_2$  trained with GradAlign"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            357,
+            205,
+            620,
+            296
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7570403a5c25707a754349395f19cf4b9d241a35cc9aebda17ce19c1ec54d36a.jpg",
+        "image_caption": [
+            "(f) ResNet18 trained with GradAlign"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            622,
+            205,
+            885,
+            296
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/d26313a50019ee9fc986785530ffce4cb8414056df6f5225922cb675f1ba34e5.jpg",
+        "image_caption": [
+            "(g) ResNet18 trained with FGSM-MEP",
+            "Figure 1. The training process of previous FAT methods with ResNet18 on CIFAR-10. Each FAT method is trained 3 times.  $\\xi = 16 / 255$ . ADV-Loss and BEN-Loss denote the classification loss of models to adversarial and benign examples during training, respectively. ADV-Acc and BEN-Acc represent the classification accuracy of models to adversarial and benign examples during testing, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            306,
+            356,
+            406
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/36780e4b0d277b67f249a6292c1612b47a45ac4e2d523f7bafd4a2dd23f657ef.jpg",
+        "image_caption": [
+            "(h) ResNet182 trained with FGSM-MEP"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            357,
+            306,
+            620,
+            406
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a205b7233de4b4082b6e17fbf138ff8447f36e6b7768b82dbd155c33980769a0.jpg",
+        "image_caption": [
+            "(i) ResNet18 trained with FGSM-MEP"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            622,
+            306,
+            885,
+            406
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "$\\xi$ . Then, the training processes of these methods have been analyzed for a better understanding of catastrophic overfitting. Finally, we detail the proposed methods.",
+        "bbox": [
+            75,
+            476,
+            468,
+            522
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Performance of FAT methods on a large  $\\xi$",
+        "text_level": 1,
+        "bbox": [
+            76,
+            529,
+            429,
+            545
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Previous FAT techniques avoid catastrophic overfitting at small  $\\xi$  ( $\\xi \\leq 8/255$ ). Here, we investigate their performance on a large  $\\xi$  ( $\\xi = 16/255$  by default).",
+        "bbox": [
+            75,
+            551,
+            468,
+            597
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FGSM-RS [40]: Based on Eq. (3), this method adopts the samples with uniformly random perturbations  $\\delta_0\\sim$ $\\mathcal{U}(-\\xi ,\\xi)$  as the attack initialization of FGSM,",
+        "bbox": [
+            75,
+            598,
+            468,
+            642
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\theta} \\mathbb {E} _ {(x, y) \\sim D} [ \\max  _ {\\delta_ {0} + \\delta \\in [ - \\xi , \\xi ]} \\mathcal {L} (f (x ^ {\\prime}; \\theta), y) ],\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            176,
+            648,
+            450,
+            674
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx ^ {\\prime} = x + \\delta_ {0} + \\delta \\quad s. t. \\quad x ^ {\\prime} \\in [ 0, 1 ], \\quad \\delta_ {0} \\sim \\mathcal {U} (- \\xi , \\xi). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            676,
+            468,
+            705
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "GradAlign [2]: This approach increases the gradient alignment between benign samples  $x$  and perturbed samples  $x + \\delta_0$ , which is denoted as",
+        "bbox": [
+            75,
+            708,
+            468,
+            752
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} _ {(x, y) \\sim D} [ 1 - \\cos (\\nabla_ {x} \\mathcal {L} (x, \\theta), \\nabla_ {x + \\delta_ {0}} \\mathcal {L} (x + \\delta_ {0}, \\theta) ], \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            758,
+            467,
+            782
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} (x, \\theta) = \\mathcal {L} (f (x; \\theta), y).\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            269,
+            779,
+            467,
+            795
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "$\\cos (\\cdot)$  computes the cosine similarity between two matrices.",
+        "bbox": [
+            75,
+            801,
+            467,
+            816
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FGSM-MEP [42]: Different from FGSM-RS, this method generates the initialization perturbations  $\\delta_0$  based on all historical adversarial perturbations from the previous epochs and introduces a regularization expressed as",
+        "bbox": [
+            75,
+            816,
+            468,
+            877
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} _ {(x, y) \\sim D} [ | | f (x ^ {\\prime}; \\theta) - f (x + \\delta_ {0}; \\theta) | | _ {2} ^ {2} ], \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            142,
+            883,
+            468,
+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $||\\cdot ||_2^2$  denotes the squared  $\\mathcal{L}_2$  distance.",
+        "bbox": [
+            500,
+            476,
+            803,
+            492
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Fig. 1 shows their detailed adversarial training processes of ResNet18 [13] on CIFAR-10 [20]. We find that they fall into catastrophic overfitting during the  $5 \\sim 20_{\\mathrm{th}}$ ,  $40 \\sim 65_{\\mathrm{th}}$  and  $10 \\sim 15_{\\mathrm{th}}$  epochs, respectively. Graphical analysis of various models and datasets is given in the supplement.",
+        "bbox": [
+            498,
+            492,
+            890,
+            568
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Analysis of training process",
+        "text_level": 1,
+        "bbox": [
+            500,
+            575,
+            746,
+            590
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "From Fig. 1, we discover several typical phenomena of catastrophic overfitting: 1) Change from a smooth convergence state to an irregular fluctuation state; 2) A slight change (increase or decrease) in the standard classification loss  $\\mathcal{L}(x,\\theta)$  and a rapid descent of the adversarial classification loss  $\\mathcal{L}(x',\\theta)$ ; 3) Rapid decline in the classification accuracy of adversarial examples.",
+        "bbox": [
+            496,
+            598,
+            890,
+            704
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "After catastrophic overfitting, the methods depicted in Fig. 1 are capable of restarting a stable FAT process, even though catastrophic overfitting may occur again. The observed phenomena during the FAT restart are: 1) Change from an irregular fluctuation state to a smooth convergence state; 2) Rapid increase in both  $\\mathcal{L}(x,\\theta)$  and  $\\mathcal{L}(x',\\theta)$  after a period of decline; 3) Rapid decrease in the classification accuracy of benign samples, while the classification accuracy of adversarial examples experiences a rapid increase.",
+        "bbox": [
+            496,
+            704,
+            890,
+            839
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "On this basis, we can make the following conclusions. 1)  $\\mathcal{L}(x,\\theta)$  is more stable than  $\\mathcal{L}(x^{\\prime},\\theta)$  and models are prone to overfitting to adversarial perturbations; 2) Catastrophic overfitting is closely correlated to the convergence insta",
+        "bbox": [
+            498,
+            839,
+            890,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4722",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "bility of adversarial training; 3) Exceptions in  $\\mathcal{L}(x,\\theta)$  and  $\\mathcal{L}(x^{\\prime},\\theta)$  occur simultaneously; 4) An oscillating adversarial training phase may trigger the FAT process to restart.",
+        "bbox": [
+            76,
+            90,
+            468,
+            137
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Smooth convergence for the stable FAT",
+        "text_level": 1,
+        "bbox": [
+            76,
+            145,
+            413,
+            161
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we describe the proposed method in detail.",
+        "bbox": [
+            94,
+            167,
+            419,
+            183
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Why did previous methods fail to prevent catastrophic overfitting? Despite the improvement in diversity achieved through random initialization in FGSM-RS, models are still susceptible to overfitting adversarial perturbations. GradAlign and FGSM-MEP enhance the stability of adversarial training through the constraints in Eqs. (5) and (6), respectively. However, Eq. (5) may reduce the stability of  $\\mathcal{L}(x,\\theta)$ . Meanwhile, the prediction probability  $f(x + \\delta_0;\\theta)$  in Eq. (6) is not the sweet spot to keep the FAT stable. Unlike these methods, we ensure the convergence stability of both  $\\mathcal{L}(x,\\theta)$  and  $\\mathcal{L}(x',\\theta)$ .",
+        "bbox": [
+            75,
+            184,
+            468,
+            349
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "How can catastrophic overfitting be solved? Since the catastrophic overfitting is usually accompanied by a slight change in  $\\mathcal{L}(x,\\theta)$  and a sharp decline in  $\\mathcal{L}(x',\\theta)$ , we consider a smooth loss convergence process to be a stable FAT process that resolves this issue. To this end, a complementary constraint  $\\mathcal{L}_{CS}$  for Eq. (3) is proposed,",
+        "bbox": [
+            75,
+            349,
+            468,
+            441
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\theta_ {t}} \\mathbb {E} _ {(x, y) \\sim D} \\left[ \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) + \\mathcal {L} _ {C S} (t) \\right], \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            450,
+            468,
+            474
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which can limit the difference in losses between adjacent epochs, expressed as",
+        "bbox": [
+            76,
+            483,
+            468,
+            513
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {C S} (t) = w _ {1} \\cdot \\left| \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) - \\mathcal {L} \\left(x _ {t - 1} ^ {\\prime}, \\theta_ {t - 1}\\right) \\right| + \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            523,
+            468,
+            547
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {2} \\cdot | \\mathcal {L} (x, \\theta_ {t}) - \\mathcal {L} (x, \\theta_ {t - 1}) |, \\quad s. t. \\quad \\mathcal {C} (x) = 1,\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            107,
+            542,
+            421,
+            558
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\theta_{t}$  represents the model weights of the  $t_{\\mathrm{th}}$  training epoch.  $w_{1}$  and  $w_{2}$  are hyper-parameters,  $w_{1}, w_{2} \\in [0,1]$ .  $|\\cdot|$  calculates the absolute value.  $x_{t}^{\\prime} = x + \\delta_{0,t} + \\delta_{t}$ .  $\\delta_{0,t}$  can be replaced by various attack initialization perturbations and  $\\delta_{t}$  is generated by",
+        "bbox": [
+            76,
+            569,
+            468,
+            645
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\max  _ {\\delta_ {t} \\in [ - \\xi , \\xi ]} \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t - 1}\\right), \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
+            655,
+            468,
+            680
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\theta_{t - 1}$  is fixed in generating  $\\delta_t$ .",
+        "bbox": [
+            76,
+            689,
+            316,
+            704
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the practical implementation of Eq. (8), storing and computing  $\\mathcal{L}(x_{t - 1}^{\\prime},\\theta_{t - 1})$  and  $\\mathcal{L}(x,\\theta_{t - 1})$  can consume a significant amount of memory. To overcome this challenge, we introduce  $u_{t - 1}^{\\prime}$  and  $u_{t - 1}$  to replace these terms, respectively.  $u_{t - 1}^{\\prime} = \\mathbb{E}_{(x,y)\\sim D}\\mathcal{L}(x_{t - 1}^{\\prime},\\theta_{t - 1})$  and  $u_{t - 1} = \\mathbb{E}_{(x,y)\\sim D}\\mathcal{L}(x,\\theta_{t - 1})$  denote the mathematical expectation of loss in the  $t - 1_{\\mathrm{th}}$  training epoch.",
+        "bbox": [
+            76,
+            704,
+            468,
+            809
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We observe that training instability is primarily caused by overfitting or underfitting of small amounts of data. Thus, in Eq. (8), the additional loss term is only applied to partial data selected by the crafted condition  $\\mathcal{C}(\\cdot)$ . Notably, exceptions in  $\\mathcal{L}(x,\\theta)$  and  $\\mathcal{L}(x',\\theta)$  occur simultaneously during training. Hence,  $\\mathcal{L}(x_t',\\theta_t)$  and  $\\mathcal{L}(x_t,\\theta_t)$  share",
+        "bbox": [
+            75,
+            810,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the same condition.  $\\mathcal{C}$  is constructed by the distance between the pointwise loss  $\\mathcal{L}(x,\\theta_t)$  and the mean value  $u_{t - 1}$ . This is because over-fitted or under-fitted data often yield excessively high or low classification losses.",
+        "bbox": [
+            496,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C} (x) = \\left(\\left| \\mathcal {L} \\left(x, \\theta_ {t}\\right) - u _ {t - 1} \\right| \\geq \\gamma_ {t}\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            581,
+            165,
+            890,
+            181
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\gamma_{t} (\\gamma_{t} \\geq 0)$  represents the convergence stride to select abnormal data. It is crucial to choose an appropriate value for  $\\gamma_{t}$  to ensure effective training. When  $\\gamma_{t} = 0$ , the adversarial training process may fail to converge as it forces the predictions of all samples to remain unchanged. On the other hand, catastrophic overfitting occurs when  $\\gamma_{t} = \\infty$ , leading to undesirable outcomes. Considering that the loss difference  $d_{t-1}(d_{t-1} = |u_{t-1} - u_{t-2}|)$  between two adjacent epochs tends to decrease non-linearly,  $\\gamma_{t}$  should be a variable that varies during the training process.",
+        "bbox": [
+            496,
+            186,
+            890,
+            338
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\gamma_ {t} = \\min  \\left(\\max  \\left(d _ {t - 1}, \\gamma_ {\\text {m i n}}\\right), \\gamma_ {\\text {m a x}}\\right), \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            573,
+            353,
+            890,
+            369
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\gamma_{min}$  and  $\\gamma_{max}$  are hyper-parameters.  $\\gamma_{max}$  controls the maximum convergence speed.  $\\gamma_{min}$  ensures that the training process is not too smooth when  $d_{t - 1} \\to 0$ .",
+        "bbox": [
+            496,
+            375,
+            890,
+            419
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Example-based ConvergeSmooth. This approach adds the constraint individually to each sample, described as",
+        "bbox": [
+            496,
+            420,
+            890,
+            450
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C S} ^ {E} (t) = w _ {1} \\cdot \\left| \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) - u _ {t - 1} ^ {\\prime} \\right| + w _ {2} \\cdot \\left| \\mathcal {L} \\left(x, \\theta_ {t}\\right) - u _ {t - 1} \\right|, \\\\ s. t. \\quad | \\mathcal {L} (x, \\theta_ {t}) - u _ {t - 1} | > \\gamma_ {t}. \\tag {12} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Batch-based ConvergeSmooth. Likewise, we can apply the complementary constraint to a data batch,",
+        "bbox": [
+            496,
+            508,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C S} ^ {B} (t) = w _ {1} \\cdot \\left| u _ {B} ^ {\\prime} - u _ {t - 1} ^ {\\prime} \\right| + w _ {2} \\cdot \\left| u _ {B} - u _ {t - 1} \\right|, \\tag {13} \\\\ s. t. \\quad | u _ {B} - u _ {t - 1} | > \\gamma_ {t}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            545,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $u_B^\\prime = \\mathbb{E}_{(x,y)\\sim B}\\mathcal{L}(x_t^\\prime ,\\theta_t),u_B = \\mathbb{E}_{(x,y)\\sim B}\\mathcal{L}(x,\\theta_t).$",
+        "bbox": [
+            500,
+            590,
+            879,
+            607
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Weight centralization. To mitigate the problem of manual parameter tuning, we introduce the weight centralization without requiring extra hyperparameters other than the coefficient  $w_{3}$ ,  $|\\theta_t - \\theta_{t-1}| = 0 \\rightarrow |\\mathcal{L}(x, \\theta_t) - \\mathcal{L}(x, \\theta_{t-1})| = 0$ ,",
+        "bbox": [
+            496,
+            607,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {C S} ^ {W} (t) = w _ {3} \\cdot | | \\theta_ {t} - \\frac {1}{l e n (\\phi)} \\cdot \\sum_ {j \\in \\phi} \\theta_ {j} | | _ {p}, \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            558,
+            676,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\| \\cdot \\|_p$  means the p-norm function  $(p = 2)$ , and  $\\phi$  denotes a set of previous model weights. The model weights  $\\theta_t$  are restricted to the center  $\\frac{1}{len(\\phi)} \\cdot \\sum_{j \\in \\phi} \\theta_j$ . The reasons behind Eq. (14) are: 1) The initial training process is stable, as indicated in Fig. 1; 2) Models at different training epochs tend to have similar weights after convergence [37].",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Experimental Results",
+        "text_level": 1,
+        "bbox": [
+            496,
+            821,
+            705,
+            838
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental settings",
+        "text_level": 1,
+        "bbox": [
+            500,
+            847,
+            702,
+            863
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Details. To demonstrate the effectiveness of the proposed method, we conduct comprehensive experiments on",
+        "bbox": [
+            496,
+            869,
+            890,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4723",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/c3c8521d1b76e9ae3048ce466e562f5ecf5e2d23f0d08eee2dc7d9aa12e229d8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">CIFAR10ξ</td><td>FGSM-RS</td><td>FGSM-MEP</td><td>B-RS</td><td>B-MEP</td></tr><tr><td>SQ↑</td><td rowspan=\"2\">16/255</td><td>19.74</td><td>22.15</td><td>28.83</td><td>29.97</td></tr><tr><td>SQ+RayS↑</td><td>18.72</td><td>20.96</td><td>27.08</td><td>28.45</td></tr></table>",
+        "bbox": [
+            78,
+            89,
+            470,
+            138
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/9cc78e2fd2dbaf9cd156da9d7c6544562d0cee308739e9288892cb3964e7ca6d.jpg",
+        "table_caption": [
+            "Table 1. Quantitative results of FAT methods against the Square and Ray-S attacks on CIFAR-10 with the backbone ResNet18."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>CIFAR10</td><td>Clean</td><td>8 255</td><td>10 255</td><td>12 255</td><td>16 255</td><td>SQ+RayS</td><td>Time</td></tr><tr><td>OAAT[1]</td><td>71.30</td><td>44.29</td><td>38.56</td><td>33.68</td><td>28.48</td><td>21.06</td><td>183</td></tr><tr><td>AWP[41]</td><td>78.86</td><td>35.91</td><td>32.70</td><td>29.89</td><td>26.95</td><td>19.36</td><td>134</td></tr><tr><td>ATES[4]</td><td>74.52</td><td>43.61</td><td>38.94</td><td>35.31</td><td>30.89</td><td>22.16</td><td>-</td></tr><tr><td>ExAT[30]</td><td>80.78</td><td>49.21</td><td>42.15</td><td>36.98</td><td>31.26</td><td>23.08</td><td>70</td></tr><tr><td>E-MEP</td><td>69.84</td><td>53.54</td><td>49.26</td><td>45.89</td><td>40.78</td><td>23.78</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>50.31</td><td>46.77</td><td>43.97</td><td>40.13</td><td>28.45</td><td>101</td></tr></table>",
+        "bbox": [
+            78,
+            191,
+            475,
+            303
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Quantitative results of methods against various levels of perturbation with ResNet18 as the backbone and CIFAR-10 as the dataset.  $\\sharp$  denotes the PGD-10 attack.",
+        "bbox": [
+            75,
+            311,
+            470,
+            354
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "several benchmark datasets, i.e. CIFAR-10 [20], CIFAR-100 [20], and Tiny ImageNet [7].",
+        "bbox": [
+            76,
+            367,
+            468,
+            398
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following previous works [40, 23, 49, 42], we adopt ResNet18 [13] as the backbone on the CIFAR-10 and CIFAR-100, and choose PreActResNet18 [14] on the Tiny ImageNet. In all experiments, models are optimized using the SGD optimizer with a batch size of 128, weight decay of 5e-4, and momentum of 0.9. The initial learning rates on CIFAR-10, CIFAR-100, and Tiny ImageNet are set as 0.1, 0.1, and 0.01, respectively. Then, we optimize models with a total training epoch of 110 and decay the learning rate at the  $100_{\\mathrm{th}}$  and  $105_{\\mathrm{th}}$  epoch with a factor of 0.1.",
+        "bbox": [
+            75,
+            398,
+            468,
+            549
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We apply the proposed ConvergeSmooth in combination with two attack initialization methods on CIFAR-10 and CIFAR-100, FGSM-RS [40] and FGSM-MEP [42]. Additionally, for the Tiny ImageNet, we use FGSM-BP [42] as the initialization method. As mentioned in [42], FGSM-MEP requires consuming memory to store the previous adversarial perturbations, which limits its application on large datasets. Regarding the hyperparameters, we set  $\\gamma_{max}$  in Eq. (11) as 0.03, 0.06, and 0.03 for CIFAR-10, CIFAR-100, and Tiny ImageNet, respectively.  $\\gamma_{max} = 1.5 \\cdot \\gamma_{min}$  and  $\\xi = 16/255$ . Specific details of hyperparameter settings for  $w_{1 \\sim 3}$  are given in the supplement. All experiments are conducted on a single GeForce RTX 3090 GPU.",
+        "bbox": [
+            75,
+            550,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We include advanced FAT methods as baselines, namely FGSM-RS [40], GradAlign [2], ZeroGrad [10], NuAT [36], ATAS [16], and FGSM-MEP [42].",
+        "bbox": [
+            76,
+            748,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. We follow [40, 16] and adopt FGSM [11], PGD-10 [25], PGD-20 [25], PGD-50 [25], C&W [3], APGD-CE [6] and Autoattack (AA) [6] to evaluate the adversarial robustness of models. PGD-n represents the PGD attack with n iterations. Autoattack combines APGD-CE and APGD-T (targeted APGD) as well as two complementary attacks (FAB [9] and Square attack [26]).",
+        "bbox": [
+            75,
+            795,
+            468,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3e97564525e8fbc6ed20f5e85e150c8587a20b3828877176d39ffb9478255b35.jpg",
+        "image_caption": [
+            "Figure 2. The training process of various FAT methods (PGD-10,  $\\xi = 16 / 255$ ) on CIFAR-10."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            514,
+            90,
+            870,
+            300
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The training easily exhibits fluctuations, and thus individual results can not objectively reflect the performance of methods. For each method, we repeat the training process three times and report the average evaluation results of the best model across the three runs (mbest). Additionally, the supplement includes the best results (best) and the average evaluation of the final model from the three runs (mfinal).",
+        "bbox": [
+            496,
+            345,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the following section, 'W-\\*', 'E-\\*', and 'B-\\*' mean 'weight centralization', 'example-based ConvergeSmooth', and 'batch-based ConvergeSmooth', respectively.",
+        "bbox": [
+            498,
+            452,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Significance of the Results",
+        "text_level": 1,
+        "bbox": [
+            500,
+            511,
+            736,
+            527
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Before evaluating the adversarial robustness of trained models, we demonstrate the significance of the results [1]. Specifically, we show that adversarial attacks with  $\\xi = 16/255$  rarely change the true label of input. 1) We generate adversarial examples for the FGSM-RS, FGSM-MEP, and our proposed methods on CIFAR10 and CIFAR100 datasets with  $\\xi = 16/255$  using the non-targeted attacks such as FGSM, PGD, C&W, APGD-CE, and the targeted attack APGD-T. The majority of the generated examples retain their true labels; 2) Tab. 1 examines the robustness of models against an ensemble of the Square (SQ) [26] and Ray-S [5] attacks, as these attacks generate strong oracle-invariant examples [1]; 3) We generate adversarial training data with  $\\xi = 16/255$  and test the robustness on various levels of perturbation. Tab. 2 provide comparative experiments between our proposed method and other AT techniques, including OAAT [1], ExAT [30], ATES [4] and AWP [41]. It is important to note that we re-implement these AT methods and apply them in the context of FAT. Overall, our methods achieve optimal performance on both oracle-invariant attacks and classical evaluation attacks. Namely, the classical evaluation attacks used in  $\\xi = 8/255$  are reliable and significant even when the value of  $\\xi$  is increased to 16/255.",
+        "bbox": [
+            496,
+            537,
+            890,
+            883
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Notably, our methods are plugged into FGSM-RS and",
+        "bbox": [
+            517,
+            885,
+            890,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "4724",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/65f4e652e24f31e3fc58298079377a3bb2b83eacc7971aa6ffe90043c2e1b25d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td colspan=\"2\">PGD-AT [29]</td><td>65.30</td><td>46.31</td><td>40.73</td><td>35.08</td><td>33.92</td><td>30.84</td><td>33.08</td><td>26.29</td><td>370</td></tr><tr><td colspan=\"2\">FGSM-RS [40]</td><td>50.12</td><td>38.28</td><td>26.13</td><td>21.55</td><td>20.43</td><td>18.96</td><td>19.40</td><td>14.84</td><td>67</td></tr><tr><td colspan=\"2\">GradAlign [2]</td><td>58.17</td><td>39.87</td><td>33.12</td><td>26.81</td><td>24.99</td><td>22.63</td><td>23.98</td><td>17.02</td><td>135</td></tr><tr><td colspan=\"2\">ZeroGrad [10]</td><td>74.16</td><td>43.96</td><td>32.67</td><td>21.98</td><td>18.37</td><td>20.76</td><td>16.44</td><td>12.07</td><td>67</td></tr><tr><td rowspan=\"3\">Ours</td><td>W-RS</td><td>70.66</td><td>45.51</td><td>36.50</td><td>27.51</td><td>24.75</td><td>23.97</td><td>23.38</td><td>17.14</td><td>71</td></tr><tr><td>E-RS</td><td>62.38</td><td>42.07</td><td>36.78</td><td>30.80</td><td>28.90</td><td>23.64</td><td>27.71</td><td>17.55</td><td>77</td></tr><tr><td>B-RS</td><td>65.42</td><td>45.94</td><td>37.54</td><td>30.01</td><td>27.85</td><td>26.28</td><td>26.52</td><td>19.43</td><td>75</td></tr><tr><td colspan=\"2\">NuAT [36]</td><td>74.62</td><td>44.92</td><td>35.22</td><td>25.93</td><td>23.67</td><td>24.07</td><td>22.37</td><td>18.43</td><td>101</td></tr><tr><td colspan=\"2\">ATAS* [16]</td><td>64.11</td><td>-</td><td>31.39</td><td>-</td><td>28.15</td><td>-</td><td>-</td><td>21.09</td><td>-</td></tr><tr><td colspan=\"2\">FGSM-MEP [42]</td><td>53.32</td><td>36.24</td><td>31.85</td><td>27.28</td><td>26.56</td><td>22.10</td><td>26.08</td><td>18.98</td><td>92</td></tr><tr><td rowspan=\"2\">Ours</td><td>E-MEP</td><td>69.84</td><td>47.18</td><td>40.90</td><td>34.17</td><td>32.72</td><td>22.69</td><td>31.12</td><td>17.74</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>45.48</td><td>40.13</td><td>34.21</td><td>32.95</td><td>28.19</td><td>32.04</td><td>23.68</td><td>101</td></tr></table>",
+        "bbox": [
+            112,
+            87,
+            857,
+            294
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/c214d09220b1bedfc314bf352f31095c408c34053f5df0faea46d6167c346efa.jpg",
+        "table_caption": [
+            "Table 3. Quantitative results of various methods ( $\\xi = 16/255$ ) on the CIFAR-10 with ResNet18 as the backbone. 'ATAS*' is the result of ATAS in [16], which is superior to our reproduction. We train each method three times. The results represent the evaluation average between the best models of three training processes. Weight centralization and regularization in MEP do not work together."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Budgets (ξ)</td><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td rowspan=\"4\">12/255</td><td>GradAlign [2]</td><td>66.52</td><td>43.06</td><td>31.66</td><td>27.95</td><td>26.04</td><td>27.05</td><td>25.99</td><td>21.65</td><td>135</td></tr><tr><td>NuAT [36]</td><td>72.79</td><td>51.80</td><td>41.75</td><td>38.60</td><td>37.54</td><td>35.99</td><td>36.71</td><td>32.01</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>74.71</td><td>52.05</td><td>38.45</td><td>36.35</td><td>35.52</td><td>33.05</td><td>33.4</td><td>27.23</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>72.63</td><td>54.40</td><td>45.23</td><td>42.85</td><td>42.14</td><td>36.81</td><td>41.62</td><td>33.26</td><td>101</td></tr><tr><td rowspan=\"4\">10/255</td><td>GradAlign [2]</td><td>83.10</td><td>55.23</td><td>36.58</td><td>30.47</td><td>28.64</td><td>31.01</td><td>26.51</td><td>23.84</td><td>135</td></tr><tr><td>NuAT [36]</td><td>75.82</td><td>55.94</td><td>45.54</td><td>43.92</td><td>43.42</td><td>41.39</td><td>42.91</td><td>38.85</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>83.43</td><td>59.51</td><td>42.76</td><td>39.28</td><td>37.33</td><td>37.26</td><td>35.91</td><td>32.52</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>75.96</td><td>57.26</td><td>47.25</td><td>45.98</td><td>45.66</td><td>41.00</td><td>45.26</td><td>39.20</td><td>101</td></tr></table>",
+        "bbox": [
+            78,
+            358,
+            895,
+            500
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/9602126751f6ae067f4fde2f01bdf75ae02067184961dfc9aa10603e85ed93dc.jpg",
+        "table_caption": [
+            "Table 4. Quantitative results of FAT methods on various  $\\xi$  with ResNet18 as the backbone and CIFAR-10 as the dataset. Models are trained and evaluated under the same  $\\xi$  . The number in bold indicates the best."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ξ = 16/255</td><td colspan=\"2\">CIFAR10</td><td colspan=\"2\">CIFAR100</td><td>Time</td></tr><tr><td>Methods</td><td>Clean</td><td>AA</td><td>Clean</td><td>AA</td><td>hours</td></tr><tr><td>GradAlign [2]</td><td>55.58</td><td>13.45</td><td>35.93</td><td>7.13</td><td>8.79</td></tr><tr><td>NuAT [36]</td><td>74.25</td><td>13.19</td><td>20.48</td><td>7.30</td><td>7.66</td></tr><tr><td>FGSM-MEP [42]</td><td>65.56</td><td>15.43</td><td>20.69</td><td>6.73</td><td>6.15</td></tr><tr><td>B-MEP (Ours)</td><td>69.94</td><td>24.27</td><td>48.64</td><td>12.05</td><td>6.72</td></tr></table>",
+        "bbox": [
+            94,
+            559,
+            454,
+            655
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 5. The adversarial accuracy of various FAT methods with WideResNet34-10 as the backbone.",
+        "bbox": [
+            76,
+            664,
+            468,
+            691
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "FGSM-MEP, which are fitted to the distribution of adversarial examples. Instead, methods such as OAAT are fitted to the distribution of benign samples and perform better on clean accuracy. Therefore, we use the settings as in OAAT and then apply OAAT and our B-OAAT to the FAT task. B-OAAT realizes  $74.12\\%$ $(+2.82\\%)$  than OAAT) clean accuracy and  $25.39\\%$  (OAAT) on SQ+RayS.",
+        "bbox": [
+            75,
+            708,
+            468,
+            815
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Results on CIFAR-10",
+        "text_level": 1,
+        "bbox": [
+            76,
+            829,
+            277,
+            844
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct our initial experiments on CIFAR-10 using the ResNet18 backbone. The default  $\\xi$  is set to 16/255. Tab. 3 presents the main comparisons. The observations",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "are as follows: (1) Compared with previous FAT methods, the proposed approaches achieve optimal adversarial robustness against different attacks, e.g. B-RS outperforms all RS-based methods and B-MEP is superior to all other methods. Meanwhile, our methods exhibit similar performance to prior work in terms of clean classification accuracy. (2) B-MEP realizes adversarial robustness approaching PGD-AT, e.g. B-MEP performs  $32.95\\%$  robustness against the PGD-50 attack, only  $0.97\\%$  lower than PGD-AT; (3) As for time consumption, B-RS takes less time (75 minutes) than GradAlign (135 minutes) and NuAT (101 minutes). This is because ConvergeSmooth only requires the additional regularization when  $|u_{B} - u_{t - 1}| > \\gamma_{t}$  instead of adding constraints on all iterations. In addition, B-MEP (102 minutes) takes a bit more calculation cost than FGSM-MEP (92 minutes) but much less than PGD-AT (370 minutes). PGD-AT takes significantly longer than FAT works; (4) B-RS and B-MEP successfully prevent catastrophic overfitting, e.g. mfinal (in the supplement) only shows a slight reduction than mbest in terms of adversarial robustness.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Fig. 2 visualizes the training process of various FAT approaches. Compared with other methods, the proposed",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "4725",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b4439e353d9945ce0713420cfe24fc84534981a821a69a6bbc5fd46f1fc8d393.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td colspan=\"2\">PGD-AT</td><td>40.57</td><td>24.72</td><td>21.46</td><td>17.94</td><td>17.38</td><td>14.98</td><td>17.02</td><td>12.63</td><td>370</td></tr><tr><td colspan=\"2\">FGSM-RS [40]</td><td>30.12</td><td>15.24</td><td>12.69</td><td>10.25</td><td>9.79</td><td>8.45</td><td>9.57</td><td>6.90</td><td>67</td></tr><tr><td colspan=\"2\">GradAlign [2]</td><td>31.91</td><td>15.71</td><td>12.56</td><td>10.28</td><td>9.71</td><td>8.22</td><td>9.47</td><td>6.61</td><td>135</td></tr><tr><td colspan=\"2\">ZeroGrad [10]</td><td>47.31</td><td>23.58</td><td>17.60</td><td>12.85</td><td>11.87</td><td>11.62</td><td>11.01</td><td>7.94</td><td>67</td></tr><tr><td rowspan=\"3\">Ours</td><td>W-RS</td><td>41.97</td><td>26.30</td><td>19.09</td><td>14.77</td><td>13.72</td><td>12.82</td><td>13.36</td><td>9.67</td><td>72</td></tr><tr><td>E-RS</td><td>41.09</td><td>22.33</td><td>18.78</td><td>15.19</td><td>14.43</td><td>12.00</td><td>13.91</td><td>9.50</td><td>78</td></tr><tr><td>B-RS</td><td>41.47</td><td>25.98</td><td>19.44</td><td>15.36</td><td>14.34</td><td>12.91</td><td>13.71</td><td>9.90</td><td>76</td></tr><tr><td colspan=\"2\">NuAT [36]</td><td>31.42</td><td>20.39</td><td>16.15</td><td>13.87</td><td>13.29</td><td>11.12</td><td>12.25</td><td>8.32</td><td>101</td></tr><tr><td colspan=\"2\">ATAS [16]</td><td>55.63</td><td>30.35</td><td>15.31</td><td>10.28</td><td>8.49</td><td>10.97</td><td>6.30</td><td>5.05</td><td>70</td></tr><tr><td colspan=\"2\">FGSM-MEP [42]</td><td>21.39</td><td>13.00</td><td>11.37</td><td>9.93</td><td>9.76</td><td>7.28</td><td>9.58</td><td>6.36</td><td>92</td></tr><tr><td rowspan=\"2\">Ours</td><td>E-MEP</td><td>44.00</td><td>24.46</td><td>20.59</td><td>17.11</td><td>16.59</td><td>13.37</td><td>16.05</td><td>10.97</td><td>106</td></tr><tr><td>B-MEP</td><td>41.86</td><td>24.86</td><td>20.84</td><td>17.30</td><td>16.59</td><td>13.96</td><td>16.25</td><td>11.38</td><td>102</td></tr></table>",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/539f6af5cf612e1f4e4d111120cfdf750ae97ab0bd7105ceaf30721e19141bd8.jpg",
+        "table_caption": [
+            "Table 6. Quantitative results of various methods  $\\left( {\\xi  = {16}/{255}}\\right)$  with ResNet18 as the backbone on CIFAR-100."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (hour)↓</td></tr><tr><td>PGD-AT</td><td>32.52</td><td>16.47</td><td>13.40</td><td>10.63</td><td>10.24</td><td>7.95</td><td>10.00</td><td>6.41</td><td>67.2</td></tr><tr><td>FGSM-RS [40]</td><td>27.48</td><td>12.46</td><td>9.59</td><td>6.97</td><td>6.47</td><td>4.99</td><td>6.19</td><td>3.63</td><td>10.5</td></tr><tr><td>GradAlign [2]</td><td>28.65</td><td>13.80</td><td>10.40</td><td>7.78</td><td>7.08</td><td>5.75</td><td>6.59</td><td>3.90</td><td>20.9</td></tr><tr><td>ZeroGrad [10]</td><td>34.66</td><td>12.26</td><td>8.22</td><td>5.29</td><td>4.82</td><td>3.71</td><td>4.23</td><td>2.21</td><td>10.5</td></tr><tr><td>NuAT [36]</td><td>35.24</td><td>15.52</td><td>12.07</td><td>8.81</td><td>8.13</td><td>6.29</td><td>7.68</td><td>4.27</td><td>24.6</td></tr><tr><td>FGSM-BP [42]</td><td>20.02</td><td>10.18</td><td>8.38</td><td>6.98</td><td>6.77</td><td>4.56</td><td>6.57</td><td>3.62</td><td>14.3</td></tr><tr><td>B-BP (Ours)</td><td>33.51</td><td>16.32</td><td>12.92</td><td>9.72</td><td>9.23</td><td>7.26</td><td>9.32</td><td>5.95</td><td>15.4</td></tr></table>",
+        "bbox": [
+            120,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 7. Quantitative results of various methods  $\\left( {\\xi  = {16}/{255}}\\right)$  with PreActResNet18 as the backbone on Tiny ImageNet.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "B-RS achieves optimal training stability and adversarial robustness, e.g. the classification accuracy of our method fluctuates slightly during three adversarial training sessions.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Various budgets. Similar experiments are performed for budgets 10/255 and 12/255. Details are given in Tab. 4. It is evident that the proposed method achieves optimal adversarial robustness across various perturbation budgets.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Various networks. We then adopt WideResNet34 with a width factor of 10 [47] as the backbone. The results are given in Tab. 5. Our proposed B-MEP also prevents the wider architectures from catastrophic overfitting.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Results on CIFAR-100",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The results on CIFAR-100 with the backbone ResNet-18 are presented in Tab. 6. (1) FAT methods perform similar training consumption on CIFAR-10 and CIFAR-100 as two datasets contain the same number and size of images; (2) All proposed methods can realize stable adversarial training, as evidenced by the comparable results of mbest and mfinal (in the supplement); (3) Among the RS-based FAT works, B-RS and E-RS achieve the best and second-best adversarial robustness against different attacks; (4) B-MEP outperforms all other FAT methods; (5) Although B-MEP performs slightly worse than PGD-AT, its training process is approximately 3.5 times faster than this competitor.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Results on Tiny ImageNet",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on the Tiny ImageNet using the PreActResNet18 backbone to demonstrate the scalability of the proposed method to large datasets. The results are given in Tab. 7. B-BP achieves higher robustness among the FAT methods and comparable robustness to PGD-AT. As for training efficiency, B-BP (15.4 hours) requires slightly more computational cost than FGSM-BP (14.3 hours), but significantly less time than PGD-AT (67.2 hours).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.6. Ablation studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In the following, B-RS is selected as the backbone. Figs. 3 and 4 conduct ablation studies on  $\\gamma_{max}$  and  $\\gamma_{max} / \\gamma_{min}$  respectively. In Fig. 3, the classification accuracy of both benign and adversarial examples increases with  $\\gamma_{max}$ . However, the model trained with a large  $\\gamma_{max}$  ( $>0.09$ ) suffers from catastrophic overfitting. Fig. 4 shows that the model with  $\\gamma_{max} / \\gamma_{min} = 1.5$  achieves optimal robustness.  $\\gamma_{max} / \\gamma_{min} = 1$  denotes the static convergence stride. All models can be trained stably when  $\\gamma_{max} = 0.06$ .",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Tabs. 8 and 9 provide the results of comparative experiments on  $w_{1}$  and  $w_{2}$  respectively. We empirically set  $w_{2}$  to 1 since too small  $w_{2}$  cannot prevent overfitting and too large  $w_{2}$  will affect the performance. In Tab. 8,  $w_{1} = 0$  achieves optimal adversarial robustness on CIFAR100 and",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "4726",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/0dab9e0d6a952d662975b0a66f009a181a37b96231ffb04234a75806a79ef74a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>w1</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Stability</td></tr><tr><td rowspan=\"5\">CIFAR100</td><td>0.0</td><td>48.13</td><td>32.13</td><td>24.25</td><td>22.67</td><td>22.21</td><td>19.04</td><td>21.29</td><td>15.28</td><td>★★★</td></tr><tr><td>0.3</td><td>46.08</td><td>30.58</td><td>23.06</td><td>21.62</td><td>21.22</td><td>17.79</td><td>20.44</td><td>15.22</td><td>★★★</td></tr><tr><td>0.5</td><td>44.04</td><td>29.96</td><td>22.64</td><td>21.34</td><td>20.99</td><td>17.55</td><td>19.16</td><td>13.84</td><td>★★★</td></tr><tr><td>0.7</td><td>43.07</td><td>28.61</td><td>22.01</td><td>20.84</td><td>20.32</td><td>16.87</td><td>18.98</td><td>13.47</td><td>★★★</td></tr><tr><td>0.9</td><td>40.45</td><td>21.05</td><td>21.62</td><td>20.54</td><td>20.15</td><td>16.33</td><td>18.91</td><td>13.53</td><td>★★★</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c99ac63b3639ee7e6daaff8d9f047762c021432397fc0f6553a0a2b1593e9ad7.jpg",
+        "table_caption": [
+            "Table 8. Quantitative results of the proposed method on various  $w_{1}$  with ResNet18 as the backbone and the perturbation budget 12/255. 'Stability' represents the number of times the model is stable in three training repetitions.  $\\gamma_{max}$  and  $w_{2}$  are set to 0.03 and 1, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>w2</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Stability</td></tr><tr><td rowspan=\"4\">CIFAR100</td><td>0.5</td><td>36.79</td><td>23.97</td><td>18.60</td><td>17.51</td><td>17.23</td><td>14.65</td><td>16.28</td><td>12.23</td><td>-</td></tr><tr><td>0.7</td><td>37.31</td><td>24.36</td><td>18.56</td><td>17.37</td><td>17.26</td><td>14.46</td><td>15.96</td><td>11.54</td><td>-</td></tr><tr><td>1.0</td><td>48.13</td><td>32.13</td><td>24.25</td><td>22.67</td><td>22.21</td><td>19.04</td><td>21.29</td><td>15.28</td><td>★★★</td></tr><tr><td>1.3</td><td>44.84</td><td>30.42</td><td>23.31</td><td>21.72</td><td>21.31</td><td>18.36</td><td>19.64</td><td>14.72</td><td>★★★</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 9. Quantitative results on various  ${w}_{2}\\left( {{\\gamma }_{max} = {0.03}}\\right.$  and  ${w}_{1} = 0)$  with ResNet18 as the backbone and  $\\xi  = {12}/{255}$  .",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b66648bc0d3b8cb0ffe73994f5c9c86e4af5bbb2d70966398399a8e131e75277.jpg",
+        "image_caption": [
+            "ResNet18 trained with ConvergeSmooth-RS on CIFAR-100",
+            "Figure 3. Ablation study of  $\\gamma_{max}(\\gamma_{max} / \\gamma_{min} = 1.5)$ . We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10,  $\\xi = 16/255$ ) on CIFAR-100."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            375,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "all settings accomplish stable FAT. According to Eqs. (7) and (8), if  $w_{1} \\neq 0$ , for the data  $x$  which satisfies  $\\mathcal{C}(x) = 1$ ,  $\\mathcal{L}(x_t', \\theta_t)$  is assigned with higher weights  $(1 + w_{1})$  or lower weights  $(1 - w_{1})$ , causing the model to excessively prioritize or neglect this portion of the data. This may weaken the performance of models. However, for Tiny ImageNet, models suffer catastrophic overfitting at  $w_{1} = 0$ . Then, we gradually increase  $w_{1}$  from 0.3 with a stride of 0.2 until the FAT process becomes stable. In addition, our weight centralization method only introduces a balance coefficient  $w_{3}$ .  $w_{3}$  is set to 0.1 since catastrophic overfitting happens when  $w_{3} = 0$  and classification performance is degraded when  $w_{3} = 0.2$ .",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we tackle the issue of catastrophic overfitting by focusing on the convergence stability of loss func",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b22b73832bd1331752bbefd95f835fb0c27d3622c1c6426d3618be637481b38b.jpg",
+        "image_caption": [
+            "ResNet18 trained with ConvergeSmooth-RS on CIFAR-100",
+            "Figure 4. Ablation study of  $\\gamma_{max} / \\gamma_{min}$  ( $\\gamma_{max} = 0.06$ ). We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10,  $\\xi = 16/255$ ) on CIFAR-100."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            373,
+            880,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "tions. Through experimental analysis, we find that this issue is accompanied by abnormal convergence behavior of losses. Motivated by this phenomenon, we propose complementary constraints, namely E-ConvergeSmooth and B-ConvergeSmooth, based on the adversarial training constraint. To alleviate the burden of parameter tuning, weight centralization is designed utilizing priors from previous epochs. Extensive experiments on different network architectures and datasets show that the proposed methods effectively solve catastrophic overfitting and exhibit superior robustness against various adversarial attacks.",
+        "bbox": [
+            496,
+            666,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments. This work was supported by the National Key R&D Program of China #2018AAA0102000 and the National Natural Science Foundation of China #62276046 and #U19B2039.",
+        "bbox": [
+            498,
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "4727",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
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+        "bbox": [
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+            514,
+            955
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+        "page_idx": 8
+    },
+    {
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+        "sub_type": "ref_text",
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+        ],
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+            "attack using generative model. In Proceedings of the AAAI Conference on Artificial Intelligence, 2021.",
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+            "[50] Wenqiang Zheng and Yan-Fu Li. Mc-fgsm: Black-box adversarial attack for deep learning system. In 2021 IEEE International Symposium on Software Reliability Engineering Workshops (ISSREW), pages 154-159. IEEE, 2021."
+        ],
+        "bbox": [
+            501,
+            92,
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+        "page_idx": 9
+    }
+]
\ No newline at end of file
diff --git a/2023/Fast Adversarial Training with Smooth Convergence/23b31082-56d8-432b-80e3-85fc235c4ff5_model.json b/2023/Fast Adversarial Training with Smooth Convergence/23b31082-56d8-432b-80e3-85fc235c4ff5_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..419dec627da06dfcfb37c344f25e25ef3484cd33
--- /dev/null
+++ b/2023/Fast Adversarial Training with Smooth Convergence/23b31082-56d8-432b-80e3-85fc235c4ff5_model.json	
@@ -0,0 +1,2464 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
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+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.22,
+                0.131,
+                0.753,
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+            "angle": 0,
+            "content": "Fast Adversarial Training with Smooth Convergence"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.258,
+                0.194,
+                0.713,
+                0.213
+            ],
+            "angle": 0,
+            "content": "Mengnan Zhao, Lihe Zhang*, Yuqiu Kong and Baocai Yin"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.326,
+                0.224,
+                0.644,
+                0.242
+            ],
+            "angle": 0,
+            "content": "Dalian University of Technology, China"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.197,
+                0.245,
+                0.772,
+                0.259
+            ],
+            "angle": 0,
+            "content": "zmnwelcome@mail.dlut.edu.cn，{zhanglihe，yqkong，ybc}@dlut.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.304,
+                0.314,
+                0.32
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.336,
+                0.473,
+                0.699
+            ],
+            "angle": 0,
+            "content": "Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, i.e. the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.729,
+                0.21,
+                0.745
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.755,
+                0.47,
+                0.878
+            ],
+            "angle": 0,
+            "content": "Recent breakthroughs in deep learning [21, 32] have aroused researchers' interest in the security of neural networks [45, 48, 39]. In particular, the advanced research proves the vulnerability of deep models to adversarial attacks [8, 11, 27]. For instance, tiny crafted perturbations can fool models in various fields into making wrong decisions [15, 50, 35, 24]. Considering the security risks brought by adversarial attacks [18, 46, 33, 44], there is a quickly grow"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.305,
+                0.892,
+                0.351
+            ],
+            "angle": 0,
+            "content": "ing body of work [43, 46, 18] on improving the adversarial robustness of neural networks. Among them, adversarial training is widely applied by practitioners [31, 12]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.353,
+                0.893,
+                0.504
+            ],
+            "angle": 0,
+            "content": "In recent years, projected gradient descent based adversarial training (PGD-AT) [25, 34] has been widely employed for its stability and effectiveness. However, this mechanism is computationally expensive. It requires multiple gradient descent steps to generate the adversarial training data [38]. An alternative of PGD-AT is the fast adversarial training (FAT) [28], which only adopts a single-step fast gradient sign method (FGSM) [11] to generate training data. Compared to PGD-AT, FAT can efficiently train models, but easily falls into catastrophic overfitting [40, 29]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.506,
+                0.895,
+                0.839
+            ],
+            "angle": 0,
+            "content": "A number of FAT methods have been proposed to mitigate catastrophic overfitting. For example, Wong et al. [40] use randomly initialized perturbations to enhance the diversity of adversarial perturbations. Based on it, Andriushchenko et al. [2] raise a complementary regularizer named GradAlign to maximize the gradient alignment between benign and adversarial examples explicitly. Similarly, NuAT [36] and FGSM-MEP [42] adopt nuclear norm or p-norm to regularize the adversarial training, thereby increasing the prediction alignment between benign and adversarial examples. However, the above methods can only resolve catastrophic overfitting within the limited perturbation budget (\\(\\xi \\leq 8/255\\)). \\(\\xi\\) specifies the perturbation degree of adversarial training data generated by various attacks. Besides, models trained by small perturbations are vulnerable to adversarial attacks with a large \\(\\xi\\), e.g. the models trained by NuAT and FGSM-MEP at \\(\\xi = 8/255\\) perform \\(53\\%\\) and \\(54\\%\\) robustness against the PGD-50 attack with \\(\\xi = 8/255\\), but only \\(22\\%\\) and \\(20\\%\\) robustness against the same attack with \\(\\xi = 16/255\\) respectively. Therefore, we aspire to prevent catastrophic overfitting to improve the adversarial robustness of neural models at larger perturbation budgets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "By analyzing adversarial training processes of representative work, we observe that catastrophic overfitting is usually accompanied by a slight fluctuation in the classification loss for benign samples and a sharp drop in the classification"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.221,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4720"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.168
+            ],
+            "angle": 0,
+            "content": "loss for adversarial examples. This motivates us to question whether a smooth loss convergence process is also a stable FAT process. Moreover, we find that an oscillating adversarial training phase may restart the FAT process after catastrophic overfitting. Fig. 1 shows the details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.168,
+                0.47,
+                0.363
+            ],
+            "angle": 0,
+            "content": "According to these observations, we introduce an oscillatory constraint that limits the difference in loss between adjacent training epochs, called ConvergeSmooth. A dynamic convergence stride of ConvergeSmooth is designed considering the nonlinear decay rate of loss functions. Inspired by the smoothness of loss convergence, we further verify the effect of the proposed weight centralization on model stability. Weight centralization refers to taking the weights average of the previously trained models as the convergence center of the current model weight. Our proposed methods are attack-agnostic and thus can be combined with existing adversarial strategies in FAT, such as FGSM-RS and FGSM-MEP, to evaluate their performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.364,
+                0.471,
+                0.56
+            ],
+            "angle": 0,
+            "content": "The contributions are summarized in four aspects: (1) We verify that previous FAT works still suffer from catastrophic overfitting at a large \\(\\xi\\) and then study catastrophic overfitting from the perspective of convergence instability of loss functions; (2) We propose a smooth convergence constraint, ConvergeSmooth, and design a dynamic convergence stride for it, to help various FAT methods avoid catastrophic overfitting on different perturbation budgets; (3) The weight centralization is proposed without introducing extra hyperparameters other than the loss balance coefficient to stabilize FAT; (4) Extensive experiments show that the proposed methods outperform the state-of-the-art FAT techniques in terms of efficiency, robustness, and stability."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.573,
+                0.219,
+                0.589
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.469,
+                0.705
+            ],
+            "angle": 0,
+            "content": "Adversarial attacks. Adversarial attacks are usually used to deceive deep-learning models. Goodfellow et al. [11] first discuss the adversarial attack (FGSM) within the classification task. They prove that adversarial examples \\( x' \\) generated by a single-step gradient backward can misclassify the model \\( f(\\cdot; \\theta) \\) with high confidence. \\( \\theta \\) denotes the fixed model weights. \\( x' \\) is generated by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.154,
+                0.713,
+                0.469,
+                0.731
+            ],
+            "angle": 0,
+            "content": "\\[\nx ^ {\\prime} = x + \\xi \\cdot \\operatorname {s g n} \\left(\\nabla_ {x} \\mathcal {L} (f (x; \\theta), y)\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.74,
+                0.469,
+                0.875
+            ],
+            "angle": 0,
+            "content": "where \\( x \\) is an input image, \\( \\xi \\) represents the perturbation budget, \\( \\operatorname{sgn}(\\cdot) \\) means the sign function, \\( \\mathcal{L}(\\cdot) \\) is usually the cross-entropy loss, \\( \\nabla_{x}\\mathcal{L}(\\cdot) \\) calculates the gradient of loss at \\( x \\), and \\( y \\) denotes the ground truth labels of \\( x \\). Following the FGSM [11], researchers propose a series of attack methods based on the iterative gradient backward, e.g. I-FGSM [22], MIM [8], and PGD [25]. Taking the PGD attack as an example, the adversarial example \\( x_{t + 1}^{\\prime} \\) produced in the iteration \\( t + 1 \\) can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.105,
+                0.885,
+                0.469,
+                0.903
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t + 1} ^ {\\prime} = \\operatorname {c l i p} _ {\\xi} \\left(x _ {t} ^ {\\prime} + \\epsilon \\cdot \\operatorname {s g n} \\left(\\nabla_ {x _ {t} ^ {\\prime}} \\mathcal {L} \\left(f \\left(x _ {t} ^ {\\prime}; \\theta\\right), y\\right)\\right)\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "where \\(\\epsilon\\) denotes the single-step stride and \\(\\mathrm{clip}_{\\xi}\\) refers to projecting adversarial perturbations to a \\(\\xi\\)-ball."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.122,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "Adversarial training. Madry et al. [25] formalize the adversarial training as a min-max optimization problem,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.569,
+                0.163,
+                0.892,
+                0.188
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\theta} \\mathbb {E} _ {(x, y) \\sim D} [ \\max  _ {\\delta \\in [ - \\xi , \\xi ]} \\mathcal {L} (f \\left(x ^ {\\prime}; \\theta\\right), y) ], \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.198,
+                0.892,
+                0.304
+            ],
+            "angle": 0,
+            "content": "where \\( x' = x + \\delta \\), \\( \\delta \\) represents the adversarial perturbations generated by various attacks such as PGD and FGSM. \\( D \\) is the data generator. The internal maximization maximizes the classification loss to generate adversarial perturbations with fixed model weights. The external minimization minimizes the classification loss on the generated adversarial examples when optimizing the model weights."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.305,
+                0.892,
+                0.515
+            ],
+            "angle": 0,
+            "content": "Actually, there is a trade-off between computational efficiency and adversarial robustness in recent adversarial training methods. Compared to PGD-AT [25], FGSM-based fast adversarial training (FAT) accelerates the training process but damages the robustness of models for the problem of catastrophic overfitting [19, 17]. To mitigate this issue, Wong et.al [40] demonstrate that the FGSM with a random start strategy (FGSM-RS) can achieve comparable performance against the PGD-AT. ZeroGrad [10] zeroes the elements of gradient that are too small to craft the perturbations. enforces the model loss to increase with the increase in perturbation size. Besides, GradAlign [2] prevents catastrophic overfitting by maximizing the alignment between gradients of benign samples and adversarial examples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.516,
+                0.892,
+                0.726
+            ],
+            "angle": 0,
+            "content": "Similarly, NuAT [36] introduces a nuclear norm regularization between logits for benign and adversarial examples and uses the Bernoulli noise as the initial perturbation. ATAS [16] learns an instantiated adaptive step size that is inversely proportional to the gradient norm. It applies the adversarial perturbations from the previous epoch as the initialization of FGSM in the current training phase. In addition, Jia et al. [42] propose several prior-guided initialization methods to replace the random start strategy of FGSM-RS. Specifically, FGSM-BP adopts the adversarial perturbations from the previous batch as the attack initialization in the current batch. FGSM-MEP employs a momentum mechanism to combine all adversarial perturbations from the previous epochs to yield adversarial initialization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.727,
+                0.892,
+                0.833
+            ],
+            "angle": 0,
+            "content": "Although these FAT methods have resolved catastrophic overfitting at small perturbation budgets, they still suffer from catastrophic overfitting under larger perturbation budgets (e.g. \\(\\xi = 16 / 255\\)). Unlike these methods, we revisit the catastrophic overfitting problem from the perspective of loss convergence instability and prevent this exception by limiting the magnitude of loss fluctuations during training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.845,
+                0.673,
+                0.863
+            ],
+            "angle": 0,
+            "content": "3. Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we first study the performance of previous FAT methods when subjected to a large perturbation budget"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4721"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.15,
+                0.094,
+                0.317,
+                0.103
+            ],
+            "angle": 0,
+            "content": "(a) ResNet18 trained with FGSM-RS"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.104,
+                0.357,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.415,
+                0.094,
+                0.581,
+                0.103
+            ],
+            "angle": 0,
+            "content": "(b) ResNet18\\(_2\\) trained with FGSM-RS"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.359,
+                0.104,
+                0.621,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.678,
+                0.094,
+                0.845,
+                0.103
+            ],
+            "angle": 0,
+            "content": "(c) ResNet18 trained with FGSM-RS"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.623,
+                0.104,
+                0.886,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.15,
+                0.197,
+                0.318,
+                0.206
+            ],
+            "angle": 0,
+            "content": "(d) ResNet18 trained with GradAlign"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.206,
+                0.357,
+                0.297
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.413,
+                0.197,
+                0.583,
+                0.206
+            ],
+            "angle": 0,
+            "content": "(e) ResNet18\\(_2\\) trained with GradAlign"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.359,
+                0.206,
+                0.621,
+                0.297
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.678,
+                0.197,
+                0.845,
+                0.206
+            ],
+            "angle": 0,
+            "content": "(f) ResNet18 trained with GradAlign"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.623,
+                0.206,
+                0.886,
+                0.297
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.147,
+                0.299,
+                0.321,
+                0.308
+            ],
+            "angle": 0,
+            "content": "(g) ResNet18 trained with FGSM-MEP"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.308,
+                0.357,
+                0.407
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.411,
+                0.299,
+                0.584,
+                0.308
+            ],
+            "angle": 0,
+            "content": "(h) ResNet182 trained with FGSM-MEP"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.359,
+                0.308,
+                0.621,
+                0.407
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.677,
+                0.299,
+                0.846,
+                0.308
+            ],
+            "angle": 0,
+            "content": "(i) ResNet18 trained with FGSM-MEP"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.623,
+                0.308,
+                0.886,
+                0.407
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.417,
+                0.892,
+                0.46
+            ],
+            "angle": 0,
+            "content": "Figure 1. The training process of previous FAT methods with ResNet18 on CIFAR-10. Each FAT method is trained 3 times. \\(\\xi = 16 / 255\\). ADV-Loss and BEN-Loss denote the classification loss of models to adversarial and benign examples during training, respectively. ADV-Acc and BEN-Acc represent the classification accuracy of models to adversarial and benign examples during testing, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.477,
+                0.469,
+                0.523
+            ],
+            "angle": 0,
+            "content": "\\(\\xi\\). Then, the training processes of these methods have been analyzed for a better understanding of catastrophic overfitting. Finally, we detail the proposed methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.53,
+                0.43,
+                0.546
+            ],
+            "angle": 0,
+            "content": "3.1. Performance of FAT methods on a large \\(\\xi\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.553,
+                0.469,
+                0.598
+            ],
+            "angle": 0,
+            "content": "Previous FAT techniques avoid catastrophic overfitting at small \\(\\xi\\) (\\(\\xi \\leq 8/255\\)). Here, we investigate their performance on a large \\(\\xi\\) (\\(\\xi = 16/255\\) by default)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.469,
+                0.643
+            ],
+            "angle": 0,
+            "content": "FGSM-RS [40]: Based on Eq. (3), this method adopts the samples with uniformly random perturbations \\(\\delta_0\\sim\\) \\(\\mathcal{U}(-\\xi ,\\xi)\\) as the attack initialization of FGSM,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.177,
+                0.65,
+                0.451,
+                0.675
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\theta} \\mathbb {E} _ {(x, y) \\sim D} [ \\max  _ {\\delta_ {0} + \\delta \\in [ - \\xi , \\xi ]} \\mathcal {L} (f (x ^ {\\prime}; \\theta), y) ],\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.678,
+                0.469,
+                0.707
+            ],
+            "angle": 0,
+            "content": "\\[\nx ^ {\\prime} = x + \\delta_ {0} + \\delta \\quad s. t. \\quad x ^ {\\prime} \\in [ 0, 1 ], \\quad \\delta_ {0} \\sim \\mathcal {U} (- \\xi , \\xi). \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.709,
+                0.469,
+                0.753
+            ],
+            "angle": 0,
+            "content": "GradAlign [2]: This approach increases the gradient alignment between benign samples \\( x \\) and perturbed samples \\( x + \\delta_0 \\), which is denoted as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.093,
+                0.76,
+                0.468,
+                0.784
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbb {E} _ {(x, y) \\sim D} [ 1 - \\cos (\\nabla_ {x} \\mathcal {L} (x, \\theta), \\nabla_ {x + \\delta_ {0}} \\mathcal {L} (x + \\delta_ {0}, \\theta) ], \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.27,
+                0.78,
+                0.468,
+                0.796
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} (x, \\theta) = \\mathcal {L} (f (x; \\theta), y).\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.803,
+                0.468,
+                0.817
+            ],
+            "angle": 0,
+            "content": "\\(\\cos (\\cdot)\\) computes the cosine similarity between two matrices."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.818,
+                0.469,
+                0.878
+            ],
+            "angle": 0,
+            "content": "FGSM-MEP [42]: Different from FGSM-RS, this method generates the initialization perturbations \\(\\delta_0\\) based on all historical adversarial perturbations from the previous epochs and introduces a regularization expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.143,
+                0.885,
+                0.469,
+                0.903
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbb {E} _ {(x, y) \\sim D} [ | | f (x ^ {\\prime}; \\theta) - f (x + \\delta_ {0}; \\theta) | | _ {2} ^ {2} ], \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.477,
+                0.804,
+                0.493
+            ],
+            "angle": 0,
+            "content": "where \\(||\\cdot ||_2^2\\) denotes the squared \\(\\mathcal{L}_2\\) distance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.493,
+                0.892,
+                0.569
+            ],
+            "angle": 0,
+            "content": "Fig. 1 shows their detailed adversarial training processes of ResNet18 [13] on CIFAR-10 [20]. We find that they fall into catastrophic overfitting during the \\(5 \\sim 20_{\\mathrm{th}}\\), \\(40 \\sim 65_{\\mathrm{th}}\\) and \\(10 \\sim 15_{\\mathrm{th}}\\) epochs, respectively. Graphical analysis of various models and datasets is given in the supplement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.576,
+                0.748,
+                0.592
+            ],
+            "angle": 0,
+            "content": "3.2. Analysis of training process"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.705
+            ],
+            "angle": 0,
+            "content": "From Fig. 1, we discover several typical phenomena of catastrophic overfitting: 1) Change from a smooth convergence state to an irregular fluctuation state; 2) A slight change (increase or decrease) in the standard classification loss \\(\\mathcal{L}(x,\\theta)\\) and a rapid descent of the adversarial classification loss \\(\\mathcal{L}(x',\\theta)\\); 3) Rapid decline in the classification accuracy of adversarial examples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "After catastrophic overfitting, the methods depicted in Fig. 1 are capable of restarting a stable FAT process, even though catastrophic overfitting may occur again. The observed phenomena during the FAT restart are: 1) Change from an irregular fluctuation state to a smooth convergence state; 2) Rapid increase in both \\(\\mathcal{L}(x,\\theta)\\) and \\(\\mathcal{L}(x',\\theta)\\) after a period of decline; 3) Rapid decrease in the classification accuracy of benign samples, while the classification accuracy of adversarial examples experiences a rapid increase."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "On this basis, we can make the following conclusions. 1) \\(\\mathcal{L}(x,\\theta)\\) is more stable than \\(\\mathcal{L}(x^{\\prime},\\theta)\\) and models are prone to overfitting to adversarial perturbations; 2) Catastrophic overfitting is closely correlated to the convergence insta"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4722"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.091,
+                0.47,
+                0.138
+            ],
+            "angle": 0,
+            "content": "bility of adversarial training; 3) Exceptions in \\(\\mathcal{L}(x,\\theta)\\) and \\(\\mathcal{L}(x^{\\prime},\\theta)\\) occur simultaneously; 4) An oscillating adversarial training phase may trigger the FAT process to restart."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.146,
+                0.414,
+                0.162
+            ],
+            "angle": 0,
+            "content": "3.3. Smooth convergence for the stable FAT"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.169,
+                0.42,
+                0.184
+            ],
+            "angle": 0,
+            "content": "Next, we describe the proposed method in detail."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.185,
+                0.469,
+                0.35
+            ],
+            "angle": 0,
+            "content": "Why did previous methods fail to prevent catastrophic overfitting? Despite the improvement in diversity achieved through random initialization in FGSM-RS, models are still susceptible to overfitting adversarial perturbations. GradAlign and FGSM-MEP enhance the stability of adversarial training through the constraints in Eqs. (5) and (6), respectively. However, Eq. (5) may reduce the stability of \\(\\mathcal{L}(x,\\theta)\\). Meanwhile, the prediction probability \\(f(x + \\delta_0;\\theta)\\) in Eq. (6) is not the sweet spot to keep the FAT stable. Unlike these methods, we ensure the convergence stability of both \\(\\mathcal{L}(x,\\theta)\\) and \\(\\mathcal{L}(x',\\theta)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.351,
+                0.469,
+                0.442
+            ],
+            "angle": 0,
+            "content": "How can catastrophic overfitting be solved? Since the catastrophic overfitting is usually accompanied by a slight change in \\(\\mathcal{L}(x,\\theta)\\) and a sharp decline in \\(\\mathcal{L}(x',\\theta)\\), we consider a smooth loss convergence process to be a stable FAT process that resolves this issue. To this end, a complementary constraint \\(\\mathcal{L}_{CS}\\) for Eq. (3) is proposed,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.153,
+                0.452,
+                0.469,
+                0.475
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\theta_ {t}} \\mathbb {E} _ {(x, y) \\sim D} \\left[ \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) + \\mathcal {L} _ {C S} (t) \\right], \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.484,
+                0.469,
+                0.515
+            ],
+            "angle": 0,
+            "content": "which can limit the difference in losses between adjacent epochs, expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.124,
+                0.525,
+                0.469,
+                0.548
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {C S} (t) = w _ {1} \\cdot \\left| \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) - \\mathcal {L} \\left(x _ {t - 1} ^ {\\prime}, \\theta_ {t - 1}\\right) \\right| + \\tag {8}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.108,
+                0.544,
+                0.422,
+                0.559
+            ],
+            "angle": 0,
+            "content": "\\[\nw _ {2} \\cdot | \\mathcal {L} (x, \\theta_ {t}) - \\mathcal {L} (x, \\theta_ {t - 1}) |, \\quad s. t. \\quad \\mathcal {C} (x) = 1,\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.57,
+                0.469,
+                0.646
+            ],
+            "angle": 0,
+            "content": "where \\(\\theta_{t}\\) represents the model weights of the \\(t_{\\mathrm{th}}\\) training epoch. \\(w_{1}\\) and \\(w_{2}\\) are hyper-parameters, \\(w_{1}, w_{2} \\in [0,1]\\). \\(|\\cdot|\\) calculates the absolute value. \\(x_{t}^{\\prime} = x + \\delta_{0,t} + \\delta_{t}\\). \\(\\delta_{0,t}\\) can be replaced by various attack initialization perturbations and \\(\\delta_{t}\\) is generated by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.202,
+                0.656,
+                0.469,
+                0.681
+            ],
+            "angle": 0,
+            "content": "\\[\n\\max  _ {\\delta_ {t} \\in [ - \\xi , \\xi ]} \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t - 1}\\right), \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.69,
+                0.318,
+                0.705
+            ],
+            "angle": 0,
+            "content": "where \\(\\theta_{t - 1}\\) is fixed in generating \\(\\delta_t\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.705,
+                0.469,
+                0.81
+            ],
+            "angle": 0,
+            "content": "In the practical implementation of Eq. (8), storing and computing \\(\\mathcal{L}(x_{t - 1}^{\\prime},\\theta_{t - 1})\\) and \\(\\mathcal{L}(x,\\theta_{t - 1})\\) can consume a significant amount of memory. To overcome this challenge, we introduce \\(u_{t - 1}^{\\prime}\\) and \\(u_{t - 1}\\) to replace these terms, respectively. \\(u_{t - 1}^{\\prime} = \\mathbb{E}_{(x,y)\\sim D}\\mathcal{L}(x_{t - 1}^{\\prime},\\theta_{t - 1})\\) and \\(u_{t - 1} = \\mathbb{E}_{(x,y)\\sim D}\\mathcal{L}(x,\\theta_{t - 1})\\) denote the mathematical expectation of loss in the \\(t - 1_{\\mathrm{th}}\\) training epoch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We observe that training instability is primarily caused by overfitting or underfitting of small amounts of data. Thus, in Eq. (8), the additional loss term is only applied to partial data selected by the crafted condition \\(\\mathcal{C}(\\cdot)\\). Notably, exceptions in \\(\\mathcal{L}(x,\\theta)\\) and \\(\\mathcal{L}(x',\\theta)\\) occur simultaneously during training. Hence, \\(\\mathcal{L}(x_t',\\theta_t)\\) and \\(\\mathcal{L}(x_t,\\theta_t)\\) share"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "the same condition. \\(\\mathcal{C}\\) is constructed by the distance between the pointwise loss \\(\\mathcal{L}(x,\\theta_t)\\) and the mean value \\(u_{t - 1}\\). This is because over-fitted or under-fitted data often yield excessively high or low classification losses."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.582,
+                0.166,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {C} (x) = \\left(\\left| \\mathcal {L} \\left(x, \\theta_ {t}\\right) - u _ {t - 1} \\right| \\geq \\gamma_ {t}\\right), \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.188,
+                0.892,
+                0.339
+            ],
+            "angle": 0,
+            "content": "where \\(\\gamma_{t} (\\gamma_{t} \\geq 0)\\) represents the convergence stride to select abnormal data. It is crucial to choose an appropriate value for \\(\\gamma_{t}\\) to ensure effective training. When \\(\\gamma_{t} = 0\\), the adversarial training process may fail to converge as it forces the predictions of all samples to remain unchanged. On the other hand, catastrophic overfitting occurs when \\(\\gamma_{t} = \\infty\\), leading to undesirable outcomes. Considering that the loss difference \\(d_{t-1}(d_{t-1} = |u_{t-1} - u_{t-2}|)\\) between two adjacent epochs tends to decrease non-linearly, \\(\\gamma_{t}\\) should be a variable that varies during the training process."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.574,
+                0.354,
+                0.892,
+                0.371
+            ],
+            "angle": 0,
+            "content": "\\[\n\\gamma_ {t} = \\min  \\left(\\max  \\left(d _ {t - 1}, \\gamma_ {\\text {m i n}}\\right), \\gamma_ {\\text {m a x}}\\right), \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.376,
+                0.892,
+                0.42
+            ],
+            "angle": 0,
+            "content": "where \\(\\gamma_{min}\\) and \\(\\gamma_{max}\\) are hyper-parameters. \\(\\gamma_{max}\\) controls the maximum convergence speed. \\(\\gamma_{min}\\) ensures that the training process is not too smooth when \\(d_{t - 1} \\to 0\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.421,
+                0.892,
+                0.451
+            ],
+            "angle": 0,
+            "content": "Example-based ConvergeSmooth. This approach adds the constraint individually to each sample, described as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.458,
+                0.896,
+                0.508
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {C S} ^ {E} (t) = w _ {1} \\cdot \\left| \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) - u _ {t - 1} ^ {\\prime} \\right| + w _ {2} \\cdot \\left| \\mathcal {L} \\left(x, \\theta_ {t}\\right) - u _ {t - 1} \\right|, \\\\ s. t. \\quad | \\mathcal {L} (x, \\theta_ {t}) - u _ {t - 1} | > \\gamma_ {t}. \\tag {12} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.509,
+                0.892,
+                0.539
+            ],
+            "angle": 0,
+            "content": "Batch-based ConvergeSmooth. Likewise, we can apply the complementary constraint to a data batch,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.546,
+                0.892,
+                0.583
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {C S} ^ {B} (t) = w _ {1} \\cdot \\left| u _ {B} ^ {\\prime} - u _ {t - 1} ^ {\\prime} \\right| + w _ {2} \\cdot \\left| u _ {B} - u _ {t - 1} \\right|, \\tag {13} \\\\ s. t. \\quad | u _ {B} - u _ {t - 1} | > \\gamma_ {t}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.592,
+                0.88,
+                0.608
+            ],
+            "angle": 0,
+            "content": "where \\(u_B^\\prime = \\mathbb{E}_{(x,y)\\sim B}\\mathcal{L}(x_t^\\prime ,\\theta_t),u_B = \\mathbb{E}_{(x,y)\\sim B}\\mathcal{L}(x,\\theta_t).\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.608,
+                0.892,
+                0.669
+            ],
+            "angle": 0,
+            "content": "Weight centralization. To mitigate the problem of manual parameter tuning, we introduce the weight centralization without requiring extra hyperparameters other than the coefficient \\( w_{3} \\), \\( |\\theta_t - \\theta_{t-1}| = 0 \\rightarrow |\\mathcal{L}(x, \\theta_t) - \\mathcal{L}(x, \\theta_{t-1})| = 0 \\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.56,
+                0.678,
+                0.892,
+                0.715
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {C S} ^ {W} (t) = w _ {3} \\cdot | | \\theta_ {t} - \\frac {1}{l e n (\\phi)} \\cdot \\sum_ {j \\in \\phi} \\theta_ {j} | | _ {p}, \\tag {14}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.811
+            ],
+            "angle": 0,
+            "content": "where \\(\\| \\cdot \\|_p\\) means the p-norm function \\((p = 2)\\), and \\(\\phi\\) denotes a set of previous model weights. The model weights \\(\\theta_t\\) are restricted to the center \\(\\frac{1}{len(\\phi)} \\cdot \\sum_{j \\in \\phi} \\theta_j\\). The reasons behind Eq. (14) are: 1) The initial training process is stable, as indicated in Fig. 1; 2) Models at different training epochs tend to have similar weights after convergence [37]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.498,
+                0.822,
+                0.706,
+                0.839
+            ],
+            "angle": 0,
+            "content": "4. Experimental Results"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.704,
+                0.864
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Details. To demonstrate the effectiveness of the proposed method, we conduct comprehensive experiments on"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4723"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.09,
+                0.472,
+                0.14
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\">CIFAR10ξ</td><td>FGSM-RS</td><td>FGSM-MEP</td><td>B-RS</td><td>B-MEP</td></tr><tr><td>SQ↑</td><td rowspan=\"2\">16/255</td><td>19.74</td><td>22.15</td><td>28.83</td><td>29.97</td></tr><tr><td>SQ+RayS↑</td><td>18.72</td><td>20.96</td><td>27.08</td><td>28.45</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.149,
+                0.47,
+                0.178
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative results of FAT methods against the Square and Ray-S attacks on CIFAR-10 with the backbone ResNet18."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.193,
+                0.476,
+                0.304
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>CIFAR10</td><td>Clean</td><td>8 255</td><td>10 255</td><td>12 255</td><td>16 255</td><td>SQ+RayS</td><td>Time</td></tr><tr><td>OAAT[1]</td><td>71.30</td><td>44.29</td><td>38.56</td><td>33.68</td><td>28.48</td><td>21.06</td><td>183</td></tr><tr><td>AWP[41]</td><td>78.86</td><td>35.91</td><td>32.70</td><td>29.89</td><td>26.95</td><td>19.36</td><td>134</td></tr><tr><td>ATES[4]</td><td>74.52</td><td>43.61</td><td>38.94</td><td>35.31</td><td>30.89</td><td>22.16</td><td>-</td></tr><tr><td>ExAT[30]</td><td>80.78</td><td>49.21</td><td>42.15</td><td>36.98</td><td>31.26</td><td>23.08</td><td>70</td></tr><tr><td>E-MEP</td><td>69.84</td><td>53.54</td><td>49.26</td><td>45.89</td><td>40.78</td><td>23.78</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>50.31</td><td>46.77</td><td>43.97</td><td>40.13</td><td>28.45</td><td>101</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.313,
+                0.471,
+                0.356
+            ],
+            "angle": 0,
+            "content": "Table 2. Quantitative results of methods against various levels of perturbation with ResNet18 as the backbone and CIFAR-10 as the dataset. \\(\\sharp\\) denotes the PGD-10 attack."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.368,
+                0.47,
+                0.399
+            ],
+            "angle": 0,
+            "content": "several benchmark datasets, i.e. CIFAR-10 [20], CIFAR-100 [20], and Tiny ImageNet [7]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.4,
+                0.47,
+                0.55
+            ],
+            "angle": 0,
+            "content": "Following previous works [40, 23, 49, 42], we adopt ResNet18 [13] as the backbone on the CIFAR-10 and CIFAR-100, and choose PreActResNet18 [14] on the Tiny ImageNet. In all experiments, models are optimized using the SGD optimizer with a batch size of 128, weight decay of 5e-4, and momentum of 0.9. The initial learning rates on CIFAR-10, CIFAR-100, and Tiny ImageNet are set as 0.1, 0.1, and 0.01, respectively. Then, we optimize models with a total training epoch of 110 and decay the learning rate at the \\(100_{\\mathrm{th}}\\) and \\(105_{\\mathrm{th}}\\) epoch with a factor of 0.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.551,
+                0.47,
+                0.748
+            ],
+            "angle": 0,
+            "content": "We apply the proposed ConvergeSmooth in combination with two attack initialization methods on CIFAR-10 and CIFAR-100, FGSM-RS [40] and FGSM-MEP [42]. Additionally, for the Tiny ImageNet, we use FGSM-BP [42] as the initialization method. As mentioned in [42], FGSM-MEP requires consuming memory to store the previous adversarial perturbations, which limits its application on large datasets. Regarding the hyperparameters, we set \\(\\gamma_{max}\\) in Eq. (11) as 0.03, 0.06, and 0.03 for CIFAR-10, CIFAR-100, and Tiny ImageNet, respectively. \\(\\gamma_{max} = 1.5 \\cdot \\gamma_{min}\\) and \\(\\xi = 16/255\\). Specific details of hyperparameter settings for \\(w_{1 \\sim 3}\\) are given in the supplement. All experiments are conducted on a single GeForce RTX 3090 GPU."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.749,
+                0.47,
+                0.795
+            ],
+            "angle": 0,
+            "content": "Baselines. We include advanced FAT methods as baselines, namely FGSM-RS [40], GradAlign [2], ZeroGrad [10], NuAT [36], ATAS [16], and FGSM-MEP [42]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Evaluation metrics. We follow [40, 16] and adopt FGSM [11], PGD-10 [25], PGD-20 [25], PGD-50 [25], C&W [3], APGD-CE [6] and Autoattack (AA) [6] to evaluate the adversarial robustness of models. PGD-n represents the PGD attack with n iterations. Autoattack combines APGD-CE and APGD-T (targeted APGD) as well as two complementary attacks (FAB [9] and Square attack [26])."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.515,
+                0.092,
+                0.872,
+                0.301
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.304,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Figure 2. The training process of various FAT methods (PGD-10, \\(\\xi = 16 / 255\\)) on CIFAR-10."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.346,
+                0.892,
+                0.452
+            ],
+            "angle": 0,
+            "content": "The training easily exhibits fluctuations, and thus individual results can not objectively reflect the performance of methods. For each method, we repeat the training process three times and report the average evaluation results of the best model across the three runs (mbest). Additionally, the supplement includes the best results (best) and the average evaluation of the final model from the three runs (mfinal)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.453,
+                0.892,
+                0.5
+            ],
+            "angle": 0,
+            "content": "In the following section, 'W-\\*', 'E-\\*', and 'B-\\*' mean 'weight centralization', 'example-based ConvergeSmooth', and 'batch-based ConvergeSmooth', respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.512,
+                0.738,
+                0.529
+            ],
+            "angle": 0,
+            "content": "4.2. Significance of the Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.538,
+                0.892,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Before evaluating the adversarial robustness of trained models, we demonstrate the significance of the results [1]. Specifically, we show that adversarial attacks with \\(\\xi = 16/255\\) rarely change the true label of input. 1) We generate adversarial examples for the FGSM-RS, FGSM-MEP, and our proposed methods on CIFAR10 and CIFAR100 datasets with \\(\\xi = 16/255\\) using the non-targeted attacks such as FGSM, PGD, C&W, APGD-CE, and the targeted attack APGD-T. The majority of the generated examples retain their true labels; 2) Tab. 1 examines the robustness of models against an ensemble of the Square (SQ) [26] and Ray-S [5] attacks, as these attacks generate strong oracle-invariant examples [1]; 3) We generate adversarial training data with \\(\\xi = 16/255\\) and test the robustness on various levels of perturbation. Tab. 2 provide comparative experiments between our proposed method and other AT techniques, including OAAT [1], ExAT [30], ATES [4] and AWP [41]. It is important to note that we re-implement these AT methods and apply them in the context of FAT. Overall, our methods achieve optimal performance on both oracle-invariant attacks and classical evaluation attacks. Namely, the classical evaluation attacks used in \\(\\xi = 8/255\\) are reliable and significant even when the value of \\(\\xi\\) is increased to 16/255."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Notably, our methods are plugged into FGSM-RS and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4724"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.114,
+                0.088,
+                0.858,
+                0.295
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\">Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td colspan=\"2\">PGD-AT [29]</td><td>65.30</td><td>46.31</td><td>40.73</td><td>35.08</td><td>33.92</td><td>30.84</td><td>33.08</td><td>26.29</td><td>370</td></tr><tr><td colspan=\"2\">FGSM-RS [40]</td><td>50.12</td><td>38.28</td><td>26.13</td><td>21.55</td><td>20.43</td><td>18.96</td><td>19.40</td><td>14.84</td><td>67</td></tr><tr><td colspan=\"2\">GradAlign [2]</td><td>58.17</td><td>39.87</td><td>33.12</td><td>26.81</td><td>24.99</td><td>22.63</td><td>23.98</td><td>17.02</td><td>135</td></tr><tr><td colspan=\"2\">ZeroGrad [10]</td><td>74.16</td><td>43.96</td><td>32.67</td><td>21.98</td><td>18.37</td><td>20.76</td><td>16.44</td><td>12.07</td><td>67</td></tr><tr><td rowspan=\"3\">Ours</td><td>W-RS</td><td>70.66</td><td>45.51</td><td>36.50</td><td>27.51</td><td>24.75</td><td>23.97</td><td>23.38</td><td>17.14</td><td>71</td></tr><tr><td>E-RS</td><td>62.38</td><td>42.07</td><td>36.78</td><td>30.80</td><td>28.90</td><td>23.64</td><td>27.71</td><td>17.55</td><td>77</td></tr><tr><td>B-RS</td><td>65.42</td><td>45.94</td><td>37.54</td><td>30.01</td><td>27.85</td><td>26.28</td><td>26.52</td><td>19.43</td><td>75</td></tr><tr><td colspan=\"2\">NuAT [36]</td><td>74.62</td><td>44.92</td><td>35.22</td><td>25.93</td><td>23.67</td><td>24.07</td><td>22.37</td><td>18.43</td><td>101</td></tr><tr><td colspan=\"2\">ATAS* [16]</td><td>64.11</td><td>-</td><td>31.39</td><td>-</td><td>28.15</td><td>-</td><td>-</td><td>21.09</td><td>-</td></tr><tr><td colspan=\"2\">FGSM-MEP [42]</td><td>53.32</td><td>36.24</td><td>31.85</td><td>27.28</td><td>26.56</td><td>22.10</td><td>26.08</td><td>18.98</td><td>92</td></tr><tr><td rowspan=\"2\">Ours</td><td>E-MEP</td><td>69.84</td><td>47.18</td><td>40.90</td><td>34.17</td><td>32.72</td><td>22.69</td><td>31.12</td><td>17.74</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>45.48</td><td>40.13</td><td>34.21</td><td>32.95</td><td>28.19</td><td>32.04</td><td>23.68</td><td>101</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.304,
+                0.895,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Table 3. Quantitative results of various methods (\\( \\xi = 16/255 \\)) on the CIFAR-10 with ResNet18 as the backbone. 'ATAS*' is the result of ATAS in [16], which is superior to our reproduction. We train each method three times. The results represent the evaluation average between the best models of three training processes. Weight centralization and regularization in MEP do not work together."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.359,
+                0.897,
+                0.501
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Budgets (ξ)</td><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td rowspan=\"4\">12/255</td><td>GradAlign [2]</td><td>66.52</td><td>43.06</td><td>31.66</td><td>27.95</td><td>26.04</td><td>27.05</td><td>25.99</td><td>21.65</td><td>135</td></tr><tr><td>NuAT [36]</td><td>72.79</td><td>51.80</td><td>41.75</td><td>38.60</td><td>37.54</td><td>35.99</td><td>36.71</td><td>32.01</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>74.71</td><td>52.05</td><td>38.45</td><td>36.35</td><td>35.52</td><td>33.05</td><td>33.4</td><td>27.23</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>72.63</td><td>54.40</td><td>45.23</td><td>42.85</td><td>42.14</td><td>36.81</td><td>41.62</td><td>33.26</td><td>101</td></tr><tr><td rowspan=\"4\">10/255</td><td>GradAlign [2]</td><td>83.10</td><td>55.23</td><td>36.58</td><td>30.47</td><td>28.64</td><td>31.01</td><td>26.51</td><td>23.84</td><td>135</td></tr><tr><td>NuAT [36]</td><td>75.82</td><td>55.94</td><td>45.54</td><td>43.92</td><td>43.42</td><td>41.39</td><td>42.91</td><td>38.85</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>83.43</td><td>59.51</td><td>42.76</td><td>39.28</td><td>37.33</td><td>37.26</td><td>35.91</td><td>32.52</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>75.96</td><td>57.26</td><td>47.25</td><td>45.98</td><td>45.66</td><td>41.00</td><td>45.26</td><td>39.20</td><td>101</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.51,
+                0.895,
+                0.539
+            ],
+            "angle": 0,
+            "content": "Table 4. Quantitative results of FAT methods on various \\( \\xi \\) with ResNet18 as the backbone and CIFAR-10 as the dataset. Models are trained and evaluated under the same \\( \\xi \\) . The number in bold indicates the best."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.095,
+                0.56,
+                0.455,
+                0.656
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>ξ = 16/255</td><td colspan=\"2\">CIFAR10</td><td colspan=\"2\">CIFAR100</td><td>Time</td></tr><tr><td>Methods</td><td>Clean</td><td>AA</td><td>Clean</td><td>AA</td><td>hours</td></tr><tr><td>GradAlign [2]</td><td>55.58</td><td>13.45</td><td>35.93</td><td>7.13</td><td>8.79</td></tr><tr><td>NuAT [36]</td><td>74.25</td><td>13.19</td><td>20.48</td><td>7.30</td><td>7.66</td></tr><tr><td>FGSM-MEP [42]</td><td>65.56</td><td>15.43</td><td>20.69</td><td>6.73</td><td>6.15</td></tr><tr><td>B-MEP (Ours)</td><td>69.94</td><td>24.27</td><td>48.64</td><td>12.05</td><td>6.72</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.665,
+                0.47,
+                0.693
+            ],
+            "angle": 0,
+            "content": "Table 5. The adversarial accuracy of various FAT methods with WideResNet34-10 as the backbone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.709,
+                0.47,
+                0.816
+            ],
+            "angle": 0,
+            "content": "FGSM-MEP, which are fitted to the distribution of adversarial examples. Instead, methods such as OAAT are fitted to the distribution of benign samples and perform better on clean accuracy. Therefore, we use the settings as in OAAT and then apply OAAT and our B-OAAT to the FAT task. B-OAAT realizes \\(74.12\\%\\) \\((+2.82\\%)\\) than OAAT) clean accuracy and \\(25.39\\%\\) (OAAT) on SQ+RayS."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.83,
+                0.279,
+                0.845
+            ],
+            "angle": 0,
+            "content": "4.3. Results on CIFAR-10"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We conduct our initial experiments on CIFAR-10 using the ResNet18 backbone. The default \\(\\xi\\) is set to 16/255. Tab. 3 presents the main comparisons. The observations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.563,
+                0.892,
+                0.865
+            ],
+            "angle": 0,
+            "content": "are as follows: (1) Compared with previous FAT methods, the proposed approaches achieve optimal adversarial robustness against different attacks, e.g. B-RS outperforms all RS-based methods and B-MEP is superior to all other methods. Meanwhile, our methods exhibit similar performance to prior work in terms of clean classification accuracy. (2) B-MEP realizes adversarial robustness approaching PGD-AT, e.g. B-MEP performs \\(32.95\\%\\) robustness against the PGD-50 attack, only \\(0.97\\%\\) lower than PGD-AT; (3) As for time consumption, B-RS takes less time (75 minutes) than GradAlign (135 minutes) and NuAT (101 minutes). This is because ConvergeSmooth only requires the additional regularization when \\(|u_{B} - u_{t - 1}| > \\gamma_{t}\\) instead of adding constraints on all iterations. In addition, B-MEP (102 minutes) takes a bit more calculation cost than FGSM-MEP (92 minutes) but much less than PGD-AT (370 minutes). PGD-AT takes significantly longer than FAT works; (4) B-RS and B-MEP successfully prevent catastrophic overfitting, e.g. mfinal (in the supplement) only shows a slight reduction than mbest in terms of adversarial robustness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Fig. 2 visualizes the training process of various FAT approaches. Compared with other methods, the proposed"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4725"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.12,
+                0.089,
+                0.852,
+                0.294
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\">Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td colspan=\"2\">PGD-AT</td><td>40.57</td><td>24.72</td><td>21.46</td><td>17.94</td><td>17.38</td><td>14.98</td><td>17.02</td><td>12.63</td><td>370</td></tr><tr><td colspan=\"2\">FGSM-RS [40]</td><td>30.12</td><td>15.24</td><td>12.69</td><td>10.25</td><td>9.79</td><td>8.45</td><td>9.57</td><td>6.90</td><td>67</td></tr><tr><td colspan=\"2\">GradAlign [2]</td><td>31.91</td><td>15.71</td><td>12.56</td><td>10.28</td><td>9.71</td><td>8.22</td><td>9.47</td><td>6.61</td><td>135</td></tr><tr><td colspan=\"2\">ZeroGrad [10]</td><td>47.31</td><td>23.58</td><td>17.60</td><td>12.85</td><td>11.87</td><td>11.62</td><td>11.01</td><td>7.94</td><td>67</td></tr><tr><td rowspan=\"3\">Ours</td><td>W-RS</td><td>41.97</td><td>26.30</td><td>19.09</td><td>14.77</td><td>13.72</td><td>12.82</td><td>13.36</td><td>9.67</td><td>72</td></tr><tr><td>E-RS</td><td>41.09</td><td>22.33</td><td>18.78</td><td>15.19</td><td>14.43</td><td>12.00</td><td>13.91</td><td>9.50</td><td>78</td></tr><tr><td>B-RS</td><td>41.47</td><td>25.98</td><td>19.44</td><td>15.36</td><td>14.34</td><td>12.91</td><td>13.71</td><td>9.90</td><td>76</td></tr><tr><td colspan=\"2\">NuAT [36]</td><td>31.42</td><td>20.39</td><td>16.15</td><td>13.87</td><td>13.29</td><td>11.12</td><td>12.25</td><td>8.32</td><td>101</td></tr><tr><td colspan=\"2\">ATAS [16]</td><td>55.63</td><td>30.35</td><td>15.31</td><td>10.28</td><td>8.49</td><td>10.97</td><td>6.30</td><td>5.05</td><td>70</td></tr><tr><td colspan=\"2\">FGSM-MEP [42]</td><td>21.39</td><td>13.00</td><td>11.37</td><td>9.93</td><td>9.76</td><td>7.28</td><td>9.58</td><td>6.36</td><td>92</td></tr><tr><td rowspan=\"2\">Ours</td><td>E-MEP</td><td>44.00</td><td>24.46</td><td>20.59</td><td>17.11</td><td>16.59</td><td>13.37</td><td>16.05</td><td>10.97</td><td>106</td></tr><tr><td>B-MEP</td><td>41.86</td><td>24.86</td><td>20.84</td><td>17.30</td><td>16.59</td><td>13.96</td><td>16.25</td><td>11.38</td><td>102</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.16,
+                0.304,
+                0.804,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Table 6. Quantitative results of various methods \\( \\left( {\\xi  = {16}/{255}}\\right) \\) with ResNet18 as the backbone on CIFAR-100."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.122,
+                0.329,
+                0.849,
+                0.46
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (hour)↓</td></tr><tr><td>PGD-AT</td><td>32.52</td><td>16.47</td><td>13.40</td><td>10.63</td><td>10.24</td><td>7.95</td><td>10.00</td><td>6.41</td><td>67.2</td></tr><tr><td>FGSM-RS [40]</td><td>27.48</td><td>12.46</td><td>9.59</td><td>6.97</td><td>6.47</td><td>4.99</td><td>6.19</td><td>3.63</td><td>10.5</td></tr><tr><td>GradAlign [2]</td><td>28.65</td><td>13.80</td><td>10.40</td><td>7.78</td><td>7.08</td><td>5.75</td><td>6.59</td><td>3.90</td><td>20.9</td></tr><tr><td>ZeroGrad [10]</td><td>34.66</td><td>12.26</td><td>8.22</td><td>5.29</td><td>4.82</td><td>3.71</td><td>4.23</td><td>2.21</td><td>10.5</td></tr><tr><td>NuAT [36]</td><td>35.24</td><td>15.52</td><td>12.07</td><td>8.81</td><td>8.13</td><td>6.29</td><td>7.68</td><td>4.27</td><td>24.6</td></tr><tr><td>FGSM-BP [42]</td><td>20.02</td><td>10.18</td><td>8.38</td><td>6.98</td><td>6.77</td><td>4.56</td><td>6.57</td><td>3.62</td><td>14.3</td></tr><tr><td>B-BP (Ours)</td><td>33.51</td><td>16.32</td><td>12.92</td><td>9.72</td><td>9.23</td><td>7.26</td><td>9.32</td><td>5.95</td><td>15.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.129,
+                0.469,
+                0.835,
+                0.484
+            ],
+            "angle": 0,
+            "content": "Table 7. Quantitative results of various methods \\( \\left( {\\xi  = {16}/{255}}\\right) \\) with PreActResNet18 as the backbone on Tiny ImageNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.501,
+                0.469,
+                0.547
+            ],
+            "angle": 0,
+            "content": "B-RS achieves optimal training stability and adversarial robustness, e.g. the classification accuracy of our method fluctuates slightly during three adversarial training sessions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.55,
+                0.469,
+                0.61
+            ],
+            "angle": 0,
+            "content": "Various budgets. Similar experiments are performed for budgets 10/255 and 12/255. Details are given in Tab. 4. It is evident that the proposed method achieves optimal adversarial robustness across various perturbation budgets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.613,
+                0.469,
+                0.675
+            ],
+            "angle": 0,
+            "content": "Various networks. We then adopt WideResNet34 with a width factor of 10 [47] as the backbone. The results are given in Tab. 5. Our proposed B-MEP also prevents the wider architectures from catastrophic overfitting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.693,
+                0.287,
+                0.709
+            ],
+            "angle": 0,
+            "content": "4.4. Results on CIFAR-100"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The results on CIFAR-100 with the backbone ResNet-18 are presented in Tab. 6. (1) FAT methods perform similar training consumption on CIFAR-10 and CIFAR-100 as two datasets contain the same number and size of images; (2) All proposed methods can realize stable adversarial training, as evidenced by the comparable results of mbest and mfinal (in the supplement); (3) Among the RS-based FAT works, B-RS and E-RS achieve the best and second-best adversarial robustness against different attacks; (4) B-MEP outperforms all other FAT methods; (5) Although B-MEP performs slightly worse than PGD-AT, its training process is approximately 3.5 times faster than this competitor."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.501,
+                0.736,
+                0.517
+            ],
+            "angle": 0,
+            "content": "4.5. Results on Tiny ImageNet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.526,
+                0.892,
+                0.648
+            ],
+            "angle": 0,
+            "content": "We conduct experiments on the Tiny ImageNet using the PreActResNet18 backbone to demonstrate the scalability of the proposed method to large datasets. The results are given in Tab. 7. B-BP achieves higher robustness among the FAT methods and comparable robustness to PGD-AT. As for training efficiency, B-BP (15.4 hours) requires slightly more computational cost than FGSM-BP (14.3 hours), but significantly less time than PGD-AT (67.2 hours)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.663,
+                0.661,
+                0.678
+            ],
+            "angle": 0,
+            "content": "4.6. Ablation studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.688,
+                0.892,
+                0.824
+            ],
+            "angle": 0,
+            "content": "In the following, B-RS is selected as the backbone. Figs. 3 and 4 conduct ablation studies on \\(\\gamma_{max}\\) and \\(\\gamma_{max} / \\gamma_{min}\\) respectively. In Fig. 3, the classification accuracy of both benign and adversarial examples increases with \\(\\gamma_{max}\\). However, the model trained with a large \\(\\gamma_{max}\\) (\\(>0.09\\)) suffers from catastrophic overfitting. Fig. 4 shows that the model with \\(\\gamma_{max} / \\gamma_{min} = 1.5\\) achieves optimal robustness. \\(\\gamma_{max} / \\gamma_{min} = 1\\) denotes the static convergence stride. All models can be trained stably when \\(\\gamma_{max} = 0.06\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Tabs. 8 and 9 provide the results of comparative experiments on \\( w_{1} \\) and \\( w_{2} \\) respectively. We empirically set \\( w_{2} \\) to 1 since too small \\( w_{2} \\) cannot prevent overfitting and too large \\( w_{2} \\) will affect the performance. In Tab. 8, \\( w_{1} = 0 \\) achieves optimal adversarial robustness on CIFAR100 and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4726"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.136,
+                0.089,
+                0.835,
+                0.184
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>w1</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Stability</td></tr><tr><td rowspan=\"5\">CIFAR100</td><td>0.0</td><td>48.13</td><td>32.13</td><td>24.25</td><td>22.67</td><td>22.21</td><td>19.04</td><td>21.29</td><td>15.28</td><td>★★★</td></tr><tr><td>0.3</td><td>46.08</td><td>30.58</td><td>23.06</td><td>21.62</td><td>21.22</td><td>17.79</td><td>20.44</td><td>15.22</td><td>★★★</td></tr><tr><td>0.5</td><td>44.04</td><td>29.96</td><td>22.64</td><td>21.34</td><td>20.99</td><td>17.55</td><td>19.16</td><td>13.84</td><td>★★★</td></tr><tr><td>0.7</td><td>43.07</td><td>28.61</td><td>22.01</td><td>20.84</td><td>20.32</td><td>16.87</td><td>18.98</td><td>13.47</td><td>★★★</td></tr><tr><td>0.9</td><td>40.45</td><td>21.05</td><td>21.62</td><td>20.54</td><td>20.15</td><td>16.33</td><td>18.91</td><td>13.53</td><td>★★★</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.193,
+                0.894,
+                0.224
+            ],
+            "angle": 0,
+            "content": "Table 8. Quantitative results of the proposed method on various \\( w_{1} \\) with ResNet18 as the backbone and the perturbation budget 12/255. 'Stability' represents the number of times the model is stable in three training repetitions. \\( \\gamma_{max} \\) and \\( w_{2} \\) are set to 0.03 and 1, respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.135,
+                0.233,
+                0.835,
+                0.314
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>w2</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Stability</td></tr><tr><td rowspan=\"4\">CIFAR100</td><td>0.5</td><td>36.79</td><td>23.97</td><td>18.60</td><td>17.51</td><td>17.23</td><td>14.65</td><td>16.28</td><td>12.23</td><td>-</td></tr><tr><td>0.7</td><td>37.31</td><td>24.36</td><td>18.56</td><td>17.37</td><td>17.26</td><td>14.46</td><td>15.96</td><td>11.54</td><td>-</td></tr><tr><td>1.0</td><td>48.13</td><td>32.13</td><td>24.25</td><td>22.67</td><td>22.21</td><td>19.04</td><td>21.29</td><td>15.28</td><td>★★★</td></tr><tr><td>1.3</td><td>44.84</td><td>30.42</td><td>23.31</td><td>21.72</td><td>21.31</td><td>18.36</td><td>19.64</td><td>14.72</td><td>★★★</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.134,
+                0.323,
+                0.83,
+                0.338
+            ],
+            "angle": 0,
+            "content": "Table 9. Quantitative results on various \\( {w}_{2}\\left( {{\\gamma }_{max} = {0.03}}\\right. \\) and \\( {w}_{1} = 0) \\) with ResNet18 as the backbone and \\( \\xi  = {12}/{255} \\) ."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.129,
+                0.363,
+                0.446,
+                0.375
+            ],
+            "angle": 0,
+            "content": "ResNet18 trained with ConvergeSmooth-RS on CIFAR-100"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.375,
+                0.451,
+                0.593
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.6,
+                0.471,
+                0.642
+            ],
+            "angle": 0,
+            "content": "Figure 3. Ablation study of \\(\\gamma_{max}(\\gamma_{max} / \\gamma_{min} = 1.5)\\). We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10, \\(\\xi = 16/255\\)) on CIFAR-100."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.651,
+                0.47,
+                0.834
+            ],
+            "angle": 0,
+            "content": "all settings accomplish stable FAT. According to Eqs. (7) and (8), if \\( w_{1} \\neq 0 \\), for the data \\( x \\) which satisfies \\( \\mathcal{C}(x) = 1 \\), \\( \\mathcal{L}(x_t', \\theta_t) \\) is assigned with higher weights \\( (1 + w_{1}) \\) or lower weights \\( (1 - w_{1}) \\), causing the model to excessively prioritize or neglect this portion of the data. This may weaken the performance of models. However, for Tiny ImageNet, models suffer catastrophic overfitting at \\( w_{1} = 0 \\). Then, we gradually increase \\( w_{1} \\) from 0.3 with a stride of 0.2 until the FAT process becomes stable. In addition, our weight centralization method only introduces a balance coefficient \\( w_{3} \\). \\( w_{3} \\) is set to 0.1 since catastrophic overfitting happens when \\( w_{3} = 0 \\) and classification performance is degraded when \\( w_{3} = 0.2 \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.845,
+                0.196,
+                0.86
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this paper, we tackle the issue of catastrophic overfitting by focusing on the convergence stability of loss func"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.564,
+                0.364,
+                0.86,
+                0.374
+            ],
+            "angle": 0,
+            "content": "ResNet18 trained with ConvergeSmooth-RS on CIFAR-100"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.374,
+                0.882,
+                0.582
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.594,
+                0.892,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Figure 4. Ablation study of \\(\\gamma_{max} / \\gamma_{min}\\) (\\(\\gamma_{max} = 0.06\\)). We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10, \\(\\xi = 16/255\\)) on CIFAR-100."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.667,
+                0.892,
+                0.834
+            ],
+            "angle": 0,
+            "content": "tions. Through experimental analysis, we find that this issue is accompanied by abnormal convergence behavior of losses. Motivated by this phenomenon, we propose complementary constraints, namely E-ConvergeSmooth and B-ConvergeSmooth, based on the adversarial training constraint. To alleviate the burden of parameter tuning, weight centralization is designed utilizing priors from previous epochs. Extensive experiments on different network architectures and datasets show that the proposed methods effectively solve catastrophic overfitting and exhibit superior robustness against various adversarial attacks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.841,
+                0.893,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Acknowledgments. This work was supported by the National Key R&D Program of China #2018AAA0102000 and the National Natural Science Foundation of China #62276046 and #U19B2039."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4727"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
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+                0.087,
+                0.115,
+                0.47,
+                0.171
+            ],
+            "angle": 0,
+            "content": "[1] Sravanti Addepalli, Samyak Jain, Gaurang Sriramananan, and R Venkatesh Babu. Scaling adversarial training to large perturbation bounds. In European Conference on Computer Vision, pages 301-316. Springer, 2022."
+        },
+        {
+            "type": "ref_text",
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+            ],
+            "angle": 0,
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+        },
+        {
+            "type": "ref_text",
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+            ],
+            "angle": 0,
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+        {
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+# Fast Adversarial Training with Smooth Convergence
+
+Mengnan Zhao, Lihe Zhang*, Yuqiu Kong and Baocai Yin
+
+Dalian University of Technology, China
+
+zmnwelcome@mail.dlut.edu.cn，{zhanglihe，yqkong，ybc}@dlut.edu.cn
+
+# Abstract
+
+Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, i.e. the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth.
+
+# 1. Introduction
+
+Recent breakthroughs in deep learning [21, 32] have aroused researchers' interest in the security of neural networks [45, 48, 39]. In particular, the advanced research proves the vulnerability of deep models to adversarial attacks [8, 11, 27]. For instance, tiny crafted perturbations can fool models in various fields into making wrong decisions [15, 50, 35, 24]. Considering the security risks brought by adversarial attacks [18, 46, 33, 44], there is a quickly grow
+
+ing body of work [43, 46, 18] on improving the adversarial robustness of neural networks. Among them, adversarial training is widely applied by practitioners [31, 12].
+
+In recent years, projected gradient descent based adversarial training (PGD-AT) [25, 34] has been widely employed for its stability and effectiveness. However, this mechanism is computationally expensive. It requires multiple gradient descent steps to generate the adversarial training data [38]. An alternative of PGD-AT is the fast adversarial training (FAT) [28], which only adopts a single-step fast gradient sign method (FGSM) [11] to generate training data. Compared to PGD-AT, FAT can efficiently train models, but easily falls into catastrophic overfitting [40, 29].
+
+A number of FAT methods have been proposed to mitigate catastrophic overfitting. For example, Wong et al. [40] use randomly initialized perturbations to enhance the diversity of adversarial perturbations. Based on it, Andriushchenko et al. [2] raise a complementary regularizer named GradAlign to maximize the gradient alignment between benign and adversarial examples explicitly. Similarly, NuAT [36] and FGSM-MEP [42] adopt nuclear norm or p-norm to regularize the adversarial training, thereby increasing the prediction alignment between benign and adversarial examples. However, the above methods can only resolve catastrophic overfitting within the limited perturbation budget ( $\xi \leq 8/255$ ).  $\xi$  specifies the perturbation degree of adversarial training data generated by various attacks. Besides, models trained by small perturbations are vulnerable to adversarial attacks with a large  $\xi$ , e.g. the models trained by NuAT and FGSM-MEP at  $\xi = 8/255$  perform  $53\%$  and  $54\%$  robustness against the PGD-50 attack with  $\xi = 8/255$ , but only  $22\%$  and  $20\%$  robustness against the same attack with  $\xi = 16/255$  respectively. Therefore, we aspire to prevent catastrophic overfitting to improve the adversarial robustness of neural models at larger perturbation budgets.
+
+By analyzing adversarial training processes of representative work, we observe that catastrophic overfitting is usually accompanied by a slight fluctuation in the classification loss for benign samples and a sharp drop in the classification
+
+loss for adversarial examples. This motivates us to question whether a smooth loss convergence process is also a stable FAT process. Moreover, we find that an oscillating adversarial training phase may restart the FAT process after catastrophic overfitting. Fig. 1 shows the details.
+
+According to these observations, we introduce an oscillatory constraint that limits the difference in loss between adjacent training epochs, called ConvergeSmooth. A dynamic convergence stride of ConvergeSmooth is designed considering the nonlinear decay rate of loss functions. Inspired by the smoothness of loss convergence, we further verify the effect of the proposed weight centralization on model stability. Weight centralization refers to taking the weights average of the previously trained models as the convergence center of the current model weight. Our proposed methods are attack-agnostic and thus can be combined with existing adversarial strategies in FAT, such as FGSM-RS and FGSM-MEP, to evaluate their performance.
+
+The contributions are summarized in four aspects: (1) We verify that previous FAT works still suffer from catastrophic overfitting at a large  $\xi$  and then study catastrophic overfitting from the perspective of convergence instability of loss functions; (2) We propose a smooth convergence constraint, ConvergeSmooth, and design a dynamic convergence stride for it, to help various FAT methods avoid catastrophic overfitting on different perturbation budgets; (3) The weight centralization is proposed without introducing extra hyperparameters other than the loss balance coefficient to stabilize FAT; (4) Extensive experiments show that the proposed methods outperform the state-of-the-art FAT techniques in terms of efficiency, robustness, and stability.
+
+# 2. Related Work
+
+Adversarial attacks. Adversarial attacks are usually used to deceive deep-learning models. Goodfellow et al. [11] first discuss the adversarial attack (FGSM) within the classification task. They prove that adversarial examples  $x'$  generated by a single-step gradient backward can misclassify the model  $f(\cdot; \theta)$  with high confidence.  $\theta$  denotes the fixed model weights.  $x'$  is generated by
+
+$$
+x ^ {\prime} = x + \xi \cdot \operatorname {s g n} \left(\nabla_ {x} \mathcal {L} (f (x; \theta), y)\right), \tag {1}
+$$
+
+where  $x$  is an input image,  $\xi$  represents the perturbation budget,  $\operatorname{sgn}(\cdot)$  means the sign function,  $\mathcal{L}(\cdot)$  is usually the cross-entropy loss,  $\nabla_{x}\mathcal{L}(\cdot)$  calculates the gradient of loss at  $x$ , and  $y$  denotes the ground truth labels of  $x$ . Following the FGSM [11], researchers propose a series of attack methods based on the iterative gradient backward, e.g. I-FGSM [22], MIM [8], and PGD [25]. Taking the PGD attack as an example, the adversarial example  $x_{t + 1}^{\prime}$  produced in the iteration  $t + 1$  can be formulated as
+
+$$
+x _ {t + 1} ^ {\prime} = \operatorname {c l i p} _ {\xi} \left(x _ {t} ^ {\prime} + \epsilon \cdot \operatorname {s g n} \left(\nabla_ {x _ {t} ^ {\prime}} \mathcal {L} \left(f \left(x _ {t} ^ {\prime}; \theta\right), y\right)\right)\right), \tag {2}
+$$
+
+where  $\epsilon$  denotes the single-step stride and  $\mathrm{clip}_{\xi}$  refers to projecting adversarial perturbations to a  $\xi$ -ball.
+
+Adversarial training. Madry et al. [25] formalize the adversarial training as a min-max optimization problem,
+
+$$
+\min  _ {\theta} \mathbb {E} _ {(x, y) \sim D} [ \max  _ {\delta \in [ - \xi , \xi ]} \mathcal {L} (f \left(x ^ {\prime}; \theta\right), y) ], \tag {3}
+$$
+
+where  $x' = x + \delta$ ,  $\delta$  represents the adversarial perturbations generated by various attacks such as PGD and FGSM.  $D$  is the data generator. The internal maximization maximizes the classification loss to generate adversarial perturbations with fixed model weights. The external minimization minimizes the classification loss on the generated adversarial examples when optimizing the model weights.
+
+Actually, there is a trade-off between computational efficiency and adversarial robustness in recent adversarial training methods. Compared to PGD-AT [25], FGSM-based fast adversarial training (FAT) accelerates the training process but damages the robustness of models for the problem of catastrophic overfitting [19, 17]. To mitigate this issue, Wong et.al [40] demonstrate that the FGSM with a random start strategy (FGSM-RS) can achieve comparable performance against the PGD-AT. ZeroGrad [10] zeroes the elements of gradient that are too small to craft the perturbations. enforces the model loss to increase with the increase in perturbation size. Besides, GradAlign [2] prevents catastrophic overfitting by maximizing the alignment between gradients of benign samples and adversarial examples.
+
+Similarly, NuAT [36] introduces a nuclear norm regularization between logits for benign and adversarial examples and uses the Bernoulli noise as the initial perturbation. ATAS [16] learns an instantiated adaptive step size that is inversely proportional to the gradient norm. It applies the adversarial perturbations from the previous epoch as the initialization of FGSM in the current training phase. In addition, Jia et al. [42] propose several prior-guided initialization methods to replace the random start strategy of FGSM-RS. Specifically, FGSM-BP adopts the adversarial perturbations from the previous batch as the attack initialization in the current batch. FGSM-MEP employs a momentum mechanism to combine all adversarial perturbations from the previous epochs to yield adversarial initialization.
+
+Although these FAT methods have resolved catastrophic overfitting at small perturbation budgets, they still suffer from catastrophic overfitting under larger perturbation budgets (e.g.  $\xi = 16 / 255$ ). Unlike these methods, we revisit the catastrophic overfitting problem from the perspective of loss convergence instability and prevent this exception by limiting the magnitude of loss fluctuations during training.
+
+# 3. Proposed Method
+
+In this section, we first study the performance of previous FAT methods when subjected to a large perturbation budget
+
+![](images/cd9ecbc383adc2a12e7ab4b5a3256b22e64a083407a68b7b5fbdf8cacf2a38fa.jpg)  
+(a) ResNet18 trained with FGSM-RS
+
+![](images/f2568362360d16210983537fbbc98350642e7fe840781af21c1099d1b6ebfb67.jpg)  
+(b) ResNet18 $_2$  trained with FGSM-RS
+
+![](images/fdd50d80d63a5e6b09bf7fb39d5738ac55fa6b9d105d1b63edcf06374cb43fd0.jpg)  
+(c) ResNet18 trained with FGSM-RS
+
+![](images/888d940547966a2de7eeb0aac3b876c80c50ae5fb0cbdda61901363669dbe86b.jpg)  
+(d) ResNet18 trained with GradAlign
+
+![](images/6b673903b39c5fb94588140a51c32a46441f9a527c1e7d9af4534d7a47470ae1.jpg)  
+(e) ResNet18 $_2$  trained with GradAlign
+
+![](images/7570403a5c25707a754349395f19cf4b9d241a35cc9aebda17ce19c1ec54d36a.jpg)  
+(f) ResNet18 trained with GradAlign
+
+![](images/d26313a50019ee9fc986785530ffce4cb8414056df6f5225922cb675f1ba34e5.jpg)  
+(g) ResNet18 trained with FGSM-MEP  
+Figure 1. The training process of previous FAT methods with ResNet18 on CIFAR-10. Each FAT method is trained 3 times.  $\xi = 16 / 255$ . ADV-Loss and BEN-Loss denote the classification loss of models to adversarial and benign examples during training, respectively. ADV-Acc and BEN-Acc represent the classification accuracy of models to adversarial and benign examples during testing, respectively.
+
+![](images/36780e4b0d277b67f249a6292c1612b47a45ac4e2d523f7bafd4a2dd23f657ef.jpg)  
+(h) ResNet182 trained with FGSM-MEP
+
+![](images/a205b7233de4b4082b6e17fbf138ff8447f36e6b7768b82dbd155c33980769a0.jpg)  
+(i) ResNet18 trained with FGSM-MEP
+
+$\xi$ . Then, the training processes of these methods have been analyzed for a better understanding of catastrophic overfitting. Finally, we detail the proposed methods.
+
+# 3.1. Performance of FAT methods on a large  $\xi$
+
+Previous FAT techniques avoid catastrophic overfitting at small  $\xi$  ( $\xi \leq 8/255$ ). Here, we investigate their performance on a large  $\xi$  ( $\xi = 16/255$  by default).
+
+FGSM-RS [40]: Based on Eq. (3), this method adopts the samples with uniformly random perturbations  $\delta_0\sim$ $\mathcal{U}(-\xi ,\xi)$  as the attack initialization of FGSM,
+
+$$
+\min  _ {\theta} \mathbb {E} _ {(x, y) \sim D} [ \max  _ {\delta_ {0} + \delta \in [ - \xi , \xi ]} \mathcal {L} (f (x ^ {\prime}; \theta), y) ],
+$$
+
+$$
+x ^ {\prime} = x + \delta_ {0} + \delta \quad s. t. \quad x ^ {\prime} \in [ 0, 1 ], \quad \delta_ {0} \sim \mathcal {U} (- \xi , \xi). \tag {4}
+$$
+
+GradAlign [2]: This approach increases the gradient alignment between benign samples  $x$  and perturbed samples  $x + \delta_0$ , which is denoted as
+
+$$
+\mathbb {E} _ {(x, y) \sim D} [ 1 - \cos (\nabla_ {x} \mathcal {L} (x, \theta), \nabla_ {x + \delta_ {0}} \mathcal {L} (x + \delta_ {0}, \theta) ], \tag {5}
+$$
+
+$$
+\mathcal {L} (x, \theta) = \mathcal {L} (f (x; \theta), y).
+$$
+
+$\cos (\cdot)$  computes the cosine similarity between two matrices.
+
+FGSM-MEP [42]: Different from FGSM-RS, this method generates the initialization perturbations  $\delta_0$  based on all historical adversarial perturbations from the previous epochs and introduces a regularization expressed as
+
+$$
+\mathbb {E} _ {(x, y) \sim D} [ | | f (x ^ {\prime}; \theta) - f (x + \delta_ {0}; \theta) | | _ {2} ^ {2} ], \tag {6}
+$$
+
+where  $||\cdot ||_2^2$  denotes the squared  $\mathcal{L}_2$  distance.
+
+Fig. 1 shows their detailed adversarial training processes of ResNet18 [13] on CIFAR-10 [20]. We find that they fall into catastrophic overfitting during the  $5 \sim 20_{\mathrm{th}}$ ,  $40 \sim 65_{\mathrm{th}}$  and  $10 \sim 15_{\mathrm{th}}$  epochs, respectively. Graphical analysis of various models and datasets is given in the supplement.
+
+# 3.2. Analysis of training process
+
+From Fig. 1, we discover several typical phenomena of catastrophic overfitting: 1) Change from a smooth convergence state to an irregular fluctuation state; 2) A slight change (increase or decrease) in the standard classification loss  $\mathcal{L}(x,\theta)$  and a rapid descent of the adversarial classification loss  $\mathcal{L}(x',\theta)$ ; 3) Rapid decline in the classification accuracy of adversarial examples.
+
+After catastrophic overfitting, the methods depicted in Fig. 1 are capable of restarting a stable FAT process, even though catastrophic overfitting may occur again. The observed phenomena during the FAT restart are: 1) Change from an irregular fluctuation state to a smooth convergence state; 2) Rapid increase in both  $\mathcal{L}(x,\theta)$  and  $\mathcal{L}(x',\theta)$  after a period of decline; 3) Rapid decrease in the classification accuracy of benign samples, while the classification accuracy of adversarial examples experiences a rapid increase.
+
+On this basis, we can make the following conclusions. 1)  $\mathcal{L}(x,\theta)$  is more stable than  $\mathcal{L}(x^{\prime},\theta)$  and models are prone to overfitting to adversarial perturbations; 2) Catastrophic overfitting is closely correlated to the convergence insta
+
+bility of adversarial training; 3) Exceptions in  $\mathcal{L}(x,\theta)$  and  $\mathcal{L}(x^{\prime},\theta)$  occur simultaneously; 4) An oscillating adversarial training phase may trigger the FAT process to restart.
+
+# 3.3. Smooth convergence for the stable FAT
+
+Next, we describe the proposed method in detail.
+
+Why did previous methods fail to prevent catastrophic overfitting? Despite the improvement in diversity achieved through random initialization in FGSM-RS, models are still susceptible to overfitting adversarial perturbations. GradAlign and FGSM-MEP enhance the stability of adversarial training through the constraints in Eqs. (5) and (6), respectively. However, Eq. (5) may reduce the stability of  $\mathcal{L}(x,\theta)$ . Meanwhile, the prediction probability  $f(x + \delta_0;\theta)$  in Eq. (6) is not the sweet spot to keep the FAT stable. Unlike these methods, we ensure the convergence stability of both  $\mathcal{L}(x,\theta)$  and  $\mathcal{L}(x',\theta)$ .
+
+How can catastrophic overfitting be solved? Since the catastrophic overfitting is usually accompanied by a slight change in  $\mathcal{L}(x,\theta)$  and a sharp decline in  $\mathcal{L}(x',\theta)$ , we consider a smooth loss convergence process to be a stable FAT process that resolves this issue. To this end, a complementary constraint  $\mathcal{L}_{CS}$  for Eq. (3) is proposed,
+
+$$
+\min  _ {\theta_ {t}} \mathbb {E} _ {(x, y) \sim D} \left[ \mathcal {L} \left(x _ {t} ^ {\prime}, \theta_ {t}\right) + \mathcal {L} _ {C S} (t) \right], \tag {7}
+$$
+
+which can limit the difference in losses between adjacent epochs, expressed as
+
+$$
+\mathcal {L} _ {C S} (t) = w _ {1} \cdot \left| \mathcal {L} \left(x _ {t} ^ {\prime}, \theta_ {t}\right) - \mathcal {L} \left(x _ {t - 1} ^ {\prime}, \theta_ {t - 1}\right) \right| + \tag {8}
+$$
+
+$$
+w _ {2} \cdot | \mathcal {L} (x, \theta_ {t}) - \mathcal {L} (x, \theta_ {t - 1}) |, \quad s. t. \quad \mathcal {C} (x) = 1,
+$$
+
+where  $\theta_{t}$  represents the model weights of the  $t_{\mathrm{th}}$  training epoch.  $w_{1}$  and  $w_{2}$  are hyper-parameters,  $w_{1}, w_{2} \in [0,1]$ .  $|\cdot|$  calculates the absolute value.  $x_{t}^{\prime} = x + \delta_{0,t} + \delta_{t}$ .  $\delta_{0,t}$  can be replaced by various attack initialization perturbations and  $\delta_{t}$  is generated by
+
+$$
+\max  _ {\delta_ {t} \in [ - \xi , \xi ]} \mathcal {L} \left(x _ {t} ^ {\prime}, \theta_ {t - 1}\right), \tag {9}
+$$
+
+where  $\theta_{t - 1}$  is fixed in generating  $\delta_t$ .
+
+In the practical implementation of Eq. (8), storing and computing  $\mathcal{L}(x_{t - 1}^{\prime},\theta_{t - 1})$  and  $\mathcal{L}(x,\theta_{t - 1})$  can consume a significant amount of memory. To overcome this challenge, we introduce  $u_{t - 1}^{\prime}$  and  $u_{t - 1}$  to replace these terms, respectively.  $u_{t - 1}^{\prime} = \mathbb{E}_{(x,y)\sim D}\mathcal{L}(x_{t - 1}^{\prime},\theta_{t - 1})$  and  $u_{t - 1} = \mathbb{E}_{(x,y)\sim D}\mathcal{L}(x,\theta_{t - 1})$  denote the mathematical expectation of loss in the  $t - 1_{\mathrm{th}}$  training epoch.
+
+We observe that training instability is primarily caused by overfitting or underfitting of small amounts of data. Thus, in Eq. (8), the additional loss term is only applied to partial data selected by the crafted condition  $\mathcal{C}(\cdot)$ . Notably, exceptions in  $\mathcal{L}(x,\theta)$  and  $\mathcal{L}(x',\theta)$  occur simultaneously during training. Hence,  $\mathcal{L}(x_t',\theta_t)$  and  $\mathcal{L}(x_t,\theta_t)$  share
+
+the same condition.  $\mathcal{C}$  is constructed by the distance between the pointwise loss  $\mathcal{L}(x,\theta_t)$  and the mean value  $u_{t - 1}$ . This is because over-fitted or under-fitted data often yield excessively high or low classification losses.
+
+$$
+\mathcal {C} (x) = \left(\left| \mathcal {L} \left(x, \theta_ {t}\right) - u _ {t - 1} \right| \geq \gamma_ {t}\right), \tag {10}
+$$
+
+where  $\gamma_{t} (\gamma_{t} \geq 0)$  represents the convergence stride to select abnormal data. It is crucial to choose an appropriate value for  $\gamma_{t}$  to ensure effective training. When  $\gamma_{t} = 0$ , the adversarial training process may fail to converge as it forces the predictions of all samples to remain unchanged. On the other hand, catastrophic overfitting occurs when  $\gamma_{t} = \infty$ , leading to undesirable outcomes. Considering that the loss difference  $d_{t-1}(d_{t-1} = |u_{t-1} - u_{t-2}|)$  between two adjacent epochs tends to decrease non-linearly,  $\gamma_{t}$  should be a variable that varies during the training process.
+
+$$
+\gamma_ {t} = \min  \left(\max  \left(d _ {t - 1}, \gamma_ {\text {m i n}}\right), \gamma_ {\text {m a x}}\right), \tag {11}
+$$
+
+where  $\gamma_{min}$  and  $\gamma_{max}$  are hyper-parameters.  $\gamma_{max}$  controls the maximum convergence speed.  $\gamma_{min}$  ensures that the training process is not too smooth when  $d_{t - 1} \to 0$ .
+
+Example-based ConvergeSmooth. This approach adds the constraint individually to each sample, described as
+
+$$
+\begin{array}{l} \mathcal {L} _ {C S} ^ {E} (t) = w _ {1} \cdot \left| \mathcal {L} \left(x _ {t} ^ {\prime}, \theta_ {t}\right) - u _ {t - 1} ^ {\prime} \right| + w _ {2} \cdot \left| \mathcal {L} \left(x, \theta_ {t}\right) - u _ {t - 1} \right|, \\ s. t. \quad | \mathcal {L} (x, \theta_ {t}) - u _ {t - 1} | > \gamma_ {t}. \tag {12} \\ \end{array}
+$$
+
+Batch-based ConvergeSmooth. Likewise, we can apply the complementary constraint to a data batch,
+
+$$
+\begin{array}{l} \mathcal {L} _ {C S} ^ {B} (t) = w _ {1} \cdot \left| u _ {B} ^ {\prime} - u _ {t - 1} ^ {\prime} \right| + w _ {2} \cdot \left| u _ {B} - u _ {t - 1} \right|, \tag {13} \\ s. t. \quad | u _ {B} - u _ {t - 1} | > \gamma_ {t}, \\ \end{array}
+$$
+
+where  $u_B^\prime = \mathbb{E}_{(x,y)\sim B}\mathcal{L}(x_t^\prime ,\theta_t),u_B = \mathbb{E}_{(x,y)\sim B}\mathcal{L}(x,\theta_t).$
+
+Weight centralization. To mitigate the problem of manual parameter tuning, we introduce the weight centralization without requiring extra hyperparameters other than the coefficient  $w_{3}$ ,  $|\theta_t - \theta_{t-1}| = 0 \rightarrow |\mathcal{L}(x, \theta_t) - \mathcal{L}(x, \theta_{t-1})| = 0$ ,
+
+$$
+\mathcal {L} _ {C S} ^ {W} (t) = w _ {3} \cdot | | \theta_ {t} - \frac {1}{l e n (\phi)} \cdot \sum_ {j \in \phi} \theta_ {j} | | _ {p}, \tag {14}
+$$
+
+where  $\| \cdot \|_p$  means the p-norm function  $(p = 2)$ , and  $\phi$  denotes a set of previous model weights. The model weights  $\theta_t$  are restricted to the center  $\frac{1}{len(\phi)} \cdot \sum_{j \in \phi} \theta_j$ . The reasons behind Eq. (14) are: 1) The initial training process is stable, as indicated in Fig. 1; 2) Models at different training epochs tend to have similar weights after convergence [37].
+
+# 4. Experimental Results
+
+# 4.1. Experimental settings
+
+Details. To demonstrate the effectiveness of the proposed method, we conduct comprehensive experiments on
+
+<table><tr><td colspan="2">CIFAR10ξ</td><td>FGSM-RS</td><td>FGSM-MEP</td><td>B-RS</td><td>B-MEP</td></tr><tr><td>SQ↑</td><td rowspan="2">16/255</td><td>19.74</td><td>22.15</td><td>28.83</td><td>29.97</td></tr><tr><td>SQ+RayS↑</td><td>18.72</td><td>20.96</td><td>27.08</td><td>28.45</td></tr></table>
+
+Table 1. Quantitative results of FAT methods against the Square and Ray-S attacks on CIFAR-10 with the backbone ResNet18.  
+
+<table><tr><td>CIFAR10</td><td>Clean</td><td>8 255</td><td>10 255</td><td>12 255</td><td>16 255</td><td>SQ+RayS</td><td>Time</td></tr><tr><td>OAAT[1]</td><td>71.30</td><td>44.29</td><td>38.56</td><td>33.68</td><td>28.48</td><td>21.06</td><td>183</td></tr><tr><td>AWP[41]</td><td>78.86</td><td>35.91</td><td>32.70</td><td>29.89</td><td>26.95</td><td>19.36</td><td>134</td></tr><tr><td>ATES[4]</td><td>74.52</td><td>43.61</td><td>38.94</td><td>35.31</td><td>30.89</td><td>22.16</td><td>-</td></tr><tr><td>ExAT[30]</td><td>80.78</td><td>49.21</td><td>42.15</td><td>36.98</td><td>31.26</td><td>23.08</td><td>70</td></tr><tr><td>E-MEP</td><td>69.84</td><td>53.54</td><td>49.26</td><td>45.89</td><td>40.78</td><td>23.78</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>50.31</td><td>46.77</td><td>43.97</td><td>40.13</td><td>28.45</td><td>101</td></tr></table>
+
+Table 2. Quantitative results of methods against various levels of perturbation with ResNet18 as the backbone and CIFAR-10 as the dataset.  $\sharp$  denotes the PGD-10 attack.
+
+several benchmark datasets, i.e. CIFAR-10 [20], CIFAR-100 [20], and Tiny ImageNet [7].
+
+Following previous works [40, 23, 49, 42], we adopt ResNet18 [13] as the backbone on the CIFAR-10 and CIFAR-100, and choose PreActResNet18 [14] on the Tiny ImageNet. In all experiments, models are optimized using the SGD optimizer with a batch size of 128, weight decay of 5e-4, and momentum of 0.9. The initial learning rates on CIFAR-10, CIFAR-100, and Tiny ImageNet are set as 0.1, 0.1, and 0.01, respectively. Then, we optimize models with a total training epoch of 110 and decay the learning rate at the  $100_{\mathrm{th}}$  and  $105_{\mathrm{th}}$  epoch with a factor of 0.1.
+
+We apply the proposed ConvergeSmooth in combination with two attack initialization methods on CIFAR-10 and CIFAR-100, FGSM-RS [40] and FGSM-MEP [42]. Additionally, for the Tiny ImageNet, we use FGSM-BP [42] as the initialization method. As mentioned in [42], FGSM-MEP requires consuming memory to store the previous adversarial perturbations, which limits its application on large datasets. Regarding the hyperparameters, we set  $\gamma_{max}$  in Eq. (11) as 0.03, 0.06, and 0.03 for CIFAR-10, CIFAR-100, and Tiny ImageNet, respectively.  $\gamma_{max} = 1.5 \cdot \gamma_{min}$  and  $\xi = 16/255$ . Specific details of hyperparameter settings for  $w_{1 \sim 3}$  are given in the supplement. All experiments are conducted on a single GeForce RTX 3090 GPU.
+
+Baselines. We include advanced FAT methods as baselines, namely FGSM-RS [40], GradAlign [2], ZeroGrad [10], NuAT [36], ATAS [16], and FGSM-MEP [42].
+
+Evaluation metrics. We follow [40, 16] and adopt FGSM [11], PGD-10 [25], PGD-20 [25], PGD-50 [25], C&W [3], APGD-CE [6] and Autoattack (AA) [6] to evaluate the adversarial robustness of models. PGD-n represents the PGD attack with n iterations. Autoattack combines APGD-CE and APGD-T (targeted APGD) as well as two complementary attacks (FAB [9] and Square attack [26]).
+
+![](images/3e97564525e8fbc6ed20f5e85e150c8587a20b3828877176d39ffb9478255b35.jpg)  
+Figure 2. The training process of various FAT methods (PGD-10,  $\xi = 16 / 255$ ) on CIFAR-10.
+
+The training easily exhibits fluctuations, and thus individual results can not objectively reflect the performance of methods. For each method, we repeat the training process three times and report the average evaluation results of the best model across the three runs (mbest). Additionally, the supplement includes the best results (best) and the average evaluation of the final model from the three runs (mfinal).
+
+In the following section, 'W-\*', 'E-\*', and 'B-\*' mean 'weight centralization', 'example-based ConvergeSmooth', and 'batch-based ConvergeSmooth', respectively.
+
+# 4.2. Significance of the Results
+
+Before evaluating the adversarial robustness of trained models, we demonstrate the significance of the results [1]. Specifically, we show that adversarial attacks with  $\xi = 16/255$  rarely change the true label of input. 1) We generate adversarial examples for the FGSM-RS, FGSM-MEP, and our proposed methods on CIFAR10 and CIFAR100 datasets with  $\xi = 16/255$  using the non-targeted attacks such as FGSM, PGD, C&W, APGD-CE, and the targeted attack APGD-T. The majority of the generated examples retain their true labels; 2) Tab. 1 examines the robustness of models against an ensemble of the Square (SQ) [26] and Ray-S [5] attacks, as these attacks generate strong oracle-invariant examples [1]; 3) We generate adversarial training data with  $\xi = 16/255$  and test the robustness on various levels of perturbation. Tab. 2 provide comparative experiments between our proposed method and other AT techniques, including OAAT [1], ExAT [30], ATES [4] and AWP [41]. It is important to note that we re-implement these AT methods and apply them in the context of FAT. Overall, our methods achieve optimal performance on both oracle-invariant attacks and classical evaluation attacks. Namely, the classical evaluation attacks used in  $\xi = 8/255$  are reliable and significant even when the value of  $\xi$  is increased to 16/255.
+
+Notably, our methods are plugged into FGSM-RS and
+
+<table><tr><td colspan="2">Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td colspan="2">PGD-AT [29]</td><td>65.30</td><td>46.31</td><td>40.73</td><td>35.08</td><td>33.92</td><td>30.84</td><td>33.08</td><td>26.29</td><td>370</td></tr><tr><td colspan="2">FGSM-RS [40]</td><td>50.12</td><td>38.28</td><td>26.13</td><td>21.55</td><td>20.43</td><td>18.96</td><td>19.40</td><td>14.84</td><td>67</td></tr><tr><td colspan="2">GradAlign [2]</td><td>58.17</td><td>39.87</td><td>33.12</td><td>26.81</td><td>24.99</td><td>22.63</td><td>23.98</td><td>17.02</td><td>135</td></tr><tr><td colspan="2">ZeroGrad [10]</td><td>74.16</td><td>43.96</td><td>32.67</td><td>21.98</td><td>18.37</td><td>20.76</td><td>16.44</td><td>12.07</td><td>67</td></tr><tr><td rowspan="3">Ours</td><td>W-RS</td><td>70.66</td><td>45.51</td><td>36.50</td><td>27.51</td><td>24.75</td><td>23.97</td><td>23.38</td><td>17.14</td><td>71</td></tr><tr><td>E-RS</td><td>62.38</td><td>42.07</td><td>36.78</td><td>30.80</td><td>28.90</td><td>23.64</td><td>27.71</td><td>17.55</td><td>77</td></tr><tr><td>B-RS</td><td>65.42</td><td>45.94</td><td>37.54</td><td>30.01</td><td>27.85</td><td>26.28</td><td>26.52</td><td>19.43</td><td>75</td></tr><tr><td colspan="2">NuAT [36]</td><td>74.62</td><td>44.92</td><td>35.22</td><td>25.93</td><td>23.67</td><td>24.07</td><td>22.37</td><td>18.43</td><td>101</td></tr><tr><td colspan="2">ATAS* [16]</td><td>64.11</td><td>-</td><td>31.39</td><td>-</td><td>28.15</td><td>-</td><td>-</td><td>21.09</td><td>-</td></tr><tr><td colspan="2">FGSM-MEP [42]</td><td>53.32</td><td>36.24</td><td>31.85</td><td>27.28</td><td>26.56</td><td>22.10</td><td>26.08</td><td>18.98</td><td>92</td></tr><tr><td rowspan="2">Ours</td><td>E-MEP</td><td>69.84</td><td>47.18</td><td>40.90</td><td>34.17</td><td>32.72</td><td>22.69</td><td>31.12</td><td>17.74</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>45.48</td><td>40.13</td><td>34.21</td><td>32.95</td><td>28.19</td><td>32.04</td><td>23.68</td><td>101</td></tr></table>
+
+Table 3. Quantitative results of various methods ( $\xi = 16/255$ ) on the CIFAR-10 with ResNet18 as the backbone. 'ATAS*' is the result of ATAS in [16], which is superior to our reproduction. We train each method three times. The results represent the evaluation average between the best models of three training processes. Weight centralization and regularization in MEP do not work together.  
+
+<table><tr><td>Budgets (ξ)</td><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td rowspan="4">12/255</td><td>GradAlign [2]</td><td>66.52</td><td>43.06</td><td>31.66</td><td>27.95</td><td>26.04</td><td>27.05</td><td>25.99</td><td>21.65</td><td>135</td></tr><tr><td>NuAT [36]</td><td>72.79</td><td>51.80</td><td>41.75</td><td>38.60</td><td>37.54</td><td>35.99</td><td>36.71</td><td>32.01</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>74.71</td><td>52.05</td><td>38.45</td><td>36.35</td><td>35.52</td><td>33.05</td><td>33.4</td><td>27.23</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>72.63</td><td>54.40</td><td>45.23</td><td>42.85</td><td>42.14</td><td>36.81</td><td>41.62</td><td>33.26</td><td>101</td></tr><tr><td rowspan="4">10/255</td><td>GradAlign [2]</td><td>83.10</td><td>55.23</td><td>36.58</td><td>30.47</td><td>28.64</td><td>31.01</td><td>26.51</td><td>23.84</td><td>135</td></tr><tr><td>NuAT [36]</td><td>75.82</td><td>55.94</td><td>45.54</td><td>43.92</td><td>43.42</td><td>41.39</td><td>42.91</td><td>38.85</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>83.43</td><td>59.51</td><td>42.76</td><td>39.28</td><td>37.33</td><td>37.26</td><td>35.91</td><td>32.52</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>75.96</td><td>57.26</td><td>47.25</td><td>45.98</td><td>45.66</td><td>41.00</td><td>45.26</td><td>39.20</td><td>101</td></tr></table>
+
+Table 4. Quantitative results of FAT methods on various  $\xi$  with ResNet18 as the backbone and CIFAR-10 as the dataset. Models are trained and evaluated under the same  $\xi$  . The number in bold indicates the best.  
+
+<table><tr><td>ξ = 16/255</td><td colspan="2">CIFAR10</td><td colspan="2">CIFAR100</td><td>Time</td></tr><tr><td>Methods</td><td>Clean</td><td>AA</td><td>Clean</td><td>AA</td><td>hours</td></tr><tr><td>GradAlign [2]</td><td>55.58</td><td>13.45</td><td>35.93</td><td>7.13</td><td>8.79</td></tr><tr><td>NuAT [36]</td><td>74.25</td><td>13.19</td><td>20.48</td><td>7.30</td><td>7.66</td></tr><tr><td>FGSM-MEP [42]</td><td>65.56</td><td>15.43</td><td>20.69</td><td>6.73</td><td>6.15</td></tr><tr><td>B-MEP (Ours)</td><td>69.94</td><td>24.27</td><td>48.64</td><td>12.05</td><td>6.72</td></tr></table>
+
+Table 5. The adversarial accuracy of various FAT methods with WideResNet34-10 as the backbone.
+
+FGSM-MEP, which are fitted to the distribution of adversarial examples. Instead, methods such as OAAT are fitted to the distribution of benign samples and perform better on clean accuracy. Therefore, we use the settings as in OAAT and then apply OAAT and our B-OAAT to the FAT task. B-OAAT realizes  $74.12\%$ $(+2.82\%)$  than OAAT) clean accuracy and  $25.39\%$  (OAAT) on SQ+RayS.
+
+# 4.3. Results on CIFAR-10
+
+We conduct our initial experiments on CIFAR-10 using the ResNet18 backbone. The default  $\xi$  is set to 16/255. Tab. 3 presents the main comparisons. The observations
+
+are as follows: (1) Compared with previous FAT methods, the proposed approaches achieve optimal adversarial robustness against different attacks, e.g. B-RS outperforms all RS-based methods and B-MEP is superior to all other methods. Meanwhile, our methods exhibit similar performance to prior work in terms of clean classification accuracy. (2) B-MEP realizes adversarial robustness approaching PGD-AT, e.g. B-MEP performs  $32.95\%$  robustness against the PGD-50 attack, only  $0.97\%$  lower than PGD-AT; (3) As for time consumption, B-RS takes less time (75 minutes) than GradAlign (135 minutes) and NuAT (101 minutes). This is because ConvergeSmooth only requires the additional regularization when  $|u_{B} - u_{t - 1}| > \gamma_{t}$  instead of adding constraints on all iterations. In addition, B-MEP (102 minutes) takes a bit more calculation cost than FGSM-MEP (92 minutes) but much less than PGD-AT (370 minutes). PGD-AT takes significantly longer than FAT works; (4) B-RS and B-MEP successfully prevent catastrophic overfitting, e.g. mfinal (in the supplement) only shows a slight reduction than mbest in terms of adversarial robustness.
+
+Fig. 2 visualizes the training process of various FAT approaches. Compared with other methods, the proposed
+
+<table><tr><td colspan="2">Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td colspan="2">PGD-AT</td><td>40.57</td><td>24.72</td><td>21.46</td><td>17.94</td><td>17.38</td><td>14.98</td><td>17.02</td><td>12.63</td><td>370</td></tr><tr><td colspan="2">FGSM-RS [40]</td><td>30.12</td><td>15.24</td><td>12.69</td><td>10.25</td><td>9.79</td><td>8.45</td><td>9.57</td><td>6.90</td><td>67</td></tr><tr><td colspan="2">GradAlign [2]</td><td>31.91</td><td>15.71</td><td>12.56</td><td>10.28</td><td>9.71</td><td>8.22</td><td>9.47</td><td>6.61</td><td>135</td></tr><tr><td colspan="2">ZeroGrad [10]</td><td>47.31</td><td>23.58</td><td>17.60</td><td>12.85</td><td>11.87</td><td>11.62</td><td>11.01</td><td>7.94</td><td>67</td></tr><tr><td rowspan="3">Ours</td><td>W-RS</td><td>41.97</td><td>26.30</td><td>19.09</td><td>14.77</td><td>13.72</td><td>12.82</td><td>13.36</td><td>9.67</td><td>72</td></tr><tr><td>E-RS</td><td>41.09</td><td>22.33</td><td>18.78</td><td>15.19</td><td>14.43</td><td>12.00</td><td>13.91</td><td>9.50</td><td>78</td></tr><tr><td>B-RS</td><td>41.47</td><td>25.98</td><td>19.44</td><td>15.36</td><td>14.34</td><td>12.91</td><td>13.71</td><td>9.90</td><td>76</td></tr><tr><td colspan="2">NuAT [36]</td><td>31.42</td><td>20.39</td><td>16.15</td><td>13.87</td><td>13.29</td><td>11.12</td><td>12.25</td><td>8.32</td><td>101</td></tr><tr><td colspan="2">ATAS [16]</td><td>55.63</td><td>30.35</td><td>15.31</td><td>10.28</td><td>8.49</td><td>10.97</td><td>6.30</td><td>5.05</td><td>70</td></tr><tr><td colspan="2">FGSM-MEP [42]</td><td>21.39</td><td>13.00</td><td>11.37</td><td>9.93</td><td>9.76</td><td>7.28</td><td>9.58</td><td>6.36</td><td>92</td></tr><tr><td rowspan="2">Ours</td><td>E-MEP</td><td>44.00</td><td>24.46</td><td>20.59</td><td>17.11</td><td>16.59</td><td>13.37</td><td>16.05</td><td>10.97</td><td>106</td></tr><tr><td>B-MEP</td><td>41.86</td><td>24.86</td><td>20.84</td><td>17.30</td><td>16.59</td><td>13.96</td><td>16.25</td><td>11.38</td><td>102</td></tr></table>
+
+Table 6. Quantitative results of various methods  $\left( {\xi  = {16}/{255}}\right)$  with ResNet18 as the backbone on CIFAR-100.  
+
+<table><tr><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (hour)↓</td></tr><tr><td>PGD-AT</td><td>32.52</td><td>16.47</td><td>13.40</td><td>10.63</td><td>10.24</td><td>7.95</td><td>10.00</td><td>6.41</td><td>67.2</td></tr><tr><td>FGSM-RS [40]</td><td>27.48</td><td>12.46</td><td>9.59</td><td>6.97</td><td>6.47</td><td>4.99</td><td>6.19</td><td>3.63</td><td>10.5</td></tr><tr><td>GradAlign [2]</td><td>28.65</td><td>13.80</td><td>10.40</td><td>7.78</td><td>7.08</td><td>5.75</td><td>6.59</td><td>3.90</td><td>20.9</td></tr><tr><td>ZeroGrad [10]</td><td>34.66</td><td>12.26</td><td>8.22</td><td>5.29</td><td>4.82</td><td>3.71</td><td>4.23</td><td>2.21</td><td>10.5</td></tr><tr><td>NuAT [36]</td><td>35.24</td><td>15.52</td><td>12.07</td><td>8.81</td><td>8.13</td><td>6.29</td><td>7.68</td><td>4.27</td><td>24.6</td></tr><tr><td>FGSM-BP [42]</td><td>20.02</td><td>10.18</td><td>8.38</td><td>6.98</td><td>6.77</td><td>4.56</td><td>6.57</td><td>3.62</td><td>14.3</td></tr><tr><td>B-BP (Ours)</td><td>33.51</td><td>16.32</td><td>12.92</td><td>9.72</td><td>9.23</td><td>7.26</td><td>9.32</td><td>5.95</td><td>15.4</td></tr></table>
+
+Table 7. Quantitative results of various methods  $\left( {\xi  = {16}/{255}}\right)$  with PreActResNet18 as the backbone on Tiny ImageNet.
+
+B-RS achieves optimal training stability and adversarial robustness, e.g. the classification accuracy of our method fluctuates slightly during three adversarial training sessions.
+
+Various budgets. Similar experiments are performed for budgets 10/255 and 12/255. Details are given in Tab. 4. It is evident that the proposed method achieves optimal adversarial robustness across various perturbation budgets.
+
+Various networks. We then adopt WideResNet34 with a width factor of 10 [47] as the backbone. The results are given in Tab. 5. Our proposed B-MEP also prevents the wider architectures from catastrophic overfitting.
+
+# 4.4. Results on CIFAR-100
+
+The results on CIFAR-100 with the backbone ResNet-18 are presented in Tab. 6. (1) FAT methods perform similar training consumption on CIFAR-10 and CIFAR-100 as two datasets contain the same number and size of images; (2) All proposed methods can realize stable adversarial training, as evidenced by the comparable results of mbest and mfinal (in the supplement); (3) Among the RS-based FAT works, B-RS and E-RS achieve the best and second-best adversarial robustness against different attacks; (4) B-MEP outperforms all other FAT methods; (5) Although B-MEP performs slightly worse than PGD-AT, its training process is approximately 3.5 times faster than this competitor.
+
+# 4.5. Results on Tiny ImageNet
+
+We conduct experiments on the Tiny ImageNet using the PreActResNet18 backbone to demonstrate the scalability of the proposed method to large datasets. The results are given in Tab. 7. B-BP achieves higher robustness among the FAT methods and comparable robustness to PGD-AT. As for training efficiency, B-BP (15.4 hours) requires slightly more computational cost than FGSM-BP (14.3 hours), but significantly less time than PGD-AT (67.2 hours).
+
+# 4.6. Ablation studies
+
+In the following, B-RS is selected as the backbone. Figs. 3 and 4 conduct ablation studies on  $\gamma_{max}$  and  $\gamma_{max} / \gamma_{min}$  respectively. In Fig. 3, the classification accuracy of both benign and adversarial examples increases with  $\gamma_{max}$ . However, the model trained with a large  $\gamma_{max}$  ( $>0.09$ ) suffers from catastrophic overfitting. Fig. 4 shows that the model with  $\gamma_{max} / \gamma_{min} = 1.5$  achieves optimal robustness.  $\gamma_{max} / \gamma_{min} = 1$  denotes the static convergence stride. All models can be trained stably when  $\gamma_{max} = 0.06$ .
+
+Tabs. 8 and 9 provide the results of comparative experiments on  $w_{1}$  and  $w_{2}$  respectively. We empirically set  $w_{2}$  to 1 since too small  $w_{2}$  cannot prevent overfitting and too large  $w_{2}$  will affect the performance. In Tab. 8,  $w_{1} = 0$  achieves optimal adversarial robustness on CIFAR100 and
+
+<table><tr><td>Dataset</td><td>w1</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Stability</td></tr><tr><td rowspan="5">CIFAR100</td><td>0.0</td><td>48.13</td><td>32.13</td><td>24.25</td><td>22.67</td><td>22.21</td><td>19.04</td><td>21.29</td><td>15.28</td><td>★★★</td></tr><tr><td>0.3</td><td>46.08</td><td>30.58</td><td>23.06</td><td>21.62</td><td>21.22</td><td>17.79</td><td>20.44</td><td>15.22</td><td>★★★</td></tr><tr><td>0.5</td><td>44.04</td><td>29.96</td><td>22.64</td><td>21.34</td><td>20.99</td><td>17.55</td><td>19.16</td><td>13.84</td><td>★★★</td></tr><tr><td>0.7</td><td>43.07</td><td>28.61</td><td>22.01</td><td>20.84</td><td>20.32</td><td>16.87</td><td>18.98</td><td>13.47</td><td>★★★</td></tr><tr><td>0.9</td><td>40.45</td><td>21.05</td><td>21.62</td><td>20.54</td><td>20.15</td><td>16.33</td><td>18.91</td><td>13.53</td><td>★★★</td></tr></table>
+
+Table 8. Quantitative results of the proposed method on various  $w_{1}$  with ResNet18 as the backbone and the perturbation budget 12/255. 'Stability' represents the number of times the model is stable in three training repetitions.  $\gamma_{max}$  and  $w_{2}$  are set to 0.03 and 1, respectively.  
+
+<table><tr><td>Dataset</td><td>w2</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Stability</td></tr><tr><td rowspan="4">CIFAR100</td><td>0.5</td><td>36.79</td><td>23.97</td><td>18.60</td><td>17.51</td><td>17.23</td><td>14.65</td><td>16.28</td><td>12.23</td><td>-</td></tr><tr><td>0.7</td><td>37.31</td><td>24.36</td><td>18.56</td><td>17.37</td><td>17.26</td><td>14.46</td><td>15.96</td><td>11.54</td><td>-</td></tr><tr><td>1.0</td><td>48.13</td><td>32.13</td><td>24.25</td><td>22.67</td><td>22.21</td><td>19.04</td><td>21.29</td><td>15.28</td><td>★★★</td></tr><tr><td>1.3</td><td>44.84</td><td>30.42</td><td>23.31</td><td>21.72</td><td>21.31</td><td>18.36</td><td>19.64</td><td>14.72</td><td>★★★</td></tr></table>
+
+Table 9. Quantitative results on various  ${w}_{2}\left( {{\gamma }_{max} = {0.03}}\right.$  and  ${w}_{1} = 0)$  with ResNet18 as the backbone and  $\xi  = {12}/{255}$  .
+
+![](images/b66648bc0d3b8cb0ffe73994f5c9c86e4af5bbb2d70966398399a8e131e75277.jpg)  
+ResNet18 trained with ConvergeSmooth-RS on CIFAR-100  
+Figure 3. Ablation study of  $\gamma_{max}(\gamma_{max} / \gamma_{min} = 1.5)$ . We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10,  $\xi = 16/255$ ) on CIFAR-100.
+
+all settings accomplish stable FAT. According to Eqs. (7) and (8), if  $w_{1} \neq 0$ , for the data  $x$  which satisfies  $\mathcal{C}(x) = 1$ ,  $\mathcal{L}(x_t', \theta_t)$  is assigned with higher weights  $(1 + w_{1})$  or lower weights  $(1 - w_{1})$ , causing the model to excessively prioritize or neglect this portion of the data. This may weaken the performance of models. However, for Tiny ImageNet, models suffer catastrophic overfitting at  $w_{1} = 0$ . Then, we gradually increase  $w_{1}$  from 0.3 with a stride of 0.2 until the FAT process becomes stable. In addition, our weight centralization method only introduces a balance coefficient  $w_{3}$ .  $w_{3}$  is set to 0.1 since catastrophic overfitting happens when  $w_{3} = 0$  and classification performance is degraded when  $w_{3} = 0.2$ .
+
+# 5. Conclusion
+
+In this paper, we tackle the issue of catastrophic overfitting by focusing on the convergence stability of loss func
+
+![](images/b22b73832bd1331752bbefd95f835fb0c27d3622c1c6426d3618be637481b38b.jpg)  
+ResNet18 trained with ConvergeSmooth-RS on CIFAR-100  
+Figure 4. Ablation study of  $\gamma_{max} / \gamma_{min}$  ( $\gamma_{max} = 0.06$ ). We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10,  $\xi = 16/255$ ) on CIFAR-100.
+
+tions. Through experimental analysis, we find that this issue is accompanied by abnormal convergence behavior of losses. Motivated by this phenomenon, we propose complementary constraints, namely E-ConvergeSmooth and B-ConvergeSmooth, based on the adversarial training constraint. To alleviate the burden of parameter tuning, weight centralization is designed utilizing priors from previous epochs. Extensive experiments on different network architectures and datasets show that the proposed methods effectively solve catastrophic overfitting and exhibit superior robustness against various adversarial attacks.
+
+Acknowledgments. This work was supported by the National Key R&D Program of China #2018AAA0102000 and the National Natural Science Foundation of China #62276046 and #U19B2039.
+
+# References
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\ No newline at end of file
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+                                    "content": "Fast adversarial training (FAT) is beneficial for improving the adversarial robustness of neural networks. However, previous FAT work has encountered a significant issue known as catastrophic overfitting when dealing with large perturbation budgets, i.e. the adversarial robustness of models declines to near zero during training. To address this, we analyze the training process of prior FAT work and observe that catastrophic overfitting is accompanied by the appearance of loss convergence outliers. Therefore, we argue a moderately smooth loss convergence process will be a stable FAT process that solves catastrophic overfitting. To obtain a smooth loss convergence process, we propose a novel oscillatory constraint (dubbed ConvergeSmooth) to limit the loss difference between adjacent epochs. The convergence stride of ConvergeSmooth is introduced to balance convergence and smoothing. Likewise, we design weight centralization without introducing additional hyperparameters other than the loss balance coefficient. Our proposed methods are attack-agnostic and thus can improve the training stability of various FAT techniques. Extensive experiments on popular datasets show that the proposed methods efficiently avoid catastrophic overfitting and outperform all previous FAT methods. Code is available at https://github.com/FAT-CS/ConvergeSmooth."
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+                                    "content": "Recent breakthroughs in deep learning [21, 32] have aroused researchers' interest in the security of neural networks [45, 48, 39]. In particular, the advanced research proves the vulnerability of deep models to adversarial attacks [8, 11, 27]. For instance, tiny crafted perturbations can fool models in various fields into making wrong decisions [15, 50, 35, 24]. Considering the security risks brought by adversarial attacks [18, 46, 33, 44], there is a quickly grow"
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+                                    "content": "ing body of work [43, 46, 18] on improving the adversarial robustness of neural networks. Among them, adversarial training is widely applied by practitioners [31, 12]."
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+                                }
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+                                    "content": "A number of FAT methods have been proposed to mitigate catastrophic overfitting. For example, Wong et al. [40] use randomly initialized perturbations to enhance the diversity of adversarial perturbations. Based on it, Andriushchenko et al. [2] raise a complementary regularizer named GradAlign to maximize the gradient alignment between benign and adversarial examples explicitly. Similarly, NuAT [36] and FGSM-MEP [42] adopt nuclear norm or p-norm to regularize the adversarial training, thereby increasing the prediction alignment between benign and adversarial examples. However, the above methods can only resolve catastrophic overfitting within the limited perturbation budget ("
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+                                    "content": " specifies the perturbation degree of adversarial training data generated by various attacks. Besides, models trained by small perturbations are vulnerable to adversarial attacks with a large "
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+                                    "content": "\\xi = 8/255"
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " robustness against the PGD-50 attack with "
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+                                    "type": "inline_equation",
+                                    "content": "\\xi = 8/255"
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+                                    "type": "inline_equation",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " robustness against the same attack with "
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+                                    "type": "inline_equation",
+                                    "content": "\\xi = 16/255"
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " respectively. Therefore, we aspire to prevent catastrophic overfitting to improve the adversarial robustness of neural models at larger perturbation budgets."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "content": "By analyzing adversarial training processes of representative work, we observe that catastrophic overfitting is usually accompanied by a slight fluctuation in the classification loss for benign samples and a sharp drop in the classification"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "type": "text",
+                                    "content": "*Corresponding author"
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+                                    "type": "text",
+                                    "content": "loss for adversarial examples. This motivates us to question whether a smooth loss convergence process is also a stable FAT process. Moreover, we find that an oscillating adversarial training phase may restart the FAT process after catastrophic overfitting. Fig. 1 shows the details."
+                                }
+                            ]
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+                                    "content": "According to these observations, we introduce an oscillatory constraint that limits the difference in loss between adjacent training epochs, called ConvergeSmooth. A dynamic convergence stride of ConvergeSmooth is designed considering the nonlinear decay rate of loss functions. Inspired by the smoothness of loss convergence, we further verify the effect of the proposed weight centralization on model stability. Weight centralization refers to taking the weights average of the previously trained models as the convergence center of the current model weight. Our proposed methods are attack-agnostic and thus can be combined with existing adversarial strategies in FAT, such as FGSM-RS and FGSM-MEP, to evaluate their performance."
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+                                    "content": "The contributions are summarized in four aspects: (1) We verify that previous FAT works still suffer from catastrophic overfitting at a large "
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+                                    "content": " and then study catastrophic overfitting from the perspective of convergence instability of loss functions; (2) We propose a smooth convergence constraint, ConvergeSmooth, and design a dynamic convergence stride for it, to help various FAT methods avoid catastrophic overfitting on different perturbation budgets; (3) The weight centralization is proposed without introducing extra hyperparameters other than the loss balance coefficient to stabilize FAT; (4) Extensive experiments show that the proposed methods outperform the state-of-the-art FAT techniques in terms of efficiency, robustness, and stability."
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+                                    "content": "2. Related Work"
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+                                    "content": "Adversarial attacks. Adversarial attacks are usually used to deceive deep-learning models. Goodfellow et al. [11] first discuss the adversarial attack (FGSM) within the classification task. They prove that adversarial examples "
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+                                    "content": " generated by a single-step gradient backward can misclassify the model "
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+                                    "content": ". Following the FGSM [11], researchers propose a series of attack methods based on the iterative gradient backward, e.g. I-FGSM [22], MIM [8], and PGD [25]. Taking the PGD attack as an example, the adversarial example "
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+                                    "content": "\\min  _ {\\theta} \\mathbb {E} _ {(x, y) \\sim D} [ \\max  _ {\\delta \\in [ - \\xi , \\xi ]} \\mathcal {L} (f \\left(x ^ {\\prime}; \\theta\\right), y) ], \\tag {3}",
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+                                    "content": " represents the adversarial perturbations generated by various attacks such as PGD and FGSM. "
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+                                    "content": " is the data generator. The internal maximization maximizes the classification loss to generate adversarial perturbations with fixed model weights. The external minimization minimizes the classification loss on the generated adversarial examples when optimizing the model weights."
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+                                    "type": "text",
+                                    "content": "Actually, there is a trade-off between computational efficiency and adversarial robustness in recent adversarial training methods. Compared to PGD-AT [25], FGSM-based fast adversarial training (FAT) accelerates the training process but damages the robustness of models for the problem of catastrophic overfitting [19, 17]. To mitigate this issue, Wong et.al [40] demonstrate that the FGSM with a random start strategy (FGSM-RS) can achieve comparable performance against the PGD-AT. ZeroGrad [10] zeroes the elements of gradient that are too small to craft the perturbations. enforces the model loss to increase with the increase in perturbation size. Besides, GradAlign [2] prevents catastrophic overfitting by maximizing the alignment between gradients of benign samples and adversarial examples."
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+                                    "content": "Similarly, NuAT [36] introduces a nuclear norm regularization between logits for benign and adversarial examples and uses the Bernoulli noise as the initial perturbation. ATAS [16] learns an instantiated adaptive step size that is inversely proportional to the gradient norm. It applies the adversarial perturbations from the previous epoch as the initialization of FGSM in the current training phase. In addition, Jia et al. [42] propose several prior-guided initialization methods to replace the random start strategy of FGSM-RS. Specifically, FGSM-BP adopts the adversarial perturbations from the previous batch as the attack initialization in the current batch. FGSM-MEP employs a momentum mechanism to combine all adversarial perturbations from the previous epochs to yield adversarial initialization."
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+                                    "type": "text",
+                                    "content": "Although these FAT methods have resolved catastrophic overfitting at small perturbation budgets, they still suffer from catastrophic overfitting under larger perturbation budgets (e.g. "
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+                                    "type": "text",
+                                    "content": "). Unlike these methods, we revisit the catastrophic overfitting problem from the perspective of loss convergence instability and prevent this exception by limiting the magnitude of loss fluctuations during training."
+                                }
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+                                    "content": "3. Proposed Method"
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+                                            "type": "text",
+                                            "content": "Figure 1. The training process of previous FAT methods with ResNet18 on CIFAR-10. Each FAT method is trained 3 times. "
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+                                            "type": "text",
+                                            "content": ". ADV-Loss and BEN-Loss denote the classification loss of models to adversarial and benign examples during training, respectively. ADV-Acc and BEN-Acc represent the classification accuracy of models to adversarial and benign examples during testing, respectively."
+                                        }
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+                                    "content": "\\xi"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Then, the training processes of these methods have been analyzed for a better understanding of catastrophic overfitting. Finally, we detail the proposed methods."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "3.1. Performance of FAT methods on a large "
+                                },
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+                                    "content": "Previous FAT techniques avoid catastrophic overfitting at small "
+                                },
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+                                    "content": "\\xi \\leq 8/255"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "). Here, we investigate their performance on a large "
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+                                    "type": "inline_equation",
+                                    "content": "\\xi = 16/255"
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+                                    "type": "text",
+                                    "content": " by default)."
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+                                    "type": "text",
+                                    "content": "FGSM-RS [40]: Based on Eq. (3), this method adopts the samples with uniformly random perturbations "
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+                                    "type": "text",
+                                    "content": " as the attack initialization of FGSM,"
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+                                    "type": "interline_equation",
+                                    "content": "\\min  _ {\\theta} \\mathbb {E} _ {(x, y) \\sim D} [ \\max  _ {\\delta_ {0} + \\delta \\in [ - \\xi , \\xi ]} \\mathcal {L} (f (x ^ {\\prime}; \\theta), y) ],",
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+                                    "type": "interline_equation",
+                                    "content": "x ^ {\\prime} = x + \\delta_ {0} + \\delta \\quad s. t. \\quad x ^ {\\prime} \\in [ 0, 1 ], \\quad \\delta_ {0} \\sim \\mathcal {U} (- \\xi , \\xi). \\tag {4}",
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+                                    "type": "text",
+                                    "content": "GradAlign [2]: This approach increases the gradient alignment between benign samples "
+                                },
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+                                    "type": "text",
+                                    "content": " and perturbed samples "
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+                                    "type": "inline_equation",
+                                    "content": "x + \\delta_0"
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+                                    "type": "text",
+                                    "content": ", which is denoted as"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbb {E} _ {(x, y) \\sim D} [ 1 - \\cos (\\nabla_ {x} \\mathcal {L} (x, \\theta), \\nabla_ {x + \\delta_ {0}} \\mathcal {L} (x + \\delta_ {0}, \\theta) ], \\tag {5}",
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} (x, \\theta) = \\mathcal {L} (f (x; \\theta), y).",
+                                    "image_path": "7cb2f1b942112c409358d93ce708924da5d6762fdb30ada47ff1dbe7bfe9c9d1.jpg"
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+                                    "type": "inline_equation",
+                                    "content": "\\cos (\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " computes the cosine similarity between two matrices."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28
+                },
+                {
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+                                    "type": "text",
+                                    "content": "FGSM-MEP [42]: Different from FGSM-RS, this method generates the initialization perturbations "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\delta_0"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " based on all historical adversarial perturbations from the previous epochs and introduces a regularization expressed as"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbb {E} _ {(x, y) \\sim D} [ | | f (x ^ {\\prime}; \\theta) - f (x + \\delta_ {0}; \\theta) | | _ {2} ^ {2} ], \\tag {6}",
+                                    "image_path": "e23d709d81928959d4e7053afc028069c6d97fe6e77746548413719a898ef589.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "||\\cdot ||_2^2"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the squared "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_2"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " distance."
+                                }
+                            ]
+                        }
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+                    "index": 31
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Fig. 1 shows their detailed adversarial training processes of ResNet18 [13] on CIFAR-10 [20]. We find that they fall into catastrophic overfitting during the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "5 \\sim 20_{\\mathrm{th}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "40 \\sim 65_{\\mathrm{th}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        390,
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+                                        450
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "10 \\sim 15_{\\mathrm{th}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " epochs, respectively. Graphical analysis of various models and datasets is given in the supplement."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.2. Analysis of training process"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "From Fig. 1, we discover several typical phenomena of catastrophic overfitting: 1) Change from a smooth convergence state to an irregular fluctuation state; 2) A slight change (increase or decrease) in the standard classification loss "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and a rapid descent of the adversarial classification loss "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x',\\theta)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
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+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": "; 3) Rapid decline in the classification accuracy of adversarial examples."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "After catastrophic overfitting, the methods depicted in Fig. 1 are capable of restarting a stable FAT process, even though catastrophic overfitting may occur again. The observed phenomena during the FAT restart are: 1) Change from an irregular fluctuation state to a smooth convergence state; 2) Rapid increase in both "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x',\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " after a period of decline; 3) Rapid decrease in the classification accuracy of benign samples, while the classification accuracy of adversarial examples experiences a rapid increase."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 35
+                },
+                {
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+                                    "content": "On this basis, we can make the following conclusions. 1) "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is more stable than "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x^{\\prime},\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                        665,
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+                                    "type": "text",
+                                    "content": " and models are prone to overfitting to adversarial perturbations; 2) Catastrophic overfitting is closely correlated to the convergence insta"
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+                                    "content": "4722"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "bility of adversarial training; 3) Exceptions in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x^{\\prime},\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " occur simultaneously; 4) An oscillating adversarial training phase may trigger the FAT process to restart."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.3. Smooth convergence for the stable FAT"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Next, we describe the proposed method in detail."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Why did previous methods fail to prevent catastrophic overfitting? Despite the improvement in diversity achieved through random initialization in FGSM-RS, models are still susceptible to overfitting adversarial perturbations. GradAlign and FGSM-MEP enhance the stability of adversarial training through the constraints in Eqs. (5) and (6), respectively. However, Eq. (5) may reduce the stability of "
+                                },
+                                {
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Meanwhile, the prediction probability "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(x + \\delta_0;\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " in Eq. (6) is not the sweet spot to keep the FAT stable. Unlike these methods, we ensure the convergence stability of both "
+                                },
+                                {
+                                    "bbox": [
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+                                        146,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
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+                                {
+                                    "bbox": [
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+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x',\\theta)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "How can catastrophic overfitting be solved? Since the catastrophic overfitting is usually accompanied by a slight change in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and a sharp decline in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x',\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we consider a smooth loss convergence process to be a stable FAT process that resolves this issue. To this end, a complementary constraint "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{CS}"
+                                },
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+                                    "type": "text",
+                                    "content": " for Eq. (3) is proposed,"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\min  _ {\\theta_ {t}} \\mathbb {E} _ {(x, y) \\sim D} \\left[ \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) + \\mathcal {L} _ {C S} (t) \\right], \\tag {7}",
+                                    "image_path": "13fc915b6b2b21b98369150ba27a99b56ad50dc3d501bb9aac420788dbfa310e.jpg"
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+                                    "type": "text",
+                                    "content": "which can limit the difference in losses between adjacent epochs, expressed as"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {C S} (t) = w _ {1} \\cdot \\left| \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) - \\mathcal {L} \\left(x _ {t - 1} ^ {\\prime}, \\theta_ {t - 1}\\right) \\right| + \\tag {8}",
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+                                    "type": "interline_equation",
+                                    "content": "w _ {2} \\cdot | \\mathcal {L} (x, \\theta_ {t}) - \\mathcal {L} (x, \\theta_ {t - 1}) |, \\quad s. t. \\quad \\mathcal {C} (x) = 1,",
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+                                    "content": "where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " represents the model weights of the "
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+                                    "type": "inline_equation",
+                                    "content": "t_{\\mathrm{th}}"
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+                                    "type": "text",
+                                    "content": " training epoch. "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " are hyper-parameters, "
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+                                    "type": "inline_equation",
+                                    "content": "w_{1}, w_{2} \\in [0,1]"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "type": "inline_equation",
+                                    "content": "|\\cdot|"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " calculates the absolute value. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{t}^{\\prime} = x + \\delta_{0,t} + \\delta_{t}"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "type": "inline_equation",
+                                    "content": "\\delta_{0,t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " can be replaced by various attack initialization perturbations and "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is generated by"
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+                                    "content": "\\max  _ {\\delta_ {t} \\in [ - \\xi , \\xi ]} \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t - 1}\\right), \\tag {9}",
+                                    "image_path": "c0ff85f4092b81cdd31b862d109e2f4e8dfc679317817e78a6062e11c44ebf73.jpg"
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is fixed in generating "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "."
+                                }
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+                {
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+                                    "type": "text",
+                                    "content": "In the practical implementation of Eq. (8), storing and computing "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "inline_equation",
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+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " can consume a significant amount of memory. To overcome this challenge, we introduce "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_{t - 1}^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_{t - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " to replace these terms, respectively. "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_{t - 1}^{\\prime} = \\mathbb{E}_{(x,y)\\sim D}\\mathcal{L}(x_{t - 1}^{\\prime},\\theta_{t - 1})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_{t - 1} = \\mathbb{E}_{(x,y)\\sim D}\\mathcal{L}(x,\\theta_{t - 1})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the mathematical expectation of loss in the "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t - 1_{\\mathrm{th}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        558,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " training epoch."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        46,
+                        642,
+                        287,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                642,
+                                287,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "We observe that training instability is primarily caused by overfitting or underfitting of small amounts of data. Thus, in Eq. (8), the additional loss term is only applied to partial data selected by the crafted condition "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ". Notably, exceptions in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x',\\theta)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " occur simultaneously during training. Hence, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x_t',\\theta_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x_t,\\theta_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " share"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        545,
+                        120
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                72,
+                                545,
+                                120
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": "the same condition. "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": " is constructed by the distance between the pointwise loss "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}(x,\\theta_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": " and the mean value "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_{t - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": ". This is because over-fitted or under-fitted data often yield excessively high or low classification losses."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                        144
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                356,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        356,
+                                        131,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {C} (x) = \\left(\\left| \\mathcal {L} \\left(x, \\theta_ {t}\\right) - u _ {t - 1} \\right| \\geq \\gamma_ {t}\\right), \\tag {10}",
+                                    "image_path": "2a74bbabcb275543f5eef2609698ff7a964980e3b325995aab8c6182814a5949.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                        268
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                545,
+                                268
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{t} (\\gamma_{t} \\geq 0)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the convergence stride to select abnormal data. It is crucial to choose an appropriate value for "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": " to ensure effective training. When "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{t} = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": ", the adversarial training process may fail to converge as it forces the predictions of all samples to remain unchanged. On the other hand, catastrophic overfitting occurs when "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{t} = \\infty"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": ", leading to undesirable outcomes. Considering that the loss difference "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d_{t-1}(d_{t-1} = |u_{t-1} - u_{t-2}|)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": " between two adjacent epochs tends to decrease non-linearly, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        148,
+                                        545,
+                                        268
+                                    ],
+                                    "type": "text",
+                                    "content": " should be a variable that varies during the training process."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        351,
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+                        293
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        351,
+                                        280,
+                                        545,
+                                        293
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\gamma_ {t} = \\min  \\left(\\max  \\left(d _ {t - 1}, \\gamma_ {\\text {m i n}}\\right), \\gamma_ {\\text {m a x}}\\right), \\tag {11}",
+                                    "image_path": "674e8d19af5eed058a625a081bbd3a549bdd2b228c911d562b2aa449bec89c66.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{min}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{max}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": " are hyper-parameters. "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{max}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": " controls the maximum convergence speed. "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{min}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": " ensures that the training process is not too smooth when "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d_{t - 1} \\to 0"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        304,
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+                        357
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        333,
+                                        545,
+                                        357
+                                    ],
+                                    "type": "text",
+                                    "content": "Example-based ConvergeSmooth. This approach adds the constraint individually to each sample, described as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
+                        306,
+                        362,
+                        548,
+                        402
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        362,
+                                        548,
+                                        402
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {C S} ^ {E} (t) = w _ {1} \\cdot \\left| \\mathcal {L} \\left(x _ {t} ^ {\\prime}, \\theta_ {t}\\right) - u _ {t - 1} ^ {\\prime} \\right| + w _ {2} \\cdot \\left| \\mathcal {L} \\left(x, \\theta_ {t}\\right) - u _ {t - 1} \\right|, \\\\ s. t. \\quad | \\mathcal {L} (x, \\theta_ {t}) - u _ {t - 1} | > \\gamma_ {t}. \\tag {12} \\\\ \\end{array}",
+                                    "image_path": "14c3edffc3f83b97de15b3e29bd5d0bebe8749180abf2c90f58a89282766a0ae.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
+                        304,
+                        403,
+                        545,
+                        426
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        403,
+                                        545,
+                                        426
+                                    ],
+                                    "type": "text",
+                                    "content": "Batch-based ConvergeSmooth. Likewise, we can apply the complementary constraint to a data batch,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
+                        318,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        318,
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+                                        461
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {C S} ^ {B} (t) = w _ {1} \\cdot \\left| u _ {B} ^ {\\prime} - u _ {t - 1} ^ {\\prime} \\right| + w _ {2} \\cdot \\left| u _ {B} - u _ {t - 1} \\right|, \\tag {13} \\\\ s. t. \\quad | u _ {B} - u _ {t - 1} | > \\gamma_ {t}, \\\\ \\end{array}",
+                                    "image_path": "4e4d814259419d995637f14c0fd016b7f52c083c4faf34a473a931ae8ba306d0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        468,
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+                                        481
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        468,
+                                        538,
+                                        481
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_B^\\prime = \\mathbb{E}_{(x,y)\\sim B}\\mathcal{L}(x_t^\\prime ,\\theta_t),u_B = \\mathbb{E}_{(x,y)\\sim B}\\mathcal{L}(x,\\theta_t)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
+                        304,
+                        481,
+                        545,
+                        529
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        481,
+                                        545,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": "Weight centralization. To mitigate the problem of manual parameter tuning, we introduce the weight centralization without requiring extra hyperparameters other than the coefficient "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        481,
+                                        545,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{3}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        481,
+                                        545,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        481,
+                                        545,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|\\theta_t - \\theta_{t-1}| = 0 \\rightarrow |\\mathcal{L}(x, \\theta_t) - \\mathcal{L}(x, \\theta_{t-1})| = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        481,
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+                                    "content": "\\mathcal {L} _ {C S} ^ {W} (t) = w _ {3} \\cdot | | \\theta_ {t} - \\frac {1}{l e n (\\phi)} \\cdot \\sum_ {j \\in \\phi} \\theta_ {j} | | _ {p}, \\tag {14}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "text",
+                                    "content": " means the p-norm function "
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+                                    "type": "inline_equation",
+                                    "content": "(p = 2)"
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "content": "\\phi"
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+                                    "type": "text",
+                                    "content": " denotes a set of previous model weights. The model weights "
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+                                    "type": "inline_equation",
+                                    "content": "\\theta_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are restricted to the center "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\frac{1}{len(\\phi)} \\cdot \\sum_{j \\in \\phi} \\theta_j"
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+                                {
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+                                    "type": "text",
+                                    "content": ". The reasons behind Eq. (14) are: 1) The initial training process is stable, as indicated in Fig. 1; 2) Models at different training epochs tend to have similar weights after convergence [37]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4. Experimental Results"
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+                                    "content": "4.1. Experimental settings"
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+                                    "type": "text",
+                                    "content": "Details. To demonstrate the effectiveness of the proposed method, we conduct comprehensive experiments on"
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+                                            "type": "table",
+                                            "html": "<table><tr><td colspan=\"2\">CIFAR10ξ</td><td>FGSM-RS</td><td>FGSM-MEP</td><td>B-RS</td><td>B-MEP</td></tr><tr><td>SQ↑</td><td rowspan=\"2\">16/255</td><td>19.74</td><td>22.15</td><td>28.83</td><td>29.97</td></tr><tr><td>SQ+RayS↑</td><td>18.72</td><td>20.96</td><td>27.08</td><td>28.45</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. Quantitative results of FAT methods against the Square and Ray-S attacks on CIFAR-10 with the backbone ResNet18."
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+                                    ]
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+                                            "html": "<table><tr><td>CIFAR10</td><td>Clean</td><td>8 255</td><td>10 255</td><td>12 255</td><td>16 255</td><td>SQ+RayS</td><td>Time</td></tr><tr><td>OAAT[1]</td><td>71.30</td><td>44.29</td><td>38.56</td><td>33.68</td><td>28.48</td><td>21.06</td><td>183</td></tr><tr><td>AWP[41]</td><td>78.86</td><td>35.91</td><td>32.70</td><td>29.89</td><td>26.95</td><td>19.36</td><td>134</td></tr><tr><td>ATES[4]</td><td>74.52</td><td>43.61</td><td>38.94</td><td>35.31</td><td>30.89</td><td>22.16</td><td>-</td></tr><tr><td>ExAT[30]</td><td>80.78</td><td>49.21</td><td>42.15</td><td>36.98</td><td>31.26</td><td>23.08</td><td>70</td></tr><tr><td>E-MEP</td><td>69.84</td><td>53.54</td><td>49.26</td><td>45.89</td><td>40.78</td><td>23.78</td><td>104</td></tr><tr><td>B-MEP</td><td>63.84</td><td>50.31</td><td>46.77</td><td>43.97</td><td>40.13</td><td>28.45</td><td>101</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 2. Quantitative results of methods against various levels of perturbation with ResNet18 as the backbone and CIFAR-10 as the dataset. "
+                                },
+                                {
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+                                    "content": " denotes the PGD-10 attack."
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+                                    "type": "text",
+                                    "content": "several benchmark datasets, i.e. CIFAR-10 [20], CIFAR-100 [20], and Tiny ImageNet [7]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Following previous works [40, 23, 49, 42], we adopt ResNet18 [13] as the backbone on the CIFAR-10 and CIFAR-100, and choose PreActResNet18 [14] on the Tiny ImageNet. In all experiments, models are optimized using the SGD optimizer with a batch size of 128, weight decay of 5e-4, and momentum of 0.9. The initial learning rates on CIFAR-10, CIFAR-100, and Tiny ImageNet are set as 0.1, 0.1, and 0.01, respectively. Then, we optimize models with a total training epoch of 110 and decay the learning rate at the "
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+                                    "content": "100_{\\mathrm{th}}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "105_{\\mathrm{th}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " epoch with a factor of 0.1."
+                                }
+                            ]
+                        }
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+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We apply the proposed ConvergeSmooth in combination with two attack initialization methods on CIFAR-10 and CIFAR-100, FGSM-RS [40] and FGSM-MEP [42]. Additionally, for the Tiny ImageNet, we use FGSM-BP [42] as the initialization method. As mentioned in [42], FGSM-MEP requires consuming memory to store the previous adversarial perturbations, which limits its application on large datasets. Regarding the hyperparameters, we set "
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+                                    "type": "text",
+                                    "content": " in Eq. (11) as 0.03, 0.06, and 0.03 for CIFAR-10, CIFAR-100, and Tiny ImageNet, respectively. "
+                                },
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+                                    "content": "\\gamma_{max} = 1.5 \\cdot \\gamma_{min}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\xi = 16/255"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Specific details of hyperparameter settings for "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{1 \\sim 3}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are given in the supplement. All experiments are conducted on a single GeForce RTX 3090 GPU."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Baselines. We include advanced FAT methods as baselines, namely FGSM-RS [40], GradAlign [2], ZeroGrad [10], NuAT [36], ATAS [16], and FGSM-MEP [42]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Evaluation metrics. We follow [40, 16] and adopt FGSM [11], PGD-10 [25], PGD-20 [25], PGD-50 [25], C&W [3], APGD-CE [6] and Autoattack (AA) [6] to evaluate the adversarial robustness of models. PGD-n represents the PGD attack with n iterations. Autoattack combines APGD-CE and APGD-T (targeted APGD) as well as two complementary attacks (FAB [9] and Square attack [26])."
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "Figure 2. The training process of various FAT methods (PGD-10, "
+                                        },
+                                        {
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+                                            "content": "\\xi = 16 / 255"
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+                                            "type": "text",
+                                            "content": ") on CIFAR-10."
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+                            "index": 10,
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+                                    "content": "The training easily exhibits fluctuations, and thus individual results can not objectively reflect the performance of methods. For each method, we repeat the training process three times and report the average evaluation results of the best model across the three runs (mbest). Additionally, the supplement includes the best results (best) and the average evaluation of the final model from the three runs (mfinal)."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "In the following section, 'W-\\*', 'E-\\*', and 'B-\\*' mean 'weight centralization', 'example-based ConvergeSmooth', and 'batch-based ConvergeSmooth', respectively."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "4.2. Significance of the Results"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Before evaluating the adversarial robustness of trained models, we demonstrate the significance of the results [1]. Specifically, we show that adversarial attacks with "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\xi = 16/255"
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+                                    "type": "text",
+                                    "content": " rarely change the true label of input. 1) We generate adversarial examples for the FGSM-RS, FGSM-MEP, and our proposed methods on CIFAR10 and CIFAR100 datasets with "
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+                                {
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+                                    "type": "text",
+                                    "content": " using the non-targeted attacks such as FGSM, PGD, C&W, APGD-CE, and the targeted attack APGD-T. The majority of the generated examples retain their true labels; 2) Tab. 1 examines the robustness of models against an ensemble of the Square (SQ) [26] and Ray-S [5] attacks, as these attacks generate strong oracle-invariant examples [1]; 3) We generate adversarial training data with "
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+                                    "type": "text",
+                                    "content": " and test the robustness on various levels of perturbation. Tab. 2 provide comparative experiments between our proposed method and other AT techniques, including OAAT [1], ExAT [30], ATES [4] and AWP [41]. It is important to note that we re-implement these AT methods and apply them in the context of FAT. Overall, our methods achieve optimal performance on both oracle-invariant attacks and classical evaluation attacks. Namely, the classical evaluation attacks used in "
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+                                    "type": "text",
+                                    "content": " are reliable and significant even when the value of "
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+                                    "type": "text",
+                                    "content": " is increased to 16/255."
+                                }
+                            ]
+                        }
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+                                    "content": "Notably, our methods are plugged into FGSM-RS and"
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+                    ],
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+                                            "type": "text",
+                                            "content": "Table 3. Quantitative results of various methods ("
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+                                            "content": ") on the CIFAR-10 with ResNet18 as the backbone. 'ATAS*' is the result of ATAS in [16], which is superior to our reproduction. We train each method three times. The results represent the evaluation average between the best models of three training processes. Weight centralization and regularization in MEP do not work together."
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+                                            "html": "<table><tr><td>Budgets (ξ)</td><td>Methods</td><td>Clean↑</td><td>FGSM↑</td><td>PGD-10↑</td><td>PGD-20↑</td><td>PGD-50↑</td><td>C&amp;W↑</td><td>APGD-CE↑</td><td>AA↑</td><td>Time (min)↓</td></tr><tr><td rowspan=\"4\">12/255</td><td>GradAlign [2]</td><td>66.52</td><td>43.06</td><td>31.66</td><td>27.95</td><td>26.04</td><td>27.05</td><td>25.99</td><td>21.65</td><td>135</td></tr><tr><td>NuAT [36]</td><td>72.79</td><td>51.80</td><td>41.75</td><td>38.60</td><td>37.54</td><td>35.99</td><td>36.71</td><td>32.01</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>74.71</td><td>52.05</td><td>38.45</td><td>36.35</td><td>35.52</td><td>33.05</td><td>33.4</td><td>27.23</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>72.63</td><td>54.40</td><td>45.23</td><td>42.85</td><td>42.14</td><td>36.81</td><td>41.62</td><td>33.26</td><td>101</td></tr><tr><td rowspan=\"4\">10/255</td><td>GradAlign [2]</td><td>83.10</td><td>55.23</td><td>36.58</td><td>30.47</td><td>28.64</td><td>31.01</td><td>26.51</td><td>23.84</td><td>135</td></tr><tr><td>NuAT [36]</td><td>75.82</td><td>55.94</td><td>45.54</td><td>43.92</td><td>43.42</td><td>41.39</td><td>42.91</td><td>38.85</td><td>101</td></tr><tr><td>FGSM-MEP [42]</td><td>83.43</td><td>59.51</td><td>42.76</td><td>39.28</td><td>37.33</td><td>37.26</td><td>35.91</td><td>32.52</td><td>92</td></tr><tr><td>B-MEP (Ours)</td><td>75.96</td><td>57.26</td><td>47.25</td><td>45.98</td><td>45.66</td><td>41.00</td><td>45.26</td><td>39.20</td><td>101</td></tr></table>",
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+                            "index": 2,
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Table 4. Quantitative results of FAT methods on various "
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+                                            "type": "text",
+                                            "content": " with ResNet18 as the backbone and CIFAR-10 as the dataset. Models are trained and evaluated under the same "
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+                                            "type": "text",
+                                            "content": " . The number in bold indicates the best."
+                                        }
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+                            "index": 3,
+                            "angle": 0,
+                            "type": "table_caption"
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+                                            "html": "<table><tr><td>ξ = 16/255</td><td colspan=\"2\">CIFAR10</td><td colspan=\"2\">CIFAR100</td><td>Time</td></tr><tr><td>Methods</td><td>Clean</td><td>AA</td><td>Clean</td><td>AA</td><td>hours</td></tr><tr><td>GradAlign [2]</td><td>55.58</td><td>13.45</td><td>35.93</td><td>7.13</td><td>8.79</td></tr><tr><td>NuAT [36]</td><td>74.25</td><td>13.19</td><td>20.48</td><td>7.30</td><td>7.66</td></tr><tr><td>FGSM-MEP [42]</td><td>65.56</td><td>15.43</td><td>20.69</td><td>6.73</td><td>6.15</td></tr><tr><td>B-MEP (Ours)</td><td>69.94</td><td>24.27</td><td>48.64</td><td>12.05</td><td>6.72</td></tr></table>",
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+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "Table 5. The adversarial accuracy of various FAT methods with WideResNet34-10 as the backbone."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "FGSM-MEP, which are fitted to the distribution of adversarial examples. Instead, methods such as OAAT are fitted to the distribution of benign samples and perform better on clean accuracy. Therefore, we use the settings as in OAAT and then apply OAAT and our B-OAAT to the FAT task. B-OAAT realizes "
+                                },
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+                                    "content": "(+2.82\\%)"
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+                                    "type": "text",
+                                    "content": " than OAAT) clean accuracy and "
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+                                    "type": "text",
+                                    "content": " (OAAT) on SQ+RayS."
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+                                    "content": "4.3. Results on CIFAR-10"
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+                                    "content": "We conduct our initial experiments on CIFAR-10 using the ResNet18 backbone. The default "
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+                                    "type": "text",
+                                    "content": " is set to 16/255. Tab. 3 presents the main comparisons. The observations"
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+                                    "type": "text",
+                                    "content": "are as follows: (1) Compared with previous FAT methods, the proposed approaches achieve optimal adversarial robustness against different attacks, e.g. B-RS outperforms all RS-based methods and B-MEP is superior to all other methods. Meanwhile, our methods exhibit similar performance to prior work in terms of clean classification accuracy. (2) B-MEP realizes adversarial robustness approaching PGD-AT, e.g. B-MEP performs "
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+                                    "content": " robustness against the PGD-50 attack, only "
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+                                    "content": " lower than PGD-AT; (3) As for time consumption, B-RS takes less time (75 minutes) than GradAlign (135 minutes) and NuAT (101 minutes). This is because ConvergeSmooth only requires the additional regularization when "
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+                                    "type": "inline_equation",
+                                    "content": "|u_{B} - u_{t - 1}| > \\gamma_{t}"
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+                                    "type": "text",
+                                    "content": " instead of adding constraints on all iterations. In addition, B-MEP (102 minutes) takes a bit more calculation cost than FGSM-MEP (92 minutes) but much less than PGD-AT (370 minutes). PGD-AT takes significantly longer than FAT works; (4) B-RS and B-MEP successfully prevent catastrophic overfitting, e.g. mfinal (in the supplement) only shows a slight reduction than mbest in terms of adversarial robustness."
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+                                    "type": "text",
+                                    "content": "Fig. 2 visualizes the training process of various FAT approaches. Compared with other methods, the proposed"
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+                                            "content": " with ResNet18 as the backbone on CIFAR-100."
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+                                    "content": "Table 7. Quantitative results of various methods "
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+                                    "type": "text",
+                                    "content": " with PreActResNet18 as the backbone on Tiny ImageNet."
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+                                    "type": "text",
+                                    "content": "B-RS achieves optimal training stability and adversarial robustness, e.g. the classification accuracy of our method fluctuates slightly during three adversarial training sessions."
+                                }
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+                                    "type": "text",
+                                    "content": "Various budgets. Similar experiments are performed for budgets 10/255 and 12/255. Details are given in Tab. 4. It is evident that the proposed method achieves optimal adversarial robustness across various perturbation budgets."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Various networks. We then adopt WideResNet34 with a width factor of 10 [47] as the backbone. The results are given in Tab. 5. Our proposed B-MEP also prevents the wider architectures from catastrophic overfitting."
+                                }
+                            ]
+                        }
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+                                    "content": "4.4. Results on CIFAR-100"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "The results on CIFAR-100 with the backbone ResNet-18 are presented in Tab. 6. (1) FAT methods perform similar training consumption on CIFAR-10 and CIFAR-100 as two datasets contain the same number and size of images; (2) All proposed methods can realize stable adversarial training, as evidenced by the comparable results of mbest and mfinal (in the supplement); (3) Among the RS-based FAT works, B-RS and E-RS achieve the best and second-best adversarial robustness against different attacks; (4) B-MEP outperforms all other FAT methods; (5) Although B-MEP performs slightly worse than PGD-AT, its training process is approximately 3.5 times faster than this competitor."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.5. Results on Tiny ImageNet"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "content": "We conduct experiments on the Tiny ImageNet using the PreActResNet18 backbone to demonstrate the scalability of the proposed method to large datasets. The results are given in Tab. 7. B-BP achieves higher robustness among the FAT methods and comparable robustness to PGD-AT. As for training efficiency, B-BP (15.4 hours) requires slightly more computational cost than FGSM-BP (14.3 hours), but significantly less time than PGD-AT (67.2 hours)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
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+                                    "type": "text",
+                                    "content": "4.6. Ablation studies"
+                                }
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+                        }
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+                                    "type": "text",
+                                    "content": "In the following, B-RS is selected as the backbone. Figs. 3 and 4 conduct ablation studies on "
+                                },
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " respectively. In Fig. 3, the classification accuracy of both benign and adversarial examples increases with "
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+                                    "type": "text",
+                                    "content": ". However, the model trained with a large "
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+                                    "type": "text",
+                                    "content": ") suffers from catastrophic overfitting. Fig. 4 shows that the model with "
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+                                    "type": "text",
+                                    "content": " achieves optimal robustness. "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " denotes the static convergence stride. All models can be trained stably when "
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+                                    "type": "text",
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+                                    "content": "Tabs. 8 and 9 provide the results of comparative experiments on "
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+                                    "content": " will affect the performance. In Tab. 8, "
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+                                    "type": "inline_equation",
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+                                    "content": " achieves optimal adversarial robustness on CIFAR100 and"
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+                                    "content": "\\mathcal{L}(x_t', \\theta_t)"
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+                                    "type": "text",
+                                    "content": " is assigned with higher weights "
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+                                    "type": "inline_equation",
+                                    "content": "(1 + w_{1})"
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+                                    "type": "text",
+                                    "content": " or lower weights "
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+                                    "type": "inline_equation",
+                                    "content": "(1 - w_{1})"
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+                                    "type": "text",
+                                    "content": ", causing the model to excessively prioritize or neglect this portion of the data. This may weaken the performance of models. However, for Tiny ImageNet, models suffer catastrophic overfitting at "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "w_{1} = 0"
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+                                    "type": "text",
+                                    "content": ". Then, we gradually increase "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " from 0.3 with a stride of 0.2 until the FAT process becomes stable. In addition, our weight centralization method only introduces a balance coefficient "
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "type": "inline_equation",
+                                    "content": "w_{3}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is set to 0.1 since catastrophic overfitting happens when "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{3} = 0"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and classification performance is degraded when "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "w_{3} = 0.2"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "content": "In this paper, we tackle the issue of catastrophic overfitting by focusing on the convergence stability of loss func"
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+                        }
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+                                            "content": "ResNet18 trained with ConvergeSmooth-RS on CIFAR-100"
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+                                            "type": "text",
+                                            "content": "Figure 4. Ablation study of "
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+                                            "type": "inline_equation",
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+                                            "content": " ("
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+                                            "content": "\\gamma_{max} = 0.06"
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+                                            "type": "text",
+                                            "content": "). We provide the classification accuracy of models (ResNet-18) to benign and adversarial examples (PGD-10, "
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+                                            "content": "\\xi = 16/255"
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+                                            "type": "text",
+                                            "content": ") on CIFAR-100."
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+                            "index": 12,
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+                },
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+                                    "type": "text",
+                                    "content": "tions. Through experimental analysis, we find that this issue is accompanied by abnormal convergence behavior of losses. Motivated by this phenomenon, we propose complementary constraints, namely E-ConvergeSmooth and B-ConvergeSmooth, based on the adversarial training constraint. To alleviate the burden of parameter tuning, weight centralization is designed utilizing priors from previous epochs. Extensive experiments on different network architectures and datasets show that the proposed methods effectively solve catastrophic overfitting and exhibit superior robustness against various adversarial attacks."
+                                }
+                            ]
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+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "Acknowledgments. This work was supported by the National Key R&D Program of China #2018AAA0102000 and the National Natural Science Foundation of China #62276046 and #U19B2039."
+                                }
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+                                }
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+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
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diff --git a/2023/Fast Full-frame Video Stabilization with Iterative Optimization/ad2d1b40-bcdd-45b6-94bd-a7d9f53481b5_content_list.json b/2023/Fast Full-frame Video Stabilization with Iterative Optimization/ad2d1b40-bcdd-45b6-94bd-a7d9f53481b5_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa20f250de16388976ab58b7364d33e24105008e
--- /dev/null
+++ b/2023/Fast Full-frame Video Stabilization with Iterative Optimization/ad2d1b40-bcdd-45b6-94bd-a7d9f53481b5_content_list.json	
@@ -0,0 +1,1600 @@
+[
+    {
+        "type": "text",
+        "text": "Fast Full-frame Video Stabilization with Iterative Optimization",
+        "text_level": 1,
+        "bbox": [
+            165,
+            130,
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+        ],
+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Weiyue Zhao $^{1}$  Xin Li $^{2}$  Zhan Peng $^{1}$  Xianrui Luo $^{1}$  Xinyi Ye $^{1}$  Hao Lu $^{1}$  Zhiguo Cao $^{1*}$ $^{1}$ Key Laboratory of Image Processing and Intelligent Control, Ministry of Education; School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China  \n $^{2}$ Department of Computer Science, University of Albany, Albany NY 12222 {zhaoweiyue, peng-zhan, xianruiluo, xinyiye, hlu, zgcao}@hust.edu.cn xli48@albany.edu",
+        "bbox": [
+            86,
+            178,
+            915,
+            287
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            314,
+            313,
+            329
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Video stabilization refers to the problem of transforming a shaky video into a visually pleasing one. The question of how to strike a good trade-off between visual quality and computational speed has remained one of the open challenges in video stabilization. Inspired by the analogy between wobbly frames and jigsaw puzzles, we propose an iterative optimization-based learning approach using synthetic datasets for video stabilization, which consists of two interacting submodules: motion trajectory smoothing and full-frame outpainting. First, we develop a two-level (coarse-to-fine) stabilizing algorithm based on the probabilistic flow field. The confidence map associated with the estimated optical flow is exploited to guide the search for shared regions through backpropagation. Second, we take a divide-and-conquer approach and propose a novel multiframe fusion strategy to render full-frame stabilized views. An important new insight brought about by our iterative optimization approach is that the target video can be interpreted as the fixed point of nonlinear mapping for video stabilization. We formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories, which guarantees convergence with the help of fixed-point theory. Extensive experimental results are reported to demonstrate the superiority of the proposed approach in terms of computational speed and visual quality. The code will be available on GitHub.",
+        "bbox": [
+            76,
+            347,
+            473,
+            739
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            771,
+            209,
+            787
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the growing popularity of short videos on social media platforms (e.g., TikTok, Instagram), video has played an increasingly important role in our daily life. However, casually captured videos are often shaky and wobbly due to",
+        "bbox": [
+            75,
+            799,
+            470,
+            859
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "amateur shooting. Although it is possible to alleviate those problems by resorting to professional equipment (e.g., dollies and steadicams), the cost of hardware-based solutions is often expensive, making it impractical for real-world applications. By contrast, software-based or computational solutions such as video stabilization algorithms [12] have become an attractive alternative to improve the visual quality of shaky video by eliminating undesirable jitter.",
+        "bbox": [
+            500,
+            315,
+            892,
+            436
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing video stabilization techniques can be classified into two categories: optimization-based and learning-based. Traditional optimization-based algorithms [11,18,21,27,39] have been widely studied due to their speed and robustness. The challenges of them are the occlusion caused by changes in depth of field and the interference caused by foreground objects on camera pose regression. Furthermore, their results often contain large missing regions at frame borders, particularly when videos with a large camera motion. In recent years, learning-based video stabilization algorithms [6, 23, 45, 50] have shown their superiority by achieving higher visual quality compared to traditional methods. However, their stabilization model is too complex for rapid computation, and its generalization property is unknown due to the scarcity of training datasets.",
+        "bbox": [
+            496,
+            441,
+            893,
+            669
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To overcome those limitations, we present an iterative optimization-based learning approach that is efficient and robust, capable of achieving high-quality stabilization results with full-frame rendering, as shown in Fig. 1. The probabilistic stabilized network addresses the issues of occlusion and interfering objects, and achieves fast pose estimation. Then the full-frame outpainting module retains the original field of view (FoV) without aggressive cropping. An important new insight brought by our approach is that the objective of video stabilization is to suppress the implicitly embedded noise in the video frames rather than the explicit noise in the pixel intensity values. This inspired us to adopt an expectation-maximization (EM)-like approach for video stabilization. Importantly, considering the strong redundancy of video in the temporal domain, we ingeniously",
+        "bbox": [
+            496,
+            674,
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+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author https://github.com/zwyking/Fast-Stab",
+        "bbox": [
+            75,
+            873,
+            400,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "23534",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/46ce70956dbb13bf03558f871ba573814a0f25c71411f32d1433c1e16de2fa95.jpg",
+        "image_caption": [
+            "Figure 1. Overview of our video stabilization framework. It consists of motion trajectory smoothing (in Sec. 3 and Sec. 4) and full-frame outpainting modules (in Sec. 5). The former adopts the two-level (coarse-to-fine) stabilizing algorithm to obtain a stabilized video. The latter further render a full-frame video with strategies of flow outpainting and multiframe fusion."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            88,
+            88,
+            467,
+            244
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/6a9817f6acb7f629182e51ff59b460f3fdc999660c43d844aeee05ce28645268.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            470,
+            89,
+            883,
+            244
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "consider stable video (the target of video stabilization) as the fixed point of nonlinear mapping. Such a fixed-point perspective allows us to formulate an optimization problem of the optical flow field in commonly shared regions. Unlike most methods that resort to the ad hoc video dataset [56] or the deblurred dataset [35] as stabilized videos, we propose to construct a synthetic training dataset to facilitate joint optimization of model parameters in different network modules.",
+        "bbox": [
+            75,
+            316,
+            468,
+            450
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To solve the formulated iterative optimization problem, we take a divide-and-conquer approach by designing two modules: probabilistic stabilization network (for motion trajectory smoothing) and video outpainting network (for full-frame video rendering). For the former, we propose to build on the previous work of PDCNet [37, 38] and extend it using a coarse-to-fine strategy to improve robustness. For a more robust estimate of the uncertainty of the optical flow, we infer masks from the optical flow by bidirectional propagation with a low computational cost (around  $1/5$  of the time Yu et al. [50]). Accordingly, we have developed a two-level (coarse-to-fine) flow smoothing strategy that first aligns adjacent frames by global affine transformation and then refines the result by warping the fields of intermediate frames. For the latter, we propose a two-stage approach (flow and image outpainting) to render full-frame video. Our experimental results have shown highly competent performance against others on three public benchmark datasets. The main contribution of this work is threefold:",
+        "bbox": [
+            75,
+            452,
+            470,
+            736
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a formulation of video stabilization as a fixed-point problem of the optical flow field and propose a novel procedure to generate a model-based synthetic dataset.",
+            "- We construct a probabilistic stabilization network based on PDCNet and propose an effective coarse-to-fine strategy for robust and efficient smoothing of optical flow fields.",
+            "- We propose a novel video outpainting network to render stabilized full-frame video by exploiting the spatial"
+        ],
+        "bbox": [
+            94,
+            742,
+            467,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "coherence in the flow field.",
+        "bbox": [
+            532,
+            316,
+            714,
+            329
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "2.1. Video Stabilization",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Most video stabilization methods can typically be summarized as a three-step procedure: motion estimation, smoothing the trajectory, and generating stable frames. Traditional methods focus primarily on 2D features or image alignment [29] when it comes to motion estimation. These methods are different in modeling approaches to motion, including the trajectory matrix [19], epipolar geometry [10, 21, 47, 53], and the optical flow field [22, 54]. Regarding the smoothing trajectory, particle filter tracking [46], space-time path smoothing [19, 40], and L1 optimization [11] have been proposed. Existing methods for generating stable frames rely mainly on 2D transformations [26], grid warping [19, 21], and dense flow field warping [22].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Compared to the 2D method, some approaches turn to 3D reconstruction [17]. However, specialized hardware such as depth camera [20] and light field camera [34] are necessary for these methods based on 3D reconstruction. Some methods [30, 43, 44, 49] tackle video stabilization from the perspective of deep learning. In [49], the optimization of video stabilization was formulated in the CNN weight space. Recent work [50] represents motion by flow field and attempts to learn a stable optical flow to warp frames. Another method [6] aims to learn stable frames by interpolation. These deep-learning methods generate stable videos with less distortion.",
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+    },
+    {
+        "type": "text",
+        "text": "2.2. Large FOV Video",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Unlike the early work (e.g., traffic video stabilization [16]), large field of view (Field Of View) video stabilization has been attracting more researchers' attention. For most video stabilization methods, cropping is inevitable, which is why the FOV is reduced. Several approaches have been proposed to maintain a high FOV ratio. OVS [45]",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "23535",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "proposed to improve FOV by extrapolation. DIFRINT [6] choose iterative interpolation to generate high-FOV frames. FuSta [23] used neural rendering to synthesize high-FOV frames from feature space. To a great extent, the performance of interpolation-based video stabilization [6,45] depends on the selected frames. If selected frames have little correspondence with each other, performance will deteriorate dramatically. Neural rendering [23] synthesizes the image by weighted summing, causing blur. Most recently, a deep neural network [33] (DNN) has jointly exploited sensor data and optical flow to stabilize videos.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Stabilization via Iterative Optimization",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Motivation. Despite rapid advances in video stabilization [30], existing methods still suffer from several notable limitations [12]. First, a systematic treatment of various uncertainty factors (e.g., low-texture regions in the background and moving objects in the foreground) in the problem formulation is still lacking. These uncertainty factors often cause occlusion-related problems and interfere with the motion estimation process. Second, the high computational cost has remained a technical barrier to real-time video processing. The motivation behind our approach is two-fold. On the one hand, we advocate for finding commonly shared regions among successive frames to address various uncertainty factors in handheld video. On the other hand, in contrast to these prestabilization algorithms [21, 23, 49, 50] based on traditional approaches, we proposed a novel high-efficiency prestabilization algorithm based on probabilistic optical flow. Flow-based methods are generally more accurate in motion estimation and deserve a high time cost. Accuracy and efficiency, we have both.",
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+    {
+        "type": "text",
+        "text": "Approach. We propose to formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories. It is enlightening to think of video stabilization as a special kind of \"video denoising\" where noise contamination is not associated with pixel intensity values, but embedded into the motion trajectories of foreground and background objects. Conceptually, for video restoration in which unknown motion is the hidden variable, we can treat video stabilization as a chicken-and-egg problem [13] - i.e., the objective of smoothing motion trajectories is intertwined with that of video frame interpolation. Note that an improved estimation of motion information can facilitate the task of frame interpolation and vice versa. Such an observation naturally inspires us to tackle the problem of video stabilization by iterative optimization.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Through divide-and-conquer, we propose to formulate video stabilization as the following optimization problem. Given a sequence of  $n$  frames along with the set of optical flows  $\\mathcal{V}$ , we first define the confidence map, which originally indicates the reliability and accuracy of the optical flow prediction at each pixel. Here, we have thresholded the",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "confidence map as a binary image, which represents accurate matches (as shown in the 4-th column of Fig. 2). Then we can denote  $n$  frames and the corresponding set of confidence maps  $\\mathcal{M}$  by:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {Y} = \\left\\{Y _ {1}, Y _ {2}, \\dots , Y _ {q} \\right\\}, \\mathcal {M} = \\left\\{M _ {1}, M _ {2}, \\dots , M _ {q} \\right\\}. \\quad (1)\n$$\n",
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+    },
+    {
+        "type": "text",
+        "text": "4. Probabilistic Stabilization Network",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The problem of video stabilization can be formulated as finding a nonlinear mapping  $f: \\mathcal{V} \\to \\hat{\\mathcal{V}}$  where  $\\hat{\\mathcal{V}}$  denotes the optical flow set of the stabilized video. We hypothesize that a desirable objective to pursue  $f$  is the well-known fixed-point property, i.e.,  $\\hat{\\mathcal{V}} = f(\\hat{\\mathcal{V}})$ . To achieve this objective, we aim to minimize an objective function  $\\mathbb{F}$  characterized by the magnitude of optical flows between commonly shared regions, as represented by  $\\mathcal{M}$ . Note that  $\\mathcal{M}$  is the hidden variable in our problem formulation (that is, we need to estimate  $\\mathcal{M}$  from  $\\hat{\\mathcal{V}}$ ). A popular strategy to address this chicken-and-egg problem is to alternatively solve the two subproblems of unknown  $\\mathcal{M}$  and  $\\hat{\\mathcal{V}}$ . More specifically, the optimization of  $\\mathbb{F}$  is decomposed into the following two subproblems:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\hat {M} _ {1}, \\dots , \\hat {M} _ {q}\\right) = \\underset {\\mathcal {M}} {\\arg \\min } \\mathbb {F} \\left(\\hat {Y} _ {1} \\odot M _ {1}, \\dots , \\hat {Y} _ {q} \\odot M _ {q}\\right), \\tag {2}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n(\\hat {Y} _ {1}, \\dots , \\hat {Y} _ {q}) = \\underset {\\mathcal {Y}} {\\arg \\min } \\mathbb {F} (Y _ {1} \\odot \\hat {M} _ {1}, \\dots , Y _ {q} \\odot \\hat {M} _ {q}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $Y / \\hat{Y}$  denotes the magnitude of the optical flow values before and after stabilization and  $\\odot$  is the Hadamard product. Instead of analyzing the estimated motion in the frequency domain, we hypothesize that stabilized videos are the fixed points of video stabilization algorithms, which minimize the above objective function. A fixed point [1] is a mathematical object that does not change under a given transformation. Numerically, fixed-point iteration is a method of computing fixed points of a function. It has been widely applied in data science [7], and image restoration [5, 25]. Here, we denote  $\\mathbb{F}$  in Eq. (2) as the function to be optimized, and the fixed point of  $\\mathbb{F}$  is defined as the stabilized video. Next, we solve these two subproblems by constructing the module of stabilization.",
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+    {
+        "type": "text",
+        "text": "4.1. Probabilistic Flow Field",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "First, we start with an interesting observation. When playing an unstable video at a slower speed (e.g., from 50fps to 30fps), the video tends to appear less wobbly. It follows from the observation that the fundamental cause of video instability is the fast frequency and the large amplitude of the still objects' motion speed. Therefore, the core task of motion smoothing is to identify the region that needs to be stabilized. As Yu et al. [50] pointed out, mismatches, moving objects, and inconsistent motion areas lead to variation of the estimated motion from the true motion trajectories and",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "23536",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a6c0690151f1ab2bb86ee086185771599464ba2e7cde3e86ede584ed8ec55c82.jpg",
+        "image_caption": [
+            "Figure 2. Visualization of confidence map back-propagation results. The flow field and confidence map are predicted by PDCNet between source and target images. The obtained masks in the last column represent the shared regions among these frames."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "should be masked. An important new insight brought about by this work is that these regions of inconsistency in the optical flow fields tend to show greater variability as the frame interval increases. Therefore, if these inconsistent regions are excluded, the video stabilization task can be simplified to the first sub-problem in Eq. (2) - i.e., minimizing  $\\mathbb{F}$  over  $\\mathcal{M}$  for a fixed  $\\mathcal{V}$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To detect unreliable matches and inconsistent regions, we have adopted the probabilistic flow network - PDCNet [37, 38], that jointly tackles the problem of dense correspondence and uncertainty estimation, as our building block. Suppose that PDCNet estimates the optical flow  $Y_{k}$  from frame  $k + d$  to frame  $k$  with the resulting confidence map  $C_k$ . Although  $C_k$  denotes the inaccuracy of the optical flow estimate in  $Y_{k}$ , it is often sensitive to the frame interval  $d$ . For example, it is difficult to identify the inconsistent region when  $d$  is small, while the common area is less controllable when  $d$  is large. Therefore, simply using an optical flow field to estimate inconsistent regions is not sufficient.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We have designed a more robust solution to the joint estimation of dense flow and confidence map based on a coarse-to-fine strategy. The basic idea is to first obtain the probabilistic flow field at a coarse scale (e.g., with the down-sampled video sequence by a factor of  $d$  along the temporal axis) and then fill in the rest (i.e., the frames between the adjacent frames in the down-sampled video) at the fine scale. Such a two-level estimation strategy effectively overcomes the limitations of PDCNet by propagating the estimation results of probabilistic flow fields bidirectionally, as we will elaborate next.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Coarse-scale strategy As shown by the second-to-last column in Fig. 2, the confidence map estimated by PDCNet can identify the mismatched region, but fails to locate the objects with small motions (e.g., people and the sky). To",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4b7a72e0ff1aa18faa8873256305d6ac94511f316b848b6dd35c65a18a39f689.jpg",
+        "image_caption": [
+            "Figure 3. Architecture of the camera pose regression network. Given the flow field and mask, our network predicts the corresponding affine transformation parameters by closed-loop iterations."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "overcome this difficulty, we introduce the binary mask as a warped and aggregated confidence map (refer to the last column of Fig. 2). Specifically, we first propose to obtain the confidence map  $\\hat{C}_{k + (n - 1)d}$  with down-sampled video (the last row of Fig. 2). In the forward direction, we estimate dense flow and confidence map using PDCNet; then  $\\hat{C}_{k + (n - 1)d}$  is backpropagated to update the binary mask  $\\hat{M}$  by thresholding and setting intersection operators. Through bidirectional propagation, the region covered by  $\\mathcal{M}$  is the shared content from frame  $k$  to frame  $k + (n - 1)d$ . The complete procedure can be found in Supp. S1.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Fine-scale strategy Based on the coarse-scale estimation result for downsampled video (i.e.,  $\\mathcal{M} = \\{\\hat{M}_k, \\hat{M}_{k+d}, \\dots, \\hat{M}_{k+(n-1)d}\\}$ ), we fill in the missing  $d-1$  frames at the fine scale. Specifically, considering the sequential frames from  $k$  to  $k+d$ , we can obtain two sets similar to Eq. (1), which are  $\\mathcal{V} = \\{Y_k, Y_{k+1}, \\dots, Y_{k+d-1}, \\hat{Y}_{k+d}\\}$  and their corresponding confidence map set  $\\mathcal{C}$ . Note that  $\\hat{M}_{k+d} \\in \\mathcal{M}$  has been calculated in coarse stage. Setting  $d=1$ , we can call the algorithm again to obtain the set of output masks  $\\mathcal{M}$  for the rest of  $d-1$  frames.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Coarse-scale Stabilizer",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To coarsely stabilize the video, we first propose aligning the adjacent frames with a global affine transformation [52]. The optimization function  $\\mathbb{F}$  in Eq. (2) is represented as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {T} ^ {*} = \\underset {\\mathbf {T}} {\\arg \\min } \\mathbf {T} (Y \\odot \\hat {M}), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{T}(\\cdot)$  denotes the image transformation applied to the shared region  $\\hat{M}$  (the result of Sec. 4.1) of the optical flow field  $Y$ . Most conventional methods [23,44,50] adopt image matching to obtain  $\\mathbf{T}(\\cdot)$ -e.g., keypoint detection [2,24,31], feature matching [2,3,51]; and camera pose estimation is implemented by OpenCV-python. However, these methods are often time-consuming and computationally expensive. For example, two adjacent frames of unstable videos usually share a large area and are free from perspective transformation. Thus, an affine transformation, including translation, rotation, and scaling, is sufficient. More importantly, within the optimization-based learning framework, we can",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "23537",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "regress these linear parameters of  $\\mathbf{T}(\\cdot)$  from the optical flow field, which characterize the relative coordinate transformation of the matched features.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We propose a novel camera pose regression network, as shown in Fig. 3. Given an optical flow field  $Y$  and the corresponding mask field  $\\hat{M}$ , our network  $\\Phi(\\cdot)$  can directly estimate the unknown parameters  $\\mathbf{T}(\\cdot) \\propto \\{\\theta, s, d_x, d_y\\} = \\Phi(Y, \\hat{M})$ . To solve the optimization problem of Eq. (3), we use the estimated parameters to iteratively compute the corresponding residual optical flow fields such that",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {Y} = Y - (S \\cdot R \\cdot V + T), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            179,
+            253,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $T$ ,  $S$ , and  $R$ , respectively, denote the translation, scaling, and rotation matrix, and  $V \\in \\mathbb{R}^{2 \\times H \\times W}$  represents an image coordination grid. Then  $\\{\\Delta \\theta, \\Delta s, \\Delta x, \\delta y\\} = \\Phi(\\bar{Y}, \\tilde{M})$  is calculated iteratively to produce the updated parameters  $\\{\\theta + \\Delta \\theta, s \\cdot \\Delta s, d_x + \\Delta x, d_y + \\Delta y\\}$ . The finally estimated affine transformation is smoothed by a moving Gaussian filter with a window size of 20 pixels.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Loss functions Our loss functions include robust loss  $\\ell_1$  and grid loss commonly applied in consistency filtering [51]. We directly calculate the  $\\ell_1$  loss between the predictions and their ground truth  $\\{\\hat{\\theta},\\hat{s},\\hat{d}_x,\\hat{d}_y\\}$",
+        "bbox": [
+            75,
+            395,
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+            455
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {g t} = \\lambda_ {\\theta} \\| | \\theta - \\hat {\\theta} \\| | _ {1} + \\lambda_ {s} \\| | 1 - \\frac {s}{\\hat {s}} \\| | _ {1} \\tag {5} \\\\ + \\lambda_ {t} \\| | d _ {x} - \\hat {d} _ {x} | + | d _ {y} - \\hat {d} _ {y} | \\| _ {1}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            129,
+            465,
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+            513
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For better supervision of the estimated pose, we calculate the loss  $L_{grid}$  with the grid  $V \\in \\mathbb{R}^{2 \\times h \\times h}$  in Eq. (4), i.e.,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {g r i d} = \\left\\| (\\hat {S} \\cdot \\hat {R} \\cdot V + \\hat {T}) - (S \\cdot R \\cdot V + T) + \\epsilon \\right\\| _ {1} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            565,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{\\cdot}$  denotes the ground truth and  $\\epsilon$  is a small value for stability. The final loss  $L_{stab}$  consists of  $L_{gt}$  and  $L_{grid}$ ,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {s t a b} = L _ {g t} + \\lambda_ {g r i d} L _ {g r i d}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Fine-scale Stabilizer",
+        "text_level": 1,
+        "bbox": [
+            76,
+            662,
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+            679
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The assumption with an affine transformation of the coarse-scale stabilizer could cause structural discontinuity and local distortion. Therefore, our objective is to refine the coarsely stabilized video by optical flow smoothing. Unlike Eq. 3 which applies an image transformation matrix to optimize the optical flow field, we optimize it at the pixel level by a flow warping field  $\\mathbf{W}$ . Thus, the function  $\\mathbb{F}$  in Eq. (2) is given by",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {W} ^ {*} = \\underset {\\mathbf {W}} {\\arg \\min } \\sum_ {i = 0} ^ {N - 1} \\mathbf {W} _ {i} \\left(Y _ {i} \\odot \\hat {M} _ {i}\\right). \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The flow smoothing network follows the U-Net architecture in [56]. We use  $N$  frames of optical flow fields  $\\mathbf{F}$  and mask",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/6fe7a98576fa7769bc42ea3ca51803b12244536840d7b80a8ef6546f35c8b5f6.jpg",
+        "image_caption": [
+            "Figure 4. Illustration of flow fields and warped images under different FOVs. The target image with large FOV presents the smoother flow field and better warped result."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
+            89,
+            880,
+            188
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "fields  $\\hat{M}$  as input and obtain  $(N - 1)$  frame warp fields  $\\mathbf{W}$  of intermediate frames. Specifically, for the optical flow field  $Y_{k}$  (from frame  $k + 1$  to frame  $k$ ), we denote the aligned matrices of each frame in Sec. 4.2 as  $H_{k} \\in \\mathbb{R}^{2 \\times 3}$  and  $H_{k + 1} \\in \\mathbb{R}^{2 \\times 3}$ , respectively. Then the input optical flow  $\\mathbf{F}_{k} \\in \\mathbb{R}^{2 \\times HW}$  can be represented by",
+        "bbox": [
+            498,
+            257,
+            890,
+            349
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} _ {k} = H _ {k + 1} \\cdot \\left[ V + Y _ {k} \\mid 1 \\right] - H _ {k} \\cdot \\left[ V \\mid 1 \\right], \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            553,
+            359,
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+            378
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $V \\in \\mathbb{R}^{2 \\times HW}$  and  $[\\cdot|1]$  denote the normalized coordinate representation. Furthermore, to better adapt the flow smoothing network to the mask field  $\\hat{M}$ , we fine-tune it using our synthetic dataset (as we will elaborate in Sec. 6.1). The loss function follows the motion loss [49]",
+        "bbox": [
+            498,
+            387,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {s m o o t h}} = \\sum_ {k = 0} ^ {N - 1} \\left(\\mathbf {F} _ {k} + \\mathbf {W} _ {k} - \\mathbf {F} _ {k} \\left(\\mathbf {W} _ {k + 1}\\right)\\right) \\odot \\hat {M}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            474,
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+            516
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_0 = \\mathbf{W}_N = 0$",
+        "bbox": [
+            500,
+            526,
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+            542
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Video Outpainting Network",
+        "text_level": 1,
+        "bbox": [
+            500,
+            555,
+            756,
+            573
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Most video stabilization methods crop an input video with a small field of view (FOV), excluding missing margin pixels due to frame warping. In contrast, full-frame video stabilization [6, 23, 26] proposes to generate a video that maintains the same FOV as the input video without cropping. They directly generate stabilized video frames with large FOV by fusing the information from neighboring frames. An important limitation of existing fusion strategies is the unequal importance of different frames (i.e., the current and neighboring frames are weighted equally), which would lead to unpleasant distortions in fast-moving situations. To overcome this weakness, we propose a two-stage framework to combine flow and image outpainting strategies [32]. In the first stage, we used flow-outpainting to iteratively align the neighboring frames with the target frame. In the second stage, we fill the target frame with adjacent aligned frame pixels by image outpainting.",
+        "bbox": [
+            496,
+            580,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Flow Outpainting Network",
+        "text_level": 1,
+        "bbox": [
+            500,
+            847,
+            743,
+            863
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let  $I^t$  denote the outpainted target image and  $I^s$  the neighboring source image. We aim to fill the missing pixel",
+        "bbox": [
+            500,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "23538",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/7b857824a8c24cae006118bc7c1c0e035fb96460916c2e667be345621f1776cd.jpg",
+        "image_caption": [
+            "Figure 5. Architecture of flow outpainting network. Given a small FOV flow field and valid mask, the network predicts the large FOV flow field."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            88,
+            460,
+            196
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "region  $M_{\\varnothing}^{t}$  of  $I^{t}$  with the pixels of  $I^{s}$ . As shown in Fig. 4, we take two different FOVs of  $I^{t}$  as input and obtain the corresponding optical flow fields and warped results  $I_{warp}^{s}$ . The small FOV  $I^{t}$  cannot guide  $I^{s}$  well to fill the regions in  $M_{\\varnothing}^{t}$ . Since the predicted optical flow field in  $M_{\\varnothing}^{t}$  is unreliable due to the lack of pixel guidance of  $I^{t}$ , the out-of-view region of  $M_{\\varnothing}^{t}$  has artifacts (marked in the last column of Fig. 4). We observe that the optical flow field of the large FOV  $I^{t}$  is continuous in  $M_{\\varnothing}^{t}$ , which inspired us to extrapolate the flow of  $M_{\\varnothing}^{t}$  using the reliable flow region (the 3rd column of Fig. 4).",
+        "bbox": [
+            75,
+            266,
+            468,
+            433
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We propose a novel flow outpainting network (Fig. 5), which extrapolates the large FOV flow field using a small FOV flow field and the corresponding valid mask. Specifically, we adopt a U-Net architecture and apply a sequence of gated convolution layers with downsampling / upsampling to obtain the large flow field of FOV  $Y_{large}$ . Note that the input flow field  $Y_{small}$  and the valid mask  $M_{valid}$  have been estimated by PDCNet (see Sec. 4.1).",
+        "bbox": [
+            75,
+            433,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Loss functions Our loss functions include robust loss  $\\ell_1$  and loss in the frequency domain [4]. We directly calculate the  $\\ell_1$  loss between  $Y_{large}$  and its ground truth  $\\hat{Y}_{large}$ ,",
+        "bbox": [
+            75,
+            560,
+            468,
+            607
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {Y} = \\lambda_ {i n} \\cdot \\| | Y _ {\\text {l a r g e}} - Y _ {\\text {s m a l l}} | \\odot M _ {\\text {v a l i d}} \\| _ {1} \\tag {11} \\\\ + \\lambda_ {o u t} \\cdot \\| | Y _ {l a r g e} - \\dot {Y} _ {l a r g e} | \\odot (\\sim M _ {v a l i d}) \\| _ {1}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            98,
+            616,
+            468,
+            651
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To encourage low frequency and smoothing  $Y_{large}$ , we add the loss in the frequency domain  $L_{F} = \\| \\hat{\\mathbf{G}}\\cdot \\mathcal{F}Y_{large}\\|_{2}$  where the normalized Gaussian map  $\\hat{\\mathbf{G}}$  with  $\\mu = 0$  and  $\\sigma = 3$  is inverted by its maximum value and  $\\mathcal{F}Y_{large}$  denotes the Fourier spectrum of  $Y_{large}$ . The final loss consists of  $L_{Y}$  and  $L_{F}$",
+        "bbox": [
+            75,
+            660,
+            468,
+            753
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {o u t p a i n t}} = L _ {Y} + \\lambda_ {F} L _ {F}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            753,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Image Margin Outpainting",
+        "text_level": 1,
+        "bbox": [
+            76,
+            786,
+            321,
+            803
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Based on our proposed flow-outpainting network, we design a margin-outpainting method by iteratively aligning frame pairs (see Fig. 6). As discussed in Sec. 5.1, we can obtain a large FOV flow field  $Y_{large}$ . The neighboring reference frame  $I^{s}$  is warped as  $I^{warp} = Y_{large}(I^{s})$  as shown in Fig. 6. In theory, the outpainted frame  $I^{result} =$",
+        "bbox": [
+            75,
+            810,
+            468,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/05918f014562ceec451629fc9b4ace86011898cec5ae90fa9887c6c10599b66a.jpg",
+        "image_caption": [
+            "Figure 6. Overview image margin outpainting. Given the target frame  $I^{t}$ , the reference frame  $I^{s}$  is coarsely aligned to  $I^{warp}$  by the predicted large-FOV flow field  $Y_{large}$ . Then, we adopt a margin fusion approach to obtain the result frame  $I^{result}$ , by carefully aggregating  $I^{t}$  and  $I^{warp}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
+            88,
+            883,
+            244
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "$I^t \\cdot M_{valid} + I^{warp} \\cdot (\\sim M_{valid})$ . However, we notice that there are obvious distortions at the image border. To further align the margins, we take a margin fusion approach (the detailed algorithm can be found in Supp. S1) We crop  $I^{warp}$  and  $I^t$  to  $I_c^s$  and  $I_c^t$ . Then, we can obtain a new warped frame  $I_c^{warp}$  by flow outpainting. In particular, we did not choose to add  $I_c^{warp}$  and  $I^t$  directly. To identify the misaligned region, we propose to outpaint the mask  $M_{I^t}$  by extending the watershed outward from the center. Instead of a preset threshold, we adaptively choose between the target image  $I^t$  and the warped image  $I_c^{warp}$ . Then, the final frame  $I^{result}$  consists of  $I^t$  and  $I_c^{warp}$ :  $I^{result} = I^t \\cdot M_{I^t} + I_c^{warp} \\cdot (\\sim M_{I^t})$ . Compared to the two results  $I^{result}$ , our strategy successfully mitigates misalignment and distortions at the boundary of video frames.",
+        "bbox": [
+            496,
+            343,
+            890,
+            570
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Multi-frame fusion During the final stage of rendering, we use a sequence of neighboring frames to outpaint the target frame, while they may have filled duplicate regions. It is important to find out which frame and which region should be selected. We proposed the selection strategy for multi-frame fusion (the details can be found in Supp. S1). By weighing the metric parameters of each frame, we finally obtain the target frame with large FOV. Note that each frame has an added margin in the stabilization process, so we need to crop them to the original resolution. Although we have outpainted the target frame, some missing pixel holes may still exit at boundaries. Here, we apply the state-of-the-art LaMa image inpainting method [36] to fill these holes using nearest-neighbor interpolation.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            805,
+            632,
+            821
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6.1. Synthetic Datasets for Supervised Learning",
+        "text_level": 1,
+        "bbox": [
+            500,
+            830,
+            867,
+            847
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Due to the limited amount of paired training data, we propose a novel model-based data generation method by carefully designing synthetic datasets for video stabiliza",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "23539",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/7cfe027c59935e040de8a2046fc98ab869833848eae4235df964d19c18b81bb1.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. Quantitative results on the NUS dataset [21], the DeepStab dataset [39] and the Selfie Dataset [48]. We evaluate the following metrics: Cropping Ratio(C.), Distortion Value(D.), Stability Score(S). * indicates the results obtained from original paper. We highlight the best method in bold and underline the second-best."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">NUS dataset [21]</td><td colspan=\"3\">DeepStab dataset [39]</td><td colspan=\"3\">Selfie dataset [48]</td></tr><tr><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td></tr><tr><td>Grundmann et al. [11]</td><td>0.71</td><td>0.76</td><td>0.62</td><td>0.77</td><td>0.87</td><td>0.80</td><td>0.75</td><td>0.81</td><td>0.83</td></tr><tr><td>Liu et al. [21]</td><td>0.81</td><td>0.78</td><td>0.82</td><td>0.80</td><td>0.90</td><td>0.85</td><td>0.74</td><td>0.89</td><td>0.8</td></tr><tr><td>Wang et al. [39]</td><td>0.67</td><td>0.72</td><td>0.41</td><td>-</td><td>-</td><td>-</td><td>0.68</td><td>0.71</td><td>0.82</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>0.78</td><td>0.77</td><td>0.82</td><td>0.85</td><td>0.89</td><td>0.76</td><td>0.79</td><td>0.77</td><td>0.84</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>0.85</td><td>0.81</td><td>0.86</td><td>0.87</td><td>0.92</td><td>0.82</td><td>0.83</td><td>0.87</td><td>0.86</td></tr><tr><td>Yu [50]+OVS* [45]</td><td>0.92</td><td>0.78</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DUT [44]</td><td>0.71</td><td>0.81</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DIFRINT [6]</td><td>1.00</td><td>0.85</td><td>0.84</td><td>1.00</td><td>0.91</td><td>0.78</td><td>1.00</td><td>0.78</td><td>0.84</td></tr><tr><td>FuSta [23]</td><td>1.00</td><td>0.87</td><td>0.86</td><td>1.00</td><td>0.92</td><td>0.82</td><td>1.00</td><td>0.83</td><td>0.87</td></tr><tr><td>Ours</td><td>1.00</td><td>0.91</td><td>0.86</td><td>1.00</td><td>0.94</td><td>0.84</td><td>1.00</td><td>0.87</td><td>0.87</td></tr></table>",
+        "bbox": [
+            178,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tion. For our base synthetic dataset, we used a collection of images from the DPED [14], CityScapes [8] and ADE20K [55] datasets. To generate a stable video, we randomly generate the homography parameters for each image, including rotation angle  $\\theta$ , scaling  $s$ , translations  $(d_x,d_y)$  and perspective factors  $(p_x,p_y)$ . Then we divide these transformation parameters into  $N$  bins equally and obtain a video of  $N$  frames by homography transformations. To simulate the presence of moving objects in real scenarios, the stable video is further augmented with additional independently moving random objects. To do so, the objects are sampled from the COCO dataset [15] and inserted on top of the synthetic video frames using their segmentation masks. Specifically, we randomly choose  $m$  objects (no more than 5), and generate randomly affine transformation parameters for each independent of the background transformation. Finally, we cropped each frame to  $720\\times 480$  around its center. For different training requirements, we apply various combinations of synthetic dataset. The implementation and training details can be found in Supp. S2, S3.",
+        "bbox": [
+            75,
+            340,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6.2.Quantitative Evaluation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            657,
+            299,
+            672
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare the results of our method with various video stabilization methods, including Grundmann et al. [11], Liu et al. [21], Wang et al. [39], Yu and Ramamoorthi [49, 50], DUT [44], OVS [45], DIFRINT [6], and FuSta [23]. We obtain the results of the compared methods from the videos released by the authors or generated from the publicly available official implementation with default parameters or pre-trained models. Note that OVS [45] does not honor their promise to provide code, thus we only report the results from their paper.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate all approaches on the NUS dataset [21], DeepStab dataset [39], and Selfie dataset [48]. The NUS dataset consists of 144 videos and the corresponding ground truths in 6 scenes. The DeepStab dataset con",
+        "bbox": [
+            75,
+            839,
+            470,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tains 61 videos and the Selfie dataset consist of 33 videos.",
+        "bbox": [
+            500,
+            340,
+            883,
+            357
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Metrics. We introduce three metrics widely used in many methods [6, 23, 50] to evaluate our model: 1) Cropping ratio measures the remaining frame area after cropping off the invalid boundaries. 2) Distortion value evaluates the anisotropic scaling of the homography between the input and output frames. 3) Stability score measures the stability of the output video. We calculate the metrics using the evaluation code provided by DIFRINT.",
+        "bbox": [
+            496,
+            378,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Quantitative comparison. The results of the NUS dataset [21] are summarized in Table 1 (Per-category result can be found in Supp. S5). Overall, our method achieves the best distortion value compared to the state-of-the-art method, FuSta [23]. Especially in the quick-rotation and zoom categories, our method outperforms pure image generation methods [6,23]. We suspect that the reduction of the shared information between frames causes the image generation methods to prefer artifacts. However, our method can ensure local structural integrity when outpainting the margin region. Furthermore, our method achieves an average cropping ratio of 1.0 and stability scores comparable to recent approaches [6, 23, 49, 50]. Since FuSta [23] uses Yu et al. [50] to obtain stabilized input videos, they have the same stability scores. It is important to note that although the stability scores are competitive, our method runs 5 times faster than [50] in the video stabilization stage. Moreover, the comparison results on DeepStab dataset [39] and Selfie dataset [48] are also reported in Table 1. Our method still shows effectiveness in different datasets, proving the generalizability of the proposed method. Note that, due to that Wang et al. [39] is trained on the DeepStab dataset, we do not report its results on the DeepStab dataset for a fair comparison. Qualitative comparisons can be found in Supp. S4 and supplementary video.",
+        "bbox": [
+            496,
+            523,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "23540",
+        "bbox": [
+            478,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b07c4ab947c05b21ce1278b311353f1ee2eafd66aeaa658f922129bb98a151c7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Stabilizer</td><td></td><td>Stability↑</td><td>Distortion↑</td></tr><tr><td rowspan=\"2\">Image-level</td><td>w.o. mask</td><td>0.76</td><td>0.88</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr><tr><td rowspan=\"2\">Pixel-level</td><td>w.o. mask</td><td>0.81</td><td>0.84</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr></table>",
+        "bbox": [
+            107,
+            88,
+            439,
+            162
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/b542d1f82c129a71a203612320e5052b98ec0e05fe13b9cd2347e221fc86f1a9.jpg",
+        "table_caption": [
+            "Table 2. The importance of mask to video stabilization. We validate on the Crowd category of NUS dataset [21]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>Distortion↑</td></tr><tr><td>PCAFlow [42]</td><td>11.34</td><td>0.50</td><td>0.72</td></tr><tr><td>Our flow outpainting</td><td>19.65</td><td>0.77</td><td>0.93</td></tr><tr><td>w.o. margin outpainting</td><td>18.04</td><td>0.64</td><td>0.81</td></tr><tr><td>w.o. mask \\( M_{I^t} \\)</td><td>20.35</td><td>0.78</td><td>0.86</td></tr><tr><td>w.o. multi-frame selection</td><td>21.99</td><td>0.84</td><td>0.90</td></tr><tr><td>Ours</td><td>23.17</td><td>0.86</td><td>0.91</td></tr></table>",
+        "bbox": [
+            83,
+            212,
+            460,
+            321
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Importance of mask generation. We investigate the influence of the mask on video stabilization at different stages. To better demonstrate the necessity of mask in complex scenarios, we choose the Crowd category of NUS dataset [21] which includes a display of moving pedestrians and occlusions. Stability and distortion at different settings are shown in Table 2. It can be seen that the performance with mask increases significantly in both stabilizers. Specifically, the mask can both improve stability globally and alleviate image warping distortion locally. This result demonstrates the importance of mask generation for video stabilization.",
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+    {
+        "type": "text",
+        "text": "Flow outpainting. We compare our flow outpainting method with the traditional flow inpainting method PCAFlow [42]. Following [50] we fit the first 5 principal components proposed by PCAFlow to the  $M_{valid} = 1$  regions of the optical flow field, and then outpaint the flow vectors in the  $M_{valid} = 0$  regions with reasonable values of the PCA Flow fitted. The result is obtained by warping the source image with the outpainted optical flow field. We perform this comparison on our synthetic validation set and evaluate it with the corresponding ground truth. Additionally, we use PSNR and SSIM [41] to evaluate the quality of the results. As shown in Table 3, ours dramatically outperforms PCAFlow [42] in all objective metrics.",
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+    {
+        "type": "text",
+        "text": "Importance of image filling strategies. We explore the following proposed strategies for image filling: margin outpainting, mask generation  $M_{It}$ , and multiframe selection. We isolate them from our method to compare their results with the complete version. The results are shown in Table 3. The proposed strategies are generally helpful in improving image quality. Especially, margin outpainting and mask  $M_{It}$  are crucial to the results.",
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+        "type": "table",
+        "img_path": "images/92723f000f91ab01b485f5125e46ec924552e68a01937aec40fc7708b2bfdc03.jpg",
+        "table_caption": [
+            "Table 3. Ablation study of image filling. The evaluation is conducted on our model-based synthetic validation set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Runtime</td></tr><tr><td>Traditional pose regression</td><td>216ms</td></tr><tr><td>Our pose regression network</td><td>21ms</td></tr><tr><td>Grundmann et al. [11]</td><td>480ms</td></tr><tr><td>Liu et al. [21]</td><td>1360ms</td></tr><tr><td>Wang et al. [39]</td><td>460ms</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>1610ms</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>570ms</td></tr><tr><td>DIFRINT [6]</td><td>1530ms</td></tr><tr><td>FuSta [23]</td><td>9820ms</td></tr><tr><td>Ours</td><td>97ms</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 4. Per-frame runtime comparison of camera pose regression and video stabilization.",
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+        "img_path": "images/84dca42383bbf2742110eb444613db34b55c7f59cc19713198a14d13c738d0d4.jpg",
+        "image_caption": [
+            "(a) shaky frames"
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+        "img_path": "images/8d25420f1065a21d7e02a10dd900842d696a5b5a32b7113e1c20e6d9b86cf614.jpg",
+        "image_caption": [
+            "(b) stable frames",
+            "Figure 7. Experiment of fixed-point iteration on shaky and stable frames. (a) Our fixed-point iteration helps the shaky frames converge to a steady state. (b) For stable frames, the fixed-point iteration guarantees the stability of results."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "6.4. Runtime Comparison",
+        "text_level": 1,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our network and pipeline are implemented with PyTorch and Python. Table 4 is a summary of the runtime per frame for various competing methods. All timing results are obtained on a desktop with an RTX3090Ti GPU and an Intel(R) Xeon(R) Gold 6226R CPU. First, we compare the run-time of pose regression. Traditional pose regression is time consuming in feature matching [2, 9], homography estimation, and SVD decomposition [28]. Although our learning-based pose regression network runs 10 times faster than the traditional framework. Then, we report the average run time of different methods, including optimization-based [21, 49] and learning-based [6, 11, 23, 39, 50]. Our method takes  $97\\mathrm{ms}$  which gives  $\\sim 5\\mathrm{x}$  speed-up. This is because our method computes the optical flow field only once and without the help of other upstream task methods and manual optimization.",
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+    {
+        "type": "text",
+        "text": "6.5. Fixed-point Experiment",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the stability of our fixed-point optimization solution, we performed an interesting toy experiment. We input a sequence of shaky frames into our coarse-to-fine stabilizers, and the stabilized result will be iteratively restabilized by our stabilizers. For each iteration, we calculate the average magnitude of optical flow filed with global transformation and flow warping for each frame. Specifi-",
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+    {
+        "type": "text",
+        "text": "cally, the regions where we calculate are marked by  $\\hat{M}$ . As shown in Fig. 7(a), the deviation of the shaky frames decreases rapidly with each iteration. Furthermore, we have pointed out that plugging a stabilized video into the stabilization system should not have an impact on the input. Thus, we plug stable frames into the coarse-to-fine stabilizers and iteratively stabilize them. The result is shown in Fig. 7(b). The deviation of each frame is perturbed around the value of zero. Obviously, our method has no effect on stable frames, which shows that stabilized video is indeed the fixed point of our developed stabilization system.",
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+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we have presented a fast full-frame video stabilization technique based on the iterative optimization strategy. Our approach can be interpreted as the combination of probabilistic stabilization network (coarse-to-fine extension of PDC-Net) and video outpainting outwork (flow-based image outpainting). When trained on synthetic data constructed within the optimization-based learning framework, our method achieves state-of-the-art performance at a fraction of the computational cost of other competing techniques. It is also empirically verified that stabilized video is the fixed point of the stabilization network.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            76,
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+            487
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+        ],
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+    },
+    {
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+    },
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new file mode 100644
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+[
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "Fast Full-frame Video Stabilization with Iterative Optimization"
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+            "content": "Weiyue Zhao\\(^{1}\\) Xin Li\\(^{2}\\) Zhan Peng\\(^{1}\\) Xianrui Luo\\(^{1}\\) Xinyi Ye\\(^{1}\\) Hao Lu\\(^{1}\\) Zhiguo Cao\\(^{1*}\\)  \n\\(^{1}\\)Key Laboratory of Image Processing and Intelligent Control, Ministry of Education; School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China  \n\\(^{2}\\)Department of Computer Science, University of Albany, Albany NY 12222 {zhaoweiyue, peng-zhan, xianruiluo, xinyiye, hlu, zgcao}@hust.edu.cn xli48@albany.edu"
+        },
+        {
+            "type": "title",
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+            "content": "Video stabilization refers to the problem of transforming a shaky video into a visually pleasing one. The question of how to strike a good trade-off between visual quality and computational speed has remained one of the open challenges in video stabilization. Inspired by the analogy between wobbly frames and jigsaw puzzles, we propose an iterative optimization-based learning approach using synthetic datasets for video stabilization, which consists of two interacting submodules: motion trajectory smoothing and full-frame outpainting. First, we develop a two-level (coarse-to-fine) stabilizing algorithm based on the probabilistic flow field. The confidence map associated with the estimated optical flow is exploited to guide the search for shared regions through backpropagation. Second, we take a divide-and-conquer approach and propose a novel multiframe fusion strategy to render full-frame stabilized views. An important new insight brought about by our iterative optimization approach is that the target video can be interpreted as the fixed point of nonlinear mapping for video stabilization. We formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories, which guarantees convergence with the help of fixed-point theory. Extensive experimental results are reported to demonstrate the superiority of the proposed approach in terms of computational speed and visual quality. The code will be available on GitHub."
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+                0.789
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.8,
+                0.471,
+                0.86
+            ],
+            "angle": 0,
+            "content": "With the growing popularity of short videos on social media platforms (e.g., TikTok, Instagram), video has played an increasingly important role in our daily life. However, casually captured videos are often shaky and wobbly due to"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.316,
+                0.893,
+                0.438
+            ],
+            "angle": 0,
+            "content": "amateur shooting. Although it is possible to alleviate those problems by resorting to professional equipment (e.g., dollies and steadicams), the cost of hardware-based solutions is often expensive, making it impractical for real-world applications. By contrast, software-based or computational solutions such as video stabilization algorithms [12] have become an attractive alternative to improve the visual quality of shaky video by eliminating undesirable jitter."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.442,
+                0.895,
+                0.67
+            ],
+            "angle": 0,
+            "content": "Existing video stabilization techniques can be classified into two categories: optimization-based and learning-based. Traditional optimization-based algorithms [11,18,21,27,39] have been widely studied due to their speed and robustness. The challenges of them are the occlusion caused by changes in depth of field and the interference caused by foreground objects on camera pose regression. Furthermore, their results often contain large missing regions at frame borders, particularly when videos with a large camera motion. In recent years, learning-based video stabilization algorithms [6, 23, 45, 50] have shown their superiority by achieving higher visual quality compared to traditional methods. However, their stabilization model is too complex for rapid computation, and its generalization property is unknown due to the scarcity of training datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.896,
+                0.902
+            ],
+            "angle": 0,
+            "content": "To overcome those limitations, we present an iterative optimization-based learning approach that is efficient and robust, capable of achieving high-quality stabilization results with full-frame rendering, as shown in Fig. 1. The probabilistic stabilized network addresses the issues of occlusion and interfering objects, and achieves fast pose estimation. Then the full-frame outpainting module retains the original field of view (FoV) without aggressive cropping. An important new insight brought by our approach is that the objective of video stabilization is to suppress the implicitly embedded noise in the video frames rather than the explicit noise in the pixel intensity values. This inspired us to adopt an expectation-maximization (EM)-like approach for video stabilization. Importantly, considering the strong redundancy of video in the temporal domain, we ingeniously"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.076,
+                0.874,
+                0.401,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Corresponding author https://github.com/zwyking/Fast-Stab"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "23534"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.089,
+                0.089,
+                0.468,
+                0.246
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.472,
+                0.09,
+                0.885,
+                0.246
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.25,
+                0.895,
+                0.293
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview of our video stabilization framework. It consists of motion trajectory smoothing (in Sec. 3 and Sec. 4) and full-frame outpainting modules (in Sec. 5). The former adopts the two-level (coarse-to-fine) stabilizing algorithm to obtain a stabilized video. The latter further render a full-frame video with strategies of flow outpainting and multiframe fusion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.317,
+                0.47,
+                0.451
+            ],
+            "angle": 0,
+            "content": "consider stable video (the target of video stabilization) as the fixed point of nonlinear mapping. Such a fixed-point perspective allows us to formulate an optimization problem of the optical flow field in commonly shared regions. Unlike most methods that resort to the ad hoc video dataset [56] or the deblurred dataset [35] as stabilized videos, we propose to construct a synthetic training dataset to facilitate joint optimization of model parameters in different network modules."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.453,
+                0.471,
+                0.737
+            ],
+            "angle": 0,
+            "content": "To solve the formulated iterative optimization problem, we take a divide-and-conquer approach by designing two modules: probabilistic stabilization network (for motion trajectory smoothing) and video outpainting network (for full-frame video rendering). For the former, we propose to build on the previous work of PDCNet [37, 38] and extend it using a coarse-to-fine strategy to improve robustness. For a more robust estimate of the uncertainty of the optical flow, we infer masks from the optical flow by bidirectional propagation with a low computational cost (around \\(1/5\\) of the time Yu et al. [50]). Accordingly, we have developed a two-level (coarse-to-fine) flow smoothing strategy that first aligns adjacent frames by global affine transformation and then refines the result by warping the fields of intermediate frames. For the latter, we propose a two-stage approach (flow and image outpainting) to render full-frame video. Our experimental results have shown highly competent performance against others on three public benchmark datasets. The main contribution of this work is threefold:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.743,
+                0.468,
+                0.801
+            ],
+            "angle": 0,
+            "content": "- We propose a formulation of video stabilization as a fixed-point problem of the optical flow field and propose a novel procedure to generate a model-based synthetic dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.807,
+                0.468,
+                0.865
+            ],
+            "angle": 0,
+            "content": "- We construct a probabilistic stabilization network based on PDCNet and propose an effective coarse-to-fine strategy for robust and efficient smoothing of optical flow fields."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.871,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "- We propose a novel video outpainting network to render stabilized full-frame video by exploiting the spatial"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.743,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.533,
+                0.317,
+                0.715,
+                0.33
+            ],
+            "angle": 0,
+            "content": "coherence in the flow field."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.348,
+                0.642,
+                0.363
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.373,
+                0.682,
+                0.387
+            ],
+            "angle": 0,
+            "content": "2.1. Video Stabilization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.397,
+                0.892,
+                0.593
+            ],
+            "angle": 0,
+            "content": "Most video stabilization methods can typically be summarized as a three-step procedure: motion estimation, smoothing the trajectory, and generating stable frames. Traditional methods focus primarily on 2D features or image alignment [29] when it comes to motion estimation. These methods are different in modeling approaches to motion, including the trajectory matrix [19], epipolar geometry [10, 21, 47, 53], and the optical flow field [22, 54]. Regarding the smoothing trajectory, particle filter tracking [46], space-time path smoothing [19, 40], and L1 optimization [11] have been proposed. Existing methods for generating stable frames rely mainly on 2D transformations [26], grid warping [19, 21], and dense flow field warping [22]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.594,
+                0.892,
+                0.774
+            ],
+            "angle": 0,
+            "content": "Compared to the 2D method, some approaches turn to 3D reconstruction [17]. However, specialized hardware such as depth camera [20] and light field camera [34] are necessary for these methods based on 3D reconstruction. Some methods [30, 43, 44, 49] tackle video stabilization from the perspective of deep learning. In [49], the optimization of video stabilization was formulated in the CNN weight space. Recent work [50] represents motion by flow field and attempts to learn a stable optical flow to warp frames. Another method [6] aims to learn stable frames by interpolation. These deep-learning methods generate stable videos with less distortion."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.673,
+                0.803
+            ],
+            "angle": 0,
+            "content": "2.2. Large FOV Video"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Unlike the early work (e.g., traffic video stabilization [16]), large field of view (Field Of View) video stabilization has been attracting more researchers' attention. For most video stabilization methods, cropping is inevitable, which is why the FOV is reduced. Several approaches have been proposed to maintain a high FOV ratio. OVS [45]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.946,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "23535"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.258
+            ],
+            "angle": 0,
+            "content": "proposed to improve FOV by extrapolation. DIFRINT [6] choose iterative interpolation to generate high-FOV frames. FuSta [23] used neural rendering to synthesize high-FOV frames from feature space. To a great extent, the performance of interpolation-based video stabilization [6,45] depends on the selected frames. If selected frames have little correspondence with each other, performance will deteriorate dramatically. Neural rendering [23] synthesizes the image by weighted summing, causing blur. Most recently, a deep neural network [33] (DNN) has jointly exploited sensor data and optical flow to stabilize videos."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.272,
+                0.431,
+                0.289
+            ],
+            "angle": 0,
+            "content": "3. Stabilization via Iterative Optimization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.296,
+                0.473,
+                0.584
+            ],
+            "angle": 0,
+            "content": "Motivation. Despite rapid advances in video stabilization [30], existing methods still suffer from several notable limitations [12]. First, a systematic treatment of various uncertainty factors (e.g., low-texture regions in the background and moving objects in the foreground) in the problem formulation is still lacking. These uncertainty factors often cause occlusion-related problems and interfere with the motion estimation process. Second, the high computational cost has remained a technical barrier to real-time video processing. The motivation behind our approach is two-fold. On the one hand, we advocate for finding commonly shared regions among successive frames to address various uncertainty factors in handheld video. On the other hand, in contrast to these prestabilization algorithms [21, 23, 49, 50] based on traditional approaches, we proposed a novel high-efficiency prestabilization algorithm based on probabilistic optical flow. Flow-based methods are generally more accurate in motion estimation and deserve a high time cost. Accuracy and efficiency, we have both."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.585,
+                0.473,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Approach. We propose to formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories. It is enlightening to think of video stabilization as a special kind of \"video denoising\" where noise contamination is not associated with pixel intensity values, but embedded into the motion trajectories of foreground and background objects. Conceptually, for video restoration in which unknown motion is the hidden variable, we can treat video stabilization as a chicken-and-egg problem [13] - i.e., the objective of smoothing motion trajectories is intertwined with that of video frame interpolation. Note that an improved estimation of motion information can facilitate the task of frame interpolation and vice versa. Such an observation naturally inspires us to tackle the problem of video stabilization by iterative optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.472,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Through divide-and-conquer, we propose to formulate video stabilization as the following optimization problem. Given a sequence of \\( n \\) frames along with the set of optical flows \\( \\mathcal{V} \\), we first define the confidence map, which originally indicates the reliability and accuracy of the optical flow prediction at each pixel. Here, we have thresholded the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "confidence map as a binary image, which represents accurate matches (as shown in the 4-th column of Fig. 2). Then we can denote \\( n \\) frames and the corresponding set of confidence maps \\( \\mathcal{M} \\) by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.515,
+                0.164,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {Y} = \\left\\{Y _ {1}, Y _ {2}, \\dots , Y _ {q} \\right\\}, \\mathcal {M} = \\left\\{M _ {1}, M _ {2}, \\dots , M _ {q} \\right\\}. \\quad (1)\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.195,
+                0.82,
+                0.211
+            ],
+            "angle": 0,
+            "content": "4. Probabilistic Stabilization Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.22,
+                0.892,
+                0.432
+            ],
+            "angle": 0,
+            "content": "The problem of video stabilization can be formulated as finding a nonlinear mapping \\( f: \\mathcal{V} \\to \\hat{\\mathcal{V}} \\) where \\( \\hat{\\mathcal{V}} \\) denotes the optical flow set of the stabilized video. We hypothesize that a desirable objective to pursue \\( f \\) is the well-known fixed-point property, i.e., \\( \\hat{\\mathcal{V}} = f(\\hat{\\mathcal{V}}) \\). To achieve this objective, we aim to minimize an objective function \\( \\mathbb{F} \\) characterized by the magnitude of optical flows between commonly shared regions, as represented by \\( \\mathcal{M} \\). Note that \\( \\mathcal{M} \\) is the hidden variable in our problem formulation (that is, we need to estimate \\( \\mathcal{M} \\) from \\( \\hat{\\mathcal{V}} \\)). A popular strategy to address this chicken-and-egg problem is to alternatively solve the two subproblems of unknown \\( \\mathcal{M} \\) and \\( \\hat{\\mathcal{V}} \\). More specifically, the optimization of \\( \\mathbb{F} \\) is decomposed into the following two subproblems:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.517,
+                0.441,
+                0.892,
+                0.474
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(\\hat {M} _ {1}, \\dots , \\hat {M} _ {q}\\right) = \\underset {\\mathcal {M}} {\\arg \\min } \\mathbb {F} \\left(\\hat {Y} _ {1} \\odot M _ {1}, \\dots , \\hat {Y} _ {q} \\odot M _ {q}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.531,
+                0.469,
+                0.859,
+                0.492
+            ],
+            "angle": 0,
+            "content": "\\[\n(\\hat {Y} _ {1}, \\dots , \\hat {Y} _ {q}) = \\underset {\\mathcal {Y}} {\\arg \\min } \\mathbb {F} (Y _ {1} \\odot \\hat {M} _ {1}, \\dots , Y _ {q} \\odot \\hat {M} _ {q}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.504,
+                0.892,
+                0.716
+            ],
+            "angle": 0,
+            "content": "where \\( Y / \\hat{Y} \\) denotes the magnitude of the optical flow values before and after stabilization and \\( \\odot \\) is the Hadamard product. Instead of analyzing the estimated motion in the frequency domain, we hypothesize that stabilized videos are the fixed points of video stabilization algorithms, which minimize the above objective function. A fixed point [1] is a mathematical object that does not change under a given transformation. Numerically, fixed-point iteration is a method of computing fixed points of a function. It has been widely applied in data science [7], and image restoration [5, 25]. Here, we denote \\( \\mathbb{F} \\) in Eq. (2) as the function to be optimized, and the fixed point of \\( \\mathbb{F} \\) is defined as the stabilized video. Next, we solve these two subproblems by constructing the module of stabilization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.727,
+                0.72,
+                0.741
+            ],
+            "angle": 0,
+            "content": "4.1. Probabilistic Flow Field"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "First, we start with an interesting observation. When playing an unstable video at a slower speed (e.g., from 50fps to 30fps), the video tends to appear less wobbly. It follows from the observation that the fundamental cause of video instability is the fast frequency and the large amplitude of the still objects' motion speed. Therefore, the core task of motion smoothing is to identify the region that needs to be stabilized. As Yu et al. [50] pointed out, mismatches, moving objects, and inconsistent motion areas lead to variation of the estimated motion from the true motion trajectories and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.946,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "23536"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.088,
+                0.46,
+                0.287
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.29,
+                0.47,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Figure 2. Visualization of confidence map back-propagation results. The flow field and confidence map are predicted by PDCNet between source and target images. The obtained masks in the last column represent the shared regions among these frames."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.375,
+                0.47,
+                0.48
+            ],
+            "angle": 0,
+            "content": "should be masked. An important new insight brought about by this work is that these regions of inconsistency in the optical flow fields tend to show greater variability as the frame interval increases. Therefore, if these inconsistent regions are excluded, the video stabilization task can be simplified to the first sub-problem in Eq. (2) - i.e., minimizing \\(\\mathbb{F}\\) over \\(\\mathcal{M}\\) for a fixed \\(\\mathcal{V}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.483,
+                0.469,
+                0.664
+            ],
+            "angle": 0,
+            "content": "To detect unreliable matches and inconsistent regions, we have adopted the probabilistic flow network - PDCNet [37, 38], that jointly tackles the problem of dense correspondence and uncertainty estimation, as our building block. Suppose that PDCNet estimates the optical flow \\( Y_{k} \\) from frame \\( k + d \\) to frame \\( k \\) with the resulting confidence map \\( C_k \\). Although \\( C_k \\) denotes the inaccuracy of the optical flow estimate in \\( Y_{k} \\), it is often sensitive to the frame interval \\( d \\). For example, it is difficult to identify the inconsistent region when \\( d \\) is small, while the common area is less controllable when \\( d \\) is large. Therefore, simply using an optical flow field to estimate inconsistent regions is not sufficient."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.666,
+                0.469,
+                0.831
+            ],
+            "angle": 0,
+            "content": "We have designed a more robust solution to the joint estimation of dense flow and confidence map based on a coarse-to-fine strategy. The basic idea is to first obtain the probabilistic flow field at a coarse scale (e.g., with the down-sampled video sequence by a factor of \\( d \\) along the temporal axis) and then fill in the rest (i.e., the frames between the adjacent frames in the down-sampled video) at the fine scale. Such a two-level estimation strategy effectively overcomes the limitations of PDCNet by propagating the estimation results of probabilistic flow fields bidirectionally, as we will elaborate next."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Coarse-scale strategy As shown by the second-to-last column in Fig. 2, the confidence map estimated by PDCNet can identify the mismatched region, but fails to locate the objects with small motions (e.g., people and the sky). To"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.09,
+                0.883,
+                0.179
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.181,
+                0.892,
+                0.235
+            ],
+            "angle": 0,
+            "content": "Figure 3. Architecture of the camera pose regression network. Given the flow field and mask, our network predicts the corresponding affine transformation parameters by closed-loop iterations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.258,
+                0.892,
+                0.426
+            ],
+            "angle": 0,
+            "content": "overcome this difficulty, we introduce the binary mask as a warped and aggregated confidence map (refer to the last column of Fig. 2). Specifically, we first propose to obtain the confidence map \\(\\hat{C}_{k + (n - 1)d}\\) with down-sampled video (the last row of Fig. 2). In the forward direction, we estimate dense flow and confidence map using PDCNet; then \\(\\hat{C}_{k + (n - 1)d}\\) is backpropagated to update the binary mask \\(\\hat{M}\\) by thresholding and setting intersection operators. Through bidirectional propagation, the region covered by \\(\\mathcal{M}\\) is the shared content from frame \\(k\\) to frame \\(k + (n - 1)d\\). The complete procedure can be found in Supp. S1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.431,
+                0.893,
+                0.596
+            ],
+            "angle": 0,
+            "content": "Fine-scale strategy Based on the coarse-scale estimation result for downsampled video (i.e., \\(\\mathcal{M} = \\{\\hat{M}_k, \\hat{M}_{k+d}, \\dots, \\hat{M}_{k+(n-1)d}\\}\\)), we fill in the missing \\(d-1\\) frames at the fine scale. Specifically, considering the sequential frames from \\(k\\) to \\(k+d\\), we can obtain two sets similar to Eq. (1), which are \\(\\mathcal{V} = \\{Y_k, Y_{k+1}, \\dots, Y_{k+d-1}, \\hat{Y}_{k+d}\\}\\) and their corresponding confidence map set \\(\\mathcal{C}\\). Note that \\(\\hat{M}_{k+d} \\in \\mathcal{M}\\) has been calculated in coarse stage. Setting \\(d=1\\), we can call the algorithm again to obtain the set of output masks \\(\\mathcal{M}\\) for the rest of \\(d-1\\) frames."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.606,
+                0.712,
+                0.621
+            ],
+            "angle": 0,
+            "content": "4.2. Coarse-scale Stabilizer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.629,
+                0.892,
+                0.675
+            ],
+            "angle": 0,
+            "content": "To coarsely stabilize the video, we first propose aligning the adjacent frames with a global affine transformation [52]. The optimization function \\(\\mathbb{F}\\) in Eq. (2) is represented as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.602,
+                0.684,
+                0.892,
+                0.71
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {T} ^ {*} = \\underset {\\mathbf {T}} {\\arg \\min } \\mathbf {T} (Y \\odot \\hat {M}), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{T}(\\cdot)\\) denotes the image transformation applied to the shared region \\(\\hat{M}\\) (the result of Sec. 4.1) of the optical flow field \\(Y\\). Most conventional methods [23,44,50] adopt image matching to obtain \\(\\mathbf{T}(\\cdot)\\)-e.g., keypoint detection [2,24,31], feature matching [2,3,51]; and camera pose estimation is implemented by OpenCV-python. However, these methods are often time-consuming and computationally expensive. For example, two adjacent frames of unstable videos usually share a large area and are free from perspective transformation. Thus, an affine transformation, including translation, rotation, and scaling, is sufficient. More importantly, within the optimization-based learning framework, we can"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "23537"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.136
+            ],
+            "angle": 0,
+            "content": "regress these linear parameters of \\(\\mathbf{T}(\\cdot)\\) from the optical flow field, which characterize the relative coordinate transformation of the matched features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.137,
+                0.471,
+                0.244
+            ],
+            "angle": 0,
+            "content": "We propose a novel camera pose regression network, as shown in Fig. 3. Given an optical flow field \\( Y \\) and the corresponding mask field \\( \\hat{M} \\), our network \\( \\Phi(\\cdot) \\) can directly estimate the unknown parameters \\( \\mathbf{T}(\\cdot) \\propto \\{\\theta, s, d_x, d_y\\} = \\Phi(Y, \\hat{M}) \\). To solve the optimization problem of Eq. (3), we use the estimated parameters to iteratively compute the corresponding residual optical flow fields such that"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.255,
+                0.47,
+                0.273
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {Y} = Y - (S \\cdot R \\cdot V + T), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.283,
+                0.47,
+                0.39
+            ],
+            "angle": 0,
+            "content": "where \\(T\\), \\(S\\), and \\(R\\), respectively, denote the translation, scaling, and rotation matrix, and \\(V \\in \\mathbb{R}^{2 \\times H \\times W}\\) represents an image coordination grid. Then \\(\\{\\Delta \\theta, \\Delta s, \\Delta x, \\delta y\\} = \\Phi(\\bar{Y}, \\tilde{M})\\) is calculated iteratively to produce the updated parameters \\(\\{\\theta + \\Delta \\theta, s \\cdot \\Delta s, d_x + \\Delta x, d_y + \\Delta y\\}\\). The finally estimated affine transformation is smoothed by a moving Gaussian filter with a window size of 20 pixels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.396,
+                0.47,
+                0.457
+            ],
+            "angle": 0,
+            "content": "Loss functions Our loss functions include robust loss \\(\\ell_1\\) and grid loss commonly applied in consistency filtering [51]. We directly calculate the \\(\\ell_1\\) loss between the predictions and their ground truth \\(\\{\\hat{\\theta},\\hat{s},\\hat{d}_x,\\hat{d}_y\\}\\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.13,
+                0.467,
+                0.47,
+                0.515
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {g t} = \\lambda_ {\\theta} \\| | \\theta - \\hat {\\theta} \\| | _ {1} + \\lambda_ {s} \\| | 1 - \\frac {s}{\\hat {s}} \\| | _ {1} \\tag {5} \\\\ + \\lambda_ {t} \\| | d _ {x} - \\hat {d} _ {x} | + | d _ {y} - \\hat {d} _ {y} | \\| _ {1}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.524,
+                0.469,
+                0.556
+            ],
+            "angle": 0,
+            "content": "For better supervision of the estimated pose, we calculate the loss \\(L_{grid}\\) with the grid \\(V \\in \\mathbb{R}^{2 \\times h \\times h}\\) in Eq. (4), i.e.,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.088,
+                0.566,
+                0.469,
+                0.585
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {g r i d} = \\left\\| (\\hat {S} \\cdot \\hat {R} \\cdot V + \\hat {T}) - (S \\cdot R \\cdot V + T) + \\epsilon \\right\\| _ {1} \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.595,
+                0.47,
+                0.627
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{\\cdot}\\) denotes the ground truth and \\(\\epsilon\\) is a small value for stability. The final loss \\(L_{stab}\\) consists of \\(L_{gt}\\) and \\(L_{grid}\\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.638,
+                0.47,
+                0.656
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {s t a b} = L _ {g t} + \\lambda_ {g r i d} L _ {g r i d}. \\tag {7}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.664,
+                0.27,
+                0.68
+            ],
+            "angle": 0,
+            "content": "4.3. Fine-scale Stabilizer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.688,
+                0.469,
+                0.809
+            ],
+            "angle": 0,
+            "content": "The assumption with an affine transformation of the coarse-scale stabilizer could cause structural discontinuity and local distortion. Therefore, our objective is to refine the coarsely stabilized video by optical flow smoothing. Unlike Eq. 3 which applies an image transformation matrix to optimize the optical flow field, we optimize it at the pixel level by a flow warping field \\(\\mathbf{W}\\). Thus, the function \\(\\mathbb{F}\\) in Eq. (2) is given by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.152,
+                0.82,
+                0.469,
+                0.861
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {W} ^ {*} = \\underset {\\mathbf {W}} {\\arg \\min } \\sum_ {i = 0} ^ {N - 1} \\mathbf {W} _ {i} \\left(Y _ {i} \\odot \\hat {M} _ {i}\\right). \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The flow smoothing network follows the U-Net architecture in [56]. We use \\(N\\) frames of optical flow fields \\(\\mathbf{F}\\) and mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.512,
+                0.09,
+                0.882,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.192,
+                0.892,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Figure 4. Illustration of flow fields and warped images under different FOVs. The target image with large FOV presents the smoother flow field and better warped result."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.258,
+                0.892,
+                0.35
+            ],
+            "angle": 0,
+            "content": "fields \\(\\hat{M}\\) as input and obtain \\((N - 1)\\) frame warp fields \\(\\mathbf{W}\\) of intermediate frames. Specifically, for the optical flow field \\(Y_{k}\\) (from frame \\(k + 1\\) to frame \\(k\\)), we denote the aligned matrices of each frame in Sec. 4.2 as \\(H_{k} \\in \\mathbb{R}^{2 \\times 3}\\) and \\(H_{k + 1} \\in \\mathbb{R}^{2 \\times 3}\\), respectively. Then the input optical flow \\(\\mathbf{F}_{k} \\in \\mathbb{R}^{2 \\times HW}\\) can be represented by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.555,
+                0.361,
+                0.892,
+                0.379
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {F} _ {k} = H _ {k + 1} \\cdot \\left[ V + Y _ {k} \\mid 1 \\right] - H _ {k} \\cdot \\left[ V \\mid 1 \\right], \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.388,
+                0.892,
+                0.465
+            ],
+            "angle": 0,
+            "content": "where \\(V \\in \\mathbb{R}^{2 \\times HW}\\) and \\([\\cdot|1]\\) denote the normalized coordinate representation. Furthermore, to better adapt the flow smoothing network to the mask field \\(\\hat{M}\\), we fine-tune it using our synthetic dataset (as we will elaborate in Sec. 6.1). The loss function follows the motion loss [49]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.516,
+                0.475,
+                0.892,
+                0.517
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {s m o o t h}} = \\sum_ {k = 0} ^ {N - 1} \\left(\\mathbf {F} _ {k} + \\mathbf {W} _ {k} - \\mathbf {F} _ {k} \\left(\\mathbf {W} _ {k + 1}\\right)\\right) \\odot \\hat {M}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.527,
+                0.666,
+                0.543
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{W}_0 = \\mathbf{W}_N = 0\\)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.556,
+                0.757,
+                0.574
+            ],
+            "angle": 0,
+            "content": "5. Video Outpainting Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.581,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Most video stabilization methods crop an input video with a small field of view (FOV), excluding missing margin pixels due to frame warping. In contrast, full-frame video stabilization [6, 23, 26] proposes to generate a video that maintains the same FOV as the input video without cropping. They directly generate stabilized video frames with large FOV by fusing the information from neighboring frames. An important limitation of existing fusion strategies is the unequal importance of different frames (i.e., the current and neighboring frames are weighted equally), which would lead to unpleasant distortions in fast-moving situations. To overcome this weakness, we propose a two-stage framework to combine flow and image outpainting strategies [32]. In the first stage, we used flow-outpainting to iteratively align the neighboring frames with the target frame. In the second stage, we fill the target frame with adjacent aligned frame pixels by image outpainting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.744,
+                0.864
+            ],
+            "angle": 0,
+            "content": "5.1. Flow Outpainting Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Let \\(I^t\\) denote the outpainted target image and \\(I^s\\) the neighboring source image. We aim to fill the missing pixel"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "23538"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.087,
+                0.089,
+                0.462,
+                0.198
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.201,
+                0.47,
+                0.243
+            ],
+            "angle": 0,
+            "content": "Figure 5. Architecture of flow outpainting network. Given a small FOV flow field and valid mask, the network predicts the large FOV flow field."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.267,
+                0.47,
+                0.434
+            ],
+            "angle": 0,
+            "content": "region \\( M_{\\varnothing}^{t} \\) of \\( I^{t} \\) with the pixels of \\( I^{s} \\). As shown in Fig. 4, we take two different FOVs of \\( I^{t} \\) as input and obtain the corresponding optical flow fields and warped results \\( I_{warp}^{s} \\). The small FOV \\( I^{t} \\) cannot guide \\( I^{s} \\) well to fill the regions in \\( M_{\\varnothing}^{t} \\). Since the predicted optical flow field in \\( M_{\\varnothing}^{t} \\) is unreliable due to the lack of pixel guidance of \\( I^{t} \\), the out-of-view region of \\( M_{\\varnothing}^{t} \\) has artifacts (marked in the last column of Fig. 4). We observe that the optical flow field of the large FOV \\( I^{t} \\) is continuous in \\( M_{\\varnothing}^{t} \\), which inspired us to extrapolate the flow of \\( M_{\\varnothing}^{t} \\) using the reliable flow region (the 3rd column of Fig. 4)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.434,
+                0.47,
+                0.555
+            ],
+            "angle": 0,
+            "content": "We propose a novel flow outpainting network (Fig. 5), which extrapolates the large FOV flow field using a small FOV flow field and the corresponding valid mask. Specifically, we adopt a U-Net architecture and apply a sequence of gated convolution layers with downsampling / upsampling to obtain the large flow field of FOV \\( Y_{large} \\). Note that the input flow field \\( Y_{small} \\) and the valid mask \\( M_{valid} \\) have been estimated by PDCNet (see Sec. 4.1)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.561,
+                0.469,
+                0.608
+            ],
+            "angle": 0,
+            "content": "Loss functions Our loss functions include robust loss \\(\\ell_1\\) and loss in the frequency domain [4]. We directly calculate the \\(\\ell_1\\) loss between \\(Y_{large}\\) and its ground truth \\(\\hat{Y}_{large}\\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.099,
+                0.617,
+                0.469,
+                0.652
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {Y} = \\lambda_ {i n} \\cdot \\| | Y _ {\\text {l a r g e}} - Y _ {\\text {s m a l l}} | \\odot M _ {\\text {v a l i d}} \\| _ {1} \\tag {11} \\\\ + \\lambda_ {o u t} \\cdot \\| | Y _ {l a r g e} - \\dot {Y} _ {l a r g e} | \\odot (\\sim M _ {v a l i d}) \\| _ {1}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.661,
+                0.469,
+                0.754
+            ],
+            "angle": 0,
+            "content": "To encourage low frequency and smoothing \\( Y_{large} \\), we add the loss in the frequency domain \\( L_{F} = \\| \\hat{\\mathbf{G}}\\cdot \\mathcal{F}Y_{large}\\|_{2} \\) where the normalized Gaussian map \\( \\hat{\\mathbf{G}} \\) with \\( \\mu = 0 \\) and \\( \\sigma = 3 \\) is inverted by its maximum value and \\( \\mathcal{F}Y_{large} \\) denotes the Fourier spectrum of \\( Y_{large} \\). The final loss consists of \\( L_{Y} \\) and \\( L_{F} \\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.755,
+                0.469,
+                0.771
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {o u t p a i n t}} = L _ {Y} + \\lambda_ {F} L _ {F}. \\tag {12}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.787,
+                0.322,
+                0.804
+            ],
+            "angle": 0,
+            "content": "5.2. Image Margin Outpainting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Based on our proposed flow-outpainting network, we design a margin-outpainting method by iteratively aligning frame pairs (see Fig. 6). As discussed in Sec. 5.1, we can obtain a large FOV flow field \\( Y_{large} \\). The neighboring reference frame \\( I^{s} \\) is warped as \\( I^{warp} = Y_{large}(I^{s}) \\) as shown in Fig. 6. In theory, the outpainted frame \\( I^{result} = \\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.089,
+                0.885,
+                0.246
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.249,
+                0.892,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Figure 6. Overview image margin outpainting. Given the target frame \\( I^{t} \\), the reference frame \\( I^{s} \\) is coarsely aligned to \\( I^{warp} \\) by the predicted large-FOV flow field \\( Y_{large} \\). Then, we adopt a margin fusion approach to obtain the result frame \\( I^{result} \\), by carefully aggregating \\( I^{t} \\) and \\( I^{warp} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.344,
+                0.892,
+                0.571
+            ],
+            "angle": 0,
+            "content": "\\(I^t \\cdot M_{valid} + I^{warp} \\cdot (\\sim M_{valid})\\). However, we notice that there are obvious distortions at the image border. To further align the margins, we take a margin fusion approach (the detailed algorithm can be found in Supp. S1) We crop \\(I^{warp}\\) and \\(I^t\\) to \\(I_c^s\\) and \\(I_c^t\\). Then, we can obtain a new warped frame \\(I_c^{warp}\\) by flow outpainting. In particular, we did not choose to add \\(I_c^{warp}\\) and \\(I^t\\) directly. To identify the misaligned region, we propose to outpaint the mask \\(M_{I^t}\\) by extending the watershed outward from the center. Instead of a preset threshold, we adaptively choose between the target image \\(I^t\\) and the warped image \\(I_c^{warp}\\). Then, the final frame \\(I^{result}\\) consists of \\(I^t\\) and \\(I_c^{warp}\\): \\(I^{result} = I^t \\cdot M_{I^t} + I_c^{warp} \\cdot (\\sim M_{I^t})\\). Compared to the two results \\(I^{result}\\), our strategy successfully mitigates misalignment and distortions at the boundary of video frames."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.579,
+                0.892,
+                0.79
+            ],
+            "angle": 0,
+            "content": "Multi-frame fusion During the final stage of rendering, we use a sequence of neighboring frames to outpaint the target frame, while they may have filled duplicate regions. It is important to find out which frame and which region should be selected. We proposed the selection strategy for multi-frame fusion (the details can be found in Supp. S1). By weighing the metric parameters of each frame, we finally obtain the target frame with large FOV. Note that each frame has an added margin in the stabilization process, so we need to crop them to the original resolution. Although we have outpainted the target frame, some missing pixel holes may still exit at boundaries. Here, we apply the state-of-the-art LaMa image inpainting method [36] to fill these holes using nearest-neighbor interpolation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.806,
+                0.633,
+                0.823
+            ],
+            "angle": 0,
+            "content": "6. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.832,
+                0.868,
+                0.848
+            ],
+            "angle": 0,
+            "content": "6.1. Synthetic Datasets for Supervised Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Due to the limited amount of paired training data, we propose a novel model-based data generation method by carefully designing synthetic datasets for video stabiliza"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "23539"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.179,
+                0.089,
+                0.795,
+                0.274
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">NUS dataset [21]</td><td colspan=\"3\">DeepStab dataset [39]</td><td colspan=\"3\">Selfie dataset [48]</td></tr><tr><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td></tr><tr><td>Grundmann et al. [11]</td><td>0.71</td><td>0.76</td><td>0.62</td><td>0.77</td><td>0.87</td><td>0.80</td><td>0.75</td><td>0.81</td><td>0.83</td></tr><tr><td>Liu et al. [21]</td><td>0.81</td><td>0.78</td><td>0.82</td><td>0.80</td><td>0.90</td><td>0.85</td><td>0.74</td><td>0.89</td><td>0.8</td></tr><tr><td>Wang et al. [39]</td><td>0.67</td><td>0.72</td><td>0.41</td><td>-</td><td>-</td><td>-</td><td>0.68</td><td>0.71</td><td>0.82</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>0.78</td><td>0.77</td><td>0.82</td><td>0.85</td><td>0.89</td><td>0.76</td><td>0.79</td><td>0.77</td><td>0.84</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>0.85</td><td>0.81</td><td>0.86</td><td>0.87</td><td>0.92</td><td>0.82</td><td>0.83</td><td>0.87</td><td>0.86</td></tr><tr><td>Yu [50]+OVS* [45]</td><td>0.92</td><td>0.78</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DUT [44]</td><td>0.71</td><td>0.81</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DIFRINT [6]</td><td>1.00</td><td>0.85</td><td>0.84</td><td>1.00</td><td>0.91</td><td>0.78</td><td>1.00</td><td>0.78</td><td>0.84</td></tr><tr><td>FuSta [23]</td><td>1.00</td><td>0.87</td><td>0.86</td><td>1.00</td><td>0.92</td><td>0.82</td><td>1.00</td><td>0.83</td><td>0.87</td></tr><tr><td>Ours</td><td>1.00</td><td>0.91</td><td>0.86</td><td>1.00</td><td>0.94</td><td>0.84</td><td>1.00</td><td>0.87</td><td>0.87</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.276,
+                0.895,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative results on the NUS dataset [21], the DeepStab dataset [39] and the Selfie Dataset [48]. We evaluate the following metrics: Cropping Ratio(C.), Distortion Value(D.), Stability Score(S). * indicates the results obtained from original paper. We highlight the best method in bold and underline the second-best."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.342,
+                0.473,
+                0.645
+            ],
+            "angle": 0,
+            "content": "tion. For our base synthetic dataset, we used a collection of images from the DPED [14], CityScapes [8] and ADE20K [55] datasets. To generate a stable video, we randomly generate the homography parameters for each image, including rotation angle \\(\\theta\\), scaling \\(s\\), translations \\((d_x,d_y)\\) and perspective factors \\((p_x,p_y)\\). Then we divide these transformation parameters into \\(N\\) bins equally and obtain a video of \\(N\\) frames by homography transformations. To simulate the presence of moving objects in real scenarios, the stable video is further augmented with additional independently moving random objects. To do so, the objects are sampled from the COCO dataset [15] and inserted on top of the synthetic video frames using their segmentation masks. Specifically, we randomly choose \\(m\\) objects (no more than 5), and generate randomly affine transformation parameters for each independent of the background transformation. Finally, we cropped each frame to \\(720\\times 480\\) around its center. For different training requirements, we apply various combinations of synthetic dataset. The implementation and training details can be found in Supp. S2, S3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.658,
+                0.3,
+                0.673
+            ],
+            "angle": 0,
+            "content": "6.2.Quantitative Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.682,
+                0.47,
+                0.834
+            ],
+            "angle": 0,
+            "content": "We compare the results of our method with various video stabilization methods, including Grundmann et al. [11], Liu et al. [21], Wang et al. [39], Yu and Ramamoorthi [49, 50], DUT [44], OVS [45], DIFRINT [6], and FuSta [23]. We obtain the results of the compared methods from the videos released by the authors or generated from the publicly available official implementation with default parameters or pre-trained models. Note that OVS [45] does not honor their promise to provide code, thus we only report the results from their paper."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Datasets. We evaluate all approaches on the NUS dataset [21], DeepStab dataset [39], and Selfie dataset [48]. The NUS dataset consists of 144 videos and the corresponding ground truths in 6 scenes. The DeepStab dataset con"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.342,
+                0.885,
+                0.358
+            ],
+            "angle": 0,
+            "content": "tains 61 videos and the Selfie dataset consist of 33 videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.38,
+                0.895,
+                0.503
+            ],
+            "angle": 0,
+            "content": "Metrics. We introduce three metrics widely used in many methods [6, 23, 50] to evaluate our model: 1) Cropping ratio measures the remaining frame area after cropping off the invalid boundaries. 2) Distortion value evaluates the anisotropic scaling of the homography between the input and output frames. 3) Stability score measures the stability of the output video. We calculate the metrics using the evaluation code provided by DIFRINT."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.524,
+                0.896,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Quantitative comparison. The results of the NUS dataset [21] are summarized in Table 1 (Per-category result can be found in Supp. S5). Overall, our method achieves the best distortion value compared to the state-of-the-art method, FuSta [23]. Especially in the quick-rotation and zoom categories, our method outperforms pure image generation methods [6,23]. We suspect that the reduction of the shared information between frames causes the image generation methods to prefer artifacts. However, our method can ensure local structural integrity when outpainting the margin region. Furthermore, our method achieves an average cropping ratio of 1.0 and stability scores comparable to recent approaches [6, 23, 49, 50]. Since FuSta [23] uses Yu et al. [50] to obtain stabilized input videos, they have the same stability scores. It is important to note that although the stability scores are competitive, our method runs 5 times faster than [50] in the video stabilization stage. Moreover, the comparison results on DeepStab dataset [39] and Selfie dataset [48] are also reported in Table 1. Our method still shows effectiveness in different datasets, proving the generalizability of the proposed method. Note that, due to that Wang et al. [39] is trained on the DeepStab dataset, we do not report its results on the DeepStab dataset for a fair comparison. Qualitative comparisons can be found in Supp. S4 and supplementary video."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "23540"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.109,
+                0.089,
+                0.44,
+                0.164
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Stabilizer</td><td></td><td>Stability↑</td><td>Distortion↑</td></tr><tr><td rowspan=\"2\">Image-level</td><td>w.o. mask</td><td>0.76</td><td>0.88</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr><tr><td rowspan=\"2\">Pixel-level</td><td>w.o. mask</td><td>0.81</td><td>0.84</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.165,
+                0.468,
+                0.193
+            ],
+            "angle": 0,
+            "content": "Table 2. The importance of mask to video stabilization. We validate on the Crowd category of NUS dataset [21]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.213,
+                0.462,
+                0.322
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>Distortion↑</td></tr><tr><td>PCAFlow [42]</td><td>11.34</td><td>0.50</td><td>0.72</td></tr><tr><td>Our flow outpainting</td><td>19.65</td><td>0.77</td><td>0.93</td></tr><tr><td>w.o. margin outpainting</td><td>18.04</td><td>0.64</td><td>0.81</td></tr><tr><td>w.o. mask \\( M_{I^t} \\)</td><td>20.35</td><td>0.78</td><td>0.86</td></tr><tr><td>w.o. multi-frame selection</td><td>21.99</td><td>0.84</td><td>0.90</td></tr><tr><td>Ours</td><td>23.17</td><td>0.86</td><td>0.91</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.322,
+                0.468,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation study of image filling. The evaluation is conducted on our model-based synthetic validation set."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.369,
+                0.23,
+                0.385
+            ],
+            "angle": 0,
+            "content": "6.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.397,
+                0.468,
+                0.562
+            ],
+            "angle": 0,
+            "content": "Importance of mask generation. We investigate the influence of the mask on video stabilization at different stages. To better demonstrate the necessity of mask in complex scenarios, we choose the Crowd category of NUS dataset [21] which includes a display of moving pedestrians and occlusions. Stability and distortion at different settings are shown in Table 2. It can be seen that the performance with mask increases significantly in both stabilizers. Specifically, the mask can both improve stability globally and alleviate image warping distortion locally. This result demonstrates the importance of mask generation for video stabilization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.574,
+                0.468,
+                0.77
+            ],
+            "angle": 0,
+            "content": "Flow outpainting. We compare our flow outpainting method with the traditional flow inpainting method PCAFlow [42]. Following [50] we fit the first 5 principal components proposed by PCAFlow to the \\( M_{valid} = 1 \\) regions of the optical flow field, and then outpaint the flow vectors in the \\( M_{valid} = 0 \\) regions with reasonable values of the PCA Flow fitted. The result is obtained by warping the source image with the outpainted optical flow field. We perform this comparison on our synthetic validation set and evaluate it with the corresponding ground truth. Additionally, we use PSNR and SSIM [41] to evaluate the quality of the results. As shown in Table 3, ours dramatically outperforms PCAFlow [42] in all objective metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Importance of image filling strategies. We explore the following proposed strategies for image filling: margin outpainting, mask generation \\( M_{It} \\), and multiframe selection. We isolate them from our method to compare their results with the complete version. The results are shown in Table 3. The proposed strategies are generally helpful in improving image quality. Especially, margin outpainting and mask \\( M_{It} \\) are crucial to the results."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.572,
+                0.089,
+                0.822,
+                0.261
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Runtime</td></tr><tr><td>Traditional pose regression</td><td>216ms</td></tr><tr><td>Our pose regression network</td><td>21ms</td></tr><tr><td>Grundmann et al. [11]</td><td>480ms</td></tr><tr><td>Liu et al. [21]</td><td>1360ms</td></tr><tr><td>Wang et al. [39]</td><td>460ms</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>1610ms</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>570ms</td></tr><tr><td>DIFRINT [6]</td><td>1530ms</td></tr><tr><td>FuSta [23]</td><td>9820ms</td></tr><tr><td>Ours</td><td>97ms</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.262,
+                0.892,
+                0.289
+            ],
+            "angle": 0,
+            "content": "Table 4. Per-frame runtime comparison of camera pose regression and video stabilization."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.511,
+                0.307,
+                0.703,
+                0.388
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.558,
+                0.393,
+                0.65,
+                0.405
+            ],
+            "angle": 0,
+            "content": "(a) shaky frames"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.706,
+                0.307,
+                0.888,
+                0.388
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.747,
+                0.393,
+                0.84,
+                0.404
+            ],
+            "angle": 0,
+            "content": "(b) stable frames"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.409,
+                0.892,
+                0.465
+            ],
+            "angle": 0,
+            "content": "Figure 7. Experiment of fixed-point iteration on shaky and stable frames. (a) Our fixed-point iteration helps the shaky frames converge to a steady state. (b) For stable frames, the fixed-point iteration guarantees the stability of results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.492,
+                0.702,
+                0.508
+            ],
+            "angle": 0,
+            "content": "6.4. Runtime Comparison"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.516,
+                0.892,
+                0.758
+            ],
+            "angle": 0,
+            "content": "Our network and pipeline are implemented with PyTorch and Python. Table 4 is a summary of the runtime per frame for various competing methods. All timing results are obtained on a desktop with an RTX3090Ti GPU and an Intel(R) Xeon(R) Gold 6226R CPU. First, we compare the run-time of pose regression. Traditional pose regression is time consuming in feature matching [2, 9], homography estimation, and SVD decomposition [28]. Although our learning-based pose regression network runs 10 times faster than the traditional framework. Then, we report the average run time of different methods, including optimization-based [21, 49] and learning-based [6, 11, 23, 39, 50]. Our method takes \\(97\\mathrm{ms}\\) which gives \\(\\sim 5\\mathrm{x}\\) speed-up. This is because our method computes the optical flow field only once and without the help of other upstream task methods and manual optimization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.771,
+                0.72,
+                0.787
+            ],
+            "angle": 0,
+            "content": "6.5. Fixed-point Experiment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To demonstrate the stability of our fixed-point optimization solution, we performed an interesting toy experiment. We input a sequence of shaky frames into our coarse-to-fine stabilizers, and the stabilized result will be iteratively restabilized by our stabilizers. For each iteration, we calculate the average magnitude of optical flow filed with global transformation and flow warping for each frame. Specifi-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "23541"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.473,
+                0.259
+            ],
+            "angle": 0,
+            "content": "cally, the regions where we calculate are marked by \\(\\hat{M}\\). As shown in Fig. 7(a), the deviation of the shaky frames decreases rapidly with each iteration. Furthermore, we have pointed out that plugging a stabilized video into the stabilization system should not have an impact on the input. Thus, we plug stable frames into the coarse-to-fine stabilizers and iteratively stabilize them. The result is shown in Fig. 7(b). The deviation of each frame is perturbed around the value of zero. Obviously, our method has no effect on stable frames, which shows that stabilized video is indeed the fixed point of our developed stabilization system."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.269,
+                0.196,
+                0.285
+            ],
+            "angle": 0,
+            "content": "7. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.295,
+                0.473,
+                0.462
+            ],
+            "angle": 0,
+            "content": "In this paper, we have presented a fast full-frame video stabilization technique based on the iterative optimization strategy. Our approach can be interpreted as the combination of probabilistic stabilization network (coarse-to-fine extension of PDC-Net) and video outpainting outwork (flow-based image outpainting). When trained on synthetic data constructed within the optimization-based learning framework, our method achieves state-of-the-art performance at a fraction of the computational cost of other competing techniques. It is also empirically verified that stabilized video is the fixed point of the stabilization network."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.472,
+                0.175,
+                0.488
+            ],
+            "angle": 0,
+            "content": "References"
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+# Fast Full-frame Video Stabilization with Iterative Optimization
+
+Weiyue Zhao $^{1}$  Xin Li $^{2}$  Zhan Peng $^{1}$  Xianrui Luo $^{1}$  Xinyi Ye $^{1}$  Hao Lu $^{1}$  Zhiguo Cao $^{1*}$ $^{1}$ Key Laboratory of Image Processing and Intelligent Control, Ministry of Education; School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China  
+ $^{2}$ Department of Computer Science, University of Albany, Albany NY 12222 {zhaoweiyue, peng-zhan, xianruiluo, xinyiye, hlu, zgcao}@hust.edu.cn xli48@albany.edu
+
+# Abstract
+
+Video stabilization refers to the problem of transforming a shaky video into a visually pleasing one. The question of how to strike a good trade-off between visual quality and computational speed has remained one of the open challenges in video stabilization. Inspired by the analogy between wobbly frames and jigsaw puzzles, we propose an iterative optimization-based learning approach using synthetic datasets for video stabilization, which consists of two interacting submodules: motion trajectory smoothing and full-frame outpainting. First, we develop a two-level (coarse-to-fine) stabilizing algorithm based on the probabilistic flow field. The confidence map associated with the estimated optical flow is exploited to guide the search for shared regions through backpropagation. Second, we take a divide-and-conquer approach and propose a novel multiframe fusion strategy to render full-frame stabilized views. An important new insight brought about by our iterative optimization approach is that the target video can be interpreted as the fixed point of nonlinear mapping for video stabilization. We formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories, which guarantees convergence with the help of fixed-point theory. Extensive experimental results are reported to demonstrate the superiority of the proposed approach in terms of computational speed and visual quality. The code will be available on GitHub.
+
+# 1. Introduction
+
+With the growing popularity of short videos on social media platforms (e.g., TikTok, Instagram), video has played an increasingly important role in our daily life. However, casually captured videos are often shaky and wobbly due to
+
+amateur shooting. Although it is possible to alleviate those problems by resorting to professional equipment (e.g., dollies and steadicams), the cost of hardware-based solutions is often expensive, making it impractical for real-world applications. By contrast, software-based or computational solutions such as video stabilization algorithms [12] have become an attractive alternative to improve the visual quality of shaky video by eliminating undesirable jitter.
+
+Existing video stabilization techniques can be classified into two categories: optimization-based and learning-based. Traditional optimization-based algorithms [11,18,21,27,39] have been widely studied due to their speed and robustness. The challenges of them are the occlusion caused by changes in depth of field and the interference caused by foreground objects on camera pose regression. Furthermore, their results often contain large missing regions at frame borders, particularly when videos with a large camera motion. In recent years, learning-based video stabilization algorithms [6, 23, 45, 50] have shown their superiority by achieving higher visual quality compared to traditional methods. However, their stabilization model is too complex for rapid computation, and its generalization property is unknown due to the scarcity of training datasets.
+
+To overcome those limitations, we present an iterative optimization-based learning approach that is efficient and robust, capable of achieving high-quality stabilization results with full-frame rendering, as shown in Fig. 1. The probabilistic stabilized network addresses the issues of occlusion and interfering objects, and achieves fast pose estimation. Then the full-frame outpainting module retains the original field of view (FoV) without aggressive cropping. An important new insight brought by our approach is that the objective of video stabilization is to suppress the implicitly embedded noise in the video frames rather than the explicit noise in the pixel intensity values. This inspired us to adopt an expectation-maximization (EM)-like approach for video stabilization. Importantly, considering the strong redundancy of video in the temporal domain, we ingeniously
+
+![](images/46ce70956dbb13bf03558f871ba573814a0f25c71411f32d1433c1e16de2fa95.jpg)  
+Figure 1. Overview of our video stabilization framework. It consists of motion trajectory smoothing (in Sec. 3 and Sec. 4) and full-frame outpainting modules (in Sec. 5). The former adopts the two-level (coarse-to-fine) stabilizing algorithm to obtain a stabilized video. The latter further render a full-frame video with strategies of flow outpainting and multiframe fusion.
+
+![](images/6a9817f6acb7f629182e51ff59b460f3fdc999660c43d844aeee05ce28645268.jpg)
+
+consider stable video (the target of video stabilization) as the fixed point of nonlinear mapping. Such a fixed-point perspective allows us to formulate an optimization problem of the optical flow field in commonly shared regions. Unlike most methods that resort to the ad hoc video dataset [56] or the deblurred dataset [35] as stabilized videos, we propose to construct a synthetic training dataset to facilitate joint optimization of model parameters in different network modules.
+
+To solve the formulated iterative optimization problem, we take a divide-and-conquer approach by designing two modules: probabilistic stabilization network (for motion trajectory smoothing) and video outpainting network (for full-frame video rendering). For the former, we propose to build on the previous work of PDCNet [37, 38] and extend it using a coarse-to-fine strategy to improve robustness. For a more robust estimate of the uncertainty of the optical flow, we infer masks from the optical flow by bidirectional propagation with a low computational cost (around  $1/5$  of the time Yu et al. [50]). Accordingly, we have developed a two-level (coarse-to-fine) flow smoothing strategy that first aligns adjacent frames by global affine transformation and then refines the result by warping the fields of intermediate frames. For the latter, we propose a two-stage approach (flow and image outpainting) to render full-frame video. Our experimental results have shown highly competent performance against others on three public benchmark datasets. The main contribution of this work is threefold:
+
+- We propose a formulation of video stabilization as a fixed-point problem of the optical flow field and propose a novel procedure to generate a model-based synthetic dataset.  
+- We construct a probabilistic stabilization network based on PDCNet and propose an effective coarse-to-fine strategy for robust and efficient smoothing of optical flow fields.  
+- We propose a novel video outpainting network to render stabilized full-frame video by exploiting the spatial
+
+coherence in the flow field.
+
+# 2. Related Work
+
+# 2.1. Video Stabilization
+
+Most video stabilization methods can typically be summarized as a three-step procedure: motion estimation, smoothing the trajectory, and generating stable frames. Traditional methods focus primarily on 2D features or image alignment [29] when it comes to motion estimation. These methods are different in modeling approaches to motion, including the trajectory matrix [19], epipolar geometry [10, 21, 47, 53], and the optical flow field [22, 54]. Regarding the smoothing trajectory, particle filter tracking [46], space-time path smoothing [19, 40], and L1 optimization [11] have been proposed. Existing methods for generating stable frames rely mainly on 2D transformations [26], grid warping [19, 21], and dense flow field warping [22].
+
+Compared to the 2D method, some approaches turn to 3D reconstruction [17]. However, specialized hardware such as depth camera [20] and light field camera [34] are necessary for these methods based on 3D reconstruction. Some methods [30, 43, 44, 49] tackle video stabilization from the perspective of deep learning. In [49], the optimization of video stabilization was formulated in the CNN weight space. Recent work [50] represents motion by flow field and attempts to learn a stable optical flow to warp frames. Another method [6] aims to learn stable frames by interpolation. These deep-learning methods generate stable videos with less distortion.
+
+# 2.2. Large FOV Video
+
+Unlike the early work (e.g., traffic video stabilization [16]), large field of view (Field Of View) video stabilization has been attracting more researchers' attention. For most video stabilization methods, cropping is inevitable, which is why the FOV is reduced. Several approaches have been proposed to maintain a high FOV ratio. OVS [45]
+
+proposed to improve FOV by extrapolation. DIFRINT [6] choose iterative interpolation to generate high-FOV frames. FuSta [23] used neural rendering to synthesize high-FOV frames from feature space. To a great extent, the performance of interpolation-based video stabilization [6,45] depends on the selected frames. If selected frames have little correspondence with each other, performance will deteriorate dramatically. Neural rendering [23] synthesizes the image by weighted summing, causing blur. Most recently, a deep neural network [33] (DNN) has jointly exploited sensor data and optical flow to stabilize videos.
+
+# 3. Stabilization via Iterative Optimization
+
+Motivation. Despite rapid advances in video stabilization [30], existing methods still suffer from several notable limitations [12]. First, a systematic treatment of various uncertainty factors (e.g., low-texture regions in the background and moving objects in the foreground) in the problem formulation is still lacking. These uncertainty factors often cause occlusion-related problems and interfere with the motion estimation process. Second, the high computational cost has remained a technical barrier to real-time video processing. The motivation behind our approach is two-fold. On the one hand, we advocate for finding commonly shared regions among successive frames to address various uncertainty factors in handheld video. On the other hand, in contrast to these prestabilization algorithms [21, 23, 49, 50] based on traditional approaches, we proposed a novel high-efficiency prestabilization algorithm based on probabilistic optical flow. Flow-based methods are generally more accurate in motion estimation and deserve a high time cost. Accuracy and efficiency, we have both.
+
+Approach. We propose to formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories. It is enlightening to think of video stabilization as a special kind of "video denoising" where noise contamination is not associated with pixel intensity values, but embedded into the motion trajectories of foreground and background objects. Conceptually, for video restoration in which unknown motion is the hidden variable, we can treat video stabilization as a chicken-and-egg problem [13] - i.e., the objective of smoothing motion trajectories is intertwined with that of video frame interpolation. Note that an improved estimation of motion information can facilitate the task of frame interpolation and vice versa. Such an observation naturally inspires us to tackle the problem of video stabilization by iterative optimization.
+
+Through divide-and-conquer, we propose to formulate video stabilization as the following optimization problem. Given a sequence of  $n$  frames along with the set of optical flows  $\mathcal{V}$ , we first define the confidence map, which originally indicates the reliability and accuracy of the optical flow prediction at each pixel. Here, we have thresholded the
+
+confidence map as a binary image, which represents accurate matches (as shown in the 4-th column of Fig. 2). Then we can denote  $n$  frames and the corresponding set of confidence maps  $\mathcal{M}$  by:
+
+$$
+\mathcal {Y} = \left\{Y _ {1}, Y _ {2}, \dots , Y _ {q} \right\}, \mathcal {M} = \left\{M _ {1}, M _ {2}, \dots , M _ {q} \right\}. \quad (1)
+$$
+
+# 4. Probabilistic Stabilization Network
+
+The problem of video stabilization can be formulated as finding a nonlinear mapping  $f: \mathcal{V} \to \hat{\mathcal{V}}$  where  $\hat{\mathcal{V}}$  denotes the optical flow set of the stabilized video. We hypothesize that a desirable objective to pursue  $f$  is the well-known fixed-point property, i.e.,  $\hat{\mathcal{V}} = f(\hat{\mathcal{V}})$ . To achieve this objective, we aim to minimize an objective function  $\mathbb{F}$  characterized by the magnitude of optical flows between commonly shared regions, as represented by  $\mathcal{M}$ . Note that  $\mathcal{M}$  is the hidden variable in our problem formulation (that is, we need to estimate  $\mathcal{M}$  from  $\hat{\mathcal{V}}$ ). A popular strategy to address this chicken-and-egg problem is to alternatively solve the two subproblems of unknown  $\mathcal{M}$  and  $\hat{\mathcal{V}}$ . More specifically, the optimization of  $\mathbb{F}$  is decomposed into the following two subproblems:
+
+$$
+\left(\hat {M} _ {1}, \dots , \hat {M} _ {q}\right) = \underset {\mathcal {M}} {\arg \min } \mathbb {F} \left(\hat {Y} _ {1} \odot M _ {1}, \dots , \hat {Y} _ {q} \odot M _ {q}\right), \tag {2}
+$$
+
+$$
+(\hat {Y} _ {1}, \dots , \hat {Y} _ {q}) = \underset {\mathcal {Y}} {\arg \min } \mathbb {F} (Y _ {1} \odot \hat {M} _ {1}, \dots , Y _ {q} \odot \hat {M} _ {q}),
+$$
+
+where  $Y / \hat{Y}$  denotes the magnitude of the optical flow values before and after stabilization and  $\odot$  is the Hadamard product. Instead of analyzing the estimated motion in the frequency domain, we hypothesize that stabilized videos are the fixed points of video stabilization algorithms, which minimize the above objective function. A fixed point [1] is a mathematical object that does not change under a given transformation. Numerically, fixed-point iteration is a method of computing fixed points of a function. It has been widely applied in data science [7], and image restoration [5, 25]. Here, we denote  $\mathbb{F}$  in Eq. (2) as the function to be optimized, and the fixed point of  $\mathbb{F}$  is defined as the stabilized video. Next, we solve these two subproblems by constructing the module of stabilization.
+
+# 4.1. Probabilistic Flow Field
+
+First, we start with an interesting observation. When playing an unstable video at a slower speed (e.g., from 50fps to 30fps), the video tends to appear less wobbly. It follows from the observation that the fundamental cause of video instability is the fast frequency and the large amplitude of the still objects' motion speed. Therefore, the core task of motion smoothing is to identify the region that needs to be stabilized. As Yu et al. [50] pointed out, mismatches, moving objects, and inconsistent motion areas lead to variation of the estimated motion from the true motion trajectories and
+
+![](images/a6c0690151f1ab2bb86ee086185771599464ba2e7cde3e86ede584ed8ec55c82.jpg)  
+Figure 2. Visualization of confidence map back-propagation results. The flow field and confidence map are predicted by PDCNet between source and target images. The obtained masks in the last column represent the shared regions among these frames.
+
+should be masked. An important new insight brought about by this work is that these regions of inconsistency in the optical flow fields tend to show greater variability as the frame interval increases. Therefore, if these inconsistent regions are excluded, the video stabilization task can be simplified to the first sub-problem in Eq. (2) - i.e., minimizing  $\mathbb{F}$  over  $\mathcal{M}$  for a fixed  $\mathcal{V}$ .
+
+To detect unreliable matches and inconsistent regions, we have adopted the probabilistic flow network - PDCNet [37, 38], that jointly tackles the problem of dense correspondence and uncertainty estimation, as our building block. Suppose that PDCNet estimates the optical flow  $Y_{k}$  from frame  $k + d$  to frame  $k$  with the resulting confidence map  $C_k$ . Although  $C_k$  denotes the inaccuracy of the optical flow estimate in  $Y_{k}$ , it is often sensitive to the frame interval  $d$ . For example, it is difficult to identify the inconsistent region when  $d$  is small, while the common area is less controllable when  $d$  is large. Therefore, simply using an optical flow field to estimate inconsistent regions is not sufficient.
+
+We have designed a more robust solution to the joint estimation of dense flow and confidence map based on a coarse-to-fine strategy. The basic idea is to first obtain the probabilistic flow field at a coarse scale (e.g., with the down-sampled video sequence by a factor of  $d$  along the temporal axis) and then fill in the rest (i.e., the frames between the adjacent frames in the down-sampled video) at the fine scale. Such a two-level estimation strategy effectively overcomes the limitations of PDCNet by propagating the estimation results of probabilistic flow fields bidirectionally, as we will elaborate next.
+
+Coarse-scale strategy As shown by the second-to-last column in Fig. 2, the confidence map estimated by PDCNet can identify the mismatched region, but fails to locate the objects with small motions (e.g., people and the sky). To
+
+![](images/4b7a72e0ff1aa18faa8873256305d6ac94511f316b848b6dd35c65a18a39f689.jpg)  
+Figure 3. Architecture of the camera pose regression network. Given the flow field and mask, our network predicts the corresponding affine transformation parameters by closed-loop iterations.
+
+overcome this difficulty, we introduce the binary mask as a warped and aggregated confidence map (refer to the last column of Fig. 2). Specifically, we first propose to obtain the confidence map  $\hat{C}_{k + (n - 1)d}$  with down-sampled video (the last row of Fig. 2). In the forward direction, we estimate dense flow and confidence map using PDCNet; then  $\hat{C}_{k + (n - 1)d}$  is backpropagated to update the binary mask  $\hat{M}$  by thresholding and setting intersection operators. Through bidirectional propagation, the region covered by  $\mathcal{M}$  is the shared content from frame  $k$  to frame  $k + (n - 1)d$ . The complete procedure can be found in Supp. S1.
+
+Fine-scale strategy Based on the coarse-scale estimation result for downsampled video (i.e.,  $\mathcal{M} = \{\hat{M}_k, \hat{M}_{k+d}, \dots, \hat{M}_{k+(n-1)d}\}$ ), we fill in the missing  $d-1$  frames at the fine scale. Specifically, considering the sequential frames from  $k$  to  $k+d$ , we can obtain two sets similar to Eq. (1), which are  $\mathcal{V} = \{Y_k, Y_{k+1}, \dots, Y_{k+d-1}, \hat{Y}_{k+d}\}$  and their corresponding confidence map set  $\mathcal{C}$ . Note that  $\hat{M}_{k+d} \in \mathcal{M}$  has been calculated in coarse stage. Setting  $d=1$ , we can call the algorithm again to obtain the set of output masks  $\mathcal{M}$  for the rest of  $d-1$  frames.
+
+# 4.2. Coarse-scale Stabilizer
+
+To coarsely stabilize the video, we first propose aligning the adjacent frames with a global affine transformation [52]. The optimization function  $\mathbb{F}$  in Eq. (2) is represented as
+
+$$
+\mathbf {T} ^ {*} = \underset {\mathbf {T}} {\arg \min } \mathbf {T} (Y \odot \hat {M}), \tag {3}
+$$
+
+where  $\mathbf{T}(\cdot)$  denotes the image transformation applied to the shared region  $\hat{M}$  (the result of Sec. 4.1) of the optical flow field  $Y$ . Most conventional methods [23,44,50] adopt image matching to obtain  $\mathbf{T}(\cdot)$ -e.g., keypoint detection [2,24,31], feature matching [2,3,51]; and camera pose estimation is implemented by OpenCV-python. However, these methods are often time-consuming and computationally expensive. For example, two adjacent frames of unstable videos usually share a large area and are free from perspective transformation. Thus, an affine transformation, including translation, rotation, and scaling, is sufficient. More importantly, within the optimization-based learning framework, we can
+
+regress these linear parameters of  $\mathbf{T}(\cdot)$  from the optical flow field, which characterize the relative coordinate transformation of the matched features.
+
+We propose a novel camera pose regression network, as shown in Fig. 3. Given an optical flow field  $Y$  and the corresponding mask field  $\hat{M}$ , our network  $\Phi(\cdot)$  can directly estimate the unknown parameters  $\mathbf{T}(\cdot) \propto \{\theta, s, d_x, d_y\} = \Phi(Y, \hat{M})$ . To solve the optimization problem of Eq. (3), we use the estimated parameters to iteratively compute the corresponding residual optical flow fields such that
+
+$$
+\bar {Y} = Y - (S \cdot R \cdot V + T), \tag {4}
+$$
+
+where  $T$ ,  $S$ , and  $R$ , respectively, denote the translation, scaling, and rotation matrix, and  $V \in \mathbb{R}^{2 \times H \times W}$  represents an image coordination grid. Then  $\{\Delta \theta, \Delta s, \Delta x, \delta y\} = \Phi(\bar{Y}, \tilde{M})$  is calculated iteratively to produce the updated parameters  $\{\theta + \Delta \theta, s \cdot \Delta s, d_x + \Delta x, d_y + \Delta y\}$ . The finally estimated affine transformation is smoothed by a moving Gaussian filter with a window size of 20 pixels.
+
+Loss functions Our loss functions include robust loss  $\ell_1$  and grid loss commonly applied in consistency filtering [51]. We directly calculate the  $\ell_1$  loss between the predictions and their ground truth  $\{\hat{\theta},\hat{s},\hat{d}_x,\hat{d}_y\}$
+
+$$
+\begin{array}{l} L _ {g t} = \lambda_ {\theta} \| | \theta - \hat {\theta} \| | _ {1} + \lambda_ {s} \| | 1 - \frac {s}{\hat {s}} \| | _ {1} \tag {5} \\ + \lambda_ {t} \| | d _ {x} - \hat {d} _ {x} | + | d _ {y} - \hat {d} _ {y} | \| _ {1}. \\ \end{array}
+$$
+
+For better supervision of the estimated pose, we calculate the loss  $L_{grid}$  with the grid  $V \in \mathbb{R}^{2 \times h \times h}$  in Eq. (4), i.e.,
+
+$$
+L _ {g r i d} = \left\| (\hat {S} \cdot \hat {R} \cdot V + \hat {T}) - (S \cdot R \cdot V + T) + \epsilon \right\| _ {1} \tag {6}
+$$
+
+where  $\hat{\cdot}$  denotes the ground truth and  $\epsilon$  is a small value for stability. The final loss  $L_{stab}$  consists of  $L_{gt}$  and  $L_{grid}$ ,
+
+$$
+L _ {s t a b} = L _ {g t} + \lambda_ {g r i d} L _ {g r i d}. \tag {7}
+$$
+
+# 4.3. Fine-scale Stabilizer
+
+The assumption with an affine transformation of the coarse-scale stabilizer could cause structural discontinuity and local distortion. Therefore, our objective is to refine the coarsely stabilized video by optical flow smoothing. Unlike Eq. 3 which applies an image transformation matrix to optimize the optical flow field, we optimize it at the pixel level by a flow warping field  $\mathbf{W}$ . Thus, the function  $\mathbb{F}$  in Eq. (2) is given by
+
+$$
+\mathbf {W} ^ {*} = \underset {\mathbf {W}} {\arg \min } \sum_ {i = 0} ^ {N - 1} \mathbf {W} _ {i} \left(Y _ {i} \odot \hat {M} _ {i}\right). \tag {8}
+$$
+
+The flow smoothing network follows the U-Net architecture in [56]. We use  $N$  frames of optical flow fields  $\mathbf{F}$  and mask
+
+![](images/6fe7a98576fa7769bc42ea3ca51803b12244536840d7b80a8ef6546f35c8b5f6.jpg)  
+Figure 4. Illustration of flow fields and warped images under different FOVs. The target image with large FOV presents the smoother flow field and better warped result.
+
+fields  $\hat{M}$  as input and obtain  $(N - 1)$  frame warp fields  $\mathbf{W}$  of intermediate frames. Specifically, for the optical flow field  $Y_{k}$  (from frame  $k + 1$  to frame  $k$ ), we denote the aligned matrices of each frame in Sec. 4.2 as  $H_{k} \in \mathbb{R}^{2 \times 3}$  and  $H_{k + 1} \in \mathbb{R}^{2 \times 3}$ , respectively. Then the input optical flow  $\mathbf{F}_{k} \in \mathbb{R}^{2 \times HW}$  can be represented by
+
+$$
+\mathbf {F} _ {k} = H _ {k + 1} \cdot \left[ V + Y _ {k} \mid 1 \right] - H _ {k} \cdot \left[ V \mid 1 \right], \tag {9}
+$$
+
+where  $V \in \mathbb{R}^{2 \times HW}$  and  $[\cdot|1]$  denote the normalized coordinate representation. Furthermore, to better adapt the flow smoothing network to the mask field  $\hat{M}$ , we fine-tune it using our synthetic dataset (as we will elaborate in Sec. 6.1). The loss function follows the motion loss [49]
+
+$$
+L _ {\text {s m o o t h}} = \sum_ {k = 0} ^ {N - 1} \left(\mathbf {F} _ {k} + \mathbf {W} _ {k} - \mathbf {F} _ {k} \left(\mathbf {W} _ {k + 1}\right)\right) \odot \hat {M}, \tag {10}
+$$
+
+where  $\mathbf{W}_0 = \mathbf{W}_N = 0$
+
+# 5. Video Outpainting Network
+
+Most video stabilization methods crop an input video with a small field of view (FOV), excluding missing margin pixels due to frame warping. In contrast, full-frame video stabilization [6, 23, 26] proposes to generate a video that maintains the same FOV as the input video without cropping. They directly generate stabilized video frames with large FOV by fusing the information from neighboring frames. An important limitation of existing fusion strategies is the unequal importance of different frames (i.e., the current and neighboring frames are weighted equally), which would lead to unpleasant distortions in fast-moving situations. To overcome this weakness, we propose a two-stage framework to combine flow and image outpainting strategies [32]. In the first stage, we used flow-outpainting to iteratively align the neighboring frames with the target frame. In the second stage, we fill the target frame with adjacent aligned frame pixels by image outpainting.
+
+# 5.1. Flow Outpainting Network
+
+Let  $I^t$  denote the outpainted target image and  $I^s$  the neighboring source image. We aim to fill the missing pixel
+
+![](images/7b857824a8c24cae006118bc7c1c0e035fb96460916c2e667be345621f1776cd.jpg)  
+Figure 5. Architecture of flow outpainting network. Given a small FOV flow field and valid mask, the network predicts the large FOV flow field.
+
+region  $M_{\varnothing}^{t}$  of  $I^{t}$  with the pixels of  $I^{s}$ . As shown in Fig. 4, we take two different FOVs of  $I^{t}$  as input and obtain the corresponding optical flow fields and warped results  $I_{warp}^{s}$ . The small FOV  $I^{t}$  cannot guide  $I^{s}$  well to fill the regions in  $M_{\varnothing}^{t}$ . Since the predicted optical flow field in  $M_{\varnothing}^{t}$  is unreliable due to the lack of pixel guidance of  $I^{t}$ , the out-of-view region of  $M_{\varnothing}^{t}$  has artifacts (marked in the last column of Fig. 4). We observe that the optical flow field of the large FOV  $I^{t}$  is continuous in  $M_{\varnothing}^{t}$ , which inspired us to extrapolate the flow of  $M_{\varnothing}^{t}$  using the reliable flow region (the 3rd column of Fig. 4).
+
+We propose a novel flow outpainting network (Fig. 5), which extrapolates the large FOV flow field using a small FOV flow field and the corresponding valid mask. Specifically, we adopt a U-Net architecture and apply a sequence of gated convolution layers with downsampling / upsampling to obtain the large flow field of FOV  $Y_{large}$ . Note that the input flow field  $Y_{small}$  and the valid mask  $M_{valid}$  have been estimated by PDCNet (see Sec. 4.1).
+
+Loss functions Our loss functions include robust loss  $\ell_1$  and loss in the frequency domain [4]. We directly calculate the  $\ell_1$  loss between  $Y_{large}$  and its ground truth  $\hat{Y}_{large}$ ,
+
+$$
+\begin{array}{l} L _ {Y} = \lambda_ {i n} \cdot \| | Y _ {\text {l a r g e}} - Y _ {\text {s m a l l}} | \odot M _ {\text {v a l i d}} \| _ {1} \tag {11} \\ + \lambda_ {o u t} \cdot \| | Y _ {l a r g e} - \dot {Y} _ {l a r g e} | \odot (\sim M _ {v a l i d}) \| _ {1}. \\ \end{array}
+$$
+
+To encourage low frequency and smoothing  $Y_{large}$ , we add the loss in the frequency domain  $L_{F} = \| \hat{\mathbf{G}}\cdot \mathcal{F}Y_{large}\|_{2}$  where the normalized Gaussian map  $\hat{\mathbf{G}}$  with  $\mu = 0$  and  $\sigma = 3$  is inverted by its maximum value and  $\mathcal{F}Y_{large}$  denotes the Fourier spectrum of  $Y_{large}$ . The final loss consists of  $L_{Y}$  and  $L_{F}$
+
+$$
+L _ {\text {o u t p a i n t}} = L _ {Y} + \lambda_ {F} L _ {F}. \tag {12}
+$$
+
+# 5.2. Image Margin Outpainting
+
+Based on our proposed flow-outpainting network, we design a margin-outpainting method by iteratively aligning frame pairs (see Fig. 6). As discussed in Sec. 5.1, we can obtain a large FOV flow field  $Y_{large}$ . The neighboring reference frame  $I^{s}$  is warped as  $I^{warp} = Y_{large}(I^{s})$  as shown in Fig. 6. In theory, the outpainted frame  $I^{result} =$
+
+![](images/05918f014562ceec451629fc9b4ace86011898cec5ae90fa9887c6c10599b66a.jpg)  
+Figure 6. Overview image margin outpainting. Given the target frame  $I^{t}$ , the reference frame  $I^{s}$  is coarsely aligned to  $I^{warp}$  by the predicted large-FOV flow field  $Y_{large}$ . Then, we adopt a margin fusion approach to obtain the result frame  $I^{result}$ , by carefully aggregating  $I^{t}$  and  $I^{warp}$ .
+
+$I^t \cdot M_{valid} + I^{warp} \cdot (\sim M_{valid})$ . However, we notice that there are obvious distortions at the image border. To further align the margins, we take a margin fusion approach (the detailed algorithm can be found in Supp. S1) We crop  $I^{warp}$  and  $I^t$  to  $I_c^s$  and  $I_c^t$ . Then, we can obtain a new warped frame  $I_c^{warp}$  by flow outpainting. In particular, we did not choose to add  $I_c^{warp}$  and  $I^t$  directly. To identify the misaligned region, we propose to outpaint the mask  $M_{I^t}$  by extending the watershed outward from the center. Instead of a preset threshold, we adaptively choose between the target image  $I^t$  and the warped image  $I_c^{warp}$ . Then, the final frame  $I^{result}$  consists of  $I^t$  and  $I_c^{warp}$ :  $I^{result} = I^t \cdot M_{I^t} + I_c^{warp} \cdot (\sim M_{I^t})$ . Compared to the two results  $I^{result}$ , our strategy successfully mitigates misalignment and distortions at the boundary of video frames.
+
+Multi-frame fusion During the final stage of rendering, we use a sequence of neighboring frames to outpaint the target frame, while they may have filled duplicate regions. It is important to find out which frame and which region should be selected. We proposed the selection strategy for multi-frame fusion (the details can be found in Supp. S1). By weighing the metric parameters of each frame, we finally obtain the target frame with large FOV. Note that each frame has an added margin in the stabilization process, so we need to crop them to the original resolution. Although we have outpainted the target frame, some missing pixel holes may still exit at boundaries. Here, we apply the state-of-the-art LaMa image inpainting method [36] to fill these holes using nearest-neighbor interpolation.
+
+# 6. Experiments
+
+# 6.1. Synthetic Datasets for Supervised Learning
+
+Due to the limited amount of paired training data, we propose a novel model-based data generation method by carefully designing synthetic datasets for video stabiliza
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">NUS dataset [21]</td><td colspan="3">DeepStab dataset [39]</td><td colspan="3">Selfie dataset [48]</td></tr><tr><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td></tr><tr><td>Grundmann et al. [11]</td><td>0.71</td><td>0.76</td><td>0.62</td><td>0.77</td><td>0.87</td><td>0.80</td><td>0.75</td><td>0.81</td><td>0.83</td></tr><tr><td>Liu et al. [21]</td><td>0.81</td><td>0.78</td><td>0.82</td><td>0.80</td><td>0.90</td><td>0.85</td><td>0.74</td><td>0.89</td><td>0.8</td></tr><tr><td>Wang et al. [39]</td><td>0.67</td><td>0.72</td><td>0.41</td><td>-</td><td>-</td><td>-</td><td>0.68</td><td>0.71</td><td>0.82</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>0.78</td><td>0.77</td><td>0.82</td><td>0.85</td><td>0.89</td><td>0.76</td><td>0.79</td><td>0.77</td><td>0.84</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>0.85</td><td>0.81</td><td>0.86</td><td>0.87</td><td>0.92</td><td>0.82</td><td>0.83</td><td>0.87</td><td>0.86</td></tr><tr><td>Yu [50]+OVS* [45]</td><td>0.92</td><td>0.78</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DUT [44]</td><td>0.71</td><td>0.81</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DIFRINT [6]</td><td>1.00</td><td>0.85</td><td>0.84</td><td>1.00</td><td>0.91</td><td>0.78</td><td>1.00</td><td>0.78</td><td>0.84</td></tr><tr><td>FuSta [23]</td><td>1.00</td><td>0.87</td><td>0.86</td><td>1.00</td><td>0.92</td><td>0.82</td><td>1.00</td><td>0.83</td><td>0.87</td></tr><tr><td>Ours</td><td>1.00</td><td>0.91</td><td>0.86</td><td>1.00</td><td>0.94</td><td>0.84</td><td>1.00</td><td>0.87</td><td>0.87</td></tr></table>
+
+Table 1. Quantitative results on the NUS dataset [21], the DeepStab dataset [39] and the Selfie Dataset [48]. We evaluate the following metrics: Cropping Ratio(C.), Distortion Value(D.), Stability Score(S). * indicates the results obtained from original paper. We highlight the best method in bold and underline the second-best.
+
+tion. For our base synthetic dataset, we used a collection of images from the DPED [14], CityScapes [8] and ADE20K [55] datasets. To generate a stable video, we randomly generate the homography parameters for each image, including rotation angle  $\theta$ , scaling  $s$ , translations  $(d_x,d_y)$  and perspective factors  $(p_x,p_y)$ . Then we divide these transformation parameters into  $N$  bins equally and obtain a video of  $N$  frames by homography transformations. To simulate the presence of moving objects in real scenarios, the stable video is further augmented with additional independently moving random objects. To do so, the objects are sampled from the COCO dataset [15] and inserted on top of the synthetic video frames using their segmentation masks. Specifically, we randomly choose  $m$  objects (no more than 5), and generate randomly affine transformation parameters for each independent of the background transformation. Finally, we cropped each frame to  $720\times 480$  around its center. For different training requirements, we apply various combinations of synthetic dataset. The implementation and training details can be found in Supp. S2, S3.
+
+# 6.2.Quantitative Evaluation
+
+We compare the results of our method with various video stabilization methods, including Grundmann et al. [11], Liu et al. [21], Wang et al. [39], Yu and Ramamoorthi [49, 50], DUT [44], OVS [45], DIFRINT [6], and FuSta [23]. We obtain the results of the compared methods from the videos released by the authors or generated from the publicly available official implementation with default parameters or pre-trained models. Note that OVS [45] does not honor their promise to provide code, thus we only report the results from their paper.
+
+Datasets. We evaluate all approaches on the NUS dataset [21], DeepStab dataset [39], and Selfie dataset [48]. The NUS dataset consists of 144 videos and the corresponding ground truths in 6 scenes. The DeepStab dataset con
+
+tains 61 videos and the Selfie dataset consist of 33 videos.
+
+Metrics. We introduce three metrics widely used in many methods [6, 23, 50] to evaluate our model: 1) Cropping ratio measures the remaining frame area after cropping off the invalid boundaries. 2) Distortion value evaluates the anisotropic scaling of the homography between the input and output frames. 3) Stability score measures the stability of the output video. We calculate the metrics using the evaluation code provided by DIFRINT.
+
+Quantitative comparison. The results of the NUS dataset [21] are summarized in Table 1 (Per-category result can be found in Supp. S5). Overall, our method achieves the best distortion value compared to the state-of-the-art method, FuSta [23]. Especially in the quick-rotation and zoom categories, our method outperforms pure image generation methods [6,23]. We suspect that the reduction of the shared information between frames causes the image generation methods to prefer artifacts. However, our method can ensure local structural integrity when outpainting the margin region. Furthermore, our method achieves an average cropping ratio of 1.0 and stability scores comparable to recent approaches [6, 23, 49, 50]. Since FuSta [23] uses Yu et al. [50] to obtain stabilized input videos, they have the same stability scores. It is important to note that although the stability scores are competitive, our method runs 5 times faster than [50] in the video stabilization stage. Moreover, the comparison results on DeepStab dataset [39] and Selfie dataset [48] are also reported in Table 1. Our method still shows effectiveness in different datasets, proving the generalizability of the proposed method. Note that, due to that Wang et al. [39] is trained on the DeepStab dataset, we do not report its results on the DeepStab dataset for a fair comparison. Qualitative comparisons can be found in Supp. S4 and supplementary video.
+
+<table><tr><td>Stabilizer</td><td></td><td>Stability↑</td><td>Distortion↑</td></tr><tr><td rowspan="2">Image-level</td><td>w.o. mask</td><td>0.76</td><td>0.88</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr><tr><td rowspan="2">Pixel-level</td><td>w.o. mask</td><td>0.81</td><td>0.84</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr></table>
+
+Table 2. The importance of mask to video stabilization. We validate on the Crowd category of NUS dataset [21].  
+
+<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>Distortion↑</td></tr><tr><td>PCAFlow [42]</td><td>11.34</td><td>0.50</td><td>0.72</td></tr><tr><td>Our flow outpainting</td><td>19.65</td><td>0.77</td><td>0.93</td></tr><tr><td>w.o. margin outpainting</td><td>18.04</td><td>0.64</td><td>0.81</td></tr><tr><td>w.o. mask \( M_{I^t} \)</td><td>20.35</td><td>0.78</td><td>0.86</td></tr><tr><td>w.o. multi-frame selection</td><td>21.99</td><td>0.84</td><td>0.90</td></tr><tr><td>Ours</td><td>23.17</td><td>0.86</td><td>0.91</td></tr></table>
+
+# 6.3. Ablation Study
+
+Importance of mask generation. We investigate the influence of the mask on video stabilization at different stages. To better demonstrate the necessity of mask in complex scenarios, we choose the Crowd category of NUS dataset [21] which includes a display of moving pedestrians and occlusions. Stability and distortion at different settings are shown in Table 2. It can be seen that the performance with mask increases significantly in both stabilizers. Specifically, the mask can both improve stability globally and alleviate image warping distortion locally. This result demonstrates the importance of mask generation for video stabilization.
+
+Flow outpainting. We compare our flow outpainting method with the traditional flow inpainting method PCAFlow [42]. Following [50] we fit the first 5 principal components proposed by PCAFlow to the  $M_{valid} = 1$  regions of the optical flow field, and then outpaint the flow vectors in the  $M_{valid} = 0$  regions with reasonable values of the PCA Flow fitted. The result is obtained by warping the source image with the outpainted optical flow field. We perform this comparison on our synthetic validation set and evaluate it with the corresponding ground truth. Additionally, we use PSNR and SSIM [41] to evaluate the quality of the results. As shown in Table 3, ours dramatically outperforms PCAFlow [42] in all objective metrics.
+
+Importance of image filling strategies. We explore the following proposed strategies for image filling: margin outpainting, mask generation  $M_{It}$ , and multiframe selection. We isolate them from our method to compare their results with the complete version. The results are shown in Table 3. The proposed strategies are generally helpful in improving image quality. Especially, margin outpainting and mask  $M_{It}$  are crucial to the results.
+
+Table 3. Ablation study of image filling. The evaluation is conducted on our model-based synthetic validation set.  
+
+<table><tr><td>Method</td><td>Runtime</td></tr><tr><td>Traditional pose regression</td><td>216ms</td></tr><tr><td>Our pose regression network</td><td>21ms</td></tr><tr><td>Grundmann et al. [11]</td><td>480ms</td></tr><tr><td>Liu et al. [21]</td><td>1360ms</td></tr><tr><td>Wang et al. [39]</td><td>460ms</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>1610ms</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>570ms</td></tr><tr><td>DIFRINT [6]</td><td>1530ms</td></tr><tr><td>FuSta [23]</td><td>9820ms</td></tr><tr><td>Ours</td><td>97ms</td></tr></table>
+
+Table 4. Per-frame runtime comparison of camera pose regression and video stabilization.
+
+![](images/84dca42383bbf2742110eb444613db34b55c7f59cc19713198a14d13c738d0d4.jpg)  
+(a) shaky frames
+
+![](images/8d25420f1065a21d7e02a10dd900842d696a5b5a32b7113e1c20e6d9b86cf614.jpg)  
+(b) stable frames  
+Figure 7. Experiment of fixed-point iteration on shaky and stable frames. (a) Our fixed-point iteration helps the shaky frames converge to a steady state. (b) For stable frames, the fixed-point iteration guarantees the stability of results.
+
+# 6.4. Runtime Comparison
+
+Our network and pipeline are implemented with PyTorch and Python. Table 4 is a summary of the runtime per frame for various competing methods. All timing results are obtained on a desktop with an RTX3090Ti GPU and an Intel(R) Xeon(R) Gold 6226R CPU. First, we compare the run-time of pose regression. Traditional pose regression is time consuming in feature matching [2, 9], homography estimation, and SVD decomposition [28]. Although our learning-based pose regression network runs 10 times faster than the traditional framework. Then, we report the average run time of different methods, including optimization-based [21, 49] and learning-based [6, 11, 23, 39, 50]. Our method takes  $97\mathrm{ms}$  which gives  $\sim 5\mathrm{x}$  speed-up. This is because our method computes the optical flow field only once and without the help of other upstream task methods and manual optimization.
+
+# 6.5. Fixed-point Experiment
+
+To demonstrate the stability of our fixed-point optimization solution, we performed an interesting toy experiment. We input a sequence of shaky frames into our coarse-to-fine stabilizers, and the stabilized result will be iteratively restabilized by our stabilizers. For each iteration, we calculate the average magnitude of optical flow filed with global transformation and flow warping for each frame. Specifi-
+
+cally, the regions where we calculate are marked by  $\hat{M}$ . As shown in Fig. 7(a), the deviation of the shaky frames decreases rapidly with each iteration. Furthermore, we have pointed out that plugging a stabilized video into the stabilization system should not have an impact on the input. Thus, we plug stable frames into the coarse-to-fine stabilizers and iteratively stabilize them. The result is shown in Fig. 7(b). The deviation of each frame is perturbed around the value of zero. Obviously, our method has no effect on stable frames, which shows that stabilized video is indeed the fixed point of our developed stabilization system.
+
+# 7. Conclusion
+
+In this paper, we have presented a fast full-frame video stabilization technique based on the iterative optimization strategy. Our approach can be interpreted as the combination of probabilistic stabilization network (coarse-to-fine extension of PDC-Net) and video outpainting outwork (flow-based image outpainting). When trained on synthetic data constructed within the optimization-based learning framework, our method achieves state-of-the-art performance at a fraction of the computational cost of other competing techniques. It is also empirically verified that stabilized video is the fixed point of the stabilization network.
+
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+                                    "content": " Xianrui Luo"
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+                                    "content": " Zhiguo Cao"
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+                                    "content": "Key Laboratory of Image Processing and Intelligent Control, Ministry of Education; School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China  \n"
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+                                    "content": "Department of Computer Science, University of Albany, Albany NY 12222 {zhaoweiyue, peng-zhan, xianruiluo, xinyiye, hlu, zgcao}@hust.edu.cn xli48@albany.edu"
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+                                    "content": "Video stabilization refers to the problem of transforming a shaky video into a visually pleasing one. The question of how to strike a good trade-off between visual quality and computational speed has remained one of the open challenges in video stabilization. Inspired by the analogy between wobbly frames and jigsaw puzzles, we propose an iterative optimization-based learning approach using synthetic datasets for video stabilization, which consists of two interacting submodules: motion trajectory smoothing and full-frame outpainting. First, we develop a two-level (coarse-to-fine) stabilizing algorithm based on the probabilistic flow field. The confidence map associated with the estimated optical flow is exploited to guide the search for shared regions through backpropagation. Second, we take a divide-and-conquer approach and propose a novel multiframe fusion strategy to render full-frame stabilized views. An important new insight brought about by our iterative optimization approach is that the target video can be interpreted as the fixed point of nonlinear mapping for video stabilization. We formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories, which guarantees convergence with the help of fixed-point theory. Extensive experimental results are reported to demonstrate the superiority of the proposed approach in terms of computational speed and visual quality. The code will be available on GitHub."
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+                                    "content": "With the growing popularity of short videos on social media platforms (e.g., TikTok, Instagram), video has played an increasingly important role in our daily life. However, casually captured videos are often shaky and wobbly due to"
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+                                    "content": "amateur shooting. Although it is possible to alleviate those problems by resorting to professional equipment (e.g., dollies and steadicams), the cost of hardware-based solutions is often expensive, making it impractical for real-world applications. By contrast, software-based or computational solutions such as video stabilization algorithms [12] have become an attractive alternative to improve the visual quality of shaky video by eliminating undesirable jitter."
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+                                    "content": "Existing video stabilization techniques can be classified into two categories: optimization-based and learning-based. Traditional optimization-based algorithms [11,18,21,27,39] have been widely studied due to their speed and robustness. The challenges of them are the occlusion caused by changes in depth of field and the interference caused by foreground objects on camera pose regression. Furthermore, their results often contain large missing regions at frame borders, particularly when videos with a large camera motion. In recent years, learning-based video stabilization algorithms [6, 23, 45, 50] have shown their superiority by achieving higher visual quality compared to traditional methods. However, their stabilization model is too complex for rapid computation, and its generalization property is unknown due to the scarcity of training datasets."
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+                                    "content": "To overcome those limitations, we present an iterative optimization-based learning approach that is efficient and robust, capable of achieving high-quality stabilization results with full-frame rendering, as shown in Fig. 1. The probabilistic stabilized network addresses the issues of occlusion and interfering objects, and achieves fast pose estimation. Then the full-frame outpainting module retains the original field of view (FoV) without aggressive cropping. An important new insight brought by our approach is that the objective of video stabilization is to suppress the implicitly embedded noise in the video frames rather than the explicit noise in the pixel intensity values. This inspired us to adopt an expectation-maximization (EM)-like approach for video stabilization. Importantly, considering the strong redundancy of video in the temporal domain, we ingeniously"
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+                                    "content": " of the time Yu et al. [50]). Accordingly, we have developed a two-level (coarse-to-fine) flow smoothing strategy that first aligns adjacent frames by global affine transformation and then refines the result by warping the fields of intermediate frames. For the latter, we propose a two-stage approach (flow and image outpainting) to render full-frame video. Our experimental results have shown highly competent performance against others on three public benchmark datasets. The main contribution of this work is threefold:"
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+                                    "type": "text",
+                                    "content": "2. Related Work"
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+                                    "content": "2.1. Video Stabilization"
+                                }
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+                                    "content": "Most video stabilization methods can typically be summarized as a three-step procedure: motion estimation, smoothing the trajectory, and generating stable frames. Traditional methods focus primarily on 2D features or image alignment [29] when it comes to motion estimation. These methods are different in modeling approaches to motion, including the trajectory matrix [19], epipolar geometry [10, 21, 47, 53], and the optical flow field [22, 54]. Regarding the smoothing trajectory, particle filter tracking [46], space-time path smoothing [19, 40], and L1 optimization [11] have been proposed. Existing methods for generating stable frames rely mainly on 2D transformations [26], grid warping [19, 21], and dense flow field warping [22]."
+                                }
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+                        }
+                    ],
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+                },
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+                                    "content": "Compared to the 2D method, some approaches turn to 3D reconstruction [17]. However, specialized hardware such as depth camera [20] and light field camera [34] are necessary for these methods based on 3D reconstruction. Some methods [30, 43, 44, 49] tackle video stabilization from the perspective of deep learning. In [49], the optimization of video stabilization was formulated in the CNN weight space. Recent work [50] represents motion by flow field and attempts to learn a stable optical flow to warp frames. Another method [6] aims to learn stable frames by interpolation. These deep-learning methods generate stable videos with less distortion."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "2.2. Large FOV Video"
+                                }
+                            ]
+                        }
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+                },
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+                                    "content": "Unlike the early work (e.g., traffic video stabilization [16]), large field of view (Field Of View) video stabilization has been attracting more researchers' attention. For most video stabilization methods, cropping is inevitable, which is why the FOV is reduced. Several approaches have been proposed to maintain a high FOV ratio. OVS [45]"
+                                }
+                            ]
+                        }
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+                                    "content": "proposed to improve FOV by extrapolation. DIFRINT [6] choose iterative interpolation to generate high-FOV frames. FuSta [23] used neural rendering to synthesize high-FOV frames from feature space. To a great extent, the performance of interpolation-based video stabilization [6,45] depends on the selected frames. If selected frames have little correspondence with each other, performance will deteriorate dramatically. Neural rendering [23] synthesizes the image by weighted summing, causing blur. Most recently, a deep neural network [33] (DNN) has jointly exploited sensor data and optical flow to stabilize videos."
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+                                    "content": "3. Stabilization via Iterative Optimization"
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+                                    "content": "Motivation. Despite rapid advances in video stabilization [30], existing methods still suffer from several notable limitations [12]. First, a systematic treatment of various uncertainty factors (e.g., low-texture regions in the background and moving objects in the foreground) in the problem formulation is still lacking. These uncertainty factors often cause occlusion-related problems and interfere with the motion estimation process. Second, the high computational cost has remained a technical barrier to real-time video processing. The motivation behind our approach is two-fold. On the one hand, we advocate for finding commonly shared regions among successive frames to address various uncertainty factors in handheld video. On the other hand, in contrast to these prestabilization algorithms [21, 23, 49, 50] based on traditional approaches, we proposed a novel high-efficiency prestabilization algorithm based on probabilistic optical flow. Flow-based methods are generally more accurate in motion estimation and deserve a high time cost. Accuracy and efficiency, we have both."
+                                }
+                            ]
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+                                    "content": "Approach. We propose to formulate video stabilization as a problem of minimizing the amount of jerkiness in motion trajectories. It is enlightening to think of video stabilization as a special kind of \"video denoising\" where noise contamination is not associated with pixel intensity values, but embedded into the motion trajectories of foreground and background objects. Conceptually, for video restoration in which unknown motion is the hidden variable, we can treat video stabilization as a chicken-and-egg problem [13] - i.e., the objective of smoothing motion trajectories is intertwined with that of video frame interpolation. Note that an improved estimation of motion information can facilitate the task of frame interpolation and vice versa. Such an observation naturally inspires us to tackle the problem of video stabilization by iterative optimization."
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+                                    "type": "text",
+                                    "content": "Through divide-and-conquer, we propose to formulate video stabilization as the following optimization problem. Given a sequence of "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " frames along with the set of optical flows "
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", we first define the confidence map, which originally indicates the reliability and accuracy of the optical flow prediction at each pixel. Here, we have thresholded the"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "confidence map as a binary image, which represents accurate matches (as shown in the 4-th column of Fig. 2). Then we can denote "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " frames and the corresponding set of confidence maps "
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+                                    "type": "text",
+                                    "content": " by:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {Y} = \\left\\{Y _ {1}, Y _ {2}, \\dots , Y _ {q} \\right\\}, \\mathcal {M} = \\left\\{M _ {1}, M _ {2}, \\dots , M _ {q} \\right\\}. \\quad (1)",
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+                                    "content": "4. Probabilistic Stabilization Network"
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+                                    "content": "The problem of video stabilization can be formulated as finding a nonlinear mapping "
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+                                    "type": "inline_equation",
+                                    "content": "f: \\mathcal{V} \\to \\hat{\\mathcal{V}}"
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+                                    "type": "text",
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+                                {
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+                                    "type": "text",
+                                    "content": " denotes the optical flow set of the stabilized video. We hypothesize that a desirable objective to pursue "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the well-known fixed-point property, i.e., "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{V}} = f(\\hat{\\mathcal{V}})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". To achieve this objective, we aim to minimize an objective function "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{F}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " characterized by the magnitude of optical flows between commonly shared regions, as represented by "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Note that "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the hidden variable in our problem formulation (that is, we need to estimate "
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+                                {
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+                                    "type": "text",
+                                    "content": " from "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{V}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "). A popular strategy to address this chicken-and-egg problem is to alternatively solve the two subproblems of unknown "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{V}}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". More specifically, the optimization of "
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+                                    "type": "text",
+                                    "content": " is decomposed into the following two subproblems:"
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+                                    "type": "interline_equation",
+                                    "content": "\\left(\\hat {M} _ {1}, \\dots , \\hat {M} _ {q}\\right) = \\underset {\\mathcal {M}} {\\arg \\min } \\mathbb {F} \\left(\\hat {Y} _ {1} \\odot M _ {1}, \\dots , \\hat {Y} _ {q} \\odot M _ {q}\\right), \\tag {2}",
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+                                    "type": "interline_equation",
+                                    "content": "(\\hat {Y} _ {1}, \\dots , \\hat {Y} _ {q}) = \\underset {\\mathcal {Y}} {\\arg \\min } \\mathbb {F} (Y _ {1} \\odot \\hat {M} _ {1}, \\dots , Y _ {q} \\odot \\hat {M} _ {q}),",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "Y / \\hat{Y}"
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+                                    "content": " denotes the magnitude of the optical flow values before and after stabilization and "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the Hadamard product. Instead of analyzing the estimated motion in the frequency domain, we hypothesize that stabilized videos are the fixed points of video stabilization algorithms, which minimize the above objective function. A fixed point [1] is a mathematical object that does not change under a given transformation. Numerically, fixed-point iteration is a method of computing fixed points of a function. It has been widely applied in data science [7], and image restoration [5, 25]. Here, we denote "
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+                                    "type": "text",
+                                    "content": " in Eq. (2) as the function to be optimized, and the fixed point of "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is defined as the stabilized video. Next, we solve these two subproblems by constructing the module of stabilization."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.1. Probabilistic Flow Field"
+                                }
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+                        }
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+                                    "content": "First, we start with an interesting observation. When playing an unstable video at a slower speed (e.g., from 50fps to 30fps), the video tends to appear less wobbly. It follows from the observation that the fundamental cause of video instability is the fast frequency and the large amplitude of the still objects' motion speed. Therefore, the core task of motion smoothing is to identify the region that needs to be stabilized. As Yu et al. [50] pointed out, mismatches, moving objects, and inconsistent motion areas lead to variation of the estimated motion from the true motion trajectories and"
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+                                            "content": "Figure 2. Visualization of confidence map back-propagation results. The flow field and confidence map are predicted by PDCNet between source and target images. The obtained masks in the last column represent the shared regions among these frames."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "should be masked. An important new insight brought about by this work is that these regions of inconsistency in the optical flow fields tend to show greater variability as the frame interval increases. Therefore, if these inconsistent regions are excluded, the video stabilization task can be simplified to the first sub-problem in Eq. (2) - i.e., minimizing "
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+                                    "content": " for a fixed "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": "To detect unreliable matches and inconsistent regions, we have adopted the probabilistic flow network - PDCNet [37, 38], that jointly tackles the problem of dense correspondence and uncertainty estimation, as our building block. Suppose that PDCNet estimates the optical flow "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " from frame "
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+                                    "type": "inline_equation",
+                                    "content": "k + d"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to frame "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "k"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with the resulting confidence map "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "C_k"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Although "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "C_k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the inaccuracy of the optical flow estimate in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{k}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", it is often sensitive to the frame interval "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". For example, it is difficult to identify the inconsistent region when "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        382,
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+                                        525
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is small, while the common area is less controllable when "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is large. Therefore, simply using an optical flow field to estimate inconsistent regions is not sufficient."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We have designed a more robust solution to the joint estimation of dense flow and confidence map based on a coarse-to-fine strategy. The basic idea is to first obtain the probabilistic flow field at a coarse scale (e.g., with the down-sampled video sequence by a factor of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " along the temporal axis) and then fill in the rest (i.e., the frames between the adjacent frames in the down-sampled video) at the fine scale. Such a two-level estimation strategy effectively overcomes the limitations of PDCNet by propagating the estimation results of probabilistic flow fields bidirectionally, as we will elaborate next."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Coarse-scale strategy As shown by the second-to-last column in Fig. 2, the confidence map estimated by PDCNet can identify the mismatched region, but fails to locate the objects with small motions (e.g., people and the sky). To"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
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+                                            "type": "text",
+                                            "content": "Figure 3. Architecture of the camera pose regression network. Given the flow field and mask, our network predicts the corresponding affine transformation parameters by closed-loop iterations."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "overcome this difficulty, we introduce the binary mask as a warped and aggregated confidence map (refer to the last column of Fig. 2). Specifically, we first propose to obtain the confidence map "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{C}_{k + (n - 1)d}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
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+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " with down-sampled video (the last row of Fig. 2). In the forward direction, we estimate dense flow and confidence map using PDCNet; then "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
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+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{C}_{k + (n - 1)d}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is backpropagated to update the binary mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
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+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " by thresholding and setting intersection operators. Through bidirectional propagation, the region covered by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the shared content from frame "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to frame "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        204,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k + (n - 1)d"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The complete procedure can be found in Supp. S1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Fine-scale strategy Based on the coarse-scale estimation result for downsampled video (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M} = \\{\\hat{M}_k, \\hat{M}_{k+d}, \\dots, \\hat{M}_{k+(n-1)d}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": "), we fill in the missing "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d-1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " frames at the fine scale. Specifically, considering the sequential frames from "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k+d"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can obtain two sets similar to Eq. (1), which are "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V} = \\{Y_k, Y_{k+1}, \\dots, Y_{k+d-1}, \\hat{Y}_{k+d}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " and their corresponding confidence map set "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}_{k+d} \\in \\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " has been calculated in coarse stage. Setting "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d=1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can call the algorithm again to obtain the set of output masks "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " for the rest of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d-1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        546,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " frames."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                        479,
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.2. Coarse-scale Stabilizer"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "To coarsely stabilize the video, we first propose aligning the adjacent frames with a global affine transformation [52]. The optimization function "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        498,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in Eq. (2) is represented as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {T} ^ {*} = \\underset {\\mathbf {T}} {\\arg \\min } \\mathbf {T} (Y \\odot \\hat {M}), \\tag {3}",
+                                    "image_path": "813aa73b22168cd808db612c6c46d7b5ea848243a05270a6f123d612b9bbe65d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{T}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the image transformation applied to the shared region "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (the result of Sec. 4.1) of the optical flow field "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Most conventional methods [23,44,50] adopt image matching to obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{T}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "-e.g., keypoint detection [2,24,31], feature matching [2,3,51]; and camera pose estimation is implemented by OpenCV-python. However, these methods are often time-consuming and computationally expensive. For example, two adjacent frames of unstable videos usually share a large area and are free from perspective transformation. Thus, an affine transformation, including translation, rotation, and scaling, is sufficient. More importantly, within the optimization-based learning framework, we can"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "23537"
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+            ],
+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        107
+                                    ],
+                                    "type": "text",
+                                    "content": "regress these linear parameters of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        107
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{T}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from the optical flow field, which characterize the relative coordinate transformation of the matched features."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": "We propose a novel camera pose regression network, as shown in Fig. 3. Given an optical flow field "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " and the corresponding mask field "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": ", our network "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Phi(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " can directly estimate the unknown parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{T}(\\cdot) \\propto \\{\\theta, s, d_x, d_y\\} = \\Phi(Y, \\hat{M})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        288,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": ". To solve the optimization problem of Eq. (3), we use the estimated parameters to iteratively compute the corresponding residual optical flow fields such that"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {Y} = Y - (S \\cdot R \\cdot V + T), \\tag {4}",
+                                    "image_path": "5d907b1f0106b8c21742929009d0856939bf3e003fe0616878357d361baf7dac.jpg"
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively, denote the translation, scaling, and rotation matrix, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V \\in \\mathbb{R}^{2 \\times H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        308
+                                    ],
+                                    "type": "text",
+                                    "content": " represents an image coordination grid. Then "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\Delta \\theta, \\Delta s, \\Delta x, \\delta y\\} = \\Phi(\\bar{Y}, \\tilde{M})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is calculated iteratively to produce the updated parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
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+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\theta + \\Delta \\theta, s \\cdot \\Delta s, d_x + \\Delta x, d_y + \\Delta y\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        308
+                                    ],
+                                    "type": "text",
+                                    "content": ". The finally estimated affine transformation is smoothed by a moving Gaussian filter with a window size of 20 pixels."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Loss functions Our loss functions include robust loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        313,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        313,
+                                        287,
+                                        361
+                                    ],
+                                    "type": "text",
+                                    "content": " and grid loss commonly applied in consistency filtering [51]. We directly calculate the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        313,
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+                                        361
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " loss between the predictions and their ground truth "
+                                },
+                                {
+                                    "bbox": [
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+                                        361
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{\\theta},\\hat{s},\\hat{d}_x,\\hat{d}_y\\}"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} L _ {g t} = \\lambda_ {\\theta} \\| | \\theta - \\hat {\\theta} \\| | _ {1} + \\lambda_ {s} \\| | 1 - \\frac {s}{\\hat {s}} \\| | _ {1} \\tag {5} \\\\ + \\lambda_ {t} \\| | d _ {x} - \\hat {d} _ {x} | + | d _ {y} - \\hat {d} _ {y} | \\| _ {1}. \\\\ \\end{array}",
+                                    "image_path": "8e5e82016f0bef50073d51e2386a938ecf9f562802f66e69599fa5ee889a1ecf.jpg"
+                                }
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For better supervision of the estimated pose, we calculate the loss "
+                                },
+                                {
+                                    "bbox": [
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+                                        440
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{grid}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with the grid "
+                                },
+                                {
+                                    "bbox": [
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+                                        415,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V \\in \\mathbb{R}^{2 \\times h \\times h}"
+                                },
+                                {
+                                    "bbox": [
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+                                        415,
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+                                        440
+                                    ],
+                                    "type": "text",
+                                    "content": " in Eq. (4), i.e.,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "L _ {g r i d} = \\left\\| (\\hat {S} \\cdot \\hat {R} \\cdot V + \\hat {T}) - (S \\cdot R \\cdot V + T) + \\epsilon \\right\\| _ {1} \\tag {6}",
+                                    "image_path": "e209662bb465214e2143ec167e2f69c7084d8f6c4bba251600f62224a112321a.jpg"
+                                }
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\cdot}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the ground truth and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\epsilon"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a small value for stability. The final loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{stab}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " consists of "
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+                                    "type": "inline_equation",
+                                    "content": "L_{gt}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "L_{grid}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ","
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                    "angle": 0,
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+                                    "type": "interline_equation",
+                                    "content": "L _ {s t a b} = L _ {g t} + \\lambda_ {g r i d} L _ {g r i d}. \\tag {7}",
+                                    "image_path": "789372202f21c4581ebb9ae845d5fab4a013cfb3b4fb4a3f606ad10e3c260864.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "4.3. Fine-scale Stabilizer"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The assumption with an affine transformation of the coarse-scale stabilizer could cause structural discontinuity and local distortion. Therefore, our objective is to refine the coarsely stabilized video by optical flow smoothing. Unlike Eq. 3 which applies an image transformation matrix to optimize the optical flow field, we optimize it at the pixel level by a flow warping field "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Thus, the function "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in Eq. (2) is given by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {W} ^ {*} = \\underset {\\mathbf {W}} {\\arg \\min } \\sum_ {i = 0} ^ {N - 1} \\mathbf {W} _ {i} \\left(Y _ {i} \\odot \\hat {M} _ {i}\\right). \\tag {8}",
+                                    "image_path": "885a4f054e1a00fa50b60d64ae78982a62816e4bf18ee71585e9d20a6e123d2e.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "The flow smoothing network follows the U-Net architecture in [56]. We use "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " frames of optical flow fields "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and mask"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                    "bbox": [
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+                                            "type": "image",
+                                            "image_path": "6fe7a98576fa7769bc42ea3ca51803b12244536840d7b80a8ef6546f35c8b5f6.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 4. Illustration of flow fields and warped images under different FOVs. The target image with large FOV presents the smoother flow field and better warped result."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "fields "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as input and obtain "
+                                },
+                                {
+                                    "bbox": [
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+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(N - 1)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " frame warp fields "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " of intermediate frames. Specifically, for the optical flow field "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
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+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " (from frame "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
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+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k + 1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " to frame "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": "), we denote the aligned matrices of each frame in Sec. 4.2 as "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{k} \\in \\mathbb{R}^{2 \\times 3}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{k + 1} \\in \\mathbb{R}^{2 \\times 3}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. Then the input optical flow "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
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+                                        277
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_{k} \\in \\mathbb{R}^{2 \\times HW}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        277
+                                    ],
+                                    "type": "text",
+                                    "content": " can be represented by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {F} _ {k} = H _ {k + 1} \\cdot \\left[ V + Y _ {k} \\mid 1 \\right] - H _ {k} \\cdot \\left[ V \\mid 1 \\right], \\tag {9}",
+                                    "image_path": "d5c826b6957b546ccc89d5a7ee547d7b499e7b8d4c7dac90e5469d484d5d9a1d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V \\in \\mathbb{R}^{2 \\times HW}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\cdot|1]"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denote the normalized coordinate representation. Furthermore, to better adapt the flow smoothing network to the mask field "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we fine-tune it using our synthetic dataset (as we will elaborate in Sec. 6.1). The loss function follows the motion loss [49]"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {\\text {s m o o t h}} = \\sum_ {k = 0} ^ {N - 1} \\left(\\mathbf {F} _ {k} + \\mathbf {W} _ {k} - \\mathbf {F} _ {k} \\left(\\mathbf {W} _ {k + 1}\\right)\\right) \\odot \\hat {M}, \\tag {10}",
+                                    "image_path": "f776ed071ad7a484a54a1d05de61731c56630c3f3481545f70a780f2125721b8.jpg"
+                                }
+                            ]
+                        }
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+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_0 = \\mathbf{W}_N = 0"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
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+                                    "type": "text",
+                                    "content": "5. Video Outpainting Network"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
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+                                    "type": "text",
+                                    "content": "Most video stabilization methods crop an input video with a small field of view (FOV), excluding missing margin pixels due to frame warping. In contrast, full-frame video stabilization [6, 23, 26] proposes to generate a video that maintains the same FOV as the input video without cropping. They directly generate stabilized video frames with large FOV by fusing the information from neighboring frames. An important limitation of existing fusion strategies is the unequal importance of different frames (i.e., the current and neighboring frames are weighted equally), which would lead to unpleasant distortions in fast-moving situations. To overcome this weakness, we propose a two-stage framework to combine flow and image outpainting strategies [32]. In the first stage, we used flow-outpainting to iteratively align the neighboring frames with the target frame. In the second stage, we fill the target frame with adjacent aligned frame pixels by image outpainting."
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+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "5.1. Flow Outpainting Network"
+                                }
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+                    ],
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+                                    "type": "text",
+                                    "content": "Let "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " denote the outpainted target image and "
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+                                    "type": "text",
+                                    "content": " the neighboring source image. We aim to fill the missing pixel"
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+                                            "content": "Figure 5. Architecture of flow outpainting network. Given a small FOV flow field and valid mask, the network predicts the large FOV flow field."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "region "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "M_{\\varnothing}^{t}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of "
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+                                {
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with the pixels of "
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+                                    "type": "inline_equation",
+                                    "content": "I^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". As shown in Fig. 4, we take two different FOVs of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as input and obtain the corresponding optical flow fields and warped results "
+                                },
+                                {
+                                    "bbox": [
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+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{warp}^{s}"
+                                },
+                                {
+                                    "bbox": [
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+                                        343
+                                    ],
+                                    "type": "text",
+                                    "content": ". The small FOV "
+                                },
+                                {
+                                    "bbox": [
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+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
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+                                        343
+                                    ],
+                                    "type": "text",
+                                    "content": " cannot guide "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
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+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        343
+                                    ],
+                                    "type": "text",
+                                    "content": " well to fill the regions in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{\\varnothing}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since the predicted optical flow field in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{\\varnothing}^{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is unreliable due to the lack of pixel guidance of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
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+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the out-of-view region of "
+                                },
+                                {
+                                    "bbox": [
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+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{\\varnothing}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "text",
+                                    "content": " has artifacts (marked in the last column of Fig. 4). We observe that the optical flow field of the large FOV "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is continuous in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{\\varnothing}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which inspired us to extrapolate the flow of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{\\varnothing}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        211,
+                                        287,
+                                        343
+                                    ],
+                                    "type": "text",
+                                    "content": " using the reliable flow region (the 3rd column of Fig. 4)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
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+                        439
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We propose a novel flow outpainting network (Fig. 5), which extrapolates the large FOV flow field using a small FOV flow field and the corresponding valid mask. Specifically, we adopt a U-Net architecture and apply a sequence of gated convolution layers with downsampling / upsampling to obtain the large flow field of FOV "
+                                },
+                                {
+                                    "bbox": [
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+                                        343,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{large}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        343,
+                                        287,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that the input flow field "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        287,
+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{small}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the valid mask "
+                                },
+                                {
+                                    "bbox": [
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+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{valid}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " have been estimated by PDCNet (see Sec. 4.1)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Loss functions Our loss functions include robust loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell_1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and loss in the frequency domain [4]. We directly calculate the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\ell_1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " loss between "
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+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{large}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and its ground truth "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{Y}_{large}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ","
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        60,
+                                        488,
+                                        287,
+                                        516
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} L _ {Y} = \\lambda_ {i n} \\cdot \\| | Y _ {\\text {l a r g e}} - Y _ {\\text {s m a l l}} | \\odot M _ {\\text {v a l i d}} \\| _ {1} \\tag {11} \\\\ + \\lambda_ {o u t} \\cdot \\| | Y _ {l a r g e} - \\dot {Y} _ {l a r g e} | \\odot (\\sim M _ {v a l i d}) \\| _ {1}. \\\\ \\end{array}",
+                                    "image_path": "e3cbed3cd3f2dfa6dc92e987a9b78c01f3d4a7a4933edeb2f2ae323a38aafece.jpg"
+                                }
+                            ]
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+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": "To encourage low frequency and smoothing "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{large}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
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+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": ", we add the loss in the frequency domain "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{F} = \\| \\hat{\\mathbf{G}}\\cdot \\mathcal{F}Y_{large}\\|_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
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+                                    ],
+                                    "type": "text",
+                                    "content": " where the normalized Gaussian map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{G}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mu = 0"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\sigma = 3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": " is inverted by its maximum value and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}Y_{large}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the Fourier spectrum of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{large}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": ". The final loss consists of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{Y}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        523,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{F}"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        111,
+                        597,
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+                        610
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                        597,
+                                        287,
+                                        610
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {\\text {o u t p a i n t}} = L _ {Y} + \\lambda_ {F} L _ {F}. \\tag {12}",
+                                    "image_path": "52fba9fe9f7a50978cfda83f9849bc77a454fbe56157c431e82358aefc28d1c2.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "5.2. Image Margin Outpainting"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Based on our proposed flow-outpainting network, we design a margin-outpainting method by iteratively aligning frame pairs (see Fig. 6). As discussed in Sec. 5.1, we can obtain a large FOV flow field "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{large}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". The neighboring reference frame "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " is warped as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{warp} = Y_{large}(I^{s})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " as shown in Fig. 6. In theory, the outpainted frame "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{result} ="
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        313,
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+                        541,
+                        194
+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
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+                                70,
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+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        194
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                313,
+                                                70,
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+                                            ],
+                                            "type": "image",
+                                            "image_path": "05918f014562ceec451629fc9b4ace86011898cec5ae90fa9887c6c10599b66a.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
+                                304,
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+                                251
+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        197,
+                                        545,
+                                        251
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 6. Overview image margin outpainting. Given the target frame "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "I^{t}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": ", the reference frame "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "I^{s}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": " is coarsely aligned to "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "I^{warp}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": " by the predicted large-FOV flow field "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "Y_{large}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": ". Then, we adopt a margin fusion approach to obtain the result frame "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "I^{result}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": ", by carefully aggregating "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "I^{t}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "I^{warp}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                197,
+                                                545,
+                                                251
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        272,
+                        545,
+                        452
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                272,
+                                545,
+                                452
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^t \\cdot M_{valid} + I^{warp} \\cdot (\\sim M_{valid})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": ". However, we notice that there are obvious distortions at the image border. To further align the margins, we take a margin fusion approach (the detailed algorithm can be found in Supp. S1) We crop "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{warp}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_c^s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_c^t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, we can obtain a new warped frame "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_c^{warp}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " by flow outpainting. In particular, we did not choose to add "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_c^{warp}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " directly. To identify the misaligned region, we propose to outpaint the mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{I^t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " by extending the watershed outward from the center. Instead of a preset threshold, we adaptively choose between the target image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " and the warped image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_c^{warp}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, the final frame "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{result}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " consists of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_c^{warp}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": ": "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{result} = I^t \\cdot M_{I^t} + I_c^{warp} \\cdot (\\sim M_{I^t})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": ". Compared to the two results "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{result}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": ", our strategy successfully mitigates misalignment and distortions at the boundary of video frames."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        304,
+                        458,
+                        545,
+                        625
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                458,
+                                545,
+                                625
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        458,
+                                        545,
+                                        625
+                                    ],
+                                    "type": "text",
+                                    "content": "Multi-frame fusion During the final stage of rendering, we use a sequence of neighboring frames to outpaint the target frame, while they may have filled duplicate regions. It is important to find out which frame and which region should be selected. We proposed the selection strategy for multi-frame fusion (the details can be found in Supp. S1). By weighing the metric parameters of each frame, we finally obtain the target frame with large FOV. Note that each frame has an added margin in the stabilization process, so we need to crop them to the original resolution. Although we have outpainted the target frame, some missing pixel holes may still exit at boundaries. Here, we apply the state-of-the-art LaMa image inpainting method [36] to fill these holes using nearest-neighbor interpolation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        306,
+                        638,
+                        387,
+                        651
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                        651
+                                    ],
+                                    "type": "text",
+                                    "content": "6. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        306,
+                        658,
+                        531,
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "6.1. Synthetic Datasets for Supervised Learning"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        304,
+                        677,
+                        545,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "Due to the limited amount of paired training data, we propose a novel model-based data generation method by carefully designing synthetic datasets for video stabiliza"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                }
+            ],
+            "discarded_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "page_number",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "23539"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                }
+            ],
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">NUS dataset [21]</td><td colspan=\"3\">DeepStab dataset [39]</td><td colspan=\"3\">Selfie dataset [48]</td></tr><tr><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td><td>C.↑</td><td>D.↑</td><td>S.↑</td></tr><tr><td>Grundmann et al. [11]</td><td>0.71</td><td>0.76</td><td>0.62</td><td>0.77</td><td>0.87</td><td>0.80</td><td>0.75</td><td>0.81</td><td>0.83</td></tr><tr><td>Liu et al. [21]</td><td>0.81</td><td>0.78</td><td>0.82</td><td>0.80</td><td>0.90</td><td>0.85</td><td>0.74</td><td>0.89</td><td>0.8</td></tr><tr><td>Wang et al. [39]</td><td>0.67</td><td>0.72</td><td>0.41</td><td>-</td><td>-</td><td>-</td><td>0.68</td><td>0.71</td><td>0.82</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>0.78</td><td>0.77</td><td>0.82</td><td>0.85</td><td>0.89</td><td>0.76</td><td>0.79</td><td>0.77</td><td>0.84</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>0.85</td><td>0.81</td><td>0.86</td><td>0.87</td><td>0.92</td><td>0.82</td><td>0.83</td><td>0.87</td><td>0.86</td></tr><tr><td>Yu [50]+OVS* [45]</td><td>0.92</td><td>0.78</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DUT [44]</td><td>0.71</td><td>0.81</td><td>0.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DIFRINT [6]</td><td>1.00</td><td>0.85</td><td>0.84</td><td>1.00</td><td>0.91</td><td>0.78</td><td>1.00</td><td>0.78</td><td>0.84</td></tr><tr><td>FuSta [23]</td><td>1.00</td><td>0.87</td><td>0.86</td><td>1.00</td><td>0.92</td><td>0.82</td><td>1.00</td><td>0.83</td><td>0.87</td></tr><tr><td>Ours</td><td>1.00</td><td>0.91</td><td>0.86</td><td>1.00</td><td>0.94</td><td>0.84</td><td>1.00</td><td>0.87</td><td>0.87</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. Quantitative results on the NUS dataset [21], the DeepStab dataset [39] and the Selfie Dataset [48]. We evaluate the following metrics: Cropping Ratio(C.), Distortion Value(D.), Stability Score(S). * indicates the results obtained from original paper. We highlight the best method in bold and underline the second-best."
+                                        }
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+                                    "type": "text",
+                                    "content": "tion. For our base synthetic dataset, we used a collection of images from the DPED [14], CityScapes [8] and ADE20K [55] datasets. To generate a stable video, we randomly generate the homography parameters for each image, including rotation angle "
+                                },
+                                {
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+                                    "content": "\\theta"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", scaling "
+                                },
+                                {
+                                    "bbox": [
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+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", translations "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        289,
+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(d_x,d_y)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
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+                                        510
+                                    ],
+                                    "type": "text",
+                                    "content": " and perspective factors "
+                                },
+                                {
+                                    "bbox": [
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+                                        270,
+                                        289,
+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(p_x,p_y)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
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+                                        510
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we divide these transformation parameters into "
+                                },
+                                {
+                                    "bbox": [
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+                                        270,
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+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " bins equally and obtain a video of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " frames by homography transformations. To simulate the presence of moving objects in real scenarios, the stable video is further augmented with additional independently moving random objects. To do so, the objects are sampled from the COCO dataset [15] and inserted on top of the synthetic video frames using their segmentation masks. Specifically, we randomly choose "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " objects (no more than 5), and generate randomly affine transformation parameters for each independent of the background transformation. Finally, we cropped each frame to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        289,
+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "720\\times 480"
+                                },
+                                {
+                                    "bbox": [
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+                                        270,
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+                                    ],
+                                    "type": "text",
+                                    "content": " around its center. For different training requirements, we apply various combinations of synthetic dataset. The implementation and training details can be found in Supp. S2, S3."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "6.2.Quantitative Evaluation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We compare the results of our method with various video stabilization methods, including Grundmann et al. [11], Liu et al. [21], Wang et al. [39], Yu and Ramamoorthi [49, 50], DUT [44], OVS [45], DIFRINT [6], and FuSta [23]. We obtain the results of the compared methods from the videos released by the authors or generated from the publicly available official implementation with default parameters or pre-trained models. Note that OVS [45] does not honor their promise to provide code, thus we only report the results from their paper."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                {
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+                                    "type": "text",
+                                    "content": "Datasets. We evaluate all approaches on the NUS dataset [21], DeepStab dataset [39], and Selfie dataset [48]. The NUS dataset consists of 144 videos and the corresponding ground truths in 6 scenes. The DeepStab dataset con"
+                                }
+                            ]
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+                {
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+                                    "type": "text",
+                                    "content": "tains 61 videos and the Selfie dataset consist of 33 videos."
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+                    "index": 6
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+                                    "type": "text",
+                                    "content": "Metrics. We introduce three metrics widely used in many methods [6, 23, 50] to evaluate our model: 1) Cropping ratio measures the remaining frame area after cropping off the invalid boundaries. 2) Distortion value evaluates the anisotropic scaling of the homography between the input and output frames. 3) Stability score measures the stability of the output video. We calculate the metrics using the evaluation code provided by DIFRINT."
+                                }
+                            ]
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+                    ],
+                    "index": 7
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+                {
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+                                    "type": "text",
+                                    "content": "Quantitative comparison. The results of the NUS dataset [21] are summarized in Table 1 (Per-category result can be found in Supp. S5). Overall, our method achieves the best distortion value compared to the state-of-the-art method, FuSta [23]. Especially in the quick-rotation and zoom categories, our method outperforms pure image generation methods [6,23]. We suspect that the reduction of the shared information between frames causes the image generation methods to prefer artifacts. However, our method can ensure local structural integrity when outpainting the margin region. Furthermore, our method achieves an average cropping ratio of 1.0 and stability scores comparable to recent approaches [6, 23, 49, 50]. Since FuSta [23] uses Yu et al. [50] to obtain stabilized input videos, they have the same stability scores. It is important to note that although the stability scores are competitive, our method runs 5 times faster than [50] in the video stabilization stage. Moreover, the comparison results on DeepStab dataset [39] and Selfie dataset [48] are also reported in Table 1. Our method still shows effectiveness in different datasets, proving the generalizability of the proposed method. Note that, due to that Wang et al. [39] is trained on the DeepStab dataset, we do not report its results on the DeepStab dataset for a fair comparison. Qualitative comparisons can be found in Supp. S4 and supplementary video."
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+                                            "html": "<table><tr><td>Stabilizer</td><td></td><td>Stability↑</td><td>Distortion↑</td></tr><tr><td rowspan=\"2\">Image-level</td><td>w.o. mask</td><td>0.76</td><td>0.88</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr><tr><td rowspan=\"2\">Pixel-level</td><td>w.o. mask</td><td>0.81</td><td>0.84</td></tr><tr><td>with mask</td><td>0.83</td><td>0.91</td></tr></table>",
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+                                            "content": "Table 2. The importance of mask to video stabilization. We validate on the Crowd category of NUS dataset [21]."
+                                        }
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+                            "angle": 0,
+                            "type": "table_caption"
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+                                            "html": "<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>Distortion↑</td></tr><tr><td>PCAFlow [42]</td><td>11.34</td><td>0.50</td><td>0.72</td></tr><tr><td>Our flow outpainting</td><td>19.65</td><td>0.77</td><td>0.93</td></tr><tr><td>w.o. margin outpainting</td><td>18.04</td><td>0.64</td><td>0.81</td></tr><tr><td>w.o. mask \\( M_{I^t} \\)</td><td>20.35</td><td>0.78</td><td>0.86</td></tr><tr><td>w.o. multi-frame selection</td><td>21.99</td><td>0.84</td><td>0.90</td></tr><tr><td>Ours</td><td>23.17</td><td>0.86</td><td>0.91</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "6.3. Ablation Study"
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+                                    "type": "text",
+                                    "content": "Importance of mask generation. We investigate the influence of the mask on video stabilization at different stages. To better demonstrate the necessity of mask in complex scenarios, we choose the Crowd category of NUS dataset [21] which includes a display of moving pedestrians and occlusions. Stability and distortion at different settings are shown in Table 2. It can be seen that the performance with mask increases significantly in both stabilizers. Specifically, the mask can both improve stability globally and alleviate image warping distortion locally. This result demonstrates the importance of mask generation for video stabilization."
+                                }
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+                                    "type": "text",
+                                    "content": "Flow outpainting. We compare our flow outpainting method with the traditional flow inpainting method PCAFlow [42]. Following [50] we fit the first 5 principal components proposed by PCAFlow to the "
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+                                    "type": "inline_equation",
+                                    "content": "M_{valid} = 1"
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+                                    "type": "text",
+                                    "content": " regions of the optical flow field, and then outpaint the flow vectors in the "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "M_{valid} = 0"
+                                },
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+                                    "type": "text",
+                                    "content": " regions with reasonable values of the PCA Flow fitted. The result is obtained by warping the source image with the outpainted optical flow field. We perform this comparison on our synthetic validation set and evaluate it with the corresponding ground truth. Additionally, we use PSNR and SSIM [41] to evaluate the quality of the results. As shown in Table 3, ours dramatically outperforms PCAFlow [42] in all objective metrics."
+                                }
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+                                    "type": "text",
+                                    "content": "Importance of image filling strategies. We explore the following proposed strategies for image filling: margin outpainting, mask generation "
+                                },
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+                                    "type": "text",
+                                    "content": ", and multiframe selection. We isolate them from our method to compare their results with the complete version. The results are shown in Table 3. The proposed strategies are generally helpful in improving image quality. Especially, margin outpainting and mask "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are crucial to the results."
+                                }
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+                                            "type": "text",
+                                            "content": "Table 3. Ablation study of image filling. The evaluation is conducted on our model-based synthetic validation set."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Method</td><td>Runtime</td></tr><tr><td>Traditional pose regression</td><td>216ms</td></tr><tr><td>Our pose regression network</td><td>21ms</td></tr><tr><td>Grundmann et al. [11]</td><td>480ms</td></tr><tr><td>Liu et al. [21]</td><td>1360ms</td></tr><tr><td>Wang et al. [39]</td><td>460ms</td></tr><tr><td>Yu and Ramamoorthi [49]</td><td>1610ms</td></tr><tr><td>Yu and Ramamoorthi [50]</td><td>570ms</td></tr><tr><td>DIFRINT [6]</td><td>1530ms</td></tr><tr><td>FuSta [23]</td><td>9820ms</td></tr><tr><td>Ours</td><td>97ms</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 4. Per-frame runtime comparison of camera pose regression and video stabilization."
+                                }
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+                                            "type": "text",
+                                            "content": "(a) shaky frames"
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+                                            "type": "text",
+                                            "content": "(b) stable frames"
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+                                            "type": "text",
+                                            "content": "Figure 7. Experiment of fixed-point iteration on shaky and stable frames. (a) Our fixed-point iteration helps the shaky frames converge to a steady state. (b) For stable frames, the fixed-point iteration guarantees the stability of results."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "6.4. Runtime Comparison"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Our network and pipeline are implemented with PyTorch and Python. Table 4 is a summary of the runtime per frame for various competing methods. All timing results are obtained on a desktop with an RTX3090Ti GPU and an Intel(R) Xeon(R) Gold 6226R CPU. First, we compare the run-time of pose regression. Traditional pose regression is time consuming in feature matching [2, 9], homography estimation, and SVD decomposition [28]. Although our learning-based pose regression network runs 10 times faster than the traditional framework. Then, we report the average run time of different methods, including optimization-based [21, 49] and learning-based [6, 11, 23, 39, 50]. Our method takes "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "97\\mathrm{ms}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " which gives "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 5\\mathrm{x}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " speed-up. This is because our method computes the optical flow field only once and without the help of other upstream task methods and manual optimization."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "6.5. Fixed-point Experiment"
+                                }
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+                                    "type": "text",
+                                    "content": "To demonstrate the stability of our fixed-point optimization solution, we performed an interesting toy experiment. We input a sequence of shaky frames into our coarse-to-fine stabilizers, and the stabilized result will be iteratively restabilized by our stabilizers. For each iteration, we calculate the average magnitude of optical flow filed with global transformation and flow warping for each frame. Specifi-"
+                                }
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+                                    "type": "text",
+                                    "content": "cally, the regions where we calculate are marked by "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". As shown in Fig. 7(a), the deviation of the shaky frames decreases rapidly with each iteration. Furthermore, we have pointed out that plugging a stabilized video into the stabilization system should not have an impact on the input. Thus, we plug stable frames into the coarse-to-fine stabilizers and iteratively stabilize them. The result is shown in Fig. 7(b). The deviation of each frame is perturbed around the value of zero. Obviously, our method has no effect on stable frames, which shows that stabilized video is indeed the fixed point of our developed stabilization system."
+                                }
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+                                    "type": "text",
+                                    "content": "7. Conclusion"
+                                }
+                            ]
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+                    "index": 1
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this paper, we have presented a fast full-frame video stabilization technique based on the iterative optimization strategy. Our approach can be interpreted as the combination of probabilistic stabilization network (coarse-to-fine extension of PDC-Net) and video outpainting outwork (flow-based image outpainting). When trained on synthetic data constructed within the optimization-based learning framework, our method achieves state-of-the-art performance at a fraction of the computational cost of other competing techniques. It is also empirically verified that stabilized video is the fixed point of the stabilization network."
+                                }
+                            ]
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[1] Ravi P Agarwal, Maria Meehan, and Donal O'regan. Fixed point theory and applications, volume 141. Cambridge university press, 2001."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                53,
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+                                470
+                            ],
+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                427,
+                                                287,
+                                                470
+                                            ],
+                                            "type": "text",
+                                            "content": "[2] Relja Arandjelović and Andrew Zisserman. Three things everyone should know to improve object retrieval. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pages 2911-2918. IEEE, 2012."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                471,
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+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                471,
+                                                287,
+                                                504
+                                            ],
+                                            "type": "text",
+                                            "content": "[3] Adam Baumberg. Reliable feature matching across widely separated views. In Proc. IEEE Conf. Comput. Vis. Pattern Recognit., volume 1, pages 774-781. IEEE, 2000."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                505,
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+                                536
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                505,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[4] Ronald Newbold Bracewell and Ronald N Bracewell. The Fourier transform and its applications, volume 31999. McGraw-hill New York, 1986."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                                    "content": "[56] Tinghui Zhou, Richard Tucker, John Flynn, Graham Fyffe, and Noah Snavely. Stereo magnification: Learning view synthesis using multiplane images. arXiv preprint arXiv:1805.09817, 2018."
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diff --git a/2023/Fast Globally Optimal Surface Normal Estimation from an Affine Correspondence/ecc07b62-9596-44a0-9745-a517e83aa84a_content_list.json b/2023/Fast Globally Optimal Surface Normal Estimation from an Affine Correspondence/ecc07b62-9596-44a0-9745-a517e83aa84a_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd1aa9312a646ee206f7d9f20813616d9d465f92
--- /dev/null
+++ b/2023/Fast Globally Optimal Surface Normal Estimation from an Affine Correspondence/ecc07b62-9596-44a0-9745-a517e83aa84a_content_list.json	
@@ -0,0 +1,2227 @@
+[
+    {
+        "type": "text",
+        "text": "Fast Globally Optimal Surface Normal from an Affine Correspondence",
+        "text_level": 1,
+        "bbox": [
+            125,
+            130,
+            843,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Levente Hajder, Lajos Lóczi  \nGeometric Computer Vision Group  \nEötvös Loránd University, Budapest, Hungary  \n{hajder, lloczi}@inf.elte.hu",
+        "bbox": [
+            125,
+            181,
+            491,
+            252
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Daniel Barath  \nComputer Vision and Geometry Group  \nETH Zurich, Switzerland  \ndbarath@inf.ethz.ch",
+        "bbox": [
+            532,
+            181,
+            843,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            286,
+            313,
+            301
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present a new solver for estimating a surface normal from a single affine correspondence in two calibrated views. The proposed approach provides a new globally optimal solution for this over-determined problem and proves that it reduces to a linear system that can be solved extremely efficiently. This allows for performing significantly faster than other recent methods, solving the same problem and obtaining the same globally optimal solution. We demonstrate on  $15k$  image pairs from standard benchmarks that the proposed approach leads to the same results as other optimal algorithms while being, on average, five times faster than the fastest alternative. Besides its theoretical value, we demonstrate that such an approach has clear benefits, e.g., in image-based visual localization, due to not requiring a dense point cloud to recover the surface normal. We show on the Cambridge Landmarks dataset that leveraging the proposed surface normal estimation further improves localization accuracy. Matlab and  $C++$  implementations are also published in the supplementary material.",
+        "bbox": [
+            75,
+            316,
+            473,
+            604
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            633,
+            209,
+            648
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Acquiring oriented point clouds is a fundamental problem both in computer vision and in robotics with a number of important real-world applications benefiting from the extra information it provides. Such applications include 3D reconstruction [1, 8, 31, 62, 72, 65, 56] and simultaneous localization and mapping [19, 23, 50], where the 3D point orientations provide useful information about the underlying structure. Image-based visual localization approaches [43, 53, 60, 61] can also benefit from known surface normals [68]. The widely used Poisson reconstruction [37, 38] is based on both the point coordinates and their orientations. The visual odometry [51, 52] of an autonomous vehicle can also benefit from understanding surface orientation to, e.g., segment ground or facades. Also, having an oriented point cloud greatly simplifies geometric model and multi-model estimation [32, 4, 5] due to allowing to design solvers that",
+        "bbox": [
+            75,
+            659,
+            470,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/0c48ef7f051b42a370dc08fa7ade8ffa2f4139ea4d5f11d69b72a1c707315bda.jpg",
+        "image_caption": [
+            "Figure 1. Geometric configuration: oriented 3D point  $\\mathbf{P} \\in \\mathbb{E}^3$  with normal  $\\mathbf{n} \\in \\mathbb{E}^3$  projected to image  $\\Pi^1$  as  $\\mathbf{p}_1 \\in \\mathbb{E}^2$  and to  $\\Pi^2$  as  $\\mathbf{p}_2 \\in \\mathbb{E}^2$ . The local patch centered at points  $\\mathbf{p}_1$  and  $\\mathbf{p}_2$  are related by the local affine transformation  $\\mathbf{A} \\in \\mathbb{R}^{2 \\times 2}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            526,
+            289,
+            864,
+            412
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "require fewer data points than their point-based counterparts [64]. Moreover, normals can also be leveraged in the numerical refinement of the reconstructed oriented 3D point cloud [27]. In this paper, we focus on a practical problem, i.e., estimating the normal at corresponding features in two images in a solely photometric manner. This can provide a lightweight approach of obtaining surface normals without requiring a dense point cloud to be known. Next, we will discuss ways of obtaining oriented points.",
+        "bbox": [
+            496,
+            518,
+            893,
+            655
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Normals from Point Clouds. After applying state-of-the-art sparse (e.g., COLMAP [63]) or dense [36, 16] reconstruction pipelines, the resulting point cloud can be straightforwardly equipped with point orientations. In this case, typically, the normals are fitted per-point, applying the widely used Principal Component Analysis (PCA) [35] to estimate tangent planes or higher-order surfaces [14, 33] from the local neighborhood centered at the current point. This procedure, while being frequently used, has two major drawbacks. First, the setting of the neighborhood size greatly affects the accuracy and is often unclear without having a metric reconstruction. Instead, using the  $k$ -nearest-neighbors [17] algorithm to find local neighborhoods is a viable solution, but the estimation becomes largely affected by the sparsity of the point cloud. Second, fitting local surfaces, independently, to the neighborhood of each 3D point",
+        "bbox": [
+            496,
+            657,
+            893,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "3390",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "in the reconstruction is an extremely expensive operation.",
+        "bbox": [
+            76,
+            90,
+            459,
+            107
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Normals from Homographies. Another method for estimating surface normals from images, without requiring the underlying 3D structure to be known, is via homographies. Homographies are projective transformations between images of co-planar 3D points that depends on the intrinsic and extrinsic camera parameters and the parameters of the underlying 3D plane [24]. A homography can be estimated from a minimum of four point correspondences in two images [30]. While this method allows the estimation of dominant planes supported by a number of correspondences in the images, it does not provide means for normal estimation for each local feature correspondence independently.",
+        "bbox": [
+            75,
+            108,
+            467,
+            289
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Normals from Local Mappings. In recent years, affine correspondences (AC) have emerged as a popular topic in computer vision, offering a valuable source of information about the underlying 3D geometry of the surrounding environment. An AC consists of a corresponding pair of points in two images and a linear transformation that maps the infinitesimal region around the point in the first image to the point in the second one. They have been used to solve various geometric problems, including relative pose estimation in the general case [15, 55, 3, 22, 10], for known vertical direction [25], planar motion [25, 26], or known feature depths [21] and homography estimation [2].",
+        "bbox": [
+            75,
+            292,
+            467,
+            474
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Traditionally, finding affine features involve four main steps: (scale-covariant) keypoint detection, orientation and affine shape estimation, and descriptor extraction. Under such paradigm, keypoint detection is typically performed on the scale pyramid with the help of a handcrafted response function, such as Hessian [13, 45], Harris [28, 45], Difference of Gaussians (DoG [42]), or learned ones like FAST [57] or Key.Net [11]. Keypoint detection obtains a triplet  $(x,y,\\mathrm{scale})$  which defines a square or circular image patch. Then the patch orientation is estimated with the help of handcrafted - dominant gradient orientation [42], center of the mass [58] - or learned methods [71, 48, 41]. Next, the affine-covariant shape [12, 48] is estimated. Finally, the patch is geometrically rectified and fed into a local patch descriptor, such as SIFT, HardNet [47], SOSNet [66], or others. In summary, all feature detectors, even recent learning-based ones like SuperPoint [20], can be made affine covariant by applying, e.g., AffNet [48] as a post-processing step on the found features.",
+        "bbox": [
+            75,
+            474,
+            467,
+            762
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The problem of surface normal estimation from ACs has been addressed in several works. The first algorithm for normal estimation from ACs was proposed by Kevin Koeser [40] assuming that the camera location is known with respect to the observed 3D point. Megyesi et al. [44] proposed a special surface normal estimator for standard (rectified) stereo, where the degree of freedom of the affine transformations decreases to two. In 2014, Molnár and Chetverikov [49] derived a formula connecting the surface",
+        "bbox": [
+            75,
+            763,
+            467,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "normals, camera parameters, affine transformations, and patch locations into a single expression for arbitrary projective functions, like the catadioptric camera model. Barath et al. [9] proposed a globally optimal estimator in the least squares sense as the solution of a quartic polynomial. Recently, Le Minh and Hajder [46] improved on this by reducing the degree and showed that the optimal solution can be found as a real root of a cubic polynomial.",
+        "bbox": [
+            496,
+            90,
+            890,
+            210
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main goal of this paper is to propose a rapid normal estimator based on affine correspondences. Our algorithm can be inserted into a 3D reconstruction system, such as Structure-from-Motion [27] (SfM) or Simultaneous Localization and Mapping (SLAM), where the normal estimation is performed many times, therefore its running time influences the time demand of the whole 3D pipeline.",
+        "bbox": [
+            496,
+            212,
+            890,
+            316
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Contribution. In this paper, we propose a new linear and globally optimal solution for surface normal estimation from a single affine correspondence. The proposed solver requires only the four basic arithmetic operations and contains 19 parameters, consisting of the coordinates of the five input vectors and the four affine parameters. This approach completely avoids root extractions, solving high-degree polynomial equations, or employing numerical or iterative methods, resulting in a particularly fast algorithm that runs for only  $0.6\\mu s$  in our experiments. The solver is five times faster than the cubic solver from [46]. Additionally, we propose a way of exploiting AC-wise normals in image-based visual localization pipelines. The algorithms are tested on 15k image pairs from standard benchmarks, and our results show superior accuracy and faster wall-clock times compared to the baselines.",
+        "bbox": [
+            496,
+            318,
+            890,
+            559
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Proposed Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            573,
+            671,
+            589
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The setting is visualized in Fig 1. We are given two images, denoted by  $\\Pi^1$  and  $\\Pi^2$ . The 2D and 3D point locations are visualized as black dots. For standard PC-based stereo vision, the 3D location can be obtained by the so-called triangulation method. The local affine transformation, denoted by  $\\mathbf{A} \\in \\mathbb{R}^{2 \\times 2}$ , is defined as the first-order Taylor-approximation of the imaging function at points  $\\mathbf{p}_1$  and  $\\mathbf{p}_2$ . It maps the infinitesimal patch around the observed points from the first to the second image. If  $\\mathbf{A}$  is known, the surface normal  $\\mathbf{n}$  can be directly estimated without knowing the actual 3D structure of the underlying scene [49].",
+        "bbox": [
+            496,
+            598,
+            890,
+            763
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Parameterization. A surface normal  $\\mathbf{n} \\in \\mathbb{R}^3$  is a 3D direction, therefore it can be represented by two parameters. Usually, it is parameterized by three coordinates  $\\mathbf{n} = [n_x, n_y, n_z]^\\top$  and its length being set to 1. However, as it turns out below, some other scaling will be more convenient in the present situation.",
+        "bbox": [
+            496,
+            763,
+            890,
+            854
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Problem Statement. Let us assume that we are given a general camera that projects the spatial location  $\\mathbf{P} = [X, Y, Z]^\\top$  to image (pixel) coordinates  $[u v]^\\top$ , and let us",
+        "bbox": [
+            496,
+            854,
+            890,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "3391",
+        "bbox": [
+            482,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "denote the projective coordinate functions by  $\\Pi_u: \\mathbb{E}^3 \\to \\mathbb{R}$  and  $\\Pi_v: \\mathbb{E}^3 \\to \\mathbb{R}$ . Function  $\\Pi_u$  calculates coordinate  $u$  of the projected point, and  $\\Pi_v$  calculates  $v$ . As Molnár and Chetverikov showed [49], the affine transformation can be defined via the spatial gradients of the projective coordinate functions  $\\Pi_u$  and  $\\Pi_v$ .",
+        "bbox": [
+            75,
+            90,
+            468,
+            181
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "An affine correspondence is represented by 2D image coordinates  $[u_1 v_1]^\\top$  and  $[u_2 v_2]^\\top$  in the stereo image pair, in conjunction with the affine transformation  $\\mathbf{A}$  that maps the surrounding area of the locations from first image to the second one. The spatial location of the corresponding spatial point is also required. It can be estimated from the image coordinates and camera parameters by standard triangulation techniques [29].",
+        "bbox": [
+            75,
+            181,
+            468,
+            304
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The normal estimation problem is written [9] as an argument minimization to determine the optimal  $\\mathbf{n}^*$  such that",
+        "bbox": [
+            76,
+            305,
+            468,
+            335
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {n} ^ {*} = \\operatorname * {a r g   m i n} _ {\\mathbf {n}} f (\\mathbf {n}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            202,
+            349,
+            339,
+            369
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with",
+        "bbox": [
+            76,
+            382,
+            109,
+            393
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf (\\mathbf {n}) := \\sum_ {i = 1} ^ {2} \\sum_ {j = 1} ^ {2} \\left(\\frac {\\mathbf {n} ^ {\\top} \\mathbf {w} _ {i j}}{\\mathbf {n} ^ {\\top} \\mathbf {w} _ {c}} - a _ {i j}\\right) ^ {2}. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
+            393,
+            468,
+            436
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here, the affine transformation yields the four affine parameters  $a_{ij}$  ( $i,j\\in [1,2]$ ) according to",
+        "bbox": [
+            76,
+            445,
+            468,
+            476
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {A} = \\left[ \\begin{array}{c c} a _ {1 1} & a _ {1 2} \\\\ a _ {2 1} & a _ {2 2} \\end{array} \\right],\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
+            487,
+            343,
+            522
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and the vectors  $\\mathbf{w}_{ij}$  and  $\\mathbf{w}_c$  are obtained as cross products of the spatial gradient vectors as follows:",
+        "bbox": [
+            76,
+            532,
+            468,
+            563
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbf {w} _ {1 1} = \\nabla \\Pi_ {v} ^ {1} \\times \\nabla \\Pi_ {u} ^ {2}, \\quad \\mathbf {w} _ {1 2} = \\nabla \\Pi_ {u} ^ {2} \\times \\nabla \\Pi_ {u} ^ {1}, \\\\ \\mathbf {w} _ {2 1} = \\nabla \\Pi_ {v} ^ {1} \\times \\nabla \\Pi_ {v} ^ {2}, \\quad \\mathbf {w} _ {2 2} = \\nabla \\Pi_ {v} ^ {2} \\times \\nabla \\Pi_ {u} ^ {1}, \\\\ \\mathbf {w} _ {c} = \\nabla \\Pi_ {u} ^ {1} \\times \\nabla \\Pi_ {v} ^ {1}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            102,
+            575,
+            406,
+            622
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where the superscripts refer to the corresponding image index. The coordinates of these vectors will be denoted by  $\\mathbf{w}_{ij,x},\\mathbf{w}_{ij,y},\\mathbf{w}_{ij,z}$ $(i,j\\in \\{1,2\\})$  and  $\\mathbf{w}_{c,x},\\mathbf{w}_{c,y},\\mathbf{w}_{c,z}$ .",
+        "bbox": [
+            76,
+            635,
+            468,
+            681
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Pin-hole (perspective) projection model. For a pin-hole camera, the projection model is as follows:",
+        "bbox": [
+            76,
+            681,
+            468,
+            710
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ \\begin{array}{c} u \\\\ v \\\\ 1 \\end{array} \\right] \\sim \\left[ \\begin{array}{c c c c} P _ {1 1} & P _ {1 2} & P _ {1 3} & P _ {1 4} \\\\ P _ {2 1} & P _ {2 2} & P _ {2 3} & P _ {2 4} \\\\ P _ {3 1} & P _ {3 2} & P _ {3 3} & P _ {3 4} \\end{array} \\right] \\left[ \\begin{array}{c} X \\\\ Y \\\\ Z \\\\ 1 \\end{array} \\right],\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            723,
+            431,
+            787
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sim$  denotes the equality up to scale operation. Therefore, image coordinates  $u$  and  $v$  are obtained as",
+        "bbox": [
+            76,
+            799,
+            468,
+            828
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\Pi_ {u} = \\frac {P _ {1 1} X + P _ {1 2} Y + P _ {1 3} Z + P _ {1 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}, \\\\ \\Pi_ {v} = \\frac {P _ {2 1} X + P _ {2 2} Y + P _ {2 3} Z + P _ {2 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            839,
+            383,
+            905
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Spatial gradients, that are  $\\nabla \\Pi = \\left[ \\begin{array}{ccc}\\frac{\\partial\\Pi}{\\partial X} & \\frac{\\partial\\Pi}{\\partial Y} & \\frac{\\partial\\Pi}{\\partial Z} \\end{array} \\right]^{\\top}$ , can be written for the pin-hole model in compact forms as",
+        "bbox": [
+            498,
+            88,
+            890,
+            122
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\begin{array}{r l} \\nabla \\Pi_ {u} & = \\frac {1}{s} \\left[ \\begin{array}{c} P _ {1 1} \\\\ P _ {1 2} \\\\ P _ {1 3} \\end{array} \\right] ^ {\\top} - \\frac {u}{s} \\left[ \\begin{array}{c} P _ {3 1} \\\\ P _ {3 2} \\\\ P _ {3 3} \\end{array} \\right] ^ {\\top}, \\end{array} \\\\ \\nabla \\Pi_ {v}   =   \\frac {1}{s} \\left[ \\begin{array}{c} P _ {2 1} \\\\ P _ {2 2} \\\\ P _ {2 3} \\end{array} \\right] ^ {\\top} - \\frac {v}{s} \\left[ \\begin{array}{c} P _ {3 1} \\\\ P _ {3 2} \\\\ P _ {3 3} \\end{array} \\right] ^ {\\top}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            547,
+            133,
+            821,
+            239
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $s = P_{31}X + P_{32}Y + P_{33}Z + P_{34}$  is the projective depth.",
+        "bbox": [
+            498,
+            250,
+            890,
+            279
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Solution. For the problem to be meaningful, we can assume that  $\\mathbf{w}_c \\neq \\mathbf{0}$ . Let us set",
+        "bbox": [
+            498,
+            280,
+            890,
+            310
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI := \\inf  _ {\\| \\mathbf {n} \\| = 1, \\mathbf {n} ^ {\\top} \\mathbf {w} _ {c} \\neq 0} f (\\mathbf {n}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            606,
+            324,
+            782,
+            348
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\| \\mathbf{n}\\| \\coloneqq \\sqrt{\\mathbf{n}^\\top\\mathbf{n}}$  denotes the standard Euclidean norm. Clearly,  $f\\geq 0$  is undefined along the \"equator\" of the unit sphere  $\\| \\mathbf{n}\\| = 1$  with  $\\mathbf{n}^{\\top}\\mathbf{w}_{c} = 0$ . Let us consider two cases.",
+        "bbox": [
+            498,
+            363,
+            890,
+            409
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "If all  $\\mathbf{w}_{ij}$  and  $\\mathbf{w}_c$  are equal, then trivially  $f(\\mathbf{n}) = \\sum_{i,j=1}^{2}(a_{ij} - 1)^2$  is a constant function.",
+        "bbox": [
+            500,
+            410,
+            890,
+            444
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Otherwise, at least one of the expressions  $\\frac{\\mathbf{n}^{\\top}\\mathbf{w}_{ij}}{\\mathbf{n}^{\\top}\\mathbf{w}_{c}}$  becomes arbitrarily large in modulus when  $\\mathbf{n}$  is chosen such that  $\\mathbf{n}^{\\top}\\mathbf{w}_c$  gets sufficiently close to 0; that is,  $|f(\\mathbf{n})|\\to +\\infty$  as  $\\mathbf{n}^{\\top}\\mathbf{w}_c\\rightarrow 0$  with  $\\| \\mathbf{n}\\| = 1$ . Therefore, by taking into account the continuity of  $f$  as well, the infimum  $I$  is in fact a minimum, and an optimal unit vector  $\\mathbf{n}^{*}$  with  $f(\\mathbf{n}^{*}) = I$  exists. In what follows, we will explicitly determine such an  $\\mathbf{n}^{*}$  as a function of the 19 parameters<sup>1</sup> by using only the four basic arithmetic operations.",
+        "bbox": [
+            498,
+            445,
+            890,
+            584
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A key observation is that  $f(\\lambda \\mathbf{n}) = f(\\mathbf{n})$  for any  $\\lambda \\neq 0$ , so (after a possible rescaling) we can assume that the last component of  $\\mathbf{n}$  is either 1 or 0. These cases, Cases A and B, respectively, will be discussed separately below. To simplify the notation, let us define two auxiliary functions",
+        "bbox": [
+            498,
+            585,
+            890,
+            660
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ng \\left(n _ {x}, n _ {y}\\right) := f \\left(n _ {x}, n _ {y}, 1\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            606,
+            674,
+            890,
+            690
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and",
+        "bbox": [
+            500,
+            703,
+            527,
+            715
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh \\left(n _ {x}, n _ {y}\\right) := f \\left(n _ {x}, n _ {y}, 0\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            719,
+            890,
+            736
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For the objective function  $g$ , we will obtain a unique candidate extremum  $\\mathbf{n}_g^* \\in \\mathbb{R}^2$ ; whereas for the function  $h$ , a one-parameter family of candidate extrema  $\\mathbf{n}_h^* \\in \\mathbb{R}^2$  will be found but with the same function value  $h(\\mathbf{n}_h^*)$ . The optimal  $\\mathbf{n}^*$  is then",
+        "bbox": [
+            498,
+            744,
+            890,
+            818
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {n} ^ {*} = \\left\\{ \\begin{array}{l l} \\left[ \\mathbf {n} _ {g} ^ {*}, 1 \\right] ^ {\\top}, & \\text {i f} g \\left(\\mathbf {n} _ {g} ^ {*}\\right) \\leq h \\left(\\mathbf {n} _ {h} ^ {*}\\right), \\\\ \\left[ \\mathbf {n} _ {h} ^ {*}, 0 \\right] ^ {\\top}, & \\text {i f} g \\left(\\mathbf {n} _ {g} ^ {*}\\right) > h \\left(\\mathbf {n} _ {h} ^ {*}\\right). \\end{array} \\right. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            557,
+            829,
+            890,
+            869
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>They are the four affine parameters  $a_{ij}$ , and the 15 components of the vectors  $\\mathbf{w}_{ij}$  and  $\\mathbf{w}_c$ .",
+        "bbox": [
+            500,
+            875,
+            890,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3392",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Remark 1 In other words, we will be utilizing the simple constraints  $n_z = 1$  or  $n_z = 0$ . We have found that other linear or non-linear constraints, such as  $\\| \\mathbf{n} \\| = 1$ , would render the symbolic calculations to minimize the objective function  $f$  infeasible.",
+        "bbox": [
+            73,
+            90,
+            472,
+            167
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Case A:  $n_z = 1$",
+        "bbox": [
+            76,
+            186,
+            189,
+            202
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use the standard technique and solve the system",
+        "bbox": [
+            76,
+            210,
+            419,
+            226
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l} \\partial_ {1} g \\left(n _ {x}, n _ {y}\\right) = 0, \\\\ \\partial_ {2} g \\left(n _ {x}, n _ {y}\\right) = 0 \\end{array} \\right. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            197,
+            238,
+            468,
+            280
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "to find the optimal vector  $\\mathbf{n}_g^* = [n_x, n_y]^\\top$  as follows.",
+        "bbox": [
+            76,
+            290,
+            426,
+            308
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By computing and putting the partial derivative",
+        "bbox": [
+            96,
+            308,
+            410,
+            321
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\partial_ {1} g (n _ {x}, n _ {y})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            228,
+            335,
+            315,
+            353
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "over a common denominator, we see that its numerator depends on  $n_x$  linearly; and it depends on  $n_y$  quadratically; so one can easily express  $n_x$  from the equation  $\\partial_1 g(n_x, n_y) = 0$  as follows:",
+        "bbox": [
+            76,
+            364,
+            468,
+            421
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nn _ {x} = \\frac {\\operatorname {n u m e r} _ {1}}{\\operatorname {d e n o m} _ {1}}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            218,
+            420,
+            468,
+            449
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where we present the expressions for  $\\mathrm{numer}_1$  and  $\\mathrm{denom}_1$  in the supplementary material. Then (6) is substituted into the other partial derivative  $\\partial_2 g(n_x, n_y)$ . The resulting rational function of  $n_y$ , also containing the other 19 parameters, can be simplified and factorized by Wolfram Mathematica's Factor command<sup>2</sup>. In this way, we obtain a fraction whose structure is the following:",
+        "bbox": [
+            76,
+            455,
+            468,
+            560
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\frac {\\operatorname {l i n e a r} _ {1} \\cdot \\operatorname {l i n e a r} _ {2}}{(\\text {q u a d r a t i c}) ^ {2}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            215,
+            571,
+            468,
+            604
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the expressions \"linear\" and \"quadratic\" denote polynomials in  $n_y$  having the corresponding degrees.",
+        "bbox": [
+            76,
+            614,
+            468,
+            645
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The optimum of  $g$  can occur when  $n_y$  is chosen such that the fraction (7), that is, its numerator is equal to 0. It can be shown that the assumption  $\\mathrm{linear}_1 = 0$  leads to a contradiction - indeed, by solving  $\\mathrm{linear}_1 = 0$  for  $n_y$ , the resulting formula would make  $\\mathrm{denom}_1$  in (6) identically equal to 0. Hence, we are only left with the equation  $\\mathrm{linear}_2 = 0$ , whose solution is",
+        "bbox": [
+            76,
+            645,
+            468,
+            750
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nn _ {y} = \\frac {\\operatorname {n u m e r} _ {2}}{\\operatorname {d e n o m} _ {2}}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            218,
+            758,
+            468,
+            787
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The actual formulas for  $\\mathrm{numer}_2$  and  $\\mathrm{denom}_2$  are found again in the supplementary material.",
+        "bbox": [
+            76,
+            797,
+            468,
+            827
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Thus, the second component of  $\\mathbf{n}_g^*$  is given by (8) (expressed in terms of the 19 parameters). Then, by using this together with (6), we obtain  $n_x$ , the first component of  $\\mathbf{n}_g^*$ .",
+        "bbox": [
+            76,
+            828,
+            468,
+            876
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Remark 2 The essential feature of these computations is that the solution of system (5) is given in a fully explicit symbolic form by using only elementary operations. Without the clever intermediate symbolic simplifications and factorizations (most notably (7)), one would need to solve a higher-degree polynomial equation to obtain  $n_y$ , requiring either taking roots or using an iterative scheme. For example, if one starts solving (5) with  $n_x$  and  $n_y$  as symbolic parameters but all the coefficients of  $g$  as floating-point numbers, then, in general, no intermediate factorizations or simplifications are possible, so in order to determine  $n_y$ , one would need to solve a quintic equation.",
+        "bbox": [
+            500,
+            90,
+            893,
+            273
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Case B:  $n_z = 0$",
+        "bbox": [
+            500,
+            290,
+            609,
+            304
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We proceed similarly and solve the system",
+        "bbox": [
+            500,
+            314,
+            782,
+            329
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l} \\partial_ {1} h \\left(n _ {x}, n _ {y}\\right) = 0, \\\\ \\partial_ {2} h \\left(n _ {x}, n _ {y}\\right) = 0. \\end{array} \\right. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            620,
+            337,
+            890,
+            378
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By expressing  $n_x$  from the first equation of (9) and substituting the resulting expression into the second equation, we find that this time the second equation is automatically satisfied. Therefore, (9) possesses a one-parameter family of solutions given by",
+        "bbox": [
+            498,
+            387,
+            892,
+            462
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nn _ {x} = \\frac {\\operatorname {n u m e r} _ {3}}{\\operatorname {d e n o m} _ {3}}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            642,
+            469,
+            890,
+            500
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "see the supplementary material. By substituting this into  $h$ , the function value  $h(\\mathbf{n}_h^*)$  appearing in (4) is obtained as",
+        "bbox": [
+            498,
+            507,
+            890,
+            539
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh \\left(\\mathbf {n} _ {h} ^ {*}\\right) = \\frac {\\operatorname {n u m e r} _ {4}}{\\operatorname {d e n o m} _ {4}}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            630,
+            546,
+            890,
+            575
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "See the supplementary material for details.",
+        "bbox": [
+            500,
+            584,
+            782,
+            599
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Remark 3 One directly checks that the value  $h(\\mathbf{n}_h^*) = h\\left(\\frac{\\mathrm{numer}_3}{\\mathrm{denom}_3}, n_y\\right)$  is indeed independent of  $n_y$ , as claimed.",
+        "bbox": [
+            498,
+            609,
+            890,
+            648
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.1. Summary of the Algorithm",
+        "text_level": 1,
+        "bbox": [
+            500,
+            657,
+            743,
+            672
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Given the elements  $a_{ij} \\in \\mathbb{R}$  in the affine transformation and 3D vectors  $\\mathbf{w}_{ij}$  and  $\\mathbf{w}_c \\neq \\mathbf{0}$ , let us define the function  $f$  by (1) for  $\\mathbf{n}$  with  $\\mathbf{n}^\\top \\mathbf{w}_c \\neq \\mathbf{0}$ , and also define the functions  $g$  and  $h$  by (2)-(3). If  $\\mathbf{w}_{11} = \\mathbf{w}_{12} = \\mathbf{w}_{21} = \\mathbf{w}_{22} = \\mathbf{w}_c$ , then any unit vector  $\\mathbf{n}^*$  can be chosen as optimal normal vector.",
+        "bbox": [
+            498,
+            681,
+            890,
+            755
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Otherwise, we compute  $\\mathbf{n}_g^* \\coloneqq [n_x, n_y]^\\top$  from (8) and (6). Then we compute  $h(\\mathbf{n}_h^*)$  from (11). Finally, the optimal  $\\mathbf{n}^*$  is determined by using (4).",
+        "bbox": [
+            498,
+            756,
+            890,
+            801
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            815,
+            632,
+            830
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We focus on the accuracy and time demand of the algorithms when testing. Both synthetic testing data, including configurations for a number of important camera motions, and standard real-world benchmarks are considered here.",
+        "bbox": [
+            498,
+            840,
+            890,
+            898
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{2}$ https://www.wolfram.com/mathematica/",
+        "bbox": [
+            94,
+            886,
+            316,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "3393",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3361adbf5f991a037b270f6cca617713817d6b0f9a68b30df32547514bbdf2f7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            88,
+            271,
+            188
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/9443b008b2f21844cc9e34eed51e5c36849a35ae5c047f53f1ef7a7de01f9ca6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            272,
+            88,
+            465,
+            188
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/7aa5f0a54ff8a3fb5ede75cbbad692e3c95bd5b99bdad1a20caee658846f7d38.jpg",
+        "image_caption": [
+            "Figure 2. Images and the reference reconstruction used from the Cambridge Landmarks dataset [39] in localization experiments."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            98,
+            202,
+            250,
+            287
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/52da8b4b8b4e061f0e13354f93a23bc7e07fd79f0a4315df454e46bb22dc7e4d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            277,
+            195,
+            464,
+            280
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Compared Algorithms. In this section, we discuss the algorithms that can be used to estimate the surface normal from a single affine correspondence.",
+        "bbox": [
+            76,
+            342,
+            468,
+            388
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. The provably most accurate algorithms are the ones that are optimal in the least squares sense. Method  $\\mathrm{OPT}_{\\mathrm{QUARTIC}}$  refers to [9] which solves the problem as a real root of a quartic polynomial equation. The cubic solution  $\\mathrm{OPT}_{\\mathrm{CUBIC}}$  is from [46]. The proposed optimal solver, as it is solved via linear equations, is called  $\\mathrm{OPT}_{\\mathrm{LINEAR}}$  in the rest of the paper.",
+            "2. The simplest and, thus, the fastest method is the Fast Normal Estimation (FNE) algorithm of [9]. A more complex variant, when all possible linear equations are considered, is also constructed here, it is denoted as  $\\mathrm{FNE}_{\\mathrm{SUPER}}$ . The modified equations can be seen in the source codes in the supplementary material.",
+            "3. Raposo and Barreto [56] proposed a solution that estimates the normal via homographies. We have not found an implementation or an exact definition of the algorithm, so we implemented it based on the description. The solution is computed via an over-determined inhomogeneous linear system of equations. The formulas are generated by the MATLAB Symbolic Toolbox. Details are given in the supplementary material. The method is called RAPOSO in the charts."
+        ],
+        "bbox": [
+            89,
+            396,
+            468,
+            738
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The synthetic tests are performed in MATLAB. In the real-world experiments, optimized  $\\mathrm{C}++$  codes run on an Intel(R) Core(TM) i9-10900K CPU @ 3.70GHz.",
+        "bbox": [
+            76,
+            747,
+            468,
+            792
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1. Synthetic Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For the synthetic tests, a spherical object is generated, thus straightforwardly allowing to sample oriented points from its surface. Two cameras are randomly generated with focal lengths from the range [500, 1500] and with image size  $2000 \\times 2000$ . Their intrinsic matrices are  $\\mathbf{K}_1$  and  $\\mathbf{K}_2$ .",
+        "bbox": [
+            76,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The 3D point was projected into both cameras. The ground truth (GT) affine parameters were calculated directly from the camera parameters and the surface normals as shown in [9]. Several camera configurations are considered to simulate various real-world scenarios. They are as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- For general stereo pose, the locations of the cameras are randomly generated inside a unit-radius sphere. The camera projection matrices are constructed as  $\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]$  and  $\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R} \\mid \\mathbf{t}]$ .",
+            "- For rectified stereo, the cameras are located next to each other with identical orientation. In this case, the projection matrices are  $\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]$  and  $\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{I} \\mid \\mathbf{t}]$ , where  $\\mathbf{t} = [\\Delta X 0 0]^\\top$ .",
+            "- Planar motion simulates the case when a camera is mounted on a vehicle that moves on a planar road with the image plane orthogonal to the ground. Such a motion can be represented by two angles around the vertical axis, one for the rotation and one for the translation. In this case, the projection matrices can be written as  $\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid 0]$  and  $\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_{\\mathrm{Y}} \\mid \\mathbf{t}]$ , where  $\\mathbf{t} = \\rho [\\cos \\beta, 0, \\sin \\beta]^\\top$  and"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {R} _ {\\mathrm {Y}} = \\left[ \\begin{array}{c c c} \\cos \\alpha & 0 & \\sin \\alpha \\\\ 0 & 1 & 0 \\\\ - \\sin \\alpha & 0 & \\cos \\alpha \\end{array} \\right].\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Moto-motion. This test case simulates a camera that is mounted on a motorcycle. If the bike leans, another rotation, the roll is involved in the problem. In this case, the camera parameters are  $\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]$  and  $\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_{\\mathrm{YZ}} \\mid \\mathbf{t}]$ , where  $\\mathbf{t} = \\rho [\\cos \\beta 0 \\sin \\beta]^\\top$  and  $\\mathbf{R}_{YZ} = \\mathbf{R}_Y \\mathbf{R}_Z$ .",
+            "- Drone-motion is another generalization of the planar motion. A camera mounted on a flying drone. Its location is arbitrary, but the orientation is limited to a vertical rotation. Therefore,  $\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]$  and  $\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_Y \\mid \\mathbf{t}]$ , where  $\\mathbf{t} = [X Y Z]^\\top$ ."
+        ],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Noise. We have added zero-mean Gaussian noise to the 2D coordinates, therefore, the point noise is given in pixels. The deviation of the noise is the parameter in the charts.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The  $2 \\times 2$  affine transformations are decomposed by SVD into two 2D rotations and another two scaling parameters. Then zero-mean Gaussian noise is added to the angle of rotations, in radians, and the scaling parameters. The standard deviation of the Gaussian noise distribution is equally set for all the four parameters.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3D Reconstruction Pipeline. In order to simulate real scenarios, first, we triangulate each generated noisy point correspondence by the optimal triangulation method proposed by Hartley and Sturm [29]. The noisy affine parameters are corrected by the method proposed in [7] to be consistent with the camera parameters.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "3394",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/e29247ae079a115614ff62377b1ca561bfb6a47a6f259aefd29da6c614187ebc.jpg",
+        "image_caption": [
+            "Figure 3. The frequencies (in 10000 runs) of the  $\\log_{10}$  errors in the  $\\log_{10}$  angular errors in degrees in the noise-free case."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Stability test. We generated 10000 random problem instances considering general camera motion and ran the normal estimators on noiseless affine correspondences. Fig. 3 shows histograms of  $\\log_{10}$  angular errors in degrees. Note that for better visualization, we replace the exact zero values by  $10^{-16}$  as it is the precision of the floating point numbers in MATLAB. The plots show that all our solvers are very stable – there is no peak close to  $10^0$ . For all methods, the majority of the errors are distributed around  $10^{-16}$  which actually is the precision of MATLAB. This means that in most of the cases, all methods are particularly stable returning almost exactly 0 error. A small peak is over  $10^{-6}$  for all methods similarly. Having  $10^{-6}$  degree error is acceptable in most of the scenarios considered in computer vision. There is no peak close to  $10^0$  implying that all solvers are stable. Note that these stability tests usually are for highlighting potential degeneracies where the error exceeds  $10^0$ .",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We also conducted tests using single-point precision in MATLAB. The OPTQUARTIC approach failed entirely under these conditions. For all other methods, we noticed an increase in error, which suggests that double precision is necessary for reliable normal estimation. Interestingly, our proposed OPTLINEAR method appears to be slightly more sensitive to precision than OPTCUBIC is. This is likely due to the fact that OPTLINEAR employs more complex formulas and, consequently, performs more stably with double precision.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Accuracy test. The accuracy of the normals is examined for all the considered camera poses independently. The results are shown in Fig 9. The effect of noise in point coordinates and affine parameters are separately evaluated. Both the mean and the median of the errors are plotted.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The observations we can make from the plots are as follows. First, the three optimal methods  $\\mathrm{OPT}_{\\mathrm{QUARTIC}}$ ,  $\\mathrm{OPT}_{\\mathrm{CUBIC}}$  and  $\\mathrm{OPT}_{\\mathrm{LINEAR}}$  always lead exactly to the same solution, thus their curves coincide in all plots. Second, the optimal methods always lead to the most accurate results if the affine parameters are contaminated by noise. This is not",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "surprising as these methods optimize the normal parameters such that the implied affine transformation is the closest to the measured one. In the case of point-noise only, the accuracy of the optimal algorithm is slightly below that of the competitors. However, it is an unlikely situation in real-world images to have noisy points but perfect local affine frames. It is usually the other way around. Third, as the FNE method uses less information, it is clearly the worst one in terms of accuracy.  $\\mathrm{FNE}_{\\mathrm{SUPER}}$  performs significantly better, however, it requires more time as the right singular vector of a  $6\\times 3$  matrix, corresponding to the smallest singular value, should be computed. Another benefit of  $\\mathrm{FNE}_{\\mathrm{SUPER}}$  is, contrary to FNE and Raposo [56], that it works in all test cases. It can cope with both planar motion and rectified stereo, similarly to the optimal algorithms.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Problematic methods. Methods FNE and Raposo [56] do not work if the cameras undergo special translations. FNE is a special method, several variants can be formed based on the selection of the affine transformations. For rectified stereo, the third and fourth elements are fixed [44], they cannot be used for the estimation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The Raposo [56] method is the most problematic one as the homography can be decomposed into the camera rotation, translation and surface normal. If the translation has zero elements, the retrieved equations are linearly dependent, and the estimation does not yield a correct solution. Due to this reason, Raposo [56] does not work for rectified stereo and planar motion. We removed these methods from the plots of the respective camera configurations.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Combined noise. In the previous experiments, noise is added either to the point coordinates or affine parameters. Here, we contaminate both types of input data. The mean and median errors of the proposed linear method are visualized in Fig. 10. As it is expected, the curves show similar trends, but the case when both the points and affines are noisy leads to higher errors.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Interpretable affine noise. In the previous experiments, the noise is added directly to the elements of the affine matrices. In Fig. 11, we consider a different way of contaminating the input to show that the proposed method acts reasonably with different noise models as well. The results of curves Aff and Comb are obtained by using the noise model from the previous sections. Comb refers to the case when both the points and the affine matrices are noisy. For AffElem and Comb-Elem, we decompose A by SVD into two orthogonal and a diagonal matrix. Fig. 11 demonstrates that the noise generation does not strongly influence the results.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Real-world Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To test normal estimators, we use the Cambridge Landmarks [39] and ScanNet datasets [18]. We chose Cambridge Landmarks, see Fig. 2 for example images, since it provides a large number of images for testing directly the",
+        "bbox": [
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+        "type": "page_number",
+        "text": "3395",
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+        "img_path": "images/b05dd400a77b1142754bc5e9cc19aa3b8a2e009f68fc685032cd21281077175e.jpg",
+        "image_caption": [
+            "Figure 4. General Motion."
+        ],
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+        "image_caption": [
+            "Figure 5. Rectified Stereo."
+        ],
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+        "image_caption": [
+            "Figure 6. Planar Motion."
+        ],
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+        "image_caption": [
+            "Figure 7. Moto Motion."
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/cdab81ac4f53dee3550ff07f2cb78219f422692eec1625340859fb715ff3ac2e.jpg",
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+        "img_path": "images/2f63d8ff61554da8b97f8bab4cd258b676cb22ba9d136c3c45a1ee820c178455.jpg",
+        "image_caption": [
+            "Figure 9. Average and median angular errors (in degrees) of surface normal estimators on synthetic data. Five camera configurations are considered. From left to right: (1) Median error; noise added to affine parameters. (2) Average error; noise added to affine parameters. (3) Median error; noise added to point coordinates. (4) Average error; noise added to point coordinates."
+        ],
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+        "image_caption": [
+            "Figure 8. Drone Motion."
+        ],
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+    {
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+    {
+        "type": "text",
+        "text": "normal accuracy and, also, we can evaluate localization as an application of the proposed procedure. Also, we chose ScanNet since the reference normals can be calculated directly from the dense depth maps which provides a complementary comparison to the tests on Cambridge Landmarks,",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where the normals come from a 3D reconstruction.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Cambridge Landmarks consists of five scenes with varying number of images, ranging from 231 to 3015. The reference pose of each image was reconstructed using the VisualSFM structure-from-motion software [70, 69] and the",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "3396",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
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+        "img_path": "images/afe3cccb487e6fa90b540974d96e7f2bfb61553b1921b007398e949eb17c0d4b.jpg",
+        "image_caption": [
+            "Figure 10. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to point coordinates (Point), affine parameters (Affine) or both (Combined)."
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/cfa87fde61ea568549103ddeb3b6007b3743ace39c2b1b98cf661245e154abdd.jpg",
+        "image_caption": [
+            "Figure 11. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to only the affine  $(A\\text{ff})$  elements and, also, to the point coordinates  $(Comb)$ . For Aff and Comb, zero-mean Gaussian noise is added directly to the affine elements. For Aff-Elem and Comb-Elem, the affine matrix is decomposed by SVD to two rotations and a diagonal matrix. Zero-mean Gaussian noise is added to the rotation angles and diagonal elements."
+        ],
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/166482e29d8bfca0ca6612feb0cd377d7bca63f7c3742e99f5ecb687fe59ba8c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "images are divided into training and testing sets. To have more accurate reference data, we ran COLMAP [63] obtaining a dense point cloud. Finally, we applied the normal estimator implemented in MeshLab<sup>3</sup> to obtain an oriented point cloud to be considered reference. The normals are fitted to the 200 nearest neighbors. For each query image, we ran DenseVLAD [67] to get 20 potential database images. In our experiments, the algorithms are tested on each obtained image pair, i.e., 20 pairs for each query image. For ScanNet, we use the 1500 image pairs used in [59].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "On Cambridge Landmarks, we detect affine correspondences by detecting DoG features [42], finding the affine shape by AffNet [48], and extracting HardNet [47] descriptors. This approach is among the leaders in the IMC 2020 benchmark [34]. On ScanNet, we detect SuperPoint [20] features, match them by SuperGlue [59], and find the affine shape by, first, estimating scale and orientation by SelfScaleOri [41] and, then, finding the affine shapes by AffNet.",
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+    },
+    {
+        "type": "text",
+        "text": "Normal Estimation. To test normal estimators, we ran all of them on the data described in the previous section. For each image pair, we iterate through all detected correspondences that are consistent with the camera pose - they have less than 5 pixels of Sampson distance. For each of",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/1bb67d9598776c047ef3944af4a4be4982d425f647c69f790568eade56b61920.jpg",
+        "image_caption": [
+            "Figure 12. The median angular error in degrees (left) and the AUC@  $10^{\\circ}$  score (right) of the estimated normals plotted as a function of the error in the detected affine correspondences on the Cambridge Landmarks dataset."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/4b414b70d67b0597142c805eaa4d8ea1d857e02ceaa495e357e61aa2c07afe43.jpg",
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+    {
+        "type": "text",
+        "text": "them, we ran multiple normal estimators, measure their angular error and run-time. To understand how the estimators proceed with respect to the error in the detected affine transformations  $\\mathbf{A}$ , we calculate the reference transformation  $\\mathbf{A}^*$  from the camera parameters and the surface normal as shown in [9]. We define the affine error as the Frobenius norm of the difference matrix  $\\| \\mathbf{A} - \\mathbf{A}^* \\|_{\\mathrm{F}}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The Area Under the recall Curve (AUC) at  $5^{\\circ}$ ,  $10^{\\circ}$  and  $20^{\\circ}$ , the avg. and med. angular errors with the standard deviation in degrees and the run-time in nanoseconds on the Cambridge Landmarks dataset are reported in Table 1. As expected, the best results are achieved by the optimal algorithms, all of them leading to exactly the same results. Our proposed linear solution of the optimal problem,  $\\mathrm{OPT}_{\\mathrm{LINEAR}}$ , is five times faster than the cubic solution  $\\mathrm{OPT}_{\\mathrm{CUBIC}}$ . While  $\\mathrm{OPT}_{\\mathrm{LINEAR}}$  is slightly slower than the fastest FNE method, it is significantly more accurate. Interestingly, while the method of Raposo et al. [56] worked well in the synthetic experiments, we did not manage to achieve good accuracy with it in the real-world experiments. Figure 12 plots the AUC@ $10^{\\circ}$  score and the median angular error as a function of the noise in the detected affine parameters. As expected, normal estimation is highly sensitive to the quality of the affine parameters. The optimal algorithms are the most stable ones.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The results on the ScanNet dataset are reported in Table 3. Similarly as on Cambridge Landmarks, all optimal solvers lead to the same accuracy while the proposed one being the fastest by a large margin.",
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+    },
+    {
+        "type": "text",
+        "text": "Visual Localization. To test the impact of surface normal estimation on localization, on the Cambridge Landmarks dataset, we applied the following procedure. We iterate through all query images, each having 10 database images retrieved by DenseVLAD. First, we estimate the relative pose between the query and a random database image by GC-RANSAC [6] with P3P [54]. Using the obtained pose, we estimate the surface normal of each inlier affine correspondence in the coordinate system of the query image. Next, we iterate through all unused database images and use",
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+        "page_idx": 7
+    },
+    {
+        "type": "page_footnote",
+        "text": "3Meshlab is an open source tool for 3D point cloud processing and visualization.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "3397",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/45c1e3e795772d2512d0efa644949931b2a50682507161b861e38e33bdd7e804.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Estimator</td><td>AUC@5°↑</td><td>@10°↑</td><td>@20°↑</td><td>Avg. err. (°) ↓</td><td>Med. err. (°) ↓</td><td>Std. dev. (°) ↓</td><td>Time (ns) ↓</td></tr><tr><td>FNE [49]</td><td>6.0</td><td>16.0</td><td>33.7</td><td>21.0</td><td>14.3</td><td>21.3</td><td>172</td></tr><tr><td>FNESUPER</td><td>8.9</td><td>22.1</td><td>42.0</td><td>10.9</td><td>16.8</td><td>15.6</td><td>1721</td></tr><tr><td>Raposo [56]</td><td>0.4</td><td>1.5</td><td>5.7</td><td>38.5</td><td>36.5</td><td>18.2</td><td>883</td></tr><tr><td>OPTQUARTIC [9]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2528</td></tr><tr><td>OPTCUBIC [46]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2484</td></tr><tr><td>Proposed OPTLINEAR</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>596</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/409f1644eb0b6a4ba44a6d75210ee1b851d9740d437615c5d1072035b03d04fe.jpg",
+        "table_caption": [
+            "Table 1. The AUC score at  $5^{\\circ}$ ,  $10^{\\circ}$ , and  $20^{\\circ}$  of the estimated surface normals, their average and median errors in degrees, the standard deviation, and the average run-time, in nanoseconds, of a single normal estimation on the Cambridge Landmarks dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Solver</td><td rowspan=\"2\">Normal estimator</td><td colspan=\"3\">Pose accuracy ↑</td><td rowspan=\"2\">Med. rot. err. (°) ↓</td><td rowspan=\"2\">Med. pos. err. (cm) ↓</td></tr><tr><td>AUC@1°, 10cm</td><td>@2.5°, 25cm</td><td>@5°, 50cm</td></tr><tr><td>P3P</td><td>-</td><td>44.3</td><td>59.1</td><td>67.5</td><td>10.1</td><td>13.5</td></tr><tr><td>P1AC</td><td>FNESUPER</td><td>47.8</td><td>62.0</td><td>69.7</td><td>6.2</td><td>12.8</td></tr><tr><td>P1AC</td><td>Proposed OPTLINEAR</td><td>48.0</td><td>62.3</td><td>69.9</td><td>5.2</td><td>1.8</td></tr><tr><td>P1AC</td><td>GT</td><td>48.4</td><td>62.9</td><td>70.4</td><td>4.6</td><td>2.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/a8f46f017481fc6419eba75c72b1d0cd8120a2ac64ab9d492c127ad9e343b269.jpg",
+        "table_caption": [
+            "Table 2. Localization AUC scores at  $(1^{\\circ}, 10\\mathrm{cm})$ ,  $(2.5^{\\circ}, 25\\mathrm{cm})$ , and  $(5^{\\circ}, 50\\mathrm{cm})$ , the median rotation (in degrees) and translation errors (in centimeters) on the Cambridge Landmarks dataset [39] when using either the P3P solver or the normal-based P1AC solver with FNEsuper or the proposed surface normal estimator OPTLINEAR. We also show the results with the reference normals. The minimal solvers are used within Graph-Cut RANSAC [6] that takes care of the robust estimation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>AUC@5↑</td><td>AUC@10↑</td><td>AUC@20↑</td><td>Time (ns)↓</td></tr><tr><td>FNE</td><td>14.8</td><td>15.4</td><td>17.0</td><td>207</td></tr><tr><td>FNESUPER</td><td>34.9</td><td>35.2</td><td>36.6</td><td>2142</td></tr><tr><td>OPTQUARTIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>18745</td></tr><tr><td>OPTCUBIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>3146</td></tr><tr><td>OPTLINEAR</td><td>35.0</td><td>35.5</td><td>37.3</td><td>747</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "the P1AC [68] solver inside GC-RANSAC to estimate the pose. P1AC requires a single AC and the surface normal. We only test the proposed solver and  $\\mathrm{FNE}_{\\mathrm{SUPER}}$ . All other optimal solvers lead exactly to the same accuracy as ours.  $\\mathrm{FNE}_{\\mathrm{SUPER}}$  is the most accurate sub-optimal algorithm.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The accuracy of the estimated pose for the database images with respect to their GT pose is reported in Table 2. All solvers, benefiting from normals and affine correspondences, are more accurate than using P3P. We also report the accuracy when using the reference normals to see the upper bound achievable using normals. The proposed optimal solver OPT LINEAR is only slightly (i.e.  $< 1$  AUC point) behind the accuracy of the GT normal, while being more accurate than the P3P-based solution. The AUC@  $10^{\\circ}$  scores on each scene are reported in Table 4. The proposed OPT LINEAR leads to the best accuracy on all but two scenes.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusions",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this work, we have presented a novel solver for estimating surface normals from affine correspondences when having calibrated cameras. The proposed method yields the",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/5dafa51b1ca9af1e1eab02f97d156dbeeca9a3d0a97c8f5f42a93489b1ea6b7f.jpg",
+        "table_caption": [
+            "Table 3. The AUC scores at  $5^{\\circ}$ ,  $10^{\\circ}$  and  $20^{\\circ}$ , and the avg. time (in nanoseconds) of normal estimators on the ScanNet datasets [18]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">P3P</td><td colspan=\"3\">P1AC</td></tr><tr><td>GT</td><td>FNESUPER</td><td>Prop. OPTLINEAR</td></tr><tr><td>St. Mary&#x27;s Church</td><td>44.2</td><td>47.7</td><td>46.1</td><td>46.5</td></tr><tr><td>Old Hospital</td><td>44.1</td><td>57.4</td><td>56.8</td><td>57.3</td></tr><tr><td>King&#x27;s College</td><td>52.1</td><td>54.2</td><td>54.1</td><td>54.0</td></tr><tr><td>Shop Facade</td><td>65.5</td><td>65.0</td><td>63.8</td><td>64.1</td></tr><tr><td>Great Court</td><td>62.7</td><td>63.2</td><td>63.0</td><td>63.5</td></tr><tr><td>Street</td><td>17.4</td><td>22.8</td><td>23.1</td><td>23.0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 4. The area under the recall curve (AUC) at  $1^{\\circ}$  rotation and 10cm position errors on the Cambridge Landmarks dataset. We combine the P1AC solver with  $\\mathrm{FNE}_{\\mathrm{SUPER}}$  and the proposed normal estimator. Also, we test it with the reference normals.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "optimal solution, in the least squares sense, with respect to the affine error, and is particularly fast as the optimal normal is obtained via linear equations. We compared our method to all existing alternatives that estimate normals from a single correspondence on both simulated and real-world data. Additionally, we provide tests that highlight the benefits of using surface normals in image-based localization. The proposed estimator has demonstrated superior accuracy compared to the fastest existing method while being the second fastest overall. Our results suggest that the proposed algorithm is a promising alternative for surface normal estimation in computer vision applications.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. The authors warmly thank the reviewers for their very valuable comments and suggestions. The work was supported by the ETH Postdoc fellowship.",
+        "bbox": [
+            498,
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+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "3398",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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+        ],
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+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[55] Carolina Raposo and Joao P Barreto. Theory and practice of structure-from-motion using affine correspondences. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5470-5478, 2016.",
+            "[56] Carolina Raposo and João Pedro Barreto. Accurate reconstruction of oriented 3d points using affine correspondences. In ECCV, volume 12373, pages 545-560. Springer, 2020.",
+            "[57] Edward Rosten and Tom Drummond. Machine learning for high-speed corner detection. In Proceedings of the 9th European Conference on Computer Vision - Volume Part I, ECCV'06, pages 430-443, Berlin, Heidelberg, 2006. Springer-Verlag.",
+            "[58] E. Rublee, V. Rabaud, K. Konolidge, and G. Bradski. ORB: An Efficient Alternative to SIFT or SURF. In ICCV, 2011.",
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+            "[62] Johannes L. Schonberger and Jan-Michael Frahm. Structure-from-motion revisited. In CVPR, 2016.",
+            "[63] Johannes L Schonberger and Jan-Michael Frahm. Structure-from-motion revisited. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4104-4113, 2016.",
+            "[64] Agnes Seiler, David Großmann, and Bert Jüttler. Spline surface fitting using normal data and norm-like functions. Comput. Aided Geom. Des., 64:37-49, 2018.",
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+        ],
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+            501,
+            90,
+            892,
+            900
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "3400",
+        "bbox": [
+            482,
+            944,
+            516,
+            955
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[69] Changchang Wu. Towards linear-time incremental structure from motion. In 2013 International Conference on 3D Vision-3DV 2013, pages 127-134. IEEE, 2013.",
+            "[70] Changchang Wu, Sameer Agarwal, Brian Curless, and Steven M Seitz. Multicore bundle adjustment. In CVPR 2011, pages 3057-3064. IEEE, 2011.",
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+            "[72] Siyu Zhu, Runze Zhang, Lei Zhou, Tianwei Shen, Tian Fang, Ping Tan, and Long Quan. Very large-scale global sfm by distributed motion averaging. In CVPR, 2018."
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "3401",
+        "bbox": [
+            482,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 11
+    }
+]
\ No newline at end of file
diff --git a/2023/Fast Globally Optimal Surface Normal Estimation from an Affine Correspondence/ecc07b62-9596-44a0-9745-a517e83aa84a_model.json b/2023/Fast Globally Optimal Surface Normal Estimation from an Affine Correspondence/ecc07b62-9596-44a0-9745-a517e83aa84a_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..4b44ddfacb1b8b1213f5b9e269554ceefa34477b
--- /dev/null
+++ b/2023/Fast Globally Optimal Surface Normal Estimation from an Affine Correspondence/ecc07b62-9596-44a0-9745-a517e83aa84a_model.json	
@@ -0,0 +1,3062 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.127,
+                0.131,
+                0.844,
+                0.154
+            ],
+            "angle": 0,
+            "content": "Fast Globally Optimal Surface Normal from an Affine Correspondence"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.126,
+                0.182,
+                0.493,
+                0.253
+            ],
+            "angle": 0,
+            "content": "Levente Hajder, Lajos Lóczi  \nGeometric Computer Vision Group  \nEötvös Loránd University, Budapest, Hungary  \n{hajder, lloczi}@inf.elte.hu"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.534,
+                0.182,
+                0.844,
+                0.252
+            ],
+            "angle": 0,
+            "content": "Daniel Barath  \nComputer Vision and Geometry Group  \nETH Zurich, Switzerland  \ndbarath@inf.ethz.ch"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.287,
+                0.314,
+                0.303
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.318,
+                0.474,
+                0.606
+            ],
+            "angle": 0,
+            "content": "We present a new solver for estimating a surface normal from a single affine correspondence in two calibrated views. The proposed approach provides a new globally optimal solution for this over-determined problem and proves that it reduces to a linear system that can be solved extremely efficiently. This allows for performing significantly faster than other recent methods, solving the same problem and obtaining the same globally optimal solution. We demonstrate on \\(15k\\) image pairs from standard benchmarks that the proposed approach leads to the same results as other optimal algorithms while being, on average, five times faster than the fastest alternative. Besides its theoretical value, we demonstrate that such an approach has clear benefits, e.g., in image-based visual localization, due to not requiring a dense point cloud to recover the surface normal. We show on the Cambridge Landmarks dataset that leveraging the proposed surface normal estimation further improves localization accuracy. Matlab and \\(C++\\) implementations are also published in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.634,
+                0.21,
+                0.65
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Acquiring oriented point clouds is a fundamental problem both in computer vision and in robotics with a number of important real-world applications benefiting from the extra information it provides. Such applications include 3D reconstruction [1, 8, 31, 62, 72, 65, 56] and simultaneous localization and mapping [19, 23, 50], where the 3D point orientations provide useful information about the underlying structure. Image-based visual localization approaches [43, 53, 60, 61] can also benefit from known surface normals [68]. The widely used Poisson reconstruction [37, 38] is based on both the point coordinates and their orientations. The visual odometry [51, 52] of an autonomous vehicle can also benefit from understanding surface orientation to, e.g., segment ground or facades. Also, having an oriented point cloud greatly simplifies geometric model and multi-model estimation [32, 4, 5] due to allowing to design solvers that"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.527,
+                0.29,
+                0.866,
+                0.413
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.43,
+                0.895,
+                0.488
+            ],
+            "angle": 0,
+            "content": "Figure 1. Geometric configuration: oriented 3D point \\(\\mathbf{P} \\in \\mathbb{E}^3\\) with normal \\(\\mathbf{n} \\in \\mathbb{E}^3\\) projected to image \\(\\Pi^1\\) as \\(\\mathbf{p}_1 \\in \\mathbb{E}^2\\) and to \\(\\Pi^2\\) as \\(\\mathbf{p}_2 \\in \\mathbb{E}^2\\). The local patch centered at points \\(\\mathbf{p}_1\\) and \\(\\mathbf{p}_2\\) are related by the local affine transformation \\(\\mathbf{A} \\in \\mathbb{R}^{2 \\times 2}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.519,
+                0.895,
+                0.656
+            ],
+            "angle": 0,
+            "content": "require fewer data points than their point-based counterparts [64]. Moreover, normals can also be leveraged in the numerical refinement of the reconstructed oriented 3D point cloud [27]. In this paper, we focus on a practical problem, i.e., estimating the normal at corresponding features in two images in a solely photometric manner. This can provide a lightweight approach of obtaining surface normals without requiring a dense point cloud to be known. Next, we will discuss ways of obtaining oriented points."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Normals from Point Clouds. After applying state-of-the-art sparse (e.g., COLMAP [63]) or dense [36, 16] reconstruction pipelines, the resulting point cloud can be straightforwardly equipped with point orientations. In this case, typically, the normals are fitted per-point, applying the widely used Principal Component Analysis (PCA) [35] to estimate tangent planes or higher-order surfaces [14, 33] from the local neighborhood centered at the current point. This procedure, while being frequently used, has two major drawbacks. First, the setting of the neighborhood size greatly affects the accuracy and is often unclear without having a metric reconstruction. Instead, using the \\(k\\)-nearest-neighbors [17] algorithm to find local neighborhoods is a viable solution, but the estimation becomes largely affected by the sparsity of the point cloud. Second, fitting local surfaces, independently, to the neighborhood of each 3D point"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3390"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.46,
+                0.108
+            ],
+            "angle": 0,
+            "content": "in the reconstruction is an extremely expensive operation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.109,
+                0.468,
+                0.29
+            ],
+            "angle": 0,
+            "content": "Normals from Homographies. Another method for estimating surface normals from images, without requiring the underlying 3D structure to be known, is via homographies. Homographies are projective transformations between images of co-planar 3D points that depends on the intrinsic and extrinsic camera parameters and the parameters of the underlying 3D plane [24]. A homography can be estimated from a minimum of four point correspondences in two images [30]. While this method allows the estimation of dominant planes supported by a number of correspondences in the images, it does not provide means for normal estimation for each local feature correspondence independently."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.293,
+                0.468,
+                0.475
+            ],
+            "angle": 0,
+            "content": "Normals from Local Mappings. In recent years, affine correspondences (AC) have emerged as a popular topic in computer vision, offering a valuable source of information about the underlying 3D geometry of the surrounding environment. An AC consists of a corresponding pair of points in two images and a linear transformation that maps the infinitesimal region around the point in the first image to the point in the second one. They have been used to solve various geometric problems, including relative pose estimation in the general case [15, 55, 3, 22, 10], for known vertical direction [25], planar motion [25, 26], or known feature depths [21] and homography estimation [2]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.476,
+                0.468,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Traditionally, finding affine features involve four main steps: (scale-covariant) keypoint detection, orientation and affine shape estimation, and descriptor extraction. Under such paradigm, keypoint detection is typically performed on the scale pyramid with the help of a handcrafted response function, such as Hessian [13, 45], Harris [28, 45], Difference of Gaussians (DoG [42]), or learned ones like FAST [57] or Key.Net [11]. Keypoint detection obtains a triplet \\((x,y,\\mathrm{scale})\\) which defines a square or circular image patch. Then the patch orientation is estimated with the help of handcrafted - dominant gradient orientation [42], center of the mass [58] - or learned methods [71, 48, 41]. Next, the affine-covariant shape [12, 48] is estimated. Finally, the patch is geometrically rectified and fed into a local patch descriptor, such as SIFT, HardNet [47], SOSNet [66], or others. In summary, all feature detectors, even recent learning-based ones like SuperPoint [20], can be made affine covariant by applying, e.g., AffNet [48] as a post-processing step on the found features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The problem of surface normal estimation from ACs has been addressed in several works. The first algorithm for normal estimation from ACs was proposed by Kevin Koeser [40] assuming that the camera location is known with respect to the observed 3D point. Megyesi et al. [44] proposed a special surface normal estimator for standard (rectified) stereo, where the degree of freedom of the affine transformations decreases to two. In 2014, Molnár and Chetverikov [49] derived a formula connecting the surface"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "normals, camera parameters, affine transformations, and patch locations into a single expression for arbitrary projective functions, like the catadioptric camera model. Barath et al. [9] proposed a globally optimal estimator in the least squares sense as the solution of a quartic polynomial. Recently, Le Minh and Hajder [46] improved on this by reducing the degree and showed that the optimal solution can be found as a real root of a cubic polynomial."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.213,
+                0.892,
+                0.318
+            ],
+            "angle": 0,
+            "content": "The main goal of this paper is to propose a rapid normal estimator based on affine correspondences. Our algorithm can be inserted into a 3D reconstruction system, such as Structure-from-Motion [27] (SfM) or Simultaneous Localization and Mapping (SLAM), where the normal estimation is performed many times, therefore its running time influences the time demand of the whole 3D pipeline."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.319,
+                0.892,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Contribution. In this paper, we propose a new linear and globally optimal solution for surface normal estimation from a single affine correspondence. The proposed solver requires only the four basic arithmetic operations and contains 19 parameters, consisting of the coordinates of the five input vectors and the four affine parameters. This approach completely avoids root extractions, solving high-degree polynomial equations, or employing numerical or iterative methods, resulting in a particularly fast algorithm that runs for only \\(0.6\\mu s\\) in our experiments. The solver is five times faster than the cubic solver from [46]. Additionally, we propose a way of exploiting AC-wise normals in image-based visual localization pipelines. The algorithms are tested on 15k image pairs from standard benchmarks, and our results show superior accuracy and faster wall-clock times compared to the baselines."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.574,
+                0.673,
+                0.59
+            ],
+            "angle": 0,
+            "content": "2. Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.765
+            ],
+            "angle": 0,
+            "content": "The setting is visualized in Fig 1. We are given two images, denoted by \\(\\Pi^1\\) and \\(\\Pi^2\\). The 2D and 3D point locations are visualized as black dots. For standard PC-based stereo vision, the 3D location can be obtained by the so-called triangulation method. The local affine transformation, denoted by \\(\\mathbf{A} \\in \\mathbb{R}^{2 \\times 2}\\), is defined as the first-order Taylor-approximation of the imaging function at points \\(\\mathbf{p}_1\\) and \\(\\mathbf{p}_2\\). It maps the infinitesimal patch around the observed points from the first to the second image. If \\(\\mathbf{A}\\) is known, the surface normal \\(\\mathbf{n}\\) can be directly estimated without knowing the actual 3D structure of the underlying scene [49]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Parameterization. A surface normal \\(\\mathbf{n} \\in \\mathbb{R}^3\\) is a 3D direction, therefore it can be represented by two parameters. Usually, it is parameterized by three coordinates \\(\\mathbf{n} = [n_x, n_y, n_z]^\\top\\) and its length being set to 1. However, as it turns out below, some other scaling will be more convenient in the present situation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Problem Statement. Let us assume that we are given a general camera that projects the spatial location \\(\\mathbf{P} = [X, Y, Z]^\\top\\) to image (pixel) coordinates \\([u v]^\\top\\), and let us"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3391"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "denote the projective coordinate functions by \\(\\Pi_u: \\mathbb{E}^3 \\to \\mathbb{R}\\) and \\(\\Pi_v: \\mathbb{E}^3 \\to \\mathbb{R}\\). Function \\(\\Pi_u\\) calculates coordinate \\(u\\) of the projected point, and \\(\\Pi_v\\) calculates \\(v\\). As Molnár and Chetverikov showed [49], the affine transformation can be defined via the spatial gradients of the projective coordinate functions \\(\\Pi_u\\) and \\(\\Pi_v\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.183,
+                0.469,
+                0.305
+            ],
+            "angle": 0,
+            "content": "An affine correspondence is represented by 2D image coordinates \\([u_1 v_1]^\\top\\) and \\([u_2 v_2]^\\top\\) in the stereo image pair, in conjunction with the affine transformation \\(\\mathbf{A}\\) that maps the surrounding area of the locations from first image to the second one. The spatial location of the corresponding spatial point is also required. It can be estimated from the image coordinates and camera parameters by standard triangulation techniques [29]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.306,
+                0.469,
+                0.336
+            ],
+            "angle": 0,
+            "content": "The normal estimation problem is written [9] as an argument minimization to determine the optimal \\(\\mathbf{n}^*\\) such that"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.204,
+                0.35,
+                0.341,
+                0.371
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {n} ^ {*} = \\operatorname * {a r g   m i n} _ {\\mathbf {n}} f (\\mathbf {n}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.383,
+                0.111,
+                0.395
+            ],
+            "angle": 0,
+            "content": "with"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.395,
+                0.469,
+                0.437
+            ],
+            "angle": 0,
+            "content": "\\[\nf (\\mathbf {n}) := \\sum_ {i = 1} ^ {2} \\sum_ {j = 1} ^ {2} \\left(\\frac {\\mathbf {n} ^ {\\top} \\mathbf {w} _ {i j}}{\\mathbf {n} ^ {\\top} \\mathbf {w} _ {c}} - a _ {i j}\\right) ^ {2}. \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.446,
+                0.469,
+                0.477
+            ],
+            "angle": 0,
+            "content": "Here, the affine transformation yields the four affine parameters \\( a_{ij} \\) (\\( i,j\\in [1,2] \\)) according to"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.202,
+                0.488,
+                0.344,
+                0.523
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {A} = \\left[ \\begin{array}{c c} a _ {1 1} & a _ {1 2} \\\\ a _ {2 1} & a _ {2 2} \\end{array} \\right],\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.534,
+                0.469,
+                0.564
+            ],
+            "angle": 0,
+            "content": "and the vectors \\(\\mathbf{w}_{ij}\\) and \\(\\mathbf{w}_c\\) are obtained as cross products of the spatial gradient vectors as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.104,
+                0.576,
+                0.408,
+                0.623
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathbf {w} _ {1 1} = \\nabla \\Pi_ {v} ^ {1} \\times \\nabla \\Pi_ {u} ^ {2}, \\quad \\mathbf {w} _ {1 2} = \\nabla \\Pi_ {u} ^ {2} \\times \\nabla \\Pi_ {u} ^ {1}, \\\\ \\mathbf {w} _ {2 1} = \\nabla \\Pi_ {v} ^ {1} \\times \\nabla \\Pi_ {v} ^ {2}, \\quad \\mathbf {w} _ {2 2} = \\nabla \\Pi_ {v} ^ {2} \\times \\nabla \\Pi_ {u} ^ {1}, \\\\ \\mathbf {w} _ {c} = \\nabla \\Pi_ {u} ^ {1} \\times \\nabla \\Pi_ {v} ^ {1}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.636,
+                0.469,
+                0.682
+            ],
+            "angle": 0,
+            "content": "where the superscripts refer to the corresponding image index. The coordinates of these vectors will be denoted by \\(\\mathbf{w}_{ij,x},\\mathbf{w}_{ij,y},\\mathbf{w}_{ij,z}\\) \\((i,j\\in \\{1,2\\})\\) and \\(\\mathbf{w}_{c,x},\\mathbf{w}_{c,y},\\mathbf{w}_{c,z}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.682,
+                0.469,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Pin-hole (perspective) projection model. For a pin-hole camera, the projection model is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.116,
+                0.724,
+                0.432,
+                0.788
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left[ \\begin{array}{c} u \\\\ v \\\\ 1 \\end{array} \\right] \\sim \\left[ \\begin{array}{c c c c} P _ {1 1} & P _ {1 2} & P _ {1 3} & P _ {1 4} \\\\ P _ {2 1} & P _ {2 2} & P _ {2 3} & P _ {2 4} \\\\ P _ {3 1} & P _ {3 2} & P _ {3 3} & P _ {3 4} \\end{array} \\right] \\left[ \\begin{array}{c} X \\\\ Y \\\\ Z \\\\ 1 \\end{array} \\right],\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.8,
+                0.469,
+                0.829
+            ],
+            "angle": 0,
+            "content": "where \\(\\sim\\) denotes the equality up to scale operation. Therefore, image coordinates \\(u\\) and \\(v\\) are obtained as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.128,
+                0.84,
+                0.384,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\Pi_ {u} = \\frac {P _ {1 1} X + P _ {1 2} Y + P _ {1 3} Z + P _ {1 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}, \\\\ \\Pi_ {v} = \\frac {P _ {2 1} X + P _ {2 2} Y + P _ {2 3} Z + P _ {2 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.089,
+                0.892,
+                0.123
+            ],
+            "angle": 0,
+            "content": "Spatial gradients, that are \\(\\nabla \\Pi = \\left[ \\begin{array}{ccc}\\frac{\\partial\\Pi}{\\partial X} & \\frac{\\partial\\Pi}{\\partial Y} & \\frac{\\partial\\Pi}{\\partial Z} \\end{array} \\right]^{\\top}\\), can be written for the pin-hole model in compact forms as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.549,
+                0.135,
+                0.822,
+                0.24
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\begin{array}{r l} \\nabla \\Pi_ {u} & = \\frac {1}{s} \\left[ \\begin{array}{c} P _ {1 1} \\\\ P _ {1 2} \\\\ P _ {1 3} \\end{array} \\right] ^ {\\top} - \\frac {u}{s} \\left[ \\begin{array}{c} P _ {3 1} \\\\ P _ {3 2} \\\\ P _ {3 3} \\end{array} \\right] ^ {\\top}, \\end{array} \\\\ \\nabla \\Pi_ {v}   =   \\frac {1}{s} \\left[ \\begin{array}{c} P _ {2 1} \\\\ P _ {2 2} \\\\ P _ {2 3} \\end{array} \\right] ^ {\\top} - \\frac {v}{s} \\left[ \\begin{array}{c} P _ {3 1} \\\\ P _ {3 2} \\\\ P _ {3 3} \\end{array} \\right] ^ {\\top}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.251,
+                0.891,
+                0.28
+            ],
+            "angle": 0,
+            "content": "where \\( s = P_{31}X + P_{32}Y + P_{33}Z + P_{34} \\) is the projective depth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.281,
+                0.891,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Solution. For the problem to be meaningful, we can assume that \\(\\mathbf{w}_c \\neq \\mathbf{0}\\). Let us set"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.607,
+                0.325,
+                0.783,
+                0.349
+            ],
+            "angle": 0,
+            "content": "\\[\nI := \\inf  _ {\\| \\mathbf {n} \\| = 1, \\mathbf {n} ^ {\\top} \\mathbf {w} _ {c} \\neq 0} f (\\mathbf {n}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.364,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "where \\(\\| \\mathbf{n}\\| \\coloneqq \\sqrt{\\mathbf{n}^\\top\\mathbf{n}}\\) denotes the standard Euclidean norm. Clearly, \\(f\\geq 0\\) is undefined along the \"equator\" of the unit sphere \\(\\| \\mathbf{n}\\| = 1\\) with \\(\\mathbf{n}^{\\top}\\mathbf{w}_{c} = 0\\). Let us consider two cases."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.411,
+                0.891,
+                0.445
+            ],
+            "angle": 0,
+            "content": "If all \\(\\mathbf{w}_{ij}\\) and \\(\\mathbf{w}_c\\) are equal, then trivially \\(f(\\mathbf{n}) = \\sum_{i,j=1}^{2}(a_{ij} - 1)^2\\) is a constant function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.446,
+                0.892,
+                0.585
+            ],
+            "angle": 0,
+            "content": "Otherwise, at least one of the expressions \\(\\frac{\\mathbf{n}^{\\top}\\mathbf{w}_{ij}}{\\mathbf{n}^{\\top}\\mathbf{w}_{c}}\\) becomes arbitrarily large in modulus when \\(\\mathbf{n}\\) is chosen such that \\(\\mathbf{n}^{\\top}\\mathbf{w}_c\\) gets sufficiently close to 0; that is, \\(|f(\\mathbf{n})|\\to +\\infty\\) as \\(\\mathbf{n}^{\\top}\\mathbf{w}_c\\rightarrow 0\\) with \\(\\| \\mathbf{n}\\| = 1\\). Therefore, by taking into account the continuity of \\(f\\) as well, the infimum \\(I\\) is in fact a minimum, and an optimal unit vector \\(\\mathbf{n}^{*}\\) with \\(f(\\mathbf{n}^{*}) = I\\) exists. In what follows, we will explicitly determine such an \\(\\mathbf{n}^{*}\\) as a function of the 19 parameters<sup>1</sup> by using only the four basic arithmetic operations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.586,
+                0.892,
+                0.661
+            ],
+            "angle": 0,
+            "content": "A key observation is that \\( f(\\lambda \\mathbf{n}) = f(\\mathbf{n}) \\) for any \\( \\lambda \\neq 0 \\), so (after a possible rescaling) we can assume that the last component of \\( \\mathbf{n} \\) is either 1 or 0. These cases, Cases A and B, respectively, will be discussed separately below. To simplify the notation, let us define two auxiliary functions"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.607,
+                0.675,
+                0.891,
+                0.691
+            ],
+            "angle": 0,
+            "content": "\\[\ng \\left(n _ {x}, n _ {y}\\right) := f \\left(n _ {x}, n _ {y}, 1\\right) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.704,
+                0.529,
+                0.717
+            ],
+            "angle": 0,
+            "content": "and"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.605,
+                0.72,
+                0.891,
+                0.737
+            ],
+            "angle": 0,
+            "content": "\\[\nh \\left(n _ {x}, n _ {y}\\right) := f \\left(n _ {x}, n _ {y}, 0\\right). \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.745,
+                0.892,
+                0.819
+            ],
+            "angle": 0,
+            "content": "For the objective function \\(g\\), we will obtain a unique candidate extremum \\(\\mathbf{n}_g^* \\in \\mathbb{R}^2\\); whereas for the function \\(h\\), a one-parameter family of candidate extrema \\(\\mathbf{n}_h^* \\in \\mathbb{R}^2\\) will be found but with the same function value \\(h(\\mathbf{n}_h^*)\\). The optimal \\(\\mathbf{n}^*\\) is then"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.83,
+                0.891,
+                0.871
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {n} ^ {*} = \\left\\{ \\begin{array}{l l} \\left[ \\mathbf {n} _ {g} ^ {*}, 1 \\right] ^ {\\top}, & \\text {i f} g \\left(\\mathbf {n} _ {g} ^ {*}\\right) \\leq h \\left(\\mathbf {n} _ {h} ^ {*}\\right), \\\\ \\left[ \\mathbf {n} _ {h} ^ {*}, 0 \\right] ^ {\\top}, & \\text {i f} g \\left(\\mathbf {n} _ {g} ^ {*}\\right) > h \\left(\\mathbf {n} _ {h} ^ {*}\\right). \\end{array} \\right. \\tag {4}\n\\]"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.875,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>They are the four affine parameters \\( a_{ij} \\), and the 15 components of the vectors \\( \\mathbf{w}_{ij} \\) and \\( \\mathbf{w}_c \\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3392"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.092,
+                0.473,
+                0.168
+            ],
+            "angle": 0,
+            "content": "Remark 1 In other words, we will be utilizing the simple constraints \\( n_z = 1 \\) or \\( n_z = 0 \\). We have found that other linear or non-linear constraints, such as \\( \\| \\mathbf{n} \\| = 1 \\), would render the symbolic calculations to minimize the objective function \\( f \\) infeasible."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.188,
+                0.191,
+                0.203
+            ],
+            "angle": 0,
+            "content": "Case A: \\(n_z = 1\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.212,
+                0.421,
+                0.227
+            ],
+            "angle": 0,
+            "content": "We use the standard technique and solve the system"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.199,
+                0.239,
+                0.469,
+                0.281
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\{ \\begin{array}{l} \\partial_ {1} g \\left(n _ {x}, n _ {y}\\right) = 0, \\\\ \\partial_ {2} g \\left(n _ {x}, n _ {y}\\right) = 0 \\end{array} \\right. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.291,
+                0.428,
+                0.309
+            ],
+            "angle": 0,
+            "content": "to find the optimal vector \\(\\mathbf{n}_g^* = [n_x, n_y]^\\top\\) as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.309,
+                0.411,
+                0.323
+            ],
+            "angle": 0,
+            "content": "By computing and putting the partial derivative"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.23,
+                0.336,
+                0.316,
+                0.354
+            ],
+            "angle": 0,
+            "content": "\\[\n\\partial_ {1} g (n _ {x}, n _ {y})\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.365,
+                0.47,
+                0.422
+            ],
+            "angle": 0,
+            "content": "over a common denominator, we see that its numerator depends on \\( n_x \\) linearly; and it depends on \\( n_y \\) quadratically; so one can easily express \\( n_x \\) from the equation \\( \\partial_1 g(n_x, n_y) = 0 \\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.22,
+                0.421,
+                0.469,
+                0.45
+            ],
+            "angle": 0,
+            "content": "\\[\nn _ {x} = \\frac {\\operatorname {n u m e r} _ {1}}{\\operatorname {d e n o m} _ {1}}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.456,
+                0.47,
+                0.561
+            ],
+            "angle": 0,
+            "content": "where we present the expressions for \\(\\mathrm{numer}_1\\) and \\(\\mathrm{denom}_1\\) in the supplementary material. Then (6) is substituted into the other partial derivative \\(\\partial_2 g(n_x, n_y)\\). The resulting rational function of \\(n_y\\), also containing the other 19 parameters, can be simplified and factorized by Wolfram Mathematica's Factor command<sup>2</sup>. In this way, we obtain a fraction whose structure is the following:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.217,
+                0.572,
+                0.469,
+                0.605
+            ],
+            "angle": 0,
+            "content": "\\[\n\\frac {\\operatorname {l i n e a r} _ {1} \\cdot \\operatorname {l i n e a r} _ {2}}{(\\text {q u a d r a t i c}) ^ {2}}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.615,
+                0.469,
+                0.646
+            ],
+            "angle": 0,
+            "content": "where the expressions \"linear\" and \"quadratic\" denote polynomials in \\( n_y \\) having the corresponding degrees."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.646,
+                0.47,
+                0.75
+            ],
+            "angle": 0,
+            "content": "The optimum of \\( g \\) can occur when \\( n_y \\) is chosen such that the fraction (7), that is, its numerator is equal to 0. It can be shown that the assumption \\( \\mathrm{linear}_1 = 0 \\) leads to a contradiction - indeed, by solving \\( \\mathrm{linear}_1 = 0 \\) for \\( n_y \\), the resulting formula would make \\( \\mathrm{denom}_1 \\) in (6) identically equal to 0. Hence, we are only left with the equation \\( \\mathrm{linear}_2 = 0 \\), whose solution is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.22,
+                0.759,
+                0.469,
+                0.788
+            ],
+            "angle": 0,
+            "content": "\\[\nn _ {y} = \\frac {\\operatorname {n u m e r} _ {2}}{\\operatorname {d e n o m} _ {2}}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.799,
+                0.469,
+                0.828
+            ],
+            "angle": 0,
+            "content": "The actual formulas for \\(\\mathrm{numer}_2\\) and \\(\\mathrm{denom}_2\\) are found again in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.829,
+                0.469,
+                0.877
+            ],
+            "angle": 0,
+            "content": "Thus, the second component of \\(\\mathbf{n}_g^*\\) is given by (8) (expressed in terms of the 19 parameters). Then, by using this together with (6), we obtain \\(n_x\\), the first component of \\(\\mathbf{n}_g^*\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.895,
+                0.274
+            ],
+            "angle": 0,
+            "content": "Remark 2 The essential feature of these computations is that the solution of system (5) is given in a fully explicit symbolic form by using only elementary operations. Without the clever intermediate symbolic simplifications and factorizations (most notably (7)), one would need to solve a higher-degree polynomial equation to obtain \\( n_y \\), requiring either taking roots or using an iterative scheme. For example, if one starts solving (5) with \\( n_x \\) and \\( n_y \\) as symbolic parameters but all the coefficients of \\( g \\) as floating-point numbers, then, in general, no intermediate factorizations or simplifications are possible, so in order to determine \\( n_y \\), one would need to solve a quintic equation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.291,
+                0.611,
+                0.305
+            ],
+            "angle": 0,
+            "content": "Case B: \\( n_z = 0 \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.315,
+                0.783,
+                0.33
+            ],
+            "angle": 0,
+            "content": "We proceed similarly and solve the system"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.621,
+                0.338,
+                0.892,
+                0.379
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\{ \\begin{array}{l} \\partial_ {1} h \\left(n _ {x}, n _ {y}\\right) = 0, \\\\ \\partial_ {2} h \\left(n _ {x}, n _ {y}\\right) = 0. \\end{array} \\right. \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.388,
+                0.893,
+                0.463
+            ],
+            "angle": 0,
+            "content": "By expressing \\( n_x \\) from the first equation of (9) and substituting the resulting expression into the second equation, we find that this time the second equation is automatically satisfied. Therefore, (9) possesses a one-parameter family of solutions given by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.643,
+                0.47,
+                0.891,
+                0.501
+            ],
+            "angle": 0,
+            "content": "\\[\nn _ {x} = \\frac {\\operatorname {n u m e r} _ {3}}{\\operatorname {d e n o m} _ {3}}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.508,
+                0.892,
+                0.54
+            ],
+            "angle": 0,
+            "content": "see the supplementary material. By substituting this into \\(h\\), the function value \\(h(\\mathbf{n}_h^*)\\) appearing in (4) is obtained as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.631,
+                0.547,
+                0.891,
+                0.577
+            ],
+            "angle": 0,
+            "content": "\\[\nh \\left(\\mathbf {n} _ {h} ^ {*}\\right) = \\frac {\\operatorname {n u m e r} _ {4}}{\\operatorname {d e n o m} _ {4}}. \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.585,
+                0.783,
+                0.6
+            ],
+            "angle": 0,
+            "content": "See the supplementary material for details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.61,
+                0.892,
+                0.65
+            ],
+            "angle": 0,
+            "content": "Remark 3 One directly checks that the value \\( h(\\mathbf{n}_h^*) = h\\left(\\frac{\\mathrm{numer}_3}{\\mathrm{denom}_3}, n_y\\right) \\) is indeed independent of \\( n_y \\), as claimed."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.659,
+                0.744,
+                0.674
+            ],
+            "angle": 0,
+            "content": "2.1. Summary of the Algorithm"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.682,
+                0.892,
+                0.756
+            ],
+            "angle": 0,
+            "content": "Given the elements \\(a_{ij} \\in \\mathbb{R}\\) in the affine transformation and 3D vectors \\(\\mathbf{w}_{ij}\\) and \\(\\mathbf{w}_c \\neq \\mathbf{0}\\), let us define the function \\(f\\) by (1) for \\(\\mathbf{n}\\) with \\(\\mathbf{n}^\\top \\mathbf{w}_c \\neq \\mathbf{0}\\), and also define the functions \\(g\\) and \\(h\\) by (2)-(3). If \\(\\mathbf{w}_{11} = \\mathbf{w}_{12} = \\mathbf{w}_{21} = \\mathbf{w}_{22} = \\mathbf{w}_c\\), then any unit vector \\(\\mathbf{n}^*\\) can be chosen as optimal normal vector."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.757,
+                0.892,
+                0.803
+            ],
+            "angle": 0,
+            "content": "Otherwise, we compute \\(\\mathbf{n}_g^* \\coloneqq [n_x, n_y]^\\top\\) from (8) and (6). Then we compute \\(h(\\mathbf{n}_h^*)\\) from (11). Finally, the optimal \\(\\mathbf{n}^*\\) is determined by using (4)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.816,
+                0.633,
+                0.832
+            ],
+            "angle": 0,
+            "content": "3. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.841,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "We focus on the accuracy and time demand of the algorithms when testing. Both synthetic testing data, including configurations for a number of important camera motions, and standard real-world benchmarks are considered here."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.095,
+                0.887,
+                0.318,
+                0.901
+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)https://www.wolfram.com/mathematica/"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3393"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.272,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.274,
+                0.089,
+                0.467,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.099,
+                0.203,
+                0.25,
+                0.288
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.278,
+                0.196,
+                0.465,
+                0.281
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.291,
+                0.47,
+                0.32
+            ],
+            "angle": 0,
+            "content": "Figure 2. Images and the reference reconstruction used from the Cambridge Landmarks dataset [39] in localization experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.343,
+                0.47,
+                0.389
+            ],
+            "angle": 0,
+            "content": "Compared Algorithms. In this section, we discuss the algorithms that can be used to estimate the surface normal from a single affine correspondence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.397,
+                0.47,
+                0.504
+            ],
+            "angle": 0,
+            "content": "1. The provably most accurate algorithms are the ones that are optimal in the least squares sense. Method \\(\\mathrm{OPT}_{\\mathrm{QUARTIC}}\\) refers to [9] which solves the problem as a real root of a quartic polynomial equation. The cubic solution \\(\\mathrm{OPT}_{\\mathrm{CUBIC}}\\) is from [46]. The proposed optimal solver, as it is solved via linear equations, is called \\(\\mathrm{OPT}_{\\mathrm{LINEAR}}\\) in the rest of the paper."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.508,
+                0.47,
+                0.599
+            ],
+            "angle": 0,
+            "content": "2. The simplest and, thus, the fastest method is the Fast Normal Estimation (FNE) algorithm of [9]. A more complex variant, when all possible linear equations are considered, is also constructed here, it is denoted as \\(\\mathrm{FNE}_{\\mathrm{SUPER}}\\). The modified equations can be seen in the source codes in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.603,
+                0.47,
+                0.739
+            ],
+            "angle": 0,
+            "content": "3. Raposo and Barreto [56] proposed a solution that estimates the normal via homographies. We have not found an implementation or an exact definition of the algorithm, so we implemented it based on the description. The solution is computed via an over-determined inhomogeneous linear system of equations. The formulas are generated by the MATLAB Symbolic Toolbox. Details are given in the supplementary material. The method is called RAPOSO in the charts."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.09,
+                0.397,
+                0.47,
+                0.739
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.748,
+                0.47,
+                0.793
+            ],
+            "angle": 0,
+            "content": "The synthetic tests are performed in MATLAB. In the real-world experiments, optimized \\(\\mathrm{C}++\\) codes run on an Intel(R) Core(TM) i9-10900K CPU @ 3.70GHz."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.802,
+                0.289,
+                0.818
+            ],
+            "angle": 0,
+            "content": "3.1. Synthetic Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.826,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For the synthetic tests, a spherical object is generated, thus straightforwardly allowing to sample oriented points from its surface. Two cameras are randomly generated with focal lengths from the range [500, 1500] and with image size \\(2000 \\times 2000\\). Their intrinsic matrices are \\(\\mathbf{K}_1\\) and \\(\\mathbf{K}_2\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "The 3D point was projected into both cameras. The ground truth (GT) affine parameters were calculated directly from the camera parameters and the surface normals as shown in [9]. Several camera configurations are considered to simulate various real-world scenarios. They are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.175,
+                0.892,
+                0.237
+            ],
+            "angle": 0,
+            "content": "- For general stereo pose, the locations of the cameras are randomly generated inside a unit-radius sphere. The camera projection matrices are constructed as \\(\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]\\) and \\(\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R} \\mid \\mathbf{t}]\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.241,
+                0.894,
+                0.302
+            ],
+            "angle": 0,
+            "content": "- For rectified stereo, the cameras are located next to each other with identical orientation. In this case, the projection matrices are \\(\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]\\) and \\(\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{I} \\mid \\mathbf{t}]\\), where \\(\\mathbf{t} = [\\Delta X 0 0]^\\top\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.306,
+                0.892,
+                0.427
+            ],
+            "angle": 0,
+            "content": "- Planar motion simulates the case when a camera is mounted on a vehicle that moves on a planar road with the image plane orthogonal to the ground. Such a motion can be represented by two angles around the vertical axis, one for the rotation and one for the translation. In this case, the projection matrices can be written as \\(\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid 0]\\) and \\(\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_{\\mathrm{Y}} \\mid \\mathbf{t}]\\), where \\(\\mathbf{t} = \\rho [\\cos \\beta, 0, \\sin \\beta]^\\top\\) and"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.175,
+                0.894,
+                0.427
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.602,
+                0.435,
+                0.821,
+                0.484
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {R} _ {\\mathrm {Y}} = \\left[ \\begin{array}{c c c} \\cos \\alpha & 0 & \\sin \\alpha \\\\ 0 & 1 & 0 \\\\ - \\sin \\alpha & 0 & \\cos \\alpha \\end{array} \\right].\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.496,
+                0.892,
+                0.587
+            ],
+            "angle": 0,
+            "content": "- Moto-motion. This test case simulates a camera that is mounted on a motorcycle. If the bike leans, another rotation, the roll is involved in the problem. In this case, the camera parameters are \\(\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]\\) and \\(\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_{\\mathrm{YZ}} \\mid \\mathbf{t}]\\), where \\(\\mathbf{t} = \\rho [\\cos \\beta 0 \\sin \\beta]^\\top\\) and \\(\\mathbf{R}_{YZ} = \\mathbf{R}_Y \\mathbf{R}_Z\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.591,
+                0.892,
+                0.668
+            ],
+            "angle": 0,
+            "content": "- Drone-motion is another generalization of the planar motion. A camera mounted on a flying drone. Its location is arbitrary, but the orientation is limited to a vertical rotation. Therefore, \\(\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]\\) and \\(\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_Y \\mid \\mathbf{t}]\\), where \\(\\mathbf{t} = [X Y Z]^\\top\\)."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.496,
+                0.892,
+                0.668
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.674,
+                0.891,
+                0.719
+            ],
+            "angle": 0,
+            "content": "Noise. We have added zero-mean Gaussian noise to the 2D coordinates, therefore, the point noise is given in pixels. The deviation of the noise is the parameter in the charts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.81
+            ],
+            "angle": 0,
+            "content": "The \\(2 \\times 2\\) affine transformations are decomposed by SVD into two 2D rotations and another two scaling parameters. Then zero-mean Gaussian noise is added to the angle of rotations, in radians, and the scaling parameters. The standard deviation of the Gaussian noise distribution is equally set for all the four parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "3D Reconstruction Pipeline. In order to simulate real scenarios, first, we triangulate each generated noisy point correspondence by the optimal triangulation method proposed by Hartley and Sturm [29]. The noisy affine parameters are corrected by the method proposed in [7] to be consistent with the camera parameters."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3394"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.14,
+                0.098,
+                0.393,
+                0.252
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.267,
+                0.47,
+                0.297
+            ],
+            "angle": 0,
+            "content": "Figure 3. The frequencies (in 10000 runs) of the \\(\\log_{10}\\) errors in the \\(\\log_{10}\\) angular errors in degrees in the noise-free case."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.47,
+                0.594
+            ],
+            "angle": 0,
+            "content": "Stability test. We generated 10000 random problem instances considering general camera motion and ran the normal estimators on noiseless affine correspondences. Fig. 3 shows histograms of \\(\\log_{10}\\) angular errors in degrees. Note that for better visualization, we replace the exact zero values by \\(10^{-16}\\) as it is the precision of the floating point numbers in MATLAB. The plots show that all our solvers are very stable – there is no peak close to \\(10^0\\). For all methods, the majority of the errors are distributed around \\(10^{-16}\\) which actually is the precision of MATLAB. This means that in most of the cases, all methods are particularly stable returning almost exactly 0 error. A small peak is over \\(10^{-6}\\) for all methods similarly. Having \\(10^{-6}\\) degree error is acceptable in most of the scenarios considered in computer vision. There is no peak close to \\(10^0\\) implying that all solvers are stable. Note that these stability tests usually are for highlighting potential degeneracies where the error exceeds \\(10^0\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.597,
+                0.468,
+                0.732
+            ],
+            "angle": 0,
+            "content": "We also conducted tests using single-point precision in MATLAB. The OPTQUARTIC approach failed entirely under these conditions. For all other methods, we noticed an increase in error, which suggests that double precision is necessary for reliable normal estimation. Interestingly, our proposed OPTLINEAR method appears to be slightly more sensitive to precision than OPTCUBIC is. This is likely due to the fact that OPTLINEAR employs more complex formulas and, consequently, performs more stably with double precision."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.734,
+                0.468,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Accuracy test. The accuracy of the normals is examined for all the considered camera poses independently. The results are shown in Fig 9. The effect of noise in point coordinates and affine parameters are separately evaluated. Both the mean and the median of the errors are plotted."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The observations we can make from the plots are as follows. First, the three optimal methods \\(\\mathrm{OPT}_{\\mathrm{QUARTIC}}\\), \\(\\mathrm{OPT}_{\\mathrm{CUBIC}}\\) and \\(\\mathrm{OPT}_{\\mathrm{LINEAR}}\\) always lead exactly to the same solution, thus their curves coincide in all plots. Second, the optimal methods always lead to the most accurate results if the affine parameters are contaminated by noise. This is not"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.318
+            ],
+            "angle": 0,
+            "content": "surprising as these methods optimize the normal parameters such that the implied affine transformation is the closest to the measured one. In the case of point-noise only, the accuracy of the optimal algorithm is slightly below that of the competitors. However, it is an unlikely situation in real-world images to have noisy points but perfect local affine frames. It is usually the other way around. Third, as the FNE method uses less information, it is clearly the worst one in terms of accuracy. \\(\\mathrm{FNE}_{\\mathrm{SUPER}}\\) performs significantly better, however, it requires more time as the right singular vector of a \\(6\\times 3\\) matrix, corresponding to the smallest singular value, should be computed. Another benefit of \\(\\mathrm{FNE}_{\\mathrm{SUPER}}\\) is, contrary to FNE and Raposo [56], that it works in all test cases. It can cope with both planar motion and rectified stereo, similarly to the optimal algorithms."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.318,
+                0.892,
+                0.407
+            ],
+            "angle": 0,
+            "content": "Problematic methods. Methods FNE and Raposo [56] do not work if the cameras undergo special translations. FNE is a special method, several variants can be formed based on the selection of the affine transformations. For rectified stereo, the third and fourth elements are fixed [44], they cannot be used for the estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.409,
+                0.892,
+                0.529
+            ],
+            "angle": 0,
+            "content": "The Raposo [56] method is the most problematic one as the homography can be decomposed into the camera rotation, translation and surface normal. If the translation has zero elements, the retrieved equations are linearly dependent, and the estimation does not yield a correct solution. Due to this reason, Raposo [56] does not work for rectified stereo and planar motion. We removed these methods from the plots of the respective camera configurations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.53,
+                0.892,
+                0.634
+            ],
+            "angle": 0,
+            "content": "Combined noise. In the previous experiments, noise is added either to the point coordinates or affine parameters. Here, we contaminate both types of input data. The mean and median errors of the proposed linear method are visualized in Fig. 10. As it is expected, the curves show similar trends, but the case when both the points and affines are noisy leads to higher errors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.636,
+                0.892,
+                0.801
+            ],
+            "angle": 0,
+            "content": "Interpretable affine noise. In the previous experiments, the noise is added directly to the elements of the affine matrices. In Fig. 11, we consider a different way of contaminating the input to show that the proposed method acts reasonably with different noise models as well. The results of curves Aff and Comb are obtained by using the noise model from the previous sections. Comb refers to the case when both the points and the affine matrices are noisy. For AffElem and Comb-Elem, we decompose A by SVD into two orthogonal and a diagonal matrix. Fig. 11 demonstrates that the noise generation does not strongly influence the results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.815,
+                0.729,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4. Real-world Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To test normal estimators, we use the Cambridge Landmarks [39] and ScanNet datasets [18]. We chose Cambridge Landmarks, see Fig. 2 for example images, since it provides a large number of images for testing directly the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3395"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.253,
+                0.094,
+                0.716,
+                0.115
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.148,
+                0.294,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.306,
+                0.148,
+                0.476,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.486,
+                0.148,
+                0.655,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.668,
+                0.148,
+                0.838,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.406,
+                0.254,
+                0.565,
+                0.267
+            ],
+            "angle": 0,
+            "content": "Figure 4. General Motion."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.272,
+                0.293,
+                0.372
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.306,
+                0.272,
+                0.475,
+                0.372
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.486,
+                0.272,
+                0.655,
+                0.372
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.668,
+                0.272,
+                0.838,
+                0.372
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.405,
+                0.376,
+                0.565,
+                0.389
+            ],
+            "angle": 0,
+            "content": "Figure 5. Rectified Stereo."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.395,
+                0.293,
+                0.495
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.306,
+                0.395,
+                0.475,
+                0.494
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.486,
+                0.395,
+                0.655,
+                0.494
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.668,
+                0.394,
+                0.838,
+                0.494
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.41,
+                0.498,
+                0.558,
+                0.512
+            ],
+            "angle": 0,
+            "content": "Figure 6. Planar Motion."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.516,
+                0.293,
+                0.617
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.306,
+                0.517,
+                0.475,
+                0.617
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.486,
+                0.516,
+                0.655,
+                0.617
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.668,
+                0.516,
+                0.838,
+                0.617
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.413,
+                0.621,
+                0.556,
+                0.634
+            ],
+            "angle": 0,
+            "content": "Figure 7. Moto Motion."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.639,
+                0.293,
+                0.739
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.306,
+                0.639,
+                0.475,
+                0.739
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.668,
+                0.639,
+                0.838,
+                0.739
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.41,
+                0.743,
+                0.558,
+                0.756
+            ],
+            "angle": 0,
+            "content": "Figure 8. Drone Motion."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.756,
+                0.894,
+                0.799
+            ],
+            "angle": 0,
+            "content": "Figure 9. Average and median angular errors (in degrees) of surface normal estimators on synthetic data. Five camera configurations are considered. From left to right: (1) Median error; noise added to affine parameters. (2) Average error; noise added to affine parameters. (3) Median error; noise added to point coordinates. (4) Average error; noise added to point coordinates."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.824,
+                0.471,
+                0.899
+            ],
+            "angle": 0,
+            "content": "normal accuracy and, also, we can evaluate localization as an application of the proposed procedure. Also, we chose ScanNet since the reference normals can be calculated directly from the dense depth maps which provides a complementary comparison to the tests on Cambridge Landmarks,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.824,
+                0.838,
+                0.837
+            ],
+            "angle": 0,
+            "content": "where the normals come from a 3D reconstruction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.841,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Cambridge Landmarks consists of five scenes with varying number of images, ranging from 231 to 3015. The reference pose of each image was reconstructed using the VisualSFM structure-from-motion software [70, 69] and the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3396"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.094,
+                0.268,
+                0.195
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.276,
+                0.094,
+                0.445,
+                0.194
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.21,
+                0.47,
+                0.252
+            ],
+            "angle": 0,
+            "content": "Figure 10. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to point coordinates (Point), affine parameters (Affine) or both (Combined)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.27,
+                0.268,
+                0.371
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.276,
+                0.271,
+                0.445,
+                0.371
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.387,
+                0.47,
+                0.484
+            ],
+            "angle": 0,
+            "content": "Figure 11. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to only the affine \\((A\\text{ff})\\) elements and, also, to the point coordinates \\((Comb)\\). For Aff and Comb, zero-mean Gaussian noise is added directly to the affine elements. For Aff-Elem and Comb-Elem, the affine matrix is decomposed by SVD to two rotations and a diagonal matrix. Zero-mean Gaussian noise is added to the rotation angles and diagonal elements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.51,
+                0.468,
+                0.661
+            ],
+            "angle": 0,
+            "content": "images are divided into training and testing sets. To have more accurate reference data, we ran COLMAP [63] obtaining a dense point cloud. Finally, we applied the normal estimator implemented in MeshLab<sup>3</sup> to obtain an oriented point cloud to be considered reference. The normals are fitted to the 200 nearest neighbors. For each query image, we ran DenseVLAD [67] to get 20 potential database images. In our experiments, the algorithms are tested on each obtained image pair, i.e., 20 pairs for each query image. For ScanNet, we use the 1500 image pairs used in [59]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.662,
+                0.468,
+                0.784
+            ],
+            "angle": 0,
+            "content": "On Cambridge Landmarks, we detect affine correspondences by detecting DoG features [42], finding the affine shape by AffNet [48], and extracting HardNet [47] descriptors. This approach is among the leaders in the IMC 2020 benchmark [34]. On ScanNet, we detect SuperPoint [20] features, match them by SuperGlue [59], and find the affine shape by, first, estimating scale and orientation by SelfScaleOri [41] and, then, finding the affine shapes by AffNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.788,
+                0.468,
+                0.863
+            ],
+            "angle": 0,
+            "content": "Normal Estimation. To test normal estimators, we ran all of them on the data described in the previous section. For each image pair, we iterate through all detected correspondences that are consistent with the camera pose - they have less than 5 pixels of Sampson distance. For each of"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.5,
+                0.097,
+                0.693,
+                0.212
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.695,
+                0.097,
+                0.886,
+                0.212
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.215,
+                0.892,
+                0.27
+            ],
+            "angle": 0,
+            "content": "Figure 12. The median angular error in degrees (left) and the AUC@ \\(10^{\\circ}\\) score (right) of the estimated normals plotted as a function of the error in the detected affine correspondences on the Cambridge Landmarks dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.301,
+                0.892,
+                0.407
+            ],
+            "angle": 0,
+            "content": "them, we ran multiple normal estimators, measure their angular error and run-time. To understand how the estimators proceed with respect to the error in the detected affine transformations \\(\\mathbf{A}\\), we calculate the reference transformation \\(\\mathbf{A}^*\\) from the camera parameters and the surface normal as shown in [9]. We define the affine error as the Frobenius norm of the difference matrix \\(\\| \\mathbf{A} - \\mathbf{A}^* \\|_{\\mathrm{F}}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.409,
+                0.893,
+                0.68
+            ],
+            "angle": 0,
+            "content": "The Area Under the recall Curve (AUC) at \\(5^{\\circ}\\), \\(10^{\\circ}\\) and \\(20^{\\circ}\\), the avg. and med. angular errors with the standard deviation in degrees and the run-time in nanoseconds on the Cambridge Landmarks dataset are reported in Table 1. As expected, the best results are achieved by the optimal algorithms, all of them leading to exactly the same results. Our proposed linear solution of the optimal problem, \\(\\mathrm{OPT}_{\\mathrm{LINEAR}}\\), is five times faster than the cubic solution \\(\\mathrm{OPT}_{\\mathrm{CUBIC}}\\). While \\(\\mathrm{OPT}_{\\mathrm{LINEAR}}\\) is slightly slower than the fastest FNE method, it is significantly more accurate. Interestingly, while the method of Raposo et al. [56] worked well in the synthetic experiments, we did not manage to achieve good accuracy with it in the real-world experiments. Figure 12 plots the AUC@\\(10^{\\circ}\\) score and the median angular error as a function of the noise in the detected affine parameters. As expected, normal estimation is highly sensitive to the quality of the affine parameters. The optimal algorithms are the most stable ones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.684,
+                0.892,
+                0.744
+            ],
+            "angle": 0,
+            "content": "The results on the ScanNet dataset are reported in Table 3. Similarly as on Cambridge Landmarks, all optimal solvers lead to the same accuracy while the proposed one being the fastest by a large margin."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visual Localization. To test the impact of surface normal estimation on localization, on the Cambridge Landmarks dataset, we applied the following procedure. We iterate through all query images, each having 10 database images retrieved by DenseVLAD. First, we estimate the relative pose between the query and a random database image by GC-RANSAC [6] with P3P [54]. Using the obtained pose, we estimate the surface normal of each inlier affine correspondence in the coordinate system of the query image. Next, we iterate through all unused database images and use"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.078,
+                0.875,
+                0.468,
+                0.899
+            ],
+            "angle": 0,
+            "content": "3Meshlab is an open source tool for 3D point cloud processing and visualization."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3397"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.089,
+                0.887,
+                0.207
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Estimator</td><td>AUC@5°↑</td><td>@10°↑</td><td>@20°↑</td><td>Avg. err. (°) ↓</td><td>Med. err. (°) ↓</td><td>Std. dev. (°) ↓</td><td>Time (ns) ↓</td></tr><tr><td>FNE [49]</td><td>6.0</td><td>16.0</td><td>33.7</td><td>21.0</td><td>14.3</td><td>21.3</td><td>172</td></tr><tr><td>FNESUPER</td><td>8.9</td><td>22.1</td><td>42.0</td><td>10.9</td><td>16.8</td><td>15.6</td><td>1721</td></tr><tr><td>Raposo [56]</td><td>0.4</td><td>1.5</td><td>5.7</td><td>38.5</td><td>36.5</td><td>18.2</td><td>883</td></tr><tr><td>OPTQUARTIC [9]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2528</td></tr><tr><td>OPTCUBIC [46]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2484</td></tr><tr><td>Proposed OPTLINEAR</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>596</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.207,
+                0.892,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Table 1. The AUC score at \\(5^{\\circ}\\), \\(10^{\\circ}\\), and \\(20^{\\circ}\\) of the estimated surface normals, their average and median errors in degrees, the standard deviation, and the average run-time, in nanoseconds, of a single normal estimation on the Cambridge Landmarks dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.137,
+                0.246,
+                0.835,
+                0.359
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Solver</td><td rowspan=\"2\">Normal estimator</td><td colspan=\"3\">Pose accuracy ↑</td><td rowspan=\"2\">Med. rot. err. (°) ↓</td><td rowspan=\"2\">Med. pos. err. (cm) ↓</td></tr><tr><td>AUC@1°, 10cm</td><td>@2.5°, 25cm</td><td>@5°, 50cm</td></tr><tr><td>P3P</td><td>-</td><td>44.3</td><td>59.1</td><td>67.5</td><td>10.1</td><td>13.5</td></tr><tr><td>P1AC</td><td>FNESUPER</td><td>47.8</td><td>62.0</td><td>69.7</td><td>6.2</td><td>12.8</td></tr><tr><td>P1AC</td><td>Proposed OPTLINEAR</td><td>48.0</td><td>62.3</td><td>69.9</td><td>5.2</td><td>1.8</td></tr><tr><td>P1AC</td><td>GT</td><td>48.4</td><td>62.9</td><td>70.4</td><td>4.6</td><td>2.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.359,
+                0.895,
+                0.415
+            ],
+            "angle": 0,
+            "content": "Table 2. Localization AUC scores at \\((1^{\\circ}, 10\\mathrm{cm})\\), \\((2.5^{\\circ}, 25\\mathrm{cm})\\), and \\((5^{\\circ}, 50\\mathrm{cm})\\), the median rotation (in degrees) and translation errors (in centimeters) on the Cambridge Landmarks dataset [39] when using either the P3P solver or the normal-based P1AC solver with FNEsuper or the proposed surface normal estimator OPTLINEAR. We also show the results with the reference normals. The minimal solvers are used within Graph-Cut RANSAC [6] that takes care of the robust estimation."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.436,
+                0.47,
+                0.526
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>AUC@5↑</td><td>AUC@10↑</td><td>AUC@20↑</td><td>Time (ns)↓</td></tr><tr><td>FNE</td><td>14.8</td><td>15.4</td><td>17.0</td><td>207</td></tr><tr><td>FNESUPER</td><td>34.9</td><td>35.2</td><td>36.6</td><td>2142</td></tr><tr><td>OPTQUARTIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>18745</td></tr><tr><td>OPTCUBIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>3146</td></tr><tr><td>OPTLINEAR</td><td>35.0</td><td>35.5</td><td>37.3</td><td>747</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.525,
+                0.47,
+                0.553
+            ],
+            "angle": 0,
+            "content": "Table 3. The AUC scores at \\(5^{\\circ}\\), \\(10^{\\circ}\\) and \\(20^{\\circ}\\), and the avg. time (in nanoseconds) of normal estimators on the ScanNet datasets [18]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.575,
+                0.469,
+                0.652
+            ],
+            "angle": 0,
+            "content": "the P1AC [68] solver inside GC-RANSAC to estimate the pose. P1AC requires a single AC and the surface normal. We only test the proposed solver and \\(\\mathrm{FNE}_{\\mathrm{SUPER}}\\). All other optimal solvers lead exactly to the same accuracy as ours. \\(\\mathrm{FNE}_{\\mathrm{SUPER}}\\) is the most accurate sub-optimal algorithm."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.652,
+                0.47,
+                0.818
+            ],
+            "angle": 0,
+            "content": "The accuracy of the estimated pose for the database images with respect to their GT pose is reported in Table 2. All solvers, benefiting from normals and affine correspondences, are more accurate than using P3P. We also report the accuracy when using the reference normals to see the upper bound achievable using normals. The proposed optimal solver OPT LINEAR is only slightly (i.e. \\(< 1\\) AUC point) behind the accuracy of the GT normal, while being more accurate than the P3P-based solution. The AUC@ \\(10^{\\circ}\\) scores on each scene are reported in Table 4. The proposed OPT LINEAR leads to the best accuracy on all but two scenes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.83,
+                0.205,
+                0.846
+            ],
+            "angle": 0,
+            "content": "5. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this work, we have presented a novel solver for estimating surface normals from affine correspondences when having calibrated cameras. The proposed method yields the"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.503,
+                0.437,
+                0.892,
+                0.556
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">P3P</td><td colspan=\"3\">P1AC</td></tr><tr><td>GT</td><td>FNESUPER</td><td>Prop. OPTLINEAR</td></tr><tr><td>St. Mary&#x27;s Church</td><td>44.2</td><td>47.7</td><td>46.1</td><td>46.5</td></tr><tr><td>Old Hospital</td><td>44.1</td><td>57.4</td><td>56.8</td><td>57.3</td></tr><tr><td>King&#x27;s College</td><td>52.1</td><td>54.2</td><td>54.1</td><td>54.0</td></tr><tr><td>Shop Facade</td><td>65.5</td><td>65.0</td><td>63.8</td><td>64.1</td></tr><tr><td>Great Court</td><td>62.7</td><td>63.2</td><td>63.0</td><td>63.5</td></tr><tr><td>Street</td><td>17.4</td><td>22.8</td><td>23.1</td><td>23.0</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.557,
+                0.892,
+                0.611
+            ],
+            "angle": 0,
+            "content": "Table 4. The area under the recall curve (AUC) at \\(1^{\\circ}\\) rotation and 10cm position errors on the Cambridge Landmarks dataset. We combine the P1AC solver with \\(\\mathrm{FNE}_{\\mathrm{SUPER}}\\) and the proposed normal estimator. Also, we test it with the reference normals."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.662,
+                0.892,
+                0.844
+            ],
+            "angle": 0,
+            "content": "optimal solution, in the least squares sense, with respect to the affine error, and is particularly fast as the optimal normal is obtained via linear equations. We compared our method to all existing alternatives that estimate normals from a single correspondence on both simulated and real-world data. Additionally, we provide tests that highlight the benefits of using surface normals in image-based localization. The proposed estimator has demonstrated superior accuracy compared to the fastest existing method while being the second fastest overall. Our results suggest that the proposed algorithm is a promising alternative for surface normal estimation in computer vision applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Acknowledgement. The authors warmly thank the reviewers for their very valuable comments and suggestions. The work was supported by the ETH Postdoc fellowship."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3398"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+            ],
+            "angle": 0,
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+        },
+        {
+            "type": "page_number",
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+]
\ No newline at end of file
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+# Fast Globally Optimal Surface Normal from an Affine Correspondence
+
+Levente Hajder, Lajos Lóczi  
+Geometric Computer Vision Group  
+Eötvös Loránd University, Budapest, Hungary  
+{hajder, lloczi}@inf.elte.hu
+
+Daniel Barath  
+Computer Vision and Geometry Group  
+ETH Zurich, Switzerland  
+dbarath@inf.ethz.ch
+
+# Abstract
+
+We present a new solver for estimating a surface normal from a single affine correspondence in two calibrated views. The proposed approach provides a new globally optimal solution for this over-determined problem and proves that it reduces to a linear system that can be solved extremely efficiently. This allows for performing significantly faster than other recent methods, solving the same problem and obtaining the same globally optimal solution. We demonstrate on  $15k$  image pairs from standard benchmarks that the proposed approach leads to the same results as other optimal algorithms while being, on average, five times faster than the fastest alternative. Besides its theoretical value, we demonstrate that such an approach has clear benefits, e.g., in image-based visual localization, due to not requiring a dense point cloud to recover the surface normal. We show on the Cambridge Landmarks dataset that leveraging the proposed surface normal estimation further improves localization accuracy. Matlab and  $C++$  implementations are also published in the supplementary material.
+
+# 1. Introduction
+
+Acquiring oriented point clouds is a fundamental problem both in computer vision and in robotics with a number of important real-world applications benefiting from the extra information it provides. Such applications include 3D reconstruction [1, 8, 31, 62, 72, 65, 56] and simultaneous localization and mapping [19, 23, 50], where the 3D point orientations provide useful information about the underlying structure. Image-based visual localization approaches [43, 53, 60, 61] can also benefit from known surface normals [68]. The widely used Poisson reconstruction [37, 38] is based on both the point coordinates and their orientations. The visual odometry [51, 52] of an autonomous vehicle can also benefit from understanding surface orientation to, e.g., segment ground or facades. Also, having an oriented point cloud greatly simplifies geometric model and multi-model estimation [32, 4, 5] due to allowing to design solvers that
+
+![](images/0c48ef7f051b42a370dc08fa7ade8ffa2f4139ea4d5f11d69b72a1c707315bda.jpg)  
+Figure 1. Geometric configuration: oriented 3D point  $\mathbf{P} \in \mathbb{E}^3$  with normal  $\mathbf{n} \in \mathbb{E}^3$  projected to image  $\Pi^1$  as  $\mathbf{p}_1 \in \mathbb{E}^2$  and to  $\Pi^2$  as  $\mathbf{p}_2 \in \mathbb{E}^2$ . The local patch centered at points  $\mathbf{p}_1$  and  $\mathbf{p}_2$  are related by the local affine transformation  $\mathbf{A} \in \mathbb{R}^{2 \times 2}$ .
+
+require fewer data points than their point-based counterparts [64]. Moreover, normals can also be leveraged in the numerical refinement of the reconstructed oriented 3D point cloud [27]. In this paper, we focus on a practical problem, i.e., estimating the normal at corresponding features in two images in a solely photometric manner. This can provide a lightweight approach of obtaining surface normals without requiring a dense point cloud to be known. Next, we will discuss ways of obtaining oriented points.
+
+Normals from Point Clouds. After applying state-of-the-art sparse (e.g., COLMAP [63]) or dense [36, 16] reconstruction pipelines, the resulting point cloud can be straightforwardly equipped with point orientations. In this case, typically, the normals are fitted per-point, applying the widely used Principal Component Analysis (PCA) [35] to estimate tangent planes or higher-order surfaces [14, 33] from the local neighborhood centered at the current point. This procedure, while being frequently used, has two major drawbacks. First, the setting of the neighborhood size greatly affects the accuracy and is often unclear without having a metric reconstruction. Instead, using the  $k$ -nearest-neighbors [17] algorithm to find local neighborhoods is a viable solution, but the estimation becomes largely affected by the sparsity of the point cloud. Second, fitting local surfaces, independently, to the neighborhood of each 3D point
+
+in the reconstruction is an extremely expensive operation.
+
+Normals from Homographies. Another method for estimating surface normals from images, without requiring the underlying 3D structure to be known, is via homographies. Homographies are projective transformations between images of co-planar 3D points that depends on the intrinsic and extrinsic camera parameters and the parameters of the underlying 3D plane [24]. A homography can be estimated from a minimum of four point correspondences in two images [30]. While this method allows the estimation of dominant planes supported by a number of correspondences in the images, it does not provide means for normal estimation for each local feature correspondence independently.
+
+Normals from Local Mappings. In recent years, affine correspondences (AC) have emerged as a popular topic in computer vision, offering a valuable source of information about the underlying 3D geometry of the surrounding environment. An AC consists of a corresponding pair of points in two images and a linear transformation that maps the infinitesimal region around the point in the first image to the point in the second one. They have been used to solve various geometric problems, including relative pose estimation in the general case [15, 55, 3, 22, 10], for known vertical direction [25], planar motion [25, 26], or known feature depths [21] and homography estimation [2].
+
+Traditionally, finding affine features involve four main steps: (scale-covariant) keypoint detection, orientation and affine shape estimation, and descriptor extraction. Under such paradigm, keypoint detection is typically performed on the scale pyramid with the help of a handcrafted response function, such as Hessian [13, 45], Harris [28, 45], Difference of Gaussians (DoG [42]), or learned ones like FAST [57] or Key.Net [11]. Keypoint detection obtains a triplet  $(x,y,\mathrm{scale})$  which defines a square or circular image patch. Then the patch orientation is estimated with the help of handcrafted - dominant gradient orientation [42], center of the mass [58] - or learned methods [71, 48, 41]. Next, the affine-covariant shape [12, 48] is estimated. Finally, the patch is geometrically rectified and fed into a local patch descriptor, such as SIFT, HardNet [47], SOSNet [66], or others. In summary, all feature detectors, even recent learning-based ones like SuperPoint [20], can be made affine covariant by applying, e.g., AffNet [48] as a post-processing step on the found features.
+
+The problem of surface normal estimation from ACs has been addressed in several works. The first algorithm for normal estimation from ACs was proposed by Kevin Koeser [40] assuming that the camera location is known with respect to the observed 3D point. Megyesi et al. [44] proposed a special surface normal estimator for standard (rectified) stereo, where the degree of freedom of the affine transformations decreases to two. In 2014, Molnár and Chetverikov [49] derived a formula connecting the surface
+
+normals, camera parameters, affine transformations, and patch locations into a single expression for arbitrary projective functions, like the catadioptric camera model. Barath et al. [9] proposed a globally optimal estimator in the least squares sense as the solution of a quartic polynomial. Recently, Le Minh and Hajder [46] improved on this by reducing the degree and showed that the optimal solution can be found as a real root of a cubic polynomial.
+
+The main goal of this paper is to propose a rapid normal estimator based on affine correspondences. Our algorithm can be inserted into a 3D reconstruction system, such as Structure-from-Motion [27] (SfM) or Simultaneous Localization and Mapping (SLAM), where the normal estimation is performed many times, therefore its running time influences the time demand of the whole 3D pipeline.
+
+Contribution. In this paper, we propose a new linear and globally optimal solution for surface normal estimation from a single affine correspondence. The proposed solver requires only the four basic arithmetic operations and contains 19 parameters, consisting of the coordinates of the five input vectors and the four affine parameters. This approach completely avoids root extractions, solving high-degree polynomial equations, or employing numerical or iterative methods, resulting in a particularly fast algorithm that runs for only  $0.6\mu s$  in our experiments. The solver is five times faster than the cubic solver from [46]. Additionally, we propose a way of exploiting AC-wise normals in image-based visual localization pipelines. The algorithms are tested on 15k image pairs from standard benchmarks, and our results show superior accuracy and faster wall-clock times compared to the baselines.
+
+# 2. Proposed Method
+
+The setting is visualized in Fig 1. We are given two images, denoted by  $\Pi^1$  and  $\Pi^2$ . The 2D and 3D point locations are visualized as black dots. For standard PC-based stereo vision, the 3D location can be obtained by the so-called triangulation method. The local affine transformation, denoted by  $\mathbf{A} \in \mathbb{R}^{2 \times 2}$ , is defined as the first-order Taylor-approximation of the imaging function at points  $\mathbf{p}_1$  and  $\mathbf{p}_2$ . It maps the infinitesimal patch around the observed points from the first to the second image. If  $\mathbf{A}$  is known, the surface normal  $\mathbf{n}$  can be directly estimated without knowing the actual 3D structure of the underlying scene [49].
+
+Parameterization. A surface normal  $\mathbf{n} \in \mathbb{R}^3$  is a 3D direction, therefore it can be represented by two parameters. Usually, it is parameterized by three coordinates  $\mathbf{n} = [n_x, n_y, n_z]^\top$  and its length being set to 1. However, as it turns out below, some other scaling will be more convenient in the present situation.
+
+Problem Statement. Let us assume that we are given a general camera that projects the spatial location  $\mathbf{P} = [X, Y, Z]^\top$  to image (pixel) coordinates  $[u v]^\top$ , and let us
+
+denote the projective coordinate functions by  $\Pi_u: \mathbb{E}^3 \to \mathbb{R}$  and  $\Pi_v: \mathbb{E}^3 \to \mathbb{R}$ . Function  $\Pi_u$  calculates coordinate  $u$  of the projected point, and  $\Pi_v$  calculates  $v$ . As Molnár and Chetverikov showed [49], the affine transformation can be defined via the spatial gradients of the projective coordinate functions  $\Pi_u$  and  $\Pi_v$ .
+
+An affine correspondence is represented by 2D image coordinates  $[u_1 v_1]^\top$  and  $[u_2 v_2]^\top$  in the stereo image pair, in conjunction with the affine transformation  $\mathbf{A}$  that maps the surrounding area of the locations from first image to the second one. The spatial location of the corresponding spatial point is also required. It can be estimated from the image coordinates and camera parameters by standard triangulation techniques [29].
+
+The normal estimation problem is written [9] as an argument minimization to determine the optimal  $\mathbf{n}^*$  such that
+
+$$
+\mathbf {n} ^ {*} = \operatorname * {a r g   m i n} _ {\mathbf {n}} f (\mathbf {n}),
+$$
+
+with
+
+$$
+f (\mathbf {n}) := \sum_ {i = 1} ^ {2} \sum_ {j = 1} ^ {2} \left(\frac {\mathbf {n} ^ {\top} \mathbf {w} _ {i j}}{\mathbf {n} ^ {\top} \mathbf {w} _ {c}} - a _ {i j}\right) ^ {2}. \tag {1}
+$$
+
+Here, the affine transformation yields the four affine parameters  $a_{ij}$  ( $i,j\in [1,2]$ ) according to
+
+$$
+\mathbf {A} = \left[ \begin{array}{c c} a _ {1 1} & a _ {1 2} \\ a _ {2 1} & a _ {2 2} \end{array} \right],
+$$
+
+and the vectors  $\mathbf{w}_{ij}$  and  $\mathbf{w}_c$  are obtained as cross products of the spatial gradient vectors as follows:
+
+$$
+\begin{array}{l} \mathbf {w} _ {1 1} = \nabla \Pi_ {v} ^ {1} \times \nabla \Pi_ {u} ^ {2}, \quad \mathbf {w} _ {1 2} = \nabla \Pi_ {u} ^ {2} \times \nabla \Pi_ {u} ^ {1}, \\ \mathbf {w} _ {2 1} = \nabla \Pi_ {v} ^ {1} \times \nabla \Pi_ {v} ^ {2}, \quad \mathbf {w} _ {2 2} = \nabla \Pi_ {v} ^ {2} \times \nabla \Pi_ {u} ^ {1}, \\ \mathbf {w} _ {c} = \nabla \Pi_ {u} ^ {1} \times \nabla \Pi_ {v} ^ {1}, \\ \end{array}
+$$
+
+where the superscripts refer to the corresponding image index. The coordinates of these vectors will be denoted by  $\mathbf{w}_{ij,x},\mathbf{w}_{ij,y},\mathbf{w}_{ij,z}$ $(i,j\in \{1,2\})$  and  $\mathbf{w}_{c,x},\mathbf{w}_{c,y},\mathbf{w}_{c,z}$ .
+
+Pin-hole (perspective) projection model. For a pin-hole camera, the projection model is as follows:
+
+$$
+\left[ \begin{array}{c} u \\ v \\ 1 \end{array} \right] \sim \left[ \begin{array}{c c c c} P _ {1 1} & P _ {1 2} & P _ {1 3} & P _ {1 4} \\ P _ {2 1} & P _ {2 2} & P _ {2 3} & P _ {2 4} \\ P _ {3 1} & P _ {3 2} & P _ {3 3} & P _ {3 4} \end{array} \right] \left[ \begin{array}{c} X \\ Y \\ Z \\ 1 \end{array} \right],
+$$
+
+where  $\sim$  denotes the equality up to scale operation. Therefore, image coordinates  $u$  and  $v$  are obtained as
+
+$$
+\begin{array}{l} \Pi_ {u} = \frac {P _ {1 1} X + P _ {1 2} Y + P _ {1 3} Z + P _ {1 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}, \\ \Pi_ {v} = \frac {P _ {2 1} X + P _ {2 2} Y + P _ {2 3} Z + P _ {2 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}. \\ \end{array}
+$$
+
+Spatial gradients, that are  $\nabla \Pi = \left[ \begin{array}{ccc}\frac{\partial\Pi}{\partial X} & \frac{\partial\Pi}{\partial Y} & \frac{\partial\Pi}{\partial Z} \end{array} \right]^{\top}$ , can be written for the pin-hole model in compact forms as
+
+$$
+\begin{array}{l} \begin{array}{r l} \nabla \Pi_ {u} & = \frac {1}{s} \left[ \begin{array}{c} P _ {1 1} \\ P _ {1 2} \\ P _ {1 3} \end{array} \right] ^ {\top} - \frac {u}{s} \left[ \begin{array}{c} P _ {3 1} \\ P _ {3 2} \\ P _ {3 3} \end{array} \right] ^ {\top}, \end{array} \\ \nabla \Pi_ {v}   =   \frac {1}{s} \left[ \begin{array}{c} P _ {2 1} \\ P _ {2 2} \\ P _ {2 3} \end{array} \right] ^ {\top} - \frac {v}{s} \left[ \begin{array}{c} P _ {3 1} \\ P _ {3 2} \\ P _ {3 3} \end{array} \right] ^ {\top}, \\ \end{array}
+$$
+
+where  $s = P_{31}X + P_{32}Y + P_{33}Z + P_{34}$  is the projective depth.
+
+Solution. For the problem to be meaningful, we can assume that  $\mathbf{w}_c \neq \mathbf{0}$ . Let us set
+
+$$
+I := \inf  _ {\| \mathbf {n} \| = 1, \mathbf {n} ^ {\top} \mathbf {w} _ {c} \neq 0} f (\mathbf {n}),
+$$
+
+where  $\| \mathbf{n}\| \coloneqq \sqrt{\mathbf{n}^\top\mathbf{n}}$  denotes the standard Euclidean norm. Clearly,  $f\geq 0$  is undefined along the "equator" of the unit sphere  $\| \mathbf{n}\| = 1$  with  $\mathbf{n}^{\top}\mathbf{w}_{c} = 0$ . Let us consider two cases.
+
+If all  $\mathbf{w}_{ij}$  and  $\mathbf{w}_c$  are equal, then trivially  $f(\mathbf{n}) = \sum_{i,j=1}^{2}(a_{ij} - 1)^2$  is a constant function.
+
+Otherwise, at least one of the expressions  $\frac{\mathbf{n}^{\top}\mathbf{w}_{ij}}{\mathbf{n}^{\top}\mathbf{w}_{c}}$  becomes arbitrarily large in modulus when  $\mathbf{n}$  is chosen such that  $\mathbf{n}^{\top}\mathbf{w}_c$  gets sufficiently close to 0; that is,  $|f(\mathbf{n})|\to +\infty$  as  $\mathbf{n}^{\top}\mathbf{w}_c\rightarrow 0$  with  $\| \mathbf{n}\| = 1$ . Therefore, by taking into account the continuity of  $f$  as well, the infimum  $I$  is in fact a minimum, and an optimal unit vector  $\mathbf{n}^{*}$  with  $f(\mathbf{n}^{*}) = I$  exists. In what follows, we will explicitly determine such an  $\mathbf{n}^{*}$  as a function of the 19 parameters<sup>1</sup> by using only the four basic arithmetic operations.
+
+A key observation is that  $f(\lambda \mathbf{n}) = f(\mathbf{n})$  for any  $\lambda \neq 0$ , so (after a possible rescaling) we can assume that the last component of  $\mathbf{n}$  is either 1 or 0. These cases, Cases A and B, respectively, will be discussed separately below. To simplify the notation, let us define two auxiliary functions
+
+$$
+g \left(n _ {x}, n _ {y}\right) := f \left(n _ {x}, n _ {y}, 1\right) \tag {2}
+$$
+
+and
+
+$$
+h \left(n _ {x}, n _ {y}\right) := f \left(n _ {x}, n _ {y}, 0\right). \tag {3}
+$$
+
+For the objective function  $g$ , we will obtain a unique candidate extremum  $\mathbf{n}_g^* \in \mathbb{R}^2$ ; whereas for the function  $h$ , a one-parameter family of candidate extrema  $\mathbf{n}_h^* \in \mathbb{R}^2$  will be found but with the same function value  $h(\mathbf{n}_h^*)$ . The optimal  $\mathbf{n}^*$  is then
+
+$$
+\mathbf {n} ^ {*} = \left\{ \begin{array}{l l} \left[ \mathbf {n} _ {g} ^ {*}, 1 \right] ^ {\top}, & \text {i f} g \left(\mathbf {n} _ {g} ^ {*}\right) \leq h \left(\mathbf {n} _ {h} ^ {*}\right), \\ \left[ \mathbf {n} _ {h} ^ {*}, 0 \right] ^ {\top}, & \text {i f} g \left(\mathbf {n} _ {g} ^ {*}\right) > h \left(\mathbf {n} _ {h} ^ {*}\right). \end{array} \right. \tag {4}
+$$
+
+Remark 1 In other words, we will be utilizing the simple constraints  $n_z = 1$  or  $n_z = 0$ . We have found that other linear or non-linear constraints, such as  $\| \mathbf{n} \| = 1$ , would render the symbolic calculations to minimize the objective function  $f$  infeasible.
+
+Case A:  $n_z = 1$
+
+We use the standard technique and solve the system
+
+$$
+\left\{ \begin{array}{l} \partial_ {1} g \left(n _ {x}, n _ {y}\right) = 0, \\ \partial_ {2} g \left(n _ {x}, n _ {y}\right) = 0 \end{array} \right. \tag {5}
+$$
+
+to find the optimal vector  $\mathbf{n}_g^* = [n_x, n_y]^\top$  as follows.
+
+By computing and putting the partial derivative
+
+$$
+\partial_ {1} g (n _ {x}, n _ {y})
+$$
+
+over a common denominator, we see that its numerator depends on  $n_x$  linearly; and it depends on  $n_y$  quadratically; so one can easily express  $n_x$  from the equation  $\partial_1 g(n_x, n_y) = 0$  as follows:
+
+$$
+n _ {x} = \frac {\operatorname {n u m e r} _ {1}}{\operatorname {d e n o m} _ {1}}, \tag {6}
+$$
+
+where we present the expressions for  $\mathrm{numer}_1$  and  $\mathrm{denom}_1$  in the supplementary material. Then (6) is substituted into the other partial derivative  $\partial_2 g(n_x, n_y)$ . The resulting rational function of  $n_y$ , also containing the other 19 parameters, can be simplified and factorized by Wolfram Mathematica's Factor command<sup>2</sup>. In this way, we obtain a fraction whose structure is the following:
+
+$$
+\frac {\operatorname {l i n e a r} _ {1} \cdot \operatorname {l i n e a r} _ {2}}{(\text {q u a d r a t i c}) ^ {2}}, \tag {7}
+$$
+
+where the expressions "linear" and "quadratic" denote polynomials in  $n_y$  having the corresponding degrees.
+
+The optimum of  $g$  can occur when  $n_y$  is chosen such that the fraction (7), that is, its numerator is equal to 0. It can be shown that the assumption  $\mathrm{linear}_1 = 0$  leads to a contradiction - indeed, by solving  $\mathrm{linear}_1 = 0$  for  $n_y$ , the resulting formula would make  $\mathrm{denom}_1$  in (6) identically equal to 0. Hence, we are only left with the equation  $\mathrm{linear}_2 = 0$ , whose solution is
+
+$$
+n _ {y} = \frac {\operatorname {n u m e r} _ {2}}{\operatorname {d e n o m} _ {2}}. \tag {8}
+$$
+
+The actual formulas for  $\mathrm{numer}_2$  and  $\mathrm{denom}_2$  are found again in the supplementary material.
+
+Thus, the second component of  $\mathbf{n}_g^*$  is given by (8) (expressed in terms of the 19 parameters). Then, by using this together with (6), we obtain  $n_x$ , the first component of  $\mathbf{n}_g^*$ .
+
+Remark 2 The essential feature of these computations is that the solution of system (5) is given in a fully explicit symbolic form by using only elementary operations. Without the clever intermediate symbolic simplifications and factorizations (most notably (7)), one would need to solve a higher-degree polynomial equation to obtain  $n_y$ , requiring either taking roots or using an iterative scheme. For example, if one starts solving (5) with  $n_x$  and  $n_y$  as symbolic parameters but all the coefficients of  $g$  as floating-point numbers, then, in general, no intermediate factorizations or simplifications are possible, so in order to determine  $n_y$ , one would need to solve a quintic equation.
+
+Case B:  $n_z = 0$
+
+We proceed similarly and solve the system
+
+$$
+\left\{ \begin{array}{l} \partial_ {1} h \left(n _ {x}, n _ {y}\right) = 0, \\ \partial_ {2} h \left(n _ {x}, n _ {y}\right) = 0. \end{array} \right. \tag {9}
+$$
+
+By expressing  $n_x$  from the first equation of (9) and substituting the resulting expression into the second equation, we find that this time the second equation is automatically satisfied. Therefore, (9) possesses a one-parameter family of solutions given by
+
+$$
+n _ {x} = \frac {\operatorname {n u m e r} _ {3}}{\operatorname {d e n o m} _ {3}}, \tag {10}
+$$
+
+see the supplementary material. By substituting this into  $h$ , the function value  $h(\mathbf{n}_h^*)$  appearing in (4) is obtained as
+
+$$
+h \left(\mathbf {n} _ {h} ^ {*}\right) = \frac {\operatorname {n u m e r} _ {4}}{\operatorname {d e n o m} _ {4}}. \tag {11}
+$$
+
+See the supplementary material for details.
+
+Remark 3 One directly checks that the value  $h(\mathbf{n}_h^*) = h\left(\frac{\mathrm{numer}_3}{\mathrm{denom}_3}, n_y\right)$  is indeed independent of  $n_y$ , as claimed.
+
+# 2.1. Summary of the Algorithm
+
+Given the elements  $a_{ij} \in \mathbb{R}$  in the affine transformation and 3D vectors  $\mathbf{w}_{ij}$  and  $\mathbf{w}_c \neq \mathbf{0}$ , let us define the function  $f$  by (1) for  $\mathbf{n}$  with  $\mathbf{n}^\top \mathbf{w}_c \neq \mathbf{0}$ , and also define the functions  $g$  and  $h$  by (2)-(3). If  $\mathbf{w}_{11} = \mathbf{w}_{12} = \mathbf{w}_{21} = \mathbf{w}_{22} = \mathbf{w}_c$ , then any unit vector  $\mathbf{n}^*$  can be chosen as optimal normal vector.
+
+Otherwise, we compute  $\mathbf{n}_g^* \coloneqq [n_x, n_y]^\top$  from (8) and (6). Then we compute  $h(\mathbf{n}_h^*)$  from (11). Finally, the optimal  $\mathbf{n}^*$  is determined by using (4).
+
+# 3. Experiments
+
+We focus on the accuracy and time demand of the algorithms when testing. Both synthetic testing data, including configurations for a number of important camera motions, and standard real-world benchmarks are considered here.
+
+![](images/3361adbf5f991a037b270f6cca617713817d6b0f9a68b30df32547514bbdf2f7.jpg)
+
+![](images/9443b008b2f21844cc9e34eed51e5c36849a35ae5c047f53f1ef7a7de01f9ca6.jpg)
+
+![](images/7aa5f0a54ff8a3fb5ede75cbbad692e3c95bd5b99bdad1a20caee658846f7d38.jpg)  
+Figure 2. Images and the reference reconstruction used from the Cambridge Landmarks dataset [39] in localization experiments.
+
+![](images/52da8b4b8b4e061f0e13354f93a23bc7e07fd79f0a4315df454e46bb22dc7e4d.jpg)
+
+Compared Algorithms. In this section, we discuss the algorithms that can be used to estimate the surface normal from a single affine correspondence.
+
+1. The provably most accurate algorithms are the ones that are optimal in the least squares sense. Method  $\mathrm{OPT}_{\mathrm{QUARTIC}}$  refers to [9] which solves the problem as a real root of a quartic polynomial equation. The cubic solution  $\mathrm{OPT}_{\mathrm{CUBIC}}$  is from [46]. The proposed optimal solver, as it is solved via linear equations, is called  $\mathrm{OPT}_{\mathrm{LINEAR}}$  in the rest of the paper.  
+2. The simplest and, thus, the fastest method is the Fast Normal Estimation (FNE) algorithm of [9]. A more complex variant, when all possible linear equations are considered, is also constructed here, it is denoted as  $\mathrm{FNE}_{\mathrm{SUPER}}$ . The modified equations can be seen in the source codes in the supplementary material.  
+3. Raposo and Barreto [56] proposed a solution that estimates the normal via homographies. We have not found an implementation or an exact definition of the algorithm, so we implemented it based on the description. The solution is computed via an over-determined inhomogeneous linear system of equations. The formulas are generated by the MATLAB Symbolic Toolbox. Details are given in the supplementary material. The method is called RAPOSO in the charts.
+
+The synthetic tests are performed in MATLAB. In the real-world experiments, optimized  $\mathrm{C}++$  codes run on an Intel(R) Core(TM) i9-10900K CPU @ 3.70GHz.
+
+# 3.1. Synthetic Experiments
+
+For the synthetic tests, a spherical object is generated, thus straightforwardly allowing to sample oriented points from its surface. Two cameras are randomly generated with focal lengths from the range [500, 1500] and with image size  $2000 \times 2000$ . Their intrinsic matrices are  $\mathbf{K}_1$  and  $\mathbf{K}_2$ .
+
+The 3D point was projected into both cameras. The ground truth (GT) affine parameters were calculated directly from the camera parameters and the surface normals as shown in [9]. Several camera configurations are considered to simulate various real-world scenarios. They are as follows:
+
+- For general stereo pose, the locations of the cameras are randomly generated inside a unit-radius sphere. The camera projection matrices are constructed as  $\mathbf{P}_1 = \mathbf{K}_1[\mathbf{I} \mid \mathbf{0}]$  and  $\mathbf{P}_2 = \mathbf{K}_2[\mathbf{R} \mid \mathbf{t}]$ .  
+- For rectified stereo, the cameras are located next to each other with identical orientation. In this case, the projection matrices are  $\mathbf{P}_1 = \mathbf{K}_1[\mathbf{I} \mid \mathbf{0}]$  and  $\mathbf{P}_2 = \mathbf{K}_2[\mathbf{I} \mid \mathbf{t}]$ , where  $\mathbf{t} = [\Delta X 0 0]^\top$ .  
+- Planar motion simulates the case when a camera is mounted on a vehicle that moves on a planar road with the image plane orthogonal to the ground. Such a motion can be represented by two angles around the vertical axis, one for the rotation and one for the translation. In this case, the projection matrices can be written as  $\mathbf{P}_1 = \mathbf{K}_1[\mathbf{I} \mid 0]$  and  $\mathbf{P}_2 = \mathbf{K}_2[\mathbf{R}_{\mathrm{Y}} \mid \mathbf{t}]$ , where  $\mathbf{t} = \rho [\cos \beta, 0, \sin \beta]^\top$  and
+
+$$
+\mathbf {R} _ {\mathrm {Y}} = \left[ \begin{array}{c c c} \cos \alpha & 0 & \sin \alpha \\ 0 & 1 & 0 \\ - \sin \alpha & 0 & \cos \alpha \end{array} \right].
+$$
+
+- Moto-motion. This test case simulates a camera that is mounted on a motorcycle. If the bike leans, another rotation, the roll is involved in the problem. In this case, the camera parameters are  $\mathbf{P}_1 = \mathbf{K}_1[\mathbf{I} \mid \mathbf{0}]$  and  $\mathbf{P}_2 = \mathbf{K}_2[\mathbf{R}_{\mathrm{YZ}} \mid \mathbf{t}]$ , where  $\mathbf{t} = \rho [\cos \beta 0 \sin \beta]^\top$  and  $\mathbf{R}_{YZ} = \mathbf{R}_Y \mathbf{R}_Z$ .  
+- Drone-motion is another generalization of the planar motion. A camera mounted on a flying drone. Its location is arbitrary, but the orientation is limited to a vertical rotation. Therefore,  $\mathbf{P}_1 = \mathbf{K}_1[\mathbf{I} \mid \mathbf{0}]$  and  $\mathbf{P}_2 = \mathbf{K}_2[\mathbf{R}_Y \mid \mathbf{t}]$ , where  $\mathbf{t} = [X Y Z]^\top$ .
+
+Noise. We have added zero-mean Gaussian noise to the 2D coordinates, therefore, the point noise is given in pixels. The deviation of the noise is the parameter in the charts.
+
+The  $2 \times 2$  affine transformations are decomposed by SVD into two 2D rotations and another two scaling parameters. Then zero-mean Gaussian noise is added to the angle of rotations, in radians, and the scaling parameters. The standard deviation of the Gaussian noise distribution is equally set for all the four parameters.
+
+3D Reconstruction Pipeline. In order to simulate real scenarios, first, we triangulate each generated noisy point correspondence by the optimal triangulation method proposed by Hartley and Sturm [29]. The noisy affine parameters are corrected by the method proposed in [7] to be consistent with the camera parameters.
+
+![](images/e29247ae079a115614ff62377b1ca561bfb6a47a6f259aefd29da6c614187ebc.jpg)  
+Figure 3. The frequencies (in 10000 runs) of the  $\log_{10}$  errors in the  $\log_{10}$  angular errors in degrees in the noise-free case.
+
+Stability test. We generated 10000 random problem instances considering general camera motion and ran the normal estimators on noiseless affine correspondences. Fig. 3 shows histograms of  $\log_{10}$  angular errors in degrees. Note that for better visualization, we replace the exact zero values by  $10^{-16}$  as it is the precision of the floating point numbers in MATLAB. The plots show that all our solvers are very stable – there is no peak close to  $10^0$ . For all methods, the majority of the errors are distributed around  $10^{-16}$  which actually is the precision of MATLAB. This means that in most of the cases, all methods are particularly stable returning almost exactly 0 error. A small peak is over  $10^{-6}$  for all methods similarly. Having  $10^{-6}$  degree error is acceptable in most of the scenarios considered in computer vision. There is no peak close to  $10^0$  implying that all solvers are stable. Note that these stability tests usually are for highlighting potential degeneracies where the error exceeds  $10^0$ .
+
+We also conducted tests using single-point precision in MATLAB. The OPTQUARTIC approach failed entirely under these conditions. For all other methods, we noticed an increase in error, which suggests that double precision is necessary for reliable normal estimation. Interestingly, our proposed OPTLINEAR method appears to be slightly more sensitive to precision than OPTCUBIC is. This is likely due to the fact that OPTLINEAR employs more complex formulas and, consequently, performs more stably with double precision.
+
+Accuracy test. The accuracy of the normals is examined for all the considered camera poses independently. The results are shown in Fig 9. The effect of noise in point coordinates and affine parameters are separately evaluated. Both the mean and the median of the errors are plotted.
+
+The observations we can make from the plots are as follows. First, the three optimal methods  $\mathrm{OPT}_{\mathrm{QUARTIC}}$ ,  $\mathrm{OPT}_{\mathrm{CUBIC}}$  and  $\mathrm{OPT}_{\mathrm{LINEAR}}$  always lead exactly to the same solution, thus their curves coincide in all plots. Second, the optimal methods always lead to the most accurate results if the affine parameters are contaminated by noise. This is not
+
+surprising as these methods optimize the normal parameters such that the implied affine transformation is the closest to the measured one. In the case of point-noise only, the accuracy of the optimal algorithm is slightly below that of the competitors. However, it is an unlikely situation in real-world images to have noisy points but perfect local affine frames. It is usually the other way around. Third, as the FNE method uses less information, it is clearly the worst one in terms of accuracy.  $\mathrm{FNE}_{\mathrm{SUPER}}$  performs significantly better, however, it requires more time as the right singular vector of a  $6\times 3$  matrix, corresponding to the smallest singular value, should be computed. Another benefit of  $\mathrm{FNE}_{\mathrm{SUPER}}$  is, contrary to FNE and Raposo [56], that it works in all test cases. It can cope with both planar motion and rectified stereo, similarly to the optimal algorithms.
+
+Problematic methods. Methods FNE and Raposo [56] do not work if the cameras undergo special translations. FNE is a special method, several variants can be formed based on the selection of the affine transformations. For rectified stereo, the third and fourth elements are fixed [44], they cannot be used for the estimation.
+
+The Raposo [56] method is the most problematic one as the homography can be decomposed into the camera rotation, translation and surface normal. If the translation has zero elements, the retrieved equations are linearly dependent, and the estimation does not yield a correct solution. Due to this reason, Raposo [56] does not work for rectified stereo and planar motion. We removed these methods from the plots of the respective camera configurations.
+
+Combined noise. In the previous experiments, noise is added either to the point coordinates or affine parameters. Here, we contaminate both types of input data. The mean and median errors of the proposed linear method are visualized in Fig. 10. As it is expected, the curves show similar trends, but the case when both the points and affines are noisy leads to higher errors.
+
+Interpretable affine noise. In the previous experiments, the noise is added directly to the elements of the affine matrices. In Fig. 11, we consider a different way of contaminating the input to show that the proposed method acts reasonably with different noise models as well. The results of curves Aff and Comb are obtained by using the noise model from the previous sections. Comb refers to the case when both the points and the affine matrices are noisy. For AffElem and Comb-Elem, we decompose A by SVD into two orthogonal and a diagonal matrix. Fig. 11 demonstrates that the noise generation does not strongly influence the results.
+
+# 4. Real-world Experiments
+
+To test normal estimators, we use the Cambridge Landmarks [39] and ScanNet datasets [18]. We chose Cambridge Landmarks, see Fig. 2 for example images, since it provides a large number of images for testing directly the
+
+![](images/e00cb504bc546457895ce0aa123a2fe0c8d9fb9be95d72a65326bff9fb5c44e0.jpg)
+
+![](images/eeacceaf62dc6d144c117dab0fba5bc60a93abeff01bb0403dca86e754fa110e.jpg)
+
+![](images/b05dd400a77b1142754bc5e9cc19aa3b8a2e009f68fc685032cd21281077175e.jpg)  
+Figure 4. General Motion.
+
+![](images/7cba10c32b4f2843d7ec8d2599b7d2f90625f6359189829e2cd5aa48f5831ad2.jpg)
+
+![](images/948ac9746a92375e8283b0ab8e0331b152b1941855a96f3683ce6ac30384690e.jpg)
+
+![](images/f5823d95f2ef91a088d04317aee25aa099e38d425f75a7c472ec120c8677a40e.jpg)
+
+![](images/0b8be2ec24e87b1682ce1ab3c497291b1d077f74ae3e305862a028e3d1829f52.jpg)  
+Figure 5. Rectified Stereo.
+
+![](images/ebb91366dee31e11c32a664398fefc899af2b32abee7350f70399503818cd040.jpg)
+
+![](images/f2f5cd5f73b8b32db8338da54395dec2b2afa99d1db88d314d5821edbb439577.jpg)
+
+![](images/d028ae3a9cc7fe72a13b88d912d1d0ed8b79c242c95d9fb6fb23d80e6c08bab8.jpg)
+
+![](images/7a3d482fe64ec4cac62e80206b50e66a1356cbbd350843476ad055bb216694d7.jpg)  
+Figure 6. Planar Motion.
+
+![](images/dd12fafc323c83b4e17753fd5ebea86cc28761dc8a09eaf89112364871bd90a7.jpg)
+
+![](images/2c9d020dc92e5aedee75bc7d4d2afafdf5d6218a4bd665f9fcce69da0ceed6a6.jpg)
+
+![](images/e0eb25234c40f4ac1dfb29acafb4ced8150fd4e857288dccf9a403dba5a08020.jpg)
+
+![](images/d4285f04584e2e24052763f147b6078dc863bcfec0635a86a9193d6f936b4ae9.jpg)  
+Figure 7. Moto Motion.
+
+![](images/44a2e7f549b351c8d796252cecccb50f32c7086737d70ced94c94b5755d43200.jpg)
+
+![](images/cdab81ac4f53dee3550ff07f2cb78219f422692eec1625340859fb715ff3ac2e.jpg)
+
+![](images/2f63d8ff61554da8b97f8bab4cd258b676cb22ba9d136c3c45a1ee820c178455.jpg)  
+Figure 9. Average and median angular errors (in degrees) of surface normal estimators on synthetic data. Five camera configurations are considered. From left to right: (1) Median error; noise added to affine parameters. (2) Average error; noise added to affine parameters. (3) Median error; noise added to point coordinates. (4) Average error; noise added to point coordinates.
+
+![](images/71f07ae3ccc694ec59f324292b47b7e713b21625dd14fc2e66ba00eb6d1f459a.jpg)  
+Figure 8. Drone Motion.
+
+![](images/438bf52d4be6ad617d635fd593c4a4d9169606aedd16012c75b9c15a72f0c273.jpg)
+
+![](images/125656e0a522fe3bbf44d20cfcd3921be0458d1b5d078f40f22ac2a806541cbd.jpg)
+
+normal accuracy and, also, we can evaluate localization as an application of the proposed procedure. Also, we chose ScanNet since the reference normals can be calculated directly from the dense depth maps which provides a complementary comparison to the tests on Cambridge Landmarks,
+
+where the normals come from a 3D reconstruction.
+
+Cambridge Landmarks consists of five scenes with varying number of images, ranging from 231 to 3015. The reference pose of each image was reconstructed using the VisualSFM structure-from-motion software [70, 69] and the
+
+![](images/afe3cccb487e6fa90b540974d96e7f2bfb61553b1921b007398e949eb17c0d4b.jpg)  
+Figure 10. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to point coordinates (Point), affine parameters (Affine) or both (Combined).
+
+![](images/b9507a16a4962393dd58f28b472a2706f878510d3e77bd11f2d4779683469989.jpg)
+
+![](images/cfa87fde61ea568549103ddeb3b6007b3743ace39c2b1b98cf661245e154abdd.jpg)  
+Figure 11. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to only the affine  $(A\text{ff})$  elements and, also, to the point coordinates  $(Comb)$ . For Aff and Comb, zero-mean Gaussian noise is added directly to the affine elements. For Aff-Elem and Comb-Elem, the affine matrix is decomposed by SVD to two rotations and a diagonal matrix. Zero-mean Gaussian noise is added to the rotation angles and diagonal elements.
+
+![](images/166482e29d8bfca0ca6612feb0cd377d7bca63f7c3742e99f5ecb687fe59ba8c.jpg)
+
+images are divided into training and testing sets. To have more accurate reference data, we ran COLMAP [63] obtaining a dense point cloud. Finally, we applied the normal estimator implemented in MeshLab<sup>3</sup> to obtain an oriented point cloud to be considered reference. The normals are fitted to the 200 nearest neighbors. For each query image, we ran DenseVLAD [67] to get 20 potential database images. In our experiments, the algorithms are tested on each obtained image pair, i.e., 20 pairs for each query image. For ScanNet, we use the 1500 image pairs used in [59].
+
+On Cambridge Landmarks, we detect affine correspondences by detecting DoG features [42], finding the affine shape by AffNet [48], and extracting HardNet [47] descriptors. This approach is among the leaders in the IMC 2020 benchmark [34]. On ScanNet, we detect SuperPoint [20] features, match them by SuperGlue [59], and find the affine shape by, first, estimating scale and orientation by SelfScaleOri [41] and, then, finding the affine shapes by AffNet.
+
+Normal Estimation. To test normal estimators, we ran all of them on the data described in the previous section. For each image pair, we iterate through all detected correspondences that are consistent with the camera pose - they have less than 5 pixels of Sampson distance. For each of
+
+![](images/1bb67d9598776c047ef3944af4a4be4982d425f647c69f790568eade56b61920.jpg)  
+Figure 12. The median angular error in degrees (left) and the AUC@  $10^{\circ}$  score (right) of the estimated normals plotted as a function of the error in the detected affine correspondences on the Cambridge Landmarks dataset.
+
+![](images/4b414b70d67b0597142c805eaa4d8ea1d857e02ceaa495e357e61aa2c07afe43.jpg)
+
+them, we ran multiple normal estimators, measure their angular error and run-time. To understand how the estimators proceed with respect to the error in the detected affine transformations  $\mathbf{A}$ , we calculate the reference transformation  $\mathbf{A}^*$  from the camera parameters and the surface normal as shown in [9]. We define the affine error as the Frobenius norm of the difference matrix  $\| \mathbf{A} - \mathbf{A}^* \|_{\mathrm{F}}$ .
+
+The Area Under the recall Curve (AUC) at  $5^{\circ}$ ,  $10^{\circ}$  and  $20^{\circ}$ , the avg. and med. angular errors with the standard deviation in degrees and the run-time in nanoseconds on the Cambridge Landmarks dataset are reported in Table 1. As expected, the best results are achieved by the optimal algorithms, all of them leading to exactly the same results. Our proposed linear solution of the optimal problem,  $\mathrm{OPT}_{\mathrm{LINEAR}}$ , is five times faster than the cubic solution  $\mathrm{OPT}_{\mathrm{CUBIC}}$ . While  $\mathrm{OPT}_{\mathrm{LINEAR}}$  is slightly slower than the fastest FNE method, it is significantly more accurate. Interestingly, while the method of Raposo et al. [56] worked well in the synthetic experiments, we did not manage to achieve good accuracy with it in the real-world experiments. Figure 12 plots the AUC@ $10^{\circ}$  score and the median angular error as a function of the noise in the detected affine parameters. As expected, normal estimation is highly sensitive to the quality of the affine parameters. The optimal algorithms are the most stable ones.
+
+The results on the ScanNet dataset are reported in Table 3. Similarly as on Cambridge Landmarks, all optimal solvers lead to the same accuracy while the proposed one being the fastest by a large margin.
+
+Visual Localization. To test the impact of surface normal estimation on localization, on the Cambridge Landmarks dataset, we applied the following procedure. We iterate through all query images, each having 10 database images retrieved by DenseVLAD. First, we estimate the relative pose between the query and a random database image by GC-RANSAC [6] with P3P [54]. Using the obtained pose, we estimate the surface normal of each inlier affine correspondence in the coordinate system of the query image. Next, we iterate through all unused database images and use
+
+<table><tr><td>Estimator</td><td>AUC@5°↑</td><td>@10°↑</td><td>@20°↑</td><td>Avg. err. (°) ↓</td><td>Med. err. (°) ↓</td><td>Std. dev. (°) ↓</td><td>Time (ns) ↓</td></tr><tr><td>FNE [49]</td><td>6.0</td><td>16.0</td><td>33.7</td><td>21.0</td><td>14.3</td><td>21.3</td><td>172</td></tr><tr><td>FNESUPER</td><td>8.9</td><td>22.1</td><td>42.0</td><td>10.9</td><td>16.8</td><td>15.6</td><td>1721</td></tr><tr><td>Raposo [56]</td><td>0.4</td><td>1.5</td><td>5.7</td><td>38.5</td><td>36.5</td><td>18.2</td><td>883</td></tr><tr><td>OPTQUARTIC [9]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2528</td></tr><tr><td>OPTCUBIC [46]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2484</td></tr><tr><td>Proposed OPTLINEAR</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>596</td></tr></table>
+
+Table 1. The AUC score at  $5^{\circ}$ ,  $10^{\circ}$ , and  $20^{\circ}$  of the estimated surface normals, their average and median errors in degrees, the standard deviation, and the average run-time, in nanoseconds, of a single normal estimation on the Cambridge Landmarks dataset.  
+
+<table><tr><td rowspan="2">Solver</td><td rowspan="2">Normal estimator</td><td colspan="3">Pose accuracy ↑</td><td rowspan="2">Med. rot. err. (°) ↓</td><td rowspan="2">Med. pos. err. (cm) ↓</td></tr><tr><td>AUC@1°, 10cm</td><td>@2.5°, 25cm</td><td>@5°, 50cm</td></tr><tr><td>P3P</td><td>-</td><td>44.3</td><td>59.1</td><td>67.5</td><td>10.1</td><td>13.5</td></tr><tr><td>P1AC</td><td>FNESUPER</td><td>47.8</td><td>62.0</td><td>69.7</td><td>6.2</td><td>12.8</td></tr><tr><td>P1AC</td><td>Proposed OPTLINEAR</td><td>48.0</td><td>62.3</td><td>69.9</td><td>5.2</td><td>1.8</td></tr><tr><td>P1AC</td><td>GT</td><td>48.4</td><td>62.9</td><td>70.4</td><td>4.6</td><td>2.1</td></tr></table>
+
+Table 2. Localization AUC scores at  $(1^{\circ}, 10\mathrm{cm})$ ,  $(2.5^{\circ}, 25\mathrm{cm})$ , and  $(5^{\circ}, 50\mathrm{cm})$ , the median rotation (in degrees) and translation errors (in centimeters) on the Cambridge Landmarks dataset [39] when using either the P3P solver or the normal-based P1AC solver with FNEsuper or the proposed surface normal estimator OPTLINEAR. We also show the results with the reference normals. The minimal solvers are used within Graph-Cut RANSAC [6] that takes care of the robust estimation.  
+
+<table><tr><td></td><td>AUC@5↑</td><td>AUC@10↑</td><td>AUC@20↑</td><td>Time (ns)↓</td></tr><tr><td>FNE</td><td>14.8</td><td>15.4</td><td>17.0</td><td>207</td></tr><tr><td>FNESUPER</td><td>34.9</td><td>35.2</td><td>36.6</td><td>2142</td></tr><tr><td>OPTQUARTIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>18745</td></tr><tr><td>OPTCUBIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>3146</td></tr><tr><td>OPTLINEAR</td><td>35.0</td><td>35.5</td><td>37.3</td><td>747</td></tr></table>
+
+the P1AC [68] solver inside GC-RANSAC to estimate the pose. P1AC requires a single AC and the surface normal. We only test the proposed solver and  $\mathrm{FNE}_{\mathrm{SUPER}}$ . All other optimal solvers lead exactly to the same accuracy as ours.  $\mathrm{FNE}_{\mathrm{SUPER}}$  is the most accurate sub-optimal algorithm.
+
+The accuracy of the estimated pose for the database images with respect to their GT pose is reported in Table 2. All solvers, benefiting from normals and affine correspondences, are more accurate than using P3P. We also report the accuracy when using the reference normals to see the upper bound achievable using normals. The proposed optimal solver OPT LINEAR is only slightly (i.e.  $< 1$  AUC point) behind the accuracy of the GT normal, while being more accurate than the P3P-based solution. The AUC@  $10^{\circ}$  scores on each scene are reported in Table 4. The proposed OPT LINEAR leads to the best accuracy on all but two scenes.
+
+# 5. Conclusions
+
+In this work, we have presented a novel solver for estimating surface normals from affine correspondences when having calibrated cameras. The proposed method yields the
+
+Table 3. The AUC scores at  $5^{\circ}$ ,  $10^{\circ}$  and  $20^{\circ}$ , and the avg. time (in nanoseconds) of normal estimators on the ScanNet datasets [18].  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">P3P</td><td colspan="3">P1AC</td></tr><tr><td>GT</td><td>FNESUPER</td><td>Prop. OPTLINEAR</td></tr><tr><td>St. Mary&#x27;s Church</td><td>44.2</td><td>47.7</td><td>46.1</td><td>46.5</td></tr><tr><td>Old Hospital</td><td>44.1</td><td>57.4</td><td>56.8</td><td>57.3</td></tr><tr><td>King&#x27;s College</td><td>52.1</td><td>54.2</td><td>54.1</td><td>54.0</td></tr><tr><td>Shop Facade</td><td>65.5</td><td>65.0</td><td>63.8</td><td>64.1</td></tr><tr><td>Great Court</td><td>62.7</td><td>63.2</td><td>63.0</td><td>63.5</td></tr><tr><td>Street</td><td>17.4</td><td>22.8</td><td>23.1</td><td>23.0</td></tr></table>
+
+Table 4. The area under the recall curve (AUC) at  $1^{\circ}$  rotation and 10cm position errors on the Cambridge Landmarks dataset. We combine the P1AC solver with  $\mathrm{FNE}_{\mathrm{SUPER}}$  and the proposed normal estimator. Also, we test it with the reference normals.
+
+optimal solution, in the least squares sense, with respect to the affine error, and is particularly fast as the optimal normal is obtained via linear equations. We compared our method to all existing alternatives that estimate normals from a single correspondence on both simulated and real-world data. Additionally, we provide tests that highlight the benefits of using surface normals in image-based localization. The proposed estimator has demonstrated superior accuracy compared to the fastest existing method while being the second fastest overall. Our results suggest that the proposed algorithm is a promising alternative for surface normal estimation in computer vision applications.
+
+Acknowledgement. The authors warmly thank the reviewers for their very valuable comments and suggestions. The work was supported by the ETH Postdoc fellowship.
+
+# References
+
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+[2] Daniel Barath and Levente Hajder. A theory of point-wise homography estimation. Pattern Recognit. Lett., 94:7-14, 2017.  
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+                                            "type": "text",
+                                            "content": " are related by the local affine transformation "
+                                        },
+                                        {
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{A} \\in \\mathbb{R}^{2 \\times 2}"
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 9
+                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "require fewer data points than their point-based counterparts [64]. Moreover, normals can also be leveraged in the numerical refinement of the reconstructed oriented 3D point cloud [27]. In this paper, we focus on a practical problem, i.e., estimating the normal at corresponding features in two images in a solely photometric manner. This can provide a lightweight approach of obtaining surface normals without requiring a dense point cloud to be known. Next, we will discuss ways of obtaining oriented points."
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "Normals from Point Clouds. After applying state-of-the-art sparse (e.g., COLMAP [63]) or dense [36, 16] reconstruction pipelines, the resulting point cloud can be straightforwardly equipped with point orientations. In this case, typically, the normals are fitted per-point, applying the widely used Principal Component Analysis (PCA) [35] to estimate tangent planes or higher-order surfaces [14, 33] from the local neighborhood centered at the current point. This procedure, while being frequently used, has two major drawbacks. First, the setting of the neighborhood size greatly affects the accuracy and is often unclear without having a metric reconstruction. Instead, using the "
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+                                    "type": "text",
+                                    "content": "-nearest-neighbors [17] algorithm to find local neighborhoods is a viable solution, but the estimation becomes largely affected by the sparsity of the point cloud. Second, fitting local surfaces, independently, to the neighborhood of each 3D point"
+                                }
+                            ]
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "in the reconstruction is an extremely expensive operation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Normals from Homographies. Another method for estimating surface normals from images, without requiring the underlying 3D structure to be known, is via homographies. Homographies are projective transformations between images of co-planar 3D points that depends on the intrinsic and extrinsic camera parameters and the parameters of the underlying 3D plane [24]. A homography can be estimated from a minimum of four point correspondences in two images [30]. While this method allows the estimation of dominant planes supported by a number of correspondences in the images, it does not provide means for normal estimation for each local feature correspondence independently."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Normals from Local Mappings. In recent years, affine correspondences (AC) have emerged as a popular topic in computer vision, offering a valuable source of information about the underlying 3D geometry of the surrounding environment. An AC consists of a corresponding pair of points in two images and a linear transformation that maps the infinitesimal region around the point in the first image to the point in the second one. They have been used to solve various geometric problems, including relative pose estimation in the general case [15, 55, 3, 22, 10], for known vertical direction [25], planar motion [25, 26], or known feature depths [21] and homography estimation [2]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Traditionally, finding affine features involve four main steps: (scale-covariant) keypoint detection, orientation and affine shape estimation, and descriptor extraction. Under such paradigm, keypoint detection is typically performed on the scale pyramid with the help of a handcrafted response function, such as Hessian [13, 45], Harris [28, 45], Difference of Gaussians (DoG [42]), or learned ones like FAST [57] or Key.Net [11]. Keypoint detection obtains a triplet "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        286,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(x,y,\\mathrm{scale})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
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+                                    ],
+                                    "type": "text",
+                                    "content": " which defines a square or circular image patch. Then the patch orientation is estimated with the help of handcrafted - dominant gradient orientation [42], center of the mass [58] - or learned methods [71, 48, 41]. Next, the affine-covariant shape [12, 48] is estimated. Finally, the patch is geometrically rectified and fed into a local patch descriptor, such as SIFT, HardNet [47], SOSNet [66], or others. In summary, all feature detectors, even recent learning-based ones like SuperPoint [20], can be made affine covariant by applying, e.g., AffNet [48] as a post-processing step on the found features."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The problem of surface normal estimation from ACs has been addressed in several works. The first algorithm for normal estimation from ACs was proposed by Kevin Koeser [40] assuming that the camera location is known with respect to the observed 3D point. Megyesi et al. [44] proposed a special surface normal estimator for standard (rectified) stereo, where the degree of freedom of the affine transformations decreases to two. In 2014, Molnár and Chetverikov [49] derived a formula connecting the surface"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        545,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "normals, camera parameters, affine transformations, and patch locations into a single expression for arbitrary projective functions, like the catadioptric camera model. Barath et al. [9] proposed a globally optimal estimator in the least squares sense as the solution of a quartic polynomial. Recently, Le Minh and Hajder [46] improved on this by reducing the degree and showed that the optimal solution can be found as a real root of a cubic polynomial."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The main goal of this paper is to propose a rapid normal estimator based on affine correspondences. Our algorithm can be inserted into a 3D reconstruction system, such as Structure-from-Motion [27] (SfM) or Simultaneous Localization and Mapping (SLAM), where the normal estimation is performed many times, therefore its running time influences the time demand of the whole 3D pipeline."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Contribution. In this paper, we propose a new linear and globally optimal solution for surface normal estimation from a single affine correspondence. The proposed solver requires only the four basic arithmetic operations and contains 19 parameters, consisting of the coordinates of the five input vectors and the four affine parameters. This approach completely avoids root extractions, solving high-degree polynomial equations, or employing numerical or iterative methods, resulting in a particularly fast algorithm that runs for only "
+                                },
+                                {
+                                    "bbox": [
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+                                        252,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "0.6\\mu s"
+                                },
+                                {
+                                    "bbox": [
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+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " in our experiments. The solver is five times faster than the cubic solver from [46]. Additionally, we propose a way of exploiting AC-wise normals in image-based visual localization pipelines. The algorithms are tested on 15k image pairs from standard benchmarks, and our results show superior accuracy and faster wall-clock times compared to the baselines."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "2. Proposed Method"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                {
+                                    "bbox": [
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+                                        474,
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+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": "The setting is visualized in Fig 1. We are given two images, denoted by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Pi^1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Pi^2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": ". The 2D and 3D point locations are visualized as black dots. For standard PC-based stereo vision, the 3D location can be obtained by the so-called triangulation method. The local affine transformation, denoted by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A} \\in \\mathbb{R}^{2 \\times 2}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": ", is defined as the first-order Taylor-approximation of the imaging function at points "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": ". It maps the infinitesimal patch around the observed points from the first to the second image. If "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": " is known, the surface normal "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        474,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": " can be directly estimated without knowing the actual 3D structure of the underlying scene [49]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
+                        605,
+                        545,
+                        677
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        677
+                                    ],
+                                    "type": "text",
+                                    "content": "Parameterization. A surface normal "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        677
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n} \\in \\mathbb{R}^3"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        677
+                                    ],
+                                    "type": "text",
+                                    "content": " is a 3D direction, therefore it can be represented by two parameters. Usually, it is parameterized by three coordinates "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        677
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n} = [n_x, n_y, n_z]^\\top"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        677
+                                    ],
+                                    "type": "text",
+                                    "content": " and its length being set to 1. However, as it turns out below, some other scaling will be more convenient in the present situation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        677,
+                        545,
+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "Problem Statement. Let us assume that we are given a general camera that projects the spatial location "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{P} = [X, Y, Z]^\\top"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " to image (pixel) coordinates "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[u v]^\\top"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ", and let us"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "denote the projective coordinate functions by "
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+                                    "type": "text",
+                                    "content": " of the projected point, and "
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+                                    "type": "text",
+                                    "content": ". As Molnár and Chetverikov showed [49], the affine transformation can be defined via the spatial gradients of the projective coordinate functions "
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+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "An affine correspondence is represented by 2D image coordinates "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "[u_1 v_1]^\\top"
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+                                    "content": "[u_2 v_2]^\\top"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in the stereo image pair, in conjunction with the affine transformation "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " that maps the surrounding area of the locations from first image to the second one. The spatial location of the corresponding spatial point is also required. It can be estimated from the image coordinates and camera parameters by standard triangulation techniques [29]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "The normal estimation problem is written [9] as an argument minimization to determine the optimal "
+                                },
+                                {
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {n} ^ {*} = \\operatorname * {a r g   m i n} _ {\\mathbf {n}} f (\\mathbf {n}),",
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "f (\\mathbf {n}) := \\sum_ {i = 1} ^ {2} \\sum_ {j = 1} ^ {2} \\left(\\frac {\\mathbf {n} ^ {\\top} \\mathbf {w} _ {i j}}{\\mathbf {n} ^ {\\top} \\mathbf {w} _ {c}} - a _ {i j}\\right) ^ {2}. \\tag {1}",
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+                                    "type": "text",
+                                    "content": "Here, the affine transformation yields the four affine parameters "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " ("
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+                                    "type": "inline_equation",
+                                    "content": "i,j\\in [1,2]"
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {A} = \\left[ \\begin{array}{c c} a _ {1 1} & a _ {1 2} \\\\ a _ {2 1} & a _ {2 2} \\end{array} \\right],",
+                                    "image_path": "c9952dc4b9a34bcbaca4bb1f77013a8a12b5e8a7d0ddaab4d0a07f875f47522a.jpg"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "and the vectors "
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+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{ij}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_c"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " are obtained as cross products of the spatial gradient vectors as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathbf {w} _ {1 1} = \\nabla \\Pi_ {v} ^ {1} \\times \\nabla \\Pi_ {u} ^ {2}, \\quad \\mathbf {w} _ {1 2} = \\nabla \\Pi_ {u} ^ {2} \\times \\nabla \\Pi_ {u} ^ {1}, \\\\ \\mathbf {w} _ {2 1} = \\nabla \\Pi_ {v} ^ {1} \\times \\nabla \\Pi_ {v} ^ {2}, \\quad \\mathbf {w} _ {2 2} = \\nabla \\Pi_ {v} ^ {2} \\times \\nabla \\Pi_ {u} ^ {1}, \\\\ \\mathbf {w} _ {c} = \\nabla \\Pi_ {u} ^ {1} \\times \\nabla \\Pi_ {v} ^ {1}, \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": "where the superscripts refer to the corresponding image index. The coordinates of these vectors will be denoted by "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{ij,x},\\mathbf{w}_{ij,y},\\mathbf{w}_{ij,z}"
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "(i,j\\in \\{1,2\\})"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{c,x},\\mathbf{w}_{c,y},\\mathbf{w}_{c,z}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Pin-hole (perspective) projection model. For a pin-hole camera, the projection model is as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\left[ \\begin{array}{c} u \\\\ v \\\\ 1 \\end{array} \\right] \\sim \\left[ \\begin{array}{c c c c} P _ {1 1} & P _ {1 2} & P _ {1 3} & P _ {1 4} \\\\ P _ {2 1} & P _ {2 2} & P _ {2 3} & P _ {2 4} \\\\ P _ {3 1} & P _ {3 2} & P _ {3 3} & P _ {3 4} \\end{array} \\right] \\left[ \\begin{array}{c} X \\\\ Y \\\\ Z \\\\ 1 \\end{array} \\right],",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\sim"
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+                                    "type": "text",
+                                    "content": " denotes the equality up to scale operation. Therefore, image coordinates "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "u"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are obtained as"
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+                            "bbox": [
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+                                665,
+                                235,
+                                717
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        78,
+                                        665,
+                                        235,
+                                        717
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\Pi_ {u} = \\frac {P _ {1 1} X + P _ {1 2} Y + P _ {1 3} Z + P _ {1 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}, \\\\ \\Pi_ {v} = \\frac {P _ {2 1} X + P _ {2 2} Y + P _ {2 3} Z + P _ {2 4}}{P _ {3 1} X + P _ {3 2} Y + P _ {3 3} Z + P _ {3 4}}. \\\\ \\end{array}",
+                                    "image_path": "a7da8a68e316b58e1da7708e7fac4a420c05e7965cefc94884a519b58e8ba947.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        305,
+                        70,
+                        545,
+                        97
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                70,
+                                545,
+                                97
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        70,
+                                        545,
+                                        97
+                                    ],
+                                    "type": "text",
+                                    "content": "Spatial gradients, that are "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        70,
+                                        545,
+                                        97
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla \\Pi = \\left[ \\begin{array}{ccc}\\frac{\\partial\\Pi}{\\partial X} & \\frac{\\partial\\Pi}{\\partial Y} & \\frac{\\partial\\Pi}{\\partial Z} \\end{array} \\right]^{\\top}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        70,
+                                        545,
+                                        97
+                                    ],
+                                    "type": "text",
+                                    "content": ", can be written for the pin-hole model in compact forms as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        335,
+                        106,
+                        503,
+                        190
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                335,
+                                106,
+                                503,
+                                190
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        335,
+                                        106,
+                                        503,
+                                        190
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\begin{array}{r l} \\nabla \\Pi_ {u} & = \\frac {1}{s} \\left[ \\begin{array}{c} P _ {1 1} \\\\ P _ {1 2} \\\\ P _ {1 3} \\end{array} \\right] ^ {\\top} - \\frac {u}{s} \\left[ \\begin{array}{c} P _ {3 1} \\\\ P _ {3 2} \\\\ P _ {3 3} \\end{array} \\right] ^ {\\top}, \\end{array} \\\\ \\nabla \\Pi_ {v}   =   \\frac {1}{s} \\left[ \\begin{array}{c} P _ {2 1} \\\\ P _ {2 2} \\\\ P _ {2 3} \\end{array} \\right] ^ {\\top} - \\frac {v}{s} \\left[ \\begin{array}{c} P _ {3 1} \\\\ P _ {3 2} \\\\ P _ {3 3} \\end{array} \\right] ^ {\\top}, \\\\ \\end{array}",
+                                    "image_path": "cfbc0a6edb86fe3b5e33ae3cbb8e64ee49a8f1177b514c9d1289629bea441c4c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        305,
+                        198,
+                        545,
+                        221
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                198,
+                                545,
+                                221
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        198,
+                                        545,
+                                        221
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        198,
+                                        545,
+                                        221
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s = P_{31}X + P_{32}Y + P_{33}Z + P_{34}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        198,
+                                        545,
+                                        221
+                                    ],
+                                    "type": "text",
+                                    "content": " is the projective depth."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        305,
+                        222,
+                        545,
+                        246
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                222,
+                                545,
+                                246
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        222,
+                                        545,
+                                        246
+                                    ],
+                                    "type": "text",
+                                    "content": "Solution. For the problem to be meaningful, we can assume that "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        222,
+                                        545,
+                                        246
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_c \\neq \\mathbf{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        222,
+                                        545,
+                                        246
+                                    ],
+                                    "type": "text",
+                                    "content": ". Let us set"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        371,
+                        257,
+                        479,
+                        276
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                371,
+                                257,
+                                479,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        371,
+                                        257,
+                                        479,
+                                        276
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "I := \\inf  _ {\\| \\mathbf {n} \\| = 1, \\mathbf {n} ^ {\\top} \\mathbf {w} _ {c} \\neq 0} f (\\mathbf {n}),",
+                                    "image_path": "8424ab976e230ad61cb7c434ca804373ed9caa3c6a2966adf0408ee68f3900f0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
+                        305,
+                        288,
+                        545,
+                        324
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                288,
+                                545,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{n}\\| \\coloneqq \\sqrt{\\mathbf{n}^\\top\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the standard Euclidean norm. Clearly, "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f\\geq 0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " is undefined along the \"equator\" of the unit sphere "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{n}\\| = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^{\\top}\\mathbf{w}_{c} = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        288,
+                                        545,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ". Let us consider two cases."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
+                        306,
+                        325,
+                        545,
+                        352
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                325,
+                                545,
+                                352
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "text",
+                                    "content": "If all "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{ij}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "text",
+                                    "content": " are equal, then trivially "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\mathbf{n}) = \\sum_{i,j=1}^{2}(a_{ij} - 1)^2"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        325,
+                                        545,
+                                        352
+                                    ],
+                                    "type": "text",
+                                    "content": " is a constant function."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
+                        305,
+                        353,
+                        545,
+                        463
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                353,
+                                545,
+                                463
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": "Otherwise, at least one of the expressions "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{\\mathbf{n}^{\\top}\\mathbf{w}_{ij}}{\\mathbf{n}^{\\top}\\mathbf{w}_{c}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " becomes arbitrarily large in modulus when "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " is chosen such that "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^{\\top}\\mathbf{w}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " gets sufficiently close to 0; that is, "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|f(\\mathbf{n})|\\to +\\infty"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " as "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^{\\top}\\mathbf{w}_c\\rightarrow 0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{n}\\| = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": ". Therefore, by taking into account the continuity of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " as well, the infimum "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " is in fact a minimum, and an optimal unit vector "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\mathbf{n}^{*}) = I"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " exists. In what follows, we will explicitly determine such an "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        353,
+                                        545,
+                                        463
+                                    ],
+                                    "type": "text",
+                                    "content": " as a function of the 19 parameters<sup>1</sup> by using only the four basic arithmetic operations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
+                        305,
+                        464,
+                        545,
+                        523
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                464,
+                                545,
+                                523
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "text",
+                                    "content": "A key observation is that "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\lambda \\mathbf{n}) = f(\\mathbf{n})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "text",
+                                    "content": " for any "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda \\neq 0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "text",
+                                    "content": ", so (after a possible rescaling) we can assume that the last component of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        464,
+                                        545,
+                                        523
+                                    ],
+                                    "type": "text",
+                                    "content": " is either 1 or 0. These cases, Cases A and B, respectively, will be discussed separately below. To simplify the notation, let us define two auxiliary functions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
+                        371,
+                        534,
+                        545,
+                        547
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                371,
+                                534,
+                                545,
+                                547
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        371,
+                                        534,
+                                        545,
+                                        547
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "g \\left(n _ {x}, n _ {y}\\right) := f \\left(n _ {x}, n _ {y}, 1\\right) \\tag {2}",
+                                    "image_path": "99a10372f8b91d234582f467ecbab871350f8d8dce41aeafce47c081fc7a20f0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "bbox": [
+                        306,
+                        557,
+                        323,
+                        567
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                557,
+                                323,
+                                567
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        557,
+                                        323,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": "and"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "bbox": [
+                        370,
+                        570,
+                        545,
+                        583
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                370,
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+                                545,
+                                583
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        370,
+                                        570,
+                                        545,
+                                        583
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "h \\left(n _ {x}, n _ {y}\\right) := f \\left(n _ {x}, n _ {y}, 0\\right). \\tag {3}",
+                                    "image_path": "1619d1634121dfd4802fe4ae410a3858f6ba2505e75a0c9cadd7f12aff67cc5e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": "For the objective function "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we will obtain a unique candidate extremum "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_g^* \\in \\mathbb{R}^2"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": "; whereas for the function "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
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+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ", a one-parameter family of candidate extrema "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_h^* \\in \\mathbb{R}^2"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
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+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " will be found but with the same function value "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h(\\mathbf{n}_h^*)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ". The optimal "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        590,
+                                        545,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " is then"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "bbox": [
+                        341,
+                        657,
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+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {n} ^ {*} = \\left\\{ \\begin{array}{l l} \\left[ \\mathbf {n} _ {g} ^ {*}, 1 \\right] ^ {\\top}, & \\text {i f} g \\left(\\mathbf {n} _ {g} ^ {*}\\right) \\leq h \\left(\\mathbf {n} _ {h} ^ {*}\\right), \\\\ \\left[ \\mathbf {n} _ {h} ^ {*}, 0 \\right] ^ {\\top}, & \\text {i f} g \\left(\\mathbf {n} _ {g} ^ {*}\\right) > h \\left(\\mathbf {n} _ {h} ^ {*}\\right). \\end{array} \\right. \\tag {4}",
+                                    "image_path": "7105f9a14969286ef389c65b47b38d0f91a780e0e9750083fc1c57f497c847f8.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "<sup>1</sup>They are the four affine parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "a_{ij}"
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+                                    "type": "text",
+                                    "content": ", and the 15 components of the vectors "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{ij}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_c"
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
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+                        }
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+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "page_number",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "3392"
+                                }
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+                }
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+            "page_idx": 2
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Remark 1 In other words, we will be utilizing the simple constraints "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_z = 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " or "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
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+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_z = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
+                                        289,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": ". We have found that other linear or non-linear constraints, such as "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
+                                        289,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{n} \\| = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
+                                        289,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": ", would render the symbolic calculations to minimize the objective function "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
+                                        289,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        72,
+                                        289,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " infeasible."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                        148,
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+                        160
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                116,
+                                160
+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Case A: "
+                                },
+                                {
+                                    "bbox": [
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+                                        116,
+                                        160
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_z = 1"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        47,
+                        167,
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+                        179
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                167,
+                                257,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
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+                                        179
+                                    ],
+                                    "type": "text",
+                                    "content": "We use the standard technique and solve the system"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                    "bbox": [
+                                        121,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\left\\{ \\begin{array}{l} \\partial_ {1} g \\left(n _ {x}, n _ {y}\\right) = 0, \\\\ \\partial_ {2} g \\left(n _ {x}, n _ {y}\\right) = 0 \\end{array} \\right. \\tag {5}",
+                                    "image_path": "623cd1867295b0aeb08c99097ed392451b5481c95ae907fc61f881ca7a5d601f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        47,
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+                        244
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                                261,
+                                244
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        230,
+                                        261,
+                                        244
+                                    ],
+                                    "type": "text",
+                                    "content": "to find the optimal vector "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        230,
+                                        261,
+                                        244
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_g^* = [n_x, n_y]^\\top"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        230,
+                                        261,
+                                        244
+                                    ],
+                                    "type": "text",
+                                    "content": " as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        59,
+                        244,
+                        251,
+                        255
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                59,
+                                244,
+                                251,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        59,
+                                        244,
+                                        251,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": "By computing and putting the partial derivative"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        140,
+                        266,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\partial_ {1} g (n _ {x}, n _ {y})",
+                                    "image_path": "5c9d7e4c10b1568188f87ccc54c71977a77b6d8db8e0fdf879459c759cd97bb8.jpg"
+                                }
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+                        }
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+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": "over a common denominator, we see that its numerator depends on "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
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+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_x"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " linearly; and it depends on "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " quadratically; so one can easily express "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_x"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " from the equation "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\partial_1 g(n_x, n_y) = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        289,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "n _ {x} = \\frac {\\operatorname {n u m e r} _ {1}}{\\operatorname {d e n o m} _ {1}}, \\tag {6}",
+                                    "image_path": "5ae6f9c0d31f5c249c6dc5963502fbfa86671f2bf6ddce041191b3e647ef6adb.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "text",
+                                    "content": "where we present the expressions for "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{numer}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{denom}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "text",
+                                    "content": " in the supplementary material. Then (6) is substituted into the other partial derivative "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\partial_2 g(n_x, n_y)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "text",
+                                    "content": ". The resulting rational function of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
+                                        287,
+                                        444
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        361,
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+                                        444
+                                    ],
+                                    "type": "text",
+                                    "content": ", also containing the other 19 parameters, can be simplified and factorized by Wolfram Mathematica's Factor command<sup>2</sup>. In this way, we obtain a fraction whose structure is the following:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
+                                        132,
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+                                    "type": "interline_equation",
+                                    "content": "\\frac {\\operatorname {l i n e a r} _ {1} \\cdot \\operatorname {l i n e a r} _ {2}}{(\\text {q u a d r a t i c}) ^ {2}}, \\tag {7}",
+                                    "image_path": "341c4983908ac883027ce2a44d65cf0ab38ed26bae76689469543ed498e69adc.jpg"
+                                }
+                            ]
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+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where the expressions \"linear\" and \"quadratic\" denote polynomials in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        487,
+                                        287,
+                                        511
+                                    ],
+                                    "type": "text",
+                                    "content": " having the corresponding degrees."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        47,
+                        511,
+                        287,
+                        594
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                511,
+                                287,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "The optimum of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": " can occur when "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": " is chosen such that the fraction (7), that is, its numerator is equal to 0. It can be shown that the assumption "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{linear}_1 = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": " leads to a contradiction - indeed, by solving "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{linear}_1 = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": " for "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": ", the resulting formula would make "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{denom}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": " in (6) identically equal to 0. Hence, we are only left with the equation "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{linear}_2 = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        511,
+                                        287,
+                                        594
+                                    ],
+                                    "type": "text",
+                                    "content": ", whose solution is"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        134,
+                        601,
+                        287,
+                        624
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                134,
+                                601,
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+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        134,
+                                        601,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "n _ {y} = \\frac {\\operatorname {n u m e r} _ {2}}{\\operatorname {d e n o m} _ {2}}. \\tag {8}",
+                                    "image_path": "21144dc20d7ef6e9f9f304d333059701752bbc610ff555990eb5a1b78f3b50ea.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        47,
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+                        655
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        632,
+                                        287,
+                                        655
+                                    ],
+                                    "type": "text",
+                                    "content": "The actual formulas for "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        632,
+                                        287,
+                                        655
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{numer}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        632,
+                                        287,
+                                        655
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        632,
+                                        287,
+                                        655
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{denom}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        632,
+                                        287,
+                                        655
+                                    ],
+                                    "type": "text",
+                                    "content": " are found again in the supplementary material."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        47,
+                        656,
+                        287,
+                        694
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                656,
+                                287,
+                                694
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "text",
+                                    "content": "Thus, the second component of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_g^*"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "text",
+                                    "content": " is given by (8) (expressed in terms of the 19 parameters). Then, by using this together with (6), we obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_x"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "text",
+                                    "content": ", the first component of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_g^*"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        656,
+                                        287,
+                                        694
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        306,
+                        72,
+                        547,
+                        217
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                72,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
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+                                        217
+                                    ],
+                                    "type": "text",
+                                    "content": "Remark 2 The essential feature of these computations is that the solution of system (5) is given in a fully explicit symbolic form by using only elementary operations. Without the clever intermediate symbolic simplifications and factorizations (most notably (7)), one would need to solve a higher-degree polynomial equation to obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "text",
+                                    "content": ", requiring either taking roots or using an iterative scheme. For example, if one starts solving (5) with "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_x"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "text",
+                                    "content": " as symbolic parameters but all the coefficients of "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "text",
+                                    "content": " as floating-point numbers, then, in general, no intermediate factorizations or simplifications are possible, so in order to determine "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        547,
+                                        217
+                                    ],
+                                    "type": "text",
+                                    "content": ", one would need to solve a quintic equation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        306,
+                        230,
+                        373,
+                        241
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                230,
+                                373,
+                                241
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        230,
+                                        373,
+                                        241
+                                    ],
+                                    "type": "text",
+                                    "content": "Case B: "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        230,
+                                        373,
+                                        241
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_z = 0"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        306,
+                        249,
+                        479,
+                        261
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                249,
+                                479,
+                                261
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        249,
+                                        479,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": "We proceed similarly and solve the system"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        380,
+                        267,
+                        545,
+                        300
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                380,
+                                267,
+                                545,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        380,
+                                        267,
+                                        545,
+                                        300
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\left\\{ \\begin{array}{l} \\partial_ {1} h \\left(n _ {x}, n _ {y}\\right) = 0, \\\\ \\partial_ {2} h \\left(n _ {x}, n _ {y}\\right) = 0. \\end{array} \\right. \\tag {9}",
+                                    "image_path": "f00eb29ec48de52cafb7b5aec57d829f523ae3754aff3eaeae1a6f6feeac6126.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
+                        305,
+                        307,
+                        546,
+                        366
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                307,
+                                546,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
+                                        546,
+                                        366
+                                    ],
+                                    "type": "text",
+                                    "content": "By expressing "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
+                                        546,
+                                        366
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_x"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        307,
+                                        546,
+                                        366
+                                    ],
+                                    "type": "text",
+                                    "content": " from the first equation of (9) and substituting the resulting expression into the second equation, we find that this time the second equation is automatically satisfied. Therefore, (9) possesses a one-parameter family of solutions given by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
+                        393,
+                        372,
+                        545,
+                        396
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                393,
+                                372,
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+                                396
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        393,
+                                        372,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "n _ {x} = \\frac {\\operatorname {n u m e r} _ {3}}{\\operatorname {d e n o m} _ {3}}, \\tag {10}",
+                                    "image_path": "c72c6bfb638d1345870765b38596e550883ef8462d586eb806bef47d6b6dd44d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
+                        305,
+                        402,
+                        545,
+                        427
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                402,
+                                545,
+                                427
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        402,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "text",
+                                    "content": "see the supplementary material. By substituting this into "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        402,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        402,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "text",
+                                    "content": ", the function value "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        402,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h(\\mathbf{n}_h^*)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        402,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "text",
+                                    "content": " appearing in (4) is obtained as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
+                        386,
+                        433,
+                        545,
+                        456
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                386,
+                                433,
+                                545,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        386,
+                                        433,
+                                        545,
+                                        456
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "h \\left(\\mathbf {n} _ {h} ^ {*}\\right) = \\frac {\\operatorname {n u m e r} _ {4}}{\\operatorname {d e n o m} _ {4}}. \\tag {11}",
+                                    "image_path": "e609c37335d87d1c0db827fd4af3dfce863f909e9c05838413cc410e68a13402.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
+                        306,
+                        463,
+                        479,
+                        475
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                463,
+                                479,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        463,
+                                        479,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": "See the supplementary material for details."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "bbox": [
+                        305,
+                        483,
+                        545,
+                        514
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                483,
+                                545,
+                                514
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        483,
+                                        545,
+                                        514
+                                    ],
+                                    "type": "text",
+                                    "content": "Remark 3 One directly checks that the value "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        483,
+                                        545,
+                                        514
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h(\\mathbf{n}_h^*) = h\\left(\\frac{\\mathrm{numer}_3}{\\mathrm{denom}_3}, n_y\\right)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        483,
+                                        545,
+                                        514
+                                    ],
+                                    "type": "text",
+                                    "content": " is indeed independent of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        483,
+                                        545,
+                                        514
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_y"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        483,
+                                        545,
+                                        514
+                                    ],
+                                    "type": "text",
+                                    "content": ", as claimed."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "bbox": [
+                        306,
+                        521,
+                        455,
+                        533
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "2.1. Summary of the Algorithm"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Given the elements "
+                                },
+                                {
+                                    "bbox": [
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+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{ij} \\in \\mathbb{R}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": " in the affine transformation and 3D vectors "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{ij}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_c \\neq \\mathbf{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": ", let us define the function "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " by (1) for "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^\\top \\mathbf{w}_c \\neq \\mathbf{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": ", and also define the functions "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": " by (2)-(3). If "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{w}_{11} = \\mathbf{w}_{12} = \\mathbf{w}_{21} = \\mathbf{w}_{22} = \\mathbf{w}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", then any unit vector "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        540,
+                                        545,
+                                        598
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be chosen as optimal normal vector."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": "Otherwise, we compute "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_g^* \\coloneqq [n_x, n_y]^\\top"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " from (8) and (6). Then we compute "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h(\\mathbf{n}_h^*)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        599,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from (11). Finally, the optimal "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}^*"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is determined by using (4)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28
+                },
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+                                    "type": "text",
+                                    "content": "3. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29
+                },
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+                                    "type": "text",
+                                    "content": "We focus on the accuracy and time demand of the algorithms when testing. Both synthetic testing data, including configurations for a number of important camera motions, and standard real-world benchmarks are considered here."
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 2. Images and the reference reconstruction used from the Cambridge Landmarks dataset [39] in localization experiments."
+                                        }
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+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "Compared Algorithms. In this section, we discuss the algorithms that can be used to estimate the surface normal from a single affine correspondence."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                            "type": "text",
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+                            "lines": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "1. The provably most accurate algorithms are the ones that are optimal in the least squares sense. Method "
+                                        },
+                                        {
+                                            "bbox": [
+                                                55,
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+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{OPT}_{\\mathrm{QUARTIC}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                55,
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+                                            ],
+                                            "type": "text",
+                                            "content": " refers to [9] which solves the problem as a real root of a quartic polynomial equation. The cubic solution "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{OPT}_{\\mathrm{CUBIC}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                55,
+                                                314,
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+                                            ],
+                                            "type": "text",
+                                            "content": " is from [46]. The proposed optimal solver, as it is solved via linear equations, is called "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{OPT}_{\\mathrm{LINEAR}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                55,
+                                                314,
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+                                            ],
+                                            "type": "text",
+                                            "content": " in the rest of the paper."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    "spans": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "2. The simplest and, thus, the fastest method is the Fast Normal Estimation (FNE) algorithm of [9]. A more complex variant, when all possible linear equations are considered, is also constructed here, it is denoted as "
+                                        },
+                                        {
+                                            "bbox": [
+                                                55,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{FNE}_{\\mathrm{SUPER}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                55,
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+                                            ],
+                                            "type": "text",
+                                            "content": ". The modified equations can be seen in the source codes in the supplementary material."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "3. Raposo and Barreto [56] proposed a solution that estimates the normal via homographies. We have not found an implementation or an exact definition of the algorithm, so we implemented it based on the description. The solution is computed via an over-determined inhomogeneous linear system of equations. The formulas are generated by the MATLAB Symbolic Toolbox. Details are given in the supplementary material. The method is called RAPOSO in the charts."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                    "type": "text",
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+                                    ],
+                                    "type": "text",
+                                    "content": "The synthetic tests are performed in MATLAB. In the real-world experiments, optimized "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{C}++"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " codes run on an Intel(R) Core(TM) i9-10900K CPU @ 3.70GHz."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
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+                                    "type": "text",
+                                    "content": "3.1. Synthetic Experiments"
+                                }
+                            ]
+                        }
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+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "For the synthetic tests, a spherical object is generated, thus straightforwardly allowing to sample oriented points from its surface. Two cameras are randomly generated with focal lengths from the range [500, 1500] and with image size "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2000 \\times 2000"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". Their intrinsic matrices are "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{K}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{K}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        654,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        305,
+                        72,
+                        545,
+                        133
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                72,
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+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": "The 3D point was projected into both cameras. The ground truth (GT) affine parameters were calculated directly from the camera parameters and the surface normals as shown in [9]. Several camera configurations are considered to simulate various real-world scenarios. They are as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        317,
+                        138,
+                        547,
+                        338
+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 17,
+                    "blocks": [
+                        {
+                            "bbox": [
+                                317,
+                                138,
+                                545,
+                                187
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        317,
+                                        138,
+                                        545,
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                138,
+                                                545,
+                                                187
+                                            ],
+                                            "type": "text",
+                                            "content": "- For general stereo pose, the locations of the cameras are randomly generated inside a unit-radius sphere. The camera projection matrices are constructed as "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                138,
+                                                545,
+                                                187
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                138,
+                                                545,
+                                                187
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                138,
+                                                545,
+                                                187
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R} \\mid \\mathbf{t}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                138,
+                                                545,
+                                                187
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                317,
+                                190,
+                                547,
+                                239
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        317,
+                                        190,
+                                        547,
+                                        239
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "text",
+                                            "content": "- For rectified stereo, the cameras are located next to each other with identical orientation. In this case, the projection matrices are "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{I} \\mid \\mathbf{t}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "text",
+                                            "content": ", where "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{t} = [\\Delta X 0 0]^\\top"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                190,
+                                                547,
+                                                239
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                317,
+                                242,
+                                545,
+                                338
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        317,
+                                        242,
+                                        545,
+                                        338
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "text",
+                                            "content": "- Planar motion simulates the case when a camera is mounted on a vehicle that moves on a planar road with the image plane orthogonal to the ground. Such a motion can be represented by two angles around the vertical axis, one for the rotation and one for the translation. In this case, the projection matrices can be written as "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid 0]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_{\\mathrm{Y}} \\mid \\mathbf{t}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "text",
+                                            "content": ", where "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{t} = \\rho [\\cos \\beta, 0, \\sin \\beta]^\\top"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                242,
+                                                545,
+                                                338
+                                            ],
+                                            "type": "text",
+                                            "content": " and"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 16
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
+                        368,
+                        344,
+                        502,
+                        383
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                368,
+                                344,
+                                502,
+                                383
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        368,
+                                        344,
+                                        502,
+                                        383
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {R} _ {\\mathrm {Y}} = \\left[ \\begin{array}{c c c} \\cos \\alpha & 0 & \\sin \\alpha \\\\ 0 & 1 & 0 \\\\ - \\sin \\alpha & 0 & \\cos \\alpha \\end{array} \\right].",
+                                    "image_path": "f78524009d87176a0e02902d585a78e9c2fe433f15e37c8c91043b48dc19e4da.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        317,
+                        392,
+                        545,
+                        529
+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 21,
+                    "blocks": [
+                        {
+                            "bbox": [
+                                317,
+                                392,
+                                545,
+                                464
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
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+                                                464
+                                            ],
+                                            "type": "text",
+                                            "content": "- Moto-motion. This test case simulates a camera that is mounted on a motorcycle. If the bike leans, another rotation, the roll is involved in the problem. In this case, the camera parameters are "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_{\\mathrm{YZ}} \\mid \\mathbf{t}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "text",
+                                            "content": ", where "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{t} = \\rho [\\cos \\beta 0 \\sin \\beta]^\\top"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{R}_{YZ} = \\mathbf{R}_Y \\mathbf{R}_Z"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                392,
+                                                545,
+                                                464
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                317,
+                                468,
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+                                529
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
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+                                            ],
+                                            "type": "text",
+                                            "content": "- Drone-motion is another generalization of the planar motion. A camera mounted on a flying drone. Its location is arbitrary, but the orientation is limited to a vertical rotation. Therefore, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
+                                                545,
+                                                529
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_1 = \\mathbf{K}_1[\\mathbf{I} \\mid \\mathbf{0}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
+                                                545,
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+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
+                                                545,
+                                                529
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{P}_2 = \\mathbf{K}_2[\\mathbf{R}_Y \\mid \\mathbf{t}]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
+                                                545,
+                                                529
+                                            ],
+                                            "type": "text",
+                                            "content": ", where "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
+                                                545,
+                                                529
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{t} = [X Y Z]^\\top"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                468,
+                                                545,
+                                                529
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 20
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
+                        305,
+                        533,
+                        545,
+                        569
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Noise. We have added zero-mean Gaussian noise to the 2D coordinates, therefore, the point noise is given in pixels. The deviation of the noise is the parameter in the charts."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
+                                        545,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2 \\times 2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": " affine transformations are decomposed by SVD into two 2D rotations and another two scaling parameters. Then zero-mean Gaussian noise is added to the angle of rotations, in radians, and the scaling parameters. The standard deviation of the Gaussian noise distribution is equally set for all the four parameters."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "3D Reconstruction Pipeline. In order to simulate real scenarios, first, we triangulate each generated noisy point correspondence by the optimal triangulation method proposed by Hartley and Sturm [29]. The noisy affine parameters are corrected by the method proposed in [7] to be consistent with the camera parameters."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "3394"
+                                }
+                            ]
+                        }
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+                    "index": 25
+                }
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+            "page_idx": 4
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+                                            "type": "text",
+                                            "content": "Figure 3. The frequencies (in 10000 runs) of the "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
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+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " errors in the "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "\\log_{10}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " angular errors in degrees in the noise-free case."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Stability test. We generated 10000 random problem instances considering general camera motion and ran the normal estimators on noiseless affine correspondences. Fig. 3 shows histograms of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\log_{10}"
+                                },
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+                                    "type": "text",
+                                    "content": " angular errors in degrees. Note that for better visualization, we replace the exact zero values by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "10^{-16}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as it is the precision of the floating point numbers in MATLAB. The plots show that all our solvers are very stable – there is no peak close to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". For all methods, the majority of the errors are distributed around "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "10^{-16}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " which actually is the precision of MATLAB. This means that in most of the cases, all methods are particularly stable returning almost exactly 0 error. A small peak is over "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "10^{-6}"
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+                                    "type": "text",
+                                    "content": " for all methods similarly. Having "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " degree error is acceptable in most of the scenarios considered in computer vision. There is no peak close to "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " implying that all solvers are stable. Note that these stability tests usually are for highlighting potential degeneracies where the error exceeds "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We also conducted tests using single-point precision in MATLAB. The OPTQUARTIC approach failed entirely under these conditions. For all other methods, we noticed an increase in error, which suggests that double precision is necessary for reliable normal estimation. Interestingly, our proposed OPTLINEAR method appears to be slightly more sensitive to precision than OPTCUBIC is. This is likely due to the fact that OPTLINEAR employs more complex formulas and, consequently, performs more stably with double precision."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Accuracy test. The accuracy of the normals is examined for all the considered camera poses independently. The results are shown in Fig 9. The effect of noise in point coordinates and affine parameters are separately evaluated. Both the mean and the median of the errors are plotted."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "The observations we can make from the plots are as follows. First, the three optimal methods "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{OPT}_{\\mathrm{QUARTIC}}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{OPT}_{\\mathrm{LINEAR}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " always lead exactly to the same solution, thus their curves coincide in all plots. Second, the optimal methods always lead to the most accurate results if the affine parameters are contaminated by noise. This is not"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "surprising as these methods optimize the normal parameters such that the implied affine transformation is the closest to the measured one. In the case of point-noise only, the accuracy of the optimal algorithm is slightly below that of the competitors. However, it is an unlikely situation in real-world images to have noisy points but perfect local affine frames. It is usually the other way around. Third, as the FNE method uses less information, it is clearly the worst one in terms of accuracy. "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{FNE}_{\\mathrm{SUPER}}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " performs significantly better, however, it requires more time as the right singular vector of a "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "6\\times 3"
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+                                {
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+                                    "type": "text",
+                                    "content": " matrix, corresponding to the smallest singular value, should be computed. Another benefit of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{FNE}_{\\mathrm{SUPER}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is, contrary to FNE and Raposo [56], that it works in all test cases. It can cope with both planar motion and rectified stereo, similarly to the optimal algorithms."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Problematic methods. Methods FNE and Raposo [56] do not work if the cameras undergo special translations. FNE is a special method, several variants can be formed based on the selection of the affine transformations. For rectified stereo, the third and fourth elements are fixed [44], they cannot be used for the estimation."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "The Raposo [56] method is the most problematic one as the homography can be decomposed into the camera rotation, translation and surface normal. If the translation has zero elements, the retrieved equations are linearly dependent, and the estimation does not yield a correct solution. Due to this reason, Raposo [56] does not work for rectified stereo and planar motion. We removed these methods from the plots of the respective camera configurations."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Combined noise. In the previous experiments, noise is added either to the point coordinates or affine parameters. Here, we contaminate both types of input data. The mean and median errors of the proposed linear method are visualized in Fig. 10. As it is expected, the curves show similar trends, but the case when both the points and affines are noisy leads to higher errors."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Interpretable affine noise. In the previous experiments, the noise is added directly to the elements of the affine matrices. In Fig. 11, we consider a different way of contaminating the input to show that the proposed method acts reasonably with different noise models as well. The results of curves Aff and Comb are obtained by using the noise model from the previous sections. Comb refers to the case when both the points and the affine matrices are noisy. For AffElem and Comb-Elem, we decompose A by SVD into two orthogonal and a diagonal matrix. Fig. 11 demonstrates that the noise generation does not strongly influence the results."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "4. Real-world Experiments"
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+                                    "content": "To test normal estimators, we use the Cambridge Landmarks [39] and ScanNet datasets [18]. We chose Cambridge Landmarks, see Fig. 2 for example images, since it provides a large number of images for testing directly the"
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+                                            "content": "Figure 10. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to point coordinates (Point), affine parameters (Affine) or both (Combined)."
+                                        }
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+                                            "type": "text",
+                                            "content": "Figure 11. Mean and median errors of the proposed OPT LINEAR normal estimator with noise added to only the affine "
+                                        },
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+                                            "content": "(A\\text{ff})"
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+                                            "type": "text",
+                                            "content": " elements and, also, to the point coordinates "
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+                                            "content": "(Comb)"
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+                                            "type": "text",
+                                            "content": ". For Aff and Comb, zero-mean Gaussian noise is added directly to the affine elements. For Aff-Elem and Comb-Elem, the affine matrix is decomposed by SVD to two rotations and a diagonal matrix. Zero-mean Gaussian noise is added to the rotation angles and diagonal elements."
+                                        }
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+                                    "type": "text",
+                                    "content": "images are divided into training and testing sets. To have more accurate reference data, we ran COLMAP [63] obtaining a dense point cloud. Finally, we applied the normal estimator implemented in MeshLab<sup>3</sup> to obtain an oriented point cloud to be considered reference. The normals are fitted to the 200 nearest neighbors. For each query image, we ran DenseVLAD [67] to get 20 potential database images. In our experiments, the algorithms are tested on each obtained image pair, i.e., 20 pairs for each query image. For ScanNet, we use the 1500 image pairs used in [59]."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "On Cambridge Landmarks, we detect affine correspondences by detecting DoG features [42], finding the affine shape by AffNet [48], and extracting HardNet [47] descriptors. This approach is among the leaders in the IMC 2020 benchmark [34]. On ScanNet, we detect SuperPoint [20] features, match them by SuperGlue [59], and find the affine shape by, first, estimating scale and orientation by SelfScaleOri [41] and, then, finding the affine shapes by AffNet."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Normal Estimation. To test normal estimators, we ran all of them on the data described in the previous section. For each image pair, we iterate through all detected correspondences that are consistent with the camera pose - they have less than 5 pixels of Sampson distance. For each of"
+                                }
+                            ]
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+                                            "type": "text",
+                                            "content": "Figure 12. The median angular error in degrees (left) and the AUC@ "
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+                                            "type": "text",
+                                            "content": " score (right) of the estimated normals plotted as a function of the error in the detected affine correspondences on the Cambridge Landmarks dataset."
+                                        }
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+                                }
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+                                    "type": "text",
+                                    "content": "them, we ran multiple normal estimators, measure their angular error and run-time. To understand how the estimators proceed with respect to the error in the detected affine transformations "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}"
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+                                {
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+                                    "type": "text",
+                                    "content": ", we calculate the reference transformation "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}^*"
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+                                    "type": "text",
+                                    "content": " from the camera parameters and the surface normal as shown in [9]. We define the affine error as the Frobenius norm of the difference matrix "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{A} - \\mathbf{A}^* \\|_{\\mathrm{F}}"
+                                },
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "The Area Under the recall Curve (AUC) at "
+                                },
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+                                    "content": ", "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", the avg. and med. angular errors with the standard deviation in degrees and the run-time in nanoseconds on the Cambridge Landmarks dataset are reported in Table 1. As expected, the best results are achieved by the optimal algorithms, all of them leading to exactly the same results. Our proposed linear solution of the optimal problem, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{OPT}_{\\mathrm{LINEAR}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", is five times faster than the cubic solution "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{OPT}_{\\mathrm{CUBIC}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". While "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{OPT}_{\\mathrm{LINEAR}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is slightly slower than the fastest FNE method, it is significantly more accurate. Interestingly, while the method of Raposo et al. [56] worked well in the synthetic experiments, we did not manage to achieve good accuracy with it in the real-world experiments. Figure 12 plots the AUC@"
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "10^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " score and the median angular error as a function of the noise in the detected affine parameters. As expected, normal estimation is highly sensitive to the quality of the affine parameters. The optimal algorithms are the most stable ones."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
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+                {
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+                                    "type": "text",
+                                    "content": "The results on the ScanNet dataset are reported in Table 3. Similarly as on Cambridge Landmarks, all optimal solvers lead to the same accuracy while the proposed one being the fastest by a large margin."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Visual Localization. To test the impact of surface normal estimation on localization, on the Cambridge Landmarks dataset, we applied the following procedure. We iterate through all query images, each having 10 database images retrieved by DenseVLAD. First, we estimate the relative pose between the query and a random database image by GC-RANSAC [6] with P3P [54]. Using the obtained pose, we estimate the surface normal of each inlier affine correspondence in the coordinate system of the query image. Next, we iterate through all unused database images and use"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3Meshlab is an open source tool for 3D point cloud processing and visualization."
+                                }
+                            ]
+                        }
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+                                            "html": "<table><tr><td>Estimator</td><td>AUC@5°↑</td><td>@10°↑</td><td>@20°↑</td><td>Avg. err. (°) ↓</td><td>Med. err. (°) ↓</td><td>Std. dev. (°) ↓</td><td>Time (ns) ↓</td></tr><tr><td>FNE [49]</td><td>6.0</td><td>16.0</td><td>33.7</td><td>21.0</td><td>14.3</td><td>21.3</td><td>172</td></tr><tr><td>FNESUPER</td><td>8.9</td><td>22.1</td><td>42.0</td><td>10.9</td><td>16.8</td><td>15.6</td><td>1721</td></tr><tr><td>Raposo [56]</td><td>0.4</td><td>1.5</td><td>5.7</td><td>38.5</td><td>36.5</td><td>18.2</td><td>883</td></tr><tr><td>OPTQUARTIC [9]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2528</td></tr><tr><td>OPTCUBIC [46]</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>2484</td></tr><tr><td>Proposed OPTLINEAR</td><td>11.7</td><td>27.3</td><td>48.7</td><td>8.8</td><td>13.6</td><td>12.9</td><td>596</td></tr></table>",
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+                                            "content": "Table 1. The AUC score at "
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+                                            "type": "text",
+                                            "content": " of the estimated surface normals, their average and median errors in degrees, the standard deviation, and the average run-time, in nanoseconds, of a single normal estimation on the Cambridge Landmarks dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "table_caption"
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+                                            "html": "<table><tr><td rowspan=\"2\">Solver</td><td rowspan=\"2\">Normal estimator</td><td colspan=\"3\">Pose accuracy ↑</td><td rowspan=\"2\">Med. rot. err. (°) ↓</td><td rowspan=\"2\">Med. pos. err. (cm) ↓</td></tr><tr><td>AUC@1°, 10cm</td><td>@2.5°, 25cm</td><td>@5°, 50cm</td></tr><tr><td>P3P</td><td>-</td><td>44.3</td><td>59.1</td><td>67.5</td><td>10.1</td><td>13.5</td></tr><tr><td>P1AC</td><td>FNESUPER</td><td>47.8</td><td>62.0</td><td>69.7</td><td>6.2</td><td>12.8</td></tr><tr><td>P1AC</td><td>Proposed OPTLINEAR</td><td>48.0</td><td>62.3</td><td>69.9</td><td>5.2</td><td>1.8</td></tr><tr><td>P1AC</td><td>GT</td><td>48.4</td><td>62.9</td><td>70.4</td><td>4.6</td><td>2.1</td></tr></table>",
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+                                            "content": "Table 2. Localization AUC scores at "
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+                                            "type": "text",
+                                            "content": ", and "
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": ", the median rotation (in degrees) and translation errors (in centimeters) on the Cambridge Landmarks dataset [39] when using either the P3P solver or the normal-based P1AC solver with FNEsuper or the proposed surface normal estimator OPTLINEAR. We also show the results with the reference normals. The minimal solvers are used within Graph-Cut RANSAC [6] that takes care of the robust estimation."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
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+                                            "html": "<table><tr><td></td><td>AUC@5↑</td><td>AUC@10↑</td><td>AUC@20↑</td><td>Time (ns)↓</td></tr><tr><td>FNE</td><td>14.8</td><td>15.4</td><td>17.0</td><td>207</td></tr><tr><td>FNESUPER</td><td>34.9</td><td>35.2</td><td>36.6</td><td>2142</td></tr><tr><td>OPTQUARTIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>18745</td></tr><tr><td>OPTCUBIC</td><td>35.0</td><td>35.5</td><td>37.3</td><td>3146</td></tr><tr><td>OPTLINEAR</td><td>35.0</td><td>35.5</td><td>37.3</td><td>747</td></tr></table>",
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+                                }
+                            ],
+                            "index": 4,
+                            "angle": 0,
+                            "type": "table_body"
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+                    ],
+                    "index": 4
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "the P1AC [68] solver inside GC-RANSAC to estimate the pose. P1AC requires a single AC and the surface normal. We only test the proposed solver and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{FNE}_{\\mathrm{SUPER}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". All other optimal solvers lead exactly to the same accuracy as ours. "
+                                },
+                                {
+                                    "bbox": [
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+                                        516
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{FNE}_{\\mathrm{SUPER}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the most accurate sub-optimal algorithm."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The accuracy of the estimated pose for the database images with respect to their GT pose is reported in Table 2. All solvers, benefiting from normals and affine correspondences, are more accurate than using P3P. We also report the accuracy when using the reference normals to see the upper bound achievable using normals. The proposed optimal solver OPT LINEAR is only slightly (i.e. "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "< 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " AUC point) behind the accuracy of the GT normal, while being more accurate than the P3P-based solution. The AUC@ "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " scores on each scene are reported in Table 4. The proposed OPT LINEAR leads to the best accuracy on all but two scenes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Conclusions"
+                                }
+                            ]
+                        }
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+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this work, we have presented a novel solver for estimating surface normals from affine correspondences when having calibrated cameras. The proposed method yields the"
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "Table 3. The AUC scores at "
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+                                            "type": "text",
+                                            "content": " and "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": ", and the avg. time (in nanoseconds) of normal estimators on the ScanNet datasets [18]."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">P3P</td><td colspan=\"3\">P1AC</td></tr><tr><td>GT</td><td>FNESUPER</td><td>Prop. OPTLINEAR</td></tr><tr><td>St. Mary&#x27;s Church</td><td>44.2</td><td>47.7</td><td>46.1</td><td>46.5</td></tr><tr><td>Old Hospital</td><td>44.1</td><td>57.4</td><td>56.8</td><td>57.3</td></tr><tr><td>King&#x27;s College</td><td>52.1</td><td>54.2</td><td>54.1</td><td>54.0</td></tr><tr><td>Shop Facade</td><td>65.5</td><td>65.0</td><td>63.8</td><td>64.1</td></tr><tr><td>Great Court</td><td>62.7</td><td>63.2</td><td>63.0</td><td>63.5</td></tr><tr><td>Street</td><td>17.4</td><td>22.8</td><td>23.1</td><td>23.0</td></tr></table>",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "Table 4. The area under the recall curve (AUC) at "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " rotation and 10cm position errors on the Cambridge Landmarks dataset. We combine the P1AC solver with "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{FNE}_{\\mathrm{SUPER}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the proposed normal estimator. Also, we test it with the reference normals."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11,
+                    "angle": 0,
+                    "type": "text"
+                },
+                {
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+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "optimal solution, in the least squares sense, with respect to the affine error, and is particularly fast as the optimal normal is obtained via linear equations. We compared our method to all existing alternatives that estimate normals from a single correspondence on both simulated and real-world data. Additionally, we provide tests that highlight the benefits of using surface normals in image-based localization. The proposed estimator has demonstrated superior accuracy compared to the fastest existing method while being the second fastest overall. Our results suggest that the proposed algorithm is a promising alternative for surface normal estimation in computer vision applications."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Acknowledgement. The authors warmly thank the reviewers for their very valuable comments and suggestions. The work was supported by the ETH Postdoc fellowship."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
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diff --git a/2023/Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction/19d05057-5302-4e5f-a291-21f3188ae791_content_list.json b/2023/Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction/19d05057-5302-4e5f-a291-21f3188ae791_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e2031ab5a3324f4fb65a09536164ec418c64a3d
--- /dev/null
+++ b/2023/Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction/19d05057-5302-4e5f-a291-21f3188ae791_content_list.json	
@@ -0,0 +1,1470 @@
+[
+    {
+        "type": "text",
+        "text": "Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction",
+        "text_level": 1,
+        "bbox": [
+            173,
+            130,
+            799,
+            176
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Takahiro Maeda Norimichi Ukita",
+        "bbox": [
+            331,
+            203,
+            638,
+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Toyota Technological Institute, Japan",
+        "bbox": [
+            336,
+            222,
+            632,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{sd21601,ukita}@toyota-ti.ac.jp",
+        "bbox": [
+            344,
+            241,
+            625,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023.",
+        "bbox": [
+            75,
+            325,
+            473,
+            703
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            737,
+            209,
+            752
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Human trajectory prediction is a challenging problem because human movements are not deterministic, unlike the billiard balls on a pool table. Starting from deterministic approaches [26, 49], to tackle its indeterministic nature, many stochastic approaches are proposed, such as Gaussian distribution-based [1, 42, 66], generative adversarial networks (GANs)-based [9, 10, 25, 57], variational autoencoder (VAE)-based [58, 71, 73], diffusion-based [24], and normalizing flow-based [59] methods. These methods",
+        "bbox": [
+            75,
+            763,
+            468,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/61587bff2e78dc4ebe9603181c4add73529e15eebc64fa2b03fd0994a5fb6b63.jpg",
+        "image_caption": [
+            "Figure 1. Effects of our FlowChain. Our FlowChain can rapidly estimate accurate density than VAE-based methods as shown in green. Furthermore, we propose an update of estimated density that only requires an instant of time, as shown in blue."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "can be applied to human-interactive systems, including autonomous vehicles [8,11,38,55,69] and social robots [4,39].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In these safety-critical applications, autonomous systems must infer the existence probability density distribution (\"density\" for brevity) of other moving objects such as pedestrians around on all prediction steps for risk assessment (i.e., collision avoidance). However, most of the indeterministic approaches mentioned above merely generate possible future trajectories and cannot estimate the density alone. We need to further apply kernel density estimation (KDE) to these future trajectories for density estimation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Thus, trajectory prediction with density estimation usually takes a larger computational cost than only generating possible trajectories. This computational cost accumulates upon every single prediction update along with highly-frequent observations. This is unacceptable to autonomous systems that work in rapidly changing environments.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To address both computational cost and density estimation, we propose a new normalizing flow-based model named FlowChain (Fig. 1). This speed and accuracy are because normalizing flows need no additional approximation such as Gaussian mixture modeling or KDE with limited samples. FlowChain can estimate a density on each prediction time step thanks to our stacked normalizing flow archi",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "9795",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "tecture unlike Flomo [59], which is closest to FlowChain. While Flomo uses one flow module that only estimates the spatial density of a trajectory, FlowChain further predicts its spatio-temporal density so that the spatial density of an agent position at each time step is also predicted. This stacking architecture also allows a rapid update of an estimated density in an instant of time e.g. less than one millisecond. This update is achieved by reusing the flow transformations and its log-det-jacobians that represent the motion trend such as going straight or turning right. This update with the reuse significantly omits the computational cost while maintaining the accuracy of density estimation because the motion trend doesn't change for several time steps.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Our contributions are three-fold as follows:",
+        "bbox": [
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a normalizing flow-based trajectory prediction network named FlowChain that rapidly estimates the accurate density of future positions on each prediction time step.",
+            "- Our update procedure for the density requires less than one millisecond by adopting new observations and reusing the motion trend as the flow transformations.",
+            "- Our FlowChain achieved comparable prediction accuracy to other computationally-intense state-of-the-art methods on several benchmarks."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            512,
+            218,
+            527
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Human Trajectory Prediction. The earliest works on human trajectory prediction [26, 49] are deterministic regression models using attractive and repulsive forces between humans and goal positions. However, human movements are indeterministic in nature. Therefore, many approaches are proposed to model this uncertainty. Social-LSTM [1] and Social-STGCNN [42] regress the parameters of the bivariate Gaussian distributions to model the uncertainty of future trajectories. These approaches [1, 42] are simple and require low computational cost but cannot catch the future multi-modality we often see at road intersections.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address this multi-modality, many stochastic prediction models are proposed. Trajectory++ [58], AgentFormer [71], and ExpertTraj [73] combined the aforementioned Gaussian regression with VAE [32]. These models predict a bivariate Gaussian mixture based on stochastically sampled latent variables [28, 52]. We can obtain the density by summing up each estimated Gaussian density map. However, these Gaussian mixture methods have limited expressive power and thus predict inaccurate distributions.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, GAN [18]-based approaches implicitly handle this uncertainty. Social-GAN [25], SoPhie [57], Goal-GAN [10], and MG-GAN [9] use a GAN architecture to predict diverse trajectories conditioned on random",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "noises. While they cannot estimate the density alone, we can estimate the density by applying KDE [48, 54] on sampled trajectories",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The denoising diffusion probabilistic model [27] can also implicitly handle uncertainty by generating multiple trajectories. Recently, denoising diffusion attracts much attention for its state-of-the-art performances in several generative tasks, including image synthesis [12] and audio generation [33]. MID [24] is a trajectory prediction model incorporating denoising diffusion, which achieves state-of-the-art performances. We can also estimate the density of MID by applying KDE. However, GAN-based and diffusion-based approaches cannot estimate accurate densities because KDE is performed on limited samples.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "On the contrary, normalizing flow [51, 64, 65]-based trajectory prediction method named Flomo [59] can rapidly generate future trajectories and their accurate probabilities thanks to the analytical computation of normalizing flows. However, this approach only estimates the probability of each future trajectory and thus cannot estimate the density of positions on each prediction step alone.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Normalizing Flows. Thanks to its bijective process, normalizing flow can compute the density analytically. This analytical computation allows us fast and accurate density estimation because it does not need additional approximation such as KDE with limited samples. For more expressive power, several bijective families were proposed such as affine coupling layers [13, 14], autoregressive maps [17, 47], invertible linear transformations [31], and invertible ResNet block [2, 6]. All flows mentioned above have a topology constraint between the base and estimated densities. This topology constraint limits the expressive power of normalizing flows. To address this constraint, some approaches incorporated stochasticity into flows [68]. However, this stochasticity makes analytical density calculation impossible. Therefore, further density approximation such as KDE is required for this stochastic normalizing flow. Other approaches [5, 7, 44] use surjective layers, which relax the topology constraint but make analytical density computation with a little looseness. In summary, the optimal normalizing flow model architecture for future trajectory density estimation is still unknown.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Density Estimation. Kernel density estimation [48, 54] is the most representative non-parametric method that estimates a continuous density from a finite set of data. Suppose that we have  $A$  input data and  $B$  points evaluated, the computational cost is  $\\mathcal{O}(AB)$ . This is a huge cost for autonomous systems. Therefore, several accelerations are proposed such as data binning [19, 60, 62, 67], fast sum updating [15, 16, 35, 61], fast Gauss transform [22, 23, 34], and dual-tree method [20, 21, 36]. However, we confirmed that the KDE implementation utilizing GPU is faster than these accelerations including [3, 45, 46]. We use the KDE utilizing",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "9796",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "GPU for comparison in Sec. 4.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Proposed Approach",
+        "text_level": 1,
+        "bbox": [
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+            119,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present our normalizing flow-based trajectory prediction named FlowChain and its update of estimated density. First, we formulate the trajectory prediction task and conditional CIFs in Sec. 3.1. and Sec. 3.2 respectively. Then, we present our FlowChain model architecture in Sec. 3.3. After that, we describe its fast update procedure of estimated density in Sec.3.4. Finally, we explain how to obtain the density map in Sec. 3.5.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We aim to estimate agents' plausible future trajectory densities from their past trajectories. The trajectory of each agent is defined as a sequence  $(\\mathbf{x}_0, \\mathbf{x}_1, \\ldots, \\mathbf{x}_T)$  of positions  $\\mathbf{x}_t = (x_t, y_t)$  over discrete timesteps  $t \\in \\{0, \\ldots, T\\}$ . Given the current time step  $t$ , we predict future  $T_{\\mathrm{f}}$ -step trajectory densities  $\\{p(\\tilde{\\mathbf{x}}_{t+1}^i | \\mathbf{o}_t), \\ldots, p(\\tilde{\\mathbf{x}}_{t+T_{\\mathrm{f}}}^i | \\mathbf{o}_t)\\}$  given  $T_{\\mathrm{o}}$ -step observed trajectory  $\\mathbf{o}_t = \\{(x_{t-T_{\\mathrm{o}}}^i - 1, \\ldots, x_t^i) | i \\in \\{1, 2, \\ldots, N_a\\}\\}$ , where  $N_a$  and  $i$  denote the number of agents and the index of each agent, respectively. This index will be omitted for brevity in later use. We denote  $\\mathbf{x}$  as an observed position,  $\\tilde{\\mathbf{x}}$  as a predicted future position, and  $\\hat{\\mathbf{x}}$  as a ground truth future position.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Conditional Continuously-indexed Flow",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Conditional normalizing flow is a density estimation method that uses a parameterized bijective transformation  $f$  conditioned on additional information  $\\mathbf{c}$  such as an encoded vector from observed trajectories, i.e.,  $\\mathbf{o}_t$ , for trajectory prediction. The bijection  $f$  transforms a base density  $p(\\mathbf{z})$  to an expressive density  $p(\\mathbf{y})$  by the analytical computation of the change-of-variables formula as follows:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {y} = f (\\mathbf {z}) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (\\mathbf {y}) = p (\\mathbf {z}) \\left| \\det  \\nabla_ {\\mathbf {y}} f ^ {- 1} (\\mathbf {y}, \\mathbf {c}) \\right| \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The parameters of bijective transformation  $f$  can be learned by maximizing the likelihood of samples  $\\hat{\\mathbf{y}}$  from datasets, or minimizing the negative log-likelihood as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nN L L = - \\log p (\\hat {\\mathbf {y}} | \\mathbf {c}) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A normalizing flow with only bijective transformations has a constraint that the topology of a base density is preserved. For example, if the base density is a simple unimodal Gaussian distribution, the normalizing flow fails to fit a distinct multi-modal density. To avoid this problem of bijective transformation, we use continuously-indexed flows (CIFs) [7], akin to an infinite mixture of normalizing flows. While CIFs potentially avoid the topology constraint, CIFs still enable analytical density computation with a little",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "looseness  $\\mathcal{E}$  because CIFs incorporate inference and generative surjections according to the survey [44]. We investigated the tradeoff between the expressive power and exactness of estimated density on CIFs. We concluded this looseness of estimated density can be ignored in trajectory prediction, as we show in the supplemental materials. Based on the above discussion, We use conditional CIFs as the base normalizing flow model of our FlowChain.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. FlowChain model",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The overview of the FlowChain model is shown in Fig. 2. Given the current time step  $t$ , we estimate future trajectory densities  $\\{p(\\tilde{\\mathbf{x}}_{t + 1}|\\mathbf{o}_t),\\dots ,p(\\tilde{\\mathbf{x}}_{t + T_{\\mathrm{f}}}|\\mathbf{o}_t)\\}$  by chaining the conditional CIFs, each of which transforms the density of the former time step  $p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)$  to the density of the next time step  $p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)$ , shown in the upper side of Fig. 2. Our formulation consists of two equations: the initial condition for the first step prediction (Eq.(4)) and the recurrence relation between the latter steps (Eq.(5)) as follows.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} p \\left(\\tilde {\\mathbf {x}} _ {t + 1} \\mid \\mathbf {o} _ {t}\\right) = \\mathcal {N} (\\mathbf {z}; \\mathbf {x} _ {t}, \\sigma) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + 1}} f _ {1} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + 1}, \\mathbf {o} _ {t}\\right) | (4) \\\\ p \\left(\\tilde {\\mathbf {x}} _ {t + n} \\mid \\mathbf {o} _ {t}\\right) = p \\left(\\tilde {\\mathbf {x}} _ {t + n - 1} \\mid \\mathbf {o} _ {t}\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n}, \\mathbf {o} _ {t}\\right) | (5) \\\\ = \\exp \\left(\\log \\mathcal {N} (\\mathbf {z}; \\mathbf {x} _ {t}, \\sigma) \\right. \\\\ \\left. + \\sum_ {n ^ {\\prime} = 1} ^ {n} \\log | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}} f _ {n ^ {\\prime}} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}, \\mathbf {o} _ {t}\\right) |\\right) (6) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $n \\in \\{2,3,\\dots,T_{\\mathrm{f}}\\}$ .  $f_{n}$  is a conditional CIF that transforms the sample  $\\tilde{\\mathbf{x}}_{t + n - 1}$  from a former density  $p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)$  to the sample  $\\tilde{\\mathbf{x}}_{t + n}$  from a next density  $p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)$  as  $\\tilde{\\mathbf{x}}_{t + n} = f_n(\\tilde{\\mathbf{x}}_{t + n - 1},\\mathbf{o}_t)$ .  $f_{1}$  transforms the sample  $\\mathbf{z}$  from a base Gaussian density  $\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)$ .  $\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)$  is created from the newest observed position  $\\mathbf{x}_t$  as a mean position. The standard deviation  $\\sigma$  is a trainable parameter of FlowChain model. All of  $f_{1}$  and  $f_{n}$  are independently trained with the loss function (Eq.(3)) in our method.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "From  $f_{n}$ , we can sample multiple trajectories for best-of-N metrics [25] by sampling multiple  $\\mathbf{z}$  as follows:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\{\\tilde {\\mathbf {x}} _ {t + 1}, \\dots , \\tilde {\\mathbf {x}} _ {t + n} \\} = \\left\\{f _ {1} (\\mathbf {z}, \\mathbf {o} _ {t}), \\dots , f _ {n} \\circ \\dots \\circ f _ {2} \\circ f _ {1} (\\mathbf {z}, \\mathbf {o} _ {t}) \\right\\} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.4. Update of estimated density",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For accurate prediction by reusing the previous predictions, we focused on two features of the observed trajectory: the newest observed position and motion trend, shown in Fig. 2. Our FlowChain generates future trajectories by transforming the newest observed position  $\\mathbf{x}_t$  based on the motion trend e.g. go straight or turning left/right, modeled",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "9797",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/bbb7e99b80d26d3aae1e45a2e55c9596c832c06ab6fc2acebc38dd25d322e822.jpg",
+        "image_caption": [
+            "Figure 2. Overview of our FlowChain model. FlowChain consists of sequential conditional CIFs denoted by  $f_{n}$ .  $f_{n}$  is conditioned on the feature vector denoted by Motion Trend from the Temporal-Social Encoder, which encodes the observed trajectories  $\\mathbf{o}_t$ . Since  $\\mathbf{o}_t$  includes the trajectories of other agents as well as an agent of interest (i.e., the target of prediction), the future trajectory is predicted while taking into account social interaction with the others.  $f_{n}$  transforms the density of the former time step  $p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)$  to the density of the next time step  $p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)$  as shown in the upper side. However, for the first step, the Gaussian distribution  $\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)$ , which is created from the newest observed position  $\\mathbf{x}_t$ , is transformed. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively. In the update procedure shown on the bottom side, the Gaussian distribution  $\\mathcal{N}(\\cdot ;\\mathbf{x}_{n + 1},\\sigma)$ , created from newest observed position  $\\mathbf{x}_{t + 1}$  at  $t + 1$ , replace the estimated density from the former time step. The other calculations are reused as shown by gray arrows. We can properly update the density by using the newest observed position at  $t + 1$ ,  $\\mathbf{x}_{t + 1}$ , instead of  $p(\\tilde{\\mathbf{x}}_{t + 1}|\\mathbf{o}_t)$ . In a toy example shown in this figure, another incorrect mode observed in the predicted densities,  $p(\\tilde{\\mathbf{x}}_{t + 2}|\\mathbf{o}_t)$  and  $p(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_t)$ , is successfully suppressed in the updated predictions  $p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 2}|\\mathbf{o}_{t + 1})$  and  $p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_{t + 1})$ . As shown in Sec. 4, our experiments validate this advantage of our proposed fast update procedure is greater than its disadvantage (i.e., a decrease in the prediction accuracy due to the reuse of the motion trend) so that the updated predictions are better than the initial predictions (e.g.,  $p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_{t + 1})$  is better than  $p(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_t)$  in the figure)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "by each flow  $f_{n}(\\mathbf{x}_{t + n},\\mathbf{o}_{t})$ . We cannot reuse the newest observed position  $\\mathbf{x}_t$  at  $t$  for the next time step because this position is a starting point of the future trajectories and thus greatly affect the accuracy of probability density estimation. Therefore, FlowChain adopt the newest observed position  $\\mathbf{x}_{t + n}$  at  $t + n$  by replacing the estimated density  $p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)$  with the Gaussian density  $\\mathcal{N}(\\cdot ;\\mathbf{x}_{t + n},\\sigma)$ , as shown in the bottom of Fig. 2. This replacement propagates the information of the newest observed position properly to the latter time steps.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "On the other hand, the motion trend can be reused because it doesn't change for several time steps unless a sudden strong external force is applied to a prediction target. Therefore, our FlowChain model reuses its trend in each flow transformation  $f_{n}(\\tilde{\\mathbf{x}}_{t + n},\\mathbf{o}_{t})$ . Specifically, we use the previously generated trajectories  $\\{\\tilde{\\mathbf{x}}_{t + 1},\\dots ,\\tilde{\\mathbf{x}}_{t + n}\\}$ . Thus, we can reuse the corresponding log-det-jacobians  $\\log |\\operatorname *{det}\\nabla_{\\tilde{\\mathbf{x}}_{t + n}}f_n^{-1}(\\tilde{\\mathbf{x}}_{t + n + 1},\\mathbf{o}_t)|$  which is the variation of the estimated densities, as shown by the gray arrows in Fig. 2. The equation of FlowChain's update is expressed",
+        "bbox": [
+            75,
+            750,
+            472,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "similar to Eq.(4) and Eq.(5) as follows:",
+        "bbox": [
+            500,
+            564,
+            759,
+            579
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + 2} \\mid \\mathbf {o} _ {t + 1}\\right) = \\mathcal {N} \\left(\\tilde {\\mathbf {x}} _ {t + 1}; \\mathbf {x} _ {t + 1}, \\sigma\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + 2}} f _ {2} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + 2}, \\mathbf {o} _ {t}\\right) | \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            590,
+            906,
+            636
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + n} \\mid \\mathbf {o} _ {t + 1}\\right) = p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + n - 1} \\mid \\mathbf {o} _ {t + 1}\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n}\\right) | (9) \\\\ = \\exp \\left(\\log \\mathcal {N} (\\tilde {\\mathbf {x}} _ {t + 1}; \\mathbf {x} _ {t + 1}, \\sigma) \\right. \\\\ \\left. + \\sum_ {n ^ {\\prime} = 2} ^ {n} \\log | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}} f _ {n ^ {\\prime}} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}, \\mathbf {o} _ {t}\\right) |\\right) (10) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            638,
+            893,
+            765
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where,  $n \\in \\{3, 4, \\ldots, T_{\\mathrm{f}}\\}$ . Thanks to reusing each flow transformation  $f_{n}(\\mathbf{x}_{t + n}, \\mathbf{o}_{t})$ , we don't need to evaluate log-det-jacobians  $\\log |\\operatorname*{det}\\nabla_{\\tilde{\\mathbf{x}}_{t + n}}f_n^{-1}(\\tilde{\\mathbf{x}}_{t + n})|$  again. This will greatly omit the computational cost. As a result, we can update the probability density by only calculating the Gaussian base distribution, summing up the log-det-jacobians, and taking exponentials, which take less than  $1ms$  in total. This rapid update is beneficial, especially for autonomous",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9798",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/52ac5db57636058d0d1358939e84c2ce76c08ffe6801a183030550912d708e22.jpg",
+        "image_caption": [
+            "Trajectories",
+            "Time steps",
+            "Figure 3. Overview of Simfork dataset. The trajectories shown in the left figure are examples of the observed and ground truth trajectories for training. The position of each step is sampled from the distributions of the middle figures. The sum of each distribution is shown in the right figure. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            233
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/49a2a5f9a20d09fb5532c5217e056cf0bdd0a2dd983c76ad9ea17624e40d3e02.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            488,
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+            233
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/272646ed6adfb81e2ef5a3be6a67db80d94dd65d0b015974e7b254183515b3f3.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            95,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "systems where computational resources are limited and often become busy by executing other computationally-intense tasks such as object detection, mapping, and path planning.",
+        "bbox": [
+            75,
+            310,
+            470,
+            371
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. How to obtain the density map",
+        "text_level": 1,
+        "bbox": [
+            76,
+            378,
+            349,
+            395
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The density map, not like the mere one-point estimate, is needed when autonomous systems perform visualization of density or successive tasks such as navigation. We can correct the possible future points with estimated density by sampling multiple trajectories from Eq.(7) and its density from Eq.(6). The density map is obtained by collecting these points with density at the same time step.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments and Results Analysis",
+        "text_level": 1,
+        "bbox": [
+            76,
+            520,
+            385,
+            537
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            545,
+            267,
+            561
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. Experiments were conducted on various datasets including our developed dataset with synthesized data Simfork, and real-image benchmarks including ETH/UCY [37, 50] and SDD [53]. On all the datasets, the numbers of past observed and future predicted steps are  $T_{o} = 8$  and  $T_{f} = 12$ , respectively. All steps have an interval of 0.4 seconds in accordance with the literature such as [25, 58].",
+        "bbox": [
+            75,
+            568,
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+            672
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Simfork is a synthesized dataset for comparison on the accuracy of predicted densities, which are produced as explained in Sec. 3.5. In all trajectories in this dataset, either of the two types of traveling directions (i.e., turning left or right) is observed after a straight trajectory, as shown in Fig. 3. Positions before and after the fork (colored by green and black, respectively, in the leftmost figure of Fig. 3) are used as past observed and future ground-truth positions, respectively. Each position of a trajectory is independently perturbed by the Gaussian noise, which results in the density at each time step.",
+        "bbox": [
+            75,
+            674,
+            468,
+            839
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Two pedestrian trajectory datasets, ETH [50] and UCY [37], are merged to ETH/UCY. This dataset has five scenes: ETH, HOTEL, UNIV, ZARA1, and ZARA2. For training and testing, we follow the standard leave-one-out",
+        "bbox": [
+            75,
+            839,
+            470,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "approach, where we train on 4 scenes and test on the remaining one. We follow the train-validation-test split of Social-GAN [25].",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$SDD$  consists of 20 scenes captured in bird's eye view using aerial drones. This dataset contains various moving agents such as pedestrians, bicycles, and cars, but we focus on pedestrians for comparison, as with Trajnet [56]. We also follow the train-test split of Trajnet [56].",
+        "bbox": [
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+            354,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Metrics Evaluation of accuracy on trajectory prediction is done with the widely-used metrics, Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE is the average L2 distance between the predicted and ground truth trajectories over time. FDE is the L2 distance between the endpoints of the predicted and ground truth trajectories. We follow the Best-of-N procedure [25] with  $N = 20$ .",
+        "bbox": [
+            496,
+            431,
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+            537
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For evaluation of the accuracy of density estimation, we use earth mover's distance (EMD) and log-probability. EMD is a measure of the distance between two densities by the minimum cost to move one density pile to the other. EMD is calculated between the estimated density and ground truth density on each prediction step. Thus, we use EMD on Simfork dataset, where the ground truth densities are available. The advantage of EMD over the widely-used KL divergence is that EMD works properly even if the two density is disjoint while KL divergence returns a constant value. We use log-probability on the pedestrian trajectory prediction datasets, where the ground truth density is unavailable. The log-probability is calculated on the ground truth trajectory instead of density.",
+        "bbox": [
+            496,
+            537,
+            892,
+            750
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Each conditional CIFs in our FlowChain used three-layer RealNVP [14] with multilayer perceptions (MLPs) of three hidden layers and 128 hidden units. All the conditional CIFs are with independent weights conditioned on the feature vectors from Trajectory++ [58] encoder as the temporal-social encoder. We used a batch size of 128 and ADAM optimizer [30] with a learning rate of  $10^{-4}$ . All experiments were conducted on a single NVIDIA A100 GPU. We use a KDE implementation utilizing GPU as mentioned in Sec. 2.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "9799",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/5d818df1050df31267b2edd0fb12bfd2a196ad86d95bd387946b1ce33363768f.jpg",
+        "table_caption": [
+            "Table 1. Quantitative results of trajectory prediction on ETH/UCY dataset with Best-of-20 metrics. T + I denotes its method takes a trajectory and an image as inputs while T denotes its method takes only a trajectory. Scores are in meters. Red and blue scores denote the best and the second-best in methods with T. Lower is better. The results of Trajectron++ [58] and MID [24] are updated according to an implementation issue #53 on the Trajectron++ GitHub page."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Input</td><td colspan=\"2\">ETH</td><td colspan=\"2\">HOTEL</td><td colspan=\"2\">UNIV</td><td colspan=\"2\">ZARA1</td><td colspan=\"2\">ZARA2</td><td colspan=\"2\">Mean</td></tr><tr><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>0.70</td><td>1.43</td><td>0.76</td><td>1.67</td><td>0.54</td><td>1.24</td><td>0.30</td><td>0.63</td><td>0.38</td><td>0.78</td><td>0.54</td><td>1.15</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>0.59</td><td>1.18</td><td>0.19</td><td>0.35</td><td>0.60</td><td>1.19</td><td>0.43</td><td>0.87</td><td>0.32</td><td>0.65</td><td>0.43</td><td>0.85</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>0.47</td><td>0.91</td><td>0.14</td><td>0.24</td><td>0.54</td><td>1.07</td><td>0.36</td><td>0.73</td><td>0.29</td><td>0.60</td><td>0.36</td><td>0.71</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>1.09</td><td>2.35</td><td>0.79</td><td>1.76</td><td>0.67</td><td>1.40</td><td>0.47</td><td>1.00</td><td>0.56</td><td>1.17</td><td>0.72</td><td>1.54</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>0.87</td><td>1.62</td><td>0.67</td><td>1.37</td><td>0.76</td><td>1.52</td><td>0.35</td><td>0.68</td><td>0.42</td><td>0.84</td><td>0.61</td><td>1.21</td></tr><tr><td>STGAT [29]</td><td>T</td><td>0.65</td><td>1.12</td><td>0.35</td><td>0.66</td><td>0.52</td><td>1.10</td><td>0.34</td><td>0.69</td><td>0.29</td><td>0.60</td><td>0.43</td><td>0.83</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>0.64</td><td>1.11</td><td>0.49</td><td>0.85</td><td>0.44</td><td>0.79</td><td>0.34</td><td>0.53</td><td>0.30</td><td>0.48</td><td>0.44</td><td>0.75</td></tr><tr><td>PECNet [41]</td><td>T</td><td>0.61</td><td>1.07</td><td>0.22</td><td>0.39</td><td>0.34</td><td>0.56</td><td>0.25</td><td>0.45</td><td>0.19</td><td>0.33</td><td>0.32</td><td>0.56</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>0.61</td><td>1.03</td><td>0.20</td><td>0.28</td><td>0.30</td><td>0.55</td><td>0.24</td><td>0.41</td><td>0.18</td><td>0.32</td><td>0.31</td><td>0.52</td></tr><tr><td>MID [24]</td><td>T</td><td>0.55</td><td>0.88</td><td>0.20</td><td>0.35</td><td>0.30</td><td>0.55</td><td>0.29</td><td>0.51</td><td>0.20</td><td>0.38</td><td>0.31</td><td>0.53</td></tr><tr><td>Social Implicit [43]</td><td>T</td><td>0.66</td><td>1.44</td><td>0.20</td><td>0.36</td><td>0.31</td><td>0.60</td><td>0.25</td><td>0.50</td><td>0.22</td><td>0.43</td><td>0.33</td><td>0.67</td></tr><tr><td>FlowChain(Ours)</td><td>T</td><td>0.55</td><td>0.99</td><td>0.20</td><td>0.35</td><td>0.29</td><td>0.54</td><td>0.22</td><td>0.40</td><td>0.20</td><td>0.34</td><td>0.29</td><td>0.52</td></tr></table>",
+        "bbox": [
+            76,
+            142,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/ddbf6351dfbee96c7272e71ca3b90ff42612cfffb64ff0afe295efafb05a877a.jpg",
+        "table_caption": [
+            "Table 2. Quantitative results of trajectory prediction on SDD dataset with Best-of-20 metrics. Scores are in pixels. See the caption of Tab. 1 also for details."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Input</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>16.27</td><td>29.38</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>12.20</td><td>22.10</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>13.60</td><td>25.80</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>31.19</td><td>56.97</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>27.25</td><td>41.44</td></tr><tr><td>STGAT [29]</td><td>T</td><td>14.85</td><td>28.17</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>20.76</td><td>33.18</td></tr><tr><td>PECNet [41]</td><td>T</td><td>9.97</td><td>15.89</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>11.40</td><td>20.12</td></tr><tr><td>MID [24]</td><td>T</td><td>10.31</td><td>17.37</td></tr><tr><td>FlowChain (Ours)</td><td>T</td><td>9.93</td><td>17.17</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Prediction Accuracy",
+        "text_level": 1,
+        "bbox": [
+            76,
+            632,
+            269,
+            648
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "A wide range of previous trajectory prediction methods is quantitatively compared with our FlowChain on ETH/UCY and SDD datasets, shown in Tab. 1 and Tab. 2. We didn't include some methods [40, 63, 70-72] due to a different train-validation-test split.",
+        "bbox": [
+            75,
+            657,
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+            731
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For ETH/UCY dataset, FlowChain achieved mean ADE/FDE of 0.29/0.52 in meters, which are the best among all trajectory prediction methods. On SDD dataset, FlowChain achieved average ADE/FDE of 9.93/17.17 in pixels, which are the best and second-best among all methods taking only trajectories as inputs [1,24,25,41,58,63].",
+        "bbox": [
+            75,
+            733,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Although our focus is on density estimation with a minimal computational cost, FlowChain is comparable with the state-of-the-art methods also in terms of errors. We didn't evaluate the accuracy of future trajectories from FlowChain's update because the trajectories do not change",
+        "bbox": [
+            75,
+            825,
+            467,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f530bdaa1cf5a2d18a228a98f412c3ee79b75f5eabac471307052eeca901d5f5.jpg",
+        "image_caption": [
+            "Figure 4. Temporal estimated densities on Simfork dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            383,
+            883,
+            686
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "in the update as mentioned in Sec. 3.4.",
+        "bbox": [
+            500,
+            729,
+            754,
+            743
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Analysis on Density Estimation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            755,
+            772,
+            771
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The results of density estimation are compared between FlowChain and previous methods based on VAE, GAN, and diffusion approaches. Trajectory++ is the representative VAE-based trajectory prediction model with density estimation by GMM. Social-GAN is a minimal model of GAN-based trajectory prediction. MID is the diffusion-based trajectory prediction model with state-of-the-art prediction accuracy. We applied KDE to Social-GAN and MID since",
+        "bbox": [
+            496,
+            779,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "9800",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/839b4e1985cd61c6514f7c80757822fc96ed14f964bc3cbf215c9e00143da48b.jpg",
+        "image_caption": [
+            "Figure 5. Temporal estimated densities on ETH/UCY dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            90,
+            455,
+            366
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "they cannot estimate the density alone. For a fair comparison, FlowChain, Social-GAN, and MID generated the same number of samples for future trajectories;  $10^{5}$  samples.",
+        "bbox": [
+            76,
+            411,
+            468,
+            457
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluated the computational time and the accuracy of density estimation of each method, as shown in Tab. 3. Social-GAN and MID take much longer time because KDE is slow in spite of running on GPU. Trajectory++ is a bit faster than our FlowChain due to its simple Gaussian mixture model but suffers from the poor quality of estimated density, as shown by the worst EMD, 2.545, on Simfork dataset and worst log-probability, -281.86, on ETH/UCY dataset. On the other hand, our FlowChain achieved the best EMD, 1.408, and the best log-probability, -0.26, in spite of the fast computation 37.0ms. Thus, our method successfully addresses both the computational cost and accurate density estimation.",
+        "bbox": [
+            75,
+            458,
+            468,
+            654
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The estimated densities on Simfork are visualized in Fig. 4. The densities estimated by Trajectory++ are too large compared to the ground truth densities. While the densities of Social-GAN and MID are stretched to the vertical axis, our FlowChain successfully estimated the tighter round-shape densities closest to the ground truth densities.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The estimated densities on  $ETH/UCY$  are shown in Fig. 5. The size of each density represents the positional uncertainty of a predicted position. As within Simfork, in  $ETH/UCY$ , an agent cannot change its traveling direction significantly in a short period (i.e.,  $T_{f} = 12$  is  $0.4 \\times 12 = 4.8$  seconds), the size of the density expected to be tight. The densities estimated by Social-GAN are tight but deviated from the ground truth trajectory. Trajectory++ generated the densities with several disconnected modes due to the approximation as a Gaussian mixture. While the densi",
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+        "img_path": "images/ba883f7cf9f760f6123000d999e38e9eeed29de25e15f81a06112c1804114af8.jpg",
+        "image_caption": [
+            "Figure 6. Temporal densities estimated by our update procedure on Simfork dataset."
+        ],
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+        "image_caption": [
+            "Figure 7. Temporal densities estimated by our update procedure on ETH/UCY dataset."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "ties from MID are close to the ground truth trajectory, MID could not suggest tight densities and their modes deviated from the ground truth trajectories. On the contrary, the density from our FlowChain covers the ground truth trajectory with tight distributions. thanks to the explicit density estimation of conditional CIFs and our expressive model architecture. We should note that the estimated density of FlowChain has some fluctuation due to the looseness of the density computation of CIFs. However, we did not observe any potential problem or failure of density estimation related to this in our experiments.",
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+    {
+        "type": "text",
+        "text": "4.4. Proposed Update of Density Estimation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As shown in Tab. 3, the accuracy of density estimation degraded along with the number of updates. However, this update is remarkably fast  $0.6ms$ , also shown in Tab. 3. Thus, autonomous systems can select the accurate prediction from scratch or the super rapid update by reusing predictions depending on the utilization of their computational resources.",
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+    {
+        "type": "text",
+        "text": "The estimated densities of our update procedure are shown in Fig. 6 and Fig. 7, which show the densities up",
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+        "type": "page_number",
+        "text": "9801",
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+    {
+        "type": "table",
+        "img_path": "images/c58c0473e9af68b3d9290cfe44242a85d1a1c22d2e8709e1187f1c8283ed923e.jpg",
+        "table_caption": [
+            "Table 3. Accuracy and computational time of density estimation. Scores are in milliseconds for computational time. While lower is better for EMD on Simfork dataset, higher is better for log-probability on ETH/UCY dataset. We report the averaged EMD and log-probability over the 12 prediction steps."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td></td><td colspan=\"2\">Comp. Time</td><td colspan=\"2\">Accuracy of Density Estimation</td></tr><tr><td></td><td>All</td><td>w/o KDE</td><td>EMD ↓</td><td>log-probability ↑</td></tr><tr><td>Social-GAN [25]</td><td></td><td>11498.8</td><td>9.8</td><td>1.544</td><td>-3.40</td></tr><tr><td>Trajectory++ [58]</td><td></td><td>33.7</td><td>-</td><td>2.545</td><td>-281.86</td></tr><tr><td>MID [24]</td><td></td><td>23904.1</td><td>12219.1</td><td>2.135</td><td>-0.90</td></tr><tr><td rowspan=\"3\">FlowChain (Ours)</td><td>Pred at t</td><td>37.0</td><td>-</td><td>1.408</td><td>-0.26</td></tr><tr><td>Update from t - 1</td><td>0.6</td><td>-</td><td>2.539</td><td>-0.45</td></tr><tr><td>Update from t - 5</td><td>0.5</td><td>-</td><td>2.899</td><td>-0.53</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/76d1a9de8abd9ffa3060dc4aa6c5873422784d1b9f4a0d21f49818c11241d778.jpg",
+        "table_caption": [
+            "Table 4. Accuracy of density estimation with the update."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\" colspan=\"2\">Method</td><td colspan=\"8\">log-probability on each step</td></tr><tr><td>t+6</td><td>t+7</td><td>t+8</td><td>t+9</td><td>t+10</td><td>t+11</td><td>t+12</td><td>mean</td></tr><tr><td colspan=\"2\">Social-GAN [25]</td><td>-2.65</td><td>-2.86</td><td>-3.07</td><td>-3.26</td><td>-3.44</td><td>-3.62</td><td>-3.80</td><td>-3.24</td></tr><tr><td colspan=\"2\">Trajectory++ [58]</td><td>-121.19</td><td>-93.61</td><td>-71.62</td><td>-51.36</td><td>-36.85</td><td>-27.92</td><td>-22.72</td><td>-97.79</td></tr><tr><td colspan=\"2\">MID [24]</td><td>-1.06</td><td>-1.43</td><td>-1.75</td><td>-2.02</td><td>-2.26</td><td>-2.46</td><td>-2.65</td><td>-1.95</td></tr><tr><td rowspan=\"2\">FlowChain</td><td>Without Update</td><td>0.21</td><td>0.36</td><td>0.44</td><td>-0.08</td><td>-0.78</td><td>-0.75</td><td>-1.19</td><td>-0.26</td></tr><tr><td>With Update</td><td>0.20</td><td>0.50</td><td>0.39</td><td>0.44</td><td>0.20</td><td>0.26</td><td>0.16</td><td>0.31</td></tr></table>",
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+    {
+        "type": "image",
+        "img_path": "images/0a76851cb4fc158b0af1c58891e65eb3faa4e67d0e242ea4c520878e06ff7c78.jpg",
+        "image_caption": [
+            "Figure 8. Comparison of standard methods and FlowChain with updates."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "dated at  $t + 1$  and  $t + 2$  from the prediction at  $t$ . On Simfork dataset, the wrong mode is successfully suppressed by exploiting the information of the new observation. On ETH/UCY dataset, the initial prediction deviated from the ground truth because the observed trajectory observed until  $t$  does not have the information on turning left. However, the updated densities covered the ground truth well by adopting the newest observed position despite the minimal computational cost.",
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+    {
+        "type": "text",
+        "text": "We further perform a comparison with a practical setting. Models usually make predictions with intervals due to the large computational cost. Therefore, we usually cannot obtain the prediction from the latest observation, as shown by the upper side of Fig. 8. For example, assume we need the density of six time-step ahead such as  $p_{t+6}$  from  $\\mathbf{x}_t$ , we cannot obtain  $p_{t+7}$  from  $\\mathbf{x}_{t+1}$  or  $p_{t+8}$  from  $\\mathbf{x}_{t+2}$  due to the",
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+    {
+        "type": "text",
+        "text": "computational overhead. However, with FlowChain's rapid update, we can obtain the update  $(p_{t + 7}, p_{t + 8})$  from the latest observation  $(\\mathbf{x}_{t + 1}, \\mathbf{x}_{t + 2})$  on every time step thanks to the minimal computational cost, as shown by the bottom side of Fig. 8. We conducted the comparison with the frame of interest as six time-step ahead  $t + 6$  and the log-probability metric. As shown by Tab. 4, our FlowChain with update achieves the highest log-probability. Therefore, we can conclude that FlowChain's update can improve the density estimation with minimal computational cost.",
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+    {
+        "type": "text",
+        "text": "5. Concluding Remarks",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper, we proposed a new normalizing flow-based trajectory prediction network named FlowChain that achieves fast and accurate probability density estimation. Furthermore, our update procedure reliably generates the density estimation of the next step based on the density estimation of the previous step in an instant. Experimental results demonstrated that FlowChain achieved comparable accuracy to the state-of-the-art trajectory prediction models and superiority in the accuracy of density estimation.",
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+        "type": "text",
+        "text": "Our FlowChain has one limitation. Our update procedure can reliably estimate the density for several steps but the performance will degrade along with the time steps because the reused flow transformations do not reflect the new observations. Our future work is determining when should we stop to use the update procedure and make predictions from scratch. Furthermore, FlowChain is the domain-agnostic model that can be applied to a wide range of prediction tasks such as stock price prediction, human motion prediction, and video prediction. We will investigate the applicability of our FlowChain on these other domains.",
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+        "text": "9802",
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+    {
+        "type": "text",
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+            "[72] Jiangbei Yue, Dinesh Manocha, and He Wang. Human trajectory prediction via neural social physics. In ECCV, pages 376-394, 2022.",
+            "[73] He Zhao and Richard P Wildes. Where are you heading? dynamic trajectory prediction with expert goal examples. In ICCV, pages 7629-7638, 2021."
+        ],
+        "bbox": [
+            78,
+            90,
+            467,
+            390
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "9805",
+        "bbox": [
+            482,
+            945,
+            514,
+            955
+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction/19d05057-5302-4e5f-a291-21f3188ae791_model.json b/2023/Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction/19d05057-5302-4e5f-a291-21f3188ae791_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..94c74975b2a3fba3750e4f8620ee192b6c855fab
--- /dev/null
+++ b/2023/Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction/19d05057-5302-4e5f-a291-21f3188ae791_model.json	
@@ -0,0 +1,2312 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.174,
+                0.131,
+                0.8,
+                0.177
+            ],
+            "angle": 0,
+            "content": "Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.333,
+                0.204,
+                0.64,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Takahiro Maeda Norimichi Ukita"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.338,
+                0.223,
+                0.633,
+                0.24
+            ],
+            "angle": 0,
+            "content": "Toyota Technological Institute, Japan"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.345,
+                0.242,
+                0.626,
+                0.257
+            ],
+            "angle": 0,
+            "content": "{sd21601,ukita}@toyota-ti.ac.jp"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.326,
+                0.474,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.738,
+                0.21,
+                0.753
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Human trajectory prediction is a challenging problem because human movements are not deterministic, unlike the billiard balls on a pool table. Starting from deterministic approaches [26, 49], to tackle its indeterministic nature, many stochastic approaches are proposed, such as Gaussian distribution-based [1, 42, 66], generative adversarial networks (GANs)-based [9, 10, 25, 57], variational autoencoder (VAE)-based [58, 71, 73], diffusion-based [24], and normalizing flow-based [59] methods. These methods"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.293,
+                0.895,
+                0.445
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.45,
+                0.894,
+                0.507
+            ],
+            "angle": 0,
+            "content": "Figure 1. Effects of our FlowChain. Our FlowChain can rapidly estimate accurate density than VAE-based methods as shown in green. Furthermore, we propose an update of estimated density that only requires an instant of time, as shown in blue."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.534,
+                0.892,
+                0.565
+            ],
+            "angle": 0,
+            "content": "can be applied to human-interactive systems, including autonomous vehicles [8,11,38,55,69] and social robots [4,39]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.566,
+                0.893,
+                0.702
+            ],
+            "angle": 0,
+            "content": "In these safety-critical applications, autonomous systems must infer the existence probability density distribution (\"density\" for brevity) of other moving objects such as pedestrians around on all prediction steps for risk assessment (i.e., collision avoidance). However, most of the indeterministic approaches mentioned above merely generate possible future trajectories and cannot estimate the density alone. We need to further apply kernel density estimation (KDE) to these future trajectories for density estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.703,
+                0.894,
+                0.794
+            ],
+            "angle": 0,
+            "content": "Thus, trajectory prediction with density estimation usually takes a larger computational cost than only generating possible trajectories. This computational cost accumulates upon every single prediction update along with highly-frequent observations. This is unacceptable to autonomous systems that work in rapidly changing environments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To address both computational cost and density estimation, we propose a new normalizing flow-based model named FlowChain (Fig. 1). This speed and accuracy are because normalizing flows need no additional approximation such as Gaussian mixture modeling or KDE with limited samples. FlowChain can estimate a density on each prediction time step thanks to our stacked normalizing flow archi"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9795"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.302
+            ],
+            "angle": 0,
+            "content": "tecture unlike Flomo [59], which is closest to FlowChain. While Flomo uses one flow module that only estimates the spatial density of a trajectory, FlowChain further predicts its spatio-temporal density so that the spatial density of an agent position at each time step is also predicted. This stacking architecture also allows a rapid update of an estimated density in an instant of time e.g. less than one millisecond. This update is achieved by reusing the flow transformations and its log-det-jacobians that represent the motion trend such as going straight or turning right. This update with the reuse significantly omits the computational cost while maintaining the accuracy of density estimation because the motion trend doesn't change for several time steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.303,
+                0.384,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Our contributions are three-fold as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.328,
+                0.468,
+                0.388
+            ],
+            "angle": 0,
+            "content": "- We propose a normalizing flow-based trajectory prediction network named FlowChain that rapidly estimates the accurate density of future positions on each prediction time step."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.399,
+                0.468,
+                0.444
+            ],
+            "angle": 0,
+            "content": "- Our update procedure for the density requires less than one millisecond by adopting new observations and reusing the motion trend as the flow transformations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.454,
+                0.468,
+                0.498
+            ],
+            "angle": 0,
+            "content": "- Our FlowChain achieved comparable prediction accuracy to other computationally-intense state-of-the-art methods on several benchmarks."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.097,
+                0.328,
+                0.468,
+                0.498
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.513,
+                0.22,
+                0.529
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.539,
+                0.47,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Human Trajectory Prediction. The earliest works on human trajectory prediction [26, 49] are deterministic regression models using attractive and repulsive forces between humans and goal positions. However, human movements are indeterministic in nature. Therefore, many approaches are proposed to model this uncertainty. Social-LSTM [1] and Social-STGCNN [42] regress the parameters of the bivariate Gaussian distributions to model the uncertainty of future trajectories. These approaches [1, 42] are simple and require low computational cost but cannot catch the future multi-modality we often see at road intersections."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.468,
+                0.84
+            ],
+            "angle": 0,
+            "content": "To address this multi-modality, many stochastic prediction models are proposed. Trajectory++ [58], AgentFormer [71], and ExpertTraj [73] combined the aforementioned Gaussian regression with VAE [32]. These models predict a bivariate Gaussian mixture based on stochastically sampled latent variables [28, 52]. We can obtain the density by summing up each estimated Gaussian density map. However, these Gaussian mixture methods have limited expressive power and thus predict inaccurate distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "On the other hand, GAN [18]-based approaches implicitly handle this uncertainty. Social-GAN [25], SoPhie [57], Goal-GAN [10], and MG-GAN [9] use a GAN architecture to predict diverse trajectories conditioned on random"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.137
+            ],
+            "angle": 0,
+            "content": "noises. While they cannot estimate the density alone, we can estimate the density by applying KDE [48, 54] on sampled trajectories"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.139,
+                0.892,
+                0.306
+            ],
+            "angle": 0,
+            "content": "The denoising diffusion probabilistic model [27] can also implicitly handle uncertainty by generating multiple trajectories. Recently, denoising diffusion attracts much attention for its state-of-the-art performances in several generative tasks, including image synthesis [12] and audio generation [33]. MID [24] is a trajectory prediction model incorporating denoising diffusion, which achieves state-of-the-art performances. We can also estimate the density of MID by applying KDE. However, GAN-based and diffusion-based approaches cannot estimate accurate densities because KDE is performed on limited samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.308,
+                0.892,
+                0.414
+            ],
+            "angle": 0,
+            "content": "On the contrary, normalizing flow [51, 64, 65]-based trajectory prediction method named Flomo [59] can rapidly generate future trajectories and their accurate probabilities thanks to the analytical computation of normalizing flows. However, this approach only estimates the probability of each future trajectory and thus cannot estimate the density of positions on each prediction step alone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.416,
+                0.892,
+                0.732
+            ],
+            "angle": 0,
+            "content": "Normalizing Flows. Thanks to its bijective process, normalizing flow can compute the density analytically. This analytical computation allows us fast and accurate density estimation because it does not need additional approximation such as KDE with limited samples. For more expressive power, several bijective families were proposed such as affine coupling layers [13, 14], autoregressive maps [17, 47], invertible linear transformations [31], and invertible ResNet block [2, 6]. All flows mentioned above have a topology constraint between the base and estimated densities. This topology constraint limits the expressive power of normalizing flows. To address this constraint, some approaches incorporated stochasticity into flows [68]. However, this stochasticity makes analytical density calculation impossible. Therefore, further density approximation such as KDE is required for this stochastic normalizing flow. Other approaches [5, 7, 44] use surjective layers, which relax the topology constraint but make analytical density computation with a little looseness. In summary, the optimal normalizing flow model architecture for future trajectory density estimation is still unknown."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Density Estimation. Kernel density estimation [48, 54] is the most representative non-parametric method that estimates a continuous density from a finite set of data. Suppose that we have \\( A \\) input data and \\( B \\) points evaluated, the computational cost is \\( \\mathcal{O}(AB) \\). This is a huge cost for autonomous systems. Therefore, several accelerations are proposed such as data binning [19, 60, 62, 67], fast sum updating [15, 16, 35, 61], fast Gauss transform [22, 23, 34], and dual-tree method [20, 21, 36]. However, we confirmed that the KDE implementation utilizing GPU is faster than these accelerations including [3, 45, 46]. We use the KDE utilizing"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9796"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.092,
+                0.283,
+                0.106
+            ],
+            "angle": 0,
+            "content": "GPU for comparison in Sec. 4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.12,
+                0.268,
+                0.138
+            ],
+            "angle": 0,
+            "content": "3. Proposed Approach"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.145,
+                0.47,
+                0.268
+            ],
+            "angle": 0,
+            "content": "In this section, we present our normalizing flow-based trajectory prediction named FlowChain and its update of estimated density. First, we formulate the trajectory prediction task and conditional CIFs in Sec. 3.1. and Sec. 3.2 respectively. Then, we present our FlowChain model architecture in Sec. 3.3. After that, we describe its fast update procedure of estimated density in Sec.3.4. Finally, we explain how to obtain the density map in Sec. 3.5."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.276,
+                0.281,
+                0.29
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.299,
+                0.471,
+                0.482
+            ],
+            "angle": 0,
+            "content": "We aim to estimate agents' plausible future trajectory densities from their past trajectories. The trajectory of each agent is defined as a sequence \\((\\mathbf{x}_0, \\mathbf{x}_1, \\ldots, \\mathbf{x}_T)\\) of positions \\(\\mathbf{x}_t = (x_t, y_t)\\) over discrete timesteps \\(t \\in \\{0, \\ldots, T\\}\\). Given the current time step \\(t\\), we predict future \\(T_{\\mathrm{f}}\\)-step trajectory densities \\(\\{p(\\tilde{\\mathbf{x}}_{t+1}^i | \\mathbf{o}_t), \\ldots, p(\\tilde{\\mathbf{x}}_{t+T_{\\mathrm{f}}}^i | \\mathbf{o}_t)\\}\\) given \\(T_{\\mathrm{o}}\\)-step observed trajectory \\(\\mathbf{o}_t = \\{(x_{t-T_{\\mathrm{o}}}^i - 1, \\ldots, x_t^i) | i \\in \\{1, 2, \\ldots, N_a\\}\\}\\), where \\(N_a\\) and \\(i\\) denote the number of agents and the index of each agent, respectively. This index will be omitted for brevity in later use. We denote \\(\\mathbf{x}\\) as an observed position, \\(\\tilde{\\mathbf{x}}\\) as a predicted future position, and \\(\\hat{\\mathbf{x}}\\) as a ground truth future position."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.491,
+                0.42,
+                0.507
+            ],
+            "angle": 0,
+            "content": "3.2. Conditional Continuously-indexed Flow"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.514,
+                0.47,
+                0.62
+            ],
+            "angle": 0,
+            "content": "Conditional normalizing flow is a density estimation method that uses a parameterized bijective transformation \\( f \\) conditioned on additional information \\( \\mathbf{c} \\) such as an encoded vector from observed trajectories, i.e., \\( \\mathbf{o}_t \\), for trajectory prediction. The bijection \\( f \\) transforms a base density \\( p(\\mathbf{z}) \\) to an expressive density \\( p(\\mathbf{y}) \\) by the analytical computation of the change-of-variables formula as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.193,
+                0.633,
+                0.469,
+                0.648
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {y} = f (\\mathbf {z}) \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.172,
+                0.652,
+                0.469,
+                0.669
+            ],
+            "angle": 0,
+            "content": "\\[\np (\\mathbf {y}) = p (\\mathbf {z}) \\left| \\det  \\nabla_ {\\mathbf {y}} f ^ {- 1} (\\mathbf {y}, \\mathbf {c}) \\right| \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.68,
+                0.469,
+                0.725
+            ],
+            "angle": 0,
+            "content": "The parameters of bijective transformation \\( f \\) can be learned by maximizing the likelihood of samples \\( \\hat{\\mathbf{y}} \\) from datasets, or minimizing the negative log-likelihood as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.202,
+                0.738,
+                0.469,
+                0.754
+            ],
+            "angle": 0,
+            "content": "\\[\nN L L = - \\log p (\\hat {\\mathbf {y}} | \\mathbf {c}) \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "A normalizing flow with only bijective transformations has a constraint that the topology of a base density is preserved. For example, if the base density is a simple unimodal Gaussian distribution, the normalizing flow fails to fit a distinct multi-modal density. To avoid this problem of bijective transformation, we use continuously-indexed flows (CIFs) [7], akin to an infinite mixture of normalizing flows. While CIFs potentially avoid the topology constraint, CIFs still enable analytical density computation with a little"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.213
+            ],
+            "angle": 0,
+            "content": "looseness \\(\\mathcal{E}\\) because CIFs incorporate inference and generative surjections according to the survey [44]. We investigated the tradeoff between the expressive power and exactness of estimated density on CIFs. We concluded this looseness of estimated density can be ignored in trajectory prediction, as we show in the supplemental materials. Based on the above discussion, We use conditional CIFs as the base normalizing flow model of our FlowChain."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.222,
+                0.673,
+                0.237
+            ],
+            "angle": 0,
+            "content": "3.3. FlowChain model"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.245,
+                0.892,
+                0.381
+            ],
+            "angle": 0,
+            "content": "The overview of the FlowChain model is shown in Fig. 2. Given the current time step \\( t \\), we estimate future trajectory densities \\( \\{p(\\tilde{\\mathbf{x}}_{t + 1}|\\mathbf{o}_t),\\dots ,p(\\tilde{\\mathbf{x}}_{t + T_{\\mathrm{f}}}|\\mathbf{o}_t)\\} \\) by chaining the conditional CIFs, each of which transforms the density of the former time step \\( p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t) \\) to the density of the next time step \\( p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t) \\), shown in the upper side of Fig. 2. Our formulation consists of two equations: the initial condition for the first step prediction (Eq.(4)) and the recurrence relation between the latter steps (Eq.(5)) as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.511,
+                0.394,
+                0.891,
+                0.538
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} p \\left(\\tilde {\\mathbf {x}} _ {t + 1} \\mid \\mathbf {o} _ {t}\\right) = \\mathcal {N} (\\mathbf {z}; \\mathbf {x} _ {t}, \\sigma) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + 1}} f _ {1} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + 1}, \\mathbf {o} _ {t}\\right) | (4) \\\\ p \\left(\\tilde {\\mathbf {x}} _ {t + n} \\mid \\mathbf {o} _ {t}\\right) = p \\left(\\tilde {\\mathbf {x}} _ {t + n - 1} \\mid \\mathbf {o} _ {t}\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n}, \\mathbf {o} _ {t}\\right) | (5) \\\\ = \\exp \\left(\\log \\mathcal {N} (\\mathbf {z}; \\mathbf {x} _ {t}, \\sigma) \\right. \\\\ \\left. + \\sum_ {n ^ {\\prime} = 1} ^ {n} \\log | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}} f _ {n ^ {\\prime}} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}, \\mathbf {o} _ {t}\\right) |\\right) (6) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.551,
+                0.892,
+                0.701
+            ],
+            "angle": 0,
+            "content": "where \\(n \\in \\{2,3,\\dots,T_{\\mathrm{f}}\\}\\). \\(f_{n}\\) is a conditional CIF that transforms the sample \\(\\tilde{\\mathbf{x}}_{t + n - 1}\\) from a former density \\(p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)\\) to the sample \\(\\tilde{\\mathbf{x}}_{t + n}\\) from a next density \\(p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)\\) as \\(\\tilde{\\mathbf{x}}_{t + n} = f_n(\\tilde{\\mathbf{x}}_{t + n - 1},\\mathbf{o}_t)\\). \\(f_{1}\\) transforms the sample \\(\\mathbf{z}\\) from a base Gaussian density \\(\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)\\). \\(\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)\\) is created from the newest observed position \\(\\mathbf{x}_t\\) as a mean position. The standard deviation \\(\\sigma\\) is a trainable parameter of FlowChain model. All of \\(f_{1}\\) and \\(f_{n}\\) are independently trained with the loss function (Eq.(3)) in our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.702,
+                0.891,
+                0.732
+            ],
+            "angle": 0,
+            "content": "From \\( f_{n} \\), we can sample multiple trajectories for best-of-N metrics [25] by sampling multiple \\( \\mathbf{z} \\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.501,
+                0.744,
+                0.911,
+                0.775
+            ],
+            "angle": 0,
+            "content": "\\[\n\\{\\tilde {\\mathbf {x}} _ {t + 1}, \\dots , \\tilde {\\mathbf {x}} _ {t + n} \\} = \\left\\{f _ {1} (\\mathbf {z}, \\mathbf {o} _ {t}), \\dots , f _ {n} \\circ \\dots \\circ f _ {2} \\circ f _ {1} (\\mathbf {z}, \\mathbf {o} _ {t}) \\right\\} \\tag {7}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.75,
+                0.804
+            ],
+            "angle": 0,
+            "content": "3.4. Update of estimated density"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For accurate prediction by reusing the previous predictions, we focused on two features of the observed trajectory: the newest observed position and motion trend, shown in Fig. 2. Our FlowChain generates future trajectories by transforming the newest observed position \\(\\mathbf{x}_t\\) based on the motion trend e.g. go straight or turning left/right, modeled"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9797"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.09,
+                0.885,
+                0.357
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.359,
+                0.896,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overview of our FlowChain model. FlowChain consists of sequential conditional CIFs denoted by \\( f_{n} \\). \\( f_{n} \\) is conditioned on the feature vector denoted by Motion Trend from the Temporal-Social Encoder, which encodes the observed trajectories \\( \\mathbf{o}_t \\). Since \\( \\mathbf{o}_t \\) includes the trajectories of other agents as well as an agent of interest (i.e., the target of prediction), the future trajectory is predicted while taking into account social interaction with the others. \\( f_{n} \\) transforms the density of the former time step \\( p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t) \\) to the density of the next time step \\( p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t) \\) as shown in the upper side. However, for the first step, the Gaussian distribution \\( \\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma) \\), which is created from the newest observed position \\( \\mathbf{x}_t \\), is transformed. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively. In the update procedure shown on the bottom side, the Gaussian distribution \\( \\mathcal{N}(\\cdot ;\\mathbf{x}_{n + 1},\\sigma) \\), created from newest observed position \\( \\mathbf{x}_{t + 1} \\) at \\( t + 1 \\), replace the estimated density from the former time step. The other calculations are reused as shown by gray arrows. We can properly update the density by using the newest observed position at \\( t + 1 \\), \\( \\mathbf{x}_{t + 1} \\), instead of \\( p(\\tilde{\\mathbf{x}}_{t + 1}|\\mathbf{o}_t) \\). In a toy example shown in this figure, another incorrect mode observed in the predicted densities, \\( p(\\tilde{\\mathbf{x}}_{t + 2}|\\mathbf{o}_t) \\) and \\( p(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_t) \\), is successfully suppressed in the updated predictions \\( p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 2}|\\mathbf{o}_{t + 1}) \\) and \\( p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_{t + 1}) \\). As shown in Sec. 4, our experiments validate this advantage of our proposed fast update procedure is greater than its disadvantage (i.e., a decrease in the prediction accuracy due to the reuse of the motion trend) so that the updated predictions are better than the initial predictions (e.g., \\( p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_{t + 1}) \\) is better than \\( p(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_t) \\) in the figure)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.565,
+                0.473,
+                0.718
+            ],
+            "angle": 0,
+            "content": "by each flow \\( f_{n}(\\mathbf{x}_{t + n},\\mathbf{o}_{t}) \\). We cannot reuse the newest observed position \\( \\mathbf{x}_t \\) at \\( t \\) for the next time step because this position is a starting point of the future trajectories and thus greatly affect the accuracy of probability density estimation. Therefore, FlowChain adopt the newest observed position \\( \\mathbf{x}_{t + n} \\) at \\( t + n \\) by replacing the estimated density \\( p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t) \\) with the Gaussian density \\( \\mathcal{N}(\\cdot ;\\mathbf{x}_{t + n},\\sigma) \\), as shown in the bottom of Fig. 2. This replacement propagates the information of the newest observed position properly to the latter time steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "On the other hand, the motion trend can be reused because it doesn't change for several time steps unless a sudden strong external force is applied to a prediction target. Therefore, our FlowChain model reuses its trend in each flow transformation \\( f_{n}(\\tilde{\\mathbf{x}}_{t + n},\\mathbf{o}_{t}) \\). Specifically, we use the previously generated trajectories \\( \\{\\tilde{\\mathbf{x}}_{t + 1},\\dots ,\\tilde{\\mathbf{x}}_{t + n}\\} \\). Thus, we can reuse the corresponding log-det-jacobians \\( \\log |\\operatorname *{det}\\nabla_{\\tilde{\\mathbf{x}}_{t + n}}f_n^{-1}(\\tilde{\\mathbf{x}}_{t + n + 1},\\mathbf{o}_t)| \\) which is the variation of the estimated densities, as shown by the gray arrows in Fig. 2. The equation of FlowChain's update is expressed"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.565,
+                0.761,
+                0.58
+            ],
+            "angle": 0,
+            "content": "similar to Eq.(4) and Eq.(5) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.592,
+                0.907,
+                0.637
+            ],
+            "angle": 0,
+            "content": "\\[\np ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + 2} \\mid \\mathbf {o} _ {t + 1}\\right) = \\mathcal {N} \\left(\\tilde {\\mathbf {x}} _ {t + 1}; \\mathbf {x} _ {t + 1}, \\sigma\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + 2}} f _ {2} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + 2}, \\mathbf {o} _ {t}\\right) | \\tag {8}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.64,
+                0.895,
+                0.766
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + n} \\mid \\mathbf {o} _ {t + 1}\\right) = p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + n - 1} \\mid \\mathbf {o} _ {t + 1}\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n}\\right) | (9) \\\\ = \\exp \\left(\\log \\mathcal {N} (\\tilde {\\mathbf {x}} _ {t + 1}; \\mathbf {x} _ {t + 1}, \\sigma) \\right. \\\\ \\left. + \\sum_ {n ^ {\\prime} = 2} ^ {n} \\log | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}} f _ {n ^ {\\prime}} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}, \\mathbf {o} _ {t}\\right) |\\right) (10) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where, \\(n \\in \\{3, 4, \\ldots, T_{\\mathrm{f}}\\}\\). Thanks to reusing each flow transformation \\(f_{n}(\\mathbf{x}_{t + n}, \\mathbf{o}_{t})\\), we don't need to evaluate log-det-jacobians \\(\\log |\\operatorname*{det}\\nabla_{\\tilde{\\mathbf{x}}_{t + n}}f_n^{-1}(\\tilde{\\mathbf{x}}_{t + n})|\\) again. This will greatly omit the computational cost. As a result, we can update the probability density by only calculating the Gaussian base distribution, summing up the log-det-jacobians, and taking exponentials, which take less than \\(1ms\\) in total. This rapid update is beneficial, especially for autonomous"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9798"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.104,
+                0.109,
+                0.195,
+                0.22
+            ],
+            "angle": 0,
+            "content": "Trajectories"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.22,
+                0.188,
+                0.233
+            ],
+            "angle": 0,
+            "content": "Time steps"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.202,
+                0.109,
+                0.485,
+                0.234
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.49,
+                0.097,
+                0.772,
+                0.234
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.775,
+                0.097,
+                0.868,
+                0.219
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.243,
+                0.895,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Figure 3. Overview of Simfork dataset. The trajectories shown in the left figure are examples of the observed and ground truth trajectories for training. The position of each step is sampled from the distributions of the middle figures. The sum of each distribution is shown in the right figure. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.311,
+                0.471,
+                0.372
+            ],
+            "angle": 0,
+            "content": "systems where computational resources are limited and often become busy by executing other computationally-intense tasks such as object detection, mapping, and path planning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.379,
+                0.35,
+                0.396
+            ],
+            "angle": 0,
+            "content": "3.5. How to obtain the density map"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.402,
+                0.47,
+                0.509
+            ],
+            "angle": 0,
+            "content": "The density map, not like the mere one-point estimate, is needed when autonomous systems perform visualization of density or successive tasks such as navigation. We can correct the possible future points with estimated density by sampling multiple trajectories from Eq.(7) and its density from Eq.(6). The density map is obtained by collecting these points with density at the same time step."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.521,
+                0.387,
+                0.539
+            ],
+            "angle": 0,
+            "content": "4. Experiments and Results Analysis"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.546,
+                0.268,
+                0.563
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.47,
+                0.674
+            ],
+            "angle": 0,
+            "content": "Datasets. Experiments were conducted on various datasets including our developed dataset with synthesized data Simfork, and real-image benchmarks including ETH/UCY [37, 50] and SDD [53]. On all the datasets, the numbers of past observed and future predicted steps are \\( T_{o} = 8 \\) and \\( T_{f} = 12 \\), respectively. All steps have an interval of 0.4 seconds in accordance with the literature such as [25, 58]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.469,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Simfork is a synthesized dataset for comparison on the accuracy of predicted densities, which are produced as explained in Sec. 3.5. In all trajectories in this dataset, either of the two types of traveling directions (i.e., turning left or right) is observed after a straight trajectory, as shown in Fig. 3. Positions before and after the fork (colored by green and black, respectively, in the leftmost figure of Fig. 3) are used as past observed and future ground-truth positions, respectively. Each position of a trajectory is independently perturbed by the Gaussian noise, which results in the density at each time step."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Two pedestrian trajectory datasets, ETH [50] and UCY [37], are merged to ETH/UCY. This dataset has five scenes: ETH, HOTEL, UNIV, ZARA1, and ZARA2. For training and testing, we follow the standard leave-one-out"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.311,
+                0.893,
+                0.355
+            ],
+            "angle": 0,
+            "content": "approach, where we train on 4 scenes and test on the remaining one. We follow the train-validation-test split of Social-GAN [25]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.356,
+                0.892,
+                0.432
+            ],
+            "angle": 0,
+            "content": "\\( SDD \\) consists of 20 scenes captured in bird's eye view using aerial drones. This dataset contains various moving agents such as pedestrians, bicycles, and cars, but we focus on pedestrians for comparison, as with Trajnet [56]. We also follow the train-test split of Trajnet [56]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.432,
+                0.893,
+                0.538
+            ],
+            "angle": 0,
+            "content": "Metrics Evaluation of accuracy on trajectory prediction is done with the widely-used metrics, Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE is the average L2 distance between the predicted and ground truth trajectories over time. FDE is the L2 distance between the endpoints of the predicted and ground truth trajectories. We follow the Best-of-N procedure [25] with \\( N = 20 \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.539,
+                0.893,
+                0.75
+            ],
+            "angle": 0,
+            "content": "For evaluation of the accuracy of density estimation, we use earth mover's distance (EMD) and log-probability. EMD is a measure of the distance between two densities by the minimum cost to move one density pile to the other. EMD is calculated between the estimated density and ground truth density on each prediction step. Thus, we use EMD on Simfork dataset, where the ground truth densities are available. The advantage of EMD over the widely-used KL divergence is that EMD works properly even if the two density is disjoint while KL divergence returns a constant value. We use log-probability on the pedestrian trajectory prediction datasets, where the ground truth density is unavailable. The log-probability is calculated on the ground truth trajectory instead of density."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Implementation Details. Each conditional CIFs in our FlowChain used three-layer RealNVP [14] with multilayer perceptions (MLPs) of three hidden layers and 128 hidden units. All the conditional CIFs are with independent weights conditioned on the feature vectors from Trajectory++ [58] encoder as the temporal-social encoder. We used a batch size of 128 and ADAM optimizer [30] with a learning rate of \\(10^{-4}\\). All experiments were conducted on a single NVIDIA A100 GPU. We use a KDE implementation utilizing GPU as mentioned in Sec. 2."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9799"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.088,
+                0.892,
+                0.142
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative results of trajectory prediction on ETH/UCY dataset with Best-of-20 metrics. T + I denotes its method takes a trajectory and an image as inputs while T denotes its method takes only a trajectory. Scores are in meters. Red and blue scores denote the best and the second-best in methods with T. Lower is better. The results of Trajectron++ [58] and MID [24] are updated according to an implementation issue #53 on the Trajectron++ GitHub page."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.143,
+                0.925,
+                0.358
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Input</td><td colspan=\"2\">ETH</td><td colspan=\"2\">HOTEL</td><td colspan=\"2\">UNIV</td><td colspan=\"2\">ZARA1</td><td colspan=\"2\">ZARA2</td><td colspan=\"2\">Mean</td></tr><tr><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>0.70</td><td>1.43</td><td>0.76</td><td>1.67</td><td>0.54</td><td>1.24</td><td>0.30</td><td>0.63</td><td>0.38</td><td>0.78</td><td>0.54</td><td>1.15</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>0.59</td><td>1.18</td><td>0.19</td><td>0.35</td><td>0.60</td><td>1.19</td><td>0.43</td><td>0.87</td><td>0.32</td><td>0.65</td><td>0.43</td><td>0.85</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>0.47</td><td>0.91</td><td>0.14</td><td>0.24</td><td>0.54</td><td>1.07</td><td>0.36</td><td>0.73</td><td>0.29</td><td>0.60</td><td>0.36</td><td>0.71</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>1.09</td><td>2.35</td><td>0.79</td><td>1.76</td><td>0.67</td><td>1.40</td><td>0.47</td><td>1.00</td><td>0.56</td><td>1.17</td><td>0.72</td><td>1.54</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>0.87</td><td>1.62</td><td>0.67</td><td>1.37</td><td>0.76</td><td>1.52</td><td>0.35</td><td>0.68</td><td>0.42</td><td>0.84</td><td>0.61</td><td>1.21</td></tr><tr><td>STGAT [29]</td><td>T</td><td>0.65</td><td>1.12</td><td>0.35</td><td>0.66</td><td>0.52</td><td>1.10</td><td>0.34</td><td>0.69</td><td>0.29</td><td>0.60</td><td>0.43</td><td>0.83</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>0.64</td><td>1.11</td><td>0.49</td><td>0.85</td><td>0.44</td><td>0.79</td><td>0.34</td><td>0.53</td><td>0.30</td><td>0.48</td><td>0.44</td><td>0.75</td></tr><tr><td>PECNet [41]</td><td>T</td><td>0.61</td><td>1.07</td><td>0.22</td><td>0.39</td><td>0.34</td><td>0.56</td><td>0.25</td><td>0.45</td><td>0.19</td><td>0.33</td><td>0.32</td><td>0.56</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>0.61</td><td>1.03</td><td>0.20</td><td>0.28</td><td>0.30</td><td>0.55</td><td>0.24</td><td>0.41</td><td>0.18</td><td>0.32</td><td>0.31</td><td>0.52</td></tr><tr><td>MID [24]</td><td>T</td><td>0.55</td><td>0.88</td><td>0.20</td><td>0.35</td><td>0.30</td><td>0.55</td><td>0.29</td><td>0.51</td><td>0.20</td><td>0.38</td><td>0.31</td><td>0.53</td></tr><tr><td>Social Implicit [43]</td><td>T</td><td>0.66</td><td>1.44</td><td>0.20</td><td>0.36</td><td>0.31</td><td>0.60</td><td>0.25</td><td>0.50</td><td>0.22</td><td>0.43</td><td>0.33</td><td>0.67</td></tr><tr><td>FlowChain(Ours)</td><td>T</td><td>0.55</td><td>0.99</td><td>0.20</td><td>0.35</td><td>0.29</td><td>0.54</td><td>0.22</td><td>0.40</td><td>0.20</td><td>0.34</td><td>0.29</td><td>0.52</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.38,
+                0.468,
+                0.42
+            ],
+            "angle": 0,
+            "content": "Table 2. Quantitative results of trajectory prediction on SDD dataset with Best-of-20 metrics. Scores are in pixels. See the caption of Tab. 1 also for details."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.104,
+                0.422,
+                0.441,
+                0.607
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Input</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>16.27</td><td>29.38</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>12.20</td><td>22.10</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>13.60</td><td>25.80</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>31.19</td><td>56.97</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>27.25</td><td>41.44</td></tr><tr><td>STGAT [29]</td><td>T</td><td>14.85</td><td>28.17</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>20.76</td><td>33.18</td></tr><tr><td>PECNet [41]</td><td>T</td><td>9.97</td><td>15.89</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>11.40</td><td>20.12</td></tr><tr><td>MID [24]</td><td>T</td><td>10.31</td><td>17.37</td></tr><tr><td>FlowChain (Ours)</td><td>T</td><td>9.93</td><td>17.17</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.633,
+                0.271,
+                0.649
+            ],
+            "angle": 0,
+            "content": "4.2. Prediction Accuracy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.658,
+                0.468,
+                0.732
+            ],
+            "angle": 0,
+            "content": "A wide range of previous trajectory prediction methods is quantitatively compared with our FlowChain on ETH/UCY and SDD datasets, shown in Tab. 1 and Tab. 2. We didn't include some methods [40, 63, 70-72] due to a different train-validation-test split."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.734,
+                0.468,
+                0.824
+            ],
+            "angle": 0,
+            "content": "For ETH/UCY dataset, FlowChain achieved mean ADE/FDE of 0.29/0.52 in meters, which are the best among all trajectory prediction methods. On SDD dataset, FlowChain achieved average ADE/FDE of 9.93/17.17 in pixels, which are the best and second-best among all methods taking only trajectories as inputs [1,24,25,41,58,63]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.826,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Although our focus is on density estimation with a minimal computational cost, FlowChain is comparable with the state-of-the-art methods also in terms of errors. We didn't evaluate the accuracy of future trajectories from FlowChain's update because the trajectories do not change"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.385,
+                0.885,
+                0.688
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.69,
+                0.871,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Figure 4. Temporal estimated densities on Simfork dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.73,
+                0.755,
+                0.744
+            ],
+            "angle": 0,
+            "content": "in the update as mentioned in Sec. 3.4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.756,
+                0.774,
+                0.772
+            ],
+            "angle": 0,
+            "content": "4.3. Analysis on Density Estimation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The results of density estimation are compared between FlowChain and previous methods based on VAE, GAN, and diffusion approaches. Trajectory++ is the representative VAE-based trajectory prediction model with density estimation by GMM. Social-GAN is a minimal model of GAN-based trajectory prediction. MID is the diffusion-based trajectory prediction model with state-of-the-art prediction accuracy. We applied KDE to Social-GAN and MID since"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9800"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.092,
+                0.457,
+                0.367
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.078,
+                0.369,
+                0.465,
+                0.384
+            ],
+            "angle": 0,
+            "content": "Figure 5. Temporal estimated densities on ETH/UCY dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.412,
+                0.469,
+                0.458
+            ],
+            "angle": 0,
+            "content": "they cannot estimate the density alone. For a fair comparison, FlowChain, Social-GAN, and MID generated the same number of samples for future trajectories; \\(10^{5}\\) samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.459,
+                0.47,
+                0.655
+            ],
+            "angle": 0,
+            "content": "We evaluated the computational time and the accuracy of density estimation of each method, as shown in Tab. 3. Social-GAN and MID take much longer time because KDE is slow in spite of running on GPU. Trajectory++ is a bit faster than our FlowChain due to its simple Gaussian mixture model but suffers from the poor quality of estimated density, as shown by the worst EMD, 2.545, on Simfork dataset and worst log-probability, -281.86, on ETH/UCY dataset. On the other hand, our FlowChain achieved the best EMD, 1.408, and the best log-probability, -0.26, in spite of the fast computation 37.0ms. Thus, our method successfully addresses both the computational cost and accurate density estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.657,
+                0.469,
+                0.748
+            ],
+            "angle": 0,
+            "content": "The estimated densities on Simfork are visualized in Fig. 4. The densities estimated by Trajectory++ are too large compared to the ground truth densities. While the densities of Social-GAN and MID are stretched to the vertical axis, our FlowChain successfully estimated the tighter round-shape densities closest to the ground truth densities."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The estimated densities on \\(ETH/UCY\\) are shown in Fig. 5. The size of each density represents the positional uncertainty of a predicted position. As within Simfork, in \\(ETH/UCY\\), an agent cannot change its traveling direction significantly in a short period (i.e., \\(T_{f} = 12\\) is \\(0.4 \\times 12 = 4.8\\) seconds), the size of the density expected to be tight. The densities estimated by Social-GAN are tight but deviated from the ground truth trajectory. Trajectory++ generated the densities with several disconnected modes due to the approximation as a Gaussian mixture. While the densi"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.092,
+                0.885,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.284,
+                0.892,
+                0.312
+            ],
+            "angle": 0,
+            "content": "Figure 6. Temporal densities estimated by our update procedure on Simfork dataset."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.321,
+                0.885,
+                0.519
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.52,
+                0.892,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Figure 7. Temporal densities estimated by our update procedure on ETH/UCY dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.567,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "ties from MID are close to the ground truth trajectory, MID could not suggest tight densities and their modes deviated from the ground truth trajectories. On the contrary, the density from our FlowChain covers the ground truth trajectory with tight distributions. thanks to the explicit density estimation of conditional CIFs and our expressive model architecture. We should note that the estimated density of FlowChain has some fluctuation due to the looseness of the density computation of CIFs. However, we did not observe any potential problem or failure of density estimation related to this in our experiments."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.742,
+                0.838,
+                0.759
+            ],
+            "angle": 0,
+            "content": "4.4. Proposed Update of Density Estimation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.869
+            ],
+            "angle": 0,
+            "content": "As shown in Tab. 3, the accuracy of density estimation degraded along with the number of updates. However, this update is remarkably fast \\(0.6ms\\), also shown in Tab. 3. Thus, autonomous systems can select the accurate prediction from scratch or the super rapid update by reusing predictions depending on the utilization of their computational resources."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The estimated densities of our update procedure are shown in Fig. 6 and Fig. 7, which show the densities up"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9801"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.088,
+                0.895,
+                0.129
+            ],
+            "angle": 0,
+            "content": "Table 3. Accuracy and computational time of density estimation. Scores are in milliseconds for computational time. While lower is better for EMD on Simfork dataset, higher is better for log-probability on ETH/UCY dataset. We report the averaged EMD and log-probability over the 12 prediction steps."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.143,
+                0.129,
+                0.825,
+                0.254
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td></td><td colspan=\"2\">Comp. Time</td><td colspan=\"2\">Accuracy of Density Estimation</td></tr><tr><td></td><td>All</td><td>w/o KDE</td><td>EMD ↓</td><td>log-probability ↑</td></tr><tr><td>Social-GAN [25]</td><td></td><td>11498.8</td><td>9.8</td><td>1.544</td><td>-3.40</td></tr><tr><td>Trajectory++ [58]</td><td></td><td>33.7</td><td>-</td><td>2.545</td><td>-281.86</td></tr><tr><td>MID [24]</td><td></td><td>23904.1</td><td>12219.1</td><td>2.135</td><td>-0.90</td></tr><tr><td rowspan=\"3\">FlowChain (Ours)</td><td>Pred at t</td><td>37.0</td><td>-</td><td>1.408</td><td>-0.26</td></tr><tr><td>Update from t - 1</td><td>0.6</td><td>-</td><td>2.539</td><td>-0.45</td></tr><tr><td>Update from t - 5</td><td>0.5</td><td>-</td><td>2.899</td><td>-0.53</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.308,
+                0.261,
+                0.662,
+                0.274
+            ],
+            "angle": 0,
+            "content": "Table 4. Accuracy of density estimation with the update."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.122,
+                0.274,
+                0.846,
+                0.384
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\" colspan=\"2\">Method</td><td colspan=\"8\">log-probability on each step</td></tr><tr><td>t+6</td><td>t+7</td><td>t+8</td><td>t+9</td><td>t+10</td><td>t+11</td><td>t+12</td><td>mean</td></tr><tr><td colspan=\"2\">Social-GAN [25]</td><td>-2.65</td><td>-2.86</td><td>-3.07</td><td>-3.26</td><td>-3.44</td><td>-3.62</td><td>-3.80</td><td>-3.24</td></tr><tr><td colspan=\"2\">Trajectory++ [58]</td><td>-121.19</td><td>-93.61</td><td>-71.62</td><td>-51.36</td><td>-36.85</td><td>-27.92</td><td>-22.72</td><td>-97.79</td></tr><tr><td colspan=\"2\">MID [24]</td><td>-1.06</td><td>-1.43</td><td>-1.75</td><td>-2.02</td><td>-2.26</td><td>-2.46</td><td>-2.65</td><td>-1.95</td></tr><tr><td rowspan=\"2\">FlowChain</td><td>Without Update</td><td>0.21</td><td>0.36</td><td>0.44</td><td>-0.08</td><td>-0.78</td><td>-0.75</td><td>-1.19</td><td>-0.26</td></tr><tr><td>With Update</td><td>0.20</td><td>0.50</td><td>0.39</td><td>0.44</td><td>0.20</td><td>0.26</td><td>0.16</td><td>0.31</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.104,
+                0.407,
+                0.436,
+                0.594
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.602,
+                0.47,
+                0.632
+            ],
+            "angle": 0,
+            "content": "Figure 8. Comparison of standard methods and FlowChain with updates."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.656,
+                0.47,
+                0.793
+            ],
+            "angle": 0,
+            "content": "dated at \\( t + 1 \\) and \\( t + 2 \\) from the prediction at \\( t \\). On Simfork dataset, the wrong mode is successfully suppressed by exploiting the information of the new observation. On ETH/UCY dataset, the initial prediction deviated from the ground truth because the observed trajectory observed until \\( t \\) does not have the information on turning left. However, the updated densities covered the ground truth well by adopting the newest observed position despite the minimal computational cost."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.471,
+                0.904
+            ],
+            "angle": 0,
+            "content": "We further perform a comparison with a practical setting. Models usually make predictions with intervals due to the large computational cost. Therefore, we usually cannot obtain the prediction from the latest observation, as shown by the upper side of Fig. 8. For example, assume we need the density of six time-step ahead such as \\( p_{t+6} \\) from \\( \\mathbf{x}_t \\), we cannot obtain \\( p_{t+7} \\) from \\( \\mathbf{x}_{t+1} \\) or \\( p_{t+8} \\) from \\( \\mathbf{x}_{t+2} \\) due to the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.405,
+                0.895,
+                0.557
+            ],
+            "angle": 0,
+            "content": "computational overhead. However, with FlowChain's rapid update, we can obtain the update \\((p_{t + 7}, p_{t + 8})\\) from the latest observation \\((\\mathbf{x}_{t + 1}, \\mathbf{x}_{t + 2})\\) on every time step thanks to the minimal computational cost, as shown by the bottom side of Fig. 8. We conducted the comparison with the frame of interest as six time-step ahead \\(t + 6\\) and the log-probability metric. As shown by Tab. 4, our FlowChain with update achieves the highest log-probability. Therefore, we can conclude that FlowChain's update can improve the density estimation with minimal computational cost."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.572,
+                0.704,
+                0.59
+            ],
+            "angle": 0,
+            "content": "5. Concluding Remarks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "In this paper, we proposed a new normalizing flow-based trajectory prediction network named FlowChain that achieves fast and accurate probability density estimation. Furthermore, our update procedure reliably generates the density estimation of the next step based on the density estimation of the previous step in an instant. Experimental results demonstrated that FlowChain achieved comparable accuracy to the state-of-the-art trajectory prediction models and superiority in the accuracy of density estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Our FlowChain has one limitation. Our update procedure can reliably estimate the density for several steps but the performance will degrade along with the time steps because the reused flow transformations do not reflect the new observations. Our future work is determining when should we stop to use the update procedure and make predictions from scratch. Furthermore, FlowChain is the domain-agnostic model that can be applied to a wide range of prediction tasks such as stock price prediction, human motion prediction, and video prediction. We will investigate the applicability of our FlowChain on these other domains."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9802"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+            ],
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+            "angle": 0,
+            "content": "[73] He Zhao and Richard P Wildes. Where are you heading? dynamic trajectory prediction with expert goal examples. In ICCV, pages 7629-7638, 2021."
+        },
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+# Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction
+
+Takahiro Maeda Norimichi Ukita
+
+Toyota Technological Institute, Japan
+
+{sd21601,ukita}@toyota-ti.ac.jp
+
+# Abstract
+
+Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023.
+
+# 1. Introduction
+
+Human trajectory prediction is a challenging problem because human movements are not deterministic, unlike the billiard balls on a pool table. Starting from deterministic approaches [26, 49], to tackle its indeterministic nature, many stochastic approaches are proposed, such as Gaussian distribution-based [1, 42, 66], generative adversarial networks (GANs)-based [9, 10, 25, 57], variational autoencoder (VAE)-based [58, 71, 73], diffusion-based [24], and normalizing flow-based [59] methods. These methods
+
+![](images/61587bff2e78dc4ebe9603181c4add73529e15eebc64fa2b03fd0994a5fb6b63.jpg)  
+Figure 1. Effects of our FlowChain. Our FlowChain can rapidly estimate accurate density than VAE-based methods as shown in green. Furthermore, we propose an update of estimated density that only requires an instant of time, as shown in blue.
+
+can be applied to human-interactive systems, including autonomous vehicles [8,11,38,55,69] and social robots [4,39].
+
+In these safety-critical applications, autonomous systems must infer the existence probability density distribution ("density" for brevity) of other moving objects such as pedestrians around on all prediction steps for risk assessment (i.e., collision avoidance). However, most of the indeterministic approaches mentioned above merely generate possible future trajectories and cannot estimate the density alone. We need to further apply kernel density estimation (KDE) to these future trajectories for density estimation.
+
+Thus, trajectory prediction with density estimation usually takes a larger computational cost than only generating possible trajectories. This computational cost accumulates upon every single prediction update along with highly-frequent observations. This is unacceptable to autonomous systems that work in rapidly changing environments.
+
+To address both computational cost and density estimation, we propose a new normalizing flow-based model named FlowChain (Fig. 1). This speed and accuracy are because normalizing flows need no additional approximation such as Gaussian mixture modeling or KDE with limited samples. FlowChain can estimate a density on each prediction time step thanks to our stacked normalizing flow archi
+
+tecture unlike Flomo [59], which is closest to FlowChain. While Flomo uses one flow module that only estimates the spatial density of a trajectory, FlowChain further predicts its spatio-temporal density so that the spatial density of an agent position at each time step is also predicted. This stacking architecture also allows a rapid update of an estimated density in an instant of time e.g. less than one millisecond. This update is achieved by reusing the flow transformations and its log-det-jacobians that represent the motion trend such as going straight or turning right. This update with the reuse significantly omits the computational cost while maintaining the accuracy of density estimation because the motion trend doesn't change for several time steps.
+
+Our contributions are three-fold as follows:
+
+- We propose a normalizing flow-based trajectory prediction network named FlowChain that rapidly estimates the accurate density of future positions on each prediction time step.  
+- Our update procedure for the density requires less than one millisecond by adopting new observations and reusing the motion trend as the flow transformations.  
+- Our FlowChain achieved comparable prediction accuracy to other computationally-intense state-of-the-art methods on several benchmarks.
+
+# 2. Related Work
+
+Human Trajectory Prediction. The earliest works on human trajectory prediction [26, 49] are deterministic regression models using attractive and repulsive forces between humans and goal positions. However, human movements are indeterministic in nature. Therefore, many approaches are proposed to model this uncertainty. Social-LSTM [1] and Social-STGCNN [42] regress the parameters of the bivariate Gaussian distributions to model the uncertainty of future trajectories. These approaches [1, 42] are simple and require low computational cost but cannot catch the future multi-modality we often see at road intersections.
+
+To address this multi-modality, many stochastic prediction models are proposed. Trajectory++ [58], AgentFormer [71], and ExpertTraj [73] combined the aforementioned Gaussian regression with VAE [32]. These models predict a bivariate Gaussian mixture based on stochastically sampled latent variables [28, 52]. We can obtain the density by summing up each estimated Gaussian density map. However, these Gaussian mixture methods have limited expressive power and thus predict inaccurate distributions.
+
+On the other hand, GAN [18]-based approaches implicitly handle this uncertainty. Social-GAN [25], SoPhie [57], Goal-GAN [10], and MG-GAN [9] use a GAN architecture to predict diverse trajectories conditioned on random
+
+noises. While they cannot estimate the density alone, we can estimate the density by applying KDE [48, 54] on sampled trajectories
+
+The denoising diffusion probabilistic model [27] can also implicitly handle uncertainty by generating multiple trajectories. Recently, denoising diffusion attracts much attention for its state-of-the-art performances in several generative tasks, including image synthesis [12] and audio generation [33]. MID [24] is a trajectory prediction model incorporating denoising diffusion, which achieves state-of-the-art performances. We can also estimate the density of MID by applying KDE. However, GAN-based and diffusion-based approaches cannot estimate accurate densities because KDE is performed on limited samples.
+
+On the contrary, normalizing flow [51, 64, 65]-based trajectory prediction method named Flomo [59] can rapidly generate future trajectories and their accurate probabilities thanks to the analytical computation of normalizing flows. However, this approach only estimates the probability of each future trajectory and thus cannot estimate the density of positions on each prediction step alone.
+
+Normalizing Flows. Thanks to its bijective process, normalizing flow can compute the density analytically. This analytical computation allows us fast and accurate density estimation because it does not need additional approximation such as KDE with limited samples. For more expressive power, several bijective families were proposed such as affine coupling layers [13, 14], autoregressive maps [17, 47], invertible linear transformations [31], and invertible ResNet block [2, 6]. All flows mentioned above have a topology constraint between the base and estimated densities. This topology constraint limits the expressive power of normalizing flows. To address this constraint, some approaches incorporated stochasticity into flows [68]. However, this stochasticity makes analytical density calculation impossible. Therefore, further density approximation such as KDE is required for this stochastic normalizing flow. Other approaches [5, 7, 44] use surjective layers, which relax the topology constraint but make analytical density computation with a little looseness. In summary, the optimal normalizing flow model architecture for future trajectory density estimation is still unknown.
+
+Density Estimation. Kernel density estimation [48, 54] is the most representative non-parametric method that estimates a continuous density from a finite set of data. Suppose that we have  $A$  input data and  $B$  points evaluated, the computational cost is  $\mathcal{O}(AB)$ . This is a huge cost for autonomous systems. Therefore, several accelerations are proposed such as data binning [19, 60, 62, 67], fast sum updating [15, 16, 35, 61], fast Gauss transform [22, 23, 34], and dual-tree method [20, 21, 36]. However, we confirmed that the KDE implementation utilizing GPU is faster than these accelerations including [3, 45, 46]. We use the KDE utilizing
+
+GPU for comparison in Sec. 4.
+
+# 3. Proposed Approach
+
+In this section, we present our normalizing flow-based trajectory prediction named FlowChain and its update of estimated density. First, we formulate the trajectory prediction task and conditional CIFs in Sec. 3.1. and Sec. 3.2 respectively. Then, we present our FlowChain model architecture in Sec. 3.3. After that, we describe its fast update procedure of estimated density in Sec.3.4. Finally, we explain how to obtain the density map in Sec. 3.5.
+
+# 3.1. Problem Formulation
+
+We aim to estimate agents' plausible future trajectory densities from their past trajectories. The trajectory of each agent is defined as a sequence  $(\mathbf{x}_0, \mathbf{x}_1, \ldots, \mathbf{x}_T)$  of positions  $\mathbf{x}_t = (x_t, y_t)$  over discrete timesteps  $t \in \{0, \ldots, T\}$ . Given the current time step  $t$ , we predict future  $T_{\mathrm{f}}$ -step trajectory densities  $\{p(\tilde{\mathbf{x}}_{t+1}^i | \mathbf{o}_t), \ldots, p(\tilde{\mathbf{x}}_{t+T_{\mathrm{f}}}^i | \mathbf{o}_t)\}$  given  $T_{\mathrm{o}}$ -step observed trajectory  $\mathbf{o}_t = \{(x_{t-T_{\mathrm{o}}}^i - 1, \ldots, x_t^i) | i \in \{1, 2, \ldots, N_a\}\}$ , where  $N_a$  and  $i$  denote the number of agents and the index of each agent, respectively. This index will be omitted for brevity in later use. We denote  $\mathbf{x}$  as an observed position,  $\tilde{\mathbf{x}}$  as a predicted future position, and  $\hat{\mathbf{x}}$  as a ground truth future position.
+
+# 3.2. Conditional Continuously-indexed Flow
+
+Conditional normalizing flow is a density estimation method that uses a parameterized bijective transformation  $f$  conditioned on additional information  $\mathbf{c}$  such as an encoded vector from observed trajectories, i.e.,  $\mathbf{o}_t$ , for trajectory prediction. The bijection  $f$  transforms a base density  $p(\mathbf{z})$  to an expressive density  $p(\mathbf{y})$  by the analytical computation of the change-of-variables formula as follows:
+
+$$
+\mathbf {y} = f (\mathbf {z}) \tag {1}
+$$
+
+$$
+p (\mathbf {y}) = p (\mathbf {z}) \left| \det  \nabla_ {\mathbf {y}} f ^ {- 1} (\mathbf {y}, \mathbf {c}) \right| \tag {2}
+$$
+
+The parameters of bijective transformation  $f$  can be learned by maximizing the likelihood of samples  $\hat{\mathbf{y}}$  from datasets, or minimizing the negative log-likelihood as follows:
+
+$$
+N L L = - \log p (\hat {\mathbf {y}} | \mathbf {c}) \tag {3}
+$$
+
+A normalizing flow with only bijective transformations has a constraint that the topology of a base density is preserved. For example, if the base density is a simple unimodal Gaussian distribution, the normalizing flow fails to fit a distinct multi-modal density. To avoid this problem of bijective transformation, we use continuously-indexed flows (CIFs) [7], akin to an infinite mixture of normalizing flows. While CIFs potentially avoid the topology constraint, CIFs still enable analytical density computation with a little
+
+looseness  $\mathcal{E}$  because CIFs incorporate inference and generative surjections according to the survey [44]. We investigated the tradeoff between the expressive power and exactness of estimated density on CIFs. We concluded this looseness of estimated density can be ignored in trajectory prediction, as we show in the supplemental materials. Based on the above discussion, We use conditional CIFs as the base normalizing flow model of our FlowChain.
+
+# 3.3. FlowChain model
+
+The overview of the FlowChain model is shown in Fig. 2. Given the current time step  $t$ , we estimate future trajectory densities  $\{p(\tilde{\mathbf{x}}_{t + 1}|\mathbf{o}_t),\dots ,p(\tilde{\mathbf{x}}_{t + T_{\mathrm{f}}}|\mathbf{o}_t)\}$  by chaining the conditional CIFs, each of which transforms the density of the former time step  $p(\tilde{\mathbf{x}}_{t + n - 1}|\mathbf{o}_t)$  to the density of the next time step  $p(\tilde{\mathbf{x}}_{t + n}|\mathbf{o}_t)$ , shown in the upper side of Fig. 2. Our formulation consists of two equations: the initial condition for the first step prediction (Eq.(4)) and the recurrence relation between the latter steps (Eq.(5)) as follows.
+
+$$
+\begin{array}{l} p \left(\tilde {\mathbf {x}} _ {t + 1} \mid \mathbf {o} _ {t}\right) = \mathcal {N} (\mathbf {z}; \mathbf {x} _ {t}, \sigma) | \det  \nabla_ {\tilde {\mathbf {x}} _ {t + 1}} f _ {1} ^ {- 1} \left(\tilde {\mathbf {x}} _ {t + 1}, \mathbf {o} _ {t}\right) | (4) \\ p \left(\tilde {\mathbf {x}} _ {t + n} \mid \mathbf {o} _ {t}\right) = p \left(\tilde {\mathbf {x}} _ {t + n - 1} \mid \mathbf {o} _ {t}\right) | \det  \nabla_ {\tilde {\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \left(\tilde {\mathbf {x}} _ {t + n}, \mathbf {o} _ {t}\right) | (5) \\ = \exp \left(\log \mathcal {N} (\mathbf {z}; \mathbf {x} _ {t}, \sigma) \right. \\ \left. + \sum_ {n ^ {\prime} = 1} ^ {n} \log | \det  \nabla_ {\tilde {\mathbf {x}} _ {t + n ^ {\prime}}} f _ {n ^ {\prime}} ^ {- 1} \left(\tilde {\mathbf {x}} _ {t + n ^ {\prime}}, \mathbf {o} _ {t}\right) |\right) (6) \\ \end{array}
+$$
+
+where  $n \in \{2,3,\dots,T_{\mathrm{f}}\}$ .  $f_{n}$  is a conditional CIF that transforms the sample  $\tilde{\mathbf{x}}_{t + n - 1}$  from a former density  $p(\tilde{\mathbf{x}}_{t + n - 1}|\mathbf{o}_t)$  to the sample  $\tilde{\mathbf{x}}_{t + n}$  from a next density  $p(\tilde{\mathbf{x}}_{t + n}|\mathbf{o}_t)$  as  $\tilde{\mathbf{x}}_{t + n} = f_n(\tilde{\mathbf{x}}_{t + n - 1},\mathbf{o}_t)$ .  $f_{1}$  transforms the sample  $\mathbf{z}$  from a base Gaussian density  $\mathcal{N}(\cdot ;\mathbf{x}_t,\sigma)$ .  $\mathcal{N}(\cdot ;\mathbf{x}_t,\sigma)$  is created from the newest observed position  $\mathbf{x}_t$  as a mean position. The standard deviation  $\sigma$  is a trainable parameter of FlowChain model. All of  $f_{1}$  and  $f_{n}$  are independently trained with the loss function (Eq.(3)) in our method.
+
+From  $f_{n}$ , we can sample multiple trajectories for best-of-N metrics [25] by sampling multiple  $\mathbf{z}$  as follows:
+
+$$
+\{\tilde {\mathbf {x}} _ {t + 1}, \dots , \tilde {\mathbf {x}} _ {t + n} \} = \left\{f _ {1} (\mathbf {z}, \mathbf {o} _ {t}), \dots , f _ {n} \circ \dots \circ f _ {2} \circ f _ {1} (\mathbf {z}, \mathbf {o} _ {t}) \right\} \tag {7}
+$$
+
+# 3.4. Update of estimated density
+
+For accurate prediction by reusing the previous predictions, we focused on two features of the observed trajectory: the newest observed position and motion trend, shown in Fig. 2. Our FlowChain generates future trajectories by transforming the newest observed position  $\mathbf{x}_t$  based on the motion trend e.g. go straight or turning left/right, modeled
+
+![](images/bbb7e99b80d26d3aae1e45a2e55c9596c832c06ab6fc2acebc38dd25d322e822.jpg)  
+Figure 2. Overview of our FlowChain model. FlowChain consists of sequential conditional CIFs denoted by  $f_{n}$ .  $f_{n}$  is conditioned on the feature vector denoted by Motion Trend from the Temporal-Social Encoder, which encodes the observed trajectories  $\mathbf{o}_t$ . Since  $\mathbf{o}_t$  includes the trajectories of other agents as well as an agent of interest (i.e., the target of prediction), the future trajectory is predicted while taking into account social interaction with the others.  $f_{n}$  transforms the density of the former time step  $p(\tilde{\mathbf{x}}_{t + n - 1}|\mathbf{o}_t)$  to the density of the next time step  $p(\tilde{\mathbf{x}}_{t + n}|\mathbf{o}_t)$  as shown in the upper side. However, for the first step, the Gaussian distribution  $\mathcal{N}(\cdot ;\mathbf{x}_t,\sigma)$ , which is created from the newest observed position  $\mathbf{x}_t$ , is transformed. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively. In the update procedure shown on the bottom side, the Gaussian distribution  $\mathcal{N}(\cdot ;\mathbf{x}_{n + 1},\sigma)$ , created from newest observed position  $\mathbf{x}_{t + 1}$  at  $t + 1$ , replace the estimated density from the former time step. The other calculations are reused as shown by gray arrows. We can properly update the density by using the newest observed position at  $t + 1$ ,  $\mathbf{x}_{t + 1}$ , instead of  $p(\tilde{\mathbf{x}}_{t + 1}|\mathbf{o}_t)$ . In a toy example shown in this figure, another incorrect mode observed in the predicted densities,  $p(\tilde{\mathbf{x}}_{t + 2}|\mathbf{o}_t)$  and  $p(\tilde{\mathbf{x}}_{t + 3}|\mathbf{o}_t)$ , is successfully suppressed in the updated predictions  $p^{\prime}(\tilde{\mathbf{x}}_{t + 2}|\mathbf{o}_{t + 1})$  and  $p^{\prime}(\tilde{\mathbf{x}}_{t + 3}|\mathbf{o}_{t + 1})$ . As shown in Sec. 4, our experiments validate this advantage of our proposed fast update procedure is greater than its disadvantage (i.e., a decrease in the prediction accuracy due to the reuse of the motion trend) so that the updated predictions are better than the initial predictions (e.g.,  $p^{\prime}(\tilde{\mathbf{x}}_{t + 3}|\mathbf{o}_{t + 1})$  is better than  $p(\tilde{\mathbf{x}}_{t + 3}|\mathbf{o}_t)$  in the figure).
+
+by each flow  $f_{n}(\mathbf{x}_{t + n},\mathbf{o}_{t})$ . We cannot reuse the newest observed position  $\mathbf{x}_t$  at  $t$  for the next time step because this position is a starting point of the future trajectories and thus greatly affect the accuracy of probability density estimation. Therefore, FlowChain adopt the newest observed position  $\mathbf{x}_{t + n}$  at  $t + n$  by replacing the estimated density  $p(\tilde{\mathbf{x}}_{t + n}|\mathbf{o}_t)$  with the Gaussian density  $\mathcal{N}(\cdot ;\mathbf{x}_{t + n},\sigma)$ , as shown in the bottom of Fig. 2. This replacement propagates the information of the newest observed position properly to the latter time steps.
+
+On the other hand, the motion trend can be reused because it doesn't change for several time steps unless a sudden strong external force is applied to a prediction target. Therefore, our FlowChain model reuses its trend in each flow transformation  $f_{n}(\tilde{\mathbf{x}}_{t + n},\mathbf{o}_{t})$ . Specifically, we use the previously generated trajectories  $\{\tilde{\mathbf{x}}_{t + 1},\dots ,\tilde{\mathbf{x}}_{t + n}\}$ . Thus, we can reuse the corresponding log-det-jacobians  $\log |\operatorname *{det}\nabla_{\tilde{\mathbf{x}}_{t + n}}f_n^{-1}(\tilde{\mathbf{x}}_{t + n + 1},\mathbf{o}_t)|$  which is the variation of the estimated densities, as shown by the gray arrows in Fig. 2. The equation of FlowChain's update is expressed
+
+similar to Eq.(4) and Eq.(5) as follows:
+
+$$
+p ^ {\prime} \left(\tilde {\mathbf {x}} _ {t + 2} \mid \mathbf {o} _ {t + 1}\right) = \mathcal {N} \left(\tilde {\mathbf {x}} _ {t + 1}; \mathbf {x} _ {t + 1}, \sigma\right) | \det  \nabla_ {\tilde {\mathbf {x}} _ {t + 2}} f _ {2} ^ {- 1} \left(\tilde {\mathbf {x}} _ {t + 2}, \mathbf {o} _ {t}\right) | \tag {8}
+$$
+
+$$
+\begin{array}{l} p ^ {\prime} \left(\tilde {\mathbf {x}} _ {t + n} \mid \mathbf {o} _ {t + 1}\right) = p ^ {\prime} \left(\tilde {\mathbf {x}} _ {t + n - 1} \mid \mathbf {o} _ {t + 1}\right) | \det  \nabla_ {\tilde {\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \left(\tilde {\mathbf {x}} _ {t + n}\right) | (9) \\ = \exp \left(\log \mathcal {N} (\tilde {\mathbf {x}} _ {t + 1}; \mathbf {x} _ {t + 1}, \sigma) \right. \\ \left. + \sum_ {n ^ {\prime} = 2} ^ {n} \log | \det  \nabla_ {\tilde {\mathbf {x}} _ {t + n ^ {\prime}}} f _ {n ^ {\prime}} ^ {- 1} \left(\tilde {\mathbf {x}} _ {t + n ^ {\prime}}, \mathbf {o} _ {t}\right) |\right) (10) \\ \end{array}
+$$
+
+where,  $n \in \{3, 4, \ldots, T_{\mathrm{f}}\}$ . Thanks to reusing each flow transformation  $f_{n}(\mathbf{x}_{t + n}, \mathbf{o}_{t})$ , we don't need to evaluate log-det-jacobians  $\log |\operatorname*{det}\nabla_{\tilde{\mathbf{x}}_{t + n}}f_n^{-1}(\tilde{\mathbf{x}}_{t + n})|$  again. This will greatly omit the computational cost. As a result, we can update the probability density by only calculating the Gaussian base distribution, summing up the log-det-jacobians, and taking exponentials, which take less than  $1ms$  in total. This rapid update is beneficial, especially for autonomous
+
+![](images/52ac5db57636058d0d1358939e84c2ce76c08ffe6801a183030550912d708e22.jpg)  
+Trajectories  
+Time steps  
+Figure 3. Overview of Simfork dataset. The trajectories shown in the left figure are examples of the observed and ground truth trajectories for training. The position of each step is sampled from the distributions of the middle figures. The sum of each distribution is shown in the right figure. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively.
+
+![](images/49a2a5f9a20d09fb5532c5217e056cf0bdd0a2dd983c76ad9ea17624e40d3e02.jpg)
+
+![](images/272646ed6adfb81e2ef5a3be6a67db80d94dd65d0b015974e7b254183515b3f3.jpg)
+
+systems where computational resources are limited and often become busy by executing other computationally-intense tasks such as object detection, mapping, and path planning.
+
+# 3.5. How to obtain the density map
+
+The density map, not like the mere one-point estimate, is needed when autonomous systems perform visualization of density or successive tasks such as navigation. We can correct the possible future points with estimated density by sampling multiple trajectories from Eq.(7) and its density from Eq.(6). The density map is obtained by collecting these points with density at the same time step.
+
+# 4. Experiments and Results Analysis
+
+# 4.1. Experimental Setup
+
+Datasets. Experiments were conducted on various datasets including our developed dataset with synthesized data Simfork, and real-image benchmarks including ETH/UCY [37, 50] and SDD [53]. On all the datasets, the numbers of past observed and future predicted steps are  $T_{o} = 8$  and  $T_{f} = 12$ , respectively. All steps have an interval of 0.4 seconds in accordance with the literature such as [25, 58].
+
+Simfork is a synthesized dataset for comparison on the accuracy of predicted densities, which are produced as explained in Sec. 3.5. In all trajectories in this dataset, either of the two types of traveling directions (i.e., turning left or right) is observed after a straight trajectory, as shown in Fig. 3. Positions before and after the fork (colored by green and black, respectively, in the leftmost figure of Fig. 3) are used as past observed and future ground-truth positions, respectively. Each position of a trajectory is independently perturbed by the Gaussian noise, which results in the density at each time step.
+
+Two pedestrian trajectory datasets, ETH [50] and UCY [37], are merged to ETH/UCY. This dataset has five scenes: ETH, HOTEL, UNIV, ZARA1, and ZARA2. For training and testing, we follow the standard leave-one-out
+
+approach, where we train on 4 scenes and test on the remaining one. We follow the train-validation-test split of Social-GAN [25].
+
+$SDD$  consists of 20 scenes captured in bird's eye view using aerial drones. This dataset contains various moving agents such as pedestrians, bicycles, and cars, but we focus on pedestrians for comparison, as with Trajnet [56]. We also follow the train-test split of Trajnet [56].
+
+Metrics Evaluation of accuracy on trajectory prediction is done with the widely-used metrics, Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE is the average L2 distance between the predicted and ground truth trajectories over time. FDE is the L2 distance between the endpoints of the predicted and ground truth trajectories. We follow the Best-of-N procedure [25] with  $N = 20$ .
+
+For evaluation of the accuracy of density estimation, we use earth mover's distance (EMD) and log-probability. EMD is a measure of the distance between two densities by the minimum cost to move one density pile to the other. EMD is calculated between the estimated density and ground truth density on each prediction step. Thus, we use EMD on Simfork dataset, where the ground truth densities are available. The advantage of EMD over the widely-used KL divergence is that EMD works properly even if the two density is disjoint while KL divergence returns a constant value. We use log-probability on the pedestrian trajectory prediction datasets, where the ground truth density is unavailable. The log-probability is calculated on the ground truth trajectory instead of density.
+
+Implementation Details. Each conditional CIFs in our FlowChain used three-layer RealNVP [14] with multilayer perceptions (MLPs) of three hidden layers and 128 hidden units. All the conditional CIFs are with independent weights conditioned on the feature vectors from Trajectory++ [58] encoder as the temporal-social encoder. We used a batch size of 128 and ADAM optimizer [30] with a learning rate of  $10^{-4}$ . All experiments were conducted on a single NVIDIA A100 GPU. We use a KDE implementation utilizing GPU as mentioned in Sec. 2.
+
+Table 1. Quantitative results of trajectory prediction on ETH/UCY dataset with Best-of-20 metrics. T + I denotes its method takes a trajectory and an image as inputs while T denotes its method takes only a trajectory. Scores are in meters. Red and blue scores denote the best and the second-best in methods with T. Lower is better. The results of Trajectron++ [58] and MID [24] are updated according to an implementation issue #53 on the Trajectron++ GitHub page.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Input</td><td colspan="2">ETH</td><td colspan="2">HOTEL</td><td colspan="2">UNIV</td><td colspan="2">ZARA1</td><td colspan="2">ZARA2</td><td colspan="2">Mean</td></tr><tr><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>0.70</td><td>1.43</td><td>0.76</td><td>1.67</td><td>0.54</td><td>1.24</td><td>0.30</td><td>0.63</td><td>0.38</td><td>0.78</td><td>0.54</td><td>1.15</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>0.59</td><td>1.18</td><td>0.19</td><td>0.35</td><td>0.60</td><td>1.19</td><td>0.43</td><td>0.87</td><td>0.32</td><td>0.65</td><td>0.43</td><td>0.85</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>0.47</td><td>0.91</td><td>0.14</td><td>0.24</td><td>0.54</td><td>1.07</td><td>0.36</td><td>0.73</td><td>0.29</td><td>0.60</td><td>0.36</td><td>0.71</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>1.09</td><td>2.35</td><td>0.79</td><td>1.76</td><td>0.67</td><td>1.40</td><td>0.47</td><td>1.00</td><td>0.56</td><td>1.17</td><td>0.72</td><td>1.54</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>0.87</td><td>1.62</td><td>0.67</td><td>1.37</td><td>0.76</td><td>1.52</td><td>0.35</td><td>0.68</td><td>0.42</td><td>0.84</td><td>0.61</td><td>1.21</td></tr><tr><td>STGAT [29]</td><td>T</td><td>0.65</td><td>1.12</td><td>0.35</td><td>0.66</td><td>0.52</td><td>1.10</td><td>0.34</td><td>0.69</td><td>0.29</td><td>0.60</td><td>0.43</td><td>0.83</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>0.64</td><td>1.11</td><td>0.49</td><td>0.85</td><td>0.44</td><td>0.79</td><td>0.34</td><td>0.53</td><td>0.30</td><td>0.48</td><td>0.44</td><td>0.75</td></tr><tr><td>PECNet [41]</td><td>T</td><td>0.61</td><td>1.07</td><td>0.22</td><td>0.39</td><td>0.34</td><td>0.56</td><td>0.25</td><td>0.45</td><td>0.19</td><td>0.33</td><td>0.32</td><td>0.56</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>0.61</td><td>1.03</td><td>0.20</td><td>0.28</td><td>0.30</td><td>0.55</td><td>0.24</td><td>0.41</td><td>0.18</td><td>0.32</td><td>0.31</td><td>0.52</td></tr><tr><td>MID [24]</td><td>T</td><td>0.55</td><td>0.88</td><td>0.20</td><td>0.35</td><td>0.30</td><td>0.55</td><td>0.29</td><td>0.51</td><td>0.20</td><td>0.38</td><td>0.31</td><td>0.53</td></tr><tr><td>Social Implicit [43]</td><td>T</td><td>0.66</td><td>1.44</td><td>0.20</td><td>0.36</td><td>0.31</td><td>0.60</td><td>0.25</td><td>0.50</td><td>0.22</td><td>0.43</td><td>0.33</td><td>0.67</td></tr><tr><td>FlowChain(Ours)</td><td>T</td><td>0.55</td><td>0.99</td><td>0.20</td><td>0.35</td><td>0.29</td><td>0.54</td><td>0.22</td><td>0.40</td><td>0.20</td><td>0.34</td><td>0.29</td><td>0.52</td></tr></table>
+
+Table 2. Quantitative results of trajectory prediction on SDD dataset with Best-of-20 metrics. Scores are in pixels. See the caption of Tab. 1 also for details.  
+
+<table><tr><td>Method</td><td>Input</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>16.27</td><td>29.38</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>12.20</td><td>22.10</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>13.60</td><td>25.80</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>31.19</td><td>56.97</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>27.25</td><td>41.44</td></tr><tr><td>STGAT [29]</td><td>T</td><td>14.85</td><td>28.17</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>20.76</td><td>33.18</td></tr><tr><td>PECNet [41]</td><td>T</td><td>9.97</td><td>15.89</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>11.40</td><td>20.12</td></tr><tr><td>MID [24]</td><td>T</td><td>10.31</td><td>17.37</td></tr><tr><td>FlowChain (Ours)</td><td>T</td><td>9.93</td><td>17.17</td></tr></table>
+
+# 4.2. Prediction Accuracy
+
+A wide range of previous trajectory prediction methods is quantitatively compared with our FlowChain on ETH/UCY and SDD datasets, shown in Tab. 1 and Tab. 2. We didn't include some methods [40, 63, 70-72] due to a different train-validation-test split.
+
+For ETH/UCY dataset, FlowChain achieved mean ADE/FDE of 0.29/0.52 in meters, which are the best among all trajectory prediction methods. On SDD dataset, FlowChain achieved average ADE/FDE of 9.93/17.17 in pixels, which are the best and second-best among all methods taking only trajectories as inputs [1,24,25,41,58,63].
+
+Although our focus is on density estimation with a minimal computational cost, FlowChain is comparable with the state-of-the-art methods also in terms of errors. We didn't evaluate the accuracy of future trajectories from FlowChain's update because the trajectories do not change
+
+![](images/f530bdaa1cf5a2d18a228a98f412c3ee79b75f5eabac471307052eeca901d5f5.jpg)  
+Figure 4. Temporal estimated densities on Simfork dataset.
+
+in the update as mentioned in Sec. 3.4.
+
+# 4.3. Analysis on Density Estimation
+
+The results of density estimation are compared between FlowChain and previous methods based on VAE, GAN, and diffusion approaches. Trajectory++ is the representative VAE-based trajectory prediction model with density estimation by GMM. Social-GAN is a minimal model of GAN-based trajectory prediction. MID is the diffusion-based trajectory prediction model with state-of-the-art prediction accuracy. We applied KDE to Social-GAN and MID since
+
+![](images/839b4e1985cd61c6514f7c80757822fc96ed14f964bc3cbf215c9e00143da48b.jpg)  
+Figure 5. Temporal estimated densities on ETH/UCY dataset.
+
+they cannot estimate the density alone. For a fair comparison, FlowChain, Social-GAN, and MID generated the same number of samples for future trajectories;  $10^{5}$  samples.
+
+We evaluated the computational time and the accuracy of density estimation of each method, as shown in Tab. 3. Social-GAN and MID take much longer time because KDE is slow in spite of running on GPU. Trajectory++ is a bit faster than our FlowChain due to its simple Gaussian mixture model but suffers from the poor quality of estimated density, as shown by the worst EMD, 2.545, on Simfork dataset and worst log-probability, -281.86, on ETH/UCY dataset. On the other hand, our FlowChain achieved the best EMD, 1.408, and the best log-probability, -0.26, in spite of the fast computation 37.0ms. Thus, our method successfully addresses both the computational cost and accurate density estimation.
+
+The estimated densities on Simfork are visualized in Fig. 4. The densities estimated by Trajectory++ are too large compared to the ground truth densities. While the densities of Social-GAN and MID are stretched to the vertical axis, our FlowChain successfully estimated the tighter round-shape densities closest to the ground truth densities.
+
+The estimated densities on  $ETH/UCY$  are shown in Fig. 5. The size of each density represents the positional uncertainty of a predicted position. As within Simfork, in  $ETH/UCY$ , an agent cannot change its traveling direction significantly in a short period (i.e.,  $T_{f} = 12$  is  $0.4 \times 12 = 4.8$  seconds), the size of the density expected to be tight. The densities estimated by Social-GAN are tight but deviated from the ground truth trajectory. Trajectory++ generated the densities with several disconnected modes due to the approximation as a Gaussian mixture. While the densi
+
+![](images/ba883f7cf9f760f6123000d999e38e9eeed29de25e15f81a06112c1804114af8.jpg)  
+Figure 6. Temporal densities estimated by our update procedure on Simfork dataset.
+
+![](images/14a0b33d57f3e80ef5505842a4b22a14ade06801bc05c2e66f6bfbaf37b077b4.jpg)  
+Figure 7. Temporal densities estimated by our update procedure on ETH/UCY dataset.
+
+ties from MID are close to the ground truth trajectory, MID could not suggest tight densities and their modes deviated from the ground truth trajectories. On the contrary, the density from our FlowChain covers the ground truth trajectory with tight distributions. thanks to the explicit density estimation of conditional CIFs and our expressive model architecture. We should note that the estimated density of FlowChain has some fluctuation due to the looseness of the density computation of CIFs. However, we did not observe any potential problem or failure of density estimation related to this in our experiments.
+
+# 4.4. Proposed Update of Density Estimation
+
+As shown in Tab. 3, the accuracy of density estimation degraded along with the number of updates. However, this update is remarkably fast  $0.6ms$ , also shown in Tab. 3. Thus, autonomous systems can select the accurate prediction from scratch or the super rapid update by reusing predictions depending on the utilization of their computational resources.
+
+The estimated densities of our update procedure are shown in Fig. 6 and Fig. 7, which show the densities up
+
+Table 3. Accuracy and computational time of density estimation. Scores are in milliseconds for computational time. While lower is better for EMD on Simfork dataset, higher is better for log-probability on ETH/UCY dataset. We report the averaged EMD and log-probability over the 12 prediction steps.  
+
+<table><tr><td rowspan="2">Method</td><td></td><td colspan="2">Comp. Time</td><td colspan="2">Accuracy of Density Estimation</td></tr><tr><td></td><td>All</td><td>w/o KDE</td><td>EMD ↓</td><td>log-probability ↑</td></tr><tr><td>Social-GAN [25]</td><td></td><td>11498.8</td><td>9.8</td><td>1.544</td><td>-3.40</td></tr><tr><td>Trajectory++ [58]</td><td></td><td>33.7</td><td>-</td><td>2.545</td><td>-281.86</td></tr><tr><td>MID [24]</td><td></td><td>23904.1</td><td>12219.1</td><td>2.135</td><td>-0.90</td></tr><tr><td rowspan="3">FlowChain (Ours)</td><td>Pred at t</td><td>37.0</td><td>-</td><td>1.408</td><td>-0.26</td></tr><tr><td>Update from t - 1</td><td>0.6</td><td>-</td><td>2.539</td><td>-0.45</td></tr><tr><td>Update from t - 5</td><td>0.5</td><td>-</td><td>2.899</td><td>-0.53</td></tr></table>
+
+Table 4. Accuracy of density estimation with the update.  
+
+<table><tr><td rowspan="2" colspan="2">Method</td><td colspan="8">log-probability on each step</td></tr><tr><td>t+6</td><td>t+7</td><td>t+8</td><td>t+9</td><td>t+10</td><td>t+11</td><td>t+12</td><td>mean</td></tr><tr><td colspan="2">Social-GAN [25]</td><td>-2.65</td><td>-2.86</td><td>-3.07</td><td>-3.26</td><td>-3.44</td><td>-3.62</td><td>-3.80</td><td>-3.24</td></tr><tr><td colspan="2">Trajectory++ [58]</td><td>-121.19</td><td>-93.61</td><td>-71.62</td><td>-51.36</td><td>-36.85</td><td>-27.92</td><td>-22.72</td><td>-97.79</td></tr><tr><td colspan="2">MID [24]</td><td>-1.06</td><td>-1.43</td><td>-1.75</td><td>-2.02</td><td>-2.26</td><td>-2.46</td><td>-2.65</td><td>-1.95</td></tr><tr><td rowspan="2">FlowChain</td><td>Without Update</td><td>0.21</td><td>0.36</td><td>0.44</td><td>-0.08</td><td>-0.78</td><td>-0.75</td><td>-1.19</td><td>-0.26</td></tr><tr><td>With Update</td><td>0.20</td><td>0.50</td><td>0.39</td><td>0.44</td><td>0.20</td><td>0.26</td><td>0.16</td><td>0.31</td></tr></table>
+
+![](images/0a76851cb4fc158b0af1c58891e65eb3faa4e67d0e242ea4c520878e06ff7c78.jpg)  
+Figure 8. Comparison of standard methods and FlowChain with updates.
+
+dated at  $t + 1$  and  $t + 2$  from the prediction at  $t$ . On Simfork dataset, the wrong mode is successfully suppressed by exploiting the information of the new observation. On ETH/UCY dataset, the initial prediction deviated from the ground truth because the observed trajectory observed until  $t$  does not have the information on turning left. However, the updated densities covered the ground truth well by adopting the newest observed position despite the minimal computational cost.
+
+We further perform a comparison with a practical setting. Models usually make predictions with intervals due to the large computational cost. Therefore, we usually cannot obtain the prediction from the latest observation, as shown by the upper side of Fig. 8. For example, assume we need the density of six time-step ahead such as  $p_{t+6}$  from  $\mathbf{x}_t$ , we cannot obtain  $p_{t+7}$  from  $\mathbf{x}_{t+1}$  or  $p_{t+8}$  from  $\mathbf{x}_{t+2}$  due to the
+
+computational overhead. However, with FlowChain's rapid update, we can obtain the update  $(p_{t + 7}, p_{t + 8})$  from the latest observation  $(\mathbf{x}_{t + 1}, \mathbf{x}_{t + 2})$  on every time step thanks to the minimal computational cost, as shown by the bottom side of Fig. 8. We conducted the comparison with the frame of interest as six time-step ahead  $t + 6$  and the log-probability metric. As shown by Tab. 4, our FlowChain with update achieves the highest log-probability. Therefore, we can conclude that FlowChain's update can improve the density estimation with minimal computational cost.
+
+# 5. Concluding Remarks
+
+In this paper, we proposed a new normalizing flow-based trajectory prediction network named FlowChain that achieves fast and accurate probability density estimation. Furthermore, our update procedure reliably generates the density estimation of the next step based on the density estimation of the previous step in an instant. Experimental results demonstrated that FlowChain achieved comparable accuracy to the state-of-the-art trajectory prediction models and superiority in the accuracy of density estimation.
+
+Our FlowChain has one limitation. Our update procedure can reliably estimate the density for several steps but the performance will degrade along with the time steps because the reused flow transformations do not reflect the new observations. Our future work is determining when should we stop to use the update procedure and make predictions from scratch. Furthermore, FlowChain is the domain-agnostic model that can be applied to a wide range of prediction tasks such as stock price prediction, human motion prediction, and video prediction. We will investigate the applicability of our FlowChain on these other domains.
+
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+[57] Amir Sadeghian, Vineet Kosaraju, Ali Sadeghian, Noriaki Hirose, Hamid Rezatofighi, and Silvio Savarese. Sophie: An attentive gan for predicting paths compliant to social and physical constraints. In CVPR, pages 1349-1358, 2019.  
+[58] Tim Salzmann, Boris Ivanovic, Punarjay Chakravarty, and Marco Pavone. Trajectory++: Dynamically-feasible trajectory forecasting with heterogeneous data. In ECCV, pages 683-700, 2020.  
+[59] Christoph Schöller and Alois Knoll. Flomo: Tractable motion prediction with normalizing flows. In IROS, pages 7977-7984, 2021.  
+[60] David W Scott. Averaged shifted histograms: effective nonparametric density estimators in several dimensions. The Annals of Statistics, pages 1024-1040, 1985.  
+[61] Burkhardt Seifert, Michael Brockmann, Joachim Engel, and Theo Gasser. Fast algorithms for nonparametric curve estimation. Journal of Computational and Graphical Statistics, 3(2):192-213, 1994.  
+[62] Bernhard W Silverman. Algorithm as 176: Kernel density estimation using the fast fourier transform. Journal of the Royal Statistical Society. Series C (Applied Statistics), 31(1):93-99, 1982.  
+[63] Jianhua Sun, Yuxuan Li, Hao-Shu Fang, and Cewu Lu. Three steps to multimodal trajectory prediction: Modality clustering, classification and synthesis. In ICCV, pages 13250-13259, 2021.  
+[64] Esteban G Tabak and Cristina V Turner. A family of nonparametric density estimation algorithms. Communications on Pure and Applied Mathematics, 66(2):145-164, 2013.  
+[65] Esteban G Tabak and Eric Vanden-Eijnden. Density estimation by dual ascent of the log-likelihood. Communications in Mathematical Sciences, 8(1):217-233, 2010.  
+[66] Anirudh Vemula, Katharina Muelling, and Jean Oh. Social attention: Modeling attention in human crowds. In ICRA, pages 4601-4607, 2018.
+
+[67] MP Wand. Fast computation of multivariate kernel estimators. Journal of Computational and Graphical Statistics, 3(4):433-445, 1994.  
+[68] Hao Wu, Jonas Kohler, and Frank Noé. Stochastic normalizing flows. NeurIPS, 33:5933-5944, 2020.  
+[69] Pengxiang Wu, Siheng Chen, and Dimitris N Metaxas. Motionnet: Joint perception and motion prediction for autonomous driving based on bird's eye view maps. In CVPR, pages 11385-11395, 2020.  
+[70] Cunjun Yu, Xiao Ma, Jiawei Ren, Haiyu Zhao, and Shuai Yi. Spatio-temporal graph transformer networks for pedestrian trajectory prediction. In ECCV, 2020.  
+[71] Ye Yuan, Xinshuo Weng, Yanglan Ou, and Kris M Kitani. Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting. In ICCV, pages 9813-9823, 2021.  
+[72] Jiangbei Yue, Dinesh Manocha, and He Wang. Human trajectory prediction via neural social physics. In ECCV, pages 376-394, 2022.  
+[73] He Zhao and Richard P Wildes. Where are you heading? dynamic trajectory prediction with expert goal examples. In ICCV, pages 7629-7638, 2021.
\ No newline at end of file
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+                                    "content": "Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023."
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+                                    "content": "can be applied to human-interactive systems, including autonomous vehicles [8,11,38,55,69] and social robots [4,39]."
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+                                    "type": "text",
+                                    "content": "tecture unlike Flomo [59], which is closest to FlowChain. While Flomo uses one flow module that only estimates the spatial density of a trajectory, FlowChain further predicts its spatio-temporal density so that the spatial density of an agent position at each time step is also predicted. This stacking architecture also allows a rapid update of an estimated density in an instant of time e.g. less than one millisecond. This update is achieved by reusing the flow transformations and its log-det-jacobians that represent the motion trend such as going straight or turning right. This update with the reuse significantly omits the computational cost while maintaining the accuracy of density estimation because the motion trend doesn't change for several time steps."
+                                }
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+                                    "content": "Our contributions are three-fold as follows:"
+                                }
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+                },
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- We propose a normalizing flow-based trajectory prediction network named FlowChain that rapidly estimates the accurate density of future positions on each prediction time step."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Our update procedure for the density requires less than one millisecond by adopting new observations and reusing the motion trend as the flow transformations."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
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+                                            "type": "text",
+                                            "content": "- Our FlowChain achieved comparable prediction accuracy to other computationally-intense state-of-the-art methods on several benchmarks."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
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+                                    "content": "2. Related Work"
+                                }
+                            ]
+                        }
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Human Trajectory Prediction. The earliest works on human trajectory prediction [26, 49] are deterministic regression models using attractive and repulsive forces between humans and goal positions. However, human movements are indeterministic in nature. Therefore, many approaches are proposed to model this uncertainty. Social-LSTM [1] and Social-STGCNN [42] regress the parameters of the bivariate Gaussian distributions to model the uncertainty of future trajectories. These approaches [1, 42] are simple and require low computational cost but cannot catch the future multi-modality we often see at road intersections."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "To address this multi-modality, many stochastic prediction models are proposed. Trajectory++ [58], AgentFormer [71], and ExpertTraj [73] combined the aforementioned Gaussian regression with VAE [32]. These models predict a bivariate Gaussian mixture based on stochastically sampled latent variables [28, 52]. We can obtain the density by summing up each estimated Gaussian density map. However, these Gaussian mixture methods have limited expressive power and thus predict inaccurate distributions."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "On the other hand, GAN [18]-based approaches implicitly handle this uncertainty. Social-GAN [25], SoPhie [57], Goal-GAN [10], and MG-GAN [9] use a GAN architecture to predict diverse trajectories conditioned on random"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "noises. While they cannot estimate the density alone, we can estimate the density by applying KDE [48, 54] on sampled trajectories"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The denoising diffusion probabilistic model [27] can also implicitly handle uncertainty by generating multiple trajectories. Recently, denoising diffusion attracts much attention for its state-of-the-art performances in several generative tasks, including image synthesis [12] and audio generation [33]. MID [24] is a trajectory prediction model incorporating denoising diffusion, which achieves state-of-the-art performances. We can also estimate the density of MID by applying KDE. However, GAN-based and diffusion-based approaches cannot estimate accurate densities because KDE is performed on limited samples."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "On the contrary, normalizing flow [51, 64, 65]-based trajectory prediction method named Flomo [59] can rapidly generate future trajectories and their accurate probabilities thanks to the analytical computation of normalizing flows. However, this approach only estimates the probability of each future trajectory and thus cannot estimate the density of positions on each prediction step alone."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Normalizing Flows. Thanks to its bijective process, normalizing flow can compute the density analytically. This analytical computation allows us fast and accurate density estimation because it does not need additional approximation such as KDE with limited samples. For more expressive power, several bijective families were proposed such as affine coupling layers [13, 14], autoregressive maps [17, 47], invertible linear transformations [31], and invertible ResNet block [2, 6]. All flows mentioned above have a topology constraint between the base and estimated densities. This topology constraint limits the expressive power of normalizing flows. To address this constraint, some approaches incorporated stochasticity into flows [68]. However, this stochasticity makes analytical density calculation impossible. Therefore, further density approximation such as KDE is required for this stochastic normalizing flow. Other approaches [5, 7, 44] use surjective layers, which relax the topology constraint but make analytical density computation with a little looseness. In summary, the optimal normalizing flow model architecture for future trajectory density estimation is still unknown."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Density Estimation. Kernel density estimation [48, 54] is the most representative non-parametric method that estimates a continuous density from a finite set of data. Suppose that we have "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " input data and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
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+                                    ],
+                                    "type": "text",
+                                    "content": " points evaluated, the computational cost is "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        545,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(AB)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This is a huge cost for autonomous systems. Therefore, several accelerations are proposed such as data binning [19, 60, 62, 67], fast sum updating [15, 16, 35, 61], fast Gauss transform [22, 23, 34], and dual-tree method [20, 21, 36]. However, we confirmed that the KDE implementation utilizing GPU is faster than these accelerations including [3, 45, 46]. We use the KDE utilizing"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                }
+            ],
+            "discarded_blocks": [
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+                                    "content": "9796"
+                                }
+                            ]
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+                    ],
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+                }
+            ],
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+            "page_idx": 1
+        },
+        {
+            "para_blocks": [
+                {
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+                    ],
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+                                    ],
+                                    "type": "text",
+                                    "content": "GPU for comparison in Sec. 4."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    ],
+                                    "type": "text",
+                                    "content": "3. Proposed Approach"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                        212
+                                    ],
+                                    "type": "text",
+                                    "content": "In this section, we present our normalizing flow-based trajectory prediction named FlowChain and its update of estimated density. First, we formulate the trajectory prediction task and conditional CIFs in Sec. 3.1. and Sec. 3.2 respectively. Then, we present our FlowChain model architecture in Sec. 3.3. After that, we describe its fast update procedure of estimated density in Sec.3.4. Finally, we explain how to obtain the density map in Sec. 3.5."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        47,
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+                        229
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        47,
+                                        218,
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+                                        229
+                                    ],
+                                    "type": "text",
+                                    "content": "3.1. Problem Formulation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": "We aim to estimate agents' plausible future trajectory densities from their past trajectories. The trajectory of each agent is defined as a sequence "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathbf{x}_0, \\mathbf{x}_1, \\ldots, \\mathbf{x}_T)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " of positions "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t = (x_t, y_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " over discrete timesteps "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t \\in \\{0, \\ldots, T\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": ". Given the current time step "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": ", we predict future "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{\\mathrm{f}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": "-step trajectory densities "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{p(\\tilde{\\mathbf{x}}_{t+1}^i | \\mathbf{o}_t), \\ldots, p(\\tilde{\\mathbf{x}}_{t+T_{\\mathrm{f}}}^i | \\mathbf{o}_t)\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " given "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{\\mathrm{o}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": "-step observed trajectory "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{o}_t = \\{(x_{t-T_{\\mathrm{o}}}^i - 1, \\ldots, x_t^i) | i \\in \\{1, 2, \\ldots, N_a\\}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the number of agents and the index of each agent, respectively. This index will be omitted for brevity in later use. We denote "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " as an observed position, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathbf{x}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " as a predicted future position, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{x}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        236,
+                                        288,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": " as a ground truth future position."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
+                        388,
+                        257,
+                        401
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        257,
+                                        401
+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Conditional Continuously-indexed Flow"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Conditional normalizing flow is a density estimation method that uses a parameterized bijective transformation "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " conditioned on additional information "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " such as an encoded vector from observed trajectories, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{o}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": ", for trajectory prediction. The bijection "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " transforms a base density "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\mathbf{z})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " to an expressive density "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\mathbf{y})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        287,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " by the analytical computation of the change-of-variables formula as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {y} = f (\\mathbf {z}) \\tag {1}",
+                                    "image_path": "ef194d8025c0457382d30b39a181edfbb6c56fae13002d4a32f151011a98e873.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "bbox": [
+                                        105,
+                                        516,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "p (\\mathbf {y}) = p (\\mathbf {z}) \\left| \\det  \\nabla_ {\\mathbf {y}} f ^ {- 1} (\\mathbf {y}, \\mathbf {c}) \\right| \\tag {2}",
+                                    "image_path": "0dddf86761fc6550a80c7a14dfaef3f3e54454655332f68575fb8573449d1813.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        538,
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+                                    ],
+                                    "type": "text",
+                                    "content": "The parameters of bijective transformation "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        538,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        538,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " can be learned by maximizing the likelihood of samples "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        538,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{y}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        538,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " from datasets, or minimizing the negative log-likelihood as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        123,
+                        584,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        123,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "N L L = - \\log p (\\hat {\\mathbf {y}} | \\mathbf {c}) \\tag {3}",
+                                    "image_path": "5c8affb14a9d7aeab8782aa1c5cd560e892b093f1a1ddd1c3424dac984a8ce4b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "A normalizing flow with only bijective transformations has a constraint that the topology of a base density is preserved. For example, if the base density is a simple unimodal Gaussian distribution, the normalizing flow fails to fit a distinct multi-modal density. To avoid this problem of bijective transformation, we use continuously-indexed flows (CIFs) [7], akin to an infinite mixture of normalizing flows. While CIFs potentially avoid the topology constraint, CIFs still enable analytical density computation with a little"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
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+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": "looseness "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        168
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{E}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": " because CIFs incorporate inference and generative surjections according to the survey [44]. We investigated the tradeoff between the expressive power and exactness of estimated density on CIFs. We concluded this looseness of estimated density can be ignored in trajectory prediction, as we show in the supplemental materials. Based on the above discussion, We use conditional CIFs as the base normalizing flow model of our FlowChain."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        306,
+                        175,
+                        411,
+                        187
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. FlowChain model"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
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+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": "The overview of the FlowChain model is shown in Fig. 2. Given the current time step "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": ", we estimate future trajectory densities "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{p(\\tilde{\\mathbf{x}}_{t + 1}|\\mathbf{o}_t),\\dots ,p(\\tilde{\\mathbf{x}}_{t + T_{\\mathrm{f}}}|\\mathbf{o}_t)\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": " by chaining the conditional CIFs, each of which transforms the density of the former time step "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": " to the density of the next time step "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        194,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": ", shown in the upper side of Fig. 2. Our formulation consists of two equations: the initial condition for the first step prediction (Eq.(4)) and the recurrence relation between the latter steps (Eq.(5)) as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
+                                        312,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} p \\left(\\tilde {\\mathbf {x}} _ {t + 1} \\mid \\mathbf {o} _ {t}\\right) = \\mathcal {N} (\\mathbf {z}; \\mathbf {x} _ {t}, \\sigma) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + 1}} f _ {1} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + 1}, \\mathbf {o} _ {t}\\right) | (4) \\\\ p \\left(\\tilde {\\mathbf {x}} _ {t + n} \\mid \\mathbf {o} _ {t}\\right) = p \\left(\\tilde {\\mathbf {x}} _ {t + n - 1} \\mid \\mathbf {o} _ {t}\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n}, \\mathbf {o} _ {t}\\right) | (5) \\\\ = \\exp \\left(\\log \\mathcal {N} (\\mathbf {z}; \\mathbf {x} _ {t}, \\sigma) \\right. \\\\ \\left. + \\sum_ {n ^ {\\prime} = 1} ^ {n} \\log | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}} f _ {n ^ {\\prime}} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}, \\mathbf {o} _ {t}\\right) |\\right) (6) \\\\ \\end{array}",
+                                    "image_path": "074805fcf994c4ddefffea771347d430e5fbdb3b9b2d9c281dd548678e1caa36.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n \\in \\{2,3,\\dots,T_{\\mathrm{f}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
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+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " is a conditional CIF that transforms the sample "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathbf{x}}_{t + n - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " from a former density "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " to the sample "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathbf{x}}_{t + n}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " from a next density "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathbf{x}}_{t + n} = f_n(\\tilde{\\mathbf{x}}_{t + n - 1},\\mathbf{o}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " transforms the sample "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " from a base Gaussian density "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " is created from the newest observed position "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " as a mean position. The standard deviation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " is a trainable parameter of FlowChain model. All of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        436,
+                                        545,
+                                        555
+                                    ],
+                                    "type": "text",
+                                    "content": " are independently trained with the loss function (Eq.(3)) in our method."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        304,
+                        555,
+                        545,
+                        579
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                555,
+                                545,
+                                579
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        555,
+                                        545,
+                                        579
+                                    ],
+                                    "type": "text",
+                                    "content": "From "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        555,
+                                        545,
+                                        579
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        555,
+                                        545,
+                                        579
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can sample multiple trajectories for best-of-N metrics [25] by sampling multiple "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        555,
+                                        545,
+                                        579
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        555,
+                                        545,
+                                        579
+                                    ],
+                                    "type": "text",
+                                    "content": " as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        306,
+                        589,
+                        557,
+                        613
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\{\\tilde {\\mathbf {x}} _ {t + 1}, \\dots , \\tilde {\\mathbf {x}} _ {t + n} \\} = \\left\\{f _ {1} (\\mathbf {z}, \\mathbf {o} _ {t}), \\dots , f _ {n} \\circ \\dots \\circ f _ {2} \\circ f _ {1} (\\mathbf {z}, \\mathbf {o} _ {t}) \\right\\} \\tag {7}",
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+                                    "type": "text",
+                                    "content": "3.4. Update of estimated density"
+                                }
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+                                    "type": "text",
+                                    "content": "For accurate prediction by reusing the previous predictions, we focused on two features of the observed trajectory: the newest observed position and motion trend, shown in Fig. 2. Our FlowChain generates future trajectories by transforming the newest observed position "
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+                                {
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+                                    "content": " based on the motion trend e.g. go straight or turning left/right, modeled"
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+                                            "type": "text",
+                                            "content": "Figure 2. Overview of our FlowChain model. FlowChain consists of sequential conditional CIFs denoted by "
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+                                            "type": "text",
+                                            "content": " is conditioned on the feature vector denoted by Motion Trend from the Temporal-Social Encoder, which encodes the observed trajectories "
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+                                            "content": ". Since "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " includes the trajectories of other agents as well as an agent of interest (i.e., the target of prediction), the future trajectory is predicted while taking into account social interaction with the others. "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " transforms the density of the former time step "
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p(\\tilde{\\mathbf{x}}_{t + n - 1}|\\mathbf{o}_t)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " to the density of the next time step "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "text",
+                                            "content": " as shown in the upper side. However, for the first step, the Gaussian distribution "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                548,
+                                                429
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{N}(\\cdot ;\\mathbf{x}_t,\\sigma)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": ", which is created from the newest observed position "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_t"
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ", is transformed. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively. In the update procedure shown on the bottom side, the Gaussian distribution "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{N}(\\cdot ;\\mathbf{x}_{n + 1},\\sigma)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": ", created from newest observed position "
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+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{t + 1}"
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+                                        {
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+                                            "type": "text",
+                                            "content": " at "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "t + 1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                284,
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+                                            ],
+                                            "type": "text",
+                                            "content": ", replace the estimated density from the former time step. The other calculations are reused as shown by gray arrows. We can properly update the density by using the newest observed position at "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": ", "
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{t + 1}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ", instead of "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p(\\tilde{\\mathbf{x}}_{t + 1}|\\mathbf{o}_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                284,
+                                                548,
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+                                            ],
+                                            "type": "text",
+                                            "content": ". In a toy example shown in this figure, another incorrect mode observed in the predicted densities, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                                429
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p(\\tilde{\\mathbf{x}}_{t + 2}|\\mathbf{o}_t)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_t)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ", is successfully suppressed in the updated predictions "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 2}|\\mathbf{o}_{t + 1})"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " and "
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_{t + 1})"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ". As shown in Sec. 4, our experiments validate this advantage of our proposed fast update procedure is greater than its disadvantage (i.e., a decrease in the prediction accuracy due to the reuse of the motion trend) so that the updated predictions are better than the initial predictions (e.g., "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p^{\\prime}(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_{t + 1})"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " is better than "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p(\\tilde{\\mathbf{x}}_{t + 3}|\\mathbf{o}_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "text",
+                                            "content": " in the figure)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
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+                        568
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "by each flow "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{n}(\\mathbf{x}_{t + n},\\mathbf{o}_{t})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We cannot reuse the newest observed position "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for the next time step because this position is a starting point of the future trajectories and thus greatly affect the accuracy of probability density estimation. Therefore, FlowChain adopt the newest observed position "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{t + n}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t + n"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " by replacing the estimated density "
+                                },
+                                {
+                                    "bbox": [
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+                                        289,
+                                        568
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\tilde{\\mathbf{x}}_{t + n}|\\mathbf{o}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        568
+                                    ],
+                                    "type": "text",
+                                    "content": " with the Gaussian density "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        568
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(\\cdot ;\\mathbf{x}_{t + n},\\sigma)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        568
+                                    ],
+                                    "type": "text",
+                                    "content": ", as shown in the bottom of Fig. 2. This replacement propagates the information of the newest observed position properly to the latter time steps."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "On the other hand, the motion trend can be reused because it doesn't change for several time steps unless a sudden strong external force is applied to a prediction target. Therefore, our FlowChain model reuses its trend in each flow transformation "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{n}(\\tilde{\\mathbf{x}}_{t + n},\\mathbf{o}_{t})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Specifically, we use the previously generated trajectories "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\tilde{\\mathbf{x}}_{t + 1},\\dots ,\\tilde{\\mathbf{x}}_{t + n}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Thus, we can reuse the corresponding log-det-jacobians "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        289,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\log |\\operatorname *{det}\\nabla_{\\tilde{\\mathbf{x}}_{t + n}}f_n^{-1}(\\tilde{\\mathbf{x}}_{t + n + 1},\\mathbf{o}_t)|"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        289,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " which is the variation of the estimated densities, as shown by the gray arrows in Fig. 2. The equation of FlowChain's update is expressed"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "similar to Eq.(4) and Eq.(5) as follows:"
+                                }
+                            ]
+                        }
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+                                    "content": "p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + 2} \\mid \\mathbf {o} _ {t + 1}\\right) = \\mathcal {N} \\left(\\tilde {\\mathbf {x}} _ {t + 1}; \\mathbf {x} _ {t + 1}, \\sigma\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + 2}} f _ {2} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + 2}, \\mathbf {o} _ {t}\\right) | \\tag {8}",
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + n} \\mid \\mathbf {o} _ {t + 1}\\right) = p ^ {\\prime} \\left(\\tilde {\\mathbf {x}} _ {t + n - 1} \\mid \\mathbf {o} _ {t + 1}\\right) | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n}} f _ {n} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n}\\right) | (9) \\\\ = \\exp \\left(\\log \\mathcal {N} (\\tilde {\\mathbf {x}} _ {t + 1}; \\mathbf {x} _ {t + 1}, \\sigma) \\right. \\\\ \\left. + \\sum_ {n ^ {\\prime} = 2} ^ {n} \\log | \\det  \\nabla_ {\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}} f _ {n ^ {\\prime}} ^ {- 1} \\left(\\tilde {\\mathbf {x}} _ {t + n ^ {\\prime}}, \\mathbf {o} _ {t}\\right) |\\right) (10) \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": "where, "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n \\in \\{3, 4, \\ldots, T_{\\mathrm{f}}\\}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Thanks to reusing each flow transformation "
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+                                {
+                                    "bbox": [
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+                                    "content": "f_{n}(\\mathbf{x}_{t + n}, \\mathbf{o}_{t})"
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+                                    "type": "text",
+                                    "content": ", we don't need to evaluate log-det-jacobians "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\log |\\operatorname*{det}\\nabla_{\\tilde{\\mathbf{x}}_{t + n}}f_n^{-1}(\\tilde{\\mathbf{x}}_{t + n})|"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " again. This will greatly omit the computational cost. As a result, we can update the probability density by only calculating the Gaussian base distribution, summing up the log-det-jacobians, and taking exponentials, which take less than "
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+                                    "type": "text",
+                                    "content": " in total. This rapid update is beneficial, especially for autonomous"
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+                                            "type": "text",
+                                            "content": "Figure 3. Overview of Simfork dataset. The trajectories shown in the left figure are examples of the observed and ground truth trajectories for training. The position of each step is sampled from the distributions of the middle figures. The sum of each distribution is shown in the right figure. The boxes of past, current (i.e., newest), and future densities are colored by red, blue, and purple, respectively."
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+                                    "type": "text",
+                                    "content": "systems where computational resources are limited and often become busy by executing other computationally-intense tasks such as object detection, mapping, and path planning."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.5. How to obtain the density map"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "The density map, not like the mere one-point estimate, is needed when autonomous systems perform visualization of density or successive tasks such as navigation. We can correct the possible future points with estimated density by sampling multiple trajectories from Eq.(7) and its density from Eq.(6). The density map is obtained by collecting these points with density at the same time step."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4. Experiments and Results Analysis"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "4.1. Experimental Setup"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Datasets. Experiments were conducted on various datasets including our developed dataset with synthesized data Simfork, and real-image benchmarks including ETH/UCY [37, 50] and SDD [53]. On all the datasets, the numbers of past observed and future predicted steps are "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "T_{o} = 8"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "T_{f} = 12"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. All steps have an interval of 0.4 seconds in accordance with the literature such as [25, 58]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Simfork is a synthesized dataset for comparison on the accuracy of predicted densities, which are produced as explained in Sec. 3.5. In all trajectories in this dataset, either of the two types of traveling directions (i.e., turning left or right) is observed after a straight trajectory, as shown in Fig. 3. Positions before and after the fork (colored by green and black, respectively, in the leftmost figure of Fig. 3) are used as past observed and future ground-truth positions, respectively. Each position of a trajectory is independently perturbed by the Gaussian noise, which results in the density at each time step."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Two pedestrian trajectory datasets, ETH [50] and UCY [37], are merged to ETH/UCY. This dataset has five scenes: ETH, HOTEL, UNIV, ZARA1, and ZARA2. For training and testing, we follow the standard leave-one-out"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "approach, where we train on 4 scenes and test on the remaining one. We follow the train-validation-test split of Social-GAN [25]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                        281,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "SDD"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " consists of 20 scenes captured in bird's eye view using aerial drones. This dataset contains various moving agents such as pedestrians, bicycles, and cars, but we focus on pedestrians for comparison, as with Trajnet [56]. We also follow the train-test split of Trajnet [56]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Metrics Evaluation of accuracy on trajectory prediction is done with the widely-used metrics, Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE is the average L2 distance between the predicted and ground truth trajectories over time. FDE is the L2 distance between the endpoints of the predicted and ground truth trajectories. We follow the Best-of-N procedure [25] with "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N = 20"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "For evaluation of the accuracy of density estimation, we use earth mover's distance (EMD) and log-probability. EMD is a measure of the distance between two densities by the minimum cost to move one density pile to the other. EMD is calculated between the estimated density and ground truth density on each prediction step. Thus, we use EMD on Simfork dataset, where the ground truth densities are available. The advantage of EMD over the widely-used KL divergence is that EMD works properly even if the two density is disjoint while KL divergence returns a constant value. We use log-probability on the pedestrian trajectory prediction datasets, where the ground truth density is unavailable. The log-probability is calculated on the ground truth trajectory instead of density."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "content": "Implementation Details. Each conditional CIFs in our FlowChain used three-layer RealNVP [14] with multilayer perceptions (MLPs) of three hidden layers and 128 hidden units. All the conditional CIFs are with independent weights conditioned on the feature vectors from Trajectory++ [58] encoder as the temporal-social encoder. We used a batch size of 128 and ADAM optimizer [30] with a learning rate of "
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+                                    "type": "inline_equation",
+                                    "content": "10^{-4}"
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+                                    "type": "text",
+                                    "content": ". All experiments were conducted on a single NVIDIA A100 GPU. We use a KDE implementation utilizing GPU as mentioned in Sec. 2."
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+                                            "type": "text",
+                                            "content": "Table 1. Quantitative results of trajectory prediction on ETH/UCY dataset with Best-of-20 metrics. T + I denotes its method takes a trajectory and an image as inputs while T denotes its method takes only a trajectory. Scores are in meters. Red and blue scores denote the best and the second-best in methods with T. Lower is better. The results of Trajectron++ [58] and MID [24] are updated according to an implementation issue #53 on the Trajectron++ GitHub page."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Input</td><td colspan=\"2\">ETH</td><td colspan=\"2\">HOTEL</td><td colspan=\"2\">UNIV</td><td colspan=\"2\">ZARA1</td><td colspan=\"2\">ZARA2</td><td colspan=\"2\">Mean</td></tr><tr><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>0.70</td><td>1.43</td><td>0.76</td><td>1.67</td><td>0.54</td><td>1.24</td><td>0.30</td><td>0.63</td><td>0.38</td><td>0.78</td><td>0.54</td><td>1.15</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>0.59</td><td>1.18</td><td>0.19</td><td>0.35</td><td>0.60</td><td>1.19</td><td>0.43</td><td>0.87</td><td>0.32</td><td>0.65</td><td>0.43</td><td>0.85</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>0.47</td><td>0.91</td><td>0.14</td><td>0.24</td><td>0.54</td><td>1.07</td><td>0.36</td><td>0.73</td><td>0.29</td><td>0.60</td><td>0.36</td><td>0.71</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>1.09</td><td>2.35</td><td>0.79</td><td>1.76</td><td>0.67</td><td>1.40</td><td>0.47</td><td>1.00</td><td>0.56</td><td>1.17</td><td>0.72</td><td>1.54</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>0.87</td><td>1.62</td><td>0.67</td><td>1.37</td><td>0.76</td><td>1.52</td><td>0.35</td><td>0.68</td><td>0.42</td><td>0.84</td><td>0.61</td><td>1.21</td></tr><tr><td>STGAT [29]</td><td>T</td><td>0.65</td><td>1.12</td><td>0.35</td><td>0.66</td><td>0.52</td><td>1.10</td><td>0.34</td><td>0.69</td><td>0.29</td><td>0.60</td><td>0.43</td><td>0.83</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>0.64</td><td>1.11</td><td>0.49</td><td>0.85</td><td>0.44</td><td>0.79</td><td>0.34</td><td>0.53</td><td>0.30</td><td>0.48</td><td>0.44</td><td>0.75</td></tr><tr><td>PECNet [41]</td><td>T</td><td>0.61</td><td>1.07</td><td>0.22</td><td>0.39</td><td>0.34</td><td>0.56</td><td>0.25</td><td>0.45</td><td>0.19</td><td>0.33</td><td>0.32</td><td>0.56</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>0.61</td><td>1.03</td><td>0.20</td><td>0.28</td><td>0.30</td><td>0.55</td><td>0.24</td><td>0.41</td><td>0.18</td><td>0.32</td><td>0.31</td><td>0.52</td></tr><tr><td>MID [24]</td><td>T</td><td>0.55</td><td>0.88</td><td>0.20</td><td>0.35</td><td>0.30</td><td>0.55</td><td>0.29</td><td>0.51</td><td>0.20</td><td>0.38</td><td>0.31</td><td>0.53</td></tr><tr><td>Social Implicit [43]</td><td>T</td><td>0.66</td><td>1.44</td><td>0.20</td><td>0.36</td><td>0.31</td><td>0.60</td><td>0.25</td><td>0.50</td><td>0.22</td><td>0.43</td><td>0.33</td><td>0.67</td></tr><tr><td>FlowChain(Ours)</td><td>T</td><td>0.55</td><td>0.99</td><td>0.20</td><td>0.35</td><td>0.29</td><td>0.54</td><td>0.22</td><td>0.40</td><td>0.20</td><td>0.34</td><td>0.29</td><td>0.52</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 2. Quantitative results of trajectory prediction on SDD dataset with Best-of-20 metrics. Scores are in pixels. See the caption of Tab. 1 also for details."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2,
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+                                            "html": "<table><tr><td>Method</td><td>Input</td><td>ADE</td><td>FDE</td></tr><tr><td>SoPhie [57]</td><td>T + I</td><td>16.27</td><td>29.38</td></tr><tr><td>Goal-GAN [10]</td><td>T + I</td><td>12.20</td><td>22.10</td></tr><tr><td>MG-GAN [9]</td><td>T + I</td><td>13.60</td><td>25.80</td></tr><tr><td>Social-LSTM [1]</td><td>T</td><td>31.19</td><td>56.97</td></tr><tr><td>Social-GAN [25]</td><td>T</td><td>27.25</td><td>41.44</td></tr><tr><td>STGAT [29]</td><td>T</td><td>14.85</td><td>28.17</td></tr><tr><td>Social-STGCNN [42]</td><td>T</td><td>20.76</td><td>33.18</td></tr><tr><td>PECNet [41]</td><td>T</td><td>9.97</td><td>15.89</td></tr><tr><td>Trajectory++ [58]</td><td>T</td><td>11.40</td><td>20.12</td></tr><tr><td>MID [24]</td><td>T</td><td>10.31</td><td>17.37</td></tr><tr><td>FlowChain (Ours)</td><td>T</td><td>9.93</td><td>17.17</td></tr></table>",
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+                                    "content": "4.2. Prediction Accuracy"
+                                }
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+                    ],
+                    "index": 4
+                },
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+                                    "type": "text",
+                                    "content": "A wide range of previous trajectory prediction methods is quantitatively compared with our FlowChain on ETH/UCY and SDD datasets, shown in Tab. 1 and Tab. 2. We didn't include some methods [40, 63, 70-72] due to a different train-validation-test split."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "For ETH/UCY dataset, FlowChain achieved mean ADE/FDE of 0.29/0.52 in meters, which are the best among all trajectory prediction methods. On SDD dataset, FlowChain achieved average ADE/FDE of 9.93/17.17 in pixels, which are the best and second-best among all methods taking only trajectories as inputs [1,24,25,41,58,63]."
+                                }
+                            ]
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+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Although our focus is on density estimation with a minimal computational cost, FlowChain is comparable with the state-of-the-art methods also in terms of errors. We didn't evaluate the accuracy of future trajectories from FlowChain's update because the trajectories do not change"
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 4. Temporal estimated densities on Simfork dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9,
+                            "angle": 0,
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "in the update as mentioned in Sec. 3.4."
+                                }
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+                        }
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+                                    "content": "4.3. Analysis on Density Estimation"
+                                }
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+                    ],
+                    "index": 11
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+                                    "content": "The results of density estimation are compared between FlowChain and previous methods based on VAE, GAN, and diffusion approaches. Trajectory++ is the representative VAE-based trajectory prediction model with density estimation by GMM. Social-GAN is a minimal model of GAN-based trajectory prediction. MID is the diffusion-based trajectory prediction model with state-of-the-art prediction accuracy. We applied KDE to Social-GAN and MID since"
+                                }
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+                                    "type": "text",
+                                    "content": "they cannot estimate the density alone. For a fair comparison, FlowChain, Social-GAN, and MID generated the same number of samples for future trajectories; "
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+                                    "type": "text",
+                                    "content": " samples."
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+                                    "content": "We evaluated the computational time and the accuracy of density estimation of each method, as shown in Tab. 3. Social-GAN and MID take much longer time because KDE is slow in spite of running on GPU. Trajectory++ is a bit faster than our FlowChain due to its simple Gaussian mixture model but suffers from the poor quality of estimated density, as shown by the worst EMD, 2.545, on Simfork dataset and worst log-probability, -281.86, on ETH/UCY dataset. On the other hand, our FlowChain achieved the best EMD, 1.408, and the best log-probability, -0.26, in spite of the fast computation 37.0ms. Thus, our method successfully addresses both the computational cost and accurate density estimation."
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+                                    "content": "The estimated densities on Simfork are visualized in Fig. 4. The densities estimated by Trajectory++ are too large compared to the ground truth densities. While the densities of Social-GAN and MID are stretched to the vertical axis, our FlowChain successfully estimated the tighter round-shape densities closest to the ground truth densities."
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+                                    "type": "text",
+                                    "content": "The estimated densities on "
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+                                    "type": "text",
+                                    "content": " are shown in Fig. 5. The size of each density represents the positional uncertainty of a predicted position. As within Simfork, in "
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+                                    "type": "text",
+                                    "content": ", an agent cannot change its traveling direction significantly in a short period (i.e., "
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+                                    "content": "0.4 \\times 12 = 4.8"
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+                                    "type": "text",
+                                    "content": " seconds), the size of the density expected to be tight. The densities estimated by Social-GAN are tight but deviated from the ground truth trajectory. Trajectory++ generated the densities with several disconnected modes due to the approximation as a Gaussian mixture. While the densi"
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+                                            "content": "Figure 6. Temporal densities estimated by our update procedure on Simfork dataset."
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+                                            "content": "Figure 7. Temporal densities estimated by our update procedure on ETH/UCY dataset."
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+                                    "type": "text",
+                                    "content": "ties from MID are close to the ground truth trajectory, MID could not suggest tight densities and their modes deviated from the ground truth trajectories. On the contrary, the density from our FlowChain covers the ground truth trajectory with tight distributions. thanks to the explicit density estimation of conditional CIFs and our expressive model architecture. We should note that the estimated density of FlowChain has some fluctuation due to the looseness of the density computation of CIFs. However, we did not observe any potential problem or failure of density estimation related to this in our experiments."
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+                                    "type": "text",
+                                    "content": "4.4. Proposed Update of Density Estimation"
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+                                    "content": "As shown in Tab. 3, the accuracy of density estimation degraded along with the number of updates. However, this update is remarkably fast "
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+                                    "type": "text",
+                                    "content": ", also shown in Tab. 3. Thus, autonomous systems can select the accurate prediction from scratch or the super rapid update by reusing predictions depending on the utilization of their computational resources."
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+                                    "content": "The estimated densities of our update procedure are shown in Fig. 6 and Fig. 7, which show the densities up"
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+                                            "content": "Table 3. Accuracy and computational time of density estimation. Scores are in milliseconds for computational time. While lower is better for EMD on Simfork dataset, higher is better for log-probability on ETH/UCY dataset. We report the averaged EMD and log-probability over the 12 prediction steps."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td></td><td colspan=\"2\">Comp. Time</td><td colspan=\"2\">Accuracy of Density Estimation</td></tr><tr><td></td><td>All</td><td>w/o KDE</td><td>EMD ↓</td><td>log-probability ↑</td></tr><tr><td>Social-GAN [25]</td><td></td><td>11498.8</td><td>9.8</td><td>1.544</td><td>-3.40</td></tr><tr><td>Trajectory++ [58]</td><td></td><td>33.7</td><td>-</td><td>2.545</td><td>-281.86</td></tr><tr><td>MID [24]</td><td></td><td>23904.1</td><td>12219.1</td><td>2.135</td><td>-0.90</td></tr><tr><td rowspan=\"3\">FlowChain (Ours)</td><td>Pred at t</td><td>37.0</td><td>-</td><td>1.408</td><td>-0.26</td></tr><tr><td>Update from t - 1</td><td>0.6</td><td>-</td><td>2.539</td><td>-0.45</td></tr><tr><td>Update from t - 5</td><td>0.5</td><td>-</td><td>2.899</td><td>-0.53</td></tr></table>",
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+                                            "content": "Table 4. Accuracy of density estimation with the update."
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+                                            "html": "<table><tr><td rowspan=\"2\" colspan=\"2\">Method</td><td colspan=\"8\">log-probability on each step</td></tr><tr><td>t+6</td><td>t+7</td><td>t+8</td><td>t+9</td><td>t+10</td><td>t+11</td><td>t+12</td><td>mean</td></tr><tr><td colspan=\"2\">Social-GAN [25]</td><td>-2.65</td><td>-2.86</td><td>-3.07</td><td>-3.26</td><td>-3.44</td><td>-3.62</td><td>-3.80</td><td>-3.24</td></tr><tr><td colspan=\"2\">Trajectory++ [58]</td><td>-121.19</td><td>-93.61</td><td>-71.62</td><td>-51.36</td><td>-36.85</td><td>-27.92</td><td>-22.72</td><td>-97.79</td></tr><tr><td colspan=\"2\">MID [24]</td><td>-1.06</td><td>-1.43</td><td>-1.75</td><td>-2.02</td><td>-2.26</td><td>-2.46</td><td>-2.65</td><td>-1.95</td></tr><tr><td rowspan=\"2\">FlowChain</td><td>Without Update</td><td>0.21</td><td>0.36</td><td>0.44</td><td>-0.08</td><td>-0.78</td><td>-0.75</td><td>-1.19</td><td>-0.26</td></tr><tr><td>With Update</td><td>0.20</td><td>0.50</td><td>0.39</td><td>0.44</td><td>0.20</td><td>0.26</td><td>0.16</td><td>0.31</td></tr></table>",
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+                                    "type": "text",
+                                    "content": " from the prediction at "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "t"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". On Simfork dataset, the wrong mode is successfully suppressed by exploiting the information of the new observation. On ETH/UCY dataset, the initial prediction deviated from the ground truth because the observed trajectory observed until "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "t"
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+                                {
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+                                    "type": "text",
+                                    "content": " does not have the information on turning left. However, the updated densities covered the ground truth well by adopting the newest observed position despite the minimal computational cost."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We further perform a comparison with a practical setting. Models usually make predictions with intervals due to the large computational cost. Therefore, we usually cannot obtain the prediction from the latest observation, as shown by the upper side of Fig. 8. For example, assume we need the density of six time-step ahead such as "
+                                },
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+                                    "type": "text",
+                                    "content": ", we cannot obtain "
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+                                    "type": "inline_equation",
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{t+1}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " or "
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+                                    "type": "text",
+                                    "content": " from "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{t+2}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " due to the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "computational overhead. However, with FlowChain's rapid update, we can obtain the update "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(p_{t + 7}, p_{t + 8})"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " from the latest observation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        320,
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+                                        441
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathbf{x}_{t + 1}, \\mathbf{x}_{t + 2})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        320,
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+                                    "type": "text",
+                                    "content": " on every time step thanks to the minimal computational cost, as shown by the bottom side of Fig. 8. We conducted the comparison with the frame of interest as six time-step ahead "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        320,
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+                                    "type": "inline_equation",
+                                    "content": "t + 6"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the log-probability metric. As shown by Tab. 4, our FlowChain with update achieves the highest log-probability. Therefore, we can conclude that FlowChain's update can improve the density estimation with minimal computational cost."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Concluding Remarks"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this paper, we proposed a new normalizing flow-based trajectory prediction network named FlowChain that achieves fast and accurate probability density estimation. Furthermore, our update procedure reliably generates the density estimation of the next step based on the density estimation of the previous step in an instant. Experimental results demonstrated that FlowChain achieved comparable accuracy to the state-of-the-art trajectory prediction models and superiority in the accuracy of density estimation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
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+                {
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+                                    "type": "text",
+                                    "content": "Our FlowChain has one limitation. Our update procedure can reliably estimate the density for several steps but the performance will degrade along with the time steps because the reused flow transformations do not reflect the new observations. Our future work is determining when should we stop to use the update procedure and make predictions from scratch. Furthermore, FlowChain is the domain-agnostic model that can be applied to a wide range of prediction tasks such as stock price prediction, human motion prediction, and video prediction. We will investigate the applicability of our FlowChain on these other domains."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
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+            ],
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                        {
+                            "bbox": [
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+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
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+                                                92,
+                                                287,
+                                                135
+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
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+                                {
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+                                        {
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+                                    ]
+                                }
+                            ],
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+                        },
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+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        {
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+                            "type": "ref_text",
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+                                {
+                                    "bbox": [
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+                                    ],
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+                                        {
+                                            "bbox": [
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
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+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[5] Jianfei Chen, Cheng Lu, Biqi Chenli, Jun Zhu, and Tian Tian. Vflow: More expressive generative flows with variational data augmentation. In ICML, pages 1660-1669, 2020."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                299,
+                                287,
+                                331
+                            ],
+                            "type": "ref_text",
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+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[6] Ricky TQ Chen, Jens Behrmann, David K Duvenaud, and Jorn-Henrik Jacobsen. Residual flows for invertible generative modeling. NeurIPS, 32, 2019."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                334,
+                                287,
+                                376
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "[7] Rob Cornish, Anthony Caterini, George Deligiannidis, and Arnaud Doucet. Relaxing bijectivity constraints with continuously indexed normalising flows. In ICML, pages 2133-2143, 2020."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                53,
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+                                434
+                            ],
+                            "type": "ref_text",
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+                            "lines": [
+                                {
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+                                        {
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                                        {
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+                                            "type": "text",
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+                                        }
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+                                        }
+                                    ]
+                                }
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+                                583
+                            ],
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+                                        {
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+                                        }
+                                    ]
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+                            "index": 12
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+                            "bbox": [
+                                48,
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[13] Laurent Dinh, David Krueger, and Yoshua Bengio. Nice: Non-linear independent components estimation. *ICLR Workshop*, 2015."
+                                        }
+                                    ]
+                                }
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+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                                            "content": "[67] MP Wand. Fast computation of multivariate kernel estimators. Journal of Computational and Graphical Statistics, 3(4):433-445, 1994."
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+                                            "content": "[68] Hao Wu, Jonas Kohler, and Frank Noé. Stochastic normalizing flows. NeurIPS, 33:5933-5944, 2020."
+                                        }
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+                                }
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+                                            "type": "text",
+                                            "content": "[69] Pengxiang Wu, Siheng Chen, and Dimitris N Metaxas. Motionnet: Joint perception and motion prediction for autonomous driving based on bird's eye view maps. In CVPR, pages 11385-11395, 2020."
+                                        }
+                                    ]
+                                }
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+                            "index": 2
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+                                            "type": "text",
+                                            "content": "[70] Cunjun Yu, Xiao Ma, Jiawei Ren, Haiyu Zhao, and Shuai Yi. Spatio-temporal graph transformer networks for pedestrian trajectory prediction. In ECCV, 2020."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
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+                                            "type": "text",
+                                            "content": "[71] Ye Yuan, Xinshuo Weng, Yanglan Ou, and Kris M Kitani. Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting. In ICCV, pages 9813-9823, 2021."
+                                        }
+                                    ]
+                                }
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+                            "index": 4
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+                                            "content": "[72] Jiangbei Yue, Dinesh Manocha, and He Wang. Human trajectory prediction via neural social physics. In ECCV, pages 376-394, 2022."
+                                        }
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+                                }
+                            ],
+                            "index": 5
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+                                            "content": "[73] He Zhao and Richard P Wildes. Where are you heading? dynamic trajectory prediction with expert goal examples. In ICCV, pages 7629-7638, 2021."
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diff --git a/2023/Fast Neural Scene Flow/ffd5b6d9-5f0d-4f78-9688-f85e6ce5fa64_content_list.json b/2023/Fast Neural Scene Flow/ffd5b6d9-5f0d-4f78-9688-f85e6ce5fa64_content_list.json
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+[
+    {
+        "type": "text",
+        "text": "Fast Neural Scene Flow",
+        "text_level": 1,
+        "bbox": [
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+            130,
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+    {
+        "type": "text",
+        "text": "Xueqian Li\\*1 Jianqiao Zheng\\* Francesco Ferroni\\*2 Jhony Kaesemodel Pontes\\*3 Simon Lucey\\*1 1The University of Adelaide 2NVIDIA 3Latitude AI",
+        "bbox": [
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+            179,
+            890,
+            217
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/42f33bc54254aecd92f7b2ef0351b6c949acfd95b315cd30d79131286e68f85a.jpg",
+        "image_caption": [
+            "(a) Lidar depth map densification"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            96,
+            244,
+            374,
+            385
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/54d9e247bdfa3c4b2fa33496b37c6945f5a17ec88ca028c376d0a7bf0ca96a32.jpg",
+        "image_caption": [
+            "(b) Efficiency of network architectures"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            382,
+            248,
+            640,
+            385
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/6e1324fa6d030cfc56e5cd611dac84ed3d0751e4de311ee5791ddb6be45afc55.jpg",
+        "image_caption": [
+            "(c) Error and computation time",
+            "Figure 1. Scene flow is an important problem as it provides low-level motion cues for many downstream tasks. State-of-the-art learning methods are usually fast and can achieve impressive performance on in-domain data, but usually fail to generalize to out-of-the-distribution (OOD) data or handle dense point clouds. In this paper, we focus on a runtime optimization-based neural scene flow pipeline. In (a) one can see its application in the densification of lidar. However, in (c) one sees that the major drawback is the extensive computation time. We identify that the common speedup strategy in network architectures for coordinate networks has little effect on scene flow acceleration [see green (b)] unlike image reconstruction [see pink (b)]. With the dominant computational burden stemming instead from the Chamfer loss function, we propose to use a distance transform-based loss function to accelerate [see purple (b)], which achieves up to  $30 \\times$  speedup and on-par estimation performance compared to NSFP [see (c)]. When tested on 8k points, it is as efficient [see (c)] as leading learning methods, achieving real-time performance."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            658,
+            246,
+            875,
+            388
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            547,
+            313,
+            563
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural Scene Flow Prior (NSFP) is of significant interest to the vision community due to its inherent robustness to out-of-distribution (OOD) effects and its ability to deal with dense lidar points. The approach utilizes a coordinate neural network to estimate scene flow at runtime, without any training. However, it is up to 100 times slower than current state-of-the-art learning methods. In other applications such as image, video, and radiance function reconstruction innovations in speeding up the runtime performance of coordinate networks have centered upon architectural changes. In this paper, we demonstrate that scene flow is different—with the dominant computational bottleneck stemming from the loss function itself (i.e., Chamfer distance). Further, we rediscover the distance transform (DT) as an efficient, correspondence-free loss function that dramatically speeds up the runtime optimization. Our fast neural scene flow (FNSF) approach reports for the first time real-time performance comparable to learning methods,",
+        "bbox": [
+            75,
+            580,
+            472,
+            853
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "*Part of the work was done while at Argo AI. Corresponding e-mail: xueqian.li@adelaide.edu.au. Code available at https://github.com/Lilac-Lee/FastNSF.git",
+        "bbox": [
+            75,
+            862,
+            470,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "without any training or OOD bias on two of the largest open autonomous driving (AV) lidar datasets Waymo Open [62] and Argoverse [8].",
+        "bbox": [
+            498,
+            549,
+            893,
+            595
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            500,
+            616,
+            632,
+            632
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural Scene Flow Prior (NSFP) [37] is considered the dominant method in open-world perception [47] and scene densification [37, 69] using lidar (see Fig. 1 (a)). NSFP achieves state-of-the-art scene flow estimates from dense lidar point clouds (up to  $150\\mathrm{k}+$  points) and works on a variety of sensor setups with little to no refinement or adaptation. Unlike supervised or unsupervised learning-based methods, NSFP does not require learning from large offline datasets and has no limits on point density ( $<8\\mathrm{k}$  for most learning methods). Instead, it leverages the architecture of a neural network to implicitly regularize the flow estimate and employs a runtime optimization that can easily scale to large out-of-distribution (OOD) scenes, which is a challenge for current learning-based methods [15, 31, 37, 47, 51].",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A fundamental drawback, however, to NSFP is the speed of its runtime optimization which is in some instances of orders of magnitude slower than its learning counterparts",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "9878",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(see Fig. 1). As a result, NSFP has widely been used offline for (i) providing scene flow supervision for efficient learning methods and (ii) as a pre-processing step for training open-world perception systems [47]. However, the considerable computational cost of NSFP limits its current applications only to these offline tasks.",
+        "bbox": [
+            75,
+            90,
+            470,
+            181
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A central narrative of our approach is that the dominant computational burden in runtime scene flow optimization (NSFP) is not the network architecture, but the loss function—specifically Chamfer distance (CD) [17]. This differs considerably from other applications of coordinate networks throughout vision and learning such as neural radiance fields (NeRF [44]) and high-fidelity image reconstruction ([61]) which have gained significant speedups through architectural innovations [83]. A visual depiction of this discrepancy can be found in Fig. 1 (b).",
+        "bbox": [
+            75,
+            181,
+            473,
+            333
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Key to our approach is the use of correspondence-free loss function—distance transform (DT) [5, 13, 58] as a proxy for the computationally expensive CD loss. Even though DT has been extensively studied by the graphics and vision community over a few decades, its application as an efficient loss function in deep geometry has largely been overlooked up until this point. We believe that the inherent efficiencies of the DT are especially pertinent for runtime network training such as in NSFP. Our approach shares similarities with Plenoxels [81]—a recent approach for efficient radiance field estimation using coordinate networks—as we trade memory consumption for computation time, allowing for significant speedups during runtime, which provides an alternative solution when exploring more efficient loss functions for dense scene flow estimation. We differ from Plenoxels, however, in that our memory consumption stems from our proposed loss function, not the neural architecture itself.",
+        "bbox": [
+            75,
+            333,
+            470,
+            589
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present for the first time an approximately real-time (for 8k points) runtime optimization method as computationally efficient as leading learning methods whilst preserving the scalability to dense point clouds and state-of-the-art performance on OOD scenes like NSFP. We compare the performance and the computation time of our approach on two of the largest open lidar AV datasets available: Waymo Open [62] and Argoverse [8]. Our fast neural scene flow achieves up to  $\\sim 30$  times speedup than NSFP [37] (our faster implementation) and of comparable speed to leading learning-based methods (see Fig. 1 (c)) with the same number of points (8,192). It opens up the possibility of employing a fast, robust, and generalizable approach for dense scene flow, which is not prone to OOD effects in real-time vision and robotic applications.",
+        "bbox": [
+            75,
+            590,
+            470,
+            816
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            833,
+            215,
+            848
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Scene flow estimation. Scene flow denotes the motion field in 3D space [67] uplifted from 2D optical flow. To reconstruct 3D flow, traditional image-based methods [2, 24,",
+        "bbox": [
+            75,
+            854,
+            470,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "25,27,28,36,53] formulate an optimization problem utilizing RGB or depth information, and learning-based RGB/RGB-D methods [6, 29, 30, 57, 60, 64, 78] rely on single/multiple image features which encode with a large amount of data supervisions. On the other hand, to estimate scene flow directly from 3D, traditional point cloud-based methods [1, 11, 50] solve for a non-rigid registration problem, while recent work prefers full-supervised learning [23, 34, 38, 39, 52, 71, 73, 75] that uses point-based features or self-supervised learning [3, 21, 45, 65, 75] that employs a self-supervised loss. Recent non-learning-based methods [37, 51] draw our attention back to runtime optimization that easily scales to large data. Graph prior [51] explicitly builds a graph on the point cloud and uses a graph Laplacian regularizer. While neural scene flow prior [37] uses the network as an implicit regularizer to smooth motions. In this paper, we explore point cloud-based scene flow using runtime optimization.",
+        "bbox": [
+            496,
+            90,
+            893,
+            349
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Accelerating coordinate networks. There exists a line of work [9, 20, 26, 46, 56, 81, 82] that focuses on accelerating coordinate networks by trading slow, memory efficient, deep network architectures for fast, memory hungry, shallow architectures. Most of these innovations have been applied to the problem of neural radiance fields most notably Plenoxels [81] and TensorRF [9]. Recently, this trend was generalized for arbitrary signals through the introduction of complex positional encoding [83] with shallow linear networks. In this paper, we claim that these architectural innovations have little utility in speeding up neural scene flow without first addressing the computational cost of the Chamfer loss it uses.",
+        "bbox": [
+            496,
+            353,
+            893,
+            549
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Distance transform. DT [4, 5, 13, 41, 58] has played an important role in image processing, especially binary image analysis [48, 66]. Further applications are also found in medical image segmentation [12, 33, 59, 70, 72], robotics motion planning [55, 76], geometric representation [7, 10, 49], and accelerated point cloud registration [19, 79]. Among them, various distance measures have been used, such as city block, chessboard, and Euclidean distance [13, 77]. Naturally, Euclidean distance is preferred in computing point distance but it is also the most difficult metric to compute due to the temporal complexity [22]. Many work attempts to speedup Euclidean DT computation including raster-scan-based algorithms [5, 18, 35, 41, 54], fast marching-based algorithms [16, 40, 68], etc., and has achieved linear time computation. In this paper, we investigate the raster-scan-based algorithm for the 3D point cloud.",
+        "bbox": [
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+        ],
+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "3. Approach",
+        "text_level": 1,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3.1. Background",
+        "text_level": 1,
+        "bbox": [
+            500,
+            835,
+            632,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Scene flow optimization. Suppose we have a moving sensor (e.g., lidar mounted on a car, depth camera tied to a robot, etc.) collecting point cloud in a dynamic environment.",
+        "bbox": [
+            496,
+            854,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "9879",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "At time  $t-1$ , a point cloud  $S_{1}$  (source) of the scene is sampled. Then given the movements of the sensor and objects in certain directions, another point cloud  $S_{2}$  (target) is sampled at time  $t$ . In order to find out all the motions in the environment, we model the translation of each point cloud  $\\mathbf{p} \\in S_{1}$  from time  $t-1$  to time  $t$  as a flow vector  $\\mathbf{f} \\in \\mathbb{R}^{3}$ , where  $\\mathbf{p}' = \\mathbf{p} + \\mathbf{f}$ . The translational vector set of all 3D points in  $S_{1}$  is defined as the scene flow  $\\mathcal{F} = \\{\\mathbf{f}_i\\}_{i=1}^{|S_1|}$ .",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Therefore, the optimization of the scene flow is to minimize the point distance between the source  $S_{1}$  and the target  $S_{2}$ . Usually, a regularization C, such as a Laplacian regularizer, is needed due to the highly unconstrained non-rigid flows. The overall optimization becomes",
+        "bbox": [
+            75,
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+            472,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} ^ {*} = \\underset {\\mathcal {F}} {\\arg \\min } \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {1}} \\mathrm {D} (\\mathbf {p} + \\mathbf {f}, \\mathcal {S} _ {2}) + \\lambda \\mathrm {C}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $D$  is a point distance function,  $\\lambda$  is a coefficient of the regularizer  $C$ .",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Neural scene flow prior. NSFP uses traditional runtime optimization to optimize a neural network. Different from learning-based methods, NSFP does not rely on any prior knowledge of large-scale datasets. And different from traditional scene flow optimization with an explicit regularizer that is mentioned above, neural scene flow prior optimizes parameters of a network which implicitly imposes a regularization by its structure:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\Theta} ^ {*} = \\underset {\\boldsymbol {\\Theta}} {\\arg \\min } \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {1}} D (\\mathbf {p} + g (\\mathbf {p}; \\boldsymbol {\\Theta}), \\mathcal {S} _ {2}). \\tag {2}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Theta$  is a parameter set of network  $g$  to be optimized.  $\\mathbf{p}$  is the input source point, and the flow  $\\mathbf{f} = g(\\mathbf{p};\\Theta)$  is the output of the network. The optimization converges at  $\\mathbf{f}^{*} = g(\\mathbf{p};\\Theta^{*})$ . The network  $g$  here is chosen to be a commonly used ReLU-MLP.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Since the points in source  $S_{1}$  and target  $S_{2}$  are not in correspondence, nor having the same number of points, i.e.,  $|S_{1}| \\neq |S_{2}|$ , we use a distance function that handles these problems as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nD (\\mathbf {p}, \\mathcal {S}) = \\min  _ {\\mathbf {x} \\in \\mathcal {S}} \\| \\mathbf {p} - \\mathbf {x} \\| _ {2} ^ {2}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Practically, a bidirectional point distance is found, yielding the above equation equivalent to the Chamfer loss [17].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Chamfer distance. In point cloud processing, Chamfer distance (CD) [17] is an important loss function and metric for computing the point distance of two point clouds that do not necessarily have points in correspondence. Chamfer distance loss computes the point distance of both source-to-target and target-to-source directions. In detail, the CD loss",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ba3b70147a46e9e29a4960e668728d47221fffca4b4b58831470bca793841440.jpg",
+        "image_caption": [
+            " Initialized DT map",
+            "Figure 2. An example of how to build a DT map of 2D points. The initialized DT map is set to all zeros. The rasterized 2D point image is set to zero if a point is presented in the grid, and set to one if the grid contains no points. After computation, the final DT map is shown in the right figure."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7dd8f1cd9ae17d1b5cd46d33439fd7062dcd1a12de5feafccfb2e358b359ebc4.jpg",
+        "image_caption": [
+            "Rasterized 2D points"
+        ],
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/0790784cd9f52965c075bbf94be5651102e85302f5870c4b294403ca2ebde626.jpg",
+        "image_caption": [
+            "Computed DT map"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "can be written as",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} C D \\left(\\mathcal {S} _ {1}, \\mathcal {S} _ {2}\\right) = \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {2}} \\mathrm {D} \\left(\\mathbf {p}, \\mathcal {S} _ {1}\\right) + \\sum_ {\\mathbf {q} \\in \\mathcal {S} _ {1}} \\mathrm {D} \\left(\\mathbf {q}, \\mathcal {S} _ {2}\\right) \\\\ = \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {2}} \\min  _ {\\mathbf {x} \\in \\mathcal {S} _ {1}} \\| \\mathbf {p} - \\mathbf {x} \\| _ {2} ^ {2} + \\sum_ {\\mathbf {q} \\in \\mathcal {S} _ {1}} \\min  _ {\\mathbf {y} \\in \\mathcal {S} _ {2}} \\| \\mathbf {q} - \\mathbf {y} \\| _ {2} ^ {2}. \\tag {4} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To compute the point distance, correspondences from source-to-target and target-to-source are searched among the nearest point neighbors. However, the exhaustive point correspondence search is extremely slow, especially when dealing with dense point clouds that contain more than 10k points (e.g., in Waymo Open and Argoverse datasets, the number of points can be up to  $150\\mathrm{k}+$ ).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Correspondence-free point distance transform",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "DT is widely used in 2D image processing, such as segmentation, boundary detection, pattern matching, skeletonization, etc. However, general usage in irregular and unordered 3D point cloud tasks is not broadly discussed. Given that the image grid is regular and ordered, a DT map is easily obtained by computing the minimum distance of each sampled point  $\\mathbf{x} \\in S$  to the vertex  $\\mathbf{q}$  of a DT map  $\\mathcal{G}$  as",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {D T} (\\mathbf {q}) = \\min  _ {\\mathbf {x} \\in \\mathcal {S}, \\mathbf {q} \\in \\mathcal {G}} \\mathrm {D} (\\mathbf {x}, \\mathbf {q}). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We extend Eq. (5) to fit in the scene flow task such that  $\\mathbf{D}$  refers to Euclidean distance,  $\\mathbf{x}$  denotes the target point, and  $\\mathbf{q}$  is the regularly spaced point in a voxel (3D).",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Approximation of DT map. However, with a large number of points in a point cloud and the grid map, directly computing Eq. (5) builds high dimensional matrices which will lead to large memory occupation. Even when we presume that each axis of the grid/voxel is separable, and the distance per axis is pre-computed, the memory consumption is still huge that cannot be processed on a single GPU. One strategy is to iteratively aggregate small",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "9880",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6a84d27d465517007a9ffc68a9a9e3ec3d25ae3c38ca967d7222e543f43f026f.jpg",
+        "image_caption": [
+            "Figure 3. Distance transform map of a target point cloud in Argoverse dataset. Purple points are the target, and green points are the source. It is important to note that the DT map is constructed from the target points, and the source points are only shown for reference purposes. The colormap denotes the DT values (in meters), with light yellow denoting a smaller distance and dark purple indicating a larger distance."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "matrix multiplications while at a cost of extensive time consumption. Another strategy is to use k-d tree query to compute the Euclidean distance. Building a k-d tree is one-time computing, but querying from a large point set to an even larger k-d tree is expensive.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Instead, we use a fast distance approximation by rasterizing the irregular points onto the nearest regular cuboid/grid. Specifically, similar to classical efficient binary image-based DT methods [12, 18], we construct two 3D binary images for target points and an initialized DT map. An example of 2D DT map is shown in Fig. 2. Specifically, the DT map is set to be all zeros, and the target binary image pixel is set to one when the grid contains no target points in it. Then a two-pass raster scan-based algorithm [18] is applied to each axis to compute the final DT, which means a 3D image needs six propagation passes (left to right, right to left, front to back, back to front, top to bottom, bottom to top). Although we rasterize target points using a binary 3D image approximation, we still compute the exact Euclidean distance between these two binary images instead of an approximated point distance. We empirically find that such discretization does not hurt performance. One reason is the local rigidity of the scene flow benefits from reasonably small but not necessarily infinitesimal DT grids/voxels.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A visualization of a 2D bird's eye view (BEV) DT map is presented in Fig. 3, where we see that when the point density is large, the distance value is relatively small, and the distance value becomes extremely large when no points exist. By choosing an appropriate grid size, the pattern of DT is distinct among different points while",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "maintaining a relatively smooth structure in the neighboring area. Evidently, the correspondence-free distance transform can act as an effective and efficient surrogate for point correspondence-based Chamfer loss.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "DT query and loss function. Once a DT map is built for the target point cloud, we can look up the pre-computed DT map to get the distance of the nearest source point in an extremely fast fashion. The loss function becomes the queried Euclidean distance between the target and the nearest deformed source points:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\min  _ {\\mathbf {y} \\in \\mathcal {S} ^ {\\prime}, \\mathbf {q} \\in \\mathcal {G}} \\| \\mathbf {y} - \\mathbf {q} \\| _ {2}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $S'$  is the deformed source point cloud. Unlike CD loss, no point correspondence search is required in Eq. (6), making the DT query exceptionally fast. Further ablation studies can be found in Sec. 4.3.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Datasets We are primarily interested in scene flow methods that are well-suited for large-scale, realistic, lidar-based OOD scenes, which are commonly encountered in autonomous driving (AV) applications. To this end, we focus on two AV datasets: Waymo Open [62] and Argoverse [8], which contain numerous challenging dynamic scenes. Unfortunately, no ground truth annotations were provided for the open-world dataset. We pre-processed the Argoverse and Waymo Open pseudo ground truth scene flow datasets following [37, 51] and [31, 80] respectively.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Metrics We follow scene flow metrics used in [37, 38, 45, 51, 75] to evaluate the performance. We also include the computation time breakdown in the table. These metrics are:",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1) 3D end-point error  $\\mathcal{E}(m)$  that measures the mean absolute point distance between estimated and target points;",
+            "2) strict accuracy  $Acc_5(\\%)$ , which is the accuracy of the estimated flow that satisfies the absolute point error  $\\mathcal{E} < 0.05\\mathrm{m}$  or the relative point error  $\\mathcal{E}' < 5\\%$ ;",
+            "3) relaxed accuracy  $Acc_{10}(\\%)$ , which is the accuracy of the estimated flow that satisfies the absolute point error  $\\mathcal{E} < 0.1\\mathrm{m}$  or the relative point error  $\\mathcal{E}' < 10\\%$ ;",
+            "4) angle error  $\\theta_{\\epsilon}(rad)$  that measures the mean angle error (in radiance) of the estimated and the pseudo ground truth translational vectors.",
+            "5) computation time  $t(ms)$  breaks down to four parts. Pre-compute includes data loading and building a DT map. Corr. / DT query counts the time needed to search point correspondences or query point distance within a DT map. We also include computation time for Network forward and backward propagation. Finally, Total time in seconds / milliseconds is measured."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9881",
+        "bbox": [
+            480,
+            944,
+            513,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Implementation details We provide the details of implementation for each algorithm we compared. Further information can be found in the supplementary materials.",
+        "bbox": [
+            76,
+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1) NSFP [37]. The original implementation is extremely slow. Based on the official code released by the authors while keeping the same parameter settings specified in the original paper, we implemented a faster version (NSFP) for a fair comparison. Note that to reflect the independence of each pair of point clouds when estimating scene flow, we randomly initialized the network before each optimization.",
+            "2) Baseline. Note that although the backward flow enforces a cycle consistency between the deformed point cloud and the original point cloud, we empirically found that removing cycle consistency does not hurt the overall performance when dealing with dense lidar point clouds, but improves the computational efficiency. Here we removed the backward flow in the original NSFP and implemented a NSFP (baseline) version as our baseline for a fair comparison—all computation times were compared with this model. We further modified the baseline model using a linear model with complex positional encodings (NSFP (baseline, linear)) to demonstrate the effect of network architecture changes. Detailed explanations can be found in Sec. 4.1 and the supplementary material.",
+            "3) Ours. We implemented a DT-based neural scene flow method with 8-layer ReLU-MLPs (Ours). We chose the grid cell size of the DT map to be 0.1 meters. Ablation studies on the choice of grid cell size can be found in Sec. 4.3. We further modified our method using a linear model with complex positional encodings (Ours (linear)) to demonstrate the effect of network architecture changes.",
+            "4) FlowStep3D [34] and FLOT [52] are fully supervised methods trained on synthetic FlyingThings3D [42] datasets. PointPWC-Net [75] can be used as a self-supervised method. We used the official code released by the authors and directly tested the pretrained model (pretrained on FlyingThings3D) on our datasets. However, as full/self-learning-based methods, they performed poorly on OOD datasets, which is also observed in [15, 31, 37, 47, 51]. Here we only chose the method with the best performance and the lowest computation time—FLOT—for comparison in the main table. The comparison of other learning-based methods is included in the supplementary material. R3DSF [21] is a weakly supervised method with no direct supervision of ground truth dynamic flows. We tested the method using the pretrained model (on KITTI [43]) provided by the authors."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "All models were implemented using CUDA 11.6-supported PyTorch. All experiments were run on a computer with a single NVIDIA RTX 3090Ti GPU and a 24 AMD Ryzen 95900X 12-Core CPU @ 4.95GHz.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/5a10fe8f3f5c48187796ab4ce9a77c3e4a182690a2b61eb3c1266e88e34bee3b.jpg",
+        "image_caption": [
+            "Figure 4. Illustration of 3D complex PE in scene flow problem. The 3D space of source points (yellow) and target points (green) is divided into small cubes. The number of cubes on each axis differs but the edge length is the same. Encoding of a point in a certain grid is the blending/interpolation of encodings of all 8 grid vertices. These grid points (blue) are encoded by complex PE along each axis. Note the vec and outer product  $(\\times)$  notation is for better visual understanding and it is equivalent to the Kronecker product."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Speedup in network architecture",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Plenoxels [81] is a method that accelerates NeRF [44] optimization by replacing deep neural networks with voxel-based spherical harmonics representations, leading to efficient volume rendering. Similar network speedup approaches can also be used in neural scene flow optimization. We incorporate recent innovations in positional encodings, specifically complex positional encoding (complex PE) [83] to represent high-frequency signals and enable a linear reconstruction model which is similar in spirit to [81].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Complex positional encodings Positional encodings (PEs) are encodings for input positions—e.g., 2D image grids, 3D voxel grids, etc.—that are usually used in coordinate networks. PEs has been shown to improve the performance and convergence speed of coordinate networks [63]. Simple PE is a simple concatenation of the encoding in each input dimension, while a complex PE is a more complicated encoding that computes the Kronecker product of the per-dimension encoding. An illustration of complex PE of scene flow is shown in Fig. 4.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With a complex PE and a linear model parameterized by  $\\mathbf{W} \\in \\mathbb{R}^{W_x W_y W_z \\times 3}$ , the scene flow can be represented as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {f} \\approx \\mathbf {B} (\\mathbf {p}; \\phi) \\operatorname {v e c} \\left(\\phi (\\mathbf {x}) \\mathbf {W} \\phi (\\mathbf {z}) ^ {T} \\phi (\\mathbf {y}) ^ {T}\\right), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            560,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{B}(\\cdot)$  is the blending function,  $\\phi (\\cdot)$  is the encoder,  $\\phi (\\mathbf{x})\\mathbf{W}\\phi (\\mathbf{z})^T\\phi (\\mathbf{y})^T$  is a simple notation for  $n$  -mode multiplication, which is equivalent to Kronecker product. The blending function interpolate the 3D regular grid encodings to handle the irregular and unordered nature of 3D point clouds. Additional details of complex PE can be found in the supplementary materials.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "9882",
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+    {
+        "type": "table",
+        "img_path": "images/6753d63ab75f620d755562fd7bfc6205a1695d2aa25db490027a5ce210c3bc2a.jpg",
+        "table_caption": [
+            "Table 1. Computation time and performance on Waymo Open Scene Flow dataset. We generated 202 testing scene flow examples where each point cloud has 8k-144k points. The upper tabular between blue bars are experiments with the full point cloud, and the lower tabular between orange bars are experiments with only 8,192 points. All query time is listed as: time per optimization step [total query time]. The speedups are marked with green  $\\times$  numbers, and the slow-downs are marked with red  $\\times$ . The computation time of using full point cloud is compared to values in the red box, and the computation time of using 8,192 points is compared to values in green box. Bold texts are the best performance, and underlined texts denote the second-best performance.  $\\uparrow$  means larger values are better while  $\\downarrow$  means smaller values are better. Corr. / DT query denotes correspondence search or DT query. Note: performance of learning methods PointPWC-Net [75], FlowStep3D [34], PV-RAFT [74] can be found in the supplementary material."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ε(m)↓</td><td rowspan=\"2\">Acc5(%)↑</td><td rowspan=\"2\">Acc10(%)↑</td><td rowspan=\"2\">θe(rad)↓</td><td colspan=\"4\">t (ms) ↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.100</td><td>76.62</td><td>88.56</td><td>0.286</td><td>—</td><td>114 [30972]</td><td>4.62 [1361]</td><td>35.51 s</td></tr><tr><td>NSFP (baseline)</td><td>0.118</td><td>74.16</td><td>86.70</td><td>0.300</td><td>—</td><td>43.1 [15036]</td><td>2.38 [904]</td><td>18.39 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.096</td><td>70.78</td><td>86.31</td><td>0.310</td><td>9.48</td><td>40.38 [8037] | 1.1×</td><td>1.53 [319] | 1.6×</td><td>10.20 s | 1.80×</td></tr><tr><td>Ours</td><td>0.072</td><td>84.73</td><td>92.24</td><td>0.280</td><td>40.85</td><td>0.25 [13] | 172×</td><td>2.89 [149] | 1.2×</td><td>0.58 s | 31.7×</td></tr><tr><td>Ours (linear)</td><td>0.109</td><td>71.27</td><td>85.80</td><td>0.321</td><td>44.88</td><td>0.23 [19] | 187×</td><td>1.62 [138] | 1.5×</td><td>0.49 s | 37.5×</td></tr><tr><td>FLOT [52]</td><td>0.702</td><td>2.46</td><td>11.30</td><td>0.808</td><td>—</td><td>—</td><td>—</td><td>99 ms</td></tr><tr><td>R3DSF [21]</td><td>0.414</td><td>35.47</td><td>44.96</td><td>0.527</td><td>—</td><td>—</td><td>—</td><td>140 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.138</td><td>53.62</td><td>78.57</td><td>0.339</td><td>—</td><td>5.42 [1285] | 21×</td><td>4.44 [1051] | 1.1×</td><td>2459 ms | 17.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.106</td><td>77.53</td><td>88.99</td><td>0.329</td><td>35.22</td><td>0.23 [6.5] | 496×</td><td>2.60 [76] | 1.8×</td><td>121 ms | 1.16×</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/aed930ce71a75ffdf34412df325a2f51800a904d91670384cbd2477f6d64435b.jpg",
+        "table_caption": [
+            "Table 2. Computation time and performance on Argoverse Scene Flow dataset. Argoverse has 212 testing scene flow examples where each point cloud has  $30\\mathrm{k - }70\\mathrm{k}$  points. Notations are the same as in the table above."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ε(m)↓</td><td rowspan=\"2\">Acc5(%)↑</td><td rowspan=\"2\">Acc10(%)↑</td><td rowspan=\"2\">θe(rad)↓</td><td colspan=\"4\">t (ms)↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.069</td><td>71.56</td><td>87.80</td><td>0.235</td><td>—</td><td>47 [14310]</td><td>4.66 [1507]</td><td>18.08 s</td></tr><tr><td>NSFP (baseline)</td><td>0.078</td><td>69.46</td><td>86.22</td><td>0.253</td><td>—</td><td>17 [5901]</td><td>2.31 [848]</td><td>8.38 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.097</td><td>67.03</td><td>83.20</td><td>0.314</td><td>9.19</td><td>14.7 [2786] | 1.1×</td><td>1.51 [297] | 1.5×</td><td>3.55 s | 2.36×</td></tr><tr><td>Ours</td><td>0.071</td><td>80.05</td><td>90.71</td><td>0.289</td><td>43.61</td><td>0.24 [14] | 71×</td><td>2.57 [149] | 1.1×</td><td>0.51 s | 16.4×</td></tr><tr><td>Ours (linear)</td><td>0.106</td><td>65.00</td><td>82.85</td><td>0.319</td><td>48.59</td><td>0.23 [20] | 74×</td><td>1.69 [149] | 1.4×</td><td>0.43 s | 19.5×</td></tr><tr><td>FLOT [52]</td><td>0.821</td><td>2.00</td><td>8.84</td><td>0.967</td><td>—</td><td>—</td><td>—</td><td>88 ms</td></tr><tr><td>R3DSF [21]</td><td>0.417</td><td>32.52</td><td>42.52</td><td>0.551</td><td>—</td><td>—</td><td>—</td><td>113 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.113</td><td>46.32</td><td>72.68</td><td>0.347</td><td>—</td><td>5.40 [1500] | 8.7×</td><td>4.42 [1233] | 1.1×</td><td>2864 ms | 25.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.118</td><td>69.93</td><td>83.55</td><td>0.352</td><td>41.57</td><td>0.22 [6.33] | 214×</td><td>2.51 [72.69] | 1.9×</td><td>124 ms | 1.10×</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Network speedup comparison We would like to point out that although various strategies have been proposed to accelerate network architectures, they do not lead to substantial speedup in neural scene flow estimation. To demonstrate this, we compare the relative efficiency of using 8-layer Relu-MLPs and complex PE with a linear model in both 2D image reconstruction and 3D scene flow tasks, shown in Fig. 1 (b). In detail, following [83], we used a size of  $256 \\times 256$  image dataset for image reconstruction. For a fair comparison, the relative efficiency is obtained by normalizing the computation time of two tasks. The computation time of single image reconstruction is  $17.63\\mathrm{s}$  and  $0.15\\mathrm{s}$  for deep network and linear network respectively, leading to  $118 \\times$  speedup. However, the linear model only results in  $\\sim 2 \\times$  and  $\\sim 1.2 \\times$  speedup for NSFP and our method respectively. Our results show that complex PE-based speedup achieves significant acceleration in 2D image reconstruction compared to deep neural networks, but the",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "benefits of such speedup are more limited when estimating neural scene flow. More detailed comparisons are in Sec. 4.2.",
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+    {
+        "type": "text",
+        "text": "4.2. Comparison of performance",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We show the performance of our method with different variants compared to NSFP, FLOT, and R3DSF on Waymo Open (Tab. 1) and Argoverse (Tab. 2) scene flow datasets. We denote results on Waymo Open (xx) and Argoverse (yy) as xx/yy. Visual results and applications of densification are shown in Fig. 5 and supplementary materials.",
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+    {
+        "type": "text",
+        "text": "Dense scene flow estimation. For dense point clouds, the baseline NSFP took  $18.39 / 8.38$  s to converge. When replacing the 8-layer MLPs with a linear network and applying complex PE, we observed a speedup of only  $1.80 / 2.36 \\times$  in total, primarily due to the network propagation speedup. When we replaced naive CD loss with the DT loss, a significant  $31.7 / 16.4 \\times$  speedup was achieved while",
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+    },
+    {
+        "type": "page_number",
+        "text": "9883",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/2e9861c823f7c6bac92698a5310c18a16c04b8e19ed13482c9b76b4b643903a0.jpg",
+        "image_caption": [
+            "Figure 5. Visual examples of the scene flow prediction using our method on Argoverse dataset. We show 3 different autonomous driving scenarios where the autonomous vehicle (AV) was making a right turn (left), the AV stopped for crossing traffic (middle), and the AV was driving in the city (right). We found that the scene flow predicted by our method is close to the ground truth flows. The upper left corner color wheel indicates the flow magnitude (color intensity) and the flow direction (angle). For example, the yellow vehicles in the middle figure are heading south with a relatively large speed wrt the AV."
+        ],
+        "image_footnote": [],
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+    },
+    {
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+        "img_path": "images/91f49666f983474bc02a473e24bb5441b7e50c4a0a9ff0f768bb2ea35f7eabb7.jpg",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b7e913dc4fcec0412dfd141d88d574f1fb57e1ba605810710b179b0fb59b6982.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "maintaining comparable high accuracy. However, replacing a deep network with a linear model when using DT loss only resulted in an additional  $1.2 / 1.2 \\times$  speedup at the cost of a decrease in flow accuracy. Specifically, the total computation time of our proposed method with DT loss is  $0.58 / 0.51$  s, and with DT loss and a linear model is  $0.49 / 0.43$  s. However, with a marginal decrease in computation time, we observed a relatively large drop in performance such that the strict accuracy of our method with DT is  $84.73 / 80.05\\%$  and  $71.27 / 65.00\\%$  with DT and a linear model. These results strongly support our argument in the previous section, which is the general strategy of simplifying or replacing network architectures to accelerate coordinate networks is not particularly effective when optimizing scene flow through coordinate networks.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Overall, the performance of our method using DT loss has on-par performance compared to NSFP while being orders of magnitude faster. We have noticed that there is an \"improved accuracy\" of our method compared to NSFP in Tab. 1, Tab. 2 based on these facts: 1. The performance of our method and NSFP is similar—our method achieves slightly higher performance on some metrics (e.g., accuracy), and NSFP achieves slightly higher performance on other metrics (e.g., angular error). These results indicate that distance transform (DT) is an effective and efficient surrogate for the Chamfer distance (CD) in the scene flow problem. 2. Compared to the \"exact\" point distance (CD), DT queries the distance based on a voxelized DT map, which naturally smooths the flow estimation. In real-world applications, we believe using a DT-accelerated deep network model will achieve both high-fidelity accuracy and efficient computation.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Computation time breakdown. A detailed time breakdown is provided in both tables, including pre-computation, correspondence search / DT distance query, and network forward / backward propagation. The naive",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Chamfer distance requires per-point correspondence search, which can be extremely slow (43.1/17 ms per iteration), especially when the point cloud is denser. For instance, correspondence search is much slower in the Waymo Open dataset than in the Argoverse dataset since Waymo Open has an average of 90k points while Argoverse has an average of 50k points in a single point cloud. DT query is a pre-defined table lookup that is exceptionally faster than the naive point correspondence search, achieving a remarkable  $172 / 71 \\times$  speedup per optimization step—the main contributor to the overall efficiency of our method. Note that the pre-computing of the DT map ( $\\sim 40$  ms) is acceptable given that it is one-time computing and the total computation time is in the range of hundreds of milliseconds. Additional complex PE and a linear model only provide a modest speedup of  $1.6 / 1.5 \\times$  in the network propagation step. Further optimization of the pre-computation and faster implementation can be achieved with full-CUDA support. Note that although in NSFP, the CD loss was implemented using PyTorch3D with CUDA acceleration, it still requires significant computation time, indicating its inherent limitations that cannot be easily overcome through engineering techniques alone.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "OOD generalizability. We further extend our model using fewer points (8,192 points) to accommodate for a fair comparison against learning-based methods [21, 34, 52, 74, 75]. For these learning models, a fixed number of points is required and they only operate on fewer points, such as 2,048 [38, 52] or 8,192 points [21, 34, 52, 75]. Also, these learning methods need to crop the point cloud to a small range. Therefore, learning models cannot be easily adapted to large-scale dense point clouds. Jund et al. explored to inference dense point cloud [32], but they did not directly process the full point cloud as the input. A simple solution to address this challenge is to iteratively predict scene flow for",
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+        "page_idx": 6
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+    {
+        "type": "page_number",
+        "text": "9884",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/af6b5027363274c10f701a2258a6af4bcd00496558e6f9e6d1c6a18196da739b.jpg",
+        "image_caption": [
+            "Figure 6. 2D DT map with different grid sizes. A larger grid size results in extremely coarse DT, as the grid cell size decreases, the DT accuracy increases. Here we zoom in on the original DT map in Fig. 3 to show the detailed distance values."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/15adaa81bf4cde9f36025e1253d956535536de24f27302b4254f5000964c02b6.jpg",
+        "image_caption": [
+            "Figure 7. Performance of distance transform with different grid cell sizes on a 2D scene from Argoverse scene flow dataset. Generally, the larger the grid cell is, the lower the accuracy becomes. The computation time and memory consumption also decrease as the grid cell size increases (the number of grids decreases). The total grid of the DT map is of size  $160 \\times 150$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "small subsets of dense point clouds using learning methods. However, this approach requires intensive computation, and it might cause out-of-memory issues [32].",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fully supervised learning methods FlowStep3D, FLOT, PV-RAFT, and self-supervised method PointPWC-Net do not generalize to new autonomous driving datasets (see Tab. 1, Tab. 2) due to the domain gap between the training and testing datasets [15, 31, 37, 47, 51]. We provide additional performance in the supplementary material. Despite its poor performance on OOD data, FLOT achieves a competitive inference time, making it one of the fastest learning-based methods available. Note that since the weakly supervised learning method R3DSF takes supervision from object segmentation and AV ego motions and was trained on a lidar point cloud-based dataset, it has a relatively high accuracy compared to full/self-supervised learning methods, but its performance is still inferior to non-learning-based methods NSFP and our method. Such evidence strongly suggests that our method—a runtime optimization—is robust to OOD effects, and can be directly applied to applications where no training data is readily available.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Towards real-time computation. Our method attains real-time performance (121/124 ms) which is comparable to learning methods and maintains high accuracy, while",
+        "bbox": [
+            75,
+            854,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/6c376d9faf336b5a839bd89f50806e65cc9e1ec0dcd99a0fa8f1c6f1c647cf58.jpg",
+        "table_caption": [
+            "Table 3. Comparison of our method and NSFP++ on Argoverse scene flow dataset with ego-motion compensation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>E↓(m)</td><td>Acc5↑(%)</td><td>Acc10↑(%)</td><td>θe↓(rad)</td><td>t↓(ms)</td></tr><tr><td>Ours</td><td>0.411</td><td>34.94</td><td>46.82</td><td>0.731</td><td>335</td></tr><tr><td>NSFP++ [47]</td><td>0.295</td><td>31.82</td><td>62.61</td><td>0.343</td><td>16188</td></tr><tr><td>NSFP++ (DT)</td><td>0.272</td><td>30.26</td><td>60.25</td><td>0.365</td><td>2001</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "learning-based methods struggle to generalize on OOD data. It indicates the significant potential of applying robust and accurate runtime optimization-based methods in many vision-based applications.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Other learning methods. Learning-based scene flow methods are usually fast and achieve good accuracy when applied to in-domain small-scale data (training and testing are on the same dataset with a specific range: e.g., KITTI data with point clouds within  $35\\mathrm{m}$  of the scene center) with a limited number of points (usually 2,048 / 8,192 points). As discussed in [15,31,37,47,51], the domain gap is a significant challenge for learning methods—a specific dataset with specific configurations—e.g., coordinate systems, viewing directions, etc.—that match the testing data needs to be used during training. However, we are interested in exploring runtime optimization-based methods that are robust to large-scale OOD data that can be employed in many real-world applications, such as autonomous driving scenarios, where no labels are readily available.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation study of DT grid size",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "DT splits the space into small grid cells, while the grid size affects the accuracy, the computation time, and the memory accuracy. We provide a performance comparison using different grid cell sizes of DT in Fig. 7. A 2D visualization of DT with different grid sizes is also shown in Fig. 6. We can clearly see that a relatively small grid cell size  $(grid \\leq 0.1m)$  is required to ensure the fidelity of the distance transform map. Note that when rasterized points are closer to the original irregular points, DT is a closer approximation to the exact Euclidean distance between two point clouds. Moreover, with a rasterized point-based DT strategy, the pre-computation of the map is no longer an overhead, and the grid cell size will largely affect the memory instead of the computation time—we trade memory consumption with computation time.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "9885",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/0996e1206160f744f23a64b3f5acd1a7afd1097427d6480dae328ef0df70051d.jpg",
+        "image_caption": [
+            "Figure 8. Failure cases on Argoverse dataset. The left figure shows some noisy motions were predicted in the background. The right figure shows our method failed to predict when the motion of some cars is relatively small to the AV."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4. Speedup in other methods",
+        "text_level": 1,
+        "bbox": [
+            76,
+            311,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The proposed DT loss is a general loss that can be used in other 3D geometry tasks. Specifically, for optimization-based methods such as RSF [14], DT could replace the nearest neighbor distance loss to speed up the overall computation. For learning methods such as PointPWCNet [75], DT could replace Chamfer loss to speed up optimization during training, especially when dealing with a large number of points. For methods using cycle consistency, when replacing CD  $(\\mathcal{O}(N^2))$  with DT, the forward flow computation will be substantially speeded up (similar speedup to the paper). The backward flow computation will also be speeded up even though the DT map will be computed in every optimization step.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We provide an example of comparing the results of our method to  $\\mathrm{NSFP}++$  [47] in Tab. 3. We used our version of  $\\mathrm{NSFP}++$  due to no publicly available official implementation. Since  $\\mathrm{NSFP}++$  requires ego-motion compensation, we also created an additional Argoverse scene flow dataset that removes the ego motions of autonomous vehicles. These ego motions are provided in the original Argoverse dataset [8].",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Following [47], we define dynamic points as points that the norm between the deformed source (i.e., source point cloud deformed by the ground truth flow) and the ego-motion compensated source (i.e., the source point cloud is transformed by the ego-motion) exceeds a threshold of 0.05. All the metrics are computed only on dynamic points. During optimization, for our method, we removed the ego-motion of the point cloud and estimated the scene flow using the full point cloud, and for NSFP++, we only used dynamic points as required.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Tab. 3, we show that our method achieves worse performance than  $\\mathrm{NSFP}++$  while being  $\\sim 50\\times$  faster. We further replaced the Chamfer distance loss used in  $\\mathrm{NSFP}++$  with our proposed distance transform (DT) loss, and we observed a  $\\sim 8\\times$  speedup. The distance transform loss can be a robust and efficient surrogate to Chamfer distance loss in many deep geometry vision tasks.",
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+        "type": "text",
+        "text": "4.5. Limitations",
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+        "type": "text",
+        "text": "One drawback of our method is that creating a DT map using rasterization can lead to discretization errors, especially when the grid size of the DT map is large. To mitigate these, it is necessary to build a DT map with relatively fine-resolution grids. In this case, the memory consumption will increase especially when dealing with high-dimensional data, such as 3D point clouds. Further engineering efforts of pre-creating an efficient high-resolution DT map are required to maintain a reasonable memory cost. However, we empirically find that in the context of scene flow estimation—specifically for scene flow in autonomous driving scenarios—a relatively smooth representation is preferred for local rigidity assumptions. Nevertheless, the tradeoff between the grid resolution, the memory consumption, and the estimation accuracy should be carefully considered and chosen based on specific real-world applications.",
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+        "text": "Failure cases. We show two typical failure cases in Fig. 8. The first case (left column) is when dynamic points are much sparser than the background, our prediction can result in noisy non-rigid motions in the background. The second case (right column) is when the dynamic motion is relatively small, our model may fail to recognize the dynamic scene and only predict rigid motions.",
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+        "type": "text",
+        "text": "5. Conclusion",
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+    {
+        "type": "text",
+        "text": "In this work, we revisit the runtime optimization-based scene flow method NSFP and propose a method that is both efficient and generalizable to large-scale OOD data and dense lidar points. We identify that common strategies for speeding up network architectures do not yield significant time reductions—the major computation overhead is the Chamfer distance loss. Therefore, we propose to use an efficient correspondence-free distance transform loss as a robust surrogate. The rediscovery of DT in scene flow estimation opens up an innovative venue to leverage its efficiency and robustness for various deep geometry tasks. Compared to NSFP, our method maintains comparable accuracy but gains up to  $\\sim 30\\times$  speedups. We report for the first time a real-time performance ( $\\sim 120\\mathrm{ms}$ ) with neural scene flow and runtime optimization when using fewer points (8,192). The efficient runtime optimization-based neural scene flow can be widely applied in lidar scenes to do point cloud densification, open-world object detection, and scene clustering, such as in autonomous driving scenarios, where no ground truth or training data are readily available.",
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+        "type": "text",
+        "text": "Acknowledgement: We would like to thank Haosen Xing for the careful review of the manuscript and the help throughout the project. We thank Kavisha Vidanapathirana for the initial implementation of NSFP++ [47].",
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+        "text": "References",
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.365,
+                0.131,
+                0.605,
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+            "angle": 0,
+            "content": "Fast Neural Scene Flow"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.18,
+                0.892,
+                0.218
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+            "angle": 0,
+            "content": "Xueqian Li\\*1 Jianqiao Zheng\\* Francesco Ferroni\\*2 Jhony Kaesemodel Pontes\\*3 Simon Lucey\\*1 1The University of Adelaide 2NVIDIA 3Latitude AI"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.097,
+                0.246,
+                0.375,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.162,
+                0.388,
+                0.327,
+                0.4
+            ],
+            "angle": 0,
+            "content": "(a) Lidar depth map densification"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.383,
+                0.249,
+                0.641,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.415,
+                0.388,
+                0.607,
+                0.399
+            ],
+            "angle": 0,
+            "content": "(b) Efficiency of network architectures"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.66,
+                0.247,
+                0.877,
+                0.389
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.691,
+                0.389,
+                0.844,
+                0.399
+            ],
+            "angle": 0,
+            "content": "(c) Error and computation time"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.404,
+                0.895,
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+            ],
+            "angle": 0,
+            "content": "Figure 1. Scene flow is an important problem as it provides low-level motion cues for many downstream tasks. State-of-the-art learning methods are usually fast and can achieve impressive performance on in-domain data, but usually fail to generalize to out-of-the-distribution (OOD) data or handle dense point clouds. In this paper, we focus on a runtime optimization-based neural scene flow pipeline. In (a) one can see its application in the densification of lidar. However, in (c) one sees that the major drawback is the extensive computation time. We identify that the common speedup strategy in network architectures for coordinate networks has little effect on scene flow acceleration [see green (b)] unlike image reconstruction [see pink (b)]. With the dominant computational burden stemming instead from the Chamfer loss function, we propose to use a distance transform-based loss function to accelerate [see purple (b)], which achieves up to \\(30 \\times\\) speedup and on-par estimation performance compared to NSFP [see (c)]. When tested on 8k points, it is as efficient [see (c)] as leading learning methods, achieving real-time performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.549,
+                0.314,
+                0.564
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.581,
+                0.473,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Neural Scene Flow Prior (NSFP) is of significant interest to the vision community due to its inherent robustness to out-of-distribution (OOD) effects and its ability to deal with dense lidar points. The approach utilizes a coordinate neural network to estimate scene flow at runtime, without any training. However, it is up to 100 times slower than current state-of-the-art learning methods. In other applications such as image, video, and radiance function reconstruction innovations in speeding up the runtime performance of coordinate networks have centered upon architectural changes. In this paper, we demonstrate that scene flow is different—with the dominant computational bottleneck stemming from the loss function itself (i.e., Chamfer distance). Further, we rediscover the distance transform (DT) as an efficient, correspondence-free loss function that dramatically speeds up the runtime optimization. Our fast neural scene flow (FNSF) approach reports for the first time real-time performance comparable to learning methods,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.863,
+                0.472,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Part of the work was done while at Argo AI. Corresponding e-mail: xueqian.li@adelaide.edu.au. Code available at https://github.com/Lilac-Lee/FastNSF.git"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.55,
+                0.894,
+                0.596
+            ],
+            "angle": 0,
+            "content": "without any training or OOD bias on two of the largest open autonomous driving (AV) lidar datasets Waymo Open [62] and Argoverse [8]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.617,
+                0.633,
+                0.633
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.895,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Neural Scene Flow Prior (NSFP) [37] is considered the dominant method in open-world perception [47] and scene densification [37, 69] using lidar (see Fig. 1 (a)). NSFP achieves state-of-the-art scene flow estimates from dense lidar point clouds (up to \\(150\\mathrm{k}+\\) points) and works on a variety of sensor setups with little to no refinement or adaptation. Unlike supervised or unsupervised learning-based methods, NSFP does not require learning from large offline datasets and has no limits on point density (\\(<8\\mathrm{k}\\) for most learning methods). Instead, it leverages the architecture of a neural network to implicitly regularize the flow estimate and employs a runtime optimization that can easily scale to large out-of-distribution (OOD) scenes, which is a challenge for current learning-based methods [15, 31, 37, 47, 51]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "A fundamental drawback, however, to NSFP is the speed of its runtime optimization which is in some instances of orders of magnitude slower than its learning counterparts"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9878"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.182
+            ],
+            "angle": 0,
+            "content": "(see Fig. 1). As a result, NSFP has widely been used offline for (i) providing scene flow supervision for efficient learning methods and (ii) as a pre-processing step for training open-world perception systems [47]. However, the considerable computational cost of NSFP limits its current applications only to these offline tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.183,
+                0.474,
+                0.334
+            ],
+            "angle": 0,
+            "content": "A central narrative of our approach is that the dominant computational burden in runtime scene flow optimization (NSFP) is not the network architecture, but the loss function—specifically Chamfer distance (CD) [17]. This differs considerably from other applications of coordinate networks throughout vision and learning such as neural radiance fields (NeRF [44]) and high-fidelity image reconstruction ([61]) which have gained significant speedups through architectural innovations [83]. A visual depiction of this discrepancy can be found in Fig. 1 (b)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.334,
+                0.471,
+                0.59
+            ],
+            "angle": 0,
+            "content": "Key to our approach is the use of correspondence-free loss function—distance transform (DT) [5, 13, 58] as a proxy for the computationally expensive CD loss. Even though DT has been extensively studied by the graphics and vision community over a few decades, its application as an efficient loss function in deep geometry has largely been overlooked up until this point. We believe that the inherent efficiencies of the DT are especially pertinent for runtime network training such as in NSFP. Our approach shares similarities with Plenoxels [81]—a recent approach for efficient radiance field estimation using coordinate networks—as we trade memory consumption for computation time, allowing for significant speedups during runtime, which provides an alternative solution when exploring more efficient loss functions for dense scene flow estimation. We differ from Plenoxels, however, in that our memory consumption stems from our proposed loss function, not the neural architecture itself."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.592,
+                0.471,
+                0.818
+            ],
+            "angle": 0,
+            "content": "In this paper, we present for the first time an approximately real-time (for 8k points) runtime optimization method as computationally efficient as leading learning methods whilst preserving the scalability to dense point clouds and state-of-the-art performance on OOD scenes like NSFP. We compare the performance and the computation time of our approach on two of the largest open lidar AV datasets available: Waymo Open [62] and Argoverse [8]. Our fast neural scene flow achieves up to \\(\\sim 30\\) times speedup than NSFP [37] (our faster implementation) and of comparable speed to leading learning-based methods (see Fig. 1 (c)) with the same number of points (8,192). It opens up the possibility of employing a fast, robust, and generalizable approach for dense scene flow, which is not prone to OOD effects in real-time vision and robotic applications."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.834,
+                0.216,
+                0.849
+            ],
+            "angle": 0,
+            "content": "2. Related work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.472,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Scene flow estimation. Scene flow denotes the motion field in 3D space [67] uplifted from 2D optical flow. To reconstruct 3D flow, traditional image-based methods [2, 24,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.35
+            ],
+            "angle": 0,
+            "content": "25,27,28,36,53] formulate an optimization problem utilizing RGB or depth information, and learning-based RGB/RGB-D methods [6, 29, 30, 57, 60, 64, 78] rely on single/multiple image features which encode with a large amount of data supervisions. On the other hand, to estimate scene flow directly from 3D, traditional point cloud-based methods [1, 11, 50] solve for a non-rigid registration problem, while recent work prefers full-supervised learning [23, 34, 38, 39, 52, 71, 73, 75] that uses point-based features or self-supervised learning [3, 21, 45, 65, 75] that employs a self-supervised loss. Recent non-learning-based methods [37, 51] draw our attention back to runtime optimization that easily scales to large data. Graph prior [51] explicitly builds a graph on the point cloud and uses a graph Laplacian regularizer. While neural scene flow prior [37] uses the network as an implicit regularizer to smooth motions. In this paper, we explore point cloud-based scene flow using runtime optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.354,
+                0.895,
+                0.55
+            ],
+            "angle": 0,
+            "content": "Accelerating coordinate networks. There exists a line of work [9, 20, 26, 46, 56, 81, 82] that focuses on accelerating coordinate networks by trading slow, memory efficient, deep network architectures for fast, memory hungry, shallow architectures. Most of these innovations have been applied to the problem of neural radiance fields most notably Plenoxels [81] and TensorRF [9]. Recently, this trend was generalized for arbitrary signals through the introduction of complex positional encoding [83] with shallow linear networks. In this paper, we claim that these architectural innovations have little utility in speeding up neural scene flow without first addressing the computational cost of the Chamfer loss it uses."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.557,
+                0.897,
+                0.799
+            ],
+            "angle": 0,
+            "content": "Distance transform. DT [4, 5, 13, 41, 58] has played an important role in image processing, especially binary image analysis [48, 66]. Further applications are also found in medical image segmentation [12, 33, 59, 70, 72], robotics motion planning [55, 76], geometric representation [7, 10, 49], and accelerated point cloud registration [19, 79]. Among them, various distance measures have been used, such as city block, chessboard, and Euclidean distance [13, 77]. Naturally, Euclidean distance is preferred in computing point distance but it is also the most difficult metric to compute due to the temporal complexity [22]. Many work attempts to speedup Euclidean DT computation including raster-scan-based algorithms [5, 18, 35, 41, 54], fast marching-based algorithms [16, 40, 68], etc., and has achieved linear time computation. In this paper, we investigate the raster-scan-based algorithm for the 3D point cloud."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.811,
+                0.61,
+                0.829
+            ],
+            "angle": 0,
+            "content": "3. Approach"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.836,
+                0.633,
+                0.853
+            ],
+            "angle": 0,
+            "content": "3.1. Background"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Scene flow optimization. Suppose we have a moving sensor (e.g., lidar mounted on a car, depth camera tied to a robot, etc.) collecting point cloud in a dynamic environment."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9879"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.215
+            ],
+            "angle": 0,
+            "content": "At time \\( t-1 \\), a point cloud \\( S_{1} \\) (source) of the scene is sampled. Then given the movements of the sensor and objects in certain directions, another point cloud \\( S_{2} \\) (target) is sampled at time \\( t \\). In order to find out all the motions in the environment, we model the translation of each point cloud \\( \\mathbf{p} \\in S_{1} \\) from time \\( t-1 \\) to time \\( t \\) as a flow vector \\( \\mathbf{f} \\in \\mathbb{R}^{3} \\), where \\( \\mathbf{p}' = \\mathbf{p} + \\mathbf{f} \\). The translational vector set of all 3D points in \\( S_{1} \\) is defined as the scene flow \\( \\mathcal{F} = \\{\\mathbf{f}_i\\}_{i=1}^{|S_1|} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.216,
+                0.473,
+                0.292
+            ],
+            "angle": 0,
+            "content": "Therefore, the optimization of the scene flow is to minimize the point distance between the source \\(S_{1}\\) and the target \\(S_{2}\\). Usually, a regularization C, such as a Laplacian regularizer, is needed due to the highly unconstrained non-rigid flows. The overall optimization becomes"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.136,
+                0.306,
+                0.47,
+                0.339
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {F} ^ {*} = \\underset {\\mathcal {F}} {\\arg \\min } \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {1}} \\mathrm {D} (\\mathbf {p} + \\mathbf {f}, \\mathcal {S} _ {2}) + \\lambda \\mathrm {C}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.352,
+                0.47,
+                0.384
+            ],
+            "angle": 0,
+            "content": "where \\(D\\) is a point distance function, \\(\\lambda\\) is a coefficient of the regularizer \\(C\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.396,
+                0.473,
+                0.518
+            ],
+            "angle": 0,
+            "content": "Neural scene flow prior. NSFP uses traditional runtime optimization to optimize a neural network. Different from learning-based methods, NSFP does not rely on any prior knowledge of large-scale datasets. And different from traditional scene flow optimization with an explicit regularizer that is mentioned above, neural scene flow prior optimizes parameters of a network which implicitly imposes a regularization by its structure:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.13,
+                0.532,
+                0.47,
+                0.565
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {\\Theta} ^ {*} = \\underset {\\boldsymbol {\\Theta}} {\\arg \\min } \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {1}} D (\\mathbf {p} + g (\\mathbf {p}; \\boldsymbol {\\Theta}), \\mathcal {S} _ {2}). \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.578,
+                0.47,
+                0.653
+            ],
+            "angle": 0,
+            "content": "where \\(\\Theta\\) is a parameter set of network \\(g\\) to be optimized. \\(\\mathbf{p}\\) is the input source point, and the flow \\(\\mathbf{f} = g(\\mathbf{p};\\Theta)\\) is the output of the network. The optimization converges at \\(\\mathbf{f}^{*} = g(\\mathbf{p};\\Theta^{*})\\). The network \\(g\\) here is chosen to be a commonly used ReLU-MLP."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.655,
+                0.471,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Since the points in source \\( S_{1} \\) and target \\( S_{2} \\) are not in correspondence, nor having the same number of points, i.e., \\( |S_{1}| \\neq |S_{2}| \\), we use a distance function that handles these problems as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.183,
+                0.73,
+                0.47,
+                0.753
+            ],
+            "angle": 0,
+            "content": "\\[\nD (\\mathbf {p}, \\mathcal {S}) = \\min  _ {\\mathbf {x} \\in \\mathcal {S}} \\| \\mathbf {p} - \\mathbf {x} \\| _ {2} ^ {2}. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.766,
+                0.469,
+                0.797
+            ],
+            "angle": 0,
+            "content": "Practically, a bidirectional point distance is found, yielding the above equation equivalent to the Chamfer loss [17]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Chamfer distance. In point cloud processing, Chamfer distance (CD) [17] is an important loss function and metric for computing the point distance of two point clouds that do not necessarily have points in correspondence. Chamfer distance loss computes the point distance of both source-to-target and target-to-source directions. In detail, the CD loss"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.091,
+                0.61,
+                0.197
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.507,
+                0.198,
+                0.607,
+                0.21
+            ],
+            "angle": 0,
+            "content": " Initialized DT map"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.092,
+                0.738,
+                0.197
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.632,
+                0.198,
+                0.742,
+                0.21
+            ],
+            "angle": 0,
+            "content": "Rasterized 2D points"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.765,
+                0.091,
+                0.889,
+                0.197
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.773,
+                0.198,
+                0.874,
+                0.21
+            ],
+            "angle": 0,
+            "content": "Computed DT map"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.215,
+                0.894,
+                0.284
+            ],
+            "angle": 0,
+            "content": "Figure 2. An example of how to build a DT map of 2D points. The initialized DT map is set to all zeros. The rasterized 2D point image is set to zero if a point is presented in the grid, and set to one if the grid contains no points. After computation, the final DT map is shown in the right figure."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.299,
+                0.616,
+                0.312
+            ],
+            "angle": 0,
+            "content": "can be written as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.323,
+                0.892,
+                0.407
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} C D \\left(\\mathcal {S} _ {1}, \\mathcal {S} _ {2}\\right) = \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {2}} \\mathrm {D} \\left(\\mathbf {p}, \\mathcal {S} _ {1}\\right) + \\sum_ {\\mathbf {q} \\in \\mathcal {S} _ {1}} \\mathrm {D} \\left(\\mathbf {q}, \\mathcal {S} _ {2}\\right) \\\\ = \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {2}} \\min  _ {\\mathbf {x} \\in \\mathcal {S} _ {1}} \\| \\mathbf {p} - \\mathbf {x} \\| _ {2} ^ {2} + \\sum_ {\\mathbf {q} \\in \\mathcal {S} _ {1}} \\min  _ {\\mathbf {y} \\in \\mathcal {S} _ {2}} \\| \\mathbf {q} - \\mathbf {y} \\| _ {2} ^ {2}. \\tag {4} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.419,
+                0.892,
+                0.526
+            ],
+            "angle": 0,
+            "content": "To compute the point distance, correspondences from source-to-target and target-to-source are searched among the nearest point neighbors. However, the exhaustive point correspondence search is extremely slow, especially when dealing with dense point clouds that contain more than 10k points (e.g., in Waymo Open and Argoverse datasets, the number of points can be up to \\(150\\mathrm{k}+\\))."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.542,
+                0.89,
+                0.558
+            ],
+            "angle": 0,
+            "content": "3.2. Correspondence-free point distance transform"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.565,
+                0.893,
+                0.671
+            ],
+            "angle": 0,
+            "content": "DT is widely used in 2D image processing, such as segmentation, boundary detection, pattern matching, skeletonization, etc. However, general usage in irregular and unordered 3D point cloud tasks is not broadly discussed. Given that the image grid is regular and ordered, a DT map is easily obtained by computing the minimum distance of each sampled point \\(\\mathbf{x} \\in S\\) to the vertex \\(\\mathbf{q}\\) of a DT map \\(\\mathcal{G}\\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.599,
+                0.683,
+                0.892,
+                0.706
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {D T} (\\mathbf {q}) = \\min  _ {\\mathbf {x} \\in \\mathcal {S}, \\mathbf {q} \\in \\mathcal {G}} \\mathrm {D} (\\mathbf {x}, \\mathbf {q}). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.716,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "We extend Eq. (5) to fit in the scene flow task such that \\(\\mathbf{D}\\) refers to Euclidean distance, \\(\\mathbf{x}\\) denotes the target point, and \\(\\mathbf{q}\\) is the regularly spaced point in a voxel (3D)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Approximation of DT map. However, with a large number of points in a point cloud and the grid map, directly computing Eq. (5) builds high dimensional matrices which will lead to large memory occupation. Even when we presume that each axis of the grid/voxel is separable, and the distance per axis is pre-computed, the memory consumption is still huge that cannot be processed on a single GPU. One strategy is to iteratively aggregate small"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9880"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.091,
+                0.089,
+                0.462,
+                0.33
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.334,
+                0.473,
+                0.435
+            ],
+            "angle": 0,
+            "content": "Figure 3. Distance transform map of a target point cloud in Argoverse dataset. Purple points are the target, and green points are the source. It is important to note that the DT map is constructed from the target points, and the source points are only shown for reference purposes. The colormap denotes the DT values (in meters), with light yellow denoting a smaller distance and dark purple indicating a larger distance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.447,
+                0.47,
+                0.522
+            ],
+            "angle": 0,
+            "content": "matrix multiplications while at a cost of extensive time consumption. Another strategy is to use k-d tree query to compute the Euclidean distance. Building a k-d tree is one-time computing, but querying from a large point set to an even larger k-d tree is expensive."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.523,
+                0.473,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Instead, we use a fast distance approximation by rasterizing the irregular points onto the nearest regular cuboid/grid. Specifically, similar to classical efficient binary image-based DT methods [12, 18], we construct two 3D binary images for target points and an initialized DT map. An example of 2D DT map is shown in Fig. 2. Specifically, the DT map is set to be all zeros, and the target binary image pixel is set to one when the grid contains no target points in it. Then a two-pass raster scan-based algorithm [18] is applied to each axis to compute the final DT, which means a 3D image needs six propagation passes (left to right, right to left, front to back, back to front, top to bottom, bottom to top). Although we rasterize target points using a binary 3D image approximation, we still compute the exact Euclidean distance between these two binary images instead of an approximated point distance. We empirically find that such discretization does not hurt performance. One reason is the local rigidity of the scene flow benefits from reasonably small but not necessarily infinitesimal DT grids/voxels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.473,
+                0.904
+            ],
+            "angle": 0,
+            "content": "A visualization of a 2D bird's eye view (BEV) DT map is presented in Fig. 3, where we see that when the point density is large, the distance value is relatively small, and the distance value becomes extremely large when no points exist. By choosing an appropriate grid size, the pattern of DT is distinct among different points while"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.152
+            ],
+            "angle": 0,
+            "content": "maintaining a relatively smooth structure in the neighboring area. Evidently, the correspondence-free distance transform can act as an effective and efficient surrogate for point correspondence-based Chamfer loss."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.166,
+                0.895,
+                0.258
+            ],
+            "angle": 0,
+            "content": "DT query and loss function. Once a DT map is built for the target point cloud, we can look up the pre-computed DT map to get the distance of the nearest source point in an extremely fast fashion. The loss function becomes the queried Euclidean distance between the target and the nearest deformed source points:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.613,
+                0.271,
+                0.895,
+                0.296
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\min  _ {\\mathbf {y} \\in \\mathcal {S} ^ {\\prime}, \\mathbf {q} \\in \\mathcal {G}} \\| \\mathbf {y} - \\mathbf {q} \\| _ {2}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.308,
+                0.895,
+                0.37
+            ],
+            "angle": 0,
+            "content": "where \\( S' \\) is the deformed source point cloud. Unlike CD loss, no point correspondence search is required in Eq. (6), making the DT query exceptionally fast. Further ablation studies can be found in Sec. 4.3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.387,
+                0.634,
+                0.405
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.414,
+                0.895,
+                0.567
+            ],
+            "angle": 0,
+            "content": "Datasets We are primarily interested in scene flow methods that are well-suited for large-scale, realistic, lidar-based OOD scenes, which are commonly encountered in autonomous driving (AV) applications. To this end, we focus on two AV datasets: Waymo Open [62] and Argoverse [8], which contain numerous challenging dynamic scenes. Unfortunately, no ground truth annotations were provided for the open-world dataset. We pre-processed the Argoverse and Waymo Open pseudo ground truth scene flow datasets following [37, 51] and [31, 80] respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.577,
+                0.895,
+                0.622
+            ],
+            "angle": 0,
+            "content": "Metrics We follow scene flow metrics used in [37, 38, 45, 51, 75] to evaluate the performance. We also include the computation time breakdown in the table. These metrics are:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.624,
+                0.894,
+                0.654
+            ],
+            "angle": 0,
+            "content": "1) 3D end-point error \\(\\mathcal{E}(m)\\) that measures the mean absolute point distance between estimated and target points;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.655,
+                0.895,
+                0.7
+            ],
+            "angle": 0,
+            "content": "2) strict accuracy \\( Acc_5(\\%) \\), which is the accuracy of the estimated flow that satisfies the absolute point error \\( \\mathcal{E} < 0.05\\mathrm{m} \\) or the relative point error \\( \\mathcal{E}' < 5\\% \\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.702,
+                0.895,
+                0.747
+            ],
+            "angle": 0,
+            "content": "3) relaxed accuracy \\( Acc_{10}(\\%) \\), which is the accuracy of the estimated flow that satisfies the absolute point error \\( \\mathcal{E} < 0.1\\mathrm{m} \\) or the relative point error \\( \\mathcal{E}' < 10\\% \\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.749,
+                0.894,
+                0.793
+            ],
+            "angle": 0,
+            "content": "4) angle error \\(\\theta_{\\epsilon}(rad)\\) that measures the mean angle error (in radiance) of the estimated and the pseudo ground truth translational vectors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "5) computation time \\( t(ms) \\) breaks down to four parts. Pre-compute includes data loading and building a DT map. Corr. / DT query counts the time needed to search point correspondences or query point distance within a DT map. We also include computation time for Network forward and backward propagation. Finally, Total time in seconds / milliseconds is measured."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.498,
+                0.624,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9881"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.138
+            ],
+            "angle": 0,
+            "content": "Implementation details We provide the details of implementation for each algorithm we compared. Further information can be found in the supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.147,
+                0.47,
+                0.254
+            ],
+            "angle": 0,
+            "content": "1) NSFP [37]. The original implementation is extremely slow. Based on the official code released by the authors while keeping the same parameter settings specified in the original paper, we implemented a faster version (NSFP) for a fair comparison. Note that to reflect the independence of each pair of point clouds when estimating scene flow, we randomly initialized the network before each optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.265,
+                0.471,
+                0.476
+            ],
+            "angle": 0,
+            "content": "2) Baseline. Note that although the backward flow enforces a cycle consistency between the deformed point cloud and the original point cloud, we empirically found that removing cycle consistency does not hurt the overall performance when dealing with dense lidar point clouds, but improves the computational efficiency. Here we removed the backward flow in the original NSFP and implemented a NSFP (baseline) version as our baseline for a fair comparison—all computation times were compared with this model. We further modified the baseline model using a linear model with complex positional encodings (NSFP (baseline, linear)) to demonstrate the effect of network architecture changes. Detailed explanations can be found in Sec. 4.1 and the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.487,
+                0.47,
+                0.593
+            ],
+            "angle": 0,
+            "content": "3) Ours. We implemented a DT-based neural scene flow method with 8-layer ReLU-MLPs (Ours). We chose the grid cell size of the DT map to be 0.1 meters. Ablation studies on the choice of grid cell size can be found in Sec. 4.3. We further modified our method using a linear model with complex positional encodings (Ours (linear)) to demonstrate the effect of network architecture changes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.603,
+                0.471,
+                0.831
+            ],
+            "angle": 0,
+            "content": "4) FlowStep3D [34] and FLOT [52] are fully supervised methods trained on synthetic FlyingThings3D [42] datasets. PointPWC-Net [75] can be used as a self-supervised method. We used the official code released by the authors and directly tested the pretrained model (pretrained on FlyingThings3D) on our datasets. However, as full/self-learning-based methods, they performed poorly on OOD datasets, which is also observed in [15, 31, 37, 47, 51]. Here we only chose the method with the best performance and the lowest computation time—FLOT—for comparison in the main table. The comparison of other learning-based methods is included in the supplementary material. R3DSF [21] is a weakly supervised method with no direct supervision of ground truth dynamic flows. We tested the method using the pretrained model (on KITTI [43]) provided by the authors."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.147,
+                0.473,
+                0.831
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "All models were implemented using CUDA 11.6-supported PyTorch. All experiments were run on a computer with a single NVIDIA RTX 3090Ti GPU and a 24 AMD Ryzen 95900X 12-Core CPU @ 4.95GHz."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.088,
+                0.895,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.27,
+                0.895,
+                0.382
+            ],
+            "angle": 0,
+            "content": "Figure 4. Illustration of 3D complex PE in scene flow problem. The 3D space of source points (yellow) and target points (green) is divided into small cubes. The number of cubes on each axis differs but the edge length is the same. Encoding of a point in a certain grid is the blending/interpolation of encodings of all 8 grid vertices. These grid points (blue) are encoded by complex PE along each axis. Note the vec and outer product \\((\\times)\\) notation is for better visual understanding and it is equivalent to the Kronecker product."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.399,
+                0.787,
+                0.415
+            ],
+            "angle": 0,
+            "content": "4.1. Speedup in network architecture"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.422,
+                0.892,
+                0.573
+            ],
+            "angle": 0,
+            "content": "Plenoxels [81] is a method that accelerates NeRF [44] optimization by replacing deep neural networks with voxel-based spherical harmonics representations, leading to efficient volume rendering. Similar network speedup approaches can also be used in neural scene flow optimization. We incorporate recent innovations in positional encodings, specifically complex positional encoding (complex PE) [83] to represent high-frequency signals and enable a linear reconstruction model which is similar in spirit to [81]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.579,
+                0.892,
+                0.729
+            ],
+            "angle": 0,
+            "content": "Complex positional encodings Positional encodings (PEs) are encodings for input positions—e.g., 2D image grids, 3D voxel grids, etc.—that are usually used in coordinate networks. PEs has been shown to improve the performance and convergence speed of coordinate networks [63]. Simple PE is a simple concatenation of the encoding in each input dimension, while a complex PE is a more complicated encoding that computes the Kronecker product of the per-dimension encoding. An illustration of complex PE of scene flow is shown in Fig. 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.73,
+                0.892,
+                0.759
+            ],
+            "angle": 0,
+            "content": "With a complex PE and a linear model parameterized by \\(\\mathbf{W} \\in \\mathbb{R}^{W_x W_y W_z \\times 3}\\), the scene flow can be represented as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.561,
+                0.768,
+                0.892,
+                0.786
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {f} \\approx \\mathbf {B} (\\mathbf {p}; \\phi) \\operatorname {v e c} \\left(\\phi (\\mathbf {x}) \\mathbf {W} \\phi (\\mathbf {z}) ^ {T} \\phi (\\mathbf {y}) ^ {T}\\right), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{B}(\\cdot)\\) is the blending function, \\(\\phi (\\cdot)\\) is the encoder, \\(\\phi (\\mathbf{x})\\mathbf{W}\\phi (\\mathbf{z})^T\\phi (\\mathbf{y})^T\\) is a simple notation for \\(n\\) -mode multiplication, which is equivalent to Kronecker product. The blending function interpolate the 3D regular grid encodings to handle the irregular and unordered nature of 3D point clouds. Additional details of complex PE can be found in the supplementary materials."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9882"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.087,
+                0.895,
+                0.199
+            ],
+            "angle": 0,
+            "content": "Table 1. Computation time and performance on Waymo Open Scene Flow dataset. We generated 202 testing scene flow examples where each point cloud has 8k-144k points. The upper tabular between blue bars are experiments with the full point cloud, and the lower tabular between orange bars are experiments with only 8,192 points. All query time is listed as: time per optimization step [total query time]. The speedups are marked with green \\(\\times\\) numbers, and the slow-downs are marked with red \\(\\times\\). The computation time of using full point cloud is compared to values in the red box, and the computation time of using 8,192 points is compared to values in green box. Bold texts are the best performance, and underlined texts denote the second-best performance. \\(\\uparrow\\) means larger values are better while \\(\\downarrow\\) means smaller values are better. Corr. / DT query denotes correspondence search or DT query. Note: performance of learning methods PointPWC-Net [75], FlowStep3D [34], PV-RAFT [74] can be found in the supplementary material."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.2,
+                0.894,
+                0.381
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ε(m)↓</td><td rowspan=\"2\">Acc5(%)↑</td><td rowspan=\"2\">Acc10(%)↑</td><td rowspan=\"2\">θe(rad)↓</td><td colspan=\"4\">t (ms) ↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.100</td><td>76.62</td><td>88.56</td><td>0.286</td><td>—</td><td>114 [30972]</td><td>4.62 [1361]</td><td>35.51 s</td></tr><tr><td>NSFP (baseline)</td><td>0.118</td><td>74.16</td><td>86.70</td><td>0.300</td><td>—</td><td>43.1 [15036]</td><td>2.38 [904]</td><td>18.39 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.096</td><td>70.78</td><td>86.31</td><td>0.310</td><td>9.48</td><td>40.38 [8037] | 1.1×</td><td>1.53 [319] | 1.6×</td><td>10.20 s | 1.80×</td></tr><tr><td>Ours</td><td>0.072</td><td>84.73</td><td>92.24</td><td>0.280</td><td>40.85</td><td>0.25 [13] | 172×</td><td>2.89 [149] | 1.2×</td><td>0.58 s | 31.7×</td></tr><tr><td>Ours (linear)</td><td>0.109</td><td>71.27</td><td>85.80</td><td>0.321</td><td>44.88</td><td>0.23 [19] | 187×</td><td>1.62 [138] | 1.5×</td><td>0.49 s | 37.5×</td></tr><tr><td>FLOT [52]</td><td>0.702</td><td>2.46</td><td>11.30</td><td>0.808</td><td>—</td><td>—</td><td>—</td><td>99 ms</td></tr><tr><td>R3DSF [21]</td><td>0.414</td><td>35.47</td><td>44.96</td><td>0.527</td><td>—</td><td>—</td><td>—</td><td>140 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.138</td><td>53.62</td><td>78.57</td><td>0.339</td><td>—</td><td>5.42 [1285] | 21×</td><td>4.44 [1051] | 1.1×</td><td>2459 ms | 17.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.106</td><td>77.53</td><td>88.99</td><td>0.329</td><td>35.22</td><td>0.23 [6.5] | 496×</td><td>2.60 [76] | 1.8×</td><td>121 ms | 1.16×</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.393,
+                0.893,
+                0.42
+            ],
+            "angle": 0,
+            "content": "Table 2. Computation time and performance on Argoverse Scene Flow dataset. Argoverse has 212 testing scene flow examples where each point cloud has \\(30\\mathrm{k - }70\\mathrm{k}\\) points. Notations are the same as in the table above."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.42,
+                0.895,
+                0.603
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ε(m)↓</td><td rowspan=\"2\">Acc5(%)↑</td><td rowspan=\"2\">Acc10(%)↑</td><td rowspan=\"2\">θe(rad)↓</td><td colspan=\"4\">t (ms)↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.069</td><td>71.56</td><td>87.80</td><td>0.235</td><td>—</td><td>47 [14310]</td><td>4.66 [1507]</td><td>18.08 s</td></tr><tr><td>NSFP (baseline)</td><td>0.078</td><td>69.46</td><td>86.22</td><td>0.253</td><td>—</td><td>17 [5901]</td><td>2.31 [848]</td><td>8.38 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.097</td><td>67.03</td><td>83.20</td><td>0.314</td><td>9.19</td><td>14.7 [2786] | 1.1×</td><td>1.51 [297] | 1.5×</td><td>3.55 s | 2.36×</td></tr><tr><td>Ours</td><td>0.071</td><td>80.05</td><td>90.71</td><td>0.289</td><td>43.61</td><td>0.24 [14] | 71×</td><td>2.57 [149] | 1.1×</td><td>0.51 s | 16.4×</td></tr><tr><td>Ours (linear)</td><td>0.106</td><td>65.00</td><td>82.85</td><td>0.319</td><td>48.59</td><td>0.23 [20] | 74×</td><td>1.69 [149] | 1.4×</td><td>0.43 s | 19.5×</td></tr><tr><td>FLOT [52]</td><td>0.821</td><td>2.00</td><td>8.84</td><td>0.967</td><td>—</td><td>—</td><td>—</td><td>88 ms</td></tr><tr><td>R3DSF [21]</td><td>0.417</td><td>32.52</td><td>42.52</td><td>0.551</td><td>—</td><td>—</td><td>—</td><td>113 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.113</td><td>46.32</td><td>72.68</td><td>0.347</td><td>—</td><td>5.40 [1500] | 8.7×</td><td>4.42 [1233] | 1.1×</td><td>2864 ms | 25.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.118</td><td>69.93</td><td>83.55</td><td>0.352</td><td>41.57</td><td>0.22 [6.33] | 214×</td><td>2.51 [72.69] | 1.9×</td><td>124 ms | 1.10×</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.625,
+                0.473,
+                0.897
+            ],
+            "angle": 0,
+            "content": "Network speedup comparison We would like to point out that although various strategies have been proposed to accelerate network architectures, they do not lead to substantial speedup in neural scene flow estimation. To demonstrate this, we compare the relative efficiency of using 8-layer Relu-MLPs and complex PE with a linear model in both 2D image reconstruction and 3D scene flow tasks, shown in Fig. 1 (b). In detail, following [83], we used a size of \\(256 \\times 256\\) image dataset for image reconstruction. For a fair comparison, the relative efficiency is obtained by normalizing the computation time of two tasks. The computation time of single image reconstruction is \\(17.63\\mathrm{s}\\) and \\(0.15\\mathrm{s}\\) for deep network and linear network respectively, leading to \\(118 \\times\\) speedup. However, the linear model only results in \\(\\sim 2 \\times\\) and \\(\\sim 1.2 \\times\\) speedup for NSFP and our method respectively. Our results show that complex PE-based speedup achieves significant acceleration in 2D image reconstruction compared to deep neural networks, but the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.625,
+                0.895,
+                0.656
+            ],
+            "angle": 0,
+            "content": "benefits of such speedup are more limited when estimating neural scene flow. More detailed comparisons are in Sec. 4.2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.668,
+                0.755,
+                0.684
+            ],
+            "angle": 0,
+            "content": "4.2. Comparison of performance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.692,
+                0.895,
+                0.783
+            ],
+            "angle": 0,
+            "content": "We show the performance of our method with different variants compared to NSFP, FLOT, and R3DSF on Waymo Open (Tab. 1) and Argoverse (Tab. 2) scene flow datasets. We denote results on Waymo Open (xx) and Argoverse (yy) as xx/yy. Visual results and applications of densification are shown in Fig. 5 and supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Dense scene flow estimation. For dense point clouds, the baseline NSFP took \\(18.39 / 8.38\\) s to converge. When replacing the 8-layer MLPs with a linear network and applying complex PE, we observed a speedup of only \\(1.80 / 2.36 \\times\\) in total, primarily due to the network propagation speedup. When we replaced naive CD loss with the DT loss, a significant \\(31.7 / 16.4 \\times\\) speedup was achieved while"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9883"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.107,
+                0.089,
+                0.374,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.376,
+                0.089,
+                0.622,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.624,
+                0.09,
+                0.871,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.28,
+                0.895,
+                0.351
+            ],
+            "angle": 0,
+            "content": "Figure 5. Visual examples of the scene flow prediction using our method on Argoverse dataset. We show 3 different autonomous driving scenarios where the autonomous vehicle (AV) was making a right turn (left), the AV stopped for crossing traffic (middle), and the AV was driving in the city (right). We found that the scene flow predicted by our method is close to the ground truth flows. The upper left corner color wheel indicates the flow magnitude (color intensity) and the flow direction (angle). For example, the yellow vehicles in the middle figure are heading south with a relatively large speed wrt the AV."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.364,
+                0.473,
+                0.59
+            ],
+            "angle": 0,
+            "content": "maintaining comparable high accuracy. However, replacing a deep network with a linear model when using DT loss only resulted in an additional \\(1.2 / 1.2 \\times\\) speedup at the cost of a decrease in flow accuracy. Specifically, the total computation time of our proposed method with DT loss is \\(0.58 / 0.51\\) s, and with DT loss and a linear model is \\(0.49 / 0.43\\) s. However, with a marginal decrease in computation time, we observed a relatively large drop in performance such that the strict accuracy of our method with DT is \\(84.73 / 80.05\\%\\) and \\(71.27 / 65.00\\%\\) with DT and a linear model. These results strongly support our argument in the previous section, which is the general strategy of simplifying or replacing network architectures to accelerate coordinate networks is not particularly effective when optimizing scene flow through coordinate networks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.59,
+                0.473,
+                0.833
+            ],
+            "angle": 0,
+            "content": "Overall, the performance of our method using DT loss has on-par performance compared to NSFP while being orders of magnitude faster. We have noticed that there is an \"improved accuracy\" of our method compared to NSFP in Tab. 1, Tab. 2 based on these facts: 1. The performance of our method and NSFP is similar—our method achieves slightly higher performance on some metrics (e.g., accuracy), and NSFP achieves slightly higher performance on other metrics (e.g., angular error). These results indicate that distance transform (DT) is an effective and efficient surrogate for the Chamfer distance (CD) in the scene flow problem. 2. Compared to the \"exact\" point distance (CD), DT queries the distance based on a voxelized DT map, which naturally smooths the flow estimation. In real-world applications, we believe using a DT-accelerated deep network model will achieve both high-fidelity accuracy and efficient computation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Computation time breakdown. A detailed time breakdown is provided in both tables, including pre-computation, correspondence search / DT distance query, and network forward / backward propagation. The naive"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.364,
+                0.895,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Chamfer distance requires per-point correspondence search, which can be extremely slow (43.1/17 ms per iteration), especially when the point cloud is denser. For instance, correspondence search is much slower in the Waymo Open dataset than in the Argoverse dataset since Waymo Open has an average of 90k points while Argoverse has an average of 50k points in a single point cloud. DT query is a pre-defined table lookup that is exceptionally faster than the naive point correspondence search, achieving a remarkable \\(172 / 71 \\times\\) speedup per optimization step—the main contributor to the overall efficiency of our method. Note that the pre-computing of the DT map (\\(\\sim 40\\) ms) is acceptable given that it is one-time computing and the total computation time is in the range of hundreds of milliseconds. Additional complex PE and a linear model only provide a modest speedup of \\(1.6 / 1.5 \\times\\) in the network propagation step. Further optimization of the pre-computation and faster implementation can be achieved with full-CUDA support. Note that although in NSFP, the CD loss was implemented using PyTorch3D with CUDA acceleration, it still requires significant computation time, indicating its inherent limitations that cannot be easily overcome through engineering techniques alone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.897,
+                0.902
+            ],
+            "angle": 0,
+            "content": "OOD generalizability. We further extend our model using fewer points (8,192 points) to accommodate for a fair comparison against learning-based methods [21, 34, 52, 74, 75]. For these learning models, a fixed number of points is required and they only operate on fewer points, such as 2,048 [38, 52] or 8,192 points [21, 34, 52, 75]. Also, these learning methods need to crop the point cloud to a small range. Therefore, learning models cannot be easily adapted to large-scale dense point clouds. Jund et al. explored to inference dense point cloud [32], but they did not directly process the full point cloud as the input. A simple solution to address this challenge is to iteratively predict scene flow for"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9884"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.088,
+                0.895,
+                0.18
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.182,
+                0.895,
+                0.21
+            ],
+            "angle": 0,
+            "content": "Figure 6. 2D DT map with different grid sizes. A larger grid size results in extremely coarse DT, as the grid cell size decreases, the DT accuracy increases. Here we zoom in on the original DT map in Fig. 3 to show the detailed distance values."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.098,
+                0.224,
+                0.446,
+                0.425
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.431,
+                0.471,
+                0.515
+            ],
+            "angle": 0,
+            "content": "Figure 7. Performance of distance transform with different grid cell sizes on a 2D scene from Argoverse scene flow dataset. Generally, the larger the grid cell is, the lower the accuracy becomes. The computation time and memory consumption also decrease as the grid cell size increases (the number of grids decreases). The total grid of the DT map is of size \\(160 \\times 150\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.53,
+                0.47,
+                0.576
+            ],
+            "angle": 0,
+            "content": "small subsets of dense point clouds using learning methods. However, this approach requires intensive computation, and it might cause out-of-memory issues [32]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.576,
+                0.471,
+                0.848
+            ],
+            "angle": 0,
+            "content": "Fully supervised learning methods FlowStep3D, FLOT, PV-RAFT, and self-supervised method PointPWC-Net do not generalize to new autonomous driving datasets (see Tab. 1, Tab. 2) due to the domain gap between the training and testing datasets [15, 31, 37, 47, 51]. We provide additional performance in the supplementary material. Despite its poor performance on OOD data, FLOT achieves a competitive inference time, making it one of the fastest learning-based methods available. Note that since the weakly supervised learning method R3DSF takes supervision from object segmentation and AV ego motions and was trained on a lidar point cloud-based dataset, it has a relatively high accuracy compared to full/self-supervised learning methods, but its performance is still inferior to non-learning-based methods NSFP and our method. Such evidence strongly suggests that our method—a runtime optimization—is robust to OOD effects, and can be directly applied to applications where no training data is readily available."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Towards real-time computation. Our method attains real-time performance (121/124 ms) which is comparable to learning methods and maintains high accuracy, while"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.22,
+                0.892,
+                0.247
+            ],
+            "angle": 0,
+            "content": "Table 3. Comparison of our method and NSFP++ on Argoverse scene flow dataset with ego-motion compensation."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.516,
+                0.248,
+                0.871,
+                0.328
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>E↓(m)</td><td>Acc5↑(%)</td><td>Acc10↑(%)</td><td>θe↓(rad)</td><td>t↓(ms)</td></tr><tr><td>Ours</td><td>0.411</td><td>34.94</td><td>46.82</td><td>0.731</td><td>335</td></tr><tr><td>NSFP++ [47]</td><td>0.295</td><td>31.82</td><td>62.61</td><td>0.343</td><td>16188</td></tr><tr><td>NSFP++ (DT)</td><td>0.272</td><td>30.26</td><td>60.25</td><td>0.365</td><td>2001</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.346,
+                0.892,
+                0.407
+            ],
+            "angle": 0,
+            "content": "learning-based methods struggle to generalize on OOD data. It indicates the significant potential of applying robust and accurate runtime optimization-based methods in many vision-based applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.414,
+                0.893,
+                0.641
+            ],
+            "angle": 0,
+            "content": "Other learning methods. Learning-based scene flow methods are usually fast and achieve good accuracy when applied to in-domain small-scale data (training and testing are on the same dataset with a specific range: e.g., KITTI data with point clouds within \\(35\\mathrm{m}\\) of the scene center) with a limited number of points (usually 2,048 / 8,192 points). As discussed in [15,31,37,47,51], the domain gap is a significant challenge for learning methods—a specific dataset with specific configurations—e.g., coordinate systems, viewing directions, etc.—that match the testing data needs to be used during training. However, we are interested in exploring runtime optimization-based methods that are robust to large-scale OOD data that can be employed in many real-world applications, such as autonomous driving scenarios, where no labels are readily available."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.651,
+                0.768,
+                0.668
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation study of DT grid size"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.674,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "DT splits the space into small grid cells, while the grid size affects the accuracy, the computation time, and the memory accuracy. We provide a performance comparison using different grid cell sizes of DT in Fig. 7. A 2D visualization of DT with different grid sizes is also shown in Fig. 6. We can clearly see that a relatively small grid cell size \\((grid \\leq 0.1m)\\) is required to ensure the fidelity of the distance transform map. Note that when rasterized points are closer to the original irregular points, DT is a closer approximation to the exact Euclidean distance between two point clouds. Moreover, with a rasterized point-based DT strategy, the pre-computation of the map is no longer an overhead, and the grid cell size will largely affect the memory instead of the computation time—we trade memory consumption with computation time."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9885"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.083,
+                0.089,
+                0.47,
+                0.239
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.242,
+                0.47,
+                0.298
+            ],
+            "angle": 0,
+            "content": "Figure 8. Failure cases on Argoverse dataset. The left figure shows some noisy motions were predicted in the background. The right figure shows our method failed to predict when the motion of some cars is relatively small to the AV."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.313,
+                0.315,
+                0.329
+            ],
+            "angle": 0,
+            "content": "4.4. Speedup in other methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.337,
+                0.47,
+                0.534
+            ],
+            "angle": 0,
+            "content": "The proposed DT loss is a general loss that can be used in other 3D geometry tasks. Specifically, for optimization-based methods such as RSF [14], DT could replace the nearest neighbor distance loss to speed up the overall computation. For learning methods such as PointPWCNet [75], DT could replace Chamfer loss to speed up optimization during training, especially when dealing with a large number of points. For methods using cycle consistency, when replacing CD \\((\\mathcal{O}(N^2))\\) with DT, the forward flow computation will be substantially speeded up (similar speedup to the paper). The backward flow computation will also be speeded up even though the DT map will be computed in every optimization step."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.536,
+                0.47,
+                0.642
+            ],
+            "angle": 0,
+            "content": "We provide an example of comparing the results of our method to \\(\\mathrm{NSFP}++\\) [47] in Tab. 3. We used our version of \\(\\mathrm{NSFP}++\\) due to no publicly available official implementation. Since \\(\\mathrm{NSFP}++\\) requires ego-motion compensation, we also created an additional Argoverse scene flow dataset that removes the ego motions of autonomous vehicles. These ego motions are provided in the original Argoverse dataset [8]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.643,
+                0.471,
+                0.794
+            ],
+            "angle": 0,
+            "content": "Following [47], we define dynamic points as points that the norm between the deformed source (i.e., source point cloud deformed by the ground truth flow) and the ego-motion compensated source (i.e., the source point cloud is transformed by the ego-motion) exceeds a threshold of 0.05. All the metrics are computed only on dynamic points. During optimization, for our method, we removed the ego-motion of the point cloud and estimated the scene flow using the full point cloud, and for NSFP++, we only used dynamic points as required."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In Tab. 3, we show that our method achieves worse performance than \\(\\mathrm{NSFP}++\\) while being \\(\\sim 50\\times\\) faster. We further replaced the Chamfer distance loss used in \\(\\mathrm{NSFP}++\\) with our proposed distance transform (DT) loss, and we observed a \\(\\sim 8\\times\\) speedup. The distance transform loss can be a robust and efficient surrogate to Chamfer distance loss in many deep geometry vision tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.091,
+                0.627,
+                0.106
+            ],
+            "angle": 0,
+            "content": "4.5. Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.114,
+                0.895,
+                0.372
+            ],
+            "angle": 0,
+            "content": "One drawback of our method is that creating a DT map using rasterization can lead to discretization errors, especially when the grid size of the DT map is large. To mitigate these, it is necessary to build a DT map with relatively fine-resolution grids. In this case, the memory consumption will increase especially when dealing with high-dimensional data, such as 3D point clouds. Further engineering efforts of pre-creating an efficient high-resolution DT map are required to maintain a reasonable memory cost. However, we empirically find that in the context of scene flow estimation—specifically for scene flow in autonomous driving scenarios—a relatively smooth representation is preferred for local rigidity assumptions. Nevertheless, the tradeoff between the grid resolution, the memory consumption, and the estimation accuracy should be carefully considered and chosen based on specific real-world applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.381,
+                0.895,
+                0.487
+            ],
+            "angle": 0,
+            "content": "Failure cases. We show two typical failure cases in Fig. 8. The first case (left column) is when dynamic points are much sparser than the background, our prediction can result in noisy non-rigid motions in the background. The second case (right column) is when the dynamic motion is relatively small, our model may fail to recognize the dynamic scene and only predict rigid motions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.502,
+                0.619,
+                0.518
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.528,
+                0.895,
+                0.831
+            ],
+            "angle": 0,
+            "content": "In this work, we revisit the runtime optimization-based scene flow method NSFP and propose a method that is both efficient and generalizable to large-scale OOD data and dense lidar points. We identify that common strategies for speeding up network architectures do not yield significant time reductions—the major computation overhead is the Chamfer distance loss. Therefore, we propose to use an efficient correspondence-free distance transform loss as a robust surrogate. The rediscovery of DT in scene flow estimation opens up an innovative venue to leverage its efficiency and robustness for various deep geometry tasks. Compared to NSFP, our method maintains comparable accuracy but gains up to \\(\\sim 30\\times\\) speedups. We report for the first time a real-time performance (\\(\\sim 120\\mathrm{ms}\\)) with neural scene flow and runtime optimization when using fewer points (8,192). The efficient runtime optimization-based neural scene flow can be widely applied in lidar scenes to do point cloud densification, open-world object detection, and scene clustering, such as in autonomous driving scenarios, where no ground truth or training data are readily available."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Acknowledgement: We would like to thank Haosen Xing for the careful review of the manuscript and the help throughout the project. We thank Kavisha Vidanapathirana for the initial implementation of NSFP++ [47]."
+        },
+        {
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+# Fast Neural Scene Flow
+
+Xueqian Li\*1 Jianqiao Zheng\* Francesco Ferroni\*2 Jhony Kaesemodel Pontes\*3 Simon Lucey\*1 1The University of Adelaide 2NVIDIA 3Latitude AI
+
+![](images/42f33bc54254aecd92f7b2ef0351b6c949acfd95b315cd30d79131286e68f85a.jpg)  
+(a) Lidar depth map densification
+
+![](images/54d9e247bdfa3c4b2fa33496b37c6945f5a17ec88ca028c376d0a7bf0ca96a32.jpg)  
+(b) Efficiency of network architectures
+
+![](images/6e1324fa6d030cfc56e5cd611dac84ed3d0751e4de311ee5791ddb6be45afc55.jpg)  
+(c) Error and computation time  
+Figure 1. Scene flow is an important problem as it provides low-level motion cues for many downstream tasks. State-of-the-art learning methods are usually fast and can achieve impressive performance on in-domain data, but usually fail to generalize to out-of-the-distribution (OOD) data or handle dense point clouds. In this paper, we focus on a runtime optimization-based neural scene flow pipeline. In (a) one can see its application in the densification of lidar. However, in (c) one sees that the major drawback is the extensive computation time. We identify that the common speedup strategy in network architectures for coordinate networks has little effect on scene flow acceleration [see green (b)] unlike image reconstruction [see pink (b)]. With the dominant computational burden stemming instead from the Chamfer loss function, we propose to use a distance transform-based loss function to accelerate [see purple (b)], which achieves up to  $30 \times$  speedup and on-par estimation performance compared to NSFP [see (c)]. When tested on 8k points, it is as efficient [see (c)] as leading learning methods, achieving real-time performance.
+
+# Abstract
+
+Neural Scene Flow Prior (NSFP) is of significant interest to the vision community due to its inherent robustness to out-of-distribution (OOD) effects and its ability to deal with dense lidar points. The approach utilizes a coordinate neural network to estimate scene flow at runtime, without any training. However, it is up to 100 times slower than current state-of-the-art learning methods. In other applications such as image, video, and radiance function reconstruction innovations in speeding up the runtime performance of coordinate networks have centered upon architectural changes. In this paper, we demonstrate that scene flow is different—with the dominant computational bottleneck stemming from the loss function itself (i.e., Chamfer distance). Further, we rediscover the distance transform (DT) as an efficient, correspondence-free loss function that dramatically speeds up the runtime optimization. Our fast neural scene flow (FNSF) approach reports for the first time real-time performance comparable to learning methods,
+
+*Part of the work was done while at Argo AI. Corresponding e-mail: xueqian.li@adelaide.edu.au. Code available at https://github.com/Lilac-Lee/FastNSF.git
+
+without any training or OOD bias on two of the largest open autonomous driving (AV) lidar datasets Waymo Open [62] and Argoverse [8].
+
+# 1. Introduction
+
+Neural Scene Flow Prior (NSFP) [37] is considered the dominant method in open-world perception [47] and scene densification [37, 69] using lidar (see Fig. 1 (a)). NSFP achieves state-of-the-art scene flow estimates from dense lidar point clouds (up to  $150\mathrm{k}+$  points) and works on a variety of sensor setups with little to no refinement or adaptation. Unlike supervised or unsupervised learning-based methods, NSFP does not require learning from large offline datasets and has no limits on point density ( $<8\mathrm{k}$  for most learning methods). Instead, it leverages the architecture of a neural network to implicitly regularize the flow estimate and employs a runtime optimization that can easily scale to large out-of-distribution (OOD) scenes, which is a challenge for current learning-based methods [15, 31, 37, 47, 51].
+
+A fundamental drawback, however, to NSFP is the speed of its runtime optimization which is in some instances of orders of magnitude slower than its learning counterparts
+
+(see Fig. 1). As a result, NSFP has widely been used offline for (i) providing scene flow supervision for efficient learning methods and (ii) as a pre-processing step for training open-world perception systems [47]. However, the considerable computational cost of NSFP limits its current applications only to these offline tasks.
+
+A central narrative of our approach is that the dominant computational burden in runtime scene flow optimization (NSFP) is not the network architecture, but the loss function—specifically Chamfer distance (CD) [17]. This differs considerably from other applications of coordinate networks throughout vision and learning such as neural radiance fields (NeRF [44]) and high-fidelity image reconstruction ([61]) which have gained significant speedups through architectural innovations [83]. A visual depiction of this discrepancy can be found in Fig. 1 (b).
+
+Key to our approach is the use of correspondence-free loss function—distance transform (DT) [5, 13, 58] as a proxy for the computationally expensive CD loss. Even though DT has been extensively studied by the graphics and vision community over a few decades, its application as an efficient loss function in deep geometry has largely been overlooked up until this point. We believe that the inherent efficiencies of the DT are especially pertinent for runtime network training such as in NSFP. Our approach shares similarities with Plenoxels [81]—a recent approach for efficient radiance field estimation using coordinate networks—as we trade memory consumption for computation time, allowing for significant speedups during runtime, which provides an alternative solution when exploring more efficient loss functions for dense scene flow estimation. We differ from Plenoxels, however, in that our memory consumption stems from our proposed loss function, not the neural architecture itself.
+
+In this paper, we present for the first time an approximately real-time (for 8k points) runtime optimization method as computationally efficient as leading learning methods whilst preserving the scalability to dense point clouds and state-of-the-art performance on OOD scenes like NSFP. We compare the performance and the computation time of our approach on two of the largest open lidar AV datasets available: Waymo Open [62] and Argoverse [8]. Our fast neural scene flow achieves up to  $\sim 30$  times speedup than NSFP [37] (our faster implementation) and of comparable speed to leading learning-based methods (see Fig. 1 (c)) with the same number of points (8,192). It opens up the possibility of employing a fast, robust, and generalizable approach for dense scene flow, which is not prone to OOD effects in real-time vision and robotic applications.
+
+# 2. Related work
+
+Scene flow estimation. Scene flow denotes the motion field in 3D space [67] uplifted from 2D optical flow. To reconstruct 3D flow, traditional image-based methods [2, 24,
+
+25,27,28,36,53] formulate an optimization problem utilizing RGB or depth information, and learning-based RGB/RGB-D methods [6, 29, 30, 57, 60, 64, 78] rely on single/multiple image features which encode with a large amount of data supervisions. On the other hand, to estimate scene flow directly from 3D, traditional point cloud-based methods [1, 11, 50] solve for a non-rigid registration problem, while recent work prefers full-supervised learning [23, 34, 38, 39, 52, 71, 73, 75] that uses point-based features or self-supervised learning [3, 21, 45, 65, 75] that employs a self-supervised loss. Recent non-learning-based methods [37, 51] draw our attention back to runtime optimization that easily scales to large data. Graph prior [51] explicitly builds a graph on the point cloud and uses a graph Laplacian regularizer. While neural scene flow prior [37] uses the network as an implicit regularizer to smooth motions. In this paper, we explore point cloud-based scene flow using runtime optimization.
+
+Accelerating coordinate networks. There exists a line of work [9, 20, 26, 46, 56, 81, 82] that focuses on accelerating coordinate networks by trading slow, memory efficient, deep network architectures for fast, memory hungry, shallow architectures. Most of these innovations have been applied to the problem of neural radiance fields most notably Plenoxels [81] and TensorRF [9]. Recently, this trend was generalized for arbitrary signals through the introduction of complex positional encoding [83] with shallow linear networks. In this paper, we claim that these architectural innovations have little utility in speeding up neural scene flow without first addressing the computational cost of the Chamfer loss it uses.
+
+Distance transform. DT [4, 5, 13, 41, 58] has played an important role in image processing, especially binary image analysis [48, 66]. Further applications are also found in medical image segmentation [12, 33, 59, 70, 72], robotics motion planning [55, 76], geometric representation [7, 10, 49], and accelerated point cloud registration [19, 79]. Among them, various distance measures have been used, such as city block, chessboard, and Euclidean distance [13, 77]. Naturally, Euclidean distance is preferred in computing point distance but it is also the most difficult metric to compute due to the temporal complexity [22]. Many work attempts to speedup Euclidean DT computation including raster-scan-based algorithms [5, 18, 35, 41, 54], fast marching-based algorithms [16, 40, 68], etc., and has achieved linear time computation. In this paper, we investigate the raster-scan-based algorithm for the 3D point cloud.
+
+# 3. Approach
+
+# 3.1. Background
+
+Scene flow optimization. Suppose we have a moving sensor (e.g., lidar mounted on a car, depth camera tied to a robot, etc.) collecting point cloud in a dynamic environment.
+
+At time  $t-1$ , a point cloud  $S_{1}$  (source) of the scene is sampled. Then given the movements of the sensor and objects in certain directions, another point cloud  $S_{2}$  (target) is sampled at time  $t$ . In order to find out all the motions in the environment, we model the translation of each point cloud  $\mathbf{p} \in S_{1}$  from time  $t-1$  to time  $t$  as a flow vector  $\mathbf{f} \in \mathbb{R}^{3}$ , where  $\mathbf{p}' = \mathbf{p} + \mathbf{f}$ . The translational vector set of all 3D points in  $S_{1}$  is defined as the scene flow  $\mathcal{F} = \{\mathbf{f}_i\}_{i=1}^{|S_1|}$ .
+
+Therefore, the optimization of the scene flow is to minimize the point distance between the source  $S_{1}$  and the target  $S_{2}$ . Usually, a regularization C, such as a Laplacian regularizer, is needed due to the highly unconstrained non-rigid flows. The overall optimization becomes
+
+$$
+\mathcal {F} ^ {*} = \underset {\mathcal {F}} {\arg \min } \sum_ {\mathbf {p} \in \mathcal {S} _ {1}} \mathrm {D} (\mathbf {p} + \mathbf {f}, \mathcal {S} _ {2}) + \lambda \mathrm {C}, \tag {1}
+$$
+
+where  $D$  is a point distance function,  $\lambda$  is a coefficient of the regularizer  $C$ .
+
+Neural scene flow prior. NSFP uses traditional runtime optimization to optimize a neural network. Different from learning-based methods, NSFP does not rely on any prior knowledge of large-scale datasets. And different from traditional scene flow optimization with an explicit regularizer that is mentioned above, neural scene flow prior optimizes parameters of a network which implicitly imposes a regularization by its structure:
+
+$$
+\boldsymbol {\Theta} ^ {*} = \underset {\boldsymbol {\Theta}} {\arg \min } \sum_ {\mathbf {p} \in \mathcal {S} _ {1}} D (\mathbf {p} + g (\mathbf {p}; \boldsymbol {\Theta}), \mathcal {S} _ {2}). \tag {2}
+$$
+
+where  $\Theta$  is a parameter set of network  $g$  to be optimized.  $\mathbf{p}$  is the input source point, and the flow  $\mathbf{f} = g(\mathbf{p};\Theta)$  is the output of the network. The optimization converges at  $\mathbf{f}^{*} = g(\mathbf{p};\Theta^{*})$ . The network  $g$  here is chosen to be a commonly used ReLU-MLP.
+
+Since the points in source  $S_{1}$  and target  $S_{2}$  are not in correspondence, nor having the same number of points, i.e.,  $|S_{1}| \neq |S_{2}|$ , we use a distance function that handles these problems as
+
+$$
+D (\mathbf {p}, \mathcal {S}) = \min  _ {\mathbf {x} \in \mathcal {S}} \| \mathbf {p} - \mathbf {x} \| _ {2} ^ {2}. \tag {3}
+$$
+
+Practically, a bidirectional point distance is found, yielding the above equation equivalent to the Chamfer loss [17].
+
+Chamfer distance. In point cloud processing, Chamfer distance (CD) [17] is an important loss function and metric for computing the point distance of two point clouds that do not necessarily have points in correspondence. Chamfer distance loss computes the point distance of both source-to-target and target-to-source directions. In detail, the CD loss
+
+![](images/ba3b70147a46e9e29a4960e668728d47221fffca4b4b58831470bca793841440.jpg)  
+ Initialized DT map  
+Figure 2. An example of how to build a DT map of 2D points. The initialized DT map is set to all zeros. The rasterized 2D point image is set to zero if a point is presented in the grid, and set to one if the grid contains no points. After computation, the final DT map is shown in the right figure.
+
+![](images/7dd8f1cd9ae17d1b5cd46d33439fd7062dcd1a12de5feafccfb2e358b359ebc4.jpg)  
+Rasterized 2D points
+
+![](images/0790784cd9f52965c075bbf94be5651102e85302f5870c4b294403ca2ebde626.jpg)  
+Computed DT map
+
+can be written as
+
+$$
+\begin{array}{l} C D \left(\mathcal {S} _ {1}, \mathcal {S} _ {2}\right) = \sum_ {\mathbf {p} \in \mathcal {S} _ {2}} \mathrm {D} \left(\mathbf {p}, \mathcal {S} _ {1}\right) + \sum_ {\mathbf {q} \in \mathcal {S} _ {1}} \mathrm {D} \left(\mathbf {q}, \mathcal {S} _ {2}\right) \\ = \sum_ {\mathbf {p} \in \mathcal {S} _ {2}} \min  _ {\mathbf {x} \in \mathcal {S} _ {1}} \| \mathbf {p} - \mathbf {x} \| _ {2} ^ {2} + \sum_ {\mathbf {q} \in \mathcal {S} _ {1}} \min  _ {\mathbf {y} \in \mathcal {S} _ {2}} \| \mathbf {q} - \mathbf {y} \| _ {2} ^ {2}. \tag {4} \\ \end{array}
+$$
+
+To compute the point distance, correspondences from source-to-target and target-to-source are searched among the nearest point neighbors. However, the exhaustive point correspondence search is extremely slow, especially when dealing with dense point clouds that contain more than 10k points (e.g., in Waymo Open and Argoverse datasets, the number of points can be up to  $150\mathrm{k}+$ ).
+
+# 3.2. Correspondence-free point distance transform
+
+DT is widely used in 2D image processing, such as segmentation, boundary detection, pattern matching, skeletonization, etc. However, general usage in irregular and unordered 3D point cloud tasks is not broadly discussed. Given that the image grid is regular and ordered, a DT map is easily obtained by computing the minimum distance of each sampled point  $\mathbf{x} \in S$  to the vertex  $\mathbf{q}$  of a DT map  $\mathcal{G}$  as
+
+$$
+\mathrm {D T} (\mathbf {q}) = \min  _ {\mathbf {x} \in \mathcal {S}, \mathbf {q} \in \mathcal {G}} \mathrm {D} (\mathbf {x}, \mathbf {q}). \tag {5}
+$$
+
+We extend Eq. (5) to fit in the scene flow task such that  $\mathbf{D}$  refers to Euclidean distance,  $\mathbf{x}$  denotes the target point, and  $\mathbf{q}$  is the regularly spaced point in a voxel (3D).
+
+Approximation of DT map. However, with a large number of points in a point cloud and the grid map, directly computing Eq. (5) builds high dimensional matrices which will lead to large memory occupation. Even when we presume that each axis of the grid/voxel is separable, and the distance per axis is pre-computed, the memory consumption is still huge that cannot be processed on a single GPU. One strategy is to iteratively aggregate small
+
+![](images/6a84d27d465517007a9ffc68a9a9e3ec3d25ae3c38ca967d7222e543f43f026f.jpg)  
+Figure 3. Distance transform map of a target point cloud in Argoverse dataset. Purple points are the target, and green points are the source. It is important to note that the DT map is constructed from the target points, and the source points are only shown for reference purposes. The colormap denotes the DT values (in meters), with light yellow denoting a smaller distance and dark purple indicating a larger distance.
+
+matrix multiplications while at a cost of extensive time consumption. Another strategy is to use k-d tree query to compute the Euclidean distance. Building a k-d tree is one-time computing, but querying from a large point set to an even larger k-d tree is expensive.
+
+Instead, we use a fast distance approximation by rasterizing the irregular points onto the nearest regular cuboid/grid. Specifically, similar to classical efficient binary image-based DT methods [12, 18], we construct two 3D binary images for target points and an initialized DT map. An example of 2D DT map is shown in Fig. 2. Specifically, the DT map is set to be all zeros, and the target binary image pixel is set to one when the grid contains no target points in it. Then a two-pass raster scan-based algorithm [18] is applied to each axis to compute the final DT, which means a 3D image needs six propagation passes (left to right, right to left, front to back, back to front, top to bottom, bottom to top). Although we rasterize target points using a binary 3D image approximation, we still compute the exact Euclidean distance between these two binary images instead of an approximated point distance. We empirically find that such discretization does not hurt performance. One reason is the local rigidity of the scene flow benefits from reasonably small but not necessarily infinitesimal DT grids/voxels.
+
+A visualization of a 2D bird's eye view (BEV) DT map is presented in Fig. 3, where we see that when the point density is large, the distance value is relatively small, and the distance value becomes extremely large when no points exist. By choosing an appropriate grid size, the pattern of DT is distinct among different points while
+
+maintaining a relatively smooth structure in the neighboring area. Evidently, the correspondence-free distance transform can act as an effective and efficient surrogate for point correspondence-based Chamfer loss.
+
+DT query and loss function. Once a DT map is built for the target point cloud, we can look up the pre-computed DT map to get the distance of the nearest source point in an extremely fast fashion. The loss function becomes the queried Euclidean distance between the target and the nearest deformed source points:
+
+$$
+\mathcal {L} = \min  _ {\mathbf {y} \in \mathcal {S} ^ {\prime}, \mathbf {q} \in \mathcal {G}} \| \mathbf {y} - \mathbf {q} \| _ {2}, \tag {6}
+$$
+
+where  $S'$  is the deformed source point cloud. Unlike CD loss, no point correspondence search is required in Eq. (6), making the DT query exceptionally fast. Further ablation studies can be found in Sec. 4.3.
+
+# 4. Experiments
+
+Datasets We are primarily interested in scene flow methods that are well-suited for large-scale, realistic, lidar-based OOD scenes, which are commonly encountered in autonomous driving (AV) applications. To this end, we focus on two AV datasets: Waymo Open [62] and Argoverse [8], which contain numerous challenging dynamic scenes. Unfortunately, no ground truth annotations were provided for the open-world dataset. We pre-processed the Argoverse and Waymo Open pseudo ground truth scene flow datasets following [37, 51] and [31, 80] respectively.
+
+Metrics We follow scene flow metrics used in [37, 38, 45, 51, 75] to evaluate the performance. We also include the computation time breakdown in the table. These metrics are:
+
+1) 3D end-point error  $\mathcal{E}(m)$  that measures the mean absolute point distance between estimated and target points;  
+2) strict accuracy  $Acc_5(\%)$ , which is the accuracy of the estimated flow that satisfies the absolute point error  $\mathcal{E} < 0.05\mathrm{m}$  or the relative point error  $\mathcal{E}' < 5\%$ ;  
+3) relaxed accuracy  $Acc_{10}(\%)$ , which is the accuracy of the estimated flow that satisfies the absolute point error  $\mathcal{E} < 0.1\mathrm{m}$  or the relative point error  $\mathcal{E}' < 10\%$ ;  
+4) angle error  $\theta_{\epsilon}(rad)$  that measures the mean angle error (in radiance) of the estimated and the pseudo ground truth translational vectors.  
+5) computation time  $t(ms)$  breaks down to four parts. Pre-compute includes data loading and building a DT map. Corr. / DT query counts the time needed to search point correspondences or query point distance within a DT map. We also include computation time for Network forward and backward propagation. Finally, Total time in seconds / milliseconds is measured.
+
+Implementation details We provide the details of implementation for each algorithm we compared. Further information can be found in the supplementary materials.
+
+1) NSFP [37]. The original implementation is extremely slow. Based on the official code released by the authors while keeping the same parameter settings specified in the original paper, we implemented a faster version (NSFP) for a fair comparison. Note that to reflect the independence of each pair of point clouds when estimating scene flow, we randomly initialized the network before each optimization.  
+2) Baseline. Note that although the backward flow enforces a cycle consistency between the deformed point cloud and the original point cloud, we empirically found that removing cycle consistency does not hurt the overall performance when dealing with dense lidar point clouds, but improves the computational efficiency. Here we removed the backward flow in the original NSFP and implemented a NSFP (baseline) version as our baseline for a fair comparison—all computation times were compared with this model. We further modified the baseline model using a linear model with complex positional encodings (NSFP (baseline, linear)) to demonstrate the effect of network architecture changes. Detailed explanations can be found in Sec. 4.1 and the supplementary material.  
+3) Ours. We implemented a DT-based neural scene flow method with 8-layer ReLU-MLPs (Ours). We chose the grid cell size of the DT map to be 0.1 meters. Ablation studies on the choice of grid cell size can be found in Sec. 4.3. We further modified our method using a linear model with complex positional encodings (Ours (linear)) to demonstrate the effect of network architecture changes.  
+4) FlowStep3D [34] and FLOT [52] are fully supervised methods trained on synthetic FlyingThings3D [42] datasets. PointPWC-Net [75] can be used as a self-supervised method. We used the official code released by the authors and directly tested the pretrained model (pretrained on FlyingThings3D) on our datasets. However, as full/self-learning-based methods, they performed poorly on OOD datasets, which is also observed in [15, 31, 37, 47, 51]. Here we only chose the method with the best performance and the lowest computation time—FLOT—for comparison in the main table. The comparison of other learning-based methods is included in the supplementary material. R3DSF [21] is a weakly supervised method with no direct supervision of ground truth dynamic flows. We tested the method using the pretrained model (on KITTI [43]) provided by the authors.
+
+All models were implemented using CUDA 11.6-supported PyTorch. All experiments were run on a computer with a single NVIDIA RTX 3090Ti GPU and a 24 AMD Ryzen 95900X 12-Core CPU @ 4.95GHz.
+
+![](images/5a10fe8f3f5c48187796ab4ce9a77c3e4a182690a2b61eb3c1266e88e34bee3b.jpg)  
+Figure 4. Illustration of 3D complex PE in scene flow problem. The 3D space of source points (yellow) and target points (green) is divided into small cubes. The number of cubes on each axis differs but the edge length is the same. Encoding of a point in a certain grid is the blending/interpolation of encodings of all 8 grid vertices. These grid points (blue) are encoded by complex PE along each axis. Note the vec and outer product  $(\times)$  notation is for better visual understanding and it is equivalent to the Kronecker product.
+
+# 4.1. Speedup in network architecture
+
+Plenoxels [81] is a method that accelerates NeRF [44] optimization by replacing deep neural networks with voxel-based spherical harmonics representations, leading to efficient volume rendering. Similar network speedup approaches can also be used in neural scene flow optimization. We incorporate recent innovations in positional encodings, specifically complex positional encoding (complex PE) [83] to represent high-frequency signals and enable a linear reconstruction model which is similar in spirit to [81].
+
+Complex positional encodings Positional encodings (PEs) are encodings for input positions—e.g., 2D image grids, 3D voxel grids, etc.—that are usually used in coordinate networks. PEs has been shown to improve the performance and convergence speed of coordinate networks [63]. Simple PE is a simple concatenation of the encoding in each input dimension, while a complex PE is a more complicated encoding that computes the Kronecker product of the per-dimension encoding. An illustration of complex PE of scene flow is shown in Fig. 4.
+
+With a complex PE and a linear model parameterized by  $\mathbf{W} \in \mathbb{R}^{W_x W_y W_z \times 3}$ , the scene flow can be represented as
+
+$$
+\mathbf {f} \approx \mathbf {B} (\mathbf {p}; \phi) \operatorname {v e c} \left(\phi (\mathbf {x}) \mathbf {W} \phi (\mathbf {z}) ^ {T} \phi (\mathbf {y}) ^ {T}\right), \tag {7}
+$$
+
+where  $\mathbf{B}(\cdot)$  is the blending function,  $\phi (\cdot)$  is the encoder,  $\phi (\mathbf{x})\mathbf{W}\phi (\mathbf{z})^T\phi (\mathbf{y})^T$  is a simple notation for  $n$  -mode multiplication, which is equivalent to Kronecker product. The blending function interpolate the 3D regular grid encodings to handle the irregular and unordered nature of 3D point clouds. Additional details of complex PE can be found in the supplementary materials.
+
+Table 1. Computation time and performance on Waymo Open Scene Flow dataset. We generated 202 testing scene flow examples where each point cloud has 8k-144k points. The upper tabular between blue bars are experiments with the full point cloud, and the lower tabular between orange bars are experiments with only 8,192 points. All query time is listed as: time per optimization step [total query time]. The speedups are marked with green  $\times$  numbers, and the slow-downs are marked with red  $\times$ . The computation time of using full point cloud is compared to values in the red box, and the computation time of using 8,192 points is compared to values in green box. Bold texts are the best performance, and underlined texts denote the second-best performance.  $\uparrow$  means larger values are better while  $\downarrow$  means smaller values are better. Corr. / DT query denotes correspondence search or DT query. Note: performance of learning methods PointPWC-Net [75], FlowStep3D [34], PV-RAFT [74] can be found in the supplementary material.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">ε(m)↓</td><td rowspan="2">Acc5(%)↑</td><td rowspan="2">Acc10(%)↑</td><td rowspan="2">θe(rad)↓</td><td colspan="4">t (ms) ↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.100</td><td>76.62</td><td>88.56</td><td>0.286</td><td>—</td><td>114 [30972]</td><td>4.62 [1361]</td><td>35.51 s</td></tr><tr><td>NSFP (baseline)</td><td>0.118</td><td>74.16</td><td>86.70</td><td>0.300</td><td>—</td><td>43.1 [15036]</td><td>2.38 [904]</td><td>18.39 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.096</td><td>70.78</td><td>86.31</td><td>0.310</td><td>9.48</td><td>40.38 [8037] | 1.1×</td><td>1.53 [319] | 1.6×</td><td>10.20 s | 1.80×</td></tr><tr><td>Ours</td><td>0.072</td><td>84.73</td><td>92.24</td><td>0.280</td><td>40.85</td><td>0.25 [13] | 172×</td><td>2.89 [149] | 1.2×</td><td>0.58 s | 31.7×</td></tr><tr><td>Ours (linear)</td><td>0.109</td><td>71.27</td><td>85.80</td><td>0.321</td><td>44.88</td><td>0.23 [19] | 187×</td><td>1.62 [138] | 1.5×</td><td>0.49 s | 37.5×</td></tr><tr><td>FLOT [52]</td><td>0.702</td><td>2.46</td><td>11.30</td><td>0.808</td><td>—</td><td>—</td><td>—</td><td>99 ms</td></tr><tr><td>R3DSF [21]</td><td>0.414</td><td>35.47</td><td>44.96</td><td>0.527</td><td>—</td><td>—</td><td>—</td><td>140 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.138</td><td>53.62</td><td>78.57</td><td>0.339</td><td>—</td><td>5.42 [1285] | 21×</td><td>4.44 [1051] | 1.1×</td><td>2459 ms | 17.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.106</td><td>77.53</td><td>88.99</td><td>0.329</td><td>35.22</td><td>0.23 [6.5] | 496×</td><td>2.60 [76] | 1.8×</td><td>121 ms | 1.16×</td></tr></table>
+
+Table 2. Computation time and performance on Argoverse Scene Flow dataset. Argoverse has 212 testing scene flow examples where each point cloud has  $30\mathrm{k - }70\mathrm{k}$  points. Notations are the same as in the table above.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">ε(m)↓</td><td rowspan="2">Acc5(%)↑</td><td rowspan="2">Acc10(%)↑</td><td rowspan="2">θe(rad)↓</td><td colspan="4">t (ms)↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.069</td><td>71.56</td><td>87.80</td><td>0.235</td><td>—</td><td>47 [14310]</td><td>4.66 [1507]</td><td>18.08 s</td></tr><tr><td>NSFP (baseline)</td><td>0.078</td><td>69.46</td><td>86.22</td><td>0.253</td><td>—</td><td>17 [5901]</td><td>2.31 [848]</td><td>8.38 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.097</td><td>67.03</td><td>83.20</td><td>0.314</td><td>9.19</td><td>14.7 [2786] | 1.1×</td><td>1.51 [297] | 1.5×</td><td>3.55 s | 2.36×</td></tr><tr><td>Ours</td><td>0.071</td><td>80.05</td><td>90.71</td><td>0.289</td><td>43.61</td><td>0.24 [14] | 71×</td><td>2.57 [149] | 1.1×</td><td>0.51 s | 16.4×</td></tr><tr><td>Ours (linear)</td><td>0.106</td><td>65.00</td><td>82.85</td><td>0.319</td><td>48.59</td><td>0.23 [20] | 74×</td><td>1.69 [149] | 1.4×</td><td>0.43 s | 19.5×</td></tr><tr><td>FLOT [52]</td><td>0.821</td><td>2.00</td><td>8.84</td><td>0.967</td><td>—</td><td>—</td><td>—</td><td>88 ms</td></tr><tr><td>R3DSF [21]</td><td>0.417</td><td>32.52</td><td>42.52</td><td>0.551</td><td>—</td><td>—</td><td>—</td><td>113 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.113</td><td>46.32</td><td>72.68</td><td>0.347</td><td>—</td><td>5.40 [1500] | 8.7×</td><td>4.42 [1233] | 1.1×</td><td>2864 ms | 25.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.118</td><td>69.93</td><td>83.55</td><td>0.352</td><td>41.57</td><td>0.22 [6.33] | 214×</td><td>2.51 [72.69] | 1.9×</td><td>124 ms | 1.10×</td></tr></table>
+
+Network speedup comparison We would like to point out that although various strategies have been proposed to accelerate network architectures, they do not lead to substantial speedup in neural scene flow estimation. To demonstrate this, we compare the relative efficiency of using 8-layer Relu-MLPs and complex PE with a linear model in both 2D image reconstruction and 3D scene flow tasks, shown in Fig. 1 (b). In detail, following [83], we used a size of  $256 \times 256$  image dataset for image reconstruction. For a fair comparison, the relative efficiency is obtained by normalizing the computation time of two tasks. The computation time of single image reconstruction is  $17.63\mathrm{s}$  and  $0.15\mathrm{s}$  for deep network and linear network respectively, leading to  $118 \times$  speedup. However, the linear model only results in  $\sim 2 \times$  and  $\sim 1.2 \times$  speedup for NSFP and our method respectively. Our results show that complex PE-based speedup achieves significant acceleration in 2D image reconstruction compared to deep neural networks, but the
+
+benefits of such speedup are more limited when estimating neural scene flow. More detailed comparisons are in Sec. 4.2.
+
+# 4.2. Comparison of performance
+
+We show the performance of our method with different variants compared to NSFP, FLOT, and R3DSF on Waymo Open (Tab. 1) and Argoverse (Tab. 2) scene flow datasets. We denote results on Waymo Open (xx) and Argoverse (yy) as xx/yy. Visual results and applications of densification are shown in Fig. 5 and supplementary materials.
+
+Dense scene flow estimation. For dense point clouds, the baseline NSFP took  $18.39 / 8.38$  s to converge. When replacing the 8-layer MLPs with a linear network and applying complex PE, we observed a speedup of only  $1.80 / 2.36 \times$  in total, primarily due to the network propagation speedup. When we replaced naive CD loss with the DT loss, a significant  $31.7 / 16.4 \times$  speedup was achieved while
+
+![](images/2e9861c823f7c6bac92698a5310c18a16c04b8e19ed13482c9b76b4b643903a0.jpg)  
+Figure 5. Visual examples of the scene flow prediction using our method on Argoverse dataset. We show 3 different autonomous driving scenarios where the autonomous vehicle (AV) was making a right turn (left), the AV stopped for crossing traffic (middle), and the AV was driving in the city (right). We found that the scene flow predicted by our method is close to the ground truth flows. The upper left corner color wheel indicates the flow magnitude (color intensity) and the flow direction (angle). For example, the yellow vehicles in the middle figure are heading south with a relatively large speed wrt the AV.
+
+![](images/91f49666f983474bc02a473e24bb5441b7e50c4a0a9ff0f768bb2ea35f7eabb7.jpg)
+
+![](images/b7e913dc4fcec0412dfd141d88d574f1fb57e1ba605810710b179b0fb59b6982.jpg)
+
+maintaining comparable high accuracy. However, replacing a deep network with a linear model when using DT loss only resulted in an additional  $1.2 / 1.2 \times$  speedup at the cost of a decrease in flow accuracy. Specifically, the total computation time of our proposed method with DT loss is  $0.58 / 0.51$  s, and with DT loss and a linear model is  $0.49 / 0.43$  s. However, with a marginal decrease in computation time, we observed a relatively large drop in performance such that the strict accuracy of our method with DT is  $84.73 / 80.05\%$  and  $71.27 / 65.00\%$  with DT and a linear model. These results strongly support our argument in the previous section, which is the general strategy of simplifying or replacing network architectures to accelerate coordinate networks is not particularly effective when optimizing scene flow through coordinate networks.
+
+Overall, the performance of our method using DT loss has on-par performance compared to NSFP while being orders of magnitude faster. We have noticed that there is an "improved accuracy" of our method compared to NSFP in Tab. 1, Tab. 2 based on these facts: 1. The performance of our method and NSFP is similar—our method achieves slightly higher performance on some metrics (e.g., accuracy), and NSFP achieves slightly higher performance on other metrics (e.g., angular error). These results indicate that distance transform (DT) is an effective and efficient surrogate for the Chamfer distance (CD) in the scene flow problem. 2. Compared to the "exact" point distance (CD), DT queries the distance based on a voxelized DT map, which naturally smooths the flow estimation. In real-world applications, we believe using a DT-accelerated deep network model will achieve both high-fidelity accuracy and efficient computation.
+
+Computation time breakdown. A detailed time breakdown is provided in both tables, including pre-computation, correspondence search / DT distance query, and network forward / backward propagation. The naive
+
+Chamfer distance requires per-point correspondence search, which can be extremely slow (43.1/17 ms per iteration), especially when the point cloud is denser. For instance, correspondence search is much slower in the Waymo Open dataset than in the Argoverse dataset since Waymo Open has an average of 90k points while Argoverse has an average of 50k points in a single point cloud. DT query is a pre-defined table lookup that is exceptionally faster than the naive point correspondence search, achieving a remarkable  $172 / 71 \times$  speedup per optimization step—the main contributor to the overall efficiency of our method. Note that the pre-computing of the DT map ( $\sim 40$  ms) is acceptable given that it is one-time computing and the total computation time is in the range of hundreds of milliseconds. Additional complex PE and a linear model only provide a modest speedup of  $1.6 / 1.5 \times$  in the network propagation step. Further optimization of the pre-computation and faster implementation can be achieved with full-CUDA support. Note that although in NSFP, the CD loss was implemented using PyTorch3D with CUDA acceleration, it still requires significant computation time, indicating its inherent limitations that cannot be easily overcome through engineering techniques alone.
+
+OOD generalizability. We further extend our model using fewer points (8,192 points) to accommodate for a fair comparison against learning-based methods [21, 34, 52, 74, 75]. For these learning models, a fixed number of points is required and they only operate on fewer points, such as 2,048 [38, 52] or 8,192 points [21, 34, 52, 75]. Also, these learning methods need to crop the point cloud to a small range. Therefore, learning models cannot be easily adapted to large-scale dense point clouds. Jund et al. explored to inference dense point cloud [32], but they did not directly process the full point cloud as the input. A simple solution to address this challenge is to iteratively predict scene flow for
+
+![](images/af6b5027363274c10f701a2258a6af4bcd00496558e6f9e6d1c6a18196da739b.jpg)  
+Figure 6. 2D DT map with different grid sizes. A larger grid size results in extremely coarse DT, as the grid cell size decreases, the DT accuracy increases. Here we zoom in on the original DT map in Fig. 3 to show the detailed distance values.
+
+![](images/15adaa81bf4cde9f36025e1253d956535536de24f27302b4254f5000964c02b6.jpg)  
+Figure 7. Performance of distance transform with different grid cell sizes on a 2D scene from Argoverse scene flow dataset. Generally, the larger the grid cell is, the lower the accuracy becomes. The computation time and memory consumption also decrease as the grid cell size increases (the number of grids decreases). The total grid of the DT map is of size  $160 \times 150$ .
+
+small subsets of dense point clouds using learning methods. However, this approach requires intensive computation, and it might cause out-of-memory issues [32].
+
+Fully supervised learning methods FlowStep3D, FLOT, PV-RAFT, and self-supervised method PointPWC-Net do not generalize to new autonomous driving datasets (see Tab. 1, Tab. 2) due to the domain gap between the training and testing datasets [15, 31, 37, 47, 51]. We provide additional performance in the supplementary material. Despite its poor performance on OOD data, FLOT achieves a competitive inference time, making it one of the fastest learning-based methods available. Note that since the weakly supervised learning method R3DSF takes supervision from object segmentation and AV ego motions and was trained on a lidar point cloud-based dataset, it has a relatively high accuracy compared to full/self-supervised learning methods, but its performance is still inferior to non-learning-based methods NSFP and our method. Such evidence strongly suggests that our method—a runtime optimization—is robust to OOD effects, and can be directly applied to applications where no training data is readily available.
+
+Towards real-time computation. Our method attains real-time performance (121/124 ms) which is comparable to learning methods and maintains high accuracy, while
+
+Table 3. Comparison of our method and NSFP++ on Argoverse scene flow dataset with ego-motion compensation.  
+
+<table><tr><td>Method</td><td>E↓(m)</td><td>Acc5↑(%)</td><td>Acc10↑(%)</td><td>θe↓(rad)</td><td>t↓(ms)</td></tr><tr><td>Ours</td><td>0.411</td><td>34.94</td><td>46.82</td><td>0.731</td><td>335</td></tr><tr><td>NSFP++ [47]</td><td>0.295</td><td>31.82</td><td>62.61</td><td>0.343</td><td>16188</td></tr><tr><td>NSFP++ (DT)</td><td>0.272</td><td>30.26</td><td>60.25</td><td>0.365</td><td>2001</td></tr></table>
+
+learning-based methods struggle to generalize on OOD data. It indicates the significant potential of applying robust and accurate runtime optimization-based methods in many vision-based applications.
+
+Other learning methods. Learning-based scene flow methods are usually fast and achieve good accuracy when applied to in-domain small-scale data (training and testing are on the same dataset with a specific range: e.g., KITTI data with point clouds within  $35\mathrm{m}$  of the scene center) with a limited number of points (usually 2,048 / 8,192 points). As discussed in [15,31,37,47,51], the domain gap is a significant challenge for learning methods—a specific dataset with specific configurations—e.g., coordinate systems, viewing directions, etc.—that match the testing data needs to be used during training. However, we are interested in exploring runtime optimization-based methods that are robust to large-scale OOD data that can be employed in many real-world applications, such as autonomous driving scenarios, where no labels are readily available.
+
+# 4.3. Ablation study of DT grid size
+
+DT splits the space into small grid cells, while the grid size affects the accuracy, the computation time, and the memory accuracy. We provide a performance comparison using different grid cell sizes of DT in Fig. 7. A 2D visualization of DT with different grid sizes is also shown in Fig. 6. We can clearly see that a relatively small grid cell size  $(grid \leq 0.1m)$  is required to ensure the fidelity of the distance transform map. Note that when rasterized points are closer to the original irregular points, DT is a closer approximation to the exact Euclidean distance between two point clouds. Moreover, with a rasterized point-based DT strategy, the pre-computation of the map is no longer an overhead, and the grid cell size will largely affect the memory instead of the computation time—we trade memory consumption with computation time.
+
+![](images/0996e1206160f744f23a64b3f5acd1a7afd1097427d6480dae328ef0df70051d.jpg)  
+Figure 8. Failure cases on Argoverse dataset. The left figure shows some noisy motions were predicted in the background. The right figure shows our method failed to predict when the motion of some cars is relatively small to the AV.
+
+# 4.4. Speedup in other methods
+
+The proposed DT loss is a general loss that can be used in other 3D geometry tasks. Specifically, for optimization-based methods such as RSF [14], DT could replace the nearest neighbor distance loss to speed up the overall computation. For learning methods such as PointPWCNet [75], DT could replace Chamfer loss to speed up optimization during training, especially when dealing with a large number of points. For methods using cycle consistency, when replacing CD  $(\mathcal{O}(N^2))$  with DT, the forward flow computation will be substantially speeded up (similar speedup to the paper). The backward flow computation will also be speeded up even though the DT map will be computed in every optimization step.
+
+We provide an example of comparing the results of our method to  $\mathrm{NSFP}++$  [47] in Tab. 3. We used our version of  $\mathrm{NSFP}++$  due to no publicly available official implementation. Since  $\mathrm{NSFP}++$  requires ego-motion compensation, we also created an additional Argoverse scene flow dataset that removes the ego motions of autonomous vehicles. These ego motions are provided in the original Argoverse dataset [8].
+
+Following [47], we define dynamic points as points that the norm between the deformed source (i.e., source point cloud deformed by the ground truth flow) and the ego-motion compensated source (i.e., the source point cloud is transformed by the ego-motion) exceeds a threshold of 0.05. All the metrics are computed only on dynamic points. During optimization, for our method, we removed the ego-motion of the point cloud and estimated the scene flow using the full point cloud, and for NSFP++, we only used dynamic points as required.
+
+In Tab. 3, we show that our method achieves worse performance than  $\mathrm{NSFP}++$  while being  $\sim 50\times$  faster. We further replaced the Chamfer distance loss used in  $\mathrm{NSFP}++$  with our proposed distance transform (DT) loss, and we observed a  $\sim 8\times$  speedup. The distance transform loss can be a robust and efficient surrogate to Chamfer distance loss in many deep geometry vision tasks.
+
+# 4.5. Limitations
+
+One drawback of our method is that creating a DT map using rasterization can lead to discretization errors, especially when the grid size of the DT map is large. To mitigate these, it is necessary to build a DT map with relatively fine-resolution grids. In this case, the memory consumption will increase especially when dealing with high-dimensional data, such as 3D point clouds. Further engineering efforts of pre-creating an efficient high-resolution DT map are required to maintain a reasonable memory cost. However, we empirically find that in the context of scene flow estimation—specifically for scene flow in autonomous driving scenarios—a relatively smooth representation is preferred for local rigidity assumptions. Nevertheless, the tradeoff between the grid resolution, the memory consumption, and the estimation accuracy should be carefully considered and chosen based on specific real-world applications.
+
+Failure cases. We show two typical failure cases in Fig. 8. The first case (left column) is when dynamic points are much sparser than the background, our prediction can result in noisy non-rigid motions in the background. The second case (right column) is when the dynamic motion is relatively small, our model may fail to recognize the dynamic scene and only predict rigid motions.
+
+# 5. Conclusion
+
+In this work, we revisit the runtime optimization-based scene flow method NSFP and propose a method that is both efficient and generalizable to large-scale OOD data and dense lidar points. We identify that common strategies for speeding up network architectures do not yield significant time reductions—the major computation overhead is the Chamfer distance loss. Therefore, we propose to use an efficient correspondence-free distance transform loss as a robust surrogate. The rediscovery of DT in scene flow estimation opens up an innovative venue to leverage its efficiency and robustness for various deep geometry tasks. Compared to NSFP, our method maintains comparable accuracy but gains up to  $\sim 30\times$  speedups. We report for the first time a real-time performance ( $\sim 120\mathrm{ms}$ ) with neural scene flow and runtime optimization when using fewer points (8,192). The efficient runtime optimization-based neural scene flow can be widely applied in lidar scenes to do point cloud densification, open-world object detection, and scene clustering, such as in autonomous driving scenarios, where no ground truth or training data are readily available.
+
+Acknowledgement: We would like to thank Haosen Xing for the careful review of the manuscript and the help throughout the project. We thank Kavisha Vidanapathirana for the initial implementation of NSFP++ [47].
+
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+[82] Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoptrees for real-time rendering of neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5752-5761, 2021. 2  
+[83] Jianqiao Zheng, Sameera Ramasinghe, Xueqian Li, and Simon Lucey. Trading positional complexity vs deepness in coordinate networks. In European Conference on Computer Vision, pages 144-160. Springer, 2022. 2, 5, 6
\ No newline at end of file
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+                                            "content": "Figure 1. Scene flow is an important problem as it provides low-level motion cues for many downstream tasks. State-of-the-art learning methods are usually fast and can achieve impressive performance on in-domain data, but usually fail to generalize to out-of-the-distribution (OOD) data or handle dense point clouds. In this paper, we focus on a runtime optimization-based neural scene flow pipeline. In (a) one can see its application in the densification of lidar. However, in (c) one sees that the major drawback is the extensive computation time. We identify that the common speedup strategy in network architectures for coordinate networks has little effect on scene flow acceleration [see green (b)] unlike image reconstruction [see pink (b)]. With the dominant computational burden stemming instead from the Chamfer loss function, we propose to use a distance transform-based loss function to accelerate [see purple (b)], which achieves up to "
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+                                            "content": " speedup and on-par estimation performance compared to NSFP [see (c)]. When tested on 8k points, it is as efficient [see (c)] as leading learning methods, achieving real-time performance."
+                                        }
+                                    ]
+                                }
+                            ],
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+                            "angle": 0,
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+                                    "content": "Abstract"
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+                                    "type": "text",
+                                    "content": "Neural Scene Flow Prior (NSFP) is of significant interest to the vision community due to its inherent robustness to out-of-distribution (OOD) effects and its ability to deal with dense lidar points. The approach utilizes a coordinate neural network to estimate scene flow at runtime, without any training. However, it is up to 100 times slower than current state-of-the-art learning methods. In other applications such as image, video, and radiance function reconstruction innovations in speeding up the runtime performance of coordinate networks have centered upon architectural changes. In this paper, we demonstrate that scene flow is different—with the dominant computational bottleneck stemming from the loss function itself (i.e., Chamfer distance). Further, we rediscover the distance transform (DT) as an efficient, correspondence-free loss function that dramatically speeds up the runtime optimization. Our fast neural scene flow (FNSF) approach reports for the first time real-time performance comparable to learning methods,"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "*Part of the work was done while at Argo AI. Corresponding e-mail: xueqian.li@adelaide.edu.au. Code available at https://github.com/Lilac-Lee/FastNSF.git"
+                                }
+                            ]
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+                {
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+                                    "type": "text",
+                                    "content": "without any training or OOD bias on two of the largest open autonomous driving (AV) lidar datasets Waymo Open [62] and Argoverse [8]."
+                                }
+                            ]
+                        }
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+                    "index": 14
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+                                    "type": "text",
+                                    "content": "1. Introduction"
+                                }
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+                },
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+                                    "content": "Neural Scene Flow Prior (NSFP) [37] is considered the dominant method in open-world perception [47] and scene densification [37, 69] using lidar (see Fig. 1 (a)). NSFP achieves state-of-the-art scene flow estimates from dense lidar point clouds (up to "
+                                },
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+                                    "type": "text",
+                                    "content": " points) and works on a variety of sensor setups with little to no refinement or adaptation. Unlike supervised or unsupervised learning-based methods, NSFP does not require learning from large offline datasets and has no limits on point density ("
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for most learning methods). Instead, it leverages the architecture of a neural network to implicitly regularize the flow estimate and employs a runtime optimization that can easily scale to large out-of-distribution (OOD) scenes, which is a challenge for current learning-based methods [15, 31, 37, 47, 51]."
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+                                    "content": "A fundamental drawback, however, to NSFP is the speed of its runtime optimization which is in some instances of orders of magnitude slower than its learning counterparts"
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+                                    "content": "(see Fig. 1). As a result, NSFP has widely been used offline for (i) providing scene flow supervision for efficient learning methods and (ii) as a pre-processing step for training open-world perception systems [47]. However, the considerable computational cost of NSFP limits its current applications only to these offline tasks."
+                                }
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+                                    "content": "A central narrative of our approach is that the dominant computational burden in runtime scene flow optimization (NSFP) is not the network architecture, but the loss function—specifically Chamfer distance (CD) [17]. This differs considerably from other applications of coordinate networks throughout vision and learning such as neural radiance fields (NeRF [44]) and high-fidelity image reconstruction ([61]) which have gained significant speedups through architectural innovations [83]. A visual depiction of this discrepancy can be found in Fig. 1 (b)."
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+                                    "type": "text",
+                                    "content": "Key to our approach is the use of correspondence-free loss function—distance transform (DT) [5, 13, 58] as a proxy for the computationally expensive CD loss. Even though DT has been extensively studied by the graphics and vision community over a few decades, its application as an efficient loss function in deep geometry has largely been overlooked up until this point. We believe that the inherent efficiencies of the DT are especially pertinent for runtime network training such as in NSFP. Our approach shares similarities with Plenoxels [81]—a recent approach for efficient radiance field estimation using coordinate networks—as we trade memory consumption for computation time, allowing for significant speedups during runtime, which provides an alternative solution when exploring more efficient loss functions for dense scene flow estimation. We differ from Plenoxels, however, in that our memory consumption stems from our proposed loss function, not the neural architecture itself."
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+                                    "content": "In this paper, we present for the first time an approximately real-time (for 8k points) runtime optimization method as computationally efficient as leading learning methods whilst preserving the scalability to dense point clouds and state-of-the-art performance on OOD scenes like NSFP. We compare the performance and the computation time of our approach on two of the largest open lidar AV datasets available: Waymo Open [62] and Argoverse [8]. Our fast neural scene flow achieves up to "
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+                                    "content": "\\sim 30"
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+                                    "type": "text",
+                                    "content": " times speedup than NSFP [37] (our faster implementation) and of comparable speed to leading learning-based methods (see Fig. 1 (c)) with the same number of points (8,192). It opens up the possibility of employing a fast, robust, and generalizable approach for dense scene flow, which is not prone to OOD effects in real-time vision and robotic applications."
+                                }
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+                                    "type": "text",
+                                    "content": "2. Related work"
+                                }
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+                                    "content": "Scene flow estimation. Scene flow denotes the motion field in 3D space [67] uplifted from 2D optical flow. To reconstruct 3D flow, traditional image-based methods [2, 24,"
+                                }
+                            ]
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+                                    "content": "25,27,28,36,53] formulate an optimization problem utilizing RGB or depth information, and learning-based RGB/RGB-D methods [6, 29, 30, 57, 60, 64, 78] rely on single/multiple image features which encode with a large amount of data supervisions. On the other hand, to estimate scene flow directly from 3D, traditional point cloud-based methods [1, 11, 50] solve for a non-rigid registration problem, while recent work prefers full-supervised learning [23, 34, 38, 39, 52, 71, 73, 75] that uses point-based features or self-supervised learning [3, 21, 45, 65, 75] that employs a self-supervised loss. Recent non-learning-based methods [37, 51] draw our attention back to runtime optimization that easily scales to large data. Graph prior [51] explicitly builds a graph on the point cloud and uses a graph Laplacian regularizer. While neural scene flow prior [37] uses the network as an implicit regularizer to smooth motions. In this paper, we explore point cloud-based scene flow using runtime optimization."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Accelerating coordinate networks. There exists a line of work [9, 20, 26, 46, 56, 81, 82] that focuses on accelerating coordinate networks by trading slow, memory efficient, deep network architectures for fast, memory hungry, shallow architectures. Most of these innovations have been applied to the problem of neural radiance fields most notably Plenoxels [81] and TensorRF [9]. Recently, this trend was generalized for arbitrary signals through the introduction of complex positional encoding [83] with shallow linear networks. In this paper, we claim that these architectural innovations have little utility in speeding up neural scene flow without first addressing the computational cost of the Chamfer loss it uses."
+                                }
+                            ]
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+                    ],
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+                                    "content": "Distance transform. DT [4, 5, 13, 41, 58] has played an important role in image processing, especially binary image analysis [48, 66]. Further applications are also found in medical image segmentation [12, 33, 59, 70, 72], robotics motion planning [55, 76], geometric representation [7, 10, 49], and accelerated point cloud registration [19, 79]. Among them, various distance measures have been used, such as city block, chessboard, and Euclidean distance [13, 77]. Naturally, Euclidean distance is preferred in computing point distance but it is also the most difficult metric to compute due to the temporal complexity [22]. Many work attempts to speedup Euclidean DT computation including raster-scan-based algorithms [5, 18, 35, 41, 54], fast marching-based algorithms [16, 40, 68], etc., and has achieved linear time computation. In this paper, we investigate the raster-scan-based algorithm for the 3D point cloud."
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+                                    "content": "3. Approach"
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+                                    "content": "3.1. Background"
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+                                    "content": "Scene flow optimization. Suppose we have a moving sensor (e.g., lidar mounted on a car, depth camera tied to a robot, etc.) collecting point cloud in a dynamic environment."
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+                                    "content": ". The translational vector set of all 3D points in "
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+                                    "content": "\\mathcal{F} = \\{\\mathbf{f}_i\\}_{i=1}^{|S_1|}"
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+                                    "content": ". Usually, a regularization C, such as a Laplacian regularizer, is needed due to the highly unconstrained non-rigid flows. The overall optimization becomes"
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+                                    "content": "Neural scene flow prior. NSFP uses traditional runtime optimization to optimize a neural network. Different from learning-based methods, NSFP does not rely on any prior knowledge of large-scale datasets. And different from traditional scene flow optimization with an explicit regularizer that is mentioned above, neural scene flow prior optimizes parameters of a network which implicitly imposes a regularization by its structure:"
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+                                    "content": "\\boldsymbol {\\Theta} ^ {*} = \\underset {\\boldsymbol {\\Theta}} {\\arg \\min } \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {1}} D (\\mathbf {p} + g (\\mathbf {p}; \\boldsymbol {\\Theta}), \\mathcal {S} _ {2}). \\tag {2}",
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+                                    "content": " to be optimized. "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the input source point, and the flow "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f} = g(\\mathbf{p};\\Theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the output of the network. The optimization converges at "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}^{*} = g(\\mathbf{p};\\Theta^{*})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". The network "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " here is chosen to be a commonly used ReLU-MLP."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Since the points in source "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_{1}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and target "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_{2}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are not in correspondence, nor having the same number of points, i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "|S_{1}| \\neq |S_{2}|"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we use a distance function that handles these problems as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "D (\\mathbf {p}, \\mathcal {S}) = \\min  _ {\\mathbf {x} \\in \\mathcal {S}} \\| \\mathbf {p} - \\mathbf {x} \\| _ {2} ^ {2}. \\tag {3}",
+                                    "image_path": "db2c0fee008f2dbd5239b275262bf1a2d077d43bfbeca3056a9d77e5e737c2e5.jpg"
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+                                    "type": "text",
+                                    "content": "Practically, a bidirectional point distance is found, yielding the above equation equivalent to the Chamfer loss [17]."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Chamfer distance. In point cloud processing, Chamfer distance (CD) [17] is an important loss function and metric for computing the point distance of two point clouds that do not necessarily have points in correspondence. Chamfer distance loss computes the point distance of both source-to-target and target-to-source directions. In detail, the CD loss"
+                                }
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+                                            "type": "text",
+                                            "content": " Initialized DT map"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12,
+                            "angle": 0,
+                            "type": "image_caption"
+                        },
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+                                            "type": "text",
+                                            "content": "Figure 2. An example of how to build a DT map of 2D points. The initialized DT map is set to all zeros. The rasterized 2D point image is set to zero if a point is presented in the grid, and set to one if the grid contains no points. After computation, the final DT map is shown in the right figure."
+                                        }
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+                                            "content": "Rasterized 2D points"
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+                                        }
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+                                    "type": "text",
+                                    "content": "can be written as"
+                                }
+                            ]
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+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} C D \\left(\\mathcal {S} _ {1}, \\mathcal {S} _ {2}\\right) = \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {2}} \\mathrm {D} \\left(\\mathbf {p}, \\mathcal {S} _ {1}\\right) + \\sum_ {\\mathbf {q} \\in \\mathcal {S} _ {1}} \\mathrm {D} \\left(\\mathbf {q}, \\mathcal {S} _ {2}\\right) \\\\ = \\sum_ {\\mathbf {p} \\in \\mathcal {S} _ {2}} \\min  _ {\\mathbf {x} \\in \\mathcal {S} _ {1}} \\| \\mathbf {p} - \\mathbf {x} \\| _ {2} ^ {2} + \\sum_ {\\mathbf {q} \\in \\mathcal {S} _ {1}} \\min  _ {\\mathbf {y} \\in \\mathcal {S} _ {2}} \\| \\mathbf {q} - \\mathbf {y} \\| _ {2} ^ {2}. \\tag {4} \\\\ \\end{array}",
+                                    "image_path": "3a398217e0510e3c239fb4cc5e0be308882ad880c8f4beb57807d9cc65cbcc91.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "To compute the point distance, correspondences from source-to-target and target-to-source are searched among the nearest point neighbors. However, the exhaustive point correspondence search is extremely slow, especially when dealing with dense point clouds that contain more than 10k points (e.g., in Waymo Open and Argoverse datasets, the number of points can be up to "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "150\\mathrm{k}+"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ")."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.2. Correspondence-free point distance transform"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
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+                                    "type": "text",
+                                    "content": "DT is widely used in 2D image processing, such as segmentation, boundary detection, pattern matching, skeletonization, etc. However, general usage in irregular and unordered 3D point cloud tasks is not broadly discussed. Given that the image grid is regular and ordered, a DT map is easily obtained by computing the minimum distance of each sampled point "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x} \\in S"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to the vertex "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of a DT map "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " as"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {D T} (\\mathbf {q}) = \\min  _ {\\mathbf {x} \\in \\mathcal {S}, \\mathbf {q} \\in \\mathcal {G}} \\mathrm {D} (\\mathbf {x}, \\mathbf {q}). \\tag {5}",
+                                    "image_path": "9427a7085f31c8551c9c24711e3d304fe59e3e6e97517a44ba60e11aadf81641.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "We extend Eq. (5) to fit in the scene flow task such that "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
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+                                    "type": "text",
+                                    "content": " refers to Euclidean distance, "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the target point, and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the regularly spaced point in a voxel (3D)."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Approximation of DT map. However, with a large number of points in a point cloud and the grid map, directly computing Eq. (5) builds high dimensional matrices which will lead to large memory occupation. Even when we presume that each axis of the grid/voxel is separable, and the distance per axis is pre-computed, the memory consumption is still huge that cannot be processed on a single GPU. One strategy is to iteratively aggregate small"
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+                                            "content": "Figure 3. Distance transform map of a target point cloud in Argoverse dataset. Purple points are the target, and green points are the source. It is important to note that the DT map is constructed from the target points, and the source points are only shown for reference purposes. The colormap denotes the DT values (in meters), with light yellow denoting a smaller distance and dark purple indicating a larger distance."
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+                                    "type": "text",
+                                    "content": "matrix multiplications while at a cost of extensive time consumption. Another strategy is to use k-d tree query to compute the Euclidean distance. Building a k-d tree is one-time computing, but querying from a large point set to an even larger k-d tree is expensive."
+                                }
+                            ]
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+                                    "content": "Instead, we use a fast distance approximation by rasterizing the irregular points onto the nearest regular cuboid/grid. Specifically, similar to classical efficient binary image-based DT methods [12, 18], we construct two 3D binary images for target points and an initialized DT map. An example of 2D DT map is shown in Fig. 2. Specifically, the DT map is set to be all zeros, and the target binary image pixel is set to one when the grid contains no target points in it. Then a two-pass raster scan-based algorithm [18] is applied to each axis to compute the final DT, which means a 3D image needs six propagation passes (left to right, right to left, front to back, back to front, top to bottom, bottom to top). Although we rasterize target points using a binary 3D image approximation, we still compute the exact Euclidean distance between these two binary images instead of an approximated point distance. We empirically find that such discretization does not hurt performance. One reason is the local rigidity of the scene flow benefits from reasonably small but not necessarily infinitesimal DT grids/voxels."
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+                                    "content": "A visualization of a 2D bird's eye view (BEV) DT map is presented in Fig. 3, where we see that when the point density is large, the distance value is relatively small, and the distance value becomes extremely large when no points exist. By choosing an appropriate grid size, the pattern of DT is distinct among different points while"
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+                                    "type": "text",
+                                    "content": "maintaining a relatively smooth structure in the neighboring area. Evidently, the correspondence-free distance transform can act as an effective and efficient surrogate for point correspondence-based Chamfer loss."
+                                }
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+                                    "type": "text",
+                                    "content": "DT query and loss function. Once a DT map is built for the target point cloud, we can look up the pre-computed DT map to get the distance of the nearest source point in an extremely fast fashion. The loss function becomes the queried Euclidean distance between the target and the nearest deformed source points:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\min  _ {\\mathbf {y} \\in \\mathcal {S} ^ {\\prime}, \\mathbf {q} \\in \\mathcal {G}} \\| \\mathbf {y} - \\mathbf {q} \\| _ {2}, \\tag {6}",
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "S'"
+                                },
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+                                    "type": "text",
+                                    "content": " is the deformed source point cloud. Unlike CD loss, no point correspondence search is required in Eq. (6), making the DT query exceptionally fast. Further ablation studies can be found in Sec. 4.3."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
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+                    "index": 9
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+                                    "type": "text",
+                                    "content": "Datasets We are primarily interested in scene flow methods that are well-suited for large-scale, realistic, lidar-based OOD scenes, which are commonly encountered in autonomous driving (AV) applications. To this end, we focus on two AV datasets: Waymo Open [62] and Argoverse [8], which contain numerous challenging dynamic scenes. Unfortunately, no ground truth annotations were provided for the open-world dataset. We pre-processed the Argoverse and Waymo Open pseudo ground truth scene flow datasets following [37, 51] and [31, 80] respectively."
+                                }
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+                                    "type": "text",
+                                    "content": "Metrics We follow scene flow metrics used in [37, 38, 45, 51, 75] to evaluate the performance. We also include the computation time breakdown in the table. These metrics are:"
+                                }
+                            ]
+                        }
+                    ],
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+                                            "type": "text",
+                                            "content": "1) 3D end-point error "
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+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{E}(m)"
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+                                            "type": "text",
+                                            "content": " that measures the mean absolute point distance between estimated and target points;"
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+                            "index": 12
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+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "2) strict accuracy "
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+                                            "content": "Acc_5(\\%)"
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+                                            "type": "text",
+                                            "content": ", which is the accuracy of the estimated flow that satisfies the absolute point error "
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+                                            "content": "\\mathcal{E} < 0.05\\mathrm{m}"
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+                                            "type": "text",
+                                            "content": " or the relative point error "
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+                                            "content": "\\mathcal{E}' < 5\\%"
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+                                            "type": "text",
+                                            "content": ";"
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+                            "index": 13
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+                        {
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+                            "type": "text",
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+                                            "type": "text",
+                                            "content": "3) relaxed accuracy "
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+                                            "content": "Acc_{10}(\\%)"
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+                                            "type": "text",
+                                            "content": ", which is the accuracy of the estimated flow that satisfies the absolute point error "
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+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{E} < 0.1\\mathrm{m}"
+                                        },
+                                        {
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+                                            "type": "text",
+                                            "content": " or the relative point error "
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+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{E}' < 10\\%"
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+                                            "content": ";"
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+                            "index": 14
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+                        {
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+                                            "type": "text",
+                                            "content": "4) angle error "
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+                                            "type": "inline_equation",
+                                            "content": "\\theta_{\\epsilon}(rad)"
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+                                            "type": "text",
+                                            "content": " that measures the mean angle error (in radiance) of the estimated and the pseudo ground truth translational vectors."
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+                            "index": 15
+                        },
+                        {
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+                                            "type": "text",
+                                            "content": "5) computation time "
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+                                            "type": "inline_equation",
+                                            "content": "t(ms)"
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+                                            "type": "text",
+                                            "content": " breaks down to four parts. Pre-compute includes data loading and building a DT map. Corr. / DT query counts the time needed to search point correspondences or query point distance within a DT map. We also include computation time for Network forward and backward propagation. Finally, Total time in seconds / milliseconds is measured."
+                                        }
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+                                    "content": "Implementation details We provide the details of implementation for each algorithm we compared. Further information can be found in the supplementary materials."
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+                                            "content": "1) NSFP [37]. The original implementation is extremely slow. Based on the official code released by the authors while keeping the same parameter settings specified in the original paper, we implemented a faster version (NSFP) for a fair comparison. Note that to reflect the independence of each pair of point clouds when estimating scene flow, we randomly initialized the network before each optimization."
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+                                            "content": "2) Baseline. Note that although the backward flow enforces a cycle consistency between the deformed point cloud and the original point cloud, we empirically found that removing cycle consistency does not hurt the overall performance when dealing with dense lidar point clouds, but improves the computational efficiency. Here we removed the backward flow in the original NSFP and implemented a NSFP (baseline) version as our baseline for a fair comparison—all computation times were compared with this model. We further modified the baseline model using a linear model with complex positional encodings (NSFP (baseline, linear)) to demonstrate the effect of network architecture changes. Detailed explanations can be found in Sec. 4.1 and the supplementary material."
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+                                            "content": "3) Ours. We implemented a DT-based neural scene flow method with 8-layer ReLU-MLPs (Ours). We chose the grid cell size of the DT map to be 0.1 meters. Ablation studies on the choice of grid cell size can be found in Sec. 4.3. We further modified our method using a linear model with complex positional encodings (Ours (linear)) to demonstrate the effect of network architecture changes."
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+                                            "content": "4) FlowStep3D [34] and FLOT [52] are fully supervised methods trained on synthetic FlyingThings3D [42] datasets. PointPWC-Net [75] can be used as a self-supervised method. We used the official code released by the authors and directly tested the pretrained model (pretrained on FlyingThings3D) on our datasets. However, as full/self-learning-based methods, they performed poorly on OOD datasets, which is also observed in [15, 31, 37, 47, 51]. Here we only chose the method with the best performance and the lowest computation time—FLOT—for comparison in the main table. The comparison of other learning-based methods is included in the supplementary material. R3DSF [21] is a weakly supervised method with no direct supervision of ground truth dynamic flows. We tested the method using the pretrained model (on KITTI [43]) provided by the authors."
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+                                    "content": "All models were implemented using CUDA 11.6-supported PyTorch. All experiments were run on a computer with a single NVIDIA RTX 3090Ti GPU and a 24 AMD Ryzen 95900X 12-Core CPU @ 4.95GHz."
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+                                            "content": "Figure 4. Illustration of 3D complex PE in scene flow problem. The 3D space of source points (yellow) and target points (green) is divided into small cubes. The number of cubes on each axis differs but the edge length is the same. Encoding of a point in a certain grid is the blending/interpolation of encodings of all 8 grid vertices. These grid points (blue) are encoded by complex PE along each axis. Note the vec and outer product "
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+                                            "content": " notation is for better visual understanding and it is equivalent to the Kronecker product."
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+                                    "content": "Plenoxels [81] is a method that accelerates NeRF [44] optimization by replacing deep neural networks with voxel-based spherical harmonics representations, leading to efficient volume rendering. Similar network speedup approaches can also be used in neural scene flow optimization. We incorporate recent innovations in positional encodings, specifically complex positional encoding (complex PE) [83] to represent high-frequency signals and enable a linear reconstruction model which is similar in spirit to [81]."
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+                                    "content": "Complex positional encodings Positional encodings (PEs) are encodings for input positions—e.g., 2D image grids, 3D voxel grids, etc.—that are usually used in coordinate networks. PEs has been shown to improve the performance and convergence speed of coordinate networks [63]. Simple PE is a simple concatenation of the encoding in each input dimension, while a complex PE is a more complicated encoding that computes the Kronecker product of the per-dimension encoding. An illustration of complex PE of scene flow is shown in Fig. 4."
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+                                    "content": "With a complex PE and a linear model parameterized by "
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+                                    "content": "\\mathbf{W} \\in \\mathbb{R}^{W_x W_y W_z \\times 3}"
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+                                    "content": ", the scene flow can be represented as"
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+                                    "content": " -mode multiplication, which is equivalent to Kronecker product. The blending function interpolate the 3D regular grid encodings to handle the irregular and unordered nature of 3D point clouds. Additional details of complex PE can be found in the supplementary materials."
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+                                            "content": "Table 1. Computation time and performance on Waymo Open Scene Flow dataset. We generated 202 testing scene flow examples where each point cloud has 8k-144k points. The upper tabular between blue bars are experiments with the full point cloud, and the lower tabular between orange bars are experiments with only 8,192 points. All query time is listed as: time per optimization step [total query time]. The speedups are marked with green "
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+                                            "content": ". The computation time of using full point cloud is compared to values in the red box, and the computation time of using 8,192 points is compared to values in green box. Bold texts are the best performance, and underlined texts denote the second-best performance. "
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+                                            "content": " means smaller values are better. Corr. / DT query denotes correspondence search or DT query. Note: performance of learning methods PointPWC-Net [75], FlowStep3D [34], PV-RAFT [74] can be found in the supplementary material."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ε(m)↓</td><td rowspan=\"2\">Acc5(%)↑</td><td rowspan=\"2\">Acc10(%)↑</td><td rowspan=\"2\">θe(rad)↓</td><td colspan=\"4\">t (ms) ↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.100</td><td>76.62</td><td>88.56</td><td>0.286</td><td>—</td><td>114 [30972]</td><td>4.62 [1361]</td><td>35.51 s</td></tr><tr><td>NSFP (baseline)</td><td>0.118</td><td>74.16</td><td>86.70</td><td>0.300</td><td>—</td><td>43.1 [15036]</td><td>2.38 [904]</td><td>18.39 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.096</td><td>70.78</td><td>86.31</td><td>0.310</td><td>9.48</td><td>40.38 [8037] | 1.1×</td><td>1.53 [319] | 1.6×</td><td>10.20 s | 1.80×</td></tr><tr><td>Ours</td><td>0.072</td><td>84.73</td><td>92.24</td><td>0.280</td><td>40.85</td><td>0.25 [13] | 172×</td><td>2.89 [149] | 1.2×</td><td>0.58 s | 31.7×</td></tr><tr><td>Ours (linear)</td><td>0.109</td><td>71.27</td><td>85.80</td><td>0.321</td><td>44.88</td><td>0.23 [19] | 187×</td><td>1.62 [138] | 1.5×</td><td>0.49 s | 37.5×</td></tr><tr><td>FLOT [52]</td><td>0.702</td><td>2.46</td><td>11.30</td><td>0.808</td><td>—</td><td>—</td><td>—</td><td>99 ms</td></tr><tr><td>R3DSF [21]</td><td>0.414</td><td>35.47</td><td>44.96</td><td>0.527</td><td>—</td><td>—</td><td>—</td><td>140 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.138</td><td>53.62</td><td>78.57</td><td>0.339</td><td>—</td><td>5.42 [1285] | 21×</td><td>4.44 [1051] | 1.1×</td><td>2459 ms | 17.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.106</td><td>77.53</td><td>88.99</td><td>0.329</td><td>35.22</td><td>0.23 [6.5] | 496×</td><td>2.60 [76] | 1.8×</td><td>121 ms | 1.16×</td></tr></table>",
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+                                            "content": "Table 2. Computation time and performance on Argoverse Scene Flow dataset. Argoverse has 212 testing scene flow examples where each point cloud has "
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+                                            "type": "inline_equation",
+                                            "content": "30\\mathrm{k - }70\\mathrm{k}"
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+                                            "type": "text",
+                                            "content": " points. Notations are the same as in the table above."
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+                            "type": "table_caption"
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ε(m)↓</td><td rowspan=\"2\">Acc5(%)↑</td><td rowspan=\"2\">Acc10(%)↑</td><td rowspan=\"2\">θe(rad)↓</td><td colspan=\"4\">t (ms)↓</td></tr><tr><td>Pre-compute</td><td>Corr. / DT query</td><td>Network</td><td>Total</td></tr><tr><td>NSFP [37]</td><td>0.069</td><td>71.56</td><td>87.80</td><td>0.235</td><td>—</td><td>47 [14310]</td><td>4.66 [1507]</td><td>18.08 s</td></tr><tr><td>NSFP (baseline)</td><td>0.078</td><td>69.46</td><td>86.22</td><td>0.253</td><td>—</td><td>17 [5901]</td><td>2.31 [848]</td><td>8.38 s</td></tr><tr><td>NSFP (baseline, linear)</td><td>0.097</td><td>67.03</td><td>83.20</td><td>0.314</td><td>9.19</td><td>14.7 [2786] | 1.1×</td><td>1.51 [297] | 1.5×</td><td>3.55 s | 2.36×</td></tr><tr><td>Ours</td><td>0.071</td><td>80.05</td><td>90.71</td><td>0.289</td><td>43.61</td><td>0.24 [14] | 71×</td><td>2.57 [149] | 1.1×</td><td>0.51 s | 16.4×</td></tr><tr><td>Ours (linear)</td><td>0.106</td><td>65.00</td><td>82.85</td><td>0.319</td><td>48.59</td><td>0.23 [20] | 74×</td><td>1.69 [149] | 1.4×</td><td>0.43 s | 19.5×</td></tr><tr><td>FLOT [52]</td><td>0.821</td><td>2.00</td><td>8.84</td><td>0.967</td><td>—</td><td>—</td><td>—</td><td>88 ms</td></tr><tr><td>R3DSF [21]</td><td>0.417</td><td>32.52</td><td>42.52</td><td>0.551</td><td>—</td><td>—</td><td>—</td><td>113 ms</td></tr><tr><td>NSFP [37] (8,192 pts)</td><td>0.113</td><td>46.32</td><td>72.68</td><td>0.347</td><td>—</td><td>5.40 [1500] | 8.7×</td><td>4.42 [1233] | 1.1×</td><td>2864 ms | 25.6×</td></tr><tr><td>Ours (8,192 pts)</td><td>0.118</td><td>69.93</td><td>83.55</td><td>0.352</td><td>41.57</td><td>0.22 [6.33] | 214×</td><td>2.51 [72.69] | 1.9×</td><td>124 ms | 1.10×</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Network speedup comparison We would like to point out that although various strategies have been proposed to accelerate network architectures, they do not lead to substantial speedup in neural scene flow estimation. To demonstrate this, we compare the relative efficiency of using 8-layer Relu-MLPs and complex PE with a linear model in both 2D image reconstruction and 3D scene flow tasks, shown in Fig. 1 (b). In detail, following [83], we used a size of "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "256 \\times 256"
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+                                    "type": "text",
+                                    "content": " image dataset for image reconstruction. For a fair comparison, the relative efficiency is obtained by normalizing the computation time of two tasks. The computation time of single image reconstruction is "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "17.63\\mathrm{s}"
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "0.15\\mathrm{s}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for deep network and linear network respectively, leading to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "118 \\times"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " speedup. However, the linear model only results in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 2 \\times"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 1.2 \\times"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " speedup for NSFP and our method respectively. Our results show that complex PE-based speedup achieves significant acceleration in 2D image reconstruction compared to deep neural networks, but the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "benefits of such speedup are more limited when estimating neural scene flow. More detailed comparisons are in Sec. 4.2."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "4.2. Comparison of performance"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "type": "text",
+                                    "content": "We show the performance of our method with different variants compared to NSFP, FLOT, and R3DSF on Waymo Open (Tab. 1) and Argoverse (Tab. 2) scene flow datasets. We denote results on Waymo Open (xx) and Argoverse (yy) as xx/yy. Visual results and applications of densification are shown in Fig. 5 and supplementary materials."
+                                }
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+                                    "content": "Dense scene flow estimation. For dense point clouds, the baseline NSFP took "
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+                                    "content": "18.39 / 8.38"
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+                                    "type": "text",
+                                    "content": " s to converge. When replacing the 8-layer MLPs with a linear network and applying complex PE, we observed a speedup of only "
+                                },
+                                {
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+                                    "content": "1.80 / 2.36 \\times"
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+                                    "type": "text",
+                                    "content": " in total, primarily due to the network propagation speedup. When we replaced naive CD loss with the DT loss, a significant "
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+                                    "type": "text",
+                                    "content": " speedup was achieved while"
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+                                            "content": "Figure 5. Visual examples of the scene flow prediction using our method on Argoverse dataset. We show 3 different autonomous driving scenarios where the autonomous vehicle (AV) was making a right turn (left), the AV stopped for crossing traffic (middle), and the AV was driving in the city (right). We found that the scene flow predicted by our method is close to the ground truth flows. The upper left corner color wheel indicates the flow magnitude (color intensity) and the flow direction (angle). For example, the yellow vehicles in the middle figure are heading south with a relatively large speed wrt the AV."
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+                                    "type": "text",
+                                    "content": "maintaining comparable high accuracy. However, replacing a deep network with a linear model when using DT loss only resulted in an additional "
+                                },
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+                                    "content": "1.2 / 1.2 \\times"
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+                                    "type": "text",
+                                    "content": " speedup at the cost of a decrease in flow accuracy. Specifically, the total computation time of our proposed method with DT loss is "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "0.58 / 0.51"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " s, and with DT loss and a linear model is "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "0.49 / 0.43"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " s. However, with a marginal decrease in computation time, we observed a relatively large drop in performance such that the strict accuracy of our method with DT is "
+                                },
+                                {
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+                                        288,
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+                                    "type": "inline_equation",
+                                    "content": "84.73 / 80.05\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "71.27 / 65.00\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        288,
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+                                    ],
+                                    "type": "text",
+                                    "content": " with DT and a linear model. These results strongly support our argument in the previous section, which is the general strategy of simplifying or replacing network architectures to accelerate coordinate networks is not particularly effective when optimizing scene flow through coordinate networks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Overall, the performance of our method using DT loss has on-par performance compared to NSFP while being orders of magnitude faster. We have noticed that there is an \"improved accuracy\" of our method compared to NSFP in Tab. 1, Tab. 2 based on these facts: 1. The performance of our method and NSFP is similar—our method achieves slightly higher performance on some metrics (e.g., accuracy), and NSFP achieves slightly higher performance on other metrics (e.g., angular error). These results indicate that distance transform (DT) is an effective and efficient surrogate for the Chamfer distance (CD) in the scene flow problem. 2. Compared to the \"exact\" point distance (CD), DT queries the distance based on a voxelized DT map, which naturally smooths the flow estimation. In real-world applications, we believe using a DT-accelerated deep network model will achieve both high-fidelity accuracy and efficient computation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Computation time breakdown. A detailed time breakdown is provided in both tables, including pre-computation, correspondence search / DT distance query, and network forward / backward propagation. The naive"
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+                                    "content": "Chamfer distance requires per-point correspondence search, which can be extremely slow (43.1/17 ms per iteration), especially when the point cloud is denser. For instance, correspondence search is much slower in the Waymo Open dataset than in the Argoverse dataset since Waymo Open has an average of 90k points while Argoverse has an average of 50k points in a single point cloud. DT query is a pre-defined table lookup that is exceptionally faster than the naive point correspondence search, achieving a remarkable "
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+                                    "type": "text",
+                                    "content": " speedup per optimization step—the main contributor to the overall efficiency of our method. Note that the pre-computing of the DT map ("
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+                                    "type": "text",
+                                    "content": " ms) is acceptable given that it is one-time computing and the total computation time is in the range of hundreds of milliseconds. Additional complex PE and a linear model only provide a modest speedup of "
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+                                    "content": "1.6 / 1.5 \\times"
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+                                    "type": "text",
+                                    "content": " in the network propagation step. Further optimization of the pre-computation and faster implementation can be achieved with full-CUDA support. Note that although in NSFP, the CD loss was implemented using PyTorch3D with CUDA acceleration, it still requires significant computation time, indicating its inherent limitations that cannot be easily overcome through engineering techniques alone."
+                                }
+                            ]
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+                                    "content": "OOD generalizability. We further extend our model using fewer points (8,192 points) to accommodate for a fair comparison against learning-based methods [21, 34, 52, 74, 75]. For these learning models, a fixed number of points is required and they only operate on fewer points, such as 2,048 [38, 52] or 8,192 points [21, 34, 52, 75]. Also, these learning methods need to crop the point cloud to a small range. Therefore, learning models cannot be easily adapted to large-scale dense point clouds. Jund et al. explored to inference dense point cloud [32], but they did not directly process the full point cloud as the input. A simple solution to address this challenge is to iteratively predict scene flow for"
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+                                            "content": "Figure 7. Performance of distance transform with different grid cell sizes on a 2D scene from Argoverse scene flow dataset. Generally, the larger the grid cell is, the lower the accuracy becomes. The computation time and memory consumption also decrease as the grid cell size increases (the number of grids decreases). The total grid of the DT map is of size "
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+                                    "content": "small subsets of dense point clouds using learning methods. However, this approach requires intensive computation, and it might cause out-of-memory issues [32]."
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+                                    "content": "Fully supervised learning methods FlowStep3D, FLOT, PV-RAFT, and self-supervised method PointPWC-Net do not generalize to new autonomous driving datasets (see Tab. 1, Tab. 2) due to the domain gap between the training and testing datasets [15, 31, 37, 47, 51]. We provide additional performance in the supplementary material. Despite its poor performance on OOD data, FLOT achieves a competitive inference time, making it one of the fastest learning-based methods available. Note that since the weakly supervised learning method R3DSF takes supervision from object segmentation and AV ego motions and was trained on a lidar point cloud-based dataset, it has a relatively high accuracy compared to full/self-supervised learning methods, but its performance is still inferior to non-learning-based methods NSFP and our method. Such evidence strongly suggests that our method—a runtime optimization—is robust to OOD effects, and can be directly applied to applications where no training data is readily available."
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+                                    "content": "Towards real-time computation. Our method attains real-time performance (121/124 ms) which is comparable to learning methods and maintains high accuracy, while"
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+                                            "content": "Table 3. Comparison of our method and NSFP++ on Argoverse scene flow dataset with ego-motion compensation."
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+                                            "html": "<table><tr><td>Method</td><td>E↓(m)</td><td>Acc5↑(%)</td><td>Acc10↑(%)</td><td>θe↓(rad)</td><td>t↓(ms)</td></tr><tr><td>Ours</td><td>0.411</td><td>34.94</td><td>46.82</td><td>0.731</td><td>335</td></tr><tr><td>NSFP++ [47]</td><td>0.295</td><td>31.82</td><td>62.61</td><td>0.343</td><td>16188</td></tr><tr><td>NSFP++ (DT)</td><td>0.272</td><td>30.26</td><td>60.25</td><td>0.365</td><td>2001</td></tr></table>",
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+                                    "content": "learning-based methods struggle to generalize on OOD data. It indicates the significant potential of applying robust and accurate runtime optimization-based methods in many vision-based applications."
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+                                    "content": "Other learning methods. Learning-based scene flow methods are usually fast and achieve good accuracy when applied to in-domain small-scale data (training and testing are on the same dataset with a specific range: e.g., KITTI data with point clouds within "
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+                                    "type": "text",
+                                    "content": " of the scene center) with a limited number of points (usually 2,048 / 8,192 points). As discussed in [15,31,37,47,51], the domain gap is a significant challenge for learning methods—a specific dataset with specific configurations—e.g., coordinate systems, viewing directions, etc.—that match the testing data needs to be used during training. However, we are interested in exploring runtime optimization-based methods that are robust to large-scale OOD data that can be employed in many real-world applications, such as autonomous driving scenarios, where no labels are readily available."
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+                                    "content": "DT splits the space into small grid cells, while the grid size affects the accuracy, the computation time, and the memory accuracy. We provide a performance comparison using different grid cell sizes of DT in Fig. 7. A 2D visualization of DT with different grid sizes is also shown in Fig. 6. We can clearly see that a relatively small grid cell size "
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+                                    "content": " is required to ensure the fidelity of the distance transform map. Note that when rasterized points are closer to the original irregular points, DT is a closer approximation to the exact Euclidean distance between two point clouds. Moreover, with a rasterized point-based DT strategy, the pre-computation of the map is no longer an overhead, and the grid cell size will largely affect the memory instead of the computation time—we trade memory consumption with computation time."
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+                                            "content": "Figure 8. Failure cases on Argoverse dataset. The left figure shows some noisy motions were predicted in the background. The right figure shows our method failed to predict when the motion of some cars is relatively small to the AV."
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+                                    "content": "The proposed DT loss is a general loss that can be used in other 3D geometry tasks. Specifically, for optimization-based methods such as RSF [14], DT could replace the nearest neighbor distance loss to speed up the overall computation. For learning methods such as PointPWCNet [75], DT could replace Chamfer loss to speed up optimization during training, especially when dealing with a large number of points. For methods using cycle consistency, when replacing CD "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{O}(N^2))"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with DT, the forward flow computation will be substantially speeded up (similar speedup to the paper). The backward flow computation will also be speeded up even though the DT map will be computed in every optimization step."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "We provide an example of comparing the results of our method to "
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+                                    "type": "text",
+                                    "content": " [47] in Tab. 3. We used our version of "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NSFP}++"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " due to no publicly available official implementation. Since "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NSFP}++"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " requires ego-motion compensation, we also created an additional Argoverse scene flow dataset that removes the ego motions of autonomous vehicles. These ego motions are provided in the original Argoverse dataset [8]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                {
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+                                    "type": "text",
+                                    "content": "Following [47], we define dynamic points as points that the norm between the deformed source (i.e., source point cloud deformed by the ground truth flow) and the ego-motion compensated source (i.e., the source point cloud is transformed by the ego-motion) exceeds a threshold of 0.05. All the metrics are computed only on dynamic points. During optimization, for our method, we removed the ego-motion of the point cloud and estimated the scene flow using the full point cloud, and for NSFP++, we only used dynamic points as required."
+                                }
+                            ]
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+                                    "content": "In Tab. 3, we show that our method achieves worse performance than "
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+                                    "type": "text",
+                                    "content": " while being "
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 50\\times"
+                                },
+                                {
+                                    "bbox": [
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+                                        630,
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+                                    "type": "text",
+                                    "content": " faster. We further replaced the Chamfer distance loss used in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NSFP}++"
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+                                    "type": "text",
+                                    "content": " with our proposed distance transform (DT) loss, and we observed a "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 8\\times"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " speedup. The distance transform loss can be a robust and efficient surrogate to Chamfer distance loss in many deep geometry vision tasks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.5. Limitations"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "One drawback of our method is that creating a DT map using rasterization can lead to discretization errors, especially when the grid size of the DT map is large. To mitigate these, it is necessary to build a DT map with relatively fine-resolution grids. In this case, the memory consumption will increase especially when dealing with high-dimensional data, such as 3D point clouds. Further engineering efforts of pre-creating an efficient high-resolution DT map are required to maintain a reasonable memory cost. However, we empirically find that in the context of scene flow estimation—specifically for scene flow in autonomous driving scenarios—a relatively smooth representation is preferred for local rigidity assumptions. Nevertheless, the tradeoff between the grid resolution, the memory consumption, and the estimation accuracy should be carefully considered and chosen based on specific real-world applications."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                                    "type": "text",
+                                    "content": "Failure cases. We show two typical failure cases in Fig. 8. The first case (left column) is when dynamic points are much sparser than the background, our prediction can result in noisy non-rigid motions in the background. The second case (right column) is when the dynamic motion is relatively small, our model may fail to recognize the dynamic scene and only predict rigid motions."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
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+                },
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+                                    "content": "In this work, we revisit the runtime optimization-based scene flow method NSFP and propose a method that is both efficient and generalizable to large-scale OOD data and dense lidar points. We identify that common strategies for speeding up network architectures do not yield significant time reductions—the major computation overhead is the Chamfer distance loss. Therefore, we propose to use an efficient correspondence-free distance transform loss as a robust surrogate. The rediscovery of DT in scene flow estimation opens up an innovative venue to leverage its efficiency and robustness for various deep geometry tasks. Compared to NSFP, our method maintains comparable accuracy but gains up to "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 30\\times"
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+                                    "type": "text",
+                                    "content": " speedups. We report for the first time a real-time performance ("
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 120\\mathrm{ms}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ") with neural scene flow and runtime optimization when using fewer points (8,192). The efficient runtime optimization-based neural scene flow can be widely applied in lidar scenes to do point cloud densification, open-world object detection, and scene clustering, such as in autonomous driving scenarios, where no ground truth or training data are readily available."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "Acknowledgement: We would like to thank Haosen Xing for the careful review of the manuscript and the help throughout the project. We thank Kavisha Vidanapathirana for the initial implementation of NSFP++ [47]."
+                                }
+                            ]
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+                                }
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+                    ],
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+                                            "content": "[83] Jianqiao Zheng, Sameera Ramasinghe, Xueqian Li, and Simon Lucey. Trading positional complexity vs deepness in coordinate networks. In European Conference on Computer Vision, pages 144-160. Springer, 2022. 2, 5, 6"
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diff --git a/2023/Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance/16d96c9b-c625-4fb0-aaab-b679d45a05de_content_list.json b/2023/Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance/16d96c9b-c625-4fb0-aaab-b679d45a05de_content_list.json
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+++ b/2023/Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance/16d96c9b-c625-4fb0-aaab-b679d45a05de_content_list.json	
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+[
+    {
+        "type": "text",
+        "text": "Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance",
+        "text_level": 1,
+        "bbox": [
+            111,
+            128,
+            859,
+            174
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Huiwen Xu  \nSeoul National University  \nSeoul, Republic of Korea  \nxuhuiwen33@snu.ac.kr",
+        "bbox": [
+            245,
+            203,
+            452,
+            273
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "U Kang Seoul National University Seoul, Republic of Korea ukang@snu.ac.kr",
+        "bbox": [
+            514,
+            203,
+            723,
+            273
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            308,
+            313,
+            325
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Given a set of pre-trained models, how can we quickly and accurately find the most useful pre-trained model for a downstream task? Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. It is used for quickly ranking pre-trained models for a given task and thus becomes a crucial step for transfer learning. Existing methods measure transferability as the discrimination ability of a source model for a target data before transfer learning, which cannot accurately estimate the fine-tuning performance. Some of them restrict the application of transferability measurement in selecting the best supervised pre-trained models that have classifiers. It is important to have a general method for measuring transferability that can be applied in a variety of situations, such as selecting the best self-supervised pre-trained models that do not have classifiers, and selecting the best transferring layer for a target task.",
+        "bbox": [
+            75,
+            340,
+            472,
+            599
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a fast and accurate algorithm to measure transferability. We view transferability as the generalization of a pre-trained model on a target task by measuring intra-class feature variance. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Extensive experiments on real-world datasets show that TMI outperforms competitors for selecting the top-5 best models, and exhibits consistently better correlation in 13 out of 17 cases.",
+        "bbox": [
+            75,
+            599,
+            472,
+            811
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            843,
+            209,
+            859
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Transfer learning is an important concept in the field of machine learning, revolutionizing the way models are",
+        "bbox": [
+            75,
+            869,
+            470,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/f3be556d27f86e0b0aa81c21d32f1f474315371c44a0984b1ad15b1bc867c58b.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of selecting the best pre-trained model for a given target task."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            321,
+            890,
+            522
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "trained and applied to various domains. Transfer learning has proven to be particularly valuable when labeled data in the target domain are scarce or costly to obtain. Within the broader scope of transfer learning, several variants have emerged, such as source-free domain adaptation [10, 27, 23, 7], multi-source transfer learning [16, 14, 7, 9], heterogeneous transfer learning [11, 15], and open-set domain adaptation [6, 21].",
+        "bbox": [
+            496,
+            625,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In transfer learning, fine-tuning a pre-trained model becomes a simple and effective way to improve the performance of a downstream task. A crucial step in transfer learning is to quickly and accurately select the most helpful pre-trained model in a set of given pre-trained models. Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. As shown in Figure. 1, transferability measurement is used for ranking pre-trained models for a given task, and is a crucial step for transfer learning.",
+        "bbox": [
+            496,
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+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "11474",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A desired method for transferability measurement should be faster than running a transfer learning algorithm, accurately select the best pre-trained model, and be general to be implemented in various common scenarios. Taskonomy [26] and Task2Vec [1] are computationally expensive due to their learning with data. NCE [18] and LEEP [13] are free of training but cannot be applied to general cases, such as selecting self-supervised pre-trained models and selecting the best transferring layer. LogMe [25] and H-Score [2] also cannot be applied theoretically to select the best transferring layer. Instead of measuring transferability, they measure how discriminative a pre-trained model is to a target task before implementing transfer learning, which cannot estimate fine-tuning performance. TransRate [5] is simple and general to be applied for transferability measurement, but too slow due to the computation of the entropy of whole hidden representations.",
+        "bbox": [
+            75,
+            90,
+            472,
+            347
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a simple but effective method for transferability measurement. We deem transferability as the generalization of a pre-trained model on a target task. To quantify the degree of generalization, we measure the intra-class variance by the conditional entropy of target representation given a label. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Large intra-class variance implies the feature is efficient for learning tasks. TMI can be used for selecting not only the best supervised model but also the best self-supervised models and the best transferring layer.",
+        "bbox": [
+            75,
+            347,
+            472,
+            589
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions are summarized as follows:",
+        "bbox": [
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+            604
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Algorithm. We propose TMI, a fast, accurate, and general method for measuring transferability. We view transferability as generalization ability of a pre-trained model on a target task. The model generalization is measured by intra-class feature variance.",
+            "- Experiments. We conduct extensive experiments on seventeen datasets with fifty supervised pre-trained models and eleven self-supervised pre-trained models. TMI outperforms competitors for selecting the top-5 pre-trained architecture in 14 out of 17 cases and selecting the best source data in all cases. TMI also shows the best trade-off of the running time and transferability, outperforming competitors in 12 out of 17 cases (see Figure. 2).",
+            "- Case study. We evaluate the transferability in more general cases, such as applying to self-supervised pretrained models and selecting the best transferring layer. Compared to competitors, TMI achieves the highest correlation coefficient in 13 out of 17 for selecting the"
+        ],
+        "bbox": [
+            94,
+            613,
+            468,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "best self-supervised pre-trained models, and in 16 out of 17 datasets for selecting the best transferring layer.",
+        "bbox": [
+            529,
+            90,
+            890,
+            121
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The rest of this paper is organized as follows. We introduce related works for transferability measurement in Section 2, and propose our method TMI in Section 3. After presenting experimental results in Section 4, we conclude in Section 5.",
+        "bbox": [
+            496,
+            132,
+            893,
+            207
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            500,
+            220,
+            650,
+            237
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We assume a pre-trained model  $\\theta = (w, h)$  in a source domain where  $w$  is a feature extractor, and  $h$  is a classifier (or head). We transfer the model  $\\theta$  to a target domain and add a new classifier  $k$  at the end of the feature extractor  $w$  before fine-tuning. Since the target task is different from the source task in most cases, the pre-trained classifier  $h$  is inappropriate to solve the target task. Thus, we fine-tune the model by minimizing the cross entropy loss on the target dataset  $D = \\{(x_i, y_i)\\}_{i=1}^n$ :",
+        "bbox": [
+            496,
+            246,
+            893,
+            383
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw ^ {*}, k ^ {*} = \\underset {w, k} {\\arg \\min } \\mathcal {L} (w, k) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            607,
+            393,
+            890,
+            420
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where a feature extractor  $w$  maps an input  $x_{i}$  to a representation  $r_i = w(x_i)$ , and a classifier  $h$  maps the representation  $r_i$  to a probability distribution  $\\hat{y}_i = \\sigma(h(r_i))$  where  $\\sigma(\\cdot)$  is an activation function. Note that  $\\hat{y}_i$  is a vector of length  $n_c$ , where  $n_c$  is the number of classes, and  $\\mathcal{L}(\\cdot)$  is the cross entropy loss, which is equivalent to the average negative log-likelihood:",
+        "bbox": [
+            496,
+            425,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} (w, k) = - \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log P \\left(\\hat {y} _ {i, c} \\mid x _ {i}; w, k\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            563,
+            541,
+            890,
+            580
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{y}_{i,c}$  is the probability of  $i$ -th input instance belonging to its ground truth.",
+        "bbox": [
+            496,
+            585,
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+            614
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The transferability of a source task  $S$  to a target task  $T$  is defined by the log-likelihood [18]:",
+        "bbox": [
+            496,
+            614,
+            890,
+            646
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT r f _ {(S \\rightarrow T)} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log P \\left(\\hat {y} _ {i, c} \\mid x _ {i}; w ^ {*}, k ^ {*}\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Taskonomy [26] and Task2Vec [1] train the source model using target data to obtain the optimal feature extractor  $w^{*}$  and the optimal classifier  $k^{*}$ . These methods are inconvenient to measure the transferability due to their training with data. There have been works focusing on estimating a bound on the log-likelihood to evaluate the transferability without training. NCE [18] proposes negative conditional entropy, which is drawn from the empirical joint distribution over ground truths and predicted labels from a pretrained model. Similarly, LEEP [13] replaces the ground truth with the average log-likelihood to evaluate the transferability. NCE and LEEP are fast, but are restricted to supervised pre-trained models because the algorithms rely",
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+        "type": "page_number",
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+            "(a) Caltech-101"
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+            "(n) Cars"
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+        "image_caption": [
+            "(0) DTD"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
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+    {
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+        "img_path": "images/6ab8e30a03644ed04531acad2e869b8f6d6e25941bb4e8c96b7c64038f320935.jpg",
+        "image_caption": [
+            "(p) Food-101",
+            "Figure 2: Total running time (seconds) vs. Kendall's Correlation between transferability scores and test accuracies for selecting the best model among fifty pre-trained models. TMI provides the best trade-off between running time and correlation."
+        ],
+        "image_footnote": [],
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+        "img_path": "images/a23dacbc109931c9493e82f68bfee0bfbe78b2a186e7887b2355b77982df373a.jpg",
+        "image_caption": [
+            "(q) Oxford-IIIT Pet"
+        ],
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+    {
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+    {
+        "type": "text",
+        "text": "on the outputs of the pre-trained classifier. To apply measurements in more general cases, LogME [25] calculates the logarithm of maximum evidence given extracted features, and H-Score [2] solves an HGR maximum correlation problem. LogMe [25] and H-Score [2] still cannot be applied to select the best transferred layer since they extract features from only the ultimate layers of the pretrained feature extractors. TransRate [5] is the most recent algorithm and applicable to self-supervised models and transferring layer selection. However, it is time-consuming since it requires to calculate mutual information between extracted feature and ground truth. To simplify the problem, [18, 13, 25, 2, 5] assume that the optimal model can be obtained by re-training the classifier while freezing the feature extractor. They estimate the performance of re-training only the classifier, which is even worse than training a target model from scratch [24]. In this paper, we propose a fast, accurate, and general transferability measurement method that predicts fine-tuned performance of a pre-trained model to a new target task.",
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+    {
+        "type": "text",
+        "text": "3. Proposed Method",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose TMI to measure the transferability between a pre-trained model and a target task.",
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+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our goal is to measure the transferability in a fast, accurate, and general manner. The following challenges need to be addressed for the goal.",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "C1 Speed. Training a pre-trained model on the target data requires a high computational cost. How can we measure the transferability without training on the target data?",
+            "C2 Accuracy. Existing methods evaluate the transferability that estimate the performance of the optimal target model obtained by re-training only the classifier, not the feature extractor, which is uncommon in transfer learning. How can we accurately measure the transferability for predicting the fine-tuning performance?",
+            "C3 Generality. How can we measure the transferability such that it is applicable to general settings, including selecting the best supervised pre-trained model, the best self-supervised pre-trained models, and the transferring layer?"
+        ],
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+    {
+        "type": "text",
+        "text": "We address the aforementioned challenges with the following main ideas:",
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+        "list_items": [
+            "I1 We assess the transferability by evaluating the compactness and sparseness of target representations with only a one-way forward propagation.",
+            "12 We relax the assumption proposed in existing methods"
+        ],
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "11476",
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+    {
+        "type": "text",
+        "text": "that the pre-trained feature extractor can extract all the information related to the target task. We view transferability as the generalization ability of a pre-trained model on a target task. We estimate the generalization ability using intra-class variance, which implies how efficient the feature is for learning tasks.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "13 We measure the transferability using intra-class variance of latent representations, which is applicable to various settings including self-supervised pre-trained models and transferring layer selection.",
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+    {
+        "type": "text",
+        "text": "3.2.TMI",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Given a pre-trained source model and a target dataset with labels, our goal is to measure the transferability between the source model and the target task to predict the fine-tuning performance. Existing methods measure the performance of re-trained classifier while freezing the feature extractor, which is time-consuming. To address the issues, our proposed TMI computes the transferability as the intra-class variance of a pre-trained model on a target task. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. It is unnecessary for TMI to obtain optimal classifier which is a time-consuming process.",
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+    },
+    {
+        "type": "text",
+        "text": "TMI The transferability of a pre-trained feature extractor  $\\omega_{s}$  from a source task  $S$  to a target task  $T$ , denoted by  $Trf_{(S\\rightarrow T)}$ , is measured by TMI with the intra-class feature variance obtained from the pre-trained model  $\\omega_{s}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT r f _ {(S \\rightarrow T)} := H \\left(\\omega_ {s} (X) | Y\\right) = \\sum_ {c = 1} ^ {C} \\frac {n _ {c}}{n} H \\left(\\omega_ {s} \\left(X _ {c}\\right)\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $X$  and  $Y$  represent the target feature and the target label, respectively.  $C$  represents the number of classes and  $X_{c} = \\{x|Y = c\\}$  is the set of target features in the  $c$ -th class.  $n$  and  $n_{c}$  represent the number of total instances and number of instances in the  $c$ -th class, respectively. We measure the intra-class variance of target representations using conditional entropy. The intra-class variance encourages the pre-trained model to have a generalization ability for learning tasks.",
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+    {
+        "type": "text",
+        "text": "How to utilize TMI? Given a set of pre-trained models and a target dataset with labels, we first obtain target representations of pre-trained models by one-way forward propagation. Next, we compute the transferability score using Equation (4). We select the pre-trained model with the highest transferability score and then fine-tune the model using the target data. We argue that the larger the TMI, the higher the transfer performance.",
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We present experimental results to answer the following questions about TMI:",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "Q1 Evaluation of transferability estimation (Section 4.2). Does TMI accurately select the best pretrained model compared to baselines? Is the transferability score measured by TMI highly correlated to the transfer performance?",
+            "Q2 Comparison of ICV measures (Section 4.3). What is the best measurement to evaluate Intra-Class Variance (ICV)?",
+            "Q3 Evaluation of generalization ability (Section 4.4). Does intra-class variance estimate generalization ability of a pre-trained model on a target task?",
+            "Q4 General applications (Section 4.5). Does TMI accurately estimate the transferability in general cases, such as selecting the best self-supervised pre-trained model and the best transferring layer?",
+            "Q5 Hyperparameter sensitivity (Section 4.6). How sensitive is TMI to hyperparameters?"
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We present pre-trained models, datasets, baselines, evaluation, estimator, and hyperparameters for our experiments.",
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+    },
+    {
+        "type": "text",
+        "text": "Pre-trained models. We use supervised model groups offered by Pytorch: ResNet, DenseNet, MnasNet, ShuffleNet V2, MobileNet V2, MobileNet V3, ResNeXt, Wide ResNet, EfficientNet, EfficientNet V2, and RegNet. We also utilize self-supervised model groups, which have only feature extractors without classifiers. We obtain Swin Transformer and Vision Transformer from Pytorch; we get MoCo v1, MoCo v2, Barlow Twins, SwAV, SimSiam, and Dino from Gitlab repositories. Note that we select fifty supervised pretrained models and eleven self-supervised pre-trained models from the aforementioned model groups.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We use seventeen image datasets summarized in Table 1. We randomly split each dataset into a train set and test set by 8:2 ratio, except for datasets that already have been separated.",
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+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare the proposed method with the following baselines. NCE [18] defines the transferability as negative conditional entropy between ground truths and predicted labels from a pre-trained model. LEEP [13] measures negative conditional entropy between ground truths and predicted average log-likelihood. H-Score [2] estimates the transferability by solving an HGR maximum correlation problem. LogME [25] proposes the logarithm of maximum evidence given extracted features. TransRate [5] measures the transferability by the mutual information between target labels and target representations. We omit the comparison with Taskonomy [26] and Task2Vec [1] due to tremendous time costs.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "11477",
+        "bbox": [
+            480,
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/2261568fa582b7a0bdce772b37610d225b81d533ba018d80ce72c42aa6e069e6.jpg",
+        "table_caption": [
+            "Table 1: Summary of datasets."
+        ],
+        "table_footnote": [
+            "<sup>1</sup>https://data.caltech.edu/records/mzrjq-6wc02",
+            "2 https://data.caltech.edu/records/nyy15-4j048",
+            "<sup>3</sup> https://www.cs.toronto.edu/~kriz/cifar.html",
+            "4 http://yann.learun.com/exdb/mnist/",
+            "5 https://github.com/zalandoresearch/fashion-mnist",
+            "$^{6}$  http://ufldl.stanford.edu/housenumbers/",
+            "$^7$  https://www.tensorflow.org/datasets/catalog/tf_flowers",
+            "8 https://github.com/phelber/eurosat",
+            "9 https://data.mendeley.com/datasets/rscbjbr9sj/2",
+            "10 http://ai.bu.edu/visda-2017/#browse",
+            "11 https://www Robots.ox.ac.uk/~vgg/data/fgvc-aircraft/",
+            "12 http://www.vision.caltech.edu/datasets/cub_200_2011/",
+            "13 https://ai.stanford.edu/~jkrause/cars/car_dataset.html",
+            "14 https://www.robots.ox.ac.uk/~vgg/data/dtd/",
+            "15 https://data.vision.ee.ethz.ch/cvl/datasetsextra/food-101/",
+            "16 https://www Robots.ox.ac.uk/~vgg/data/pets/"
+        ],
+        "table_body": "<table><tr><td>Dataset</td><td># of instances (train / test)</td><td># of classes</td><td>Category</td></tr><tr><td>Caltech-1011</td><td>7,315 / 1,829</td><td>101</td><td>Multiple domains</td></tr><tr><td>Caltech-2562</td><td>24,485 / 6,122</td><td>256</td><td>Multiple domains</td></tr><tr><td>CIFAR-103</td><td>50,000 / 10,000</td><td>10</td><td>Multiple domains</td></tr><tr><td>CIFAR-1003</td><td>50,000 / 10,000</td><td>100</td><td>Multiple domains</td></tr><tr><td>MNIST4</td><td>60,000 / 10,000</td><td>10</td><td>Digit</td></tr><tr><td>FashionMNIST5</td><td>60,000 / 10,000</td><td>10</td><td>Fashion</td></tr><tr><td>SVHN6</td><td>73,257 / 26,032</td><td>10</td><td>Digit</td></tr><tr><td>FlowerPhotos7</td><td>2,936 / 734</td><td>5</td><td>Flower</td></tr><tr><td>EuroSAT8</td><td>21,600 / 5,400</td><td>10</td><td>Landscape</td></tr><tr><td>Chest X-Ray9</td><td>5,216 / 623</td><td>2</td><td>Medicine</td></tr><tr><td>VisDA10</td><td>152,397 / 72,372</td><td>212</td><td>Multiple domains</td></tr><tr><td>FGVC-Aircraft11</td><td>3,334 / 3,333</td><td>100</td><td>Aircraft</td></tr><tr><td>CUB-20012</td><td>9,430 / 2,358</td><td>200</td><td>Animal</td></tr><tr><td>Cars13</td><td>8,144 / 8,041</td><td>196</td><td>Auto</td></tr><tr><td>DTD14</td><td>4,512 / 1,128</td><td>47</td><td>Texture</td></tr><tr><td>Food-10115</td><td>80,800 / 20,200</td><td>101</td><td>Food</td></tr><tr><td>Oxford-IIIT Pet16</td><td>3,680 / 3,669</td><td>37</td><td>Animal</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation. We evaluate the performance of transferability measurement methods in two ways. First, do they accurately predict the best model? Second, are the transferability scores correlated to fine-tuned accuracy? We adopt Kendall correlation coefficient to measure the correlations between the transferability and fine-tuned accuracy. Kendall correlation coefficient tests the ordinal association between two measured quantities. Kendall correlation coefficient has values between -1 and 1, and correlations between two variables are high when the values are close to 1.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Estimator. We adopt  $k$ -nearest estimator [8] to evaluate the continuous entropy in Equation (4). Compared to kernel density estimators [12, 17],  $k$ -nearest estimator vastly reduces errors by sacrificing time, especially when data are too big. TMI greatly reduces the size of data to be calculated at once because it computes conditional entropy of representation given label.",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Hyperparameters. We use greedy searching algorithm to find the best hyperparameters for fine-tuning. For transferability measurement, the only hyperparameter in our proposed TMI is the number  $n_k$  of neighbors, which is used in the entropy estimator [8]. We discuss the hyperparameter sensitivity to transferability in Section 4.6.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Ratio of target tasks where their top-5 best source models include the model estimated by each transferability measurement method. The best result is in bold. Note that TMI gives the best ratio, accurately selecting the best pretrained models in 14 out of 17 cases.",
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/23777e577da089b5b969e9cb617481c0299354687082ad4a3465982aa180eff1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-5</td><td>3 / 17</td><td>5 / 17</td><td>4 / 17</td><td>8 / 17</td><td>9 / 17</td><td>14 / 17</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Evaluation of Transferability Estimation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Remind that our goal is to quickly and accurately select the best pre-trained model among a pool of well-trained models. A pre-trained model is determined by two components, source data and model architecture. Thus, we conduct experiments to select the best model architecture and the best source data.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Selecting the best model architecture. We evaluate how the transferability measurement methods accurately select the best source model for a target model. Table 2 shows the ratio of targets tasks where their top-5 best source models include the model estimated by each transferability measurement method. Note that TMI gives the best ratio, accurately selecting the best pre-trained models in 14 out of 17 cases, which is much better than the ratio  $9 / 17$  of the second-best model TransRate.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We also compare the correlations between fine-tuned accuracies and transferability scores in Table 3. Note that our proposed TMI shows the best Kendall correlation in 13 out of 17 datasets, outperforming all the competitors. Some baselines even give negative coefficients, which means that their predictions are far from the correct ranking.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Selecting the best source data. We fine-tune eighteen pre-trained models with the same model architecture ResNet-50, but different source datasets, including ImageNet and seventeen datasets introduced in Section 4.1. We predict the best source data and compare correlations with the ground truths. Table 4 shows that our proposed TMI accurately predicts the best source data in all the 17 cases, outperforming all the competitors. Our proposed TMI gives the best Kendall correlation consistently in 12 out of 17 cases, as shown in Table 5.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Comparison of ICV Measures",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Intra-Class Variance (ICV) is a general concept widely used in metric learning. In addition to the conditional entropy introduced in Section 3, we additionally choose four metric learning methods, Contrast [4], Center [20], SNCA [22], and MS [19]. We use the intra-class variance parts of their objective functions to measure the transferability. We apply the five aforementioned methods to measure",
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "11478",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/abfbeb347e3afef8e613d4358e47fe7fd03843fb9e5dd4e4e70679428b92b038.jpg",
+        "table_caption": [
+            "Table 3: Correlations between fine-tuned accuracies and transferability scores when transferring supervised pre-trained models trained on ImageNet. The best result is in bold. Our proposed TMI gives the best Kendall correlation in 13 out of 17 cases, outperforming competitors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"6\">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>0.429</td><td>0.425</td><td>0.316</td><td>0.362</td><td>0.474</td><td>0.524</td></tr><tr><td>Caltech-256</td><td>0.686</td><td>0.455</td><td>0.492</td><td>0.503</td><td>0.509</td><td>0.481</td></tr><tr><td>CIFAR-10</td><td>-0.140</td><td>0.324</td><td>0.275</td><td>0.323</td><td>0.364</td><td>0.527</td></tr><tr><td>CIFAR-100</td><td>-0.202</td><td>0.340</td><td>0.351</td><td>0.398</td><td>0.432</td><td>0.497</td></tr><tr><td>MNIST</td><td>0.057</td><td>0.282</td><td>0.083</td><td>0.137</td><td>0.038</td><td>0.137</td></tr><tr><td>FashionMNIST</td><td>-0.328</td><td>0.127</td><td>-0.038</td><td>0.121</td><td>0.125</td><td>0.467</td></tr><tr><td>SVHN</td><td>-0.023</td><td>0.091</td><td>-0.002</td><td>0.092</td><td>0.206</td><td>0.394</td></tr><tr><td>FlowerPhotos</td><td>0.117</td><td>0.139</td><td>0.224</td><td>0.321</td><td>0.392</td><td>0.499</td></tr><tr><td>EuroSAT</td><td>0.269</td><td>0.082</td><td>-0.005</td><td>0.102</td><td>0.051</td><td>0.085</td></tr><tr><td>Chest X-Ray</td><td>0.071</td><td>0.152</td><td>0.171</td><td>0.333</td><td>0.285</td><td>0.395</td></tr><tr><td>VisDA</td><td>0.298</td><td>0.240</td><td>0.329</td><td>0.334</td><td>0.304</td><td>0.341</td></tr><tr><td>FGVC-Aircraft</td><td>0.366</td><td>-0.011</td><td>0.216</td><td>0.498</td><td>0.421</td><td>0.500</td></tr><tr><td>CUB-200</td><td>0.415</td><td>0.098</td><td>0.325</td><td>0.410</td><td>0.519</td><td>0.523</td></tr><tr><td>Cars</td><td>0.270</td><td>0.506</td><td>0.175</td><td>0.432</td><td>0.455</td><td>0.521</td></tr><tr><td>DTD</td><td>-0.074</td><td>0.501</td><td>0.479</td><td>0.366</td><td>0.499</td><td>0.401</td></tr><tr><td>Food-101</td><td>0.261</td><td>0.515</td><td>0.395</td><td>0.421</td><td>0.448</td><td>0.537</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.536</td><td>0.527</td><td>0.418</td><td>0.493</td><td>0.500</td><td>0.576</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/86ad4169e3bd318844a9f37d12d16f95c936bde71f72ca34ac575fcb76e57f83.jpg",
+        "table_caption": [
+            "Table 4: Ratio of target tasks where the transferability measurement methods accurately find the best source data. The best method is in bold. TMI predicts the best source data in all cases, outperforming competitors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-1</td><td>1 / 17</td><td>2 / 17</td><td>3 / 17</td><td>2 / 17</td><td>13 / 17</td><td>17 / 17</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the correlations between fine-tuned accuracies and transferability scores. Conditional Entropy (CE) shows the best correlations than the other four metric learning measurements in 15 out of 17 datasets, outperforming all the competitors, as shown in Table 6. M. Boudiaf et al. [3] demonstrate that the conditional entropy is a lower bound of intra-class variance of the four metric learning methods.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Evaluation of Generalization Ability",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "We perform experiments on two control groups to demonstrate that transferability is relevant to the generalization ability of a pre-trained model on a target task. In Group A, we use a pre-trained ResNet-50 model trained on ImageNet and fine-tune it using the dataset  $D$ . In Group B, we train a ResNet-50 model trained from scratch on dataset  $D$  and fine-tune it on the same dataset. Dataset  $D$  is one of the datasets introduced in Section 4.1.",
+        "bbox": [
+            75,
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+    },
+    {
+        "type": "text",
+        "text": "Table 7 shows the difference of fine-tuning performance and that of transferability between two groups. “+” rep",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "resents the difference is larger than 0 while “-” represents that is less than 0. Group A has higher transfer accuracies than Group B in most cases since models in Group A have learned a large amount of information from the ImageNet, which can potentially benefit downstream tasks.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our proposed TMI and TransRate have the same symbols for transfer accuracy in 14 out of 17 cases, while the other four baselines do not provide similar symbols. TransRate also estimates well, but it is computationally expensive since it measures the mutual information between target representation and label. In contrast, TMI is more efficient as it considers only intra-class features.",
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+    },
+    {
+        "type": "text",
+        "text": "4.5. General Applications",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Applying to self-supervised pre-trained models. TMI not only measures the transferability between supervised pre-trained models and classification tasks but also can be extended to self-supervised pre-trained models. We prepare eleven self-supervised pre-trained models already trained on ImageNet provided by Github repositories introduced in Section 4.1. NCE [18] and LEEP [13] cannot measure the transferability between a self-supervised pre-trained model and a downstream task because they dig out the relationship between target ground truth and predicted label or probability. Thus, we compare the proposed TMI to LogME [25], H-Score [2], and TransRate [5] in Table 8; TMI outperforms competitors in 13 out of 17 classification datasets.",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "11479",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f9ccf95c3210a5588e9edac8509ea68cf8be26aa939154cc7887356e28551ee6.jpg",
+        "table_caption": [
+            "Table 5: Correlations between fine-tuned accuracies and transferability scores when transferring ResNet-50 models trained on different source data. The best result is in bold. TMI shows the best Kendall correlation in 12 out of 17 cases, outperforming all the competitors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"6\">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.294</td><td>0.542</td><td>0.353</td><td>0.647</td><td>0.425</td><td>0.699</td></tr><tr><td>Caltech-256</td><td>-0.268</td><td>0.542</td><td>0.437</td><td>0.660</td><td>0.477</td><td>0.699</td></tr><tr><td>CIFAR-10</td><td>-0.216</td><td>0.373</td><td>0.383</td><td>0.490</td><td>0.399</td><td>0.630</td></tr><tr><td>CIFAR-100</td><td>-0.098</td><td>0.556</td><td>0.686</td><td>0.345</td><td>0.542</td><td>0.699</td></tr><tr><td>MNIST</td><td>-0.061</td><td>0.439</td><td>0.372</td><td>-0.007</td><td>0.115</td><td>0.162</td></tr><tr><td>FashionMNIST</td><td>-0.086</td><td>0.362</td><td>0.430</td><td>0.475</td><td>0.046</td><td>0.150</td></tr><tr><td>SVHN</td><td>0.039</td><td>0.285</td><td>-0.033</td><td>0.393</td><td>0.170</td><td>0.407</td></tr><tr><td>FlowerPhotos</td><td>-0.359</td><td>0.412</td><td>0.456</td><td>0.307</td><td>0.490</td><td>0.516</td></tr><tr><td>EuroSAT</td><td>-0.388</td><td>0.428</td><td>0.490</td><td>0.322</td><td>0.467</td><td>0.704</td></tr><tr><td>Chest X-Ray</td><td>-0.072</td><td>0.164</td><td>0.359</td><td>-0.111</td><td>0.425</td><td>-0.123</td></tr><tr><td>VisDA</td><td>-0.538</td><td>0.498</td><td>0.094</td><td>-0.039</td><td>0.498</td><td>0.546</td></tr><tr><td>FGVC-Aircraft</td><td>-0.033</td><td>0.373</td><td>0.339</td><td>0.556</td><td>0.399</td><td>0.688</td></tr><tr><td>CUB-200</td><td>-0.503</td><td>0.582</td><td>0.455</td><td>0.464</td><td>0.647</td><td>0.723</td></tr><tr><td>Cars</td><td>-0.294</td><td>0.529</td><td>0.403</td><td>0.752</td><td>0.542</td><td>0.804</td></tr><tr><td>DTD</td><td>-0.438</td><td>0.595</td><td>0.393</td><td>0.647</td><td>0.542</td><td>0.757</td></tr><tr><td>Food-101</td><td>-0.020</td><td>0.281</td><td>0.092</td><td>0.046</td><td>0.229</td><td>0.225</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.268</td><td>0.569</td><td>0.660</td><td>0.503</td><td>0.516</td><td>0.248</td></tr></table>",
+        "bbox": [
+            210,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/4bf5cacc516bd8b3e4945abbf7645da4b39378740f2ba26d29e1d4500de17c44.jpg",
+        "table_caption": [
+            "Table 6: Comparison of intra-class variance measurements. Conditional Entropy (CE) shows the best correlations consistently in 15 out of 17 cases. The best result is in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"5\">Kendall Correlation Coefficient</td></tr><tr><td>Contrast</td><td>Center</td><td>SNCA</td><td>MS</td><td>CE</td></tr><tr><td>Caltech-101</td><td>0.274</td><td>0.283</td><td>0.380</td><td>0.358</td><td>0.442</td></tr><tr><td>Caltech-256</td><td>0.295</td><td>0.347</td><td>0.261</td><td>0.347</td><td>0.354</td></tr><tr><td>CIFAR-10</td><td>0.328</td><td>0.322</td><td>0.275</td><td>0.299</td><td>0.369</td></tr><tr><td>CIFAR-100</td><td>0.374</td><td>0.282</td><td>0.207</td><td>0.200</td><td>0.376</td></tr><tr><td>MNIST</td><td>0.383</td><td>0.267</td><td>0.306</td><td>0.228</td><td>0.374</td></tr><tr><td>FashionMNIST</td><td>0.332</td><td>0.225</td><td>0.260</td><td>0.337</td><td>0.374</td></tr><tr><td>SVHN</td><td>0.303</td><td>0.359</td><td>0.369</td><td>0.360</td><td>0.383</td></tr><tr><td>FlowerPhotos</td><td>0.209</td><td>0.263</td><td>0.291</td><td>0.277</td><td>0.372</td></tr><tr><td>EuroSAT</td><td>0.292</td><td>0.237</td><td>0.367</td><td>0.268</td><td>0.400</td></tr><tr><td>Chest X-Ray</td><td>0.292</td><td>0.289</td><td>0.210</td><td>0.232</td><td>0.357</td></tr><tr><td>VisDA</td><td>0.259</td><td>0.352</td><td>0.200</td><td>0.329</td><td>0.352</td></tr><tr><td>FGVC-Aircraft</td><td>0.220</td><td>0.322</td><td>0.244</td><td>0.315</td><td>0.351</td></tr><tr><td>CUB-200</td><td>0.368</td><td>0.252</td><td>0.379</td><td>0.385</td><td>0.431</td></tr><tr><td>Cars</td><td>0.351</td><td>0.285</td><td>0.398</td><td>0.268</td><td>0.248</td></tr><tr><td>DTD</td><td>0.236</td><td>0.322</td><td>0.228</td><td>0.206</td><td>0.327</td></tr><tr><td>Food-101</td><td>0.322</td><td>0.267</td><td>0.246</td><td>0.269</td><td>0.484</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.301</td><td>0.202</td><td>0.363</td><td>0.274</td><td>0.449</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Selecting the best transferring layer. Given a ResNet-18 trained on ImageNet, we can easily determine the best transferring layer, which produces the best fine-tuning performance for a target task by measuring transferability. We compare the correlations of LogME [25], H-Score [2], and TransRate to select the best transferring layer for fine",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/fcecd8c634032bc5b009ab8ae35f6b731f2fc16ed4bee9bf3b2fde1570844d74.jpg",
+        "table_caption": [
+            "Table 7: Comparison of the consistency of fine-tuning accuracy and transferability. “+” represents the difference is larger than 0 while “-” represents the difference is less than 0. TMI has consistent signs with fine-tuning accuracy in 14 out of 17 cases, outperforming its competitors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Accuracy (A-B)</td><td colspan=\"6\">Transferability (A-B)</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogME</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Caltech-256</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-10</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-100</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>MNIST</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FashionMNIST</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>SVHN</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>FlowerPhotos</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>EuroSAT</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>Chest X-Ray</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>VisDA</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FGVC-Aircraft</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CUB-200</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Cars</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>DTD</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Food-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Oxford-IIIT Pet</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tuning. Theoretically, LogME [25] and H-Score [2] cannot deal with layer selection because they rely on features from the ultimate layer of the feature extractor. However, we extract features from each layer and directly put them into LogME and H-Score algorithms to calculate the trans",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "11480",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/be0ce93f694e5c1485661c53e9de06f01740fa39c6cd56abb89f8ec397054dc2.jpg",
+        "table_caption": [
+            "Table 8: Correlations between fine-tuned accuracies and transferability scores when transferring self-supervised pretrained models to classification tasks. The best result is in bold. TMI shows the best Kendall correlation consistently in 13 out of 17 cases, outperforming all the competitors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">Kendall Correlation Coefficient</td></tr><tr><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.278</td><td>0.183</td><td>0.000</td><td>0.367</td></tr><tr><td>Caltech-256</td><td>-0.561</td><td>0.345</td><td>0.164</td><td>0.600</td></tr><tr><td>CIFAR-10</td><td>-0.337</td><td>0.018</td><td>0.164</td><td>0.624</td></tr><tr><td>CIFAR-100</td><td>-0.561</td><td>0.673</td><td>0.236</td><td>0.697</td></tr><tr><td>MNIST</td><td>-0.574</td><td>-0.262</td><td>-0.426</td><td>0.246</td></tr><tr><td>FashionMNIST</td><td>-0.330</td><td>-0.220</td><td>-0.330</td><td>0.094</td></tr><tr><td>SVHN</td><td>0.055</td><td>0.309</td><td>-0.345</td><td>0.075</td></tr><tr><td>FlowerPhotos</td><td>0.389</td><td>-0.241</td><td>0.130</td><td>0.075</td></tr><tr><td>EuroSAT</td><td>-0.073</td><td>-0.037</td><td>0.037</td><td>-0.208</td></tr><tr><td>Chest X-Ray</td><td>-0.037</td><td>-0.037</td><td>-0.257</td><td>0.175</td></tr><tr><td>VisDA</td><td>0.550</td><td>0.055</td><td>0.309</td><td>-0.597</td></tr><tr><td>FGVC-Aircraft</td><td>-0.345</td><td>0.091</td><td>-0.309</td><td>0.150</td></tr><tr><td>CUB-200</td><td>-0.112</td><td>-0.018</td><td>0.091</td><td>0.564</td></tr><tr><td>Cars</td><td>0.000</td><td>0.382</td><td>-0.200</td><td>0.262</td></tr><tr><td>DTD</td><td>0.382</td><td>0.018</td><td>0.224</td><td>0.455</td></tr><tr><td>Food-101</td><td>-0.411</td><td>-0.018</td><td>-0.018</td><td>0.204</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.585</td><td>0.294</td><td>0.073</td><td>0.807</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c98a0030dc307929921556676a29d661d875515f1787899a5231af92281004ef.jpg",
+        "image_caption": [
+            "Figure 3: Sensitivity to the hyperparameter  $n_k$  in entropy estimator."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            140,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ferability. The size of extracted features is quite large in the early layers, resulting in much higher computational cost for transferability measurement. To reduce this cost, we add an avgpool2d layer to the end of transferring layer to reduce the dimension of extracted features. Table 9 shows that TMI achieves the highest correlation coefficients in 16 out of 17 datasets. Correlation coefficients of MNIST, SVHN, and Chest X-Ray are much lower than those of the other datasets because their ranges of minimum and maximum accuracies obtained by layer transfer are smaller than  $0.5\\%$ , making it challenging to rank these dataset accurately.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.6. Hyperparameter Sensitivity",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "An advantage of TMI is that it does not train models on target datasets because it is time-consuming and sensitive to hyperparameters which may cause different results. The only hyperparameter in TMI is  $n_k$  used in the entropy estimator. In Figure. 3, the correlation between pre-trained",
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+        "type": "table",
+        "img_path": "images/132aac5f08356d6efc99d7f4c6332f736ce396e9c4a10bb4c143a652bf9b80be.jpg",
+        "table_caption": [
+            "Table 9: Correlations between fine-tuned accuracies and transferability scores when transferring specific layers of pre-trained models. The best result is in bold. TMI shows the best correlations consistently in 16 out of 17 cases."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">Kendall Correlation Coefficient</td></tr><tr><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>0.346</td><td>0.935</td><td>0.752</td><td>0.941</td></tr><tr><td>Caltech-256</td><td>0.973</td><td>0.317</td><td>0.800</td><td>0.984</td></tr><tr><td>CIFAR-10</td><td>0.360</td><td>0.743</td><td>0.704</td><td>0.746</td></tr><tr><td>CIFAR-100</td><td>0.460</td><td>0.774</td><td>0.774</td><td>0.801</td></tr><tr><td>MNIST</td><td>0.180</td><td>0.055</td><td>0.179</td><td>0.184</td></tr><tr><td>FashionMNIST</td><td>0.294</td><td>0.241</td><td>0.298</td><td>0.308</td></tr><tr><td>SVHN</td><td>0.087</td><td>0.106</td><td>0.040</td><td>0.113</td></tr><tr><td>FlowerPhotos</td><td>0.779</td><td>0.198</td><td>0.687</td><td>0.792</td></tr><tr><td>EuroSAT</td><td>0.691</td><td>0.709</td><td>0.495</td><td>0.735</td></tr><tr><td>Chest X-Ray</td><td>0.113</td><td>0.154</td><td>0.100</td><td>0.054</td></tr><tr><td>VisDA</td><td>0.665</td><td>0.866</td><td>0.826</td><td>0.904</td></tr><tr><td>FGVC-Aircraft</td><td>0.791</td><td>0.302</td><td>0.595</td><td>0.817</td></tr><tr><td>CUB-200</td><td>0.317</td><td>0.970</td><td>0.787</td><td>0.954</td></tr><tr><td>Cars</td><td>0.330</td><td>0.869</td><td>0.752</td><td>0.882</td></tr><tr><td>DTD</td><td>0.924</td><td>0.401</td><td>0.761</td><td>0.931</td></tr><tr><td>Food-101</td><td>0.409</td><td>0.948</td><td>0.869</td><td>0.970</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.349</td><td>0.970</td><td>0.826</td><td>0.990</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "models and TMI shows consistency in most ranges for  $n_k$ .",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We propose TMI, a fast, accurate, and general algorithm to measure the transferability. TMI quantifies the degree of generalization of a pre-trained model to a new task by estimating the intra-class feature variance. We conduct experiments on seventeen datasets with fifty supervised pretrained models and eleven self-supervised pre-trained models. TMI selects the top-5 pre-trained architecture in 14 out of 17 cases and selects the best source data in all cases, outperforming its competitors. We measure the correlation between the fine-tuning performance and transferability, and our proposed TMI outperforms competitors in 13 out of 17 cases.",
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+    {
+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) [No.2020-0-00894, Flexible and Efficient Model Compression Method for Various Applications and Environments], [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)], and [NO.2021-0-02068, Artificial Intelligence Innovation Hub (Artificial Intelligence Institute, Seoul National University)]. The Institute of Engineering Research at Seoul National University provided research facilities for this work. The ICT at Seoul National University provides research facilities for this study. U Kang is the corresponding author.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Alessandro Achille, Michael Lam, Rahul Tewari, Avinash Ravichandran, Subhransu Maji, Charless C. Fowlkes, Stefano Soatto, and Pietro Perona. Task2vec: Task embedding for meta-learning. In ICCV, 2019.",
+            "[2] Yajie Bao, Yang Li, Shao-Lun Huang, Lin Zhang, Lizhong Zheng, Amir Roshan Zamir, and Leonidas J. Guibas. An information-theoretic approach to transferability in task transfer learning. In ICIP, 2019.",
+            "[3] Malik Boudiaf, Jérôme Rony, Imtiaz Masud Ziko, Eric Granger, Marco Pedersoli, Pablo Piantanida, and Ismail Ben Ayed. A unifying mutual information view of metric learning: Cross-entropy vs. pairwise losses. In Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part VI, volume 12351 of Lecture Notes in Computer Science, pages 548-564. Springer, 2020.",
+            "[4] Raia Hadsell, Sumit Chopra, and Yann LeCun. Dimensionality reduction by learning an invariant mapping. In 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2006), 17-22 June 2006, New York, NY, USA, pages 1735-1742. IEEE Computer Society, 2006.",
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+            "[7] Lee S. Jeon, H. and U Kang. Unsupervised multi-source domain adaptation with no observable source data. *PloS one*, 16(7), 2021.",
+            "[8] Alexander Kraskov, Harald Stögbauer, and Peter Grassberger. Estimating mutual information. Physical Review E, 2004.",
+            "[9] Jeon H. Lee, S. and U Kang. Multi-epl: Accurate multisource domain adaptation. PloS one, 16(8), 2021.",
+            "[10] Jian Liang, Dapeng Hu, Jiashi Feng, and Ran He. Dine: Domain adaptation from single and multiple black-box predictors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022.",
+            "[11] Feng Liu, Guangquan Zhang, and Jie Lu. Heterogeneous domain adaptation: An unsupervised approach. IEEE Transactions on Neural Networks and Learning Systems.",
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+            "[13] Cuong Nguyen, Tal Hassner, Matthias W. Seeger, and Cedric Archambeau. LEEP: A new measure to evaluate transferability of learned representations. In ICML, 2020.",
+            "[14] Tuan Nguyen, Trung Le, He Zhao, Quan Hung Tran, Truyen Nguyen, and Dinh Phung. Most: multi-source domain adaptation via optimal transport for student-teacher learning. In Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, pages 225–235, 2021.",
+            "[15] Seungcheol Park, Huiwen Xu, Taehun Kim, Inhwan Hwang, Kyung-Jun Kim, and U Kang. Fast and accurate transferabil"
+        ],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "ity measurement for heterogeneous multivariate data. CoRR, abs/1912.13366, 2019.",
+            "[16] Chuan-Xian Ren, Yong Hui Liu, Xiwen Zhang, and Ke-Kun Huang. Multi-source unsupervised domain adaptation via pseudo target domain. IEEE Trans. Image Process., 31:2122-2135, 2022.",
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+            "[18] Anh Tuan Tran, Cuong V. Nguyen, and Tal Hassner. Transferability and hardness of supervised classification tasks. In ICCV, 2019.",
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+            "[20] Yandong Wen, Kaipeng Zhang, Zhifeng Li, and Yu Qiao. A discriminative feature learning approach for deep face recognition. In Computer Vision - ECCV 2016 - 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part VII, volume 9911 of Lecture Notes in Computer Science, pages 499-515. Springer, 2016.",
+            "[21] Jun Wu and Jingrui He. Domain adaptation with dynamic open-set targets. In KDD '22: The 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Washington, DC, USA, August 14 - 18, 2022, pages 2039-2049. ACM, 2022.",
+            "[22] Zhirong Wu, Alexei A. Efros, and Stella X. Yu. Improving generalization via scalable neighborhood component analysis. In Computer Vision - ECCV 2018 - 15th European Conference, Munich, Germany, September 8-14, 2018, Proceedings, Part VII, volume 11211 of Lecture Notes in Computer Science, pages 712-728.",
+            "[23] Huiwen Xu and U Kang. Transfer alignment network for blind unsupervised domain adaptation. Knowl. Inf. Syst., 63(11):2861-2881, 2021.",
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+            "[25] Kaichao You, Yong Liu, Jianmin Wang, and Mingsheng Long. Logme: Practical assessment of pre-trained models for transfer learning. In ICML, 2021.",
+            "[26] Amir R. Zamir, Alexander Sax, William B. Shen, Leonidas J. Guibas, Jitendra Malik, and Silvio Savarese. Taskonomy: Disentangling task transfer learning. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, 2018.",
+            "[27] Haojian Zhang, Yabin Zhang, Kui Jia, and Lei Zhang. Unsupervised domain adaptation of black-box source models. arXiv preprint arXiv:2101.02839, 2021."
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            854
+        ],
+        "page_idx": 8
+    },
+    {
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+        "text": "11482",
+        "bbox": [
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+            955
+        ],
+        "page_idx": 8
+    }
+]
\ No newline at end of file
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+++ b/2023/Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance/16d96c9b-c625-4fb0-aaab-b679d45a05de_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Huiwen Xu  \nSeoul National University  \nSeoul, Republic of Korea  \nxuhuiwen33@snu.ac.kr"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.516,
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+            ],
+            "angle": 0,
+            "content": "U Kang Seoul National University Seoul, Republic of Korea ukang@snu.ac.kr"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
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+            "angle": 0,
+            "content": "Abstract"
+        },
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+            "type": "text",
+            "bbox": [
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+                0.6
+            ],
+            "angle": 0,
+            "content": "Given a set of pre-trained models, how can we quickly and accurately find the most useful pre-trained model for a downstream task? Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. It is used for quickly ranking pre-trained models for a given task and thus becomes a crucial step for transfer learning. Existing methods measure transferability as the discrimination ability of a source model for a target data before transfer learning, which cannot accurately estimate the fine-tuning performance. Some of them restrict the application of transferability measurement in selecting the best supervised pre-trained models that have classifiers. It is important to have a general method for measuring transferability that can be applied in a variety of situations, such as selecting the best self-supervised pre-trained models that do not have classifiers, and selecting the best transferring layer for a target task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.601,
+                0.473,
+                0.813
+            ],
+            "angle": 0,
+            "content": "In this work, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a fast and accurate algorithm to measure transferability. We view transferability as the generalization of a pre-trained model on a target task by measuring intra-class feature variance. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Extensive experiments on real-world datasets show that TMI outperforms competitors for selecting the top-5 best models, and exhibits consistently better correlation in 13 out of 17 cases."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+            ],
+            "angle": 0,
+            "content": "Transfer learning is an important concept in the field of machine learning, revolutionizing the way models are"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
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+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1: Illustration of selecting the best pre-trained model for a given target task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "trained and applied to various domains. Transfer learning has proven to be particularly valuable when labeled data in the target domain are scarce or costly to obtain. Within the broader scope of transfer learning, several variants have emerged, such as source-free domain adaptation [10, 27, 23, 7], multi-source transfer learning [16, 14, 7, 9], heterogeneous transfer learning [11, 15], and open-set domain adaptation [6, 21]."
+        },
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+            "content": "In transfer learning, fine-tuning a pre-trained model becomes a simple and effective way to improve the performance of a downstream task. A crucial step in transfer learning is to quickly and accurately select the most helpful pre-trained model in a set of given pre-trained models. Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. As shown in Figure. 1, transferability measurement is used for ranking pre-trained models for a given task, and is a crucial step for transfer learning."
+        },
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+            "type": "page_number",
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+            "bbox": [
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+            "angle": 0,
+            "content": "A desired method for transferability measurement should be faster than running a transfer learning algorithm, accurately select the best pre-trained model, and be general to be implemented in various common scenarios. Taskonomy [26] and Task2Vec [1] are computationally expensive due to their learning with data. NCE [18] and LEEP [13] are free of training but cannot be applied to general cases, such as selecting self-supervised pre-trained models and selecting the best transferring layer. LogMe [25] and H-Score [2] also cannot be applied theoretically to select the best transferring layer. Instead of measuring transferability, they measure how discriminative a pre-trained model is to a target task before implementing transfer learning, which cannot estimate fine-tuning performance. TransRate [5] is simple and general to be applied for transferability measurement, but too slow due to the computation of the entropy of whole hidden representations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.348,
+                0.473,
+                0.59
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a simple but effective method for transferability measurement. We deem transferability as the generalization of a pre-trained model on a target task. To quantify the degree of generalization, we measure the intra-class variance by the conditional entropy of target representation given a label. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Large intra-class variance implies the feature is efficient for learning tasks. TMI can be used for selecting not only the best supervised model but also the best self-supervised models and the best transferring layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
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+            "angle": 0,
+            "content": "Our contributions are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.614,
+                0.47,
+                0.689
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+            "angle": 0,
+            "content": "- Algorithm. We propose TMI, a fast, accurate, and general method for measuring transferability. We view transferability as generalization ability of a pre-trained model on a target task. The model generalization is measured by intra-class feature variance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.69,
+                0.47,
+                0.825
+            ],
+            "angle": 0,
+            "content": "- Experiments. We conduct extensive experiments on seventeen datasets with fifty supervised pre-trained models and eleven self-supervised pre-trained models. TMI outperforms competitors for selecting the top-5 pre-trained architecture in 14 out of 17 cases and selecting the best source data in all cases. TMI also shows the best trade-off of the running time and transferability, outperforming competitors in 12 out of 17 cases (see Figure. 2)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.826,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "- Case study. We evaluate the transferability in more general cases, such as applying to self-supervised pretrained models and selecting the best transferring layer. Compared to competitors, TMI achieves the highest correlation coefficient in 13 out of 17 for selecting the"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.614,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "best self-supervised pre-trained models, and in 16 out of 17 datasets for selecting the best transferring layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.133,
+                0.894,
+                0.208
+            ],
+            "angle": 0,
+            "content": "The rest of this paper is organized as follows. We introduce related works for transferability measurement in Section 2, and propose our method TMI in Section 3. After presenting experimental results in Section 4, we conclude in Section 5."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
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+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.247,
+                0.895,
+                0.385
+            ],
+            "angle": 0,
+            "content": "We assume a pre-trained model \\(\\theta = (w, h)\\) in a source domain where \\(w\\) is a feature extractor, and \\(h\\) is a classifier (or head). We transfer the model \\(\\theta\\) to a target domain and add a new classifier \\(k\\) at the end of the feature extractor \\(w\\) before fine-tuning. Since the target task is different from the source task in most cases, the pre-trained classifier \\(h\\) is inappropriate to solve the target task. Thus, we fine-tune the model by minimizing the cross entropy loss on the target dataset \\(D = \\{(x_i, y_i)\\}_{i=1}^n\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.608,
+                0.395,
+                0.892,
+                0.421
+            ],
+            "angle": 0,
+            "content": "\\[\nw ^ {*}, k ^ {*} = \\underset {w, k} {\\arg \\min } \\mathcal {L} (w, k) \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.426,
+                0.894,
+                0.532
+            ],
+            "angle": 0,
+            "content": "where a feature extractor \\( w \\) maps an input \\( x_{i} \\) to a representation \\( r_i = w(x_i) \\), and a classifier \\( h \\) maps the representation \\( r_i \\) to a probability distribution \\( \\hat{y}_i = \\sigma(h(r_i)) \\) where \\( \\sigma(\\cdot) \\) is an activation function. Note that \\( \\hat{y}_i \\) is a vector of length \\( n_c \\), where \\( n_c \\) is the number of classes, and \\( \\mathcal{L}(\\cdot) \\) is the cross entropy loss, which is equivalent to the average negative log-likelihood:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.565,
+                0.542,
+                0.892,
+                0.582
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} (w, k) = - \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log P \\left(\\hat {y} _ {i, c} \\mid x _ {i}; w, k\\right) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.587,
+                0.892,
+                0.616
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{y}_{i,c}\\) is the probability of \\(i\\)-th input instance belonging to its ground truth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.616,
+                0.892,
+                0.647
+            ],
+            "angle": 0,
+            "content": "The transferability of a source task \\( S \\) to a target task \\( T \\) is defined by the log-likelihood [18]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.555,
+                0.657,
+                0.892,
+                0.696
+            ],
+            "angle": 0,
+            "content": "\\[\nT r f _ {(S \\rightarrow T)} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log P \\left(\\hat {y} _ {i, c} \\mid x _ {i}; w ^ {*}, k ^ {*}\\right) \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Taskonomy [26] and Task2Vec [1] train the source model using target data to obtain the optimal feature extractor \\( w^{*} \\) and the optimal classifier \\( k^{*} \\). These methods are inconvenient to measure the transferability due to their training with data. There have been works focusing on estimating a bound on the log-likelihood to evaluate the transferability without training. NCE [18] proposes negative conditional entropy, which is drawn from the empirical joint distribution over ground truths and predicted labels from a pretrained model. Similarly, LEEP [13] replaces the ground truth with the average log-likelihood to evaluate the transferability. NCE and LEEP are fast, but are restricted to supervised pre-trained models because the algorithms rely"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "11475"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.091,
+                0.222,
+                0.188
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.113,
+                0.19,
+                0.207,
+                0.202
+            ],
+            "angle": 0,
+            "content": "(a) Caltech-101"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.226,
+                0.092,
+                0.351,
+                0.188
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.24,
+                0.19,
+                0.335,
+                0.202
+            ],
+            "angle": 0,
+            "content": "(b) Caltech-256"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.092,
+                0.475,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.372,
+                0.19,
+                0.456,
+                0.202
+            ],
+            "angle": 0,
+            "content": "(c) CIFAR-10"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.483,
+                0.092,
+                0.607,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.19,
+                0.591,
+                0.202
+            ],
+            "angle": 0,
+            "content": "(d) CIFAR-100"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.616,
+                0.092,
+                0.738,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.643,
+                0.19,
+                0.71,
+                0.202
+            ],
+            "angle": 0,
+            "content": "(e) MNIST"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.747,
+                0.092,
+                0.868,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.751,
+                0.19,
+                0.863,
+                0.202
+            ],
+            "angle": 0,
+            "content": "(f) FashionMNIST"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.099,
+                0.209,
+                0.222,
+                0.302
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.13,
+                0.305,
+                0.192,
+                0.317
+            ],
+            "angle": 0,
+            "content": "(g) SVHN"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.227,
+                0.209,
+                0.35,
+                0.303
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.238,
+                0.305,
+                0.337,
+                0.316
+            ],
+            "angle": 0,
+            "content": "(h)FlowerPhotos"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.208,
+                0.475,
+                0.303
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.377,
+                0.305,
+                0.45,
+                0.317
+            ],
+            "angle": 0,
+            "content": "(i) EuroSAT"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.48,
+                0.207,
+                0.61,
+                0.303
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.497,
+                0.305,
+                0.592,
+                0.318
+            ],
+            "angle": 0,
+            "content": "(j) Chest X-Ray"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.617,
+                0.208,
+                0.738,
+                0.303
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.646,
+                0.305,
+                0.707,
+                0.317
+            ],
+            "angle": 0,
+            "content": "(k) VisDA"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.746,
+                0.209,
+                0.868,
+                0.303
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.752,
+                0.305,
+                0.862,
+                0.317
+            ],
+            "angle": 0,
+            "content": "(1) FGVC-Aircraft"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.099,
+                0.322,
+                0.222,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.119,
+                0.418,
+                0.203,
+                0.43
+            ],
+            "angle": 0,
+            "content": "(m) CUB-200"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.227,
+                0.322,
+                0.35,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.263,
+                0.418,
+                0.313,
+                0.43
+            ],
+            "angle": 0,
+            "content": "(n) Cars"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.322,
+                0.475,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.387,
+                0.418,
+                0.44,
+                0.43
+            ],
+            "angle": 0,
+            "content": "(0) DTD"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.483,
+                0.322,
+                0.606,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.505,
+                0.418,
+                0.583,
+                0.43
+            ],
+            "angle": 0,
+            "content": "(p) Food-101"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.616,
+                0.322,
+                0.739,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.618,
+                0.418,
+                0.734,
+                0.43
+            ],
+            "angle": 0,
+            "content": "(q) Oxford-IIIT Pet"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.749,
+                0.33,
+                0.871,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.444,
+                0.892,
+                0.475
+            ],
+            "angle": 0,
+            "content": "Figure 2: Total running time (seconds) vs. Kendall's Correlation between transferability scores and test accuracies for selecting the best model among fifty pre-trained models. TMI provides the best trade-off between running time and correlation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.501,
+                0.473,
+                0.804
+            ],
+            "angle": 0,
+            "content": "on the outputs of the pre-trained classifier. To apply measurements in more general cases, LogME [25] calculates the logarithm of maximum evidence given extracted features, and H-Score [2] solves an HGR maximum correlation problem. LogMe [25] and H-Score [2] still cannot be applied to select the best transferred layer since they extract features from only the ultimate layers of the pretrained feature extractors. TransRate [5] is the most recent algorithm and applicable to self-supervised models and transferring layer selection. However, it is time-consuming since it requires to calculate mutual information between extracted feature and ground truth. To simplify the problem, [18, 13, 25, 2, 5] assume that the optimal model can be obtained by re-training the classifier while freezing the feature extractor. They estimate the performance of re-training only the classifier, which is even worse than training a target model from scratch [24]. In this paper, we propose a fast, accurate, and general transferability measurement method that predicts fine-tuned performance of a pre-trained model to a new target task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.838,
+                0.25,
+                0.856
+            ],
+            "angle": 0,
+            "content": "3. Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We propose TMI to measure the transferability between a pre-trained model and a target task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.5,
+                0.61,
+                0.515
+            ],
+            "angle": 0,
+            "content": "3.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.527,
+                0.892,
+                0.573
+            ],
+            "angle": 0,
+            "content": "Our goal is to measure the transferability in a fast, accurate, and general manner. The following challenges need to be addressed for the goal."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.577,
+                0.892,
+                0.635
+            ],
+            "angle": 0,
+            "content": "C1 Speed. Training a pre-trained model on the target data requires a high computational cost. How can we measure the transferability without training on the target data?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.637,
+                0.892,
+                0.728
+            ],
+            "angle": 0,
+            "content": "C2 Accuracy. Existing methods evaluate the transferability that estimate the performance of the optimal target model obtained by re-training only the classifier, not the feature extractor, which is uncommon in transfer learning. How can we accurately measure the transferability for predicting the fine-tuning performance?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.728,
+                0.892,
+                0.804
+            ],
+            "angle": 0,
+            "content": "C3 Generality. How can we measure the transferability such that it is applicable to general settings, including selecting the best supervised pre-trained model, the best self-supervised pre-trained models, and the transferring layer?"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.505,
+                0.577,
+                0.892,
+                0.804
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.807,
+                0.891,
+                0.837
+            ],
+            "angle": 0,
+            "content": "We address the aforementioned challenges with the following main ideas:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.84,
+                0.892,
+                0.886
+            ],
+            "angle": 0,
+            "content": "I1 We assess the transferability by evaluating the compactness and sparseness of target representations with only a one-way forward propagation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "12 We relax the assumption proposed in existing methods"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.51,
+                0.84,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11476"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.108,
+                0.092,
+                0.468,
+                0.182
+            ],
+            "angle": 0,
+            "content": "that the pre-trained feature extractor can extract all the information related to the target task. We view transferability as the generalization ability of a pre-trained model on a target task. We estimate the generalization ability using intra-class variance, which implies how efficient the feature is for learning tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.183,
+                0.468,
+                0.243
+            ],
+            "angle": 0,
+            "content": "13 We measure the transferability using intra-class variance of latent representations, which is applicable to various settings including self-supervised pre-trained models and transferring layer selection."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.25,
+                0.146,
+                0.264
+            ],
+            "angle": 0,
+            "content": "3.2.TMI"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.273,
+                0.468,
+                0.454
+            ],
+            "angle": 0,
+            "content": "Given a pre-trained source model and a target dataset with labels, our goal is to measure the transferability between the source model and the target task to predict the fine-tuning performance. Existing methods measure the performance of re-trained classifier while freezing the feature extractor, which is time-consuming. To address the issues, our proposed TMI computes the transferability as the intra-class variance of a pre-trained model on a target task. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. It is unnecessary for TMI to obtain optimal classifier which is a time-consuming process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.455,
+                0.468,
+                0.515
+            ],
+            "angle": 0,
+            "content": "TMI The transferability of a pre-trained feature extractor \\(\\omega_{s}\\) from a source task \\(S\\) to a target task \\(T\\), denoted by \\(Trf_{(S\\rightarrow T)}\\), is measured by TMI with the intra-class feature variance obtained from the pre-trained model \\(\\omega_{s}\\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.532,
+                0.468,
+                0.573
+            ],
+            "angle": 0,
+            "content": "\\[\nT r f _ {(S \\rightarrow T)} := H \\left(\\omega_ {s} (X) | Y\\right) = \\sum_ {c = 1} ^ {C} \\frac {n _ {c}}{n} H \\left(\\omega_ {s} \\left(X _ {c}\\right)\\right) \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.578,
+                0.468,
+                0.713
+            ],
+            "angle": 0,
+            "content": "where \\( X \\) and \\( Y \\) represent the target feature and the target label, respectively. \\( C \\) represents the number of classes and \\( X_{c} = \\{x|Y = c\\} \\) is the set of target features in the \\( c \\)-th class. \\( n \\) and \\( n_{c} \\) represent the number of total instances and number of instances in the \\( c \\)-th class, respectively. We measure the intra-class variance of target representations using conditional entropy. The intra-class variance encourages the pre-trained model to have a generalization ability for learning tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.713,
+                0.468,
+                0.834
+            ],
+            "angle": 0,
+            "content": "How to utilize TMI? Given a set of pre-trained models and a target dataset with labels, we first obtain target representations of pre-trained models by one-way forward propagation. Next, we compute the transferability score using Equation (4). We select the pre-trained model with the highest transferability score and then fine-tune the model using the target data. We argue that the larger the TMI, the higher the transfer performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.846,
+                0.209,
+                0.862
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We present experimental results to answer the following questions about TMI:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.092,
+                0.891,
+                0.167
+            ],
+            "angle": 0,
+            "content": "Q1 Evaluation of transferability estimation (Section 4.2). Does TMI accurately select the best pretrained model compared to baselines? Is the transferability score measured by TMI highly correlated to the transfer performance?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.167,
+                0.891,
+                0.211
+            ],
+            "angle": 0,
+            "content": "Q2 Comparison of ICV measures (Section 4.3). What is the best measurement to evaluate Intra-Class Variance (ICV)?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.213,
+                0.891,
+                0.257
+            ],
+            "angle": 0,
+            "content": "Q3 Evaluation of generalization ability (Section 4.4). Does intra-class variance estimate generalization ability of a pre-trained model on a target task?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.258,
+                0.891,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Q4 General applications (Section 4.5). Does TMI accurately estimate the transferability in general cases, such as selecting the best self-supervised pre-trained model and the best transferring layer?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.318,
+                0.89,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Q5 Hyperparameter sensitivity (Section 4.6). How sensitive is TMI to hyperparameters?"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.505,
+                0.092,
+                0.891,
+                0.348
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.36,
+                0.69,
+                0.375
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.383,
+                0.891,
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+            "angle": 0,
+            "content": "We present pre-trained models, datasets, baselines, evaluation, estimator, and hyperparameters for our experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.435,
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+            "angle": 0,
+            "content": "Pre-trained models. We use supervised model groups offered by Pytorch: ResNet, DenseNet, MnasNet, ShuffleNet V2, MobileNet V2, MobileNet V3, ResNeXt, Wide ResNet, EfficientNet, EfficientNet V2, and RegNet. We also utilize self-supervised model groups, which have only feature extractors without classifiers. We obtain Swin Transformer and Vision Transformer from Pytorch; we get MoCo v1, MoCo v2, Barlow Twins, SwAV, SimSiam, and Dino from Gitlab repositories. Note that we select fifty supervised pretrained models and eleven self-supervised pre-trained models from the aforementioned model groups."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.623,
+                0.891,
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+            ],
+            "angle": 0,
+            "content": "Datasets. We use seventeen image datasets summarized in Table 1. We randomly split each dataset into a train set and test set by 8:2 ratio, except for datasets that already have been separated."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Baselines. We compare the proposed method with the following baselines. NCE [18] defines the transferability as negative conditional entropy between ground truths and predicted labels from a pre-trained model. LEEP [13] measures negative conditional entropy between ground truths and predicted average log-likelihood. H-Score [2] estimates the transferability by solving an HGR maximum correlation problem. LogME [25] proposes the logarithm of maximum evidence given extracted features. TransRate [5] measures the transferability by the mutual information between target labels and target representations. We omit the comparison with Taskonomy [26] and Task2Vec [1] due to tremendous time costs."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "11477"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.172,
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+            ],
+            "angle": 0,
+            "content": "Table 1: Summary of datasets."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td># of instances (train / test)</td><td># of classes</td><td>Category</td></tr><tr><td>Caltech-1011</td><td>7,315 / 1,829</td><td>101</td><td>Multiple domains</td></tr><tr><td>Caltech-2562</td><td>24,485 / 6,122</td><td>256</td><td>Multiple domains</td></tr><tr><td>CIFAR-103</td><td>50,000 / 10,000</td><td>10</td><td>Multiple domains</td></tr><tr><td>CIFAR-1003</td><td>50,000 / 10,000</td><td>100</td><td>Multiple domains</td></tr><tr><td>MNIST4</td><td>60,000 / 10,000</td><td>10</td><td>Digit</td></tr><tr><td>FashionMNIST5</td><td>60,000 / 10,000</td><td>10</td><td>Fashion</td></tr><tr><td>SVHN6</td><td>73,257 / 26,032</td><td>10</td><td>Digit</td></tr><tr><td>FlowerPhotos7</td><td>2,936 / 734</td><td>5</td><td>Flower</td></tr><tr><td>EuroSAT8</td><td>21,600 / 5,400</td><td>10</td><td>Landscape</td></tr><tr><td>Chest X-Ray9</td><td>5,216 / 623</td><td>2</td><td>Medicine</td></tr><tr><td>VisDA10</td><td>152,397 / 72,372</td><td>212</td><td>Multiple domains</td></tr><tr><td>FGVC-Aircraft11</td><td>3,334 / 3,333</td><td>100</td><td>Aircraft</td></tr><tr><td>CUB-20012</td><td>9,430 / 2,358</td><td>200</td><td>Animal</td></tr><tr><td>Cars13</td><td>8,144 / 8,041</td><td>196</td><td>Auto</td></tr><tr><td>DTD14</td><td>4,512 / 1,128</td><td>47</td><td>Texture</td></tr><tr><td>Food-10115</td><td>80,800 / 20,200</td><td>101</td><td>Food</td></tr><tr><td>Oxford-IIIT Pet16</td><td>3,680 / 3,669</td><td>37</td><td>Animal</td></tr></table>"
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+            "content": "\\(^7\\) https://www.tensorflow.org/datasets/catalog/tf_flowers"
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+        },
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+            "bbox": [
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+            "angle": 0,
+            "content": "9 https://data.mendeley.com/datasets/rscbjbr9sj/2"
+        },
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+        },
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+            "bbox": [
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+            "angle": 0,
+            "content": "11 https://www Robots.ox.ac.uk/~vgg/data/fgvc-aircraft/"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "12 http://www.vision.caltech.edu/datasets/cub_200_2011/"
+        },
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+            "bbox": [
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+        },
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+            "type": "table_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "14 https://www.robots.ox.ac.uk/~vgg/data/dtd/"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
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+            "content": "15 https://data.vision.ee.ethz.ch/cvl/datasetsextra/food-101/"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.084,
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+            "angle": 0,
+            "content": "16 https://www Robots.ox.ac.uk/~vgg/data/pets/"
+        },
+        {
+            "type": "list",
+            "bbox": [
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+                0.32,
+                0.417,
+                0.454
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.485,
+                0.47,
+                0.636
+            ],
+            "angle": 0,
+            "content": "Evaluation. We evaluate the performance of transferability measurement methods in two ways. First, do they accurately predict the best model? Second, are the transferability scores correlated to fine-tuned accuracy? We adopt Kendall correlation coefficient to measure the correlations between the transferability and fine-tuned accuracy. Kendall correlation coefficient tests the ordinal association between two measured quantities. Kendall correlation coefficient has values between -1 and 1, and correlations between two variables are high when the values are close to 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.67,
+                0.47,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Estimator. We adopt \\( k \\)-nearest estimator [8] to evaluate the continuous entropy in Equation (4). Compared to kernel density estimators [12, 17], \\( k \\)-nearest estimator vastly reduces errors by sacrificing time, especially when data are too big. TMI greatly reduces the size of data to be calculated at once because it computes conditional entropy of representation given label."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Hyperparameters. We use greedy searching algorithm to find the best hyperparameters for fine-tuning. For transferability measurement, the only hyperparameter in our proposed TMI is the number \\( n_k \\) of neighbors, which is used in the entropy estimator [8]. We discuss the hyperparameter sensitivity to transferability in Section 4.6."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.089,
+                0.892,
+                0.164
+            ],
+            "angle": 0,
+            "content": "Table 2: Ratio of target tasks where their top-5 best source models include the model estimated by each transferability measurement method. The best result is in bold. Note that TMI gives the best ratio, accurately selecting the best pretrained models in 14 out of 17 cases."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.506,
+                0.177,
+                0.888,
+                0.214
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-5</td><td>3 / 17</td><td>5 / 17</td><td>4 / 17</td><td>8 / 17</td><td>9 / 17</td><td>14 / 17</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.236,
+                0.848,
+                0.252
+            ],
+            "angle": 0,
+            "content": "4.2. Evaluation of Transferability Estimation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.259,
+                0.892,
+                0.349
+            ],
+            "angle": 0,
+            "content": "Remind that our goal is to quickly and accurately select the best pre-trained model among a pool of well-trained models. A pre-trained model is determined by two components, source data and model architecture. Thus, we conduct experiments to select the best model architecture and the best source data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.367,
+                0.892,
+                0.502
+            ],
+            "angle": 0,
+            "content": "Selecting the best model architecture. We evaluate how the transferability measurement methods accurately select the best source model for a target model. Table 2 shows the ratio of targets tasks where their top-5 best source models include the model estimated by each transferability measurement method. Note that TMI gives the best ratio, accurately selecting the best pre-trained models in 14 out of 17 cases, which is much better than the ratio \\(9 / 17\\) of the second-best model TransRate."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.504,
+                0.892,
+                0.594
+            ],
+            "angle": 0,
+            "content": "We also compare the correlations between fine-tuned accuracies and transferability scores in Table 3. Note that our proposed TMI shows the best Kendall correlation in 13 out of 17 datasets, outperforming all the competitors. Some baselines even give negative coefficients, which means that their predictions are far from the correct ranking."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.612,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Selecting the best source data. We fine-tune eighteen pre-trained models with the same model architecture ResNet-50, but different source datasets, including ImageNet and seventeen datasets introduced in Section 4.1. We predict the best source data and compare correlations with the ground truths. Table 4 shows that our proposed TMI accurately predicts the best source data in all the 17 cases, outperforming all the competitors. Our proposed TMI gives the best Kendall correlation consistently in 12 out of 17 cases, as shown in Table 5."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.772,
+                0.766,
+                0.788
+            ],
+            "angle": 0,
+            "content": "4.3. Comparison of ICV Measures"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Intra-Class Variance (ICV) is a general concept widely used in metric learning. In addition to the conditional entropy introduced in Section 3, we additionally choose four metric learning methods, Contrast [4], Center [20], SNCA [22], and MS [19]. We use the intra-class variance parts of their objective functions to measure the transferability. We apply the five aforementioned methods to measure"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11478"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.089,
+                0.895,
+                0.137
+            ],
+            "angle": 0,
+            "content": "Table 3: Correlations between fine-tuned accuracies and transferability scores when transferring supervised pre-trained models trained on ImageNet. The best result is in bold. Our proposed TMI gives the best Kendall correlation in 13 out of 17 cases, outperforming competitors."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.214,
+                0.147,
+                0.761,
+                0.451
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"6\">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>0.429</td><td>0.425</td><td>0.316</td><td>0.362</td><td>0.474</td><td>0.524</td></tr><tr><td>Caltech-256</td><td>0.686</td><td>0.455</td><td>0.492</td><td>0.503</td><td>0.509</td><td>0.481</td></tr><tr><td>CIFAR-10</td><td>-0.140</td><td>0.324</td><td>0.275</td><td>0.323</td><td>0.364</td><td>0.527</td></tr><tr><td>CIFAR-100</td><td>-0.202</td><td>0.340</td><td>0.351</td><td>0.398</td><td>0.432</td><td>0.497</td></tr><tr><td>MNIST</td><td>0.057</td><td>0.282</td><td>0.083</td><td>0.137</td><td>0.038</td><td>0.137</td></tr><tr><td>FashionMNIST</td><td>-0.328</td><td>0.127</td><td>-0.038</td><td>0.121</td><td>0.125</td><td>0.467</td></tr><tr><td>SVHN</td><td>-0.023</td><td>0.091</td><td>-0.002</td><td>0.092</td><td>0.206</td><td>0.394</td></tr><tr><td>FlowerPhotos</td><td>0.117</td><td>0.139</td><td>0.224</td><td>0.321</td><td>0.392</td><td>0.499</td></tr><tr><td>EuroSAT</td><td>0.269</td><td>0.082</td><td>-0.005</td><td>0.102</td><td>0.051</td><td>0.085</td></tr><tr><td>Chest X-Ray</td><td>0.071</td><td>0.152</td><td>0.171</td><td>0.333</td><td>0.285</td><td>0.395</td></tr><tr><td>VisDA</td><td>0.298</td><td>0.240</td><td>0.329</td><td>0.334</td><td>0.304</td><td>0.341</td></tr><tr><td>FGVC-Aircraft</td><td>0.366</td><td>-0.011</td><td>0.216</td><td>0.498</td><td>0.421</td><td>0.500</td></tr><tr><td>CUB-200</td><td>0.415</td><td>0.098</td><td>0.325</td><td>0.410</td><td>0.519</td><td>0.523</td></tr><tr><td>Cars</td><td>0.270</td><td>0.506</td><td>0.175</td><td>0.432</td><td>0.455</td><td>0.521</td></tr><tr><td>DTD</td><td>-0.074</td><td>0.501</td><td>0.479</td><td>0.366</td><td>0.499</td><td>0.401</td></tr><tr><td>Food-101</td><td>0.261</td><td>0.515</td><td>0.395</td><td>0.421</td><td>0.448</td><td>0.537</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.536</td><td>0.527</td><td>0.418</td><td>0.493</td><td>0.500</td><td>0.576</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.473,
+                0.472,
+                0.536
+            ],
+            "angle": 0,
+            "content": "Table 4: Ratio of target tasks where the transferability measurement methods accurately find the best source data. The best method is in bold. TMI predicts the best source data in all cases, outperforming competitors."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.083,
+                0.545,
+                0.465,
+                0.582
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-1</td><td>1 / 17</td><td>2 / 17</td><td>3 / 17</td><td>2 / 17</td><td>13 / 17</td><td>17 / 17</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.608,
+                0.47,
+                0.714
+            ],
+            "angle": 0,
+            "content": "the correlations between fine-tuned accuracies and transferability scores. Conditional Entropy (CE) shows the best correlations than the other four metric learning measurements in 15 out of 17 datasets, outperforming all the competitors, as shown in Table 6. M. Boudiaf et al. [3] demonstrate that the conditional entropy is a lower bound of intra-class variance of the four metric learning methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.394,
+                0.743
+            ],
+            "angle": 0,
+            "content": "4.4. Evaluation of Generalization Ability"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.869
+            ],
+            "angle": 0,
+            "content": "We perform experiments on two control groups to demonstrate that transferability is relevant to the generalization ability of a pre-trained model on a target task. In Group A, we use a pre-trained ResNet-50 model trained on ImageNet and fine-tune it using the dataset \\( D \\). In Group B, we train a ResNet-50 model trained from scratch on dataset \\( D \\) and fine-tune it on the same dataset. Dataset \\( D \\) is one of the datasets introduced in Section 4.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Table 7 shows the difference of fine-tuning performance and that of transferability between two groups. “+” rep"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.475,
+                0.892,
+                0.552
+            ],
+            "angle": 0,
+            "content": "resents the difference is larger than 0 while “-” represents that is less than 0. Group A has higher transfer accuracies than Group B in most cases since models in Group A have learned a large amount of information from the ImageNet, which can potentially benefit downstream tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.554,
+                0.892,
+                0.66
+            ],
+            "angle": 0,
+            "content": "Our proposed TMI and TransRate have the same symbols for transfer accuracy in 14 out of 17 cases, while the other four baselines do not provide similar symbols. TransRate also estimates well, but it is computationally expensive since it measures the mutual information between target representation and label. In contrast, TMI is more efficient as it considers only intra-class features."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.678,
+                0.7,
+                0.695
+            ],
+            "angle": 0,
+            "content": "4.5. General Applications"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Applying to self-supervised pre-trained models. TMI not only measures the transferability between supervised pre-trained models and classification tasks but also can be extended to self-supervised pre-trained models. We prepare eleven self-supervised pre-trained models already trained on ImageNet provided by Github repositories introduced in Section 4.1. NCE [18] and LEEP [13] cannot measure the transferability between a self-supervised pre-trained model and a downstream task because they dig out the relationship between target ground truth and predicted label or probability. Thus, we compare the proposed TMI to LogME [25], H-Score [2], and TransRate [5] in Table 8; TMI outperforms competitors in 13 out of 17 classification datasets."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "11479"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.089,
+                0.895,
+                0.137
+            ],
+            "angle": 0,
+            "content": "Table 5: Correlations between fine-tuned accuracies and transferability scores when transferring ResNet-50 models trained on different source data. The best result is in bold. TMI shows the best Kendall correlation in 12 out of 17 cases, outperforming all the competitors."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.212,
+                0.147,
+                0.761,
+                0.451
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"6\">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.294</td><td>0.542</td><td>0.353</td><td>0.647</td><td>0.425</td><td>0.699</td></tr><tr><td>Caltech-256</td><td>-0.268</td><td>0.542</td><td>0.437</td><td>0.660</td><td>0.477</td><td>0.699</td></tr><tr><td>CIFAR-10</td><td>-0.216</td><td>0.373</td><td>0.383</td><td>0.490</td><td>0.399</td><td>0.630</td></tr><tr><td>CIFAR-100</td><td>-0.098</td><td>0.556</td><td>0.686</td><td>0.345</td><td>0.542</td><td>0.699</td></tr><tr><td>MNIST</td><td>-0.061</td><td>0.439</td><td>0.372</td><td>-0.007</td><td>0.115</td><td>0.162</td></tr><tr><td>FashionMNIST</td><td>-0.086</td><td>0.362</td><td>0.430</td><td>0.475</td><td>0.046</td><td>0.150</td></tr><tr><td>SVHN</td><td>0.039</td><td>0.285</td><td>-0.033</td><td>0.393</td><td>0.170</td><td>0.407</td></tr><tr><td>FlowerPhotos</td><td>-0.359</td><td>0.412</td><td>0.456</td><td>0.307</td><td>0.490</td><td>0.516</td></tr><tr><td>EuroSAT</td><td>-0.388</td><td>0.428</td><td>0.490</td><td>0.322</td><td>0.467</td><td>0.704</td></tr><tr><td>Chest X-Ray</td><td>-0.072</td><td>0.164</td><td>0.359</td><td>-0.111</td><td>0.425</td><td>-0.123</td></tr><tr><td>VisDA</td><td>-0.538</td><td>0.498</td><td>0.094</td><td>-0.039</td><td>0.498</td><td>0.546</td></tr><tr><td>FGVC-Aircraft</td><td>-0.033</td><td>0.373</td><td>0.339</td><td>0.556</td><td>0.399</td><td>0.688</td></tr><tr><td>CUB-200</td><td>-0.503</td><td>0.582</td><td>0.455</td><td>0.464</td><td>0.647</td><td>0.723</td></tr><tr><td>Cars</td><td>-0.294</td><td>0.529</td><td>0.403</td><td>0.752</td><td>0.542</td><td>0.804</td></tr><tr><td>DTD</td><td>-0.438</td><td>0.595</td><td>0.393</td><td>0.647</td><td>0.542</td><td>0.757</td></tr><tr><td>Food-101</td><td>-0.020</td><td>0.281</td><td>0.092</td><td>0.046</td><td>0.229</td><td>0.225</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.268</td><td>0.569</td><td>0.660</td><td>0.503</td><td>0.516</td><td>0.248</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.473,
+                0.472,
+                0.521
+            ],
+            "angle": 0,
+            "content": "Table 6: Comparison of intra-class variance measurements. Conditional Entropy (CE) shows the best correlations consistently in 15 out of 17 cases. The best result is in bold."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.093,
+                0.53,
+                0.456,
+                0.774
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"5\">Kendall Correlation Coefficient</td></tr><tr><td>Contrast</td><td>Center</td><td>SNCA</td><td>MS</td><td>CE</td></tr><tr><td>Caltech-101</td><td>0.274</td><td>0.283</td><td>0.380</td><td>0.358</td><td>0.442</td></tr><tr><td>Caltech-256</td><td>0.295</td><td>0.347</td><td>0.261</td><td>0.347</td><td>0.354</td></tr><tr><td>CIFAR-10</td><td>0.328</td><td>0.322</td><td>0.275</td><td>0.299</td><td>0.369</td></tr><tr><td>CIFAR-100</td><td>0.374</td><td>0.282</td><td>0.207</td><td>0.200</td><td>0.376</td></tr><tr><td>MNIST</td><td>0.383</td><td>0.267</td><td>0.306</td><td>0.228</td><td>0.374</td></tr><tr><td>FashionMNIST</td><td>0.332</td><td>0.225</td><td>0.260</td><td>0.337</td><td>0.374</td></tr><tr><td>SVHN</td><td>0.303</td><td>0.359</td><td>0.369</td><td>0.360</td><td>0.383</td></tr><tr><td>FlowerPhotos</td><td>0.209</td><td>0.263</td><td>0.291</td><td>0.277</td><td>0.372</td></tr><tr><td>EuroSAT</td><td>0.292</td><td>0.237</td><td>0.367</td><td>0.268</td><td>0.400</td></tr><tr><td>Chest X-Ray</td><td>0.292</td><td>0.289</td><td>0.210</td><td>0.232</td><td>0.357</td></tr><tr><td>VisDA</td><td>0.259</td><td>0.352</td><td>0.200</td><td>0.329</td><td>0.352</td></tr><tr><td>FGVC-Aircraft</td><td>0.220</td><td>0.322</td><td>0.244</td><td>0.315</td><td>0.351</td></tr><tr><td>CUB-200</td><td>0.368</td><td>0.252</td><td>0.379</td><td>0.385</td><td>0.431</td></tr><tr><td>Cars</td><td>0.351</td><td>0.285</td><td>0.398</td><td>0.268</td><td>0.248</td></tr><tr><td>DTD</td><td>0.236</td><td>0.322</td><td>0.228</td><td>0.206</td><td>0.327</td></tr><tr><td>Food-101</td><td>0.322</td><td>0.267</td><td>0.246</td><td>0.269</td><td>0.484</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.301</td><td>0.202</td><td>0.363</td><td>0.274</td><td>0.449</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Selecting the best transferring layer. Given a ResNet-18 trained on ImageNet, we can easily determine the best transferring layer, which produces the best fine-tuning performance for a target task by measuring transferability. We compare the correlations of LogME [25], H-Score [2], and TransRate to select the best transferring layer for fine"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.473,
+                0.895,
+                0.552
+            ],
+            "angle": 0,
+            "content": "Table 7: Comparison of the consistency of fine-tuning accuracy and transferability. “+” represents the difference is larger than 0 while “-” represents the difference is less than 0. TMI has consistent signs with fine-tuning accuracy in 14 out of 17 cases, outperforming its competitors."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.56,
+                0.895,
+                0.791
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Accuracy (A-B)</td><td colspan=\"6\">Transferability (A-B)</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogME</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Caltech-256</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-10</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-100</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>MNIST</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FashionMNIST</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>SVHN</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>FlowerPhotos</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>EuroSAT</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>Chest X-Ray</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>VisDA</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FGVC-Aircraft</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CUB-200</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Cars</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>DTD</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Food-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Oxford-IIIT Pet</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "tuning. Theoretically, LogME [25] and H-Score [2] cannot deal with layer selection because they rely on features from the ultimate layer of the feature extractor. However, we extract features from each layer and directly put them into LogME and H-Score algorithms to calculate the trans"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "11480"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.089,
+                0.472,
+                0.166
+            ],
+            "angle": 0,
+            "content": "Table 8: Correlations between fine-tuned accuracies and transferability scores when transferring self-supervised pretrained models to classification tasks. The best result is in bold. TMI shows the best Kendall correlation consistently in 13 out of 17 cases, outperforming all the competitors."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.103,
+                0.177,
+                0.446,
+                0.421
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">Kendall Correlation Coefficient</td></tr><tr><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.278</td><td>0.183</td><td>0.000</td><td>0.367</td></tr><tr><td>Caltech-256</td><td>-0.561</td><td>0.345</td><td>0.164</td><td>0.600</td></tr><tr><td>CIFAR-10</td><td>-0.337</td><td>0.018</td><td>0.164</td><td>0.624</td></tr><tr><td>CIFAR-100</td><td>-0.561</td><td>0.673</td><td>0.236</td><td>0.697</td></tr><tr><td>MNIST</td><td>-0.574</td><td>-0.262</td><td>-0.426</td><td>0.246</td></tr><tr><td>FashionMNIST</td><td>-0.330</td><td>-0.220</td><td>-0.330</td><td>0.094</td></tr><tr><td>SVHN</td><td>0.055</td><td>0.309</td><td>-0.345</td><td>0.075</td></tr><tr><td>FlowerPhotos</td><td>0.389</td><td>-0.241</td><td>0.130</td><td>0.075</td></tr><tr><td>EuroSAT</td><td>-0.073</td><td>-0.037</td><td>0.037</td><td>-0.208</td></tr><tr><td>Chest X-Ray</td><td>-0.037</td><td>-0.037</td><td>-0.257</td><td>0.175</td></tr><tr><td>VisDA</td><td>0.550</td><td>0.055</td><td>0.309</td><td>-0.597</td></tr><tr><td>FGVC-Aircraft</td><td>-0.345</td><td>0.091</td><td>-0.309</td><td>0.150</td></tr><tr><td>CUB-200</td><td>-0.112</td><td>-0.018</td><td>0.091</td><td>0.564</td></tr><tr><td>Cars</td><td>0.000</td><td>0.382</td><td>-0.200</td><td>0.262</td></tr><tr><td>DTD</td><td>0.382</td><td>0.018</td><td>0.224</td><td>0.455</td></tr><tr><td>Food-101</td><td>-0.411</td><td>-0.018</td><td>-0.018</td><td>0.204</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.585</td><td>0.294</td><td>0.073</td><td>0.807</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.142,
+                0.457,
+                0.408,
+                0.541
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.558,
+                0.47,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Figure 3: Sensitivity to the hyperparameter \\( n_k \\) in entropy estimator."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.622,
+                0.47,
+                0.789
+            ],
+            "angle": 0,
+            "content": "ferability. The size of extracted features is quite large in the early layers, resulting in much higher computational cost for transferability measurement. To reduce this cost, we add an avgpool2d layer to the end of transferring layer to reduce the dimension of extracted features. Table 9 shows that TMI achieves the highest correlation coefficients in 16 out of 17 datasets. Correlation coefficients of MNIST, SVHN, and Chest X-Ray are much lower than those of the other datasets because their ranges of minimum and maximum accuracies obtained by layer transfer are smaller than \\(0.5\\%\\), making it challenging to rank these dataset accurately."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.801,
+                0.327,
+                0.818
+            ],
+            "angle": 0,
+            "content": "4.6. Hyperparameter Sensitivity"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "An advantage of TMI is that it does not train models on target datasets because it is time-consuming and sensitive to hyperparameters which may cause different results. The only hyperparameter in TMI is \\( n_k \\) used in the entropy estimator. In Figure. 3, the correlation between pre-trained"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.089,
+                0.895,
+                0.151
+            ],
+            "angle": 0,
+            "content": "Table 9: Correlations between fine-tuned accuracies and transferability scores when transferring specific layers of pre-trained models. The best result is in bold. TMI shows the best correlations consistently in 16 out of 17 cases."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.527,
+                0.162,
+                0.866,
+                0.405
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">Kendall Correlation Coefficient</td></tr><tr><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>0.346</td><td>0.935</td><td>0.752</td><td>0.941</td></tr><tr><td>Caltech-256</td><td>0.973</td><td>0.317</td><td>0.800</td><td>0.984</td></tr><tr><td>CIFAR-10</td><td>0.360</td><td>0.743</td><td>0.704</td><td>0.746</td></tr><tr><td>CIFAR-100</td><td>0.460</td><td>0.774</td><td>0.774</td><td>0.801</td></tr><tr><td>MNIST</td><td>0.180</td><td>0.055</td><td>0.179</td><td>0.184</td></tr><tr><td>FashionMNIST</td><td>0.294</td><td>0.241</td><td>0.298</td><td>0.308</td></tr><tr><td>SVHN</td><td>0.087</td><td>0.106</td><td>0.040</td><td>0.113</td></tr><tr><td>FlowerPhotos</td><td>0.779</td><td>0.198</td><td>0.687</td><td>0.792</td></tr><tr><td>EuroSAT</td><td>0.691</td><td>0.709</td><td>0.495</td><td>0.735</td></tr><tr><td>Chest X-Ray</td><td>0.113</td><td>0.154</td><td>0.100</td><td>0.054</td></tr><tr><td>VisDA</td><td>0.665</td><td>0.866</td><td>0.826</td><td>0.904</td></tr><tr><td>FGVC-Aircraft</td><td>0.791</td><td>0.302</td><td>0.595</td><td>0.817</td></tr><tr><td>CUB-200</td><td>0.317</td><td>0.970</td><td>0.787</td><td>0.954</td></tr><tr><td>Cars</td><td>0.330</td><td>0.869</td><td>0.752</td><td>0.882</td></tr><tr><td>DTD</td><td>0.924</td><td>0.401</td><td>0.761</td><td>0.931</td></tr><tr><td>Food-101</td><td>0.409</td><td>0.948</td><td>0.869</td><td>0.970</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.349</td><td>0.970</td><td>0.826</td><td>0.990</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.431,
+                0.888,
+                0.446
+            ],
+            "angle": 0,
+            "content": "models and TMI shows consistency in most ranges for \\( n_k \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.459,
+                0.618,
+                0.475
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.484,
+                0.892,
+                0.665
+            ],
+            "angle": 0,
+            "content": "We propose TMI, a fast, accurate, and general algorithm to measure the transferability. TMI quantifies the degree of generalization of a pre-trained model to a new task by estimating the intra-class feature variance. We conduct experiments on seventeen datasets with fifty supervised pretrained models and eleven self-supervised pre-trained models. TMI selects the top-5 pre-trained architecture in 14 out of 17 cases and selects the best source data in all cases, outperforming its competitors. We measure the correlation between the fine-tuning performance and transferability, and our proposed TMI outperforms competitors in 13 out of 17 cases."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.68,
+                0.66,
+                0.696
+            ],
+            "angle": 0,
+            "content": "Acknowledgments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) [No.2020-0-00894, Flexible and Efficient Model Compression Method for Various Applications and Environments], [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)], and [NO.2021-0-02068, Artificial Intelligence Innovation Hub (Artificial Intelligence Institute, Seoul National University)]. The Institute of Engineering Research at Seoul National University provided research facilities for this work. The ICT at Seoul National University provides research facilities for this study. U Kang is the corresponding author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.956
+            ],
+            "angle": 0,
+            "content": "11481"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.115,
+                0.47,
+                0.17
+            ],
+            "angle": 0,
+            "content": "[1] Alessandro Achille, Michael Lam, Rahul Tewari, Avinash Ravichandran, Subhransu Maji, Charless C. Fowlkes, Stefano Soatto, and Pietro Perona. Task2vec: Task embedding for meta-learning. In ICCV, 2019."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
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+# Fast and Accurate Transferability Measurement by Evaluating Intra-class Feature Variance
+
+Huiwen Xu  
+Seoul National University  
+Seoul, Republic of Korea  
+xuhuiwen33@snu.ac.kr
+
+U Kang Seoul National University Seoul, Republic of Korea ukang@snu.ac.kr
+
+# Abstract
+
+Given a set of pre-trained models, how can we quickly and accurately find the most useful pre-trained model for a downstream task? Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. It is used for quickly ranking pre-trained models for a given task and thus becomes a crucial step for transfer learning. Existing methods measure transferability as the discrimination ability of a source model for a target data before transfer learning, which cannot accurately estimate the fine-tuning performance. Some of them restrict the application of transferability measurement in selecting the best supervised pre-trained models that have classifiers. It is important to have a general method for measuring transferability that can be applied in a variety of situations, such as selecting the best self-supervised pre-trained models that do not have classifiers, and selecting the best transferring layer for a target task.
+
+In this work, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a fast and accurate algorithm to measure transferability. We view transferability as the generalization of a pre-trained model on a target task by measuring intra-class feature variance. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Extensive experiments on real-world datasets show that TMI outperforms competitors for selecting the top-5 best models, and exhibits consistently better correlation in 13 out of 17 cases.
+
+# 1. Introduction
+
+Transfer learning is an important concept in the field of machine learning, revolutionizing the way models are
+
+![](images/f3be556d27f86e0b0aa81c21d32f1f474315371c44a0984b1ad15b1bc867c58b.jpg)  
+Figure 1: Illustration of selecting the best pre-trained model for a given target task.
+
+trained and applied to various domains. Transfer learning has proven to be particularly valuable when labeled data in the target domain are scarce or costly to obtain. Within the broader scope of transfer learning, several variants have emerged, such as source-free domain adaptation [10, 27, 23, 7], multi-source transfer learning [16, 14, 7, 9], heterogeneous transfer learning [11, 15], and open-set domain adaptation [6, 21].
+
+In transfer learning, fine-tuning a pre-trained model becomes a simple and effective way to improve the performance of a downstream task. A crucial step in transfer learning is to quickly and accurately select the most helpful pre-trained model in a set of given pre-trained models. Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. As shown in Figure. 1, transferability measurement is used for ranking pre-trained models for a given task, and is a crucial step for transfer learning.
+
+A desired method for transferability measurement should be faster than running a transfer learning algorithm, accurately select the best pre-trained model, and be general to be implemented in various common scenarios. Taskonomy [26] and Task2Vec [1] are computationally expensive due to their learning with data. NCE [18] and LEEP [13] are free of training but cannot be applied to general cases, such as selecting self-supervised pre-trained models and selecting the best transferring layer. LogMe [25] and H-Score [2] also cannot be applied theoretically to select the best transferring layer. Instead of measuring transferability, they measure how discriminative a pre-trained model is to a target task before implementing transfer learning, which cannot estimate fine-tuning performance. TransRate [5] is simple and general to be applied for transferability measurement, but too slow due to the computation of the entropy of whole hidden representations.
+
+In this paper, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a simple but effective method for transferability measurement. We deem transferability as the generalization of a pre-trained model on a target task. To quantify the degree of generalization, we measure the intra-class variance by the conditional entropy of target representation given a label. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Large intra-class variance implies the feature is efficient for learning tasks. TMI can be used for selecting not only the best supervised model but also the best self-supervised models and the best transferring layer.
+
+Our contributions are summarized as follows:
+
+- Algorithm. We propose TMI, a fast, accurate, and general method for measuring transferability. We view transferability as generalization ability of a pre-trained model on a target task. The model generalization is measured by intra-class feature variance.  
+- Experiments. We conduct extensive experiments on seventeen datasets with fifty supervised pre-trained models and eleven self-supervised pre-trained models. TMI outperforms competitors for selecting the top-5 pre-trained architecture in 14 out of 17 cases and selecting the best source data in all cases. TMI also shows the best trade-off of the running time and transferability, outperforming competitors in 12 out of 17 cases (see Figure. 2).  
+- Case study. We evaluate the transferability in more general cases, such as applying to self-supervised pretrained models and selecting the best transferring layer. Compared to competitors, TMI achieves the highest correlation coefficient in 13 out of 17 for selecting the
+
+best self-supervised pre-trained models, and in 16 out of 17 datasets for selecting the best transferring layer.
+
+The rest of this paper is organized as follows. We introduce related works for transferability measurement in Section 2, and propose our method TMI in Section 3. After presenting experimental results in Section 4, we conclude in Section 5.
+
+# 2. Related Works
+
+We assume a pre-trained model  $\theta = (w, h)$  in a source domain where  $w$  is a feature extractor, and  $h$  is a classifier (or head). We transfer the model  $\theta$  to a target domain and add a new classifier  $k$  at the end of the feature extractor  $w$  before fine-tuning. Since the target task is different from the source task in most cases, the pre-trained classifier  $h$  is inappropriate to solve the target task. Thus, we fine-tune the model by minimizing the cross entropy loss on the target dataset  $D = \{(x_i, y_i)\}_{i=1}^n$ :
+
+$$
+w ^ {*}, k ^ {*} = \underset {w, k} {\arg \min } \mathcal {L} (w, k) \tag {1}
+$$
+
+where a feature extractor  $w$  maps an input  $x_{i}$  to a representation  $r_i = w(x_i)$ , and a classifier  $h$  maps the representation  $r_i$  to a probability distribution  $\hat{y}_i = \sigma(h(r_i))$  where  $\sigma(\cdot)$  is an activation function. Note that  $\hat{y}_i$  is a vector of length  $n_c$ , where  $n_c$  is the number of classes, and  $\mathcal{L}(\cdot)$  is the cross entropy loss, which is equivalent to the average negative log-likelihood:
+
+$$
+\mathcal {L} (w, k) = - \frac {1}{n} \sum_ {i = 1} ^ {n} \log P \left(\hat {y} _ {i, c} \mid x _ {i}; w, k\right) \tag {2}
+$$
+
+where  $\hat{y}_{i,c}$  is the probability of  $i$ -th input instance belonging to its ground truth.
+
+The transferability of a source task  $S$  to a target task  $T$  is defined by the log-likelihood [18]:
+
+$$
+T r f _ {(S \rightarrow T)} = \frac {1}{n} \sum_ {i = 1} ^ {n} \log P \left(\hat {y} _ {i, c} \mid x _ {i}; w ^ {*}, k ^ {*}\right) \tag {3}
+$$
+
+Taskonomy [26] and Task2Vec [1] train the source model using target data to obtain the optimal feature extractor  $w^{*}$  and the optimal classifier  $k^{*}$ . These methods are inconvenient to measure the transferability due to their training with data. There have been works focusing on estimating a bound on the log-likelihood to evaluate the transferability without training. NCE [18] proposes negative conditional entropy, which is drawn from the empirical joint distribution over ground truths and predicted labels from a pretrained model. Similarly, LEEP [13] replaces the ground truth with the average log-likelihood to evaluate the transferability. NCE and LEEP are fast, but are restricted to supervised pre-trained models because the algorithms rely
+
+![](images/a9731248f7c35c157c6bdbcaeba07a3b58c6254bcfa6867e1c80149c32113399.jpg)  
+(a) Caltech-101
+
+![](images/f2afcec31899d62037b3846c2bce0ef393923ecb52c0bca1818c9bae03f88285.jpg)  
+(b) Caltech-256
+
+![](images/dae8c4d07881c56e467ea24debcf0df2b5294e9a7dcad15de1b74a7809b6da91.jpg)  
+(c) CIFAR-10
+
+![](images/62d8dba0ea2141c6f26444e17e624502d6a31a3907e837e37150af86bc68318f.jpg)  
+(d) CIFAR-100
+
+![](images/1ff58ff1b9aba23a0248e1fd808e99aff809542a7cf20344225a0fb800bc4de0.jpg)  
+(e) MNIST
+
+![](images/796bdb29190ae4c7ddbdfc8fea9dd77c86c1f589ef99bac0603dc9789815ea95.jpg)  
+(f) FashionMNIST
+
+![](images/47e5d3a24defa41fbb9996e6df75604c9c3fc6ac5129c586c2f6733d5c29a6a8.jpg)  
+(g) SVHN
+
+![](images/3e8269311f49908d6804ea194d7029f75205a9aa22efccf0d29a356ccc8522b2.jpg)  
+(h)FlowerPhotos
+
+![](images/563d544d5a3b8acfb5cf300e8b0e4890ddcfab206c133e280fac8885c3a4d437.jpg)  
+(i) EuroSAT
+
+![](images/231512f9b597aa897b309293edd853d04399ed061e886e74be47772a4f2774d6.jpg)  
+(j) Chest X-Ray
+
+![](images/a2d4e46bf4c2ba04433013f4b21e03d8178f515fe6ba4d679dc14d4cdf72fb27.jpg)  
+(k) VisDA
+
+![](images/1597aec12dfd9d10ffd9932fa5dadb1e6042b3553185e33d3edd482aa6d52216.jpg)  
+(1) FGVC-Aircraft
+
+![](images/490baa3b51fb19ee1879503f13f2cab59a100f99020df1bcbf1a6b1d206ddaca.jpg)  
+(m) CUB-200
+
+![](images/6442787cf94ddc90ad887a2d8906d67e4abfa52fd238b4d731296a587c0375bc.jpg)  
+(n) Cars
+
+![](images/60f66bbe2c739c9e84b585b92a6da91dcee89670844ec0f0da5951447e45cfff.jpg)  
+(0) DTD
+
+![](images/6ab8e30a03644ed04531acad2e869b8f6d6e25941bb4e8c96b7c64038f320935.jpg)  
+(p) Food-101  
+Figure 2: Total running time (seconds) vs. Kendall's Correlation between transferability scores and test accuracies for selecting the best model among fifty pre-trained models. TMI provides the best trade-off between running time and correlation.
+
+![](images/a23dacbc109931c9493e82f68bfee0bfbe78b2a186e7887b2355b77982df373a.jpg)  
+(q) Oxford-IIIT Pet
+
+![](images/6f9ba93d8c11955ece7591be98cff4c64123f005d356866d04f60ab5c3d85e8e.jpg)
+
+on the outputs of the pre-trained classifier. To apply measurements in more general cases, LogME [25] calculates the logarithm of maximum evidence given extracted features, and H-Score [2] solves an HGR maximum correlation problem. LogMe [25] and H-Score [2] still cannot be applied to select the best transferred layer since they extract features from only the ultimate layers of the pretrained feature extractors. TransRate [5] is the most recent algorithm and applicable to self-supervised models and transferring layer selection. However, it is time-consuming since it requires to calculate mutual information between extracted feature and ground truth. To simplify the problem, [18, 13, 25, 2, 5] assume that the optimal model can be obtained by re-training the classifier while freezing the feature extractor. They estimate the performance of re-training only the classifier, which is even worse than training a target model from scratch [24]. In this paper, we propose a fast, accurate, and general transferability measurement method that predicts fine-tuned performance of a pre-trained model to a new target task.
+
+# 3. Proposed Method
+
+We propose TMI to measure the transferability between a pre-trained model and a target task.
+
+# 3.1. Overview
+
+Our goal is to measure the transferability in a fast, accurate, and general manner. The following challenges need to be addressed for the goal.
+
+C1 Speed. Training a pre-trained model on the target data requires a high computational cost. How can we measure the transferability without training on the target data?  
+C2 Accuracy. Existing methods evaluate the transferability that estimate the performance of the optimal target model obtained by re-training only the classifier, not the feature extractor, which is uncommon in transfer learning. How can we accurately measure the transferability for predicting the fine-tuning performance?  
+C3 Generality. How can we measure the transferability such that it is applicable to general settings, including selecting the best supervised pre-trained model, the best self-supervised pre-trained models, and the transferring layer?
+
+We address the aforementioned challenges with the following main ideas:
+
+I1 We assess the transferability by evaluating the compactness and sparseness of target representations with only a one-way forward propagation.  
+12 We relax the assumption proposed in existing methods
+
+that the pre-trained feature extractor can extract all the information related to the target task. We view transferability as the generalization ability of a pre-trained model on a target task. We estimate the generalization ability using intra-class variance, which implies how efficient the feature is for learning tasks.
+
+13 We measure the transferability using intra-class variance of latent representations, which is applicable to various settings including self-supervised pre-trained models and transferring layer selection.
+
+# 3.2.TMI
+
+Given a pre-trained source model and a target dataset with labels, our goal is to measure the transferability between the source model and the target task to predict the fine-tuning performance. Existing methods measure the performance of re-trained classifier while freezing the feature extractor, which is time-consuming. To address the issues, our proposed TMI computes the transferability as the intra-class variance of a pre-trained model on a target task. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. It is unnecessary for TMI to obtain optimal classifier which is a time-consuming process.
+
+TMI The transferability of a pre-trained feature extractor  $\omega_{s}$  from a source task  $S$  to a target task  $T$ , denoted by  $Trf_{(S\rightarrow T)}$ , is measured by TMI with the intra-class feature variance obtained from the pre-trained model  $\omega_{s}$ .
+
+$$
+T r f _ {(S \rightarrow T)} := H \left(\omega_ {s} (X) | Y\right) = \sum_ {c = 1} ^ {C} \frac {n _ {c}}{n} H \left(\omega_ {s} \left(X _ {c}\right)\right) \tag {4}
+$$
+
+where  $X$  and  $Y$  represent the target feature and the target label, respectively.  $C$  represents the number of classes and  $X_{c} = \{x|Y = c\}$  is the set of target features in the  $c$ -th class.  $n$  and  $n_{c}$  represent the number of total instances and number of instances in the  $c$ -th class, respectively. We measure the intra-class variance of target representations using conditional entropy. The intra-class variance encourages the pre-trained model to have a generalization ability for learning tasks.
+
+How to utilize TMI? Given a set of pre-trained models and a target dataset with labels, we first obtain target representations of pre-trained models by one-way forward propagation. Next, we compute the transferability score using Equation (4). We select the pre-trained model with the highest transferability score and then fine-tune the model using the target data. We argue that the larger the TMI, the higher the transfer performance.
+
+# 4. Experiments
+
+We present experimental results to answer the following questions about TMI:
+
+Q1 Evaluation of transferability estimation (Section 4.2). Does TMI accurately select the best pretrained model compared to baselines? Is the transferability score measured by TMI highly correlated to the transfer performance?  
+Q2 Comparison of ICV measures (Section 4.3). What is the best measurement to evaluate Intra-Class Variance (ICV)?  
+Q3 Evaluation of generalization ability (Section 4.4). Does intra-class variance estimate generalization ability of a pre-trained model on a target task?  
+Q4 General applications (Section 4.5). Does TMI accurately estimate the transferability in general cases, such as selecting the best self-supervised pre-trained model and the best transferring layer?  
+Q5 Hyperparameter sensitivity (Section 4.6). How sensitive is TMI to hyperparameters?
+
+# 4.1. Experimental Setup
+
+We present pre-trained models, datasets, baselines, evaluation, estimator, and hyperparameters for our experiments.
+
+Pre-trained models. We use supervised model groups offered by Pytorch: ResNet, DenseNet, MnasNet, ShuffleNet V2, MobileNet V2, MobileNet V3, ResNeXt, Wide ResNet, EfficientNet, EfficientNet V2, and RegNet. We also utilize self-supervised model groups, which have only feature extractors without classifiers. We obtain Swin Transformer and Vision Transformer from Pytorch; we get MoCo v1, MoCo v2, Barlow Twins, SwAV, SimSiam, and Dino from Gitlab repositories. Note that we select fifty supervised pretrained models and eleven self-supervised pre-trained models from the aforementioned model groups.
+
+Datasets. We use seventeen image datasets summarized in Table 1. We randomly split each dataset into a train set and test set by 8:2 ratio, except for datasets that already have been separated.
+
+Baselines. We compare the proposed method with the following baselines. NCE [18] defines the transferability as negative conditional entropy between ground truths and predicted labels from a pre-trained model. LEEP [13] measures negative conditional entropy between ground truths and predicted average log-likelihood. H-Score [2] estimates the transferability by solving an HGR maximum correlation problem. LogME [25] proposes the logarithm of maximum evidence given extracted features. TransRate [5] measures the transferability by the mutual information between target labels and target representations. We omit the comparison with Taskonomy [26] and Task2Vec [1] due to tremendous time costs.
+
+Table 1: Summary of datasets.  
+
+<table><tr><td>Dataset</td><td># of instances (train / test)</td><td># of classes</td><td>Category</td></tr><tr><td>Caltech-1011</td><td>7,315 / 1,829</td><td>101</td><td>Multiple domains</td></tr><tr><td>Caltech-2562</td><td>24,485 / 6,122</td><td>256</td><td>Multiple domains</td></tr><tr><td>CIFAR-103</td><td>50,000 / 10,000</td><td>10</td><td>Multiple domains</td></tr><tr><td>CIFAR-1003</td><td>50,000 / 10,000</td><td>100</td><td>Multiple domains</td></tr><tr><td>MNIST4</td><td>60,000 / 10,000</td><td>10</td><td>Digit</td></tr><tr><td>FashionMNIST5</td><td>60,000 / 10,000</td><td>10</td><td>Fashion</td></tr><tr><td>SVHN6</td><td>73,257 / 26,032</td><td>10</td><td>Digit</td></tr><tr><td>FlowerPhotos7</td><td>2,936 / 734</td><td>5</td><td>Flower</td></tr><tr><td>EuroSAT8</td><td>21,600 / 5,400</td><td>10</td><td>Landscape</td></tr><tr><td>Chest X-Ray9</td><td>5,216 / 623</td><td>2</td><td>Medicine</td></tr><tr><td>VisDA10</td><td>152,397 / 72,372</td><td>212</td><td>Multiple domains</td></tr><tr><td>FGVC-Aircraft11</td><td>3,334 / 3,333</td><td>100</td><td>Aircraft</td></tr><tr><td>CUB-20012</td><td>9,430 / 2,358</td><td>200</td><td>Animal</td></tr><tr><td>Cars13</td><td>8,144 / 8,041</td><td>196</td><td>Auto</td></tr><tr><td>DTD14</td><td>4,512 / 1,128</td><td>47</td><td>Texture</td></tr><tr><td>Food-10115</td><td>80,800 / 20,200</td><td>101</td><td>Food</td></tr><tr><td>Oxford-IIIT Pet16</td><td>3,680 / 3,669</td><td>37</td><td>Animal</td></tr></table>
+
+<sup>1</sup>https://data.caltech.edu/records/mzrjq-6wc02  
+2 https://data.caltech.edu/records/nyy15-4j048  
+<sup>3</sup> https://www.cs.toronto.edu/~kriz/cifar.html  
+4 http://yann.learun.com/exdb/mnist/  
+5 https://github.com/zalandoresearch/fashion-mnist  
+$^{6}$  http://ufldl.stanford.edu/housenumbers/  
+$^7$  https://www.tensorflow.org/datasets/catalog/tf_flowers  
+8 https://github.com/phelber/eurosat  
+9 https://data.mendeley.com/datasets/rscbjbr9sj/2  
+10 http://ai.bu.edu/visda-2017/#browse  
+11 https://www Robots.ox.ac.uk/~vgg/data/fgvc-aircraft/  
+12 http://www.vision.caltech.edu/datasets/cub_200_2011/  
+13 https://ai.stanford.edu/~jkrause/cars/car_dataset.html  
+14 https://www.robots.ox.ac.uk/~vgg/data/dtd/  
+15 https://data.vision.ee.ethz.ch/cvl/datasetsextra/food-101/  
+16 https://www Robots.ox.ac.uk/~vgg/data/pets/
+
+Evaluation. We evaluate the performance of transferability measurement methods in two ways. First, do they accurately predict the best model? Second, are the transferability scores correlated to fine-tuned accuracy? We adopt Kendall correlation coefficient to measure the correlations between the transferability and fine-tuned accuracy. Kendall correlation coefficient tests the ordinal association between two measured quantities. Kendall correlation coefficient has values between -1 and 1, and correlations between two variables are high when the values are close to 1.
+
+Estimator. We adopt  $k$ -nearest estimator [8] to evaluate the continuous entropy in Equation (4). Compared to kernel density estimators [12, 17],  $k$ -nearest estimator vastly reduces errors by sacrificing time, especially when data are too big. TMI greatly reduces the size of data to be calculated at once because it computes conditional entropy of representation given label.
+
+Hyperparameters. We use greedy searching algorithm to find the best hyperparameters for fine-tuning. For transferability measurement, the only hyperparameter in our proposed TMI is the number  $n_k$  of neighbors, which is used in the entropy estimator [8]. We discuss the hyperparameter sensitivity to transferability in Section 4.6.
+
+Table 2: Ratio of target tasks where their top-5 best source models include the model estimated by each transferability measurement method. The best result is in bold. Note that TMI gives the best ratio, accurately selecting the best pretrained models in 14 out of 17 cases.
+
+<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-5</td><td>3 / 17</td><td>5 / 17</td><td>4 / 17</td><td>8 / 17</td><td>9 / 17</td><td>14 / 17</td></tr></table>
+
+# 4.2. Evaluation of Transferability Estimation
+
+Remind that our goal is to quickly and accurately select the best pre-trained model among a pool of well-trained models. A pre-trained model is determined by two components, source data and model architecture. Thus, we conduct experiments to select the best model architecture and the best source data.
+
+Selecting the best model architecture. We evaluate how the transferability measurement methods accurately select the best source model for a target model. Table 2 shows the ratio of targets tasks where their top-5 best source models include the model estimated by each transferability measurement method. Note that TMI gives the best ratio, accurately selecting the best pre-trained models in 14 out of 17 cases, which is much better than the ratio  $9 / 17$  of the second-best model TransRate.
+
+We also compare the correlations between fine-tuned accuracies and transferability scores in Table 3. Note that our proposed TMI shows the best Kendall correlation in 13 out of 17 datasets, outperforming all the competitors. Some baselines even give negative coefficients, which means that their predictions are far from the correct ranking.
+
+Selecting the best source data. We fine-tune eighteen pre-trained models with the same model architecture ResNet-50, but different source datasets, including ImageNet and seventeen datasets introduced in Section 4.1. We predict the best source data and compare correlations with the ground truths. Table 4 shows that our proposed TMI accurately predicts the best source data in all the 17 cases, outperforming all the competitors. Our proposed TMI gives the best Kendall correlation consistently in 12 out of 17 cases, as shown in Table 5.
+
+# 4.3. Comparison of ICV Measures
+
+Intra-Class Variance (ICV) is a general concept widely used in metric learning. In addition to the conditional entropy introduced in Section 3, we additionally choose four metric learning methods, Contrast [4], Center [20], SNCA [22], and MS [19]. We use the intra-class variance parts of their objective functions to measure the transferability. We apply the five aforementioned methods to measure
+
+Table 3: Correlations between fine-tuned accuracies and transferability scores when transferring supervised pre-trained models trained on ImageNet. The best result is in bold. Our proposed TMI gives the best Kendall correlation in 13 out of 17 cases, outperforming competitors.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="6">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>0.429</td><td>0.425</td><td>0.316</td><td>0.362</td><td>0.474</td><td>0.524</td></tr><tr><td>Caltech-256</td><td>0.686</td><td>0.455</td><td>0.492</td><td>0.503</td><td>0.509</td><td>0.481</td></tr><tr><td>CIFAR-10</td><td>-0.140</td><td>0.324</td><td>0.275</td><td>0.323</td><td>0.364</td><td>0.527</td></tr><tr><td>CIFAR-100</td><td>-0.202</td><td>0.340</td><td>0.351</td><td>0.398</td><td>0.432</td><td>0.497</td></tr><tr><td>MNIST</td><td>0.057</td><td>0.282</td><td>0.083</td><td>0.137</td><td>0.038</td><td>0.137</td></tr><tr><td>FashionMNIST</td><td>-0.328</td><td>0.127</td><td>-0.038</td><td>0.121</td><td>0.125</td><td>0.467</td></tr><tr><td>SVHN</td><td>-0.023</td><td>0.091</td><td>-0.002</td><td>0.092</td><td>0.206</td><td>0.394</td></tr><tr><td>FlowerPhotos</td><td>0.117</td><td>0.139</td><td>0.224</td><td>0.321</td><td>0.392</td><td>0.499</td></tr><tr><td>EuroSAT</td><td>0.269</td><td>0.082</td><td>-0.005</td><td>0.102</td><td>0.051</td><td>0.085</td></tr><tr><td>Chest X-Ray</td><td>0.071</td><td>0.152</td><td>0.171</td><td>0.333</td><td>0.285</td><td>0.395</td></tr><tr><td>VisDA</td><td>0.298</td><td>0.240</td><td>0.329</td><td>0.334</td><td>0.304</td><td>0.341</td></tr><tr><td>FGVC-Aircraft</td><td>0.366</td><td>-0.011</td><td>0.216</td><td>0.498</td><td>0.421</td><td>0.500</td></tr><tr><td>CUB-200</td><td>0.415</td><td>0.098</td><td>0.325</td><td>0.410</td><td>0.519</td><td>0.523</td></tr><tr><td>Cars</td><td>0.270</td><td>0.506</td><td>0.175</td><td>0.432</td><td>0.455</td><td>0.521</td></tr><tr><td>DTD</td><td>-0.074</td><td>0.501</td><td>0.479</td><td>0.366</td><td>0.499</td><td>0.401</td></tr><tr><td>Food-101</td><td>0.261</td><td>0.515</td><td>0.395</td><td>0.421</td><td>0.448</td><td>0.537</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.536</td><td>0.527</td><td>0.418</td><td>0.493</td><td>0.500</td><td>0.576</td></tr></table>
+
+Table 4: Ratio of target tasks where the transferability measurement methods accurately find the best source data. The best method is in bold. TMI predicts the best source data in all cases, outperforming competitors.  
+
+<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-1</td><td>1 / 17</td><td>2 / 17</td><td>3 / 17</td><td>2 / 17</td><td>13 / 17</td><td>17 / 17</td></tr></table>
+
+the correlations between fine-tuned accuracies and transferability scores. Conditional Entropy (CE) shows the best correlations than the other four metric learning measurements in 15 out of 17 datasets, outperforming all the competitors, as shown in Table 6. M. Boudiaf et al. [3] demonstrate that the conditional entropy is a lower bound of intra-class variance of the four metric learning methods.
+
+# 4.4. Evaluation of Generalization Ability
+
+We perform experiments on two control groups to demonstrate that transferability is relevant to the generalization ability of a pre-trained model on a target task. In Group A, we use a pre-trained ResNet-50 model trained on ImageNet and fine-tune it using the dataset  $D$ . In Group B, we train a ResNet-50 model trained from scratch on dataset  $D$  and fine-tune it on the same dataset. Dataset  $D$  is one of the datasets introduced in Section 4.1.
+
+Table 7 shows the difference of fine-tuning performance and that of transferability between two groups. “+” rep
+
+resents the difference is larger than 0 while “-” represents that is less than 0. Group A has higher transfer accuracies than Group B in most cases since models in Group A have learned a large amount of information from the ImageNet, which can potentially benefit downstream tasks.
+
+Our proposed TMI and TransRate have the same symbols for transfer accuracy in 14 out of 17 cases, while the other four baselines do not provide similar symbols. TransRate also estimates well, but it is computationally expensive since it measures the mutual information between target representation and label. In contrast, TMI is more efficient as it considers only intra-class features.
+
+# 4.5. General Applications
+
+Applying to self-supervised pre-trained models. TMI not only measures the transferability between supervised pre-trained models and classification tasks but also can be extended to self-supervised pre-trained models. We prepare eleven self-supervised pre-trained models already trained on ImageNet provided by Github repositories introduced in Section 4.1. NCE [18] and LEEP [13] cannot measure the transferability between a self-supervised pre-trained model and a downstream task because they dig out the relationship between target ground truth and predicted label or probability. Thus, we compare the proposed TMI to LogME [25], H-Score [2], and TransRate [5] in Table 8; TMI outperforms competitors in 13 out of 17 classification datasets.
+
+Table 5: Correlations between fine-tuned accuracies and transferability scores when transferring ResNet-50 models trained on different source data. The best result is in bold. TMI shows the best Kendall correlation in 12 out of 17 cases, outperforming all the competitors.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="6">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.294</td><td>0.542</td><td>0.353</td><td>0.647</td><td>0.425</td><td>0.699</td></tr><tr><td>Caltech-256</td><td>-0.268</td><td>0.542</td><td>0.437</td><td>0.660</td><td>0.477</td><td>0.699</td></tr><tr><td>CIFAR-10</td><td>-0.216</td><td>0.373</td><td>0.383</td><td>0.490</td><td>0.399</td><td>0.630</td></tr><tr><td>CIFAR-100</td><td>-0.098</td><td>0.556</td><td>0.686</td><td>0.345</td><td>0.542</td><td>0.699</td></tr><tr><td>MNIST</td><td>-0.061</td><td>0.439</td><td>0.372</td><td>-0.007</td><td>0.115</td><td>0.162</td></tr><tr><td>FashionMNIST</td><td>-0.086</td><td>0.362</td><td>0.430</td><td>0.475</td><td>0.046</td><td>0.150</td></tr><tr><td>SVHN</td><td>0.039</td><td>0.285</td><td>-0.033</td><td>0.393</td><td>0.170</td><td>0.407</td></tr><tr><td>FlowerPhotos</td><td>-0.359</td><td>0.412</td><td>0.456</td><td>0.307</td><td>0.490</td><td>0.516</td></tr><tr><td>EuroSAT</td><td>-0.388</td><td>0.428</td><td>0.490</td><td>0.322</td><td>0.467</td><td>0.704</td></tr><tr><td>Chest X-Ray</td><td>-0.072</td><td>0.164</td><td>0.359</td><td>-0.111</td><td>0.425</td><td>-0.123</td></tr><tr><td>VisDA</td><td>-0.538</td><td>0.498</td><td>0.094</td><td>-0.039</td><td>0.498</td><td>0.546</td></tr><tr><td>FGVC-Aircraft</td><td>-0.033</td><td>0.373</td><td>0.339</td><td>0.556</td><td>0.399</td><td>0.688</td></tr><tr><td>CUB-200</td><td>-0.503</td><td>0.582</td><td>0.455</td><td>0.464</td><td>0.647</td><td>0.723</td></tr><tr><td>Cars</td><td>-0.294</td><td>0.529</td><td>0.403</td><td>0.752</td><td>0.542</td><td>0.804</td></tr><tr><td>DTD</td><td>-0.438</td><td>0.595</td><td>0.393</td><td>0.647</td><td>0.542</td><td>0.757</td></tr><tr><td>Food-101</td><td>-0.020</td><td>0.281</td><td>0.092</td><td>0.046</td><td>0.229</td><td>0.225</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.268</td><td>0.569</td><td>0.660</td><td>0.503</td><td>0.516</td><td>0.248</td></tr></table>
+
+Table 6: Comparison of intra-class variance measurements. Conditional Entropy (CE) shows the best correlations consistently in 15 out of 17 cases. The best result is in bold.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="5">Kendall Correlation Coefficient</td></tr><tr><td>Contrast</td><td>Center</td><td>SNCA</td><td>MS</td><td>CE</td></tr><tr><td>Caltech-101</td><td>0.274</td><td>0.283</td><td>0.380</td><td>0.358</td><td>0.442</td></tr><tr><td>Caltech-256</td><td>0.295</td><td>0.347</td><td>0.261</td><td>0.347</td><td>0.354</td></tr><tr><td>CIFAR-10</td><td>0.328</td><td>0.322</td><td>0.275</td><td>0.299</td><td>0.369</td></tr><tr><td>CIFAR-100</td><td>0.374</td><td>0.282</td><td>0.207</td><td>0.200</td><td>0.376</td></tr><tr><td>MNIST</td><td>0.383</td><td>0.267</td><td>0.306</td><td>0.228</td><td>0.374</td></tr><tr><td>FashionMNIST</td><td>0.332</td><td>0.225</td><td>0.260</td><td>0.337</td><td>0.374</td></tr><tr><td>SVHN</td><td>0.303</td><td>0.359</td><td>0.369</td><td>0.360</td><td>0.383</td></tr><tr><td>FlowerPhotos</td><td>0.209</td><td>0.263</td><td>0.291</td><td>0.277</td><td>0.372</td></tr><tr><td>EuroSAT</td><td>0.292</td><td>0.237</td><td>0.367</td><td>0.268</td><td>0.400</td></tr><tr><td>Chest X-Ray</td><td>0.292</td><td>0.289</td><td>0.210</td><td>0.232</td><td>0.357</td></tr><tr><td>VisDA</td><td>0.259</td><td>0.352</td><td>0.200</td><td>0.329</td><td>0.352</td></tr><tr><td>FGVC-Aircraft</td><td>0.220</td><td>0.322</td><td>0.244</td><td>0.315</td><td>0.351</td></tr><tr><td>CUB-200</td><td>0.368</td><td>0.252</td><td>0.379</td><td>0.385</td><td>0.431</td></tr><tr><td>Cars</td><td>0.351</td><td>0.285</td><td>0.398</td><td>0.268</td><td>0.248</td></tr><tr><td>DTD</td><td>0.236</td><td>0.322</td><td>0.228</td><td>0.206</td><td>0.327</td></tr><tr><td>Food-101</td><td>0.322</td><td>0.267</td><td>0.246</td><td>0.269</td><td>0.484</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.301</td><td>0.202</td><td>0.363</td><td>0.274</td><td>0.449</td></tr></table>
+
+Selecting the best transferring layer. Given a ResNet-18 trained on ImageNet, we can easily determine the best transferring layer, which produces the best fine-tuning performance for a target task by measuring transferability. We compare the correlations of LogME [25], H-Score [2], and TransRate to select the best transferring layer for fine
+
+Table 7: Comparison of the consistency of fine-tuning accuracy and transferability. “+” represents the difference is larger than 0 while “-” represents the difference is less than 0. TMI has consistent signs with fine-tuning accuracy in 14 out of 17 cases, outperforming its competitors.  
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Accuracy (A-B)</td><td colspan="6">Transferability (A-B)</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogME</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Caltech-256</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-10</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-100</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>MNIST</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FashionMNIST</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>SVHN</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>FlowerPhotos</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>EuroSAT</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>Chest X-Ray</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>VisDA</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FGVC-Aircraft</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CUB-200</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Cars</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>DTD</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Food-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Oxford-IIIT Pet</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr></table>
+
+tuning. Theoretically, LogME [25] and H-Score [2] cannot deal with layer selection because they rely on features from the ultimate layer of the feature extractor. However, we extract features from each layer and directly put them into LogME and H-Score algorithms to calculate the trans
+
+Table 8: Correlations between fine-tuned accuracies and transferability scores when transferring self-supervised pretrained models to classification tasks. The best result is in bold. TMI shows the best Kendall correlation consistently in 13 out of 17 cases, outperforming all the competitors.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="4">Kendall Correlation Coefficient</td></tr><tr><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.278</td><td>0.183</td><td>0.000</td><td>0.367</td></tr><tr><td>Caltech-256</td><td>-0.561</td><td>0.345</td><td>0.164</td><td>0.600</td></tr><tr><td>CIFAR-10</td><td>-0.337</td><td>0.018</td><td>0.164</td><td>0.624</td></tr><tr><td>CIFAR-100</td><td>-0.561</td><td>0.673</td><td>0.236</td><td>0.697</td></tr><tr><td>MNIST</td><td>-0.574</td><td>-0.262</td><td>-0.426</td><td>0.246</td></tr><tr><td>FashionMNIST</td><td>-0.330</td><td>-0.220</td><td>-0.330</td><td>0.094</td></tr><tr><td>SVHN</td><td>0.055</td><td>0.309</td><td>-0.345</td><td>0.075</td></tr><tr><td>FlowerPhotos</td><td>0.389</td><td>-0.241</td><td>0.130</td><td>0.075</td></tr><tr><td>EuroSAT</td><td>-0.073</td><td>-0.037</td><td>0.037</td><td>-0.208</td></tr><tr><td>Chest X-Ray</td><td>-0.037</td><td>-0.037</td><td>-0.257</td><td>0.175</td></tr><tr><td>VisDA</td><td>0.550</td><td>0.055</td><td>0.309</td><td>-0.597</td></tr><tr><td>FGVC-Aircraft</td><td>-0.345</td><td>0.091</td><td>-0.309</td><td>0.150</td></tr><tr><td>CUB-200</td><td>-0.112</td><td>-0.018</td><td>0.091</td><td>0.564</td></tr><tr><td>Cars</td><td>0.000</td><td>0.382</td><td>-0.200</td><td>0.262</td></tr><tr><td>DTD</td><td>0.382</td><td>0.018</td><td>0.224</td><td>0.455</td></tr><tr><td>Food-101</td><td>-0.411</td><td>-0.018</td><td>-0.018</td><td>0.204</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.585</td><td>0.294</td><td>0.073</td><td>0.807</td></tr></table>
+
+![](images/c98a0030dc307929921556676a29d661d875515f1787899a5231af92281004ef.jpg)  
+Figure 3: Sensitivity to the hyperparameter  $n_k$  in entropy estimator.
+
+ferability. The size of extracted features is quite large in the early layers, resulting in much higher computational cost for transferability measurement. To reduce this cost, we add an avgpool2d layer to the end of transferring layer to reduce the dimension of extracted features. Table 9 shows that TMI achieves the highest correlation coefficients in 16 out of 17 datasets. Correlation coefficients of MNIST, SVHN, and Chest X-Ray are much lower than those of the other datasets because their ranges of minimum and maximum accuracies obtained by layer transfer are smaller than  $0.5\%$ , making it challenging to rank these dataset accurately.
+
+# 4.6. Hyperparameter Sensitivity
+
+An advantage of TMI is that it does not train models on target datasets because it is time-consuming and sensitive to hyperparameters which may cause different results. The only hyperparameter in TMI is  $n_k$  used in the entropy estimator. In Figure. 3, the correlation between pre-trained
+
+Table 9: Correlations between fine-tuned accuracies and transferability scores when transferring specific layers of pre-trained models. The best result is in bold. TMI shows the best correlations consistently in 16 out of 17 cases.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="4">Kendall Correlation Coefficient</td></tr><tr><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>0.346</td><td>0.935</td><td>0.752</td><td>0.941</td></tr><tr><td>Caltech-256</td><td>0.973</td><td>0.317</td><td>0.800</td><td>0.984</td></tr><tr><td>CIFAR-10</td><td>0.360</td><td>0.743</td><td>0.704</td><td>0.746</td></tr><tr><td>CIFAR-100</td><td>0.460</td><td>0.774</td><td>0.774</td><td>0.801</td></tr><tr><td>MNIST</td><td>0.180</td><td>0.055</td><td>0.179</td><td>0.184</td></tr><tr><td>FashionMNIST</td><td>0.294</td><td>0.241</td><td>0.298</td><td>0.308</td></tr><tr><td>SVHN</td><td>0.087</td><td>0.106</td><td>0.040</td><td>0.113</td></tr><tr><td>FlowerPhotos</td><td>0.779</td><td>0.198</td><td>0.687</td><td>0.792</td></tr><tr><td>EuroSAT</td><td>0.691</td><td>0.709</td><td>0.495</td><td>0.735</td></tr><tr><td>Chest X-Ray</td><td>0.113</td><td>0.154</td><td>0.100</td><td>0.054</td></tr><tr><td>VisDA</td><td>0.665</td><td>0.866</td><td>0.826</td><td>0.904</td></tr><tr><td>FGVC-Aircraft</td><td>0.791</td><td>0.302</td><td>0.595</td><td>0.817</td></tr><tr><td>CUB-200</td><td>0.317</td><td>0.970</td><td>0.787</td><td>0.954</td></tr><tr><td>Cars</td><td>0.330</td><td>0.869</td><td>0.752</td><td>0.882</td></tr><tr><td>DTD</td><td>0.924</td><td>0.401</td><td>0.761</td><td>0.931</td></tr><tr><td>Food-101</td><td>0.409</td><td>0.948</td><td>0.869</td><td>0.970</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.349</td><td>0.970</td><td>0.826</td><td>0.990</td></tr></table>
+
+models and TMI shows consistency in most ranges for  $n_k$ .
+
+# 5. Conclusion
+
+We propose TMI, a fast, accurate, and general algorithm to measure the transferability. TMI quantifies the degree of generalization of a pre-trained model to a new task by estimating the intra-class feature variance. We conduct experiments on seventeen datasets with fifty supervised pretrained models and eleven self-supervised pre-trained models. TMI selects the top-5 pre-trained architecture in 14 out of 17 cases and selects the best source data in all cases, outperforming its competitors. We measure the correlation between the fine-tuning performance and transferability, and our proposed TMI outperforms competitors in 13 out of 17 cases.
+
+# Acknowledgments
+
+This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) [No.2020-0-00894, Flexible and Efficient Model Compression Method for Various Applications and Environments], [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)], and [NO.2021-0-02068, Artificial Intelligence Innovation Hub (Artificial Intelligence Institute, Seoul National University)]. The Institute of Engineering Research at Seoul National University provided research facilities for this work. The ICT at Seoul National University provides research facilities for this study. U Kang is the corresponding author.
+
+# References
+
+[1] Alessandro Achille, Michael Lam, Rahul Tewari, Avinash Ravichandran, Subhransu Maji, Charless C. Fowlkes, Stefano Soatto, and Pietro Perona. Task2vec: Task embedding for meta-learning. In ICCV, 2019.  
+[2] Yajie Bao, Yang Li, Shao-Lun Huang, Lin Zhang, Lizhong Zheng, Amir Roshan Zamir, and Leonidas J. Guibas. An information-theoretic approach to transferability in task transfer learning. In ICIP, 2019.  
+[3] Malik Boudiaf, Jérôme Rony, Imtiaz Masud Ziko, Eric Granger, Marco Pedersoli, Pablo Piantanida, and Ismail Ben Ayed. A unifying mutual information view of metric learning: Cross-entropy vs. pairwise losses. In Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part VI, volume 12351 of Lecture Notes in Computer Science, pages 548-564. Springer, 2020.  
+[4] Raia Hadsell, Sumit Chopra, and Yann LeCun. Dimensionality reduction by learning an invariant mapping. In 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2006), 17-22 June 2006, New York, NY, USA, pages 1735-1742. IEEE Computer Society, 2006.  
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+[7] Lee S. Jeon, H. and U Kang. Unsupervised multi-source domain adaptation with no observable source data. *PloS one*, 16(7), 2021.  
+[8] Alexander Kraskov, Harald Stögbauer, and Peter Grassberger. Estimating mutual information. Physical Review E, 2004.  
+[9] Jeon H. Lee, S. and U Kang. Multi-epl: Accurate multisource domain adaptation. PloS one, 16(8), 2021.  
+[10] Jian Liang, Dapeng Hu, Jiashi Feng, and Ran He. Dine: Domain adaptation from single and multiple black-box predictors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022.  
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+[15] Seungcheol Park, Huiwen Xu, Taehun Kim, Inhwan Hwang, Kyung-Jun Kim, and U Kang. Fast and accurate transferabil
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+ity measurement for heterogeneous multivariate data. CoRR, abs/1912.13366, 2019.  
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+                                            "content": "Figure 1: Illustration of selecting the best pre-trained model for a given target task."
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+                                    "content": "trained and applied to various domains. Transfer learning has proven to be particularly valuable when labeled data in the target domain are scarce or costly to obtain. Within the broader scope of transfer learning, several variants have emerged, such as source-free domain adaptation [10, 27, 23, 7], multi-source transfer learning [16, 14, 7, 9], heterogeneous transfer learning [11, 15], and open-set domain adaptation [6, 21]."
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+                                    "content": "In transfer learning, fine-tuning a pre-trained model becomes a simple and effective way to improve the performance of a downstream task. A crucial step in transfer learning is to quickly and accurately select the most helpful pre-trained model in a set of given pre-trained models. Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. As shown in Figure. 1, transferability measurement is used for ranking pre-trained models for a given task, and is a crucial step for transfer learning."
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "A desired method for transferability measurement should be faster than running a transfer learning algorithm, accurately select the best pre-trained model, and be general to be implemented in various common scenarios. Taskonomy [26] and Task2Vec [1] are computationally expensive due to their learning with data. NCE [18] and LEEP [13] are free of training but cannot be applied to general cases, such as selecting self-supervised pre-trained models and selecting the best transferring layer. LogMe [25] and H-Score [2] also cannot be applied theoretically to select the best transferring layer. Instead of measuring transferability, they measure how discriminative a pre-trained model is to a target task before implementing transfer learning, which cannot estimate fine-tuning performance. TransRate [5] is simple and general to be applied for transferability measurement, but too slow due to the computation of the entropy of whole hidden representations."
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+                                    "content": "In this paper, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a simple but effective method for transferability measurement. We deem transferability as the generalization of a pre-trained model on a target task. To quantify the degree of generalization, we measure the intra-class variance by the conditional entropy of target representation given a label. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Large intra-class variance implies the feature is efficient for learning tasks. TMI can be used for selecting not only the best supervised model but also the best self-supervised models and the best transferring layer."
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+                                    "type": "text",
+                                    "content": "Our contributions are summarized as follows:"
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+                                            "type": "text",
+                                            "content": "- Algorithm. We propose TMI, a fast, accurate, and general method for measuring transferability. We view transferability as generalization ability of a pre-trained model on a target task. The model generalization is measured by intra-class feature variance."
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+                                    ]
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+                                            "type": "text",
+                                            "content": "- Experiments. We conduct extensive experiments on seventeen datasets with fifty supervised pre-trained models and eleven self-supervised pre-trained models. TMI outperforms competitors for selecting the top-5 pre-trained architecture in 14 out of 17 cases and selecting the best source data in all cases. TMI also shows the best trade-off of the running time and transferability, outperforming competitors in 12 out of 17 cases (see Figure. 2)."
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+                                            "type": "text",
+                                            "content": "- Case study. We evaluate the transferability in more general cases, such as applying to self-supervised pretrained models and selecting the best transferring layer. Compared to competitors, TMI achieves the highest correlation coefficient in 13 out of 17 for selecting the"
+                                        }
+                                    ]
+                                }
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+                                    "content": "best self-supervised pre-trained models, and in 16 out of 17 datasets for selecting the best transferring layer."
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+                                    "content": "The rest of this paper is organized as follows. We introduce related works for transferability measurement in Section 2, and propose our method TMI in Section 3. After presenting experimental results in Section 4, we conclude in Section 5."
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+                                    "content": "2. Related Works"
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+                                    "type": "text",
+                                    "content": " is a feature extractor, and "
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+                                    "content": " is a classifier (or head). We transfer the model "
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+                                    "content": " to a target domain and add a new classifier "
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+                                    "content": " at the end of the feature extractor "
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+                                    "type": "text",
+                                    "content": " before fine-tuning. Since the target task is different from the source task in most cases, the pre-trained classifier "
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+                                    "content": " is inappropriate to solve the target task. Thus, we fine-tune the model by minimizing the cross entropy loss on the target dataset "
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+                                    "type": "inline_equation",
+                                    "content": "D = \\{(x_i, y_i)\\}_{i=1}^n"
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+                                    "type": "interline_equation",
+                                    "content": "w ^ {*}, k ^ {*} = \\underset {w, k} {\\arg \\min } \\mathcal {L} (w, k) \\tag {1}",
+                                    "image_path": "14a5e33249457572041607b76d8c2cc0e8fb98956cb694803e0e9cbeffa4074c.jpg"
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+                                    "type": "text",
+                                    "content": "where a feature extractor "
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+                                    "content": " maps an input "
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+                                    "type": "text",
+                                    "content": " to a representation "
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+                                    "type": "inline_equation",
+                                    "content": "r_i = w(x_i)"
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+                                    "type": "text",
+                                    "content": ", and a classifier "
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+                                    "content": " maps the representation "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{y}_i = \\sigma(h(r_i))"
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+                                    "type": "text",
+                                    "content": " is an activation function. Note that "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "content": "on the outputs of the pre-trained classifier. To apply measurements in more general cases, LogME [25] calculates the logarithm of maximum evidence given extracted features, and H-Score [2] solves an HGR maximum correlation problem. LogMe [25] and H-Score [2] still cannot be applied to select the best transferred layer since they extract features from only the ultimate layers of the pretrained feature extractors. TransRate [5] is the most recent algorithm and applicable to self-supervised models and transferring layer selection. However, it is time-consuming since it requires to calculate mutual information between extracted feature and ground truth. To simplify the problem, [18, 13, 25, 2, 5] assume that the optimal model can be obtained by re-training the classifier while freezing the feature extractor. They estimate the performance of re-training only the classifier, which is even worse than training a target model from scratch [24]. In this paper, we propose a fast, accurate, and general transferability measurement method that predicts fine-tuned performance of a pre-trained model to a new target task."
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+                                            "type": "text",
+                                            "content": "C2 Accuracy. Existing methods evaluate the transferability that estimate the performance of the optimal target model obtained by re-training only the classifier, not the feature extractor, which is uncommon in transfer learning. How can we accurately measure the transferability for predicting the fine-tuning performance?"
+                                        }
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+                                            "type": "text",
+                                            "content": "C3 Generality. How can we measure the transferability such that it is applicable to general settings, including selecting the best supervised pre-trained model, the best self-supervised pre-trained models, and the transferring layer?"
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "We address the aforementioned challenges with the following main ideas:"
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+                                            "type": "text",
+                                            "content": "I1 We assess the transferability by evaluating the compactness and sparseness of target representations with only a one-way forward propagation."
+                                        }
+                                    ]
+                                }
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+                        },
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+                                            "type": "text",
+                                            "content": "12 We relax the assumption proposed in existing methods"
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+                                    "type": "text",
+                                    "content": "that the pre-trained feature extractor can extract all the information related to the target task. We view transferability as the generalization ability of a pre-trained model on a target task. We estimate the generalization ability using intra-class variance, which implies how efficient the feature is for learning tasks."
+                                }
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+                                    "content": "13 We measure the transferability using intra-class variance of latent representations, which is applicable to various settings including self-supervised pre-trained models and transferring layer selection."
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+                                    "content": "3.2.TMI"
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+                                    "type": "text",
+                                    "content": "Given a pre-trained source model and a target dataset with labels, our goal is to measure the transferability between the source model and the target task to predict the fine-tuning performance. Existing methods measure the performance of re-trained classifier while freezing the feature extractor, which is time-consuming. To address the issues, our proposed TMI computes the transferability as the intra-class variance of a pre-trained model on a target task. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. It is unnecessary for TMI to obtain optimal classifier which is a time-consuming process."
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+                                    "content": "TMI The transferability of a pre-trained feature extractor "
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+                                    "content": " to a target task "
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+                                    "type": "text",
+                                    "content": ", denoted by "
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+                                    "type": "inline_equation",
+                                    "content": "Trf_{(S\\rightarrow T)}"
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+                                    "type": "text",
+                                    "content": ", is measured by TMI with the intra-class feature variance obtained from the pre-trained model "
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "interline_equation",
+                                    "content": "T r f _ {(S \\rightarrow T)} := H \\left(\\omega_ {s} (X) | Y\\right) = \\sum_ {c = 1} ^ {C} \\frac {n _ {c}}{n} H \\left(\\omega_ {s} \\left(X _ {c}\\right)\\right) \\tag {4}",
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+                                    "type": "text",
+                                    "content": " represent the target feature and the target label, respectively. "
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+                                    "content": " represents the number of classes and "
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+                                    "type": "inline_equation",
+                                    "content": "X_{c} = \\{x|Y = c\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the set of target features in the "
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+                                    "type": "text",
+                                    "content": " represent the number of total instances and number of instances in the "
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+                                    "type": "text",
+                                    "content": "-th class, respectively. We measure the intra-class variance of target representations using conditional entropy. The intra-class variance encourages the pre-trained model to have a generalization ability for learning tasks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "How to utilize TMI? Given a set of pre-trained models and a target dataset with labels, we first obtain target representations of pre-trained models by one-way forward propagation. Next, we compute the transferability score using Equation (4). We select the pre-trained model with the highest transferability score and then fine-tune the model using the target data. We argue that the larger the TMI, the higher the transfer performance."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
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+                    "index": 8
+                },
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+                                    "content": "We present experimental results to answer the following questions about TMI:"
+                                }
+                            ]
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Q1 Evaluation of transferability estimation (Section 4.2). Does TMI accurately select the best pretrained model compared to baselines? Is the transferability score measured by TMI highly correlated to the transfer performance?"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Q2 Comparison of ICV measures (Section 4.3). What is the best measurement to evaluate Intra-Class Variance (ICV)?"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Q3 Evaluation of generalization ability (Section 4.4). Does intra-class variance estimate generalization ability of a pre-trained model on a target task?"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Q4 General applications (Section 4.5). Does TMI accurately estimate the transferability in general cases, such as selecting the best self-supervised pre-trained model and the best transferring layer?"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
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+                                            "content": "Q5 Hyperparameter sensitivity (Section 4.6). How sensitive is TMI to hyperparameters?"
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+                                }
+                            ],
+                            "index": 14
+                        }
+                    ],
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+                                    "content": "4.1. Experimental Setup"
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+                                    "content": "We present pre-trained models, datasets, baselines, evaluation, estimator, and hyperparameters for our experiments."
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+                                    "content": "Pre-trained models. We use supervised model groups offered by Pytorch: ResNet, DenseNet, MnasNet, ShuffleNet V2, MobileNet V2, MobileNet V3, ResNeXt, Wide ResNet, EfficientNet, EfficientNet V2, and RegNet. We also utilize self-supervised model groups, which have only feature extractors without classifiers. We obtain Swin Transformer and Vision Transformer from Pytorch; we get MoCo v1, MoCo v2, Barlow Twins, SwAV, SimSiam, and Dino from Gitlab repositories. Note that we select fifty supervised pretrained models and eleven self-supervised pre-trained models from the aforementioned model groups."
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+                                    "content": "Datasets. We use seventeen image datasets summarized in Table 1. We randomly split each dataset into a train set and test set by 8:2 ratio, except for datasets that already have been separated."
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+                            ]
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+                                    "type": "text",
+                                    "content": "Baselines. We compare the proposed method with the following baselines. NCE [18] defines the transferability as negative conditional entropy between ground truths and predicted labels from a pre-trained model. LEEP [13] measures negative conditional entropy between ground truths and predicted average log-likelihood. H-Score [2] estimates the transferability by solving an HGR maximum correlation problem. LogME [25] proposes the logarithm of maximum evidence given extracted features. TransRate [5] measures the transferability by the mutual information between target labels and target representations. We omit the comparison with Taskonomy [26] and Task2Vec [1] due to tremendous time costs."
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+                                            "content": "<sup>3</sup> https://www.cs.toronto.edu/~kriz/cifar.html"
+                                        }
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+                                            "content": "4 http://yann.learun.com/exdb/mnist/"
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+                                            "content": " https://www.tensorflow.org/datasets/catalog/tf_flowers"
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "content": "15 https://data.vision.ee.ethz.ch/cvl/datasetsextra/food-101/"
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+                                            "content": "16 https://www Robots.ox.ac.uk/~vgg/data/pets/"
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+                                    "type": "text",
+                                    "content": "Evaluation. We evaluate the performance of transferability measurement methods in two ways. First, do they accurately predict the best model? Second, are the transferability scores correlated to fine-tuned accuracy? We adopt Kendall correlation coefficient to measure the correlations between the transferability and fine-tuned accuracy. Kendall correlation coefficient tests the ordinal association between two measured quantities. Kendall correlation coefficient has values between -1 and 1, and correlations between two variables are high when the values are close to 1."
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+                                    "type": "text",
+                                    "content": "Estimator. We adopt "
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+                                    "type": "text",
+                                    "content": "-nearest estimator [8] to evaluate the continuous entropy in Equation (4). Compared to kernel density estimators [12, 17], "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-nearest estimator vastly reduces errors by sacrificing time, especially when data are too big. TMI greatly reduces the size of data to be calculated at once because it computes conditional entropy of representation given label."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Hyperparameters. We use greedy searching algorithm to find the best hyperparameters for fine-tuning. For transferability measurement, the only hyperparameter in our proposed TMI is the number "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " of neighbors, which is used in the entropy estimator [8]. We discuss the hyperparameter sensitivity to transferability in Section 4.6."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Table 2: Ratio of target tasks where their top-5 best source models include the model estimated by each transferability measurement method. The best result is in bold. Note that TMI gives the best ratio, accurately selecting the best pretrained models in 14 out of 17 cases."
+                                }
+                            ]
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+                                            "html": "<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-5</td><td>3 / 17</td><td>5 / 17</td><td>4 / 17</td><td>8 / 17</td><td>9 / 17</td><td>14 / 17</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "4.2. Evaluation of Transferability Estimation"
+                                }
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+                        }
+                    ],
+                    "index": 24
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+                {
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+                                    "type": "text",
+                                    "content": "Remind that our goal is to quickly and accurately select the best pre-trained model among a pool of well-trained models. A pre-trained model is determined by two components, source data and model architecture. Thus, we conduct experiments to select the best model architecture and the best source data."
+                                }
+                            ]
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+                    ],
+                    "index": 25
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Selecting the best model architecture. We evaluate how the transferability measurement methods accurately select the best source model for a target model. Table 2 shows the ratio of targets tasks where their top-5 best source models include the model estimated by each transferability measurement method. Note that TMI gives the best ratio, accurately selecting the best pre-trained models in 14 out of 17 cases, which is much better than the ratio "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "9 / 17"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the second-best model TransRate."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We also compare the correlations between fine-tuned accuracies and transferability scores in Table 3. Note that our proposed TMI shows the best Kendall correlation in 13 out of 17 datasets, outperforming all the competitors. Some baselines even give negative coefficients, which means that their predictions are far from the correct ranking."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Selecting the best source data. We fine-tune eighteen pre-trained models with the same model architecture ResNet-50, but different source datasets, including ImageNet and seventeen datasets introduced in Section 4.1. We predict the best source data and compare correlations with the ground truths. Table 4 shows that our proposed TMI accurately predicts the best source data in all the 17 cases, outperforming all the competitors. Our proposed TMI gives the best Kendall correlation consistently in 12 out of 17 cases, as shown in Table 5."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.3. Comparison of ICV Measures"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Intra-Class Variance (ICV) is a general concept widely used in metric learning. In addition to the conditional entropy introduced in Section 3, we additionally choose four metric learning methods, Contrast [4], Center [20], SNCA [22], and MS [19]. We use the intra-class variance parts of their objective functions to measure the transferability. We apply the five aforementioned methods to measure"
+                                }
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+                                            "content": "Table 3: Correlations between fine-tuned accuracies and transferability scores when transferring supervised pre-trained models trained on ImageNet. The best result is in bold. Our proposed TMI gives the best Kendall correlation in 13 out of 17 cases, outperforming competitors."
+                                        }
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+                                            "type": "text",
+                                            "content": "Table 4: Ratio of target tasks where the transferability measurement methods accurately find the best source data. The best method is in bold. TMI predicts the best source data in all cases, outperforming competitors."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "html": "<table><tr><td>Methods</td><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Top-1</td><td>1 / 17</td><td>2 / 17</td><td>3 / 17</td><td>2 / 17</td><td>13 / 17</td><td>17 / 17</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "the correlations between fine-tuned accuracies and transferability scores. Conditional Entropy (CE) shows the best correlations than the other four metric learning measurements in 15 out of 17 datasets, outperforming all the competitors, as shown in Table 6. M. Boudiaf et al. [3] demonstrate that the conditional entropy is a lower bound of intra-class variance of the four metric learning methods."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "4.4. Evaluation of Generalization Ability"
+                                }
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+                    ],
+                    "index": 5
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+                {
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+                                    "type": "text",
+                                    "content": "We perform experiments on two control groups to demonstrate that transferability is relevant to the generalization ability of a pre-trained model on a target task. In Group A, we use a pre-trained ResNet-50 model trained on ImageNet and fine-tune it using the dataset "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". In Group B, we train a ResNet-50 model trained from scratch on dataset "
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and fine-tune it on the same dataset. Dataset "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is one of the datasets introduced in Section 4.1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
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+                {
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+                                    "content": "Table 7 shows the difference of fine-tuning performance and that of transferability between two groups. “+” rep"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "resents the difference is larger than 0 while “-” represents that is less than 0. Group A has higher transfer accuracies than Group B in most cases since models in Group A have learned a large amount of information from the ImageNet, which can potentially benefit downstream tasks."
+                                }
+                            ]
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+                                    "content": "Our proposed TMI and TransRate have the same symbols for transfer accuracy in 14 out of 17 cases, while the other four baselines do not provide similar symbols. TransRate also estimates well, but it is computationally expensive since it measures the mutual information between target representation and label. In contrast, TMI is more efficient as it considers only intra-class features."
+                                }
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+                                    "type": "text",
+                                    "content": "4.5. General Applications"
+                                }
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+                                    "content": "Applying to self-supervised pre-trained models. TMI not only measures the transferability between supervised pre-trained models and classification tasks but also can be extended to self-supervised pre-trained models. We prepare eleven self-supervised pre-trained models already trained on ImageNet provided by Github repositories introduced in Section 4.1. NCE [18] and LEEP [13] cannot measure the transferability between a self-supervised pre-trained model and a downstream task because they dig out the relationship between target ground truth and predicted label or probability. Thus, we compare the proposed TMI to LogME [25], H-Score [2], and TransRate [5] in Table 8; TMI outperforms competitors in 13 out of 17 classification datasets."
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+                                            "content": "Table 5: Correlations between fine-tuned accuracies and transferability scores when transferring ResNet-50 models trained on different source data. The best result is in bold. TMI shows the best Kendall correlation in 12 out of 17 cases, outperforming all the competitors."
+                                        }
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+                                            "html": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"6\">Kendall Correlation Coefficient</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogMe</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>-0.294</td><td>0.542</td><td>0.353</td><td>0.647</td><td>0.425</td><td>0.699</td></tr><tr><td>Caltech-256</td><td>-0.268</td><td>0.542</td><td>0.437</td><td>0.660</td><td>0.477</td><td>0.699</td></tr><tr><td>CIFAR-10</td><td>-0.216</td><td>0.373</td><td>0.383</td><td>0.490</td><td>0.399</td><td>0.630</td></tr><tr><td>CIFAR-100</td><td>-0.098</td><td>0.556</td><td>0.686</td><td>0.345</td><td>0.542</td><td>0.699</td></tr><tr><td>MNIST</td><td>-0.061</td><td>0.439</td><td>0.372</td><td>-0.007</td><td>0.115</td><td>0.162</td></tr><tr><td>FashionMNIST</td><td>-0.086</td><td>0.362</td><td>0.430</td><td>0.475</td><td>0.046</td><td>0.150</td></tr><tr><td>SVHN</td><td>0.039</td><td>0.285</td><td>-0.033</td><td>0.393</td><td>0.170</td><td>0.407</td></tr><tr><td>FlowerPhotos</td><td>-0.359</td><td>0.412</td><td>0.456</td><td>0.307</td><td>0.490</td><td>0.516</td></tr><tr><td>EuroSAT</td><td>-0.388</td><td>0.428</td><td>0.490</td><td>0.322</td><td>0.467</td><td>0.704</td></tr><tr><td>Chest X-Ray</td><td>-0.072</td><td>0.164</td><td>0.359</td><td>-0.111</td><td>0.425</td><td>-0.123</td></tr><tr><td>VisDA</td><td>-0.538</td><td>0.498</td><td>0.094</td><td>-0.039</td><td>0.498</td><td>0.546</td></tr><tr><td>FGVC-Aircraft</td><td>-0.033</td><td>0.373</td><td>0.339</td><td>0.556</td><td>0.399</td><td>0.688</td></tr><tr><td>CUB-200</td><td>-0.503</td><td>0.582</td><td>0.455</td><td>0.464</td><td>0.647</td><td>0.723</td></tr><tr><td>Cars</td><td>-0.294</td><td>0.529</td><td>0.403</td><td>0.752</td><td>0.542</td><td>0.804</td></tr><tr><td>DTD</td><td>-0.438</td><td>0.595</td><td>0.393</td><td>0.647</td><td>0.542</td><td>0.757</td></tr><tr><td>Food-101</td><td>-0.020</td><td>0.281</td><td>0.092</td><td>0.046</td><td>0.229</td><td>0.225</td></tr><tr><td>Oxford-IIIT Pet</td><td>-0.268</td><td>0.569</td><td>0.660</td><td>0.503</td><td>0.516</td><td>0.248</td></tr></table>",
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+                                            "content": "Table 6: Comparison of intra-class variance measurements. Conditional Entropy (CE) shows the best correlations consistently in 15 out of 17 cases. The best result is in bold."
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+                                            "html": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"5\">Kendall Correlation Coefficient</td></tr><tr><td>Contrast</td><td>Center</td><td>SNCA</td><td>MS</td><td>CE</td></tr><tr><td>Caltech-101</td><td>0.274</td><td>0.283</td><td>0.380</td><td>0.358</td><td>0.442</td></tr><tr><td>Caltech-256</td><td>0.295</td><td>0.347</td><td>0.261</td><td>0.347</td><td>0.354</td></tr><tr><td>CIFAR-10</td><td>0.328</td><td>0.322</td><td>0.275</td><td>0.299</td><td>0.369</td></tr><tr><td>CIFAR-100</td><td>0.374</td><td>0.282</td><td>0.207</td><td>0.200</td><td>0.376</td></tr><tr><td>MNIST</td><td>0.383</td><td>0.267</td><td>0.306</td><td>0.228</td><td>0.374</td></tr><tr><td>FashionMNIST</td><td>0.332</td><td>0.225</td><td>0.260</td><td>0.337</td><td>0.374</td></tr><tr><td>SVHN</td><td>0.303</td><td>0.359</td><td>0.369</td><td>0.360</td><td>0.383</td></tr><tr><td>FlowerPhotos</td><td>0.209</td><td>0.263</td><td>0.291</td><td>0.277</td><td>0.372</td></tr><tr><td>EuroSAT</td><td>0.292</td><td>0.237</td><td>0.367</td><td>0.268</td><td>0.400</td></tr><tr><td>Chest X-Ray</td><td>0.292</td><td>0.289</td><td>0.210</td><td>0.232</td><td>0.357</td></tr><tr><td>VisDA</td><td>0.259</td><td>0.352</td><td>0.200</td><td>0.329</td><td>0.352</td></tr><tr><td>FGVC-Aircraft</td><td>0.220</td><td>0.322</td><td>0.244</td><td>0.315</td><td>0.351</td></tr><tr><td>CUB-200</td><td>0.368</td><td>0.252</td><td>0.379</td><td>0.385</td><td>0.431</td></tr><tr><td>Cars</td><td>0.351</td><td>0.285</td><td>0.398</td><td>0.268</td><td>0.248</td></tr><tr><td>DTD</td><td>0.236</td><td>0.322</td><td>0.228</td><td>0.206</td><td>0.327</td></tr><tr><td>Food-101</td><td>0.322</td><td>0.267</td><td>0.246</td><td>0.269</td><td>0.484</td></tr><tr><td>Oxford-IIIT Pet</td><td>0.301</td><td>0.202</td><td>0.363</td><td>0.274</td><td>0.449</td></tr></table>",
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+                                    "content": "Selecting the best transferring layer. Given a ResNet-18 trained on ImageNet, we can easily determine the best transferring layer, which produces the best fine-tuning performance for a target task by measuring transferability. We compare the correlations of LogME [25], H-Score [2], and TransRate to select the best transferring layer for fine"
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+                                            "content": "Table 7: Comparison of the consistency of fine-tuning accuracy and transferability. “+” represents the difference is larger than 0 while “-” represents the difference is less than 0. TMI has consistent signs with fine-tuning accuracy in 14 out of 17 cases, outperforming its competitors."
+                                        }
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+                                            "html": "<table><tr><td rowspan=\"2\">Dataset</td><td rowspan=\"2\">Accuracy (A-B)</td><td colspan=\"6\">Transferability (A-B)</td></tr><tr><td>NCE</td><td>LEEP</td><td>LogME</td><td>H-Score</td><td>TransRate</td><td>TMI</td></tr><tr><td>Caltech-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Caltech-256</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-10</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CIFAR-100</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>MNIST</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FashionMNIST</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>SVHN</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>FlowerPhotos</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>EuroSAT</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>Chest X-Ray</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>VisDA</td><td>+</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td><td>+</td></tr><tr><td>FGVC-Aircraft</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>CUB-200</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Cars</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>DTD</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Food-101</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Oxford-IIIT Pet</td><td>+</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr></table>",
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+                                        }
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+                                    "type": "text",
+                                    "content": "tuning. Theoretically, LogME [25] and H-Score [2] cannot deal with layer selection because they rely on features from the ultimate layer of the feature extractor. However, we extract features from each layer and directly put them into LogME and H-Score algorithms to calculate the trans"
+                                }
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+                                            "content": "Table 8: Correlations between fine-tuned accuracies and transferability scores when transferring self-supervised pretrained models to classification tasks. The best result is in bold. TMI shows the best Kendall correlation consistently in 13 out of 17 cases, outperforming all the competitors."
+                                        }
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+                                    "content": "ferability. The size of extracted features is quite large in the early layers, resulting in much higher computational cost for transferability measurement. To reduce this cost, we add an avgpool2d layer to the end of transferring layer to reduce the dimension of extracted features. Table 9 shows that TMI achieves the highest correlation coefficients in 16 out of 17 datasets. Correlation coefficients of MNIST, SVHN, and Chest X-Ray are much lower than those of the other datasets because their ranges of minimum and maximum accuracies obtained by layer transfer are smaller than "
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+                                    "content": "An advantage of TMI is that it does not train models on target datasets because it is time-consuming and sensitive to hyperparameters which may cause different results. The only hyperparameter in TMI is "
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+                                    "content": " used in the entropy estimator. In Figure. 3, the correlation between pre-trained"
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+                                            "content": "Table 9: Correlations between fine-tuned accuracies and transferability scores when transferring specific layers of pre-trained models. The best result is in bold. TMI shows the best correlations consistently in 16 out of 17 cases."
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+                                    "content": "models and TMI shows consistency in most ranges for "
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "type": "text",
+                                    "content": "We propose TMI, a fast, accurate, and general algorithm to measure the transferability. TMI quantifies the degree of generalization of a pre-trained model to a new task by estimating the intra-class feature variance. We conduct experiments on seventeen datasets with fifty supervised pretrained models and eleven self-supervised pre-trained models. TMI selects the top-5 pre-trained architecture in 14 out of 17 cases and selects the best source data in all cases, outperforming its competitors. We measure the correlation between the fine-tuning performance and transferability, and our proposed TMI outperforms competitors in 13 out of 17 cases."
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+                                    "type": "text",
+                                    "content": "Acknowledgments"
+                                }
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+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) [No.2020-0-00894, Flexible and Efficient Model Compression Method for Various Applications and Environments], [No.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)], and [NO.2021-0-02068, Artificial Intelligence Innovation Hub (Artificial Intelligence Institute, Seoul National University)]. The Institute of Engineering Research at Seoul National University provided research facilities for this work. The ICT at Seoul National University provides research facilities for this study. U Kang is the corresponding author."
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+                                }
+                            ]
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+                    ],
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+                },
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+                                            "bbox": [
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+                                            "content": "[1] Alessandro Achille, Michael Lam, Rahul Tewari, Avinash Ravichandran, Subhransu Maji, Charless C. Fowlkes, Stefano Soatto, and Pietro Perona. Task2vec: Task embedding for meta-learning. In ICCV, 2019."
+                                        }
+                                    ]
+                                }
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+                                    ]
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
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diff --git a/2023/FastRecon_ Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction/3fc31964-ced1-48a5-b5b7-b2709febc3e3_content_list.json b/2023/FastRecon_ Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction/3fc31964-ced1-48a5-b5b7-b2709febc3e3_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d5488dc65842f5b283e59c37ab435cb998049f7
--- /dev/null
+++ b/2023/FastRecon_ Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction/3fc31964-ced1-48a5-b5b7-b2709febc3e3_content_list.json	
@@ -0,0 +1,1567 @@
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+        "text": "Zheng Fang $^{1,2\\dagger}$  Xiaoyang Wang $^{1,2\\dagger}$  Haocheng Li $^{3}$  Jiejie Liu $^{1,3}$  Qiugui Hu $^{3}$  Jimin Xiao $^{1*}$ $^{1}$ XJTLU  $^{2}$ Metavisioncn  $^{3}$ Dinnar Automation Technology  \n{fz.jun26th, haocheng.li789}@gmail.com,  \n{xiaoyang.wang20, jiejie.liu22}@student.xjtlu.edu.cn, jimin.xiao@xjtlu.edu.cn",
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+        "type": "text",
+        "text": "In industrial anomaly detection, data efficiency and the ability for fast migration across products become the main concerns when developing detection algorithms. Existing methods tend to be data-hungry and work in the one-model-one-category way, which hinders their effectiveness in real-world industrial scenarios. In this paper, we propose a few-shot anomaly detection strategy that works in a low-data regime and can generalize across products at no cost. Given a defective query sample, we propose to utilize a few normal samples as a reference to reconstruct its normal version, where the final anomaly detection can be achieved by sample alignment. Specifically, we introduce a novel regression with distribution regularization to obtain the optimal transformation from support to query features, which guarantees the reconstruction result shares visual similarity with the query sample and meanwhile maintains the property of normal samples. Experimental results show that our method significantly outperforms previous state-of-the-art at both image and pixel-level AUROC performances from 2 to 8-shot scenarios. Besides, with only a limited number of training samples (less than 8 samples), our method reaches competitive performance with vanilla AD methods which are trained with extensive normal samples. The code is available at https://github.com/FzJun26th/ FastRecon.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Anomaly detection (AD) in computer vision aims to identify rare observations that deviate significantly from the majority of the data and do not conform to a well-defined notion of normal behavior [4]. In industrial settings, AD is widely used to detect the anomalies on the surface of the product, which has been attracting a lot of attention re",
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+        "img_path": "images/9fda1f949d8e508731215874e634e9f814685f13d6abc49238c6e450cd7865b7.jpg",
+        "image_caption": [
+            "Figure 1: Comparison of our FastRecon with (a) Vanilla Reconstruction-based method and (b) Vanilla Feature-Matching-based method. Compared with (a), our method needs no training session and requires less normal samples for feature reconstruction. Compared with (b), our method applies direct pixel-to-pixel alignment between the test sample and reconstruction result for anomaly detection without an exhaustive feature searching process, thus being more efficient in inference."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "cently [31, 16, 9]. The difficulty of industrial AD lies in the diversity of the defects, which can take different forms, from subtle flaws like slight bruises, to obvious ones such as missing components [3]. This makes it difficult to detect and classify anomalies. Primal researches focus on utilizing supervised learning to tackle industrial AD [5, 17]. However, such a learning paradigm often requires an exhaustive set of anomalous samples for each category, which can be",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "$\\dagger$  Equal contribution.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "* Corresponding author.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "17481",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "naturally rare to collect, making it inefficient for real-world industrial scenarios.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recent works pay attention to learning with limited or even no supervision to overcome the problem caused by the lack of anomalous samples. As shown in Fig. 1 (a), reconstruction-based industrial AD [34, 10, 26, 14] utilizes generative models such as autoencoder to learn the distribution of normal samples through the cumbersome training process. As in Fig. 1 (b), recent researches favor feature-matching strategy [28, 7] that conducts feature comparison between the test sample and memory bank of normal features, where the feature searching causes high computational complexity. Both lines of work require massive normal samples either for model training or memory construction, only to achieve detection for a single product category, and fail to quickly generalize across products.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we state that well-generalized industrial AD can be achieved in an extremely data-efficient way. We propose a training-free, few-shot AD method named FastRecon, to meet the demand for industrial scenarios, which works under the situation that only a limited number of normal samples are available. Given a query sample to detect, we propose to construct its normal version at the feature level through a linear transformation based on features extracted from limited normal samples. This constructed sample shares low-frequency features with the original query image but differs in the defect regions, making the anomaly apparent when directly compared to the original. The comparisons on the methodology of our method and previous mainstream works are shown in Fig. 1. The key lies in finding the optimal transformation. On the one hand, the transformation should bring the constructed sample somewhere close to the query sample so they share visual features on the normal parts. On the other hand, the constructed sample should maintain the property of a normal sample so the difference between the two samples can fully reveal the anomaly regions. With this goal, we proposed a distributional regularization term upon the classical ridge regression algorithm. We first utilize normal features to fit a Gaussian distribution. When finding the transformation from normal features to the query sample, we simultaneously push the reconstructed sample toward the center of the built distribution to enhance its normality. Note that our proposed optimization process admits a closed-form solution just as ridge regression, which allows fast computation with low cost, ensuring the adaptation and migration of our method from old products to novel ones.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Experiments on the benchmark datasets for industrial defection, MVTec [3] and MDPP [15], as well as comparisons with various existing state-of-the-art FSAD methods [19, 13], indicate the effectiveness of our model. Compared with previous state-of-the-art [13], our method achieves improvements of  $5.27\\%$ ,  $6.04\\%$ ,  $3.99\\%$  on MVTec, and",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "10.25%, 11.55%, 10.60% on MPDD, at image-level AUROC under 2-shot, 4-shot and 8-shot scenarios, respectively. The contributions of this work are summarized below:",
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+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. We propose a few-shot and category-agnostic industrial AD strategy which adopts sample alignment between the original test sample and its reconstructed normal version.",
+            "2. We propose a regression algorithm with distribution regularization which has a closed-form solution for the transformation estimation, keeping the reconstructed result close to the query image while maintaining the property of normal samples.",
+            "3. Our proposed method achieves state-of-the-art few-shot AD performance under various datasets and settings."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2.1. Anomaly Detection",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Industrial visual anomaly detection (AD) is a rising topic in computer vision. The mainstream AD methods can be categorized as reconstruction-based model and feature-matching-based models. Previous reconstruction-based models classified anomalous samples either though reconstruction loss [2, 33, 30] or via comparison between reconstructed normal samples and test sample [21, 22, 29] with generative models. Another line of works, feature-matching-based models, take full advantage of pre-trained features. For example, SPADE [6] firstly put forward memory banks comprising various feature hierarchies for fine-grained, KNN-based [8] anomaly segmentation and image-level anomaly detection. Similarly, PaDiM [7] and PatchCore [28] investigated AD performance on MVTec in unsupervised learning settings. However, both two lines of methods show greatly high data dependence which would hinder their industrial application.",
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+    {
+        "type": "text",
+        "text": "2.2. Few-shot Anomaly Detection",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot anomaly detection (FSAD) has developed to meet the demands of fast manufacturing changeover. TDG [23] proposes a hierarchical generative model that captures the multi-scale patch distribution of each support image. DiffNet [19] leverages the descriptiveness of features extracted by convolutional neural networks to estimate their density using a normalizing flow, which is a tool well-suited to estimate distributions from a few support samples. RegAD [13] explored a new paradigm for FSAD, by learning a common model shared among multiple categories in a meta-learning style. Despite of their decent inference performances under few-shot settings, the training process be",
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "17482",
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/9241ee867b0ed2781334d255d99c3846fa3dbbd76bd9a2403adf16dfdbfb0092.jpg",
+        "image_caption": [
+            "Figure 2: Overview of our method. Feature maps of each query sample and support samples are exacted by a pre-trained encoder. Features from support images are aggregated into a support feature pool. This pool is down-sampled through greedy coreset selection as  $S$  to reduce data redundancy and improve inference speed. The coreset  $S$  and the original query feature map  $Q$  are then input to our proposed regression with distribution regularization as shown in the grey region. An optimal transformation  $\\bar{W}$  between  $S$  and  $Q$  is obtained by the regression to make sure the reconstructed sample  $\\bar{W} S$ , denoted as  $\\bar{Q}$ , to share similarity with  $Q$  but keeps all the property of normal samples. Finally, we align  $\\bar{Q}$  and  $Q$  for direct comparison to obtaining the anomaly estimation."
+        ],
+        "image_footnote": [],
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "comes the main obstacle for fast model migration in real industrial scenarios.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we introduce the details of FastRecon. Firstly, we define the one-class classification problem in industrial anomaly detection. FastRecon contains 3 parts: feature extraction and coreset selection, regression with distribution regularization, and anomaly detection with reconstruction. The overview of our method is shown in Fig. 2.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Definition",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We formally define the problem for one-class classification of industrial anomaly detection. Following the few-shot learning setting, in an  $n$ -way and  $k$ -shot episode, a support set consisting of normal samples from  $n$  categories is given, i.e.,  $S = \\bigcup_{i=1}^{n} T_i$ , where the subset  $T_i$  consists of  $k$  normal samples from category  $c_i$ . During test time, a query sample, whether normal or anomalous, is presented. The model predicts whether or not the sample is anomalous at the pixel and image level.",
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+    {
+        "type": "text",
+        "text": "3.2. Feature Extraction and Coreset Selection",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Existing studies [7, 28] have shown that extracted features from pre-trained CNNs perform well in the anomaly",
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+    {
+        "type": "text",
+        "text": "detection task. We also utilize a pre-trained ResNet-50 to output a patch-level feature map of an image.  $\\phi_{i,j}$  is used to denote hierarchy-level  $j$  of the pre-trained network  $\\phi$  for the image  $x_{i} \\in X$  (dataset  $X$ ), where  $j \\in \\{1,2,3,4\\}$ . We adopt the intermediate features of the hierarchy-level, i.e.,  $j \\in \\{2,3\\}$ . The resulting feature map has a dimension of  $H \\times W \\times D$ , where  $H$ ,  $W$  are the height and width of the largest activation map used to generate the embedding, and  $D$  is the total number of channels of both activation maps used to generate embedding.",
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+    {
+        "type": "text",
+        "text": "To facilitate calculations, the feature map is reshaped from 3-dimension  $H \\times W \\times D$  to 2-dimension  $R \\times D$ , where  $R = H \\times W$ . Features in the reshaped map represent embedding vectors, i.e., the local aware patch features. In a  $k$ -shot setting, our ultimate support feature pool is obtained by concatenating features of  $k$  support images, with a size of  $k \\times R \\times D$ . Besides, following [18], we take a coreset sampling operation to get a coreset  $S \\in R^{c \\times d}$ , where  $c$  is the number of clustering centers computed with K-greedy algorithm. The coverage of  $S$  is comparable to the original support feature pools but with a smaller scale so that the computational complexity and the performance of detection could be balanced. For a query image, with the same pretrained network, it is also extracted to patch-level feature map  $Q$ . The process of feature extraction and coreset is",
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+        "page_idx": 2
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+    {
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+        "text": "17483",
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+        "page_idx": 2
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+    {
+        "type": "image",
+        "img_path": "images/bbbe522c9704579f22d0deca006c444f872309059e8ea90e60897d8a0aca9285.jpg",
+        "image_caption": [
+            "(a)"
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/c4ba3066bcf10205a6fab0fdc0d852489e2018de9609714be369b157a0362cce.jpg",
+        "image_caption": [
+            "(b)"
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/08488c3ef5d5bc7e0d0ca5a9506aa17c463cf117848aa0762173fb41c0122d94.jpg",
+        "image_caption": [
+            "(c)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/b45c840814b9645ca7a9ec0f8c80753cd8249d4ea6b4d5b781753f4e32cc218f.jpg",
+        "image_caption": [
+            "(d)",
+            "Figure 3: Visual comparison of decoding results on reconstructed features. We train a decoder on features of the whole dataset for image recovery, which is used to probe the transformed features from the encoder. (a) The original query image with defects region in red boxes. (b) Decoding results on original query features. (c) Decoding results on transformed features by ridge regression. The defects regions are reconstructed as on original query features. (d) Decoding results on transformed features by the proposed regression, which shares visual similarity with the original query image but with the property of normal samples."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "shown in the brown region in Fig. 2.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Regression with Distribution Regularization",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Why Ridge Regression fails. The goal is to reconstruct query feature map  $Q$  as a linear transformation of S-coreset  $S$  by finding an optimal transformation weight  $W$  such that  $WS \\approx Q$  and meanwhile  $WS$  has most properties of normal samples. Searching for optimal weight  $W$  amounts to solving the linear least-squares problem [25]. With original ridge regression, the optimization takes the following form:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {\\boldsymbol {W}} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2} + \\lambda \\| \\boldsymbol {W} \\| ^ {2}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  is the weight of the penalty term and  $\\| \\cdot \\|$  representing the Frobenius norm. The penalty term in ridge regression, i.e.,  $\\| W\\|^2$ , ensures tractability when the linear system is over- or under-constrained. However, the transformation obtained from ridge regression can cause the reconstructed sample to deviate significantly from the distribution of normal samples, i.e., after the transformation, the result  $WS$  can be too close to  $Q$  so that features of defect regions are reconstructed as in  $Q$ . As shown in Fig. 3 column (c), the decoding results on reconstructed features share excessively high similarity with the original query image with defects regions being reconstructed.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The distribution regularization. In our work, we propose a distributional regularization term to replace the original penalty term in ridge regression, which effectively enhances the normality of the reconstruction result  $W S$ . We first model the distribution of normal feature maps by an isotropic Gaussian density function denoted as  $f(\\boldsymbol{X}|\\boldsymbol{\\mu},\\boldsymbol{\\Sigma})$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\pmb{\\mu},\\pmb{\\Sigma}$  is the mean and co-variance estimated by the support set feature maps. We design the regularization term as  $|f(WS) - f(\\pmb{\\mu})|$  and the proposed regression has the form as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {\\boldsymbol {W}} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2} + \\lambda | f (\\boldsymbol {W} \\boldsymbol {S}) - f (\\boldsymbol {\\mu}) |, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  denotes the coefficient that controls the contribution of the regularization. When searching the optimal transformation  $W$ , the optimization of the first term  $\\|Q - WS\\|^2$  naturally pushes  $WS$  towards original query feature maps  $Q$ , while with the proposed regularization  $|f(WS) - f(\\pmb{\\mu})|$ , we force the constructed  $WS$  to lie in the high probability density region in the distribution, that is, somewhere close to the distribution center. The visualization of distribution regularization is shown in the grey region of Fig. 2.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The approximation for closed-form solution. The density function inside the regularization term in Eq. (2) prevents us from having a closed-form solution for the regression, which hinders fast calculation of the transformation. Thus, we propose an approximated version of Eq. (2) with the help of Taylor's theorem for multivariable functions on the distribution density function  $f$ . Taylor's expansion for  $f(x)$  at  $a$  is shown as follows:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf (\\boldsymbol {x}) \\approx f (\\boldsymbol {a}) + \\nabla f (\\boldsymbol {a}) (\\mathbf {x} - \\boldsymbol {a}) + \\frac {1}{2} (\\mathbf {x} - \\boldsymbol {a}) ^ {T} H f (\\boldsymbol {a}) (\\mathbf {x} - \\boldsymbol {a}), \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $Hf(\\pmb{a})$  denotes Hessian matrix of  $f(\\pmb{x})$  at  $\\pmb{a}$ . And we approximate the density function with the first and second-order term of Taylor's expansion, where the first-order term is 0 at  $\\pmb{\\mu}$ . Following Eq. (3), we expand the probability density function  $f(WS)$  at  $\\pmb{\\mu}$  as:",
+        "bbox": [
+            498,
+            523,
+            890,
+            599
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} f (\\boldsymbol {W} \\boldsymbol {S}) \\approx f (\\boldsymbol {\\mu}) + \\nabla f (\\boldsymbol {\\mu}) (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) \\\\ + \\frac {1}{2} (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) ^ {T} H f (\\boldsymbol {\\mu}) (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}). \\tag {4} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            504,
+            609,
+            890,
+            669
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since our assumed data distribution is isotropic Gaussian, its covariance matrix can be represented as  $\\pmb{\\Sigma} = \\sigma^2\\pmb{I}$ , where  $\\sigma^2$  is the variance for all dimensions. Then, we have the term  $\\nabla f(\\pmb{\\mu})(\\pmb{W}\\pmb{S} - \\pmb{\\mu})$  as 0, and  $Hf(\\pmb{\\mu})$  equals the  $\\pmb{\\Sigma}^{-1}$  which is the inverse of the covariance matrix. Then, by placing  $f(\\pmb{\\mu})$  to the left, we have",
+        "bbox": [
+            498,
+            670,
+            890,
+            762
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} f (\\boldsymbol {W} \\boldsymbol {S}) - f (\\boldsymbol {\\mu}) \\approx \\frac {1}{2} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) ^ {T} \\boldsymbol {\\Sigma} ^ {- 1} (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) \\\\ = \\frac {1}{2 \\sigma^ {2}} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) ^ {T} \\boldsymbol {I} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) \\tag {5} \\\\ = \\frac {1}{2 \\sigma^ {2}} \\| \\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu} \\| ^ {2}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            771,
+            890,
+            861
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $I$  is an identity matrix. Then we merge the coefficient  $\\frac{1}{2\\sigma^2}$  into  $\\lambda$  and the approximated version of the optimization",
+        "bbox": [
+            500,
+            869,
+            890,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "17484",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "target in Eq. (2) is:",
+        "bbox": [
+            76,
+            90,
+            204,
+            104
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {W} = \\underset {W} {\\arg \\min } \\| Q - W S \\| ^ {2} + \\lambda \\| W S - \\mu \\| ^ {2}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            102,
+            112,
+            468,
+            138
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finding the optimal transformation. Knowing that the following optimization target of least square error (LSE) of",
+        "bbox": [
+            76,
+            146,
+            468,
+            176
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {W} ^ {\\prime} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            168,
+            188,
+            468,
+            214
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "has the closed-form solution as",
+        "bbox": [
+            76,
+            219,
+            285,
+            232
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {W} ^ {\\prime} = \\boldsymbol {Q} \\boldsymbol {S} ^ {\\top} \\left(\\boldsymbol {S} ^ {\\top} \\boldsymbol {S}\\right) ^ {- 1}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            187,
+            238,
+            468,
+            267
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "to utilize the conclusion from Eq. (8), we transform Eq. (6) by variable substitution to fit the form of Eq. (8). Let  $Q_*$  and  $S_*$  be the column-wise augmented version of  $Q$  and  $S$  respectively:",
+        "bbox": [
+            76,
+            273,
+            468,
+            334
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {S} _ {*} = \\left[ \\boldsymbol {S} \\sqrt {\\lambda} \\boldsymbol {S} \\right], \\quad \\boldsymbol {Q} _ {*} = \\left[ \\boldsymbol {Q} \\sqrt {\\lambda} \\boldsymbol {\\mu} \\right], \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            143,
+            340,
+            468,
+            359
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  is the coefficient of the regularization term which is always set as a positive number. Hence, equality holds for",
+        "bbox": [
+            76,
+            367,
+            468,
+            411
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\| Q _ {*} - W S _ {*} \\right\\| ^ {2} = \\left\\| Q - W S \\right\\| ^ {2} + \\lambda \\left\\| \\boldsymbol {\\mu} - W S \\right\\| ^ {2}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            93,
+            419,
+            468,
+            450
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and the form in Eq. (6) can be written as",
+        "bbox": [
+            76,
+            452,
+            346,
+            465
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {W} = \\underset {W} {\\arg \\min } \\| Q _ {*} - W S _ {*} \\| ^ {2}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            473,
+            468,
+            500
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Based on the conclusion in Eq. (8), the solution for our optimization process is",
+        "bbox": [
+            76,
+            507,
+            468,
+            537
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\bar {W} = Q _ {*} S _ {*} ^ {\\top} \\left(S _ {*} ^ {\\top} S _ {*}\\right) ^ {- 1} \\tag {12} \\\\ = \\left(\\boldsymbol {Q} \\boldsymbol {S} ^ {\\top} + \\lambda \\cdot \\boldsymbol {\\mu} \\boldsymbol {S} ^ {\\top}\\right) \\left(\\boldsymbol {S} ^ {\\top} \\boldsymbol {S} + \\lambda \\cdot \\boldsymbol {S} \\boldsymbol {S} ^ {\\top}\\right) ^ {- 1}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
+            544,
+            468,
+            603
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Anomaly Detection with Reconstruction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            609,
+            419,
+            625
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After getting the reconstruction query feature maps  $\\bar{Q}$ , we align it with those from the original query sample  $\\mathbf{Q}$  to estimate the pixel-level anomaly segmentation map and image-level anomaly score. For pixel  $i$  in the query image, the anomaly score  $m_{i}$  is calculated as:",
+        "bbox": [
+            76,
+            632,
+            468,
+            708
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nm _ {i} = \\left\\| Q _ {i} - \\bar {Q} _ {i} \\right\\| ^ {2}, i \\in \\mathcal {N}, \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            176,
+            715,
+            468,
+            736
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{N}$  denotes the collection of all pixel indices in  $Q$ .  $Q_{i}$  denotes the relevant feature vector of pixel  $i$ . For image-level classification, we use the maximum distance score  $s^{*}$  among all the pixels to represent the image-level score as",
+        "bbox": [
+            76,
+            743,
+            467,
+            804
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ns ^ {*} = \\max  \\left\\{\\left\\| Q _ {i} - \\bar {Q} _ {i} \\right\\| ^ {2} \\mid i \\in \\mathcal {N} \\right\\}. \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            811,
+            468,
+            833
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Besides, similar to [28, 7], to match the original input resolution, the segmentation map should be up-scaled with bilinear interpolation. Finally, we smoothed the segmentation map with a Gaussian of kernel width of 4.",
+        "bbox": [
+            76,
+            839,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiment",
+        "text_level": 1,
+        "bbox": [
+            500,
+            90,
+            624,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setups",
+        "text_level": 1,
+        "bbox": [
+            500,
+            114,
+            696,
+            131
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset. We evaluated the performance of our model by using the MVTec AD dataset [3] and MPDD [15], which are the real-world benchmarks for AD. MVTec dataset includes 5354 images in 15 categories. 3629 of these images are defect-free and the remaining 1725 have defects. Each category has an average of five different types of defects. The image resolution ranges from  $700 \\times 700$  to  $1024 \\times 1024$ . MPDD dataset contains 6 classes of metal productions. Images taken from different distances and spatial directions, as well as the non-uniform backgrounds, make the AD task on this dataset extremely difficult. The MPDD dataset includes 888 normal images in the training set and 176 normal images and 282 abnormal images in the test set with the resolution of  $1024 \\times 1024$ . Additionally, both datasets provide ground truth of defective regions on pixel level.",
+        "bbox": [
+            496,
+            138,
+            890,
+            366
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Competing Methods. We compare our method with previous state-of-the-art FSAD and also full-data AD methods. The methods for comparison include GANomaly [1], ARNet [27], MKD [20], CutPaste [24], FYD [32], PaDiM [7], PatchCore [18], CflowAD [11], TDG [23], DiffNet [19] and RegAD [13].",
+        "bbox": [
+            496,
+            372,
+            890,
+            463
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Protocols. We measure the model performance with the area under the Receiver Operating Characteristic curve (AUROC) on classification results. We use image-level AUROC to evaluate the sample detection results and pixel-level AUROC to measure the defects localization performance.",
+        "bbox": [
+            496,
+            470,
+            890,
+            560
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. In our experiment, we used a ResNet-50 [12] model pre-trained on ImageNet for feature extraction. We extract features from the 2 middle-level layers of the model. For both MVtec and MPDD datasets, all the support and query images are reshaped to  $368 \\times 368$  for training and inference. For all the experiments, the coefficient  $\\lambda$  for our regularization term is set as 0.3, and the corset selection sampling rate  $s$  is set as 0.15. All the experiments are conducted on one NVIDIA GTX 3090 GPU.",
+        "bbox": [
+            496,
+            568,
+            890,
+            703
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Experiment Results",
+        "text_level": 1,
+        "bbox": [
+            500,
+            715,
+            687,
+            731
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2.1 Comparison with State-of-the-art Methods",
+        "text_level": 1,
+        "bbox": [
+            500,
+            739,
+            849,
+            753
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Few-shot AD averaged performance. Tab. 1 shows FSAD averaged performance on both MVTec and MPDD datasets. Our method (FastRecon) obtains the best performances under all experimental settings. Specifically, FastRecon improves image-level AUROC by  $5.27\\%$ ,  $6.04\\%$ ,  $3.99\\%$  on MVTec and  $10.25\\%$ ,  $11.55\\%$ $10.60\\%$  on MPDD over the current state-of-the-art FSAD method RegAD for 2-shot, 4-shot, and 8-shot scenarios respectively. For pixel-level AUROC, FastRecon also outperforms RegAD",
+        "bbox": [
+            496,
+            763,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "17485",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/67397eb50dafb5311e2bfdc10313eb969415c67e8c2422813060e7e6d7bb936d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td colspan=\"6\">AUROC at Image-level</td><td colspan=\"4\">AUROC at Pixel-level</td></tr><tr><td>Dataset</td><td>k</td><td>TDG [23]</td><td>DiffNet [19]</td><td>RegAD [13]</td><td>PaDiM [7]</td><td>PatchCore [18]</td><td>FastRcon (ours)</td><td>RegAD [13]</td><td>PaDiM [7]</td><td>PatchCore [18]</td><td>FastRcon (ours)</td></tr><tr><td rowspan=\"3\">MVTec</td><td>2</td><td>71.20</td><td>80.60</td><td>85.70</td><td>78.90</td><td>87.81</td><td>90.97</td><td>94.60</td><td>90.50</td><td>94.75</td><td>95.86</td></tr><tr><td>4</td><td>72.70</td><td>81.30</td><td>88.20</td><td>71.60</td><td>89.49</td><td>94.24</td><td>95.80</td><td>80.20</td><td>94.99</td><td>96.98</td></tr><tr><td>8</td><td>75.20</td><td>83.20</td><td>91.20</td><td>75.30</td><td>94.31</td><td>95.19</td><td>96.70</td><td>80.50</td><td>95.60</td><td>97.27</td></tr><tr><td rowspan=\"3\">MPDD</td><td>2</td><td>60.30</td><td>60.20</td><td>63.40</td><td>-</td><td>59.55</td><td>73.65</td><td>93.20</td><td>-</td><td>79.15</td><td>97.03</td></tr><tr><td>4</td><td>63.50</td><td>63.30</td><td>68.30</td><td>-</td><td>59.78</td><td>79.85</td><td>93.90</td><td>-</td><td>79.82</td><td>97.60</td></tr><tr><td>8</td><td>68.20</td><td>68.50</td><td>71.90</td><td>-</td><td>59.95</td><td>82.50</td><td>95.10</td><td>-</td><td>80.30</td><td>97.92</td></tr></table>",
+        "bbox": [
+            117,
+            88,
+            859,
+            237
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/e8dbc819ef7009f2d24cac97c5af964650068c0bfd71eb3b802bda6e6a68870f.jpg",
+        "table_caption": [
+            "Table 1: FSAD performance comparisons on MVtec and MPDD dataset. The results are averaged over all categories. Both image-level and pixel-level performances are reported in AUROC (\\%)  $\\uparrow$ .  $k$  denotes the number of shots in our few-shot settings. The best results for different settings are in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">RegAD [13]</td><td colspan=\"2\">PatchCore [18]</td><td colspan=\"2\">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bottle</td><td>99.40</td><td>98.40</td><td>99.60</td><td>98.60</td><td>99.44</td><td>98.50</td></tr><tr><td>Cable</td><td>76.10</td><td>92.70</td><td>97.40</td><td>97.90</td><td>93.79</td><td>96.12</td></tr><tr><td>Capsule</td><td>72.40</td><td>97.60</td><td>66.30</td><td>97.70</td><td>90.07</td><td>98.96</td></tr><tr><td>Carpet</td><td>97.90</td><td>98.90</td><td>99.00</td><td>99.00</td><td>99.90</td><td>99.15</td></tr><tr><td>Grid</td><td>91.20</td><td>85.70</td><td>63.00</td><td>70.60</td><td>88.81</td><td>86.32</td></tr><tr><td>Hazelnut</td><td>95.80</td><td>98.00</td><td>92.80</td><td>97.00</td><td>99.32</td><td>98.59</td></tr><tr><td>Leather</td><td>100.00</td><td>99.10</td><td>100.00</td><td>96.90</td><td>100.00</td><td>99.20</td></tr><tr><td>Metal_Nut</td><td>94.60</td><td>97.80</td><td>94.70</td><td>97.00</td><td>99.12</td><td>98.72</td></tr><tr><td>Pill</td><td>80.80</td><td>97.40</td><td>89.00</td><td>96.90</td><td>93.48</td><td>98.32</td></tr><tr><td>Screw</td><td>56.60</td><td>95.00</td><td>54.10</td><td>92.10</td><td>62.46</td><td>97.10</td></tr><tr><td>Tile</td><td>95.50</td><td>94.90</td><td>100.00</td><td>96.00</td><td>100.00</td><td>96.73</td></tr><tr><td>Toothbrush</td><td>90.90</td><td>98.50</td><td>95.20</td><td>98.80</td><td>93.61</td><td>99.04</td></tr><tr><td>Transistor</td><td>85.20</td><td>93.80</td><td>98.40</td><td>95.00</td><td>97.29</td><td>94.18</td></tr><tr><td>Wood</td><td>98.60</td><td>94.70</td><td>97.40</td><td>93.10</td><td>99.29</td><td>94.94</td></tr><tr><td>Zipper</td><td>88.50</td><td>94.00</td><td>95.50</td><td>98.30</td><td>96.95</td><td>98.89</td></tr><tr><td>Average</td><td>88.20</td><td>95.80</td><td>89.49</td><td>94.99</td><td>94.24</td><td>96.98</td></tr></table>",
+        "bbox": [
+            78,
+            316,
+            468,
+            583
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "by  $1.26\\%$ ,  $1.18\\%$ ,  $0.57\\%$  on MVTev and  $3.83\\%$ ,  $3.70\\%$ ,  $2.82\\%$  on MPDD respectively.",
+        "bbox": [
+            75,
+            680,
+            468,
+            710
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Few-shot AD categorical performances. Tab. 2 and Tab. 3 show the FSAD categorical performance. As shown in Tab. 2, FastRecon outperforms all the baselines in 10 out of 15 categories at the image level and in 12 out of 15 categories at the pixel level. And as shown in Tab. 3, FastRecon outperforms all the baselines in 4 out of 6 categories at the image level and in all categories at the pixel level.",
+        "bbox": [
+            75,
+            715,
+            468,
+            821
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Comparison with full-data AD. Tab. 4 shows the comparison of our method with AD methods which utilize the whole normal samples. Results show that our FastRecon has competitive performance compared with full-data methods, indicating the high data efficiency of our model.",
+        "bbox": [
+            75,
+            824,
+            468,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/3a50dbce58c7fc218e572f8e1bc126b4818ffcc3dd12f7efde7d9a76d3eee651.jpg",
+        "table_caption": [
+            "Table 2: FSAD categorical performance comparisons in AUROC (\\%)  $\\uparrow$  on MVTec dataset. Results are from the setting of shot  $k = 4$ . The best results are in bold. Our method achieves the best performance in most categories."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">RegAD [13]</td><td colspan=\"2\">PatchCore [18]</td><td colspan=\"2\">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bracket/black</td><td>63.80</td><td>-</td><td>58.90</td><td>79.10</td><td>71.81</td><td>95.54</td></tr><tr><td>Bracket_brown</td><td>66.10</td><td>-</td><td>70.80</td><td>77.30</td><td>63.34</td><td>95.93</td></tr><tr><td>Bracket_white</td><td>59.30</td><td>-</td><td>70.70</td><td>69.30</td><td>69.44</td><td>98.89</td></tr><tr><td>Connector</td><td>77.20</td><td>-</td><td>59.40</td><td>86.40</td><td>97.62</td><td>98.04</td></tr><tr><td>Metal_plate</td><td>78.60</td><td>-</td><td>64.40</td><td>86.70</td><td>100.00</td><td>99.29</td></tr><tr><td>Tubes</td><td>67.50</td><td>-</td><td>34.50</td><td>80.10</td><td>76.90</td><td>97.89</td></tr><tr><td>Average</td><td>68.30</td><td>93.90</td><td>59.78</td><td>79.82</td><td>79.85</td><td>97.60</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/78140d570edcf7928347bb6461ba46bdf8bb9fa1b11d87734be76999e08da429.jpg",
+        "table_caption": [
+            "Table 3: FSAD categorical performance comparisons in AUROC (\\%)  $\\uparrow$  on MPDD dataset. Results are from the setting of shot  $k = 4$ . The best results are in bold. Our method achieves the best performance in most categories."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\"></td><td colspan=\"2\">MVTec AD</td><td colspan=\"2\">MPDD</td></tr><tr><td>Method</td><td>Data</td><td>Backbone</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>FastRecon</td><td>2</td><td>WRN50</td><td>90.97</td><td>95.86</td><td>73.65</td><td>97.03</td></tr><tr><td>FastRecon</td><td>4</td><td>WRN50</td><td>94.24</td><td>96.98</td><td>79.85</td><td>97.60</td></tr><tr><td>FastRecon</td><td>8</td><td>WRN50</td><td>95.19</td><td>97.27</td><td>82.50</td><td>97.92</td></tr><tr><td>GANomaly [1]</td><td>Full</td><td>Unet</td><td>80.50</td><td>-</td><td>64.80</td><td>-</td></tr><tr><td>ARNet [27]</td><td>Full</td><td>Unet</td><td>83.90</td><td>-</td><td>69.70</td><td>-</td></tr><tr><td>MKD [20]</td><td>Full</td><td>Res18</td><td>87.70</td><td>90.70</td><td>-</td><td>-</td></tr><tr><td>FYD [32]</td><td>Full</td><td>Res18</td><td>97.30</td><td>97.40</td><td>-</td><td>-</td></tr><tr><td>PaDiM [7]</td><td>Full</td><td>WRN50</td><td>97.90</td><td>97.50</td><td>74.80</td><td>96.70</td></tr><tr><td>PatchCore [18]</td><td>Full</td><td>WRN50</td><td>99.10</td><td>98.10</td><td>82.10</td><td>95.70</td></tr><tr><td>CflowAD [11]</td><td>Full</td><td>WRN50</td><td>98.60</td><td>98.60</td><td>86.10</td><td>97.70</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4: AD performance comparisons in AUROC  $(\\%)$  ↑ on MVTec and MPDD dataset with full-data methods which utilize the whole dataset in training. Both image-level and pixel-level performances are averaged over all categories. The Data column denotes different usage of the dataset.",
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+    {
+        "type": "text",
+        "text": "Speed performance of FastRecon. Speed comparisons on both training and inference are shown in the following Tab. 5. For FastRecon, training stage consists of feature extraction, feature subsampling and calculation on transfor",
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+        "text": "17486",
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+    {
+        "type": "image",
+        "img_path": "images/d776065b7544db0615f0589064a6374347446c6200f668fc5ea0292674a077b7.jpg",
+        "image_caption": [
+            "Figure 4: Qualitative results of anomaly localization for both MVTec and MPDD datasets. The first row in the red box presents the support sample for each category while the second row indicates the query samples. The results show that our method can provide accurate localization of defect regions even for more complicated patterns in MPDD."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c0cd66bc11cfb004d56653a5475a5a52a02710423a7fe22f3d1a845ef5523617.jpg",
+        "image_caption": [
+            "Figure 5: Visualization of decoding results on reconstructed query features. With a pretrained image decoder, we investigate the transformed query features in the MVtec dataset. The first row shows the original query image, and the middle row shows the images decoded from the original query features. The last row represents the image decoded from the reconstructed query feature map. Our method can reveal the normal side of the defective query samples."
+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/6d8c5a4ab2a871f8420b283964a81fe28fc54fa83741b4d8628b4a5fcf41713a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Aggregated Training</td><td>Training Time</td><td>Inference Time</td></tr><tr><td>PatchCore</td><td>No</td><td>80.37</td><td>0.60</td></tr><tr><td>RegAD (k=2)</td><td>Yes</td><td>660.80</td><td>0.05</td></tr><tr><td>FastRecon (k=8)</td><td>No</td><td>1.95</td><td>0.04</td></tr><tr><td>FastRecon (k=2)</td><td>No</td><td>0.52</td><td>0.04</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Training and inference speed comparisons in seconds. RegAD requires additional training on aggregated features. The inference speed is evaluated as averaged inference time per query sample. FastRecon achieves overall best speed performance with 2 and 8 shots.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "mation matrix. FastRecon achieves the best performance.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Visualization",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Localization of anomaly detection Fig. 4 demonstrates visual examples of anomaly detection on MVTec and MPDD. Most defects can be accurately identified.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Decoding results on reconstructed query feature. In order to better reflect the reconstruction ability of FastRecon, a feature decoder is built to visualize the query sample from reconstructed feature maps. The decoder is trained with full MVTec dataset to learn to decode image sample from feature maps. Fig. 5 shows that, images decoded from reconstructed feature maps maintain the normality of the normal samples, which illustrates the effectiveness of our approach.",
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "17487",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b04dbb283130a3c3550b987e19a2e32336bb190697feeef75804ea3f163e4a16.jpg",
+        "image_caption": [
+            "(a) Sampling Rate  $s$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/9bf3c50330417414c6c713a50630eee1a728d5061ed36a96435c04aacd3a323e.jpg",
+        "image_caption": [
+            "(b) Coefficient  $\\lambda$  of Regularization Term"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/f5b51b470c35bdefd27e1e6afcba4f56ecfa70483c4117db9eecfe649271df19.jpg",
+        "image_caption": [
+            "(c) Resolution  $r$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/fc77ce6651bcabc7e720c752faaf4c21744a254ecb3fec5714b576c3795631ee.jpg",
+        "image_caption": [
+            "Figure 6: Effect of three hyper-parameters comparisons in AUROC (\\%) on MVTec dataset. (a) AD performance with different sampling rate  $s$ . (b) AD performance with different coefficient  $\\lambda$ . (c) AD performance with different resolution  $r$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/92a55d12dd9fb1a76aaf04e9858e180b5aeda32c34fe0c914e37d594757be312.jpg",
+        "image_caption": [
+            "Figure 7: AD performance comparisons in AUROC (\\%) on MVTec dataset between ridge regression and proposed regularization. Our results, displayed in blue, are better than ridge regression at both image and pixel levels."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this section, we ablate the core parts of our proposed method to investigate its impact on the final performance. We also discuss the effect of hyper-parameters, which are the coefficient of regularization term  $\\lambda$ , the resolution of input data, and the coreset selection sampling ratio  $s$ .",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effect of sampling Rate  $s$ . Fig. 6 (a) illustrates the relationship between the Sampling Rate  $s$  and AUROC performance. The sampling rate  $s$  decides the number of feature points in the support feature pool. As shown in Fig. 6 (a), the optimal sampling rate is around 0.45.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Impact of the distribution regularization term and coefficient  $\\lambda$ . In Fig. 7, FastRecon obtains better AUROC performance at both image and pixel levels. It reflects the significance of our proposed distribution regularization. Fig. 6 (b) shows the relationship between coefficient  $\\lambda$  of regularization term and AUROC performance for 4-shot and 8-shot scenarios. When  $\\lambda$  equals 0.3, the AUROC performances are best at both image and pixel levels.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effect of image resolution  $r$ . In our experiment, images, no matter how much the original resolutions are, should be reshaped to new resolution  $r \\times r$ . Fig. 6 (c) reflects the relationship between resolution  $r$  and AUROC performance. The resolution will affect the feature points. As shown in Fig. 6 (c), when the resolution equals 368, FastRecon performs well at both image and pixel levels.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, a novel method FastRecon is proposed for few-shot anomaly detection based on feature reconstruction. For each query sample, we construct their normal version, referenced by a limited number of normal features. To ensure the reconstructed result shares high visual similarity with the query sample while maintaining the property of the normal sample, a regression equation with proposed distribution regularization is proposed, to obtain the optimal transformation from support to query features. With this fast and accurate reconstruction, the final anomaly detection could be accomplished by a simple alignment. Experimental results show the state-of-the-art performance of our method for 2-shot, 4-shot, and 8-shot scenarios.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by National Key R&D Program of China (No.2022YFE0200300), National Natural Science Foundation of China (No.61972323).",
+        "bbox": [
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+        "type": "page_number",
+        "text": "17488",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+    }
+]
\ No newline at end of file
diff --git a/2023/FastRecon_ Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction/3fc31964-ced1-48a5-b5b7-b2709febc3e3_model.json b/2023/FastRecon_ Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction/3fc31964-ced1-48a5-b5b7-b2709febc3e3_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..0f714bec2a4e2c24c65adaf4ca5d576b029aff29
--- /dev/null
+++ b/2023/FastRecon_ Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction/3fc31964-ced1-48a5-b5b7-b2709febc3e3_model.json	
@@ -0,0 +1,2046 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.044
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.048
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.184,
+                0.131,
+                0.79,
+                0.175
+            ],
+            "angle": 0,
+            "content": "FastRecon: Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.086,
+                0.202,
+                0.887,
+                0.277
+            ],
+            "angle": 0,
+            "content": "Zheng Fang\\(^{1,2\\dagger}\\) Xiaoyang Wang\\(^{1,2\\dagger}\\) Haocheng Li\\(^{3}\\) Jiejie Liu\\(^{1,3}\\) Qiugui Hu\\(^{3}\\) Jimin Xiao\\(^{1*}\\)  \n\\(^{1}\\)XJTLU \\(^{2}\\)Metavisioncn \\(^{3}\\)Dinnar Automation Technology  \n{fz.jun26th, haocheng.li789}@gmail.com,  \n{xiaoyang.wang20, jiejie.liu22}@student.xjtlu.edu.cn, jimin.xiao@xjtlu.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.309,
+                0.314,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.341,
+                0.474,
+                0.719
+            ],
+            "angle": 0,
+            "content": "In industrial anomaly detection, data efficiency and the ability for fast migration across products become the main concerns when developing detection algorithms. Existing methods tend to be data-hungry and work in the one-model-one-category way, which hinders their effectiveness in real-world industrial scenarios. In this paper, we propose a few-shot anomaly detection strategy that works in a low-data regime and can generalize across products at no cost. Given a defective query sample, we propose to utilize a few normal samples as a reference to reconstruct its normal version, where the final anomaly detection can be achieved by sample alignment. Specifically, we introduce a novel regression with distribution regularization to obtain the optimal transformation from support to query features, which guarantees the reconstruction result shares visual similarity with the query sample and meanwhile maintains the property of normal samples. Experimental results show that our method significantly outperforms previous state-of-the-art at both image and pixel-level AUROC performances from 2 to 8-shot scenarios. Besides, with only a limited number of training samples (less than 8 samples), our method reaches competitive performance with vanilla AD methods which are trained with extensive normal samples. The code is available at https://github.com/FzJun26th/ FastRecon."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.748,
+                0.21,
+                0.765
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.774,
+                0.471,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Anomaly detection (AD) in computer vision aims to identify rare observations that deviate significantly from the majority of the data and do not conform to a well-defined notion of normal behavior [4]. In industrial settings, AD is widely used to detect the anomalies on the surface of the product, which has been attracting a lot of attention re"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.308,
+                0.892,
+                0.402
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.406,
+                0.892,
+                0.499
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.503,
+                0.892,
+                0.607
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.616,
+                0.895,
+                0.753
+            ],
+            "angle": 0,
+            "content": "Figure 1: Comparison of our FastRecon with (a) Vanilla Reconstruction-based method and (b) Vanilla Feature-Matching-based method. Compared with (a), our method needs no training session and requires less normal samples for feature reconstruction. Compared with (b), our method applies direct pixel-to-pixel alignment between the test sample and reconstruction result for anomaly detection without an exhaustive feature searching process, thus being more efficient in inference."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "cently [31, 16, 9]. The difficulty of industrial AD lies in the diversity of the defects, which can take different forms, from subtle flaws like slight bruises, to obvious ones such as missing components [3]. This makes it difficult to detect and classify anomalies. Primal researches focus on utilizing supervised learning to tackle industrial AD [5, 17]. However, such a learning paradigm often requires an exhaustive set of anomalous samples for each category, which can be"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.875,
+                0.204,
+                0.888
+            ],
+            "angle": 0,
+            "content": "\\(\\dagger\\) Equal contribution."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.098,
+                0.888,
+                0.222,
+                0.9
+            ],
+            "angle": 0,
+            "content": "* Corresponding author."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.875,
+                0.222,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17481"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.121
+            ],
+            "angle": 0,
+            "content": "naturally rare to collect, making it inefficient for real-world industrial scenarios."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.125,
+                0.468,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Recent works pay attention to learning with limited or even no supervision to overcome the problem caused by the lack of anomalous samples. As shown in Fig. 1 (a), reconstruction-based industrial AD [34, 10, 26, 14] utilizes generative models such as autoencoder to learn the distribution of normal samples through the cumbersome training process. As in Fig. 1 (b), recent researches favor feature-matching strategy [28, 7] that conducts feature comparison between the test sample and memory bank of normal features, where the feature searching causes high computational complexity. Both lines of work require massive normal samples either for model training or memory construction, only to achieve detection for a single product category, and fail to quickly generalize across products."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.339,
+                0.47,
+                0.807
+            ],
+            "angle": 0,
+            "content": "In this paper, we state that well-generalized industrial AD can be achieved in an extremely data-efficient way. We propose a training-free, few-shot AD method named FastRecon, to meet the demand for industrial scenarios, which works under the situation that only a limited number of normal samples are available. Given a query sample to detect, we propose to construct its normal version at the feature level through a linear transformation based on features extracted from limited normal samples. This constructed sample shares low-frequency features with the original query image but differs in the defect regions, making the anomaly apparent when directly compared to the original. The comparisons on the methodology of our method and previous mainstream works are shown in Fig. 1. The key lies in finding the optimal transformation. On the one hand, the transformation should bring the constructed sample somewhere close to the query sample so they share visual features on the normal parts. On the other hand, the constructed sample should maintain the property of a normal sample so the difference between the two samples can fully reveal the anomaly regions. With this goal, we proposed a distributional regularization term upon the classical ridge regression algorithm. We first utilize normal features to fit a Gaussian distribution. When finding the transformation from normal features to the query sample, we simultaneously push the reconstructed sample toward the center of the built distribution to enhance its normality. Note that our proposed optimization process admits a closed-form solution just as ridge regression, which allows fast computation with low cost, ensuring the adaptation and migration of our method from old products to novel ones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.811,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Experiments on the benchmark datasets for industrial defection, MVTec [3] and MDPP [15], as well as comparisons with various existing state-of-the-art FSAD methods [19, 13], indicate the effectiveness of our model. Compared with previous state-of-the-art [13], our method achieves improvements of \\(5.27\\%\\), \\(6.04\\%\\), \\(3.99\\%\\) on MVTec, and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.15
+            ],
+            "angle": 0,
+            "content": "10.25%, 11.55%, 10.60% on MPDD, at image-level AUROC under 2-shot, 4-shot and 8-shot scenarios, respectively. The contributions of this work are summarized below:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.165,
+                0.892,
+                0.224
+            ],
+            "angle": 0,
+            "content": "1. We propose a few-shot and category-agnostic industrial AD strategy which adopts sample alignment between the original test sample and its reconstructed normal version."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.236,
+                0.892,
+                0.311
+            ],
+            "angle": 0,
+            "content": "2. We propose a regression algorithm with distribution regularization which has a closed-form solution for the transformation estimation, keeping the reconstructed result close to the query image while maintaining the property of normal samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.322,
+                0.892,
+                0.367
+            ],
+            "angle": 0,
+            "content": "3. Our proposed method achieves state-of-the-art few-shot AD performance under various datasets and settings."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.513,
+                0.165,
+                0.892,
+                0.367
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.381,
+                0.642,
+                0.397
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.407,
+                0.684,
+                0.422
+            ],
+            "angle": 0,
+            "content": "2.1. Anomaly Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.43,
+                0.892,
+                0.686
+            ],
+            "angle": 0,
+            "content": "Industrial visual anomaly detection (AD) is a rising topic in computer vision. The mainstream AD methods can be categorized as reconstruction-based model and feature-matching-based models. Previous reconstruction-based models classified anomalous samples either though reconstruction loss [2, 33, 30] or via comparison between reconstructed normal samples and test sample [21, 22, 29] with generative models. Another line of works, feature-matching-based models, take full advantage of pre-trained features. For example, SPADE [6] firstly put forward memory banks comprising various feature hierarchies for fine-grained, KNN-based [8] anomaly segmentation and image-level anomaly detection. Similarly, PaDiM [7] and PatchCore [28] investigated AD performance on MVTec in unsupervised learning settings. However, both two lines of methods show greatly high data dependence which would hinder their industrial application."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.697,
+                0.757,
+                0.712
+            ],
+            "angle": 0,
+            "content": "2.2. Few-shot Anomaly Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Few-shot anomaly detection (FSAD) has developed to meet the demands of fast manufacturing changeover. TDG [23] proposes a hierarchical generative model that captures the multi-scale patch distribution of each support image. DiffNet [19] leverages the descriptiveness of features extracted by convolutional neural networks to estimate their density using a normalizing flow, which is a tool well-suited to estimate distributions from a few support samples. RegAD [13] explored a new paradigm for FSAD, by learning a common model shared among multiple categories in a meta-learning style. Despite of their decent inference performances under few-shot settings, the training process be"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.956
+            ],
+            "angle": 0,
+            "content": "17482"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.087,
+                0.895,
+                0.367
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.377,
+                0.893,
+                0.483
+            ],
+            "angle": 0,
+            "content": "Figure 2: Overview of our method. Feature maps of each query sample and support samples are exacted by a pre-trained encoder. Features from support images are aggregated into a support feature pool. This pool is down-sampled through greedy coreset selection as \\( S \\) to reduce data redundancy and improve inference speed. The coreset \\( S \\) and the original query feature map \\( Q \\) are then input to our proposed regression with distribution regularization as shown in the grey region. An optimal transformation \\( \\bar{W} \\) between \\( S \\) and \\( Q \\) is obtained by the regression to make sure the reconstructed sample \\( \\bar{W} S \\), denoted as \\( \\bar{Q} \\), to share similarity with \\( Q \\) but keeps all the property of normal samples. Finally, we align \\( \\bar{Q} \\) and \\( Q \\) for direct comparison to obtaining the anomaly estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.51,
+                0.47,
+                0.54
+            ],
+            "angle": 0,
+            "content": "comes the main obstacle for fast model migration in real industrial scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.553,
+                0.214,
+                0.571
+            ],
+            "angle": 0,
+            "content": "3. Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.579,
+                0.47,
+                0.671
+            ],
+            "angle": 0,
+            "content": "In this section, we introduce the details of FastRecon. Firstly, we define the one-class classification problem in industrial anomaly detection. FastRecon contains 3 parts: feature extraction and coreset selection, regression with distribution regularization, and anomaly detection with reconstruction. The overview of our method is shown in Fig. 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.679,
+                0.262,
+                0.695
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Definition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.702,
+                0.471,
+                0.839
+            ],
+            "angle": 0,
+            "content": "We formally define the problem for one-class classification of industrial anomaly detection. Following the few-shot learning setting, in an \\( n \\)-way and \\( k \\)-shot episode, a support set consisting of normal samples from \\( n \\) categories is given, i.e., \\( S = \\bigcup_{i=1}^{n} T_i \\), where the subset \\( T_i \\) consists of \\( k \\) normal samples from category \\( c_i \\). During test time, a query sample, whether normal or anomalous, is presented. The model predicts whether or not the sample is anomalous at the pixel and image level."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.43,
+                0.864
+            ],
+            "angle": 0,
+            "content": "3.2. Feature Extraction and Coreset Selection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Existing studies [7, 28] have shown that extracted features from pre-trained CNNs perform well in the anomaly"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.51,
+                0.895,
+                0.661
+            ],
+            "angle": 0,
+            "content": "detection task. We also utilize a pre-trained ResNet-50 to output a patch-level feature map of an image. \\(\\phi_{i,j}\\) is used to denote hierarchy-level \\(j\\) of the pre-trained network \\(\\phi\\) for the image \\(x_{i} \\in X\\) (dataset \\(X\\)), where \\(j \\in \\{1,2,3,4\\}\\). We adopt the intermediate features of the hierarchy-level, i.e., \\(j \\in \\{2,3\\}\\). The resulting feature map has a dimension of \\(H \\times W \\times D\\), where \\(H\\), \\(W\\) are the height and width of the largest activation map used to generate the embedding, and \\(D\\) is the total number of channels of both activation maps used to generate embedding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To facilitate calculations, the feature map is reshaped from 3-dimension \\( H \\times W \\times D \\) to 2-dimension \\( R \\times D \\), where \\( R = H \\times W \\). Features in the reshaped map represent embedding vectors, i.e., the local aware patch features. In a \\( k \\)-shot setting, our ultimate support feature pool is obtained by concatenating features of \\( k \\) support images, with a size of \\( k \\times R \\times D \\). Besides, following [18], we take a coreset sampling operation to get a coreset \\( S \\in R^{c \\times d} \\), where \\( c \\) is the number of clustering centers computed with K-greedy algorithm. The coverage of \\( S \\) is comparable to the original support feature pools but with a smaller scale so that the computational complexity and the performance of detection could be balanced. For a query image, with the same pretrained network, it is also extracted to patch-level feature map \\( Q \\). The process of feature extraction and coreset is"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17483"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.089,
+                0.18,
+                0.213
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.132,
+                0.216,
+                0.147,
+                0.226
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.184,
+                0.089,
+                0.265,
+                0.213
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.215,
+                0.216,
+                0.231,
+                0.226
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.268,
+                0.089,
+                0.348,
+                0.213
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.299,
+                0.216,
+                0.315,
+                0.226
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.349,
+                0.089,
+                0.43,
+                0.213
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.381,
+                0.216,
+                0.397,
+                0.226
+            ],
+            "angle": 0,
+            "content": "(d)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.238,
+                0.473,
+                0.405
+            ],
+            "angle": 0,
+            "content": "Figure 3: Visual comparison of decoding results on reconstructed features. We train a decoder on features of the whole dataset for image recovery, which is used to probe the transformed features from the encoder. (a) The original query image with defects region in red boxes. (b) Decoding results on original query features. (c) Decoding results on transformed features by ridge regression. The defects regions are reconstructed as on original query features. (d) Decoding results on transformed features by the proposed regression, which shares visual similarity with the original query image but with the property of normal samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.43,
+                0.319,
+                0.446
+            ],
+            "angle": 0,
+            "content": "shown in the brown region in Fig. 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.453,
+                0.452,
+                0.47
+            ],
+            "angle": 0,
+            "content": "3.3. Regression with Distribution Regularization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.477,
+                0.47,
+                0.584
+            ],
+            "angle": 0,
+            "content": "Why Ridge Regression fails. The goal is to reconstruct query feature map \\( Q \\) as a linear transformation of S-coreset \\( S \\) by finding an optimal transformation weight \\( W \\) such that \\( WS \\approx Q \\) and meanwhile \\( WS \\) has most properties of normal samples. Searching for optimal weight \\( W \\) amounts to solving the linear least-squares problem [25]. With original ridge regression, the optimization takes the following form:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.138,
+                0.595,
+                0.469,
+                0.621
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {\\boldsymbol {W}} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2} + \\lambda \\| \\boldsymbol {W} \\| ^ {2}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.627,
+                0.469,
+                0.808
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) is the weight of the penalty term and \\(\\| \\cdot \\|\\) representing the Frobenius norm. The penalty term in ridge regression, i.e., \\(\\| W\\|^2\\), ensures tractability when the linear system is over- or under-constrained. However, the transformation obtained from ridge regression can cause the reconstructed sample to deviate significantly from the distribution of normal samples, i.e., after the transformation, the result \\(WS\\) can be too close to \\(Q\\) so that features of defect regions are reconstructed as in \\(Q\\). As shown in Fig. 3 column (c), the decoding results on reconstructed features share excessively high similarity with the original query image with defects regions being reconstructed."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The distribution regularization. In our work, we propose a distributional regularization term to replace the original penalty term in ridge regression, which effectively enhances the normality of the reconstruction result \\( W S \\). We first model the distribution of normal feature maps by an isotropic Gaussian density function denoted as \\( f(\\boldsymbol{X}|\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}) \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.151
+            ],
+            "angle": 0,
+            "content": "where \\(\\pmb{\\mu},\\pmb{\\Sigma}\\) is the mean and co-variance estimated by the support set feature maps. We design the regularization term as \\(|f(WS) - f(\\pmb{\\mu})|\\) and the proposed regression has the form as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.511,
+                0.161,
+                0.892,
+                0.188
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {\\boldsymbol {W}} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2} + \\lambda | f (\\boldsymbol {W} \\boldsymbol {S}) - f (\\boldsymbol {\\mu}) |, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.198,
+                0.892,
+                0.349
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) denotes the coefficient that controls the contribution of the regularization. When searching the optimal transformation \\(W\\), the optimization of the first term \\(\\|Q - WS\\|^2\\) naturally pushes \\(WS\\) towards original query feature maps \\(Q\\), while with the proposed regularization \\(|f(WS) - f(\\pmb{\\mu})|\\), we force the constructed \\(WS\\) to lie in the high probability density region in the distribution, that is, somewhere close to the distribution center. The visualization of distribution regularization is shown in the grey region of Fig. 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.352,
+                0.892,
+                0.473
+            ],
+            "angle": 0,
+            "content": "The approximation for closed-form solution. The density function inside the regularization term in Eq. (2) prevents us from having a closed-form solution for the regression, which hinders fast calculation of the transformation. Thus, we propose an approximated version of Eq. (2) with the help of Taylor's theorem for multivariable functions on the distribution density function \\( f \\). Taylor's expansion for \\( f(x) \\) at \\( a \\) is shown as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.483,
+                0.891,
+                0.524
+            ],
+            "angle": 0,
+            "content": "\\[\nf (\\boldsymbol {x}) \\approx f (\\boldsymbol {a}) + \\nabla f (\\boldsymbol {a}) (\\mathbf {x} - \\boldsymbol {a}) + \\frac {1}{2} (\\mathbf {x} - \\boldsymbol {a}) ^ {T} H f (\\boldsymbol {a}) (\\mathbf {x} - \\boldsymbol {a}), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.524,
+                0.892,
+                0.6
+            ],
+            "angle": 0,
+            "content": "where \\(Hf(\\pmb{a})\\) denotes Hessian matrix of \\(f(\\pmb{x})\\) at \\(\\pmb{a}\\). And we approximate the density function with the first and second-order term of Taylor's expansion, where the first-order term is 0 at \\(\\pmb{\\mu}\\). Following Eq. (3), we expand the probability density function \\(f(WS)\\) at \\(\\pmb{\\mu}\\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.506,
+                0.61,
+                0.891,
+                0.67
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} f (\\boldsymbol {W} \\boldsymbol {S}) \\approx f (\\boldsymbol {\\mu}) + \\nabla f (\\boldsymbol {\\mu}) (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) \\\\ + \\frac {1}{2} (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) ^ {T} H f (\\boldsymbol {\\mu}) (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}). \\tag {4} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.671,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Since our assumed data distribution is isotropic Gaussian, its covariance matrix can be represented as \\(\\pmb{\\Sigma} = \\sigma^2\\pmb{I}\\), where \\(\\sigma^2\\) is the variance for all dimensions. Then, we have the term \\(\\nabla f(\\pmb{\\mu})(\\pmb{W}\\pmb{S} - \\pmb{\\mu})\\) as 0, and \\(Hf(\\pmb{\\mu})\\) equals the \\(\\pmb{\\Sigma}^{-1}\\) which is the inverse of the covariance matrix. Then, by placing \\(f(\\pmb{\\mu})\\) to the left, we have"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.508,
+                0.772,
+                0.891,
+                0.862
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} f (\\boldsymbol {W} \\boldsymbol {S}) - f (\\boldsymbol {\\mu}) \\approx \\frac {1}{2} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) ^ {T} \\boldsymbol {\\Sigma} ^ {- 1} (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) \\\\ = \\frac {1}{2 \\sigma^ {2}} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) ^ {T} \\boldsymbol {I} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) \\tag {5} \\\\ = \\frac {1}{2 \\sigma^ {2}} \\| \\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu} \\| ^ {2}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.904
+            ],
+            "angle": 0,
+            "content": "where \\(I\\) is an identity matrix. Then we merge the coefficient \\(\\frac{1}{2\\sigma^2}\\) into \\(\\lambda\\) and the approximated version of the optimization"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17484"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.205,
+                0.106
+            ],
+            "angle": 0,
+            "content": "target in Eq. (2) is:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.103,
+                0.113,
+                0.469,
+                0.139
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {W} = \\underset {W} {\\arg \\min } \\| Q - W S \\| ^ {2} + \\lambda \\| W S - \\mu \\| ^ {2}. \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.147,
+                0.47,
+                0.178
+            ],
+            "angle": 0,
+            "content": "Finding the optimal transformation. Knowing that the following optimization target of least square error (LSE) of"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.169,
+                0.189,
+                0.469,
+                0.215
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {W} ^ {\\prime} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.22,
+                0.286,
+                0.233
+            ],
+            "angle": 0,
+            "content": "has the closed-form solution as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.239,
+                0.469,
+                0.268
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {W} ^ {\\prime} = \\boldsymbol {Q} \\boldsymbol {S} ^ {\\top} \\left(\\boldsymbol {S} ^ {\\top} \\boldsymbol {S}\\right) ^ {- 1}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.274,
+                0.469,
+                0.335
+            ],
+            "angle": 0,
+            "content": "to utilize the conclusion from Eq. (8), we transform Eq. (6) by variable substitution to fit the form of Eq. (8). Let \\( Q_* \\) and \\( S_* \\) be the column-wise augmented version of \\( Q \\) and \\( S \\) respectively:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.144,
+                0.342,
+                0.469,
+                0.361
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {S} _ {*} = \\left[ \\boldsymbol {S} \\sqrt {\\lambda} \\boldsymbol {S} \\right], \\quad \\boldsymbol {Q} _ {*} = \\left[ \\boldsymbol {Q} \\sqrt {\\lambda} \\boldsymbol {\\mu} \\right], \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.368,
+                0.469,
+                0.412
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) is the coefficient of the regularization term which is always set as a positive number. Hence, equality holds for"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.094,
+                0.42,
+                0.469,
+                0.451
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\| Q _ {*} - W S _ {*} \\right\\| ^ {2} = \\left\\| Q - W S \\right\\| ^ {2} + \\lambda \\left\\| \\boldsymbol {\\mu} - W S \\right\\| ^ {2}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.453,
+                0.347,
+                0.467
+            ],
+            "angle": 0,
+            "content": "and the form in Eq. (6) can be written as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.165,
+                0.474,
+                0.469,
+                0.5
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {W} = \\underset {W} {\\arg \\min } \\| Q _ {*} - W S _ {*} \\| ^ {2}. \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.508,
+                0.469,
+                0.539
+            ],
+            "angle": 0,
+            "content": "Based on the conclusion in Eq. (8), the solution for our optimization process is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.545,
+                0.469,
+                0.604
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\bar {W} = Q _ {*} S _ {*} ^ {\\top} \\left(S _ {*} ^ {\\top} S _ {*}\\right) ^ {- 1} \\tag {12} \\\\ = \\left(\\boldsymbol {Q} \\boldsymbol {S} ^ {\\top} + \\lambda \\cdot \\boldsymbol {\\mu} \\boldsymbol {S} ^ {\\top}\\right) \\left(\\boldsymbol {S} ^ {\\top} \\boldsymbol {S} + \\lambda \\cdot \\boldsymbol {S} \\boldsymbol {S} ^ {\\top}\\right) ^ {- 1}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.611,
+                0.42,
+                0.626
+            ],
+            "angle": 0,
+            "content": "3.4. Anomaly Detection with Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.633,
+                0.469,
+                0.709
+            ],
+            "angle": 0,
+            "content": "After getting the reconstruction query feature maps \\(\\bar{Q}\\), we align it with those from the original query sample \\(\\mathbf{Q}\\) to estimate the pixel-level anomaly segmentation map and image-level anomaly score. For pixel \\(i\\) in the query image, the anomaly score \\(m_{i}\\) is calculated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.177,
+                0.716,
+                0.469,
+                0.737
+            ],
+            "angle": 0,
+            "content": "\\[\nm _ {i} = \\left\\| Q _ {i} - \\bar {Q} _ {i} \\right\\| ^ {2}, i \\in \\mathcal {N}, \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.744,
+                0.468,
+                0.805
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{N}\\) denotes the collection of all pixel indices in \\(Q\\). \\(Q_{i}\\) denotes the relevant feature vector of pixel \\(i\\). For image-level classification, we use the maximum distance score \\(s^{*}\\) among all the pixels to represent the image-level score as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.154,
+                0.813,
+                0.469,
+                0.834
+            ],
+            "angle": 0,
+            "content": "\\[\ns ^ {*} = \\max  \\left\\{\\left\\| Q _ {i} - \\bar {Q} _ {i} \\right\\| ^ {2} \\mid i \\in \\mathcal {N} \\right\\}. \\tag {14}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.84,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Besides, similar to [28, 7], to match the original input resolution, the segmentation map should be up-scaled with bilinear interpolation. Finally, we smoothed the segmentation map with a Gaussian of kernel width of 4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.091,
+                0.625,
+                0.107
+            ],
+            "angle": 0,
+            "content": "4. Experiment"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.116,
+                0.697,
+                0.132
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setups"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.139,
+                0.892,
+                0.367
+            ],
+            "angle": 0,
+            "content": "Dataset. We evaluated the performance of our model by using the MVTec AD dataset [3] and MPDD [15], which are the real-world benchmarks for AD. MVTec dataset includes 5354 images in 15 categories. 3629 of these images are defect-free and the remaining 1725 have defects. Each category has an average of five different types of defects. The image resolution ranges from \\(700 \\times 700\\) to \\(1024 \\times 1024\\). MPDD dataset contains 6 classes of metal productions. Images taken from different distances and spatial directions, as well as the non-uniform backgrounds, make the AD task on this dataset extremely difficult. The MPDD dataset includes 888 normal images in the training set and 176 normal images and 282 abnormal images in the test set with the resolution of \\(1024 \\times 1024\\). Additionally, both datasets provide ground truth of defective regions on pixel level."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.373,
+                0.892,
+                0.464
+            ],
+            "angle": 0,
+            "content": "Competing Methods. We compare our method with previous state-of-the-art FSAD and also full-data AD methods. The methods for comparison include GANomaly [1], ARNet [27], MKD [20], CutPaste [24], FYD [32], PaDiM [7], PatchCore [18], CflowAD [11], TDG [23], DiffNet [19] and RegAD [13]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.471,
+                0.891,
+                0.561
+            ],
+            "angle": 0,
+            "content": "Evaluation Protocols. We measure the model performance with the area under the Receiver Operating Characteristic curve (AUROC) on classification results. We use image-level AUROC to evaluate the sample detection results and pixel-level AUROC to measure the defects localization performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Implementation Details. In our experiment, we used a ResNet-50 [12] model pre-trained on ImageNet for feature extraction. We extract features from the 2 middle-level layers of the model. For both MVtec and MPDD datasets, all the support and query images are reshaped to \\(368 \\times 368\\) for training and inference. For all the experiments, the coefficient \\(\\lambda\\) for our regularization term is set as 0.3, and the corset selection sampling rate \\(s\\) is set as 0.15. All the experiments are conducted on one NVIDIA GTX 3090 GPU."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.716,
+                0.688,
+                0.732
+            ],
+            "angle": 0,
+            "content": "4.2. Experiment Results"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.74,
+                0.851,
+                0.755
+            ],
+            "angle": 0,
+            "content": "4.2.1 Comparison with State-of-the-art Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Few-shot AD averaged performance. Tab. 1 shows FSAD averaged performance on both MVTec and MPDD datasets. Our method (FastRecon) obtains the best performances under all experimental settings. Specifically, FastRecon improves image-level AUROC by \\(5.27\\%\\), \\(6.04\\%\\), \\(3.99\\%\\) on MVTec and \\(10.25\\%\\), \\(11.55\\%\\) \\(10.60\\%\\) on MPDD over the current state-of-the-art FSAD method RegAD for 2-shot, 4-shot, and 8-shot scenarios respectively. For pixel-level AUROC, FastRecon also outperforms RegAD"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17485"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.119,
+                0.089,
+                0.86,
+                0.238
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td></td><td colspan=\"6\">AUROC at Image-level</td><td colspan=\"4\">AUROC at Pixel-level</td></tr><tr><td>Dataset</td><td>k</td><td>TDG [23]</td><td>DiffNet [19]</td><td>RegAD [13]</td><td>PaDiM [7]</td><td>PatchCore [18]</td><td>FastRcon (ours)</td><td>RegAD [13]</td><td>PaDiM [7]</td><td>PatchCore [18]</td><td>FastRcon (ours)</td></tr><tr><td rowspan=\"3\">MVTec</td><td>2</td><td>71.20</td><td>80.60</td><td>85.70</td><td>78.90</td><td>87.81</td><td>90.97</td><td>94.60</td><td>90.50</td><td>94.75</td><td>95.86</td></tr><tr><td>4</td><td>72.70</td><td>81.30</td><td>88.20</td><td>71.60</td><td>89.49</td><td>94.24</td><td>95.80</td><td>80.20</td><td>94.99</td><td>96.98</td></tr><tr><td>8</td><td>75.20</td><td>83.20</td><td>91.20</td><td>75.30</td><td>94.31</td><td>95.19</td><td>96.70</td><td>80.50</td><td>95.60</td><td>97.27</td></tr><tr><td rowspan=\"3\">MPDD</td><td>2</td><td>60.30</td><td>60.20</td><td>63.40</td><td>-</td><td>59.55</td><td>73.65</td><td>93.20</td><td>-</td><td>79.15</td><td>97.03</td></tr><tr><td>4</td><td>63.50</td><td>63.30</td><td>68.30</td><td>-</td><td>59.78</td><td>79.85</td><td>93.90</td><td>-</td><td>79.82</td><td>97.60</td></tr><tr><td>8</td><td>68.20</td><td>68.50</td><td>71.90</td><td>-</td><td>59.95</td><td>82.50</td><td>95.10</td><td>-</td><td>80.30</td><td>97.92</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.249,
+                0.895,
+                0.296
+            ],
+            "angle": 0,
+            "content": "Table 1: FSAD performance comparisons on MVtec and MPDD dataset. The results are averaged over all categories. Both image-level and pixel-level performances are reported in AUROC (\\%) \\(\\uparrow\\). \\(k\\) denotes the number of shots in our few-shot settings. The best results for different settings are in bold."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.318,
+                0.469,
+                0.584
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td colspan=\"2\">RegAD [13]</td><td colspan=\"2\">PatchCore [18]</td><td colspan=\"2\">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bottle</td><td>99.40</td><td>98.40</td><td>99.60</td><td>98.60</td><td>99.44</td><td>98.50</td></tr><tr><td>Cable</td><td>76.10</td><td>92.70</td><td>97.40</td><td>97.90</td><td>93.79</td><td>96.12</td></tr><tr><td>Capsule</td><td>72.40</td><td>97.60</td><td>66.30</td><td>97.70</td><td>90.07</td><td>98.96</td></tr><tr><td>Carpet</td><td>97.90</td><td>98.90</td><td>99.00</td><td>99.00</td><td>99.90</td><td>99.15</td></tr><tr><td>Grid</td><td>91.20</td><td>85.70</td><td>63.00</td><td>70.60</td><td>88.81</td><td>86.32</td></tr><tr><td>Hazelnut</td><td>95.80</td><td>98.00</td><td>92.80</td><td>97.00</td><td>99.32</td><td>98.59</td></tr><tr><td>Leather</td><td>100.00</td><td>99.10</td><td>100.00</td><td>96.90</td><td>100.00</td><td>99.20</td></tr><tr><td>Metal_Nut</td><td>94.60</td><td>97.80</td><td>94.70</td><td>97.00</td><td>99.12</td><td>98.72</td></tr><tr><td>Pill</td><td>80.80</td><td>97.40</td><td>89.00</td><td>96.90</td><td>93.48</td><td>98.32</td></tr><tr><td>Screw</td><td>56.60</td><td>95.00</td><td>54.10</td><td>92.10</td><td>62.46</td><td>97.10</td></tr><tr><td>Tile</td><td>95.50</td><td>94.90</td><td>100.00</td><td>96.00</td><td>100.00</td><td>96.73</td></tr><tr><td>Toothbrush</td><td>90.90</td><td>98.50</td><td>95.20</td><td>98.80</td><td>93.61</td><td>99.04</td></tr><tr><td>Transistor</td><td>85.20</td><td>93.80</td><td>98.40</td><td>95.00</td><td>97.29</td><td>94.18</td></tr><tr><td>Wood</td><td>98.60</td><td>94.70</td><td>97.40</td><td>93.10</td><td>99.29</td><td>94.94</td></tr><tr><td>Zipper</td><td>88.50</td><td>94.00</td><td>95.50</td><td>98.30</td><td>96.95</td><td>98.89</td></tr><tr><td>Average</td><td>88.20</td><td>95.80</td><td>89.49</td><td>94.99</td><td>94.24</td><td>96.98</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.593,
+                0.472,
+                0.655
+            ],
+            "angle": 0,
+            "content": "Table 2: FSAD categorical performance comparisons in AUROC (\\%) \\(\\uparrow\\) on MVTec dataset. Results are from the setting of shot \\(k = 4\\). The best results are in bold. Our method achieves the best performance in most categories."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.681,
+                0.47,
+                0.711
+            ],
+            "angle": 0,
+            "content": "by \\(1.26\\%\\), \\(1.18\\%\\), \\(0.57\\%\\) on MVTev and \\(3.83\\%\\), \\(3.70\\%\\), \\(2.82\\%\\) on MPDD respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.716,
+                0.47,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Few-shot AD categorical performances. Tab. 2 and Tab. 3 show the FSAD categorical performance. As shown in Tab. 2, FastRecon outperforms all the baselines in 10 out of 15 categories at the image level and in 12 out of 15 categories at the pixel level. And as shown in Tab. 3, FastRecon outperforms all the baselines in 4 out of 6 categories at the image level and in all categories at the pixel level."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Comparison with full-data AD. Tab. 4 shows the comparison of our method with AD methods which utilize the whole normal samples. Results show that our FastRecon has competitive performance compared with full-data methods, indicating the high data efficiency of our model."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.501,
+                0.318,
+                0.9,
+                0.461
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td colspan=\"2\">RegAD [13]</td><td colspan=\"2\">PatchCore [18]</td><td colspan=\"2\">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bracket/black</td><td>63.80</td><td>-</td><td>58.90</td><td>79.10</td><td>71.81</td><td>95.54</td></tr><tr><td>Bracket_brown</td><td>66.10</td><td>-</td><td>70.80</td><td>77.30</td><td>63.34</td><td>95.93</td></tr><tr><td>Bracket_white</td><td>59.30</td><td>-</td><td>70.70</td><td>69.30</td><td>69.44</td><td>98.89</td></tr><tr><td>Connector</td><td>77.20</td><td>-</td><td>59.40</td><td>86.40</td><td>97.62</td><td>98.04</td></tr><tr><td>Metal_plate</td><td>78.60</td><td>-</td><td>64.40</td><td>86.70</td><td>100.00</td><td>99.29</td></tr><tr><td>Tubes</td><td>67.50</td><td>-</td><td>34.50</td><td>80.10</td><td>76.90</td><td>97.89</td></tr><tr><td>Average</td><td>68.30</td><td>93.90</td><td>59.78</td><td>79.82</td><td>79.85</td><td>97.60</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.471,
+                0.895,
+                0.533
+            ],
+            "angle": 0,
+            "content": "Table 3: FSAD categorical performance comparisons in AUROC (\\%) \\(\\uparrow\\) on MPDD dataset. Results are from the setting of shot \\(k = 4\\). The best results are in bold. Our method achieves the best performance in most categories."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.55,
+                0.897,
+                0.722
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"3\"></td><td colspan=\"2\">MVTec AD</td><td colspan=\"2\">MPDD</td></tr><tr><td>Method</td><td>Data</td><td>Backbone</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>FastRecon</td><td>2</td><td>WRN50</td><td>90.97</td><td>95.86</td><td>73.65</td><td>97.03</td></tr><tr><td>FastRecon</td><td>4</td><td>WRN50</td><td>94.24</td><td>96.98</td><td>79.85</td><td>97.60</td></tr><tr><td>FastRecon</td><td>8</td><td>WRN50</td><td>95.19</td><td>97.27</td><td>82.50</td><td>97.92</td></tr><tr><td>GANomaly [1]</td><td>Full</td><td>Unet</td><td>80.50</td><td>-</td><td>64.80</td><td>-</td></tr><tr><td>ARNet [27]</td><td>Full</td><td>Unet</td><td>83.90</td><td>-</td><td>69.70</td><td>-</td></tr><tr><td>MKD [20]</td><td>Full</td><td>Res18</td><td>87.70</td><td>90.70</td><td>-</td><td>-</td></tr><tr><td>FYD [32]</td><td>Full</td><td>Res18</td><td>97.30</td><td>97.40</td><td>-</td><td>-</td></tr><tr><td>PaDiM [7]</td><td>Full</td><td>WRN50</td><td>97.90</td><td>97.50</td><td>74.80</td><td>96.70</td></tr><tr><td>PatchCore [18]</td><td>Full</td><td>WRN50</td><td>99.10</td><td>98.10</td><td>82.10</td><td>95.70</td></tr><tr><td>CflowAD [11]</td><td>Full</td><td>WRN50</td><td>98.60</td><td>98.60</td><td>86.10</td><td>97.70</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.733,
+                0.895,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Table 4: AD performance comparisons in AUROC \\((\\%)\\) ↑ on MVTec and MPDD dataset with full-data methods which utilize the whole dataset in training. Both image-level and pixel-level performances are averaged over all categories. The Data column denotes different usage of the dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Speed performance of FastRecon. Speed comparisons on both training and inference are shown in the following Tab. 5. For FastRecon, training stage consists of feature extraction, feature subsampling and calculation on transfor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17486"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.089,
+                0.87,
+                0.33
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.341,
+                0.896,
+                0.388
+            ],
+            "angle": 0,
+            "content": "Figure 4: Qualitative results of anomaly localization for both MVTec and MPDD datasets. The first row in the red box presents the support sample for each category while the second row indicates the query samples. The results show that our method can provide accurate localization of defect regions even for more complicated patterns in MPDD."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.399,
+                0.87,
+                0.58
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.59,
+                0.893,
+                0.651
+            ],
+            "angle": 0,
+            "content": "Figure 5: Visualization of decoding results on reconstructed query features. With a pretrained image decoder, we investigate the transformed query features in the MVtec dataset. The first row shows the original query image, and the middle row shows the images decoded from the original query features. The last row represents the image decoded from the reconstructed query feature map. Our method can reveal the normal side of the defective query samples."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.674,
+                0.472,
+                0.748
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Aggregated Training</td><td>Training Time</td><td>Inference Time</td></tr><tr><td>PatchCore</td><td>No</td><td>80.37</td><td>0.60</td></tr><tr><td>RegAD (k=2)</td><td>Yes</td><td>660.80</td><td>0.05</td></tr><tr><td>FastRecon (k=8)</td><td>No</td><td>1.95</td><td>0.04</td></tr><tr><td>FastRecon (k=2)</td><td>No</td><td>0.52</td><td>0.04</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.758,
+                0.47,
+                0.834
+            ],
+            "angle": 0,
+            "content": "Table 5: Training and inference speed comparisons in seconds. RegAD requires additional training on aggregated features. The inference speed is evaluated as averaged inference time per query sample. FastRecon achieves overall best speed performance with 2 and 8 shots."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.886,
+                0.456,
+                0.901
+            ],
+            "angle": 0,
+            "content": "mation matrix. FastRecon achieves the best performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.677,
+                0.637,
+                0.691
+            ],
+            "angle": 0,
+            "content": "4.3. Visualization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.705,
+                0.892,
+                0.751
+            ],
+            "angle": 0,
+            "content": "Localization of anomaly detection Fig. 4 demonstrates visual examples of anomaly detection on MVTec and MPDD. Most defects can be accurately identified."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.78,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Decoding results on reconstructed query feature. In order to better reflect the reconstruction ability of FastRecon, a feature decoder is built to visualize the query sample from reconstructed feature maps. The decoder is trained with full MVTec dataset to learn to decode image sample from feature maps. Fig. 5 shows that, images decoded from reconstructed feature maps maintain the normality of the normal samples, which illustrates the effectiveness of our approach."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17487"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.089,
+                0.351,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.159,
+                0.257,
+                0.278,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(a) Sampling Rate \\( s \\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.089,
+                0.617,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.365,
+                0.256,
+                0.605,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(b) Coefficient \\(\\lambda\\) of Regularization Term"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.62,
+                0.09,
+                0.885,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.704,
+                0.257,
+                0.8,
+                0.269
+            ],
+            "angle": 0,
+            "content": "(c) Resolution \\(r\\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.282,
+                0.893,
+                0.313
+            ],
+            "angle": 0,
+            "content": "Figure 6: Effect of three hyper-parameters comparisons in AUROC (\\%) on MVTec dataset. (a) AD performance with different sampling rate \\( s \\). (b) AD performance with different coefficient \\( \\lambda \\). (c) AD performance with different resolution \\( r \\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.089,
+                0.338,
+                0.459,
+                0.462
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.477,
+                0.459,
+                0.616
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.629,
+                0.47,
+                0.69
+            ],
+            "angle": 0,
+            "content": "Figure 7: AD performance comparisons in AUROC (\\%) on MVTec dataset between ridge regression and proposed regularization. Our results, displayed in blue, are better than ridge regression at both image and pixel levels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.718,
+                0.241,
+                0.733
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.742,
+                0.47,
+                0.819
+            ],
+            "angle": 0,
+            "content": "In this section, we ablate the core parts of our proposed method to investigate its impact on the final performance. We also discuss the effect of hyper-parameters, which are the coefficient of regularization term \\(\\lambda\\), the resolution of input data, and the coreset selection sampling ratio \\(s\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Effect of sampling Rate \\( s \\). Fig. 6 (a) illustrates the relationship between the Sampling Rate \\( s \\) and AUROC performance. The sampling rate \\( s \\) decides the number of feature points in the support feature pool. As shown in Fig. 6 (a), the optimal sampling rate is around 0.45."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.34,
+                0.893,
+                0.461
+            ],
+            "angle": 0,
+            "content": "Impact of the distribution regularization term and coefficient \\(\\lambda\\). In Fig. 7, FastRecon obtains better AUROC performance at both image and pixel levels. It reflects the significance of our proposed distribution regularization. Fig. 6 (b) shows the relationship between coefficient \\(\\lambda\\) of regularization term and AUROC performance for 4-shot and 8-shot scenarios. When \\(\\lambda\\) equals 0.3, the AUROC performances are best at both image and pixel levels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.475,
+                0.892,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Effect of image resolution \\( r \\). In our experiment, images, no matter how much the original resolutions are, should be reshaped to new resolution \\( r \\times r \\). Fig. 6 (c) reflects the relationship between resolution \\( r \\) and AUROC performance. The resolution will affect the feature points. As shown in Fig. 6 (c), when the resolution equals 368, FastRecon performs well at both image and pixel levels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.602,
+                0.619,
+                0.617
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.893,
+                0.825
+            ],
+            "angle": 0,
+            "content": "In this paper, a novel method FastRecon is proposed for few-shot anomaly detection based on feature reconstruction. For each query sample, we construct their normal version, referenced by a limited number of normal features. To ensure the reconstructed result shares high visual similarity with the query sample while maintaining the property of the normal sample, a regression equation with proposed distribution regularization is proposed, to obtain the optimal transformation from support to query features. With this fast and accurate reconstruction, the final anomaly detection could be accomplished by a simple alignment. Experimental results show the state-of-the-art performance of our method for 2-shot, 4-shot, and 8-shot scenarios."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work was supported by National Key R&D Program of China (No.2022YFE0200300), National Natural Science Foundation of China (No.61972323)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.956
+            ],
+            "angle": 0,
+            "content": "17488"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
+                0.09,
+                0.176,
+                0.107
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
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+                0.116,
+                0.47,
+                0.171
+            ],
+            "angle": 0,
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+# FastRecon: Few-shot Industrial Anomaly Detection via Fast Feature Reconstruction
+
+Zheng Fang $^{1,2\dagger}$  Xiaoyang Wang $^{1,2\dagger}$  Haocheng Li $^{3}$  Jiejie Liu $^{1,3}$  Qiugui Hu $^{3}$  Jimin Xiao $^{1*}$ $^{1}$ XJTLU  $^{2}$ Metavisioncn  $^{3}$ Dinnar Automation Technology  
+{fz.jun26th, haocheng.li789}@gmail.com,  
+{xiaoyang.wang20, jiejie.liu22}@student.xjtlu.edu.cn, jimin.xiao@xjtlu.edu.cn
+
+# Abstract
+
+In industrial anomaly detection, data efficiency and the ability for fast migration across products become the main concerns when developing detection algorithms. Existing methods tend to be data-hungry and work in the one-model-one-category way, which hinders their effectiveness in real-world industrial scenarios. In this paper, we propose a few-shot anomaly detection strategy that works in a low-data regime and can generalize across products at no cost. Given a defective query sample, we propose to utilize a few normal samples as a reference to reconstruct its normal version, where the final anomaly detection can be achieved by sample alignment. Specifically, we introduce a novel regression with distribution regularization to obtain the optimal transformation from support to query features, which guarantees the reconstruction result shares visual similarity with the query sample and meanwhile maintains the property of normal samples. Experimental results show that our method significantly outperforms previous state-of-the-art at both image and pixel-level AUROC performances from 2 to 8-shot scenarios. Besides, with only a limited number of training samples (less than 8 samples), our method reaches competitive performance with vanilla AD methods which are trained with extensive normal samples. The code is available at https://github.com/FzJun26th/ FastRecon.
+
+# 1. Introduction
+
+Anomaly detection (AD) in computer vision aims to identify rare observations that deviate significantly from the majority of the data and do not conform to a well-defined notion of normal behavior [4]. In industrial settings, AD is widely used to detect the anomalies on the surface of the product, which has been attracting a lot of attention re
+
+![](images/e36e138b1980f80a9a1a97463b5aa7085394029a12dcfeb7dbbf6ed9cd543a65.jpg)
+
+![](images/66f3e4b66eaa45a62d97b2c1f92bd69ed2c28c29251c65728ce3a087ad2dc57a.jpg)
+
+![](images/9fda1f949d8e508731215874e634e9f814685f13d6abc49238c6e450cd7865b7.jpg)  
+Figure 1: Comparison of our FastRecon with (a) Vanilla Reconstruction-based method and (b) Vanilla Feature-Matching-based method. Compared with (a), our method needs no training session and requires less normal samples for feature reconstruction. Compared with (b), our method applies direct pixel-to-pixel alignment between the test sample and reconstruction result for anomaly detection without an exhaustive feature searching process, thus being more efficient in inference.
+
+cently [31, 16, 9]. The difficulty of industrial AD lies in the diversity of the defects, which can take different forms, from subtle flaws like slight bruises, to obvious ones such as missing components [3]. This makes it difficult to detect and classify anomalies. Primal researches focus on utilizing supervised learning to tackle industrial AD [5, 17]. However, such a learning paradigm often requires an exhaustive set of anomalous samples for each category, which can be
+
+naturally rare to collect, making it inefficient for real-world industrial scenarios.
+
+Recent works pay attention to learning with limited or even no supervision to overcome the problem caused by the lack of anomalous samples. As shown in Fig. 1 (a), reconstruction-based industrial AD [34, 10, 26, 14] utilizes generative models such as autoencoder to learn the distribution of normal samples through the cumbersome training process. As in Fig. 1 (b), recent researches favor feature-matching strategy [28, 7] that conducts feature comparison between the test sample and memory bank of normal features, where the feature searching causes high computational complexity. Both lines of work require massive normal samples either for model training or memory construction, only to achieve detection for a single product category, and fail to quickly generalize across products.
+
+In this paper, we state that well-generalized industrial AD can be achieved in an extremely data-efficient way. We propose a training-free, few-shot AD method named FastRecon, to meet the demand for industrial scenarios, which works under the situation that only a limited number of normal samples are available. Given a query sample to detect, we propose to construct its normal version at the feature level through a linear transformation based on features extracted from limited normal samples. This constructed sample shares low-frequency features with the original query image but differs in the defect regions, making the anomaly apparent when directly compared to the original. The comparisons on the methodology of our method and previous mainstream works are shown in Fig. 1. The key lies in finding the optimal transformation. On the one hand, the transformation should bring the constructed sample somewhere close to the query sample so they share visual features on the normal parts. On the other hand, the constructed sample should maintain the property of a normal sample so the difference between the two samples can fully reveal the anomaly regions. With this goal, we proposed a distributional regularization term upon the classical ridge regression algorithm. We first utilize normal features to fit a Gaussian distribution. When finding the transformation from normal features to the query sample, we simultaneously push the reconstructed sample toward the center of the built distribution to enhance its normality. Note that our proposed optimization process admits a closed-form solution just as ridge regression, which allows fast computation with low cost, ensuring the adaptation and migration of our method from old products to novel ones.
+
+Experiments on the benchmark datasets for industrial defection, MVTec [3] and MDPP [15], as well as comparisons with various existing state-of-the-art FSAD methods [19, 13], indicate the effectiveness of our model. Compared with previous state-of-the-art [13], our method achieves improvements of  $5.27\%$ ,  $6.04\%$ ,  $3.99\%$  on MVTec, and
+
+10.25%, 11.55%, 10.60% on MPDD, at image-level AUROC under 2-shot, 4-shot and 8-shot scenarios, respectively. The contributions of this work are summarized below:
+
+1. We propose a few-shot and category-agnostic industrial AD strategy which adopts sample alignment between the original test sample and its reconstructed normal version.  
+2. We propose a regression algorithm with distribution regularization which has a closed-form solution for the transformation estimation, keeping the reconstructed result close to the query image while maintaining the property of normal samples.  
+3. Our proposed method achieves state-of-the-art few-shot AD performance under various datasets and settings.
+
+# 2. Related Work
+
+# 2.1. Anomaly Detection
+
+Industrial visual anomaly detection (AD) is a rising topic in computer vision. The mainstream AD methods can be categorized as reconstruction-based model and feature-matching-based models. Previous reconstruction-based models classified anomalous samples either though reconstruction loss [2, 33, 30] or via comparison between reconstructed normal samples and test sample [21, 22, 29] with generative models. Another line of works, feature-matching-based models, take full advantage of pre-trained features. For example, SPADE [6] firstly put forward memory banks comprising various feature hierarchies for fine-grained, KNN-based [8] anomaly segmentation and image-level anomaly detection. Similarly, PaDiM [7] and PatchCore [28] investigated AD performance on MVTec in unsupervised learning settings. However, both two lines of methods show greatly high data dependence which would hinder their industrial application.
+
+# 2.2. Few-shot Anomaly Detection
+
+Few-shot anomaly detection (FSAD) has developed to meet the demands of fast manufacturing changeover. TDG [23] proposes a hierarchical generative model that captures the multi-scale patch distribution of each support image. DiffNet [19] leverages the descriptiveness of features extracted by convolutional neural networks to estimate their density using a normalizing flow, which is a tool well-suited to estimate distributions from a few support samples. RegAD [13] explored a new paradigm for FSAD, by learning a common model shared among multiple categories in a meta-learning style. Despite of their decent inference performances under few-shot settings, the training process be
+
+![](images/9241ee867b0ed2781334d255d99c3846fa3dbbd76bd9a2403adf16dfdbfb0092.jpg)  
+Figure 2: Overview of our method. Feature maps of each query sample and support samples are exacted by a pre-trained encoder. Features from support images are aggregated into a support feature pool. This pool is down-sampled through greedy coreset selection as  $S$  to reduce data redundancy and improve inference speed. The coreset  $S$  and the original query feature map  $Q$  are then input to our proposed regression with distribution regularization as shown in the grey region. An optimal transformation  $\bar{W}$  between  $S$  and  $Q$  is obtained by the regression to make sure the reconstructed sample  $\bar{W} S$ , denoted as  $\bar{Q}$ , to share similarity with  $Q$  but keeps all the property of normal samples. Finally, we align  $\bar{Q}$  and  $Q$  for direct comparison to obtaining the anomaly estimation.
+
+comes the main obstacle for fast model migration in real industrial scenarios.
+
+# 3. Methodology
+
+In this section, we introduce the details of FastRecon. Firstly, we define the one-class classification problem in industrial anomaly detection. FastRecon contains 3 parts: feature extraction and coreset selection, regression with distribution regularization, and anomaly detection with reconstruction. The overview of our method is shown in Fig. 2.
+
+# 3.1. Problem Definition
+
+We formally define the problem for one-class classification of industrial anomaly detection. Following the few-shot learning setting, in an  $n$ -way and  $k$ -shot episode, a support set consisting of normal samples from  $n$  categories is given, i.e.,  $S = \bigcup_{i=1}^{n} T_i$ , where the subset  $T_i$  consists of  $k$  normal samples from category  $c_i$ . During test time, a query sample, whether normal or anomalous, is presented. The model predicts whether or not the sample is anomalous at the pixel and image level.
+
+# 3.2. Feature Extraction and Coreset Selection
+
+Existing studies [7, 28] have shown that extracted features from pre-trained CNNs perform well in the anomaly
+
+detection task. We also utilize a pre-trained ResNet-50 to output a patch-level feature map of an image.  $\phi_{i,j}$  is used to denote hierarchy-level  $j$  of the pre-trained network  $\phi$  for the image  $x_{i} \in X$  (dataset  $X$ ), where  $j \in \{1,2,3,4\}$ . We adopt the intermediate features of the hierarchy-level, i.e.,  $j \in \{2,3\}$ . The resulting feature map has a dimension of  $H \times W \times D$ , where  $H$ ,  $W$  are the height and width of the largest activation map used to generate the embedding, and  $D$  is the total number of channels of both activation maps used to generate embedding.
+
+To facilitate calculations, the feature map is reshaped from 3-dimension  $H \times W \times D$  to 2-dimension  $R \times D$ , where  $R = H \times W$ . Features in the reshaped map represent embedding vectors, i.e., the local aware patch features. In a  $k$ -shot setting, our ultimate support feature pool is obtained by concatenating features of  $k$  support images, with a size of  $k \times R \times D$ . Besides, following [18], we take a coreset sampling operation to get a coreset  $S \in R^{c \times d}$ , where  $c$  is the number of clustering centers computed with K-greedy algorithm. The coverage of  $S$  is comparable to the original support feature pools but with a smaller scale so that the computational complexity and the performance of detection could be balanced. For a query image, with the same pretrained network, it is also extracted to patch-level feature map  $Q$ . The process of feature extraction and coreset is
+
+![](images/bbbe522c9704579f22d0deca006c444f872309059e8ea90e60897d8a0aca9285.jpg)  
+(a)
+
+![](images/c4ba3066bcf10205a6fab0fdc0d852489e2018de9609714be369b157a0362cce.jpg)  
+(b)
+
+![](images/08488c3ef5d5bc7e0d0ca5a9506aa17c463cf117848aa0762173fb41c0122d94.jpg)  
+(c)
+
+![](images/b45c840814b9645ca7a9ec0f8c80753cd8249d4ea6b4d5b781753f4e32cc218f.jpg)  
+(d)  
+Figure 3: Visual comparison of decoding results on reconstructed features. We train a decoder on features of the whole dataset for image recovery, which is used to probe the transformed features from the encoder. (a) The original query image with defects region in red boxes. (b) Decoding results on original query features. (c) Decoding results on transformed features by ridge regression. The defects regions are reconstructed as on original query features. (d) Decoding results on transformed features by the proposed regression, which shares visual similarity with the original query image but with the property of normal samples.
+
+shown in the brown region in Fig. 2.
+
+# 3.3. Regression with Distribution Regularization
+
+Why Ridge Regression fails. The goal is to reconstruct query feature map  $Q$  as a linear transformation of S-coreset  $S$  by finding an optimal transformation weight  $W$  such that  $WS \approx Q$  and meanwhile  $WS$  has most properties of normal samples. Searching for optimal weight  $W$  amounts to solving the linear least-squares problem [25]. With original ridge regression, the optimization takes the following form:
+
+$$
+\bar {\boldsymbol {W}} = \underset {\boldsymbol {W}} {\arg \min } \| \boldsymbol {Q} - \boldsymbol {W} \boldsymbol {S} \| ^ {2} + \lambda \| \boldsymbol {W} \| ^ {2}, \tag {1}
+$$
+
+where  $\lambda$  is the weight of the penalty term and  $\| \cdot \|$  representing the Frobenius norm. The penalty term in ridge regression, i.e.,  $\| W\|^2$ , ensures tractability when the linear system is over- or under-constrained. However, the transformation obtained from ridge regression can cause the reconstructed sample to deviate significantly from the distribution of normal samples, i.e., after the transformation, the result  $WS$  can be too close to  $Q$  so that features of defect regions are reconstructed as in  $Q$ . As shown in Fig. 3 column (c), the decoding results on reconstructed features share excessively high similarity with the original query image with defects regions being reconstructed.
+
+The distribution regularization. In our work, we propose a distributional regularization term to replace the original penalty term in ridge regression, which effectively enhances the normality of the reconstruction result  $W S$ . We first model the distribution of normal feature maps by an isotropic Gaussian density function denoted as  $f(\boldsymbol{X}|\boldsymbol{\mu},\boldsymbol{\Sigma})$
+
+where  $\pmb{\mu},\pmb{\Sigma}$  is the mean and co-variance estimated by the support set feature maps. We design the regularization term as  $|f(WS) - f(\pmb{\mu})|$  and the proposed regression has the form as:
+
+$$
+\bar {\boldsymbol {W}} = \underset {\boldsymbol {W}} {\arg \min } \| \boldsymbol {Q} - \boldsymbol {W} \boldsymbol {S} \| ^ {2} + \lambda | f (\boldsymbol {W} \boldsymbol {S}) - f (\boldsymbol {\mu}) |, \tag {2}
+$$
+
+where  $\lambda$  denotes the coefficient that controls the contribution of the regularization. When searching the optimal transformation  $W$ , the optimization of the first term  $\|Q - WS\|^2$  naturally pushes  $WS$  towards original query feature maps  $Q$ , while with the proposed regularization  $|f(WS) - f(\pmb{\mu})|$ , we force the constructed  $WS$  to lie in the high probability density region in the distribution, that is, somewhere close to the distribution center. The visualization of distribution regularization is shown in the grey region of Fig. 2.
+
+The approximation for closed-form solution. The density function inside the regularization term in Eq. (2) prevents us from having a closed-form solution for the regression, which hinders fast calculation of the transformation. Thus, we propose an approximated version of Eq. (2) with the help of Taylor's theorem for multivariable functions on the distribution density function  $f$ . Taylor's expansion for  $f(x)$  at  $a$  is shown as follows:
+
+$$
+f (\boldsymbol {x}) \approx f (\boldsymbol {a}) + \nabla f (\boldsymbol {a}) (\mathbf {x} - \boldsymbol {a}) + \frac {1}{2} (\mathbf {x} - \boldsymbol {a}) ^ {T} H f (\boldsymbol {a}) (\mathbf {x} - \boldsymbol {a}), \tag {3}
+$$
+
+where  $Hf(\pmb{a})$  denotes Hessian matrix of  $f(\pmb{x})$  at  $\pmb{a}$ . And we approximate the density function with the first and second-order term of Taylor's expansion, where the first-order term is 0 at  $\pmb{\mu}$ . Following Eq. (3), we expand the probability density function  $f(WS)$  at  $\pmb{\mu}$  as:
+
+$$
+\begin{array}{l} f (\boldsymbol {W} \boldsymbol {S}) \approx f (\boldsymbol {\mu}) + \nabla f (\boldsymbol {\mu}) (\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}) \\ + \frac {1}{2} (\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}) ^ {T} H f (\boldsymbol {\mu}) (\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}). \tag {4} \\ \end{array}
+$$
+
+Since our assumed data distribution is isotropic Gaussian, its covariance matrix can be represented as  $\pmb{\Sigma} = \sigma^2\pmb{I}$ , where  $\sigma^2$  is the variance for all dimensions. Then, we have the term  $\nabla f(\pmb{\mu})(\pmb{W}\pmb{S} - \pmb{\mu})$  as 0, and  $Hf(\pmb{\mu})$  equals the  $\pmb{\Sigma}^{-1}$  which is the inverse of the covariance matrix. Then, by placing  $f(\pmb{\mu})$  to the left, we have
+
+$$
+\begin{array}{l} f (\boldsymbol {W} \boldsymbol {S}) - f (\boldsymbol {\mu}) \approx \frac {1}{2} \left(\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}\right) ^ {T} \boldsymbol {\Sigma} ^ {- 1} (\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}) \\ = \frac {1}{2 \sigma^ {2}} \left(\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}\right) ^ {T} \boldsymbol {I} \left(\boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu}\right) \tag {5} \\ = \frac {1}{2 \sigma^ {2}} \| \boldsymbol {W} \boldsymbol {S} - \boldsymbol {\mu} \| ^ {2}, \\ \end{array}
+$$
+
+where  $I$  is an identity matrix. Then we merge the coefficient  $\frac{1}{2\sigma^2}$  into  $\lambda$  and the approximated version of the optimization
+
+target in Eq. (2) is:
+
+$$
+\bar {W} = \underset {W} {\arg \min } \| Q - W S \| ^ {2} + \lambda \| W S - \mu \| ^ {2}. \tag {6}
+$$
+
+Finding the optimal transformation. Knowing that the following optimization target of least square error (LSE) of
+
+$$
+\boldsymbol {W} ^ {\prime} = \underset {\boldsymbol {W}} {\arg \min } \| \boldsymbol {Q} - \boldsymbol {W} \boldsymbol {S} \| ^ {2}, \tag {7}
+$$
+
+has the closed-form solution as
+
+$$
+\boldsymbol {W} ^ {\prime} = \boldsymbol {Q} \boldsymbol {S} ^ {\top} \left(\boldsymbol {S} ^ {\top} \boldsymbol {S}\right) ^ {- 1}, \tag {8}
+$$
+
+to utilize the conclusion from Eq. (8), we transform Eq. (6) by variable substitution to fit the form of Eq. (8). Let  $Q_*$  and  $S_*$  be the column-wise augmented version of  $Q$  and  $S$  respectively:
+
+$$
+\boldsymbol {S} _ {*} = \left[ \boldsymbol {S} \sqrt {\lambda} \boldsymbol {S} \right], \quad \boldsymbol {Q} _ {*} = \left[ \boldsymbol {Q} \sqrt {\lambda} \boldsymbol {\mu} \right], \tag {9}
+$$
+
+where  $\lambda$  is the coefficient of the regularization term which is always set as a positive number. Hence, equality holds for
+
+$$
+\left\| Q _ {*} - W S _ {*} \right\| ^ {2} = \left\| Q - W S \right\| ^ {2} + \lambda \left\| \boldsymbol {\mu} - W S \right\| ^ {2}, \tag {10}
+$$
+
+and the form in Eq. (6) can be written as
+
+$$
+\bar {W} = \underset {W} {\arg \min } \| Q _ {*} - W S _ {*} \| ^ {2}. \tag {11}
+$$
+
+Based on the conclusion in Eq. (8), the solution for our optimization process is
+
+$$
+\begin{array}{l} \bar {W} = Q _ {*} S _ {*} ^ {\top} \left(S _ {*} ^ {\top} S _ {*}\right) ^ {- 1} \tag {12} \\ = \left(\boldsymbol {Q} \boldsymbol {S} ^ {\top} + \lambda \cdot \boldsymbol {\mu} \boldsymbol {S} ^ {\top}\right) \left(\boldsymbol {S} ^ {\top} \boldsymbol {S} + \lambda \cdot \boldsymbol {S} \boldsymbol {S} ^ {\top}\right) ^ {- 1}. \\ \end{array}
+$$
+
+# 3.4. Anomaly Detection with Reconstruction
+
+After getting the reconstruction query feature maps  $\bar{Q}$ , we align it with those from the original query sample  $\mathbf{Q}$  to estimate the pixel-level anomaly segmentation map and image-level anomaly score. For pixel  $i$  in the query image, the anomaly score  $m_{i}$  is calculated as:
+
+$$
+m _ {i} = \left\| Q _ {i} - \bar {Q} _ {i} \right\| ^ {2}, i \in \mathcal {N}, \tag {13}
+$$
+
+where  $\mathcal{N}$  denotes the collection of all pixel indices in  $Q$ .  $Q_{i}$  denotes the relevant feature vector of pixel  $i$ . For image-level classification, we use the maximum distance score  $s^{*}$  among all the pixels to represent the image-level score as
+
+$$
+s ^ {*} = \max  \left\{\left\| Q _ {i} - \bar {Q} _ {i} \right\| ^ {2} \mid i \in \mathcal {N} \right\}. \tag {14}
+$$
+
+Besides, similar to [28, 7], to match the original input resolution, the segmentation map should be up-scaled with bilinear interpolation. Finally, we smoothed the segmentation map with a Gaussian of kernel width of 4.
+
+# 4. Experiment
+
+# 4.1. Experimental Setups
+
+Dataset. We evaluated the performance of our model by using the MVTec AD dataset [3] and MPDD [15], which are the real-world benchmarks for AD. MVTec dataset includes 5354 images in 15 categories. 3629 of these images are defect-free and the remaining 1725 have defects. Each category has an average of five different types of defects. The image resolution ranges from  $700 \times 700$  to  $1024 \times 1024$ . MPDD dataset contains 6 classes of metal productions. Images taken from different distances and spatial directions, as well as the non-uniform backgrounds, make the AD task on this dataset extremely difficult. The MPDD dataset includes 888 normal images in the training set and 176 normal images and 282 abnormal images in the test set with the resolution of  $1024 \times 1024$ . Additionally, both datasets provide ground truth of defective regions on pixel level.
+
+Competing Methods. We compare our method with previous state-of-the-art FSAD and also full-data AD methods. The methods for comparison include GANomaly [1], ARNet [27], MKD [20], CutPaste [24], FYD [32], PaDiM [7], PatchCore [18], CflowAD [11], TDG [23], DiffNet [19] and RegAD [13].
+
+Evaluation Protocols. We measure the model performance with the area under the Receiver Operating Characteristic curve (AUROC) on classification results. We use image-level AUROC to evaluate the sample detection results and pixel-level AUROC to measure the defects localization performance.
+
+Implementation Details. In our experiment, we used a ResNet-50 [12] model pre-trained on ImageNet for feature extraction. We extract features from the 2 middle-level layers of the model. For both MVtec and MPDD datasets, all the support and query images are reshaped to  $368 \times 368$  for training and inference. For all the experiments, the coefficient  $\lambda$  for our regularization term is set as 0.3, and the corset selection sampling rate  $s$  is set as 0.15. All the experiments are conducted on one NVIDIA GTX 3090 GPU.
+
+# 4.2. Experiment Results
+
+# 4.2.1 Comparison with State-of-the-art Methods
+
+Few-shot AD averaged performance. Tab. 1 shows FSAD averaged performance on both MVTec and MPDD datasets. Our method (FastRecon) obtains the best performances under all experimental settings. Specifically, FastRecon improves image-level AUROC by  $5.27\%$ ,  $6.04\%$ ,  $3.99\%$  on MVTec and  $10.25\%$ ,  $11.55\%$ $10.60\%$  on MPDD over the current state-of-the-art FSAD method RegAD for 2-shot, 4-shot, and 8-shot scenarios respectively. For pixel-level AUROC, FastRecon also outperforms RegAD
+
+<table><tr><td></td><td></td><td colspan="6">AUROC at Image-level</td><td colspan="4">AUROC at Pixel-level</td></tr><tr><td>Dataset</td><td>k</td><td>TDG [23]</td><td>DiffNet [19]</td><td>RegAD [13]</td><td>PaDiM [7]</td><td>PatchCore [18]</td><td>FastRcon (ours)</td><td>RegAD [13]</td><td>PaDiM [7]</td><td>PatchCore [18]</td><td>FastRcon (ours)</td></tr><tr><td rowspan="3">MVTec</td><td>2</td><td>71.20</td><td>80.60</td><td>85.70</td><td>78.90</td><td>87.81</td><td>90.97</td><td>94.60</td><td>90.50</td><td>94.75</td><td>95.86</td></tr><tr><td>4</td><td>72.70</td><td>81.30</td><td>88.20</td><td>71.60</td><td>89.49</td><td>94.24</td><td>95.80</td><td>80.20</td><td>94.99</td><td>96.98</td></tr><tr><td>8</td><td>75.20</td><td>83.20</td><td>91.20</td><td>75.30</td><td>94.31</td><td>95.19</td><td>96.70</td><td>80.50</td><td>95.60</td><td>97.27</td></tr><tr><td rowspan="3">MPDD</td><td>2</td><td>60.30</td><td>60.20</td><td>63.40</td><td>-</td><td>59.55</td><td>73.65</td><td>93.20</td><td>-</td><td>79.15</td><td>97.03</td></tr><tr><td>4</td><td>63.50</td><td>63.30</td><td>68.30</td><td>-</td><td>59.78</td><td>79.85</td><td>93.90</td><td>-</td><td>79.82</td><td>97.60</td></tr><tr><td>8</td><td>68.20</td><td>68.50</td><td>71.90</td><td>-</td><td>59.95</td><td>82.50</td><td>95.10</td><td>-</td><td>80.30</td><td>97.92</td></tr></table>
+
+Table 1: FSAD performance comparisons on MVtec and MPDD dataset. The results are averaged over all categories. Both image-level and pixel-level performances are reported in AUROC (\%)  $\uparrow$ .  $k$  denotes the number of shots in our few-shot settings. The best results for different settings are in bold.  
+
+<table><tr><td></td><td colspan="2">RegAD [13]</td><td colspan="2">PatchCore [18]</td><td colspan="2">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bottle</td><td>99.40</td><td>98.40</td><td>99.60</td><td>98.60</td><td>99.44</td><td>98.50</td></tr><tr><td>Cable</td><td>76.10</td><td>92.70</td><td>97.40</td><td>97.90</td><td>93.79</td><td>96.12</td></tr><tr><td>Capsule</td><td>72.40</td><td>97.60</td><td>66.30</td><td>97.70</td><td>90.07</td><td>98.96</td></tr><tr><td>Carpet</td><td>97.90</td><td>98.90</td><td>99.00</td><td>99.00</td><td>99.90</td><td>99.15</td></tr><tr><td>Grid</td><td>91.20</td><td>85.70</td><td>63.00</td><td>70.60</td><td>88.81</td><td>86.32</td></tr><tr><td>Hazelnut</td><td>95.80</td><td>98.00</td><td>92.80</td><td>97.00</td><td>99.32</td><td>98.59</td></tr><tr><td>Leather</td><td>100.00</td><td>99.10</td><td>100.00</td><td>96.90</td><td>100.00</td><td>99.20</td></tr><tr><td>Metal_Nut</td><td>94.60</td><td>97.80</td><td>94.70</td><td>97.00</td><td>99.12</td><td>98.72</td></tr><tr><td>Pill</td><td>80.80</td><td>97.40</td><td>89.00</td><td>96.90</td><td>93.48</td><td>98.32</td></tr><tr><td>Screw</td><td>56.60</td><td>95.00</td><td>54.10</td><td>92.10</td><td>62.46</td><td>97.10</td></tr><tr><td>Tile</td><td>95.50</td><td>94.90</td><td>100.00</td><td>96.00</td><td>100.00</td><td>96.73</td></tr><tr><td>Toothbrush</td><td>90.90</td><td>98.50</td><td>95.20</td><td>98.80</td><td>93.61</td><td>99.04</td></tr><tr><td>Transistor</td><td>85.20</td><td>93.80</td><td>98.40</td><td>95.00</td><td>97.29</td><td>94.18</td></tr><tr><td>Wood</td><td>98.60</td><td>94.70</td><td>97.40</td><td>93.10</td><td>99.29</td><td>94.94</td></tr><tr><td>Zipper</td><td>88.50</td><td>94.00</td><td>95.50</td><td>98.30</td><td>96.95</td><td>98.89</td></tr><tr><td>Average</td><td>88.20</td><td>95.80</td><td>89.49</td><td>94.99</td><td>94.24</td><td>96.98</td></tr></table>
+
+by  $1.26\%$ ,  $1.18\%$ ,  $0.57\%$  on MVTev and  $3.83\%$ ,  $3.70\%$ ,  $2.82\%$  on MPDD respectively.
+
+Few-shot AD categorical performances. Tab. 2 and Tab. 3 show the FSAD categorical performance. As shown in Tab. 2, FastRecon outperforms all the baselines in 10 out of 15 categories at the image level and in 12 out of 15 categories at the pixel level. And as shown in Tab. 3, FastRecon outperforms all the baselines in 4 out of 6 categories at the image level and in all categories at the pixel level.
+
+Comparison with full-data AD. Tab. 4 shows the comparison of our method with AD methods which utilize the whole normal samples. Results show that our FastRecon has competitive performance compared with full-data methods, indicating the high data efficiency of our model.
+
+Table 2: FSAD categorical performance comparisons in AUROC (\%)  $\uparrow$  on MVTec dataset. Results are from the setting of shot  $k = 4$ . The best results are in bold. Our method achieves the best performance in most categories.  
+
+<table><tr><td></td><td colspan="2">RegAD [13]</td><td colspan="2">PatchCore [18]</td><td colspan="2">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bracket/black</td><td>63.80</td><td>-</td><td>58.90</td><td>79.10</td><td>71.81</td><td>95.54</td></tr><tr><td>Bracket_brown</td><td>66.10</td><td>-</td><td>70.80</td><td>77.30</td><td>63.34</td><td>95.93</td></tr><tr><td>Bracket_white</td><td>59.30</td><td>-</td><td>70.70</td><td>69.30</td><td>69.44</td><td>98.89</td></tr><tr><td>Connector</td><td>77.20</td><td>-</td><td>59.40</td><td>86.40</td><td>97.62</td><td>98.04</td></tr><tr><td>Metal_plate</td><td>78.60</td><td>-</td><td>64.40</td><td>86.70</td><td>100.00</td><td>99.29</td></tr><tr><td>Tubes</td><td>67.50</td><td>-</td><td>34.50</td><td>80.10</td><td>76.90</td><td>97.89</td></tr><tr><td>Average</td><td>68.30</td><td>93.90</td><td>59.78</td><td>79.82</td><td>79.85</td><td>97.60</td></tr></table>
+
+Table 3: FSAD categorical performance comparisons in AUROC (\%)  $\uparrow$  on MPDD dataset. Results are from the setting of shot  $k = 4$ . The best results are in bold. Our method achieves the best performance in most categories.  
+
+<table><tr><td colspan="3"></td><td colspan="2">MVTec AD</td><td colspan="2">MPDD</td></tr><tr><td>Method</td><td>Data</td><td>Backbone</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>FastRecon</td><td>2</td><td>WRN50</td><td>90.97</td><td>95.86</td><td>73.65</td><td>97.03</td></tr><tr><td>FastRecon</td><td>4</td><td>WRN50</td><td>94.24</td><td>96.98</td><td>79.85</td><td>97.60</td></tr><tr><td>FastRecon</td><td>8</td><td>WRN50</td><td>95.19</td><td>97.27</td><td>82.50</td><td>97.92</td></tr><tr><td>GANomaly [1]</td><td>Full</td><td>Unet</td><td>80.50</td><td>-</td><td>64.80</td><td>-</td></tr><tr><td>ARNet [27]</td><td>Full</td><td>Unet</td><td>83.90</td><td>-</td><td>69.70</td><td>-</td></tr><tr><td>MKD [20]</td><td>Full</td><td>Res18</td><td>87.70</td><td>90.70</td><td>-</td><td>-</td></tr><tr><td>FYD [32]</td><td>Full</td><td>Res18</td><td>97.30</td><td>97.40</td><td>-</td><td>-</td></tr><tr><td>PaDiM [7]</td><td>Full</td><td>WRN50</td><td>97.90</td><td>97.50</td><td>74.80</td><td>96.70</td></tr><tr><td>PatchCore [18]</td><td>Full</td><td>WRN50</td><td>99.10</td><td>98.10</td><td>82.10</td><td>95.70</td></tr><tr><td>CflowAD [11]</td><td>Full</td><td>WRN50</td><td>98.60</td><td>98.60</td><td>86.10</td><td>97.70</td></tr></table>
+
+Table 4: AD performance comparisons in AUROC  $(\%)$  ↑ on MVTec and MPDD dataset with full-data methods which utilize the whole dataset in training. Both image-level and pixel-level performances are averaged over all categories. The Data column denotes different usage of the dataset.
+
+Speed performance of FastRecon. Speed comparisons on both training and inference are shown in the following Tab. 5. For FastRecon, training stage consists of feature extraction, feature subsampling and calculation on transfor
+
+![](images/d776065b7544db0615f0589064a6374347446c6200f668fc5ea0292674a077b7.jpg)  
+Figure 4: Qualitative results of anomaly localization for both MVTec and MPDD datasets. The first row in the red box presents the support sample for each category while the second row indicates the query samples. The results show that our method can provide accurate localization of defect regions even for more complicated patterns in MPDD.
+
+![](images/c0cd66bc11cfb004d56653a5475a5a52a02710423a7fe22f3d1a845ef5523617.jpg)  
+Figure 5: Visualization of decoding results on reconstructed query features. With a pretrained image decoder, we investigate the transformed query features in the MVtec dataset. The first row shows the original query image, and the middle row shows the images decoded from the original query features. The last row represents the image decoded from the reconstructed query feature map. Our method can reveal the normal side of the defective query samples.
+
+<table><tr><td></td><td>Aggregated Training</td><td>Training Time</td><td>Inference Time</td></tr><tr><td>PatchCore</td><td>No</td><td>80.37</td><td>0.60</td></tr><tr><td>RegAD (k=2)</td><td>Yes</td><td>660.80</td><td>0.05</td></tr><tr><td>FastRecon (k=8)</td><td>No</td><td>1.95</td><td>0.04</td></tr><tr><td>FastRecon (k=2)</td><td>No</td><td>0.52</td><td>0.04</td></tr></table>
+
+Table 5: Training and inference speed comparisons in seconds. RegAD requires additional training on aggregated features. The inference speed is evaluated as averaged inference time per query sample. FastRecon achieves overall best speed performance with 2 and 8 shots.
+
+mation matrix. FastRecon achieves the best performance.
+
+# 4.3. Visualization
+
+Localization of anomaly detection Fig. 4 demonstrates visual examples of anomaly detection on MVTec and MPDD. Most defects can be accurately identified.
+
+Decoding results on reconstructed query feature. In order to better reflect the reconstruction ability of FastRecon, a feature decoder is built to visualize the query sample from reconstructed feature maps. The decoder is trained with full MVTec dataset to learn to decode image sample from feature maps. Fig. 5 shows that, images decoded from reconstructed feature maps maintain the normality of the normal samples, which illustrates the effectiveness of our approach.
+
+![](images/b04dbb283130a3c3550b987e19a2e32336bb190697feeef75804ea3f163e4a16.jpg)  
+(a) Sampling Rate  $s$
+
+![](images/9bf3c50330417414c6c713a50630eee1a728d5061ed36a96435c04aacd3a323e.jpg)  
+(b) Coefficient  $\lambda$  of Regularization Term
+
+![](images/f5b51b470c35bdefd27e1e6afcba4f56ecfa70483c4117db9eecfe649271df19.jpg)  
+(c) Resolution  $r$
+
+![](images/fc77ce6651bcabc7e720c752faaf4c21744a254ecb3fec5714b576c3795631ee.jpg)  
+Figure 6: Effect of three hyper-parameters comparisons in AUROC (\%) on MVTec dataset. (a) AD performance with different sampling rate  $s$ . (b) AD performance with different coefficient  $\lambda$ . (c) AD performance with different resolution  $r$ .
+
+![](images/92a55d12dd9fb1a76aaf04e9858e180b5aeda32c34fe0c914e37d594757be312.jpg)  
+Figure 7: AD performance comparisons in AUROC (\%) on MVTec dataset between ridge regression and proposed regularization. Our results, displayed in blue, are better than ridge regression at both image and pixel levels.
+
+# 4.4. Ablation Studies
+
+In this section, we ablate the core parts of our proposed method to investigate its impact on the final performance. We also discuss the effect of hyper-parameters, which are the coefficient of regularization term  $\lambda$ , the resolution of input data, and the coreset selection sampling ratio  $s$ .
+
+Effect of sampling Rate  $s$ . Fig. 6 (a) illustrates the relationship between the Sampling Rate  $s$  and AUROC performance. The sampling rate  $s$  decides the number of feature points in the support feature pool. As shown in Fig. 6 (a), the optimal sampling rate is around 0.45.
+
+Impact of the distribution regularization term and coefficient  $\lambda$ . In Fig. 7, FastRecon obtains better AUROC performance at both image and pixel levels. It reflects the significance of our proposed distribution regularization. Fig. 6 (b) shows the relationship between coefficient  $\lambda$  of regularization term and AUROC performance for 4-shot and 8-shot scenarios. When  $\lambda$  equals 0.3, the AUROC performances are best at both image and pixel levels.
+
+Effect of image resolution  $r$ . In our experiment, images, no matter how much the original resolutions are, should be reshaped to new resolution  $r \times r$ . Fig. 6 (c) reflects the relationship between resolution  $r$  and AUROC performance. The resolution will affect the feature points. As shown in Fig. 6 (c), when the resolution equals 368, FastRecon performs well at both image and pixel levels.
+
+# 5. Conclusion
+
+In this paper, a novel method FastRecon is proposed for few-shot anomaly detection based on feature reconstruction. For each query sample, we construct their normal version, referenced by a limited number of normal features. To ensure the reconstructed result shares high visual similarity with the query sample while maintaining the property of the normal sample, a regression equation with proposed distribution regularization is proposed, to obtain the optimal transformation from support to query features. With this fast and accurate reconstruction, the final anomaly detection could be accomplished by a simple alignment. Experimental results show the state-of-the-art performance of our method for 2-shot, 4-shot, and 8-shot scenarios.
+
+Acknowledgements. This work was supported by National Key R&D Program of China (No.2022YFE0200300), National Natural Science Foundation of China (No.61972323).
+
+# References
+
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\ No newline at end of file
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+                                    "content": "In industrial anomaly detection, data efficiency and the ability for fast migration across products become the main concerns when developing detection algorithms. Existing methods tend to be data-hungry and work in the one-model-one-category way, which hinders their effectiveness in real-world industrial scenarios. In this paper, we propose a few-shot anomaly detection strategy that works in a low-data regime and can generalize across products at no cost. Given a defective query sample, we propose to utilize a few normal samples as a reference to reconstruct its normal version, where the final anomaly detection can be achieved by sample alignment. Specifically, we introduce a novel regression with distribution regularization to obtain the optimal transformation from support to query features, which guarantees the reconstruction result shares visual similarity with the query sample and meanwhile maintains the property of normal samples. Experimental results show that our method significantly outperforms previous state-of-the-art at both image and pixel-level AUROC performances from 2 to 8-shot scenarios. Besides, with only a limited number of training samples (less than 8 samples), our method reaches competitive performance with vanilla AD methods which are trained with extensive normal samples. The code is available at https://github.com/FzJun26th/ FastRecon."
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+                                            "content": "Figure 1: Comparison of our FastRecon with (a) Vanilla Reconstruction-based method and (b) Vanilla Feature-Matching-based method. Compared with (a), our method needs no training session and requires less normal samples for feature reconstruction. Compared with (b), our method applies direct pixel-to-pixel alignment between the test sample and reconstruction result for anomaly detection without an exhaustive feature searching process, thus being more efficient in inference."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "content": "cently [31, 16, 9]. The difficulty of industrial AD lies in the diversity of the defects, which can take different forms, from subtle flaws like slight bruises, to obvious ones such as missing components [3]. This makes it difficult to detect and classify anomalies. Primal researches focus on utilizing supervised learning to tackle industrial AD [5, 17]. However, such a learning paradigm often requires an exhaustive set of anomalous samples for each category, which can be"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+                                    "content": "naturally rare to collect, making it inefficient for real-world industrial scenarios."
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+                                    "content": "Recent works pay attention to learning with limited or even no supervision to overcome the problem caused by the lack of anomalous samples. As shown in Fig. 1 (a), reconstruction-based industrial AD [34, 10, 26, 14] utilizes generative models such as autoencoder to learn the distribution of normal samples through the cumbersome training process. As in Fig. 1 (b), recent researches favor feature-matching strategy [28, 7] that conducts feature comparison between the test sample and memory bank of normal features, where the feature searching causes high computational complexity. Both lines of work require massive normal samples either for model training or memory construction, only to achieve detection for a single product category, and fail to quickly generalize across products."
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+                                    "content": "10.25%, 11.55%, 10.60% on MPDD, at image-level AUROC under 2-shot, 4-shot and 8-shot scenarios, respectively. The contributions of this work are summarized below:"
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+                                            "content": "1. We propose a few-shot and category-agnostic industrial AD strategy which adopts sample alignment between the original test sample and its reconstructed normal version."
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+                                            "type": "text",
+                                            "content": ", to share similarity with "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " but keeps all the property of normal samples. Finally, we align "
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+                                            "type": "inline_equation",
+                                            "content": "\\bar{Q}"
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+                                            "type": "text",
+                                            "content": " and "
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+                                            "type": "text",
+                                            "content": " for direct comparison to obtaining the anomaly estimation."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "comes the main obstacle for fast model migration in real industrial scenarios."
+                                }
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+                    ],
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+                                    "content": "3. Methodology"
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+                                    "content": "In this section, we introduce the details of FastRecon. Firstly, we define the one-class classification problem in industrial anomaly detection. FastRecon contains 3 parts: feature extraction and coreset selection, regression with distribution regularization, and anomaly detection with reconstruction. The overview of our method is shown in Fig. 2."
+                                }
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+                                    "content": "3.1. Problem Definition"
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+                                    "content": "We formally define the problem for one-class classification of industrial anomaly detection. Following the few-shot learning setting, in an "
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+                                    "content": " categories is given, i.e., "
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+                                    "type": "inline_equation",
+                                    "content": "S = \\bigcup_{i=1}^{n} T_i"
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+                                    "type": "text",
+                                    "content": ", where the subset "
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+                                    "content": " consists of "
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " normal samples from category "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". During test time, a query sample, whether normal or anomalous, is presented. The model predicts whether or not the sample is anomalous at the pixel and image level."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "3.2. Feature Extraction and Coreset Selection"
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+                                    "type": "text",
+                                    "content": "Existing studies [7, 28] have shown that extracted features from pre-trained CNNs perform well in the anomaly"
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+                                    "type": "text",
+                                    "content": "detection task. We also utilize a pre-trained ResNet-50 to output a patch-level feature map of an image. "
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+                                    "type": "inline_equation",
+                                    "content": "\\phi_{i,j}"
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+                                    "type": "text",
+                                    "content": " is used to denote hierarchy-level "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " of the pre-trained network "
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+                                    "type": "inline_equation",
+                                    "content": "\\phi"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for the image "
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+                                    "type": "inline_equation",
+                                    "content": "x_{i} \\in X"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (dataset "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "j \\in \\{1,2,3,4\\}"
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+                                    "type": "text",
+                                    "content": ". We adopt the intermediate features of the hierarchy-level, i.e., "
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+                                    "content": "j \\in \\{2,3\\}"
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+                                    "type": "text",
+                                    "content": ". The resulting feature map has a dimension of "
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+                                    "type": "inline_equation",
+                                    "content": "H \\times W \\times D"
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "text",
+                                    "content": ", "
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are the height and width of the largest activation map used to generate the embedding, and "
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+                                    "type": "text",
+                                    "content": " is the total number of channels of both activation maps used to generate embedding."
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+                                    "content": "To facilitate calculations, the feature map is reshaped from 3-dimension "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". Features in the reshaped map represent embedding vectors, i.e., the local aware patch features. In a "
+                                },
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+                                    "content": "-shot setting, our ultimate support feature pool is obtained by concatenating features of "
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+                                    "type": "text",
+                                    "content": ". Besides, following [18], we take a coreset sampling operation to get a coreset "
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+                                    "type": "text",
+                                    "content": " is the number of clustering centers computed with K-greedy algorithm. The coverage of "
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+                                    "content": " is comparable to the original support feature pools but with a smaller scale so that the computational complexity and the performance of detection could be balanced. For a query image, with the same pretrained network, it is also extracted to patch-level feature map "
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+                                    "type": "text",
+                                    "content": ". The process of feature extraction and coreset is"
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+                                            "type": "text",
+                                            "content": "Figure 3: Visual comparison of decoding results on reconstructed features. We train a decoder on features of the whole dataset for image recovery, which is used to probe the transformed features from the encoder. (a) The original query image with defects region in red boxes. (b) Decoding results on original query features. (c) Decoding results on transformed features by ridge regression. The defects regions are reconstructed as on original query features. (d) Decoding results on transformed features by the proposed regression, which shares visual similarity with the original query image but with the property of normal samples."
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+                                    "type": "text",
+                                    "content": "shown in the brown region in Fig. 2."
+                                }
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+                                    "content": "3.3. Regression with Distribution Regularization"
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+                                    "type": "text",
+                                    "content": "Why Ridge Regression fails. The goal is to reconstruct query feature map "
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+                                    "type": "text",
+                                    "content": " as a linear transformation of S-coreset "
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+                                    "type": "text",
+                                    "content": " by finding an optimal transformation weight "
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+                                    "type": "text",
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+                                    "content": " has most properties of normal samples. Searching for optimal weight "
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+                                    "type": "text",
+                                    "content": " amounts to solving the linear least-squares problem [25]. With original ridge regression, the optimization takes the following form:"
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {\\boldsymbol {W}} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2} + \\lambda \\| \\boldsymbol {W} \\| ^ {2}, \\tag {1}",
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+                                    "type": "text",
+                                    "content": " is the weight of the penalty term and "
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+                                    "type": "inline_equation",
+                                    "content": "\\| \\cdot \\|"
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+                                    "type": "text",
+                                    "content": " representing the Frobenius norm. The penalty term in ridge regression, i.e., "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\| W\\|^2"
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+                                    "type": "text",
+                                    "content": ", ensures tractability when the linear system is over- or under-constrained. However, the transformation obtained from ridge regression can cause the reconstructed sample to deviate significantly from the distribution of normal samples, i.e., after the transformation, the result "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " can be too close to "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " so that features of defect regions are reconstructed as in "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". As shown in Fig. 3 column (c), the decoding results on reconstructed features share excessively high similarity with the original query image with defects regions being reconstructed."
+                                }
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+                                    "type": "text",
+                                    "content": "The distribution regularization. In our work, we propose a distributional regularization term to replace the original penalty term in ridge regression, which effectively enhances the normality of the reconstruction result "
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+                                    "type": "inline_equation",
+                                    "content": "W S"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". We first model the distribution of normal feature maps by an isotropic Gaussian density function denoted as "
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+                                    "type": "inline_equation",
+                                    "content": "f(\\boldsymbol{X}|\\boldsymbol{\\mu},\\boldsymbol{\\Sigma})"
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+                                    "type": "text",
+                                    "content": " is the mean and co-variance estimated by the support set feature maps. We design the regularization term as "
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+                                    "type": "inline_equation",
+                                    "content": "|f(WS) - f(\\pmb{\\mu})|"
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+                                    "type": "text",
+                                    "content": " and the proposed regression has the form as:"
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {\\boldsymbol {W}} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2} + \\lambda | f (\\boldsymbol {W} \\boldsymbol {S}) - f (\\boldsymbol {\\mu}) |, \\tag {2}",
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+                                    "type": "text",
+                                    "content": " denotes the coefficient that controls the contribution of the regularization. When searching the optimal transformation "
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+                                    "type": "text",
+                                    "content": ", the optimization of the first term "
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+                                    "type": "inline_equation",
+                                    "content": "\\|Q - WS\\|^2"
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+                                    "type": "text",
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+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "WS"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " towards original query feature maps "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", while with the proposed regularization "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|f(WS) - f(\\pmb{\\mu})|"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", we force the constructed "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "WS"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        156,
+                                        545,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " to lie in the high probability density region in the distribution, that is, somewhere close to the distribution center. The visualization of distribution regularization is shown in the grey region of Fig. 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        305,
+                        278,
+                        545,
+                        374
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                278,
+                                545,
+                                374
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": "The approximation for closed-form solution. The density function inside the regularization term in Eq. (2) prevents us from having a closed-form solution for the regression, which hinders fast calculation of the transformation. Thus, we propose an approximated version of Eq. (2) with the help of Taylor's theorem for multivariable functions on the distribution density function "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": ". Taylor's expansion for "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(x)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        278,
+                                        545,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " is shown as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                        382,
+                        545,
+                        415
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                382,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        382,
+                                        545,
+                                        415
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "f (\\boldsymbol {x}) \\approx f (\\boldsymbol {a}) + \\nabla f (\\boldsymbol {a}) (\\mathbf {x} - \\boldsymbol {a}) + \\frac {1}{2} (\\mathbf {x} - \\boldsymbol {a}) ^ {T} H f (\\boldsymbol {a}) (\\mathbf {x} - \\boldsymbol {a}), \\tag {3}",
+                                    "image_path": "f5549e4870eddb777718d0bd9a927259d43566b539cc4a2152eb594334964081.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
+                        305,
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+                        475
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                415,
+                                545,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Hf(\\pmb{a})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes Hessian matrix of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\pmb{x})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{a}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": ". And we approximate the density function with the first and second-order term of Taylor's expansion, where the first-order term is 0 at "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\mu}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": ". Following Eq. (3), we expand the probability density function "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(WS)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\mu}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        415,
+                                        545,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        309,
+                                        483,
+                                        545,
+                                        530
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} f (\\boldsymbol {W} \\boldsymbol {S}) \\approx f (\\boldsymbol {\\mu}) + \\nabla f (\\boldsymbol {\\mu}) (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) \\\\ + \\frac {1}{2} (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) ^ {T} H f (\\boldsymbol {\\mu}) (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}). \\tag {4} \\\\ \\end{array}",
+                                    "image_path": "b78456622fed9de1c49f8c2d9d1b4c80b1d0466dd13dd90f081dc6d027a30f9c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": "Since our assumed data distribution is isotropic Gaussian, its covariance matrix can be represented as "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\Sigma} = \\sigma^2\\pmb{I}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma^2"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " is the variance for all dimensions. Then, we have the term "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla f(\\pmb{\\mu})(\\pmb{W}\\pmb{S} - \\pmb{\\mu})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " as 0, and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Hf(\\pmb{\\mu})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " equals the "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\Sigma}^{-1}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " which is the inverse of the covariance matrix. Then, by placing "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
+                                        545,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\pmb{\\mu})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        531,
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+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " to the left, we have"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} f (\\boldsymbol {W} \\boldsymbol {S}) - f (\\boldsymbol {\\mu}) \\approx \\frac {1}{2} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) ^ {T} \\boldsymbol {\\Sigma} ^ {- 1} (\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}) \\\\ = \\frac {1}{2 \\sigma^ {2}} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) ^ {T} \\boldsymbol {I} \\left(\\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu}\\right) \\tag {5} \\\\ = \\frac {1}{2 \\sigma^ {2}} \\| \\boldsymbol {W} \\boldsymbol {S} - \\boldsymbol {\\mu} \\| ^ {2}, \\\\ \\end{array}",
+                                    "image_path": "619462e716f98f414dc6829293c1cad2f18cd0eca602611025bc053f5cea7bd2.jpg"
+                                }
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+                    "index": 23
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+                {
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is an identity matrix. Then we merge the coefficient "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{1}{2\\sigma^2}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " into "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the approximated version of the optimization"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "target in Eq. (2) is:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\bar {W} = \\underset {W} {\\arg \\min } \\| Q - W S \\| ^ {2} + \\lambda \\| W S - \\mu \\| ^ {2}. \\tag {6}",
+                                    "image_path": "ddbff2b972afe0d8e974e909e9caae8d3b6b637735abba9cf77356f276a3da71.jpg"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Finding the optimal transformation. Knowing that the following optimization target of least square error (LSE) of"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {W} ^ {\\prime} = \\underset {\\boldsymbol {W}} {\\arg \\min } \\| \\boldsymbol {Q} - \\boldsymbol {W} \\boldsymbol {S} \\| ^ {2}, \\tag {7}",
+                                    "image_path": "8e1d2b77955ba70f343cddb701e517ded6029bdde745f2511b50183bfafd5f62.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "has the closed-form solution as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {W} ^ {\\prime} = \\boldsymbol {Q} \\boldsymbol {S} ^ {\\top} \\left(\\boldsymbol {S} ^ {\\top} \\boldsymbol {S}\\right) ^ {- 1}, \\tag {8}",
+                                    "image_path": "1fb4f26af187140a06cab7d1a0394d58c6b03703474771343664f663fdfaa37c.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "to utilize the conclusion from Eq. (8), we transform Eq. (6) by variable substitution to fit the form of Eq. (8). Let "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "S_*"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        217,
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+                                    ],
+                                    "type": "text",
+                                    "content": " be the column-wise augmented version of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " respectively:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {S} _ {*} = \\left[ \\boldsymbol {S} \\sqrt {\\lambda} \\boldsymbol {S} \\right], \\quad \\boldsymbol {Q} _ {*} = \\left[ \\boldsymbol {Q} \\sqrt {\\lambda} \\boldsymbol {\\mu} \\right], \\tag {9}",
+                                    "image_path": "9c07d6ae36189bc35e672f73a9b246216787eee6bb164ce264ae8535cc817a84.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the coefficient of the regularization term which is always set as a positive number. Hence, equality holds for"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\left\\| Q _ {*} - W S _ {*} \\right\\| ^ {2} = \\left\\| Q - W S \\right\\| ^ {2} + \\lambda \\left\\| \\boldsymbol {\\mu} - W S \\right\\| ^ {2}, \\tag {10}",
+                                    "image_path": "65c4de9ef761e89542a7397c1fb2cd57afd8083fab8d1c7554392b1d8c0cd819.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "and the form in Eq. (6) can be written as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {W} = \\underset {W} {\\arg \\min } \\| Q _ {*} - W S _ {*} \\| ^ {2}. \\tag {11}",
+                                    "image_path": "d8b2ee8d28bba2ee812014cbc0a696898f7fc87ca24135ef04b503b269c21d30.jpg"
+                                }
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Based on the conclusion in Eq. (8), the solution for our optimization process is"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\bar {W} = Q _ {*} S _ {*} ^ {\\top} \\left(S _ {*} ^ {\\top} S _ {*}\\right) ^ {- 1} \\tag {12} \\\\ = \\left(\\boldsymbol {Q} \\boldsymbol {S} ^ {\\top} + \\lambda \\cdot \\boldsymbol {\\mu} \\boldsymbol {S} ^ {\\top}\\right) \\left(\\boldsymbol {S} ^ {\\top} \\boldsymbol {S} + \\lambda \\cdot \\boldsymbol {S} \\boldsymbol {S} ^ {\\top}\\right) ^ {- 1}. \\\\ \\end{array}",
+                                    "image_path": "73d5e8b3856f4360b6ad755b6de398d3607db3f9a8c8bea6a091cc5d6c3e2938.jpg"
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+                                    "type": "text",
+                                    "content": "3.4. Anomaly Detection with Reconstruction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "After getting the reconstruction query feature maps "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{Q}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
+                                        287,
+                                        561
+                                    ],
+                                    "type": "text",
+                                    "content": ", we align it with those from the original query sample "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
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+                                        561
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Q}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
+                                        287,
+                                        561
+                                    ],
+                                    "type": "text",
+                                    "content": " to estimate the pixel-level anomaly segmentation map and image-level anomaly score. For pixel "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
+                                        287,
+                                        561
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
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+                                        561
+                                    ],
+                                    "type": "text",
+                                    "content": " in the query image, the anomaly score "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
+                                        287,
+                                        561
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        501,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is calculated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "m _ {i} = \\left\\| Q _ {i} - \\bar {Q} _ {i} \\right\\| ^ {2}, i \\in \\mathcal {N}, \\tag {13}",
+                                    "image_path": "af918148a4dcf69c51359eea8946420369860895ecc8001c2ca7eb912c19d9d4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
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+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the collection of all pixel indices in "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the relevant feature vector of pixel "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "text",
+                                    "content": ". For image-level classification, we use the maximum distance score "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        589,
+                                        286,
+                                        637
+                                    ],
+                                    "type": "text",
+                                    "content": " among all the pixels to represent the image-level score as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        94,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "s ^ {*} = \\max  \\left\\{\\left\\| Q _ {i} - \\bar {Q} _ {i} \\right\\| ^ {2} \\mid i \\in \\mathcal {N} \\right\\}. \\tag {14}",
+                                    "image_path": "c533d15fba735530d57507d1838ecc00dc1b7493680ec7aa62cd7f217ffe2310.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        47,
+                                        665,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Besides, similar to [28, 7], to match the original input resolution, the segmentation map should be up-scaled with bilinear interpolation. Finally, we smoothed the segmentation map with a Gaussian of kernel width of 4."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4. Experiment"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "4.1. Experimental Setups"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Dataset. We evaluated the performance of our model by using the MVTec AD dataset [3] and MPDD [15], which are the real-world benchmarks for AD. MVTec dataset includes 5354 images in 15 categories. 3629 of these images are defect-free and the remaining 1725 have defects. Each category has an average of five different types of defects. The image resolution ranges from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        110,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "700 \\times 700"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        110,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        110,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1024 \\times 1024"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        110,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "text",
+                                    "content": ". MPDD dataset contains 6 classes of metal productions. Images taken from different distances and spatial directions, as well as the non-uniform backgrounds, make the AD task on this dataset extremely difficult. The MPDD dataset includes 888 normal images in the training set and 176 normal images and 282 abnormal images in the test set with the resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        110,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1024 \\times 1024"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        110,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "text",
+                                    "content": ". Additionally, both datasets provide ground truth of defective regions on pixel level."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        295,
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+                                        367
+                                    ],
+                                    "type": "text",
+                                    "content": "Competing Methods. We compare our method with previous state-of-the-art FSAD and also full-data AD methods. The methods for comparison include GANomaly [1], ARNet [27], MKD [20], CutPaste [24], FYD [32], PaDiM [7], PatchCore [18], CflowAD [11], TDG [23], DiffNet [19] and RegAD [13]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
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+                        545,
+                        444
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "content": "Evaluation Protocols. We measure the model performance with the area under the Receiver Operating Characteristic curve (AUROC) on classification results. We use image-level AUROC to evaluate the sample detection results and pixel-level AUROC to measure the defects localization performance."
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+                                    "content": "Implementation Details. In our experiment, we used a ResNet-50 [12] model pre-trained on ImageNet for feature extraction. We extract features from the 2 middle-level layers of the model. For both MVtec and MPDD datasets, all the support and query images are reshaped to "
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+                                    "content": " for training and inference. For all the experiments, the coefficient "
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+                                    "content": " for our regularization term is set as 0.3, and the corset selection sampling rate "
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+                                    "content": " is set as 0.15. All the experiments are conducted on one NVIDIA GTX 3090 GPU."
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+                                    "content": "4.2. Experiment Results"
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+                                    "content": " on MPDD over the current state-of-the-art FSAD method RegAD for 2-shot, 4-shot, and 8-shot scenarios respectively. For pixel-level AUROC, FastRecon also outperforms RegAD"
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+                                            "content": " denotes the number of shots in our few-shot settings. The best results for different settings are in bold."
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+                                    "content": "Comparison with full-data AD. Tab. 4 shows the comparison of our method with AD methods which utilize the whole normal samples. Results show that our FastRecon has competitive performance compared with full-data methods, indicating the high data efficiency of our model."
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+                                            "content": " on MVTec dataset. Results are from the setting of shot "
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+                                            "content": ". The best results are in bold. Our method achieves the best performance in most categories."
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+                                            "html": "<table><tr><td></td><td colspan=\"2\">RegAD [13]</td><td colspan=\"2\">PatchCore [18]</td><td colspan=\"2\">FastRecon</td></tr><tr><td>Category</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>Bracket/black</td><td>63.80</td><td>-</td><td>58.90</td><td>79.10</td><td>71.81</td><td>95.54</td></tr><tr><td>Bracket_brown</td><td>66.10</td><td>-</td><td>70.80</td><td>77.30</td><td>63.34</td><td>95.93</td></tr><tr><td>Bracket_white</td><td>59.30</td><td>-</td><td>70.70</td><td>69.30</td><td>69.44</td><td>98.89</td></tr><tr><td>Connector</td><td>77.20</td><td>-</td><td>59.40</td><td>86.40</td><td>97.62</td><td>98.04</td></tr><tr><td>Metal_plate</td><td>78.60</td><td>-</td><td>64.40</td><td>86.70</td><td>100.00</td><td>99.29</td></tr><tr><td>Tubes</td><td>67.50</td><td>-</td><td>34.50</td><td>80.10</td><td>76.90</td><td>97.89</td></tr><tr><td>Average</td><td>68.30</td><td>93.90</td><td>59.78</td><td>79.82</td><td>79.85</td><td>97.60</td></tr></table>",
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+                                            "content": " on MPDD dataset. Results are from the setting of shot "
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+                                            "content": ". The best results are in bold. Our method achieves the best performance in most categories."
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+                                            "html": "<table><tr><td colspan=\"3\"></td><td colspan=\"2\">MVTec AD</td><td colspan=\"2\">MPDD</td></tr><tr><td>Method</td><td>Data</td><td>Backbone</td><td>Image</td><td>Pixel</td><td>Image</td><td>Pixel</td></tr><tr><td>FastRecon</td><td>2</td><td>WRN50</td><td>90.97</td><td>95.86</td><td>73.65</td><td>97.03</td></tr><tr><td>FastRecon</td><td>4</td><td>WRN50</td><td>94.24</td><td>96.98</td><td>79.85</td><td>97.60</td></tr><tr><td>FastRecon</td><td>8</td><td>WRN50</td><td>95.19</td><td>97.27</td><td>82.50</td><td>97.92</td></tr><tr><td>GANomaly [1]</td><td>Full</td><td>Unet</td><td>80.50</td><td>-</td><td>64.80</td><td>-</td></tr><tr><td>ARNet [27]</td><td>Full</td><td>Unet</td><td>83.90</td><td>-</td><td>69.70</td><td>-</td></tr><tr><td>MKD [20]</td><td>Full</td><td>Res18</td><td>87.70</td><td>90.70</td><td>-</td><td>-</td></tr><tr><td>FYD [32]</td><td>Full</td><td>Res18</td><td>97.30</td><td>97.40</td><td>-</td><td>-</td></tr><tr><td>PaDiM [7]</td><td>Full</td><td>WRN50</td><td>97.90</td><td>97.50</td><td>74.80</td><td>96.70</td></tr><tr><td>PatchCore [18]</td><td>Full</td><td>WRN50</td><td>99.10</td><td>98.10</td><td>82.10</td><td>95.70</td></tr><tr><td>CflowAD [11]</td><td>Full</td><td>WRN50</td><td>98.60</td><td>98.60</td><td>86.10</td><td>97.70</td></tr></table>",
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+                                    "content": " ↑ on MVTec and MPDD dataset with full-data methods which utilize the whole dataset in training. Both image-level and pixel-level performances are averaged over all categories. The Data column denotes different usage of the dataset."
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+                                    "content": "Speed performance of FastRecon. Speed comparisons on both training and inference are shown in the following Tab. 5. For FastRecon, training stage consists of feature extraction, feature subsampling and calculation on transfor"
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+                                            "content": "Figure 6: Effect of three hyper-parameters comparisons in AUROC (\\%) on MVTec dataset. (a) AD performance with different sampling rate "
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+                                    "content": ", the resolution of input data, and the coreset selection sampling ratio "
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+                                    "type": "text",
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+                                    "content": ". Fig. 6 (a) illustrates the relationship between the Sampling Rate "
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+                                    "type": "text",
+                                    "content": " decides the number of feature points in the support feature pool. As shown in Fig. 6 (a), the optimal sampling rate is around 0.45."
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+                                    "type": "text",
+                                    "content": ". In Fig. 7, FastRecon obtains better AUROC performance at both image and pixel levels. It reflects the significance of our proposed distribution regularization. Fig. 6 (b) shows the relationship between coefficient "
+                                },
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+                                    "content": " of regularization term and AUROC performance for 4-shot and 8-shot scenarios. When "
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+                                    "type": "text",
+                                    "content": ". In our experiment, images, no matter how much the original resolutions are, should be reshaped to new resolution "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "r \\times r"
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+                                    "type": "text",
+                                    "content": ". Fig. 6 (c) reflects the relationship between resolution "
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+                                    "type": "text",
+                                    "content": " and AUROC performance. The resolution will affect the feature points. As shown in Fig. 6 (c), when the resolution equals 368, FastRecon performs well at both image and pixel levels."
+                                }
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+                                    "type": "text",
+                                    "content": "In this paper, a novel method FastRecon is proposed for few-shot anomaly detection based on feature reconstruction. For each query sample, we construct their normal version, referenced by a limited number of normal features. To ensure the reconstructed result shares high visual similarity with the query sample while maintaining the property of the normal sample, a regression equation with proposed distribution regularization is proposed, to obtain the optimal transformation from support to query features. With this fast and accurate reconstruction, the final anomaly detection could be accomplished by a simple alignment. Experimental results show the state-of-the-art performance of our method for 2-shot, 4-shot, and 8-shot scenarios."
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work was supported by National Key R&D Program of China (No.2022YFE0200300), National Natural Science Foundation of China (No.61972323)."
+                                }
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+                                        }
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diff --git a/2023/FastViT_ A Fast Hybrid Vision Transformer Using Structural Reparameterization/63912104-d421-4e14-8cba-166c1f78904b_content_list.json b/2023/FastViT_ A Fast Hybrid Vision Transformer Using Structural Reparameterization/63912104-d421-4e14-8cba-166c1f78904b_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..6fbfb5915d2c64249e511c4a437ecdcfbcf33d25
--- /dev/null
+++ b/2023/FastViT_ A Fast Hybrid Vision Transformer Using Structural Reparameterization/63912104-d421-4e14-8cba-166c1f78904b_content_list.json	
@@ -0,0 +1,1371 @@
+[
+    {
+        "type": "text",
+        "text": "FastViT: A Fast Hybrid Vision Transformer using Structural Reparameterization",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Pavan Kumar Anasosalu Vasu† James Gabriel Jeff Zhu Oncel Tuzel Anurag Ranjan†",
+        "bbox": [
+            112,
+            202,
+            854,
+            222
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Apple",
+        "bbox": [
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+            257
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The recent amalgamation of transformer and convolutional designs has led to steady improvements in accuracy and efficiency of the models. In this work, we introduce FastViT, a hybrid vision transformer architecture that obtains the state-of-the-art latency-accuracy trade-off. To this end, we introduce a novel token mixing operator, RepMixer, a building block of FastViT, that uses structural reparameterization to lower the memory access cost by removing skip-connections in the network. We further apply train-time overparametrization and large kernel convolutions to boost accuracy and empirically show that these choices have minimal effect on latency. We show that – our model is  $3.5 \\times$  faster than CMT, a recent state-of-the-art hybrid transformer architecture,  $4.9 \\times$  faster than EfficientNet, and  $1.9 \\times$  faster than ConvNeXt on a mobile device for the same accuracy on the ImageNet dataset. At similar latency, our model obtains  $4.2\\%$  better Top-1 accuracy on ImageNet than MobileOne. Our model consistently outperforms competing architectures across several tasks – image classification, detection, segmentation and 3D mesh regression with significant improvement in latency on both a mobile device and a desktop GPU. Furthermore, our model is highly robust to out-of-distribution samples and corruptions, improving over competing robust models. Code and models are available at https://github.com/apple/ml-fastvit",
+        "bbox": [
+            76,
+            323,
+            472,
+            715
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            744,
+            209,
+            762
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Vision Transformers [14] have achieved state-of-the-art performance on several tasks such as image classification, detection and segmentation [35]. However, these models have traditionally been computationally expensive. Recent works [66, 39, 41, 57, 29] have proposed methods to lower the compute and memory requirements of vision transformers. Recent hybrid architectures [41, 17, 10, 62] effectively",
+        "bbox": [
+            75,
+            771,
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+            878
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "combine the strengths of convolutional architectures and transformers to build architectures that are highly competitive on a wide range of computer vision tasks. Our goal is to build a model that achieves state-of-the-art latency-accuracy trade-off.",
+        "bbox": [
+            500,
+            292,
+            890,
+            366
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent vision and hybrid transformer models [51, 17, 42, 41] follow the Metaformer [65] architecture, which consists of a token mixer with a skip connection followed by Feed Forward Network (FFN) with another skip connection. These skip connections account for a significant overhead in latency due to increased memory access cost [13, 55]. To address this latency overhead, we introduce RepMixer, a fully reparameterizable token mixer that uses structural reparameterization to remove the skip-connections. The RepMixer block also uses depthwise convolutions for spatial mixing of information similar to ConvMixer [53]. However, the key difference is that our module can be reparameterized at inference to remove any branches.",
+        "bbox": [
+            496,
+            368,
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+            565
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To further improve on latency, FLOPs and parameter count, we replace all dense  $\\mathrm{k} \\times \\mathrm{k}$  convolutions with their factorized version, i.e. depthwise followed by pointwise convolutions. This is a common approach used by efficient architectures [26, 46, 25] to improve on efficiency metrics, but, naively using this approach hurts performance as seen in Table 1. In order to increase capacity of the these layers, we use linear train-time overparameterization as introduced in [13, 11, 12, 55, 18]. These additional branches are only introduced during training and are reparameterized at inference.",
+        "bbox": [
+            496,
+            566,
+            893,
+            731
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In addition, we use large kernel convolutions in our network. This is because, although self-attention based token mixing is highly effective to attain competitive accuracy, they are inefficient in terms of latency [39]. Therefore, we incorporate large kernel convolutions in Feed Forward Network (FFN) [14] layer and patch embedding layers. These changes have minimal impact on overall latency of the model while improving performance.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Thus, we introduce FastViT that is based on three key design principles - i) use of RepMixer block to remove skip connections, ii) use of linear train-time overparameteriza",
+        "bbox": [
+            498,
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+            0,
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "corresponding authors: {panasosaluvasu, anuragr}  $@$  apple.com",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "5785",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/b122794dd42f482b77e210d5a0f445450eb738dd5a4962f1da9daa75c5364e27.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/ad0fb8dfced8e49e158dcd41f23fb7cc32974f177837b46c0972ed95d059c5da.jpg",
+        "image_caption": [
+            "(b)",
+            "Figure 1: (a) Accuracy vs. Mobile latency scaling curves of recent methods. The models are benchmarked on an iPhone 12 Pro following [55]. (b) Accuracy vs. GPU latency scaling curves of recent methods. For better readability only models with Top-1 accuracy better than  $79\\%$  are plotted. See supplementary materials for more plots. Across both compute fabrics, our model has the best accuracy-latency tradeoff."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "tion to improve accuracy, iii) use of large convolutional kernels to substitute self-attention layers in early stages.",
+        "bbox": [
+            75,
+            407,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "FastViT achieves significant improvements in latency compared to other hybrid vision transformer architectures while maintaining accuracy on several tasks like - image classification, object detection, semantic segmentation and 3d hand mesh estimation. We perform a comprehensive analysis by deploying recent state-of-the-art architectures on an iPhone 12 Pro device and an NVIDIA RTX-2080Ti desktop GPU.",
+        "bbox": [
+            75,
+            441,
+            468,
+            561
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In Figure 1, we show that, at ImageNet Top-1 accuracy of  $83.9\\%$ , our model is  $4.9 \\times$  faster than EfficientNet-B5 [48],  $1.6 \\times$  faster than EfficientNetV2-S [49],  $3.5 \\times$  faster than CMT-S [17] and  $1.9 \\times$  faster than ConvNeXt-B [36] on an iPhone 12 Pro mobile device. At ImageNet Top-1 accuracy of  $84.9\\%$  our model is just as fast as NFNet-F1 [1] on a desktop GPU while being  $66.7\\%$  smaller, using  $50.1\\%$  less FLOPs and  $42.8\\%$  faster on mobile device. At latency of  $0.8\\mathrm{ms}$  on an iPhone 12 Pro mobile device, our model obtains  $4.2\\%$  better Top-1 accuracy on ImageNet than MobileOne-S0. For object detection and instance segmentation on MS COCO using Mask-RCNN [20] head, our model attains comparable performance to CMT-S [17] while incurring  $4.3 \\times$  lower backbone latency. For semantic segmentation on ADE20K, our model improves over PoolFormer-M36 [65] by  $5.2\\%$ , while incurring a  $1.5 \\times$  lower backbone latency on an iPhone 12 Pro mobile device. On 3D hand mesh estimation task, our model is  $1.9 \\times$  faster than MobileHand [16] and  $2.8 \\times$  faster than recent state-of-the-art MobRecon [4] when benchmarked on GPU.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In addition to accuracy metrics, we also study the robustness of our models to corruption and out-of-distribution",
+        "bbox": [
+            76,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "samples which does not always correlate well with accuracy. For example, PVT [58] achieves highly competitive performance on ImageNet dataset, but has very poor robustness to corruption and out-of-distribution samples as reported in Mao et al. [38]. In real world applications, using a robust model in such a scenario can significantly improve user experience. We demonstrate the robustness of our architecture on popular benchmarks and show that our models are highly robust to corruption and out-of-distribution samples while being significantly faster than competing robust models. In summary, our contributions are as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We introduce FastViT, a hybrid vision transformer that uses structural reparameterization to obtain lower memory access cost and increased capacity, achieving state-of-the-art accuracy-latency trade-off.",
+            "- We show that our models are the fastest in terms of latency on two widely used platforms - mobile device and desktop GPU.",
+            "- We show that our models generalize to many tasks - image classification, object detection, semantics segmentation, and 3D hand mesh regression.",
+            "- We show that our models are robust to corruption and out-of-distribution samples and significantly faster than competing robust models."
+        ],
+        "bbox": [
+            500,
+            580,
+            890,
+            787
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            799,
+            640,
+            815
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For the past decade, convolutional neural networks have been the standard architecture for vision models [21, 43, 64, 48, 49, 26, 46, 25, 36, 13, 55]. More recently, transformers have shown great success on computer vision tasks [14, 63, 51, 35, 58, 52, 42, 41]. Unlike convolutional",
+        "bbox": [
+            496,
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+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "5786",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "layers, the self-attention layers in vision transformers provide a global context by modeling long-range dependencies. Unfortunately, this global scope often comes at a high computational price [39]. Works like [41, 57, 29, 39] address ways to alleviate computational costs associated with self-attention layers. In our work, we explore an efficient alternative to self-attention layers for lower latency.",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Hybrid Vision Transformers In order to design efficient networks while maintaining accuracy, recent works introduce hybrid architectures that combine convolutional and transformer design to effectively capture local and global information. Some designs replace the patchify stem [14] with convolutional layers [63], introduce early convolutional stages [9, 41] or implicitly hybridize through windowed attention [35, 7]. More recent works build explicit hybrid structures for better exchange of information between tokens (or patches) [17, 10, 62]. In majority of the hybrid architectures, token mixers are predominantly self-attention based. Recently, MetaFormer [65] introduced Pooling, a simple and efficient candidate for token mixing.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Structural Reparameterization Recent work [13, 55] shows the benefits of reparameterizing skip connections to lower memory access cost. In our model, we introduce a novel architectural component RepMixer, that is reparameterizable at inference. For better efficiency, works like [26, 46, 25, 37, 69] introduce factorized  $\\mathrm{k}\\times \\mathrm{k}$  convolutions using depthwise or grouped convolutions followed by  $1\\times 1$  pointwise convolutions. While this approach is highly effective in improving the overall efficiency of the model, the lower parameter count can lead to reduced capacity. Recently, linear train-time over overparameterization was introduced in [55, 11, 12] to improve capacity of such models. We use factorized  $\\mathrm{k}\\times \\mathrm{k}$  convolutions in our model and boost the capacity of these layers using linear train-time overparameterization. To the best of our knowledge, structural reparameterization to remove skip connections and linear overparameterization has not been attempted in any prior hybrid transformer architecture.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Architecture",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FastViT is a hybrid transformer and has four distinct stages which operate at different scales as shown in Figure 2. We detail all the FastViT variants in Table 2.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FastViT uses RepMixer, a token mixer that reparameterizes a skip connection, which helps in alleviating memory access cost (see Figure 2d). To further improve efficiency and performance, we replace dense  $\\mathrm{k} \\times \\mathrm{k}$  convolutions commonly found in stem and patch embedding layers with its factorized version that uses train-time overparameterization (see Figure 2a).",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "table",
+        "img_path": "images/930e789a11a608de248e5c23bb28e8c66db553b4afd083e4163deb1afa6f78c9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Architectural Choices</td><td>Params (M)</td><td>FLOPs (G)</td><td>Mobile Latency (ms)</td><td>Top-1 (%)</td></tr><tr><td rowspan=\"2\">PoolFormer-S12 (Baseline) + 224 → 256</td><td>11.9</td><td>1.8</td><td>1.50</td><td>77.2</td></tr><tr><td>11.9</td><td>2.4</td><td>2.25</td><td>77.6</td></tr><tr><td>Section 3.2.1 + Pooling → RepMixer</td><td>11.9</td><td>2.4</td><td>1.58</td><td>78.5</td></tr><tr><td rowspan=\"2\">Section 3.2.2 + Factorized dense conv. + Train-Time Overparam.</td><td>8.7</td><td>1.7</td><td>1.26</td><td>78.0</td></tr><tr><td>8.7</td><td>1.7</td><td>1.26</td><td>78.9</td></tr><tr><td rowspan=\"2\">Section 3.2.3 + LK. conv. FFN + LK. conv. Patch Emb.</td><td>8.7</td><td>1.8</td><td>1.33</td><td>79.4</td></tr><tr><td>8.8</td><td>1.8</td><td>1.40</td><td>79.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Analysis of architectural choices made to obtain FastViT-S12 variant, starting from PoolFormer-S12. \"LK.\" stands for Large Kernel.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-attention [14] token mixers are computationally expensive, especially at higher resolutions [42, 39]. While efficient versions of self-attention layers are explored in [17, 41], we use large kernel convolutions as an efficient alternative to improve receptive field in early stages of the network architecture (see Figure 2c).",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We analyze various architectural choices made in designing FastViT from a PoolFormer [65] baseline in Table 1 and detail our approach below.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. FastViT",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Reparameterizing Skip Connections",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "RepMixer Convolutional mixing was first introduced in ConvMixer[53]. For an input tensor  $X$ , the mixing block in the layer was implemented as,",
+        "bbox": [
+            496,
+            541,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nY = \\operatorname {B N} \\left(\\sigma (\\operatorname {D W C o n v} (X))\\right) + X \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            576,
+            590,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma$  is a non-linear activation function and BN is Batch Normalization [27] layer and DwConv is depthwise convolutional layer. While this block was shown to be effective, in RepMixer, we simply rearrange the operations and remove the non-linear activation function as shown below,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nY = \\operatorname {D W C o n v} (\\mathrm {B N} (X) + X \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The main benefit of our design is that it can be reparameterized at inference time to a single depthwise convolutional layer as shown below and in Figure 2d.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nY = \\operatorname {D W C o n v} (X) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            627,
+            757,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Positional Encodings We use conditional positional encodings [7, 8] that is dynamically generated and conditioned on the local neighborhood of the input tokens. These encodings are generated as a result of a depth-wise convolution operator and are added to the patch embeddings. Note the lack of non-linearities in this group of operations, hence this block is reparameterized as shown in Figure 2a.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "5787",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7b97ca9d4077121df847565fc5b97467a4ae9d2cd1c7e0e84dfd5de061b8d5da.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            89,
+            85,
+            480,
+            469
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/dfb8afdf58c91ab460891b28c6cfc93e6a495e8fb08b72be1ec87a03c81ee220.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            480,
+            88,
+            877,
+            327
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/eb2e674b910ba0857abd1206e23a0d354686262bff98afa1bbc332a5c586108f.jpg",
+        "image_caption": [
+            "(b)",
+            "(d)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            480,
+            340,
+            875,
+            468
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/f1e86708b9b78362605ba1d6a3cb1bf805a54cab875c5024d0543a0c01ce84ab.jpg",
+        "image_caption": [
+            "Figure 2: (a) Overview of FastViT architecture which decouples train-time and inference-time architecture. Stages 1, 2, and 3 have the same architecture and uses RepMixer for token mixing. In stage 4, self attention layers are used for token mixing. (b) Architecture of the convolutional stem. (c) Architecture of convolutional-FFN (d) Overview of RepMixer block, which reparameterizes a skip connection at inference.",
+            "Figure 3: Latency comparison of a MetaFormer (S12) architecture with Pooling and RepMixer as a choice for token mixing; measured on iPhone 12 Pro for various image resolutions. Both models have  $\\sim 1.8\\mathrm{G}$  FLOPs. Absence of a skip connection in RepMixer lowers the overall memory access cost leading to lower latency."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            563,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Empirical Analysis In order to verify the benefits of reparameterizing skip connections, we ablate over the using one of the most efficient (in terms of latency) token mixer, i.e. Pooling and RepMixer in a MetaFormer S12 architecture. Both the models being ablated have  $\\sim 1.8\\mathrm{G}$  FLOPs.",
+        "bbox": [
+            75,
+            824,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We time the models for various input resolutions starting from  $224 \\times 224$  to  $1024 \\times 1024$  on an iPhone 12 Pro mobile device. From Figure 3, we see that RepMixer significantly improves over Pooling, especially at higher resolutions. At  $384 \\times 384$ , using RepMixer will lower the latency by  $25.1\\%$  and at larger resolutions like  $1024 \\times 1024$ , latency is lowered significantly by  $43.9\\%$ .",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Linear Train-time Overparameterization",
+        "text_level": 1,
+        "bbox": [
+            498,
+            680,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In order to further improve efficiency (parameter count, FLOPs, and latency), we replace all dense  $\\mathrm{k} \\times \\mathrm{k}$  convolutions with its factorized version, i.e.  $\\mathrm{k} \\times \\mathrm{k}$  depthwise followed by  $1 \\times 1$  pointwise convolutions. However, the lower parameter count from factorization can diminish the capacity of the model. In order to increase capacity of the factorized layers, we perform linear train-time overparameterization as described in MobileOne [55]. MobileOne-style overparameterization in stem, patch embedding, and projection layers help in boosting performance. From Table 3, we note that train-time overparameterization improves Top-1 accuracy on ImageNet by  $0.6\\%$  on FastViT-SA12 model. On a smaller FastViT-S12 variant, Top-1 accuracy improves",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5788",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/bea44622b1e4214c888cc5ffc1e7b977aca809ab70c43a8d99e192fac57778f8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Stage</td><td rowspan=\"2\">#Tokens</td><td rowspan=\"2\" colspan=\"2\">Layer Spec.</td><td colspan=\"7\">FastViT</td></tr><tr><td>T8</td><td>T12</td><td>S12</td><td>SA12</td><td>SA24</td><td>SA36</td><td>MA36</td></tr><tr><td rowspan=\"3\">Stem</td><td rowspan=\"3\">H×W</td><td rowspan=\"3\" colspan=\"2\">Conv.</td><td colspan=\"7\">3 × 3, stride 2</td></tr><tr><td colspan=\"7\">3 × 3 MobileOne Style, stride 2</td></tr><tr><td>48</td><td colspan=\"5\">64</td><td>76</td></tr><tr><td rowspan=\"5\">1</td><td rowspan=\"2\">H/4 × W/4</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>48</td><td colspan=\"5\">64</td><td>76</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"7\">RepMixer</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td rowspan=\"5\">2</td><td rowspan=\"2\">H/8 × W/8</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>96</td><td colspan=\"5\">128</td><td>152</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"7\">RepMixer</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td rowspan=\"5\">3</td><td rowspan=\"2\">H/16 × W/16</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>192</td><td colspan=\"5\">256</td><td>304</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"7\">RepMixer</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>4</td><td>6</td><td>6</td><td>6</td><td>12</td><td>18</td><td>18</td></tr><tr><td rowspan=\"5\">4</td><td rowspan=\"2\">H/32 × W/32</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>384</td><td colspan=\"5\">512</td><td>608</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"2\">RepMixer</td><td colspan=\"5\">Attention</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td colspan=\"4\">Parameters (M)</td><td>3.6</td><td>6.8</td><td>8.8</td><td>10.9</td><td>20.6</td><td>30.4</td><td>42.7</td></tr><tr><td colspan=\"4\">FLOPs (G)</td><td>0.7</td><td>1.4</td><td>1.8</td><td>1.9</td><td>3.8</td><td>5.6</td><td>7.9</td></tr></table>",
+        "bbox": [
+            80,
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "by  $0.9\\%$  as shown in Table 1.",
+        "bbox": [
+            76,
+            662,
+            274,
+            678
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However, train-time overparameterization results in increased training time due to computational overhead from the added branches. In our architecture, we only overparameterize those layers that replace dense  $\\mathrm{k} \\times \\mathrm{k}$  convolutions with its factorized form as described above. These layers are found in the convolutional stem, patch embedding and projection layers. The computational cost incurred in these layers are lower than the rest of the network, hence overparameterizing these layers do not result in significant increases to train time. For example, FastViT-SA12 takes  $6.7\\%$  longer and FastViT-SA36 takes  $4.4\\%$  longer to train with train-time overparameterization as opposed to training those variants without it under the same settings described in Section 4.1.",
+        "bbox": [
+            75,
+            700,
+            470,
+            912
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/65b5b38e4a5553fdc185c772fc50c6fd44080ce7ddeb4024bcd4f1d3ad3ee117.jpg",
+        "table_caption": [
+            "Table 2: Architecture details of FastViT variants. Models with smaller embedding dimensions, i.e. [64, 128, 256, 512] are prefixed with \"S\" and models that contain Self-Attention layers are prefixed with \"SA\". Models with bigger embedding dimensions, i.e. [76, 152, 304, 608] are prefixed with \"M\". Models with MLP expansion ratio less than 4 are prefixed with \"T\". The number in the notation denotes total number of FastViT blocks. FLOP count is computed by fvcore[15] library."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Ablation</td><td>Top-1 (%)</td><td>Train Time (hrs)</td></tr><tr><td rowspan=\"2\">FastViT-SA12</td><td>Without Train-Time Overparam.</td><td>80.0</td><td>31.3</td></tr><tr><td>With Train-Time Overparam.</td><td>80.6</td><td>33.4</td></tr><tr><td rowspan=\"2\">FastViT-SA36</td><td>Without Train-Time Overparam.</td><td>83.3</td><td>73.5</td></tr><tr><td>With Train-Time Overparam.</td><td>83.6</td><td>76.7</td></tr></table>",
+        "bbox": [
+            504,
+            89,
+            890,
+            157
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Comparison of FastViT variants with and without linear train-time overparameterization when trained on ImageNet-1k dataset. Train time is wall clock time elapsed at the end of a training run.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.3 Large Kernel Convolutions",
+        "text_level": 1,
+        "bbox": [
+            500,
+            239,
+            741,
+            255
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The receptive field of RepMixer is local compared to self-attention token mixers. However, self-attention based token mixers are computationally expensive. A computationally efficient approach to improve the receptive field of early stages that do not use self-attention is by incorporating depthwise large kernel convolutions. We introduce depthwise large kernel convolutions in FFN and patch embedding layers. From Table 4, we note that variants using depthwise large kernel convolutions can be highly competitive to variants using self-attention layers while incurring a modest increase in latency. When we compare V5 with V3, model size increases by  $11.2\\%$ , and latency increases by a factor of  $2.3 \\times$  for a relatively small gain of  $0.4\\%$  in Top-1 accuracy. V2 is larger than V4 by  $20\\%$  and has  $7.1\\%$  higher latency than V4 while attaining similar Top-1 accuracy on ImageNet. Further ablations on kernel sizes and latency is provided in the supplementary materials. In Table 1, we ablate over large kernel convolutions in FFN and patch embedding layers. Overall, large kernel convolutions provide  $0.9\\%$  improvement in Top-1 accuracy on FastViT-S12.",
+        "bbox": [
+            496,
+            263,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The architecture of our FFN and patch embedding layer is shown in Figure 2. Our FFN block has a structure similar to ConvNeXt [36] block with a few key differences, see Figure 2c. We use Batch Normalization as opposed to Layer Normalization, as it can be fused with the preceding layer at inference. Also, it does not require additional reshape operations to obtain appropriate tensor layout for LayerNorm as done in the original implementation of ConvNeXt block.",
+        "bbox": [
+            496,
+            566,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Along with increased receptive field, large kernel convolutions help in improving model robustness as observed in [59] and convolutional-FFN blocks generally tend to be more robust than vanilla-FFN blocks as observed in [38]. Hence, incorporating large kernel convolutions is an efficient way to improve model performance and robustness.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            791,
+            633,
+            808
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Image Classification",
+        "text_level": 1,
+        "bbox": [
+            500,
+            816,
+            691,
+            832
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We report results on the widely used ImageNet-1K dataset [45] which contains  $\\sim 1.3\\mathrm{M}$  training images and  $50\\mathrm{K}$  validation images. We follow the training recipe prescribed in [51, 65], i.e. the models are trained for 300",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5789",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/d89da0e3014cf81111039eba9f866f37a40b6e29e7f31273970344c68f1d5411.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Variant</td><td colspan=\"4\">Stages</td><td>Params</td><td>Top-1</td><td>Mobile</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>(M)</td><td>(%)</td><td>Latency (ms)</td></tr><tr><td colspan=\"8\">Standard Setting</td></tr><tr><td>V1</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.7</td><td>78.9</td><td>1.3</td></tr><tr><td>V2</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.8</td><td>79.9</td><td>1.5</td></tr><tr><td>V3</td><td>RM</td><td>RM</td><td>SA</td><td>SA</td><td>12.4</td><td>81.0</td><td>3.7</td></tr><tr><td colspan=\"8\">Large Kernel Convolutions (7×7)</td></tr><tr><td>V4</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.8</td><td>79.8</td><td>1.4</td></tr><tr><td>V5</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.9</td><td>80.6</td><td>1.6</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "epochs using AdamW optimizer with weight decay of 0.05 and peak learning rate  $10^{-3}$  for a total batch size of 1024. The number of warmup epochs is set to 5 and cosine schedule is used to decay the learning rate. Our implementation uses timm library [60] and all the models were trained on 8 NVIDIA A100 GPUs. See supplementary materials for details on hyper parameters used for all the variants. For  $384 \\times 384$  input size, we fine-tune the models for 30 epochs with weight decay of  $10^{-8}$  and learning rate of  $5 \\times 10^{-5}$  and batch size of 512 following [36]. To measure latency, we use the input sizes corresponding to the respective methods. For iPhone latency measurements, we export the models using Core ML Tools (v6.0) and run it on iPhone12 Pro Max with iOS 16 and batch size is set to 1 for all the models. We follow the same protocol as [55]. For GPU latency measurements, we export the traced model to TensorRT (v8.0.1.6) format and run it on NVIDIA RTX-2080Ti with batch size of 8. We report the median latency estimate from 100 runs.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Comparison with SOTA Models In Table 5, we compare our models against recent state-of-the-art models on ImageNet-1k dataset. For a fair comparison, we modify ConvNeXt [36] from official implementation by avoiding costly reshape operations, see supplementary materials for more details. We were unable to reliably export LITv2 [41] due to poor support for deformable convolutions in either library. Our model obtains the best accuracy-latency trade-off when compared to recent state-of-the-art models on two different compute fabrics, i.e. desktop-grade GPU and mobile device. Our models improve over LITv2 [41] on both parameter count and FLOPs, at Top-1 accuracy of  $84.9\\%$ , FastViT-MA36 is  $49.3\\%$  smaller and consumes  $55.4\\%$  less FLOPs than LITv2-B. FastViT-S12 is  $26.3\\%$  faster than MobileOne-S4 [55] on iPhone 12 Pro and  $26.9\\%$  faster on",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/afd609cee60a4cd78f85925125d8852b448b0054286745965e89664960af943f.jpg",
+        "table_caption": [
+            "Table 4: Ablation on using large kernel convolutions as a substitute for self-attention layers. \"RM\" indicates [RepMixer-FFN] block is used in the stage. \"SA\" indicates [Self Attention-FFN] block is used in the stage. Standard setting uses  $3 \\times 3$  factorized convolutions in patch embedding and stem layers and  $1 \\times 1$  convolutions for FFN. In variants V4 and V5, large kernel convolutions  $(7 \\times 7)$  are used in patch embedding and FFN layers."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>MobileOne-S0[55]</td><td>224</td><td>2.1</td><td>0.3</td><td>1.0</td><td>0.8</td><td>71.4</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>75.6</td></tr><tr><td>MobileOne-S3[55]</td><td>224</td><td>10.1</td><td>1.8</td><td>2.1</td><td>1.5</td><td>78.1</td></tr><tr><td>CMT-T* [17]</td><td>160</td><td>9.5</td><td>0.6</td><td>4.5</td><td>3.8</td><td>79.1</td></tr><tr><td>EfficientNet-B1[48]</td><td>256</td><td>7.8</td><td>0.7</td><td>3.2</td><td>2.5</td><td>79.1</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>79.1</td></tr><tr><td>MobileOne-S4[55]</td><td>224</td><td>14.8</td><td>2.9</td><td>2.6</td><td>1.9</td><td>79.4</td></tr><tr><td>RSB-ResNet50[61]</td><td>224</td><td>25.6</td><td>4.1</td><td>2.3</td><td>2.6</td><td>79.8</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22.0</td><td>4.6</td><td>5.2</td><td>5.3</td><td>79.8</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>79.8</td></tr><tr><td>RegNetY-8G[43]</td><td>224</td><td>39.2</td><td>8.0</td><td>5.8</td><td>3.8</td><td>79.9</td></tr><tr><td>EfficientNet-B2[48]</td><td>288</td><td>9.2</td><td>1.0</td><td>4.1</td><td>3.5</td><td>80.1</td></tr><tr><td>PoolFormer-S24[65]</td><td>224</td><td>21.0</td><td>3.4</td><td>15.7</td><td>2.5</td><td>80.3</td></tr><tr><td>RegNetY-16G [43]</td><td>224</td><td>83.6</td><td>16.0</td><td>8.1</td><td>7.5</td><td>80.4</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>80.6</td></tr><tr><td>ResNeSt50[67]</td><td>224</td><td>27.5</td><td>5.4</td><td>51.5</td><td>29.9</td><td>81.1</td></tr><tr><td>Swin-T[35]</td><td>224</td><td>29.0</td><td>4.5</td><td>-</td><td>9.3</td><td>81.3</td></tr><tr><td>PoolFormer-S36[65]</td><td>224</td><td>31.0</td><td>5.0</td><td>23.7</td><td>3.5</td><td>81.4</td></tr><tr><td>EfficientNet-B3[48]</td><td>300</td><td>12.0</td><td>1.8</td><td>5.3</td><td>7.1</td><td>81.6</td></tr><tr><td>CvT-13[62]</td><td>224</td><td>20.1</td><td>4.5</td><td>18.1</td><td>62.6</td><td>81.6</td></tr><tr><td>CoAtNet-0[9]</td><td>224</td><td>25.0</td><td>4.2</td><td>-</td><td>6.7</td><td>81.6</td></tr><tr><td>CMT-XS* [17]</td><td>192</td><td>15.2</td><td>1.5</td><td>8.3</td><td>6.3</td><td>81.8</td></tr><tr><td>DeiT-B [51]</td><td>224</td><td>86.0</td><td>17.5</td><td>11.6</td><td>11.6</td><td>81.8</td></tr><tr><td>RSB-ResNet152[61]</td><td>224</td><td>60.2</td><td>11.6</td><td>5.4</td><td>4.7</td><td>81.8</td></tr><tr><td>LITv2-S[41]</td><td>224</td><td>28.0</td><td>3.7</td><td>-</td><td>-</td><td>82.0</td></tr><tr><td>ConvNeXt-T†[36]</td><td>224</td><td>29.0</td><td>4.5</td><td>6.3</td><td>3.7</td><td>82.1</td></tr><tr><td>PoolFormer-M48[65]</td><td>224</td><td>73.0</td><td>11.6</td><td>30.2</td><td>7.6</td><td>82.5</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>82.6</td></tr><tr><td>ResNeSt101[67]</td><td>224</td><td>48.2</td><td>10.2</td><td>75.5</td><td>37.7</td><td>83.0</td></tr><tr><td>Swin-S[35]</td><td>224</td><td>50.0</td><td>8.7</td><td>-</td><td>13.0</td><td>83.0</td></tr><tr><td>ConvNeXt-S†[36]</td><td>224</td><td>50.0</td><td>8.7</td><td>10.3</td><td>5.4</td><td>83.1</td></tr><tr><td>MOAT-0[5]</td><td>224</td><td>27.8</td><td>5.7</td><td>-</td><td>4.9</td><td>83.3</td></tr><tr><td>CoAtNet-1[9]</td><td>224</td><td>42.0</td><td>8.4</td><td>-</td><td>13.4</td><td>83.3</td></tr><tr><td>Swin-B [35]</td><td>224</td><td>88.0</td><td>15.4</td><td>-</td><td>18.5</td><td>83.5</td></tr><tr><td>CMT-S* [17]</td><td>224</td><td>25.1</td><td>4.0</td><td>13.8</td><td>15.6</td><td>83.5</td></tr><tr><td>MaxViT-T[54]</td><td>224</td><td>31.0</td><td>5.6</td><td>-</td><td>31.5</td><td>83.6</td></tr><tr><td>LITv2-B[41]</td><td>224</td><td>87.0</td><td>13.2</td><td>-</td><td>-</td><td>83.6</td></tr><tr><td>EfficientNet-B5[48]</td><td>456</td><td>30.0</td><td>9.9</td><td>24.2</td><td>22.1</td><td>83.6</td></tr><tr><td>NFNet-F0[1]</td><td>256</td><td>71.5</td><td>12.4</td><td>6.2</td><td>6.4</td><td>83.6</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>83.6</td></tr><tr><td>ConvNeXt-B†[36]</td><td>224</td><td>89.0</td><td>15.4</td><td>13.6</td><td>8.4</td><td>83.8</td></tr><tr><td>CoAtNet-0</td><td>384</td><td>25.0</td><td>13.4</td><td>-</td><td>20.1</td><td>83.9</td></tr><tr><td>EfficientNetV2-S[49]</td><td>384</td><td>22.0</td><td>8.8</td><td>8.2</td><td>7.1</td><td>83.9</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>83.9</td></tr><tr><td>EfficientNet-B6[48]</td><td>528</td><td>43.0</td><td>19.0</td><td>44.3</td><td>51.7</td><td>84.0</td></tr><tr><td>CoAtNet-2[9]</td><td>224</td><td>75.0</td><td>15.7</td><td>-</td><td>19.6</td><td>84.1</td></tr><tr><td>MOAT-1[5]</td><td>224</td><td>41.6</td><td>9.1</td><td>-</td><td>8.3</td><td>84.2</td></tr><tr><td>EfficientNet-B7[48]</td><td>600</td><td>66.0</td><td>37.0</td><td>72.6</td><td>85.5</td><td>84.3</td></tr><tr><td>CMT-B* [17]</td><td>256</td><td>45.7</td><td>9.3</td><td>26.9</td><td>20.6</td><td>84.5</td></tr><tr><td>Swin-B[35]</td><td>384</td><td>88.0</td><td>47.0</td><td>-</td><td>57.2</td><td>84.5</td></tr><tr><td>MaxViT-S[54]</td><td>224</td><td>69.0</td><td>11.7</td><td>-</td><td>48.7</td><td>84.5</td></tr><tr><td>FastViT-SA36</td><td>384</td><td>30.4</td><td>12.6</td><td>12.8</td><td>7.4</td><td>84.5</td></tr><tr><td>MOAT-0[5]</td><td>384</td><td>27.8</td><td>18.2</td><td>-</td><td>24.3</td><td>84.6</td></tr><tr><td>NFNet-F1[1]</td><td>320</td><td>132.6</td><td>35.5</td><td>16.9</td><td>16.1</td><td>84.7</td></tr><tr><td>MOAT-2[5]</td><td>224</td><td>73.4</td><td>17.2</td><td>-</td><td>12.6</td><td>84.7</td></tr><tr><td>LITv2-B[41]</td><td>384</td><td>87.0</td><td>39.7</td><td>-</td><td>-</td><td>84.7</td></tr><tr><td>FastViT-MA36</td><td>384</td><td>42.7</td><td>17.7</td><td>16.5</td><td>9.2</td><td>84.9</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Comparison of different state-of-the-art methods on ImageNet-1k classification. HardSwish is not well supported by Core ML, * denotes we replace it with GELU for fair comparison. “†” denotes that model has been modified from original implementation for efficient deployment. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”.",
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+            800,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "5790",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/184ba1df46563ce82f571707f80fa2e7009be5093aae50b2d2658aa579abee9c.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 6: Comparison of different state-of-the-art methods on ImageNet-1k classification when trained using distillation objective specified by [51]. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>76.7</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>80.3</td></tr><tr><td>CaiT XXS-36[52]</td><td>224</td><td>17.3</td><td>3.8</td><td>15.8</td><td>-</td><td>79.7</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>80.9</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22</td><td>4.6</td><td>5.2</td><td>6.7</td><td>81.2</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>81.9</td></tr><tr><td>EfficientFormer-L3[31]</td><td>224</td><td>31.3</td><td>3.9</td><td>3.6</td><td>3.0</td><td>82.4</td></tr><tr><td>EfficientFormer-L7[31]</td><td>224</td><td>82.1</td><td>10.2</td><td>7.5</td><td>7.0</td><td>83.3</td></tr><tr><td>DeiT-B[51]</td><td>224</td><td>87</td><td>17.6</td><td>11.6</td><td>11.6</td><td>83.4</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>83.4</td></tr><tr><td>CaiT S-24[52]</td><td>224</td><td>46.9</td><td>9.4</td><td>19.1</td><td>-</td><td>83.5</td></tr><tr><td>CaiT XS-24[52]</td><td>384</td><td>26.6</td><td>19.3</td><td>77.7</td><td>-</td><td>84.1</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>84.2</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>84.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "GPU. At Top-1 accuracy of  $83.9\\%$ , FastViT-MA36 is  $1.9 \\times$  faster than an optimized ConvNeXt-B model on iPhone 12 Pro and  $2.0 \\times$  faster on GPU. At Top-1 accuracy of  $84.9\\%$ , FastViT-MA36 is just as fast as NFNet-F1 [1] on GPU while being  $66.7\\%$  smaller and using  $50.1\\%$  less FLOPs and  $42.8\\%$  faster on mobile device.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Knowledge distillation We report performance of our models when trained with distillation objective in Table 6. We follow the setting described in DeiT [51], with RegNet-16GF [43] as the teacher model. Following DeiT [51], we use hard distillation where hard decision of the teacher is set as true label. Our models are trained for 300 epochs. Unlike [51, 52, 31], we do not introduce an additional classification head for distillation. FastViT outperforms recent state-of-the-art model EfficientFormer [31]. FastViT-SA24 attains similar performance as EfficientFormer-L7 while having  $3.8 \\times$  less parameters,  $2.7 \\times$  less FLOPs and  $2.7 \\times$  lower latency.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Robustness Evaluation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            724,
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+            739
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our models for out-of-distribution robustness on the following benchmarks - (i) ImageNet-A [24], a dataset that contains naturally occurring examples that are misclassified by ResNets; (ii) ImageNet-R [22], a dataset that contains natural renditions of ImageNet object classes with different textures and local image statistics; (iii) ImageNet-Sketch [56], a dataset that contains black and white sketches of all ImageNet classes, obtained using google image queries; and (iv) ImageNet-C [23], a dataset that consists of algorithmically generated corruption",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5060c92d498bd9fda8079b60cdc0445a37d3f1ead82a37f688534650f9207ad3.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 7: Results on robustness benchmark datasets. Models are grouped based on FLOPs. Performance of competing models is reported by [38] and [36]. *ResNet-50 model is trained with AugMix to improve robustness as reported in [38]. For ImageNet-C mean corruption error is reported (lower is better) and for other datasets Top-1 accuracy is reported (higher is better). The best results are in bold and second best results are underlined."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>#Params</td><td>#FLOPs</td><td>Clean</td><td>IN-C (↓)</td><td>IN-A</td><td>IN-R</td><td>IN-SK</td></tr><tr><td>PVT-Tiny</td><td>13.2</td><td>1.9</td><td>75.0</td><td>79.6</td><td>7.9</td><td>33.9</td><td>21.5</td></tr><tr><td>RVT-Ti</td><td>8.6</td><td>1.3</td><td>78.4</td><td>58.2</td><td>13.3</td><td>43.7</td><td>30.0</td></tr><tr><td>FastViT-SA12</td><td>10.9</td><td>1.9</td><td>80.6</td><td>62.2</td><td>17.2</td><td>42.6</td><td>29.7</td></tr><tr><td>PVT-Small</td><td>24.5</td><td>3.8</td><td>79.9</td><td>66.9</td><td>18.0</td><td>40.1</td><td>27.2</td></tr><tr><td>ResNet-50*</td><td>25.6</td><td>4.1</td><td>79.0</td><td>65.5</td><td>5.9</td><td>42.5</td><td>31.5</td></tr><tr><td>ResNeXt50-32x4d</td><td>25.0</td><td>4.3</td><td>79.8</td><td>64.7</td><td>10.7</td><td>41.5</td><td>29.3</td></tr><tr><td>FastViT-SA24</td><td>20.6</td><td>3.8</td><td>82.6</td><td>55.3</td><td>26.0</td><td>46.5</td><td>34.0</td></tr><tr><td>Swin-T</td><td>28.3</td><td>4.5</td><td>81.2</td><td>62.0</td><td>21.6</td><td>41.3</td><td>29.1</td></tr><tr><td>ConViT-S</td><td>27.8</td><td>5.4</td><td>81.5</td><td>49.8</td><td>24.5</td><td>45.4</td><td>33.1</td></tr><tr><td>RVT-S</td><td>22.1</td><td>4.7</td><td>81.7</td><td>50.1</td><td>24.1</td><td>46.9</td><td>35.0</td></tr><tr><td>ConvNeXt-T</td><td>28.6</td><td>4.5</td><td>82.1</td><td>53.2</td><td>24.2</td><td>47.2</td><td>33.8</td></tr><tr><td>EfficientNet-B4</td><td>19.3</td><td>4.2</td><td>83.0</td><td>71.1</td><td>26.3</td><td>47.1</td><td>34.1</td></tr><tr><td>FastViT-SA36</td><td>30.4</td><td>5.6</td><td>83.6</td><td>51.8</td><td>32.3</td><td>48.1</td><td>35.8</td></tr><tr><td>ConvNeXt-S</td><td>50.0</td><td>8.7</td><td>83.1</td><td>51.2</td><td>31.2</td><td>49.5</td><td>37.1</td></tr><tr><td>FastViT-MA36</td><td>42.7</td><td>7.9</td><td>83.9</td><td>49.9</td><td>34.6</td><td>49.5</td><td>36.6</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "tions (blur, noise) applied to the ImageNet test-set. We evaluate our models using the implementation provided by [38]. Our models are more robust than recent vision transformers while being faster than pure-CNN based models which exhibit low robustness as seen Table 7. Architectural choices like using a large kernel convolutions in FFN and patch-embedding layers in combination with self-attention layers helps in improving the robustness of our model as discussed in Section 3.2.3. All the models compared in Table 7 are trained only on ImageNet-1k dataset using similar training recipes. From Table 7, our model is highly competitive to RVT and ConvNeXt, in fact FastViT-M36 has better clean accuracy, better robustness to corruptions and similar out-of-distribution robustness as ConvNeXt-S which has 6.1M more parameters and has  $10\\%$  more FLOPs than our model.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. 3D Hand mesh estimation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Recent works on real-time 3D hand mesh estimation introduce complex mesh regression layers over CNN based backbones. The backbones usually belong to ResNet or MobileNet family of architectures with the exception of METRO and MeshGraphormer which use HRNets [47] for feature extraction. While most hardware devices are highly optimized for feature extraction from 2D CNNs, the same is not true for the complex mesh regression heads used in these methods. In our method, we replace the complex mesh regression head with a simple regression module which regresses weak perspective camera, pose and shape parameters of the MANO model [44]. We argue that using a feature",
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+    },
+    {
+        "type": "page_number",
+        "text": "5791",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8bc5ccc15667961f918c485afa62d4dcf3eb151b9261ed558508ffd9d9fefcd9.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 8: Results on the FreiHAND test dataset. FPS is computed on NVIDIA RTX-2080Ti under similar setting as MobRecon [4]. Performance of competing methods obtained from training exclusively on FreiHand dataset."
+        ],
+        "table_body": "<table><tr><td>Method</td><td>Backbone</td><td colspan=\"5\">PJ ↓ PV ↓ F@5 ↑ F@15 ↑ FPS ↑</td></tr><tr><td colspan=\"7\">Non Real-Time methods</td></tr><tr><td>HIU-DMTL [68]</td><td>Customized</td><td>7.1</td><td>7.3</td><td>0.699</td><td>0.974</td><td>5</td></tr><tr><td>METRO [32]</td><td>HRNet</td><td>6.3</td><td>6.5</td><td>0.731</td><td>0.984</td><td>4.2</td></tr><tr><td>MeshGraphormer [33]</td><td>HRNet</td><td>5.9</td><td>6.0</td><td>0.764</td><td>0.986</td><td>2.6</td></tr><tr><td colspan=\"7\">Real-Time methods</td></tr><tr><td>Hasson et al. [19]</td><td>ResNet18</td><td>-</td><td>13.2</td><td>0.436</td><td>0.908</td><td>20</td></tr><tr><td>MobileHand [16]</td><td>MobileNetV3</td><td>-</td><td>13.1</td><td>0.439</td><td>0.902</td><td>110</td></tr><tr><td>YoutubeHand [30]</td><td>ResNet50</td><td>8.4</td><td>8.6</td><td>0.614</td><td>0.966</td><td>60</td></tr><tr><td>I2L-MeshNet [40]</td><td>ResNet50</td><td>7.4</td><td>7.6</td><td>0.681</td><td>0.973</td><td>33.3</td></tr><tr><td>Pose2Mesh [6]</td><td>Customized</td><td>7.4</td><td>7.6</td><td>0.683</td><td>0.973</td><td>20</td></tr><tr><td>I2UV-HandNet [2]</td><td>ResNet50</td><td>7.2</td><td>7.4</td><td>0.682</td><td>0.973</td><td>-</td></tr><tr><td>Tang et al. [50]</td><td>ResNet50</td><td>7.1</td><td>7.1</td><td>0.706</td><td>0.977</td><td>39.1</td></tr><tr><td>MobRecon[4]</td><td>DenseStack</td><td>6.9</td><td>7.2</td><td>0.694</td><td>0.979</td><td>77</td></tr><tr><td>CMR [3]</td><td>ResNet50*</td><td>6.9</td><td>7.0</td><td>0.715</td><td>0.977</td><td>-</td></tr><tr><td>Ours</td><td>FastViT-MA36</td><td>6.6</td><td>6.7</td><td>0.722</td><td>0.981</td><td>218</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "extraction backbone that learns a good representation for underlying images can alleviate learning challenges in mesh regression. While other real-time methods compensate for weak feature extraction backbone with complex mesh regression layers, we use a better feature extraction backbone with a simple mesh regression layer. We compare our approach with other published methods on the FreiHand [71] dataset. For a fair comparison, we cite results of methods that only used FreiHand dataset for training as some methods either pre-train, train, or fine-tune with additional pose datasets. We only use ImageNet-1k dataset for pretraining and then train exclusively on the FreiHand dataset using the experimental setup described in [32]. For more details, please see supplementary materials. From Table 8, amongst real-time methods, our method outperforms other methods on all joint and vertex error related metrics while being  $1.9 \\times$  faster than MobileHand [16] and  $2.8 \\times$  faster than recent state-of-art MobRecon.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Semantic Segmentation and Object Detection",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For semantic segmentation, we validate the performance of our models on ADE20k [70]. The dataset contains 20K training images and 2K validation images with 150 semantic categories. We train semantic segmentation models with Semantic FPN [28] decoder. Models with Semantic FPN head use the same settings as [65]. All models are initialized with pretrained weights from their corresponding image classification models. FLOPs and backbone latency are estimated on image crops of  $512 \\times 512$ . Due to higher resolution of input image, GPU latencies are estimated over a batch size of 2 in both Table 9 and Table 10. In Table 9, we compare our models with recent works. FastViT-MA36 model obtains  $5.2\\%$  higher mIoU than PoolFormer-M36",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/b6329ee2e4c03714aaa80806c8801cdd416718b166644402ec2ba9609dba276a.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 9: Performance of different backbones on ADE20K semantic segmentation task. Following common convention, FLOPs and backbone latencies are measured on crops of  $512 \\times 512$ ."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Backbone</td><td rowspan=\"2\">GPU Latency</td><td rowspan=\"2\">Mobile Latency</td><td colspan=\"3\">Semantic FPN 80k</td></tr><tr><td>Param(M)</td><td>FLOPs(G)</td><td>mIoU(%)</td></tr><tr><td>ResNet-50</td><td>2.7</td><td>8.7</td><td>28.5</td><td>46</td><td>36.7</td></tr><tr><td>PoolFormer-S12[65]</td><td>9.7</td><td>6.2</td><td>15.7</td><td>31</td><td>37.2</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>14.1</td><td>29</td><td>38.0</td></tr><tr><td>ResNet-101</td><td>4.6</td><td>12.4</td><td>47.5</td><td>65</td><td>38.8</td></tr><tr><td>PVT-Small[58]</td><td>-</td><td>-</td><td>28.2</td><td>41</td><td>39.8</td></tr><tr><td>PoolFormer-S24[65]</td><td>18.9</td><td>10.7</td><td>23.2</td><td>48</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>23.8</td><td>37</td><td>41.0</td></tr><tr><td>PoolFormer-S36[65]</td><td>28.0</td><td>17.0</td><td>34.6</td><td>48</td><td>42.0</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>33.6</td><td>44</td><td>42.9</td></tr><tr><td>PVT-Medium[58]</td><td>-</td><td>-</td><td>48.0</td><td>55</td><td>41.6</td></tr><tr><td>PoolFormer-M36[65]</td><td>41.4</td><td>24.8</td><td>59.8</td><td>68</td><td>42.4</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.7</td><td>53</td><td>44.6</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/25b4eef0159f2ae2fbfeab081b5f9196af7d81d1fe5a07d975e0469d232c12d3.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 10: Results for object detection and instance segmentation on MS-COCO val2017 split using Mask-RCNN [20] framework using 1x training schedule, i.e. 12 epochs used for training the models. Backbone latencies are measured on crops of  $512 \\times 512$ ."
+        ],
+        "table_body": "<table><tr><td>Backbone</td><td>GPU Latency</td><td>Mobile Latency</td><td>\\(AP^b\\)</td><td>\\(AP^{b}_{50}\\)</td><td>\\(AP^{b}_{75}\\)</td><td>\\(AP^m\\)</td><td>\\(AP^{m}_{50}\\)</td><td>\\(AP^{m}_{75}\\)</td></tr><tr><td>Poolfomer-S12[65]</td><td>9.7</td><td>6.2</td><td>37.3</td><td>59.0</td><td>40.1</td><td>34.6</td><td>55.8</td><td>36.9</td></tr><tr><td>ResNet-50 [21]</td><td>2.7</td><td>8.7</td><td>38.0</td><td>58.6</td><td>41.4</td><td>34.4</td><td>55.1</td><td>36.7</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>38.9</td><td>60.5</td><td>42.2</td><td>35.9</td><td>57.6</td><td>38.1</td></tr><tr><td>ResNet-101 [21]</td><td>4.6</td><td>12.4</td><td>40.0</td><td>60.5</td><td>44.0</td><td>36.1</td><td>57.5</td><td>38.6</td></tr><tr><td>Poolfomer-S24[65]</td><td>18.9</td><td>10.7</td><td>40.1</td><td>62.2</td><td>43.4</td><td>37.0</td><td>59.1</td><td>39.6</td></tr><tr><td>PVT-S [58]</td><td>-</td><td>-</td><td>40.4</td><td>62.9</td><td>43.8</td><td>37.8</td><td>60.1</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>42.0</td><td>63.5</td><td>45.8</td><td>38.0</td><td>60.5</td><td>40.5</td></tr><tr><td>Swin-T [35]</td><td>-</td><td>-</td><td>42.2</td><td>64.6</td><td>46.2</td><td>39.1</td><td>61.6</td><td>42.0</td></tr><tr><td>Twins-SVT-S [7]</td><td>-</td><td>-</td><td>42.7</td><td>65.6</td><td>46.7</td><td>39.6</td><td>62.5</td><td>42.6</td></tr><tr><td>Twins-PCPVT-S [7]</td><td>-</td><td>52.1</td><td>42.9</td><td>65.8</td><td>47.1</td><td>40.0</td><td>62.7</td><td>42.9</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>43.8</td><td>65.1</td><td>47.9</td><td>39.4</td><td>62.0</td><td>42.3</td></tr><tr><td>CMT-S [17]</td><td>19.9</td><td>70.9</td><td>44.6</td><td>66.8</td><td>48.9</td><td>40.7</td><td>63.9</td><td>43.4</td></tr><tr><td>Poolfomer-S36[65]</td><td>28.0</td><td>17.0</td><td>41.0</td><td>63.1</td><td>44.8</td><td>37.7</td><td>60.1</td><td>40.0</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.1</td><td>66.8</td><td>49.5</td><td>40.5</td><td>63.8</td><td>43.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "which has higher FLOPs, parameter count and latency on both desktop GPU and mobile device.",
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+    {
+        "type": "text",
+        "text": "We train object detection on the MS-COCO [34] dataset with 80 classes containing 118K training and 5K validation images. In Table 10, we compare our models with recent works. All the models are trained with 1x schedule following [65] using a Mask-RCNN [20] head. All models are initialized with pretrained weights from their corresponding image classification models. We show that our models achieve state-of-the-art performance under multiple latency regimes. FastViT-MA36 model has similar performance as CMT-S, while being  $2.4 \\times$  and  $4.3 \\times$  faster on desktop GPU and mobile device respectively.",
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+    },
+    {
+        "type": "page_number",
+        "text": "5792",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We have proposed a general purpose hybrid vision transformer that is highly efficient on multiple compute fabrics: mobile devices and desktop grade GPUs. Through structural reparameterization, our model incurs reduced memory access cost. This leads to significant improvements in runtime especially at higher resolutions. In addition, we propose further architectural changes that boosts performance on ImageNet classification task and other downstream tasks like object detection, semantic segmentation and 3D hand mesh estimation. We empirically show that our backbone is highly robust to out-of-distribution samples, while being significantly faster than competing robust models.",
+        "bbox": [
+            75,
+            114,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements We thank Jen-Hao Rick Chang, Skyker Seto and Hadi Pouransari for helpful discussions and reviewing the manuscript.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            377,
+            174,
+            392
+        ],
+        "page_idx": 8
+    },
+    {
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diff --git a/2023/FastViT_ A Fast Hybrid Vision Transformer Using Structural Reparameterization/63912104-d421-4e14-8cba-166c1f78904b_model.json b/2023/FastViT_ A Fast Hybrid Vision Transformer Using Structural Reparameterization/63912104-d421-4e14-8cba-166c1f78904b_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..59a8e7a4a4523582d3c943c7c900589c3a8818e0
--- /dev/null
+++ b/2023/FastViT_ A Fast Hybrid Vision Transformer Using Structural Reparameterization/63912104-d421-4e14-8cba-166c1f78904b_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
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+            "type": "header",
+            "bbox": [
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
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+            "content": "FastViT: A Fast Hybrid Vision Transformer using Structural Reparameterization"
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+            "type": "text",
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+            "angle": 0,
+            "content": "Pavan Kumar Anasosalu Vasu† James Gabriel Jeff Zhu Oncel Tuzel Anurag Ranjan†"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Apple"
+        },
+        {
+            "type": "title",
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+            "angle": 0,
+            "content": "Abstract"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "The recent amalgamation of transformer and convolutional designs has led to steady improvements in accuracy and efficiency of the models. In this work, we introduce FastViT, a hybrid vision transformer architecture that obtains the state-of-the-art latency-accuracy trade-off. To this end, we introduce a novel token mixing operator, RepMixer, a building block of FastViT, that uses structural reparameterization to lower the memory access cost by removing skip-connections in the network. We further apply train-time overparametrization and large kernel convolutions to boost accuracy and empirically show that these choices have minimal effect on latency. We show that – our model is \\(3.5 \\times\\) faster than CMT, a recent state-of-the-art hybrid transformer architecture, \\(4.9 \\times\\) faster than EfficientNet, and \\(1.9 \\times\\) faster than ConvNeXt on a mobile device for the same accuracy on the ImageNet dataset. At similar latency, our model obtains \\(4.2\\%\\) better Top-1 accuracy on ImageNet than MobileOne. Our model consistently outperforms competing architectures across several tasks – image classification, detection, segmentation and 3D mesh regression with significant improvement in latency on both a mobile device and a desktop GPU. Furthermore, our model is highly robust to out-of-distribution samples and corruptions, improving over competing robust models. Code and models are available at https://github.com/apple/ml-fastvit"
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+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "1. Introduction"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Vision Transformers [14] have achieved state-of-the-art performance on several tasks such as image classification, detection and segmentation [35]. However, these models have traditionally been computationally expensive. Recent works [66, 39, 41, 57, 29] have proposed methods to lower the compute and memory requirements of vision transformers. Recent hybrid architectures [41, 17, 10, 62] effectively"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "combine the strengths of convolutional architectures and transformers to build architectures that are highly competitive on a wide range of computer vision tasks. Our goal is to build a model that achieves state-of-the-art latency-accuracy trade-off."
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+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "Recent vision and hybrid transformer models [51, 17, 42, 41] follow the Metaformer [65] architecture, which consists of a token mixer with a skip connection followed by Feed Forward Network (FFN) with another skip connection. These skip connections account for a significant overhead in latency due to increased memory access cost [13, 55]. To address this latency overhead, we introduce RepMixer, a fully reparameterizable token mixer that uses structural reparameterization to remove the skip-connections. The RepMixer block also uses depthwise convolutions for spatial mixing of information similar to ConvMixer [53]. However, the key difference is that our module can be reparameterized at inference to remove any branches."
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+            "type": "text",
+            "bbox": [
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+            "content": "To further improve on latency, FLOPs and parameter count, we replace all dense \\( \\mathrm{k} \\times \\mathrm{k} \\) convolutions with their factorized version, i.e. depthwise followed by pointwise convolutions. This is a common approach used by efficient architectures [26, 46, 25] to improve on efficiency metrics, but, naively using this approach hurts performance as seen in Table 1. In order to increase capacity of the these layers, we use linear train-time overparameterization as introduced in [13, 11, 12, 55, 18]. These additional branches are only introduced during training and are reparameterized at inference."
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+            "type": "text",
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+            "content": "In addition, we use large kernel convolutions in our network. This is because, although self-attention based token mixing is highly effective to attain competitive accuracy, they are inefficient in terms of latency [39]. Therefore, we incorporate large kernel convolutions in Feed Forward Network (FFN) [14] layer and patch embedding layers. These changes have minimal impact on overall latency of the model while improving performance."
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+            "content": "Thus, we introduce FastViT that is based on three key design principles - i) use of RepMixer block to remove skip connections, ii) use of linear train-time overparameteriza"
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+            "content": "corresponding authors: {panasosaluvasu, anuragr} \\(@\\) apple.com"
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+            "bbox": [
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+            "angle": 0,
+            "content": "(a)"
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+        {
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+            "content": "Figure 1: (a) Accuracy vs. Mobile latency scaling curves of recent methods. The models are benchmarked on an iPhone 12 Pro following [55]. (b) Accuracy vs. GPU latency scaling curves of recent methods. For better readability only models with Top-1 accuracy better than \\(79\\%\\) are plotted. See supplementary materials for more plots. Across both compute fabrics, our model has the best accuracy-latency tradeoff."
+        },
+        {
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+            "angle": 0,
+            "content": "tion to improve accuracy, iii) use of large convolutional kernels to substitute self-attention layers in early stages."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "FastViT achieves significant improvements in latency compared to other hybrid vision transformer architectures while maintaining accuracy on several tasks like - image classification, object detection, semantic segmentation and 3d hand mesh estimation. We perform a comprehensive analysis by deploying recent state-of-the-art architectures on an iPhone 12 Pro device and an NVIDIA RTX-2080Ti desktop GPU."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In Figure 1, we show that, at ImageNet Top-1 accuracy of \\(83.9\\%\\), our model is \\(4.9 \\times\\) faster than EfficientNet-B5 [48], \\(1.6 \\times\\) faster than EfficientNetV2-S [49], \\(3.5 \\times\\) faster than CMT-S [17] and \\(1.9 \\times\\) faster than ConvNeXt-B [36] on an iPhone 12 Pro mobile device. At ImageNet Top-1 accuracy of \\(84.9\\%\\) our model is just as fast as NFNet-F1 [1] on a desktop GPU while being \\(66.7\\%\\) smaller, using \\(50.1\\%\\) less FLOPs and \\(42.8\\%\\) faster on mobile device. At latency of \\(0.8\\mathrm{ms}\\) on an iPhone 12 Pro mobile device, our model obtains \\(4.2\\%\\) better Top-1 accuracy on ImageNet than MobileOne-S0. For object detection and instance segmentation on MS COCO using Mask-RCNN [20] head, our model attains comparable performance to CMT-S [17] while incurring \\(4.3 \\times\\) lower backbone latency. For semantic segmentation on ADE20K, our model improves over PoolFormer-M36 [65] by \\(5.2\\%\\), while incurring a \\(1.5 \\times\\) lower backbone latency on an iPhone 12 Pro mobile device. On 3D hand mesh estimation task, our model is \\(1.9 \\times\\) faster than MobileHand [16] and \\(2.8 \\times\\) faster than recent state-of-the-art MobRecon [4] when benchmarked on GPU."
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+            "angle": 0,
+            "content": "In addition to accuracy metrics, we also study the robustness of our models to corruption and out-of-distribution"
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+                0.892,
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+            ],
+            "angle": 0,
+            "content": "samples which does not always correlate well with accuracy. For example, PVT [58] achieves highly competitive performance on ImageNet dataset, but has very poor robustness to corruption and out-of-distribution samples as reported in Mao et al. [38]. In real world applications, using a robust model in such a scenario can significantly improve user experience. We demonstrate the robustness of our architecture on popular benchmarks and show that our models are highly robust to corruption and out-of-distribution samples while being significantly faster than competing robust models. In summary, our contributions are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.581,
+                0.892,
+                0.643
+            ],
+            "angle": 0,
+            "content": "- We introduce FastViT, a hybrid vision transformer that uses structural reparameterization to obtain lower memory access cost and increased capacity, achieving state-of-the-art accuracy-latency trade-off."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.645,
+                0.892,
+                0.691
+            ],
+            "angle": 0,
+            "content": "- We show that our models are the fastest in terms of latency on two widely used platforms - mobile device and desktop GPU."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.694,
+                0.892,
+                0.739
+            ],
+            "angle": 0,
+            "content": "- We show that our models generalize to many tasks - image classification, object detection, semantics segmentation, and 3D hand mesh regression."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.742,
+                0.892,
+                0.788
+            ],
+            "angle": 0,
+            "content": "- We show that our models are robust to corruption and out-of-distribution samples and significantly faster than competing robust models."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.5,
+                0.581,
+                0.892,
+                0.788
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.8,
+                0.642,
+                0.816
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For the past decade, convolutional neural networks have been the standard architecture for vision models [21, 43, 64, 48, 49, 26, 46, 25, 36, 13, 55]. More recently, transformers have shown great success on computer vision tasks [14, 63, 51, 35, 58, 52, 42, 41]. Unlike convolutional"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "5786"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.198
+            ],
+            "angle": 0,
+            "content": "layers, the self-attention layers in vision transformers provide a global context by modeling long-range dependencies. Unfortunately, this global scope often comes at a high computational price [39]. Works like [41, 57, 29, 39] address ways to alleviate computational costs associated with self-attention layers. In our work, we explore an efficient alternative to self-attention layers for lower latency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.207,
+                0.473,
+                0.404
+            ],
+            "angle": 0,
+            "content": "Hybrid Vision Transformers In order to design efficient networks while maintaining accuracy, recent works introduce hybrid architectures that combine convolutional and transformer design to effectively capture local and global information. Some designs replace the patchify stem [14] with convolutional layers [63], introduce early convolutional stages [9, 41] or implicitly hybridize through windowed attention [35, 7]. More recent works build explicit hybrid structures for better exchange of information between tokens (or patches) [17, 10, 62]. In majority of the hybrid architectures, token mixers are predominantly self-attention based. Recently, MetaFormer [65] introduced Pooling, a simple and efficient candidate for token mixing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.413,
+                0.473,
+                0.685
+            ],
+            "angle": 0,
+            "content": "Structural Reparameterization Recent work [13, 55] shows the benefits of reparameterizing skip connections to lower memory access cost. In our model, we introduce a novel architectural component RepMixer, that is reparameterizable at inference. For better efficiency, works like [26, 46, 25, 37, 69] introduce factorized \\(\\mathrm{k}\\times \\mathrm{k}\\) convolutions using depthwise or grouped convolutions followed by \\(1\\times 1\\) pointwise convolutions. While this approach is highly effective in improving the overall efficiency of the model, the lower parameter count can lead to reduced capacity. Recently, linear train-time over overparameterization was introduced in [55, 11, 12] to improve capacity of such models. We use factorized \\(\\mathrm{k}\\times \\mathrm{k}\\) convolutions in our model and boost the capacity of these layers using linear train-time overparameterization. To the best of our knowledge, structural reparameterization to remove skip connections and linear overparameterization has not been attempted in any prior hybrid transformer architecture."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.7,
+                0.21,
+                0.715
+            ],
+            "angle": 0,
+            "content": "3. Architecture"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.188,
+                0.74
+            ],
+            "angle": 0,
+            "content": "3.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.794
+            ],
+            "angle": 0,
+            "content": "FastViT is a hybrid transformer and has four distinct stages which operate at different scales as shown in Figure 2. We detail all the FastViT variants in Table 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "FastViT uses RepMixer, a token mixer that reparameterizes a skip connection, which helps in alleviating memory access cost (see Figure 2d). To further improve efficiency and performance, we replace dense \\( \\mathrm{k} \\times \\mathrm{k} \\) convolutions commonly found in stem and patch embedding layers with its factorized version that uses train-time overparameterization (see Figure 2a)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.089,
+                0.878,
+                0.264
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Architectural Choices</td><td>Params (M)</td><td>FLOPs (G)</td><td>Mobile Latency (ms)</td><td>Top-1 (%)</td></tr><tr><td rowspan=\"2\">PoolFormer-S12 (Baseline) + 224 → 256</td><td>11.9</td><td>1.8</td><td>1.50</td><td>77.2</td></tr><tr><td>11.9</td><td>2.4</td><td>2.25</td><td>77.6</td></tr><tr><td>Section 3.2.1 + Pooling → RepMixer</td><td>11.9</td><td>2.4</td><td>1.58</td><td>78.5</td></tr><tr><td rowspan=\"2\">Section 3.2.2 + Factorized dense conv. + Train-Time Overparam.</td><td>8.7</td><td>1.7</td><td>1.26</td><td>78.0</td></tr><tr><td>8.7</td><td>1.7</td><td>1.26</td><td>78.9</td></tr><tr><td rowspan=\"2\">Section 3.2.3 + LK. conv. FFN + LK. conv. Patch Emb.</td><td>8.7</td><td>1.8</td><td>1.33</td><td>79.4</td></tr><tr><td>8.8</td><td>1.8</td><td>1.40</td><td>79.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.273,
+                0.894,
+                0.32
+            ],
+            "angle": 0,
+            "content": "Table 1: Analysis of architectural choices made to obtain FastViT-S12 variant, starting from PoolFormer-S12. \"LK.\" stands for Large Kernel."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.347,
+                0.892,
+                0.437
+            ],
+            "angle": 0,
+            "content": "Self-attention [14] token mixers are computationally expensive, especially at higher resolutions [42, 39]. While efficient versions of self-attention layers are explored in [17, 41], we use large kernel convolutions as an efficient alternative to improve receptive field in early stages of the network architecture (see Figure 2c)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.438,
+                0.894,
+                0.484
+            ],
+            "angle": 0,
+            "content": "We analyze various architectural choices made in designing FastViT from a PoolFormer [65] baseline in Table 1 and detail our approach below."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.494,
+                0.6,
+                0.509
+            ],
+            "angle": 0,
+            "content": "3.2. FastViT"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.518,
+                0.807,
+                0.535
+            ],
+            "angle": 0,
+            "content": "3.2.1 Reparameterizing Skip Connections"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.542,
+                0.894,
+                0.589
+            ],
+            "angle": 0,
+            "content": "RepMixer Convolutional mixing was first introduced in ConvMixer[53]. For an input tensor \\(X\\), the mixing block in the layer was implemented as,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.577,
+                0.592,
+                0.891,
+                0.608
+            ],
+            "angle": 0,
+            "content": "\\[\nY = \\operatorname {B N} \\left(\\sigma (\\operatorname {D W C o n v} (X))\\right) + X \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.611,
+                0.892,
+                0.686
+            ],
+            "angle": 0,
+            "content": "where \\(\\sigma\\) is a non-linear activation function and BN is Batch Normalization [27] layer and DwConv is depthwise convolutional layer. While this block was shown to be effective, in RepMixer, we simply rearrange the operations and remove the non-linear activation function as shown below,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.597,
+                0.69,
+                0.891,
+                0.706
+            ],
+            "angle": 0,
+            "content": "\\[\nY = \\operatorname {D W C o n v} (\\mathrm {B N} (X) + X \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.709,
+                0.892,
+                0.754
+            ],
+            "angle": 0,
+            "content": "The main benefit of our design is that it can be reparameterized at inference time to a single depthwise convolutional layer as shown below and in Figure 2d."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.629,
+                0.758,
+                0.891,
+                0.773
+            ],
+            "angle": 0,
+            "content": "\\[\nY = \\operatorname {D W C o n v} (X) \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Positional Encodings We use conditional positional encodings [7, 8] that is dynamically generated and conditioned on the local neighborhood of the input tokens. These encodings are generated as a result of a depth-wise convolution operator and are added to the patch embeddings. Note the lack of non-linearities in this group of operations, hence this block is reparameterized as shown in Figure 2a."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5787"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.091,
+                0.087,
+                0.482,
+                0.47
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.346,
+                0.47,
+                0.366,
+                0.482
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.482,
+                0.089,
+                0.878,
+                0.328
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.669,
+                0.329,
+                0.69,
+                0.342
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.482,
+                0.342,
+                0.877,
+                0.469
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.731,
+                0.47,
+                0.75,
+                0.482
+            ],
+            "angle": 0,
+            "content": "(d)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.493,
+                0.892,
+                0.555
+            ],
+            "angle": 0,
+            "content": "Figure 2: (a) Overview of FastViT architecture which decouples train-time and inference-time architecture. Stages 1, 2, and 3 have the same architecture and uses RepMixer for token mixing. In stage 4, self attention layers are used for token mixing. (b) Architecture of the convolutional stem. (c) Architecture of convolutional-FFN (d) Overview of RepMixer block, which reparameterizes a skip connection at inference."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.564,
+                0.473,
+                0.71
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.719,
+                0.47,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Figure 3: Latency comparison of a MetaFormer (S12) architecture with Pooling and RepMixer as a choice for token mixing; measured on iPhone 12 Pro for various image resolutions. Both models have \\(\\sim 1.8\\mathrm{G}\\) FLOPs. Absence of a skip connection in RepMixer lowers the overall memory access cost leading to lower latency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Empirical Analysis In order to verify the benefits of reparameterizing skip connections, we ablate over the using one of the most efficient (in terms of latency) token mixer, i.e. Pooling and RepMixer in a MetaFormer S12 architecture. Both the models being ablated have \\(\\sim 1.8\\mathrm{G}\\) FLOPs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.567,
+                0.892,
+                0.674
+            ],
+            "angle": 0,
+            "content": "We time the models for various input resolutions starting from \\(224 \\times 224\\) to \\(1024 \\times 1024\\) on an iPhone 12 Pro mobile device. From Figure 3, we see that RepMixer significantly improves over Pooling, especially at higher resolutions. At \\(384 \\times 384\\), using RepMixer will lower the latency by \\(25.1\\%\\) and at larger resolutions like \\(1024 \\times 1024\\), latency is lowered significantly by \\(43.9\\%\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.681,
+                0.84,
+                0.696
+            ],
+            "angle": 0,
+            "content": "3.2.2 Linear Train-time Overparameterization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In order to further improve efficiency (parameter count, FLOPs, and latency), we replace all dense \\(\\mathrm{k} \\times \\mathrm{k}\\) convolutions with its factorized version, i.e. \\(\\mathrm{k} \\times \\mathrm{k}\\) depthwise followed by \\(1 \\times 1\\) pointwise convolutions. However, the lower parameter count from factorization can diminish the capacity of the model. In order to increase capacity of the factorized layers, we perform linear train-time overparameterization as described in MobileOne [55]. MobileOne-style overparameterization in stem, patch embedding, and projection layers help in boosting performance. From Table 3, we note that train-time overparameterization improves Top-1 accuracy on ImageNet by \\(0.6\\%\\) on FastViT-SA12 model. On a smaller FastViT-S12 variant, Top-1 accuracy improves"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5788"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.09,
+                0.468,
+                0.457
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Stage</td><td rowspan=\"2\">#Tokens</td><td rowspan=\"2\" colspan=\"2\">Layer Spec.</td><td colspan=\"7\">FastViT</td></tr><tr><td>T8</td><td>T12</td><td>S12</td><td>SA12</td><td>SA24</td><td>SA36</td><td>MA36</td></tr><tr><td rowspan=\"3\">Stem</td><td rowspan=\"3\">H×W</td><td rowspan=\"3\" colspan=\"2\">Conv.</td><td colspan=\"7\">3 × 3, stride 2</td></tr><tr><td colspan=\"7\">3 × 3 MobileOne Style, stride 2</td></tr><tr><td>48</td><td colspan=\"5\">64</td><td>76</td></tr><tr><td rowspan=\"5\">1</td><td rowspan=\"2\">H/4 × W/4</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>48</td><td colspan=\"5\">64</td><td>76</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"7\">RepMixer</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td rowspan=\"5\">2</td><td rowspan=\"2\">H/8 × W/8</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>96</td><td colspan=\"5\">128</td><td>152</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"7\">RepMixer</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td rowspan=\"5\">3</td><td rowspan=\"2\">H/16 × W/16</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>192</td><td colspan=\"5\">256</td><td>304</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"7\">RepMixer</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>4</td><td>6</td><td>6</td><td>6</td><td>12</td><td>18</td><td>18</td></tr><tr><td rowspan=\"5\">4</td><td rowspan=\"2\">H/32 × W/32</td><td rowspan=\"2\" colspan=\"2\">Patch Embed.</td><td colspan=\"7\">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>384</td><td colspan=\"5\">512</td><td>608</td></tr><tr><td rowspan=\"3\">FastViTBlock</td><td colspan=\"2\">Mixer</td><td colspan=\"2\">RepMixer</td><td colspan=\"5\">Attention</td></tr><tr><td colspan=\"2\">Exp.</td><td colspan=\"2\">3</td><td colspan=\"5\">4</td></tr><tr><td colspan=\"2\">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td colspan=\"4\">Parameters (M)</td><td>3.6</td><td>6.8</td><td>8.8</td><td>10.9</td><td>20.6</td><td>30.4</td><td>42.7</td></tr><tr><td colspan=\"4\">FLOPs (G)</td><td>0.7</td><td>1.4</td><td>1.8</td><td>1.9</td><td>3.8</td><td>5.6</td><td>7.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.467,
+                0.47,
+                0.604
+            ],
+            "angle": 0,
+            "content": "Table 2: Architecture details of FastViT variants. Models with smaller embedding dimensions, i.e. [64, 128, 256, 512] are prefixed with \"S\" and models that contain Self-Attention layers are prefixed with \"SA\". Models with bigger embedding dimensions, i.e. [76, 152, 304, 608] are prefixed with \"M\". Models with MLP expansion ratio less than 4 are prefixed with \"T\". The number in the notation denotes total number of FastViT blocks. FLOP count is computed by fvcore[15] library."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.663,
+                0.275,
+                0.679
+            ],
+            "angle": 0,
+            "content": "by \\(0.9\\%\\) as shown in Table 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.702,
+                0.471,
+                0.913
+            ],
+            "angle": 0,
+            "content": "However, train-time overparameterization results in increased training time due to computational overhead from the added branches. In our architecture, we only overparameterize those layers that replace dense \\( \\mathrm{k} \\times \\mathrm{k} \\) convolutions with its factorized form as described above. These layers are found in the convolutional stem, patch embedding and projection layers. The computational cost incurred in these layers are lower than the rest of the network, hence overparameterizing these layers do not result in significant increases to train time. For example, FastViT-SA12 takes \\( 6.7\\% \\) longer and FastViT-SA36 takes \\( 4.4\\% \\) longer to train with train-time overparameterization as opposed to training those variants without it under the same settings described in Section 4.1."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.09,
+                0.891,
+                0.158
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Ablation</td><td>Top-1 (%)</td><td>Train Time (hrs)</td></tr><tr><td rowspan=\"2\">FastViT-SA12</td><td>Without Train-Time Overparam.</td><td>80.0</td><td>31.3</td></tr><tr><td>With Train-Time Overparam.</td><td>80.6</td><td>33.4</td></tr><tr><td rowspan=\"2\">FastViT-SA36</td><td>Without Train-Time Overparam.</td><td>83.3</td><td>73.5</td></tr><tr><td>With Train-Time Overparam.</td><td>83.6</td><td>76.7</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.167,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "Table 3: Comparison of FastViT variants with and without linear train-time overparameterization when trained on ImageNet-1k dataset. Train time is wall clock time elapsed at the end of a training run."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.241,
+                0.743,
+                0.256
+            ],
+            "angle": 0,
+            "content": "3.2.3 Large Kernel Convolutions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.264,
+                0.892,
+                0.566
+            ],
+            "angle": 0,
+            "content": "The receptive field of RepMixer is local compared to self-attention token mixers. However, self-attention based token mixers are computationally expensive. A computationally efficient approach to improve the receptive field of early stages that do not use self-attention is by incorporating depthwise large kernel convolutions. We introduce depthwise large kernel convolutions in FFN and patch embedding layers. From Table 4, we note that variants using depthwise large kernel convolutions can be highly competitive to variants using self-attention layers while incurring a modest increase in latency. When we compare V5 with V3, model size increases by \\(11.2\\%\\), and latency increases by a factor of \\(2.3 \\times\\) for a relatively small gain of \\(0.4\\%\\) in Top-1 accuracy. V2 is larger than V4 by \\(20\\%\\) and has \\(7.1\\%\\) higher latency than V4 while attaining similar Top-1 accuracy on ImageNet. Further ablations on kernel sizes and latency is provided in the supplementary materials. In Table 1, we ablate over large kernel convolutions in FFN and patch embedding layers. Overall, large kernel convolutions provide \\(0.9\\%\\) improvement in Top-1 accuracy on FastViT-S12."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.567,
+                0.892,
+                0.687
+            ],
+            "angle": 0,
+            "content": "The architecture of our FFN and patch embedding layer is shown in Figure 2. Our FFN block has a structure similar to ConvNeXt [36] block with a few key differences, see Figure 2c. We use Batch Normalization as opposed to Layer Normalization, as it can be fused with the preceding layer at inference. Also, it does not require additional reshape operations to obtain appropriate tensor layout for LayerNorm as done in the original implementation of ConvNeXt block."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.688,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Along with increased receptive field, large kernel convolutions help in improving model robustness as observed in [59] and convolutional-FFN blocks generally tend to be more robust than vanilla-FFN blocks as observed in [38]. Hence, incorporating large kernel convolutions is an efficient way to improve model performance and robustness."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.792,
+                0.634,
+                0.809
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.817,
+                0.692,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.1. Image Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We report results on the widely used ImageNet-1K dataset [45] which contains \\(\\sim 1.3\\mathrm{M}\\) training images and \\(50\\mathrm{K}\\) validation images. We follow the training recipe prescribed in [51, 65], i.e. the models are trained for 300"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5789"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.089,
+                0.464,
+                0.228
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Variant</td><td colspan=\"4\">Stages</td><td>Params</td><td>Top-1</td><td>Mobile</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>(M)</td><td>(%)</td><td>Latency (ms)</td></tr><tr><td colspan=\"8\">Standard Setting</td></tr><tr><td>V1</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.7</td><td>78.9</td><td>1.3</td></tr><tr><td>V2</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.8</td><td>79.9</td><td>1.5</td></tr><tr><td>V3</td><td>RM</td><td>RM</td><td>SA</td><td>SA</td><td>12.4</td><td>81.0</td><td>3.7</td></tr><tr><td colspan=\"8\">Large Kernel Convolutions (7×7)</td></tr><tr><td>V4</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.8</td><td>79.8</td><td>1.4</td></tr><tr><td>V5</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.9</td><td>80.6</td><td>1.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.239,
+                0.47,
+                0.359
+            ],
+            "angle": 0,
+            "content": "Table 4: Ablation on using large kernel convolutions as a substitute for self-attention layers. \"RM\" indicates [RepMixer-FFN] block is used in the stage. \"SA\" indicates [Self Attention-FFN] block is used in the stage. Standard setting uses \\(3 \\times 3\\) factorized convolutions in patch embedding and stem layers and \\(1 \\times 1\\) convolutions for FFN. In variants V4 and V5, large kernel convolutions \\((7 \\times 7)\\) are used in patch embedding and FFN layers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.387,
+                0.47,
+                0.659
+            ],
+            "angle": 0,
+            "content": "epochs using AdamW optimizer with weight decay of 0.05 and peak learning rate \\(10^{-3}\\) for a total batch size of 1024. The number of warmup epochs is set to 5 and cosine schedule is used to decay the learning rate. Our implementation uses timm library [60] and all the models were trained on 8 NVIDIA A100 GPUs. See supplementary materials for details on hyper parameters used for all the variants. For \\(384 \\times 384\\) input size, we fine-tune the models for 30 epochs with weight decay of \\(10^{-8}\\) and learning rate of \\(5 \\times 10^{-5}\\) and batch size of 512 following [36]. To measure latency, we use the input sizes corresponding to the respective methods. For iPhone latency measurements, we export the models using Core ML Tools (v6.0) and run it on iPhone12 Pro Max with iOS 16 and batch size is set to 1 for all the models. We follow the same protocol as [55]. For GPU latency measurements, we export the traced model to TensorRT (v8.0.1.6) format and run it on NVIDIA RTX-2080Ti with batch size of 8. We report the median latency estimate from 100 runs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Comparison with SOTA Models In Table 5, we compare our models against recent state-of-the-art models on ImageNet-1k dataset. For a fair comparison, we modify ConvNeXt [36] from official implementation by avoiding costly reshape operations, see supplementary materials for more details. We were unable to reliably export LITv2 [41] due to poor support for deformable convolutions in either library. Our model obtains the best accuracy-latency trade-off when compared to recent state-of-the-art models on two different compute fabrics, i.e. desktop-grade GPU and mobile device. Our models improve over LITv2 [41] on both parameter count and FLOPs, at Top-1 accuracy of \\(84.9\\%\\), FastViT-MA36 is \\(49.3\\%\\) smaller and consumes \\(55.4\\%\\) less FLOPs than LITv2-B. FastViT-S12 is \\(26.3\\%\\) faster than MobileOne-S4 [55] on iPhone 12 Pro and \\(26.9\\%\\) faster on"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.513,
+                0.089,
+                0.88,
+                0.791
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>MobileOne-S0[55]</td><td>224</td><td>2.1</td><td>0.3</td><td>1.0</td><td>0.8</td><td>71.4</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>75.6</td></tr><tr><td>MobileOne-S3[55]</td><td>224</td><td>10.1</td><td>1.8</td><td>2.1</td><td>1.5</td><td>78.1</td></tr><tr><td>CMT-T* [17]</td><td>160</td><td>9.5</td><td>0.6</td><td>4.5</td><td>3.8</td><td>79.1</td></tr><tr><td>EfficientNet-B1[48]</td><td>256</td><td>7.8</td><td>0.7</td><td>3.2</td><td>2.5</td><td>79.1</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>79.1</td></tr><tr><td>MobileOne-S4[55]</td><td>224</td><td>14.8</td><td>2.9</td><td>2.6</td><td>1.9</td><td>79.4</td></tr><tr><td>RSB-ResNet50[61]</td><td>224</td><td>25.6</td><td>4.1</td><td>2.3</td><td>2.6</td><td>79.8</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22.0</td><td>4.6</td><td>5.2</td><td>5.3</td><td>79.8</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>79.8</td></tr><tr><td>RegNetY-8G[43]</td><td>224</td><td>39.2</td><td>8.0</td><td>5.8</td><td>3.8</td><td>79.9</td></tr><tr><td>EfficientNet-B2[48]</td><td>288</td><td>9.2</td><td>1.0</td><td>4.1</td><td>3.5</td><td>80.1</td></tr><tr><td>PoolFormer-S24[65]</td><td>224</td><td>21.0</td><td>3.4</td><td>15.7</td><td>2.5</td><td>80.3</td></tr><tr><td>RegNetY-16G [43]</td><td>224</td><td>83.6</td><td>16.0</td><td>8.1</td><td>7.5</td><td>80.4</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>80.6</td></tr><tr><td>ResNeSt50[67]</td><td>224</td><td>27.5</td><td>5.4</td><td>51.5</td><td>29.9</td><td>81.1</td></tr><tr><td>Swin-T[35]</td><td>224</td><td>29.0</td><td>4.5</td><td>-</td><td>9.3</td><td>81.3</td></tr><tr><td>PoolFormer-S36[65]</td><td>224</td><td>31.0</td><td>5.0</td><td>23.7</td><td>3.5</td><td>81.4</td></tr><tr><td>EfficientNet-B3[48]</td><td>300</td><td>12.0</td><td>1.8</td><td>5.3</td><td>7.1</td><td>81.6</td></tr><tr><td>CvT-13[62]</td><td>224</td><td>20.1</td><td>4.5</td><td>18.1</td><td>62.6</td><td>81.6</td></tr><tr><td>CoAtNet-0[9]</td><td>224</td><td>25.0</td><td>4.2</td><td>-</td><td>6.7</td><td>81.6</td></tr><tr><td>CMT-XS* [17]</td><td>192</td><td>15.2</td><td>1.5</td><td>8.3</td><td>6.3</td><td>81.8</td></tr><tr><td>DeiT-B [51]</td><td>224</td><td>86.0</td><td>17.5</td><td>11.6</td><td>11.6</td><td>81.8</td></tr><tr><td>RSB-ResNet152[61]</td><td>224</td><td>60.2</td><td>11.6</td><td>5.4</td><td>4.7</td><td>81.8</td></tr><tr><td>LITv2-S[41]</td><td>224</td><td>28.0</td><td>3.7</td><td>-</td><td>-</td><td>82.0</td></tr><tr><td>ConvNeXt-T†[36]</td><td>224</td><td>29.0</td><td>4.5</td><td>6.3</td><td>3.7</td><td>82.1</td></tr><tr><td>PoolFormer-M48[65]</td><td>224</td><td>73.0</td><td>11.6</td><td>30.2</td><td>7.6</td><td>82.5</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>82.6</td></tr><tr><td>ResNeSt101[67]</td><td>224</td><td>48.2</td><td>10.2</td><td>75.5</td><td>37.7</td><td>83.0</td></tr><tr><td>Swin-S[35]</td><td>224</td><td>50.0</td><td>8.7</td><td>-</td><td>13.0</td><td>83.0</td></tr><tr><td>ConvNeXt-S†[36]</td><td>224</td><td>50.0</td><td>8.7</td><td>10.3</td><td>5.4</td><td>83.1</td></tr><tr><td>MOAT-0[5]</td><td>224</td><td>27.8</td><td>5.7</td><td>-</td><td>4.9</td><td>83.3</td></tr><tr><td>CoAtNet-1[9]</td><td>224</td><td>42.0</td><td>8.4</td><td>-</td><td>13.4</td><td>83.3</td></tr><tr><td>Swin-B [35]</td><td>224</td><td>88.0</td><td>15.4</td><td>-</td><td>18.5</td><td>83.5</td></tr><tr><td>CMT-S* [17]</td><td>224</td><td>25.1</td><td>4.0</td><td>13.8</td><td>15.6</td><td>83.5</td></tr><tr><td>MaxViT-T[54]</td><td>224</td><td>31.0</td><td>5.6</td><td>-</td><td>31.5</td><td>83.6</td></tr><tr><td>LITv2-B[41]</td><td>224</td><td>87.0</td><td>13.2</td><td>-</td><td>-</td><td>83.6</td></tr><tr><td>EfficientNet-B5[48]</td><td>456</td><td>30.0</td><td>9.9</td><td>24.2</td><td>22.1</td><td>83.6</td></tr><tr><td>NFNet-F0[1]</td><td>256</td><td>71.5</td><td>12.4</td><td>6.2</td><td>6.4</td><td>83.6</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>83.6</td></tr><tr><td>ConvNeXt-B†[36]</td><td>224</td><td>89.0</td><td>15.4</td><td>13.6</td><td>8.4</td><td>83.8</td></tr><tr><td>CoAtNet-0</td><td>384</td><td>25.0</td><td>13.4</td><td>-</td><td>20.1</td><td>83.9</td></tr><tr><td>EfficientNetV2-S[49]</td><td>384</td><td>22.0</td><td>8.8</td><td>8.2</td><td>7.1</td><td>83.9</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>83.9</td></tr><tr><td>EfficientNet-B6[48]</td><td>528</td><td>43.0</td><td>19.0</td><td>44.3</td><td>51.7</td><td>84.0</td></tr><tr><td>CoAtNet-2[9]</td><td>224</td><td>75.0</td><td>15.7</td><td>-</td><td>19.6</td><td>84.1</td></tr><tr><td>MOAT-1[5]</td><td>224</td><td>41.6</td><td>9.1</td><td>-</td><td>8.3</td><td>84.2</td></tr><tr><td>EfficientNet-B7[48]</td><td>600</td><td>66.0</td><td>37.0</td><td>72.6</td><td>85.5</td><td>84.3</td></tr><tr><td>CMT-B* [17]</td><td>256</td><td>45.7</td><td>9.3</td><td>26.9</td><td>20.6</td><td>84.5</td></tr><tr><td>Swin-B[35]</td><td>384</td><td>88.0</td><td>47.0</td><td>-</td><td>57.2</td><td>84.5</td></tr><tr><td>MaxViT-S[54]</td><td>224</td><td>69.0</td><td>11.7</td><td>-</td><td>48.7</td><td>84.5</td></tr><tr><td>FastViT-SA36</td><td>384</td><td>30.4</td><td>12.6</td><td>12.8</td><td>7.4</td><td>84.5</td></tr><tr><td>MOAT-0[5]</td><td>384</td><td>27.8</td><td>18.2</td><td>-</td><td>24.3</td><td>84.6</td></tr><tr><td>NFNet-F1[1]</td><td>320</td><td>132.6</td><td>35.5</td><td>16.9</td><td>16.1</td><td>84.7</td></tr><tr><td>MOAT-2[5]</td><td>224</td><td>73.4</td><td>17.2</td><td>-</td><td>12.6</td><td>84.7</td></tr><tr><td>LITv2-B[41]</td><td>384</td><td>87.0</td><td>39.7</td><td>-</td><td>-</td><td>84.7</td></tr><tr><td>FastViT-MA36</td><td>384</td><td>42.7</td><td>17.7</td><td>16.5</td><td>9.2</td><td>84.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.801,
+                0.892,
+                0.907
+            ],
+            "angle": 0,
+            "content": "Table 5: Comparison of different state-of-the-art methods on ImageNet-1k classification. HardSwish is not well supported by Core ML, * denotes we replace it with GELU for fair comparison. “†” denotes that model has been modified from original implementation for efficient deployment. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5790"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.467,
+                0.319
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>76.7</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>80.3</td></tr><tr><td>CaiT XXS-36[52]</td><td>224</td><td>17.3</td><td>3.8</td><td>15.8</td><td>-</td><td>79.7</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>80.9</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22</td><td>4.6</td><td>5.2</td><td>6.7</td><td>81.2</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>81.9</td></tr><tr><td>EfficientFormer-L3[31]</td><td>224</td><td>31.3</td><td>3.9</td><td>3.6</td><td>3.0</td><td>82.4</td></tr><tr><td>EfficientFormer-L7[31]</td><td>224</td><td>82.1</td><td>10.2</td><td>7.5</td><td>7.0</td><td>83.3</td></tr><tr><td>DeiT-B[51]</td><td>224</td><td>87</td><td>17.6</td><td>11.6</td><td>11.6</td><td>83.4</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>83.4</td></tr><tr><td>CaiT S-24[52]</td><td>224</td><td>46.9</td><td>9.4</td><td>19.1</td><td>-</td><td>83.5</td></tr><tr><td>CaiT XS-24[52]</td><td>384</td><td>26.6</td><td>19.3</td><td>77.7</td><td>-</td><td>84.1</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>84.2</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>84.6</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.33,
+                0.47,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Table 6: Comparison of different state-of-the-art methods on ImageNet-1k classification when trained using distillation objective specified by [51]. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.427,
+                0.47,
+                0.518
+            ],
+            "angle": 0,
+            "content": "GPU. At Top-1 accuracy of \\(83.9\\%\\), FastViT-MA36 is \\(1.9 \\times\\) faster than an optimized ConvNeXt-B model on iPhone 12 Pro and \\(2.0 \\times\\) faster on GPU. At Top-1 accuracy of \\(84.9\\%\\), FastViT-MA36 is just as fast as NFNet-F1 [1] on GPU while being \\(66.7\\%\\) smaller and using \\(50.1\\%\\) less FLOPs and \\(42.8\\%\\) faster on mobile device."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.534,
+                0.47,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Knowledge distillation We report performance of our models when trained with distillation objective in Table 6. We follow the setting described in DeiT [51], with RegNet-16GF [43] as the teacher model. Following DeiT [51], we use hard distillation where hard decision of the teacher is set as true label. Our models are trained for 300 epochs. Unlike [51, 52, 31], we do not introduce an additional classification head for distillation. FastViT outperforms recent state-of-the-art model EfficientFormer [31]. FastViT-SA24 attains similar performance as EfficientFormer-L7 while having \\(3.8 \\times\\) less parameters, \\(2.7 \\times\\) less FLOPs and \\(2.7 \\times\\) lower latency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.726,
+                0.288,
+                0.74
+            ],
+            "angle": 0,
+            "content": "4.2. Robustness Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We evaluate our models for out-of-distribution robustness on the following benchmarks - (i) ImageNet-A [24], a dataset that contains naturally occurring examples that are misclassified by ResNets; (ii) ImageNet-R [22], a dataset that contains natural renditions of ImageNet object classes with different textures and local image statistics; (iii) ImageNet-Sketch [56], a dataset that contains black and white sketches of all ImageNet classes, obtained using google image queries; and (iv) ImageNet-C [23], a dataset that consists of algorithmically generated corruption"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.891,
+                0.292
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>#Params</td><td>#FLOPs</td><td>Clean</td><td>IN-C (↓)</td><td>IN-A</td><td>IN-R</td><td>IN-SK</td></tr><tr><td>PVT-Tiny</td><td>13.2</td><td>1.9</td><td>75.0</td><td>79.6</td><td>7.9</td><td>33.9</td><td>21.5</td></tr><tr><td>RVT-Ti</td><td>8.6</td><td>1.3</td><td>78.4</td><td>58.2</td><td>13.3</td><td>43.7</td><td>30.0</td></tr><tr><td>FastViT-SA12</td><td>10.9</td><td>1.9</td><td>80.6</td><td>62.2</td><td>17.2</td><td>42.6</td><td>29.7</td></tr><tr><td>PVT-Small</td><td>24.5</td><td>3.8</td><td>79.9</td><td>66.9</td><td>18.0</td><td>40.1</td><td>27.2</td></tr><tr><td>ResNet-50*</td><td>25.6</td><td>4.1</td><td>79.0</td><td>65.5</td><td>5.9</td><td>42.5</td><td>31.5</td></tr><tr><td>ResNeXt50-32x4d</td><td>25.0</td><td>4.3</td><td>79.8</td><td>64.7</td><td>10.7</td><td>41.5</td><td>29.3</td></tr><tr><td>FastViT-SA24</td><td>20.6</td><td>3.8</td><td>82.6</td><td>55.3</td><td>26.0</td><td>46.5</td><td>34.0</td></tr><tr><td>Swin-T</td><td>28.3</td><td>4.5</td><td>81.2</td><td>62.0</td><td>21.6</td><td>41.3</td><td>29.1</td></tr><tr><td>ConViT-S</td><td>27.8</td><td>5.4</td><td>81.5</td><td>49.8</td><td>24.5</td><td>45.4</td><td>33.1</td></tr><tr><td>RVT-S</td><td>22.1</td><td>4.7</td><td>81.7</td><td>50.1</td><td>24.1</td><td>46.9</td><td>35.0</td></tr><tr><td>ConvNeXt-T</td><td>28.6</td><td>4.5</td><td>82.1</td><td>53.2</td><td>24.2</td><td>47.2</td><td>33.8</td></tr><tr><td>EfficientNet-B4</td><td>19.3</td><td>4.2</td><td>83.0</td><td>71.1</td><td>26.3</td><td>47.1</td><td>34.1</td></tr><tr><td>FastViT-SA36</td><td>30.4</td><td>5.6</td><td>83.6</td><td>51.8</td><td>32.3</td><td>48.1</td><td>35.8</td></tr><tr><td>ConvNeXt-S</td><td>50.0</td><td>8.7</td><td>83.1</td><td>51.2</td><td>31.2</td><td>49.5</td><td>37.1</td></tr><tr><td>FastViT-MA36</td><td>42.7</td><td>7.9</td><td>83.9</td><td>49.9</td><td>34.6</td><td>49.5</td><td>36.6</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.498,
+                0.303,
+                0.893,
+                0.424
+            ],
+            "angle": 0,
+            "content": "Table 7: Results on robustness benchmark datasets. Models are grouped based on FLOPs. Performance of competing models is reported by [38] and [36]. *ResNet-50 model is trained with AugMix to improve robustness as reported in [38]. For ImageNet-C mean corruption error is reported (lower is better) and for other datasets Top-1 accuracy is reported (higher is better). The best results are in bold and second best results are underlined."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.454,
+                0.893,
+                0.681
+            ],
+            "angle": 0,
+            "content": "tions (blur, noise) applied to the ImageNet test-set. We evaluate our models using the implementation provided by [38]. Our models are more robust than recent vision transformers while being faster than pure-CNN based models which exhibit low robustness as seen Table 7. Architectural choices like using a large kernel convolutions in FFN and patch-embedding layers in combination with self-attention layers helps in improving the robustness of our model as discussed in Section 3.2.3. All the models compared in Table 7 are trained only on ImageNet-1k dataset using similar training recipes. From Table 7, our model is highly competitive to RVT and ConvNeXt, in fact FastViT-M36 has better clean accuracy, better robustness to corruptions and similar out-of-distribution robustness as ConvNeXt-S which has 6.1M more parameters and has \\(10\\%\\) more FLOPs than our model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.695,
+                0.734,
+                0.71
+            ],
+            "angle": 0,
+            "content": "4.3. 3D Hand mesh estimation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Recent works on real-time 3D hand mesh estimation introduce complex mesh regression layers over CNN based backbones. The backbones usually belong to ResNet or MobileNet family of architectures with the exception of METRO and MeshGraphormer which use HRNets [47] for feature extraction. While most hardware devices are highly optimized for feature extraction from 2D CNNs, the same is not true for the complex mesh regression heads used in these methods. In our method, we replace the complex mesh regression head with a simple regression module which regresses weak perspective camera, pose and shape parameters of the MANO model [44]. We argue that using a feature"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5791"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.477,
+                0.304
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Backbone</td><td colspan=\"5\">PJ ↓ PV ↓ F@5 ↑ F@15 ↑ FPS ↑</td></tr><tr><td colspan=\"7\">Non Real-Time methods</td></tr><tr><td>HIU-DMTL [68]</td><td>Customized</td><td>7.1</td><td>7.3</td><td>0.699</td><td>0.974</td><td>5</td></tr><tr><td>METRO [32]</td><td>HRNet</td><td>6.3</td><td>6.5</td><td>0.731</td><td>0.984</td><td>4.2</td></tr><tr><td>MeshGraphormer [33]</td><td>HRNet</td><td>5.9</td><td>6.0</td><td>0.764</td><td>0.986</td><td>2.6</td></tr><tr><td colspan=\"7\">Real-Time methods</td></tr><tr><td>Hasson et al. [19]</td><td>ResNet18</td><td>-</td><td>13.2</td><td>0.436</td><td>0.908</td><td>20</td></tr><tr><td>MobileHand [16]</td><td>MobileNetV3</td><td>-</td><td>13.1</td><td>0.439</td><td>0.902</td><td>110</td></tr><tr><td>YoutubeHand [30]</td><td>ResNet50</td><td>8.4</td><td>8.6</td><td>0.614</td><td>0.966</td><td>60</td></tr><tr><td>I2L-MeshNet [40]</td><td>ResNet50</td><td>7.4</td><td>7.6</td><td>0.681</td><td>0.973</td><td>33.3</td></tr><tr><td>Pose2Mesh [6]</td><td>Customized</td><td>7.4</td><td>7.6</td><td>0.683</td><td>0.973</td><td>20</td></tr><tr><td>I2UV-HandNet [2]</td><td>ResNet50</td><td>7.2</td><td>7.4</td><td>0.682</td><td>0.973</td><td>-</td></tr><tr><td>Tang et al. [50]</td><td>ResNet50</td><td>7.1</td><td>7.1</td><td>0.706</td><td>0.977</td><td>39.1</td></tr><tr><td>MobRecon[4]</td><td>DenseStack</td><td>6.9</td><td>7.2</td><td>0.694</td><td>0.979</td><td>77</td></tr><tr><td>CMR [3]</td><td>ResNet50*</td><td>6.9</td><td>7.0</td><td>0.715</td><td>0.977</td><td>-</td></tr><tr><td>Ours</td><td>FastViT-MA36</td><td>6.6</td><td>6.7</td><td>0.722</td><td>0.981</td><td>218</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.313,
+                0.471,
+                0.375
+            ],
+            "angle": 0,
+            "content": "Table 8: Results on the FreiHAND test dataset. FPS is computed on NVIDIA RTX-2080Ti under similar setting as MobRecon [4]. Performance of competing methods obtained from training exclusively on FreiHand dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.4,
+                0.472,
+                0.673
+            ],
+            "angle": 0,
+            "content": "extraction backbone that learns a good representation for underlying images can alleviate learning challenges in mesh regression. While other real-time methods compensate for weak feature extraction backbone with complex mesh regression layers, we use a better feature extraction backbone with a simple mesh regression layer. We compare our approach with other published methods on the FreiHand [71] dataset. For a fair comparison, we cite results of methods that only used FreiHand dataset for training as some methods either pre-train, train, or fine-tune with additional pose datasets. We only use ImageNet-1k dataset for pretraining and then train exclusively on the FreiHand dataset using the experimental setup described in [32]. For more details, please see supplementary materials. From Table 8, amongst real-time methods, our method outperforms other methods on all joint and vertex error related metrics while being \\(1.9 \\times\\) faster than MobileHand [16] and \\(2.8 \\times\\) faster than recent state-of-art MobRecon."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.682,
+                0.462,
+                0.699
+            ],
+            "angle": 0,
+            "content": "4.4. Semantic Segmentation and Object Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For semantic segmentation, we validate the performance of our models on ADE20k [70]. The dataset contains 20K training images and 2K validation images with 150 semantic categories. We train semantic segmentation models with Semantic FPN [28] decoder. Models with Semantic FPN head use the same settings as [65]. All models are initialized with pretrained weights from their corresponding image classification models. FLOPs and backbone latency are estimated on image crops of \\(512 \\times 512\\). Due to higher resolution of input image, GPU latencies are estimated over a batch size of 2 in both Table 9 and Table 10. In Table 9, we compare our models with recent works. FastViT-MA36 model obtains \\(5.2\\%\\) higher mIoU than PoolFormer-M36"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.895,
+                0.276
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Backbone</td><td rowspan=\"2\">GPU Latency</td><td rowspan=\"2\">Mobile Latency</td><td colspan=\"3\">Semantic FPN 80k</td></tr><tr><td>Param(M)</td><td>FLOPs(G)</td><td>mIoU(%)</td></tr><tr><td>ResNet-50</td><td>2.7</td><td>8.7</td><td>28.5</td><td>46</td><td>36.7</td></tr><tr><td>PoolFormer-S12[65]</td><td>9.7</td><td>6.2</td><td>15.7</td><td>31</td><td>37.2</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>14.1</td><td>29</td><td>38.0</td></tr><tr><td>ResNet-101</td><td>4.6</td><td>12.4</td><td>47.5</td><td>65</td><td>38.8</td></tr><tr><td>PVT-Small[58]</td><td>-</td><td>-</td><td>28.2</td><td>41</td><td>39.8</td></tr><tr><td>PoolFormer-S24[65]</td><td>18.9</td><td>10.7</td><td>23.2</td><td>48</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>23.8</td><td>37</td><td>41.0</td></tr><tr><td>PoolFormer-S36[65]</td><td>28.0</td><td>17.0</td><td>34.6</td><td>48</td><td>42.0</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>33.6</td><td>44</td><td>42.9</td></tr><tr><td>PVT-Medium[58]</td><td>-</td><td>-</td><td>48.0</td><td>55</td><td>41.6</td></tr><tr><td>PoolFormer-M36[65]</td><td>41.4</td><td>24.8</td><td>59.8</td><td>68</td><td>42.4</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.7</td><td>53</td><td>44.6</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.498,
+                0.285,
+                0.895,
+                0.346
+            ],
+            "angle": 0,
+            "content": "Table 9: Performance of different backbones on ADE20K semantic segmentation task. Following common convention, FLOPs and backbone latencies are measured on crops of \\(512 \\times 512\\)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.373,
+                0.892,
+                0.578
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Backbone</td><td>GPU Latency</td><td>Mobile Latency</td><td>\\(AP^b\\)</td><td>\\(AP^{b}_{50}\\)</td><td>\\(AP^{b}_{75}\\)</td><td>\\(AP^m\\)</td><td>\\(AP^{m}_{50}\\)</td><td>\\(AP^{m}_{75}\\)</td></tr><tr><td>Poolfomer-S12[65]</td><td>9.7</td><td>6.2</td><td>37.3</td><td>59.0</td><td>40.1</td><td>34.6</td><td>55.8</td><td>36.9</td></tr><tr><td>ResNet-50 [21]</td><td>2.7</td><td>8.7</td><td>38.0</td><td>58.6</td><td>41.4</td><td>34.4</td><td>55.1</td><td>36.7</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>38.9</td><td>60.5</td><td>42.2</td><td>35.9</td><td>57.6</td><td>38.1</td></tr><tr><td>ResNet-101 [21]</td><td>4.6</td><td>12.4</td><td>40.0</td><td>60.5</td><td>44.0</td><td>36.1</td><td>57.5</td><td>38.6</td></tr><tr><td>Poolfomer-S24[65]</td><td>18.9</td><td>10.7</td><td>40.1</td><td>62.2</td><td>43.4</td><td>37.0</td><td>59.1</td><td>39.6</td></tr><tr><td>PVT-S [58]</td><td>-</td><td>-</td><td>40.4</td><td>62.9</td><td>43.8</td><td>37.8</td><td>60.1</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>42.0</td><td>63.5</td><td>45.8</td><td>38.0</td><td>60.5</td><td>40.5</td></tr><tr><td>Swin-T [35]</td><td>-</td><td>-</td><td>42.2</td><td>64.6</td><td>46.2</td><td>39.1</td><td>61.6</td><td>42.0</td></tr><tr><td>Twins-SVT-S [7]</td><td>-</td><td>-</td><td>42.7</td><td>65.6</td><td>46.7</td><td>39.6</td><td>62.5</td><td>42.6</td></tr><tr><td>Twins-PCPVT-S [7]</td><td>-</td><td>52.1</td><td>42.9</td><td>65.8</td><td>47.1</td><td>40.0</td><td>62.7</td><td>42.9</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>43.8</td><td>65.1</td><td>47.9</td><td>39.4</td><td>62.0</td><td>42.3</td></tr><tr><td>CMT-S [17]</td><td>19.9</td><td>70.9</td><td>44.6</td><td>66.8</td><td>48.9</td><td>40.7</td><td>63.9</td><td>43.4</td></tr><tr><td>Poolfomer-S36[65]</td><td>28.0</td><td>17.0</td><td>41.0</td><td>63.1</td><td>44.8</td><td>37.7</td><td>60.1</td><td>40.0</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.1</td><td>66.8</td><td>49.5</td><td>40.5</td><td>63.8</td><td>43.4</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.498,
+                0.587,
+                0.895,
+                0.664
+            ],
+            "angle": 0,
+            "content": "Table 10: Results for object detection and instance segmentation on MS-COCO val2017 split using Mask-RCNN [20] framework using 1x training schedule, i.e. 12 epochs used for training the models. Backbone latencies are measured on crops of \\(512 \\times 512\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.703,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "which has higher FLOPs, parameter count and latency on both desktop GPU and mobile device."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.739,
+                0.895,
+                0.906
+            ],
+            "angle": 0,
+            "content": "We train object detection on the MS-COCO [34] dataset with 80 classes containing 118K training and 5K validation images. In Table 10, we compare our models with recent works. All the models are trained with 1x schedule following [65] using a Mask-RCNN [20] head. All models are initialized with pretrained weights from their corresponding image classification models. We show that our models achieve state-of-the-art performance under multiple latency regimes. FastViT-MA36 model has similar performance as CMT-S, while being \\(2.4 \\times\\) and \\(4.3 \\times\\) faster on desktop GPU and mobile device respectively."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.958
+            ],
+            "angle": 0,
+            "content": "5792"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.09,
+                0.196,
+                0.106
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.116,
+                0.473,
+                0.298
+            ],
+            "angle": 0,
+            "content": "We have proposed a general purpose hybrid vision transformer that is highly efficient on multiple compute fabrics: mobile devices and desktop grade GPUs. Through structural reparameterization, our model incurs reduced memory access cost. This leads to significant improvements in runtime especially at higher resolutions. In addition, we propose further architectural changes that boosts performance on ImageNet classification task and other downstream tasks like object detection, semantic segmentation and 3D hand mesh estimation. We empirically show that our backbone is highly robust to out-of-distribution samples, while being significantly faster than competing robust models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.318,
+                0.471,
+                0.364
+            ],
+            "angle": 0,
+            "content": "Acknowledgements We thank Jen-Hao Rick Chang, Skyker Seto and Hadi Pouransari for helpful discussions and reviewing the manuscript."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
+                0.378,
+                0.175,
+                0.393
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.403,
+                0.469,
+                0.444
+            ],
+            "angle": 0,
+            "content": "[1] Andrew Brock, Soham De, Samuel L. Smith, and Karen Simonyan. High-performance large-scale image recognition without normalization. 2021."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.446,
+                0.469,
+                0.516
+            ],
+            "angle": 0,
+            "content": "[2] Ping Chen, Yujin Chen, Dong Yang, Fangyin Wu, Qin Li, Qingpei Xia, and Yong Tan. I2uv-handnet: Image-to-uv prediction network for accurate and high-fidelity 3d hand mesh modeling. In International Conference on Computer Vision (ICCV), 2021."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.517,
+                0.469,
+                0.6
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+# FastViT: A Fast Hybrid Vision Transformer using Structural Reparameterization
+
+Pavan Kumar Anasosalu Vasu† James Gabriel Jeff Zhu Oncel Tuzel Anurag Ranjan†
+
+Apple
+
+# Abstract
+
+The recent amalgamation of transformer and convolutional designs has led to steady improvements in accuracy and efficiency of the models. In this work, we introduce FastViT, a hybrid vision transformer architecture that obtains the state-of-the-art latency-accuracy trade-off. To this end, we introduce a novel token mixing operator, RepMixer, a building block of FastViT, that uses structural reparameterization to lower the memory access cost by removing skip-connections in the network. We further apply train-time overparametrization and large kernel convolutions to boost accuracy and empirically show that these choices have minimal effect on latency. We show that – our model is  $3.5 \times$  faster than CMT, a recent state-of-the-art hybrid transformer architecture,  $4.9 \times$  faster than EfficientNet, and  $1.9 \times$  faster than ConvNeXt on a mobile device for the same accuracy on the ImageNet dataset. At similar latency, our model obtains  $4.2\%$  better Top-1 accuracy on ImageNet than MobileOne. Our model consistently outperforms competing architectures across several tasks – image classification, detection, segmentation and 3D mesh regression with significant improvement in latency on both a mobile device and a desktop GPU. Furthermore, our model is highly robust to out-of-distribution samples and corruptions, improving over competing robust models. Code and models are available at https://github.com/apple/ml-fastvit
+
+# 1. Introduction
+
+Vision Transformers [14] have achieved state-of-the-art performance on several tasks such as image classification, detection and segmentation [35]. However, these models have traditionally been computationally expensive. Recent works [66, 39, 41, 57, 29] have proposed methods to lower the compute and memory requirements of vision transformers. Recent hybrid architectures [41, 17, 10, 62] effectively
+
+combine the strengths of convolutional architectures and transformers to build architectures that are highly competitive on a wide range of computer vision tasks. Our goal is to build a model that achieves state-of-the-art latency-accuracy trade-off.
+
+Recent vision and hybrid transformer models [51, 17, 42, 41] follow the Metaformer [65] architecture, which consists of a token mixer with a skip connection followed by Feed Forward Network (FFN) with another skip connection. These skip connections account for a significant overhead in latency due to increased memory access cost [13, 55]. To address this latency overhead, we introduce RepMixer, a fully reparameterizable token mixer that uses structural reparameterization to remove the skip-connections. The RepMixer block also uses depthwise convolutions for spatial mixing of information similar to ConvMixer [53]. However, the key difference is that our module can be reparameterized at inference to remove any branches.
+
+To further improve on latency, FLOPs and parameter count, we replace all dense  $\mathrm{k} \times \mathrm{k}$  convolutions with their factorized version, i.e. depthwise followed by pointwise convolutions. This is a common approach used by efficient architectures [26, 46, 25] to improve on efficiency metrics, but, naively using this approach hurts performance as seen in Table 1. In order to increase capacity of the these layers, we use linear train-time overparameterization as introduced in [13, 11, 12, 55, 18]. These additional branches are only introduced during training and are reparameterized at inference.
+
+In addition, we use large kernel convolutions in our network. This is because, although self-attention based token mixing is highly effective to attain competitive accuracy, they are inefficient in terms of latency [39]. Therefore, we incorporate large kernel convolutions in Feed Forward Network (FFN) [14] layer and patch embedding layers. These changes have minimal impact on overall latency of the model while improving performance.
+
+Thus, we introduce FastViT that is based on three key design principles - i) use of RepMixer block to remove skip connections, ii) use of linear train-time overparameteriza
+
+![](images/b122794dd42f482b77e210d5a0f445450eb738dd5a4962f1da9daa75c5364e27.jpg)  
+(a)
+
+![](images/ad0fb8dfced8e49e158dcd41f23fb7cc32974f177837b46c0972ed95d059c5da.jpg)  
+(b)  
+Figure 1: (a) Accuracy vs. Mobile latency scaling curves of recent methods. The models are benchmarked on an iPhone 12 Pro following [55]. (b) Accuracy vs. GPU latency scaling curves of recent methods. For better readability only models with Top-1 accuracy better than  $79\%$  are plotted. See supplementary materials for more plots. Across both compute fabrics, our model has the best accuracy-latency tradeoff.
+
+tion to improve accuracy, iii) use of large convolutional kernels to substitute self-attention layers in early stages.
+
+FastViT achieves significant improvements in latency compared to other hybrid vision transformer architectures while maintaining accuracy on several tasks like - image classification, object detection, semantic segmentation and 3d hand mesh estimation. We perform a comprehensive analysis by deploying recent state-of-the-art architectures on an iPhone 12 Pro device and an NVIDIA RTX-2080Ti desktop GPU.
+
+In Figure 1, we show that, at ImageNet Top-1 accuracy of  $83.9\%$ , our model is  $4.9 \times$  faster than EfficientNet-B5 [48],  $1.6 \times$  faster than EfficientNetV2-S [49],  $3.5 \times$  faster than CMT-S [17] and  $1.9 \times$  faster than ConvNeXt-B [36] on an iPhone 12 Pro mobile device. At ImageNet Top-1 accuracy of  $84.9\%$  our model is just as fast as NFNet-F1 [1] on a desktop GPU while being  $66.7\%$  smaller, using  $50.1\%$  less FLOPs and  $42.8\%$  faster on mobile device. At latency of  $0.8\mathrm{ms}$  on an iPhone 12 Pro mobile device, our model obtains  $4.2\%$  better Top-1 accuracy on ImageNet than MobileOne-S0. For object detection and instance segmentation on MS COCO using Mask-RCNN [20] head, our model attains comparable performance to CMT-S [17] while incurring  $4.3 \times$  lower backbone latency. For semantic segmentation on ADE20K, our model improves over PoolFormer-M36 [65] by  $5.2\%$ , while incurring a  $1.5 \times$  lower backbone latency on an iPhone 12 Pro mobile device. On 3D hand mesh estimation task, our model is  $1.9 \times$  faster than MobileHand [16] and  $2.8 \times$  faster than recent state-of-the-art MobRecon [4] when benchmarked on GPU.
+
+In addition to accuracy metrics, we also study the robustness of our models to corruption and out-of-distribution
+
+samples which does not always correlate well with accuracy. For example, PVT [58] achieves highly competitive performance on ImageNet dataset, but has very poor robustness to corruption and out-of-distribution samples as reported in Mao et al. [38]. In real world applications, using a robust model in such a scenario can significantly improve user experience. We demonstrate the robustness of our architecture on popular benchmarks and show that our models are highly robust to corruption and out-of-distribution samples while being significantly faster than competing robust models. In summary, our contributions are as follows:
+
+- We introduce FastViT, a hybrid vision transformer that uses structural reparameterization to obtain lower memory access cost and increased capacity, achieving state-of-the-art accuracy-latency trade-off.  
+- We show that our models are the fastest in terms of latency on two widely used platforms - mobile device and desktop GPU.  
+- We show that our models generalize to many tasks - image classification, object detection, semantics segmentation, and 3D hand mesh regression.  
+- We show that our models are robust to corruption and out-of-distribution samples and significantly faster than competing robust models.
+
+# 2. Related Work
+
+For the past decade, convolutional neural networks have been the standard architecture for vision models [21, 43, 64, 48, 49, 26, 46, 25, 36, 13, 55]. More recently, transformers have shown great success on computer vision tasks [14, 63, 51, 35, 58, 52, 42, 41]. Unlike convolutional
+
+layers, the self-attention layers in vision transformers provide a global context by modeling long-range dependencies. Unfortunately, this global scope often comes at a high computational price [39]. Works like [41, 57, 29, 39] address ways to alleviate computational costs associated with self-attention layers. In our work, we explore an efficient alternative to self-attention layers for lower latency.
+
+Hybrid Vision Transformers In order to design efficient networks while maintaining accuracy, recent works introduce hybrid architectures that combine convolutional and transformer design to effectively capture local and global information. Some designs replace the patchify stem [14] with convolutional layers [63], introduce early convolutional stages [9, 41] or implicitly hybridize through windowed attention [35, 7]. More recent works build explicit hybrid structures for better exchange of information between tokens (or patches) [17, 10, 62]. In majority of the hybrid architectures, token mixers are predominantly self-attention based. Recently, MetaFormer [65] introduced Pooling, a simple and efficient candidate for token mixing.
+
+Structural Reparameterization Recent work [13, 55] shows the benefits of reparameterizing skip connections to lower memory access cost. In our model, we introduce a novel architectural component RepMixer, that is reparameterizable at inference. For better efficiency, works like [26, 46, 25, 37, 69] introduce factorized  $\mathrm{k}\times \mathrm{k}$  convolutions using depthwise or grouped convolutions followed by  $1\times 1$  pointwise convolutions. While this approach is highly effective in improving the overall efficiency of the model, the lower parameter count can lead to reduced capacity. Recently, linear train-time over overparameterization was introduced in [55, 11, 12] to improve capacity of such models. We use factorized  $\mathrm{k}\times \mathrm{k}$  convolutions in our model and boost the capacity of these layers using linear train-time overparameterization. To the best of our knowledge, structural reparameterization to remove skip connections and linear overparameterization has not been attempted in any prior hybrid transformer architecture.
+
+# 3. Architecture
+
+# 3.1. Overview
+
+FastViT is a hybrid transformer and has four distinct stages which operate at different scales as shown in Figure 2. We detail all the FastViT variants in Table 2.
+
+FastViT uses RepMixer, a token mixer that reparameterizes a skip connection, which helps in alleviating memory access cost (see Figure 2d). To further improve efficiency and performance, we replace dense  $\mathrm{k} \times \mathrm{k}$  convolutions commonly found in stem and patch embedding layers with its factorized version that uses train-time overparameterization (see Figure 2a).
+
+<table><tr><td>Architectural Choices</td><td>Params (M)</td><td>FLOPs (G)</td><td>Mobile Latency (ms)</td><td>Top-1 (%)</td></tr><tr><td rowspan="2">PoolFormer-S12 (Baseline) + 224 → 256</td><td>11.9</td><td>1.8</td><td>1.50</td><td>77.2</td></tr><tr><td>11.9</td><td>2.4</td><td>2.25</td><td>77.6</td></tr><tr><td>Section 3.2.1 + Pooling → RepMixer</td><td>11.9</td><td>2.4</td><td>1.58</td><td>78.5</td></tr><tr><td rowspan="2">Section 3.2.2 + Factorized dense conv. + Train-Time Overparam.</td><td>8.7</td><td>1.7</td><td>1.26</td><td>78.0</td></tr><tr><td>8.7</td><td>1.7</td><td>1.26</td><td>78.9</td></tr><tr><td rowspan="2">Section 3.2.3 + LK. conv. FFN + LK. conv. Patch Emb.</td><td>8.7</td><td>1.8</td><td>1.33</td><td>79.4</td></tr><tr><td>8.8</td><td>1.8</td><td>1.40</td><td>79.8</td></tr></table>
+
+Table 1: Analysis of architectural choices made to obtain FastViT-S12 variant, starting from PoolFormer-S12. "LK." stands for Large Kernel.
+
+Self-attention [14] token mixers are computationally expensive, especially at higher resolutions [42, 39]. While efficient versions of self-attention layers are explored in [17, 41], we use large kernel convolutions as an efficient alternative to improve receptive field in early stages of the network architecture (see Figure 2c).
+
+We analyze various architectural choices made in designing FastViT from a PoolFormer [65] baseline in Table 1 and detail our approach below.
+
+# 3.2. FastViT
+
+# 3.2.1 Reparameterizing Skip Connections
+
+RepMixer Convolutional mixing was first introduced in ConvMixer[53]. For an input tensor  $X$ , the mixing block in the layer was implemented as,
+
+$$
+Y = \operatorname {B N} \left(\sigma (\operatorname {D W C o n v} (X))\right) + X \tag {1}
+$$
+
+where  $\sigma$  is a non-linear activation function and BN is Batch Normalization [27] layer and DwConv is depthwise convolutional layer. While this block was shown to be effective, in RepMixer, we simply rearrange the operations and remove the non-linear activation function as shown below,
+
+$$
+Y = \operatorname {D W C o n v} (\mathrm {B N} (X) + X \tag {2}
+$$
+
+The main benefit of our design is that it can be reparameterized at inference time to a single depthwise convolutional layer as shown below and in Figure 2d.
+
+$$
+Y = \operatorname {D W C o n v} (X) \tag {3}
+$$
+
+Positional Encodings We use conditional positional encodings [7, 8] that is dynamically generated and conditioned on the local neighborhood of the input tokens. These encodings are generated as a result of a depth-wise convolution operator and are added to the patch embeddings. Note the lack of non-linearities in this group of operations, hence this block is reparameterized as shown in Figure 2a.
+
+![](images/7b97ca9d4077121df847565fc5b97467a4ae9d2cd1c7e0e84dfd5de061b8d5da.jpg)  
+(a)
+
+![](images/dfb8afdf58c91ab460891b28c6cfc93e6a495e8fb08b72be1ec87a03c81ee220.jpg)
+
+![](images/eb2e674b910ba0857abd1206e23a0d354686262bff98afa1bbc332a5c586108f.jpg)  
+(b)  
+(d)
+
+![](images/f1e86708b9b78362605ba1d6a3cb1bf805a54cab875c5024d0543a0c01ce84ab.jpg)  
+Figure 2: (a) Overview of FastViT architecture which decouples train-time and inference-time architecture. Stages 1, 2, and 3 have the same architecture and uses RepMixer for token mixing. In stage 4, self attention layers are used for token mixing. (b) Architecture of the convolutional stem. (c) Architecture of convolutional-FFN (d) Overview of RepMixer block, which reparameterizes a skip connection at inference.  
+Figure 3: Latency comparison of a MetaFormer (S12) architecture with Pooling and RepMixer as a choice for token mixing; measured on iPhone 12 Pro for various image resolutions. Both models have  $\sim 1.8\mathrm{G}$  FLOPs. Absence of a skip connection in RepMixer lowers the overall memory access cost leading to lower latency.
+
+Empirical Analysis In order to verify the benefits of reparameterizing skip connections, we ablate over the using one of the most efficient (in terms of latency) token mixer, i.e. Pooling and RepMixer in a MetaFormer S12 architecture. Both the models being ablated have  $\sim 1.8\mathrm{G}$  FLOPs.
+
+We time the models for various input resolutions starting from  $224 \times 224$  to  $1024 \times 1024$  on an iPhone 12 Pro mobile device. From Figure 3, we see that RepMixer significantly improves over Pooling, especially at higher resolutions. At  $384 \times 384$ , using RepMixer will lower the latency by  $25.1\%$  and at larger resolutions like  $1024 \times 1024$ , latency is lowered significantly by  $43.9\%$ .
+
+# 3.2.2 Linear Train-time Overparameterization
+
+In order to further improve efficiency (parameter count, FLOPs, and latency), we replace all dense  $\mathrm{k} \times \mathrm{k}$  convolutions with its factorized version, i.e.  $\mathrm{k} \times \mathrm{k}$  depthwise followed by  $1 \times 1$  pointwise convolutions. However, the lower parameter count from factorization can diminish the capacity of the model. In order to increase capacity of the factorized layers, we perform linear train-time overparameterization as described in MobileOne [55]. MobileOne-style overparameterization in stem, patch embedding, and projection layers help in boosting performance. From Table 3, we note that train-time overparameterization improves Top-1 accuracy on ImageNet by  $0.6\%$  on FastViT-SA12 model. On a smaller FastViT-S12 variant, Top-1 accuracy improves
+
+<table><tr><td rowspan="2">Stage</td><td rowspan="2">#Tokens</td><td rowspan="2" colspan="2">Layer Spec.</td><td colspan="7">FastViT</td></tr><tr><td>T8</td><td>T12</td><td>S12</td><td>SA12</td><td>SA24</td><td>SA36</td><td>MA36</td></tr><tr><td rowspan="3">Stem</td><td rowspan="3">H×W</td><td rowspan="3" colspan="2">Conv.</td><td colspan="7">3 × 3, stride 2</td></tr><tr><td colspan="7">3 × 3 MobileOne Style, stride 2</td></tr><tr><td>48</td><td colspan="5">64</td><td>76</td></tr><tr><td rowspan="5">1</td><td rowspan="2">H/4 × W/4</td><td rowspan="2" colspan="2">Patch Embed.</td><td colspan="7">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>48</td><td colspan="5">64</td><td>76</td></tr><tr><td rowspan="3">FastViTBlock</td><td colspan="2">Mixer</td><td colspan="7">RepMixer</td></tr><tr><td colspan="2">Exp.</td><td colspan="2">3</td><td colspan="5">4</td></tr><tr><td colspan="2">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td rowspan="5">2</td><td rowspan="2">H/8 × W/8</td><td rowspan="2" colspan="2">Patch Embed.</td><td colspan="7">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>96</td><td colspan="5">128</td><td>152</td></tr><tr><td rowspan="3">FastViTBlock</td><td colspan="2">Mixer</td><td colspan="7">RepMixer</td></tr><tr><td colspan="2">Exp.</td><td colspan="2">3</td><td colspan="5">4</td></tr><tr><td colspan="2">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td rowspan="5">3</td><td rowspan="2">H/16 × W/16</td><td rowspan="2" colspan="2">Patch Embed.</td><td colspan="7">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>192</td><td colspan="5">256</td><td>304</td></tr><tr><td rowspan="3">FastViTBlock</td><td colspan="2">Mixer</td><td colspan="7">RepMixer</td></tr><tr><td colspan="2">Exp.</td><td colspan="2">3</td><td colspan="5">4</td></tr><tr><td colspan="2">Blocks</td><td>4</td><td>6</td><td>6</td><td>6</td><td>12</td><td>18</td><td>18</td></tr><tr><td rowspan="5">4</td><td rowspan="2">H/32 × W/32</td><td rowspan="2" colspan="2">Patch Embed.</td><td colspan="7">7 × 7 MobileOne Style, stride 2</td></tr><tr><td>384</td><td colspan="5">512</td><td>608</td></tr><tr><td rowspan="3">FastViTBlock</td><td colspan="2">Mixer</td><td colspan="2">RepMixer</td><td colspan="5">Attention</td></tr><tr><td colspan="2">Exp.</td><td colspan="2">3</td><td colspan="5">4</td></tr><tr><td colspan="2">Blocks</td><td>2</td><td>2</td><td>2</td><td>2</td><td>4</td><td>6</td><td>6</td></tr><tr><td colspan="4">Parameters (M)</td><td>3.6</td><td>6.8</td><td>8.8</td><td>10.9</td><td>20.6</td><td>30.4</td><td>42.7</td></tr><tr><td colspan="4">FLOPs (G)</td><td>0.7</td><td>1.4</td><td>1.8</td><td>1.9</td><td>3.8</td><td>5.6</td><td>7.9</td></tr></table>
+
+by  $0.9\%$  as shown in Table 1.
+
+However, train-time overparameterization results in increased training time due to computational overhead from the added branches. In our architecture, we only overparameterize those layers that replace dense  $\mathrm{k} \times \mathrm{k}$  convolutions with its factorized form as described above. These layers are found in the convolutional stem, patch embedding and projection layers. The computational cost incurred in these layers are lower than the rest of the network, hence overparameterizing these layers do not result in significant increases to train time. For example, FastViT-SA12 takes  $6.7\%$  longer and FastViT-SA36 takes  $4.4\%$  longer to train with train-time overparameterization as opposed to training those variants without it under the same settings described in Section 4.1.
+
+Table 2: Architecture details of FastViT variants. Models with smaller embedding dimensions, i.e. [64, 128, 256, 512] are prefixed with "S" and models that contain Self-Attention layers are prefixed with "SA". Models with bigger embedding dimensions, i.e. [76, 152, 304, 608] are prefixed with "M". Models with MLP expansion ratio less than 4 are prefixed with "T". The number in the notation denotes total number of FastViT blocks. FLOP count is computed by fvcore[15] library.  
+
+<table><tr><td>Model</td><td>Ablation</td><td>Top-1 (%)</td><td>Train Time (hrs)</td></tr><tr><td rowspan="2">FastViT-SA12</td><td>Without Train-Time Overparam.</td><td>80.0</td><td>31.3</td></tr><tr><td>With Train-Time Overparam.</td><td>80.6</td><td>33.4</td></tr><tr><td rowspan="2">FastViT-SA36</td><td>Without Train-Time Overparam.</td><td>83.3</td><td>73.5</td></tr><tr><td>With Train-Time Overparam.</td><td>83.6</td><td>76.7</td></tr></table>
+
+Table 3: Comparison of FastViT variants with and without linear train-time overparameterization when trained on ImageNet-1k dataset. Train time is wall clock time elapsed at the end of a training run.
+
+# 3.2.3 Large Kernel Convolutions
+
+The receptive field of RepMixer is local compared to self-attention token mixers. However, self-attention based token mixers are computationally expensive. A computationally efficient approach to improve the receptive field of early stages that do not use self-attention is by incorporating depthwise large kernel convolutions. We introduce depthwise large kernel convolutions in FFN and patch embedding layers. From Table 4, we note that variants using depthwise large kernel convolutions can be highly competitive to variants using self-attention layers while incurring a modest increase in latency. When we compare V5 with V3, model size increases by  $11.2\%$ , and latency increases by a factor of  $2.3 \times$  for a relatively small gain of  $0.4\%$  in Top-1 accuracy. V2 is larger than V4 by  $20\%$  and has  $7.1\%$  higher latency than V4 while attaining similar Top-1 accuracy on ImageNet. Further ablations on kernel sizes and latency is provided in the supplementary materials. In Table 1, we ablate over large kernel convolutions in FFN and patch embedding layers. Overall, large kernel convolutions provide  $0.9\%$  improvement in Top-1 accuracy on FastViT-S12.
+
+The architecture of our FFN and patch embedding layer is shown in Figure 2. Our FFN block has a structure similar to ConvNeXt [36] block with a few key differences, see Figure 2c. We use Batch Normalization as opposed to Layer Normalization, as it can be fused with the preceding layer at inference. Also, it does not require additional reshape operations to obtain appropriate tensor layout for LayerNorm as done in the original implementation of ConvNeXt block.
+
+Along with increased receptive field, large kernel convolutions help in improving model robustness as observed in [59] and convolutional-FFN blocks generally tend to be more robust than vanilla-FFN blocks as observed in [38]. Hence, incorporating large kernel convolutions is an efficient way to improve model performance and robustness.
+
+# 4. Experiments
+
+# 4.1. Image Classification
+
+We report results on the widely used ImageNet-1K dataset [45] which contains  $\sim 1.3\mathrm{M}$  training images and  $50\mathrm{K}$  validation images. We follow the training recipe prescribed in [51, 65], i.e. the models are trained for 300
+
+<table><tr><td rowspan="2">Variant</td><td colspan="4">Stages</td><td>Params</td><td>Top-1</td><td>Mobile</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>(M)</td><td>(%)</td><td>Latency (ms)</td></tr><tr><td colspan="8">Standard Setting</td></tr><tr><td>V1</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.7</td><td>78.9</td><td>1.3</td></tr><tr><td>V2</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.8</td><td>79.9</td><td>1.5</td></tr><tr><td>V3</td><td>RM</td><td>RM</td><td>SA</td><td>SA</td><td>12.4</td><td>81.0</td><td>3.7</td></tr><tr><td colspan="8">Large Kernel Convolutions (7×7)</td></tr><tr><td>V4</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.8</td><td>79.8</td><td>1.4</td></tr><tr><td>V5</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.9</td><td>80.6</td><td>1.6</td></tr></table>
+
+epochs using AdamW optimizer with weight decay of 0.05 and peak learning rate  $10^{-3}$  for a total batch size of 1024. The number of warmup epochs is set to 5 and cosine schedule is used to decay the learning rate. Our implementation uses timm library [60] and all the models were trained on 8 NVIDIA A100 GPUs. See supplementary materials for details on hyper parameters used for all the variants. For  $384 \times 384$  input size, we fine-tune the models for 30 epochs with weight decay of  $10^{-8}$  and learning rate of  $5 \times 10^{-5}$  and batch size of 512 following [36]. To measure latency, we use the input sizes corresponding to the respective methods. For iPhone latency measurements, we export the models using Core ML Tools (v6.0) and run it on iPhone12 Pro Max with iOS 16 and batch size is set to 1 for all the models. We follow the same protocol as [55]. For GPU latency measurements, we export the traced model to TensorRT (v8.0.1.6) format and run it on NVIDIA RTX-2080Ti with batch size of 8. We report the median latency estimate from 100 runs.
+
+Comparison with SOTA Models In Table 5, we compare our models against recent state-of-the-art models on ImageNet-1k dataset. For a fair comparison, we modify ConvNeXt [36] from official implementation by avoiding costly reshape operations, see supplementary materials for more details. We were unable to reliably export LITv2 [41] due to poor support for deformable convolutions in either library. Our model obtains the best accuracy-latency trade-off when compared to recent state-of-the-art models on two different compute fabrics, i.e. desktop-grade GPU and mobile device. Our models improve over LITv2 [41] on both parameter count and FLOPs, at Top-1 accuracy of  $84.9\%$ , FastViT-MA36 is  $49.3\%$  smaller and consumes  $55.4\%$  less FLOPs than LITv2-B. FastViT-S12 is  $26.3\%$  faster than MobileOne-S4 [55] on iPhone 12 Pro and  $26.9\%$  faster on
+
+Table 4: Ablation on using large kernel convolutions as a substitute for self-attention layers. "RM" indicates [RepMixer-FFN] block is used in the stage. "SA" indicates [Self Attention-FFN] block is used in the stage. Standard setting uses  $3 \times 3$  factorized convolutions in patch embedding and stem layers and  $1 \times 1$  convolutions for FFN. In variants V4 and V5, large kernel convolutions  $(7 \times 7)$  are used in patch embedding and FFN layers.  
+
+<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>MobileOne-S0[55]</td><td>224</td><td>2.1</td><td>0.3</td><td>1.0</td><td>0.8</td><td>71.4</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>75.6</td></tr><tr><td>MobileOne-S3[55]</td><td>224</td><td>10.1</td><td>1.8</td><td>2.1</td><td>1.5</td><td>78.1</td></tr><tr><td>CMT-T* [17]</td><td>160</td><td>9.5</td><td>0.6</td><td>4.5</td><td>3.8</td><td>79.1</td></tr><tr><td>EfficientNet-B1[48]</td><td>256</td><td>7.8</td><td>0.7</td><td>3.2</td><td>2.5</td><td>79.1</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>79.1</td></tr><tr><td>MobileOne-S4[55]</td><td>224</td><td>14.8</td><td>2.9</td><td>2.6</td><td>1.9</td><td>79.4</td></tr><tr><td>RSB-ResNet50[61]</td><td>224</td><td>25.6</td><td>4.1</td><td>2.3</td><td>2.6</td><td>79.8</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22.0</td><td>4.6</td><td>5.2</td><td>5.3</td><td>79.8</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>79.8</td></tr><tr><td>RegNetY-8G[43]</td><td>224</td><td>39.2</td><td>8.0</td><td>5.8</td><td>3.8</td><td>79.9</td></tr><tr><td>EfficientNet-B2[48]</td><td>288</td><td>9.2</td><td>1.0</td><td>4.1</td><td>3.5</td><td>80.1</td></tr><tr><td>PoolFormer-S24[65]</td><td>224</td><td>21.0</td><td>3.4</td><td>15.7</td><td>2.5</td><td>80.3</td></tr><tr><td>RegNetY-16G [43]</td><td>224</td><td>83.6</td><td>16.0</td><td>8.1</td><td>7.5</td><td>80.4</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>80.6</td></tr><tr><td>ResNeSt50[67]</td><td>224</td><td>27.5</td><td>5.4</td><td>51.5</td><td>29.9</td><td>81.1</td></tr><tr><td>Swin-T[35]</td><td>224</td><td>29.0</td><td>4.5</td><td>-</td><td>9.3</td><td>81.3</td></tr><tr><td>PoolFormer-S36[65]</td><td>224</td><td>31.0</td><td>5.0</td><td>23.7</td><td>3.5</td><td>81.4</td></tr><tr><td>EfficientNet-B3[48]</td><td>300</td><td>12.0</td><td>1.8</td><td>5.3</td><td>7.1</td><td>81.6</td></tr><tr><td>CvT-13[62]</td><td>224</td><td>20.1</td><td>4.5</td><td>18.1</td><td>62.6</td><td>81.6</td></tr><tr><td>CoAtNet-0[9]</td><td>224</td><td>25.0</td><td>4.2</td><td>-</td><td>6.7</td><td>81.6</td></tr><tr><td>CMT-XS* [17]</td><td>192</td><td>15.2</td><td>1.5</td><td>8.3</td><td>6.3</td><td>81.8</td></tr><tr><td>DeiT-B [51]</td><td>224</td><td>86.0</td><td>17.5</td><td>11.6</td><td>11.6</td><td>81.8</td></tr><tr><td>RSB-ResNet152[61]</td><td>224</td><td>60.2</td><td>11.6</td><td>5.4</td><td>4.7</td><td>81.8</td></tr><tr><td>LITv2-S[41]</td><td>224</td><td>28.0</td><td>3.7</td><td>-</td><td>-</td><td>82.0</td></tr><tr><td>ConvNeXt-T†[36]</td><td>224</td><td>29.0</td><td>4.5</td><td>6.3</td><td>3.7</td><td>82.1</td></tr><tr><td>PoolFormer-M48[65]</td><td>224</td><td>73.0</td><td>11.6</td><td>30.2</td><td>7.6</td><td>82.5</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>82.6</td></tr><tr><td>ResNeSt101[67]</td><td>224</td><td>48.2</td><td>10.2</td><td>75.5</td><td>37.7</td><td>83.0</td></tr><tr><td>Swin-S[35]</td><td>224</td><td>50.0</td><td>8.7</td><td>-</td><td>13.0</td><td>83.0</td></tr><tr><td>ConvNeXt-S†[36]</td><td>224</td><td>50.0</td><td>8.7</td><td>10.3</td><td>5.4</td><td>83.1</td></tr><tr><td>MOAT-0[5]</td><td>224</td><td>27.8</td><td>5.7</td><td>-</td><td>4.9</td><td>83.3</td></tr><tr><td>CoAtNet-1[9]</td><td>224</td><td>42.0</td><td>8.4</td><td>-</td><td>13.4</td><td>83.3</td></tr><tr><td>Swin-B [35]</td><td>224</td><td>88.0</td><td>15.4</td><td>-</td><td>18.5</td><td>83.5</td></tr><tr><td>CMT-S* [17]</td><td>224</td><td>25.1</td><td>4.0</td><td>13.8</td><td>15.6</td><td>83.5</td></tr><tr><td>MaxViT-T[54]</td><td>224</td><td>31.0</td><td>5.6</td><td>-</td><td>31.5</td><td>83.6</td></tr><tr><td>LITv2-B[41]</td><td>224</td><td>87.0</td><td>13.2</td><td>-</td><td>-</td><td>83.6</td></tr><tr><td>EfficientNet-B5[48]</td><td>456</td><td>30.0</td><td>9.9</td><td>24.2</td><td>22.1</td><td>83.6</td></tr><tr><td>NFNet-F0[1]</td><td>256</td><td>71.5</td><td>12.4</td><td>6.2</td><td>6.4</td><td>83.6</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>83.6</td></tr><tr><td>ConvNeXt-B†[36]</td><td>224</td><td>89.0</td><td>15.4</td><td>13.6</td><td>8.4</td><td>83.8</td></tr><tr><td>CoAtNet-0</td><td>384</td><td>25.0</td><td>13.4</td><td>-</td><td>20.1</td><td>83.9</td></tr><tr><td>EfficientNetV2-S[49]</td><td>384</td><td>22.0</td><td>8.8</td><td>8.2</td><td>7.1</td><td>83.9</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>83.9</td></tr><tr><td>EfficientNet-B6[48]</td><td>528</td><td>43.0</td><td>19.0</td><td>44.3</td><td>51.7</td><td>84.0</td></tr><tr><td>CoAtNet-2[9]</td><td>224</td><td>75.0</td><td>15.7</td><td>-</td><td>19.6</td><td>84.1</td></tr><tr><td>MOAT-1[5]</td><td>224</td><td>41.6</td><td>9.1</td><td>-</td><td>8.3</td><td>84.2</td></tr><tr><td>EfficientNet-B7[48]</td><td>600</td><td>66.0</td><td>37.0</td><td>72.6</td><td>85.5</td><td>84.3</td></tr><tr><td>CMT-B* [17]</td><td>256</td><td>45.7</td><td>9.3</td><td>26.9</td><td>20.6</td><td>84.5</td></tr><tr><td>Swin-B[35]</td><td>384</td><td>88.0</td><td>47.0</td><td>-</td><td>57.2</td><td>84.5</td></tr><tr><td>MaxViT-S[54]</td><td>224</td><td>69.0</td><td>11.7</td><td>-</td><td>48.7</td><td>84.5</td></tr><tr><td>FastViT-SA36</td><td>384</td><td>30.4</td><td>12.6</td><td>12.8</td><td>7.4</td><td>84.5</td></tr><tr><td>MOAT-0[5]</td><td>384</td><td>27.8</td><td>18.2</td><td>-</td><td>24.3</td><td>84.6</td></tr><tr><td>NFNet-F1[1]</td><td>320</td><td>132.6</td><td>35.5</td><td>16.9</td><td>16.1</td><td>84.7</td></tr><tr><td>MOAT-2[5]</td><td>224</td><td>73.4</td><td>17.2</td><td>-</td><td>12.6</td><td>84.7</td></tr><tr><td>LITv2-B[41]</td><td>384</td><td>87.0</td><td>39.7</td><td>-</td><td>-</td><td>84.7</td></tr><tr><td>FastViT-MA36</td><td>384</td><td>42.7</td><td>17.7</td><td>16.5</td><td>9.2</td><td>84.9</td></tr></table>
+
+Table 5: Comparison of different state-of-the-art methods on ImageNet-1k classification. HardSwish is not well supported by Core ML, * denotes we replace it with GELU for fair comparison. “†” denotes that model has been modified from original implementation for efficient deployment. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”.
+
+<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>76.7</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>80.3</td></tr><tr><td>CaiT XXS-36[52]</td><td>224</td><td>17.3</td><td>3.8</td><td>15.8</td><td>-</td><td>79.7</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>80.9</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22</td><td>4.6</td><td>5.2</td><td>6.7</td><td>81.2</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>81.9</td></tr><tr><td>EfficientFormer-L3[31]</td><td>224</td><td>31.3</td><td>3.9</td><td>3.6</td><td>3.0</td><td>82.4</td></tr><tr><td>EfficientFormer-L7[31]</td><td>224</td><td>82.1</td><td>10.2</td><td>7.5</td><td>7.0</td><td>83.3</td></tr><tr><td>DeiT-B[51]</td><td>224</td><td>87</td><td>17.6</td><td>11.6</td><td>11.6</td><td>83.4</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>83.4</td></tr><tr><td>CaiT S-24[52]</td><td>224</td><td>46.9</td><td>9.4</td><td>19.1</td><td>-</td><td>83.5</td></tr><tr><td>CaiT XS-24[52]</td><td>384</td><td>26.6</td><td>19.3</td><td>77.7</td><td>-</td><td>84.1</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>84.2</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>84.6</td></tr></table>
+
+Table 6: Comparison of different state-of-the-art methods on ImageNet-1k classification when trained using distillation objective specified by [51]. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”.
+
+GPU. At Top-1 accuracy of  $83.9\%$ , FastViT-MA36 is  $1.9 \times$  faster than an optimized ConvNeXt-B model on iPhone 12 Pro and  $2.0 \times$  faster on GPU. At Top-1 accuracy of  $84.9\%$ , FastViT-MA36 is just as fast as NFNet-F1 [1] on GPU while being  $66.7\%$  smaller and using  $50.1\%$  less FLOPs and  $42.8\%$  faster on mobile device.
+
+Knowledge distillation We report performance of our models when trained with distillation objective in Table 6. We follow the setting described in DeiT [51], with RegNet-16GF [43] as the teacher model. Following DeiT [51], we use hard distillation where hard decision of the teacher is set as true label. Our models are trained for 300 epochs. Unlike [51, 52, 31], we do not introduce an additional classification head for distillation. FastViT outperforms recent state-of-the-art model EfficientFormer [31]. FastViT-SA24 attains similar performance as EfficientFormer-L7 while having  $3.8 \times$  less parameters,  $2.7 \times$  less FLOPs and  $2.7 \times$  lower latency.
+
+# 4.2. Robustness Evaluation
+
+We evaluate our models for out-of-distribution robustness on the following benchmarks - (i) ImageNet-A [24], a dataset that contains naturally occurring examples that are misclassified by ResNets; (ii) ImageNet-R [22], a dataset that contains natural renditions of ImageNet object classes with different textures and local image statistics; (iii) ImageNet-Sketch [56], a dataset that contains black and white sketches of all ImageNet classes, obtained using google image queries; and (iv) ImageNet-C [23], a dataset that consists of algorithmically generated corruption
+
+<table><tr><td>Model</td><td>#Params</td><td>#FLOPs</td><td>Clean</td><td>IN-C (↓)</td><td>IN-A</td><td>IN-R</td><td>IN-SK</td></tr><tr><td>PVT-Tiny</td><td>13.2</td><td>1.9</td><td>75.0</td><td>79.6</td><td>7.9</td><td>33.9</td><td>21.5</td></tr><tr><td>RVT-Ti</td><td>8.6</td><td>1.3</td><td>78.4</td><td>58.2</td><td>13.3</td><td>43.7</td><td>30.0</td></tr><tr><td>FastViT-SA12</td><td>10.9</td><td>1.9</td><td>80.6</td><td>62.2</td><td>17.2</td><td>42.6</td><td>29.7</td></tr><tr><td>PVT-Small</td><td>24.5</td><td>3.8</td><td>79.9</td><td>66.9</td><td>18.0</td><td>40.1</td><td>27.2</td></tr><tr><td>ResNet-50*</td><td>25.6</td><td>4.1</td><td>79.0</td><td>65.5</td><td>5.9</td><td>42.5</td><td>31.5</td></tr><tr><td>ResNeXt50-32x4d</td><td>25.0</td><td>4.3</td><td>79.8</td><td>64.7</td><td>10.7</td><td>41.5</td><td>29.3</td></tr><tr><td>FastViT-SA24</td><td>20.6</td><td>3.8</td><td>82.6</td><td>55.3</td><td>26.0</td><td>46.5</td><td>34.0</td></tr><tr><td>Swin-T</td><td>28.3</td><td>4.5</td><td>81.2</td><td>62.0</td><td>21.6</td><td>41.3</td><td>29.1</td></tr><tr><td>ConViT-S</td><td>27.8</td><td>5.4</td><td>81.5</td><td>49.8</td><td>24.5</td><td>45.4</td><td>33.1</td></tr><tr><td>RVT-S</td><td>22.1</td><td>4.7</td><td>81.7</td><td>50.1</td><td>24.1</td><td>46.9</td><td>35.0</td></tr><tr><td>ConvNeXt-T</td><td>28.6</td><td>4.5</td><td>82.1</td><td>53.2</td><td>24.2</td><td>47.2</td><td>33.8</td></tr><tr><td>EfficientNet-B4</td><td>19.3</td><td>4.2</td><td>83.0</td><td>71.1</td><td>26.3</td><td>47.1</td><td>34.1</td></tr><tr><td>FastViT-SA36</td><td>30.4</td><td>5.6</td><td>83.6</td><td>51.8</td><td>32.3</td><td>48.1</td><td>35.8</td></tr><tr><td>ConvNeXt-S</td><td>50.0</td><td>8.7</td><td>83.1</td><td>51.2</td><td>31.2</td><td>49.5</td><td>37.1</td></tr><tr><td>FastViT-MA36</td><td>42.7</td><td>7.9</td><td>83.9</td><td>49.9</td><td>34.6</td><td>49.5</td><td>36.6</td></tr></table>
+
+Table 7: Results on robustness benchmark datasets. Models are grouped based on FLOPs. Performance of competing models is reported by [38] and [36]. *ResNet-50 model is trained with AugMix to improve robustness as reported in [38]. For ImageNet-C mean corruption error is reported (lower is better) and for other datasets Top-1 accuracy is reported (higher is better). The best results are in bold and second best results are underlined.
+
+tions (blur, noise) applied to the ImageNet test-set. We evaluate our models using the implementation provided by [38]. Our models are more robust than recent vision transformers while being faster than pure-CNN based models which exhibit low robustness as seen Table 7. Architectural choices like using a large kernel convolutions in FFN and patch-embedding layers in combination with self-attention layers helps in improving the robustness of our model as discussed in Section 3.2.3. All the models compared in Table 7 are trained only on ImageNet-1k dataset using similar training recipes. From Table 7, our model is highly competitive to RVT and ConvNeXt, in fact FastViT-M36 has better clean accuracy, better robustness to corruptions and similar out-of-distribution robustness as ConvNeXt-S which has 6.1M more parameters and has  $10\%$  more FLOPs than our model.
+
+# 4.3. 3D Hand mesh estimation
+
+Recent works on real-time 3D hand mesh estimation introduce complex mesh regression layers over CNN based backbones. The backbones usually belong to ResNet or MobileNet family of architectures with the exception of METRO and MeshGraphormer which use HRNets [47] for feature extraction. While most hardware devices are highly optimized for feature extraction from 2D CNNs, the same is not true for the complex mesh regression heads used in these methods. In our method, we replace the complex mesh regression head with a simple regression module which regresses weak perspective camera, pose and shape parameters of the MANO model [44]. We argue that using a feature
+
+<table><tr><td>Method</td><td>Backbone</td><td colspan="5">PJ ↓ PV ↓ F@5 ↑ F@15 ↑ FPS ↑</td></tr><tr><td colspan="7">Non Real-Time methods</td></tr><tr><td>HIU-DMTL [68]</td><td>Customized</td><td>7.1</td><td>7.3</td><td>0.699</td><td>0.974</td><td>5</td></tr><tr><td>METRO [32]</td><td>HRNet</td><td>6.3</td><td>6.5</td><td>0.731</td><td>0.984</td><td>4.2</td></tr><tr><td>MeshGraphormer [33]</td><td>HRNet</td><td>5.9</td><td>6.0</td><td>0.764</td><td>0.986</td><td>2.6</td></tr><tr><td colspan="7">Real-Time methods</td></tr><tr><td>Hasson et al. [19]</td><td>ResNet18</td><td>-</td><td>13.2</td><td>0.436</td><td>0.908</td><td>20</td></tr><tr><td>MobileHand [16]</td><td>MobileNetV3</td><td>-</td><td>13.1</td><td>0.439</td><td>0.902</td><td>110</td></tr><tr><td>YoutubeHand [30]</td><td>ResNet50</td><td>8.4</td><td>8.6</td><td>0.614</td><td>0.966</td><td>60</td></tr><tr><td>I2L-MeshNet [40]</td><td>ResNet50</td><td>7.4</td><td>7.6</td><td>0.681</td><td>0.973</td><td>33.3</td></tr><tr><td>Pose2Mesh [6]</td><td>Customized</td><td>7.4</td><td>7.6</td><td>0.683</td><td>0.973</td><td>20</td></tr><tr><td>I2UV-HandNet [2]</td><td>ResNet50</td><td>7.2</td><td>7.4</td><td>0.682</td><td>0.973</td><td>-</td></tr><tr><td>Tang et al. [50]</td><td>ResNet50</td><td>7.1</td><td>7.1</td><td>0.706</td><td>0.977</td><td>39.1</td></tr><tr><td>MobRecon[4]</td><td>DenseStack</td><td>6.9</td><td>7.2</td><td>0.694</td><td>0.979</td><td>77</td></tr><tr><td>CMR [3]</td><td>ResNet50*</td><td>6.9</td><td>7.0</td><td>0.715</td><td>0.977</td><td>-</td></tr><tr><td>Ours</td><td>FastViT-MA36</td><td>6.6</td><td>6.7</td><td>0.722</td><td>0.981</td><td>218</td></tr></table>
+
+Table 8: Results on the FreiHAND test dataset. FPS is computed on NVIDIA RTX-2080Ti under similar setting as MobRecon [4]. Performance of competing methods obtained from training exclusively on FreiHand dataset.
+
+extraction backbone that learns a good representation for underlying images can alleviate learning challenges in mesh regression. While other real-time methods compensate for weak feature extraction backbone with complex mesh regression layers, we use a better feature extraction backbone with a simple mesh regression layer. We compare our approach with other published methods on the FreiHand [71] dataset. For a fair comparison, we cite results of methods that only used FreiHand dataset for training as some methods either pre-train, train, or fine-tune with additional pose datasets. We only use ImageNet-1k dataset for pretraining and then train exclusively on the FreiHand dataset using the experimental setup described in [32]. For more details, please see supplementary materials. From Table 8, amongst real-time methods, our method outperforms other methods on all joint and vertex error related metrics while being  $1.9 \times$  faster than MobileHand [16] and  $2.8 \times$  faster than recent state-of-art MobRecon.
+
+# 4.4. Semantic Segmentation and Object Detection
+
+For semantic segmentation, we validate the performance of our models on ADE20k [70]. The dataset contains 20K training images and 2K validation images with 150 semantic categories. We train semantic segmentation models with Semantic FPN [28] decoder. Models with Semantic FPN head use the same settings as [65]. All models are initialized with pretrained weights from their corresponding image classification models. FLOPs and backbone latency are estimated on image crops of  $512 \times 512$ . Due to higher resolution of input image, GPU latencies are estimated over a batch size of 2 in both Table 9 and Table 10. In Table 9, we compare our models with recent works. FastViT-MA36 model obtains  $5.2\%$  higher mIoU than PoolFormer-M36
+
+<table><tr><td rowspan="2">Backbone</td><td rowspan="2">GPU Latency</td><td rowspan="2">Mobile Latency</td><td colspan="3">Semantic FPN 80k</td></tr><tr><td>Param(M)</td><td>FLOPs(G)</td><td>mIoU(%)</td></tr><tr><td>ResNet-50</td><td>2.7</td><td>8.7</td><td>28.5</td><td>46</td><td>36.7</td></tr><tr><td>PoolFormer-S12[65]</td><td>9.7</td><td>6.2</td><td>15.7</td><td>31</td><td>37.2</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>14.1</td><td>29</td><td>38.0</td></tr><tr><td>ResNet-101</td><td>4.6</td><td>12.4</td><td>47.5</td><td>65</td><td>38.8</td></tr><tr><td>PVT-Small[58]</td><td>-</td><td>-</td><td>28.2</td><td>41</td><td>39.8</td></tr><tr><td>PoolFormer-S24[65]</td><td>18.9</td><td>10.7</td><td>23.2</td><td>48</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>23.8</td><td>37</td><td>41.0</td></tr><tr><td>PoolFormer-S36[65]</td><td>28.0</td><td>17.0</td><td>34.6</td><td>48</td><td>42.0</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>33.6</td><td>44</td><td>42.9</td></tr><tr><td>PVT-Medium[58]</td><td>-</td><td>-</td><td>48.0</td><td>55</td><td>41.6</td></tr><tr><td>PoolFormer-M36[65]</td><td>41.4</td><td>24.8</td><td>59.8</td><td>68</td><td>42.4</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.7</td><td>53</td><td>44.6</td></tr></table>
+
+Table 9: Performance of different backbones on ADE20K semantic segmentation task. Following common convention, FLOPs and backbone latencies are measured on crops of  $512 \times 512$ .
+
+<table><tr><td>Backbone</td><td>GPU Latency</td><td>Mobile Latency</td><td>\(AP^b\)</td><td>\(AP^{b}_{50}\)</td><td>\(AP^{b}_{75}\)</td><td>\(AP^m\)</td><td>\(AP^{m}_{50}\)</td><td>\(AP^{m}_{75}\)</td></tr><tr><td>Poolfomer-S12[65]</td><td>9.7</td><td>6.2</td><td>37.3</td><td>59.0</td><td>40.1</td><td>34.6</td><td>55.8</td><td>36.9</td></tr><tr><td>ResNet-50 [21]</td><td>2.7</td><td>8.7</td><td>38.0</td><td>58.6</td><td>41.4</td><td>34.4</td><td>55.1</td><td>36.7</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>38.9</td><td>60.5</td><td>42.2</td><td>35.9</td><td>57.6</td><td>38.1</td></tr><tr><td>ResNet-101 [21]</td><td>4.6</td><td>12.4</td><td>40.0</td><td>60.5</td><td>44.0</td><td>36.1</td><td>57.5</td><td>38.6</td></tr><tr><td>Poolfomer-S24[65]</td><td>18.9</td><td>10.7</td><td>40.1</td><td>62.2</td><td>43.4</td><td>37.0</td><td>59.1</td><td>39.6</td></tr><tr><td>PVT-S [58]</td><td>-</td><td>-</td><td>40.4</td><td>62.9</td><td>43.8</td><td>37.8</td><td>60.1</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>42.0</td><td>63.5</td><td>45.8</td><td>38.0</td><td>60.5</td><td>40.5</td></tr><tr><td>Swin-T [35]</td><td>-</td><td>-</td><td>42.2</td><td>64.6</td><td>46.2</td><td>39.1</td><td>61.6</td><td>42.0</td></tr><tr><td>Twins-SVT-S [7]</td><td>-</td><td>-</td><td>42.7</td><td>65.6</td><td>46.7</td><td>39.6</td><td>62.5</td><td>42.6</td></tr><tr><td>Twins-PCPVT-S [7]</td><td>-</td><td>52.1</td><td>42.9</td><td>65.8</td><td>47.1</td><td>40.0</td><td>62.7</td><td>42.9</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>43.8</td><td>65.1</td><td>47.9</td><td>39.4</td><td>62.0</td><td>42.3</td></tr><tr><td>CMT-S [17]</td><td>19.9</td><td>70.9</td><td>44.6</td><td>66.8</td><td>48.9</td><td>40.7</td><td>63.9</td><td>43.4</td></tr><tr><td>Poolfomer-S36[65]</td><td>28.0</td><td>17.0</td><td>41.0</td><td>63.1</td><td>44.8</td><td>37.7</td><td>60.1</td><td>40.0</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.1</td><td>66.8</td><td>49.5</td><td>40.5</td><td>63.8</td><td>43.4</td></tr></table>
+
+Table 10: Results for object detection and instance segmentation on MS-COCO val2017 split using Mask-RCNN [20] framework using 1x training schedule, i.e. 12 epochs used for training the models. Backbone latencies are measured on crops of  $512 \times 512$ .
+
+which has higher FLOPs, parameter count and latency on both desktop GPU and mobile device.
+
+We train object detection on the MS-COCO [34] dataset with 80 classes containing 118K training and 5K validation images. In Table 10, we compare our models with recent works. All the models are trained with 1x schedule following [65] using a Mask-RCNN [20] head. All models are initialized with pretrained weights from their corresponding image classification models. We show that our models achieve state-of-the-art performance under multiple latency regimes. FastViT-MA36 model has similar performance as CMT-S, while being  $2.4 \times$  and  $4.3 \times$  faster on desktop GPU and mobile device respectively.
+
+# 5. Conclusion
+
+We have proposed a general purpose hybrid vision transformer that is highly efficient on multiple compute fabrics: mobile devices and desktop grade GPUs. Through structural reparameterization, our model incurs reduced memory access cost. This leads to significant improvements in runtime especially at higher resolutions. In addition, we propose further architectural changes that boosts performance on ImageNet classification task and other downstream tasks like object detection, semantic segmentation and 3D hand mesh estimation. We empirically show that our backbone is highly robust to out-of-distribution samples, while being significantly faster than competing robust models.
+
+Acknowledgements We thank Jen-Hao Rick Chang, Skyker Seto and Hadi Pouransari for helpful discussions and reviewing the manuscript.
+
+# References
+
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+                                    "content": " convolutions with their factorized version, i.e. depthwise followed by pointwise convolutions. This is a common approach used by efficient architectures [26, 46, 25] to improve on efficiency metrics, but, naively using this approach hurts performance as seen in Table 1. In order to increase capacity of the these layers, we use linear train-time overparameterization as introduced in [13, 11, 12, 55, 18]. These additional branches are only introduced during training and are reparameterized at inference."
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+                                            "content": "- We show that our models are robust to corruption and out-of-distribution samples and significantly faster than competing robust models."
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+                                    "content": "2. Related Work"
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+                                    "content": "For the past decade, convolutional neural networks have been the standard architecture for vision models [21, 43, 64, 48, 49, 26, 46, 25, 36, 13, 55]. More recently, transformers have shown great success on computer vision tasks [14, 63, 51, 35, 58, 52, 42, 41]. Unlike convolutional"
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+                                    "content": "layers, the self-attention layers in vision transformers provide a global context by modeling long-range dependencies. Unfortunately, this global scope often comes at a high computational price [39]. Works like [41, 57, 29, 39] address ways to alleviate computational costs associated with self-attention layers. In our work, we explore an efficient alternative to self-attention layers for lower latency."
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+                                    "content": "Hybrid Vision Transformers In order to design efficient networks while maintaining accuracy, recent works introduce hybrid architectures that combine convolutional and transformer design to effectively capture local and global information. Some designs replace the patchify stem [14] with convolutional layers [63], introduce early convolutional stages [9, 41] or implicitly hybridize through windowed attention [35, 7]. More recent works build explicit hybrid structures for better exchange of information between tokens (or patches) [17, 10, 62]. In majority of the hybrid architectures, token mixers are predominantly self-attention based. Recently, MetaFormer [65] introduced Pooling, a simple and efficient candidate for token mixing."
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+                                    "content": "Structural Reparameterization Recent work [13, 55] shows the benefits of reparameterizing skip connections to lower memory access cost. In our model, we introduce a novel architectural component RepMixer, that is reparameterizable at inference. For better efficiency, works like [26, 46, 25, 37, 69] introduce factorized "
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+                                    "content": " convolutions using depthwise or grouped convolutions followed by "
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+                                    "content": " pointwise convolutions. While this approach is highly effective in improving the overall efficiency of the model, the lower parameter count can lead to reduced capacity. Recently, linear train-time over overparameterization was introduced in [55, 11, 12] to improve capacity of such models. We use factorized "
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+                                    "type": "text",
+                                    "content": " convolutions in our model and boost the capacity of these layers using linear train-time overparameterization. To the best of our knowledge, structural reparameterization to remove skip connections and linear overparameterization has not been attempted in any prior hybrid transformer architecture."
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+                                    "content": "3. Architecture"
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+                                    "content": "3.1. Overview"
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+                                    "content": "FastViT is a hybrid transformer and has four distinct stages which operate at different scales as shown in Figure 2. We detail all the FastViT variants in Table 2."
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+                                    "content": "FastViT uses RepMixer, a token mixer that reparameterizes a skip connection, which helps in alleviating memory access cost (see Figure 2d). To further improve efficiency and performance, we replace dense "
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+                                    "content": " convolutions commonly found in stem and patch embedding layers with its factorized version that uses train-time overparameterization (see Figure 2a)."
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+                                            "html": "<table><tr><td>Architectural Choices</td><td>Params (M)</td><td>FLOPs (G)</td><td>Mobile Latency (ms)</td><td>Top-1 (%)</td></tr><tr><td rowspan=\"2\">PoolFormer-S12 (Baseline) + 224 → 256</td><td>11.9</td><td>1.8</td><td>1.50</td><td>77.2</td></tr><tr><td>11.9</td><td>2.4</td><td>2.25</td><td>77.6</td></tr><tr><td>Section 3.2.1 + Pooling → RepMixer</td><td>11.9</td><td>2.4</td><td>1.58</td><td>78.5</td></tr><tr><td rowspan=\"2\">Section 3.2.2 + Factorized dense conv. + Train-Time Overparam.</td><td>8.7</td><td>1.7</td><td>1.26</td><td>78.0</td></tr><tr><td>8.7</td><td>1.7</td><td>1.26</td><td>78.9</td></tr><tr><td rowspan=\"2\">Section 3.2.3 + LK. conv. FFN + LK. conv. Patch Emb.</td><td>8.7</td><td>1.8</td><td>1.33</td><td>79.4</td></tr><tr><td>8.8</td><td>1.8</td><td>1.40</td><td>79.8</td></tr></table>",
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+                                    "content": "Table 1: Analysis of architectural choices made to obtain FastViT-S12 variant, starting from PoolFormer-S12. \"LK.\" stands for Large Kernel."
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+                                    "content": "Self-attention [14] token mixers are computationally expensive, especially at higher resolutions [42, 39]. While efficient versions of self-attention layers are explored in [17, 41], we use large kernel convolutions as an efficient alternative to improve receptive field in early stages of the network architecture (see Figure 2c)."
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+                                    "content": "We analyze various architectural choices made in designing FastViT from a PoolFormer [65] baseline in Table 1 and detail our approach below."
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+                                    "content": ", the mixing block in the layer was implemented as,"
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+                                            "type": "text",
+                                            "content": "Figure 2: (a) Overview of FastViT architecture which decouples train-time and inference-time architecture. Stages 1, 2, and 3 have the same architecture and uses RepMixer for token mixing. In stage 4, self attention layers are used for token mixing. (b) Architecture of the convolutional stem. (c) Architecture of convolutional-FFN (d) Overview of RepMixer block, which reparameterizes a skip connection at inference."
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+                                            "type": "text",
+                                            "content": "Figure 3: Latency comparison of a MetaFormer (S12) architecture with Pooling and RepMixer as a choice for token mixing; measured on iPhone 12 Pro for various image resolutions. Both models have "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "\\sim 1.8\\mathrm{G}"
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+                                            "type": "text",
+                                            "content": " FLOPs. Absence of a skip connection in RepMixer lowers the overall memory access cost leading to lower latency."
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+                                    "type": "text",
+                                    "content": "Empirical Analysis In order to verify the benefits of reparameterizing skip connections, we ablate over the using one of the most efficient (in terms of latency) token mixer, i.e. Pooling and RepMixer in a MetaFormer S12 architecture. Both the models being ablated have "
+                                },
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+                                    "type": "text",
+                                    "content": " FLOPs."
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+                                    "type": "text",
+                                    "content": "We time the models for various input resolutions starting from "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " on an iPhone 12 Pro mobile device. From Figure 3, we see that RepMixer significantly improves over Pooling, especially at higher resolutions. At "
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+                                    "type": "text",
+                                    "content": ", using RepMixer will lower the latency by "
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+                                    "content": "25.1\\%"
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+                                    "type": "text",
+                                    "content": " and at larger resolutions like "
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+                                    "type": "text",
+                                    "content": ", latency is lowered significantly by "
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+                                    "type": "text",
+                                    "content": "."
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+                        }
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+                                    "content": "3.2.2 Linear Train-time Overparameterization"
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+                                    "content": "In order to further improve efficiency (parameter count, FLOPs, and latency), we replace all dense "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " convolutions with its factorized version, i.e. "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " depthwise followed by "
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+                                    "content": " pointwise convolutions. However, the lower parameter count from factorization can diminish the capacity of the model. In order to increase capacity of the factorized layers, we perform linear train-time overparameterization as described in MobileOne [55]. MobileOne-style overparameterization in stem, patch embedding, and projection layers help in boosting performance. From Table 3, we note that train-time overparameterization improves Top-1 accuracy on ImageNet by "
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+                                    "content": " on FastViT-SA12 model. On a smaller FastViT-S12 variant, Top-1 accuracy improves"
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+                                    "content": " as shown in Table 1."
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+                                    "content": "However, train-time overparameterization results in increased training time due to computational overhead from the added branches. In our architecture, we only overparameterize those layers that replace dense "
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+                                    "content": " convolutions with its factorized form as described above. These layers are found in the convolutional stem, patch embedding and projection layers. The computational cost incurred in these layers are lower than the rest of the network, hence overparameterizing these layers do not result in significant increases to train time. For example, FastViT-SA12 takes "
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+                                    "content": " longer and FastViT-SA36 takes "
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+                                    "content": " longer to train with train-time overparameterization as opposed to training those variants without it under the same settings described in Section 4.1."
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+                                            "type": "text",
+                                            "content": "Table 2: Architecture details of FastViT variants. Models with smaller embedding dimensions, i.e. [64, 128, 256, 512] are prefixed with \"S\" and models that contain Self-Attention layers are prefixed with \"SA\". Models with bigger embedding dimensions, i.e. [76, 152, 304, 608] are prefixed with \"M\". Models with MLP expansion ratio less than 4 are prefixed with \"T\". The number in the notation denotes total number of FastViT blocks. FLOP count is computed by fvcore[15] library."
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+                                            "html": "<table><tr><td>Model</td><td>Ablation</td><td>Top-1 (%)</td><td>Train Time (hrs)</td></tr><tr><td rowspan=\"2\">FastViT-SA12</td><td>Without Train-Time Overparam.</td><td>80.0</td><td>31.3</td></tr><tr><td>With Train-Time Overparam.</td><td>80.6</td><td>33.4</td></tr><tr><td rowspan=\"2\">FastViT-SA36</td><td>Without Train-Time Overparam.</td><td>83.3</td><td>73.5</td></tr><tr><td>With Train-Time Overparam.</td><td>83.6</td><td>76.7</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 3: Comparison of FastViT variants with and without linear train-time overparameterization when trained on ImageNet-1k dataset. Train time is wall clock time elapsed at the end of a training run."
+                                }
+                            ]
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+                                    "content": "3.2.3 Large Kernel Convolutions"
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+                                    "content": "The receptive field of RepMixer is local compared to self-attention token mixers. However, self-attention based token mixers are computationally expensive. A computationally efficient approach to improve the receptive field of early stages that do not use self-attention is by incorporating depthwise large kernel convolutions. We introduce depthwise large kernel convolutions in FFN and patch embedding layers. From Table 4, we note that variants using depthwise large kernel convolutions can be highly competitive to variants using self-attention layers while incurring a modest increase in latency. When we compare V5 with V3, model size increases by "
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+                                    "content": ", and latency increases by a factor of "
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+                                    "content": "2.3 \\times"
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+                                    "type": "text",
+                                    "content": " for a relatively small gain of "
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+                                    "type": "text",
+                                    "content": " in Top-1 accuracy. V2 is larger than V4 by "
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+                                    "content": " and has "
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+                                    "type": "text",
+                                    "content": " higher latency than V4 while attaining similar Top-1 accuracy on ImageNet. Further ablations on kernel sizes and latency is provided in the supplementary materials. In Table 1, we ablate over large kernel convolutions in FFN and patch embedding layers. Overall, large kernel convolutions provide "
+                                },
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+                                    "type": "text",
+                                    "content": " improvement in Top-1 accuracy on FastViT-S12."
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+                },
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+                                    "type": "text",
+                                    "content": "The architecture of our FFN and patch embedding layer is shown in Figure 2. Our FFN block has a structure similar to ConvNeXt [36] block with a few key differences, see Figure 2c. We use Batch Normalization as opposed to Layer Normalization, as it can be fused with the preceding layer at inference. Also, it does not require additional reshape operations to obtain appropriate tensor layout for LayerNorm as done in the original implementation of ConvNeXt block."
+                                }
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Along with increased receptive field, large kernel convolutions help in improving model robustness as observed in [59] and convolutional-FFN blocks generally tend to be more robust than vanilla-FFN blocks as observed in [38]. Hence, incorporating large kernel convolutions is an efficient way to improve model performance and robustness."
+                                }
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+                                    "type": "text",
+                                    "content": "4. Experiments"
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+                                    "content": "4.1. Image Classification"
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+                                    "content": "We report results on the widely used ImageNet-1K dataset [45] which contains "
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+                                    "content": "\\sim 1.3\\mathrm{M}"
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+                                    "content": " training images and "
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+                                    "type": "inline_equation",
+                                    "content": "50\\mathrm{K}"
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+                                    "type": "text",
+                                    "content": " validation images. We follow the training recipe prescribed in [51, 65], i.e. the models are trained for 300"
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+                                            "html": "<table><tr><td rowspan=\"2\">Variant</td><td colspan=\"4\">Stages</td><td>Params</td><td>Top-1</td><td>Mobile</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>(M)</td><td>(%)</td><td>Latency (ms)</td></tr><tr><td colspan=\"8\">Standard Setting</td></tr><tr><td>V1</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.7</td><td>78.9</td><td>1.3</td></tr><tr><td>V2</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.8</td><td>79.9</td><td>1.5</td></tr><tr><td>V3</td><td>RM</td><td>RM</td><td>SA</td><td>SA</td><td>12.4</td><td>81.0</td><td>3.7</td></tr><tr><td colspan=\"8\">Large Kernel Convolutions (7×7)</td></tr><tr><td>V4</td><td>RM</td><td>RM</td><td>RM</td><td>RM</td><td>8.8</td><td>79.8</td><td>1.4</td></tr><tr><td>V5</td><td>RM</td><td>RM</td><td>RM</td><td>SA</td><td>10.9</td><td>80.6</td><td>1.6</td></tr></table>",
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+                                    "content": "epochs using AdamW optimizer with weight decay of 0.05 and peak learning rate "
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+                                    "content": " for a total batch size of 1024. The number of warmup epochs is set to 5 and cosine schedule is used to decay the learning rate. Our implementation uses timm library [60] and all the models were trained on 8 NVIDIA A100 GPUs. See supplementary materials for details on hyper parameters used for all the variants. For "
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+                                    "type": "text",
+                                    "content": " input size, we fine-tune the models for 30 epochs with weight decay of "
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+                                    "content": " and learning rate of "
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+                                    "type": "inline_equation",
+                                    "content": "5 \\times 10^{-5}"
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+                                    "type": "text",
+                                    "content": " and batch size of 512 following [36]. To measure latency, we use the input sizes corresponding to the respective methods. For iPhone latency measurements, we export the models using Core ML Tools (v6.0) and run it on iPhone12 Pro Max with iOS 16 and batch size is set to 1 for all the models. We follow the same protocol as [55]. For GPU latency measurements, we export the traced model to TensorRT (v8.0.1.6) format and run it on NVIDIA RTX-2080Ti with batch size of 8. We report the median latency estimate from 100 runs."
+                                }
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+                                    "content": "Comparison with SOTA Models In Table 5, we compare our models against recent state-of-the-art models on ImageNet-1k dataset. For a fair comparison, we modify ConvNeXt [36] from official implementation by avoiding costly reshape operations, see supplementary materials for more details. We were unable to reliably export LITv2 [41] due to poor support for deformable convolutions in either library. Our model obtains the best accuracy-latency trade-off when compared to recent state-of-the-art models on two different compute fabrics, i.e. desktop-grade GPU and mobile device. Our models improve over LITv2 [41] on both parameter count and FLOPs, at Top-1 accuracy of "
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+                                    "content": ", FastViT-MA36 is "
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+                                    "content": " smaller and consumes "
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+                                    "content": " less FLOPs than LITv2-B. FastViT-S12 is "
+                                },
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+                                    "content": " faster than MobileOne-S4 [55] on iPhone 12 Pro and "
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+                                    "content": " faster on"
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+                                            "content": "Table 4: Ablation on using large kernel convolutions as a substitute for self-attention layers. \"RM\" indicates [RepMixer-FFN] block is used in the stage. \"SA\" indicates [Self Attention-FFN] block is used in the stage. Standard setting uses "
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+                                            "content": " factorized convolutions in patch embedding and stem layers and "
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+                                            "content": " convolutions for FFN. In variants V4 and V5, large kernel convolutions "
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+                                            "content": " are used in patch embedding and FFN layers."
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+                            "type": "table_caption"
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+                                            "html": "<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>MobileOne-S0[55]</td><td>224</td><td>2.1</td><td>0.3</td><td>1.0</td><td>0.8</td><td>71.4</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>75.6</td></tr><tr><td>MobileOne-S3[55]</td><td>224</td><td>10.1</td><td>1.8</td><td>2.1</td><td>1.5</td><td>78.1</td></tr><tr><td>CMT-T* [17]</td><td>160</td><td>9.5</td><td>0.6</td><td>4.5</td><td>3.8</td><td>79.1</td></tr><tr><td>EfficientNet-B1[48]</td><td>256</td><td>7.8</td><td>0.7</td><td>3.2</td><td>2.5</td><td>79.1</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>79.1</td></tr><tr><td>MobileOne-S4[55]</td><td>224</td><td>14.8</td><td>2.9</td><td>2.6</td><td>1.9</td><td>79.4</td></tr><tr><td>RSB-ResNet50[61]</td><td>224</td><td>25.6</td><td>4.1</td><td>2.3</td><td>2.6</td><td>79.8</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22.0</td><td>4.6</td><td>5.2</td><td>5.3</td><td>79.8</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>79.8</td></tr><tr><td>RegNetY-8G[43]</td><td>224</td><td>39.2</td><td>8.0</td><td>5.8</td><td>3.8</td><td>79.9</td></tr><tr><td>EfficientNet-B2[48]</td><td>288</td><td>9.2</td><td>1.0</td><td>4.1</td><td>3.5</td><td>80.1</td></tr><tr><td>PoolFormer-S24[65]</td><td>224</td><td>21.0</td><td>3.4</td><td>15.7</td><td>2.5</td><td>80.3</td></tr><tr><td>RegNetY-16G [43]</td><td>224</td><td>83.6</td><td>16.0</td><td>8.1</td><td>7.5</td><td>80.4</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>80.6</td></tr><tr><td>ResNeSt50[67]</td><td>224</td><td>27.5</td><td>5.4</td><td>51.5</td><td>29.9</td><td>81.1</td></tr><tr><td>Swin-T[35]</td><td>224</td><td>29.0</td><td>4.5</td><td>-</td><td>9.3</td><td>81.3</td></tr><tr><td>PoolFormer-S36[65]</td><td>224</td><td>31.0</td><td>5.0</td><td>23.7</td><td>3.5</td><td>81.4</td></tr><tr><td>EfficientNet-B3[48]</td><td>300</td><td>12.0</td><td>1.8</td><td>5.3</td><td>7.1</td><td>81.6</td></tr><tr><td>CvT-13[62]</td><td>224</td><td>20.1</td><td>4.5</td><td>18.1</td><td>62.6</td><td>81.6</td></tr><tr><td>CoAtNet-0[9]</td><td>224</td><td>25.0</td><td>4.2</td><td>-</td><td>6.7</td><td>81.6</td></tr><tr><td>CMT-XS* [17]</td><td>192</td><td>15.2</td><td>1.5</td><td>8.3</td><td>6.3</td><td>81.8</td></tr><tr><td>DeiT-B [51]</td><td>224</td><td>86.0</td><td>17.5</td><td>11.6</td><td>11.6</td><td>81.8</td></tr><tr><td>RSB-ResNet152[61]</td><td>224</td><td>60.2</td><td>11.6</td><td>5.4</td><td>4.7</td><td>81.8</td></tr><tr><td>LITv2-S[41]</td><td>224</td><td>28.0</td><td>3.7</td><td>-</td><td>-</td><td>82.0</td></tr><tr><td>ConvNeXt-T†[36]</td><td>224</td><td>29.0</td><td>4.5</td><td>6.3</td><td>3.7</td><td>82.1</td></tr><tr><td>PoolFormer-M48[65]</td><td>224</td><td>73.0</td><td>11.6</td><td>30.2</td><td>7.6</td><td>82.5</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>82.6</td></tr><tr><td>ResNeSt101[67]</td><td>224</td><td>48.2</td><td>10.2</td><td>75.5</td><td>37.7</td><td>83.0</td></tr><tr><td>Swin-S[35]</td><td>224</td><td>50.0</td><td>8.7</td><td>-</td><td>13.0</td><td>83.0</td></tr><tr><td>ConvNeXt-S†[36]</td><td>224</td><td>50.0</td><td>8.7</td><td>10.3</td><td>5.4</td><td>83.1</td></tr><tr><td>MOAT-0[5]</td><td>224</td><td>27.8</td><td>5.7</td><td>-</td><td>4.9</td><td>83.3</td></tr><tr><td>CoAtNet-1[9]</td><td>224</td><td>42.0</td><td>8.4</td><td>-</td><td>13.4</td><td>83.3</td></tr><tr><td>Swin-B [35]</td><td>224</td><td>88.0</td><td>15.4</td><td>-</td><td>18.5</td><td>83.5</td></tr><tr><td>CMT-S* [17]</td><td>224</td><td>25.1</td><td>4.0</td><td>13.8</td><td>15.6</td><td>83.5</td></tr><tr><td>MaxViT-T[54]</td><td>224</td><td>31.0</td><td>5.6</td><td>-</td><td>31.5</td><td>83.6</td></tr><tr><td>LITv2-B[41]</td><td>224</td><td>87.0</td><td>13.2</td><td>-</td><td>-</td><td>83.6</td></tr><tr><td>EfficientNet-B5[48]</td><td>456</td><td>30.0</td><td>9.9</td><td>24.2</td><td>22.1</td><td>83.6</td></tr><tr><td>NFNet-F0[1]</td><td>256</td><td>71.5</td><td>12.4</td><td>6.2</td><td>6.4</td><td>83.6</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>83.6</td></tr><tr><td>ConvNeXt-B†[36]</td><td>224</td><td>89.0</td><td>15.4</td><td>13.6</td><td>8.4</td><td>83.8</td></tr><tr><td>CoAtNet-0</td><td>384</td><td>25.0</td><td>13.4</td><td>-</td><td>20.1</td><td>83.9</td></tr><tr><td>EfficientNetV2-S[49]</td><td>384</td><td>22.0</td><td>8.8</td><td>8.2</td><td>7.1</td><td>83.9</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>83.9</td></tr><tr><td>EfficientNet-B6[48]</td><td>528</td><td>43.0</td><td>19.0</td><td>44.3</td><td>51.7</td><td>84.0</td></tr><tr><td>CoAtNet-2[9]</td><td>224</td><td>75.0</td><td>15.7</td><td>-</td><td>19.6</td><td>84.1</td></tr><tr><td>MOAT-1[5]</td><td>224</td><td>41.6</td><td>9.1</td><td>-</td><td>8.3</td><td>84.2</td></tr><tr><td>EfficientNet-B7[48]</td><td>600</td><td>66.0</td><td>37.0</td><td>72.6</td><td>85.5</td><td>84.3</td></tr><tr><td>CMT-B* [17]</td><td>256</td><td>45.7</td><td>9.3</td><td>26.9</td><td>20.6</td><td>84.5</td></tr><tr><td>Swin-B[35]</td><td>384</td><td>88.0</td><td>47.0</td><td>-</td><td>57.2</td><td>84.5</td></tr><tr><td>MaxViT-S[54]</td><td>224</td><td>69.0</td><td>11.7</td><td>-</td><td>48.7</td><td>84.5</td></tr><tr><td>FastViT-SA36</td><td>384</td><td>30.4</td><td>12.6</td><td>12.8</td><td>7.4</td><td>84.5</td></tr><tr><td>MOAT-0[5]</td><td>384</td><td>27.8</td><td>18.2</td><td>-</td><td>24.3</td><td>84.6</td></tr><tr><td>NFNet-F1[1]</td><td>320</td><td>132.6</td><td>35.5</td><td>16.9</td><td>16.1</td><td>84.7</td></tr><tr><td>MOAT-2[5]</td><td>224</td><td>73.4</td><td>17.2</td><td>-</td><td>12.6</td><td>84.7</td></tr><tr><td>LITv2-B[41]</td><td>384</td><td>87.0</td><td>39.7</td><td>-</td><td>-</td><td>84.7</td></tr><tr><td>FastViT-MA36</td><td>384</td><td>42.7</td><td>17.7</td><td>16.5</td><td>9.2</td><td>84.9</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 5: Comparison of different state-of-the-art methods on ImageNet-1k classification. HardSwish is not well supported by Core ML, * denotes we replace it with GELU for fair comparison. “†” denotes that model has been modified from original implementation for efficient deployment. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”."
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+                                            "html": "<table><tr><td>Model</td><td>Eval Image Size</td><td>Param (M)</td><td>FLOPs (G)</td><td>GPU Latency (ms)</td><td>Mobile Latency (ms)</td><td>Top-1 Acc. (%)</td></tr><tr><td>FastViT-T8</td><td>256</td><td>3.6</td><td>0.7</td><td>1.7</td><td>0.8</td><td>76.7</td></tr><tr><td>FastViT-T12</td><td>256</td><td>6.8</td><td>1.4</td><td>2.1</td><td>1.2</td><td>80.3</td></tr><tr><td>CaiT XXS-36[52]</td><td>224</td><td>17.3</td><td>3.8</td><td>15.8</td><td>-</td><td>79.7</td></tr><tr><td>FastViT-S12</td><td>256</td><td>8.8</td><td>1.8</td><td>2.2</td><td>1.4</td><td>80.9</td></tr><tr><td>DeiT-S[51]</td><td>224</td><td>22</td><td>4.6</td><td>5.2</td><td>6.7</td><td>81.2</td></tr><tr><td>FastViT-SA12</td><td>256</td><td>10.9</td><td>1.9</td><td>2.5</td><td>1.6</td><td>81.9</td></tr><tr><td>EfficientFormer-L3[31]</td><td>224</td><td>31.3</td><td>3.9</td><td>3.6</td><td>3.0</td><td>82.4</td></tr><tr><td>EfficientFormer-L7[31]</td><td>224</td><td>82.1</td><td>10.2</td><td>7.5</td><td>7.0</td><td>83.3</td></tr><tr><td>DeiT-B[51]</td><td>224</td><td>87</td><td>17.6</td><td>11.6</td><td>11.6</td><td>83.4</td></tr><tr><td>FastViT-SA24</td><td>256</td><td>20.6</td><td>3.8</td><td>3.8</td><td>2.6</td><td>83.4</td></tr><tr><td>CaiT S-24[52]</td><td>224</td><td>46.9</td><td>9.4</td><td>19.1</td><td>-</td><td>83.5</td></tr><tr><td>CaiT XS-24[52]</td><td>384</td><td>26.6</td><td>19.3</td><td>77.7</td><td>-</td><td>84.1</td></tr><tr><td>FastViT-SA36</td><td>256</td><td>30.4</td><td>5.6</td><td>5.2</td><td>3.5</td><td>84.2</td></tr><tr><td>FastViT-MA36</td><td>256</td><td>42.7</td><td>7.9</td><td>6.7</td><td>4.5</td><td>84.6</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 6: Comparison of different state-of-the-art methods on ImageNet-1k classification when trained using distillation objective specified by [51]. Models which could not be reliably exported either by TensorRT or Core ML Tools are annotated by “-”."
+                                        }
+                                    ]
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+                                    "type": "text",
+                                    "content": "GPU. At Top-1 accuracy of "
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+                                    "type": "text",
+                                    "content": ", FastViT-MA36 is "
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+                                    "type": "text",
+                                    "content": " faster than an optimized ConvNeXt-B model on iPhone 12 Pro and "
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+                                    "content": "2.0 \\times"
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+                                    "type": "text",
+                                    "content": " faster on GPU. At Top-1 accuracy of "
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+                                    "type": "text",
+                                    "content": ", FastViT-MA36 is just as fast as NFNet-F1 [1] on GPU while being "
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+                                    "type": "text",
+                                    "content": " smaller and using "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " less FLOPs and "
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+                                    "type": "text",
+                                    "content": " faster on mobile device."
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+                            ]
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+                    ],
+                    "index": 2
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+                {
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+                                    "type": "text",
+                                    "content": "Knowledge distillation We report performance of our models when trained with distillation objective in Table 6. We follow the setting described in DeiT [51], with RegNet-16GF [43] as the teacher model. Following DeiT [51], we use hard distillation where hard decision of the teacher is set as true label. Our models are trained for 300 epochs. Unlike [51, 52, 31], we do not introduce an additional classification head for distillation. FastViT outperforms recent state-of-the-art model EfficientFormer [31]. FastViT-SA24 attains similar performance as EfficientFormer-L7 while having "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "3.8 \\times"
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+                                    "type": "text",
+                                    "content": " less parameters, "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "2.7 \\times"
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+                                    "type": "text",
+                                    "content": " less FLOPs and "
+                                },
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+                                    "content": "2.7 \\times"
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+                                    "type": "text",
+                                    "content": " lower latency."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.2. Robustness Evaluation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
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+                                    "content": "We evaluate our models for out-of-distribution robustness on the following benchmarks - (i) ImageNet-A [24], a dataset that contains naturally occurring examples that are misclassified by ResNets; (ii) ImageNet-R [22], a dataset that contains natural renditions of ImageNet object classes with different textures and local image statistics; (iii) ImageNet-Sketch [56], a dataset that contains black and white sketches of all ImageNet classes, obtained using google image queries; and (iv) ImageNet-C [23], a dataset that consists of algorithmically generated corruption"
+                                }
+                            ]
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+                    ],
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Model</td><td>#Params</td><td>#FLOPs</td><td>Clean</td><td>IN-C (↓)</td><td>IN-A</td><td>IN-R</td><td>IN-SK</td></tr><tr><td>PVT-Tiny</td><td>13.2</td><td>1.9</td><td>75.0</td><td>79.6</td><td>7.9</td><td>33.9</td><td>21.5</td></tr><tr><td>RVT-Ti</td><td>8.6</td><td>1.3</td><td>78.4</td><td>58.2</td><td>13.3</td><td>43.7</td><td>30.0</td></tr><tr><td>FastViT-SA12</td><td>10.9</td><td>1.9</td><td>80.6</td><td>62.2</td><td>17.2</td><td>42.6</td><td>29.7</td></tr><tr><td>PVT-Small</td><td>24.5</td><td>3.8</td><td>79.9</td><td>66.9</td><td>18.0</td><td>40.1</td><td>27.2</td></tr><tr><td>ResNet-50*</td><td>25.6</td><td>4.1</td><td>79.0</td><td>65.5</td><td>5.9</td><td>42.5</td><td>31.5</td></tr><tr><td>ResNeXt50-32x4d</td><td>25.0</td><td>4.3</td><td>79.8</td><td>64.7</td><td>10.7</td><td>41.5</td><td>29.3</td></tr><tr><td>FastViT-SA24</td><td>20.6</td><td>3.8</td><td>82.6</td><td>55.3</td><td>26.0</td><td>46.5</td><td>34.0</td></tr><tr><td>Swin-T</td><td>28.3</td><td>4.5</td><td>81.2</td><td>62.0</td><td>21.6</td><td>41.3</td><td>29.1</td></tr><tr><td>ConViT-S</td><td>27.8</td><td>5.4</td><td>81.5</td><td>49.8</td><td>24.5</td><td>45.4</td><td>33.1</td></tr><tr><td>RVT-S</td><td>22.1</td><td>4.7</td><td>81.7</td><td>50.1</td><td>24.1</td><td>46.9</td><td>35.0</td></tr><tr><td>ConvNeXt-T</td><td>28.6</td><td>4.5</td><td>82.1</td><td>53.2</td><td>24.2</td><td>47.2</td><td>33.8</td></tr><tr><td>EfficientNet-B4</td><td>19.3</td><td>4.2</td><td>83.0</td><td>71.1</td><td>26.3</td><td>47.1</td><td>34.1</td></tr><tr><td>FastViT-SA36</td><td>30.4</td><td>5.6</td><td>83.6</td><td>51.8</td><td>32.3</td><td>48.1</td><td>35.8</td></tr><tr><td>ConvNeXt-S</td><td>50.0</td><td>8.7</td><td>83.1</td><td>51.2</td><td>31.2</td><td>49.5</td><td>37.1</td></tr><tr><td>FastViT-MA36</td><td>42.7</td><td>7.9</td><td>83.9</td><td>49.9</td><td>34.6</td><td>49.5</td><td>36.6</td></tr></table>",
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+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Table 7: Results on robustness benchmark datasets. Models are grouped based on FLOPs. Performance of competing models is reported by [38] and [36]. *ResNet-50 model is trained with AugMix to improve robustness as reported in [38]. For ImageNet-C mean corruption error is reported (lower is better) and for other datasets Top-1 accuracy is reported (higher is better). The best results are in bold and second best results are underlined."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
+                            "angle": 0,
+                            "type": "table_footnote"
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+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "tions (blur, noise) applied to the ImageNet test-set. We evaluate our models using the implementation provided by [38]. Our models are more robust than recent vision transformers while being faster than pure-CNN based models which exhibit low robustness as seen Table 7. Architectural choices like using a large kernel convolutions in FFN and patch-embedding layers in combination with self-attention layers helps in improving the robustness of our model as discussed in Section 3.2.3. All the models compared in Table 7 are trained only on ImageNet-1k dataset using similar training recipes. From Table 7, our model is highly competitive to RVT and ConvNeXt, in fact FastViT-M36 has better clean accuracy, better robustness to corruptions and similar out-of-distribution robustness as ConvNeXt-S which has 6.1M more parameters and has "
+                                },
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+                                    "type": "text",
+                                    "content": " more FLOPs than our model."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                                    "type": "text",
+                                    "content": "4.3. 3D Hand mesh estimation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Recent works on real-time 3D hand mesh estimation introduce complex mesh regression layers over CNN based backbones. The backbones usually belong to ResNet or MobileNet family of architectures with the exception of METRO and MeshGraphormer which use HRNets [47] for feature extraction. While most hardware devices are highly optimized for feature extraction from 2D CNNs, the same is not true for the complex mesh regression heads used in these methods. In our method, we replace the complex mesh regression head with a simple regression module which regresses weak perspective camera, pose and shape parameters of the MANO model [44]. We argue that using a feature"
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Method</td><td>Backbone</td><td colspan=\"5\">PJ ↓ PV ↓ F@5 ↑ F@15 ↑ FPS ↑</td></tr><tr><td colspan=\"7\">Non Real-Time methods</td></tr><tr><td>HIU-DMTL [68]</td><td>Customized</td><td>7.1</td><td>7.3</td><td>0.699</td><td>0.974</td><td>5</td></tr><tr><td>METRO [32]</td><td>HRNet</td><td>6.3</td><td>6.5</td><td>0.731</td><td>0.984</td><td>4.2</td></tr><tr><td>MeshGraphormer [33]</td><td>HRNet</td><td>5.9</td><td>6.0</td><td>0.764</td><td>0.986</td><td>2.6</td></tr><tr><td colspan=\"7\">Real-Time methods</td></tr><tr><td>Hasson et al. [19]</td><td>ResNet18</td><td>-</td><td>13.2</td><td>0.436</td><td>0.908</td><td>20</td></tr><tr><td>MobileHand [16]</td><td>MobileNetV3</td><td>-</td><td>13.1</td><td>0.439</td><td>0.902</td><td>110</td></tr><tr><td>YoutubeHand [30]</td><td>ResNet50</td><td>8.4</td><td>8.6</td><td>0.614</td><td>0.966</td><td>60</td></tr><tr><td>I2L-MeshNet [40]</td><td>ResNet50</td><td>7.4</td><td>7.6</td><td>0.681</td><td>0.973</td><td>33.3</td></tr><tr><td>Pose2Mesh [6]</td><td>Customized</td><td>7.4</td><td>7.6</td><td>0.683</td><td>0.973</td><td>20</td></tr><tr><td>I2UV-HandNet [2]</td><td>ResNet50</td><td>7.2</td><td>7.4</td><td>0.682</td><td>0.973</td><td>-</td></tr><tr><td>Tang et al. [50]</td><td>ResNet50</td><td>7.1</td><td>7.1</td><td>0.706</td><td>0.977</td><td>39.1</td></tr><tr><td>MobRecon[4]</td><td>DenseStack</td><td>6.9</td><td>7.2</td><td>0.694</td><td>0.979</td><td>77</td></tr><tr><td>CMR [3]</td><td>ResNet50*</td><td>6.9</td><td>7.0</td><td>0.715</td><td>0.977</td><td>-</td></tr><tr><td>Ours</td><td>FastViT-MA36</td><td>6.6</td><td>6.7</td><td>0.722</td><td>0.981</td><td>218</td></tr></table>",
+                                            "image_path": "8bc5ccc15667961f918c485afa62d4dcf3eb151b9261ed558508ffd9d9fefcd9.jpg"
+                                        }
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+                                            "type": "text",
+                                            "content": "Table 8: Results on the FreiHAND test dataset. FPS is computed on NVIDIA RTX-2080Ti under similar setting as MobRecon [4]. Performance of competing methods obtained from training exclusively on FreiHand dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
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+                                    "type": "text",
+                                    "content": "extraction backbone that learns a good representation for underlying images can alleviate learning challenges in mesh regression. While other real-time methods compensate for weak feature extraction backbone with complex mesh regression layers, we use a better feature extraction backbone with a simple mesh regression layer. We compare our approach with other published methods on the FreiHand [71] dataset. For a fair comparison, we cite results of methods that only used FreiHand dataset for training as some methods either pre-train, train, or fine-tune with additional pose datasets. We only use ImageNet-1k dataset for pretraining and then train exclusively on the FreiHand dataset using the experimental setup described in [32]. For more details, please see supplementary materials. From Table 8, amongst real-time methods, our method outperforms other methods on all joint and vertex error related metrics while being "
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+                                    "type": "text",
+                                    "content": " faster than MobileHand [16] and "
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+                                    "type": "text",
+                                    "content": " faster than recent state-of-art MobRecon."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
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+                                    "type": "text",
+                                    "content": "4.4. Semantic Segmentation and Object Detection"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "For semantic segmentation, we validate the performance of our models on ADE20k [70]. The dataset contains 20K training images and 2K validation images with 150 semantic categories. We train semantic segmentation models with Semantic FPN [28] decoder. Models with Semantic FPN head use the same settings as [65]. All models are initialized with pretrained weights from their corresponding image classification models. FLOPs and backbone latency are estimated on image crops of "
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+                                    "type": "text",
+                                    "content": ". Due to higher resolution of input image, GPU latencies are estimated over a batch size of 2 in both Table 9 and Table 10. In Table 9, we compare our models with recent works. FastViT-MA36 model obtains "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "5.2\\%"
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+                                    "type": "text",
+                                    "content": " higher mIoU than PoolFormer-M36"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    "bbox": [
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+                            "bbox": [
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">Backbone</td><td rowspan=\"2\">GPU Latency</td><td rowspan=\"2\">Mobile Latency</td><td colspan=\"3\">Semantic FPN 80k</td></tr><tr><td>Param(M)</td><td>FLOPs(G)</td><td>mIoU(%)</td></tr><tr><td>ResNet-50</td><td>2.7</td><td>8.7</td><td>28.5</td><td>46</td><td>36.7</td></tr><tr><td>PoolFormer-S12[65]</td><td>9.7</td><td>6.2</td><td>15.7</td><td>31</td><td>37.2</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>14.1</td><td>29</td><td>38.0</td></tr><tr><td>ResNet-101</td><td>4.6</td><td>12.4</td><td>47.5</td><td>65</td><td>38.8</td></tr><tr><td>PVT-Small[58]</td><td>-</td><td>-</td><td>28.2</td><td>41</td><td>39.8</td></tr><tr><td>PoolFormer-S24[65]</td><td>18.9</td><td>10.7</td><td>23.2</td><td>48</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>23.8</td><td>37</td><td>41.0</td></tr><tr><td>PoolFormer-S36[65]</td><td>28.0</td><td>17.0</td><td>34.6</td><td>48</td><td>42.0</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>33.6</td><td>44</td><td>42.9</td></tr><tr><td>PVT-Medium[58]</td><td>-</td><td>-</td><td>48.0</td><td>55</td><td>41.6</td></tr><tr><td>PoolFormer-M36[65]</td><td>41.4</td><td>24.8</td><td>59.8</td><td>68</td><td>42.4</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.7</td><td>53</td><td>44.6</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 9: Performance of different backbones on ADE20K semantic segmentation task. Following common convention, FLOPs and backbone latencies are measured on crops of "
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+                                            "html": "<table><tr><td>Backbone</td><td>GPU Latency</td><td>Mobile Latency</td><td>\\(AP^b\\)</td><td>\\(AP^{b}_{50}\\)</td><td>\\(AP^{b}_{75}\\)</td><td>\\(AP^m\\)</td><td>\\(AP^{m}_{50}\\)</td><td>\\(AP^{m}_{75}\\)</td></tr><tr><td>Poolfomer-S12[65]</td><td>9.7</td><td>6.2</td><td>37.3</td><td>59.0</td><td>40.1</td><td>34.6</td><td>55.8</td><td>36.9</td></tr><tr><td>ResNet-50 [21]</td><td>2.7</td><td>8.7</td><td>38.0</td><td>58.6</td><td>41.4</td><td>34.4</td><td>55.1</td><td>36.7</td></tr><tr><td>FastViT-SA12</td><td>2.5</td><td>5.6</td><td>38.9</td><td>60.5</td><td>42.2</td><td>35.9</td><td>57.6</td><td>38.1</td></tr><tr><td>ResNet-101 [21]</td><td>4.6</td><td>12.4</td><td>40.0</td><td>60.5</td><td>44.0</td><td>36.1</td><td>57.5</td><td>38.6</td></tr><tr><td>Poolfomer-S24[65]</td><td>18.9</td><td>10.7</td><td>40.1</td><td>62.2</td><td>43.4</td><td>37.0</td><td>59.1</td><td>39.6</td></tr><tr><td>PVT-S [58]</td><td>-</td><td>-</td><td>40.4</td><td>62.9</td><td>43.8</td><td>37.8</td><td>60.1</td><td>40.3</td></tr><tr><td>FastViT-SA24</td><td>4.4</td><td>9.3</td><td>42.0</td><td>63.5</td><td>45.8</td><td>38.0</td><td>60.5</td><td>40.5</td></tr><tr><td>Swin-T [35]</td><td>-</td><td>-</td><td>42.2</td><td>64.6</td><td>46.2</td><td>39.1</td><td>61.6</td><td>42.0</td></tr><tr><td>Twins-SVT-S [7]</td><td>-</td><td>-</td><td>42.7</td><td>65.6</td><td>46.7</td><td>39.6</td><td>62.5</td><td>42.6</td></tr><tr><td>Twins-PCPVT-S [7]</td><td>-</td><td>52.1</td><td>42.9</td><td>65.8</td><td>47.1</td><td>40.0</td><td>62.7</td><td>42.9</td></tr><tr><td>FastViT-SA36</td><td>6.1</td><td>12.9</td><td>43.8</td><td>65.1</td><td>47.9</td><td>39.4</td><td>62.0</td><td>42.3</td></tr><tr><td>CMT-S [17]</td><td>19.9</td><td>70.9</td><td>44.6</td><td>66.8</td><td>48.9</td><td>40.7</td><td>63.9</td><td>43.4</td></tr><tr><td>Poolfomer-S36[65]</td><td>28.0</td><td>17.0</td><td>41.0</td><td>63.1</td><td>44.8</td><td>37.7</td><td>60.1</td><td>40.0</td></tr><tr><td>FastViT-MA36</td><td>8.2</td><td>16.3</td><td>45.1</td><td>66.8</td><td>49.5</td><td>40.5</td><td>63.8</td><td>43.4</td></tr></table>",
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+                                        }
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+                            "index": 7,
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Table 10: Results for object detection and instance segmentation on MS-COCO val2017 split using Mask-RCNN [20] framework using 1x training schedule, i.e. 12 epochs used for training the models. Backbone latencies are measured on crops of "
+                                        },
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+                            ],
+                            "index": 8,
+                            "angle": 0,
+                            "type": "table_footnote"
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "which has higher FLOPs, parameter count and latency on both desktop GPU and mobile device."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We train object detection on the MS-COCO [34] dataset with 80 classes containing 118K training and 5K validation images. In Table 10, we compare our models with recent works. All the models are trained with 1x schedule following [65] using a Mask-RCNN [20] head. All models are initialized with pretrained weights from their corresponding image classification models. We show that our models achieve state-of-the-art performance under multiple latency regimes. FastViT-MA36 model has similar performance as CMT-S, while being "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "2.4 \\times"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "4.3 \\times"
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+                                    "type": "text",
+                                    "content": " faster on desktop GPU and mobile device respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
+                            ]
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+                },
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+                                    "content": "We have proposed a general purpose hybrid vision transformer that is highly efficient on multiple compute fabrics: mobile devices and desktop grade GPUs. Through structural reparameterization, our model incurs reduced memory access cost. This leads to significant improvements in runtime especially at higher resolutions. In addition, we propose further architectural changes that boosts performance on ImageNet classification task and other downstream tasks like object detection, semantic segmentation and 3D hand mesh estimation. We empirically show that our backbone is highly robust to out-of-distribution samples, while being significantly faster than competing robust models."
+                                }
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+                                    "type": "text",
+                                    "content": "Acknowledgements We thank Jen-Hao Rick Chang, Skyker Seto and Hadi Pouransari for helpful discussions and reviewing the manuscript."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "content": "References"
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diff --git a/2023/FateZero_ Fusing Attentions for Zero-shot Text-based Video Editing/e5894958-e0d6-43ea-919c-f4a78223bdd8_content_list.json b/2023/FateZero_ Fusing Attentions for Zero-shot Text-based Video Editing/e5894958-e0d6-43ea-919c-f4a78223bdd8_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..4045df05b92ec13399711910923ef8d2bd374486
--- /dev/null
+++ b/2023/FateZero_ Fusing Attentions for Zero-shot Text-based Video Editing/e5894958-e0d6-43ea-919c-f4a78223bdd8_content_list.json	
@@ -0,0 +1,1980 @@
+[
+    {
+        "type": "text",
+        "text": "FateZero: Fusing Attentions for Zero-shot Text-based Video Editing",
+        "text_level": 1,
+        "bbox": [
+            140,
+            130,
+            828,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Chenyang Qi $^{1*}$  Xiaodong Cun $^{2\\dagger}$  Yong Zhang $^{2}$  Chenyang Lei $^{3}$  Xintao Wang $^{2}$  Ying Shan $^{2}$  Qifeng Chen $^{1\\dagger}$",
+        "bbox": [
+            189,
+            178,
+            777,
+            219
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ HKUST  $^{2}$ Tencent AI Lab  $^{3}$ CAIR, HKISI-CAS",
+        "bbox": [
+            256,
+            232,
+            712,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "https://fate-zero-edit.github.io",
+        "bbox": [
+            290,
+            268,
+            673,
+            287
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/d3be8d22c7445e65d4844eb9cb13a73c3ac156801810d3bcb6237999fd2e3576.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            321,
+            890,
+            426
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Source Video Prompt: A silver jeep driving down a curvy road in the countryside.",
+        "bbox": [
+            212,
+            426,
+            750,
+            440
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/e356623977af9a159898539d6064163ffcc7b0749c4f8249e02b3fee2299daf2.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            441,
+            890,
+            546
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot object shape editing with pre-trained video diffusion model [52]: silver jeep  $\\rightarrow$  Porsche car.",
+        "bbox": [
+            148,
+            546,
+            815,
+            560
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/914d4e31b5e3482e93451761f0b45d62f71774e96257c02567f9ee78663f154b.jpg",
+        "image_caption": [
+            "Figure 1. Zero-shot text-driven video editing. We present a zero-shot approach for shape-aware local object editing and video style editing from pre-trained diffusion models [42, 52] without any optimization for each target prompt."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            560,
+            890,
+            665
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot video style editing with pre-trained image diffusion model [42]: watercolor painting.",
+        "bbox": [
+            166,
+            665,
+            790,
+            680
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            739,
+            313,
+            757
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The diffusion-based generative models have achieved remarkable success in text-based image generation. However, since it contains enormous randomness in generation progress, it is still challenging to apply such models for real-world visual content editing, especially in videos. In this paper, we propose FateZero, a zero-shot text-based",
+        "bbox": [
+            75,
+            772,
+            470,
+            864
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "editing method on real-world videos without per-prompt training or use-specific mask. To edit videos consistently, we propose several techniques based on the pre-trained models. Firstly, in contrast to the straightforward DDIM inversion technique, our approach captures intermediate attention maps during inversion, which effectively retain both structural and motion information. These maps are directly fused in the editing process rather than generated during denoising. To further minimize semantic leakage of the source video, we then fuse self-attention with a blending",
+        "bbox": [
+            496,
+            742,
+            893,
+            893
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "* Work done during an internship at Tencent AI Lab.",
+        "bbox": [
+            76,
+            875,
+            356,
+            887
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding Authors.",
+        "bbox": [
+            78,
+            887,
+            215,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "15932",
+        "bbox": [
+            480,
+            945,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "mask obtained by cross-attention features from the source prompt. Furthermore, we have implemented a reform of the self-attention mechanism in denoising UNet by introducing spatial-temporal attention to ensure frame consistency. Yet succinct, our method is the first one to show the ability of zero-shot text-driven video style and local attribute editing from the trained text-to-image model. We also have a better zero-shot shape-aware editing ability based on the text-to-video model [52]. Extensive experiments demonstrate our superior temporal consistency and editing capability than previous works.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            265,
+            209,
+            280
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Diffusion-based models [19] can generate diverse and high-quality images [40, 42, 44] and videos [15, 18, 32, 45, 56] through text prompts. It also brings large opportunities to edit real-world visual content from these generative priors.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Previous or concurrent diffusion-based editing methods [2, 3, 6, 16, 38, 48] majorly work on images. To edit real images, their methods utilize deterministic DDIM [46] for the image-to-noise inversion, and then, the inverted noise gradually generates the edited images under the condition of the target prompt. Based on this pipeline, several methods have been proposed in terms of cross-attention guidance [38], plug-and-play feature [48], and optimization [25, 35].",
+        "bbox": [
+            75,
+            354,
+            470,
+            474
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Manipulating videos through generative priors as image editing methods above contains many challenges (Fig. 7). First, there are no publicly available generic text-to-video models [18, 45]. Thus, a framework based on image models can be more valuable than on video ones [36], thanks to the various open-sourced image models in the community [1, 37, 42, 54]. However, the text-to-image models [42] lack the consideration of temporal-aware information, e.g., motion and 3D shape understanding. Directly applying the image editing methods [33, 35] to the video will show obverse flickering. Second, although we can use previous video editing methods [4, 24, 28] via keyframe [21] or atlas editing [4, 24], these methods still need atlas learning [4, 24], keyframe selection [21], and per-prompt tunning [4, 28]. Moreover, while they may work well on the attribute [4, 24] and style [21] editing, the shape editing is still a big challenge [28]. Finally, as introduced above, current editing methods use DDIM for inversion and then denoising via the new prompt. However, in video inversion, the inverted noise in the  $T$  step might break the motion and structure of the original video because of error accumulation (Fig. 4 and 9).",
+        "bbox": [
+            73,
+            477,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose FateZero, a simple yet effective method for zero-shot video editing since we do not need to train for each target prompt individually [4, 24, 28] and have no user-specific mask [2, 3]. Different from image editing, video editing needs to keep the temporal consistency of the edited video, which is not learned by the original trained text-to-image model. We tackle this problem by using two",
+        "bbox": [
+            75,
+            795,
+            470,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "novel designs. Firstly, instead of solely relying on inversion and generation [16, 35, 48], we adopt a different approach by storing all the self and cross-attention maps at every step of the inversion process. This enables us to subsequently replace them during the denoising steps of the DDIM pipeline. Specifically, we find these self-attention blocks store better motion information and the cross-attention can be used as a threshold mask for self-attention blending spatially. This attention blending operation can keep the original structures unchanged. Furthermore, we reform the self-attention blocks to the spatial-temporal attention blocks as in [52] to make the appearance more consistent. Powered by our novel designs, we can directly edit the style and the attribute of the real-world video (Fig. 6) using the pre-trained text-to-image model [42]. Also, after getting the video diffusion model (e.g., pretrained Tune-A-Video [52]), our method shows better object editing (Fig. 5) ability in test-time than simple DDIM inversion [46]. The extensive experiments provide evidence of the advantages offered by the proposed method for both video and image editing.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions are summarized as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We present the first framework for temporal-consistent zero-shot text-based video editing using pretrained text-to-image model.",
+            "- We propose to fuse the attention maps in the inversion process and generation process to preserve the motion and structure consistency during editing.",
+            "- Our novel Attention Blending Block utilizes the source prompt's cross-attention map during attention fusion to prevent source semantic leakage and improve the shape-editing capability.",
+            "- We show extensive applications of our method in video style editing, video local attribute editing, video object shape editing, etc."
+        ],
+        "bbox": [
+            517,
+            419,
+            890,
+            648
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            662,
+            640,
+            679
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Video Editing. Video can be edited via several aspects. For video stylizing editing, current methods [11, 21] rely on the example as the style guide and these methods may fail when the track is lost. By processing frames individually using image style transfer [13, 22], some works also learn to reduce the temporal consistency [5, 27, 29, 30] in a post-process way. However, the style may still be imperfect since the style transfer only measures the perceptual distance [55]. Several works also show better consistency but on the specific domain, e.g., portrait video [12, 53]. For video local editing, layer-atlas based methods [4, 24] show a promising direction by editing the video on a flattened texture map. However, the 2d atlas lacks 3d motion perception to support shape editing, and prompt-specific optimization is required.",
+        "bbox": [
+            496,
+            688,
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+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "15933",
+        "bbox": [
+            480,
+            944,
+            517,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/9c16df1981ca8dc5b5c87e7700e8c469e93990b5928c75f2423d275b84f0a8ed.jpg",
+        "image_caption": [
+            "Figure 2. The overview of our approach. Our input is the user-provided source prompt  $p_{src}$ , target prompt  $p_{edit}$  and clean latent  $z = \\{z^1, z^2, \\ldots, z^n\\}$  encoded from input source video  $x = \\{x^1, x^2, \\ldots, x^n\\}$  with number frames  $n$  in a video sequence. On the left, we first invert the video using DDIM inversion pipeline into noisy latent  $z_T$  using the source prompt  $p_{src}$  and an inflated 3D U-Net  $\\varepsilon_\\theta$ . During each inversion timestep  $t$ , we store both spatial-temporal self-attention maps  $s_t^{src}$  and cross-attention maps  $c_t^{src}$ . At the editing stage of the DDIM denoising, we denoise the latent  $z_T$  back to clean image  $\\hat{z}_0$  conditioned on target prompt  $p_{edit}$ . At each denoising timestep  $t$ , we fuse the attention maps  $(s_t^{edit}$  and  $c_t^{edit}$  ) in  $\\varepsilon_\\theta$  with stored attention map  $(s_t^{src}, c_t^{src})$  using the proposed Attention Blending Block. Right: Specifically, we replace the cross-attention maps  $c_t^{edit}$  of un-edited words (e.g., road and countryside) with source maps  $c_t^{src}$  of them. In addition, we blend the self-attention map during inversion  $s_t^{src}$  and editing  $s_t^{edit}$  with an adaptive spatial mask obtained from cross-attention maps  $c_t^{src}$  of edited words (e.g., silver and jeep), which represents the areas that the user wants to edit."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7c3a0f61c23aa1b9f5927f17038247d6d172d6d36f2e52cc15614ce365846851.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A more challenging topic is to edit the object shape in the real-world video. Current method shows obvious artifacts even with the optimization on generative priors [28]. The stronger prior of the diffusion-based model also draws the attention of current researchers. e.g., gen1 [9] trains a conditional model for depth and text-guided video generation, which can edit the appearance of the generated images on the fly. Dreamix [36] finetunes a stronger diffusion-based video model [18] for editing with stronger generative priors. Both of these methods need private and powerful video diffusion models for editing. Thus, the applications of the current larger-scale fine-tuned text-to-image models [1] cannot be used directly.",
+        "bbox": [
+            75,
+            473,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Image and Video Generation Models. Image generation is a basic and hot topic in computer vision. Early works mainly use VAE [26] or GAN [14] to model the distribution on the specific domain. Recent works adopt VQVAE [49] and transformer [10] for image generation. However, due to the difficulties in training these models, they only work well on the specific domain, e.g., face [23]. On the other hand, the editing ability of these models is relatively weak since the feature space of GAN is high-level, and the quantified tokens can not be considered individually. Another type of method focuses on text-to-image generation. DALL-E [40, 41] and CogView [8] train an image generative pre-training transformer (GPT) to generate images from a CLIP [34] text embedding. Recent models [42, 44] benefit from the stability of training diffusion-based model [19]. These mod",
+        "bbox": [
+            75,
+            674,
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+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "els can be scaled by a huge dataset and show surprisingly good results on text-to-image generation by integrating large language model conditions since its latent space has spatial structure, which provides a stronger edit ability than previous GAN [23] based methods. Generating videos is much more difficult than images. Current methods rely on the larger cascaded models [18, 45] and dataset. Differently, magic-video [56] and gen1 [9] initialize the model from text-to-image [42] and generate the continuous contents through extra time-aware layers. Recently, Tune-A-Video [52] overfits a single video for text-based video generation. After training, the model can generate related motion from similar prompts. However, the results from this model are too flickering to achieve realistic local editing. Inspired by the image editing methods and tune-a-video, our method can edit the style of the real-world video and images using the trained text-to-image model [42] and shows better object replacing performance than the one-shot finetuned video diffusion model [52] with simple DDIM inversion [46] in real videos (Fig. 7).",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Image Editing in Diffusion Model. Many recent works adopt the trained diffusion model for editing. SDEdit [33] generates content for a new prompt by adding noise to the image first. DiffEdit [6] computes the edit mask by the noise differences of the text prompts, and then, blends the inversion noises into the image generation process. Similar work has also been proposed by Blended Diffusion [2, 3], which combines the features of each step for image blending. Plug-",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "15934",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and-play [48] gets the inversion noise and applies the denoising for feature reconstruction. After that, the self-attention features in editing are replaced with that in reconstruction directly. Pix2pix-Zero [38] edits the image with the cross-attention guidance. Prompt-to-Prompt [16] proves that images can be edited via reweighting the cross-attention map of different prompts. There are also some methods to achieve better editing ability via optimization [25, 35]. However, a naive frame-wise application of these image methods to video results in flickering and inconsistency among frames.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3. Methods",
+        "text_level": 1,
+        "bbox": [
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+            256,
+            174,
+            272
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We target zero-shot text-driven video editing (e.g., style, attribute, and shape) without optimization for each target prompt or the user-provided mask. In Sec. 3.1, we first give the details of the latent diffusion and DDIM inversion. After that, we introduce our method that enables video appearance editing (Sec. 3.2) via the pre-trained text-to-image models [42]. Finally, we discuss a more challenging case that also enables the shape-aware editing of video using the video diffusion model in Sec. 3.3. Notice that, the proposed method is a general editing method and can be used in various text-to-image or text-to-video models. In this paper, we majorly use Stable Diffusion [42] and the video generation model based on Stable Diffusion (Tune-A-Video [52]) for its popularity and generalization ability.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminary: Latent Diffusion and Inversion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Latent Diffusion Models [42] are introduced to diffuse and denoise the latent space of an autoencoder. First, an encoder  $\\mathcal{E}$  compresses a RGB image  $x$  to a low-resolution latent  $z = \\mathcal{E}(x)$ , which can be reconstructed back to image  $\\mathcal{D}(z) \\approx x$  by decoder  $\\mathcal{D}$ . Second, a U-Net [43]  $\\varepsilon_{\\theta}$  containing cross-attention and self-attention [50] is trained to remove the artificial noise using the objective:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min _ {\\theta} E _ {z _ {0}, \\varepsilon \\sim N (0, I), t \\sim \\mathrm {U n i f o r m} (1, T)} \\| \\varepsilon - \\varepsilon_ {\\theta} (z _ {t}, t, p) \\| _ {2} ^ {2}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $p$  is the embedding of the conditional text prompt and  $z_{t}$  is a noisy sample of  $z_{0}$  at timestep  $t$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "DDIM Inversion [46]. During inference, deterministic DDIM sampling is employed to convert a random noise  $z_{T}$  to a clean latent  $z_{0}$  in a sequence of timestep  $t: T \\to 1$ :",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\frac {z _ {t} - \\sqrt {1 - \\alpha_ {t}} \\varepsilon_ {\\theta}}{\\sqrt {\\alpha_ {t}}} + \\sqrt {1 - \\alpha_ {t - 1}} \\varepsilon_ {\\theta}, \\tag {2}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "where  $\\alpha_{t}$  is a parameter for noise scheduling [19,46]",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Based on the ODE limit analysis of the diffusion process, DDIM inversion [7,46] is proposed to map a clean latent  $z_0$  back to a noised latent  $\\hat{z}_T$  in revered steps  $t:1\\to T$ :",
+        "bbox": [
+            76,
+            813,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {z} _ {t} = \\sqrt {\\alpha_ {t}} \\frac {\\hat {z} _ {t - 1} - \\sqrt {1 - \\alpha_ {t - 1}} \\varepsilon_ {\\theta}}{\\sqrt {\\alpha_ {t - 1}}} + \\sqrt {1 - \\alpha_ {t}} \\varepsilon_ {\\theta}, \\tag {3}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/f223838b035a975bf23718868468c70067a720a96ab5bde2622407776420f6ec.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/caa50adb795a90892b67c8b0fa22a3ed6f7cbcb3e1641752b48670e3704f901f.jpg",
+        "image_caption": [
+            "Figure 3. Zero-shot local attributed editing (cat  $\\rightarrow$  tiger) using stable diffusion. In contrast to fusion with attention during reconstruction (a) in previous work [16, 38, 48], our inversion attention fusion (b) provides more accurate structure guidance and editing ability, as visualized on the right side."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            220,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where each  $\\varepsilon_{\\theta}$  stands for the noise  $\\varepsilon_{\\theta}(z_{t - 1},t - 1,p_{src})$  predicted at  $t - 1$  timestep.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Such that the inverted latent  $\\hat{z}_T$  can reconstruct a latent  $\\hat{z}_0(p_{src}) = \\mathrm{DDIM}(\\hat{z}_T, p_{src})$  similar to the clean latent  $z_0$  at classifier-free guidance scale  $s_{cfg} = 1$ . Recently, image editing methods [16,35,38,48] use a large classifier-free guidance scale  $s_{cfg} \\gg 1$  to edit the latent as  $\\hat{z}_0(p_{edit}) = \\mathrm{DDIM}(\\hat{z}_T, p_{edit})$  (second row in Fig 3(a)), where a reconstruction of  $\\hat{z}_0(p_{src})$  is conducted in parallel to provide attention constraints. (first row in Fig 3(a)).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. FateZero Video Editing",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 2, we use the pretrained text-to-image model, i.e., Stable Diffusion, as our base model, which contains a UNet for  $T$ -timestep denoising. Instead of straightforwardly exploiting the regular pipeline of latent editing guided by reconstruction attention, we have made several critical modifications for video editing as follows.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Inversion Attention Fusion. Direct editing using the inverted noise results in frame inconsistency, which may be attributed to two factors. First, the invertible property of DDIM discussed in Eq. (2) and Eq. (3) only holds in the limit of small steps [46, 47]. Nevertheless, the present requirements of 50 DDIM denoising steps lead to an accumulation of errors with each subsequent step. Second, using a large classifier-free guidance  $s_{cfg} \\gg 1$  can increase the edit ability in denoising, but the large editing freedom leads to inconsistent neighboring frames. Therefore, previous methods require optimization of text-embedding [16] or other",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "15935",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "regularization [38].",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "While the issues seem trivial in the context of single-frame editing they can become magnified when working with video as even minor discrepancies among frames will be accentuated along the temporal indexes.",
+        "bbox": [
+            75,
+            108,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To alleviate these issues, our framework utilizes the attention maps during inversion steps (Eq. (3)), which is available because the source prompt  $p_{src}$  and initial latent  $z_0$  are provided to the UNet during inversion. Formally, during inversion, we store the intermediate self-attention maps  $[s_t^{\\mathrm{src}}]_{t=1}^T$ , cross-attention maps  $[c_t^{\\mathrm{src}}]_{t=1}^T$  at each timestep  $t$  and the final latent feature maps  $z_T$  as",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {T}, \\left[ c _ {t} ^ {\\mathrm {s r c}} \\right] _ {t = 1} ^ {T}, \\left[ s _ {t} ^ {\\mathrm {s r c}} \\right] _ {t = 1} ^ {T} = \\operatorname {D D I M} - \\operatorname {I N V} \\left(z _ {0}, p _ {s r c}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            291,
+            470,
+            310
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where DDIM-INV stands for the DDIM inversion pipeline discussed in Eq. (3). During the editing stage, we can obtain the noise to remove by fusing the attention from inversion:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\epsilon} _ {t} = \\text {A T T - F U S I O N} \\left(\\varepsilon_ {\\theta}, z _ {t}, t, p _ {\\text {e d i t}}, c _ {t} ^ {\\text {s r c}}, s _ {t} ^ {\\text {s r c}}\\right). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            130,
+            380,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $p_{\\mathrm{edit}}$  represents the modified prompt. In function ATT-FUSION, we inject the cross-attention maps of the unchanged part of the prompt similar to Prompt-to-Prompt [16]. We also replace self-attention maps to preserve the original structure and motion during the style and attribute editing.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Fig. 3 shows a toy comparison example between our attention fusion method and the typical method with simply inversion and then generation as in [16, 35] for image editing. The cross-attention map during inversion captures the silhouette and the pose of the cat in the source image, but the map during reconstruction has a noticeable difference. While in the video, the attention consistency might influence the temporal consistency as shown in Fig. 8. This is because the spatial-temporal self-attention maps represent the correspondence between frames and the temporal modeling ability of existing video diffusion model [52] is not satisfactory.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Attention Map Blending. Inversion-time attention fusion might be insufficient in local attrition editing, as shown in an image example in Fig. 4. In the third column, replacing self-attention  $s^{edit} \\in \\mathbb{R}^{hw \\times hw}$  with  $s^{src}$  brings unnecessary structure leakage and the generated image has unpleasant blending artifacts in the visualization. On the other hand, if we keep  $s^{edit}$  during the DDIM denoising pipeline, the structure of the background and watermelon has unwanted changes, and the pose of the original rabbit is also lost. Inspired by the fact that the cross-attention map provides the semantic layout of the image [16], as visualized in the second row of Fig. 4, we obtain a binary mask  $M_t$  by thresholding the cross-attention map of the edited words during inversion by a constant  $\\tau$  [2, 3]. Then, the self-attention maps of editing stage  $s_t^{edit}$  and inversion stage  $s_t^{src}$  are blended with the binary mask  $M_t$ , as illustrated in Fig. 2. Formally, the",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3df5b143cc33b90ca438f09492ccf9886740deea4c2a24985c4694b00c4470f4.jpg",
+        "image_caption": [
+            "Input Frame"
+        ],
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+    {
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+        "img_path": "images/fef4547c66d29be430730642c6d9de20ca8df1a116d405c4b12f95e5ba9dd6d8.jpg",
+        "image_caption": [
+            "Reconstruction Frame Inversion attention"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/36eaaef284887bc6de1812720164d4ca7190c69b3495071d7676aba70ea3d68b.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/15bc5adcda924096ab0176c07bf895a2610b6708b2676183a12e01b79a527e87.jpg",
+        "image_caption": [
+            "Our Blended Self-Attention"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/618f2b3e94f75b98ae3ffe07bf2e5ea2d2881fdd6bc5efcd2b052eedc8e7cc4c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1d8dc5021df4891690fbe9b29d11b3fc5a2573ae2e86b3bc274b5049b8c42987.jpg",
+        "image_caption": [
+            "No Self-Attention",
+            "Figure 4. Study of blended self-attention in zero-shot shape editing (rabbit  $\\rightarrow$  tiger) using stable diffusion. Forth and fifth columns: Ignoring self-attention can not preserve the original structure and background, and naive replacement causes artifacts. Third column: Blending the self-attention using the cross-attention map (the second row) obtains both new shape from the target text with a similar pose and background from the input frame."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/759f9c3b78b3a47092735f8262c7cdfed20a170190a352322f8776412bb078c7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/56155934d9a13e7c157f2af8a6443f1cfd089c3c256123d09fecc23259c02120.jpg",
+        "image_caption": [
+            "Self-Attention without Mask"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "attention map fusion is implemented as",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM _ {t} = \\text {H E A V I S I D E S T E P} \\left(c _ {t} ^ {\\text {s r c}}, \\tau\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ns _ {t} ^ {\\text {f u s e d}} = M _ {t} \\odot s _ {t} ^ {\\text {e d i t}} + (1 - M _ {t}) \\odot s _ {t} ^ {\\text {s r c}}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Spatial-Temporal Self-Attention. The previous two designs make our method a strong editing method that can preserve the better structure, and also a big potential in video editing. However, denoising each frame individually still produces inconsistent video. Inspired by the casual self-attention [15, 20,50,51] and recent one-shot video generation method [52], we reshape the original self-attention to Spatial-Temporal Self-Attention without changing pretrained weights. Specifically, we implement ATTENTION  $(Q,K,V)$  for feature  $z^i$  at temporal index  $i\\in [1,n]$  as",
+        "bbox": [
+            496,
+            448,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ = W ^ {Q} \\mathbf {z} ^ {i}, K = W ^ {K} \\left[ \\mathbf {z} ^ {i}; \\mathbf {z} ^ {\\mathrm {w}} \\right], V = W ^ {V} \\left[ \\mathbf {z} ^ {i}; \\mathbf {z} ^ {\\mathrm {w}} \\right], \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            607,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $[\\cdot ]$  denotes the concatenation operation and  $W^{Q},W^{K}$ $W^{V}$  are the projection matrices from pretrained model. Empirically, we find it is enough to warp the middle frame  $\\mathbf{z}^{\\mathrm{w}} = z^{\\mathrm{Round}\\left[\\frac{n}{2}\\right]}$  for attribute and style editing. Thus, the spatial-temporal self-attention map is represented as  $s_t^{src}\\in$ $R^{hw\\times fhw}$ , where  $f = 2$  is the number of frames used as key and value. It captures both the structure of a single frame and the temporal correspondence with the key frame features.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Overall, the proposed method produces a new editing method for zero-shot real-world video editing. We replace the attention maps in the denoising steps with their corresponding maps during the inversion steps. After that, we utilize cross-attention maps as masks to prevent semantic leaks. Finally, we reform the self-attention of UNet to spatial-temporal attention for better temporal consistency among different temporal frames. We have included a formal algorithm in the supplementary materials for reference purposes.",
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "15936",
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+    {
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+        "img_path": "images/293e9ed6d8a00fb0e65a3c74cdbb20e47818b8995279dccaebf4409c68e922f6.jpg",
+        "image_caption": [
+            "Source Prompt: A black swan with a red beak swimming in a river near a wall and bushes."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/77ee74c1a8b62ca7d804636b7095ffc6a1c0fd4cc8af7bc6c77e4c13ddd617b4.jpg",
+        "image_caption": [
+            "black swan  $\\rightarrow$  white duck."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
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+            250
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/9f97b55dc6e9813cd1c759812b239f9f07fd4e98be31d0b124312953d29e6995.jpg",
+        "image_caption": [
+            "black swan  $\\rightarrow$  pink flamingo."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
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+        "img_path": "images/600614f59755dd5b7d058a602dc9b9ee61da026669215c47b849505aae41ebed.jpg",
+        "image_caption": [
+            "Figure 5. Zero-shot object shape editing on pre-trained video diffusion model [52]: Our framework can directly edit the shape of the object in videos driven by text prompts using a trained video diffusion model [52]",
+            "Source Prompt from Fig 5: black  $\\rightarrow$  Swarovski crystal"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/580180d32db41a0a80bef39d1db7df6554fe5cf38daf2c6b5e253b7244e5965c.jpg",
+        "image_caption": [
+            "A man with round helmet surfing on a white wave  $\\rightarrow$  The Ukiyo-e style painting of a man ..."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/0a9b13c55186e8aea30655e93c76263e0cccece822067a37695e96eb5a2e405e.jpg",
+        "image_caption": [
+            "A train traveling down tracks next to a forest and a man on the side of the track  $\\rightarrow$  ..., Makoto Shinkai style",
+            "Figure 6. Zero-shot attribute and style editing results using Stable Diffusion [42]. Our framework supports abstract attribute and style editing like 'Swarovski crystal', 'Ukiyo-e', and 'Makoto Shinkai'. Best viewed with zoom-in."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "text": "15937",
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+    {
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+    {
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+        "img_path": "images/869e4fb61a12f4aa4b0369b52b3c3a3f387828f11a2498d5424850f1f79172a5.jpg",
+        "image_caption": [
+            "Tune-A-Video + Ours"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
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+    {
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+        "img_path": "images/e2db527c2146e7e2276eed6e9c91b37c5a4ed755ae36dc3a2ed472f267e0d277.jpg",
+        "image_caption": [
+            "Shape-aware Editing"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
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+    {
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+        "img_path": "images/f34d13f6c1d44759b991a22bd98b0371e6ab2fb4edf7c11e91bc74e6c64b2025.jpg",
+        "image_caption": [
+            "Tune-A-Video + DDIM Inv"
+        ],
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+        ],
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+    {
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+        "image_caption": [],
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+    },
+    {
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+        "img_path": "images/13d0950d9c1449a77dbc32bce0813e988ed1a8b9c6d7657366677dc6aea63563.jpg",
+        "image_caption": [
+            "$\\mathrm{NLA + }$  Null-Inv"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            "Framewise Null-Inv",
+            "Figure 7. Qualitative comparison of our methods with other baselines. Inputs are in Fig. 5 and Fig 6. Our results have the best temporal consistency, image fidelity, and editing quality. Best viewed with zoom-in."
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+    {
+        "type": "text",
+        "text": "3.3. Shape-Aware Video Editing",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Different from appearance editing, reforming the shape of a specific object in the video is much more challenging. To this end, a pretrained video diffusion model is needed. Since there is no publicly-available generic video diffusion model, we perform the editing on the one-shot video diffusion model [52] instead. In this case, we compare our editing method with simple DDIM inversion [46], where our method also achieves better performance in terms of editing ability, motion consistency, and temporal consistency. It might be because it is hard for an inflated model to overfit the exact motion of the input video. While in our method, the motion and structure are represented by high-quality spatial-temporal attention maps  $s_t^{src} \\in R^{hw \\times fhw}$  during inversion, which is further fused with the attention maps during editing. More details can be founded in Fig. 7 and the supp. video.",
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+        "text": "4. Experiments",
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+        "text": "4.1. Implementation Details",
+        "text_level": 1,
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+        "type": "text",
+        "text": "For zero-shot style and attribute editing, we directly use the trained stable diffusion v1.4 [42] as the base model, we fuse the attentions in the interval of  $t \\in [0.2 \\times T, T]$  of the DDIM step with total timestep  $T = 50$ . For shape editing, we utilize the pretrained model of the specific video [52] at 100 iterations and fuse the attention at DDIM timestep  $t \\in [0.5 \\times T, T]$ , giving more freedom for new shape generation. Following previous works [4,9], we use videos from DAVIS [39] and other in-the-wild videos to evaluate our approach. The source prompt of the video is generated via the image caption model [31]. Finally, we design the target prompt for each video by replacing or adding several words.",
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+    {
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+        "text": "4.2. Applications",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Local attribute and global style editing. Using pretrained text-to-image diffusion model [42], our framework supports zero-shot local attribute and global style editing, as shown in Fig. 6 and third row in Fig.1. In the first row, the texture",
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+    {
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+        "table_body": "<table><tr><td>Method</td><td colspan=\"2\">CLIP Metrics↑</td><td colspan=\"3\">User Study↓</td></tr><tr><td>Inversion &amp; Editing</td><td>Tem-Con</td><td>Fram-Acc</td><td>Edit</td><td>Image</td><td>Temp</td></tr><tr><td>Frameswise Null &amp; p2p [16,35]</td><td>0.852</td><td>0.958</td><td>3.55</td><td>4.11</td><td>4.38</td></tr><tr><td>Frameswise SDEdit [33]</td><td>0.910</td><td>0.819</td><td>3.69</td><td>3.28</td><td>3.62</td></tr><tr><td>NLA, Null &amp; p2p [16,24,35]</td><td>0.949</td><td>0.600</td><td>3.17</td><td>3.02</td><td>2.60</td></tr><tr><td>Tune-A-Video &amp; DDIM [46,52]</td><td>0.958</td><td>0.750</td><td>2.78</td><td>2.80</td><td>2.70</td></tr><tr><td>Ours</td><td>0.965</td><td>0.903</td><td>1.82</td><td>1.79</td><td>1.69</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Quantitative evaluation against baselines. In our user study, the results of our method are preferred over those from baselines. For CLIP-Score, we achieve the best temporal consistency and comparable framewise editing accuracy against an optimization-based image editing method [35].",
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+    {
+        "type": "text",
+        "text": "and color of the feather are modified by the target prompt Swarovski crystal and kept consistent across frames. In the second and third rows, our framework applies abstract style (Ukiyo-e and Makoto Shinkai). The image structure and temporal motion can be well preserved since we fuse both the spatial-temporal self-attention and cross-attention during the inversion and editing stage.",
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+    {
+        "type": "text",
+        "text": "Shape-aware editing. Fig. 5 and the second row in Fig.1 present the result of difficult object shape editing, with a pretrained video model [52]. This task is challenging because a naive full-resolution fusion of the spatial-temporal self-attention maps results in inaccurate shape results and wrong temporal motion, as shown in the ablation (Fig.9). Thanks to the proposed Attention Blending, we combine the motion of generated shape from the editing target and inverted attention from the input video. Results of porsche, duck and flamingo show that we generate new content with poses and positions similar to input videos.",
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+    {
+        "type": "text",
+        "text": "Zero-shot image editing. In addition, our framework can serve as a zero-shot image editing method such as local attribute editing (Fig. 3) and object shape editing (Fig. 4) by considering an image as a video with a single frame. We provide more results in our supplementary material.",
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+        "text": "15938",
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+        "image_caption": [
+            "Ours Inversion Cross-Attention",
+            "Figure 8. Inversion attention compared with reconstruction attention using prompt 'deserted shore  $\\rightarrow$  'glacier shore'. The attention maps obtained from the reconstruction stage fail to detect the boat's position, and can not provide suitable motion guidance for zero-shot video editing."
+        ],
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+    {
+        "type": "text",
+        "text": "4.3. Baseline Comparisons",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Since there are no available zero-shot video editing methods based on diffusion models, we build the following four state-of-the-art baselines for comparison. (1) Tune-A-Video [52] overfits an inflated diffusion model on a single video to generate similar content. (2) The Neural Layered Atlas [24] (NLA) based method is combined with keyframe-editing via state-of-the-art image editing methods [16, 35]. (3) Frame-wise Null-text optimization [35] and then edit by prompt2prompt [16]. (4) Frame-wise zero-shot editing using SDEdit [33]. For attention-based editing (2,3,4), we use the same timesteps fusion parameters as ours.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We conduct the quantitative evaluation using the trained CLIP [34] model as previous methods [9, 38, 52]. Specially, we show the 'Tem-Con' [9] to measure the temporal consistency in frames by computing the cosine similarity between all pairs of consecutive frames. 'Frame-Acc' [17, 34, 38] is the frame-wise editing accuracy, which is the percentage of frames where the edited image has a higher CLIP similarity to the target prompt than the source prompt. In addition, three user studies metrics (denoted as 'Edit', 'Image', and 'Temp') are conducted to measure the editing quality, overall frame-wise image fidelity, and temporal consistency of the video, respectively. We ask 20 subjects to rank different methods with 9 sets of comparisons in each study. From Tab. 1, the proposed zero-shot method achieves the best temporal consistency against baselines and shows a comparable frame-wise editing accuracy as the pre-frame optimization method [35]. As for the user studies, the average ranking of our method earns user preferences the best in three aspects.",
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+    {
+        "type": "text",
+        "text": "To provide a qualitative comparison, Fig.7 provides the results of our method and other baselines at two different frames. The editing result of framewise SDEdit [33] can not be localized and varies a lot among different frames. Framewise Null inversion achieves local editing at the cost of 500-iterations optimization for each frame but is still temporally inconsistent. NLA-based [24] method preserves the exact",
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+        "image_caption": [
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+        "img_path": "images/506d147c9834e1aca378c461814cd906765fc5044199b2df5a604085e763568f.jpg",
+        "image_caption": [
+            "w/o Self-attention"
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+        "img_path": "images/44965cb4022d541742284a8d784e35793d912c721700c7badba20f04b307f1ed.jpg",
+        "image_caption": [
+            "Figure 9. Ablation study of blended self-attention. Without self-attention fusion, the generated video can not preserve the details of input videos (e.g., fence, trees, and car identity). If we replace full self-attention without a spatial mask, the structure of the original jeep misleads the generation of the Porsche car."
+        ],
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+    {
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+        "img_path": "images/99f92576b9424fb7c7b7fda0f93ef273938ce53d7a1d3e8e3d0c28e3e0b21db0.jpg",
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+    {
+        "type": "text",
+        "text": "pixels in the atlas. However, it struggles to perform editing that involves new shapes or 3D structures. In addition, it takes hours to optimize the neural atlas for each input video. While Tune-A-Video [52] with DDIM [46] ranks second in editing quality and image fidelity of Tab. 1, we observe that it has difficulty in reproducing the exact motion and spatial position as input video (right side of Fig.7). Besides, the background has annoying artifacts. Different from the above baselines, our method preserves the motion by fusion the attention during inversion and editing. Thus, our results outperform others by a large margin in our user study and frame consistency measured by CLIP.",
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+    {
+        "type": "text",
+        "text": "4.4. Ablation Studies",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Although we have proved the effectiveness of the proposed strategies in Fig. 4 and Fig. 3 using toy image examples, here, we ablate these designs in the video.",
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+    {
+        "type": "text",
+        "text": "Attention during inversion. In the right column of Fig. 8, we use the attention map during reconstruction instead of inversion for zero-shot background editing. The visualized cross-attention map of the word 'boat' in the first and last frame can not capture the correct position and structure of the boat, which may be caused by the poor temporal modeling capacity of the image diffusion model and the accumulation of errors in DDIM inversion. In contrast, we propose using attention during inversion as the middle column, which provides stable guidance of semantic layout in the original video. We observe this huge difference in attention maps between inversion and reconstruction exists in most videos.",
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+    {
+        "type": "text",
+        "text": "Attention Blending Block is studied in Fig. 9, where we remove all self-attention fusion or fuse all self-attention with",
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+        "page_idx": 7
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+    {
+        "type": "page_number",
+        "text": "15939",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "out a spatial mask. The third column shows that removing all self-attention maps brings a loss of fine details ( e.g., fences, poles, and trees in the background) and inconsistency of car identity over time. In contrast, if we fuse full-resolution self-attention as in the previous work [16], the shape editing ability of the framework can be severely degraded so that the geometry of generated car resembles the input video, especially in the last few frames. Therefore, we propose to blend the self-attention maps with a mask obtained from cross-attention to preserve unedited details and ensure temporal consistency while editing the object shape.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a new text-driven video editing framework FateZero that performs temporal consistent zero-shot editing of attribute, style, and shape. We make the first attempt to study and utilize the cross-attention and spatial-temporal self-attention during DDIM inversion, which provides fine-grained motion and structure guidance at each denoising step. A new Attention Blending Block is further proposed to enhance the shape editing performance of our framework. Our framework benefits video editing using widely existing image diffusion models, which we believe will contribute to a lot of new video applications.",
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+        "type": "text",
+        "text": "Limitation & Future Work. While our method achieves impressive results, it still has some limitations. During shape editing, since the motion is produced by the one-shot video diffusion model [52], it is difficult to generate totally new motion (e.g., 'swim'  $\\rightarrow$  'fly') or very different shape (e.g., 'swan'  $\\rightarrow$  'pterosaur'). We will test our method on the generic pretrained video diffusion model for better editing abilities.",
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+        "text": "References",
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+    },
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+        "type": "list",
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+        "list_items": [
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+        ],
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new file mode 100644
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+            "content": "CVF"
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "FateZero: Fusing Attentions for Zero-shot Text-based Video Editing"
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+            "content": "Chenyang Qi\\(^{1*}\\) Xiaodong Cun\\(^{2\\dagger}\\) Yong Zhang\\(^{2}\\) Chenyang Lei\\(^{3}\\) Xintao Wang\\(^{2}\\) Ying Shan\\(^{2}\\) Qifeng Chen\\(^{1\\dagger}\\)"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{1}\\)HKUST \\(^{2}\\)Tencent AI Lab \\(^{3}\\)CAIR, HKISI-CAS"
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+        {
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+            "angle": 0,
+            "content": "Source Video Prompt: A silver jeep driving down a curvy road in the countryside."
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+        {
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+            "content": "Zero-shot object shape editing with pre-trained video diffusion model [52]: silver jeep \\(\\rightarrow\\) Porsche car."
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+            "content": "Zero-shot video style editing with pre-trained image diffusion model [42]: watercolor painting."
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+            "bbox": [
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+            "content": "Figure 1. Zero-shot text-driven video editing. We present a zero-shot approach for shape-aware local object editing and video style editing from pre-trained diffusion models [42, 52] without any optimization for each target prompt."
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+        {
+            "type": "title",
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+            "content": "The diffusion-based generative models have achieved remarkable success in text-based image generation. However, since it contains enormous randomness in generation progress, it is still challenging to apply such models for real-world visual content editing, especially in videos. In this paper, we propose FateZero, a zero-shot text-based"
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+            "angle": 0,
+            "content": "* Work done during an internship at Tencent AI Lab."
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+            "angle": 0,
+            "content": "editing method on real-world videos without per-prompt training or use-specific mask. To edit videos consistently, we propose several techniques based on the pre-trained models. Firstly, in contrast to the straightforward DDIM inversion technique, our approach captures intermediate attention maps during inversion, which effectively retain both structural and motion information. These maps are directly fused in the editing process rather than generated during denoising. To further minimize semantic leakage of the source video, we then fuse self-attention with a blending"
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+            "bbox": [
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+            "angle": 0,
+            "content": "mask obtained by cross-attention features from the source prompt. Furthermore, we have implemented a reform of the self-attention mechanism in denoising UNet by introducing spatial-temporal attention to ensure frame consistency. Yet succinct, our method is the first one to show the ability of zero-shot text-driven video style and local attribute editing from the trained text-to-image model. We also have a better zero-shot shape-aware editing ability based on the text-to-video model [52]. Extensive experiments demonstrate our superior temporal consistency and editing capability than previous works."
+        },
+        {
+            "type": "title",
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+            "angle": 0,
+            "content": "1. Introduction"
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+        {
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+            "content": "Diffusion-based models [19] can generate diverse and high-quality images [40, 42, 44] and videos [15, 18, 32, 45, 56] through text prompts. It also brings large opportunities to edit real-world visual content from these generative priors."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Previous or concurrent diffusion-based editing methods [2, 3, 6, 16, 38, 48] majorly work on images. To edit real images, their methods utilize deterministic DDIM [46] for the image-to-noise inversion, and then, the inverted noise gradually generates the edited images under the condition of the target prompt. Based on this pipeline, several methods have been proposed in terms of cross-attention guidance [38], plug-and-play feature [48], and optimization [25, 35]."
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+            ],
+            "angle": 0,
+            "content": "Manipulating videos through generative priors as image editing methods above contains many challenges (Fig. 7). First, there are no publicly available generic text-to-video models [18, 45]. Thus, a framework based on image models can be more valuable than on video ones [36], thanks to the various open-sourced image models in the community [1, 37, 42, 54]. However, the text-to-image models [42] lack the consideration of temporal-aware information, e.g., motion and 3D shape understanding. Directly applying the image editing methods [33, 35] to the video will show obverse flickering. Second, although we can use previous video editing methods [4, 24, 28] via keyframe [21] or atlas editing [4, 24], these methods still need atlas learning [4, 24], keyframe selection [21], and per-prompt tunning [4, 28]. Moreover, while they may work well on the attribute [4, 24] and style [21] editing, the shape editing is still a big challenge [28]. Finally, as introduced above, current editing methods use DDIM for inversion and then denoising via the new prompt. However, in video inversion, the inverted noise in the \\(T\\) step might break the motion and structure of the original video because of error accumulation (Fig. 4 and 9)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose FateZero, a simple yet effective method for zero-shot video editing since we do not need to train for each target prompt individually [4, 24, 28] and have no user-specific mask [2, 3]. Different from image editing, video editing needs to keep the temporal consistency of the edited video, which is not learned by the original trained text-to-image model. We tackle this problem by using two"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.394
+            ],
+            "angle": 0,
+            "content": "novel designs. Firstly, instead of solely relying on inversion and generation [16, 35, 48], we adopt a different approach by storing all the self and cross-attention maps at every step of the inversion process. This enables us to subsequently replace them during the denoising steps of the DDIM pipeline. Specifically, we find these self-attention blocks store better motion information and the cross-attention can be used as a threshold mask for self-attention blending spatially. This attention blending operation can keep the original structures unchanged. Furthermore, we reform the self-attention blocks to the spatial-temporal attention blocks as in [52] to make the appearance more consistent. Powered by our novel designs, we can directly edit the style and the attribute of the real-world video (Fig. 6) using the pre-trained text-to-image model [42]. Also, after getting the video diffusion model (e.g., pretrained Tune-A-Video [52]), our method shows better object editing (Fig. 5) ability in test-time than simple DDIM inversion [46]. The extensive experiments provide evidence of the advantages offered by the proposed method for both video and image editing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.394,
+                0.822,
+                0.408
+            ],
+            "angle": 0,
+            "content": "Our contributions are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.42,
+                0.892,
+                0.464
+            ],
+            "angle": 0,
+            "content": "- We present the first framework for temporal-consistent zero-shot text-based video editing using pretrained text-to-image model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.476,
+                0.891,
+                0.521
+            ],
+            "angle": 0,
+            "content": "- We propose to fuse the attention maps in the inversion process and generation process to preserve the motion and structure consistency during editing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.533,
+                0.891,
+                0.593
+            ],
+            "angle": 0,
+            "content": "- Our novel Attention Blending Block utilizes the source prompt's cross-attention map during attention fusion to prevent source semantic leakage and improve the shape-editing capability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.604,
+                0.891,
+                0.649
+            ],
+            "angle": 0,
+            "content": "- We show extensive applications of our method in video style editing, video local attribute editing, video object shape editing, etc."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.42,
+                0.892,
+                0.649
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.664,
+                0.642,
+                0.68
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Video Editing. Video can be edited via several aspects. For video stylizing editing, current methods [11, 21] rely on the example as the style guide and these methods may fail when the track is lost. By processing frames individually using image style transfer [13, 22], some works also learn to reduce the temporal consistency [5, 27, 29, 30] in a post-process way. However, the style may still be imperfect since the style transfer only measures the perceptual distance [55]. Several works also show better consistency but on the specific domain, e.g., portrait video [12, 53]. For video local editing, layer-atlas based methods [4, 24] show a promising direction by editing the video on a flattened texture map. However, the 2d atlas lacks 3d motion perception to support shape editing, and prompt-specific optimization is required."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15933"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.087,
+                0.511,
+                0.31
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.518,
+                0.087,
+                0.895,
+                0.31
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.322,
+                0.897,
+                0.448
+            ],
+            "angle": 0,
+            "content": "Figure 2. The overview of our approach. Our input is the user-provided source prompt \\( p_{src} \\), target prompt \\( p_{edit} \\) and clean latent \\( z = \\{z^1, z^2, \\ldots, z^n\\} \\) encoded from input source video \\( x = \\{x^1, x^2, \\ldots, x^n\\} \\) with number frames \\( n \\) in a video sequence. On the left, we first invert the video using DDIM inversion pipeline into noisy latent \\( z_T \\) using the source prompt \\( p_{src} \\) and an inflated 3D U-Net \\( \\varepsilon_\\theta \\). During each inversion timestep \\( t \\), we store both spatial-temporal self-attention maps \\( s_t^{src} \\) and cross-attention maps \\( c_t^{src} \\). At the editing stage of the DDIM denoising, we denoise the latent \\( z_T \\) back to clean image \\( \\hat{z}_0 \\) conditioned on target prompt \\( p_{edit} \\). At each denoising timestep \\( t \\), we fuse the attention maps \\( (s_t^{edit} \\) and \\( c_t^{edit} \\) ) in \\( \\varepsilon_\\theta \\) with stored attention map \\( (s_t^{src}, c_t^{src}) \\) using the proposed Attention Blending Block. Right: Specifically, we replace the cross-attention maps \\( c_t^{edit} \\) of un-edited words (e.g., road and countryside) with source maps \\( c_t^{src} \\) of them. In addition, we blend the self-attention map during inversion \\( s_t^{src} \\) and editing \\( s_t^{edit} \\) with an adaptive spatial mask obtained from cross-attention maps \\( c_t^{src} \\) of edited words (e.g., silver and jeep), which represents the areas that the user wants to edit."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.474,
+                0.473,
+                0.671
+            ],
+            "angle": 0,
+            "content": "A more challenging topic is to edit the object shape in the real-world video. Current method shows obvious artifacts even with the optimization on generative priors [28]. The stronger prior of the diffusion-based model also draws the attention of current researchers. e.g., gen1 [9] trains a conditional model for depth and text-guided video generation, which can edit the appearance of the generated images on the fly. Dreamix [36] finetunes a stronger diffusion-based video model [18] for editing with stronger generative priors. Both of these methods need private and powerful video diffusion models for editing. Thus, the applications of the current larger-scale fine-tuned text-to-image models [1] cannot be used directly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Image and Video Generation Models. Image generation is a basic and hot topic in computer vision. Early works mainly use VAE [26] or GAN [14] to model the distribution on the specific domain. Recent works adopt VQVAE [49] and transformer [10] for image generation. However, due to the difficulties in training these models, they only work well on the specific domain, e.g., face [23]. On the other hand, the editing ability of these models is relatively weak since the feature space of GAN is high-level, and the quantified tokens can not be considered individually. Another type of method focuses on text-to-image generation. DALL-E [40, 41] and CogView [8] train an image generative pre-training transformer (GPT) to generate images from a CLIP [34] text embedding. Recent models [42, 44] benefit from the stability of training diffusion-based model [19]. These mod"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.474,
+                0.896,
+                0.776
+            ],
+            "angle": 0,
+            "content": "els can be scaled by a huge dataset and show surprisingly good results on text-to-image generation by integrating large language model conditions since its latent space has spatial structure, which provides a stronger edit ability than previous GAN [23] based methods. Generating videos is much more difficult than images. Current methods rely on the larger cascaded models [18, 45] and dataset. Differently, magic-video [56] and gen1 [9] initialize the model from text-to-image [42] and generate the continuous contents through extra time-aware layers. Recently, Tune-A-Video [52] overfits a single video for text-based video generation. After training, the model can generate related motion from similar prompts. However, the results from this model are too flickering to achieve realistic local editing. Inspired by the image editing methods and tune-a-video, our method can edit the style of the real-world video and images using the trained text-to-image model [42] and shows better object replacing performance than the one-shot finetuned video diffusion model [52] with simple DDIM inversion [46] in real videos (Fig. 7)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.897,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Image Editing in Diffusion Model. Many recent works adopt the trained diffusion model for editing. SDEdit [33] generates content for a new prompt by adding noise to the image first. DiffEdit [6] computes the edit mask by the noise differences of the text prompts, and then, blends the inversion noises into the image generation process. Similar work has also been proposed by Blended Diffusion [2, 3], which combines the features of each step for image blending. Plug-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15934"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.244
+            ],
+            "angle": 0,
+            "content": "and-play [48] gets the inversion noise and applies the denoising for feature reconstruction. After that, the self-attention features in editing are replaced with that in reconstruction directly. Pix2pix-Zero [38] edits the image with the cross-attention guidance. Prompt-to-Prompt [16] proves that images can be edited via reweighting the cross-attention map of different prompts. There are also some methods to achieve better editing ability via optimization [25, 35]. However, a naive frame-wise application of these image methods to video results in flickering and inconsistency among frames."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.257,
+                0.176,
+                0.273
+            ],
+            "angle": 0,
+            "content": "3. Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.283,
+                0.474,
+                0.495
+            ],
+            "angle": 0,
+            "content": "We target zero-shot text-driven video editing (e.g., style, attribute, and shape) without optimization for each target prompt or the user-provided mask. In Sec. 3.1, we first give the details of the latent diffusion and DDIM inversion. After that, we introduce our method that enables video appearance editing (Sec. 3.2) via the pre-trained text-to-image models [42]. Finally, we discuss a more challenging case that also enables the shape-aware editing of video using the video diffusion model in Sec. 3.3. Notice that, the proposed method is a general editing method and can be used in various text-to-image or text-to-video models. In this paper, we majorly use Stable Diffusion [42] and the video generation model based on Stable Diffusion (Tune-A-Video [52]) for its popularity and generalization ability."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.504,
+                0.453,
+                0.52
+            ],
+            "angle": 0,
+            "content": "3.1. Preliminary: Latent Diffusion and Inversion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.527,
+                0.47,
+                0.633
+            ],
+            "angle": 0,
+            "content": "Latent Diffusion Models [42] are introduced to diffuse and denoise the latent space of an autoencoder. First, an encoder \\(\\mathcal{E}\\) compresses a RGB image \\(x\\) to a low-resolution latent \\(z = \\mathcal{E}(x)\\), which can be reconstructed back to image \\(\\mathcal{D}(z) \\approx x\\) by decoder \\(\\mathcal{D}\\). Second, a U-Net [43] \\(\\varepsilon_{\\theta}\\) containing cross-attention and self-attention [50] is trained to remove the artificial noise using the objective:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.638,
+                0.473,
+                0.662
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min _ {\\theta} E _ {z _ {0}, \\varepsilon \\sim N (0, I), t \\sim \\mathrm {U n i f o r m} (1, T)} \\| \\varepsilon - \\varepsilon_ {\\theta} (z _ {t}, t, p) \\| _ {2} ^ {2}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.672,
+                0.47,
+                0.702
+            ],
+            "angle": 0,
+            "content": "where \\( p \\) is the embedding of the conditional text prompt and \\( z_{t} \\) is a noisy sample of \\( z_{0} \\) at timestep \\( t \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.703,
+                0.47,
+                0.749
+            ],
+            "angle": 0,
+            "content": "DDIM Inversion [46]. During inference, deterministic DDIM sampling is employed to convert a random noise \\( z_{T} \\) to a clean latent \\( z_{0} \\) in a sequence of timestep \\( t: T \\to 1 \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.097,
+                0.754,
+                0.47,
+                0.789
+            ],
+            "angle": 0,
+            "content": "\\[\nz _ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\frac {z _ {t} - \\sqrt {1 - \\alpha_ {t}} \\varepsilon_ {\\theta}}{\\sqrt {\\alpha_ {t}}} + \\sqrt {1 - \\alpha_ {t - 1}} \\varepsilon_ {\\theta}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.798,
+                0.428,
+                0.814
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha_{t}\\) is a parameter for noise scheduling [19,46]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.814,
+                0.471,
+                0.859
+            ],
+            "angle": 0,
+            "content": "Based on the ODE limit analysis of the diffusion process, DDIM inversion [7,46] is proposed to map a clean latent \\(z_0\\) back to a noised latent \\(\\hat{z}_T\\) in revered steps \\(t:1\\to T\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.115,
+                0.87,
+                0.47,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {z} _ {t} = \\sqrt {\\alpha_ {t}} \\frac {\\hat {z} _ {t - 1} - \\sqrt {1 - \\alpha_ {t - 1}} \\varepsilon_ {\\theta}}{\\sqrt {\\alpha_ {t - 1}}} + \\sqrt {1 - \\alpha_ {t}} \\varepsilon_ {\\theta}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.088,
+                0.895,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.221,
+                0.895,
+                0.346
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.356,
+                0.895,
+                0.427
+            ],
+            "angle": 0,
+            "content": "Figure 3. Zero-shot local attributed editing (cat \\(\\rightarrow\\) tiger) using stable diffusion. In contrast to fusion with attention during reconstruction (a) in previous work [16, 38, 48], our inversion attention fusion (b) provides more accurate structure guidance and editing ability, as visualized on the right side."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.455,
+                0.895,
+                0.485
+            ],
+            "angle": 0,
+            "content": "where each \\(\\varepsilon_{\\theta}\\) stands for the noise \\(\\varepsilon_{\\theta}(z_{t - 1},t - 1,p_{src})\\) predicted at \\(t - 1\\) timestep."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.486,
+                0.895,
+                0.607
+            ],
+            "angle": 0,
+            "content": "Such that the inverted latent \\(\\hat{z}_T\\) can reconstruct a latent \\(\\hat{z}_0(p_{src}) = \\mathrm{DDIM}(\\hat{z}_T, p_{src})\\) similar to the clean latent \\(z_0\\) at classifier-free guidance scale \\(s_{cfg} = 1\\). Recently, image editing methods [16,35,38,48] use a large classifier-free guidance scale \\(s_{cfg} \\gg 1\\) to edit the latent as \\(\\hat{z}_0(p_{edit}) = \\mathrm{DDIM}(\\hat{z}_T, p_{edit})\\) (second row in Fig 3(a)), where a reconstruction of \\(\\hat{z}_0(p_{src})\\) is conducted in parallel to provide attention constraints. (first row in Fig 3(a))."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.619,
+                0.719,
+                0.635
+            ],
+            "angle": 0,
+            "content": "3.2. FateZero Video Editing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.894,
+                0.734
+            ],
+            "angle": 0,
+            "content": "As shown in Fig. 2, we use the pretrained text-to-image model, i.e., Stable Diffusion, as our base model, which contains a UNet for \\( T \\)-timestep denoising. Instead of straightforwardly exploiting the regular pipeline of latent editing guided by reconstruction attention, we have made several critical modifications for video editing as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Inversion Attention Fusion. Direct editing using the inverted noise results in frame inconsistency, which may be attributed to two factors. First, the invertible property of DDIM discussed in Eq. (2) and Eq. (3) only holds in the limit of small steps [46, 47]. Nevertheless, the present requirements of 50 DDIM denoising steps lead to an accumulation of errors with each subsequent step. Second, using a large classifier-free guidance \\( s_{cfg} \\gg 1 \\) can increase the edit ability in denoising, but the large editing freedom leads to inconsistent neighboring frames. Therefore, previous methods require optimization of text-embedding [16] or other"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15935"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.208,
+                0.106
+            ],
+            "angle": 0,
+            "content": "regularization [38]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.109,
+                0.471,
+                0.169
+            ],
+            "angle": 0,
+            "content": "While the issues seem trivial in the context of single-frame editing they can become magnified when working with video as even minor discrepancies among frames will be accentuated along the temporal indexes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.171,
+                0.473,
+                0.277
+            ],
+            "angle": 0,
+            "content": "To alleviate these issues, our framework utilizes the attention maps during inversion steps (Eq. (3)), which is available because the source prompt \\( p_{src} \\) and initial latent \\( z_0 \\) are provided to the UNet during inversion. Formally, during inversion, we store the intermediate self-attention maps \\( [s_t^{\\mathrm{src}}]_{t=1}^T \\), cross-attention maps \\( [c_t^{\\mathrm{src}}]_{t=1}^T \\) at each timestep \\( t \\) and the final latent feature maps \\( z_T \\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.117,
+                0.292,
+                0.471,
+                0.311
+            ],
+            "angle": 0,
+            "content": "\\[\nz _ {T}, \\left[ c _ {t} ^ {\\mathrm {s r c}} \\right] _ {t = 1} ^ {T}, \\left[ s _ {t} ^ {\\mathrm {s r c}} \\right] _ {t = 1} ^ {T} = \\operatorname {D D I M} - \\operatorname {I N V} \\left(z _ {0}, p _ {s r c}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.319,
+                0.47,
+                0.366
+            ],
+            "angle": 0,
+            "content": "where DDIM-INV stands for the DDIM inversion pipeline discussed in Eq. (3). During the editing stage, we can obtain the noise to remove by fusing the attention from inversion:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.131,
+                0.381,
+                0.47,
+                0.399
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\epsilon} _ {t} = \\text {A T T - F U S I O N} \\left(\\varepsilon_ {\\theta}, z _ {t}, t, p _ {\\text {e d i t}}, c _ {t} ^ {\\text {s r c}}, s _ {t} ^ {\\text {s r c}}\\right). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.414,
+                0.471,
+                0.49
+            ],
+            "angle": 0,
+            "content": "where \\( p_{\\mathrm{edit}} \\) represents the modified prompt. In function ATT-FUSION, we inject the cross-attention maps of the unchanged part of the prompt similar to Prompt-to-Prompt [16]. We also replace self-attention maps to preserve the original structure and motion during the style and attribute editing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.471,
+                0.658
+            ],
+            "angle": 0,
+            "content": "Fig. 3 shows a toy comparison example between our attention fusion method and the typical method with simply inversion and then generation as in [16, 35] for image editing. The cross-attention map during inversion captures the silhouette and the pose of the cat in the source image, but the map during reconstruction has a noticeable difference. While in the video, the attention consistency might influence the temporal consistency as shown in Fig. 8. This is because the spatial-temporal self-attention maps represent the correspondence between frames and the temporal modeling ability of existing video diffusion model [52] is not satisfactory."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Attention Map Blending. Inversion-time attention fusion might be insufficient in local attrition editing, as shown in an image example in Fig. 4. In the third column, replacing self-attention \\( s^{edit} \\in \\mathbb{R}^{hw \\times hw} \\) with \\( s^{src} \\) brings unnecessary structure leakage and the generated image has unpleasant blending artifacts in the visualization. On the other hand, if we keep \\( s^{edit} \\) during the DDIM denoising pipeline, the structure of the background and watermelon has unwanted changes, and the pose of the original rabbit is also lost. Inspired by the fact that the cross-attention map provides the semantic layout of the image [16], as visualized in the second row of Fig. 4, we obtain a binary mask \\( M_t \\) by thresholding the cross-attention map of the edited words during inversion by a constant \\( \\tau \\) [2, 3]. Then, the self-attention maps of editing stage \\( s_t^{edit} \\) and inversion stage \\( s_t^{src} \\) are blended with the binary mask \\( M_t \\), as illustrated in Fig. 2. Formally, the"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.089,
+                0.582,
+                0.147
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.519,
+                0.151,
+                0.566,
+                0.159
+            ],
+            "angle": 0,
+            "content": "Input Frame"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.582,
+                0.089,
+                0.658,
+                0.147
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.148,
+                0.658,
+                0.207
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.578,
+                0.208,
+                0.661,
+                0.225
+            ],
+            "angle": 0,
+            "content": "Reconstruction Frame Inversion attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.659,
+                0.09,
+                0.735,
+                0.146
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.148,
+                0.734,
+                0.207
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.671,
+                0.208,
+                0.726,
+                0.225
+            ],
+            "angle": 0,
+            "content": "Our Blended Self-Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.735,
+                0.089,
+                0.812,
+                0.146
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.148,
+                0.812,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.746,
+                0.209,
+                0.8,
+                0.225
+            ],
+            "angle": 0,
+            "content": "No Self-Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.813,
+                0.089,
+                0.888,
+                0.146
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.148,
+                0.888,
+                0.207
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.821,
+                0.209,
+                0.877,
+                0.225
+            ],
+            "angle": 0,
+            "content": "Self-Attention without Mask"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.235,
+                0.894,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Figure 4. Study of blended self-attention in zero-shot shape editing (rabbit \\(\\rightarrow\\) tiger) using stable diffusion. Forth and fifth columns: Ignoring self-attention can not preserve the original structure and background, and naive replacement causes artifacts. Third column: Blending the self-attention using the cross-attention map (the second row) obtains both new shape from the target text with a similar pose and background from the input frame."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.365,
+                0.761,
+                0.38
+            ],
+            "angle": 0,
+            "content": "attention map fusion is implemented as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.568,
+                0.396,
+                0.892,
+                0.412
+            ],
+            "angle": 0,
+            "content": "\\[\nM _ {t} = \\text {H E A V I S I D E S T E P} \\left(c _ {t} ^ {\\text {s r c}}, \\tau\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.414,
+                0.892,
+                0.431
+            ],
+            "angle": 0,
+            "content": "\\[\ns _ {t} ^ {\\text {f u s e d}} = M _ {t} \\odot s _ {t} ^ {\\text {e d i t}} + (1 - M _ {t}) \\odot s _ {t} ^ {\\text {s r c}}. \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.449,
+                0.895,
+                0.601
+            ],
+            "angle": 0,
+            "content": "Spatial-Temporal Self-Attention. The previous two designs make our method a strong editing method that can preserve the better structure, and also a big potential in video editing. However, denoising each frame individually still produces inconsistent video. Inspired by the casual self-attention [15, 20,50,51] and recent one-shot video generation method [52], we reshape the original self-attention to Spatial-Temporal Self-Attention without changing pretrained weights. Specifically, we implement ATTENTION \\((Q,K,V)\\) for feature \\(z^i\\) at temporal index \\(i\\in [1,n]\\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.513,
+                0.608,
+                0.892,
+                0.629
+            ],
+            "angle": 0,
+            "content": "\\[\nQ = W ^ {Q} \\mathbf {z} ^ {i}, K = W ^ {K} \\left[ \\mathbf {z} ^ {i}; \\mathbf {z} ^ {\\mathrm {w}} \\right], V = W ^ {V} \\left[ \\mathbf {z} ^ {i}; \\mathbf {z} ^ {\\mathrm {w}} \\right], \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.641,
+                0.894,
+                0.763
+            ],
+            "angle": 0,
+            "content": "where \\([\\cdot ]\\) denotes the concatenation operation and \\(W^{Q},W^{K}\\) \\(W^{V}\\) are the projection matrices from pretrained model. Empirically, we find it is enough to warp the middle frame \\(\\mathbf{z}^{\\mathrm{w}} = z^{\\mathrm{Round}\\left[\\frac{n}{2}\\right]}\\) for attribute and style editing. Thus, the spatial-temporal self-attention map is represented as \\(s_t^{src}\\in\\) \\(R^{hw\\times fhw}\\), where \\(f = 2\\) is the number of frames used as key and value. It captures both the structure of a single frame and the temporal correspondence with the key frame features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Overall, the proposed method produces a new editing method for zero-shot real-world video editing. We replace the attention maps in the denoising steps with their corresponding maps during the inversion steps. After that, we utilize cross-attention maps as masks to prevent semantic leaks. Finally, we reform the self-attention of UNet to spatial-temporal attention for better temporal consistency among different temporal frames. We have included a formal algorithm in the supplementary materials for reference purposes."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15936"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.077,
+                0.891,
+                0.156
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.187,
+                0.156,
+                0.778,
+                0.169
+            ],
+            "angle": 0,
+            "content": "Source Prompt: A black swan with a red beak swimming in a river near a wall and bushes."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.17,
+                0.891,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.398,
+                0.25,
+                0.573,
+                0.262
+            ],
+            "angle": 0,
+            "content": "black swan \\(\\rightarrow\\) white duck."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.263,
+                0.891,
+                0.343
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.391,
+                0.343,
+                0.584,
+                0.357
+            ],
+            "angle": 0,
+            "content": "black swan \\(\\rightarrow\\) pink flamingo."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.369,
+                0.893,
+                0.397
+            ],
+            "angle": 0,
+            "content": "Figure 5. Zero-shot object shape editing on pre-trained video diffusion model [52]: Our framework can directly edit the shape of the object in videos driven by text prompts using a trained video diffusion model [52]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.4,
+                0.891,
+                0.478
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.308,
+                0.479,
+                0.667,
+                0.492
+            ],
+            "angle": 0,
+            "content": "Source Prompt from Fig 5: black \\(\\rightarrow\\) Swarovski crystal"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.493,
+                0.891,
+                0.65
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.18,
+                0.65,
+                0.79,
+                0.664
+            ],
+            "angle": 0,
+            "content": "A man with round helmet surfing on a white wave \\(\\rightarrow\\) The Ukiyo-e style painting of a man ..."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.664,
+                0.891,
+                0.821
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.134,
+                0.821,
+                0.836,
+                0.836
+            ],
+            "angle": 0,
+            "content": "A train traveling down tracks next to a forest and a man on the side of the track \\(\\rightarrow\\) ..., Makoto Shinkai style"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.848,
+                0.893,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Figure 6. Zero-shot attribute and style editing results using Stable Diffusion [42]. Our framework supports abstract attribute and style editing like 'Swarovski crystal', 'Ukiyo-e', and 'Makoto Shinkai'. Best viewed with zoom-in."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15937"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.257,
+                0.089,
+                0.35,
+                0.099
+            ],
+            "angle": 0,
+            "content": "Shape-aware Editing"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.1,
+                0.168,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.169,
+                0.168,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.092,
+                0.24,
+                0.157,
+                0.247
+            ],
+            "angle": 0,
+            "content": "Tune-A-Video + Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.17,
+                0.1,
+                0.258,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.172,
+                0.239,
+                0.253,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Tune-A-Video + DDIM Inv"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.261,
+                0.1,
+                0.348,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.279,
+                0.24,
+                0.328,
+                0.246
+            ],
+            "angle": 0,
+            "content": "\\(\\mathrm{NLA + }\\) Null-Inv"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.1,
+                0.438,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.363,
+                0.24,
+                0.423,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Framewise Null-Inv"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.44,
+                0.1,
+                0.528,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.169,
+                0.528,
+                0.237
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.455,
+                0.24,
+                0.513,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Frameswise SDEdit"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.683,
+                0.089,
+                0.743,
+                0.099
+            ],
+            "angle": 0,
+            "content": "Style Editing"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.534,
+                0.1,
+                0.622,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.169,
+                0.622,
+                0.237
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.557,
+                0.24,
+                0.59,
+                0.246
+            ],
+            "angle": 0,
+            "content": "SD + Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.624,
+                0.1,
+                0.712,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.624,
+                0.169,
+                0.712,
+                0.237
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.627,
+                0.239,
+                0.708,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Tune-A-Video + DDIM Inv"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.714,
+                0.1,
+                0.802,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.169,
+                0.801,
+                0.237
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.727,
+                0.239,
+                0.786,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Framewise Null-Inv"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.804,
+                0.1,
+                0.892,
+                0.169
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.804,
+                0.169,
+                0.892,
+                0.237
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.819,
+                0.239,
+                0.875,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Frameswise SDEdit"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.261,
+                0.894,
+                0.29
+            ],
+            "angle": 0,
+            "content": "Figure 7. Qualitative comparison of our methods with other baselines. Inputs are in Fig. 5 and Fig 6. Our results have the best temporal consistency, image fidelity, and editing quality. Best viewed with zoom-in."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.315,
+                0.327,
+                0.332
+            ],
+            "angle": 0,
+            "content": "3.3. Shape-Aware Video Editing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.339,
+                0.474,
+                0.566
+            ],
+            "angle": 0,
+            "content": "Different from appearance editing, reforming the shape of a specific object in the video is much more challenging. To this end, a pretrained video diffusion model is needed. Since there is no publicly-available generic video diffusion model, we perform the editing on the one-shot video diffusion model [52] instead. In this case, we compare our editing method with simple DDIM inversion [46], where our method also achieves better performance in terms of editing ability, motion consistency, and temporal consistency. It might be because it is hard for an inflated model to overfit the exact motion of the input video. While in our method, the motion and structure are represented by high-quality spatial-temporal attention maps \\( s_t^{src} \\in R^{hw \\times fhw} \\) during inversion, which is further fused with the attention maps during editing. More details can be founded in Fig. 7 and the supp. video."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.581,
+                0.21,
+                0.599
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.607,
+                0.295,
+                0.623
+            ],
+            "angle": 0,
+            "content": "4.1. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.631,
+                0.47,
+                0.812
+            ],
+            "angle": 0,
+            "content": "For zero-shot style and attribute editing, we directly use the trained stable diffusion v1.4 [42] as the base model, we fuse the attentions in the interval of \\( t \\in [0.2 \\times T, T] \\) of the DDIM step with total timestep \\( T = 50 \\). For shape editing, we utilize the pretrained model of the specific video [52] at 100 iterations and fuse the attention at DDIM timestep \\( t \\in [0.5 \\times T, T] \\), giving more freedom for new shape generation. Following previous works [4,9], we use videos from DAVIS [39] and other in-the-wild videos to evaluate our approach. The source prompt of the video is generated via the image caption model [31]. Finally, we design the target prompt for each video by replacing or adding several words."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.817,
+                0.212,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.2. Applications"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Local attribute and global style editing. Using pretrained text-to-image diffusion model [42], our framework supports zero-shot local attribute and global style editing, as shown in Fig. 6 and third row in Fig.1. In the first row, the texture"
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td colspan=\"2\">CLIP Metrics↑</td><td colspan=\"3\">User Study↓</td></tr><tr><td>Inversion &amp; Editing</td><td>Tem-Con</td><td>Fram-Acc</td><td>Edit</td><td>Image</td><td>Temp</td></tr><tr><td>Frameswise Null &amp; p2p [16,35]</td><td>0.852</td><td>0.958</td><td>3.55</td><td>4.11</td><td>4.38</td></tr><tr><td>Frameswise SDEdit [33]</td><td>0.910</td><td>0.819</td><td>3.69</td><td>3.28</td><td>3.62</td></tr><tr><td>NLA, Null &amp; p2p [16,24,35]</td><td>0.949</td><td>0.600</td><td>3.17</td><td>3.02</td><td>2.60</td></tr><tr><td>Tune-A-Video &amp; DDIM [46,52]</td><td>0.958</td><td>0.750</td><td>2.78</td><td>2.80</td><td>2.70</td></tr><tr><td>Ours</td><td>0.965</td><td>0.903</td><td>1.82</td><td>1.79</td><td>1.69</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.433,
+                0.894,
+                0.504
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative evaluation against baselines. In our user study, the results of our method are preferred over those from baselines. For CLIP-Score, we achieve the best temporal consistency and comparable framewise editing accuracy against an optimization-based image editing method [35]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.542,
+                0.895,
+                0.648
+            ],
+            "angle": 0,
+            "content": "and color of the feather are modified by the target prompt Swarovski crystal and kept consistent across frames. In the second and third rows, our framework applies abstract style (Ukiyo-e and Makoto Shinkai). The image structure and temporal motion can be well preserved since we fuse both the spatial-temporal self-attention and cross-attention during the inversion and editing stage."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.653,
+                0.895,
+                0.82
+            ],
+            "angle": 0,
+            "content": "Shape-aware editing. Fig. 5 and the second row in Fig.1 present the result of difficult object shape editing, with a pretrained video model [52]. This task is challenging because a naive full-resolution fusion of the spatial-temporal self-attention maps results in inaccurate shape results and wrong temporal motion, as shown in the ablation (Fig.9). Thanks to the proposed Attention Blending, we combine the motion of generated shape from the editing target and inverted attention from the input video. Results of porsche, duck and flamingo show that we generate new content with poses and positions similar to input videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Zero-shot image editing. In addition, our framework can serve as a zero-shot image editing method such as local attribute editing (Fig. 3) and object shape editing (Fig. 4) by considering an image as a video with a single frame. We provide more results in our supplementary material."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15938"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.097,
+                0.089,
+                0.143,
+                0.098
+            ],
+            "angle": 0,
+            "content": "Input Video"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.098,
+                0.159,
+                0.217
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.178,
+                0.089,
+                0.3,
+                0.097
+            ],
+            "angle": 0,
+            "content": "Ours Inversion Cross-Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.163,
+                0.098,
+                0.313,
+                0.218
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.331,
+                0.089,
+                0.452,
+                0.097
+            ],
+            "angle": 0,
+            "content": "Reconstruction Cross-Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.316,
+                0.098,
+                0.467,
+                0.218
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.229,
+                0.47,
+                0.299
+            ],
+            "angle": 0,
+            "content": "Figure 8. Inversion attention compared with reconstruction attention using prompt 'deserted shore \\(\\rightarrow\\) 'glacier shore'. The attention maps obtained from the reconstruction stage fail to detect the boat's position, and can not provide suitable motion guidance for zero-shot video editing."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.328,
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+            ],
+            "angle": 0,
+            "content": "4.3. Baseline Comparisons"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.354,
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+            "angle": 0,
+            "content": "Since there are no available zero-shot video editing methods based on diffusion models, we build the following four state-of-the-art baselines for comparison. (1) Tune-A-Video [52] overfits an inflated diffusion model on a single video to generate similar content. (2) The Neural Layered Atlas [24] (NLA) based method is combined with keyframe-editing via state-of-the-art image editing methods [16, 35]. (3) Frame-wise Null-text optimization [35] and then edit by prompt2prompt [16]. (4) Frame-wise zero-shot editing using SDEdit [33]. For attention-based editing (2,3,4), we use the same timesteps fusion parameters as ours."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.522,
+                0.47,
+                0.793
+            ],
+            "angle": 0,
+            "content": "We conduct the quantitative evaluation using the trained CLIP [34] model as previous methods [9, 38, 52]. Specially, we show the 'Tem-Con' [9] to measure the temporal consistency in frames by computing the cosine similarity between all pairs of consecutive frames. 'Frame-Acc' [17, 34, 38] is the frame-wise editing accuracy, which is the percentage of frames where the edited image has a higher CLIP similarity to the target prompt than the source prompt. In addition, three user studies metrics (denoted as 'Edit', 'Image', and 'Temp') are conducted to measure the editing quality, overall frame-wise image fidelity, and temporal consistency of the video, respectively. We ask 20 subjects to rank different methods with 9 sets of comparisons in each study. From Tab. 1, the proposed zero-shot method achieves the best temporal consistency against baselines and shows a comparable frame-wise editing accuracy as the pre-frame optimization method [35]. As for the user studies, the average ranking of our method earns user preferences the best in three aspects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To provide a qualitative comparison, Fig.7 provides the results of our method and other baselines at two different frames. The editing result of framewise SDEdit [33] can not be localized and varies a lot among different frames. Framewise Null inversion achieves local editing at the cost of 500-iterations optimization for each frame but is still temporally inconsistent. NLA-based [24] method preserves the exact"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.536,
+                0.089,
+                0.574,
+                0.097
+            ],
+            "angle": 0,
+            "content": "Input Video"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.097,
+                0.603,
+                0.168
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.642,
+                0.089,
+                0.66,
+                0.097
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.605,
+                0.097,
+                0.698,
+                0.168
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.717,
+                0.089,
+                0.775,
+                0.097
+            ],
+            "angle": 0,
+            "content": "w/o Self-attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.699,
+                0.097,
+                0.792,
+                0.168
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.802,
+                0.089,
+                0.88,
+                0.097
+            ],
+            "angle": 0,
+            "content": "Self-attention w/o Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.795,
+                0.097,
+                0.888,
+                0.243
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.244,
+                0.603,
+                0.319
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.605,
+                0.244,
+                0.699,
+                0.319
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.699,
+                0.244,
+                0.793,
+                0.319
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.795,
+                0.244,
+                0.888,
+                0.319
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.33,
+                0.895,
+                0.4
+            ],
+            "angle": 0,
+            "content": "Figure 9. Ablation study of blended self-attention. Without self-attention fusion, the generated video can not preserve the details of input videos (e.g., fence, trees, and car identity). If we replace full self-attention without a spatial mask, the structure of the original jeep misleads the generation of the Porsche car."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.427,
+                0.895,
+                0.609
+            ],
+            "angle": 0,
+            "content": "pixels in the atlas. However, it struggles to perform editing that involves new shapes or 3D structures. In addition, it takes hours to optimize the neural atlas for each input video. While Tune-A-Video [52] with DDIM [46] ranks second in editing quality and image fidelity of Tab. 1, we observe that it has difficulty in reproducing the exact motion and spatial position as input video (right side of Fig.7). Besides, the background has annoying artifacts. Different from the above baselines, our method preserves the motion by fusion the attention during inversion and editing. Thus, our results outperform others by a large margin in our user study and frame consistency measured by CLIP."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.62,
+                0.665,
+                0.634
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.895,
+                0.688
+            ],
+            "angle": 0,
+            "content": "Although we have proved the effectiveness of the proposed strategies in Fig. 4 and Fig. 3 using toy image examples, here, we ablate these designs in the video."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.895,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Attention during inversion. In the right column of Fig. 8, we use the attention map during reconstruction instead of inversion for zero-shot background editing. The visualized cross-attention map of the word 'boat' in the first and last frame can not capture the correct position and structure of the boat, which may be caused by the poor temporal modeling capacity of the image diffusion model and the accumulation of errors in DDIM inversion. In contrast, we propose using attention during inversion as the middle column, which provides stable guidance of semantic layout in the original video. We observe this huge difference in attention maps between inversion and reconstruction exists in most videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.895,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Attention Blending Block is studied in Fig. 9, where we remove all self-attention fusion or fuse all self-attention with"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15939"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.258
+            ],
+            "angle": 0,
+            "content": "out a spatial mask. The third column shows that removing all self-attention maps brings a loss of fine details ( e.g., fences, poles, and trees in the background) and inconsistency of car identity over time. In contrast, if we fuse full-resolution self-attention as in the previous work [16], the shape editing ability of the framework can be severely degraded so that the geometry of generated car resembles the input video, especially in the last few frames. Therefore, we propose to blend the self-attention maps with a mask obtained from cross-attention to preserve unedited details and ensure temporal consistency while editing the object shape."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.274,
+                0.196,
+                0.289
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.3,
+                0.47,
+                0.465
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a new text-driven video editing framework FateZero that performs temporal consistent zero-shot editing of attribute, style, and shape. We make the first attempt to study and utilize the cross-attention and spatial-temporal self-attention during DDIM inversion, which provides fine-grained motion and structure guidance at each denoising step. A new Attention Blending Block is further proposed to enhance the shape editing performance of our framework. Our framework benefits video editing using widely existing image diffusion models, which we believe will contribute to a lot of new video applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.467,
+                0.473,
+                0.573
+            ],
+            "angle": 0,
+            "content": "Limitation & Future Work. While our method achieves impressive results, it still has some limitations. During shape editing, since the motion is produced by the one-shot video diffusion model [52], it is difficult to generate totally new motion (e.g., 'swim' \\(\\rightarrow\\) 'fly') or very different shape (e.g., 'swan' \\(\\rightarrow\\) 'pterosaur'). We will test our method on the generic pretrained video diffusion model for better editing abilities."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
+                0.588,
+                0.175,
+                0.604
+            ],
+            "angle": 0,
+            "content": "References"
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+# FateZero: Fusing Attentions for Zero-shot Text-based Video Editing
+
+Chenyang Qi $^{1*}$  Xiaodong Cun $^{2\dagger}$  Yong Zhang $^{2}$  Chenyang Lei $^{3}$  Xintao Wang $^{2}$  Ying Shan $^{2}$  Qifeng Chen $^{1\dagger}$
+
+$^{1}$ HKUST  $^{2}$ Tencent AI Lab  $^{3}$ CAIR, HKISI-CAS
+
+https://fate-zero-edit.github.io
+
+![](images/d3be8d22c7445e65d4844eb9cb13a73c3ac156801810d3bcb6237999fd2e3576.jpg)
+
+Source Video Prompt: A silver jeep driving down a curvy road in the countryside.
+
+![](images/e356623977af9a159898539d6064163ffcc7b0749c4f8249e02b3fee2299daf2.jpg)
+
+Zero-shot object shape editing with pre-trained video diffusion model [52]: silver jeep  $\rightarrow$  Porsche car.
+
+![](images/914d4e31b5e3482e93451761f0b45d62f71774e96257c02567f9ee78663f154b.jpg)  
+Figure 1. Zero-shot text-driven video editing. We present a zero-shot approach for shape-aware local object editing and video style editing from pre-trained diffusion models [42, 52] without any optimization for each target prompt.
+
+Zero-shot video style editing with pre-trained image diffusion model [42]: watercolor painting.
+
+# Abstract
+
+The diffusion-based generative models have achieved remarkable success in text-based image generation. However, since it contains enormous randomness in generation progress, it is still challenging to apply such models for real-world visual content editing, especially in videos. In this paper, we propose FateZero, a zero-shot text-based
+
+editing method on real-world videos without per-prompt training or use-specific mask. To edit videos consistently, we propose several techniques based on the pre-trained models. Firstly, in contrast to the straightforward DDIM inversion technique, our approach captures intermediate attention maps during inversion, which effectively retain both structural and motion information. These maps are directly fused in the editing process rather than generated during denoising. To further minimize semantic leakage of the source video, we then fuse self-attention with a blending
+
+mask obtained by cross-attention features from the source prompt. Furthermore, we have implemented a reform of the self-attention mechanism in denoising UNet by introducing spatial-temporal attention to ensure frame consistency. Yet succinct, our method is the first one to show the ability of zero-shot text-driven video style and local attribute editing from the trained text-to-image model. We also have a better zero-shot shape-aware editing ability based on the text-to-video model [52]. Extensive experiments demonstrate our superior temporal consistency and editing capability than previous works.
+
+# 1. Introduction
+
+Diffusion-based models [19] can generate diverse and high-quality images [40, 42, 44] and videos [15, 18, 32, 45, 56] through text prompts. It also brings large opportunities to edit real-world visual content from these generative priors.
+
+Previous or concurrent diffusion-based editing methods [2, 3, 6, 16, 38, 48] majorly work on images. To edit real images, their methods utilize deterministic DDIM [46] for the image-to-noise inversion, and then, the inverted noise gradually generates the edited images under the condition of the target prompt. Based on this pipeline, several methods have been proposed in terms of cross-attention guidance [38], plug-and-play feature [48], and optimization [25, 35].
+
+Manipulating videos through generative priors as image editing methods above contains many challenges (Fig. 7). First, there are no publicly available generic text-to-video models [18, 45]. Thus, a framework based on image models can be more valuable than on video ones [36], thanks to the various open-sourced image models in the community [1, 37, 42, 54]. However, the text-to-image models [42] lack the consideration of temporal-aware information, e.g., motion and 3D shape understanding. Directly applying the image editing methods [33, 35] to the video will show obverse flickering. Second, although we can use previous video editing methods [4, 24, 28] via keyframe [21] or atlas editing [4, 24], these methods still need atlas learning [4, 24], keyframe selection [21], and per-prompt tunning [4, 28]. Moreover, while they may work well on the attribute [4, 24] and style [21] editing, the shape editing is still a big challenge [28]. Finally, as introduced above, current editing methods use DDIM for inversion and then denoising via the new prompt. However, in video inversion, the inverted noise in the  $T$  step might break the motion and structure of the original video because of error accumulation (Fig. 4 and 9).
+
+In this paper, we propose FateZero, a simple yet effective method for zero-shot video editing since we do not need to train for each target prompt individually [4, 24, 28] and have no user-specific mask [2, 3]. Different from image editing, video editing needs to keep the temporal consistency of the edited video, which is not learned by the original trained text-to-image model. We tackle this problem by using two
+
+novel designs. Firstly, instead of solely relying on inversion and generation [16, 35, 48], we adopt a different approach by storing all the self and cross-attention maps at every step of the inversion process. This enables us to subsequently replace them during the denoising steps of the DDIM pipeline. Specifically, we find these self-attention blocks store better motion information and the cross-attention can be used as a threshold mask for self-attention blending spatially. This attention blending operation can keep the original structures unchanged. Furthermore, we reform the self-attention blocks to the spatial-temporal attention blocks as in [52] to make the appearance more consistent. Powered by our novel designs, we can directly edit the style and the attribute of the real-world video (Fig. 6) using the pre-trained text-to-image model [42]. Also, after getting the video diffusion model (e.g., pretrained Tune-A-Video [52]), our method shows better object editing (Fig. 5) ability in test-time than simple DDIM inversion [46]. The extensive experiments provide evidence of the advantages offered by the proposed method for both video and image editing.
+
+Our contributions are summarized as follows:
+
+- We present the first framework for temporal-consistent zero-shot text-based video editing using pretrained text-to-image model.  
+- We propose to fuse the attention maps in the inversion process and generation process to preserve the motion and structure consistency during editing.  
+- Our novel Attention Blending Block utilizes the source prompt's cross-attention map during attention fusion to prevent source semantic leakage and improve the shape-editing capability.  
+- We show extensive applications of our method in video style editing, video local attribute editing, video object shape editing, etc.
+
+# 2. Related Work
+
+Video Editing. Video can be edited via several aspects. For video stylizing editing, current methods [11, 21] rely on the example as the style guide and these methods may fail when the track is lost. By processing frames individually using image style transfer [13, 22], some works also learn to reduce the temporal consistency [5, 27, 29, 30] in a post-process way. However, the style may still be imperfect since the style transfer only measures the perceptual distance [55]. Several works also show better consistency but on the specific domain, e.g., portrait video [12, 53]. For video local editing, layer-atlas based methods [4, 24] show a promising direction by editing the video on a flattened texture map. However, the 2d atlas lacks 3d motion perception to support shape editing, and prompt-specific optimization is required.
+
+![](images/9c16df1981ca8dc5b5c87e7700e8c469e93990b5928c75f2423d275b84f0a8ed.jpg)  
+Figure 2. The overview of our approach. Our input is the user-provided source prompt  $p_{src}$ , target prompt  $p_{edit}$  and clean latent  $z = \{z^1, z^2, \ldots, z^n\}$  encoded from input source video  $x = \{x^1, x^2, \ldots, x^n\}$  with number frames  $n$  in a video sequence. On the left, we first invert the video using DDIM inversion pipeline into noisy latent  $z_T$  using the source prompt  $p_{src}$  and an inflated 3D U-Net  $\varepsilon_\theta$ . During each inversion timestep  $t$ , we store both spatial-temporal self-attention maps  $s_t^{src}$  and cross-attention maps  $c_t^{src}$ . At the editing stage of the DDIM denoising, we denoise the latent  $z_T$  back to clean image  $\hat{z}_0$  conditioned on target prompt  $p_{edit}$ . At each denoising timestep  $t$ , we fuse the attention maps  $(s_t^{edit}$  and  $c_t^{edit}$  ) in  $\varepsilon_\theta$  with stored attention map  $(s_t^{src}, c_t^{src})$  using the proposed Attention Blending Block. Right: Specifically, we replace the cross-attention maps  $c_t^{edit}$  of un-edited words (e.g., road and countryside) with source maps  $c_t^{src}$  of them. In addition, we blend the self-attention map during inversion  $s_t^{src}$  and editing  $s_t^{edit}$  with an adaptive spatial mask obtained from cross-attention maps  $c_t^{src}$  of edited words (e.g., silver and jeep), which represents the areas that the user wants to edit.
+
+![](images/7c3a0f61c23aa1b9f5927f17038247d6d172d6d36f2e52cc15614ce365846851.jpg)
+
+A more challenging topic is to edit the object shape in the real-world video. Current method shows obvious artifacts even with the optimization on generative priors [28]. The stronger prior of the diffusion-based model also draws the attention of current researchers. e.g., gen1 [9] trains a conditional model for depth and text-guided video generation, which can edit the appearance of the generated images on the fly. Dreamix [36] finetunes a stronger diffusion-based video model [18] for editing with stronger generative priors. Both of these methods need private and powerful video diffusion models for editing. Thus, the applications of the current larger-scale fine-tuned text-to-image models [1] cannot be used directly.
+
+Image and Video Generation Models. Image generation is a basic and hot topic in computer vision. Early works mainly use VAE [26] or GAN [14] to model the distribution on the specific domain. Recent works adopt VQVAE [49] and transformer [10] for image generation. However, due to the difficulties in training these models, they only work well on the specific domain, e.g., face [23]. On the other hand, the editing ability of these models is relatively weak since the feature space of GAN is high-level, and the quantified tokens can not be considered individually. Another type of method focuses on text-to-image generation. DALL-E [40, 41] and CogView [8] train an image generative pre-training transformer (GPT) to generate images from a CLIP [34] text embedding. Recent models [42, 44] benefit from the stability of training diffusion-based model [19]. These mod
+
+els can be scaled by a huge dataset and show surprisingly good results on text-to-image generation by integrating large language model conditions since its latent space has spatial structure, which provides a stronger edit ability than previous GAN [23] based methods. Generating videos is much more difficult than images. Current methods rely on the larger cascaded models [18, 45] and dataset. Differently, magic-video [56] and gen1 [9] initialize the model from text-to-image [42] and generate the continuous contents through extra time-aware layers. Recently, Tune-A-Video [52] overfits a single video for text-based video generation. After training, the model can generate related motion from similar prompts. However, the results from this model are too flickering to achieve realistic local editing. Inspired by the image editing methods and tune-a-video, our method can edit the style of the real-world video and images using the trained text-to-image model [42] and shows better object replacing performance than the one-shot finetuned video diffusion model [52] with simple DDIM inversion [46] in real videos (Fig. 7).
+
+Image Editing in Diffusion Model. Many recent works adopt the trained diffusion model for editing. SDEdit [33] generates content for a new prompt by adding noise to the image first. DiffEdit [6] computes the edit mask by the noise differences of the text prompts, and then, blends the inversion noises into the image generation process. Similar work has also been proposed by Blended Diffusion [2, 3], which combines the features of each step for image blending. Plug-
+
+and-play [48] gets the inversion noise and applies the denoising for feature reconstruction. After that, the self-attention features in editing are replaced with that in reconstruction directly. Pix2pix-Zero [38] edits the image with the cross-attention guidance. Prompt-to-Prompt [16] proves that images can be edited via reweighting the cross-attention map of different prompts. There are also some methods to achieve better editing ability via optimization [25, 35]. However, a naive frame-wise application of these image methods to video results in flickering and inconsistency among frames.
+
+# 3. Methods
+
+We target zero-shot text-driven video editing (e.g., style, attribute, and shape) without optimization for each target prompt or the user-provided mask. In Sec. 3.1, we first give the details of the latent diffusion and DDIM inversion. After that, we introduce our method that enables video appearance editing (Sec. 3.2) via the pre-trained text-to-image models [42]. Finally, we discuss a more challenging case that also enables the shape-aware editing of video using the video diffusion model in Sec. 3.3. Notice that, the proposed method is a general editing method and can be used in various text-to-image or text-to-video models. In this paper, we majorly use Stable Diffusion [42] and the video generation model based on Stable Diffusion (Tune-A-Video [52]) for its popularity and generalization ability.
+
+# 3.1. Preliminary: Latent Diffusion and Inversion
+
+Latent Diffusion Models [42] are introduced to diffuse and denoise the latent space of an autoencoder. First, an encoder  $\mathcal{E}$  compresses a RGB image  $x$  to a low-resolution latent  $z = \mathcal{E}(x)$ , which can be reconstructed back to image  $\mathcal{D}(z) \approx x$  by decoder  $\mathcal{D}$ . Second, a U-Net [43]  $\varepsilon_{\theta}$  containing cross-attention and self-attention [50] is trained to remove the artificial noise using the objective:
+
+$$
+\min _ {\theta} E _ {z _ {0}, \varepsilon \sim N (0, I), t \sim \mathrm {U n i f o r m} (1, T)} \| \varepsilon - \varepsilon_ {\theta} (z _ {t}, t, p) \| _ {2} ^ {2}, \tag {1}
+$$
+
+where  $p$  is the embedding of the conditional text prompt and  $z_{t}$  is a noisy sample of  $z_{0}$  at timestep  $t$ .
+
+DDIM Inversion [46]. During inference, deterministic DDIM sampling is employed to convert a random noise  $z_{T}$  to a clean latent  $z_{0}$  in a sequence of timestep  $t: T \to 1$ :
+
+$$
+z _ {t - 1} = \sqrt {\alpha_ {t - 1}} \frac {z _ {t} - \sqrt {1 - \alpha_ {t}} \varepsilon_ {\theta}}{\sqrt {\alpha_ {t}}} + \sqrt {1 - \alpha_ {t - 1}} \varepsilon_ {\theta}, \tag {2}
+$$
+
+where  $\alpha_{t}$  is a parameter for noise scheduling [19,46]
+
+Based on the ODE limit analysis of the diffusion process, DDIM inversion [7,46] is proposed to map a clean latent  $z_0$  back to a noised latent  $\hat{z}_T$  in revered steps  $t:1\to T$ :
+
+$$
+\hat {z} _ {t} = \sqrt {\alpha_ {t}} \frac {\hat {z} _ {t - 1} - \sqrt {1 - \alpha_ {t - 1}} \varepsilon_ {\theta}}{\sqrt {\alpha_ {t - 1}}} + \sqrt {1 - \alpha_ {t}} \varepsilon_ {\theta}, \tag {3}
+$$
+
+![](images/f223838b035a975bf23718868468c70067a720a96ab5bde2622407776420f6ec.jpg)
+
+![](images/caa50adb795a90892b67c8b0fa22a3ed6f7cbcb3e1641752b48670e3704f901f.jpg)  
+Figure 3. Zero-shot local attributed editing (cat  $\rightarrow$  tiger) using stable diffusion. In contrast to fusion with attention during reconstruction (a) in previous work [16, 38, 48], our inversion attention fusion (b) provides more accurate structure guidance and editing ability, as visualized on the right side.
+
+where each  $\varepsilon_{\theta}$  stands for the noise  $\varepsilon_{\theta}(z_{t - 1},t - 1,p_{src})$  predicted at  $t - 1$  timestep.
+
+Such that the inverted latent  $\hat{z}_T$  can reconstruct a latent  $\hat{z}_0(p_{src}) = \mathrm{DDIM}(\hat{z}_T, p_{src})$  similar to the clean latent  $z_0$  at classifier-free guidance scale  $s_{cfg} = 1$ . Recently, image editing methods [16,35,38,48] use a large classifier-free guidance scale  $s_{cfg} \gg 1$  to edit the latent as  $\hat{z}_0(p_{edit}) = \mathrm{DDIM}(\hat{z}_T, p_{edit})$  (second row in Fig 3(a)), where a reconstruction of  $\hat{z}_0(p_{src})$  is conducted in parallel to provide attention constraints. (first row in Fig 3(a)).
+
+# 3.2. FateZero Video Editing
+
+As shown in Fig. 2, we use the pretrained text-to-image model, i.e., Stable Diffusion, as our base model, which contains a UNet for  $T$ -timestep denoising. Instead of straightforwardly exploiting the regular pipeline of latent editing guided by reconstruction attention, we have made several critical modifications for video editing as follows.
+
+Inversion Attention Fusion. Direct editing using the inverted noise results in frame inconsistency, which may be attributed to two factors. First, the invertible property of DDIM discussed in Eq. (2) and Eq. (3) only holds in the limit of small steps [46, 47]. Nevertheless, the present requirements of 50 DDIM denoising steps lead to an accumulation of errors with each subsequent step. Second, using a large classifier-free guidance  $s_{cfg} \gg 1$  can increase the edit ability in denoising, but the large editing freedom leads to inconsistent neighboring frames. Therefore, previous methods require optimization of text-embedding [16] or other
+
+regularization [38].
+
+While the issues seem trivial in the context of single-frame editing they can become magnified when working with video as even minor discrepancies among frames will be accentuated along the temporal indexes.
+
+To alleviate these issues, our framework utilizes the attention maps during inversion steps (Eq. (3)), which is available because the source prompt  $p_{src}$  and initial latent  $z_0$  are provided to the UNet during inversion. Formally, during inversion, we store the intermediate self-attention maps  $[s_t^{\mathrm{src}}]_{t=1}^T$ , cross-attention maps  $[c_t^{\mathrm{src}}]_{t=1}^T$  at each timestep  $t$  and the final latent feature maps  $z_T$  as
+
+$$
+z _ {T}, \left[ c _ {t} ^ {\mathrm {s r c}} \right] _ {t = 1} ^ {T}, \left[ s _ {t} ^ {\mathrm {s r c}} \right] _ {t = 1} ^ {T} = \operatorname {D D I M} - \operatorname {I N V} \left(z _ {0}, p _ {s r c}\right), \tag {4}
+$$
+
+where DDIM-INV stands for the DDIM inversion pipeline discussed in Eq. (3). During the editing stage, we can obtain the noise to remove by fusing the attention from inversion:
+
+$$
+\hat {\epsilon} _ {t} = \text {A T T - F U S I O N} \left(\varepsilon_ {\theta}, z _ {t}, t, p _ {\text {e d i t}}, c _ {t} ^ {\text {s r c}}, s _ {t} ^ {\text {s r c}}\right). \tag {5}
+$$
+
+where  $p_{\mathrm{edit}}$  represents the modified prompt. In function ATT-FUSION, we inject the cross-attention maps of the unchanged part of the prompt similar to Prompt-to-Prompt [16]. We also replace self-attention maps to preserve the original structure and motion during the style and attribute editing.
+
+Fig. 3 shows a toy comparison example between our attention fusion method and the typical method with simply inversion and then generation as in [16, 35] for image editing. The cross-attention map during inversion captures the silhouette and the pose of the cat in the source image, but the map during reconstruction has a noticeable difference. While in the video, the attention consistency might influence the temporal consistency as shown in Fig. 8. This is because the spatial-temporal self-attention maps represent the correspondence between frames and the temporal modeling ability of existing video diffusion model [52] is not satisfactory.
+
+Attention Map Blending. Inversion-time attention fusion might be insufficient in local attrition editing, as shown in an image example in Fig. 4. In the third column, replacing self-attention  $s^{edit} \in \mathbb{R}^{hw \times hw}$  with  $s^{src}$  brings unnecessary structure leakage and the generated image has unpleasant blending artifacts in the visualization. On the other hand, if we keep  $s^{edit}$  during the DDIM denoising pipeline, the structure of the background and watermelon has unwanted changes, and the pose of the original rabbit is also lost. Inspired by the fact that the cross-attention map provides the semantic layout of the image [16], as visualized in the second row of Fig. 4, we obtain a binary mask  $M_t$  by thresholding the cross-attention map of the edited words during inversion by a constant  $\tau$  [2, 3]. Then, the self-attention maps of editing stage  $s_t^{edit}$  and inversion stage  $s_t^{src}$  are blended with the binary mask  $M_t$ , as illustrated in Fig. 2. Formally, the
+
+![](images/3df5b143cc33b90ca438f09492ccf9886740deea4c2a24985c4694b00c4470f4.jpg)  
+Input Frame
+
+![](images/d45e6c2f52fd4e78a7f90107ee6077f7c0a0e44f408ff39d7d69b04bb5592dde.jpg)
+
+![](images/fef4547c66d29be430730642c6d9de20ca8df1a116d405c4b12f95e5ba9dd6d8.jpg)  
+Reconstruction Frame Inversion attention
+
+![](images/36eaaef284887bc6de1812720164d4ca7190c69b3495071d7676aba70ea3d68b.jpg)
+
+![](images/15bc5adcda924096ab0176c07bf895a2610b6708b2676183a12e01b79a527e87.jpg)  
+Our Blended Self-Attention
+
+![](images/618f2b3e94f75b98ae3ffe07bf2e5ea2d2881fdd6bc5efcd2b052eedc8e7cc4c.jpg)
+
+![](images/1d8dc5021df4891690fbe9b29d11b3fc5a2573ae2e86b3bc274b5049b8c42987.jpg)  
+No Self-Attention  
+Figure 4. Study of blended self-attention in zero-shot shape editing (rabbit  $\rightarrow$  tiger) using stable diffusion. Forth and fifth columns: Ignoring self-attention can not preserve the original structure and background, and naive replacement causes artifacts. Third column: Blending the self-attention using the cross-attention map (the second row) obtains both new shape from the target text with a similar pose and background from the input frame.
+
+![](images/759f9c3b78b3a47092735f8262c7cdfed20a170190a352322f8776412bb078c7.jpg)
+
+![](images/56155934d9a13e7c157f2af8a6443f1cfd089c3c256123d09fecc23259c02120.jpg)  
+Self-Attention without Mask
+
+attention map fusion is implemented as
+
+$$
+M _ {t} = \text {H E A V I S I D E S T E P} \left(c _ {t} ^ {\text {s r c}}, \tau\right), \tag {6}
+$$
+
+$$
+s _ {t} ^ {\text {f u s e d}} = M _ {t} \odot s _ {t} ^ {\text {e d i t}} + (1 - M _ {t}) \odot s _ {t} ^ {\text {s r c}}. \tag {7}
+$$
+
+Spatial-Temporal Self-Attention. The previous two designs make our method a strong editing method that can preserve the better structure, and also a big potential in video editing. However, denoising each frame individually still produces inconsistent video. Inspired by the casual self-attention [15, 20,50,51] and recent one-shot video generation method [52], we reshape the original self-attention to Spatial-Temporal Self-Attention without changing pretrained weights. Specifically, we implement ATTENTION  $(Q,K,V)$  for feature  $z^i$  at temporal index  $i\in [1,n]$  as
+
+$$
+Q = W ^ {Q} \mathbf {z} ^ {i}, K = W ^ {K} \left[ \mathbf {z} ^ {i}; \mathbf {z} ^ {\mathrm {w}} \right], V = W ^ {V} \left[ \mathbf {z} ^ {i}; \mathbf {z} ^ {\mathrm {w}} \right], \tag {8}
+$$
+
+where  $[\cdot ]$  denotes the concatenation operation and  $W^{Q},W^{K}$ $W^{V}$  are the projection matrices from pretrained model. Empirically, we find it is enough to warp the middle frame  $\mathbf{z}^{\mathrm{w}} = z^{\mathrm{Round}\left[\frac{n}{2}\right]}$  for attribute and style editing. Thus, the spatial-temporal self-attention map is represented as  $s_t^{src}\in$ $R^{hw\times fhw}$ , where  $f = 2$  is the number of frames used as key and value. It captures both the structure of a single frame and the temporal correspondence with the key frame features.
+
+Overall, the proposed method produces a new editing method for zero-shot real-world video editing. We replace the attention maps in the denoising steps with their corresponding maps during the inversion steps. After that, we utilize cross-attention maps as masks to prevent semantic leaks. Finally, we reform the self-attention of UNet to spatial-temporal attention for better temporal consistency among different temporal frames. We have included a formal algorithm in the supplementary materials for reference purposes.
+
+![](images/293e9ed6d8a00fb0e65a3c74cdbb20e47818b8995279dccaebf4409c68e922f6.jpg)  
+Source Prompt: A black swan with a red beak swimming in a river near a wall and bushes.
+
+![](images/77ee74c1a8b62ca7d804636b7095ffc6a1c0fd4cc8af7bc6c77e4c13ddd617b4.jpg)  
+black swan  $\rightarrow$  white duck.
+
+![](images/9f97b55dc6e9813cd1c759812b239f9f07fd4e98be31d0b124312953d29e6995.jpg)  
+black swan  $\rightarrow$  pink flamingo.
+
+![](images/600614f59755dd5b7d058a602dc9b9ee61da026669215c47b849505aae41ebed.jpg)  
+Figure 5. Zero-shot object shape editing on pre-trained video diffusion model [52]: Our framework can directly edit the shape of the object in videos driven by text prompts using a trained video diffusion model [52]  
+Source Prompt from Fig 5: black  $\rightarrow$  Swarovski crystal
+
+![](images/580180d32db41a0a80bef39d1db7df6554fe5cf38daf2c6b5e253b7244e5965c.jpg)  
+A man with round helmet surfing on a white wave  $\rightarrow$  The Ukiyo-e style painting of a man ...
+
+![](images/0a9b13c55186e8aea30655e93c76263e0cccece822067a37695e96eb5a2e405e.jpg)  
+A train traveling down tracks next to a forest and a man on the side of the track  $\rightarrow$  ..., Makoto Shinkai style  
+Figure 6. Zero-shot attribute and style editing results using Stable Diffusion [42]. Our framework supports abstract attribute and style editing like 'Swarovski crystal', 'Ukiyo-e', and 'Makoto Shinkai'. Best viewed with zoom-in.
+
+![](images/d0a86b04e3c1e96cda2894d08d24300463e1862ff5a101050fd61ffcf18a06e5.jpg)
+
+![](images/869e4fb61a12f4aa4b0369b52b3c3a3f387828f11a2498d5424850f1f79172a5.jpg)  
+Tune-A-Video + Ours
+
+![](images/e2db527c2146e7e2276eed6e9c91b37c5a4ed755ae36dc3a2ed472f267e0d277.jpg)  
+Shape-aware Editing
+
+![](images/f34d13f6c1d44759b991a22bd98b0371e6ab2fb4edf7c11e91bc74e6c64b2025.jpg)  
+Tune-A-Video + DDIM Inv
+
+![](images/8cdf37b76203707cd190961687b01dd2bf81b0b54ff15856ec5399598eda9a86.jpg)
+
+![](images/13d0950d9c1449a77dbc32bce0813e988ed1a8b9c6d7657366677dc6aea63563.jpg)  
+$\mathrm{NLA + }$  Null-Inv
+
+![](images/2226ab2734c05c4b7f1d09224fb5e161c31a8ee88184cd4e58220446bbfd92b8.jpg)
+
+![](images/e989a52398632ed61aa6c40fbee9ee1a793435c2e5c1e22ee32ea6b42939db98.jpg)  
+Framewise Null-Inv  
+Figure 7. Qualitative comparison of our methods with other baselines. Inputs are in Fig. 5 and Fig 6. Our results have the best temporal consistency, image fidelity, and editing quality. Best viewed with zoom-in.
+
+![](images/ffb33ded8c4b3108cbe5f7e5bc0cc5d5aacd92d116f1d1463ad5564d4e1c28d2.jpg)
+
+![](images/07c04c350e2b2ba37c27ea35c6c73a9f6ac926d5d0f83b2452d8e5c2381af4b9.jpg)  
+Frameswise SDEdit
+
+![](images/2351c2d297753273fd87b301ca68346ae46caec78f1701b3bbd626d2c9362007.jpg)
+
+![](images/16fedcc3871b820bc1258729de319c52298ac87a2dd167304cb2e9d6be496608.jpg)  
+SD + Ours
+
+![](images/5a7fa87b4a1338ea605cc6c391038eb08f722f19f4512101de7aba1efea28d80.jpg)  
+Style Editing
+
+![](images/2da21aabda475161f9ffe44da0a9583a1b610a2ae5106d1145fd22234a611d28.jpg)  
+Tune-A-Video + DDIM Inv
+
+![](images/e0bde75599bcd79fa774d2e774108cd19f8568e24d5d58aa0dd86c9439574503.jpg)
+
+![](images/1c5e6ff3fbbc98da2b16e23552e22be2797eb3d8a866d24f19037e4a9b4dacae.jpg)  
+Framewise Null-Inv
+
+![](images/76a760298486f63b21538d5f0971437d3856ced34f5af65fee407d59babd6dcd.jpg)
+
+![](images/16593b7de9ef85b1414884601e63118f9ea50059629fc17e975e76e56f9d2802.jpg)  
+Frameswise SDEdit
+
+# 3.3. Shape-Aware Video Editing
+
+Different from appearance editing, reforming the shape of a specific object in the video is much more challenging. To this end, a pretrained video diffusion model is needed. Since there is no publicly-available generic video diffusion model, we perform the editing on the one-shot video diffusion model [52] instead. In this case, we compare our editing method with simple DDIM inversion [46], where our method also achieves better performance in terms of editing ability, motion consistency, and temporal consistency. It might be because it is hard for an inflated model to overfit the exact motion of the input video. While in our method, the motion and structure are represented by high-quality spatial-temporal attention maps  $s_t^{src} \in R^{hw \times fhw}$  during inversion, which is further fused with the attention maps during editing. More details can be founded in Fig. 7 and the supp. video.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+For zero-shot style and attribute editing, we directly use the trained stable diffusion v1.4 [42] as the base model, we fuse the attentions in the interval of  $t \in [0.2 \times T, T]$  of the DDIM step with total timestep  $T = 50$ . For shape editing, we utilize the pretrained model of the specific video [52] at 100 iterations and fuse the attention at DDIM timestep  $t \in [0.5 \times T, T]$ , giving more freedom for new shape generation. Following previous works [4,9], we use videos from DAVIS [39] and other in-the-wild videos to evaluate our approach. The source prompt of the video is generated via the image caption model [31]. Finally, we design the target prompt for each video by replacing or adding several words.
+
+# 4.2. Applications
+
+Local attribute and global style editing. Using pretrained text-to-image diffusion model [42], our framework supports zero-shot local attribute and global style editing, as shown in Fig. 6 and third row in Fig.1. In the first row, the texture
+
+<table><tr><td>Method</td><td colspan="2">CLIP Metrics↑</td><td colspan="3">User Study↓</td></tr><tr><td>Inversion &amp; Editing</td><td>Tem-Con</td><td>Fram-Acc</td><td>Edit</td><td>Image</td><td>Temp</td></tr><tr><td>Frameswise Null &amp; p2p [16,35]</td><td>0.852</td><td>0.958</td><td>3.55</td><td>4.11</td><td>4.38</td></tr><tr><td>Frameswise SDEdit [33]</td><td>0.910</td><td>0.819</td><td>3.69</td><td>3.28</td><td>3.62</td></tr><tr><td>NLA, Null &amp; p2p [16,24,35]</td><td>0.949</td><td>0.600</td><td>3.17</td><td>3.02</td><td>2.60</td></tr><tr><td>Tune-A-Video &amp; DDIM [46,52]</td><td>0.958</td><td>0.750</td><td>2.78</td><td>2.80</td><td>2.70</td></tr><tr><td>Ours</td><td>0.965</td><td>0.903</td><td>1.82</td><td>1.79</td><td>1.69</td></tr></table>
+
+Table 1. Quantitative evaluation against baselines. In our user study, the results of our method are preferred over those from baselines. For CLIP-Score, we achieve the best temporal consistency and comparable framewise editing accuracy against an optimization-based image editing method [35].
+
+and color of the feather are modified by the target prompt Swarovski crystal and kept consistent across frames. In the second and third rows, our framework applies abstract style (Ukiyo-e and Makoto Shinkai). The image structure and temporal motion can be well preserved since we fuse both the spatial-temporal self-attention and cross-attention during the inversion and editing stage.
+
+Shape-aware editing. Fig. 5 and the second row in Fig.1 present the result of difficult object shape editing, with a pretrained video model [52]. This task is challenging because a naive full-resolution fusion of the spatial-temporal self-attention maps results in inaccurate shape results and wrong temporal motion, as shown in the ablation (Fig.9). Thanks to the proposed Attention Blending, we combine the motion of generated shape from the editing target and inverted attention from the input video. Results of porsche, duck and flamingo show that we generate new content with poses and positions similar to input videos.
+
+Zero-shot image editing. In addition, our framework can serve as a zero-shot image editing method such as local attribute editing (Fig. 3) and object shape editing (Fig. 4) by considering an image as a video with a single frame. We provide more results in our supplementary material.
+
+![](images/3ac1674f1fc0d8e2baa20fd6308de9680ffa74851b4a142f1d98cfea86081640.jpg)  
+Input Video
+
+![](images/9a378ef30f46429fb596a299a7f0e042cb99174318966aae58ed97071d4d7706.jpg)  
+Ours Inversion Cross-Attention  
+Figure 8. Inversion attention compared with reconstruction attention using prompt 'deserted shore  $\rightarrow$  'glacier shore'. The attention maps obtained from the reconstruction stage fail to detect the boat's position, and can not provide suitable motion guidance for zero-shot video editing.
+
+![](images/b16a21f62ff64070eb37349517708ecbaca3d6bb778242a459f7b338372f74bd.jpg)  
+Reconstruction Cross-Attention
+
+# 4.3. Baseline Comparisons
+
+Since there are no available zero-shot video editing methods based on diffusion models, we build the following four state-of-the-art baselines for comparison. (1) Tune-A-Video [52] overfits an inflated diffusion model on a single video to generate similar content. (2) The Neural Layered Atlas [24] (NLA) based method is combined with keyframe-editing via state-of-the-art image editing methods [16, 35]. (3) Frame-wise Null-text optimization [35] and then edit by prompt2prompt [16]. (4) Frame-wise zero-shot editing using SDEdit [33]. For attention-based editing (2,3,4), we use the same timesteps fusion parameters as ours.
+
+We conduct the quantitative evaluation using the trained CLIP [34] model as previous methods [9, 38, 52]. Specially, we show the 'Tem-Con' [9] to measure the temporal consistency in frames by computing the cosine similarity between all pairs of consecutive frames. 'Frame-Acc' [17, 34, 38] is the frame-wise editing accuracy, which is the percentage of frames where the edited image has a higher CLIP similarity to the target prompt than the source prompt. In addition, three user studies metrics (denoted as 'Edit', 'Image', and 'Temp') are conducted to measure the editing quality, overall frame-wise image fidelity, and temporal consistency of the video, respectively. We ask 20 subjects to rank different methods with 9 sets of comparisons in each study. From Tab. 1, the proposed zero-shot method achieves the best temporal consistency against baselines and shows a comparable frame-wise editing accuracy as the pre-frame optimization method [35]. As for the user studies, the average ranking of our method earns user preferences the best in three aspects.
+
+To provide a qualitative comparison, Fig.7 provides the results of our method and other baselines at two different frames. The editing result of framewise SDEdit [33] can not be localized and varies a lot among different frames. Framewise Null inversion achieves local editing at the cost of 500-iterations optimization for each frame but is still temporally inconsistent. NLA-based [24] method preserves the exact
+
+![](images/9aafe56fdc958e03a1818294609aa88cad604807eeb05eda8ce0e7fe424f4451.jpg)  
+Input Video
+
+![](images/c17d5314dea72d57d908da9f993a25f8e00c78a27ed2f97c3d4ff023d39390be.jpg)  
+Ours
+
+![](images/506d147c9834e1aca378c461814cd906765fc5044199b2df5a604085e763568f.jpg)  
+w/o Self-attention
+
+![](images/2b58f9c3c4c6838d4e15b04db67250469864629479812aeeb91d0efa1bada3c7.jpg)  
+Self-attention w/o Mask
+
+![](images/44965cb4022d541742284a8d784e35793d912c721700c7badba20f04b307f1ed.jpg)  
+Figure 9. Ablation study of blended self-attention. Without self-attention fusion, the generated video can not preserve the details of input videos (e.g., fence, trees, and car identity). If we replace full self-attention without a spatial mask, the structure of the original jeep misleads the generation of the Porsche car.
+
+![](images/37e7f6c6d916b0fdf129eed30e49feccb714be09d0e48c4f527c26530de22da6.jpg)
+
+![](images/3cf9bea00656f77dce436d4fb6e0cfb9e32d25b3221dad1d255c5d6943ed75b6.jpg)
+
+![](images/99f92576b9424fb7c7b7fda0f93ef273938ce53d7a1d3e8e3d0c28e3e0b21db0.jpg)
+
+pixels in the atlas. However, it struggles to perform editing that involves new shapes or 3D structures. In addition, it takes hours to optimize the neural atlas for each input video. While Tune-A-Video [52] with DDIM [46] ranks second in editing quality and image fidelity of Tab. 1, we observe that it has difficulty in reproducing the exact motion and spatial position as input video (right side of Fig.7). Besides, the background has annoying artifacts. Different from the above baselines, our method preserves the motion by fusion the attention during inversion and editing. Thus, our results outperform others by a large margin in our user study and frame consistency measured by CLIP.
+
+# 4.4. Ablation Studies
+
+Although we have proved the effectiveness of the proposed strategies in Fig. 4 and Fig. 3 using toy image examples, here, we ablate these designs in the video.
+
+Attention during inversion. In the right column of Fig. 8, we use the attention map during reconstruction instead of inversion for zero-shot background editing. The visualized cross-attention map of the word 'boat' in the first and last frame can not capture the correct position and structure of the boat, which may be caused by the poor temporal modeling capacity of the image diffusion model and the accumulation of errors in DDIM inversion. In contrast, we propose using attention during inversion as the middle column, which provides stable guidance of semantic layout in the original video. We observe this huge difference in attention maps between inversion and reconstruction exists in most videos.
+
+Attention Blending Block is studied in Fig. 9, where we remove all self-attention fusion or fuse all self-attention with
+
+out a spatial mask. The third column shows that removing all self-attention maps brings a loss of fine details ( e.g., fences, poles, and trees in the background) and inconsistency of car identity over time. In contrast, if we fuse full-resolution self-attention as in the previous work [16], the shape editing ability of the framework can be severely degraded so that the geometry of generated car resembles the input video, especially in the last few frames. Therefore, we propose to blend the self-attention maps with a mask obtained from cross-attention to preserve unedited details and ensure temporal consistency while editing the object shape.
+
+# 5. Conclusion
+
+In this paper, we propose a new text-driven video editing framework FateZero that performs temporal consistent zero-shot editing of attribute, style, and shape. We make the first attempt to study and utilize the cross-attention and spatial-temporal self-attention during DDIM inversion, which provides fine-grained motion and structure guidance at each denoising step. A new Attention Blending Block is further proposed to enhance the shape editing performance of our framework. Our framework benefits video editing using widely existing image diffusion models, which we believe will contribute to a lot of new video applications.
+
+Limitation & Future Work. While our method achieves impressive results, it still has some limitations. During shape editing, since the motion is produced by the one-shot video diffusion model [52], it is difficult to generate totally new motion (e.g., 'swim'  $\rightarrow$  'fly') or very different shape (e.g., 'swan'  $\rightarrow$  'pterosaur'). We will test our method on the generic pretrained video diffusion model for better editing abilities.
+
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+                                    "content": "The diffusion-based generative models have achieved remarkable success in text-based image generation. However, since it contains enormous randomness in generation progress, it is still challenging to apply such models for real-world visual content editing, especially in videos. In this paper, we propose FateZero, a zero-shot text-based"
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+                                    "type": "text",
+                                    "content": "editing method on real-world videos without per-prompt training or use-specific mask. To edit videos consistently, we propose several techniques based on the pre-trained models. Firstly, in contrast to the straightforward DDIM inversion technique, our approach captures intermediate attention maps during inversion, which effectively retain both structural and motion information. These maps are directly fused in the editing process rather than generated during denoising. To further minimize semantic leakage of the source video, we then fuse self-attention with a blending"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "* Work done during an internship at Tencent AI Lab."
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+                                    "content": "mask obtained by cross-attention features from the source prompt. Furthermore, we have implemented a reform of the self-attention mechanism in denoising UNet by introducing spatial-temporal attention to ensure frame consistency. Yet succinct, our method is the first one to show the ability of zero-shot text-driven video style and local attribute editing from the trained text-to-image model. We also have a better zero-shot shape-aware editing ability based on the text-to-video model [52]. Extensive experiments demonstrate our superior temporal consistency and editing capability than previous works."
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+                                    "content": "Diffusion-based models [19] can generate diverse and high-quality images [40, 42, 44] and videos [15, 18, 32, 45, 56] through text prompts. It also brings large opportunities to edit real-world visual content from these generative priors."
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+                                    "content": "Previous or concurrent diffusion-based editing methods [2, 3, 6, 16, 38, 48] majorly work on images. To edit real images, their methods utilize deterministic DDIM [46] for the image-to-noise inversion, and then, the inverted noise gradually generates the edited images under the condition of the target prompt. Based on this pipeline, several methods have been proposed in terms of cross-attention guidance [38], plug-and-play feature [48], and optimization [25, 35]."
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+                                    "content": "Manipulating videos through generative priors as image editing methods above contains many challenges (Fig. 7). First, there are no publicly available generic text-to-video models [18, 45]. Thus, a framework based on image models can be more valuable than on video ones [36], thanks to the various open-sourced image models in the community [1, 37, 42, 54]. However, the text-to-image models [42] lack the consideration of temporal-aware information, e.g., motion and 3D shape understanding. Directly applying the image editing methods [33, 35] to the video will show obverse flickering. Second, although we can use previous video editing methods [4, 24, 28] via keyframe [21] or atlas editing [4, 24], these methods still need atlas learning [4, 24], keyframe selection [21], and per-prompt tunning [4, 28]. Moreover, while they may work well on the attribute [4, 24] and style [21] editing, the shape editing is still a big challenge [28]. Finally, as introduced above, current editing methods use DDIM for inversion and then denoising via the new prompt. However, in video inversion, the inverted noise in the "
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+                                    "content": " step might break the motion and structure of the original video because of error accumulation (Fig. 4 and 9)."
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+                                    "content": "In this paper, we propose FateZero, a simple yet effective method for zero-shot video editing since we do not need to train for each target prompt individually [4, 24, 28] and have no user-specific mask [2, 3]. Different from image editing, video editing needs to keep the temporal consistency of the edited video, which is not learned by the original trained text-to-image model. We tackle this problem by using two"
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+                                    "content": "novel designs. Firstly, instead of solely relying on inversion and generation [16, 35, 48], we adopt a different approach by storing all the self and cross-attention maps at every step of the inversion process. This enables us to subsequently replace them during the denoising steps of the DDIM pipeline. Specifically, we find these self-attention blocks store better motion information and the cross-attention can be used as a threshold mask for self-attention blending spatially. This attention blending operation can keep the original structures unchanged. Furthermore, we reform the self-attention blocks to the spatial-temporal attention blocks as in [52] to make the appearance more consistent. Powered by our novel designs, we can directly edit the style and the attribute of the real-world video (Fig. 6) using the pre-trained text-to-image model [42]. Also, after getting the video diffusion model (e.g., pretrained Tune-A-Video [52]), our method shows better object editing (Fig. 5) ability in test-time than simple DDIM inversion [46]. The extensive experiments provide evidence of the advantages offered by the proposed method for both video and image editing."
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+                                    "content": "Our contributions are summarized as follows:"
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+                                            "content": "- We present the first framework for temporal-consistent zero-shot text-based video editing using pretrained text-to-image model."
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+                                            "content": "- We propose to fuse the attention maps in the inversion process and generation process to preserve the motion and structure consistency during editing."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "content": "- Our novel Attention Blending Block utilizes the source prompt's cross-attention map during attention fusion to prevent source semantic leakage and improve the shape-editing capability."
+                                        }
+                                    ]
+                                }
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+                            "index": 10
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+                                            "content": "- We show extensive applications of our method in video style editing, video local attribute editing, video object shape editing, etc."
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+                                    "content": "2. Related Work"
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+                                    "content": "Video Editing. Video can be edited via several aspects. For video stylizing editing, current methods [11, 21] rely on the example as the style guide and these methods may fail when the track is lost. By processing frames individually using image style transfer [13, 22], some works also learn to reduce the temporal consistency [5, 27, 29, 30] in a post-process way. However, the style may still be imperfect since the style transfer only measures the perceptual distance [55]. Several works also show better consistency but on the specific domain, e.g., portrait video [12, 53]. For video local editing, layer-atlas based methods [4, 24] show a promising direction by editing the video on a flattened texture map. However, the 2d atlas lacks 3d motion perception to support shape editing, and prompt-specific optimization is required."
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+                                            "content": "Figure 2. The overview of our approach. Our input is the user-provided source prompt "
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+                                            "type": "inline_equation",
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+                                            "content": " and clean latent "
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+                                            "type": "inline_equation",
+                                            "content": "z = \\{z^1, z^2, \\ldots, z^n\\}"
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+                                            "content": " encoded from input source video "
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+                                            "content": "x = \\{x^1, x^2, \\ldots, x^n\\}"
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+                                            "type": "text",
+                                            "content": " with number frames "
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+                                            "content": "n"
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+                                            "type": "text",
+                                            "content": " in a video sequence. On the left, we first invert the video using DDIM inversion pipeline into noisy latent "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "z_T"
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+                                            "type": "text",
+                                            "content": " using the source prompt "
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+                                            "type": "inline_equation",
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+                                            "content": " and an inflated 3D U-Net "
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+                                            "type": "text",
+                                            "content": ". During each inversion timestep "
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+                                            "content": ", we store both spatial-temporal self-attention maps "
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+                                            "type": "text",
+                                            "content": ". At the editing stage of the DDIM denoising, we denoise the latent "
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+                                            "content": " back to clean image "
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+                                            "type": "text",
+                                            "content": ". At each denoising timestep "
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+                                            "content": " with stored attention map "
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+                                            "type": "text",
+                                            "content": " using the proposed Attention Blending Block. Right: Specifically, we replace the cross-attention maps "
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+                                            "content": " of un-edited words (e.g., road and countryside) with source maps "
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+                                            "content": " of them. In addition, we blend the self-attention map during inversion "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " of edited words (e.g., silver and jeep), which represents the areas that the user wants to edit."
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+                                    "content": "A more challenging topic is to edit the object shape in the real-world video. Current method shows obvious artifacts even with the optimization on generative priors [28]. The stronger prior of the diffusion-based model also draws the attention of current researchers. e.g., gen1 [9] trains a conditional model for depth and text-guided video generation, which can edit the appearance of the generated images on the fly. Dreamix [36] finetunes a stronger diffusion-based video model [18] for editing with stronger generative priors. Both of these methods need private and powerful video diffusion models for editing. Thus, the applications of the current larger-scale fine-tuned text-to-image models [1] cannot be used directly."
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+                                    "content": "Image and Video Generation Models. Image generation is a basic and hot topic in computer vision. Early works mainly use VAE [26] or GAN [14] to model the distribution on the specific domain. Recent works adopt VQVAE [49] and transformer [10] for image generation. However, due to the difficulties in training these models, they only work well on the specific domain, e.g., face [23]. On the other hand, the editing ability of these models is relatively weak since the feature space of GAN is high-level, and the quantified tokens can not be considered individually. Another type of method focuses on text-to-image generation. DALL-E [40, 41] and CogView [8] train an image generative pre-training transformer (GPT) to generate images from a CLIP [34] text embedding. Recent models [42, 44] benefit from the stability of training diffusion-based model [19]. These mod"
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+                                    "content": "els can be scaled by a huge dataset and show surprisingly good results on text-to-image generation by integrating large language model conditions since its latent space has spatial structure, which provides a stronger edit ability than previous GAN [23] based methods. Generating videos is much more difficult than images. Current methods rely on the larger cascaded models [18, 45] and dataset. Differently, magic-video [56] and gen1 [9] initialize the model from text-to-image [42] and generate the continuous contents through extra time-aware layers. Recently, Tune-A-Video [52] overfits a single video for text-based video generation. After training, the model can generate related motion from similar prompts. However, the results from this model are too flickering to achieve realistic local editing. Inspired by the image editing methods and tune-a-video, our method can edit the style of the real-world video and images using the trained text-to-image model [42] and shows better object replacing performance than the one-shot finetuned video diffusion model [52] with simple DDIM inversion [46] in real videos (Fig. 7)."
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+                                    "content": "Image Editing in Diffusion Model. Many recent works adopt the trained diffusion model for editing. SDEdit [33] generates content for a new prompt by adding noise to the image first. DiffEdit [6] computes the edit mask by the noise differences of the text prompts, and then, blends the inversion noises into the image generation process. Similar work has also been proposed by Blended Diffusion [2, 3], which combines the features of each step for image blending. Plug-"
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+                                    "content": "and-play [48] gets the inversion noise and applies the denoising for feature reconstruction. After that, the self-attention features in editing are replaced with that in reconstruction directly. Pix2pix-Zero [38] edits the image with the cross-attention guidance. Prompt-to-Prompt [16] proves that images can be edited via reweighting the cross-attention map of different prompts. There are also some methods to achieve better editing ability via optimization [25, 35]. However, a naive frame-wise application of these image methods to video results in flickering and inconsistency among frames."
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+                                    "content": "We target zero-shot text-driven video editing (e.g., style, attribute, and shape) without optimization for each target prompt or the user-provided mask. In Sec. 3.1, we first give the details of the latent diffusion and DDIM inversion. After that, we introduce our method that enables video appearance editing (Sec. 3.2) via the pre-trained text-to-image models [42]. Finally, we discuss a more challenging case that also enables the shape-aware editing of video using the video diffusion model in Sec. 3.3. Notice that, the proposed method is a general editing method and can be used in various text-to-image or text-to-video models. In this paper, we majorly use Stable Diffusion [42] and the video generation model based on Stable Diffusion (Tune-A-Video [52]) for its popularity and generalization ability."
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+                                            "type": "text",
+                                            "content": "Figure 3. Zero-shot local attributed editing (cat "
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+                                            "type": "text",
+                                            "content": " tiger) using stable diffusion. In contrast to fusion with attention during reconstruction (a) in previous work [16, 38, 48], our inversion attention fusion (b) provides more accurate structure guidance and editing ability, as visualized on the right side."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "content": " stands for the noise "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " predicted at "
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+                                    "type": "text",
+                                    "content": " timestep."
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+                                    "type": "text",
+                                    "content": "Such that the inverted latent "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{z}_T"
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+                                    "type": "text",
+                                    "content": " can reconstruct a latent "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{z}_0(p_{src}) = \\mathrm{DDIM}(\\hat{z}_T, p_{src})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " similar to the clean latent "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " at classifier-free guidance scale "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "s_{cfg} = 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Recently, image editing methods [16,35,38,48] use a large classifier-free guidance scale "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "s_{cfg} \\gg 1"
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+                                    "type": "text",
+                                    "content": " to edit the latent as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{z}_0(p_{edit}) = \\mathrm{DDIM}(\\hat{z}_T, p_{edit})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (second row in Fig 3(a)), where a reconstruction of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{z}_0(p_{src})"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is conducted in parallel to provide attention constraints. (first row in Fig 3(a))."
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "3.2. FateZero Video Editing"
+                                }
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+                                    "type": "text",
+                                    "content": "As shown in Fig. 2, we use the pretrained text-to-image model, i.e., Stable Diffusion, as our base model, which contains a UNet for "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": "-timestep denoising. Instead of straightforwardly exploiting the regular pipeline of latent editing guided by reconstruction attention, we have made several critical modifications for video editing as follows."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Inversion Attention Fusion. Direct editing using the inverted noise results in frame inconsistency, which may be attributed to two factors. First, the invertible property of DDIM discussed in Eq. (2) and Eq. (3) only holds in the limit of small steps [46, 47]. Nevertheless, the present requirements of 50 DDIM denoising steps lead to an accumulation of errors with each subsequent step. Second, using a large classifier-free guidance "
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+                                    "type": "text",
+                                    "content": " can increase the edit ability in denoising, but the large editing freedom leads to inconsistent neighboring frames. Therefore, previous methods require optimization of text-embedding [16] or other"
+                                }
+                            ]
+                        }
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+                                    "content": "While the issues seem trivial in the context of single-frame editing they can become magnified when working with video as even minor discrepancies among frames will be accentuated along the temporal indexes."
+                                }
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+                                    "type": "text",
+                                    "content": "To alleviate these issues, our framework utilizes the attention maps during inversion steps (Eq. (3)), which is available because the source prompt "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "content": " and initial latent "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " are provided to the UNet during inversion. Formally, during inversion, we store the intermediate self-attention maps "
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+                                    "type": "inline_equation",
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+                                    "content": " at each timestep "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and the final latent feature maps "
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+                                    "type": "interline_equation",
+                                    "content": "z _ {T}, \\left[ c _ {t} ^ {\\mathrm {s r c}} \\right] _ {t = 1} ^ {T}, \\left[ s _ {t} ^ {\\mathrm {s r c}} \\right] _ {t = 1} ^ {T} = \\operatorname {D D I M} - \\operatorname {I N V} \\left(z _ {0}, p _ {s r c}\\right), \\tag {4}",
+                                    "image_path": "f4a57eb97f4d2d2aa09cc3b8c24586b23689f2ac241d647afa1987476667b459.jpg"
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+                                    "type": "text",
+                                    "content": "where DDIM-INV stands for the DDIM inversion pipeline discussed in Eq. (3). During the editing stage, we can obtain the noise to remove by fusing the attention from inversion:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {\\epsilon} _ {t} = \\text {A T T - F U S I O N} \\left(\\varepsilon_ {\\theta}, z _ {t}, t, p _ {\\text {e d i t}}, c _ {t} ^ {\\text {s r c}}, s _ {t} ^ {\\text {s r c}}\\right). \\tag {5}",
+                                    "image_path": "2aa78e8faee815b7eb0cc1cb950c565a0b4f49ee4a51345447c3ccd7a89c28a1.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "content": " represents the modified prompt. In function ATT-FUSION, we inject the cross-attention maps of the unchanged part of the prompt similar to Prompt-to-Prompt [16]. We also replace self-attention maps to preserve the original structure and motion during the style and attribute editing."
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+                                    "content": "Fig. 3 shows a toy comparison example between our attention fusion method and the typical method with simply inversion and then generation as in [16, 35] for image editing. The cross-attention map during inversion captures the silhouette and the pose of the cat in the source image, but the map during reconstruction has a noticeable difference. While in the video, the attention consistency might influence the temporal consistency as shown in Fig. 8. This is because the spatial-temporal self-attention maps represent the correspondence between frames and the temporal modeling ability of existing video diffusion model [52] is not satisfactory."
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+                                    "content": "Attention Map Blending. Inversion-time attention fusion might be insufficient in local attrition editing, as shown in an image example in Fig. 4. In the third column, replacing self-attention "
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+                                    "content": "Different from appearance editing, reforming the shape of a specific object in the video is much more challenging. To this end, a pretrained video diffusion model is needed. Since there is no publicly-available generic video diffusion model, we perform the editing on the one-shot video diffusion model [52] instead. In this case, we compare our editing method with simple DDIM inversion [46], where our method also achieves better performance in terms of editing ability, motion consistency, and temporal consistency. It might be because it is hard for an inflated model to overfit the exact motion of the input video. While in our method, the motion and structure are represented by high-quality spatial-temporal attention maps "
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+                                    "content": " during inversion, which is further fused with the attention maps during editing. More details can be founded in Fig. 7 and the supp. video."
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+                                    "content": ". For shape editing, we utilize the pretrained model of the specific video [52] at 100 iterations and fuse the attention at DDIM timestep "
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+                                    "content": ", giving more freedom for new shape generation. Following previous works [4,9], we use videos from DAVIS [39] and other in-the-wild videos to evaluate our approach. The source prompt of the video is generated via the image caption model [31]. Finally, we design the target prompt for each video by replacing or adding several words."
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+                                            "html": "<table><tr><td>Method</td><td colspan=\"2\">CLIP Metrics↑</td><td colspan=\"3\">User Study↓</td></tr><tr><td>Inversion &amp; Editing</td><td>Tem-Con</td><td>Fram-Acc</td><td>Edit</td><td>Image</td><td>Temp</td></tr><tr><td>Frameswise Null &amp; p2p [16,35]</td><td>0.852</td><td>0.958</td><td>3.55</td><td>4.11</td><td>4.38</td></tr><tr><td>Frameswise SDEdit [33]</td><td>0.910</td><td>0.819</td><td>3.69</td><td>3.28</td><td>3.62</td></tr><tr><td>NLA, Null &amp; p2p [16,24,35]</td><td>0.949</td><td>0.600</td><td>3.17</td><td>3.02</td><td>2.60</td></tr><tr><td>Tune-A-Video &amp; DDIM [46,52]</td><td>0.958</td><td>0.750</td><td>2.78</td><td>2.80</td><td>2.70</td></tr><tr><td>Ours</td><td>0.965</td><td>0.903</td><td>1.82</td><td>1.79</td><td>1.69</td></tr></table>",
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+                                    "content": "Table 1. Quantitative evaluation against baselines. In our user study, the results of our method are preferred over those from baselines. For CLIP-Score, we achieve the best temporal consistency and comparable framewise editing accuracy against an optimization-based image editing method [35]."
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+                                    "content": "and color of the feather are modified by the target prompt Swarovski crystal and kept consistent across frames. In the second and third rows, our framework applies abstract style (Ukiyo-e and Makoto Shinkai). The image structure and temporal motion can be well preserved since we fuse both the spatial-temporal self-attention and cross-attention during the inversion and editing stage."
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+                                    "content": "Shape-aware editing. Fig. 5 and the second row in Fig.1 present the result of difficult object shape editing, with a pretrained video model [52]. This task is challenging because a naive full-resolution fusion of the spatial-temporal self-attention maps results in inaccurate shape results and wrong temporal motion, as shown in the ablation (Fig.9). Thanks to the proposed Attention Blending, we combine the motion of generated shape from the editing target and inverted attention from the input video. Results of porsche, duck and flamingo show that we generate new content with poses and positions similar to input videos."
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+                                    "content": "Zero-shot image editing. In addition, our framework can serve as a zero-shot image editing method such as local attribute editing (Fig. 3) and object shape editing (Fig. 4) by considering an image as a video with a single frame. We provide more results in our supplementary material."
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+                                            "content": "Figure 8. Inversion attention compared with reconstruction attention using prompt 'deserted shore "
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+                                            "content": " 'glacier shore'. The attention maps obtained from the reconstruction stage fail to detect the boat's position, and can not provide suitable motion guidance for zero-shot video editing."
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+                                    "content": "Since there are no available zero-shot video editing methods based on diffusion models, we build the following four state-of-the-art baselines for comparison. (1) Tune-A-Video [52] overfits an inflated diffusion model on a single video to generate similar content. (2) The Neural Layered Atlas [24] (NLA) based method is combined with keyframe-editing via state-of-the-art image editing methods [16, 35]. (3) Frame-wise Null-text optimization [35] and then edit by prompt2prompt [16]. (4) Frame-wise zero-shot editing using SDEdit [33]. For attention-based editing (2,3,4), we use the same timesteps fusion parameters as ours."
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+                                    "content": "We conduct the quantitative evaluation using the trained CLIP [34] model as previous methods [9, 38, 52]. Specially, we show the 'Tem-Con' [9] to measure the temporal consistency in frames by computing the cosine similarity between all pairs of consecutive frames. 'Frame-Acc' [17, 34, 38] is the frame-wise editing accuracy, which is the percentage of frames where the edited image has a higher CLIP similarity to the target prompt than the source prompt. In addition, three user studies metrics (denoted as 'Edit', 'Image', and 'Temp') are conducted to measure the editing quality, overall frame-wise image fidelity, and temporal consistency of the video, respectively. We ask 20 subjects to rank different methods with 9 sets of comparisons in each study. From Tab. 1, the proposed zero-shot method achieves the best temporal consistency against baselines and shows a comparable frame-wise editing accuracy as the pre-frame optimization method [35]. As for the user studies, the average ranking of our method earns user preferences the best in three aspects."
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+                                    "content": "To provide a qualitative comparison, Fig.7 provides the results of our method and other baselines at two different frames. The editing result of framewise SDEdit [33] can not be localized and varies a lot among different frames. Framewise Null inversion achieves local editing at the cost of 500-iterations optimization for each frame but is still temporally inconsistent. NLA-based [24] method preserves the exact"
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+                                    "content": "pixels in the atlas. However, it struggles to perform editing that involves new shapes or 3D structures. In addition, it takes hours to optimize the neural atlas for each input video. While Tune-A-Video [52] with DDIM [46] ranks second in editing quality and image fidelity of Tab. 1, we observe that it has difficulty in reproducing the exact motion and spatial position as input video (right side of Fig.7). Besides, the background has annoying artifacts. Different from the above baselines, our method preserves the motion by fusion the attention during inversion and editing. Thus, our results outperform others by a large margin in our user study and frame consistency measured by CLIP."
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+                                    "type": "text",
+                                    "content": "Attention during inversion. In the right column of Fig. 8, we use the attention map during reconstruction instead of inversion for zero-shot background editing. The visualized cross-attention map of the word 'boat' in the first and last frame can not capture the correct position and structure of the boat, which may be caused by the poor temporal modeling capacity of the image diffusion model and the accumulation of errors in DDIM inversion. In contrast, we propose using attention during inversion as the middle column, which provides stable guidance of semantic layout in the original video. We observe this huge difference in attention maps between inversion and reconstruction exists in most videos."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Attention Blending Block is studied in Fig. 9, where we remove all self-attention fusion or fuse all self-attention with"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "out a spatial mask. The third column shows that removing all self-attention maps brings a loss of fine details ( e.g., fences, poles, and trees in the background) and inconsistency of car identity over time. In contrast, if we fuse full-resolution self-attention as in the previous work [16], the shape editing ability of the framework can be severely degraded so that the geometry of generated car resembles the input video, especially in the last few frames. Therefore, we propose to blend the self-attention maps with a mask obtained from cross-attention to preserve unedited details and ensure temporal consistency while editing the object shape."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this paper, we propose a new text-driven video editing framework FateZero that performs temporal consistent zero-shot editing of attribute, style, and shape. We make the first attempt to study and utilize the cross-attention and spatial-temporal self-attention during DDIM inversion, which provides fine-grained motion and structure guidance at each denoising step. A new Attention Blending Block is further proposed to enhance the shape editing performance of our framework. Our framework benefits video editing using widely existing image diffusion models, which we believe will contribute to a lot of new video applications."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Limitation & Future Work. While our method achieves impressive results, it still has some limitations. During shape editing, since the motion is produced by the one-shot video diffusion model [52], it is difficult to generate totally new motion (e.g., 'swim' "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\rightarrow"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " 'fly') or very different shape (e.g., 'swan' "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        369,
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+                                    "type": "inline_equation",
+                                    "content": "\\rightarrow"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        369,
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+                                        453
+                                    ],
+                                    "type": "text",
+                                    "content": " 'pterosaur'). We will test our method on the generic pretrained video diffusion model for better editing abilities."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                            ],
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[1] https://civitai.com, 2020. 2, 3"
+                                        }
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+                            "lines": [
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                670,
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+                                            "bbox": [
+                                                53,
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+                                            "type": "text",
+                                            "content": "[6] Guillaume Couairon, Jakob Verbeek, Holger Schwenk, and Matthieu Cord. Diffedit: Diffusion-based semantic image editing with mask guidance. arXiv preprint arXiv:2210.11427, 2022. 2, 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
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+                                            "bbox": [
+                                                312,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[7] Prafulla Dhariwal and Alex Nichol. Diffusion models beat gans on image synthesis. Neural Information Processing Systems, 2021. 4"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                312,
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+                                            "bbox": [
+                                                312,
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+                                            "type": "text",
+                                            "content": "[8] Ming Ding, Zhuoyi Yang, Wenyi Hong, Wendi Zheng, Chang Zhou, Da Yin, Junyang Lin, Xu Zou, Zhou Shao, Hongxia Yang, et al. Cogview: Mastering text-to-image generation via transformers. Advances in Neural Information Processing Systems, 34:19822-19835, 2021. 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                312,
+                                162,
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+                            ],
+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
+                                                312,
+                                                162,
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+                                                205
+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                308,
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+                                            "type": "text",
+                                            "content": "[10] Patrick Esser, Robin Rombach, and Bjorn Ommer. Taming transformers for high-resolution image synthesis. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 12873-12883, 2021. 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                308,
+                                250,
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+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[11] Jakub Fiser, Ondrej Jamriška, Michal Lukáč, Eli Shechtman, Paul Arente, Jingwan Lu, and Daniel Sykora. Stylit: illumination-guided example-based stylization of 3d renderings. ACM Transactions on Graphics (TOG), 35(4):1-11, 2016. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                308,
+                                304,
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+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
+                                308,
+                                350,
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+                                392
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
+                                308,
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+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
+                                                308,
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+                                            "type": "text",
+                                            "content": "[14] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11):139–144, 2020. 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
+                            "bbox": [
+                                308,
+                                437,
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+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[15] Yingqing He, Tianyu Yang, Yong Zhang, Ying Shan, and Qifeng Chen. Latent video diffusion models for high-fidelity video generation with arbitrary lengths. arXiv preprint arXiv:2211.13221, 2022. 2, 5"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
+                                308,
+                                482,
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+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[16] Amir Hertz, Ron Mokady, Jay Tenenbaum, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or. Prompt-to-prompt image editing with cross attention control. arXiv preprint arXiv:2208.01626, 2022. 2, 4, 5, 7, 8, 9"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                                            "type": "text",
+                                            "content": "[17] Jack Hessel, Ari Holtzman, Maxwell Forbes, Ronan Le Bras, and Yejin Choi. Clipscore: A reference-free evaluation metric for image captioning. Empirical Methods in Natural Language Processing, 2021. 8"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22
+                        },
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+                                        }
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diff --git a/2023/Fcaformer_ Forward Cross Attention in Hybrid Vision Transformer/5726ddf1-d837-42aa-9a96-e54cdcd1f294_content_list.json b/2023/Fcaformer_ Forward Cross Attention in Hybrid Vision Transformer/5726ddf1-d837-42aa-9a96-e54cdcd1f294_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad7a131cbd4b6ba4a8c8ec88f0e76e6213993c1c
--- /dev/null
+++ b/2023/Fcaformer_ Forward Cross Attention in Hybrid Vision Transformer/5726ddf1-d837-42aa-9a96-e54cdcd1f294_content_list.json	
@@ -0,0 +1,1570 @@
+[
+    {
+        "type": "text",
+        "text": "Fcaformer: Forward Cross Attention in Hybrid Vision Transformer",
+        "text_level": 1,
+        "bbox": [
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+            130,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Haokui Zhang $^{1,2}$ , Wenze Hu $^{1}$ , Xiaoyu Wang $^{3}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup>Intellifusion <sup>2</sup>Yan'an University",
+        "bbox": [
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+            198,
+            614,
+            217
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>3</sup>The Hong Kong University of Science and Technology (Guangzhou)",
+        "bbox": [
+            210,
+            215,
+            759,
+            234
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
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+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Currently, one main research line in designing a more efficient vision transformer is reducing the computational cost of self attention modules by adopting sparse attention or using local attention windows. In contrast, we propose a different approach that aims to improve the performance of transformer-based architectures by densifying the attention pattern. Specifically, we proposed forward cross attention for hybrid vision transformer (FcaFormer), where tokens from previous blocks in the same stage are secondary used. To achieve this, the FcaFormer leverages two innovative components: learnable scale factors (LSFs) and a token merge and enhancement module (TME). The LSFs enable efficient processing of cross tokens, while the TME generates representative cross tokens. By integrating these components, the proposed FcaFormer enhances the interactions of tokens across blocks with potentially different semantics, and encourages more information flows to the lower levels. Based on the forward cross attention (Fca), we have designed a series of FcaFormer models that achieve the best trade-off between model size, computational cost, memory cost, and accuracy. For example, without the need for knowledge distillation to strengthen training, our FcaFormer achieves  $83.1\\%$  top-1 accuracy on Imagenet with only 16.3 million parameters and about 3.6 billion MACs. This saves almost half of the parameters and a few computational costs while achieving  $0.7\\%$  higher accuracy compared to distilled EfficientFormer. Code is available at https://github.com/hkzhang-git/FcaFormer",
+        "bbox": [
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+            300,
+            472,
+            738
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            768,
+            209,
+            784
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the rapid adoption of transformer structures in the computer vision community, several types of attention patterns have been proposed to enhance the performance or speed of transformer models. For instance, ViT [5] employs the vanilla global multi-head self-attention, Swin Transformers [20] uses local windowed attention, MaxViT [32] incorporates grid attention across interleaved",
+        "bbox": [
+            75,
+            794,
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+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "tokens, and Dynamic ViT [28] utilizes attention on progressively pruned tokens. These approaches aim to sparsify the attention patterns of the original ViT to achieve a better trade-off between speed and accuracy.",
+        "bbox": [
+            496,
+            268,
+            890,
+            330
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In contrast, we propose a new model block as well as a family of models called FcaFormer, which improves the performance of vision transformers by further densifying the attention patterns at a limited extra cost. Specifically, we propose to connect the input of the standard multi-head attention (MHA) module with extra tokens transformed from previous blocks in the same stage, while still restricting the attention module to output the original amount of tokens. To further reduce the computational cost, we merge the tokens from previous blocks by using depthwise convolutions with large strides. These tokens are further calibrated by scaling them with learned parameters, before being taken into the attention units in subsequent blocks.",
+        "bbox": [
+            496,
+            333,
+            892,
+            529
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The new forward cross attention connection has several advantages: 1) it helps transformers further exploit the interactions of tokens across different levels; 2) it reuses the previously generated tokens so that some of the information no longer needs to be preserved by the subsequent transformer operations, leading to potentially smaller models with similar accuracy; 3) similar to the residual connections in ResNet, this extra cross layer connection encourages more information flows to the lower levels of the network, which further accelerate the convergence.",
+        "bbox": [
+            496,
+            532,
+            893,
+            683
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The newly densified connections come with a limited increase in computational cost. As explained in Section 3.3, this cost increase is linear rather than quadratic, since we keep the number of output tokens the same as in standard ViTs. Furthermore, most of the computation cost in most hybrid vision transformer architectures is in the feed forward network (FFN) rather than the MHA part of transformer blocks. Thus, the linear growth of computational complexity from densified connections does not significantly affect the overall computation cost. Finally, to further reduce the number of extra inputs, we use depthwise convolutions with large kernels and long strides to aggregate tokens from previous blocks.",
+        "bbox": [
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+            686,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We have incorporated the proposed Fca design into two",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            2,
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+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "6060",
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+    {
+        "type": "text",
+        "text": "typical classes of transformer models: the plain ViT model used in DeiT, and the hybrid ConvNet and transformer structures frequently seen in recent works [24, 9, 17]. Our experiments demonstrate that the Fca block can seamlessly replace the corresponding transformer blocks in these architectures, leading to significantly improved performance compared to their corresponding baselines. Specifically, FcaFormer-L1 achieves a top-1 accuracy of  $80.3\\%$  with approximately 6.2 million parameters and about 1.4 billion MACs. This is achieved while saving almost half the number of parameters, and achieving  $1.1\\%$  higher accuracy compared to the recently proposed EfficientFormer. Table 2 displays the comparison results.",
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+        "type": "text",
+        "text": "The contribution of this paper is summarized as follows.",
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+            "- Opposite to many recent works that use sparse attentions to improve transformer models, we propose to design more efficient models by densifying the attention connection patterns, which open up a new and worthwhile research avenue for consideration.",
+            "- We propose the FcaFormer block, which leverages existing tokens and enhance interactions across different levels. To achieve this, we introduce two new components: learnable scale factors (LSFs) and a token merge and enhancement module (TME). The LSFs allow us to effectively process cross tokens, while the TME generates representative cross tokens. Together, these components improve the performance of the FcaFormer models.",
+            "- Based on the proposed FcaFormer block, we constructed several new models which have demonstrated better performance than various other recently proposed models."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.1. Pure vision transformers",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Dosovitskiy et al. introduced transformer model into vision tasks and proposed the ViT [5]. It cropped an image into  $16 \\times 16$  patches as an input token sequence to the transformer and used positional encoding to model spatial relations among tokens. DeiT [31] lowered the difficulty of ViT model training by knowledge distillation, and achieved competitive accuracy with less pretraining data. To further improve the model architecture, researchers attempted to optimize the ViT toward improving its computational efficiency. Among them, the Swin transformer [20] computes self attention among shifted local windows. The MaxViT [32] uses block attention and grid attention alternatively to keep spatially global information exchange while significantly reduce the number of tokens involved in the self attention computation. The DynamicViT [28] prunes redundant tokens progressively and dynamically depending on",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "the input features. Mohsen et al. [7] proposed a differentiable parameter-free adaptive token sampler and plugged it into ViTs to sample part tokens for attention computation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Except for the DeiT, all methods above keep pure vision transformer architectures and seek to achieve better accuracy speed trade-off by using sparse attention via reducing the number of tokens in attention patterns. In contrast, we propose to achieve this goal by densifying the attention pattern, reusing existing tokens from previous blocks. Such interactions promote attentions across features of different semantic levels, which is very common in ConvNets and many methods before the wide adoption of deep learning.",
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+    {
+        "type": "text",
+        "text": "2.2. Hybrid ConvNet and vision transformers",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Rather than simplifying ViTs, another popular line of research is to combine elements of ViTs and ConvNets to form new backbones. Two early attempts can be found in [9, 39], where ConvNet blocks are employed to extract low level information in early stages and ViT blocks are adopted in deep stages. Such a hybrid structure improves optimization stability and model performance. Similarly, BoTNet [30] replaces the standard convolution with multi-head attention in the last few blocks of ResNet. In [24], the deeper stages of MobileNetv2 [29] are replaced with their proposed MobileViT block. There are other hybrid models which mix convolution operation with self attention and channel mixer operations. For example, ConViT[6] incorporates soft convolutional inductive biases via a gated positional self-attention. CMT [10] and Next-ViT [15] insert both convolution operation and self attention module into a single block. PVT v1 [36], PVT v2 [37], LIT [27] and LIT v2 [26] insert convolutional operations into each stage of ViT models to reduce the number of tokens, and build hybrid multi-stage structures.",
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+    {
+        "type": "text",
+        "text": "Generally speaking, hybrid models achieve better tradeoff between model cost and accuracy compared with pure vision transformer models. Therefore, we mainly focus on applying forward cross attention design on hybrid models to evaluate its effects. Our work is complementary to these hybrid design attempts, and can be used to replace the transformer part for most of these models.",
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+    {
+        "type": "text",
+        "text": "2.3. Skip connections in ConvNets",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In retrospect, our work is also related to several key improvements in ConvNets design that introduces extra connections to improve the information flows.",
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+    {
+        "type": "text",
+        "text": "ResNet [13] employs shortcut connections to overcome the degradation problem, where accuracy gets saturated and then degrades rapidly with the increasing convolutional network depth. DenseNet [14] connects each layer to every other layer in a feedforward fashion. As with ResNet that builds the whole network by stacking several residual units, DenseNet consists of multiple dense blocks. Wang et",
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "6061",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/0bdc43c6ca161f3e4e25ee7230d62a58a6882fc6deb904d9e8fb6a457d68b903.jpg",
+        "image_caption": [
+            "Figure 1. A FcaFormer stage which consists of  $L$  FcaFormer blocks. Compared with standard ViT blocks, we add token merge and enhancement (TME) part, which uses long stride large kernel convolutions to merge tokens spatially as cross tokens, and small kernel convolutions to further enhance tokens for channel mixing (FFN). The cross tokens are then used in later blocks as extra tokens for multi-head attention, after being calibrated by multiplying them with learned scaling factors (LSFs,  $\\alpha$ )."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "al. [35] further improve DenseNet by using two-way dense layers to obtain different receptive fields. With limited extra computational cost, these model design choices solved bottlenecks existed in ConvNets and are still widely used in both academia and industry. Skip connection is also used in transformer models. For instance, Denseformer [22] reuses the first layer CLS token into subsequent layers.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Our proposed forward cross attention is similar to the works above in that it reuses existing intermediate results and introduces extra connections to the overall network structure. As experiments show, our work introduces similar benefits to transformer models such as better model performance and faster model convergence.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.4. Cross attention transformers",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "In transformers, cross attention is usually used to mix two different embedding sequences. In [34, 8], the output of encoder is fed to decoder via cross attention. CrossViT [1] mixes small-patch and large-patch tokens with cross attention to extract multi-scale feature. Our proposed FcaFormer shares the basic idea of integrating information with cross attention. However, unlike previous models, our FcaFormer integrates tokens from different semantic levels using TME and LSFs to overcome their distinct characteristics.",
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+    {
+        "type": "text",
+        "text": "3. The proposed FcaFormer",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.1. FcaFormer block and FcaFormer stage",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Fig.1 shows the major parts and connection relations of a FcaFormer stage which consists of  $L$  FcaFormer blocks. Each FcaFormer block is composed of three major parts, which are cross multi-head attention (CMHA), token merge and enhancement (TME), and feed forward network (FFN) respectively.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "CMHA and LSFs. Different from the standard ViT block, our proposed FcaFormer block receives two sets of tokens as input. The block in turn generates two sets of tokens as well, which are denoted as  $x^{l}$  and  $\\bar{x}^{l}$  respectively.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Taking the block at depth  $l$  as an example, the inputs are the regular tokens from its previous block  $x^{l-1}$  and a set of block cross tokens  $(\\bar{x}^{l-2}, \\bar{x}^{l-3} \\dots \\bar{x}^1)$  from earlier blocks in the stage. The CMHA takes both  $x^{l-1}$  and  $(\\bar{x}^{l-2}, \\bar{x}^{l-3} \\dots \\bar{x}^1)$  as input, but only generates  $n$  tokens  $\\tilde{y}^k$  as its output.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It is worth noting that the cross tokens are scaled by learned calibration coefficients (learnable scale factors LSFs)  $\\alpha$  before they are used in the CMHA. We found that the statistics of tokens from different semantic levels are very different. Without this calibration operation, cross tokens are hard to integrate to regular tokens in current blocks to work as we expected. Details are shown and analyzed in our ablation study part.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Specifically, given the inputs above, the query, key and value for multi-head attention modules are constructed as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nQ = W ^ {Q} x ^ {l - 1} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\nK = W ^ {K} \\left[ x ^ {l - 1}, \\left(\\mathbf {1} \\alpha^ {l}\\right) ^ {T} \\otimes \\left(\\bar {x} ^ {l - 2}, \\dots , \\bar {x} ^ {1}\\right) \\right] \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\nV = W ^ {V} \\left[ x ^ {l - 1}, \\left(\\mathbf {1} \\alpha^ {l}\\right) ^ {T} \\otimes \\left(\\bar {x} ^ {l - 2}, \\dots , \\bar {x} ^ {1}\\right) \\right] \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $W^{K}, W^{V}, W^{Q}$  are the three weight matrices transforming input into key, value and query tokens respectively. Elements in  $\\alpha \\in \\mathbb{R}^{(l - 2)\\bar{n} \\times 1}$  are the learnable scale factors for cross tokens and  $\\otimes$  denotes the element-wise multiplication where each token in  $\\bar{x}$  is multiplied by a corresponding scaling scalar in  $\\alpha$ .  $\\bar{n}$  represents the number of cross tokens for each layer.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The computed  $Q, K, V$  are then connected to the standard dot product attention operators as in the original transformer [34], which computes the globally mixed intermediate tokens  $y^{l}$ .",
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+        "page_idx": 2
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+    {
+        "type": "equation",
+        "text": "\n$$\ny ^ {l} = x ^ {l - 1} + W ^ {P} \\left[ \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}} + B\\right) V \\right] \\tag {4}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The  $B$  in Eqn.4 is a learnable matrix consisting of two parts, which are relative position bias for  $x$  and relative depth bias for  $\\bar{x}$ . The query has only  $n$  tokens, so the output  $y^{l}$  is of size  $n\\times d$ .",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "6062",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/ecfb24c89be6c5a072219f42bbafdb6d19fc43782190dbb15483c249e225b920.jpg",
+        "image_caption": [
+            "Figure 2. The detailed structure of the token merge and enhancement (TME) module."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "TME. The intermediate tokens  $y^{l}$  are then passed to the added token merge and enhancement (TME) part, which computes the cross tokens  $\\bar{x}^{l}$  and locally enhanced tokens  $z^{l}$  using two separate depthwise convolutions. As shown in Fig 2, our TME has two branches. In the token merge branch, we use a large kernel  $(7 \\times 7)$  large stride  $(s = 4)$  depthwise convolution to generate  $\\bar{x}^{l}$ , resulting in a small number of cross tokens to be used by subsequent blocks. In token enhancement branch, a standard depth wise convolution  $(3 \\times 3, s = 1)$  is used to locally mix the tokens so as to enhance the 2d spatial relations in the token sequence.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "FFN. The locally enhanced tokens  $z^l$  are then used in the standard FFN part of ViT to compute the output token  $x^l$ , which together with  $\\bar{x}^l$  are the entire output of a FcaFormer block at depth  $l$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In summary, our FcaFormer are different from vanilla ViT in following ways:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Asymmetric input and output. In our FcaFormer, CMHA part takes both regular tokens and cross tokens as input but keep the output sequence length fixed to  $n$  as in regular transformers. This is the key point that why our proposed FcaFormer only introduce limited extra computational cost. More details are explained in section 3.3.",
+            "- Cross token scale. LSFs are used to facilitate the integration of cross tokens into regular tokens. Without this calibration process, cross tokens may not function as expected. As shown in Fig 5.",
+            "- Relative depth embedding. In the CMHA part, we choose to use relative positional encoding instead of absolute ones. Apart from its generally better performance, the choice also gives model the flexibility to encode relative depth of the cross tokens, which simplifies the model design."
+        ],
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. FcaFormer Models",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The FcaFormer block is a generic block that can be grouped as FcaFormer stages to construct models. To demonstrate the universal effectiveness of our new attention",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/b344df2cc1bed0bd97968a95eb0c1c12dfa6de3bcf229c33462443f619eb210f.jpg",
+        "image_caption": [
+            "Figure 3. The overall structure of FcaFormer Mobels for image classification tasks. (a) Plain FcaFormer model. This model is directly modified from the DeiT structure. (b) Hybrid FcaFormer model. The ConvNet stages are composed of ConvNext blocks. The detailed model scaling hyperparameters are specified in Sec.3.2"
+        ],
+        "image_footnote": [],
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "pattern, we build two types of FcaFormer based models, each falls into one of the major categories of transformer related computer vision models as described in Sec. 2. The overall structure of these models for classification task are illustrated in Fig.3.",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Plain FcaFormer. As shown in Fig 3 (a), following the style of vanilla ViT, we construct our plain FcaFormer model (denoted as FcaFormer-L0). The model essentially uses one block of FcaFormer after the patch embedding layer that crops  $16 \\times 16$  patches and converts them into a token sequence. The corresponding task related head is kept unchanged compared with the original ViT model.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Hybrid FcaFormer. As illustrated in Fig 3 (b). Following the trend of combining ConvNet structures and transformer structures to build hybrid models, we also propose to build hybrid FcaFormer. Following LeViT [9] and ViTC[39], we adopt the most straightforward way to build our Hybrid FcaFormers, where there are two conventional ConvNet stages followed by two FcaFormer stages. The ConvNet stage is composed of ConvNext blocks [21] plus a downsampling layer that uses pointwise and depthwise convolutions to reduce the feature map resolution by  $4\\times$  and increases the feature map channels.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Based on the above overall structure, we build models of different sizes to compare with other works. The key scaling hyper-parameters is summarized below, where  $D$  denotes the channel size:",
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+    {
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+        "sub_type": "text",
+        "list_items": [
+            "- FcaFormer-L0:  $\\mathrm{D} = {192},\\mathrm{\\;L} = {12}$",
+            "- FcaFormer-L1:  $\\mathrm{D} = (64,128,192,320)$ ,  $\\mathrm{L} = (2,2,6,2)$",
+            "- FcaFormer-L2:  $\\mathrm{D} = (96,192,320,480)$ ,  $\\mathrm{L} = (2,2,7,2)$"
+        ],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "6063",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/07e590efac5d797eef80da9500c72857cd161383fce4687c48770f29ea8891d8.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/28ad74d18a1d6131fca9777b3b6c2148fcc36cab536efd672a7c70da99170fc0.jpg",
+        "image_caption": [
+            "(b)"
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+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/9d0b144f8b10ae0d457fbc928ede1a3606c51b547569d109055ab3deb29c5fb2.jpg",
+        "image_caption": [
+            "(c)",
+            "Figure 4. Computational cost analysis. (a) Detailed analysis on the number of parameters and MACs for a transformer block; (b)-(c) Computation decompositions in blocks of stage 3 of DeiT-Tiny and stage 4 of EfficientFormer-L1 respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Computational Complexity of FcaFormer",
+        "text_level": 1,
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "In terms of computational complexity, transformers are notorious for its  $\\mathcal{O}(n^2)$  scaling property, which is why so many prior works try to reduce the inputs to the MHA model. However, the extra computational cost of densifying the attention pattern is rather limited in our FcaFormer models, because of the following reasons:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1) The added extra computation is restricted to the MHA part, since we keep the output sequence length of MHA fixed to  $n$  as in regular transformers. This leads to linear scaling cost in terms of the number of additional input tokens, which itself is a small  $\\left( (l - 1) * n / s^2 \\right)$  compared with  $n$ . The computational cost of FFN part is kept unchanged compared with original ViT blocks.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2) In vision transformer model families, the FFN part actually constitutes the majority of computations. In [19], Liu et al. also emphasized that larger models incur higher computational costs, primarily due to FFNs. Here, we delve into a more detailed analysis. This is paradoxical to the fact that MHA scales at  $\\mathcal{O}(n^2)$  while FFN scales at  $\\mathcal{O}(n)$ , largely because that the neglected constant token size  $d$  in big O analysis is rather large and scales poorly. Fig. 4 details the exact adds and multiplications (MACs) of a standard ViT block in terms of the number of tokens  $n$  and the dimension of tokens  $d$ . Taking the transformer block DeiT-Tiny as an example, because  $n = 196$  and  $d = 192$  are at the same scale, the  $2n^2 d$  MACs in MHA is much less compared with that  $(8nd^2)$  of FFN ( $15\\%$  vs  $56\\%$  respectively). For models in pyramid shapes such as swim transformers where  $n < d$ , the majority skews even more towards FFN because of the local windowing effect. Compared with the reference models, our FcaFormer variants only introduce about  $13\\%$  extra computational cost.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "It looks like that the proposed FcaFormer is heavier than its reference model as it introduces extra computations. However, the counter-intuitive fact is that FcaFormer can",
+        "bbox": [
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+            854,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/db8e8d476bc26d1ad2c22b8cc18473e9499c3a0d5abd6ec0b7764eeb4666c88d.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. Comparison with baselines. The plain version FcaFormer is based on DeiT-T. The hybrid ViT FcaFormer models are based on ConvNext and Swin Transformers.  $\\ddagger$ means our implementation"
+        ],
+        "table_body": "<table><tr><td>Models</td><td># params. (M)</td><td>FLOPs (G)</td><td>Top1 acc</td></tr><tr><td>DeiT-T [31]</td><td>5.5</td><td>1.23</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>5.9.</td><td>1.49</td><td>74.3</td></tr><tr><td>Swin-1G‡</td><td>6.3</td><td>1.5</td><td>78.4</td></tr><tr><td>FcaFormer-L1</td><td>6.2</td><td>1.4</td><td>80.3</td></tr><tr><td>ConvNext-Tiny [21]</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>Swin-Tiny [20]</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>FcaFormer-L2</td><td>16.3</td><td>3.6</td><td>83.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "be more light-weight than its reference model. As is mentioned in introduction, FcaFormer reuses tokens from previous blocks, enhances interaction of tokens across blocks and improve information flow. Compared with the vanilla ViT, FcaFormer has better parameter efficiency. Therefore, FcaFormer can get comparable or even better performance with fewer layers and channels. Our experiments further verifies this advantage.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In addition to the detailed analysis above, we want to point out that the prior efforts to sparsify the attention patterns spatially in Sec.2.1 and our proposal to densify the attention patterns across semantic levels are complementary to each other. While not the key emphasis of this paper, it is definitely worth exploring if the two types of designs can be combined to yield even more efficient and performant models.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct image classification experiments on Imagenet-1K [3], semantic segmentation experiments on ADE20K [44], and object detection experiments on MS-COCO [18] to evaluate our proposed models. We first compare the proposed FcaFormers with our baselines and the previous SOTA methods. Then, we conduct detailed study to show the effectiveness of our design choices.",
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+    },
+    {
+        "type": "text",
+        "text": "4.1. ImageNet classification",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Experiment settings. The FcaFormer-L0 is implemented based on code of DeiT<sup>1</sup>. The hybrid FcaFormer models are implemented based on code of ConvNext<sup>2</sup> and Swin<sup>3</sup>. We follow the training recipes in DeiT [31] to train our FcaFormer-L0, except that we did not use the knowledge distillation. To train the hybrid FcaFormers, we use the same training hyper parameters and augmentations as used in ConvNext except that the batch size is restricted to 1024 and the initial learning rate is reduced to 2e-3. This change is because we don't have enough GPUs to support the default batch size of 4096 in ConvNext.",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "$^{1}$ https://github.com/facebookresearch/deit",
+            "$^{2}$ https://github.com/facebookresearch/ConvNeXt",
+            "<sup>3</sup>https://github.com/microsoft/Swin-Transformer"
+        ],
+        "bbox": [
+            517,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "6064",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/f479625fc575a7542f5b2a0d1708406a7df536f2e9dad1503aeec632b75b1361.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 2. Comparison with the SOTA methods on ImageNet-1K validation set. KD means knowledge distillation is used. ‡ indicates implemented by us, where models are trained following the training setting used in ConvNext. Accuracy and FLOPs are calculated on input image size  ${224} \\times  {224}$  . † borrowed from [2]"
+        ],
+        "table_body": "<table><tr><td>Models</td><td>KD</td><td>Type</td><td>Param.</td><td>MACs</td><td>Top1</td></tr><tr><td>DeiT-Tiny [31]</td><td>Y</td><td>ViT</td><td>6</td><td>-</td><td>74.5</td></tr><tr><td>DeiT-Tiny [31]</td><td>-</td><td>ViT</td><td>6</td><td>-</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>-</td><td>ViT</td><td>6</td><td>-</td><td>74.3</td></tr><tr><td>LeViT-128 [9]</td><td>Y</td><td>Hybrid</td><td>9</td><td>0.4</td><td>78.6</td></tr><tr><td>EfficientFormer-L1 [17]</td><td>Y</td><td>Hybrid</td><td>12</td><td>1.3</td><td>79.2</td></tr><tr><td>ParCNet [43]</td><td>-</td><td>Conv</td><td>5</td><td>1.7</td><td>78.6</td></tr><tr><td>TNT-Ti [12]</td><td>-</td><td>ViT</td><td>6</td><td>1.4</td><td>73.9</td></tr><tr><td>Swin-1G† [20]</td><td>-</td><td>ViT</td><td>7</td><td>1.0</td><td>77.3</td></tr><tr><td>Swin-2G† [20]</td><td>-</td><td>ViT</td><td>13</td><td>2.0</td><td>79.2</td></tr><tr><td>EfficientFormer-L1‡</td><td>-</td><td>Hybrid</td><td>12</td><td>1.3</td><td>76.1</td></tr><tr><td>MobileViT-V1 [24]</td><td>-</td><td>Hybrid</td><td>6</td><td>2.0</td><td>78.4</td></tr><tr><td>EdgeViT-XS [25]</td><td>-</td><td>Hybrid</td><td>7</td><td>1.1</td><td>77.5</td></tr><tr><td>MobileViTV2[29]</td><td>-</td><td>Hybrid</td><td>5</td><td>1.8</td><td>78.1</td></tr><tr><td>CoaT-Tiny [40]</td><td>-</td><td>Hybrid</td><td>6</td><td>4.4</td><td>78.3</td></tr><tr><td>PVT-V2-B1 [37]</td><td>-</td><td>Hybrid</td><td>13</td><td>2.1</td><td>78.7</td></tr><tr><td>Mobile-Former [2]</td><td>-</td><td>Hybrid</td><td>14</td><td>0.5</td><td>79.3</td></tr><tr><td>Edgenext [23]</td><td>-</td><td>Hybrid</td><td>6</td><td>1.3</td><td>79.4</td></tr><tr><td>MobileOne-S4 [33]</td><td>-</td><td>Hybrid</td><td>15</td><td>3.0</td><td>79.4</td></tr><tr><td>FcaFormer-L1</td><td>-</td><td>Hybrid</td><td>6</td><td>1.4</td><td>80.3</td></tr><tr><td>DeiT-S [31]</td><td>Y</td><td>ViT</td><td>22</td><td>4.6</td><td>81.2</td></tr><tr><td>LeViT-256 [9]</td><td>Y</td><td>Hybrid</td><td>19</td><td>1.1</td><td>81.6</td></tr><tr><td>EfficientFormer-L3 [31]</td><td>Y</td><td>Hybrid</td><td>31</td><td>3.9</td><td>82.4</td></tr><tr><td>ResNet50 [13]</td><td>-</td><td>Conv</td><td>25</td><td>4.1</td><td>78.8</td></tr><tr><td>ResNet50‡</td><td>-</td><td>Conv</td><td>25</td><td>4.1</td><td>79.1</td></tr><tr><td>PoolFormer-S24 [41]</td><td>-</td><td>Conv</td><td>21</td><td>3.4</td><td>80.3</td></tr><tr><td>PoolFormer-S36 [41]</td><td>-</td><td>Conv</td><td>31</td><td>5.0</td><td>81.4</td></tr><tr><td>ConvNext-Tiny [21]</td><td>-</td><td>Conv</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>VAN-B2 [11]</td><td>-</td><td>Conv</td><td>27</td><td>5.0</td><td>82.8</td></tr><tr><td>DeiT-S [31]</td><td>-</td><td>ViT</td><td>22</td><td>4.6</td><td>79.9</td></tr><tr><td>Swin-T [20]</td><td>-</td><td>ViT</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>T2T-ViT-14 [42]</td><td>-</td><td>ViT</td><td>22</td><td>4.8</td><td>81.5</td></tr><tr><td>T2T-ViT-19 [42]</td><td>-</td><td>ViT</td><td>39</td><td>8.5</td><td>81.9</td></tr><tr><td>MViTv2-T [16]</td><td>-</td><td>ViT</td><td>24</td><td>4.7</td><td>82.3</td></tr><tr><td>CSWin-T [4]</td><td>-</td><td>ViT</td><td>23</td><td>4.3</td><td>82.7</td></tr><tr><td>MobileViTV2 [29]</td><td>-</td><td>Hybrid</td><td>19</td><td>7.5</td><td>81.2</td></tr><tr><td>LITV2 [26]</td><td>-</td><td>Hybrid</td><td>28</td><td>3.7</td><td>82.0</td></tr><tr><td>Next-ViT-S [15]</td><td>-</td><td>Hybrid</td><td>32</td><td>5.8</td><td>82.5</td></tr><tr><td>FcaFormer-L2</td><td>-</td><td>Hybrid</td><td>16</td><td>3.6</td><td>83.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Comparison with baselines. The results are summarized in Table 1, from which we can see that both types of our proposed FcaFormer models outperform their reference models by a significant margin. Compared with DeiT, FcaFormer-L0 does have  $0.4\\mathrm{M}$  more parameters, but it achieves  $2.1\\%$  higher accuracy. Our hybrid FcaFormers achieve better performance in all three metrics: accuracy, model size and computational cost. FcaFormer-L1 achieves  $1.9\\%$  higher top-1 accuracy compared with sim",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c18118e69828d95be3fdcc2150256f4aa79cb314056364feb6f40c72f3ea64f6.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3. Semantic segmentation on the ADE20K dataset. We use UperNet as our segmentation method and compare our performance using the same method with other popular backbones."
+        ],
+        "table_body": "<table><tr><td>Method</td><td>Backbone</td><td>mIOU</td><td># params.</td><td>MACs</td></tr><tr><td>DANet</td><td>ResNet-101</td><td>45.2</td><td>69</td><td>1119</td></tr><tr><td>DpLab.v3+</td><td>ResNet-101</td><td>44.1</td><td>63</td><td>1021</td></tr><tr><td>ACNet</td><td>ResNet-101</td><td>45.9</td><td>-</td><td>-</td></tr><tr><td>DNL</td><td>ResNet-101</td><td>46.0</td><td>69</td><td>1249</td></tr><tr><td>OCRNet</td><td>ResNet-101</td><td>45.3</td><td>56</td><td>923</td></tr><tr><td>UperNet</td><td>ResNet-101</td><td>44.9</td><td>86</td><td>1029</td></tr><tr><td>UperNet</td><td>DeiT III (ViT-S)</td><td>46.8</td><td>42</td><td>588</td></tr><tr><td>UperNet</td><td>Swin-T</td><td>45.8</td><td>60</td><td>945</td></tr><tr><td>UperNet</td><td>ConvNext-T</td><td>46.7</td><td>60</td><td>939</td></tr><tr><td>UperNet</td><td>FcaFormer-L2</td><td>47.6</td><td>46</td><td>730</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "arily sized Swin-1G. FcaFormer-L1 also has good scalability. The scaled up version FcaFormer-L2 outperforms the ConvNext-Tiny by  $1.0\\%$  with  $20\\%$  less computational cost and  $44\\%$  fewer parameters. FcaFormer-L2 also surpasses Swin-T by  $1.8\\%$  while using fewer parameters and less computation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In summary, our proposed forward cross attention design universally improves performances of both plain version and hybrid ViT models without increasing too much extra computation cost or even saving parameters and FLOPs.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison with other models. In Table 2, we make a comparison with other models proposed in recent two years. Compared to the latest state-of-the-arts, including ConvNets, ViTs and Hybrid models, our proposed FcaFormer models achieve the best accuracy under the condition of having similar model sizes. In addition, the proposed models beat models strengthened by knowledge distillation in classification accuracy.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Specifically, FcaFormer-L1 outperforms MobileOne and EdgeNext by  $0.9\\%$  in classification accuracy, while keeping comparable or smaller model size and fewer computational cost. Among models having about 25 million parameters, FcaFormer-L2 achieves the highest classification accuracy with the fewest parameters. Compared with Next-ViT-S which achieves the second highest accuracy, FcaFormer-L2 saves about half parameters and  $38\\%$  computational cost, while gaining 0.6 percentage points higher accuracy. Also, note that both EfficientFormer-L3 and LeViT-256 are trained with knowledge distillation, which has been verified to improve accuracy significantly [31]. Even so, FcaFormer-L2 still has better accuracy and smaller model size compared with these two models.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Semantic segmentation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training setting. To evaluate the proposed FcaFormers on downstream tasks. We apply them on the ADE20K semantic segmentation task. Following Swin and ConvNext, we adopt UperNet [38] as our base framework and imple",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6065",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/a5b3ef2d2ea3252d545595ebf3e9deea120fce0d50d24786834517916fe992e7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Backbone</td><td>#Params.MACs</td><td>APb</td><td>APb50</td><td>APb75</td><td>APm</td><td>APm50</td><td>APm75</td></tr><tr><td colspan=\"8\">Mask-RCNN 3× schedule</td></tr><tr><td>SWin-T</td><td>48</td><td>267</td><td>46.0</td><td>68.1</td><td>50.3</td><td>41.6</td><td>65.1</td></tr><tr><td>ConvNext-T</td><td>48</td><td>262</td><td>46.2</td><td>67.9</td><td>50.8</td><td>41.7</td><td>65.0</td></tr><tr><td>FcaFormer-L2</td><td>37</td><td>249</td><td>47.0</td><td>68.9</td><td>51.8</td><td>42.1</td><td>65.7</td></tr><tr><td colspan=\"8\">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50</td><td>82</td><td>739</td><td>46.3</td><td>64.3</td><td>50.5</td><td>40.1</td><td>61.7</td></tr><tr><td>DeiT-S</td><td>80</td><td>889</td><td>48.0</td><td>67.2</td><td>51.7</td><td>41.4</td><td>64.2</td></tr><tr><td>X101-32</td><td>101</td><td>819</td><td>48.1</td><td>66.5</td><td>52.4</td><td>41.6</td><td>63.9</td></tr><tr><td>X101-64</td><td>140</td><td>972</td><td>48.3</td><td>66.4</td><td>52.3</td><td>41.7</td><td>64.0</td></tr><tr><td>Swin-T</td><td>86</td><td>745</td><td>50.4</td><td>69.2</td><td>54.7</td><td>43.7</td><td>66.6</td></tr><tr><td>ConvNext-T</td><td>86</td><td>741</td><td>50.4</td><td>69.1</td><td>54.8</td><td>43.7</td><td>66.5</td></tr><tr><td>FcaFormer-L2</td><td>74</td><td>728</td><td>51.0</td><td>69.4</td><td>55.5</td><td>43.9</td><td>67.0</td></tr><tr><td>Swin-S</td><td>107</td><td>838</td><td>51.9</td><td>70.7</td><td>56.3</td><td>45.0</td><td>68.2</td></tr><tr><td>ConvNext-S</td><td>108</td><td>827</td><td>51.9</td><td>70.8</td><td>56.5</td><td>45.0</td><td>68.4</td></tr><tr><td>FcaFormer-L3</td><td>86</td><td>792</td><td>52.4</td><td>71.1</td><td>57.2</td><td>44.9</td><td>68.4</td></tr><tr><td>Swin-B</td><td>145</td><td>982</td><td>51.9</td><td>70.5</td><td>56.4</td><td>45.0</td><td>68.1</td></tr><tr><td>ConvNext-B</td><td>146</td><td>964</td><td>52.7</td><td>71.3</td><td>57.2</td><td>45.6</td><td>68.9</td></tr><tr><td>FcaFormer-L4</td><td>124</td><td>970</td><td>53.7</td><td>72.4</td><td>58.2</td><td>46.3</td><td>69.7</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Object detection on the COCO dataset.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ment segmentation experiments on mmseg  $^{4}$ . FcaFormerL2 is trained for 160K iterations with a batch size of 16. Model pretrained on ImageNet-1K is used to initialize segmentation model. More details are presented in supplementary materials.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Comparison with baselines. The results are summarized in Tab.3, compared with Swin-Tiny, FcaFormer-L2 achieves  $1.8\\%$  higher mIoU. Compared with ConvNext-Tiny, FcaFormer-L2 achieves  $0.9\\%$  higher mIoU. Compared with Swin-T and ConvNext-T, the last two stages of FcaFormer-L2 are narrower (384 vs 320, 768 vs 480), which saves parameters and computational cost. Therefore, our FcaFormer-L2 achieves higher mIoU, while saving  $23\\%$  parameters and  $22 - 23\\%$  computation cost.",
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+    {
+        "type": "text",
+        "text": "4.3. Object detection",
+        "text_level": 1,
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+        "text": "Training setting. Object detection experiments are conducted on COCO 2017 and implemented on mmdet  $^{5}$ . Following [20] and [21], we fintune MASK-RCNN and Cascade Mask R-CNN on the COCO dataset with FcaFormer pretrained on ImageNet-1k. We use multi-scale training, AdamW optimizer, and a  $3 \\times$  schedule. More details are presented in supplementary materials.",
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+    {
+        "type": "text",
+        "text": "Comparison with baselines. The results are summarized in Tab.4. Experimental results on objection detection show a similar trend with that on semantic segmentation. Compared with Swin-Tiny and ConvNext-Tiny, FcaFormer-L2 achieves higher values on all six metrics, while having",
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+    {
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+        "img_path": "images/caa01a68b1e1cce41ef7ebe737e863e8471d8f5ed914d53379c0f3284e9d597f.jpg",
+        "image_caption": [
+            "Figure 5. Effects of LSFs. Attention scores for cross tokens are marked with red boxes. From rows 1-4, attention maps are from blocks 2,4 and 6 of stage3, and block 2 of stage 4 respectively."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "fewer parameters and less computational cost.",
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+    {
+        "type": "text",
+        "text": "4.4. Ablation study",
+        "text_level": 1,
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+        "text": "In this section, we conduct ablation analysis on components proposed in our FcaFormer.",
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+        "type": "text",
+        "text": "Effects of the learnable scale factors (LSFs). Fig 5 shows the attention score maps of several FcaFormer blocks trained with and without LSFs. It can be seen that without LSFs, the attention between cross tokens and regular tokens are generally weak, and become weaker as the depth goes deeper (down on the figure). This verifies our hypothesis that characteristics of tokens in different levels can be very different. Comparing the two columns of attention maps, it clearly shows that the LSFs helps increasing the correlation between regular tokens and the cross tokens, thus encourages the reuse of previously generated tokens.",
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+        "type": "text",
+        "text": "From baseline to FcaFormer. The high performance of FcaFormer models is based on two key factors: combining the strengths of ViTs and ConvNets, and utilizing a dense but not heavy forward cross attention design. Table 5 shows how we integrate these two key points in designing our models. To evaluate the performance of the proposed FcaFormer on real-world applications, we deployed each model on the edge device Rockchip 3288, which is widely used in various embedded applications. We collected latency and memory usage information for each model.",
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+    {
+        "type": "text",
+        "text": "The first row in Table 5 provides a baseline micro model to speed up experiments. The second row uses the simplest way to build a hybrid model, which inherits some advantages of ConvNets and ViTs. Compared to the baseline, the",
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+        "type": "page_footnote",
+        "text": "4https://github.com/open-mmlab/mmsegmentation",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{5}$ https://github.com/open-mmlab/mmdetetection",
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+        "type": "page_number",
+        "text": "6066",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Rows</td><td>Models</td><td>Model differences</td><td>#Param. (M)</td><td>MACs (B)</td><td>Latency (ms)</td><td>Memory (M)</td><td>Top1 acc (%)</td></tr><tr><td>1</td><td>Swin-1G</td><td>baseline</td><td>6.25</td><td>1.49</td><td>340</td><td>46.64</td><td>78.4</td></tr><tr><td>2</td><td>ConvSwin</td><td>+early convolution</td><td>6.11</td><td>1.26</td><td>269</td><td>38.34</td><td>78.8 (+0.4)</td></tr><tr><td>3</td><td>ConvViT</td><td>+global attention</td><td>6.11</td><td>1.32</td><td>300</td><td>42.01</td><td>79.4 (+1.0)</td></tr><tr><td>4</td><td>FcaFormer</td><td>+naive forward cross attention.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.4 (+1.0)</td></tr><tr><td>5</td><td>FcaFormer</td><td>+learnable scale factors.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.9 (+1.5)</td></tr><tr><td>6</td><td>FcaFormer</td><td>+TME.</td><td>6.19</td><td>1.37</td><td>312</td><td>42.31</td><td>80.3 (+1.9)</td></tr><tr><td>7</td><td>FcaFormer</td><td>scale up to L2</td><td>16.3</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 5. Ablation study on Imagenet-1K. Steps 1-7 depict the process we followed to develop our FcaFormer models from the Swin-1G. We evaluated the latency and memory usage of the models on ARM Quad Core Cortex-A17. To conduct our experiments, we utilized the RK3288 platform, which is commonly employed in real-world applications such as smart TV and AI entrance guard systems."
+        ],
+        "table_footnote": [
+            "Table 6. Batch size=1, image size=224, four threads. ARM:Quad Core Cortex-A17."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Models</td><td colspan=\"2\"># params.MACs</td><td colspan=\"2\">Latency</td><td rowspan=\"2\">Memory Acc (%)</td></tr><tr><td>(M)</td><td>(B)</td><td>ARM(ms)</td><td>(M)</td></tr><tr><td>ConvNext-Tiny</td><td>29</td><td>4.5</td><td>875</td><td>129</td><td>82.1</td></tr><tr><td>ConvNext-Small</td><td>50</td><td>8.7</td><td>1618</td><td>211</td><td>83.1</td></tr><tr><td>ConvNext-Base</td><td>89</td><td>15.4</td><td>2708</td><td>364</td><td>83.8</td></tr><tr><td>ConvNext-Large</td><td>198</td><td>34.4</td><td>5604</td><td>764</td><td>84.3</td></tr><tr><td>Swin-Tiny</td><td>29</td><td>4.5</td><td>855</td><td>139</td><td>81.3</td></tr><tr><td>Swin-Small</td><td>50</td><td>8.7</td><td>1576</td><td>222</td><td>83.0</td></tr><tr><td>Swin-Base</td><td>88</td><td>15.4</td><td>2624</td><td>378</td><td>83.5</td></tr><tr><td>FcaFormer-L1(Micro)</td><td>6.2</td><td>1.4</td><td>312</td><td>42</td><td>80.3</td></tr><tr><td>FcaFormer-L2(Tiny)</td><td>16</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr><tr><td>FcaFormer-L3(Small)</td><td>28</td><td>6.7</td><td>1344</td><td>148</td><td>84.2</td></tr><tr><td>FcaFormer-L4(Base)</td><td>66</td><td>14.5</td><td>2624</td><td>328</td><td>84.9</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "early convolution structure achieves higher accuracy while requiring less computation and memory usage. In the third row, we replaced window attention with global attention based on computational complexity analysis in section 3.3. This improved the accuracy by  $0.6\\%$  while introducing very limited extra cost. However, latency increased by  $11\\%$ , and memory usage increased by  $7.7\\mathrm{M}$ .",
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+    {
+        "type": "text",
+        "text": "Rows 4 and 5 attempt to introduce forward cross attention. In row 4, cross tokens are not calibrated, which only introduces extra cost and has no benefit to accuracy. In row 5, we adopted LSFs to adjust cross tokens, which further improved the accuracy by  $0.5\\%$ . So far, FcaFormer has outperformed the baseline by  $1.5\\%$  while utilizing fewer parameters and incurring lower computational costs compared to the baseline.",
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+    },
+    {
+        "type": "text",
+        "text": "In row 6, we introduced the TME module to generate representative cross tokens and enhance regular tokens, which improved the final accuracy to  $80.3\\%$ ,  $1.9\\%$  higher than the baseline. Finally, we scaled up the micro size model and got FcaFormer-L2. This new model achieved top-1 accuracy of  $83.1\\%$ , meeting the requirements for some practical applications with low latency, taking less than 1 second and minimal memory usage, below 100M.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f3a44c8587141390065651227734465afc10644c9145023606ae0e4377d5b9b0.jpg",
+        "image_caption": [
+            "Figure 6. Comparison experiments. Left: Params vs. acc vs. MACs. Right: Latency vs. acc vs. MACs. The latency is measured on a single NVIDIA RTX 3090 GPU with batchsize=64."
+        ],
+        "image_footnote": [],
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+    },
+    {
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+        "img_path": "images/8f1a38cdd75b5b6a89af5caeffbdfd04c606dc4edc3beed062a2332914d6bf49.jpg",
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+    {
+        "type": "text",
+        "text": "4.5. Test on different devices",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We deployed our proposed models on two different devices, the widely used edge device RK3288 and GPU device RTX3090, to test their inference efficiency. We also built larger models, FcaFormer-L3 (D=(96,192,320,512), L=(3,6,12,3)), and FcaFormer-L4 (D=(128,256,512,768), L=(3,6,12,3)), to validate the scalability of FcaFormer. We repeated two sets of experiments for 100 and 1000 times, respectively. The average cost is listed in Table 6 and shown in Fig 6. Our models achieved higher accuracy compared with ConvNexts while having far fewer parameters, less memory usage, and lower latency. Furthermore, our network demonstrated good scalability. From tiny model to base model, FcaFormers consistently maintained a clear advantage compared to both Swin and ConvNext models.",
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+    {
+        "type": "text",
+        "text": "5. Discussions",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we introduce a new type of attention pattern for hybrid vision models. This attention pattern leverages previously generated tokens to create forward cross-attentions that span different semantic levels. Our experiments show that this approach is effective across different model scales and vision tasks. For future work, we propose combining this design with prior research on sparsifying spatial attention patterns, which could lead to even more efficient model backbones for a range of applications",
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+        "type": "page_number",
+        "text": "6067",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "page_idx": 8
+    },
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+            "[37] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pvt v2: Improved baselines with pyramid vision transformer. Computational Visual Media, 8(3):415-424, 2022. 2, 6",
+            "[38] Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In Proceedings of the European conference on computer vision (ECCV), pages 418-434, 2018. 6"
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
+            900
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[39] Tete Xiao, Mannat Singh, Eric Mintun, Trevor Darrell, Piotr Dollar, and Ross Girshick. Early convolutions help transformers see better. Advances in Neural Information Processing Systems, 34:30392-30400, 2021. 2, 4",
+            "[40] Weijian Xu, Yifan Xu, Tyler Chang, and Zhuowen Tu. Coscale conv-attentional image transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9981–9990, 2021. 6",
+            "[41] Weihao Yu, Mi Luo, Pan Zhou, Chenyang Si, Yichen Zhou, Xinchao Wang, Jiashi Feng, and Shuicheng Yan. Metaformer is actually what you need for vision. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10819-10829, 2022. 6",
+            "[42] Li Yuan, Yunpeng Chen, Tao Wang, Weihao Yu, Yujun Shi, Zi-Hang Jiang, Francis EH Tay, Jiashi Feng, and Shuicheng Yan. Tokens-to-token vit: Training vision transformers from scratch onImagenet. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 558-567, 2021. 6",
+            "[43] Haokui Zhang, Wenze Hu, and Xiaoyu Wang. Parc-net: Position aware circular convolution with merits from convnets and transformer. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXVI, pages 613-630. Springer, 2022. 6",
+            "[44] Bolei Zhou, Hang Zhao, Xavier Puig, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Scene parsing through ade20k dataset. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 5"
+        ],
+        "bbox": [
+            501,
+            92,
+            893,
+            498
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "6069",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 9
+    }
+]
\ No newline at end of file
diff --git a/2023/Fcaformer_ Forward Cross Attention in Hybrid Vision Transformer/5726ddf1-d837-42aa-9a96-e54cdcd1f294_model.json b/2023/Fcaformer_ Forward Cross Attention in Hybrid Vision Transformer/5726ddf1-d837-42aa-9a96-e54cdcd1f294_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..67eb4e203bb0e63c82d81e9fa90b7535d151a815
--- /dev/null
+++ b/2023/Fcaformer_ Forward Cross Attention in Hybrid Vision Transformer/5726ddf1-d837-42aa-9a96-e54cdcd1f294_model.json	
@@ -0,0 +1,2222 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.807,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.143,
+                0.131,
+                0.83,
+                0.152
+            ],
+            "angle": 0,
+            "content": "Fcaformer: Forward Cross Attention in Hybrid Vision Transformer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.305,
+                0.18,
+                0.664,
+                0.199
+            ],
+            "angle": 0,
+            "content": "Haokui Zhang\\(^{1,2}\\), Wenze Hu\\(^{1}\\), Xiaoyu Wang\\(^{3}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.355,
+                0.199,
+                0.616,
+                0.218
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>Intellifusion <sup>2</sup>Yan'an University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.212,
+                0.217,
+                0.76,
+                0.235
+            ],
+            "angle": 0,
+            "content": "<sup>3</sup>The Hong Kong University of Science and Technology (Guangzhou)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.269,
+                0.314,
+                0.285
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.301,
+                0.473,
+                0.739
+            ],
+            "angle": 0,
+            "content": "Currently, one main research line in designing a more efficient vision transformer is reducing the computational cost of self attention modules by adopting sparse attention or using local attention windows. In contrast, we propose a different approach that aims to improve the performance of transformer-based architectures by densifying the attention pattern. Specifically, we proposed forward cross attention for hybrid vision transformer (FcaFormer), where tokens from previous blocks in the same stage are secondary used. To achieve this, the FcaFormer leverages two innovative components: learnable scale factors (LSFs) and a token merge and enhancement module (TME). The LSFs enable efficient processing of cross tokens, while the TME generates representative cross tokens. By integrating these components, the proposed FcaFormer enhances the interactions of tokens across blocks with potentially different semantics, and encourages more information flows to the lower levels. Based on the forward cross attention (Fca), we have designed a series of FcaFormer models that achieve the best trade-off between model size, computational cost, memory cost, and accuracy. For example, without the need for knowledge distillation to strengthen training, our FcaFormer achieves \\(83.1\\%\\) top-1 accuracy on Imagenet with only 16.3 million parameters and about 3.6 billion MACs. This saves almost half of the parameters and a few computational costs while achieving \\(0.7\\%\\) higher accuracy compared to distilled EfficientFormer. Code is available at https://github.com/hkzhang-git/FcaFormer"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.769,
+                0.21,
+                0.785
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "With the rapid adoption of transformer structures in the computer vision community, several types of attention patterns have been proposed to enhance the performance or speed of transformer models. For instance, ViT [5] employs the vanilla global multi-head self-attention, Swin Transformers [20] uses local windowed attention, MaxViT [32] incorporates grid attention across interleaved"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.27,
+                0.892,
+                0.331
+            ],
+            "angle": 0,
+            "content": "tokens, and Dynamic ViT [28] utilizes attention on progressively pruned tokens. These approaches aim to sparsify the attention patterns of the original ViT to achieve a better trade-off between speed and accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.334,
+                0.893,
+                0.53
+            ],
+            "angle": 0,
+            "content": "In contrast, we propose a new model block as well as a family of models called FcaFormer, which improves the performance of vision transformers by further densifying the attention patterns at a limited extra cost. Specifically, we propose to connect the input of the standard multi-head attention (MHA) module with extra tokens transformed from previous blocks in the same stage, while still restricting the attention module to output the original amount of tokens. To further reduce the computational cost, we merge the tokens from previous blocks by using depthwise convolutions with large strides. These tokens are further calibrated by scaling them with learned parameters, before being taken into the attention units in subsequent blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.533,
+                0.895,
+                0.684
+            ],
+            "angle": 0,
+            "content": "The new forward cross attention connection has several advantages: 1) it helps transformers further exploit the interactions of tokens across different levels; 2) it reuses the previously generated tokens so that some of the information no longer needs to be preserved by the subsequent transformer operations, leading to potentially smaller models with similar accuracy; 3) similar to the residual connections in ResNet, this extra cross layer connection encourages more information flows to the lower levels of the network, which further accelerate the convergence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.687,
+                0.895,
+                0.883
+            ],
+            "angle": 0,
+            "content": "The newly densified connections come with a limited increase in computational cost. As explained in Section 3.3, this cost increase is linear rather than quadratic, since we keep the number of output tokens the same as in standard ViTs. Furthermore, most of the computation cost in most hybrid vision transformer architectures is in the feed forward network (FFN) rather than the MHA part of transformer blocks. Thus, the linear growth of computational complexity from densified connections does not significantly affect the overall computation cost. Finally, to further reduce the number of extra inputs, we use depthwise convolutions with large kernels and long strides to aggregate tokens from previous blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We have incorporated the proposed Fca design into two"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6060"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.288
+            ],
+            "angle": 0,
+            "content": "typical classes of transformer models: the plain ViT model used in DeiT, and the hybrid ConvNet and transformer structures frequently seen in recent works [24, 9, 17]. Our experiments demonstrate that the Fca block can seamlessly replace the corresponding transformer blocks in these architectures, leading to significantly improved performance compared to their corresponding baselines. Specifically, FcaFormer-L1 achieves a top-1 accuracy of \\(80.3\\%\\) with approximately 6.2 million parameters and about 1.4 billion MACs. This is achieved while saving almost half the number of parameters, and achieving \\(1.1\\%\\) higher accuracy compared to the recently proposed EfficientFormer. Table 2 displays the comparison results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.288,
+                0.468,
+                0.303
+            ],
+            "angle": 0,
+            "content": "The contribution of this paper is summarized as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.312,
+                0.468,
+                0.386
+            ],
+            "angle": 0,
+            "content": "- Opposite to many recent works that use sparse attentions to improve transformer models, we propose to design more efficient models by densifying the attention connection patterns, which open up a new and worthwhile research avenue for consideration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.391,
+                0.468,
+                0.526
+            ],
+            "angle": 0,
+            "content": "- We propose the FcaFormer block, which leverages existing tokens and enhance interactions across different levels. To achieve this, we introduce two new components: learnable scale factors (LSFs) and a token merge and enhancement module (TME). The LSFs allow us to effectively process cross tokens, while the TME generates representative cross tokens. Together, these components improve the performance of the FcaFormer models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.531,
+                0.468,
+                0.591
+            ],
+            "angle": 0,
+            "content": "- Based on the proposed FcaFormer block, we constructed several new models which have demonstrated better performance than various other recently proposed models."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.312,
+                0.468,
+                0.591
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.612,
+                0.227,
+                0.627
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.636,
+                0.305,
+                0.651
+            ],
+            "angle": 0,
+            "content": "2.1. Pure vision transformers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Dosovitskiy et al. introduced transformer model into vision tasks and proposed the ViT [5]. It cropped an image into \\(16 \\times 16\\) patches as an input token sequence to the transformer and used positional encoding to model spatial relations among tokens. DeiT [31] lowered the difficulty of ViT model training by knowledge distillation, and achieved competitive accuracy with less pretraining data. To further improve the model architecture, researchers attempted to optimize the ViT toward improving its computational efficiency. Among them, the Swin transformer [20] computes self attention among shifted local windows. The MaxViT [32] uses block attention and grid attention alternatively to keep spatially global information exchange while significantly reduce the number of tokens involved in the self attention computation. The DynamicViT [28] prunes redundant tokens progressively and dynamically depending on"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.137
+            ],
+            "angle": 0,
+            "content": "the input features. Mohsen et al. [7] proposed a differentiable parameter-free adaptive token sampler and plugged it into ViTs to sample part tokens for attention computation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.138,
+                0.892,
+                0.274
+            ],
+            "angle": 0,
+            "content": "Except for the DeiT, all methods above keep pure vision transformer architectures and seek to achieve better accuracy speed trade-off by using sparse attention via reducing the number of tokens in attention patterns. In contrast, we propose to achieve this goal by densifying the attention pattern, reusing existing tokens from previous blocks. Such interactions promote attentions across features of different semantic levels, which is very common in ConvNets and many methods before the wide adoption of deep learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.284,
+                0.852,
+                0.3
+            ],
+            "angle": 0,
+            "content": "2.2. Hybrid ConvNet and vision transformers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.307,
+                0.892,
+                0.609
+            ],
+            "angle": 0,
+            "content": "Rather than simplifying ViTs, another popular line of research is to combine elements of ViTs and ConvNets to form new backbones. Two early attempts can be found in [9, 39], where ConvNet blocks are employed to extract low level information in early stages and ViT blocks are adopted in deep stages. Such a hybrid structure improves optimization stability and model performance. Similarly, BoTNet [30] replaces the standard convolution with multi-head attention in the last few blocks of ResNet. In [24], the deeper stages of MobileNetv2 [29] are replaced with their proposed MobileViT block. There are other hybrid models which mix convolution operation with self attention and channel mixer operations. For example, ConViT[6] incorporates soft convolutional inductive biases via a gated positional self-attention. CMT [10] and Next-ViT [15] insert both convolution operation and self attention module into a single block. PVT v1 [36], PVT v2 [37], LIT [27] and LIT v2 [26] insert convolutional operations into each stage of ViT models to reduce the number of tokens, and build hybrid multi-stage structures."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.61,
+                0.892,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Generally speaking, hybrid models achieve better tradeoff between model cost and accuracy compared with pure vision transformer models. Therefore, we mainly focus on applying forward cross attention design on hybrid models to evaluate its effects. Our work is complementary to these hybrid design attempts, and can be used to replace the transformer part for most of these models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.726,
+                0.765,
+                0.742
+            ],
+            "angle": 0,
+            "content": "2.3. Skip connections in ConvNets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "In retrospect, our work is also related to several key improvements in ConvNets design that introduces extra connections to improve the information flows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "ResNet [13] employs shortcut connections to overcome the degradation problem, where accuracy gets saturated and then degrades rapidly with the increasing convolutional network depth. DenseNet [14] connects each layer to every other layer in a feedforward fashion. As with ResNet that builds the whole network by stacking several residual units, DenseNet consists of multiple dense blocks. Wang et"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6061"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.1,
+                0.867,
+                0.246
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.247,
+                0.894,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Figure 1. A FcaFormer stage which consists of \\( L \\) FcaFormer blocks. Compared with standard ViT blocks, we add token merge and enhancement (TME) part, which uses long stride large kernel convolutions to merge tokens spatially as cross tokens, and small kernel convolutions to further enhance tokens for channel mixing (FFN). The cross tokens are then used in later blocks as extra tokens for multi-head attention, after being calibrated by multiplying them with learned scaling factors (LSFs, \\( \\alpha \\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.317,
+                0.47,
+                0.422
+            ],
+            "angle": 0,
+            "content": "al. [35] further improve DenseNet by using two-way dense layers to obtain different receptive fields. With limited extra computational cost, these model design choices solved bottlenecks existed in ConvNets and are still widely used in both academia and industry. Skip connection is also used in transformer models. For instance, Denseformer [22] reuses the first layer CLS token into subsequent layers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.423,
+                0.471,
+                0.514
+            ],
+            "angle": 0,
+            "content": "Our proposed forward cross attention is similar to the works above in that it reuses existing intermediate results and introduces extra connections to the overall network structure. As experiments show, our work introduces similar benefits to transformer models such as better model performance and faster model convergence."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.525,
+                0.336,
+                0.54
+            ],
+            "angle": 0,
+            "content": "2.4. Cross attention transformers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.549,
+                0.47,
+                0.685
+            ],
+            "angle": 0,
+            "content": "In transformers, cross attention is usually used to mix two different embedding sequences. In [34, 8], the output of encoder is fed to decoder via cross attention. CrossViT [1] mixes small-patch and large-patch tokens with cross attention to extract multi-scale feature. Our proposed FcaFormer shares the basic idea of integrating information with cross attention. However, unlike previous models, our FcaFormer integrates tokens from different semantic levels using TME and LSFs to overcome their distinct characteristics."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.7,
+                0.317,
+                0.718
+            ],
+            "angle": 0,
+            "content": "3. The proposed FcaFormer"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.415,
+                0.743
+            ],
+            "angle": 0,
+            "content": "3.1. FcaFormer block and FcaFormer stage"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.469,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Fig.1 shows the major parts and connection relations of a FcaFormer stage which consists of \\(L\\) FcaFormer blocks. Each FcaFormer block is composed of three major parts, which are cross multi-head attention (CMHA), token merge and enhancement (TME), and feed forward network (FFN) respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "CMHA and LSFs. Different from the standard ViT block, our proposed FcaFormer block receives two sets of tokens as input. The block in turn generates two sets of tokens as well, which are denoted as \\( x^{l} \\) and \\( \\bar{x}^{l} \\) respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.317,
+                0.892,
+                0.394
+            ],
+            "angle": 0,
+            "content": "Taking the block at depth \\( l \\) as an example, the inputs are the regular tokens from its previous block \\( x^{l-1} \\) and a set of block cross tokens \\( (\\bar{x}^{l-2}, \\bar{x}^{l-3} \\dots \\bar{x}^1) \\) from earlier blocks in the stage. The CMHA takes both \\( x^{l-1} \\) and \\( (\\bar{x}^{l-2}, \\bar{x}^{l-3} \\dots \\bar{x}^1) \\) as input, but only generates \\( n \\) tokens \\( \\tilde{y}^k \\) as its output."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.395,
+                0.893,
+                0.515
+            ],
+            "angle": 0,
+            "content": "It is worth noting that the cross tokens are scaled by learned calibration coefficients (learnable scale factors LSFs) \\(\\alpha\\) before they are used in the CMHA. We found that the statistics of tokens from different semantic levels are very different. Without this calibration operation, cross tokens are hard to integrate to regular tokens in current blocks to work as we expected. Details are shown and analyzed in our ablation study part."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.515,
+                0.892,
+                0.545
+            ],
+            "angle": 0,
+            "content": "Specifically, given the inputs above, the query, key and value for multi-head attention modules are constructed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.537,
+                0.551,
+                0.891,
+                0.568
+            ],
+            "angle": 0,
+            "content": "\\[\nQ = W ^ {Q} x ^ {l - 1} \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.537,
+                0.569,
+                0.891,
+                0.588
+            ],
+            "angle": 0,
+            "content": "\\[\nK = W ^ {K} \\left[ x ^ {l - 1}, \\left(\\mathbf {1} \\alpha^ {l}\\right) ^ {T} \\otimes \\left(\\bar {x} ^ {l - 2}, \\dots , \\bar {x} ^ {1}\\right) \\right] \\tag {2}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.538,
+                0.59,
+                0.891,
+                0.61
+            ],
+            "angle": 0,
+            "content": "\\[\nV = W ^ {V} \\left[ x ^ {l - 1}, \\left(\\mathbf {1} \\alpha^ {l}\\right) ^ {T} \\otimes \\left(\\bar {x} ^ {l - 2}, \\dots , \\bar {x} ^ {1}\\right) \\right] \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.615,
+                0.892,
+                0.721
+            ],
+            "angle": 0,
+            "content": "where \\( W^{K}, W^{V}, W^{Q} \\) are the three weight matrices transforming input into key, value and query tokens respectively. Elements in \\( \\alpha \\in \\mathbb{R}^{(l - 2)\\bar{n} \\times 1} \\) are the learnable scale factors for cross tokens and \\( \\otimes \\) denotes the element-wise multiplication where each token in \\( \\bar{x} \\) is multiplied by a corresponding scaling scalar in \\( \\alpha \\). \\( \\bar{n} \\) represents the number of cross tokens for each layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.722,
+                0.892,
+                0.782
+            ],
+            "angle": 0,
+            "content": "The computed \\( Q, K, V \\) are then connected to the standard dot product attention operators as in the original transformer [34], which computes the globally mixed intermediate tokens \\( y^{l} \\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.538,
+                0.801,
+                0.892,
+                0.836
+            ],
+            "angle": 0,
+            "content": "\\[\ny ^ {l} = x ^ {l - 1} + W ^ {P} \\left[ \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}} + B\\right) V \\right] \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.9
+            ],
+            "angle": 0,
+            "content": "The \\(B\\) in Eqn.4 is a learnable matrix consisting of two parts, which are relative position bias for \\(x\\) and relative depth bias for \\(\\bar{x}\\). The query has only \\(n\\) tokens, so the output \\(y^{l}\\) is of size \\(n\\times d\\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6062"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.119,
+                0.092,
+                0.434,
+                0.226
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.228,
+                0.47,
+                0.256
+            ],
+            "angle": 0,
+            "content": "Figure 2. The detailed structure of the token merge and enhancement (TME) module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.28,
+                0.47,
+                0.446
+            ],
+            "angle": 0,
+            "content": "TME. The intermediate tokens \\( y^{l} \\) are then passed to the added token merge and enhancement (TME) part, which computes the cross tokens \\( \\bar{x}^{l} \\) and locally enhanced tokens \\( z^{l} \\) using two separate depthwise convolutions. As shown in Fig 2, our TME has two branches. In the token merge branch, we use a large kernel \\( (7 \\times 7) \\) large stride \\( (s = 4) \\) depthwise convolution to generate \\( \\bar{x}^{l} \\), resulting in a small number of cross tokens to be used by subsequent blocks. In token enhancement branch, a standard depth wise convolution \\( (3 \\times 3, s = 1) \\) is used to locally mix the tokens so as to enhance the 2d spatial relations in the token sequence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.447,
+                0.469,
+                0.507
+            ],
+            "angle": 0,
+            "content": "FFN. The locally enhanced tokens \\( z^l \\) are then used in the standard FFN part of ViT to compute the output token \\( x^l \\), which together with \\( \\bar{x}^l \\) are the entire output of a FcaFormer block at depth \\( l \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.507,
+                0.469,
+                0.539
+            ],
+            "angle": 0,
+            "content": "In summary, our FcaFormer are different from vanilla ViT in following ways:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.547,
+                0.47,
+                0.652
+            ],
+            "angle": 0,
+            "content": "- Asymmetric input and output. In our FcaFormer, CMHA part takes both regular tokens and cross tokens as input but keep the output sequence length fixed to \\( n \\) as in regular transformers. This is the key point that why our proposed FcaFormer only introduce limited extra computational cost. More details are explained in section 3.3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.658,
+                0.469,
+                0.718
+            ],
+            "angle": 0,
+            "content": "- Cross token scale. LSFs are used to facilitate the integration of cross tokens into regular tokens. Without this calibration process, cross tokens may not function as expected. As shown in Fig 5."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.723,
+                0.469,
+                0.813
+            ],
+            "angle": 0,
+            "content": "- Relative depth embedding. In the CMHA part, we choose to use relative positional encoding instead of absolute ones. Apart from its generally better performance, the choice also gives model the flexibility to encode relative depth of the cross tokens, which simplifies the model design."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.547,
+                0.47,
+                0.813
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.833,
+                0.262,
+                0.848
+            ],
+            "angle": 0,
+            "content": "3.2. FcaFormer Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.9
+            ],
+            "angle": 0,
+            "content": "The FcaFormer block is a generic block that can be grouped as FcaFormer stages to construct models. To demonstrate the universal effectiveness of our new attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.087,
+                0.889,
+                0.312
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.314,
+                0.892,
+                0.398
+            ],
+            "angle": 0,
+            "content": "Figure 3. The overall structure of FcaFormer Mobels for image classification tasks. (a) Plain FcaFormer model. This model is directly modified from the DeiT structure. (b) Hybrid FcaFormer model. The ConvNet stages are composed of ConvNext blocks. The detailed model scaling hyperparameters are specified in Sec.3.2"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.421,
+                0.892,
+                0.496
+            ],
+            "angle": 0,
+            "content": "pattern, we build two types of FcaFormer based models, each falls into one of the major categories of transformer related computer vision models as described in Sec. 2. The overall structure of these models for classification task are illustrated in Fig.3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.497,
+                0.892,
+                0.601
+            ],
+            "angle": 0,
+            "content": "Plain FcaFormer. As shown in Fig 3 (a), following the style of vanilla ViT, we construct our plain FcaFormer model (denoted as FcaFormer-L0). The model essentially uses one block of FcaFormer after the patch embedding layer that crops \\(16 \\times 16\\) patches and converts them into a token sequence. The corresponding task related head is kept unchanged compared with the original ViT model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.602,
+                0.892,
+                0.767
+            ],
+            "angle": 0,
+            "content": "Hybrid FcaFormer. As illustrated in Fig 3 (b). Following the trend of combining ConvNet structures and transformer structures to build hybrid models, we also propose to build hybrid FcaFormer. Following LeViT [9] and ViTC[39], we adopt the most straightforward way to build our Hybrid FcaFormers, where there are two conventional ConvNet stages followed by two FcaFormer stages. The ConvNet stage is composed of ConvNext blocks [21] plus a downsampling layer that uses pointwise and depthwise convolutions to reduce the feature map resolution by \\(4\\times\\) and increases the feature map channels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.768,
+                0.892,
+                0.827
+            ],
+            "angle": 0,
+            "content": "Based on the above overall structure, we build models of different sizes to compare with other works. The key scaling hyper-parameters is summarized below, where \\(D\\) denotes the channel size:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.838,
+                0.732,
+                0.852
+            ],
+            "angle": 0,
+            "content": "- FcaFormer-L0: \\( \\mathrm{D} = {192},\\mathrm{\\;L} = {12} \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.861,
+                0.858,
+                0.877
+            ],
+            "angle": 0,
+            "content": "- FcaFormer-L1: \\( \\mathrm{D} = (64,128,192,320) \\), \\( \\mathrm{L} = (2,2,6,2) \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.886,
+                0.858,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- FcaFormer-L2: \\( \\mathrm{D} = (96,192,320,480) \\), \\( \\mathrm{L} = (2,2,7,2) \\)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.838,
+                0.858,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6063"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.089,
+                0.235,
+                0.26
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.144,
+                0.264,
+                0.156,
+                0.272
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.257,
+                0.088,
+                0.391,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.318,
+                0.164,
+                0.331,
+                0.172
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.258,
+                0.181,
+                0.39,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.318,
+                0.264,
+                0.331,
+                0.272
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.276,
+                0.47,
+                0.332
+            ],
+            "angle": 0,
+            "content": "Figure 4. Computational cost analysis. (a) Detailed analysis on the number of parameters and MACs for a transformer block; (b)-(c) Computation decompositions in blocks of stage 3 of DeiT-Tiny and stage 4 of EfficientFormer-L1 respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.346,
+                0.433,
+                0.363
+            ],
+            "angle": 0,
+            "content": "3.3. Computational Complexity of FcaFormer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.371,
+                0.47,
+                0.461
+            ],
+            "angle": 0,
+            "content": "In terms of computational complexity, transformers are notorious for its \\(\\mathcal{O}(n^2)\\) scaling property, which is why so many prior works try to reduce the inputs to the MHA model. However, the extra computational cost of densifying the attention pattern is rather limited in our FcaFormer models, because of the following reasons:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.462,
+                0.47,
+                0.567
+            ],
+            "angle": 0,
+            "content": "1) The added extra computation is restricted to the MHA part, since we keep the output sequence length of MHA fixed to \\( n \\) as in regular transformers. This leads to linear scaling cost in terms of the number of additional input tokens, which itself is a small \\( \\left( (l - 1) * n / s^2 \\right) \\) compared with \\( n \\). The computational cost of FFN part is kept unchanged compared with original ViT blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.568,
+                0.471,
+                0.854
+            ],
+            "angle": 0,
+            "content": "2) In vision transformer model families, the FFN part actually constitutes the majority of computations. In [19], Liu et al. also emphasized that larger models incur higher computational costs, primarily due to FFNs. Here, we delve into a more detailed analysis. This is paradoxical to the fact that MHA scales at \\(\\mathcal{O}(n^2)\\) while FFN scales at \\(\\mathcal{O}(n)\\), largely because that the neglected constant token size \\(d\\) in big O analysis is rather large and scales poorly. Fig. 4 details the exact adds and multiplications (MACs) of a standard ViT block in terms of the number of tokens \\(n\\) and the dimension of tokens \\(d\\). Taking the transformer block DeiT-Tiny as an example, because \\(n = 196\\) and \\(d = 192\\) are at the same scale, the \\(2n^2 d\\) MACs in MHA is much less compared with that \\((8nd^2)\\) of FFN (\\(15\\%\\) vs \\(56\\%\\) respectively). For models in pyramid shapes such as swim transformers where \\(n < d\\), the majority skews even more towards FFN because of the local windowing effect. Compared with the reference models, our FcaFormer variants only introduce about \\(13\\%\\) extra computational cost."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "It looks like that the proposed FcaFormer is heavier than its reference model as it introduces extra computations. However, the counter-intuitive fact is that FcaFormer can"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.089,
+                0.892,
+                0.219
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Models</td><td># params. (M)</td><td>FLOPs (G)</td><td>Top1 acc</td></tr><tr><td>DeiT-T [31]</td><td>5.5</td><td>1.23</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>5.9.</td><td>1.49</td><td>74.3</td></tr><tr><td>Swin-1G‡</td><td>6.3</td><td>1.5</td><td>78.4</td></tr><tr><td>FcaFormer-L1</td><td>6.2</td><td>1.4</td><td>80.3</td></tr><tr><td>ConvNext-Tiny [21]</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>Swin-Tiny [20]</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>FcaFormer-L2</td><td>16.3</td><td>3.6</td><td>83.1</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.499,
+                0.22,
+                0.892,
+                0.261
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison with baselines. The plain version FcaFormer is based on DeiT-T. The hybrid ViT FcaFormer models are based on ConvNext and Swin Transformers. \\(\\ddagger\\)means our implementation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.274,
+                0.892,
+                0.394
+            ],
+            "angle": 0,
+            "content": "be more light-weight than its reference model. As is mentioned in introduction, FcaFormer reuses tokens from previous blocks, enhances interaction of tokens across blocks and improve information flow. Compared with the vanilla ViT, FcaFormer has better parameter efficiency. Therefore, FcaFormer can get comparable or even better performance with fewer layers and channels. Our experiments further verifies this advantage."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.395,
+                0.893,
+                0.514
+            ],
+            "angle": 0,
+            "content": "In addition to the detailed analysis above, we want to point out that the prior efforts to sparsify the attention patterns spatially in Sec.2.1 and our proposal to densify the attention patterns across semantic levels are complementary to each other. While not the key emphasis of this paper, it is definitely worth exploring if the two types of designs can be combined to yield even more efficient and performant models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.528,
+                0.633,
+                0.545
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.553,
+                0.892,
+                0.659
+            ],
+            "angle": 0,
+            "content": "In this section, we conduct image classification experiments on Imagenet-1K [3], semantic segmentation experiments on ADE20K [44], and object detection experiments on MS-COCO [18] to evaluate our proposed models. We first compare the proposed FcaFormers with our baselines and the previous SOTA methods. Then, we conduct detailed study to show the effectiveness of our design choices."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.668,
+                0.715,
+                0.684
+            ],
+            "angle": 0,
+            "content": "4.1. ImageNet classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.691,
+                0.892,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Experiment settings. The FcaFormer-L0 is implemented based on code of DeiT<sup>1</sup>. The hybrid FcaFormer models are implemented based on code of ConvNext<sup>2</sup> and Swin<sup>3</sup>. We follow the training recipes in DeiT [31] to train our FcaFormer-L0, except that we did not use the knowledge distillation. To train the hybrid FcaFormers, we use the same training hyper parameters and augmentations as used in ConvNext except that the batch size is restricted to 1024 and the initial learning rate is reduced to 2e-3. This change is because we don't have enough GPUs to support the default batch size of 4096 in ConvNext."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.863,
+                0.741,
+                0.876
+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)https://github.com/facebookresearch/deit"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.876,
+                0.778,
+                0.888
+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)https://github.com/facebookresearch/ConvNeXt"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.888,
+                0.777,
+                0.9
+            ],
+            "angle": 0,
+            "content": "<sup>3</sup>https://github.com/microsoft/Swin-Transformer"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.863,
+                0.778,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "6064"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.089,
+                0.47,
+                0.685
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Models</td><td>KD</td><td>Type</td><td>Param.</td><td>MACs</td><td>Top1</td></tr><tr><td>DeiT-Tiny [31]</td><td>Y</td><td>ViT</td><td>6</td><td>-</td><td>74.5</td></tr><tr><td>DeiT-Tiny [31]</td><td>-</td><td>ViT</td><td>6</td><td>-</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>-</td><td>ViT</td><td>6</td><td>-</td><td>74.3</td></tr><tr><td>LeViT-128 [9]</td><td>Y</td><td>Hybrid</td><td>9</td><td>0.4</td><td>78.6</td></tr><tr><td>EfficientFormer-L1 [17]</td><td>Y</td><td>Hybrid</td><td>12</td><td>1.3</td><td>79.2</td></tr><tr><td>ParCNet [43]</td><td>-</td><td>Conv</td><td>5</td><td>1.7</td><td>78.6</td></tr><tr><td>TNT-Ti [12]</td><td>-</td><td>ViT</td><td>6</td><td>1.4</td><td>73.9</td></tr><tr><td>Swin-1G† [20]</td><td>-</td><td>ViT</td><td>7</td><td>1.0</td><td>77.3</td></tr><tr><td>Swin-2G† [20]</td><td>-</td><td>ViT</td><td>13</td><td>2.0</td><td>79.2</td></tr><tr><td>EfficientFormer-L1‡</td><td>-</td><td>Hybrid</td><td>12</td><td>1.3</td><td>76.1</td></tr><tr><td>MobileViT-V1 [24]</td><td>-</td><td>Hybrid</td><td>6</td><td>2.0</td><td>78.4</td></tr><tr><td>EdgeViT-XS [25]</td><td>-</td><td>Hybrid</td><td>7</td><td>1.1</td><td>77.5</td></tr><tr><td>MobileViTV2[29]</td><td>-</td><td>Hybrid</td><td>5</td><td>1.8</td><td>78.1</td></tr><tr><td>CoaT-Tiny [40]</td><td>-</td><td>Hybrid</td><td>6</td><td>4.4</td><td>78.3</td></tr><tr><td>PVT-V2-B1 [37]</td><td>-</td><td>Hybrid</td><td>13</td><td>2.1</td><td>78.7</td></tr><tr><td>Mobile-Former [2]</td><td>-</td><td>Hybrid</td><td>14</td><td>0.5</td><td>79.3</td></tr><tr><td>Edgenext [23]</td><td>-</td><td>Hybrid</td><td>6</td><td>1.3</td><td>79.4</td></tr><tr><td>MobileOne-S4 [33]</td><td>-</td><td>Hybrid</td><td>15</td><td>3.0</td><td>79.4</td></tr><tr><td>FcaFormer-L1</td><td>-</td><td>Hybrid</td><td>6</td><td>1.4</td><td>80.3</td></tr><tr><td>DeiT-S [31]</td><td>Y</td><td>ViT</td><td>22</td><td>4.6</td><td>81.2</td></tr><tr><td>LeViT-256 [9]</td><td>Y</td><td>Hybrid</td><td>19</td><td>1.1</td><td>81.6</td></tr><tr><td>EfficientFormer-L3 [31]</td><td>Y</td><td>Hybrid</td><td>31</td><td>3.9</td><td>82.4</td></tr><tr><td>ResNet50 [13]</td><td>-</td><td>Conv</td><td>25</td><td>4.1</td><td>78.8</td></tr><tr><td>ResNet50‡</td><td>-</td><td>Conv</td><td>25</td><td>4.1</td><td>79.1</td></tr><tr><td>PoolFormer-S24 [41]</td><td>-</td><td>Conv</td><td>21</td><td>3.4</td><td>80.3</td></tr><tr><td>PoolFormer-S36 [41]</td><td>-</td><td>Conv</td><td>31</td><td>5.0</td><td>81.4</td></tr><tr><td>ConvNext-Tiny [21]</td><td>-</td><td>Conv</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>VAN-B2 [11]</td><td>-</td><td>Conv</td><td>27</td><td>5.0</td><td>82.8</td></tr><tr><td>DeiT-S [31]</td><td>-</td><td>ViT</td><td>22</td><td>4.6</td><td>79.9</td></tr><tr><td>Swin-T [20]</td><td>-</td><td>ViT</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>T2T-ViT-14 [42]</td><td>-</td><td>ViT</td><td>22</td><td>4.8</td><td>81.5</td></tr><tr><td>T2T-ViT-19 [42]</td><td>-</td><td>ViT</td><td>39</td><td>8.5</td><td>81.9</td></tr><tr><td>MViTv2-T [16]</td><td>-</td><td>ViT</td><td>24</td><td>4.7</td><td>82.3</td></tr><tr><td>CSWin-T [4]</td><td>-</td><td>ViT</td><td>23</td><td>4.3</td><td>82.7</td></tr><tr><td>MobileViTV2 [29]</td><td>-</td><td>Hybrid</td><td>19</td><td>7.5</td><td>81.2</td></tr><tr><td>LITV2 [26]</td><td>-</td><td>Hybrid</td><td>28</td><td>3.7</td><td>82.0</td></tr><tr><td>Next-ViT-S [15]</td><td>-</td><td>Hybrid</td><td>32</td><td>5.8</td><td>82.5</td></tr><tr><td>FcaFormer-L2</td><td>-</td><td>Hybrid</td><td>16</td><td>3.6</td><td>83.1</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.077,
+                0.686,
+                0.47,
+                0.755
+            ],
+            "angle": 0,
+            "content": "Table 2. Comparison with the SOTA methods on ImageNet-1K validation set. KD means knowledge distillation is used. ‡ indicates implemented by us, where models are trained following the training setting used in ConvNext. Accuracy and FLOPs are calculated on input image size \\( {224} \\times  {224} \\) . † borrowed from [2]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Comparison with baselines. The results are summarized in Table 1, from which we can see that both types of our proposed FcaFormer models outperform their reference models by a significant margin. Compared with DeiT, FcaFormer-L0 does have \\(0.4\\mathrm{M}\\) more parameters, but it achieves \\(2.1\\%\\) higher accuracy. Our hybrid FcaFormers achieve better performance in all three metrics: accuracy, model size and computational cost. FcaFormer-L1 achieves \\(1.9\\%\\) higher top-1 accuracy compared with sim"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.507,
+                0.09,
+                0.888,
+                0.261
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Backbone</td><td>mIOU</td><td># params.</td><td>MACs</td></tr><tr><td>DANet</td><td>ResNet-101</td><td>45.2</td><td>69</td><td>1119</td></tr><tr><td>DpLab.v3+</td><td>ResNet-101</td><td>44.1</td><td>63</td><td>1021</td></tr><tr><td>ACNet</td><td>ResNet-101</td><td>45.9</td><td>-</td><td>-</td></tr><tr><td>DNL</td><td>ResNet-101</td><td>46.0</td><td>69</td><td>1249</td></tr><tr><td>OCRNet</td><td>ResNet-101</td><td>45.3</td><td>56</td><td>923</td></tr><tr><td>UperNet</td><td>ResNet-101</td><td>44.9</td><td>86</td><td>1029</td></tr><tr><td>UperNet</td><td>DeiT III (ViT-S)</td><td>46.8</td><td>42</td><td>588</td></tr><tr><td>UperNet</td><td>Swin-T</td><td>45.8</td><td>60</td><td>945</td></tr><tr><td>UperNet</td><td>ConvNext-T</td><td>46.7</td><td>60</td><td>939</td></tr><tr><td>UperNet</td><td>FcaFormer-L2</td><td>47.6</td><td>46</td><td>730</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.262,
+                0.892,
+                0.303
+            ],
+            "angle": 0,
+            "content": "Table 3. Semantic segmentation on the ADE20K dataset. We use UperNet as our segmentation method and compare our performance using the same method with other popular backbones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.322,
+                0.892,
+                0.412
+            ],
+            "angle": 0,
+            "content": "arily sized Swin-1G. FcaFormer-L1 also has good scalability. The scaled up version FcaFormer-L2 outperforms the ConvNext-Tiny by \\(1.0\\%\\) with \\(20\\%\\) less computational cost and \\(44\\%\\) fewer parameters. FcaFormer-L2 also surpasses Swin-T by \\(1.8\\%\\) while using fewer parameters and less computation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.413,
+                0.892,
+                0.473
+            ],
+            "angle": 0,
+            "content": "In summary, our proposed forward cross attention design universally improves performances of both plain version and hybrid ViT models without increasing too much extra computation cost or even saving parameters and FLOPs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.474,
+                0.892,
+                0.594
+            ],
+            "angle": 0,
+            "content": "Comparison with other models. In Table 2, we make a comparison with other models proposed in recent two years. Compared to the latest state-of-the-arts, including ConvNets, ViTs and Hybrid models, our proposed FcaFormer models achieve the best accuracy under the condition of having similar model sizes. In addition, the proposed models beat models strengthened by knowledge distillation in classification accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.595,
+                0.892,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Specifically, FcaFormer-L1 outperforms MobileOne and EdgeNext by \\(0.9\\%\\) in classification accuracy, while keeping comparable or smaller model size and fewer computational cost. Among models having about 25 million parameters, FcaFormer-L2 achieves the highest classification accuracy with the fewest parameters. Compared with Next-ViT-S which achieves the second highest accuracy, FcaFormer-L2 saves about half parameters and \\(38\\%\\) computational cost, while gaining 0.6 percentage points higher accuracy. Also, note that both EfficientFormer-L3 and LeViT-256 are trained with knowledge distillation, which has been verified to improve accuracy significantly [31]. Even so, FcaFormer-L2 still has better accuracy and smaller model size compared with these two models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.817,
+                0.715,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.2. Semantic segmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Training setting. To evaluate the proposed FcaFormers on downstream tasks. We apply them on the ADE20K semantic segmentation task. Following Swin and ConvNext, we adopt UperNet [38] as our base framework and imple"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6065"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.09,
+                0.464,
+                0.406
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Backbone</td><td>#Params.MACs</td><td>APb</td><td>APb50</td><td>APb75</td><td>APm</td><td>APm50</td><td>APm75</td></tr><tr><td colspan=\"8\">Mask-RCNN 3× schedule</td></tr><tr><td>SWin-T</td><td>48</td><td>267</td><td>46.0</td><td>68.1</td><td>50.3</td><td>41.6</td><td>65.1</td></tr><tr><td>ConvNext-T</td><td>48</td><td>262</td><td>46.2</td><td>67.9</td><td>50.8</td><td>41.7</td><td>65.0</td></tr><tr><td>FcaFormer-L2</td><td>37</td><td>249</td><td>47.0</td><td>68.9</td><td>51.8</td><td>42.1</td><td>65.7</td></tr><tr><td colspan=\"8\">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50</td><td>82</td><td>739</td><td>46.3</td><td>64.3</td><td>50.5</td><td>40.1</td><td>61.7</td></tr><tr><td>DeiT-S</td><td>80</td><td>889</td><td>48.0</td><td>67.2</td><td>51.7</td><td>41.4</td><td>64.2</td></tr><tr><td>X101-32</td><td>101</td><td>819</td><td>48.1</td><td>66.5</td><td>52.4</td><td>41.6</td><td>63.9</td></tr><tr><td>X101-64</td><td>140</td><td>972</td><td>48.3</td><td>66.4</td><td>52.3</td><td>41.7</td><td>64.0</td></tr><tr><td>Swin-T</td><td>86</td><td>745</td><td>50.4</td><td>69.2</td><td>54.7</td><td>43.7</td><td>66.6</td></tr><tr><td>ConvNext-T</td><td>86</td><td>741</td><td>50.4</td><td>69.1</td><td>54.8</td><td>43.7</td><td>66.5</td></tr><tr><td>FcaFormer-L2</td><td>74</td><td>728</td><td>51.0</td><td>69.4</td><td>55.5</td><td>43.9</td><td>67.0</td></tr><tr><td>Swin-S</td><td>107</td><td>838</td><td>51.9</td><td>70.7</td><td>56.3</td><td>45.0</td><td>68.2</td></tr><tr><td>ConvNext-S</td><td>108</td><td>827</td><td>51.9</td><td>70.8</td><td>56.5</td><td>45.0</td><td>68.4</td></tr><tr><td>FcaFormer-L3</td><td>86</td><td>792</td><td>52.4</td><td>71.1</td><td>57.2</td><td>44.9</td><td>68.4</td></tr><tr><td>Swin-B</td><td>145</td><td>982</td><td>51.9</td><td>70.5</td><td>56.4</td><td>45.0</td><td>68.1</td></tr><tr><td>ConvNext-B</td><td>146</td><td>964</td><td>52.7</td><td>71.3</td><td>57.2</td><td>45.6</td><td>68.9</td></tr><tr><td>FcaFormer-L4</td><td>124</td><td>970</td><td>53.7</td><td>72.4</td><td>58.2</td><td>46.3</td><td>69.7</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.133,
+                0.406,
+                0.415,
+                0.419
+            ],
+            "angle": 0,
+            "content": "Table 4. Object detection on the COCO dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.438,
+                0.469,
+                0.514
+            ],
+            "angle": 0,
+            "content": "ment segmentation experiments on mmseg \\(^{4}\\). FcaFormerL2 is trained for 160K iterations with a batch size of 16. Model pretrained on ImageNet-1K is used to initialize segmentation model. More details are presented in supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.514,
+                0.469,
+                0.651
+            ],
+            "angle": 0,
+            "content": "Comparison with baselines. The results are summarized in Tab.3, compared with Swin-Tiny, FcaFormer-L2 achieves \\(1.8\\%\\) higher mIoU. Compared with ConvNext-Tiny, FcaFormer-L2 achieves \\(0.9\\%\\) higher mIoU. Compared with Swin-T and ConvNext-T, the last two stages of FcaFormer-L2 are narrower (384 vs 320, 768 vs 480), which saves parameters and computational cost. Therefore, our FcaFormer-L2 achieves higher mIoU, while saving \\(23\\%\\) parameters and \\(22 - 23\\%\\) computation cost."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.66,
+                0.24,
+                0.675
+            ],
+            "angle": 0,
+            "content": "4.3. Object detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.683,
+                0.469,
+                0.789
+            ],
+            "angle": 0,
+            "content": "Training setting. Object detection experiments are conducted on COCO 2017 and implemented on mmdet \\(^{5}\\). Following [20] and [21], we fintune MASK-RCNN and Cascade Mask R-CNN on the COCO dataset with FcaFormer pretrained on ImageNet-1k. We use multi-scale training, AdamW optimizer, and a \\(3 \\times\\) schedule. More details are presented in supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.79,
+                0.469,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Comparison with baselines. The results are summarized in Tab.4. Experimental results on objection detection show a similar trend with that on semantic segmentation. Compared with Swin-Tiny and ConvNext-Tiny, FcaFormer-L2 achieves higher values on all six metrics, while having"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.544,
+                0.09,
+                0.842,
+                0.379
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.382,
+                0.892,
+                0.425
+            ],
+            "angle": 0,
+            "content": "Figure 5. Effects of LSFs. Attention scores for cross tokens are marked with red boxes. From rows 1-4, attention maps are from blocks 2,4 and 6 of stage3, and block 2 of stage 4 respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.443,
+                0.804,
+                0.457
+            ],
+            "angle": 0,
+            "content": "fewer parameters and less computational cost."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.469,
+                0.65,
+                0.485
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.492,
+                0.891,
+                0.521
+            ],
+            "angle": 0,
+            "content": "In this section, we conduct ablation analysis on components proposed in our FcaFormer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.523,
+                0.892,
+                0.688
+            ],
+            "angle": 0,
+            "content": "Effects of the learnable scale factors (LSFs). Fig 5 shows the attention score maps of several FcaFormer blocks trained with and without LSFs. It can be seen that without LSFs, the attention between cross tokens and regular tokens are generally weak, and become weaker as the depth goes deeper (down on the figure). This verifies our hypothesis that characteristics of tokens in different levels can be very different. Comparing the two columns of attention maps, it clearly shows that the LSFs helps increasing the correlation between regular tokens and the cross tokens, thus encourages the reuse of previously generated tokens."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "From baseline to FcaFormer. The high performance of FcaFormer models is based on two key factors: combining the strengths of ViTs and ConvNets, and utilizing a dense but not heavy forward cross attention design. Table 5 shows how we integrate these two key points in designing our models. To evaluate the performance of the proposed FcaFormer on real-world applications, we deployed each model on the edge device Rockchip 3288, which is widely used in various embedded applications. We collected latency and memory usage information for each model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The first row in Table 5 provides a baseline micro model to speed up experiments. The second row uses the simplest way to build a hybrid model, which inherits some advantages of ConvNets and ViTs. Compared to the baseline, the"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.094,
+                0.875,
+                0.364,
+                0.888
+            ],
+            "angle": 0,
+            "content": "4https://github.com/open-mmlab/mmsegmentation"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.097,
+                0.888,
+                0.342,
+                0.9
+            ],
+            "angle": 0,
+            "content": "\\(^{5}\\)https://github.com/open-mmlab/mmdetetection"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.094,
+                0.875,
+                0.364,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "6066"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.891,
+                0.218
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Rows</td><td>Models</td><td>Model differences</td><td>#Param. (M)</td><td>MACs (B)</td><td>Latency (ms)</td><td>Memory (M)</td><td>Top1 acc (%)</td></tr><tr><td>1</td><td>Swin-1G</td><td>baseline</td><td>6.25</td><td>1.49</td><td>340</td><td>46.64</td><td>78.4</td></tr><tr><td>2</td><td>ConvSwin</td><td>+early convolution</td><td>6.11</td><td>1.26</td><td>269</td><td>38.34</td><td>78.8 (+0.4)</td></tr><tr><td>3</td><td>ConvViT</td><td>+global attention</td><td>6.11</td><td>1.32</td><td>300</td><td>42.01</td><td>79.4 (+1.0)</td></tr><tr><td>4</td><td>FcaFormer</td><td>+naive forward cross attention.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.4 (+1.0)</td></tr><tr><td>5</td><td>FcaFormer</td><td>+learnable scale factors.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.9 (+1.5)</td></tr><tr><td>6</td><td>FcaFormer</td><td>+TME.</td><td>6.19</td><td>1.37</td><td>312</td><td>42.31</td><td>80.3 (+1.9)</td></tr><tr><td>7</td><td>FcaFormer</td><td>scale up to L2</td><td>16.3</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.218,
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+            ],
+            "angle": 0,
+            "content": "Table 5. Ablation study on Imagenet-1K. Steps 1-7 depict the process we followed to develop our FcaFormer models from the Swin-1G. We evaluated the latency and memory usage of the models on ARM Quad Core Cortex-A17. To conduct our experiments, we utilized the RK3288 platform, which is commonly employed in real-world applications such as smart TV and AI entrance guard systems."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Models</td><td colspan=\"2\"># params.MACs</td><td colspan=\"2\">Latency</td><td rowspan=\"2\">Memory Acc (%)</td></tr><tr><td>(M)</td><td>(B)</td><td>ARM(ms)</td><td>(M)</td></tr><tr><td>ConvNext-Tiny</td><td>29</td><td>4.5</td><td>875</td><td>129</td><td>82.1</td></tr><tr><td>ConvNext-Small</td><td>50</td><td>8.7</td><td>1618</td><td>211</td><td>83.1</td></tr><tr><td>ConvNext-Base</td><td>89</td><td>15.4</td><td>2708</td><td>364</td><td>83.8</td></tr><tr><td>ConvNext-Large</td><td>198</td><td>34.4</td><td>5604</td><td>764</td><td>84.3</td></tr><tr><td>Swin-Tiny</td><td>29</td><td>4.5</td><td>855</td><td>139</td><td>81.3</td></tr><tr><td>Swin-Small</td><td>50</td><td>8.7</td><td>1576</td><td>222</td><td>83.0</td></tr><tr><td>Swin-Base</td><td>88</td><td>15.4</td><td>2624</td><td>378</td><td>83.5</td></tr><tr><td>FcaFormer-L1(Micro)</td><td>6.2</td><td>1.4</td><td>312</td><td>42</td><td>80.3</td></tr><tr><td>FcaFormer-L2(Tiny)</td><td>16</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr><tr><td>FcaFormer-L3(Small)</td><td>28</td><td>6.7</td><td>1344</td><td>148</td><td>84.2</td></tr><tr><td>FcaFormer-L4(Base)</td><td>66</td><td>14.5</td><td>2624</td><td>328</td><td>84.9</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.078,
+                0.478,
+                0.471,
+                0.505
+            ],
+            "angle": 0,
+            "content": "Table 6. Batch size=1, image size=224, four threads. ARM:Quad Core Cortex-A17."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.541,
+                0.47,
+                0.648
+            ],
+            "angle": 0,
+            "content": "early convolution structure achieves higher accuracy while requiring less computation and memory usage. In the third row, we replaced window attention with global attention based on computational complexity analysis in section 3.3. This improved the accuracy by \\(0.6\\%\\) while introducing very limited extra cost. However, latency increased by \\(11\\%\\), and memory usage increased by \\(7.7\\mathrm{M}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.653,
+                0.47,
+                0.775
+            ],
+            "angle": 0,
+            "content": "Rows 4 and 5 attempt to introduce forward cross attention. In row 4, cross tokens are not calibrated, which only introduces extra cost and has no benefit to accuracy. In row 5, we adopted LSFs to adjust cross tokens, which further improved the accuracy by \\(0.5\\%\\). So far, FcaFormer has outperformed the baseline by \\(1.5\\%\\) while utilizing fewer parameters and incurring lower computational costs compared to the baseline."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In row 6, we introduced the TME module to generate representative cross tokens and enhance regular tokens, which improved the final accuracy to \\(80.3\\%\\), \\(1.9\\%\\) higher than the baseline. Finally, we scaled up the micro size model and got FcaFormer-L2. This new model achieved top-1 accuracy of \\(83.1\\%\\), meeting the requirements for some practical applications with low latency, taking less than 1 second and minimal memory usage, below 100M."
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.283,
+                0.695,
+                0.435
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.697,
+                0.283,
+                0.889,
+                0.435
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.438,
+                0.892,
+                0.48
+            ],
+            "angle": 0,
+            "content": "Figure 6. Comparison experiments. Left: Params vs. acc vs. MACs. Right: Latency vs. acc vs. MACs. The latency is measured on a single NVIDIA RTX 3090 GPU with batchsize=64."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.492,
+                0.722,
+                0.507
+            ],
+            "angle": 0,
+            "content": "4.5. Test on different devices"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.515,
+                0.893,
+                0.728
+            ],
+            "angle": 0,
+            "content": "We deployed our proposed models on two different devices, the widely used edge device RK3288 and GPU device RTX3090, to test their inference efficiency. We also built larger models, FcaFormer-L3 (D=(96,192,320,512), L=(3,6,12,3)), and FcaFormer-L4 (D=(128,256,512,768), L=(3,6,12,3)), to validate the scalability of FcaFormer. We repeated two sets of experiments for 100 and 1000 times, respectively. The average cost is listed in Table 6 and shown in Fig 6. Our models achieved higher accuracy compared with ConvNexts while having far fewer parameters, less memory usage, and lower latency. Furthermore, our network demonstrated good scalability. From tiny model to base model, FcaFormers consistently maintained a clear advantage compared to both Swin and ConvNext models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.74,
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+                0.755
+            ],
+            "angle": 0,
+            "content": "5. Discussions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this paper, we introduce a new type of attention pattern for hybrid vision models. This attention pattern leverages previously generated tokens to create forward cross-attentions that span different semantic levels. Our experiments show that this approach is effective across different model scales and vision tasks. For future work, we propose combining this design with prior research on sparsifying spatial attention patterns, which could lead to even more efficient model backbones for a range of applications"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6067"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
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+            ],
+            "angle": 0,
+            "content": "References"
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\ No newline at end of file
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+# Fcaformer: Forward Cross Attention in Hybrid Vision Transformer
+
+Haokui Zhang $^{1,2}$ , Wenze Hu $^{1}$ , Xiaoyu Wang $^{3}$
+
+<sup>1</sup>Intellifusion <sup>2</sup>Yan'an University
+
+<sup>3</sup>The Hong Kong University of Science and Technology (Guangzhou)
+
+# Abstract
+
+Currently, one main research line in designing a more efficient vision transformer is reducing the computational cost of self attention modules by adopting sparse attention or using local attention windows. In contrast, we propose a different approach that aims to improve the performance of transformer-based architectures by densifying the attention pattern. Specifically, we proposed forward cross attention for hybrid vision transformer (FcaFormer), where tokens from previous blocks in the same stage are secondary used. To achieve this, the FcaFormer leverages two innovative components: learnable scale factors (LSFs) and a token merge and enhancement module (TME). The LSFs enable efficient processing of cross tokens, while the TME generates representative cross tokens. By integrating these components, the proposed FcaFormer enhances the interactions of tokens across blocks with potentially different semantics, and encourages more information flows to the lower levels. Based on the forward cross attention (Fca), we have designed a series of FcaFormer models that achieve the best trade-off between model size, computational cost, memory cost, and accuracy. For example, without the need for knowledge distillation to strengthen training, our FcaFormer achieves  $83.1\%$  top-1 accuracy on Imagenet with only 16.3 million parameters and about 3.6 billion MACs. This saves almost half of the parameters and a few computational costs while achieving  $0.7\%$  higher accuracy compared to distilled EfficientFormer. Code is available at https://github.com/hkzhang-git/FcaFormer
+
+# 1. Introduction
+
+With the rapid adoption of transformer structures in the computer vision community, several types of attention patterns have been proposed to enhance the performance or speed of transformer models. For instance, ViT [5] employs the vanilla global multi-head self-attention, Swin Transformers [20] uses local windowed attention, MaxViT [32] incorporates grid attention across interleaved
+
+tokens, and Dynamic ViT [28] utilizes attention on progressively pruned tokens. These approaches aim to sparsify the attention patterns of the original ViT to achieve a better trade-off between speed and accuracy.
+
+In contrast, we propose a new model block as well as a family of models called FcaFormer, which improves the performance of vision transformers by further densifying the attention patterns at a limited extra cost. Specifically, we propose to connect the input of the standard multi-head attention (MHA) module with extra tokens transformed from previous blocks in the same stage, while still restricting the attention module to output the original amount of tokens. To further reduce the computational cost, we merge the tokens from previous blocks by using depthwise convolutions with large strides. These tokens are further calibrated by scaling them with learned parameters, before being taken into the attention units in subsequent blocks.
+
+The new forward cross attention connection has several advantages: 1) it helps transformers further exploit the interactions of tokens across different levels; 2) it reuses the previously generated tokens so that some of the information no longer needs to be preserved by the subsequent transformer operations, leading to potentially smaller models with similar accuracy; 3) similar to the residual connections in ResNet, this extra cross layer connection encourages more information flows to the lower levels of the network, which further accelerate the convergence.
+
+The newly densified connections come with a limited increase in computational cost. As explained in Section 3.3, this cost increase is linear rather than quadratic, since we keep the number of output tokens the same as in standard ViTs. Furthermore, most of the computation cost in most hybrid vision transformer architectures is in the feed forward network (FFN) rather than the MHA part of transformer blocks. Thus, the linear growth of computational complexity from densified connections does not significantly affect the overall computation cost. Finally, to further reduce the number of extra inputs, we use depthwise convolutions with large kernels and long strides to aggregate tokens from previous blocks.
+
+We have incorporated the proposed Fca design into two
+
+typical classes of transformer models: the plain ViT model used in DeiT, and the hybrid ConvNet and transformer structures frequently seen in recent works [24, 9, 17]. Our experiments demonstrate that the Fca block can seamlessly replace the corresponding transformer blocks in these architectures, leading to significantly improved performance compared to their corresponding baselines. Specifically, FcaFormer-L1 achieves a top-1 accuracy of  $80.3\%$  with approximately 6.2 million parameters and about 1.4 billion MACs. This is achieved while saving almost half the number of parameters, and achieving  $1.1\%$  higher accuracy compared to the recently proposed EfficientFormer. Table 2 displays the comparison results.
+
+The contribution of this paper is summarized as follows.
+
+- Opposite to many recent works that use sparse attentions to improve transformer models, we propose to design more efficient models by densifying the attention connection patterns, which open up a new and worthwhile research avenue for consideration.  
+- We propose the FcaFormer block, which leverages existing tokens and enhance interactions across different levels. To achieve this, we introduce two new components: learnable scale factors (LSFs) and a token merge and enhancement module (TME). The LSFs allow us to effectively process cross tokens, while the TME generates representative cross tokens. Together, these components improve the performance of the FcaFormer models.  
+- Based on the proposed FcaFormer block, we constructed several new models which have demonstrated better performance than various other recently proposed models.
+
+# 2. Related Works
+
+# 2.1. Pure vision transformers
+
+Dosovitskiy et al. introduced transformer model into vision tasks and proposed the ViT [5]. It cropped an image into  $16 \times 16$  patches as an input token sequence to the transformer and used positional encoding to model spatial relations among tokens. DeiT [31] lowered the difficulty of ViT model training by knowledge distillation, and achieved competitive accuracy with less pretraining data. To further improve the model architecture, researchers attempted to optimize the ViT toward improving its computational efficiency. Among them, the Swin transformer [20] computes self attention among shifted local windows. The MaxViT [32] uses block attention and grid attention alternatively to keep spatially global information exchange while significantly reduce the number of tokens involved in the self attention computation. The DynamicViT [28] prunes redundant tokens progressively and dynamically depending on
+
+the input features. Mohsen et al. [7] proposed a differentiable parameter-free adaptive token sampler and plugged it into ViTs to sample part tokens for attention computation.
+
+Except for the DeiT, all methods above keep pure vision transformer architectures and seek to achieve better accuracy speed trade-off by using sparse attention via reducing the number of tokens in attention patterns. In contrast, we propose to achieve this goal by densifying the attention pattern, reusing existing tokens from previous blocks. Such interactions promote attentions across features of different semantic levels, which is very common in ConvNets and many methods before the wide adoption of deep learning.
+
+# 2.2. Hybrid ConvNet and vision transformers
+
+Rather than simplifying ViTs, another popular line of research is to combine elements of ViTs and ConvNets to form new backbones. Two early attempts can be found in [9, 39], where ConvNet blocks are employed to extract low level information in early stages and ViT blocks are adopted in deep stages. Such a hybrid structure improves optimization stability and model performance. Similarly, BoTNet [30] replaces the standard convolution with multi-head attention in the last few blocks of ResNet. In [24], the deeper stages of MobileNetv2 [29] are replaced with their proposed MobileViT block. There are other hybrid models which mix convolution operation with self attention and channel mixer operations. For example, ConViT[6] incorporates soft convolutional inductive biases via a gated positional self-attention. CMT [10] and Next-ViT [15] insert both convolution operation and self attention module into a single block. PVT v1 [36], PVT v2 [37], LIT [27] and LIT v2 [26] insert convolutional operations into each stage of ViT models to reduce the number of tokens, and build hybrid multi-stage structures.
+
+Generally speaking, hybrid models achieve better tradeoff between model cost and accuracy compared with pure vision transformer models. Therefore, we mainly focus on applying forward cross attention design on hybrid models to evaluate its effects. Our work is complementary to these hybrid design attempts, and can be used to replace the transformer part for most of these models.
+
+# 2.3. Skip connections in ConvNets
+
+In retrospect, our work is also related to several key improvements in ConvNets design that introduces extra connections to improve the information flows.
+
+ResNet [13] employs shortcut connections to overcome the degradation problem, where accuracy gets saturated and then degrades rapidly with the increasing convolutional network depth. DenseNet [14] connects each layer to every other layer in a feedforward fashion. As with ResNet that builds the whole network by stacking several residual units, DenseNet consists of multiple dense blocks. Wang et
+
+![](images/0bdc43c6ca161f3e4e25ee7230d62a58a6882fc6deb904d9e8fb6a457d68b903.jpg)  
+Figure 1. A FcaFormer stage which consists of  $L$  FcaFormer blocks. Compared with standard ViT blocks, we add token merge and enhancement (TME) part, which uses long stride large kernel convolutions to merge tokens spatially as cross tokens, and small kernel convolutions to further enhance tokens for channel mixing (FFN). The cross tokens are then used in later blocks as extra tokens for multi-head attention, after being calibrated by multiplying them with learned scaling factors (LSFs,  $\alpha$ ).
+
+al. [35] further improve DenseNet by using two-way dense layers to obtain different receptive fields. With limited extra computational cost, these model design choices solved bottlenecks existed in ConvNets and are still widely used in both academia and industry. Skip connection is also used in transformer models. For instance, Denseformer [22] reuses the first layer CLS token into subsequent layers.
+
+Our proposed forward cross attention is similar to the works above in that it reuses existing intermediate results and introduces extra connections to the overall network structure. As experiments show, our work introduces similar benefits to transformer models such as better model performance and faster model convergence.
+
+# 2.4. Cross attention transformers
+
+In transformers, cross attention is usually used to mix two different embedding sequences. In [34, 8], the output of encoder is fed to decoder via cross attention. CrossViT [1] mixes small-patch and large-patch tokens with cross attention to extract multi-scale feature. Our proposed FcaFormer shares the basic idea of integrating information with cross attention. However, unlike previous models, our FcaFormer integrates tokens from different semantic levels using TME and LSFs to overcome their distinct characteristics.
+
+# 3. The proposed FcaFormer
+
+# 3.1. FcaFormer block and FcaFormer stage
+
+Fig.1 shows the major parts and connection relations of a FcaFormer stage which consists of  $L$  FcaFormer blocks. Each FcaFormer block is composed of three major parts, which are cross multi-head attention (CMHA), token merge and enhancement (TME), and feed forward network (FFN) respectively.
+
+CMHA and LSFs. Different from the standard ViT block, our proposed FcaFormer block receives two sets of tokens as input. The block in turn generates two sets of tokens as well, which are denoted as  $x^{l}$  and  $\bar{x}^{l}$  respectively.
+
+Taking the block at depth  $l$  as an example, the inputs are the regular tokens from its previous block  $x^{l-1}$  and a set of block cross tokens  $(\bar{x}^{l-2}, \bar{x}^{l-3} \dots \bar{x}^1)$  from earlier blocks in the stage. The CMHA takes both  $x^{l-1}$  and  $(\bar{x}^{l-2}, \bar{x}^{l-3} \dots \bar{x}^1)$  as input, but only generates  $n$  tokens  $\tilde{y}^k$  as its output.
+
+It is worth noting that the cross tokens are scaled by learned calibration coefficients (learnable scale factors LSFs)  $\alpha$  before they are used in the CMHA. We found that the statistics of tokens from different semantic levels are very different. Without this calibration operation, cross tokens are hard to integrate to regular tokens in current blocks to work as we expected. Details are shown and analyzed in our ablation study part.
+
+Specifically, given the inputs above, the query, key and value for multi-head attention modules are constructed as:
+
+$$
+Q = W ^ {Q} x ^ {l - 1} \tag {1}
+$$
+
+$$
+K = W ^ {K} \left[ x ^ {l - 1}, \left(\mathbf {1} \alpha^ {l}\right) ^ {T} \otimes \left(\bar {x} ^ {l - 2}, \dots , \bar {x} ^ {1}\right) \right] \tag {2}
+$$
+
+$$
+V = W ^ {V} \left[ x ^ {l - 1}, \left(\mathbf {1} \alpha^ {l}\right) ^ {T} \otimes \left(\bar {x} ^ {l - 2}, \dots , \bar {x} ^ {1}\right) \right] \tag {3}
+$$
+
+where  $W^{K}, W^{V}, W^{Q}$  are the three weight matrices transforming input into key, value and query tokens respectively. Elements in  $\alpha \in \mathbb{R}^{(l - 2)\bar{n} \times 1}$  are the learnable scale factors for cross tokens and  $\otimes$  denotes the element-wise multiplication where each token in  $\bar{x}$  is multiplied by a corresponding scaling scalar in  $\alpha$ .  $\bar{n}$  represents the number of cross tokens for each layer.
+
+The computed  $Q, K, V$  are then connected to the standard dot product attention operators as in the original transformer [34], which computes the globally mixed intermediate tokens  $y^{l}$ .
+
+$$
+y ^ {l} = x ^ {l - 1} + W ^ {P} \left[ \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d}} + B\right) V \right] \tag {4}
+$$
+
+The  $B$  in Eqn.4 is a learnable matrix consisting of two parts, which are relative position bias for  $x$  and relative depth bias for  $\bar{x}$ . The query has only  $n$  tokens, so the output  $y^{l}$  is of size  $n\times d$ .
+
+![](images/ecfb24c89be6c5a072219f42bbafdb6d19fc43782190dbb15483c249e225b920.jpg)  
+Figure 2. The detailed structure of the token merge and enhancement (TME) module.
+
+TME. The intermediate tokens  $y^{l}$  are then passed to the added token merge and enhancement (TME) part, which computes the cross tokens  $\bar{x}^{l}$  and locally enhanced tokens  $z^{l}$  using two separate depthwise convolutions. As shown in Fig 2, our TME has two branches. In the token merge branch, we use a large kernel  $(7 \times 7)$  large stride  $(s = 4)$  depthwise convolution to generate  $\bar{x}^{l}$ , resulting in a small number of cross tokens to be used by subsequent blocks. In token enhancement branch, a standard depth wise convolution  $(3 \times 3, s = 1)$  is used to locally mix the tokens so as to enhance the 2d spatial relations in the token sequence.
+
+FFN. The locally enhanced tokens  $z^l$  are then used in the standard FFN part of ViT to compute the output token  $x^l$ , which together with  $\bar{x}^l$  are the entire output of a FcaFormer block at depth  $l$ .
+
+In summary, our FcaFormer are different from vanilla ViT in following ways:
+
+- Asymmetric input and output. In our FcaFormer, CMHA part takes both regular tokens and cross tokens as input but keep the output sequence length fixed to  $n$  as in regular transformers. This is the key point that why our proposed FcaFormer only introduce limited extra computational cost. More details are explained in section 3.3.  
+- Cross token scale. LSFs are used to facilitate the integration of cross tokens into regular tokens. Without this calibration process, cross tokens may not function as expected. As shown in Fig 5.  
+- Relative depth embedding. In the CMHA part, we choose to use relative positional encoding instead of absolute ones. Apart from its generally better performance, the choice also gives model the flexibility to encode relative depth of the cross tokens, which simplifies the model design.
+
+# 3.2. FcaFormer Models
+
+The FcaFormer block is a generic block that can be grouped as FcaFormer stages to construct models. To demonstrate the universal effectiveness of our new attention
+
+![](images/b344df2cc1bed0bd97968a95eb0c1c12dfa6de3bcf229c33462443f619eb210f.jpg)  
+Figure 3. The overall structure of FcaFormer Mobels for image classification tasks. (a) Plain FcaFormer model. This model is directly modified from the DeiT structure. (b) Hybrid FcaFormer model. The ConvNet stages are composed of ConvNext blocks. The detailed model scaling hyperparameters are specified in Sec.3.2
+
+pattern, we build two types of FcaFormer based models, each falls into one of the major categories of transformer related computer vision models as described in Sec. 2. The overall structure of these models for classification task are illustrated in Fig.3.
+
+Plain FcaFormer. As shown in Fig 3 (a), following the style of vanilla ViT, we construct our plain FcaFormer model (denoted as FcaFormer-L0). The model essentially uses one block of FcaFormer after the patch embedding layer that crops  $16 \times 16$  patches and converts them into a token sequence. The corresponding task related head is kept unchanged compared with the original ViT model.
+
+Hybrid FcaFormer. As illustrated in Fig 3 (b). Following the trend of combining ConvNet structures and transformer structures to build hybrid models, we also propose to build hybrid FcaFormer. Following LeViT [9] and ViTC[39], we adopt the most straightforward way to build our Hybrid FcaFormers, where there are two conventional ConvNet stages followed by two FcaFormer stages. The ConvNet stage is composed of ConvNext blocks [21] plus a downsampling layer that uses pointwise and depthwise convolutions to reduce the feature map resolution by  $4\times$  and increases the feature map channels.
+
+Based on the above overall structure, we build models of different sizes to compare with other works. The key scaling hyper-parameters is summarized below, where  $D$  denotes the channel size:
+
+- FcaFormer-L0:  $\mathrm{D} = {192},\mathrm{\;L} = {12}$  
+- FcaFormer-L1:  $\mathrm{D} = (64,128,192,320)$ ,  $\mathrm{L} = (2,2,6,2)$  
+- FcaFormer-L2:  $\mathrm{D} = (96,192,320,480)$ ,  $\mathrm{L} = (2,2,7,2)$
+
+![](images/07e590efac5d797eef80da9500c72857cd161383fce4687c48770f29ea8891d8.jpg)  
+(a)
+
+![](images/28ad74d18a1d6131fca9777b3b6c2148fcc36cab536efd672a7c70da99170fc0.jpg)  
+(b)
+
+![](images/9d0b144f8b10ae0d457fbc928ede1a3606c51b547569d109055ab3deb29c5fb2.jpg)  
+(c)  
+Figure 4. Computational cost analysis. (a) Detailed analysis on the number of parameters and MACs for a transformer block; (b)-(c) Computation decompositions in blocks of stage 3 of DeiT-Tiny and stage 4 of EfficientFormer-L1 respectively.
+
+# 3.3. Computational Complexity of FcaFormer
+
+In terms of computational complexity, transformers are notorious for its  $\mathcal{O}(n^2)$  scaling property, which is why so many prior works try to reduce the inputs to the MHA model. However, the extra computational cost of densifying the attention pattern is rather limited in our FcaFormer models, because of the following reasons:
+
+1) The added extra computation is restricted to the MHA part, since we keep the output sequence length of MHA fixed to  $n$  as in regular transformers. This leads to linear scaling cost in terms of the number of additional input tokens, which itself is a small  $\left( (l - 1) * n / s^2 \right)$  compared with  $n$ . The computational cost of FFN part is kept unchanged compared with original ViT blocks.
+
+2) In vision transformer model families, the FFN part actually constitutes the majority of computations. In [19], Liu et al. also emphasized that larger models incur higher computational costs, primarily due to FFNs. Here, we delve into a more detailed analysis. This is paradoxical to the fact that MHA scales at  $\mathcal{O}(n^2)$  while FFN scales at  $\mathcal{O}(n)$ , largely because that the neglected constant token size  $d$  in big O analysis is rather large and scales poorly. Fig. 4 details the exact adds and multiplications (MACs) of a standard ViT block in terms of the number of tokens  $n$  and the dimension of tokens  $d$ . Taking the transformer block DeiT-Tiny as an example, because  $n = 196$  and  $d = 192$  are at the same scale, the  $2n^2 d$  MACs in MHA is much less compared with that  $(8nd^2)$  of FFN ( $15\%$  vs  $56\%$  respectively). For models in pyramid shapes such as swim transformers where  $n < d$ , the majority skews even more towards FFN because of the local windowing effect. Compared with the reference models, our FcaFormer variants only introduce about  $13\%$  extra computational cost.
+
+It looks like that the proposed FcaFormer is heavier than its reference model as it introduces extra computations. However, the counter-intuitive fact is that FcaFormer can
+
+<table><tr><td>Models</td><td># params. (M)</td><td>FLOPs (G)</td><td>Top1 acc</td></tr><tr><td>DeiT-T [31]</td><td>5.5</td><td>1.23</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>5.9.</td><td>1.49</td><td>74.3</td></tr><tr><td>Swin-1G‡</td><td>6.3</td><td>1.5</td><td>78.4</td></tr><tr><td>FcaFormer-L1</td><td>6.2</td><td>1.4</td><td>80.3</td></tr><tr><td>ConvNext-Tiny [21]</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>Swin-Tiny [20]</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>FcaFormer-L2</td><td>16.3</td><td>3.6</td><td>83.1</td></tr></table>
+
+Table 1. Comparison with baselines. The plain version FcaFormer is based on DeiT-T. The hybrid ViT FcaFormer models are based on ConvNext and Swin Transformers.  $\ddagger$ means our implementation
+
+be more light-weight than its reference model. As is mentioned in introduction, FcaFormer reuses tokens from previous blocks, enhances interaction of tokens across blocks and improve information flow. Compared with the vanilla ViT, FcaFormer has better parameter efficiency. Therefore, FcaFormer can get comparable or even better performance with fewer layers and channels. Our experiments further verifies this advantage.
+
+In addition to the detailed analysis above, we want to point out that the prior efforts to sparsify the attention patterns spatially in Sec.2.1 and our proposal to densify the attention patterns across semantic levels are complementary to each other. While not the key emphasis of this paper, it is definitely worth exploring if the two types of designs can be combined to yield even more efficient and performant models.
+
+# 4. Experiments
+
+In this section, we conduct image classification experiments on Imagenet-1K [3], semantic segmentation experiments on ADE20K [44], and object detection experiments on MS-COCO [18] to evaluate our proposed models. We first compare the proposed FcaFormers with our baselines and the previous SOTA methods. Then, we conduct detailed study to show the effectiveness of our design choices.
+
+# 4.1. ImageNet classification
+
+Experiment settings. The FcaFormer-L0 is implemented based on code of DeiT<sup>1</sup>. The hybrid FcaFormer models are implemented based on code of ConvNext<sup>2</sup> and Swin<sup>3</sup>. We follow the training recipes in DeiT [31] to train our FcaFormer-L0, except that we did not use the knowledge distillation. To train the hybrid FcaFormers, we use the same training hyper parameters and augmentations as used in ConvNext except that the batch size is restricted to 1024 and the initial learning rate is reduced to 2e-3. This change is because we don't have enough GPUs to support the default batch size of 4096 in ConvNext.
+
+$^{1}$ https://github.com/facebookresearch/deit  
+$^{2}$ https://github.com/facebookresearch/ConvNeXt  
+<sup>3</sup>https://github.com/microsoft/Swin-Transformer
+
+<table><tr><td>Models</td><td>KD</td><td>Type</td><td>Param.</td><td>MACs</td><td>Top1</td></tr><tr><td>DeiT-Tiny [31]</td><td>Y</td><td>ViT</td><td>6</td><td>-</td><td>74.5</td></tr><tr><td>DeiT-Tiny [31]</td><td>-</td><td>ViT</td><td>6</td><td>-</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>-</td><td>ViT</td><td>6</td><td>-</td><td>74.3</td></tr><tr><td>LeViT-128 [9]</td><td>Y</td><td>Hybrid</td><td>9</td><td>0.4</td><td>78.6</td></tr><tr><td>EfficientFormer-L1 [17]</td><td>Y</td><td>Hybrid</td><td>12</td><td>1.3</td><td>79.2</td></tr><tr><td>ParCNet [43]</td><td>-</td><td>Conv</td><td>5</td><td>1.7</td><td>78.6</td></tr><tr><td>TNT-Ti [12]</td><td>-</td><td>ViT</td><td>6</td><td>1.4</td><td>73.9</td></tr><tr><td>Swin-1G† [20]</td><td>-</td><td>ViT</td><td>7</td><td>1.0</td><td>77.3</td></tr><tr><td>Swin-2G† [20]</td><td>-</td><td>ViT</td><td>13</td><td>2.0</td><td>79.2</td></tr><tr><td>EfficientFormer-L1‡</td><td>-</td><td>Hybrid</td><td>12</td><td>1.3</td><td>76.1</td></tr><tr><td>MobileViT-V1 [24]</td><td>-</td><td>Hybrid</td><td>6</td><td>2.0</td><td>78.4</td></tr><tr><td>EdgeViT-XS [25]</td><td>-</td><td>Hybrid</td><td>7</td><td>1.1</td><td>77.5</td></tr><tr><td>MobileViTV2[29]</td><td>-</td><td>Hybrid</td><td>5</td><td>1.8</td><td>78.1</td></tr><tr><td>CoaT-Tiny [40]</td><td>-</td><td>Hybrid</td><td>6</td><td>4.4</td><td>78.3</td></tr><tr><td>PVT-V2-B1 [37]</td><td>-</td><td>Hybrid</td><td>13</td><td>2.1</td><td>78.7</td></tr><tr><td>Mobile-Former [2]</td><td>-</td><td>Hybrid</td><td>14</td><td>0.5</td><td>79.3</td></tr><tr><td>Edgenext [23]</td><td>-</td><td>Hybrid</td><td>6</td><td>1.3</td><td>79.4</td></tr><tr><td>MobileOne-S4 [33]</td><td>-</td><td>Hybrid</td><td>15</td><td>3.0</td><td>79.4</td></tr><tr><td>FcaFormer-L1</td><td>-</td><td>Hybrid</td><td>6</td><td>1.4</td><td>80.3</td></tr><tr><td>DeiT-S [31]</td><td>Y</td><td>ViT</td><td>22</td><td>4.6</td><td>81.2</td></tr><tr><td>LeViT-256 [9]</td><td>Y</td><td>Hybrid</td><td>19</td><td>1.1</td><td>81.6</td></tr><tr><td>EfficientFormer-L3 [31]</td><td>Y</td><td>Hybrid</td><td>31</td><td>3.9</td><td>82.4</td></tr><tr><td>ResNet50 [13]</td><td>-</td><td>Conv</td><td>25</td><td>4.1</td><td>78.8</td></tr><tr><td>ResNet50‡</td><td>-</td><td>Conv</td><td>25</td><td>4.1</td><td>79.1</td></tr><tr><td>PoolFormer-S24 [41]</td><td>-</td><td>Conv</td><td>21</td><td>3.4</td><td>80.3</td></tr><tr><td>PoolFormer-S36 [41]</td><td>-</td><td>Conv</td><td>31</td><td>5.0</td><td>81.4</td></tr><tr><td>ConvNext-Tiny [21]</td><td>-</td><td>Conv</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>VAN-B2 [11]</td><td>-</td><td>Conv</td><td>27</td><td>5.0</td><td>82.8</td></tr><tr><td>DeiT-S [31]</td><td>-</td><td>ViT</td><td>22</td><td>4.6</td><td>79.9</td></tr><tr><td>Swin-T [20]</td><td>-</td><td>ViT</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>T2T-ViT-14 [42]</td><td>-</td><td>ViT</td><td>22</td><td>4.8</td><td>81.5</td></tr><tr><td>T2T-ViT-19 [42]</td><td>-</td><td>ViT</td><td>39</td><td>8.5</td><td>81.9</td></tr><tr><td>MViTv2-T [16]</td><td>-</td><td>ViT</td><td>24</td><td>4.7</td><td>82.3</td></tr><tr><td>CSWin-T [4]</td><td>-</td><td>ViT</td><td>23</td><td>4.3</td><td>82.7</td></tr><tr><td>MobileViTV2 [29]</td><td>-</td><td>Hybrid</td><td>19</td><td>7.5</td><td>81.2</td></tr><tr><td>LITV2 [26]</td><td>-</td><td>Hybrid</td><td>28</td><td>3.7</td><td>82.0</td></tr><tr><td>Next-ViT-S [15]</td><td>-</td><td>Hybrid</td><td>32</td><td>5.8</td><td>82.5</td></tr><tr><td>FcaFormer-L2</td><td>-</td><td>Hybrid</td><td>16</td><td>3.6</td><td>83.1</td></tr></table>
+
+Table 2. Comparison with the SOTA methods on ImageNet-1K validation set. KD means knowledge distillation is used. ‡ indicates implemented by us, where models are trained following the training setting used in ConvNext. Accuracy and FLOPs are calculated on input image size  ${224} \times  {224}$  . † borrowed from [2]
+
+Comparison with baselines. The results are summarized in Table 1, from which we can see that both types of our proposed FcaFormer models outperform their reference models by a significant margin. Compared with DeiT, FcaFormer-L0 does have  $0.4\mathrm{M}$  more parameters, but it achieves  $2.1\%$  higher accuracy. Our hybrid FcaFormers achieve better performance in all three metrics: accuracy, model size and computational cost. FcaFormer-L1 achieves  $1.9\%$  higher top-1 accuracy compared with sim
+
+<table><tr><td>Method</td><td>Backbone</td><td>mIOU</td><td># params.</td><td>MACs</td></tr><tr><td>DANet</td><td>ResNet-101</td><td>45.2</td><td>69</td><td>1119</td></tr><tr><td>DpLab.v3+</td><td>ResNet-101</td><td>44.1</td><td>63</td><td>1021</td></tr><tr><td>ACNet</td><td>ResNet-101</td><td>45.9</td><td>-</td><td>-</td></tr><tr><td>DNL</td><td>ResNet-101</td><td>46.0</td><td>69</td><td>1249</td></tr><tr><td>OCRNet</td><td>ResNet-101</td><td>45.3</td><td>56</td><td>923</td></tr><tr><td>UperNet</td><td>ResNet-101</td><td>44.9</td><td>86</td><td>1029</td></tr><tr><td>UperNet</td><td>DeiT III (ViT-S)</td><td>46.8</td><td>42</td><td>588</td></tr><tr><td>UperNet</td><td>Swin-T</td><td>45.8</td><td>60</td><td>945</td></tr><tr><td>UperNet</td><td>ConvNext-T</td><td>46.7</td><td>60</td><td>939</td></tr><tr><td>UperNet</td><td>FcaFormer-L2</td><td>47.6</td><td>46</td><td>730</td></tr></table>
+
+Table 3. Semantic segmentation on the ADE20K dataset. We use UperNet as our segmentation method and compare our performance using the same method with other popular backbones.
+
+arily sized Swin-1G. FcaFormer-L1 also has good scalability. The scaled up version FcaFormer-L2 outperforms the ConvNext-Tiny by  $1.0\%$  with  $20\%$  less computational cost and  $44\%$  fewer parameters. FcaFormer-L2 also surpasses Swin-T by  $1.8\%$  while using fewer parameters and less computation.
+
+In summary, our proposed forward cross attention design universally improves performances of both plain version and hybrid ViT models without increasing too much extra computation cost or even saving parameters and FLOPs.
+
+Comparison with other models. In Table 2, we make a comparison with other models proposed in recent two years. Compared to the latest state-of-the-arts, including ConvNets, ViTs and Hybrid models, our proposed FcaFormer models achieve the best accuracy under the condition of having similar model sizes. In addition, the proposed models beat models strengthened by knowledge distillation in classification accuracy.
+
+Specifically, FcaFormer-L1 outperforms MobileOne and EdgeNext by  $0.9\%$  in classification accuracy, while keeping comparable or smaller model size and fewer computational cost. Among models having about 25 million parameters, FcaFormer-L2 achieves the highest classification accuracy with the fewest parameters. Compared with Next-ViT-S which achieves the second highest accuracy, FcaFormer-L2 saves about half parameters and  $38\%$  computational cost, while gaining 0.6 percentage points higher accuracy. Also, note that both EfficientFormer-L3 and LeViT-256 are trained with knowledge distillation, which has been verified to improve accuracy significantly [31]. Even so, FcaFormer-L2 still has better accuracy and smaller model size compared with these two models.
+
+# 4.2. Semantic segmentation
+
+Training setting. To evaluate the proposed FcaFormers on downstream tasks. We apply them on the ADE20K semantic segmentation task. Following Swin and ConvNext, we adopt UperNet [38] as our base framework and imple
+
+<table><tr><td>Backbone</td><td>#Params.MACs</td><td>APb</td><td>APb50</td><td>APb75</td><td>APm</td><td>APm50</td><td>APm75</td></tr><tr><td colspan="8">Mask-RCNN 3× schedule</td></tr><tr><td>SWin-T</td><td>48</td><td>267</td><td>46.0</td><td>68.1</td><td>50.3</td><td>41.6</td><td>65.1</td></tr><tr><td>ConvNext-T</td><td>48</td><td>262</td><td>46.2</td><td>67.9</td><td>50.8</td><td>41.7</td><td>65.0</td></tr><tr><td>FcaFormer-L2</td><td>37</td><td>249</td><td>47.0</td><td>68.9</td><td>51.8</td><td>42.1</td><td>65.7</td></tr><tr><td colspan="8">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50</td><td>82</td><td>739</td><td>46.3</td><td>64.3</td><td>50.5</td><td>40.1</td><td>61.7</td></tr><tr><td>DeiT-S</td><td>80</td><td>889</td><td>48.0</td><td>67.2</td><td>51.7</td><td>41.4</td><td>64.2</td></tr><tr><td>X101-32</td><td>101</td><td>819</td><td>48.1</td><td>66.5</td><td>52.4</td><td>41.6</td><td>63.9</td></tr><tr><td>X101-64</td><td>140</td><td>972</td><td>48.3</td><td>66.4</td><td>52.3</td><td>41.7</td><td>64.0</td></tr><tr><td>Swin-T</td><td>86</td><td>745</td><td>50.4</td><td>69.2</td><td>54.7</td><td>43.7</td><td>66.6</td></tr><tr><td>ConvNext-T</td><td>86</td><td>741</td><td>50.4</td><td>69.1</td><td>54.8</td><td>43.7</td><td>66.5</td></tr><tr><td>FcaFormer-L2</td><td>74</td><td>728</td><td>51.0</td><td>69.4</td><td>55.5</td><td>43.9</td><td>67.0</td></tr><tr><td>Swin-S</td><td>107</td><td>838</td><td>51.9</td><td>70.7</td><td>56.3</td><td>45.0</td><td>68.2</td></tr><tr><td>ConvNext-S</td><td>108</td><td>827</td><td>51.9</td><td>70.8</td><td>56.5</td><td>45.0</td><td>68.4</td></tr><tr><td>FcaFormer-L3</td><td>86</td><td>792</td><td>52.4</td><td>71.1</td><td>57.2</td><td>44.9</td><td>68.4</td></tr><tr><td>Swin-B</td><td>145</td><td>982</td><td>51.9</td><td>70.5</td><td>56.4</td><td>45.0</td><td>68.1</td></tr><tr><td>ConvNext-B</td><td>146</td><td>964</td><td>52.7</td><td>71.3</td><td>57.2</td><td>45.6</td><td>68.9</td></tr><tr><td>FcaFormer-L4</td><td>124</td><td>970</td><td>53.7</td><td>72.4</td><td>58.2</td><td>46.3</td><td>69.7</td></tr></table>
+
+Table 4. Object detection on the COCO dataset.
+
+ment segmentation experiments on mmseg  $^{4}$ . FcaFormerL2 is trained for 160K iterations with a batch size of 16. Model pretrained on ImageNet-1K is used to initialize segmentation model. More details are presented in supplementary materials.
+
+Comparison with baselines. The results are summarized in Tab.3, compared with Swin-Tiny, FcaFormer-L2 achieves  $1.8\%$  higher mIoU. Compared with ConvNext-Tiny, FcaFormer-L2 achieves  $0.9\%$  higher mIoU. Compared with Swin-T and ConvNext-T, the last two stages of FcaFormer-L2 are narrower (384 vs 320, 768 vs 480), which saves parameters and computational cost. Therefore, our FcaFormer-L2 achieves higher mIoU, while saving  $23\%$  parameters and  $22 - 23\%$  computation cost.
+
+# 4.3. Object detection
+
+Training setting. Object detection experiments are conducted on COCO 2017 and implemented on mmdet  $^{5}$ . Following [20] and [21], we fintune MASK-RCNN and Cascade Mask R-CNN on the COCO dataset with FcaFormer pretrained on ImageNet-1k. We use multi-scale training, AdamW optimizer, and a  $3 \times$  schedule. More details are presented in supplementary materials.
+
+Comparison with baselines. The results are summarized in Tab.4. Experimental results on objection detection show a similar trend with that on semantic segmentation. Compared with Swin-Tiny and ConvNext-Tiny, FcaFormer-L2 achieves higher values on all six metrics, while having
+
+![](images/caa01a68b1e1cce41ef7ebe737e863e8471d8f5ed914d53379c0f3284e9d597f.jpg)  
+Figure 5. Effects of LSFs. Attention scores for cross tokens are marked with red boxes. From rows 1-4, attention maps are from blocks 2,4 and 6 of stage3, and block 2 of stage 4 respectively.
+
+fewer parameters and less computational cost.
+
+# 4.4. Ablation study
+
+In this section, we conduct ablation analysis on components proposed in our FcaFormer.
+
+Effects of the learnable scale factors (LSFs). Fig 5 shows the attention score maps of several FcaFormer blocks trained with and without LSFs. It can be seen that without LSFs, the attention between cross tokens and regular tokens are generally weak, and become weaker as the depth goes deeper (down on the figure). This verifies our hypothesis that characteristics of tokens in different levels can be very different. Comparing the two columns of attention maps, it clearly shows that the LSFs helps increasing the correlation between regular tokens and the cross tokens, thus encourages the reuse of previously generated tokens.
+
+From baseline to FcaFormer. The high performance of FcaFormer models is based on two key factors: combining the strengths of ViTs and ConvNets, and utilizing a dense but not heavy forward cross attention design. Table 5 shows how we integrate these two key points in designing our models. To evaluate the performance of the proposed FcaFormer on real-world applications, we deployed each model on the edge device Rockchip 3288, which is widely used in various embedded applications. We collected latency and memory usage information for each model.
+
+The first row in Table 5 provides a baseline micro model to speed up experiments. The second row uses the simplest way to build a hybrid model, which inherits some advantages of ConvNets and ViTs. Compared to the baseline, the
+
+<table><tr><td>Rows</td><td>Models</td><td>Model differences</td><td>#Param. (M)</td><td>MACs (B)</td><td>Latency (ms)</td><td>Memory (M)</td><td>Top1 acc (%)</td></tr><tr><td>1</td><td>Swin-1G</td><td>baseline</td><td>6.25</td><td>1.49</td><td>340</td><td>46.64</td><td>78.4</td></tr><tr><td>2</td><td>ConvSwin</td><td>+early convolution</td><td>6.11</td><td>1.26</td><td>269</td><td>38.34</td><td>78.8 (+0.4)</td></tr><tr><td>3</td><td>ConvViT</td><td>+global attention</td><td>6.11</td><td>1.32</td><td>300</td><td>42.01</td><td>79.4 (+1.0)</td></tr><tr><td>4</td><td>FcaFormer</td><td>+naive forward cross attention.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.4 (+1.0)</td></tr><tr><td>5</td><td>FcaFormer</td><td>+learnable scale factors.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.9 (+1.5)</td></tr><tr><td>6</td><td>FcaFormer</td><td>+TME.</td><td>6.19</td><td>1.37</td><td>312</td><td>42.31</td><td>80.3 (+1.9)</td></tr><tr><td>7</td><td>FcaFormer</td><td>scale up to L2</td><td>16.3</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr></table>
+
+Table 5. Ablation study on Imagenet-1K. Steps 1-7 depict the process we followed to develop our FcaFormer models from the Swin-1G. We evaluated the latency and memory usage of the models on ARM Quad Core Cortex-A17. To conduct our experiments, we utilized the RK3288 platform, which is commonly employed in real-world applications such as smart TV and AI entrance guard systems.  
+
+<table><tr><td rowspan="2">Models</td><td colspan="2"># params.MACs</td><td colspan="2">Latency</td><td rowspan="2">Memory Acc (%)</td></tr><tr><td>(M)</td><td>(B)</td><td>ARM(ms)</td><td>(M)</td></tr><tr><td>ConvNext-Tiny</td><td>29</td><td>4.5</td><td>875</td><td>129</td><td>82.1</td></tr><tr><td>ConvNext-Small</td><td>50</td><td>8.7</td><td>1618</td><td>211</td><td>83.1</td></tr><tr><td>ConvNext-Base</td><td>89</td><td>15.4</td><td>2708</td><td>364</td><td>83.8</td></tr><tr><td>ConvNext-Large</td><td>198</td><td>34.4</td><td>5604</td><td>764</td><td>84.3</td></tr><tr><td>Swin-Tiny</td><td>29</td><td>4.5</td><td>855</td><td>139</td><td>81.3</td></tr><tr><td>Swin-Small</td><td>50</td><td>8.7</td><td>1576</td><td>222</td><td>83.0</td></tr><tr><td>Swin-Base</td><td>88</td><td>15.4</td><td>2624</td><td>378</td><td>83.5</td></tr><tr><td>FcaFormer-L1(Micro)</td><td>6.2</td><td>1.4</td><td>312</td><td>42</td><td>80.3</td></tr><tr><td>FcaFormer-L2(Tiny)</td><td>16</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr><tr><td>FcaFormer-L3(Small)</td><td>28</td><td>6.7</td><td>1344</td><td>148</td><td>84.2</td></tr><tr><td>FcaFormer-L4(Base)</td><td>66</td><td>14.5</td><td>2624</td><td>328</td><td>84.9</td></tr></table>
+
+Table 6. Batch size=1, image size=224, four threads. ARM:Quad Core Cortex-A17.
+
+early convolution structure achieves higher accuracy while requiring less computation and memory usage. In the third row, we replaced window attention with global attention based on computational complexity analysis in section 3.3. This improved the accuracy by  $0.6\%$  while introducing very limited extra cost. However, latency increased by  $11\%$ , and memory usage increased by  $7.7\mathrm{M}$ .
+
+Rows 4 and 5 attempt to introduce forward cross attention. In row 4, cross tokens are not calibrated, which only introduces extra cost and has no benefit to accuracy. In row 5, we adopted LSFs to adjust cross tokens, which further improved the accuracy by  $0.5\%$ . So far, FcaFormer has outperformed the baseline by  $1.5\%$  while utilizing fewer parameters and incurring lower computational costs compared to the baseline.
+
+In row 6, we introduced the TME module to generate representative cross tokens and enhance regular tokens, which improved the final accuracy to  $80.3\%$ ,  $1.9\%$  higher than the baseline. Finally, we scaled up the micro size model and got FcaFormer-L2. This new model achieved top-1 accuracy of  $83.1\%$ , meeting the requirements for some practical applications with low latency, taking less than 1 second and minimal memory usage, below 100M.
+
+![](images/f3a44c8587141390065651227734465afc10644c9145023606ae0e4377d5b9b0.jpg)  
+Figure 6. Comparison experiments. Left: Params vs. acc vs. MACs. Right: Latency vs. acc vs. MACs. The latency is measured on a single NVIDIA RTX 3090 GPU with batchsize=64.
+
+![](images/8f1a38cdd75b5b6a89af5caeffbdfd04c606dc4edc3beed062a2332914d6bf49.jpg)
+
+# 4.5. Test on different devices
+
+We deployed our proposed models on two different devices, the widely used edge device RK3288 and GPU device RTX3090, to test their inference efficiency. We also built larger models, FcaFormer-L3 (D=(96,192,320,512), L=(3,6,12,3)), and FcaFormer-L4 (D=(128,256,512,768), L=(3,6,12,3)), to validate the scalability of FcaFormer. We repeated two sets of experiments for 100 and 1000 times, respectively. The average cost is listed in Table 6 and shown in Fig 6. Our models achieved higher accuracy compared with ConvNexts while having far fewer parameters, less memory usage, and lower latency. Furthermore, our network demonstrated good scalability. From tiny model to base model, FcaFormers consistently maintained a clear advantage compared to both Swin and ConvNext models.
+
+# 5. Discussions
+
+In this paper, we introduce a new type of attention pattern for hybrid vision models. This attention pattern leverages previously generated tokens to create forward cross-attentions that span different semantic levels. Our experiments show that this approach is effective across different model scales and vision tasks. For future work, we propose combining this design with prior research on sparsifying spatial attention patterns, which could lead to even more efficient model backbones for a range of applications
+
+# References
+
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+[16] Yanghao Li, Chao-Yuan Wu, Haoqi Fan, Karttikeya Mangalam, Bo Xiong, Jitendra Malik, and Christoph Feichtenhofer. Mviv2: Improved multiscale vision transformers for classification and detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4804-4814, 2022. 6  
+[17] Yanyu Li, Geng Yuan, Yang Wen, Eric Hu, Georgios Evangelidis, Sergey Tulyakov, Yanzhi Wang, and Jian Ren. Efficientformer: Vision transformers at mobilenet speed. arXiv preprint arXiv:2206.01191, 2022. 2, 6  
+[18] T. Y. Lin, M. Maire, S. Belongie, J. Hays, and C. L. Zitnick. Microsoft coco: Common objects in context. Springer International Publishing, 2014. 5  
+[19] Jing Liu, Zizheng Pan, Haoyu He, Jianfei Cai, and Bohan Zhuang. Ecoformer: Energy-saving attention with linear complexity. Advances in Neural Information Processing Systems, 35:10295-10308, 2022. 5  
+[20] Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10012-10022, 2021. 1, 2, 5, 6, 7  
+[21] Zhuang Liu, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie. A convnet for the 2020s. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11976-11986, 2022. 4, 5, 6, 7  
+[22] Haoyan Ma, Xiang Li, Xia Yuan, and Chunxia Zhao. Denseformer: A dense transformer framework for person re-identification. IET Computer Vision, 2022. 3  
+[23] Muhammad Maaz, Abdelrahman Shaker, Hisham Cholakkal, Salman Khan, Syed Waqas Zamir, Rao Muhammad Anwer, and Fahad Shahbaz Khan. Edgenext: efficiently amalgamated cnn-transformer architecture for mobile vision applications. In Computer Vision-ECCV 2022 Workshops: Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part VII, pages 3-20. Springer, 2023. 6  
+[24] Sachin Mehta and Mohammad Rastegari. Mobilevit: lightweight, general-purpose, and mobile-friendly vision transformer. arXiv preprint arXiv:2110.02178, 2021. 2, 6  
+[25] Junting Pan, Adrian Bulat, Fuwen Tan, Xiatian Zhu, Lukasz Dudziak, Hongsheng Li, Georgios Tzimiropoulos, and Brais Martinez. Edgevits: Competing light-weight cnns on mobile devices with vision transformers. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel,
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+October 23-27, 2022, Proceedings, Part XI, pages 294-311. Springer, 2022. 6  
+[26] Zizheng Pan, Jianfei Cai, and Bohan Zhuang. Fast vision transformers with hilo attention. arXiv preprint arXiv:2205.13213, 2022. 2, 6  
+[27] Zizheng Pan, Bohan Zhuang, Haoyu He, Jing Liu, and Jianfei Cai. Less is more: Pay less attention in vision transformers. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 2035-2043, 2022. 2  
+[28] Yongming Rao, Wenliang Zhao, Benlin Liu, Jiwen Lu, Jie Zhou, and Cho-Jui Hsieh. Dynamicvit: Efficient vision transformers with dynamic token sparsification. In Advances in Neural Information Processing Systems (NeurIPS), 2021. 1, 2  
+[29] Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zh-moginov, and Liang-Chieh Chen. Mobilenetv2: Inverted residuals and linear bottlenecks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4510-4520, 2018. 2, 6  
+[30] Aravind Srinivas, Tsung-Yi Lin, Niki Parmar, Jonathon Shlens, Pieter Abbeel, and Ashish Vaswani. Bottleneck transformers for visual recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 16519-16529, 2021. 2  
+[31] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training data-efficient image transformers & distillation through attention. In International Conference on Machine Learning, pages 10347-10357. PMLR, 2021. 2, 5, 6  
+[32] Zhengzhong Tu, Hossein Talebi, Han Zhang, Feng Yang, Peyman Milanfar, Alan Bovik, and Yinxiao Li. Maxvit: Multi-axis vision transformer. ECCV, 2022. 1, 2  
+[33] Pavan Kumar Anasosalu Vasu, James Gabriel, Jeff Zhu, Oncel Tuzel, and Anurag Ranjan. An improved one millisecond mobile backbone. arXiv preprint arXiv:2206.04040, 2022. 6  
+[34] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017. 3  
+[35] Robert J Wang, Xiang Li, and Charles X Ling. Pelee: A real-time object detection system on mobile devices. Advances in neural information processing systems, 31, 2018. 3  
+[36] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyramid vision transformer: A versatile backbone for dense prediction without convolutions. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 568-578, 2021. 2  
+[37] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pvt v2: Improved baselines with pyramid vision transformer. Computational Visual Media, 8(3):415-424, 2022. 2, 6  
+[38] Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuning Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In Proceedings of the European conference on computer vision (ECCV), pages 418-434, 2018. 6
+
+[39] Tete Xiao, Mannat Singh, Eric Mintun, Trevor Darrell, Piotr Dollar, and Ross Girshick. Early convolutions help transformers see better. Advances in Neural Information Processing Systems, 34:30392-30400, 2021. 2, 4  
+[40] Weijian Xu, Yifan Xu, Tyler Chang, and Zhuowen Tu. Coscale conv-attentional image transformers. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9981–9990, 2021. 6  
+[41] Weihao Yu, Mi Luo, Pan Zhou, Chenyang Si, Yichen Zhou, Xinchao Wang, Jiashi Feng, and Shuicheng Yan. Metaformer is actually what you need for vision. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10819-10829, 2022. 6  
+[42] Li Yuan, Yunpeng Chen, Tao Wang, Weihao Yu, Yujun Shi, Zi-Hang Jiang, Francis EH Tay, Jiashi Feng, and Shuicheng Yan. Tokens-to-token vit: Training vision transformers from scratch onImagenet. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 558-567, 2021. 6  
+[43] Haokui Zhang, Wenze Hu, and Xiaoyu Wang. Parc-net: Position aware circular convolution with merits from convnets and transformer. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXVI, pages 613-630. Springer, 2022. 6  
+[44] Bolei Zhou, Hang Zhao, Xavier Puig, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Scene parsing through ade20k dataset. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 5
\ No newline at end of file
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+                                    "content": " top-1 accuracy on Imagenet with only 16.3 million parameters and about 3.6 billion MACs. This saves almost half of the parameters and a few computational costs while achieving "
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+                                }
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+                                }
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+                                    "content": "typical classes of transformer models: the plain ViT model used in DeiT, and the hybrid ConvNet and transformer structures frequently seen in recent works [24, 9, 17]. Our experiments demonstrate that the Fca block can seamlessly replace the corresponding transformer blocks in these architectures, leading to significantly improved performance compared to their corresponding baselines. Specifically, FcaFormer-L1 achieves a top-1 accuracy of "
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+                                    "content": " higher accuracy compared to the recently proposed EfficientFormer. Table 2 displays the comparison results."
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+                                            "content": "- Opposite to many recent works that use sparse attentions to improve transformer models, we propose to design more efficient models by densifying the attention connection patterns, which open up a new and worthwhile research avenue for consideration."
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+                                    "content": " patches as an input token sequence to the transformer and used positional encoding to model spatial relations among tokens. DeiT [31] lowered the difficulty of ViT model training by knowledge distillation, and achieved competitive accuracy with less pretraining data. To further improve the model architecture, researchers attempted to optimize the ViT toward improving its computational efficiency. Among them, the Swin transformer [20] computes self attention among shifted local windows. The MaxViT [32] uses block attention and grid attention alternatively to keep spatially global information exchange while significantly reduce the number of tokens involved in the self attention computation. The DynamicViT [28] prunes redundant tokens progressively and dynamically depending on"
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+                                    "content": "the input features. Mohsen et al. [7] proposed a differentiable parameter-free adaptive token sampler and plugged it into ViTs to sample part tokens for attention computation."
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+                                    "content": "al. [35] further improve DenseNet by using two-way dense layers to obtain different receptive fields. With limited extra computational cost, these model design choices solved bottlenecks existed in ConvNets and are still widely used in both academia and industry. Skip connection is also used in transformer models. For instance, Denseformer [22] reuses the first layer CLS token into subsequent layers."
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+                                    "content": "Our proposed forward cross attention is similar to the works above in that it reuses existing intermediate results and introduces extra connections to the overall network structure. As experiments show, our work introduces similar benefits to transformer models such as better model performance and faster model convergence."
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+                                    "content": " are then used in the standard FFN part of ViT to compute the output token "
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+                                            "content": "- Asymmetric input and output. In our FcaFormer, CMHA part takes both regular tokens and cross tokens as input but keep the output sequence length fixed to "
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+                                            "content": " as in regular transformers. This is the key point that why our proposed FcaFormer only introduce limited extra computational cost. More details are explained in section 3.3."
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+                                            "content": "- Cross token scale. LSFs are used to facilitate the integration of cross tokens into regular tokens. Without this calibration process, cross tokens may not function as expected. As shown in Fig 5."
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+                                            "content": "- Relative depth embedding. In the CMHA part, we choose to use relative positional encoding instead of absolute ones. Apart from its generally better performance, the choice also gives model the flexibility to encode relative depth of the cross tokens, which simplifies the model design."
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+                                            "content": "Figure 3. The overall structure of FcaFormer Mobels for image classification tasks. (a) Plain FcaFormer model. This model is directly modified from the DeiT structure. (b) Hybrid FcaFormer model. The ConvNet stages are composed of ConvNext blocks. The detailed model scaling hyperparameters are specified in Sec.3.2"
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+                                    "content": "pattern, we build two types of FcaFormer based models, each falls into one of the major categories of transformer related computer vision models as described in Sec. 2. The overall structure of these models for classification task are illustrated in Fig.3."
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+                                    "content": "Plain FcaFormer. As shown in Fig 3 (a), following the style of vanilla ViT, we construct our plain FcaFormer model (denoted as FcaFormer-L0). The model essentially uses one block of FcaFormer after the patch embedding layer that crops "
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+                                    "type": "text",
+                                    "content": " patches and converts them into a token sequence. The corresponding task related head is kept unchanged compared with the original ViT model."
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+                                    "content": "Hybrid FcaFormer. As illustrated in Fig 3 (b). Following the trend of combining ConvNet structures and transformer structures to build hybrid models, we also propose to build hybrid FcaFormer. Following LeViT [9] and ViTC[39], we adopt the most straightforward way to build our Hybrid FcaFormers, where there are two conventional ConvNet stages followed by two FcaFormer stages. The ConvNet stage is composed of ConvNext blocks [21] plus a downsampling layer that uses pointwise and depthwise convolutions to reduce the feature map resolution by "
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+                                    "content": " and increases the feature map channels."
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+                                    "content": "Based on the above overall structure, we build models of different sizes to compare with other works. The key scaling hyper-parameters is summarized below, where "
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+                                    "content": " denotes the channel size:"
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+                                            "content": "- FcaFormer-L0: "
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+                                            "content": "\\mathrm{D} = {192},\\mathrm{\\;L} = {12}"
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+                                            "content": "- FcaFormer-L1: "
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+                                            "content": "Figure 4. Computational cost analysis. (a) Detailed analysis on the number of parameters and MACs for a transformer block; (b)-(c) Computation decompositions in blocks of stage 3 of DeiT-Tiny and stage 4 of EfficientFormer-L1 respectively."
+                                        }
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+                                    "content": "3.3. Computational Complexity of FcaFormer"
+                                }
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+                        }
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+                },
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+                                    "type": "text",
+                                    "content": "In terms of computational complexity, transformers are notorious for its "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(n^2)"
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+                                    "type": "text",
+                                    "content": " scaling property, which is why so many prior works try to reduce the inputs to the MHA model. However, the extra computational cost of densifying the attention pattern is rather limited in our FcaFormer models, because of the following reasons:"
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "1) The added extra computation is restricted to the MHA part, since we keep the output sequence length of MHA fixed to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as in regular transformers. This leads to linear scaling cost in terms of the number of additional input tokens, which itself is a small "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "inline_equation",
+                                    "content": "\\left( (l - 1) * n / s^2 \\right)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        365,
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+                                    ],
+                                    "type": "text",
+                                    "content": " compared with "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". The computational cost of FFN part is kept unchanged compared with original ViT blocks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "2) In vision transformer model families, the FFN part actually constitutes the majority of computations. In [19], Liu et al. also emphasized that larger models incur higher computational costs, primarily due to FFNs. Here, we delve into a more detailed analysis. This is paradoxical to the fact that MHA scales at "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(n^2)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " while FFN scales at "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(n)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", largely because that the neglected constant token size "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in big O analysis is rather large and scales poorly. Fig. 4 details the exact adds and multiplications (MACs) of a standard ViT block in terms of the number of tokens "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and the dimension of tokens "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Taking the transformer block DeiT-Tiny as an example, because "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n = 196"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "d = 192"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are at the same scale, the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "2n^2 d"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " MACs in MHA is much less compared with that "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(8nd^2)"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of FFN ("
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "15\\%"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " vs "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "56\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " respectively). For models in pyramid shapes such as swim transformers where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n < d"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", the majority skews even more towards FFN because of the local windowing effect. Compared with the reference models, our FcaFormer variants only introduce about "
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+                                    "content": " extra computational cost."
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+                                    "content": "It looks like that the proposed FcaFormer is heavier than its reference model as it introduces extra computations. However, the counter-intuitive fact is that FcaFormer can"
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+                                            "html": "<table><tr><td>Models</td><td># params. (M)</td><td>FLOPs (G)</td><td>Top1 acc</td></tr><tr><td>DeiT-T [31]</td><td>5.5</td><td>1.23</td><td>72.2</td></tr><tr><td>FcaFormer-L0</td><td>5.9.</td><td>1.49</td><td>74.3</td></tr><tr><td>Swin-1G‡</td><td>6.3</td><td>1.5</td><td>78.4</td></tr><tr><td>FcaFormer-L1</td><td>6.2</td><td>1.4</td><td>80.3</td></tr><tr><td>ConvNext-Tiny [21]</td><td>29</td><td>4.5</td><td>82.1</td></tr><tr><td>Swin-Tiny [20]</td><td>29</td><td>4.5</td><td>81.3</td></tr><tr><td>FcaFormer-L2</td><td>16.3</td><td>3.6</td><td>83.1</td></tr></table>",
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+                                            "content": "Table 1. Comparison with baselines. The plain version FcaFormer is based on DeiT-T. The hybrid ViT FcaFormer models are based on ConvNext and Swin Transformers. "
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+                                            "content": "means our implementation"
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+                                    "type": "text",
+                                    "content": "be more light-weight than its reference model. As is mentioned in introduction, FcaFormer reuses tokens from previous blocks, enhances interaction of tokens across blocks and improve information flow. Compared with the vanilla ViT, FcaFormer has better parameter efficiency. Therefore, FcaFormer can get comparable or even better performance with fewer layers and channels. Our experiments further verifies this advantage."
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+                                    "content": "In addition to the detailed analysis above, we want to point out that the prior efforts to sparsify the attention patterns spatially in Sec.2.1 and our proposal to densify the attention patterns across semantic levels are complementary to each other. While not the key emphasis of this paper, it is definitely worth exploring if the two types of designs can be combined to yield even more efficient and performant models."
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+                                    "type": "text",
+                                    "content": "4. Experiments"
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+                                    "content": "In this section, we conduct image classification experiments on Imagenet-1K [3], semantic segmentation experiments on ADE20K [44], and object detection experiments on MS-COCO [18] to evaluate our proposed models. We first compare the proposed FcaFormers with our baselines and the previous SOTA methods. Then, we conduct detailed study to show the effectiveness of our design choices."
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+                                    "content": "Experiment settings. The FcaFormer-L0 is implemented based on code of DeiT<sup>1</sup>. The hybrid FcaFormer models are implemented based on code of ConvNext<sup>2</sup> and Swin<sup>3</sup>. We follow the training recipes in DeiT [31] to train our FcaFormer-L0, except that we did not use the knowledge distillation. To train the hybrid FcaFormers, we use the same training hyper parameters and augmentations as used in ConvNext except that the batch size is restricted to 1024 and the initial learning rate is reduced to 2e-3. This change is because we don't have enough GPUs to support the default batch size of 4096 in ConvNext."
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+                                            "content": "Table 2. Comparison with the SOTA methods on ImageNet-1K validation set. KD means knowledge distillation is used. ‡ indicates implemented by us, where models are trained following the training setting used in ConvNext. Accuracy and FLOPs are calculated on input image size "
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+                                    "content": "Comparison with baselines. The results are summarized in Table 1, from which we can see that both types of our proposed FcaFormer models outperform their reference models by a significant margin. Compared with DeiT, FcaFormer-L0 does have "
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+                                    "type": "text",
+                                    "content": " higher accuracy. Our hybrid FcaFormers achieve better performance in all three metrics: accuracy, model size and computational cost. FcaFormer-L1 achieves "
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+                                    "content": " higher top-1 accuracy compared with sim"
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+                                            "html": "<table><tr><td>Method</td><td>Backbone</td><td>mIOU</td><td># params.</td><td>MACs</td></tr><tr><td>DANet</td><td>ResNet-101</td><td>45.2</td><td>69</td><td>1119</td></tr><tr><td>DpLab.v3+</td><td>ResNet-101</td><td>44.1</td><td>63</td><td>1021</td></tr><tr><td>ACNet</td><td>ResNet-101</td><td>45.9</td><td>-</td><td>-</td></tr><tr><td>DNL</td><td>ResNet-101</td><td>46.0</td><td>69</td><td>1249</td></tr><tr><td>OCRNet</td><td>ResNet-101</td><td>45.3</td><td>56</td><td>923</td></tr><tr><td>UperNet</td><td>ResNet-101</td><td>44.9</td><td>86</td><td>1029</td></tr><tr><td>UperNet</td><td>DeiT III (ViT-S)</td><td>46.8</td><td>42</td><td>588</td></tr><tr><td>UperNet</td><td>Swin-T</td><td>45.8</td><td>60</td><td>945</td></tr><tr><td>UperNet</td><td>ConvNext-T</td><td>46.7</td><td>60</td><td>939</td></tr><tr><td>UperNet</td><td>FcaFormer-L2</td><td>47.6</td><td>46</td><td>730</td></tr></table>",
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+                                            "content": "Table 3. Semantic segmentation on the ADE20K dataset. We use UperNet as our segmentation method and compare our performance using the same method with other popular backbones."
+                                        }
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+                                    "content": "arily sized Swin-1G. FcaFormer-L1 also has good scalability. The scaled up version FcaFormer-L2 outperforms the ConvNext-Tiny by "
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+                                    "type": "text",
+                                    "content": " less computational cost and "
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+                                    "type": "text",
+                                    "content": " fewer parameters. FcaFormer-L2 also surpasses Swin-T by "
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+                                    "type": "text",
+                                    "content": " while using fewer parameters and less computation."
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+                                    "type": "text",
+                                    "content": "In summary, our proposed forward cross attention design universally improves performances of both plain version and hybrid ViT models without increasing too much extra computation cost or even saving parameters and FLOPs."
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+                                    "content": "Comparison with other models. In Table 2, we make a comparison with other models proposed in recent two years. Compared to the latest state-of-the-arts, including ConvNets, ViTs and Hybrid models, our proposed FcaFormer models achieve the best accuracy under the condition of having similar model sizes. In addition, the proposed models beat models strengthened by knowledge distillation in classification accuracy."
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+                                    "content": "Specifically, FcaFormer-L1 outperforms MobileOne and EdgeNext by "
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+                                    "content": " in classification accuracy, while keeping comparable or smaller model size and fewer computational cost. Among models having about 25 million parameters, FcaFormer-L2 achieves the highest classification accuracy with the fewest parameters. Compared with Next-ViT-S which achieves the second highest accuracy, FcaFormer-L2 saves about half parameters and "
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+                                    "type": "text",
+                                    "content": " computational cost, while gaining 0.6 percentage points higher accuracy. Also, note that both EfficientFormer-L3 and LeViT-256 are trained with knowledge distillation, which has been verified to improve accuracy significantly [31]. Even so, FcaFormer-L2 still has better accuracy and smaller model size compared with these two models."
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+                                    "content": "4.2. Semantic segmentation"
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+                                    "content": "Training setting. To evaluate the proposed FcaFormers on downstream tasks. We apply them on the ADE20K semantic segmentation task. Following Swin and ConvNext, we adopt UperNet [38] as our base framework and imple"
+                                }
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+                                            "html": "<table><tr><td>Backbone</td><td>#Params.MACs</td><td>APb</td><td>APb50</td><td>APb75</td><td>APm</td><td>APm50</td><td>APm75</td></tr><tr><td colspan=\"8\">Mask-RCNN 3× schedule</td></tr><tr><td>SWin-T</td><td>48</td><td>267</td><td>46.0</td><td>68.1</td><td>50.3</td><td>41.6</td><td>65.1</td></tr><tr><td>ConvNext-T</td><td>48</td><td>262</td><td>46.2</td><td>67.9</td><td>50.8</td><td>41.7</td><td>65.0</td></tr><tr><td>FcaFormer-L2</td><td>37</td><td>249</td><td>47.0</td><td>68.9</td><td>51.8</td><td>42.1</td><td>65.7</td></tr><tr><td colspan=\"8\">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50</td><td>82</td><td>739</td><td>46.3</td><td>64.3</td><td>50.5</td><td>40.1</td><td>61.7</td></tr><tr><td>DeiT-S</td><td>80</td><td>889</td><td>48.0</td><td>67.2</td><td>51.7</td><td>41.4</td><td>64.2</td></tr><tr><td>X101-32</td><td>101</td><td>819</td><td>48.1</td><td>66.5</td><td>52.4</td><td>41.6</td><td>63.9</td></tr><tr><td>X101-64</td><td>140</td><td>972</td><td>48.3</td><td>66.4</td><td>52.3</td><td>41.7</td><td>64.0</td></tr><tr><td>Swin-T</td><td>86</td><td>745</td><td>50.4</td><td>69.2</td><td>54.7</td><td>43.7</td><td>66.6</td></tr><tr><td>ConvNext-T</td><td>86</td><td>741</td><td>50.4</td><td>69.1</td><td>54.8</td><td>43.7</td><td>66.5</td></tr><tr><td>FcaFormer-L2</td><td>74</td><td>728</td><td>51.0</td><td>69.4</td><td>55.5</td><td>43.9</td><td>67.0</td></tr><tr><td>Swin-S</td><td>107</td><td>838</td><td>51.9</td><td>70.7</td><td>56.3</td><td>45.0</td><td>68.2</td></tr><tr><td>ConvNext-S</td><td>108</td><td>827</td><td>51.9</td><td>70.8</td><td>56.5</td><td>45.0</td><td>68.4</td></tr><tr><td>FcaFormer-L3</td><td>86</td><td>792</td><td>52.4</td><td>71.1</td><td>57.2</td><td>44.9</td><td>68.4</td></tr><tr><td>Swin-B</td><td>145</td><td>982</td><td>51.9</td><td>70.5</td><td>56.4</td><td>45.0</td><td>68.1</td></tr><tr><td>ConvNext-B</td><td>146</td><td>964</td><td>52.7</td><td>71.3</td><td>57.2</td><td>45.6</td><td>68.9</td></tr><tr><td>FcaFormer-L4</td><td>124</td><td>970</td><td>53.7</td><td>72.4</td><td>58.2</td><td>46.3</td><td>69.7</td></tr></table>",
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+                                    "content": "Table 4. Object detection on the COCO dataset."
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+                                    "type": "text",
+                                    "content": "ment segmentation experiments on mmseg "
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+                                    "type": "text",
+                                    "content": ". FcaFormerL2 is trained for 160K iterations with a batch size of 16. Model pretrained on ImageNet-1K is used to initialize segmentation model. More details are presented in supplementary materials."
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+                                    "content": "Comparison with baselines. The results are summarized in Tab.3, compared with Swin-Tiny, FcaFormer-L2 achieves "
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+                                    "content": " higher mIoU. Compared with ConvNext-Tiny, FcaFormer-L2 achieves "
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+                                    "content": " higher mIoU. Compared with Swin-T and ConvNext-T, the last two stages of FcaFormer-L2 are narrower (384 vs 320, 768 vs 480), which saves parameters and computational cost. Therefore, our FcaFormer-L2 achieves higher mIoU, while saving "
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+                                    "type": "text",
+                                    "content": " computation cost."
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+                                    "content": ". Following [20] and [21], we fintune MASK-RCNN and Cascade Mask R-CNN on the COCO dataset with FcaFormer pretrained on ImageNet-1k. We use multi-scale training, AdamW optimizer, and a "
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+                                    "type": "text",
+                                    "content": " schedule. More details are presented in supplementary materials."
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+                                    "content": "Comparison with baselines. The results are summarized in Tab.4. Experimental results on objection detection show a similar trend with that on semantic segmentation. Compared with Swin-Tiny and ConvNext-Tiny, FcaFormer-L2 achieves higher values on all six metrics, while having"
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+                                            "content": "Figure 5. Effects of LSFs. Attention scores for cross tokens are marked with red boxes. From rows 1-4, attention maps are from blocks 2,4 and 6 of stage3, and block 2 of stage 4 respectively."
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+                                    "content": "In this section, we conduct ablation analysis on components proposed in our FcaFormer."
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+                                    "content": "Effects of the learnable scale factors (LSFs). Fig 5 shows the attention score maps of several FcaFormer blocks trained with and without LSFs. It can be seen that without LSFs, the attention between cross tokens and regular tokens are generally weak, and become weaker as the depth goes deeper (down on the figure). This verifies our hypothesis that characteristics of tokens in different levels can be very different. Comparing the two columns of attention maps, it clearly shows that the LSFs helps increasing the correlation between regular tokens and the cross tokens, thus encourages the reuse of previously generated tokens."
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+                                    "content": "From baseline to FcaFormer. The high performance of FcaFormer models is based on two key factors: combining the strengths of ViTs and ConvNets, and utilizing a dense but not heavy forward cross attention design. Table 5 shows how we integrate these two key points in designing our models. To evaluate the performance of the proposed FcaFormer on real-world applications, we deployed each model on the edge device Rockchip 3288, which is widely used in various embedded applications. We collected latency and memory usage information for each model."
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+                                    "content": "The first row in Table 5 provides a baseline micro model to speed up experiments. The second row uses the simplest way to build a hybrid model, which inherits some advantages of ConvNets and ViTs. Compared to the baseline, the"
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+                                            "html": "<table><tr><td>Rows</td><td>Models</td><td>Model differences</td><td>#Param. (M)</td><td>MACs (B)</td><td>Latency (ms)</td><td>Memory (M)</td><td>Top1 acc (%)</td></tr><tr><td>1</td><td>Swin-1G</td><td>baseline</td><td>6.25</td><td>1.49</td><td>340</td><td>46.64</td><td>78.4</td></tr><tr><td>2</td><td>ConvSwin</td><td>+early convolution</td><td>6.11</td><td>1.26</td><td>269</td><td>38.34</td><td>78.8 (+0.4)</td></tr><tr><td>3</td><td>ConvViT</td><td>+global attention</td><td>6.11</td><td>1.32</td><td>300</td><td>42.01</td><td>79.4 (+1.0)</td></tr><tr><td>4</td><td>FcaFormer</td><td>+naive forward cross attention.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.4 (+1.0)</td></tr><tr><td>5</td><td>FcaFormer</td><td>+learnable scale factors.</td><td>6.11</td><td>1.37</td><td>311</td><td>42.07</td><td>79.9 (+1.5)</td></tr><tr><td>6</td><td>FcaFormer</td><td>+TME.</td><td>6.19</td><td>1.37</td><td>312</td><td>42.31</td><td>80.3 (+1.9)</td></tr><tr><td>7</td><td>FcaFormer</td><td>scale up to L2</td><td>16.3</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr></table>",
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+                                            "content": "Table 5. Ablation study on Imagenet-1K. Steps 1-7 depict the process we followed to develop our FcaFormer models from the Swin-1G. We evaluated the latency and memory usage of the models on ARM Quad Core Cortex-A17. To conduct our experiments, we utilized the RK3288 platform, which is commonly employed in real-world applications such as smart TV and AI entrance guard systems."
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+                                            "html": "<table><tr><td rowspan=\"2\">Models</td><td colspan=\"2\"># params.MACs</td><td colspan=\"2\">Latency</td><td rowspan=\"2\">Memory Acc (%)</td></tr><tr><td>(M)</td><td>(B)</td><td>ARM(ms)</td><td>(M)</td></tr><tr><td>ConvNext-Tiny</td><td>29</td><td>4.5</td><td>875</td><td>129</td><td>82.1</td></tr><tr><td>ConvNext-Small</td><td>50</td><td>8.7</td><td>1618</td><td>211</td><td>83.1</td></tr><tr><td>ConvNext-Base</td><td>89</td><td>15.4</td><td>2708</td><td>364</td><td>83.8</td></tr><tr><td>ConvNext-Large</td><td>198</td><td>34.4</td><td>5604</td><td>764</td><td>84.3</td></tr><tr><td>Swin-Tiny</td><td>29</td><td>4.5</td><td>855</td><td>139</td><td>81.3</td></tr><tr><td>Swin-Small</td><td>50</td><td>8.7</td><td>1576</td><td>222</td><td>83.0</td></tr><tr><td>Swin-Base</td><td>88</td><td>15.4</td><td>2624</td><td>378</td><td>83.5</td></tr><tr><td>FcaFormer-L1(Micro)</td><td>6.2</td><td>1.4</td><td>312</td><td>42</td><td>80.3</td></tr><tr><td>FcaFormer-L2(Tiny)</td><td>16</td><td>3.6</td><td>728</td><td>95</td><td>83.1</td></tr><tr><td>FcaFormer-L3(Small)</td><td>28</td><td>6.7</td><td>1344</td><td>148</td><td>84.2</td></tr><tr><td>FcaFormer-L4(Base)</td><td>66</td><td>14.5</td><td>2624</td><td>328</td><td>84.9</td></tr></table>",
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+                                    "content": "Rows 4 and 5 attempt to introduce forward cross attention. In row 4, cross tokens are not calibrated, which only introduces extra cost and has no benefit to accuracy. In row 5, we adopted LSFs to adjust cross tokens, which further improved the accuracy by "
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+                                    "content": " higher than the baseline. Finally, we scaled up the micro size model and got FcaFormer-L2. This new model achieved top-1 accuracy of "
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+                                    "content": ", meeting the requirements for some practical applications with low latency, taking less than 1 second and minimal memory usage, below 100M."
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+                                            "content": "Figure 6. Comparison experiments. Left: Params vs. acc vs. MACs. Right: Latency vs. acc vs. MACs. The latency is measured on a single NVIDIA RTX 3090 GPU with batchsize=64."
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+                                    "content": "4.5. Test on different devices"
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+                                    "content": "We deployed our proposed models on two different devices, the widely used edge device RK3288 and GPU device RTX3090, to test their inference efficiency. We also built larger models, FcaFormer-L3 (D=(96,192,320,512), L=(3,6,12,3)), and FcaFormer-L4 (D=(128,256,512,768), L=(3,6,12,3)), to validate the scalability of FcaFormer. We repeated two sets of experiments for 100 and 1000 times, respectively. The average cost is listed in Table 6 and shown in Fig 6. Our models achieved higher accuracy compared with ConvNexts while having far fewer parameters, less memory usage, and lower latency. Furthermore, our network demonstrated good scalability. From tiny model to base model, FcaFormers consistently maintained a clear advantage compared to both Swin and ConvNext models."
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+                                    "content": "5. Discussions"
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+                                    "content": "In this paper, we introduce a new type of attention pattern for hybrid vision models. This attention pattern leverages previously generated tokens to create forward cross-attentions that span different semantic levels. Our experiments show that this approach is effective across different model scales and vision tasks. For future work, we propose combining this design with prior research on sparsifying spatial attention patterns, which could lead to even more efficient model backbones for a range of applications"
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+                                }
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+                                        }
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+                                        }
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+                                        }
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diff --git a/2023/FeatEnHancer_ Enhancing Hierarchical Features for Object Detection and Beyond Under Low-Light Vision/d981278d-dbe2-41ac-9aab-c72923dbfb19_content_list.json b/2023/FeatEnHancer_ Enhancing Hierarchical Features for Object Detection and Beyond Under Low-Light Vision/d981278d-dbe2-41ac-9aab-c72923dbfb19_content_list.json
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+    {
+        "type": "text",
+        "text": "FeatEnHancer: Enhancing Hierarchical Features for Object Detection and Beyond Under Low-Light Vision",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Khurram Azeem Hashmi $^{1,2}$ , Goutham Kallempudi $^{2}$ , Didier Stricker $^{1,2}$  and Muhammad Zeshan Afzal $^{1,2}$",
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+        "type": "text",
+        "text": "$^{1}$ DFKI - German Research Center for Artificial Intelligence,  $^{2}$ RPTU Kaiserslautern, {khurram.azeem Hashmi, didier.stricker, muhammad.zeshan.afzal}@dfki.de, kallempu@rptu.de",
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+        "img_path": "images/863d1335d99571d2dc51cd9855a417f29a2a5144b35e057861987f654bcc283d.jpg",
+        "image_caption": [
+            "GT",
+            "Hierarchical Representation",
+            "Figure 1: Learned hierarchical representation and enhanced image from our FeatEnHancer. We train our FeatEnHancer on a downstream object detection task and visualize these images from the validation set. These maps and enhanced images show that despite producing less visually appealing images, our model enhances task-related features. Best viewed on the screen."
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Extracting useful visual cues for the downstream tasks is especially challenging under low-light vision. Prior works create enhanced representations by either correlating visual quality with machine perception or designing illumination-degrading transformation methods that require pre-training on synthetic datasets. We argue that optimizing enhanced image representation pertaining to the loss of the downstream task can result in more expressive representations. Therefore, in this work, we propose a novel module, FeatEnHancer, that hierarchically combines multiscale features using multi-headed attention guided by task-related loss function to create suitable representations. Furthermore, our intra-scale enhancement improves the quality of features extracted at each scale or level, as well as combines features from different scales in a way that reflects their relative importance for the task at hand. FeatEnHancer is a general-purpose plug-and-play module and can be incorporated into any low-light vision pipeline. We show with extensive experimentation that the enhanced representation produced with FeatEnHancer significantly and consistently improves results in several low",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "light vision tasks, including dark object detection (+5.7 mAP on ExDark), face detection (+1.5 mAP on DARK FACE), nighttime semantic segmentation (+5.1 mIoU on ACDC), and video object detection (+1.8 mAP on DarkVision), highlighting the effectiveness of enhancing hierarchical features under low-light vision.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent remarkable advancements in high-level vision tasks have shown that given a high-quality image, current vision backbone networks [20, 15, 12, 32, 31], object detectors [42, 28, 43, 19, 2, 3, 49, 4, 71, 64, 65] and semantic segmentation models [34, 48, 57, 7, 58] can effectively learn desired features to perform vision tasks. Similarly, modern low-light image enhancement (LLIE) methods [44, 67, 14, 21, 17, 25] are capable of transforming a low-light image into a visual-friendly representation. However, a naive combination of the two brings sub-optimal gains when it comes to high-level vision tasks under low-light vision.",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "6725",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This work explores the underlying reasons for the low performance of the combination of LLIE with high-level vision methods and observes the following limitations: 1) Although existing LLIE methods push the envelope of visual perception for human eyes, they do not align with vision backbone networks [20, 12, 15, 32, 31] due to lack of multiscale features. For instance, it is likely that the enhancement method increases brightness in some regions. However, it simultaneously corrupts the edges and texture information of objects. 2) The pixel distribution among different low-light images may have huge variance owing to the disparity in less illuminated environments [17, 25, 68]. This increases intra-class variance in some cases (see Fig. 3, where only one bicycle is recognized by [17] instead of two bicycles in the ground-truth). 3) Current LLIE approaches [14, 17, 25, 21, 44, 56, 67] employ enhancement loss functions to optimize the enhancement networks. These loss functions compel the network to attend to all pixels equally, lacking the learning of informative details necessary for high-level downstream vision tasks such as object pose and shape for object detection. Furthermore, to train these enhancement networks, most of them [44, 14, 67, 56] require a set of high-quality images, which is hardly available in a real-world setting.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Motivated by these observations and inspired by recent developments in LLIE [17, 25] and vision-based backbone networks [15, 32, 31], this paper aims to bridge the gap by exploring an end-to-end trainable recipe that jointly optimizes the enhancement and downstream task objectives in a single network. To this end, we present FeatEnHancer, a general-purpose feature enhancer that learns to enrich multiscale hierarchical features favourable for downstream vision tasks in a low-light setting. An example of learned hierarchical representation and the enhanced image is illustrated in Fig. 1.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In particular, our FeatEnHancer first downsamples a low-light RGB input image to construct multi-scale hierarchical representations. Subsequently, these representations are fed to our Feature Enhancement Network (FEN), which is a deep convolutional network, employed to enrich intra-scale semantic representations. Note that the parameters of FEN can be adjusted through task-related loss functions, which pushes the FEN to only enhance the task-related features. This multiscale learning allows the network to enhance both global and local information from higher and lower-resolution features, respectively. Once the enhanced representations on different scales are obtained, the remaining obstacle is to fuse them effectively. To achieve, this, we select two different strategies to capture both global and local information from higher and lower-resolution features. First, to merge high-resolution features, inspired by multi-head attention in [50], we design a Scale-aware Attentional Feature Aggregation (SAFA) method that jointly attends information from differ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "ent scales. Second, for lower-resolution features, the skip connection [20] scheme is adopted to merge the enhanced representation from SAFA to lower-resolution features. With these jointly learned hierarchical features, our FeatEnHancer provides semantically powerful representations which can be exploited by advanced methods such as feature pyramid networks [27] for object detection [43] and instance segmentation [19], or UNet [45] for semantic segmentation [34].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main contributions of this work can be summarized as follows:",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. We propose FeatEnHancer, a novel module that enhances hierarchical features to boost downstream vision tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. FeatEnHancer is a general-purpose plug-and-play module that can be trained end-to-end with any high-level vision task.",
+            "2. To the best of our knowledge, this is the first work that fully exploits multi-scale hierarchical features in low-light scenarios and generalizes to several downstream vision tasks such as object detection, semantic segmentation, and video object detection.",
+            "3. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods and task-specific state-of-the-art approaches."
+        ],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "page_idx": 1
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+        "type": "text",
+        "text": "2.1. Enhancing Low-Light Images",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Deep learning-based LLIE methods focus on improving the visual quality of low-light images that satisfies human visual perception [23, 22]. Most LLIE approaches [14, 44, 56, 67] operate under a supervised learning paradigm, requiring paired data during training. Unsupervised GAN-based methods [21] eliminate the need for paired data during the training. However, their performance relies on the careful choice of unpaired data. Recently, zero-reference methods [17, 25, 68] discard the need for both paired and unpaired data to enhance low-light images by designing a set of non-reference loss functions. Inspired by these recent developments, this work aims to bridge low-light enhancement and downstream vision tasks (such as object detection [10, 33, 62], semantic segmentation [60, 47], and video object detection [63]) by enhancing multi-scale hierarchical features without needing paired or unpaired data to boost performance.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "6726",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.2. Enhancing Low-Light for Downstream Vision Tasks",
+        "text_level": 1,
+        "bbox": [
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+            90,
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+            119
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "These approaches consider machine perception as the criteria for success while enhancing images to improve downstream vision tasks. One obvious way to achieve this goal is to apply the LLIE methods as an initial step [70, 17]. However, this leads to unsatisfactory results (see Table 2, 4, and 5). Recently, another line of work has explored end-to-end pipelines, optimizing both enhancement and individual tasks during training, and our work follows the same spirit.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Face detection. Liang et al. [26] propose an effective information extraction scheme from low-light images by exploiting multi-exposure generation. Furthermore, bi-directional domain adaptation [52, 51] and parallel architecture that jointly performs enhancement and detection [37] are presented to advance the research. However, these approaches are carefully designed to tackle face detection [62, 53] only and deliver minor improvements when applied to generic object detection [51]. Contrarily, our FeatEnHancer is a general-purpose module. It significantly improves several downstream vision tasks. Hence, we refrain from comparing our method to architectures only evaluated for face detection.",
+        "bbox": [
+            76,
+            250,
+            468,
+            444
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Dark object detection. Dark (low-light) object detection [10, 30] methods have emerged recently, thanks to the real-world low illumination datasets [33, 39]. IA-YOLO [30] introduces a convolutional neural network (CNN)-based parameter predictor that learns the optimal configuration for the filters employed in the differential image processing module. Most related to our work is MAET [10], which investigates the physical noise model and image signal processing (ISP) pipeline under low illumination and learns the model to predict degradation parameters and object features. To avoid feature entanglement, they impose orthogonal tangent regularity to penalize cosine similarity between objects and degrading features. However, owing to the weather-specific hyperparameters in [30] and degradation parameters in [10], these works rely on large synthetic datasets to achieve desired performance. Unlike them, our FeatEnHancer is optimized from the task-related loss functions and does not require any pre-training on synthetic datasets mimicking low-light or harsh weather conditions.",
+        "bbox": [
+            76,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Other high-level vision tasks. Besides face and object detection, recent research has explored high-level computer vision tasks like semantic segmentation [6, 34]. Xue et al. [60] devise a contrastive-learning strategy to improve visual and machine perception simultaneously, achieving impressive performance on nighttime semantic segmentation of adverse conditions dataset with correspondences (ACDC) dataset [47]. Furthermore, DarkVision [63] has emerged recently to tackle video object detection under low-light vision. In this work, thanks to [47, 63], we apply FeatEnHancer",
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "to semantic segmentation and video object detection under low-light vision to investigate its generalization capabilities.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Learning Multi-scale Hierarchical Features",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Representing objects at varying scales is one of the main difficulties in computer vision. Therefore, the work in this domain goes back to the era of hand-engineered features [36, 11, 38, 24]. Modern object detectors [43, 28, 2, 71, 49, 40, 65] exploit multi-scale features to tackle this challenge. Similarly, multi-scale representations [34] and pyramid pooling schemes [69] have been proposed for effective semantic segmentation. Moreover, current improvements in vision-based backbone networks [15, 31, 32] demonstrate that learning hierarchical features during feature extraction directly uplifts the downstream vision tasks [19, 57, 2]. However, the multi-scale and hierarchical structures of CNN have not been fully explored for low-light vision tasks.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Under harsh weather conditions, DENet [41] employs Laplacian Pyramid [1] to decompose images into low and high-frequency components for object detection. Despite the encouraging results, the multi-scale feature learning in DENet relies on the Laplacian pyramid, which is susceptible to noise and may produce inconsistencies in regions with high contrast or sharp edges. Alternatively, aligned with the multi-scale learning in modern vision backbone networks [27, 32, 31], our FeatEnHancer employs CNN to generate multi-scale feature representations, which are fused through the scale-aware attentional feature aggregation and skip connections. Our approach is much more flexible and aligns with downstream vision tasks, boosting state-of-the-art results on multiple downstream vision tasks.",
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+    {
+        "type": "text",
+        "text": "3. Proposed Approach",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The key idea of this paper is to design a general-purpose pluggable module that strengthens machine perception under low-light vision to solve several downstream vision tasks such as object detection, semantic segmentation, and video object detection. The overall architecture of FeatEnHancer is exhibited in Fig. 2. Our FeatEnHancer takes a low-light image as input and adaptively boosts its semantic representation by enriching task-related hierarchical features. We now discuss the key components of FeatEnHancer in detail.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Hierarchical Feature Enhancement",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Inspired by the recent improvements in vision-based backbone networks [15, 31, 32], we introduce the enhancement of hierarchical features through jointly optimizing feature enhancement and downstream tasks under low-light vision. Unlike [15, 31, 32], our goal is to extract spatial features from low-light images and generate meaningful semantic representations. In order to enhance hierarchical features, we first construct multi-scale representations from the low-light input image. Later, we feed these multi-scale",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "6727",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/8a4cddd9bf1b856dac24761aa9df2f581fff9eff945b5b88a5797b08d431e3ad.jpg",
+        "image_caption": [
+            "Figure 2: Network architecture of the proposed FeatEnHancer employed in a downstream vision task. Our FeatEnHancer takes a low-light image and adaptively boosts its semantic representation by enriching task-related hierarchical features. Zoom in for the best view."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "representations to our feature enhancement network.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Constructing multi-scale representations. We take a lowlight RGB image  $I\\in \\mathbb{R}^{H\\times W\\times C}$  as input and employ regular convolutional operator Conv.) on  $I$  to generate  $I_{q}\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}\\times 3}$  and  $I_{o}\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times 3}$  representing the quarter and octa scale of an input image, respectively. To summarize, it can be written as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI _ {q} = \\operatorname {C o n v} (I) \\quad K = 7, S = 4, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI _ {o} = \\mathbf {C o n v} (I _ {q}) \\quad K = 3, S = 2,\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
+            546,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $K$  and  $S$  denote kernel size and stride, and  $H$ ,  $W$ , and  $C$  represent the height, width, and channels of an image.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Feature enhancement network. In order to enhance features at each scale, we require an enhancement network that learns to enhance spatial information important for downstream tasks. Inspired by low-light image enhancement networks [17, 25], we design a fully convolutional intra-scale feature extraction network (FEN). However, unlike [17, 25], our FEN introduces a single convolutional layer at the beginning that generates a feature map  $F \\in \\mathbb{R}^{H \\times W \\times C}$ , where  $C$  is transformed from 3 to 32 by keeping the resolution  $(H \\times W)$  same as the input. Then a series of six convolutional layers with symmetrical skip concatenation is applied, where each convolutional layer, with  $K = 3$  and  $S = 1$ , is accompanied by the ReLU activation function. We apply FEN on each scale  $I$ ,  $I_{q}$ , and  $I_{o}$  separately, and obtain multiscale feature representations, denoted as  $F$ ,  $F_{q}$ , and  $F_{o}$ , respectively. This multi-scale learning allows the network to enhance both global and local information from higher and lower-resolution features. Hence, we ignore down-sampling and batch normalization to preserve semantic relations be",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tween neighbouring pixels which is similar to [17]. However, we discard the last convolutional layer of DCENet [17] in our FEN and propagate the final enhanced feature representations from each scale for the multi-scale feature fusion. Note that the implementation details of FEN in FeatEnHancer are independent of the proposed module, and even more, advanced image enhancement networks such as [68] can be applied to improve performance. Now, we discuss multiscale feature fusion in detail.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Multi-scale Feature Fusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since we already have multi-scale feature representations  $(F, F_{q},$  and  $F_{o})$  from FEN, the remaining obstacle is to fuse them effectively. Lower-scale features  $(F_{o})$  contain fine details and edges. In contrast, higher-resolution features  $(F_{q})$  capture more abstract information, such as shapes and patterns. Therefore, naive aggregation leads to inferior performance (see Table 6a). Hence, we adopt two different strategies to capture both global and local information from higher and lower-resolution features. First, inspired by multi-head attention in [50] that enables the network to jointly learn information from different channels, we design a scale-aware attentional feature aggregation (SAFA) module that jointly attends to features from different scales. Second, we adopt a skip connection [20] (SC) scheme to integrate low-level information from  $F_{o}$  and the enhanced representation from SAFA to obtain the final enhanced hierarchical representation. Adopting SAFA for merging high-resolution features and SC for lower-resolution features leads to a more robust hierarchical representation (see Table 6b). Now, we discuss SAFA in detail.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Scale-aware Attentional Feature Aggregation. Even though high-resolution features assist in capturing fine de",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "6728",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tails, such as recognizing small objects, applying an attentional operation to them is computationally demanding. Thus, in SAFA, we propose an efficient multi-scale aggregation strategy where enhanced high-resolution hierarchical features are projected to a smaller resolution prior to attentional feature aggregation. As illustrated in Figure 2, SAFA transforms  $F \\in \\mathbb{R}^{H \\times W \\times C}$  to  $Q \\in \\mathbb{R}^{\\frac{H}{8} \\times \\frac{W}{8} \\times C}$  with two convolutional layers ( $K = 7$ ,  $S = 4$ ;  $K = 3$ ,  $S = 2$ ) and  $F_{q} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}$  to  $K \\in \\mathbb{R}^{\\frac{H}{8} \\times \\frac{W}{8} \\times C}$  with a single convolutional layer ( $K = 3$ ,  $S = 2$ ). Note that the weights of the convolutional layer ( $K = 3$ ,  $S = 2$ ) are not shared because, in addition to down-scaling the high-resolution features, it serves as an embedding network before computing the attentional weights. Later,  $Q$  and  $K$  are concatenated to form the set of hierarchical features  $F_{q + k}$ , which are split into N blocks along the channel dimension  $C$ :",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {q + k} ^ {n} = F _ {q + k} [:,:, (n - 1) \\frac {C}{N}: n \\frac {C}{N} ], \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            343,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $n\\in \\{1,2,\\dots,N\\}$  and  $\\mathbf{N}$  is the total number of attentional blocks. The  $F_{q + k}^{n}\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times \\frac{C}{N}}$  is used to compute attentional weights  $W$  in a single attention block as follows:",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {q + k} ^ {n} = F _ {q} ^ {n} \\cdot F _ {k} ^ {n}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {\\mathbf {W}} _ {q + k} ^ {n} = \\frac {\\exp \\left(W _ {q + k} ^ {n}\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(W _ {q + k} ^ {n}\\right)}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            174,
+            467,
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+            507
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{q + k}^{n}$  is the attentional weights of  $F_{q}^{n}$  and  $F_{k}^{n}$  for  $n$ -th block, and  $\\overline{\\mathbf{W}}_{q + k}^{n}$  is the normalized form of  $W_{q + k}^{n}$ . Derived from the  $n$ -th block of normalized attention weights, we apply weighted sum to compute the  $n$ -th block of enhanced hierarchical representation  $\\overline{\\mathbf{F}}_h^n\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times \\frac{C}{N}}$  as follows:",
+        "bbox": [
+            76,
+            511,
+            468,
+            592
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {\\mathbf {F}} _ {h} ^ {n} = \\sum_ {l = 1} ^ {L} \\bar {\\mathbf {W}} _ {q + k} ^ {n} \\cdot F _ {q + k} ^ {n}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            187,
+            603,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "now we concatenate all  $\\bar{\\mathbf{F}}_h^n$  along the channel dimension to obtain  $\\bar{\\mathbf{F}}_h\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times C}$ . Note that although  $\\bar{\\mathbf{F}}_h$  is the same size as  $Q$  and  $K$ , it contains far richer representations, encompassing information from multi-scale high-resolution features.",
+        "bbox": [
+            76,
+            656,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Subsequently, as explained earlier in Sec. 3.2, with the help of skip connections (SC), we integrate  $F_{o}$  and  $\\bar{\\mathbf{F}}_h$  to obtain the final enhanced hierarchical representation covering both global and local features, as illustrated in Figure 1 and 2. Note that prior to the skip connection, we upsample  $\\bar{\\mathbf{F}}_h$  and  $F_{o}$ , where the upsampling operation  $U(.)\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times C}\\to \\mathbb{R}^{H\\times W\\times C}$  is performed with simple bi-linear interpolation operation, which is much faster than using transposed convolutions [13]. Unlike image enhancement in existing works [17, 25, 10], with a multi-scale hierarchical feature enhancement strategy, our FeatEnHancer",
+        "bbox": [
+            76,
+            734,
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+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "learns a powerful semantic representation by capturing both local and global features. This makes it a general-purpose module to enhance hierarchical features, boosting machine perception under low-light vision.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/8bb65d7b304956a537b26c991e27288de14cc6496e18aa6e62953493b272c6f9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Task</td><td>#Cls</td><td>#Train</td><td>#Val</td></tr><tr><td>ExDark [33]</td><td>Dark object detection</td><td>12</td><td>4800</td><td>2563</td></tr><tr><td>DARK FACE [62]</td><td>Face detection</td><td>1</td><td>5400</td><td>600</td></tr><tr><td>ACDC Nighttime [47]</td><td>Semantic segmentation</td><td>19</td><td>400</td><td>106</td></tr><tr><td>DarkVision [63]</td><td>Video object detection</td><td>4</td><td>26</td><td>6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Statistics of the datasets used to report results on four different downstream vision tasks. #Cls is the number of classes, whereas #Train and #Val denote number of training and validation samples for each dataset, respectively.",
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We conduct extensive experiments for evaluating the proposed FeatEnHancer module to several downstream tasks under the low-light vision, including generic object detection [33, 39], face detection [62], semantic segmentation [47], and video object detection [63]. Table 1 summarizes the crucial statistics of the employed datasets. This section first compares the proposed method with powerful baselines, existing LLIE approaches, and task-specific state-of-the-art methods. Then, we ablate the important design choices of our FeatEnHancer. We provide complete implementation details for each experiment in Appendix A.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1. Dark Object Detection",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Settings. For dark object detection experiments on the real-world data, we consider the exclusively dark (ExDark) [33] dataset (see Table 1). We adopt RetinaNet [28] as a typical detector and Featurized Query R-CNN [65] (FQ R-CNN) as an advanced object detection framework to report results. In the case of both detectors, pre-trained models on COCO [29] are fine-tuned on each dataset. For RetinaNet, images are resized to  $640 \\times 640$ , and we train the network using  $1 \\times$  schedule in mmdetection [5] (12 epochs using SGD optimizer [46] with an initial learning rate of 0.001). For Featurized Query R-CNN, we employ multiscale training [4, 49, 65] (shorter side ranging from 400 to 800 with a longer side of 1333). The FQ R-CNN is trained for 50000 iterations using ADAMW [35] optimizer (initial learning rate of 0.0000025, weight decay of 0.0001, and batch size of 8). Note that for each object detection framework, we adopt the same settings while reproducing results of our work, baseline, LLIE approaches, and task-specific state-of-the-art methods.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We compare our FeatEnHancer to several state-of-the-art LLIE methods, including KIND [67], RAUS [44], EnGAN [21], MBLLEN [14], Zero-DCE [17], Zero-DCE++ [17], and state-of-the-art dark object detection method, MAET [10]. For LLIE methods, all images are",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "6729",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/c884d801f1827575e00199fd40fda2b5bd6d0b5e58fa1ef462092ca294b98826.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">RetinaNet</td><td colspan=\"2\">FQ R-CNN</td><td rowspan=\"2\">Methods</td><td colspan=\"2\">RetinaNet</td><td colspan=\"2\">FQ R-CNN</td><td>Method</td><td>mIoU</td></tr><tr><td>\\( mAP_{50} \\)</td><td>mAP</td><td>\\( mAP_{50} \\)</td><td>mAP</td><td>\\( AP_{50} \\)</td><td>AP</td><td>\\( AP_{50} \\)</td><td>AP</td><td>Baseline [7]</td><td>45.7</td></tr><tr><td>Baseline</td><td>72.1</td><td>46.3</td><td>74.5</td><td>47.0</td><td>Baseline</td><td>47.3</td><td>19.9</td><td>67.5</td><td>28.6</td><td>RetinexNet [54]</td><td>41.9</td></tr><tr><td>RAUS [44]</td><td>64.7</td><td>44.0</td><td>77.0</td><td>48.1</td><td>RAUS [44]</td><td>42.1</td><td>17.6</td><td>65.5</td><td>27.4</td><td>DRBN [59]</td><td>43.3</td></tr><tr><td>KIND [67]</td><td>70.7</td><td>45.1</td><td>80.5</td><td>51.5</td><td>KIND [67]</td><td>47.2</td><td>19.8</td><td>65.0</td><td>27.5</td><td>FIDE [61]</td><td>43.4</td></tr><tr><td>Zero-DCE++ [25]</td><td>70.3</td><td>45.2</td><td>79.5</td><td>49.2</td><td>Zero-DCE++ [25]</td><td>47.3</td><td>20.1</td><td>66.2</td><td>28.2</td><td>KIND [67]</td><td>43.0</td></tr><tr><td>EnGAN [21]</td><td>70.4</td><td>44.9</td><td>80.0</td><td>51.9</td><td>EnGAN [21]</td><td>45.1</td><td>19.3</td><td>67.4</td><td>28.4</td><td>EnGAN [21]</td><td>43.8</td></tr><tr><td>MBLLEN [14]</td><td>70.6</td><td>45.1</td><td>80.0</td><td>51.0</td><td>MBLLEN [14]</td><td>47.1</td><td>19.8</td><td>67.3</td><td>27.1</td><td>ZeroDCE [17]</td><td>43.4</td></tr><tr><td>Zero-DCE [17]</td><td>71.0</td><td>45.2</td><td>80.6</td><td>52.0</td><td>Zero-DCE [17]</td><td>47.4</td><td>20.1</td><td>66.9</td><td>27.5</td><td>SSIENet [66]</td><td>41.4</td></tr><tr><td>MAET [10]</td><td>71.8</td><td>45.7</td><td>81.6</td><td>52.4</td><td>MAET [10]</td><td>44.3</td><td>18.7</td><td>66.1</td><td>27.1</td><td>Xue et al. [60]</td><td>49.8</td></tr><tr><td>FeatEnHancer</td><td>72.6</td><td>46.4</td><td>86.3</td><td>56.5</td><td>FeatEnHancer</td><td>47.2</td><td>19.9</td><td>69.0</td><td>29.4</td><td>FeatEnHancer</td><td>54.9</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "enhanced from their released checkpoints and propagated to the detector. In case of MAET [10], we pre-train the detector using their proposed degrading pipeline and then fine-tune it on both datasets to establish a direct comparison.",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results on ExDark. Table 2 lists the results of LLIE works, MAET, and the proposed method on both object detection frameworks. It is evident that our FeatEnHancer brings consistent and significant gains over prior methods. Note that, while the performance of MAET and our method is comparable on RetinaNet  $(\\approx 72\\mathrm{AP}_{50})$ , the proposed FeatEnHancer outperforms MAET by a significant margin on FQ R-CNN, achieving the new state-of-the-art  $\\mathrm{AP}_{50}$  of 86.3. Furthermore, Figure 3 shows four detection examples from our method and the two best competitors using FQ R-CNN as a detector. These results illustrate that despite the inferior visual quality, our FeatEnHancer enhances hierarchical features that are favourable for dark object detection, producing state-of-the-art results.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Face Detection on DARK FACE",
+        "text_level": 1,
+        "bbox": [
+            76,
+            650,
+            357,
+            666
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Settings. The DARK FACE [53, 62] is a challenging face detection dataset released for the  $\\mathrm{UG}^2$  competition. For experiments on the DARK FACE (see Table 1), the images are resized to a larger resolution of  $1500 \\times 1000$  for all methods. We adopt the same object detection frameworks of RetinaNet and FQ R-CNN and follow identical experimental settings, as explained in Sec. 4.1.",
+        "bbox": [
+            75,
+            672,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results. The performance of FeatEnHancer, MAET, and six LLIE methods, using RetinaNet and Featurized Query R-CNN, are summarized in Table 3. Note that a few LLIE methods [17, 25, 67] yield superior results than our approach in the case of RetinaNet. We argue that due to tiny faces with highly dark images in the DARK FACE dataset, RetinaNet fails to capture information even from the enhanced hierarchical features. We discuss this behaviour with an ex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/1959ea2c2e90caa562b9d8158d45f49c3a7fffc053838c6c7f2a6fe46e1d5632.jpg",
+        "table_caption": [
+            "Table 2: Quantitative comparison on ExDark dataset. Results obtained on the commonly used evaluation metrics are highlighted. Our FeatEnHancer brings consistent improvements and achieves new state-of-the-art results with FQ R-CNN.",
+            "Table 3: Comparing FeatEnHancer on the DARK FACE dataset. With RetinaNet, FeatEnHancer performs on par with other methods. However, with FQ R-CNN, FeatEnHancer surpasses all of them.",
+            "Table 4: Quantitative comparison on the ACDC dataset. Huge gains from our FeatEnhancer lead to new state-of-the-art results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>GT</td><td>MAET</td><td>ZeroDCE</td><td>Ours</td></tr></table>",
+        "bbox": [
+            503,
+            351,
+            890,
+            558
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figure 3: Visual comparison of FeatEnHancer with the two previous best competitors on the ExDark dataset. Zoom in for the best view.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ample in Appendix B. On the other hand, LLIE approaches directly provides well-lit images that bring slightly bigger gains  $(+0.1\\mathrm{mAP}_{50})$  in this case. However, note that with the more strong detector, our FeatEnHancer surpasses all the LLIE methods and MAET by a significant margin  $(+1.5\\mathrm{mAP}_{50})$ , achieving  $\\mathrm{mAP}_{50}$  of 69.0.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Nighttime Semantic Segmentation on ACDC",
+        "text_level": 1,
+        "bbox": [
+            500,
+            737,
+            877,
+            753
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Settings. We utilize nighttime images from the ACDC dataset [47] (see Table 1) to report results on semantic segmentation in a low-light setting. DeepLabV3+ [7] is adopted as the segmentation baseline from mmseg [8] for straightforward comparison with the concurrent work [60]. We follow identical experimental settings as in [60]. Refer to Appendix A for complete implementation details.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results. We compare our method with several state-of-the-art LLIE methods, including RetinexNet [54] KIND [67],",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6730",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/583e4c022fb3f1109eddbc843d4ac1187a968270d8c68a001c9e58241dc08358.jpg",
+        "image_caption": [
+            "Figure 4: Qualitative comparison of FeatEnHancer with previous best work [60] on the ACDC nighttime semantic segmentation. FeatEnHancer provides more accurate segmentations."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            88,
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+            406
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ee17390905bce7b0c317712c41cd86183fdc7fe00b30cac1eacc6ca68ffa1455.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Illumination (3.2) \nmAP</td><td>Illumination (0.2) \nmAP</td></tr><tr><td>Baseline [55]</td><td>32.8</td><td>10.4</td></tr><tr><td>RAUS [44]</td><td>7.42</td><td>5.19</td></tr><tr><td>EnGAN [21]</td><td>7.83</td><td>5.41</td></tr><tr><td>MBLLEN [14]</td><td>7.82</td><td>5.39</td></tr><tr><td>KIND [67]</td><td>7.43</td><td>5.25</td></tr><tr><td>Zero-DCE++ [25]</td><td>7.51</td><td>5.02</td></tr><tr><td>Zero-DCE [17]</td><td>7.83</td><td>5.43</td></tr><tr><td>FeatEnHancer</td><td>34.6</td><td>11.2</td></tr></table>",
+        "bbox": [
+            84,
+            483,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Comparing FeatEnHancer with LLIE methods on the DarkVision dataset. FeatEnHancer is the only method that boosts the performance of the powerful baseline method on both illumination levels.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "FIDE [61], DRBN [59], EnGAN [21], SSIONet [66], ZeroDCE [17], and current state-of-the-art nighttime semantic segmentation method Xue et al. [60]. As shown in Table 4, our FeatEnHancer brings remarkable improvements in the baseline with a mIoU of 54.9, outperforming the previous best result by 5.1 points. Moreover, we present a qualitative comparison with the previous best competitor [60] in Figure 4. Evidently, our FeatEnHancer generates more accurate segmentation for both bigger and smaller objects, such as terrain and traffic signs in the last row. These results affirm the effectiveness of FeatEnHancer as a general-purpose module achieving state-of-the-art results in both dark object",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "detection and nighttime semantic segmentation.",
+        "bbox": [
+            500,
+            90,
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+            107
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Video Object Detection on DarkVision",
+        "text_level": 1,
+        "bbox": [
+            500,
+            116,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Settings. We extend our experiments from static images to video domain to test the generalization capabilities of our method. The video object detection under low-light vision is evaluated on the recently emerged DarkVision dataset [63] (see Table 1 for dataset details). Although the dataset is not publicly available yet, we sincerely thank the authors of [63] for providing prompt access. To evaluate our FeatEnHancer under low light settings, we take the low-end camera split on two different illumination levels, i.e., 0.2 and 3.2. For ablation studies, we adopt a  $3.2\\%$  illumination level split. We consider SELSA [55] as our baseline and follow identical experimental settings with the ResNet-50 backbone network in the mmtracking [9]. To establish a direct comparison, we enhance all video frames first through LLIE methods and feed these frames to the baseline, as done in Sec. 4.1. As a common practice in video object detection [16, 18, 55], the mAP@IoU=0.5 is utilized as an evaluation metric to report results. More details can be found in Appendix A.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results. Table 5 compares our FeatEnHancer with several LLIE methods [44, 21, 14, 67, 17, 25] and the powerful video object detection baseline [55]. Evidently, our FeatEnHancer provides considerable gains to the baseline with  $34.6\\mathrm{mAP}$  and  $11.2\\mathrm{mAP}$  under illumination levels of 3.2 and 0.2, respectively. Note that our FeatEnHancer is the only method that boosts performance under both image and video modalities. In contrast, as shown in Table 5, existing LLIE methods not only fail to assist the baseline method but also deteriorate the performance. This poor generalization of LLIE approaches highlights that learning from domain-specific paired data [14, 67, 44], unpaired data [21], and curve estimation without data [17, 25] are not the optimal solutions for generalized enhancement methods. Hence, more research is required.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "This section ablates important design choices in the proposed FeatEnHancer when plugged into RetinaNet, DeeplabV3+, and SELSA on ExDark (dark object detection), ACDC (nighttime semantic segmentation), and DarkVision with illumination level of  $3.2\\%$  (video object detection), respectively.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "SAFA in FeatEnHancer. The important component of the proposed FeatEnHancer is the scale-aware attentional feature aggregation (SAFA) that aggregates high-resolution features. To validate its effectiveness, we conduct multiple experiments where SAFA is replaced with simple averaging or skip connections (SC) [20] to fuse enhanced multi-scale features  $F$  and  $F_{q}$  (see Sec. 3.2). The experiment results are",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "6731",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/cdcbc01cfd54f957abc6c47e4423bac2d44578d55f16a5371a0ca9e5d0e50bc9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>simple averaging</td><td>69.5</td><td>50.3</td><td>32.9</td></tr><tr><td>skip connections [20]</td><td>70.3</td><td>51.7</td><td>33.1</td></tr><tr><td>SAFA</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fe240b9d6904c3bbe9ed2a79a14f56272945ac557718431d6b3d5e7f31c75842.jpg",
+        "table_caption": [
+            "(a) Effectiveness of SAFA."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>SC, SC</td><td>69.7</td><td>51.7</td><td>32.8</td></tr><tr><td>SAFA, SAFA</td><td>70.2</td><td>52.6</td><td>33.4</td></tr><tr><td>SC, SAFA</td><td>70.9</td><td>52.9</td><td>33.8</td></tr><tr><td>SAFA, SC</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(b) Various combinations of multi-scale fusion.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/b6e3adae28f71c1a8ec34b610c18af49f5725f28d44bf9a9e2a5bfac0564b2d3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>maxpool</td><td>69.3</td><td>51.3</td><td>32.9</td></tr><tr><td>adavgpool [68]</td><td>69.9</td><td>50.7</td><td>32.9</td></tr><tr><td>interpolation [30]</td><td>70.7</td><td>51.5</td><td>33.1</td></tr><tr><td>Convolution</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>",
+        "bbox": [
+            98,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/9af82a46f87d27ff98a2b579c89bb82dca2bf045ed2a017548cbc05d1c015afe.jpg",
+        "table_caption": [
+            "(c) Downsampling approaches."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Scale</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>(2, 4)</td><td>71.8</td><td>52.7</td><td>34.1</td></tr><tr><td>(4, 8)</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>(4, 16)</td><td>71.5</td><td>51.4</td><td>33.9</td></tr><tr><td>(8, 16)</td><td>68.7</td><td>45.6</td><td>31.9</td></tr></table>",
+        "bbox": [
+            401,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/f9293d20b99d64edeb50c5135fbbd976d4c2ef23d6c8197912e10d2b5cb70332.jpg",
+        "table_caption": [
+            "(d) Scales for  $I_{q}$  and  $I_{o}$ , respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>N</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>2</td><td>72.1</td><td>53.9</td><td>34.2</td></tr><tr><td>4</td><td>72.4</td><td>54.3</td><td>34.5</td></tr><tr><td>8</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>12</td><td>72.4</td><td>54.3</td><td>34.1</td></tr></table>",
+        "bbox": [
+            650,
+            188,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(e) # attentional blocks in SAFA.",
+        "bbox": [
+            655,
+            273,
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+            286
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Ablations for the proposed FeatEnHancer on three benchmarks. (a) We investigate the effectiveness of SAFA by replacing it with different aggregation methods to fuse  $F$  and  $F_{q}$ . (b) We experiment with various combinations of SAFA and skip connection (SC) to justify an optimal design choice. Here, (SC, SC) means employing only skip connections to merge both  $F_{q}$  and  $F_{o}$  with  $F$ . (c) Besides convolution, we experiment with other downsampling techniques to generate lower resolutions. Here, adavgpool denotes adaptive average pooling as done in [68]. (d) We vary scale sizes to generate lower-scale representations. Here, (2, 4) means  $I_{q} \\in \\mathbb{R}^{\\frac{H}{2} \\times \\frac{W}{2} \\times 3}$  and  $I_{o} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times 3}$ . (e) We vary number of attentional blocks  $N$  in SAFA of FeatEnHancer. Default settings are highlighted.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "summarized in Table 6a. It is clear that SAFA outperforms both averaging and SC strategies by  $+2.3\\mathrm{mAP}$  on ExDark,  $+3.2\\mathrm{mIoU}$  on ACDC, and  $+1.5\\mathrm{mAP}$  on DarkVision. These significant boosts across all three benchmarks indicate that scale-aware attention leads to optimal multi-scale feature aggregation in the proposed FeatEnHancer.",
+        "bbox": [
+            73,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Multi-scale feature fusion. We experiment with various combinations of SAFA and SC to find an optimal design choice to fuse  $F_{q}$  and  $F_{o}$  with  $F$  (see Sec. 3.2). As shown in Table 6b, there is a clear increase in performance, achieving (72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision) when SAFA is applied to fuse  $F$  and  $F_{q}$  first, and then  $F_{o}$  is merged with the output of SAFA using skip connection. Hence, we use this approach as the default setting.",
+        "bbox": [
+            75,
+            521,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Convolutional Downsampling. Table 6c summarizes results from different downsampling techniques applied on the input image  $I$  to generate lower-resolutions  $I_{q}$  and  $I_{o}$  (see Sec 3.1). Our proposed convolutional downsampling yields impressive gains of  $+1.9\\mathrm{mAP}$  on ExDark,  $+3.4\\mathrm{mIoU}$ , and  $+1.5\\mathrm{mAP}$  on DarkVision compared to max-pooling, adaptive average pooling [68], and bilinear interpolation [30]. These results demonstrate the effectiveness of convolutional downsampling since it is better aligned with various vision backbone networks [32, 15, 27].",
+        "bbox": [
+            73,
+            657,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Different Scale sizes. We analyse the effect of different scale sizes to generate lower resolutions in Table 6d. Here, for instance, (2, 4) means that the resolution of input image  $I \\in \\mathbb{R}^{H \\times W \\times 3}$  is reduced by a factor of 2 and 4 to generate  $I_{q} \\in \\mathbb{R}^{\\frac{H}{2} \\times \\frac{W}{2} \\times 3}$  and  $I_{o} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times 3}$ , respectively. Note that all these scales are generated through regular convolutional",
+        "bbox": [
+            75,
+            810,
+            470,
+            901
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "operator  $\\mathbf{Conv}(.)$ , as explained in Eq. 1. Looking at results in Table 6d, the top performance on all three tasks is achieved with the scale size of (4, 8), thereby, preferred as a default setting.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Number of Attention Blocks in SAFA. Table 6e studies the effect of the number of attention blocks  $N$  in our SAFA. The performance rises for all three tasks with the increase in  $N$ . This demonstrates that more attentional blocks in SAFA bring additional gains. The best performance with 72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision is achieved when  $N$  reaches 8, and after that, it tends to saturate. Hence,  $N = 8$  is used as the default setting.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This paper proposes FeatEnHancer, a novel general-purpose feature enhancement module designed to enrich hierarchical features favourable for downstream tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. Furthermore, our FeatEnHancer neither requires pre-training on synthetic datasets nor relies on enhancement loss functions. These architectural innovations make FeatEnHancer a plug-and-play module. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods, and task-specific state-of-the-art approaches.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "6732",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
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+        "list_items": [
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+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.71,
+                0.47,
+                0.804,
+                0.478
+            ],
+            "angle": 0,
+            "content": "Hierarchical Representation"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.801,
+                0.329,
+                0.892,
+                0.47
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.817,
+                0.47,
+                0.875,
+                0.478
+            ],
+            "angle": 0,
+            "content": "Enhanced Image"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.491,
+                0.893,
+                0.551
+            ],
+            "angle": 0,
+            "content": "Figure 1: Learned hierarchical representation and enhanced image from our FeatEnHancer. We train our FeatEnHancer on a downstream object detection task and visualize these images from the validation set. These maps and enhanced images show that despite producing less visually appealing images, our model enhances task-related features. Best viewed on the screen."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.565,
+                0.314,
+                0.58
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.474,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Extracting useful visual cues for the downstream tasks is especially challenging under low-light vision. Prior works create enhanced representations by either correlating visual quality with machine perception or designing illumination-degrading transformation methods that require pre-training on synthetic datasets. We argue that optimizing enhanced image representation pertaining to the loss of the downstream task can result in more expressive representations. Therefore, in this work, we propose a novel module, FeatEnHancer, that hierarchically combines multiscale features using multi-headed attention guided by task-related loss function to create suitable representations. Furthermore, our intra-scale enhancement improves the quality of features extracted at each scale or level, as well as combines features from different scales in a way that reflects their relative importance for the task at hand. FeatEnHancer is a general-purpose plug-and-play module and can be incorporated into any low-light vision pipeline. We show with extensive experimentation that the enhanced representation produced with FeatEnHancer significantly and consistently improves results in several low"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.566,
+                0.895,
+                0.657
+            ],
+            "angle": 0,
+            "content": "light vision tasks, including dark object detection (+5.7 mAP on ExDark), face detection (+1.5 mAP on DARK FACE), nighttime semantic segmentation (+5.1 mIoU on ACDC), and video object detection (+1.8 mAP on DarkVision), highlighting the effectiveness of enhancing hierarchical features under low-light vision."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.692,
+                0.633,
+                0.708
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.897,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Recent remarkable advancements in high-level vision tasks have shown that given a high-quality image, current vision backbone networks [20, 15, 12, 32, 31], object detectors [42, 28, 43, 19, 2, 3, 49, 4, 71, 64, 65] and semantic segmentation models [34, 48, 57, 7, 58] can effectively learn desired features to perform vision tasks. Similarly, modern low-light image enhancement (LLIE) methods [44, 67, 14, 21, 17, 25] are capable of transforming a low-light image into a visual-friendly representation. However, a naive combination of the two brings sub-optimal gains when it comes to high-level vision tasks under low-light vision."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6725"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.455
+            ],
+            "angle": 0,
+            "content": "This work explores the underlying reasons for the low performance of the combination of LLIE with high-level vision methods and observes the following limitations: 1) Although existing LLIE methods push the envelope of visual perception for human eyes, they do not align with vision backbone networks [20, 12, 15, 32, 31] due to lack of multiscale features. For instance, it is likely that the enhancement method increases brightness in some regions. However, it simultaneously corrupts the edges and texture information of objects. 2) The pixel distribution among different low-light images may have huge variance owing to the disparity in less illuminated environments [17, 25, 68]. This increases intra-class variance in some cases (see Fig. 3, where only one bicycle is recognized by [17] instead of two bicycles in the ground-truth). 3) Current LLIE approaches [14, 17, 25, 21, 44, 56, 67] employ enhancement loss functions to optimize the enhancement networks. These loss functions compel the network to attend to all pixels equally, lacking the learning of informative details necessary for high-level downstream vision tasks such as object pose and shape for object detection. Furthermore, to train these enhancement networks, most of them [44, 14, 67, 56] require a set of high-quality images, which is hardly available in a real-world setting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.459,
+                0.473,
+                0.626
+            ],
+            "angle": 0,
+            "content": "Motivated by these observations and inspired by recent developments in LLIE [17, 25] and vision-based backbone networks [15, 32, 31], this paper aims to bridge the gap by exploring an end-to-end trainable recipe that jointly optimizes the enhancement and downstream task objectives in a single network. To this end, we present FeatEnHancer, a general-purpose feature enhancer that learns to enrich multiscale hierarchical features favourable for downstream vision tasks in a low-light setting. An example of learned hierarchical representation and the enhanced image is illustrated in Fig. 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.629,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In particular, our FeatEnHancer first downsamples a low-light RGB input image to construct multi-scale hierarchical representations. Subsequently, these representations are fed to our Feature Enhancement Network (FEN), which is a deep convolutional network, employed to enrich intra-scale semantic representations. Note that the parameters of FEN can be adjusted through task-related loss functions, which pushes the FEN to only enhance the task-related features. This multiscale learning allows the network to enhance both global and local information from higher and lower-resolution features, respectively. Once the enhanced representations on different scales are obtained, the remaining obstacle is to fuse them effectively. To achieve, this, we select two different strategies to capture both global and local information from higher and lower-resolution features. First, to merge high-resolution features, inspired by multi-head attention in [50], we design a Scale-aware Attentional Feature Aggregation (SAFA) method that jointly attends information from differ"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.213
+            ],
+            "angle": 0,
+            "content": "ent scales. Second, for lower-resolution features, the skip connection [20] scheme is adopted to merge the enhanced representation from SAFA to lower-resolution features. With these jointly learned hierarchical features, our FeatEnHancer provides semantically powerful representations which can be exploited by advanced methods such as feature pyramid networks [27] for object detection [43] and instance segmentation [19], or UNet [45] for semantic segmentation [34]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.215,
+                0.895,
+                0.245
+            ],
+            "angle": 0,
+            "content": "The main contributions of this work can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.514,
+                0.263,
+                0.897,
+                0.399
+            ],
+            "angle": 0,
+            "content": "1. We propose FeatEnHancer, a novel module that enhances hierarchical features to boost downstream vision tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. FeatEnHancer is a general-purpose plug-and-play module that can be trained end-to-end with any high-level vision task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.414,
+                0.895,
+                0.49
+            ],
+            "angle": 0,
+            "content": "2. To the best of our knowledge, this is the first work that fully exploits multi-scale hierarchical features in low-light scenarios and generalizes to several downstream vision tasks such as object detection, semantic segmentation, and video object detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.504,
+                0.895,
+                0.58
+            ],
+            "angle": 0,
+            "content": "3. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods and task-specific state-of-the-art approaches."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.513,
+                0.263,
+                0.897,
+                0.58
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.594,
+                0.642,
+                0.61
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.622,
+                0.766,
+                0.639
+            ],
+            "angle": 0,
+            "content": "2.1. Enhancing Low-Light Images"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.648,
+                0.897,
+                0.905
+            ],
+            "angle": 0,
+            "content": "Deep learning-based LLIE methods focus on improving the visual quality of low-light images that satisfies human visual perception [23, 22]. Most LLIE approaches [14, 44, 56, 67] operate under a supervised learning paradigm, requiring paired data during training. Unsupervised GAN-based methods [21] eliminate the need for paired data during the training. However, their performance relies on the careful choice of unpaired data. Recently, zero-reference methods [17, 25, 68] discard the need for both paired and unpaired data to enhance low-light images by designing a set of non-reference loss functions. Inspired by these recent developments, this work aims to bridge low-light enhancement and downstream vision tasks (such as object detection [10, 33, 62], semantic segmentation [60, 47], and video object detection [63]) by enhancing multi-scale hierarchical features without needing paired or unpaired data to boost performance."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.517,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6726"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.47,
+                0.121
+            ],
+            "angle": 0,
+            "content": "2.2. Enhancing Low-Light for Downstream Vision Tasks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.13,
+                0.471,
+                0.25
+            ],
+            "angle": 0,
+            "content": "These approaches consider machine perception as the criteria for success while enhancing images to improve downstream vision tasks. One obvious way to achieve this goal is to apply the LLIE methods as an initial step [70, 17]. However, this leads to unsatisfactory results (see Table 2, 4, and 5). Recently, another line of work has explored end-to-end pipelines, optimizing both enhancement and individual tasks during training, and our work follows the same spirit."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.251,
+                0.47,
+                0.445
+            ],
+            "angle": 0,
+            "content": "Face detection. Liang et al. [26] propose an effective information extraction scheme from low-light images by exploiting multi-exposure generation. Furthermore, bi-directional domain adaptation [52, 51] and parallel architecture that jointly performs enhancement and detection [37] are presented to advance the research. However, these approaches are carefully designed to tackle face detection [62, 53] only and deliver minor improvements when applied to generic object detection [51]. Contrarily, our FeatEnHancer is a general-purpose module. It significantly improves several downstream vision tasks. Hence, we refrain from comparing our method to architectures only evaluated for face detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.446,
+                0.471,
+                0.746
+            ],
+            "angle": 0,
+            "content": "Dark object detection. Dark (low-light) object detection [10, 30] methods have emerged recently, thanks to the real-world low illumination datasets [33, 39]. IA-YOLO [30] introduces a convolutional neural network (CNN)-based parameter predictor that learns the optimal configuration for the filters employed in the differential image processing module. Most related to our work is MAET [10], which investigates the physical noise model and image signal processing (ISP) pipeline under low illumination and learns the model to predict degradation parameters and object features. To avoid feature entanglement, they impose orthogonal tangent regularity to penalize cosine similarity between objects and degrading features. However, owing to the weather-specific hyperparameters in [30] and degradation parameters in [10], these works rely on large synthetic datasets to achieve desired performance. Unlike them, our FeatEnHancer is optimized from the task-related loss functions and does not require any pre-training on synthetic datasets mimicking low-light or harsh weather conditions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.75,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Other high-level vision tasks. Besides face and object detection, recent research has explored high-level computer vision tasks like semantic segmentation [6, 34]. Xue et al. [60] devise a contrastive-learning strategy to improve visual and machine perception simultaneously, achieving impressive performance on nighttime semantic segmentation of adverse conditions dataset with correspondences (ACDC) dataset [47]. Furthermore, DarkVision [63] has emerged recently to tackle video object detection under low-light vision. In this work, thanks to [47, 63], we apply FeatEnHancer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.894,
+                0.123
+            ],
+            "angle": 0,
+            "content": "to semantic segmentation and video object detection under low-light vision to investigate its generalization capabilities."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.13,
+                0.869,
+                0.146
+            ],
+            "angle": 0,
+            "content": "2.3. Learning Multi-scale Hierarchical Features"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.153,
+                0.895,
+                0.349
+            ],
+            "angle": 0,
+            "content": "Representing objects at varying scales is one of the main difficulties in computer vision. Therefore, the work in this domain goes back to the era of hand-engineered features [36, 11, 38, 24]. Modern object detectors [43, 28, 2, 71, 49, 40, 65] exploit multi-scale features to tackle this challenge. Similarly, multi-scale representations [34] and pyramid pooling schemes [69] have been proposed for effective semantic segmentation. Moreover, current improvements in vision-based backbone networks [15, 31, 32] demonstrate that learning hierarchical features during feature extraction directly uplifts the downstream vision tasks [19, 57, 2]. However, the multi-scale and hierarchical structures of CNN have not been fully explored for low-light vision tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.35,
+                0.895,
+                0.561
+            ],
+            "angle": 0,
+            "content": "Under harsh weather conditions, DENet [41] employs Laplacian Pyramid [1] to decompose images into low and high-frequency components for object detection. Despite the encouraging results, the multi-scale feature learning in DENet relies on the Laplacian pyramid, which is susceptible to noise and may produce inconsistencies in regions with high contrast or sharp edges. Alternatively, aligned with the multi-scale learning in modern vision backbone networks [27, 32, 31], our FeatEnHancer employs CNN to generate multi-scale feature representations, which are fused through the scale-aware attentional feature aggregation and skip connections. Our approach is much more flexible and aligns with downstream vision tasks, boosting state-of-the-art results on multiple downstream vision tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.573,
+                0.691,
+                0.59
+            ],
+            "angle": 0,
+            "content": "3. Proposed Approach"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.894,
+                0.734
+            ],
+            "angle": 0,
+            "content": "The key idea of this paper is to design a general-purpose pluggable module that strengthens machine perception under low-light vision to solve several downstream vision tasks such as object detection, semantic segmentation, and video object detection. The overall architecture of FeatEnHancer is exhibited in Fig. 2. Our FeatEnHancer takes a low-light image as input and adaptively boosts its semantic representation by enriching task-related hierarchical features. We now discuss the key components of FeatEnHancer in detail."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.742,
+                0.807,
+                0.757
+            ],
+            "angle": 0,
+            "content": "3.1. Hierarchical Feature Enhancement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Inspired by the recent improvements in vision-based backbone networks [15, 31, 32], we introduce the enhancement of hierarchical features through jointly optimizing feature enhancement and downstream tasks under low-light vision. Unlike [15, 31, 32], our goal is to extract spatial features from low-light images and generate meaningful semantic representations. In order to enhance hierarchical features, we first construct multi-scale representations from the low-light input image. Later, we feed these multi-scale"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6727"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.088,
+                0.895,
+                0.315
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.336,
+                0.895,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Figure 2: Network architecture of the proposed FeatEnHancer employed in a downstream vision task. Our FeatEnHancer takes a low-light image and adaptively boosts its semantic representation by enriching task-related hierarchical features. Zoom in for the best view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.397,
+                0.424,
+                0.412
+            ],
+            "angle": 0,
+            "content": "representations to our feature enhancement network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.426,
+                0.473,
+                0.517
+            ],
+            "angle": 0,
+            "content": "Constructing multi-scale representations. We take a lowlight RGB image \\(I\\in \\mathbb{R}^{H\\times W\\times C}\\) as input and employ regular convolutional operator Conv.) on \\(I\\) to generate \\(I_{q}\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}\\times 3}\\) and \\(I_{o}\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times 3}\\) representing the quarter and octa scale of an input image, respectively. To summarize, it can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.156,
+                0.525,
+                0.47,
+                0.549
+            ],
+            "angle": 0,
+            "content": "\\[\nI _ {q} = \\operatorname {C o n v} (I) \\quad K = 7, S = 4, \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.158,
+                0.547,
+                0.39,
+                0.561
+            ],
+            "angle": 0,
+            "content": "\\[\nI _ {o} = \\mathbf {C o n v} (I _ {q}) \\quad K = 3, S = 2,\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.471,
+                0.6
+            ],
+            "angle": 0,
+            "content": "where \\(K\\) and \\(S\\) denote kernel size and stride, and \\(H\\), \\(W\\), and \\(C\\) represent the height, width, and channels of an image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.614,
+                0.473,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Feature enhancement network. In order to enhance features at each scale, we require an enhancement network that learns to enhance spatial information important for downstream tasks. Inspired by low-light image enhancement networks [17, 25], we design a fully convolutional intra-scale feature extraction network (FEN). However, unlike [17, 25], our FEN introduces a single convolutional layer at the beginning that generates a feature map \\( F \\in \\mathbb{R}^{H \\times W \\times C} \\), where \\( C \\) is transformed from 3 to 32 by keeping the resolution \\( (H \\times W) \\) same as the input. Then a series of six convolutional layers with symmetrical skip concatenation is applied, where each convolutional layer, with \\( K = 3 \\) and \\( S = 1 \\), is accompanied by the ReLU activation function. We apply FEN on each scale \\( I \\), \\( I_{q} \\), and \\( I_{o} \\) separately, and obtain multiscale feature representations, denoted as \\( F \\), \\( F_{q} \\), and \\( F_{o} \\), respectively. This multi-scale learning allows the network to enhance both global and local information from higher and lower-resolution features. Hence, we ignore down-sampling and batch normalization to preserve semantic relations be"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.396,
+                0.895,
+                0.532
+            ],
+            "angle": 0,
+            "content": "tween neighbouring pixels which is similar to [17]. However, we discard the last convolutional layer of DCENet [17] in our FEN and propagate the final enhanced feature representations from each scale for the multi-scale feature fusion. Note that the implementation details of FEN in FeatEnHancer are independent of the proposed module, and even more, advanced image enhancement networks such as [68] can be applied to improve performance. Now, we discuss multiscale feature fusion in detail."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.544,
+                0.744,
+                0.558
+            ],
+            "angle": 0,
+            "content": "3.2. Multi-scale Feature Fusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.568,
+                0.895,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Since we already have multi-scale feature representations \\((F, F_{q},\\) and \\(F_{o})\\) from FEN, the remaining obstacle is to fuse them effectively. Lower-scale features \\((F_{o})\\) contain fine details and edges. In contrast, higher-resolution features \\((F_{q})\\) capture more abstract information, such as shapes and patterns. Therefore, naive aggregation leads to inferior performance (see Table 6a). Hence, we adopt two different strategies to capture both global and local information from higher and lower-resolution features. First, inspired by multi-head attention in [50] that enables the network to jointly learn information from different channels, we design a scale-aware attentional feature aggregation (SAFA) module that jointly attends to features from different scales. Second, we adopt a skip connection [20] (SC) scheme to integrate low-level information from \\(F_{o}\\) and the enhanced representation from SAFA to obtain the final enhanced hierarchical representation. Adopting SAFA for merging high-resolution features and SC for lower-resolution features leads to a more robust hierarchical representation (see Table 6b). Now, we discuss SAFA in detail."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Scale-aware Attentional Feature Aggregation. Even though high-resolution features assist in capturing fine de"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6728"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.333
+            ],
+            "angle": 0,
+            "content": "tails, such as recognizing small objects, applying an attentional operation to them is computationally demanding. Thus, in SAFA, we propose an efficient multi-scale aggregation strategy where enhanced high-resolution hierarchical features are projected to a smaller resolution prior to attentional feature aggregation. As illustrated in Figure 2, SAFA transforms \\( F \\in \\mathbb{R}^{H \\times W \\times C} \\) to \\( Q \\in \\mathbb{R}^{\\frac{H}{8} \\times \\frac{W}{8} \\times C} \\) with two convolutional layers (\\( K = 7 \\), \\( S = 4 \\); \\( K = 3 \\), \\( S = 2 \\)) and \\( F_{q} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C} \\) to \\( K \\in \\mathbb{R}^{\\frac{H}{8} \\times \\frac{W}{8} \\times C} \\) with a single convolutional layer (\\( K = 3 \\), \\( S = 2 \\)). Note that the weights of the convolutional layer (\\( K = 3 \\), \\( S = 2 \\)) are not shared because, in addition to down-scaling the high-resolution features, it serves as an embedding network before computing the attentional weights. Later, \\( Q \\) and \\( K \\) are concatenated to form the set of hierarchical features \\( F_{q + k} \\), which are split into N blocks along the channel dimension \\( C \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.344,
+                0.471,
+                0.375
+            ],
+            "angle": 0,
+            "content": "\\[\nF _ {q + k} ^ {n} = F _ {q + k} [:,:, (n - 1) \\frac {C}{N}: n \\frac {C}{N} ], \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.384,
+                0.472,
+                0.432
+            ],
+            "angle": 0,
+            "content": "where \\(n\\in \\{1,2,\\dots,N\\}\\) and \\(\\mathbf{N}\\) is the total number of attentional blocks. The \\(F_{q + k}^{n}\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times \\frac{C}{N}}\\) is used to compute attentional weights \\(W\\) in a single attention block as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.211,
+                0.445,
+                0.47,
+                0.465
+            ],
+            "angle": 0,
+            "content": "\\[\nW _ {q + k} ^ {n} = F _ {q} ^ {n} \\cdot F _ {k} ^ {n}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.176,
+                0.468,
+                0.47,
+                0.508
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {\\mathbf {W}} _ {q + k} ^ {n} = \\frac {\\exp \\left(W _ {q + k} ^ {n}\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(W _ {q + k} ^ {n}\\right)}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.512,
+                0.47,
+                0.593
+            ],
+            "angle": 0,
+            "content": "where \\( W_{q + k}^{n} \\) is the attentional weights of \\( F_{q}^{n} \\) and \\( F_{k}^{n} \\) for \\( n \\)-th block, and \\( \\overline{\\mathbf{W}}_{q + k}^{n} \\) is the normalized form of \\( W_{q + k}^{n} \\). Derived from the \\( n \\)-th block of normalized attention weights, we apply weighted sum to compute the \\( n \\)-th block of enhanced hierarchical representation \\( \\overline{\\mathbf{F}}_h^n\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times \\frac{C}{N}} \\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.604,
+                0.47,
+                0.645
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {\\mathbf {F}} _ {h} ^ {n} = \\sum_ {l = 1} ^ {L} \\bar {\\mathbf {W}} _ {q + k} ^ {n} \\cdot F _ {q + k} ^ {n}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.657,
+                0.47,
+                0.734
+            ],
+            "angle": 0,
+            "content": "now we concatenate all \\(\\bar{\\mathbf{F}}_h^n\\) along the channel dimension to obtain \\(\\bar{\\mathbf{F}}_h\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times C}\\). Note that although \\(\\bar{\\mathbf{F}}_h\\) is the same size as \\(Q\\) and \\(K\\), it contains far richer representations, encompassing information from multi-scale high-resolution features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.735,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Subsequently, as explained earlier in Sec. 3.2, with the help of skip connections (SC), we integrate \\( F_{o} \\) and \\( \\bar{\\mathbf{F}}_h \\) to obtain the final enhanced hierarchical representation covering both global and local features, as illustrated in Figure 1 and 2. Note that prior to the skip connection, we upsample \\( \\bar{\\mathbf{F}}_h \\) and \\( F_{o} \\), where the upsampling operation \\( U(.)\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times C}\\to \\mathbb{R}^{H\\times W\\times C} \\) is performed with simple bi-linear interpolation operation, which is much faster than using transposed convolutions [13]. Unlike image enhancement in existing works [17, 25, 10], with a multi-scale hierarchical feature enhancement strategy, our FeatEnHancer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "learns a powerful semantic representation by capturing both local and global features. This makes it a general-purpose module to enhance hierarchical features, boosting machine perception under low-light vision."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.163,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>Task</td><td>#Cls</td><td>#Train</td><td>#Val</td></tr><tr><td>ExDark [33]</td><td>Dark object detection</td><td>12</td><td>4800</td><td>2563</td></tr><tr><td>DARK FACE [62]</td><td>Face detection</td><td>1</td><td>5400</td><td>600</td></tr><tr><td>ACDC Nighttime [47]</td><td>Semantic segmentation</td><td>19</td><td>400</td><td>106</td></tr><tr><td>DarkVision [63]</td><td>Video object detection</td><td>4</td><td>26</td><td>6</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.239,
+                0.894,
+                0.3
+            ],
+            "angle": 0,
+            "content": "Table 1: Statistics of the datasets used to report results on four different downstream vision tasks. #Cls is the number of classes, whereas #Train and #Val denote number of training and validation samples for each dataset, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.315,
+                0.634,
+                0.332
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.34,
+                0.895,
+                0.507
+            ],
+            "angle": 0,
+            "content": "We conduct extensive experiments for evaluating the proposed FeatEnHancer module to several downstream tasks under the low-light vision, including generic object detection [33, 39], face detection [62], semantic segmentation [47], and video object detection [63]. Table 1 summarizes the crucial statistics of the employed datasets. This section first compares the proposed method with powerful baselines, existing LLIE approaches, and task-specific state-of-the-art methods. Then, we ablate the important design choices of our FeatEnHancer. We provide complete implementation details for each experiment in Appendix A."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.515,
+                0.712,
+                0.531
+            ],
+            "angle": 0,
+            "content": "4.1. Dark Object Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.539,
+                0.895,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Settings. For dark object detection experiments on the real-world data, we consider the exclusively dark (ExDark) [33] dataset (see Table 1). We adopt RetinaNet [28] as a typical detector and Featurized Query R-CNN [65] (FQ R-CNN) as an advanced object detection framework to report results. In the case of both detectors, pre-trained models on COCO [29] are fine-tuned on each dataset. For RetinaNet, images are resized to \\(640 \\times 640\\), and we train the network using \\(1 \\times\\) schedule in mmdetection [5] (12 epochs using SGD optimizer [46] with an initial learning rate of 0.001). For Featurized Query R-CNN, we employ multiscale training [4, 49, 65] (shorter side ranging from 400 to 800 with a longer side of 1333). The FQ R-CNN is trained for 50000 iterations using ADAMW [35] optimizer (initial learning rate of 0.0000025, weight decay of 0.0001, and batch size of 8). Note that for each object detection framework, we adopt the same settings while reproducing results of our work, baseline, LLIE approaches, and task-specific state-of-the-art methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We compare our FeatEnHancer to several state-of-the-art LLIE methods, including KIND [67], RAUS [44], EnGAN [21], MBLLEN [14], Zero-DCE [17], Zero-DCE++ [17], and state-of-the-art dark object detection method, MAET [10]. For LLIE methods, all images are"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6729"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.09,
+                0.891,
+                0.239
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">RetinaNet</td><td colspan=\"2\">FQ R-CNN</td><td rowspan=\"2\">Methods</td><td colspan=\"2\">RetinaNet</td><td colspan=\"2\">FQ R-CNN</td><td>Method</td><td>mIoU</td></tr><tr><td>\\( mAP_{50} \\)</td><td>mAP</td><td>\\( mAP_{50} \\)</td><td>mAP</td><td>\\( AP_{50} \\)</td><td>AP</td><td>\\( AP_{50} \\)</td><td>AP</td><td>Baseline [7]</td><td>45.7</td></tr><tr><td>Baseline</td><td>72.1</td><td>46.3</td><td>74.5</td><td>47.0</td><td>Baseline</td><td>47.3</td><td>19.9</td><td>67.5</td><td>28.6</td><td>RetinexNet [54]</td><td>41.9</td></tr><tr><td>RAUS [44]</td><td>64.7</td><td>44.0</td><td>77.0</td><td>48.1</td><td>RAUS [44]</td><td>42.1</td><td>17.6</td><td>65.5</td><td>27.4</td><td>DRBN [59]</td><td>43.3</td></tr><tr><td>KIND [67]</td><td>70.7</td><td>45.1</td><td>80.5</td><td>51.5</td><td>KIND [67]</td><td>47.2</td><td>19.8</td><td>65.0</td><td>27.5</td><td>FIDE [61]</td><td>43.4</td></tr><tr><td>Zero-DCE++ [25]</td><td>70.3</td><td>45.2</td><td>79.5</td><td>49.2</td><td>Zero-DCE++ [25]</td><td>47.3</td><td>20.1</td><td>66.2</td><td>28.2</td><td>KIND [67]</td><td>43.0</td></tr><tr><td>EnGAN [21]</td><td>70.4</td><td>44.9</td><td>80.0</td><td>51.9</td><td>EnGAN [21]</td><td>45.1</td><td>19.3</td><td>67.4</td><td>28.4</td><td>EnGAN [21]</td><td>43.8</td></tr><tr><td>MBLLEN [14]</td><td>70.6</td><td>45.1</td><td>80.0</td><td>51.0</td><td>MBLLEN [14]</td><td>47.1</td><td>19.8</td><td>67.3</td><td>27.1</td><td>ZeroDCE [17]</td><td>43.4</td></tr><tr><td>Zero-DCE [17]</td><td>71.0</td><td>45.2</td><td>80.6</td><td>52.0</td><td>Zero-DCE [17]</td><td>47.4</td><td>20.1</td><td>66.9</td><td>27.5</td><td>SSIENet [66]</td><td>41.4</td></tr><tr><td>MAET [10]</td><td>71.8</td><td>45.7</td><td>81.6</td><td>52.4</td><td>MAET [10]</td><td>44.3</td><td>18.7</td><td>66.1</td><td>27.1</td><td>Xue et al. [60]</td><td>49.8</td></tr><tr><td>FeatEnHancer</td><td>72.6</td><td>46.4</td><td>86.3</td><td>56.5</td><td>FeatEnHancer</td><td>47.2</td><td>19.9</td><td>69.0</td><td>29.4</td><td>FeatEnHancer</td><td>54.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.247,
+                0.409,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Table 2: Quantitative comparison on ExDark dataset. Results obtained on the commonly used evaluation metrics are highlighted. Our FeatEnHancer brings consistent improvements and achieves new state-of-the-art results with FQ R-CNN."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.413,
+                0.247,
+                0.721,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Table 3: Comparing FeatEnHancer on the DARK FACE dataset. With RetinaNet, FeatEnHancer performs on par with other methods. However, with FQ R-CNN, FeatEnHancer surpasses all of them."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.724,
+                0.249,
+                0.892,
+                0.339
+            ],
+            "angle": 0,
+            "content": "Table 4: Quantitative comparison on the ACDC dataset. Huge gains from our FeatEnhancer lead to new state-of-the-art results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.354,
+                0.47,
+                0.415
+            ],
+            "angle": 0,
+            "content": "enhanced from their released checkpoints and propagated to the detector. In case of MAET [10], we pre-train the detector using their proposed degrading pipeline and then fine-tune it on both datasets to establish a direct comparison."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.43,
+                0.473,
+                0.641
+            ],
+            "angle": 0,
+            "content": "Results on ExDark. Table 2 lists the results of LLIE works, MAET, and the proposed method on both object detection frameworks. It is evident that our FeatEnHancer brings consistent and significant gains over prior methods. Note that, while the performance of MAET and our method is comparable on RetinaNet \\((\\approx 72\\mathrm{AP}_{50})\\), the proposed FeatEnHancer outperforms MAET by a significant margin on FQ R-CNN, achieving the new state-of-the-art \\(\\mathrm{AP}_{50}\\) of 86.3. Furthermore, Figure 3 shows four detection examples from our method and the two best competitors using FQ R-CNN as a detector. These results illustrate that despite the inferior visual quality, our FeatEnHancer enhances hierarchical features that are favourable for dark object detection, producing state-of-the-art results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.651,
+                0.358,
+                0.667
+            ],
+            "angle": 0,
+            "content": "4.2. Face Detection on DARK FACE"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.47,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Settings. The DARK FACE [53, 62] is a challenging face detection dataset released for the \\(\\mathrm{UG}^2\\) competition. For experiments on the DARK FACE (see Table 1), the images are resized to a larger resolution of \\(1500 \\times 1000\\) for all methods. We adopt the same object detection frameworks of RetinaNet and FQ R-CNN and follow identical experimental settings, as explained in Sec. 4.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Results. The performance of FeatEnHancer, MAET, and six LLIE methods, using RetinaNet and Featurized Query R-CNN, are summarized in Table 3. Note that a few LLIE methods [17, 25, 67] yield superior results than our approach in the case of RetinaNet. We argue that due to tiny faces with highly dark images in the DARK FACE dataset, RetinaNet fails to capture information even from the enhanced hierarchical features. We discuss this behaviour with an ex"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.352,
+                0.892,
+                0.559
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>GT</td><td>MAET</td><td>ZeroDCE</td><td>Ours</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.569,
+                0.894,
+                0.614
+            ],
+            "angle": 0,
+            "content": "Figure 3: Visual comparison of FeatEnHancer with the two previous best competitors on the ExDark dataset. Zoom in for the best view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.633,
+                0.892,
+                0.724
+            ],
+            "angle": 0,
+            "content": "ample in Appendix B. On the other hand, LLIE approaches directly provides well-lit images that bring slightly bigger gains \\((+0.1\\mathrm{mAP}_{50})\\) in this case. However, note that with the more strong detector, our FeatEnHancer surpasses all the LLIE methods and MAET by a significant margin \\((+1.5\\mathrm{mAP}_{50})\\), achieving \\(\\mathrm{mAP}_{50}\\) of 69.0."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.738,
+                0.878,
+                0.755
+            ],
+            "angle": 0,
+            "content": "4.3. Nighttime Semantic Segmentation on ACDC"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.763,
+                0.894,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Settings. We utilize nighttime images from the ACDC dataset [47] (see Table 1) to report results on semantic segmentation in a low-light setting. DeepLabV3+ [7] is adopted as the segmentation baseline from mmseg [8] for straightforward comparison with the concurrent work [60]. We follow identical experimental settings as in [60]. Refer to Appendix A for complete implementation details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Results. We compare our method with several state-of-the-art LLIE methods, including RetinexNet [54] KIND [67],"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6730"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.473,
+                0.407
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.416,
+                0.472,
+                0.476
+            ],
+            "angle": 0,
+            "content": "Figure 4: Qualitative comparison of FeatEnHancer with previous best work [60] on the ACDC nighttime semantic segmentation. FeatEnHancer provides more accurate segmentations."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.484,
+                0.465,
+                0.633
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Illumination (3.2) \nmAP</td><td>Illumination (0.2) \nmAP</td></tr><tr><td>Baseline [55]</td><td>32.8</td><td>10.4</td></tr><tr><td>RAUS [44]</td><td>7.42</td><td>5.19</td></tr><tr><td>EnGAN [21]</td><td>7.83</td><td>5.41</td></tr><tr><td>MBLLEN [14]</td><td>7.82</td><td>5.39</td></tr><tr><td>KIND [67]</td><td>7.43</td><td>5.25</td></tr><tr><td>Zero-DCE++ [25]</td><td>7.51</td><td>5.02</td></tr><tr><td>Zero-DCE [17]</td><td>7.83</td><td>5.43</td></tr><tr><td>FeatEnHancer</td><td>34.6</td><td>11.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.643,
+                0.472,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Table 5: Comparing FeatEnHancer with LLIE methods on the DarkVision dataset. FeatEnHancer is the only method that boosts the performance of the powerful baseline method on both illumination levels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.719,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "FIDE [61], DRBN [59], EnGAN [21], SSIONet [66], ZeroDCE [17], and current state-of-the-art nighttime semantic segmentation method Xue et al. [60]. As shown in Table 4, our FeatEnHancer brings remarkable improvements in the baseline with a mIoU of 54.9, outperforming the previous best result by 5.1 points. Moreover, we present a qualitative comparison with the previous best competitor [60] in Figure 4. Evidently, our FeatEnHancer generates more accurate segmentation for both bigger and smaller objects, such as terrain and traffic signs in the last row. These results affirm the effectiveness of FeatEnHancer as a general-purpose module achieving state-of-the-art results in both dark object"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.816,
+                0.108
+            ],
+            "angle": 0,
+            "content": "detection and nighttime semantic segmentation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.117,
+                0.83,
+                0.133
+            ],
+            "angle": 0,
+            "content": "4.4. Video Object Detection on DarkVision"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.141,
+                0.895,
+                0.429
+            ],
+            "angle": 0,
+            "content": "Settings. We extend our experiments from static images to video domain to test the generalization capabilities of our method. The video object detection under low-light vision is evaluated on the recently emerged DarkVision dataset [63] (see Table 1 for dataset details). Although the dataset is not publicly available yet, we sincerely thank the authors of [63] for providing prompt access. To evaluate our FeatEnHancer under low light settings, we take the low-end camera split on two different illumination levels, i.e., 0.2 and 3.2. For ablation studies, we adopt a \\(3.2\\%\\) illumination level split. We consider SELSA [55] as our baseline and follow identical experimental settings with the ResNet-50 backbone network in the mmtracking [9]. To establish a direct comparison, we enhance all video frames first through LLIE methods and feed these frames to the baseline, as done in Sec. 4.1. As a common practice in video object detection [16, 18, 55], the mAP@IoU=0.5 is utilized as an evaluation metric to report results. More details can be found in Appendix A."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.443,
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+            ],
+            "angle": 0,
+            "content": "Results. Table 5 compares our FeatEnHancer with several LLIE methods [44, 21, 14, 67, 17, 25] and the powerful video object detection baseline [55]. Evidently, our FeatEnHancer provides considerable gains to the baseline with \\(34.6\\mathrm{mAP}\\) and \\(11.2\\mathrm{mAP}\\) under illumination levels of 3.2 and 0.2, respectively. Note that our FeatEnHancer is the only method that boosts performance under both image and video modalities. In contrast, as shown in Table 5, existing LLIE methods not only fail to assist the baseline method but also deteriorate the performance. This poor generalization of LLIE approaches highlights that learning from domain-specific paired data [14, 67, 44], unpaired data [21], and curve estimation without data [17, 25] are not the optimal solutions for generalized enhancement methods. Hence, more research is required."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4.5. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "This section ablates important design choices in the proposed FeatEnHancer when plugged into RetinaNet, DeeplabV3+, and SELSA on ExDark (dark object detection), ACDC (nighttime semantic segmentation), and DarkVision with illumination level of \\(3.2\\%\\) (video object detection), respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.896,
+                0.903
+            ],
+            "angle": 0,
+            "content": "SAFA in FeatEnHancer. The important component of the proposed FeatEnHancer is the scale-aware attentional feature aggregation (SAFA) that aggregates high-resolution features. To validate its effectiveness, we conduct multiple experiments where SAFA is replaced with simple averaging or skip connections (SC) [20] to fuse enhanced multi-scale features \\(F\\) and \\(F_{q}\\) (see Sec. 3.2). The experiment results are"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
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+            "angle": 0,
+            "content": "6731"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>simple averaging</td><td>69.5</td><td>50.3</td><td>32.9</td></tr><tr><td>skip connections [20]</td><td>70.3</td><td>51.7</td><td>33.1</td></tr><tr><td>SAFA</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.24,
+                0.174,
+                0.406,
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+            "angle": 0,
+            "content": "(a) Effectiveness of SAFA."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>SC, SC</td><td>69.7</td><td>51.7</td><td>32.8</td></tr><tr><td>SAFA, SAFA</td><td>70.2</td><td>52.6</td><td>33.4</td></tr><tr><td>SC, SAFA</td><td>70.9</td><td>52.9</td><td>33.8</td></tr><tr><td>SAFA, SC</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.524,
+                0.174,
+                0.81,
+                0.187
+            ],
+            "angle": 0,
+            "content": "(b) Various combinations of multi-scale fusion."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.099,
+                0.189,
+                0.402,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>maxpool</td><td>69.3</td><td>51.3</td><td>32.9</td></tr><tr><td>adavgpool [68]</td><td>69.9</td><td>50.7</td><td>32.9</td></tr><tr><td>interpolation [30]</td><td>70.7</td><td>51.5</td><td>33.1</td></tr><tr><td>Convolution</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.152,
+                0.274,
+                0.348,
+                0.287
+            ],
+            "angle": 0,
+            "content": "(c) Downsampling approaches."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.403,
+                0.189,
+                0.648,
+                0.267
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Scale</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>(2, 4)</td><td>71.8</td><td>52.7</td><td>34.1</td></tr><tr><td>(4, 8)</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>(4, 16)</td><td>71.5</td><td>51.4</td><td>33.9</td></tr><tr><td>(8, 16)</td><td>68.7</td><td>45.6</td><td>31.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.411,
+                0.274,
+                0.64,
+                0.288
+            ],
+            "angle": 0,
+            "content": "(d) Scales for \\(I_{q}\\) and \\(I_{o}\\), respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.651,
+                0.189,
+                0.871,
+                0.267
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>N</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>2</td><td>72.1</td><td>53.9</td><td>34.2</td></tr><tr><td>4</td><td>72.4</td><td>54.3</td><td>34.5</td></tr><tr><td>8</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>12</td><td>72.4</td><td>54.3</td><td>34.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.656,
+                0.274,
+                0.865,
+                0.287
+            ],
+            "angle": 0,
+            "content": "(e) # attentional blocks in SAFA."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.3,
+                0.894,
+                0.409
+            ],
+            "angle": 0,
+            "content": "Table 6: Ablations for the proposed FeatEnHancer on three benchmarks. (a) We investigate the effectiveness of SAFA by replacing it with different aggregation methods to fuse \\( F \\) and \\( F_{q} \\). (b) We experiment with various combinations of SAFA and skip connection (SC) to justify an optimal design choice. Here, (SC, SC) means employing only skip connections to merge both \\( F_{q} \\) and \\( F_{o} \\) with \\( F \\). (c) Besides convolution, we experiment with other downsampling techniques to generate lower resolutions. Here, adavgpool denotes adaptive average pooling as done in [68]. (d) We vary scale sizes to generate lower-scale representations. Here, (2, 4) means \\( I_{q} \\in \\mathbb{R}^{\\frac{H}{2} \\times \\frac{W}{2} \\times 3} \\) and \\( I_{o} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times 3} \\). (e) We vary number of attentional blocks \\( N \\) in SAFA of FeatEnHancer. Default settings are highlighted."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.43,
+                0.47,
+                0.521
+            ],
+            "angle": 0,
+            "content": "summarized in Table 6a. It is clear that SAFA outperforms both averaging and SC strategies by \\(+2.3\\mathrm{mAP}\\) on ExDark, \\(+3.2\\mathrm{mIoU}\\) on ACDC, and \\(+1.5\\mathrm{mAP}\\) on DarkVision. These significant boosts across all three benchmarks indicate that scale-aware attention leads to optimal multi-scale feature aggregation in the proposed FeatEnHancer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.522,
+                0.47,
+                0.658
+            ],
+            "angle": 0,
+            "content": "Multi-scale feature fusion. We experiment with various combinations of SAFA and SC to find an optimal design choice to fuse \\( F_{q} \\) and \\( F_{o} \\) with \\( F \\) (see Sec. 3.2). As shown in Table 6b, there is a clear increase in performance, achieving (72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision) when SAFA is applied to fuse \\( F \\) and \\( F_{q} \\) first, and then \\( F_{o} \\) is merged with the output of SAFA using skip connection. Hence, we use this approach as the default setting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.659,
+                0.471,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Convolutional Downsampling. Table 6c summarizes results from different downsampling techniques applied on the input image \\(I\\) to generate lower-resolutions \\(I_{q}\\) and \\(I_{o}\\) (see Sec 3.1). Our proposed convolutional downsampling yields impressive gains of \\(+1.9\\mathrm{mAP}\\) on ExDark, \\(+3.4\\mathrm{mIoU}\\), and \\(+1.5\\mathrm{mAP}\\) on DarkVision compared to max-pooling, adaptive average pooling [68], and bilinear interpolation [30]. These results demonstrate the effectiveness of convolutional downsampling since it is better aligned with various vision backbone networks [32, 15, 27]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Different Scale sizes. We analyse the effect of different scale sizes to generate lower resolutions in Table 6d. Here, for instance, (2, 4) means that the resolution of input image \\( I \\in \\mathbb{R}^{H \\times W \\times 3} \\) is reduced by a factor of 2 and 4 to generate \\( I_{q} \\in \\mathbb{R}^{\\frac{H}{2} \\times \\frac{W}{2} \\times 3} \\) and \\( I_{o} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times 3} \\), respectively. Note that all these scales are generated through regular convolutional"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.43,
+                0.893,
+                0.491
+            ],
+            "angle": 0,
+            "content": "operator \\(\\mathbf{Conv}(.)\\), as explained in Eq. 1. Looking at results in Table 6d, the top performance on all three tasks is achieved with the scale size of (4, 8), thereby, preferred as a default setting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.895,
+                0.629
+            ],
+            "angle": 0,
+            "content": "Number of Attention Blocks in SAFA. Table 6e studies the effect of the number of attention blocks \\( N \\) in our SAFA. The performance rises for all three tasks with the increase in \\( N \\). This demonstrates that more attentional blocks in SAFA bring additional gains. The best performance with 72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision is achieved when \\( N \\) reaches 8, and after that, it tends to saturate. Hence, \\( N = 8 \\) is used as the default setting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.648,
+                0.619,
+                0.663
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This paper proposes FeatEnHancer, a novel general-purpose feature enhancement module designed to enrich hierarchical features favourable for downstream tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. Furthermore, our FeatEnHancer neither requires pre-training on synthetic datasets nor relies on enhancement loss functions. These architectural innovations make FeatEnHancer a plug-and-play module. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods, and task-specific state-of-the-art approaches."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6732"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+        },
+        {
+            "type": "ref_text",
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+                0.503,
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+            ],
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+            "content": "[70] Ziqiang Zheng, Yang Wu, Xinran Han, and Jianbo Shi. Forkgan: Seeing into the rainy night. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020, pages 155-170, Cham, 2020. Springer International Publishing."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
+                0.686,
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+            ],
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+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.503,
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+                0.894,
+                0.74
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+            "content": null
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+        }
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+]
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+# FeatEnHancer: Enhancing Hierarchical Features for Object Detection and Beyond Under Low-Light Vision
+
+Khurram Azeem Hashmi $^{1,2}$ , Goutham Kallempudi $^{2}$ , Didier Stricker $^{1,2}$  and Muhammad Zeshan Afzal $^{1,2}$
+
+$^{1}$ DFKI - German Research Center for Artificial Intelligence,  $^{2}$ RPTU Kaiserslautern, {khurram.azeem Hashmi, didier.stricker, muhammad.zeshan.afzal}@dfki.de, kallempu@rptu.de
+
+![](images/863d1335d99571d2dc51cd9855a417f29a2a5144b35e057861987f654bcc283d.jpg)  
+GT  
+Hierarchical Representation  
+Figure 1: Learned hierarchical representation and enhanced image from our FeatEnHancer. We train our FeatEnHancer on a downstream object detection task and visualize these images from the validation set. These maps and enhanced images show that despite producing less visually appealing images, our model enhances task-related features. Best viewed on the screen.
+
+![](images/476ae4d9f37ba48ab5990a8998327e746f14fe862b38976df8f40bef15c9f74e.jpg)
+
+![](images/e532ee4956db7ebd3a680b3d2ccea7f469c3c66908e70d7548cbedba69117cf9.jpg)  
+Enhanced Image
+
+![](images/09222f8001683392d6a149c2b10e34959d0c78841ab27762493f0080971e464b.jpg)  
+GT  
+Hierarchical Representation
+
+![](images/ea3409686da6db885fc1552070d4e6a3a194b9e2d7a90e1e3e6376b307c4839f.jpg)
+
+![](images/f72267d5259ddaa8ed5a4eb89fb8f88a7408e837a942d23b7d9abea0eea55ab6.jpg)  
+Enhanced Image
+
+![](images/627d5c5350ea0657248f2ae834ef7cddf8f80bcced6c85b86546b2ff3d5c3881.jpg)  
+GT  
+Hierarchical Representation
+
+![](images/9d9165a26c3406bc470654e61b52d491c4363639ed7b96a3b086bb0e0e3c8091.jpg)
+
+![](images/9749056543c7d336c48a8e4e7f78f8d06d8b774e8a9537bc1694589e3f82ed85.jpg)  
+Enhanced Image
+
+# Abstract
+
+Extracting useful visual cues for the downstream tasks is especially challenging under low-light vision. Prior works create enhanced representations by either correlating visual quality with machine perception or designing illumination-degrading transformation methods that require pre-training on synthetic datasets. We argue that optimizing enhanced image representation pertaining to the loss of the downstream task can result in more expressive representations. Therefore, in this work, we propose a novel module, FeatEnHancer, that hierarchically combines multiscale features using multi-headed attention guided by task-related loss function to create suitable representations. Furthermore, our intra-scale enhancement improves the quality of features extracted at each scale or level, as well as combines features from different scales in a way that reflects their relative importance for the task at hand. FeatEnHancer is a general-purpose plug-and-play module and can be incorporated into any low-light vision pipeline. We show with extensive experimentation that the enhanced representation produced with FeatEnHancer significantly and consistently improves results in several low
+
+light vision tasks, including dark object detection (+5.7 mAP on ExDark), face detection (+1.5 mAP on DARK FACE), nighttime semantic segmentation (+5.1 mIoU on ACDC), and video object detection (+1.8 mAP on DarkVision), highlighting the effectiveness of enhancing hierarchical features under low-light vision.
+
+# 1. Introduction
+
+Recent remarkable advancements in high-level vision tasks have shown that given a high-quality image, current vision backbone networks [20, 15, 12, 32, 31], object detectors [42, 28, 43, 19, 2, 3, 49, 4, 71, 64, 65] and semantic segmentation models [34, 48, 57, 7, 58] can effectively learn desired features to perform vision tasks. Similarly, modern low-light image enhancement (LLIE) methods [44, 67, 14, 21, 17, 25] are capable of transforming a low-light image into a visual-friendly representation. However, a naive combination of the two brings sub-optimal gains when it comes to high-level vision tasks under low-light vision.
+
+This work explores the underlying reasons for the low performance of the combination of LLIE with high-level vision methods and observes the following limitations: 1) Although existing LLIE methods push the envelope of visual perception for human eyes, they do not align with vision backbone networks [20, 12, 15, 32, 31] due to lack of multiscale features. For instance, it is likely that the enhancement method increases brightness in some regions. However, it simultaneously corrupts the edges and texture information of objects. 2) The pixel distribution among different low-light images may have huge variance owing to the disparity in less illuminated environments [17, 25, 68]. This increases intra-class variance in some cases (see Fig. 3, where only one bicycle is recognized by [17] instead of two bicycles in the ground-truth). 3) Current LLIE approaches [14, 17, 25, 21, 44, 56, 67] employ enhancement loss functions to optimize the enhancement networks. These loss functions compel the network to attend to all pixels equally, lacking the learning of informative details necessary for high-level downstream vision tasks such as object pose and shape for object detection. Furthermore, to train these enhancement networks, most of them [44, 14, 67, 56] require a set of high-quality images, which is hardly available in a real-world setting.
+
+Motivated by these observations and inspired by recent developments in LLIE [17, 25] and vision-based backbone networks [15, 32, 31], this paper aims to bridge the gap by exploring an end-to-end trainable recipe that jointly optimizes the enhancement and downstream task objectives in a single network. To this end, we present FeatEnHancer, a general-purpose feature enhancer that learns to enrich multiscale hierarchical features favourable for downstream vision tasks in a low-light setting. An example of learned hierarchical representation and the enhanced image is illustrated in Fig. 1.
+
+In particular, our FeatEnHancer first downsamples a low-light RGB input image to construct multi-scale hierarchical representations. Subsequently, these representations are fed to our Feature Enhancement Network (FEN), which is a deep convolutional network, employed to enrich intra-scale semantic representations. Note that the parameters of FEN can be adjusted through task-related loss functions, which pushes the FEN to only enhance the task-related features. This multiscale learning allows the network to enhance both global and local information from higher and lower-resolution features, respectively. Once the enhanced representations on different scales are obtained, the remaining obstacle is to fuse them effectively. To achieve, this, we select two different strategies to capture both global and local information from higher and lower-resolution features. First, to merge high-resolution features, inspired by multi-head attention in [50], we design a Scale-aware Attentional Feature Aggregation (SAFA) method that jointly attends information from differ
+
+ent scales. Second, for lower-resolution features, the skip connection [20] scheme is adopted to merge the enhanced representation from SAFA to lower-resolution features. With these jointly learned hierarchical features, our FeatEnHancer provides semantically powerful representations which can be exploited by advanced methods such as feature pyramid networks [27] for object detection [43] and instance segmentation [19], or UNet [45] for semantic segmentation [34].
+
+The main contributions of this work can be summarized as follows:
+
+1. We propose FeatEnHancer, a novel module that enhances hierarchical features to boost downstream vision tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. FeatEnHancer is a general-purpose plug-and-play module that can be trained end-to-end with any high-level vision task.  
+2. To the best of our knowledge, this is the first work that fully exploits multi-scale hierarchical features in low-light scenarios and generalizes to several downstream vision tasks such as object detection, semantic segmentation, and video object detection.  
+3. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods and task-specific state-of-the-art approaches.
+
+# 2. Related Work
+
+# 2.1. Enhancing Low-Light Images
+
+Deep learning-based LLIE methods focus on improving the visual quality of low-light images that satisfies human visual perception [23, 22]. Most LLIE approaches [14, 44, 56, 67] operate under a supervised learning paradigm, requiring paired data during training. Unsupervised GAN-based methods [21] eliminate the need for paired data during the training. However, their performance relies on the careful choice of unpaired data. Recently, zero-reference methods [17, 25, 68] discard the need for both paired and unpaired data to enhance low-light images by designing a set of non-reference loss functions. Inspired by these recent developments, this work aims to bridge low-light enhancement and downstream vision tasks (such as object detection [10, 33, 62], semantic segmentation [60, 47], and video object detection [63]) by enhancing multi-scale hierarchical features without needing paired or unpaired data to boost performance.
+
+# 2.2. Enhancing Low-Light for Downstream Vision Tasks
+
+These approaches consider machine perception as the criteria for success while enhancing images to improve downstream vision tasks. One obvious way to achieve this goal is to apply the LLIE methods as an initial step [70, 17]. However, this leads to unsatisfactory results (see Table 2, 4, and 5). Recently, another line of work has explored end-to-end pipelines, optimizing both enhancement and individual tasks during training, and our work follows the same spirit.
+
+Face detection. Liang et al. [26] propose an effective information extraction scheme from low-light images by exploiting multi-exposure generation. Furthermore, bi-directional domain adaptation [52, 51] and parallel architecture that jointly performs enhancement and detection [37] are presented to advance the research. However, these approaches are carefully designed to tackle face detection [62, 53] only and deliver minor improvements when applied to generic object detection [51]. Contrarily, our FeatEnHancer is a general-purpose module. It significantly improves several downstream vision tasks. Hence, we refrain from comparing our method to architectures only evaluated for face detection.
+
+Dark object detection. Dark (low-light) object detection [10, 30] methods have emerged recently, thanks to the real-world low illumination datasets [33, 39]. IA-YOLO [30] introduces a convolutional neural network (CNN)-based parameter predictor that learns the optimal configuration for the filters employed in the differential image processing module. Most related to our work is MAET [10], which investigates the physical noise model and image signal processing (ISP) pipeline under low illumination and learns the model to predict degradation parameters and object features. To avoid feature entanglement, they impose orthogonal tangent regularity to penalize cosine similarity between objects and degrading features. However, owing to the weather-specific hyperparameters in [30] and degradation parameters in [10], these works rely on large synthetic datasets to achieve desired performance. Unlike them, our FeatEnHancer is optimized from the task-related loss functions and does not require any pre-training on synthetic datasets mimicking low-light or harsh weather conditions.
+
+Other high-level vision tasks. Besides face and object detection, recent research has explored high-level computer vision tasks like semantic segmentation [6, 34]. Xue et al. [60] devise a contrastive-learning strategy to improve visual and machine perception simultaneously, achieving impressive performance on nighttime semantic segmentation of adverse conditions dataset with correspondences (ACDC) dataset [47]. Furthermore, DarkVision [63] has emerged recently to tackle video object detection under low-light vision. In this work, thanks to [47, 63], we apply FeatEnHancer
+
+to semantic segmentation and video object detection under low-light vision to investigate its generalization capabilities.
+
+# 2.3. Learning Multi-scale Hierarchical Features
+
+Representing objects at varying scales is one of the main difficulties in computer vision. Therefore, the work in this domain goes back to the era of hand-engineered features [36, 11, 38, 24]. Modern object detectors [43, 28, 2, 71, 49, 40, 65] exploit multi-scale features to tackle this challenge. Similarly, multi-scale representations [34] and pyramid pooling schemes [69] have been proposed for effective semantic segmentation. Moreover, current improvements in vision-based backbone networks [15, 31, 32] demonstrate that learning hierarchical features during feature extraction directly uplifts the downstream vision tasks [19, 57, 2]. However, the multi-scale and hierarchical structures of CNN have not been fully explored for low-light vision tasks.
+
+Under harsh weather conditions, DENet [41] employs Laplacian Pyramid [1] to decompose images into low and high-frequency components for object detection. Despite the encouraging results, the multi-scale feature learning in DENet relies on the Laplacian pyramid, which is susceptible to noise and may produce inconsistencies in regions with high contrast or sharp edges. Alternatively, aligned with the multi-scale learning in modern vision backbone networks [27, 32, 31], our FeatEnHancer employs CNN to generate multi-scale feature representations, which are fused through the scale-aware attentional feature aggregation and skip connections. Our approach is much more flexible and aligns with downstream vision tasks, boosting state-of-the-art results on multiple downstream vision tasks.
+
+# 3. Proposed Approach
+
+The key idea of this paper is to design a general-purpose pluggable module that strengthens machine perception under low-light vision to solve several downstream vision tasks such as object detection, semantic segmentation, and video object detection. The overall architecture of FeatEnHancer is exhibited in Fig. 2. Our FeatEnHancer takes a low-light image as input and adaptively boosts its semantic representation by enriching task-related hierarchical features. We now discuss the key components of FeatEnHancer in detail.
+
+# 3.1. Hierarchical Feature Enhancement
+
+Inspired by the recent improvements in vision-based backbone networks [15, 31, 32], we introduce the enhancement of hierarchical features through jointly optimizing feature enhancement and downstream tasks under low-light vision. Unlike [15, 31, 32], our goal is to extract spatial features from low-light images and generate meaningful semantic representations. In order to enhance hierarchical features, we first construct multi-scale representations from the low-light input image. Later, we feed these multi-scale
+
+![](images/8a4cddd9bf1b856dac24761aa9df2f581fff9eff945b5b88a5797b08d431e3ad.jpg)  
+Figure 2: Network architecture of the proposed FeatEnHancer employed in a downstream vision task. Our FeatEnHancer takes a low-light image and adaptively boosts its semantic representation by enriching task-related hierarchical features. Zoom in for the best view.
+
+representations to our feature enhancement network.
+
+Constructing multi-scale representations. We take a lowlight RGB image  $I\in \mathbb{R}^{H\times W\times C}$  as input and employ regular convolutional operator Conv.) on  $I$  to generate  $I_{q}\in \mathbb{R}^{\frac{H}{4}\times \frac{W}{4}\times 3}$  and  $I_{o}\in \mathbb{R}^{\frac{H}{8}\times \frac{W}{8}\times 3}$  representing the quarter and octa scale of an input image, respectively. To summarize, it can be written as:
+
+$$
+I _ {q} = \operatorname {C o n v} (I) \quad K = 7, S = 4, \tag {1}
+$$
+
+$$
+I _ {o} = \mathbf {C o n v} (I _ {q}) \quad K = 3, S = 2,
+$$
+
+where  $K$  and  $S$  denote kernel size and stride, and  $H$ ,  $W$ , and  $C$  represent the height, width, and channels of an image.
+
+Feature enhancement network. In order to enhance features at each scale, we require an enhancement network that learns to enhance spatial information important for downstream tasks. Inspired by low-light image enhancement networks [17, 25], we design a fully convolutional intra-scale feature extraction network (FEN). However, unlike [17, 25], our FEN introduces a single convolutional layer at the beginning that generates a feature map  $F \in \mathbb{R}^{H \times W \times C}$ , where  $C$  is transformed from 3 to 32 by keeping the resolution  $(H \times W)$  same as the input. Then a series of six convolutional layers with symmetrical skip concatenation is applied, where each convolutional layer, with  $K = 3$  and  $S = 1$ , is accompanied by the ReLU activation function. We apply FEN on each scale  $I$ ,  $I_{q}$ , and  $I_{o}$  separately, and obtain multiscale feature representations, denoted as  $F$ ,  $F_{q}$ , and  $F_{o}$ , respectively. This multi-scale learning allows the network to enhance both global and local information from higher and lower-resolution features. Hence, we ignore down-sampling and batch normalization to preserve semantic relations be
+
+tween neighbouring pixels which is similar to [17]. However, we discard the last convolutional layer of DCENet [17] in our FEN and propagate the final enhanced feature representations from each scale for the multi-scale feature fusion. Note that the implementation details of FEN in FeatEnHancer are independent of the proposed module, and even more, advanced image enhancement networks such as [68] can be applied to improve performance. Now, we discuss multiscale feature fusion in detail.
+
+# 3.2. Multi-scale Feature Fusion
+
+Since we already have multi-scale feature representations  $(F, F_{q},$  and  $F_{o})$  from FEN, the remaining obstacle is to fuse them effectively. Lower-scale features  $(F_{o})$  contain fine details and edges. In contrast, higher-resolution features  $(F_{q})$  capture more abstract information, such as shapes and patterns. Therefore, naive aggregation leads to inferior performance (see Table 6a). Hence, we adopt two different strategies to capture both global and local information from higher and lower-resolution features. First, inspired by multi-head attention in [50] that enables the network to jointly learn information from different channels, we design a scale-aware attentional feature aggregation (SAFA) module that jointly attends to features from different scales. Second, we adopt a skip connection [20] (SC) scheme to integrate low-level information from  $F_{o}$  and the enhanced representation from SAFA to obtain the final enhanced hierarchical representation. Adopting SAFA for merging high-resolution features and SC for lower-resolution features leads to a more robust hierarchical representation (see Table 6b). Now, we discuss SAFA in detail.
+
+Scale-aware Attentional Feature Aggregation. Even though high-resolution features assist in capturing fine de
+
+tails, such as recognizing small objects, applying an attentional operation to them is computationally demanding. Thus, in SAFA, we propose an efficient multi-scale aggregation strategy where enhanced high-resolution hierarchical features are projected to a smaller resolution prior to attentional feature aggregation. As illustrated in Figure 2, SAFA transforms  $F \in \mathbb{R}^{H \times W \times C}$  to  $Q \in \mathbb{R}^{\frac{H}{8} \times \frac{W}{8} \times C}$  with two convolutional layers ( $K = 7$ ,  $S = 4$ ;  $K = 3$ ,  $S = 2$ ) and  $F_{q} \in \mathbb{R}^{\frac{H}{4} \times \frac{W}{4} \times C}$  to  $K \in \mathbb{R}^{\frac{H}{8} \times \frac{W}{8} \times C}$  with a single convolutional layer ( $K = 3$ ,  $S = 2$ ). Note that the weights of the convolutional layer ( $K = 3$ ,  $S = 2$ ) are not shared because, in addition to down-scaling the high-resolution features, it serves as an embedding network before computing the attentional weights. Later,  $Q$  and  $K$  are concatenated to form the set of hierarchical features  $F_{q + k}$ , which are split into N blocks along the channel dimension  $C$ :
+
+$$
+F _ {q + k} ^ {n} = F _ {q + k} [:,:, (n - 1) \frac {C}{N}: n \frac {C}{N} ], \tag {2}
+$$
+
+where  $n\in \{1,2,\dots,N\}$  and  $\mathbf{N}$  is the total number of attentional blocks. The  $F_{q + k}^{n}\in \mathbb{R}^{\frac{H}{8}\times \frac{W}{8}\times \frac{C}{N}}$  is used to compute attentional weights  $W$  in a single attention block as follows:
+
+$$
+W _ {q + k} ^ {n} = F _ {q} ^ {n} \cdot F _ {k} ^ {n}, \tag {3}
+$$
+
+$$
+\bar {\mathbf {W}} _ {q + k} ^ {n} = \frac {\exp \left(W _ {q + k} ^ {n}\right)}{\sum_ {l = 1} ^ {L} \exp \left(W _ {q + k} ^ {n}\right)}, \tag {4}
+$$
+
+where  $W_{q + k}^{n}$  is the attentional weights of  $F_{q}^{n}$  and  $F_{k}^{n}$  for  $n$ -th block, and  $\overline{\mathbf{W}}_{q + k}^{n}$  is the normalized form of  $W_{q + k}^{n}$ . Derived from the  $n$ -th block of normalized attention weights, we apply weighted sum to compute the  $n$ -th block of enhanced hierarchical representation  $\overline{\mathbf{F}}_h^n\in \mathbb{R}^{\frac{H}{8}\times \frac{W}{8}\times \frac{C}{N}}$  as follows:
+
+$$
+\bar {\mathbf {F}} _ {h} ^ {n} = \sum_ {l = 1} ^ {L} \bar {\mathbf {W}} _ {q + k} ^ {n} \cdot F _ {q + k} ^ {n}, \tag {5}
+$$
+
+now we concatenate all  $\bar{\mathbf{F}}_h^n$  along the channel dimension to obtain  $\bar{\mathbf{F}}_h\in \mathbb{R}^{\frac{H}{8}\times \frac{W}{8}\times C}$ . Note that although  $\bar{\mathbf{F}}_h$  is the same size as  $Q$  and  $K$ , it contains far richer representations, encompassing information from multi-scale high-resolution features.
+
+Subsequently, as explained earlier in Sec. 3.2, with the help of skip connections (SC), we integrate  $F_{o}$  and  $\bar{\mathbf{F}}_h$  to obtain the final enhanced hierarchical representation covering both global and local features, as illustrated in Figure 1 and 2. Note that prior to the skip connection, we upsample  $\bar{\mathbf{F}}_h$  and  $F_{o}$ , where the upsampling operation  $U(.)\in \mathbb{R}^{\frac{H}{8}\times \frac{W}{8}\times C}\to \mathbb{R}^{H\times W\times C}$  is performed with simple bi-linear interpolation operation, which is much faster than using transposed convolutions [13]. Unlike image enhancement in existing works [17, 25, 10], with a multi-scale hierarchical feature enhancement strategy, our FeatEnHancer
+
+learns a powerful semantic representation by capturing both local and global features. This makes it a general-purpose module to enhance hierarchical features, boosting machine perception under low-light vision.
+
+<table><tr><td>Dataset</td><td>Task</td><td>#Cls</td><td>#Train</td><td>#Val</td></tr><tr><td>ExDark [33]</td><td>Dark object detection</td><td>12</td><td>4800</td><td>2563</td></tr><tr><td>DARK FACE [62]</td><td>Face detection</td><td>1</td><td>5400</td><td>600</td></tr><tr><td>ACDC Nighttime [47]</td><td>Semantic segmentation</td><td>19</td><td>400</td><td>106</td></tr><tr><td>DarkVision [63]</td><td>Video object detection</td><td>4</td><td>26</td><td>6</td></tr></table>
+
+Table 1: Statistics of the datasets used to report results on four different downstream vision tasks. #Cls is the number of classes, whereas #Train and #Val denote number of training and validation samples for each dataset, respectively.
+
+# 4. Experiments
+
+We conduct extensive experiments for evaluating the proposed FeatEnHancer module to several downstream tasks under the low-light vision, including generic object detection [33, 39], face detection [62], semantic segmentation [47], and video object detection [63]. Table 1 summarizes the crucial statistics of the employed datasets. This section first compares the proposed method with powerful baselines, existing LLIE approaches, and task-specific state-of-the-art methods. Then, we ablate the important design choices of our FeatEnHancer. We provide complete implementation details for each experiment in Appendix A.
+
+# 4.1. Dark Object Detection
+
+Settings. For dark object detection experiments on the real-world data, we consider the exclusively dark (ExDark) [33] dataset (see Table 1). We adopt RetinaNet [28] as a typical detector and Featurized Query R-CNN [65] (FQ R-CNN) as an advanced object detection framework to report results. In the case of both detectors, pre-trained models on COCO [29] are fine-tuned on each dataset. For RetinaNet, images are resized to  $640 \times 640$ , and we train the network using  $1 \times$  schedule in mmdetection [5] (12 epochs using SGD optimizer [46] with an initial learning rate of 0.001). For Featurized Query R-CNN, we employ multiscale training [4, 49, 65] (shorter side ranging from 400 to 800 with a longer side of 1333). The FQ R-CNN is trained for 50000 iterations using ADAMW [35] optimizer (initial learning rate of 0.0000025, weight decay of 0.0001, and batch size of 8). Note that for each object detection framework, we adopt the same settings while reproducing results of our work, baseline, LLIE approaches, and task-specific state-of-the-art methods.
+
+We compare our FeatEnHancer to several state-of-the-art LLIE methods, including KIND [67], RAUS [44], EnGAN [21], MBLLEN [14], Zero-DCE [17], Zero-DCE++ [17], and state-of-the-art dark object detection method, MAET [10]. For LLIE methods, all images are
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">RetinaNet</td><td colspan="2">FQ R-CNN</td><td rowspan="2">Methods</td><td colspan="2">RetinaNet</td><td colspan="2">FQ R-CNN</td><td>Method</td><td>mIoU</td></tr><tr><td>\( mAP_{50} \)</td><td>mAP</td><td>\( mAP_{50} \)</td><td>mAP</td><td>\( AP_{50} \)</td><td>AP</td><td>\( AP_{50} \)</td><td>AP</td><td>Baseline [7]</td><td>45.7</td></tr><tr><td>Baseline</td><td>72.1</td><td>46.3</td><td>74.5</td><td>47.0</td><td>Baseline</td><td>47.3</td><td>19.9</td><td>67.5</td><td>28.6</td><td>RetinexNet [54]</td><td>41.9</td></tr><tr><td>RAUS [44]</td><td>64.7</td><td>44.0</td><td>77.0</td><td>48.1</td><td>RAUS [44]</td><td>42.1</td><td>17.6</td><td>65.5</td><td>27.4</td><td>DRBN [59]</td><td>43.3</td></tr><tr><td>KIND [67]</td><td>70.7</td><td>45.1</td><td>80.5</td><td>51.5</td><td>KIND [67]</td><td>47.2</td><td>19.8</td><td>65.0</td><td>27.5</td><td>FIDE [61]</td><td>43.4</td></tr><tr><td>Zero-DCE++ [25]</td><td>70.3</td><td>45.2</td><td>79.5</td><td>49.2</td><td>Zero-DCE++ [25]</td><td>47.3</td><td>20.1</td><td>66.2</td><td>28.2</td><td>KIND [67]</td><td>43.0</td></tr><tr><td>EnGAN [21]</td><td>70.4</td><td>44.9</td><td>80.0</td><td>51.9</td><td>EnGAN [21]</td><td>45.1</td><td>19.3</td><td>67.4</td><td>28.4</td><td>EnGAN [21]</td><td>43.8</td></tr><tr><td>MBLLEN [14]</td><td>70.6</td><td>45.1</td><td>80.0</td><td>51.0</td><td>MBLLEN [14]</td><td>47.1</td><td>19.8</td><td>67.3</td><td>27.1</td><td>ZeroDCE [17]</td><td>43.4</td></tr><tr><td>Zero-DCE [17]</td><td>71.0</td><td>45.2</td><td>80.6</td><td>52.0</td><td>Zero-DCE [17]</td><td>47.4</td><td>20.1</td><td>66.9</td><td>27.5</td><td>SSIENet [66]</td><td>41.4</td></tr><tr><td>MAET [10]</td><td>71.8</td><td>45.7</td><td>81.6</td><td>52.4</td><td>MAET [10]</td><td>44.3</td><td>18.7</td><td>66.1</td><td>27.1</td><td>Xue et al. [60]</td><td>49.8</td></tr><tr><td>FeatEnHancer</td><td>72.6</td><td>46.4</td><td>86.3</td><td>56.5</td><td>FeatEnHancer</td><td>47.2</td><td>19.9</td><td>69.0</td><td>29.4</td><td>FeatEnHancer</td><td>54.9</td></tr></table>
+
+enhanced from their released checkpoints and propagated to the detector. In case of MAET [10], we pre-train the detector using their proposed degrading pipeline and then fine-tune it on both datasets to establish a direct comparison.
+
+Results on ExDark. Table 2 lists the results of LLIE works, MAET, and the proposed method on both object detection frameworks. It is evident that our FeatEnHancer brings consistent and significant gains over prior methods. Note that, while the performance of MAET and our method is comparable on RetinaNet  $(\approx 72\mathrm{AP}_{50})$ , the proposed FeatEnHancer outperforms MAET by a significant margin on FQ R-CNN, achieving the new state-of-the-art  $\mathrm{AP}_{50}$  of 86.3. Furthermore, Figure 3 shows four detection examples from our method and the two best competitors using FQ R-CNN as a detector. These results illustrate that despite the inferior visual quality, our FeatEnHancer enhances hierarchical features that are favourable for dark object detection, producing state-of-the-art results.
+
+# 4.2. Face Detection on DARK FACE
+
+Settings. The DARK FACE [53, 62] is a challenging face detection dataset released for the  $\mathrm{UG}^2$  competition. For experiments on the DARK FACE (see Table 1), the images are resized to a larger resolution of  $1500 \times 1000$  for all methods. We adopt the same object detection frameworks of RetinaNet and FQ R-CNN and follow identical experimental settings, as explained in Sec. 4.1.
+
+Results. The performance of FeatEnHancer, MAET, and six LLIE methods, using RetinaNet and Featurized Query R-CNN, are summarized in Table 3. Note that a few LLIE methods [17, 25, 67] yield superior results than our approach in the case of RetinaNet. We argue that due to tiny faces with highly dark images in the DARK FACE dataset, RetinaNet fails to capture information even from the enhanced hierarchical features. We discuss this behaviour with an ex
+
+Table 2: Quantitative comparison on ExDark dataset. Results obtained on the commonly used evaluation metrics are highlighted. Our FeatEnHancer brings consistent improvements and achieves new state-of-the-art results with FQ R-CNN.  
+Table 3: Comparing FeatEnHancer on the DARK FACE dataset. With RetinaNet, FeatEnHancer performs on par with other methods. However, with FQ R-CNN, FeatEnHancer surpasses all of them.  
+Table 4: Quantitative comparison on the ACDC dataset. Huge gains from our FeatEnhancer lead to new state-of-the-art results.  
+
+<table><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>GT</td><td>MAET</td><td>ZeroDCE</td><td>Ours</td></tr></table>
+
+Figure 3: Visual comparison of FeatEnHancer with the two previous best competitors on the ExDark dataset. Zoom in for the best view.
+
+ample in Appendix B. On the other hand, LLIE approaches directly provides well-lit images that bring slightly bigger gains  $(+0.1\mathrm{mAP}_{50})$  in this case. However, note that with the more strong detector, our FeatEnHancer surpasses all the LLIE methods and MAET by a significant margin  $(+1.5\mathrm{mAP}_{50})$ , achieving  $\mathrm{mAP}_{50}$  of 69.0.
+
+# 4.3. Nighttime Semantic Segmentation on ACDC
+
+Settings. We utilize nighttime images from the ACDC dataset [47] (see Table 1) to report results on semantic segmentation in a low-light setting. DeepLabV3+ [7] is adopted as the segmentation baseline from mmseg [8] for straightforward comparison with the concurrent work [60]. We follow identical experimental settings as in [60]. Refer to Appendix A for complete implementation details.
+
+Results. We compare our method with several state-of-the-art LLIE methods, including RetinexNet [54] KIND [67],
+
+![](images/583e4c022fb3f1109eddbc843d4ac1187a968270d8c68a001c9e58241dc08358.jpg)  
+Figure 4: Qualitative comparison of FeatEnHancer with previous best work [60] on the ACDC nighttime semantic segmentation. FeatEnHancer provides more accurate segmentations.
+
+<table><tr><td>Method</td><td>Illumination (3.2) 
+mAP</td><td>Illumination (0.2) 
+mAP</td></tr><tr><td>Baseline [55]</td><td>32.8</td><td>10.4</td></tr><tr><td>RAUS [44]</td><td>7.42</td><td>5.19</td></tr><tr><td>EnGAN [21]</td><td>7.83</td><td>5.41</td></tr><tr><td>MBLLEN [14]</td><td>7.82</td><td>5.39</td></tr><tr><td>KIND [67]</td><td>7.43</td><td>5.25</td></tr><tr><td>Zero-DCE++ [25]</td><td>7.51</td><td>5.02</td></tr><tr><td>Zero-DCE [17]</td><td>7.83</td><td>5.43</td></tr><tr><td>FeatEnHancer</td><td>34.6</td><td>11.2</td></tr></table>
+
+Table 5: Comparing FeatEnHancer with LLIE methods on the DarkVision dataset. FeatEnHancer is the only method that boosts the performance of the powerful baseline method on both illumination levels.
+
+FIDE [61], DRBN [59], EnGAN [21], SSIONet [66], ZeroDCE [17], and current state-of-the-art nighttime semantic segmentation method Xue et al. [60]. As shown in Table 4, our FeatEnHancer brings remarkable improvements in the baseline with a mIoU of 54.9, outperforming the previous best result by 5.1 points. Moreover, we present a qualitative comparison with the previous best competitor [60] in Figure 4. Evidently, our FeatEnHancer generates more accurate segmentation for both bigger and smaller objects, such as terrain and traffic signs in the last row. These results affirm the effectiveness of FeatEnHancer as a general-purpose module achieving state-of-the-art results in both dark object
+
+detection and nighttime semantic segmentation.
+
+# 4.4. Video Object Detection on DarkVision
+
+Settings. We extend our experiments from static images to video domain to test the generalization capabilities of our method. The video object detection under low-light vision is evaluated on the recently emerged DarkVision dataset [63] (see Table 1 for dataset details). Although the dataset is not publicly available yet, we sincerely thank the authors of [63] for providing prompt access. To evaluate our FeatEnHancer under low light settings, we take the low-end camera split on two different illumination levels, i.e., 0.2 and 3.2. For ablation studies, we adopt a  $3.2\%$  illumination level split. We consider SELSA [55] as our baseline and follow identical experimental settings with the ResNet-50 backbone network in the mmtracking [9]. To establish a direct comparison, we enhance all video frames first through LLIE methods and feed these frames to the baseline, as done in Sec. 4.1. As a common practice in video object detection [16, 18, 55], the mAP@IoU=0.5 is utilized as an evaluation metric to report results. More details can be found in Appendix A.
+
+Results. Table 5 compares our FeatEnHancer with several LLIE methods [44, 21, 14, 67, 17, 25] and the powerful video object detection baseline [55]. Evidently, our FeatEnHancer provides considerable gains to the baseline with  $34.6\mathrm{mAP}$  and  $11.2\mathrm{mAP}$  under illumination levels of 3.2 and 0.2, respectively. Note that our FeatEnHancer is the only method that boosts performance under both image and video modalities. In contrast, as shown in Table 5, existing LLIE methods not only fail to assist the baseline method but also deteriorate the performance. This poor generalization of LLIE approaches highlights that learning from domain-specific paired data [14, 67, 44], unpaired data [21], and curve estimation without data [17, 25] are not the optimal solutions for generalized enhancement methods. Hence, more research is required.
+
+# 4.5. Ablation Studies
+
+This section ablates important design choices in the proposed FeatEnHancer when plugged into RetinaNet, DeeplabV3+, and SELSA on ExDark (dark object detection), ACDC (nighttime semantic segmentation), and DarkVision with illumination level of  $3.2\%$  (video object detection), respectively.
+
+SAFA in FeatEnHancer. The important component of the proposed FeatEnHancer is the scale-aware attentional feature aggregation (SAFA) that aggregates high-resolution features. To validate its effectiveness, we conduct multiple experiments where SAFA is replaced with simple averaging or skip connections (SC) [20] to fuse enhanced multi-scale features  $F$  and  $F_{q}$  (see Sec. 3.2). The experiment results are
+
+<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>simple averaging</td><td>69.5</td><td>50.3</td><td>32.9</td></tr><tr><td>skip connections [20]</td><td>70.3</td><td>51.7</td><td>33.1</td></tr><tr><td>SAFA</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>
+
+(a) Effectiveness of SAFA.  
+
+<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>SC, SC</td><td>69.7</td><td>51.7</td><td>32.8</td></tr><tr><td>SAFA, SAFA</td><td>70.2</td><td>52.6</td><td>33.4</td></tr><tr><td>SC, SAFA</td><td>70.9</td><td>52.9</td><td>33.8</td></tr><tr><td>SAFA, SC</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>
+
+(b) Various combinations of multi-scale fusion.
+
+<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>maxpool</td><td>69.3</td><td>51.3</td><td>32.9</td></tr><tr><td>adavgpool [68]</td><td>69.9</td><td>50.7</td><td>32.9</td></tr><tr><td>interpolation [30]</td><td>70.7</td><td>51.5</td><td>33.1</td></tr><tr><td>Convolution</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>
+
+(c) Downsampling approaches.  
+
+<table><tr><td>Scale</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>(2, 4)</td><td>71.8</td><td>52.7</td><td>34.1</td></tr><tr><td>(4, 8)</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>(4, 16)</td><td>71.5</td><td>51.4</td><td>33.9</td></tr><tr><td>(8, 16)</td><td>68.7</td><td>45.6</td><td>31.9</td></tr></table>
+
+(d) Scales for  $I_{q}$  and  $I_{o}$ , respectively.  
+
+<table><tr><td>N</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>2</td><td>72.1</td><td>53.9</td><td>34.2</td></tr><tr><td>4</td><td>72.4</td><td>54.3</td><td>34.5</td></tr><tr><td>8</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>12</td><td>72.4</td><td>54.3</td><td>34.1</td></tr></table>
+
+(e) # attentional blocks in SAFA.
+
+Table 6: Ablations for the proposed FeatEnHancer on three benchmarks. (a) We investigate the effectiveness of SAFA by replacing it with different aggregation methods to fuse  $F$  and  $F_{q}$ . (b) We experiment with various combinations of SAFA and skip connection (SC) to justify an optimal design choice. Here, (SC, SC) means employing only skip connections to merge both  $F_{q}$  and  $F_{o}$  with  $F$ . (c) Besides convolution, we experiment with other downsampling techniques to generate lower resolutions. Here, adavgpool denotes adaptive average pooling as done in [68]. (d) We vary scale sizes to generate lower-scale representations. Here, (2, 4) means  $I_{q} \in \mathbb{R}^{\frac{H}{2} \times \frac{W}{2} \times 3}$  and  $I_{o} \in \mathbb{R}^{\frac{H}{4} \times \frac{W}{4} \times 3}$ . (e) We vary number of attentional blocks  $N$  in SAFA of FeatEnHancer. Default settings are highlighted.
+
+summarized in Table 6a. It is clear that SAFA outperforms both averaging and SC strategies by  $+2.3\mathrm{mAP}$  on ExDark,  $+3.2\mathrm{mIoU}$  on ACDC, and  $+1.5\mathrm{mAP}$  on DarkVision. These significant boosts across all three benchmarks indicate that scale-aware attention leads to optimal multi-scale feature aggregation in the proposed FeatEnHancer.
+
+Multi-scale feature fusion. We experiment with various combinations of SAFA and SC to find an optimal design choice to fuse  $F_{q}$  and  $F_{o}$  with  $F$  (see Sec. 3.2). As shown in Table 6b, there is a clear increase in performance, achieving (72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision) when SAFA is applied to fuse  $F$  and  $F_{q}$  first, and then  $F_{o}$  is merged with the output of SAFA using skip connection. Hence, we use this approach as the default setting.
+
+Convolutional Downsampling. Table 6c summarizes results from different downsampling techniques applied on the input image  $I$  to generate lower-resolutions  $I_{q}$  and  $I_{o}$  (see Sec 3.1). Our proposed convolutional downsampling yields impressive gains of  $+1.9\mathrm{mAP}$  on ExDark,  $+3.4\mathrm{mIoU}$ , and  $+1.5\mathrm{mAP}$  on DarkVision compared to max-pooling, adaptive average pooling [68], and bilinear interpolation [30]. These results demonstrate the effectiveness of convolutional downsampling since it is better aligned with various vision backbone networks [32, 15, 27].
+
+Different Scale sizes. We analyse the effect of different scale sizes to generate lower resolutions in Table 6d. Here, for instance, (2, 4) means that the resolution of input image  $I \in \mathbb{R}^{H \times W \times 3}$  is reduced by a factor of 2 and 4 to generate  $I_{q} \in \mathbb{R}^{\frac{H}{2} \times \frac{W}{2} \times 3}$  and  $I_{o} \in \mathbb{R}^{\frac{H}{4} \times \frac{W}{4} \times 3}$ , respectively. Note that all these scales are generated through regular convolutional
+
+operator  $\mathbf{Conv}(.)$ , as explained in Eq. 1. Looking at results in Table 6d, the top performance on all three tasks is achieved with the scale size of (4, 8), thereby, preferred as a default setting.
+
+Number of Attention Blocks in SAFA. Table 6e studies the effect of the number of attention blocks  $N$  in our SAFA. The performance rises for all three tasks with the increase in  $N$ . This demonstrates that more attentional blocks in SAFA bring additional gains. The best performance with 72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision is achieved when  $N$  reaches 8, and after that, it tends to saturate. Hence,  $N = 8$  is used as the default setting.
+
+# 5. Conclusion
+
+This paper proposes FeatEnHancer, a novel general-purpose feature enhancement module designed to enrich hierarchical features favourable for downstream tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. Furthermore, our FeatEnHancer neither requires pre-training on synthetic datasets nor relies on enhancement loss functions. These architectural innovations make FeatEnHancer a plug-and-play module. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods, and task-specific state-of-the-art approaches.
+
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+                                    "content": "Extracting useful visual cues for the downstream tasks is especially challenging under low-light vision. Prior works create enhanced representations by either correlating visual quality with machine perception or designing illumination-degrading transformation methods that require pre-training on synthetic datasets. We argue that optimizing enhanced image representation pertaining to the loss of the downstream task can result in more expressive representations. Therefore, in this work, we propose a novel module, FeatEnHancer, that hierarchically combines multiscale features using multi-headed attention guided by task-related loss function to create suitable representations. Furthermore, our intra-scale enhancement improves the quality of features extracted at each scale or level, as well as combines features from different scales in a way that reflects their relative importance for the task at hand. FeatEnHancer is a general-purpose plug-and-play module and can be incorporated into any low-light vision pipeline. We show with extensive experimentation that the enhanced representation produced with FeatEnHancer significantly and consistently improves results in several low"
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+                                    "content": "light vision tasks, including dark object detection (+5.7 mAP on ExDark), face detection (+1.5 mAP on DARK FACE), nighttime semantic segmentation (+5.1 mIoU on ACDC), and video object detection (+1.8 mAP on DarkVision), highlighting the effectiveness of enhancing hierarchical features under low-light vision."
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+                                    "content": "Recent remarkable advancements in high-level vision tasks have shown that given a high-quality image, current vision backbone networks [20, 15, 12, 32, 31], object detectors [42, 28, 43, 19, 2, 3, 49, 4, 71, 64, 65] and semantic segmentation models [34, 48, 57, 7, 58] can effectively learn desired features to perform vision tasks. Similarly, modern low-light image enhancement (LLIE) methods [44, 67, 14, 21, 17, 25] are capable of transforming a low-light image into a visual-friendly representation. However, a naive combination of the two brings sub-optimal gains when it comes to high-level vision tasks under low-light vision."
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "This work explores the underlying reasons for the low performance of the combination of LLIE with high-level vision methods and observes the following limitations: 1) Although existing LLIE methods push the envelope of visual perception for human eyes, they do not align with vision backbone networks [20, 12, 15, 32, 31] due to lack of multiscale features. For instance, it is likely that the enhancement method increases brightness in some regions. However, it simultaneously corrupts the edges and texture information of objects. 2) The pixel distribution among different low-light images may have huge variance owing to the disparity in less illuminated environments [17, 25, 68]. This increases intra-class variance in some cases (see Fig. 3, where only one bicycle is recognized by [17] instead of two bicycles in the ground-truth). 3) Current LLIE approaches [14, 17, 25, 21, 44, 56, 67] employ enhancement loss functions to optimize the enhancement networks. These loss functions compel the network to attend to all pixels equally, lacking the learning of informative details necessary for high-level downstream vision tasks such as object pose and shape for object detection. Furthermore, to train these enhancement networks, most of them [44, 14, 67, 56] require a set of high-quality images, which is hardly available in a real-world setting."
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+                                    "content": "Motivated by these observations and inspired by recent developments in LLIE [17, 25] and vision-based backbone networks [15, 32, 31], this paper aims to bridge the gap by exploring an end-to-end trainable recipe that jointly optimizes the enhancement and downstream task objectives in a single network. To this end, we present FeatEnHancer, a general-purpose feature enhancer that learns to enrich multiscale hierarchical features favourable for downstream vision tasks in a low-light setting. An example of learned hierarchical representation and the enhanced image is illustrated in Fig. 1."
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+                                    "content": "In particular, our FeatEnHancer first downsamples a low-light RGB input image to construct multi-scale hierarchical representations. Subsequently, these representations are fed to our Feature Enhancement Network (FEN), which is a deep convolutional network, employed to enrich intra-scale semantic representations. Note that the parameters of FEN can be adjusted through task-related loss functions, which pushes the FEN to only enhance the task-related features. This multiscale learning allows the network to enhance both global and local information from higher and lower-resolution features, respectively. Once the enhanced representations on different scales are obtained, the remaining obstacle is to fuse them effectively. To achieve, this, we select two different strategies to capture both global and local information from higher and lower-resolution features. First, to merge high-resolution features, inspired by multi-head attention in [50], we design a Scale-aware Attentional Feature Aggregation (SAFA) method that jointly attends information from differ"
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+                                    "content": "ent scales. Second, for lower-resolution features, the skip connection [20] scheme is adopted to merge the enhanced representation from SAFA to lower-resolution features. With these jointly learned hierarchical features, our FeatEnHancer provides semantically powerful representations which can be exploited by advanced methods such as feature pyramid networks [27] for object detection [43] and instance segmentation [19], or UNet [45] for semantic segmentation [34]."
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+                                            "content": "1. We propose FeatEnHancer, a novel module that enhances hierarchical features to boost downstream vision tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. FeatEnHancer is a general-purpose plug-and-play module that can be trained end-to-end with any high-level vision task."
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+                                    "content": "Deep learning-based LLIE methods focus on improving the visual quality of low-light images that satisfies human visual perception [23, 22]. Most LLIE approaches [14, 44, 56, 67] operate under a supervised learning paradigm, requiring paired data during training. Unsupervised GAN-based methods [21] eliminate the need for paired data during the training. However, their performance relies on the careful choice of unpaired data. Recently, zero-reference methods [17, 25, 68] discard the need for both paired and unpaired data to enhance low-light images by designing a set of non-reference loss functions. Inspired by these recent developments, this work aims to bridge low-light enhancement and downstream vision tasks (such as object detection [10, 33, 62], semantic segmentation [60, 47], and video object detection [63]) by enhancing multi-scale hierarchical features without needing paired or unpaired data to boost performance."
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+                                    "content": "These approaches consider machine perception as the criteria for success while enhancing images to improve downstream vision tasks. One obvious way to achieve this goal is to apply the LLIE methods as an initial step [70, 17]. However, this leads to unsatisfactory results (see Table 2, 4, and 5). Recently, another line of work has explored end-to-end pipelines, optimizing both enhancement and individual tasks during training, and our work follows the same spirit."
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+                                    "content": "Face detection. Liang et al. [26] propose an effective information extraction scheme from low-light images by exploiting multi-exposure generation. Furthermore, bi-directional domain adaptation [52, 51] and parallel architecture that jointly performs enhancement and detection [37] are presented to advance the research. However, these approaches are carefully designed to tackle face detection [62, 53] only and deliver minor improvements when applied to generic object detection [51]. Contrarily, our FeatEnHancer is a general-purpose module. It significantly improves several downstream vision tasks. Hence, we refrain from comparing our method to architectures only evaluated for face detection."
+                                }
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+                                    "type": "text",
+                                    "content": "Dark object detection. Dark (low-light) object detection [10, 30] methods have emerged recently, thanks to the real-world low illumination datasets [33, 39]. IA-YOLO [30] introduces a convolutional neural network (CNN)-based parameter predictor that learns the optimal configuration for the filters employed in the differential image processing module. Most related to our work is MAET [10], which investigates the physical noise model and image signal processing (ISP) pipeline under low illumination and learns the model to predict degradation parameters and object features. To avoid feature entanglement, they impose orthogonal tangent regularity to penalize cosine similarity between objects and degrading features. However, owing to the weather-specific hyperparameters in [30] and degradation parameters in [10], these works rely on large synthetic datasets to achieve desired performance. Unlike them, our FeatEnHancer is optimized from the task-related loss functions and does not require any pre-training on synthetic datasets mimicking low-light or harsh weather conditions."
+                                }
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+                                    "content": "Other high-level vision tasks. Besides face and object detection, recent research has explored high-level computer vision tasks like semantic segmentation [6, 34]. Xue et al. [60] devise a contrastive-learning strategy to improve visual and machine perception simultaneously, achieving impressive performance on nighttime semantic segmentation of adverse conditions dataset with correspondences (ACDC) dataset [47]. Furthermore, DarkVision [63] has emerged recently to tackle video object detection under low-light vision. In this work, thanks to [47, 63], we apply FeatEnHancer"
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+                                    "content": "to semantic segmentation and video object detection under low-light vision to investigate its generalization capabilities."
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+                                    "content": "2.3. Learning Multi-scale Hierarchical Features"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Representing objects at varying scales is one of the main difficulties in computer vision. Therefore, the work in this domain goes back to the era of hand-engineered features [36, 11, 38, 24]. Modern object detectors [43, 28, 2, 71, 49, 40, 65] exploit multi-scale features to tackle this challenge. Similarly, multi-scale representations [34] and pyramid pooling schemes [69] have been proposed for effective semantic segmentation. Moreover, current improvements in vision-based backbone networks [15, 31, 32] demonstrate that learning hierarchical features during feature extraction directly uplifts the downstream vision tasks [19, 57, 2]. However, the multi-scale and hierarchical structures of CNN have not been fully explored for low-light vision tasks."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Under harsh weather conditions, DENet [41] employs Laplacian Pyramid [1] to decompose images into low and high-frequency components for object detection. Despite the encouraging results, the multi-scale feature learning in DENet relies on the Laplacian pyramid, which is susceptible to noise and may produce inconsistencies in regions with high contrast or sharp edges. Alternatively, aligned with the multi-scale learning in modern vision backbone networks [27, 32, 31], our FeatEnHancer employs CNN to generate multi-scale feature representations, which are fused through the scale-aware attentional feature aggregation and skip connections. Our approach is much more flexible and aligns with downstream vision tasks, boosting state-of-the-art results on multiple downstream vision tasks."
+                                }
+                            ]
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+                                    "content": "3. Proposed Approach"
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+                                    "content": "The key idea of this paper is to design a general-purpose pluggable module that strengthens machine perception under low-light vision to solve several downstream vision tasks such as object detection, semantic segmentation, and video object detection. The overall architecture of FeatEnHancer is exhibited in Fig. 2. Our FeatEnHancer takes a low-light image as input and adaptively boosts its semantic representation by enriching task-related hierarchical features. We now discuss the key components of FeatEnHancer in detail."
+                                }
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+                                    "content": "where "
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+                                    "type": "text",
+                                    "content": " denote kernel size and stride, and "
+                                },
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+                                    "content": ", "
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                        450,
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+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " represent the height, width, and channels of an image."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Feature enhancement network. In order to enhance features at each scale, we require an enhancement network that learns to enhance spatial information important for downstream tasks. Inspired by low-light image enhancement networks [17, 25], we design a fully convolutional intra-scale feature extraction network (FEN). However, unlike [17, 25], our FEN introduces a single convolutional layer at the beginning that generates a feature map "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "F \\in \\mathbb{R}^{H \\times W \\times C}"
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+                                {
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+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is transformed from 3 to 32 by keeping the resolution "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(H \\times W)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
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+                                    ],
+                                    "type": "text",
+                                    "content": " same as the input. Then a series of six convolutional layers with symmetrical skip concatenation is applied, where each convolutional layer, with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", is accompanied by the ReLU activation function. We apply FEN on each scale "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{o}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " separately, and obtain multiscale feature representations, denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{o}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        486,
+                                        289,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. This multi-scale learning allows the network to enhance both global and local information from higher and lower-resolution features. Hence, we ignore down-sampling and batch normalization to preserve semantic relations be"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        304,
+                        313,
+                        547,
+                        421
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "tween neighbouring pixels which is similar to [17]. However, we discard the last convolutional layer of DCENet [17] in our FEN and propagate the final enhanced feature representations from each scale for the multi-scale feature fusion. Note that the implementation details of FEN in FeatEnHancer are independent of the proposed module, and even more, advanced image enhancement networks such as [68] can be applied to improve performance. Now, we discuss multiscale feature fusion in detail."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Multi-scale Feature Fusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Since we already have multi-scale feature representations "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(F, F_{q},"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{o})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from FEN, the remaining obstacle is to fuse them effectively. Lower-scale features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
+                                        547,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(F_{o})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
+                                        547,
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+                                    ],
+                                    "type": "text",
+                                    "content": " contain fine details and edges. In contrast, higher-resolution features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
+                                        547,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(F_{q})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
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+                                    ],
+                                    "type": "text",
+                                    "content": " capture more abstract information, such as shapes and patterns. Therefore, naive aggregation leads to inferior performance (see Table 6a). Hence, we adopt two different strategies to capture both global and local information from higher and lower-resolution features. First, inspired by multi-head attention in [50] that enables the network to jointly learn information from different channels, we design a scale-aware attentional feature aggregation (SAFA) module that jointly attends to features from different scales. Second, we adopt a skip connection [20] (SC) scheme to integrate low-level information from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        449,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{o}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the enhanced representation from SAFA to obtain the final enhanced hierarchical representation. Adopting SAFA for merging high-resolution features and SC for lower-resolution features leads to a more robust hierarchical representation (see Table 6b). Now, we discuss SAFA in detail."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Scale-aware Attentional Feature Aggregation. Even though high-resolution features assist in capturing fine de"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
+            "discarded_blocks": [
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+                                }
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+                }
+            ],
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+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    "type": "text",
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+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "tails, such as recognizing small objects, applying an attentional operation to them is computationally demanding. Thus, in SAFA, we propose an efficient multi-scale aggregation strategy where enhanced high-resolution hierarchical features are projected to a smaller resolution prior to attentional feature aggregation. As illustrated in Figure 2, SAFA transforms "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F \\in \\mathbb{R}^{H \\times W \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q \\in \\mathbb{R}^{\\frac{H}{8} \\times \\frac{W}{8} \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " with two convolutional layers ("
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 7"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "S = 4"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "; "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K = 3"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S = 2"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ") and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{q} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K \\in \\mathbb{R}^{\\frac{H}{8} \\times \\frac{W}{8} \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " with a single convolutional layer ("
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 3"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S = 2"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": "). Note that the weights of the convolutional layer ("
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 3"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S = 2"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": ") are not shared because, in addition to down-scaling the high-resolution features, it serves as an embedding network before computing the attentional weights. Later, "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " are concatenated to form the set of hierarchical features "
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+                                    "content": " is the total number of attentional blocks. The "
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+                                    "content": "W _ {q + k} ^ {n} = F _ {q} ^ {n} \\cdot F _ {k} ^ {n}, \\tag {3}",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "-th block, and "
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+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{W}}_{q + k}^{n}"
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+                                    "type": "inline_equation",
+                                    "content": "W_{q + k}^{n}"
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+                                    "type": "text",
+                                    "content": ". Derived from the "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "-th block of normalized attention weights, we apply weighted sum to compute the "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{F}}_h^n\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times \\frac{C}{N}}"
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {\\mathbf {F}} _ {h} ^ {n} = \\sum_ {l = 1} ^ {L} \\bar {\\mathbf {W}} _ {q + k} ^ {n} \\cdot F _ {q + k} ^ {n}, \\tag {5}",
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+                                    "content": "now we concatenate all "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " along the channel dimension to obtain "
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+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbf{F}}_h\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times C}"
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+                                    "type": "text",
+                                    "content": ". Note that although "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": ", it contains far richer representations, encompassing information from multi-scale high-resolution features."
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+                                    "content": "Subsequently, as explained earlier in Sec. 3.2, with the help of skip connections (SC), we integrate "
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+                                    "type": "text",
+                                    "content": " to obtain the final enhanced hierarchical representation covering both global and local features, as illustrated in Figure 1 and 2. Note that prior to the skip connection, we upsample "
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+                                    "content": ", where the upsampling operation "
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+                                    "type": "inline_equation",
+                                    "content": "U(.)\\in \\mathbb{R}^{\\frac{H}{8}\\times \\frac{W}{8}\\times C}\\to \\mathbb{R}^{H\\times W\\times C}"
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+                                {
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+                                    "type": "text",
+                                    "content": " is performed with simple bi-linear interpolation operation, which is much faster than using transposed convolutions [13]. Unlike image enhancement in existing works [17, 25, 10], with a multi-scale hierarchical feature enhancement strategy, our FeatEnHancer"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "learns a powerful semantic representation by capturing both local and global features. This makes it a general-purpose module to enhance hierarchical features, boosting machine perception under low-light vision."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Dataset</td><td>Task</td><td>#Cls</td><td>#Train</td><td>#Val</td></tr><tr><td>ExDark [33]</td><td>Dark object detection</td><td>12</td><td>4800</td><td>2563</td></tr><tr><td>DARK FACE [62]</td><td>Face detection</td><td>1</td><td>5400</td><td>600</td></tr><tr><td>ACDC Nighttime [47]</td><td>Semantic segmentation</td><td>19</td><td>400</td><td>106</td></tr><tr><td>DarkVision [63]</td><td>Video object detection</td><td>4</td><td>26</td><td>6</td></tr></table>",
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+                                        }
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+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Table 1: Statistics of the datasets used to report results on four different downstream vision tasks. #Cls is the number of classes, whereas #Train and #Val denote number of training and validation samples for each dataset, respectively."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4. Experiments"
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+                                    "content": "We conduct extensive experiments for evaluating the proposed FeatEnHancer module to several downstream tasks under the low-light vision, including generic object detection [33, 39], face detection [62], semantic segmentation [47], and video object detection [63]. Table 1 summarizes the crucial statistics of the employed datasets. This section first compares the proposed method with powerful baselines, existing LLIE approaches, and task-specific state-of-the-art methods. Then, we ablate the important design choices of our FeatEnHancer. We provide complete implementation details for each experiment in Appendix A."
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+                                    "content": "4.1. Dark Object Detection"
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+                                    "type": "text",
+                                    "content": "Settings. For dark object detection experiments on the real-world data, we consider the exclusively dark (ExDark) [33] dataset (see Table 1). We adopt RetinaNet [28] as a typical detector and Featurized Query R-CNN [65] (FQ R-CNN) as an advanced object detection framework to report results. In the case of both detectors, pre-trained models on COCO [29] are fine-tuned on each dataset. For RetinaNet, images are resized to "
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+                                    "type": "text",
+                                    "content": ", and we train the network using "
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+                                    "type": "inline_equation",
+                                    "content": "1 \\times"
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+                                    "type": "text",
+                                    "content": " schedule in mmdetection [5] (12 epochs using SGD optimizer [46] with an initial learning rate of 0.001). For Featurized Query R-CNN, we employ multiscale training [4, 49, 65] (shorter side ranging from 400 to 800 with a longer side of 1333). The FQ R-CNN is trained for 50000 iterations using ADAMW [35] optimizer (initial learning rate of 0.0000025, weight decay of 0.0001, and batch size of 8). Note that for each object detection framework, we adopt the same settings while reproducing results of our work, baseline, LLIE approaches, and task-specific state-of-the-art methods."
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+                                    "content": "We compare our FeatEnHancer to several state-of-the-art LLIE methods, including KIND [67], RAUS [44], EnGAN [21], MBLLEN [14], Zero-DCE [17], Zero-DCE++ [17], and state-of-the-art dark object detection method, MAET [10]. For LLIE methods, all images are"
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">RetinaNet</td><td colspan=\"2\">FQ R-CNN</td><td rowspan=\"2\">Methods</td><td colspan=\"2\">RetinaNet</td><td colspan=\"2\">FQ R-CNN</td><td>Method</td><td>mIoU</td></tr><tr><td>\\( mAP_{50} \\)</td><td>mAP</td><td>\\( mAP_{50} \\)</td><td>mAP</td><td>\\( AP_{50} \\)</td><td>AP</td><td>\\( AP_{50} \\)</td><td>AP</td><td>Baseline [7]</td><td>45.7</td></tr><tr><td>Baseline</td><td>72.1</td><td>46.3</td><td>74.5</td><td>47.0</td><td>Baseline</td><td>47.3</td><td>19.9</td><td>67.5</td><td>28.6</td><td>RetinexNet [54]</td><td>41.9</td></tr><tr><td>RAUS [44]</td><td>64.7</td><td>44.0</td><td>77.0</td><td>48.1</td><td>RAUS [44]</td><td>42.1</td><td>17.6</td><td>65.5</td><td>27.4</td><td>DRBN [59]</td><td>43.3</td></tr><tr><td>KIND [67]</td><td>70.7</td><td>45.1</td><td>80.5</td><td>51.5</td><td>KIND [67]</td><td>47.2</td><td>19.8</td><td>65.0</td><td>27.5</td><td>FIDE [61]</td><td>43.4</td></tr><tr><td>Zero-DCE++ [25]</td><td>70.3</td><td>45.2</td><td>79.5</td><td>49.2</td><td>Zero-DCE++ [25]</td><td>47.3</td><td>20.1</td><td>66.2</td><td>28.2</td><td>KIND [67]</td><td>43.0</td></tr><tr><td>EnGAN [21]</td><td>70.4</td><td>44.9</td><td>80.0</td><td>51.9</td><td>EnGAN [21]</td><td>45.1</td><td>19.3</td><td>67.4</td><td>28.4</td><td>EnGAN [21]</td><td>43.8</td></tr><tr><td>MBLLEN [14]</td><td>70.6</td><td>45.1</td><td>80.0</td><td>51.0</td><td>MBLLEN [14]</td><td>47.1</td><td>19.8</td><td>67.3</td><td>27.1</td><td>ZeroDCE [17]</td><td>43.4</td></tr><tr><td>Zero-DCE [17]</td><td>71.0</td><td>45.2</td><td>80.6</td><td>52.0</td><td>Zero-DCE [17]</td><td>47.4</td><td>20.1</td><td>66.9</td><td>27.5</td><td>SSIENet [66]</td><td>41.4</td></tr><tr><td>MAET [10]</td><td>71.8</td><td>45.7</td><td>81.6</td><td>52.4</td><td>MAET [10]</td><td>44.3</td><td>18.7</td><td>66.1</td><td>27.1</td><td>Xue et al. [60]</td><td>49.8</td></tr><tr><td>FeatEnHancer</td><td>72.6</td><td>46.4</td><td>86.3</td><td>56.5</td><td>FeatEnHancer</td><td>47.2</td><td>19.9</td><td>69.0</td><td>29.4</td><td>FeatEnHancer</td><td>54.9</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "enhanced from their released checkpoints and propagated to the detector. In case of MAET [10], we pre-train the detector using their proposed degrading pipeline and then fine-tune it on both datasets to establish a direct comparison."
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+                                    "content": "Results on ExDark. Table 2 lists the results of LLIE works, MAET, and the proposed method on both object detection frameworks. It is evident that our FeatEnHancer brings consistent and significant gains over prior methods. Note that, while the performance of MAET and our method is comparable on RetinaNet "
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+                                    "content": ", the proposed FeatEnHancer outperforms MAET by a significant margin on FQ R-CNN, achieving the new state-of-the-art "
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+                                    "type": "text",
+                                    "content": " of 86.3. Furthermore, Figure 3 shows four detection examples from our method and the two best competitors using FQ R-CNN as a detector. These results illustrate that despite the inferior visual quality, our FeatEnHancer enhances hierarchical features that are favourable for dark object detection, producing state-of-the-art results."
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+                                    "content": "Settings. The DARK FACE [53, 62] is a challenging face detection dataset released for the "
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+                                    "content": " competition. For experiments on the DARK FACE (see Table 1), the images are resized to a larger resolution of "
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+                                    "content": " for all methods. We adopt the same object detection frameworks of RetinaNet and FQ R-CNN and follow identical experimental settings, as explained in Sec. 4.1."
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+                                    "content": "Results. The performance of FeatEnHancer, MAET, and six LLIE methods, using RetinaNet and Featurized Query R-CNN, are summarized in Table 3. Note that a few LLIE methods [17, 25, 67] yield superior results than our approach in the case of RetinaNet. We argue that due to tiny faces with highly dark images in the DARK FACE dataset, RetinaNet fails to capture information even from the enhanced hierarchical features. We discuss this behaviour with an ex"
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+                                            "content": "Table 2: Quantitative comparison on ExDark dataset. Results obtained on the commonly used evaluation metrics are highlighted. Our FeatEnHancer brings consistent improvements and achieves new state-of-the-art results with FQ R-CNN."
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+                                            "content": "Table 3: Comparing FeatEnHancer on the DARK FACE dataset. With RetinaNet, FeatEnHancer performs on par with other methods. However, with FQ R-CNN, FeatEnHancer surpasses all of them."
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+                                            "content": "Table 4: Quantitative comparison on the ACDC dataset. Huge gains from our FeatEnhancer lead to new state-of-the-art results."
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+                                    "content": "Figure 3: Visual comparison of FeatEnHancer with the two previous best competitors on the ExDark dataset. Zoom in for the best view."
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+                                    "content": "ample in Appendix B. On the other hand, LLIE approaches directly provides well-lit images that bring slightly bigger gains "
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+                                    "content": " in this case. However, note that with the more strong detector, our FeatEnHancer surpasses all the LLIE methods and MAET by a significant margin "
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+                                    "content": "4.3. Nighttime Semantic Segmentation on ACDC"
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+                                    "content": "Settings. We utilize nighttime images from the ACDC dataset [47] (see Table 1) to report results on semantic segmentation in a low-light setting. DeepLabV3+ [7] is adopted as the segmentation baseline from mmseg [8] for straightforward comparison with the concurrent work [60]. We follow identical experimental settings as in [60]. Refer to Appendix A for complete implementation details."
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+                                    "content": "Results. We compare our method with several state-of-the-art LLIE methods, including RetinexNet [54] KIND [67],"
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+                                            "content": "Figure 4: Qualitative comparison of FeatEnHancer with previous best work [60] on the ACDC nighttime semantic segmentation. FeatEnHancer provides more accurate segmentations."
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+                                            "html": "<table><tr><td>Method</td><td>Illumination (3.2) \nmAP</td><td>Illumination (0.2) \nmAP</td></tr><tr><td>Baseline [55]</td><td>32.8</td><td>10.4</td></tr><tr><td>RAUS [44]</td><td>7.42</td><td>5.19</td></tr><tr><td>EnGAN [21]</td><td>7.83</td><td>5.41</td></tr><tr><td>MBLLEN [14]</td><td>7.82</td><td>5.39</td></tr><tr><td>KIND [67]</td><td>7.43</td><td>5.25</td></tr><tr><td>Zero-DCE++ [25]</td><td>7.51</td><td>5.02</td></tr><tr><td>Zero-DCE [17]</td><td>7.83</td><td>5.43</td></tr><tr><td>FeatEnHancer</td><td>34.6</td><td>11.2</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 5: Comparing FeatEnHancer with LLIE methods on the DarkVision dataset. FeatEnHancer is the only method that boosts the performance of the powerful baseline method on both illumination levels."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "FIDE [61], DRBN [59], EnGAN [21], SSIONet [66], ZeroDCE [17], and current state-of-the-art nighttime semantic segmentation method Xue et al. [60]. As shown in Table 4, our FeatEnHancer brings remarkable improvements in the baseline with a mIoU of 54.9, outperforming the previous best result by 5.1 points. Moreover, we present a qualitative comparison with the previous best competitor [60] in Figure 4. Evidently, our FeatEnHancer generates more accurate segmentation for both bigger and smaller objects, such as terrain and traffic signs in the last row. These results affirm the effectiveness of FeatEnHancer as a general-purpose module achieving state-of-the-art results in both dark object"
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+                                    "type": "text",
+                                    "content": "detection and nighttime semantic segmentation."
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+                                    "content": "4.4. Video Object Detection on DarkVision"
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+                                    "type": "text",
+                                    "content": "Settings. We extend our experiments from static images to video domain to test the generalization capabilities of our method. The video object detection under low-light vision is evaluated on the recently emerged DarkVision dataset [63] (see Table 1 for dataset details). Although the dataset is not publicly available yet, we sincerely thank the authors of [63] for providing prompt access. To evaluate our FeatEnHancer under low light settings, we take the low-end camera split on two different illumination levels, i.e., 0.2 and 3.2. For ablation studies, we adopt a "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "3.2\\%"
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+                                    "type": "text",
+                                    "content": " illumination level split. We consider SELSA [55] as our baseline and follow identical experimental settings with the ResNet-50 backbone network in the mmtracking [9]. To establish a direct comparison, we enhance all video frames first through LLIE methods and feed these frames to the baseline, as done in Sec. 4.1. As a common practice in video object detection [16, 18, 55], the mAP@IoU=0.5 is utilized as an evaluation metric to report results. More details can be found in Appendix A."
+                                }
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+                                    "type": "text",
+                                    "content": "Results. Table 5 compares our FeatEnHancer with several LLIE methods [44, 21, 14, 67, 17, 25] and the powerful video object detection baseline [55]. Evidently, our FeatEnHancer provides considerable gains to the baseline with "
+                                },
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+                                    "content": "34.6\\mathrm{mAP}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "11.2\\mathrm{mAP}"
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+                                    "type": "text",
+                                    "content": " under illumination levels of 3.2 and 0.2, respectively. Note that our FeatEnHancer is the only method that boosts performance under both image and video modalities. In contrast, as shown in Table 5, existing LLIE methods not only fail to assist the baseline method but also deteriorate the performance. This poor generalization of LLIE approaches highlights that learning from domain-specific paired data [14, 67, 44], unpaired data [21], and curve estimation without data [17, 25] are not the optimal solutions for generalized enhancement methods. Hence, more research is required."
+                                }
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+                                    "content": "4.5. Ablation Studies"
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+                                    "content": "This section ablates important design choices in the proposed FeatEnHancer when plugged into RetinaNet, DeeplabV3+, and SELSA on ExDark (dark object detection), ACDC (nighttime semantic segmentation), and DarkVision with illumination level of "
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+                                    "type": "text",
+                                    "content": " (video object detection), respectively."
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+                                    "content": "SAFA in FeatEnHancer. The important component of the proposed FeatEnHancer is the scale-aware attentional feature aggregation (SAFA) that aggregates high-resolution features. To validate its effectiveness, we conduct multiple experiments where SAFA is replaced with simple averaging or skip connections (SC) [20] to fuse enhanced multi-scale features "
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+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": " (see Sec. 3.2). The experiment results are"
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+                                            "html": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>simple averaging</td><td>69.5</td><td>50.3</td><td>32.9</td></tr><tr><td>skip connections [20]</td><td>70.3</td><td>51.7</td><td>33.1</td></tr><tr><td>SAFA</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>",
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+                                            "content": "(a) Effectiveness of SAFA."
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+                                            "html": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>SC, SC</td><td>69.7</td><td>51.7</td><td>32.8</td></tr><tr><td>SAFA, SAFA</td><td>70.2</td><td>52.6</td><td>33.4</td></tr><tr><td>SC, SAFA</td><td>70.9</td><td>52.9</td><td>33.8</td></tr><tr><td>SAFA, SC</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>",
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+                                            "html": "<table><tr><td>Method</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>maxpool</td><td>69.3</td><td>51.3</td><td>32.9</td></tr><tr><td>adavgpool [68]</td><td>69.9</td><td>50.7</td><td>32.9</td></tr><tr><td>interpolation [30]</td><td>70.7</td><td>51.5</td><td>33.1</td></tr><tr><td>Convolution</td><td>72.6</td><td>54.9</td><td>34.6</td></tr></table>",
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+                                            "html": "<table><tr><td>Scale</td><td>ExDark (mAP)</td><td>ACDC (mIoU)</td><td>DarkVision (mAP)</td></tr><tr><td>(2, 4)</td><td>71.8</td><td>52.7</td><td>34.1</td></tr><tr><td>(4, 8)</td><td>72.6</td><td>54.9</td><td>34.6</td></tr><tr><td>(4, 16)</td><td>71.5</td><td>51.4</td><td>33.9</td></tr><tr><td>(8, 16)</td><td>68.7</td><td>45.6</td><td>31.9</td></tr></table>",
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+                                            "type": "text",
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+                                    "type": "text",
+                                    "content": "(e) # attentional blocks in SAFA."
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+                                    "type": "text",
+                                    "content": "Table 6: Ablations for the proposed FeatEnHancer on three benchmarks. (a) We investigate the effectiveness of SAFA by replacing it with different aggregation methods to fuse "
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+                                    "type": "text",
+                                    "content": ". (b) We experiment with various combinations of SAFA and skip connection (SC) to justify an optimal design choice. Here, (SC, SC) means employing only skip connections to merge both "
+                                },
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+                                    "bbox": [
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+                                    "content": " with "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". (c) Besides convolution, we experiment with other downsampling techniques to generate lower resolutions. Here, adavgpool denotes adaptive average pooling as done in [68]. (d) We vary scale sizes to generate lower-scale representations. Here, (2, 4) means "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "I_{q} \\in \\mathbb{R}^{\\frac{H}{2} \\times \\frac{W}{2} \\times 3}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "I_{o} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times 3}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". (e) We vary number of attentional blocks "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " in SAFA of FeatEnHancer. Default settings are highlighted."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
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+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "summarized in Table 6a. It is clear that SAFA outperforms both averaging and SC strategies by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "+2.3\\mathrm{mAP}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " on ExDark, "
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+                                    "type": "inline_equation",
+                                    "content": "+3.2\\mathrm{mIoU}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " on ACDC, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "+1.5\\mathrm{mAP}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " on DarkVision. These significant boosts across all three benchmarks indicate that scale-aware attention leads to optimal multi-scale feature aggregation in the proposed FeatEnHancer."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "content": "Multi-scale feature fusion. We experiment with various combinations of SAFA and SC to find an optimal design choice to fuse "
+                                },
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+                                {
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+                                    "content": " with "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (see Sec. 3.2). As shown in Table 6b, there is a clear increase in performance, achieving (72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision) when SAFA is applied to fuse "
+                                },
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "F_{q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " first, and then "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{o}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is merged with the output of SAFA using skip connection. Hence, we use this approach as the default setting."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Convolutional Downsampling. Table 6c summarizes results from different downsampling techniques applied on the input image "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " to generate lower-resolutions "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "I_{o}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " (see Sec 3.1). Our proposed convolutional downsampling yields impressive gains of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "+1.9\\mathrm{mAP}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " on ExDark, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "+3.4\\mathrm{mIoU}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "+1.5\\mathrm{mAP}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " on DarkVision compared to max-pooling, adaptive average pooling [68], and bilinear interpolation [30]. These results demonstrate the effectiveness of convolutional downsampling since it is better aligned with various vision backbone networks [32, 15, 27]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Different Scale sizes. We analyse the effect of different scale sizes to generate lower resolutions in Table 6d. Here, for instance, (2, 4) means that the resolution of input image "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "I \\in \\mathbb{R}^{H \\times W \\times 3}"
+                                },
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+                                    "type": "text",
+                                    "content": " is reduced by a factor of 2 and 4 to generate "
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+                                    "type": "inline_equation",
+                                    "content": "I_{q} \\in \\mathbb{R}^{\\frac{H}{2} \\times \\frac{W}{2} \\times 3}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "I_{o} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times 3}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", respectively. Note that all these scales are generated through regular convolutional"
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+                            ]
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+                    ],
+                    "index": 14
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+                                    "type": "text",
+                                    "content": "operator "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Conv}(.)"
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+                                    "type": "text",
+                                    "content": ", as explained in Eq. 1. Looking at results in Table 6d, the top performance on all three tasks is achieved with the scale size of (4, 8), thereby, preferred as a default setting."
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+                    ],
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+                                    "type": "text",
+                                    "content": "Number of Attention Blocks in SAFA. Table 6e studies the effect of the number of attention blocks "
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+                                    "type": "text",
+                                    "content": " in our SAFA. The performance rises for all three tasks with the increase in "
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+                                    "type": "text",
+                                    "content": ". This demonstrates that more attentional blocks in SAFA bring additional gains. The best performance with 72.6 mAP on ExDark, 54.9 mIoU on ACDC, and 34.6 mAP on DarkVision is achieved when "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N"
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+                                    "type": "text",
+                                    "content": " reaches 8, and after that, it tends to saturate. Hence, "
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+                                    "type": "inline_equation",
+                                    "content": "N = 8"
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+                                    "type": "text",
+                                    "content": " is used as the default setting."
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+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "This paper proposes FeatEnHancer, a novel general-purpose feature enhancement module designed to enrich hierarchical features favourable for downstream tasks under low-light vision. Our intra-scale feature enhancement and scale-aware attentional feature aggregation schemes are aligned with vision backbone networks and produce powerful semantic representations. Furthermore, our FeatEnHancer neither requires pre-training on synthetic datasets nor relies on enhancement loss functions. These architectural innovations make FeatEnHancer a plug-and-play module. Extensive experiments on four different downstream visions tasks covering both images and videos demonstrate that our method brings consistent and significant improvements over baselines, LLIE methods, and task-specific state-of-the-art approaches."
+                                }
+                            ]
+                        }
+                    ],
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+            ],
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                        }
+                                    ]
+                                }
+                            ],
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diff --git a/2023/Feature Modulation Transformer_ Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution/358910c2-9bed-4301-a68b-c93d03912323_content_list.json b/2023/Feature Modulation Transformer_ Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution/358910c2-9bed-4301-a68b-c93d03912323_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..b83348b0b8a21c4223d4a1dcd24e4322b74aff27
--- /dev/null
+++ b/2023/Feature Modulation Transformer_ Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution/358910c2-9bed-4301-a68b-c93d03912323_content_list.json	
@@ -0,0 +1,3093 @@
+[
+    {
+        "type": "text",
+        "text": "Feature Modulation Transformer: Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Ao Li $^{1}$ , Le Zhang $^{1*}$ , Yun Liu $^{2}$ , Ce Zhu $^{1}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup>University of Electronic Science and Technology of China, <sup>2</sup>I2R, A*STAR",
+        "bbox": [
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+            244,
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+            261
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "aoli@std.uestc.edu.cn, {lezhang,eczhu}@uestc.edu.cn, vagrantlyun@gmail.com",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            309,
+            312,
+            323
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Transformer-based methods have exhibited remarkable potential in single image super-resolution (SISR) by effectively extracting long-range dependencies. However, most of the current research in this area has prioritized the design of transformer blocks to capture global information, while overlooking the importance of incorporating high-frequency priors, which we believe could be beneficial. In our study, we conducted a series of experiments and found that transformer structures are more adept at capturing low-frequency information, but have limited capacity in constructing high-frequency representations when compared to their convolutional counterparts. Our proposed solution, the cross-refinement adaptive feature modulation transformer (CRAFT), integrates the strengths of both convolutional and transformer structures. It comprises three key components: the high-frequency enhancement residual block (HFERB) for extracting high-frequency information, the shift rectangle window attention block (SRWAB) for capturing global information, and the hybrid fusion block (HFB) for refining the global representation. Our experiments on multiple datasets demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB while using fewer parameters. The source code will be made available at: https://github.com/AVC2-UESTC/CRAFT-SR.git.",
+        "bbox": [
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+            338,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            208,
+            724
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Single image super-resolution (SISR) has garnered significant attention in recent years, owing to its promising applications across diverse domains, such as surveillance video and medical image enhancement [31, 10], old image reconstruction [21, 17], and efficient image transmission [47]. Despite its practical value, SISR remains an ill-posed problem, given the existence of multiple solutions for a given low-resolution (LR) image. To tackle this challenge,",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "a multitude of classical approaches have been proposed, including  $\\mathrm{A + }$  [36], SC [41], and ANR [35]. However, these methods exhibit limitations in their performance, primarily attributed to their constrained model capacities.",
+        "bbox": [
+            499,
+            309,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In recent years, deep learning has experienced significant growth and demonstrated remarkable success in SISR [7, 20, 45, 22]. Prior research efforts have introduced residual and dense connectives to facilitate the stacking of deep convolutional neural networks (CNNs) [16, 37], while others [46, 40, 29, 30] have leveraged attention mechanisms to enhance performance. Notably, the emergence of transformer architectures has demonstrated their efficacy in capturing long-range dependencies and attaining state-of-the-art performance [21, 6, 4, 18, 25]. Despite these advancements, these works have mainly focused on designing transformer blocks to obtain global information and overlooked the potential of incorporating high-frequency priors [32, 8] to further bolster performance in SISR. Additionally, there is limited detailed analysis of the impact of frequency on performance.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we investigate the influence of high-frequency information on the performance of CNN and transformer structures in SISR. We achieve this by discarding different ratios of high-frequency components from the input image and observing the corresponding performance changes. Our empirical findings reveal that transformers tend to prioritize low-frequency information and exhibit limited capability in constructing high-frequency representations when compared to CNNs. To address this issue, we proposed a cross-refinement adaptive feature modulation transformer (CRAFT) that integrates the strengths of both structures. Specifically, CRAFT comprises three key components, namely the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB), which work collaboratively to capture high-frequency details, extract long-range dependencies, and refine the output for better representation. Experimental results show that CRAFT outperforms state-of-the-art performance with relatively fewer parameters. The main contributions of this paper are as fol",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "12514",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "lows:",
+        "bbox": [
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+            138
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We study the impact of CNN and transformer structures on performance from a frequency perspective and observe that transformer is more effective in capturing low-frequency information while having limited capacity for constructing high-frequency representations compared to CNN.",
+            "- Based on the observation, we design a parallel structure to explore different frequency features. We utilize the HFERB branch to introduce high-frequency information, which is beneficial to SISR, and the SRWAB branch to acquire global information.",
+            "- We propose a fuse strategy that integrates the strengths of CNN and transformer. Specifically, we treat the HFERB branch as high-frequency prior and the output of SRWAB as key and value for inter-attention, resulting in improved performance.",
+            "- Extensive experimental results on multiple datasets show that the proposed method performs on par with the existing state-of-the-art SISR methods while using fewer parameters."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. CNN-based SISR",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since the pioneering work SRCNN [7] has achieved significant progress in SISR, various CNN-based works have been proposed. Kim et al. [15] presented an SR method using deep networks by cascading 20 layers, demonstrating promising results. Building upon this, Lim et al. [23] introduced the enhanced deep super-resolution (EDSR) network, which achieved a significant performance boost by removing the batch normalization layer [14] from the residual block and incorporating additional convolution layers. Ahn et al. [2] designed an architecture with an increased number of residual blocks and dense connections, further improving the SR performance. In pursuit of lightweight models, Hui et al. [13] proposed a selective fusion approach, employing cascaded information multi-distillation blocks to construct an efficient model. Li et al. [19] introduced a method involving predefined filters and utilized a CNN to learn coefficients, which were then linearly combined to obtain the final results. Sun et al. [34] proposed a hybrid pixel-unshuffled network (HPUN) by introducing an efficient and effective downsampling module into the SR task.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Transformer-based SISR",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Liang et al. [21] proposed SwinIR, a robust baseline model for image restoration, leveraging the Swin Trans",
+        "bbox": [
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+            838,
+            468,
+            866
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "former [24]. CAT [6] modified the window shape and introduced a rectangle window attention to obtaining better performance. Chen et al. [4] proposed a pre-trained image processing transformer and showed that pre-trained mechanism could significantly improve the performance for low-level tasks. Li et al. [18] comprehensively analyzed the effect of pre-training and proposed a versatile model to tackle different low-level tasks. Lu et al. [25] proposed a lightweight transformer to capture long-range dependencies between similar patches in an image with the help of the specially designed efficient transformer and efficient attention mechanism. Zhang et al. [44] introduced a shift convolution and a group-wise multi-scale self-attention to reduce the complexity of transformer. HAT [5] introduced a hybrid attention mechanism to enhance the performance of window-based transformers.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Analysis of Frequency Impact",
+        "text_level": 1,
+        "bbox": [
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+            359,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This section delves into the influence of performance from a frequency perspective. To analyze the impact of various frequencies on CNN and transformer, we conduct two sets of experiments using four common used benchmarks, as illustrated in Figure 1.",
+        "bbox": [
+            497,
+            382,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We select CARN [2], IMDN [13], EDSR [23], and SwinIR [21], CAT [6], HAT [5] as representatives of CNN and transformer structures. The process of dropping frequency components is depicted in Figure 1(c). Given a high-resolution (HR) image  $X^{HR}$ , we perform a fast Fourier transform (FFT) on it to obtain its frequency spectrum. Subsequently, we flatten this spectrum into a sequence and arrange it in ascending order based on the magnitudes. With a sequence length of  $L$ , we define a threshold determined by the drop ratio  $\\gamma$ ,  $0 \\leq \\gamma \\leq 1$ , located at the magnitude corresponding to the position  $\\gamma \\cdot L$ . Frequency components with magnitudes below this threshold are set to zero. Following this, we perform an inverse fast Fourier transform (IFFT) to generate the HR image with dropped frequencies, referred to as  $X_{drop}^{HR}(\\gamma)$ . The formulation for this process is as follows",
+        "bbox": [
+            497,
+            451,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {d r o p} ^ {H R} (\\gamma) = I F F T (D r o p \\left(\\left| F F T \\left(X ^ {H R}\\right) \\right|, \\gamma)\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Afterward, we downsample  $X_{drop}^{HR}(\\gamma)$  using bicubic interpolation to obtain the LR version  $X_{drop}^{LR}(\\gamma)$  (e.g.  $\\times 4$  down-sampling). Finally, we employ CNN-based and transformer-based SR models to generate the super-resolved counterpart  $X_{drop}^{SR}(\\gamma)$ .",
+        "bbox": [
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+            709,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To analyze the dependency of CNN and transformer on high-frequency information, we compute the peak signal-to-noise ratio (PSNR)  $P^{D}(\\gamma)$  between  $X_{drop}^{SR}(\\gamma)$  and  $X_{drop}^{HR}$ . We then plot the PSNR drop trend to visualize the difference between the two structures. As shown in Figure 1(a), the PSNR drop ratio for each drop ratio is defined",
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+    {
+        "type": "page_number",
+        "text": "12515",
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+    {
+        "type": "image",
+        "img_path": "images/648fc695cb737893a695877192d32b3052c591287d9511d4c42a1c8e674d1403.jpg",
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+        "image_caption": [
+            "(a) Dependency of different structures on high-frequency information."
+        ],
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+            "(b) Effectiveness of reconstructing high-frequency information."
+        ],
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+        "img_path": "images/09ddec8e32b675e128e76acc080c3cf256b5911981a6ece9631fcd3ba87f2425.jpg",
+        "image_caption": [
+            "(c) The procedure of dropping high-frequency.",
+            "Figure 1. The influence of high-frequency information on the performance of CNN and transformer architectures. Dashed and solid lines correspond to CNN and transformer methods, respectively. (a) With an increase in the high-frequency drop ratio, transformer models exhibit a smaller change in PSNR compared to CNN, suggesting their superiority in capturing low-frequency information. (b) As the high-frequency drop ratio increases, transformer models show a more pronounced change in PSNR compared to CNN, indicating their limited ability to reconstruct high-frequency information from low-frequency."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {d r o p} ^ {D} (\\gamma) = \\frac {P (0) - P ^ {D} (\\gamma)}{P (0)}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            561,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $P(0)$  represents the PSNR without dropping, calculated between  $X^{SR}$  and  $X^{HR}$ . The figures illustrate that the transformer model exhibits reduced sensitivity to high-frequency information and excels in capturing low-frequency information, as evidenced by the smaller PSNR change compared to the CNN model as the proportion of discarded high-frequency information increases.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we conduct another experiment to evaluate the effectiveness of different structures in reconstructing high-frequency information. Specifically, we calculate the PSNR  $P^{E}(\\gamma)$  between  $X_{drop}^{SR}(\\gamma)$  and  $X^{HR}$  and plot the performance drop trend as previously depicted. The PSNR drop ratio for each drop ratio can be expressed as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {d r o p} ^ {E} (\\gamma) = \\frac {P ^ {E} (\\gamma) - P (0)}{P (0)}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "From Figure 1(b), we observe that as the proportion of discarded high-frequency information increases, the transformer model experiences a larger PSNR change compared",
+        "bbox": [
+            75,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "to the CNN model, indicating its limited ability to reconstruct high-frequency information from low-frequency.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Based on these observations, we argue that the transformer requires the assistance of CNN to enhance its capability to recover intricate details. To address this, we propose a method that combines the strengths of both CNN and transformer. Specifically, we introduce CNN information as a high-frequency prior to aid the transformer in refining the global representation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4. Proposed Method",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The CRAFT network comprises three key components: Shallow feature extraction, residual cross-refinement fusion groups (RCRFGs), and reconstruction as shown in Figure 2. The shallow feature extraction module comprises a single convolutional layer, while the reconstruction module is followed by the SwinIR [21]. The RCRFG component consists of several cross-refinement fusion blocks (CRFBs), each comprising three types of blocks: the high-frequency enhancement residual blocks (HFERBs), the shift rectangle window attention blocks (SRWABs), and the hybrid fusion blocks (HFBs). We first describe the overall structure of",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "12516",
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+    {
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+    {
+        "type": "image",
+        "img_path": "images/d7fb07312b7cac3f0a784677041c3f3d296ba9b545c87e6b639ec28b812d5a5a.jpg",
+        "image_caption": [],
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+    {
+        "type": "image",
+        "img_path": "images/6acca8e4cb112b52fca9f753fd260605b0098efe6ed7ad8288191494d5fe0cf2.jpg",
+        "image_caption": [
+            "Figure 2. The framework of CRAFT. HFERB extracts the high frequency from the input features, SRWAB captures the long-range dependency of input features, and HFB integrates the output of HFERB and SRWAB to cross refine the global features. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            110,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "CRAFT and then elaborate on the three key designs, including HFERB, SRWAB, and HFB.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Model Overview",
+        "text_level": 1,
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The input LR image is processed by a  $3 \\times 3$  convolutional layer to obtain shallow features. These features are then fed into a serial of RCRFGs to learn deep features. After the last RCRFG, a  $3 \\times 3$  convolutional layer aggregates the features, and a residual connection is established between its output and the shallow features for facilitating training. The reconstruction module employs a  $3 \\times 3$  convolutional layer to aggregate the features, and a shuffle layer [33] is used to obtain the final SR output image.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. High-frequency Enhancement Residual Block",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The HFERB aims to enhance the high-frequency information, as shown in Figure 2. It comprises the local feature extraction (LFE) branch and the high-frequency enhancement (HFE) branch. Specifically, we split the input features",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$F_{in}\\in \\mathbb{R}^{H\\times W\\times C}$  into two parts, and then processed by the two branches separately",
+        "bbox": [
+            499,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {i n} ^ {L F E}, F _ {i n} ^ {H F E} = \\operatorname {S p l i t} \\left(F _ {i n}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
+            631,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $F_{in}^{LFE}, F_{in}^{HFE} \\in \\mathbb{R}^{H \\times W \\times C / 2}$  represent the input of LFE and HFE. For the LFE branch, we utilize a  $3 \\times 3$  convolutional layer followed by a GELU activation function to extract local high-frequency features",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {F} _ {i n} ^ {L F E} = f _ {a} \\left(\\operatorname {C o n v} _ {3 \\times 3} \\left(F _ {i n} ^ {L F E}\\right)\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            584,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the  $Conv_{3\\times 3}(\\cdot)$  refers to the convolutional layer and the  $f_{a}(\\cdot)$  represents the GELU activation layer. For the HFE branch, we employ a max-pooling layer to extract high-frequency information from the input features  $F_{in}^{HFE}$ . Then, we use a  $1\\times 1$  convolutional layer followed by a GELU activation function to enhance the high-frequency features,",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {F} _ {i n} ^ {H F E} = f _ {a} \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {M a x P o o l i n g} \\left(F _ {i n} ^ {H F E}\\right)\\right)\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12517",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the  $Conv_{1\\times 1}(\\cdot)$  indicates the convolutional layer, the MaxPooling  $(\\cdot)$  means the max-pooling layer and the  $f_{a}(\\cdot)$  represents the GELU activation layer. The outputs of the two branches are then concatenated and fed into a  $1\\times 1$  convolutional layer to fuse the information thoroughly. To make the network benefit from multi-scale information and maintain training stability, a skip connection is introduced. The whole process can be formulated as",
+        "bbox": [
+            75,
+            125,
+            472,
+            237
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {H} = C o n v _ {1 \\times 1} (C o n c a t (\\hat {F} _ {i n} ^ {L F E}, \\hat {F} _ {i n} ^ {H F E})) + F _ {i n}, (7)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            95,
+            245,
+            468,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the  $\\text{Concat}(\\cdot)$  refers to the concatenation operation and the  $\\text{Conv}_{1 \\times 1}(\\cdot)$  represents the convolutional layer.",
+        "bbox": [
+            75,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Shift Rectangle Window Attention Block",
+        "text_level": 1,
+        "bbox": [
+            77,
+            313,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We utilize the shift rectangle window (SRWin) to expand the receptive field, which can benefit SISR [6]. Unlike square windows, the SRWin uses rectangle windows to capture more relevant information along the longer axis. In detail, given an input  $X_{in} \\in \\mathbb{R}^{H \\times W \\times C}$ , we divide it into  $\\frac{H \\times W}{rh \\times rw}$  rectangle windows, where  $rh$  and  $rw$  refer to the height and width of the rectangle window. For the  $i$ -th rectangle window feature  $X_{i} \\in \\mathbb{R}^{(rh \\times rw) \\times C}$ , we compute the query, key, and value as follows",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {Q} _ {i} = X _ {i} W _ {i} ^ {Q}, \\boldsymbol {K} _ {i} = X _ {i} W _ {i} ^ {K}, \\boldsymbol {V} _ {i} = X _ {i} W _ {i} ^ {V}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            124,
+            469,
+            468,
+            488
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the  $W_{i}^{Q}\\in \\mathbb{R}^{C\\times d}$ $W_{i}^{K}\\in \\mathbb{R}^{C\\times d}$  and  $W_{i}^{V}\\in \\mathbb{R}^{C\\times d}$  represent the projection matrices and  $d$  is projection dimension which is commonly set to  $d = \\frac{C}{M}$  where the  $M$  is the number of heads. The self-attention can be formulated as",
+        "bbox": [
+            75,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} \\left(\\boldsymbol {Q} _ {i}, \\boldsymbol {K} _ {i}, \\boldsymbol {V} _ {i}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {\\boldsymbol {Q} _ {i} \\boldsymbol {K} _ {i} ^ {T}}{\\sqrt {d}} + B\\right) \\boldsymbol {V} _ {i}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            85,
+            564,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $B$  is the dynamic relative position encoding [38]. Moreover, a convolutional operation on the value is introduced to enhance local extraction capability. To capture information from different axes, we utilize two types of rectangle windows: Horizontal and vertical windows. Unlike traditional operations that utilize attention masks to limit calculations to the same window, in practice, we eliminate the mask and enable more extensive information interaction across different windows. Accordingly, we split the attention heads into two equal groups and compute the self-attention within each group separately. We then concatenate the outputs of the two groups to obtain the final output. The procedure can be expressed as",
+        "bbox": [
+            75,
+            605,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR \\operatorname {w i n} - S A (X) = \\operatorname {C o n c a t} (V - R \\operatorname {w i n}, H - R \\operatorname {w i n}) W ^ {p}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            87,
+            796,
+            468,
+            814
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the  $W^{p}\\in \\mathbb{R}^{C\\times C}$  represents the linear projection to fuse the features,  $V$  -Rwin and  $H$  Rwin indicate the vertical and horizontal rectangle window attention. In addition,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "a multi-layer perceptron (MLP) is used for further feature transformations. The whole process can be formulated as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} X = R \\operatorname {w i n} - S A \\left(L N \\left(X _ {i n}\\right)\\right) + X _ {i n} \\\\ X = M P (L N (X)) - X \\end{array} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            576,
+            161,
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+            182
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {S} = M L P (L N (X)) + X,\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            579,
+            178,
+            771,
+            192
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the  $LN$  represents the LayerNorm layer.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.4. Hybrid Fusion Block",
+        "text_level": 1,
+        "bbox": [
+            499,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To better integrate the merits of CNN and transformer (HFERB and SRWAB), we have designed a hybrid fusion block (HFB), which is illustrated in Figure 2. We formulate the output of HFERB as the high frequency prior query and the output of SRWAB as key, value and calculate the inter-attention to refine the global features which are obtained from SRWAB. Moreover, most existing methods focus on spatial relations and overlook channel information. To overcome this limitation, we perform inter-attention based on the channel dimension to explore channel dependencies. This design will significantly reduce complexity. Traditional methods that utilize spatial attention tend to result in significant computational complexity (e.g.,  $O(N^2 C)$ ,  $N \\gg C$ ), where  $N$  represents the length of the sequence and  $C$  represents the channel dimension. In contrast, our channel attention design can transfer the quadratic component to the channel dimension (e.g.,  $O(NC^2)$ ), effectively reducing complexity.",
+        "bbox": [
+            497,
+            241,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Specifically, as shown in Figure 2, we use a  $1\\times 1$  convolutional layer followed by a  $3\\times 3$  depth-wise convolutional layer to generate the high frequency query  $\\pmb{Q}\\in \\mathbb{R}^{H\\times W\\times C}$  based on the output of HFERB,  $X_{H}$ . As to the output of SRWAB,  $X_{S}$ , we first normalize the features by LayerNorm layer and then use the same operation as the query  $\\pmb{Q}$  to get the key  $\\pmb {K}\\in \\mathbb{R}^{H\\times W\\times C}$  and the value  $\\pmb {V}\\in \\mathbb{R}^{H\\times W\\times C}$ . Following the [42], we perform the reshape operation on  $\\pmb{Q}$ ,  $\\pmb{K}$  and  $\\pmb{V}$  to get the  $\\hat{\\pmb{Q}}\\in \\mathbb{R}^{C\\times (HW)}$ ,  $\\hat{\\pmb{K}}\\in \\mathbb{R}^{C\\times (HW)}$  and  $\\hat{\\pmb{V}}\\in \\mathbb{R}^{C\\times (HW)}$ . After that, we compute the inter-attention as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} (\\hat {\\boldsymbol {Q}}, \\hat {\\boldsymbol {K}}, \\hat {\\boldsymbol {V}}) = \\operatorname {S o f t m a x} \\left(\\frac {\\hat {\\boldsymbol {Q}} \\hat {\\boldsymbol {K}} ^ {T}}{\\alpha}\\right) \\hat {\\boldsymbol {V}}, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            524,
+            646,
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+            676
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the  $\\alpha$  represents the learnable parameter. Meanwhile, we add the refinement features to the  $X_{S}$  to get the fusion output  $X_{fuse}$ . In addition, we feed  $X_{fuse}$  to an improved feed-forward network [42] to aggregate the features further. The details of this structure are shown in Figure 2. It introduced a gate mechanism to fully extract the spatial and channel information and gain better performance. The whole process can be formulated as",
+        "bbox": [
+            497,
+            681,
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+            792
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {f u s e} = \\text {I n t e r - A t t e n} (L N \\left(X _ {S}\\right), X _ {H}) + X _ {S} \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            539,
+            799,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {H F B} = I M L P (L N (X)) + X _ {f u s e},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            539,
+            817,
+            771,
+            832
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the  $LN$  means LayerNorm operation, IMLP represents the improved MLP, and Inter-Atten indicates",
+        "bbox": [
+            497,
+            838,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12518",
+        "bbox": [
+            465,
+            885,
+            505,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/6df7866a445b63b3f6cd9463057a530aeaf12d6633429bed44cc6c71a3deb9ba.jpg",
+        "table_caption": [
+            "Table 1. Performance comparison of different SISR models on five benchmarks. Params represents the total number of network parameters. Results for the best and second best candidates are highlighted, and underlined."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Scale</td><td>Model</td><td>Params</td><td>Set5 (PSNR/SSIM)</td><td>Set14 (PSNR/SSIM)</td><td>BSD100 (PSNR/SSIM)</td><td>Urban100 (PSNR/SSIM)</td><td>Manga109 (PSNR/SSIM)</td></tr><tr><td rowspan=\"10\">×2</td><td>EDSR-baseline [23]</td><td>1370K</td><td>37.99/0.9604</td><td>33.57/0.9175</td><td>32.16/0.8994</td><td>31.98/0.9272</td><td>38.54/0.9769</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>37.76/0.9590</td><td>33.52/0.9166</td><td>32.09/0.8978</td><td>31.92/0.9256</td><td>38.36/0.9765</td></tr><tr><td>IMDN [13]</td><td>694K</td><td>38.00/0.9605</td><td>33.63/0.9177</td><td>32.19/0.8996</td><td>32.17/0.9283</td><td>38.88/0.9774</td></tr><tr><td>LatticeNet [26]</td><td>756K</td><td>38.06/0.9607</td><td>33.70/0.9187</td><td>32.20/0.8999</td><td>32.25/0.9288</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>548k</td><td>38.01/0.9605</td><td>33.62/0.9183</td><td>32.19/0.8999</td><td>32.10/0.9283</td><td>38.67/0.9772</td></tr><tr><td>HPUN-L [34]</td><td>714K</td><td>38.09/0.9608</td><td>33.79/0.9198</td><td>32.25/0.9006</td><td>32.37/0.9307</td><td>39.07/0.9779</td></tr><tr><td>SwinIR-light [21]</td><td>878K</td><td>38.14/0.9611</td><td>33.86/0.9206</td><td>32.31/0.9012</td><td>32.76/0.9340</td><td>39.12/0.9783</td></tr><tr><td>ESRT [25]</td><td>777K</td><td>38.03/0.9600</td><td>33.75/0.9184</td><td>32.25/0.9001</td><td>32.58/0.9318</td><td>39.12/0.9774</td></tr><tr><td>ELAN-light [44]</td><td>582K</td><td>38.17/0.9611</td><td>33.94/0.9207</td><td>32.30/0.9012</td><td>32.76/0.9340</td><td>39.11/0.9782</td></tr><tr><td>CRAFT (Ours)</td><td>737K</td><td>38.23/0.9615</td><td>33.92/0.9211</td><td>32.33/0.9016</td><td>32.86/0.9343</td><td>39.39/0.9786</td></tr><tr><td rowspan=\"11\">×3</td><td>EDSR-baseline [23]</td><td>1555K</td><td>34.37/0.9270</td><td>30.28/0.8417</td><td>29.09/0.8052</td><td>28.15/0.8527</td><td>33.45/0.9439</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>34.29/0.9255</td><td>30.29/0.8407</td><td>29.06/0.8034</td><td>28.06/0.8493</td><td>33.50/0.9440</td></tr><tr><td>IMDN [13]</td><td>703K</td><td>34.36/0.9270</td><td>30.32/0.8417</td><td>29.09/0.8046</td><td>28.17/0.8519</td><td>33.61/0.9445</td></tr><tr><td>LatticeNet [26]</td><td>765K</td><td>34.53/0.9281</td><td>30.39/0.8424</td><td>29.15/0.8059</td><td>28.33/0.8538</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>544k</td><td>34.36/0.9267</td><td>30.34/0.8421</td><td>29.11/0.8054</td><td>28.15/0.8523</td><td>33.51/0.9441</td></tr><tr><td>HPUN-L [34]</td><td>723K</td><td>34.56/0.9281</td><td>30.45/0.8445</td><td>29.18/0.8072</td><td>28.37/0.8572</td><td>33.90/0.9463</td></tr><tr><td>SwinIR-light [21]</td><td>886K</td><td>34.62/0.9289</td><td>30.54/0.8463</td><td>29.20/0.8082</td><td>28.66/0.8624</td><td>33.98/0.9478</td></tr><tr><td>LBNet [9]</td><td>736K</td><td>34.47/0.277</td><td>30.38/0.8417</td><td>29.13/0.8061</td><td>28.42/0.8559</td><td>33.82/0.9406</td></tr><tr><td>ESRT [25]</td><td>770K</td><td>34.42/0.9268</td><td>30.43/0.8433</td><td>29.15/0.8063</td><td>28.46/0.8574</td><td>33.95/0.9455</td></tr><tr><td>ELAN-light [44]</td><td>590K</td><td>34.61/0.9288</td><td>30.55/0.8463</td><td>29.21/0.8081</td><td>28.69/0.8624</td><td>34.00/0.9478</td></tr><tr><td>CRAFT (Ours)</td><td>744K</td><td>34.71/0.9295</td><td>30.61/0.8469</td><td>29.24/0.8093</td><td>28.77/0.8635</td><td>34.29/0.9491</td></tr><tr><td rowspan=\"11\">×4</td><td>EDSR-baseline [23]</td><td>1518K</td><td>32.09/0.8938</td><td>28.58/0.7813</td><td>27.57/0.7357</td><td>26.04/0.7849</td><td>30.35/0.9067</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>32.13/0.8937</td><td>28.60/0.7806</td><td>27.58/0.7349</td><td>26.07/0.7837</td><td>30.47/0.9084</td></tr><tr><td>IMDN [13]</td><td>715K</td><td>32.21/0.8948</td><td>28.58/0.7811</td><td>27.56/0.7353</td><td>26.04/0.7838</td><td>30.45/0.9075</td></tr><tr><td>LatticeNet [26]</td><td>777K</td><td>32.18/0.8943</td><td>28.61/0.7812</td><td>27.57/0.7355</td><td>26.14/0.7844</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>659k</td><td>32.15/0.8944</td><td>28.61/0.7818</td><td>27.61/0.7366</td><td>26.14/0.7871</td><td>30.42/0.9074</td></tr><tr><td>HPUN-L [34]</td><td>734K</td><td>32.31/0.8962</td><td>28.73/0.7842</td><td>27.66/0.7386</td><td>26.27/0.7918</td><td>30.77/0.9109</td></tr><tr><td>SwinIR-light [21]</td><td>897K</td><td>32.44/0.8976</td><td>28.77/0.7858</td><td>27.69/0.7406</td><td>26.47/0.7980</td><td>30.92/0.9151</td></tr><tr><td>LBNet [9]</td><td>742K</td><td>32.29/0.8960</td><td>28.68/0.7832</td><td>27.62/0.7382</td><td>26.27/0.7906</td><td>30.76/0.9111</td></tr><tr><td>ESRT [25]</td><td>751K</td><td>32.19/0.8947</td><td>28.69/0.7833</td><td>27.69/0.7379</td><td>26.39/0.7962</td><td>30.75/0.9100</td></tr><tr><td>ELAN-light [44]</td><td>601K</td><td>32.43/0.8975</td><td>28.78/0.7858</td><td>27.69/0.7406</td><td>26.54/0.7982</td><td>30.92/0.9150</td></tr><tr><td>CRAFT (Ours)</td><td>753K</td><td>32.52/0.8989</td><td>28.85/0.7872</td><td>27.72/0.7418</td><td>26.56/0.7995</td><td>31.18/0.9168</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the proposed inter-attention mechanism, which introduces high-frequency prior to refining the global representations.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            77,
+            570,
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+            586
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Data and Metrics",
+        "text_level": 1,
+        "bbox": [
+            77,
+            592,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we adopt the DIV2K [1] as the training dataset, which includes 800 training images. Meanwhile, five benchmarks are used for evaluation, including Set5 [3], Set14 [43], BSD100 [27], Urban100 [12], and Manga109 [28] with three magnification factors:  $\\times 2$ ,  $\\times 3$ , and  $\\times 4$ . The quality of the images is evaluated using PSNR, and SSIM [39]. The complexity of the model is indicated by its parameters.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            77,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Following the general setting, we use bicubic to obtain the corresponding LR images from the original HR images. During training, we randomly crop the images into  $64 \\times 64$  patches, and the total training iterations are  $500\\mathrm{K}$ . Meanwhile, data augmentation is performed, such as random horizontal flipping and  $90^{\\circ}$  rotation. The Adam optimizer with  $\\beta_{1} = 0.9$  and  $\\beta_{2} = 0.999$  is adopted to minimize the  $\\mathcal{L}_1$  Loss. The batch size is set to 64, the initial learning",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "rate is set to  $2 \\times 10^{-4}$  and reduced by half at the milestone [250K, 400K, 450K, 475K]. In addition, the model is trained on 4 NVIDIA 3090 GPUs using the PyTorch toolbox. In CRAFT, we have set the RCRFG number to 4 and the CRFB number to 2 for each RCRFG. Each CRFB is comprised of 1 HFERB and 2 SRWABs for efficiency. The feature channel, attention head, and MLP expansion ratio are set to 48, 6, and 2, respectively. We also set the IMLP expansion ratio to 2.66, as in [42]. To obtain two types of rectangle windows, we have set the rectangle window size to  $[sh, sw]$  as [4, 16] and [16, 4].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3. Comparison with state-of-the-art methods",
+        "text_level": 1,
+        "bbox": [
+            499,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We compare with several state-of-the-art SISR methods to demonstrate the effective of the proposed CRAFT model, including EDSR [23], CARN [2], IMDN [13], LatticeNet [26], LAPAR [19], SwinIR [21], HPUN [34], ESRT [25], LBNet [9], and ELAN [44].",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Results. The experimental results for SISR are presented in Table 1, where the proposed CRAFT model demonstrates competitive performance across all benchmarks. Particularly, when compared to traditional CNN-based methods like EDSR, the proposed CRAFT achieves significant performance improvements of  $0.85\\mathrm{dB}$",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "12519",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/c495e9681d5e0d09b2bd5e98fe8f968813d63083893cb9036b995236a91ff42b.jpg",
+        "image_caption": [
+            "Img012  $(\\times 4)$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
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+    {
+        "type": "image",
+        "img_path": "images/65a61369fef1c96d6d23be3b3fef9d66f258c2d987779da8f593826bbfcd71ec.jpg",
+        "image_caption": [
+            "Bicubic"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/093c3a17b0589b525e28998089edc54410ca8a423eefd0dd134c8f157386314b.jpg",
+        "image_caption": [
+            "EDSR [23]"
+        ],
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+        ],
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+    {
+        "type": "image",
+        "img_path": "images/c4b9eb406c13ad4ea62fe2b604f61f9ed70661b6f3c067c5424b713e40aa3b30.jpg",
+        "image_caption": [
+            "CARN [2]"
+        ],
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+        "image_caption": [
+            "LBNet [9]"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7c51d892601651c47c1b45dc2cfa6c92d917fedf513e1b9c4da664ed459a8dbe.jpg",
+        "image_caption": [
+            "YumeiroCook  $(\\times 4)$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/dab4afd1bfb5314d489ae5efd826eb75d9bdfcc21a10b7f0e0eb53fe088dce87.jpg",
+        "image_caption": [
+            "SwinIR [21]"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4448ad44e0bd9ed1f531eddd325dc977c311fc941e7528f487764cc6d44de6af.jpg",
+        "image_caption": [
+            "ESRT [25]"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
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+        "img_path": "images/858e9791738bbc720b939b24116974dbc72313d788782b6ffd05afa68d5d3c3c.jpg",
+        "image_caption": [
+            "CRAFT (Ours)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/54b746e826baf6ea00cc184728a287183be3fd4a5ecf573b166ef8fd6c2f1db3.jpg",
+        "image_caption": [
+            "HR"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/fa57e7794cb28c2880c0f82b6fbcfc42d5d67e95c8563f45dd59a0c5d1dbfdff.jpg",
+        "image_caption": [
+            "UchuKigekiM774  $(\\times 4)$",
+            "Figure 3. Visual quality comparison with SOTA methods. CRAFT achieves better restoration quality in both line direction and details."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
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+        "img_path": "images/4403ce67762ab1900fa8fb9610fe2f09c72bc86c3ba39645d974474d3c716819.jpg",
+        "image_caption": [
+            "Bicubic"
+        ],
+        "image_footnote": [],
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+        ],
+        "page_idx": 6
+    },
+    {
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+        "image_caption": [
+            "EDSR [23]"
+        ],
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+        ],
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+    },
+    {
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+        "img_path": "images/d72ea7180661dad3325cc3d4d24c5018397afc4ad39e6cd4b3eb63671d171423.jpg",
+        "image_caption": [
+            "CARN [2]"
+        ],
+        "image_footnote": [],
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+    {
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+        "image_caption": [
+            "LBNet [9]"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/c5a6c00210dad90a00d288b2523a9c3fd64e11860eff46ae64a085bebf1e0e74.jpg",
+        "image_caption": [
+            "SwinIR [21]"
+        ],
+        "image_footnote": [],
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+        "page_idx": 6
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+    {
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+    {
+        "type": "text",
+        "text": "0.84dB, and 0.83dB at magnification factors  $\\times 2$ ,  $\\times 3$ , and  $\\times 4$ , respectively, while using  $46\\%$ ,  $52\\%$ , and  $50\\%$  fewer parameters on the Manga109 dataset. Furthermore, compared to recent channel attention methods such as CARN, the proposed CRAFT achieves improvements of 1.03dB, 0.79dB, and 0.71dB at magnification factors  $\\times 2$ ,  $\\times 3$ , and  $\\times 4$ , respectively, with a  $54\\%$ ,  $53\\%$ , and  $52\\%$  reduction in the number of parameters on the Manga109 dataset. Regarding transformer-based methods [25, 21, 44], the proposed CRAFT gains performance improvements of 0.34dB, 0.31dB, and 0.29dB, respectively, with a comparable number of parameters under the magnification factor of  $\\times 3$  on the Manga109 dataset.",
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+    {
+        "type": "text",
+        "text": "Qualitative Results. We present a visual comparison  $(\\times 4)$  in Figure 3 and analyze the results. Our proposed CRAFT model integrates the strengths of both CNN and transformer structures, leading to accurate line direction recovery while preserving image details. To further investigate the performance, we compare the local attribution map (LAM) [11] between CRAFT and SwinIR, as shown in Figure 4. LAM indicates the correlation between the significance of each pixel in LR and the SR of the patch that is outlined with the red box. By leveraging a broader range of information, our model achieves improved results. Furthermore, we examine the diffusion index (DI), which signifies the range of pixels involved. A larger DI indicates a",
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+    {
+        "type": "text",
+        "text": "wider scope of attention. Compared to SwinIR, our model exhibits a higher DI, implying that it can capture more contextual information. These results demonstrate the effectiveness of the proposed CRAFT method.",
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+    {
+        "type": "text",
+        "text": "5.4. Ablation study",
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+        "text": "5.4.1 Effectiveness of HFERB and SRWAB",
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+        "text": "We conduct several experiments to show the effectiveness of HFERB and SRWAB in Table 2. Specifically, we removed SRWAB and HFERB separately to assess their contributions. We observed that using local or global information alone, as in  $\\mathrm{CRAFT}_{conv}$  and  $\\mathrm{CRAFT}_{transformer}$ , respectively, is insufficient to learn a better representation (lower performance). Furthermore, we found that SRWAB provides the most significant performance improvement, demonstrating the benefits of the long-range dependencies learned by the transformer. In addition, high-frequency priors from CNN are also helpful in restoring details, cross-refining learned features and further improving performance. Meanwhile, we also analyzed the properties of HFERB and SRWAB from a frequency perspective. We visualized the features extracted from two blocks in different RCRFGs and plotted the Fourier spectrum to observe what each block learns. The results, shown in Figure 5, indicate that HFERB focuses more on high-frequency information, while SRWAB extracts more global informa",
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+        "img_path": "images/c31392aebcb7b7d92cab2df42dd5742bd16ee729d8410c489ea6b0ea0134e1dc.jpg",
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+            "DI: 12.88"
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+    {
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+        "img_path": "images/f9ae1c653d87f11dad2215979a85c2f98e1ee90f22ed27f92d4a436f612c9b93.jpg",
+        "table_caption": [
+            "Table 2. Study of HFERB, SRWAB, and HFB on SISR. The results  $(\\times 4)$  are obtained from the Manga109 dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>HFERB</td><td>SRWAB</td><td>HFB</td><td>Concat</td><td>PSNR</td></tr><tr><td>CRAFTconv</td><td>✓</td><td></td><td>✓</td><td></td><td>30.79</td></tr><tr><td>CRAFTtransformer</td><td></td><td>✓</td><td>✓</td><td></td><td>31.12</td></tr><tr><td>CRAFTconcat</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>30.92</td></tr><tr><td>CRAFT</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>31.18</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "tion. Specifically, the top row of each image indicates the Fourier spectrum of each block, and the bottom row indicates the feature maps of each block. The figure shows that SRWAB has a weaker response and focuses more on the low-frequency parts, which correspond to flat regions, while HFERB shows a stronger response and focuses more on intricate parts of features, such as edges and corners. The feature maps on the bottom row also support this conclusion. HFERB captures more details such as window edges and cornices, while SRWAB pays more attention to flat areas such as windows and walls.",
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+    {
+        "type": "text",
+        "text": "5.4.2 Effectiveness of HFB",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the effectiveness of HFB, we conducted an experiment where we modified the fusion method to a concatenation formulation. This involved concatenating the",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/1fd7e8247457fd5b3270b4ccec2d6ea3b9ad34aa9d03e86ab44d7de5a2f7f51b.jpg",
+        "table_caption": [
+            "Table 3. Effectiveness of high-frequency prior. The results  $(\\times 4)$  are obtained from the Manga109 dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Regular</td><td>Swap</td><td>Cascade</td><td>PSNR</td><td>SSIM</td></tr><tr><td>CRAFTswap</td><td></td><td>✓</td><td></td><td>30.67</td><td>0.9113</td></tr><tr><td>CRAFT cascade</td><td></td><td></td><td>✓</td><td>30.88</td><td>0.9141</td></tr><tr><td>CRAFT</td><td>✓</td><td></td><td></td><td>31.18</td><td>0.9168</td></tr></table>",
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+    {
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+        "img_path": "images/8f2b93c1e8ceb3c1a4adf3daa890a307c9581a610b8b086c04055101a80ecedc.jpg",
+        "table_caption": [
+            "Table 4. Complexity analysis compared to SwinIR."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>#Params. (K)</td><td>#FLOPs (G)</td><td>#GPU Mem. (M)</td><td>Ave. Time (ms)</td></tr><tr><td>SwinIR</td><td>897</td><td>32.2</td><td>141.2</td><td>72.0</td></tr><tr><td>CRAFT</td><td>753</td><td>26.1</td><td>79.5</td><td>42.8</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "HFERB and SRWAB output and replacing the HFB with a  $3 \\times 3$  convolutional layer to obtain the final output. The results are presented in Table 2, where  $\\mathrm{CRAFT}_{\\text {concat }}$  denotes the modified version. The result shows that our proposed method outperforms the concatenation structure by  $0.26\\mathrm{dB}$ , demonstrating the effectiveness of our HFB. The observed result can be attributed to SRWAB and HFERB focusing on disparate frequency information. Stacking features directly impedes the ability of the network to learn the relationship between high-frequency and low-frequency components. Conversely, the inter-attention mechanism presents a viable solution for integrating features with different distributions.",
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+        "text": "12521",
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+            "HPE LFE SW with Altex (c) Visualization of the spectrum of the 4th RCFG"
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+        "image_caption": [
+            "(a) Visualization of the spectrum of the 2nd RCRFG",
+            "HFE"
+        ],
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+    {
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+        "image_caption": [
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+    {
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+        "img_path": "images/66301d83520ae9980cb3295fb85addd20bc42ce9e85da34db7ca2aa67de1fa02.jpg",
+        "image_caption": [
+            "LR Image",
+            "Figure 5. Visualization of HFERB and SRWAB. The LFE indicates the local feature extraction branch in HFERB, the HFE means the high-frequency enhancement branch in HFERB, and the SRWin-Attention represents the self-attention part in SRWAB."
+        ],
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+    {
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+        "img_path": "images/6a070bcdf4e8e5f894784428d2586804d2909f9760c63e57251b95255e5b074e.jpg",
+        "image_caption": [
+            "(d) Visualization of the feature of the 4th RCFIG",
+            "HFE"
+        ],
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+    {
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+    {
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+        "img_path": "images/b62cd49dbf879601291a33c0a37faced1ca2a997dae6abbf296c74cafdea6618.jpg",
+        "image_caption": [
+            "(e) Visualization of the spectrum of the 2nd RCRFG",
+            "HFE",
+            "(f) Visualization of the feature of the 2nd RCRFG"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "image_caption": [
+            "HFE",
+            "(h) Visualization of the feature of the 4th RCRFG"
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/62cd6ebb64ae8b498e5754f53fe73abae9f7f9f941ff83c78882de10fd3f953a.jpg",
+        "image_caption": [
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+    {
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+        "img_path": "images/0b1104d9f7f06785ff3694f36c2174987df1ed1f30193bdeb7613171c36963c2.jpg",
+        "image_caption": [
+            "SRWin-Attention"
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+    {
+        "type": "text",
+        "text": "5.4.3 Effectiveness of High-Frequency Prior",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We conducted several experiments to investigate the effectiveness of high-frequency prior. Firstly, we swapped the input of  $Q$  and  $K$ ,  $V$  in HFB and treated the output of SRWAB as  $Q$  and the output of HFERB as  $K$ ,  $V$  to verify whether global features are dominant in restoration and high-frequency features only serve as a prior for refining the global representation. As shown in Table 3, compared to the original design, swapping the input leads to a significant drop in performance, with a 0.51dB decrease in PSNR. Furthermore, we also performed an experiment to formulate the model as a cascade structure to verify the effectiveness of the design introducing high-frequency priors. As shown in Table 3, the  $\\mathrm{CRAFT}_{\\text{ cascade}}$  structure resulted in a performance drop, with a 0.3dB decrease in PSNR compared to CRAFT. These results demonstrate the effectiveness of high-frequency priors in the CRAFT model.",
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+        "text": "5.4.4 Complexity analysis",
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+        "text": "We compared CRAFT with SwinIR in terms of complexity using an input size of  $128 \\times 128$ , as shown in Table 4. The analysis considered parameters, FLOPs, GPU memory consumption, and average inference time. GPU memory was measured using the official PyTorch function, and time cost was calculated based on 100 inference runs. Compared to SwinIR, CRAFT has fewer parameters and FLOPs, and requires less memory consumption and inference time. Additionally, we analyzed the complexity of our CRAFT framework and summarized the findings in Table 5. We observed that SRWAB contributes approximately  $46\\%$  of the total complexity, while HFERB involves fewer convolution operations, resulting in reduced FLOPs. Furthermore, the HFB module's channel-wise attention effectively reduces",
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+        "table_caption": [
+            "Table 5. Complexity analysis of each block."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>CRAFT\nw/o HFERB</td><td>CRAFT\nw/o SRWAB</td><td>CRAFT\nw/o HFB</td><td>CRAFT</td></tr><tr><td>#Params. (K)</td><td>688</td><td>441</td><td>503</td><td>753</td></tr><tr><td>#FLOPs (G)</td><td>23.8</td><td>14.2</td><td>20.0</td><td>26.1</td></tr></table>",
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+        "text": "the computational burden.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
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+        "text": "This paper investigates the impact of frequency on the performance of CNN and transformer structures in SISR and finds that transformer structures are more adept at capturing low-frequency information, but have limited capability to reconstruct high-frequency representations compared to CNN. To address this issue, we design a feature modulation transformer, named cross-refinement adaptive feature modulation transformer (CRAFT), which comprises three key components: the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB). The HFERB is designed to extract high-frequency features, while the SRWAB captures global representations. In the HFB, we treat the output of HFERB as a high-frequency prior and the output of SRWAB as key and value, and use interattention to refine the global representation. Experimental results demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB with relatively fewer parameters.",
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+        "text": "This work is supported by the National Natural Science Foundation of China (NSFC) under Grant U19A2052 and Grant 62020106011, as well as by the National Key Lab of Autonomous Intelligent Unmanned Systems.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+            124,
+            171,
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+        ],
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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diff --git a/2023/Feature Modulation Transformer_ Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution/358910c2-9bed-4301-a68b-c93d03912323_model.json b/2023/Feature Modulation Transformer_ Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution/358910c2-9bed-4301-a68b-c93d03912323_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..74d37f5225c6b47e4771d13c971432c0cd66b9bf
--- /dev/null
+++ b/2023/Feature Modulation Transformer_ Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution/358910c2-9bed-4301-a68b-c93d03912323_model.json	
@@ -0,0 +1,4369 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.254,
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+                0.79,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Feature Modulation Transformer: Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Ao Li\\(^{1}\\), Le Zhang\\(^{1*}\\), Yun Liu\\(^{2}\\), Ce Zhu\\(^{1}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.187,
+                0.245,
+                0.783,
+                0.262
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>University of Electronic Science and Technology of China, <sup>2</sup>I2R, A*STAR"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.158,
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+            ],
+            "angle": 0,
+            "content": "aoli@std.uestc.edu.cn, {lezhang,eczhu}@uestc.edu.cn, vagrantlyun@gmail.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
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+            "angle": 0,
+            "content": "Abstract"
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+            "type": "text",
+            "bbox": [
+                0.076,
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+            ],
+            "angle": 0,
+            "content": "Transformer-based methods have exhibited remarkable potential in single image super-resolution (SISR) by effectively extracting long-range dependencies. However, most of the current research in this area has prioritized the design of transformer blocks to capture global information, while overlooking the importance of incorporating high-frequency priors, which we believe could be beneficial. In our study, we conducted a series of experiments and found that transformer structures are more adept at capturing low-frequency information, but have limited capacity in constructing high-frequency representations when compared to their convolutional counterparts. Our proposed solution, the cross-refinement adaptive feature modulation transformer (CRAFT), integrates the strengths of both convolutional and transformer structures. It comprises three key components: the high-frequency enhancement residual block (HFERB) for extracting high-frequency information, the shift rectangle window attention block (SRWAB) for capturing global information, and the hybrid fusion block (HFB) for refining the global representation. Our experiments on multiple datasets demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB while using fewer parameters. The source code will be made available at: https://github.com/AVC2-UESTC/CRAFT-SR.git."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.734,
+                0.47,
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+            "angle": 0,
+            "content": "Single image super-resolution (SISR) has garnered significant attention in recent years, owing to its promising applications across diverse domains, such as surveillance video and medical image enhancement [31, 10], old image reconstruction [21, 17], and efficient image transmission [47]. Despite its practical value, SISR remains an ill-posed problem, given the existence of multiple solutions for a given low-resolution (LR) image. To tackle this challenge,"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "a multitude of classical approaches have been proposed, including \\(\\mathrm{A + }\\) [36], SC [41], and ANR [35]. However, these methods exhibit limitations in their performance, primarily attributed to their constrained model capacities."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In recent years, deep learning has experienced significant growth and demonstrated remarkable success in SISR [7, 20, 45, 22]. Prior research efforts have introduced residual and dense connectives to facilitate the stacking of deep convolutional neural networks (CNNs) [16, 37], while others [46, 40, 29, 30] have leveraged attention mechanisms to enhance performance. Notably, the emergence of transformer architectures has demonstrated their efficacy in capturing long-range dependencies and attaining state-of-the-art performance [21, 6, 4, 18, 25]. Despite these advancements, these works have mainly focused on designing transformer blocks to obtain global information and overlooked the potential of incorporating high-frequency priors [32, 8] to further bolster performance in SISR. Additionally, there is limited detailed analysis of the impact of frequency on performance."
+        },
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+            "type": "text",
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+            "content": "In this paper, we investigate the influence of high-frequency information on the performance of CNN and transformer structures in SISR. We achieve this by discarding different ratios of high-frequency components from the input image and observing the corresponding performance changes. Our empirical findings reveal that transformers tend to prioritize low-frequency information and exhibit limited capability in constructing high-frequency representations when compared to CNNs. To address this issue, we proposed a cross-refinement adaptive feature modulation transformer (CRAFT) that integrates the strengths of both structures. Specifically, CRAFT comprises three key components, namely the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB), which work collaboratively to capture high-frequency details, extract long-range dependencies, and refine the output for better representation. Experimental results show that CRAFT outperforms state-of-the-art performance with relatively fewer parameters. The main contributions of this paper are as fol"
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+            "angle": 0,
+            "content": "*Corresponding author."
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+            "content": "- We study the impact of CNN and transformer structures on performance from a frequency perspective and observe that transformer is more effective in capturing low-frequency information while having limited capacity for constructing high-frequency representations compared to CNN."
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+            ],
+            "angle": 0,
+            "content": "- Based on the observation, we design a parallel structure to explore different frequency features. We utilize the HFERB branch to introduce high-frequency information, which is beneficial to SISR, and the SRWAB branch to acquire global information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.32,
+                0.469,
+                0.389
+            ],
+            "angle": 0,
+            "content": "- We propose a fuse strategy that integrates the strengths of CNN and transformer. Specifically, we treat the HFERB branch as high-frequency prior and the output of SRWAB as key and value for inter-attention, resulting in improved performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.398,
+                0.469,
+                0.453
+            ],
+            "angle": 0,
+            "content": "- Extensive experimental results on multiple datasets show that the proposed method performs on par with the existing state-of-the-art SISR methods while using fewer parameters."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.15,
+                0.469,
+                0.453
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.476,
+                0.227,
+                0.49
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.498,
+                0.247,
+                0.511
+            ],
+            "angle": 0,
+            "content": "2.1. CNN-based SISR"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.519,
+                0.47,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Since the pioneering work SRCNN [7] has achieved significant progress in SISR, various CNN-based works have been proposed. Kim et al. [15] presented an SR method using deep networks by cascading 20 layers, demonstrating promising results. Building upon this, Lim et al. [23] introduced the enhanced deep super-resolution (EDSR) network, which achieved a significant performance boost by removing the batch normalization layer [14] from the residual block and incorporating additional convolution layers. Ahn et al. [2] designed an architecture with an increased number of residual blocks and dense connections, further improving the SR performance. In pursuit of lightweight models, Hui et al. [13] proposed a selective fusion approach, employing cascaded information multi-distillation blocks to construct an efficient model. Li et al. [19] introduced a method involving predefined filters and utilized a CNN to learn coefficients, which were then linearly combined to obtain the final results. Sun et al. [34] proposed a hybrid pixel-unshuffled network (HPUN) by introducing an efficient and effective downsampling module into the SR task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.818,
+                0.305,
+                0.831
+            ],
+            "angle": 0,
+            "content": "2.2. Transformer-based SISR"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.839,
+                0.469,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Liang et al. [21] proposed SwinIR, a robust baseline model for image restoration, leveraging the Swin Trans"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.127,
+                0.892,
+                0.347
+            ],
+            "angle": 0,
+            "content": "former [24]. CAT [6] modified the window shape and introduced a rectangle window attention to obtaining better performance. Chen et al. [4] proposed a pre-trained image processing transformer and showed that pre-trained mechanism could significantly improve the performance for low-level tasks. Li et al. [18] comprehensively analyzed the effect of pre-training and proposed a versatile model to tackle different low-level tasks. Lu et al. [25] proposed a lightweight transformer to capture long-range dependencies between similar patches in an image with the help of the specially designed efficient transformer and efficient attention mechanism. Zhang et al. [44] introduced a shift convolution and a group-wise multi-scale self-attention to reduce the complexity of transformer. HAT [5] introduced a hybrid attention mechanism to enhance the performance of window-based transformers."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.36,
+                0.776,
+                0.376
+            ],
+            "angle": 0,
+            "content": "3. Analysis of Frequency Impact"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.383,
+                0.891,
+                0.451
+            ],
+            "angle": 0,
+            "content": "This section delves into the influence of performance from a frequency perspective. To analyze the impact of various frequencies on CNN and transformer, we conduct two sets of experiments using four common used benchmarks, as illustrated in Figure 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.452,
+                0.892,
+                0.673
+            ],
+            "angle": 0,
+            "content": "We select CARN [2], IMDN [13], EDSR [23], and SwinIR [21], CAT [6], HAT [5] as representatives of CNN and transformer structures. The process of dropping frequency components is depicted in Figure 1(c). Given a high-resolution (HR) image \\(X^{HR}\\), we perform a fast Fourier transform (FFT) on it to obtain its frequency spectrum. Subsequently, we flatten this spectrum into a sequence and arrange it in ascending order based on the magnitudes. With a sequence length of \\(L\\), we define a threshold determined by the drop ratio \\(\\gamma\\), \\(0 \\leq \\gamma \\leq 1\\), located at the magnitude corresponding to the position \\(\\gamma \\cdot L\\). Frequency components with magnitudes below this threshold are set to zero. Following this, we perform an inverse fast Fourier transform (IFFT) to generate the HR image with dropped frequencies, referred to as \\(X_{drop}^{HR}(\\gamma)\\). The formulation for this process is as follows"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.538,
+                0.682,
+                0.891,
+                0.701
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {d r o p} ^ {H R} (\\gamma) = I F F T (D r o p \\left(\\left| F F T \\left(X ^ {H R}\\right) \\right|, \\gamma)\\right). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.71,
+                0.891,
+                0.783
+            ],
+            "angle": 0,
+            "content": "Afterward, we downsample \\(X_{drop}^{HR}(\\gamma)\\) using bicubic interpolation to obtain the LR version \\(X_{drop}^{LR}(\\gamma)\\) (e.g. \\(\\times 4\\) down-sampling). Finally, we employ CNN-based and transformer-based SR models to generate the super-resolved counterpart \\(X_{drop}^{SR}(\\gamma)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.782,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "To analyze the dependency of CNN and transformer on high-frequency information, we compute the peak signal-to-noise ratio (PSNR) \\( P^{D}(\\gamma) \\) between \\( X_{drop}^{SR}(\\gamma) \\) and \\( X_{drop}^{HR} \\). We then plot the PSNR drop trend to visualize the difference between the two structures. As shown in Figure 1(a), the PSNR drop ratio for each drop ratio is defined"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.887,
+                0.505,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12515"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.119,
+                0.278,
+                0.221
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.284,
+                0.12,
+                0.473,
+                0.22
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.483,
+                0.12,
+                0.673,
+                0.22
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.687,
+                0.121,
+                0.871,
+                0.22
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.297,
+                0.224,
+                0.666,
+                0.235
+            ],
+            "angle": 0,
+            "content": "(a) Dependency of different structures on high-frequency information."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.246,
+                0.27,
+                0.343
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.284,
+                0.242,
+                0.475,
+                0.342
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.484,
+                0.244,
+                0.674,
+                0.342
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.688,
+                0.244,
+                0.875,
+                0.342
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.318,
+                0.346,
+                0.652,
+                0.358
+            ],
+            "angle": 0,
+            "content": "(b) Effectiveness of reconstructing high-frequency information."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.119,
+                0.365,
+                0.852,
+                0.452
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.361,
+                0.455,
+                0.608,
+                0.466
+            ],
+            "angle": 0,
+            "content": "(c) The procedure of dropping high-frequency."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.465,
+                0.893,
+                0.53
+            ],
+            "angle": 0,
+            "content": "Figure 1. The influence of high-frequency information on the performance of CNN and transformer architectures. Dashed and solid lines correspond to CNN and transformer methods, respectively. (a) With an increase in the high-frequency drop ratio, transformer models exhibit a smaller change in PSNR compared to CNN, suggesting their superiority in capturing low-frequency information. (b) As the high-frequency drop ratio increases, transformer models show a more pronounced change in PSNR compared to CNN, indicating their limited ability to reconstruct high-frequency information from low-frequency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.554,
+                0.097,
+                0.564
+            ],
+            "angle": 0,
+            "content": "as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.175,
+                0.562,
+                0.469,
+                0.592
+            ],
+            "angle": 0,
+            "content": "\\[\nR _ {d r o p} ^ {D} (\\gamma) = \\frac {P (0) - P ^ {D} (\\gamma)}{P (0)}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.597,
+                0.469,
+                0.693
+            ],
+            "angle": 0,
+            "content": "where \\(P(0)\\) represents the PSNR without dropping, calculated between \\(X^{SR}\\) and \\(X^{HR}\\). The figures illustrate that the transformer model exhibits reduced sensitivity to high-frequency information and excels in capturing low-frequency information, as evidenced by the smaller PSNR change compared to the CNN model as the proportion of discarded high-frequency information increases."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.695,
+                0.469,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Furthermore, we conduct another experiment to evaluate the effectiveness of different structures in reconstructing high-frequency information. Specifically, we calculate the PSNR \\( P^{E}(\\gamma) \\) between \\( X_{drop}^{SR}(\\gamma) \\) and \\( X^{HR} \\) and plot the performance drop trend as previously depicted. The PSNR drop ratio for each drop ratio can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.175,
+                0.785,
+                0.469,
+                0.817
+            ],
+            "angle": 0,
+            "content": "\\[\nR _ {d r o p} ^ {E} (\\gamma) = \\frac {P ^ {E} (\\gamma) - P (0)}{P (0)}. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.867
+            ],
+            "angle": 0,
+            "content": "From Figure 1(b), we observe that as the proportion of discarded high-frequency information increases, the transformer model experiences a larger PSNR change compared"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.552,
+                0.89,
+                0.579
+            ],
+            "angle": 0,
+            "content": "to the CNN model, indicating its limited ability to reconstruct high-frequency information from low-frequency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.58,
+                0.891,
+                0.676
+            ],
+            "angle": 0,
+            "content": "Based on these observations, we argue that the transformer requires the assistance of CNN to enhance its capability to recover intricate details. To address this, we propose a method that combines the strengths of both CNN and transformer. Specifically, we introduce CNN information as a high-frequency prior to aid the transformer in refining the global representation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.691,
+                0.673,
+                0.707
+            ],
+            "angle": 0,
+            "content": "4. Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.715,
+                0.892,
+                0.866
+            ],
+            "angle": 0,
+            "content": "The CRAFT network comprises three key components: Shallow feature extraction, residual cross-refinement fusion groups (RCRFGs), and reconstruction as shown in Figure 2. The shallow feature extraction module comprises a single convolutional layer, while the reconstruction module is followed by the SwinIR [21]. The RCRFG component consists of several cross-refinement fusion blocks (CRFBs), each comprising three types of blocks: the high-frequency enhancement residual blocks (HFERBs), the shift rectangle window attention blocks (SRWABs), and the hybrid fusion blocks (HFBs). We first describe the overall structure of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.887,
+                0.506,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12516"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.11,
+                0.123,
+                0.862,
+                0.238
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.111,
+                0.24,
+                0.856,
+                0.374
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.112,
+                0.376,
+                0.856,
+                0.546
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.548,
+                0.893,
+                0.575
+            ],
+            "angle": 0,
+            "content": "Figure 2. The framework of CRAFT. HFERB extracts the high frequency from the input features, SRWAB captures the long-range dependency of input features, and HFB integrates the output of HFERB and SRWAB to cross refine the global features. Best viewed in color."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.597,
+                0.471,
+                0.625
+            ],
+            "angle": 0,
+            "content": "CRAFT and then elaborate on the three key designs, including HFERB, SRWAB, and HFB."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.634,
+                0.242,
+                0.648
+            ],
+            "angle": 0,
+            "content": "4.1. Model Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.655,
+                0.47,
+                0.781
+            ],
+            "angle": 0,
+            "content": "The input LR image is processed by a \\(3 \\times 3\\) convolutional layer to obtain shallow features. These features are then fed into a serial of RCRFGs to learn deep features. After the last RCRFG, a \\(3 \\times 3\\) convolutional layer aggregates the features, and a residual connection is established between its output and the shallow features for facilitating training. The reconstruction module employs a \\(3 \\times 3\\) convolutional layer to aggregate the features, and a shuffle layer [33] is used to obtain the final SR output image."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.79,
+                0.466,
+                0.805
+            ],
+            "angle": 0,
+            "content": "4.2. High-frequency Enhancement Residual Block"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.47,
+                0.868
+            ],
+            "angle": 0,
+            "content": "The HFERB aims to enhance the high-frequency information, as shown in Figure 2. It comprises the local feature extraction (LFE) branch and the high-frequency enhancement (HFE) branch. Specifically, we split the input features"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.595,
+                0.891,
+                0.625
+            ],
+            "angle": 0,
+            "content": "\\(F_{in}\\in \\mathbb{R}^{H\\times W\\times C}\\) into two parts, and then processed by the two branches separately"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.597,
+                0.632,
+                0.892,
+                0.65
+            ],
+            "angle": 0,
+            "content": "\\[\nF _ {i n} ^ {L F E}, F _ {i n} ^ {H F E} = \\operatorname {S p l i t} \\left(F _ {i n}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.656,
+                0.894,
+                0.714
+            ],
+            "angle": 0,
+            "content": "where \\(F_{in}^{LFE}, F_{in}^{HFE} \\in \\mathbb{R}^{H \\times W \\times C / 2}\\) represent the input of LFE and HFE. For the LFE branch, we utilize a \\(3 \\times 3\\) convolutional layer followed by a GELU activation function to extract local high-frequency features"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.586,
+                0.72,
+                0.892,
+                0.739
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {F} _ {i n} ^ {L F E} = f _ {a} \\left(\\operatorname {C o n v} _ {3 \\times 3} \\left(F _ {i n} ^ {L F E}\\right)\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.746,
+                0.893,
+                0.843
+            ],
+            "angle": 0,
+            "content": "where the \\(Conv_{3\\times 3}(\\cdot)\\) refers to the convolutional layer and the \\(f_{a}(\\cdot)\\) represents the GELU activation layer. For the HFE branch, we employ a max-pooling layer to extract high-frequency information from the input features \\(F_{in}^{HFE}\\). Then, we use a \\(1\\times 1\\) convolutional layer followed by a GELU activation function to enhance the high-frequency features,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.85,
+                0.892,
+                0.869
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {F} _ {i n} ^ {H F E} = f _ {a} \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {M a x P o o l i n g} \\left(F _ {i n} ^ {H F E}\\right)\\right)\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.887,
+                0.506,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12517"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.126,
+                0.473,
+                0.238
+            ],
+            "angle": 0,
+            "content": "where the \\(Conv_{1\\times 1}(\\cdot)\\) indicates the convolutional layer, the MaxPooling \\((\\cdot)\\) means the max-pooling layer and the \\(f_{a}(\\cdot)\\) represents the GELU activation layer. The outputs of the two branches are then concatenated and fed into a \\(1\\times 1\\) convolutional layer to fuse the information thoroughly. To make the network benefit from multi-scale information and maintain training stability, a skip connection is introduced. The whole process can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.096,
+                0.247,
+                0.47,
+                0.267
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {H} = C o n v _ {1 \\times 1} (C o n c a t (\\hat {F} _ {i n} ^ {L F E}, \\hat {F} _ {i n} ^ {H F E})) + F _ {i n}, (7)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.276,
+                0.47,
+                0.306
+            ],
+            "angle": 0,
+            "content": "where the \\( \\text{Concat}(\\cdot) \\) refers to the concatenation operation and the \\( \\text{Conv}_{1 \\times 1}(\\cdot) \\) represents the convolutional layer."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.314,
+                0.427,
+                0.329
+            ],
+            "angle": 0,
+            "content": "4.3. Shift Rectangle Window Attention Block"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.336,
+                0.47,
+                0.461
+            ],
+            "angle": 0,
+            "content": "We utilize the shift rectangle window (SRWin) to expand the receptive field, which can benefit SISR [6]. Unlike square windows, the SRWin uses rectangle windows to capture more relevant information along the longer axis. In detail, given an input \\( X_{in} \\in \\mathbb{R}^{H \\times W \\times C} \\), we divide it into \\( \\frac{H \\times W}{rh \\times rw} \\) rectangle windows, where \\( rh \\) and \\( rw \\) refer to the height and width of the rectangle window. For the \\( i \\)-th rectangle window feature \\( X_{i} \\in \\mathbb{R}^{(rh \\times rw) \\times C} \\), we compute the query, key, and value as follows"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.125,
+                0.47,
+                0.47,
+                0.489
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {Q} _ {i} = X _ {i} W _ {i} ^ {Q}, \\boldsymbol {K} _ {i} = X _ {i} W _ {i} ^ {K}, \\boldsymbol {V} _ {i} = X _ {i} W _ {i} ^ {V}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.498,
+                0.47,
+                0.556
+            ],
+            "angle": 0,
+            "content": "where the \\(W_{i}^{Q}\\in \\mathbb{R}^{C\\times d}\\) \\(W_{i}^{K}\\in \\mathbb{R}^{C\\times d}\\) and \\(W_{i}^{V}\\in \\mathbb{R}^{C\\times d}\\) represent the projection matrices and \\(d\\) is projection dimension which is commonly set to \\(d = \\frac{C}{M}\\) where the \\(M\\) is the number of heads. The self-attention can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.086,
+                0.565,
+                0.47,
+                0.598
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A t t e n t i o n} \\left(\\boldsymbol {Q} _ {i}, \\boldsymbol {K} _ {i}, \\boldsymbol {V} _ {i}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {\\boldsymbol {Q} _ {i} \\boldsymbol {K} _ {i} ^ {T}}{\\sqrt {d}} + B\\right) \\boldsymbol {V} _ {i}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.606,
+                0.47,
+                0.787
+            ],
+            "angle": 0,
+            "content": "where \\( B \\) is the dynamic relative position encoding [38]. Moreover, a convolutional operation on the value is introduced to enhance local extraction capability. To capture information from different axes, we utilize two types of rectangle windows: Horizontal and vertical windows. Unlike traditional operations that utilize attention masks to limit calculations to the same window, in practice, we eliminate the mask and enable more extensive information interaction across different windows. Accordingly, we split the attention heads into two equal groups and compute the self-attention within each group separately. We then concatenate the outputs of the two groups to obtain the final output. The procedure can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.088,
+                0.798,
+                0.469,
+                0.815
+            ],
+            "angle": 0,
+            "content": "\\[\nR \\operatorname {w i n} - S A (X) = \\operatorname {C o n c a t} (V - R \\operatorname {w i n}, H - R \\operatorname {w i n}) W ^ {p}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.824,
+                0.47,
+                0.867
+            ],
+            "angle": 0,
+            "content": "where the \\(W^{p}\\in \\mathbb{R}^{C\\times C}\\) represents the linear projection to fuse the features, \\(V\\) -Rwin and \\(H\\) Rwin indicate the vertical and horizontal rectangle window attention. In addition,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.126,
+                0.892,
+                0.154
+            ],
+            "angle": 0,
+            "content": "a multi-layer perceptron (MLP) is used for further feature transformations. The whole process can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.577,
+                0.162,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} X = R \\operatorname {w i n} - S A \\left(L N \\left(X _ {i n}\\right)\\right) + X _ {i n} \\\\ X = M P (L N (X)) - X \\end{array} \\tag {11}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.179,
+                0.773,
+                0.193
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {S} = M L P (L N (X)) + X,\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.2,
+                0.813,
+                0.215
+            ],
+            "angle": 0,
+            "content": "where the \\(LN\\) represents the LayerNorm layer."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.221,
+                0.698,
+                0.236
+            ],
+            "angle": 0,
+            "content": "4.4. Hybrid Fusion Block"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.242,
+                0.892,
+                0.492
+            ],
+            "angle": 0,
+            "content": "To better integrate the merits of CNN and transformer (HFERB and SRWAB), we have designed a hybrid fusion block (HFB), which is illustrated in Figure 2. We formulate the output of HFERB as the high frequency prior query and the output of SRWAB as key, value and calculate the inter-attention to refine the global features which are obtained from SRWAB. Moreover, most existing methods focus on spatial relations and overlook channel information. To overcome this limitation, we perform inter-attention based on the channel dimension to explore channel dependencies. This design will significantly reduce complexity. Traditional methods that utilize spatial attention tend to result in significant computational complexity (e.g., \\(O(N^2 C)\\), \\(N \\gg C\\)), where \\(N\\) represents the length of the sequence and \\(C\\) represents the channel dimension. In contrast, our channel attention design can transfer the quadratic component to the channel dimension (e.g., \\(O(NC^2)\\)), effectively reducing complexity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.893,
+                0.643
+            ],
+            "angle": 0,
+            "content": "Specifically, as shown in Figure 2, we use a \\(1\\times 1\\) convolutional layer followed by a \\(3\\times 3\\) depth-wise convolutional layer to generate the high frequency query \\(\\pmb{Q}\\in \\mathbb{R}^{H\\times W\\times C}\\) based on the output of HFERB, \\(X_{H}\\). As to the output of SRWAB, \\(X_{S}\\), we first normalize the features by LayerNorm layer and then use the same operation as the query \\(\\pmb{Q}\\) to get the key \\(\\pmb {K}\\in \\mathbb{R}^{H\\times W\\times C}\\) and the value \\(\\pmb {V}\\in \\mathbb{R}^{H\\times W\\times C}\\). Following the [42], we perform the reshape operation on \\(\\pmb{Q}\\), \\(\\pmb{K}\\) and \\(\\pmb{V}\\) to get the \\(\\hat{\\pmb{Q}}\\in \\mathbb{R}^{C\\times (HW)}\\), \\(\\hat{\\pmb{K}}\\in \\mathbb{R}^{C\\times (HW)}\\) and \\(\\hat{\\pmb{V}}\\in \\mathbb{R}^{C\\times (HW)}\\). After that, we compute the inter-attention as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.525,
+                0.647,
+                0.892,
+                0.678
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A t t e n t i o n} (\\hat {\\boldsymbol {Q}}, \\hat {\\boldsymbol {K}}, \\hat {\\boldsymbol {V}}) = \\operatorname {S o f t m a x} \\left(\\frac {\\hat {\\boldsymbol {Q}} \\hat {\\boldsymbol {K}} ^ {T}}{\\alpha}\\right) \\hat {\\boldsymbol {V}}, \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.682,
+                0.892,
+                0.793
+            ],
+            "angle": 0,
+            "content": "where the \\(\\alpha\\) represents the learnable parameter. Meanwhile, we add the refinement features to the \\(X_{S}\\) to get the fusion output \\(X_{fuse}\\). In addition, we feed \\(X_{fuse}\\) to an improved feed-forward network [42] to aggregate the features further. The details of this structure are shown in Figure 2. It introduced a gate mechanism to fully extract the spatial and channel information and gain better performance. The whole process can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.54,
+                0.8,
+                0.892,
+                0.821
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {f u s e} = \\text {I n t e r - A t t e n} (L N \\left(X _ {S}\\right), X _ {H}) + X _ {S} \\tag {13}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.54,
+                0.818,
+                0.773,
+                0.833
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {H F B} = I M L P (L N (X)) + X _ {f u s e},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.839,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "where the \\(LN\\) means LayerNorm operation, IMLP represents the improved MLP, and Inter-Atten indicates"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.887,
+                0.506,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12518"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.123,
+                0.892,
+                0.147
+            ],
+            "angle": 0,
+            "content": "Table 1. Performance comparison of different SISR models on five benchmarks. Params represents the total number of network parameters. Results for the best and second best candidates are highlighted, and underlined."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.148,
+                0.88,
+                0.523
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Scale</td><td>Model</td><td>Params</td><td>Set5 (PSNR/SSIM)</td><td>Set14 (PSNR/SSIM)</td><td>BSD100 (PSNR/SSIM)</td><td>Urban100 (PSNR/SSIM)</td><td>Manga109 (PSNR/SSIM)</td></tr><tr><td rowspan=\"10\">×2</td><td>EDSR-baseline [23]</td><td>1370K</td><td>37.99/0.9604</td><td>33.57/0.9175</td><td>32.16/0.8994</td><td>31.98/0.9272</td><td>38.54/0.9769</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>37.76/0.9590</td><td>33.52/0.9166</td><td>32.09/0.8978</td><td>31.92/0.9256</td><td>38.36/0.9765</td></tr><tr><td>IMDN [13]</td><td>694K</td><td>38.00/0.9605</td><td>33.63/0.9177</td><td>32.19/0.8996</td><td>32.17/0.9283</td><td>38.88/0.9774</td></tr><tr><td>LatticeNet [26]</td><td>756K</td><td>38.06/0.9607</td><td>33.70/0.9187</td><td>32.20/0.8999</td><td>32.25/0.9288</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>548k</td><td>38.01/0.9605</td><td>33.62/0.9183</td><td>32.19/0.8999</td><td>32.10/0.9283</td><td>38.67/0.9772</td></tr><tr><td>HPUN-L [34]</td><td>714K</td><td>38.09/0.9608</td><td>33.79/0.9198</td><td>32.25/0.9006</td><td>32.37/0.9307</td><td>39.07/0.9779</td></tr><tr><td>SwinIR-light [21]</td><td>878K</td><td>38.14/0.9611</td><td>33.86/0.9206</td><td>32.31/0.9012</td><td>32.76/0.9340</td><td>39.12/0.9783</td></tr><tr><td>ESRT [25]</td><td>777K</td><td>38.03/0.9600</td><td>33.75/0.9184</td><td>32.25/0.9001</td><td>32.58/0.9318</td><td>39.12/0.9774</td></tr><tr><td>ELAN-light [44]</td><td>582K</td><td>38.17/0.9611</td><td>33.94/0.9207</td><td>32.30/0.9012</td><td>32.76/0.9340</td><td>39.11/0.9782</td></tr><tr><td>CRAFT (Ours)</td><td>737K</td><td>38.23/0.9615</td><td>33.92/0.9211</td><td>32.33/0.9016</td><td>32.86/0.9343</td><td>39.39/0.9786</td></tr><tr><td rowspan=\"11\">×3</td><td>EDSR-baseline [23]</td><td>1555K</td><td>34.37/0.9270</td><td>30.28/0.8417</td><td>29.09/0.8052</td><td>28.15/0.8527</td><td>33.45/0.9439</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>34.29/0.9255</td><td>30.29/0.8407</td><td>29.06/0.8034</td><td>28.06/0.8493</td><td>33.50/0.9440</td></tr><tr><td>IMDN [13]</td><td>703K</td><td>34.36/0.9270</td><td>30.32/0.8417</td><td>29.09/0.8046</td><td>28.17/0.8519</td><td>33.61/0.9445</td></tr><tr><td>LatticeNet [26]</td><td>765K</td><td>34.53/0.9281</td><td>30.39/0.8424</td><td>29.15/0.8059</td><td>28.33/0.8538</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>544k</td><td>34.36/0.9267</td><td>30.34/0.8421</td><td>29.11/0.8054</td><td>28.15/0.8523</td><td>33.51/0.9441</td></tr><tr><td>HPUN-L [34]</td><td>723K</td><td>34.56/0.9281</td><td>30.45/0.8445</td><td>29.18/0.8072</td><td>28.37/0.8572</td><td>33.90/0.9463</td></tr><tr><td>SwinIR-light [21]</td><td>886K</td><td>34.62/0.9289</td><td>30.54/0.8463</td><td>29.20/0.8082</td><td>28.66/0.8624</td><td>33.98/0.9478</td></tr><tr><td>LBNet [9]</td><td>736K</td><td>34.47/0.277</td><td>30.38/0.8417</td><td>29.13/0.8061</td><td>28.42/0.8559</td><td>33.82/0.9406</td></tr><tr><td>ESRT [25]</td><td>770K</td><td>34.42/0.9268</td><td>30.43/0.8433</td><td>29.15/0.8063</td><td>28.46/0.8574</td><td>33.95/0.9455</td></tr><tr><td>ELAN-light [44]</td><td>590K</td><td>34.61/0.9288</td><td>30.55/0.8463</td><td>29.21/0.8081</td><td>28.69/0.8624</td><td>34.00/0.9478</td></tr><tr><td>CRAFT (Ours)</td><td>744K</td><td>34.71/0.9295</td><td>30.61/0.8469</td><td>29.24/0.8093</td><td>28.77/0.8635</td><td>34.29/0.9491</td></tr><tr><td rowspan=\"11\">×4</td><td>EDSR-baseline [23]</td><td>1518K</td><td>32.09/0.8938</td><td>28.58/0.7813</td><td>27.57/0.7357</td><td>26.04/0.7849</td><td>30.35/0.9067</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>32.13/0.8937</td><td>28.60/0.7806</td><td>27.58/0.7349</td><td>26.07/0.7837</td><td>30.47/0.9084</td></tr><tr><td>IMDN [13]</td><td>715K</td><td>32.21/0.8948</td><td>28.58/0.7811</td><td>27.56/0.7353</td><td>26.04/0.7838</td><td>30.45/0.9075</td></tr><tr><td>LatticeNet [26]</td><td>777K</td><td>32.18/0.8943</td><td>28.61/0.7812</td><td>27.57/0.7355</td><td>26.14/0.7844</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>659k</td><td>32.15/0.8944</td><td>28.61/0.7818</td><td>27.61/0.7366</td><td>26.14/0.7871</td><td>30.42/0.9074</td></tr><tr><td>HPUN-L [34]</td><td>734K</td><td>32.31/0.8962</td><td>28.73/0.7842</td><td>27.66/0.7386</td><td>26.27/0.7918</td><td>30.77/0.9109</td></tr><tr><td>SwinIR-light [21]</td><td>897K</td><td>32.44/0.8976</td><td>28.77/0.7858</td><td>27.69/0.7406</td><td>26.47/0.7980</td><td>30.92/0.9151</td></tr><tr><td>LBNet [9]</td><td>742K</td><td>32.29/0.8960</td><td>28.68/0.7832</td><td>27.62/0.7382</td><td>26.27/0.7906</td><td>30.76/0.9111</td></tr><tr><td>ESRT [25]</td><td>751K</td><td>32.19/0.8947</td><td>28.69/0.7833</td><td>27.69/0.7379</td><td>26.39/0.7962</td><td>30.75/0.9100</td></tr><tr><td>ELAN-light [44]</td><td>601K</td><td>32.43/0.8975</td><td>28.78/0.7858</td><td>27.69/0.7406</td><td>26.54/0.7982</td><td>30.92/0.9150</td></tr><tr><td>CRAFT (Ours)</td><td>753K</td><td>32.52/0.8989</td><td>28.85/0.7872</td><td>27.72/0.7418</td><td>26.56/0.7995</td><td>31.18/0.9168</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.53,
+                0.47,
+                0.559
+            ],
+            "angle": 0,
+            "content": "the proposed inter-attention mechanism, which introduces high-frequency prior to refining the global representations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.571,
+                0.21,
+                0.587
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.593,
+                0.248,
+                0.607
+            ],
+            "angle": 0,
+            "content": "5.1. Data and Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.615,
+                0.47,
+                0.725
+            ],
+            "angle": 0,
+            "content": "In this paper, we adopt the DIV2K [1] as the training dataset, which includes 800 training images. Meanwhile, five benchmarks are used for evaluation, including Set5 [3], Set14 [43], BSD100 [27], Urban100 [12], and Manga109 [28] with three magnification factors: \\(\\times 2\\), \\(\\times 3\\), and \\(\\times 4\\). The quality of the images is evaluated using PSNR, and SSIM [39]. The complexity of the model is indicated by its parameters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.735,
+                0.295,
+                0.75
+            ],
+            "angle": 0,
+            "content": "5.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.756,
+                0.47,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Following the general setting, we use bicubic to obtain the corresponding LR images from the original HR images. During training, we randomly crop the images into \\(64 \\times 64\\) patches, and the total training iterations are \\(500\\mathrm{K}\\). Meanwhile, data augmentation is performed, such as random horizontal flipping and \\(90^{\\circ}\\) rotation. The Adam optimizer with \\(\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999\\) is adopted to minimize the \\(\\mathcal{L}_1\\) Loss. The batch size is set to 64, the initial learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.53,
+                0.892,
+                0.683
+            ],
+            "angle": 0,
+            "content": "rate is set to \\(2 \\times 10^{-4}\\) and reduced by half at the milestone [250K, 400K, 450K, 475K]. In addition, the model is trained on 4 NVIDIA 3090 GPUs using the PyTorch toolbox. In CRAFT, we have set the RCRFG number to 4 and the CRFB number to 2 for each RCRFG. Each CRFB is comprised of 1 HFERB and 2 SRWABs for efficiency. The feature channel, attention head, and MLP expansion ratio are set to 48, 6, and 2, respectively. We also set the IMLP expansion ratio to 2.66, as in [42]. To obtain two types of rectangle windows, we have set the rectangle window size to \\([sh, sw]\\) as [4, 16] and [16, 4]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.692,
+                0.86,
+                0.707
+            ],
+            "angle": 0,
+            "content": "5.3. Comparison with state-of-the-art methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.714,
+                0.892,
+                0.783
+            ],
+            "angle": 0,
+            "content": "We compare with several state-of-the-art SISR methods to demonstrate the effective of the proposed CRAFT model, including EDSR [23], CARN [2], IMDN [13], LatticeNet [26], LAPAR [19], SwinIR [21], HPUN [34], ESRT [25], LBNet [9], and ELAN [44]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.784,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Quantitative Results. The experimental results for SISR are presented in Table 1, where the proposed CRAFT model demonstrates competitive performance across all benchmarks. Particularly, when compared to traditional CNN-based methods like EDSR, the proposed CRAFT achieves significant performance improvements of \\(0.85\\mathrm{dB}\\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.887,
+                0.506,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12519"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.116,
+                0.121,
+                0.311,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.182,
+                0.225,
+                0.255,
+                0.235
+            ],
+            "angle": 0,
+            "content": "Img012 \\((\\times 4)\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.322,
+                0.122,
+                0.449,
+                0.168
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.365,
+                0.168,
+                0.407,
+                0.177
+            ],
+            "angle": 0,
+            "content": "Bicubic"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.456,
+                0.122,
+                0.585,
+                0.168
+            ],
+            "angle": 0,
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+            "content": "ESRT [25]"
+        },
+        {
+            "type": "image",
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+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "CRAFT (Ours)"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "HR"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Figure 3. Visual quality comparison with SOTA methods. CRAFT achieves better restoration quality in both line direction and details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.496,
+                0.47,
+                0.676
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+            "angle": 0,
+            "content": "0.84dB, and 0.83dB at magnification factors \\(\\times 2\\), \\(\\times 3\\), and \\(\\times 4\\), respectively, while using \\(46\\%\\), \\(52\\%\\), and \\(50\\%\\) fewer parameters on the Manga109 dataset. Furthermore, compared to recent channel attention methods such as CARN, the proposed CRAFT achieves improvements of 1.03dB, 0.79dB, and 0.71dB at magnification factors \\(\\times 2\\), \\(\\times 3\\), and \\(\\times 4\\), respectively, with a \\(54\\%\\), \\(53\\%\\), and \\(52\\%\\) reduction in the number of parameters on the Manga109 dataset. Regarding transformer-based methods [25, 21, 44], the proposed CRAFT gains performance improvements of 0.34dB, 0.31dB, and 0.29dB, respectively, with a comparable number of parameters under the magnification factor of \\(\\times 3\\) on the Manga109 dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.687,
+                0.471,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Qualitative Results. We present a visual comparison \\((\\times 4)\\) in Figure 3 and analyze the results. Our proposed CRAFT model integrates the strengths of both CNN and transformer structures, leading to accurate line direction recovery while preserving image details. To further investigate the performance, we compare the local attribution map (LAM) [11] between CRAFT and SwinIR, as shown in Figure 4. LAM indicates the correlation between the significance of each pixel in LR and the SR of the patch that is outlined with the red box. By leveraging a broader range of information, our model achieves improved results. Furthermore, we examine the diffusion index (DI), which signifies the range of pixels involved. A larger DI indicates a"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.496,
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+                0.552
+            ],
+            "angle": 0,
+            "content": "wider scope of attention. Compared to SwinIR, our model exhibits a higher DI, implying that it can capture more contextual information. These results demonstrate the effectiveness of the proposed CRAFT method."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5.4. Ablation study"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5.4.1 Effectiveness of HFERB and SRWAB"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "We conduct several experiments to show the effectiveness of HFERB and SRWAB in Table 2. Specifically, we removed SRWAB and HFERB separately to assess their contributions. We observed that using local or global information alone, as in \\(\\mathrm{CRAFT}_{conv}\\) and \\(\\mathrm{CRAFT}_{transformer}\\), respectively, is insufficient to learn a better representation (lower performance). Furthermore, we found that SRWAB provides the most significant performance improvement, demonstrating the benefits of the long-range dependencies learned by the transformer. In addition, high-frequency priors from CNN are also helpful in restoring details, cross-refining learned features and further improving performance. Meanwhile, we also analyzed the properties of HFERB and SRWAB from a frequency perspective. We visualized the features extracted from two blocks in different RCRFGs and plotted the Fourier spectrum to observe what each block learns. The results, shown in Figure 5, indicate that HFERB focuses more on high-frequency information, while SRWAB extracts more global informa"
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+        },
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+        },
+        {
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+            "bbox": [
+                0.076,
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+                0.497
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+            "angle": 0,
+            "content": "Figure 4. Comparison of the LAM results of SwinIR [21] and CRAFT. LAM indicates the correlation between the significance of each pixel in LR and the SR of the patch that is outlined with the red box. CRAFT utilizes a broader range of information to obtain better performance. DI quantifies the LAM results, CRAFT has a higher DI score, indicating its ability to capture more contextual information."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
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+            "angle": 0,
+            "content": "Table 2. Study of HFERB, SRWAB, and HFB on SISR. The results \\((\\times 4)\\) are obtained from the Manga109 dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "content": "<table><tr><td>Model</td><td>HFERB</td><td>SRWAB</td><td>HFB</td><td>Concat</td><td>PSNR</td></tr><tr><td>CRAFTconv</td><td>✓</td><td></td><td>✓</td><td></td><td>30.79</td></tr><tr><td>CRAFTtransformer</td><td></td><td>✓</td><td>✓</td><td></td><td>31.12</td></tr><tr><td>CRAFTconcat</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>30.92</td></tr><tr><td>CRAFT</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>31.18</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "tion. Specifically, the top row of each image indicates the Fourier spectrum of each block, and the bottom row indicates the feature maps of each block. The figure shows that SRWAB has a weaker response and focuses more on the low-frequency parts, which correspond to flat regions, while HFERB shows a stronger response and focuses more on intricate parts of features, such as edges and corners. The feature maps on the bottom row also support this conclusion. HFERB captures more details such as window edges and cornices, while SRWAB pays more attention to flat areas such as windows and walls."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5.4.2 Effectiveness of HFB"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
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+            ],
+            "angle": 0,
+            "content": "To evaluate the effectiveness of HFB, we conducted an experiment where we modified the fusion method to a concatenation formulation. This involved concatenating the"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
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+            ],
+            "angle": 0,
+            "content": "Table 3. Effectiveness of high-frequency prior. The results \\((\\times 4)\\) are obtained from the Manga109 dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Regular</td><td>Swap</td><td>Cascade</td><td>PSNR</td><td>SSIM</td></tr><tr><td>CRAFTswap</td><td></td><td>✓</td><td></td><td>30.67</td><td>0.9113</td></tr><tr><td>CRAFT cascade</td><td></td><td></td><td>✓</td><td>30.88</td><td>0.9141</td></tr><tr><td>CRAFT</td><td>✓</td><td></td><td></td><td>31.18</td><td>0.9168</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.545,
+                0.608,
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+            "angle": 0,
+            "content": "Table 4. Complexity analysis compared to SwinIR."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.503,
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+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>#Params. (K)</td><td>#FLOPs (G)</td><td>#GPU Mem. (M)</td><td>Ave. Time (ms)</td></tr><tr><td>SwinIR</td><td>897</td><td>32.2</td><td>141.2</td><td>72.0</td></tr><tr><td>CRAFT</td><td>753</td><td>26.1</td><td>79.5</td><td>42.8</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "HFERB and SRWAB output and replacing the HFB with a \\(3 \\times 3\\) convolutional layer to obtain the final output. The results are presented in Table 2, where \\(\\mathrm{CRAFT}_{\\text {concat }}\\) denotes the modified version. The result shows that our proposed method outperforms the concatenation structure by \\(0.26\\mathrm{dB}\\), demonstrating the effectiveness of our HFB. The observed result can be attributed to SRWAB and HFERB focusing on disparate frequency information. Stacking features directly impedes the ability of the network to learn the relationship between high-frequency and low-frequency components. Conversely, the inter-attention mechanism presents a viable solution for integrating features with different distributions."
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+            "bbox": [
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+            "angle": 0,
+            "content": "(a) Visualization of the spectrum of the 2nd RCRFG"
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+            "content": "HPE LFE SW with Altex (c) Visualization of the spectrum of the 4th RCFG"
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+        {
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+        {
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+        },
+        {
+            "type": "image",
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+        },
+        {
+            "type": "image",
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+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "LFE"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.783,
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+            "angle": 0,
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+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "SRWin-Attention"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "(d) Visualization of the feature of the 4th RCFIG"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "LR Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "HFE"
+        },
+        {
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+            "bbox": [
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+        {
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+            "bbox": [
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+        {
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+        {
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+        {
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+        {
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+        {
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+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
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+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "SRWin-Attention"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.359,
+                0.293,
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+            "angle": 0,
+            "content": "(e) Visualization of the spectrum of the 2nd RCRFG"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "content": "HFE"
+        },
+        {
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+            "content": "LFE"
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+        {
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+            "bbox": [
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+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "SRWin-Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "HFE"
+        },
+        {
+            "type": "image",
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+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "LFE"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.803,
+                0.344,
+                0.858,
+                0.349
+            ],
+            "angle": 0,
+            "content": "SRWin-Attention"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.363,
+                0.35,
+                0.565,
+                0.358
+            ],
+            "angle": 0,
+            "content": "(f) Visualization of the feature of the 2nd RCRFG"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.638,
+                0.35,
+                0.838,
+                0.358
+            ],
+            "angle": 0,
+            "content": "(h) Visualization of the feature of the 4th RCRFG"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.363,
+                0.892,
+                0.389
+            ],
+            "angle": 0,
+            "content": "Figure 5. Visualization of HFERB and SRWAB. The LFE indicates the local feature extraction branch in HFERB, the HFE means the high-frequency enhancement branch in HFERB, and the SRWin-Attention represents the self-attention part in SRWAB."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.395,
+                0.398,
+                0.41
+            ],
+            "angle": 0,
+            "content": "5.4.3 Effectiveness of High-Frequency Prior"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.418,
+                0.471,
+                0.64
+            ],
+            "angle": 0,
+            "content": "We conducted several experiments to investigate the effectiveness of high-frequency prior. Firstly, we swapped the input of \\( Q \\) and \\( K \\), \\( V \\) in HFB and treated the output of SRWAB as \\( Q \\) and the output of HFERB as \\( K \\), \\( V \\) to verify whether global features are dominant in restoration and high-frequency features only serve as a prior for refining the global representation. As shown in Table 3, compared to the original design, swapping the input leads to a significant drop in performance, with a 0.51dB decrease in PSNR. Furthermore, we also performed an experiment to formulate the model as a cascade structure to verify the effectiveness of the design introducing high-frequency priors. As shown in Table 3, the \\( \\mathrm{CRAFT}_{\\text{ cascade}} \\) structure resulted in a performance drop, with a 0.3dB decrease in PSNR compared to CRAFT. These results demonstrate the effectiveness of high-frequency priors in the CRAFT model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.651,
+                0.272,
+                0.666
+            ],
+            "angle": 0,
+            "content": "5.4.4 Complexity analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.673,
+                0.47,
+                0.867
+            ],
+            "angle": 0,
+            "content": "We compared CRAFT with SwinIR in terms of complexity using an input size of \\(128 \\times 128\\), as shown in Table 4. The analysis considered parameters, FLOPs, GPU memory consumption, and average inference time. GPU memory was measured using the official PyTorch function, and time cost was calculated based on 100 inference runs. Compared to SwinIR, CRAFT has fewer parameters and FLOPs, and requires less memory consumption and inference time. Additionally, we analyzed the complexity of our CRAFT framework and summarized the findings in Table 5. We observed that SRWAB contributes approximately \\(46\\%\\) of the total complexity, while HFERB involves fewer convolution operations, resulting in reduced FLOPs. Furthermore, the HFB module's channel-wise attention effectively reduces"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.565,
+                0.392,
+                0.826,
+                0.404
+            ],
+            "angle": 0,
+            "content": "Table 5. Complexity analysis of each block."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>CRAFT\nw/o HFERB</td><td>CRAFT\nw/o SRWAB</td><td>CRAFT\nw/o HFB</td><td>CRAFT</td></tr><tr><td>#Params. (K)</td><td>688</td><td>441</td><td>503</td><td>753</td></tr><tr><td>#FLOPs (G)</td><td>23.8</td><td>14.2</td><td>20.0</td><td>26.1</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.464,
+                0.675,
+                0.477
+            ],
+            "angle": 0,
+            "content": "the computational burden."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.49,
+                0.618,
+                0.504
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.513,
+                0.892,
+                0.775
+            ],
+            "angle": 0,
+            "content": "This paper investigates the impact of frequency on the performance of CNN and transformer structures in SISR and finds that transformer structures are more adept at capturing low-frequency information, but have limited capability to reconstruct high-frequency representations compared to CNN. To address this issue, we design a feature modulation transformer, named cross-refinement adaptive feature modulation transformer (CRAFT), which comprises three key components: the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB). The HFERB is designed to extract high-frequency features, while the SRWAB captures global representations. In the HFB, we treat the output of HFERB as a high-frequency prior and the output of SRWAB as key and value, and use interattention to refine the global representation. Experimental results demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB with relatively fewer parameters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.788,
+                0.667,
+                0.804
+            ],
+            "angle": 0,
+            "content": "Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "This work is supported by the National Natural Science Foundation of China (NSFC) under Grant U19A2052 and Grant 62020106011, as well as by the National Key Lab of Autonomous Intelligent Unmanned Systems."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.887,
+                0.506,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12522"
+        }
+    ],
+    [
+        {
+            "type": "title",
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+                0.139
+            ],
+            "angle": 0,
+            "content": "References"
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+# Feature Modulation Transformer: Cross-Refinement of Global Representation via High-Frequency Prior for Image Super-Resolution
+
+Ao Li $^{1}$ , Le Zhang $^{1*}$ , Yun Liu $^{2}$ , Ce Zhu $^{1}$
+
+<sup>1</sup>University of Electronic Science and Technology of China, <sup>2</sup>I2R, A*STAR
+
+aoli@std.uestc.edu.cn, {lezhang,eczhu}@uestc.edu.cn, vagrantlyun@gmail.com
+
+# Abstract
+
+Transformer-based methods have exhibited remarkable potential in single image super-resolution (SISR) by effectively extracting long-range dependencies. However, most of the current research in this area has prioritized the design of transformer blocks to capture global information, while overlooking the importance of incorporating high-frequency priors, which we believe could be beneficial. In our study, we conducted a series of experiments and found that transformer structures are more adept at capturing low-frequency information, but have limited capacity in constructing high-frequency representations when compared to their convolutional counterparts. Our proposed solution, the cross-refinement adaptive feature modulation transformer (CRAFT), integrates the strengths of both convolutional and transformer structures. It comprises three key components: the high-frequency enhancement residual block (HFERB) for extracting high-frequency information, the shift rectangle window attention block (SRWAB) for capturing global information, and the hybrid fusion block (HFB) for refining the global representation. Our experiments on multiple datasets demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB while using fewer parameters. The source code will be made available at: https://github.com/AVC2-UESTC/CRAFT-SR.git.
+
+# 1. Introduction
+
+Single image super-resolution (SISR) has garnered significant attention in recent years, owing to its promising applications across diverse domains, such as surveillance video and medical image enhancement [31, 10], old image reconstruction [21, 17], and efficient image transmission [47]. Despite its practical value, SISR remains an ill-posed problem, given the existence of multiple solutions for a given low-resolution (LR) image. To tackle this challenge,
+
+a multitude of classical approaches have been proposed, including  $\mathrm{A + }$  [36], SC [41], and ANR [35]. However, these methods exhibit limitations in their performance, primarily attributed to their constrained model capacities.
+
+In recent years, deep learning has experienced significant growth and demonstrated remarkable success in SISR [7, 20, 45, 22]. Prior research efforts have introduced residual and dense connectives to facilitate the stacking of deep convolutional neural networks (CNNs) [16, 37], while others [46, 40, 29, 30] have leveraged attention mechanisms to enhance performance. Notably, the emergence of transformer architectures has demonstrated their efficacy in capturing long-range dependencies and attaining state-of-the-art performance [21, 6, 4, 18, 25]. Despite these advancements, these works have mainly focused on designing transformer blocks to obtain global information and overlooked the potential of incorporating high-frequency priors [32, 8] to further bolster performance in SISR. Additionally, there is limited detailed analysis of the impact of frequency on performance.
+
+In this paper, we investigate the influence of high-frequency information on the performance of CNN and transformer structures in SISR. We achieve this by discarding different ratios of high-frequency components from the input image and observing the corresponding performance changes. Our empirical findings reveal that transformers tend to prioritize low-frequency information and exhibit limited capability in constructing high-frequency representations when compared to CNNs. To address this issue, we proposed a cross-refinement adaptive feature modulation transformer (CRAFT) that integrates the strengths of both structures. Specifically, CRAFT comprises three key components, namely the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB), which work collaboratively to capture high-frequency details, extract long-range dependencies, and refine the output for better representation. Experimental results show that CRAFT outperforms state-of-the-art performance with relatively fewer parameters. The main contributions of this paper are as fol
+
+lows:
+
+- We study the impact of CNN and transformer structures on performance from a frequency perspective and observe that transformer is more effective in capturing low-frequency information while having limited capacity for constructing high-frequency representations compared to CNN.  
+- Based on the observation, we design a parallel structure to explore different frequency features. We utilize the HFERB branch to introduce high-frequency information, which is beneficial to SISR, and the SRWAB branch to acquire global information.  
+- We propose a fuse strategy that integrates the strengths of CNN and transformer. Specifically, we treat the HFERB branch as high-frequency prior and the output of SRWAB as key and value for inter-attention, resulting in improved performance.  
+- Extensive experimental results on multiple datasets show that the proposed method performs on par with the existing state-of-the-art SISR methods while using fewer parameters.
+
+# 2. Related Works
+
+# 2.1. CNN-based SISR
+
+Since the pioneering work SRCNN [7] has achieved significant progress in SISR, various CNN-based works have been proposed. Kim et al. [15] presented an SR method using deep networks by cascading 20 layers, demonstrating promising results. Building upon this, Lim et al. [23] introduced the enhanced deep super-resolution (EDSR) network, which achieved a significant performance boost by removing the batch normalization layer [14] from the residual block and incorporating additional convolution layers. Ahn et al. [2] designed an architecture with an increased number of residual blocks and dense connections, further improving the SR performance. In pursuit of lightweight models, Hui et al. [13] proposed a selective fusion approach, employing cascaded information multi-distillation blocks to construct an efficient model. Li et al. [19] introduced a method involving predefined filters and utilized a CNN to learn coefficients, which were then linearly combined to obtain the final results. Sun et al. [34] proposed a hybrid pixel-unshuffled network (HPUN) by introducing an efficient and effective downsampling module into the SR task.
+
+# 2.2. Transformer-based SISR
+
+Liang et al. [21] proposed SwinIR, a robust baseline model for image restoration, leveraging the Swin Trans
+
+former [24]. CAT [6] modified the window shape and introduced a rectangle window attention to obtaining better performance. Chen et al. [4] proposed a pre-trained image processing transformer and showed that pre-trained mechanism could significantly improve the performance for low-level tasks. Li et al. [18] comprehensively analyzed the effect of pre-training and proposed a versatile model to tackle different low-level tasks. Lu et al. [25] proposed a lightweight transformer to capture long-range dependencies between similar patches in an image with the help of the specially designed efficient transformer and efficient attention mechanism. Zhang et al. [44] introduced a shift convolution and a group-wise multi-scale self-attention to reduce the complexity of transformer. HAT [5] introduced a hybrid attention mechanism to enhance the performance of window-based transformers.
+
+# 3. Analysis of Frequency Impact
+
+This section delves into the influence of performance from a frequency perspective. To analyze the impact of various frequencies on CNN and transformer, we conduct two sets of experiments using four common used benchmarks, as illustrated in Figure 1.
+
+We select CARN [2], IMDN [13], EDSR [23], and SwinIR [21], CAT [6], HAT [5] as representatives of CNN and transformer structures. The process of dropping frequency components is depicted in Figure 1(c). Given a high-resolution (HR) image  $X^{HR}$ , we perform a fast Fourier transform (FFT) on it to obtain its frequency spectrum. Subsequently, we flatten this spectrum into a sequence and arrange it in ascending order based on the magnitudes. With a sequence length of  $L$ , we define a threshold determined by the drop ratio  $\gamma$ ,  $0 \leq \gamma \leq 1$ , located at the magnitude corresponding to the position  $\gamma \cdot L$ . Frequency components with magnitudes below this threshold are set to zero. Following this, we perform an inverse fast Fourier transform (IFFT) to generate the HR image with dropped frequencies, referred to as  $X_{drop}^{HR}(\gamma)$ . The formulation for this process is as follows
+
+$$
+X _ {d r o p} ^ {H R} (\gamma) = I F F T (D r o p \left(\left| F F T \left(X ^ {H R}\right) \right|, \gamma)\right). \tag {1}
+$$
+
+Afterward, we downsample  $X_{drop}^{HR}(\gamma)$  using bicubic interpolation to obtain the LR version  $X_{drop}^{LR}(\gamma)$  (e.g.  $\times 4$  down-sampling). Finally, we employ CNN-based and transformer-based SR models to generate the super-resolved counterpart  $X_{drop}^{SR}(\gamma)$ .
+
+To analyze the dependency of CNN and transformer on high-frequency information, we compute the peak signal-to-noise ratio (PSNR)  $P^{D}(\gamma)$  between  $X_{drop}^{SR}(\gamma)$  and  $X_{drop}^{HR}$ . We then plot the PSNR drop trend to visualize the difference between the two structures. As shown in Figure 1(a), the PSNR drop ratio for each drop ratio is defined
+
+![](images/648fc695cb737893a695877192d32b3052c591287d9511d4c42a1c8e674d1403.jpg)
+
+![](images/069fe64e7fe1eb334081d2ad88952db8b0b68b191bc0908c8bbed89a821c1c59.jpg)  
+(a) Dependency of different structures on high-frequency information.
+
+![](images/d6afe61221bfc4572297c54174e287fd5c61c254ae7b2fee78b849c0a8e264a2.jpg)
+
+![](images/8ef01f291728dc5b48d43e204c83cb58090a60cfd760e20e221d2ac264618ab3.jpg)
+
+![](images/473cf9228e4ebf9f482d172f3dce520dd09866d0c94e1477ce36ef4c3b2a78f4.jpg)
+
+![](images/32f04f4bd5c0c05c8bf9fade37952dcb8f0b51e9ff10e8647a4881f18799b55c.jpg)  
+(b) Effectiveness of reconstructing high-frequency information.
+
+![](images/e5532c51a66d35fb17d43da1d99957be99eaac66632f1a7a6c69bba5b3b3d35e.jpg)
+
+![](images/3e91ec8d6fc29965691472ed79f50454bfeb5b0d3a393598a26b7f047d3c3399.jpg)
+
+![](images/09ddec8e32b675e128e76acc080c3cf256b5911981a6ece9631fcd3ba87f2425.jpg)  
+(c) The procedure of dropping high-frequency.  
+Figure 1. The influence of high-frequency information on the performance of CNN and transformer architectures. Dashed and solid lines correspond to CNN and transformer methods, respectively. (a) With an increase in the high-frequency drop ratio, transformer models exhibit a smaller change in PSNR compared to CNN, suggesting their superiority in capturing low-frequency information. (b) As the high-frequency drop ratio increases, transformer models show a more pronounced change in PSNR compared to CNN, indicating their limited ability to reconstruct high-frequency information from low-frequency.
+
+as
+
+$$
+R _ {d r o p} ^ {D} (\gamma) = \frac {P (0) - P ^ {D} (\gamma)}{P (0)}, \tag {2}
+$$
+
+where  $P(0)$  represents the PSNR without dropping, calculated between  $X^{SR}$  and  $X^{HR}$ . The figures illustrate that the transformer model exhibits reduced sensitivity to high-frequency information and excels in capturing low-frequency information, as evidenced by the smaller PSNR change compared to the CNN model as the proportion of discarded high-frequency information increases.
+
+Furthermore, we conduct another experiment to evaluate the effectiveness of different structures in reconstructing high-frequency information. Specifically, we calculate the PSNR  $P^{E}(\gamma)$  between  $X_{drop}^{SR}(\gamma)$  and  $X^{HR}$  and plot the performance drop trend as previously depicted. The PSNR drop ratio for each drop ratio can be expressed as
+
+$$
+R _ {d r o p} ^ {E} (\gamma) = \frac {P ^ {E} (\gamma) - P (0)}{P (0)}. \tag {3}
+$$
+
+From Figure 1(b), we observe that as the proportion of discarded high-frequency information increases, the transformer model experiences a larger PSNR change compared
+
+to the CNN model, indicating its limited ability to reconstruct high-frequency information from low-frequency.
+
+Based on these observations, we argue that the transformer requires the assistance of CNN to enhance its capability to recover intricate details. To address this, we propose a method that combines the strengths of both CNN and transformer. Specifically, we introduce CNN information as a high-frequency prior to aid the transformer in refining the global representation.
+
+# 4. Proposed Method
+
+The CRAFT network comprises three key components: Shallow feature extraction, residual cross-refinement fusion groups (RCRFGs), and reconstruction as shown in Figure 2. The shallow feature extraction module comprises a single convolutional layer, while the reconstruction module is followed by the SwinIR [21]. The RCRFG component consists of several cross-refinement fusion blocks (CRFBs), each comprising three types of blocks: the high-frequency enhancement residual blocks (HFERBs), the shift rectangle window attention blocks (SRWABs), and the hybrid fusion blocks (HFBs). We first describe the overall structure of
+
+![](images/16b7cf32c72a2bc15b9df958d565e2f245d450fa5c2c3fbb223362422cbbc05f.jpg)
+
+![](images/d7fb07312b7cac3f0a784677041c3f3d296ba9b545c87e6b639ec28b812d5a5a.jpg)
+
+![](images/6acca8e4cb112b52fca9f753fd260605b0098efe6ed7ad8288191494d5fe0cf2.jpg)  
+Figure 2. The framework of CRAFT. HFERB extracts the high frequency from the input features, SRWAB captures the long-range dependency of input features, and HFB integrates the output of HFERB and SRWAB to cross refine the global features. Best viewed in color.
+
+CRAFT and then elaborate on the three key designs, including HFERB, SRWAB, and HFB.
+
+# 4.1. Model Overview
+
+The input LR image is processed by a  $3 \times 3$  convolutional layer to obtain shallow features. These features are then fed into a serial of RCRFGs to learn deep features. After the last RCRFG, a  $3 \times 3$  convolutional layer aggregates the features, and a residual connection is established between its output and the shallow features for facilitating training. The reconstruction module employs a  $3 \times 3$  convolutional layer to aggregate the features, and a shuffle layer [33] is used to obtain the final SR output image.
+
+# 4.2. High-frequency Enhancement Residual Block
+
+The HFERB aims to enhance the high-frequency information, as shown in Figure 2. It comprises the local feature extraction (LFE) branch and the high-frequency enhancement (HFE) branch. Specifically, we split the input features
+
+$F_{in}\in \mathbb{R}^{H\times W\times C}$  into two parts, and then processed by the two branches separately
+
+$$
+F _ {i n} ^ {L F E}, F _ {i n} ^ {H F E} = \operatorname {S p l i t} \left(F _ {i n}\right), \tag {4}
+$$
+
+where  $F_{in}^{LFE}, F_{in}^{HFE} \in \mathbb{R}^{H \times W \times C / 2}$  represent the input of LFE and HFE. For the LFE branch, we utilize a  $3 \times 3$  convolutional layer followed by a GELU activation function to extract local high-frequency features
+
+$$
+\hat {F} _ {i n} ^ {L F E} = f _ {a} \left(\operatorname {C o n v} _ {3 \times 3} \left(F _ {i n} ^ {L F E}\right)\right), \tag {5}
+$$
+
+where the  $Conv_{3\times 3}(\cdot)$  refers to the convolutional layer and the  $f_{a}(\cdot)$  represents the GELU activation layer. For the HFE branch, we employ a max-pooling layer to extract high-frequency information from the input features  $F_{in}^{HFE}$ . Then, we use a  $1\times 1$  convolutional layer followed by a GELU activation function to enhance the high-frequency features,
+
+$$
+\hat {F} _ {i n} ^ {H F E} = f _ {a} \left(\operatorname {C o n v} _ {1 \times 1} \left(\operatorname {M a x P o o l i n g} \left(F _ {i n} ^ {H F E}\right)\right)\right), \tag {6}
+$$
+
+where the  $Conv_{1\times 1}(\cdot)$  indicates the convolutional layer, the MaxPooling  $(\cdot)$  means the max-pooling layer and the  $f_{a}(\cdot)$  represents the GELU activation layer. The outputs of the two branches are then concatenated and fed into a  $1\times 1$  convolutional layer to fuse the information thoroughly. To make the network benefit from multi-scale information and maintain training stability, a skip connection is introduced. The whole process can be formulated as
+
+$$
+X _ {H} = C o n v _ {1 \times 1} (C o n c a t (\hat {F} _ {i n} ^ {L F E}, \hat {F} _ {i n} ^ {H F E})) + F _ {i n}, (7)
+$$
+
+where the  $\text{Concat}(\cdot)$  refers to the concatenation operation and the  $\text{Conv}_{1 \times 1}(\cdot)$  represents the convolutional layer.
+
+# 4.3. Shift Rectangle Window Attention Block
+
+We utilize the shift rectangle window (SRWin) to expand the receptive field, which can benefit SISR [6]. Unlike square windows, the SRWin uses rectangle windows to capture more relevant information along the longer axis. In detail, given an input  $X_{in} \in \mathbb{R}^{H \times W \times C}$ , we divide it into  $\frac{H \times W}{rh \times rw}$  rectangle windows, where  $rh$  and  $rw$  refer to the height and width of the rectangle window. For the  $i$ -th rectangle window feature  $X_{i} \in \mathbb{R}^{(rh \times rw) \times C}$ , we compute the query, key, and value as follows
+
+$$
+\boldsymbol {Q} _ {i} = X _ {i} W _ {i} ^ {Q}, \boldsymbol {K} _ {i} = X _ {i} W _ {i} ^ {K}, \boldsymbol {V} _ {i} = X _ {i} W _ {i} ^ {V}, \tag {8}
+$$
+
+where the  $W_{i}^{Q}\in \mathbb{R}^{C\times d}$ $W_{i}^{K}\in \mathbb{R}^{C\times d}$  and  $W_{i}^{V}\in \mathbb{R}^{C\times d}$  represent the projection matrices and  $d$  is projection dimension which is commonly set to  $d = \frac{C}{M}$  where the  $M$  is the number of heads. The self-attention can be formulated as
+
+$$
+\operatorname {A t t e n t i o n} \left(\boldsymbol {Q} _ {i}, \boldsymbol {K} _ {i}, \boldsymbol {V} _ {i}\right) = \operatorname {S o f t m a x} \left(\frac {\boldsymbol {Q} _ {i} \boldsymbol {K} _ {i} ^ {T}}{\sqrt {d}} + B\right) \boldsymbol {V} _ {i}, \tag {9}
+$$
+
+where  $B$  is the dynamic relative position encoding [38]. Moreover, a convolutional operation on the value is introduced to enhance local extraction capability. To capture information from different axes, we utilize two types of rectangle windows: Horizontal and vertical windows. Unlike traditional operations that utilize attention masks to limit calculations to the same window, in practice, we eliminate the mask and enable more extensive information interaction across different windows. Accordingly, we split the attention heads into two equal groups and compute the self-attention within each group separately. We then concatenate the outputs of the two groups to obtain the final output. The procedure can be expressed as
+
+$$
+R \operatorname {w i n} - S A (X) = \operatorname {C o n c a t} (V - R \operatorname {w i n}, H - R \operatorname {w i n}) W ^ {p}, \tag {10}
+$$
+
+where the  $W^{p}\in \mathbb{R}^{C\times C}$  represents the linear projection to fuse the features,  $V$  -Rwin and  $H$  Rwin indicate the vertical and horizontal rectangle window attention. In addition,
+
+a multi-layer perceptron (MLP) is used for further feature transformations. The whole process can be formulated as
+
+$$
+\begin{array}{l} X = R \operatorname {w i n} - S A \left(L N \left(X _ {i n}\right)\right) + X _ {i n} \\ X = M P (L N (X)) - X \end{array} \tag {11}
+$$
+
+$$
+X _ {S} = M L P (L N (X)) + X,
+$$
+
+where the  $LN$  represents the LayerNorm layer.
+
+# 4.4. Hybrid Fusion Block
+
+To better integrate the merits of CNN and transformer (HFERB and SRWAB), we have designed a hybrid fusion block (HFB), which is illustrated in Figure 2. We formulate the output of HFERB as the high frequency prior query and the output of SRWAB as key, value and calculate the inter-attention to refine the global features which are obtained from SRWAB. Moreover, most existing methods focus on spatial relations and overlook channel information. To overcome this limitation, we perform inter-attention based on the channel dimension to explore channel dependencies. This design will significantly reduce complexity. Traditional methods that utilize spatial attention tend to result in significant computational complexity (e.g.,  $O(N^2 C)$ ,  $N \gg C$ ), where  $N$  represents the length of the sequence and  $C$  represents the channel dimension. In contrast, our channel attention design can transfer the quadratic component to the channel dimension (e.g.,  $O(NC^2)$ ), effectively reducing complexity.
+
+Specifically, as shown in Figure 2, we use a  $1\times 1$  convolutional layer followed by a  $3\times 3$  depth-wise convolutional layer to generate the high frequency query  $\pmb{Q}\in \mathbb{R}^{H\times W\times C}$  based on the output of HFERB,  $X_{H}$ . As to the output of SRWAB,  $X_{S}$ , we first normalize the features by LayerNorm layer and then use the same operation as the query  $\pmb{Q}$  to get the key  $\pmb {K}\in \mathbb{R}^{H\times W\times C}$  and the value  $\pmb {V}\in \mathbb{R}^{H\times W\times C}$ . Following the [42], we perform the reshape operation on  $\pmb{Q}$ ,  $\pmb{K}$  and  $\pmb{V}$  to get the  $\hat{\pmb{Q}}\in \mathbb{R}^{C\times (HW)}$ ,  $\hat{\pmb{K}}\in \mathbb{R}^{C\times (HW)}$  and  $\hat{\pmb{V}}\in \mathbb{R}^{C\times (HW)}$ . After that, we compute the inter-attention as
+
+$$
+\operatorname {A t t e n t i o n} (\hat {\boldsymbol {Q}}, \hat {\boldsymbol {K}}, \hat {\boldsymbol {V}}) = \operatorname {S o f t m a x} \left(\frac {\hat {\boldsymbol {Q}} \hat {\boldsymbol {K}} ^ {T}}{\alpha}\right) \hat {\boldsymbol {V}}, \tag {12}
+$$
+
+where the  $\alpha$  represents the learnable parameter. Meanwhile, we add the refinement features to the  $X_{S}$  to get the fusion output  $X_{fuse}$ . In addition, we feed  $X_{fuse}$  to an improved feed-forward network [42] to aggregate the features further. The details of this structure are shown in Figure 2. It introduced a gate mechanism to fully extract the spatial and channel information and gain better performance. The whole process can be formulated as
+
+$$
+X _ {f u s e} = \text {I n t e r - A t t e n} (L N \left(X _ {S}\right), X _ {H}) + X _ {S} \tag {13}
+$$
+
+$$
+X _ {H F B} = I M L P (L N (X)) + X _ {f u s e},
+$$
+
+where the  $LN$  means LayerNorm operation, IMLP represents the improved MLP, and Inter-Atten indicates
+
+Table 1. Performance comparison of different SISR models on five benchmarks. Params represents the total number of network parameters. Results for the best and second best candidates are highlighted, and underlined.  
+
+<table><tr><td>Scale</td><td>Model</td><td>Params</td><td>Set5 (PSNR/SSIM)</td><td>Set14 (PSNR/SSIM)</td><td>BSD100 (PSNR/SSIM)</td><td>Urban100 (PSNR/SSIM)</td><td>Manga109 (PSNR/SSIM)</td></tr><tr><td rowspan="10">×2</td><td>EDSR-baseline [23]</td><td>1370K</td><td>37.99/0.9604</td><td>33.57/0.9175</td><td>32.16/0.8994</td><td>31.98/0.9272</td><td>38.54/0.9769</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>37.76/0.9590</td><td>33.52/0.9166</td><td>32.09/0.8978</td><td>31.92/0.9256</td><td>38.36/0.9765</td></tr><tr><td>IMDN [13]</td><td>694K</td><td>38.00/0.9605</td><td>33.63/0.9177</td><td>32.19/0.8996</td><td>32.17/0.9283</td><td>38.88/0.9774</td></tr><tr><td>LatticeNet [26]</td><td>756K</td><td>38.06/0.9607</td><td>33.70/0.9187</td><td>32.20/0.8999</td><td>32.25/0.9288</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>548k</td><td>38.01/0.9605</td><td>33.62/0.9183</td><td>32.19/0.8999</td><td>32.10/0.9283</td><td>38.67/0.9772</td></tr><tr><td>HPUN-L [34]</td><td>714K</td><td>38.09/0.9608</td><td>33.79/0.9198</td><td>32.25/0.9006</td><td>32.37/0.9307</td><td>39.07/0.9779</td></tr><tr><td>SwinIR-light [21]</td><td>878K</td><td>38.14/0.9611</td><td>33.86/0.9206</td><td>32.31/0.9012</td><td>32.76/0.9340</td><td>39.12/0.9783</td></tr><tr><td>ESRT [25]</td><td>777K</td><td>38.03/0.9600</td><td>33.75/0.9184</td><td>32.25/0.9001</td><td>32.58/0.9318</td><td>39.12/0.9774</td></tr><tr><td>ELAN-light [44]</td><td>582K</td><td>38.17/0.9611</td><td>33.94/0.9207</td><td>32.30/0.9012</td><td>32.76/0.9340</td><td>39.11/0.9782</td></tr><tr><td>CRAFT (Ours)</td><td>737K</td><td>38.23/0.9615</td><td>33.92/0.9211</td><td>32.33/0.9016</td><td>32.86/0.9343</td><td>39.39/0.9786</td></tr><tr><td rowspan="11">×3</td><td>EDSR-baseline [23]</td><td>1555K</td><td>34.37/0.9270</td><td>30.28/0.8417</td><td>29.09/0.8052</td><td>28.15/0.8527</td><td>33.45/0.9439</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>34.29/0.9255</td><td>30.29/0.8407</td><td>29.06/0.8034</td><td>28.06/0.8493</td><td>33.50/0.9440</td></tr><tr><td>IMDN [13]</td><td>703K</td><td>34.36/0.9270</td><td>30.32/0.8417</td><td>29.09/0.8046</td><td>28.17/0.8519</td><td>33.61/0.9445</td></tr><tr><td>LatticeNet [26]</td><td>765K</td><td>34.53/0.9281</td><td>30.39/0.8424</td><td>29.15/0.8059</td><td>28.33/0.8538</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>544k</td><td>34.36/0.9267</td><td>30.34/0.8421</td><td>29.11/0.8054</td><td>28.15/0.8523</td><td>33.51/0.9441</td></tr><tr><td>HPUN-L [34]</td><td>723K</td><td>34.56/0.9281</td><td>30.45/0.8445</td><td>29.18/0.8072</td><td>28.37/0.8572</td><td>33.90/0.9463</td></tr><tr><td>SwinIR-light [21]</td><td>886K</td><td>34.62/0.9289</td><td>30.54/0.8463</td><td>29.20/0.8082</td><td>28.66/0.8624</td><td>33.98/0.9478</td></tr><tr><td>LBNet [9]</td><td>736K</td><td>34.47/0.277</td><td>30.38/0.8417</td><td>29.13/0.8061</td><td>28.42/0.8559</td><td>33.82/0.9406</td></tr><tr><td>ESRT [25]</td><td>770K</td><td>34.42/0.9268</td><td>30.43/0.8433</td><td>29.15/0.8063</td><td>28.46/0.8574</td><td>33.95/0.9455</td></tr><tr><td>ELAN-light [44]</td><td>590K</td><td>34.61/0.9288</td><td>30.55/0.8463</td><td>29.21/0.8081</td><td>28.69/0.8624</td><td>34.00/0.9478</td></tr><tr><td>CRAFT (Ours)</td><td>744K</td><td>34.71/0.9295</td><td>30.61/0.8469</td><td>29.24/0.8093</td><td>28.77/0.8635</td><td>34.29/0.9491</td></tr><tr><td rowspan="11">×4</td><td>EDSR-baseline [23]</td><td>1518K</td><td>32.09/0.8938</td><td>28.58/0.7813</td><td>27.57/0.7357</td><td>26.04/0.7849</td><td>30.35/0.9067</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>32.13/0.8937</td><td>28.60/0.7806</td><td>27.58/0.7349</td><td>26.07/0.7837</td><td>30.47/0.9084</td></tr><tr><td>IMDN [13]</td><td>715K</td><td>32.21/0.8948</td><td>28.58/0.7811</td><td>27.56/0.7353</td><td>26.04/0.7838</td><td>30.45/0.9075</td></tr><tr><td>LatticeNet [26]</td><td>777K</td><td>32.18/0.8943</td><td>28.61/0.7812</td><td>27.57/0.7355</td><td>26.14/0.7844</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>659k</td><td>32.15/0.8944</td><td>28.61/0.7818</td><td>27.61/0.7366</td><td>26.14/0.7871</td><td>30.42/0.9074</td></tr><tr><td>HPUN-L [34]</td><td>734K</td><td>32.31/0.8962</td><td>28.73/0.7842</td><td>27.66/0.7386</td><td>26.27/0.7918</td><td>30.77/0.9109</td></tr><tr><td>SwinIR-light [21]</td><td>897K</td><td>32.44/0.8976</td><td>28.77/0.7858</td><td>27.69/0.7406</td><td>26.47/0.7980</td><td>30.92/0.9151</td></tr><tr><td>LBNet [9]</td><td>742K</td><td>32.29/0.8960</td><td>28.68/0.7832</td><td>27.62/0.7382</td><td>26.27/0.7906</td><td>30.76/0.9111</td></tr><tr><td>ESRT [25]</td><td>751K</td><td>32.19/0.8947</td><td>28.69/0.7833</td><td>27.69/0.7379</td><td>26.39/0.7962</td><td>30.75/0.9100</td></tr><tr><td>ELAN-light [44]</td><td>601K</td><td>32.43/0.8975</td><td>28.78/0.7858</td><td>27.69/0.7406</td><td>26.54/0.7982</td><td>30.92/0.9150</td></tr><tr><td>CRAFT (Ours)</td><td>753K</td><td>32.52/0.8989</td><td>28.85/0.7872</td><td>27.72/0.7418</td><td>26.56/0.7995</td><td>31.18/0.9168</td></tr></table>
+
+the proposed inter-attention mechanism, which introduces high-frequency prior to refining the global representations.
+
+# 5. Experiments
+
+# 5.1. Data and Metrics
+
+In this paper, we adopt the DIV2K [1] as the training dataset, which includes 800 training images. Meanwhile, five benchmarks are used for evaluation, including Set5 [3], Set14 [43], BSD100 [27], Urban100 [12], and Manga109 [28] with three magnification factors:  $\times 2$ ,  $\times 3$ , and  $\times 4$ . The quality of the images is evaluated using PSNR, and SSIM [39]. The complexity of the model is indicated by its parameters.
+
+# 5.2. Implementation Details
+
+Following the general setting, we use bicubic to obtain the corresponding LR images from the original HR images. During training, we randomly crop the images into  $64 \times 64$  patches, and the total training iterations are  $500\mathrm{K}$ . Meanwhile, data augmentation is performed, such as random horizontal flipping and  $90^{\circ}$  rotation. The Adam optimizer with  $\beta_{1} = 0.9$  and  $\beta_{2} = 0.999$  is adopted to minimize the  $\mathcal{L}_1$  Loss. The batch size is set to 64, the initial learning
+
+rate is set to  $2 \times 10^{-4}$  and reduced by half at the milestone [250K, 400K, 450K, 475K]. In addition, the model is trained on 4 NVIDIA 3090 GPUs using the PyTorch toolbox. In CRAFT, we have set the RCRFG number to 4 and the CRFB number to 2 for each RCRFG. Each CRFB is comprised of 1 HFERB and 2 SRWABs for efficiency. The feature channel, attention head, and MLP expansion ratio are set to 48, 6, and 2, respectively. We also set the IMLP expansion ratio to 2.66, as in [42]. To obtain two types of rectangle windows, we have set the rectangle window size to  $[sh, sw]$  as [4, 16] and [16, 4].
+
+# 5.3. Comparison with state-of-the-art methods
+
+We compare with several state-of-the-art SISR methods to demonstrate the effective of the proposed CRAFT model, including EDSR [23], CARN [2], IMDN [13], LatticeNet [26], LAPAR [19], SwinIR [21], HPUN [34], ESRT [25], LBNet [9], and ELAN [44].
+
+Quantitative Results. The experimental results for SISR are presented in Table 1, where the proposed CRAFT model demonstrates competitive performance across all benchmarks. Particularly, when compared to traditional CNN-based methods like EDSR, the proposed CRAFT achieves significant performance improvements of  $0.85\mathrm{dB}$
+
+![](images/c495e9681d5e0d09b2bd5e98fe8f968813d63083893cb9036b995236a91ff42b.jpg)  
+Img012  $(\times 4)$
+
+![](images/65a61369fef1c96d6d23be3b3fef9d66f258c2d987779da8f593826bbfcd71ec.jpg)  
+Bicubic
+
+![](images/093c3a17b0589b525e28998089edc54410ca8a423eefd0dd134c8f157386314b.jpg)  
+EDSR [23]
+
+![](images/c4b9eb406c13ad4ea62fe2b604f61f9ed70661b6f3c067c5424b713e40aa3b30.jpg)  
+CARN [2]
+
+![](images/1fc32a6d33e4bab4abc90c3429f5e7c5391164632cba562273d37e1b975c4b48.jpg)  
+LBNet [9]
+
+![](images/7c51d892601651c47c1b45dc2cfa6c92d917fedf513e1b9c4da664ed459a8dbe.jpg)  
+YumeiroCook  $(\times 4)$
+
+![](images/dab4afd1bfb5314d489ae5efd826eb75d9bdfcc21a10b7f0e0eb53fe088dce87.jpg)  
+SwinIR [21]
+
+![](images/4448ad44e0bd9ed1f531eddd325dc977c311fc941e7528f487764cc6d44de6af.jpg)  
+ESRT [25]
+
+![](images/858e9791738bbc720b939b24116974dbc72313d788782b6ffd05afa68d5d3c3c.jpg)  
+CRAFT (Ours)
+
+![](images/54b746e826baf6ea00cc184728a287183be3fd4a5ecf573b166ef8fd6c2f1db3.jpg)  
+HR
+
+![](images/fa57e7794cb28c2880c0f82b6fbcfc42d5d67e95c8563f45dd59a0c5d1dbfdff.jpg)  
+UchuKigekiM774  $(\times 4)$  
+Figure 3. Visual quality comparison with SOTA methods. CRAFT achieves better restoration quality in both line direction and details.
+
+![](images/4403ce67762ab1900fa8fb9610fe2f09c72bc86c3ba39645d974474d3c716819.jpg)  
+Bicubic
+
+![](images/eaef64edc23c72770dc60d2af235f4e222824348f48e8135b2b08abf3b3d4e5d.jpg)  
+EDSR [23]
+
+![](images/d72ea7180661dad3325cc3d4d24c5018397afc4ad39e6cd4b3eb63671d171423.jpg)  
+CARN [2]
+
+![](images/7c2fd22b3aa2fde2a2baa987b786d8bf4f821fb0ed6f82f242422a1c7a7c699d.jpg)  
+LBNet [9]
+
+![](images/c5a6c00210dad90a00d288b2523a9c3fd64e11860eff46ae64a085bebf1e0e74.jpg)  
+SwinIR [21]
+
+![](images/86078475e0135025e6334c07ba30e7c02e50c4f4a7bf317bee5ee6d5f99294b0.jpg)  
+ESRT [25]
+
+![](images/8873dc980532e7a47e529ad5de281b37f34346fb92a8f646c76514fa6232ddf9.jpg)  
+CRAFT (Ours)
+
+![](images/4d25ab33715ec0f2c74f128212e24115eb23c39f06570ea49ee4585fa446d95c.jpg)  
+HR
+
+![](images/bfb505ddaa6cd88701837403dd02883edeb15671791f3b45ee320f6b5c551da4.jpg)  
+Bicubic
+
+![](images/330be183b956ade9e6c947cc1977dad403b9d20db74ca7060444a6d960678e9e.jpg)  
+EDSR [23]
+
+![](images/12b0764feaa857233aba5643730def9bdd60a741a363fd84cc99615730d7f6cd.jpg)  
+CARN [2]
+
+![](images/bccc42d4864f838c5fe0992669e689fa253b174c8b8012f571b479fca95f02cc.jpg)  
+LBNet [9]
+
+![](images/102590e88af721789c14382e4ba2d90da724e6c40406baec2ab22681c1fa5e9a.jpg)  
+SwinIR [21]
+
+![](images/2e9b6bc68874334cd9cf02c3c661d07580f555b1552f6de5ec78edb813f92376.jpg)  
+ESRT [25]
+
+![](images/267d4bf705d57a85356746c0564cf08bdba9d95b612387ef24b139ef87ccda25.jpg)  
+CRAFT (Ours)
+
+![](images/eff5b539c52a715d2f85e5faeb733fe0690e101b1e6651287e0f5f13ff7e0534.jpg)  
+HR
+
+0.84dB, and 0.83dB at magnification factors  $\times 2$ ,  $\times 3$ , and  $\times 4$ , respectively, while using  $46\%$ ,  $52\%$ , and  $50\%$  fewer parameters on the Manga109 dataset. Furthermore, compared to recent channel attention methods such as CARN, the proposed CRAFT achieves improvements of 1.03dB, 0.79dB, and 0.71dB at magnification factors  $\times 2$ ,  $\times 3$ , and  $\times 4$ , respectively, with a  $54\%$ ,  $53\%$ , and  $52\%$  reduction in the number of parameters on the Manga109 dataset. Regarding transformer-based methods [25, 21, 44], the proposed CRAFT gains performance improvements of 0.34dB, 0.31dB, and 0.29dB, respectively, with a comparable number of parameters under the magnification factor of  $\times 3$  on the Manga109 dataset.
+
+Qualitative Results. We present a visual comparison  $(\times 4)$  in Figure 3 and analyze the results. Our proposed CRAFT model integrates the strengths of both CNN and transformer structures, leading to accurate line direction recovery while preserving image details. To further investigate the performance, we compare the local attribution map (LAM) [11] between CRAFT and SwinIR, as shown in Figure 4. LAM indicates the correlation between the significance of each pixel in LR and the SR of the patch that is outlined with the red box. By leveraging a broader range of information, our model achieves improved results. Furthermore, we examine the diffusion index (DI), which signifies the range of pixels involved. A larger DI indicates a
+
+wider scope of attention. Compared to SwinIR, our model exhibits a higher DI, implying that it can capture more contextual information. These results demonstrate the effectiveness of the proposed CRAFT method.
+
+# 5.4. Ablation study
+
+# 5.4.1 Effectiveness of HFERB and SRWAB
+
+We conduct several experiments to show the effectiveness of HFERB and SRWAB in Table 2. Specifically, we removed SRWAB and HFERB separately to assess their contributions. We observed that using local or global information alone, as in  $\mathrm{CRAFT}_{conv}$  and  $\mathrm{CRAFT}_{transformer}$ , respectively, is insufficient to learn a better representation (lower performance). Furthermore, we found that SRWAB provides the most significant performance improvement, demonstrating the benefits of the long-range dependencies learned by the transformer. In addition, high-frequency priors from CNN are also helpful in restoring details, cross-refining learned features and further improving performance. Meanwhile, we also analyzed the properties of HFERB and SRWAB from a frequency perspective. We visualized the features extracted from two blocks in different RCRFGs and plotted the Fourier spectrum to observe what each block learns. The results, shown in Figure 5, indicate that HFERB focuses more on high-frequency information, while SRWAB extracts more global informa
+
+![](images/75459e4518ff85b52ab333d67d04a890646573b9130d9f1d5c16f226db884782.jpg)  
+LAM
+
+![](images/3f960a9e87c25f312171bab883fbe3051b70eb62e91e0382caba622f60f94484.jpg)  
+HR
+
+![](images/4082c725fa4f84f1563d13719cc4a0d6ac62854d4c8db9466c9f6acd063f7735.jpg)  
+SwinIR
+
+![](images/13212703f9b84706f40b8d98c5af053fba5b3e39a6b9d85b84e007ed8d0b26be.jpg)  
+CRAFT
+
+![](images/1498004e0697864d6c0c4429a531efe9ad7a94715b9c2312bb121862c52de381.jpg)
+
+![](images/7a2a0f3fdbada2ba406083373643211ad064a704814262852f795fbfc26b06e6.jpg)
+
+![](images/fcd012267c0e616fe8fb654f5f16713b7ba463d1772d022d7b07c054d09fdb85.jpg)  
+DI: 10.78
+
+![](images/08048a59ce1eb6e38f730a7fd027831a43f93555979b86dc355123cff06e163f.jpg)  
+DI:30,34
+
+![](images/3c0432f6cf094c466dba66d0b831a29623337473fb9ee1db09dfd57a4cd12713.jpg)  
+LR  
+HR  
+LAM
+
+![](images/5a22c2dc61adfd85d15150aeb17224a8ae1750401236ad55459fd54d32c4e028.jpg)  
+SwinIR
+
+![](images/a0ae3d55990974e278dcd8b933a8469dc6a27fa40d0671d6f228c08c0f76358b.jpg)  
+CRAFT
+
+![](images/0d9329b2d7036cd6f8b206d4fa107dbf9bbc2cac97b00cb2394f9b911279c0f2.jpg)
+
+![](images/0769aeba478650a5420b34514b92f995c2791887affe0912c4e3fd93c7f04107.jpg)
+
+![](images/64dfd74d97f4aa0dab5a1e672ce6e040b0d1b1709ebde46b29ae0a58f089804d.jpg)  
+LR  
+#
+
+![](images/c03c145925703e9be7de83817e8c1e96b2f57503c40c45eb01dcdc8ee2184318.jpg)  
+DI: 7.36
+
+![](images/6898e8883984c630b2b1a020688ff9270cf46c185c834ebef2ca333850dca5af.jpg)  
+DI:18.89
+
+![](images/d2e9f344f067546a8773ce21f04b9fffd12c51be062c0fc8f5835b4659ddd92e.jpg)  
+HR  
+Rnnaaee aaeaae
+
+![](images/81c6be0e27a3a46f121c416f95541f985b74b3b8679f6535344905964aa3eacc.jpg)  
+rrrnnnne  
+LR
+
+![](images/344540d6893f7e27c21acae59cec41239bc73919423ac3acb4c334a336a3c38a.jpg)  
+SwinIR
+
+![](images/db04f757e508eaebba25a0913d853688392ce6ff46969f915d65ee3f4b04a46c.jpg)  
+CRAFT
+
+![](images/08792f10838112cd22164f0694f824742f25e9b2c2c673dcf7e487b225d710dc.jpg)
+
+![](images/c1ebb8c29e122480a34bc2c27e03c164d182628f80262351d075a15379336280.jpg)
+
+![](images/1ab2afb408d6c5623ed76866b85fae1a9550b0535fd4f4887082ff0da5f8bcb8.jpg)  
+DI: 9.37
+
+![](images/45767dec8989c19da15740682e6429ac972c296ec214520272519f64e5eeff12.jpg)  
+DI:30.94
+
+![](images/002caf5f01dcc767f0241b0f0fae49be0ee03131cfe0fb66f5c5a7cec9dc9c30.jpg)  
+SwinIR  
+LAM Results
+
+![](images/595ce45ee9a999efaedca3ec3abc313d98fbd53667ea6c62b9384b5c8cd18acf.jpg)
+
+![](images/b41c92630815a32241f7ce1606532ce1dd7da669b19961093901994937f41004.jpg)
+
+![](images/aff93ff8f380ebfdd4529ad5e908c339d6983eac4f1eeace838fcf98f9dfb304.jpg)
+
+![](images/e5713eaa1a28daa4d7a780a57263c18c0cf5f0b6aaba820165f62a12a4db3916.jpg)  
+DI: 9.30  
+Figure 4. Comparison of the LAM results of SwinIR [21] and CRAFT. LAM indicates the correlation between the significance of each pixel in LR and the SR of the patch that is outlined with the red box. CRAFT utilizes a broader range of information to obtain better performance. DI quantifies the LAM results, CRAFT has a higher DI score, indicating its ability to capture more contextual information.
+
+![](images/0974c78326bf84f08834f3e148ce91fd786beacb2d0f33fb991590ed29b7315d.jpg)  
+DI: 17.98
+
+![](images/1959c51bbcc020a4f1682e2ec10c36b373a3b1945a9318476f99fea8ea58b93a.jpg)  
+HR  
+PAA
+
+![](images/d76c8f0cbd2e382f78d2d7ee8c635289e90db4a2c8a272a68175ed0932c6d079.jpg)  
+LR  
+Raaes
+
+![](images/826318197116386b07bca21b12362f46586a597bf05e1c603a246bf0c437f782.jpg)  
+SwinIR
+
+![](images/8ae2d1f05a7571a9b992cc9a1a919c8238ab53be4684396cd3f499ebaa96443e.jpg)  
+CRAFT
+
+![](images/249f05eecd52da86314150fb352b294ce6d1c43fdb39b4d0c42015f4737d145e.jpg)
+
+![](images/8023baf200259d01b3833fffefe4ad95e01b362d72931a2f359376e4fa9fd2ff.jpg)
+
+![](images/1d96ecadd2aadff40307964a7bf921a7d8065bc8c2489d7a7b5c6121e4eb85ef.jpg)
+
+![](images/cc6f6d67480c450b6221358fc5cd5dfb3657718792d89b5c94a7d32ad9937f43.jpg)  
+DI:13.03
+
+![](images/4f6d43a1730eee4294e7896a3af978587aecfd2128d4d222289ccb3713b19337.jpg)  
+DI:30.87
+
+![](images/7706a0cd3189ef4868616d01426bd47a9ca3d1dde927ef61565c8efb02a35ed3.jpg)  
+Rarnnnnns
+
+![](images/ff8b7153a541e9c08af9e05d1778eec1c30b4461378e4531b5c9f29b5cd8b9c6.jpg)  
+SwinIR  
+CRAFT
+
+![](images/9bc640ed2e2a407f72e339e11e7a65ac45ca9d78bfe113b10dc08d100da7452b.jpg)
+
+![](images/9a84bb6db563797e70b2644218f8bafde13b50875633d13da66a5ce2eaa015f4.jpg)
+
+![](images/2b495aece478447e52fd49d9a78e4ad1bc988b687467b6ba0e858e508bc9306a.jpg)  
+DI:32.17
+
+![](images/c31392aebcb7b7d92cab2df42dd5742bd16ee729d8410c489ea6b0ea0134e1dc.jpg)  
+DI: 12.88
+
+Table 2. Study of HFERB, SRWAB, and HFB on SISR. The results  $(\times 4)$  are obtained from the Manga109 dataset.  
+
+<table><tr><td>Model</td><td>HFERB</td><td>SRWAB</td><td>HFB</td><td>Concat</td><td>PSNR</td></tr><tr><td>CRAFTconv</td><td>✓</td><td></td><td>✓</td><td></td><td>30.79</td></tr><tr><td>CRAFTtransformer</td><td></td><td>✓</td><td>✓</td><td></td><td>31.12</td></tr><tr><td>CRAFTconcat</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>30.92</td></tr><tr><td>CRAFT</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>31.18</td></tr></table>
+
+tion. Specifically, the top row of each image indicates the Fourier spectrum of each block, and the bottom row indicates the feature maps of each block. The figure shows that SRWAB has a weaker response and focuses more on the low-frequency parts, which correspond to flat regions, while HFERB shows a stronger response and focuses more on intricate parts of features, such as edges and corners. The feature maps on the bottom row also support this conclusion. HFERB captures more details such as window edges and cornices, while SRWAB pays more attention to flat areas such as windows and walls.
+
+# 5.4.2 Effectiveness of HFB
+
+To evaluate the effectiveness of HFB, we conducted an experiment where we modified the fusion method to a concatenation formulation. This involved concatenating the
+
+Table 3. Effectiveness of high-frequency prior. The results  $(\times 4)$  are obtained from the Manga109 dataset.  
+
+<table><tr><td>Model</td><td>Regular</td><td>Swap</td><td>Cascade</td><td>PSNR</td><td>SSIM</td></tr><tr><td>CRAFTswap</td><td></td><td>✓</td><td></td><td>30.67</td><td>0.9113</td></tr><tr><td>CRAFT cascade</td><td></td><td></td><td>✓</td><td>30.88</td><td>0.9141</td></tr><tr><td>CRAFT</td><td>✓</td><td></td><td></td><td>31.18</td><td>0.9168</td></tr></table>
+
+Table 4. Complexity analysis compared to SwinIR.  
+
+<table><tr><td>Model</td><td>#Params. (K)</td><td>#FLOPs (G)</td><td>#GPU Mem. (M)</td><td>Ave. Time (ms)</td></tr><tr><td>SwinIR</td><td>897</td><td>32.2</td><td>141.2</td><td>72.0</td></tr><tr><td>CRAFT</td><td>753</td><td>26.1</td><td>79.5</td><td>42.8</td></tr></table>
+
+HFERB and SRWAB output and replacing the HFB with a  $3 \times 3$  convolutional layer to obtain the final output. The results are presented in Table 2, where  $\mathrm{CRAFT}_{\text {concat }}$  denotes the modified version. The result shows that our proposed method outperforms the concatenation structure by  $0.26\mathrm{dB}$ , demonstrating the effectiveness of our HFB. The observed result can be attributed to SRWAB and HFERB focusing on disparate frequency information. Stacking features directly impedes the ability of the network to learn the relationship between high-frequency and low-frequency components. Conversely, the inter-attention mechanism presents a viable solution for integrating features with different distributions.
+
+![](images/d48c53f0844a844d93442b9518e408245a824e8ca6f33726d1a01448fba9c9c2.jpg)  
+LR Image
+
+![](images/8caed29b1309146f155d284eb82e285fca73922b90daafbbd4a415037f619a38.jpg)  
+HFE
+
+![](images/b370c5391373108dbef1fce0512e24ad43e21aa8973bbfcb1d3fee86ab2cd8e5.jpg)  
+LFE
+
+![](images/f81695209cdbeacbe2f76f557bcb87912bf8dc89b5132488edbde64542ddfb7e.jpg)  
+SRWin-Attention
+
+![](images/1fed3dd8a8bdb7e31b99131f5eff4bbfbd0419f632ac879b61e68db499c09d27.jpg)  
+HFE
+
+![](images/fa1402d7226214f67adb404f55a3e969062c6370e7e720ceceb4e21fe5ac952f.jpg)  
+HPE LFE SW with Altex (c) Visualization of the spectrum of the 4th RCFG
+
+![](images/eb800c15fb8c024da9a1cafe83fd48183d142cfc3520e0676ef2f0cfb3465d8d.jpg)
+
+![](images/06a96c77a4e2357f322708c850f7ac7bafb2afbe650958bd8e70a99944d59f3d.jpg)  
+(a) Visualization of the spectrum of the 2nd RCRFG  
+HFE
+
+![](images/17babca7efc5b92b10698aeeb33388401d534f1f8b63ca4fd3579ffe19f5636e.jpg)  
+LFE
+
+![](images/36fa3ce2d1a06a4f084e875ff33be5845db796f3a92d2202c33ced215fa21bdb.jpg)  
+SRWin-Attention
+
+![](images/1d7bd5a5736253541aff75ee4e085ba4110d90e72b6fb97e7fe439295c1925fc.jpg)  
+HFE
+
+![](images/144a8bcdea7bd22cc9fb064efece512c87fe1b452135a245348746e989b05908.jpg)  
+LFE
+
+![](images/ffaac01498d101944bbe1be99937186e1f440a0dcdf258e4eda2da493eb09b53.jpg)  
+SRWin-Attention
+
+![](images/66301d83520ae9980cb3295fb85addd20bc42ce9e85da34db7ca2aa67de1fa02.jpg)  
+LR Image  
+Figure 5. Visualization of HFERB and SRWAB. The LFE indicates the local feature extraction branch in HFERB, the HFE means the high-frequency enhancement branch in HFERB, and the SRWin-Attention represents the self-attention part in SRWAB.
+
+![](images/438fbef71629da920d854c7b18d30d1b2fa5a48f9a08382eee40abf3c94c7a48.jpg)  
+HFE
+
+![](images/dfb8793e8a5f62238badfa83480b7e4ba713792b49fcc7ac86b48aa37dba3d88.jpg)  
+LFE
+
+![](images/1b7745056eeccfae6daa64a72f5b92af48887b9beba1ff86d9fb66db9d786ac3.jpg)  
+SRWin-Attention
+
+![](images/6a070bcdf4e8e5f894784428d2586804d2909f9760c63e57251b95255e5b074e.jpg)  
+(d) Visualization of the feature of the 4th RCFIG  
+HFE
+
+![](images/7441afb4098e491e2cd8f192b35b78ffa524a52e26ed91feeb6e72937334e0b2.jpg)  
+LFE
+
+![](images/a678fc06465aaccb0c7a4e1f3bc82e7d03ac16d144be354e4e9152dab49c8e0f.jpg)  
+SRWin-Attention
+
+![](images/b62cd49dbf879601291a33c0a37faced1ca2a997dae6abbf296c74cafdea6618.jpg)  
+(e) Visualization of the spectrum of the 2nd RCRFG  
+HFE  
+(f) Visualization of the feature of the 2nd RCRFG
+
+![](images/6b6e1016d84d54addf76c98394dd48d72f6fd6039b1c9481751e63ea4efaf5e5.jpg)  
+LFE
+
+![](images/cdb031420f99ade962da4bc82ef9db9dec0c796077598548c49e6d304d296f8e.jpg)  
+SRWin-Attention
+
+![](images/8e8c89f6fffb20fc5e6005fc6169e0fcd7eece9f191328d3c81f114f0bc22b48.jpg)  
+HFE  
+(h) Visualization of the feature of the 4th RCRFG
+
+![](images/62cd6ebb64ae8b498e5754f53fe73abae9f7f9f941ff83c78882de10fd3f953a.jpg)  
+LFE
+
+![](images/0b1104d9f7f06785ff3694f36c2174987df1ed1f30193bdeb7613171c36963c2.jpg)  
+SRWin-Attention
+
+# 5.4.3 Effectiveness of High-Frequency Prior
+
+We conducted several experiments to investigate the effectiveness of high-frequency prior. Firstly, we swapped the input of  $Q$  and  $K$ ,  $V$  in HFB and treated the output of SRWAB as  $Q$  and the output of HFERB as  $K$ ,  $V$  to verify whether global features are dominant in restoration and high-frequency features only serve as a prior for refining the global representation. As shown in Table 3, compared to the original design, swapping the input leads to a significant drop in performance, with a 0.51dB decrease in PSNR. Furthermore, we also performed an experiment to formulate the model as a cascade structure to verify the effectiveness of the design introducing high-frequency priors. As shown in Table 3, the  $\mathrm{CRAFT}_{\text{ cascade}}$  structure resulted in a performance drop, with a 0.3dB decrease in PSNR compared to CRAFT. These results demonstrate the effectiveness of high-frequency priors in the CRAFT model.
+
+# 5.4.4 Complexity analysis
+
+We compared CRAFT with SwinIR in terms of complexity using an input size of  $128 \times 128$ , as shown in Table 4. The analysis considered parameters, FLOPs, GPU memory consumption, and average inference time. GPU memory was measured using the official PyTorch function, and time cost was calculated based on 100 inference runs. Compared to SwinIR, CRAFT has fewer parameters and FLOPs, and requires less memory consumption and inference time. Additionally, we analyzed the complexity of our CRAFT framework and summarized the findings in Table 5. We observed that SRWAB contributes approximately  $46\%$  of the total complexity, while HFERB involves fewer convolution operations, resulting in reduced FLOPs. Furthermore, the HFB module's channel-wise attention effectively reduces
+
+Table 5. Complexity analysis of each block.  
+
+<table><tr><td>Model</td><td>CRAFT
+w/o HFERB</td><td>CRAFT
+w/o SRWAB</td><td>CRAFT
+w/o HFB</td><td>CRAFT</td></tr><tr><td>#Params. (K)</td><td>688</td><td>441</td><td>503</td><td>753</td></tr><tr><td>#FLOPs (G)</td><td>23.8</td><td>14.2</td><td>20.0</td><td>26.1</td></tr></table>
+
+the computational burden.
+
+# 6. Conclusion
+
+This paper investigates the impact of frequency on the performance of CNN and transformer structures in SISR and finds that transformer structures are more adept at capturing low-frequency information, but have limited capability to reconstruct high-frequency representations compared to CNN. To address this issue, we design a feature modulation transformer, named cross-refinement adaptive feature modulation transformer (CRAFT), which comprises three key components: the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB). The HFERB is designed to extract high-frequency features, while the SRWAB captures global representations. In the HFB, we treat the output of HFERB as a high-frequency prior and the output of SRWAB as key and value, and use interattention to refine the global representation. Experimental results demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB with relatively fewer parameters.
+
+# Acknowledgements
+
+This work is supported by the National Natural Science Foundation of China (NSFC) under Grant U19A2052 and Grant 62020106011, as well as by the National Key Lab of Autonomous Intelligent Unmanned Systems.
+
+# References
+
+[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshop (CVPRW), pages 126-135, 2017. 6  
+[2] Namhyuk Ahn, Byungkon Kang, and Kyung Ah Sohn. Fast, accurate, and lightweight super-resolution with cascading residual network. In Proceedings of the European Conference on Computer Vision (ECCV), pages 256-272, 2018. 2, 6, 7  
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+Proceedings of the IEEE/CVF Conference on Computer Vision (ICCV), pages 10012-10022, 2021. 2  
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "*Corresponding author."
+                                }
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+                                    "content": "lows:"
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+                                            "type": "text",
+                                            "content": "- We study the impact of CNN and transformer structures on performance from a frequency perspective and observe that transformer is more effective in capturing low-frequency information while having limited capacity for constructing high-frequency representations compared to CNN."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
+                                            "content": "- Based on the observation, we design a parallel structure to explore different frequency features. We utilize the HFERB branch to introduce high-frequency information, which is beneficial to SISR, and the SRWAB branch to acquire global information."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
+                                            "content": "- We propose a fuse strategy that integrates the strengths of CNN and transformer. Specifically, we treat the HFERB branch as high-frequency prior and the output of SRWAB as key and value for inter-attention, resulting in improved performance."
+                                        }
+                                    ]
+                                }
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+                                            "content": "- Extensive experimental results on multiple datasets show that the proposed method performs on par with the existing state-of-the-art SISR methods while using fewer parameters."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "2. Related Works"
+                                }
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+                                    "type": "text",
+                                    "content": "2.1. CNN-based SISR"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Since the pioneering work SRCNN [7] has achieved significant progress in SISR, various CNN-based works have been proposed. Kim et al. [15] presented an SR method using deep networks by cascading 20 layers, demonstrating promising results. Building upon this, Lim et al. [23] introduced the enhanced deep super-resolution (EDSR) network, which achieved a significant performance boost by removing the batch normalization layer [14] from the residual block and incorporating additional convolution layers. Ahn et al. [2] designed an architecture with an increased number of residual blocks and dense connections, further improving the SR performance. In pursuit of lightweight models, Hui et al. [13] proposed a selective fusion approach, employing cascaded information multi-distillation blocks to construct an efficient model. Li et al. [19] introduced a method involving predefined filters and utilized a CNN to learn coefficients, which were then linearly combined to obtain the final results. Sun et al. [34] proposed a hybrid pixel-unshuffled network (HPUN) by introducing an efficient and effective downsampling module into the SR task."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "2.2. Transformer-based SISR"
+                                }
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+                                    "type": "text",
+                                    "content": "Liang et al. [21] proposed SwinIR, a robust baseline model for image restoration, leveraging the Swin Trans"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "former [24]. CAT [6] modified the window shape and introduced a rectangle window attention to obtaining better performance. Chen et al. [4] proposed a pre-trained image processing transformer and showed that pre-trained mechanism could significantly improve the performance for low-level tasks. Li et al. [18] comprehensively analyzed the effect of pre-training and proposed a versatile model to tackle different low-level tasks. Lu et al. [25] proposed a lightweight transformer to capture long-range dependencies between similar patches in an image with the help of the specially designed efficient transformer and efficient attention mechanism. Zhang et al. [44] introduced a shift convolution and a group-wise multi-scale self-attention to reduce the complexity of transformer. HAT [5] introduced a hybrid attention mechanism to enhance the performance of window-based transformers."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. Analysis of Frequency Impact"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "This section delves into the influence of performance from a frequency perspective. To analyze the impact of various frequencies on CNN and transformer, we conduct two sets of experiments using four common used benchmarks, as illustrated in Figure 1."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "We select CARN [2], IMDN [13], EDSR [23], and SwinIR [21], CAT [6], HAT [5] as representatives of CNN and transformer structures. The process of dropping frequency components is depicted in Figure 1(c). Given a high-resolution (HR) image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X^{HR}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we perform a fast Fourier transform (FFT) on it to obtain its frequency spectrum. Subsequently, we flatten this spectrum into a sequence and arrange it in ascending order based on the magnitudes. With a sequence length of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "L"
+                                },
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+                                    "type": "text",
+                                    "content": ", we define a threshold determined by the drop ratio "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "0 \\leq \\gamma \\leq 1"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        380,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", located at the magnitude corresponding to the position "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma \\cdot L"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Frequency components with magnitudes below this threshold are set to zero. Following this, we perform an inverse fast Fourier transform (IFFT) to generate the HR image with dropped frequencies, referred to as "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        380,
+                                        530,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{drop}^{HR}(\\gamma)"
+                                },
+                                {
+                                    "bbox": [
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+                                        380,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The formulation for this process is as follows"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
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+                                    "type": "interline_equation",
+                                    "content": "X _ {d r o p} ^ {H R} (\\gamma) = I F F T (D r o p \\left(\\left| F F T \\left(X ^ {H R}\\right) \\right|, \\gamma)\\right). \\tag {1}",
+                                    "image_path": "b9d6acaba340a69a98049279cbc24ac61630221347e64ddfaebc4fccc8e9398c.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Afterward, we downsample "
+                                },
+                                {
+                                    "bbox": [
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+                                        597,
+                                        530,
+                                        659
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{drop}^{HR}(\\gamma)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        597,
+                                        530,
+                                        659
+                                    ],
+                                    "type": "text",
+                                    "content": " using bicubic interpolation to obtain the LR version "
+                                },
+                                {
+                                    "bbox": [
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+                                        597,
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+                                        659
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{drop}^{LR}(\\gamma)"
+                                },
+                                {
+                                    "bbox": [
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+                                        597,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (e.g. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\times 4"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        597,
+                                        530,
+                                        659
+                                    ],
+                                    "type": "text",
+                                    "content": " down-sampling). Finally, we employ CNN-based and transformer-based SR models to generate the super-resolved counterpart "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        597,
+                                        530,
+                                        659
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{drop}^{SR}(\\gamma)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "To analyze the dependency of CNN and transformer on high-frequency information, we compute the peak signal-to-noise ratio (PSNR) "
+                                },
+                                {
+                                    "bbox": [
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+                                        658,
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+                                        730
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P^{D}(\\gamma)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " between "
+                                },
+                                {
+                                    "bbox": [
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+                                        658,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{drop}^{SR}(\\gamma)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        658,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        658,
+                                        530,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{drop}^{HR}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        658,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then plot the PSNR drop trend to visualize the difference between the two structures. As shown in Figure 1(a), the PSNR drop ratio for each drop ratio is defined"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                }
+            ],
+            "discarded_blocks": [
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+                                    "content": "R _ {d r o p} ^ {D} (\\gamma) = \\frac {P (0) - P ^ {D} (\\gamma)}{P (0)}, \\tag {2}",
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+                                    "content": " represents the PSNR without dropping, calculated between "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": ". The figures illustrate that the transformer model exhibits reduced sensitivity to high-frequency information and excels in capturing low-frequency information, as evidenced by the smaller PSNR change compared to the CNN model as the proportion of discarded high-frequency information increases."
+                                }
+                            ]
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+                                    "content": "Furthermore, we conduct another experiment to evaluate the effectiveness of different structures in reconstructing high-frequency information. Specifically, we calculate the PSNR "
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+                                    "type": "text",
+                                    "content": " and plot the performance drop trend as previously depicted. The PSNR drop ratio for each drop ratio can be expressed as"
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+                                    "content": "R _ {d r o p} ^ {E} (\\gamma) = \\frac {P ^ {E} (\\gamma) - P (0)}{P (0)}. \\tag {3}",
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+                                    "content": "to the CNN model, indicating its limited ability to reconstruct high-frequency information from low-frequency."
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+                                    "content": "Based on these observations, we argue that the transformer requires the assistance of CNN to enhance its capability to recover intricate details. To address this, we propose a method that combines the strengths of both CNN and transformer. Specifically, we introduce CNN information as a high-frequency prior to aid the transformer in refining the global representation."
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+                                    "content": "The CRAFT network comprises three key components: Shallow feature extraction, residual cross-refinement fusion groups (RCRFGs), and reconstruction as shown in Figure 2. The shallow feature extraction module comprises a single convolutional layer, while the reconstruction module is followed by the SwinIR [21]. The RCRFG component consists of several cross-refinement fusion blocks (CRFBs), each comprising three types of blocks: the high-frequency enhancement residual blocks (HFERBs), the shift rectangle window attention blocks (SRWABs), and the hybrid fusion blocks (HFBs). We first describe the overall structure of"
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+                                            "content": "Figure 2. The framework of CRAFT. HFERB extracts the high frequency from the input features, SRWAB captures the long-range dependency of input features, and HFB integrates the output of HFERB and SRWAB to cross refine the global features. Best viewed in color."
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+                                    "type": "text",
+                                    "content": "CRAFT and then elaborate on the three key designs, including HFERB, SRWAB, and HFB."
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+                                    "content": "4.1. Model Overview"
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+                                    "content": "The input LR image is processed by a "
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+                                    "type": "inline_equation",
+                                    "content": "3 \\times 3"
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+                                    "type": "text",
+                                    "content": " convolutional layer to obtain shallow features. These features are then fed into a serial of RCRFGs to learn deep features. After the last RCRFG, a "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "3 \\times 3"
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+                                    "type": "text",
+                                    "content": " convolutional layer aggregates the features, and a residual connection is established between its output and the shallow features for facilitating training. The reconstruction module employs a "
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+                                    "type": "inline_equation",
+                                    "content": "3 \\times 3"
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+                                    "type": "text",
+                                    "content": " convolutional layer to aggregate the features, and a shuffle layer [33] is used to obtain the final SR output image."
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+                                    "content": "4.2. High-frequency Enhancement Residual Block"
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+                                    "content": "The HFERB aims to enhance the high-frequency information, as shown in Figure 2. It comprises the local feature extraction (LFE) branch and the high-frequency enhancement (HFE) branch. Specifically, we split the input features"
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+                                    "content": "F_{in}\\in \\mathbb{R}^{H\\times W\\times C}"
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+                                    "type": "text",
+                                    "content": " into two parts, and then processed by the two branches separately"
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+                                    "content": "F _ {i n} ^ {L F E}, F _ {i n} ^ {H F E} = \\operatorname {S p l i t} \\left(F _ {i n}\\right), \\tag {4}",
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+                                    "type": "inline_equation",
+                                    "content": "F_{in}^{LFE}, F_{in}^{HFE} \\in \\mathbb{R}^{H \\times W \\times C / 2}"
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+                                    "type": "text",
+                                    "content": " represent the input of LFE and HFE. For the LFE branch, we utilize a "
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+                                    "content": "\\hat {F} _ {i n} ^ {L F E} = f _ {a} \\left(\\operatorname {C o n v} _ {3 \\times 3} \\left(F _ {i n} ^ {L F E}\\right)\\right), \\tag {5}",
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+                                    "content": "where the "
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+                                    "type": "inline_equation",
+                                    "content": "Conv_{3\\times 3}(\\cdot)"
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+                                    "type": "text",
+                                    "content": " refers to the convolutional layer and the "
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+                                    "content": "f_{a}(\\cdot)"
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+                                {
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+                                    "type": "text",
+                                    "content": " represents the GELU activation layer. For the HFE branch, we employ a max-pooling layer to extract high-frequency information from the input features "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". Then, we use a "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " convolutional layer followed by a GELU activation function to enhance the high-frequency features,"
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+                                    "content": "\\hat {F} _ {i n} ^ {H F E} = f _ {a} \\left(\\operatorname {C o n v} _ {1 \\times 1} \\left(\\operatorname {M a x P o o l i n g} \\left(F _ {i n} ^ {H F E}\\right)\\right)\\right), \\tag {6}",
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+                                    "content": " means the max-pooling layer and the "
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+                                    "content": " represents the GELU activation layer. The outputs of the two branches are then concatenated and fed into a "
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+                                    "type": "text",
+                                    "content": " convolutional layer to fuse the information thoroughly. To make the network benefit from multi-scale information and maintain training stability, a skip connection is introduced. The whole process can be formulated as"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "X _ {H} = C o n v _ {1 \\times 1} (C o n c a t (\\hat {F} _ {i n} ^ {L F E}, \\hat {F} _ {i n} ^ {H F E})) + F _ {i n}, (7)",
+                                    "image_path": "1a685081c896f4d59c0360a0f4ca213e4b8be8b3cec7ff2d7c9559027396382a.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\text{Concat}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " refers to the concatenation operation and the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\text{Conv}_{1 \\times 1}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the convolutional layer."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.3. Shift Rectangle Window Attention Block"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We utilize the shift rectangle window (SRWin) to expand the receptive field, which can benefit SISR [6]. Unlike square windows, the SRWin uses rectangle windows to capture more relevant information along the longer axis. In detail, given an input "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X_{in} \\in \\mathbb{R}^{H \\times W \\times C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we divide it into "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{H \\times W}{rh \\times rw}"
+                                },
+                                {
+                                    "bbox": [
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+                                        282,
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+                                    ],
+                                    "type": "text",
+                                    "content": " rectangle windows, where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "rh"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "rw"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        282,
+                                        279,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " refer to the height and width of the rectangle window. For the "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        282,
+                                        279,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        282,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th rectangle window feature "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        282,
+                                        279,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i} \\in \\mathbb{R}^{(rh \\times rw) \\times C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we compute the query, key, and value as follows"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {Q} _ {i} = X _ {i} W _ {i} ^ {Q}, \\boldsymbol {K} _ {i} = X _ {i} W _ {i} ^ {K}, \\boldsymbol {V} _ {i} = X _ {i} W _ {i} ^ {V}, \\tag {8}",
+                                    "image_path": "781f0b1f4024841043c11111f8096cb9aa53e1eabb8102e5420e8750777c9f0f.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "where the "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "W_{i}^{Q}\\in \\mathbb{R}^{C\\times d}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "W_{i}^{K}\\in \\mathbb{R}^{C\\times d}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "W_{i}^{V}\\in \\mathbb{R}^{C\\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        419,
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+                                        468
+                                    ],
+                                    "type": "text",
+                                    "content": " represent the projection matrices and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is projection dimension which is commonly set to "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        419,
+                                        279,
+                                        468
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d = \\frac{C}{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                        468
+                                    ],
+                                    "type": "text",
+                                    "content": " where the "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of heads. The self-attention can be formulated as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {A t t e n t i o n} \\left(\\boldsymbol {Q} _ {i}, \\boldsymbol {K} _ {i}, \\boldsymbol {V} _ {i}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {\\boldsymbol {Q} _ {i} \\boldsymbol {K} _ {i} ^ {T}}{\\sqrt {d}} + B\\right) \\boldsymbol {V} _ {i}, \\tag {9}",
+                                    "image_path": "915a43fd92b6bd0162fd402805c763a1c285aa1bed521bd869ac57b1f326f0ab.jpg"
+                                }
+                            ]
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+                {
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the dynamic relative position encoding [38]. Moreover, a convolutional operation on the value is introduced to enhance local extraction capability. To capture information from different axes, we utilize two types of rectangle windows: Horizontal and vertical windows. Unlike traditional operations that utilize attention masks to limit calculations to the same window, in practice, we eliminate the mask and enable more extensive information interaction across different windows. Accordingly, we split the attention heads into two equal groups and compute the self-attention within each group separately. We then concatenate the outputs of the two groups to obtain the final output. The procedure can be expressed as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "R \\operatorname {w i n} - S A (X) = \\operatorname {C o n c a t} (V - R \\operatorname {w i n}, H - R \\operatorname {w i n}) W ^ {p}, \\tag {10}",
+                                    "image_path": "eb7a16770b3b052521f8ceec7f8a6ad78747fa80523e27198e1718e126e63189.jpg"
+                                }
+                            ]
+                        }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where the "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W^{p}\\in \\mathbb{R}^{C\\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the linear projection to fuse the features, "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " -Rwin and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " Rwin indicate the vertical and horizontal rectangle window attention. In addition,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": "a multi-layer perceptron (MLP) is used for further feature transformations. The whole process can be formulated as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} X = R \\operatorname {w i n} - S A \\left(L N \\left(X _ {i n}\\right)\\right) + X _ {i n} \\\\ X = M P (L N (X)) - X \\end{array} \\tag {11}",
+                                    "image_path": "12d1225af560a939602b56f0579eb6b10ab1d3bc09fa8893b070dfb5c6591454.jpg"
+                                }
+                            ]
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "X _ {S} = M L P (L N (X)) + X,",
+                                    "image_path": "2b98c2793e62525f4fd068cc84146f9831e7b66eefca8aa6e9a1b2dcbb569bb5.jpg"
+                                }
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+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where the "
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "LN"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the LayerNorm layer."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.4. Hybrid Fusion Block"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "To better integrate the merits of CNN and transformer (HFERB and SRWAB), we have designed a hybrid fusion block (HFB), which is illustrated in Figure 2. We formulate the output of HFERB as the high frequency prior query and the output of SRWAB as key, value and calculate the inter-attention to refine the global features which are obtained from SRWAB. Moreover, most existing methods focus on spatial relations and overlook channel information. To overcome this limitation, we perform inter-attention based on the channel dimension to explore channel dependencies. This design will significantly reduce complexity. Traditional methods that utilize spatial attention tend to result in significant computational complexity (e.g., "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        203,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "O(N^2 C)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N \\gg C"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": "), where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": " represents the length of the sequence and "
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+                                    "type": "text",
+                                    "content": " represents the channel dimension. In contrast, our channel attention design can transfer the quadratic component to the channel dimension (e.g., "
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+                                    "type": "text",
+                                    "content": ". As to the output of SRWAB, "
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+                                    "content": ". Following the [42], we perform the reshape operation on "
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+                                    "type": "text",
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " represents the learnable parameter. Meanwhile, we add the refinement features to the "
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+                                    "type": "text",
+                                    "content": " to get the fusion output "
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+                                    "type": "text",
+                                    "content": ". In addition, we feed "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to an improved feed-forward network [42] to aggregate the features further. The details of this structure are shown in Figure 2. It introduced a gate mechanism to fully extract the spatial and channel information and gain better performance. The whole process can be formulated as"
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+                                    "content": "X _ {f u s e} = \\text {I n t e r - A t t e n} (L N \\left(X _ {S}\\right), X _ {H}) + X _ {S} \\tag {13}",
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+                                    "content": "X _ {H F B} = I M L P (L N (X)) + X _ {f u s e},",
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+                                    "content": " means LayerNorm operation, IMLP represents the improved MLP, and Inter-Atten indicates"
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+                                            "content": "Table 1. Performance comparison of different SISR models on five benchmarks. Params represents the total number of network parameters. Results for the best and second best candidates are highlighted, and underlined."
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+                                            "html": "<table><tr><td>Scale</td><td>Model</td><td>Params</td><td>Set5 (PSNR/SSIM)</td><td>Set14 (PSNR/SSIM)</td><td>BSD100 (PSNR/SSIM)</td><td>Urban100 (PSNR/SSIM)</td><td>Manga109 (PSNR/SSIM)</td></tr><tr><td rowspan=\"10\">×2</td><td>EDSR-baseline [23]</td><td>1370K</td><td>37.99/0.9604</td><td>33.57/0.9175</td><td>32.16/0.8994</td><td>31.98/0.9272</td><td>38.54/0.9769</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>37.76/0.9590</td><td>33.52/0.9166</td><td>32.09/0.8978</td><td>31.92/0.9256</td><td>38.36/0.9765</td></tr><tr><td>IMDN [13]</td><td>694K</td><td>38.00/0.9605</td><td>33.63/0.9177</td><td>32.19/0.8996</td><td>32.17/0.9283</td><td>38.88/0.9774</td></tr><tr><td>LatticeNet [26]</td><td>756K</td><td>38.06/0.9607</td><td>33.70/0.9187</td><td>32.20/0.8999</td><td>32.25/0.9288</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>548k</td><td>38.01/0.9605</td><td>33.62/0.9183</td><td>32.19/0.8999</td><td>32.10/0.9283</td><td>38.67/0.9772</td></tr><tr><td>HPUN-L [34]</td><td>714K</td><td>38.09/0.9608</td><td>33.79/0.9198</td><td>32.25/0.9006</td><td>32.37/0.9307</td><td>39.07/0.9779</td></tr><tr><td>SwinIR-light [21]</td><td>878K</td><td>38.14/0.9611</td><td>33.86/0.9206</td><td>32.31/0.9012</td><td>32.76/0.9340</td><td>39.12/0.9783</td></tr><tr><td>ESRT [25]</td><td>777K</td><td>38.03/0.9600</td><td>33.75/0.9184</td><td>32.25/0.9001</td><td>32.58/0.9318</td><td>39.12/0.9774</td></tr><tr><td>ELAN-light [44]</td><td>582K</td><td>38.17/0.9611</td><td>33.94/0.9207</td><td>32.30/0.9012</td><td>32.76/0.9340</td><td>39.11/0.9782</td></tr><tr><td>CRAFT (Ours)</td><td>737K</td><td>38.23/0.9615</td><td>33.92/0.9211</td><td>32.33/0.9016</td><td>32.86/0.9343</td><td>39.39/0.9786</td></tr><tr><td rowspan=\"11\">×3</td><td>EDSR-baseline [23]</td><td>1555K</td><td>34.37/0.9270</td><td>30.28/0.8417</td><td>29.09/0.8052</td><td>28.15/0.8527</td><td>33.45/0.9439</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>34.29/0.9255</td><td>30.29/0.8407</td><td>29.06/0.8034</td><td>28.06/0.8493</td><td>33.50/0.9440</td></tr><tr><td>IMDN [13]</td><td>703K</td><td>34.36/0.9270</td><td>30.32/0.8417</td><td>29.09/0.8046</td><td>28.17/0.8519</td><td>33.61/0.9445</td></tr><tr><td>LatticeNet [26]</td><td>765K</td><td>34.53/0.9281</td><td>30.39/0.8424</td><td>29.15/0.8059</td><td>28.33/0.8538</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>544k</td><td>34.36/0.9267</td><td>30.34/0.8421</td><td>29.11/0.8054</td><td>28.15/0.8523</td><td>33.51/0.9441</td></tr><tr><td>HPUN-L [34]</td><td>723K</td><td>34.56/0.9281</td><td>30.45/0.8445</td><td>29.18/0.8072</td><td>28.37/0.8572</td><td>33.90/0.9463</td></tr><tr><td>SwinIR-light [21]</td><td>886K</td><td>34.62/0.9289</td><td>30.54/0.8463</td><td>29.20/0.8082</td><td>28.66/0.8624</td><td>33.98/0.9478</td></tr><tr><td>LBNet [9]</td><td>736K</td><td>34.47/0.277</td><td>30.38/0.8417</td><td>29.13/0.8061</td><td>28.42/0.8559</td><td>33.82/0.9406</td></tr><tr><td>ESRT [25]</td><td>770K</td><td>34.42/0.9268</td><td>30.43/0.8433</td><td>29.15/0.8063</td><td>28.46/0.8574</td><td>33.95/0.9455</td></tr><tr><td>ELAN-light [44]</td><td>590K</td><td>34.61/0.9288</td><td>30.55/0.8463</td><td>29.21/0.8081</td><td>28.69/0.8624</td><td>34.00/0.9478</td></tr><tr><td>CRAFT (Ours)</td><td>744K</td><td>34.71/0.9295</td><td>30.61/0.8469</td><td>29.24/0.8093</td><td>28.77/0.8635</td><td>34.29/0.9491</td></tr><tr><td rowspan=\"11\">×4</td><td>EDSR-baseline [23]</td><td>1518K</td><td>32.09/0.8938</td><td>28.58/0.7813</td><td>27.57/0.7357</td><td>26.04/0.7849</td><td>30.35/0.9067</td></tr><tr><td>CARN [2]</td><td>1592K</td><td>32.13/0.8937</td><td>28.60/0.7806</td><td>27.58/0.7349</td><td>26.07/0.7837</td><td>30.47/0.9084</td></tr><tr><td>IMDN [13]</td><td>715K</td><td>32.21/0.8948</td><td>28.58/0.7811</td><td>27.56/0.7353</td><td>26.04/0.7838</td><td>30.45/0.9075</td></tr><tr><td>LatticeNet [26]</td><td>777K</td><td>32.18/0.8943</td><td>28.61/0.7812</td><td>27.57/0.7355</td><td>26.14/0.7844</td><td>-/-</td></tr><tr><td>LAPAR-A [19]</td><td>659k</td><td>32.15/0.8944</td><td>28.61/0.7818</td><td>27.61/0.7366</td><td>26.14/0.7871</td><td>30.42/0.9074</td></tr><tr><td>HPUN-L [34]</td><td>734K</td><td>32.31/0.8962</td><td>28.73/0.7842</td><td>27.66/0.7386</td><td>26.27/0.7918</td><td>30.77/0.9109</td></tr><tr><td>SwinIR-light [21]</td><td>897K</td><td>32.44/0.8976</td><td>28.77/0.7858</td><td>27.69/0.7406</td><td>26.47/0.7980</td><td>30.92/0.9151</td></tr><tr><td>LBNet [9]</td><td>742K</td><td>32.29/0.8960</td><td>28.68/0.7832</td><td>27.62/0.7382</td><td>26.27/0.7906</td><td>30.76/0.9111</td></tr><tr><td>ESRT [25]</td><td>751K</td><td>32.19/0.8947</td><td>28.69/0.7833</td><td>27.69/0.7379</td><td>26.39/0.7962</td><td>30.75/0.9100</td></tr><tr><td>ELAN-light [44]</td><td>601K</td><td>32.43/0.8975</td><td>28.78/0.7858</td><td>27.69/0.7406</td><td>26.54/0.7982</td><td>30.92/0.9150</td></tr><tr><td>CRAFT (Ours)</td><td>753K</td><td>32.52/0.8989</td><td>28.85/0.7872</td><td>27.72/0.7418</td><td>26.56/0.7995</td><td>31.18/0.9168</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "the proposed inter-attention mechanism, which introduces high-frequency prior to refining the global representations."
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+                                    "content": "5. Experiments"
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+                                    "content": "5.1. Data and Metrics"
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+                                    "content": "In this paper, we adopt the DIV2K [1] as the training dataset, which includes 800 training images. Meanwhile, five benchmarks are used for evaluation, including Set5 [3], Set14 [43], BSD100 [27], Urban100 [12], and Manga109 [28] with three magnification factors: "
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "text",
+                                    "content": ". The quality of the images is evaluated using PSNR, and SSIM [39]. The complexity of the model is indicated by its parameters."
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+                                    "content": "5.2. Implementation Details"
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+                                    "content": "Following the general setting, we use bicubic to obtain the corresponding LR images from the original HR images. During training, we randomly crop the images into "
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+                                    "type": "text",
+                                    "content": " patches, and the total training iterations are "
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+                                    "type": "text",
+                                    "content": ". Meanwhile, data augmentation is performed, such as random horizontal flipping and "
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+                                    "type": "text",
+                                    "content": " rotation. The Adam optimizer with "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\beta_{2} = 0.999"
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+                                    "type": "text",
+                                    "content": " is adopted to minimize the "
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+                                    "type": "text",
+                                    "content": " Loss. The batch size is set to 64, the initial learning"
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+                                    "type": "text",
+                                    "content": "rate is set to "
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+                                    "type": "inline_equation",
+                                    "content": "2 \\times 10^{-4}"
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+                                    "type": "text",
+                                    "content": " and reduced by half at the milestone [250K, 400K, 450K, 475K]. In addition, the model is trained on 4 NVIDIA 3090 GPUs using the PyTorch toolbox. In CRAFT, we have set the RCRFG number to 4 and the CRFB number to 2 for each RCRFG. Each CRFB is comprised of 1 HFERB and 2 SRWABs for efficiency. The feature channel, attention head, and MLP expansion ratio are set to 48, 6, and 2, respectively. We also set the IMLP expansion ratio to 2.66, as in [42]. To obtain two types of rectangle windows, we have set the rectangle window size to "
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+                                    "content": "[sh, sw]"
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+                                    "type": "text",
+                                    "content": " as [4, 16] and [16, 4]."
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+                                    "content": "5.3. Comparison with state-of-the-art methods"
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+                                    "content": "We compare with several state-of-the-art SISR methods to demonstrate the effective of the proposed CRAFT model, including EDSR [23], CARN [2], IMDN [13], LatticeNet [26], LAPAR [19], SwinIR [21], HPUN [34], ESRT [25], LBNet [9], and ELAN [44]."
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+                                    "type": "text",
+                                    "content": "Quantitative Results. The experimental results for SISR are presented in Table 1, where the proposed CRAFT model demonstrates competitive performance across all benchmarks. Particularly, when compared to traditional CNN-based methods like EDSR, the proposed CRAFT achieves significant performance improvements of "
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+                                    "content": " reduction in the number of parameters on the Manga109 dataset. Regarding transformer-based methods [25, 21, 44], the proposed CRAFT gains performance improvements of 0.34dB, 0.31dB, and 0.29dB, respectively, with a comparable number of parameters under the magnification factor of "
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+                                    "content": "Qualitative Results. We present a visual comparison "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " in Figure 3 and analyze the results. Our proposed CRAFT model integrates the strengths of both CNN and transformer structures, leading to accurate line direction recovery while preserving image details. To further investigate the performance, we compare the local attribution map (LAM) [11] between CRAFT and SwinIR, as shown in Figure 4. LAM indicates the correlation between the significance of each pixel in LR and the SR of the patch that is outlined with the red box. By leveraging a broader range of information, our model achieves improved results. Furthermore, we examine the diffusion index (DI), which signifies the range of pixels involved. A larger DI indicates a"
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+                                    "type": "text",
+                                    "content": "wider scope of attention. Compared to SwinIR, our model exhibits a higher DI, implying that it can capture more contextual information. These results demonstrate the effectiveness of the proposed CRAFT method."
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+                                    "content": " in HFB and treated the output of SRWAB as "
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+                                    "content": " to verify whether global features are dominant in restoration and high-frequency features only serve as a prior for refining the global representation. As shown in Table 3, compared to the original design, swapping the input leads to a significant drop in performance, with a 0.51dB decrease in PSNR. Furthermore, we also performed an experiment to formulate the model as a cascade structure to verify the effectiveness of the design introducing high-frequency priors. As shown in Table 3, the "
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+                                    "content": ", as shown in Table 4. The analysis considered parameters, FLOPs, GPU memory consumption, and average inference time. GPU memory was measured using the official PyTorch function, and time cost was calculated based on 100 inference runs. Compared to SwinIR, CRAFT has fewer parameters and FLOPs, and requires less memory consumption and inference time. Additionally, we analyzed the complexity of our CRAFT framework and summarized the findings in Table 5. We observed that SRWAB contributes approximately "
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+                                    "content": "the computational burden."
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+                                    "content": "6. Conclusion"
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+                                    "content": "This paper investigates the impact of frequency on the performance of CNN and transformer structures in SISR and finds that transformer structures are more adept at capturing low-frequency information, but have limited capability to reconstruct high-frequency representations compared to CNN. To address this issue, we design a feature modulation transformer, named cross-refinement adaptive feature modulation transformer (CRAFT), which comprises three key components: the high-frequency enhancement residual block (HFERB), the shift rectangle window attention block (SRWAB), and the hybrid fusion block (HFB). The HFERB is designed to extract high-frequency features, while the SRWAB captures global representations. In the HFB, we treat the output of HFERB as a high-frequency prior and the output of SRWAB as key and value, and use interattention to refine the global representation. Experimental results demonstrate that CRAFT outperforms state-of-the-art methods by up to 0.29dB with relatively fewer parameters."
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+                                    "content": "Acknowledgements"
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+                                    "content": "This work is supported by the National Natural Science Foundation of China (NSFC) under Grant U19A2052 and Grant 62020106011, as well as by the National Key Lab of Autonomous Intelligent Unmanned Systems."
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+                                        }
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+                                        }
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+                                            "type": "text",
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+                                        }
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+                        {
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+                                299,
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+                        },
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+                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
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+                                        }
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+                        },
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+                                            "content": "[46] Yulun Zhang, Kunpeng Li, Kai Li, Lichen Wang, Bineng Zhong, and Yun Fu. Image super-resolution using very deep residual channel attention networks. In Proceedings of the European Conference on Computer Vision (ECCV), pages 294-310, 2018. 1"
+                                        }
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+                                            "content": "[47] Zhengdong Zhang and Vivienne Sze. Fast: A framework to accelerate super-resolution processing on compressed videos. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 1015-1024, 2017. 1"
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diff --git a/2023/Feature Prediction Diffusion Model for Video Anomaly Detection/b7c9cb2d-d935-41b6-bf79-feb2138dade6_content_list.json b/2023/Feature Prediction Diffusion Model for Video Anomaly Detection/b7c9cb2d-d935-41b6-bf79-feb2138dade6_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..9c28309a08dccb781a3854345f6477c6f71bc831
--- /dev/null
+++ b/2023/Feature Prediction Diffusion Model for Video Anomaly Detection/b7c9cb2d-d935-41b6-bf79-feb2138dade6_content_list.json	
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+[
+    {
+        "type": "text",
+        "text": "Feature Prediction Diffusion Model for Video Anomaly Detection",
+        "text_level": 1,
+        "bbox": [
+            155,
+            130,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Cheng Yan $^{1}$ , Shiyu Zhang $^{1}$ , Yang Liu $^{2}$ , Guansong Pang $^{3*}$ , Wenjun Wang $^{1}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ Tianjin University  $^{2}$ Zhejiang University  $^{3}$ Singapore Management University",
+        "bbox": [
+            158,
+            205,
+            808,
+            226
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            258,
+            313,
+            276
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anomaly detection in the video is an important research area and a challenging task in real applications. Due to the unavailability of large-scale annotated anomaly events, most existing video anomaly detection (VAD) methods focus on learning the distribution of normal samples to detect the substantially deviated samples as anomalies. To well learn the distribution of normal motion and appearance, many auxiliary networks are employed to extract foreground object or action information. These high-level semantic features effectively filter the noise from the background to decrease its influence on detection models. However, the capability of these extra semantic models heavily affects the performance of the VAD methods. Motivated by the impressive generative and anti-noise capacity of diffusion model (DM), in this work, we introduce a novel DM-based method to predict the features of video frames for anomaly detection. We aim to learn the distribution of normal samples without any extra high-level semantic feature extraction models involved. To this end, we build two denoising diffusion implicit modules to predict and refine the features. The first module concentrates on feature motion learning, while the last focuses on feature appearance learning. To the best of our knowledge, it is the first DM-based method to predict frame features for VAD. The strong capacity of DMs also enables our method to more accurately predict the normal features than non-DM-based feature prediction-based VAD methods. Extensive experiments show that the proposed approach substantially outperforms state-of-the-art competing methods. The code is available atFPDM.",
+        "bbox": [
+            75,
+            292,
+            473,
+            731
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            761,
+            209,
+            777
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Video anomaly detection (VAD) aims at identifying the unusual events that rarely appear and are different from normal behaviors in videos. Successfully detecting the anomalies, such as traffic accidents, violence, and stampedes, is of great importance in ubiquitous video surveillance for pub-",
+        "bbox": [
+            75,
+            787,
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+            864
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/dc0103f01572b2a8b4542ad89abc4707b626c5992a4924da8e0cd5ba2c086d88.jpg",
+        "image_caption": [
+            "Figure 1. Overview of three generative VAD approaches. Existing state-of-the-art GAN-based or auto-encoder-based approaches heavily rely on foreground object or action information extracted by auxiliary models, such as object detection, action recognition or optical flow network, to generate features/images for effective performance. By contrast, our proposed diffusion model-based approach does not have this reliance and can make accurate feature prediction using only simple networks as encoder to extract basic image features as input."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            263,
+            879,
+            433
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "lic safety. However, VAD is a challenging task since the anomaly events are unbounded in real-world applications and it is difficult to collect large-scale labeled data.",
+        "bbox": [
+            496,
+            595,
+            892,
+            641
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There have been many VAD methods [9, 10, 14, 19, 23, 33, 34, 39, 45, 46, 57, 62, 68, 71] proposed over the years to handle this issue, in which one-class learning-based methods are preferred due to the relatively accessible normal training set and their capacity to achieve better performance [44]. The one-class VAD methods assume the availability of the training data in which all samples are normal, and build different models to learn the distribution of normal data. Generative modeling is a widely-used technique in this line since the normal samples can be better generated than anomalies after training. Generative Adversarial Networks (GAN) [22, 52, 71, 72] and Auto-Encoder (AE) [24, 29, 40, 46] are two popular frameworks. Although these generative approaches achieve promising performance in VAD, there are three main challenges: (1) the GAN/AE-based methods suffer from the weak generative capacity, leading to more noise from the low-quality generated image, which reduces the",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Guansong Pang is the corresponding author, e-mail: pangguansong@gmail.com",
+        "bbox": [
+            76,
+            875,
+            468,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "5527",
+        "bbox": [
+            482,
+            944,
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+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "performance, (2) current SOTA methods often employ some auxiliary models, e.g., object detection and action recognition models, to capture the features of the foreground object or action information, and as a result, the performance relies heavily on the representation capacity of these high-level semantic models, and (3) the anomaly events are often characterized by the novel appearance and/or abnormal motion, which increase the difficulty of the generative models to capture the normality/abnormality in both aspects.",
+        "bbox": [
+            75,
+            90,
+            468,
+            226
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In very recent years, diffusion models (DMs) [26, 53], have been attracting increasing attention due to their powerful generative capacity and excellent performance in various tasks [5, 17, 49, 53]. Different from GAN and AE, the diffusion models inject Gaussian noise into the training data and then learn to recover the samples from those noisy data. The DMs are featured by minor modifications and rectification of the generated samples in each step, enabling a more stable generation of more realistic samples. Therefore, the DM-based approaches outperform the GAN/AE-based approaches in many generative tasks [6, 12, 50, 63].",
+        "bbox": [
+            75,
+            227,
+            470,
+            393
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Motivated by the powerful generative capacity of these diffusion models, we propose a novel DM-based approach for anomaly detection. For the second and third challenges mentioned above, as shown in Fig. 1, we devise two complementary denoising DM modules to learn the distribution of normal samples. One module emphasizes learning the distribution of motion, while another module focuses on appearance learning. We employ a simple neural network as the encoder for extracting basic 2D features. Many previous studies [21, 49] have shown that many simple pre-trained networks can effectively extract basic texture information of images even if there are novel classes beyond the training data. Therefore, we adopt a basic 2D feature extractor, which is different from many existing generative methods that utilize high-level semantic models for 3D feature extraction. Based on this, our goal is to learn the distribution of normal features and predict the features of samples for anomaly detection.",
+        "bbox": [
+            75,
+            393,
+            470,
+            664
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, there are three main contributions:",
+        "bbox": [
+            96,
+            666,
+            410,
+            681
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We introduce a novel diffusion model-based method to predict the features of each sample for VAD. To the best of our knowledge, it is the first work in utilizing DMs for VAD.",
+            "- We design two types of DDIM module for respective motion and appearance learning from the normal samples to guarantee the generative quality of predicted features.",
+            "- The proposed model takes 2D images as input with no auxiliary semantic networks, while achieving a highly comparable performance to the methods utilizing high-level 3D semantic features."
+        ],
+        "bbox": [
+            96,
+            695,
+            467,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Experimental results on four publicly available video anomaly detection datasets demonstrate that our method substantially outperforms the image feature-based VAD counterparts and performs comparably well to methods using 3D semantic features.",
+        "bbox": [
+            498,
+            90,
+            890,
+            167
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            180,
+            635,
+            196
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For different application scenarios, the video anomaly detection methods can be generally classified into three categories, semi-supervised, one-class, and unsupervised VAD, according to the annotation of training samples. Since our method belongs to the one-class type, we only review one-class VAD methods.",
+        "bbox": [
+            498,
+            205,
+            890,
+            295
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The early one-class VAD methods are two-step approaches in which feature extraction and learning are separated. They first use hand-crafted feature descriptors to present each frame, such as 3D gradients features [38], histogram of gradient (HOG) [16], histogram optical flow (HOF) [16], bag of words (BOW) etc., then build a shallow model to learn the normal distribution, such as dictionary-based models [75], probabilistic models [13, 41], and reconstruction models [16, 38, 75]. These traditional methods suffer from the poor performance of hand-crafted features. With the development of deep learning [35, 36, 64-67], convolutional neural network-based methods followed close on another. The CNN integrates feature extraction and learning into an end-to-end frame [42, 43, 70]. The majority of these CNN-based methods belong to the generative approach, in which the model applies feature learning on normality and detects anomalies according to the difference between the generated and original samples. The generative adversarial network (GAN) [20, 51, 73] and auto-encoder-based network (AE) [25, 27, 56] are widely used for such normal feature learning. Based on these frameworks, memory module [24], and feature prediction module [33] are proposed to enhance the capacity of feature learning. To further improve performance, some high-level feature extraction models, e.g., object detection [23, 37], action recognition [62], and optical flow [33], are employed to obtain foreground or motion information for the learning of normality. The auxiliary models bring the benefit to these VAD methods while increasing the dependency on semantic presentations.",
+        "bbox": [
+            498,
+            297,
+            890,
+            734
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, diffusion models have achieved state-of-the-art performance on many generative tasks and become a hot research topic [5, 17, 26, 49, 53]. Many applications have already emerged in computer vision, such as image inpainting [7, 15, 54], image manipulation [47], image superresolution [7, 18], and image-to-image translation [50, 76]. The state-of-the-art performance of these applications confirms that the DM-based models have remarkable generative capacity. To further expand DMs to mainstream computer vision tasks, some DM-based latent representation learning methods have been proposed, such as DiffusionDet for ob",
+        "bbox": [
+            498,
+            734,
+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "5528",
+        "bbox": [
+            482,
+            945,
+            514,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/00271f01bcafe7d845cd92647365d3e5d85a16492f2ed1a8a3093fa89f189edb.jpg",
+        "image_caption": [
+            "Figure 2. The framework of the proposed method. It contains a frame-level 2D encoder and two DM-based modules, including a feature prediction diffusion module and a feature refinement diffusion module. The feature prediction diffusion module adopts consecutive  $k$  features as input, in which only the last one accepts the diffusion process. With the temporal information from the consecutive frames, this module emphasizes learning the distribution of normal motion. The feature refinement diffusion module takes the sampling output of previous module as input and the  $k$ -th original features as a condition for training, which focuses on the appearance learning."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            150,
+            90,
+            831,
+            385
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ject detection [12], SegDiff for segmentation [2], and SBG classifier for classification [77]. These discriminative tasks usually require more powerful models that are not easy to be disturbed by background. Therefore the success of these methods on different tasks verifies the anti-noise ability of DM. The early diffusion models, such as the denoising diffusion probabilistic model (DDPM), have quite a few denoising steps required in the sampling stage due to the Markov process converting data distribution via tiny modification. To accelerate the sampling process, many speed-up diffusion methods have been proposed [30, 53, 74]. The denoising diffusion implicit model (DDIM) is widely used due to its training-free property. The DDIM requires no extra training and can directly apply the advanced sampling algorithms with fewer steps and higher fidelity. Therefore DDIM-based methods are more likely to be adopted in real applications.",
+        "bbox": [
+            75,
+            486,
+            472,
+            744
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            763,
+            168,
+            779
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our key motivation is to design a diffusion model-based approach to well learn the distribution of normal motion and appearance without the help of 3D feature extraction networks. In the inference stage, the feature of a normal sample is more easily predicted by the optimized model than that of the abnormal one.",
+        "bbox": [
+            75,
+            792,
+            468,
+            881
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 2, our framework contains three parts,",
+        "bbox": [
+            96,
+            885,
+            468,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "i.e. a frame encoder, a feature prediction diffusion module, and a feature refinement diffusion module. First, we employ an encoder to extract the feature of each frame. Any pretrained CNN can be used as the encoder. Here we adopt a slight encoder from [48] since (1) the size of output feature map is 64 times spatially smaller than that of the original image and contains only four channels, which significantly reduces the computation of the following diffusion modules, and (2) the pretraining of this encoder is unsupervised, which is more accessible. To predict the feature, we design two DDIM-based modules to predict and refine the feature of each frame. Notice that DDIM has the same training procedure as DDPM but is more efficient in the sampling stage since it adopts a jump-step implicit sampler rather than extracting noise information step by step. The feature prediction diffusion module emphasizes learning the distribution of motion, and the feature refinement diffusion module focuses on appearance distribution learning.",
+        "bbox": [
+            496,
+            486,
+            890,
+            758
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            770,
+            702,
+            786
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The problem aims to address is to generate a feature by giving several continuous video frames and then estimate whether this feature belongs to the learned distribution. Formally, given a video clip with  $k$  consecutive frames  $X = \\{\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_k\\}$  our goal is to predict the feature of  $k$  -th frame denoted as  $\\ddot{f} (\\mathbf{x}_k)$  and  $\\ddot{f}_k$  for short. We use  $\\dot{f}_k$  and  $\\ddot{f}_k$  to denote the output of the feature prediction and re",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "5529",
+        "bbox": [
+            482,
+            944,
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+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "finement diffusion module. Since the time step is involved, we use  $f_{k}^{t}$  to denote the feature of  $k$ -the frame at time step  $t$ . To this end,  $f_{k}^{0}$  refers to the  $k$ -th feature at time step 0, which is equivalent to  $f_{k}$ . Compared with the original feature denoted as  $f_{k}$ , the anomaly score of the  $k$ -th frame can be calculated by Mean Square Error between  $f_{k}$  and  $\\ddot{f}_{k}$ .",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Feature prediction diffusion module",
+        "text_level": 1,
+        "bbox": [
+            76,
+            190,
+            390,
+            207
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Different the previous work [33] that adopts  $k$  samples to predict the  $(k + 1)$ -th sample, we take the features  $\\{f_1^0,f_2^0,\\dots ,f_{k - 1}^0\\}$  of 1 to  $k - 1$  frames and the noisy feature  $f_{k}^{t}$  of the  $k$ -th frame together as the input, to predict the feature  $\\dot{f}_k^0$ . To this end, we build a feature prediction diffusion module to progressively remove the noise of  $f_{k}^{t}$  by using implicit sampling [53] to generate  $\\dot{f}_k^0$ .",
+        "bbox": [
+            75,
+            213,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For training, the goal of our diffusion models is to learn a distribution  $p_{\\theta}(f^0)$  that approximates the original data distribution  $q(f^0)$ . In forward process, the posterior  $q(f^{1:T}|f^0)$  is fixed to a Markov chain:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(f ^ {1: T} \\mid f ^ {0}\\right) := \\prod_ {t = 1} ^ {T} q \\left(f ^ {t} \\mid f ^ {t - 1}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            169,
+            393,
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+            435
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $t\\in [1,T]$  is the time step, and:",
+        "bbox": [
+            76,
+            440,
+            326,
+            455
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(f ^ {t} \\mid f ^ {t - 1}\\right) := \\mathcal {N} \\left(f ^ {t}; \\sqrt {\\alpha_ {t}} f ^ {t - 1}, \\left(1 - \\alpha_ {t}\\right) \\mathbf {I}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            465,
+            468,
+            484
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha_{t}\\in \\{\\alpha_{t}\\}_{t = 1}^{T}$  is a schedule to control the percentage of  $f^{t - 1}$ ,  $(1 - \\alpha_{t})$  controls the percentage of noise. With time step  $t$  increase,  $\\alpha_{t}$  decrease. Based on these properties, the  $f^t$  can be presented by the linear combination of  $f^0$  and standard Gaussian noise  $\\epsilon$  as following:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf ^ {t} = \\sqrt {\\alpha_ {t}} f ^ {0} + \\sqrt {1 - \\alpha_ {t}} \\epsilon . \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            583,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To learn the distribution  $p_{\\theta}(f^0)$ , we build a U-net diffusion network  $\\epsilon_{\\theta}(\\cdot)$  based on the LDM [49]. To well predict the features, we modify two parts of the LDM: (1) we discard the latent condition part and modify all the cross-attention layers to traditional attention layers, and (2) each input sample contains  $k$  features  $\\{f_1^0,f_2^0,\\dots ,f_k^t\\}$  where only the  $k$ -th feature is applied diffusion forward process. There are two reasons for such modification: (1) we expect to learn the distribution of features from normal samples without any other latent condition involved, and (2) combined with the consecutive features of previous frames, we can provide the motion information to the  $\\epsilon_{\\theta}(\\cdot)$ , making this diffusion module focus on feature motion learning.",
+        "bbox": [
+            75,
+            606,
+            468,
+            801
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Following [26,53], the simplified version of the objective is used for training defined as:",
+        "bbox": [
+            75,
+            801,
+            468,
+            833
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\theta} = \\mathbb {E} \\left[ | | \\epsilon_ {\\theta} \\left(f _ {1} ^ {0}, f _ {2} ^ {0}, \\dots , f _ {k} ^ {t}, t\\right) - \\epsilon | | _ {2} ^ {2} \\right], \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            845,
+            468,
+            864
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $t$  is the time step,  $\\epsilon_{\\theta}(\\cdot ,t)$  is the prediction noise at time  $t$ . Substituting  $f^{t}$  of Eq. (3) into Eq. (4), the parameter",
+        "bbox": [
+            75,
+            869,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$\\theta$  can be optimized by given sufficient feature samples and random time step  $t \\in [1, T]$ .",
+        "bbox": [
+            498,
+            90,
+            890,
+            119
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the reverse process, the features of the  $k$ -th sample at time  $t-1$  can be generated once given  $\\{f_1^0, f_2^0, \\dots, f_k^t\\}$  by the following formula:",
+        "bbox": [
+            498,
+            121,
+            890,
+            166
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} f _ {k} ^ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\left(\\frac {f _ {k} ^ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\theta} \\left(f _ {1} ^ {0} , f _ {2} ^ {0} , \\cdots , f _ {k} ^ {t} , t\\right)}{\\sqrt {\\alpha t}}\\right) \\tag {5} \\\\ + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\theta} \\left(f _ {1} ^ {0}, f _ {2} ^ {0}, \\dots , f _ {k} ^ {t}, t\\right) + \\sigma_ {t} \\epsilon \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            509,
+            186,
+            890,
+            248
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma_t \\in \\{\\sigma_t\\}_{t=1}^T$  is a schedule to control the added noise for each step. At sampling stage, the (t-1)-th step takes the features  $\\{f_1^0, f_2^0, \\dots, f_k^t\\}$  as input to predict  $f_k^{t-1}$ .",
+        "bbox": [
+            498,
+            257,
+            890,
+            305
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The consecutive supervision on the reverse process can effectively guarantee the motion prediction while it may miss some appearance details since the non-noisy  $k-1$  features are helpful for motion learning while having an effect on appearance learning. To this end, we create another DDIM module to refine the appearance information.",
+        "bbox": [
+            498,
+            305,
+            890,
+            393
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Feature refinement diffusion module",
+        "text_level": 1,
+        "bbox": [
+            500,
+            402,
+            815,
+            417
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We build a feature refinement diffusion module next to the prediction module. This refinement model places emphasis on learning the appearance distribution of features. Similarly, we adopt the LDM-based U-net as the diffusion network for refining, in which the condition part is maintained. We take the output of the previous prediction module, i.e. the denoised feature  $\\dot{f}_k^0$  as input, and use the original feature  $f_{k}^{0}$  of the  $k$ -th frame as condition, to generate the refined features denoted as  $\\ddot{f}_k^0$ . The condition  $f_{k}^{0}$  is used for cross-attention to guarantee the feature appearance learning. The goal of the feature refinement diffusion module is to learn a distribution  $p_{\\varphi}(\\dot{f}^{0})$  that approximates  $q(f^0)$ .",
+        "bbox": [
+            498,
+            426,
+            890,
+            609
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Same with the previous feature prediction module, the posterior  $q(\\dot{f}^{1:T}|\\dot{f}^{0})$  is fixed to a Markov chain, and the input  $\\dot{f}^t$  at time step  $t$  can be calculated according to Eq. (3) by given  $\\dot{f}^{0}$  and a Gaussian noise  $\\epsilon$ .",
+        "bbox": [
+            498,
+            609,
+            890,
+            667
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To make this refinement network  $\\epsilon_{\\varphi}(\\cdot)$  focus on appearance learning, we augment the underlying UNet backbone with cross-attention mechanism and take the original feature  $f_{k}^{0}$  as the condition into the cross-attention layers. We flatten the feature  $f_{k}^{0}$ , then use a linear transform to obtain a  $d$ -dimensional vector, which is defined as  $\\widehat{f}_{k}^{0}$ . The cross-attention is implemented according to:",
+        "bbox": [
+            498,
+            669,
+            890,
+            777
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}}\\right) V, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            609,
+            787,
+            890,
+            821
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ = W _ {q} \\cdot \\widehat {f} _ {k} ^ {0}, K = W _ {k} \\cdot \\phi \\left(\\dot {f} _ {k} ^ {t}\\right), V = W _ {v} \\cdot \\phi \\left(\\dot {f} _ {k} ^ {t}\\right), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            521,
+            840,
+            890,
+            859
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{k}$ ,  $W_{q}$ ,  $W_{v}$  are learnable projection matrices and  $\\phi(\\dot{f}_{k}^{t})$  is the input feature map of each cross-attention layer.",
+        "bbox": [
+            500,
+            868,
+            890,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5530",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The  $\\widehat{f}_k^0$  is changeless for different cross-attention layer that provides a consistent appearance supervision on feature learning. The loss function is also the simplified version of DDIM, defined as:",
+        "bbox": [
+            75,
+            89,
+            468,
+            150
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\varphi} = \\mathbb {E} \\left[ | | \\epsilon_ {\\varphi} \\left(\\dot {f} _ {k} ^ {t}, \\widehat {f} _ {k} ^ {0}, t\\right) - \\epsilon | | _ {2} ^ {2} \\right]. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            162,
+            468,
+            188
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For reverse process, we can obtain the feature at  $t - 1$  time step by:",
+        "bbox": [
+            76,
+            194,
+            468,
+            223
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\dot {f} _ {k} ^ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\left(\\frac {\\dot {f} _ {k} ^ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\varphi} \\left(\\dot {f} _ {k} ^ {t} , \\widehat {f} _ {k} ^ {0} , t\\right)}{\\sqrt {\\alpha t}}\\right) \\tag {9} \\\\ + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\varphi} (\\dot {f} _ {k} ^ {t}, \\widehat {f} _ {k} ^ {0}, t) + \\sigma_ {t} \\epsilon , \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            247,
+            468,
+            311
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the parameters  $\\alpha$  and  $\\sigma$  are same as that of Eq. (5). With a certain time step  $t$ , the refined feature  $\\tilde{f}_k^0$  can be obtained through Eq. (9).",
+        "bbox": [
+            76,
+            321,
+            467,
+            366
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For testing, we use MSE to calculate the anomaly score between  $\\tilde{f}_k^0$  and the original feature  $f_{k}^{0}$ , defined as:",
+        "bbox": [
+            76,
+            367,
+            468,
+            398
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {S c o r e} = M S E \\left(\\tilde {f} _ {k} ^ {0}, f _ {k} ^ {0}\\right). \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            189,
+            411,
+            468,
+            429
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the training stage, we train the two diffusion modules separately, i.e. train the refinement module after the prediction module reaching convergence. It is because the input of the refinement module is the sampling output of the prediction module, which is of low quality at the beginning of training. Joint learning has a negative impact on the performance of the refinement module (see the results of Table 3). Therefore, we adopt separate training. The pseudo-code for training and inference is shown in Algorithm 1.",
+        "bbox": [
+            75,
+            436,
+            468,
+            571
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments and discussions",
+        "text_level": 1,
+        "bbox": [
+            76,
+            585,
+            341,
+            603
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets",
+        "text_level": 1,
+        "bbox": [
+            76,
+            611,
+            178,
+            626
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Empirical evaluations are carried out on four video anomaly detection datasets, CUHK Avenue [38], ShanghaiTech [39], UCF-Crime datasets [31] and UBnormal [1]. The ShanghaiTech and UCF-Crime are large-scale real-world VAD datasets, and UBnormal is a generated dataset. The details are as follows:",
+        "bbox": [
+            75,
+            633,
+            468,
+            724
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- The CUHK Avenue (Ave) Dataset contains 16 training and 21 testing video clips. The videos are captured in CUHK campus avenue with over  $30\\mathrm{k}$  frames. This dataset is proposed for one-class video anomaly detection with anomaly annotations provided only in the testing set, while the training split contains only normal samples.",
+            "- The ShanghaiTech (ShT) dataset is collected from ShanghaiTech campus in different monitoring angles and lighting conditions. It contains 13 scenes with over"
+        ],
+        "bbox": [
+            94,
+            738,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1: The pseudocode for training and inference"
+        ],
+        "code_body": "Training:   \nfor S Epochs do Random choose t from [1,T] Calculate  $f^t$  at time t by Eq. (3) Update  $\\epsilon_{\\theta}$  by Minimizing Eq. (4)   \nend   \nfor S Epochs do Random choose t from [1,T] Calculate  $f^t$  by at time t Eq. (3) Sample  $\\dot{f}^{0}$  through Eq. (5) Update  $\\epsilon_{\\varphi}$  by Minimizing Eq. (8)   \nend   \nInference:   \nforeach Sample in X do Choose a certain t Calculate  $f_{k}^{t}$  at time t by Eq. (3) Sample  $\\dot{f}_k^0$  through Eq. (5) Calculate  $\\dot{f}_k^t$  at time t by Eq. (3) Sample  $\\ddot{f}_k^0$  through Eq. (9) Calculate anomaly score by Eq. (10)   \nend",
+        "bbox": [
+            516,
+            125,
+            792,
+            446
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "270k frames in 330 training videos and 130 abnormal events covered in 13 testing videos. This dataset is also for one-class video anomaly detection with anomaly annotations provided only in the testing set.",
+        "bbox": [
+            529,
+            481,
+            890,
+            542
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- The UCF-Crime (UCF) dataset is collected from real-world surveillance. It is a large-scale dataset containing over 128 hours of 1,900 long and untrimmed videos with more than  $10\\mathrm{m}$  frames. The real anomalies consist of 13 events that have a significant impact on public safety. In one-class VAD setting, the video-level annotations are discarded.",
+            "- The UBnormal (UB) benchmark is a supervised open-set dataset composed of multiple virtual scenes for video anomaly detection. It is generated by using the Cinema4D software, containing a total of 29 scenes with over 236k frames. We use the default training and testing sets for one-class VAD to evaluate our method."
+        ],
+        "bbox": [
+            517,
+            556,
+            890,
+            767
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Performance evaluation metrics",
+        "text_level": 1,
+        "bbox": [
+            500,
+            785,
+            779,
+            800
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following previous works [23, 34, 45, 46, 57], the Area Under the ROC Curve (AUC) is used as the evaluation metrics. The AUC is calculated by using ground truth and the frame-level anomaly scores. In our model, the anomaly scores are defined as the mean squared error (MSE) of each frame as in Eq. (10).",
+        "bbox": [
+            496,
+            809,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5531",
+        "bbox": [
+            482,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/4de3d33afdb89cbc6cf5ea0a853caf62a9ad017814a06d5c3bedfead53ab7336.jpg",
+        "table_caption": [
+            "Table 1. AUC of different one-class VAD methods. OD refers to the foreground bounding box from the object detection method, while I3D, R3D and A3D refer to the 3D features from ConvNet3D, ResNext3D and action recognition networks, respectively. 'FPM' indicates that the model also takes a Frame Prediction-based Method for VAD."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Venue</td><td>Feature</td><td>Framework</td><td>Ave</td><td>ShT</td><td>UCF</td><td>UB</td></tr><tr><td>sRNN [39]</td><td>ICCV-17</td><td>Image</td><td>Encoder</td><td>81.7%</td><td>68.0%</td><td>-</td><td>-</td></tr><tr><td>AnoPCN [68]</td><td>ACMMM-19</td><td>Image</td><td>AE (FPM)</td><td>86.2%</td><td>73.6%</td><td>-</td><td>-</td></tr><tr><td>MemAE [24]</td><td>ICCV-19</td><td>Image</td><td>AE</td><td>83.3%</td><td>71.2%</td><td>-</td><td>-</td></tr><tr><td>Bman [32]</td><td>TIP-20</td><td>Image</td><td>AE (FPM)</td><td>90.0%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>STC [55]</td><td>ACMMM-20</td><td>Image</td><td>AE</td><td>80.9%</td><td>74.7%</td><td>72.7%</td><td>-</td></tr><tr><td>CDAE [10]</td><td>ECCV-20</td><td>Image</td><td>AE (FPM)</td><td>86.0%</td><td>73.3%</td><td>-</td><td>-</td></tr><tr><td>RUVAD [61]</td><td>TNNLS-21</td><td>Image</td><td>AE (FPM)</td><td>88.3%</td><td>76.6%</td><td>-</td><td>-</td></tr><tr><td>MemG [46]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.5%</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>ITAE [14]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.0%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>OGNet [71]</td><td>CVPR-20</td><td>Image</td><td>GAN</td><td>-</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>AMMC [8]</td><td>AAAI-21</td><td>Image</td><td>AE (FPM)</td><td>86.6%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FFP [40]</td><td>TPAMI-21</td><td>Image</td><td>AE (FPM)</td><td>85.1%</td><td>72.8%</td><td>-</td><td>-</td></tr><tr><td>LNTR [3]</td><td>CVPR-21</td><td>Image</td><td>AE</td><td>84.9%</td><td>75.9%</td><td>-</td><td>-</td></tr><tr><td>NGOF [59]</td><td>CVPR-21</td><td>Image</td><td>AE (FPM)</td><td>88.4%</td><td>75.3%</td><td>-</td><td>-</td></tr><tr><td>CT-D2GAN [22]</td><td>ACMMM-21</td><td>Image</td><td>GAN (FPM)</td><td>85.9%</td><td>77.7%</td><td>-</td><td>-</td></tr><tr><td>PB-S [4]</td><td>NC-23</td><td>Image</td><td>GAN (FPM)</td><td>87.1%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr><tr><td>BODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>68.2%</td><td>-</td></tr><tr><td>GODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>69.4%</td><td>-</td></tr><tr><td>VEC [69]</td><td>ACMMM-20</td><td>OD</td><td>AE (FPM)</td><td>90.2%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>CAC [62]</td><td>ACMMM-20</td><td>A3D</td><td>Encoder</td><td>87.0%</td><td>79.3%</td><td>-</td><td>-</td></tr><tr><td>HF2 [37]</td><td>ICCV-21</td><td>OD</td><td>AE (FPM)</td><td>91.1%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>BAF [23]</td><td>TPAMI-21</td><td>OD</td><td>AE</td><td>92.3%</td><td>82.7%</td><td>-</td><td>59.3%</td></tr><tr><td>BDPN [11]</td><td>AAAI-22</td><td>OD</td><td>AE (FPM)</td><td>90.0%</td><td>78.1%</td><td>-</td><td>-</td></tr><tr><td>GCL [72]</td><td>CVPR-22</td><td>R3D</td><td>GAN</td><td>-</td><td>79.6%</td><td>74.2%</td><td>-</td></tr><tr><td>SSL [58]</td><td>ECCV-22</td><td>OD</td><td>Encoder</td><td>92.2%</td><td>84.3%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Implementation details",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Following many previous works [24, 34, 45], the input size of images is set to  $256 \\times 256$ . Since the encoder has four  $2 \\times$  downsampling layers, the size of the final feature map is  $32 \\times 32 \\times 4$  for each sample. We use four consecutive neighbor frames to predict the fifth according to the setting of the first prediction framework in video anomaly detection [33]. Specifically, we create a cube with four original features and a noised feature from the fifth feature as input for training and testing. We use the recommended settings of  $\\alpha$  and  $\\sigma$  in DDIM [53]. In the training stage, the number of training epochs  $S$  is set to 60, including 12 warm-up epochs at the beginning, and the time step  $T$  and learning rate are set to  $1\\mathrm{k}$  and  $10^{-5}$  respectively. In the inference stage, we adopt a 200 steps sampling schedule  $T'$  according to [53], i.e. each step in  $T'$  equals five steps in  $T$ . More",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "over, we set  $t = 0.25T'$  for sampling because this was found to be the best in [28, 63]. Therefore, the sampling stage is  $20 \\times$  speed-up compared with DDPM.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Competing methods",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We examine the performance of the proposed FPDM on all four datasets. We compare our method with 15 state-of-the-art one-class VAD methods that use images as input, as well as another 7 methods that employ different high-level semantic features for training, e.g., foreground bounding box from object detection, 3D features from action recognition models et. al..",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "On all four datasets, FPDM outperforms all the competing image-based one-class methods, verifying the advanced performance of our method. Compared with the methods with 3D features, we still have the best AUC results on UCF-Crime and UBnormal datasets. Notice that the VEC,",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "5532",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/af68bc62930ea92e9c57dbd99c766b78ddafe3470b78869abc44b78198c3c908.jpg",
+        "image_caption": [
+            "Normality"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/06bc98c96cf86828f68883b92ee27554f840dbeb8b819326036dc8c3375d6874.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7607a44d15687e821db8e9d330381b04953e55f8e25eed9e4e1c83c458291a5d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/2a4a553f887cdfdd1999bc1d8df3957dc47469f846c9468048c314ed0afea604.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            220
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e3f999f3a90de24345f18c627fed1a52afb3f331b09ccedce88421592bdd6c0c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            125,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/745fda283249e5b3fb20dcee971b3410eb78792c92de0a2b2ce81e7e137664ea.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8a509859bcf02383e3735289cc05fd9d6cbefa5e5599fcba1b241dd8130c6865.jpg",
+        "image_caption": [
+            "Anomaly",
+            "Input",
+            "Figure 3. The visualization results. We use the frozen decoder from [48] to visualize the features of each module. The top and bottom lines are two examples of normal and abnormal samples. The first column is the original input, and the next four columns named Noised, Predicted, Refined and Output are the decoded images of noised feature, predicted feature, refined feature and original feature respectively. The column named FFP is the predicted frames of FFP approach [40]."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ef6fec2535c6219f2c71e07e9f5838b0093592792e252a8f4f56b46062d9f5c8.jpg",
+        "image_caption": [
+            "Noised"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            253,
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+            349
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/14bc35f9c05cd49cc7632ea34158169375abbf782ddd5a75067a88dc546c128d.jpg",
+        "image_caption": [
+            "Predicted"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f8059c5600014efc9555524c084b938ae07c1c1198e7bb85019d68d4d0cca223.jpg",
+        "image_caption": [
+            "Refined"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/df86ade291a3124923190c158aa60ef9cbfdc03ab9645933784947febce2b243.jpg",
+        "image_caption": [
+            "Output"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b791818ccd0b87e6e8388f57f3d0883eb3da05c2835a1e2cefe1492d37f11b77.jpg",
+        "image_caption": [
+            "FFP"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            253,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "HF2, and DBPN employ object detection methods to extract the foreground, which can greatly reduce the influence of various noises from the background. While our method still beats these methods, illustrating the anti-noise capability of the diffusion model.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Visualization results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            544,
+            267,
+            559
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To give a more intuitive presentation of the outputs from each proposed module, we present two series of visualization results from normal and abnormal samples. Here we employ the decoder from [48] that matches our encoder to recover an auto-encoder for feature map decoding.",
+        "bbox": [
+            75,
+            568,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The results are shown in Fig. 3, where the first column is the original input. The next four columns show the output of the decoder with four different features, including noised features after the diffusion process in the feature prediction module, the predicted features from the reverse process of the prediction module, the refined features from the reverse process of refinement module, and the features from the encoder respectively. For a more intuitive comparison, we present the predicted frames of FFP [40] in the last column.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "From the results of normality one shown in the top line, we can see that the predicted features well capture the motion information and predict the position of each foreground object, but missing some detail information, such as legs and head of the person dressed in a white T-shirt, the head of the person in black clothing et. al.. These missing details are restored by the refinement module, as shown in the refined column. Comparing the last three, the quality of the",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "refined one is significantly higher than that of the FFP and very close to that of the decoded output from the original feature. This example demonstrates that our model can accurately predict normal features.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The bottom line shows a visual example of the anomaly detection process. According to the results, the predicted feature in the third column also captures the global information of the foreground person but missing some details around this person. With the help of Refined module, the details of the bicycle, e.g., the two wheels are still blurred, illustrating the lack of refinement capacity for the bicycle. The quality of the person/bicycle in the refined column is much better/worse than that of the FFP, verifying our refinement module has greater discriminate capacity than the frame prediction auto-encoder approach The Visualization results verify that the distribution of appearance is so well learned by our model that the anomaly bicycle can't be restored.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.6. Ablation study",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the importance of two key diffusion modules with six variations on ShT and UCF datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "First, we employ the decoder from [48] and discard the two diffusion modules. This setting is to present the performance of the feature extractor. We show the results of the original AE as well as the trained AE using our training data for auto-encoder training. As shown on the top two rows in Table. 2, the results of both original AE and trained AE are far behind the proposed FPDM, demonstrating that the",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "5533",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "improvement of our FPDM model is based on the two designed diffusion modules. We also train the AE using training data before optimizing FPDM and present the result in the third row. Comparing the result of directly optimizing FPDM, it has almost the same performance, which confirms the unnecessary process of training AE before FPDM.",
+        "bbox": [
+            78,
+            90,
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+            181
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c8b3c5fe0143fe32943898dbeee021b28ba2d97a767c5f15f4b99bf6109f5488.jpg",
+        "table_caption": [
+            "Table 2. AUC of our model FPDM and its variants. PM and RM refer to our prediction module and refinement module, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">FPDM and its Variants</td><td>ShT</td><td>UCF</td></tr><tr><td>AE</td><td>without training</td><td>67.5%</td><td>50.8%</td></tr><tr><td>AE</td><td>with training</td><td>69.1%</td><td>53.1%</td></tr><tr><td>FPDM</td><td>with trained AE</td><td>78.6%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>with only PM</td><td>77.3%</td><td>74.2%</td></tr><tr><td>FPDM</td><td>with only RM</td><td>76.8%</td><td>72.5%</td></tr><tr><td>FPDM</td><td>with decoder</td><td>78.3%</td><td>74.1%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.7%</td></tr></table>",
+        "bbox": [
+            114,
+            224,
+            431,
+            375
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Then we keep the prediction/refinement diffusion module with the other one discarded to test the capacity of each module. From the results on the fourth and fifth rows, we can see that the performance decreases when only one module is utilized. The feature prediction module learns the motion information as well as some appearance information, helping achieve better performance than the refinement module.",
+        "bbox": [
+            78,
+            404,
+            467,
+            523
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Finally, we present the results of FPDM with the decoder. We also use the decoder from [48] to decode the  $\\ddot{f}_k^0$  and calculate the MSE between the input and the decoded one. The declining result of FPDM with decoder shows that the information could be lost through the decoder, e.g., the details of the background (also see the fence and curb on the last column in Fig. 3), which leads to the decrease of performance. Since the specific information of background is usually not relevant to VAD, discarding the decoder is a better choice.",
+        "bbox": [
+            78,
+            525,
+            467,
+            674
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.7. Analysis of training settings",
+        "text_level": 1,
+        "bbox": [
+            78,
+            685,
+            323,
+            700
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/9d0e589137520b91c6ee83d11d2dce3a959b7dcd76f957c3cc6186b4a69b62c6.jpg",
+        "table_caption": [
+            "Table 3. The results of FPDM with different training mode settings. PM, RM, J(.), S(. refer to prediction module, refinement module, joint training, and separated training respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Training Mode</td><td>ShT</td><td>UCF</td></tr><tr><td>FPDM</td><td>J(PM &amp; RM)</td><td>70.8%</td><td>68.1%</td></tr><tr><td>FPDM</td><td>S(PM&amp;RM) → J(PM&amp;RM)</td><td>78.2%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.8%</td></tr></table>",
+        "bbox": [
+            78,
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+            856
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We first evaluate the performance of FPDM with differ",
+        "bbox": [
+            99,
+            886,
+            467,
+            898
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ent training mode settings. For the proposed two modules, we present the results of joint learning for the whole training, joint learning after separated learning, and the default setting of FPDM in Table. 3. We can see that the performance of joint learning for the whole training, i.e. J(PM & RM), is far behind that of the default setting. It may be due to the low quality of predicted features at the beginning of training, negatively impacting refinement learning. The performance of joint learning after separated learning, i.e. S(PM&RM)  $\\rightarrow$  J(PM&RM), falls slightly behind the default setting. The reason may be that the distribution of  $\\dot{f}_k^0$  changes in the training process of the prediction module, leading to the instability of refinement learning.",
+        "bbox": [
+            503,
+            90,
+            888,
+            287
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/7db139fe94ab3741368c347935e5377b75fdd1ca6357622b55783002ab6c1327.jpg",
+        "table_caption": [
+            "Table 4. The results of FPDM with different number of neighbors on the ShanghaiTech dataset. ShT-3, ShT-11 and ShT-all refer to the 3-rd, 11-th and all scenes of ShanghaiTech dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td># Neighbors</td><td>ShT-3</td><td>ShT-11</td><td>ShT-all</td></tr><tr><td>FPDM</td><td>12</td><td>81.7</td><td>96.6</td><td>79.0</td></tr><tr><td>FPDM</td><td>8</td><td>80.3</td><td>96.4</td><td>78.9</td></tr><tr><td>FPDM</td><td>4</td><td>79.2</td><td>96.5</td><td>78.6</td></tr><tr><td>FPDM</td><td>0</td><td>73.8</td><td>96.3</td><td>76.2</td></tr></table>",
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+        "type": "text",
+        "text": "Then we evaluate the performance of FPDM with different numbers of neighbors in the prediction module. We present the results of 0, 4, 8, and 12 neighbors on two representative scenes, i.e., scene-3 and scene-11 of ShanghaiTech dataset. These two scenes are chosen because the anomalies are all action/appearance-based abnormal events. From the results, we can see that the performance increases observably on the action anomaly test set with more neighbors for training. When the number of neighbors is set to zero, the prediction module degrades to a prediction refinement module with no condition, leading to the decline of the motion learning capacity. While for the appearance-based anomalies, the number of neighbors has little influence on the performance.",
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+        "text": "5. Conclusions",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This paper introduces the first feature prediction diffusion model for video anomaly detection. We further devise two DDIM modules, namely the feature prediction diffusion module and feature refinement diffusion module, for motion and appearance learning from the normal samples. It is impressive that although our model takes images as input to predict features for anomaly detection, it achieves a competing performance compared with the methods utilizing high-level 3D semantic features. Extensive empirical results also demonstrate the superiority of our approach against the SOTA 2D image feature-based VAD models.",
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+        "text": "References",
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diff --git a/2023/Feature Prediction Diffusion Model for Video Anomaly Detection/b7c9cb2d-d935-41b6-bf79-feb2138dade6_model.json b/2023/Feature Prediction Diffusion Model for Video Anomaly Detection/b7c9cb2d-d935-41b6-bf79-feb2138dade6_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..d902714ea81d82a3cb3ed05d7e4422b00a9ffa6e
--- /dev/null
+++ b/2023/Feature Prediction Diffusion Model for Video Anomaly Detection/b7c9cb2d-d935-41b6-bf79-feb2138dade6_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
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+                0.043
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
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+                0.001,
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Feature Prediction Diffusion Model for Video Anomaly Detection"
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+        {
+            "type": "text",
+            "bbox": [
+                0.157,
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+            "angle": 0,
+            "content": "Cheng Yan\\(^{1}\\), Shiyu Zhang\\(^{1}\\), Yang Liu\\(^{2}\\), Guansong Pang\\(^{3*}\\), Wenjun Wang\\(^{1}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.16,
+                0.206,
+                0.81,
+                0.227
+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)Tianjin University \\(^{2}\\)Zhejiang University \\(^{3}\\)Singapore Management University"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.26,
+                0.314,
+                0.277
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
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+            "bbox": [
+                0.076,
+                0.293,
+                0.474,
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+            ],
+            "angle": 0,
+            "content": "Anomaly detection in the video is an important research area and a challenging task in real applications. Due to the unavailability of large-scale annotated anomaly events, most existing video anomaly detection (VAD) methods focus on learning the distribution of normal samples to detect the substantially deviated samples as anomalies. To well learn the distribution of normal motion and appearance, many auxiliary networks are employed to extract foreground object or action information. These high-level semantic features effectively filter the noise from the background to decrease its influence on detection models. However, the capability of these extra semantic models heavily affects the performance of the VAD methods. Motivated by the impressive generative and anti-noise capacity of diffusion model (DM), in this work, we introduce a novel DM-based method to predict the features of video frames for anomaly detection. We aim to learn the distribution of normal samples without any extra high-level semantic feature extraction models involved. To this end, we build two denoising diffusion implicit modules to predict and refine the features. The first module concentrates on feature motion learning, while the last focuses on feature appearance learning. To the best of our knowledge, it is the first DM-based method to predict frame features for VAD. The strong capacity of DMs also enables our method to more accurately predict the normal features than non-DM-based feature prediction-based VAD methods. Extensive experiments show that the proposed approach substantially outperforms state-of-the-art competing methods. The code is available atFPDM."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.762,
+                0.21,
+                0.779
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.788,
+                0.47,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Video anomaly detection (VAD) aims at identifying the unusual events that rarely appear and are different from normal behaviors in videos. Successfully detecting the anomalies, such as traffic accidents, violence, and stampedes, is of great importance in ubiquitous video surveillance for pub-"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.264,
+                0.88,
+                0.434
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.442,
+                0.895,
+                0.568
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview of three generative VAD approaches. Existing state-of-the-art GAN-based or auto-encoder-based approaches heavily rely on foreground object or action information extracted by auxiliary models, such as object detection, action recognition or optical flow network, to generate features/images for effective performance. By contrast, our proposed diffusion model-based approach does not have this reliance and can make accurate feature prediction using only simple networks as encoder to extract basic image features as input."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.597,
+                0.893,
+                0.642
+            ],
+            "angle": 0,
+            "content": "lic safety. However, VAD is a challenging task since the anomaly events are unbounded in real-world applications and it is difficult to collect large-scale labeled data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "There have been many VAD methods [9, 10, 14, 19, 23, 33, 34, 39, 45, 46, 57, 62, 68, 71] proposed over the years to handle this issue, in which one-class learning-based methods are preferred due to the relatively accessible normal training set and their capacity to achieve better performance [44]. The one-class VAD methods assume the availability of the training data in which all samples are normal, and build different models to learn the distribution of normal data. Generative modeling is a widely-used technique in this line since the normal samples can be better generated than anomalies after training. Generative Adversarial Networks (GAN) [22, 52, 71, 72] and Auto-Encoder (AE) [24, 29, 40, 46] are two popular frameworks. Although these generative approaches achieve promising performance in VAD, there are three main challenges: (1) the GAN/AE-based methods suffer from the weak generative capacity, leading to more noise from the low-quality generated image, which reduces the"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Guansong Pang is the corresponding author, e-mail: pangguansong@gmail.com"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.958
+            ],
+            "angle": 0,
+            "content": "5527"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.227
+            ],
+            "angle": 0,
+            "content": "performance, (2) current SOTA methods often employ some auxiliary models, e.g., object detection and action recognition models, to capture the features of the foreground object or action information, and as a result, the performance relies heavily on the representation capacity of these high-level semantic models, and (3) the anomaly events are often characterized by the novel appearance and/or abnormal motion, which increase the difficulty of the generative models to capture the normality/abnormality in both aspects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.228,
+                0.471,
+                0.394
+            ],
+            "angle": 0,
+            "content": "In very recent years, diffusion models (DMs) [26, 53], have been attracting increasing attention due to their powerful generative capacity and excellent performance in various tasks [5, 17, 49, 53]. Different from GAN and AE, the diffusion models inject Gaussian noise into the training data and then learn to recover the samples from those noisy data. The DMs are featured by minor modifications and rectification of the generated samples in each step, enabling a more stable generation of more realistic samples. Therefore, the DM-based approaches outperform the GAN/AE-based approaches in many generative tasks [6, 12, 50, 63]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.395,
+                0.471,
+                0.665
+            ],
+            "angle": 0,
+            "content": "Motivated by the powerful generative capacity of these diffusion models, we propose a novel DM-based approach for anomaly detection. For the second and third challenges mentioned above, as shown in Fig. 1, we devise two complementary denoising DM modules to learn the distribution of normal samples. One module emphasizes learning the distribution of motion, while another module focuses on appearance learning. We employ a simple neural network as the encoder for extracting basic 2D features. Many previous studies [21, 49] have shown that many simple pre-trained networks can effectively extract basic texture information of images even if there are novel classes beyond the training data. Therefore, we adopt a basic 2D feature extractor, which is different from many existing generative methods that utilize high-level semantic models for 3D feature extraction. Based on this, our goal is to learn the distribution of normal features and predict the features of samples for anomaly detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.667,
+                0.411,
+                0.682
+            ],
+            "angle": 0,
+            "content": "In summary, there are three main contributions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.696,
+                0.468,
+                0.755
+            ],
+            "angle": 0,
+            "content": "- We introduce a novel diffusion model-based method to predict the features of each sample for VAD. To the best of our knowledge, it is the first work in utilizing DMs for VAD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.768,
+                0.468,
+                0.827
+            ],
+            "angle": 0,
+            "content": "- We design two types of DDIM module for respective motion and appearance learning from the normal samples to guarantee the generative quality of predicted features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.84,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "- The proposed model takes 2D images as input with no auxiliary semantic networks, while achieving a highly comparable performance to the methods utilizing high-level 3D semantic features."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.097,
+                0.696,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "Experimental results on four publicly available video anomaly detection datasets demonstrate that our method substantially outperforms the image feature-based VAD counterparts and performs comparably well to methods using 3D semantic features."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.181,
+                0.637,
+                0.197
+            ],
+            "angle": 0,
+            "content": "2. Related work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.207,
+                0.892,
+                0.296
+            ],
+            "angle": 0,
+            "content": "For different application scenarios, the video anomaly detection methods can be generally classified into three categories, semi-supervised, one-class, and unsupervised VAD, according to the annotation of training samples. Since our method belongs to the one-class type, we only review one-class VAD methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.298,
+                0.892,
+                0.735
+            ],
+            "angle": 0,
+            "content": "The early one-class VAD methods are two-step approaches in which feature extraction and learning are separated. They first use hand-crafted feature descriptors to present each frame, such as 3D gradients features [38], histogram of gradient (HOG) [16], histogram optical flow (HOF) [16], bag of words (BOW) etc., then build a shallow model to learn the normal distribution, such as dictionary-based models [75], probabilistic models [13, 41], and reconstruction models [16, 38, 75]. These traditional methods suffer from the poor performance of hand-crafted features. With the development of deep learning [35, 36, 64-67], convolutional neural network-based methods followed close on another. The CNN integrates feature extraction and learning into an end-to-end frame [42, 43, 70]. The majority of these CNN-based methods belong to the generative approach, in which the model applies feature learning on normality and detects anomalies according to the difference between the generated and original samples. The generative adversarial network (GAN) [20, 51, 73] and auto-encoder-based network (AE) [25, 27, 56] are widely used for such normal feature learning. Based on these frameworks, memory module [24], and feature prediction module [33] are proposed to enhance the capacity of feature learning. To further improve performance, some high-level feature extraction models, e.g., object detection [23, 37], action recognition [62], and optical flow [33], are employed to obtain foreground or motion information for the learning of normality. The auxiliary models bring the benefit to these VAD methods while increasing the dependency on semantic presentations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Recently, diffusion models have achieved state-of-the-art performance on many generative tasks and become a hot research topic [5, 17, 26, 49, 53]. Many applications have already emerged in computer vision, such as image inpainting [7, 15, 54], image manipulation [47], image superresolution [7, 18], and image-to-image translation [50, 76]. The state-of-the-art performance of these applications confirms that the DM-based models have remarkable generative capacity. To further expand DMs to mainstream computer vision tasks, some DM-based latent representation learning methods have been proposed, such as DiffusionDet for ob"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5528"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.151,
+                0.092,
+                0.833,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.393,
+                0.895,
+                0.466
+            ],
+            "angle": 0,
+            "content": "Figure 2. The framework of the proposed method. It contains a frame-level 2D encoder and two DM-based modules, including a feature prediction diffusion module and a feature refinement diffusion module. The feature prediction diffusion module adopts consecutive \\( k \\) features as input, in which only the last one accepts the diffusion process. With the temporal information from the consecutive frames, this module emphasizes learning the distribution of normal motion. The feature refinement diffusion module takes the sampling output of previous module as input and the \\( k \\)-th original features as a condition for training, which focuses on the appearance learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.487,
+                0.473,
+                0.745
+            ],
+            "angle": 0,
+            "content": "ject detection [12], SegDiff for segmentation [2], and SBG classifier for classification [77]. These discriminative tasks usually require more powerful models that are not easy to be disturbed by background. Therefore the success of these methods on different tasks verifies the anti-noise ability of DM. The early diffusion models, such as the denoising diffusion probabilistic model (DDPM), have quite a few denoising steps required in the sampling stage due to the Markov process converting data distribution via tiny modification. To accelerate the sampling process, many speed-up diffusion methods have been proposed [30, 53, 74]. The denoising diffusion implicit model (DDIM) is widely used due to its training-free property. The DDIM requires no extra training and can directly apply the advanced sampling algorithms with fewer steps and higher fidelity. Therefore DDIM-based methods are more likely to be adopted in real applications."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.765,
+                0.169,
+                0.78
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.793,
+                0.47,
+                0.882
+            ],
+            "angle": 0,
+            "content": "Our key motivation is to design a diffusion model-based approach to well learn the distribution of normal motion and appearance without the help of 3D feature extraction networks. In the inference stage, the feature of a normal sample is more easily predicted by the optimized model than that of the abnormal one."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "As shown in Fig. 2, our framework contains three parts,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.487,
+                0.892,
+                0.76
+            ],
+            "angle": 0,
+            "content": "i.e. a frame encoder, a feature prediction diffusion module, and a feature refinement diffusion module. First, we employ an encoder to extract the feature of each frame. Any pretrained CNN can be used as the encoder. Here we adopt a slight encoder from [48] since (1) the size of output feature map is 64 times spatially smaller than that of the original image and contains only four channels, which significantly reduces the computation of the following diffusion modules, and (2) the pretraining of this encoder is unsupervised, which is more accessible. To predict the feature, we design two DDIM-based modules to predict and refine the feature of each frame. Notice that DDIM has the same training procedure as DDPM but is more efficient in the sampling stage since it adopts a jump-step implicit sampler rather than extracting noise information step by step. The feature prediction diffusion module emphasizes learning the distribution of motion, and the feature refinement diffusion module focuses on appearance distribution learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.771,
+                0.704,
+                0.787
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The problem aims to address is to generate a feature by giving several continuous video frames and then estimate whether this feature belongs to the learned distribution. Formally, given a video clip with \\(k\\) consecutive frames \\(X = \\{\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_k\\}\\) our goal is to predict the feature of \\(k\\) -th frame denoted as \\(\\ddot{f} (\\mathbf{x}_k)\\) and \\(\\ddot{f}_k\\) for short. We use \\(\\dot{f}_k\\) and \\(\\ddot{f}_k\\) to denote the output of the feature prediction and re"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5529"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.184
+            ],
+            "angle": 0,
+            "content": "finement diffusion module. Since the time step is involved, we use \\( f_{k}^{t} \\) to denote the feature of \\( k \\)-the frame at time step \\( t \\). To this end, \\( f_{k}^{0} \\) refers to the \\( k \\)-th feature at time step 0, which is equivalent to \\( f_{k} \\). Compared with the original feature denoted as \\( f_{k} \\), the anomaly score of the \\( k \\)-th frame can be calculated by Mean Square Error between \\( f_{k} \\) and \\( \\ddot{f}_{k} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.191,
+                0.391,
+                0.208
+            ],
+            "angle": 0,
+            "content": "3.2. Feature prediction diffusion module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.214,
+                0.469,
+                0.323
+            ],
+            "angle": 0,
+            "content": "Different the previous work [33] that adopts \\(k\\) samples to predict the \\((k + 1)\\)-th sample, we take the features \\(\\{f_1^0,f_2^0,\\dots ,f_{k - 1}^0\\}\\) of 1 to \\(k - 1\\) frames and the noisy feature \\(f_{k}^{t}\\) of the \\(k\\)-th frame together as the input, to predict the feature \\(\\dot{f}_k^0\\). To this end, we build a feature prediction diffusion module to progressively remove the noise of \\(f_{k}^{t}\\) by using implicit sampling [53] to generate \\(\\dot{f}_k^0\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.469,
+                0.384
+            ],
+            "angle": 0,
+            "content": "For training, the goal of our diffusion models is to learn a distribution \\( p_{\\theta}(f^0) \\) that approximates the original data distribution \\( q(f^0) \\). In forward process, the posterior \\( q(f^{1:T}|f^0) \\) is fixed to a Markov chain:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.17,
+                0.395,
+                0.47,
+                0.436
+            ],
+            "angle": 0,
+            "content": "\\[\nq \\left(f ^ {1: T} \\mid f ^ {0}\\right) := \\prod_ {t = 1} ^ {T} q \\left(f ^ {t} \\mid f ^ {t - 1}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.441,
+                0.328,
+                0.457
+            ],
+            "angle": 0,
+            "content": "where \\(t\\in [1,T]\\) is the time step, and:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.128,
+                0.466,
+                0.469,
+                0.485
+            ],
+            "angle": 0,
+            "content": "\\[\nq \\left(f ^ {t} \\mid f ^ {t - 1}\\right) := \\mathcal {N} \\left(f ^ {t}; \\sqrt {\\alpha_ {t}} f ^ {t - 1}, \\left(1 - \\alpha_ {t}\\right) \\mathbf {I}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.494,
+                0.469,
+                0.571
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha_{t}\\in \\{\\alpha_{t}\\}_{t = 1}^{T}\\) is a schedule to control the percentage of \\(f^{t - 1}\\), \\((1 - \\alpha_{t})\\) controls the percentage of noise. With time step \\(t\\) increase, \\(\\alpha_{t}\\) decrease. Based on these properties, the \\(f^t\\) can be presented by the linear combination of \\(f^0\\) and standard Gaussian noise \\(\\epsilon\\) as following:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.185,
+                0.584,
+                0.469,
+                0.601
+            ],
+            "angle": 0,
+            "content": "\\[\nf ^ {t} = \\sqrt {\\alpha_ {t}} f ^ {0} + \\sqrt {1 - \\alpha_ {t}} \\epsilon . \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.607,
+                0.469,
+                0.802
+            ],
+            "angle": 0,
+            "content": "To learn the distribution \\(p_{\\theta}(f^0)\\), we build a U-net diffusion network \\(\\epsilon_{\\theta}(\\cdot)\\) based on the LDM [49]. To well predict the features, we modify two parts of the LDM: (1) we discard the latent condition part and modify all the cross-attention layers to traditional attention layers, and (2) each input sample contains \\(k\\) features \\(\\{f_1^0,f_2^0,\\dots ,f_k^t\\}\\) where only the \\(k\\)-th feature is applied diffusion forward process. There are two reasons for such modification: (1) we expect to learn the distribution of features from normal samples without any other latent condition involved, and (2) combined with the consecutive features of previous frames, we can provide the motion information to the \\(\\epsilon_{\\theta}(\\cdot)\\), making this diffusion module focus on feature motion learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.803,
+                0.469,
+                0.834
+            ],
+            "angle": 0,
+            "content": "Following [26,53], the simplified version of the objective is used for training defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.847,
+                0.469,
+                0.866
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\theta} = \\mathbb {E} \\left[ | | \\epsilon_ {\\theta} \\left(f _ {1} ^ {0}, f _ {2} ^ {0}, \\dots , f _ {k} ^ {t}, t\\right) - \\epsilon | | _ {2} ^ {2} \\right], \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(t\\) is the time step, \\(\\epsilon_{\\theta}(\\cdot ,t)\\) is the prediction noise at time \\(t\\). Substituting \\(f^{t}\\) of Eq. (3) into Eq. (4), the parameter"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "\\(\\theta\\) can be optimized by given sufficient feature samples and random time step \\(t \\in [1, T]\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.122,
+                0.892,
+                0.167
+            ],
+            "angle": 0,
+            "content": "For the reverse process, the features of the \\(k\\)-th sample at time \\(t-1\\) can be generated once given \\(\\{f_1^0, f_2^0, \\dots, f_k^t\\}\\) by the following formula:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.511,
+                0.187,
+                0.892,
+                0.249
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} f _ {k} ^ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\left(\\frac {f _ {k} ^ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\theta} \\left(f _ {1} ^ {0} , f _ {2} ^ {0} , \\cdots , f _ {k} ^ {t} , t\\right)}{\\sqrt {\\alpha t}}\\right) \\tag {5} \\\\ + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\theta} \\left(f _ {1} ^ {0}, f _ {2} ^ {0}, \\dots , f _ {k} ^ {t}, t\\right) + \\sigma_ {t} \\epsilon \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.258,
+                0.892,
+                0.306
+            ],
+            "angle": 0,
+            "content": "where \\(\\sigma_t \\in \\{\\sigma_t\\}_{t=1}^T\\) is a schedule to control the added noise for each step. At sampling stage, the (t-1)-th step takes the features \\(\\{f_1^0, f_2^0, \\dots, f_k^t\\}\\) as input to predict \\(f_k^{t-1}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.306,
+                0.892,
+                0.395
+            ],
+            "angle": 0,
+            "content": "The consecutive supervision on the reverse process can effectively guarantee the motion prediction while it may miss some appearance details since the non-noisy \\(k-1\\) features are helpful for motion learning while having an effect on appearance learning. To this end, we create another DDIM module to refine the appearance information."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.403,
+                0.816,
+                0.418
+            ],
+            "angle": 0,
+            "content": "3.3. Feature refinement diffusion module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.427,
+                0.892,
+                0.61
+            ],
+            "angle": 0,
+            "content": "We build a feature refinement diffusion module next to the prediction module. This refinement model places emphasis on learning the appearance distribution of features. Similarly, we adopt the LDM-based U-net as the diffusion network for refining, in which the condition part is maintained. We take the output of the previous prediction module, i.e. the denoised feature \\(\\dot{f}_k^0\\) as input, and use the original feature \\(f_{k}^{0}\\) of the \\(k\\)-th frame as condition, to generate the refined features denoted as \\(\\ddot{f}_k^0\\). The condition \\(f_{k}^{0}\\) is used for cross-attention to guarantee the feature appearance learning. The goal of the feature refinement diffusion module is to learn a distribution \\(p_{\\varphi}(\\dot{f}^{0})\\) that approximates \\(q(f^0)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.61,
+                0.892,
+                0.669
+            ],
+            "angle": 0,
+            "content": "Same with the previous feature prediction module, the posterior \\( q(\\dot{f}^{1:T}|\\dot{f}^{0}) \\) is fixed to a Markov chain, and the input \\( \\dot{f}^t \\) at time step \\( t \\) can be calculated according to Eq. (3) by given \\( \\dot{f}^{0} \\) and a Gaussian noise \\( \\epsilon \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.67,
+                0.892,
+                0.778
+            ],
+            "angle": 0,
+            "content": "To make this refinement network \\(\\epsilon_{\\varphi}(\\cdot)\\) focus on appearance learning, we augment the underlying UNet backbone with cross-attention mechanism and take the original feature \\(f_{k}^{0}\\) as the condition into the cross-attention layers. We flatten the feature \\(f_{k}^{0}\\), then use a linear transform to obtain a \\(d\\)-dimensional vector, which is defined as \\(\\widehat{f}_{k}^{0}\\). The cross-attention is implemented according to:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.611,
+                0.788,
+                0.892,
+                0.823
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}}\\right) V, \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.522,
+                0.841,
+                0.892,
+                0.861
+            ],
+            "angle": 0,
+            "content": "\\[\nQ = W _ {q} \\cdot \\widehat {f} _ {k} ^ {0}, K = W _ {k} \\cdot \\phi \\left(\\dot {f} _ {k} ^ {t}\\right), V = W _ {v} \\cdot \\phi \\left(\\dot {f} _ {k} ^ {t}\\right), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.869,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where \\( W_{k} \\), \\( W_{q} \\), \\( W_{v} \\) are learnable projection matrices and \\( \\phi(\\dot{f}_{k}^{t}) \\) is the input feature map of each cross-attention layer."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5530"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.09,
+                0.47,
+                0.151
+            ],
+            "angle": 0,
+            "content": "The \\(\\widehat{f}_k^0\\) is changeless for different cross-attention layer that provides a consistent appearance supervision on feature learning. The loss function is also the simplified version of DDIM, defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.165,
+                0.163,
+                0.469,
+                0.189
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\varphi} = \\mathbb {E} \\left[ | | \\epsilon_ {\\varphi} \\left(\\dot {f} _ {k} ^ {t}, \\widehat {f} _ {k} ^ {0}, t\\right) - \\epsilon | | _ {2} ^ {2} \\right]. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.195,
+                0.469,
+                0.224
+            ],
+            "angle": 0,
+            "content": "For reverse process, we can obtain the feature at \\( t - 1 \\) time step by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.124,
+                0.248,
+                0.469,
+                0.312
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\dot {f} _ {k} ^ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\left(\\frac {\\dot {f} _ {k} ^ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\varphi} \\left(\\dot {f} _ {k} ^ {t} , \\widehat {f} _ {k} ^ {0} , t\\right)}{\\sqrt {\\alpha t}}\\right) \\tag {9} \\\\ + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\varphi} (\\dot {f} _ {k} ^ {t}, \\widehat {f} _ {k} ^ {0}, t) + \\sigma_ {t} \\epsilon , \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.323,
+                0.468,
+                0.367
+            ],
+            "angle": 0,
+            "content": "where the parameters \\(\\alpha\\) and \\(\\sigma\\) are same as that of Eq. (5). With a certain time step \\(t\\), the refined feature \\(\\tilde{f}_k^0\\) can be obtained through Eq. (9)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.368,
+                0.469,
+                0.399
+            ],
+            "angle": 0,
+            "content": "For testing, we use MSE to calculate the anomaly score between \\(\\tilde{f}_k^0\\) and the original feature \\(f_{k}^{0}\\), defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.19,
+                0.412,
+                0.469,
+                0.43
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {S c o r e} = M S E \\left(\\tilde {f} _ {k} ^ {0}, f _ {k} ^ {0}\\right). \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.438,
+                0.469,
+                0.573
+            ],
+            "angle": 0,
+            "content": "In the training stage, we train the two diffusion modules separately, i.e. train the refinement module after the prediction module reaching convergence. It is because the input of the refinement module is the sampling output of the prediction module, which is of low quality at the beginning of training. Joint learning has a negative impact on the performance of the refinement module (see the results of Table 3). Therefore, we adopt separate training. The pseudo-code for training and inference is shown in Algorithm 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.587,
+                0.342,
+                0.604
+            ],
+            "angle": 0,
+            "content": "4. Experiments and discussions"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.612,
+                0.179,
+                0.627
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.635,
+                0.469,
+                0.725
+            ],
+            "angle": 0,
+            "content": "Empirical evaluations are carried out on four video anomaly detection datasets, CUHK Avenue [38], ShanghaiTech [39], UCF-Crime datasets [31] and UBnormal [1]. The ShanghaiTech and UCF-Crime are large-scale real-world VAD datasets, and UBnormal is a generated dataset. The details are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.739,
+                0.469,
+                0.844
+            ],
+            "angle": 0,
+            "content": "- The CUHK Avenue (Ave) Dataset contains 16 training and 21 testing video clips. The videos are captured in CUHK campus avenue with over \\(30\\mathrm{k}\\) frames. This dataset is proposed for one-class video anomaly detection with anomaly annotations provided only in the testing set, while the training split contains only normal samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.855,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- The ShanghaiTech (ShT) dataset is collected from ShanghaiTech campus in different monitoring angles and lighting conditions. It contains 13 scenes with over"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.739,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.51,
+                0.095,
+                0.848,
+                0.124
+            ],
+            "angle": 0,
+            "content": "Algorithm 1: The pseudocode for training and inference"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.517,
+                0.126,
+                0.794,
+                0.448
+            ],
+            "angle": 0,
+            "content": "Training:   \nfor S Epochs do Random choose t from [1,T] Calculate \\(f^t\\) at time t by Eq. (3) Update \\(\\epsilon_{\\theta}\\) by Minimizing Eq. (4)   \nend   \nfor S Epochs do Random choose t from [1,T] Calculate \\(f^t\\) by at time t Eq. (3) Sample \\(\\dot{f}^{0}\\) through Eq. (5) Update \\(\\epsilon_{\\varphi}\\) by Minimizing Eq. (8)   \nend   \nInference:   \nforeach Sample in X do Choose a certain t Calculate \\(f_{k}^{t}\\) at time t by Eq. (3) Sample \\(\\dot{f}_k^0\\) through Eq. (5) Calculate \\(\\dot{f}_k^t\\) at time t by Eq. (3) Sample \\(\\ddot{f}_k^0\\) through Eq. (9) Calculate anomaly score by Eq. (10)   \nend"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.531,
+                0.482,
+                0.892,
+                0.543
+            ],
+            "angle": 0,
+            "content": "270k frames in 330 training videos and 130 abnormal events covered in 13 testing videos. This dataset is also for one-class video anomaly detection with anomaly annotations provided only in the testing set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.557,
+                0.892,
+                0.662
+            ],
+            "angle": 0,
+            "content": "- The UCF-Crime (UCF) dataset is collected from real-world surveillance. It is a large-scale dataset containing over 128 hours of 1,900 long and untrimmed videos with more than \\(10\\mathrm{m}\\) frames. The real anomalies consist of 13 events that have a significant impact on public safety. In one-class VAD setting, the video-level annotations are discarded."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.678,
+                0.892,
+                0.768
+            ],
+            "angle": 0,
+            "content": "- The UBnormal (UB) benchmark is a supervised open-set dataset composed of multiple virtual scenes for video anomaly detection. It is generated by using the Cinema4D software, containing a total of 29 scenes with over 236k frames. We use the default training and testing sets for one-class VAD to evaluate our method."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.557,
+                0.892,
+                0.768
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.786,
+                0.78,
+                0.801
+            ],
+            "angle": 0,
+            "content": "4.2. Performance evaluation metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Following previous works [23, 34, 45, 46, 57], the Area Under the ROC Curve (AUC) is used as the evaluation metrics. The AUC is calculated by using ground truth and the frame-level anomaly scores. In our model, the anomaly scores are defined as the mean squared error (MSE) of each frame as in Eq. (10)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5531"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.087,
+                0.894,
+                0.129
+            ],
+            "angle": 0,
+            "content": "Table 1. AUC of different one-class VAD methods. OD refers to the foreground bounding box from the object detection method, while I3D, R3D and A3D refer to the 3D features from ConvNet3D, ResNext3D and action recognition networks, respectively. 'FPM' indicates that the model also takes a Frame Prediction-based Method for VAD."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.154,
+                0.13,
+                0.819,
+                0.606
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Venue</td><td>Feature</td><td>Framework</td><td>Ave</td><td>ShT</td><td>UCF</td><td>UB</td></tr><tr><td>sRNN [39]</td><td>ICCV-17</td><td>Image</td><td>Encoder</td><td>81.7%</td><td>68.0%</td><td>-</td><td>-</td></tr><tr><td>AnoPCN [68]</td><td>ACMMM-19</td><td>Image</td><td>AE (FPM)</td><td>86.2%</td><td>73.6%</td><td>-</td><td>-</td></tr><tr><td>MemAE [24]</td><td>ICCV-19</td><td>Image</td><td>AE</td><td>83.3%</td><td>71.2%</td><td>-</td><td>-</td></tr><tr><td>Bman [32]</td><td>TIP-20</td><td>Image</td><td>AE (FPM)</td><td>90.0%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>STC [55]</td><td>ACMMM-20</td><td>Image</td><td>AE</td><td>80.9%</td><td>74.7%</td><td>72.7%</td><td>-</td></tr><tr><td>CDAE [10]</td><td>ECCV-20</td><td>Image</td><td>AE (FPM)</td><td>86.0%</td><td>73.3%</td><td>-</td><td>-</td></tr><tr><td>RUVAD [61]</td><td>TNNLS-21</td><td>Image</td><td>AE (FPM)</td><td>88.3%</td><td>76.6%</td><td>-</td><td>-</td></tr><tr><td>MemG [46]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.5%</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>ITAE [14]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.0%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>OGNet [71]</td><td>CVPR-20</td><td>Image</td><td>GAN</td><td>-</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>AMMC [8]</td><td>AAAI-21</td><td>Image</td><td>AE (FPM)</td><td>86.6%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FFP [40]</td><td>TPAMI-21</td><td>Image</td><td>AE (FPM)</td><td>85.1%</td><td>72.8%</td><td>-</td><td>-</td></tr><tr><td>LNTR [3]</td><td>CVPR-21</td><td>Image</td><td>AE</td><td>84.9%</td><td>75.9%</td><td>-</td><td>-</td></tr><tr><td>NGOF [59]</td><td>CVPR-21</td><td>Image</td><td>AE (FPM)</td><td>88.4%</td><td>75.3%</td><td>-</td><td>-</td></tr><tr><td>CT-D2GAN [22]</td><td>ACMMM-21</td><td>Image</td><td>GAN (FPM)</td><td>85.9%</td><td>77.7%</td><td>-</td><td>-</td></tr><tr><td>PB-S [4]</td><td>NC-23</td><td>Image</td><td>GAN (FPM)</td><td>87.1%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr><tr><td>BODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>68.2%</td><td>-</td></tr><tr><td>GODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>69.4%</td><td>-</td></tr><tr><td>VEC [69]</td><td>ACMMM-20</td><td>OD</td><td>AE (FPM)</td><td>90.2%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>CAC [62]</td><td>ACMMM-20</td><td>A3D</td><td>Encoder</td><td>87.0%</td><td>79.3%</td><td>-</td><td>-</td></tr><tr><td>HF2 [37]</td><td>ICCV-21</td><td>OD</td><td>AE (FPM)</td><td>91.1%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>BAF [23]</td><td>TPAMI-21</td><td>OD</td><td>AE</td><td>92.3%</td><td>82.7%</td><td>-</td><td>59.3%</td></tr><tr><td>BDPN [11]</td><td>AAAI-22</td><td>OD</td><td>AE (FPM)</td><td>90.0%</td><td>78.1%</td><td>-</td><td>-</td></tr><tr><td>GCL [72]</td><td>CVPR-22</td><td>R3D</td><td>GAN</td><td>-</td><td>79.6%</td><td>74.2%</td><td>-</td></tr><tr><td>SSL [58]</td><td>ECCV-22</td><td>OD</td><td>Encoder</td><td>92.2%</td><td>84.3%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.643,
+                0.292,
+                0.66
+            ],
+            "angle": 0,
+            "content": "4.3. Implementation details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Following many previous works [24, 34, 45], the input size of images is set to \\(256 \\times 256\\). Since the encoder has four \\(2 \\times\\) downsampling layers, the size of the final feature map is \\(32 \\times 32 \\times 4\\) for each sample. We use four consecutive neighbor frames to predict the fifth according to the setting of the first prediction framework in video anomaly detection [33]. Specifically, we create a cube with four original features and a noised feature from the fifth feature as input for training and testing. We use the recommended settings of \\(\\alpha\\) and \\(\\sigma\\) in DDIM [53]. In the training stage, the number of training epochs \\(S\\) is set to 60, including 12 warm-up epochs at the beginning, and the time step \\(T\\) and learning rate are set to \\(1\\mathrm{k}\\) and \\(10^{-5}\\) respectively. In the inference stage, we adopt a 200 steps sampling schedule \\(T'\\) according to [53], i.e. each step in \\(T'\\) equals five steps in \\(T\\). More"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.892,
+                0.69
+            ],
+            "angle": 0,
+            "content": "over, we set \\( t = 0.25T' \\) for sampling because this was found to be the best in [28, 63]. Therefore, the sampling stage is \\( 20 \\times \\) speed-up compared with DDPM."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.697,
+                0.693,
+                0.714
+            ],
+            "angle": 0,
+            "content": "4.4. Competing methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.825
+            ],
+            "angle": 0,
+            "content": "We examine the performance of the proposed FPDM on all four datasets. We compare our method with 15 state-of-the-art one-class VAD methods that use images as input, as well as another 7 methods that employ different high-level semantic features for training, e.g., foreground bounding box from object detection, 3D features from action recognition models et. al.."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "On all four datasets, FPDM outperforms all the competing image-based one-class methods, verifying the advanced performance of our method. Compared with the methods with 3D features, we still have the best AUC results on UCF-Crime and UBnormal datasets. Notice that the VEC,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5532"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.094,
+                0.105,
+                0.177,
+                0.122
+            ],
+            "angle": 0,
+            "content": "Normality"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.124,
+                0.216,
+                0.222
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.223,
+                0.125,
+                0.349,
+                0.221
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.357,
+                0.125,
+                0.482,
+                0.221
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.49,
+                0.125,
+                0.614,
+                0.221
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.622,
+                0.125,
+                0.747,
+                0.221
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.757,
+                0.125,
+                0.883,
+                0.221
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.095,
+                0.235,
+                0.169,
+                0.251
+            ],
+            "angle": 0,
+            "content": "Anomaly"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.254,
+                0.216,
+                0.351
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.132,
+                0.358,
+                0.175,
+                0.374
+            ],
+            "angle": 0,
+            "content": "Input"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.223,
+                0.254,
+                0.349,
+                0.351
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.255,
+                0.357,
+                0.312,
+                0.372
+            ],
+            "angle": 0,
+            "content": "Noised"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.357,
+                0.254,
+                0.482,
+                0.351
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.377,
+                0.357,
+                0.452,
+                0.372
+            ],
+            "angle": 0,
+            "content": "Predicted"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.49,
+                0.254,
+                0.615,
+                0.351
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.52,
+                0.357,
+                0.583,
+                0.373
+            ],
+            "angle": 0,
+            "content": "Refined"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.622,
+                0.254,
+                0.747,
+                0.351
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.65,
+                0.357,
+                0.706,
+                0.374
+            ],
+            "angle": 0,
+            "content": "Output"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.757,
+                0.254,
+                0.883,
+                0.351
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.802,
+                0.357,
+                0.837,
+                0.372
+            ],
+            "angle": 0,
+            "content": "FFP"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.379,
+                0.892,
+                0.435
+            ],
+            "angle": 0,
+            "content": "Figure 3. The visualization results. We use the frozen decoder from [48] to visualize the features of each module. The top and bottom lines are two examples of normal and abnormal samples. The first column is the original input, and the next four columns named Noised, Predicted, Refined and Output are the decoded images of noised feature, predicted feature, refined feature and original feature respectively. The column named FFP is the predicted frames of FFP approach [40]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.461,
+                0.469,
+                0.536
+            ],
+            "angle": 0,
+            "content": "HF2, and DBPN employ object detection methods to extract the foreground, which can greatly reduce the influence of various noises from the background. While our method still beats these methods, illustrating the anti-noise capability of the diffusion model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.545,
+                0.269,
+                0.56
+            ],
+            "angle": 0,
+            "content": "4.5. Visualization results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.469,
+                0.644
+            ],
+            "angle": 0,
+            "content": "To give a more intuitive presentation of the outputs from each proposed module, we present two series of visualization results from normal and abnormal samples. Here we employ the decoder from [48] that matches our encoder to recover an auto-encoder for feature map decoding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.644,
+                0.469,
+                0.78
+            ],
+            "angle": 0,
+            "content": "The results are shown in Fig. 3, where the first column is the original input. The next four columns show the output of the decoder with four different features, including noised features after the diffusion process in the feature prediction module, the predicted features from the reverse process of the prediction module, the refined features from the reverse process of refinement module, and the features from the encoder respectively. For a more intuitive comparison, we present the predicted frames of FFP [40] in the last column."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "From the results of normality one shown in the top line, we can see that the predicted features well capture the motion information and predict the position of each foreground object, but missing some detail information, such as legs and head of the person dressed in a white T-shirt, the head of the person in black clothing et. al.. These missing details are restored by the refinement module, as shown in the refined column. Comparing the last three, the quality of the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.461,
+                0.892,
+                0.52
+            ],
+            "angle": 0,
+            "content": "refined one is significantly higher than that of the FFP and very close to that of the decoded output from the original feature. This example demonstrates that our model can accurately predict normal features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.892,
+                0.732
+            ],
+            "angle": 0,
+            "content": "The bottom line shows a visual example of the anomaly detection process. According to the results, the predicted feature in the third column also captures the global information of the foreground person but missing some details around this person. With the help of Refined module, the details of the bicycle, e.g., the two wheels are still blurred, illustrating the lack of refinement capacity for the bicycle. The quality of the person/bicycle in the refined column is much better/worse than that of the FFP, verifying our refinement module has greater discriminate capacity than the frame prediction auto-encoder approach The Visualization results verify that the distribution of appearance is so well learned by our model that the anomaly bicycle can't be restored."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.742,
+                0.65,
+                0.759
+            ],
+            "angle": 0,
+            "content": "4.6. Ablation study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.765,
+                0.89,
+                0.794
+            ],
+            "angle": 0,
+            "content": "We evaluate the importance of two key diffusion modules with six variations on ShT and UCF datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "First, we employ the decoder from [48] and discard the two diffusion modules. This setting is to present the performance of the feature extractor. We show the results of the original AE as well as the trained AE using our training data for auto-encoder training. As shown on the top two rows in Table. 2, the results of both original AE and trained AE are far behind the proposed FPDM, demonstrating that the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5533"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.468,
+                0.182
+            ],
+            "angle": 0,
+            "content": "improvement of our FPDM model is based on the two designed diffusion modules. We also train the AE using training data before optimizing FPDM and present the result in the third row. Comparing the result of directly optimizing FPDM, it has almost the same performance, which confirms the unnecessary process of training AE before FPDM."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.08,
+                0.194,
+                0.468,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Table 2. AUC of our model FPDM and its variants. PM and RM refer to our prediction module and refinement module, respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.115,
+                0.225,
+                0.433,
+                0.376
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\">FPDM and its Variants</td><td>ShT</td><td>UCF</td></tr><tr><td>AE</td><td>without training</td><td>67.5%</td><td>50.8%</td></tr><tr><td>AE</td><td>with training</td><td>69.1%</td><td>53.1%</td></tr><tr><td>FPDM</td><td>with trained AE</td><td>78.6%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>with only PM</td><td>77.3%</td><td>74.2%</td></tr><tr><td>FPDM</td><td>with only RM</td><td>76.8%</td><td>72.5%</td></tr><tr><td>FPDM</td><td>with decoder</td><td>78.3%</td><td>74.1%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.7%</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.405,
+                0.468,
+                0.524
+            ],
+            "angle": 0,
+            "content": "Then we keep the prediction/refinement diffusion module with the other one discarded to test the capacity of each module. From the results on the fourth and fifth rows, we can see that the performance decreases when only one module is utilized. The feature prediction module learns the motion information as well as some appearance information, helping achieve better performance than the refinement module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.526,
+                0.468,
+                0.675
+            ],
+            "angle": 0,
+            "content": "Finally, we present the results of FPDM with the decoder. We also use the decoder from [48] to decode the \\( \\ddot{f}_k^0 \\) and calculate the MSE between the input and the decoded one. The declining result of FPDM with decoder shows that the information could be lost through the decoder, e.g., the details of the background (also see the fence and curb on the last column in Fig. 3), which leads to the decrease of performance. Since the specific information of background is usually not relevant to VAD, discarding the decoder is a better choice."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.686,
+                0.325,
+                0.701
+            ],
+            "angle": 0,
+            "content": "4.7. Analysis of training settings"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.08,
+                0.721,
+                0.468,
+                0.762
+            ],
+            "angle": 0,
+            "content": "Table 3. The results of FPDM with different training mode settings. PM, RM, J(.), S(. refer to prediction module, refinement module, joint training, and separated training respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.778,
+                0.472,
+                0.857
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Training Mode</td><td>ShT</td><td>UCF</td></tr><tr><td>FPDM</td><td>J(PM &amp; RM)</td><td>70.8%</td><td>68.1%</td></tr><tr><td>FPDM</td><td>S(PM&amp;RM) → J(PM&amp;RM)</td><td>78.2%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.8%</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.101,
+                0.887,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "We first evaluate the performance of FPDM with differ"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.89,
+                0.288
+            ],
+            "angle": 0,
+            "content": "ent training mode settings. For the proposed two modules, we present the results of joint learning for the whole training, joint learning after separated learning, and the default setting of FPDM in Table. 3. We can see that the performance of joint learning for the whole training, i.e. J(PM & RM), is far behind that of the default setting. It may be due to the low quality of predicted features at the beginning of training, negatively impacting refinement learning. The performance of joint learning after separated learning, i.e. S(PM&RM) \\(\\rightarrow\\) J(PM&RM), falls slightly behind the default setting. The reason may be that the distribution of \\(\\dot{f}_k^0\\) changes in the training process of the prediction module, leading to the instability of refinement learning."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.504,
+                0.303,
+                0.89,
+                0.344
+            ],
+            "angle": 0,
+            "content": "Table 4. The results of FPDM with different number of neighbors on the ShanghaiTech dataset. ShT-3, ShT-11 and ShT-all refer to the 3-rd, 11-th and all scenes of ShanghaiTech dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.515,
+                0.348,
+                0.879,
+                0.445
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td># Neighbors</td><td>ShT-3</td><td>ShT-11</td><td>ShT-all</td></tr><tr><td>FPDM</td><td>12</td><td>81.7</td><td>96.6</td><td>79.0</td></tr><tr><td>FPDM</td><td>8</td><td>80.3</td><td>96.4</td><td>78.9</td></tr><tr><td>FPDM</td><td>4</td><td>79.2</td><td>96.5</td><td>78.6</td></tr><tr><td>FPDM</td><td>0</td><td>73.8</td><td>96.3</td><td>76.2</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.478,
+                0.89,
+                0.688
+            ],
+            "angle": 0,
+            "content": "Then we evaluate the performance of FPDM with different numbers of neighbors in the prediction module. We present the results of 0, 4, 8, and 12 neighbors on two representative scenes, i.e., scene-3 and scene-11 of ShanghaiTech dataset. These two scenes are chosen because the anomalies are all action/appearance-based abnormal events. From the results, we can see that the performance increases observably on the action anomaly test set with more neighbors for training. When the number of neighbors is set to zero, the prediction module degrades to a prediction refinement module with no condition, leading to the decline of the motion learning capacity. While for the appearance-based anomalies, the number of neighbors has little influence on the performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.708,
+                0.624,
+                0.723
+            ],
+            "angle": 0,
+            "content": "5. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.735,
+                0.89,
+                0.9
+            ],
+            "angle": 0,
+            "content": "This paper introduces the first feature prediction diffusion model for video anomaly detection. We further devise two DDIM modules, namely the feature prediction diffusion module and feature refinement diffusion module, for motion and appearance learning from the normal samples. It is impressive that although our model takes images as input to predict features for anomaly detection, it achieves a competing performance compared with the methods utilizing high-level 3D semantic features. Extensive empirical results also demonstrate the superiority of our approach against the SOTA 2D image feature-based VAD models."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.485,
+                0.947,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5534"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.091,
+                0.174,
+                0.105
+            ],
+            "angle": 0,
+            "content": "References"
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\ No newline at end of file
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+# Feature Prediction Diffusion Model for Video Anomaly Detection
+
+Cheng Yan $^{1}$ , Shiyu Zhang $^{1}$ , Yang Liu $^{2}$ , Guansong Pang $^{3*}$ , Wenjun Wang $^{1}$
+
+$^{1}$ Tianjin University  $^{2}$ Zhejiang University  $^{3}$ Singapore Management University
+
+# Abstract
+
+Anomaly detection in the video is an important research area and a challenging task in real applications. Due to the unavailability of large-scale annotated anomaly events, most existing video anomaly detection (VAD) methods focus on learning the distribution of normal samples to detect the substantially deviated samples as anomalies. To well learn the distribution of normal motion and appearance, many auxiliary networks are employed to extract foreground object or action information. These high-level semantic features effectively filter the noise from the background to decrease its influence on detection models. However, the capability of these extra semantic models heavily affects the performance of the VAD methods. Motivated by the impressive generative and anti-noise capacity of diffusion model (DM), in this work, we introduce a novel DM-based method to predict the features of video frames for anomaly detection. We aim to learn the distribution of normal samples without any extra high-level semantic feature extraction models involved. To this end, we build two denoising diffusion implicit modules to predict and refine the features. The first module concentrates on feature motion learning, while the last focuses on feature appearance learning. To the best of our knowledge, it is the first DM-based method to predict frame features for VAD. The strong capacity of DMs also enables our method to more accurately predict the normal features than non-DM-based feature prediction-based VAD methods. Extensive experiments show that the proposed approach substantially outperforms state-of-the-art competing methods. The code is available atFPDM.
+
+# 1. Introduction
+
+Video anomaly detection (VAD) aims at identifying the unusual events that rarely appear and are different from normal behaviors in videos. Successfully detecting the anomalies, such as traffic accidents, violence, and stampedes, is of great importance in ubiquitous video surveillance for pub-
+
+![](images/dc0103f01572b2a8b4542ad89abc4707b626c5992a4924da8e0cd5ba2c086d88.jpg)  
+Figure 1. Overview of three generative VAD approaches. Existing state-of-the-art GAN-based or auto-encoder-based approaches heavily rely on foreground object or action information extracted by auxiliary models, such as object detection, action recognition or optical flow network, to generate features/images for effective performance. By contrast, our proposed diffusion model-based approach does not have this reliance and can make accurate feature prediction using only simple networks as encoder to extract basic image features as input.
+
+lic safety. However, VAD is a challenging task since the anomaly events are unbounded in real-world applications and it is difficult to collect large-scale labeled data.
+
+There have been many VAD methods [9, 10, 14, 19, 23, 33, 34, 39, 45, 46, 57, 62, 68, 71] proposed over the years to handle this issue, in which one-class learning-based methods are preferred due to the relatively accessible normal training set and their capacity to achieve better performance [44]. The one-class VAD methods assume the availability of the training data in which all samples are normal, and build different models to learn the distribution of normal data. Generative modeling is a widely-used technique in this line since the normal samples can be better generated than anomalies after training. Generative Adversarial Networks (GAN) [22, 52, 71, 72] and Auto-Encoder (AE) [24, 29, 40, 46] are two popular frameworks. Although these generative approaches achieve promising performance in VAD, there are three main challenges: (1) the GAN/AE-based methods suffer from the weak generative capacity, leading to more noise from the low-quality generated image, which reduces the
+
+performance, (2) current SOTA methods often employ some auxiliary models, e.g., object detection and action recognition models, to capture the features of the foreground object or action information, and as a result, the performance relies heavily on the representation capacity of these high-level semantic models, and (3) the anomaly events are often characterized by the novel appearance and/or abnormal motion, which increase the difficulty of the generative models to capture the normality/abnormality in both aspects.
+
+In very recent years, diffusion models (DMs) [26, 53], have been attracting increasing attention due to their powerful generative capacity and excellent performance in various tasks [5, 17, 49, 53]. Different from GAN and AE, the diffusion models inject Gaussian noise into the training data and then learn to recover the samples from those noisy data. The DMs are featured by minor modifications and rectification of the generated samples in each step, enabling a more stable generation of more realistic samples. Therefore, the DM-based approaches outperform the GAN/AE-based approaches in many generative tasks [6, 12, 50, 63].
+
+Motivated by the powerful generative capacity of these diffusion models, we propose a novel DM-based approach for anomaly detection. For the second and third challenges mentioned above, as shown in Fig. 1, we devise two complementary denoising DM modules to learn the distribution of normal samples. One module emphasizes learning the distribution of motion, while another module focuses on appearance learning. We employ a simple neural network as the encoder for extracting basic 2D features. Many previous studies [21, 49] have shown that many simple pre-trained networks can effectively extract basic texture information of images even if there are novel classes beyond the training data. Therefore, we adopt a basic 2D feature extractor, which is different from many existing generative methods that utilize high-level semantic models for 3D feature extraction. Based on this, our goal is to learn the distribution of normal features and predict the features of samples for anomaly detection.
+
+In summary, there are three main contributions:
+
+- We introduce a novel diffusion model-based method to predict the features of each sample for VAD. To the best of our knowledge, it is the first work in utilizing DMs for VAD.  
+- We design two types of DDIM module for respective motion and appearance learning from the normal samples to guarantee the generative quality of predicted features.  
+- The proposed model takes 2D images as input with no auxiliary semantic networks, while achieving a highly comparable performance to the methods utilizing high-level 3D semantic features.
+
+Experimental results on four publicly available video anomaly detection datasets demonstrate that our method substantially outperforms the image feature-based VAD counterparts and performs comparably well to methods using 3D semantic features.
+
+# 2. Related work
+
+For different application scenarios, the video anomaly detection methods can be generally classified into three categories, semi-supervised, one-class, and unsupervised VAD, according to the annotation of training samples. Since our method belongs to the one-class type, we only review one-class VAD methods.
+
+The early one-class VAD methods are two-step approaches in which feature extraction and learning are separated. They first use hand-crafted feature descriptors to present each frame, such as 3D gradients features [38], histogram of gradient (HOG) [16], histogram optical flow (HOF) [16], bag of words (BOW) etc., then build a shallow model to learn the normal distribution, such as dictionary-based models [75], probabilistic models [13, 41], and reconstruction models [16, 38, 75]. These traditional methods suffer from the poor performance of hand-crafted features. With the development of deep learning [35, 36, 64-67], convolutional neural network-based methods followed close on another. The CNN integrates feature extraction and learning into an end-to-end frame [42, 43, 70]. The majority of these CNN-based methods belong to the generative approach, in which the model applies feature learning on normality and detects anomalies according to the difference between the generated and original samples. The generative adversarial network (GAN) [20, 51, 73] and auto-encoder-based network (AE) [25, 27, 56] are widely used for such normal feature learning. Based on these frameworks, memory module [24], and feature prediction module [33] are proposed to enhance the capacity of feature learning. To further improve performance, some high-level feature extraction models, e.g., object detection [23, 37], action recognition [62], and optical flow [33], are employed to obtain foreground or motion information for the learning of normality. The auxiliary models bring the benefit to these VAD methods while increasing the dependency on semantic presentations.
+
+Recently, diffusion models have achieved state-of-the-art performance on many generative tasks and become a hot research topic [5, 17, 26, 49, 53]. Many applications have already emerged in computer vision, such as image inpainting [7, 15, 54], image manipulation [47], image superresolution [7, 18], and image-to-image translation [50, 76]. The state-of-the-art performance of these applications confirms that the DM-based models have remarkable generative capacity. To further expand DMs to mainstream computer vision tasks, some DM-based latent representation learning methods have been proposed, such as DiffusionDet for ob
+
+![](images/00271f01bcafe7d845cd92647365d3e5d85a16492f2ed1a8a3093fa89f189edb.jpg)  
+Figure 2. The framework of the proposed method. It contains a frame-level 2D encoder and two DM-based modules, including a feature prediction diffusion module and a feature refinement diffusion module. The feature prediction diffusion module adopts consecutive  $k$  features as input, in which only the last one accepts the diffusion process. With the temporal information from the consecutive frames, this module emphasizes learning the distribution of normal motion. The feature refinement diffusion module takes the sampling output of previous module as input and the  $k$ -th original features as a condition for training, which focuses on the appearance learning.
+
+ject detection [12], SegDiff for segmentation [2], and SBG classifier for classification [77]. These discriminative tasks usually require more powerful models that are not easy to be disturbed by background. Therefore the success of these methods on different tasks verifies the anti-noise ability of DM. The early diffusion models, such as the denoising diffusion probabilistic model (DDPM), have quite a few denoising steps required in the sampling stage due to the Markov process converting data distribution via tiny modification. To accelerate the sampling process, many speed-up diffusion methods have been proposed [30, 53, 74]. The denoising diffusion implicit model (DDIM) is widely used due to its training-free property. The DDIM requires no extra training and can directly apply the advanced sampling algorithms with fewer steps and higher fidelity. Therefore DDIM-based methods are more likely to be adopted in real applications.
+
+# 3. Method
+
+Our key motivation is to design a diffusion model-based approach to well learn the distribution of normal motion and appearance without the help of 3D feature extraction networks. In the inference stage, the feature of a normal sample is more easily predicted by the optimized model than that of the abnormal one.
+
+As shown in Fig. 2, our framework contains three parts,
+
+i.e. a frame encoder, a feature prediction diffusion module, and a feature refinement diffusion module. First, we employ an encoder to extract the feature of each frame. Any pretrained CNN can be used as the encoder. Here we adopt a slight encoder from [48] since (1) the size of output feature map is 64 times spatially smaller than that of the original image and contains only four channels, which significantly reduces the computation of the following diffusion modules, and (2) the pretraining of this encoder is unsupervised, which is more accessible. To predict the feature, we design two DDIM-based modules to predict and refine the feature of each frame. Notice that DDIM has the same training procedure as DDPM but is more efficient in the sampling stage since it adopts a jump-step implicit sampler rather than extracting noise information step by step. The feature prediction diffusion module emphasizes learning the distribution of motion, and the feature refinement diffusion module focuses on appearance distribution learning.
+
+# 3.1. Problem Formulation
+
+The problem aims to address is to generate a feature by giving several continuous video frames and then estimate whether this feature belongs to the learned distribution. Formally, given a video clip with  $k$  consecutive frames  $X = \{\mathbf{x}_1,\mathbf{x}_2,\dots ,\mathbf{x}_k\}$  our goal is to predict the feature of  $k$  -th frame denoted as  $\ddot{f} (\mathbf{x}_k)$  and  $\ddot{f}_k$  for short. We use  $\dot{f}_k$  and  $\ddot{f}_k$  to denote the output of the feature prediction and re
+
+finement diffusion module. Since the time step is involved, we use  $f_{k}^{t}$  to denote the feature of  $k$ -the frame at time step  $t$ . To this end,  $f_{k}^{0}$  refers to the  $k$ -th feature at time step 0, which is equivalent to  $f_{k}$ . Compared with the original feature denoted as  $f_{k}$ , the anomaly score of the  $k$ -th frame can be calculated by Mean Square Error between  $f_{k}$  and  $\ddot{f}_{k}$ .
+
+# 3.2. Feature prediction diffusion module
+
+Different the previous work [33] that adopts  $k$  samples to predict the  $(k + 1)$ -th sample, we take the features  $\{f_1^0,f_2^0,\dots ,f_{k - 1}^0\}$  of 1 to  $k - 1$  frames and the noisy feature  $f_{k}^{t}$  of the  $k$ -th frame together as the input, to predict the feature  $\dot{f}_k^0$ . To this end, we build a feature prediction diffusion module to progressively remove the noise of  $f_{k}^{t}$  by using implicit sampling [53] to generate  $\dot{f}_k^0$ .
+
+For training, the goal of our diffusion models is to learn a distribution  $p_{\theta}(f^0)$  that approximates the original data distribution  $q(f^0)$ . In forward process, the posterior  $q(f^{1:T}|f^0)$  is fixed to a Markov chain:
+
+$$
+q \left(f ^ {1: T} \mid f ^ {0}\right) := \prod_ {t = 1} ^ {T} q \left(f ^ {t} \mid f ^ {t - 1}\right), \tag {1}
+$$
+
+where  $t\in [1,T]$  is the time step, and:
+
+$$
+q \left(f ^ {t} \mid f ^ {t - 1}\right) := \mathcal {N} \left(f ^ {t}; \sqrt {\alpha_ {t}} f ^ {t - 1}, \left(1 - \alpha_ {t}\right) \mathbf {I}\right), \tag {2}
+$$
+
+where  $\alpha_{t}\in \{\alpha_{t}\}_{t = 1}^{T}$  is a schedule to control the percentage of  $f^{t - 1}$ ,  $(1 - \alpha_{t})$  controls the percentage of noise. With time step  $t$  increase,  $\alpha_{t}$  decrease. Based on these properties, the  $f^t$  can be presented by the linear combination of  $f^0$  and standard Gaussian noise  $\epsilon$  as following:
+
+$$
+f ^ {t} = \sqrt {\alpha_ {t}} f ^ {0} + \sqrt {1 - \alpha_ {t}} \epsilon . \tag {3}
+$$
+
+To learn the distribution  $p_{\theta}(f^0)$ , we build a U-net diffusion network  $\epsilon_{\theta}(\cdot)$  based on the LDM [49]. To well predict the features, we modify two parts of the LDM: (1) we discard the latent condition part and modify all the cross-attention layers to traditional attention layers, and (2) each input sample contains  $k$  features  $\{f_1^0,f_2^0,\dots ,f_k^t\}$  where only the  $k$ -th feature is applied diffusion forward process. There are two reasons for such modification: (1) we expect to learn the distribution of features from normal samples without any other latent condition involved, and (2) combined with the consecutive features of previous frames, we can provide the motion information to the  $\epsilon_{\theta}(\cdot)$ , making this diffusion module focus on feature motion learning.
+
+Following [26,53], the simplified version of the objective is used for training defined as:
+
+$$
+L _ {\theta} = \mathbb {E} \left[ | | \epsilon_ {\theta} \left(f _ {1} ^ {0}, f _ {2} ^ {0}, \dots , f _ {k} ^ {t}, t\right) - \epsilon | | _ {2} ^ {2} \right], \tag {4}
+$$
+
+where  $t$  is the time step,  $\epsilon_{\theta}(\cdot ,t)$  is the prediction noise at time  $t$ . Substituting  $f^{t}$  of Eq. (3) into Eq. (4), the parameter
+
+$\theta$  can be optimized by given sufficient feature samples and random time step  $t \in [1, T]$ .
+
+For the reverse process, the features of the  $k$ -th sample at time  $t-1$  can be generated once given  $\{f_1^0, f_2^0, \dots, f_k^t\}$  by the following formula:
+
+$$
+\begin{array}{l} f _ {k} ^ {t - 1} = \sqrt {\alpha_ {t - 1}} \left(\frac {f _ {k} ^ {t} - \sqrt {1 - \alpha_ {t}} \epsilon_ {\theta} \left(f _ {1} ^ {0} , f _ {2} ^ {0} , \cdots , f _ {k} ^ {t} , t\right)}{\sqrt {\alpha t}}\right) \tag {5} \\ + \sqrt {1 - \alpha_ {t - 1} - \sigma_ {t} ^ {2}} \epsilon_ {\theta} \left(f _ {1} ^ {0}, f _ {2} ^ {0}, \dots , f _ {k} ^ {t}, t\right) + \sigma_ {t} \epsilon \\ \end{array}
+$$
+
+where  $\sigma_t \in \{\sigma_t\}_{t=1}^T$  is a schedule to control the added noise for each step. At sampling stage, the (t-1)-th step takes the features  $\{f_1^0, f_2^0, \dots, f_k^t\}$  as input to predict  $f_k^{t-1}$ .
+
+The consecutive supervision on the reverse process can effectively guarantee the motion prediction while it may miss some appearance details since the non-noisy  $k-1$  features are helpful for motion learning while having an effect on appearance learning. To this end, we create another DDIM module to refine the appearance information.
+
+# 3.3. Feature refinement diffusion module
+
+We build a feature refinement diffusion module next to the prediction module. This refinement model places emphasis on learning the appearance distribution of features. Similarly, we adopt the LDM-based U-net as the diffusion network for refining, in which the condition part is maintained. We take the output of the previous prediction module, i.e. the denoised feature  $\dot{f}_k^0$  as input, and use the original feature  $f_{k}^{0}$  of the  $k$ -th frame as condition, to generate the refined features denoted as  $\ddot{f}_k^0$ . The condition  $f_{k}^{0}$  is used for cross-attention to guarantee the feature appearance learning. The goal of the feature refinement diffusion module is to learn a distribution  $p_{\varphi}(\dot{f}^{0})$  that approximates  $q(f^0)$ .
+
+Same with the previous feature prediction module, the posterior  $q(\dot{f}^{1:T}|\dot{f}^{0})$  is fixed to a Markov chain, and the input  $\dot{f}^t$  at time step  $t$  can be calculated according to Eq. (3) by given  $\dot{f}^{0}$  and a Gaussian noise  $\epsilon$ .
+
+To make this refinement network  $\epsilon_{\varphi}(\cdot)$  focus on appearance learning, we augment the underlying UNet backbone with cross-attention mechanism and take the original feature  $f_{k}^{0}$  as the condition into the cross-attention layers. We flatten the feature  $f_{k}^{0}$ , then use a linear transform to obtain a  $d$ -dimensional vector, which is defined as  $\widehat{f}_{k}^{0}$ . The cross-attention is implemented according to:
+
+$$
+\operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d}}\right) V, \tag {6}
+$$
+
+$$
+Q = W _ {q} \cdot \widehat {f} _ {k} ^ {0}, K = W _ {k} \cdot \phi \left(\dot {f} _ {k} ^ {t}\right), V = W _ {v} \cdot \phi \left(\dot {f} _ {k} ^ {t}\right), \tag {7}
+$$
+
+where  $W_{k}$ ,  $W_{q}$ ,  $W_{v}$  are learnable projection matrices and  $\phi(\dot{f}_{k}^{t})$  is the input feature map of each cross-attention layer.
+
+The  $\widehat{f}_k^0$  is changeless for different cross-attention layer that provides a consistent appearance supervision on feature learning. The loss function is also the simplified version of DDIM, defined as:
+
+$$
+L _ {\varphi} = \mathbb {E} \left[ | | \epsilon_ {\varphi} \left(\dot {f} _ {k} ^ {t}, \widehat {f} _ {k} ^ {0}, t\right) - \epsilon | | _ {2} ^ {2} \right]. \tag {8}
+$$
+
+For reverse process, we can obtain the feature at  $t - 1$  time step by:
+
+$$
+\begin{array}{l} \dot {f} _ {k} ^ {t - 1} = \sqrt {\alpha_ {t - 1}} \left(\frac {\dot {f} _ {k} ^ {t} - \sqrt {1 - \alpha_ {t}} \epsilon_ {\varphi} \left(\dot {f} _ {k} ^ {t} , \widehat {f} _ {k} ^ {0} , t\right)}{\sqrt {\alpha t}}\right) \tag {9} \\ + \sqrt {1 - \alpha_ {t - 1} - \sigma_ {t} ^ {2}} \epsilon_ {\varphi} (\dot {f} _ {k} ^ {t}, \widehat {f} _ {k} ^ {0}, t) + \sigma_ {t} \epsilon , \\ \end{array}
+$$
+
+where the parameters  $\alpha$  and  $\sigma$  are same as that of Eq. (5). With a certain time step  $t$ , the refined feature  $\tilde{f}_k^0$  can be obtained through Eq. (9).
+
+For testing, we use MSE to calculate the anomaly score between  $\tilde{f}_k^0$  and the original feature  $f_{k}^{0}$ , defined as:
+
+$$
+\operatorname {S c o r e} = M S E \left(\tilde {f} _ {k} ^ {0}, f _ {k} ^ {0}\right). \tag {10}
+$$
+
+In the training stage, we train the two diffusion modules separately, i.e. train the refinement module after the prediction module reaching convergence. It is because the input of the refinement module is the sampling output of the prediction module, which is of low quality at the beginning of training. Joint learning has a negative impact on the performance of the refinement module (see the results of Table 3). Therefore, we adopt separate training. The pseudo-code for training and inference is shown in Algorithm 1.
+
+# 4. Experiments and discussions
+
+# 4.1. Datasets
+
+Empirical evaluations are carried out on four video anomaly detection datasets, CUHK Avenue [38], ShanghaiTech [39], UCF-Crime datasets [31] and UBnormal [1]. The ShanghaiTech and UCF-Crime are large-scale real-world VAD datasets, and UBnormal is a generated dataset. The details are as follows:
+
+- The CUHK Avenue (Ave) Dataset contains 16 training and 21 testing video clips. The videos are captured in CUHK campus avenue with over  $30\mathrm{k}$  frames. This dataset is proposed for one-class video anomaly detection with anomaly annotations provided only in the testing set, while the training split contains only normal samples.  
+- The ShanghaiTech (ShT) dataset is collected from ShanghaiTech campus in different monitoring angles and lighting conditions. It contains 13 scenes with over
+
+Algorithm 1: The pseudocode for training and inference  
+Training:   
+for S Epochs do Random choose t from [1,T] Calculate  $f^t$  at time t by Eq. (3) Update  $\epsilon_{\theta}$  by Minimizing Eq. (4)   
+end   
+for S Epochs do Random choose t from [1,T] Calculate  $f^t$  by at time t Eq. (3) Sample  $\dot{f}^{0}$  through Eq. (5) Update  $\epsilon_{\varphi}$  by Minimizing Eq. (8)   
+end   
+Inference:   
+foreach Sample in X do Choose a certain t Calculate  $f_{k}^{t}$  at time t by Eq. (3) Sample  $\dot{f}_k^0$  through Eq. (5) Calculate  $\dot{f}_k^t$  at time t by Eq. (3) Sample  $\ddot{f}_k^0$  through Eq. (9) Calculate anomaly score by Eq. (10)   
+end
+
+270k frames in 330 training videos and 130 abnormal events covered in 13 testing videos. This dataset is also for one-class video anomaly detection with anomaly annotations provided only in the testing set.
+
+- The UCF-Crime (UCF) dataset is collected from real-world surveillance. It is a large-scale dataset containing over 128 hours of 1,900 long and untrimmed videos with more than  $10\mathrm{m}$  frames. The real anomalies consist of 13 events that have a significant impact on public safety. In one-class VAD setting, the video-level annotations are discarded.  
+- The UBnormal (UB) benchmark is a supervised open-set dataset composed of multiple virtual scenes for video anomaly detection. It is generated by using the Cinema4D software, containing a total of 29 scenes with over 236k frames. We use the default training and testing sets for one-class VAD to evaluate our method.
+
+# 4.2. Performance evaluation metrics
+
+Following previous works [23, 34, 45, 46, 57], the Area Under the ROC Curve (AUC) is used as the evaluation metrics. The AUC is calculated by using ground truth and the frame-level anomaly scores. In our model, the anomaly scores are defined as the mean squared error (MSE) of each frame as in Eq. (10).
+
+Table 1. AUC of different one-class VAD methods. OD refers to the foreground bounding box from the object detection method, while I3D, R3D and A3D refer to the 3D features from ConvNet3D, ResNext3D and action recognition networks, respectively. 'FPM' indicates that the model also takes a Frame Prediction-based Method for VAD.  
+
+<table><tr><td>Method</td><td>Venue</td><td>Feature</td><td>Framework</td><td>Ave</td><td>ShT</td><td>UCF</td><td>UB</td></tr><tr><td>sRNN [39]</td><td>ICCV-17</td><td>Image</td><td>Encoder</td><td>81.7%</td><td>68.0%</td><td>-</td><td>-</td></tr><tr><td>AnoPCN [68]</td><td>ACMMM-19</td><td>Image</td><td>AE (FPM)</td><td>86.2%</td><td>73.6%</td><td>-</td><td>-</td></tr><tr><td>MemAE [24]</td><td>ICCV-19</td><td>Image</td><td>AE</td><td>83.3%</td><td>71.2%</td><td>-</td><td>-</td></tr><tr><td>Bman [32]</td><td>TIP-20</td><td>Image</td><td>AE (FPM)</td><td>90.0%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>STC [55]</td><td>ACMMM-20</td><td>Image</td><td>AE</td><td>80.9%</td><td>74.7%</td><td>72.7%</td><td>-</td></tr><tr><td>CDAE [10]</td><td>ECCV-20</td><td>Image</td><td>AE (FPM)</td><td>86.0%</td><td>73.3%</td><td>-</td><td>-</td></tr><tr><td>RUVAD [61]</td><td>TNNLS-21</td><td>Image</td><td>AE (FPM)</td><td>88.3%</td><td>76.6%</td><td>-</td><td>-</td></tr><tr><td>MemG [46]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.5%</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>ITAE [14]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.0%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>OGNet [71]</td><td>CVPR-20</td><td>Image</td><td>GAN</td><td>-</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>AMMC [8]</td><td>AAAI-21</td><td>Image</td><td>AE (FPM)</td><td>86.6%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FFP [40]</td><td>TPAMI-21</td><td>Image</td><td>AE (FPM)</td><td>85.1%</td><td>72.8%</td><td>-</td><td>-</td></tr><tr><td>LNTR [3]</td><td>CVPR-21</td><td>Image</td><td>AE</td><td>84.9%</td><td>75.9%</td><td>-</td><td>-</td></tr><tr><td>NGOF [59]</td><td>CVPR-21</td><td>Image</td><td>AE (FPM)</td><td>88.4%</td><td>75.3%</td><td>-</td><td>-</td></tr><tr><td>CT-D2GAN [22]</td><td>ACMMM-21</td><td>Image</td><td>GAN (FPM)</td><td>85.9%</td><td>77.7%</td><td>-</td><td>-</td></tr><tr><td>PB-S [4]</td><td>NC-23</td><td>Image</td><td>GAN (FPM)</td><td>87.1%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr><tr><td>BODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>68.2%</td><td>-</td></tr><tr><td>GODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>69.4%</td><td>-</td></tr><tr><td>VEC [69]</td><td>ACMMM-20</td><td>OD</td><td>AE (FPM)</td><td>90.2%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>CAC [62]</td><td>ACMMM-20</td><td>A3D</td><td>Encoder</td><td>87.0%</td><td>79.3%</td><td>-</td><td>-</td></tr><tr><td>HF2 [37]</td><td>ICCV-21</td><td>OD</td><td>AE (FPM)</td><td>91.1%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>BAF [23]</td><td>TPAMI-21</td><td>OD</td><td>AE</td><td>92.3%</td><td>82.7%</td><td>-</td><td>59.3%</td></tr><tr><td>BDPN [11]</td><td>AAAI-22</td><td>OD</td><td>AE (FPM)</td><td>90.0%</td><td>78.1%</td><td>-</td><td>-</td></tr><tr><td>GCL [72]</td><td>CVPR-22</td><td>R3D</td><td>GAN</td><td>-</td><td>79.6%</td><td>74.2%</td><td>-</td></tr><tr><td>SSL [58]</td><td>ECCV-22</td><td>OD</td><td>Encoder</td><td>92.2%</td><td>84.3%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr></table>
+
+# 4.3. Implementation details
+
+Following many previous works [24, 34, 45], the input size of images is set to  $256 \times 256$ . Since the encoder has four  $2 \times$  downsampling layers, the size of the final feature map is  $32 \times 32 \times 4$  for each sample. We use four consecutive neighbor frames to predict the fifth according to the setting of the first prediction framework in video anomaly detection [33]. Specifically, we create a cube with four original features and a noised feature from the fifth feature as input for training and testing. We use the recommended settings of  $\alpha$  and  $\sigma$  in DDIM [53]. In the training stage, the number of training epochs  $S$  is set to 60, including 12 warm-up epochs at the beginning, and the time step  $T$  and learning rate are set to  $1\mathrm{k}$  and  $10^{-5}$  respectively. In the inference stage, we adopt a 200 steps sampling schedule  $T'$  according to [53], i.e. each step in  $T'$  equals five steps in  $T$ . More
+
+over, we set  $t = 0.25T'$  for sampling because this was found to be the best in [28, 63]. Therefore, the sampling stage is  $20 \times$  speed-up compared with DDPM.
+
+# 4.4. Competing methods
+
+We examine the performance of the proposed FPDM on all four datasets. We compare our method with 15 state-of-the-art one-class VAD methods that use images as input, as well as another 7 methods that employ different high-level semantic features for training, e.g., foreground bounding box from object detection, 3D features from action recognition models et. al..
+
+On all four datasets, FPDM outperforms all the competing image-based one-class methods, verifying the advanced performance of our method. Compared with the methods with 3D features, we still have the best AUC results on UCF-Crime and UBnormal datasets. Notice that the VEC,
+
+![](images/af68bc62930ea92e9c57dbd99c766b78ddafe3470b78869abc44b78198c3c908.jpg)  
+Normality
+
+![](images/06bc98c96cf86828f68883b92ee27554f840dbeb8b819326036dc8c3375d6874.jpg)
+
+![](images/7607a44d15687e821db8e9d330381b04953e55f8e25eed9e4e1c83c458291a5d.jpg)
+
+![](images/2a4a553f887cdfdd1999bc1d8df3957dc47469f846c9468048c314ed0afea604.jpg)
+
+![](images/e3f999f3a90de24345f18c627fed1a52afb3f331b09ccedce88421592bdd6c0c.jpg)
+
+![](images/745fda283249e5b3fb20dcee971b3410eb78792c92de0a2b2ce81e7e137664ea.jpg)
+
+![](images/8a509859bcf02383e3735289cc05fd9d6cbefa5e5599fcba1b241dd8130c6865.jpg)  
+Anomaly  
+Input  
+Figure 3. The visualization results. We use the frozen decoder from [48] to visualize the features of each module. The top and bottom lines are two examples of normal and abnormal samples. The first column is the original input, and the next four columns named Noised, Predicted, Refined and Output are the decoded images of noised feature, predicted feature, refined feature and original feature respectively. The column named FFP is the predicted frames of FFP approach [40].
+
+![](images/ef6fec2535c6219f2c71e07e9f5838b0093592792e252a8f4f56b46062d9f5c8.jpg)  
+Noised
+
+![](images/14bc35f9c05cd49cc7632ea34158169375abbf782ddd5a75067a88dc546c128d.jpg)  
+Predicted
+
+![](images/f8059c5600014efc9555524c084b938ae07c1c1198e7bb85019d68d4d0cca223.jpg)  
+Refined
+
+![](images/df86ade291a3124923190c158aa60ef9cbfdc03ab9645933784947febce2b243.jpg)  
+Output
+
+![](images/b791818ccd0b87e6e8388f57f3d0883eb3da05c2835a1e2cefe1492d37f11b77.jpg)  
+FFP
+
+HF2, and DBPN employ object detection methods to extract the foreground, which can greatly reduce the influence of various noises from the background. While our method still beats these methods, illustrating the anti-noise capability of the diffusion model.
+
+# 4.5. Visualization results
+
+To give a more intuitive presentation of the outputs from each proposed module, we present two series of visualization results from normal and abnormal samples. Here we employ the decoder from [48] that matches our encoder to recover an auto-encoder for feature map decoding.
+
+The results are shown in Fig. 3, where the first column is the original input. The next four columns show the output of the decoder with four different features, including noised features after the diffusion process in the feature prediction module, the predicted features from the reverse process of the prediction module, the refined features from the reverse process of refinement module, and the features from the encoder respectively. For a more intuitive comparison, we present the predicted frames of FFP [40] in the last column.
+
+From the results of normality one shown in the top line, we can see that the predicted features well capture the motion information and predict the position of each foreground object, but missing some detail information, such as legs and head of the person dressed in a white T-shirt, the head of the person in black clothing et. al.. These missing details are restored by the refinement module, as shown in the refined column. Comparing the last three, the quality of the
+
+refined one is significantly higher than that of the FFP and very close to that of the decoded output from the original feature. This example demonstrates that our model can accurately predict normal features.
+
+The bottom line shows a visual example of the anomaly detection process. According to the results, the predicted feature in the third column also captures the global information of the foreground person but missing some details around this person. With the help of Refined module, the details of the bicycle, e.g., the two wheels are still blurred, illustrating the lack of refinement capacity for the bicycle. The quality of the person/bicycle in the refined column is much better/worse than that of the FFP, verifying our refinement module has greater discriminate capacity than the frame prediction auto-encoder approach The Visualization results verify that the distribution of appearance is so well learned by our model that the anomaly bicycle can't be restored.
+
+# 4.6. Ablation study
+
+We evaluate the importance of two key diffusion modules with six variations on ShT and UCF datasets.
+
+First, we employ the decoder from [48] and discard the two diffusion modules. This setting is to present the performance of the feature extractor. We show the results of the original AE as well as the trained AE using our training data for auto-encoder training. As shown on the top two rows in Table. 2, the results of both original AE and trained AE are far behind the proposed FPDM, demonstrating that the
+
+improvement of our FPDM model is based on the two designed diffusion modules. We also train the AE using training data before optimizing FPDM and present the result in the third row. Comparing the result of directly optimizing FPDM, it has almost the same performance, which confirms the unnecessary process of training AE before FPDM.
+
+Table 2. AUC of our model FPDM and its variants. PM and RM refer to our prediction module and refinement module, respectively.  
+
+<table><tr><td colspan="2">FPDM and its Variants</td><td>ShT</td><td>UCF</td></tr><tr><td>AE</td><td>without training</td><td>67.5%</td><td>50.8%</td></tr><tr><td>AE</td><td>with training</td><td>69.1%</td><td>53.1%</td></tr><tr><td>FPDM</td><td>with trained AE</td><td>78.6%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>with only PM</td><td>77.3%</td><td>74.2%</td></tr><tr><td>FPDM</td><td>with only RM</td><td>76.8%</td><td>72.5%</td></tr><tr><td>FPDM</td><td>with decoder</td><td>78.3%</td><td>74.1%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.7%</td></tr></table>
+
+Then we keep the prediction/refinement diffusion module with the other one discarded to test the capacity of each module. From the results on the fourth and fifth rows, we can see that the performance decreases when only one module is utilized. The feature prediction module learns the motion information as well as some appearance information, helping achieve better performance than the refinement module.
+
+Finally, we present the results of FPDM with the decoder. We also use the decoder from [48] to decode the  $\ddot{f}_k^0$  and calculate the MSE between the input and the decoded one. The declining result of FPDM with decoder shows that the information could be lost through the decoder, e.g., the details of the background (also see the fence and curb on the last column in Fig. 3), which leads to the decrease of performance. Since the specific information of background is usually not relevant to VAD, discarding the decoder is a better choice.
+
+# 4.7. Analysis of training settings
+
+Table 3. The results of FPDM with different training mode settings. PM, RM, J(.), S(. refer to prediction module, refinement module, joint training, and separated training respectively.  
+
+<table><tr><td></td><td>Training Mode</td><td>ShT</td><td>UCF</td></tr><tr><td>FPDM</td><td>J(PM &amp; RM)</td><td>70.8%</td><td>68.1%</td></tr><tr><td>FPDM</td><td>S(PM&amp;RM) → J(PM&amp;RM)</td><td>78.2%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.8%</td></tr></table>
+
+We first evaluate the performance of FPDM with differ
+
+ent training mode settings. For the proposed two modules, we present the results of joint learning for the whole training, joint learning after separated learning, and the default setting of FPDM in Table. 3. We can see that the performance of joint learning for the whole training, i.e. J(PM & RM), is far behind that of the default setting. It may be due to the low quality of predicted features at the beginning of training, negatively impacting refinement learning. The performance of joint learning after separated learning, i.e. S(PM&RM)  $\rightarrow$  J(PM&RM), falls slightly behind the default setting. The reason may be that the distribution of  $\dot{f}_k^0$  changes in the training process of the prediction module, leading to the instability of refinement learning.
+
+Table 4. The results of FPDM with different number of neighbors on the ShanghaiTech dataset. ShT-3, ShT-11 and ShT-all refer to the 3-rd, 11-th and all scenes of ShanghaiTech dataset.  
+
+<table><tr><td></td><td># Neighbors</td><td>ShT-3</td><td>ShT-11</td><td>ShT-all</td></tr><tr><td>FPDM</td><td>12</td><td>81.7</td><td>96.6</td><td>79.0</td></tr><tr><td>FPDM</td><td>8</td><td>80.3</td><td>96.4</td><td>78.9</td></tr><tr><td>FPDM</td><td>4</td><td>79.2</td><td>96.5</td><td>78.6</td></tr><tr><td>FPDM</td><td>0</td><td>73.8</td><td>96.3</td><td>76.2</td></tr></table>
+
+Then we evaluate the performance of FPDM with different numbers of neighbors in the prediction module. We present the results of 0, 4, 8, and 12 neighbors on two representative scenes, i.e., scene-3 and scene-11 of ShanghaiTech dataset. These two scenes are chosen because the anomalies are all action/appearance-based abnormal events. From the results, we can see that the performance increases observably on the action anomaly test set with more neighbors for training. When the number of neighbors is set to zero, the prediction module degrades to a prediction refinement module with no condition, leading to the decline of the motion learning capacity. While for the appearance-based anomalies, the number of neighbors has little influence on the performance.
+
+# 5. Conclusions
+
+This paper introduces the first feature prediction diffusion model for video anomaly detection. We further devise two DDIM modules, namely the feature prediction diffusion module and feature refinement diffusion module, for motion and appearance learning from the normal samples. It is impressive that although our model takes images as input to predict features for anomaly detection, it achieves a competing performance compared with the methods utilizing high-level 3D semantic features. Extensive empirical results also demonstrate the superiority of our approach against the SOTA 2D image feature-based VAD models.
+
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+                                    "content": "Anomaly detection in the video is an important research area and a challenging task in real applications. Due to the unavailability of large-scale annotated anomaly events, most existing video anomaly detection (VAD) methods focus on learning the distribution of normal samples to detect the substantially deviated samples as anomalies. To well learn the distribution of normal motion and appearance, many auxiliary networks are employed to extract foreground object or action information. These high-level semantic features effectively filter the noise from the background to decrease its influence on detection models. However, the capability of these extra semantic models heavily affects the performance of the VAD methods. Motivated by the impressive generative and anti-noise capacity of diffusion model (DM), in this work, we introduce a novel DM-based method to predict the features of video frames for anomaly detection. We aim to learn the distribution of normal samples without any extra high-level semantic feature extraction models involved. To this end, we build two denoising diffusion implicit modules to predict and refine the features. The first module concentrates on feature motion learning, while the last focuses on feature appearance learning. To the best of our knowledge, it is the first DM-based method to predict frame features for VAD. The strong capacity of DMs also enables our method to more accurately predict the normal features than non-DM-based feature prediction-based VAD methods. Extensive experiments show that the proposed approach substantially outperforms state-of-the-art competing methods. The code is available atFPDM."
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+                                    "type": "text",
+                                    "content": "*Guansong Pang is the corresponding author, e-mail: pangguansong@gmail.com"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "performance, (2) current SOTA methods often employ some auxiliary models, e.g., object detection and action recognition models, to capture the features of the foreground object or action information, and as a result, the performance relies heavily on the representation capacity of these high-level semantic models, and (3) the anomaly events are often characterized by the novel appearance and/or abnormal motion, which increase the difficulty of the generative models to capture the normality/abnormality in both aspects."
+                                }
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+                                    "type": "text",
+                                    "content": "In very recent years, diffusion models (DMs) [26, 53], have been attracting increasing attention due to their powerful generative capacity and excellent performance in various tasks [5, 17, 49, 53]. Different from GAN and AE, the diffusion models inject Gaussian noise into the training data and then learn to recover the samples from those noisy data. The DMs are featured by minor modifications and rectification of the generated samples in each step, enabling a more stable generation of more realistic samples. Therefore, the DM-based approaches outperform the GAN/AE-based approaches in many generative tasks [6, 12, 50, 63]."
+                                }
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+                    ],
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+                                    "type": "text",
+                                    "content": "Motivated by the powerful generative capacity of these diffusion models, we propose a novel DM-based approach for anomaly detection. For the second and third challenges mentioned above, as shown in Fig. 1, we devise two complementary denoising DM modules to learn the distribution of normal samples. One module emphasizes learning the distribution of motion, while another module focuses on appearance learning. We employ a simple neural network as the encoder for extracting basic 2D features. Many previous studies [21, 49] have shown that many simple pre-trained networks can effectively extract basic texture information of images even if there are novel classes beyond the training data. Therefore, we adopt a basic 2D feature extractor, which is different from many existing generative methods that utilize high-level semantic models for 3D feature extraction. Based on this, our goal is to learn the distribution of normal features and predict the features of samples for anomaly detection."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "In summary, there are three main contributions:"
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+                                            "content": "- We introduce a novel diffusion model-based method to predict the features of each sample for VAD. To the best of our knowledge, it is the first work in utilizing DMs for VAD."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "content": "- We design two types of DDIM module for respective motion and appearance learning from the normal samples to guarantee the generative quality of predicted features."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
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+                                            "type": "text",
+                                            "content": "- The proposed model takes 2D images as input with no auxiliary semantic networks, while achieving a highly comparable performance to the methods utilizing high-level 3D semantic features."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
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+                                    "content": "Experimental results on four publicly available video anomaly detection datasets demonstrate that our method substantially outperforms the image feature-based VAD counterparts and performs comparably well to methods using 3D semantic features."
+                                }
+                            ]
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+                    ],
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+                                    "content": "2. Related work"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "For different application scenarios, the video anomaly detection methods can be generally classified into three categories, semi-supervised, one-class, and unsupervised VAD, according to the annotation of training samples. Since our method belongs to the one-class type, we only review one-class VAD methods."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The early one-class VAD methods are two-step approaches in which feature extraction and learning are separated. They first use hand-crafted feature descriptors to present each frame, such as 3D gradients features [38], histogram of gradient (HOG) [16], histogram optical flow (HOF) [16], bag of words (BOW) etc., then build a shallow model to learn the normal distribution, such as dictionary-based models [75], probabilistic models [13, 41], and reconstruction models [16, 38, 75]. These traditional methods suffer from the poor performance of hand-crafted features. With the development of deep learning [35, 36, 64-67], convolutional neural network-based methods followed close on another. The CNN integrates feature extraction and learning into an end-to-end frame [42, 43, 70]. The majority of these CNN-based methods belong to the generative approach, in which the model applies feature learning on normality and detects anomalies according to the difference between the generated and original samples. The generative adversarial network (GAN) [20, 51, 73] and auto-encoder-based network (AE) [25, 27, 56] are widely used for such normal feature learning. Based on these frameworks, memory module [24], and feature prediction module [33] are proposed to enhance the capacity of feature learning. To further improve performance, some high-level feature extraction models, e.g., object detection [23, 37], action recognition [62], and optical flow [33], are employed to obtain foreground or motion information for the learning of normality. The auxiliary models bring the benefit to these VAD methods while increasing the dependency on semantic presentations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Recently, diffusion models have achieved state-of-the-art performance on many generative tasks and become a hot research topic [5, 17, 26, 49, 53]. Many applications have already emerged in computer vision, such as image inpainting [7, 15, 54], image manipulation [47], image superresolution [7, 18], and image-to-image translation [50, 76]. The state-of-the-art performance of these applications confirms that the DM-based models have remarkable generative capacity. To further expand DMs to mainstream computer vision tasks, some DM-based latent representation learning methods have been proposed, such as DiffusionDet for ob"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+                                            "type": "text",
+                                            "content": "Figure 2. The framework of the proposed method. It contains a frame-level 2D encoder and two DM-based modules, including a feature prediction diffusion module and a feature refinement diffusion module. The feature prediction diffusion module adopts consecutive "
+                                        },
+                                        {
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+                                            "type": "text",
+                                            "content": " features as input, in which only the last one accepts the diffusion process. With the temporal information from the consecutive frames, this module emphasizes learning the distribution of normal motion. The feature refinement diffusion module takes the sampling output of previous module as input and the "
+                                        },
+                                        {
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+                                            "type": "text",
+                                            "content": "-th original features as a condition for training, which focuses on the appearance learning."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
+                    "index": 0
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+                {
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+                                    "type": "text",
+                                    "content": "ject detection [12], SegDiff for segmentation [2], and SBG classifier for classification [77]. These discriminative tasks usually require more powerful models that are not easy to be disturbed by background. Therefore the success of these methods on different tasks verifies the anti-noise ability of DM. The early diffusion models, such as the denoising diffusion probabilistic model (DDPM), have quite a few denoising steps required in the sampling stage due to the Markov process converting data distribution via tiny modification. To accelerate the sampling process, many speed-up diffusion methods have been proposed [30, 53, 74]. The denoising diffusion implicit model (DDIM) is widely used due to its training-free property. The DDIM requires no extra training and can directly apply the advanced sampling algorithms with fewer steps and higher fidelity. Therefore DDIM-based methods are more likely to be adopted in real applications."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
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+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Our key motivation is to design a diffusion model-based approach to well learn the distribution of normal motion and appearance without the help of 3D feature extraction networks. In the inference stage, the feature of a normal sample is more easily predicted by the optimized model than that of the abnormal one."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "As shown in Fig. 2, our framework contains three parts,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "i.e. a frame encoder, a feature prediction diffusion module, and a feature refinement diffusion module. First, we employ an encoder to extract the feature of each frame. Any pretrained CNN can be used as the encoder. Here we adopt a slight encoder from [48] since (1) the size of output feature map is 64 times spatially smaller than that of the original image and contains only four channels, which significantly reduces the computation of the following diffusion modules, and (2) the pretraining of this encoder is unsupervised, which is more accessible. To predict the feature, we design two DDIM-based modules to predict and refine the feature of each frame. Notice that DDIM has the same training procedure as DDPM but is more efficient in the sampling stage since it adopts a jump-step implicit sampler rather than extracting noise information step by step. The feature prediction diffusion module emphasizes learning the distribution of motion, and the feature refinement diffusion module focuses on appearance distribution learning."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
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+                {
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+                                    "content": "3.1. Problem Formulation"
+                                }
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+                },
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+                                    "content": "The problem aims to address is to generate a feature by giving several continuous video frames and then estimate whether this feature belongs to the learned distribution. Formally, given a video clip with "
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+                                    "content": " consecutive frames "
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+                                    "type": "inline_equation",
+                                    "content": "X = \\{\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_k\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " our goal is to predict the feature of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
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+                                    ],
+                                    "type": "text",
+                                    "content": " -th frame denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ddot{f} (\\mathbf{x}_k)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ddot{f}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " for short. We use "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\dot{f}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ddot{f}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the output of the feature prediction and re"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                }
+            ],
+            "discarded_blocks": [
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+                                    "content": "5529"
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+                    "angle": 0,
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+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": "finement diffusion module. Since the time step is involved, we use "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the feature of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": "-the frame at time step "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ". To this end, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " refers to the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": "-th feature at time step 0, which is equivalent to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ". Compared with the original feature denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ", the anomaly score of the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": "-th frame can be calculated by Mean Square Error between "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ddot{f}_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                        164
+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Feature prediction diffusion module"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": "Different the previous work [33] that adopts "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
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+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
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+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": " samples to predict the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(k + 1)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
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+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": "-th sample, we take the features "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{f_1^0,f_2^0,\\dots ,f_{k - 1}^0\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": " of 1 to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
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+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k - 1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": " frames and the noisy feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": " of the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": "-th frame together as the input, to predict the feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\dot{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": ". To this end, we build a feature prediction diffusion module to progressively remove the noise of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": " by using implicit sampling [53] to generate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\dot{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        169,
+                                        287,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For training, the goal of our diffusion models is to learn a distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
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+                                        304
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_{\\theta}(f^0)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
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+                                        304
+                                    ],
+                                    "type": "text",
+                                    "content": " that approximates the original data distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q(f^0)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
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+                                        304
+                                    ],
+                                    "type": "text",
+                                    "content": ". In forward process, the posterior "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        304
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q(f^{1:T}|f^0)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
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+                                        304
+                                    ],
+                                    "type": "text",
+                                    "content": " is fixed to a Markov chain:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "q \\left(f ^ {1: T} \\mid f ^ {0}\\right) := \\prod_ {t = 1} ^ {T} q \\left(f ^ {t} \\mid f ^ {t - 1}\\right), \\tag {1}",
+                                    "image_path": "381cd6ad7a92e8e84c78ea4c8a0d7205abc75ae39a3f9b7cef2df883c188f258.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t\\in [1,T]"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the time step, and:"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "q \\left(f ^ {t} \\mid f ^ {t - 1}\\right) := \\mathcal {N} \\left(f ^ {t}; \\sqrt {\\alpha_ {t}} f ^ {t - 1}, \\left(1 - \\alpha_ {t}\\right) \\mathbf {I}\\right), \\tag {2}",
+                                    "image_path": "2a0f14346d00cf7efc636d286dcc957ca64cea831a0e074852a48093c6350596.jpg"
+                                }
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+                                    "type": "text",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{t}\\in \\{\\alpha_{t}\\}_{t = 1}^{T}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a schedule to control the percentage of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f^{t - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(1 - \\alpha_{t})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " controls the percentage of noise. With time step "
+                                },
+                                {
+                                    "bbox": [
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+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " increase, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " decrease. Based on these properties, the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f^t"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be presented by the linear combination of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f^0"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and standard Gaussian noise "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        391,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as following:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "f ^ {t} = \\sqrt {\\alpha_ {t}} f ^ {0} + \\sqrt {1 - \\alpha_ {t}} \\epsilon . \\tag {3}",
+                                    "image_path": "edcc0b0fd552d6f0ece5aebe1ca356f5068f216d5ccfa39f1f6f2c28e1e70c1a.jpg"
+                                }
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+                    ],
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+                },
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+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": "To learn the distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_{\\theta}(f^0)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": ", we build a U-net diffusion network "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon_{\\theta}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " based on the LDM [49]. To well predict the features, we modify two parts of the LDM: (1) we discard the latent condition part and modify all the cross-attention layers to traditional attention layers, and (2) each input sample contains "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
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+                                    ],
+                                    "type": "text",
+                                    "content": " features "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{f_1^0,f_2^0,\\dots ,f_k^t\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " where only the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th feature is applied diffusion forward process. There are two reasons for such modification: (1) we expect to learn the distribution of features from normal samples without any other latent condition involved, and (2) combined with the consecutive features of previous frames, we can provide the motion information to the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon_{\\theta}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": ", making this diffusion module focus on feature motion learning."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                        660
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Following [26,53], the simplified version of the objective is used for training defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {\\theta} = \\mathbb {E} \\left[ | | \\epsilon_ {\\theta} \\left(f _ {1} ^ {0}, f _ {2} ^ {0}, \\dots , f _ {k} ^ {t}, t\\right) - \\epsilon | | _ {2} ^ {2} \\right], \\tag {4}",
+                                    "image_path": "f37bb7f02a9cd0cf140ee709468676df6e85c8bae02464e34fc3a89cce82eb69.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        46,
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+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " is the time step, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon_{\\theta}(\\cdot ,t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " is the prediction noise at time "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Substituting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " of Eq. (3) into Eq. (4), the parameter"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                        95
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                        95
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "text",
+                                    "content": " can be optimized by given sufficient feature samples and random time step "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t \\in [1, T]"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        305,
+                        96,
+                        545,
+                        132
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                96,
+                                545,
+                                132
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": "For the reverse process, the features of the "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": "-th sample at time "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t-1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": " can be generated once given "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{f_1^0, f_2^0, \\dots, f_k^t\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
+                                        545,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": " by the following formula:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        312,
+                        148,
+                        545,
+                        197
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        312,
+                                        148,
+                                        545,
+                                        197
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} f _ {k} ^ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\left(\\frac {f _ {k} ^ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\theta} \\left(f _ {1} ^ {0} , f _ {2} ^ {0} , \\cdots , f _ {k} ^ {t} , t\\right)}{\\sqrt {\\alpha t}}\\right) \\tag {5} \\\\ + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\theta} \\left(f _ {1} ^ {0}, f _ {2} ^ {0}, \\dots , f _ {k} ^ {t}, t\\right) + \\sigma_ {t} \\epsilon \\\\ \\end{array}",
+                                    "image_path": "667a67b287bc9f7c5e4355af4d4a3838341990cc41c44e9204fab3de2fe8f376.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        305,
+                        204,
+                        545,
+                        242
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                204,
+                                545,
+                                242
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma_t \\in \\{\\sigma_t\\}_{t=1}^T"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "text",
+                                    "content": " is a schedule to control the added noise for each step. At sampling stage, the (t-1)-th step takes the features "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{f_1^0, f_2^0, \\dots, f_k^t\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "text",
+                                    "content": " as input to predict "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_k^{t-1}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        204,
+                                        545,
+                                        242
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        305,
+                        242,
+                        545,
+                        312
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                242,
+                                545,
+                                312
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        242,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": "The consecutive supervision on the reverse process can effectively guarantee the motion prediction while it may miss some appearance details since the non-noisy "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        242,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k-1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        242,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " features are helpful for motion learning while having an effect on appearance learning. To this end, we create another DDIM module to refine the appearance information."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                        331
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Feature refinement diffusion module"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": "We build a feature refinement diffusion module next to the prediction module. This refinement model places emphasis on learning the appearance distribution of features. Similarly, we adopt the LDM-based U-net as the diffusion network for refining, in which the condition part is maintained. We take the output of the previous prediction module, i.e. the denoised feature "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\dot{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": " as input, and use the original feature "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": " of the "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": "-th frame as condition, to generate the refined features denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ddot{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": ". The condition "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": " is used for cross-attention to guarantee the feature appearance learning. The goal of the feature refinement diffusion module is to learn a distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_{\\varphi}(\\dot{f}^{0})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": " that approximates "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q(f^0)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        338,
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
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+                                    "type": "text",
+                                    "content": "Same with the previous feature prediction module, the posterior "
+                                },
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+                                    "content": "q(\\dot{f}^{1:T}|\\dot{f}^{0})"
+                                },
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+                                    "type": "text",
+                                    "content": " is fixed to a Markov chain, and the input "
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+                                    "type": "inline_equation",
+                                    "content": "\\dot{f}^t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " at time step "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " can be calculated according to Eq. (3) by given "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and a Gaussian noise "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\epsilon"
+                                },
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "To make this refinement network "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\epsilon_{\\varphi}(\\cdot)"
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+                                    "type": "text",
+                                    "content": " focus on appearance learning, we augment the underlying UNet backbone with cross-attention mechanism and take the original feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as the condition into the cross-attention layers. We flatten the feature "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", then use a linear transform to obtain a "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "-dimensional vector, which is defined as "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\widehat{f}_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The cross-attention is implemented according to:"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}}\\right) V, \\tag {6}",
+                                    "image_path": "e39123522affe28da063509c78c53c4524ff237131bd03d986c6b02d9a1bd343.jpg"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "Q = W _ {q} \\cdot \\widehat {f} _ {k} ^ {0}, K = W _ {k} \\cdot \\phi \\left(\\dot {f} _ {k} ^ {t}\\right), V = W _ {v} \\cdot \\phi \\left(\\dot {f} _ {k} ^ {t}\\right), \\tag {7}",
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+                                    "content": "W_{v}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are learnable projection matrices and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\phi(\\dot{f}_{k}^{t})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the input feature map of each cross-attention layer."
+                                }
+                            ]
+                        }
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+                    "index": 24
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "The "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{f}_k^0"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is changeless for different cross-attention layer that provides a consistent appearance supervision on feature learning. The loss function is also the simplified version of DDIM, defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "L _ {\\varphi} = \\mathbb {E} \\left[ | | \\epsilon_ {\\varphi} \\left(\\dot {f} _ {k} ^ {t}, \\widehat {f} _ {k} ^ {0}, t\\right) - \\epsilon | | _ {2} ^ {2} \\right]. \\tag {8}",
+                                    "image_path": "0b61c4cb383558a61fb4d1ff6ea7b3aae1d7523049488973e5c6d44e4ce46228.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "For reverse process, we can obtain the feature at "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        154,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t - 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " time step by:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\dot {f} _ {k} ^ {t - 1} = \\sqrt {\\alpha_ {t - 1}} \\left(\\frac {\\dot {f} _ {k} ^ {t} - \\sqrt {1 - \\alpha_ {t}} \\epsilon_ {\\varphi} \\left(\\dot {f} _ {k} ^ {t} , \\widehat {f} _ {k} ^ {0} , t\\right)}{\\sqrt {\\alpha t}}\\right) \\tag {9} \\\\ + \\sqrt {1 - \\alpha_ {t - 1} - \\sigma_ {t} ^ {2}} \\epsilon_ {\\varphi} (\\dot {f} _ {k} ^ {t}, \\widehat {f} _ {k} ^ {0}, t) + \\sigma_ {t} \\epsilon , \\\\ \\end{array}",
+                                    "image_path": "f96fdd1a74a1811b0fb87365c153d822e9854605d750ce78df90150015d34880.jpg"
+                                }
+                            ]
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+                    ],
+                    "index": 3
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+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where the parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        255,
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+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        255,
+                                        286,
+                                        290
+                                    ],
+                                    "type": "text",
+                                    "content": " are same as that of Eq. (5). With a certain time step "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        255,
+                                        286,
+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        255,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the refined feature "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        255,
+                                        286,
+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        255,
+                                        286,
+                                        290
+                                    ],
+                                    "type": "text",
+                                    "content": " can be obtained through Eq. (9)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For testing, we use MSE to calculate the anomaly score between "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the original feature "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{0}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        116,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {S c o r e} = M S E \\left(\\tilde {f} _ {k} ^ {0}, f _ {k} ^ {0}\\right). \\tag {10}",
+                                    "image_path": "b057b255f56228cc91d63f1b105ff2de9c0dfb10850154dd7740d504a98d4b4e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "In the training stage, we train the two diffusion modules separately, i.e. train the refinement module after the prediction module reaching convergence. It is because the input of the refinement module is the sampling output of the prediction module, which is of low quality at the beginning of training. Joint learning has a negative impact on the performance of the refinement module (see the results of Table 3). Therefore, we adopt separate training. The pseudo-code for training and inference is shown in Algorithm 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4. Experiments and discussions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.1. Datasets"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Empirical evaluations are carried out on four video anomaly detection datasets, CUHK Avenue [38], ShanghaiTech [39], UCF-Crime datasets [31] and UBnormal [1]. The ShanghaiTech and UCF-Crime are large-scale real-world VAD datasets, and UBnormal is a generated dataset. The details are as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                            "type": "text",
+                                            "content": "- The CUHK Avenue (Ave) Dataset contains 16 training and 21 testing video clips. The videos are captured in CUHK campus avenue with over "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "30\\mathrm{k}"
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " frames. This dataset is proposed for one-class video anomaly detection with anomaly annotations provided only in the testing set, while the training split contains only normal samples."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                58,
+                                677,
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- The ShanghaiTech (ShT) dataset is collected from ShanghaiTech campus in different monitoring angles and lighting conditions. It contains 13 scenes with over"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "sub_type": "text"
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+                {
+                    "type": "code",
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+                                            "type": "text",
+                                            "content": "Algorithm 1: The pseudocode for training and inference"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14,
+                            "angle": 0,
+                            "type": "code_caption"
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+                                            "type": "text",
+                                            "content": "Training:   \nfor S Epochs do Random choose t from [1,T] Calculate "
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+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "f^t"
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " at time t by Eq. (3) Update "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\epsilon_{\\theta}"
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " by Minimizing Eq. (4)   \nend   \nfor S Epochs do Random choose t from [1,T] Calculate "
+                                        },
+                                        {
+                                            "bbox": [
+                                                316,
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+                                            "type": "inline_equation",
+                                            "content": "f^t"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " by at time t Eq. (3) Sample "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\dot{f}^{0}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " through Eq. (5) Update "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "\\epsilon_{\\varphi}"
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+                                            "type": "text",
+                                            "content": " by Minimizing Eq. (8)   \nend   \nInference:   \nforeach Sample in X do Choose a certain t Calculate "
+                                        },
+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "f_{k}^{t}"
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+                                        {
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+                                            "type": "text",
+                                            "content": " at time t by Eq. (3) Sample "
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+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "\\dot{f}_k^0"
+                                        },
+                                        {
+                                            "bbox": [
+                                                316,
+                                                99,
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+                                            ],
+                                            "type": "text",
+                                            "content": " through Eq. (5) Calculate "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                485,
+                                                354
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\dot{f}_k^t"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " at time t by Eq. (3) Sample "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                354
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\ddot{f}_k^0"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " through Eq. (9) Calculate anomaly score by Eq. (10)   \nend"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "angle": 0,
+                            "type": "code_body"
+                        }
+                    ],
+                    "index": 15,
+                    "sub_type": "algorithm"
+                },
+                {
+                    "bbox": [
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+                        430
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                324,
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+                            ],
+                            "spans": [
+                                {
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+                                    "type": "text",
+                                    "content": "270k frames in 330 training videos and 130 abnormal events covered in 13 testing videos. This dataset is also for one-class video anomaly detection with anomaly annotations provided only in the testing set."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 19,
+                    "blocks": [
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- The UCF-Crime (UCF) dataset is collected from real-world surveillance. It is a large-scale dataset containing over 128 hours of 1,900 long and untrimmed videos with more than "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "10\\mathrm{m}"
+                                        },
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+                                            "type": "text",
+                                            "content": " frames. The real anomalies consist of 13 events that have a significant impact on public safety. In one-class VAD setting, the video-level annotations are discarded."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- The UBnormal (UB) benchmark is a supervised open-set dataset composed of multiple virtual scenes for video anomaly detection. It is generated by using the Cinema4D software, containing a total of 29 scenes with over 236k frames. We use the default training and testing sets for one-class VAD to evaluate our method."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.2. Performance evaluation metrics"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Following previous works [23, 34, 45, 46, 57], the Area Under the ROC Curve (AUC) is used as the evaluation metrics. The AUC is calculated by using ground truth and the frame-level anomaly scores. In our model, the anomaly scores are defined as the mean squared error (MSE) of each frame as in Eq. (10)."
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+                                            "type": "text",
+                                            "content": "Table 1. AUC of different one-class VAD methods. OD refers to the foreground bounding box from the object detection method, while I3D, R3D and A3D refer to the 3D features from ConvNet3D, ResNext3D and action recognition networks, respectively. 'FPM' indicates that the model also takes a Frame Prediction-based Method for VAD."
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+                                            "html": "<table><tr><td>Method</td><td>Venue</td><td>Feature</td><td>Framework</td><td>Ave</td><td>ShT</td><td>UCF</td><td>UB</td></tr><tr><td>sRNN [39]</td><td>ICCV-17</td><td>Image</td><td>Encoder</td><td>81.7%</td><td>68.0%</td><td>-</td><td>-</td></tr><tr><td>AnoPCN [68]</td><td>ACMMM-19</td><td>Image</td><td>AE (FPM)</td><td>86.2%</td><td>73.6%</td><td>-</td><td>-</td></tr><tr><td>MemAE [24]</td><td>ICCV-19</td><td>Image</td><td>AE</td><td>83.3%</td><td>71.2%</td><td>-</td><td>-</td></tr><tr><td>Bman [32]</td><td>TIP-20</td><td>Image</td><td>AE (FPM)</td><td>90.0%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>STC [55]</td><td>ACMMM-20</td><td>Image</td><td>AE</td><td>80.9%</td><td>74.7%</td><td>72.7%</td><td>-</td></tr><tr><td>CDAE [10]</td><td>ECCV-20</td><td>Image</td><td>AE (FPM)</td><td>86.0%</td><td>73.3%</td><td>-</td><td>-</td></tr><tr><td>RUVAD [61]</td><td>TNNLS-21</td><td>Image</td><td>AE (FPM)</td><td>88.3%</td><td>76.6%</td><td>-</td><td>-</td></tr><tr><td>MemG [46]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.5%</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>ITAE [14]</td><td>CVPR-20</td><td>Image</td><td>AE</td><td>88.0%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>OGNet [71]</td><td>CVPR-20</td><td>Image</td><td>GAN</td><td>-</td><td>70.5%</td><td>-</td><td>-</td></tr><tr><td>AMMC [8]</td><td>AAAI-21</td><td>Image</td><td>AE (FPM)</td><td>86.6%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FFP [40]</td><td>TPAMI-21</td><td>Image</td><td>AE (FPM)</td><td>85.1%</td><td>72.8%</td><td>-</td><td>-</td></tr><tr><td>LNTR [3]</td><td>CVPR-21</td><td>Image</td><td>AE</td><td>84.9%</td><td>75.9%</td><td>-</td><td>-</td></tr><tr><td>NGOF [59]</td><td>CVPR-21</td><td>Image</td><td>AE (FPM)</td><td>88.4%</td><td>75.3%</td><td>-</td><td>-</td></tr><tr><td>CT-D2GAN [22]</td><td>ACMMM-21</td><td>Image</td><td>GAN (FPM)</td><td>85.9%</td><td>77.7%</td><td>-</td><td>-</td></tr><tr><td>PB-S [4]</td><td>NC-23</td><td>Image</td><td>GAN (FPM)</td><td>87.1%</td><td>73.7%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr><tr><td>BODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>68.2%</td><td>-</td></tr><tr><td>GODS [60]</td><td>CVPR-19</td><td>I3D</td><td>AE</td><td>-</td><td>-</td><td>69.4%</td><td>-</td></tr><tr><td>VEC [69]</td><td>ACMMM-20</td><td>OD</td><td>AE (FPM)</td><td>90.2%</td><td>74.8%</td><td>-</td><td>-</td></tr><tr><td>CAC [62]</td><td>ACMMM-20</td><td>A3D</td><td>Encoder</td><td>87.0%</td><td>79.3%</td><td>-</td><td>-</td></tr><tr><td>HF2 [37]</td><td>ICCV-21</td><td>OD</td><td>AE (FPM)</td><td>91.1%</td><td>76.2%</td><td>-</td><td>-</td></tr><tr><td>BAF [23]</td><td>TPAMI-21</td><td>OD</td><td>AE</td><td>92.3%</td><td>82.7%</td><td>-</td><td>59.3%</td></tr><tr><td>BDPN [11]</td><td>AAAI-22</td><td>OD</td><td>AE (FPM)</td><td>90.0%</td><td>78.1%</td><td>-</td><td>-</td></tr><tr><td>GCL [72]</td><td>CVPR-22</td><td>R3D</td><td>GAN</td><td>-</td><td>79.6%</td><td>74.2%</td><td>-</td></tr><tr><td>SSL [58]</td><td>ECCV-22</td><td>OD</td><td>Encoder</td><td>92.2%</td><td>84.3%</td><td>-</td><td>-</td></tr><tr><td>FPDM (Ours)</td><td>-</td><td>Image</td><td>DDIM</td><td>90.1%</td><td>78.6%</td><td>74.7%</td><td>62.7%</td></tr></table>",
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+                                    "content": "Following many previous works [24, 34, 45], the input size of images is set to "
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+                                    "type": "text",
+                                    "content": ". Since the encoder has four "
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+                                    "type": "text",
+                                    "content": " downsampling layers, the size of the final feature map is "
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+                                    "type": "inline_equation",
+                                    "content": "32 \\times 32 \\times 4"
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+                                    "type": "text",
+                                    "content": " for each sample. We use four consecutive neighbor frames to predict the fifth according to the setting of the first prediction framework in video anomaly detection [33]. Specifically, we create a cube with four original features and a noised feature from the fifth feature as input for training and testing. We use the recommended settings of "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in DDIM [53]. In the training stage, the number of training epochs "
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+                                    "content": " is set to 60, including 12 warm-up epochs at the beginning, and the time step "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and learning rate are set to "
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+                                    "type": "inline_equation",
+                                    "content": "1\\mathrm{k}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "10^{-5}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " respectively. In the inference stage, we adopt a 200 steps sampling schedule "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "T'"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " according to [53], i.e. each step in "
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+                                    "type": "inline_equation",
+                                    "content": "T'"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " equals five steps in "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". More"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "over, we set "
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+                                    "type": "inline_equation",
+                                    "content": "t = 0.25T'"
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+                                    "type": "text",
+                                    "content": " for sampling because this was found to be the best in [28, 63]. Therefore, the sampling stage is "
+                                },
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+                                    "content": "20 \\times"
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+                                    "type": "text",
+                                    "content": " speed-up compared with DDPM."
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+                                    "content": "4.4. Competing methods"
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+                                    "content": "We examine the performance of the proposed FPDM on all four datasets. We compare our method with 15 state-of-the-art one-class VAD methods that use images as input, as well as another 7 methods that employ different high-level semantic features for training, e.g., foreground bounding box from object detection, 3D features from action recognition models et. al.."
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+                                            "content": "Figure 3. The visualization results. We use the frozen decoder from [48] to visualize the features of each module. The top and bottom lines are two examples of normal and abnormal samples. The first column is the original input, and the next four columns named Noised, Predicted, Refined and Output are the decoded images of noised feature, predicted feature, refined feature and original feature respectively. The column named FFP is the predicted frames of FFP approach [40]."
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+                                    "content": "HF2, and DBPN employ object detection methods to extract the foreground, which can greatly reduce the influence of various noises from the background. While our method still beats these methods, illustrating the anti-noise capability of the diffusion model."
+                                }
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+                                    "content": "To give a more intuitive presentation of the outputs from each proposed module, we present two series of visualization results from normal and abnormal samples. Here we employ the decoder from [48] that matches our encoder to recover an auto-encoder for feature map decoding."
+                                }
+                            ]
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+                                    "content": "The results are shown in Fig. 3, where the first column is the original input. The next four columns show the output of the decoder with four different features, including noised features after the diffusion process in the feature prediction module, the predicted features from the reverse process of the prediction module, the refined features from the reverse process of refinement module, and the features from the encoder respectively. For a more intuitive comparison, we present the predicted frames of FFP [40] in the last column."
+                                }
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+                                    "content": "From the results of normality one shown in the top line, we can see that the predicted features well capture the motion information and predict the position of each foreground object, but missing some detail information, such as legs and head of the person dressed in a white T-shirt, the head of the person in black clothing et. al.. These missing details are restored by the refinement module, as shown in the refined column. Comparing the last three, the quality of the"
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+                                    "type": "text",
+                                    "content": "refined one is significantly higher than that of the FFP and very close to that of the decoded output from the original feature. This example demonstrates that our model can accurately predict normal features."
+                                }
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+                                    "type": "text",
+                                    "content": "The bottom line shows a visual example of the anomaly detection process. According to the results, the predicted feature in the third column also captures the global information of the foreground person but missing some details around this person. With the help of Refined module, the details of the bicycle, e.g., the two wheels are still blurred, illustrating the lack of refinement capacity for the bicycle. The quality of the person/bicycle in the refined column is much better/worse than that of the FFP, verifying our refinement module has greater discriminate capacity than the frame prediction auto-encoder approach The Visualization results verify that the distribution of appearance is so well learned by our model that the anomaly bicycle can't be restored."
+                                }
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+                                    "content": "4.6. Ablation study"
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+                                    "content": "We evaluate the importance of two key diffusion modules with six variations on ShT and UCF datasets."
+                                }
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+                                    "content": "First, we employ the decoder from [48] and discard the two diffusion modules. This setting is to present the performance of the feature extractor. We show the results of the original AE as well as the trained AE using our training data for auto-encoder training. As shown on the top two rows in Table. 2, the results of both original AE and trained AE are far behind the proposed FPDM, demonstrating that the"
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+                                    "type": "text",
+                                    "content": "improvement of our FPDM model is based on the two designed diffusion modules. We also train the AE using training data before optimizing FPDM and present the result in the third row. Comparing the result of directly optimizing FPDM, it has almost the same performance, which confirms the unnecessary process of training AE before FPDM."
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+                                            "content": "Table 2. AUC of our model FPDM and its variants. PM and RM refer to our prediction module and refinement module, respectively."
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+                                            "html": "<table><tr><td colspan=\"2\">FPDM and its Variants</td><td>ShT</td><td>UCF</td></tr><tr><td>AE</td><td>without training</td><td>67.5%</td><td>50.8%</td></tr><tr><td>AE</td><td>with training</td><td>69.1%</td><td>53.1%</td></tr><tr><td>FPDM</td><td>with trained AE</td><td>78.6%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>with only PM</td><td>77.3%</td><td>74.2%</td></tr><tr><td>FPDM</td><td>with only RM</td><td>76.8%</td><td>72.5%</td></tr><tr><td>FPDM</td><td>with decoder</td><td>78.3%</td><td>74.1%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.7%</td></tr></table>",
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+                                    "content": "Then we keep the prediction/refinement diffusion module with the other one discarded to test the capacity of each module. From the results on the fourth and fifth rows, we can see that the performance decreases when only one module is utilized. The feature prediction module learns the motion information as well as some appearance information, helping achieve better performance than the refinement module."
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+                                    "content": "Finally, we present the results of FPDM with the decoder. We also use the decoder from [48] to decode the "
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+                                    "content": " and calculate the MSE between the input and the decoded one. The declining result of FPDM with decoder shows that the information could be lost through the decoder, e.g., the details of the background (also see the fence and curb on the last column in Fig. 3), which leads to the decrease of performance. Since the specific information of background is usually not relevant to VAD, discarding the decoder is a better choice."
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+                                    "type": "text",
+                                    "content": "4.7. Analysis of training settings"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
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+                                            "type": "text",
+                                            "content": "Table 3. The results of FPDM with different training mode settings. PM, RM, J(.), S(. refer to prediction module, refinement module, joint training, and separated training respectively."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6,
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+                                            "html": "<table><tr><td></td><td>Training Mode</td><td>ShT</td><td>UCF</td></tr><tr><td>FPDM</td><td>J(PM &amp; RM)</td><td>70.8%</td><td>68.1%</td></tr><tr><td>FPDM</td><td>S(PM&amp;RM) → J(PM&amp;RM)</td><td>78.2%</td><td>74.5%</td></tr><tr><td>FPDM</td><td>default</td><td>78.6%</td><td>74.8%</td></tr></table>",
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+                            ],
+                            "index": 7,
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+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We first evaluate the performance of FPDM with differ"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                    "type": "text",
+                                    "content": "ent training mode settings. For the proposed two modules, we present the results of joint learning for the whole training, joint learning after separated learning, and the default setting of FPDM in Table. 3. We can see that the performance of joint learning for the whole training, i.e. J(PM & RM), is far behind that of the default setting. It may be due to the low quality of predicted features at the beginning of training, negatively impacting refinement learning. The performance of joint learning after separated learning, i.e. S(PM&RM) "
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+                                    "type": "text",
+                                    "content": " J(PM&RM), falls slightly behind the default setting. The reason may be that the distribution of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\dot{f}_k^0"
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " changes in the training process of the prediction module, leading to the instability of refinement learning."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "table",
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+                                            "type": "text",
+                                            "content": "Table 4. The results of FPDM with different number of neighbors on the ShanghaiTech dataset. ShT-3, ShT-11 and ShT-all refer to the 3-rd, 11-th and all scenes of ShanghaiTech dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
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+                                            "type": "table",
+                                            "html": "<table><tr><td></td><td># Neighbors</td><td>ShT-3</td><td>ShT-11</td><td>ShT-all</td></tr><tr><td>FPDM</td><td>12</td><td>81.7</td><td>96.6</td><td>79.0</td></tr><tr><td>FPDM</td><td>8</td><td>80.3</td><td>96.4</td><td>78.9</td></tr><tr><td>FPDM</td><td>4</td><td>79.2</td><td>96.5</td><td>78.6</td></tr><tr><td>FPDM</td><td>0</td><td>73.8</td><td>96.3</td><td>76.2</td></tr></table>",
+                                            "image_path": "7db139fe94ab3741368c347935e5377b75fdd1ca6357622b55783002ab6c1327.jpg"
+                                        }
+                                    ]
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+                            ],
+                            "index": 11,
+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Then we evaluate the performance of FPDM with different numbers of neighbors in the prediction module. We present the results of 0, 4, 8, and 12 neighbors on two representative scenes, i.e., scene-3 and scene-11 of ShanghaiTech dataset. These two scenes are chosen because the anomalies are all action/appearance-based abnormal events. From the results, we can see that the performance increases observably on the action anomaly test set with more neighbors for training. When the number of neighbors is set to zero, the prediction module degrades to a prediction refinement module with no condition, leading to the decline of the motion learning capacity. While for the appearance-based anomalies, the number of neighbors has little influence on the performance."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
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+                                    "type": "text",
+                                    "content": "5. Conclusions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "This paper introduces the first feature prediction diffusion model for video anomaly detection. We further devise two DDIM modules, namely the feature prediction diffusion module and feature refinement diffusion module, for motion and appearance learning from the normal samples. It is impressive that although our model takes images as input to predict features for anomaly detection, it achieves a competing performance compared with the methods utilizing high-level 3D semantic features. Extensive empirical results also demonstrate the superiority of our approach against the SOTA 2D image feature-based VAD models."
+                                }
+                            ]
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+                                    "content": "References"
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+                                        }
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+                                }
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+                                        }
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+                                }
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+                            ],
+                            "type": "ref_text",
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+                                {
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+                        },
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+                        }
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diff --git a/2023/Feature Proliferation -- the 'Cancer' in StyleGAN and its Treatments/585d65ee-f18b-4e36-8941-f08943b3d7c2_content_list.json b/2023/Feature Proliferation -- the 'Cancer' in StyleGAN and its Treatments/585d65ee-f18b-4e36-8941-f08943b3d7c2_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..160690e25f89d6898479faea94311c99e577a3be
--- /dev/null
+++ b/2023/Feature Proliferation -- the 'Cancer' in StyleGAN and its Treatments/585d65ee-f18b-4e36-8941-f08943b3d7c2_content_list.json	
@@ -0,0 +1,2172 @@
+[
+    {
+        "type": "text",
+        "text": "Feature Proliferation — the “Cancer” in StyleGAN and its Treatments",
+        "text_level": 1,
+        "bbox": [
+            129,
+            130,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Shuang Song Yuanbang Liang Jing Wu Yu-Kun Lai Yipeng Qin* Cardiff University",
+        "bbox": [
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+            782,
+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{songs7, liangy32, wuj11, laiy4, qiny16}@cardiff.ac.uk",
+        "bbox": [
+            263,
+            222,
+            705,
+            237
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            272,
+            313,
+            287
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite the success of StyleGAN in image synthesis, the images it synthesizes are not always perfect and the well-known truncation trick has become a standard post-processing technique for StyleGAN to synthesize high quality images. Although effective, it has long been noted that the truncation trick tends to reduce the diversity of synthesized images and unnecessarily sacrifices many distinct image features. To address this issue, in this paper, we first delve into the StyleGAN image synthesis mechanism and discover an important phenomenon, namely Feature Proliferation, which demonstrates how specific features reproduce with forward propagation. Then, we show how the occurrence of Feature Proliferation results in StyleGAN image artifacts. As an analogy, we refer to it as the \"cancer\" in StyleGAN from its proliferating and malignant nature. Finally, we propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation. Thanks to our discovery of Feature Proliferation, the proposed feature rescaling method is less destructive and retains more useful image features than the truncation trick, as it is more fine-grained and works in a lower-level feature space rather than a high-level latent space. Experimental results justify the validity of our claims and the effectiveness of the proposed feature rescaling method. Our code is available at https://github.com/songc42/Feature-proliferation.",
+        "bbox": [
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+            303,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            724,
+            209,
+            739
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep learning has entered the era of large models. For instance, the GPT-3 [7] developed by OpenAI has 175 billion parameters and can easily cost around 15 million dollars to train for a single run, let alone the GPT-3.5 underpinning the recently hyped ChatGPT; Stability.ai trained their Stable-diffusion-v1-4 $^2$  using 256 Nvidia A100 GPUs for 150,000 GPU hours; Nvidia spent 92 GPU years and",
+        "bbox": [
+            75,
+            748,
+            470,
+            854
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "225 MWh of electricity with an in-house cluster of NVIDIA V100 GPUs to develop StyleGAN3 [15] and 4 weeks on 64 NVIDIA A100s for a \"constrained\" training of their recent StyleGAN-T [27]. As a result, although the performance of large models is impressive, their high costs have become a critical concern, e.g., OpenAI admitted that there was a bug in their GPT-3 model but cannot afford to retrain it due to the high cost [7]. This motivates us to do our best to avoid retraining large neural network models. In this work, we focus on the StyleGAN family [16, 17, 15, 27] as they are inherently more efficient (i.e., generating images with a single pass), allow for excellent semantic interpolation in their latent spaces, and are comparable to the quality of diffusion models [27]. For the StyleGAN series, although there were no obvious bugs in the training, the synthesized images are not always perfect. While instead of attempting to solve this problem by improving the model design which requires multiple retraining, StyleGAN follows the \"no retraining\" philosophy and resorts to a post-processing technique called truncation trick [20, 6]. In short, the truncation trick improves the quality of StyleGAN synthesized images by normalizing their corresponding latent codes towards their mean in the latent space. However, despite its popularity, it has long been noted that the truncation trick tends to reduce the diversity of synthesized images and unnecessarily sacrifices many distinct image features [16].",
+        "bbox": [
+            500,
+            273,
+            893,
+            667
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we address the low-quality images synthesized by StyleGAN from a different perspective, i.e., its mechanism for image synthesis in the feature space. Specifically, we delved into the architectural details of the StyleGAN generator and discovered an important phenomenon, namely Feature Proliferation, which demonstrates how specific features reproduce with forward propagation. In short, Feature Proliferation denotes the phenomenon where the ratio of the occurrence of a certain type of feature (those with abnormally large values) in a layer increases with forward propagation. Our analysis points out that such a phenomenon is a by-product of the weight modulation and demodulation techniques used in StyleGAN2/3 [17, 15] and the latest StyleGAN-T [27]. Interestingly, we observed that Feature Proliferation usually leads to artifacts in Style-",
+        "bbox": [
+            498,
+            674,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author: Yipeng Qin",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "1 https://openai.com/blog/chatgpt",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "2https://huggingface.co/CompVis/stable-diffusion-v1-4",
+        "bbox": [
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+        ],
+        "page_idx": 0
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+    {
+        "type": "page_number",
+        "text": "2360",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/5390750f0a06c84b3e25e62d3e60319b32f34c339afd2e82eca021304ff7e6d6.jpg",
+        "image_caption": [
+            "Figure 1. Top: StyleGAN synthesized images with artifacts. Bottom: images \"cured\" by our method."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "GAN synthesized images and these artifacts can be easily removed by a simple feature rescaling method. To minimize the unnecessary interference with useful image features, we propose a novel method to identify the risky features prone to proliferation in the earliest layers, thereby removing the least amount of them. As a result, our method significantly outperforms the truncation trick in terms of retaining useful image features while improving the quality of StyleGAN synthesized images. Experimental results justify the validity of our claims and the effectiveness of the proposed feature rescaling method. Our contributions include:",
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+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We discover an important phenomenon, namely Feature Proliferation, which shows how specific features reproduce with forward propagation. We also show that it is a by-product of the weight modulation and demodulation techniques used in modern StyleGANs.",
+            "- We discover a strong causal relationship between the occurrence of Feature Proliferation and StyleGAN image artifacts.",
+            "- We propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation, thereby achieving a better trade-off between quality and diversity of StyleGAN synthesized images than the popular truncation trick."
+        ],
+        "bbox": [
+            96,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            784,
+            215,
+            800
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since the seminal work of Goodfellow et al. [10], Generative Adversarial Networks (GANs) have become one of the most promising deep generative models that have numerous applications in computer vision and graphics. Nevertheless, GANs are known to be notoriously difficult to train and a variety of techniques have been proposed to",
+        "bbox": [
+            75,
+            809,
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+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "stabilize their training from different perspectives, including architectures [25, 11], loss functions [4, 19], regularization [22, 23], and the interactions between them [24]. Thanks to the massive efforts from the community, the StyleGAN series [16, 17, 15, 27] have become one of the most influential models in the GAN family, as it can generate high-resolution and realistic images that are almost indistinguishable from real photos by human inspectors. Examples of its applications include GAN inversion and editing [1, 2, 29, 3], image-to-image translation [26], superresolution [21], 3D shape generation [32], etc. We refer interested audiences to [5] for a survey on StyleGAN and its applications. Nevertheless, despite its success, the quality of images synthesized by StyleGAN varies, and a post-processing method known as the truncation trick [20, 6] has widely been adopted to obtain higher quality images. However, the truncation trick has long been noted as \"destructive\" as it unnecessarily sacrifices useful image features and tends to reduce the diversity of synthesized images. In this paper, we address this issue by investigating the StyleGAN image synthesis mechanism and propose a feature rescaling method that can precisely identify the risky features causing image artifacts, thereby improving image quality by modulating these features at the minimal cost.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Feature Proliferation in StyleGAN",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first introduce two new phenomena that we discovered in the forward propagation of deep neural networks, i.e. feature domination and proliferation. We then show that they are by-products of the weight modulation and demodulation techniques used in modern StyleGANs. Finally, we show how they affect StyleGAN and lead to artifacts in synthesized images.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2361",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/16306bd1efdc357289432a5cae9afd58f1691123fc77aec27eeb502b52359222.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of feature domination.  $y$  is dominated by  $x_{j}$  and its perturbations  $x_{i} \\approx x_{j}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Feature Domination and Proliferation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Throughout the history of machine learning, the weighted sum method has been built to last from the classical linear regression, to the theoretically elegant support vector machines and the deep neural networks that are now taking both academia and industry by storm. For deep neural networks, we usually refer to the output of neurons as features that are the elements to be weighted and summed. However, due to the differences among weights and input features, the output of a neuron can occasionally be dominated by one or a small amount of input features, which leads to a phenomenon we call Feature Domination.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Definition 3.1 (Feature Domination) Let  $y = \\mathbf{w}^{\\mathrm{T}}\\mathbf{x} + b$  be the output of a neuron,  $\\mathbf{x}$  and  $\\mathbf{w}$  are the input and weight vectors respectively,  $b$  denotes the bias, we define Feature Domination as the case where  $y \\approx (\\sum_{i} w_{i}) x_{j} + b$  is dominated by feature  $x_{j}$  and its perturbations  $x_{i} \\approx x_{j}$ , where  $i$  indicates the  $i$ -th element in  $\\mathbf{w}$  and  $\\mathbf{x}$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In a nutshell, the proposed Feature Domination describes the phenomenon that one or a small number of similar input features may dominate the weighted sum if their products with associated weights significantly outweigh others (Fig. 2), making  $y$  similar to  $x_{i} / x_{j}$ . In practice, we observed that the dominant features are highly likely to be those that deviate significantly from the mean of their distributions:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Observation 3.1 (Feature Domination in StyleGAN)",
+        "text_level": 1,
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let  $t$  be an empirically obtained threshold, and  $x_{l,j}$  be the feature map of channel  $j$  of layer  $l$  of the generator.  $x_{l,j}$  is highly likely to be dominant if  $\\frac{|\\mathrm{mean}(x_{l,j}) - \\mu_{x_{l,j}}|}{\\sigma_{x_{l,j}}} > t$ , where  $\\mathrm{mean}(x_{l,j})$  is the mean value of all elements in  $x_{l,j}$ ,  $\\mu_{x_{l,j}}$  and  $\\sigma_{x_{l,j}}$  are the mean and standard deviation of the distribution of  $x_{l,j}$  over the training dataset.",
+        "bbox": [
+            73,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In practice, we use Observation 3.1 to identify dominant features in StyleGANs. Furthermore, Feature Proliferation happens when the same type of Feature Domination proliferates during the forward propagation.",
+        "bbox": [
+            75,
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/608b2de0a7c965e9bb157312ab3ee4dea22f6fd21c154b9a3a33de43103f6f88.jpg",
+        "image_caption": [
+            "(a) Mean of inputs"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            95,
+            700,
+            191
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7d379999759b68822a9bf4cc1d1e2e34fb85bcf72954ca71a6cedc3d8db9d46e.jpg",
+        "image_caption": [
+            "(b) Standard deviation of inputs",
+            "Figure 3. Histograms of mean and standard deviation of the input feature maps from 10,000 StyleGAN2 synthesized images."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            705,
+            95,
+            901,
+            191
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Definition 3.2 (Feature Proliferation) Following Definition 3.1, let  $\\mathbf{Y}_d(x_j)$  be the set consisting of all outputs  $y$  dominated by feature  $x_j$  in a single neural network layer, we define Feature Proliferation as the increase of  $\\eta(x_j) = |\\mathbf{Y}_d(x_j)| / |\\mathbf{Y}|$  during forward propagation, where  $\\mathbf{Y}$  is the set of all outputs in a single neural network layer and  $|\\cdot|$  denotes the cardinality of a set.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "When Feature Proliferation happens, one or a small number of features will dominate the output of the entire network, leading to artifacts in StyleGAN synthesized images. As an analogy, we refer to it as the \"cancer\" in StyleGAN from its proliferating and malignant nature.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Remark. For simplicity, Definitions 3.1 and 3.2 are introduced with fully-connected layers. However, both definitions can be easily extended to other types of neural networks, e.g., convolutional neural networks (CNNs) [30], as the weighted sum operation is widely used in almost all deep neural networks due to its benefits in parallelization.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Root Causes of Feature Proliferation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            555,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We ascribe feature proliferation to the strong statistical assumption used in the weight modulation and demodulation of StyleGAN2/3/T [17, 15, 27], i.e., \"the input activations are i.i.d. random variables with unit standard deviation\", rather than the statistics (i.e., mean and standard deviation) of the actual feature maps used in the AdaIN of StyleGAN1 [16].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Specifically, weight demodulation assumes that all input activations (modulated feature maps) are already normalized to be of unit standard deviation, thereby eliminating the step of feature map normalization  $\\frac{\\mathbf{x}_i - \\mu(\\mathbf{x}_i)}{\\sigma(\\mathbf{x}_i)}$  used in AdaIN. Since the standard deviations of output feature maps are determined by the products of those of their input feature maps (assumed to be unit ones as mentioned above) and convolutional weights, the abovementioned assumption ensures the unit standard deviations of output feature maps by only \"demodulating\" the convolutional weights to be of unit standard deviations [17]:",
+        "bbox": [
+            498,
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+            852
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {i j k} ^ {\\prime \\prime} = w _ {i j k} ^ {\\prime} / \\sqrt {\\sum_ {i} w _ {i j k} ^ {\\prime 2} + \\epsilon}, w _ {i j k} ^ {\\prime} = s _ {i} \\cdot w _ {i j k} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            539,
+            862,
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+            905
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "2362",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/565ba8404032a99ac810907a99496f7401dac5d4382c8dde99226605bb904d29.jpg",
+        "image_caption": [
+            "Figure 4. Left: ('Cancer' Proliferation) the Feature Proliferation phenomenon leads to image artifacts; (Curing) setting the visually identified proliferating feature map in Layer 3 to zero (blue arrow) mitigates feature proliferation. Right: (Normal Generation) a proper StyleGAN image synthesis process; (Inserted 'Cancer' Proliferation) inserting the \"cancer\" features identified in the left part results in feature proliferation and similar image artifacts (red arrow). The yellow boxes in feature maps highlight the feature proliferation process.  $\\eta$  in red: the ratio of dominated features in a layer."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            90,
+            880,
+            251
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $s_i$  is the scaling parameter corresponding to the  $i$ -th input feature map,  $j$  and  $k$  enumerate the output feature maps and spatial footprint of the convolution, respectively. While in practice, the assumption of the unit standard deviation of input activations does not hold (Fig. 3). As a result, weight demodulation cannot ensure the unit standard deviations of output feature maps. Instead, the standard deviations of output feature maps are determined by those of input ones, causing feature domination and proliferation.",
+        "bbox": [
+            75,
+            359,
+            472,
+            494
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Remark. AdaIN explicitly normalizes each feature map according to its mean and standard deviation so the mean and standard deviation of its output are solely determined by the style parameters  $\\mathbf{y} = (\\mathbf{y}_s, \\mathbf{y}_b)$  but not those of its input feature map  $\\mathbf{x}_i$  [16]:",
+        "bbox": [
+            75,
+            503,
+            470,
+            580
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A d a I N} \\left(\\mathbf {x} _ {i}, \\mathbf {y}\\right) = \\mathbf {y} _ {s, i} \\frac {\\mathbf {x} _ {i} - \\mu \\left(\\mathbf {x} _ {i}\\right)}{\\sigma \\left(\\mathbf {x} _ {i}\\right)} + \\mathbf {y} _ {b, i} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            135,
+            592,
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+            626
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This breaks the chain of feature proliferation in forward propagation and we did not observe significant proliferation in our experiments. However, as shown in [17], AdaIN has its own problems (i.e., the \"characteristic artifacts\", which is why weight demodulation is used in StyleGAN2/3) and may not be a good solution to feature proliferation.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Impact of Feature Proliferation on StyleGAN",
+        "text_level": 1,
+        "bbox": [
+            76,
+            739,
+            460,
+            757
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As Fig. 4 shows, the synthesized images suffer from obvious artifacts when Feature Proliferation happens and we observed a strong spatial correlation between the proliferated feature maps and the artifacts in synthesized images. To justify the causality between them, we show that i) the artifacts can be \"cured\" by removing corresponding features before their proliferation in Fig. 4 (left) and ii) the artifacts can be added to high-quality images by inducing feature proliferation in Fig. 4 (right).",
+        "bbox": [
+            75,
+            763,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Curing the \"Cancer\" in StyleGAN",
+        "text_level": 1,
+        "bbox": [
+            498,
+            357,
+            812,
+            376
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first introduce how to identify the risky features for feature proliferation and then introduce a simple but effective feature rescaling method to adjust the identified features and mitigate the feature proliferation.",
+        "bbox": [
+            496,
+            383,
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+            444
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Feature Proliferation (\"Cancer\") Identification",
+        "text_level": 1,
+        "bbox": [
+            498,
+            453,
+            890,
+            469
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Naively, one of the most straightforward methods for feature proliferation identification is to extract all similar pairs of feature maps in the successive layers of a neural network. However, let  $k$  be the number of successive pairs of layers and  $n$  be the number of neurons per layer, the time complexity of this strategy is  $O(kn^2)$  per image, which is inefficient and makes it infeasible for frequent use.",
+        "bbox": [
+            496,
+            477,
+            890,
+            583
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Addressing this issue, we employ a heuristic stemming from Observation 3.1 that the dominant features are likely to be those that deviate significantly from the mean of their distributions. Specifically, we estimate the mean  $\\mu_{l,j}$  and standard deviation  $\\sigma_{l,j}$  with a large number (e.g., 3,000) of randomly sampled images and identify  $x_{l,j}$  as a high risk feature for proliferation if:",
+        "bbox": [
+            496,
+            584,
+            892,
+            688
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr _ {l, j} = \\frac {\\left| \\operatorname {m e a n} \\left(x _ {l , j}\\right) - \\mu_ {l , j} \\right|}{\\max  \\left(\\sigma_ {l , j} , c\\right)} > t \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            700,
+            890,
+            736
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{mean}(x_{l,j})$  is the mean value of all elements in  $x_{l,j}$ ,  $r_{l,j}$  denotes the amount of risk of feature proliferation,  $t$  is a user-defined threshold obtained empirically,  $c = 0.1$  is a small constant introduced to avoid the mis-identification when  $\\sigma_{l,j}$  is small.",
+        "bbox": [
+            496,
+            744,
+            893,
+            821
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Curing the \"Cancer\" by Feature Rescaling",
+        "text_level": 1,
+        "bbox": [
+            498,
+            830,
+            864,
+            848
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since the risky features identified by Eq. 3 proliferate with forward propagation, we propose a simple yet effective feature scaling method to address the proliferation in the",
+        "bbox": [
+            496,
+            854,
+            892,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "2363",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c0fe9ca54f2c165341f470d1805d3b589382ee83c00b143b220ea93d60e9a9f5.jpg",
+        "image_caption": [
+            "(a) StyleGAN2 pretrained with FFHQ dataset"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            91,
+            98,
+            480,
+            244
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0eb3b7060c48bedec43a032b587bd16b0c1af6364bd87473cf5f62bbcf5af292.jpg",
+        "image_caption": [
+            "(b) StyleGAN2 pretrained with AFHQ-Cat dataset"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            491,
+            98,
+            880,
+            244
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1090d187e93b4504772c81717fbeab73c4f2f9efb0dbd43811a1e8feba04ae8a.jpg",
+        "image_caption": [
+            "(c) StyleGAN3 pretrained on FFHQ dataset"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            287,
+            478,
+            467
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/304458e6c7a917b43c4edd1ba590f99b6665430e184a12317b0b6e24fc95bcf0.jpg",
+        "image_caption": [
+            "(d) StyleGAN3 pretrained on AFHQ dataset",
+            "Figure 5. Curated StyleGAN2/3 [17, 15] synthesized images, those processed by the truncation trick  $(\\psi = 0.7)$ , and our method."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            488,
+            287,
+            879,
+            465
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "earliest layers, thereby removing the least amount of them and minimizing the unnecessary interference with useful image features. Let  $x_{c}$  be a \"cancer\" feature map with risk  $r$  (Eq. 3), we have",
+        "bbox": [
+            75,
+            546,
+            468,
+            606
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {c} ^ {m} = \\frac {x _ {c}}{p \\cdot r} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            230,
+            607,
+            468,
+            635
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $x_{c}^{m}$  denotes the modified feature map,  $p$  is the scaling hyper-parameter. By rescaling  $x_{c}$ , we reduce the values of its elements and thus prevent it from Feature Domination (Definition 3.1) and Proliferation (Definition 3.2), thereby improving the quality of StyleGAN synthesized images.",
+        "bbox": [
+            75,
+            642,
+            468,
+            719
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            733,
+            209,
+            750
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Please see the supplement for more experiments.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The proposed method does not require network training. We run the proposed method with pretrained deep generative models on a workstation with an Intel(R) Core(TM) i7-10875H CPU and a GeForce RTX 3080 GPU. The pretrained StyleGAN2 [17] models (using FFHQ [16], MetFace [14] and AFHQ-Cat [8] datasets) used in all our experi",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "iments are publicly-released on  $\\mathrm{Gibthub}^3$ . Unless specified, we use hyperparameters  $t = 2$  and  $p = 2$  for our method, and  $\\psi = 0.7$  for the truncation trick that has been suggested for the best trade-off between quality and diversity of synthesized images [16, 6].",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.2. Qualitative Evaluation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            635,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As Fig. 5 shows, we compare the performance of our method against the truncation trick [20, 6] on StyleGAN2 and StyleGAN3 models pretrained on FFHQ, MetFace and AFHQ-Cat datasets. In Fig. 5(a), it can be observed that: i) all the StyleGAN2 synthesized images in the top row, except the third one, contain obvious artifacts; ii) for the third column (high-quality image), our method retains useful image features better than the truncation trick; iii) for the other columns, our method not only removes the artifacts but also retains useful image features in a better way, e.g., the truncation trick eliminates the eyeglasses in column 1 while our method retains them and other fine facial details like the beard. Similar results can be observed in Fig. 5(b), which demonstrates the versatility of our method across datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "3StyleGAN2: https://github.com/NVlabs/stylegan2",
+        "bbox": [
+            514,
+            886,
+            790,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "2364",
+        "bbox": [
+            482,
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+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/5bc56dc84fdb2b2622535afcb1966f0f74607234cc6f1c9454262f18706302b5.jpg",
+        "image_caption": [
+            "Figure 6. Comparison of precision and recall [18] between the truncation trick [20, 6] and our method on StyleGAN2.  $p$  and  $t$  are hyperparameters of our method and  $\\psi$  is the hyperparameter for the truncation trick. \"StyleGAN2\" (bottom-right corner): precision and recall of the original StyleGAN2; Blue ( $\\psi = 0.7$ ): best  $\\psi$  recommended by StyleGAN2 [17]; Cyan ( $p = 2$ ,  $t = 2$ ): best  $p$  and  $t$  of our method; Red: the upper bound of StyleGAN \"correction\" methods where every error is corrected (precision=1.0) without sacrificing diversity (recall remains constant); Orange: the closer to the dashed line, the less sacrifice of diversity; Gray: region of uninterest where too much diversity has been sacrificed. Ours is closer to the dashed line in the region of interest, indicating that it strikes a better balance between precision and recall."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            88,
+            464,
+            272
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/fd934a4ad6347a263a02851c8bd4da65cfbc858243fc7e8c97e2efdab9e15963.jpg",
+        "table_caption": [
+            "Table 1. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31], ID (identity preservation using the Arc-Face [9]) and FID [12] computed with 10K images on StyleGAN2."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset Method</td><td colspan=\"2\">AFHQ-Cat</td><td colspan=\"2\">MetFace</td><td colspan=\"2\">FFHQ</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>3.66</td><td>4.11</td><td>5.33</td><td>10.45</td><td>3.80</td><td>4.28</td></tr><tr><td>SSIM↑</td><td>0.79</td><td>0.81</td><td>0.81</td><td>0.87</td><td>0.74</td><td>0.68</td></tr><tr><td>LPIPS↓</td><td>0.15</td><td>0.14</td><td>0.22</td><td>0.14</td><td>0.31</td><td>0.24</td></tr><tr><td>ID↑</td><td>0.74</td><td>0.84</td><td>0.77</td><td>0.87</td><td>0.71</td><td>0.77</td></tr><tr><td>FID↓</td><td>7.43</td><td>4.47</td><td>23.02</td><td>17.51</td><td>12.56</td><td>11.91</td></tr></table>",
+        "bbox": [
+            78,
+            512,
+            475,
+            633
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figs. 5(c) and 5(d) show synthesized results of the truncation trick and our method on StyleGAN3 [15] models pretrained on FFHQ and AFHQ datasets<sup>4</sup>. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3.Quantitative Evaluation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            744,
+            299,
+            762
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Precision and Recall. Fig. 6 shows the comparison of precision and recall [18] between the truncation trick [20, 6] and our method on StyleGAN2. It can be observed that our method strikes a better balance between precision and recall  $(p = 2, t = 2)$  in the region of interest (right side, white region) while the truncation trick sacrifices too much diversity to achieve the same level of precision. Recognizing that",
+        "bbox": [
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+            768,
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+            876
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/d8e55e6cdeb46afffa08ec79df7edd2c1cfd5bd3f1eec79ba83a7a05bd3628c7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            90,
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+            152
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/356110c1cbbee4d519a7a129c7c91939893f5195c9bab93c95df94bd5b344704.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            154,
+            883,
+            214
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/356d002fa7f08cc09353319b2a0c975f69fd965753bb3059ff8e525503e7378a.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            217,
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+            277
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/20803eb84e03f29686d4a8786aab0eb0826ce89025c068030141106cb4c1ab47.jpg",
+        "image_caption": [
+            "StyleGAN2",
+            "Truncation Trick",
+            "Difference Map (Truncation Trick)",
+            "Ours",
+            "Difference Map (Ours)",
+            "Figure 7. Comparison of difference maps of truncation trick [20, 6] and our method. The numbers at the bottom right corner of the difference images are PSNR scores."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            503,
+            281,
+            883,
+            343
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b71122abe1b80c9d3b3a645b87c9bdd1dda4aada9a432c7e9eb4ef7ae2de8307.jpg",
+        "table_caption": [
+            "Table 2. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31] and FID [12] computed with 10K images on StyleGAN3."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset Method</td><td colspan=\"2\">FFHQ</td><td colspan=\"2\">AFHQ-Cat</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>16.23</td><td>18.07</td><td>16.03</td><td>17.72</td></tr><tr><td>SSIM↑</td><td>0.70</td><td>0.78</td><td>0.70</td><td>0.76</td></tr><tr><td>LPIPS↓</td><td>0.33</td><td>0.22</td><td>0.16</td><td>0.13</td></tr><tr><td>FID↓</td><td>22.45</td><td>14.31</td><td>24.02</td><td>17.36</td></tr></table>",
+        "bbox": [
+            545,
+            455,
+            846,
+            563
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the aims of StyleGAN correction methods are to maximize image quality (i.e., precision) without sacrificing diversity (i.e., recall), our method has made a concrete step towards the ultimate solution (red point in Fig. 6).",
+        "bbox": [
+            496,
+            590,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Image Similarity Metrics. Although less effective in assessing the trade-off between quality and diversity, for the sake of completeness, we also quantitatively compare the extent to which image features are retained by our method and the truncation trick [20, 6]. As Table 1 shows, for StyleGAN2, it can be observed that i) for PSNR, SSIM [33] and LPIPS [31], our method outperforms the truncation trick in most cases, which demonstrates that our method better retains the useful features in the original image. However, the SSIM of our method is slightly worse than that of the truncation trick for the FFHQ dataset. We ascribe this to the superior power of our method in removing structural artifacts that are common in StyleGAN pretrained with the FFHQ dataset. ii) For ID, we used the ArcFace [9] to compute the identity similarity scores between the original and the processed images. Interestingly, we observe that although",
+        "bbox": [
+            496,
+            657,
+            892,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>4</sup>https://github.com/NVlabs/stylegan3",
+        "bbox": [
+            94,
+            886,
+            297,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "2365",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/5abda7285b49d244f92b3938a5bc5b06127a23f3cd0d4868dffeb839d86c6ef7.jpg",
+        "image_caption": [
+            "Figure 8. Choice of hyper-parameters. Top row: images generated with truncation trick with  $\\psi = 0.55$  to 0.95. Rows 2-4: images generated with our method with  $t = 0.0$  to 4.0,  $p = 1$  to 3. Our method removes the artifacts while retaining almost all important features of the original image, indicating that it achieves a better trade-off between image quality and diversity than the truncation trick."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            91,
+            102,
+            890,
+            381
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "trained on human face datasets, ArcFace [9] generalizes to AFHQ-Cat [8] and MetFace [14] images and provides meaningful scores. iii) For FID [12], our method outperforms the truncation trick in all three datasets, which again demonstrates that our method better retains the useful features in the original image. We also show the difference maps in Fig. 7 to facilitate intuitive understanding. The results on StyleGAN3 [15] are shown in Table 2. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method.",
+        "bbox": [
+            75,
+            436,
+            472,
+            587
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4. Choice of Hyper-parameters",
+        "text_level": 1,
+        "bbox": [
+            76,
+            599,
+            333,
+            616
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Similar to  $\\psi$  in the truncation trick [20, 6], we use two hyperparameters  $t$  and  $p$  for the trade-off between quality and diversity in our method. Between them,  $t$  determines how many feature maps are identified as risky ones for feature proliferation, and  $p$  adjusts the extent to which we rescale such feature maps. In general, the more risky feature maps identified, the stronger rescaling, and the higher quality but less diversity of synthesized images.",
+        "bbox": [
+            75,
+            623,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Qualitative Justification. As Fig. 8 shows, we visualize the results generated with the truncation trick with  $\\psi = 0.6$  to 1.0 and our method with  $t = 0.0$  to 4.0 and  $p = 1.0$  to 3.0, and identify the best choice ( $p = 2$ ,  $t = 2$ ) through visual inspection. In general, the smaller the  $t$ , the more features are identified as risky (Eq. 3) for rescaling; the larger the  $p$ , the stronger the rescaling. In this way,  $t$  and  $p$  work together to modify only the problematic features, thus achieving a better trade-off between quality and diversity than the truncation trick.",
+        "bbox": [
+            75,
+            750,
+            470,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2c1d01c665fec3691af33ac8ea08d74ce4e0d1579995422f5d5cd9345ce75343.jpg",
+        "image_caption": [
+            "Figure 9. Choice of Hyper-parameters (Quantitative). It can be observed that  $p = 2, t = 2$  (cyan) achieves the best trade-off between precision and recall, which is consistent with the visual inspection results in Fig. 8."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            435,
+            883,
+            619
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Justification. We quantitatively justify the choice of hyper-parameters  $p$  and  $t$  by comparing their precision and recall. As Fig. 9 shows,  $p = 2$ ,  $t = 2$  achieves the best trade-off between precision and recall, which is consistent with the qualitative results in Fig. 8.",
+        "bbox": [
+            496,
+            693,
+            893,
+            768
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
+            781,
+            653,
+            797
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To justify the effectiveness of our channel-wise feature identification and rescaling strategy (Sec. 4), we demonstrate its superiority over its layer-wise and pixel-wise variants as follows.",
+        "bbox": [
+            496,
+            805,
+            892,
+            864
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Layer-wise \"Cancer\" Curing. As in Sec. 4, let  $x_{l,j}$  be a \"cancer\" feature map identified using Eq. 3, we compute the",
+        "bbox": [
+            498,
+            869,
+            893,
+            901
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "2366",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b7c6da152fe16a839786ab59200439c6e4e7bfc70b1fc46009033cbbb2c95d31.jpg",
+        "image_caption": [
+            "Figure 10. Successful cases of the layer-wise variant of our method (threshold  $t'$  ranges from 0.3 to 0.9). It can be observed that this variant is effective in removing artifacts of background intrusion."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            94,
+            92,
+            455,
+            243
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "mean absolute \"cancer\" feature map for layer  $l$  as:",
+        "bbox": [
+            76,
+            311,
+            410,
+            327
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {x} _ {l} = \\operatorname {m e a n} _ {j} (| x _ {l, j} |) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            205,
+            338,
+            468,
+            356
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where we take the absolute value  $|x_{l,j}|$  to capture their magnitude and avoid them canceling each other out when added together. In order to make the same choice of hyperparameters applicable to all layers, we normalize  $\\hat{x}_l$  to  $\\bar{x}_l$  with mean  $\\mu = 0$  and  $\\sigma = 1$ :",
+        "bbox": [
+            76,
+            364,
+            468,
+            441
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {x} _ {l} = \\frac {\\hat {x} _ {l} - \\mu (\\hat {x} _ {l})}{\\sigma (\\hat {x} _ {l})} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            214,
+            450,
+            468,
+            484
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Then we measure the \"correlation\" between each  $|x_{l,j}|$  and its corresponding  $\\bar{x}_l$  as:",
+        "bbox": [
+            76,
+            493,
+            468,
+            523
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nc _ {l, j} = \\frac {\\left| x _ {l , j} \\right| * \\bar {x} _ {l}}{\\sum_ {\\text {e l e m e n t}} \\left| x _ {l , j} \\right|} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            196,
+            534,
+            468,
+            568
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sum_{\\mathrm{element}}|x_{l,j}|$  is the sum for all elements in  $|x_{l,j}|$ . Let  $t^\\prime$  be a threshold hyper-parameter, if  $c_{l,j} > t^{\\prime}$ , we mark  $x_{l,j}$  as a layer-wise \"cancer\" feature map and perform the same feature rescaling on it to remove image artifacts. As Fig. 10 shows, this layer-wise variant of our method is also effective for certain types of image artifacts (e.g., background intrusion). While for some other types of artifacts (e.g., alien objects), it becomes less effective (Fig. 11).",
+        "bbox": [
+            76,
+            577,
+            468,
+            698
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Pixel-wise \"Cancer\" Curing. We follow ProGAN [13] and apply its pixel-wise feature vector normalization technique, which was originally proposed to stabilize GAN training by resolving the potentially exploding magnitudes in the generator and discriminator, to pre-trained StyleGAN2. However, we observed that even the normally synthesized images become unrealistic (Fig. 12), indicating that it is not applicable to our problem.",
+        "bbox": [
+            75,
+            700,
+            468,
+            823
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.6. Time Complexity",
+        "text_level": 1,
+        "bbox": [
+            76,
+            830,
+            246,
+            848
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3 shows the time costs of generating a single image for StyleGAN2, ours implemented in serial, and ours implemented in parallel on an Nvidia V100 GPU. It can",
+        "bbox": [
+            76,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/065d5d9200064f36b62c0cd3641a4da964878ebf576178491bc042eb8f281526.jpg",
+        "image_caption": [
+            "Figure 11. Failure cases of the layer-wise variant of our method (threshold  $t' = 0.5$ ). It can be observed that this variant is ineffective in removing artifacts of alien objects (e.g., color blocks on faces) while our method can remove them effectively. Top row: low-quality images synthesized by StyleGAN2; Middle row: results of the layer-wise variant of our method; Bottom row: results of our method."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            98,
+            898,
+            314
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/7e0662d8d3671e8f5a1b268949b7a8dca6e81f696bf25eb2c73f0bc0889b255c.jpg",
+        "image_caption": [
+            "Figure 12. Effects of pixel-wise feature vector normalization on StyleGAN2 pre-trained on FFHQ dataset. Top row: normal images synthesized by StyleGAN2. Bottom row: images after applying pixel-wise feature vector normalization, which become unrealistic."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            441,
+            890,
+            542
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/627ffb590fdc9908edbd2f6e8e714134e288c913369b9d1e145e7e992cd27092.jpg",
+        "table_caption": [
+            "Table 3. Time costs of generating a single image for StyleGAN2, Ours (Serial) and Ours (Parallel) on an Nvidia V100 GPU. The time is averaged over 100 runs."
+        ],
+        "table_footnote": [],
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+            "Fig. 14 shows similar observations for StyleGAN image editing. These suggest that our method preserves StyleGAN latent semantics and is thus compatible with various StyleGAN latent space operations."
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+        "text": "6. Conclusion",
+        "text_level": 1,
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+        "text": "In this paper, we propose a novel feature identification and rescaling method to address the artifacts in StyleGAN synthesized images. The rationale of the proposed feature rescaling method stems from the Feature Proliferation phenomenon we discovered that has a strong causal relationship with StyleGAN image artifacts. Specifically, we observed that the features that deviate significantly from the mean of their distribution are highly likely to dominate the output of a neuron and proliferate in the forward propagation. As a result, the output of the entire network will be dominated by a small number of features. We ascribe this to the strong statistical assumption used in the weight modulation and demodulation used by the StyleGAN family. Intuitively, we name Feature Proliferation as the \"cancer\" in StyleGANs from its proliferating and malignant nature. Experimental results demonstrate that our method achieves a better tradeoff between quality and diversity of StyleGAN synthesized images than the popular truncation trick.",
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+        "text": "Limitation and Future Work. Although effective and significantly better than the truncation trick, the proposed method is not perfect as it can still remove some useful image features and make minor changes to high-quality StyleGAN synthesized images. We plan to design more precise",
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+    {
+        "type": "text",
+        "text": "methods to identify and process proliferating features in future work. In addition, we believe that Feature Proliferation is not a problem exclusive to StyleGAN and may occur in other works as long as weight modulation and demodulation techniques are used (Sec. 3.2). Thus, we plan to investigate in future work whether feature proliferation is a common phenomenon in various network architectures and its consequences in different tasks.",
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+    {
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+        "text": "Potential Negative Social Impact. Although our method works as a post-hoc \"cure\" for StyleGAN synthesized images and can save millions of dollars in training costs and energy consumption, it may also lead to potentially negative social impacts. For example, it can further improve the quality of StyleGAN synthesized images, which may facilitate the creation of fake portrait photos/videos for fake social media accounts and fake news. Nevertheless, we still believe that our work will make a positive contribution to the field and provide new insights into the mechanisms of generative models that may help identify such fake content.",
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+    {
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+        "text": "Acknowledgements",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We thank the reviewers for their constructive comments that helped improve this paper. This work was partially supported by the China Scholarship Council (CSC) under Grant No. 202106150033 and the UK Engineering and Physical Sciences Research Council (EPSRC) through the Doctoral Training Partnerships (DTP) with No. EP/T517951/1 (2599521).",
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+        "text": "2368",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "versarial networks with limited data. Advances in Neural Information Processing Systems, 33:12104-12114, 2020.",
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+            "[16] Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4401-4410, 2019.",
+            "[17] Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of StyleGAN. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8110-8119, 2020.",
+            "[18] Tuomas Kynkänniemi, Tero Karras, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Improved precision and recall metric for assessing generative models. Advances in Neural Information Processing Systems, 32, 2019.",
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+            "[20] Marco Marchesi. Megapixel size image creation using generative adversarial networks. arXiv preprint arXiv:1706.00082, 2017.",
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+            "[24] Yipeng Qin, Niloy Mitra, and Peter Wonka. How does Lipschitz regularization influences GAN training? In European Conference on Computer Vision, pages 310-326. Springer, 2020.",
+            "[25] Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434, 2015.",
+            "[26] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, and Daniel Cohen-Or. Encoding in style: a StyleGAN encoder for image-to-image translation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2287–2296, 2021.",
+            "[27] Axel Sauer, Tero Karras, Samuli Laine, Andreas Geiger, and Timo Aila. StyleGAN-T: Unlocking the power of GANs for fast large-scale text-to-image synthesis. arXiv preprint arXiv:2301.09515, 2023.",
+            "[28] Yuri Viazovetskyi, Vladimir Ivashkin, and Evgeny Kashin. Stylegan2 distillation for feed-forward image manipulation."
+        ],
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+            503,
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+        "page_idx": 9
+    },
+    {
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+        "text": "2369",
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+        "page_idx": 9
+    },
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+        "sub_type": "ref_text",
+        "list_items": [
+            "In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXII 16, pages 170-186. Springer, 2020.",
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+            "[31] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018.",
+            "[32] X Zheng, Yang Liu, P Wang, and Xin Tong. SDF-StyleGAN: Implicit SDF-based StyleGAN for 3D shape generation. In Computer Graphics Forum, volume 41, pages 52–63. Wiley Online Library, 2022.",
+            "[33] Wang Zhou. Image quality assessment: from error measurement to structural similarity. IEEE transactions on image processing, 13:600-613, 2004."
+        ],
+        "bbox": [
+            78,
+            90,
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+        ],
+        "page_idx": 10
+    },
+    {
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+        "page_idx": 10
+    }
+]
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diff --git a/2023/Feature Proliferation -- the 'Cancer' in StyleGAN and its Treatments/585d65ee-f18b-4e36-8941-f08943b3d7c2_model.json b/2023/Feature Proliferation -- the 'Cancer' in StyleGAN and its Treatments/585d65ee-f18b-4e36-8941-f08943b3d7c2_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..d07801364bf9a4ec7ece0ff827c515c6fe3b0dcc
--- /dev/null
+++ b/2023/Feature Proliferation -- the 'Cancer' in StyleGAN and its Treatments/585d65ee-f18b-4e36-8941-f08943b3d7c2_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Feature Proliferation — the “Cancer” in StyleGAN and its Treatments"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Shuang Song Yuanbang Liang Jing Wu Yu-Kun Lai Yipeng Qin* Cardiff University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.264,
+                0.223,
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+                0.238
+            ],
+            "angle": 0,
+            "content": "{songs7, liangy32, wuj11, laiy4, qiny16}@cardiff.ac.uk"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.273,
+                0.314,
+                0.289
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.304,
+                0.474,
+                0.699
+            ],
+            "angle": 0,
+            "content": "Despite the success of StyleGAN in image synthesis, the images it synthesizes are not always perfect and the well-known truncation trick has become a standard post-processing technique for StyleGAN to synthesize high quality images. Although effective, it has long been noted that the truncation trick tends to reduce the diversity of synthesized images and unnecessarily sacrifices many distinct image features. To address this issue, in this paper, we first delve into the StyleGAN image synthesis mechanism and discover an important phenomenon, namely Feature Proliferation, which demonstrates how specific features reproduce with forward propagation. Then, we show how the occurrence of Feature Proliferation results in StyleGAN image artifacts. As an analogy, we refer to it as the \"cancer\" in StyleGAN from its proliferating and malignant nature. Finally, we propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation. Thanks to our discovery of Feature Proliferation, the proposed feature rescaling method is less destructive and retains more useful image features than the truncation trick, as it is more fine-grained and works in a lower-level feature space rather than a high-level latent space. Experimental results justify the validity of our claims and the effectiveness of the proposed feature rescaling method. Our code is available at https://github.com/songc42/Feature-proliferation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.725,
+                0.21,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.749,
+                0.471,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Deep learning has entered the era of large models. For instance, the GPT-3 [7] developed by OpenAI has 175 billion parameters and can easily cost around 15 million dollars to train for a single run, let alone the GPT-3.5 underpinning the recently hyped ChatGPT; Stability.ai trained their Stable-diffusion-v1-4\\(^2\\) using 256 Nvidia A100 GPUs for 150,000 GPU hours; Nvidia spent 92 GPU years and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.274,
+                0.895,
+                0.668
+            ],
+            "angle": 0,
+            "content": "225 MWh of electricity with an in-house cluster of NVIDIA V100 GPUs to develop StyleGAN3 [15] and 4 weeks on 64 NVIDIA A100s for a \"constrained\" training of their recent StyleGAN-T [27]. As a result, although the performance of large models is impressive, their high costs have become a critical concern, e.g., OpenAI admitted that there was a bug in their GPT-3 model but cannot afford to retrain it due to the high cost [7]. This motivates us to do our best to avoid retraining large neural network models. In this work, we focus on the StyleGAN family [16, 17, 15, 27] as they are inherently more efficient (i.e., generating images with a single pass), allow for excellent semantic interpolation in their latent spaces, and are comparable to the quality of diffusion models [27]. For the StyleGAN series, although there were no obvious bugs in the training, the synthesized images are not always perfect. While instead of attempting to solve this problem by improving the model design which requires multiple retraining, StyleGAN follows the \"no retraining\" philosophy and resorts to a post-processing technique called truncation trick [20, 6]. In short, the truncation trick improves the quality of StyleGAN synthesized images by normalizing their corresponding latent codes towards their mean in the latent space. However, despite its popularity, it has long been noted that the truncation trick tends to reduce the diversity of synthesized images and unnecessarily sacrifices many distinct image features [16]."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In this paper, we address the low-quality images synthesized by StyleGAN from a different perspective, i.e., its mechanism for image synthesis in the feature space. Specifically, we delved into the architectural details of the StyleGAN generator and discovered an important phenomenon, namely Feature Proliferation, which demonstrates how specific features reproduce with forward propagation. In short, Feature Proliferation denotes the phenomenon where the ratio of the occurrence of a certain type of feature (those with abnormally large values) in a layer increases with forward propagation. Our analysis points out that such a phenomenon is a by-product of the weight modulation and demodulation techniques used in StyleGAN2/3 [17, 15] and the latest StyleGAN-T [27]. Interestingly, we observed that Feature Proliferation usually leads to artifacts in Style-"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "*Corresponding author: Yipeng Qin"
+        },
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+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "1 https://openai.com/blog/chatgpt"
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+            "content": "2https://huggingface.co/CompVis/stable-diffusion-v1-4"
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+            "bbox": [
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+            "angle": 0,
+            "content": "2360"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.089,
+                0.885,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.185,
+                0.342,
+                0.784,
+                0.358
+            ],
+            "angle": 0,
+            "content": "Figure 1. Top: StyleGAN synthesized images with artifacts. Bottom: images \"cured\" by our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.375,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "GAN synthesized images and these artifacts can be easily removed by a simple feature rescaling method. To minimize the unnecessary interference with useful image features, we propose a novel method to identify the risky features prone to proliferation in the earliest layers, thereby removing the least amount of them. As a result, our method significantly outperforms the truncation trick in terms of retaining useful image features while improving the quality of StyleGAN synthesized images. Experimental results justify the validity of our claims and the effectiveness of the proposed feature rescaling method. Our contributions include:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.552,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "- We discover an important phenomenon, namely Feature Proliferation, which shows how specific features reproduce with forward propagation. We also show that it is a by-product of the weight modulation and demodulation techniques used in modern StyleGANs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.639,
+                0.47,
+                0.684
+            ],
+            "angle": 0,
+            "content": "- We discover a strong causal relationship between the occurrence of Feature Proliferation and StyleGAN image artifacts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.695,
+                0.47,
+                0.771
+            ],
+            "angle": 0,
+            "content": "- We propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation, thereby achieving a better trade-off between quality and diversity of StyleGAN synthesized images than the popular truncation trick."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+            "angle": 0,
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+        },
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+            "type": "title",
+            "bbox": [
+                0.078,
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+            "angle": 0,
+            "content": "2. Related work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Since the seminal work of Goodfellow et al. [10], Generative Adversarial Networks (GANs) have become one of the most promising deep generative models that have numerous applications in computer vision and graphics. Nevertheless, GANs are known to be notoriously difficult to train and a variety of techniques have been proposed to"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.375,
+                0.892,
+                0.737
+            ],
+            "angle": 0,
+            "content": "stabilize their training from different perspectives, including architectures [25, 11], loss functions [4, 19], regularization [22, 23], and the interactions between them [24]. Thanks to the massive efforts from the community, the StyleGAN series [16, 17, 15, 27] have become one of the most influential models in the GAN family, as it can generate high-resolution and realistic images that are almost indistinguishable from real photos by human inspectors. Examples of its applications include GAN inversion and editing [1, 2, 29, 3], image-to-image translation [26], superresolution [21], 3D shape generation [32], etc. We refer interested audiences to [5] for a survey on StyleGAN and its applications. Nevertheless, despite its success, the quality of images synthesized by StyleGAN varies, and a post-processing method known as the truncation trick [20, 6] has widely been adopted to obtain higher quality images. However, the truncation trick has long been noted as \"destructive\" as it unnecessarily sacrifices useful image features and tends to reduce the diversity of synthesized images. In this paper, we address this issue by investigating the StyleGAN image synthesis mechanism and propose a feature rescaling method that can precisely identify the risky features causing image artifacts, thereby improving image quality by modulating these features at the minimal cost."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.765,
+                0.813,
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+            ],
+            "angle": 0,
+            "content": "3. Feature Proliferation in StyleGAN"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, we first introduce two new phenomena that we discovered in the forward propagation of deep neural networks, i.e. feature domination and proliferation. We then show that they are by-products of the weight modulation and demodulation techniques used in modern StyleGANs. Finally, we show how they affect StyleGAN and lead to artifacts in synthesized images."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2361"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.091,
+                0.089,
+                0.469,
+                0.243
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.246,
+                0.47,
+                0.276
+            ],
+            "angle": 0,
+            "content": "Figure 2. Illustration of feature domination. \\( y \\) is dominated by \\( x_{j} \\) and its perturbations \\( x_{i} \\approx x_{j} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.297,
+                0.407,
+                0.314
+            ],
+            "angle": 0,
+            "content": "3.1. Feature Domination and Proliferation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.32,
+                0.473,
+                0.488
+            ],
+            "angle": 0,
+            "content": "Throughout the history of machine learning, the weighted sum method has been built to last from the classical linear regression, to the theoretically elegant support vector machines and the deep neural networks that are now taking both academia and industry by storm. For deep neural networks, we usually refer to the output of neurons as features that are the elements to be weighted and summed. However, due to the differences among weights and input features, the output of a neuron can occasionally be dominated by one or a small amount of input features, which leads to a phenomenon we call Feature Domination."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.497,
+                0.473,
+                0.589
+            ],
+            "angle": 0,
+            "content": "Definition 3.1 (Feature Domination) Let \\( y = \\mathbf{w}^{\\mathrm{T}}\\mathbf{x} + b \\) be the output of a neuron, \\( \\mathbf{x} \\) and \\( \\mathbf{w} \\) are the input and weight vectors respectively, \\( b \\) denotes the bias, we define Feature Domination as the case where \\( y \\approx (\\sum_{i} w_{i}) x_{j} + b \\) is dominated by feature \\( x_{j} \\) and its perturbations \\( x_{i} \\approx x_{j} \\), where \\( i \\) indicates the \\( i \\)-th element in \\( \\mathbf{w} \\) and \\( \\mathbf{x} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.47,
+                0.706
+            ],
+            "angle": 0,
+            "content": "In a nutshell, the proposed Feature Domination describes the phenomenon that one or a small number of similar input features may dominate the weighted sum if their products with associated weights significantly outweigh others (Fig. 2), making \\( y \\) similar to \\( x_{i} / x_{j} \\). In practice, we observed that the dominant features are highly likely to be those that deviate significantly from the mean of their distributions:"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.076,
+                0.715,
+                0.442,
+                0.73
+            ],
+            "angle": 0,
+            "content": "Observation 3.1 (Feature Domination in StyleGAN)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.73,
+                0.47,
+                0.832
+            ],
+            "angle": 0,
+            "content": "Let \\( t \\) be an empirically obtained threshold, and \\( x_{l,j} \\) be the feature map of channel \\( j \\) of layer \\( l \\) of the generator. \\( x_{l,j} \\) is highly likely to be dominant if \\( \\frac{|\\mathrm{mean}(x_{l,j}) - \\mu_{x_{l,j}}|}{\\sigma_{x_{l,j}}} > t \\), where \\( \\mathrm{mean}(x_{l,j}) \\) is the mean value of all elements in \\( x_{l,j} \\), \\( \\mu_{x_{l,j}} \\) and \\( \\sigma_{x_{l,j}} \\) are the mean and standard deviation of the distribution of \\( x_{l,j} \\) over the training dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In practice, we use Observation 3.1 to identify dominant features in StyleGANs. Furthermore, Feature Proliferation happens when the same type of Feature Domination proliferates during the forward propagation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.096,
+                0.701,
+                0.193
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.553,
+                0.198,
+                0.656,
+                0.212
+            ],
+            "angle": 0,
+            "content": "(a) Mean of inputs"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.706,
+                0.097,
+                0.902,
+                0.193
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.72,
+                0.198,
+                0.891,
+                0.212
+            ],
+            "angle": 0,
+            "content": "(b) Standard deviation of inputs"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.215,
+                0.893,
+                0.243
+            ],
+            "angle": 0,
+            "content": "Figure 3. Histograms of mean and standard deviation of the input feature maps from 10,000 StyleGAN2 synthesized images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.253,
+                0.894,
+                0.36
+            ],
+            "angle": 0,
+            "content": "Definition 3.2 (Feature Proliferation) Following Definition 3.1, let \\(\\mathbf{Y}_d(x_j)\\) be the set consisting of all outputs \\(y\\) dominated by feature \\(x_j\\) in a single neural network layer, we define Feature Proliferation as the increase of \\(\\eta(x_j) = |\\mathbf{Y}_d(x_j)| / |\\mathbf{Y}|\\) during forward propagation, where \\(\\mathbf{Y}\\) is the set of all outputs in a single neural network layer and \\(|\\cdot|\\) denotes the cardinality of a set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.372,
+                0.894,
+                0.449
+            ],
+            "angle": 0,
+            "content": "When Feature Proliferation happens, one or a small number of features will dominate the output of the entire network, leading to artifacts in StyleGAN synthesized images. As an analogy, we refer to it as the \"cancer\" in StyleGAN from its proliferating and malignant nature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.455,
+                0.894,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Remark. For simplicity, Definitions 3.1 and 3.2 are introduced with fully-connected layers. However, both definitions can be easily extended to other types of neural networks, e.g., convolutional neural networks (CNNs) [30], as the weighted sum operation is widely used in almost all deep neural networks due to its benefits in parallelization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.556,
+                0.818,
+                0.57
+            ],
+            "angle": 0,
+            "content": "3.2. Root Causes of Feature Proliferation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.578,
+                0.894,
+                0.684
+            ],
+            "angle": 0,
+            "content": "We ascribe feature proliferation to the strong statistical assumption used in the weight modulation and demodulation of StyleGAN2/3/T [17, 15, 27], i.e., \"the input activations are i.i.d. random variables with unit standard deviation\", rather than the statistics (i.e., mean and standard deviation) of the actual feature maps used in the AdaIN of StyleGAN1 [16]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.684,
+                0.895,
+                0.853
+            ],
+            "angle": 0,
+            "content": "Specifically, weight demodulation assumes that all input activations (modulated feature maps) are already normalized to be of unit standard deviation, thereby eliminating the step of feature map normalization \\(\\frac{\\mathbf{x}_i - \\mu(\\mathbf{x}_i)}{\\sigma(\\mathbf{x}_i)}\\) used in AdaIN. Since the standard deviations of output feature maps are determined by the products of those of their input feature maps (assumed to be unit ones as mentioned above) and convolutional weights, the abovementioned assumption ensures the unit standard deviations of output feature maps by only \"demodulating\" the convolutional weights to be of unit standard deviations [17]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.54,
+                0.863,
+                0.893,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\nw _ {i j k} ^ {\\prime \\prime} = w _ {i j k} ^ {\\prime} / \\sqrt {\\sum_ {i} w _ {i j k} ^ {\\prime 2} + \\epsilon}, w _ {i j k} ^ {\\prime} = s _ {i} \\cdot w _ {i j k} \\tag {1}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2362"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.092,
+                0.882,
+                0.252
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.265,
+                0.894,
+                0.337
+            ],
+            "angle": 0,
+            "content": "Figure 4. Left: ('Cancer' Proliferation) the Feature Proliferation phenomenon leads to image artifacts; (Curing) setting the visually identified proliferating feature map in Layer 3 to zero (blue arrow) mitigates feature proliferation. Right: (Normal Generation) a proper StyleGAN image synthesis process; (Inserted 'Cancer' Proliferation) inserting the \"cancer\" features identified in the left part results in feature proliferation and similar image artifacts (red arrow). The yellow boxes in feature maps highlight the feature proliferation process. \\(\\eta\\) in red: the ratio of dominated features in a layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.36,
+                0.473,
+                0.496
+            ],
+            "angle": 0,
+            "content": "where \\( s_i \\) is the scaling parameter corresponding to the \\( i \\)-th input feature map, \\( j \\) and \\( k \\) enumerate the output feature maps and spatial footprint of the convolution, respectively. While in practice, the assumption of the unit standard deviation of input activations does not hold (Fig. 3). As a result, weight demodulation cannot ensure the unit standard deviations of output feature maps. Instead, the standard deviations of output feature maps are determined by those of input ones, causing feature domination and proliferation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.504,
+                0.471,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Remark. AdaIN explicitly normalizes each feature map according to its mean and standard deviation so the mean and standard deviation of its output are solely determined by the style parameters \\(\\mathbf{y} = (\\mathbf{y}_s, \\mathbf{y}_b)\\) but not those of its input feature map \\(\\mathbf{x}_i\\) [16]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.137,
+                0.593,
+                0.47,
+                0.627
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A d a I N} \\left(\\mathbf {x} _ {i}, \\mathbf {y}\\right) = \\mathbf {y} _ {s, i} \\frac {\\mathbf {x} _ {i} - \\mu \\left(\\mathbf {x} _ {i}\\right)}{\\sigma \\left(\\mathbf {x} _ {i}\\right)} + \\mathbf {y} _ {b, i} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.637,
+                0.47,
+                0.73
+            ],
+            "angle": 0,
+            "content": "This breaks the chain of feature proliferation in forward propagation and we did not observe significant proliferation in our experiments. However, as shown in [17], AdaIN has its own problems (i.e., the \"characteristic artifacts\", which is why weight demodulation is used in StyleGAN2/3) and may not be a good solution to feature proliferation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.741,
+                0.462,
+                0.758
+            ],
+            "angle": 0,
+            "content": "3.3. Impact of Feature Proliferation on StyleGAN"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "As Fig. 4 shows, the synthesized images suffer from obvious artifacts when Feature Proliferation happens and we observed a strong spatial correlation between the proliferated feature maps and the artifacts in synthesized images. To justify the causality between them, we show that i) the artifacts can be \"cured\" by removing corresponding features before their proliferation in Fig. 4 (left) and ii) the artifacts can be added to high-quality images by inducing feature proliferation in Fig. 4 (right)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.358,
+                0.813,
+                0.377
+            ],
+            "angle": 0,
+            "content": "4. Curing the \"Cancer\" in StyleGAN"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.384,
+                0.893,
+                0.445
+            ],
+            "angle": 0,
+            "content": "In this section, we first introduce how to identify the risky features for feature proliferation and then introduce a simple but effective feature rescaling method to adjust the identified features and mitigate the feature proliferation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.454,
+                0.892,
+                0.47
+            ],
+            "angle": 0,
+            "content": "4.1. Feature Proliferation (\"Cancer\") Identification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.478,
+                0.892,
+                0.584
+            ],
+            "angle": 0,
+            "content": "Naively, one of the most straightforward methods for feature proliferation identification is to extract all similar pairs of feature maps in the successive layers of a neural network. However, let \\( k \\) be the number of successive pairs of layers and \\( n \\) be the number of neurons per layer, the time complexity of this strategy is \\( O(kn^2) \\) per image, which is inefficient and makes it infeasible for frequent use."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.585,
+                0.893,
+                0.689
+            ],
+            "angle": 0,
+            "content": "Addressing this issue, we employ a heuristic stemming from Observation 3.1 that the dominant features are likely to be those that deviate significantly from the mean of their distributions. Specifically, we estimate the mean \\(\\mu_{l,j}\\) and standard deviation \\(\\sigma_{l,j}\\) with a large number (e.g., 3,000) of randomly sampled images and identify \\(x_{l,j}\\) as a high risk feature for proliferation if:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.701,
+                0.892,
+                0.737
+            ],
+            "angle": 0,
+            "content": "\\[\nr _ {l, j} = \\frac {\\left| \\operatorname {m e a n} \\left(x _ {l , j}\\right) - \\mu_ {l , j} \\right|}{\\max  \\left(\\sigma_ {l , j} , c\\right)} > t \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.746,
+                0.894,
+                0.822
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathrm{mean}(x_{l,j})\\) is the mean value of all elements in \\(x_{l,j}\\), \\(r_{l,j}\\) denotes the amount of risk of feature proliferation, \\(t\\) is a user-defined threshold obtained empirically, \\(c = 0.1\\) is a small constant introduced to avoid the mis-identification when \\(\\sigma_{l,j}\\) is small."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.832,
+                0.866,
+                0.849
+            ],
+            "angle": 0,
+            "content": "4.2. Curing the \"Cancer\" by Feature Rescaling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Since the risky features identified by Eq. 3 proliferate with forward propagation, we propose a simple yet effective feature scaling method to address the proliferation in the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2363"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.092,
+                0.099,
+                0.482,
+                0.246
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.163,
+                0.257,
+                0.408,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(a) StyleGAN2 pretrained with FFHQ dataset"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.493,
+                0.099,
+                0.882,
+                0.246
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.551,
+                0.257,
+                0.822,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(b) StyleGAN2 pretrained with AFHQ-Cat dataset"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.288,
+                0.48,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.167,
+                0.477,
+                0.4,
+                0.49
+            ],
+            "angle": 0,
+            "content": "(c) StyleGAN3 pretrained on FFHQ dataset"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.49,
+                0.288,
+                0.88,
+                0.466
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.565,
+                0.477,
+                0.802,
+                0.49
+            ],
+            "angle": 0,
+            "content": "(d) StyleGAN3 pretrained on AFHQ dataset"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.108,
+                0.508,
+                0.855,
+                0.523
+            ],
+            "angle": 0,
+            "content": "Figure 5. Curated StyleGAN2/3 [17, 15] synthesized images, those processed by the truncation trick \\((\\psi = 0.7)\\), and our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.547,
+                0.47,
+                0.607
+            ],
+            "angle": 0,
+            "content": "earliest layers, thereby removing the least amount of them and minimizing the unnecessary interference with useful image features. Let \\( x_{c} \\) be a \"cancer\" feature map with risk \\( r \\) (Eq. 3), we have"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.232,
+                0.608,
+                0.47,
+                0.636
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {c} ^ {m} = \\frac {x _ {c}}{p \\cdot r} \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.643,
+                0.47,
+                0.72
+            ],
+            "angle": 0,
+            "content": "where \\( x_{c}^{m} \\) denotes the modified feature map, \\( p \\) is the scaling hyper-parameter. By rescaling \\( x_{c} \\), we reduce the values of its elements and thus prevent it from Feature Domination (Definition 3.1) and Proliferation (Definition 3.2), thereby improving the quality of StyleGAN synthesized images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.734,
+                0.21,
+                0.751
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.76,
+                0.424,
+                0.775
+            ],
+            "angle": 0,
+            "content": "Please see the supplement for more experiments."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.786,
+                0.267,
+                0.803
+            ],
+            "angle": 0,
+            "content": "5.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The proposed method does not require network training. We run the proposed method with pretrained deep generative models on a workstation with an Intel(R) Core(TM) i7-10875H CPU and a GeForce RTX 3080 GPU. The pretrained StyleGAN2 [17] models (using FFHQ [16], MetFace [14] and AFHQ-Cat [8] datasets) used in all our experi"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.546,
+                0.892,
+                0.623
+            ],
+            "angle": 0,
+            "content": "iments are publicly-released on \\(\\mathrm{Gibthub}^3\\). Unless specified, we use hyperparameters \\(t = 2\\) and \\(p = 2\\) for our method, and \\(\\psi = 0.7\\) for the truncation trick that has been suggested for the best trade-off between quality and diversity of synthesized images [16, 6]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.636,
+                0.71,
+                0.652
+            ],
+            "angle": 0,
+            "content": "5.2. Qualitative Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.661,
+                0.893,
+                0.872
+            ],
+            "angle": 0,
+            "content": "As Fig. 5 shows, we compare the performance of our method against the truncation trick [20, 6] on StyleGAN2 and StyleGAN3 models pretrained on FFHQ, MetFace and AFHQ-Cat datasets. In Fig. 5(a), it can be observed that: i) all the StyleGAN2 synthesized images in the top row, except the third one, contain obvious artifacts; ii) for the third column (high-quality image), our method retains useful image features better than the truncation trick; iii) for the other columns, our method not only removes the artifacts but also retains useful image features in a better way, e.g., the truncation trick eliminates the eyeglasses in column 1 while our method retains them and other fine facial details like the beard. Similar results can be observed in Fig. 5(b), which demonstrates the versatility of our method across datasets."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.516,
+                0.887,
+                0.791,
+                0.901
+            ],
+            "angle": 0,
+            "content": "3StyleGAN2: https://github.com/NVlabs/stylegan2"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2364"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.089,
+                0.465,
+                0.273
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.278,
+                0.473,
+                0.46
+            ],
+            "angle": 0,
+            "content": "Figure 6. Comparison of precision and recall [18] between the truncation trick [20, 6] and our method on StyleGAN2. \\( p \\) and \\( t \\) are hyperparameters of our method and \\( \\psi \\) is the hyperparameter for the truncation trick. \"StyleGAN2\" (bottom-right corner): precision and recall of the original StyleGAN2; Blue (\\( \\psi = 0.7 \\)): best \\( \\psi \\) recommended by StyleGAN2 [17]; Cyan (\\( p = 2 \\), \\( t = 2 \\)): best \\( p \\) and \\( t \\) of our method; Red: the upper bound of StyleGAN \"correction\" methods where every error is corrected (precision=1.0) without sacrificing diversity (recall remains constant); Orange: the closer to the dashed line, the less sacrifice of diversity; Gray: region of uninterest where too much diversity has been sacrificed. Ours is closer to the dashed line in the region of interest, indicating that it strikes a better balance between precision and recall."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.47,
+                0.472,
+                0.512
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31], ID (identity preservation using the Arc-Face [9]) and FID [12] computed with 10K images on StyleGAN2."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.513,
+                0.477,
+                0.634
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset Method</td><td colspan=\"2\">AFHQ-Cat</td><td colspan=\"2\">MetFace</td><td colspan=\"2\">FFHQ</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>3.66</td><td>4.11</td><td>5.33</td><td>10.45</td><td>3.80</td><td>4.28</td></tr><tr><td>SSIM↑</td><td>0.79</td><td>0.81</td><td>0.81</td><td>0.87</td><td>0.74</td><td>0.68</td></tr><tr><td>LPIPS↓</td><td>0.15</td><td>0.14</td><td>0.22</td><td>0.14</td><td>0.31</td><td>0.24</td></tr><tr><td>ID↑</td><td>0.74</td><td>0.84</td><td>0.77</td><td>0.87</td><td>0.71</td><td>0.77</td></tr><tr><td>FID↓</td><td>7.43</td><td>4.47</td><td>23.02</td><td>17.51</td><td>12.56</td><td>11.91</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.47,
+                0.737
+            ],
+            "angle": 0,
+            "content": "Figs. 5(c) and 5(d) show synthesized results of the truncation trick and our method on StyleGAN3 [15] models pretrained on FFHQ and AFHQ datasets<sup>4</sup>. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.746,
+                0.3,
+                0.763
+            ],
+            "angle": 0,
+            "content": "5.3.Quantitative Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.77,
+                0.47,
+                0.877
+            ],
+            "angle": 0,
+            "content": "Precision and Recall. Fig. 6 shows the comparison of precision and recall [18] between the truncation trick [20, 6] and our method on StyleGAN2. It can be observed that our method strikes a better balance between precision and recall \\((p = 2, t = 2)\\) in the region of interest (right side, white region) while the truncation trick sacrifices too much diversity to achieve the same level of precision. Recognizing that"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.091,
+                0.885,
+                0.153
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.155,
+                0.885,
+                0.215
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.218,
+                0.885,
+                0.279
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.282,
+                0.885,
+                0.344
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.521,
+                0.347,
+                0.561,
+                0.357
+            ],
+            "angle": 0,
+            "content": "StyleGAN2"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.588,
+                0.345,
+                0.646,
+                0.356
+            ],
+            "angle": 0,
+            "content": "Truncation Trick"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.662,
+                0.345,
+                0.723,
+                0.359
+            ],
+            "angle": 0,
+            "content": "Difference Map (Truncation Trick)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.756,
+                0.346,
+                0.775,
+                0.358
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.815,
+                0.345,
+                0.872,
+                0.361
+            ],
+            "angle": 0,
+            "content": "Difference Map (Ours)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.367,
+                0.892,
+                0.409
+            ],
+            "angle": 0,
+            "content": "Figure 7. Comparison of difference maps of truncation trick [20, 6] and our method. The numbers at the bottom right corner of the difference images are PSNR scores."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.415,
+                0.892,
+                0.457
+            ],
+            "angle": 0,
+            "content": "Table 2. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31] and FID [12] computed with 10K images on StyleGAN3."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.547,
+                0.457,
+                0.848,
+                0.564
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset Method</td><td colspan=\"2\">FFHQ</td><td colspan=\"2\">AFHQ-Cat</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>16.23</td><td>18.07</td><td>16.03</td><td>17.72</td></tr><tr><td>SSIM↑</td><td>0.70</td><td>0.78</td><td>0.70</td><td>0.76</td></tr><tr><td>LPIPS↓</td><td>0.33</td><td>0.22</td><td>0.16</td><td>0.13</td></tr><tr><td>FID↓</td><td>22.45</td><td>14.31</td><td>24.02</td><td>17.36</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.591,
+                0.892,
+                0.652
+            ],
+            "angle": 0,
+            "content": "the aims of StyleGAN correction methods are to maximize image quality (i.e., precision) without sacrificing diversity (i.e., recall), our method has made a concrete step towards the ultimate solution (red point in Fig. 6)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Image Similarity Metrics. Although less effective in assessing the trade-off between quality and diversity, for the sake of completeness, we also quantitatively compare the extent to which image features are retained by our method and the truncation trick [20, 6]. As Table 1 shows, for StyleGAN2, it can be observed that i) for PSNR, SSIM [33] and LPIPS [31], our method outperforms the truncation trick in most cases, which demonstrates that our method better retains the useful features in the original image. However, the SSIM of our method is slightly worse than that of the truncation trick for the FFHQ dataset. We ascribe this to the superior power of our method in removing structural artifacts that are common in StyleGAN pretrained with the FFHQ dataset. ii) For ID, we used the ArcFace [9] to compute the identity similarity scores between the original and the processed images. Interestingly, we observe that although"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.298,
+                0.901
+            ],
+            "angle": 0,
+            "content": "<sup>4</sup>https://github.com/NVlabs/stylegan3"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2365"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.092,
+                0.103,
+                0.891,
+                0.382
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.384,
+                0.893,
+                0.427
+            ],
+            "angle": 0,
+            "content": "Figure 8. Choice of hyper-parameters. Top row: images generated with truncation trick with \\(\\psi = 0.55\\) to 0.95. Rows 2-4: images generated with our method with \\(t = 0.0\\) to 4.0, \\(p = 1\\) to 3. Our method removes the artifacts while retaining almost all important features of the original image, indicating that it achieves a better trade-off between image quality and diversity than the truncation trick."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.437,
+                0.473,
+                0.588
+            ],
+            "angle": 0,
+            "content": "trained on human face datasets, ArcFace [9] generalizes to AFHQ-Cat [8] and MetFace [14] images and provides meaningful scores. iii) For FID [12], our method outperforms the truncation trick in all three datasets, which again demonstrates that our method better retains the useful features in the original image. We also show the difference maps in Fig. 7 to facilitate intuitive understanding. The results on StyleGAN3 [15] are shown in Table 2. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.6,
+                0.334,
+                0.617
+            ],
+            "angle": 0,
+            "content": "5.4. Choice of Hyper-parameters"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.624,
+                0.47,
+                0.746
+            ],
+            "angle": 0,
+            "content": "Similar to \\(\\psi\\) in the truncation trick [20, 6], we use two hyperparameters \\(t\\) and \\(p\\) for the trade-off between quality and diversity in our method. Between them, \\(t\\) determines how many feature maps are identified as risky ones for feature proliferation, and \\(p\\) adjusts the extent to which we rescale such feature maps. In general, the more risky feature maps identified, the stronger rescaling, and the higher quality but less diversity of synthesized images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Qualitative Justification. As Fig. 8 shows, we visualize the results generated with the truncation trick with \\(\\psi = 0.6\\) to 1.0 and our method with \\(t = 0.0\\) to 4.0 and \\(p = 1.0\\) to 3.0, and identify the best choice (\\(p = 2\\), \\(t = 2\\)) through visual inspection. In general, the smaller the \\(t\\), the more features are identified as risky (Eq. 3) for rescaling; the larger the \\(p\\), the stronger the rescaling. In this way, \\(t\\) and \\(p\\) work together to modify only the problematic features, thus achieving a better trade-off between quality and diversity than the truncation trick."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.436,
+                0.885,
+                0.62
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.626,
+                0.895,
+                0.682
+            ],
+            "angle": 0,
+            "content": "Figure 9. Choice of Hyper-parameters (Quantitative). It can be observed that \\( p = 2, t = 2 \\) (cyan) achieves the best trade-off between precision and recall, which is consistent with the visual inspection results in Fig. 8."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.694,
+                0.894,
+                0.77
+            ],
+            "angle": 0,
+            "content": "Quantitative Justification. We quantitatively justify the choice of hyper-parameters \\( p \\) and \\( t \\) by comparing their precision and recall. As Fig. 9 shows, \\( p = 2 \\), \\( t = 2 \\) achieves the best trade-off between precision and recall, which is consistent with the qualitative results in Fig. 8."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.782,
+                0.655,
+                0.798
+            ],
+            "angle": 0,
+            "content": "5.5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.806,
+                0.893,
+                0.866
+            ],
+            "angle": 0,
+            "content": "To justify the effectiveness of our channel-wise feature identification and rescaling strategy (Sec. 4), we demonstrate its superiority over its layer-wise and pixel-wise variants as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Layer-wise \"Cancer\" Curing. As in Sec. 4, let \\( x_{l,j} \\) be a \"cancer\" feature map identified using Eq. 3, we compute the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "2366"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.095,
+                0.093,
+                0.457,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.246,
+                0.47,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Figure 10. Successful cases of the layer-wise variant of our method (threshold \\( t' \\) ranges from 0.3 to 0.9). It can be observed that this variant is effective in removing artifacts of background intrusion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.313,
+                0.411,
+                0.328
+            ],
+            "angle": 0,
+            "content": "mean absolute \"cancer\" feature map for layer \\(l\\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.207,
+                0.339,
+                0.469,
+                0.357
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {x} _ {l} = \\operatorname {m e a n} _ {j} (| x _ {l, j} |) \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.366,
+                0.469,
+                0.442
+            ],
+            "angle": 0,
+            "content": "where we take the absolute value \\( |x_{l,j}| \\) to capture their magnitude and avoid them canceling each other out when added together. In order to make the same choice of hyperparameters applicable to all layers, we normalize \\( \\hat{x}_l \\) to \\( \\bar{x}_l \\) with mean \\( \\mu = 0 \\) and \\( \\sigma = 1 \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.215,
+                0.451,
+                0.469,
+                0.485
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {x} _ {l} = \\frac {\\hat {x} _ {l} - \\mu (\\hat {x} _ {l})}{\\sigma (\\hat {x} _ {l})} \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.494,
+                0.469,
+                0.525
+            ],
+            "angle": 0,
+            "content": "Then we measure the \"correlation\" between each \\( |x_{l,j}| \\) and its corresponding \\( \\bar{x}_l \\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.197,
+                0.535,
+                0.469,
+                0.569
+            ],
+            "angle": 0,
+            "content": "\\[\nc _ {l, j} = \\frac {\\left| x _ {l , j} \\right| * \\bar {x} _ {l}}{\\sum_ {\\text {e l e m e n t}} \\left| x _ {l , j} \\right|} \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.578,
+                0.469,
+                0.699
+            ],
+            "angle": 0,
+            "content": "where \\(\\sum_{\\mathrm{element}}|x_{l,j}|\\) is the sum for all elements in \\(|x_{l,j}|\\). Let \\(t^\\prime\\) be a threshold hyper-parameter, if \\(c_{l,j} > t^{\\prime}\\), we mark \\(x_{l,j}\\) as a layer-wise \"cancer\" feature map and perform the same feature rescaling on it to remove image artifacts. As Fig. 10 shows, this layer-wise variant of our method is also effective for certain types of image artifacts (e.g., background intrusion). While for some other types of artifacts (e.g., alien objects), it becomes less effective (Fig. 11)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.702,
+                0.469,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Pixel-wise \"Cancer\" Curing. We follow ProGAN [13] and apply its pixel-wise feature vector normalization technique, which was originally proposed to stabilize GAN training by resolving the potentially exploding magnitudes in the generator and discriminator, to pre-trained StyleGAN2. However, we observed that even the normally synthesized images become unrealistic (Fig. 12), indicating that it is not applicable to our problem."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.832,
+                0.247,
+                0.849
+            ],
+            "angle": 0,
+            "content": "5.6. Time Complexity"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Table 3 shows the time costs of generating a single image for StyleGAN2, ours implemented in serial, and ours implemented in parallel on an Nvidia V100 GPU. It can"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.099,
+                0.9,
+                0.315
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.335,
+                0.892,
+                0.432
+            ],
+            "angle": 0,
+            "content": "Figure 11. Failure cases of the layer-wise variant of our method (threshold \\( t' = 0.5 \\)). It can be observed that this variant is ineffective in removing artifacts of alien objects (e.g., color blocks on faces) while our method can remove them effectively. Top row: low-quality images synthesized by StyleGAN2; Middle row: results of the layer-wise variant of our method; Bottom row: results of our method."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.442,
+                0.892,
+                0.544
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.547,
+                0.892,
+                0.616
+            ],
+            "angle": 0,
+            "content": "Figure 12. Effects of pixel-wise feature vector normalization on StyleGAN2 pre-trained on FFHQ dataset. Top row: normal images synthesized by StyleGAN2. Bottom row: images after applying pixel-wise feature vector normalization, which become unrealistic."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.626,
+                0.892,
+                0.667
+            ],
+            "angle": 0,
+            "content": "Table 3. Time costs of generating a single image for StyleGAN2, Ours (Serial) and Ours (Parallel) on an Nvidia V100 GPU. The time is averaged over 100 runs."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.571,
+                0.673,
+                0.818,
+                0.75
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>FFHQ</td><td>AFHQ</td></tr><tr><td>SG2</td><td>0.075s</td><td>0.031s</td></tr><tr><td>Ours (Serial)</td><td>0.972s</td><td>0.721s</td></tr><tr><td>Ours (Parallel)</td><td>0.409s</td><td>0.189s</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.762,
+                0.892,
+                0.837
+            ],
+            "angle": 0,
+            "content": "be observed that the parallel implementation of our method significantly reduces the time costs from a factor of approximately 15-20 (Serial) to approximately 5 times those of the original StyleGAN2 (SG2). We leave further acceleration of our method to future work."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.847,
+                0.854,
+                0.864
+            ],
+            "angle": 0,
+            "content": "5.7. Applications in Interpolation and Editing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Fig. 13 shows that our method can remove image artifacts while retaining smooth StyleGAN interpolations, and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2367"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.086,
+                0.107,
+                0.138,
+                0.117
+            ],
+            "angle": 0,
+            "content": "StyleGAN2"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.087,
+                0.14,
+                0.155,
+                0.15
+            ],
+            "angle": 0,
+            "content": "Feature Rescaling"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.087,
+                0.173,
+                0.111,
+                0.181
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.147,
+                0.09,
+                0.207,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.167,
+                0.139,
+                0.182,
+                0.15
+            ],
+            "angle": 0,
+            "content": "#"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.212,
+                0.09,
+                0.272,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.235,
+                0.139,
+                0.249,
+                0.15
+            ],
+            "angle": 0,
+            "content": "↓"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.279,
+                0.09,
+                0.339,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.303,
+                0.139,
+                0.317,
+                0.15
+            ],
+            "angle": 0,
+            "content": "#"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.371,
+                0.09,
+                0.405,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.369,
+                0.139,
+                0.383,
+                0.15
+            ],
+            "angle": 0,
+            "content": "↓"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.413,
+                0.09,
+                0.472,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.437,
+                0.139,
+                0.449,
+                0.15
+            ],
+            "angle": 0,
+            "content": "↓"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.478,
+                0.09,
+                0.539,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.515,
+                0.15
+            ],
+            "angle": 0,
+            "content": "#"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.605,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.568,
+                0.139,
+                0.582,
+                0.15
+            ],
+            "angle": 0,
+            "content": "↓"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.598,
+                0.09,
+                0.67,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.636,
+                0.139,
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+            "content": "Figure 14. Our method is compatible with StyleGAN image editing [28]. StyleGAN2: interpolation between defective images synthesized by StyleGAN2; Ours: images \"corrected\" by our feature rescaling method."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Fig. 14 shows similar observations for StyleGAN image editing. These suggest that our method preserves StyleGAN latent semantics and is thus compatible with various StyleGAN latent space operations."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In this paper, we propose a novel feature identification and rescaling method to address the artifacts in StyleGAN synthesized images. The rationale of the proposed feature rescaling method stems from the Feature Proliferation phenomenon we discovered that has a strong causal relationship with StyleGAN image artifacts. Specifically, we observed that the features that deviate significantly from the mean of their distribution are highly likely to dominate the output of a neuron and proliferate in the forward propagation. As a result, the output of the entire network will be dominated by a small number of features. We ascribe this to the strong statistical assumption used in the weight modulation and demodulation used by the StyleGAN family. Intuitively, we name Feature Proliferation as the \"cancer\" in StyleGANs from its proliferating and malignant nature. Experimental results demonstrate that our method achieves a better tradeoff between quality and diversity of StyleGAN synthesized images than the popular truncation trick."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Limitation and Future Work. Although effective and significantly better than the truncation trick, the proposed method is not perfect as it can still remove some useful image features and make minor changes to high-quality StyleGAN synthesized images. We plan to design more precise"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.447,
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+            "angle": 0,
+            "content": "methods to identify and process proliferating features in future work. In addition, we believe that Feature Proliferation is not a problem exclusive to StyleGAN and may occur in other works as long as weight modulation and demodulation techniques are used (Sec. 3.2). Thus, we plan to investigate in future work whether feature proliferation is a common phenomenon in various network architectures and its consequences in different tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.578,
+                0.893,
+                0.745
+            ],
+            "angle": 0,
+            "content": "Potential Negative Social Impact. Although our method works as a post-hoc \"cure\" for StyleGAN synthesized images and can save millions of dollars in training costs and energy consumption, it may also lead to potentially negative social impacts. For example, it can further improve the quality of StyleGAN synthesized images, which may facilitate the creation of fake portrait photos/videos for fake social media accounts and fake news. Nevertheless, we still believe that our work will make a positive contribution to the field and provide new insights into the mechanisms of generative models that may help identify such fake content."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We thank the reviewers for their constructive comments that helped improve this paper. This work was partially supported by the China Scholarship Council (CSC) under Grant No. 202106150033 and the UK Engineering and Physical Sciences Research Council (EPSRC) through the Doctoral Training Partnerships (DTP) with No. EP/T517951/1 (2599521)."
+        },
+        {
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+            "angle": 0,
+            "content": "2368"
+        }
+    ],
+    [
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "References"
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+# Feature Proliferation — the “Cancer” in StyleGAN and its Treatments
+
+Shuang Song Yuanbang Liang Jing Wu Yu-Kun Lai Yipeng Qin* Cardiff University
+
+{songs7, liangy32, wuj11, laiy4, qiny16}@cardiff.ac.uk
+
+# Abstract
+
+Despite the success of StyleGAN in image synthesis, the images it synthesizes are not always perfect and the well-known truncation trick has become a standard post-processing technique for StyleGAN to synthesize high quality images. Although effective, it has long been noted that the truncation trick tends to reduce the diversity of synthesized images and unnecessarily sacrifices many distinct image features. To address this issue, in this paper, we first delve into the StyleGAN image synthesis mechanism and discover an important phenomenon, namely Feature Proliferation, which demonstrates how specific features reproduce with forward propagation. Then, we show how the occurrence of Feature Proliferation results in StyleGAN image artifacts. As an analogy, we refer to it as the "cancer" in StyleGAN from its proliferating and malignant nature. Finally, we propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation. Thanks to our discovery of Feature Proliferation, the proposed feature rescaling method is less destructive and retains more useful image features than the truncation trick, as it is more fine-grained and works in a lower-level feature space rather than a high-level latent space. Experimental results justify the validity of our claims and the effectiveness of the proposed feature rescaling method. Our code is available at https://github.com/songc42/Feature-proliferation.
+
+# 1. Introduction
+
+Deep learning has entered the era of large models. For instance, the GPT-3 [7] developed by OpenAI has 175 billion parameters and can easily cost around 15 million dollars to train for a single run, let alone the GPT-3.5 underpinning the recently hyped ChatGPT; Stability.ai trained their Stable-diffusion-v1-4 $^2$  using 256 Nvidia A100 GPUs for 150,000 GPU hours; Nvidia spent 92 GPU years and
+
+225 MWh of electricity with an in-house cluster of NVIDIA V100 GPUs to develop StyleGAN3 [15] and 4 weeks on 64 NVIDIA A100s for a "constrained" training of their recent StyleGAN-T [27]. As a result, although the performance of large models is impressive, their high costs have become a critical concern, e.g., OpenAI admitted that there was a bug in their GPT-3 model but cannot afford to retrain it due to the high cost [7]. This motivates us to do our best to avoid retraining large neural network models. In this work, we focus on the StyleGAN family [16, 17, 15, 27] as they are inherently more efficient (i.e., generating images with a single pass), allow for excellent semantic interpolation in their latent spaces, and are comparable to the quality of diffusion models [27]. For the StyleGAN series, although there were no obvious bugs in the training, the synthesized images are not always perfect. While instead of attempting to solve this problem by improving the model design which requires multiple retraining, StyleGAN follows the "no retraining" philosophy and resorts to a post-processing technique called truncation trick [20, 6]. In short, the truncation trick improves the quality of StyleGAN synthesized images by normalizing their corresponding latent codes towards their mean in the latent space. However, despite its popularity, it has long been noted that the truncation trick tends to reduce the diversity of synthesized images and unnecessarily sacrifices many distinct image features [16].
+
+In this paper, we address the low-quality images synthesized by StyleGAN from a different perspective, i.e., its mechanism for image synthesis in the feature space. Specifically, we delved into the architectural details of the StyleGAN generator and discovered an important phenomenon, namely Feature Proliferation, which demonstrates how specific features reproduce with forward propagation. In short, Feature Proliferation denotes the phenomenon where the ratio of the occurrence of a certain type of feature (those with abnormally large values) in a layer increases with forward propagation. Our analysis points out that such a phenomenon is a by-product of the weight modulation and demodulation techniques used in StyleGAN2/3 [17, 15] and the latest StyleGAN-T [27]. Interestingly, we observed that Feature Proliferation usually leads to artifacts in Style-
+
+![](images/5390750f0a06c84b3e25e62d3e60319b32f34c339afd2e82eca021304ff7e6d6.jpg)  
+Figure 1. Top: StyleGAN synthesized images with artifacts. Bottom: images "cured" by our method.
+
+GAN synthesized images and these artifacts can be easily removed by a simple feature rescaling method. To minimize the unnecessary interference with useful image features, we propose a novel method to identify the risky features prone to proliferation in the earliest layers, thereby removing the least amount of them. As a result, our method significantly outperforms the truncation trick in terms of retaining useful image features while improving the quality of StyleGAN synthesized images. Experimental results justify the validity of our claims and the effectiveness of the proposed feature rescaling method. Our contributions include:
+
+- We discover an important phenomenon, namely Feature Proliferation, which shows how specific features reproduce with forward propagation. We also show that it is a by-product of the weight modulation and demodulation techniques used in modern StyleGANs.  
+- We discover a strong causal relationship between the occurrence of Feature Proliferation and StyleGAN image artifacts.  
+- We propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation, thereby achieving a better trade-off between quality and diversity of StyleGAN synthesized images than the popular truncation trick.
+
+# 2. Related work
+
+Since the seminal work of Goodfellow et al. [10], Generative Adversarial Networks (GANs) have become one of the most promising deep generative models that have numerous applications in computer vision and graphics. Nevertheless, GANs are known to be notoriously difficult to train and a variety of techniques have been proposed to
+
+stabilize their training from different perspectives, including architectures [25, 11], loss functions [4, 19], regularization [22, 23], and the interactions between them [24]. Thanks to the massive efforts from the community, the StyleGAN series [16, 17, 15, 27] have become one of the most influential models in the GAN family, as it can generate high-resolution and realistic images that are almost indistinguishable from real photos by human inspectors. Examples of its applications include GAN inversion and editing [1, 2, 29, 3], image-to-image translation [26], superresolution [21], 3D shape generation [32], etc. We refer interested audiences to [5] for a survey on StyleGAN and its applications. Nevertheless, despite its success, the quality of images synthesized by StyleGAN varies, and a post-processing method known as the truncation trick [20, 6] has widely been adopted to obtain higher quality images. However, the truncation trick has long been noted as "destructive" as it unnecessarily sacrifices useful image features and tends to reduce the diversity of synthesized images. In this paper, we address this issue by investigating the StyleGAN image synthesis mechanism and propose a feature rescaling method that can precisely identify the risky features causing image artifacts, thereby improving image quality by modulating these features at the minimal cost.
+
+# 3. Feature Proliferation in StyleGAN
+
+In this section, we first introduce two new phenomena that we discovered in the forward propagation of deep neural networks, i.e. feature domination and proliferation. We then show that they are by-products of the weight modulation and demodulation techniques used in modern StyleGANs. Finally, we show how they affect StyleGAN and lead to artifacts in synthesized images.
+
+![](images/16306bd1efdc357289432a5cae9afd58f1691123fc77aec27eeb502b52359222.jpg)  
+Figure 2. Illustration of feature domination.  $y$  is dominated by  $x_{j}$  and its perturbations  $x_{i} \approx x_{j}$ .
+
+# 3.1. Feature Domination and Proliferation
+
+Throughout the history of machine learning, the weighted sum method has been built to last from the classical linear regression, to the theoretically elegant support vector machines and the deep neural networks that are now taking both academia and industry by storm. For deep neural networks, we usually refer to the output of neurons as features that are the elements to be weighted and summed. However, due to the differences among weights and input features, the output of a neuron can occasionally be dominated by one or a small amount of input features, which leads to a phenomenon we call Feature Domination.
+
+Definition 3.1 (Feature Domination) Let  $y = \mathbf{w}^{\mathrm{T}}\mathbf{x} + b$  be the output of a neuron,  $\mathbf{x}$  and  $\mathbf{w}$  are the input and weight vectors respectively,  $b$  denotes the bias, we define Feature Domination as the case where  $y \approx (\sum_{i} w_{i}) x_{j} + b$  is dominated by feature  $x_{j}$  and its perturbations  $x_{i} \approx x_{j}$ , where  $i$  indicates the  $i$ -th element in  $\mathbf{w}$  and  $\mathbf{x}$ .
+
+In a nutshell, the proposed Feature Domination describes the phenomenon that one or a small number of similar input features may dominate the weighted sum if their products with associated weights significantly outweigh others (Fig. 2), making  $y$  similar to  $x_{i} / x_{j}$ . In practice, we observed that the dominant features are highly likely to be those that deviate significantly from the mean of their distributions:
+
+# Observation 3.1 (Feature Domination in StyleGAN)
+
+Let  $t$  be an empirically obtained threshold, and  $x_{l,j}$  be the feature map of channel  $j$  of layer  $l$  of the generator.  $x_{l,j}$  is highly likely to be dominant if  $\frac{|\mathrm{mean}(x_{l,j}) - \mu_{x_{l,j}}|}{\sigma_{x_{l,j}}} > t$ , where  $\mathrm{mean}(x_{l,j})$  is the mean value of all elements in  $x_{l,j}$ ,  $\mu_{x_{l,j}}$  and  $\sigma_{x_{l,j}}$  are the mean and standard deviation of the distribution of  $x_{l,j}$  over the training dataset.
+
+In practice, we use Observation 3.1 to identify dominant features in StyleGANs. Furthermore, Feature Proliferation happens when the same type of Feature Domination proliferates during the forward propagation.
+
+![](images/608b2de0a7c965e9bb157312ab3ee4dea22f6fd21c154b9a3a33de43103f6f88.jpg)  
+(a) Mean of inputs
+
+![](images/7d379999759b68822a9bf4cc1d1e2e34fb85bcf72954ca71a6cedc3d8db9d46e.jpg)  
+(b) Standard deviation of inputs  
+Figure 3. Histograms of mean and standard deviation of the input feature maps from 10,000 StyleGAN2 synthesized images.
+
+Definition 3.2 (Feature Proliferation) Following Definition 3.1, let  $\mathbf{Y}_d(x_j)$  be the set consisting of all outputs  $y$  dominated by feature  $x_j$  in a single neural network layer, we define Feature Proliferation as the increase of  $\eta(x_j) = |\mathbf{Y}_d(x_j)| / |\mathbf{Y}|$  during forward propagation, where  $\mathbf{Y}$  is the set of all outputs in a single neural network layer and  $|\cdot|$  denotes the cardinality of a set.
+
+When Feature Proliferation happens, one or a small number of features will dominate the output of the entire network, leading to artifacts in StyleGAN synthesized images. As an analogy, we refer to it as the "cancer" in StyleGAN from its proliferating and malignant nature.
+
+Remark. For simplicity, Definitions 3.1 and 3.2 are introduced with fully-connected layers. However, both definitions can be easily extended to other types of neural networks, e.g., convolutional neural networks (CNNs) [30], as the weighted sum operation is widely used in almost all deep neural networks due to its benefits in parallelization.
+
+# 3.2. Root Causes of Feature Proliferation
+
+We ascribe feature proliferation to the strong statistical assumption used in the weight modulation and demodulation of StyleGAN2/3/T [17, 15, 27], i.e., "the input activations are i.i.d. random variables with unit standard deviation", rather than the statistics (i.e., mean and standard deviation) of the actual feature maps used in the AdaIN of StyleGAN1 [16].
+
+Specifically, weight demodulation assumes that all input activations (modulated feature maps) are already normalized to be of unit standard deviation, thereby eliminating the step of feature map normalization  $\frac{\mathbf{x}_i - \mu(\mathbf{x}_i)}{\sigma(\mathbf{x}_i)}$  used in AdaIN. Since the standard deviations of output feature maps are determined by the products of those of their input feature maps (assumed to be unit ones as mentioned above) and convolutional weights, the abovementioned assumption ensures the unit standard deviations of output feature maps by only "demodulating" the convolutional weights to be of unit standard deviations [17]:
+
+$$
+w _ {i j k} ^ {\prime \prime} = w _ {i j k} ^ {\prime} / \sqrt {\sum_ {i} w _ {i j k} ^ {\prime 2} + \epsilon}, w _ {i j k} ^ {\prime} = s _ {i} \cdot w _ {i j k} \tag {1}
+$$
+
+![](images/565ba8404032a99ac810907a99496f7401dac5d4382c8dde99226605bb904d29.jpg)  
+Figure 4. Left: ('Cancer' Proliferation) the Feature Proliferation phenomenon leads to image artifacts; (Curing) setting the visually identified proliferating feature map in Layer 3 to zero (blue arrow) mitigates feature proliferation. Right: (Normal Generation) a proper StyleGAN image synthesis process; (Inserted 'Cancer' Proliferation) inserting the "cancer" features identified in the left part results in feature proliferation and similar image artifacts (red arrow). The yellow boxes in feature maps highlight the feature proliferation process.  $\eta$  in red: the ratio of dominated features in a layer.
+
+where  $s_i$  is the scaling parameter corresponding to the  $i$ -th input feature map,  $j$  and  $k$  enumerate the output feature maps and spatial footprint of the convolution, respectively. While in practice, the assumption of the unit standard deviation of input activations does not hold (Fig. 3). As a result, weight demodulation cannot ensure the unit standard deviations of output feature maps. Instead, the standard deviations of output feature maps are determined by those of input ones, causing feature domination and proliferation.
+
+Remark. AdaIN explicitly normalizes each feature map according to its mean and standard deviation so the mean and standard deviation of its output are solely determined by the style parameters  $\mathbf{y} = (\mathbf{y}_s, \mathbf{y}_b)$  but not those of its input feature map  $\mathbf{x}_i$  [16]:
+
+$$
+\operatorname {A d a I N} \left(\mathbf {x} _ {i}, \mathbf {y}\right) = \mathbf {y} _ {s, i} \frac {\mathbf {x} _ {i} - \mu \left(\mathbf {x} _ {i}\right)}{\sigma \left(\mathbf {x} _ {i}\right)} + \mathbf {y} _ {b, i} \tag {2}
+$$
+
+This breaks the chain of feature proliferation in forward propagation and we did not observe significant proliferation in our experiments. However, as shown in [17], AdaIN has its own problems (i.e., the "characteristic artifacts", which is why weight demodulation is used in StyleGAN2/3) and may not be a good solution to feature proliferation.
+
+# 3.3. Impact of Feature Proliferation on StyleGAN
+
+As Fig. 4 shows, the synthesized images suffer from obvious artifacts when Feature Proliferation happens and we observed a strong spatial correlation between the proliferated feature maps and the artifacts in synthesized images. To justify the causality between them, we show that i) the artifacts can be "cured" by removing corresponding features before their proliferation in Fig. 4 (left) and ii) the artifacts can be added to high-quality images by inducing feature proliferation in Fig. 4 (right).
+
+# 4. Curing the "Cancer" in StyleGAN
+
+In this section, we first introduce how to identify the risky features for feature proliferation and then introduce a simple but effective feature rescaling method to adjust the identified features and mitigate the feature proliferation.
+
+# 4.1. Feature Proliferation ("Cancer") Identification
+
+Naively, one of the most straightforward methods for feature proliferation identification is to extract all similar pairs of feature maps in the successive layers of a neural network. However, let  $k$  be the number of successive pairs of layers and  $n$  be the number of neurons per layer, the time complexity of this strategy is  $O(kn^2)$  per image, which is inefficient and makes it infeasible for frequent use.
+
+Addressing this issue, we employ a heuristic stemming from Observation 3.1 that the dominant features are likely to be those that deviate significantly from the mean of their distributions. Specifically, we estimate the mean  $\mu_{l,j}$  and standard deviation  $\sigma_{l,j}$  with a large number (e.g., 3,000) of randomly sampled images and identify  $x_{l,j}$  as a high risk feature for proliferation if:
+
+$$
+r _ {l, j} = \frac {\left| \operatorname {m e a n} \left(x _ {l , j}\right) - \mu_ {l , j} \right|}{\max  \left(\sigma_ {l , j} , c\right)} > t \tag {3}
+$$
+
+where  $\mathrm{mean}(x_{l,j})$  is the mean value of all elements in  $x_{l,j}$ ,  $r_{l,j}$  denotes the amount of risk of feature proliferation,  $t$  is a user-defined threshold obtained empirically,  $c = 0.1$  is a small constant introduced to avoid the mis-identification when  $\sigma_{l,j}$  is small.
+
+# 4.2. Curing the "Cancer" by Feature Rescaling
+
+Since the risky features identified by Eq. 3 proliferate with forward propagation, we propose a simple yet effective feature scaling method to address the proliferation in the
+
+![](images/c0fe9ca54f2c165341f470d1805d3b589382ee83c00b143b220ea93d60e9a9f5.jpg)  
+(a) StyleGAN2 pretrained with FFHQ dataset
+
+![](images/0eb3b7060c48bedec43a032b587bd16b0c1af6364bd87473cf5f62bbcf5af292.jpg)  
+(b) StyleGAN2 pretrained with AFHQ-Cat dataset
+
+![](images/1090d187e93b4504772c81717fbeab73c4f2f9efb0dbd43811a1e8feba04ae8a.jpg)  
+(c) StyleGAN3 pretrained on FFHQ dataset
+
+![](images/304458e6c7a917b43c4edd1ba590f99b6665430e184a12317b0b6e24fc95bcf0.jpg)  
+(d) StyleGAN3 pretrained on AFHQ dataset  
+Figure 5. Curated StyleGAN2/3 [17, 15] synthesized images, those processed by the truncation trick  $(\psi = 0.7)$ , and our method.
+
+earliest layers, thereby removing the least amount of them and minimizing the unnecessary interference with useful image features. Let  $x_{c}$  be a "cancer" feature map with risk  $r$  (Eq. 3), we have
+
+$$
+x _ {c} ^ {m} = \frac {x _ {c}}{p \cdot r} \tag {4}
+$$
+
+where  $x_{c}^{m}$  denotes the modified feature map,  $p$  is the scaling hyper-parameter. By rescaling  $x_{c}$ , we reduce the values of its elements and thus prevent it from Feature Domination (Definition 3.1) and Proliferation (Definition 3.2), thereby improving the quality of StyleGAN synthesized images.
+
+# 5. Experiments
+
+Please see the supplement for more experiments.
+
+# 5.1. Experimental Setup
+
+The proposed method does not require network training. We run the proposed method with pretrained deep generative models on a workstation with an Intel(R) Core(TM) i7-10875H CPU and a GeForce RTX 3080 GPU. The pretrained StyleGAN2 [17] models (using FFHQ [16], MetFace [14] and AFHQ-Cat [8] datasets) used in all our experi
+
+iments are publicly-released on  $\mathrm{Gibthub}^3$ . Unless specified, we use hyperparameters  $t = 2$  and  $p = 2$  for our method, and  $\psi = 0.7$  for the truncation trick that has been suggested for the best trade-off between quality and diversity of synthesized images [16, 6].
+
+# 5.2. Qualitative Evaluation
+
+As Fig. 5 shows, we compare the performance of our method against the truncation trick [20, 6] on StyleGAN2 and StyleGAN3 models pretrained on FFHQ, MetFace and AFHQ-Cat datasets. In Fig. 5(a), it can be observed that: i) all the StyleGAN2 synthesized images in the top row, except the third one, contain obvious artifacts; ii) for the third column (high-quality image), our method retains useful image features better than the truncation trick; iii) for the other columns, our method not only removes the artifacts but also retains useful image features in a better way, e.g., the truncation trick eliminates the eyeglasses in column 1 while our method retains them and other fine facial details like the beard. Similar results can be observed in Fig. 5(b), which demonstrates the versatility of our method across datasets.
+
+![](images/5bc56dc84fdb2b2622535afcb1966f0f74607234cc6f1c9454262f18706302b5.jpg)  
+Figure 6. Comparison of precision and recall [18] between the truncation trick [20, 6] and our method on StyleGAN2.  $p$  and  $t$  are hyperparameters of our method and  $\psi$  is the hyperparameter for the truncation trick. "StyleGAN2" (bottom-right corner): precision and recall of the original StyleGAN2; Blue ( $\psi = 0.7$ ): best  $\psi$  recommended by StyleGAN2 [17]; Cyan ( $p = 2$ ,  $t = 2$ ): best  $p$  and  $t$  of our method; Red: the upper bound of StyleGAN "correction" methods where every error is corrected (precision=1.0) without sacrificing diversity (recall remains constant); Orange: the closer to the dashed line, the less sacrifice of diversity; Gray: region of uninterest where too much diversity has been sacrificed. Ours is closer to the dashed line in the region of interest, indicating that it strikes a better balance between precision and recall.
+
+Table 1. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31], ID (identity preservation using the Arc-Face [9]) and FID [12] computed with 10K images on StyleGAN2.  
+
+<table><tr><td rowspan="2">Dataset Method</td><td colspan="2">AFHQ-Cat</td><td colspan="2">MetFace</td><td colspan="2">FFHQ</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>3.66</td><td>4.11</td><td>5.33</td><td>10.45</td><td>3.80</td><td>4.28</td></tr><tr><td>SSIM↑</td><td>0.79</td><td>0.81</td><td>0.81</td><td>0.87</td><td>0.74</td><td>0.68</td></tr><tr><td>LPIPS↓</td><td>0.15</td><td>0.14</td><td>0.22</td><td>0.14</td><td>0.31</td><td>0.24</td></tr><tr><td>ID↑</td><td>0.74</td><td>0.84</td><td>0.77</td><td>0.87</td><td>0.71</td><td>0.77</td></tr><tr><td>FID↓</td><td>7.43</td><td>4.47</td><td>23.02</td><td>17.51</td><td>12.56</td><td>11.91</td></tr></table>
+
+Figs. 5(c) and 5(d) show synthesized results of the truncation trick and our method on StyleGAN3 [15] models pretrained on FFHQ and AFHQ datasets<sup>4</sup>. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method.
+
+# 5.3.Quantitative Evaluation
+
+Precision and Recall. Fig. 6 shows the comparison of precision and recall [18] between the truncation trick [20, 6] and our method on StyleGAN2. It can be observed that our method strikes a better balance between precision and recall  $(p = 2, t = 2)$  in the region of interest (right side, white region) while the truncation trick sacrifices too much diversity to achieve the same level of precision. Recognizing that
+
+![](images/d8e55e6cdeb46afffa08ec79df7edd2c1cfd5bd3f1eec79ba83a7a05bd3628c7.jpg)
+
+![](images/356110c1cbbee4d519a7a129c7c91939893f5195c9bab93c95df94bd5b344704.jpg)
+
+![](images/356d002fa7f08cc09353319b2a0c975f69fd965753bb3059ff8e525503e7378a.jpg)
+
+![](images/20803eb84e03f29686d4a8786aab0eb0826ce89025c068030141106cb4c1ab47.jpg)  
+StyleGAN2  
+Truncation Trick  
+Difference Map (Truncation Trick)  
+Ours  
+Difference Map (Ours)  
+Figure 7. Comparison of difference maps of truncation trick [20, 6] and our method. The numbers at the bottom right corner of the difference images are PSNR scores.
+
+Table 2. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31] and FID [12] computed with 10K images on StyleGAN3.  
+
+<table><tr><td rowspan="2">Dataset Method</td><td colspan="2">FFHQ</td><td colspan="2">AFHQ-Cat</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>16.23</td><td>18.07</td><td>16.03</td><td>17.72</td></tr><tr><td>SSIM↑</td><td>0.70</td><td>0.78</td><td>0.70</td><td>0.76</td></tr><tr><td>LPIPS↓</td><td>0.33</td><td>0.22</td><td>0.16</td><td>0.13</td></tr><tr><td>FID↓</td><td>22.45</td><td>14.31</td><td>24.02</td><td>17.36</td></tr></table>
+
+the aims of StyleGAN correction methods are to maximize image quality (i.e., precision) without sacrificing diversity (i.e., recall), our method has made a concrete step towards the ultimate solution (red point in Fig. 6).
+
+Image Similarity Metrics. Although less effective in assessing the trade-off between quality and diversity, for the sake of completeness, we also quantitatively compare the extent to which image features are retained by our method and the truncation trick [20, 6]. As Table 1 shows, for StyleGAN2, it can be observed that i) for PSNR, SSIM [33] and LPIPS [31], our method outperforms the truncation trick in most cases, which demonstrates that our method better retains the useful features in the original image. However, the SSIM of our method is slightly worse than that of the truncation trick for the FFHQ dataset. We ascribe this to the superior power of our method in removing structural artifacts that are common in StyleGAN pretrained with the FFHQ dataset. ii) For ID, we used the ArcFace [9] to compute the identity similarity scores between the original and the processed images. Interestingly, we observe that although
+
+![](images/5abda7285b49d244f92b3938a5bc5b06127a23f3cd0d4868dffeb839d86c6ef7.jpg)  
+Figure 8. Choice of hyper-parameters. Top row: images generated with truncation trick with  $\psi = 0.55$  to 0.95. Rows 2-4: images generated with our method with  $t = 0.0$  to 4.0,  $p = 1$  to 3. Our method removes the artifacts while retaining almost all important features of the original image, indicating that it achieves a better trade-off between image quality and diversity than the truncation trick.
+
+trained on human face datasets, ArcFace [9] generalizes to AFHQ-Cat [8] and MetFace [14] images and provides meaningful scores. iii) For FID [12], our method outperforms the truncation trick in all three datasets, which again demonstrates that our method better retains the useful features in the original image. We also show the difference maps in Fig. 7 to facilitate intuitive understanding. The results on StyleGAN3 [15] are shown in Table 2. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method.
+
+# 5.4. Choice of Hyper-parameters
+
+Similar to  $\psi$  in the truncation trick [20, 6], we use two hyperparameters  $t$  and  $p$  for the trade-off between quality and diversity in our method. Between them,  $t$  determines how many feature maps are identified as risky ones for feature proliferation, and  $p$  adjusts the extent to which we rescale such feature maps. In general, the more risky feature maps identified, the stronger rescaling, and the higher quality but less diversity of synthesized images.
+
+Qualitative Justification. As Fig. 8 shows, we visualize the results generated with the truncation trick with  $\psi = 0.6$  to 1.0 and our method with  $t = 0.0$  to 4.0 and  $p = 1.0$  to 3.0, and identify the best choice ( $p = 2$ ,  $t = 2$ ) through visual inspection. In general, the smaller the  $t$ , the more features are identified as risky (Eq. 3) for rescaling; the larger the  $p$ , the stronger the rescaling. In this way,  $t$  and  $p$  work together to modify only the problematic features, thus achieving a better trade-off between quality and diversity than the truncation trick.
+
+![](images/2c1d01c665fec3691af33ac8ea08d74ce4e0d1579995422f5d5cd9345ce75343.jpg)  
+Figure 9. Choice of Hyper-parameters (Quantitative). It can be observed that  $p = 2, t = 2$  (cyan) achieves the best trade-off between precision and recall, which is consistent with the visual inspection results in Fig. 8.
+
+Quantitative Justification. We quantitatively justify the choice of hyper-parameters  $p$  and  $t$  by comparing their precision and recall. As Fig. 9 shows,  $p = 2$ ,  $t = 2$  achieves the best trade-off between precision and recall, which is consistent with the qualitative results in Fig. 8.
+
+# 5.5. Ablation Study
+
+To justify the effectiveness of our channel-wise feature identification and rescaling strategy (Sec. 4), we demonstrate its superiority over its layer-wise and pixel-wise variants as follows.
+
+Layer-wise "Cancer" Curing. As in Sec. 4, let  $x_{l,j}$  be a "cancer" feature map identified using Eq. 3, we compute the
+
+![](images/b7c6da152fe16a839786ab59200439c6e4e7bfc70b1fc46009033cbbb2c95d31.jpg)  
+Figure 10. Successful cases of the layer-wise variant of our method (threshold  $t'$  ranges from 0.3 to 0.9). It can be observed that this variant is effective in removing artifacts of background intrusion.
+
+mean absolute "cancer" feature map for layer  $l$  as:
+
+$$
+\hat {x} _ {l} = \operatorname {m e a n} _ {j} (| x _ {l, j} |) \tag {5}
+$$
+
+where we take the absolute value  $|x_{l,j}|$  to capture their magnitude and avoid them canceling each other out when added together. In order to make the same choice of hyperparameters applicable to all layers, we normalize  $\hat{x}_l$  to  $\bar{x}_l$  with mean  $\mu = 0$  and  $\sigma = 1$ :
+
+$$
+\bar {x} _ {l} = \frac {\hat {x} _ {l} - \mu (\hat {x} _ {l})}{\sigma (\hat {x} _ {l})} \tag {6}
+$$
+
+Then we measure the "correlation" between each  $|x_{l,j}|$  and its corresponding  $\bar{x}_l$  as:
+
+$$
+c _ {l, j} = \frac {\left| x _ {l , j} \right| * \bar {x} _ {l}}{\sum_ {\text {e l e m e n t}} \left| x _ {l , j} \right|} \tag {7}
+$$
+
+where  $\sum_{\mathrm{element}}|x_{l,j}|$  is the sum for all elements in  $|x_{l,j}|$ . Let  $t^\prime$  be a threshold hyper-parameter, if  $c_{l,j} > t^{\prime}$ , we mark  $x_{l,j}$  as a layer-wise "cancer" feature map and perform the same feature rescaling on it to remove image artifacts. As Fig. 10 shows, this layer-wise variant of our method is also effective for certain types of image artifacts (e.g., background intrusion). While for some other types of artifacts (e.g., alien objects), it becomes less effective (Fig. 11).
+
+Pixel-wise "Cancer" Curing. We follow ProGAN [13] and apply its pixel-wise feature vector normalization technique, which was originally proposed to stabilize GAN training by resolving the potentially exploding magnitudes in the generator and discriminator, to pre-trained StyleGAN2. However, we observed that even the normally synthesized images become unrealistic (Fig. 12), indicating that it is not applicable to our problem.
+
+# 5.6. Time Complexity
+
+Table 3 shows the time costs of generating a single image for StyleGAN2, ours implemented in serial, and ours implemented in parallel on an Nvidia V100 GPU. It can
+
+![](images/065d5d9200064f36b62c0cd3641a4da964878ebf576178491bc042eb8f281526.jpg)  
+Figure 11. Failure cases of the layer-wise variant of our method (threshold  $t' = 0.5$ ). It can be observed that this variant is ineffective in removing artifacts of alien objects (e.g., color blocks on faces) while our method can remove them effectively. Top row: low-quality images synthesized by StyleGAN2; Middle row: results of the layer-wise variant of our method; Bottom row: results of our method.
+
+![](images/7e0662d8d3671e8f5a1b268949b7a8dca6e81f696bf25eb2c73f0bc0889b255c.jpg)  
+Figure 12. Effects of pixel-wise feature vector normalization on StyleGAN2 pre-trained on FFHQ dataset. Top row: normal images synthesized by StyleGAN2. Bottom row: images after applying pixel-wise feature vector normalization, which become unrealistic.
+
+Table 3. Time costs of generating a single image for StyleGAN2, Ours (Serial) and Ours (Parallel) on an Nvidia V100 GPU. The time is averaged over 100 runs.  
+
+<table><tr><td>Dataset</td><td>FFHQ</td><td>AFHQ</td></tr><tr><td>SG2</td><td>0.075s</td><td>0.031s</td></tr><tr><td>Ours (Serial)</td><td>0.972s</td><td>0.721s</td></tr><tr><td>Ours (Parallel)</td><td>0.409s</td><td>0.189s</td></tr></table>
+
+be observed that the parallel implementation of our method significantly reduces the time costs from a factor of approximately 15-20 (Serial) to approximately 5 times those of the original StyleGAN2 (SG2). We leave further acceleration of our method to future work.
+
+# 5.7. Applications in Interpolation and Editing
+
+Fig. 13 shows that our method can remove image artifacts while retaining smooth StyleGAN interpolations, and
+
+![](images/f634e13300fbe4507e0485dd51274993cd3e71437f1fe8fc9974b6ca11d979e9.jpg)  
+StyleGAN2  
+#
+
+![](images/294e8605bc9f06f084e2b54b2865ecb40932bba95d046c60d893de52410de501.jpg)  
+↓
+
+![](images/e583a60dc8c8a0641c26067bfb37f0419d6c649dd1aab6a3fee94db154a04a3c.jpg)  
+#
+
+![](images/b1e5c907387fd8f7a856206768132523520df541c5bf4b69de859eb491fcdcd4.jpg)  
+↓
+
+![](images/f16b51d0bea50a036da272e6af86c0b8a5d7db9b187adb2629772a13c8957b31.jpg)  
+↓
+
+![](images/91f386131838be8bce293cf56b08d299ad199d0c2b7a85ffa660c6ab4c32d623.jpg)  
+#
+
+![](images/dd17b0a3dc70acbdd569ef05c3949877b1d9980c50a04abf5750837797f12494.jpg)  
+↓
+
+![](images/411d74ee2387eca40656bcc8cd8b59e2ab7993ac2acb276dd52e6bba4985a97a.jpg)  
+↓
+
+![](images/6b14da3003014b7fa549c4d536a3c1278e14ae7590205fa74e1472fd6f226e05.jpg)  
+↓
+
+![](images/367cbc4e0011efa80f91e30e3532156217b1d37454f96868c85f2a56901da897.jpg)  
+↓
+
+![](images/8fc298b532db06034c09f19ff4b7c65b6d2a19e9833875ab9a060345746d88f3.jpg)  
+↓
+
+![](images/2eecaee1dead4913b65e7f52d4000d6d9abdb380f1f1d1cd8764e8344f2d0112.jpg)  
+Feature Rescaling  
+Figure 13. Our method is compatible with StyleGAN interpolations. StyleGAN2: interpolation between defective images synthesized by StyleGAN2; Ours: images "corrected" by our feature rescaling method.
+
+![](images/461c0d0f8cfb36f48d9f7cb3e3442272b605475e822e1db5292acfaf1b60a780.jpg)  
+Ours
+
+![](images/d828f019ff0ca1a909c0b109d5a5746ea83d190a7c64d1ffa5ef7b0253ae413d.jpg)
+
+![](images/295f6281dc18d53306911a0e4eb26998bdf3d7cc689a3acfa26d4af30dd70b90.jpg)
+
+![](images/6d22dee999d028ca22b337d1c92a069cf916a0298f7c19e4e139ca54e9db2edf.jpg)
+
+![](images/722cdd719bdfb4d384fdd2a4ee00d4966f463e8092ecff8dfbac19f7580b2ab4.jpg)
+
+![](images/e54dac4bd29afc74a843a014c63f5b0d1bfb24f0d3e4dd72a193a87b155747d8.jpg)
+
+![](images/037f4f7273533e3fc60aab37a10a343d1f6326e3253652bac2f694f4a0866225.jpg)
+
+![](images/ba63d5d0ec46749adb47a0e8bc4efbc207bf28c83df2d8dd836b2c7a6b4794aa.jpg)
+
+![](images/0087ab36da4f444a910032035dac36aea706c6e4efbcc39fe6b9203a7f5292c2.jpg)
+
+![](images/e7bf427235d003f76e660b01cda08144b9a755a1ae32654214557402408ee972.jpg)
+
+![](images/cc1f6fefb3761fc4505a63d15e2adeead74255eb3e8856d093b62dd2c662f624.jpg)  
+StyleGAN2  
+Feature Rescaling  
+Ours  
+#
+
+![](images/68ba081301377f53bfaaee902c9a51e5982f8163745f226edc345e56566c5a18.jpg)  
+↓
+
+![](images/148a3ddb5a10b52102a706c2944571047c599eb124d814bb5a1cfc15617ac5ef.jpg)  
+#
+
+![](images/d3384ea5a5afd27455b064cf0ad9abc01b0bae99b57fc06e4db2917866cff6c3.jpg)  
+#
+
+![](images/9b4b29122f52010ea293235e77f10f3ea11a3c563efd6c119f9164f589b499d2.jpg)  
+#
+
+![](images/83c4e1b75985402b7ebe08be14122347bdad51b444ec34b25e67eda4e058c558.jpg)  
+#
+
+![](images/77e2907f300acde88f7bf1962ea098b993fd9fc188e55c3d8a21a4032350ddb7.jpg)  
+#
+
+![](images/e7cf7d55eeff041ea6924ef8e4e38373479e300931c9591b0d0721e027737155.jpg)  
+Figure 14. Our method is compatible with StyleGAN image editing [28]. StyleGAN2: interpolation between defective images synthesized by StyleGAN2; Ours: images "corrected" by our feature rescaling method.  
+Fig. 14 shows similar observations for StyleGAN image editing. These suggest that our method preserves StyleGAN latent semantics and is thus compatible with various StyleGAN latent space operations.
+
+![](images/aa08e0f76583eede797989d1d1e3cc89fe62034cb79736bcba847c772eac5a2c.jpg)  
+#
+
+![](images/2bd6d6ab3a1437470eb1eb071b83856d8e940bf2c428c2900563ebcccca91f49.jpg)
+
+![](images/8726c33a435ad64ecc371cb2be217a751f80975ef593942fcb1ada5fe2da4037.jpg)  
+#
+
+![](images/635d3a55946f2e4a284d131d1feeb8056dce6597bc7e4e6ff29f9ee785a474d2.jpg)
+
+![](images/929613357275ce0339439328443fb252ed4228f53627e6666f99ba0a16de3a6a.jpg)  
+#
+
+![](images/85c35d482047d56b4df7a69309b7fd36c6b5b05e9ad6e4e009a0c94361cfafb3.jpg)
+
+![](images/99588d5e4c8a011b5d56af7ee62fa435f2a9169a837aadecb4d5eb557ad3a97a.jpg)  
+#
+
+![](images/ddfa9e322d116a2d6c7266d6c9430e3aef23542396c7e42d93eec15b62399e16.jpg)
+
+# 6. Conclusion
+
+In this paper, we propose a novel feature identification and rescaling method to address the artifacts in StyleGAN synthesized images. The rationale of the proposed feature rescaling method stems from the Feature Proliferation phenomenon we discovered that has a strong causal relationship with StyleGAN image artifacts. Specifically, we observed that the features that deviate significantly from the mean of their distribution are highly likely to dominate the output of a neuron and proliferate in the forward propagation. As a result, the output of the entire network will be dominated by a small number of features. We ascribe this to the strong statistical assumption used in the weight modulation and demodulation used by the StyleGAN family. Intuitively, we name Feature Proliferation as the "cancer" in StyleGANs from its proliferating and malignant nature. Experimental results demonstrate that our method achieves a better tradeoff between quality and diversity of StyleGAN synthesized images than the popular truncation trick.
+
+Limitation and Future Work. Although effective and significantly better than the truncation trick, the proposed method is not perfect as it can still remove some useful image features and make minor changes to high-quality StyleGAN synthesized images. We plan to design more precise
+
+methods to identify and process proliferating features in future work. In addition, we believe that Feature Proliferation is not a problem exclusive to StyleGAN and may occur in other works as long as weight modulation and demodulation techniques are used (Sec. 3.2). Thus, we plan to investigate in future work whether feature proliferation is a common phenomenon in various network architectures and its consequences in different tasks.
+
+Potential Negative Social Impact. Although our method works as a post-hoc "cure" for StyleGAN synthesized images and can save millions of dollars in training costs and energy consumption, it may also lead to potentially negative social impacts. For example, it can further improve the quality of StyleGAN synthesized images, which may facilitate the creation of fake portrait photos/videos for fake social media accounts and fake news. Nevertheless, we still believe that our work will make a positive contribution to the field and provide new insights into the mechanisms of generative models that may help identify such fake content.
+
+# Acknowledgements
+
+We thank the reviewers for their constructive comments that helped improve this paper. This work was partially supported by the China Scholarship Council (CSC) under Grant No. 202106150033 and the UK Engineering and Physical Sciences Research Council (EPSRC) through the Doctoral Training Partnerships (DTP) with No. EP/T517951/1 (2599521).
+
+# References
+
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+[2] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2StyleGAN++: How to edit the embedded images? In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8296-8305, 2020.  
+[3] Yuval Alaluf, Omer Tov, Ron Mokady, Rinon Gal, and Amit Bermano. HyperStyle: StyleGAN inversion with hypernetworks for real image editing. In Proceedings of the IEEE/CVF conference on computer Vision and pattern recognition, pages 18511-18521, 2022.  
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+
+versarial networks with limited data. Advances in Neural Information Processing Systems, 33:12104-12114, 2020.  
+[15] Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Alias-free generative adversarial networks. Advances in Neural Information Processing Systems, 34, 2021.  
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+[22] Lars Mescheder, Andreas Geiger, and Sebastian Nowozin. Which training methods for GANs do actually converge? In International conference on machine learning, pages 3481-3490. PMLR, 2018.  
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+[26] Elad Richardson, Yuval Alaluf, Or Patashnik, Yotam Nitzan, Yaniv Azar, Stav Shapiro, and Daniel Cohen-Or. Encoding in style: a StyleGAN encoder for image-to-image translation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2287–2296, 2021.  
+[27] Axel Sauer, Tero Karras, Samuli Laine, Andreas Geiger, and Timo Aila. StyleGAN-T: Unlocking the power of GANs for fast large-scale text-to-image synthesis. arXiv preprint arXiv:2301.09515, 2023.  
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+In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXII 16, pages 170-186. Springer, 2020.  
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\ No newline at end of file
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+                                            "type": "text",
+                                            "content": "- We propose a novel feature rescaling method that identifies and modulates risky features to mitigate feature proliferation, thereby achieving a better trade-off between quality and diversity of StyleGAN synthesized images than the popular truncation trick."
+                                        }
+                                    ]
+                                }
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+                                    "content": "2. Related work"
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+                                    "content": "Since the seminal work of Goodfellow et al. [10], Generative Adversarial Networks (GANs) have become one of the most promising deep generative models that have numerous applications in computer vision and graphics. Nevertheless, GANs are known to be notoriously difficult to train and a variety of techniques have been proposed to"
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+                                    "content": "stabilize their training from different perspectives, including architectures [25, 11], loss functions [4, 19], regularization [22, 23], and the interactions between them [24]. Thanks to the massive efforts from the community, the StyleGAN series [16, 17, 15, 27] have become one of the most influential models in the GAN family, as it can generate high-resolution and realistic images that are almost indistinguishable from real photos by human inspectors. Examples of its applications include GAN inversion and editing [1, 2, 29, 3], image-to-image translation [26], superresolution [21], 3D shape generation [32], etc. We refer interested audiences to [5] for a survey on StyleGAN and its applications. Nevertheless, despite its success, the quality of images synthesized by StyleGAN varies, and a post-processing method known as the truncation trick [20, 6] has widely been adopted to obtain higher quality images. However, the truncation trick has long been noted as \"destructive\" as it unnecessarily sacrifices useful image features and tends to reduce the diversity of synthesized images. In this paper, we address this issue by investigating the StyleGAN image synthesis mechanism and propose a feature rescaling method that can precisely identify the risky features causing image artifacts, thereby improving image quality by modulating these features at the minimal cost."
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+                                    "content": "3. Feature Proliferation in StyleGAN"
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+                                    "content": "In this section, we first introduce two new phenomena that we discovered in the forward propagation of deep neural networks, i.e. feature domination and proliferation. We then show that they are by-products of the weight modulation and demodulation techniques used in modern StyleGANs. Finally, we show how they affect StyleGAN and lead to artifacts in synthesized images."
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+                                            "content": "Figure 2. Illustration of feature domination. "
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+                                            "type": "text",
+                                            "content": " and its perturbations "
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+                                    "content": "3.1. Feature Domination and Proliferation"
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+                                    "content": "Throughout the history of machine learning, the weighted sum method has been built to last from the classical linear regression, to the theoretically elegant support vector machines and the deep neural networks that are now taking both academia and industry by storm. For deep neural networks, we usually refer to the output of neurons as features that are the elements to be weighted and summed. However, due to the differences among weights and input features, the output of a neuron can occasionally be dominated by one or a small amount of input features, which leads to a phenomenon we call Feature Domination."
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+                                    "content": "Definition 3.1 (Feature Domination) Let "
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+                                    "content": " be the output of a neuron, "
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+                                    "content": " denotes the bias, we define Feature Domination as the case where "
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+                                    "content": "In a nutshell, the proposed Feature Domination describes the phenomenon that one or a small number of similar input features may dominate the weighted sum if their products with associated weights significantly outweigh others (Fig. 2), making "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". In practice, we observed that the dominant features are highly likely to be those that deviate significantly from the mean of their distributions:"
+                                }
+                            ]
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+                                    "content": "Observation 3.1 (Feature Domination in StyleGAN)"
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+                                    "content": " of the generator. "
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+                                    "content": " is highly likely to be dominant if "
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+                                    "type": "inline_equation",
+                                    "content": "\\frac{|\\mathrm{mean}(x_{l,j}) - \\mu_{x_{l,j}}|}{\\sigma_{x_{l,j}}} > t"
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+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": " are the mean and standard deviation of the distribution of "
+                                },
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+                                    "type": "text",
+                                    "content": " over the training dataset."
+                                }
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+                                    "content": "In practice, we use Observation 3.1 to identify dominant features in StyleGANs. Furthermore, Feature Proliferation happens when the same type of Feature Domination proliferates during the forward propagation."
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+                                            "content": "(a) Mean of inputs"
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+                                            "content": "(b) Standard deviation of inputs"
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+                                            "content": "Figure 3. Histograms of mean and standard deviation of the input feature maps from 10,000 StyleGAN2 synthesized images."
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+                                    "content": "Definition 3.2 (Feature Proliferation) Following Definition 3.1, let "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y}_d(x_j)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " be the set consisting of all outputs "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " dominated by feature "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " in a single neural network layer, we define Feature Proliferation as the increase of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\eta(x_j) = |\\mathbf{Y}_d(x_j)| / |\\mathbf{Y}|"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " during forward propagation, where "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the set of all outputs in a single neural network layer and "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " denotes the cardinality of a set."
+                                }
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+                                    "type": "text",
+                                    "content": "When Feature Proliferation happens, one or a small number of features will dominate the output of the entire network, leading to artifacts in StyleGAN synthesized images. As an analogy, we refer to it as the \"cancer\" in StyleGAN from its proliferating and malignant nature."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Remark. For simplicity, Definitions 3.1 and 3.2 are introduced with fully-connected layers. However, both definitions can be easily extended to other types of neural networks, e.g., convolutional neural networks (CNNs) [30], as the weighted sum operation is widely used in almost all deep neural networks due to its benefits in parallelization."
+                                }
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+                                    "type": "text",
+                                    "content": "3.2. Root Causes of Feature Proliferation"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "We ascribe feature proliferation to the strong statistical assumption used in the weight modulation and demodulation of StyleGAN2/3/T [17, 15, 27], i.e., \"the input activations are i.i.d. random variables with unit standard deviation\", rather than the statistics (i.e., mean and standard deviation) of the actual feature maps used in the AdaIN of StyleGAN1 [16]."
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+                                    "type": "text",
+                                    "content": "Specifically, weight demodulation assumes that all input activations (modulated feature maps) are already normalized to be of unit standard deviation, thereby eliminating the step of feature map normalization "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\frac{\\mathbf{x}_i - \\mu(\\mathbf{x}_i)}{\\sigma(\\mathbf{x}_i)}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": " used in AdaIN. Since the standard deviations of output feature maps are determined by the products of those of their input feature maps (assumed to be unit ones as mentioned above) and convolutional weights, the abovementioned assumption ensures the unit standard deviations of output feature maps by only \"demodulating\" the convolutional weights to be of unit standard deviations [17]:"
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+                                    "type": "interline_equation",
+                                    "content": "w _ {i j k} ^ {\\prime \\prime} = w _ {i j k} ^ {\\prime} / \\sqrt {\\sum_ {i} w _ {i j k} ^ {\\prime 2} + \\epsilon}, w _ {i j k} ^ {\\prime} = s _ {i} \\cdot w _ {i j k} \\tag {1}",
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+                                            "content": "Figure 4. Left: ('Cancer' Proliferation) the Feature Proliferation phenomenon leads to image artifacts; (Curing) setting the visually identified proliferating feature map in Layer 3 to zero (blue arrow) mitigates feature proliferation. Right: (Normal Generation) a proper StyleGAN image synthesis process; (Inserted 'Cancer' Proliferation) inserting the \"cancer\" features identified in the left part results in feature proliferation and similar image artifacts (red arrow). The yellow boxes in feature maps highlight the feature proliferation process. "
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+                                            "type": "text",
+                                            "content": " in red: the ratio of dominated features in a layer."
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+                                    "content": " is the scaling parameter corresponding to the "
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+                                    "type": "text",
+                                    "content": "-th input feature map, "
+                                },
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+                                    "type": "inline_equation",
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+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "k"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " enumerate the output feature maps and spatial footprint of the convolution, respectively. While in practice, the assumption of the unit standard deviation of input activations does not hold (Fig. 3). As a result, weight demodulation cannot ensure the unit standard deviations of output feature maps. Instead, the standard deviations of output feature maps are determined by those of input ones, causing feature domination and proliferation."
+                                }
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+                                    "type": "text",
+                                    "content": "Remark. AdaIN explicitly normalizes each feature map according to its mean and standard deviation so the mean and standard deviation of its output are solely determined by the style parameters "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y} = (\\mathbf{y}_s, \\mathbf{y}_b)"
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+                                    "type": "text",
+                                    "content": " but not those of its input feature map "
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+                                    "type": "text",
+                                    "content": " [16]:"
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {A d a I N} \\left(\\mathbf {x} _ {i}, \\mathbf {y}\\right) = \\mathbf {y} _ {s, i} \\frac {\\mathbf {x} _ {i} - \\mu \\left(\\mathbf {x} _ {i}\\right)}{\\sigma \\left(\\mathbf {x} _ {i}\\right)} + \\mathbf {y} _ {b, i} \\tag {2}",
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+                                    "type": "text",
+                                    "content": "This breaks the chain of feature proliferation in forward propagation and we did not observe significant proliferation in our experiments. However, as shown in [17], AdaIN has its own problems (i.e., the \"characteristic artifacts\", which is why weight demodulation is used in StyleGAN2/3) and may not be a good solution to feature proliferation."
+                                }
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+                                    "type": "text",
+                                    "content": "3.3. Impact of Feature Proliferation on StyleGAN"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "As Fig. 4 shows, the synthesized images suffer from obvious artifacts when Feature Proliferation happens and we observed a strong spatial correlation between the proliferated feature maps and the artifacts in synthesized images. To justify the causality between them, we show that i) the artifacts can be \"cured\" by removing corresponding features before their proliferation in Fig. 4 (left) and ii) the artifacts can be added to high-quality images by inducing feature proliferation in Fig. 4 (right)."
+                                }
+                            ]
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+                                    "content": "4. Curing the \"Cancer\" in StyleGAN"
+                                }
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+                                    "content": "In this section, we first introduce how to identify the risky features for feature proliferation and then introduce a simple but effective feature rescaling method to adjust the identified features and mitigate the feature proliferation."
+                                }
+                            ]
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+                                    "content": "4.1. Feature Proliferation (\"Cancer\") Identification"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Naively, one of the most straightforward methods for feature proliferation identification is to extract all similar pairs of feature maps in the successive layers of a neural network. However, let "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " be the number of successive pairs of layers and "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " be the number of neurons per layer, the time complexity of this strategy is "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "O(kn^2)"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " per image, which is inefficient and makes it infeasible for frequent use."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Addressing this issue, we employ a heuristic stemming from Observation 3.1 that the dominant features are likely to be those that deviate significantly from the mean of their distributions. Specifically, we estimate the mean "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mu_{l,j}"
+                                },
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+                                    "type": "text",
+                                    "content": " and standard deviation "
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+                                    "type": "inline_equation",
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+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " with a large number (e.g., 3,000) of randomly sampled images and identify "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " as a high risk feature for proliferation if:"
+                                }
+                            ]
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+                    ],
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+                                    "content": "r _ {l, j} = \\frac {\\left| \\operatorname {m e a n} \\left(x _ {l , j}\\right) - \\mu_ {l , j} \\right|}{\\max  \\left(\\sigma_ {l , j} , c\\right)} > t \\tag {3}",
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+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{mean}(x_{l,j})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the mean value of all elements in "
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+                                    "content": " denotes the amount of risk of feature proliferation, "
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+                                    "content": " is a user-defined threshold obtained empirically, "
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+                                    "content": "c = 0.1"
+                                },
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+                                    "type": "text",
+                                    "content": " is a small constant introduced to avoid the mis-identification when "
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+                                    "type": "text",
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+                                }
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+                                            "content": "(d) StyleGAN3 pretrained on AFHQ dataset"
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+                                            "content": "Figure 5. Curated StyleGAN2/3 [17, 15] synthesized images, those processed by the truncation trick "
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+                                            "type": "text",
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+                                    "content": "earliest layers, thereby removing the least amount of them and minimizing the unnecessary interference with useful image features. Let "
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+                                    "type": "text",
+                                    "content": " be a \"cancer\" feature map with risk "
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+                                    "type": "text",
+                                    "content": " (Eq. 3), we have"
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+                                    "type": "interline_equation",
+                                    "content": "x _ {c} ^ {m} = \\frac {x _ {c}}{p \\cdot r} \\tag {4}",
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+                                    "type": "text",
+                                    "content": " denotes the modified feature map, "
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+                                    "type": "text",
+                                    "content": " is the scaling hyper-parameter. By rescaling "
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+                                    "type": "text",
+                                    "content": ", we reduce the values of its elements and thus prevent it from Feature Domination (Definition 3.1) and Proliferation (Definition 3.2), thereby improving the quality of StyleGAN synthesized images."
+                                }
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+                        }
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+                {
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+                                    "content": "5. Experiments"
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+                                    "type": "text",
+                                    "content": "Please see the supplement for more experiments."
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+                                    "content": "5.1. Experimental Setup"
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+                                    "type": "text",
+                                    "content": "The proposed method does not require network training. We run the proposed method with pretrained deep generative models on a workstation with an Intel(R) Core(TM) i7-10875H CPU and a GeForce RTX 3080 GPU. The pretrained StyleGAN2 [17] models (using FFHQ [16], MetFace [14] and AFHQ-Cat [8] datasets) used in all our experi"
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+                                    "type": "text",
+                                    "content": "iments are publicly-released on "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". Unless specified, we use hyperparameters "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for our method, and "
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " for the truncation trick that has been suggested for the best trade-off between quality and diversity of synthesized images [16, 6]."
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+                            ]
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+                                    "type": "text",
+                                    "content": "As Fig. 5 shows, we compare the performance of our method against the truncation trick [20, 6] on StyleGAN2 and StyleGAN3 models pretrained on FFHQ, MetFace and AFHQ-Cat datasets. In Fig. 5(a), it can be observed that: i) all the StyleGAN2 synthesized images in the top row, except the third one, contain obvious artifacts; ii) for the third column (high-quality image), our method retains useful image features better than the truncation trick; iii) for the other columns, our method not only removes the artifacts but also retains useful image features in a better way, e.g., the truncation trick eliminates the eyeglasses in column 1 while our method retains them and other fine facial details like the beard. Similar results can be observed in Fig. 5(b), which demonstrates the versatility of our method across datasets."
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+                                            "content": " of our method; Red: the upper bound of StyleGAN \"correction\" methods where every error is corrected (precision=1.0) without sacrificing diversity (recall remains constant); Orange: the closer to the dashed line, the less sacrifice of diversity; Gray: region of uninterest where too much diversity has been sacrificed. Ours is closer to the dashed line in the region of interest, indicating that it strikes a better balance between precision and recall."
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+                                    "content": "Figs. 5(c) and 5(d) show synthesized results of the truncation trick and our method on StyleGAN3 [15] models pretrained on FFHQ and AFHQ datasets<sup>4</sup>. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method."
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+                                            "content": "Table 2. Comparison with Truncation Trick (TT) [6] using PSNR, SSIM [33], LPIPS [31] and FID [12] computed with 10K images on StyleGAN3."
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+                                            "html": "<table><tr><td rowspan=\"2\">Dataset Method</td><td colspan=\"2\">FFHQ</td><td colspan=\"2\">AFHQ-Cat</td></tr><tr><td>TT</td><td>Ours</td><td>TT</td><td>Ours</td></tr><tr><td>PSNR↑</td><td>16.23</td><td>18.07</td><td>16.03</td><td>17.72</td></tr><tr><td>SSIM↑</td><td>0.70</td><td>0.78</td><td>0.70</td><td>0.76</td></tr><tr><td>LPIPS↓</td><td>0.33</td><td>0.22</td><td>0.16</td><td>0.13</td></tr><tr><td>FID↓</td><td>22.45</td><td>14.31</td><td>24.02</td><td>17.36</td></tr></table>",
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+                                    "content": "the aims of StyleGAN correction methods are to maximize image quality (i.e., precision) without sacrificing diversity (i.e., recall), our method has made a concrete step towards the ultimate solution (red point in Fig. 6)."
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+                                    "content": "Image Similarity Metrics. Although less effective in assessing the trade-off between quality and diversity, for the sake of completeness, we also quantitatively compare the extent to which image features are retained by our method and the truncation trick [20, 6]. As Table 1 shows, for StyleGAN2, it can be observed that i) for PSNR, SSIM [33] and LPIPS [31], our method outperforms the truncation trick in most cases, which demonstrates that our method better retains the useful features in the original image. However, the SSIM of our method is slightly worse than that of the truncation trick for the FFHQ dataset. We ascribe this to the superior power of our method in removing structural artifacts that are common in StyleGAN pretrained with the FFHQ dataset. ii) For ID, we used the ArcFace [9] to compute the identity similarity scores between the original and the processed images. Interestingly, we observe that although"
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+                                    "content": "<sup>4</sup>https://github.com/NVlabs/stylegan3"
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+                                            "content": "Figure 8. Choice of hyper-parameters. Top row: images generated with truncation trick with "
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+                                            "type": "text",
+                                            "content": " to 0.95. Rows 2-4: images generated with our method with "
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+                                            "content": "p = 1"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " to 3. Our method removes the artifacts while retaining almost all important features of the original image, indicating that it achieves a better trade-off between image quality and diversity than the truncation trick."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "trained on human face datasets, ArcFace [9] generalizes to AFHQ-Cat [8] and MetFace [14] images and provides meaningful scores. iii) For FID [12], our method outperforms the truncation trick in all three datasets, which again demonstrates that our method better retains the useful features in the original image. We also show the difference maps in Fig. 7 to facilitate intuitive understanding. The results on StyleGAN3 [15] are shown in Table 2. It can be observed that our claims still hold on StyleGAN3, which further justifies the superiority of our method."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "content": "5.4. Choice of Hyper-parameters"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Similar to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\psi"
+                                },
+                                {
+                                    "bbox": [
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+                                        494,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in the truncation trick [20, 6], we use two hyperparameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        494,
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+                                        590
+                                    ],
+                                    "type": "text",
+                                    "content": " for the trade-off between quality and diversity in our method. Between them, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        494,
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+                                        590
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        494,
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+                                    ],
+                                    "type": "text",
+                                    "content": " determines how many feature maps are identified as risky ones for feature proliferation, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        494,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " adjusts the extent to which we rescale such feature maps. In general, the more risky feature maps identified, the stronger rescaling, and the higher quality but less diversity of synthesized images."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Qualitative Justification. As Fig. 8 shows, we visualize the results generated with the truncation trick with "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to 1.0 and our method with "
+                                },
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+                                    "type": "text",
+                                    "content": " to 4.0 and "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to 3.0, and identify the best choice ("
+                                },
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+                                    "type": "inline_equation",
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+                                },
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ") through visual inspection. In general, the smaller the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", the more features are identified as risky (Eq. 3) for rescaling; the larger the "
+                                },
+                                {
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the stronger the rescaling. In this way, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " work together to modify only the problematic features, thus achieving a better trade-off between quality and diversity than the truncation trick."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                            "type": "text",
+                                            "content": "Figure 9. Choice of Hyper-parameters (Quantitative). It can be observed that "
+                                        },
+                                        {
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " (cyan) achieves the best trade-off between precision and recall, which is consistent with the visual inspection results in Fig. 8."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
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+                                    "type": "text",
+                                    "content": "Quantitative Justification. We quantitatively justify the choice of hyper-parameters "
+                                },
+                                {
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+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " by comparing their precision and recall. As Fig. 9 shows, "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "t = 2"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " achieves the best trade-off between precision and recall, which is consistent with the qualitative results in Fig. 8."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "5.5. Ablation Study"
+                                }
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+                                    "type": "text",
+                                    "content": "To justify the effectiveness of our channel-wise feature identification and rescaling strategy (Sec. 4), we demonstrate its superiority over its layer-wise and pixel-wise variants as follows."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Layer-wise \"Cancer\" Curing. As in Sec. 4, let "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "x_{l,j}"
+                                },
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+                                    "type": "text",
+                                    "content": " be a \"cancer\" feature map identified using Eq. 3, we compute the"
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 10. Successful cases of the layer-wise variant of our method (threshold "
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+                                            "content": " ranges from 0.3 to 0.9). It can be observed that this variant is effective in removing artifacts of background intrusion."
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {x} _ {l} = \\operatorname {m e a n} _ {j} (| x _ {l, j} |) \\tag {5}",
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+                                    "type": "text",
+                                    "content": "where we take the absolute value "
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+                                    "type": "text",
+                                    "content": " to capture their magnitude and avoid them canceling each other out when added together. In order to make the same choice of hyperparameters applicable to all layers, we normalize "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with mean "
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+                                    "content": "\\mu = 0"
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+                                    "type": "text",
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+                                    "content": "\\sigma = 1"
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+                                    "type": "text",
+                                    "content": ":"
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {x} _ {l} = \\frac {\\hat {x} _ {l} - \\mu (\\hat {x} _ {l})}{\\sigma (\\hat {x} _ {l})} \\tag {6}",
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+                                    "type": "text",
+                                    "content": "Then we measure the \"correlation\" between each "
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+                                    "type": "text",
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+                                    "content": "c _ {l, j} = \\frac {\\left| x _ {l , j} \\right| * \\bar {x} _ {l}}{\\sum_ {\\text {e l e m e n t}} \\left| x _ {l , j} \\right|} \\tag {7}",
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+                                    "type": "text",
+                                    "content": ". Let "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " be a threshold hyper-parameter, if "
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+                                    "type": "text",
+                                    "content": ", we mark "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " as a layer-wise \"cancer\" feature map and perform the same feature rescaling on it to remove image artifacts. As Fig. 10 shows, this layer-wise variant of our method is also effective for certain types of image artifacts (e.g., background intrusion). While for some other types of artifacts (e.g., alien objects), it becomes less effective (Fig. 11)."
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+                                    "type": "text",
+                                    "content": "Pixel-wise \"Cancer\" Curing. We follow ProGAN [13] and apply its pixel-wise feature vector normalization technique, which was originally proposed to stabilize GAN training by resolving the potentially exploding magnitudes in the generator and discriminator, to pre-trained StyleGAN2. However, we observed that even the normally synthesized images become unrealistic (Fig. 12), indicating that it is not applicable to our problem."
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+                                    "content": "5.6. Time Complexity"
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+                                    "content": "Table 3 shows the time costs of generating a single image for StyleGAN2, ours implemented in serial, and ours implemented in parallel on an Nvidia V100 GPU. It can"
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+                                            "type": "text",
+                                            "content": "Figure 11. Failure cases of the layer-wise variant of our method (threshold "
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+                                            "type": "text",
+                                            "content": "). It can be observed that this variant is ineffective in removing artifacts of alien objects (e.g., color blocks on faces) while our method can remove them effectively. Top row: low-quality images synthesized by StyleGAN2; Middle row: results of the layer-wise variant of our method; Bottom row: results of our method."
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+                                            "type": "text",
+                                            "content": "Table 3. Time costs of generating a single image for StyleGAN2, Ours (Serial) and Ours (Parallel) on an Nvidia V100 GPU. The time is averaged over 100 runs."
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+                                            "html": "<table><tr><td>Dataset</td><td>FFHQ</td><td>AFHQ</td></tr><tr><td>SG2</td><td>0.075s</td><td>0.031s</td></tr><tr><td>Ours (Serial)</td><td>0.972s</td><td>0.721s</td></tr><tr><td>Ours (Parallel)</td><td>0.409s</td><td>0.189s</td></tr></table>",
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+                                    "content": "be observed that the parallel implementation of our method significantly reduces the time costs from a factor of approximately 15-20 (Serial) to approximately 5 times those of the original StyleGAN2 (SG2). We leave further acceleration of our method to future work."
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+                                    "content": "In this paper, we propose a novel feature identification and rescaling method to address the artifacts in StyleGAN synthesized images. The rationale of the proposed feature rescaling method stems from the Feature Proliferation phenomenon we discovered that has a strong causal relationship with StyleGAN image artifacts. Specifically, we observed that the features that deviate significantly from the mean of their distribution are highly likely to dominate the output of a neuron and proliferate in the forward propagation. As a result, the output of the entire network will be dominated by a small number of features. We ascribe this to the strong statistical assumption used in the weight modulation and demodulation used by the StyleGAN family. Intuitively, we name Feature Proliferation as the \"cancer\" in StyleGANs from its proliferating and malignant nature. Experimental results demonstrate that our method achieves a better tradeoff between quality and diversity of StyleGAN synthesized images than the popular truncation trick."
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+                                    "content": "Limitation and Future Work. Although effective and significantly better than the truncation trick, the proposed method is not perfect as it can still remove some useful image features and make minor changes to high-quality StyleGAN synthesized images. We plan to design more precise"
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+                                    "content": "methods to identify and process proliferating features in future work. In addition, we believe that Feature Proliferation is not a problem exclusive to StyleGAN and may occur in other works as long as weight modulation and demodulation techniques are used (Sec. 3.2). Thus, we plan to investigate in future work whether feature proliferation is a common phenomenon in various network architectures and its consequences in different tasks."
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+                                    "content": "Potential Negative Social Impact. Although our method works as a post-hoc \"cure\" for StyleGAN synthesized images and can save millions of dollars in training costs and energy consumption, it may also lead to potentially negative social impacts. For example, it can further improve the quality of StyleGAN synthesized images, which may facilitate the creation of fake portrait photos/videos for fake social media accounts and fake news. Nevertheless, we still believe that our work will make a positive contribution to the field and provide new insights into the mechanisms of generative models that may help identify such fake content."
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+                                    "content": "Acknowledgements"
+                                }
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+                                    "content": "We thank the reviewers for their constructive comments that helped improve this paper. This work was partially supported by the China Scholarship Council (CSC) under Grant No. 202106150033 and the UK Engineering and Physical Sciences Research Council (EPSRC) through the Doctoral Training Partnerships (DTP) with No. EP/T517951/1 (2599521)."
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+                                }
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+                                            "type": "text",
+                                            "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2StyleGAN: How to embed images into the StyleGAN latent space? In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4432-4441, 2019."
+                                        }
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+                                        }
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+                                        }
+                                    ]
+                                }
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+                            "index": 0
+                        },
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+                                        }
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+                                        }
+                                    ]
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+                                        }
+                                    ]
+                                }
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+                            "index": 5
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diff --git a/2023/FeatureNeRF_ Learning Generalizable NeRFs by Distilling Foundation Models/77c2128e-07a6-41a1-8c05-52f5da1cd81d_content_list.json b/2023/FeatureNeRF_ Learning Generalizable NeRFs by Distilling Foundation Models/77c2128e-07a6-41a1-8c05-52f5da1cd81d_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..809c65c2231216d35119798534d04427def32ccf
--- /dev/null
+++ b/2023/FeatureNeRF_ Learning Generalizable NeRFs by Distilling Foundation Models/77c2128e-07a6-41a1-8c05-52f5da1cd81d_content_list.json	
@@ -0,0 +1,1726 @@
+[
+    {
+        "type": "text",
+        "text": "FeatureNeRF: Learning Generalizable NeRFs by Distilling Foundation Models",
+        "text_level": 1,
+        "bbox": [
+            86,
+            130,
+            880,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Jianglong Ye<sup>1</sup> Naiyan Wang<sup>2</sup> Xiaolong Wang<sup>1</sup>  \n<sup>1</sup>UC San Diego <sup>2</sup>TuSimple",
+        "bbox": [
+            264,
+            178,
+            702,
+            219
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/21fb390b2f40c0010e19ee41d23f8a40107b54f8fcb8e189ad79ccf1740aa8df.jpg",
+        "image_caption": [
+            "Figure 1: While most generalizable NeRFs focus on novel-view synthesis, we propose a framework named FeatureNeRF to learn 3D semantic representations by distilling vision foundation models. After distillation, FeatureNeRF allows to render novel-view feature maps given a single input image (a), which can be leveraged to various downstream tasks. Here, we show how we propagate part segmentation labels and keypoints to different views and instances in both 2D and 3D domains (b)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            244,
+            303,
+            414
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/c07f48ba6b67bcfbbfd5d604adb0f028366dc77bc0bb75193b63a6e4135bf3c3.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            310,
+            244,
+            893,
+            414
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            496,
+            313,
+            512
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent works on generalizable NeRFs have shown promising results on novel view synthesis from single or few images. However, such models have rarely been applied on other downstream tasks beyond synthesis such as semantic understanding and parsing. In this paper, we propose a novel framework named FeatureNeRF to learn generalizable NeRFs by distilling pre-trained vision foundation models (e.g., DINO, Latent Diffusion). FeatureNeRF leverages 2D pre-trained foundation models to 3D space via neural rendering, and then extract deep features for 3D query points from NeRF MLPs. Consequently, it allows to map 2D images to continuous 3D semantic feature volumes, which can be used for various downstream tasks. We evaluate FeatureNeRF on tasks of 2D/3D semantic keypoint transfer and 2D/3D object part segmentation. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor. Our project page is available at https://jianglongye.com/featuresenerf/.",
+        "bbox": [
+            75,
+            527,
+            473,
+            816
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            844,
+            209,
+            859
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural fields have emerged as a compelling paradigm for representing a variety of visual signals [8, 10, 31, 32, 37]. In",
+        "bbox": [
+            76,
+            869,
+            470,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "particular, the Neural Radiance Fields (NeRF [32]), which implicitly encodes density and color via Multi-Layer Perceptrons (MLPs), has shown high quality novel view synthesis results from dense input images. A body of follow-up works [7, 27, 45, 54, 66] further reduce the dependency on dense inputs and generalize NeRF to unseen objects by learning priors from large-scale multi-view image datasets. With the remarkable abilities on reconstruction and view synthesis of generalizable NeRFs, we ask the question: Can we adapt such models to learn 3D representations as foundations for general 3D applications (e.g., recognition, matching) beyond view synthesis?",
+        "bbox": [
+            496,
+            497,
+            892,
+            679
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent years have witnessed the rise of vision foundation models [5, 40, 43, 67] that are pre-trained on web-scale image datasets and demonstrate generalization capabilities across massive vision tasks (e.g., CLIP [40], DINO [5], Latent Diffusion [47]). The feature space constructed by foundation models captures rich semantic and structural information of 2D visual data and make it possible to identify object categories, parts and correspondences even without extra supervisions [1, 5, 30]. Motivated by these works, our goal is to leverage the powerful 2D foundations models to obtain generalizable 3D features.",
+        "bbox": [
+            496,
+            684,
+            893,
+            849
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling pretrained 2D vision foundation models. Unlike previous gen",
+        "bbox": [
+            498,
+            854,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "8962",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "eralizable NeRFs [45, 66], which utilize 2D encoder solely for novel view synthesis, FeatureNeRF explores the use of deep features extracted from NeRFs as generalizable 3D visual descriptors. We show that distilling 2D foundation models into 3D space via neural rendering equips the NeRF features with rich semantic information. As a result, FeatureNeRF allows to predict a continuous 3D semantic feature volume from a single or a few images, which can be applied to various downstream tasks such as semantic keypoint transfer and object part co-segmentation. Examples of these applications are shown in Fig. 1.",
+        "bbox": [
+            80,
+            90,
+            467,
+            256
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Specifically, we adopt an encoder to map 2D images to corresponding 3D NeRF volume similar to previous generalizable NeRFs. Apart from density and color, we propose to extract deep features of the query 3D points from the intermediate layers of NeRF MLP. To enrich semantic information of the NeRF features, we further transfer knowledge from the foundation models to the encoder via neural rendering during training: The rendered feature outputs should be consistent with the feature extracted from the foundation models, which is enforced by a distillation loss.",
+        "bbox": [
+            80,
+            257,
+            467,
+            407
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To evaluate FeatureNeRF, we tackle the tasks of 2D/3D semantic keypoint transfer and object part segmentation. To the best of our knowledge, our work is the first to resolve these 3D semantic understanding tasks without 3D supervision. We validate our framework with two foundation models: (i) DINO [5], a self-supervised vision transformer aware of object correspondences, and (ii) Latent Diffusion [47], a diffusion-based model that achieves state-of-the-art text-to-image generation performance. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor.",
+        "bbox": [
+            80,
+            407,
+            467,
+            574
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            80,
+            588,
+            215,
+            603
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Generalizable NeRFs. In the past few years, neural fields have gained significant attention and led to rapid progress in representing various visual signals [8, 10, 25, 31, 32, 36, 37, 50, 52, 61]. In particular, NeRF [32] achieves photo-realistic results on novel view synthesis by mapping 3D coordinates and 2D viewing directions to density and color via MLPs. However, the original NeRF requires enormous posed images and time-consuming optimization for each single scene. To address these issues, a large number of follow-up methods [9, 23, 27, 45, 46, 54, 56, 66] propose to learn generalizable NeRFs from large-scale multi-view image datasets. For example, PixelNeRF [66] employs an image encoder to condition NeRF on image features, which enables novel views synthesis from a single image and generalizes NeRF to unseen objects. CodeNeRF [23] learns to disentangle shape and texture by learning separate embeddings, allowing shape and texture editing by varying the latent codes. Recent work TransINR [9] is proposed to infer NeRF parameters directly with a vision transformer to over",
+        "bbox": [
+            80,
+            613,
+            467,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "come the information bottleneck of encoder-decoder architecture. However, most of these works focus only on view synthesis. Our work differs from them by learning general-purpose 3D representations for multiple downstream tasks.",
+        "bbox": [
+            503,
+            90,
+            888,
+            151
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Vision Foundation Models. The term foundation model is introduced in [3] to refer to the model pre-trained from data at scale and capable of generalizing to a wide range of downstream tasks. After demonstrating huge impacts in NLP [4, 15, 41], a large family of vision foundation models [5, 40, 42, 43, 47, 58, 62, 67] have been proposed and effectively transferred to various vision tasks. For example, the CLIP model [40] is trained from large-scale image-text data using contrastive learning, and it is shown to be transferable to multiple tasks in a zero-shot manner. The DINO model [5] has shown object segment can emerge automatically with only self-supervision, and the learned feature can be applied in a wide range of visual correspondence and recognition tasks [1, 12, 30, 57]. Besides contrastive learning, recent text-conditioned generative model such as diffusion models [16, 21, 35, 47] have been introduced and shown astonishing performance on image generation. Subsequently, feature spaces learned by these generative models have also been used for recognition tasks such as semantic segmentation [2, 59]. In contrast to the success of 2D foundation models, the 3D counterparts are still suffering from the lack of large-scale annotated datasets and effective architectures [18, 49, 60]. In this paper, we propose to distill the features from 2D foundation models to 3D space via the generalizable NeRFs.",
+        "bbox": [
+            503,
+            154,
+            888,
+            531
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Feature Distillation. For the purpose of model compression and knowledge transfer, distillation has been widely studied by the community. After the pioneering work by Hinton et al. [20], which matches the softmax output distribution of the teacher model to that of the student, numerous methods have been proposed to tackle various tasks [19, 22, 38, 39, 53, 64]. Recently, researchers also propose to distill features from 2D models to 3D space by optimizing neural feature fields [26, 55]. Multiple editing tasks are shown as applications. However, these methods not only require test-time optimization for each single scene, but the learned features are also not generalizable to unseen objects, which makes them unsuitable for general semantic understanding tasks and differ from our work fundamentally.",
+        "bbox": [
+            503,
+            534,
+            888,
+            746
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Semantic Correspondences. Given a pair of visual observation, semantic correspondences learning aims to find corresponding points between them. Several supervised [13, 24, 51] and self-supervised [1, 11, 28] methods have been proposed to resolve this task in 2D and 3D domain respectively. In particular, Amir et al. [1] show that utilizing pre-trained 2D foundation models in a zero-shot manner can achieve competitive results with supervised methods on semantic correspondences. Cheng et al. [11] propose to learn point cloud correspondences via",
+        "bbox": [
+            503,
+            750,
+            888,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "8963",
+        "bbox": [
+            483,
+            946,
+            513,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/1e830e67dec17bdf6c37b72751bb6589f18f335c8bac3b241caf141368b54645.jpg",
+        "image_caption": [
+            "Figure 2: Pipeline of FeatureNeRF. Given a single image  $I$  as input, FeatureNeRF adopts an encoder to extract the image feature  $E_{\\pi(\\mathbf{x})}$ , and then concatenate it with the query point  $\\mathbf{x}$  as well as the view direction  $\\mathbf{d}$  as the inputs for NeRF MLPs. Apart from density  $\\sigma$  and color  $\\mathbf{c}$ , we add two MLP branches to predict the feature vector  $\\mathbf{v}$  and coordinate  $\\hat{\\mathbf{x}}$ , which are supervised by two novel loss terms  $\\mathcal{L}_{\\mathrm{distill}}$  and  $\\mathcal{L}_{\\mathrm{coord}}$  respectively. Consequently, we distill knowledge from 2D vision foundation models to FeatureNeRF. Besides, we propose to extract internal NeRF feature  $\\mathbf{v}_{\\mathrm{NeRF}}$  as 3D-consistent feature representation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            87,
+            885,
+            299
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "self-reconstruction and cross-reconstruction of 3D shapes. To the best of our knowledge, our work is the first to address semantic correspondences in both 2D and 3D space with only 2D observations.",
+        "bbox": [
+            75,
+            426,
+            470,
+            487
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            500,
+            171,
+            513
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We present FeatureNeRF, a unified framework for learning generalizable NeRF from vision foundation models. We give an overview of generalizable NeRFs in Sec. 3.1 and elaborate our feature distillation process in Sec. 3.2. Then we introduce how to learn internal NeRF features for 3D semantic understanding in Sec. 3.3 and downstream applications in Sec. 3.4. The overall pipeline of FeatureNeRF is illustrated in Fig. 2.",
+        "bbox": [
+            75,
+            523,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminary: Generalizable NeRF",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Neural Radiance Fields (NeRF [32]) consists of two functions:  $\\sigma (\\mathbf{x}):\\mathbb{R}^3\\mapsto \\mathbb{R}_+$  that maps a 3D point  $\\mathbf{x}$  to the density  $\\sigma$  and  $\\mathbf{c}(\\mathbf{x},\\mathbf{d}):\\mathbb{R}^{3\\times 3}\\mapsto \\mathbb{R}^3$  that maps a 3D point as well as a unit viewing direction  $\\mathbf{d}$  to color. The radiance field can be rendered and optimized via differentiable volume rendering [29]. Given a pixel's camera ray  $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}$ , which is defined by the camera origin  $\\mathbf{o}\\in \\mathbb{R}^3$ , view direction  $\\mathbf{d}$  and depth  $t$  with bounds  $[t_n,t_f]$ , the estimated color of the ray can be calculated by:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {C}} (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) \\mathbf {c} (\\mathbf {r} (t), \\mathbf {d}) \\mathrm {d} t, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $T(t) = \\exp \\left(-\\int_{t_n}^t\\sigma (s)ds\\right)$ . In practice, the integral is approximated with numerical quadrature by sam",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "pling points along the ray. NeRF is optimized to a single scene with multi-view posed images by minimizing the following reconstruction loss:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e c}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\mathbf {C} (\\mathbf {r}) - \\hat {\\mathbf {C}} (\\mathbf {r}) \\right\\| _ {2} ^ {2}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            591,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{C}(\\mathbf{r})$  is the ground truth color of the ray and  $\\mathcal{R}$  is the set of rays generated from camera poses.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In order to generalize to novel scenes, the NeRF model can be conditioned on the input image  $I \\in \\mathbb{R}^{H \\times W \\times 3}$ :",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma (\\mathbf {x}, I) = g _ {\\sigma} \\left(\\mathbf {x}, f (I) _ {\\pi (\\mathbf {x})}\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            581,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {c}} \\left(\\mathbf {x}, \\mathbf {d}, f (I) _ {\\pi (\\mathbf {x})}\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            584,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $g_{\\sigma}$  and  $g_{\\mathbf{c}}$  are MLPs that predict density and color respectively,  $f$  is an image encoder and  $\\pi$  is the projection function.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As shown in the left part of Fig. 2, the image  $I$  is firstly passed to an encoder  $f_{\\mathrm{enc}}$  (blue blocks in the figure) to obtain a feature map  $E = f(I)$ . The query point  $\\mathbf{x}$  is projected onto the image plane using known pose and intrinsics to extract the corresponding feature vector  $E_{\\pi (\\mathbf{x})}$ . Then the feature vectors are concatenated with the positional-encoded point  $\\mathbf{x}$  and direction  $\\mathbf{d}$ , and passed to subsequent MLPs  $g_{\\sigma}$  and  $g_{\\mathbf{c}}$  (yellow blocks in the figure) to predict appearance and geometry. When multi-view images are available, feature vectors from different views are aggregated with the average pooling before passing to MLPs.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Feature Distillation from Foundation Models",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "While most generalizable NeRFs only predict density  $\\sigma$  and color c, it's possible to extend NeRF to predict other",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "8964",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "quantities of interests. For example, SemanticNeRF [68] and PanopticNeRF [17] propose to add a branch to predict segmentation labels to achieve a 3D-consistent semantic segmentation of a scene. However, these methods require expensive semantic labels during optimization, which is impractical for general cases. In this paper, we aim to transfer knowledge from a pre-trained foundation model  $f_{\\mathrm{teacher}}$  to our generalizable NeRFs to perform 3D semantic understanding. To this end, we add a branch to output a high-dimensional feature vector  $\\mathbf{v} \\in \\mathbb{R}^{D}$  for the query point  $\\mathbf{x}$ , where  $D$  is the feature channels. Similar to the color rendering (Eq. 1), we can aggregate the feature vectors along a ray as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {V}} (\\mathbf {r}, I) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t), I) \\mathbf {v} (\\mathbf {r} (t), \\mathbf {d}, I) d t \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {v} \\left(\\mathbf {x}, \\mathbf {d}, I\\right) = g _ {\\mathbf {v}} \\left(\\mathbf {x}, \\mathbf {d}, f (I) _ {\\pi (\\mathbf {x})}\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            330,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $g_{\\mathbf{v}}$  is the MLP that predicts future vectors. Note that our model is still conditioned on the image  $I$  in the above equation.",
+        "bbox": [
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+            354,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We then minimize the difference between rendered pixel feature vector  $\\hat{\\mathbf{V}}$  and the teacher's feature  $\\mathbf{V} = f_{\\mathrm{teacher}}(I)_{\\pi (\\mathbf{x})}$ . In this way, we distill the teacher network into our generalizable NeRFs via neural rendering. We add a distillation loss to penalize the difference:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t i l l}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\mathbf {V} (\\mathbf {r}) - \\hat {\\mathbf {V}} (\\mathbf {r}) \\right\\| _ {2} ^ {2}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "FeatureNeRF can be trained jointly for image reconstruction and feature distillation by combing two losses (Eq. 2 and Eq. 5). We show both color rendering and feature rendering processes in the right part of Fig. 2. We emphasize that, after distillation, FeatureNeRF can obtain a 3D semantic feature function  $\\mathbf{v}$  in a single forward pass, which can be used for downstream applications. Our experiments show that the feature function  $\\mathbf{v}$ , learned with only 2D observation, contains accurate 3D semantic information.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our framework can be built on top of any foundation model, and in this work we employ DINO [5] and Latent Diffusion [47] as teacher networks. DINO is a vision transformer trained with self-distillation, and we simply extract features from the deepest layer as teacher features. Latent Diffusion firstly transforms input image  $I$  to the latent space, and utilizes a U-Net [48] architecture to estimate the noise for the backward diffusion process. Besides, the denoising module can be conditioned on inputs like text and segmentation maps. We add noise to the original image, condition the pre-trained model with fixed language prompts (e.g. \"Car\", \"Chair\") and extract features from the intermediate layers of U-Net. Distilling these foundation models that pre-trained on large-scale image datasets brings open-world knowledge to our generalizable 3D representation.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Learning Internal NeRF Features for 3D Semantic Understanding",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Although we have distilled features from foundation models, it is still questionable whether the final feature output is best suitable for 3D semantic understanding. Here we explore using internal NeRF features as view-independent representations for 3D semantic understanding and introduce a new coordinate loss for learning spatial-aware NeRF features.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "While previous works only utilize final outputs of MLPs, we explore whether we can use features from intermediate layers as continuous 3D visual descriptors. Given a input image  $I$ , we firstly learn a function  $\\mathbf{v}_{\\mathrm{NeRF}}(\\mathbf{x},I)$  to predict NeRF features and utilize several shallow MLPs to predict other quantities:",
+        "bbox": [
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+            236,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I) = g _ {\\mathrm {N e R F}} \\left(\\mathbf {x}, f (I) _ {\\pi (\\mathbf {x})}\\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            571,
+            339,
+            815,
+            357
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma (\\mathbf {x}, I) = g _ {\\sigma} \\left(\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            358,
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+            383
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {c}} \\left(\\mathbf {d}, \\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            571,
+            378,
+            794,
+            393
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {v} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {v}} \\left(\\mathbf {d}, \\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            571,
+            397,
+            805,
+            412
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $g_{\\mathrm{NeRF}}$  is MLP that predicts NeRF features. Note that the proposed function  $\\mathbf{v}_{\\mathrm{NeRF}}$  can be learned without the feature distillation introduced in Sec. 3.2, therefore it can be applied to all generalizable NeRFs. The feature extraction process is demonstrated in the bottom of Fig. 2. We compare the performance of NeRF features with and without feature distillation in our experiments.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Even for the feature distillation version, since teacher's features  $\\mathbf{V}$  are always not 3D-consistent, using a view-independent representation  $\\mathbf{v}_{\\mathrm{NeRF}}$  and modeling view-dependent effect using another MLP  $g_{\\mathbf{v}}$  that conditioned on view direction  $\\mathbf{d}$  further boosts the performance (See Sec. 4.4 for the ablation study).",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The supervision of most generalizable NeRFs are RGB values, which do not contain spatial information. To enhance the spatial perception of the NeRF feature, we propose to utilize another MLP branch  $g_{\\mathbf{x}}$  (shown at the top of Fig. 2) to regress the input coordinates  $\\mathbf{x}$  given the NeRF feature  $\\mathbf{v}_{\\mathrm{NeRF}}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {x}} = g _ {\\mathbf {x}} \\left(\\mathbf {v} _ {\\text {N e R F}} (\\mathbf {x}, I)\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We add a cycle-consistent loss to penalize the difference:",
+        "bbox": [
+            500,
+            757,
+            877,
+            772
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c o o r d}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\sum_ {t = t _ {n}} ^ {t _ {f}} \\| \\mathbf {r} (t) - g _ {\\mathbf {x}} \\left(\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {r} (t), I)\\right) \\| _ {2} ^ {2}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            785,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The final loss function is the weighted sum of all three losses:  $\\mathcal{L} = \\mathcal{L}_{\\mathrm{rec}} + \\lambda_{\\mathrm{distill}}\\mathcal{L}_{\\mathrm{distill}} + \\lambda_{\\mathrm{coord}}\\mathcal{L}_{\\mathrm{coord}}$ , where  $\\lambda_{\\mathrm{distill}}$  and  $\\lambda_{\\mathrm{coord}}$  are weights for different losses. All losses and their forward flows are shown in Fig. 2.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "8965",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Applications of FeatureNeRF",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            336,
+            107
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We demonstrate the effectiveness of the learned 3D semantic NeRF feature function  $\\mathbf{v}_{\\mathrm{NeRF}}$  on various downstream applications: 2D/3D semantic keypoint transfer and object part segmentation. We deliberately apply simple, zero-shot methodologies on NeRF features, without any fine-tuning or post-process, to validate the proposed representations.",
+        "bbox": [
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+            114,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2D Tasks. Given a single image  $I$ , we can render its NeRF feature map  $F \\in \\mathbb{R}^{H \\times W \\times D}$  using Eq. 4. Then we can render novel-view feature map  $F'$  from other viewpoints. For feature vectors  $\\mathbf{V}$  and  $\\mathbf{V}'$  of two pixels from  $F$  and  $F'$ , we use cosine similarity to measure their distance in the feature space:  $D(\\mathbf{V}, \\mathbf{V}') = \\frac{\\mathbf{V} \\cdot \\mathbf{V}'}{\\|\\mathbf{V}\\|_2 \\cdot \\|\\mathbf{V}'\\|_2}$ . For the part co-segmentation task, for each pixel feature  $\\mathbf{V}'$  in  $F'$ , we take the segmentation label of its closest pixel feature  $\\mathbf{V}$  in  $F$  as the predicted segmentation label. For the keypoint transfer task, we adopt a similar process, for the feature  $\\mathbf{V}$  of each keypoint in  $F$ , we take the pixel location of its closest feature in  $F'$  as the predicted keypoint.",
+        "bbox": [
+            75,
+            220,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since FeatureNeRF is a generalizable NeRF conditioned on the input image, it can be further applied to cross-instance tasks in addition to novel-view tasks for a single instance. Given images  $I_{1}$  and  $I_{2}$  of two instances, we can render their feature maps  $F_{1}$  and  $F_{2}$ . Then we can resolve semantic correspondence tasks in a process similar to the novel-view tasks.",
+        "bbox": [
+            75,
+            407,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3D Tasks. The FeatureNeRF model learned with only 2D observations can also be leveraged to 3D tasks. Given images  $I_{1}$  and  $I_{2}$  of two instances, we can construct two continuous 3D feature fields. For feature vectors  $\\mathbf{v}_1$  and  $\\mathbf{v}_2$  of two 3D points  $\\mathbf{x}_1$  and  $\\mathbf{x}_2$ , we still utilize cosine similarity to measure their distance:  $D(\\mathbf{v}_1,\\mathbf{v}_2) = \\frac{\\mathbf{v}_1\\cdot\\mathbf{v}_2}{\\|\\mathbf{v}_1\\|_2\\cdot\\|\\mathbf{v}_2\\|_2}$ . Then we can resolve semantic correspondence tasks in a process similar to the 2D tasks.",
+        "bbox": [
+            75,
+            513,
+            467,
+            635
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            654,
+            207,
+            671
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setting",
+        "text_level": 1,
+        "bbox": [
+            76,
+            679,
+            276,
+            695
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. Our experiments are mainly conducted on 6 categories from the ShapeNet [6] dataset: Chair, Car, Airplane, Table, Bottle and Motorcycle. We evaluate our model using annotations from KeypointNet [65], ShapeNet part dataset [63] and PartNet [34]. In addition, we train our model on the real-world CO3D [45] dataset and evaluate its keypoint transfer performance on the Spair [33] dataset. For ShapeNet, we split each category into training (70%), validation (10%), and testing (20%) splits. All shapes are normalized so that the longest edges of the bounding box are equal. For the training set, 50 random camera poses from the upper hemisphere are sampled. For validation and testing sets, 50 fixed camera poses are used. We employ",
+        "bbox": [
+            75,
+            704,
+            467,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "blender [14] to render RGB images, with a resolution of  $128 \\times 128$ , the same as in PixelNeRF [66]. For PartNet, we use level-1 annotations. All annotations are in 3D and can be used for the evaluation of 3D tasks directly. For the evaluation of 2D tasks, we employ PyTorch3D [44] rasterizer to render 2D part segmentation labels and 2D keypoints.",
+        "bbox": [
+            498,
+            90,
+            890,
+            181
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We mainly compare FeatureNeRF quantitatively and qualitatively to two foundation models DINO [5] and Latent Diffusion [47]. We extend PixelNeRF [66] with the mechanisms mentioned in Sec. 3.3 to make it possible for semantic understanding tasks and report its performance as \"NeRF feature\" in all results. In addition, for the 2D cosegmentation task, we re-implement a one-shot generalizable SemanticNeRF* [68] by adding a semantic branch in PixelNeRF, and train it with the source segmentation labels.",
+        "bbox": [
+            498,
+            181,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Following PixelNeRF [66], we employ a ResNet-34 model pre-trained on ImageNet as the image encoder  $f$ . The batch size is 4 (objects) and 1024 rays per object. We train a single model for each object category for 500k steps. The weights for different losses are  $\\lambda_{\\mathrm{distill}} = 0.25$  and  $\\lambda_{\\mathrm{coord}} = 0.25$ . The dimension of the internal NeRF feature is 512. MLP for NeRF feature  $g_{\\mathrm{NeRF}}$  is 4-layer, all other shallow MLPs for final outputs  $(g_{\\sigma}, g_{\\mathbf{c}}, g_{\\mathbf{v}}$  and  $g_{\\mathbf{x}})$  are one-layer.",
+        "bbox": [
+            498,
+            319,
+            890,
+            455
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Teacher Networks. We employ DINO [5] and Latent Diffusion [47] as teacher networks, which are pre-trained and publicly available. The patch size of DINO is 8. The final feature map has dimension  $32 \\times 32 \\times 384$ . For Latent Diffusion, we extract the outputs of the 4th layer in U-Net as teacher features. The language prompts used to condition denoising modules are class names (e.g. \"Chair\", \"Car\") from ShapeNet. The final feature map has dimension  $128 \\times 128 \\times 960$ . The weights of teacher networks are fixed during distillation.",
+        "bbox": [
+            498,
+            455,
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+            606
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. 2D Semantic Understanding Tasks",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in Sec. 3.4, we evaluate FeatureNeRF on tasks of 2D keypoints transfer and part segmentation labels transfer under two settings: (i) Cross-instance: given images of two instances, we transfer keypoints/segmentation labels from the source image to the target image and compare the transferred labels in the target image with the ground truth. (ii) Novel-view: given a single image of an instance, we render a novel-view feature map, transfer labels from the source viewpoint to the target viewpoint and compare the transferred labels in the target viewpoint with the ground truth.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Metrics. For the task of 2D keypoints transfer, we report the percentage of predicted keypoints whose distances from their corresponding ground truths are below thresholds of (2.5, 5.0, 7.5, 10.0) pixels in the target image. We denote this percentage as Correspondence Accuracy in the following. For the task of part segmentation labels trans",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "8966",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/360d8db1b2d2280f22c67cab75b17c30e502f3f62fadff49ec50ffeb0768fff1.jpg",
+        "image_caption": [
+            "Figure 3: Correspondence accuracy for cross-instance semantic keypoints transfer. The first row is for 2D keypoints transfer and the second row is for 3D. Our approach distilled with different features consistently outperforms baselines for all categories in both 2D and 3D domains."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/1f5183ce13abb3eed031c8a185792b740687f60d3fb8e164770aa727edcc6254.jpg",
+        "image_caption": [
+            "(a) 2D results"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/af49cbbf127baf049ffa3f7c025dfea8b0e13e1dc7dfa392c82d9f0697021259.jpg",
+        "image_caption": [
+            "(b) 3D results",
+            "Figure 4: Qualitative results for cross-instance semantic keypoints transfer. Both 2D (a) and 3D (b) results are presented here. Each row contains a source image with keypoints annotations and its pairwise transfer results."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "fer, we calculate the mean intersection over union  $(mIoU)$  over every part category for each object class. For both settings, we randomly generate 1000 combinations per category. While generating, we make sure that the source viewpoints/instances and target viewpoints/instances have intersecting keypoints/segmentation labels.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "2D Keypoints Transfer. We report correspondence accuracy of 2D cross-instance keypoints transfer in the first row of Fig. 3. We show that for all 6 categories, keypoints transferred via our proposed method are more accurate than baselines. The performances of distilling diffusion and DINO features are similar. Using NeRF feature without distilling foundation models (denoted as \"NeRF feature\" in the figure) also achieves a reasonable performance compared to 2D foundation model baselines. Fig. 4 (a) shows the qual",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "itative results for 2D keypoints transfer. It can be seen that despite various appearances and structures of instances, our method can successfully transfer keypoints based on semantic understanding, while baselines often fail.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "FeatureNeRF learns a 3D representation from 2D observations, which allows to synthesize novel-view feature maps for different viewpoints and performs keypoints transfer on top of it. Fig. 6 (a) shows qualitative results of novel-view keypoints transfer. Since 2D foundation models can not synthesize novel-view feature maps, we do not apply them to this novel-view setting.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "2D Part Segmentation Label Transfer. We report mIoU results of 2D cross-instance part segmentation label transfer in the left part of Tab. 1. FeatureNeRF distilled with DINO features significantly outperforms other approaches",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "8967",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/119a059fe338ffddf927ebc2f18602def9f13db319267be7828d1646a0ee201e.jpg",
+        "image_caption": [
+            "Figure 5: Qualitative results for cross-instance part segmentation label transfer. Each row contains a source image and its 2D/3D transfer results. After distilling, FeatureNeRF learns richer semantic information, produces better boundaries and preserves details like small parts. Note that the segmentation label for the source instance is omitted."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ed8d458f02cbc0aed0f3aaa0c54148705d5fd48672817211b906ee2e7b75c030.jpg",
+        "image_caption": [
+            "Figure 6: Qualitative results of novel-view keypoints transfer and part co-segmentation. FeatureNeRF learns a 3D representation from 2D observations, which makes it possible to synthesize feature maps from other viewpoints and transfer keypoints and segmentation labels to them."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            101,
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+            472,
+            513
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/146ce826a2e62b2e21ada216e32a980f976bb22e339e261ecdf596b0683e9139.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            490,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c1335c98a0ac95c18fbeba3e7aec667ddba31b05baaa4851d4cac2d54cad681e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"6\">2D part co-segmentation</td><td colspan=\"6\">3D part co-segmentation</td></tr><tr><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>SemanticNeRF*</td><td>50.32</td><td>34.61</td><td>56.19</td><td>54.87</td><td>51.58</td><td>27.62</td><td></td><td></td><td></td><td>-</td><td></td><td></td></tr><tr><td>Diffusion Baseline</td><td>41.59</td><td>42.46</td><td>44.60</td><td>57.77</td><td>41.72</td><td>25.50</td><td>33.60</td><td>24.74</td><td>30.45</td><td>44.34</td><td>53.81</td><td>20.01</td></tr><tr><td>DINO Baseline</td><td>62.43</td><td>54.59</td><td>57.81</td><td>64.01</td><td>59.73</td><td>37.05</td><td>52.67</td><td>29.72</td><td>40.16</td><td>49.98</td><td>70.79</td><td>29.25</td></tr><tr><td>NeRF Feature</td><td>72.02</td><td>58.57</td><td>72.57</td><td>70.41</td><td>55.87</td><td>44.00</td><td>65.23</td><td>59.19</td><td>71.23</td><td>61.64</td><td>66.63</td><td>44.88</td></tr><tr><td>Ours (Diffusion)</td><td>65.39</td><td>63.02</td><td>72.95</td><td>70.59</td><td>53.91</td><td>44.84</td><td>63.65</td><td>61.27</td><td>73.41</td><td>63.93</td><td>66.91</td><td>49.05</td></tr><tr><td>Ours (DINO)</td><td>76.55</td><td>66.85</td><td>74.60</td><td>74.06</td><td>61.13</td><td>49.56</td><td>73.85</td><td>64.99</td><td>74.20</td><td>66.52</td><td>72.33</td><td>52.56</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Cross-instance part segmentation label transfer results. We report mIoU of part co-segmentation for each category. The left part is for 2D and the right is for 3D. By distilling features to the 3D space, our proposed representation contains richer semantic information which is apt for this co-segmentation task.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "for all 6 categories. However, the performance of FeatureNeRF distilled with diffusion features is not as good as the DINO one. This is possible since the keypoints transfer task may focus on predicting accurate locations of sparse pixels that contain the richest semantic information, but part cosegmentation requires denser correspondences. Qualitative results are shown Fig. 5 (a). We can find that NeRF feature often produces unexpected artifacts. We attribute this phenomenon to NeRF feature's training only relying on RGB",
+        "bbox": [
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+            751,
+            472,
+            888
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "information. In contrast, by distilling pre-trained features, our method produces better boundaries and preserves details like small parts. Note that the segmentation label of the source object is also required during the transfer process, which is omitted in the figure.",
+        "bbox": [
+            496,
+            751,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also perform novel-view part co-segmentation and report both quantitative and qualitative results in Tab. 2 and Fig. 6 (b) respectively. The rendered feature maps from other viewpoints still exhibit promising performance for co",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "8968",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/19aa2a1102f840ace5e2ced29dceae3843fdfe7dbeed6f86eaab627017142b3f.jpg",
+        "image_caption": [
+            "Figure 7: Keypoints transfer on SPair. Our method outperforms NeRF feature on 5 categories on the real-world dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            114,
+            85,
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+            239
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/51ebca655e2ba3e3319f4254220cc26bf476fb546ebc6f33d554ff7e2a730ce1.jpg",
+        "image_caption": [
+            "Figure 8: Keypoints and segmentation label transfer on CO3D. After training on CO3D, our method can accurately transfer keypoints and segmentation labels with in-the-wild image inputs"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            268,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation.",
+        "bbox": [
+            75,
+            565,
+            467,
+            595
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Real-world Experiments. To show the generalizability to real-world images, we fine-tune our model on CO3D datasets and evaluate its keypoints transfer performance on two categories from the SPair dataset. The results in Fig. 7 confirm the effectiveness of our approach over NeRF feature on real images. The qualitative results on CO3D are shown in Fig. 8. Even with in-the-wild images, our method can still transfer keypoints and segmentation labels accurately. Note that pre-process steps (e.g. segment and normalize the foreground object) are required.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3. 3D Semantic Understanding Tasks",
+        "text_level": 1,
+        "bbox": [
+            76,
+            756,
+            377,
+            772
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We further validate our proposed method on 3D semantic understanding tasks, which aims to find semantic correspondences between two sets of 3D points based on image observations. We only evaluate under the cross-instance setting for 3D tasks.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Metrics. The metrics for 3D tasks are 3D versions of their counterparts in 2D tasks. For the keypoints transfer, we utilize Euclidean distance instead of 2D pixel distance with",
+        "bbox": [
+            75,
+            854,
+            467,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/9c989eade534af8d5d290f8302cafb125c349aff3450bd164811b8235be308f4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>NeRF Feat.</td><td>80.73</td><td>75.10</td><td>69.45</td><td>84.65</td><td>87.14</td><td>67.49</td></tr><tr><td>Ours (Diff.)</td><td>73.45</td><td>71.16</td><td>59.16</td><td>83.91</td><td>88.01</td><td>64.28</td></tr><tr><td>Ours (DINO)</td><td>81.93</td><td>76.50</td><td>71.57</td><td>87.97</td><td>87.89</td><td>68.22</td></tr></table>",
+        "bbox": [
+            509,
+            273,
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+            328
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Novel-view 2D part segmentation label transfer results. The rendered feature maps from other viewpoints still exhibit promising performance for co-segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation.",
+        "bbox": [
+            498,
+            330,
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+            406
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "the threshold of (0.025, 0.05, 0.075, 0.1) in the normalized space. For the part co-segmentation, we calculate mIoU based on point clouds instead of pixels. We randomly generate 1000 combinations per category for the evaluation.",
+        "bbox": [
+            498,
+            440,
+            890,
+            501
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3D Keypoints Transfer. For each 3D keypoint from the source shape, we try to find its corresponding point from a set of sampled candidate points from the target shape. For DINO and diffusion baselines, we simply project the 3D points onto 2D feature maps and utilize the interpolated feature vectors for matching. As those features are not 3D-aware, it is expected that their performance will be suboptimal. The quantitative results are shown in the second row of Fig 3. We can find that our method has a larger advantage in 3D tasks, which can also be observed from the qualitative results in Fig 4. Our learned 3D representation contains accurate semantic information and thus are able to transfer 3D keypoints in a more accurate way.",
+        "bbox": [
+            498,
+            503,
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+            700
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3D Part Segmentation Label Transfer. Similar to keypoints transfer, we try to propagate segmentation labels from the source point cloud to the target point cloud based on image observations. Note that the point cloud is only used as a query for segmentation, our method constructs a semantic feature volume for the whole 3D space and allows predicting feature vectors for any given 3D points. The right part of Tab 1 reports mIoUs for all methods. FeatureNeRF consistently outperforms all baselines in all categories, suggesting that distilling feature to 3D-aware representation leads to improved 3D co-segmentation performance. Fig. 5 presents qualitative results. Note that even for occluded areas in 2D images, FeatureNeRF can transfer its labels cor",
+        "bbox": [
+            496,
+            703,
+            890,
+            898
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8969",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e689201fb3de0908318216cddec155f1cd9d260b0242e8b90c66cdccf6448502.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Chair</td><td>Plane</td></tr><tr><td>w/o Lcoord</td><td>75.39</td><td>72.83</td></tr><tr><td>w/o internal features</td><td>74.62</td><td>72.29</td></tr><tr><td>full model</td><td>76.55</td><td>74.60</td></tr></table>",
+        "bbox": [
+            148,
+            88,
+            395,
+            143
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/1ea89a17913dd4cb9552ee52cfb0e09197dec0ce1ea6c1ec34b42a749c1fea31.jpg",
+        "table_caption": [
+            "Table 3: Ablation study. The coordinate loss and the use of internal NeRF features both boost performance."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td rowspan=\"3\">PSNR</td><td>PixelNeRF [66]</td><td>23.29</td><td>22.86</td><td>24.46</td><td>25.61</td><td>26.04</td><td>20.36</td></tr><tr><td>Ours (Diff.)</td><td>23.36</td><td>23.09</td><td>24.39</td><td>25.42</td><td>25.75</td><td>20.64</td></tr><tr><td>Ours (DINO)</td><td>23.20</td><td>22.92</td><td>24.49</td><td>25.69</td><td>26.01</td><td>20.59</td></tr><tr><td rowspan=\"3\">SSIM</td><td>PixelNeRF [66]</td><td>0.92</td><td>0.91</td><td>0.93</td><td>0.89</td><td>0.89</td><td>0.80</td></tr><tr><td>Ours (Diff.)</td><td>0.92</td><td>0.91</td><td>0.91</td><td>0.87</td><td>0.89</td><td>0.81</td></tr><tr><td>Ours (DINO)</td><td>0.91</td><td>0.91</td><td>0.91</td><td>0.89</td><td>0.90</td><td>0.80</td></tr></table>",
+        "bbox": [
+            78,
+            196,
+            478,
+            292
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Novel-view synthesis results. The proposed distillation process does not hurt the performance of novel-view synthesis, our method achieves comparable performance with PixelNeRF on novel-view synthesis.",
+        "bbox": [
+            75,
+            300,
+            468,
+            359
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "rectly in 3D space.",
+        "bbox": [
+            76,
+            388,
+            204,
+            402
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
+            415,
+            228,
+            430
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We mainly ablate the coordinate loss  $\\mathcal{L}_{\\mathrm{coord}}$  and the use of internal NeRF features  $\\mathbf{v}_{\\mathrm{NeRF}}$  (instead of final output feature vector  $\\mathbf{v}$ ) for semantic understanding. We conduct experiments of 2D parts co-segmentation on the Chair and Plane classes. The mIoU results are reported in Tab. 3. We can see that both design choices boost performance.",
+        "bbox": [
+            75,
+            438,
+            468,
+            527
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In addition, we compare the performance of novel-view synthesis with PixelNeRF [66] to see if the proposed feature distillation technique hurts the synthesis ability. Both FeatureNeRF and PixelNeRF are trained on our rendered dataset with the same parameters. From Tab. 4, we see that our method achieves comparable performance with PixelNeRF on novel-view synthesis.",
+        "bbox": [
+            75,
+            529,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.5. Editing Applications",
+        "text_level": 1,
+        "bbox": [
+            76,
+            646,
+            272,
+            662
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The learned FeatureNeRF model can also be leveraged to editing applications. Here, we take the 3D part texture swapping as an example. Given a source image and its part segmentation label, we can construct a 3D feature volume for the source image. Then, for a target image, we also construct its 3D feature volume and transfer the segmentation label from the source image to it. When rendering the target image, for a 3D point  $\\mathbf{x}_{\\mathrm{tgt}}$  that belongs to the part of interests (e.g. chair back) in the target feature volume, we find its closet point in the source feature volume:",
+        "bbox": [
+            75,
+            670,
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+            820
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf{x}_{\\text{closet}} = \\operatorname *{arg  min}_{\\mathbf{x}_{\\text{src}}}\\left\\| v_{\\text{NeRF}}\\left(\\mathbf{x}_{\\text{tgt}}\\right) - v_{\\text{NeRF}}\\left(\\mathbf{x}_{\\text{src}}\\right)\\right\\|_{2},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            834,
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+    {
+        "type": "text",
+        "text": "where  $\\mathbf{x}_{\\mathrm{src}} \\in \\mathbf{X}_{\\mathrm{src}}$  and  $\\mathbf{X}_{\\mathrm{src}}$  is the set of sampled points in the source feature volume. Finally, we use the color of the",
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+        "img_path": "images/5b6af87b3df73cb0fc7c2cce048dfa125678cc6b462b8dfdf94b8ada80e77bf8.jpg",
+        "image_caption": [
+            "Figure 9: Editing application: 3D part texture swapping. The part textures from source images are successfully transferred to the target images. Note that the edited target objects can also be rendered from novel views, please see our video for 3D visualizations."
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "closet point  $\\mathbf{x}_{\\mathrm{closet}}$  to replace the original color of  $\\mathbf{x}_{\\mathrm{tgt}}$  for the rendering.",
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+    {
+        "type": "text",
+        "text": "The results are shown in Fig. 9. We can find that the part textures from source images are successfully transferred to the target images. Besides, the details are also well preserved (the brown boundary from the source image at the second row still exists in the target images). Note that the edited target instances can also be rendered from novel views, please see our video for 3D visualizations.",
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+        "text": "5. Conclusion",
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+    {
+        "type": "text",
+        "text": "In contrast to the success of 2D foundation models, it is still unclear how to build foundation models in 3D given the lack of web-scale datasets and effective architecture. In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling 2D vision foundation models. FeatureNeRF explores the use of internal NeRF features as 3D visual descriptors and distills knowledge from 2D foundation models into 3D space via neural rendering. Given a single image, FeatureNeRF allows to predict a 3D semantic feature representation, which can be leveraged for downstream tasks. Specifically, we demonstrate the effectiveness of FeatureNeRF on the tasks of 2D/3D keypoints transfer and part co-segmentation from a single image. In addition, FeatureNeRF can also serve as a general-purpose feature extractor for downstream 3D tasks such as open-world 3D classification/segmentation and robotics tasks.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements. Prof. Wang's lab was supported, in part, by Amazon Research Award, Sony Research Award, Adobe Data Science Research Award, and gifts from Qualcomm.",
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+        "text": "References",
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+        ],
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+        ],
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diff --git a/2023/FeatureNeRF_ Learning Generalizable NeRFs by Distilling Foundation Models/77c2128e-07a6-41a1-8c05-52f5da1cd81d_model.json b/2023/FeatureNeRF_ Learning Generalizable NeRFs by Distilling Foundation Models/77c2128e-07a6-41a1-8c05-52f5da1cd81d_model.json
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
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+            "content": "Jianglong Ye<sup>1</sup> Naiyan Wang<sup>2</sup> Xiaolong Wang<sup>1</sup>  \n<sup>1</sup>UC San Diego <sup>2</sup>TuSimple"
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+            "content": "Figure 1: While most generalizable NeRFs focus on novel-view synthesis, we propose a framework named FeatureNeRF to learn 3D semantic representations by distilling vision foundation models. After distillation, FeatureNeRF allows to render novel-view feature maps given a single input image (a), which can be leveraged to various downstream tasks. Here, we show how we propagate part segmentation labels and keypoints to different views and instances in both 2D and 3D domains (b)."
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+        {
+            "type": "title",
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+            "content": "Recent works on generalizable NeRFs have shown promising results on novel view synthesis from single or few images. However, such models have rarely been applied on other downstream tasks beyond synthesis such as semantic understanding and parsing. In this paper, we propose a novel framework named FeatureNeRF to learn generalizable NeRFs by distilling pre-trained vision foundation models (e.g., DINO, Latent Diffusion). FeatureNeRF leverages 2D pre-trained foundation models to 3D space via neural rendering, and then extract deep features for 3D query points from NeRF MLPs. Consequently, it allows to map 2D images to continuous 3D semantic feature volumes, which can be used for various downstream tasks. We evaluate FeatureNeRF on tasks of 2D/3D semantic keypoint transfer and 2D/3D object part segmentation. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor. Our project page is available at https://jianglongye.com/featuresenerf/."
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+                0.845,
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+                0.86
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Neural fields have emerged as a compelling paradigm for representing a variety of visual signals [8, 10, 31, 32, 37]. In"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.498,
+                0.893,
+                0.68
+            ],
+            "angle": 0,
+            "content": "particular, the Neural Radiance Fields (NeRF [32]), which implicitly encodes density and color via Multi-Layer Perceptrons (MLPs), has shown high quality novel view synthesis results from dense input images. A body of follow-up works [7, 27, 45, 54, 66] further reduce the dependency on dense inputs and generalize NeRF to unseen objects by learning priors from large-scale multi-view image datasets. With the remarkable abilities on reconstruction and view synthesis of generalizable NeRFs, we ask the question: Can we adapt such models to learn 3D representations as foundations for general 3D applications (e.g., recognition, matching) beyond view synthesis?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.685,
+                0.895,
+                0.851
+            ],
+            "angle": 0,
+            "content": "Recent years have witnessed the rise of vision foundation models [5, 40, 43, 67] that are pre-trained on web-scale image datasets and demonstrate generalization capabilities across massive vision tasks (e.g., CLIP [40], DINO [5], Latent Diffusion [47]). The feature space constructed by foundation models captures rich semantic and structural information of 2D visual data and make it possible to identify object categories, parts and correspondences even without extra supervisions [1, 5, 30]. Motivated by these works, our goal is to leverage the powerful 2D foundations models to obtain generalizable 3D features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling pretrained 2D vision foundation models. Unlike previous gen"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8962"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.092,
+                0.468,
+                0.257
+            ],
+            "angle": 0,
+            "content": "eralizable NeRFs [45, 66], which utilize 2D encoder solely for novel view synthesis, FeatureNeRF explores the use of deep features extracted from NeRFs as generalizable 3D visual descriptors. We show that distilling 2D foundation models into 3D space via neural rendering equips the NeRF features with rich semantic information. As a result, FeatureNeRF allows to predict a continuous 3D semantic feature volume from a single or a few images, which can be applied to various downstream tasks such as semantic keypoint transfer and object part co-segmentation. Examples of these applications are shown in Fig. 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.258,
+                0.468,
+                0.408
+            ],
+            "angle": 0,
+            "content": "Specifically, we adopt an encoder to map 2D images to corresponding 3D NeRF volume similar to previous generalizable NeRFs. Apart from density and color, we propose to extract deep features of the query 3D points from the intermediate layers of NeRF MLP. To enrich semantic information of the NeRF features, we further transfer knowledge from the foundation models to the encoder via neural rendering during training: The rendered feature outputs should be consistent with the feature extracted from the foundation models, which is enforced by a distillation loss."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.409,
+                0.468,
+                0.575
+            ],
+            "angle": 0,
+            "content": "To evaluate FeatureNeRF, we tackle the tasks of 2D/3D semantic keypoint transfer and object part segmentation. To the best of our knowledge, our work is the first to resolve these 3D semantic understanding tasks without 3D supervision. We validate our framework with two foundation models: (i) DINO [5], a self-supervised vision transformer aware of object correspondences, and (ii) Latent Diffusion [47], a diffusion-based model that achieves state-of-the-art text-to-image generation performance. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.081,
+                0.589,
+                0.216,
+                0.604
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.614,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Generalizable NeRFs. In the past few years, neural fields have gained significant attention and led to rapid progress in representing various visual signals [8, 10, 25, 31, 32, 36, 37, 50, 52, 61]. In particular, NeRF [32] achieves photo-realistic results on novel view synthesis by mapping 3D coordinates and 2D viewing directions to density and color via MLPs. However, the original NeRF requires enormous posed images and time-consuming optimization for each single scene. To address these issues, a large number of follow-up methods [9, 23, 27, 45, 46, 54, 56, 66] propose to learn generalizable NeRFs from large-scale multi-view image datasets. For example, PixelNeRF [66] employs an image encoder to condition NeRF on image features, which enables novel views synthesis from a single image and generalizes NeRF to unseen objects. CodeNeRF [23] learns to disentangle shape and texture by learning separate embeddings, allowing shape and texture editing by varying the latent codes. Recent work TransINR [9] is proposed to infer NeRF parameters directly with a vision transformer to over"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.89,
+                0.152
+            ],
+            "angle": 0,
+            "content": "come the information bottleneck of encoder-decoder architecture. However, most of these works focus only on view synthesis. Our work differs from them by learning general-purpose 3D representations for multiple downstream tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.155,
+                0.89,
+                0.532
+            ],
+            "angle": 0,
+            "content": "Vision Foundation Models. The term foundation model is introduced in [3] to refer to the model pre-trained from data at scale and capable of generalizing to a wide range of downstream tasks. After demonstrating huge impacts in NLP [4, 15, 41], a large family of vision foundation models [5, 40, 42, 43, 47, 58, 62, 67] have been proposed and effectively transferred to various vision tasks. For example, the CLIP model [40] is trained from large-scale image-text data using contrastive learning, and it is shown to be transferable to multiple tasks in a zero-shot manner. The DINO model [5] has shown object segment can emerge automatically with only self-supervision, and the learned feature can be applied in a wide range of visual correspondence and recognition tasks [1, 12, 30, 57]. Besides contrastive learning, recent text-conditioned generative model such as diffusion models [16, 21, 35, 47] have been introduced and shown astonishing performance on image generation. Subsequently, feature spaces learned by these generative models have also been used for recognition tasks such as semantic segmentation [2, 59]. In contrast to the success of 2D foundation models, the 3D counterparts are still suffering from the lack of large-scale annotated datasets and effective architectures [18, 49, 60]. In this paper, we propose to distill the features from 2D foundation models to 3D space via the generalizable NeRFs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.535,
+                0.89,
+                0.747
+            ],
+            "angle": 0,
+            "content": "Feature Distillation. For the purpose of model compression and knowledge transfer, distillation has been widely studied by the community. After the pioneering work by Hinton et al. [20], which matches the softmax output distribution of the teacher model to that of the student, numerous methods have been proposed to tackle various tasks [19, 22, 38, 39, 53, 64]. Recently, researchers also propose to distill features from 2D models to 3D space by optimizing neural feature fields [26, 55]. Multiple editing tasks are shown as applications. However, these methods not only require test-time optimization for each single scene, but the learned features are also not generalizable to unseen objects, which makes them unsuitable for general semantic understanding tasks and differ from our work fundamentally."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.75,
+                0.89,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Semantic Correspondences. Given a pair of visual observation, semantic correspondences learning aims to find corresponding points between them. Several supervised [13, 24, 51] and self-supervised [1, 11, 28] methods have been proposed to resolve this task in 2D and 3D domain respectively. In particular, Amir et al. [1] show that utilizing pre-trained 2D foundation models in a zero-shot manner can achieve competitive results with supervised methods on semantic correspondences. Cheng et al. [11] propose to learn point cloud correspondences via"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.485,
+                0.947,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8963"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.088,
+                0.887,
+                0.3
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.313,
+                0.896,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Figure 2: Pipeline of FeatureNeRF. Given a single image \\(I\\) as input, FeatureNeRF adopts an encoder to extract the image feature \\(E_{\\pi(\\mathbf{x})}\\), and then concatenate it with the query point \\(\\mathbf{x}\\) as well as the view direction \\(\\mathbf{d}\\) as the inputs for NeRF MLPs. Apart from density \\(\\sigma\\) and color \\(\\mathbf{c}\\), we add two MLP branches to predict the feature vector \\(\\mathbf{v}\\) and coordinate \\(\\hat{\\mathbf{x}}\\), which are supervised by two novel loss terms \\(\\mathcal{L}_{\\mathrm{distill}}\\) and \\(\\mathcal{L}_{\\mathrm{coord}}\\) respectively. Consequently, we distill knowledge from 2D vision foundation models to FeatureNeRF. Besides, we propose to extract internal NeRF feature \\(\\mathbf{v}_{\\mathrm{NeRF}}\\) as 3D-consistent feature representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.427,
+                0.471,
+                0.488
+            ],
+            "angle": 0,
+            "content": "self-reconstruction and cross-reconstruction of 3D shapes. To the best of our knowledge, our work is the first to address semantic correspondences in both 2D and 3D space with only 2D observations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.5,
+                0.172,
+                0.515
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.525,
+                0.47,
+                0.646
+            ],
+            "angle": 0,
+            "content": "We present FeatureNeRF, a unified framework for learning generalizable NeRF from vision foundation models. We give an overview of generalizable NeRFs in Sec. 3.1 and elaborate our feature distillation process in Sec. 3.2. Then we introduce how to learn internal NeRF features for 3D semantic understanding in Sec. 3.3 and downstream applications in Sec. 3.4. The overall pipeline of FeatureNeRF is illustrated in Fig. 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.654,
+                0.377,
+                0.67
+            ],
+            "angle": 0,
+            "content": "3.1. Preliminary: Generalizable NeRF"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.677,
+                0.47,
+                0.814
+            ],
+            "angle": 0,
+            "content": "Neural Radiance Fields (NeRF [32]) consists of two functions: \\(\\sigma (\\mathbf{x}):\\mathbb{R}^3\\mapsto \\mathbb{R}_+\\) that maps a 3D point \\(\\mathbf{x}\\) to the density \\(\\sigma\\) and \\(\\mathbf{c}(\\mathbf{x},\\mathbf{d}):\\mathbb{R}^{3\\times 3}\\mapsto \\mathbb{R}^3\\) that maps a 3D point as well as a unit viewing direction \\(\\mathbf{d}\\) to color. The radiance field can be rendered and optimized via differentiable volume rendering [29]. Given a pixel's camera ray \\(\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}\\), which is defined by the camera origin \\(\\mathbf{o}\\in \\mathbb{R}^3\\), view direction \\(\\mathbf{d}\\) and depth \\(t\\) with bounds \\([t_n,t_f]\\), the estimated color of the ray can be calculated by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.139,
+                0.821,
+                0.47,
+                0.856
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathbf {C}} (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) \\mathbf {c} (\\mathbf {r} (t), \\mathbf {d}) \\mathrm {d} t, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.865,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where \\( T(t) = \\exp \\left(-\\int_{t_n}^t\\sigma (s)ds\\right) \\). In practice, the integral is approximated with numerical quadrature by sam"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.427,
+                0.893,
+                0.472
+            ],
+            "angle": 0,
+            "content": "pling points along the ray. NeRF is optimized to a single scene with multi-view posed images by minimizing the following reconstruction loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.593,
+                0.478,
+                0.892,
+                0.515
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {r e c}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\mathbf {C} (\\mathbf {r}) - \\hat {\\mathbf {C}} (\\mathbf {r}) \\right\\| _ {2} ^ {2}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.52,
+                0.892,
+                0.551
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{C}(\\mathbf{r})\\) is the ground truth color of the ray and \\(\\mathcal{R}\\) is the set of rays generated from camera poses."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.551,
+                0.892,
+                0.581
+            ],
+            "angle": 0,
+            "content": "In order to generalize to novel scenes, the NeRF model can be conditioned on the input image \\(I \\in \\mathbb{R}^{H \\times W \\times 3}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.583,
+                0.586,
+                0.891,
+                0.611
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sigma (\\mathbf {x}, I) = g _ {\\sigma} \\left(\\mathbf {x}, f (I) _ {\\pi (\\mathbf {x})}\\right) \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.586,
+                0.607,
+                0.807,
+                0.625
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {c}} \\left(\\mathbf {x}, \\mathbf {d}, f (I) _ {\\pi (\\mathbf {x})}\\right),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.892,
+                0.673
+            ],
+            "angle": 0,
+            "content": "where \\( g_{\\sigma} \\) and \\( g_{\\mathbf{c}} \\) are MLPs that predict density and color respectively, \\( f \\) is an image encoder and \\( \\pi \\) is the projection function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.674,
+                0.893,
+                0.841
+            ],
+            "angle": 0,
+            "content": "As shown in the left part of Fig. 2, the image \\(I\\) is firstly passed to an encoder \\(f_{\\mathrm{enc}}\\) (blue blocks in the figure) to obtain a feature map \\(E = f(I)\\). The query point \\(\\mathbf{x}\\) is projected onto the image plane using known pose and intrinsics to extract the corresponding feature vector \\(E_{\\pi (\\mathbf{x})}\\). Then the feature vectors are concatenated with the positional-encoded point \\(\\mathbf{x}\\) and direction \\(\\mathbf{d}\\), and passed to subsequent MLPs \\(g_{\\sigma}\\) and \\(g_{\\mathbf{c}}\\) (yellow blocks in the figure) to predict appearance and geometry. When multi-view images are available, feature vectors from different views are aggregated with the average pooling before passing to MLPs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.88,
+                0.862
+            ],
+            "angle": 0,
+            "content": "3.2. Feature Distillation from Foundation Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "While most generalizable NeRFs only predict density \\(\\sigma\\) and color c, it's possible to extend NeRF to predict other"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8964"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.288
+            ],
+            "angle": 0,
+            "content": "quantities of interests. For example, SemanticNeRF [68] and PanopticNeRF [17] propose to add a branch to predict segmentation labels to achieve a 3D-consistent semantic segmentation of a scene. However, these methods require expensive semantic labels during optimization, which is impractical for general cases. In this paper, we aim to transfer knowledge from a pre-trained foundation model \\( f_{\\mathrm{teacher}} \\) to our generalizable NeRFs to perform 3D semantic understanding. To this end, we add a branch to output a high-dimensional feature vector \\( \\mathbf{v} \\in \\mathbb{R}^{D} \\) for the query point \\( \\mathbf{x} \\), where \\( D \\) is the feature channels. Similar to the color rendering (Eq. 1), we can aggregate the feature vectors along a ray as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.116,
+                0.294,
+                0.47,
+                0.329
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathbf {V}} (\\mathbf {r}, I) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t), I) \\mathbf {v} (\\mathbf {r} (t), \\mathbf {d}, I) d t \\tag {4}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.117,
+                0.331,
+                0.348,
+                0.35
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {v} \\left(\\mathbf {x}, \\mathbf {d}, I\\right) = g _ {\\mathbf {v}} \\left(\\mathbf {x}, \\mathbf {d}, f (I) _ {\\pi (\\mathbf {x})}\\right),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.355,
+                0.47,
+                0.399
+            ],
+            "angle": 0,
+            "content": "where \\( g_{\\mathbf{v}} \\) is the MLP that predicts future vectors. Note that our model is still conditioned on the image \\( I \\) in the above equation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.4,
+                0.47,
+                0.476
+            ],
+            "angle": 0,
+            "content": "We then minimize the difference between rendered pixel feature vector \\(\\hat{\\mathbf{V}}\\) and the teacher's feature \\(\\mathbf{V} = f_{\\mathrm{teacher}}(I)_{\\pi (\\mathbf{x})}\\). In this way, we distill the teacher network into our generalizable NeRFs via neural rendering. We add a distillation loss to penalize the difference:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.162,
+                0.481,
+                0.469,
+                0.518
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {d i s t i l l}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\mathbf {V} (\\mathbf {r}) - \\hat {\\mathbf {V}} (\\mathbf {r}) \\right\\| _ {2} ^ {2}. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.524,
+                0.47,
+                0.659
+            ],
+            "angle": 0,
+            "content": "FeatureNeRF can be trained jointly for image reconstruction and feature distillation by combing two losses (Eq. 2 and Eq. 5). We show both color rendering and feature rendering processes in the right part of Fig. 2. We emphasize that, after distillation, FeatureNeRF can obtain a 3D semantic feature function \\(\\mathbf{v}\\) in a single forward pass, which can be used for downstream applications. Our experiments show that the feature function \\(\\mathbf{v}\\), learned with only 2D observation, contains accurate 3D semantic information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our framework can be built on top of any foundation model, and in this work we employ DINO [5] and Latent Diffusion [47] as teacher networks. DINO is a vision transformer trained with self-distillation, and we simply extract features from the deepest layer as teacher features. Latent Diffusion firstly transforms input image \\(I\\) to the latent space, and utilizes a U-Net [48] architecture to estimate the noise for the backward diffusion process. Besides, the denoising module can be conditioned on inputs like text and segmentation maps. We add noise to the original image, condition the pre-trained model with fixed language prompts (e.g. \"Car\", \"Chair\") and extract features from the intermediate layers of U-Net. Distilling these foundation models that pre-trained on large-scale image datasets brings open-world knowledge to our generalizable 3D representation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.091,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "3.3. Learning Internal NeRF Features for 3D Semantic Understanding"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.13,
+                0.894,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Although we have distilled features from foundation models, it is still questionable whether the final feature output is best suitable for 3D semantic understanding. Here we explore using internal NeRF features as view-independent representations for 3D semantic understanding and introduce a new coordinate loss for learning spatial-aware NeRF features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.237,
+                0.894,
+                0.327
+            ],
+            "angle": 0,
+            "content": "While previous works only utilize final outputs of MLPs, we explore whether we can use features from intermediate layers as continuous 3D visual descriptors. Given a input image \\(I\\), we firstly learn a function \\(\\mathbf{v}_{\\mathrm{NeRF}}(\\mathbf{x},I)\\) to predict NeRF features and utilize several shallow MLPs to predict other quantities:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.573,
+                0.34,
+                0.816,
+                0.358
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I) = g _ {\\mathrm {N e R F}} \\left(\\mathbf {x}, f (I) _ {\\pi (\\mathbf {x})}\\right)\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.573,
+                0.359,
+                0.892,
+                0.384
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sigma (\\mathbf {x}, I) = g _ {\\sigma} \\left(\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right) \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.573,
+                0.38,
+                0.795,
+                0.395
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {c}} \\left(\\mathbf {d}, \\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right)\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.573,
+                0.398,
+                0.806,
+                0.414
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {v} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {v}} \\left(\\mathbf {d}, \\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.426,
+                0.892,
+                0.531
+            ],
+            "angle": 0,
+            "content": "where \\( g_{\\mathrm{NeRF}} \\) is MLP that predicts NeRF features. Note that the proposed function \\( \\mathbf{v}_{\\mathrm{NeRF}} \\) can be learned without the feature distillation introduced in Sec. 3.2, therefore it can be applied to all generalizable NeRFs. The feature extraction process is demonstrated in the bottom of Fig. 2. We compare the performance of NeRF features with and without feature distillation in our experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.533,
+                0.892,
+                0.623
+            ],
+            "angle": 0,
+            "content": "Even for the feature distillation version, since teacher's features \\(\\mathbf{V}\\) are always not 3D-consistent, using a view-independent representation \\(\\mathbf{v}_{\\mathrm{NeRF}}\\) and modeling view-dependent effect using another MLP \\(g_{\\mathbf{v}}\\) that conditioned on view direction \\(\\mathbf{d}\\) further boosts the performance (See Sec. 4.4 for the ablation study)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.624,
+                0.892,
+                0.715
+            ],
+            "angle": 0,
+            "content": "The supervision of most generalizable NeRFs are RGB values, which do not contain spatial information. To enhance the spatial perception of the NeRF feature, we propose to utilize another MLP branch \\( g_{\\mathbf{x}} \\) (shown at the top of Fig. 2) to regress the input coordinates \\( \\mathbf{x} \\) given the NeRF feature \\( \\mathbf{v}_{\\mathrm{NeRF}} \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.616,
+                0.729,
+                0.892,
+                0.745
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathbf {x}} = g _ {\\mathbf {x}} \\left(\\mathbf {v} _ {\\text {N e R F}} (\\mathbf {x}, I)\\right). \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.758,
+                0.878,
+                0.773
+            ],
+            "angle": 0,
+            "content": "We add a cycle-consistent loss to penalize the difference:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.516,
+                0.786,
+                0.892,
+                0.829
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {c o o r d}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\sum_ {t = t _ {n}} ^ {t _ {f}} \\| \\mathbf {r} (t) - g _ {\\mathbf {x}} \\left(\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {r} (t), I)\\right) \\| _ {2} ^ {2}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The final loss function is the weighted sum of all three losses: \\(\\mathcal{L} = \\mathcal{L}_{\\mathrm{rec}} + \\lambda_{\\mathrm{distill}}\\mathcal{L}_{\\mathrm{distill}} + \\lambda_{\\mathrm{coord}}\\mathcal{L}_{\\mathrm{coord}}\\), where \\(\\lambda_{\\mathrm{distill}}\\) and \\(\\lambda_{\\mathrm{coord}}\\) are weights for different losses. All losses and their forward flows are shown in Fig. 2."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8965"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.338,
+                0.108
+            ],
+            "angle": 0,
+            "content": "3.4. Applications of FeatureNeRF"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.115,
+                0.468,
+                0.22
+            ],
+            "angle": 0,
+            "content": "We demonstrate the effectiveness of the learned 3D semantic NeRF feature function \\(\\mathbf{v}_{\\mathrm{NeRF}}\\) on various downstream applications: 2D/3D semantic keypoint transfer and object part segmentation. We deliberately apply simple, zero-shot methodologies on NeRF features, without any fine-tuning or post-process, to validate the proposed representations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.222,
+                0.468,
+                0.406
+            ],
+            "angle": 0,
+            "content": "2D Tasks. Given a single image \\(I\\), we can render its NeRF feature map \\(F \\in \\mathbb{R}^{H \\times W \\times D}\\) using Eq. 4. Then we can render novel-view feature map \\(F'\\) from other viewpoints. For feature vectors \\(\\mathbf{V}\\) and \\(\\mathbf{V}'\\) of two pixels from \\(F\\) and \\(F'\\), we use cosine similarity to measure their distance in the feature space: \\(D(\\mathbf{V}, \\mathbf{V}') = \\frac{\\mathbf{V} \\cdot \\mathbf{V}'}{\\|\\mathbf{V}\\|_2 \\cdot \\|\\mathbf{V}'\\|_2}\\). For the part co-segmentation task, for each pixel feature \\(\\mathbf{V}'\\) in \\(F'\\), we take the segmentation label of its closest pixel feature \\(\\mathbf{V}\\) in \\(F\\) as the predicted segmentation label. For the keypoint transfer task, we adopt a similar process, for the feature \\(\\mathbf{V}\\) of each keypoint in \\(F\\), we take the pixel location of its closest feature in \\(F'\\) as the predicted keypoint."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.408,
+                0.468,
+                0.512
+            ],
+            "angle": 0,
+            "content": "Since FeatureNeRF is a generalizable NeRF conditioned on the input image, it can be further applied to cross-instance tasks in addition to novel-view tasks for a single instance. Given images \\( I_{1} \\) and \\( I_{2} \\) of two instances, we can render their feature maps \\( F_{1} \\) and \\( F_{2} \\). Then we can resolve semantic correspondence tasks in a process similar to the novel-view tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.514,
+                0.468,
+                0.636
+            ],
+            "angle": 0,
+            "content": "3D Tasks. The FeatureNeRF model learned with only 2D observations can also be leveraged to 3D tasks. Given images \\(I_{1}\\) and \\(I_{2}\\) of two instances, we can construct two continuous 3D feature fields. For feature vectors \\(\\mathbf{v}_1\\) and \\(\\mathbf{v}_2\\) of two 3D points \\(\\mathbf{x}_1\\) and \\(\\mathbf{x}_2\\), we still utilize cosine similarity to measure their distance: \\(D(\\mathbf{v}_1,\\mathbf{v}_2) = \\frac{\\mathbf{v}_1\\cdot\\mathbf{v}_2}{\\|\\mathbf{v}_1\\|_2\\cdot\\|\\mathbf{v}_2\\|_2}\\). Then we can resolve semantic correspondence tasks in a process similar to the 2D tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.655,
+                0.209,
+                0.672
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.68,
+                0.277,
+                0.696
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets. Our experiments are mainly conducted on 6 categories from the ShapeNet [6] dataset: Chair, Car, Airplane, Table, Bottle and Motorcycle. We evaluate our model using annotations from KeypointNet [65], ShapeNet part dataset [63] and PartNet [34]. In addition, we train our model on the real-world CO3D [45] dataset and evaluate its keypoint transfer performance on the Spair [33] dataset. For ShapeNet, we split each category into training (70%), validation (10%), and testing (20%) splits. All shapes are normalized so that the longest edges of the bounding box are equal. For the training set, 50 random camera poses from the upper hemisphere are sampled. For validation and testing sets, 50 fixed camera poses are used. We employ"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "blender [14] to render RGB images, with a resolution of \\(128 \\times 128\\), the same as in PixelNeRF [66]. For PartNet, we use level-1 annotations. All annotations are in 3D and can be used for the evaluation of 3D tasks directly. For the evaluation of 2D tasks, we employ PyTorch3D [44] rasterizer to render 2D part segmentation labels and 2D keypoints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.183,
+                0.892,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Baselines. We mainly compare FeatureNeRF quantitatively and qualitatively to two foundation models DINO [5] and Latent Diffusion [47]. We extend PixelNeRF [66] with the mechanisms mentioned in Sec. 3.3 to make it possible for semantic understanding tasks and report its performance as \"NeRF feature\" in all results. In addition, for the 2D cosegmentation task, we re-implement a one-shot generalizable SemanticNeRF* [68] by adding a semantic branch in PixelNeRF, and train it with the source segmentation labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.32,
+                0.892,
+                0.456
+            ],
+            "angle": 0,
+            "content": "Implementation Details. Following PixelNeRF [66], we employ a ResNet-34 model pre-trained on ImageNet as the image encoder \\( f \\). The batch size is 4 (objects) and 1024 rays per object. We train a single model for each object category for 500k steps. The weights for different losses are \\( \\lambda_{\\mathrm{distill}} = 0.25 \\) and \\( \\lambda_{\\mathrm{coord}} = 0.25 \\). The dimension of the internal NeRF feature is 512. MLP for NeRF feature \\( g_{\\mathrm{NeRF}} \\) is 4-layer, all other shallow MLPs for final outputs \\( (g_{\\sigma}, g_{\\mathbf{c}}, g_{\\mathbf{v}} \\) and \\( g_{\\mathbf{x}}) \\) are one-layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.457,
+                0.892,
+                0.607
+            ],
+            "angle": 0,
+            "content": "Teacher Networks. We employ DINO [5] and Latent Diffusion [47] as teacher networks, which are pre-trained and publicly available. The patch size of DINO is 8. The final feature map has dimension \\(32 \\times 32 \\times 384\\). For Latent Diffusion, we extract the outputs of the 4th layer in U-Net as teacher features. The language prompts used to condition denoising modules are class names (e.g. \"Chair\", \"Car\") from ShapeNet. The final feature map has dimension \\(128 \\times 128 \\times 960\\). The weights of teacher networks are fixed during distillation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.62,
+                0.802,
+                0.636
+            ],
+            "angle": 0,
+            "content": "4.2. 2D Semantic Understanding Tasks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.644,
+                0.892,
+                0.809
+            ],
+            "angle": 0,
+            "content": "As mentioned in Sec. 3.4, we evaluate FeatureNeRF on tasks of 2D keypoints transfer and part segmentation labels transfer under two settings: (i) Cross-instance: given images of two instances, we transfer keypoints/segmentation labels from the source image to the target image and compare the transferred labels in the target image with the ground truth. (ii) Novel-view: given a single image of an instance, we render a novel-view feature map, transfer labels from the source viewpoint to the target viewpoint and compare the transferred labels in the target viewpoint with the ground truth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Metrics. For the task of 2D keypoints transfer, we report the percentage of predicted keypoints whose distances from their corresponding ground truths are below thresholds of (2.5, 5.0, 7.5, 10.0) pixels in the target image. We denote this percentage as Correspondence Accuracy in the following. For the task of part segmentation labels trans"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8966"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.086,
+                0.895,
+                0.341
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.344,
+                0.895,
+                0.391
+            ],
+            "angle": 0,
+            "content": "Figure 3: Correspondence accuracy for cross-instance semantic keypoints transfer. The first row is for 2D keypoints transfer and the second row is for 3D. Our approach distilled with different features consistently outperforms baselines for all categories in both 2D and 3D domains."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.083,
+                0.399,
+                0.512,
+                0.587
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.259,
+                0.595,
+                0.343,
+                0.608
+            ],
+            "angle": 0,
+            "content": "(a) 2D results"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.516,
+                0.399,
+                0.892,
+                0.591
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.658,
+                0.595,
+                0.743,
+                0.608
+            ],
+            "angle": 0,
+            "content": "(b) 3D results"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.613,
+                0.895,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Figure 4: Qualitative results for cross-instance semantic keypoints transfer. Both 2D (a) and 3D (b) results are presented here. Each row contains a source image with keypoints annotations and its pairwise transfer results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.666,
+                0.471,
+                0.756
+            ],
+            "angle": 0,
+            "content": "fer, we calculate the mean intersection over union \\((mIoU)\\) over every part category for each object class. For both settings, we randomly generate 1000 combinations per category. While generating, we make sure that the source viewpoints/instances and target viewpoints/instances have intersecting keypoints/segmentation labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "2D Keypoints Transfer. We report correspondence accuracy of 2D cross-instance keypoints transfer in the first row of Fig. 3. We show that for all 6 categories, keypoints transferred via our proposed method are more accurate than baselines. The performances of distilling diffusion and DINO features are similar. Using NeRF feature without distilling foundation models (denoted as \"NeRF feature\" in the figure) also achieves a reasonable performance compared to 2D foundation model baselines. Fig. 4 (a) shows the qual"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.666,
+                0.892,
+                0.726
+            ],
+            "angle": 0,
+            "content": "itative results for 2D keypoints transfer. It can be seen that despite various appearances and structures of instances, our method can successfully transfer keypoints based on semantic understanding, while baselines often fail."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.73,
+                0.895,
+                0.837
+            ],
+            "angle": 0,
+            "content": "FeatureNeRF learns a 3D representation from 2D observations, which allows to synthesize novel-view feature maps for different viewpoints and performs keypoints transfer on top of it. Fig. 6 (a) shows qualitative results of novel-view keypoints transfer. Since 2D foundation models can not synthesize novel-view feature maps, we do not apply them to this novel-view setting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "2D Part Segmentation Label Transfer. We report mIoU results of 2D cross-instance part segmentation label transfer in the left part of Tab. 1. FeatureNeRF distilled with DINO features significantly outperforms other approaches"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8967"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.094,
+                0.885,
+                0.297
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.303,
+                0.897,
+                0.351
+            ],
+            "angle": 0,
+            "content": "Figure 5: Qualitative results for cross-instance part segmentation label transfer. Each row contains a source image and its 2D/3D transfer results. After distilling, FeatureNeRF learns richer semantic information, produces better boundaries and preserves details like small parts. Note that the segmentation label for the source instance is omitted."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.102,
+                0.357,
+                0.473,
+                0.514
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.491,
+                0.357,
+                0.871,
+                0.515
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.523,
+                0.895,
+                0.569
+            ],
+            "angle": 0,
+            "content": "Figure 6: Qualitative results of novel-view keypoints transfer and part co-segmentation. FeatureNeRF learns a 3D representation from 2D observations, which makes it possible to synthesize feature maps from other viewpoints and transfer keypoints and segmentation labels to them."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.122,
+                0.573,
+                0.846,
+                0.682
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td colspan=\"6\">2D part co-segmentation</td><td colspan=\"6\">3D part co-segmentation</td></tr><tr><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>SemanticNeRF*</td><td>50.32</td><td>34.61</td><td>56.19</td><td>54.87</td><td>51.58</td><td>27.62</td><td></td><td></td><td></td><td>-</td><td></td><td></td></tr><tr><td>Diffusion Baseline</td><td>41.59</td><td>42.46</td><td>44.60</td><td>57.77</td><td>41.72</td><td>25.50</td><td>33.60</td><td>24.74</td><td>30.45</td><td>44.34</td><td>53.81</td><td>20.01</td></tr><tr><td>DINO Baseline</td><td>62.43</td><td>54.59</td><td>57.81</td><td>64.01</td><td>59.73</td><td>37.05</td><td>52.67</td><td>29.72</td><td>40.16</td><td>49.98</td><td>70.79</td><td>29.25</td></tr><tr><td>NeRF Feature</td><td>72.02</td><td>58.57</td><td>72.57</td><td>70.41</td><td>55.87</td><td>44.00</td><td>65.23</td><td>59.19</td><td>71.23</td><td>61.64</td><td>66.63</td><td>44.88</td></tr><tr><td>Ours (Diffusion)</td><td>65.39</td><td>63.02</td><td>72.95</td><td>70.59</td><td>53.91</td><td>44.84</td><td>63.65</td><td>61.27</td><td>73.41</td><td>63.93</td><td>66.91</td><td>49.05</td></tr><tr><td>Ours (DINO)</td><td>76.55</td><td>66.85</td><td>74.60</td><td>74.06</td><td>61.13</td><td>49.56</td><td>73.85</td><td>64.99</td><td>74.20</td><td>66.52</td><td>72.33</td><td>52.56</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.684,
+                0.895,
+                0.731
+            ],
+            "angle": 0,
+            "content": "Table 1: Cross-instance part segmentation label transfer results. We report mIoU of part co-segmentation for each category. The left part is for 2D and the right is for 3D. By distilling features to the 3D space, our proposed representation contains richer semantic information which is apt for this co-segmentation task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.752,
+                0.473,
+                0.89
+            ],
+            "angle": 0,
+            "content": "for all 6 categories. However, the performance of FeatureNeRF distilled with diffusion features is not as good as the DINO one. This is possible since the keypoints transfer task may focus on predicting accurate locations of sparse pixels that contain the richest semantic information, but part cosegmentation requires denser correspondences. Qualitative results are shown Fig. 5 (a). We can find that NeRF feature often produces unexpected artifacts. We attribute this phenomenon to NeRF feature's training only relying on RGB"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.752,
+                0.895,
+                0.829
+            ],
+            "angle": 0,
+            "content": "information. In contrast, by distilling pre-trained features, our method produces better boundaries and preserves details like small parts. Note that the segmentation label of the source object is also required during the transfer process, which is omitted in the figure."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We also perform novel-view part co-segmentation and report both quantitative and qualitative results in Tab. 2 and Fig. 6 (b) respectively. The rendered feature maps from other viewpoints still exhibit promising performance for co"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8968"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.116,
+                0.086,
+                0.852,
+                0.24
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.084,
+                0.243,
+                0.882,
+                0.259
+            ],
+            "angle": 0,
+            "content": "Figure 7: Keypoints transfer on SPair. Our method outperforms NeRF feature on 5 categories on the real-world dataset."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.269,
+                0.456,
+                0.49
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.492,
+                0.47,
+                0.553
+            ],
+            "angle": 0,
+            "content": "Figure 8: Keypoints and segmentation label transfer on CO3D. After training on CO3D, our method can accurately transfer keypoints and segmentation labels with in-the-wild image inputs"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.566,
+                0.468,
+                0.596
+            ],
+            "angle": 0,
+            "content": "segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.596,
+                0.468,
+                0.747
+            ],
+            "angle": 0,
+            "content": "Real-world Experiments. To show the generalizability to real-world images, we fine-tune our model on CO3D datasets and evaluate its keypoints transfer performance on two categories from the SPair dataset. The results in Fig. 7 confirm the effectiveness of our approach over NeRF feature on real images. The qualitative results on CO3D are shown in Fig. 8. Even with in-the-wild images, our method can still transfer keypoints and segmentation labels accurately. Note that pre-process steps (e.g. segment and normalize the foreground object) are required."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.757,
+                0.379,
+                0.773
+            ],
+            "angle": 0,
+            "content": "4.3. 3D Semantic Understanding Tasks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.468,
+                0.854
+            ],
+            "angle": 0,
+            "content": "We further validate our proposed method on 3D semantic understanding tasks, which aims to find semantic correspondences between two sets of 3D points based on image observations. We only evaluate under the cross-instance setting for 3D tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Metrics. The metrics for 3D tasks are 3D versions of their counterparts in 2D tasks. For the keypoints transfer, we utilize Euclidean distance instead of 2D pixel distance with"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.51,
+                0.274,
+                0.88,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>NeRF Feat.</td><td>80.73</td><td>75.10</td><td>69.45</td><td>84.65</td><td>87.14</td><td>67.49</td></tr><tr><td>Ours (Diff.)</td><td>73.45</td><td>71.16</td><td>59.16</td><td>83.91</td><td>88.01</td><td>64.28</td></tr><tr><td>Ours (DINO)</td><td>81.93</td><td>76.50</td><td>71.57</td><td>87.97</td><td>87.89</td><td>68.22</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.332,
+                0.892,
+                0.407
+            ],
+            "angle": 0,
+            "content": "Table 2: Novel-view 2D part segmentation label transfer results. The rendered feature maps from other viewpoints still exhibit promising performance for co-segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.441,
+                0.892,
+                0.502
+            ],
+            "angle": 0,
+            "content": "the threshold of (0.025, 0.05, 0.075, 0.1) in the normalized space. For the part co-segmentation, we calculate mIoU based on point clouds instead of pixels. We randomly generate 1000 combinations per category for the evaluation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.505,
+                0.892,
+                0.701
+            ],
+            "angle": 0,
+            "content": "3D Keypoints Transfer. For each 3D keypoint from the source shape, we try to find its corresponding point from a set of sampled candidate points from the target shape. For DINO and diffusion baselines, we simply project the 3D points onto 2D feature maps and utilize the interpolated feature vectors for matching. As those features are not 3D-aware, it is expected that their performance will be suboptimal. The quantitative results are shown in the second row of Fig 3. We can find that our method has a larger advantage in 3D tasks, which can also be observed from the qualitative results in Fig 4. Our learned 3D representation contains accurate semantic information and thus are able to transfer 3D keypoints in a more accurate way."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "3D Part Segmentation Label Transfer. Similar to keypoints transfer, we try to propagate segmentation labels from the source point cloud to the target point cloud based on image observations. Note that the point cloud is only used as a query for segmentation, our method constructs a semantic feature volume for the whole 3D space and allows predicting feature vectors for any given 3D points. The right part of Tab 1 reports mIoUs for all methods. FeatureNeRF consistently outperforms all baselines in all categories, suggesting that distilling feature to 3D-aware representation leads to improved 3D co-segmentation performance. Fig. 5 presents qualitative results. Note that even for occluded areas in 2D images, FeatureNeRF can transfer its labels cor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8969"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.149,
+                0.089,
+                0.396,
+                0.145
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Chair</td><td>Plane</td></tr><tr><td>w/o Lcoord</td><td>75.39</td><td>72.83</td></tr><tr><td>w/o internal features</td><td>74.62</td><td>72.29</td></tr><tr><td>full model</td><td>76.55</td><td>74.60</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.151,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "Table 3: Ablation study. The coordinate loss and the use of internal NeRF features both boost performance."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.198,
+                0.48,
+                0.294
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\"></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td rowspan=\"3\">PSNR</td><td>PixelNeRF [66]</td><td>23.29</td><td>22.86</td><td>24.46</td><td>25.61</td><td>26.04</td><td>20.36</td></tr><tr><td>Ours (Diff.)</td><td>23.36</td><td>23.09</td><td>24.39</td><td>25.42</td><td>25.75</td><td>20.64</td></tr><tr><td>Ours (DINO)</td><td>23.20</td><td>22.92</td><td>24.49</td><td>25.69</td><td>26.01</td><td>20.59</td></tr><tr><td rowspan=\"3\">SSIM</td><td>PixelNeRF [66]</td><td>0.92</td><td>0.91</td><td>0.93</td><td>0.89</td><td>0.89</td><td>0.80</td></tr><tr><td>Ours (Diff.)</td><td>0.92</td><td>0.91</td><td>0.91</td><td>0.87</td><td>0.89</td><td>0.81</td></tr><tr><td>Ours (DINO)</td><td>0.91</td><td>0.91</td><td>0.91</td><td>0.89</td><td>0.90</td><td>0.80</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.301,
+                0.47,
+                0.361
+            ],
+            "angle": 0,
+            "content": "Table 4: Novel-view synthesis results. The proposed distillation process does not hurt the performance of novel-view synthesis, our method achieves comparable performance with PixelNeRF on novel-view synthesis."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.39,
+                0.205,
+                0.404
+            ],
+            "angle": 0,
+            "content": "rectly in 3D space."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.416,
+                0.23,
+                0.431
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.439,
+                0.469,
+                0.529
+            ],
+            "angle": 0,
+            "content": "We mainly ablate the coordinate loss \\(\\mathcal{L}_{\\mathrm{coord}}\\) and the use of internal NeRF features \\(\\mathbf{v}_{\\mathrm{NeRF}}\\) (instead of final output feature vector \\(\\mathbf{v}\\)) for semantic understanding. We conduct experiments of 2D parts co-segmentation on the Chair and Plane classes. The mIoU results are reported in Tab. 3. We can see that both design choices boost performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.53,
+                0.469,
+                0.636
+            ],
+            "angle": 0,
+            "content": "In addition, we compare the performance of novel-view synthesis with PixelNeRF [66] to see if the proposed feature distillation technique hurts the synthesis ability. Both FeatureNeRF and PixelNeRF are trained on our rendered dataset with the same parameters. From Tab. 4, we see that our method achieves comparable performance with PixelNeRF on novel-view synthesis."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.647,
+                0.273,
+                0.663
+            ],
+            "angle": 0,
+            "content": "4.5. Editing Applications"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.671,
+                0.469,
+                0.821
+            ],
+            "angle": 0,
+            "content": "The learned FeatureNeRF model can also be leveraged to editing applications. Here, we take the 3D part texture swapping as an example. Given a source image and its part segmentation label, we can construct a 3D feature volume for the source image. Then, for a target image, we also construct its 3D feature volume and transfer the segmentation label from the source image to it. When rendering the target image, for a 3D point \\(\\mathbf{x}_{\\mathrm{tgt}}\\) that belongs to the part of interests (e.g. chair back) in the target feature volume, we find its closet point in the source feature volume:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.1,
+                0.835,
+                0.445,
+                0.859
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf{x}_{\\text{closet}} = \\operatorname *{arg  min}_{\\mathbf{x}_{\\text{src}}}\\left\\| v_{\\text{NeRF}}\\left(\\mathbf{x}_{\\text{tgt}}\\right) - v_{\\text{NeRF}}\\left(\\mathbf{x}_{\\text{src}}\\right)\\right\\|_{2},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{x}_{\\mathrm{src}} \\in \\mathbf{X}_{\\mathrm{src}}\\) and \\(\\mathbf{X}_{\\mathrm{src}}\\) is the set of sampled points in the source feature volume. Finally, we use the color of the"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.088,
+                0.895,
+                0.285
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.305,
+                0.892,
+                0.38
+            ],
+            "angle": 0,
+            "content": "Figure 9: Editing application: 3D part texture swapping. The part textures from source images are successfully transferred to the target images. Note that the edited target objects can also be rendered from novel views, please see our video for 3D visualizations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.401,
+                0.892,
+                0.431
+            ],
+            "angle": 0,
+            "content": "closet point \\(\\mathbf{x}_{\\mathrm{closet}}\\) to replace the original color of \\(\\mathbf{x}_{\\mathrm{tgt}}\\) for the rendering."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.432,
+                0.892,
+                0.538
+            ],
+            "angle": 0,
+            "content": "The results are shown in Fig. 9. We can find that the part textures from source images are successfully transferred to the target images. Besides, the details are also well preserved (the brown boundary from the source image at the second row still exists in the target images). Note that the edited target instances can also be rendered from novel views, please see our video for 3D visualizations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.556,
+                0.619,
+                0.571
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.838
+            ],
+            "angle": 0,
+            "content": "In contrast to the success of 2D foundation models, it is still unclear how to build foundation models in 3D given the lack of web-scale datasets and effective architecture. In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling 2D vision foundation models. FeatureNeRF explores the use of internal NeRF features as 3D visual descriptors and distills knowledge from 2D foundation models into 3D space via neural rendering. Given a single image, FeatureNeRF allows to predict a 3D semantic feature representation, which can be leveraged for downstream tasks. Specifically, we demonstrate the effectiveness of FeatureNeRF on the tasks of 2D/3D keypoints transfer and part co-segmentation from a single image. In addition, FeatureNeRF can also serve as a general-purpose feature extractor for downstream 3D tasks such as open-world 3D classification/segmentation and robotics tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.84,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. Prof. Wang's lab was supported, in part, by Amazon Research Award, Sony Research Award, Adobe Data Science Research Award, and gifts from Qualcomm."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8970"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+# FeatureNeRF: Learning Generalizable NeRFs by Distilling Foundation Models
+
+Jianglong Ye<sup>1</sup> Naiyan Wang<sup>2</sup> Xiaolong Wang<sup>1</sup>  
+<sup>1</sup>UC San Diego <sup>2</sup>TuSimple
+
+![](images/21fb390b2f40c0010e19ee41d23f8a40107b54f8fcb8e189ad79ccf1740aa8df.jpg)  
+Figure 1: While most generalizable NeRFs focus on novel-view synthesis, we propose a framework named FeatureNeRF to learn 3D semantic representations by distilling vision foundation models. After distillation, FeatureNeRF allows to render novel-view feature maps given a single input image (a), which can be leveraged to various downstream tasks. Here, we show how we propagate part segmentation labels and keypoints to different views and instances in both 2D and 3D domains (b).
+
+![](images/c07f48ba6b67bcfbbfd5d604adb0f028366dc77bc0bb75193b63a6e4135bf3c3.jpg)
+
+# Abstract
+
+Recent works on generalizable NeRFs have shown promising results on novel view synthesis from single or few images. However, such models have rarely been applied on other downstream tasks beyond synthesis such as semantic understanding and parsing. In this paper, we propose a novel framework named FeatureNeRF to learn generalizable NeRFs by distilling pre-trained vision foundation models (e.g., DINO, Latent Diffusion). FeatureNeRF leverages 2D pre-trained foundation models to 3D space via neural rendering, and then extract deep features for 3D query points from NeRF MLPs. Consequently, it allows to map 2D images to continuous 3D semantic feature volumes, which can be used for various downstream tasks. We evaluate FeatureNeRF on tasks of 2D/3D semantic keypoint transfer and 2D/3D object part segmentation. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor. Our project page is available at https://jianglongye.com/featuresenerf/.
+
+# 1. Introduction
+
+Neural fields have emerged as a compelling paradigm for representing a variety of visual signals [8, 10, 31, 32, 37]. In
+
+particular, the Neural Radiance Fields (NeRF [32]), which implicitly encodes density and color via Multi-Layer Perceptrons (MLPs), has shown high quality novel view synthesis results from dense input images. A body of follow-up works [7, 27, 45, 54, 66] further reduce the dependency on dense inputs and generalize NeRF to unseen objects by learning priors from large-scale multi-view image datasets. With the remarkable abilities on reconstruction and view synthesis of generalizable NeRFs, we ask the question: Can we adapt such models to learn 3D representations as foundations for general 3D applications (e.g., recognition, matching) beyond view synthesis?
+
+Recent years have witnessed the rise of vision foundation models [5, 40, 43, 67] that are pre-trained on web-scale image datasets and demonstrate generalization capabilities across massive vision tasks (e.g., CLIP [40], DINO [5], Latent Diffusion [47]). The feature space constructed by foundation models captures rich semantic and structural information of 2D visual data and make it possible to identify object categories, parts and correspondences even without extra supervisions [1, 5, 30]. Motivated by these works, our goal is to leverage the powerful 2D foundations models to obtain generalizable 3D features.
+
+In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling pretrained 2D vision foundation models. Unlike previous gen
+
+eralizable NeRFs [45, 66], which utilize 2D encoder solely for novel view synthesis, FeatureNeRF explores the use of deep features extracted from NeRFs as generalizable 3D visual descriptors. We show that distilling 2D foundation models into 3D space via neural rendering equips the NeRF features with rich semantic information. As a result, FeatureNeRF allows to predict a continuous 3D semantic feature volume from a single or a few images, which can be applied to various downstream tasks such as semantic keypoint transfer and object part co-segmentation. Examples of these applications are shown in Fig. 1.
+
+Specifically, we adopt an encoder to map 2D images to corresponding 3D NeRF volume similar to previous generalizable NeRFs. Apart from density and color, we propose to extract deep features of the query 3D points from the intermediate layers of NeRF MLP. To enrich semantic information of the NeRF features, we further transfer knowledge from the foundation models to the encoder via neural rendering during training: The rendered feature outputs should be consistent with the feature extracted from the foundation models, which is enforced by a distillation loss.
+
+To evaluate FeatureNeRF, we tackle the tasks of 2D/3D semantic keypoint transfer and object part segmentation. To the best of our knowledge, our work is the first to resolve these 3D semantic understanding tasks without 3D supervision. We validate our framework with two foundation models: (i) DINO [5], a self-supervised vision transformer aware of object correspondences, and (ii) Latent Diffusion [47], a diffusion-based model that achieves state-of-the-art text-to-image generation performance. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor.
+
+# 2. Related Work
+
+Generalizable NeRFs. In the past few years, neural fields have gained significant attention and led to rapid progress in representing various visual signals [8, 10, 25, 31, 32, 36, 37, 50, 52, 61]. In particular, NeRF [32] achieves photo-realistic results on novel view synthesis by mapping 3D coordinates and 2D viewing directions to density and color via MLPs. However, the original NeRF requires enormous posed images and time-consuming optimization for each single scene. To address these issues, a large number of follow-up methods [9, 23, 27, 45, 46, 54, 56, 66] propose to learn generalizable NeRFs from large-scale multi-view image datasets. For example, PixelNeRF [66] employs an image encoder to condition NeRF on image features, which enables novel views synthesis from a single image and generalizes NeRF to unseen objects. CodeNeRF [23] learns to disentangle shape and texture by learning separate embeddings, allowing shape and texture editing by varying the latent codes. Recent work TransINR [9] is proposed to infer NeRF parameters directly with a vision transformer to over
+
+come the information bottleneck of encoder-decoder architecture. However, most of these works focus only on view synthesis. Our work differs from them by learning general-purpose 3D representations for multiple downstream tasks.
+
+Vision Foundation Models. The term foundation model is introduced in [3] to refer to the model pre-trained from data at scale and capable of generalizing to a wide range of downstream tasks. After demonstrating huge impacts in NLP [4, 15, 41], a large family of vision foundation models [5, 40, 42, 43, 47, 58, 62, 67] have been proposed and effectively transferred to various vision tasks. For example, the CLIP model [40] is trained from large-scale image-text data using contrastive learning, and it is shown to be transferable to multiple tasks in a zero-shot manner. The DINO model [5] has shown object segment can emerge automatically with only self-supervision, and the learned feature can be applied in a wide range of visual correspondence and recognition tasks [1, 12, 30, 57]. Besides contrastive learning, recent text-conditioned generative model such as diffusion models [16, 21, 35, 47] have been introduced and shown astonishing performance on image generation. Subsequently, feature spaces learned by these generative models have also been used for recognition tasks such as semantic segmentation [2, 59]. In contrast to the success of 2D foundation models, the 3D counterparts are still suffering from the lack of large-scale annotated datasets and effective architectures [18, 49, 60]. In this paper, we propose to distill the features from 2D foundation models to 3D space via the generalizable NeRFs.
+
+Feature Distillation. For the purpose of model compression and knowledge transfer, distillation has been widely studied by the community. After the pioneering work by Hinton et al. [20], which matches the softmax output distribution of the teacher model to that of the student, numerous methods have been proposed to tackle various tasks [19, 22, 38, 39, 53, 64]. Recently, researchers also propose to distill features from 2D models to 3D space by optimizing neural feature fields [26, 55]. Multiple editing tasks are shown as applications. However, these methods not only require test-time optimization for each single scene, but the learned features are also not generalizable to unseen objects, which makes them unsuitable for general semantic understanding tasks and differ from our work fundamentally.
+
+Semantic Correspondences. Given a pair of visual observation, semantic correspondences learning aims to find corresponding points between them. Several supervised [13, 24, 51] and self-supervised [1, 11, 28] methods have been proposed to resolve this task in 2D and 3D domain respectively. In particular, Amir et al. [1] show that utilizing pre-trained 2D foundation models in a zero-shot manner can achieve competitive results with supervised methods on semantic correspondences. Cheng et al. [11] propose to learn point cloud correspondences via
+
+![](images/1e830e67dec17bdf6c37b72751bb6589f18f335c8bac3b241caf141368b54645.jpg)  
+Figure 2: Pipeline of FeatureNeRF. Given a single image  $I$  as input, FeatureNeRF adopts an encoder to extract the image feature  $E_{\pi(\mathbf{x})}$ , and then concatenate it with the query point  $\mathbf{x}$  as well as the view direction  $\mathbf{d}$  as the inputs for NeRF MLPs. Apart from density  $\sigma$  and color  $\mathbf{c}$ , we add two MLP branches to predict the feature vector  $\mathbf{v}$  and coordinate  $\hat{\mathbf{x}}$ , which are supervised by two novel loss terms  $\mathcal{L}_{\mathrm{distill}}$  and  $\mathcal{L}_{\mathrm{coord}}$  respectively. Consequently, we distill knowledge from 2D vision foundation models to FeatureNeRF. Besides, we propose to extract internal NeRF feature  $\mathbf{v}_{\mathrm{NeRF}}$  as 3D-consistent feature representation.
+
+self-reconstruction and cross-reconstruction of 3D shapes. To the best of our knowledge, our work is the first to address semantic correspondences in both 2D and 3D space with only 2D observations.
+
+# 3. Method
+
+We present FeatureNeRF, a unified framework for learning generalizable NeRF from vision foundation models. We give an overview of generalizable NeRFs in Sec. 3.1 and elaborate our feature distillation process in Sec. 3.2. Then we introduce how to learn internal NeRF features for 3D semantic understanding in Sec. 3.3 and downstream applications in Sec. 3.4. The overall pipeline of FeatureNeRF is illustrated in Fig. 2.
+
+# 3.1. Preliminary: Generalizable NeRF
+
+Neural Radiance Fields (NeRF [32]) consists of two functions:  $\sigma (\mathbf{x}):\mathbb{R}^3\mapsto \mathbb{R}_+$  that maps a 3D point  $\mathbf{x}$  to the density  $\sigma$  and  $\mathbf{c}(\mathbf{x},\mathbf{d}):\mathbb{R}^{3\times 3}\mapsto \mathbb{R}^3$  that maps a 3D point as well as a unit viewing direction  $\mathbf{d}$  to color. The radiance field can be rendered and optimized via differentiable volume rendering [29]. Given a pixel's camera ray  $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d}$ , which is defined by the camera origin  $\mathbf{o}\in \mathbb{R}^3$ , view direction  $\mathbf{d}$  and depth  $t$  with bounds  $[t_n,t_f]$ , the estimated color of the ray can be calculated by:
+
+$$
+\hat {\mathbf {C}} (\mathbf {r}) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \sigma (\mathbf {r} (t)) \mathbf {c} (\mathbf {r} (t), \mathbf {d}) \mathrm {d} t, \tag {1}
+$$
+
+where  $T(t) = \exp \left(-\int_{t_n}^t\sigma (s)ds\right)$ . In practice, the integral is approximated with numerical quadrature by sam
+
+pling points along the ray. NeRF is optimized to a single scene with multi-view posed images by minimizing the following reconstruction loss:
+
+$$
+\mathcal {L} _ {\mathrm {r e c}} = \sum_ {\mathbf {r} \in \mathcal {R}} \left\| \mathbf {C} (\mathbf {r}) - \hat {\mathbf {C}} (\mathbf {r}) \right\| _ {2} ^ {2}, \tag {2}
+$$
+
+where  $\mathbf{C}(\mathbf{r})$  is the ground truth color of the ray and  $\mathcal{R}$  is the set of rays generated from camera poses.
+
+In order to generalize to novel scenes, the NeRF model can be conditioned on the input image  $I \in \mathbb{R}^{H \times W \times 3}$ :
+
+$$
+\sigma (\mathbf {x}, I) = g _ {\sigma} \left(\mathbf {x}, f (I) _ {\pi (\mathbf {x})}\right) \tag {3}
+$$
+
+$$
+\mathbf {c} (\mathbf {x}, \mathbf {d}, I) = g _ {\mathbf {c}} \left(\mathbf {x}, \mathbf {d}, f (I) _ {\pi (\mathbf {x})}\right),
+$$
+
+where  $g_{\sigma}$  and  $g_{\mathbf{c}}$  are MLPs that predict density and color respectively,  $f$  is an image encoder and  $\pi$  is the projection function.
+
+As shown in the left part of Fig. 2, the image  $I$  is firstly passed to an encoder  $f_{\mathrm{enc}}$  (blue blocks in the figure) to obtain a feature map  $E = f(I)$ . The query point  $\mathbf{x}$  is projected onto the image plane using known pose and intrinsics to extract the corresponding feature vector  $E_{\pi (\mathbf{x})}$ . Then the feature vectors are concatenated with the positional-encoded point  $\mathbf{x}$  and direction  $\mathbf{d}$ , and passed to subsequent MLPs  $g_{\sigma}$  and  $g_{\mathbf{c}}$  (yellow blocks in the figure) to predict appearance and geometry. When multi-view images are available, feature vectors from different views are aggregated with the average pooling before passing to MLPs.
+
+# 3.2. Feature Distillation from Foundation Models
+
+While most generalizable NeRFs only predict density  $\sigma$  and color c, it's possible to extend NeRF to predict other
+
+quantities of interests. For example, SemanticNeRF [68] and PanopticNeRF [17] propose to add a branch to predict segmentation labels to achieve a 3D-consistent semantic segmentation of a scene. However, these methods require expensive semantic labels during optimization, which is impractical for general cases. In this paper, we aim to transfer knowledge from a pre-trained foundation model  $f_{\mathrm{teacher}}$  to our generalizable NeRFs to perform 3D semantic understanding. To this end, we add a branch to output a high-dimensional feature vector  $\mathbf{v} \in \mathbb{R}^{D}$  for the query point  $\mathbf{x}$ , where  $D$  is the feature channels. Similar to the color rendering (Eq. 1), we can aggregate the feature vectors along a ray as follows:
+
+$$
+\hat {\mathbf {V}} (\mathbf {r}, I) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \sigma (\mathbf {r} (t), I) \mathbf {v} (\mathbf {r} (t), \mathbf {d}, I) d t \tag {4}
+$$
+
+$$
+\mathbf {v} \left(\mathbf {x}, \mathbf {d}, I\right) = g _ {\mathbf {v}} \left(\mathbf {x}, \mathbf {d}, f (I) _ {\pi (\mathbf {x})}\right),
+$$
+
+where  $g_{\mathbf{v}}$  is the MLP that predicts future vectors. Note that our model is still conditioned on the image  $I$  in the above equation.
+
+We then minimize the difference between rendered pixel feature vector  $\hat{\mathbf{V}}$  and the teacher's feature  $\mathbf{V} = f_{\mathrm{teacher}}(I)_{\pi (\mathbf{x})}$ . In this way, we distill the teacher network into our generalizable NeRFs via neural rendering. We add a distillation loss to penalize the difference:
+
+$$
+\mathcal {L} _ {\text {d i s t i l l}} = \sum_ {\mathbf {r} \in \mathcal {R}} \left\| \mathbf {V} (\mathbf {r}) - \hat {\mathbf {V}} (\mathbf {r}) \right\| _ {2} ^ {2}. \tag {5}
+$$
+
+FeatureNeRF can be trained jointly for image reconstruction and feature distillation by combing two losses (Eq. 2 and Eq. 5). We show both color rendering and feature rendering processes in the right part of Fig. 2. We emphasize that, after distillation, FeatureNeRF can obtain a 3D semantic feature function  $\mathbf{v}$  in a single forward pass, which can be used for downstream applications. Our experiments show that the feature function  $\mathbf{v}$ , learned with only 2D observation, contains accurate 3D semantic information.
+
+Our framework can be built on top of any foundation model, and in this work we employ DINO [5] and Latent Diffusion [47] as teacher networks. DINO is a vision transformer trained with self-distillation, and we simply extract features from the deepest layer as teacher features. Latent Diffusion firstly transforms input image  $I$  to the latent space, and utilizes a U-Net [48] architecture to estimate the noise for the backward diffusion process. Besides, the denoising module can be conditioned on inputs like text and segmentation maps. We add noise to the original image, condition the pre-trained model with fixed language prompts (e.g. "Car", "Chair") and extract features from the intermediate layers of U-Net. Distilling these foundation models that pre-trained on large-scale image datasets brings open-world knowledge to our generalizable 3D representation.
+
+# 3.3. Learning Internal NeRF Features for 3D Semantic Understanding
+
+Although we have distilled features from foundation models, it is still questionable whether the final feature output is best suitable for 3D semantic understanding. Here we explore using internal NeRF features as view-independent representations for 3D semantic understanding and introduce a new coordinate loss for learning spatial-aware NeRF features.
+
+While previous works only utilize final outputs of MLPs, we explore whether we can use features from intermediate layers as continuous 3D visual descriptors. Given a input image  $I$ , we firstly learn a function  $\mathbf{v}_{\mathrm{NeRF}}(\mathbf{x},I)$  to predict NeRF features and utilize several shallow MLPs to predict other quantities:
+
+$$
+\mathbf {v} _ {\mathrm {N e R F}} (\mathbf {x}, I) = g _ {\mathrm {N e R F}} \left(\mathbf {x}, f (I) _ {\pi (\mathbf {x})}\right)
+$$
+
+$$
+\sigma (\mathbf {x}, I) = g _ {\sigma} \left(\mathbf {v} _ {\mathrm {N e R F}} (\mathbf {x}, I)\right) \tag {6}
+$$
+
+$$
+\mathbf {c} (\mathbf {x}, \mathbf {d}, I) = g _ {\mathbf {c}} \left(\mathbf {d}, \mathbf {v} _ {\mathrm {N e R F}} (\mathbf {x}, I)\right)
+$$
+
+$$
+\mathbf {v} (\mathbf {x}, \mathbf {d}, I) = g _ {\mathbf {v}} \left(\mathbf {d}, \mathbf {v} _ {\mathrm {N e R F}} (\mathbf {x}, I)\right),
+$$
+
+where  $g_{\mathrm{NeRF}}$  is MLP that predicts NeRF features. Note that the proposed function  $\mathbf{v}_{\mathrm{NeRF}}$  can be learned without the feature distillation introduced in Sec. 3.2, therefore it can be applied to all generalizable NeRFs. The feature extraction process is demonstrated in the bottom of Fig. 2. We compare the performance of NeRF features with and without feature distillation in our experiments.
+
+Even for the feature distillation version, since teacher's features  $\mathbf{V}$  are always not 3D-consistent, using a view-independent representation  $\mathbf{v}_{\mathrm{NeRF}}$  and modeling view-dependent effect using another MLP  $g_{\mathbf{v}}$  that conditioned on view direction  $\mathbf{d}$  further boosts the performance (See Sec. 4.4 for the ablation study).
+
+The supervision of most generalizable NeRFs are RGB values, which do not contain spatial information. To enhance the spatial perception of the NeRF feature, we propose to utilize another MLP branch  $g_{\mathbf{x}}$  (shown at the top of Fig. 2) to regress the input coordinates  $\mathbf{x}$  given the NeRF feature  $\mathbf{v}_{\mathrm{NeRF}}$ :
+
+$$
+\hat {\mathbf {x}} = g _ {\mathbf {x}} \left(\mathbf {v} _ {\text {N e R F}} (\mathbf {x}, I)\right). \tag {7}
+$$
+
+We add a cycle-consistent loss to penalize the difference:
+
+$$
+\mathcal {L} _ {\mathrm {c o o r d}} = \sum_ {\mathbf {r} \in \mathcal {R}} \sum_ {t = t _ {n}} ^ {t _ {f}} \| \mathbf {r} (t) - g _ {\mathbf {x}} \left(\mathbf {v} _ {\mathrm {N e R F}} (\mathbf {r} (t), I)\right) \| _ {2} ^ {2}. \tag {8}
+$$
+
+The final loss function is the weighted sum of all three losses:  $\mathcal{L} = \mathcal{L}_{\mathrm{rec}} + \lambda_{\mathrm{distill}}\mathcal{L}_{\mathrm{distill}} + \lambda_{\mathrm{coord}}\mathcal{L}_{\mathrm{coord}}$ , where  $\lambda_{\mathrm{distill}}$  and  $\lambda_{\mathrm{coord}}$  are weights for different losses. All losses and their forward flows are shown in Fig. 2.
+
+# 3.4. Applications of FeatureNeRF
+
+We demonstrate the effectiveness of the learned 3D semantic NeRF feature function  $\mathbf{v}_{\mathrm{NeRF}}$  on various downstream applications: 2D/3D semantic keypoint transfer and object part segmentation. We deliberately apply simple, zero-shot methodologies on NeRF features, without any fine-tuning or post-process, to validate the proposed representations.
+
+2D Tasks. Given a single image  $I$ , we can render its NeRF feature map  $F \in \mathbb{R}^{H \times W \times D}$  using Eq. 4. Then we can render novel-view feature map  $F'$  from other viewpoints. For feature vectors  $\mathbf{V}$  and  $\mathbf{V}'$  of two pixels from  $F$  and  $F'$ , we use cosine similarity to measure their distance in the feature space:  $D(\mathbf{V}, \mathbf{V}') = \frac{\mathbf{V} \cdot \mathbf{V}'}{\|\mathbf{V}\|_2 \cdot \|\mathbf{V}'\|_2}$ . For the part co-segmentation task, for each pixel feature  $\mathbf{V}'$  in  $F'$ , we take the segmentation label of its closest pixel feature  $\mathbf{V}$  in  $F$  as the predicted segmentation label. For the keypoint transfer task, we adopt a similar process, for the feature  $\mathbf{V}$  of each keypoint in  $F$ , we take the pixel location of its closest feature in  $F'$  as the predicted keypoint.
+
+Since FeatureNeRF is a generalizable NeRF conditioned on the input image, it can be further applied to cross-instance tasks in addition to novel-view tasks for a single instance. Given images  $I_{1}$  and  $I_{2}$  of two instances, we can render their feature maps  $F_{1}$  and  $F_{2}$ . Then we can resolve semantic correspondence tasks in a process similar to the novel-view tasks.
+
+3D Tasks. The FeatureNeRF model learned with only 2D observations can also be leveraged to 3D tasks. Given images  $I_{1}$  and  $I_{2}$  of two instances, we can construct two continuous 3D feature fields. For feature vectors  $\mathbf{v}_1$  and  $\mathbf{v}_2$  of two 3D points  $\mathbf{x}_1$  and  $\mathbf{x}_2$ , we still utilize cosine similarity to measure their distance:  $D(\mathbf{v}_1,\mathbf{v}_2) = \frac{\mathbf{v}_1\cdot\mathbf{v}_2}{\|\mathbf{v}_1\|_2\cdot\|\mathbf{v}_2\|_2}$ . Then we can resolve semantic correspondence tasks in a process similar to the 2D tasks.
+
+# 4. Experiments
+
+# 4.1. Experimental Setting
+
+Datasets. Our experiments are mainly conducted on 6 categories from the ShapeNet [6] dataset: Chair, Car, Airplane, Table, Bottle and Motorcycle. We evaluate our model using annotations from KeypointNet [65], ShapeNet part dataset [63] and PartNet [34]. In addition, we train our model on the real-world CO3D [45] dataset and evaluate its keypoint transfer performance on the Spair [33] dataset. For ShapeNet, we split each category into training (70%), validation (10%), and testing (20%) splits. All shapes are normalized so that the longest edges of the bounding box are equal. For the training set, 50 random camera poses from the upper hemisphere are sampled. For validation and testing sets, 50 fixed camera poses are used. We employ
+
+blender [14] to render RGB images, with a resolution of  $128 \times 128$ , the same as in PixelNeRF [66]. For PartNet, we use level-1 annotations. All annotations are in 3D and can be used for the evaluation of 3D tasks directly. For the evaluation of 2D tasks, we employ PyTorch3D [44] rasterizer to render 2D part segmentation labels and 2D keypoints.
+
+Baselines. We mainly compare FeatureNeRF quantitatively and qualitatively to two foundation models DINO [5] and Latent Diffusion [47]. We extend PixelNeRF [66] with the mechanisms mentioned in Sec. 3.3 to make it possible for semantic understanding tasks and report its performance as "NeRF feature" in all results. In addition, for the 2D cosegmentation task, we re-implement a one-shot generalizable SemanticNeRF* [68] by adding a semantic branch in PixelNeRF, and train it with the source segmentation labels.
+
+Implementation Details. Following PixelNeRF [66], we employ a ResNet-34 model pre-trained on ImageNet as the image encoder  $f$ . The batch size is 4 (objects) and 1024 rays per object. We train a single model for each object category for 500k steps. The weights for different losses are  $\lambda_{\mathrm{distill}} = 0.25$  and  $\lambda_{\mathrm{coord}} = 0.25$ . The dimension of the internal NeRF feature is 512. MLP for NeRF feature  $g_{\mathrm{NeRF}}$  is 4-layer, all other shallow MLPs for final outputs  $(g_{\sigma}, g_{\mathbf{c}}, g_{\mathbf{v}}$  and  $g_{\mathbf{x}})$  are one-layer.
+
+Teacher Networks. We employ DINO [5] and Latent Diffusion [47] as teacher networks, which are pre-trained and publicly available. The patch size of DINO is 8. The final feature map has dimension  $32 \times 32 \times 384$ . For Latent Diffusion, we extract the outputs of the 4th layer in U-Net as teacher features. The language prompts used to condition denoising modules are class names (e.g. "Chair", "Car") from ShapeNet. The final feature map has dimension  $128 \times 128 \times 960$ . The weights of teacher networks are fixed during distillation.
+
+# 4.2. 2D Semantic Understanding Tasks
+
+As mentioned in Sec. 3.4, we evaluate FeatureNeRF on tasks of 2D keypoints transfer and part segmentation labels transfer under two settings: (i) Cross-instance: given images of two instances, we transfer keypoints/segmentation labels from the source image to the target image and compare the transferred labels in the target image with the ground truth. (ii) Novel-view: given a single image of an instance, we render a novel-view feature map, transfer labels from the source viewpoint to the target viewpoint and compare the transferred labels in the target viewpoint with the ground truth.
+
+Metrics. For the task of 2D keypoints transfer, we report the percentage of predicted keypoints whose distances from their corresponding ground truths are below thresholds of (2.5, 5.0, 7.5, 10.0) pixels in the target image. We denote this percentage as Correspondence Accuracy in the following. For the task of part segmentation labels trans
+
+![](images/360d8db1b2d2280f22c67cab75b17c30e502f3f62fadff49ec50ffeb0768fff1.jpg)  
+Figure 3: Correspondence accuracy for cross-instance semantic keypoints transfer. The first row is for 2D keypoints transfer and the second row is for 3D. Our approach distilled with different features consistently outperforms baselines for all categories in both 2D and 3D domains.
+
+![](images/1f5183ce13abb3eed031c8a185792b740687f60d3fb8e164770aa727edcc6254.jpg)  
+(a) 2D results
+
+![](images/af49cbbf127baf049ffa3f7c025dfea8b0e13e1dc7dfa392c82d9f0697021259.jpg)  
+(b) 3D results  
+Figure 4: Qualitative results for cross-instance semantic keypoints transfer. Both 2D (a) and 3D (b) results are presented here. Each row contains a source image with keypoints annotations and its pairwise transfer results.
+
+fer, we calculate the mean intersection over union  $(mIoU)$  over every part category for each object class. For both settings, we randomly generate 1000 combinations per category. While generating, we make sure that the source viewpoints/instances and target viewpoints/instances have intersecting keypoints/segmentation labels.
+
+2D Keypoints Transfer. We report correspondence accuracy of 2D cross-instance keypoints transfer in the first row of Fig. 3. We show that for all 6 categories, keypoints transferred via our proposed method are more accurate than baselines. The performances of distilling diffusion and DINO features are similar. Using NeRF feature without distilling foundation models (denoted as "NeRF feature" in the figure) also achieves a reasonable performance compared to 2D foundation model baselines. Fig. 4 (a) shows the qual
+
+itative results for 2D keypoints transfer. It can be seen that despite various appearances and structures of instances, our method can successfully transfer keypoints based on semantic understanding, while baselines often fail.
+
+FeatureNeRF learns a 3D representation from 2D observations, which allows to synthesize novel-view feature maps for different viewpoints and performs keypoints transfer on top of it. Fig. 6 (a) shows qualitative results of novel-view keypoints transfer. Since 2D foundation models can not synthesize novel-view feature maps, we do not apply them to this novel-view setting.
+
+2D Part Segmentation Label Transfer. We report mIoU results of 2D cross-instance part segmentation label transfer in the left part of Tab. 1. FeatureNeRF distilled with DINO features significantly outperforms other approaches
+
+![](images/119a059fe338ffddf927ebc2f18602def9f13db319267be7828d1646a0ee201e.jpg)  
+Figure 5: Qualitative results for cross-instance part segmentation label transfer. Each row contains a source image and its 2D/3D transfer results. After distilling, FeatureNeRF learns richer semantic information, produces better boundaries and preserves details like small parts. Note that the segmentation label for the source instance is omitted.
+
+![](images/ed8d458f02cbc0aed0f3aaa0c54148705d5fd48672817211b906ee2e7b75c030.jpg)  
+Figure 6: Qualitative results of novel-view keypoints transfer and part co-segmentation. FeatureNeRF learns a 3D representation from 2D observations, which makes it possible to synthesize feature maps from other viewpoints and transfer keypoints and segmentation labels to them.
+
+![](images/146ce826a2e62b2e21ada216e32a980f976bb22e339e261ecdf596b0683e9139.jpg)
+
+<table><tr><td rowspan="2"></td><td colspan="6">2D part co-segmentation</td><td colspan="6">3D part co-segmentation</td></tr><tr><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>SemanticNeRF*</td><td>50.32</td><td>34.61</td><td>56.19</td><td>54.87</td><td>51.58</td><td>27.62</td><td></td><td></td><td></td><td>-</td><td></td><td></td></tr><tr><td>Diffusion Baseline</td><td>41.59</td><td>42.46</td><td>44.60</td><td>57.77</td><td>41.72</td><td>25.50</td><td>33.60</td><td>24.74</td><td>30.45</td><td>44.34</td><td>53.81</td><td>20.01</td></tr><tr><td>DINO Baseline</td><td>62.43</td><td>54.59</td><td>57.81</td><td>64.01</td><td>59.73</td><td>37.05</td><td>52.67</td><td>29.72</td><td>40.16</td><td>49.98</td><td>70.79</td><td>29.25</td></tr><tr><td>NeRF Feature</td><td>72.02</td><td>58.57</td><td>72.57</td><td>70.41</td><td>55.87</td><td>44.00</td><td>65.23</td><td>59.19</td><td>71.23</td><td>61.64</td><td>66.63</td><td>44.88</td></tr><tr><td>Ours (Diffusion)</td><td>65.39</td><td>63.02</td><td>72.95</td><td>70.59</td><td>53.91</td><td>44.84</td><td>63.65</td><td>61.27</td><td>73.41</td><td>63.93</td><td>66.91</td><td>49.05</td></tr><tr><td>Ours (DINO)</td><td>76.55</td><td>66.85</td><td>74.60</td><td>74.06</td><td>61.13</td><td>49.56</td><td>73.85</td><td>64.99</td><td>74.20</td><td>66.52</td><td>72.33</td><td>52.56</td></tr></table>
+
+Table 1: Cross-instance part segmentation label transfer results. We report mIoU of part co-segmentation for each category. The left part is for 2D and the right is for 3D. By distilling features to the 3D space, our proposed representation contains richer semantic information which is apt for this co-segmentation task.
+
+for all 6 categories. However, the performance of FeatureNeRF distilled with diffusion features is not as good as the DINO one. This is possible since the keypoints transfer task may focus on predicting accurate locations of sparse pixels that contain the richest semantic information, but part cosegmentation requires denser correspondences. Qualitative results are shown Fig. 5 (a). We can find that NeRF feature often produces unexpected artifacts. We attribute this phenomenon to NeRF feature's training only relying on RGB
+
+information. In contrast, by distilling pre-trained features, our method produces better boundaries and preserves details like small parts. Note that the segmentation label of the source object is also required during the transfer process, which is omitted in the figure.
+
+We also perform novel-view part co-segmentation and report both quantitative and qualitative results in Tab. 2 and Fig. 6 (b) respectively. The rendered feature maps from other viewpoints still exhibit promising performance for co
+
+![](images/19aa2a1102f840ace5e2ced29dceae3843fdfe7dbeed6f86eaab627017142b3f.jpg)  
+Figure 7: Keypoints transfer on SPair. Our method outperforms NeRF feature on 5 categories on the real-world dataset.
+
+![](images/51ebca655e2ba3e3319f4254220cc26bf476fb546ebc6f33d554ff7e2a730ce1.jpg)  
+Figure 8: Keypoints and segmentation label transfer on CO3D. After training on CO3D, our method can accurately transfer keypoints and segmentation labels with in-the-wild image inputs
+
+segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation.
+
+Real-world Experiments. To show the generalizability to real-world images, we fine-tune our model on CO3D datasets and evaluate its keypoints transfer performance on two categories from the SPair dataset. The results in Fig. 7 confirm the effectiveness of our approach over NeRF feature on real images. The qualitative results on CO3D are shown in Fig. 8. Even with in-the-wild images, our method can still transfer keypoints and segmentation labels accurately. Note that pre-process steps (e.g. segment and normalize the foreground object) are required.
+
+# 4.3. 3D Semantic Understanding Tasks
+
+We further validate our proposed method on 3D semantic understanding tasks, which aims to find semantic correspondences between two sets of 3D points based on image observations. We only evaluate under the cross-instance setting for 3D tasks.
+
+Metrics. The metrics for 3D tasks are 3D versions of their counterparts in 2D tasks. For the keypoints transfer, we utilize Euclidean distance instead of 2D pixel distance with
+
+<table><tr><td></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>NeRF Feat.</td><td>80.73</td><td>75.10</td><td>69.45</td><td>84.65</td><td>87.14</td><td>67.49</td></tr><tr><td>Ours (Diff.)</td><td>73.45</td><td>71.16</td><td>59.16</td><td>83.91</td><td>88.01</td><td>64.28</td></tr><tr><td>Ours (DINO)</td><td>81.93</td><td>76.50</td><td>71.57</td><td>87.97</td><td>87.89</td><td>68.22</td></tr></table>
+
+Table 2: Novel-view 2D part segmentation label transfer results. The rendered feature maps from other viewpoints still exhibit promising performance for co-segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation.
+
+the threshold of (0.025, 0.05, 0.075, 0.1) in the normalized space. For the part co-segmentation, we calculate mIoU based on point clouds instead of pixels. We randomly generate 1000 combinations per category for the evaluation.
+
+3D Keypoints Transfer. For each 3D keypoint from the source shape, we try to find its corresponding point from a set of sampled candidate points from the target shape. For DINO and diffusion baselines, we simply project the 3D points onto 2D feature maps and utilize the interpolated feature vectors for matching. As those features are not 3D-aware, it is expected that their performance will be suboptimal. The quantitative results are shown in the second row of Fig 3. We can find that our method has a larger advantage in 3D tasks, which can also be observed from the qualitative results in Fig 4. Our learned 3D representation contains accurate semantic information and thus are able to transfer 3D keypoints in a more accurate way.
+
+3D Part Segmentation Label Transfer. Similar to keypoints transfer, we try to propagate segmentation labels from the source point cloud to the target point cloud based on image observations. Note that the point cloud is only used as a query for segmentation, our method constructs a semantic feature volume for the whole 3D space and allows predicting feature vectors for any given 3D points. The right part of Tab 1 reports mIoUs for all methods. FeatureNeRF consistently outperforms all baselines in all categories, suggesting that distilling feature to 3D-aware representation leads to improved 3D co-segmentation performance. Fig. 5 presents qualitative results. Note that even for occluded areas in 2D images, FeatureNeRF can transfer its labels cor
+
+<table><tr><td>Method</td><td>Chair</td><td>Plane</td></tr><tr><td>w/o Lcoord</td><td>75.39</td><td>72.83</td></tr><tr><td>w/o internal features</td><td>74.62</td><td>72.29</td></tr><tr><td>full model</td><td>76.55</td><td>74.60</td></tr></table>
+
+Table 3: Ablation study. The coordinate loss and the use of internal NeRF features both boost performance.  
+
+<table><tr><td colspan="2"></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td rowspan="3">PSNR</td><td>PixelNeRF [66]</td><td>23.29</td><td>22.86</td><td>24.46</td><td>25.61</td><td>26.04</td><td>20.36</td></tr><tr><td>Ours (Diff.)</td><td>23.36</td><td>23.09</td><td>24.39</td><td>25.42</td><td>25.75</td><td>20.64</td></tr><tr><td>Ours (DINO)</td><td>23.20</td><td>22.92</td><td>24.49</td><td>25.69</td><td>26.01</td><td>20.59</td></tr><tr><td rowspan="3">SSIM</td><td>PixelNeRF [66]</td><td>0.92</td><td>0.91</td><td>0.93</td><td>0.89</td><td>0.89</td><td>0.80</td></tr><tr><td>Ours (Diff.)</td><td>0.92</td><td>0.91</td><td>0.91</td><td>0.87</td><td>0.89</td><td>0.81</td></tr><tr><td>Ours (DINO)</td><td>0.91</td><td>0.91</td><td>0.91</td><td>0.89</td><td>0.90</td><td>0.80</td></tr></table>
+
+Table 4: Novel-view synthesis results. The proposed distillation process does not hurt the performance of novel-view synthesis, our method achieves comparable performance with PixelNeRF on novel-view synthesis.
+
+rectly in 3D space.
+
+# 4.4. Ablation Study
+
+We mainly ablate the coordinate loss  $\mathcal{L}_{\mathrm{coord}}$  and the use of internal NeRF features  $\mathbf{v}_{\mathrm{NeRF}}$  (instead of final output feature vector  $\mathbf{v}$ ) for semantic understanding. We conduct experiments of 2D parts co-segmentation on the Chair and Plane classes. The mIoU results are reported in Tab. 3. We can see that both design choices boost performance.
+
+In addition, we compare the performance of novel-view synthesis with PixelNeRF [66] to see if the proposed feature distillation technique hurts the synthesis ability. Both FeatureNeRF and PixelNeRF are trained on our rendered dataset with the same parameters. From Tab. 4, we see that our method achieves comparable performance with PixelNeRF on novel-view synthesis.
+
+# 4.5. Editing Applications
+
+The learned FeatureNeRF model can also be leveraged to editing applications. Here, we take the 3D part texture swapping as an example. Given a source image and its part segmentation label, we can construct a 3D feature volume for the source image. Then, for a target image, we also construct its 3D feature volume and transfer the segmentation label from the source image to it. When rendering the target image, for a 3D point  $\mathbf{x}_{\mathrm{tgt}}$  that belongs to the part of interests (e.g. chair back) in the target feature volume, we find its closet point in the source feature volume:
+
+$$
+\mathbf{x}_{\text{closet}} = \operatorname *{arg  min}_{\mathbf{x}_{\text{src}}}\left\| v_{\text{NeRF}}\left(\mathbf{x}_{\text{tgt}}\right) - v_{\text{NeRF}}\left(\mathbf{x}_{\text{src}}\right)\right\|_{2},
+$$
+
+where  $\mathbf{x}_{\mathrm{src}} \in \mathbf{X}_{\mathrm{src}}$  and  $\mathbf{X}_{\mathrm{src}}$  is the set of sampled points in the source feature volume. Finally, we use the color of the
+
+![](images/5b6af87b3df73cb0fc7c2cce048dfa125678cc6b462b8dfdf94b8ada80e77bf8.jpg)  
+Figure 9: Editing application: 3D part texture swapping. The part textures from source images are successfully transferred to the target images. Note that the edited target objects can also be rendered from novel views, please see our video for 3D visualizations.
+
+closet point  $\mathbf{x}_{\mathrm{closet}}$  to replace the original color of  $\mathbf{x}_{\mathrm{tgt}}$  for the rendering.
+
+The results are shown in Fig. 9. We can find that the part textures from source images are successfully transferred to the target images. Besides, the details are also well preserved (the brown boundary from the source image at the second row still exists in the target images). Note that the edited target instances can also be rendered from novel views, please see our video for 3D visualizations.
+
+# 5. Conclusion
+
+In contrast to the success of 2D foundation models, it is still unclear how to build foundation models in 3D given the lack of web-scale datasets and effective architecture. In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling 2D vision foundation models. FeatureNeRF explores the use of internal NeRF features as 3D visual descriptors and distills knowledge from 2D foundation models into 3D space via neural rendering. Given a single image, FeatureNeRF allows to predict a 3D semantic feature representation, which can be leveraged for downstream tasks. Specifically, we demonstrate the effectiveness of FeatureNeRF on the tasks of 2D/3D keypoints transfer and part co-segmentation from a single image. In addition, FeatureNeRF can also serve as a general-purpose feature extractor for downstream 3D tasks such as open-world 3D classification/segmentation and robotics tasks.
+
+Acknowledgements. Prof. Wang's lab was supported, in part, by Amazon Research Award, Sony Research Award, Adobe Data Science Research Award, and gifts from Qualcomm.
+
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+[61] Yiheng Xie, Towaki Takikawa, Shunsuke Saito, Or Litany, Shiqin Yan, Numair Khan, Federico Tombari, James Tompkin, Vincent Sitzmann, and Srinath Sridhar. Neural fields in visual computing and beyond. In Computer Graphics Forum, volume 41, pages 641-676. Wiley Online Library, 2022. 2  
+[62] Zhenda Xie, Yutong Lin, Zhuliang Yao, Zheng Zhang, Qi Dai, Yue Cao, and Han Hu. Self-supervised learning with swim transformers. arXiv preprint arXiv:2105.04553, 2021. 2  
+[63] Li Yi, Vladimir G. Kim, Duygu Ceylan, I-Chao Shen, Mengyan Yan, Hao Su, Cewu Lu, Qixing Huang, Alla Sheffer, and Leonidas Guibas. A scalable active framework for region annotation in 3d shape collections. SIGGRAPH Asia, 2016. 5  
+[64] Junho Yim, Donggyu Joo, Ji-Hoon Bae, and Junmo Kim. A gift from knowledge distillation: Fast optimization, network minimization and transfer learning. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 7130-7138, 2017. 2  
+[65] Yang You, Yujing Lou, Chengkun Li, Zhoujun Cheng, Liangwei Li, Lizhuang Ma, Cewu Lu, and Weiming Wang. Keypointnet: A large-scale 3d keypoint dataset aggregated from numerous human annotations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13647-13656, 2020. 5  
+[66] Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelnerf: Neural radiance fields from one or few images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4578-4587, 2021. 1, 2, 5, 9  
+[67] Lu Yuan, Dongdong Chen, Yi-Ling Chen, Noel Codella, Xiyang Dai, Jianfeng Gao, Houdong Hu, Xuedong Huang, Boxin Li, Chunyuan Li, et al. Florence: A new
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+foundation model for computer vision. arXiv preprint arXiv:2111.11432, 2021. 1, 2  
+[68] Shuaifeng Zhi, Tristan Laidlow, Stefan Leutenegger, and Andrew J Davison. In-place scene labelling and understanding with implicit scene representation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 15838-15847, 2021. 4, 5
\ No newline at end of file
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+                                            "content": "Figure 1: While most generalizable NeRFs focus on novel-view synthesis, we propose a framework named FeatureNeRF to learn 3D semantic representations by distilling vision foundation models. After distillation, FeatureNeRF allows to render novel-view feature maps given a single input image (a), which can be leveraged to various downstream tasks. Here, we show how we propagate part segmentation labels and keypoints to different views and instances in both 2D and 3D domains (b)."
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+                                    "content": "Recent works on generalizable NeRFs have shown promising results on novel view synthesis from single or few images. However, such models have rarely been applied on other downstream tasks beyond synthesis such as semantic understanding and parsing. In this paper, we propose a novel framework named FeatureNeRF to learn generalizable NeRFs by distilling pre-trained vision foundation models (e.g., DINO, Latent Diffusion). FeatureNeRF leverages 2D pre-trained foundation models to 3D space via neural rendering, and then extract deep features for 3D query points from NeRF MLPs. Consequently, it allows to map 2D images to continuous 3D semantic feature volumes, which can be used for various downstream tasks. We evaluate FeatureNeRF on tasks of 2D/3D semantic keypoint transfer and 2D/3D object part segmentation. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor. Our project page is available at https://jianglongye.com/featuresenerf/."
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+                                    "content": "Neural fields have emerged as a compelling paradigm for representing a variety of visual signals [8, 10, 31, 32, 37]. In"
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+                            ]
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+                                    "content": "particular, the Neural Radiance Fields (NeRF [32]), which implicitly encodes density and color via Multi-Layer Perceptrons (MLPs), has shown high quality novel view synthesis results from dense input images. A body of follow-up works [7, 27, 45, 54, 66] further reduce the dependency on dense inputs and generalize NeRF to unseen objects by learning priors from large-scale multi-view image datasets. With the remarkable abilities on reconstruction and view synthesis of generalizable NeRFs, we ask the question: Can we adapt such models to learn 3D representations as foundations for general 3D applications (e.g., recognition, matching) beyond view synthesis?"
+                                }
+                            ]
+                        }
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+                                    "content": "Recent years have witnessed the rise of vision foundation models [5, 40, 43, 67] that are pre-trained on web-scale image datasets and demonstrate generalization capabilities across massive vision tasks (e.g., CLIP [40], DINO [5], Latent Diffusion [47]). The feature space constructed by foundation models captures rich semantic and structural information of 2D visual data and make it possible to identify object categories, parts and correspondences even without extra supervisions [1, 5, 30]. Motivated by these works, our goal is to leverage the powerful 2D foundations models to obtain generalizable 3D features."
+                                }
+                            ]
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+                                    "content": "In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling pretrained 2D vision foundation models. Unlike previous gen"
+                                }
+                            ]
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+                    "index": 13
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+                                    "type": "text",
+                                    "content": "eralizable NeRFs [45, 66], which utilize 2D encoder solely for novel view synthesis, FeatureNeRF explores the use of deep features extracted from NeRFs as generalizable 3D visual descriptors. We show that distilling 2D foundation models into 3D space via neural rendering equips the NeRF features with rich semantic information. As a result, FeatureNeRF allows to predict a continuous 3D semantic feature volume from a single or a few images, which can be applied to various downstream tasks such as semantic keypoint transfer and object part co-segmentation. Examples of these applications are shown in Fig. 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                                    "content": "Specifically, we adopt an encoder to map 2D images to corresponding 3D NeRF volume similar to previous generalizable NeRFs. Apart from density and color, we propose to extract deep features of the query 3D points from the intermediate layers of NeRF MLP. To enrich semantic information of the NeRF features, we further transfer knowledge from the foundation models to the encoder via neural rendering during training: The rendered feature outputs should be consistent with the feature extracted from the foundation models, which is enforced by a distillation loss."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        49,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "To evaluate FeatureNeRF, we tackle the tasks of 2D/3D semantic keypoint transfer and object part segmentation. To the best of our knowledge, our work is the first to resolve these 3D semantic understanding tasks without 3D supervision. We validate our framework with two foundation models: (i) DINO [5], a self-supervised vision transformer aware of object correspondences, and (ii) Latent Diffusion [47], a diffusion-based model that achieves state-of-the-art text-to-image generation performance. Our extensive experiments demonstrate the effectiveness of FeatureNeRF as a generalizable 3D semantic feature extractor."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "content": "2. Related Work"
+                                }
+                            ]
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+                },
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+                                    "content": "Generalizable NeRFs. In the past few years, neural fields have gained significant attention and led to rapid progress in representing various visual signals [8, 10, 25, 31, 32, 36, 37, 50, 52, 61]. In particular, NeRF [32] achieves photo-realistic results on novel view synthesis by mapping 3D coordinates and 2D viewing directions to density and color via MLPs. However, the original NeRF requires enormous posed images and time-consuming optimization for each single scene. To address these issues, a large number of follow-up methods [9, 23, 27, 45, 46, 54, 56, 66] propose to learn generalizable NeRFs from large-scale multi-view image datasets. For example, PixelNeRF [66] employs an image encoder to condition NeRF on image features, which enables novel views synthesis from a single image and generalizes NeRF to unseen objects. CodeNeRF [23] learns to disentangle shape and texture by learning separate embeddings, allowing shape and texture editing by varying the latent codes. Recent work TransINR [9] is proposed to infer NeRF parameters directly with a vision transformer to over"
+                                }
+                            ]
+                        }
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+                    "index": 4
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+                                    "type": "text",
+                                    "content": "come the information bottleneck of encoder-decoder architecture. However, most of these works focus only on view synthesis. Our work differs from them by learning general-purpose 3D representations for multiple downstream tasks."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Vision Foundation Models. The term foundation model is introduced in [3] to refer to the model pre-trained from data at scale and capable of generalizing to a wide range of downstream tasks. After demonstrating huge impacts in NLP [4, 15, 41], a large family of vision foundation models [5, 40, 42, 43, 47, 58, 62, 67] have been proposed and effectively transferred to various vision tasks. For example, the CLIP model [40] is trained from large-scale image-text data using contrastive learning, and it is shown to be transferable to multiple tasks in a zero-shot manner. The DINO model [5] has shown object segment can emerge automatically with only self-supervision, and the learned feature can be applied in a wide range of visual correspondence and recognition tasks [1, 12, 30, 57]. Besides contrastive learning, recent text-conditioned generative model such as diffusion models [16, 21, 35, 47] have been introduced and shown astonishing performance on image generation. Subsequently, feature spaces learned by these generative models have also been used for recognition tasks such as semantic segmentation [2, 59]. In contrast to the success of 2D foundation models, the 3D counterparts are still suffering from the lack of large-scale annotated datasets and effective architectures [18, 49, 60]. In this paper, we propose to distill the features from 2D foundation models to 3D space via the generalizable NeRFs."
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+                                    "content": "Feature Distillation. For the purpose of model compression and knowledge transfer, distillation has been widely studied by the community. After the pioneering work by Hinton et al. [20], which matches the softmax output distribution of the teacher model to that of the student, numerous methods have been proposed to tackle various tasks [19, 22, 38, 39, 53, 64]. Recently, researchers also propose to distill features from 2D models to 3D space by optimizing neural feature fields [26, 55]. Multiple editing tasks are shown as applications. However, these methods not only require test-time optimization for each single scene, but the learned features are also not generalizable to unseen objects, which makes them unsuitable for general semantic understanding tasks and differ from our work fundamentally."
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+                                    "content": "Semantic Correspondences. Given a pair of visual observation, semantic correspondences learning aims to find corresponding points between them. Several supervised [13, 24, 51] and self-supervised [1, 11, 28] methods have been proposed to resolve this task in 2D and 3D domain respectively. In particular, Amir et al. [1] show that utilizing pre-trained 2D foundation models in a zero-shot manner can achieve competitive results with supervised methods on semantic correspondences. Cheng et al. [11] propose to learn point cloud correspondences via"
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+                                            "content": "Figure 2: Pipeline of FeatureNeRF. Given a single image "
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+                                            "content": " as well as the view direction "
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+                                            "content": " as the inputs for NeRF MLPs. Apart from density "
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+                                            "content": ", we add two MLP branches to predict the feature vector "
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+                                            "content": ", which are supervised by two novel loss terms "
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+                                            "type": "text",
+                                            "content": " respectively. Consequently, we distill knowledge from 2D vision foundation models to FeatureNeRF. Besides, we propose to extract internal NeRF feature "
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+                                            "content": " as 3D-consistent feature representation."
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+                                    "content": "self-reconstruction and cross-reconstruction of 3D shapes. To the best of our knowledge, our work is the first to address semantic correspondences in both 2D and 3D space with only 2D observations."
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+                                    "content": "3. Method"
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+                                    "content": "We present FeatureNeRF, a unified framework for learning generalizable NeRF from vision foundation models. We give an overview of generalizable NeRFs in Sec. 3.1 and elaborate our feature distillation process in Sec. 3.2. Then we introduce how to learn internal NeRF features for 3D semantic understanding in Sec. 3.3 and downstream applications in Sec. 3.4. The overall pipeline of FeatureNeRF is illustrated in Fig. 2."
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+                                    "content": "\\mathbf{c}(\\mathbf{x},\\mathbf{d}):\\mathbb{R}^{3\\times 3}\\mapsto \\mathbb{R}^3"
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+                                    "type": "text",
+                                    "content": " that maps a 3D point as well as a unit viewing direction "
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+                                    "content": " to color. The radiance field can be rendered and optimized via differentiable volume rendering [29]. Given a pixel's camera ray "
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+                                    "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}"
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+                                    "type": "inline_equation",
+                                    "content": "[t_n,t_f]"
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+                                    "content": ", the estimated color of the ray can be calculated by:"
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+                                    "content": "\\hat {\\mathbf {C}} (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) \\mathbf {c} (\\mathbf {r} (t), \\mathbf {d}) \\mathrm {d} t, \\tag {1}",
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+                                    "content": "T(t) = \\exp \\left(-\\int_{t_n}^t\\sigma (s)ds\\right)"
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+                                    "type": "text",
+                                    "content": ". In practice, the integral is approximated with numerical quadrature by sam"
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+                                    "content": "pling points along the ray. NeRF is optimized to a single scene with multi-view posed images by minimizing the following reconstruction loss:"
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+                                    "content": "\\mathcal {L} _ {\\mathrm {r e c}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\mathbf {C} (\\mathbf {r}) - \\hat {\\mathbf {C}} (\\mathbf {r}) \\right\\| _ {2} ^ {2}, \\tag {2}",
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+                                    "content": "\\mathbf{C}(\\mathbf{r})"
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+                                    "type": "text",
+                                    "content": " is the ground truth color of the ray and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}"
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+                                    "type": "text",
+                                    "content": " is the set of rays generated from camera poses."
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+                                    "type": "text",
+                                    "content": "In order to generalize to novel scenes, the NeRF model can be conditioned on the input image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "I \\in \\mathbb{R}^{H \\times W \\times 3}"
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\sigma (\\mathbf {x}, I) = g _ {\\sigma} \\left(\\mathbf {x}, f (I) _ {\\pi (\\mathbf {x})}\\right) \\tag {3}",
+                                    "image_path": "26871655339790b8d7f6b34173260a13b76b871a7ba8b92772589022c40e8c65.jpg"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {c}} \\left(\\mathbf {x}, \\mathbf {d}, f (I) _ {\\pi (\\mathbf {x})}\\right),",
+                                    "image_path": "11635a7957e23553e4b8e1c213ee4d88bf6b698cd8a37f0cef87e805cc4c36d8.jpg"
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+                                    "content": "where "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are MLPs that predict density and color respectively, "
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+                                    "type": "inline_equation",
+                                    "content": "f"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is an image encoder and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\pi"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the projection function."
+                                }
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+                {
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+                                    "type": "text",
+                                    "content": "As shown in the left part of Fig. 2, the image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is firstly passed to an encoder "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (blue blocks in the figure) to obtain a feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "E = f(I)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The query point "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
+                                        546,
+                                        666
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
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+                                        666
+                                    ],
+                                    "type": "text",
+                                    "content": " is projected onto the image plane using known pose and intrinsics to extract the corresponding feature vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
+                                        546,
+                                        666
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E_{\\pi (\\mathbf{x})}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
+                                        546,
+                                        666
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then the feature vectors are concatenated with the positional-encoded point "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
+                                        546,
+                                        666
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and direction "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and passed to subsequent MLPs "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
+                                        546,
+                                        666
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\sigma}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        533,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathbf{c}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " (yellow blocks in the figure) to predict appearance and geometry. When multi-view images are available, feature vectors from different views are aggregated with the average pooling before passing to MLPs."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.2. Feature Distillation from Foundation Models"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "While most generalizable NeRFs only predict density "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\sigma"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and color c, it's possible to extend NeRF to predict other"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                }
+            ],
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "quantities of interests. For example, SemanticNeRF [68] and PanopticNeRF [17] propose to add a branch to predict segmentation labels to achieve a 3D-consistent semantic segmentation of a scene. However, these methods require expensive semantic labels during optimization, which is impractical for general cases. In this paper, we aim to transfer knowledge from a pre-trained foundation model "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{teacher}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to our generalizable NeRFs to perform 3D semantic understanding. To this end, we add a branch to output a high-dimensional feature vector "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v} \\in \\mathbb{R}^{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " for the query point "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " is the feature channels. Similar to the color rendering (Eq. 1), we can aggregate the feature vectors along a ray as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {\\mathbf {V}} (\\mathbf {r}, I) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t), I) \\mathbf {v} (\\mathbf {r} (t), \\mathbf {d}, I) d t \\tag {4}",
+                                    "image_path": "eef8084f8f31fe3ab66eef91f3b1128a1f9e81d680218bdcde4ebd1881e81750.jpg"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {v} \\left(\\mathbf {x}, \\mathbf {d}, I\\right) = g _ {\\mathbf {v}} \\left(\\mathbf {x}, \\mathbf {d}, f (I) _ {\\pi (\\mathbf {x})}\\right),",
+                                    "image_path": "213b717dbe899f0df636b54fc2ab2b70a3b7d976d34fca72566e9b271a2c012a.jpg"
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathbf{v}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the MLP that predicts future vectors. Note that our model is still conditioned on the image "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in the above equation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We then minimize the difference between rendered pixel feature vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{V}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and the teacher's feature "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        316,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V} = f_{\\mathrm{teacher}}(I)_{\\pi (\\mathbf{x})}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        316,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "text",
+                                    "content": ". In this way, we distill the teacher network into our generalizable NeRFs via neural rendering. We add a distillation loss to penalize the difference:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
+                                        99,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {d i s t i l l}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\mathbf {V} (\\mathbf {r}) - \\hat {\\mathbf {V}} (\\mathbf {r}) \\right\\| _ {2} ^ {2}. \\tag {5}",
+                                    "image_path": "ef3804af149d751e5eab94e33704c8ea45a1f47d843fe27bbce719b10ad9f5f3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "FeatureNeRF can be trained jointly for image reconstruction and feature distillation by combing two losses (Eq. 2 and Eq. 5). We show both color rendering and feature rendering processes in the right part of Fig. 2. We emphasize that, after distillation, FeatureNeRF can obtain a 3D semantic feature function "
+                                },
+                                {
+                                    "bbox": [
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+                                        415,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        415,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in a single forward pass, which can be used for downstream applications. Our experiments show that the feature function "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        415,
+                                        287,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        415,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", learned with only 2D observation, contains accurate 3D semantic information."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        46,
+                        522,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Our framework can be built on top of any foundation model, and in this work we employ DINO [5] and Latent Diffusion [47] as teacher networks. DINO is a vision transformer trained with self-distillation, and we simply extract features from the deepest layer as teacher features. Latent Diffusion firstly transforms input image "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        522,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        522,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to the latent space, and utilizes a U-Net [48] architecture to estimate the noise for the backward diffusion process. Besides, the denoising module can be conditioned on inputs like text and segmentation maps. We add noise to the original image, condition the pre-trained model with fixed language prompts (e.g. \"Car\", \"Chair\") and extract features from the intermediate layers of U-Net. Distilling these foundation models that pre-trained on large-scale image datasets brings open-world knowledge to our generalizable 3D representation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "3.3. Learning Internal NeRF Features for 3D Semantic Understanding"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Although we have distilled features from foundation models, it is still questionable whether the final feature output is best suitable for 3D semantic understanding. Here we explore using internal NeRF features as view-independent representations for 3D semantic understanding and introduce a new coordinate loss for learning spatial-aware NeRF features."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "bbox": [
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+                                        258
+                                    ],
+                                    "type": "text",
+                                    "content": "While previous works only utilize final outputs of MLPs, we explore whether we can use features from intermediate layers as continuous 3D visual descriptors. Given a input image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        187,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "text",
+                                    "content": ", we firstly learn a function "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        187,
+                                        547,
+                                        258
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_{\\mathrm{NeRF}}(\\mathbf{x},I)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        187,
+                                        547,
+                                        258
+                                    ],
+                                    "type": "text",
+                                    "content": " to predict NeRF features and utilize several shallow MLPs to predict other quantities:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I) = g _ {\\mathrm {N e R F}} \\left(\\mathbf {x}, f (I) _ {\\pi (\\mathbf {x})}\\right)",
+                                    "image_path": "69423c45d40c3fe0438b3a19751c45821bdfbf6387dd0e1d57bdd5d890bb529b.jpg"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\sigma (\\mathbf {x}, I) = g _ {\\sigma} \\left(\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right) \\tag {6}",
+                                    "image_path": "529a454ea8944e1f71467c75011138242ee00ed3b94cd7d38f690d323e853b53.jpg"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {c} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {c}} \\left(\\mathbf {d}, \\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right)",
+                                    "image_path": "39b621dbbda6bb5889f1b86a88e6cee6df62ad022dfdf139b5773d6571b72b6d.jpg"
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {v} (\\mathbf {x}, \\mathbf {d}, I) = g _ {\\mathbf {v}} \\left(\\mathbf {d}, \\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {x}, I)\\right),",
+                                    "image_path": "ef66d9e0ff3ff71f2160dba571fff7757d53a7a29dea6a7830c3f617c8de15dc.jpg"
+                                }
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+                },
+                {
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+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        420
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathrm{NeRF}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        420
+                                    ],
+                                    "type": "text",
+                                    "content": " is MLP that predicts NeRF features. Note that the proposed function "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        420
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_{\\mathrm{NeRF}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                        420
+                                    ],
+                                    "type": "text",
+                                    "content": " can be learned without the feature distillation introduced in Sec. 3.2, therefore it can be applied to all generalizable NeRFs. The feature extraction process is demonstrated in the bottom of Fig. 2. We compare the performance of NeRF features with and without feature distillation in our experiments."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                        493
+                                    ],
+                                    "type": "text",
+                                    "content": "Even for the feature distillation version, since teacher's features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "text",
+                                    "content": " are always not 3D-consistent, using a view-independent representation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_{\\mathrm{NeRF}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "text",
+                                    "content": " and modeling view-dependent effect using another MLP "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathbf{v}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "text",
+                                    "content": " that conditioned on view direction "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        422,
+                                        545,
+                                        493
+                                    ],
+                                    "type": "text",
+                                    "content": " further boosts the performance (See Sec. 4.4 for the ablation study)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The supervision of most generalizable NeRFs are RGB values, which do not contain spatial information. To enhance the spatial perception of the NeRF feature, we propose to utilize another MLP branch "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathbf{x}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        494,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " (shown at the top of Fig. 2) to regress the input coordinates "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        494,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        494,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " given the NeRF feature "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        494,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_{\\mathrm{NeRF}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        494,
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+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        376,
+                                        577,
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+                                        590
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {\\mathbf {x}} = g _ {\\mathbf {x}} \\left(\\mathbf {v} _ {\\text {N e R F}} (\\mathbf {x}, I)\\right). \\tag {7}",
+                                    "image_path": "fb68c40d6ce5a89d6956381f5fa43fb4410d6f1a230b4a8cd0f9464781632636.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        600,
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+                                    ],
+                                    "type": "text",
+                                    "content": "We add a cycle-consistent loss to penalize the difference:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                                {
+                                    "bbox": [
+                                        315,
+                                        622,
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+                                        656
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {c o o r d}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\sum_ {t = t _ {n}} ^ {t _ {f}} \\| \\mathbf {r} (t) - g _ {\\mathbf {x}} \\left(\\mathbf {v} _ {\\mathrm {N e R F}} (\\mathbf {r} (t), I)\\right) \\| _ {2} ^ {2}. \\tag {8}",
+                                    "image_path": "33d91f84d1ffe527afb7bd24a072873d49192115bebbbbdb19b67825e05a3b47.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The final loss function is the weighted sum of all three losses: "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L} = \\mathcal{L}_{\\mathrm{rec}} + \\lambda_{\\mathrm{distill}}\\mathcal{L}_{\\mathrm{distill}} + \\lambda_{\\mathrm{coord}}\\mathcal{L}_{\\mathrm{coord}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{\\mathrm{distill}}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are weights for different losses. All losses and their forward flows are shown in Fig. 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "3.4. Applications of FeatureNeRF"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We demonstrate the effectiveness of the learned 3D semantic NeRF feature function "
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+                                    "type": "text",
+                                    "content": " on various downstream applications: 2D/3D semantic keypoint transfer and object part segmentation. We deliberately apply simple, zero-shot methodologies on NeRF features, without any fine-tuning or post-process, to validate the proposed representations."
+                                }
+                            ]
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+                    ],
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+                },
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+                                    ],
+                                    "type": "text",
+                                    "content": "2D Tasks. Given a single image "
+                                },
+                                {
+                                    "bbox": [
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+                                        175,
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we can render its NeRF feature map "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "F \\in \\mathbb{R}^{H \\times W \\times D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " using Eq. 4. Then we can render novel-view feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
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+                                    "type": "inline_equation",
+                                    "content": "F'"
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+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
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+                                    "type": "text",
+                                    "content": " from other viewpoints. For feature vectors "
+                                },
+                                {
+                                    "bbox": [
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+                                        175,
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+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}'"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " of two pixels from "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
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+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F'"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", we use cosine similarity to measure their distance in the feature space: "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D(\\mathbf{V}, \\mathbf{V}') = \\frac{\\mathbf{V} \\cdot \\mathbf{V}'}{\\|\\mathbf{V}\\|_2 \\cdot \\|\\mathbf{V}'\\|_2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ". For the part co-segmentation task, for each pixel feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}'"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
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+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F'"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", we take the segmentation label of its closest pixel feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " as the predicted segmentation label. For the keypoint transfer task, we adopt a similar process, for the feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " of each keypoint in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", we take the pixel location of its closest feature in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F'"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        175,
+                                        286,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " as the predicted keypoint."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        323,
+                        286,
+                        405
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": "Since FeatureNeRF is a generalizable NeRF conditioned on the input image, it can be further applied to cross-instance tasks in addition to novel-view tasks for a single instance. Given images "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{1}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
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+                                    "type": "inline_equation",
+                                    "content": "I_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": " of two instances, we can render their feature maps "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we can resolve semantic correspondence tasks in a process similar to the novel-view tasks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                        286,
+                        503
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": "3D Tasks. The FeatureNeRF model learned with only 2D observations can also be leveraged to 3D tasks. Given images "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": " of two instances, we can construct two continuous 3D feature fields. For feature vectors "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": " of two 3D points "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": ", we still utilize cosine similarity to measure their distance: "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D(\\mathbf{v}_1,\\mathbf{v}_2) = \\frac{\\mathbf{v}_1\\cdot\\mathbf{v}_2}{\\|\\mathbf{v}_1\\|_2\\cdot\\|\\mathbf{v}_2\\|_2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        407,
+                                        286,
+                                        503
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we can resolve semantic correspondence tasks in a process similar to the 2D tasks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
+                        518,
+                        127,
+                        532
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        47,
+                        538,
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+                    ],
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+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.1. Experimental Setting"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        46,
+                        558,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Datasets. Our experiments are mainly conducted on 6 categories from the ShapeNet [6] dataset: Chair, Car, Airplane, Table, Bottle and Motorcycle. We evaluate our model using annotations from KeypointNet [65], ShapeNet part dataset [63] and PartNet [34]. In addition, we train our model on the real-world CO3D [45] dataset and evaluate its keypoint transfer performance on the Spair [33] dataset. For ShapeNet, we split each category into training (70%), validation (10%), and testing (20%) splits. All shapes are normalized so that the longest edges of the bounding box are equal. For the training set, 50 random camera poses from the upper hemisphere are sampled. For validation and testing sets, 50 fixed camera poses are used. We employ"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        305,
+                        72,
+                        545,
+                        144
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": "blender [14] to render RGB images, with a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "128 \\times 128"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ", the same as in PixelNeRF [66]. For PartNet, we use level-1 annotations. All annotations are in 3D and can be used for the evaluation of 3D tasks directly. For the evaluation of 2D tasks, we employ PyTorch3D [44] rasterizer to render 2D part segmentation labels and 2D keypoints."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        305,
+                        144,
+                        545,
+                        251
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        144,
+                                        545,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": "Baselines. We mainly compare FeatureNeRF quantitatively and qualitatively to two foundation models DINO [5] and Latent Diffusion [47]. We extend PixelNeRF [66] with the mechanisms mentioned in Sec. 3.3 to make it possible for semantic understanding tasks and report its performance as \"NeRF feature\" in all results. In addition, for the 2D cosegmentation task, we re-implement a one-shot generalizable SemanticNeRF* [68] by adding a semantic branch in PixelNeRF, and train it with the source segmentation labels."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Implementation Details. Following PixelNeRF [66], we employ a ResNet-34 model pre-trained on ImageNet as the image encoder "
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+                                    "type": "text",
+                                    "content": ". The batch size is 4 (objects) and 1024 rays per object. We train a single model for each object category for 500k steps. The weights for different losses are "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{\\mathrm{distill}} = 0.25"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{\\mathrm{coord}} = 0.25"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The dimension of the internal NeRF feature is 512. MLP for NeRF feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathrm{NeRF}}"
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+                                    "type": "text",
+                                    "content": " is 4-layer, all other shallow MLPs for final outputs "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(g_{\\sigma}, g_{\\mathbf{c}}, g_{\\mathbf{v}}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathbf{x}})"
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+                                {
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+                                    "type": "text",
+                                    "content": " are one-layer."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Teacher Networks. We employ DINO [5] and Latent Diffusion [47] as teacher networks, which are pre-trained and publicly available. The patch size of DINO is 8. The final feature map has dimension "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "32 \\times 32 \\times 384"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". For Latent Diffusion, we extract the outputs of the 4th layer in U-Net as teacher features. The language prompts used to condition denoising modules are class names (e.g. \"Chair\", \"Car\") from ShapeNet. The final feature map has dimension "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "128 \\times 128 \\times 960"
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+                                    "type": "text",
+                                    "content": ". The weights of teacher networks are fixed during distillation."
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+                                    "type": "text",
+                                    "content": "4.2. 2D Semantic Understanding Tasks"
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+                                    "type": "text",
+                                    "content": "As mentioned in Sec. 3.4, we evaluate FeatureNeRF on tasks of 2D keypoints transfer and part segmentation labels transfer under two settings: (i) Cross-instance: given images of two instances, we transfer keypoints/segmentation labels from the source image to the target image and compare the transferred labels in the target image with the ground truth. (ii) Novel-view: given a single image of an instance, we render a novel-view feature map, transfer labels from the source viewpoint to the target viewpoint and compare the transferred labels in the target viewpoint with the ground truth."
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+                                    "content": "Metrics. For the task of 2D keypoints transfer, we report the percentage of predicted keypoints whose distances from their corresponding ground truths are below thresholds of (2.5, 5.0, 7.5, 10.0) pixels in the target image. We denote this percentage as Correspondence Accuracy in the following. For the task of part segmentation labels trans"
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+                                            "content": "Figure 3: Correspondence accuracy for cross-instance semantic keypoints transfer. The first row is for 2D keypoints transfer and the second row is for 3D. Our approach distilled with different features consistently outperforms baselines for all categories in both 2D and 3D domains."
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+                                            "type": "text",
+                                            "content": "Figure 4: Qualitative results for cross-instance semantic keypoints transfer. Both 2D (a) and 3D (b) results are presented here. Each row contains a source image with keypoints annotations and its pairwise transfer results."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "fer, we calculate the mean intersection over union "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "(mIoU)"
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+                                    "type": "text",
+                                    "content": " over every part category for each object class. For both settings, we randomly generate 1000 combinations per category. While generating, we make sure that the source viewpoints/instances and target viewpoints/instances have intersecting keypoints/segmentation labels."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "2D Keypoints Transfer. We report correspondence accuracy of 2D cross-instance keypoints transfer in the first row of Fig. 3. We show that for all 6 categories, keypoints transferred via our proposed method are more accurate than baselines. The performances of distilling diffusion and DINO features are similar. Using NeRF feature without distilling foundation models (denoted as \"NeRF feature\" in the figure) also achieves a reasonable performance compared to 2D foundation model baselines. Fig. 4 (a) shows the qual"
+                                }
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+                                    "type": "text",
+                                    "content": "itative results for 2D keypoints transfer. It can be seen that despite various appearances and structures of instances, our method can successfully transfer keypoints based on semantic understanding, while baselines often fail."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "FeatureNeRF learns a 3D representation from 2D observations, which allows to synthesize novel-view feature maps for different viewpoints and performs keypoints transfer on top of it. Fig. 6 (a) shows qualitative results of novel-view keypoints transfer. Since 2D foundation models can not synthesize novel-view feature maps, we do not apply them to this novel-view setting."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "2D Part Segmentation Label Transfer. We report mIoU results of 2D cross-instance part segmentation label transfer in the left part of Tab. 1. FeatureNeRF distilled with DINO features significantly outperforms other approaches"
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 5: Qualitative results for cross-instance part segmentation label transfer. Each row contains a source image and its 2D/3D transfer results. After distilling, FeatureNeRF learns richer semantic information, produces better boundaries and preserves details like small parts. Note that the segmentation label for the source instance is omitted."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td colspan=\"6\">2D part co-segmentation</td><td colspan=\"6\">3D part co-segmentation</td></tr><tr><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>SemanticNeRF*</td><td>50.32</td><td>34.61</td><td>56.19</td><td>54.87</td><td>51.58</td><td>27.62</td><td></td><td></td><td></td><td>-</td><td></td><td></td></tr><tr><td>Diffusion Baseline</td><td>41.59</td><td>42.46</td><td>44.60</td><td>57.77</td><td>41.72</td><td>25.50</td><td>33.60</td><td>24.74</td><td>30.45</td><td>44.34</td><td>53.81</td><td>20.01</td></tr><tr><td>DINO Baseline</td><td>62.43</td><td>54.59</td><td>57.81</td><td>64.01</td><td>59.73</td><td>37.05</td><td>52.67</td><td>29.72</td><td>40.16</td><td>49.98</td><td>70.79</td><td>29.25</td></tr><tr><td>NeRF Feature</td><td>72.02</td><td>58.57</td><td>72.57</td><td>70.41</td><td>55.87</td><td>44.00</td><td>65.23</td><td>59.19</td><td>71.23</td><td>61.64</td><td>66.63</td><td>44.88</td></tr><tr><td>Ours (Diffusion)</td><td>65.39</td><td>63.02</td><td>72.95</td><td>70.59</td><td>53.91</td><td>44.84</td><td>63.65</td><td>61.27</td><td>73.41</td><td>63.93</td><td>66.91</td><td>49.05</td></tr><tr><td>Ours (DINO)</td><td>76.55</td><td>66.85</td><td>74.60</td><td>74.06</td><td>61.13</td><td>49.56</td><td>73.85</td><td>64.99</td><td>74.20</td><td>66.52</td><td>72.33</td><td>52.56</td></tr></table>",
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+                                    "content": "Table 1: Cross-instance part segmentation label transfer results. We report mIoU of part co-segmentation for each category. The left part is for 2D and the right is for 3D. By distilling features to the 3D space, our proposed representation contains richer semantic information which is apt for this co-segmentation task."
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+                                    "content": "for all 6 categories. However, the performance of FeatureNeRF distilled with diffusion features is not as good as the DINO one. This is possible since the keypoints transfer task may focus on predicting accurate locations of sparse pixels that contain the richest semantic information, but part cosegmentation requires denser correspondences. Qualitative results are shown Fig. 5 (a). We can find that NeRF feature often produces unexpected artifacts. We attribute this phenomenon to NeRF feature's training only relying on RGB"
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+                                    "content": "information. In contrast, by distilling pre-trained features, our method produces better boundaries and preserves details like small parts. Note that the segmentation label of the source object is also required during the transfer process, which is omitted in the figure."
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+                                    "content": "We also perform novel-view part co-segmentation and report both quantitative and qualitative results in Tab. 2 and Fig. 6 (b) respectively. The rendered feature maps from other viewpoints still exhibit promising performance for co"
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+                                    "type": "text",
+                                    "content": "segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation."
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+                                    "content": "Real-world Experiments. To show the generalizability to real-world images, we fine-tune our model on CO3D datasets and evaluate its keypoints transfer performance on two categories from the SPair dataset. The results in Fig. 7 confirm the effectiveness of our approach over NeRF feature on real images. The qualitative results on CO3D are shown in Fig. 8. Even with in-the-wild images, our method can still transfer keypoints and segmentation labels accurately. Note that pre-process steps (e.g. segment and normalize the foreground object) are required."
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+                                    "content": "4.3. 3D Semantic Understanding Tasks"
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+                                    "content": "We further validate our proposed method on 3D semantic understanding tasks, which aims to find semantic correspondences between two sets of 3D points based on image observations. We only evaluate under the cross-instance setting for 3D tasks."
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+                                    "content": "Metrics. The metrics for 3D tasks are 3D versions of their counterparts in 2D tasks. For the keypoints transfer, we utilize Euclidean distance instead of 2D pixel distance with"
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+                                            "html": "<table><tr><td></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td>NeRF Feat.</td><td>80.73</td><td>75.10</td><td>69.45</td><td>84.65</td><td>87.14</td><td>67.49</td></tr><tr><td>Ours (Diff.)</td><td>73.45</td><td>71.16</td><td>59.16</td><td>83.91</td><td>88.01</td><td>64.28</td></tr><tr><td>Ours (DINO)</td><td>81.93</td><td>76.50</td><td>71.57</td><td>87.97</td><td>87.89</td><td>68.22</td></tr></table>",
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+                                    "content": "Table 2: Novel-view 2D part segmentation label transfer results. The rendered feature maps from other viewpoints still exhibit promising performance for co-segmentation, which proves that FeatureNeRF learns a 3D-consistent feature representation."
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+                                    "type": "text",
+                                    "content": "the threshold of (0.025, 0.05, 0.075, 0.1) in the normalized space. For the part co-segmentation, we calculate mIoU based on point clouds instead of pixels. We randomly generate 1000 combinations per category for the evaluation."
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+                                    "type": "text",
+                                    "content": "3D Keypoints Transfer. For each 3D keypoint from the source shape, we try to find its corresponding point from a set of sampled candidate points from the target shape. For DINO and diffusion baselines, we simply project the 3D points onto 2D feature maps and utilize the interpolated feature vectors for matching. As those features are not 3D-aware, it is expected that their performance will be suboptimal. The quantitative results are shown in the second row of Fig 3. We can find that our method has a larger advantage in 3D tasks, which can also be observed from the qualitative results in Fig 4. Our learned 3D representation contains accurate semantic information and thus are able to transfer 3D keypoints in a more accurate way."
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+                                    "content": "3D Part Segmentation Label Transfer. Similar to keypoints transfer, we try to propagate segmentation labels from the source point cloud to the target point cloud based on image observations. Note that the point cloud is only used as a query for segmentation, our method constructs a semantic feature volume for the whole 3D space and allows predicting feature vectors for any given 3D points. The right part of Tab 1 reports mIoUs for all methods. FeatureNeRF consistently outperforms all baselines in all categories, suggesting that distilling feature to 3D-aware representation leads to improved 3D co-segmentation performance. Fig. 5 presents qualitative results. Note that even for occluded areas in 2D images, FeatureNeRF can transfer its labels cor"
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+                                            "html": "<table><tr><td>Method</td><td>Chair</td><td>Plane</td></tr><tr><td>w/o Lcoord</td><td>75.39</td><td>72.83</td></tr><tr><td>w/o internal features</td><td>74.62</td><td>72.29</td></tr><tr><td>full model</td><td>76.55</td><td>74.60</td></tr></table>",
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+                                            "content": "Table 3: Ablation study. The coordinate loss and the use of internal NeRF features both boost performance."
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+                                            "html": "<table><tr><td colspan=\"2\"></td><td>Chair</td><td>Car</td><td>Plane</td><td>Table</td><td>Bottle</td><td>Motorbike</td></tr><tr><td rowspan=\"3\">PSNR</td><td>PixelNeRF [66]</td><td>23.29</td><td>22.86</td><td>24.46</td><td>25.61</td><td>26.04</td><td>20.36</td></tr><tr><td>Ours (Diff.)</td><td>23.36</td><td>23.09</td><td>24.39</td><td>25.42</td><td>25.75</td><td>20.64</td></tr><tr><td>Ours (DINO)</td><td>23.20</td><td>22.92</td><td>24.49</td><td>25.69</td><td>26.01</td><td>20.59</td></tr><tr><td rowspan=\"3\">SSIM</td><td>PixelNeRF [66]</td><td>0.92</td><td>0.91</td><td>0.93</td><td>0.89</td><td>0.89</td><td>0.80</td></tr><tr><td>Ours (Diff.)</td><td>0.92</td><td>0.91</td><td>0.91</td><td>0.87</td><td>0.89</td><td>0.81</td></tr><tr><td>Ours (DINO)</td><td>0.91</td><td>0.91</td><td>0.91</td><td>0.89</td><td>0.90</td><td>0.80</td></tr></table>",
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+                                    "content": "Table 4: Novel-view synthesis results. The proposed distillation process does not hurt the performance of novel-view synthesis, our method achieves comparable performance with PixelNeRF on novel-view synthesis."
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+                                    "content": "rectly in 3D space."
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+                                    "content": "4.4. Ablation Study"
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+                                    "content": "We mainly ablate the coordinate loss "
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+                                    "type": "text",
+                                    "content": " and the use of internal NeRF features "
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+                                    "content": "\\mathbf{v}_{\\mathrm{NeRF}}"
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+                                    "type": "text",
+                                    "content": " (instead of final output feature vector "
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+                                    "type": "text",
+                                    "content": ") for semantic understanding. We conduct experiments of 2D parts co-segmentation on the Chair and Plane classes. The mIoU results are reported in Tab. 3. We can see that both design choices boost performance."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "In addition, we compare the performance of novel-view synthesis with PixelNeRF [66] to see if the proposed feature distillation technique hurts the synthesis ability. Both FeatureNeRF and PixelNeRF are trained on our rendered dataset with the same parameters. From Tab. 4, we see that our method achieves comparable performance with PixelNeRF on novel-view synthesis."
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+                                    "type": "text",
+                                    "content": "4.5. Editing Applications"
+                                }
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+                                    "type": "text",
+                                    "content": "The learned FeatureNeRF model can also be leveraged to editing applications. Here, we take the 3D part texture swapping as an example. Given a source image and its part segmentation label, we can construct a 3D feature volume for the source image. Then, for a target image, we also construct its 3D feature volume and transfer the segmentation label from the source image to it. When rendering the target image, for a 3D point "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{\\mathrm{tgt}}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " that belongs to the part of interests (e.g. chair back) in the target feature volume, we find its closet point in the source feature volume:"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf{x}_{\\text{closet}} = \\operatorname *{arg  min}_{\\mathbf{x}_{\\text{src}}}\\left\\| v_{\\text{NeRF}}\\left(\\mathbf{x}_{\\text{tgt}}\\right) - v_{\\text{NeRF}}\\left(\\mathbf{x}_{\\text{src}}\\right)\\right\\|_{2},",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{\\mathrm{src}} \\in \\mathbf{X}_{\\mathrm{src}}"
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " is the set of sampled points in the source feature volume. Finally, we use the color of the"
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 9: Editing application: 3D part texture swapping. The part textures from source images are successfully transferred to the target images. Note that the edited target objects can also be rendered from novel views, please see our video for 3D visualizations."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "content": "closet point "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to replace the original color of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{\\mathrm{tgt}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for the rendering."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "The results are shown in Fig. 9. We can find that the part textures from source images are successfully transferred to the target images. Besides, the details are also well preserved (the brown boundary from the source image at the second row still exists in the target images). Note that the edited target instances can also be rendered from novel views, please see our video for 3D visualizations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "lines": [
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+                                    "type": "text",
+                                    "content": "In contrast to the success of 2D foundation models, it is still unclear how to build foundation models in 3D given the lack of web-scale datasets and effective architecture. In this paper, we present FeatureNeRF, a unified framework for learning generalizable NeRFs from distilling 2D vision foundation models. FeatureNeRF explores the use of internal NeRF features as 3D visual descriptors and distills knowledge from 2D foundation models into 3D space via neural rendering. Given a single image, FeatureNeRF allows to predict a 3D semantic feature representation, which can be leveraged for downstream tasks. Specifically, we demonstrate the effectiveness of FeatureNeRF on the tasks of 2D/3D keypoints transfer and part co-segmentation from a single image. In addition, FeatureNeRF can also serve as a general-purpose feature extractor for downstream 3D tasks such as open-world 3D classification/segmentation and robotics tasks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Acknowledgements. Prof. Wang's lab was supported, in part, by Amazon Research Award, Sony Research Award, Adobe Data Science Research Award, and gifts from Qualcomm."
+                                }
+                            ]
+                        }
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+                    "index": 18
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diff --git a/2023/FedPD_ Federated Open Set Recognition with Parameter Disentanglement/edefee4b-642c-4a0c-ba36-c80cdd791aa1_content_list.json b/2023/FedPD_ Federated Open Set Recognition with Parameter Disentanglement/edefee4b-642c-4a0c-ba36-c80cdd791aa1_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..9ba2779793bde03653a765a3770f5eeee7bda02a
--- /dev/null
+++ b/2023/FedPD_ Federated Open Set Recognition with Parameter Disentanglement/edefee4b-642c-4a0c-ba36-c80cdd791aa1_content_list.json	
@@ -0,0 +1,1684 @@
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+        "text": "<sup>1</sup>City University of Hong Kong",
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+    {
+        "type": "text",
+        "text": "2The Chinese University of Hong Kong",
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+    {
+        "type": "text",
+        "text": "{cyang53, meiluzhu2}-c@my.cityu.edu.hk 1155195605@link.cuhk.edu.hk yxyuan@ee.cuhk.edu.hk",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Existing federated learning (FL) approaches are deployed under the unrealistic closed-set setting, with both training and testing classes belong to the same set, which makes the global model fail to identify the unseen classes as 'unknown'. To this end, we aim to study a novel problem of federated open-set recognition (FedOSR), which learns an open-set recognition (OSR) model under federated paradigm such that it classifies seen classes while at the same time detects unknown classes. In this work, we propose a parameter disentanglement guided federated open-set recognition (FedPD) algorithm to address two core challenges of FedOSR: cross-client inter-set interference between learning closed-set and open-set knowledge and cross-client intra-set inconsistency by data heterogeneity. The proposed FedPD framework mainly leverages two modules, i.e., local parameter disentanglement (LPD) and global divide-and-conquer aggregation (GDCA), to first disentangle client OSR model into different subnetworks, then align the corresponding parts cross clients for matched model aggregation. Specifically, on the client side, LPD decouples an OSR model into a closed-set subnetwork and an open-set subnetwork by the task-related importance, thus preventing inter-set interference. On the server side, GDCA first partitions the two subnetworks into specific and shared parts, and subsequently aligns the corresponding parts through optimal transport to eliminate parameter misalignment. Extensive experiments on various datasets demonstrate the superior performance of our proposed method.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Deep learning algorithms rely on the availability of large-scale data to achieve remarkable performance. However, in reality, data is scattered across different organiza",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/42158c9670bec7e8408c21cb65edc777235df594b2af20162ccfde6dbe50ed0d.jpg",
+        "image_caption": [
+            "Figure 1. Parameter disentanglement on FedOSR models and comparison of various aggregation strategies on FedOSR setting. (a) FedAvg simply aggregates multiple OSR models, leading to model collapse; (b) Our FedPD first aligns corresponding close-specific, open-specific and shared parts by optimal transport (OT), then aggregates aligned parameters. The curves inside the network box represent different parameter distribution of each parts."
+        ],
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+    {
+        "type": "text",
+        "text": "tions and difficult to integrate into a centralized dataset, owing to increasing privacy and ethical concerns, especially for those sensitive data such as location-based services or health information [22]. To break this dilemma, federated learning (FL) [5, 23, 20] provides a privacy-preserving paradigm that allows local clients to collaboratively train a shared global model without data sharing.",
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+    {
+        "type": "text",
+        "text": "Although FL has recently achieved promising progress, existing FL works [23, 20, 5] are generally evaluated in a closed-set scenario, where the categories of training and testing samples are identical. The closed-set setting is irrational since unknown classes may appear at the test time and would be classified into known classes. This problem seriously impedes the deployment of FL models in many real-world applications due to enormous risk, such as clinical diagnosis and autonomous driving. Current open-set recognition (OSR) methods [3, 43, 2, 6] attempt to improve the",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "*Yixuan Yuan is the corresponding author.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "This work was supported by Hong Kong Research Grants Council(RGC) General Research Fund 1422062214204321, and Innovation and Technology Commission-Innovation and Technology Fund ITS/100/20.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "4882",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ability of models in recognizing unknown classes, but they are designed for the centralized setting. In this work, we represent the first effort to formulate a challenging and unexplored problem of Federated Open Set Recognition (FedOSR). FedOSR aims to unite multiple distributed clients to learn a global model and reduce privacy as well as security risk, which not only exactly classifies known classes but also recognizes unknown classes in the testing stage.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Directly applying existing OSR methods into the FL setting for FedOSR mainly undergoes two troublesome challenges. The first challenge lies in the cross-client inter-set interference between learning closed-set and open-set knowledge. According to the previous study [34], the partial parameters of a client model are in charge of learning knowledge of known classes, and the rest are related to open set. The known classes-related parameters of a client is probably polluted by the open set-related parameters from other clients after server communication, leading to the performance degradation on closed set. Similarly, open set-related parameters of a client are also affected by closed-set knowledge of other clients. In this situation, a unknown samples would be possibly misclassified into known classes. The second one is cross-client intra-set inconsistency by data heterogeneity. Even though we aggregate corresponding closed-related parameters of OSR models from different clients, these parameters are still misaligned due to the permutation invariance property of neural networks and data heterogeneity [37]. Aggregation of local client parameters directly at the server can result in inconsistent models among the clients, leading to significant divergence of client models. This inconsistency issue can cause slow and unstable convergence [19], ultimately resulting in sub-optimal performance of the entire FL system [17, 37].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To achieve FedOSR, we conquer these intractable challenges from a new perspective, i.e., parameter disentanglement. Based on the lottery ticket hypothesis [7, 11, 36], we divide parameters of a client model into a closed-set subnetwork and an open-set subnetwork. These two subnetworks have their own specific parameters, which are only related to known classes and unknown classes respectively. Meanwhile, they also share partial parameters since known and unknown samples might have some similar patterns [35]. The parameter disentanglement of client models can preserve the high performance of closed set by reducing the interference from open-set subnetworks. As shown in Fig. 1, the closed-set subnetworks and the open-set subnetworks of different client models distribute in different positions with some overlaps. Directly aggregating all client OSR models by FedAvg [23] on the server side may encounter the parameter misalignment problem and lead to model collapse as shown in Fig. 1 (a). These destroyed parameters are transmitted to clients and slow down the convergence of the federated system due to bad model initialization to the",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "next training step. Therefore, aligning these subnetworks before model aggregation is a crucial step to solve the inconsistency problem of parameter distributions.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "To tackle these challenges in FedOSR, we propose a novel parameter disentanglement guided federated OSR (FedPD) algorithm in this paper, which effectively addresses the local parameter misalignment problem occurred on the global model aggregation. Specifically, we design a local parameter disentanglement strategy (LPD) to firstly decouple an OSR model into two subnetworks: an open-set subnetwork and a closed-set subnetwork by task-related metrics. To overcome the parameter misalignment caused by simply parameter averaging on whole client OSR models, we propose a global divide-and-conquer aggregation (GDCA) method to firstly divide two subnetworks into specific parts and shared parts, then align corresponding parameter components by optimal transport [13, 30] and aggregate them. As shown in Fig. 1 (b), our FedPD enables reasonable model aggregation and reliable global model to boost federated training.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "The major contribution of this paper are summarized as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We address a practical FL problem, namely Federated Open-Set Recognition (FedOSR). To the best of our knowledge, this is the first work to improve the ability of detecting novel category for federated models.",
+            "- We propose a novel Parameter Disentanglement guided Federated algorithm (FedPD) to solve parameter misalignment problem in FedOSR.",
+            "- On the client side, we introduce the Local Parameter Disentanglement (LPD) approach, which leverages task-related importance on model parameters to decouple the local OSR model into a closed-set subnetwork and an open-set subnetwork.",
+            "- On the server side, we design a Global Divide-and-Conquer Aggregation (GDCA) strategy to partition the two subnetworks into specific and shared parts, align the corresponding parts via optimal transport, and subsequently fuse them to alleviate the misalignment problem in FedOSR."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Federated Learning",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Federated learning [23, 20, 38, 37, 19, 29, 24, 42] provides a promising privacy-preserving solution for multi-site data collaboration, which develops a global model from decentralized datasets by aggregating the parameters of each local client while keeping data locally. Representatively, McMahan [23] proposed the popular FedAvg algorithm",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "4883",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "for communication-efficient federated training of deep networks. There are two lines to improve FedAvg: improvement on local training and on global aggregation.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Regarding improving local training, FedProx [19] introduced a proximal term to the clients' objective, which regulates the local updates to be closer to the initial global model. Meanwhile, MOON [18] proposed a model contrastive loss that corrects local updates by maximizing the agreement of the representation learned by the current local model and the global model, and minimizing the agreement of the representation learned by the current local model and the previous local model.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As for studies on improving the global aggregation phase, FedMA [37] utilizes Bayesian non-parametric methods to match and average weights in a layer-wise manner. To preserve personalization of local clients, FedBN [20] aggregates parameters except BN layers on the server side. Chen [5] proposed to aggregate client model parameters on the frequency domain. Even if these works [37, 21] try to solve parameter misalignment, they are applied to the closed-set recognition task, which can't be directly transferred to open-set recognition due to complex parameter composition in open-set recognition.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Open Set Recognition",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To deploy the classification models to real-world scenario with high stability, open-set recognition (OSR) [40, 41, 33, 3, 43] was proposed to classify known classes while detect unknown classes at the same time. Recent deep learning-based OSR methods can be classified into three categories: discriminative-based models, prototype-based models and generative-based models.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Discriminative model-based methods calibrate the classification logistics to detect unknown samples. Softmax scores are initially utilized to identify out-of-distribution data by argmax thresholding. OpenMax [2] improves softmax scores with an OpenMax layer and fits outputs probabilities with Weibull distributions.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Prototype-based methods [4, 3, 26] apply prototype learning to identify unknown samples on the feature space. ARPL [3] enhanced prototype learning with generated fake samples to achieve prediction-level and feature-level detection. Even if prototype-based methods show outstanding performance on open-set recognition, they are not suitable to be applied on FL since the uploaded prototype may cause leakage of privacy.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Generative model-based methods generate unknown samples using GANs [10] and autoencoders [1] to help the classifier learning the decision boundary between known and unknown distributions. OSRCI [27] utilized GAN [10] architecture to generate counterfactual examples. PROSER [43] set up the open space between class boundaries to keep classes far from each other based on manifold mixup. Generally, there are a closed-set loss based on su",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "pervision from known samples and an open-set loss by generated unknown samples or boundary constrains [9, 32].",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3. Problem Definition",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We begin with formal definition of Federated Learning (FL) and Open-Set Recognition (OSR). Then we define Federated Open-Set Recognition (FedOSR) and its challenges.",
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+        "text": "Open-Set Recognition: In the standard open-set recognition, the model is trained with a labelled closed training set  $\\mathcal{D}_{train} = \\{(x_i,y_i)\\}_{i=1}^N \\subset \\mathcal{X} \\times \\mathcal{C}$ , where  $\\mathcal{X}$  is the input images and  $\\mathcal{C}$  is the set of 'known' classes. On the testing phase, the testing set  $\\mathcal{D}_{test} = \\{(x_i,y_i)\\}_{i=1}^M \\subset \\mathcal{X} \\times (\\mathcal{C} \\cup \\mathcal{U})$  contains both seen classes  $\\mathcal{C}$  and unseen classes  $\\mathcal{U}$ . In addition to returning the distribution  $p(y|x,y \\in \\mathcal{C})$  over known classes, the model also returns a score  $\\mathcal{O}(y \\in \\mathcal{C}|x)$  to indicate whether or not the test sample belongs to any of the known classes. Since generative model-based approaches show superior performance, we utilize these methods as our baseline. There are two loss components of generative model-based approaches: closed-set loss based on supervision from known samples and an open-set loss by generated unknown samples or boundary constrains:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {c l s}} = \\mathcal {L} _ {\\text {c l o s e}} + \\lambda \\cdot \\mathcal {L} _ {\\text {o p e n}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{close}$  is the cross entropy loss between model prediction and known ground truth,  $\\mathcal{L}_{open}$  is to constrain open space or generated unknown samples.",
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+    {
+        "type": "text",
+        "text": "Federated Open-Set Recognition: We then extend conventional open-set recognition to Federated Open-Set Recognition (FedOSR). Given  $K$  local clients  $\\{\\mathcal{S}^l\\}_{l=1}^K$  with the same known classes  $\\mathcal{C}$  and a global central server  $G$ , for the federated round  $t$ , every client  $\\mathcal{S}^k$  will receive the same global model weights  $G_{t-1}$  from the central server and update the model with their local data  $\\mathcal{D}_k$  for  $E$  epochs. The central server then collects the local parameters  $\\mathcal{S}_t^k$  from all clients and aggregates them to update the global model  $G_t$ . This process repeats until the global model converges. In this paper, we consider the most popular federated averaging algorithm (FedAvg) [23], which aggregates the local parameters with weights of each local dataset to update the global model  $G = \\frac{1}{K} \\sum_{k=1}^{K} \\mathcal{S}^k$ .",
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+    },
+    {
+        "type": "text",
+        "text": "Challenges: Based on the conclusion that closed-set ability is related to certain parameters of an OSR model [34], the simple merging of OSR models may result in the mixing of closed-related parameters from one client with closed-unrelated parameters from other clients, thereby rendering the related parameters ineffective. Furthermore, even if we aggregate the corresponding closed-related parameters of different OSR models, they may still be misaligned due to the inconsistent distribution of locations. These two challenges pose difficulties in globally aggregating OSR models.",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4884",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/df625baa03220ac63dcd02a31e8dfa7a77080b777a0358f7d4e8fcaf95ca75fd.jpg",
+        "image_caption": [
+            "Figure 2. Framework of the proposed FedPD. It consists of a local parameter disentanglement strategy (LPD) and a global divide-and-conquer aggregation approach (GDCA). On the client side, an OSR model is generated with closed-set loss and open-set loss on samples of known classes. Then, LPD decouples the local OSR model into a closed-set subnetwork and an open-set subnetwork by task-related parameter importance. On the server side, GDCA first extracts close-specific, open-specific and shared parameters from the uploaded subnetworks, and then align the corresponding parts by optimal transport and fuse them to generate global model."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. The Proposed FedPD",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The overview of our method is depicted in Fig. 2. To address the FedOSR requirements, our method solves parameter misalignment via a local parameter disentanglement (LPD) strategy (Section 4.1) and a global divide-and-conquer aggregation (GDCA) approach (Section 4.2). For the federated round  $t$ , every client  $S^k$  will receive the same global model weights  $G_{t-1}$  from the last round and update the model with their local known data  $D_k$  by a closed-set loss and an open-set loss. The LPD then decouples the updated local OSR model  $S_t^k$  into a closed-set subnetwork  $\\mathcal{M}_{close}^k$  and an open-set subnetwork  $\\mathcal{M}_{open}^k$ . The local model  $S^k$  together with two subnetworks  $\\mathcal{M}_{close}^k$  and  $\\mathcal{M}_{open}^k$  are uploaded to the server for global divide-and-conquer aggregation. Specifically, the central server first divides two subnetworks into specific parts  $\\mathcal{P}_{close}^k$ ,  $\\mathcal{P}_{open}^k$  and shared part  $\\mathcal{P}_{share}^k$ , then aligns corresponding parts of all clients by optimal transport. At last, the aligned models are averaged to generate the global model  $G_t$ .",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Local Parameter Disentanglement",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "To address the parameter misalignment problem caused by cross-client inter-set inference, we propose a local parameter disentanglement (LPD) strategy to analyze parameter components in FedOSR and decouple an OSR model",
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "into a closed-set subnetwork and an open-set subnetwork. Specifically, motivated by the lottery ticket hypothesis [7, 11, 36] which shows that only partial parameters are significant for generalization, we find that partial parameters of an OSR model are important to closed-set classification and some parameters are significant to open-set detection.",
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+        "img_path": "images/887cd63fae782a5f1e2a7ceaef64b1f58eeca43f938586cde31eb53808744738.jpg",
+        "image_caption": [
+            "Figure 3. Parameter distribution of closed-set subnetwork and open-set subnetwork on an OSR model on MNIST dataset."
+        ],
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+    {
+        "type": "text",
+        "text": "The Lottery Ticket Hypothesis We first review the lottery ticket hypothesis [7, 11, 36], which generates subnetwork to achieve better generalization. For subtask  $\\mathbf{t}$ , if parameter  $h_i$  is essential to it, the change of loss would be large once we remove  $h_i$  (i.e.,  $h_i = 0$ ) [25]. We define the difference value  $\\Omega^{\\mathrm{t}}$  to represent the importance score of the parameter as shown in Eq. 2.",
+        "bbox": [
+            496,
+            732,
+            890,
+            839
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Omega^ {\\mathbf {t}} \\left(h _ {i}\\right) = \\left| \\mathcal {L} ^ {\\mathbf {t}} \\left(H, h _ {i} = 0\\right) - \\mathcal {L} ^ {\\mathbf {t}} \\left(H, h _ {i}\\right) \\right|, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            560,
+            849,
+            890,
+            867
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $H$  refers to other parameters except  $h_i$ . Since it's inefficient to evaluate the importance by parameter traversal,",
+        "bbox": [
+            496,
+            869,
+            890,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4885",
+        "bbox": [
+            480,
+            924,
+            514,
+            936
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "we approximate it with Taylor Expansion [39] and obtain:",
+        "bbox": [
+            76,
+            90,
+            460,
+            107
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Omega^ {\\mathbf {t}} \\left(h _ {i}\\right) = \\left| \\frac {\\partial \\mathcal {L} ^ {\\mathbf {t}} (H , h _ {i})}{\\partial h _ {i}} h _ {i} \\right| = \\left| \\nabla \\mathcal {L} _ {\\mathbf {t}} \\left(h _ {i}\\right) \\times h _ {i} \\right|. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            119,
+            126,
+            468,
+            159
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After deriving the importance score of parameters for subtask  $\\mathbf{t}$  based on input  $(\\mathcal{X}_{\\mathbf{t}},\\mathcal{Y}_{\\mathbf{t}})$ , parameters with the higher score are selected as the subnetwork for  $\\mathbf{t}$ . It can be indicated by a mask  $M_{t}$ , where  $M^{\\mathbf{t}}(h_i) = 1$  if  $h_i$  belongs to the subnetwork, and  $M^{\\mathbf{t}}(h_i) = 0$  otherwise.",
+        "bbox": [
+            76,
+            167,
+            468,
+            243
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Parameter Disentanglement on OSR Based on the lottery ticket hypothesis, we apply parameter disentanglement to decouple an OSR model into closed-set subnetwork and open-set subnetwork. Specifically, given a local OSR model  $S^k$ , we define two task-related metric  $\\mathcal{T}_{close}$  and  $\\mathcal{T}_{open}$  to judge the importance of each parameter contributing to closed-set classification and open-set detection based on the Eq. 3:",
+        "bbox": [
+            76,
+            244,
+            468,
+            364
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {T} _ {\\text {c l o s e}} ^ {k} (i) = \\left| \\nabla \\mathcal {L} _ {\\text {c l o s e}} \\left(\\omega_ {i}\\right) \\times \\omega_ {i} \\right|, i \\in [ m _ {*} ]. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            132,
+            375,
+            468,
+            393
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {T} _ {\\text {o p e n}} ^ {k} (i) = | \\nabla \\mathcal {L} _ {\\text {o p e n}} (\\omega_ {i}) \\times \\omega_ {i} |, i \\in [ m _ {*} ]. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            133,
+            417,
+            468,
+            438
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $m_*$  is the parameter number of a module in an OSR network and  $w_i$  is the corresponding parameters of the module. The larger the value of  $\\mathcal{T}(i)$  is, the more this parameter contributes to the task-related loss function.",
+        "bbox": [
+            76,
+            443,
+            468,
+            502
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After deriving the importance score  $\\mathcal{T}_{close}$ ,  $\\mathcal{T}_{open}$  of parameters for closed-set loss and open-set loss, we choose the top-K highest scores as most valuable weights and set them as 1 with the rest as 0 to generate closed-set subnetwork and open-set subnetwork respectively:",
+        "bbox": [
+            76,
+            503,
+            468,
+            579
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {M} _ {\\text {c l o s e}} ^ {k} (i) = \\left\\{ \\begin{array}{l} 1, \\mathcal {T} _ {\\text {c l o s e}} ^ {k} (i) > \\delta_ {\\text {c l o s e}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            589,
+            468,
+            631
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {M} _ {\\text {o p e n}} ^ {k} (i) = \\left\\{ \\begin{array}{l} 1, \\mathcal {T} _ {\\text {o p e n}} ^ {k} (i) > \\delta_ {\\text {o p e n}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            643,
+            468,
+            683
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\delta_{close}$  and  $\\delta_{open}$  are the threshold to filter out redundant parameters and we choose the threshold based on ratio of parameter numbers. Here we set the masking ratio as 0.5 based on our experimental observation.",
+        "bbox": [
+            76,
+            688,
+            468,
+            748
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We visualize the subnetworks in the first convolution layer as illustrated in Fig. 3. It's obvious that open-set and closed-set subnetworks hold different distribution.",
+        "bbox": [
+            76,
+            750,
+            468,
+            792
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Parameter Disentanglement on FedOSR Given a set of local OSR models  $\\{\\mathcal{S}^k\\}_{k = 1}^K$ , we apply parameter disentanglement on these models, and plot closed-set subnetworks  $\\{\\mathcal{M}_close^k\\}_{k = 1}^K$  and open-set subnetworks  $\\{\\mathcal{M}_{open}^k\\}_{k = 1}^K$  as shown in Fig. 4. It illustrates that there exists parameter misalignment in both closed-set subnetworks and open-set subnetworks among these clients. Simply aggregating the",
+        "bbox": [
+            76,
+            794,
+            468,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "client OSR modes into one global model may ignore the complex parameter composition and lead to model collapse due to unmatched averaging. For example, the parameter averaging on a closed-set subnetwork and an open-set subnetwork on the same position may generate chaotic neuron weights. This phenomenon motivates us to develop a new model aggregation approach for FedOSR.",
+        "bbox": [
+            496,
+            90,
+            890,
+            196
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/ca2d5d3bf3d680d1c8672dcc293b2977d46ba0dd4d61c5c29d5a80725262170e.jpg",
+        "image_caption": [
+            "Figure 4. Parameter distribution of closed-set parameters and open-set parameters in federated framework on HDR-FL dataset. The horizontal direction of the picture represents channel numbers, and the vertical of it denotes client numbers."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            513,
+            213,
+            883,
+            349
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Global Divide-and-Conquer Aggregation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            425,
+            849,
+            441
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During model communication on the server side, parameter misalignment problem will significantly destroy the global model, thus providing bad model initialization for local training in next step. To further remedy the aggregation catastrophe by cross-client intra-set inconsistency, we design a global divide-and-conquer aggregation (GDCA) method to first divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters, and then align and aggregate the corresponding parts respectively.",
+        "bbox": [
+            496,
+            448,
+            890,
+            599
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Learning to divide Based on the results of local parameter disentanglement, an OSR model can be decoupled into a closed-set subnetwork and an open-set subnetwork as shown in Fig. 4. Since there are overlaps between these two subnetworks, we further divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters.",
+        "bbox": [
+            496,
+            599,
+            890,
+            705
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {P} _ {\\text {c l o s e}} = \\mathcal {M} _ {\\text {c l o s e}} \\odot \\overline {{\\mathcal {M} _ {\\text {o p e n}}}}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            714,
+            890,
+            732
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {P} _ {\\text {o p e n}} = \\mathcal {M} _ {\\text {o p e n}} \\odot \\overline {{\\mathcal {M} _ {\\text {c l o s e}}}}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            734,
+            890,
+            751
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {P} _ {\\text {s h a r e}} = \\mathcal {M} _ {\\text {o p e n}} \\odot \\mathcal {M} _ {\\text {c l o s e}}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            753,
+            890,
+            770
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\overline{\\mathcal{M}}$  is the negation of the binary mask  $\\mathcal{M}$ . Compared with two subnetworks, the three non-overlapping parts are more suitable to deal with since the overlapping parameters may cause conflicts after alignment.",
+        "bbox": [
+            496,
+            779,
+            890,
+            839
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Learning to conquer We disentangle the OSR model of each client into three parts and align the corresponding parts before aggregation. The neuron weights are considered as a distribution, and we use optimal transport (OT) to achieve",
+        "bbox": [
+            496,
+            839,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "4886",
+        "bbox": [
+            482,
+            926,
+            514,
+            936
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "distribution alignment as shown in Fig. 2. OT is a technique used to solve distribution matching problems by finding a minimal effort solution to transport a given mass of dirt into a given hole. It has been successfully applied to various problems such as domain adaptation and GANs. We compute the transport map layer by layer to achieve alignment between two models  $W_{A}$  and  $W_{B}$ .",
+        "bbox": [
+            75,
+            90,
+            468,
+            196
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Taking two models  $\\mathbf{W}_A$  and  $\\mathbf{W}_B$  as an example, we align parameters of  $\\mathbf{W}_A$  on  $\\mathbf{W}_B$  by channel-wise distribution matching. Let us assume that we are at one convolution layer  $\\mathbf{W}^{(\\ell)} \\in (\\mathcal{C}_{in}^{\\ell},\\mathcal{C}_{out}^{\\ell},F^{\\ell})$  and the previous layers have already been aligned, where  $F = k\\times k$  is the square of filter size. The transport matrix of the last convolution layer  $\\mathbf{W}^{(\\ell -1)}\\in (\\mathcal{C}_{in}^{\\ell -1},\\mathcal{C}_{out}^{\\ell -1},F^{\\ell -1})$  is denoted as  $T^{(\\ell -1)} \\in (\\mathcal{C}_{out}^{\\ell -1},\\mathcal{C}_{out}^{\\ell -1})$ . Since the output of last layer has been permuted by  $T^{(\\ell -1)}$ , we conduct post-multiplying on current layer with transport map of previous layer such that the order of current layer input  $\\mathcal{C}_{out}^{\\ell -1}$  can match the order of  $\\mathcal{C}_{in}^{\\ell}$ . Then the current layer can be transformed as:",
+        "bbox": [
+            75,
+            196,
+            470,
+            378
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widehat {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)} \\leftarrow \\boldsymbol {W} _ {A} ^ {(\\ell) ^ {\\top}} \\boldsymbol {T} ^ {(\\ell - 1)}, \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            174,
+            388,
+            468,
+            412
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\widehat{\\pmb{W}}_A^{(\\ell, \\ell-1)}$  is the post-processed layer, and  $\\pmb{W}_A^{(\\ell)}$  is transposed as  $(\\mathcal{C}_{in}^{\\ell}, F^{\\ell}, \\mathcal{C}_{out}^{\\ell})$  to achieve matrix multiplication.",
+        "bbox": [
+            75,
+            415,
+            468,
+            462
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "With current layer permuted, we compute the optimal transport map  $\\pmb{T}^{(\\ell)}$  between  $\\widehat{\\pmb{W}}_A^{(\\ell,\\ell-1)}, \\pmb{W}_B^{(\\ell)}$ , i.e.,  $\\pmb{T}^{(\\ell)}$ ,  $d \\gets \\mathrm{OT}(\\widehat{\\pmb{W}}_A^{(\\ell,\\ell-1)}, \\pmb{W}_B^{(\\ell)})$ , where  $d$  denotes the obtained Wasserstein-distance. We use this transport map  $\\pmb{T}^{(\\ell)}$  to align the neurons weights of the first model  $(\\pmb{W}_A)$  with respect to the second  $(\\pmb{W}_B)$ ,",
+        "bbox": [
+            75,
+            464,
+            468,
+            559
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)} \\leftarrow \\boldsymbol {T} ^ {(\\ell) ^ {\\top}} \\widehat {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)}, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            169,
+            569,
+            468,
+            590
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\widetilde{W}_A^{(\\ell, \\ell-1)}$  is the aligned layer from model  $W_A$  to  $W_B$ . To simplify this alignment process, we define  $\\widetilde{W}_A = OT(W_A, W_B)$ . Through the alignment of model parameters, model  $W_A$  will only change the orders of feature channels without affecting the model prediction.",
+        "bbox": [
+            75,
+            594,
+            468,
+            675
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "When we align the parameters of the OSR model for all clients, we can choose any client as the target client and align other clients with the target client. For example, we use the second client as the target client as shown in Fig. 2. The alignment process can be denoted as:",
+        "bbox": [
+            75,
+            676,
+            468,
+            751
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {S} _ {\\text {c l o s e}} ^ {k} = O T \\left(\\mathcal {S} ^ {k} \\odot \\mathcal {P} _ {\\text {c l o s e}} ^ {k}, \\mathcal {S} ^ {2} \\odot \\mathcal {P} _ {\\text {c l o s e}} ^ {2}\\right), \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            119,
+            757,
+            468,
+            776
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathcal {S}} _ {\\text {o p e n}} ^ {k} = O T \\left(S ^ {k} \\odot \\mathcal {P} _ {\\text {o p e n}} ^ {k}, S ^ {2} \\odot \\mathcal {P} _ {\\text {o p e n}} ^ {2}\\right), \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            777,
+            468,
+            797
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathcal {S}} _ {\\text {s h a r e}} ^ {k} = O T \\left(\\mathcal {S} ^ {k} \\odot \\mathcal {P} _ {\\text {s h a r e}} ^ {k}, \\mathcal {S} ^ {2} \\odot \\mathcal {P} _ {\\text {s h a r e}} ^ {2}\\right). \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            117,
+            800,
+            468,
+            819
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "After that, the global model  $G$  can be represented as:",
+        "bbox": [
+            96,
+            825,
+            446,
+            840
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nG = \\frac {1}{K} \\left(\\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {c l o s e}} ^ {k} + \\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {o p e n}} ^ {k} + \\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {s h a r e}} ^ {k}\\right). \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            848,
+            468,
+            890
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 summarizes the FedPD algorithm.",
+        "bbox": [
+            76,
+            897,
+            387,
+            912
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 FedPD"
+        ],
+        "code_body": "Server OPERATIONS  \nInputs: Round number  $T$ , Set of clients  $K$   \nOutput: Global OSR model  $G$   \nfor  $t = 0,1,\\ldots,T-1$  do  \nfor client  $k \\in K$  in parallel do  \n $\\mathcal{S}^k, \\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k \\gets \\text{CLIENTOPERATIONS}(G_{t-1})$   \nend for  \n $\\mathcal{P}_{close}^k = \\mathcal{M}_{close}^k \\odot \\overline{\\mathcal{M}_{open}^k}$ $\\mathcal{P}_{open}^k = \\mathcal{M}_{open}^k \\odot \\overline{\\mathcal{M}_{close}^k}$ $\\mathcal{P}_{share}^k = \\mathcal{M}_{close}^k \\odot \\mathcal{M}_{open}^k$ $\\widetilde{S}_{close}^k = OT(S^k \\odot \\mathcal{P}_{close}^k, S^2 \\odot \\mathcal{P}_{close}^2)$ $\\widetilde{S}_{open}^k = OT(S^k \\odot \\mathcal{P}_{open}^k, S^2 \\odot \\mathcal{P}_{open}^2)$ $\\widetilde{S}_{share}^k = OT(S^k \\odot \\mathcal{P}_{share}^k, S^2 \\odot \\mathcal{P}_{share}^2)$ $G_t \\gets \\frac{1}{K} (\\sum_{k=1}^{K} \\widetilde{S}_{close}^k + \\sum_{k=1}^{K} \\widetilde{S}_{open}^k + \\sum_{k=1}^{K} \\widetilde{S}_{share}^k)$   \nend for  \nObtain global OSR model  $G$   \nCLIENT OPERATIONS  \nInput: Model weights  $G_{t-1}$   \nOutput: Updated local OSR model weights  $\\mathcal{S}_t^k$ , closed-set subnetwork  $\\mathcal{M}_{close}^k$ , open-set subnetwork  $\\mathcal{M}_{open}^k$   \nfor epoch  $e = 0,1,\\ldots,E-1$  do  \nfor batch  $\\{x,y\\} \\in D_m$  do  \n $\\mathcal{L}_{local} = \\mathcal{L}_{close}(x,y) + \\mathcal{L}_{open}(x,y)$ $\\mathcal{T}_{close}^k = |\\nabla \\mathcal{L}_{close}(\\omega) \\times \\omega|$ $\\mathcal{T}_{open}^k = |\\nabla \\mathcal{L}_{open}(\\omega) \\times \\omega|$ $\\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k = TopK(\\mathcal{T}_{close}^k, \\mathcal{T}_{open}^k)$ $\\mathcal{S}_t^k \\gets update(\\mathcal{S}_t^k, \\mathcal{L}_{local})$   \nend for  \nend for  \nSend model weights  $\\mathcal{S}_t^k$  and subnetworks  $\\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k$  to the server",
+        "bbox": [
+            503,
+            112,
+            880,
+            489
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiment",
+        "text_level": 1,
+        "bbox": [
+            500,
+            520,
+            624,
+            537
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Datasets and Evaluation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            547,
+            722,
+            561
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct extensive experiments on both heterogeneous federated learning benchmark Handwritten digital recognition FL Dataset (HDR-FL) and homogeneous federated learning benchmark CIFAR-10. The closed-set classification and open-set detection performances are evaluated by accuracy (ACC) and AUROC (AUC) respectively.",
+        "bbox": [
+            496,
+            573,
+            890,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "HDR-FL: It consists of five datasets: MNIST [16], SVHN [28], USPS [12], SynthDigits [8] and MNIST-M [8]. These datasets are 10-class handwritten digital images from various scenarios. Each dataset is set as a client for Non-IID FedOSR. To achieve open-set recognition, six classes are chosen to be known and four classes are to be unknown classes. We keep the same known classes and unknown classes for all clients.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "CIFAR-10: It contains 60000 images in 10 classes, with 6000 images per class [15]. We first divide 10 classes into known classes and unknown classes, then split them into five equal parts to construct homogeneous federated setting. Specifically, we try different ratio between the known and the unknown to validate our method (e.g. 4:6, 6:4 and 8:2).",
+        "bbox": [
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+            809,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "4887",
+        "bbox": [
+            480,
+            926,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/06983856021c414183878a8ffcc4e426e82a73e5ff0453744cef798fc473b91f.jpg",
+        "table_caption": [
+            "Table 1. Performance comparisons between our method and other baseline methods on HDR-FL benchmark."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">Closed-set ACC</td><td colspan=\"6\">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>SoftMax</td><td>96.69</td><td>76.06</td><td>97.97</td><td>83.99</td><td>83.69</td><td>87.68</td><td>77.38</td><td>65.41</td><td>88.80</td><td>70.53</td><td>66.24</td><td>73.67</td></tr><tr><td>OpenMax[2](CVPR&#x27;16)</td><td>95.54</td><td>63.13</td><td>97.97</td><td>81.15</td><td>76.57</td><td>82.87</td><td>77.78</td><td>57.37</td><td>89.21</td><td>69.78</td><td>60.88</td><td>71.00</td></tr><tr><td>RPL[4](ECCV&#x27;20)</td><td>98.33</td><td>77.22</td><td>98.13</td><td>84.76</td><td>86.32</td><td>88.95</td><td>77.87</td><td>66.70</td><td>89.53</td><td>73.17</td><td>73.23</td><td>76.10</td></tr><tr><td>PROSER[43](CVPR&#x27;21)</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>ARPL[3](TPAMI&#x27;21)</td><td>97.17</td><td>69.83</td><td>96.44</td><td>84.64</td><td>84.22</td><td>86.46</td><td>85.65</td><td>59.79</td><td>92.53</td><td>69.70</td><td>68.17</td><td>75.16</td></tr><tr><td>DIAS[26](ECCV&#x27;22)</td><td>97.50</td><td>70.66</td><td>97.62</td><td>86.11</td><td>86.81</td><td>87.74</td><td>82.90</td><td>67.33</td><td>90.69</td><td>77.48</td><td>71.92</td><td>78.06</td></tr><tr><td>SSB[35](ICLR&#x27;22)</td><td>96.41</td><td>60.12</td><td>97.46</td><td>82.82</td><td>74.86</td><td>82.33</td><td>88.53</td><td>57.68</td><td>90.45</td><td>73.40</td><td>70.01</td><td>76.01</td></tr><tr><td>FedPD(Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/67700c217b00b8d5c3c34f342828dbbb752d4c0068624dd97e32442f7efa9083.jpg",
+        "table_caption": [
+            "Table 2. Performance comparisons between our method and other baseline methods on CIFAR-10 benchmark."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Known=4</td><td colspan=\"2\">Known=6</td><td colspan=\"2\">Known=8</td></tr><tr><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td></tr><tr><td>SoftMax</td><td>83.23 ±0.28</td><td>65.70±0.14</td><td>83.14±0.38</td><td>72.00±0.44</td><td>72.17±0.41</td><td>61.11±0.45</td></tr><tr><td>\\( OpenMax[2]_{(CVPR&#x27;16)} \\)</td><td>83.24 ±0.08</td><td>65.96±0.14</td><td>84.56±0.24</td><td>81.69±0.59</td><td>72.72±0.40</td><td>61.52±0.38</td></tr><tr><td>\\( RPL[4]_{(ECCV&#x27;20)} \\)</td><td>81.23 ±0.11</td><td>65.10±0.05</td><td>78.78±0.43</td><td>68.72±0.43</td><td>72.98±0.33</td><td>61.36±0.32</td></tr><tr><td>\\( PROSER[43]_{(CVPR&#x27;21)} \\)</td><td>84.15 ±0.13</td><td>69.04±0.07</td><td>85.77±0.48</td><td>80.69±0.27</td><td>70.50±0.21</td><td>60.48±0.41</td></tr><tr><td>\\( ARPL[3]_{(TPAMI&#x27;21)} \\)</td><td>83.91 ±0.09</td><td>69.02±0.12</td><td>86.54±0.53</td><td>79.83±0.69</td><td>73.63±0.37</td><td>66.78±0.64</td></tr><tr><td>\\( DIAS[26]_{(ECCV&#x27;22)} \\)</td><td>84.85 ±0.04</td><td>70.32±0.09</td><td>87.74±0.16</td><td>81.66±0.25</td><td>74.53±0.37</td><td>67.75±0.34</td></tr><tr><td>\\( SSB[35]_{(ICLR&#x27;22)} \\)</td><td>84.27±0.06</td><td>68.85±0.11</td><td>86.04±0.70</td><td>82.41±0.33</td><td>75.54±0.18</td><td>67.97±0.23</td></tr><tr><td>\\( FedPD(Ours) \\)</td><td>86.28±0.07</td><td>71.50±0.07</td><td>89.43±0.22</td><td>85.07±0.50</td><td>75.87±0.16</td><td>69.12±0.45</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "On local training, we apply PROSER [43] for open-set training with a closed-set loss and an open-set loss. On global aggregation, we utilize FedAvg [23] to average OSR models for comparison methods. For handwritten digital recognition, we apply a six-layer CNN. During the training process, we utilize the SGD optimizer [31] with learning rate  $10^{-2}$  for closed-set loss and  $10^{-4}$  for open-set loss, we set batch size to 32 and training epochs to 100. Global model is updated every epoch by FedAvg [23] aggregation. For CIFAR-10 Dataset, we use WideResNet for classification. Networks are trained by Adam optimizer [14] with batch size of 128. The learning rates of closed-set loss and open-set loss are initialized as  $10^{-1}$  and  $10^{-3}$  respectively. The communication is conducted after every  $\\mathrm{E} = 5$  epochs in local training until reaching  $\\mathrm{T} = 250$  epochs in total. All experiments of these two benchmarks are performed on NVIDIA 2080Ti card with Pytorch library. Detailed model architecture for both benchmarks is shown in the supplementary material.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Comparison with state-of-the-arts",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare the performance of FedPD with the state-of-the-art OSR methods, including SoftMax, OpenMax [2], RPL [4], PROSER [43], ARPL [3], DIAS [26], SSB [35]. These comparison methods are implemented by FedAvg [23] on each client OSR models. Our FedPD utilizes the popular generative-based method PROSER [43] for local open-set training.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "HDR-FL: As shown in Table 1, our FedPD outperforms existing OSR approaches with a large margin not only in closed-set classification but also in open-set detection. In addition, our FedPD achieves consistent improvements on",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "all clients. Specifically, our method can surpass existing approaches with a promising  $90.60\\%$  average closed-set ACC and 80.78 average open-set AUC, outperforming the state-of-the-art OSR method DIAS [26] with  $2.76\\%$  in ACC and  $2.72\\%$  in AUC. It validates that our method could enable better global model aggregation for open-set recognition, which verifies the effectiveness of our divide-and-conquer approach to address parameter misalignment in FedOSR. Moreover, some generate-based methods (e.g. SSB [26]) may encounter serious model collapse problem due to unmatched parameter of local OSR models, leading to  $8.17\\%$  performance gap in average ACC.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "CIFAR-10: Comparison results on CIFAR-10 benchmark are shown in Table 2. To validate the stability of our method, we conduct experiments on different ratios between known classes and unknown classes. In these three settings, our FedPD achieves the best open-set AUC of  $71.70\\%$ ,  $85.07\\%$  and  $69.12\\%$ . The consistent performance improvement over different openness demonstrate the effectiveness of our FedPD to promote the ability of detecting novel category for federated models.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4. Ablation Analysis of Our Method",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4.1 Effectiveness of LPD",
+        "text_level": 1,
+        "bbox": [
+            500,
+            750,
+            700,
+            763
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/39bb85aa67553d8675ae938974762bda2dc3a7b41ab455e26ff1f82e01f0368f.jpg",
+        "table_caption": [
+            "Table 4. Comparison to different network splitting methods."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Splitting Method</td><td>None</td><td>Grad</td><td>Grad × Weight (Ours)</td></tr><tr><td>Closed-set ACC</td><td>85.61</td><td>89.04</td><td>90.96</td></tr><tr><td>Open-set AUC</td><td>76.19</td><td>80.95</td><td>81.36</td></tr></table>",
+        "bbox": [
+            501,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the advantage of local parameter disentanglement, we compare it with no splitting and network splitting by grad as shown in Table 4. It shows that conducting network splitting according to task gradients results in large",
+        "bbox": [
+            496,
+            839,
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+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "4888",
+        "bbox": [
+            482,
+            926,
+            514,
+            936
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/72149ab1b4aed5c1bf72a3e3dcfaca9ef13e497891204b4163348a65d286739f.jpg",
+        "table_caption": [
+            "Table 3. Ablation study for key components."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">closed-set ACC</td><td colspan=\"6\">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>Baseline + FedAvg</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>Baseline + FedMA</td><td>97.21</td><td>60.72</td><td>98.22</td><td>86.18</td><td>85.72</td><td>85.61</td><td>83.09</td><td>66.47</td><td>88.81</td><td>73.13</td><td>69.46</td><td>76.19</td></tr><tr><td>Baseline + FedPD (Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr><tr><td>Ours w/o Divide</td><td>98.39</td><td>77.60</td><td>98.22</td><td>88.65</td><td>89.66</td><td>90.50</td><td>89.56</td><td>69.91</td><td>92.72</td><td>79.05</td><td>72.67</td><td>80.78</td></tr><tr><td>Ours w/o Conquer</td><td>97.43</td><td>72.74</td><td>97.62</td><td>85.82</td><td>85.22</td><td>87.76</td><td>84.41</td><td>65.78</td><td>91.60</td><td>72.51</td><td>70.81</td><td>77.02</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/581e695f7cd5e84386930de1a35ac2d30010078481d4747338e7f3e0a2b65755.jpg",
+        "image_caption": [
+            "Figure 5. Ablation study for the masking ratio of the parameter disentanglement."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            106,
+            220,
+            267,
+            308
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/ed5663815be86a8074d318bcb748b0488ab085b843c01d6fc1503655eb9c6607.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "performance gain. Combining gradient and weight information makes better model decoupling, which corresponds to our theoretical analysis in Eq. 3.",
+        "bbox": [
+            75,
+            366,
+            468,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4.2 Effectiveness of GDCA",
+        "text_level": 1,
+        "bbox": [
+            76,
+            412,
+            290,
+            426
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Learning to Divide To validate the advantage of dividing two subnetworks into specific parts and shared parts, we conduct experiments on two different aggregation strategy: align two subnetworks then average (Ours w/o Divide) and align three parts then average (Ours). Comparison results in Table 3 illustrates that aligning three parts outperforms aligning two subnetworks with performance gain of  $0.46\\%$  in ACC and  $0.58\\%$  in AUC. It is because that the overlapping parameters between these two subnetworks may have different distribution after alignment, thus leading to ambiguous parameters.",
+        "bbox": [
+            75,
+            433,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Learning to Conquer To validate the effectiveness of divide-and-conquer aggregation, we compare our method with traditional aggregation methods FedAvg and FedMA. Unlike obvious improvement on closed-set setting, FedMA shows inferior performance than FedAvg as shown in Table 3. It is consistent with our observation that parameter components in open-set models are more complex than those in closed-set models due to multiple optimization directions. Compared with directly averaging three parts with alignment (Ours w/o Conquer), conducting our proposed aggregation strategy brings performance boost on of  $3.2\\%$  in ACC and  $4.34\\%$  in AUC, demonstrating that our FedPD can alleviate parameter misalignment problem.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4.3 Effect of Masking Ratio",
+        "text_level": 1,
+        "bbox": [
+            76,
+            801,
+            297,
+            816
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To investigate the effect of masking ratio to the FedOSR performance, we design ablation experiments under HDRFL setting, as shown in Fig. 5. It is observed that small masking ratio (e.g. 0.1) may filter out too much parameters, leading to empty shared parameter. Large masking ratio",
+        "bbox": [
+            75,
+            824,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/099acd292bf2f2d4773a2b9d20c037e0ab4d78851e448ba723d07668fce3aea8.jpg",
+        "image_caption": [
+            "Figure 6. Parameter distribution of closed-set subnetworks and open-set subnetworks on CIFAR-10 dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            535,
+            217,
+            859,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(e.g. 0.9) can't choose valuable weights for the closed-set task and the open-set task, thus leading to invalid decoupling. In this paper, we choose suitable masking ratio as 0.5 based on our experimental observation that it achieves the best closed-set ACC and open-set AUC.",
+        "bbox": [
+            496,
+            393,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.5. Analysis of Parameter Misalignment",
+        "text_level": 1,
+        "bbox": [
+            500,
+            470,
+            816,
+            486
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To verify the parameter misalignment problem in FedOSR, we visualize the weights distributions of closed-set subnetwork and open-set subnetwork on CIFAR-10 homogeneous benchmark as shown in Fig. 6. Different clients still hold inconsistent parameter distribution on both closed-set subnetwork and open-set subnetwork. Different from results shown in Fig. 4, where parameter misalignment may come from domain shift in heterogeneous federated datasets. Fig. 6 further emphasize that the parameter misalignment in FedOSR mainly comes from gradient divergence of closed-set loss and open-set loss.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            667,
+            617,
+            683
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a novel and practical problem of federated open-set recognition (FedOSR) for the first time. To alleviate the parameter misalignment problem in FedOSR, we design a novel parameter disentanglement guided federated algorithm (FedPD). Specifically, on the client side, a local parameter disentanglement is developed to decouple the local OSR models into closed-set subnetworks and open-set subnetworks. On the server side, a global divide-and-conquer aggregation strategy is proposed to divide two subnetworks into specific parts and shared parts, then align corresponding parts by optimal transport and fuse them to generate global model. Extensive experiments on both IID and Non-IID benchmark datasets demonstrate the effectiveness of FedPD.",
+        "bbox": [
+            496,
+            689,
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+            898
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "4889",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+        "page_idx": 8
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+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[38] Jiacheng Wang, Yueming Jin, and Liansheng Wang. Personalizing federated medical image segmentation via local calibration. arXiv preprint arXiv:2207.04655, 2022. 2",
+            "[39] Runxin Xu, Fuli Luo, Baobao Chang, Songfang Huang, and Fei Huang. S4-tuning: A simple cross-lingual sub-network tuning method-tuning: A simple cross-lingual sub-network tuning method. In ACL, pages 530–537, 2022. 5",
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+            "[41] Hongjie Zhang, Ang Li, Jie Guo, and Yanwen Guo. Hybrid models for open set recognition. In ECCV, pages 102-117. Springer, 2020. 3",
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+            "[43] Da-Wei Zhou, Han-Jia Ye, and De-Chuan Zhan. Learning placeholders for open-set recognition. In CVPR, pages 4401-4410, 2021. 1, 3, 7"
+        ],
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diff --git a/2023/FedPD_ Federated Open Set Recognition with Parameter Disentanglement/edefee4b-642c-4a0c-ba36-c80cdd791aa1_model.json b/2023/FedPD_ Federated Open Set Recognition with Parameter Disentanglement/edefee4b-642c-4a0c-ba36-c80cdd791aa1_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..b7fbb22564138cae4a699909df94c0181042219f
--- /dev/null
+++ b/2023/FedPD_ Federated Open Set Recognition with Parameter Disentanglement/edefee4b-642c-4a0c-ba36-c80cdd791aa1_model.json	
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+[
+    [
+        {
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "FedPD: Federated Open Set Recognition with Parameter Disentanglement"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Chen Yang<sup>1</sup>"
+        },
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+            "bbox": [
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+            "angle": 0,
+            "content": "Meilu Zhu"
+        },
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+            "angle": 0,
+            "content": "Yifan Liu2"
+        },
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+            "content": "<sup>1</sup>City University of Hong Kong"
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+            "angle": 0,
+            "content": "2The Chinese University of Hong Kong"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "{cyang53, meiluzhu2}-c@my.cityu.edu.hk 1155195605@link.cuhk.edu.hk yxyuan@ee.cuhk.edu.hk"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Existing federated learning (FL) approaches are deployed under the unrealistic closed-set setting, with both training and testing classes belong to the same set, which makes the global model fail to identify the unseen classes as 'unknown'. To this end, we aim to study a novel problem of federated open-set recognition (FedOSR), which learns an open-set recognition (OSR) model under federated paradigm such that it classifies seen classes while at the same time detects unknown classes. In this work, we propose a parameter disentanglement guided federated open-set recognition (FedPD) algorithm to address two core challenges of FedOSR: cross-client inter-set interference between learning closed-set and open-set knowledge and cross-client intra-set inconsistency by data heterogeneity. The proposed FedPD framework mainly leverages two modules, i.e., local parameter disentanglement (LPD) and global divide-and-conquer aggregation (GDCA), to first disentangle client OSR model into different subnetworks, then align the corresponding parts cross clients for matched model aggregation. Specifically, on the client side, LPD decouples an OSR model into a closed-set subnetwork and an open-set subnetwork by the task-related importance, thus preventing inter-set interference. On the server side, GDCA first partitions the two subnetworks into specific and shared parts, and subsequently aligns the corresponding parts through optimal transport to eliminate parameter misalignment. Extensive experiments on various datasets demonstrate the superior performance of our proposed method."
+        },
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+            "bbox": [
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+            "content": "1. Introduction"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Deep learning algorithms rely on the availability of large-scale data to achieve remarkable performance. However, in reality, data is scattered across different organiza"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "bbox": [
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+            "content": "Figure 1. Parameter disentanglement on FedOSR models and comparison of various aggregation strategies on FedOSR setting. (a) FedAvg simply aggregates multiple OSR models, leading to model collapse; (b) Our FedPD first aligns corresponding close-specific, open-specific and shared parts by optimal transport (OT), then aggregates aligned parameters. The curves inside the network box represent different parameter distribution of each parts."
+        },
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+            "bbox": [
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+            "angle": 0,
+            "content": "tions and difficult to integrate into a centralized dataset, owing to increasing privacy and ethical concerns, especially for those sensitive data such as location-based services or health information [22]. To break this dilemma, federated learning (FL) [5, 23, 20] provides a privacy-preserving paradigm that allows local clients to collaboratively train a shared global model without data sharing."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Although FL has recently achieved promising progress, existing FL works [23, 20, 5] are generally evaluated in a closed-set scenario, where the categories of training and testing samples are identical. The closed-set setting is irrational since unknown classes may appear at the test time and would be classified into known classes. This problem seriously impedes the deployment of FL models in many real-world applications due to enormous risk, such as clinical diagnosis and autonomous driving. Current open-set recognition (OSR) methods [3, 43, 2, 6] attempt to improve the"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "*Yixuan Yuan is the corresponding author."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+                0.864,
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+            ],
+            "angle": 0,
+            "content": "This work was supported by Hong Kong Research Grants Council(RGC) General Research Fund 1422062214204321, and Innovation and Technology Commission-Innovation and Technology Fund ITS/100/20."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+            "bbox": [
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+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.213
+            ],
+            "angle": 0,
+            "content": "ability of models in recognizing unknown classes, but they are designed for the centralized setting. In this work, we represent the first effort to formulate a challenging and unexplored problem of Federated Open Set Recognition (FedOSR). FedOSR aims to unite multiple distributed clients to learn a global model and reduce privacy as well as security risk, which not only exactly classifies known classes but also recognizes unknown classes in the testing stage."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.217,
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+            "angle": 0,
+            "content": "Directly applying existing OSR methods into the FL setting for FedOSR mainly undergoes two troublesome challenges. The first challenge lies in the cross-client inter-set interference between learning closed-set and open-set knowledge. According to the previous study [34], the partial parameters of a client model are in charge of learning knowledge of known classes, and the rest are related to open set. The known classes-related parameters of a client is probably polluted by the open set-related parameters from other clients after server communication, leading to the performance degradation on closed set. Similarly, open set-related parameters of a client are also affected by closed-set knowledge of other clients. In this situation, a unknown samples would be possibly misclassified into known classes. The second one is cross-client intra-set inconsistency by data heterogeneity. Even though we aggregate corresponding closed-related parameters of OSR models from different clients, these parameters are still misaligned due to the permutation invariance property of neural networks and data heterogeneity [37]. Aggregation of local client parameters directly at the server can result in inconsistent models among the clients, leading to significant divergence of client models. This inconsistency issue can cause slow and unstable convergence [19], ultimately resulting in sub-optimal performance of the entire FL system [17, 37]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "To achieve FedOSR, we conquer these intractable challenges from a new perspective, i.e., parameter disentanglement. Based on the lottery ticket hypothesis [7, 11, 36], we divide parameters of a client model into a closed-set subnetwork and an open-set subnetwork. These two subnetworks have their own specific parameters, which are only related to known classes and unknown classes respectively. Meanwhile, they also share partial parameters since known and unknown samples might have some similar patterns [35]. The parameter disentanglement of client models can preserve the high performance of closed set by reducing the interference from open-set subnetworks. As shown in Fig. 1, the closed-set subnetworks and the open-set subnetworks of different client models distribute in different positions with some overlaps. Directly aggregating all client OSR models by FedAvg [23] on the server side may encounter the parameter misalignment problem and lead to model collapse as shown in Fig. 1 (a). These destroyed parameters are transmitted to clients and slow down the convergence of the federated system due to bad model initialization to the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.137
+            ],
+            "angle": 0,
+            "content": "next training step. Therefore, aligning these subnetworks before model aggregation is a crucial step to solve the inconsistency problem of parameter distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.137,
+                0.893,
+                0.394
+            ],
+            "angle": 0,
+            "content": "To tackle these challenges in FedOSR, we propose a novel parameter disentanglement guided federated OSR (FedPD) algorithm in this paper, which effectively addresses the local parameter misalignment problem occurred on the global model aggregation. Specifically, we design a local parameter disentanglement strategy (LPD) to firstly decouple an OSR model into two subnetworks: an open-set subnetwork and a closed-set subnetwork by task-related metrics. To overcome the parameter misalignment caused by simply parameter averaging on whole client OSR models, we propose a global divide-and-conquer aggregation (GDCA) method to firstly divide two subnetworks into specific parts and shared parts, then align corresponding parameter components by optimal transport [13, 30] and aggregate them. As shown in Fig. 1 (b), our FedPD enables reasonable model aggregation and reliable global model to boost federated training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.395,
+                0.892,
+                0.424
+            ],
+            "angle": 0,
+            "content": "The major contribution of this paper are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.439,
+                0.892,
+                0.5
+            ],
+            "angle": 0,
+            "content": "- We address a practical FL problem, namely Federated Open-Set Recognition (FedOSR). To the best of our knowledge, this is the first work to improve the ability of detecting novel category for federated models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.512,
+                0.892,
+                0.557
+            ],
+            "angle": 0,
+            "content": "- We propose a novel Parameter Disentanglement guided Federated algorithm (FedPD) to solve parameter misalignment problem in FedOSR."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.568,
+                0.892,
+                0.644
+            ],
+            "angle": 0,
+            "content": "- On the client side, we introduce the Local Parameter Disentanglement (LPD) approach, which leverages task-related importance on model parameters to decouple the local OSR model into a closed-set subnetwork and an open-set subnetwork."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.655,
+                0.892,
+                0.746
+            ],
+            "angle": 0,
+            "content": "- On the server side, we design a Global Divide-and-Conquer Aggregation (GDCA) strategy to partition the two subnetworks into specific and shared parts, align the corresponding parts via optimal transport, and subsequently fuse them to alleviate the misalignment problem in FedOSR."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.439,
+                0.892,
+                0.746
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.762,
+                0.642,
+                0.777
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.691,
+                0.803
+            ],
+            "angle": 0,
+            "content": "2.1. Federated Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Federated learning [23, 20, 38, 37, 19, 29, 24, 42] provides a promising privacy-preserving solution for multi-site data collaboration, which develops a global model from decentralized datasets by aggregating the parameters of each local client while keeping data locally. Representatively, McMahan [23] proposed the popular FedAvg algorithm"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.925,
+                0.516,
+                0.937
+            ],
+            "angle": 0,
+            "content": "4883"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "for communication-efficient federated training of deep networks. There are two lines to improve FedAvg: improvement on local training and on global aggregation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.137,
+                0.468,
+                0.272
+            ],
+            "angle": 0,
+            "content": "Regarding improving local training, FedProx [19] introduced a proximal term to the clients' objective, which regulates the local updates to be closer to the initial global model. Meanwhile, MOON [18] proposed a model contrastive loss that corrects local updates by maximizing the agreement of the representation learned by the current local model and the global model, and minimizing the agreement of the representation learned by the current local model and the previous local model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.273,
+                0.468,
+                0.438
+            ],
+            "angle": 0,
+            "content": "As for studies on improving the global aggregation phase, FedMA [37] utilizes Bayesian non-parametric methods to match and average weights in a layer-wise manner. To preserve personalization of local clients, FedBN [20] aggregates parameters except BN layers on the server side. Chen [5] proposed to aggregate client model parameters on the frequency domain. Even if these works [37, 21] try to solve parameter misalignment, they are applied to the closed-set recognition task, which can't be directly transferred to open-set recognition due to complex parameter composition in open-set recognition."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.44,
+                0.281,
+                0.456
+            ],
+            "angle": 0,
+            "content": "2.2. Open Set Recognition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.463,
+                0.468,
+                0.568
+            ],
+            "angle": 0,
+            "content": "To deploy the classification models to real-world scenario with high stability, open-set recognition (OSR) [40, 41, 33, 3, 43] was proposed to classify known classes while detect unknown classes at the same time. Recent deep learning-based OSR methods can be classified into three categories: discriminative-based models, prototype-based models and generative-based models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.468,
+                0.658
+            ],
+            "angle": 0,
+            "content": "Discriminative model-based methods calibrate the classification logistics to detect unknown samples. Softmax scores are initially utilized to identify out-of-distribution data by argmax thresholding. OpenMax [2] improves softmax scores with an OpenMax layer and fits outputs probabilities with Weibull distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.468,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Prototype-based methods [4, 3, 26] apply prototype learning to identify unknown samples on the feature space. ARPL [3] enhanced prototype learning with generated fake samples to achieve prediction-level and feature-level detection. Even if prototype-based methods show outstanding performance on open-set recognition, they are not suitable to be applied on FL since the uploaded prototype may cause leakage of privacy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.781,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Generative model-based methods generate unknown samples using GANs [10] and autoencoders [1] to help the classifier learning the decision boundary between known and unknown distributions. OSRCI [27] utilized GAN [10] architecture to generate counterfactual examples. PROSER [43] set up the open space between class boundaries to keep classes far from each other based on manifold mixup. Generally, there are a closed-set loss based on su"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.89,
+                0.122
+            ],
+            "angle": 0,
+            "content": "pervision from known samples and an open-set loss by generated unknown samples or boundary constrains [9, 32]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.126,
+                0.685,
+                0.142
+            ],
+            "angle": 0,
+            "content": "3. Problem Definition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.152,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "We begin with formal definition of Federated Learning (FL) and Open-Set Recognition (OSR). Then we define Federated Open-Set Recognition (FedOSR) and its challenges."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.213,
+                0.892,
+                0.439
+            ],
+            "angle": 0,
+            "content": "Open-Set Recognition: In the standard open-set recognition, the model is trained with a labelled closed training set \\(\\mathcal{D}_{train} = \\{(x_i,y_i)\\}_{i=1}^N \\subset \\mathcal{X} \\times \\mathcal{C}\\), where \\(\\mathcal{X}\\) is the input images and \\(\\mathcal{C}\\) is the set of 'known' classes. On the testing phase, the testing set \\(\\mathcal{D}_{test} = \\{(x_i,y_i)\\}_{i=1}^M \\subset \\mathcal{X} \\times (\\mathcal{C} \\cup \\mathcal{U})\\) contains both seen classes \\(\\mathcal{C}\\) and unseen classes \\(\\mathcal{U}\\). In addition to returning the distribution \\(p(y|x,y \\in \\mathcal{C})\\) over known classes, the model also returns a score \\(\\mathcal{O}(y \\in \\mathcal{C}|x)\\) to indicate whether or not the test sample belongs to any of the known classes. Since generative model-based approaches show superior performance, we utilize these methods as our baseline. There are two loss components of generative model-based approaches: closed-set loss based on supervision from known samples and an open-set loss by generated unknown samples or boundary constrains:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.605,
+                0.449,
+                0.891,
+                0.466
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {c l s}} = \\mathcal {L} _ {\\text {c l o s e}} + \\lambda \\cdot \\mathcal {L} _ {\\text {o p e n}}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.478,
+                0.89,
+                0.522
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}_{close}\\) is the cross entropy loss between model prediction and known ground truth, \\(\\mathcal{L}_{open}\\) is to constrain open space or generated unknown samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.524,
+                0.892,
+                0.736
+            ],
+            "angle": 0,
+            "content": "Federated Open-Set Recognition: We then extend conventional open-set recognition to Federated Open-Set Recognition (FedOSR). Given \\(K\\) local clients \\(\\{\\mathcal{S}^l\\}_{l=1}^K\\) with the same known classes \\(\\mathcal{C}\\) and a global central server \\(G\\), for the federated round \\(t\\), every client \\(\\mathcal{S}^k\\) will receive the same global model weights \\(G_{t-1}\\) from the central server and update the model with their local data \\(\\mathcal{D}_k\\) for \\(E\\) epochs. The central server then collects the local parameters \\(\\mathcal{S}_t^k\\) from all clients and aggregates them to update the global model \\(G_t\\). This process repeats until the global model converges. In this paper, we consider the most popular federated averaging algorithm (FedAvg) [23], which aggregates the local parameters with weights of each local dataset to update the global model \\(G = \\frac{1}{K} \\sum_{k=1}^{K} \\mathcal{S}^k\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Challenges: Based on the conclusion that closed-set ability is related to certain parameters of an OSR model [34], the simple merging of OSR models may result in the mixing of closed-related parameters from one client with closed-unrelated parameters from other clients, thereby rendering the related parameters ineffective. Furthermore, even if we aggregate the corresponding closed-related parameters of different OSR models, they may still be misaligned due to the inconsistent distribution of locations. These two challenges pose difficulties in globally aggregating OSR models."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.926,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "4884"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.117,
+                0.09,
+                0.842,
+                0.41
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.412,
+                0.895,
+                0.484
+            ],
+            "angle": 0,
+            "content": "Figure 2. Framework of the proposed FedPD. It consists of a local parameter disentanglement strategy (LPD) and a global divide-and-conquer aggregation approach (GDCA). On the client side, an OSR model is generated with closed-set loss and open-set loss on samples of known classes. Then, LPD decouples the local OSR model into a closed-set subnetwork and an open-set subnetwork by task-related parameter importance. On the server side, GDCA first extracts close-specific, open-specific and shared parameters from the uploaded subnetworks, and then align the corresponding parts by optimal transport and fuse them to generate global model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.501,
+                0.281,
+                0.519
+            ],
+            "angle": 0,
+            "content": "4. The Proposed FedPD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.528,
+                0.474,
+                0.804
+            ],
+            "angle": 0,
+            "content": "The overview of our method is depicted in Fig. 2. To address the FedOSR requirements, our method solves parameter misalignment via a local parameter disentanglement (LPD) strategy (Section 4.1) and a global divide-and-conquer aggregation (GDCA) approach (Section 4.2). For the federated round \\( t \\), every client \\( S^k \\) will receive the same global model weights \\( G_{t-1} \\) from the last round and update the model with their local known data \\( D_k \\) by a closed-set loss and an open-set loss. The LPD then decouples the updated local OSR model \\( S_t^k \\) into a closed-set subnetwork \\( \\mathcal{M}_{close}^k \\) and an open-set subnetwork \\( \\mathcal{M}_{open}^k \\). The local model \\( S^k \\) together with two subnetworks \\( \\mathcal{M}_{close}^k \\) and \\( \\mathcal{M}_{open}^k \\) are uploaded to the server for global divide-and-conquer aggregation. Specifically, the central server first divides two subnetworks into specific parts \\( \\mathcal{P}_{close}^k \\), \\( \\mathcal{P}_{open}^k \\) and shared part \\( \\mathcal{P}_{share}^k \\), then aligns corresponding parts of all clients by optimal transport. At last, the aligned models are averaged to generate the global model \\( G_t \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.816,
+                0.378,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.1. Local Parameter Disentanglement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "To address the parameter misalignment problem caused by cross-client inter-set inference, we propose a local parameter disentanglement (LPD) strategy to analyze parameter components in FedOSR and decouple an OSR model"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.503,
+                0.892,
+                0.595
+            ],
+            "angle": 0,
+            "content": "into a closed-set subnetwork and an open-set subnetwork. Specifically, motivated by the lottery ticket hypothesis [7, 11, 36] which shows that only partial parameters are significant for generalization, we find that partial parameters of an OSR model are important to closed-set classification and some parameters are significant to open-set detection."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.512,
+                0.606,
+                0.882,
+                0.689
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.693,
+                0.892,
+                0.721
+            ],
+            "angle": 0,
+            "content": "Figure 3. Parameter distribution of closed-set subnetwork and open-set subnetwork on an OSR model on MNIST dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.733,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "The Lottery Ticket Hypothesis We first review the lottery ticket hypothesis [7, 11, 36], which generates subnetwork to achieve better generalization. For subtask \\(\\mathbf{t}\\), if parameter \\(h_i\\) is essential to it, the change of loss would be large once we remove \\(h_i\\) (i.e., \\(h_i = 0\\)) [25]. We define the difference value \\(\\Omega^{\\mathrm{t}}\\) to represent the importance score of the parameter as shown in Eq. 2."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.561,
+                0.85,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "\\[\n\\Omega^ {\\mathbf {t}} \\left(h _ {i}\\right) = \\left| \\mathcal {L} ^ {\\mathbf {t}} \\left(H, h _ {i} = 0\\right) - \\mathcal {L} ^ {\\mathbf {t}} \\left(H, h _ {i}\\right) \\right|, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(H\\) refers to other parameters except \\(h_i\\). Since it's inefficient to evaluate the importance by parameter traversal,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.925,
+                0.516,
+                0.937
+            ],
+            "angle": 0,
+            "content": "4885"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.092,
+                0.462,
+                0.108
+            ],
+            "angle": 0,
+            "content": "we approximate it with Taylor Expansion [39] and obtain:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.12,
+                0.127,
+                0.47,
+                0.16
+            ],
+            "angle": 0,
+            "content": "\\[\n\\Omega^ {\\mathbf {t}} \\left(h _ {i}\\right) = \\left| \\frac {\\partial \\mathcal {L} ^ {\\mathbf {t}} (H , h _ {i})}{\\partial h _ {i}} h _ {i} \\right| = \\left| \\nabla \\mathcal {L} _ {\\mathbf {t}} \\left(h _ {i}\\right) \\times h _ {i} \\right|. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.169,
+                0.469,
+                0.244
+            ],
+            "angle": 0,
+            "content": "After deriving the importance score of parameters for subtask \\( \\mathbf{t} \\) based on input \\( (\\mathcal{X}_{\\mathbf{t}},\\mathcal{Y}_{\\mathbf{t}}) \\), parameters with the higher score are selected as the subnetwork for \\( \\mathbf{t} \\). It can be indicated by a mask \\( M_{t} \\), where \\( M^{\\mathbf{t}}(h_i) = 1 \\) if \\( h_i \\) belongs to the subnetwork, and \\( M^{\\mathbf{t}}(h_i) = 0 \\) otherwise."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.245,
+                0.469,
+                0.365
+            ],
+            "angle": 0,
+            "content": "Parameter Disentanglement on OSR Based on the lottery ticket hypothesis, we apply parameter disentanglement to decouple an OSR model into closed-set subnetwork and open-set subnetwork. Specifically, given a local OSR model \\( S^k \\), we define two task-related metric \\( \\mathcal{T}_{close} \\) and \\( \\mathcal{T}_{open} \\) to judge the importance of each parameter contributing to closed-set classification and open-set detection based on the Eq. 3:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.133,
+                0.376,
+                0.47,
+                0.395
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {T} _ {\\text {c l o s e}} ^ {k} (i) = \\left| \\nabla \\mathcal {L} _ {\\text {c l o s e}} \\left(\\omega_ {i}\\right) \\times \\omega_ {i} \\right|, i \\in [ m _ {*} ]. \\tag {4}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.135,
+                0.419,
+                0.469,
+                0.439
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {T} _ {\\text {o p e n}} ^ {k} (i) = | \\nabla \\mathcal {L} _ {\\text {o p e n}} (\\omega_ {i}) \\times \\omega_ {i} |, i \\in [ m _ {*} ]. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.444,
+                0.469,
+                0.503
+            ],
+            "angle": 0,
+            "content": "where \\( m_* \\) is the parameter number of a module in an OSR network and \\( w_i \\) is the corresponding parameters of the module. The larger the value of \\( \\mathcal{T}(i) \\) is, the more this parameter contributes to the task-related loss function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.504,
+                0.469,
+                0.58
+            ],
+            "angle": 0,
+            "content": "After deriving the importance score \\(\\mathcal{T}_{close}\\), \\(\\mathcal{T}_{open}\\) of parameters for closed-set loss and open-set loss, we choose the top-K highest scores as most valuable weights and set them as 1 with the rest as 0 to generate closed-set subnetwork and open-set subnetwork respectively:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.152,
+                0.59,
+                0.469,
+                0.632
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {M} _ {\\text {c l o s e}} ^ {k} (i) = \\left\\{ \\begin{array}{l} 1, \\mathcal {T} _ {\\text {c l o s e}} ^ {k} (i) > \\delta_ {\\text {c l o s e}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.155,
+                0.644,
+                0.469,
+                0.684
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {M} _ {\\text {o p e n}} ^ {k} (i) = \\left\\{ \\begin{array}{l} 1, \\mathcal {T} _ {\\text {o p e n}} ^ {k} (i) > \\delta_ {\\text {o p e n}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.689,
+                0.469,
+                0.749
+            ],
+            "angle": 0,
+            "content": "where \\(\\delta_{close}\\) and \\(\\delta_{open}\\) are the threshold to filter out redundant parameters and we choose the threshold based on ratio of parameter numbers. Here we set the masking ratio as 0.5 based on our experimental observation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.75,
+                0.469,
+                0.794
+            ],
+            "angle": 0,
+            "content": "We visualize the subnetworks in the first convolution layer as illustrated in Fig. 3. It's obvious that open-set and closed-set subnetworks hold different distribution."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.795,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Parameter Disentanglement on FedOSR Given a set of local OSR models \\(\\{\\mathcal{S}^k\\}_{k = 1}^K\\), we apply parameter disentanglement on these models, and plot closed-set subnetworks \\(\\{\\mathcal{M}_close^k\\}_{k = 1}^K\\) and open-set subnetworks \\(\\{\\mathcal{M}_{open}^k\\}_{k = 1}^K\\) as shown in Fig. 4. It illustrates that there exists parameter misalignment in both closed-set subnetworks and open-set subnetworks among these clients. Simply aggregating the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.198
+            ],
+            "angle": 0,
+            "content": "client OSR modes into one global model may ignore the complex parameter composition and lead to model collapse due to unmatched averaging. For example, the parameter averaging on a closed-set subnetwork and an open-set subnetwork on the same position may generate chaotic neuron weights. This phenomenon motivates us to develop a new model aggregation approach for FedOSR."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.514,
+                0.214,
+                0.885,
+                0.35
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.355,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Figure 4. Parameter distribution of closed-set parameters and open-set parameters in federated framework on HDR-FL dataset. The horizontal direction of the picture represents channel numbers, and the vertical of it denotes client numbers."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.426,
+                0.851,
+                0.442
+            ],
+            "angle": 0,
+            "content": "4.2. Global Divide-and-Conquer Aggregation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.449,
+                0.892,
+                0.6
+            ],
+            "angle": 0,
+            "content": "During model communication on the server side, parameter misalignment problem will significantly destroy the global model, thus providing bad model initialization for local training in next step. To further remedy the aggregation catastrophe by cross-client intra-set inconsistency, we design a global divide-and-conquer aggregation (GDCA) method to first divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters, and then align and aggregate the corresponding parts respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.6,
+                0.892,
+                0.706
+            ],
+            "angle": 0,
+            "content": "Learning to divide Based on the results of local parameter disentanglement, an OSR model can be decoupled into a closed-set subnetwork and an open-set subnetwork as shown in Fig. 4. Since there are overlaps between these two subnetworks, we further divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.715,
+                0.891,
+                0.733
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {P} _ {\\text {c l o s e}} = \\mathcal {M} _ {\\text {c l o s e}} \\odot \\overline {{\\mathcal {M} _ {\\text {o p e n}}}}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.591,
+                0.735,
+                0.891,
+                0.752
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {P} _ {\\text {o p e n}} = \\mathcal {M} _ {\\text {o p e n}} \\odot \\overline {{\\mathcal {M} _ {\\text {c l o s e}}}}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.587,
+                0.755,
+                0.891,
+                0.771
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {P} _ {\\text {s h a r e}} = \\mathcal {M} _ {\\text {o p e n}} \\odot \\mathcal {M} _ {\\text {c l o s e}}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.891,
+                0.84
+            ],
+            "angle": 0,
+            "content": "where \\(\\overline{\\mathcal{M}}\\) is the negation of the binary mask \\(\\mathcal{M}\\). Compared with two subnetworks, the three non-overlapping parts are more suitable to deal with since the overlapping parameters may cause conflicts after alignment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Learning to conquer We disentangle the OSR model of each client into three parts and align the corresponding parts before aggregation. The neuron weights are considered as a distribution, and we use optimal transport (OT) to achieve"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "4886"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.197
+            ],
+            "angle": 0,
+            "content": "distribution alignment as shown in Fig. 2. OT is a technique used to solve distribution matching problems by finding a minimal effort solution to transport a given mass of dirt into a given hole. It has been successfully applied to various problems such as domain adaptation and GANs. We compute the transport map layer by layer to achieve alignment between two models \\( W_{A} \\) and \\( W_{B} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.198,
+                0.471,
+                0.379
+            ],
+            "angle": 0,
+            "content": "Taking two models \\( \\mathbf{W}_A \\) and \\( \\mathbf{W}_B \\) as an example, we align parameters of \\( \\mathbf{W}_A \\) on \\( \\mathbf{W}_B \\) by channel-wise distribution matching. Let us assume that we are at one convolution layer \\( \\mathbf{W}^{(\\ell)} \\in (\\mathcal{C}_{in}^{\\ell},\\mathcal{C}_{out}^{\\ell},F^{\\ell}) \\) and the previous layers have already been aligned, where \\( F = k\\times k \\) is the square of filter size. The transport matrix of the last convolution layer \\( \\mathbf{W}^{(\\ell -1)}\\in (\\mathcal{C}_{in}^{\\ell -1},\\mathcal{C}_{out}^{\\ell -1},F^{\\ell -1}) \\) is denoted as \\( T^{(\\ell -1)} \\in (\\mathcal{C}_{out}^{\\ell -1},\\mathcal{C}_{out}^{\\ell -1}) \\). Since the output of last layer has been permuted by \\( T^{(\\ell -1)} \\), we conduct post-multiplying on current layer with transport map of previous layer such that the order of current layer input \\( \\mathcal{C}_{out}^{\\ell -1} \\) can match the order of \\( \\mathcal{C}_{in}^{\\ell} \\). Then the current layer can be transformed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.176,
+                0.389,
+                0.47,
+                0.413
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widehat {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)} \\leftarrow \\boldsymbol {W} _ {A} ^ {(\\ell) ^ {\\top}} \\boldsymbol {T} ^ {(\\ell - 1)}, \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.416,
+                0.469,
+                0.463
+            ],
+            "angle": 0,
+            "content": "where \\(\\widehat{\\pmb{W}}_A^{(\\ell, \\ell-1)}\\) is the post-processed layer, and \\(\\pmb{W}_A^{(\\ell)}\\) is transposed as \\((\\mathcal{C}_{in}^{\\ell}, F^{\\ell}, \\mathcal{C}_{out}^{\\ell})\\) to achieve matrix multiplication."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.465,
+                0.469,
+                0.56
+            ],
+            "angle": 0,
+            "content": "With current layer permuted, we compute the optimal transport map \\( \\pmb{T}^{(\\ell)} \\) between \\( \\widehat{\\pmb{W}}_A^{(\\ell,\\ell-1)}, \\pmb{W}_B^{(\\ell)} \\), i.e., \\( \\pmb{T}^{(\\ell)} \\), \\( d \\gets \\mathrm{OT}(\\widehat{\\pmb{W}}_A^{(\\ell,\\ell-1)}, \\pmb{W}_B^{(\\ell)}) \\), where \\( d \\) denotes the obtained Wasserstein-distance. We use this transport map \\( \\pmb{T}^{(\\ell)} \\) to align the neurons weights of the first model \\( (\\pmb{W}_A) \\) with respect to the second \\( (\\pmb{W}_B) \\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.17,
+                0.57,
+                0.469,
+                0.592
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)} \\leftarrow \\boldsymbol {T} ^ {(\\ell) ^ {\\top}} \\widehat {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)}, \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.595,
+                0.469,
+                0.676
+            ],
+            "angle": 0,
+            "content": "where \\(\\widetilde{W}_A^{(\\ell, \\ell-1)}\\) is the aligned layer from model \\(W_A\\) to \\(W_B\\). To simplify this alignment process, we define \\(\\widetilde{W}_A = OT(W_A, W_B)\\). Through the alignment of model parameters, model \\(W_A\\) will only change the orders of feature channels without affecting the model prediction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.677,
+                0.469,
+                0.752
+            ],
+            "angle": 0,
+            "content": "When we align the parameters of the OSR model for all clients, we can choose any client as the target client and align other clients with the target client. For example, we use the second client as the target client as shown in Fig. 2. The alignment process can be denoted as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.12,
+                0.758,
+                0.469,
+                0.777
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {S} _ {\\text {c l o s e}} ^ {k} = O T \\left(\\mathcal {S} ^ {k} \\odot \\mathcal {P} _ {\\text {c l o s e}} ^ {k}, \\mathcal {S} ^ {2} \\odot \\mathcal {P} _ {\\text {c l o s e}} ^ {2}\\right), \\tag {13}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.124,
+                0.779,
+                0.469,
+                0.799
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\mathcal {S}} _ {\\text {o p e n}} ^ {k} = O T \\left(S ^ {k} \\odot \\mathcal {P} _ {\\text {o p e n}} ^ {k}, S ^ {2} \\odot \\mathcal {P} _ {\\text {o p e n}} ^ {2}\\right), \\tag {14}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.119,
+                0.801,
+                0.469,
+                0.82
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\mathcal {S}} _ {\\text {s h a r e}} ^ {k} = O T \\left(\\mathcal {S} ^ {k} \\odot \\mathcal {P} _ {\\text {s h a r e}} ^ {k}, \\mathcal {S} ^ {2} \\odot \\mathcal {P} _ {\\text {s h a r e}} ^ {2}\\right). \\tag {15}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.098,
+                0.827,
+                0.447,
+                0.842
+            ],
+            "angle": 0,
+            "content": "After that, the global model \\(G\\) can be represented as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.101,
+                0.849,
+                0.469,
+                0.891
+            ],
+            "angle": 0,
+            "content": "\\[\nG = \\frac {1}{K} \\left(\\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {c l o s e}} ^ {k} + \\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {o p e n}} ^ {k} + \\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {s h a r e}} ^ {k}\\right). \\tag {16}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.898,
+                0.388,
+                0.913
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 summarizes the FedPD algorithm."
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.502,
+                0.092,
+                0.64,
+                0.106
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 FedPD"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.504,
+                0.113,
+                0.882,
+                0.491
+            ],
+            "angle": 0,
+            "content": "Server OPERATIONS  \nInputs: Round number \\(T\\), Set of clients \\(K\\)  \nOutput: Global OSR model \\(G\\)  \nfor \\(t = 0,1,\\ldots,T-1\\) do  \nfor client \\(k \\in K\\) in parallel do  \n\\(\\mathcal{S}^k, \\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k \\gets \\text{CLIENTOPERATIONS}(G_{t-1})\\)  \nend for  \n\\(\\mathcal{P}_{close}^k = \\mathcal{M}_{close}^k \\odot \\overline{\\mathcal{M}_{open}^k}\\)  \n\\(\\mathcal{P}_{open}^k = \\mathcal{M}_{open}^k \\odot \\overline{\\mathcal{M}_{close}^k}\\)  \n\\(\\mathcal{P}_{share}^k = \\mathcal{M}_{close}^k \\odot \\mathcal{M}_{open}^k\\)  \n\\(\\widetilde{S}_{close}^k = OT(S^k \\odot \\mathcal{P}_{close}^k, S^2 \\odot \\mathcal{P}_{close}^2)\\)  \n\\(\\widetilde{S}_{open}^k = OT(S^k \\odot \\mathcal{P}_{open}^k, S^2 \\odot \\mathcal{P}_{open}^2)\\)  \n\\(\\widetilde{S}_{share}^k = OT(S^k \\odot \\mathcal{P}_{share}^k, S^2 \\odot \\mathcal{P}_{share}^2)\\)  \n\\(G_t \\gets \\frac{1}{K} (\\sum_{k=1}^{K} \\widetilde{S}_{close}^k + \\sum_{k=1}^{K} \\widetilde{S}_{open}^k + \\sum_{k=1}^{K} \\widetilde{S}_{share}^k)\\)  \nend for  \nObtain global OSR model \\(G\\)  \nCLIENT OPERATIONS  \nInput: Model weights \\(G_{t-1}\\)  \nOutput: Updated local OSR model weights \\(\\mathcal{S}_t^k\\), closed-set subnetwork \\(\\mathcal{M}_{close}^k\\), open-set subnetwork \\(\\mathcal{M}_{open}^k\\)  \nfor epoch \\(e = 0,1,\\ldots,E-1\\) do  \nfor batch \\(\\{x,y\\} \\in D_m\\) do  \n\\(\\mathcal{L}_{local} = \\mathcal{L}_{close}(x,y) + \\mathcal{L}_{open}(x,y)\\)  \n\\(\\mathcal{T}_{close}^k = |\\nabla \\mathcal{L}_{close}(\\omega) \\times \\omega|\\)  \n\\(\\mathcal{T}_{open}^k = |\\nabla \\mathcal{L}_{open}(\\omega) \\times \\omega|\\)  \n\\(\\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k = TopK(\\mathcal{T}_{close}^k, \\mathcal{T}_{open}^k)\\)  \n\\(\\mathcal{S}_t^k \\gets update(\\mathcal{S}_t^k, \\mathcal{L}_{local})\\)  \nend for  \nend for  \nSend model weights \\(\\mathcal{S}_t^k\\) and subnetworks \\(\\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k\\) to the server"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.521,
+                0.625,
+                0.538
+            ],
+            "angle": 0,
+            "content": "5. Experiment"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.548,
+                0.723,
+                0.563
+            ],
+            "angle": 0,
+            "content": "5.1. Datasets and Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.574,
+                0.892,
+                0.665
+            ],
+            "angle": 0,
+            "content": "We conduct extensive experiments on both heterogeneous federated learning benchmark Handwritten digital recognition FL Dataset (HDR-FL) and homogeneous federated learning benchmark CIFAR-10. The closed-set classification and open-set detection performances are evaluated by accuracy (ACC) and AUROC (AUC) respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.677,
+                0.892,
+                0.797
+            ],
+            "angle": 0,
+            "content": "HDR-FL: It consists of five datasets: MNIST [16], SVHN [28], USPS [12], SynthDigits [8] and MNIST-M [8]. These datasets are 10-class handwritten digital images from various scenarios. Each dataset is set as a client for Non-IID FedOSR. To achieve open-set recognition, six classes are chosen to be known and four classes are to be unknown classes. We keep the same known classes and unknown classes for all clients."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "CIFAR-10: It contains 60000 images in 10 classes, with 6000 images per class [15]. We first divide 10 classes into known classes and unknown classes, then split them into five equal parts to construct homogeneous federated setting. Specifically, we try different ratio between the known and the unknown to validate our method (e.g. 4:6, 6:4 and 8:2)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "4887"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.163,
+                0.088,
+                0.805,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Table 1. Performance comparisons between our method and other baseline methods on HDR-FL benchmark."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.098,
+                0.1,
+                0.877,
+                0.228
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">Closed-set ACC</td><td colspan=\"6\">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>SoftMax</td><td>96.69</td><td>76.06</td><td>97.97</td><td>83.99</td><td>83.69</td><td>87.68</td><td>77.38</td><td>65.41</td><td>88.80</td><td>70.53</td><td>66.24</td><td>73.67</td></tr><tr><td>OpenMax[2](CVPR&#x27;16)</td><td>95.54</td><td>63.13</td><td>97.97</td><td>81.15</td><td>76.57</td><td>82.87</td><td>77.78</td><td>57.37</td><td>89.21</td><td>69.78</td><td>60.88</td><td>71.00</td></tr><tr><td>RPL[4](ECCV&#x27;20)</td><td>98.33</td><td>77.22</td><td>98.13</td><td>84.76</td><td>86.32</td><td>88.95</td><td>77.87</td><td>66.70</td><td>89.53</td><td>73.17</td><td>73.23</td><td>76.10</td></tr><tr><td>PROSER[43](CVPR&#x27;21)</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>ARPL[3](TPAMI&#x27;21)</td><td>97.17</td><td>69.83</td><td>96.44</td><td>84.64</td><td>84.22</td><td>86.46</td><td>85.65</td><td>59.79</td><td>92.53</td><td>69.70</td><td>68.17</td><td>75.16</td></tr><tr><td>DIAS[26](ECCV&#x27;22)</td><td>97.50</td><td>70.66</td><td>97.62</td><td>86.11</td><td>86.81</td><td>87.74</td><td>82.90</td><td>67.33</td><td>90.69</td><td>77.48</td><td>71.92</td><td>78.06</td></tr><tr><td>SSB[35](ICLR&#x27;22)</td><td>96.41</td><td>60.12</td><td>97.46</td><td>82.82</td><td>74.86</td><td>82.33</td><td>88.53</td><td>57.68</td><td>90.45</td><td>73.40</td><td>70.01</td><td>76.01</td></tr><tr><td>FedPD(Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.158,
+                0.239,
+                0.809,
+                0.251
+            ],
+            "angle": 0,
+            "content": "Table 2. Performance comparisons between our method and other baseline methods on CIFAR-10 benchmark."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.102,
+                0.252,
+                0.868,
+                0.38
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Known=4</td><td colspan=\"2\">Known=6</td><td colspan=\"2\">Known=8</td></tr><tr><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td></tr><tr><td>SoftMax</td><td>83.23 ±0.28</td><td>65.70±0.14</td><td>83.14±0.38</td><td>72.00±0.44</td><td>72.17±0.41</td><td>61.11±0.45</td></tr><tr><td>\\( OpenMax[2]_{(CVPR&#x27;16)} \\)</td><td>83.24 ±0.08</td><td>65.96±0.14</td><td>84.56±0.24</td><td>81.69±0.59</td><td>72.72±0.40</td><td>61.52±0.38</td></tr><tr><td>\\( RPL[4]_{(ECCV&#x27;20)} \\)</td><td>81.23 ±0.11</td><td>65.10±0.05</td><td>78.78±0.43</td><td>68.72±0.43</td><td>72.98±0.33</td><td>61.36±0.32</td></tr><tr><td>\\( PROSER[43]_{(CVPR&#x27;21)} \\)</td><td>84.15 ±0.13</td><td>69.04±0.07</td><td>85.77±0.48</td><td>80.69±0.27</td><td>70.50±0.21</td><td>60.48±0.41</td></tr><tr><td>\\( ARPL[3]_{(TPAMI&#x27;21)} \\)</td><td>83.91 ±0.09</td><td>69.02±0.12</td><td>86.54±0.53</td><td>79.83±0.69</td><td>73.63±0.37</td><td>66.78±0.64</td></tr><tr><td>\\( DIAS[26]_{(ECCV&#x27;22)} \\)</td><td>84.85 ±0.04</td><td>70.32±0.09</td><td>87.74±0.16</td><td>81.66±0.25</td><td>74.53±0.37</td><td>67.75±0.34</td></tr><tr><td>\\( SSB[35]_{(ICLR&#x27;22)} \\)</td><td>84.27±0.06</td><td>68.85±0.11</td><td>86.04±0.70</td><td>82.41±0.33</td><td>75.54±0.18</td><td>67.97±0.23</td></tr><tr><td>\\( FedPD(Ours) \\)</td><td>86.28±0.07</td><td>71.50±0.07</td><td>89.43±0.22</td><td>85.07±0.50</td><td>75.87±0.16</td><td>69.12±0.45</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.403,
+                0.295,
+                0.42
+            ],
+            "angle": 0,
+            "content": "5.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.427,
+                0.473,
+                0.714
+            ],
+            "angle": 0,
+            "content": "On local training, we apply PROSER [43] for open-set training with a closed-set loss and an open-set loss. On global aggregation, we utilize FedAvg [23] to average OSR models for comparison methods. For handwritten digital recognition, we apply a six-layer CNN. During the training process, we utilize the SGD optimizer [31] with learning rate \\(10^{-2}\\) for closed-set loss and \\(10^{-4}\\) for open-set loss, we set batch size to 32 and training epochs to 100. Global model is updated every epoch by FedAvg [23] aggregation. For CIFAR-10 Dataset, we use WideResNet for classification. Networks are trained by Adam optimizer [14] with batch size of 128. The learning rates of closed-set loss and open-set loss are initialized as \\(10^{-1}\\) and \\(10^{-3}\\) respectively. The communication is conducted after every \\(\\mathrm{E} = 5\\) epochs in local training until reaching \\(\\mathrm{T} = 250\\) epochs in total. All experiments of these two benchmarks are performed on NVIDIA 2080Ti card with Pytorch library. Detailed model architecture for both benchmarks is shown in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.715,
+                0.376,
+                0.731
+            ],
+            "angle": 0,
+            "content": "5.3. Comparison with state-of-the-arts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.47,
+                0.841
+            ],
+            "angle": 0,
+            "content": "We compare the performance of FedPD with the state-of-the-art OSR methods, including SoftMax, OpenMax [2], RPL [4], PROSER [43], ARPL [3], DIAS [26], SSB [35]. These comparison methods are implemented by FedAvg [23] on each client OSR models. Our FedPD utilizes the popular generative-based method PROSER [43] for local open-set training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "HDR-FL: As shown in Table 1, our FedPD outperforms existing OSR approaches with a large margin not only in closed-set classification but also in open-set detection. In addition, our FedPD achieves consistent improvements on"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.404,
+                0.892,
+                0.587
+            ],
+            "angle": 0,
+            "content": "all clients. Specifically, our method can surpass existing approaches with a promising \\(90.60\\%\\) average closed-set ACC and 80.78 average open-set AUC, outperforming the state-of-the-art OSR method DIAS [26] with \\(2.76\\%\\) in ACC and \\(2.72\\%\\) in AUC. It validates that our method could enable better global model aggregation for open-set recognition, which verifies the effectiveness of our divide-and-conquer approach to address parameter misalignment in FedOSR. Moreover, some generate-based methods (e.g. SSB [26]) may encounter serious model collapse problem due to unmatched parameter of local OSR models, leading to \\(8.17\\%\\) performance gap in average ACC."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.592,
+                0.893,
+                0.728
+            ],
+            "angle": 0,
+            "content": "CIFAR-10: Comparison results on CIFAR-10 benchmark are shown in Table 2. To validate the stability of our method, we conduct experiments on different ratios between known classes and unknown classes. In these three settings, our FedPD achieves the best open-set AUC of \\(71.70\\%\\), \\(85.07\\%\\) and \\(69.12\\%\\). The consistent performance improvement over different openness demonstrate the effectiveness of our FedPD to promote the ability of detecting novel category for federated models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.734,
+                0.795,
+                0.749
+            ],
+            "angle": 0,
+            "content": "5.4. Ablation Analysis of Our Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.751,
+                0.702,
+                0.765
+            ],
+            "angle": 0,
+            "content": "5.4.1 Effectiveness of LPD"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.774,
+                0.856,
+                0.787
+            ],
+            "angle": 0,
+            "content": "Table 4. Comparison to different network splitting methods."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.787,
+                0.892,
+                0.833
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Splitting Method</td><td>None</td><td>Grad</td><td>Grad × Weight (Ours)</td></tr><tr><td>Closed-set ACC</td><td>85.61</td><td>89.04</td><td>90.96</td></tr><tr><td>Open-set AUC</td><td>76.19</td><td>80.95</td><td>81.36</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To demonstrate the advantage of local parameter disentanglement, we compare it with no splitting and network splitting by grad as shown in Table 4. It shows that conducting network splitting according to task gradients results in large"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "4888"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.352,
+                0.089,
+                0.616,
+                0.101
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation study for key components."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.094,
+                0.101,
+                0.878,
+                0.191
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">closed-set ACC</td><td colspan=\"6\">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>Baseline + FedAvg</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>Baseline + FedMA</td><td>97.21</td><td>60.72</td><td>98.22</td><td>86.18</td><td>85.72</td><td>85.61</td><td>83.09</td><td>66.47</td><td>88.81</td><td>73.13</td><td>69.46</td><td>76.19</td></tr><tr><td>Baseline + FedPD (Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr><tr><td>Ours w/o Divide</td><td>98.39</td><td>77.60</td><td>98.22</td><td>88.65</td><td>89.66</td><td>90.50</td><td>89.56</td><td>69.91</td><td>92.72</td><td>79.05</td><td>72.67</td><td>80.78</td></tr><tr><td>Ours w/o Conquer</td><td>97.43</td><td>72.74</td><td>97.62</td><td>85.82</td><td>85.22</td><td>87.76</td><td>84.41</td><td>65.78</td><td>91.60</td><td>72.51</td><td>70.81</td><td>77.02</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.107,
+                0.222,
+                0.268,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.27,
+                0.223,
+                0.432,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.313,
+                0.47,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Figure 5. Ablation study for the masking ratio of the parameter disentanglement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.367,
+                0.469,
+                0.412
+            ],
+            "angle": 0,
+            "content": "performance gain. Combining gradient and weight information makes better model decoupling, which corresponds to our theoretical analysis in Eq. 3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.414,
+                0.292,
+                0.427
+            ],
+            "angle": 0,
+            "content": "5.4.2 Effectiveness of GDCA"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.434,
+                0.469,
+                0.599
+            ],
+            "angle": 0,
+            "content": "Learning to Divide To validate the advantage of dividing two subnetworks into specific parts and shared parts, we conduct experiments on two different aggregation strategy: align two subnetworks then average (Ours w/o Divide) and align three parts then average (Ours). Comparison results in Table 3 illustrates that aligning three parts outperforms aligning two subnetworks with performance gain of \\(0.46\\%\\) in ACC and \\(0.58\\%\\) in AUC. It is because that the overlapping parameters between these two subnetworks may have different distribution after alignment, thus leading to ambiguous parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.601,
+                0.469,
+                0.796
+            ],
+            "angle": 0,
+            "content": "Learning to Conquer To validate the effectiveness of divide-and-conquer aggregation, we compare our method with traditional aggregation methods FedAvg and FedMA. Unlike obvious improvement on closed-set setting, FedMA shows inferior performance than FedAvg as shown in Table 3. It is consistent with our observation that parameter components in open-set models are more complex than those in closed-set models due to multiple optimization directions. Compared with directly averaging three parts with alignment (Ours w/o Conquer), conducting our proposed aggregation strategy brings performance boost on of \\(3.2\\%\\) in ACC and \\(4.34\\%\\) in AUC, demonstrating that our FedPD can alleviate parameter misalignment problem."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.802,
+                0.298,
+                0.817
+            ],
+            "angle": 0,
+            "content": "5.4.3 Effect of Masking Ratio"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To investigate the effect of masking ratio to the FedOSR performance, we design ablation experiments under HDRFL setting, as shown in Fig. 5. It is observed that small masking ratio (e.g. 0.1) may filter out too much parameters, leading to empty shared parameter. Large masking ratio"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.536,
+                0.218,
+                0.861,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.342,
+                0.892,
+                0.37
+            ],
+            "angle": 0,
+            "content": "Figure 6. Parameter distribution of closed-set subnetworks and open-set subnetworks on CIFAR-10 dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.394,
+                0.892,
+                0.47
+            ],
+            "angle": 0,
+            "content": "(e.g. 0.9) can't choose valuable weights for the closed-set task and the open-set task, thus leading to invalid decoupling. In this paper, we choose suitable masking ratio as 0.5 based on our experimental observation that it achieves the best closed-set ACC and open-set AUC."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.472,
+                0.817,
+                0.487
+            ],
+            "angle": 0,
+            "content": "5.5. Analysis of Parameter Misalignment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.495,
+                0.892,
+                0.661
+            ],
+            "angle": 0,
+            "content": "To verify the parameter misalignment problem in FedOSR, we visualize the weights distributions of closed-set subnetwork and open-set subnetwork on CIFAR-10 homogeneous benchmark as shown in Fig. 6. Different clients still hold inconsistent parameter distribution on both closed-set subnetwork and open-set subnetwork. Different from results shown in Fig. 4, where parameter misalignment may come from domain shift in heterogeneous federated datasets. Fig. 6 further emphasize that the parameter misalignment in FedOSR mainly comes from gradient divergence of closed-set loss and open-set loss."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.668,
+                0.619,
+                0.684
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.69,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "In this work, we propose a novel and practical problem of federated open-set recognition (FedOSR) for the first time. To alleviate the parameter misalignment problem in FedOSR, we design a novel parameter disentanglement guided federated algorithm (FedPD). Specifically, on the client side, a local parameter disentanglement is developed to decouple the local OSR models into closed-set subnetworks and open-set subnetworks. On the server side, a global divide-and-conquer aggregation strategy is proposed to divide two subnetworks into specific parts and shared parts, then align corresponding parts by optimal transport and fuse them to generate global model. Extensive experiments on both IID and Non-IID benchmark datasets demonstrate the effectiveness of FedPD."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "4889"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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\ No newline at end of file
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+# FedPD: Federated Open Set Recognition with Parameter Disentanglement
+
+Chen Yang<sup>1</sup>
+
+Meilu Zhu
+
+Yifan Liu2
+
+Yixuan Yuan $^{1,2*}$
+
+<sup>1</sup>City University of Hong Kong
+
+2The Chinese University of Hong Kong
+
+{cyang53, meiluzhu2}-c@my.cityu.edu.hk 1155195605@link.cuhk.edu.hk yxyuan@ee.cuhk.edu.hk
+
+# Abstract
+
+Existing federated learning (FL) approaches are deployed under the unrealistic closed-set setting, with both training and testing classes belong to the same set, which makes the global model fail to identify the unseen classes as 'unknown'. To this end, we aim to study a novel problem of federated open-set recognition (FedOSR), which learns an open-set recognition (OSR) model under federated paradigm such that it classifies seen classes while at the same time detects unknown classes. In this work, we propose a parameter disentanglement guided federated open-set recognition (FedPD) algorithm to address two core challenges of FedOSR: cross-client inter-set interference between learning closed-set and open-set knowledge and cross-client intra-set inconsistency by data heterogeneity. The proposed FedPD framework mainly leverages two modules, i.e., local parameter disentanglement (LPD) and global divide-and-conquer aggregation (GDCA), to first disentangle client OSR model into different subnetworks, then align the corresponding parts cross clients for matched model aggregation. Specifically, on the client side, LPD decouples an OSR model into a closed-set subnetwork and an open-set subnetwork by the task-related importance, thus preventing inter-set interference. On the server side, GDCA first partitions the two subnetworks into specific and shared parts, and subsequently aligns the corresponding parts through optimal transport to eliminate parameter misalignment. Extensive experiments on various datasets demonstrate the superior performance of our proposed method.
+
+# 1. Introduction
+
+Deep learning algorithms rely on the availability of large-scale data to achieve remarkable performance. However, in reality, data is scattered across different organiza
+
+![](images/42158c9670bec7e8408c21cb65edc777235df594b2af20162ccfde6dbe50ed0d.jpg)  
+Figure 1. Parameter disentanglement on FedOSR models and comparison of various aggregation strategies on FedOSR setting. (a) FedAvg simply aggregates multiple OSR models, leading to model collapse; (b) Our FedPD first aligns corresponding close-specific, open-specific and shared parts by optimal transport (OT), then aggregates aligned parameters. The curves inside the network box represent different parameter distribution of each parts.
+
+tions and difficult to integrate into a centralized dataset, owing to increasing privacy and ethical concerns, especially for those sensitive data such as location-based services or health information [22]. To break this dilemma, federated learning (FL) [5, 23, 20] provides a privacy-preserving paradigm that allows local clients to collaboratively train a shared global model without data sharing.
+
+Although FL has recently achieved promising progress, existing FL works [23, 20, 5] are generally evaluated in a closed-set scenario, where the categories of training and testing samples are identical. The closed-set setting is irrational since unknown classes may appear at the test time and would be classified into known classes. This problem seriously impedes the deployment of FL models in many real-world applications due to enormous risk, such as clinical diagnosis and autonomous driving. Current open-set recognition (OSR) methods [3, 43, 2, 6] attempt to improve the
+
+ability of models in recognizing unknown classes, but they are designed for the centralized setting. In this work, we represent the first effort to formulate a challenging and unexplored problem of Federated Open Set Recognition (FedOSR). FedOSR aims to unite multiple distributed clients to learn a global model and reduce privacy as well as security risk, which not only exactly classifies known classes but also recognizes unknown classes in the testing stage.
+
+Directly applying existing OSR methods into the FL setting for FedOSR mainly undergoes two troublesome challenges. The first challenge lies in the cross-client inter-set interference between learning closed-set and open-set knowledge. According to the previous study [34], the partial parameters of a client model are in charge of learning knowledge of known classes, and the rest are related to open set. The known classes-related parameters of a client is probably polluted by the open set-related parameters from other clients after server communication, leading to the performance degradation on closed set. Similarly, open set-related parameters of a client are also affected by closed-set knowledge of other clients. In this situation, a unknown samples would be possibly misclassified into known classes. The second one is cross-client intra-set inconsistency by data heterogeneity. Even though we aggregate corresponding closed-related parameters of OSR models from different clients, these parameters are still misaligned due to the permutation invariance property of neural networks and data heterogeneity [37]. Aggregation of local client parameters directly at the server can result in inconsistent models among the clients, leading to significant divergence of client models. This inconsistency issue can cause slow and unstable convergence [19], ultimately resulting in sub-optimal performance of the entire FL system [17, 37].
+
+To achieve FedOSR, we conquer these intractable challenges from a new perspective, i.e., parameter disentanglement. Based on the lottery ticket hypothesis [7, 11, 36], we divide parameters of a client model into a closed-set subnetwork and an open-set subnetwork. These two subnetworks have their own specific parameters, which are only related to known classes and unknown classes respectively. Meanwhile, they also share partial parameters since known and unknown samples might have some similar patterns [35]. The parameter disentanglement of client models can preserve the high performance of closed set by reducing the interference from open-set subnetworks. As shown in Fig. 1, the closed-set subnetworks and the open-set subnetworks of different client models distribute in different positions with some overlaps. Directly aggregating all client OSR models by FedAvg [23] on the server side may encounter the parameter misalignment problem and lead to model collapse as shown in Fig. 1 (a). These destroyed parameters are transmitted to clients and slow down the convergence of the federated system due to bad model initialization to the
+
+next training step. Therefore, aligning these subnetworks before model aggregation is a crucial step to solve the inconsistency problem of parameter distributions.
+
+To tackle these challenges in FedOSR, we propose a novel parameter disentanglement guided federated OSR (FedPD) algorithm in this paper, which effectively addresses the local parameter misalignment problem occurred on the global model aggregation. Specifically, we design a local parameter disentanglement strategy (LPD) to firstly decouple an OSR model into two subnetworks: an open-set subnetwork and a closed-set subnetwork by task-related metrics. To overcome the parameter misalignment caused by simply parameter averaging on whole client OSR models, we propose a global divide-and-conquer aggregation (GDCA) method to firstly divide two subnetworks into specific parts and shared parts, then align corresponding parameter components by optimal transport [13, 30] and aggregate them. As shown in Fig. 1 (b), our FedPD enables reasonable model aggregation and reliable global model to boost federated training.
+
+The major contribution of this paper are summarized as follows:
+
+- We address a practical FL problem, namely Federated Open-Set Recognition (FedOSR). To the best of our knowledge, this is the first work to improve the ability of detecting novel category for federated models.  
+- We propose a novel Parameter Disentanglement guided Federated algorithm (FedPD) to solve parameter misalignment problem in FedOSR.  
+- On the client side, we introduce the Local Parameter Disentanglement (LPD) approach, which leverages task-related importance on model parameters to decouple the local OSR model into a closed-set subnetwork and an open-set subnetwork.  
+- On the server side, we design a Global Divide-and-Conquer Aggregation (GDCA) strategy to partition the two subnetworks into specific and shared parts, align the corresponding parts via optimal transport, and subsequently fuse them to alleviate the misalignment problem in FedOSR.
+
+# 2. Related Work
+
+# 2.1. Federated Learning
+
+Federated learning [23, 20, 38, 37, 19, 29, 24, 42] provides a promising privacy-preserving solution for multi-site data collaboration, which develops a global model from decentralized datasets by aggregating the parameters of each local client while keeping data locally. Representatively, McMahan [23] proposed the popular FedAvg algorithm
+
+for communication-efficient federated training of deep networks. There are two lines to improve FedAvg: improvement on local training and on global aggregation.
+
+Regarding improving local training, FedProx [19] introduced a proximal term to the clients' objective, which regulates the local updates to be closer to the initial global model. Meanwhile, MOON [18] proposed a model contrastive loss that corrects local updates by maximizing the agreement of the representation learned by the current local model and the global model, and minimizing the agreement of the representation learned by the current local model and the previous local model.
+
+As for studies on improving the global aggregation phase, FedMA [37] utilizes Bayesian non-parametric methods to match and average weights in a layer-wise manner. To preserve personalization of local clients, FedBN [20] aggregates parameters except BN layers on the server side. Chen [5] proposed to aggregate client model parameters on the frequency domain. Even if these works [37, 21] try to solve parameter misalignment, they are applied to the closed-set recognition task, which can't be directly transferred to open-set recognition due to complex parameter composition in open-set recognition.
+
+# 2.2. Open Set Recognition
+
+To deploy the classification models to real-world scenario with high stability, open-set recognition (OSR) [40, 41, 33, 3, 43] was proposed to classify known classes while detect unknown classes at the same time. Recent deep learning-based OSR methods can be classified into three categories: discriminative-based models, prototype-based models and generative-based models.
+
+Discriminative model-based methods calibrate the classification logistics to detect unknown samples. Softmax scores are initially utilized to identify out-of-distribution data by argmax thresholding. OpenMax [2] improves softmax scores with an OpenMax layer and fits outputs probabilities with Weibull distributions.
+
+Prototype-based methods [4, 3, 26] apply prototype learning to identify unknown samples on the feature space. ARPL [3] enhanced prototype learning with generated fake samples to achieve prediction-level and feature-level detection. Even if prototype-based methods show outstanding performance on open-set recognition, they are not suitable to be applied on FL since the uploaded prototype may cause leakage of privacy.
+
+Generative model-based methods generate unknown samples using GANs [10] and autoencoders [1] to help the classifier learning the decision boundary between known and unknown distributions. OSRCI [27] utilized GAN [10] architecture to generate counterfactual examples. PROSER [43] set up the open space between class boundaries to keep classes far from each other based on manifold mixup. Generally, there are a closed-set loss based on su
+
+pervision from known samples and an open-set loss by generated unknown samples or boundary constrains [9, 32].
+
+# 3. Problem Definition
+
+We begin with formal definition of Federated Learning (FL) and Open-Set Recognition (OSR). Then we define Federated Open-Set Recognition (FedOSR) and its challenges.
+
+Open-Set Recognition: In the standard open-set recognition, the model is trained with a labelled closed training set  $\mathcal{D}_{train} = \{(x_i,y_i)\}_{i=1}^N \subset \mathcal{X} \times \mathcal{C}$ , where  $\mathcal{X}$  is the input images and  $\mathcal{C}$  is the set of 'known' classes. On the testing phase, the testing set  $\mathcal{D}_{test} = \{(x_i,y_i)\}_{i=1}^M \subset \mathcal{X} \times (\mathcal{C} \cup \mathcal{U})$  contains both seen classes  $\mathcal{C}$  and unseen classes  $\mathcal{U}$ . In addition to returning the distribution  $p(y|x,y \in \mathcal{C})$  over known classes, the model also returns a score  $\mathcal{O}(y \in \mathcal{C}|x)$  to indicate whether or not the test sample belongs to any of the known classes. Since generative model-based approaches show superior performance, we utilize these methods as our baseline. There are two loss components of generative model-based approaches: closed-set loss based on supervision from known samples and an open-set loss by generated unknown samples or boundary constrains:
+
+$$
+\mathcal {L} _ {\text {c l s}} = \mathcal {L} _ {\text {c l o s e}} + \lambda \cdot \mathcal {L} _ {\text {o p e n}}, \tag {1}
+$$
+
+where  $\mathcal{L}_{close}$  is the cross entropy loss between model prediction and known ground truth,  $\mathcal{L}_{open}$  is to constrain open space or generated unknown samples.
+
+Federated Open-Set Recognition: We then extend conventional open-set recognition to Federated Open-Set Recognition (FedOSR). Given  $K$  local clients  $\{\mathcal{S}^l\}_{l=1}^K$  with the same known classes  $\mathcal{C}$  and a global central server  $G$ , for the federated round  $t$ , every client  $\mathcal{S}^k$  will receive the same global model weights  $G_{t-1}$  from the central server and update the model with their local data  $\mathcal{D}_k$  for  $E$  epochs. The central server then collects the local parameters  $\mathcal{S}_t^k$  from all clients and aggregates them to update the global model  $G_t$ . This process repeats until the global model converges. In this paper, we consider the most popular federated averaging algorithm (FedAvg) [23], which aggregates the local parameters with weights of each local dataset to update the global model  $G = \frac{1}{K} \sum_{k=1}^{K} \mathcal{S}^k$ .
+
+Challenges: Based on the conclusion that closed-set ability is related to certain parameters of an OSR model [34], the simple merging of OSR models may result in the mixing of closed-related parameters from one client with closed-unrelated parameters from other clients, thereby rendering the related parameters ineffective. Furthermore, even if we aggregate the corresponding closed-related parameters of different OSR models, they may still be misaligned due to the inconsistent distribution of locations. These two challenges pose difficulties in globally aggregating OSR models.
+
+![](images/df625baa03220ac63dcd02a31e8dfa7a77080b777a0358f7d4e8fcaf95ca75fd.jpg)  
+Figure 2. Framework of the proposed FedPD. It consists of a local parameter disentanglement strategy (LPD) and a global divide-and-conquer aggregation approach (GDCA). On the client side, an OSR model is generated with closed-set loss and open-set loss on samples of known classes. Then, LPD decouples the local OSR model into a closed-set subnetwork and an open-set subnetwork by task-related parameter importance. On the server side, GDCA first extracts close-specific, open-specific and shared parameters from the uploaded subnetworks, and then align the corresponding parts by optimal transport and fuse them to generate global model.
+
+# 4. The Proposed FedPD
+
+The overview of our method is depicted in Fig. 2. To address the FedOSR requirements, our method solves parameter misalignment via a local parameter disentanglement (LPD) strategy (Section 4.1) and a global divide-and-conquer aggregation (GDCA) approach (Section 4.2). For the federated round  $t$ , every client  $S^k$  will receive the same global model weights  $G_{t-1}$  from the last round and update the model with their local known data  $D_k$  by a closed-set loss and an open-set loss. The LPD then decouples the updated local OSR model  $S_t^k$  into a closed-set subnetwork  $\mathcal{M}_{close}^k$  and an open-set subnetwork  $\mathcal{M}_{open}^k$ . The local model  $S^k$  together with two subnetworks  $\mathcal{M}_{close}^k$  and  $\mathcal{M}_{open}^k$  are uploaded to the server for global divide-and-conquer aggregation. Specifically, the central server first divides two subnetworks into specific parts  $\mathcal{P}_{close}^k$ ,  $\mathcal{P}_{open}^k$  and shared part  $\mathcal{P}_{share}^k$ , then aligns corresponding parts of all clients by optimal transport. At last, the aligned models are averaged to generate the global model  $G_t$ .
+
+# 4.1. Local Parameter Disentanglement
+
+To address the parameter misalignment problem caused by cross-client inter-set inference, we propose a local parameter disentanglement (LPD) strategy to analyze parameter components in FedOSR and decouple an OSR model
+
+into a closed-set subnetwork and an open-set subnetwork. Specifically, motivated by the lottery ticket hypothesis [7, 11, 36] which shows that only partial parameters are significant for generalization, we find that partial parameters of an OSR model are important to closed-set classification and some parameters are significant to open-set detection.
+
+![](images/887cd63fae782a5f1e2a7ceaef64b1f58eeca43f938586cde31eb53808744738.jpg)  
+Figure 3. Parameter distribution of closed-set subnetwork and open-set subnetwork on an OSR model on MNIST dataset.
+
+The Lottery Ticket Hypothesis We first review the lottery ticket hypothesis [7, 11, 36], which generates subnetwork to achieve better generalization. For subtask  $\mathbf{t}$ , if parameter  $h_i$  is essential to it, the change of loss would be large once we remove  $h_i$  (i.e.,  $h_i = 0$ ) [25]. We define the difference value  $\Omega^{\mathrm{t}}$  to represent the importance score of the parameter as shown in Eq. 2.
+
+$$
+\Omega^ {\mathbf {t}} \left(h _ {i}\right) = \left| \mathcal {L} ^ {\mathbf {t}} \left(H, h _ {i} = 0\right) - \mathcal {L} ^ {\mathbf {t}} \left(H, h _ {i}\right) \right|, \tag {2}
+$$
+
+where  $H$  refers to other parameters except  $h_i$ . Since it's inefficient to evaluate the importance by parameter traversal,
+
+we approximate it with Taylor Expansion [39] and obtain:
+
+$$
+\Omega^ {\mathbf {t}} \left(h _ {i}\right) = \left| \frac {\partial \mathcal {L} ^ {\mathbf {t}} (H , h _ {i})}{\partial h _ {i}} h _ {i} \right| = \left| \nabla \mathcal {L} _ {\mathbf {t}} \left(h _ {i}\right) \times h _ {i} \right|. \tag {3}
+$$
+
+After deriving the importance score of parameters for subtask  $\mathbf{t}$  based on input  $(\mathcal{X}_{\mathbf{t}},\mathcal{Y}_{\mathbf{t}})$ , parameters with the higher score are selected as the subnetwork for  $\mathbf{t}$ . It can be indicated by a mask  $M_{t}$ , where  $M^{\mathbf{t}}(h_i) = 1$  if  $h_i$  belongs to the subnetwork, and  $M^{\mathbf{t}}(h_i) = 0$  otherwise.
+
+Parameter Disentanglement on OSR Based on the lottery ticket hypothesis, we apply parameter disentanglement to decouple an OSR model into closed-set subnetwork and open-set subnetwork. Specifically, given a local OSR model  $S^k$ , we define two task-related metric  $\mathcal{T}_{close}$  and  $\mathcal{T}_{open}$  to judge the importance of each parameter contributing to closed-set classification and open-set detection based on the Eq. 3:
+
+$$
+\mathcal {T} _ {\text {c l o s e}} ^ {k} (i) = \left| \nabla \mathcal {L} _ {\text {c l o s e}} \left(\omega_ {i}\right) \times \omega_ {i} \right|, i \in [ m _ {*} ]. \tag {4}
+$$
+
+$$
+\mathcal {T} _ {\text {o p e n}} ^ {k} (i) = | \nabla \mathcal {L} _ {\text {o p e n}} (\omega_ {i}) \times \omega_ {i} |, i \in [ m _ {*} ]. \tag {5}
+$$
+
+where  $m_*$  is the parameter number of a module in an OSR network and  $w_i$  is the corresponding parameters of the module. The larger the value of  $\mathcal{T}(i)$  is, the more this parameter contributes to the task-related loss function.
+
+After deriving the importance score  $\mathcal{T}_{close}$ ,  $\mathcal{T}_{open}$  of parameters for closed-set loss and open-set loss, we choose the top-K highest scores as most valuable weights and set them as 1 with the rest as 0 to generate closed-set subnetwork and open-set subnetwork respectively:
+
+$$
+\mathcal {M} _ {\text {c l o s e}} ^ {k} (i) = \left\{ \begin{array}{l} 1, \mathcal {T} _ {\text {c l o s e}} ^ {k} (i) > \delta_ {\text {c l o s e}} \\ 0, \text {o t h e r w i s e} \end{array} \right. \tag {6}
+$$
+
+$$
+\mathcal {M} _ {\text {o p e n}} ^ {k} (i) = \left\{ \begin{array}{l} 1, \mathcal {T} _ {\text {o p e n}} ^ {k} (i) > \delta_ {\text {o p e n}} \\ 0, \text {o t h e r w i s e} \end{array} \right. \tag {7}
+$$
+
+where  $\delta_{close}$  and  $\delta_{open}$  are the threshold to filter out redundant parameters and we choose the threshold based on ratio of parameter numbers. Here we set the masking ratio as 0.5 based on our experimental observation.
+
+We visualize the subnetworks in the first convolution layer as illustrated in Fig. 3. It's obvious that open-set and closed-set subnetworks hold different distribution.
+
+Parameter Disentanglement on FedOSR Given a set of local OSR models  $\{\mathcal{S}^k\}_{k = 1}^K$ , we apply parameter disentanglement on these models, and plot closed-set subnetworks  $\{\mathcal{M}_close^k\}_{k = 1}^K$  and open-set subnetworks  $\{\mathcal{M}_{open}^k\}_{k = 1}^K$  as shown in Fig. 4. It illustrates that there exists parameter misalignment in both closed-set subnetworks and open-set subnetworks among these clients. Simply aggregating the
+
+client OSR modes into one global model may ignore the complex parameter composition and lead to model collapse due to unmatched averaging. For example, the parameter averaging on a closed-set subnetwork and an open-set subnetwork on the same position may generate chaotic neuron weights. This phenomenon motivates us to develop a new model aggregation approach for FedOSR.
+
+![](images/ca2d5d3bf3d680d1c8672dcc293b2977d46ba0dd4d61c5c29d5a80725262170e.jpg)  
+Figure 4. Parameter distribution of closed-set parameters and open-set parameters in federated framework on HDR-FL dataset. The horizontal direction of the picture represents channel numbers, and the vertical of it denotes client numbers.
+
+# 4.2. Global Divide-and-Conquer Aggregation
+
+During model communication on the server side, parameter misalignment problem will significantly destroy the global model, thus providing bad model initialization for local training in next step. To further remedy the aggregation catastrophe by cross-client intra-set inconsistency, we design a global divide-and-conquer aggregation (GDCA) method to first divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters, and then align and aggregate the corresponding parts respectively.
+
+Learning to divide Based on the results of local parameter disentanglement, an OSR model can be decoupled into a closed-set subnetwork and an open-set subnetwork as shown in Fig. 4. Since there are overlaps between these two subnetworks, we further divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters.
+
+$$
+\mathcal {P} _ {\text {c l o s e}} = \mathcal {M} _ {\text {c l o s e}} \odot \overline {{\mathcal {M} _ {\text {o p e n}}}}, \tag {8}
+$$
+
+$$
+\mathcal {P} _ {\text {o p e n}} = \mathcal {M} _ {\text {o p e n}} \odot \overline {{\mathcal {M} _ {\text {c l o s e}}}}, \tag {9}
+$$
+
+$$
+\mathcal {P} _ {\text {s h a r e}} = \mathcal {M} _ {\text {o p e n}} \odot \mathcal {M} _ {\text {c l o s e}}, \tag {10}
+$$
+
+where  $\overline{\mathcal{M}}$  is the negation of the binary mask  $\mathcal{M}$ . Compared with two subnetworks, the three non-overlapping parts are more suitable to deal with since the overlapping parameters may cause conflicts after alignment.
+
+Learning to conquer We disentangle the OSR model of each client into three parts and align the corresponding parts before aggregation. The neuron weights are considered as a distribution, and we use optimal transport (OT) to achieve
+
+distribution alignment as shown in Fig. 2. OT is a technique used to solve distribution matching problems by finding a minimal effort solution to transport a given mass of dirt into a given hole. It has been successfully applied to various problems such as domain adaptation and GANs. We compute the transport map layer by layer to achieve alignment between two models  $W_{A}$  and  $W_{B}$ .
+
+Taking two models  $\mathbf{W}_A$  and  $\mathbf{W}_B$  as an example, we align parameters of  $\mathbf{W}_A$  on  $\mathbf{W}_B$  by channel-wise distribution matching. Let us assume that we are at one convolution layer  $\mathbf{W}^{(\ell)} \in (\mathcal{C}_{in}^{\ell},\mathcal{C}_{out}^{\ell},F^{\ell})$  and the previous layers have already been aligned, where  $F = k\times k$  is the square of filter size. The transport matrix of the last convolution layer  $\mathbf{W}^{(\ell -1)}\in (\mathcal{C}_{in}^{\ell -1},\mathcal{C}_{out}^{\ell -1},F^{\ell -1})$  is denoted as  $T^{(\ell -1)} \in (\mathcal{C}_{out}^{\ell -1},\mathcal{C}_{out}^{\ell -1})$ . Since the output of last layer has been permuted by  $T^{(\ell -1)}$ , we conduct post-multiplying on current layer with transport map of previous layer such that the order of current layer input  $\mathcal{C}_{out}^{\ell -1}$  can match the order of  $\mathcal{C}_{in}^{\ell}$ . Then the current layer can be transformed as:
+
+$$
+\widehat {\boldsymbol {W}} _ {A} ^ {(\ell , \ell - 1)} \leftarrow \boldsymbol {W} _ {A} ^ {(\ell) ^ {\top}} \boldsymbol {T} ^ {(\ell - 1)}, \tag {11}
+$$
+
+where  $\widehat{\pmb{W}}_A^{(\ell, \ell-1)}$  is the post-processed layer, and  $\pmb{W}_A^{(\ell)}$  is transposed as  $(\mathcal{C}_{in}^{\ell}, F^{\ell}, \mathcal{C}_{out}^{\ell})$  to achieve matrix multiplication.
+
+With current layer permuted, we compute the optimal transport map  $\pmb{T}^{(\ell)}$  between  $\widehat{\pmb{W}}_A^{(\ell,\ell-1)}, \pmb{W}_B^{(\ell)}$ , i.e.,  $\pmb{T}^{(\ell)}$ ,  $d \gets \mathrm{OT}(\widehat{\pmb{W}}_A^{(\ell,\ell-1)}, \pmb{W}_B^{(\ell)})$ , where  $d$  denotes the obtained Wasserstein-distance. We use this transport map  $\pmb{T}^{(\ell)}$  to align the neurons weights of the first model  $(\pmb{W}_A)$  with respect to the second  $(\pmb{W}_B)$ ,
+
+$$
+\widetilde {\boldsymbol {W}} _ {A} ^ {(\ell , \ell - 1)} \leftarrow \boldsymbol {T} ^ {(\ell) ^ {\top}} \widehat {\boldsymbol {W}} _ {A} ^ {(\ell , \ell - 1)}, \tag {12}
+$$
+
+where  $\widetilde{W}_A^{(\ell, \ell-1)}$  is the aligned layer from model  $W_A$  to  $W_B$ . To simplify this alignment process, we define  $\widetilde{W}_A = OT(W_A, W_B)$ . Through the alignment of model parameters, model  $W_A$  will only change the orders of feature channels without affecting the model prediction.
+
+When we align the parameters of the OSR model for all clients, we can choose any client as the target client and align other clients with the target client. For example, we use the second client as the target client as shown in Fig. 2. The alignment process can be denoted as:
+
+$$
+\tilde {S} _ {\text {c l o s e}} ^ {k} = O T \left(\mathcal {S} ^ {k} \odot \mathcal {P} _ {\text {c l o s e}} ^ {k}, \mathcal {S} ^ {2} \odot \mathcal {P} _ {\text {c l o s e}} ^ {2}\right), \tag {13}
+$$
+
+$$
+\widetilde {\mathcal {S}} _ {\text {o p e n}} ^ {k} = O T \left(S ^ {k} \odot \mathcal {P} _ {\text {o p e n}} ^ {k}, S ^ {2} \odot \mathcal {P} _ {\text {o p e n}} ^ {2}\right), \tag {14}
+$$
+
+$$
+\widetilde {\mathcal {S}} _ {\text {s h a r e}} ^ {k} = O T \left(\mathcal {S} ^ {k} \odot \mathcal {P} _ {\text {s h a r e}} ^ {k}, \mathcal {S} ^ {2} \odot \mathcal {P} _ {\text {s h a r e}} ^ {2}\right). \tag {15}
+$$
+
+After that, the global model  $G$  can be represented as:
+
+$$
+G = \frac {1}{K} \left(\sum_ {k = 1} ^ {K} \widetilde {S} _ {\text {c l o s e}} ^ {k} + \sum_ {k = 1} ^ {K} \widetilde {S} _ {\text {o p e n}} ^ {k} + \sum_ {k = 1} ^ {K} \widetilde {S} _ {\text {s h a r e}} ^ {k}\right). \tag {16}
+$$
+
+Algorithm 1 summarizes the FedPD algorithm.
+
+Algorithm 1 FedPD  
+Server OPERATIONS  
+Inputs: Round number  $T$ , Set of clients  $K$   
+Output: Global OSR model  $G$   
+for  $t = 0,1,\ldots,T-1$  do  
+for client  $k \in K$  in parallel do  
+ $\mathcal{S}^k, \mathcal{M}_{close}^k, \mathcal{M}_{open}^k \gets \text{CLIENTOPERATIONS}(G_{t-1})$   
+end for  
+ $\mathcal{P}_{close}^k = \mathcal{M}_{close}^k \odot \overline{\mathcal{M}_{open}^k}$ $\mathcal{P}_{open}^k = \mathcal{M}_{open}^k \odot \overline{\mathcal{M}_{close}^k}$ $\mathcal{P}_{share}^k = \mathcal{M}_{close}^k \odot \mathcal{M}_{open}^k$ $\widetilde{S}_{close}^k = OT(S^k \odot \mathcal{P}_{close}^k, S^2 \odot \mathcal{P}_{close}^2)$ $\widetilde{S}_{open}^k = OT(S^k \odot \mathcal{P}_{open}^k, S^2 \odot \mathcal{P}_{open}^2)$ $\widetilde{S}_{share}^k = OT(S^k \odot \mathcal{P}_{share}^k, S^2 \odot \mathcal{P}_{share}^2)$ $G_t \gets \frac{1}{K} (\sum_{k=1}^{K} \widetilde{S}_{close}^k + \sum_{k=1}^{K} \widetilde{S}_{open}^k + \sum_{k=1}^{K} \widetilde{S}_{share}^k)$   
+end for  
+Obtain global OSR model  $G$   
+CLIENT OPERATIONS  
+Input: Model weights  $G_{t-1}$   
+Output: Updated local OSR model weights  $\mathcal{S}_t^k$ , closed-set subnetwork  $\mathcal{M}_{close}^k$ , open-set subnetwork  $\mathcal{M}_{open}^k$   
+for epoch  $e = 0,1,\ldots,E-1$  do  
+for batch  $\{x,y\} \in D_m$  do  
+ $\mathcal{L}_{local} = \mathcal{L}_{close}(x,y) + \mathcal{L}_{open}(x,y)$ $\mathcal{T}_{close}^k = |\nabla \mathcal{L}_{close}(\omega) \times \omega|$ $\mathcal{T}_{open}^k = |\nabla \mathcal{L}_{open}(\omega) \times \omega|$ $\mathcal{M}_{close}^k, \mathcal{M}_{open}^k = TopK(\mathcal{T}_{close}^k, \mathcal{T}_{open}^k)$ $\mathcal{S}_t^k \gets update(\mathcal{S}_t^k, \mathcal{L}_{local})$   
+end for  
+end for  
+Send model weights  $\mathcal{S}_t^k$  and subnetworks  $\mathcal{M}_{close}^k, \mathcal{M}_{open}^k$  to the server
+
+# 5. Experiment
+
+# 5.1. Datasets and Evaluation
+
+We conduct extensive experiments on both heterogeneous federated learning benchmark Handwritten digital recognition FL Dataset (HDR-FL) and homogeneous federated learning benchmark CIFAR-10. The closed-set classification and open-set detection performances are evaluated by accuracy (ACC) and AUROC (AUC) respectively.
+
+HDR-FL: It consists of five datasets: MNIST [16], SVHN [28], USPS [12], SynthDigits [8] and MNIST-M [8]. These datasets are 10-class handwritten digital images from various scenarios. Each dataset is set as a client for Non-IID FedOSR. To achieve open-set recognition, six classes are chosen to be known and four classes are to be unknown classes. We keep the same known classes and unknown classes for all clients.
+
+CIFAR-10: It contains 60000 images in 10 classes, with 6000 images per class [15]. We first divide 10 classes into known classes and unknown classes, then split them into five equal parts to construct homogeneous federated setting. Specifically, we try different ratio between the known and the unknown to validate our method (e.g. 4:6, 6:4 and 8:2).
+
+Table 1. Performance comparisons between our method and other baseline methods on HDR-FL benchmark.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="6">Closed-set ACC</td><td colspan="6">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>SoftMax</td><td>96.69</td><td>76.06</td><td>97.97</td><td>83.99</td><td>83.69</td><td>87.68</td><td>77.38</td><td>65.41</td><td>88.80</td><td>70.53</td><td>66.24</td><td>73.67</td></tr><tr><td>OpenMax[2](CVPR&#x27;16)</td><td>95.54</td><td>63.13</td><td>97.97</td><td>81.15</td><td>76.57</td><td>82.87</td><td>77.78</td><td>57.37</td><td>89.21</td><td>69.78</td><td>60.88</td><td>71.00</td></tr><tr><td>RPL[4](ECCV&#x27;20)</td><td>98.33</td><td>77.22</td><td>98.13</td><td>84.76</td><td>86.32</td><td>88.95</td><td>77.87</td><td>66.70</td><td>89.53</td><td>73.17</td><td>73.23</td><td>76.10</td></tr><tr><td>PROSER[43](CVPR&#x27;21)</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>ARPL[3](TPAMI&#x27;21)</td><td>97.17</td><td>69.83</td><td>96.44</td><td>84.64</td><td>84.22</td><td>86.46</td><td>85.65</td><td>59.79</td><td>92.53</td><td>69.70</td><td>68.17</td><td>75.16</td></tr><tr><td>DIAS[26](ECCV&#x27;22)</td><td>97.50</td><td>70.66</td><td>97.62</td><td>86.11</td><td>86.81</td><td>87.74</td><td>82.90</td><td>67.33</td><td>90.69</td><td>77.48</td><td>71.92</td><td>78.06</td></tr><tr><td>SSB[35](ICLR&#x27;22)</td><td>96.41</td><td>60.12</td><td>97.46</td><td>82.82</td><td>74.86</td><td>82.33</td><td>88.53</td><td>57.68</td><td>90.45</td><td>73.40</td><td>70.01</td><td>76.01</td></tr><tr><td>FedPD(Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr></table>
+
+Table 2. Performance comparisons between our method and other baseline methods on CIFAR-10 benchmark.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Known=4</td><td colspan="2">Known=6</td><td colspan="2">Known=8</td></tr><tr><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td></tr><tr><td>SoftMax</td><td>83.23 ±0.28</td><td>65.70±0.14</td><td>83.14±0.38</td><td>72.00±0.44</td><td>72.17±0.41</td><td>61.11±0.45</td></tr><tr><td>\( OpenMax[2]_{(CVPR&#x27;16)} \)</td><td>83.24 ±0.08</td><td>65.96±0.14</td><td>84.56±0.24</td><td>81.69±0.59</td><td>72.72±0.40</td><td>61.52±0.38</td></tr><tr><td>\( RPL[4]_{(ECCV&#x27;20)} \)</td><td>81.23 ±0.11</td><td>65.10±0.05</td><td>78.78±0.43</td><td>68.72±0.43</td><td>72.98±0.33</td><td>61.36±0.32</td></tr><tr><td>\( PROSER[43]_{(CVPR&#x27;21)} \)</td><td>84.15 ±0.13</td><td>69.04±0.07</td><td>85.77±0.48</td><td>80.69±0.27</td><td>70.50±0.21</td><td>60.48±0.41</td></tr><tr><td>\( ARPL[3]_{(TPAMI&#x27;21)} \)</td><td>83.91 ±0.09</td><td>69.02±0.12</td><td>86.54±0.53</td><td>79.83±0.69</td><td>73.63±0.37</td><td>66.78±0.64</td></tr><tr><td>\( DIAS[26]_{(ECCV&#x27;22)} \)</td><td>84.85 ±0.04</td><td>70.32±0.09</td><td>87.74±0.16</td><td>81.66±0.25</td><td>74.53±0.37</td><td>67.75±0.34</td></tr><tr><td>\( SSB[35]_{(ICLR&#x27;22)} \)</td><td>84.27±0.06</td><td>68.85±0.11</td><td>86.04±0.70</td><td>82.41±0.33</td><td>75.54±0.18</td><td>67.97±0.23</td></tr><tr><td>\( FedPD(Ours) \)</td><td>86.28±0.07</td><td>71.50±0.07</td><td>89.43±0.22</td><td>85.07±0.50</td><td>75.87±0.16</td><td>69.12±0.45</td></tr></table>
+
+# 5.2. Implementation Details
+
+On local training, we apply PROSER [43] for open-set training with a closed-set loss and an open-set loss. On global aggregation, we utilize FedAvg [23] to average OSR models for comparison methods. For handwritten digital recognition, we apply a six-layer CNN. During the training process, we utilize the SGD optimizer [31] with learning rate  $10^{-2}$  for closed-set loss and  $10^{-4}$  for open-set loss, we set batch size to 32 and training epochs to 100. Global model is updated every epoch by FedAvg [23] aggregation. For CIFAR-10 Dataset, we use WideResNet for classification. Networks are trained by Adam optimizer [14] with batch size of 128. The learning rates of closed-set loss and open-set loss are initialized as  $10^{-1}$  and  $10^{-3}$  respectively. The communication is conducted after every  $\mathrm{E} = 5$  epochs in local training until reaching  $\mathrm{T} = 250$  epochs in total. All experiments of these two benchmarks are performed on NVIDIA 2080Ti card with Pytorch library. Detailed model architecture for both benchmarks is shown in the supplementary material.
+
+# 5.3. Comparison with state-of-the-arts
+
+We compare the performance of FedPD with the state-of-the-art OSR methods, including SoftMax, OpenMax [2], RPL [4], PROSER [43], ARPL [3], DIAS [26], SSB [35]. These comparison methods are implemented by FedAvg [23] on each client OSR models. Our FedPD utilizes the popular generative-based method PROSER [43] for local open-set training.
+
+HDR-FL: As shown in Table 1, our FedPD outperforms existing OSR approaches with a large margin not only in closed-set classification but also in open-set detection. In addition, our FedPD achieves consistent improvements on
+
+all clients. Specifically, our method can surpass existing approaches with a promising  $90.60\%$  average closed-set ACC and 80.78 average open-set AUC, outperforming the state-of-the-art OSR method DIAS [26] with  $2.76\%$  in ACC and  $2.72\%$  in AUC. It validates that our method could enable better global model aggregation for open-set recognition, which verifies the effectiveness of our divide-and-conquer approach to address parameter misalignment in FedOSR. Moreover, some generate-based methods (e.g. SSB [26]) may encounter serious model collapse problem due to unmatched parameter of local OSR models, leading to  $8.17\%$  performance gap in average ACC.
+
+CIFAR-10: Comparison results on CIFAR-10 benchmark are shown in Table 2. To validate the stability of our method, we conduct experiments on different ratios between known classes and unknown classes. In these three settings, our FedPD achieves the best open-set AUC of  $71.70\%$ ,  $85.07\%$  and  $69.12\%$ . The consistent performance improvement over different openness demonstrate the effectiveness of our FedPD to promote the ability of detecting novel category for federated models.
+
+# 5.4. Ablation Analysis of Our Method
+
+# 5.4.1 Effectiveness of LPD
+
+Table 4. Comparison to different network splitting methods.  
+
+<table><tr><td>Splitting Method</td><td>None</td><td>Grad</td><td>Grad × Weight (Ours)</td></tr><tr><td>Closed-set ACC</td><td>85.61</td><td>89.04</td><td>90.96</td></tr><tr><td>Open-set AUC</td><td>76.19</td><td>80.95</td><td>81.36</td></tr></table>
+
+To demonstrate the advantage of local parameter disentanglement, we compare it with no splitting and network splitting by grad as shown in Table 4. It shows that conducting network splitting according to task gradients results in large
+
+Table 3. Ablation study for key components.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="6">closed-set ACC</td><td colspan="6">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>Baseline + FedAvg</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>Baseline + FedMA</td><td>97.21</td><td>60.72</td><td>98.22</td><td>86.18</td><td>85.72</td><td>85.61</td><td>83.09</td><td>66.47</td><td>88.81</td><td>73.13</td><td>69.46</td><td>76.19</td></tr><tr><td>Baseline + FedPD (Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr><tr><td>Ours w/o Divide</td><td>98.39</td><td>77.60</td><td>98.22</td><td>88.65</td><td>89.66</td><td>90.50</td><td>89.56</td><td>69.91</td><td>92.72</td><td>79.05</td><td>72.67</td><td>80.78</td></tr><tr><td>Ours w/o Conquer</td><td>97.43</td><td>72.74</td><td>97.62</td><td>85.82</td><td>85.22</td><td>87.76</td><td>84.41</td><td>65.78</td><td>91.60</td><td>72.51</td><td>70.81</td><td>77.02</td></tr></table>
+
+![](images/581e695f7cd5e84386930de1a35ac2d30010078481d4747338e7f3e0a2b65755.jpg)  
+Figure 5. Ablation study for the masking ratio of the parameter disentanglement.
+
+![](images/ed5663815be86a8074d318bcb748b0488ab085b843c01d6fc1503655eb9c6607.jpg)
+
+performance gain. Combining gradient and weight information makes better model decoupling, which corresponds to our theoretical analysis in Eq. 3.
+
+# 5.4.2 Effectiveness of GDCA
+
+Learning to Divide To validate the advantage of dividing two subnetworks into specific parts and shared parts, we conduct experiments on two different aggregation strategy: align two subnetworks then average (Ours w/o Divide) and align three parts then average (Ours). Comparison results in Table 3 illustrates that aligning three parts outperforms aligning two subnetworks with performance gain of  $0.46\%$  in ACC and  $0.58\%$  in AUC. It is because that the overlapping parameters between these two subnetworks may have different distribution after alignment, thus leading to ambiguous parameters.
+
+Learning to Conquer To validate the effectiveness of divide-and-conquer aggregation, we compare our method with traditional aggregation methods FedAvg and FedMA. Unlike obvious improvement on closed-set setting, FedMA shows inferior performance than FedAvg as shown in Table 3. It is consistent with our observation that parameter components in open-set models are more complex than those in closed-set models due to multiple optimization directions. Compared with directly averaging three parts with alignment (Ours w/o Conquer), conducting our proposed aggregation strategy brings performance boost on of  $3.2\%$  in ACC and  $4.34\%$  in AUC, demonstrating that our FedPD can alleviate parameter misalignment problem.
+
+# 5.4.3 Effect of Masking Ratio
+
+To investigate the effect of masking ratio to the FedOSR performance, we design ablation experiments under HDRFL setting, as shown in Fig. 5. It is observed that small masking ratio (e.g. 0.1) may filter out too much parameters, leading to empty shared parameter. Large masking ratio
+
+![](images/099acd292bf2f2d4773a2b9d20c037e0ab4d78851e448ba723d07668fce3aea8.jpg)  
+Figure 6. Parameter distribution of closed-set subnetworks and open-set subnetworks on CIFAR-10 dataset.
+
+(e.g. 0.9) can't choose valuable weights for the closed-set task and the open-set task, thus leading to invalid decoupling. In this paper, we choose suitable masking ratio as 0.5 based on our experimental observation that it achieves the best closed-set ACC and open-set AUC.
+
+# 5.5. Analysis of Parameter Misalignment
+
+To verify the parameter misalignment problem in FedOSR, we visualize the weights distributions of closed-set subnetwork and open-set subnetwork on CIFAR-10 homogeneous benchmark as shown in Fig. 6. Different clients still hold inconsistent parameter distribution on both closed-set subnetwork and open-set subnetwork. Different from results shown in Fig. 4, where parameter misalignment may come from domain shift in heterogeneous federated datasets. Fig. 6 further emphasize that the parameter misalignment in FedOSR mainly comes from gradient divergence of closed-set loss and open-set loss.
+
+# 6. Conclusion
+
+In this work, we propose a novel and practical problem of federated open-set recognition (FedOSR) for the first time. To alleviate the parameter misalignment problem in FedOSR, we design a novel parameter disentanglement guided federated algorithm (FedPD). Specifically, on the client side, a local parameter disentanglement is developed to decouple the local OSR models into closed-set subnetworks and open-set subnetworks. On the server side, a global divide-and-conquer aggregation strategy is proposed to divide two subnetworks into specific parts and shared parts, then align corresponding parts by optimal transport and fuse them to generate global model. Extensive experiments on both IID and Non-IID benchmark datasets demonstrate the effectiveness of FedPD.
+
+# References
+
+[1] Jinwon An and Sungzoon Cho. Variational autoencoder based anomaly detection using reconstruction probability. Special Lecture on IE, 2(1):1-18, 2015. 3  
+[2] Abhijit Bendale and Terrance E Boult. Towards open set deep networks. In CVPR, pages 1563-1572, 2016. 1, 3, 7  
+[3] Guangyao Chen, Peixi Peng, Xiangqian Wang, and Yonghong Tian. Adversarial reciprocal points learning for open set recognition. IEEE Trans. Pattern Anal. Mach. Intell., 2021. 1, 3, 7  
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+                                            "content": "Figure 1. Parameter disentanglement on FedOSR models and comparison of various aggregation strategies on FedOSR setting. (a) FedAvg simply aggregates multiple OSR models, leading to model collapse; (b) Our FedPD first aligns corresponding close-specific, open-specific and shared parts by optimal transport (OT), then aggregates aligned parameters. The curves inside the network box represent different parameter distribution of each parts."
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+                                    "content": "tions and difficult to integrate into a centralized dataset, owing to increasing privacy and ethical concerns, especially for those sensitive data such as location-based services or health information [22]. To break this dilemma, federated learning (FL) [5, 23, 20] provides a privacy-preserving paradigm that allows local clients to collaboratively train a shared global model without data sharing."
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+                                    "type": "text",
+                                    "content": "This work was supported by Hong Kong Research Grants Council(RGC) General Research Fund 1422062214204321, and Innovation and Technology Commission-Innovation and Technology Fund ITS/100/20."
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+                                    "type": "text",
+                                    "content": "ability of models in recognizing unknown classes, but they are designed for the centralized setting. In this work, we represent the first effort to formulate a challenging and unexplored problem of Federated Open Set Recognition (FedOSR). FedOSR aims to unite multiple distributed clients to learn a global model and reduce privacy as well as security risk, which not only exactly classifies known classes but also recognizes unknown classes in the testing stage."
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+                                    "content": "Directly applying existing OSR methods into the FL setting for FedOSR mainly undergoes two troublesome challenges. The first challenge lies in the cross-client inter-set interference between learning closed-set and open-set knowledge. According to the previous study [34], the partial parameters of a client model are in charge of learning knowledge of known classes, and the rest are related to open set. The known classes-related parameters of a client is probably polluted by the open set-related parameters from other clients after server communication, leading to the performance degradation on closed set. Similarly, open set-related parameters of a client are also affected by closed-set knowledge of other clients. In this situation, a unknown samples would be possibly misclassified into known classes. The second one is cross-client intra-set inconsistency by data heterogeneity. Even though we aggregate corresponding closed-related parameters of OSR models from different clients, these parameters are still misaligned due to the permutation invariance property of neural networks and data heterogeneity [37]. Aggregation of local client parameters directly at the server can result in inconsistent models among the clients, leading to significant divergence of client models. This inconsistency issue can cause slow and unstable convergence [19], ultimately resulting in sub-optimal performance of the entire FL system [17, 37]."
+                                }
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+                                    "type": "text",
+                                    "content": "To achieve FedOSR, we conquer these intractable challenges from a new perspective, i.e., parameter disentanglement. Based on the lottery ticket hypothesis [7, 11, 36], we divide parameters of a client model into a closed-set subnetwork and an open-set subnetwork. These two subnetworks have their own specific parameters, which are only related to known classes and unknown classes respectively. Meanwhile, they also share partial parameters since known and unknown samples might have some similar patterns [35]. The parameter disentanglement of client models can preserve the high performance of closed set by reducing the interference from open-set subnetworks. As shown in Fig. 1, the closed-set subnetworks and the open-set subnetworks of different client models distribute in different positions with some overlaps. Directly aggregating all client OSR models by FedAvg [23] on the server side may encounter the parameter misalignment problem and lead to model collapse as shown in Fig. 1 (a). These destroyed parameters are transmitted to clients and slow down the convergence of the federated system due to bad model initialization to the"
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+                                    "type": "text",
+                                    "content": "next training step. Therefore, aligning these subnetworks before model aggregation is a crucial step to solve the inconsistency problem of parameter distributions."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "To tackle these challenges in FedOSR, we propose a novel parameter disentanglement guided federated OSR (FedPD) algorithm in this paper, which effectively addresses the local parameter misalignment problem occurred on the global model aggregation. Specifically, we design a local parameter disentanglement strategy (LPD) to firstly decouple an OSR model into two subnetworks: an open-set subnetwork and a closed-set subnetwork by task-related metrics. To overcome the parameter misalignment caused by simply parameter averaging on whole client OSR models, we propose a global divide-and-conquer aggregation (GDCA) method to firstly divide two subnetworks into specific parts and shared parts, then align corresponding parameter components by optimal transport [13, 30] and aggregate them. As shown in Fig. 1 (b), our FedPD enables reasonable model aggregation and reliable global model to boost federated training."
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+                                    "content": "The major contribution of this paper are summarized as follows:"
+                                }
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+                                            "type": "text",
+                                            "content": "- We address a practical FL problem, namely Federated Open-Set Recognition (FedOSR). To the best of our knowledge, this is the first work to improve the ability of detecting novel category for federated models."
+                                        }
+                                    ]
+                                }
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+                        {
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+                                            "content": "- We propose a novel Parameter Disentanglement guided Federated algorithm (FedPD) to solve parameter misalignment problem in FedOSR."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
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+                                            "type": "text",
+                                            "content": "- On the client side, we introduce the Local Parameter Disentanglement (LPD) approach, which leverages task-related importance on model parameters to decouple the local OSR model into a closed-set subnetwork and an open-set subnetwork."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "type": "text",
+                                            "content": "- On the server side, we design a Global Divide-and-Conquer Aggregation (GDCA) strategy to partition the two subnetworks into specific and shared parts, align the corresponding parts via optimal transport, and subsequently fuse them to alleviate the misalignment problem in FedOSR."
+                                        }
+                                    ]
+                                }
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+                                    "content": "2. Related Work"
+                                }
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+                                    "content": "2.1. Federated Learning"
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+                                    "type": "text",
+                                    "content": "Federated learning [23, 20, 38, 37, 19, 29, 24, 42] provides a promising privacy-preserving solution for multi-site data collaboration, which develops a global model from decentralized datasets by aggregating the parameters of each local client while keeping data locally. Representatively, McMahan [23] proposed the popular FedAvg algorithm"
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+                                    "type": "text",
+                                    "content": "for communication-efficient federated training of deep networks. There are two lines to improve FedAvg: improvement on local training and on global aggregation."
+                                }
+                            ]
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+                                    "content": "Regarding improving local training, FedProx [19] introduced a proximal term to the clients' objective, which regulates the local updates to be closer to the initial global model. Meanwhile, MOON [18] proposed a model contrastive loss that corrects local updates by maximizing the agreement of the representation learned by the current local model and the global model, and minimizing the agreement of the representation learned by the current local model and the previous local model."
+                                }
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+                                    "type": "text",
+                                    "content": "As for studies on improving the global aggregation phase, FedMA [37] utilizes Bayesian non-parametric methods to match and average weights in a layer-wise manner. To preserve personalization of local clients, FedBN [20] aggregates parameters except BN layers on the server side. Chen [5] proposed to aggregate client model parameters on the frequency domain. Even if these works [37, 21] try to solve parameter misalignment, they are applied to the closed-set recognition task, which can't be directly transferred to open-set recognition due to complex parameter composition in open-set recognition."
+                                }
+                            ]
+                        }
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+                                    "content": "2.2. Open Set Recognition"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
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+                                    "type": "text",
+                                    "content": "To deploy the classification models to real-world scenario with high stability, open-set recognition (OSR) [40, 41, 33, 3, 43] was proposed to classify known classes while detect unknown classes at the same time. Recent deep learning-based OSR methods can be classified into three categories: discriminative-based models, prototype-based models and generative-based models."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Discriminative model-based methods calibrate the classification logistics to detect unknown samples. Softmax scores are initially utilized to identify out-of-distribution data by argmax thresholding. OpenMax [2] improves softmax scores with an OpenMax layer and fits outputs probabilities with Weibull distributions."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Prototype-based methods [4, 3, 26] apply prototype learning to identify unknown samples on the feature space. ARPL [3] enhanced prototype learning with generated fake samples to achieve prediction-level and feature-level detection. Even if prototype-based methods show outstanding performance on open-set recognition, they are not suitable to be applied on FL since the uploaded prototype may cause leakage of privacy."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Generative model-based methods generate unknown samples using GANs [10] and autoencoders [1] to help the classifier learning the decision boundary between known and unknown distributions. OSRCI [27] utilized GAN [10] architecture to generate counterfactual examples. PROSER [43] set up the open space between class boundaries to keep classes far from each other based on manifold mixup. Generally, there are a closed-set loss based on su"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "pervision from known samples and an open-set loss by generated unknown samples or boundary constrains [9, 32]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3. Problem Definition"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We begin with formal definition of Federated Learning (FL) and Open-Set Recognition (OSR). Then we define Federated Open-Set Recognition (FedOSR) and its challenges."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Open-Set Recognition: In the standard open-set recognition, the model is trained with a labelled closed training set "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
+                                        545,
+                                        347
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{train} = \\{(x_i,y_i)\\}_{i=1}^N \\subset \\mathcal{X} \\times \\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                        168,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
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+                                        347
+                                    ],
+                                    "type": "text",
+                                    "content": " is the input images and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
+                                        545,
+                                        347
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
+                                        545,
+                                        347
+                                    ],
+                                    "type": "text",
+                                    "content": " is the set of 'known' classes. On the testing phase, the testing set "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{test} = \\{(x_i,y_i)\\}_{i=1}^M \\subset \\mathcal{X} \\times (\\mathcal{C} \\cup \\mathcal{U})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
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+                                    ],
+                                    "type": "text",
+                                    "content": " contains both seen classes "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
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+                                        347
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and unseen classes "
+                                },
+                                {
+                                    "bbox": [
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+                                        168,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
+                                        545,
+                                        347
+                                    ],
+                                    "type": "text",
+                                    "content": ". In addition to returning the distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        168,
+                                        545,
+                                        347
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(y|x,y \\in \\mathcal{C})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " over known classes, the model also returns a score "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(y \\in \\mathcal{C}|x)"
+                                },
+                                {
+                                    "bbox": [
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+                                        168,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to indicate whether or not the test sample belongs to any of the known classes. Since generative model-based approaches show superior performance, we utilize these methods as our baseline. There are two loss components of generative model-based approaches: closed-set loss based on supervision from known samples and an open-set loss by generated unknown samples or boundary constrains:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {c l s}} = \\mathcal {L} _ {\\text {c l o s e}} + \\lambda \\cdot \\mathcal {L} _ {\\text {o p e n}}, \\tag {1}",
+                                    "image_path": "642ffbfdcf406dac009f6430c2792539b9b0a2148960cb8a385cc0efde94405b.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{close}"
+                                },
+                                {
+                                    "bbox": [
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+                                        413
+                                    ],
+                                    "type": "text",
+                                    "content": " is the cross entropy loss between model prediction and known ground truth, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{open}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is to constrain open space or generated unknown samples."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Federated Open-Set Recognition: We then extend conventional open-set recognition to Federated Open-Set Recognition (FedOSR). Given "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " local clients "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{S}^l\\}_{l=1}^K"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with the same known classes "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and a global central server "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", for the federated round "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", every client "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{S}^k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " will receive the same global model weights "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_{t-1}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " from the central server and update the model with their local data "
+                                },
+                                {
+                                    "bbox": [
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+                                        415,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " epochs. The central server then collects the local parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{S}_t^k"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from all clients and aggregates them to update the global model "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_t"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This process repeats until the global model converges. In this paper, we consider the most popular federated averaging algorithm (FedAvg) [23], which aggregates the local parameters with weights of each local dataset to update the global model "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G = \\frac{1}{K} \\sum_{k=1}^{K} \\mathcal{S}^k"
+                                },
+                                {
+                                    "bbox": [
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+                                        415,
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Challenges: Based on the conclusion that closed-set ability is related to certain parameters of an OSR model [34], the simple merging of OSR models may result in the mixing of closed-related parameters from one client with closed-unrelated parameters from other clients, thereby rendering the related parameters ineffective. Furthermore, even if we aggregate the corresponding closed-related parameters of different OSR models, they may still be misaligned due to the inconsistent distribution of locations. These two challenges pose difficulties in globally aggregating OSR models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                }
+            ],
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+                                    "content": "4884"
+                                }
+                            ]
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+                }
+            ],
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+        {
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+                                        }
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+                            "index": 0,
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+                            "type": "image_body"
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 2. Framework of the proposed FedPD. It consists of a local parameter disentanglement strategy (LPD) and a global divide-and-conquer aggregation approach (GDCA). On the client side, an OSR model is generated with closed-set loss and open-set loss on samples of known classes. Then, LPD decouples the local OSR model into a closed-set subnetwork and an open-set subnetwork by task-related parameter importance. On the server side, GDCA first extracts close-specific, open-specific and shared parameters from the uploaded subnetworks, and then align the corresponding parts by optimal transport and fuse them to generate global model."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
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+                        }
+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "4. The Proposed FedPD"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The overview of our method is depicted in Fig. 2. To address the FedOSR requirements, our method solves parameter misalignment via a local parameter disentanglement (LPD) strategy (Section 4.1) and a global divide-and-conquer aggregation (GDCA) approach (Section 4.2). For the federated round "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", every client "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                        636
+                                    ],
+                                    "type": "text",
+                                    "content": " will receive the same global model weights "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
+                                        290,
+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_{t-1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
+                                        290,
+                                        636
+                                    ],
+                                    "type": "text",
+                                    "content": " from the last round and update the model with their local known data "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D_k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
+                                        290,
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+                                    ],
+                                    "type": "text",
+                                    "content": " by a closed-set loss and an open-set loss. The LPD then decouples the updated local OSR model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_t^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "text",
+                                    "content": " into a closed-set subnetwork "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
+                                        290,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}_{close}^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and an open-set subnetwork "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}_{open}^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The local model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S^k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " together with two subnetworks "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}_{close}^k"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}_{open}^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are uploaded to the server for global divide-and-conquer aggregation. Specifically, the central server first divides two subnetworks into specific parts "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{close}^k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{open}^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                        636
+                                    ],
+                                    "type": "text",
+                                    "content": " and shared part "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
+                                        290,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{share}^k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", then aligns corresponding parts of all clients by optimal transport. At last, the aligned models are averaged to generate the global model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        418,
+                                        290,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        47,
+                        646,
+                        231,
+                        659
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "4.1. Local Parameter Disentanglement"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "To address the parameter misalignment problem caused by cross-client inter-set inference, we propose a local parameter disentanglement (LPD) strategy to analyze parameter components in FedOSR and decouple an OSR model"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "into a closed-set subnetwork and an open-set subnetwork. Specifically, motivated by the lottery ticket hypothesis [7, 11, 36] which shows that only partial parameters are significant for generalization, we find that partial parameters of an OSR model are important to closed-set classification and some parameters are significant to open-set detection."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                                {
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 3. Parameter distribution of closed-set subnetwork and open-set subnetwork on an OSR model on MNIST dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The Lottery Ticket Hypothesis We first review the lottery ticket hypothesis [7, 11, 36], which generates subnetwork to achieve better generalization. For subtask "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", if parameter "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is essential to it, the change of loss would be large once we remove "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        580,
+                                        545,
+                                        665
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        580,
+                                        545,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        580,
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+                                    ],
+                                    "type": "text",
+                                    "content": ") [25]. We define the difference value "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        580,
+                                        545,
+                                        665
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Omega^{\\mathrm{t}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        580,
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+                                        665
+                                    ],
+                                    "type": "text",
+                                    "content": " to represent the importance score of the parameter as shown in Eq. 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\Omega^ {\\mathbf {t}} \\left(h _ {i}\\right) = \\left| \\mathcal {L} ^ {\\mathbf {t}} \\left(H, h _ {i} = 0\\right) - \\mathcal {L} ^ {\\mathbf {t}} \\left(H, h _ {i}\\right) \\right|, \\tag {2}",
+                                    "image_path": "bd3f5ef9366e79d0d12edc2941fb7c07d47d60a97b999d0824f83b34e1ae59b7.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " refers to other parameters except "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        689,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        689,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since it's inefficient to evaluate the importance by parameter traversal,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
+            "discarded_blocks": [
+                {
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+                    ],
+                    "type": "page_number",
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+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "4885"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
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+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
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+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "we approximate it with Taylor Expansion [39] and obtain:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\Omega^ {\\mathbf {t}} \\left(h _ {i}\\right) = \\left| \\frac {\\partial \\mathcal {L} ^ {\\mathbf {t}} (H , h _ {i})}{\\partial h _ {i}} h _ {i} \\right| = \\left| \\nabla \\mathcal {L} _ {\\mathbf {t}} \\left(h _ {i}\\right) \\times h _ {i} \\right|. \\tag {3}",
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+                    "angle": 0,
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+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "After deriving the importance score of parameters for subtask "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " based on input "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{X}_{\\mathbf{t}},\\mathcal{Y}_{\\mathbf{t}})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": ", parameters with the higher score are selected as the subnetwork for "
+                                },
+                                {
+                                    "bbox": [
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+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": ". It can be indicated by a mask "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M^{\\mathbf{t}}(h_i) = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
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+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " if "
+                                },
+                                {
+                                    "bbox": [
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+                                        133,
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+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " belongs to the subnetwork, and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M^{\\mathbf{t}}(h_i) = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " otherwise."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        47,
+                                        194,
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+                                        289
+                                    ],
+                                    "type": "text",
+                                    "content": "Parameter Disentanglement on OSR Based on the lottery ticket hypothesis, we apply parameter disentanglement to decouple an OSR model into closed-set subnetwork and open-set subnetwork. Specifically, given a local OSR model "
+                                },
+                                {
+                                    "bbox": [
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+                                        289
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S^k"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        194,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we define two task-related metric "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        194,
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+                                        289
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{close}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        194,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{open}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        194,
+                                        287,
+                                        289
+                                    ],
+                                    "type": "text",
+                                    "content": " to judge the importance of each parameter contributing to closed-set classification and open-set detection based on the Eq. 3:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
+                                        81,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {T} _ {\\text {c l o s e}} ^ {k} (i) = \\left| \\nabla \\mathcal {L} _ {\\text {c l o s e}} \\left(\\omega_ {i}\\right) \\times \\omega_ {i} \\right|, i \\in [ m _ {*} ]. \\tag {4}",
+                                    "image_path": "ff189e7d9236b0eceed865ccadaa1348d22d082a0a6f44e04f454d3af11f95b9.jpg"
+                                }
+                            ]
+                        }
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+                            "spans": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {T} _ {\\text {o p e n}} ^ {k} (i) = | \\nabla \\mathcal {L} _ {\\text {o p e n}} (\\omega_ {i}) \\times \\omega_ {i} |, i \\in [ m _ {*} ]. \\tag {5}",
+                                    "image_path": "f49cf96fd616e6ccdfa5a3a82a0243b61e91cfe2c49262cf1738d5ce7a1d496f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the parameter number of a module in an OSR network and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_i"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the corresponding parameters of the module. The larger the value of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}(i)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is, the more this parameter contributes to the task-related loss function."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "After deriving the importance score "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{close}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{open}"
+                                },
+                                {
+                                    "bbox": [
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+                                        399,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of parameters for closed-set loss and open-set loss, we choose the top-K highest scores as most valuable weights and set them as 1 with the rest as 0 to generate closed-set subnetwork and open-set subnetwork respectively:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {M} _ {\\text {c l o s e}} ^ {k} (i) = \\left\\{ \\begin{array}{l} 1, \\mathcal {T} _ {\\text {c l o s e}} ^ {k} (i) > \\delta_ {\\text {c l o s e}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {6}",
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {M} _ {\\text {o p e n}} ^ {k} (i) = \\left\\{ \\begin{array}{l} 1, \\mathcal {T} _ {\\text {o p e n}} ^ {k} (i) > \\delta_ {\\text {o p e n}} \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{close}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        545,
+                                        287,
+                                        593
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{open}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        545,
+                                        287,
+                                        593
+                                    ],
+                                    "type": "text",
+                                    "content": " are the threshold to filter out redundant parameters and we choose the threshold based on ratio of parameter numbers. Here we set the masking ratio as 0.5 based on our experimental observation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                        594,
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+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": "We visualize the subnetworks in the first convolution layer as illustrated in Fig. 3. It's obvious that open-set and closed-set subnetworks hold different distribution."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Parameter Disentanglement on FedOSR Given a set of local OSR models "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{S}^k\\}_{k = 1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", we apply parameter disentanglement on these models, and plot closed-set subnetworks "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{M}_close^k\\}_{k = 1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and open-set subnetworks "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
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+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{M}_{open}^k\\}_{k = 1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " as shown in Fig. 4. It illustrates that there exists parameter misalignment in both closed-set subnetworks and open-set subnetworks among these clients. Simply aggregating the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        545,
+                        156
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": "client OSR modes into one global model may ignore the complex parameter composition and lead to model collapse due to unmatched averaging. For example, the parameter averaging on a closed-set subnetwork and an open-set subnetwork on the same position may generate chaotic neuron weights. This phenomenon motivates us to develop a new model aggregation approach for FedOSR."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "image",
+                    "bbox": [
+                        314,
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+                    ],
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+                                            "image_path": "ca2d5d3bf3d680d1c8672dcc293b2977d46ba0dd4d61c5c29d5a80725262170e.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
+                                304,
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+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        {
+                                            "bbox": [
+                                                304,
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 4. Parameter distribution of closed-set parameters and open-set parameters in federated framework on HDR-FL dataset. The horizontal direction of the picture represents channel numbers, and the vertical of it denotes client numbers."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. Global Divide-and-Conquer Aggregation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "During model communication on the server side, parameter misalignment problem will significantly destroy the global model, thus providing bad model initialization for local training in next step. To further remedy the aggregation catastrophe by cross-client intra-set inconsistency, we design a global divide-and-conquer aggregation (GDCA) method to first divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters, and then align and aggregate the corresponding parts respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        475,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Learning to divide Based on the results of local parameter disentanglement, an OSR model can be decoupled into a closed-set subnetwork and an open-set subnetwork as shown in Fig. 4. Since there are overlaps between these two subnetworks, we further divide an OSR model into three non-overlapping parts: close-specific parameters, open-specific parameters and shared parameters."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {P} _ {\\text {c l o s e}} = \\mathcal {M} _ {\\text {c l o s e}} \\odot \\overline {{\\mathcal {M} _ {\\text {o p e n}}}}, \\tag {8}",
+                                    "image_path": "5af60fb17c516148cbad7518d0410ef8bac2f8d91ab60eccdcf7ed8dd991eaa0.jpg"
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {P} _ {\\text {o p e n}} = \\mathcal {M} _ {\\text {o p e n}} \\odot \\overline {{\\mathcal {M} _ {\\text {c l o s e}}}}, \\tag {9}",
+                                    "image_path": "628746a4bbb52a0a781cba0b820670423e706607d24a395fbd4968d4af1d17e2.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {P} _ {\\text {s h a r e}} = \\mathcal {M} _ {\\text {o p e n}} \\odot \\mathcal {M} _ {\\text {c l o s e}}, \\tag {10}",
+                                    "image_path": "937f913e117d80259d8f735da0727ca30a5c90b45e6220fe9e63eb68092244bc.jpg"
+                                }
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+                {
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+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        617,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathcal{M}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        617,
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+                                        665
+                                    ],
+                                    "type": "text",
+                                    "content": " is the negation of the binary mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        617,
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+                                        665
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        617,
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+                                        665
+                                    ],
+                                    "type": "text",
+                                    "content": ". Compared with two subnetworks, the three non-overlapping parts are more suitable to deal with since the overlapping parameters may cause conflicts after alignment."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Learning to conquer We disentangle the OSR model of each client into three parts and align the corresponding parts before aggregation. The neuron weights are considered as a distribution, and we use optimal transport (OT) to achieve"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                }
+            ],
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+            ],
+            "page_idx": 4
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
+                        46,
+                        72,
+                        287,
+                        156
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": "distribution alignment as shown in Fig. 2. OT is a technique used to solve distribution matching problems by finding a minimal effort solution to transport a given mass of dirt into a given hole. It has been successfully applied to various problems such as domain adaptation and GANs. We compute the transport map layer by layer to achieve alignment between two models "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        156
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        156
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
+                        156,
+                        288,
+                        300
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                156,
+                                288,
+                                300
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": "Taking two models "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " as an example, we align parameters of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " on "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " by channel-wise distribution matching. Let us assume that we are at one convolution layer "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}^{(\\ell)} \\in (\\mathcal{C}_{in}^{\\ell},\\mathcal{C}_{out}^{\\ell},F^{\\ell})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " and the previous layers have already been aligned, where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F = k\\times k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " is the square of filter size. The transport matrix of the last convolution layer "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}^{(\\ell -1)}\\in (\\mathcal{C}_{in}^{\\ell -1},\\mathcal{C}_{out}^{\\ell -1},F^{\\ell -1})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " is denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T^{(\\ell -1)} \\in (\\mathcal{C}_{out}^{\\ell -1},\\mathcal{C}_{out}^{\\ell -1})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since the output of last layer has been permuted by "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T^{(\\ell -1)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": ", we conduct post-multiplying on current layer with transport map of previous layer such that the order of current layer input "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{out}^{\\ell -1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": " can match the order of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{in}^{\\ell}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        156,
+                                        288,
+                                        300
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then the current layer can be transformed as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        107,
+                        308,
+                        287,
+                        327
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                107,
+                                308,
+                                287,
+                                327
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        308,
+                                        287,
+                                        327
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widehat {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)} \\leftarrow \\boldsymbol {W} _ {A} ^ {(\\ell) ^ {\\top}} \\boldsymbol {T} ^ {(\\ell - 1)}, \\tag {11}",
+                                    "image_path": "efcda5061921272805478665d48e437f4ad64da7b6886d6b79ad402582c30db5.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        329,
+                        287,
+                        366
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                329,
+                                287,
+                                366
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\pmb{W}}_A^{(\\ell, \\ell-1)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "text",
+                                    "content": " is the post-processed layer, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{W}_A^{(\\ell)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "text",
+                                    "content": " is transposed as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{C}_{in}^{\\ell}, F^{\\ell}, \\mathcal{C}_{out}^{\\ell})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        287,
+                                        366
+                                    ],
+                                    "type": "text",
+                                    "content": " to achieve matrix multiplication."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        368,
+                        287,
+                        443
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                368,
+                                287,
+                                443
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": "With current layer permuted, we compute the optimal transport map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{T}^{(\\ell)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " between "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\pmb{W}}_A^{(\\ell,\\ell-1)}, \\pmb{W}_B^{(\\ell)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{T}^{(\\ell)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d \\gets \\mathrm{OT}(\\widehat{\\pmb{W}}_A^{(\\ell,\\ell-1)}, \\pmb{W}_B^{(\\ell)})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the obtained Wasserstein-distance. We use this transport map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{T}^{(\\ell)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " to align the neurons weights of the first model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\pmb{W}_A)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " with respect to the second "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\pmb{W}_B)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        368,
+                                        287,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": ","
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        104,
+                        451,
+                        287,
+                        468
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                104,
+                                451,
+                                287,
+                                468
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        104,
+                                        451,
+                                        287,
+                                        468
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)} \\leftarrow \\boldsymbol {T} ^ {(\\ell) ^ {\\top}} \\widehat {\\boldsymbol {W}} _ {A} ^ {(\\ell , \\ell - 1)}, \\tag {12}",
+                                    "image_path": "fc8a86759d35ba02f16f99838a264605c305dfb14ee363ded7647938e9daca67.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        46,
+                        471,
+                        287,
+                        535
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                471,
+                                287,
+                                535
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{W}_A^{(\\ell, \\ell-1)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "text",
+                                    "content": " is the aligned layer from model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "text",
+                                    "content": ". To simplify this alignment process, we define "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{W}_A = OT(W_A, W_B)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "text",
+                                    "content": ". Through the alignment of model parameters, model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        471,
+                                        287,
+                                        535
+                                    ],
+                                    "type": "text",
+                                    "content": " will only change the orders of feature channels without affecting the model prediction."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        46,
+                        536,
+                        287,
+                        595
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                536,
+                                287,
+                                595
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        536,
+                                        287,
+                                        595
+                                    ],
+                                    "type": "text",
+                                    "content": "When we align the parameters of the OSR model for all clients, we can choose any client as the target client and align other clients with the target client. For example, we use the second client as the target client as shown in Fig. 2. The alignment process can be denoted as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        73,
+                        600,
+                        287,
+                        615
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                73,
+                                600,
+                                287,
+                                615
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        73,
+                                        600,
+                                        287,
+                                        615
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\tilde {S} _ {\\text {c l o s e}} ^ {k} = O T \\left(\\mathcal {S} ^ {k} \\odot \\mathcal {P} _ {\\text {c l o s e}} ^ {k}, \\mathcal {S} ^ {2} \\odot \\mathcal {P} _ {\\text {c l o s e}} ^ {2}\\right), \\tag {13}",
+                                    "image_path": "e64a555903cd05c8000bc1197b574572b288bce07b0ac3876a2a3c86a80b8469.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        75,
+                        616,
+                        287,
+                        632
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                75,
+                                616,
+                                287,
+                                632
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        75,
+                                        616,
+                                        287,
+                                        632
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\mathcal {S}} _ {\\text {o p e n}} ^ {k} = O T \\left(S ^ {k} \\odot \\mathcal {P} _ {\\text {o p e n}} ^ {k}, S ^ {2} \\odot \\mathcal {P} _ {\\text {o p e n}} ^ {2}\\right), \\tag {14}",
+                                    "image_path": "d28334caffa6b73b6aa1e14dc923aebb8b2c95276f68713c6de87e253e9e555e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        72,
+                        634,
+                        287,
+                        649
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                72,
+                                634,
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+                                649
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        72,
+                                        634,
+                                        287,
+                                        649
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\mathcal {S}} _ {\\text {s h a r e}} ^ {k} = O T \\left(\\mathcal {S} ^ {k} \\odot \\mathcal {P} _ {\\text {s h a r e}} ^ {k}, \\mathcal {S} ^ {2} \\odot \\mathcal {P} _ {\\text {s h a r e}} ^ {2}\\right). \\tag {15}",
+                                    "image_path": "31b56d451e9d9faa90923246e1c5d0ccd8dd3b87eebe5e5687e06df713bc4d74.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        59,
+                        654,
+                        273,
+                        666
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                59,
+                                654,
+                                273,
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        59,
+                                        654,
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+                                    ],
+                                    "type": "text",
+                                    "content": "After that, the global model "
+                                },
+                                {
+                                    "bbox": [
+                                        59,
+                                        654,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
+                                        59,
+                                        654,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be represented as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        61,
+                        672,
+                        287,
+                        705
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                61,
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        61,
+                                        672,
+                                        287,
+                                        705
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "G = \\frac {1}{K} \\left(\\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {c l o s e}} ^ {k} + \\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {o p e n}} ^ {k} + \\sum_ {k = 1} ^ {K} \\widetilde {S} _ {\\text {s h a r e}} ^ {k}\\right). \\tag {16}",
+                                    "image_path": "83fda3a2b31ed584312dd61e15374697a60fb99905722976a2819f5f54273347.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        47,
+                        711,
+                        237,
+                        723
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                711,
+                                237,
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+                            ],
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+                                {
+                                    "bbox": [
+                                        47,
+                                        711,
+                                        237,
+                                        723
+                                    ],
+                                    "type": "text",
+                                    "content": "Algorithm 1 summarizes the FedPD algorithm."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "code",
+                    "bbox": [
+                        308,
+                        89,
+                        539,
+                        388
+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
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+                                    "spans": [
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+                                            "bbox": [
+                                                307,
+                                                72,
+                                                391,
+                                                83
+                                            ],
+                                            "type": "text",
+                                            "content": "Algorithm 1 FedPD"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14,
+                            "angle": 0,
+                            "type": "code_caption"
+                        },
+                        {
+                            "bbox": [
+                                308,
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+                            "lines": [
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+                                    "bbox": [
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+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "Server OPERATIONS  \nInputs: Round number "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "T"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": ", Set of clients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "K"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nOutput: Global OSR model "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "G"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nfor "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "t = 0,1,\\ldots,T-1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": " do  \nfor client "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "k \\in K"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": " in parallel do  \n"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{S}^k, \\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k \\gets \\text{CLIENTOPERATIONS}(G_{t-1})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nend for  \n"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{P}_{close}^k = \\mathcal{M}_{close}^k \\odot \\overline{\\mathcal{M}_{open}^k}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{P}_{open}^k = \\mathcal{M}_{open}^k \\odot \\overline{\\mathcal{M}_{close}^k}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{P}_{share}^k = \\mathcal{M}_{close}^k \\odot \\mathcal{M}_{open}^k"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\widetilde{S}_{close}^k = OT(S^k \\odot \\mathcal{P}_{close}^k, S^2 \\odot \\mathcal{P}_{close}^2)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\widetilde{S}_{open}^k = OT(S^k \\odot \\mathcal{P}_{open}^k, S^2 \\odot \\mathcal{P}_{open}^2)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\widetilde{S}_{share}^k = OT(S^k \\odot \\mathcal{P}_{share}^k, S^2 \\odot \\mathcal{P}_{share}^2)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "G_t \\gets \\frac{1}{K} (\\sum_{k=1}^{K} \\widetilde{S}_{close}^k + \\sum_{k=1}^{K} \\widetilde{S}_{open}^k + \\sum_{k=1}^{K} \\widetilde{S}_{share}^k)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nend for  \nObtain global OSR model "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "G"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nCLIENT OPERATIONS  \nInput: Model weights "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "G_{t-1}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nOutput: Updated local OSR model weights "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{S}_t^k"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": ", closed-set subnetwork "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{M}_{close}^k"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": ", open-set subnetwork "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{M}_{open}^k"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nfor epoch "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "e = 0,1,\\ldots,E-1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": " do  \nfor batch "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{x,y\\} \\in D_m"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": " do  \n"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{L}_{local} = \\mathcal{L}_{close}(x,y) + \\mathcal{L}_{open}(x,y)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{T}_{close}^k = |\\nabla \\mathcal{L}_{close}(\\omega) \\times \\omega|"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{T}_{open}^k = |\\nabla \\mathcal{L}_{open}(\\omega) \\times \\omega|"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k = TopK(\\mathcal{T}_{close}^k, \\mathcal{T}_{open}^k)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{S}_t^k \\gets update(\\mathcal{S}_t^k, \\mathcal{L}_{local})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": "  \nend for  \nend for  \nSend model weights "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{S}_t^k"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": " and subnetworks "
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{M}_{close}^k, \\mathcal{M}_{open}^k"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
+                                                89,
+                                                539,
+                                                388
+                                            ],
+                                            "type": "text",
+                                            "content": " to the server"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "angle": 0,
+                            "type": "code_body"
+                        }
+                    ],
+                    "index": 15,
+                    "sub_type": "algorithm"
+                },
+                {
+                    "bbox": [
+                        306,
+                        412,
+                        382,
+                        426
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
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+                            ],
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+                                    "bbox": [
+                                        306,
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+                                        426
+                                    ],
+                                    "type": "text",
+                                    "content": "5. Experiment"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        306,
+                        434,
+                        442,
+                        445
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "type": "text",
+                                    "content": "5.1. Datasets and Evaluation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        304,
+                        454,
+                        545,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "We conduct extensive experiments on both heterogeneous federated learning benchmark Handwritten digital recognition FL Dataset (HDR-FL) and homogeneous federated learning benchmark CIFAR-10. The closed-set classification and open-set detection performances are evaluated by accuracy (ACC) and AUROC (AUC) respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        304,
+                        536,
+                        545,
+                        631
+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
+                                        536,
+                                        545,
+                                        631
+                                    ],
+                                    "type": "text",
+                                    "content": "HDR-FL: It consists of five datasets: MNIST [16], SVHN [28], USPS [12], SynthDigits [8] and MNIST-M [8]. These datasets are 10-class handwritten digital images from various scenarios. Each dataset is set as a client for Non-IID FedOSR. To achieve open-set recognition, six classes are chosen to be known and four classes are to be unknown classes. We keep the same known classes and unknown classes for all clients."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
+                        304,
+                        641,
+                        545,
+                        713
+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
+                                        304,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "CIFAR-10: It contains 60000 images in 10 classes, with 6000 images per class [15]. We first divide 10 classes into known classes and unknown classes, then split them into five equal parts to construct homogeneous federated setting. Specifically, we try different ratio between the known and the unknown to validate our method (e.g. 4:6, 6:4 and 8:2)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "4887"
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+                        }
+                    ],
+                    "index": 21
+                }
+            ],
+            "page_size": [
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+            "page_idx": 5
+        },
+        {
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
+                        59,
+                        79,
+                        536,
+                        180
+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
+                                99,
+                                69,
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+                                79
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+                                    "bbox": [
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+                                            "type": "text",
+                                            "content": "Table 1. Performance comparisons between our method and other baseline methods on HDR-FL benchmark."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">Closed-set ACC</td><td colspan=\"6\">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>SoftMax</td><td>96.69</td><td>76.06</td><td>97.97</td><td>83.99</td><td>83.69</td><td>87.68</td><td>77.38</td><td>65.41</td><td>88.80</td><td>70.53</td><td>66.24</td><td>73.67</td></tr><tr><td>OpenMax[2](CVPR&#x27;16)</td><td>95.54</td><td>63.13</td><td>97.97</td><td>81.15</td><td>76.57</td><td>82.87</td><td>77.78</td><td>57.37</td><td>89.21</td><td>69.78</td><td>60.88</td><td>71.00</td></tr><tr><td>RPL[4](ECCV&#x27;20)</td><td>98.33</td><td>77.22</td><td>98.13</td><td>84.76</td><td>86.32</td><td>88.95</td><td>77.87</td><td>66.70</td><td>89.53</td><td>73.17</td><td>73.23</td><td>76.10</td></tr><tr><td>PROSER[43](CVPR&#x27;21)</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>ARPL[3](TPAMI&#x27;21)</td><td>97.17</td><td>69.83</td><td>96.44</td><td>84.64</td><td>84.22</td><td>86.46</td><td>85.65</td><td>59.79</td><td>92.53</td><td>69.70</td><td>68.17</td><td>75.16</td></tr><tr><td>DIAS[26](ECCV&#x27;22)</td><td>97.50</td><td>70.66</td><td>97.62</td><td>86.11</td><td>86.81</td><td>87.74</td><td>82.90</td><td>67.33</td><td>90.69</td><td>77.48</td><td>71.92</td><td>78.06</td></tr><tr><td>SSB[35](ICLR&#x27;22)</td><td>96.41</td><td>60.12</td><td>97.46</td><td>82.82</td><td>74.86</td><td>82.33</td><td>88.53</td><td>57.68</td><td>90.45</td><td>73.40</td><td>70.01</td><td>76.01</td></tr><tr><td>FedPD(Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr></table>",
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+                                            "content": "Table 2. Performance comparisons between our method and other baseline methods on CIFAR-10 benchmark."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Known=4</td><td colspan=\"2\">Known=6</td><td colspan=\"2\">Known=8</td></tr><tr><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td><td>Closed-set ACC</td><td>Open-set AUC</td></tr><tr><td>SoftMax</td><td>83.23 ±0.28</td><td>65.70±0.14</td><td>83.14±0.38</td><td>72.00±0.44</td><td>72.17±0.41</td><td>61.11±0.45</td></tr><tr><td>\\( OpenMax[2]_{(CVPR&#x27;16)} \\)</td><td>83.24 ±0.08</td><td>65.96±0.14</td><td>84.56±0.24</td><td>81.69±0.59</td><td>72.72±0.40</td><td>61.52±0.38</td></tr><tr><td>\\( RPL[4]_{(ECCV&#x27;20)} \\)</td><td>81.23 ±0.11</td><td>65.10±0.05</td><td>78.78±0.43</td><td>68.72±0.43</td><td>72.98±0.33</td><td>61.36±0.32</td></tr><tr><td>\\( PROSER[43]_{(CVPR&#x27;21)} \\)</td><td>84.15 ±0.13</td><td>69.04±0.07</td><td>85.77±0.48</td><td>80.69±0.27</td><td>70.50±0.21</td><td>60.48±0.41</td></tr><tr><td>\\( ARPL[3]_{(TPAMI&#x27;21)} \\)</td><td>83.91 ±0.09</td><td>69.02±0.12</td><td>86.54±0.53</td><td>79.83±0.69</td><td>73.63±0.37</td><td>66.78±0.64</td></tr><tr><td>\\( DIAS[26]_{(ECCV&#x27;22)} \\)</td><td>84.85 ±0.04</td><td>70.32±0.09</td><td>87.74±0.16</td><td>81.66±0.25</td><td>74.53±0.37</td><td>67.75±0.34</td></tr><tr><td>\\( SSB[35]_{(ICLR&#x27;22)} \\)</td><td>84.27±0.06</td><td>68.85±0.11</td><td>86.04±0.70</td><td>82.41±0.33</td><td>75.54±0.18</td><td>67.97±0.23</td></tr><tr><td>\\( FedPD(Ours) \\)</td><td>86.28±0.07</td><td>71.50±0.07</td><td>89.43±0.22</td><td>85.07±0.50</td><td>75.87±0.16</td><td>69.12±0.45</td></tr></table>",
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+                                    "content": "5.2. Implementation Details"
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+                                    "content": "On local training, we apply PROSER [43] for open-set training with a closed-set loss and an open-set loss. On global aggregation, we utilize FedAvg [23] to average OSR models for comparison methods. For handwritten digital recognition, we apply a six-layer CNN. During the training process, we utilize the SGD optimizer [31] with learning rate "
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+                                    "content": " for closed-set loss and "
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+                                    "type": "text",
+                                    "content": " for open-set loss, we set batch size to 32 and training epochs to 100. Global model is updated every epoch by FedAvg [23] aggregation. For CIFAR-10 Dataset, we use WideResNet for classification. Networks are trained by Adam optimizer [14] with batch size of 128. The learning rates of closed-set loss and open-set loss are initialized as "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": " respectively. The communication is conducted after every "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{E} = 5"
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+                                    "type": "text",
+                                    "content": " epochs in local training until reaching "
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+                                    "content": "\\mathrm{T} = 250"
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+                                    "type": "text",
+                                    "content": " epochs in total. All experiments of these two benchmarks are performed on NVIDIA 2080Ti card with Pytorch library. Detailed model architecture for both benchmarks is shown in the supplementary material."
+                                }
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+                                    "content": "5.3. Comparison with state-of-the-arts"
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+                                    "content": "We compare the performance of FedPD with the state-of-the-art OSR methods, including SoftMax, OpenMax [2], RPL [4], PROSER [43], ARPL [3], DIAS [26], SSB [35]. These comparison methods are implemented by FedAvg [23] on each client OSR models. Our FedPD utilizes the popular generative-based method PROSER [43] for local open-set training."
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+                                    "type": "text",
+                                    "content": "HDR-FL: As shown in Table 1, our FedPD outperforms existing OSR approaches with a large margin not only in closed-set classification but also in open-set detection. In addition, our FedPD achieves consistent improvements on"
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+                                    "type": "text",
+                                    "content": "all clients. Specifically, our method can surpass existing approaches with a promising "
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+                                    "type": "text",
+                                    "content": " average closed-set ACC and 80.78 average open-set AUC, outperforming the state-of-the-art OSR method DIAS [26] with "
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+                                    "type": "text",
+                                    "content": " in AUC. It validates that our method could enable better global model aggregation for open-set recognition, which verifies the effectiveness of our divide-and-conquer approach to address parameter misalignment in FedOSR. Moreover, some generate-based methods (e.g. SSB [26]) may encounter serious model collapse problem due to unmatched parameter of local OSR models, leading to "
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+                                    "content": " performance gap in average ACC."
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+                                    "content": "CIFAR-10: Comparison results on CIFAR-10 benchmark are shown in Table 2. To validate the stability of our method, we conduct experiments on different ratios between known classes and unknown classes. In these three settings, our FedPD achieves the best open-set AUC of "
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+                                    "type": "text",
+                                    "content": ". The consistent performance improvement over different openness demonstrate the effectiveness of our FedPD to promote the ability of detecting novel category for federated models."
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+                                    "content": "5.4. Ablation Analysis of Our Method"
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+                                    "content": "5.4.1 Effectiveness of LPD"
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+                                            "content": "Table 4. Comparison to different network splitting methods."
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Splitting Method</td><td>None</td><td>Grad</td><td>Grad × Weight (Ours)</td></tr><tr><td>Closed-set ACC</td><td>85.61</td><td>89.04</td><td>90.96</td></tr><tr><td>Open-set AUC</td><td>76.19</td><td>80.95</td><td>81.36</td></tr></table>",
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+                                    "content": "To demonstrate the advantage of local parameter disentanglement, we compare it with no splitting and network splitting by grad as shown in Table 4. It shows that conducting network splitting according to task gradients results in large"
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+                                            "content": "Table 3. Ablation study for key components."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">closed-set ACC</td><td colspan=\"6\">Open-set AUC</td></tr><tr><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td><td>MNIST</td><td>SVHN</td><td>USPS</td><td>Synth</td><td>MNIST-M</td><td>Avg</td></tr><tr><td>Baseline + FedAvg</td><td>98.04</td><td>75.81</td><td>97.20</td><td>86.92</td><td>84.93</td><td>88.58</td><td>83.63</td><td>65.57</td><td>90.28</td><td>71.76</td><td>69.75</td><td>76.20</td></tr><tr><td>Baseline + FedMA</td><td>97.21</td><td>60.72</td><td>98.22</td><td>86.18</td><td>85.72</td><td>85.61</td><td>83.09</td><td>66.47</td><td>88.81</td><td>73.13</td><td>69.46</td><td>76.19</td></tr><tr><td>Baseline + FedPD (Ours)</td><td>98.73</td><td>78.06</td><td>98.56</td><td>89.32</td><td>90.14</td><td>90.96</td><td>90.98</td><td>69.46</td><td>93.31</td><td>79.43</td><td>73.64</td><td>81.36</td></tr><tr><td>Ours w/o Divide</td><td>98.39</td><td>77.60</td><td>98.22</td><td>88.65</td><td>89.66</td><td>90.50</td><td>89.56</td><td>69.91</td><td>92.72</td><td>79.05</td><td>72.67</td><td>80.78</td></tr><tr><td>Ours w/o Conquer</td><td>97.43</td><td>72.74</td><td>97.62</td><td>85.82</td><td>85.22</td><td>87.76</td><td>84.41</td><td>65.78</td><td>91.60</td><td>72.51</td><td>70.81</td><td>77.02</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "performance gain. Combining gradient and weight information makes better model decoupling, which corresponds to our theoretical analysis in Eq. 3."
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+                                    "type": "text",
+                                    "content": "Learning to Divide To validate the advantage of dividing two subnetworks into specific parts and shared parts, we conduct experiments on two different aggregation strategy: align two subnetworks then average (Ours w/o Divide) and align three parts then average (Ours). Comparison results in Table 3 illustrates that aligning three parts outperforms aligning two subnetworks with performance gain of "
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+                                    "content": " in ACC and "
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+                                    "type": "text",
+                                    "content": " in AUC. It is because that the overlapping parameters between these two subnetworks may have different distribution after alignment, thus leading to ambiguous parameters."
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+                                    "type": "text",
+                                    "content": "Learning to Conquer To validate the effectiveness of divide-and-conquer aggregation, we compare our method with traditional aggregation methods FedAvg and FedMA. Unlike obvious improvement on closed-set setting, FedMA shows inferior performance than FedAvg as shown in Table 3. It is consistent with our observation that parameter components in open-set models are more complex than those in closed-set models due to multiple optimization directions. Compared with directly averaging three parts with alignment (Ours w/o Conquer), conducting our proposed aggregation strategy brings performance boost on of "
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+                                    "type": "text",
+                                    "content": " in AUC, demonstrating that our FedPD can alleviate parameter misalignment problem."
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+                                    "content": "5.4.3 Effect of Masking Ratio"
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+                                    "content": "To investigate the effect of masking ratio to the FedOSR performance, we design ablation experiments under HDRFL setting, as shown in Fig. 5. It is observed that small masking ratio (e.g. 0.1) may filter out too much parameters, leading to empty shared parameter. Large masking ratio"
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+                                            "content": "Figure 6. Parameter distribution of closed-set subnetworks and open-set subnetworks on CIFAR-10 dataset."
+                                        }
+                                    ]
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+                            ],
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+                                    "type": "text",
+                                    "content": "(e.g. 0.9) can't choose valuable weights for the closed-set task and the open-set task, thus leading to invalid decoupling. In this paper, we choose suitable masking ratio as 0.5 based on our experimental observation that it achieves the best closed-set ACC and open-set AUC."
+                                }
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+                                    "type": "text",
+                                    "content": "5.5. Analysis of Parameter Misalignment"
+                                }
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+                    "index": 14
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+                                    "type": "text",
+                                    "content": "To verify the parameter misalignment problem in FedOSR, we visualize the weights distributions of closed-set subnetwork and open-set subnetwork on CIFAR-10 homogeneous benchmark as shown in Fig. 6. Different clients still hold inconsistent parameter distribution on both closed-set subnetwork and open-set subnetwork. Different from results shown in Fig. 4, where parameter misalignment may come from domain shift in heterogeneous federated datasets. Fig. 6 further emphasize that the parameter misalignment in FedOSR mainly comes from gradient divergence of closed-set loss and open-set loss."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "6. Conclusion"
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+                                    "type": "text",
+                                    "content": "In this work, we propose a novel and practical problem of federated open-set recognition (FedOSR) for the first time. To alleviate the parameter misalignment problem in FedOSR, we design a novel parameter disentanglement guided federated algorithm (FedPD). Specifically, on the client side, a local parameter disentanglement is developed to decouple the local OSR models into closed-set subnetworks and open-set subnetworks. On the server side, a global divide-and-conquer aggregation strategy is proposed to divide two subnetworks into specific parts and shared parts, then align corresponding parts by optimal transport and fuse them to generate global model. Extensive experiments on both IID and Non-IID benchmark datasets demonstrate the effectiveness of FedPD."
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diff --git a/2023/FedPerfix_ Towards Partial Model Personalization of Vision Transformers in Federated Learning/d543e771-be91-4881-a9ae-44abbc36ec5b_content_list.json b/2023/FedPerfix_ Towards Partial Model Personalization of Vision Transformers in Federated Learning/d543e771-be91-4881-a9ae-44abbc36ec5b_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..8e6909cf78be0bd0f3e041be23f28f05cb80a9d5
--- /dev/null
+++ b/2023/FedPerfix_ Towards Partial Model Personalization of Vision Transformers in Federated Learning/d543e771-be91-4881-a9ae-44abbc36ec5b_content_list.json	
@@ -0,0 +1,1600 @@
+[
+    {
+        "type": "text",
+        "text": "FedPerfix: Towards Partial Model Personalization of Vision Transformers in Federated Learning",
+        "text_level": 1,
+        "bbox": [
+            99,
+            128,
+            870,
+            176
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Guangyu Sun<sup>1</sup>, Matias Mendieta<sup>1</sup>, Jun Luo<sup>2</sup>, Shandong Wu<sup>3</sup>, Chen Chen<sup>1</sup>",
+        "bbox": [
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+            202,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup>Center for Research in Computer Vision, University of Central Florida, USA  \n<sup>2</sup>Intelligent Systems Program, University of Pittsburgh, USA  \n<sup>3</sup>Department of Radiology, Biomedical Informatics, and Bioengineering, University of Pittsburgh, USA  \n{guangyu.sun, matias.mendieta}@ucf.edu; jul117@pitt.edu; wus3@upmc.edu; chen.chen@crcv.ucf.edu",
+        "bbox": [
+            179,
+            238,
+            790,
+            344
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            378,
+            313,
+            395
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Personalized Federated Learning (PFL) represents a promising solution for decentralized learning in heterogeneous data environments. Partial model personalization has been proposed to improve the efficiency of PFL by selectively updating local model parameters instead of aggregating all of them. However, previous work on partial model personalization has mainly focused on Convolutional Neural Networks (CNNs), leaving a gap in understanding how it can be applied to other popular models such as Vision Transformers (ViTs). In this work, we investigate where and how to partially personalize a ViT model. Specifically, we empirically evaluate the sensitivity to data distribution of each type of layer. Based on the insights that the self-attention layer and the classification head are the most sensitive parts of a ViT, we propose a novel approach called FedPerfix, which leverages plugins to transfer information from the aggregated model to the local client as a personalization. Finally, we evaluate the proposed approach on CIFAR-100, OrganAM-NIST, and Office-Home datasets and demonstrate its effectiveness in improving the model's performance compared to several advanced PFL methods. Code is available at https://github.com/imguangyu/FedPerfix",
+        "bbox": [
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+            411,
+            472,
+            758
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            784,
+            209,
+            800
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Federated learning (FL) [25] has emerged as a promising method for training machine learning models on decentralized data without requiring direct data sharing. However, data heterogeneity among participating clients can present a significant challenge. Due to the various circumstances of the clients, the data across the clients can",
+        "bbox": [
+            75,
+            809,
+            470,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "be non-independent and non-identically distributed (non-IID). Therefore, achieving satisfactory performance using a one-model-fits-all approach is difficult, and personalized models are often needed to achieve the best results. This has inspired the study of Personalized Federated Learning (PFL), where the focus is shifted from the performance of the global model on the server to the local models on the clients.",
+        "bbox": [
+            496,
+            380,
+            893,
+            501
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In the context of personalized federated learning, previous literature has explored two main approaches: full model personalization [9, 6, 23] and partial model personalization [31, 27, 18, 5, 1]. Full model personalization involves maintaining a separate local model for each client and updating it based on a joint objective, while partial model personalization aims to personalize only a subset of the model parameters. A convergence analysis [31] suggests that partial model personalization can achieve most of the benefits of full model personalization with fewer shared parameters, offering advantages in terms of computation, communication, and privacy to enable the deployment of larger models on the clients.",
+        "bbox": [
+            496,
+            505,
+            893,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However, recent literature shows that where and how to perform partial model personalization has a high correlation to the model architectures and the tasks [31], which requires further study when applied to a new architecture. Despite the multitude of approaches proposed in the literature, the majority of methods have only been evaluated on Convolutional Neural Networks (CNNs). Meanwhile, Vision Transformers (ViTs) [8] have demonstrated superior performance compared to CNNs in several tasks, such as image classification [37] and object detection [42, 3], making them an attractive option for personalized federated learning. However, to the best of our knowledge, the application of ViT in the federated learning community has received limited at",
+        "bbox": [
+            496,
+            704,
+            895,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "4988",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "tention in the existing literature [32]. Given the advantages of ViT shown under centralized training, it is reasonable to expect that these benefits can also be realized in PFL by offering a more robust model for improved performance on the clients. Therefore, in this work, we investigate where and how to partially personalize a ViT model.",
+        "bbox": [
+            75,
+            90,
+            470,
+            181
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Drawing from previous research on CNNs, layers that serve specific engineering purposes, such as feature extraction, normalization, or classification, have been identified as suitable candidates for partial model personalization [27, 18, 5]. These layers might have a higher sensitivity to the distribution of the training data. Therefore, aggregating the model weights trained from different data distributions may result in an inaccurate feature, while keeping them updated locally can gain a better feature for the local data distribution. Similarly, we select some candidates from ViT and conduct an empirical study to investigate the sensitivity of each type of layer. Specifically, we quantitatively evaluate the impact of keeping certain layers updated locally without aggregation with other clients. This evaluation shows that the self-attention layers and the classification head have a higher sensitivity than other layers, providing insights about where to personalize.",
+        "bbox": [
+            75,
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+        "type": "text",
+        "text": "To personalize the sensitive parts, one intuitive approach is to keep them completely local. However, the global aggregation has shown the capability to provide a more general global model than local models [24]. Completely preventing the sharing with the global model will severely hinder the potential benefits of leveraging general knowledge from the aggregated global model. Therefore, we desire to train a personalization module to bridge the general knowledge and the client-specific knowledge.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As existing works in transfer learning suggest, the same pre-trained model can be transferred to different downstream data by adding different tiny architectures [30, 15, 20, 12]. We refer to these tiny architectures as plugins since they are small-sized parameters plugged into the pretrained model. These plugins are trained while the weights of the pre-trained model are frozen. The plugged model can achieve comparable performance as the fully fine-tuned model [29]. Since the model can maintain the same level of performance without changing the weights of the pretrained model, the downstream-specific knowledge is captured by the plugins. Therefore, the plugins show the capability to personalize the same model to satisfy different downstream data. In federated learning, we can consider the aggregated model as an inferior version of the \"pre-trained\" model, and the data on different clients as the downstream data, as shown in Fig. 1. With this perspective, we can therefore exploit the capability of the plugins in the federated learning context to capture client-specific knowledge for personalization.",
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+    {
+        "type": "text",
+        "text": "Therefore, we select and adapt a specific family of plu",
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+        "img_path": "images/4c5b523e57c066de4c40d87c11cd53ad1b0f2ee48e65d345b28783d66ba42ee1.jpg",
+        "image_caption": [
+            "Personalized Federated Learning",
+            "Figure 1. Analogy between transfer learning and personalized federated learning. A pre-trained model can be transferred to different downstream data with different plugins. In personalized federated learning, we are seeking different personalization modules (PM) to transfer the aggregated model to different client data."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "gin, Prefixes, to personalize the self-attention layer and propose a novel approach FedPerfix, short for Federated Personalized Prefix-tuning.",
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+        "type": "text",
+        "text": "The main contributions of this paper are as follows:",
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+        "list_items": [
+            "- We perform an empirical study to reveal the sensitivity to data distribution of each type of layer in a ViT for PFL and locate the self-attention layer and classification head as the sensitive part to be personalized. (Section 3.3)",
+            "- We propose a novel partial model personalization approach on ViT, FedPerfix, inspired by the connection between PFL and transfer learning. Specifically, we exploit Prefix plugins to capture client-specific knowledge for personalization. (Section 3.5)",
+            "- We conduct evaluations on CIFAR-100 [2], OrganAMINIST [40], and Office-home [38], which are across different domains, and degrees of data heterogeneity and achieve state-of-the-art performance compared with several competitive methods with lower resource requirements. (Section 4.2)"
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Personalized Federated Learning. Personalized Federated Learning focuses on training a client-specific model to achieve satisfying performance on each client instead of a unified global model to fit all the client data. In terms of the shared parameters, full model personalization keeps a separate personalized model for each client and designs different training objectives, where the global model is usually served as the regularization term [36, 17, 43, 19, 13, 26].",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "4989",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The training objectives are designed with the idea of meta-learning [9], Moreau Envelopes [7], model interpolation [6], decoupling [4], etc. In contrast, partial model personalization focuses on personalizing some specific parameters inside a model. Some works simply keep these parameters, e.g., the classification head [1, 27], and the batch normalization layers [18] updated locally, while some works design additional parameters, e.g., prototypes for each class [36] or hypernetworks [34], to further personalized these parameters. Our proposed method focuses on the self-attention layers in a ViT and leverages plugins in transfer learning, enabling personalization without introducing significant overhead. Our experimental results demonstrate that FedPerfix outperforms existing methods in terms of both efficiency and effectiveness.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Vision Transformer. ViTs, a type of attention-based neural network, have shown superior performance in several fields compared to CNNs. In particular, ViTs have achieved state-of-the-art performance on various benchmarks [8, 22, 21]. ViTs employ self-attention mechanisms to learn the dependencies between different regions of an image and can capture long-range dependencies more effectively than CNNs. Despite their success, the use of ViTs in federated learning has not been as widely explored as CNNs. Qu et al. [32] studied the performance of ViT under conventional FL settings and found that simply replacing CNNs with ViTs can greatly accelerate convergence and reach a better global model, especially when dealing with heterogeneous data, demonstrating the potential of ViTs in FL. In this paper, we extend the application of ViT to PFL and propose a novel approach to better personalize a ViT.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Parameter-efficient Fine-tuning and Plugins. Finetuning is a popular technique for adapting a pre-trained model to a new task. However, fine-tuning can be computationally expensive, especially for large models [10, 41]. Parameter-efficient fine-tuning (PEFT) has been proposed to address this issue by selectively updating only a subset of the model's parameters or a few added parameters. These added parameters are plugged into the pre-trained model; therefore, they are summarised as \"Plugins\" in this paper. Although the location of the plugins for a transformer is various, including the input [15], the self-attention layer [20], and the feed-forward network [30], all of them can be trained to achieve comparable performance as fine-tuning without updating the weights of the pre-trained model. The plugins have also been applied to conventional FL to enable large pre-trained models and reduce the communication cost [35]. In the PFL, inspired by analogy from fine-tuning to the local training, the plugins can similarly be employed to personalize the representation from the global model to the local data distribution. Based on our empirical study, we choose prefixes [20] since the parameters are directly applied to the self-attention layer and propose our",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "method, FedPerfix.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We consider a classification problem in Computer Vision (CV). A dataset  $\\mathcal{D} = \\{(x,y)|x\\in X,y\\in Y\\}$  is separated on  $N$  clients, where  $X$  is the input space and  $Y$  is the label space. Data on each client is denoted as  $\\mathcal{D}_i$ , and the distribution  $P_{i}$ . The client distributions are not identical. Each client has access to  $m_{i}$  samples drawn IID from the distribution  $P_{i}$ . The total number of samples is  $M = \\sum_{i = 1}^{N}m_{i}$ . The hypothesis (model) on each client is noted as  $h_i$ , and the expected loss on the  $i^{\\mathrm{th}}$  client is denoted as",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathcal {D} _ {i}} \\left(h _ {i}\\right) = \\mathbb {E} _ {(x, y) \\sim P _ {i}} [ \\ell (h (x), y) ] \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\ell$  is the loss function. Further, considering the partial model personalization, the parameters in each client model can be divided into two parts: global parameters  $u$  and local parameters  $v_{i}$ , i.e.,  $h_i = u\\cup v_i$ . Specifically,  $v_{i} = \\varnothing$  indicates full model personalization.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In each communication round  $t \\in [T]$ , each client will receive  $u^{(t-1)}$  from the server and plug  $v_i^{(t-1)}$  into  $u^{(t-1)}$ . Then,  $u_i^{(t)}, v_i^{(t)}$  are trained on the local data. After the local training, only the  $u_i^{(t)}$  of  $K$  sampled clients will be sent to the server and participate in the global aggregation. The sampled ratio (client participation rate) is denoted as  $r = K/N$ . The global aggregation is formulated as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nu ^ {(t)} = \\sum_ {i = 1} ^ {K} \\alpha_ {i} u _ {i} ^ {(t)} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha_{i}$  is the aggregation coefficient. Federated Averaging (FedAVG) is the most common aggregation algorithm where  $\\alpha_{i} = \\frac{m_{i}}{M}$ . After  $T$  rounds of communication, each client model will receive a copy of the newest global parameters and plug its own local parameters into the global parameters. Then, the model will be evaluated on its own test data drawn IID from  $P_{i}$ . To assess the overall performance, the mean and standard deviation of the Top-1 classification accuracy (Acc) for all clients will be reported.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Recap: Partial Model Personalization for CNN",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we provide a brief recap of the approaches for partial model personalization in CNNs. We aim to leverage the insights and experiences gained from previous research to explore the strategy to personalize ViTs partially.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "FedRep [5] is a partial model personalization method that aims to preserve client-specific information while leveraging common knowledge in the earlier layers of a CNN by keeping the last classification layer and a few blocks local",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4990",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0266517e54401fa4723d251661c546485559d0ecd223180ca0dc0db433ef2b90.jpg",
+        "table_caption": [
+            "Table 1. Sensitivity to data distribution of each type of layer in a Vision Transformer. The mean and standard deviation of the client's Top-1 Accuracy are reported for each type of layer (Stand-alone). Considering the classification head is the most sensitive type of layer, we also report the performance when a type of layer is kept updated locally along with the classification head (Combined). The overall performance is the mean of the standalone accuracy and combined accuracy."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Type</td><td>Stand-alone</td><td>Combined</td><td>Overall</td></tr><tr><td>All Local</td><td>34.74±9.36</td><td>-</td><td>-</td></tr><tr><td>All Global</td><td>23.29±11.31</td><td>-</td><td>-</td></tr><tr><td>Classification Head</td><td>44.42±7.98</td><td>-</td><td>-</td></tr><tr><td>Patch Embedding</td><td>27.61±10.02</td><td>43.45±8.69</td><td>35.53</td></tr><tr><td>Position Embedding</td><td>23.80±11.42</td><td>45.04±8.08</td><td>34.42</td></tr><tr><td>LayerNorm</td><td>23.94±11.19</td><td>44.60±7.96</td><td>34.27</td></tr><tr><td>Self-attention</td><td>42.95±8.68</td><td>44.63±8.67</td><td>43.79</td></tr><tr><td>MLP</td><td>42.53±8.82</td><td>42.63±8.84</td><td>42.58</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "and aggregating the rest. FedBN [18] is a partial model personalization method that updates Batch normalization (BN) [14] layers locally while aggregating the rest of the model. This method leverages the local statistics of the BN layer to adapt to the data distribution of each client while maintaining a global representation of the model, achieving a better balance between personalization and global representation. FedBABU [27] focuses on personalizing the classification head to address the issue of inconsistent feature spaces among clients. Unlike FedRep, FedBABU freezes the classification head and fine-tunes it for several steps before evaluation. By doing so, FedBABU can mitigate the negative impact of classification head drift and encourage consistent feature spaces across all clients.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In summary, previous approaches to partial model personalization for CNNs provide valuable insights to answer the \"where to personalize\" question for ViTs: The layers to be personalized are usually designed with some engineering purpose, thus, are sensitive to data distribution. For instance, the normalization layers are designed to capture the statistical characters of the data, while classification heads are designed to map the feature to a predicted class. Building on these insights, we group the layers in ViT by their engineering purpose and conduct an empirical study to determine the layers in ViT that are the most sensitive to data distribution. We evaluated the performance of ViT while keeping some specific types of layers updated locally without aggregating with other clients. The results of our study are presented in Section 3.3.",
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+    {
+        "type": "text",
+        "text": "3.3. Empirical Study: Partial ViT Personalization",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In a ViT, we consider the following layers as candidates to be personalized and evaluate their sensitivity to data distribution when they are updated locally: Patch Embedding layer converts the input image to a sequence of patches, then applies a linear projection to map each patch into an embedding vector. Position Embedding layer is responsible for injecting positional information into the sequence of patches produced by the patch embedding layer, allowing the model to capture the spatial arrangement of the image. LayerNorm is a normalization layer commonly used in ViT to normalize the feature maps across the channel dimension. Self-attention layer allows the model to attend to different regions of the input image and capture long-range dependencies between them. MLP layers, following the self-attention layer, enable the model to capture nonlinear relationships between the image patches. Classification Head applies a linear projection from the [CLS] token to a predicted class.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We perform experiments on CIFAR-100 with our default setting, which will be introduced in Section 4.1. We keep the specified type of layer updated locally and report the mean and standard deviation of the Top-1 Accuracy across all clients as the metrics to indicate the sensitivity to data distribution. The result is shown in the second column of Table 1.",
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+    },
+    {
+        "type": "text",
+        "text": "From the table, we can draw several insights. Keeping all layers local yields better performance than aggregating all layers. This suggests that aggregation of heterogeneous data may have a negative impact on some layers. Meanwhile, keeping each type of layer updated locally allows for greater adaptability to each client's data, leading to different degrees of improvement compared with keeping every layer global. Among all types of layers, the classification head is the most sensitive to data distribution, leading to the highest stand-alone performance, which is as expected. Except for the classification head, self-attention layer is more sensitive to data distribution than other components, showing a higher standard-alone performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Considering the vital importance of the classification head, we also reported the combined performance when a type of layer is kept updated locally along with the classification head, as shown in the third column of Table 1. To decide the most sensitive layers to be personalized, we averaged the performance under the two settings as the overall performance.",
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+    {
+        "type": "text",
+        "text": "Based on the overall performance, personalizing the self-attention and classification head is one possible answer to the question of where to personalize. Besides, a vanilla baseline to keep the self-attention layers and classification head updated locally is proposed, which is referred to as Vanilla Attention as described in Fig. 2 (a).",
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+        "page_idx": 3
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+    {
+        "type": "page_number",
+        "text": "4991",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/0ad70d1540205e32b92e02a31b063e5f4199c88c315714265c6526a9b5024527.jpg",
+        "image_caption": [
+            "Figure 2. Several designs to personalize the self-attention layer in a ViT. SDP is short for Scaled Dot Product, the red part indicates the local parameters, the blue part indicates the global parameters and the gray parts are vectors or modules with no learnable parameter. (a) Vanilla attention simply keeps the self-attention and classification updated locally. (b) Vanilla prefix-tuning only keeps the prefixes updated locally and aggregates the original self-attention layer. (c) FedPerfix uses a local adapter to generate the prefixes and aggregates the original self-attention layer. The adapter is composed of a scale-down, an activation, and a scale-up layer."
+        ],
+        "image_footnote": [],
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/2ae7d7ff43b5e214e749e77dda4863902feb9f8d624f4b3ed2e03d8805b20949.jpg",
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+    {
+        "type": "text",
+        "text": "3.4. Proposed Baseline: Vanilla Prefix-tuning",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Building upon the insights about where to personalize gained in the previous section, we move to the next question about how to personalize the selected layers. As obtained from our empirical study, Vanilla Attention is a baseline to personalize the self-attention layer by completely keeping the self-attention updated locally. However, it will also prevent it from learning general information for the global model.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As explained in Section 1, the plugins can be trained on the local data to capture the client-specific knowledge as a personalization module. There are three widely used plugins for ViTs: a) Prompts that are learnable embeddings appended to the inputs, b) Adapters that are inserted into the MLP layers, and c) Prefixes that are appended to the key and value matrix of the self-attention layer. Given that the self-attention layer is one of the most sensitive layers, It is plausible that the Prefixes integrated nearest to the self-attention layer are capable of capturing the most relevant client-specific information pertaining to the self-attention mechanism. Besides, we further compare the effectiveness of all three plugins and discuss it in Section 5.3. Therefore, we select Prefixes as our personalization module.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Specifically, learnable prefixes are appended to the self-attention layer and kept updated locally on the client. Meanwhile, the original self-attention layer is shared across all clients as normal to capture global dependencies. We refer to this approach as Vanilla Prefix-tuning.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "An illustration of how Prefixes cooperate with the self-attention layer is shown in Fig. 2 (b). Besides, we formulate",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "the output of one head of the self-attention layer as",
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+    {
+        "type": "equation",
+        "text": "\n$$\nh e a d _ {i} = A t t e n t i o n \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {q} ^ {(i)}\\right),\n$$\n",
+        "text_format": "latex",
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+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {Z} ^ {l - 1} \\left[ \\boldsymbol {P} _ {k}, \\boldsymbol {W} _ {k} ^ {(i)} \\right], \\tag {3}\n$$\n",
+        "text_format": "latex",
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+        "type": "equation",
+        "text": "\n$$\n\\left. \\boldsymbol {Z} ^ {l - 1} \\left[ \\boldsymbol {P} _ {v}, \\boldsymbol {W} _ {v} ^ {(i)} \\right]\\right))\n$$\n",
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+        "type": "text",
+        "text": "where  $Z^{l-1}$  is the output from the last layer,  $P_k$  and  $P_v$  are prefixes,  $W_q^{(i)}, W_k^{(i)}$ , and  $W_v^{(i)}$  are the parameters in the self-attention layer, and [,] is the concatenate operation.",
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+    {
+        "type": "text",
+        "text": "3.5. FedPerfix: Stabilize the Prefix",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In Vanilla Prefix-tuning, the prefixes are randomly initialized, which can result in unstable performance when initialized with different weights. We later conduct an experiment to demonstrate such instability in Section 5.3 when Vanilla Prefix-tuning is initialized with different weights. To address this issue, we draw inspiration from the parallel attention design [41], which uses adapters to stabilize the prefixes. Similarly, we propose to use adapters in Vanilla Prefix-tuning to stabilize the prefix initialization. Specifically, we add a parallel adapter to prepare the prefixes for each layer, as shown in Fig. 2. Meanwhile, we add a hyperparameter  $s$  to control the efficiency of the adapter. Following the design of parallel attention, the prefixes are generated as",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {P} _ {k}, \\boldsymbol {P} _ {v} = \\operatorname {A d a p t e r} \\left(\\boldsymbol {Z} ^ {l - 1}\\right) = \\operatorname {T a n h} \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {\\text {d o w n}}\\right) \\boldsymbol {W} _ {u p} \\tag {4}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\mathrm{Tanh}$  is the activation function,  $W_{down}$  and  $W_{up}$  are parameters of the scaling layers of the adapter. As a result, the output of one head of the self-attention layer with paral",
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+        "type": "page_number",
+        "text": "4992",
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+        "type": "text",
+        "text": "IeI attention is shown in Fig. 2(c) and formulated as",
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+    {
+        "type": "equation",
+        "text": "\n$$\nh e a d _ {i} = A t t e n t i o n \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {q} ^ {(i)}\\right),\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {Z} ^ {l - 1} \\left[ s \\boldsymbol {P} _ {k}, \\boldsymbol {W} _ {k} ^ {(i)} \\right], \\tag {5}\n$$\n",
+        "text_format": "latex",
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+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {Z} ^ {l - 1} [ s \\boldsymbol {P} _ {v}, \\boldsymbol {W} _ {v} ^ {(i)} ]).\n$$\n",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "In conclusion, FedPerfix is proposed as a novel approach to transfer the information from the aggregated self-attention layer to fit the local data better, leveraging the plugins in transfer learning. The local prefixes are trained for personalization, while the global self-attention layer captures global dependencies. Therefore, FedPerfix provides a promising solution to address the question of how to perform personalization for ViTs.",
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+    {
+        "type": "text",
+        "text": "4. Experiment",
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+    {
+        "type": "text",
+        "text": "4.1. Experiment Details",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Dataset. We use three popular datasets to evaluate the performance: CIFAR-100 [16], OrganAMNIST [40], and Office-Home [38]. CIFAR-100 is a widely-used image classification dataset consisting of 50,000 RGB images across 100 classes. Office-Home is a domain adaptation dataset for object recognition tasks, which contains 15,500 images across 65 categories, captured from four different domains: Artistic images, Clipart, Product images, and Real-World images. OrganAMNIST is a medical image classification dataset that includes 58,850 gray-scale images of organs and tissues from human anatomy. The images are classified into 11 different classes. These datasets are chosen to evaluate the performance in various scenarios, including different data scales, domains, and the number of classes.",
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+    {
+        "type": "text",
+        "text": "Federated learning settings. We conduct  $T = 50$  communication rounds with each local training consisting of 10 epochs. To account for the various factors that can affect federated learning performance, we adjust the default settings for each dataset to focus on different scenarios with varying degrees of data heterogeneity of label skew and concept skew. For CIFAR-100, which has a relatively high number of samples and classes, we simulate a federated learning environment with  $N = 64$  clients using a Dirichlet distribution with  $\\alpha = 0.1$  and sampling  $K = 8$  clients with a ratio  $r = 0.125$  for each round. For OrganAMNIST, which has a similar number of samples but fewer classes than CIFAR-100, we partition the data using a Dirichlet distribution with a larger  $\\alpha = 0.5$  and apply the same client settings as CIFAR-100. As for Office-Home, which has fewer samples captured from 4 different domains, we focus on concept skew by partitioning the data from each domain into four different clients using a Dirichlet distribution with  $\\alpha = 1.0$ , resulting in a total of  $N = 16$  clients. In each communication round, we randomly sample  $K = 4$  clients",
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+    {
+        "type": "text",
+        "text": "from any domain with a ratio  $r = 0.25$ . A visualization of the data partitioning is provided in Supplementary A.1.",
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+    {
+        "type": "text",
+        "text": "Model Architecture and Baselines. We choose ViT-Small (ViT-S) [8] with a patch size of 16 and an image size of 224 as our model for evaluation. We compare our proposed FedPerfix method against a range of baseline methods, including widely used approaches like FedAVG and local training without aggregation (Local). We also compare our method against advanced full model personalization methods, namely APFL [6] and Per-FedAVG [9], and three partial model personalization methods, namely FedBN, FedRep, and FedBABU. Besides, we also include the performance of Vanilla Attention, which keeps the self-attention layer and the classification head updated locally, as a reference. APFL adapts the global and local model through an adaptive mixture coefficient, while Per-FedAVG employs meta-learning to improve the global model. These methods are model-agnostic and can be applied to ViTs. FedBN keeps the batch normalization layer updated locally and aggregates the remaining layers in the server with FedAVG. To adapt it to ViTs, we replace the batch normalization layer with the layer normalization layer. FedRep keeps the classification head updated locally while aggregating the other layers in the server. FedBABU freezes the classification head and aggregates the remaining layers in the server, then fine-tunes the classification head on the local data for one step before the evaluation.",
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+    {
+        "type": "text",
+        "text": "Evaluation Metrics. We report the final mean and standard deviation of Top-1 accuracy among all clients after all communication rounds finish as the evaluation metrics. Besides, to evaluate the feasibility of the methods, an analysis of storage, computation, and communication costs is reported in Section 4.4.",
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+    {
+        "type": "text",
+        "text": "Implement Details. All hyperparameters in each method are tuned as optimal in a range. Each model is optimized with the SGD [33] optimizer with the optimal learning rate, which is 0.01 for most methods. The server and all the clients are simulated in one machine, and we resize the images in all datasets as  $224 \\times 224$  RGB images to fit the model and set the batch size of the client data as 64. The model is implemented from the TIMM [39] library. All the experiments are implemented in Pytorch [28] and performed on 4 Nvidia A5000 GPUs. More details are provided in Supplementary A.2.",
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+    {
+        "type": "text",
+        "text": "4.2. Performance Evaluation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Based on the evaluation results presented in Table 2, several insights can be drawn regarding the performance of the compared methods. It can be observed that FedAVG performs worse than Local when facing a large label skew, i.e., on CIFAR-100. This indicates the importance of addressing data heterogeneity in federated learning scenarios. However, when the label skew is not that extreme, the informa",
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+    {
+        "type": "page_number",
+        "text": "4993",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/dd942a5fbfd2136e28f489933674a504293ca894358e14c17fa1a49f2a79d046.jpg",
+        "table_caption": [
+            "Table 2. Performance and required resources for each method. The mean and standard deviation of the Top-1 Accuracy among all clients are reported. The bold style indicates the best performance in each dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>CIFAR-100</td><td>Performance OrganAMNIST</td><td>Office-Home</td><td>Storage (# Params)</td><td>Computation (FLOPs)</td><td>Communication (# Params)</td></tr><tr><td>FedAvg</td><td>23.29±11.31</td><td>87.31±5.98</td><td>21.47±6.24</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.03M (100%)</td></tr><tr><td>Local</td><td>34.74±9.36</td><td>78.26±11.07</td><td>20.39±7.26</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>0 (0%)</td></tr><tr><td>APFL</td><td>44.88±10.50</td><td>89.74±5.83</td><td>24.23±7.02</td><td>42.06M (200%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>Per-FedAVG</td><td>33.86±8.01</td><td>82.81±7.13</td><td>17.09±4.83</td><td>21.03M (100%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>FedBN</td><td>23.94±11.19</td><td>87.63±5.78</td><td>21.25±5.89</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.01M (100%)</td></tr><tr><td>FedBABU</td><td>41.41±8.87</td><td>88.38±7.16</td><td>19.50±7.71</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>FedRep</td><td>44.42±7.80</td><td>92.63±3.77</td><td>23.67±5.97</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>Vanilla Attention</td><td>44.63±8.67</td><td>88.90±5.87</td><td>22.55±6.37</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>13.89M (66%)</td></tr><tr><td>FedPerfix (ours)</td><td>48.10±7.76</td><td>93.17±3.51</td><td>24.38±8.47</td><td>24.42M (116%)</td><td>66.58M (101%)</td><td>20.66M (98%)</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "tion gathered from the global aggregation can alleviate the overfitting due to few training samples on the client, leading to higher performance.",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "In addition, it is worth noting that the methods that focus on the global objective instead of information transferring from the global to the client model, such as Per-FedAVG, achieve better performance than FedAVG but still show inferior performance compared to Local when facing extreme label skew or concept skew, i.e., CIFAR-100 and OfficeHome. This suggests that direct modification of the global objective may not always be the most effective way when using ViTs. Performing meta-learning on relatively small-size client data for a relatively large ViT is a challenging task, which limits the effectiveness of Per-FedAVG.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "On the other hand, how to leverage the information provided in the global model is crucial for partial model personalization. The layer normalization version of FedBN shows little impact on the performance, leading to a negligible improvement based on FedAVG. However, APFL, FedRep, Vanilla Attention, FedBABU, and FedPerfix find a more suitable way to transfer the information from the global model, leading to superior performance than other methods. Consistent with the conclusion we draw from the empirical study, FedRep, FedBABU, and Vanilla Attention personalized the sensitive parts in ViT, thus outperforming FedAVG and Local by a significant margin. As an extension, APFL and our method, FedPerfix, balance the information between the local and global models in a proper manner, leading to the highest two performances considering the performance across all three datasets.",
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+    {
+        "type": "text",
+        "text": "Surprisingly, we find that there is a connection between FedPerfix and APFL. Equation 3, which shows the output",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "of a self-attention with Prefixes, can be rewritten as",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} h e a d (x) = (1 - \\lambda (x)) \\underbrace {A t t n (x \\boldsymbol {W} _ {q} , x \\boldsymbol {W} _ {k} , x \\boldsymbol {W} _ {v})} _ {\\text {a g g r e g a t e d a t t e n t i o n}} \\\\ + \\lambda (x) \\underbrace {A t t n \\left(x \\boldsymbol {W} _ {q} , x \\boldsymbol {P} _ {k} , x \\boldsymbol {P} _ {v}\\right)} _ {\\text {p e r s o n a l i z e d a t t e n t i o n}} \\tag {6} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda(x)$  is a scalar representing the normalized attention weights on the prefixes [10]. More details are provided in Supplementary B. It reveals that the local prefixes are learned as a mixture coefficient between the aggregated attention from the global model and the personalized attention from the prefixes. The high performance of both APFL and FedPerfix indicates the effectiveness of a mixture between the local and global models in PFL. Compared with APFL, FedPerfix only mixed the sensitive self-attention layers instead of the entire model, leading to higher performance. Meanwhile, FedPerfix trains the Prefix, which can be considered as the mixture coefficient, and the model simultaneously, while APFL needs separate training for the personalized model. Therefore, FedPerfix can achieve higher performance with fewer storage, computation, and communication resources. Furthermore, we provide a more detailed resource requirements analysis of each method in the following Section 4.4.",
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+    {
+        "type": "text",
+        "text": "4.3. Client-wise Performance",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 3, we present a density plot depicting the performance gain of each method in comparison to Local. Notably, FedPerfix demonstrates an average performance gain of over  $10\\%$ , surpassing all other methods. Moreover, FedPerfix outperforms all other methods by achieving up to  $30\\%$  performance gains for certain clients. Conversely, some clients experience performance degradation under other methods, while FedPerfix ensures performance",
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+    {
+        "type": "page_number",
+        "text": "4994",
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+        "page_idx": 6
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+    {
+        "type": "image",
+        "img_path": "images/f5594d0f9572b88eb47551aff750420cc3d2b9f4f2a7b855f495d0ec8164079d.jpg",
+        "image_caption": [
+            "Figure 3. Client-wise performance for each method on CIFAR-100. Density of the accuracy gain compared with Local training is plotted. FedPerfix provides highest upper and lower bounds among all the methods."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "gains for nearly all clients. In conclusion, FedPerfix shows a higher upper bound while maintaining a high lower bound, which will encourage more clients to involve in the federated training with performance-gaining guarantees for almost all clients.",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "4.4. Resource Requirements Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In federated learning, it is crucial to consider the practicality of each method in terms of the storage, computation, and communication resources required by each participating client. As such, it is imperative to analyze the resource demands of each approach to determine its feasibility in realistic federated settings.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We present a resource analysis of the evaluated methods, taking into account the storage, computation, and communication demands, which are crucial aspects in practical federated learning scenarios where clients may have limited resources. Table 2 reports the parameter size required to store the model, the FLOPs needed for training, and the parameter size required for communication. Notably, FedPerfix achieves superior performance compared to other methods with slightly more resources for storage and computation but fewer resources for communication.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Overall, our proposed FedPerfix approach demonstrates the highest efficiency in terms of achieving superior performance while utilizing fewer storage, computation, and communication resources compared to other methods. These findings highlight the potential of our approach to effectively address the resource constraints often encountered in realistic federated learning scenarios.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In this section, we conduct an ablation study on the CIFAR-100 dataset to evaluate the robustness of FedPerfix under various federated learning settings and to investigate FedPerfix with different designs.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/77b6d6bf1246fd47a742baffcfc5526669b7e416b5a849796d404b92ee5ee953.jpg",
+        "table_caption": [
+            "Table 3. Performance on CIFAR-100 with different backbones."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ResNet50</td><td>ViT-Small</td></tr><tr><td>FedAVG</td><td>17.87±13.16</td><td>23.29±11.31</td></tr><tr><td>Local</td><td>28.34±9.83</td><td>34.74±9.36</td></tr><tr><td>APFL</td><td>30.71±9.89</td><td>44.88±10.50</td></tr><tr><td>Per-FedAVG</td><td>28.82±8.53</td><td>33.86±8.01</td></tr><tr><td>FedBN</td><td>19.33±10.25</td><td>23.94±11.19</td></tr><tr><td>FedBABU</td><td>24.56±7.82</td><td>41.41±8.87</td></tr><tr><td>FedRep</td><td>39.52±10.92</td><td>44.42±7.80</td></tr><tr><td>FedPerfix</td><td>-</td><td>48.10±7.76</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.1. Performance Comparison with CNN Backbone",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To further demonstrate the motivation behind our work, i.e., addressing PFL with ViT, we conduct experiments to compare ViT and CNN as different backbones for the same set of methods. Given that the comparison methods are originally designed with a CNN backbone, we conduct experiments on CIFAR-100 with a CNN backbone as a reference to investigate the impact of replacing the CNNs with ViTs in these methods. To fairly compare the performance, we choose ResNet50 [11] as the CNN backbone due to its similar parameter size (24.37M) to ViT-Small [8] (21.03M).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The result is shown in Table 3. Simply replacing the CNN backbone with the ViT backbone significantly improves performance for each method without additional operations. It suggests that the advantages of ViTs that demonstrated superior performance compared to CNNs in centralized settings may also translate to personalized federated learning scenarios.",
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+    {
+        "type": "text",
+        "text": "The success of ViTs in existing methods highlights their potential for personalized federated learning. However, there is a lack of approaches specifically designed for ViTs. To address this gap, we propose FedPerfix, which is tailored for ViTs and focuses on personalizing the sensitive parts of the network. By doing so, FedPerfix further improves performance compared to existing methods that incorporate ViTs. Our approach fills an important research gap and suggests that there is still much to be gained from exploring the unique properties of ViTs for personalized federated learning.",
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+        "text": "5.2. Different FL Settings",
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+        "type": "text",
+        "text": "In order to assess the robustness of FedPerfix in more challenging federated learning scenarios, we conduct experiments that involve varying the number of clients with fewer samples per client and a lower client participation rate. We also compare the performance of FedPerfix with other competitive methods and report the results in Table 4. Our experimental results demonstrate that FedPerfix exhibits robust performance in different federated learning settings,",
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+        "type": "table",
+        "img_path": "images/da444334ba5ea72ae2d4d52d98d10cf7584ca3fad207971d047e286cc2e03818.jpg",
+        "table_caption": [
+            "Table 4. Performance on CIFAR-100 under different federated learning settings."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">N = 64</td><td colspan=\"2\">N = 128</td></tr><tr><td>r = 6.25%</td><td>r = 12.5%</td><td>r = 6.25%</td><td>r = 12.5%</td></tr><tr><td>FedAvg</td><td>19.76±9.35</td><td>23.29±11.31</td><td>19.64±10.01</td><td>23.29±11.81</td></tr><tr><td>Local</td><td>32.35±11.64</td><td>34.74±9.36</td><td>31.79±12.00</td><td>36.03±9.57</td></tr><tr><td>APFL</td><td>42.55±13.51</td><td>44.88±10.50</td><td>41.64±12.77</td><td>43.92±9.40</td></tr><tr><td>FedRep</td><td>35.72±10.33</td><td>44.42±7.80</td><td>35.88±9.59</td><td>44.70±8.40</td></tr><tr><td>FedPerfix</td><td>43.80±11.56</td><td>48.10±7.76</td><td>43.96±10.42</td><td>46.96±9.00</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "outperforming all other methods consistently. Thus, FedPerfix can be considered a reliable solution for extreme federated learning scenarios.",
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+    {
+        "type": "text",
+        "text": "5.3. Investigation of FedPerfix",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this subsection, we investigate the impact of the model size of FedPerfix and verify its effectiveness compared with other designs.",
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+    {
+        "type": "text",
+        "text": "Impact of Model Size. The model size is a crucial factor in federated learning, as it determines the resource requirements for storage, computation, and communication. To examine the impact of model size on the performance of FedPerfix, we conducted experiments with three different ViT backbones: ViT-Tiny, ViT-Small (Default), and ViT-Base. Additionally, we included the results of the baselines and two competitive methods as a reference. As shown in Table 5, FedPerfix still yields superior performance with different model sizes. Besides, the larger models generally performed better, with ViT-Base achieving the highest performance for each method. However, we note that the performance improvement decreases as the model size increases, suggesting a potential trade-off between model size and performance. This finding highlights the importance of selecting an appropriate model size to achieve the optimal balance between performance and resource requirements, particularly in resource-constrained environments where storage and computation resources are limited.",
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+        "type": "text",
+        "text": "FedPerfix vs. Vanilla Prefix-tuning. As mentioned in Section 3.5, the initialization of the Prefixes will affect the performance. To show the effectiveness of the parallel attention design in FedPerfix, we conduct experiments with Vanilla Prefix-tuning under two different initialization, initialized with zero (Prefix-Z) and random initialization (Prefix-R). Then, we compare the results with FedPerfix. The result is shown in Table 6. As expected, the prefixes generated from the parallel attention yield better performance than the other two manually initialized prefixes, highlighting the effectiveness of the parallel attention design in FedPerfix.",
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+    {
+        "type": "text",
+        "text": "FedPerfix vs. Prompts & Adapters. Prompts and adapters are also popular plugins that are widely used. To verify whether FedPerfix is the most effective among all families of the plugins, we also apply Prompts and Adapters",
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+        "table_caption": [
+            "Table 5. Performance on CIFAR-100 with different model sizes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ViT-Tiny</td><td>ViT-Small</td><td>ViT-Base</td></tr><tr><td>FedAVG</td><td>19.56±10.27</td><td>23.29±11.31</td><td>24.82±11.53</td></tr><tr><td>Local</td><td>33.73±9.20</td><td>34.74±9.36</td><td>38.93±10.08</td></tr><tr><td>APFL</td><td>37.66±10.04</td><td>44.88±10.50</td><td>47.57±9.57</td></tr><tr><td>FedRep</td><td>41.58±7.19</td><td>44.42±7.80</td><td>44.34±8.35</td></tr><tr><td>FedPerfix</td><td>44.71±8.47</td><td>48.10±7.76</td><td>48.40±8.18</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "to personalized federated learning. Specifically, we append several trainable Prompts to the input embeddings and keep them updated locally as the implementation of Prompt-tuning [15]. Meanwhile, we add Adapters to the MLP layers as the implementation of Adatper-tuning [30]. The results are shown in Table 6. Adding personalized Prompts doesn't improve the performance compared with simply keeping the classification head updated locally, indicating that the transformation to the input is not effective in PFL. However, adding Adapters to the MLP layers can also lead to a promising result as FedPerfix. Recap the result of our empirical study shown in Table 1, MLP layers are also sensitive to data distribution in a ViT. We note that as another instance to show the effectiveness of adding plugins to the sensitive parts of a ViT in PFL.",
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+        "type": "table",
+        "img_path": "images/7c712b9aa67e3d3372627cfe9607a38108be759852045227e6c217859ae44b3d.jpg",
+        "table_caption": [
+            "Table 6. Performance of different designs on CIFAR-100. Prefix-Z and Prefix-R mean vanilla prefix-tuning with zero and random initialization."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>FedPerfix</td><td>Prefix-Z</td><td>Prefix-R</td><td>Prompts</td><td>Adapters</td></tr><tr><td>48.10±7.76</td><td>47.37±8.47</td><td>46.98±8.10</td><td>44.19±8.13</td><td>47.99±8.59</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
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+    {
+        "type": "text",
+        "text": "In this work, we studied two research questions of where and how to personalize a ViT in federated learning. We conducted an empirical study to reveal that the self-attention and classification layers are the most sensitive layers for personalization. Based on that, we proposed FedPerfix, a novel method that introduces Prefixes with parallel attention to personalize the self-attention layers. Through extensive experiments on various datasets with different degrees of data heterogeneity, we demonstrated that FedPerfix achieves state-of-the-art performance while also reducing resource requirements. Our work focuses on ViTs and represents a shift in attention from the extensively researched CNNs, serving as inspiration for further investigation.",
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+        "type": "text",
+        "text": "7. Acknowledgement",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This work is partially supported by the NSF/Intel Partnership on MLWiNS under Grant No. 2003198.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
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+    },
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+        "list_items": [
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+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+            "content": "<sup>1</sup>Center for Research in Computer Vision, University of Central Florida, USA  \n<sup>2</sup>Intelligent Systems Program, University of Pittsburgh, USA  \n<sup>3</sup>Department of Radiology, Biomedical Informatics, and Bioengineering, University of Pittsburgh, USA  \n{guangyu.sun, matias.mendieta}@ucf.edu; jul117@pitt.edu; wus3@upmc.edu; chen.chen@crcv.ucf.edu"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
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+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+            ],
+            "angle": 0,
+            "content": "Personalized Federated Learning (PFL) represents a promising solution for decentralized learning in heterogeneous data environments. Partial model personalization has been proposed to improve the efficiency of PFL by selectively updating local model parameters instead of aggregating all of them. However, previous work on partial model personalization has mainly focused on Convolutional Neural Networks (CNNs), leaving a gap in understanding how it can be applied to other popular models such as Vision Transformers (ViTs). In this work, we investigate where and how to partially personalize a ViT model. Specifically, we empirically evaluate the sensitivity to data distribution of each type of layer. Based on the insights that the self-attention layer and the classification head are the most sensitive parts of a ViT, we propose a novel approach called FedPerfix, which leverages plugins to transfer information from the aggregated model to the local client as a personalization. Finally, we evaluate the proposed approach on CIFAR-100, OrganAM-NIST, and Office-Home datasets and demonstrate its effectiveness in improving the model's performance compared to several advanced PFL methods. Code is available at https://github.com/imguangyu/FedPerfix"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.785,
+                0.21,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Federated learning (FL) [25] has emerged as a promising method for training machine learning models on decentralized data without requiring direct data sharing. However, data heterogeneity among participating clients can present a significant challenge. Due to the various circumstances of the clients, the data across the clients can"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.381,
+                0.895,
+                0.502
+            ],
+            "angle": 0,
+            "content": "be non-independent and non-identically distributed (non-IID). Therefore, achieving satisfactory performance using a one-model-fits-all approach is difficult, and personalized models are often needed to achieve the best results. This has inspired the study of Personalized Federated Learning (PFL), where the focus is shifted from the performance of the global model on the server to the local models on the clients."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.506,
+                0.895,
+                0.701
+            ],
+            "angle": 0,
+            "content": "In the context of personalized federated learning, previous literature has explored two main approaches: full model personalization [9, 6, 23] and partial model personalization [31, 27, 18, 5, 1]. Full model personalization involves maintaining a separate local model for each client and updating it based on a joint objective, while partial model personalization aims to personalize only a subset of the model parameters. A convergence analysis [31] suggests that partial model personalization can achieve most of the benefits of full model personalization with fewer shared parameters, offering advantages in terms of computation, communication, and privacy to enable the deployment of larger models on the clients."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.896,
+                0.901
+            ],
+            "angle": 0,
+            "content": "However, recent literature shows that where and how to perform partial model personalization has a high correlation to the model architectures and the tasks [31], which requires further study when applied to a new architecture. Despite the multitude of approaches proposed in the literature, the majority of methods have only been evaluated on Convolutional Neural Networks (CNNs). Meanwhile, Vision Transformers (ViTs) [8] have demonstrated superior performance compared to CNNs in several tasks, such as image classification [37] and object detection [42, 3], making them an attractive option for personalized federated learning. However, to the best of our knowledge, the application of ViT in the federated learning community has received limited at"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4988"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.182
+            ],
+            "angle": 0,
+            "content": "tention in the existing literature [32]. Given the advantages of ViT shown under centralized training, it is reasonable to expect that these benefits can also be realized in PFL by offering a more robust model for improved performance on the clients. Therefore, in this work, we investigate where and how to partially personalize a ViT model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.185,
+                0.47,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Drawing from previous research on CNNs, layers that serve specific engineering purposes, such as feature extraction, normalization, or classification, have been identified as suitable candidates for partial model personalization [27, 18, 5]. These layers might have a higher sensitivity to the distribution of the training data. Therefore, aggregating the model weights trained from different data distributions may result in an inaccurate feature, while keeping them updated locally can gain a better feature for the local data distribution. Similarly, we select some candidates from ViT and conduct an empirical study to investigate the sensitivity of each type of layer. Specifically, we quantitatively evaluate the impact of keeping certain layers updated locally without aggregation with other clients. This evaluation shows that the self-attention layers and the classification head have a higher sensitivity than other layers, providing insights about where to personalize."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.444,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "To personalize the sensitive parts, one intuitive approach is to keep them completely local. However, the global aggregation has shown the capability to provide a more general global model than local models [24]. Completely preventing the sharing with the global model will severely hinder the potential benefits of leveraging general knowledge from the aggregated global model. Therefore, we desire to train a personalization module to bridge the general knowledge and the client-specific knowledge."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.582,
+                0.471,
+                0.884
+            ],
+            "angle": 0,
+            "content": "As existing works in transfer learning suggest, the same pre-trained model can be transferred to different downstream data by adding different tiny architectures [30, 15, 20, 12]. We refer to these tiny architectures as plugins since they are small-sized parameters plugged into the pretrained model. These plugins are trained while the weights of the pre-trained model are frozen. The plugged model can achieve comparable performance as the fully fine-tuned model [29]. Since the model can maintain the same level of performance without changing the weights of the pretrained model, the downstream-specific knowledge is captured by the plugins. Therefore, the plugins show the capability to personalize the same model to satisfy different downstream data. In federated learning, we can consider the aggregated model as an inferior version of the \"pre-trained\" model, and the data on different clients as the downstream data, as shown in Fig. 1. With this perspective, we can therefore exploit the capability of the plugins in the federated learning context to capture client-specific knowledge for personalization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Therefore, we select and adapt a specific family of plu"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.515,
+                0.097,
+                0.736,
+                0.111
+            ],
+            "angle": 0,
+            "content": "Personalized Federated Learning"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.524,
+                0.114,
+                0.882,
+                0.334
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.339,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Figure 1. Analogy between transfer learning and personalized federated learning. A pre-trained model can be transferred to different downstream data with different plugins. In personalized federated learning, we are seeking different personalization modules (PM) to transfer the aggregated model to different client data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.435,
+                0.892,
+                0.481
+            ],
+            "angle": 0,
+            "content": "gin, Prefixes, to personalize the self-attention layer and propose a novel approach FedPerfix, short for Federated Personalized Prefix-tuning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.481,
+                0.86,
+                0.496
+            ],
+            "angle": 0,
+            "content": "The main contributions of this paper are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.498,
+                0.891,
+                0.572
+            ],
+            "angle": 0,
+            "content": "- We perform an empirical study to reveal the sensitivity to data distribution of each type of layer in a ViT for PFL and locate the self-attention layer and classification head as the sensitive part to be personalized. (Section 3.3)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.573,
+                0.892,
+                0.648
+            ],
+            "angle": 0,
+            "content": "- We propose a novel partial model personalization approach on ViT, FedPerfix, inspired by the connection between PFL and transfer learning. Specifically, we exploit Prefix plugins to capture client-specific knowledge for personalization. (Section 3.5)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.648,
+                0.892,
+                0.738
+            ],
+            "angle": 0,
+            "content": "- We conduct evaluations on CIFAR-100 [2], OrganAMINIST [40], and Office-home [38], which are across different domains, and degrees of data heterogeneity and achieve state-of-the-art performance compared with several competitive methods with lower resource requirements. (Section 4.2)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.498,
+                0.892,
+                0.738
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.754,
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+                0.77
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Personalized Federated Learning. Personalized Federated Learning focuses on training a client-specific model to achieve satisfying performance on each client instead of a unified global model to fit all the client data. In terms of the shared parameters, full model personalization keeps a separate personalized model for each client and designs different training objectives, where the global model is usually served as the regularization term [36, 17, 43, 19, 13, 26]."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4989"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.318
+            ],
+            "angle": 0,
+            "content": "The training objectives are designed with the idea of meta-learning [9], Moreau Envelopes [7], model interpolation [6], decoupling [4], etc. In contrast, partial model personalization focuses on personalizing some specific parameters inside a model. Some works simply keep these parameters, e.g., the classification head [1, 27], and the batch normalization layers [18] updated locally, while some works design additional parameters, e.g., prototypes for each class [36] or hypernetworks [34], to further personalized these parameters. Our proposed method focuses on the self-attention layers in a ViT and leverages plugins in transfer learning, enabling personalization without introducing significant overhead. Our experimental results demonstrate that FedPerfix outperforms existing methods in terms of both efficiency and effectiveness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.473,
+                0.566
+            ],
+            "angle": 0,
+            "content": "Vision Transformer. ViTs, a type of attention-based neural network, have shown superior performance in several fields compared to CNNs. In particular, ViTs have achieved state-of-the-art performance on various benchmarks [8, 22, 21]. ViTs employ self-attention mechanisms to learn the dependencies between different regions of an image and can capture long-range dependencies more effectively than CNNs. Despite their success, the use of ViTs in federated learning has not been as widely explored as CNNs. Qu et al. [32] studied the performance of ViT under conventional FL settings and found that simply replacing CNNs with ViTs can greatly accelerate convergence and reach a better global model, especially when dealing with heterogeneous data, demonstrating the potential of ViTs in FL. In this paper, we extend the application of ViT to PFL and propose a novel approach to better personalize a ViT."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Parameter-efficient Fine-tuning and Plugins. Finetuning is a popular technique for adapting a pre-trained model to a new task. However, fine-tuning can be computationally expensive, especially for large models [10, 41]. Parameter-efficient fine-tuning (PEFT) has been proposed to address this issue by selectively updating only a subset of the model's parameters or a few added parameters. These added parameters are plugged into the pre-trained model; therefore, they are summarised as \"Plugins\" in this paper. Although the location of the plugins for a transformer is various, including the input [15], the self-attention layer [20], and the feed-forward network [30], all of them can be trained to achieve comparable performance as fine-tuning without updating the weights of the pre-trained model. The plugins have also been applied to conventional FL to enable large pre-trained models and reduce the communication cost [35]. In the PFL, inspired by analogy from fine-tuning to the local training, the plugins can similarly be employed to personalize the representation from the global model to the local data distribution. Based on our empirical study, we choose prefixes [20] since the parameters are directly applied to the self-attention layer and propose our"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.63,
+                0.106
+            ],
+            "angle": 0,
+            "content": "method, FedPerfix."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.12,
+                0.593,
+                0.136
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.145,
+                0.704,
+                0.16
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.168,
+                0.895,
+                0.306
+            ],
+            "angle": 0,
+            "content": "We consider a classification problem in Computer Vision (CV). A dataset \\(\\mathcal{D} = \\{(x,y)|x\\in X,y\\in Y\\}\\) is separated on \\(N\\) clients, where \\(X\\) is the input space and \\(Y\\) is the label space. Data on each client is denoted as \\(\\mathcal{D}_i\\), and the distribution \\(P_{i}\\). The client distributions are not identical. Each client has access to \\(m_{i}\\) samples drawn IID from the distribution \\(P_{i}\\). The total number of samples is \\(M = \\sum_{i = 1}^{N}m_{i}\\). The hypothesis (model) on each client is noted as \\(h_i\\), and the expected loss on the \\(i^{\\mathrm{th}}\\) client is denoted as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.585,
+                0.316,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathcal {D} _ {i}} \\left(h _ {i}\\right) = \\mathbb {E} _ {(x, y) \\sim P _ {i}} [ \\ell (h (x), y) ] \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.344,
+                0.895,
+                0.42
+            ],
+            "angle": 0,
+            "content": "where \\(\\ell\\) is the loss function. Further, considering the partial model personalization, the parameters in each client model can be divided into two parts: global parameters \\(u\\) and local parameters \\(v_{i}\\), i.e., \\(h_i = u\\cup v_i\\). Specifically, \\(v_{i} = \\varnothing\\) indicates full model personalization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.42,
+                0.895,
+                0.535
+            ],
+            "angle": 0,
+            "content": "In each communication round \\( t \\in [T] \\), each client will receive \\( u^{(t-1)} \\) from the server and plug \\( v_i^{(t-1)} \\) into \\( u^{(t-1)} \\). Then, \\( u_i^{(t)}, v_i^{(t)} \\) are trained on the local data. After the local training, only the \\( u_i^{(t)} \\) of \\( K \\) sampled clients will be sent to the server and participate in the global aggregation. The sampled ratio (client participation rate) is denoted as \\( r = K/N \\). The global aggregation is formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.636,
+                0.545,
+                0.892,
+                0.587
+            ],
+            "angle": 0,
+            "content": "\\[\nu ^ {(t)} = \\sum_ {i = 1} ^ {K} \\alpha_ {i} u _ {i} ^ {(t)} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.597,
+                0.895,
+                0.735
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha_{i}\\) is the aggregation coefficient. Federated Averaging (FedAVG) is the most common aggregation algorithm where \\(\\alpha_{i} = \\frac{m_{i}}{M}\\). After \\(T\\) rounds of communication, each client model will receive a copy of the newest global parameters and plug its own local parameters into the global parameters. Then, the model will be evaluated on its own test data drawn IID from \\(P_{i}\\). To assess the overall performance, the mean and standard deviation of the Top-1 classification accuracy (Acc) for all clients will be reported."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.742,
+                0.892,
+                0.759
+            ],
+            "angle": 0,
+            "content": "3.2. Recap: Partial Model Personalization for CNN"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.894,
+                0.841
+            ],
+            "angle": 0,
+            "content": "In this section, we provide a brief recap of the approaches for partial model personalization in CNNs. We aim to leverage the insights and experiences gained from previous research to explore the strategy to personalize ViTs partially."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "FedRep [5] is a partial model personalization method that aims to preserve client-specific information while leveraging common knowledge in the earlier layers of a CNN by keeping the last classification layer and a few blocks local"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4990"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.472,
+                0.199
+            ],
+            "angle": 0,
+            "content": "Table 1. Sensitivity to data distribution of each type of layer in a Vision Transformer. The mean and standard deviation of the client's Top-1 Accuracy are reported for each type of layer (Stand-alone). Considering the classification head is the most sensitive type of layer, we also report the performance when a type of layer is kept updated locally along with the classification head (Combined). The overall performance is the mean of the standalone accuracy and combined accuracy."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.223,
+                0.47,
+                0.37
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Type</td><td>Stand-alone</td><td>Combined</td><td>Overall</td></tr><tr><td>All Local</td><td>34.74±9.36</td><td>-</td><td>-</td></tr><tr><td>All Global</td><td>23.29±11.31</td><td>-</td><td>-</td></tr><tr><td>Classification Head</td><td>44.42±7.98</td><td>-</td><td>-</td></tr><tr><td>Patch Embedding</td><td>27.61±10.02</td><td>43.45±8.69</td><td>35.53</td></tr><tr><td>Position Embedding</td><td>23.80±11.42</td><td>45.04±8.08</td><td>34.42</td></tr><tr><td>LayerNorm</td><td>23.94±11.19</td><td>44.60±7.96</td><td>34.27</td></tr><tr><td>Self-attention</td><td>42.95±8.68</td><td>44.63±8.67</td><td>43.79</td></tr><tr><td>MLP</td><td>42.53±8.82</td><td>42.63±8.84</td><td>42.58</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.444,
+                0.47,
+                0.656
+            ],
+            "angle": 0,
+            "content": "and aggregating the rest. FedBN [18] is a partial model personalization method that updates Batch normalization (BN) [14] layers locally while aggregating the rest of the model. This method leverages the local statistics of the BN layer to adapt to the data distribution of each client while maintaining a global representation of the model, achieving a better balance between personalization and global representation. FedBABU [27] focuses on personalizing the classification head to address the issue of inconsistent feature spaces among clients. Unlike FedRep, FedBABU freezes the classification head and fine-tunes it for several steps before evaluation. By doing so, FedBABU can mitigate the negative impact of classification head drift and encourage consistent feature spaces across all clients."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In summary, previous approaches to partial model personalization for CNNs provide valuable insights to answer the \"where to personalize\" question for ViTs: The layers to be personalized are usually designed with some engineering purpose, thus, are sensitive to data distribution. For instance, the normalization layers are designed to capture the statistical characters of the data, while classification heads are designed to map the feature to a predicted class. Building on these insights, we group the layers in ViT by their engineering purpose and conduct an empirical study to determine the layers in ViT that are the most sensitive to data distribution. We evaluated the performance of ViT while keeping some specific types of layers updated locally without aggregating with other clients. The results of our study are presented in Section 3.3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.091,
+                0.885,
+                0.108
+            ],
+            "angle": 0,
+            "content": "3.3. Empirical Study: Partial ViT Personalization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.117,
+                0.892,
+                0.389
+            ],
+            "angle": 0,
+            "content": "In a ViT, we consider the following layers as candidates to be personalized and evaluate their sensitivity to data distribution when they are updated locally: Patch Embedding layer converts the input image to a sequence of patches, then applies a linear projection to map each patch into an embedding vector. Position Embedding layer is responsible for injecting positional information into the sequence of patches produced by the patch embedding layer, allowing the model to capture the spatial arrangement of the image. LayerNorm is a normalization layer commonly used in ViT to normalize the feature maps across the channel dimension. Self-attention layer allows the model to attend to different regions of the input image and capture long-range dependencies between them. MLP layers, following the self-attention layer, enable the model to capture nonlinear relationships between the image patches. Classification Head applies a linear projection from the [CLS] token to a predicted class."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.393,
+                0.892,
+                0.497
+            ],
+            "angle": 0,
+            "content": "We perform experiments on CIFAR-100 with our default setting, which will be introduced in Section 4.1. We keep the specified type of layer updated locally and report the mean and standard deviation of the Top-1 Accuracy across all clients as the metrics to indicate the sensitivity to data distribution. The result is shown in the second column of Table 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.502,
+                0.892,
+                0.698
+            ],
+            "angle": 0,
+            "content": "From the table, we can draw several insights. Keeping all layers local yields better performance than aggregating all layers. This suggests that aggregation of heterogeneous data may have a negative impact on some layers. Meanwhile, keeping each type of layer updated locally allows for greater adaptability to each client's data, leading to different degrees of improvement compared with keeping every layer global. Among all types of layers, the classification head is the most sensitive to data distribution, leading to the highest stand-alone performance, which is as expected. Except for the classification head, self-attention layer is more sensitive to data distribution than other components, showing a higher standard-alone performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.701,
+                0.892,
+                0.807
+            ],
+            "angle": 0,
+            "content": "Considering the vital importance of the classification head, we also reported the combined performance when a type of layer is kept updated locally along with the classification head, as shown in the third column of Table 1. To decide the most sensitive layers to be personalized, we averaged the performance under the two settings as the overall performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Based on the overall performance, personalizing the self-attention and classification head is one possible answer to the question of where to personalize. Besides, a vanilla baseline to keep the self-attention layers and classification head updated locally is proposed, which is referred to as Vanilla Attention as described in Fig. 2 (a)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4991"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.09,
+                0.446,
+                0.277
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.451,
+                0.091,
+                0.895,
+                0.273
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.283,
+                0.893,
+                0.354
+            ],
+            "angle": 0,
+            "content": "Figure 2. Several designs to personalize the self-attention layer in a ViT. SDP is short for Scaled Dot Product, the red part indicates the local parameters, the blue part indicates the global parameters and the gray parts are vectors or modules with no learnable parameter. (a) Vanilla attention simply keeps the self-attention and classification updated locally. (b) Vanilla prefix-tuning only keeps the prefixes updated locally and aggregates the original self-attention layer. (c) FedPerfix uses a local adapter to generate the prefixes and aggregates the original self-attention layer. The adapter is composed of a scale-down, an activation, and a scale-up layer."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.377,
+                0.427,
+                0.394
+            ],
+            "angle": 0,
+            "content": "3.4. Proposed Baseline: Vanilla Prefix-tuning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.416,
+                0.471,
+                0.537
+            ],
+            "angle": 0,
+            "content": "Building upon the insights about where to personalize gained in the previous section, we move to the next question about how to personalize the selected layers. As obtained from our empirical study, Vanilla Attention is a baseline to personalize the self-attention layer by completely keeping the self-attention updated locally. However, it will also prevent it from learning general information for the global model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.553,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "As explained in Section 1, the plugins can be trained on the local data to capture the client-specific knowledge as a personalization module. There are three widely used plugins for ViTs: a) Prompts that are learnable embeddings appended to the inputs, b) Adapters that are inserted into the MLP layers, and c) Prefixes that are appended to the key and value matrix of the self-attention layer. Given that the self-attention layer is one of the most sensitive layers, It is plausible that the Prefixes integrated nearest to the self-attention layer are capable of capturing the most relevant client-specific information pertaining to the self-attention mechanism. Besides, we further compare the effectiveness of all three plugins and discuss it in Section 5.3. Therefore, we select Prefixes as our personalization module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Specifically, learnable prefixes are appended to the self-attention layer and kept updated locally on the client. Meanwhile, the original self-attention layer is shared across all clients as normal to capture global dependencies. We refer to this approach as Vanilla Prefix-tuning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "An illustration of how Prefixes cooperate with the self-attention layer is shown in Fig. 2 (b). Besides, we formulate"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.378,
+                0.838,
+                0.394
+            ],
+            "angle": 0,
+            "content": "the output of one head of the self-attention layer as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.587,
+                0.411,
+                0.804,
+                0.431
+            ],
+            "angle": 0,
+            "content": "\\[\nh e a d _ {i} = A t t e n t i o n \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {q} ^ {(i)}\\right),\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.648,
+                0.433,
+                0.891,
+                0.453
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {Z} ^ {l - 1} \\left[ \\boldsymbol {P} _ {k}, \\boldsymbol {W} _ {k} ^ {(i)} \\right], \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.648,
+                0.455,
+                0.771,
+                0.474
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left. \\boldsymbol {Z} ^ {l - 1} \\left[ \\boldsymbol {P} _ {v}, \\boldsymbol {W} _ {v} ^ {(i)} \\right]\\right))\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.493,
+                0.893,
+                0.543
+            ],
+            "angle": 0,
+            "content": "where \\( Z^{l-1} \\) is the output from the last layer, \\( P_k \\) and \\( P_v \\) are prefixes, \\( W_q^{(i)}, W_k^{(i)} \\), and \\( W_v^{(i)} \\) are the parameters in the self-attention layer, and [,] is the concatenate operation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.561,
+                0.768,
+                0.577
+            ],
+            "angle": 0,
+            "content": "3.5. FedPerfix: Stabilize the Prefix"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.588,
+                0.892,
+                0.799
+            ],
+            "angle": 0,
+            "content": "In Vanilla Prefix-tuning, the prefixes are randomly initialized, which can result in unstable performance when initialized with different weights. We later conduct an experiment to demonstrate such instability in Section 5.3 when Vanilla Prefix-tuning is initialized with different weights. To address this issue, we draw inspiration from the parallel attention design [41], which uses adapters to stabilize the prefixes. Similarly, we propose to use adapters in Vanilla Prefix-tuning to stabilize the prefix initialization. Specifically, we add a parallel adapter to prepare the prefixes for each layer, as shown in Fig. 2. Meanwhile, we add a hyperparameter \\( s \\) to control the efficiency of the adapter. Following the design of parallel attention, the prefixes are generated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.818,
+                0.892,
+                0.836
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {P} _ {k}, \\boldsymbol {P} _ {v} = \\operatorname {A d a p t e r} \\left(\\boldsymbol {Z} ^ {l - 1}\\right) = \\operatorname {T a n h} \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {\\text {d o w n}}\\right) \\boldsymbol {W} _ {u p} \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathrm{Tanh}\\) is the activation function, \\(W_{down}\\) and \\(W_{up}\\) are parameters of the scaling layers of the adapter. As a result, the output of one head of the self-attention layer with paral"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4992"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.419,
+                0.106
+            ],
+            "angle": 0,
+            "content": "IeI attention is shown in Fig. 2(c) and formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.165,
+                0.117,
+                0.382,
+                0.137
+            ],
+            "angle": 0,
+            "content": "\\[\nh e a d _ {i} = A t t e n t i o n \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {q} ^ {(i)}\\right),\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.225,
+                0.139,
+                0.469,
+                0.16
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {Z} ^ {l - 1} \\left[ s \\boldsymbol {P} _ {k}, \\boldsymbol {W} _ {k} ^ {(i)} \\right], \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.225,
+                0.162,
+                0.353,
+                0.182
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {Z} ^ {l - 1} [ s \\boldsymbol {P} _ {v}, \\boldsymbol {W} _ {v} ^ {(i)} ]).\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.191,
+                0.47,
+                0.31
+            ],
+            "angle": 0,
+            "content": "In conclusion, FedPerfix is proposed as a novel approach to transfer the information from the aggregated self-attention layer to fit the local data better, leveraging the plugins in transfer learning. The local prefixes are trained for personalization, while the global self-attention layer captures global dependencies. Therefore, FedPerfix provides a promising solution to address the question of how to perform personalization for ViTs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.325,
+                0.201,
+                0.342
+            ],
+            "angle": 0,
+            "content": "4. Experiment"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.349,
+                0.262,
+                0.365
+            ],
+            "angle": 0,
+            "content": "4.1. Experiment Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.373,
+                0.47,
+                0.597
+            ],
+            "angle": 0,
+            "content": "Dataset. We use three popular datasets to evaluate the performance: CIFAR-100 [16], OrganAMNIST [40], and Office-Home [38]. CIFAR-100 is a widely-used image classification dataset consisting of 50,000 RGB images across 100 classes. Office-Home is a domain adaptation dataset for object recognition tasks, which contains 15,500 images across 65 categories, captured from four different domains: Artistic images, Clipart, Product images, and Real-World images. OrganAMNIST is a medical image classification dataset that includes 58,850 gray-scale images of organs and tissues from human anatomy. The images are classified into 11 different classes. These datasets are chosen to evaluate the performance in various scenarios, including different data scales, domains, and the number of classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Federated learning settings. We conduct \\( T = 50 \\) communication rounds with each local training consisting of 10 epochs. To account for the various factors that can affect federated learning performance, we adjust the default settings for each dataset to focus on different scenarios with varying degrees of data heterogeneity of label skew and concept skew. For CIFAR-100, which has a relatively high number of samples and classes, we simulate a federated learning environment with \\( N = 64 \\) clients using a Dirichlet distribution with \\( \\alpha = 0.1 \\) and sampling \\( K = 8 \\) clients with a ratio \\( r = 0.125 \\) for each round. For OrganAMNIST, which has a similar number of samples but fewer classes than CIFAR-100, we partition the data using a Dirichlet distribution with a larger \\( \\alpha = 0.5 \\) and apply the same client settings as CIFAR-100. As for Office-Home, which has fewer samples captured from 4 different domains, we focus on concept skew by partitioning the data from each domain into four different clients using a Dirichlet distribution with \\( \\alpha = 1.0 \\), resulting in a total of \\( N = 16 \\) clients. In each communication round, we randomly sample \\( K = 4 \\) clients"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "from any domain with a ratio \\( r = 0.25 \\). A visualization of the data partitioning is provided in Supplementary A.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.123,
+                0.892,
+                0.5
+            ],
+            "angle": 0,
+            "content": "Model Architecture and Baselines. We choose ViT-Small (ViT-S) [8] with a patch size of 16 and an image size of 224 as our model for evaluation. We compare our proposed FedPerfix method against a range of baseline methods, including widely used approaches like FedAVG and local training without aggregation (Local). We also compare our method against advanced full model personalization methods, namely APFL [6] and Per-FedAVG [9], and three partial model personalization methods, namely FedBN, FedRep, and FedBABU. Besides, we also include the performance of Vanilla Attention, which keeps the self-attention layer and the classification head updated locally, as a reference. APFL adapts the global and local model through an adaptive mixture coefficient, while Per-FedAVG employs meta-learning to improve the global model. These methods are model-agnostic and can be applied to ViTs. FedBN keeps the batch normalization layer updated locally and aggregates the remaining layers in the server with FedAVG. To adapt it to ViTs, we replace the batch normalization layer with the layer normalization layer. FedRep keeps the classification head updated locally while aggregating the other layers in the server. FedBABU freezes the classification head and aggregates the remaining layers in the server, then fine-tunes the classification head on the local data for one step before the evaluation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.501,
+                0.892,
+                0.59
+            ],
+            "angle": 0,
+            "content": "Evaluation Metrics. We report the final mean and standard deviation of Top-1 accuracy among all clients after all communication rounds finish as the evaluation metrics. Besides, to evaluate the feasibility of the methods, an analysis of storage, computation, and communication costs is reported in Section 4.4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.593,
+                0.892,
+                0.759
+            ],
+            "angle": 0,
+            "content": "Implement Details. All hyperparameters in each method are tuned as optimal in a range. Each model is optimized with the SGD [33] optimizer with the optimal learning rate, which is 0.01 for most methods. The server and all the clients are simulated in one machine, and we resize the images in all datasets as \\(224 \\times 224\\) RGB images to fit the model and set the batch size of the client data as 64. The model is implemented from the TIMM [39] library. All the experiments are implemented in Pytorch [28] and performed on 4 Nvidia A5000 GPUs. More details are provided in Supplementary A.2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.771,
+                0.724,
+                0.787
+            ],
+            "angle": 0,
+            "content": "4.2. Performance Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Based on the evaluation results presented in Table 2, several insights can be drawn regarding the performance of the compared methods. It can be observed that FedAVG performs worse than Local when facing a large label skew, i.e., on CIFAR-100. This indicates the importance of addressing data heterogeneity in federated learning scenarios. However, when the label skew is not that extreme, the informa"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4993"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.895,
+                0.119
+            ],
+            "angle": 0,
+            "content": "Table 2. Performance and required resources for each method. The mean and standard deviation of the Top-1 Accuracy among all clients are reported. The bold style indicates the best performance in each dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.139,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>CIFAR-100</td><td>Performance OrganAMNIST</td><td>Office-Home</td><td>Storage (# Params)</td><td>Computation (FLOPs)</td><td>Communication (# Params)</td></tr><tr><td>FedAvg</td><td>23.29±11.31</td><td>87.31±5.98</td><td>21.47±6.24</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.03M (100%)</td></tr><tr><td>Local</td><td>34.74±9.36</td><td>78.26±11.07</td><td>20.39±7.26</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>0 (0%)</td></tr><tr><td>APFL</td><td>44.88±10.50</td><td>89.74±5.83</td><td>24.23±7.02</td><td>42.06M (200%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>Per-FedAVG</td><td>33.86±8.01</td><td>82.81±7.13</td><td>17.09±4.83</td><td>21.03M (100%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>FedBN</td><td>23.94±11.19</td><td>87.63±5.78</td><td>21.25±5.89</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.01M (100%)</td></tr><tr><td>FedBABU</td><td>41.41±8.87</td><td>88.38±7.16</td><td>19.50±7.71</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>FedRep</td><td>44.42±7.80</td><td>92.63±3.77</td><td>23.67±5.97</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>Vanilla Attention</td><td>44.63±8.67</td><td>88.90±5.87</td><td>22.55±6.37</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>13.89M (66%)</td></tr><tr><td>FedPerfix (ours)</td><td>48.10±7.76</td><td>93.17±3.51</td><td>24.38±8.47</td><td>24.42M (116%)</td><td>66.58M (101%)</td><td>20.66M (98%)</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.369,
+                0.471,
+                0.416
+            ],
+            "angle": 0,
+            "content": "tion gathered from the global aggregation can alleviate the overfitting due to few training samples on the client, leading to higher performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.431,
+                0.471,
+                0.598
+            ],
+            "angle": 0,
+            "content": "In addition, it is worth noting that the methods that focus on the global objective instead of information transferring from the global to the client model, such as Per-FedAVG, achieve better performance than FedAVG but still show inferior performance compared to Local when facing extreme label skew or concept skew, i.e., CIFAR-100 and OfficeHome. This suggests that direct modification of the global objective may not always be the most effective way when using ViTs. Performing meta-learning on relatively small-size client data for a relatively large ViT is a challenging task, which limits the effectiveness of Per-FedAVG."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.613,
+                0.47,
+                0.855
+            ],
+            "angle": 0,
+            "content": "On the other hand, how to leverage the information provided in the global model is crucial for partial model personalization. The layer normalization version of FedBN shows little impact on the performance, leading to a negligible improvement based on FedAVG. However, APFL, FedRep, Vanilla Attention, FedBABU, and FedPerfix find a more suitable way to transfer the information from the global model, leading to superior performance than other methods. Consistent with the conclusion we draw from the empirical study, FedRep, FedBABU, and Vanilla Attention personalized the sensitive parts in ViT, thus outperforming FedAVG and Local by a significant margin. As an extension, APFL and our method, FedPerfix, balance the information between the local and global models in a proper manner, leading to the highest two performances considering the performance across all three datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Surprisingly, we find that there is a connection between FedPerfix and APFL. Equation 3, which shows the output"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.369,
+                0.842,
+                0.384
+            ],
+            "angle": 0,
+            "content": "of a self-attention with Prefixes, can be rewritten as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.526,
+                0.391,
+                0.89,
+                0.467
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} h e a d (x) = (1 - \\lambda (x)) \\underbrace {A t t n (x \\boldsymbol {W} _ {q} , x \\boldsymbol {W} _ {k} , x \\boldsymbol {W} _ {v})} _ {\\text {a g g r e g a t e d a t t e n t i o n}} \\\\ + \\lambda (x) \\underbrace {A t t n \\left(x \\boldsymbol {W} _ {q} , x \\boldsymbol {P} _ {k} , x \\boldsymbol {P} _ {v}\\right)} _ {\\text {p e r s o n a l i z e d a t t e n t i o n}} \\tag {6} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.477,
+                0.893,
+                0.75
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda(x)\\) is a scalar representing the normalized attention weights on the prefixes [10]. More details are provided in Supplementary B. It reveals that the local prefixes are learned as a mixture coefficient between the aggregated attention from the global model and the personalized attention from the prefixes. The high performance of both APFL and FedPerfix indicates the effectiveness of a mixture between the local and global models in PFL. Compared with APFL, FedPerfix only mixed the sensitive self-attention layers instead of the entire model, leading to higher performance. Meanwhile, FedPerfix trains the Prefix, which can be considered as the mixture coefficient, and the model simultaneously, while APFL needs separate training for the personalized model. Therefore, FedPerfix can achieve higher performance with fewer storage, computation, and communication resources. Furthermore, we provide a more detailed resource requirements analysis of each method in the following Section 4.4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.757,
+                0.727,
+                0.772
+            ],
+            "angle": 0,
+            "content": "4.3. Client-wise Performance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In Fig. 3, we present a density plot depicting the performance gain of each method in comparison to Local. Notably, FedPerfix demonstrates an average performance gain of over \\(10\\%\\), surpassing all other methods. Moreover, FedPerfix outperforms all other methods by achieving up to \\(30\\%\\) performance gains for certain clients. Conversely, some clients experience performance degradation under other methods, while FedPerfix ensures performance"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4994"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.087,
+                0.09,
+                0.468,
+                0.257
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.261,
+                0.47,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Figure 3. Client-wise performance for each method on CIFAR-100. Density of the accuracy gain compared with Local training is plotted. FedPerfix provides highest upper and lower bounds among all the methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.343,
+                0.47,
+                0.418
+            ],
+            "angle": 0,
+            "content": "gains for nearly all clients. In conclusion, FedPerfix shows a higher upper bound while maintaining a high lower bound, which will encourage more clients to involve in the federated training with performance-gaining guarantees for almost all clients."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.429,
+                0.366,
+                0.445
+            ],
+            "angle": 0,
+            "content": "4.4. Resource Requirements Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.452,
+                0.469,
+                0.543
+            ],
+            "angle": 0,
+            "content": "In federated learning, it is crucial to consider the practicality of each method in terms of the storage, computation, and communication resources required by each participating client. As such, it is imperative to analyze the resource demands of each approach to determine its feasibility in realistic federated settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.543,
+                0.469,
+                0.693
+            ],
+            "angle": 0,
+            "content": "We present a resource analysis of the evaluated methods, taking into account the storage, computation, and communication demands, which are crucial aspects in practical federated learning scenarios where clients may have limited resources. Table 2 reports the parameter size required to store the model, the FLOPs needed for training, and the parameter size required for communication. Notably, FedPerfix achieves superior performance compared to other methods with slightly more resources for storage and computation but fewer resources for communication."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.695,
+                0.469,
+                0.801
+            ],
+            "angle": 0,
+            "content": "Overall, our proposed FedPerfix approach demonstrates the highest efficiency in terms of achieving superior performance while utilizing fewer storage, computation, and communication resources compared to other methods. These findings highlight the potential of our approach to effectively address the resource constraints often encountered in realistic federated learning scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.815,
+                0.229,
+                0.833
+            ],
+            "angle": 0,
+            "content": "5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we conduct an ablation study on the CIFAR-100 dataset to evaluate the robustness of FedPerfix under various federated learning settings and to investigate FedPerfix with different designs."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.088,
+                0.874,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 3. Performance on CIFAR-100 with different backbones."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.546,
+                0.111,
+                0.849,
+                0.264
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>ResNet50</td><td>ViT-Small</td></tr><tr><td>FedAVG</td><td>17.87±13.16</td><td>23.29±11.31</td></tr><tr><td>Local</td><td>28.34±9.83</td><td>34.74±9.36</td></tr><tr><td>APFL</td><td>30.71±9.89</td><td>44.88±10.50</td></tr><tr><td>Per-FedAVG</td><td>28.82±8.53</td><td>33.86±8.01</td></tr><tr><td>FedBN</td><td>19.33±10.25</td><td>23.94±11.19</td></tr><tr><td>FedBABU</td><td>24.56±7.82</td><td>41.41±8.87</td></tr><tr><td>FedRep</td><td>39.52±10.92</td><td>44.42±7.80</td></tr><tr><td>FedPerfix</td><td>-</td><td>48.10±7.76</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.301,
+                0.892,
+                0.317
+            ],
+            "angle": 0,
+            "content": "5.1. Performance Comparison with CNN Backbone"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.324,
+                0.892,
+                0.475
+            ],
+            "angle": 0,
+            "content": "To further demonstrate the motivation behind our work, i.e., addressing PFL with ViT, we conduct experiments to compare ViT and CNN as different backbones for the same set of methods. Given that the comparison methods are originally designed with a CNN backbone, we conduct experiments on CIFAR-100 with a CNN backbone as a reference to investigate the impact of replacing the CNNs with ViTs in these methods. To fairly compare the performance, we choose ResNet50 [11] as the CNN backbone due to its similar parameter size (24.37M) to ViT-Small [8] (21.03M)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.475,
+                0.892,
+                0.581
+            ],
+            "angle": 0,
+            "content": "The result is shown in Table 3. Simply replacing the CNN backbone with the ViT backbone significantly improves performance for each method without additional operations. It suggests that the advantages of ViTs that demonstrated superior performance compared to CNNs in centralized settings may also translate to personalized federated learning scenarios."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.581,
+                0.892,
+                0.747
+            ],
+            "angle": 0,
+            "content": "The success of ViTs in existing methods highlights their potential for personalized federated learning. However, there is a lack of approaches specifically designed for ViTs. To address this gap, we propose FedPerfix, which is tailored for ViTs and focuses on personalizing the sensitive parts of the network. By doing so, FedPerfix further improves performance compared to existing methods that incorporate ViTs. Our approach fills an important research gap and suggests that there is still much to be gained from exploring the unique properties of ViTs for personalized federated learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.757,
+                0.698,
+                0.773
+            ],
+            "angle": 0,
+            "content": "5.2. Different FL Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In order to assess the robustness of FedPerfix in more challenging federated learning scenarios, we conduct experiments that involve varying the number of clients with fewer samples per client and a lower client participation rate. We also compare the performance of FedPerfix with other competitive methods and report the results in Table 4. Our experimental results demonstrate that FedPerfix exhibits robust performance in different federated learning settings,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4995"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.47,
+                0.116
+            ],
+            "angle": 0,
+            "content": "Table 4. Performance on CIFAR-100 under different federated learning settings."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.127,
+                0.466,
+                0.223
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">N = 64</td><td colspan=\"2\">N = 128</td></tr><tr><td>r = 6.25%</td><td>r = 12.5%</td><td>r = 6.25%</td><td>r = 12.5%</td></tr><tr><td>FedAvg</td><td>19.76±9.35</td><td>23.29±11.31</td><td>19.64±10.01</td><td>23.29±11.81</td></tr><tr><td>Local</td><td>32.35±11.64</td><td>34.74±9.36</td><td>31.79±12.00</td><td>36.03±9.57</td></tr><tr><td>APFL</td><td>42.55±13.51</td><td>44.88±10.50</td><td>41.64±12.77</td><td>43.92±9.40</td></tr><tr><td>FedRep</td><td>35.72±10.33</td><td>44.42±7.80</td><td>35.88±9.59</td><td>44.70±8.40</td></tr><tr><td>FedPerfix</td><td>43.80±11.56</td><td>48.10±7.76</td><td>43.96±10.42</td><td>46.96±9.00</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.261,
+                0.469,
+                0.307
+            ],
+            "angle": 0,
+            "content": "outperforming all other methods consistently. Thus, FedPerfix can be considered a reliable solution for extreme federated learning scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.317,
+                0.311,
+                0.334
+            ],
+            "angle": 0,
+            "content": "5.3. Investigation of FedPerfix"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.341,
+                0.469,
+                0.386
+            ],
+            "angle": 0,
+            "content": "In this subsection, we investigate the impact of the model size of FedPerfix and verify its effectiveness compared with other designs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.386,
+                0.469,
+                0.673
+            ],
+            "angle": 0,
+            "content": "Impact of Model Size. The model size is a crucial factor in federated learning, as it determines the resource requirements for storage, computation, and communication. To examine the impact of model size on the performance of FedPerfix, we conducted experiments with three different ViT backbones: ViT-Tiny, ViT-Small (Default), and ViT-Base. Additionally, we included the results of the baselines and two competitive methods as a reference. As shown in Table 5, FedPerfix still yields superior performance with different model sizes. Besides, the larger models generally performed better, with ViT-Base achieving the highest performance for each method. However, we note that the performance improvement decreases as the model size increases, suggesting a potential trade-off between model size and performance. This finding highlights the importance of selecting an appropriate model size to achieve the optimal balance between performance and resource requirements, particularly in resource-constrained environments where storage and computation resources are limited."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.673,
+                0.469,
+                0.839
+            ],
+            "angle": 0,
+            "content": "FedPerfix vs. Vanilla Prefix-tuning. As mentioned in Section 3.5, the initialization of the Prefixes will affect the performance. To show the effectiveness of the parallel attention design in FedPerfix, we conduct experiments with Vanilla Prefix-tuning under two different initialization, initialized with zero (Prefix-Z) and random initialization (Prefix-R). Then, we compare the results with FedPerfix. The result is shown in Table 6. As expected, the prefixes generated from the parallel attention yield better performance than the other two manually initialized prefixes, highlighting the effectiveness of the parallel attention design in FedPerfix."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.84,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "FedPerfix vs. Prompts & Adapters. Prompts and adapters are also popular plugins that are widely used. To verify whether FedPerfix is the most effective among all families of the plugins, we also apply Prompts and Adapters"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.088,
+                0.881,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 5. Performance on CIFAR-100 with different model sizes."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.111,
+                0.889,
+                0.218
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>ViT-Tiny</td><td>ViT-Small</td><td>ViT-Base</td></tr><tr><td>FedAVG</td><td>19.56±10.27</td><td>23.29±11.31</td><td>24.82±11.53</td></tr><tr><td>Local</td><td>33.73±9.20</td><td>34.74±9.36</td><td>38.93±10.08</td></tr><tr><td>APFL</td><td>37.66±10.04</td><td>44.88±10.50</td><td>47.57±9.57</td></tr><tr><td>FedRep</td><td>41.58±7.19</td><td>44.42±7.80</td><td>44.34±8.35</td></tr><tr><td>FedPerfix</td><td>44.71±8.47</td><td>48.10±7.76</td><td>48.40±8.18</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.227,
+                0.892,
+                0.453
+            ],
+            "angle": 0,
+            "content": "to personalized federated learning. Specifically, we append several trainable Prompts to the input embeddings and keep them updated locally as the implementation of Prompt-tuning [15]. Meanwhile, we add Adapters to the MLP layers as the implementation of Adatper-tuning [30]. The results are shown in Table 6. Adding personalized Prompts doesn't improve the performance compared with simply keeping the classification head updated locally, indicating that the transformation to the input is not effective in PFL. However, adding Adapters to the MLP layers can also lead to a promising result as FedPerfix. Recap the result of our empirical study shown in Table 1, MLP layers are also sensitive to data distribution in a ViT. We note that as another instance to show the effectiveness of adding plugins to the sensitive parts of a ViT in PFL."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.464,
+                0.892,
+                0.505
+            ],
+            "angle": 0,
+            "content": "Table 6. Performance of different designs on CIFAR-100. Prefix-Z and Prefix-R mean vanilla prefix-tuning with zero and random initialization."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.53,
+                0.892,
+                0.57
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>FedPerfix</td><td>Prefix-Z</td><td>Prefix-R</td><td>Prompts</td><td>Adapters</td></tr><tr><td>48.10±7.76</td><td>47.37±8.47</td><td>46.98±8.10</td><td>44.19±8.13</td><td>47.99±8.59</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.611,
+                0.619,
+                0.627
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.636,
+                0.892,
+                0.832
+            ],
+            "angle": 0,
+            "content": "In this work, we studied two research questions of where and how to personalize a ViT in federated learning. We conducted an empirical study to reveal that the self-attention and classification layers are the most sensitive layers for personalization. Based on that, we proposed FedPerfix, a novel method that introduces Prefixes with parallel attention to personalize the self-attention layers. Through extensive experiments on various datasets with different degrees of data heterogeneity, we demonstrated that FedPerfix achieves state-of-the-art performance while also reducing resource requirements. Our work focuses on ViTs and represents a shift in attention from the extensively researched CNNs, serving as inspiration for further investigation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.845,
+                0.681,
+                0.863
+            ],
+            "angle": 0,
+            "content": "7. Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This work is partially supported by the NSF/Intel Partnership on MLWiNS under Grant No. 2003198."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4996"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+# FedPerfix: Towards Partial Model Personalization of Vision Transformers in Federated Learning
+
+Guangyu Sun<sup>1</sup>, Matias Mendieta<sup>1</sup>, Jun Luo<sup>2</sup>, Shandong Wu<sup>3</sup>, Chen Chen<sup>1</sup>
+
+<sup>1</sup>Center for Research in Computer Vision, University of Central Florida, USA  
+<sup>2</sup>Intelligent Systems Program, University of Pittsburgh, USA  
+<sup>3</sup>Department of Radiology, Biomedical Informatics, and Bioengineering, University of Pittsburgh, USA  
+{guangyu.sun, matias.mendieta}@ucf.edu; jul117@pitt.edu; wus3@upmc.edu; chen.chen@crcv.ucf.edu
+
+# Abstract
+
+Personalized Federated Learning (PFL) represents a promising solution for decentralized learning in heterogeneous data environments. Partial model personalization has been proposed to improve the efficiency of PFL by selectively updating local model parameters instead of aggregating all of them. However, previous work on partial model personalization has mainly focused on Convolutional Neural Networks (CNNs), leaving a gap in understanding how it can be applied to other popular models such as Vision Transformers (ViTs). In this work, we investigate where and how to partially personalize a ViT model. Specifically, we empirically evaluate the sensitivity to data distribution of each type of layer. Based on the insights that the self-attention layer and the classification head are the most sensitive parts of a ViT, we propose a novel approach called FedPerfix, which leverages plugins to transfer information from the aggregated model to the local client as a personalization. Finally, we evaluate the proposed approach on CIFAR-100, OrganAM-NIST, and Office-Home datasets and demonstrate its effectiveness in improving the model's performance compared to several advanced PFL methods. Code is available at https://github.com/imguangyu/FedPerfix
+
+# 1. Introduction
+
+Federated learning (FL) [25] has emerged as a promising method for training machine learning models on decentralized data without requiring direct data sharing. However, data heterogeneity among participating clients can present a significant challenge. Due to the various circumstances of the clients, the data across the clients can
+
+be non-independent and non-identically distributed (non-IID). Therefore, achieving satisfactory performance using a one-model-fits-all approach is difficult, and personalized models are often needed to achieve the best results. This has inspired the study of Personalized Federated Learning (PFL), where the focus is shifted from the performance of the global model on the server to the local models on the clients.
+
+In the context of personalized federated learning, previous literature has explored two main approaches: full model personalization [9, 6, 23] and partial model personalization [31, 27, 18, 5, 1]. Full model personalization involves maintaining a separate local model for each client and updating it based on a joint objective, while partial model personalization aims to personalize only a subset of the model parameters. A convergence analysis [31] suggests that partial model personalization can achieve most of the benefits of full model personalization with fewer shared parameters, offering advantages in terms of computation, communication, and privacy to enable the deployment of larger models on the clients.
+
+However, recent literature shows that where and how to perform partial model personalization has a high correlation to the model architectures and the tasks [31], which requires further study when applied to a new architecture. Despite the multitude of approaches proposed in the literature, the majority of methods have only been evaluated on Convolutional Neural Networks (CNNs). Meanwhile, Vision Transformers (ViTs) [8] have demonstrated superior performance compared to CNNs in several tasks, such as image classification [37] and object detection [42, 3], making them an attractive option for personalized federated learning. However, to the best of our knowledge, the application of ViT in the federated learning community has received limited at
+
+tention in the existing literature [32]. Given the advantages of ViT shown under centralized training, it is reasonable to expect that these benefits can also be realized in PFL by offering a more robust model for improved performance on the clients. Therefore, in this work, we investigate where and how to partially personalize a ViT model.
+
+Drawing from previous research on CNNs, layers that serve specific engineering purposes, such as feature extraction, normalization, or classification, have been identified as suitable candidates for partial model personalization [27, 18, 5]. These layers might have a higher sensitivity to the distribution of the training data. Therefore, aggregating the model weights trained from different data distributions may result in an inaccurate feature, while keeping them updated locally can gain a better feature for the local data distribution. Similarly, we select some candidates from ViT and conduct an empirical study to investigate the sensitivity of each type of layer. Specifically, we quantitatively evaluate the impact of keeping certain layers updated locally without aggregation with other clients. This evaluation shows that the self-attention layers and the classification head have a higher sensitivity than other layers, providing insights about where to personalize.
+
+To personalize the sensitive parts, one intuitive approach is to keep them completely local. However, the global aggregation has shown the capability to provide a more general global model than local models [24]. Completely preventing the sharing with the global model will severely hinder the potential benefits of leveraging general knowledge from the aggregated global model. Therefore, we desire to train a personalization module to bridge the general knowledge and the client-specific knowledge.
+
+As existing works in transfer learning suggest, the same pre-trained model can be transferred to different downstream data by adding different tiny architectures [30, 15, 20, 12]. We refer to these tiny architectures as plugins since they are small-sized parameters plugged into the pretrained model. These plugins are trained while the weights of the pre-trained model are frozen. The plugged model can achieve comparable performance as the fully fine-tuned model [29]. Since the model can maintain the same level of performance without changing the weights of the pretrained model, the downstream-specific knowledge is captured by the plugins. Therefore, the plugins show the capability to personalize the same model to satisfy different downstream data. In federated learning, we can consider the aggregated model as an inferior version of the "pre-trained" model, and the data on different clients as the downstream data, as shown in Fig. 1. With this perspective, we can therefore exploit the capability of the plugins in the federated learning context to capture client-specific knowledge for personalization.
+
+Therefore, we select and adapt a specific family of plu
+
+![](images/4c5b523e57c066de4c40d87c11cd53ad1b0f2ee48e65d345b28783d66ba42ee1.jpg)  
+Personalized Federated Learning  
+Figure 1. Analogy between transfer learning and personalized federated learning. A pre-trained model can be transferred to different downstream data with different plugins. In personalized federated learning, we are seeking different personalization modules (PM) to transfer the aggregated model to different client data.
+
+gin, Prefixes, to personalize the self-attention layer and propose a novel approach FedPerfix, short for Federated Personalized Prefix-tuning.
+
+The main contributions of this paper are as follows:
+
+- We perform an empirical study to reveal the sensitivity to data distribution of each type of layer in a ViT for PFL and locate the self-attention layer and classification head as the sensitive part to be personalized. (Section 3.3)  
+- We propose a novel partial model personalization approach on ViT, FedPerfix, inspired by the connection between PFL and transfer learning. Specifically, we exploit Prefix plugins to capture client-specific knowledge for personalization. (Section 3.5)  
+- We conduct evaluations on CIFAR-100 [2], OrganAMINIST [40], and Office-home [38], which are across different domains, and degrees of data heterogeneity and achieve state-of-the-art performance compared with several competitive methods with lower resource requirements. (Section 4.2)
+
+# 2. Related Work
+
+Personalized Federated Learning. Personalized Federated Learning focuses on training a client-specific model to achieve satisfying performance on each client instead of a unified global model to fit all the client data. In terms of the shared parameters, full model personalization keeps a separate personalized model for each client and designs different training objectives, where the global model is usually served as the regularization term [36, 17, 43, 19, 13, 26].
+
+The training objectives are designed with the idea of meta-learning [9], Moreau Envelopes [7], model interpolation [6], decoupling [4], etc. In contrast, partial model personalization focuses on personalizing some specific parameters inside a model. Some works simply keep these parameters, e.g., the classification head [1, 27], and the batch normalization layers [18] updated locally, while some works design additional parameters, e.g., prototypes for each class [36] or hypernetworks [34], to further personalized these parameters. Our proposed method focuses on the self-attention layers in a ViT and leverages plugins in transfer learning, enabling personalization without introducing significant overhead. Our experimental results demonstrate that FedPerfix outperforms existing methods in terms of both efficiency and effectiveness.
+
+Vision Transformer. ViTs, a type of attention-based neural network, have shown superior performance in several fields compared to CNNs. In particular, ViTs have achieved state-of-the-art performance on various benchmarks [8, 22, 21]. ViTs employ self-attention mechanisms to learn the dependencies between different regions of an image and can capture long-range dependencies more effectively than CNNs. Despite their success, the use of ViTs in federated learning has not been as widely explored as CNNs. Qu et al. [32] studied the performance of ViT under conventional FL settings and found that simply replacing CNNs with ViTs can greatly accelerate convergence and reach a better global model, especially when dealing with heterogeneous data, demonstrating the potential of ViTs in FL. In this paper, we extend the application of ViT to PFL and propose a novel approach to better personalize a ViT.
+
+Parameter-efficient Fine-tuning and Plugins. Finetuning is a popular technique for adapting a pre-trained model to a new task. However, fine-tuning can be computationally expensive, especially for large models [10, 41]. Parameter-efficient fine-tuning (PEFT) has been proposed to address this issue by selectively updating only a subset of the model's parameters or a few added parameters. These added parameters are plugged into the pre-trained model; therefore, they are summarised as "Plugins" in this paper. Although the location of the plugins for a transformer is various, including the input [15], the self-attention layer [20], and the feed-forward network [30], all of them can be trained to achieve comparable performance as fine-tuning without updating the weights of the pre-trained model. The plugins have also been applied to conventional FL to enable large pre-trained models and reduce the communication cost [35]. In the PFL, inspired by analogy from fine-tuning to the local training, the plugins can similarly be employed to personalize the representation from the global model to the local data distribution. Based on our empirical study, we choose prefixes [20] since the parameters are directly applied to the self-attention layer and propose our
+
+method, FedPerfix.
+
+# 3. Method
+
+# 3.1. Problem Formulation
+
+We consider a classification problem in Computer Vision (CV). A dataset  $\mathcal{D} = \{(x,y)|x\in X,y\in Y\}$  is separated on  $N$  clients, where  $X$  is the input space and  $Y$  is the label space. Data on each client is denoted as  $\mathcal{D}_i$ , and the distribution  $P_{i}$ . The client distributions are not identical. Each client has access to  $m_{i}$  samples drawn IID from the distribution  $P_{i}$ . The total number of samples is  $M = \sum_{i = 1}^{N}m_{i}$ . The hypothesis (model) on each client is noted as  $h_i$ , and the expected loss on the  $i^{\mathrm{th}}$  client is denoted as
+
+$$
+\mathcal {L} _ {\mathcal {D} _ {i}} \left(h _ {i}\right) = \mathbb {E} _ {(x, y) \sim P _ {i}} [ \ell (h (x), y) ] \tag {1}
+$$
+
+where  $\ell$  is the loss function. Further, considering the partial model personalization, the parameters in each client model can be divided into two parts: global parameters  $u$  and local parameters  $v_{i}$ , i.e.,  $h_i = u\cup v_i$ . Specifically,  $v_{i} = \varnothing$  indicates full model personalization.
+
+In each communication round  $t \in [T]$ , each client will receive  $u^{(t-1)}$  from the server and plug  $v_i^{(t-1)}$  into  $u^{(t-1)}$ . Then,  $u_i^{(t)}, v_i^{(t)}$  are trained on the local data. After the local training, only the  $u_i^{(t)}$  of  $K$  sampled clients will be sent to the server and participate in the global aggregation. The sampled ratio (client participation rate) is denoted as  $r = K/N$ . The global aggregation is formulated as
+
+$$
+u ^ {(t)} = \sum_ {i = 1} ^ {K} \alpha_ {i} u _ {i} ^ {(t)} \tag {2}
+$$
+
+where  $\alpha_{i}$  is the aggregation coefficient. Federated Averaging (FedAVG) is the most common aggregation algorithm where  $\alpha_{i} = \frac{m_{i}}{M}$ . After  $T$  rounds of communication, each client model will receive a copy of the newest global parameters and plug its own local parameters into the global parameters. Then, the model will be evaluated on its own test data drawn IID from  $P_{i}$ . To assess the overall performance, the mean and standard deviation of the Top-1 classification accuracy (Acc) for all clients will be reported.
+
+# 3.2. Recap: Partial Model Personalization for CNN
+
+In this section, we provide a brief recap of the approaches for partial model personalization in CNNs. We aim to leverage the insights and experiences gained from previous research to explore the strategy to personalize ViTs partially.
+
+FedRep [5] is a partial model personalization method that aims to preserve client-specific information while leveraging common knowledge in the earlier layers of a CNN by keeping the last classification layer and a few blocks local
+
+Table 1. Sensitivity to data distribution of each type of layer in a Vision Transformer. The mean and standard deviation of the client's Top-1 Accuracy are reported for each type of layer (Stand-alone). Considering the classification head is the most sensitive type of layer, we also report the performance when a type of layer is kept updated locally along with the classification head (Combined). The overall performance is the mean of the standalone accuracy and combined accuracy.  
+
+<table><tr><td>Type</td><td>Stand-alone</td><td>Combined</td><td>Overall</td></tr><tr><td>All Local</td><td>34.74±9.36</td><td>-</td><td>-</td></tr><tr><td>All Global</td><td>23.29±11.31</td><td>-</td><td>-</td></tr><tr><td>Classification Head</td><td>44.42±7.98</td><td>-</td><td>-</td></tr><tr><td>Patch Embedding</td><td>27.61±10.02</td><td>43.45±8.69</td><td>35.53</td></tr><tr><td>Position Embedding</td><td>23.80±11.42</td><td>45.04±8.08</td><td>34.42</td></tr><tr><td>LayerNorm</td><td>23.94±11.19</td><td>44.60±7.96</td><td>34.27</td></tr><tr><td>Self-attention</td><td>42.95±8.68</td><td>44.63±8.67</td><td>43.79</td></tr><tr><td>MLP</td><td>42.53±8.82</td><td>42.63±8.84</td><td>42.58</td></tr></table>
+
+and aggregating the rest. FedBN [18] is a partial model personalization method that updates Batch normalization (BN) [14] layers locally while aggregating the rest of the model. This method leverages the local statistics of the BN layer to adapt to the data distribution of each client while maintaining a global representation of the model, achieving a better balance between personalization and global representation. FedBABU [27] focuses on personalizing the classification head to address the issue of inconsistent feature spaces among clients. Unlike FedRep, FedBABU freezes the classification head and fine-tunes it for several steps before evaluation. By doing so, FedBABU can mitigate the negative impact of classification head drift and encourage consistent feature spaces across all clients.
+
+In summary, previous approaches to partial model personalization for CNNs provide valuable insights to answer the "where to personalize" question for ViTs: The layers to be personalized are usually designed with some engineering purpose, thus, are sensitive to data distribution. For instance, the normalization layers are designed to capture the statistical characters of the data, while classification heads are designed to map the feature to a predicted class. Building on these insights, we group the layers in ViT by their engineering purpose and conduct an empirical study to determine the layers in ViT that are the most sensitive to data distribution. We evaluated the performance of ViT while keeping some specific types of layers updated locally without aggregating with other clients. The results of our study are presented in Section 3.3.
+
+# 3.3. Empirical Study: Partial ViT Personalization
+
+In a ViT, we consider the following layers as candidates to be personalized and evaluate their sensitivity to data distribution when they are updated locally: Patch Embedding layer converts the input image to a sequence of patches, then applies a linear projection to map each patch into an embedding vector. Position Embedding layer is responsible for injecting positional information into the sequence of patches produced by the patch embedding layer, allowing the model to capture the spatial arrangement of the image. LayerNorm is a normalization layer commonly used in ViT to normalize the feature maps across the channel dimension. Self-attention layer allows the model to attend to different regions of the input image and capture long-range dependencies between them. MLP layers, following the self-attention layer, enable the model to capture nonlinear relationships between the image patches. Classification Head applies a linear projection from the [CLS] token to a predicted class.
+
+We perform experiments on CIFAR-100 with our default setting, which will be introduced in Section 4.1. We keep the specified type of layer updated locally and report the mean and standard deviation of the Top-1 Accuracy across all clients as the metrics to indicate the sensitivity to data distribution. The result is shown in the second column of Table 1.
+
+From the table, we can draw several insights. Keeping all layers local yields better performance than aggregating all layers. This suggests that aggregation of heterogeneous data may have a negative impact on some layers. Meanwhile, keeping each type of layer updated locally allows for greater adaptability to each client's data, leading to different degrees of improvement compared with keeping every layer global. Among all types of layers, the classification head is the most sensitive to data distribution, leading to the highest stand-alone performance, which is as expected. Except for the classification head, self-attention layer is more sensitive to data distribution than other components, showing a higher standard-alone performance.
+
+Considering the vital importance of the classification head, we also reported the combined performance when a type of layer is kept updated locally along with the classification head, as shown in the third column of Table 1. To decide the most sensitive layers to be personalized, we averaged the performance under the two settings as the overall performance.
+
+Based on the overall performance, personalizing the self-attention and classification head is one possible answer to the question of where to personalize. Besides, a vanilla baseline to keep the self-attention layers and classification head updated locally is proposed, which is referred to as Vanilla Attention as described in Fig. 2 (a).
+
+![](images/0ad70d1540205e32b92e02a31b063e5f4199c88c315714265c6526a9b5024527.jpg)  
+Figure 2. Several designs to personalize the self-attention layer in a ViT. SDP is short for Scaled Dot Product, the red part indicates the local parameters, the blue part indicates the global parameters and the gray parts are vectors or modules with no learnable parameter. (a) Vanilla attention simply keeps the self-attention and classification updated locally. (b) Vanilla prefix-tuning only keeps the prefixes updated locally and aggregates the original self-attention layer. (c) FedPerfix uses a local adapter to generate the prefixes and aggregates the original self-attention layer. The adapter is composed of a scale-down, an activation, and a scale-up layer.
+
+![](images/2ae7d7ff43b5e214e749e77dda4863902feb9f8d624f4b3ed2e03d8805b20949.jpg)
+
+# 3.4. Proposed Baseline: Vanilla Prefix-tuning
+
+Building upon the insights about where to personalize gained in the previous section, we move to the next question about how to personalize the selected layers. As obtained from our empirical study, Vanilla Attention is a baseline to personalize the self-attention layer by completely keeping the self-attention updated locally. However, it will also prevent it from learning general information for the global model.
+
+As explained in Section 1, the plugins can be trained on the local data to capture the client-specific knowledge as a personalization module. There are three widely used plugins for ViTs: a) Prompts that are learnable embeddings appended to the inputs, b) Adapters that are inserted into the MLP layers, and c) Prefixes that are appended to the key and value matrix of the self-attention layer. Given that the self-attention layer is one of the most sensitive layers, It is plausible that the Prefixes integrated nearest to the self-attention layer are capable of capturing the most relevant client-specific information pertaining to the self-attention mechanism. Besides, we further compare the effectiveness of all three plugins and discuss it in Section 5.3. Therefore, we select Prefixes as our personalization module.
+
+Specifically, learnable prefixes are appended to the self-attention layer and kept updated locally on the client. Meanwhile, the original self-attention layer is shared across all clients as normal to capture global dependencies. We refer to this approach as Vanilla Prefix-tuning.
+
+An illustration of how Prefixes cooperate with the self-attention layer is shown in Fig. 2 (b). Besides, we formulate
+
+the output of one head of the self-attention layer as
+
+$$
+h e a d _ {i} = A t t e n t i o n \left(\boldsymbol {Z} ^ {l - 1} \boldsymbol {W} _ {q} ^ {(i)}\right),
+$$
+
+$$
+\boldsymbol {Z} ^ {l - 1} \left[ \boldsymbol {P} _ {k}, \boldsymbol {W} _ {k} ^ {(i)} \right], \tag {3}
+$$
+
+$$
+\left. \boldsymbol {Z} ^ {l - 1} \left[ \boldsymbol {P} _ {v}, \boldsymbol {W} _ {v} ^ {(i)} \right]\right))
+$$
+
+where  $Z^{l-1}$  is the output from the last layer,  $P_k$  and  $P_v$  are prefixes,  $W_q^{(i)}, W_k^{(i)}$ , and  $W_v^{(i)}$  are the parameters in the self-attention layer, and [,] is the concatenate operation.
+
+# 3.5. FedPerfix: Stabilize the Prefix
+
+In Vanilla Prefix-tuning, the prefixes are randomly initialized, which can result in unstable performance when initialized with different weights. We later conduct an experiment to demonstrate such instability in Section 5.3 when Vanilla Prefix-tuning is initialized with different weights. To address this issue, we draw inspiration from the parallel attention design [41], which uses adapters to stabilize the prefixes. Similarly, we propose to use adapters in Vanilla Prefix-tuning to stabilize the prefix initialization. Specifically, we add a parallel adapter to prepare the prefixes for each layer, as shown in Fig. 2. Meanwhile, we add a hyperparameter  $s$  to control the efficiency of the adapter. Following the design of parallel attention, the prefixes are generated as
+
+$$
+\boldsymbol {P} _ {k}, \boldsymbol {P} _ {v} = \operatorname {A d a p t e r} \left(\boldsymbol {Z} ^ {l - 1}\right) = \operatorname {T a n h} \left(\boldsymbol {Z} ^ {l - 1} \boldsymbol {W} _ {\text {d o w n}}\right) \boldsymbol {W} _ {u p} \tag {4}
+$$
+
+where  $\mathrm{Tanh}$  is the activation function,  $W_{down}$  and  $W_{up}$  are parameters of the scaling layers of the adapter. As a result, the output of one head of the self-attention layer with paral
+
+IeI attention is shown in Fig. 2(c) and formulated as
+
+$$
+h e a d _ {i} = A t t e n t i o n \left(\boldsymbol {Z} ^ {l - 1} \boldsymbol {W} _ {q} ^ {(i)}\right),
+$$
+
+$$
+\boldsymbol {Z} ^ {l - 1} \left[ s \boldsymbol {P} _ {k}, \boldsymbol {W} _ {k} ^ {(i)} \right], \tag {5}
+$$
+
+$$
+\boldsymbol {Z} ^ {l - 1} [ s \boldsymbol {P} _ {v}, \boldsymbol {W} _ {v} ^ {(i)} ]).
+$$
+
+In conclusion, FedPerfix is proposed as a novel approach to transfer the information from the aggregated self-attention layer to fit the local data better, leveraging the plugins in transfer learning. The local prefixes are trained for personalization, while the global self-attention layer captures global dependencies. Therefore, FedPerfix provides a promising solution to address the question of how to perform personalization for ViTs.
+
+# 4. Experiment
+
+# 4.1. Experiment Details
+
+Dataset. We use three popular datasets to evaluate the performance: CIFAR-100 [16], OrganAMNIST [40], and Office-Home [38]. CIFAR-100 is a widely-used image classification dataset consisting of 50,000 RGB images across 100 classes. Office-Home is a domain adaptation dataset for object recognition tasks, which contains 15,500 images across 65 categories, captured from four different domains: Artistic images, Clipart, Product images, and Real-World images. OrganAMNIST is a medical image classification dataset that includes 58,850 gray-scale images of organs and tissues from human anatomy. The images are classified into 11 different classes. These datasets are chosen to evaluate the performance in various scenarios, including different data scales, domains, and the number of classes.
+
+Federated learning settings. We conduct  $T = 50$  communication rounds with each local training consisting of 10 epochs. To account for the various factors that can affect federated learning performance, we adjust the default settings for each dataset to focus on different scenarios with varying degrees of data heterogeneity of label skew and concept skew. For CIFAR-100, which has a relatively high number of samples and classes, we simulate a federated learning environment with  $N = 64$  clients using a Dirichlet distribution with  $\alpha = 0.1$  and sampling  $K = 8$  clients with a ratio  $r = 0.125$  for each round. For OrganAMNIST, which has a similar number of samples but fewer classes than CIFAR-100, we partition the data using a Dirichlet distribution with a larger  $\alpha = 0.5$  and apply the same client settings as CIFAR-100. As for Office-Home, which has fewer samples captured from 4 different domains, we focus on concept skew by partitioning the data from each domain into four different clients using a Dirichlet distribution with  $\alpha = 1.0$ , resulting in a total of  $N = 16$  clients. In each communication round, we randomly sample  $K = 4$  clients
+
+from any domain with a ratio  $r = 0.25$ . A visualization of the data partitioning is provided in Supplementary A.1.
+
+Model Architecture and Baselines. We choose ViT-Small (ViT-S) [8] with a patch size of 16 and an image size of 224 as our model for evaluation. We compare our proposed FedPerfix method against a range of baseline methods, including widely used approaches like FedAVG and local training without aggregation (Local). We also compare our method against advanced full model personalization methods, namely APFL [6] and Per-FedAVG [9], and three partial model personalization methods, namely FedBN, FedRep, and FedBABU. Besides, we also include the performance of Vanilla Attention, which keeps the self-attention layer and the classification head updated locally, as a reference. APFL adapts the global and local model through an adaptive mixture coefficient, while Per-FedAVG employs meta-learning to improve the global model. These methods are model-agnostic and can be applied to ViTs. FedBN keeps the batch normalization layer updated locally and aggregates the remaining layers in the server with FedAVG. To adapt it to ViTs, we replace the batch normalization layer with the layer normalization layer. FedRep keeps the classification head updated locally while aggregating the other layers in the server. FedBABU freezes the classification head and aggregates the remaining layers in the server, then fine-tunes the classification head on the local data for one step before the evaluation.
+
+Evaluation Metrics. We report the final mean and standard deviation of Top-1 accuracy among all clients after all communication rounds finish as the evaluation metrics. Besides, to evaluate the feasibility of the methods, an analysis of storage, computation, and communication costs is reported in Section 4.4.
+
+Implement Details. All hyperparameters in each method are tuned as optimal in a range. Each model is optimized with the SGD [33] optimizer with the optimal learning rate, which is 0.01 for most methods. The server and all the clients are simulated in one machine, and we resize the images in all datasets as  $224 \times 224$  RGB images to fit the model and set the batch size of the client data as 64. The model is implemented from the TIMM [39] library. All the experiments are implemented in Pytorch [28] and performed on 4 Nvidia A5000 GPUs. More details are provided in Supplementary A.2.
+
+# 4.2. Performance Evaluation
+
+Based on the evaluation results presented in Table 2, several insights can be drawn regarding the performance of the compared methods. It can be observed that FedAVG performs worse than Local when facing a large label skew, i.e., on CIFAR-100. This indicates the importance of addressing data heterogeneity in federated learning scenarios. However, when the label skew is not that extreme, the informa
+
+Table 2. Performance and required resources for each method. The mean and standard deviation of the Top-1 Accuracy among all clients are reported. The bold style indicates the best performance in each dataset.  
+
+<table><tr><td>Method</td><td>CIFAR-100</td><td>Performance OrganAMNIST</td><td>Office-Home</td><td>Storage (# Params)</td><td>Computation (FLOPs)</td><td>Communication (# Params)</td></tr><tr><td>FedAvg</td><td>23.29±11.31</td><td>87.31±5.98</td><td>21.47±6.24</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.03M (100%)</td></tr><tr><td>Local</td><td>34.74±9.36</td><td>78.26±11.07</td><td>20.39±7.26</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>0 (0%)</td></tr><tr><td>APFL</td><td>44.88±10.50</td><td>89.74±5.83</td><td>24.23±7.02</td><td>42.06M (200%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>Per-FedAVG</td><td>33.86±8.01</td><td>82.81±7.13</td><td>17.09±4.83</td><td>21.03M (100%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>FedBN</td><td>23.94±11.19</td><td>87.63±5.78</td><td>21.25±5.89</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.01M (100%)</td></tr><tr><td>FedBABU</td><td>41.41±8.87</td><td>88.38±7.16</td><td>19.50±7.71</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>FedRep</td><td>44.42±7.80</td><td>92.63±3.77</td><td>23.67±5.97</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>Vanilla Attention</td><td>44.63±8.67</td><td>88.90±5.87</td><td>22.55±6.37</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>13.89M (66%)</td></tr><tr><td>FedPerfix (ours)</td><td>48.10±7.76</td><td>93.17±3.51</td><td>24.38±8.47</td><td>24.42M (116%)</td><td>66.58M (101%)</td><td>20.66M (98%)</td></tr></table>
+
+tion gathered from the global aggregation can alleviate the overfitting due to few training samples on the client, leading to higher performance.
+
+In addition, it is worth noting that the methods that focus on the global objective instead of information transferring from the global to the client model, such as Per-FedAVG, achieve better performance than FedAVG but still show inferior performance compared to Local when facing extreme label skew or concept skew, i.e., CIFAR-100 and OfficeHome. This suggests that direct modification of the global objective may not always be the most effective way when using ViTs. Performing meta-learning on relatively small-size client data for a relatively large ViT is a challenging task, which limits the effectiveness of Per-FedAVG.
+
+On the other hand, how to leverage the information provided in the global model is crucial for partial model personalization. The layer normalization version of FedBN shows little impact on the performance, leading to a negligible improvement based on FedAVG. However, APFL, FedRep, Vanilla Attention, FedBABU, and FedPerfix find a more suitable way to transfer the information from the global model, leading to superior performance than other methods. Consistent with the conclusion we draw from the empirical study, FedRep, FedBABU, and Vanilla Attention personalized the sensitive parts in ViT, thus outperforming FedAVG and Local by a significant margin. As an extension, APFL and our method, FedPerfix, balance the information between the local and global models in a proper manner, leading to the highest two performances considering the performance across all three datasets.
+
+Surprisingly, we find that there is a connection between FedPerfix and APFL. Equation 3, which shows the output
+
+of a self-attention with Prefixes, can be rewritten as
+
+$$
+\begin{array}{l} h e a d (x) = (1 - \lambda (x)) \underbrace {A t t n (x \boldsymbol {W} _ {q} , x \boldsymbol {W} _ {k} , x \boldsymbol {W} _ {v})} _ {\text {a g g r e g a t e d a t t e n t i o n}} \\ + \lambda (x) \underbrace {A t t n \left(x \boldsymbol {W} _ {q} , x \boldsymbol {P} _ {k} , x \boldsymbol {P} _ {v}\right)} _ {\text {p e r s o n a l i z e d a t t e n t i o n}} \tag {6} \\ \end{array}
+$$
+
+where  $\lambda(x)$  is a scalar representing the normalized attention weights on the prefixes [10]. More details are provided in Supplementary B. It reveals that the local prefixes are learned as a mixture coefficient between the aggregated attention from the global model and the personalized attention from the prefixes. The high performance of both APFL and FedPerfix indicates the effectiveness of a mixture between the local and global models in PFL. Compared with APFL, FedPerfix only mixed the sensitive self-attention layers instead of the entire model, leading to higher performance. Meanwhile, FedPerfix trains the Prefix, which can be considered as the mixture coefficient, and the model simultaneously, while APFL needs separate training for the personalized model. Therefore, FedPerfix can achieve higher performance with fewer storage, computation, and communication resources. Furthermore, we provide a more detailed resource requirements analysis of each method in the following Section 4.4.
+
+# 4.3. Client-wise Performance
+
+In Fig. 3, we present a density plot depicting the performance gain of each method in comparison to Local. Notably, FedPerfix demonstrates an average performance gain of over  $10\%$ , surpassing all other methods. Moreover, FedPerfix outperforms all other methods by achieving up to  $30\%$  performance gains for certain clients. Conversely, some clients experience performance degradation under other methods, while FedPerfix ensures performance
+
+![](images/f5594d0f9572b88eb47551aff750420cc3d2b9f4f2a7b855f495d0ec8164079d.jpg)  
+Figure 3. Client-wise performance for each method on CIFAR-100. Density of the accuracy gain compared with Local training is plotted. FedPerfix provides highest upper and lower bounds among all the methods.
+
+gains for nearly all clients. In conclusion, FedPerfix shows a higher upper bound while maintaining a high lower bound, which will encourage more clients to involve in the federated training with performance-gaining guarantees for almost all clients.
+
+# 4.4. Resource Requirements Analysis
+
+In federated learning, it is crucial to consider the practicality of each method in terms of the storage, computation, and communication resources required by each participating client. As such, it is imperative to analyze the resource demands of each approach to determine its feasibility in realistic federated settings.
+
+We present a resource analysis of the evaluated methods, taking into account the storage, computation, and communication demands, which are crucial aspects in practical federated learning scenarios where clients may have limited resources. Table 2 reports the parameter size required to store the model, the FLOPs needed for training, and the parameter size required for communication. Notably, FedPerfix achieves superior performance compared to other methods with slightly more resources for storage and computation but fewer resources for communication.
+
+Overall, our proposed FedPerfix approach demonstrates the highest efficiency in terms of achieving superior performance while utilizing fewer storage, computation, and communication resources compared to other methods. These findings highlight the potential of our approach to effectively address the resource constraints often encountered in realistic federated learning scenarios.
+
+# 5. Ablation Study
+
+In this section, we conduct an ablation study on the CIFAR-100 dataset to evaluate the robustness of FedPerfix under various federated learning settings and to investigate FedPerfix with different designs.
+
+Table 3. Performance on CIFAR-100 with different backbones.  
+
+<table><tr><td>Method</td><td>ResNet50</td><td>ViT-Small</td></tr><tr><td>FedAVG</td><td>17.87±13.16</td><td>23.29±11.31</td></tr><tr><td>Local</td><td>28.34±9.83</td><td>34.74±9.36</td></tr><tr><td>APFL</td><td>30.71±9.89</td><td>44.88±10.50</td></tr><tr><td>Per-FedAVG</td><td>28.82±8.53</td><td>33.86±8.01</td></tr><tr><td>FedBN</td><td>19.33±10.25</td><td>23.94±11.19</td></tr><tr><td>FedBABU</td><td>24.56±7.82</td><td>41.41±8.87</td></tr><tr><td>FedRep</td><td>39.52±10.92</td><td>44.42±7.80</td></tr><tr><td>FedPerfix</td><td>-</td><td>48.10±7.76</td></tr></table>
+
+# 5.1. Performance Comparison with CNN Backbone
+
+To further demonstrate the motivation behind our work, i.e., addressing PFL with ViT, we conduct experiments to compare ViT and CNN as different backbones for the same set of methods. Given that the comparison methods are originally designed with a CNN backbone, we conduct experiments on CIFAR-100 with a CNN backbone as a reference to investigate the impact of replacing the CNNs with ViTs in these methods. To fairly compare the performance, we choose ResNet50 [11] as the CNN backbone due to its similar parameter size (24.37M) to ViT-Small [8] (21.03M).
+
+The result is shown in Table 3. Simply replacing the CNN backbone with the ViT backbone significantly improves performance for each method without additional operations. It suggests that the advantages of ViTs that demonstrated superior performance compared to CNNs in centralized settings may also translate to personalized federated learning scenarios.
+
+The success of ViTs in existing methods highlights their potential for personalized federated learning. However, there is a lack of approaches specifically designed for ViTs. To address this gap, we propose FedPerfix, which is tailored for ViTs and focuses on personalizing the sensitive parts of the network. By doing so, FedPerfix further improves performance compared to existing methods that incorporate ViTs. Our approach fills an important research gap and suggests that there is still much to be gained from exploring the unique properties of ViTs for personalized federated learning.
+
+# 5.2. Different FL Settings
+
+In order to assess the robustness of FedPerfix in more challenging federated learning scenarios, we conduct experiments that involve varying the number of clients with fewer samples per client and a lower client participation rate. We also compare the performance of FedPerfix with other competitive methods and report the results in Table 4. Our experimental results demonstrate that FedPerfix exhibits robust performance in different federated learning settings,
+
+Table 4. Performance on CIFAR-100 under different federated learning settings.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">N = 64</td><td colspan="2">N = 128</td></tr><tr><td>r = 6.25%</td><td>r = 12.5%</td><td>r = 6.25%</td><td>r = 12.5%</td></tr><tr><td>FedAvg</td><td>19.76±9.35</td><td>23.29±11.31</td><td>19.64±10.01</td><td>23.29±11.81</td></tr><tr><td>Local</td><td>32.35±11.64</td><td>34.74±9.36</td><td>31.79±12.00</td><td>36.03±9.57</td></tr><tr><td>APFL</td><td>42.55±13.51</td><td>44.88±10.50</td><td>41.64±12.77</td><td>43.92±9.40</td></tr><tr><td>FedRep</td><td>35.72±10.33</td><td>44.42±7.80</td><td>35.88±9.59</td><td>44.70±8.40</td></tr><tr><td>FedPerfix</td><td>43.80±11.56</td><td>48.10±7.76</td><td>43.96±10.42</td><td>46.96±9.00</td></tr></table>
+
+outperforming all other methods consistently. Thus, FedPerfix can be considered a reliable solution for extreme federated learning scenarios.
+
+# 5.3. Investigation of FedPerfix
+
+In this subsection, we investigate the impact of the model size of FedPerfix and verify its effectiveness compared with other designs.
+
+Impact of Model Size. The model size is a crucial factor in federated learning, as it determines the resource requirements for storage, computation, and communication. To examine the impact of model size on the performance of FedPerfix, we conducted experiments with three different ViT backbones: ViT-Tiny, ViT-Small (Default), and ViT-Base. Additionally, we included the results of the baselines and two competitive methods as a reference. As shown in Table 5, FedPerfix still yields superior performance with different model sizes. Besides, the larger models generally performed better, with ViT-Base achieving the highest performance for each method. However, we note that the performance improvement decreases as the model size increases, suggesting a potential trade-off between model size and performance. This finding highlights the importance of selecting an appropriate model size to achieve the optimal balance between performance and resource requirements, particularly in resource-constrained environments where storage and computation resources are limited.
+
+FedPerfix vs. Vanilla Prefix-tuning. As mentioned in Section 3.5, the initialization of the Prefixes will affect the performance. To show the effectiveness of the parallel attention design in FedPerfix, we conduct experiments with Vanilla Prefix-tuning under two different initialization, initialized with zero (Prefix-Z) and random initialization (Prefix-R). Then, we compare the results with FedPerfix. The result is shown in Table 6. As expected, the prefixes generated from the parallel attention yield better performance than the other two manually initialized prefixes, highlighting the effectiveness of the parallel attention design in FedPerfix.
+
+FedPerfix vs. Prompts & Adapters. Prompts and adapters are also popular plugins that are widely used. To verify whether FedPerfix is the most effective among all families of the plugins, we also apply Prompts and Adapters
+
+Table 5. Performance on CIFAR-100 with different model sizes.  
+
+<table><tr><td>Method</td><td>ViT-Tiny</td><td>ViT-Small</td><td>ViT-Base</td></tr><tr><td>FedAVG</td><td>19.56±10.27</td><td>23.29±11.31</td><td>24.82±11.53</td></tr><tr><td>Local</td><td>33.73±9.20</td><td>34.74±9.36</td><td>38.93±10.08</td></tr><tr><td>APFL</td><td>37.66±10.04</td><td>44.88±10.50</td><td>47.57±9.57</td></tr><tr><td>FedRep</td><td>41.58±7.19</td><td>44.42±7.80</td><td>44.34±8.35</td></tr><tr><td>FedPerfix</td><td>44.71±8.47</td><td>48.10±7.76</td><td>48.40±8.18</td></tr></table>
+
+to personalized federated learning. Specifically, we append several trainable Prompts to the input embeddings and keep them updated locally as the implementation of Prompt-tuning [15]. Meanwhile, we add Adapters to the MLP layers as the implementation of Adatper-tuning [30]. The results are shown in Table 6. Adding personalized Prompts doesn't improve the performance compared with simply keeping the classification head updated locally, indicating that the transformation to the input is not effective in PFL. However, adding Adapters to the MLP layers can also lead to a promising result as FedPerfix. Recap the result of our empirical study shown in Table 1, MLP layers are also sensitive to data distribution in a ViT. We note that as another instance to show the effectiveness of adding plugins to the sensitive parts of a ViT in PFL.
+
+Table 6. Performance of different designs on CIFAR-100. Prefix-Z and Prefix-R mean vanilla prefix-tuning with zero and random initialization.  
+
+<table><tr><td>FedPerfix</td><td>Prefix-Z</td><td>Prefix-R</td><td>Prompts</td><td>Adapters</td></tr><tr><td>48.10±7.76</td><td>47.37±8.47</td><td>46.98±8.10</td><td>44.19±8.13</td><td>47.99±8.59</td></tr></table>
+
+# 6. Conclusion
+
+In this work, we studied two research questions of where and how to personalize a ViT in federated learning. We conducted an empirical study to reveal that the self-attention and classification layers are the most sensitive layers for personalization. Based on that, we proposed FedPerfix, a novel method that introduces Prefixes with parallel attention to personalize the self-attention layers. Through extensive experiments on various datasets with different degrees of data heterogeneity, we demonstrated that FedPerfix achieves state-of-the-art performance while also reducing resource requirements. Our work focuses on ViTs and represents a shift in attention from the extensively researched CNNs, serving as inspiration for further investigation.
+
+# 7. Acknowledgement
+
+This work is partially supported by the NSF/Intel Partnership on MLWiNS under Grant No. 2003198.
+
+# References
+
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\ No newline at end of file
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+                                    "content": "Personalized Federated Learning (PFL) represents a promising solution for decentralized learning in heterogeneous data environments. Partial model personalization has been proposed to improve the efficiency of PFL by selectively updating local model parameters instead of aggregating all of them. However, previous work on partial model personalization has mainly focused on Convolutional Neural Networks (CNNs), leaving a gap in understanding how it can be applied to other popular models such as Vision Transformers (ViTs). In this work, we investigate where and how to partially personalize a ViT model. Specifically, we empirically evaluate the sensitivity to data distribution of each type of layer. Based on the insights that the self-attention layer and the classification head are the most sensitive parts of a ViT, we propose a novel approach called FedPerfix, which leverages plugins to transfer information from the aggregated model to the local client as a personalization. Finally, we evaluate the proposed approach on CIFAR-100, OrganAM-NIST, and Office-Home datasets and demonstrate its effectiveness in improving the model's performance compared to several advanced PFL methods. Code is available at https://github.com/imguangyu/FedPerfix"
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+                                    "content": "In the context of personalized federated learning, previous literature has explored two main approaches: full model personalization [9, 6, 23] and partial model personalization [31, 27, 18, 5, 1]. Full model personalization involves maintaining a separate local model for each client and updating it based on a joint objective, while partial model personalization aims to personalize only a subset of the model parameters. A convergence analysis [31] suggests that partial model personalization can achieve most of the benefits of full model personalization with fewer shared parameters, offering advantages in terms of computation, communication, and privacy to enable the deployment of larger models on the clients."
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+                                    "content": "However, recent literature shows that where and how to perform partial model personalization has a high correlation to the model architectures and the tasks [31], which requires further study when applied to a new architecture. Despite the multitude of approaches proposed in the literature, the majority of methods have only been evaluated on Convolutional Neural Networks (CNNs). Meanwhile, Vision Transformers (ViTs) [8] have demonstrated superior performance compared to CNNs in several tasks, such as image classification [37] and object detection [42, 3], making them an attractive option for personalized federated learning. However, to the best of our knowledge, the application of ViT in the federated learning community has received limited at"
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+                                    "content": "tention in the existing literature [32]. Given the advantages of ViT shown under centralized training, it is reasonable to expect that these benefits can also be realized in PFL by offering a more robust model for improved performance on the clients. Therefore, in this work, we investigate where and how to partially personalize a ViT model."
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+                                    "content": "Drawing from previous research on CNNs, layers that serve specific engineering purposes, such as feature extraction, normalization, or classification, have been identified as suitable candidates for partial model personalization [27, 18, 5]. These layers might have a higher sensitivity to the distribution of the training data. Therefore, aggregating the model weights trained from different data distributions may result in an inaccurate feature, while keeping them updated locally can gain a better feature for the local data distribution. Similarly, we select some candidates from ViT and conduct an empirical study to investigate the sensitivity of each type of layer. Specifically, we quantitatively evaluate the impact of keeping certain layers updated locally without aggregation with other clients. This evaluation shows that the self-attention layers and the classification head have a higher sensitivity than other layers, providing insights about where to personalize."
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+                                    "content": "To personalize the sensitive parts, one intuitive approach is to keep them completely local. However, the global aggregation has shown the capability to provide a more general global model than local models [24]. Completely preventing the sharing with the global model will severely hinder the potential benefits of leveraging general knowledge from the aggregated global model. Therefore, we desire to train a personalization module to bridge the general knowledge and the client-specific knowledge."
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+                                    "content": "As existing works in transfer learning suggest, the same pre-trained model can be transferred to different downstream data by adding different tiny architectures [30, 15, 20, 12]. We refer to these tiny architectures as plugins since they are small-sized parameters plugged into the pretrained model. These plugins are trained while the weights of the pre-trained model are frozen. The plugged model can achieve comparable performance as the fully fine-tuned model [29]. Since the model can maintain the same level of performance without changing the weights of the pretrained model, the downstream-specific knowledge is captured by the plugins. Therefore, the plugins show the capability to personalize the same model to satisfy different downstream data. In federated learning, we can consider the aggregated model as an inferior version of the \"pre-trained\" model, and the data on different clients as the downstream data, as shown in Fig. 1. With this perspective, we can therefore exploit the capability of the plugins in the federated learning context to capture client-specific knowledge for personalization."
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+                                            "content": "Figure 1. Analogy between transfer learning and personalized federated learning. A pre-trained model can be transferred to different downstream data with different plugins. In personalized federated learning, we are seeking different personalization modules (PM) to transfer the aggregated model to different client data."
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+                                    "content": "gin, Prefixes, to personalize the self-attention layer and propose a novel approach FedPerfix, short for Federated Personalized Prefix-tuning."
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+                                    "content": "The main contributions of this paper are as follows:"
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+                                            "type": "text",
+                                            "content": "- We perform an empirical study to reveal the sensitivity to data distribution of each type of layer in a ViT for PFL and locate the self-attention layer and classification head as the sensitive part to be personalized. (Section 3.3)"
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+                                }
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+                                            "content": "- We propose a novel partial model personalization approach on ViT, FedPerfix, inspired by the connection between PFL and transfer learning. Specifically, we exploit Prefix plugins to capture client-specific knowledge for personalization. (Section 3.5)"
+                                        }
+                                    ]
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+                                            "content": "- We conduct evaluations on CIFAR-100 [2], OrganAMINIST [40], and Office-home [38], which are across different domains, and degrees of data heterogeneity and achieve state-of-the-art performance compared with several competitive methods with lower resource requirements. (Section 4.2)"
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+                                    "content": "2. Related Work"
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+                                    "content": "Personalized Federated Learning. Personalized Federated Learning focuses on training a client-specific model to achieve satisfying performance on each client instead of a unified global model to fit all the client data. In terms of the shared parameters, full model personalization keeps a separate personalized model for each client and designs different training objectives, where the global model is usually served as the regularization term [36, 17, 43, 19, 13, 26]."
+                                }
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+                                    "content": "The training objectives are designed with the idea of meta-learning [9], Moreau Envelopes [7], model interpolation [6], decoupling [4], etc. In contrast, partial model personalization focuses on personalizing some specific parameters inside a model. Some works simply keep these parameters, e.g., the classification head [1, 27], and the batch normalization layers [18] updated locally, while some works design additional parameters, e.g., prototypes for each class [36] or hypernetworks [34], to further personalized these parameters. Our proposed method focuses on the self-attention layers in a ViT and leverages plugins in transfer learning, enabling personalization without introducing significant overhead. Our experimental results demonstrate that FedPerfix outperforms existing methods in terms of both efficiency and effectiveness."
+                                }
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+                                    "content": "Vision Transformer. ViTs, a type of attention-based neural network, have shown superior performance in several fields compared to CNNs. In particular, ViTs have achieved state-of-the-art performance on various benchmarks [8, 22, 21]. ViTs employ self-attention mechanisms to learn the dependencies between different regions of an image and can capture long-range dependencies more effectively than CNNs. Despite their success, the use of ViTs in federated learning has not been as widely explored as CNNs. Qu et al. [32] studied the performance of ViT under conventional FL settings and found that simply replacing CNNs with ViTs can greatly accelerate convergence and reach a better global model, especially when dealing with heterogeneous data, demonstrating the potential of ViTs in FL. In this paper, we extend the application of ViT to PFL and propose a novel approach to better personalize a ViT."
+                                }
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+                                    "content": "Parameter-efficient Fine-tuning and Plugins. Finetuning is a popular technique for adapting a pre-trained model to a new task. However, fine-tuning can be computationally expensive, especially for large models [10, 41]. Parameter-efficient fine-tuning (PEFT) has been proposed to address this issue by selectively updating only a subset of the model's parameters or a few added parameters. These added parameters are plugged into the pre-trained model; therefore, they are summarised as \"Plugins\" in this paper. Although the location of the plugins for a transformer is various, including the input [15], the self-attention layer [20], and the feed-forward network [30], all of them can be trained to achieve comparable performance as fine-tuning without updating the weights of the pre-trained model. The plugins have also been applied to conventional FL to enable large pre-trained models and reduce the communication cost [35]. In the PFL, inspired by analogy from fine-tuning to the local training, the plugins can similarly be employed to personalize the representation from the global model to the local data distribution. Based on our empirical study, we choose prefixes [20] since the parameters are directly applied to the self-attention layer and propose our"
+                                }
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+                                    "type": "text",
+                                    "content": "method, FedPerfix."
+                                }
+                            ]
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+                                    "content": "3. Method"
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+                {
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+                    ],
+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "3.1. Problem Formulation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    ],
+                                    "type": "text",
+                                    "content": "We consider a classification problem in Computer Vision (CV). A dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D} = \\{(x,y)|x\\in X,y\\in Y\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is separated on "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                    ],
+                                    "type": "text",
+                                    "content": " clients, where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the input space and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the label space. Data on each client is denoted as "
+                                },
+                                {
+                                    "bbox": [
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+                                        133,
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+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and the distribution "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The client distributions are not identical. Each client has access to "
+                                },
+                                {
+                                    "bbox": [
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+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                        133,
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+                                    ],
+                                    "type": "text",
+                                    "content": " samples drawn IID from the distribution "
+                                },
+                                {
+                                    "bbox": [
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+                                        133,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        547,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The total number of samples is "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        547,
+                                        242
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M = \\sum_{i = 1}^{N}m_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                        242
+                                    ],
+                                    "type": "text",
+                                    "content": ". The hypothesis (model) on each client is noted as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and the expected loss on the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i^{\\mathrm{th}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " client is denoted as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathcal {D} _ {i}} \\left(h _ {i}\\right) = \\mathbb {E} _ {(x, y) \\sim P _ {i}} [ \\ell (h (x), y) ] \\tag {1}",
+                                    "image_path": "48df4cfb587e9fd2b4c4f378e453453079217f6b0746f8c9084a39422995dedc.jpg"
+                                }
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+                    ],
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+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": " is the loss function. Further, considering the partial model personalization, the parameters in each client model can be divided into two parts: global parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and local parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "v_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_i = u\\cup v_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Specifically, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        272,
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+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "v_{i} = \\varnothing"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates full model personalization."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "In each communication round "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t \\in [T]"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", each client will receive "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u^{(t-1)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from the server and plug "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        332,
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+                                        423
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "v_i^{(t-1)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " into "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u^{(t-1)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        332,
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+                                        423
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        332,
+                                        547,
+                                        423
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_i^{(t)}, v_i^{(t)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        332,
+                                        547,
+                                        423
+                                    ],
+                                    "type": "text",
+                                    "content": " are trained on the local data. After the local training, only the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        332,
+                                        547,
+                                        423
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_i^{(t)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " sampled clients will be sent to the server and participate in the global aggregation. The sampled ratio (client participation rate) is denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r = K/N"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The global aggregation is formulated as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "u ^ {(t)} = \\sum_ {i = 1} ^ {K} \\alpha_ {i} u _ {i} ^ {(t)} \\tag {2}",
+                                    "image_path": "93bbec865e0557a16e1ee8f5978d52057c11eefe842a72ce64fabe13eb6a2b4d.jpg"
+                                }
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+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        472,
+                                        547,
+                                        582
+                                    ],
+                                    "type": "text",
+                                    "content": " is the aggregation coefficient. Federated Averaging (FedAVG) is the most common aggregation algorithm where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        472,
+                                        547,
+                                        582
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{i} = \\frac{m_{i}}{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        472,
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+                                        582
+                                    ],
+                                    "type": "text",
+                                    "content": ". After "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        472,
+                                        547,
+                                        582
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        472,
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+                                    ],
+                                    "type": "text",
+                                    "content": " rounds of communication, each client model will receive a copy of the newest global parameters and plug its own local parameters into the global parameters. Then, the model will be evaluated on its own test data drawn IID from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        472,
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+                                        582
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        582
+                                    ],
+                                    "type": "text",
+                                    "content": ". To assess the overall performance, the mean and standard deviation of the Top-1 classification accuracy (Acc) for all clients will be reported."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.2. Recap: Partial Model Personalization for CNN"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this section, we provide a brief recap of the approaches for partial model personalization in CNNs. We aim to leverage the insights and experiences gained from previous research to explore the strategy to personalize ViTs partially."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "FedRep [5] is a partial model personalization method that aims to preserve client-specific information while leveraging common knowledge in the earlier layers of a CNN by keeping the last classification layer and a few blocks local"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                }
+            ],
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+                    "type": "table",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Table 1. Sensitivity to data distribution of each type of layer in a Vision Transformer. The mean and standard deviation of the client's Top-1 Accuracy are reported for each type of layer (Stand-alone). Considering the classification head is the most sensitive type of layer, we also report the performance when a type of layer is kept updated locally along with the classification head (Combined). The overall performance is the mean of the standalone accuracy and combined accuracy."
+                                        }
+                                    ]
+                                }
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+                                            "html": "<table><tr><td>Type</td><td>Stand-alone</td><td>Combined</td><td>Overall</td></tr><tr><td>All Local</td><td>34.74±9.36</td><td>-</td><td>-</td></tr><tr><td>All Global</td><td>23.29±11.31</td><td>-</td><td>-</td></tr><tr><td>Classification Head</td><td>44.42±7.98</td><td>-</td><td>-</td></tr><tr><td>Patch Embedding</td><td>27.61±10.02</td><td>43.45±8.69</td><td>35.53</td></tr><tr><td>Position Embedding</td><td>23.80±11.42</td><td>45.04±8.08</td><td>34.42</td></tr><tr><td>LayerNorm</td><td>23.94±11.19</td><td>44.60±7.96</td><td>34.27</td></tr><tr><td>Self-attention</td><td>42.95±8.68</td><td>44.63±8.67</td><td>43.79</td></tr><tr><td>MLP</td><td>42.53±8.82</td><td>42.63±8.84</td><td>42.58</td></tr></table>",
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+                                    "content": "and aggregating the rest. FedBN [18] is a partial model personalization method that updates Batch normalization (BN) [14] layers locally while aggregating the rest of the model. This method leverages the local statistics of the BN layer to adapt to the data distribution of each client while maintaining a global representation of the model, achieving a better balance between personalization and global representation. FedBABU [27] focuses on personalizing the classification head to address the issue of inconsistent feature spaces among clients. Unlike FedRep, FedBABU freezes the classification head and fine-tunes it for several steps before evaluation. By doing so, FedBABU can mitigate the negative impact of classification head drift and encourage consistent feature spaces across all clients."
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+                                    "content": "In summary, previous approaches to partial model personalization for CNNs provide valuable insights to answer the \"where to personalize\" question for ViTs: The layers to be personalized are usually designed with some engineering purpose, thus, are sensitive to data distribution. For instance, the normalization layers are designed to capture the statistical characters of the data, while classification heads are designed to map the feature to a predicted class. Building on these insights, we group the layers in ViT by their engineering purpose and conduct an empirical study to determine the layers in ViT that are the most sensitive to data distribution. We evaluated the performance of ViT while keeping some specific types of layers updated locally without aggregating with other clients. The results of our study are presented in Section 3.3."
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+                                    "content": "3.3. Empirical Study: Partial ViT Personalization"
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+                                    "content": "In a ViT, we consider the following layers as candidates to be personalized and evaluate their sensitivity to data distribution when they are updated locally: Patch Embedding layer converts the input image to a sequence of patches, then applies a linear projection to map each patch into an embedding vector. Position Embedding layer is responsible for injecting positional information into the sequence of patches produced by the patch embedding layer, allowing the model to capture the spatial arrangement of the image. LayerNorm is a normalization layer commonly used in ViT to normalize the feature maps across the channel dimension. Self-attention layer allows the model to attend to different regions of the input image and capture long-range dependencies between them. MLP layers, following the self-attention layer, enable the model to capture nonlinear relationships between the image patches. Classification Head applies a linear projection from the [CLS] token to a predicted class."
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+                                    "content": "We perform experiments on CIFAR-100 with our default setting, which will be introduced in Section 4.1. We keep the specified type of layer updated locally and report the mean and standard deviation of the Top-1 Accuracy across all clients as the metrics to indicate the sensitivity to data distribution. The result is shown in the second column of Table 1."
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+                                    "content": "From the table, we can draw several insights. Keeping all layers local yields better performance than aggregating all layers. This suggests that aggregation of heterogeneous data may have a negative impact on some layers. Meanwhile, keeping each type of layer updated locally allows for greater adaptability to each client's data, leading to different degrees of improvement compared with keeping every layer global. Among all types of layers, the classification head is the most sensitive to data distribution, leading to the highest stand-alone performance, which is as expected. Except for the classification head, self-attention layer is more sensitive to data distribution than other components, showing a higher standard-alone performance."
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+                                    "content": "Considering the vital importance of the classification head, we also reported the combined performance when a type of layer is kept updated locally along with the classification head, as shown in the third column of Table 1. To decide the most sensitive layers to be personalized, we averaged the performance under the two settings as the overall performance."
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+                                    "content": "Based on the overall performance, personalizing the self-attention and classification head is one possible answer to the question of where to personalize. Besides, a vanilla baseline to keep the self-attention layers and classification head updated locally is proposed, which is referred to as Vanilla Attention as described in Fig. 2 (a)."
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+                                            "content": "Figure 2. Several designs to personalize the self-attention layer in a ViT. SDP is short for Scaled Dot Product, the red part indicates the local parameters, the blue part indicates the global parameters and the gray parts are vectors or modules with no learnable parameter. (a) Vanilla attention simply keeps the self-attention and classification updated locally. (b) Vanilla prefix-tuning only keeps the prefixes updated locally and aggregates the original self-attention layer. (c) FedPerfix uses a local adapter to generate the prefixes and aggregates the original self-attention layer. The adapter is composed of a scale-down, an activation, and a scale-up layer."
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+                                    "content": "Building upon the insights about where to personalize gained in the previous section, we move to the next question about how to personalize the selected layers. As obtained from our empirical study, Vanilla Attention is a baseline to personalize the self-attention layer by completely keeping the self-attention updated locally. However, it will also prevent it from learning general information for the global model."
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+                                    "content": " are prefixes, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "W_q^{(i)}, W_k^{(i)}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "W_v^{(i)}"
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+                                    "type": "text",
+                                    "content": " are the parameters in the self-attention layer, and [,] is the concatenate operation."
+                                }
+                            ]
+                        }
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+                                    "content": "3.5. FedPerfix: Stabilize the Prefix"
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+                                    "type": "text",
+                                    "content": "In Vanilla Prefix-tuning, the prefixes are randomly initialized, which can result in unstable performance when initialized with different weights. We later conduct an experiment to demonstrate such instability in Section 5.3 when Vanilla Prefix-tuning is initialized with different weights. To address this issue, we draw inspiration from the parallel attention design [41], which uses adapters to stabilize the prefixes. Similarly, we propose to use adapters in Vanilla Prefix-tuning to stabilize the prefix initialization. Specifically, we add a parallel adapter to prepare the prefixes for each layer, as shown in Fig. 2. Meanwhile, we add a hyperparameter "
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+                                    "type": "text",
+                                    "content": " to control the efficiency of the adapter. Following the design of parallel attention, the prefixes are generated as"
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+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {P} _ {k}, \\boldsymbol {P} _ {v} = \\operatorname {A d a p t e r} \\left(\\boldsymbol {Z} ^ {l - 1}\\right) = \\operatorname {T a n h} \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {\\text {d o w n}}\\right) \\boldsymbol {W} _ {u p} \\tag {4}",
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " are parameters of the scaling layers of the adapter. As a result, the output of one head of the self-attention layer with paral"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "IeI attention is shown in Fig. 2(c) and formulated as"
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+                                    "content": "h e a d _ {i} = A t t e n t i o n \\left(\\boldsymbol {Z} ^ {l - 1} \\boldsymbol {W} _ {q} ^ {(i)}\\right),",
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+                                    "content": "\\boldsymbol {Z} ^ {l - 1} \\left[ s \\boldsymbol {P} _ {k}, \\boldsymbol {W} _ {k} ^ {(i)} \\right], \\tag {5}",
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+                                    "content": "\\boldsymbol {Z} ^ {l - 1} [ s \\boldsymbol {P} _ {v}, \\boldsymbol {W} _ {v} ^ {(i)} ]).",
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+                                    "type": "text",
+                                    "content": "In conclusion, FedPerfix is proposed as a novel approach to transfer the information from the aggregated self-attention layer to fit the local data better, leveraging the plugins in transfer learning. The local prefixes are trained for personalization, while the global self-attention layer captures global dependencies. Therefore, FedPerfix provides a promising solution to address the question of how to perform personalization for ViTs."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4. Experiment"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "4.1. Experiment Details"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "Dataset. We use three popular datasets to evaluate the performance: CIFAR-100 [16], OrganAMNIST [40], and Office-Home [38]. CIFAR-100 is a widely-used image classification dataset consisting of 50,000 RGB images across 100 classes. Office-Home is a domain adaptation dataset for object recognition tasks, which contains 15,500 images across 65 categories, captured from four different domains: Artistic images, Clipart, Product images, and Real-World images. OrganAMNIST is a medical image classification dataset that includes 58,850 gray-scale images of organs and tissues from human anatomy. The images are classified into 11 different classes. These datasets are chosen to evaluate the performance in various scenarios, including different data scales, domains, and the number of classes."
+                                }
+                            ]
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+                    ],
+                    "index": 7
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+                {
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+                                    "type": "text",
+                                    "content": "Federated learning settings. We conduct "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "T = 50"
+                                },
+                                {
+                                    "bbox": [
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+                                        474,
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+                                    ],
+                                    "type": "text",
+                                    "content": " communication rounds with each local training consisting of 10 epochs. To account for the various factors that can affect federated learning performance, we adjust the default settings for each dataset to focus on different scenarios with varying degrees of data heterogeneity of label skew and concept skew. For CIFAR-100, which has a relatively high number of samples and classes, we simulate a federated learning environment with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N = 64"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " clients using a Dirichlet distribution with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha = 0.1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and sampling "
+                                },
+                                {
+                                    "bbox": [
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+                                        474,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 8"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " clients with a ratio "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r = 0.125"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " for each round. For OrganAMNIST, which has a similar number of samples but fewer classes than CIFAR-100, we partition the data using a Dirichlet distribution with a larger "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha = 0.5"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and apply the same client settings as CIFAR-100. As for Office-Home, which has fewer samples captured from 4 different domains, we focus on concept skew by partitioning the data from each domain into four different clients using a Dirichlet distribution with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha = 1.0"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", resulting in a total of "
+                                },
+                                {
+                                    "bbox": [
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N = 16"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " clients. In each communication round, we randomly sample "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 4"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " clients"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "from any domain with a ratio "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r = 0.25"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". A visualization of the data partitioning is provided in Supplementary A.1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
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+                        396
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Model Architecture and Baselines. We choose ViT-Small (ViT-S) [8] with a patch size of 16 and an image size of 224 as our model for evaluation. We compare our proposed FedPerfix method against a range of baseline methods, including widely used approaches like FedAVG and local training without aggregation (Local). We also compare our method against advanced full model personalization methods, namely APFL [6] and Per-FedAVG [9], and three partial model personalization methods, namely FedBN, FedRep, and FedBABU. Besides, we also include the performance of Vanilla Attention, which keeps the self-attention layer and the classification head updated locally, as a reference. APFL adapts the global and local model through an adaptive mixture coefficient, while Per-FedAVG employs meta-learning to improve the global model. These methods are model-agnostic and can be applied to ViTs. FedBN keeps the batch normalization layer updated locally and aggregates the remaining layers in the server with FedAVG. To adapt it to ViTs, we replace the batch normalization layer with the layer normalization layer. FedRep keeps the classification head updated locally while aggregating the other layers in the server. FedBABU freezes the classification head and aggregates the remaining layers in the server, then fine-tunes the classification head on the local data for one step before the evaluation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Evaluation Metrics. We report the final mean and standard deviation of Top-1 accuracy among all clients after all communication rounds finish as the evaluation metrics. Besides, to evaluate the feasibility of the methods, an analysis of storage, computation, and communication costs is reported in Section 4.4."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "content": "Implement Details. All hyperparameters in each method are tuned as optimal in a range. Each model is optimized with the SGD [33] optimizer with the optimal learning rate, which is 0.01 for most methods. The server and all the clients are simulated in one machine, and we resize the images in all datasets as "
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+                                    "content": " RGB images to fit the model and set the batch size of the client data as 64. The model is implemented from the TIMM [39] library. All the experiments are implemented in Pytorch [28] and performed on 4 Nvidia A5000 GPUs. More details are provided in Supplementary A.2."
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+                                    "content": "4.2. Performance Evaluation"
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+                                    "content": "Based on the evaluation results presented in Table 2, several insights can be drawn regarding the performance of the compared methods. It can be observed that FedAVG performs worse than Local when facing a large label skew, i.e., on CIFAR-100. This indicates the importance of addressing data heterogeneity in federated learning scenarios. However, when the label skew is not that extreme, the informa"
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+                                            "content": "Table 2. Performance and required resources for each method. The mean and standard deviation of the Top-1 Accuracy among all clients are reported. The bold style indicates the best performance in each dataset."
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+                                            "html": "<table><tr><td>Method</td><td>CIFAR-100</td><td>Performance OrganAMNIST</td><td>Office-Home</td><td>Storage (# Params)</td><td>Computation (FLOPs)</td><td>Communication (# Params)</td></tr><tr><td>FedAvg</td><td>23.29±11.31</td><td>87.31±5.98</td><td>21.47±6.24</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.03M (100%)</td></tr><tr><td>Local</td><td>34.74±9.36</td><td>78.26±11.07</td><td>20.39±7.26</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>0 (0%)</td></tr><tr><td>APFL</td><td>44.88±10.50</td><td>89.74±5.83</td><td>24.23±7.02</td><td>42.06M (200%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>Per-FedAVG</td><td>33.86±8.01</td><td>82.81±7.13</td><td>17.09±4.83</td><td>21.03M (100%)</td><td>131.30M (200%)</td><td>21.03M (100%)</td></tr><tr><td>FedBN</td><td>23.94±11.19</td><td>87.63±5.78</td><td>21.25±5.89</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>21.01M (100%)</td></tr><tr><td>FedBABU</td><td>41.41±8.87</td><td>88.38±7.16</td><td>19.50±7.71</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>FedRep</td><td>44.42±7.80</td><td>92.63±3.77</td><td>23.67±5.97</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>20.66M (98%)</td></tr><tr><td>Vanilla Attention</td><td>44.63±8.67</td><td>88.90±5.87</td><td>22.55±6.37</td><td>21.03M (100%)</td><td>65.65M (100%)</td><td>13.89M (66%)</td></tr><tr><td>FedPerfix (ours)</td><td>48.10±7.76</td><td>93.17±3.51</td><td>24.38±8.47</td><td>24.42M (116%)</td><td>66.58M (101%)</td><td>20.66M (98%)</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "tion gathered from the global aggregation can alleviate the overfitting due to few training samples on the client, leading to higher performance."
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+                                    "content": "In addition, it is worth noting that the methods that focus on the global objective instead of information transferring from the global to the client model, such as Per-FedAVG, achieve better performance than FedAVG but still show inferior performance compared to Local when facing extreme label skew or concept skew, i.e., CIFAR-100 and OfficeHome. This suggests that direct modification of the global objective may not always be the most effective way when using ViTs. Performing meta-learning on relatively small-size client data for a relatively large ViT is a challenging task, which limits the effectiveness of Per-FedAVG."
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+                                    "content": "On the other hand, how to leverage the information provided in the global model is crucial for partial model personalization. The layer normalization version of FedBN shows little impact on the performance, leading to a negligible improvement based on FedAVG. However, APFL, FedRep, Vanilla Attention, FedBABU, and FedPerfix find a more suitable way to transfer the information from the global model, leading to superior performance than other methods. Consistent with the conclusion we draw from the empirical study, FedRep, FedBABU, and Vanilla Attention personalized the sensitive parts in ViT, thus outperforming FedAVG and Local by a significant margin. As an extension, APFL and our method, FedPerfix, balance the information between the local and global models in a proper manner, leading to the highest two performances considering the performance across all three datasets."
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+                                    "content": "Surprisingly, we find that there is a connection between FedPerfix and APFL. Equation 3, which shows the output"
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+                                    "content": "of a self-attention with Prefixes, can be rewritten as"
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+                                    "content": "\\begin{array}{l} h e a d (x) = (1 - \\lambda (x)) \\underbrace {A t t n (x \\boldsymbol {W} _ {q} , x \\boldsymbol {W} _ {k} , x \\boldsymbol {W} _ {v})} _ {\\text {a g g r e g a t e d a t t e n t i o n}} \\\\ + \\lambda (x) \\underbrace {A t t n \\left(x \\boldsymbol {W} _ {q} , x \\boldsymbol {P} _ {k} , x \\boldsymbol {P} _ {v}\\right)} _ {\\text {p e r s o n a l i z e d a t t e n t i o n}} \\tag {6} \\\\ \\end{array}",
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+                                    "content": "where "
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+                                    "content": " is a scalar representing the normalized attention weights on the prefixes [10]. More details are provided in Supplementary B. It reveals that the local prefixes are learned as a mixture coefficient between the aggregated attention from the global model and the personalized attention from the prefixes. The high performance of both APFL and FedPerfix indicates the effectiveness of a mixture between the local and global models in PFL. Compared with APFL, FedPerfix only mixed the sensitive self-attention layers instead of the entire model, leading to higher performance. Meanwhile, FedPerfix trains the Prefix, which can be considered as the mixture coefficient, and the model simultaneously, while APFL needs separate training for the personalized model. Therefore, FedPerfix can achieve higher performance with fewer storage, computation, and communication resources. Furthermore, we provide a more detailed resource requirements analysis of each method in the following Section 4.4."
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+                                    "content": "In Fig. 3, we present a density plot depicting the performance gain of each method in comparison to Local. Notably, FedPerfix demonstrates an average performance gain of over "
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+                                    "content": ", surpassing all other methods. Moreover, FedPerfix outperforms all other methods by achieving up to "
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+                                    "content": " performance gains for certain clients. Conversely, some clients experience performance degradation under other methods, while FedPerfix ensures performance"
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+                                    "content": "gains for nearly all clients. In conclusion, FedPerfix shows a higher upper bound while maintaining a high lower bound, which will encourage more clients to involve in the federated training with performance-gaining guarantees for almost all clients."
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+                                    "type": "text",
+                                    "content": "We present a resource analysis of the evaluated methods, taking into account the storage, computation, and communication demands, which are crucial aspects in practical federated learning scenarios where clients may have limited resources. Table 2 reports the parameter size required to store the model, the FLOPs needed for training, and the parameter size required for communication. Notably, FedPerfix achieves superior performance compared to other methods with slightly more resources for storage and computation but fewer resources for communication."
+                                }
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+                                    "content": "Overall, our proposed FedPerfix approach demonstrates the highest efficiency in terms of achieving superior performance while utilizing fewer storage, computation, and communication resources compared to other methods. These findings highlight the potential of our approach to effectively address the resource constraints often encountered in realistic federated learning scenarios."
+                                }
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+                                    "content": "5. Ablation Study"
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+                                    "content": "In this section, we conduct an ablation study on the CIFAR-100 dataset to evaluate the robustness of FedPerfix under various federated learning settings and to investigate FedPerfix with different designs."
+                                }
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+                                            "content": "Table 3. Performance on CIFAR-100 with different backbones."
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+                                            "html": "<table><tr><td>Method</td><td>ResNet50</td><td>ViT-Small</td></tr><tr><td>FedAVG</td><td>17.87±13.16</td><td>23.29±11.31</td></tr><tr><td>Local</td><td>28.34±9.83</td><td>34.74±9.36</td></tr><tr><td>APFL</td><td>30.71±9.89</td><td>44.88±10.50</td></tr><tr><td>Per-FedAVG</td><td>28.82±8.53</td><td>33.86±8.01</td></tr><tr><td>FedBN</td><td>19.33±10.25</td><td>23.94±11.19</td></tr><tr><td>FedBABU</td><td>24.56±7.82</td><td>41.41±8.87</td></tr><tr><td>FedRep</td><td>39.52±10.92</td><td>44.42±7.80</td></tr><tr><td>FedPerfix</td><td>-</td><td>48.10±7.76</td></tr></table>",
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+                                    "content": "5.1. Performance Comparison with CNN Backbone"
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+                                    "type": "text",
+                                    "content": "To further demonstrate the motivation behind our work, i.e., addressing PFL with ViT, we conduct experiments to compare ViT and CNN as different backbones for the same set of methods. Given that the comparison methods are originally designed with a CNN backbone, we conduct experiments on CIFAR-100 with a CNN backbone as a reference to investigate the impact of replacing the CNNs with ViTs in these methods. To fairly compare the performance, we choose ResNet50 [11] as the CNN backbone due to its similar parameter size (24.37M) to ViT-Small [8] (21.03M)."
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+                                    "type": "text",
+                                    "content": "The result is shown in Table 3. Simply replacing the CNN backbone with the ViT backbone significantly improves performance for each method without additional operations. It suggests that the advantages of ViTs that demonstrated superior performance compared to CNNs in centralized settings may also translate to personalized federated learning scenarios."
+                                }
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+                                    "type": "text",
+                                    "content": "The success of ViTs in existing methods highlights their potential for personalized federated learning. However, there is a lack of approaches specifically designed for ViTs. To address this gap, we propose FedPerfix, which is tailored for ViTs and focuses on personalizing the sensitive parts of the network. By doing so, FedPerfix further improves performance compared to existing methods that incorporate ViTs. Our approach fills an important research gap and suggests that there is still much to be gained from exploring the unique properties of ViTs for personalized federated learning."
+                                }
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+                                    "content": "5.2. Different FL Settings"
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+                                    "content": "In order to assess the robustness of FedPerfix in more challenging federated learning scenarios, we conduct experiments that involve varying the number of clients with fewer samples per client and a lower client participation rate. We also compare the performance of FedPerfix with other competitive methods and report the results in Table 4. Our experimental results demonstrate that FedPerfix exhibits robust performance in different federated learning settings,"
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+                                            "content": "Table 4. Performance on CIFAR-100 under different federated learning settings."
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+                            "index": 0,
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">N = 64</td><td colspan=\"2\">N = 128</td></tr><tr><td>r = 6.25%</td><td>r = 12.5%</td><td>r = 6.25%</td><td>r = 12.5%</td></tr><tr><td>FedAvg</td><td>19.76±9.35</td><td>23.29±11.31</td><td>19.64±10.01</td><td>23.29±11.81</td></tr><tr><td>Local</td><td>32.35±11.64</td><td>34.74±9.36</td><td>31.79±12.00</td><td>36.03±9.57</td></tr><tr><td>APFL</td><td>42.55±13.51</td><td>44.88±10.50</td><td>41.64±12.77</td><td>43.92±9.40</td></tr><tr><td>FedRep</td><td>35.72±10.33</td><td>44.42±7.80</td><td>35.88±9.59</td><td>44.70±8.40</td></tr><tr><td>FedPerfix</td><td>43.80±11.56</td><td>48.10±7.76</td><td>43.96±10.42</td><td>46.96±9.00</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "outperforming all other methods consistently. Thus, FedPerfix can be considered a reliable solution for extreme federated learning scenarios."
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+                                    "content": "5.3. Investigation of FedPerfix"
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+                                    "content": "In this subsection, we investigate the impact of the model size of FedPerfix and verify its effectiveness compared with other designs."
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+                                    "content": "Impact of Model Size. The model size is a crucial factor in federated learning, as it determines the resource requirements for storage, computation, and communication. To examine the impact of model size on the performance of FedPerfix, we conducted experiments with three different ViT backbones: ViT-Tiny, ViT-Small (Default), and ViT-Base. Additionally, we included the results of the baselines and two competitive methods as a reference. As shown in Table 5, FedPerfix still yields superior performance with different model sizes. Besides, the larger models generally performed better, with ViT-Base achieving the highest performance for each method. However, we note that the performance improvement decreases as the model size increases, suggesting a potential trade-off between model size and performance. This finding highlights the importance of selecting an appropriate model size to achieve the optimal balance between performance and resource requirements, particularly in resource-constrained environments where storage and computation resources are limited."
+                                }
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+                                    "type": "text",
+                                    "content": "FedPerfix vs. Vanilla Prefix-tuning. As mentioned in Section 3.5, the initialization of the Prefixes will affect the performance. To show the effectiveness of the parallel attention design in FedPerfix, we conduct experiments with Vanilla Prefix-tuning under two different initialization, initialized with zero (Prefix-Z) and random initialization (Prefix-R). Then, we compare the results with FedPerfix. The result is shown in Table 6. As expected, the prefixes generated from the parallel attention yield better performance than the other two manually initialized prefixes, highlighting the effectiveness of the parallel attention design in FedPerfix."
+                                }
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+                                    "content": "FedPerfix vs. Prompts & Adapters. Prompts and adapters are also popular plugins that are widely used. To verify whether FedPerfix is the most effective among all families of the plugins, we also apply Prompts and Adapters"
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+                                            "content": "Table 5. Performance on CIFAR-100 with different model sizes."
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+                                            "html": "<table><tr><td>Method</td><td>ViT-Tiny</td><td>ViT-Small</td><td>ViT-Base</td></tr><tr><td>FedAVG</td><td>19.56±10.27</td><td>23.29±11.31</td><td>24.82±11.53</td></tr><tr><td>Local</td><td>33.73±9.20</td><td>34.74±9.36</td><td>38.93±10.08</td></tr><tr><td>APFL</td><td>37.66±10.04</td><td>44.88±10.50</td><td>47.57±9.57</td></tr><tr><td>FedRep</td><td>41.58±7.19</td><td>44.42±7.80</td><td>44.34±8.35</td></tr><tr><td>FedPerfix</td><td>44.71±8.47</td><td>48.10±7.76</td><td>48.40±8.18</td></tr></table>",
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+                                    "content": "to personalized federated learning. Specifically, we append several trainable Prompts to the input embeddings and keep them updated locally as the implementation of Prompt-tuning [15]. Meanwhile, we add Adapters to the MLP layers as the implementation of Adatper-tuning [30]. The results are shown in Table 6. Adding personalized Prompts doesn't improve the performance compared with simply keeping the classification head updated locally, indicating that the transformation to the input is not effective in PFL. However, adding Adapters to the MLP layers can also lead to a promising result as FedPerfix. Recap the result of our empirical study shown in Table 1, MLP layers are also sensitive to data distribution in a ViT. We note that as another instance to show the effectiveness of adding plugins to the sensitive parts of a ViT in PFL."
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+                                            "content": "Table 6. Performance of different designs on CIFAR-100. Prefix-Z and Prefix-R mean vanilla prefix-tuning with zero and random initialization."
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+                                            "html": "<table><tr><td>FedPerfix</td><td>Prefix-Z</td><td>Prefix-R</td><td>Prompts</td><td>Adapters</td></tr><tr><td>48.10±7.76</td><td>47.37±8.47</td><td>46.98±8.10</td><td>44.19±8.13</td><td>47.99±8.59</td></tr></table>",
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+                                    "content": "6. Conclusion"
+                                }
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+                                    "content": "In this work, we studied two research questions of where and how to personalize a ViT in federated learning. We conducted an empirical study to reveal that the self-attention and classification layers are the most sensitive layers for personalization. Based on that, we proposed FedPerfix, a novel method that introduces Prefixes with parallel attention to personalize the self-attention layers. Through extensive experiments on various datasets with different degrees of data heterogeneity, we demonstrated that FedPerfix achieves state-of-the-art performance while also reducing resource requirements. Our work focuses on ViTs and represents a shift in attention from the extensively researched CNNs, serving as inspiration for further investigation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
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+                                    "type": "text",
+                                    "content": "7. Acknowledgement"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "content": "This work is partially supported by the NSF/Intel Partnership on MLWiNS under Grant No. 2003198."
+                                }
+                            ]
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+            ],
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+                                    "content": "References"
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+                                            "content": "[41] Bruce X. B. Yu, Jianlong Chang, Lingbo Liu, Qi Tian, and Chang Wen Chen. Towards a Unified View on Visual Parameter-Efficient Transfer Learning, Oct. 2022. arXiv:2210.00788 [cs]. 3, 5"
+                                        }
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+                                            "content": "[42] Hao Zhang, Feng Li, Shilong Liu, Lei Zhang, Hang Su, Jun Zhu, Lionel M. Ni, and Heung-Yeung Shum. DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection, Apr. 2022. arXiv:2203.03605 [cs] version: 3.1"
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+                                            "content": "[43] Michael Zhang, Karan Sapra, Sanja Fidler, Serena Yeung, and Jose M. Alvarez. Personalized Federated Learning with First Order Model Optimization. Jan. 2023. 2"
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diff --git a/2023/Federated Learning Over Images_ Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat/9da08db2-59f8-4fa7-be0b-195e30685450_content_list.json b/2023/Federated Learning Over Images_ Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat/9da08db2-59f8-4fa7-be0b-195e30685450_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..ae484cc9bdd43052ec6ba09175407585ebe99f52
--- /dev/null
+++ b/2023/Federated Learning Over Images_ Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat/9da08db2-59f8-4fa7-be0b-195e30685450_content_list.json	
@@ -0,0 +1,1820 @@
+[
+    {
+        "type": "text",
+        "text": "Federated Learning Over Images: Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat",
+        "text_level": 1,
+        "bbox": [
+            114,
+            130,
+            854,
+            176
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Erdong Hu<sup>1</sup>, Yuxin Tang<sup>1</sup>, Anastasios Kyrillidis, Chris Jermaine Rice University",
+        "bbox": [
+            225,
+            202,
+            746,
+            237
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{eh51, yuxin.tang, anastasios, cmj4}@rice.edu",
+        "bbox": [
+            222,
+            239,
+            750,
+            258
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We carefully evaluate a number of algorithms for learning in a federated environment, and test their utility for a variety of image classification tasks. We consider many issues that have not been adequately considered before: whether learning over data sets that do not have diverse sets of images affects the results; whether to use a pre-trained feature extraction \"backbone\"; how to evaluate learner performance (we argue that classification accuracy is not enough), among others. Overall, across a wide variety of settings, we find that vertically decomposing a neural network seems to give the best results, and outperforms more standard reconciliation-used methods.",
+        "bbox": [
+            73,
+            323,
+            473,
+            505
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            537,
+            209,
+            553
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There has been a recent influx of work aimed at developing and evaluating new algorithms for Federated Learning (FL) [2, 6, 20, 29], particularly for image classification [3, 14, 18, 27, 28, 31, 35, 50, 53]. Most papers are primarily concerned with the development of innovative algorithms, and less concerned with the design of appropriate benchmarks and especially, appropriate baselines to test against. This paper, in contrast, is concerned with benchmarking: Which existing methods for FL work best, and under what conditions do they work, or not work? As such, our primary contribution is a set of carefully-designed experiments, rather than the introduction of a new FL algorithm. Our benchmarks are designed to address the following concerns regarding the design of FL benchmarks and baselines.",
+        "bbox": [
+            73,
+            563,
+            470,
+            790
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(1) Learning algorithms are typically evaluated on a few diverse data sets, rather than a large variety of more focused data sets. The most common benchmark for evaluating federated image classification is CIFAR-100 [25]. This dataset includes whales, chairs, dinosaurs, and so on. This is a very",
+        "bbox": [
+            75,
+            797,
+            470,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "diverse set of classes, and we are concerned that few FL tasks will involve differentiating dinosaurs from rabbits.",
+        "bbox": [
+            500,
+            292,
+            890,
+            323
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "For example, imagine that the members of a bird watching club taking pictures with their smartphones; club members label the pictures with the bird species, and FL is used to build a classifier. Or, a set of companies who are typically competitors—and hence cannot exchange data—want to work together to classify pictures of industrial drill bits based on whether they are going to fail. Both of these deployments involve narrow domains, and the classification problems involve fine-grained differentiation [13, 48] among members of a narrow category. True, not all applications of FL will be narrow, but they are likely to be far narrower than classifying whales versus chairs. We argue that, while evaluating on a broad data set—such as CIFAR-100—is useful, it is also necessary to evaluate FL algorithms on a variety of more narrow data sets.",
+        "bbox": [
+            496,
+            325,
+            893,
+            554
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(2) Most evaluations focus on final accuracy or the number of communication rounds required for convergence. FL algorithms are often evaluated by reporting final accuracies (after convergence), or by plotting test accuracy as a function of the number of epochs, or the number of communication rounds. However, final accuracy, at least in isolation, is not really a useful metric. After all, the simplest \"FL\" algorithm is classical, data parallel learning [33,41,52]. That is, run distributed gradient descent; compute gradients locally over mini-batches in a fully synchronous way, then do an all-reduce. As this is functionally equivalent to centralized learning, it is invariant to data distribution, and is likely to be the most accurate method in terms of final accuracy. However, it is inefficient in a federated environment.",
+        "bbox": [
+            496,
+            563,
+            893,
+            776
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Likewise, considering accuracy as a function of communication rounds ignores the computation or communication cost of each round. Communication and computation costs can vary across methods, and are typically far more important than the number of rounds. A method that can quickly achieve high accuracy with a relatively large number of very inexpensive communication rounds—where a small fraction of the model is communicated at each round—is proba",
+        "bbox": [
+            496,
+            779,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            805,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{1}$ Equal contribution.",
+        "bbox": [
+            94,
+            886,
+            205,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "19385",
+        "bbox": [
+            480,
+            944,
+            517,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "bly preferred to one that uses few rounds, but must transmit a huge amount of data. Similarly, for computation, given similar accuracies, an algorithm that performs one forward and one backward gradient descent pass is preferred over one that performs two additional forward passes, as extra overhead [28], even though both operate in the same number of communication rounds.",
+        "bbox": [
+            75,
+            90,
+            472,
+            196
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "(3) Pre-trained feature extractors need to be a standard baseline. Training the feature-extraction backbone that is used in most deep image processing networks—that is, the series of convolutional and pooling layers and without the final classification layer—is not easy. It is difficult to get the training process right, and training a good backbone requires a lot of computation.",
+        "bbox": [
+            75,
+            205,
+            472,
+            311
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Researchers have recently suggested using pre-trained backbones, especially for few-shot training [7, 16]. In a pre-trained backbone, a pre-trained feature extractor such as a convolutional neural network (CNN) [15, 19, 39] or vision transformer [10] is used without modification to embed an image in a high-dimensional space. Learning is then performed on the resulting vectors, and not on the original images. The goal is to leverage an existing, well-trained model on the new learning problem. Given the resource constraints in many FL scenarios, it is unclear why attempting to fully train such a backbone from scratch in a federated environment would be the first approach. Instead, we suggest simply taking a standard, pre-trained backbone (such as a ResNet [15], or a DenseNet [19], or both used together) and directly using that backbone as a feature extractor, without training.",
+        "bbox": [
+            75,
+            313,
+            472,
+            555
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The benefit is that each training image only needs to be pushed through the backbone one time to obtain a compact set of features, and then that set can be used during training. As the backbone need not to be communicated or repeatedly used to process the input images, both CPU/GPU cycles and communication are saved during federated training. Furthermore, final accuracies might actually be better, as this approach sidesteps the difficulty of training the backbone.",
+        "bbox": [
+            75,
+            556,
+            472,
+            691
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "(4) Off-the-shelf performance is really what matters, but it is often neglected in research studies. In a centralized environment, it is feasible to train and re-train many times, as various parameters (learning rate, proximal weight, exact neural architecture, etc.) are tuned. In FL, this is much less feasible. Most FL scenarios imagine a resource-constrained environment (possibly involving edge devices), where one cannot ignore the cost of tuning. FL is typically happening on someone else's hardware, and so running an algorithm many times during parameter tuning is likely to make participation in training far less palatable.",
+        "bbox": [
+            75,
+            700,
+            472,
+            867
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Further, application-specific tuning may simply be impossible. A device may enter the federated training and then",
+        "bbox": [
+            76,
+            869,
+            470,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "drop out shortly after, never to be seen again. One cannot access a missing device's data to perform validation, and clearly, one cannot retrain over data that cannot be accessed.",
+        "bbox": [
+            496,
+            90,
+            893,
+            136
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As such, we argue that \"off-the-shelf\" performance is more important than in centralized learning. That is, it becomes important to settle on one set of universal parameters that tend to work in most deployments, such that the learning algorithm can be universally deployed without further tuning. At the very least, this is an important use case that should be covered in most experiments.",
+        "bbox": [
+            496,
+            136,
+            893,
+            242
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our Contributions. Our contributions are as follows.",
+        "bbox": [
+            498,
+            248,
+            857,
+            263
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We suggest several rules-of-thumb governing benchmark and baseline development for FL over images, and use those rules to devise an extensive FL image classification benchmark, and use that benchmark.",
+            "- We show that using pre-trained features and other model reduction tools are necessary for practical FL.",
+            "- We highlight some surprising behaviors of current FL algorithms, including the effect of client population size, that to our knowledge are not sufficiently explored in current literature.",
+            "- Our source code is publicly available at https://github.com/huerdong/FedVert-Experiments"
+        ],
+        "bbox": [
+            500,
+            268,
+            893,
+            492
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Background",
+        "text_level": 1,
+        "bbox": [
+            500,
+            506,
+            629,
+            523
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The common setting for FL is the following: There are total  $N$  devices participating in the optimization. To protect data privacy (or due to communication constraints), devices are not allowed to share local data samples to others. Each device has its own local objective function  $f_{i}$  parameterized by its own model  $w_{i}$ . The coefficient  $p_i = n_i / n$  is the number of data samples  $n_i$  on each device, divided by the unified total data sample  $n = \\sum_{i=1}^{N} n_i$ . There will be a central server that collects all the parameters  $w_{i}$  uploaded by each device and aggregate them into a single model  $w$ .",
+        "bbox": [
+            496,
+            532,
+            893,
+            683
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The common formulation of FL is to optimize a global optimization function  $L(w)$ :",
+        "bbox": [
+            496,
+            683,
+            893,
+            713
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {w} L (w) = \\sum_ {i = 1} ^ {N} p _ {i} L \\left(w _ {i}; \\left\\{x _ {\\text {l o c}}, y _ {\\text {l o c}} \\right\\}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
+            715,
+            890,
+            757
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $L(w_{i};\\{x_{\\mathrm{loc}},y_{\\mathrm{loc}}\\})$  represents the local objective for device  $i$ , based on local data  $\\{x_{\\mathrm{loc}},y_{\\mathrm{loc}}\\}$ . The natural algorithm that arises from this objective is FedAvg [37] which directly applies stochastic gradient descent (SGD) to learn  $w_{i}$ 's. In the most basic case, where FedAvg performs only one local gradient step, the above formulation becomes equivalent to data parallel SGD [33,41,52].",
+        "bbox": [
+            496,
+            763,
+            893,
+            869
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In real-world applications of FL, local data distributions are often skewed towards specific classes: i.e., the natural",
+        "bbox": [
+            498,
+            869,
+            893,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "19386",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "distribution of real data can be very skewed, with certain classes only existing in a very small segment of clients' devices. In these heavily non-i.i.d. scenarios, the learned  $w_{i}$  in Eq. (1) can diverge in drastically different directions and, in the most extreme cases, diverge in opposite directions. When FL is performed in this scenario, the averaging can result in a model drastically different from any of the client models and has degraded performance as a consequence; a phenomenon often called client drift [54]. It is this concern that has motivated the development of a number of FL methods beyond FedAvg [21,28,30,43], a few of which will be described in the next section.",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Federated Learning Methods Tested",
+        "text_level": 1,
+        "bbox": [
+            76,
+            285,
+            406,
+            303
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. The Methods",
+        "text_level": 1,
+        "bbox": [
+            76,
+            310,
+            215,
+            324
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In our experiments, we consider the following FL methods, chosen as a representative set of the state-of-the-art.",
+        "bbox": [
+            76,
+            333,
+            468,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FedAvg. Federated averaging [37] is the most simple averaging algorithm and is the basis of the others, whereby client models are trained locally by (stochastic) gradient descent. These local models are aggregated by directly averaging their weights, or equivalently averaging their computed gradients using this averaged gradient for one global round of gradient descent.",
+        "bbox": [
+            75,
+            369,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FedProx. FedProx [30] is a modification on FedAvg that introduces an additional  $\\ell_2$ -norm term to the local loss function, that takes the difference between the previously communicated global model and the current model. The aim is to avoid client drift by biasing the training towards an established model. Again, the clients then compute local models whose weights are averaged. Given the model weights  $w_0$  from the previous communication round, the FedProx modification to the FedAvg objective is:",
+        "bbox": [
+            75,
+            481,
+            468,
+            617
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min _ {w _ {i}} \\left\\{L (w _ {i}; \\{x _ {\\mathrm {l o c}}, y _ {\\mathrm {l o c}} \\}) + \\frac {\\mu}{2} \\| w _ {i} - w _ {0} \\| _ {2} ^ {2} \\right\\}, i \\in [ N ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
+            627,
+            449,
+            651
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu$  is a regularization parameter.",
+        "bbox": [
+            76,
+            660,
+            328,
+            676
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "MOON. MOON (Model-Contrastive) [28] uses a similar principle as FedProx by comparing the current model with the previous model. However, it utilizes a cross-entropy loss, rather than  $\\ell_2$ -norm loss, as in:",
+        "bbox": [
+            76,
+            681,
+            468,
+            742
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {w _ {i}} \\left\\{L (w _ {i}; \\{x _ {\\mathrm {l o c}}, y _ {\\mathrm {l o c}} \\}) - \\mu \\log \\frac {e ^ {\\sin (z , z _ {\\mathrm {g l o b}}) / \\tau}}{e ^ {\\sin (z , z _ {\\mathrm {g l o b}}) / \\tau} + e ^ {\\sin (z , z _ {\\mathrm {p r e v}}) / \\tau}} \\right\\}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            78,
+            750,
+            465,
+            779
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{sim}()$  is the cosine similarity function, and  $z, z_{\\text{glob}}, z_{\\text{prev}}$  are representations of the data generated by the respective model (respectively: learned, current global, previous local).  $\\tau$  is a temperature hyperparameter.",
+        "bbox": [
+            76,
+            787,
+            468,
+            849
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FedAdam. While the above algorithms modify the local training process of FedAvg, FedAdam [40] modifies the aggregation step. Once the averaged weights are computed",
+        "bbox": [
+            76,
+            854,
+            468,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "via local gradient descent and their average is computed, it is used to compute a global gradient surrogate to be used in the Adam algorithm [22].",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "FedNova. FedNova [43] introduces a client gradient reweighting scheme when accumulating the models parameters/gradients and generalizes FedAvg and FedProx as specific parameterizations. However, we use the specific formulation specified in [43], where these weights are normalizations of the local gradients.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "IST. We consider the previous set of learning algorithms to be \"reconciliation-used\"; in that, they attempt to train a copy of the model at each site. In contrast, IST, or independent subnet training [51] does not utilize averaging or some other method to try to reconcile versions of the model trained at the various sites. Instead, IST decomposes the model and sends non-overlapping parts of the model to different sites. In one training round, all neurons (or activations) in a neural network are randomly partitioned to the active sites. A weight is only sent to a site if it connects two neurons that have been assigned to the site. Thus, each site is assigned only a very small subnet network, which is trained locally for a number of gradient descent steps. At the end of local training, the updated weights are shuffled (with or without the aid of a central server) and the process is repeated. Since subnetworks are independent, there is no averaging or other form of reconciliation needed. There are many variants of this approach in the literature, including FjORD [17], HeteroFL [9], LotteryFL [26], FedSelect [4], FedRolex [1], Federated Dropout [5], PVT [47], and the independent subnet network training approach in the non-FL setting [11, 32, 44, 45, 51]. It is this latter version of the approach (for MLPs) that we apply here.",
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+    },
+    {
+        "type": "text",
+        "text": "ISTProx. This is IST, but with a proximal term added to the loss function.",
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+    {
+        "type": "text",
+        "text": "3.2. Analytic Comparison",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The focus of our experiments will be on comparing each of the methods based on their ability to produce high test accuracy with a low cost. In the paper, we will define cost in terms of floating point operations (FLOPs) required to reach a given accuracy, and in terms of floating point numbers transferred. As such, we begin by considering the number of FLOPS required and the floating point numbers that must be transferred to complete one gradient descent step for each of the methods.",
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+        "type": "text",
+        "text": "In our analysis, we assume that we are using a pretrained backbone to transform each input image into a vector, and we are learning a MLP with two weight matrices. The MLP accepts an  $n_1$ -dimensional input. It has a hidden layer of  $n_2$  neurons, and has  $n_3$  outputs. Assume a batch size of  $b$  at each of  $s$  sites. Since each image only goes through the pre-trained backbone once, the FLOP cost",
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+    {
+        "type": "page_number",
+        "text": "19387",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "of the pre-trained backbone is negligible when amortized over many gradient descent steps. We will consider only the FLOPs associated with the weights, as the cost associated with updating weights dominates the cost associated with the activation layers.",
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+    {
+        "type": "text",
+        "text": "Begin with FedAvg. In this case, to push a batch through, we have approximately  $2b(n_{1}n_{2} + n_{2}n_{3})$  FLOPs for the forward pass and approximately  $2b(n_{1}n_{2} + 2n_{2}n_{3})$  for the backward pass, for a total of  $4n_{1}n_{2}b + 6n_{2}n_{3}b$  FLOPs at each site. Coordination requires  $2s(n_{1}n_{2} + n_{2}n_{3})$  floating point numbers be sent (the model needs to be distributed to all sites, and then the updated model needs to be collected from all sites). The number of FLOPs incurred during averaging is typically not significant, as we are simply average  $s$  copies of the two weight matrices, having  $n_{1}n_{2}$  and  $n_{2}n_{3}$  floating point numbers each, and this may be done using a distributed algorithm.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Adding a proximal term in the case of FedProx may have little effect, as this changes the backward pass at each site by adding FLOP computations that scales linearly with the weight matrices, but does not scale with the batch size  $b$ . Thus, for any reasonable batch size, it is insignificant. If multiple gradient update steps are performed at each site, it also requires storing an older copy of the weight matrices at each site.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "FedAdam is a federated version of the Adam algorithm and as such, it requires storing four additional matrices—typically at a coordinator—two of which are associated with each of the MLP's weight matrices. It must approximate the gradient and run the Adam algorithm at the coordinator during each update. However, this does not affect the memory, computation, or communication requirements at each site, and so any differences may not be of practical importance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "FedNova requires a normalization step at each site during the local gradient computation, but this only requires multiplying each gradient by a scalar, which is likely insignificant and so it is also, for practical purposes, computationally no more expensive than FedAvg. MOON is more expensive than FedAvg in terms of FLOPs, as it needs to compute multiple representations of each training iteration. The obvious MOON implementation will require  $4bn_{1}n_{2}$  additional FLOPs compared to FedAvg at each site. In addition, MOON needs to locally maintain two additional copies of the weight matrices.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Next, consider IST. At each site,  $n_2$  is effectively cut by a fraction  $s$ , because the neurons in the hidden layer is partitioned  $s$  ways and only the weights associated with neurons assigned to a site are actually sent or used there. Hence, the total number of FLOPs is  $(4n_1n_2b + 6n_2n_3b) / s$ , and coordination requires that only  $2(n_{1}n_{2} + n_{2}n_{3})$  floating point numbers be sent and received; each weight is assigned to exactly one site. There are no FLOPs associated with coordination, as there is no averaging done; weights are sim",
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+    },
+    {
+        "type": "text",
+        "text": "ply updated and sent around. Due to the partitioning, the memory usage at each site is on average smaller than that of FedAvg by a factor of  $s$ . Like FedAvg, adding a proximal term has little effect on either FLOPs or bytes transferred.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Experimental Setup",
+        "text_level": 1,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Pre-Trained Backbones",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "All of the methods we tested (except for one baseline) utilize pre-trained backbones. That is, we take a pre-trained feature image classifiers: ResNet101 [15] and DenseNet121 [19], and remove the classification layers to produce two \"backbones.\" When processing an image, we simply concatenate the feature vectors produced by the two backbones to produce a 3072 dimensional vector. We also evaluate FedProx, but without a pre-trained backbone. This version of FedProx (called \"FedFull\") uses a ResNet18 instead of a single-hidden layer MLP.",
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+    {
+        "type": "text",
+        "text": "4.2. Data Sets and Hyperparameters",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Overall, we conduct experiments on a diverse and broad range of image classification data sets: (1) CUB-200-2011 (Birds) [42], (2) Stanford Cars (Cars) [23], (3) VGGFlowers (Flwrs) [38], (4) Aircraft (Aircraft) [36], (5) Describable Textures (Textre) [8], and (6) CIFAR 100 (CFAR) [24]. The only processing we apply on these data sets, besides using the pre-trained feature extractors, is the standard cropping and resizing of image data. For the Aircraft data set, there are multiple levels of specificity of labels - manufacturer, family, variant - we chose variant for the finest-grained classes.",
+        "bbox": [
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+        "type": "text",
+        "text": "We use the Birds data set to tune the methods. After extensive experimentation on Birds, we chose a learning rate of 0.01, as we found this to give stable convergence in all algorithms, except FedAdam, where we choose a learning rate of 0.03. For all algorithms except for IST, ISTProx, and FedFull, tuning led us to a single-hidden-layer, multi-layer perceptron (MLP) with 1,000 hidden neurons sitting on top of the feature extractor. FedFull was trained with its \"out of the box\" configuration. For IST and ISTProx, we find scaling the hidden neurons based on the number of concurrent training sites made sense (3000 neurons for ten sites, 6000 for 20, 9000 for 30, 18000 for 60, and so on). This ensures that the client models are not too small.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "A number of other hyperparameters were also optimized using the Birds data set. For the various hyperparameters in each algorithm, we applied a grid search on a set list of parameter values, as described in the next subsection. We consider the number of local iterations of stochastic gradient descent as a hyperparameter with either 1, 5, or 25 local training batches, before a communication round. We use a batch size of 32 images. For FedProx, FedNova, and IST-Prox, we tuned the additional proximal hyperparameter  $\\mu$ . For MOON, we have a similar weight parameter  $\\mu$  (the co",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19388",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/40d5922de81e3d4fe2b83274b90791f1b7d2af2ddc7b916acad319a9191f2661.jpg",
+        "table_caption": [
+            "(a) Final accuracies"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>73.5</td><td>66.7</td><td>95.9</td><td>48.8</td><td>74.3</td><td>76.7</td></tr><tr><td>FedProx</td><td>74.0</td><td>65.7</td><td>95.8</td><td>48.9</td><td>74.7</td><td>75.1</td></tr><tr><td>MOON</td><td>74.3</td><td>66.0</td><td>95.6</td><td>48.9</td><td>74.6</td><td>75.3</td></tr><tr><td>FedAdam</td><td>67.6</td><td>51.1</td><td>92.4</td><td>41.9</td><td>72.8</td><td>70.1</td></tr><tr><td>FedNova</td><td>73.3</td><td>66.8</td><td>95.6</td><td>49.0</td><td>74.7</td><td>74.7</td></tr><tr><td>FedFull</td><td>5.2</td><td>2.8</td><td>35.1</td><td>5.4</td><td>40.3</td><td>7.8</td></tr><tr><td>IST</td><td>74.6</td><td>67.8</td><td>96.4</td><td>50.6</td><td>74.6</td><td>76.2</td></tr><tr><td>ISTProx</td><td>74.8</td><td>66.8</td><td>96.5</td><td>50.4</td><td>74.7</td><td>76.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/4cf466ed26a700cb187709bbcbdc3bbd71ed2ba632565ef742cd596e26e4527f.jpg",
+        "table_caption": [
+            "(b) Communication (GB) to threshold acc."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>9</td><td>6</td><td>4</td><td>13</td><td>3</td><td>10</td></tr><tr><td>FedProx</td><td>13</td><td>FAIL</td><td>6</td><td>21</td><td>5</td><td>15</td></tr><tr><td>MOON</td><td>13</td><td>43</td><td>6</td><td>21</td><td>4</td><td>16</td></tr><tr><td>FedAdam</td><td>8</td><td>FAIL</td><td>2</td><td>FAIL</td><td>1</td><td>7</td></tr><tr><td>FedNova</td><td>57</td><td>138</td><td>17</td><td>84</td><td>12</td><td>68</td></tr><tr><td>FedFull</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>IST</td><td>3</td><td>288</td><td>1</td><td>3</td><td>1</td><td>3</td></tr><tr><td>ISTProx</td><td>3</td><td>FAIL</td><td>2</td><td>3</td><td>1</td><td>3</td></tr></table>",
+        "bbox": [
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+            268,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/1affc9672ab746424f88b7f9f1ade5ba63d9cce6063aca02e53fde12e4d7ec4e.jpg",
+        "table_caption": [
+            "(c) GFLOPs to threshold acc."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>904</td><td>642</td><td>445</td><td>1334</td><td>275</td><td>979</td></tr><tr><td>FedProx</td><td>53</td><td>FAIL</td><td>23</td><td>86</td><td>18</td><td>62</td></tr><tr><td>MOON</td><td>110</td><td>FAIL</td><td>46</td><td>178</td><td>34</td><td>121</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>170</td><td>FAIL</td><td>152</td><td>750</td></tr><tr><td>FedNova</td><td>1140</td><td>2768</td><td>333</td><td>1680</td><td>232</td><td>1355</td></tr><tr><td>FedFull</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>IST</td><td>11</td><td>1152</td><td>6</td><td>14</td><td>3</td><td>12</td></tr><tr><td>ISTProx</td><td>11</td><td>FAIL</td><td>6</td><td>14</td><td>3</td><td>13</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1: i.i.d. results, 100 sites,  ${10}\\%$  participation.",
+        "bbox": [
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+            602
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "efficient of the contrastive term) and  $\\tau$ , the temperature of the contrastive term. FedAdam has a central learning rate as well, which we set to 0.01. Exact values for all of our hyperparameters are given in the appendix. We stress that, while we performed careful tuning on the Birds data set, all hyperparameters were re-used blindly and without modification, on all other data sets.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Choosing an evaluation metric is among the most difficult aspects of evaluating FL methods, but does not seem to have received much attention in the literature. Most papers focus on final accuracy: What is the accuracy that a FL method exhibits on a test set after training? Unfortunately, final accuracy as a metric makes little sense in isolation from other considerations. After all, the method that likely gives the very best final accuracy is simple dis",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/120d7737c1cb9b1bf36300a48a46bb1efa4187107380753166f40bccc5f1d659.jpg",
+        "image_caption": [
+            "Figure 1: Accuracy as a function of time for FedProx and FedFull on the Stanford Cars data set."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "tributed mini-batch training, where each site computes gradients over a small subset of its local data; those gradients are summed and a central site updates the model. This is algorithmically equivalent to centralized training, but it is typically not tested, because it is generally assumed that the convergence would be too \"slow,\" for some implicit definition of \"slow.\" Thus, a more carefully-defined evaluation framework (beyond simple accuracy) is needed.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Hence, we consider three metrics: final accuracy, computational efficiency, and communication efficiency [34, 46]. Of the three, we assert that final accuracy should be considered the least important; it is most useful as a way to contextualize the other two metrics (e.g., \"what final accuracy can I achieve in GigaFLOPs of computation?\").",
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Tuning and Evaluation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "For a given method, using the Birds data set, we first perform a grid search over the various hyperparameters, and for each hyperparameter set, we run the method for a \"long time,\" where a \"long time\" allows a maximum of  $10^{14}$  floating point operations (or 100 teraFLOPs, where floating point operations are summed across all devices participating in federated training) and five terabytes of data communicated (assuming single-precision floating point computations). Note that 100 teraFLOPs corresponds to around 14 hours of CPU time on a single mobile phone, or perhaps several hundred hours of processor time on a limited IoT device. Once a method exceeds 100 teraFLOPs or five terabytes of communication, we take its very best observed test accuracy, averaged over ten communication rounds. The best average observed over all hyperparameter settings is taken as the method's \"final accuracy\".",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Once we have the method's final accuracy, we then perform a grid search over all hyperparameters to find the two sets of parameter settings for the method that (a) minimize the number of FLOPs to reach  $90\\%$  of the final accuracy, and (b) minimize the number of GB of communication necessary to reach  $90\\%$  of the final accuracy. Now we have",
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+    },
+    {
+        "type": "page_number",
+        "text": "19389",
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+        "page_idx": 4
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+    {
+        "type": "image",
+        "img_path": "images/9038faca4e44741825b1c6bd4a9494d0e9d684221c840f7585de7032377faa79.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/d4764527bafd910e254a4513e30409f3e597cff464bccb79f439b37f3aaef35c.jpg",
+        "image_caption": [
+            "(b) Skewed, Cars, one round accuracy."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/01582e4c09836aca10f90f1a0a7c621262118f57b09ae8edf17cdb54dc85e4f6.jpg",
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+    {
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+        "img_path": "images/3e4d0f784678468c327912c37d21c88264f12be7c0e8147d9cf484947e58d91e.jpg",
+        "image_caption": [
+            "(a) i.i.d., Cars, one round accuracy.",
+            "(d) i.i.d., Flowers, one round accuracy.",
+            "Figure 2: Comparison of similarity of the FL descent direction to a centrally-computed descent direction. One means the directions are identical; 0 represents de-correlation. At left is i.i.d. data; center is skewed data, similarity computed over one descent step; right is skewed data, similarity computed over 20 descent steps."
+        ],
+        "image_footnote": [],
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+        "img_path": "images/cfa75b3671a4d1b4cdd36d457e96f97fe472f3f9cfb7ce1836d43371163559ac.jpg",
+        "image_caption": [
+            "(e) Skewed, Flowers, one round accuracy."
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/1e73ae70bd38e22fb95082657336c958f3197d608c81da4244281cee8c2544ee.jpg",
+        "image_caption": [
+            "(c) Skewed, Cars, 20 rounds accuracy.",
+            "(f) Skewed, Flowers, 20 rounds accuracy."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            632,
+            250,
+            888,
+            383
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "three sets of hyperparameters: one optimized for accuracy, one for gigaFLOPs, and one for communication. The reason that we use three sets of hyperparameters is that the goals of maximizing accuracy, minimizing FLOPs and minimizing communication are often in direct opposition to one another, and these resources can often be traded (e.g., more local iterations and FLOPs for less communication).",
+        "bbox": [
+            75,
+            491,
+            467,
+            595
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Next, we consider each data set in sequence. We first run each method to 100 teraFLOPs or five terabytes of communication on the data set, using the accuracy-optimized parameters. We then compute the maximum accuracy that any method obtained on the data set, and set  $90\\%$  of this accuracy as a target. Then, for each method and each data set, we compute two additional numbers: the number of gigaFLOPs required to reach the target accuracy for five consecutive rounds (using the FLOP-optimized settings), and the number of gigabytes of communication required to reach the target accuracy (using the communication-optimized settings). If a method is unable to reach the target accuracy within the 100 teraFLOPs/five terabytes limit, it is said to have failed (indicated as FAIL in tables).",
+        "bbox": [
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+            597,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We estimate the amount of FLOPs used during training using the FlopCountAnalysis tool in the Python fvmcore [12]. Similarly, for our communication costs we estimate the size of a model in bytes with the Python torchinfo [49] package.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The reason for this evaluation strategy is simple. In practice, the preferred FL method is likely to be the one that",
+        "bbox": [
+            76,
+            869,
+            467,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "reaches a high level of accuracy with little cost. Hence, we (somewhat arbitrarily, but precisely) define \"high level of accuracy\" as  $90\\%$  of the peak accuracy observed over all methods for a given data set. Given this target, evaluation is then a matter of counting floating point operations and bytes to reach that target.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Note that other metrics are possible: power usage and elapsed wall clock time are two of the most obvious. However, both of these will be closely related to FLOPs and communication required, and hence we stick to these two.",
+        "bbox": [
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+            580,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Identically Distributed Data",
+        "text_level": 1,
+        "bbox": [
+            500,
+            655,
+            758,
+            671
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
+            680,
+            578,
+            696
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In our first set of experiments, the images are randomly partitioned across the sites, so that each site has a randomly-selected (with replacement) subset of the overall set of images in the training data set. After a round of communication finishes, ten sites are randomly selected as being \"on the network\" and those sites participate in the present round of training. After local training finishes and all of the results have been communicated, another set of ten sites are randomly selected and the process continues.",
+        "bbox": [
+            496,
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+            839
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For this simple \"i.i.d.\" setup, our experiments will answer a few key questions. First and foremost, should we be doing full backpropagation through a convolutional network, or should we be exclusively using a pre-trained back",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "19390",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/149f0b4d2156e0c36b1eba4708d24b6aee112259ebc2f882920647db978cfa49.jpg",
+        "table_caption": [
+            "(a) Final accuracies"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>61.5</td><td>56.4</td><td>88.9</td><td>40.2</td><td>68.1</td><td>61.4</td></tr><tr><td>FedProx</td><td>58.4</td><td>50.1</td><td>85.4</td><td>35.6</td><td>66.8</td><td>60.5</td></tr><tr><td>MOON</td><td>57.7</td><td>48.0</td><td>86.9</td><td>37.6</td><td>66.2</td><td>58.6</td></tr><tr><td>FedAdam</td><td>49.4</td><td>16.9</td><td>81.0</td><td>28.9</td><td>54.0</td><td>40.5</td></tr><tr><td>FedNova</td><td>58.4</td><td>47.1</td><td>83.6</td><td>37.0</td><td>64.3</td><td>60.3</td></tr><tr><td>IST</td><td>64.3</td><td>50.8</td><td>90.7</td><td>39.8</td><td>69.5</td><td>49.4</td></tr><tr><td>ISTProx</td><td>64.8</td><td>50.3</td><td>91.3</td><td>40.6</td><td>68.2</td><td>56.7</td></tr></table>",
+        "bbox": [
+            84,
+            103,
+            454,
+            228
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/faa80177175832587eccb862bc4593cf72b0b1f44e18a8b181aea1807ebb95dd.jpg",
+        "table_caption": [
+            "(b) Communication (GB) to threshold acc."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>131</td><td>62</td><td>51</td><td>79</td><td>55</td><td>59</td></tr><tr><td>FedProx</td><td>250</td><td>FAIL</td><td>124</td><td>FAIL</td><td>71</td><td>54</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>193</td><td>FAIL</td><td>143</td><td>74</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>743</td><td>FAIL</td><td>430</td><td>608</td><td>309</td><td>160</td></tr><tr><td>IST</td><td>79</td><td>FAIL</td><td>37</td><td>119</td><td>69</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>72</td><td>FAIL</td><td>59</td><td>134</td><td>72</td><td>219</td></tr></table>",
+        "bbox": [
+            86,
+            255,
+            460,
+            378
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/9626e3e98a899cd004514ed0b7cece8fa95a1ad085d3a7d150b2c4ea465b5a3b.jpg",
+        "table_caption": [
+            "(c) GFLOPs to threshold acc"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>13121</td><td>6245</td><td>5150</td><td>7892</td><td>5461</td><td>5884</td></tr><tr><td>FedProx</td><td>1000</td><td>FAIL</td><td>495</td><td>FAIL</td><td>283</td><td>218</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>581</td><td>1243</td><td>653</td><td>1207</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>14872</td><td>FAIL</td><td>8614</td><td>12172</td><td>6181</td><td>3200</td></tr><tr><td>IST</td><td>315</td><td>FAIL</td><td>148</td><td>475</td><td>277</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>287</td><td>FAIL</td><td>238</td><td>535</td><td>288</td><td>875</td></tr></table>",
+        "bbox": [
+            84,
+            406,
+            460,
+            530
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Skewed data results, 100 sites,  ${10}\\%$  participation.",
+        "bbox": [
+            78,
+            541,
+            465,
+            556
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "bone? Second, when one considers computation and communication (rather than just final accuracy) do the methods compare differently than when the only metric is accuracy? And finally, does the data set used matter? Results are shown in Table 1. For each data set, the best result is indicated in bold.",
+        "bbox": [
+            75,
+            587,
+            468,
+            676
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Discussion",
+        "text_level": 1,
+        "bbox": [
+            76,
+            693,
+            192,
+            708
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "There are a few clear results. First, except for FedAdam and FedFull, the methods generally have very similar final accuracy, with the two IST-based methods being slightly higher. Thus, one key finding is that for data without skewness across sites, if one is only interested in final accuracy, it does not seem to matter much which method is used, and this result holds across data sets. The two exceptions to this are FedAdam and FedFull. FedAdam does not reach the same final accuracy as the other methods, but it generally does quite a good job reaching high accuracy with relatively little communication. This corresponds to the fact that it tends to converge in relatively few communication rounds.",
+        "bbox": [
+            75,
+            719,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "FedFull is a very interesting case. Note that it has poor final accuracy—only  $3\\%$  in the case of the Cars data set. As a result, it is labeled as “FAIL” in every case, because it can never reach  $90\\%$  of the peak accuracy observed for the other methods on a given data set. One might ask, Why is FedFull such a poor choice? The answer is simple: as we put a 100 teraFLOP/five terabyte “timeout” on the computation, FedFull timed out in every case. That is, it always hit the 100 teraFLOP/five terabyte limit. Were FedFull allowed infinite computation and infinite communication, it is actually the preferred method, as the pre-trained backbones limit accuracy. For example, consider Figure 1, which plots accuracy as a function of FLOPs for both FedFull and FedProx on Cars. FedFull eventually reaches  $90\\%$  accuracy, but it takes nearly four orders of magnitude more FLOPs to top out compared to FedProx. This FLOP usage gap is apparent in Fig. 1 where even the first communication round of FedFull requires more FLOPs than the amount required for the entire FedProx training. As a result, we would argue that full backpropagation is effectively unusable in resource-constrained FL. Note, however, that our FedFull was trained using an initialization consisting of random weights. Perhaps a hybrid method makes sense, where one begins with FedProx (with a pre-trained backbone) and then once the MLP begins to reach peak accuracy, we allow backpropagation over the backbone to begin. This issue deserves further investigation. That said, given our maximum FLOP count and communication, FedFull is not competitive and in the interest of space, we will not consider it further.",
+        "bbox": [
+            496,
+            90,
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+            529
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The final observation we make is the general superiority of IST, over each of the six data sets. It is perhaps not surprising that IST is efficient in terms of communication and in terms of computation. Each site obtains only a fraction of the MLP that is being trained, saving communication and computation at each site. However, it is surprising that it is also generally the most accurate method, in terms of final accuracy (or close to it) in every case. We will examine this finding more fully, later in the paper.",
+        "bbox": [
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+            530,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6. Effect of Data Skewness",
+        "text_level": 1,
+        "bbox": [
+            500,
+            684,
+            723,
+            699
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6.1. Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
+            709,
+            580,
+            726
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "How might these results change if data are not uniformly distributed across sites? To answer this question, we modify our experiments as follows. Rather than assigning each training image to each site with uniform probability, we sample the class probabilities for each site from a Dirichlet(0.01) distribution, and rerun our experiments (with 100 sites and 10 sites active in each round). This creates a relatively extreme—yet still realistic—amount of skew. For the six data sets we tested, the three-tuple (number of classes in data set, min number of classes at any site, max number of classes at any site) is: for Birds (200, 7,",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "19391",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/33d8db3c9c0c05c7d00ad2eed59f10a4ac8ec766449fe7cb80387b33d4e989ea.jpg",
+        "table_caption": [
+            "(a) 1000 sites",
+            "Change in acc.,  $2\\% \\rightarrow 6\\%$  participation"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.1</td><td>-0.8</td><td>0</td><td>0</td><td>-1.1</td><td>1.3</td></tr><tr><td>FedProx</td><td>0.1</td><td>-2</td><td>0.4</td><td>0.8</td><td>1</td><td>1.1</td></tr><tr><td>MOON</td><td>0.3</td><td>2.9</td><td>0.5</td><td>0.5</td><td>-0.2</td><td>1.4</td></tr><tr><td>FedAdam</td><td>12.8</td><td>16.8</td><td>7</td><td>12.5</td><td>12.1</td><td>12.4</td></tr><tr><td>FedNova</td><td>0.6</td><td>-0.5</td><td>-0.5</td><td>0</td><td>0.6</td><td>0.8</td></tr><tr><td></td><td>1.2</td><td>7.3</td><td>0.5</td><td>2.4</td><td>0.7</td><td>4.9</td></tr><tr><td>ISTProx</td><td>0.4</td><td>6.3</td><td>0.4</td><td>1.8</td><td>7.6</td><td>4.1</td></tr></table>",
+        "bbox": [
+            80,
+            119,
+            459,
+            243
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/ef9a910b940d30bd4b92e1962503a20bf34065d2d26aff16fe5d58837fca943a.jpg",
+        "table_caption": [
+            "(b) 100 sites",
+            "Change in acc.,  $10\\% \\rightarrow 30\\%$  participation"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>-0.5</td><td>-0.8</td><td>0.6</td><td>-0.1</td><td>1.2</td><td>4</td></tr><tr><td>FedProx</td><td>-0.4</td><td>-2</td><td>3.7</td><td>2.1</td><td>-0.6</td><td>0</td></tr><tr><td>MOON</td><td>1.5</td><td>2.9</td><td>-0.5</td><td>-0.3</td><td>-0.1</td><td>2.8</td></tr><tr><td>FedAdam</td><td>2</td><td>14.9</td><td>-0.9</td><td>0.6</td><td>0.4</td><td>5</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>2.3</td><td>7.3</td><td>-1.7</td><td>0.1</td><td>0.1</td><td>6.2</td></tr><tr><td>ISTProx</td><td>3</td><td>6.3</td><td>-0.9</td><td>3</td><td>1.3</td><td>2.2</td></tr></table>",
+        "bbox": [
+            80,
+            285,
+            459,
+            409
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Observed change in accuracy, computed as “(correct with fewer sites) - (% correct with more sites)”, when active sites increase. Red indicates negative change.",
+        "bbox": [
+            75,
+            420,
+            468,
+            465
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "20), Aircraft (100, 2, 15), Stanford Cars (196, 4, 20), Flowers (102, 3, 15), Textures (47, 1, 9), and CIFAR100 (100, 1, 13). This matches the realistic case where each site has access to only a few of the classes, and from this limited local information, an accurate global model must be constructed. Results are shown in Table 2.",
+        "bbox": [
+            75,
+            494,
+            468,
+            585
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6.2. Discussion",
+        "text_level": 1,
+        "bbox": [
+            76,
+            601,
+            194,
+            616
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Probably the single most interesting finding is that for a highly-skewed situation, there seems to be divergence in performance, depending upon the data set. The two IST methods seem to perform best overall, with either IST or ISTProx being the superior option in terms of final accuracy, FLOPs, or communication for four of the six data sets. However, IST does relatively poorly on the venerable CFAR data set. CFAR is a somewhat strange benchmark, as the images are tiny  $(32 \\times 32)$  and widely varied within the data set, and both IST variants have problems with this. Nevertheless, it is a good stress test. Note that in the two cases where IST does not do the best, it is either simple FedAvg or FedProx that is the best performer. One of the most surprising findings is that FedAvg dominates all other methods in all metrics (accuracy, FLOPs, communication) on Cars.",
+        "bbox": [
+            75,
+            626,
+            468,
+            852
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Overall, across the two experiments (i.i.d. and skewed), we find that adding a proximal term to FedAvg (to obtain FedProx) seems to have little effect on accuracy, but does",
+        "bbox": [
+            75,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c49647ab02103e758bd212a22262a8d39c73d8b6680085006d8d3dabe66c9b1c.jpg",
+        "table_caption": [
+            "(a) 1000 sites",
+            "Change in comm.,  $2\\% \\rightarrow 6\\%$  participation"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>3.02</td><td>2.41</td><td>2.53</td><td>4.28</td><td>2.25</td><td>2.07</td></tr><tr><td>FedProx</td><td>2.76</td><td>NA</td><td>2.34</td><td>2.98</td><td>2</td><td>2.12</td></tr><tr><td>MOON</td><td>2.78</td><td>0.88</td><td>2.52</td><td>2.91</td><td>2.28</td><td>2.11</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>0</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>FedNova</td><td>2.6</td><td>3.81</td><td>2.43</td><td>3.73</td><td>2.77</td><td>3.12</td></tr><tr><td>IST</td><td>1.41</td><td>0</td><td>1.07</td><td>1.95</td><td>1.03</td><td>NA</td></tr><tr><td>ISTProx</td><td>1.29</td><td>NA</td><td>1.15</td><td>2.2</td><td>0.48</td><td>NA</td></tr></table>",
+        "bbox": [
+            506,
+            119,
+            875,
+            243
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/31815d82a14aec86d95d05601b72f52f815fd20a248315bf151d98d914a0bde0.jpg",
+        "table_caption": [
+            "(b) 100 sites",
+            "Change in comm.,  $10\\% \\rightarrow 30\\%$  participation"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.65</td><td>NA</td><td>1.97</td><td>0.24</td><td>1.24</td><td>0</td></tr><tr><td>FedProx</td><td>∞</td><td>3.13</td><td>2.82</td><td>6.43</td><td>1.75</td><td>2.41</td></tr><tr><td>MOON</td><td>∞</td><td>NA</td><td>1.27</td><td>NA</td><td>5.31</td><td>7.39</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>1.29</td><td>NA</td><td>2.23</td><td>2.89</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>∞</td><td>NA</td><td>1.09</td><td>∞</td><td>2.73</td><td>6.44</td></tr><tr><td>ISTProx</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4: Multiplicative change in communication when tripling the number of active sites. Red text indicates more than a  $3 \\times$  increase; black indicates less than a  $3 \\times$  increase. \"NA\" indicates the case when there was a FAIL in both bases.  $\\infty$  indicates a change from non-fail to a FAIL, and 0 indicates a change from FAIL to non-fail.",
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+    {
+        "type": "text",
+        "text": "speedup convergence, both in terms of reducing communication and FLOPs. However, IST seems to be the best performer overall, allowing for significant reductions in communication and FLOPs. The addition of a proximal term does not seem to help IST much. The other methods tested all seem to under-perform.",
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+    {
+        "type": "text",
+        "text": "6.3. FL, Approximating Centralized Learning",
+        "text_level": 1,
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+        "type": "text",
+        "text": "How does the training process for a method (such as FedAvg and FedProx) that trains the entire model at each site and then reconciles the various versions of the model, compare with IST, which avoids this through decomposition?",
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+        "type": "text",
+        "text": "To examine, we centrally train a model from initialization through convergence using min-batch gradient descent, obtaining model parameters  $M_{i}$  for the  $i$ th training epoch. Then, using FL, we start training in a federated setting from  $M_{i}$  for some number of communication rounds, to obtain new model parameters  $\\hat{M}_i$ . We refer to the set of model parameters we would have obtained after processing exactly the same set of data centrally, via a series of mini-batches, as  $M_i^*$ . Then the cosine similarity of the directions both methods move, defined as  $(\\hat{M}_i - M_i)\\cdot (M_i^* -M_i) / (||\\hat{M}_i - M_i||\\times ||M_i^* -M_i||)$ ,",
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+    },
+    {
+        "type": "page_number",
+        "text": "19392",
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+    {
+        "type": "text",
+        "text": "shows the utility of FL as an approximation for centralized learning. Cosine similarity close to one means FL and centralized training move in the same direction. Zero implies de-correlation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Some results obtained in this way are plotted in Figure 2, where we consider FedAvg, FedProx, IST, and ISTProx. These plots depict this cosine similarity as a function of the training epochs. We plot running averages to smooth the data. The top three plots are for Cars, the bottom three Flwrs. The results for identically distributed data are at left, whereas skewed data are in the center, and at the right.",
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+    {
+        "type": "text",
+        "text": "FedAvg and FedProx are shown to approximate the centralized gradient descent direction well early on, but the similarity drops after initial training. This makes sense, as initially, with a random initialization, learning is \"easy\" as the model is far from optimal. In the i.i.d. case FedAvg and FedProx perform well. But in the skewed case, after the initial training period, similarity to the centralized training direction drops. IST seems more well-behaved, with less variance. Especially considering how well the methods approximate the direction of centralized training through twenty rounds on skewed data (the right column), the IST-based methods seem to do better. This is especially pronounced for the Flwrs data set through the first 20 epochs, where IST averages a similarity of 0.035, compared to 0.01 for the averaging-based methods. Perhaps this is due to the high variance of the directions computed by FedAvg and FedProx—as estimators for the centrally-predicted direction—compared to IST. Examining why this is deserves further investigation in future work.",
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+    {
+        "type": "text",
+        "text": "7. Varying Sites and Connectivity",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "7.1. Setup",
+        "text_level": 1,
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+        "type": "text",
+        "text": "All of our experiments thus far have focused on the simple case of 100 sites, where at each communication round,  $10\\%$  of the sites are connected. We now ask: how do things change when the number of sites changes and/or the number of sites connected at each communication round changes? Keeping all of the other settings the same, we try 1000 sites, with either  $2\\%$  or  $6\\%$  of the sites connected at each communication round, and 100 sites, with either  $10\\%$  of  $30\\%$  of the sites connected at each round. Due to space constraints, we consider accuracy and communication here, and provide further results of these experiments in the appendix. In Table 3, we show the absolute change in percentage accuracy moving from  $2\\%$  to  $6\\%$  connectivity, and from  $10\\%$  to  $30\\%$  connectivity. In Table 4, we show the multiplicative change in communication required. Note that, as we increase the number of active sites by  $3\\times$ , we might expect a  $3\\times$  increase in communication if the same number of communication rounds are required. If fewer rounds are required, we would see an increase that is less than  $3\\times$ .",
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+    {
+        "type": "text",
+        "text": "7.2. Discussion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "FedAdam, IST, and ISTProx are generally helped a bit by increasing participation. But for the other methods, the results obtained by increasing participation rates are mixed, with a surprising number of red values in both Table 3 and Table 4, indicating a decrease in accuracy or communication efficiency via the addition of extra active sites. In addition, it seems that the increase from  $2\\%$  participation to  $6\\%$  participation is much more helpful than  $10\\%$  to  $30\\%$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The lack of clear benefit to increasing the rate of participation is not surprising in retrospect. Aside from FedFull, each of the methods was able to run to convergence in the allotted FLOP/communication budget. The central question becomes: can we run to convergence in fewer rounds by doing more work in each round? This seems very unlikely, as this is akin to increasing the batch size in centralized learning, and expecting a significant decrease in the number of batches required for convergence. There is typically some decrease in the number of batches with increasing batch size, but it often is not significant. In reconciliation-based methods, this may be particularly inefficient as local training rounds cause the active sites to diverge and simply makes it more difficult to reconcile them. IST may have another advantage in that regard, in that more active sites does not increase communication for IST, it simply means that each site gets less of the full model. As long as each site can tolerate local learning using a smaller model (due to partitioning more ways), the learning may benefit from seeing a greater variety of data in each round. This certainly seems to be the case in when moving from  $2\\%$  to  $6\\%$ , which benefits IST.",
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+    },
+    {
+        "type": "text",
+        "text": "8. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We have designed a set of experiments to evaluate FL methods. Among the issues considered were what were the appropriate evaluation metrics (accuracy alone makes little sense), whether to use a pre-trained backbone, and the effect of connectivity on the efficiency of the learning. We find that overall, the method of decomposition of a neural network into independent subnetworks seems to be the best option. This has the benefit of decreasing communication and computation compared to \"reconciliation-based\" methods that train a copy of the model at each site, as the model is sharded, rather than broadcasted.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. We would like thank the anonymous reviewers for their comments on the submitted version of the paper. Work presented in this paper has been supported by an NIH CTSA, award No. UL1TR003167 and by the NSF under grant Nos. 1918651, 1910803, 2008240, and 2131294.",
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+        "type": "page_number",
+        "text": "19393",
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+    {
+        "type": "text",
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "19396",
+        "bbox": [
+            480,
+            945,
+            517,
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+        ],
+        "page_idx": 11
+    }
+]
\ No newline at end of file
diff --git a/2023/Federated Learning Over Images_ Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat/9da08db2-59f8-4fa7-be0b-195e30685450_model.json b/2023/Federated Learning Over Images_ Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat/9da08db2-59f8-4fa7-be0b-195e30685450_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..096ec41c7796c4cfcf4819d53006a342061781b3
--- /dev/null
+++ b/2023/Federated Learning Over Images_ Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat/9da08db2-59f8-4fa7-be0b-195e30685450_model.json	
@@ -0,0 +1,2556 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.807,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.116,
+                0.131,
+                0.856,
+                0.177
+            ],
+            "angle": 0,
+            "content": "Federated Learning Over Images: Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.226,
+                0.203,
+                0.748,
+                0.238
+            ],
+            "angle": 0,
+            "content": "Erdong Hu<sup>1</sup>, Yuxin Tang<sup>1</sup>, Anastasios Kyrillidis, Chris Jermaine Rice University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.223,
+                0.24,
+                0.75,
+                0.259
+            ],
+            "angle": 0,
+            "content": "{eh51, yuxin.tang, anastasios, cmj4}@rice.edu"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.324,
+                0.474,
+                0.506
+            ],
+            "angle": 0,
+            "content": "We carefully evaluate a number of algorithms for learning in a federated environment, and test their utility for a variety of image classification tasks. We consider many issues that have not been adequately considered before: whether learning over data sets that do not have diverse sets of images affects the results; whether to use a pre-trained feature extraction \"backbone\"; how to evaluate learner performance (we argue that classification accuracy is not enough), among others. Overall, across a wide variety of settings, we find that vertically decomposing a neural network seems to give the best results, and outperforms more standard reconciliation-used methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.538,
+                0.21,
+                0.554
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.564,
+                0.471,
+                0.791
+            ],
+            "angle": 0,
+            "content": "There has been a recent influx of work aimed at developing and evaluating new algorithms for Federated Learning (FL) [2, 6, 20, 29], particularly for image classification [3, 14, 18, 27, 28, 31, 35, 50, 53]. Most papers are primarily concerned with the development of innovative algorithms, and less concerned with the design of appropriate benchmarks and especially, appropriate baselines to test against. This paper, in contrast, is concerned with benchmarking: Which existing methods for FL work best, and under what conditions do they work, or not work? As such, our primary contribution is a set of carefully-designed experiments, rather than the introduction of a new FL algorithm. Our benchmarks are designed to address the following concerns regarding the design of FL benchmarks and baselines."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.798,
+                0.471,
+                0.876
+            ],
+            "angle": 0,
+            "content": "(1) Learning algorithms are typically evaluated on a few diverse data sets, rather than a large variety of more focused data sets. The most common benchmark for evaluating federated image classification is CIFAR-100 [25]. This dataset includes whales, chairs, dinosaurs, and so on. This is a very"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.293,
+                0.892,
+                0.324
+            ],
+            "angle": 0,
+            "content": "diverse set of classes, and we are concerned that few FL tasks will involve differentiating dinosaurs from rabbits."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.327,
+                0.895,
+                0.555
+            ],
+            "angle": 0,
+            "content": "For example, imagine that the members of a bird watching club taking pictures with their smartphones; club members label the pictures with the bird species, and FL is used to build a classifier. Or, a set of companies who are typically competitors—and hence cannot exchange data—want to work together to classify pictures of industrial drill bits based on whether they are going to fail. Both of these deployments involve narrow domains, and the classification problems involve fine-grained differentiation [13, 48] among members of a narrow category. True, not all applications of FL will be narrow, but they are likely to be far narrower than classifying whales versus chairs. We argue that, while evaluating on a broad data set—such as CIFAR-100—is useful, it is also necessary to evaluate FL algorithms on a variety of more narrow data sets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.564,
+                0.895,
+                0.777
+            ],
+            "angle": 0,
+            "content": "(2) Most evaluations focus on final accuracy or the number of communication rounds required for convergence. FL algorithms are often evaluated by reporting final accuracies (after convergence), or by plotting test accuracy as a function of the number of epochs, or the number of communication rounds. However, final accuracy, at least in isolation, is not really a useful metric. After all, the simplest \"FL\" algorithm is classical, data parallel learning [33,41,52]. That is, run distributed gradient descent; compute gradients locally over mini-batches in a fully synchronous way, then do an all-reduce. As this is functionally equivalent to centralized learning, it is invariant to data distribution, and is likely to be the most accurate method in terms of final accuracy. However, it is inefficient in a federated environment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Likewise, considering accuracy as a function of communication rounds ignores the computation or communication cost of each round. Communication and computation costs can vary across methods, and are typically far more important than the number of rounds. A method that can quickly achieve high accuracy with a relatively large number of very inexpensive communication rounds—where a small fraction of the model is communicated at each round—is proba"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.206,
+                0.901
+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)Equal contribution."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19385"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.198
+            ],
+            "angle": 0,
+            "content": "bly preferred to one that uses few rounds, but must transmit a huge amount of data. Similarly, for computation, given similar accuracies, an algorithm that performs one forward and one backward gradient descent pass is preferred over one that performs two additional forward passes, as extra overhead [28], even though both operate in the same number of communication rounds."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.206,
+                0.473,
+                0.312
+            ],
+            "angle": 0,
+            "content": "(3) Pre-trained feature extractors need to be a standard baseline. Training the feature-extraction backbone that is used in most deep image processing networks—that is, the series of convolutional and pooling layers and without the final classification layer—is not easy. It is difficult to get the training process right, and training a good backbone requires a lot of computation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.314,
+                0.473,
+                0.556
+            ],
+            "angle": 0,
+            "content": "Researchers have recently suggested using pre-trained backbones, especially for few-shot training [7, 16]. In a pre-trained backbone, a pre-trained feature extractor such as a convolutional neural network (CNN) [15, 19, 39] or vision transformer [10] is used without modification to embed an image in a high-dimensional space. Learning is then performed on the resulting vectors, and not on the original images. The goal is to leverage an existing, well-trained model on the new learning problem. Given the resource constraints in many FL scenarios, it is unclear why attempting to fully train such a backbone from scratch in a federated environment would be the first approach. Instead, we suggest simply taking a standard, pre-trained backbone (such as a ResNet [15], or a DenseNet [19], or both used together) and directly using that backbone as a feature extractor, without training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.558,
+                0.473,
+                0.693
+            ],
+            "angle": 0,
+            "content": "The benefit is that each training image only needs to be pushed through the backbone one time to obtain a compact set of features, and then that set can be used during training. As the backbone need not to be communicated or repeatedly used to process the input images, both CPU/GPU cycles and communication are saved during federated training. Furthermore, final accuracies might actually be better, as this approach sidesteps the difficulty of training the backbone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.702,
+                0.473,
+                0.868
+            ],
+            "angle": 0,
+            "content": "(4) Off-the-shelf performance is really what matters, but it is often neglected in research studies. In a centralized environment, it is feasible to train and re-train many times, as various parameters (learning rate, proximal weight, exact neural architecture, etc.) are tuned. In FL, this is much less feasible. Most FL scenarios imagine a resource-constrained environment (possibly involving edge devices), where one cannot ignore the cost of tuning. FL is typically happening on someone else's hardware, and so running an algorithm many times during parameter tuning is likely to make participation in training far less palatable."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.472,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Further, application-specific tuning may simply be impossible. A device may enter the federated training and then"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.894,
+                0.137
+            ],
+            "angle": 0,
+            "content": "drop out shortly after, never to be seen again. One cannot access a missing device's data to perform validation, and clearly, one cannot retrain over data that cannot be accessed."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.137,
+                0.895,
+                0.243
+            ],
+            "angle": 0,
+            "content": "As such, we argue that \"off-the-shelf\" performance is more important than in centralized learning. That is, it becomes important to settle on one set of universal parameters that tend to work in most deployments, such that the learning algorithm can be universally deployed without further tuning. At the very least, this is an important use case that should be covered in most experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.249,
+                0.859,
+                0.264
+            ],
+            "angle": 0,
+            "content": "Our Contributions. Our contributions are as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.269,
+                0.894,
+                0.33
+            ],
+            "angle": 0,
+            "content": "- We suggest several rules-of-thumb governing benchmark and baseline development for FL over images, and use those rules to devise an extensive FL image classification benchmark, and use that benchmark."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.335,
+                0.894,
+                0.366
+            ],
+            "angle": 0,
+            "content": "- We show that using pre-trained features and other model reduction tools are necessary for practical FL."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.376,
+                0.893,
+                0.436
+            ],
+            "angle": 0,
+            "content": "- We highlight some surprising behaviors of current FL algorithms, including the effect of client population size, that to our knowledge are not sufficiently explored in current literature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.448,
+                0.894,
+                0.493
+            ],
+            "angle": 0,
+            "content": "- Our source code is publicly available at https://github.com/huerdong/FedVert-Experiments"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.5,
+                0.269,
+                0.894,
+                0.493
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.507,
+                0.63,
+                0.525
+            ],
+            "angle": 0,
+            "content": "2. Background"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.533,
+                0.895,
+                0.684
+            ],
+            "angle": 0,
+            "content": "The common setting for FL is the following: There are total \\(N\\) devices participating in the optimization. To protect data privacy (or due to communication constraints), devices are not allowed to share local data samples to others. Each device has its own local objective function \\(f_{i}\\) parameterized by its own model \\(w_{i}\\). The coefficient \\(p_i = n_i / n\\) is the number of data samples \\(n_i\\) on each device, divided by the unified total data sample \\(n = \\sum_{i=1}^{N} n_i\\). There will be a central server that collects all the parameters \\(w_{i}\\) uploaded by each device and aggregate them into a single model \\(w\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.684,
+                0.894,
+                0.714
+            ],
+            "angle": 0,
+            "content": "The common formulation of FL is to optimize a global optimization function \\( L(w) \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.567,
+                0.717,
+                0.892,
+                0.758
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {w} L (w) = \\sum_ {i = 1} ^ {N} p _ {i} L \\left(w _ {i}; \\left\\{x _ {\\text {l o c}}, y _ {\\text {l o c}} \\right\\}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.894,
+                0.87
+            ],
+            "angle": 0,
+            "content": "where \\( L(w_{i};\\{x_{\\mathrm{loc}},y_{\\mathrm{loc}}\\}) \\) represents the local objective for device \\( i \\), based on local data \\( \\{x_{\\mathrm{loc}},y_{\\mathrm{loc}}\\} \\). The natural algorithm that arises from this objective is FedAvg [37] which directly applies stochastic gradient descent (SGD) to learn \\( w_{i} \\)'s. In the most basic case, where FedAvg performs only one local gradient step, the above formulation becomes equivalent to data parallel SGD [33,41,52]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In real-world applications of FL, local data distributions are often skewed towards specific classes: i.e., the natural"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19386"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "distribution of real data can be very skewed, with certain classes only existing in a very small segment of clients' devices. In these heavily non-i.i.d. scenarios, the learned \\( w_{i} \\) in Eq. (1) can diverge in drastically different directions and, in the most extreme cases, diverge in opposite directions. When FL is performed in this scenario, the averaging can result in a model drastically different from any of the client models and has degraded performance as a consequence; a phenomenon often called client drift [54]. It is this concern that has motivated the development of a number of FL methods beyond FedAvg [21,28,30,43], a few of which will be described in the next section."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.286,
+                0.407,
+                0.304
+            ],
+            "angle": 0,
+            "content": "3. Federated Learning Methods Tested"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.311,
+                0.216,
+                0.325
+            ],
+            "angle": 0,
+            "content": "3.1. The Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.334,
+                0.469,
+                0.365
+            ],
+            "angle": 0,
+            "content": "In our experiments, we consider the following FL methods, chosen as a representative set of the state-of-the-art."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.371,
+                0.469,
+                0.476
+            ],
+            "angle": 0,
+            "content": "FedAvg. Federated averaging [37] is the most simple averaging algorithm and is the basis of the others, whereby client models are trained locally by (stochastic) gradient descent. These local models are aggregated by directly averaging their weights, or equivalently averaging their computed gradients using this averaged gradient for one global round of gradient descent."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.482,
+                0.47,
+                0.618
+            ],
+            "angle": 0,
+            "content": "FedProx. FedProx [30] is a modification on FedAvg that introduces an additional \\(\\ell_2\\)-norm term to the local loss function, that takes the difference between the previously communicated global model and the current model. The aim is to avoid client drift by biasing the training towards an established model. Again, the clients then compute local models whose weights are averaged. Given the model weights \\(w_0\\) from the previous communication round, the FedProx modification to the FedAvg objective is:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.097,
+                0.628,
+                0.45,
+                0.652
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min _ {w _ {i}} \\left\\{L (w _ {i}; \\{x _ {\\mathrm {l o c}}, y _ {\\mathrm {l o c}} \\}) + \\frac {\\mu}{2} \\| w _ {i} - w _ {0} \\| _ {2} ^ {2} \\right\\}, i \\in [ N ]\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.661,
+                0.33,
+                0.677
+            ],
+            "angle": 0,
+            "content": "where \\(\\mu\\) is a regularization parameter."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.682,
+                0.47,
+                0.743
+            ],
+            "angle": 0,
+            "content": "MOON. MOON (Model-Contrastive) [28] uses a similar principle as FedProx by comparing the current model with the previous model. However, it utilizes a cross-entropy loss, rather than \\(\\ell_2\\)-norm loss, as in:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.08,
+                0.751,
+                0.466,
+                0.78
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {w _ {i}} \\left\\{L (w _ {i}; \\{x _ {\\mathrm {l o c}}, y _ {\\mathrm {l o c}} \\}) - \\mu \\log \\frac {e ^ {\\sin (z , z _ {\\mathrm {g l o b}}) / \\tau}}{e ^ {\\sin (z , z _ {\\mathrm {g l o b}}) / \\tau} + e ^ {\\sin (z , z _ {\\mathrm {p r e v}}) / \\tau}} \\right\\}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.789,
+                0.469,
+                0.851
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathrm{sim}()\\) is the cosine similarity function, and \\(z, z_{\\text{glob}}, z_{\\text{prev}}\\) are representations of the data generated by the respective model (respectively: learned, current global, previous local). \\(\\tau\\) is a temperature hyperparameter."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "FedAdam. While the above algorithms modify the local training process of FedAvg, FedAdam [40] modifies the aggregation step. Once the averaged weights are computed"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.138
+            ],
+            "angle": 0,
+            "content": "via local gradient descent and their average is computed, it is used to compute a global gradient surrogate to be used in the Adam algorithm [22]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.143,
+                0.892,
+                0.234
+            ],
+            "angle": 0,
+            "content": "FedNova. FedNova [43] introduces a client gradient reweighting scheme when accumulating the models parameters/gradients and generalizes FedAvg and FedProx as specific parameterizations. However, we use the specific formulation specified in [43], where these weights are normalizations of the local gradients."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.241,
+                0.893,
+                0.589
+            ],
+            "angle": 0,
+            "content": "IST. We consider the previous set of learning algorithms to be \"reconciliation-used\"; in that, they attempt to train a copy of the model at each site. In contrast, IST, or independent subnet training [51] does not utilize averaging or some other method to try to reconcile versions of the model trained at the various sites. Instead, IST decomposes the model and sends non-overlapping parts of the model to different sites. In one training round, all neurons (or activations) in a neural network are randomly partitioned to the active sites. A weight is only sent to a site if it connects two neurons that have been assigned to the site. Thus, each site is assigned only a very small subnet network, which is trained locally for a number of gradient descent steps. At the end of local training, the updated weights are shuffled (with or without the aid of a central server) and the process is repeated. Since subnetworks are independent, there is no averaging or other form of reconciliation needed. There are many variants of this approach in the literature, including FjORD [17], HeteroFL [9], LotteryFL [26], FedSelect [4], FedRolex [1], Federated Dropout [5], PVT [47], and the independent subnet network training approach in the non-FL setting [11, 32, 44, 45, 51]. It is this latter version of the approach (for MLPs) that we apply here."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.595,
+                0.892,
+                0.624
+            ],
+            "angle": 0,
+            "content": "ISTProx. This is IST, but with a proximal term added to the loss function."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.635,
+                0.702,
+                0.652
+            ],
+            "angle": 0,
+            "content": "3.2. Analytic Comparison"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "The focus of our experiments will be on comparing each of the methods based on their ability to produce high test accuracy with a low cost. In the paper, we will define cost in terms of floating point operations (FLOPs) required to reach a given accuracy, and in terms of floating point numbers transferred. As such, we begin by considering the number of FLOPS required and the floating point numbers that must be transferred to complete one gradient descent step for each of the methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In our analysis, we assume that we are using a pretrained backbone to transform each input image into a vector, and we are learning a MLP with two weight matrices. The MLP accepts an \\( n_1 \\)-dimensional input. It has a hidden layer of \\( n_2 \\) neurons, and has \\( n_3 \\) outputs. Assume a batch size of \\( b \\) at each of \\( s \\) sites. Since each image only goes through the pre-trained backbone once, the FLOP cost"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19387"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.168
+            ],
+            "angle": 0,
+            "content": "of the pre-trained backbone is negligible when amortized over many gradient descent steps. We will consider only the FLOPs associated with the weights, as the cost associated with updating weights dominates the cost associated with the activation layers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.169,
+                0.47,
+                0.35
+            ],
+            "angle": 0,
+            "content": "Begin with FedAvg. In this case, to push a batch through, we have approximately \\(2b(n_{1}n_{2} + n_{2}n_{3})\\) FLOPs for the forward pass and approximately \\(2b(n_{1}n_{2} + 2n_{2}n_{3})\\) for the backward pass, for a total of \\(4n_{1}n_{2}b + 6n_{2}n_{3}b\\) FLOPs at each site. Coordination requires \\(2s(n_{1}n_{2} + n_{2}n_{3})\\) floating point numbers be sent (the model needs to be distributed to all sites, and then the updated model needs to be collected from all sites). The number of FLOPs incurred during averaging is typically not significant, as we are simply average \\(s\\) copies of the two weight matrices, having \\(n_{1}n_{2}\\) and \\(n_{2}n_{3}\\) floating point numbers each, and this may be done using a distributed algorithm."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.352,
+                0.47,
+                0.472
+            ],
+            "angle": 0,
+            "content": "Adding a proximal term in the case of FedProx may have little effect, as this changes the backward pass at each site by adding FLOP computations that scales linearly with the weight matrices, but does not scale with the batch size \\( b \\). Thus, for any reasonable batch size, it is insignificant. If multiple gradient update steps are performed at each site, it also requires storing an older copy of the weight matrices at each site."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.475,
+                0.47,
+                0.597
+            ],
+            "angle": 0,
+            "content": "FedAdam is a federated version of the Adam algorithm and as such, it requires storing four additional matrices—typically at a coordinator—two of which are associated with each of the MLP's weight matrices. It must approximate the gradient and run the Adam algorithm at the coordinator during each update. However, this does not affect the memory, computation, or communication requirements at each site, and so any differences may not be of practical importance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.47,
+                0.763
+            ],
+            "angle": 0,
+            "content": "FedNova requires a normalization step at each site during the local gradient computation, but this only requires multiplying each gradient by a scalar, which is likely insignificant and so it is also, for practical purposes, computationally no more expensive than FedAvg. MOON is more expensive than FedAvg in terms of FLOPs, as it needs to compute multiple representations of each training iteration. The obvious MOON implementation will require \\( 4bn_{1}n_{2} \\) additional FLOPs compared to FedAvg at each site. In addition, MOON needs to locally maintain two additional copies of the weight matrices."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Next, consider IST. At each site, \\( n_2 \\) is effectively cut by a fraction \\( s \\), because the neurons in the hidden layer is partitioned \\( s \\) ways and only the weights associated with neurons assigned to a site are actually sent or used there. Hence, the total number of FLOPs is \\( (4n_1n_2b + 6n_2n_3b) / s \\), and coordination requires that only \\( 2(n_{1}n_{2} + n_{2}n_{3}) \\) floating point numbers be sent and received; each weight is assigned to exactly one site. There are no FLOPs associated with coordination, as there is no averaging done; weights are sim"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.153
+            ],
+            "angle": 0,
+            "content": "ply updated and sent around. Due to the partitioning, the memory usage at each site is on average smaller than that of FedAvg by a factor of \\( s \\). Like FedAvg, adding a proximal term has little effect on either FLOPs or bytes transferred."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.167,
+                0.693,
+                0.185
+            ],
+            "angle": 0,
+            "content": "4. Experimental Setup"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.193,
+                0.719,
+                0.208
+            ],
+            "angle": 0,
+            "content": "4.1. Pre-Trained Backbones"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.216,
+                0.892,
+                0.368
+            ],
+            "angle": 0,
+            "content": "All of the methods we tested (except for one baseline) utilize pre-trained backbones. That is, we take a pre-trained feature image classifiers: ResNet101 [15] and DenseNet121 [19], and remove the classification layers to produce two \"backbones.\" When processing an image, we simply concatenate the feature vectors produced by the two backbones to produce a 3072 dimensional vector. We also evaluate FedProx, but without a pre-trained backbone. This version of FedProx (called \"FedFull\") uses a ResNet18 instead of a single-hidden layer MLP."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.378,
+                0.783,
+                0.394
+            ],
+            "angle": 0,
+            "content": "4.2. Data Sets and Hyperparameters"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.402,
+                0.892,
+                0.553
+            ],
+            "angle": 0,
+            "content": "Overall, we conduct experiments on a diverse and broad range of image classification data sets: (1) CUB-200-2011 (Birds) [42], (2) Stanford Cars (Cars) [23], (3) VGGFlowers (Flwrs) [38], (4) Aircraft (Aircraft) [36], (5) Describable Textures (Textre) [8], and (6) CIFAR 100 (CFAR) [24]. The only processing we apply on these data sets, besides using the pre-trained feature extractors, is the standard cropping and resizing of image data. For the Aircraft data set, there are multiple levels of specificity of labels - manufacturer, family, variant - we chose variant for the finest-grained classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.554,
+                0.892,
+                0.749
+            ],
+            "angle": 0,
+            "content": "We use the Birds data set to tune the methods. After extensive experimentation on Birds, we chose a learning rate of 0.01, as we found this to give stable convergence in all algorithms, except FedAdam, where we choose a learning rate of 0.03. For all algorithms except for IST, ISTProx, and FedFull, tuning led us to a single-hidden-layer, multi-layer perceptron (MLP) with 1,000 hidden neurons sitting on top of the feature extractor. FedFull was trained with its \"out of the box\" configuration. For IST and ISTProx, we find scaling the hidden neurons based on the number of concurrent training sites made sense (3000 neurons for ten sites, 6000 for 20, 9000 for 30, 18000 for 60, and so on). This ensures that the client models are not too small."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "A number of other hyperparameters were also optimized using the Birds data set. For the various hyperparameters in each algorithm, we applied a grid search on a set list of parameter values, as described in the next subsection. We consider the number of local iterations of stochastic gradient descent as a hyperparameter with either 1, 5, or 25 local training batches, before a communication round. We use a batch size of 32 images. For FedProx, FedNova, and IST-Prox, we tuned the additional proximal hyperparameter \\(\\mu\\). For MOON, we have a similar weight parameter \\(\\mu\\) (the co"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19388"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.206,
+                0.09,
+                0.338,
+                0.104
+            ],
+            "angle": 0,
+            "content": "(a) Final accuracies"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.104,
+                0.457,
+                0.244
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>73.5</td><td>66.7</td><td>95.9</td><td>48.8</td><td>74.3</td><td>76.7</td></tr><tr><td>FedProx</td><td>74.0</td><td>65.7</td><td>95.8</td><td>48.9</td><td>74.7</td><td>75.1</td></tr><tr><td>MOON</td><td>74.3</td><td>66.0</td><td>95.6</td><td>48.9</td><td>74.6</td><td>75.3</td></tr><tr><td>FedAdam</td><td>67.6</td><td>51.1</td><td>92.4</td><td>41.9</td><td>72.8</td><td>70.1</td></tr><tr><td>FedNova</td><td>73.3</td><td>66.8</td><td>95.6</td><td>49.0</td><td>74.7</td><td>74.7</td></tr><tr><td>FedFull</td><td>5.2</td><td>2.8</td><td>35.1</td><td>5.4</td><td>40.3</td><td>7.8</td></tr><tr><td>IST</td><td>74.6</td><td>67.8</td><td>96.4</td><td>50.6</td><td>74.6</td><td>76.2</td></tr><tr><td>ISTProx</td><td>74.8</td><td>66.8</td><td>96.5</td><td>50.4</td><td>74.7</td><td>76.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.131,
+                0.256,
+                0.411,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(b) Communication (GB) to threshold acc."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.27,
+                0.459,
+                0.41
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>9</td><td>6</td><td>4</td><td>13</td><td>3</td><td>10</td></tr><tr><td>FedProx</td><td>13</td><td>FAIL</td><td>6</td><td>21</td><td>5</td><td>15</td></tr><tr><td>MOON</td><td>13</td><td>43</td><td>6</td><td>21</td><td>4</td><td>16</td></tr><tr><td>FedAdam</td><td>8</td><td>FAIL</td><td>2</td><td>FAIL</td><td>1</td><td>7</td></tr><tr><td>FedNova</td><td>57</td><td>138</td><td>17</td><td>84</td><td>12</td><td>68</td></tr><tr><td>FedFull</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>IST</td><td>3</td><td>288</td><td>1</td><td>3</td><td>1</td><td>3</td></tr><tr><td>ISTProx</td><td>3</td><td>FAIL</td><td>2</td><td>3</td><td>1</td><td>3</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.174,
+                0.423,
+                0.368,
+                0.437
+            ],
+            "angle": 0,
+            "content": "(c) GFLOPs to threshold acc."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.437,
+                0.458,
+                0.576
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>904</td><td>642</td><td>445</td><td>1334</td><td>275</td><td>979</td></tr><tr><td>FedProx</td><td>53</td><td>FAIL</td><td>23</td><td>86</td><td>18</td><td>62</td></tr><tr><td>MOON</td><td>110</td><td>FAIL</td><td>46</td><td>178</td><td>34</td><td>121</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>170</td><td>FAIL</td><td>152</td><td>750</td></tr><tr><td>FedNova</td><td>1140</td><td>2768</td><td>333</td><td>1680</td><td>232</td><td>1355</td></tr><tr><td>FedFull</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>IST</td><td>11</td><td>1152</td><td>6</td><td>14</td><td>3</td><td>12</td></tr><tr><td>ISTProx</td><td>11</td><td>FAIL</td><td>6</td><td>14</td><td>3</td><td>13</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.106,
+                0.587,
+                0.441,
+                0.603
+            ],
+            "angle": 0,
+            "content": "Table 1: i.i.d. results, 100 sites, \\( {10}\\% \\) participation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.633,
+                0.47,
+                0.739
+            ],
+            "angle": 0,
+            "content": "efficient of the contrastive term) and \\(\\tau\\), the temperature of the contrastive term. FedAdam has a central learning rate as well, which we set to 0.01. Exact values for all of our hyperparameters are given in the appendix. We stress that, while we performed careful tuning on the Birds data set, all hyperparameters were re-used blindly and without modification, on all other data sets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.755,
+                0.262,
+                0.77
+            ],
+            "angle": 0,
+            "content": "4.3. Evaluation Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Choosing an evaluation metric is among the most difficult aspects of evaluating FL methods, but does not seem to have received much attention in the literature. Most papers focus on final accuracy: What is the accuracy that a FL method exhibits on a test set after training? Unfortunately, final accuracy as a metric makes little sense in isolation from other considerations. After all, the method that likely gives the very best final accuracy is simple dis"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.518,
+                0.093,
+                0.878,
+                0.245
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.257,
+                0.892,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Figure 1: Accuracy as a function of time for FedProx and FedFull on the Stanford Cars data set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.317,
+                0.892,
+                0.438
+            ],
+            "angle": 0,
+            "content": "tributed mini-batch training, where each site computes gradients over a small subset of its local data; those gradients are summed and a central site updates the model. This is algorithmically equivalent to centralized training, but it is typically not tested, because it is generally assumed that the convergence would be too \"slow,\" for some implicit definition of \"slow.\" Thus, a more carefully-defined evaluation framework (beyond simple accuracy) is needed."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.439,
+                0.892,
+                0.531
+            ],
+            "angle": 0,
+            "content": "Hence, we consider three metrics: final accuracy, computational efficiency, and communication efficiency [34, 46]. Of the three, we assert that final accuracy should be considered the least important; it is most useful as a way to contextualize the other two metrics (e.g., \"what final accuracy can I achieve in GigaFLOPs of computation?\")."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.543,
+                0.714,
+                0.559
+            ],
+            "angle": 0,
+            "content": "4.4. Tuning and Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.568,
+                0.892,
+                0.809
+            ],
+            "angle": 0,
+            "content": "For a given method, using the Birds data set, we first perform a grid search over the various hyperparameters, and for each hyperparameter set, we run the method for a \"long time,\" where a \"long time\" allows a maximum of \\(10^{14}\\) floating point operations (or 100 teraFLOPs, where floating point operations are summed across all devices participating in federated training) and five terabytes of data communicated (assuming single-precision floating point computations). Note that 100 teraFLOPs corresponds to around 14 hours of CPU time on a single mobile phone, or perhaps several hundred hours of processor time on a limited IoT device. Once a method exceeds 100 teraFLOPs or five terabytes of communication, we take its very best observed test accuracy, averaged over ten communication rounds. The best average observed over all hyperparameter settings is taken as the method's \"final accuracy\"."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Once we have the method's final accuracy, we then perform a grid search over all hyperparameters to find the two sets of parameter settings for the method that (a) minimize the number of FLOPs to reach \\(90\\%\\) of the final accuracy, and (b) minimize the number of GB of communication necessary to reach \\(90\\%\\) of the final accuracy. Now we have"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19389"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.09,
+                0.34,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.107,
+                0.235,
+                0.314,
+                0.248
+            ],
+            "angle": 0,
+            "content": "(a) i.i.d., Cars, one round accuracy."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.357,
+                0.091,
+                0.614,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.371,
+                0.234,
+                0.598,
+                0.247
+            ],
+            "angle": 0,
+            "content": "(b) Skewed, Cars, one round accuracy."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.092,
+                0.888,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.648,
+                0.235,
+                0.872,
+                0.248
+            ],
+            "angle": 0,
+            "content": "(c) Skewed, Cars, 20 rounds accuracy."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.25,
+                0.338,
+                0.384
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.096,
+                0.392,
+                0.325,
+                0.406
+            ],
+            "angle": 0,
+            "content": "(d) i.i.d., Flowers, one round accuracy."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.357,
+                0.25,
+                0.614,
+                0.383
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.362,
+                0.392,
+                0.609,
+                0.406
+            ],
+            "angle": 0,
+            "content": "(e) Skewed, Flowers, one round accuracy."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.25,
+                0.889,
+                0.384
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.639,
+                0.392,
+                0.882,
+                0.406
+            ],
+            "angle": 0,
+            "content": "(f) Skewed, Flowers, 20 rounds accuracy."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.419,
+                0.893,
+                0.465
+            ],
+            "angle": 0,
+            "content": "Figure 2: Comparison of similarity of the FL descent direction to a centrally-computed descent direction. One means the directions are identical; 0 represents de-correlation. At left is i.i.d. data; center is skewed data, similarity computed over one descent step; right is skewed data, similarity computed over 20 descent steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.468,
+                0.596
+            ],
+            "angle": 0,
+            "content": "three sets of hyperparameters: one optimized for accuracy, one for gigaFLOPs, and one for communication. The reason that we use three sets of hyperparameters is that the goals of maximizing accuracy, minimizing FLOPs and minimizing communication are often in direct opposition to one another, and these resources can often be traded (e.g., more local iterations and FLOPs for less communication)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.468,
+                0.808
+            ],
+            "angle": 0,
+            "content": "Next, we consider each data set in sequence. We first run each method to 100 teraFLOPs or five terabytes of communication on the data set, using the accuracy-optimized parameters. We then compute the maximum accuracy that any method obtained on the data set, and set \\(90\\%\\) of this accuracy as a target. Then, for each method and each data set, we compute two additional numbers: the number of gigaFLOPs required to reach the target accuracy for five consecutive rounds (using the FLOP-optimized settings), and the number of gigabytes of communication required to reach the target accuracy (using the communication-optimized settings). If a method is unable to reach the target accuracy within the 100 teraFLOPs/five terabytes limit, it is said to have failed (indicated as FAIL in tables)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.468,
+                0.87
+            ],
+            "angle": 0,
+            "content": "We estimate the amount of FLOPs used during training using the FlopCountAnalysis tool in the Python fvmcore [12]. Similarly, for our communication costs we estimate the size of a model in bytes with the Python torchinfo [49] package."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The reason for this evaluation strategy is simple. In practice, the preferred FL method is likely to be the one that"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.491,
+                0.892,
+                0.581
+            ],
+            "angle": 0,
+            "content": "reaches a high level of accuracy with little cost. Hence, we (somewhat arbitrarily, but precisely) define \"high level of accuracy\" as \\(90\\%\\) of the peak accuracy observed over all methods for a given data set. Given this target, evaluation is then a matter of counting floating point operations and bytes to reach that target."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.582,
+                0.892,
+                0.642
+            ],
+            "angle": 0,
+            "content": "Note that other metrics are possible: power usage and elapsed wall clock time are two of the most obvious. However, both of these will be closely related to FLOPs and communication required, and hence we stick to these two."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.656,
+                0.759,
+                0.672
+            ],
+            "angle": 0,
+            "content": "5. Identically Distributed Data"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.681,
+                0.58,
+                0.697
+            ],
+            "angle": 0,
+            "content": "5.1. Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "In our first set of experiments, the images are randomly partitioned across the sites, so that each site has a randomly-selected (with replacement) subset of the overall set of images in the training data set. After a round of communication finishes, ten sites are randomly selected as being \"on the network\" and those sites participate in the present round of training. After local training finishes and all of the results have been communicated, another set of ten sites are randomly selected and the process continues."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.841,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For this simple \"i.i.d.\" setup, our experiments will answer a few key questions. First and foremost, should we be doing full backpropagation through a convolutional network, or should we be exclusively using a pre-trained back"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19390"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.205,
+                0.09,
+                0.335,
+                0.103
+            ],
+            "angle": 0,
+            "content": "(a) Final accuracies"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.104,
+                0.455,
+                0.229
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>61.5</td><td>56.4</td><td>88.9</td><td>40.2</td><td>68.1</td><td>61.4</td></tr><tr><td>FedProx</td><td>58.4</td><td>50.1</td><td>85.4</td><td>35.6</td><td>66.8</td><td>60.5</td></tr><tr><td>MOON</td><td>57.7</td><td>48.0</td><td>86.9</td><td>37.6</td><td>66.2</td><td>58.6</td></tr><tr><td>FedAdam</td><td>49.4</td><td>16.9</td><td>81.0</td><td>28.9</td><td>54.0</td><td>40.5</td></tr><tr><td>FedNova</td><td>58.4</td><td>47.1</td><td>83.6</td><td>37.0</td><td>64.3</td><td>60.3</td></tr><tr><td>IST</td><td>64.3</td><td>50.8</td><td>90.7</td><td>39.8</td><td>69.5</td><td>49.4</td></tr><tr><td>ISTProx</td><td>64.8</td><td>50.3</td><td>91.3</td><td>40.6</td><td>68.2</td><td>56.7</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.134,
+                0.241,
+                0.412,
+                0.255
+            ],
+            "angle": 0,
+            "content": "(b) Communication (GB) to threshold acc."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.256,
+                0.461,
+                0.38
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>131</td><td>62</td><td>51</td><td>79</td><td>55</td><td>59</td></tr><tr><td>FedProx</td><td>250</td><td>FAIL</td><td>124</td><td>FAIL</td><td>71</td><td>54</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>193</td><td>FAIL</td><td>143</td><td>74</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>743</td><td>FAIL</td><td>430</td><td>608</td><td>309</td><td>160</td></tr><tr><td>IST</td><td>79</td><td>FAIL</td><td>37</td><td>119</td><td>69</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>72</td><td>FAIL</td><td>59</td><td>134</td><td>72</td><td>219</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.182,
+                0.393,
+                0.367,
+                0.406
+            ],
+            "angle": 0,
+            "content": "(c) GFLOPs to threshold acc"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.085,
+                0.407,
+                0.462,
+                0.531
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>13121</td><td>6245</td><td>5150</td><td>7892</td><td>5461</td><td>5884</td></tr><tr><td>FedProx</td><td>1000</td><td>FAIL</td><td>495</td><td>FAIL</td><td>283</td><td>218</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>581</td><td>1243</td><td>653</td><td>1207</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>14872</td><td>FAIL</td><td>8614</td><td>12172</td><td>6181</td><td>3200</td></tr><tr><td>IST</td><td>315</td><td>FAIL</td><td>148</td><td>475</td><td>277</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>287</td><td>FAIL</td><td>238</td><td>535</td><td>288</td><td>875</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.08,
+                0.542,
+                0.466,
+                0.557
+            ],
+            "angle": 0,
+            "content": "Table 2: Skewed data results, 100 sites, \\( {10}\\% \\) participation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.588,
+                0.469,
+                0.678
+            ],
+            "angle": 0,
+            "content": "bone? Second, when one considers computation and communication (rather than just final accuracy) do the methods compare differently than when the only metric is accuracy? And finally, does the data set used matter? Results are shown in Table 1. For each data set, the best result is indicated in bold."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.694,
+                0.194,
+                0.709
+            ],
+            "angle": 0,
+            "content": "5.2. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "There are a few clear results. First, except for FedAdam and FedFull, the methods generally have very similar final accuracy, with the two IST-based methods being slightly higher. Thus, one key finding is that for data without skewness across sites, if one is only interested in final accuracy, it does not seem to matter much which method is used, and this result holds across data sets. The two exceptions to this are FedAdam and FedFull. FedAdam does not reach the same final accuracy as the other methods, but it generally does quite a good job reaching high accuracy with relatively little communication. This corresponds to the fact that it tends to converge in relatively few communication rounds."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.53
+            ],
+            "angle": 0,
+            "content": "FedFull is a very interesting case. Note that it has poor final accuracy—only \\(3\\%\\) in the case of the Cars data set. As a result, it is labeled as “FAIL” in every case, because it can never reach \\(90\\%\\) of the peak accuracy observed for the other methods on a given data set. One might ask, Why is FedFull such a poor choice? The answer is simple: as we put a 100 teraFLOP/five terabyte “timeout” on the computation, FedFull timed out in every case. That is, it always hit the 100 teraFLOP/five terabyte limit. Were FedFull allowed infinite computation and infinite communication, it is actually the preferred method, as the pre-trained backbones limit accuracy. For example, consider Figure 1, which plots accuracy as a function of FLOPs for both FedFull and FedProx on Cars. FedFull eventually reaches \\(90\\%\\) accuracy, but it takes nearly four orders of magnitude more FLOPs to top out compared to FedProx. This FLOP usage gap is apparent in Fig. 1 where even the first communication round of FedFull requires more FLOPs than the amount required for the entire FedProx training. As a result, we would argue that full backpropagation is effectively unusable in resource-constrained FL. Note, however, that our FedFull was trained using an initialization consisting of random weights. Perhaps a hybrid method makes sense, where one begins with FedProx (with a pre-trained backbone) and then once the MLP begins to reach peak accuracy, we allow backpropagation over the backbone to begin. This issue deserves further investigation. That said, given our maximum FLOP count and communication, FedFull is not competitive and in the interest of space, we will not consider it further."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.531,
+                0.892,
+                0.668
+            ],
+            "angle": 0,
+            "content": "The final observation we make is the general superiority of IST, over each of the six data sets. It is perhaps not surprising that IST is efficient in terms of communication and in terms of computation. Each site obtains only a fraction of the MLP that is being trained, saving communication and computation at each site. However, it is surprising that it is also generally the most accurate method, in terms of final accuracy (or close to it) in every case. We will examine this finding more fully, later in the paper."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.685,
+                0.725,
+                0.7
+            ],
+            "angle": 0,
+            "content": "6. Effect of Data Skewness"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.71,
+                0.581,
+                0.727
+            ],
+            "angle": 0,
+            "content": "6.1. Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "How might these results change if data are not uniformly distributed across sites? To answer this question, we modify our experiments as follows. Rather than assigning each training image to each site with uniform probability, we sample the class probabilities for each site from a Dirichlet(0.01) distribution, and rerun our experiments (with 100 sites and 10 sites active in each round). This creates a relatively extreme—yet still realistic—amount of skew. For the six data sets we tested, the three-tuple (number of classes in data set, min number of classes at any site, max number of classes at any site) is: for Birds (200, 7,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19391"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.223,
+                0.09,
+                0.317,
+                0.104
+            ],
+            "angle": 0,
+            "content": "(a) 1000 sites"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.138,
+                0.105,
+                0.402,
+                0.119
+            ],
+            "angle": 0,
+            "content": "Change in acc., \\(2\\% \\rightarrow 6\\%\\) participation"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.12,
+                0.46,
+                0.244
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.1</td><td>-0.8</td><td>0</td><td>0</td><td>-1.1</td><td>1.3</td></tr><tr><td>FedProx</td><td>0.1</td><td>-2</td><td>0.4</td><td>0.8</td><td>1</td><td>1.1</td></tr><tr><td>MOON</td><td>0.3</td><td>2.9</td><td>0.5</td><td>0.5</td><td>-0.2</td><td>1.4</td></tr><tr><td>FedAdam</td><td>12.8</td><td>16.8</td><td>7</td><td>12.5</td><td>12.1</td><td>12.4</td></tr><tr><td>FedNova</td><td>0.6</td><td>-0.5</td><td>-0.5</td><td>0</td><td>0.6</td><td>0.8</td></tr><tr><td></td><td>1.2</td><td>7.3</td><td>0.5</td><td>2.4</td><td>0.7</td><td>4.9</td></tr><tr><td>ISTProx</td><td>0.4</td><td>6.3</td><td>0.4</td><td>1.8</td><td>7.6</td><td>4.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.227,
+                0.256,
+                0.312,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(b) 100 sites"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.13,
+                0.272,
+                0.409,
+                0.286
+            ],
+            "angle": 0,
+            "content": "Change in acc., \\(10\\% \\rightarrow 30\\%\\) participation"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.286,
+                0.46,
+                0.41
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>-0.5</td><td>-0.8</td><td>0.6</td><td>-0.1</td><td>1.2</td><td>4</td></tr><tr><td>FedProx</td><td>-0.4</td><td>-2</td><td>3.7</td><td>2.1</td><td>-0.6</td><td>0</td></tr><tr><td>MOON</td><td>1.5</td><td>2.9</td><td>-0.5</td><td>-0.3</td><td>-0.1</td><td>2.8</td></tr><tr><td>FedAdam</td><td>2</td><td>14.9</td><td>-0.9</td><td>0.6</td><td>0.4</td><td>5</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>2.3</td><td>7.3</td><td>-1.7</td><td>0.1</td><td>0.1</td><td>6.2</td></tr><tr><td>ISTProx</td><td>3</td><td>6.3</td><td>-0.9</td><td>3</td><td>1.3</td><td>2.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.421,
+                0.47,
+                0.467
+            ],
+            "angle": 0,
+            "content": "Table 3: Observed change in accuracy, computed as “(correct with fewer sites) - (% correct with more sites)”, when active sites increase. Red indicates negative change."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.496,
+                0.469,
+                0.587
+            ],
+            "angle": 0,
+            "content": "20), Aircraft (100, 2, 15), Stanford Cars (196, 4, 20), Flowers (102, 3, 15), Textures (47, 1, 9), and CIFAR100 (100, 1, 13). This matches the realistic case where each site has access to only a few of the classes, and from this limited local information, an accurate global model must be constructed. Results are shown in Table 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.602,
+                0.195,
+                0.617
+            ],
+            "angle": 0,
+            "content": "6.2. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.627,
+                0.469,
+                0.853
+            ],
+            "angle": 0,
+            "content": "Probably the single most interesting finding is that for a highly-skewed situation, there seems to be divergence in performance, depending upon the data set. The two IST methods seem to perform best overall, with either IST or ISTProx being the superior option in terms of final accuracy, FLOPs, or communication for four of the six data sets. However, IST does relatively poorly on the venerable CFAR data set. CFAR is a somewhat strange benchmark, as the images are tiny \\((32 \\times 32)\\) and widely varied within the data set, and both IST variants have problems with this. Nevertheless, it is a good stress test. Note that in the two cases where IST does not do the best, it is either simple FedAvg or FedProx that is the best performer. One of the most surprising findings is that FedAvg dominates all other methods in all metrics (accuracy, FLOPs, communication) on Cars."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Overall, across the two experiments (i.i.d. and skewed), we find that adding a proximal term to FedAvg (to obtain FedProx) seems to have little effect on accuracy, but does"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.646,
+                0.09,
+                0.739,
+                0.104
+            ],
+            "angle": 0,
+            "content": "(a) 1000 sites"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.551,
+                0.105,
+                0.834,
+                0.119
+            ],
+            "angle": 0,
+            "content": "Change in comm., \\(2\\% \\rightarrow 6\\%\\) participation"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.12,
+                0.877,
+                0.244
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>3.02</td><td>2.41</td><td>2.53</td><td>4.28</td><td>2.25</td><td>2.07</td></tr><tr><td>FedProx</td><td>2.76</td><td>NA</td><td>2.34</td><td>2.98</td><td>2</td><td>2.12</td></tr><tr><td>MOON</td><td>2.78</td><td>0.88</td><td>2.52</td><td>2.91</td><td>2.28</td><td>2.11</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>0</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>FedNova</td><td>2.6</td><td>3.81</td><td>2.43</td><td>3.73</td><td>2.77</td><td>3.12</td></tr><tr><td>IST</td><td>1.41</td><td>0</td><td>1.07</td><td>1.95</td><td>1.03</td><td>NA</td></tr><tr><td>ISTProx</td><td>1.29</td><td>NA</td><td>1.15</td><td>2.2</td><td>0.48</td><td>NA</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.651,
+                0.256,
+                0.735,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(b) 100 sites"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.544,
+                0.272,
+                0.842,
+                0.286
+            ],
+            "angle": 0,
+            "content": "Change in comm., \\(10\\% \\rightarrow 30\\%\\) participation"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.286,
+                0.877,
+                0.41
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.65</td><td>NA</td><td>1.97</td><td>0.24</td><td>1.24</td><td>0</td></tr><tr><td>FedProx</td><td>∞</td><td>3.13</td><td>2.82</td><td>6.43</td><td>1.75</td><td>2.41</td></tr><tr><td>MOON</td><td>∞</td><td>NA</td><td>1.27</td><td>NA</td><td>5.31</td><td>7.39</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>1.29</td><td>NA</td><td>2.23</td><td>2.89</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>∞</td><td>NA</td><td>1.09</td><td>∞</td><td>2.73</td><td>6.44</td></tr><tr><td>ISTProx</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.421,
+                0.892,
+                0.511
+            ],
+            "angle": 0,
+            "content": "Table 4: Multiplicative change in communication when tripling the number of active sites. Red text indicates more than a \\(3 \\times\\) increase; black indicates less than a \\(3 \\times\\) increase. \"NA\" indicates the case when there was a FAIL in both bases. \\(\\infty\\) indicates a change from non-fail to a FAIL, and 0 indicates a change from FAIL to non-fail."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.542,
+                0.892,
+                0.633
+            ],
+            "angle": 0,
+            "content": "speedup convergence, both in terms of reducing communication and FLOPs. However, IST seems to be the best performer overall, allowing for significant reductions in communication and FLOPs. The addition of a proximal term does not seem to help IST much. The other methods tested all seem to under-perform."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.647,
+                0.855,
+                0.664
+            ],
+            "angle": 0,
+            "content": "6.3. FL, Approximating Centralized Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.673,
+                0.891,
+                0.734
+            ],
+            "angle": 0,
+            "content": "How does the training process for a method (such as FedAvg and FedProx) that trains the entire model at each site and then reconciles the various versions of the model, compare with IST, which avoids this through decomposition?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To examine, we centrally train a model from initialization through convergence using min-batch gradient descent, obtaining model parameters \\(M_{i}\\) for the \\(i\\)th training epoch. Then, using FL, we start training in a federated setting from \\(M_{i}\\) for some number of communication rounds, to obtain new model parameters \\(\\hat{M}_i\\). We refer to the set of model parameters we would have obtained after processing exactly the same set of data centrally, via a series of mini-batches, as \\(M_i^*\\). Then the cosine similarity of the directions both methods move, defined as \\((\\hat{M}_i - M_i)\\cdot (M_i^* -M_i) / (||\\hat{M}_i - M_i||\\times ||M_i^* -M_i||)\\),"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19392"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.468,
+                0.151
+            ],
+            "angle": 0,
+            "content": "shows the utility of FL as an approximation for centralized learning. Cosine similarity close to one means FL and centralized training move in the same direction. Zero implies de-correlation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.153,
+                0.468,
+                0.259
+            ],
+            "angle": 0,
+            "content": "Some results obtained in this way are plotted in Figure 2, where we consider FedAvg, FedProx, IST, and ISTProx. These plots depict this cosine similarity as a function of the training epochs. We plot running averages to smooth the data. The top three plots are for Cars, the bottom three Flwrs. The results for identically distributed data are at left, whereas skewed data are in the center, and at the right."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.261,
+                0.468,
+                0.547
+            ],
+            "angle": 0,
+            "content": "FedAvg and FedProx are shown to approximate the centralized gradient descent direction well early on, but the similarity drops after initial training. This makes sense, as initially, with a random initialization, learning is \"easy\" as the model is far from optimal. In the i.i.d. case FedAvg and FedProx perform well. But in the skewed case, after the initial training period, similarity to the centralized training direction drops. IST seems more well-behaved, with less variance. Especially considering how well the methods approximate the direction of centralized training through twenty rounds on skewed data (the right column), the IST-based methods seem to do better. This is especially pronounced for the Flwrs data set through the first 20 epochs, where IST averages a similarity of 0.035, compared to 0.01 for the averaging-based methods. Perhaps this is due to the high variance of the directions computed by FedAvg and FedProx—as estimators for the centrally-predicted direction—compared to IST. Examining why this is deserves further investigation in future work."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.564,
+                0.358,
+                0.581
+            ],
+            "angle": 0,
+            "content": "7. Varying Sites and Connectivity"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.59,
+                0.157,
+                0.606
+            ],
+            "angle": 0,
+            "content": "7.1. Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.614,
+                0.468,
+                0.899
+            ],
+            "angle": 0,
+            "content": "All of our experiments thus far have focused on the simple case of 100 sites, where at each communication round, \\(10\\%\\) of the sites are connected. We now ask: how do things change when the number of sites changes and/or the number of sites connected at each communication round changes? Keeping all of the other settings the same, we try 1000 sites, with either \\(2\\%\\) or \\(6\\%\\) of the sites connected at each communication round, and 100 sites, with either \\(10\\%\\) of \\(30\\%\\) of the sites connected at each round. Due to space constraints, we consider accuracy and communication here, and provide further results of these experiments in the appendix. In Table 3, we show the absolute change in percentage accuracy moving from \\(2\\%\\) to \\(6\\%\\) connectivity, and from \\(10\\%\\) to \\(30\\%\\) connectivity. In Table 4, we show the multiplicative change in communication required. Note that, as we increase the number of active sites by \\(3\\times\\), we might expect a \\(3\\times\\) increase in communication if the same number of communication rounds are required. If fewer rounds are required, we would see an increase that is less than \\(3\\times\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.092,
+                0.616,
+                0.106
+            ],
+            "angle": 0,
+            "content": "7.2. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.119,
+                0.891,
+                0.239
+            ],
+            "angle": 0,
+            "content": "FedAdam, IST, and ISTProx are generally helped a bit by increasing participation. But for the other methods, the results obtained by increasing participation rates are mixed, with a surprising number of red values in both Table 3 and Table 4, indicating a decrease in accuracy or communication efficiency via the addition of extra active sites. In addition, it seems that the increase from \\(2\\%\\) participation to \\(6\\%\\) participation is much more helpful than \\(10\\%\\) to \\(30\\%\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.244,
+                0.891,
+                0.575
+            ],
+            "angle": 0,
+            "content": "The lack of clear benefit to increasing the rate of participation is not surprising in retrospect. Aside from FedFull, each of the methods was able to run to convergence in the allotted FLOP/communication budget. The central question becomes: can we run to convergence in fewer rounds by doing more work in each round? This seems very unlikely, as this is akin to increasing the batch size in centralized learning, and expecting a significant decrease in the number of batches required for convergence. There is typically some decrease in the number of batches with increasing batch size, but it often is not significant. In reconciliation-based methods, this may be particularly inefficient as local training rounds cause the active sites to diverge and simply makes it more difficult to reconcile them. IST may have another advantage in that regard, in that more active sites does not increase communication for IST, it simply means that each site gets less of the full model. As long as each site can tolerate local learning using a smaller model (due to partitioning more ways), the learning may benefit from seeing a greater variety of data in each round. This certainly seems to be the case in when moving from \\(2\\%\\) to \\(6\\%\\), which benefits IST."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.604,
+                0.617,
+                0.619
+            ],
+            "angle": 0,
+            "content": "8. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.634,
+                0.891,
+                0.798
+            ],
+            "angle": 0,
+            "content": "We have designed a set of experiments to evaluate FL methods. Among the issues considered were what were the appropriate evaluation metrics (accuracy alone makes little sense), whether to use a pre-trained backbone, and the effect of connectivity on the efficiency of the learning. We find that overall, the method of decomposition of a neural network into independent subnetworks seems to be the best option. This has the benefit of decreasing communication and computation compared to \"reconciliation-based\" methods that train a copy of the model at each site, as the model is sharded, rather than broadcasted."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.811,
+                0.891,
+                0.899
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. We would like thank the anonymous reviewers for their comments on the submitted version of the paper. Work presented in this paper has been supported by an NIH CTSA, award No. UL1TR003167 and by the NSF under grant Nos. 1918651, 1910803, 2008240, and 2131294."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.947,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19393"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
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+                0.174,
+                0.106
+            ],
+            "angle": 0,
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+# Federated Learning Over Images: Vertical Decompositions and Pre-Trained Backbones Are Difficult to Beat
+
+Erdong Hu<sup>1</sup>, Yuxin Tang<sup>1</sup>, Anastasios Kyrillidis, Chris Jermaine Rice University
+
+{eh51, yuxin.tang, anastasios, cmj4}@rice.edu
+
+# Abstract
+
+We carefully evaluate a number of algorithms for learning in a federated environment, and test their utility for a variety of image classification tasks. We consider many issues that have not been adequately considered before: whether learning over data sets that do not have diverse sets of images affects the results; whether to use a pre-trained feature extraction "backbone"; how to evaluate learner performance (we argue that classification accuracy is not enough), among others. Overall, across a wide variety of settings, we find that vertically decomposing a neural network seems to give the best results, and outperforms more standard reconciliation-used methods.
+
+# 1. Introduction
+
+There has been a recent influx of work aimed at developing and evaluating new algorithms for Federated Learning (FL) [2, 6, 20, 29], particularly for image classification [3, 14, 18, 27, 28, 31, 35, 50, 53]. Most papers are primarily concerned with the development of innovative algorithms, and less concerned with the design of appropriate benchmarks and especially, appropriate baselines to test against. This paper, in contrast, is concerned with benchmarking: Which existing methods for FL work best, and under what conditions do they work, or not work? As such, our primary contribution is a set of carefully-designed experiments, rather than the introduction of a new FL algorithm. Our benchmarks are designed to address the following concerns regarding the design of FL benchmarks and baselines.
+
+(1) Learning algorithms are typically evaluated on a few diverse data sets, rather than a large variety of more focused data sets. The most common benchmark for evaluating federated image classification is CIFAR-100 [25]. This dataset includes whales, chairs, dinosaurs, and so on. This is a very
+
+diverse set of classes, and we are concerned that few FL tasks will involve differentiating dinosaurs from rabbits.
+
+For example, imagine that the members of a bird watching club taking pictures with their smartphones; club members label the pictures with the bird species, and FL is used to build a classifier. Or, a set of companies who are typically competitors—and hence cannot exchange data—want to work together to classify pictures of industrial drill bits based on whether they are going to fail. Both of these deployments involve narrow domains, and the classification problems involve fine-grained differentiation [13, 48] among members of a narrow category. True, not all applications of FL will be narrow, but they are likely to be far narrower than classifying whales versus chairs. We argue that, while evaluating on a broad data set—such as CIFAR-100—is useful, it is also necessary to evaluate FL algorithms on a variety of more narrow data sets.
+
+(2) Most evaluations focus on final accuracy or the number of communication rounds required for convergence. FL algorithms are often evaluated by reporting final accuracies (after convergence), or by plotting test accuracy as a function of the number of epochs, or the number of communication rounds. However, final accuracy, at least in isolation, is not really a useful metric. After all, the simplest "FL" algorithm is classical, data parallel learning [33,41,52]. That is, run distributed gradient descent; compute gradients locally over mini-batches in a fully synchronous way, then do an all-reduce. As this is functionally equivalent to centralized learning, it is invariant to data distribution, and is likely to be the most accurate method in terms of final accuracy. However, it is inefficient in a federated environment.
+
+Likewise, considering accuracy as a function of communication rounds ignores the computation or communication cost of each round. Communication and computation costs can vary across methods, and are typically far more important than the number of rounds. A method that can quickly achieve high accuracy with a relatively large number of very inexpensive communication rounds—where a small fraction of the model is communicated at each round—is proba
+
+bly preferred to one that uses few rounds, but must transmit a huge amount of data. Similarly, for computation, given similar accuracies, an algorithm that performs one forward and one backward gradient descent pass is preferred over one that performs two additional forward passes, as extra overhead [28], even though both operate in the same number of communication rounds.
+
+(3) Pre-trained feature extractors need to be a standard baseline. Training the feature-extraction backbone that is used in most deep image processing networks—that is, the series of convolutional and pooling layers and without the final classification layer—is not easy. It is difficult to get the training process right, and training a good backbone requires a lot of computation.
+
+Researchers have recently suggested using pre-trained backbones, especially for few-shot training [7, 16]. In a pre-trained backbone, a pre-trained feature extractor such as a convolutional neural network (CNN) [15, 19, 39] or vision transformer [10] is used without modification to embed an image in a high-dimensional space. Learning is then performed on the resulting vectors, and not on the original images. The goal is to leverage an existing, well-trained model on the new learning problem. Given the resource constraints in many FL scenarios, it is unclear why attempting to fully train such a backbone from scratch in a federated environment would be the first approach. Instead, we suggest simply taking a standard, pre-trained backbone (such as a ResNet [15], or a DenseNet [19], or both used together) and directly using that backbone as a feature extractor, without training.
+
+The benefit is that each training image only needs to be pushed through the backbone one time to obtain a compact set of features, and then that set can be used during training. As the backbone need not to be communicated or repeatedly used to process the input images, both CPU/GPU cycles and communication are saved during federated training. Furthermore, final accuracies might actually be better, as this approach sidesteps the difficulty of training the backbone.
+
+(4) Off-the-shelf performance is really what matters, but it is often neglected in research studies. In a centralized environment, it is feasible to train and re-train many times, as various parameters (learning rate, proximal weight, exact neural architecture, etc.) are tuned. In FL, this is much less feasible. Most FL scenarios imagine a resource-constrained environment (possibly involving edge devices), where one cannot ignore the cost of tuning. FL is typically happening on someone else's hardware, and so running an algorithm many times during parameter tuning is likely to make participation in training far less palatable.
+
+Further, application-specific tuning may simply be impossible. A device may enter the federated training and then
+
+drop out shortly after, never to be seen again. One cannot access a missing device's data to perform validation, and clearly, one cannot retrain over data that cannot be accessed.
+
+As such, we argue that "off-the-shelf" performance is more important than in centralized learning. That is, it becomes important to settle on one set of universal parameters that tend to work in most deployments, such that the learning algorithm can be universally deployed without further tuning. At the very least, this is an important use case that should be covered in most experiments.
+
+Our Contributions. Our contributions are as follows.
+
+- We suggest several rules-of-thumb governing benchmark and baseline development for FL over images, and use those rules to devise an extensive FL image classification benchmark, and use that benchmark.  
+- We show that using pre-trained features and other model reduction tools are necessary for practical FL.  
+- We highlight some surprising behaviors of current FL algorithms, including the effect of client population size, that to our knowledge are not sufficiently explored in current literature.  
+- Our source code is publicly available at https://github.com/huerdong/FedVert-Experiments
+
+# 2. Background
+
+The common setting for FL is the following: There are total  $N$  devices participating in the optimization. To protect data privacy (or due to communication constraints), devices are not allowed to share local data samples to others. Each device has its own local objective function  $f_{i}$  parameterized by its own model  $w_{i}$ . The coefficient  $p_i = n_i / n$  is the number of data samples  $n_i$  on each device, divided by the unified total data sample  $n = \sum_{i=1}^{N} n_i$ . There will be a central server that collects all the parameters  $w_{i}$  uploaded by each device and aggregate them into a single model  $w$ .
+
+The common formulation of FL is to optimize a global optimization function  $L(w)$ :
+
+$$
+\min  _ {w} L (w) = \sum_ {i = 1} ^ {N} p _ {i} L \left(w _ {i}; \left\{x _ {\text {l o c}}, y _ {\text {l o c}} \right\}\right), \tag {1}
+$$
+
+where  $L(w_{i};\{x_{\mathrm{loc}},y_{\mathrm{loc}}\})$  represents the local objective for device  $i$ , based on local data  $\{x_{\mathrm{loc}},y_{\mathrm{loc}}\}$ . The natural algorithm that arises from this objective is FedAvg [37] which directly applies stochastic gradient descent (SGD) to learn  $w_{i}$ 's. In the most basic case, where FedAvg performs only one local gradient step, the above formulation becomes equivalent to data parallel SGD [33,41,52].
+
+In real-world applications of FL, local data distributions are often skewed towards specific classes: i.e., the natural
+
+distribution of real data can be very skewed, with certain classes only existing in a very small segment of clients' devices. In these heavily non-i.i.d. scenarios, the learned  $w_{i}$  in Eq. (1) can diverge in drastically different directions and, in the most extreme cases, diverge in opposite directions. When FL is performed in this scenario, the averaging can result in a model drastically different from any of the client models and has degraded performance as a consequence; a phenomenon often called client drift [54]. It is this concern that has motivated the development of a number of FL methods beyond FedAvg [21,28,30,43], a few of which will be described in the next section.
+
+# 3. Federated Learning Methods Tested
+
+# 3.1. The Methods
+
+In our experiments, we consider the following FL methods, chosen as a representative set of the state-of-the-art.
+
+FedAvg. Federated averaging [37] is the most simple averaging algorithm and is the basis of the others, whereby client models are trained locally by (stochastic) gradient descent. These local models are aggregated by directly averaging their weights, or equivalently averaging their computed gradients using this averaged gradient for one global round of gradient descent.
+
+FedProx. FedProx [30] is a modification on FedAvg that introduces an additional  $\ell_2$ -norm term to the local loss function, that takes the difference between the previously communicated global model and the current model. The aim is to avoid client drift by biasing the training towards an established model. Again, the clients then compute local models whose weights are averaged. Given the model weights  $w_0$  from the previous communication round, the FedProx modification to the FedAvg objective is:
+
+$$
+\min _ {w _ {i}} \left\{L (w _ {i}; \{x _ {\mathrm {l o c}}, y _ {\mathrm {l o c}} \}) + \frac {\mu}{2} \| w _ {i} - w _ {0} \| _ {2} ^ {2} \right\}, i \in [ N ]
+$$
+
+where  $\mu$  is a regularization parameter.
+
+MOON. MOON (Model-Contrastive) [28] uses a similar principle as FedProx by comparing the current model with the previous model. However, it utilizes a cross-entropy loss, rather than  $\ell_2$ -norm loss, as in:
+
+$$
+\min  _ {w _ {i}} \left\{L (w _ {i}; \{x _ {\mathrm {l o c}}, y _ {\mathrm {l o c}} \}) - \mu \log \frac {e ^ {\sin (z , z _ {\mathrm {g l o b}}) / \tau}}{e ^ {\sin (z , z _ {\mathrm {g l o b}}) / \tau} + e ^ {\sin (z , z _ {\mathrm {p r e v}}) / \tau}} \right\}
+$$
+
+where  $\mathrm{sim}()$  is the cosine similarity function, and  $z, z_{\text{glob}}, z_{\text{prev}}$  are representations of the data generated by the respective model (respectively: learned, current global, previous local).  $\tau$  is a temperature hyperparameter.
+
+FedAdam. While the above algorithms modify the local training process of FedAvg, FedAdam [40] modifies the aggregation step. Once the averaged weights are computed
+
+via local gradient descent and their average is computed, it is used to compute a global gradient surrogate to be used in the Adam algorithm [22].
+
+FedNova. FedNova [43] introduces a client gradient reweighting scheme when accumulating the models parameters/gradients and generalizes FedAvg and FedProx as specific parameterizations. However, we use the specific formulation specified in [43], where these weights are normalizations of the local gradients.
+
+IST. We consider the previous set of learning algorithms to be "reconciliation-used"; in that, they attempt to train a copy of the model at each site. In contrast, IST, or independent subnet training [51] does not utilize averaging or some other method to try to reconcile versions of the model trained at the various sites. Instead, IST decomposes the model and sends non-overlapping parts of the model to different sites. In one training round, all neurons (or activations) in a neural network are randomly partitioned to the active sites. A weight is only sent to a site if it connects two neurons that have been assigned to the site. Thus, each site is assigned only a very small subnet network, which is trained locally for a number of gradient descent steps. At the end of local training, the updated weights are shuffled (with or without the aid of a central server) and the process is repeated. Since subnetworks are independent, there is no averaging or other form of reconciliation needed. There are many variants of this approach in the literature, including FjORD [17], HeteroFL [9], LotteryFL [26], FedSelect [4], FedRolex [1], Federated Dropout [5], PVT [47], and the independent subnet network training approach in the non-FL setting [11, 32, 44, 45, 51]. It is this latter version of the approach (for MLPs) that we apply here.
+
+ISTProx. This is IST, but with a proximal term added to the loss function.
+
+# 3.2. Analytic Comparison
+
+The focus of our experiments will be on comparing each of the methods based on their ability to produce high test accuracy with a low cost. In the paper, we will define cost in terms of floating point operations (FLOPs) required to reach a given accuracy, and in terms of floating point numbers transferred. As such, we begin by considering the number of FLOPS required and the floating point numbers that must be transferred to complete one gradient descent step for each of the methods.
+
+In our analysis, we assume that we are using a pretrained backbone to transform each input image into a vector, and we are learning a MLP with two weight matrices. The MLP accepts an  $n_1$ -dimensional input. It has a hidden layer of  $n_2$  neurons, and has  $n_3$  outputs. Assume a batch size of  $b$  at each of  $s$  sites. Since each image only goes through the pre-trained backbone once, the FLOP cost
+
+of the pre-trained backbone is negligible when amortized over many gradient descent steps. We will consider only the FLOPs associated with the weights, as the cost associated with updating weights dominates the cost associated with the activation layers.
+
+Begin with FedAvg. In this case, to push a batch through, we have approximately  $2b(n_{1}n_{2} + n_{2}n_{3})$  FLOPs for the forward pass and approximately  $2b(n_{1}n_{2} + 2n_{2}n_{3})$  for the backward pass, for a total of  $4n_{1}n_{2}b + 6n_{2}n_{3}b$  FLOPs at each site. Coordination requires  $2s(n_{1}n_{2} + n_{2}n_{3})$  floating point numbers be sent (the model needs to be distributed to all sites, and then the updated model needs to be collected from all sites). The number of FLOPs incurred during averaging is typically not significant, as we are simply average  $s$  copies of the two weight matrices, having  $n_{1}n_{2}$  and  $n_{2}n_{3}$  floating point numbers each, and this may be done using a distributed algorithm.
+
+Adding a proximal term in the case of FedProx may have little effect, as this changes the backward pass at each site by adding FLOP computations that scales linearly with the weight matrices, but does not scale with the batch size  $b$ . Thus, for any reasonable batch size, it is insignificant. If multiple gradient update steps are performed at each site, it also requires storing an older copy of the weight matrices at each site.
+
+FedAdam is a federated version of the Adam algorithm and as such, it requires storing four additional matrices—typically at a coordinator—two of which are associated with each of the MLP's weight matrices. It must approximate the gradient and run the Adam algorithm at the coordinator during each update. However, this does not affect the memory, computation, or communication requirements at each site, and so any differences may not be of practical importance.
+
+FedNova requires a normalization step at each site during the local gradient computation, but this only requires multiplying each gradient by a scalar, which is likely insignificant and so it is also, for practical purposes, computationally no more expensive than FedAvg. MOON is more expensive than FedAvg in terms of FLOPs, as it needs to compute multiple representations of each training iteration. The obvious MOON implementation will require  $4bn_{1}n_{2}$  additional FLOPs compared to FedAvg at each site. In addition, MOON needs to locally maintain two additional copies of the weight matrices.
+
+Next, consider IST. At each site,  $n_2$  is effectively cut by a fraction  $s$ , because the neurons in the hidden layer is partitioned  $s$  ways and only the weights associated with neurons assigned to a site are actually sent or used there. Hence, the total number of FLOPs is  $(4n_1n_2b + 6n_2n_3b) / s$ , and coordination requires that only  $2(n_{1}n_{2} + n_{2}n_{3})$  floating point numbers be sent and received; each weight is assigned to exactly one site. There are no FLOPs associated with coordination, as there is no averaging done; weights are sim
+
+ply updated and sent around. Due to the partitioning, the memory usage at each site is on average smaller than that of FedAvg by a factor of  $s$ . Like FedAvg, adding a proximal term has little effect on either FLOPs or bytes transferred.
+
+# 4. Experimental Setup
+
+# 4.1. Pre-Trained Backbones
+
+All of the methods we tested (except for one baseline) utilize pre-trained backbones. That is, we take a pre-trained feature image classifiers: ResNet101 [15] and DenseNet121 [19], and remove the classification layers to produce two "backbones." When processing an image, we simply concatenate the feature vectors produced by the two backbones to produce a 3072 dimensional vector. We also evaluate FedProx, but without a pre-trained backbone. This version of FedProx (called "FedFull") uses a ResNet18 instead of a single-hidden layer MLP.
+
+# 4.2. Data Sets and Hyperparameters
+
+Overall, we conduct experiments on a diverse and broad range of image classification data sets: (1) CUB-200-2011 (Birds) [42], (2) Stanford Cars (Cars) [23], (3) VGGFlowers (Flwrs) [38], (4) Aircraft (Aircraft) [36], (5) Describable Textures (Textre) [8], and (6) CIFAR 100 (CFAR) [24]. The only processing we apply on these data sets, besides using the pre-trained feature extractors, is the standard cropping and resizing of image data. For the Aircraft data set, there are multiple levels of specificity of labels - manufacturer, family, variant - we chose variant for the finest-grained classes.
+
+We use the Birds data set to tune the methods. After extensive experimentation on Birds, we chose a learning rate of 0.01, as we found this to give stable convergence in all algorithms, except FedAdam, where we choose a learning rate of 0.03. For all algorithms except for IST, ISTProx, and FedFull, tuning led us to a single-hidden-layer, multi-layer perceptron (MLP) with 1,000 hidden neurons sitting on top of the feature extractor. FedFull was trained with its "out of the box" configuration. For IST and ISTProx, we find scaling the hidden neurons based on the number of concurrent training sites made sense (3000 neurons for ten sites, 6000 for 20, 9000 for 30, 18000 for 60, and so on). This ensures that the client models are not too small.
+
+A number of other hyperparameters were also optimized using the Birds data set. For the various hyperparameters in each algorithm, we applied a grid search on a set list of parameter values, as described in the next subsection. We consider the number of local iterations of stochastic gradient descent as a hyperparameter with either 1, 5, or 25 local training batches, before a communication round. We use a batch size of 32 images. For FedProx, FedNova, and IST-Prox, we tuned the additional proximal hyperparameter  $\mu$ . For MOON, we have a similar weight parameter  $\mu$  (the co
+
+(a) Final accuracies  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>73.5</td><td>66.7</td><td>95.9</td><td>48.8</td><td>74.3</td><td>76.7</td></tr><tr><td>FedProx</td><td>74.0</td><td>65.7</td><td>95.8</td><td>48.9</td><td>74.7</td><td>75.1</td></tr><tr><td>MOON</td><td>74.3</td><td>66.0</td><td>95.6</td><td>48.9</td><td>74.6</td><td>75.3</td></tr><tr><td>FedAdam</td><td>67.6</td><td>51.1</td><td>92.4</td><td>41.9</td><td>72.8</td><td>70.1</td></tr><tr><td>FedNova</td><td>73.3</td><td>66.8</td><td>95.6</td><td>49.0</td><td>74.7</td><td>74.7</td></tr><tr><td>FedFull</td><td>5.2</td><td>2.8</td><td>35.1</td><td>5.4</td><td>40.3</td><td>7.8</td></tr><tr><td>IST</td><td>74.6</td><td>67.8</td><td>96.4</td><td>50.6</td><td>74.6</td><td>76.2</td></tr><tr><td>ISTProx</td><td>74.8</td><td>66.8</td><td>96.5</td><td>50.4</td><td>74.7</td><td>76.1</td></tr></table>
+
+(b) Communication (GB) to threshold acc.  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>9</td><td>6</td><td>4</td><td>13</td><td>3</td><td>10</td></tr><tr><td>FedProx</td><td>13</td><td>FAIL</td><td>6</td><td>21</td><td>5</td><td>15</td></tr><tr><td>MOON</td><td>13</td><td>43</td><td>6</td><td>21</td><td>4</td><td>16</td></tr><tr><td>FedAdam</td><td>8</td><td>FAIL</td><td>2</td><td>FAIL</td><td>1</td><td>7</td></tr><tr><td>FedNova</td><td>57</td><td>138</td><td>17</td><td>84</td><td>12</td><td>68</td></tr><tr><td>FedFull</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>IST</td><td>3</td><td>288</td><td>1</td><td>3</td><td>1</td><td>3</td></tr><tr><td>ISTProx</td><td>3</td><td>FAIL</td><td>2</td><td>3</td><td>1</td><td>3</td></tr></table>
+
+(c) GFLOPs to threshold acc.  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>904</td><td>642</td><td>445</td><td>1334</td><td>275</td><td>979</td></tr><tr><td>FedProx</td><td>53</td><td>FAIL</td><td>23</td><td>86</td><td>18</td><td>62</td></tr><tr><td>MOON</td><td>110</td><td>FAIL</td><td>46</td><td>178</td><td>34</td><td>121</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>170</td><td>FAIL</td><td>152</td><td>750</td></tr><tr><td>FedNova</td><td>1140</td><td>2768</td><td>333</td><td>1680</td><td>232</td><td>1355</td></tr><tr><td>FedFull</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>IST</td><td>11</td><td>1152</td><td>6</td><td>14</td><td>3</td><td>12</td></tr><tr><td>ISTProx</td><td>11</td><td>FAIL</td><td>6</td><td>14</td><td>3</td><td>13</td></tr></table>
+
+Table 1: i.i.d. results, 100 sites,  ${10}\%$  participation.
+
+efficient of the contrastive term) and  $\tau$ , the temperature of the contrastive term. FedAdam has a central learning rate as well, which we set to 0.01. Exact values for all of our hyperparameters are given in the appendix. We stress that, while we performed careful tuning on the Birds data set, all hyperparameters were re-used blindly and without modification, on all other data sets.
+
+# 4.3. Evaluation Metrics
+
+Choosing an evaluation metric is among the most difficult aspects of evaluating FL methods, but does not seem to have received much attention in the literature. Most papers focus on final accuracy: What is the accuracy that a FL method exhibits on a test set after training? Unfortunately, final accuracy as a metric makes little sense in isolation from other considerations. After all, the method that likely gives the very best final accuracy is simple dis
+
+![](images/120d7737c1cb9b1bf36300a48a46bb1efa4187107380753166f40bccc5f1d659.jpg)  
+Figure 1: Accuracy as a function of time for FedProx and FedFull on the Stanford Cars data set.
+
+tributed mini-batch training, where each site computes gradients over a small subset of its local data; those gradients are summed and a central site updates the model. This is algorithmically equivalent to centralized training, but it is typically not tested, because it is generally assumed that the convergence would be too "slow," for some implicit definition of "slow." Thus, a more carefully-defined evaluation framework (beyond simple accuracy) is needed.
+
+Hence, we consider three metrics: final accuracy, computational efficiency, and communication efficiency [34, 46]. Of the three, we assert that final accuracy should be considered the least important; it is most useful as a way to contextualize the other two metrics (e.g., "what final accuracy can I achieve in GigaFLOPs of computation?").
+
+# 4.4. Tuning and Evaluation
+
+For a given method, using the Birds data set, we first perform a grid search over the various hyperparameters, and for each hyperparameter set, we run the method for a "long time," where a "long time" allows a maximum of  $10^{14}$  floating point operations (or 100 teraFLOPs, where floating point operations are summed across all devices participating in federated training) and five terabytes of data communicated (assuming single-precision floating point computations). Note that 100 teraFLOPs corresponds to around 14 hours of CPU time on a single mobile phone, or perhaps several hundred hours of processor time on a limited IoT device. Once a method exceeds 100 teraFLOPs or five terabytes of communication, we take its very best observed test accuracy, averaged over ten communication rounds. The best average observed over all hyperparameter settings is taken as the method's "final accuracy".
+
+Once we have the method's final accuracy, we then perform a grid search over all hyperparameters to find the two sets of parameter settings for the method that (a) minimize the number of FLOPs to reach  $90\%$  of the final accuracy, and (b) minimize the number of GB of communication necessary to reach  $90\%$  of the final accuracy. Now we have
+
+![](images/9038faca4e44741825b1c6bd4a9494d0e9d684221c840f7585de7032377faa79.jpg)
+
+![](images/d4764527bafd910e254a4513e30409f3e597cff464bccb79f439b37f3aaef35c.jpg)  
+(b) Skewed, Cars, one round accuracy.
+
+![](images/01582e4c09836aca10f90f1a0a7c621262118f57b09ae8edf17cdb54dc85e4f6.jpg)
+
+![](images/3e4d0f784678468c327912c37d21c88264f12be7c0e8147d9cf484947e58d91e.jpg)  
+(a) i.i.d., Cars, one round accuracy.  
+(d) i.i.d., Flowers, one round accuracy.  
+Figure 2: Comparison of similarity of the FL descent direction to a centrally-computed descent direction. One means the directions are identical; 0 represents de-correlation. At left is i.i.d. data; center is skewed data, similarity computed over one descent step; right is skewed data, similarity computed over 20 descent steps.
+
+![](images/cfa75b3671a4d1b4cdd36d457e96f97fe472f3f9cfb7ce1836d43371163559ac.jpg)  
+(e) Skewed, Flowers, one round accuracy.
+
+![](images/1e73ae70bd38e22fb95082657336c958f3197d608c81da4244281cee8c2544ee.jpg)  
+(c) Skewed, Cars, 20 rounds accuracy.  
+(f) Skewed, Flowers, 20 rounds accuracy.
+
+three sets of hyperparameters: one optimized for accuracy, one for gigaFLOPs, and one for communication. The reason that we use three sets of hyperparameters is that the goals of maximizing accuracy, minimizing FLOPs and minimizing communication are often in direct opposition to one another, and these resources can often be traded (e.g., more local iterations and FLOPs for less communication).
+
+Next, we consider each data set in sequence. We first run each method to 100 teraFLOPs or five terabytes of communication on the data set, using the accuracy-optimized parameters. We then compute the maximum accuracy that any method obtained on the data set, and set  $90\%$  of this accuracy as a target. Then, for each method and each data set, we compute two additional numbers: the number of gigaFLOPs required to reach the target accuracy for five consecutive rounds (using the FLOP-optimized settings), and the number of gigabytes of communication required to reach the target accuracy (using the communication-optimized settings). If a method is unable to reach the target accuracy within the 100 teraFLOPs/five terabytes limit, it is said to have failed (indicated as FAIL in tables).
+
+We estimate the amount of FLOPs used during training using the FlopCountAnalysis tool in the Python fvmcore [12]. Similarly, for our communication costs we estimate the size of a model in bytes with the Python torchinfo [49] package.
+
+The reason for this evaluation strategy is simple. In practice, the preferred FL method is likely to be the one that
+
+reaches a high level of accuracy with little cost. Hence, we (somewhat arbitrarily, but precisely) define "high level of accuracy" as  $90\%$  of the peak accuracy observed over all methods for a given data set. Given this target, evaluation is then a matter of counting floating point operations and bytes to reach that target.
+
+Note that other metrics are possible: power usage and elapsed wall clock time are two of the most obvious. However, both of these will be closely related to FLOPs and communication required, and hence we stick to these two.
+
+# 5. Identically Distributed Data
+
+# 5.1. Setup
+
+In our first set of experiments, the images are randomly partitioned across the sites, so that each site has a randomly-selected (with replacement) subset of the overall set of images in the training data set. After a round of communication finishes, ten sites are randomly selected as being "on the network" and those sites participate in the present round of training. After local training finishes and all of the results have been communicated, another set of ten sites are randomly selected and the process continues.
+
+For this simple "i.i.d." setup, our experiments will answer a few key questions. First and foremost, should we be doing full backpropagation through a convolutional network, or should we be exclusively using a pre-trained back
+
+(a) Final accuracies  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>61.5</td><td>56.4</td><td>88.9</td><td>40.2</td><td>68.1</td><td>61.4</td></tr><tr><td>FedProx</td><td>58.4</td><td>50.1</td><td>85.4</td><td>35.6</td><td>66.8</td><td>60.5</td></tr><tr><td>MOON</td><td>57.7</td><td>48.0</td><td>86.9</td><td>37.6</td><td>66.2</td><td>58.6</td></tr><tr><td>FedAdam</td><td>49.4</td><td>16.9</td><td>81.0</td><td>28.9</td><td>54.0</td><td>40.5</td></tr><tr><td>FedNova</td><td>58.4</td><td>47.1</td><td>83.6</td><td>37.0</td><td>64.3</td><td>60.3</td></tr><tr><td>IST</td><td>64.3</td><td>50.8</td><td>90.7</td><td>39.8</td><td>69.5</td><td>49.4</td></tr><tr><td>ISTProx</td><td>64.8</td><td>50.3</td><td>91.3</td><td>40.6</td><td>68.2</td><td>56.7</td></tr></table>
+
+(b) Communication (GB) to threshold acc.  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>131</td><td>62</td><td>51</td><td>79</td><td>55</td><td>59</td></tr><tr><td>FedProx</td><td>250</td><td>FAIL</td><td>124</td><td>FAIL</td><td>71</td><td>54</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>193</td><td>FAIL</td><td>143</td><td>74</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>743</td><td>FAIL</td><td>430</td><td>608</td><td>309</td><td>160</td></tr><tr><td>IST</td><td>79</td><td>FAIL</td><td>37</td><td>119</td><td>69</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>72</td><td>FAIL</td><td>59</td><td>134</td><td>72</td><td>219</td></tr></table>
+
+(c) GFLOPs to threshold acc  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>13121</td><td>6245</td><td>5150</td><td>7892</td><td>5461</td><td>5884</td></tr><tr><td>FedProx</td><td>1000</td><td>FAIL</td><td>495</td><td>FAIL</td><td>283</td><td>218</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>581</td><td>1243</td><td>653</td><td>1207</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>14872</td><td>FAIL</td><td>8614</td><td>12172</td><td>6181</td><td>3200</td></tr><tr><td>IST</td><td>315</td><td>FAIL</td><td>148</td><td>475</td><td>277</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>287</td><td>FAIL</td><td>238</td><td>535</td><td>288</td><td>875</td></tr></table>
+
+Table 2: Skewed data results, 100 sites,  ${10}\%$  participation.
+
+bone? Second, when one considers computation and communication (rather than just final accuracy) do the methods compare differently than when the only metric is accuracy? And finally, does the data set used matter? Results are shown in Table 1. For each data set, the best result is indicated in bold.
+
+# 5.2. Discussion
+
+There are a few clear results. First, except for FedAdam and FedFull, the methods generally have very similar final accuracy, with the two IST-based methods being slightly higher. Thus, one key finding is that for data without skewness across sites, if one is only interested in final accuracy, it does not seem to matter much which method is used, and this result holds across data sets. The two exceptions to this are FedAdam and FedFull. FedAdam does not reach the same final accuracy as the other methods, but it generally does quite a good job reaching high accuracy with relatively little communication. This corresponds to the fact that it tends to converge in relatively few communication rounds.
+
+FedFull is a very interesting case. Note that it has poor final accuracy—only  $3\%$  in the case of the Cars data set. As a result, it is labeled as “FAIL” in every case, because it can never reach  $90\%$  of the peak accuracy observed for the other methods on a given data set. One might ask, Why is FedFull such a poor choice? The answer is simple: as we put a 100 teraFLOP/five terabyte “timeout” on the computation, FedFull timed out in every case. That is, it always hit the 100 teraFLOP/five terabyte limit. Were FedFull allowed infinite computation and infinite communication, it is actually the preferred method, as the pre-trained backbones limit accuracy. For example, consider Figure 1, which plots accuracy as a function of FLOPs for both FedFull and FedProx on Cars. FedFull eventually reaches  $90\%$  accuracy, but it takes nearly four orders of magnitude more FLOPs to top out compared to FedProx. This FLOP usage gap is apparent in Fig. 1 where even the first communication round of FedFull requires more FLOPs than the amount required for the entire FedProx training. As a result, we would argue that full backpropagation is effectively unusable in resource-constrained FL. Note, however, that our FedFull was trained using an initialization consisting of random weights. Perhaps a hybrid method makes sense, where one begins with FedProx (with a pre-trained backbone) and then once the MLP begins to reach peak accuracy, we allow backpropagation over the backbone to begin. This issue deserves further investigation. That said, given our maximum FLOP count and communication, FedFull is not competitive and in the interest of space, we will not consider it further.
+
+The final observation we make is the general superiority of IST, over each of the six data sets. It is perhaps not surprising that IST is efficient in terms of communication and in terms of computation. Each site obtains only a fraction of the MLP that is being trained, saving communication and computation at each site. However, it is surprising that it is also generally the most accurate method, in terms of final accuracy (or close to it) in every case. We will examine this finding more fully, later in the paper.
+
+# 6. Effect of Data Skewness
+
+# 6.1. Setup
+
+How might these results change if data are not uniformly distributed across sites? To answer this question, we modify our experiments as follows. Rather than assigning each training image to each site with uniform probability, we sample the class probabilities for each site from a Dirichlet(0.01) distribution, and rerun our experiments (with 100 sites and 10 sites active in each round). This creates a relatively extreme—yet still realistic—amount of skew. For the six data sets we tested, the three-tuple (number of classes in data set, min number of classes at any site, max number of classes at any site) is: for Birds (200, 7,
+
+(a) 1000 sites  
+Change in acc.,  $2\% \rightarrow 6\%$  participation  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.1</td><td>-0.8</td><td>0</td><td>0</td><td>-1.1</td><td>1.3</td></tr><tr><td>FedProx</td><td>0.1</td><td>-2</td><td>0.4</td><td>0.8</td><td>1</td><td>1.1</td></tr><tr><td>MOON</td><td>0.3</td><td>2.9</td><td>0.5</td><td>0.5</td><td>-0.2</td><td>1.4</td></tr><tr><td>FedAdam</td><td>12.8</td><td>16.8</td><td>7</td><td>12.5</td><td>12.1</td><td>12.4</td></tr><tr><td>FedNova</td><td>0.6</td><td>-0.5</td><td>-0.5</td><td>0</td><td>0.6</td><td>0.8</td></tr><tr><td></td><td>1.2</td><td>7.3</td><td>0.5</td><td>2.4</td><td>0.7</td><td>4.9</td></tr><tr><td>ISTProx</td><td>0.4</td><td>6.3</td><td>0.4</td><td>1.8</td><td>7.6</td><td>4.1</td></tr></table>
+
+(b) 100 sites  
+Change in acc.,  $10\% \rightarrow 30\%$  participation  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>-0.5</td><td>-0.8</td><td>0.6</td><td>-0.1</td><td>1.2</td><td>4</td></tr><tr><td>FedProx</td><td>-0.4</td><td>-2</td><td>3.7</td><td>2.1</td><td>-0.6</td><td>0</td></tr><tr><td>MOON</td><td>1.5</td><td>2.9</td><td>-0.5</td><td>-0.3</td><td>-0.1</td><td>2.8</td></tr><tr><td>FedAdam</td><td>2</td><td>14.9</td><td>-0.9</td><td>0.6</td><td>0.4</td><td>5</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>2.3</td><td>7.3</td><td>-1.7</td><td>0.1</td><td>0.1</td><td>6.2</td></tr><tr><td>ISTProx</td><td>3</td><td>6.3</td><td>-0.9</td><td>3</td><td>1.3</td><td>2.2</td></tr></table>
+
+Table 3: Observed change in accuracy, computed as “(correct with fewer sites) - (% correct with more sites)”, when active sites increase. Red indicates negative change.
+
+20), Aircraft (100, 2, 15), Stanford Cars (196, 4, 20), Flowers (102, 3, 15), Textures (47, 1, 9), and CIFAR100 (100, 1, 13). This matches the realistic case where each site has access to only a few of the classes, and from this limited local information, an accurate global model must be constructed. Results are shown in Table 2.
+
+# 6.2. Discussion
+
+Probably the single most interesting finding is that for a highly-skewed situation, there seems to be divergence in performance, depending upon the data set. The two IST methods seem to perform best overall, with either IST or ISTProx being the superior option in terms of final accuracy, FLOPs, or communication for four of the six data sets. However, IST does relatively poorly on the venerable CFAR data set. CFAR is a somewhat strange benchmark, as the images are tiny  $(32 \times 32)$  and widely varied within the data set, and both IST variants have problems with this. Nevertheless, it is a good stress test. Note that in the two cases where IST does not do the best, it is either simple FedAvg or FedProx that is the best performer. One of the most surprising findings is that FedAvg dominates all other methods in all metrics (accuracy, FLOPs, communication) on Cars.
+
+Overall, across the two experiments (i.i.d. and skewed), we find that adding a proximal term to FedAvg (to obtain FedProx) seems to have little effect on accuracy, but does
+
+(a) 1000 sites  
+Change in comm.,  $2\% \rightarrow 6\%$  participation  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>3.02</td><td>2.41</td><td>2.53</td><td>4.28</td><td>2.25</td><td>2.07</td></tr><tr><td>FedProx</td><td>2.76</td><td>NA</td><td>2.34</td><td>2.98</td><td>2</td><td>2.12</td></tr><tr><td>MOON</td><td>2.78</td><td>0.88</td><td>2.52</td><td>2.91</td><td>2.28</td><td>2.11</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>0</td><td>NA</td><td>NA</td><td>NA</td></tr><tr><td>FedNova</td><td>2.6</td><td>3.81</td><td>2.43</td><td>3.73</td><td>2.77</td><td>3.12</td></tr><tr><td>IST</td><td>1.41</td><td>0</td><td>1.07</td><td>1.95</td><td>1.03</td><td>NA</td></tr><tr><td>ISTProx</td><td>1.29</td><td>NA</td><td>1.15</td><td>2.2</td><td>0.48</td><td>NA</td></tr></table>
+
+(b) 100 sites  
+Change in comm.,  $10\% \rightarrow 30\%$  participation  
+
+<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.65</td><td>NA</td><td>1.97</td><td>0.24</td><td>1.24</td><td>0</td></tr><tr><td>FedProx</td><td>∞</td><td>3.13</td><td>2.82</td><td>6.43</td><td>1.75</td><td>2.41</td></tr><tr><td>MOON</td><td>∞</td><td>NA</td><td>1.27</td><td>NA</td><td>5.31</td><td>7.39</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>1.29</td><td>NA</td><td>2.23</td><td>2.89</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>∞</td><td>NA</td><td>1.09</td><td>∞</td><td>2.73</td><td>6.44</td></tr><tr><td>ISTProx</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr></table>
+
+Table 4: Multiplicative change in communication when tripling the number of active sites. Red text indicates more than a  $3 \times$  increase; black indicates less than a  $3 \times$  increase. "NA" indicates the case when there was a FAIL in both bases.  $\infty$  indicates a change from non-fail to a FAIL, and 0 indicates a change from FAIL to non-fail.
+
+speedup convergence, both in terms of reducing communication and FLOPs. However, IST seems to be the best performer overall, allowing for significant reductions in communication and FLOPs. The addition of a proximal term does not seem to help IST much. The other methods tested all seem to under-perform.
+
+# 6.3. FL, Approximating Centralized Learning
+
+How does the training process for a method (such as FedAvg and FedProx) that trains the entire model at each site and then reconciles the various versions of the model, compare with IST, which avoids this through decomposition?
+
+To examine, we centrally train a model from initialization through convergence using min-batch gradient descent, obtaining model parameters  $M_{i}$  for the  $i$ th training epoch. Then, using FL, we start training in a federated setting from  $M_{i}$  for some number of communication rounds, to obtain new model parameters  $\hat{M}_i$ . We refer to the set of model parameters we would have obtained after processing exactly the same set of data centrally, via a series of mini-batches, as  $M_i^*$ . Then the cosine similarity of the directions both methods move, defined as  $(\hat{M}_i - M_i)\cdot (M_i^* -M_i) / (||\hat{M}_i - M_i||\times ||M_i^* -M_i||)$ ,
+
+shows the utility of FL as an approximation for centralized learning. Cosine similarity close to one means FL and centralized training move in the same direction. Zero implies de-correlation.
+
+Some results obtained in this way are plotted in Figure 2, where we consider FedAvg, FedProx, IST, and ISTProx. These plots depict this cosine similarity as a function of the training epochs. We plot running averages to smooth the data. The top three plots are for Cars, the bottom three Flwrs. The results for identically distributed data are at left, whereas skewed data are in the center, and at the right.
+
+FedAvg and FedProx are shown to approximate the centralized gradient descent direction well early on, but the similarity drops after initial training. This makes sense, as initially, with a random initialization, learning is "easy" as the model is far from optimal. In the i.i.d. case FedAvg and FedProx perform well. But in the skewed case, after the initial training period, similarity to the centralized training direction drops. IST seems more well-behaved, with less variance. Especially considering how well the methods approximate the direction of centralized training through twenty rounds on skewed data (the right column), the IST-based methods seem to do better. This is especially pronounced for the Flwrs data set through the first 20 epochs, where IST averages a similarity of 0.035, compared to 0.01 for the averaging-based methods. Perhaps this is due to the high variance of the directions computed by FedAvg and FedProx—as estimators for the centrally-predicted direction—compared to IST. Examining why this is deserves further investigation in future work.
+
+# 7. Varying Sites and Connectivity
+
+# 7.1. Setup
+
+All of our experiments thus far have focused on the simple case of 100 sites, where at each communication round,  $10\%$  of the sites are connected. We now ask: how do things change when the number of sites changes and/or the number of sites connected at each communication round changes? Keeping all of the other settings the same, we try 1000 sites, with either  $2\%$  or  $6\%$  of the sites connected at each communication round, and 100 sites, with either  $10\%$  of  $30\%$  of the sites connected at each round. Due to space constraints, we consider accuracy and communication here, and provide further results of these experiments in the appendix. In Table 3, we show the absolute change in percentage accuracy moving from  $2\%$  to  $6\%$  connectivity, and from  $10\%$  to  $30\%$  connectivity. In Table 4, we show the multiplicative change in communication required. Note that, as we increase the number of active sites by  $3\times$ , we might expect a  $3\times$  increase in communication if the same number of communication rounds are required. If fewer rounds are required, we would see an increase that is less than  $3\times$ .
+
+# 7.2. Discussion
+
+FedAdam, IST, and ISTProx are generally helped a bit by increasing participation. But for the other methods, the results obtained by increasing participation rates are mixed, with a surprising number of red values in both Table 3 and Table 4, indicating a decrease in accuracy or communication efficiency via the addition of extra active sites. In addition, it seems that the increase from  $2\%$  participation to  $6\%$  participation is much more helpful than  $10\%$  to  $30\%$ .
+
+The lack of clear benefit to increasing the rate of participation is not surprising in retrospect. Aside from FedFull, each of the methods was able to run to convergence in the allotted FLOP/communication budget. The central question becomes: can we run to convergence in fewer rounds by doing more work in each round? This seems very unlikely, as this is akin to increasing the batch size in centralized learning, and expecting a significant decrease in the number of batches required for convergence. There is typically some decrease in the number of batches with increasing batch size, but it often is not significant. In reconciliation-based methods, this may be particularly inefficient as local training rounds cause the active sites to diverge and simply makes it more difficult to reconcile them. IST may have another advantage in that regard, in that more active sites does not increase communication for IST, it simply means that each site gets less of the full model. As long as each site can tolerate local learning using a smaller model (due to partitioning more ways), the learning may benefit from seeing a greater variety of data in each round. This certainly seems to be the case in when moving from  $2\%$  to  $6\%$ , which benefits IST.
+
+# 8. Conclusion
+
+We have designed a set of experiments to evaluate FL methods. Among the issues considered were what were the appropriate evaluation metrics (accuracy alone makes little sense), whether to use a pre-trained backbone, and the effect of connectivity on the efficiency of the learning. We find that overall, the method of decomposition of a neural network into independent subnetworks seems to be the best option. This has the benefit of decreasing communication and computation compared to "reconciliation-based" methods that train a copy of the model at each site, as the model is sharded, rather than broadcasted.
+
+Acknowledgements. We would like thank the anonymous reviewers for their comments on the submitted version of the paper. Work presented in this paper has been supported by an NIH CTSA, award No. UL1TR003167 and by the NSF under grant Nos. 1918651, 1910803, 2008240, and 2131294.
+
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+                                    "content": "Erdong Hu<sup>1</sup>, Yuxin Tang<sup>1</sup>, Anastasios Kyrillidis, Chris Jermaine Rice University"
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+                                    "content": "{eh51, yuxin.tang, anastasios, cmj4}@rice.edu"
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+                                    "content": "Abstract"
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+                                    "content": "We carefully evaluate a number of algorithms for learning in a federated environment, and test their utility for a variety of image classification tasks. We consider many issues that have not been adequately considered before: whether learning over data sets that do not have diverse sets of images affects the results; whether to use a pre-trained feature extraction \"backbone\"; how to evaluate learner performance (we argue that classification accuracy is not enough), among others. Overall, across a wide variety of settings, we find that vertically decomposing a neural network seems to give the best results, and outperforms more standard reconciliation-used methods."
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+                                    "content": "1. Introduction"
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+                                    "content": "There has been a recent influx of work aimed at developing and evaluating new algorithms for Federated Learning (FL) [2, 6, 20, 29], particularly for image classification [3, 14, 18, 27, 28, 31, 35, 50, 53]. Most papers are primarily concerned with the development of innovative algorithms, and less concerned with the design of appropriate benchmarks and especially, appropriate baselines to test against. This paper, in contrast, is concerned with benchmarking: Which existing methods for FL work best, and under what conditions do they work, or not work? As such, our primary contribution is a set of carefully-designed experiments, rather than the introduction of a new FL algorithm. Our benchmarks are designed to address the following concerns regarding the design of FL benchmarks and baselines."
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+                                    "content": "(1) Learning algorithms are typically evaluated on a few diverse data sets, rather than a large variety of more focused data sets. The most common benchmark for evaluating federated image classification is CIFAR-100 [25]. This dataset includes whales, chairs, dinosaurs, and so on. This is a very"
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+                                    "content": "diverse set of classes, and we are concerned that few FL tasks will involve differentiating dinosaurs from rabbits."
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+                                    "content": "For example, imagine that the members of a bird watching club taking pictures with their smartphones; club members label the pictures with the bird species, and FL is used to build a classifier. Or, a set of companies who are typically competitors—and hence cannot exchange data—want to work together to classify pictures of industrial drill bits based on whether they are going to fail. Both of these deployments involve narrow domains, and the classification problems involve fine-grained differentiation [13, 48] among members of a narrow category. True, not all applications of FL will be narrow, but they are likely to be far narrower than classifying whales versus chairs. We argue that, while evaluating on a broad data set—such as CIFAR-100—is useful, it is also necessary to evaluate FL algorithms on a variety of more narrow data sets."
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+                                    "content": "(2) Most evaluations focus on final accuracy or the number of communication rounds required for convergence. FL algorithms are often evaluated by reporting final accuracies (after convergence), or by plotting test accuracy as a function of the number of epochs, or the number of communication rounds. However, final accuracy, at least in isolation, is not really a useful metric. After all, the simplest \"FL\" algorithm is classical, data parallel learning [33,41,52]. That is, run distributed gradient descent; compute gradients locally over mini-batches in a fully synchronous way, then do an all-reduce. As this is functionally equivalent to centralized learning, it is invariant to data distribution, and is likely to be the most accurate method in terms of final accuracy. However, it is inefficient in a federated environment."
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+                                    "content": "Likewise, considering accuracy as a function of communication rounds ignores the computation or communication cost of each round. Communication and computation costs can vary across methods, and are typically far more important than the number of rounds. A method that can quickly achieve high accuracy with a relatively large number of very inexpensive communication rounds—where a small fraction of the model is communicated at each round—is proba"
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+                                    "content": "bly preferred to one that uses few rounds, but must transmit a huge amount of data. Similarly, for computation, given similar accuracies, an algorithm that performs one forward and one backward gradient descent pass is preferred over one that performs two additional forward passes, as extra overhead [28], even though both operate in the same number of communication rounds."
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+                                    "content": "(3) Pre-trained feature extractors need to be a standard baseline. Training the feature-extraction backbone that is used in most deep image processing networks—that is, the series of convolutional and pooling layers and without the final classification layer—is not easy. It is difficult to get the training process right, and training a good backbone requires a lot of computation."
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+                                    "content": "Researchers have recently suggested using pre-trained backbones, especially for few-shot training [7, 16]. In a pre-trained backbone, a pre-trained feature extractor such as a convolutional neural network (CNN) [15, 19, 39] or vision transformer [10] is used without modification to embed an image in a high-dimensional space. Learning is then performed on the resulting vectors, and not on the original images. The goal is to leverage an existing, well-trained model on the new learning problem. Given the resource constraints in many FL scenarios, it is unclear why attempting to fully train such a backbone from scratch in a federated environment would be the first approach. Instead, we suggest simply taking a standard, pre-trained backbone (such as a ResNet [15], or a DenseNet [19], or both used together) and directly using that backbone as a feature extractor, without training."
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+                                    "content": "The benefit is that each training image only needs to be pushed through the backbone one time to obtain a compact set of features, and then that set can be used during training. As the backbone need not to be communicated or repeatedly used to process the input images, both CPU/GPU cycles and communication are saved during federated training. Furthermore, final accuracies might actually be better, as this approach sidesteps the difficulty of training the backbone."
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+                                    "content": "(4) Off-the-shelf performance is really what matters, but it is often neglected in research studies. In a centralized environment, it is feasible to train and re-train many times, as various parameters (learning rate, proximal weight, exact neural architecture, etc.) are tuned. In FL, this is much less feasible. Most FL scenarios imagine a resource-constrained environment (possibly involving edge devices), where one cannot ignore the cost of tuning. FL is typically happening on someone else's hardware, and so running an algorithm many times during parameter tuning is likely to make participation in training far less palatable."
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+                                    "content": "Further, application-specific tuning may simply be impossible. A device may enter the federated training and then"
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+                                    "type": "text",
+                                    "content": "drop out shortly after, never to be seen again. One cannot access a missing device's data to perform validation, and clearly, one cannot retrain over data that cannot be accessed."
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+                                    "content": "As such, we argue that \"off-the-shelf\" performance is more important than in centralized learning. That is, it becomes important to settle on one set of universal parameters that tend to work in most deployments, such that the learning algorithm can be universally deployed without further tuning. At the very least, this is an important use case that should be covered in most experiments."
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+                                    "content": "Our Contributions. Our contributions are as follows."
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+                                            "type": "text",
+                                            "content": "- We suggest several rules-of-thumb governing benchmark and baseline development for FL over images, and use those rules to devise an extensive FL image classification benchmark, and use that benchmark."
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+                                            ],
+                                            "type": "text",
+                                            "content": "- We show that using pre-trained features and other model reduction tools are necessary for practical FL."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10
+                        },
+                        {
+                            "bbox": [
+                                306,
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+                                345
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    ],
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "- We highlight some surprising behaviors of current FL algorithms, including the effect of client population size, that to our knowledge are not sufficiently explored in current literature."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "- Our source code is publicly available at https://github.com/huerdong/FedVert-Experiments"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                                    "type": "text",
+                                    "content": "2. Background"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The common setting for FL is the following: There are total "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " devices participating in the optimization. To protect data privacy (or due to communication constraints), devices are not allowed to share local data samples to others. Each device has its own local objective function "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{i}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " parameterized by its own model "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "w_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". The coefficient "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_i = n_i / n"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the number of data samples "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " on each device, divided by the unified total data sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "n = \\sum_{i=1}^{N} n_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". There will be a central server that collects all the parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " uploaded by each device and aggregate them into a single model "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
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+                                    "type": "text",
+                                    "content": "The common formulation of FL is to optimize a global optimization function "
+                                },
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+                                    "content": "L(w)"
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\min  _ {w} L (w) = \\sum_ {i = 1} ^ {N} p _ {i} L \\left(w _ {i}; \\left\\{x _ {\\text {l o c}}, y _ {\\text {l o c}} \\right\\}\\right), \\tag {1}",
+                                    "image_path": "69f2a566d8691efee898a10ec23f1f095277a31ceeddab4dd9dddd64fe7a3be4.jpg"
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+                {
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "L(w_{i};\\{x_{\\mathrm{loc}},y_{\\mathrm{loc}}\\})"
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+                                    "type": "text",
+                                    "content": " represents the local objective for device "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", based on local data "
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". The natural algorithm that arises from this objective is FedAvg [37] which directly applies stochastic gradient descent (SGD) to learn "
+                                },
+                                {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "'s. In the most basic case, where FedAvg performs only one local gradient step, the above formulation becomes equivalent to data parallel SGD [33,41,52]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In real-world applications of FL, local data distributions are often skewed towards specific classes: i.e., the natural"
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+                                    "type": "text",
+                                    "content": "distribution of real data can be very skewed, with certain classes only existing in a very small segment of clients' devices. In these heavily non-i.i.d. scenarios, the learned "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " in Eq. (1) can diverge in drastically different directions and, in the most extreme cases, diverge in opposite directions. When FL is performed in this scenario, the averaging can result in a model drastically different from any of the client models and has degraded performance as a consequence; a phenomenon often called client drift [54]. It is this concern that has motivated the development of a number of FL methods beyond FedAvg [21,28,30,43], a few of which will be described in the next section."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. Federated Learning Methods Tested"
+                                }
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+                                    "content": "3.1. The Methods"
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+                                    "content": "In our experiments, we consider the following FL methods, chosen as a representative set of the state-of-the-art."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "FedAvg. Federated averaging [37] is the most simple averaging algorithm and is the basis of the others, whereby client models are trained locally by (stochastic) gradient descent. These local models are aggregated by directly averaging their weights, or equivalently averaging their computed gradients using this averaged gradient for one global round of gradient descent."
+                                }
+                            ]
+                        }
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+                                    "content": "FedProx. FedProx [30] is a modification on FedAvg that introduces an additional "
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+                                    "type": "text",
+                                    "content": "-norm term to the local loss function, that takes the difference between the previously communicated global model and the current model. The aim is to avoid client drift by biasing the training towards an established model. Again, the clients then compute local models whose weights are averaged. Given the model weights "
+                                },
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+                                    "content": " from the previous communication round, the FedProx modification to the FedAvg objective is:"
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+                                    "content": "\\min _ {w _ {i}} \\left\\{L (w _ {i}; \\{x _ {\\mathrm {l o c}}, y _ {\\mathrm {l o c}} \\}) + \\frac {\\mu}{2} \\| w _ {i} - w _ {0} \\| _ {2} ^ {2} \\right\\}, i \\in [ N ]",
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+                                    "content": " is a regularization parameter."
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+                                    "type": "text",
+                                    "content": "MOON. MOON (Model-Contrastive) [28] uses a similar principle as FedProx by comparing the current model with the previous model. However, it utilizes a cross-entropy loss, rather than "
+                                },
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+                                    "content": "\\min  _ {w _ {i}} \\left\\{L (w _ {i}; \\{x _ {\\mathrm {l o c}}, y _ {\\mathrm {l o c}} \\}) - \\mu \\log \\frac {e ^ {\\sin (z , z _ {\\mathrm {g l o b}}) / \\tau}}{e ^ {\\sin (z , z _ {\\mathrm {g l o b}}) / \\tau} + e ^ {\\sin (z , z _ {\\mathrm {p r e v}}) / \\tau}} \\right\\}",
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+                                    "type": "text",
+                                    "content": " is the cosine similarity function, and "
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+                                    "content": "z, z_{\\text{glob}}, z_{\\text{prev}}"
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+                                    "type": "text",
+                                    "content": " are representations of the data generated by the respective model (respectively: learned, current global, previous local). "
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+                                    "type": "text",
+                                    "content": " is a temperature hyperparameter."
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+                                    "type": "text",
+                                    "content": "FedAdam. While the above algorithms modify the local training process of FedAvg, FedAdam [40] modifies the aggregation step. Once the averaged weights are computed"
+                                }
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+                                    "type": "text",
+                                    "content": "via local gradient descent and their average is computed, it is used to compute a global gradient surrogate to be used in the Adam algorithm [22]."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "FedNova. FedNova [43] introduces a client gradient reweighting scheme when accumulating the models parameters/gradients and generalizes FedAvg and FedProx as specific parameterizations. However, we use the specific formulation specified in [43], where these weights are normalizations of the local gradients."
+                                }
+                            ]
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+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "IST. We consider the previous set of learning algorithms to be \"reconciliation-used\"; in that, they attempt to train a copy of the model at each site. In contrast, IST, or independent subnet training [51] does not utilize averaging or some other method to try to reconcile versions of the model trained at the various sites. Instead, IST decomposes the model and sends non-overlapping parts of the model to different sites. In one training round, all neurons (or activations) in a neural network are randomly partitioned to the active sites. A weight is only sent to a site if it connects two neurons that have been assigned to the site. Thus, each site is assigned only a very small subnet network, which is trained locally for a number of gradient descent steps. At the end of local training, the updated weights are shuffled (with or without the aid of a central server) and the process is repeated. Since subnetworks are independent, there is no averaging or other form of reconciliation needed. There are many variants of this approach in the literature, including FjORD [17], HeteroFL [9], LotteryFL [26], FedSelect [4], FedRolex [1], Federated Dropout [5], PVT [47], and the independent subnet network training approach in the non-FL setting [11, 32, 44, 45, 51]. It is this latter version of the approach (for MLPs) that we apply here."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "ISTProx. This is IST, but with a proximal term added to the loss function."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.2. Analytic Comparison"
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+                                    "content": "The focus of our experiments will be on comparing each of the methods based on their ability to produce high test accuracy with a low cost. In the paper, we will define cost in terms of floating point operations (FLOPs) required to reach a given accuracy, and in terms of floating point numbers transferred. As such, we begin by considering the number of FLOPS required and the floating point numbers that must be transferred to complete one gradient descent step for each of the methods."
+                                }
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+                                    "content": "In our analysis, we assume that we are using a pretrained backbone to transform each input image into a vector, and we are learning a MLP with two weight matrices. The MLP accepts an "
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+                                    "content": "-dimensional input. It has a hidden layer of "
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+                                    "content": " neurons, and has "
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+                                    "type": "text",
+                                    "content": " outputs. Assume a batch size of "
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+                                    "type": "text",
+                                    "content": " at each of "
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+                                    "type": "text",
+                                    "content": " sites. Since each image only goes through the pre-trained backbone once, the FLOP cost"
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+                                    "content": "of the pre-trained backbone is negligible when amortized over many gradient descent steps. We will consider only the FLOPs associated with the weights, as the cost associated with updating weights dominates the cost associated with the activation layers."
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+                                    "content": "Begin with FedAvg. In this case, to push a batch through, we have approximately "
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+                                    "content": " FLOPs for the forward pass and approximately "
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+                                    "content": "2b(n_{1}n_{2} + 2n_{2}n_{3})"
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+                                    "type": "text",
+                                    "content": " for the backward pass, for a total of "
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+                                    "content": " FLOPs at each site. Coordination requires "
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+                                    "type": "inline_equation",
+                                    "content": "2s(n_{1}n_{2} + n_{2}n_{3})"
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+                                    "type": "text",
+                                    "content": " floating point numbers be sent (the model needs to be distributed to all sites, and then the updated model needs to be collected from all sites). The number of FLOPs incurred during averaging is typically not significant, as we are simply average "
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+                                    "type": "text",
+                                    "content": " copies of the two weight matrices, having "
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+                                    "content": " and "
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+                                    "content": " floating point numbers each, and this may be done using a distributed algorithm."
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+                                    "content": "Adding a proximal term in the case of FedProx may have little effect, as this changes the backward pass at each site by adding FLOP computations that scales linearly with the weight matrices, but does not scale with the batch size "
+                                },
+                                {
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+                                    "content": ". Thus, for any reasonable batch size, it is insignificant. If multiple gradient update steps are performed at each site, it also requires storing an older copy of the weight matrices at each site."
+                                }
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+                                    "type": "text",
+                                    "content": "FedAdam is a federated version of the Adam algorithm and as such, it requires storing four additional matrices—typically at a coordinator—two of which are associated with each of the MLP's weight matrices. It must approximate the gradient and run the Adam algorithm at the coordinator during each update. However, this does not affect the memory, computation, or communication requirements at each site, and so any differences may not be of practical importance."
+                                }
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+                                    "content": "FedNova requires a normalization step at each site during the local gradient computation, but this only requires multiplying each gradient by a scalar, which is likely insignificant and so it is also, for practical purposes, computationally no more expensive than FedAvg. MOON is more expensive than FedAvg in terms of FLOPs, as it needs to compute multiple representations of each training iteration. The obvious MOON implementation will require "
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+                                    "type": "text",
+                                    "content": " additional FLOPs compared to FedAvg at each site. In addition, MOON needs to locally maintain two additional copies of the weight matrices."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
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+                                    "type": "text",
+                                    "content": "Next, consider IST. At each site, "
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+                                    "type": "text",
+                                    "content": " is effectively cut by a fraction "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", because the neurons in the hidden layer is partitioned "
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+                                    "type": "text",
+                                    "content": " ways and only the weights associated with neurons assigned to a site are actually sent or used there. Hence, the total number of FLOPs is "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(4n_1n_2b + 6n_2n_3b) / s"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and coordination requires that only "
+                                },
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2(n_{1}n_{2} + n_{2}n_{3})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " floating point numbers be sent and received; each weight is assigned to exactly one site. There are no FLOPs associated with coordination, as there is no averaging done; weights are sim"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "ply updated and sent around. Due to the partitioning, the memory usage at each site is on average smaller than that of FedAvg by a factor of "
+                                },
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+                                    "type": "text",
+                                    "content": ". Like FedAvg, adding a proximal term has little effect on either FLOPs or bytes transferred."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4. Experimental Setup"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "4.1. Pre-Trained Backbones"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                    "type": "text",
+                                    "content": "All of the methods we tested (except for one baseline) utilize pre-trained backbones. That is, we take a pre-trained feature image classifiers: ResNet101 [15] and DenseNet121 [19], and remove the classification layers to produce two \"backbones.\" When processing an image, we simply concatenate the feature vectors produced by the two backbones to produce a 3072 dimensional vector. We also evaluate FedProx, but without a pre-trained backbone. This version of FedProx (called \"FedFull\") uses a ResNet18 instead of a single-hidden layer MLP."
+                                }
+                            ]
+                        }
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+                                    "content": "4.2. Data Sets and Hyperparameters"
+                                }
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+                        }
+                    ],
+                    "index": 10
+                },
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+                                    "type": "text",
+                                    "content": "Overall, we conduct experiments on a diverse and broad range of image classification data sets: (1) CUB-200-2011 (Birds) [42], (2) Stanford Cars (Cars) [23], (3) VGGFlowers (Flwrs) [38], (4) Aircraft (Aircraft) [36], (5) Describable Textures (Textre) [8], and (6) CIFAR 100 (CFAR) [24]. The only processing we apply on these data sets, besides using the pre-trained feature extractors, is the standard cropping and resizing of image data. For the Aircraft data set, there are multiple levels of specificity of labels - manufacturer, family, variant - we chose variant for the finest-grained classes."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "We use the Birds data set to tune the methods. After extensive experimentation on Birds, we chose a learning rate of 0.01, as we found this to give stable convergence in all algorithms, except FedAdam, where we choose a learning rate of 0.03. For all algorithms except for IST, ISTProx, and FedFull, tuning led us to a single-hidden-layer, multi-layer perceptron (MLP) with 1,000 hidden neurons sitting on top of the feature extractor. FedFull was trained with its \"out of the box\" configuration. For IST and ISTProx, we find scaling the hidden neurons based on the number of concurrent training sites made sense (3000 neurons for ten sites, 6000 for 20, 9000 for 30, 18000 for 60, and so on). This ensures that the client models are not too small."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "A number of other hyperparameters were also optimized using the Birds data set. For the various hyperparameters in each algorithm, we applied a grid search on a set list of parameter values, as described in the next subsection. We consider the number of local iterations of stochastic gradient descent as a hyperparameter with either 1, 5, or 25 local training batches, before a communication round. We use a batch size of 32 images. For FedProx, FedNova, and IST-Prox, we tuned the additional proximal hyperparameter "
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+                                    "type": "text",
+                                    "content": ". For MOON, we have a similar weight parameter "
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+                                    "content": " (the co"
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+                                            "content": "(a) Final accuracies"
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+                                            "content": "(b) Communication (GB) to threshold acc."
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+                                    "content": "efficient of the contrastive term) and "
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+                                    "content": ", the temperature of the contrastive term. FedAdam has a central learning rate as well, which we set to 0.01. Exact values for all of our hyperparameters are given in the appendix. We stress that, while we performed careful tuning on the Birds data set, all hyperparameters were re-used blindly and without modification, on all other data sets."
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+                                    "content": "4.3. Evaluation Metrics"
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+                                    "content": "Choosing an evaluation metric is among the most difficult aspects of evaluating FL methods, but does not seem to have received much attention in the literature. Most papers focus on final accuracy: What is the accuracy that a FL method exhibits on a test set after training? Unfortunately, final accuracy as a metric makes little sense in isolation from other considerations. After all, the method that likely gives the very best final accuracy is simple dis"
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+                                            "content": "Figure 1: Accuracy as a function of time for FedProx and FedFull on the Stanford Cars data set."
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+                                    "content": "tributed mini-batch training, where each site computes gradients over a small subset of its local data; those gradients are summed and a central site updates the model. This is algorithmically equivalent to centralized training, but it is typically not tested, because it is generally assumed that the convergence would be too \"slow,\" for some implicit definition of \"slow.\" Thus, a more carefully-defined evaluation framework (beyond simple accuracy) is needed."
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+                                    "content": "Hence, we consider three metrics: final accuracy, computational efficiency, and communication efficiency [34, 46]. Of the three, we assert that final accuracy should be considered the least important; it is most useful as a way to contextualize the other two metrics (e.g., \"what final accuracy can I achieve in GigaFLOPs of computation?\")."
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+                                    "content": "For a given method, using the Birds data set, we first perform a grid search over the various hyperparameters, and for each hyperparameter set, we run the method for a \"long time,\" where a \"long time\" allows a maximum of "
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+                                    "content": " floating point operations (or 100 teraFLOPs, where floating point operations are summed across all devices participating in federated training) and five terabytes of data communicated (assuming single-precision floating point computations). Note that 100 teraFLOPs corresponds to around 14 hours of CPU time on a single mobile phone, or perhaps several hundred hours of processor time on a limited IoT device. Once a method exceeds 100 teraFLOPs or five terabytes of communication, we take its very best observed test accuracy, averaged over ten communication rounds. The best average observed over all hyperparameter settings is taken as the method's \"final accuracy\"."
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+                                    "type": "text",
+                                    "content": "Next, we consider each data set in sequence. We first run each method to 100 teraFLOPs or five terabytes of communication on the data set, using the accuracy-optimized parameters. We then compute the maximum accuracy that any method obtained on the data set, and set "
+                                },
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+                                    "type": "text",
+                                    "content": " of this accuracy as a target. Then, for each method and each data set, we compute two additional numbers: the number of gigaFLOPs required to reach the target accuracy for five consecutive rounds (using the FLOP-optimized settings), and the number of gigabytes of communication required to reach the target accuracy (using the communication-optimized settings). If a method is unable to reach the target accuracy within the 100 teraFLOPs/five terabytes limit, it is said to have failed (indicated as FAIL in tables)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
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+                                    "type": "text",
+                                    "content": "We estimate the amount of FLOPs used during training using the FlopCountAnalysis tool in the Python fvmcore [12]. Similarly, for our communication costs we estimate the size of a model in bytes with the Python torchinfo [49] package."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "The reason for this evaluation strategy is simple. In practice, the preferred FL method is likely to be the one that"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "reaches a high level of accuracy with little cost. Hence, we (somewhat arbitrarily, but precisely) define \"high level of accuracy\" as "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " of the peak accuracy observed over all methods for a given data set. Given this target, evaluation is then a matter of counting floating point operations and bytes to reach that target."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Note that other metrics are possible: power usage and elapsed wall clock time are two of the most obvious. However, both of these will be closely related to FLOPs and communication required, and hence we stick to these two."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "5. Identically Distributed Data"
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+                                    "content": "5.1. Setup"
+                                }
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+                                    "content": "In our first set of experiments, the images are randomly partitioned across the sites, so that each site has a randomly-selected (with replacement) subset of the overall set of images in the training data set. After a round of communication finishes, ten sites are randomly selected as being \"on the network\" and those sites participate in the present round of training. After local training finishes and all of the results have been communicated, another set of ten sites are randomly selected and the process continues."
+                                }
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+                                    "content": "For this simple \"i.i.d.\" setup, our experiments will answer a few key questions. First and foremost, should we be doing full backpropagation through a convolutional network, or should we be exclusively using a pre-trained back"
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+                            ]
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+                                            "content": "(a) Final accuracies"
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+                                            "type": "text",
+                                            "content": "(b) Communication (GB) to threshold acc."
+                                        }
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+                            "index": 2,
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+                            "type": "table_caption"
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+                                            "html": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>131</td><td>62</td><td>51</td><td>79</td><td>55</td><td>59</td></tr><tr><td>FedProx</td><td>250</td><td>FAIL</td><td>124</td><td>FAIL</td><td>71</td><td>54</td></tr><tr><td>MOON</td><td>FAIL</td><td>FAIL</td><td>193</td><td>FAIL</td><td>143</td><td>74</td></tr><tr><td>FedAdam</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td><td>FAIL</td></tr><tr><td>FedNova</td><td>743</td><td>FAIL</td><td>430</td><td>608</td><td>309</td><td>160</td></tr><tr><td>IST</td><td>79</td><td>FAIL</td><td>37</td><td>119</td><td>69</td><td>FAIL</td></tr><tr><td>ISTProx</td><td>72</td><td>FAIL</td><td>59</td><td>134</td><td>72</td><td>219</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "(c) GFLOPs to threshold acc"
+                                        }
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+                                        }
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+                                    "type": "text",
+                                    "content": "Table 2: Skewed data results, 100 sites, "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "{10}\\%"
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+                                    "type": "text",
+                                    "content": " participation."
+                                }
+                            ]
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+                {
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+                                    "type": "text",
+                                    "content": "bone? Second, when one considers computation and communication (rather than just final accuracy) do the methods compare differently than when the only metric is accuracy? And finally, does the data set used matter? Results are shown in Table 1. For each data set, the best result is indicated in bold."
+                                }
+                            ]
+                        }
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+                                    "content": "5.2. Discussion"
+                                }
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+                                    "type": "text",
+                                    "content": "There are a few clear results. First, except for FedAdam and FedFull, the methods generally have very similar final accuracy, with the two IST-based methods being slightly higher. Thus, one key finding is that for data without skewness across sites, if one is only interested in final accuracy, it does not seem to matter much which method is used, and this result holds across data sets. The two exceptions to this are FedAdam and FedFull. FedAdam does not reach the same final accuracy as the other methods, but it generally does quite a good job reaching high accuracy with relatively little communication. This corresponds to the fact that it tends to converge in relatively few communication rounds."
+                                }
+                            ]
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+                                    "content": "FedFull is a very interesting case. Note that it has poor final accuracy—only "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " in the case of the Cars data set. As a result, it is labeled as “FAIL” in every case, because it can never reach "
+                                },
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+                                    "type": "text",
+                                    "content": " of the peak accuracy observed for the other methods on a given data set. One might ask, Why is FedFull such a poor choice? The answer is simple: as we put a 100 teraFLOP/five terabyte “timeout” on the computation, FedFull timed out in every case. That is, it always hit the 100 teraFLOP/five terabyte limit. Were FedFull allowed infinite computation and infinite communication, it is actually the preferred method, as the pre-trained backbones limit accuracy. For example, consider Figure 1, which plots accuracy as a function of FLOPs for both FedFull and FedProx on Cars. FedFull eventually reaches "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "90\\%"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " accuracy, but it takes nearly four orders of magnitude more FLOPs to top out compared to FedProx. This FLOP usage gap is apparent in Fig. 1 where even the first communication round of FedFull requires more FLOPs than the amount required for the entire FedProx training. As a result, we would argue that full backpropagation is effectively unusable in resource-constrained FL. Note, however, that our FedFull was trained using an initialization consisting of random weights. Perhaps a hybrid method makes sense, where one begins with FedProx (with a pre-trained backbone) and then once the MLP begins to reach peak accuracy, we allow backpropagation over the backbone to begin. This issue deserves further investigation. That said, given our maximum FLOP count and communication, FedFull is not competitive and in the interest of space, we will not consider it further."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The final observation we make is the general superiority of IST, over each of the six data sets. It is perhaps not surprising that IST is efficient in terms of communication and in terms of computation. Each site obtains only a fraction of the MLP that is being trained, saving communication and computation at each site. However, it is surprising that it is also generally the most accurate method, in terms of final accuracy (or close to it) in every case. We will examine this finding more fully, later in the paper."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "6. Effect of Data Skewness"
+                                }
+                            ]
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+                                    "content": "6.1. Setup"
+                                }
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+                                    "content": "How might these results change if data are not uniformly distributed across sites? To answer this question, we modify our experiments as follows. Rather than assigning each training image to each site with uniform probability, we sample the class probabilities for each site from a Dirichlet(0.01) distribution, and rerun our experiments (with 100 sites and 10 sites active in each round). This creates a relatively extreme—yet still realistic—amount of skew. For the six data sets we tested, the three-tuple (number of classes in data set, min number of classes at any site, max number of classes at any site) is: for Birds (200, 7,"
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+                                            "content": "(a) 1000 sites"
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+                                            "content": "Change in acc., "
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+                                    "type": "text",
+                                    "content": "Table 3: Observed change in accuracy, computed as “(correct with fewer sites) - (% correct with more sites)”, when active sites increase. Red indicates negative change."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "20), Aircraft (100, 2, 15), Stanford Cars (196, 4, 20), Flowers (102, 3, 15), Textures (47, 1, 9), and CIFAR100 (100, 1, 13). This matches the realistic case where each site has access to only a few of the classes, and from this limited local information, an accurate global model must be constructed. Results are shown in Table 2."
+                                }
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+                                    "content": "Probably the single most interesting finding is that for a highly-skewed situation, there seems to be divergence in performance, depending upon the data set. The two IST methods seem to perform best overall, with either IST or ISTProx being the superior option in terms of final accuracy, FLOPs, or communication for four of the six data sets. However, IST does relatively poorly on the venerable CFAR data set. CFAR is a somewhat strange benchmark, as the images are tiny "
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+                                    "content": " and widely varied within the data set, and both IST variants have problems with this. Nevertheless, it is a good stress test. Note that in the two cases where IST does not do the best, it is either simple FedAvg or FedProx that is the best performer. One of the most surprising findings is that FedAvg dominates all other methods in all metrics (accuracy, FLOPs, communication) on Cars."
+                                }
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+                                }
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+                                            "content": "Change in comm., "
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+                                            "html": "<table><tr><td></td><td>Birds</td><td>Cars</td><td>Flwrs</td><td>Aircraft</td><td>Textre</td><td>CFAR</td></tr><tr><td>FedAvg</td><td>0.65</td><td>NA</td><td>1.97</td><td>0.24</td><td>1.24</td><td>0</td></tr><tr><td>FedProx</td><td>∞</td><td>3.13</td><td>2.82</td><td>6.43</td><td>1.75</td><td>2.41</td></tr><tr><td>MOON</td><td>∞</td><td>NA</td><td>1.27</td><td>NA</td><td>5.31</td><td>7.39</td></tr><tr><td>FedAdam</td><td>NA</td><td>NA</td><td>1.29</td><td>NA</td><td>2.23</td><td>2.89</td></tr><tr><td>FedNova</td><td>0.3</td><td>-0.5</td><td>4.3</td><td>-0.7</td><td>-0.6</td><td>-0.3</td></tr><tr><td>IST</td><td>∞</td><td>NA</td><td>1.09</td><td>∞</td><td>2.73</td><td>6.44</td></tr><tr><td>ISTProx</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr></table>",
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+                                    "content": "Table 4: Multiplicative change in communication when tripling the number of active sites. Red text indicates more than a "
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+                                    "content": " increase; black indicates less than a "
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+                                    "type": "text",
+                                    "content": " increase. \"NA\" indicates the case when there was a FAIL in both bases. "
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+                                    "content": " indicates a change from non-fail to a FAIL, and 0 indicates a change from FAIL to non-fail."
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+                    ],
+                    "index": 17,
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+                    "type": "text",
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+                                    "type": "text",
+                                    "content": "speedup convergence, both in terms of reducing communication and FLOPs. However, IST seems to be the best performer overall, allowing for significant reductions in communication and FLOPs. The addition of a proximal term does not seem to help IST much. The other methods tested all seem to under-perform."
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+                                    "type": "text",
+                                    "content": "6.3. FL, Approximating Centralized Learning"
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+                                    "type": "text",
+                                    "content": "How does the training process for a method (such as FedAvg and FedProx) that trains the entire model at each site and then reconciles the various versions of the model, compare with IST, which avoids this through decomposition?"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "To examine, we centrally train a model from initialization through convergence using min-batch gradient descent, obtaining model parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "M_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for the "
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+                                    "type": "inline_equation",
+                                    "content": "i"
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+                                {
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+                                    "type": "text",
+                                    "content": "th training epoch. Then, using FL, we start training in a federated setting from "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "M_{i}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for some number of communication rounds, to obtain new model parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". We refer to the set of model parameters we would have obtained after processing exactly the same set of data centrally, via a series of mini-batches, as "
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Then the cosine similarity of the directions both methods move, defined as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(\\hat{M}_i - M_i)\\cdot (M_i^* -M_i) / (||\\hat{M}_i - M_i||\\times ||M_i^* -M_i||)"
+                                },
+                                {
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+                                    "type": "text",
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+        {
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+                                    "type": "text",
+                                    "content": "shows the utility of FL as an approximation for centralized learning. Cosine similarity close to one means FL and centralized training move in the same direction. Zero implies de-correlation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        48,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Some results obtained in this way are plotted in Figure 2, where we consider FedAvg, FedProx, IST, and ISTProx. These plots depict this cosine similarity as a function of the training epochs. We plot running averages to smooth the data. The top three plots are for Cars, the bottom three Flwrs. The results for identically distributed data are at left, whereas skewed data are in the center, and at the right."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        433
+                                    ],
+                                    "type": "text",
+                                    "content": "FedAvg and FedProx are shown to approximate the centralized gradient descent direction well early on, but the similarity drops after initial training. This makes sense, as initially, with a random initialization, learning is \"easy\" as the model is far from optimal. In the i.i.d. case FedAvg and FedProx perform well. But in the skewed case, after the initial training period, similarity to the centralized training direction drops. IST seems more well-behaved, with less variance. Especially considering how well the methods approximate the direction of centralized training through twenty rounds on skewed data (the right column), the IST-based methods seem to do better. This is especially pronounced for the Flwrs data set through the first 20 epochs, where IST averages a similarity of 0.035, compared to 0.01 for the averaging-based methods. Perhaps this is due to the high variance of the directions computed by FedAvg and FedProx—as estimators for the centrally-predicted direction—compared to IST. Examining why this is deserves further investigation in future work."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        48,
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "7. Varying Sites and Connectivity"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "7.1. Setup"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "All of our experiments thus far have focused on the simple case of 100 sites, where at each communication round, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "10\\%"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of the sites are connected. We now ask: how do things change when the number of sites changes and/or the number of sites connected at each communication round changes? Keeping all of the other settings the same, we try 1000 sites, with either "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " or "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "6\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        48,
+                                        486,
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+                                    "type": "text",
+                                    "content": " of the sites connected at each communication round, and 100 sites, with either "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "10\\%"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "30\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        48,
+                                        486,
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+                                    "type": "text",
+                                    "content": " of the sites connected at each round. Due to space constraints, we consider accuracy and communication here, and provide further results of these experiments in the appendix. In Table 3, we show the absolute change in percentage accuracy moving from "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": " to "
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+                                    "content": "6\\%"
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+                                {
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+                                    "type": "text",
+                                    "content": " connectivity, and from "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "10\\%"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "30\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        48,
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+                                    "type": "text",
+                                    "content": " connectivity. In Table 4, we show the multiplicative change in communication required. Note that, as we increase the number of active sites by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we might expect a "
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+                                    "type": "text",
+                                    "content": " increase in communication if the same number of communication rounds are required. If fewer rounds are required, we would see an increase that is less than "
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "7.2. Discussion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "FedAdam, IST, and ISTProx are generally helped a bit by increasing participation. But for the other methods, the results obtained by increasing participation rates are mixed, with a surprising number of red values in both Table 3 and Table 4, indicating a decrease in accuracy or communication efficiency via the addition of extra active sites. In addition, it seems that the increase from "
+                                },
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+                                    "type": "text",
+                                    "content": " participation to "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
+                                        308,
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+                                    "type": "text",
+                                    "content": " participation is much more helpful than "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "The lack of clear benefit to increasing the rate of participation is not surprising in retrospect. Aside from FedFull, each of the methods was able to run to convergence in the allotted FLOP/communication budget. The central question becomes: can we run to convergence in fewer rounds by doing more work in each round? This seems very unlikely, as this is akin to increasing the batch size in centralized learning, and expecting a significant decrease in the number of batches required for convergence. There is typically some decrease in the number of batches with increasing batch size, but it often is not significant. In reconciliation-based methods, this may be particularly inefficient as local training rounds cause the active sites to diverge and simply makes it more difficult to reconcile them. IST may have another advantage in that regard, in that more active sites does not increase communication for IST, it simply means that each site gets less of the full model. As long as each site can tolerate local learning using a smaller model (due to partitioning more ways), the learning may benefit from seeing a greater variety of data in each round. This certainly seems to be the case in when moving from "
+                                },
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+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "6\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", which benefits IST."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "8. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We have designed a set of experiments to evaluate FL methods. Among the issues considered were what were the appropriate evaluation metrics (accuracy alone makes little sense), whether to use a pre-trained backbone, and the effect of connectivity on the efficiency of the learning. We find that overall, the method of decomposition of a neural network into independent subnetworks seems to be the best option. This has the benefit of decreasing communication and computation compared to \"reconciliation-based\" methods that train a copy of the model at each site, as the model is sharded, rather than broadcasted."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Acknowledgements. We would like thank the anonymous reviewers for their comments on the submitted version of the paper. Work presented in this paper has been supported by an NIH CTSA, award No. UL1TR003167 and by the NSF under grant Nos. 1918651, 1910803, 2008240, and 2131294."
+                                }
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+                                        }
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diff --git a/2023/FemtoDet_ An Object Detection Baseline for Energy Versus Performance Tradeoffs/ae3858f0-bbf1-4f71-acdc-96b1b40f62b6_content_list.json b/2023/FemtoDet_ An Object Detection Baseline for Energy Versus Performance Tradeoffs/ae3858f0-bbf1-4f71-acdc-96b1b40f62b6_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..ffbac1e131d20a2797038c883209bb40d8d149c5
--- /dev/null
+++ b/2023/FemtoDet_ An Object Detection Baseline for Energy Versus Performance Tradeoffs/ae3858f0-bbf1-4f71-acdc-96b1b40f62b6_content_list.json	
@@ -0,0 +1,1489 @@
+[
+    {
+        "type": "text",
+        "text": "FemtoDet: An Object Detection Baseline for Energy Versus Performance Tradeoffs",
+        "text_level": 1,
+        "bbox": [
+            117,
+            128,
+            851,
+            174
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Peng Tu $^{1}$ , Xu Xie $^{1}$ , GUO AI $^{1}$ , Yuexiang Li $^{2}$ , Yawen Huang $^{2*}$ , Yefeng Zheng $^{2}$ $^{1}$  MicroBT Inc.  \n $^{2}$  Jarvis Lab, Tencent",
+        "bbox": [
+            169,
+            200,
+            797,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            275,
+            313,
+            291
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Efficient detectors for edge devices are often optimized for parameters or speed count metrics, which remain in weak correlation with the energy of detectors. However, some vision applications of convolutional neural networks, such as always-on surveillance cameras, are critical for energy constraints. This paper aims to serve as a baseline by designing detectors to reach tradeoffs between energy and performance from two perspectives: 1) We extensively analyze various CNNs to identify low-energy architectures, including selecting activation functions, convolutions operators, and feature fusion structures on necks. These underappreciated details in past work seriously affect the energy consumption of detectors; 2) To break through the dilemmacatic energy-performance problem, we propose a balanced detector driven by energy using discovered low-energy components named FemtoDet. In addition to the novel construction, we improve FemtoDet by considering convolutions and training strategy optimizations. Specifically, we develop a new instance boundary enhancement (IBE) module for convolution optimization to overcome the contradiction between the limited capacity of CNNs and detection tasks in diverse spatial representations, and propose a recursive warm_restart (RecWR) for optimizing training strategy to escape the sub-optimization of light-weight detectors by considering the data shift produced in popular augmentations. As a result, FemtoDet with only 68.77k parameters achieves a competitive score of 46.3 AP50 on PASCAL VOC and 1.11 W & 64.47 FPS on Qualcomm Snapdragon 865 CPU platforms. Extensive experiments on COCO and TJUDHD datasets indicate that the proposed method achieves competitive results in diverse scenes.",
+        "bbox": [
+            76,
+            306,
+            472,
+            777
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            801,
+            209,
+            816
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The deployment of efficient convolutional neural networks (CNNs) enabled immense progress [23, 29, 30, 31, 4, 9, 41] in vision detectors for edge devices, in which they",
+        "bbox": [
+            76,
+            828,
+            468,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "consistently reduce parameters and speed counts for improving accuracy. However, these metrics are not correlated well with the efficiency of the models in terms of energy. Evaluation metrics, such as parameters, do not take into account the energy cost of models, resulting in a nontrivial effect on the energy cost of detectors. Compared with the same architecture, the parameters of models are positively correlated with their energy cost (shown in Table 2). However, in the case of equal model parameters, their energy consumption may be negatively correlated or even irrelevant to the model parameters (shown in Table 1). Considering that various activation functions, convolution operators, and feature fuse structures may not increase model parameters, but generate more energy costs. Similarly, the speed count is also not well correlated with energy, as it can be optimized by the degree of parallelism. These disconnections will leave customized efficient detectors unavailable, when they are deployed under severe energy constraints like the always-on surveillance cameras.",
+        "bbox": [
+            500,
+            276,
+            893,
+            564
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "This paper aims to reduce the energy costs of efficient object detectors, while improving their performances by achieving energy versus performance tradeoffs. Specifically, these bottlenecks fall into several categories:",
+        "bbox": [
+            498,
+            565,
+            893,
+            626
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1) Detector components with unknown energy. Most current object detection methods focus either on latency-oriented [5, 34, 44] or accuracy-oriented [9, 38, 32, 36] works. There are very limited works toward the energy cost of the detector components, which is the first obstacle to designing energy-performance-balanced detectors. To identify energy-efficient components of detectors, we followed [42] to benchmark their energy metrics from three types of structures, i.e., activation functions, convolution operators, and necks of detectors. The following finding is acquired: Firstly, some activation functions have been widely used, because of their ability to improve models without adding more parameters. They have increased costs, yet received very limited attention. As shown in Table 1, we set ReLU [1] based models as a baseline. When replacing the ReLU with the GELU [16],  $4.40\\%$  performance is gained, while  $12.50\\%$  energy cost is increased, and the corresponding factor of the mean energy versus the perfor",
+        "bbox": [
+            498,
+            628,
+            893,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author; First author's Email: yh.peng.tu@gmail.com",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "13318",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "mance tradeoffs (Eq. 1) drops  $7.16\\%$ . In addition, although large kernel convolutions [25] can improve models (Table 2), the increased energy cost is unacceptable. As seen in Table 2, the large kernel convolutions are equipped to enable the model to rise by around  $1.87\\%$  in performance, but with more energy costs  $(16.20\\%)$  than in the small kernel size of convolutions (shown in the second row of Table 2). Finally, the standard FPN [21, 22, 39, 10, 37] in the detectors also causes significant energy costs. We observe that this situation is happened due to multi-feature fusion paths following either bottom-to-up or top-to-down way, resulting in frequent data reading in memory for data coverage. However, it is shown that the up-down fusion between multi-features may not necessary. As shown in Table 3, we propose a simple SharedNeck for replacing FPN to reduce around  $5.77\\%$  energy costs, while obtaining  $6.25\\%$  performance gains. SharedNeck uses an adaptive fusion between multi-features by learning convolution, instead of feature-by-feature bottom-to-up or top-to-down fusions, as operated in FPN. Based on these analyses, we further build upon a low-energy detector, named FemtoDet. Surprisingly, FemtoDet just has  $68.77\\mathrm{k}$  parameters and  $1.1\\mathrm{W}$  power on the platform. 2) Optimization for CNN is another bottleneck, since obtaining a favorable detector is very challenging, especially for a small number of parameters. Light-weight detectors are restricted by their limited capacities [6], which will cause obfuscation on feature maps of the instances' boundaries of interesting objects, as shown in Figure 2 (b). Ambiguous instance boundaries on the features may raise the risk of false detection in the models. For this problem, we propose a novel instance boundary enhancement module (IBE), which emphasizes the potential of the object boundary information: The parameter reuse mechanism is first applied to integrate local descriptors with convolution operation to make robust and diverse instance boundary feature representation. But this operation would cause feature un-alignment between normal features and integrated features. Then, in order to sufficiently exploit these two types of features, we design dual-normalization in IBE, as to realign the features (Fig. 4 of the Appendix). IBE employs a shared convolution yet an independent batch normalization layer for separate normalization is also adopted. Finally, we add normal and integrated features together behind the dual-normalization layer. IBE provides a novel form of parameter reuse to generate new local descriptors from shared convolution operators. This method can capture object boundary information by integrating gradient cues around the learned convolution. After trained, IBE modules can be folded into simple convolution operators, thus requiring no extra computations anymore; In addition, data augmentation is a common approach for efficient detector training. Using well-designed strong augmentations is conducive to improving the generalization of mod",
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+    {
+        "type": "text",
+        "text": "els [31, 9]. However, how to prevent data shifts between training and validation images has not been explored, while training data suffers strong augmentations. It is found that the produced data shifts by strong augmentations would prevent light-weight detectors from moving toward global optimization. A common view is that strong image augmentations can effectively encourage networks to learn diverse features [11]. But for light-weight detectors, these diverse features cannot assist the models in making better generalizations in the validation set. In other words, light-weight detectors are more susceptible to these ignored data shifts because of their limited capacities. Furthermore, we propose an effective training strategy, namely recursive warm-start (RecWR), to adapt these diverse features to improve the model's generalization. RecWR works based on multistage training while gradually weakening data augmentation strength. This method can help the limited-capacity detectors jump out of local optima under the assistance of high-dimension & diverse features. The effectiveness of the IBE and RecWR has been evaluated on PASCAL VOC dataset. And the experimental results show that IBE can improve FemtoDet  $\\sim 7.72\\%$  performance, while incurring no extra parameter burdens, as compared to the original architecture; RecWR can improve FemtoDet  $\\sim 6.19\\%$  performance by gradually weakening the data augmentation strength in multi-stage learning. By jointly training FemtoDet with IBE and RecWR, our proposed methodology can go over the YOLOX [9] by  $51.34\\%$  in performance when using the same-level parameters.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Something worth mentioning is that FemtoDet is specially designed for hierarchical intelligent chips to enable always-on alerts: the always-on low power, high-recall, and decent accuracy - it achieved 85.8 AR20 & 76.3 AP20 (Table 7) while performing pedestrian detection on TJU-DHD. In addition, FemtoDet is poor in detecting small objects but is excellent in detecting medium and large objects, which they are more interested in, with 88.8 AR20-m & 94.1 AP20-m / 95.3 AR20-1 & 98.6 AP20-1 (Table 7) on TJU-DHD. Information can be passed to other models after identifying possible objects of interest, and high-precision robust models are then initiated for accurate recognition. The always-on smart products have a wide range of applications, e.g., in-home monitoring or robots. Hence, the loose metric (e.g., AP50 or AP20) and data scenario with moderate difficulty (e.g., VOC) can well reflect the application ability of FemtoDet. Further, the experiments on COCO datasets have verified that the proposed method is suitable for diverse scenarios resulting in competitive results.",
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+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "2.1. Object Detection",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Object detection is a classic computer vision task for identifying the category and location of object in pictures",
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+    {
+        "type": "page_number",
+        "text": "13319",
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+    {
+        "type": "text",
+        "text": "or videos. The existing object detectors can be divided into two categories: two-stage detectors and one-stage detectors. Two-stage detectors [32, 36, 14, 21] are anchor-based devices that generate region proposals from the image and then produce the final prediction boxes from these proposals. Further, FPN [21] improves the two-stage detectors by fusing multi-level features. Despite their higher accuracy compared to the one-stage detectors, two-stage detectors are still difficult to achieve low latency when deployed on edge devices.",
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+    {
+        "type": "text",
+        "text": "Specifically, there are two types of one-stage detectors: anchor-based and anchor-free, which depends on anchor priors injecting into whole images to enable box regression. SSD [23], as a classical anchor-based one-stage detector, discretizes the output space of bounding boxes into a set of default anchors with different aspect ratios and scales per feature map location. This operation helps detecting tiny objects. Another typical anchor-based detector is the YOLO series [30, 31, 4]. YOLOv2 [30] explores bag of freebies to improve the performances of one-stage detectors. YOLOv3 [31] proposes cross-scale features and novel nms (Non-Maximum Suppression) to obtain more confident predictions. YOLOv4 [4] finds that the repeated gradient of network optimization aggravates detector latency, and thus designs Cross-Stage-Partial-connection modules to reduce the latency of detectors while maintaining detection performance. Anchor-free detectors [29, 9, 19, 38] aim to eliminate the pre-defined set of anchor boxes. YOLO [29], as an anchor-free one-stage detector, divides an image into multiple grids and predict boxes at grids near the object's center. CornerNet [19] detects an object as a pair of key points (through the top-left corner and bottom-right corner of the bounding box). A single convolutional network was leveraged in CornerNet to predict a heatmap for all top-left corners of instances of the same object category, a heatmap for all bottom-right corners, and an embedding vector for each detected corner. Indeed, CornerNet is a new pipeline for object detection. FCOS [38] eliminates the anchor setting by proposing a fully convolutional one-stage object detector, which can solve object detection in a per-pixel prediction manner. The anchor-free detectors solve the problem happened in anchor-based detectors, which reduce the memory cost and increase accuracy of the bounding box.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Both one-stage and two-stage object detection methods have obtained high performance on many challenging public datasets, i.e., COCO and TJU-DHD [27]. These methods provide the accuracy-oriented detectors. However, the critical problem for detectors serving edge devices is detection latency and its power. In other words, detectors obtain higher performance in challenging scenes, which is not a necessary option for detectors deployed on edge devices. For the detection latency, a lot of effort [5, 34, 44] have been devoted to achieving the balance between accuracy",
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+    },
+    {
+        "type": "text",
+        "text": "and efficiency. FastYOLO [34] is an optimized architecture extended from YOLOv2 with fewer parameters and  $2\\%$  performance drop, which makes FastYOLO run at an average of  $\\sim 18$  FPS on an Nvidia Jetson TX1 embedded system. YOLObite [5] focuses on pruning redundancy object detectors to be real-time by designing in a compression- compilation way. NanoDet uses ShuffleNetV2 [26] as its backbone to make the model lighter, and further uses ATSS [47] and GFL [20] to improve its accuracy. It is worth noting that NanoDet also reached  $\\sim 60$  FPS on an ARM CPU. These light-weight detectors are latency-oriented. Actually, neither accuracy-oriented nor latency-oriented detectors take their energy cost into account. High energy cost detectors are unfriendly to devices deployed at edges.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "This paper aims to develop a light-weight detector that can achieve tradeoffs between energy and performance.",
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+    {
+        "type": "text",
+        "text": "2.2. Energy-Oriented Convolutional Neural Networks",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Besides the manual design of deep neural networks, a great deal of work has been done to improve the effectiveness and efficiency of deep neural networks via network pruning [45], quantization [13, 2], architecture search [12, 40]. ECC [42] proposes the end-to-end classifier training framework, which provides quantitative energy consumption guarantees by using weighted sparse projection and input masking. Zhang et al. [46] specialized in video broadcast and leveraged distillation techniques to reduce memory consumption by approximating the video frame data. MIME [3] is an algorithm-hardware co-design approach that reuses the weight parameters of a trained parent task and learns task-specific threshold parameters for inferring on multiple child tasks. However, the above works are all in service for image classification, and we can observe that fewer parameters represent lower energy costs in the same architecture. Object detection on edge devices is still a challenging topic, considering that the conflict between the limited capacity of CNNs and diverse spatial representations. This paper is the first work to provide a systematized solution for energy-oriented light-weight detectors.",
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+    },
+    {
+        "type": "text",
+        "text": "3. FemtoDet",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This section will be divided into two subsections to describe how FemtoDet achieves energy versus performance tradeoffs. 1) Benchmarks for Low-energy Detectors: We provide benchmarks for designing low-energy detectors, including the exploring of activation functions, convolution operators, and neck of detectors. 2) Energy-Oriented FemtoDet: Based on the benchmarks for designing low-energy detectors, an energy-oriented light-weight detector named FemtoDet is provided, which stacks layers from depthwise separable convolutions (DSC), BN and ReLU. FemtoDet involves only  $68.77\\mathrm{k}$  parameters and power of  $1.11\\mathrm{W}$  on",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "13320",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "the Qualcomm Snapdragon 865 CPU platform. Moreover, FemtoDet can be optimized with two designs: Firstly, instance boundary enhancement (IBE) modules are used to improve the DSC in FemtoDet, overcoming the bottleneck of light-weight models' representation optimization (i.e., models will learn obfuscation features because of their limited capacity, as shown in Fig. 2(b)). Second, the recursive warm_restart (RecWR) training strategy is a multi-stage recursive warm_restart learning procedure, which can surmount data shifts produced from strong data augmentations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.1. Benchmarks for Low-energy Detectors' Designing",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1.1 Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Top1-Acc (top1 accuracy, for image classification), and AP (average precision, for object detection) are widely used measures to evaluate the performance of CNN. In addition to the commonly used metrics top1 - Acc and AP, we propose the Power (energy costs) and mEPT (mean energy versus performance tradeoffs) to comprehensively evaluate the energy costs of the models and their ability to achieve energy versus performance tradeoffs. Specifically, Power and mEPT are represented by",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {m E P T} = \\left(\\frac {1}{\\mathrm {N}} \\sum_ {\\mathrm {i}} ^ {\\mathrm {N}} \\mathrm {P}\\right) / (\\text {P o w e r}), \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {s . t .} \\quad \\operatorname {P o w e r} = \\frac {1}{\\mathrm {T} _ {\\text {t i m e}}} \\sum_ {\\mathrm {i}} ^ {\\mathrm {N}} \\left(\\varepsilon \\left(\\mathbf {W}, \\mathrm {x} _ {\\mathrm {i}}\\right) - \\varepsilon \\left(\\hat {\\mathbf {W}}, \\mathrm {x} _ {\\mathrm {i}}\\right)\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{T}_{\\mathrm{time}}$  indicates the total times required to evaluate  $\\mathbf{N}$  images,  $\\varepsilon(\\mathbf{W}, \\mathrm{x_i})$  represents the energy costs while models evaluate i-th image  $\\mathrm{x_i}$  with trained parameters  $\\mathbf{W}$ .  $\\varepsilon(\\hat{\\mathbf{W}}, \\mathrm{x_i})$  is similar to  $\\varepsilon(\\mathbf{W}, \\mathrm{x_i})$ . The difference is that we set a value of 1 for each layer of channels, where the model parameter is  $\\hat{\\mathbf{W}}$ .  $\\varepsilon(\\hat{\\mathbf{W}}, \\mathrm{x_i})$  indicates that the model is an empty state. P denotes the model performance (top1-Acc for image classification while evaluating activation functions and convolution operators, AP50 for object detection while evaluating necks of detectors in Sec. 3.1.2) in image  $\\mathrm{x_i}$ . For the power metric, the value is expected to be as small as possible. For the mEPT metric, the result is expected as greater as possible.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1.2 Components to Be Evaluated",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To identify low-energy components of detectors, we followed [42] to benchmark their energy costs from three types of structures: activation functions, convolution operators and necks of detectors:",
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+    },
+    {
+        "type": "text",
+        "text": "Activation Functions. Rectified Linear Unit (ReLU) [29, 23], GELU [16], Swish [9], SiLU [8], and etc. are widely used for object detection because they have fewer",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "parameters and flops. We calculate the energy costs of different activation functions in the same architecture to explore which activation function is more friendly for designing an energy-oriented detector.",
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+    },
+    {
+        "type": "text",
+        "text": "Convolution Operators can automatically learn fiber weights while CNNs are trained to summarize helpful information, including horizontal, vertical, edged, diagonal, and etc. features from images. Vanilla convolutions (van-Conv) [18], depthwise separable convolutions (DSC) [17] and their large kernel size versions [25] are widely used. Ding et al. [7] pointed out that when CNNs are constructed based on enough large convolution kernels, results can be comparable to the transformer [24]. Here, we set up energy consumption comparison experiments with different convolutions (vanCon and DSC) and multi-scale convolution kernel sizes  $(3\\times 3$ , and  $5\\times 5)$  on different network structures (ResNet and MobileNetV2). It is important that for each experiment case, the convolution operator type or kernel size would be the only variable.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Necks of Detectors: Feature pyramid networks (FPN) are essential components for two-stage or one-stage detectors. FPN-based necks of detectors fuse multiple low-resolution and high-resolution feature inputs for better representations, leading to a series of studies for designing manually complex fusion methods [21, 22, 39]. However, they only presented favorable results brought by FPN but ignored its energy costs. We form a series of experiments on Fem-toDet by using different neck types, e.g. FPN [21], PAN [22], and our proposed SharedNeck (details can be found in Sec. 3.2.1) to study corresponding metrics (including energy costs, parameters, and detection precision on PASCAL VOC) changes.",
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+    {
+        "type": "text",
+        "text": "All related experiments can be found in Sec. 4.1. We can observe that DSC and ReLU are more energy friendly than vanCon and other activation functions. In addition, by comparing with the necks of detectors such as FPN and PAN, the proposed SharedNeck is more suitable for light-weight detectors.",
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+    {
+        "type": "text",
+        "text": "3.2. Energy-Oriented FemtoDet",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Building FemtoDet",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Backbone: The backbone of FemtoDet contains an initial full convolution layer with 8 filters. We use ReLU as the non-linearity and BN as the batch normalization. From the second layer beginning, all the convolution operators use DSC. The reason is that we follow the results of our benchmarks (the results can be seen in Sec. 4.1) to select the energy friendly components. The whole backbone is described in Appendix Table 9; Neck: We customize a neck for FemtoDet to achieve better tradeoffs between energy and performance. In detail, SharedNeck first aligns the scale information of inputs from backbones, and then merges these alignment features with elements addition. Fi",
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+        "type": "page_number",
+        "text": "13321",
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+    {
+        "type": "image",
+        "img_path": "images/06bd57ad96ee3fdfb9f4c4a448b04f286cf71feda743b5d60b754ee4e418c9d1.jpg",
+        "image_caption": [
+            "(a) FPN"
+        ],
+        "image_footnote": [],
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/2a041fe89340f182df35050ee1988fbade5fdcb721cbf6e643b8df719853de2c.jpg",
+        "image_caption": [
+            "(c) PAN"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "nally, a DSC performs adaptive multi-scale information fusion between merged features. The implementation details of SharedNeck, and how it differs from other necks are shown in Fig. 1; Head and Training Loss: Here, we use the decouple head of YOLOX as the head of our proposed detector with the same training loss as YOLOX.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Instance Boundary Enhancement Module",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "Optimizing light-weight detectors is a notoriously challenging problem. The reason for this is that limited by their representation, features learned by detectors are diffuse, as shown in Fig. 2 (b). Instance boundary enhancement (IBE) modules are designed to improve the DSC in FemtoDet, thus overcoming the bottleneck of light-weight models' representation optimization. IBE is similar to modules introduced in [45, 35, 43], except that our modules are designed for convolutional layers that are factorized into depthwise and pointwise layers. We further introduce a dual-normalization mechanism, such that the IBE modules can be used for object detection, while the modules in [45, 35, 43] just working for low-level tasks. Based on the DSC block, the basic block of IBE includes  $3 \\times 3$  depthwise convolution followed by  $1 \\times 1$  convolution. IBE enhances DSC by designing a new local descriptor, semantic projector, and dual-normalization layer. Specifically, the  $1 \\times 1$  local descriptor is a parameter reusing mechanism generated by the linear transformation of the integrating gradient cues around shared depthwise convolution. Therefore, the object boundary information can be found in the local descriptors. Previously, the local descriptor is known as the difference convolution [45, 35, 43] used for low-level tasks. Although the idea is easy to get that using these object boundary information to enhance the noisy feature representation (shown in Fig. 2 (b)) of the above standard operators, such",
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+        "type": "image",
+        "img_path": "images/36bae9606241a317307a361f0de81a1ccf9aac9c38bf99830ca97d4b30aaa54f.jpg",
+        "image_caption": [
+            "Figure 1: (a) FPN: A top-down multi-scale feature fusion architecture that outputs multiple predictions; (b) Shared-Neck: Simple adaptive multi-scale feature fusion architecture with single prediction, enabling tradeoffs between energy and performance; (c) PAN [22]: Exploring extra bottom-to-up multi-scale feature fusions with many predictions based on FPN.",
+            "(a) Inputs",
+            "Figure 2: Feature visualization of the trained light-weight detector. (a) Inputs: RGB images from PASCAL VOC; (b) FemtoDet*: Trained FemtoDet detector consisting of pure depthwise separable convolution; (c) FemtoDet: Trained FemtoDet detector, which was trained with the IBE modules."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/6cd4b946411753c56682ccdd4f60d324676cab9766785ade88838c8683998264.jpg",
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+        "img_path": "images/cda1b05584e5331fa31ba682af0dbf853d08d22eeb433f9421ee29700a0ca7cd.jpg",
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+        "img_path": "images/2c28f1ff0570646fa2facb343fdfb93d880a450cfcce1099843a7a7f3b545367.jpg",
+        "image_caption": [
+            "(b) FemtoDet\\*"
+        ],
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+    },
+    {
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+        "img_path": "images/b4aef114acfc5290183754d239b9ef6411fa3a4f870034ec4d472e18e7d38946.jpg",
+        "image_caption": [],
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+    {
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+        "img_path": "images/d40514d11bf29b56f94aed71445c3185d980d0d2acad8d4edabc7163baf7bbb2.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a83e98d1cce1b288ffafb328523c9f0425b2f9d41e6c28c6d5b2e159ec9b7ae4.jpg",
+        "image_caption": [
+            "(c) FemtoDet"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "as depthwise convolution, in practice, the original difference convolution architecture cannot serve for high-level semantic tasks. We observe that features obtained by the difference convolution are unaligned with the features obtained by standard convolution (the figure shown in Fig. 4 of the Appendix). On the one hand, the difference convolution captures diverse information about object boundaries by integrating gradient cues around  $3 \\times 3$  or with larger convolution. On the other hand, high-level tasks encourage standard convolution to summarize the abstract semantic information of images. That is the reason that the classical difference convolution cannot serve high-level tasks. To simultaneously solve this problem, we propose a semantic projector and a dual-normalization layer. The semantic projector is the linear transformation of depthwise convolution to transfer operators related to semantic information extraction; The dual-normalization layer consists of two independent batch normalization modules specifically designed for aligning the unaligned features. After that, we incorporate the object boundary cues from the feature addition between the local descriptor and depthwise convolution to guide the model in learning an effective representation of the instance (refined results can be seen in Fig. 2 (c)).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The description of IBE modules is given in Fig. 3 of the Appendix. For the depthwise convolution of kernel size  $3$ ,  $\\mathbf{C}_{\\mathrm{in}}$  denotes the input channel dimension,  $\\mathbf{C}_{\\mathrm{out}}$  represents the output channel dimension, the weight matrix can be denoted as  $\\mathbf{W}_{\\mathrm{conv}} \\in \\mathbb{R}^{1 \\times \\mathbf{C}_{\\mathrm{in}} \\times 3 \\times 3}$ , and the bias is represented as  $\\mathbf{b} \\in \\mathbb{R}^{\\mathrm{D}}$ . The local descriptor of kernel size 1 can be",
+        "bbox": [
+            496,
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "13322",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "generated from the depthwise convolution by reusing parameters. Its weight matric is denoted as  $\\mathbf{W}_{\\mathrm{des}}$ , which is integrating the gradient cues around  $\\mathbf{W}_{\\mathrm{conv}}$ :",
+        "bbox": [
+            76,
+            90,
+            468,
+            137
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {W} _ {\\text {d e s}} = - \\theta_ {1}. \\sum_ {\\mathrm {p} _ {\\mathrm {n}} \\in \\mathbf {R}} \\mathbf {W} _ {\\text {c o n v}} \\left(\\mathrm {p} _ {\\mathrm {n}}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            174,
+            148,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_{\\mathrm{des}} \\in \\mathbb{R}^{C_{\\mathrm{out}} \\times C_{\\mathrm{in}}}$ ,  $\\theta_1 \\in [0,1], \\in \\mathbb{R}^{1 \\times 1}$  is a learnable parameter projection factor.  $\\mathbf{R}$  represents the  $3 \\times 3$  convolution in  $\\mathbf{W}_{\\mathrm{conv}}$ , and  $\\mathfrak{p}_{\\mathrm{n}}$  is the n-the weight value. Integrating the gradient cues around  $\\mathbf{W}_{\\mathrm{conv}}$  can help the local descriptors capture the object boundary information effectively. The semantic projector is generated from the depthwise convolution, while diverse semantic presentations can be obtained through a learnable linear transformation, shown as follows:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {W} _ {\\text {p r o}} = \\theta_ {2}. \\mathbf {W} _ {\\text {c o n v}}, \\mathbf {W} _ {\\text {p r o}} \\in \\mathbb {R} ^ {C _ {\\text {o u t}} \\times C _ {\\text {i n}} \\times 3 \\times 3}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\theta_{2} \\in [0,1], \\mathbb{R}^{1 \\times 1}$  is another learnable parameter as the projection factor. Subsequently, the IBE modules perform four steps to refine the feature representation under the guidance of object boundary information. 1) inputs  $\\mathrm{x}_{\\mathrm{in}}$  will be convolved with the obtained three convolution operators, and the corresponding results are denoted as  $\\mathrm{x}_{22}, \\mathrm{x}_{21}$ , and  $\\mathrm{x}_{23}$ , respectively; 2) elements addition are conducted between  $\\mathrm{x}_{22}$  and  $\\mathrm{x}_{21}$ ; 3) the dual-normalization layer enables feature distribution normalization on  $\\mathrm{x}_{21}$  and  $\\mathrm{x}_{23}$ ; 4) the two outputs from the dual-normalization layer can be added together; As a result, the aforementioned added features are convolved through pointwise convolution as the final output of the IBE module.",
+        "bbox": [
+            76,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In addition, we leverage the homogeneity and additivity of the convolutions to fold IBM modules into the simpler depthwise separable convolution in the inference stage without performance degradation. The details can be seen in Appendix C.",
+        "bbox": [
+            76,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3. Recursive Warm-restart Training Strategy",
+        "text_level": 1,
+        "bbox": [
+            76,
+            665,
+            437,
+            681
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Strong augmentations (SA) are widely used for object detection, and [9, 31] shows well-designed SA effectively improves detectors. However, we find that well-designed SA does not always benefit light-weight detectors, because the current training strategies cannot sufficiently exploit diverse training representations to boost the generalization ability on real validation data. For example, YOLOX [9] points out MixUp reduces YOLOX-nano's performance by about  $5\\%$ . We argue that the limited capacity detectors fit the diverse data generated by SA as much as possible during training, such that the modules have no surplus capacity to adjust learned features to boost the generalization ability of modules on real validation data. In other words, SA produces diverse representations that are equal to the data",
+        "bbox": [
+            76,
+            688,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "shifts, thus breaking the generalization ability of the module. We also propose an effective training strategy to adjust these diverse features to improve the generalization ability, namely recursive warm_restart (RecWR).",
+        "bbox": [
+            498,
+            90,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 5 of the Appendix, the whole training procedure can be divided into four stages. Starting from the 1-st stage to 4-th stage training, the intensity of image augmentations gradually decreases. Specifically, in the 1-st training stage, some SA types will be combined, such as MixUp, Mosaic, and RandomAffine. Starting from the 2-nd training stage, the above SA types are gradually unloaded in each training stage, until the 4-th training stage. For the last training stage, only the random flip and random scales are performed on the training data. In addition, before starting each training stage, the waiting training detectors load the trained weights of the previous training stage as the initialization.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We can see that in Appendix D, after training FemtoDet with RecWR, MixUp also help such extremely small detectors obtain better performance. In other words, RecWR takes advantage of diversity features learned from SA to get FemtoDet out of sub-optimization.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            435,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We used VOC, COCO, TJU, and ImageNet datasets to conduct experiments and validate the proposed method. Specifically, whole experiments can be divided into two sections, i.e., identifying low-energy components of detectors mentioned in Sec. 3.1.2, and validating the effectiveness of our designed FemtoDet, where the Power metric was measured in GTX 3090.",
+        "bbox": [
+            496,
+            460,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Comparisons of energy-related metrics in MobileNetV2 0.25 (MBV2) [33] used different activation functions. We trained a classifier on ImageNet to evaluate relevant metrics.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/41a90c4c9acdb059cefd95950ac925899937327260f95ae64ca55fff779ef944.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Activation Functions</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td>ReLU [1]</td><td></td><td>5.04</td><td>45.22</td><td>8.97</td></tr><tr><td>GELU [16]</td><td></td><td>5.67</td><td>47.21</td><td>8.33</td></tr><tr><td>Swish [9]</td><td>1.48</td><td>5.47</td><td>47.45</td><td>8.67</td></tr><tr><td>HSwish [44]</td><td></td><td>5.33</td><td>47.60</td><td>8.93</td></tr><tr><td>SiLU [8]</td><td></td><td>5.73</td><td>47.25</td><td>8.25</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Benchmark to Find Low-energy Components",
+        "text_level": 1,
+        "bbox": [
+            500,
+            775,
+            880,
+            791
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1.1 Activation Functions",
+        "text_level": 1,
+        "bbox": [
+            500,
+            799,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows the energy-related metric results using different activation functions under the same architecture (MobileNetV2 0.25). We observe that the activation functions can significantly improve models without extra parameters (Param). On the other hand, such activation functions incur",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "13323",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "unacceptable overhead on some metrics which are inconvenient to measure. For example, Swish improves ReLU-based models performance by  $4.93\\%$ , but produces more than  $8.53\\%$  more energy cost. The mEPT metric also demonstrate that ReLU results in the best energy versus performance tradeoffs.",
+        "bbox": [
+            75,
+            90,
+            470,
+            181
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Comparisons of energy-related metrics in MobileNetV2 0.75 and ResNet18 [15]. The two CNNs can present the two typical convolution operators: vanilla convolutions and depthwise separable convolutions. We compare different convolution operators with different kernel sizes on the same convolution operators. Here,  $\\clubsuit$ , and  $\\diamond$  indicate two kernel sizes of  $3 \\times 3$ , and  $5 \\times 5$ . In this experiment, we also evaluate models by training them on ImageNet.",
+        "bbox": [
+            75,
+            186,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/9e6fea790dd85ae44d9962515f1e331e89d3cadc62d45703c43267528593fca9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>CNNs</td><td>Convolution Operators</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td rowspan=\"2\">Res18</td><td>vanConv♣</td><td>12.46</td><td>170.64</td><td>69.93</td><td>0.41</td></tr><tr><td>vanConv◇</td><td>31.99</td><td>198.28</td><td>71.24</td><td>0.36</td></tr><tr><td rowspan=\"2\">MBV2</td><td>DSC♣</td><td>2.29</td><td>5.56</td><td>69.51</td><td>12.50</td></tr><tr><td>DSC◇</td><td>2.35</td><td>6.07</td><td>70.96</td><td>11.69</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1.2 Convolution Operators",
+        "text_level": 1,
+        "bbox": [
+            76,
+            459,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "This sub-section compares energy-related metrics while training an image classifier on the ImageNet dataset based on the different convolution operators (vanCon and DSC), and the different kernel sizes  $(3\\times 3$ , and  $5\\times 5)$  on the same convolution operator. Experimental results in Table 2 show that: 1) When CNNs were constructed with the same kernel size, mobilenetv2 generated much lower energy costs than resnet18, as shown in Table 2 of vanConv and DSC. In other words, DSC is more energy friendly than vanConv while achieving similar performance; 2) When CNNs were constructed with different kernel sizes and the same types of operators, the smaller kernel generated much lower energy costs than the larger kernel, as shown in Table 2 of vanConv and vanConv. However, the performance gain from the large kernels is not so impressive.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1.3 Necks of Detectors",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Here we evaluated the effects of different necks (including FPN, PAN, and SharedNeck) in FemtoDet. Experimental results are shown in Table 3, and some observation are summarized as follow: 1) Although FPN enables FemtoDet to achieve preferable results, it not only consumes more energy but also has a large parameter overhead; 2) Due to the limited representation of light-weight models, the top-down and bottom-up feature fusion of PAN is poor; 3) SharedNeck achieves the best results in the metrics of parameter, energy cost, object detection performance, and factors of",
+        "bbox": [
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+            750,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "mean energy versus performance tradeoffs by performing adaptive feature fusion.",
+        "bbox": [
+            498,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/19f909d487d8f12b952e01dfcd7446101db3d4b611923b7e7b0b324d21050b6f.jpg",
+        "table_caption": [
+            "Table 3: Comparisons of energy-related metrics in Fem-toDet with different necks: FPN, PAN, and our proposed SharedNeck, respectively. The detector was trained on the PASCAL VOC."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Necks of Detectors</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>FPN</td><td>176.31</td><td>8.31</td><td>40.04</td><td>4.82</td></tr><tr><td>PAN</td><td>79.83</td><td>7.97</td><td>39.91</td><td>5.01</td></tr><tr><td>SharedNeck</td><td>69.77</td><td>7.83</td><td>42.50</td><td>5.43</td></tr></table>",
+        "bbox": [
+            511,
+            200,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/26c313478f6eafb189fdf436036090e88827cdea25a837be504c691a3baf1b6f.jpg",
+        "table_caption": [
+            "Table 4: PASCAL VOC object detection results with YOLOX, NanoDet Plus, and FemtoDet."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>70.39</td><td>10.42</td><td>30.60</td><td>2.94</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>11.29</td><td>38.44</td><td>3.40</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>7.83</td><td>46.31</td><td>5.91</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>13.60</td><td>3.00</td><td>5.10</td><td>16.60</td></tr><tr><td>NanoDet Plus</td><td>20.78</td><td>4.02</td><td>8.07</td><td>25.48</td></tr><tr><td>FemtoDet</td><td>22.90</td><td>1.10</td><td>8.40</td><td>28.50</td></tr></table>",
+        "bbox": [
+            519,
+            335,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/784854827bd56f62c51879f102dea5a43c55ad101551c954933cb627941d19c2.jpg",
+        "table_caption": [
+            "Table 5: Inference speed (FPS) and power of trained detectors (YOLOX, NanoDet Plus, and FemtoDet were trained on PASCAL VOC) on Qualcomm Snapdragon 865 CPU platforms."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Param (k)</td><td rowspan=\"2\">AP50</td><td colspan=\"2\">Inference</td></tr><tr><td>Power (W)</td><td>FPS</td></tr><tr><td>YOLOX</td><td>70.39</td><td>30.60</td><td>1.41</td><td>38.04</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>38.44</td><td>1.37</td><td>47.80</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>46.31</td><td>1.11</td><td>64.47</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Validating the Effectiveness of FemtoDet",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We verify the effectiveness of FemtoDet on three datasets: PASCAL VOC, COCO, and TJU-DHD, while resizing inputs to  $640 \\times 640$  for training and resizing inputs to  $416 \\times 416$  for validating. Two datasets, PASCAL VOC and TJU-DHD two datasets are converted to the COCO data types for evaluation. In addition, we extract campus data from the TJU-DHD dataset to evaluate the pedestrian detection performance of our proposed extremely light detector, i.e., FemtoDet. Considering extremely light-weight detectors are challenging to fit the complex COCO dataset with poor detection performance, we pull the corresponding results to Appendix E. Also, we compare the detection performance of FemtoDet with YOLOX, and NanoDet Plus [28], in which they are at the same parameter level to ensure fairness. All the detector backbones are pretrained on the Ima",
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+    {
+        "type": "text",
+        "text": "geNet for 100 epochs, and the metric of mEPT presented in this section is calculated between AP50 and Power.",
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+    {
+        "type": "text",
+        "text": "4.2.1 Results on PASCAL VOC",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Experimental results are presented in Table 4, which shows light-weight detectors with eight metrics: parameter (Param), energy cost (Power), AP50, factors of mean energy versus performance tradeoffs (mEPT), mAP, mAP of small size objects (mAP-s), mAP of medium size objects (mAP-m), and mAP of large size of objects (mAP-1) respectively. We can see that although YOLOX has a large number of parameters, it is much lower than FemtoDet in many metrics. NanoDet Plus has the parameter comparable to that of FemtoDet, but only outperforming FemtoDet in the metrics of mAP-s. We believe that for such extremely light-weight detectors, their performances on large-scale objects are the most critical. FemtoDet also presented better results than YOLOX and NanoDet Plus on the metrics of mAP-1. Although the metrics i.e. mEPT, used to evaluate performance and energy balance, FemtoDet achieves the best balance compared to the other two models.",
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+    },
+    {
+        "type": "text",
+        "text": "In addition, we evaluated the inference speed (FPS) and power of trained detectors on Qualcomm Snapdragon 865 CPU platforms. As shown in Tab. 5, our FemtoDet also achieves the smallest energy costs and inference speed on edge devices.",
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+        "type": "table",
+        "img_path": "images/9611945c61c616e70d0e80d8649eb4fcb48308c5cf701d1d218d6d35ef560742.jpg",
+        "table_caption": [
+            "Table 6: TJU-DHD pedestrian detection results with YOLOX, and FemtoDet."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>59.40</td><td>6.03</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>66.90</td><td>9.67</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>29.00</td><td>11.50</td><td>37.60</td><td>54.20</td></tr><tr><td>FemtoDet</td><td>33.10</td><td>17.60</td><td>50.20</td><td>61.50</td></tr></table>",
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+        "img_path": "images/541d3ee95b3f665c739bc36896cdfa8ed5ec4331412736889ef1c892cc903588.jpg",
+        "table_caption": [
+            "Table 7: Loose metric on TJU-DHD pedestrian detection with YOLOX, and FemtoDet."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AR20</td><td>AP20</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>90.40</td><td>42.10</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>85.80</td><td>76.30</td></tr><tr><td>Methods</td><td>AR20-m</td><td>AP20-m</td><td>AR20-1</td><td>AP20-1</td></tr><tr><td>YOLOX</td><td>83.70</td><td>34.80</td><td>96.10</td><td>55.60</td></tr><tr><td>FemtoDet</td><td>94.10</td><td>88.80</td><td>98.60</td><td>95.30</td></tr></table>",
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+        "type": "text",
+        "text": "4.2.2 Results on TJU-DHD",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Extremely light-weight detectors like FemtoDet have broad application prospects in surveillance scenarios. Hence, we",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "evaluate the performance of FemtoDet in pedestrian detection using the campus dataset of TJU-DHD, and show the performance of the detectors on the less stringent metric AP20. Table 6 and 7 demonstrate that FemtoDet is competent for pedestrian detection in common surveillance scenarios: 1) FemtoDet has lower energy costs in deployment, which is  $29.74\\%$  lower than YOLOX; 2) FemtoDet obtains  $76.3\\%$  AP20, while YOLOX with the same parameters only obtain  $71.80\\%$  AP20.",
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+        "type": "table",
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+        "table_caption": [
+            "Table 8: Ablation study on the effectiveness of our IBE modules and RecWR training strategy. Where FemtoDet* denotes FemtoDet consists of pure DSC without the enhancement of IBE, 300e and 1200e mean the detector training with the same data augmentation with 300 or 1200 epochs."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>\\</td><td>IBE</td><td>RecWR</td><td>300e</td><td>1200e</td><td>AP50</td></tr><tr><td rowspan=\"5\">FemtoDet*</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>42.50</td></tr><tr><td>X</td><td>X</td><td>X</td><td>✓</td><td>42.11</td></tr><tr><td>X</td><td>✓</td><td>X</td><td>X</td><td>45.13</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>X</td><td>45.78</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>46.31</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.2.3 Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We conduct a series of ablation studies on PASCAL VOC to demonstrate the effectiveness and efficiency of our IBE modules and RecWR training strategy. As shown in Table 8: 1) The second and third rows present that by training with 300 and 1200 epochs for FemtoDet*, such a longer epochs do not yield better gains. 2) The fourth and fifth rows present FemtoDet* was trained with RecWR and 300 epochs with the enhancement of IBE, respectively. Results show that independently equipping IBE and RecWR can improve model performance. 3) The six rows demonstrate that jointly using IBE and RecWR enables FemtoDet to achieve the best performance.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper presented a baseline to encourage the research on energy and performance balance detectors. Our experimental results clearly showed that boosting performance can also cause problem of growth in energy consumption. Conversely, the simple components like ReLU are suitable for building energy-oriented detectors. In addition, we also proposed a novel IBE module and RecWR training strategy to overcome the optimization problem of extremely lightweight detectors. Compared to other state-of-the-art methods under the same parameters setting, IBE and RecWR support these baselines achieving the best performance on VOC, COCO, and TJU-DHD datasets, while consuming the",
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+    {
+        "type": "text",
+        "text": "least energy. In the future, we will continue improving the detectors on the balance of energy and performance.",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
+            78,
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+        "page_idx": 8
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diff --git a/2023/FemtoDet_ An Object Detection Baseline for Energy Versus Performance Tradeoffs/ae3858f0-bbf1-4f71-acdc-96b1b40f62b6_model.json b/2023/FemtoDet_ An Object Detection Baseline for Energy Versus Performance Tradeoffs/ae3858f0-bbf1-4f71-acdc-96b1b40f62b6_model.json
new file mode 100644
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+++ b/2023/FemtoDet_ An Object Detection Baseline for Energy Versus Performance Tradeoffs/ae3858f0-bbf1-4f71-acdc-96b1b40f62b6_model.json	
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+            "content": "Efficient detectors for edge devices are often optimized for parameters or speed count metrics, which remain in weak correlation with the energy of detectors. However, some vision applications of convolutional neural networks, such as always-on surveillance cameras, are critical for energy constraints. This paper aims to serve as a baseline by designing detectors to reach tradeoffs between energy and performance from two perspectives: 1) We extensively analyze various CNNs to identify low-energy architectures, including selecting activation functions, convolutions operators, and feature fusion structures on necks. These underappreciated details in past work seriously affect the energy consumption of detectors; 2) To break through the dilemmacatic energy-performance problem, we propose a balanced detector driven by energy using discovered low-energy components named FemtoDet. In addition to the novel construction, we improve FemtoDet by considering convolutions and training strategy optimizations. Specifically, we develop a new instance boundary enhancement (IBE) module for convolution optimization to overcome the contradiction between the limited capacity of CNNs and detection tasks in diverse spatial representations, and propose a recursive warm_restart (RecWR) for optimizing training strategy to escape the sub-optimization of light-weight detectors by considering the data shift produced in popular augmentations. As a result, FemtoDet with only 68.77k parameters achieves a competitive score of 46.3 AP50 on PASCAL VOC and 1.11 W & 64.47 FPS on Qualcomm Snapdragon 865 CPU platforms. Extensive experiments on COCO and TJUDHD datasets indicate that the proposed method achieves competitive results in diverse scenes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.803,
+                0.21,
+                0.818
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.829,
+                0.47,
+                0.876
+            ],
+            "angle": 0,
+            "content": "The deployment of efficient convolutional neural networks (CNNs) enabled immense progress [23, 29, 30, 31, 4, 9, 41] in vision detectors for edge devices, in which they"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.277,
+                0.895,
+                0.565
+            ],
+            "angle": 0,
+            "content": "consistently reduce parameters and speed counts for improving accuracy. However, these metrics are not correlated well with the efficiency of the models in terms of energy. Evaluation metrics, such as parameters, do not take into account the energy cost of models, resulting in a nontrivial effect on the energy cost of detectors. Compared with the same architecture, the parameters of models are positively correlated with their energy cost (shown in Table 2). However, in the case of equal model parameters, their energy consumption may be negatively correlated or even irrelevant to the model parameters (shown in Table 1). Considering that various activation functions, convolution operators, and feature fuse structures may not increase model parameters, but generate more energy costs. Similarly, the speed count is also not well correlated with energy, as it can be optimized by the degree of parallelism. These disconnections will leave customized efficient detectors unavailable, when they are deployed under severe energy constraints like the always-on surveillance cameras."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.566,
+                0.894,
+                0.627
+            ],
+            "angle": 0,
+            "content": "This paper aims to reduce the energy costs of efficient object detectors, while improving their performances by achieving energy versus performance tradeoffs. Specifically, these bottlenecks fall into several categories:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.629,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "1) Detector components with unknown energy. Most current object detection methods focus either on latency-oriented [5, 34, 44] or accuracy-oriented [9, 38, 32, 36] works. There are very limited works toward the energy cost of the detector components, which is the first obstacle to designing energy-performance-balanced detectors. To identify energy-efficient components of detectors, we followed [42] to benchmark their energy metrics from three types of structures, i.e., activation functions, convolution operators, and necks of detectors. The following finding is acquired: Firstly, some activation functions have been widely used, because of their ability to improve models without adding more parameters. They have increased costs, yet received very limited attention. As shown in Table 1, we set ReLU [1] based models as a baseline. When replacing the ReLU with the GELU [16], \\(4.40\\%\\) performance is gained, while \\(12.50\\%\\) energy cost is increased, and the corresponding factor of the mean energy versus the perfor"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.101,
+                0.887,
+                0.468,
+                0.902
+            ],
+            "angle": 0,
+            "content": "*Corresponding author; First author's Email: yh.peng.tu@gmail.com"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13318"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.473,
+                0.896
+            ],
+            "angle": 0,
+            "content": "mance tradeoffs (Eq. 1) drops \\(7.16\\%\\). In addition, although large kernel convolutions [25] can improve models (Table 2), the increased energy cost is unacceptable. As seen in Table 2, the large kernel convolutions are equipped to enable the model to rise by around \\(1.87\\%\\) in performance, but with more energy costs \\((16.20\\%)\\) than in the small kernel size of convolutions (shown in the second row of Table 2). Finally, the standard FPN [21, 22, 39, 10, 37] in the detectors also causes significant energy costs. We observe that this situation is happened due to multi-feature fusion paths following either bottom-to-up or top-to-down way, resulting in frequent data reading in memory for data coverage. However, it is shown that the up-down fusion between multi-features may not necessary. As shown in Table 3, we propose a simple SharedNeck for replacing FPN to reduce around \\(5.77\\%\\) energy costs, while obtaining \\(6.25\\%\\) performance gains. SharedNeck uses an adaptive fusion between multi-features by learning convolution, instead of feature-by-feature bottom-to-up or top-to-down fusions, as operated in FPN. Based on these analyses, we further build upon a low-energy detector, named FemtoDet. Surprisingly, FemtoDet just has \\(68.77\\mathrm{k}\\) parameters and \\(1.1\\mathrm{W}\\) power on the platform. 2) Optimization for CNN is another bottleneck, since obtaining a favorable detector is very challenging, especially for a small number of parameters. Light-weight detectors are restricted by their limited capacities [6], which will cause obfuscation on feature maps of the instances' boundaries of interesting objects, as shown in Figure 2 (b). Ambiguous instance boundaries on the features may raise the risk of false detection in the models. For this problem, we propose a novel instance boundary enhancement module (IBE), which emphasizes the potential of the object boundary information: The parameter reuse mechanism is first applied to integrate local descriptors with convolution operation to make robust and diverse instance boundary feature representation. But this operation would cause feature un-alignment between normal features and integrated features. Then, in order to sufficiently exploit these two types of features, we design dual-normalization in IBE, as to realign the features (Fig. 4 of the Appendix). IBE employs a shared convolution yet an independent batch normalization layer for separate normalization is also adopted. Finally, we add normal and integrated features together behind the dual-normalization layer. IBE provides a novel form of parameter reuse to generate new local descriptors from shared convolution operators. This method can capture object boundary information by integrating gradient cues around the learned convolution. After trained, IBE modules can be folded into simple convolution operators, thus requiring no extra computations anymore; In addition, data augmentation is a common approach for efficient detector training. Using well-designed strong augmentations is conducive to improving the generalization of mod"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.53
+            ],
+            "angle": 0,
+            "content": "els [31, 9]. However, how to prevent data shifts between training and validation images has not been explored, while training data suffers strong augmentations. It is found that the produced data shifts by strong augmentations would prevent light-weight detectors from moving toward global optimization. A common view is that strong image augmentations can effectively encourage networks to learn diverse features [11]. But for light-weight detectors, these diverse features cannot assist the models in making better generalizations in the validation set. In other words, light-weight detectors are more susceptible to these ignored data shifts because of their limited capacities. Furthermore, we propose an effective training strategy, namely recursive warm-start (RecWR), to adapt these diverse features to improve the model's generalization. RecWR works based on multistage training while gradually weakening data augmentation strength. This method can help the limited-capacity detectors jump out of local optima under the assistance of high-dimension & diverse features. The effectiveness of the IBE and RecWR has been evaluated on PASCAL VOC dataset. And the experimental results show that IBE can improve FemtoDet \\(\\sim 7.72\\%\\) performance, while incurring no extra parameter burdens, as compared to the original architecture; RecWR can improve FemtoDet \\(\\sim 6.19\\%\\) performance by gradually weakening the data augmentation strength in multi-stage learning. By jointly training FemtoDet with IBE and RecWR, our proposed methodology can go over the YOLOX [9] by \\(51.34\\%\\) in performance when using the same-level parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.53,
+                0.897,
+                0.817
+            ],
+            "angle": 0,
+            "content": "Something worth mentioning is that FemtoDet is specially designed for hierarchical intelligent chips to enable always-on alerts: the always-on low power, high-recall, and decent accuracy - it achieved 85.8 AR20 & 76.3 AP20 (Table 7) while performing pedestrian detection on TJU-DHD. In addition, FemtoDet is poor in detecting small objects but is excellent in detecting medium and large objects, which they are more interested in, with 88.8 AR20-m & 94.1 AP20-m / 95.3 AR20-1 & 98.6 AP20-1 (Table 7) on TJU-DHD. Information can be passed to other models after identifying possible objects of interest, and high-precision robust models are then initiated for accurate recognition. The always-on smart products have a wide range of applications, e.g., in-home monitoring or robots. Hence, the loose metric (e.g., AP50 or AP20) and data scenario with moderate difficulty (e.g., VOC) can well reflect the application ability of FemtoDet. Further, the experiments on COCO datasets have verified that the proposed method is suitable for diverse scenarios resulting in competitive results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.823,
+                0.652,
+                0.838
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.668,
+                0.864
+            ],
+            "angle": 0,
+            "content": "2.1. Object Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Object detection is a classic computer vision task for identifying the category and location of object in pictures"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "13319"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.242
+            ],
+            "angle": 0,
+            "content": "or videos. The existing object detectors can be divided into two categories: two-stage detectors and one-stage detectors. Two-stage detectors [32, 36, 14, 21] are anchor-based devices that generate region proposals from the image and then produce the final prediction boxes from these proposals. Further, FPN [21] improves the two-stage detectors by fusing multi-level features. Despite their higher accuracy compared to the one-stage detectors, two-stage detectors are still difficult to achieve low latency when deployed on edge devices."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.247,
+                0.473,
+                0.746
+            ],
+            "angle": 0,
+            "content": "Specifically, there are two types of one-stage detectors: anchor-based and anchor-free, which depends on anchor priors injecting into whole images to enable box regression. SSD [23], as a classical anchor-based one-stage detector, discretizes the output space of bounding boxes into a set of default anchors with different aspect ratios and scales per feature map location. This operation helps detecting tiny objects. Another typical anchor-based detector is the YOLO series [30, 31, 4]. YOLOv2 [30] explores bag of freebies to improve the performances of one-stage detectors. YOLOv3 [31] proposes cross-scale features and novel nms (Non-Maximum Suppression) to obtain more confident predictions. YOLOv4 [4] finds that the repeated gradient of network optimization aggravates detector latency, and thus designs Cross-Stage-Partial-connection modules to reduce the latency of detectors while maintaining detection performance. Anchor-free detectors [29, 9, 19, 38] aim to eliminate the pre-defined set of anchor boxes. YOLO [29], as an anchor-free one-stage detector, divides an image into multiple grids and predict boxes at grids near the object's center. CornerNet [19] detects an object as a pair of key points (through the top-left corner and bottom-right corner of the bounding box). A single convolutional network was leveraged in CornerNet to predict a heatmap for all top-left corners of instances of the same object category, a heatmap for all bottom-right corners, and an embedding vector for each detected corner. Indeed, CornerNet is a new pipeline for object detection. FCOS [38] eliminates the anchor setting by proposing a fully convolutional one-stage object detector, which can solve object detection in a per-pixel prediction manner. The anchor-free detectors solve the problem happened in anchor-based detectors, which reduce the memory cost and increase accuracy of the bounding box."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Both one-stage and two-stage object detection methods have obtained high performance on many challenging public datasets, i.e., COCO and TJU-DHD [27]. These methods provide the accuracy-oriented detectors. However, the critical problem for detectors serving edge devices is detection latency and its power. In other words, detectors obtain higher performance in challenging scenes, which is not a necessary option for detectors deployed on edge devices. For the detection latency, a lot of effort [5, 34, 44] have been devoted to achieving the balance between accuracy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.304
+            ],
+            "angle": 0,
+            "content": "and efficiency. FastYOLO [34] is an optimized architecture extended from YOLOv2 with fewer parameters and \\(2\\%\\) performance drop, which makes FastYOLO run at an average of \\(\\sim 18\\) FPS on an Nvidia Jetson TX1 embedded system. YOLObite [5] focuses on pruning redundancy object detectors to be real-time by designing in a compression- compilation way. NanoDet uses ShuffleNetV2 [26] as its backbone to make the model lighter, and further uses ATSS [47] and GFL [20] to improve its accuracy. It is worth noting that NanoDet also reached \\(\\sim 60\\) FPS on an ARM CPU. These light-weight detectors are latency-oriented. Actually, neither accuracy-oriented nor latency-oriented detectors take their energy cost into account. High energy cost detectors are unfriendly to devices deployed at edges."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.304,
+                0.895,
+                0.334
+            ],
+            "angle": 0,
+            "content": "This paper aims to develop a light-weight detector that can achieve tradeoffs between energy and performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.344,
+                0.895,
+                0.375
+            ],
+            "angle": 0,
+            "content": "2.2. Energy-Oriented Convolutional Neural Networks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.383,
+                0.895,
+                0.702
+            ],
+            "angle": 0,
+            "content": "Besides the manual design of deep neural networks, a great deal of work has been done to improve the effectiveness and efficiency of deep neural networks via network pruning [45], quantization [13, 2], architecture search [12, 40]. ECC [42] proposes the end-to-end classifier training framework, which provides quantitative energy consumption guarantees by using weighted sparse projection and input masking. Zhang et al. [46] specialized in video broadcast and leveraged distillation techniques to reduce memory consumption by approximating the video frame data. MIME [3] is an algorithm-hardware co-design approach that reuses the weight parameters of a trained parent task and learns task-specific threshold parameters for inferring on multiple child tasks. However, the above works are all in service for image classification, and we can observe that fewer parameters represent lower energy costs in the same architecture. Object detection on edge devices is still a challenging topic, considering that the conflict between the limited capacity of CNNs and diverse spatial representations. This paper is the first work to provide a systematized solution for energy-oriented light-weight detectors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.709,
+                0.61,
+                0.725
+            ],
+            "angle": 0,
+            "content": "3. FemtoDet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.897,
+                0.903
+            ],
+            "angle": 0,
+            "content": "This section will be divided into two subsections to describe how FemtoDet achieves energy versus performance tradeoffs. 1) Benchmarks for Low-energy Detectors: We provide benchmarks for designing low-energy detectors, including the exploring of activation functions, convolution operators, and neck of detectors. 2) Energy-Oriented FemtoDet: Based on the benchmarks for designing low-energy detectors, an energy-oriented light-weight detector named FemtoDet is provided, which stacks layers from depthwise separable convolutions (DSC), BN and ReLU. FemtoDet involves only \\(68.77\\mathrm{k}\\) parameters and power of \\(1.11\\mathrm{W}\\) on"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "13320"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.244
+            ],
+            "angle": 0,
+            "content": "the Qualcomm Snapdragon 865 CPU platform. Moreover, FemtoDet can be optimized with two designs: Firstly, instance boundary enhancement (IBE) modules are used to improve the DSC in FemtoDet, overcoming the bottleneck of light-weight models' representation optimization (i.e., models will learn obfuscation features because of their limited capacity, as shown in Fig. 2(b)). Second, the recursive warm_restart (RecWR) training strategy is a multi-stage recursive warm_restart learning procedure, which can surmount data shifts produced from strong data augmentations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.248,
+                0.471,
+                0.28
+            ],
+            "angle": 0,
+            "content": "3.1. Benchmarks for Low-energy Detectors' Designing"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.287,
+                0.266,
+                0.302
+            ],
+            "angle": 0,
+            "content": "3.1.1 Evaluation Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.312,
+                0.473,
+                0.449
+            ],
+            "angle": 0,
+            "content": "Top1-Acc (top1 accuracy, for image classification), and AP (average precision, for object detection) are widely used measures to evaluate the performance of CNN. In addition to the commonly used metrics top1 - Acc and AP, we propose the Power (energy costs) and mEPT (mean energy versus performance tradeoffs) to comprehensively evaluate the energy costs of the models and their ability to achieve energy versus performance tradeoffs. Specifically, Power and mEPT are represented by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.177,
+                0.454,
+                0.47,
+                0.497
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {m E P T} = \\left(\\frac {1}{\\mathrm {N}} \\sum_ {\\mathrm {i}} ^ {\\mathrm {N}} \\mathrm {P}\\right) / (\\text {P o w e r}), \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.126,
+                0.508,
+                0.47,
+                0.55
+            ],
+            "angle": 0,
+            "content": "\\[\n\\text {s . t .} \\quad \\operatorname {P o w e r} = \\frac {1}{\\mathrm {T} _ {\\text {t i m e}}} \\sum_ {\\mathrm {i}} ^ {\\mathrm {N}} \\left(\\varepsilon \\left(\\mathbf {W}, \\mathrm {x} _ {\\mathrm {i}}\\right) - \\varepsilon \\left(\\hat {\\mathbf {W}}, \\mathrm {x} _ {\\mathrm {i}}\\right)\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.558,
+                0.473,
+                0.753
+            ],
+            "angle": 0,
+            "content": "where \\( \\mathrm{T}_{\\mathrm{time}} \\) indicates the total times required to evaluate \\( \\mathbf{N} \\) images, \\( \\varepsilon(\\mathbf{W}, \\mathrm{x_i}) \\) represents the energy costs while models evaluate i-th image \\( \\mathrm{x_i} \\) with trained parameters \\( \\mathbf{W} \\). \\( \\varepsilon(\\hat{\\mathbf{W}}, \\mathrm{x_i}) \\) is similar to \\( \\varepsilon(\\mathbf{W}, \\mathrm{x_i}) \\). The difference is that we set a value of 1 for each layer of channels, where the model parameter is \\( \\hat{\\mathbf{W}} \\). \\( \\varepsilon(\\hat{\\mathbf{W}}, \\mathrm{x_i}) \\) indicates that the model is an empty state. P denotes the model performance (top1-Acc for image classification while evaluating activation functions and convolution operators, AP50 for object detection while evaluating necks of detectors in Sec. 3.1.2) in image \\( \\mathrm{x_i} \\). For the power metric, the value is expected to be as small as possible. For the mEPT metric, the result is expected as greater as possible."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.77,
+                0.334,
+                0.785
+            ],
+            "angle": 0,
+            "content": "3.1.2 Components to Be Evaluated"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.794,
+                0.47,
+                0.854
+            ],
+            "angle": 0,
+            "content": "To identify low-energy components of detectors, we followed [42] to benchmark their energy costs from three types of structures: activation functions, convolution operators and necks of detectors:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Activation Functions. Rectified Linear Unit (ReLU) [29, 23], GELU [16], Swish [9], SiLU [8], and etc. are widely used for object detection because they have fewer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "parameters and flops. We calculate the energy costs of different activation functions in the same architecture to explore which activation function is more friendly for designing an energy-oriented detector."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.153,
+                0.893,
+                0.379
+            ],
+            "angle": 0,
+            "content": "Convolution Operators can automatically learn fiber weights while CNNs are trained to summarize helpful information, including horizontal, vertical, edged, diagonal, and etc. features from images. Vanilla convolutions (van-Conv) [18], depthwise separable convolutions (DSC) [17] and their large kernel size versions [25] are widely used. Ding et al. [7] pointed out that when CNNs are constructed based on enough large convolution kernels, results can be comparable to the transformer [24]. Here, we set up energy consumption comparison experiments with different convolutions (vanCon and DSC) and multi-scale convolution kernel sizes \\((3\\times 3\\), and \\(5\\times 5)\\) on different network structures (ResNet and MobileNetV2). It is important that for each experiment case, the convolution operator type or kernel size would be the only variable."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.381,
+                0.892,
+                0.577
+            ],
+            "angle": 0,
+            "content": "Necks of Detectors: Feature pyramid networks (FPN) are essential components for two-stage or one-stage detectors. FPN-based necks of detectors fuse multiple low-resolution and high-resolution feature inputs for better representations, leading to a series of studies for designing manually complex fusion methods [21, 22, 39]. However, they only presented favorable results brought by FPN but ignored its energy costs. We form a series of experiments on Fem-toDet by using different neck types, e.g. FPN [21], PAN [22], and our proposed SharedNeck (details can be found in Sec. 3.2.1) to study corresponding metrics (including energy costs, parameters, and detection precision on PASCAL VOC) changes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.578,
+                0.892,
+                0.667
+            ],
+            "angle": 0,
+            "content": "All related experiments can be found in Sec. 4.1. We can observe that DSC and ReLU are more energy friendly than vanCon and other activation functions. In addition, by comparing with the necks of detectors such as FPN and PAN, the proposed SharedNeck is more suitable for light-weight detectors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.669,
+                0.747,
+                0.685
+            ],
+            "angle": 0,
+            "content": "3.2. Energy-Oriented FemtoDet"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.694,
+                0.688,
+                0.709
+            ],
+            "angle": 0,
+            "content": "3.2.1 Building FemtoDet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Backbone: The backbone of FemtoDet contains an initial full convolution layer with 8 filters. We use ReLU as the non-linearity and BN as the batch normalization. From the second layer beginning, all the convolution operators use DSC. The reason is that we follow the results of our benchmarks (the results can be seen in Sec. 4.1) to select the energy friendly components. The whole backbone is described in Appendix Table 9; Neck: We customize a neck for FemtoDet to achieve better tradeoffs between energy and performance. In detail, SharedNeck first aligns the scale information of inputs from backbones, and then merges these alignment features with elements addition. Fi"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.518,
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+            ],
+            "angle": 0,
+            "content": "13321"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.082,
+                0.465,
+                0.144
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.155,
+                0.149,
+                0.204,
+                0.161
+            ],
+            "angle": 0,
+            "content": "(a) FPN"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.136,
+                0.163,
+                0.418,
+                0.222
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.249,
+                0.229,
+                0.299,
+                0.242
+            ],
+            "angle": 0,
+            "content": "(c) PAN"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.255,
+                0.47,
+                0.36
+            ],
+            "angle": 0,
+            "content": "Figure 1: (a) FPN: A top-down multi-scale feature fusion architecture that outputs multiple predictions; (b) Shared-Neck: Simple adaptive multi-scale feature fusion architecture with single prediction, enabling tradeoffs between energy and performance; (c) PAN [22]: Exploring extra bottom-to-up multi-scale feature fusions with many predictions based on FPN."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.383,
+                0.469,
+                0.473
+            ],
+            "angle": 0,
+            "content": "nally, a DSC performs adaptive multi-scale information fusion between merged features. The implementation details of SharedNeck, and how it differs from other necks are shown in Fig. 1; Head and Training Loss: Here, we use the decouple head of YOLOX as the head of our proposed detector with the same training loss as YOLOX."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.484,
+                0.422,
+                0.498
+            ],
+            "angle": 0,
+            "content": "3.2.2 Instance Boundary Enhancement Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.508,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Optimizing light-weight detectors is a notoriously challenging problem. The reason for this is that limited by their representation, features learned by detectors are diffuse, as shown in Fig. 2 (b). Instance boundary enhancement (IBE) modules are designed to improve the DSC in FemtoDet, thus overcoming the bottleneck of light-weight models' representation optimization. IBE is similar to modules introduced in [45, 35, 43], except that our modules are designed for convolutional layers that are factorized into depthwise and pointwise layers. We further introduce a dual-normalization mechanism, such that the IBE modules can be used for object detection, while the modules in [45, 35, 43] just working for low-level tasks. Based on the DSC block, the basic block of IBE includes \\(3 \\times 3\\) depthwise convolution followed by \\(1 \\times 1\\) convolution. IBE enhances DSC by designing a new local descriptor, semantic projector, and dual-normalization layer. Specifically, the \\(1 \\times 1\\) local descriptor is a parameter reusing mechanism generated by the linear transformation of the integrating gradient cues around shared depthwise convolution. Therefore, the object boundary information can be found in the local descriptors. Previously, the local descriptor is known as the difference convolution [45, 35, 43] used for low-level tasks. Although the idea is easy to get that using these object boundary information to enhance the noisy feature representation (shown in Fig. 2 (b)) of the above standard operators, such"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.089,
+                0.631,
+                0.163
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.165,
+                0.631,
+                0.238
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.239,
+                0.631,
+                0.312
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.538,
+                0.319,
+                0.597,
+                0.332
+            ],
+            "angle": 0,
+            "content": "(a) Inputs"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.089,
+                0.759,
+                0.163
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.165,
+                0.759,
+                0.238
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.239,
+                0.759,
+                0.312
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.652,
+                0.318,
+                0.741,
+                0.332
+            ],
+            "angle": 0,
+            "content": "(b) FemtoDet\\*"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.763,
+                0.089,
+                0.89,
+                0.163
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.763,
+                0.165,
+                0.89,
+                0.238
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.763,
+                0.239,
+                0.89,
+                0.312
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.786,
+                0.319,
+                0.867,
+                0.332
+            ],
+            "angle": 0,
+            "content": "(c) FemtoDet"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.341,
+                0.892,
+                0.43
+            ],
+            "angle": 0,
+            "content": "Figure 2: Feature visualization of the trained light-weight detector. (a) Inputs: RGB images from PASCAL VOC; (b) FemtoDet*: Trained FemtoDet detector consisting of pure depthwise separable convolution; (c) FemtoDet: Trained FemtoDet detector, which was trained with the IBE modules."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.46,
+                0.892,
+                0.807
+            ],
+            "angle": 0,
+            "content": "as depthwise convolution, in practice, the original difference convolution architecture cannot serve for high-level semantic tasks. We observe that features obtained by the difference convolution are unaligned with the features obtained by standard convolution (the figure shown in Fig. 4 of the Appendix). On the one hand, the difference convolution captures diverse information about object boundaries by integrating gradient cues around \\(3 \\times 3\\) or with larger convolution. On the other hand, high-level tasks encourage standard convolution to summarize the abstract semantic information of images. That is the reason that the classical difference convolution cannot serve high-level tasks. To simultaneously solve this problem, we propose a semantic projector and a dual-normalization layer. The semantic projector is the linear transformation of depthwise convolution to transfer operators related to semantic information extraction; The dual-normalization layer consists of two independent batch normalization modules specifically designed for aligning the unaligned features. After that, we incorporate the object boundary cues from the feature addition between the local descriptor and depthwise convolution to guide the model in learning an effective representation of the instance (refined results can be seen in Fig. 2 (c))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.893,
+                0.9
+            ],
+            "angle": 0,
+            "content": "The description of IBE modules is given in Fig. 3 of the Appendix. For the depthwise convolution of kernel size \\(3\\), \\(\\mathbf{C}_{\\mathrm{in}}\\) denotes the input channel dimension, \\(\\mathbf{C}_{\\mathrm{out}}\\) represents the output channel dimension, the weight matrix can be denoted as \\(\\mathbf{W}_{\\mathrm{conv}} \\in \\mathbb{R}^{1 \\times \\mathbf{C}_{\\mathrm{in}} \\times 3 \\times 3}\\), and the bias is represented as \\(\\mathbf{b} \\in \\mathbb{R}^{\\mathrm{D}}\\). The local descriptor of kernel size 1 can be"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13322"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.138
+            ],
+            "angle": 0,
+            "content": "generated from the depthwise convolution by reusing parameters. Its weight matric is denoted as \\(\\mathbf{W}_{\\mathrm{des}}\\), which is integrating the gradient cues around \\(\\mathbf{W}_{\\mathrm{conv}}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.176,
+                0.15,
+                0.47,
+                0.185
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {W} _ {\\text {d e s}} = - \\theta_ {1}. \\sum_ {\\mathrm {p} _ {\\mathrm {n}} \\in \\mathbf {R}} \\mathbf {W} _ {\\text {c o n v}} \\left(\\mathrm {p} _ {\\mathrm {n}}\\right), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.198,
+                0.469,
+                0.336
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{W}_{\\mathrm{des}} \\in \\mathbb{R}^{C_{\\mathrm{out}} \\times C_{\\mathrm{in}}}\\), \\(\\theta_1 \\in [0,1], \\in \\mathbb{R}^{1 \\times 1}\\) is a learnable parameter projection factor. \\(\\mathbf{R}\\) represents the \\(3 \\times 3\\) convolution in \\(\\mathbf{W}_{\\mathrm{conv}}\\), and \\(\\mathfrak{p}_{\\mathrm{n}}\\) is the n-the weight value. Integrating the gradient cues around \\(\\mathbf{W}_{\\mathrm{conv}}\\) can help the local descriptors capture the object boundary information effectively. The semantic projector is generated from the depthwise convolution, while diverse semantic presentations can be obtained through a learnable linear transformation, shown as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.132,
+                0.348,
+                0.469,
+                0.367
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {W} _ {\\text {p r o}} = \\theta_ {2}. \\mathbf {W} _ {\\text {c o n v}}, \\mathbf {W} _ {\\text {p r o}} \\in \\mathbb {R} ^ {C _ {\\text {o u t}} \\times C _ {\\text {i n}} \\times 3 \\times 3}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.38,
+                0.469,
+                0.576
+            ],
+            "angle": 0,
+            "content": "where \\(\\theta_{2} \\in [0,1], \\mathbb{R}^{1 \\times 1}\\) is another learnable parameter as the projection factor. Subsequently, the IBE modules perform four steps to refine the feature representation under the guidance of object boundary information. 1) inputs \\(\\mathrm{x}_{\\mathrm{in}}\\) will be convolved with the obtained three convolution operators, and the corresponding results are denoted as \\(\\mathrm{x}_{22}, \\mathrm{x}_{21}\\), and \\(\\mathrm{x}_{23}\\), respectively; 2) elements addition are conducted between \\(\\mathrm{x}_{22}\\) and \\(\\mathrm{x}_{21}\\); 3) the dual-normalization layer enables feature distribution normalization on \\(\\mathrm{x}_{21}\\) and \\(\\mathrm{x}_{23}\\); 4) the two outputs from the dual-normalization layer can be added together; As a result, the aforementioned added features are convolved through pointwise convolution as the final output of the IBE module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.578,
+                0.469,
+                0.654
+            ],
+            "angle": 0,
+            "content": "In addition, we leverage the homogeneity and additivity of the convolutions to fold IBM modules into the simpler depthwise separable convolution in the inference stage without performance degradation. The details can be seen in Appendix C."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.666,
+                0.439,
+                0.683
+            ],
+            "angle": 0,
+            "content": "3.3. Recursive Warm-restart Training Strategy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.689,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Strong augmentations (SA) are widely used for object detection, and [9, 31] shows well-designed SA effectively improves detectors. However, we find that well-designed SA does not always benefit light-weight detectors, because the current training strategies cannot sufficiently exploit diverse training representations to boost the generalization ability on real validation data. For example, YOLOX [9] points out MixUp reduces YOLOX-nano's performance by about \\(5\\%\\). We argue that the limited capacity detectors fit the diverse data generated by SA as much as possible during training, such that the modules have no surplus capacity to adjust learned features to boost the generalization ability of modules on real validation data. In other words, SA produces diverse representations that are equal to the data"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "shifts, thus breaking the generalization ability of the module. We also propose an effective training strategy to adjust these diverse features to improve the generalization ability, namely recursive warm_restart (RecWR)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.153,
+                0.892,
+                0.348
+            ],
+            "angle": 0,
+            "content": "As shown in Fig. 5 of the Appendix, the whole training procedure can be divided into four stages. Starting from the 1-st stage to 4-th stage training, the intensity of image augmentations gradually decreases. Specifically, in the 1-st training stage, some SA types will be combined, such as MixUp, Mosaic, and RandomAffine. Starting from the 2-nd training stage, the above SA types are gradually unloaded in each training stage, until the 4-th training stage. For the last training stage, only the random flip and random scales are performed on the training data. In addition, before starting each training stage, the waiting training detectors load the trained weights of the previous training stage as the initialization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.35,
+                0.892,
+                0.426
+            ],
+            "angle": 0,
+            "content": "We can see that in Appendix D, after training FemtoDet with RecWR, MixUp also help such extremely small detectors obtain better performance. In other words, RecWR takes advantage of diversity features learned from SA to get FemtoDet out of sub-optimization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.436,
+                0.633,
+                0.453
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.462,
+                0.892,
+                0.567
+            ],
+            "angle": 0,
+            "content": "We used VOC, COCO, TJU, and ImageNet datasets to conduct experiments and validate the proposed method. Specifically, whole experiments can be divided into two sections, i.e., identifying low-energy components of detectors mentioned in Sec. 3.1.2, and validating the effectiveness of our designed FemtoDet, where the Power metric was measured in GTX 3090."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.574,
+                0.892,
+                0.634
+            ],
+            "angle": 0,
+            "content": "Table 1: Comparisons of energy-related metrics in MobileNetV2 0.25 (MBV2) [33] used different activation functions. We trained a classifier on ImageNet to evaluate relevant metrics."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.533,
+                0.646,
+                0.858,
+                0.75
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Activation Functions</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td>ReLU [1]</td><td></td><td>5.04</td><td>45.22</td><td>8.97</td></tr><tr><td>GELU [16]</td><td></td><td>5.67</td><td>47.21</td><td>8.33</td></tr><tr><td>Swish [9]</td><td>1.48</td><td>5.47</td><td>47.45</td><td>8.67</td></tr><tr><td>HSwish [44]</td><td></td><td>5.33</td><td>47.60</td><td>8.93</td></tr><tr><td>SiLU [8]</td><td></td><td>5.73</td><td>47.25</td><td>8.25</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.776,
+                0.882,
+                0.792
+            ],
+            "angle": 0,
+            "content": "4.1. Benchmark to Find Low-energy Components"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.8,
+                0.699,
+                0.814
+            ],
+            "angle": 0,
+            "content": "4.1.1 Activation Functions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Table 1 shows the energy-related metric results using different activation functions under the same architecture (MobileNetV2 0.25). We observe that the activation functions can significantly improve models without extra parameters (Param). On the other hand, such activation functions incur"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13323"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.182
+            ],
+            "angle": 0,
+            "content": "unacceptable overhead on some metrics which are inconvenient to measure. For example, Swish improves ReLU-based models performance by \\(4.93\\%\\), but produces more than \\(8.53\\%\\) more energy cost. The mEPT metric also demonstrate that ReLU results in the best energy versus performance tradeoffs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.187,
+                0.471,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Table 2: Comparisons of energy-related metrics in MobileNetV2 0.75 and ResNet18 [15]. The two CNNs can present the two typical convolution operators: vanilla convolutions and depthwise separable convolutions. We compare different convolution operators with different kernel sizes on the same convolution operators. Here, \\(\\clubsuit\\), and \\(\\diamond\\) indicate two kernel sizes of \\(3 \\times 3\\), and \\(5 \\times 5\\). In this experiment, we also evaluate models by training them on ImageNet."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.335,
+                0.468,
+                0.434
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>CNNs</td><td>Convolution Operators</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td rowspan=\"2\">Res18</td><td>vanConv♣</td><td>12.46</td><td>170.64</td><td>69.93</td><td>0.41</td></tr><tr><td>vanConv◇</td><td>31.99</td><td>198.28</td><td>71.24</td><td>0.36</td></tr><tr><td rowspan=\"2\">MBV2</td><td>DSC♣</td><td>2.29</td><td>5.56</td><td>69.51</td><td>12.50</td></tr><tr><td>DSC◇</td><td>2.35</td><td>6.07</td><td>70.96</td><td>11.69</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.46,
+                0.295,
+                0.476
+            ],
+            "angle": 0,
+            "content": "4.1.2 Convolution Operators"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.485,
+                0.471,
+                0.711
+            ],
+            "angle": 0,
+            "content": "This sub-section compares energy-related metrics while training an image classifier on the ImageNet dataset based on the different convolution operators (vanCon and DSC), and the different kernel sizes \\((3\\times 3\\), and \\(5\\times 5)\\) on the same convolution operator. Experimental results in Table 2 show that: 1) When CNNs were constructed with the same kernel size, mobilenetv2 generated much lower energy costs than resnet18, as shown in Table 2 of vanConv and DSC. In other words, DSC is more energy friendly than vanConv while achieving similar performance; 2) When CNNs were constructed with different kernel sizes and the same types of operators, the smaller kernel generated much lower energy costs than the larger kernel, as shown in Table 2 of vanConv and vanConv. However, the performance gain from the large kernels is not so impressive."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.726,
+                0.262,
+                0.74
+            ],
+            "angle": 0,
+            "content": "4.1.3 Necks of Detectors"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Here we evaluated the effects of different necks (including FPN, PAN, and SharedNeck) in FemtoDet. Experimental results are shown in Table 3, and some observation are summarized as follow: 1) Although FPN enables FemtoDet to achieve preferable results, it not only consumes more energy but also has a large parameter overhead; 2) Due to the limited representation of light-weight models, the top-down and bottom-up feature fusion of PAN is poor; 3) SharedNeck achieves the best results in the metrics of parameter, energy cost, object detection performance, and factors of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "mean energy versus performance tradeoffs by performing adaptive feature fusion."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.129,
+                0.894,
+                0.189
+            ],
+            "angle": 0,
+            "content": "Table 3: Comparisons of energy-related metrics in Fem-toDet with different necks: FPN, PAN, and our proposed SharedNeck, respectively. The detector was trained on the PASCAL VOC."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.513,
+                0.202,
+                0.879,
+                0.278
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Necks of Detectors</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>FPN</td><td>176.31</td><td>8.31</td><td>40.04</td><td>4.82</td></tr><tr><td>PAN</td><td>79.83</td><td>7.97</td><td>39.91</td><td>5.01</td></tr><tr><td>SharedNeck</td><td>69.77</td><td>7.83</td><td>42.50</td><td>5.43</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.295,
+                0.892,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Table 4: PASCAL VOC object detection results with YOLOX, NanoDet Plus, and FemtoDet."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.52,
+                0.337,
+                0.871,
+                0.472
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>70.39</td><td>10.42</td><td>30.60</td><td>2.94</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>11.29</td><td>38.44</td><td>3.40</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>7.83</td><td>46.31</td><td>5.91</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>13.60</td><td>3.00</td><td>5.10</td><td>16.60</td></tr><tr><td>NanoDet Plus</td><td>20.78</td><td>4.02</td><td>8.07</td><td>25.48</td></tr><tr><td>FemtoDet</td><td>22.90</td><td>1.10</td><td>8.40</td><td>28.50</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.489,
+                0.892,
+                0.55
+            ],
+            "angle": 0,
+            "content": "Table 5: Inference speed (FPS) and power of trained detectors (YOLOX, NanoDet Plus, and FemtoDet were trained on PASCAL VOC) on Qualcomm Snapdragon 865 CPU platforms."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.561,
+                0.884,
+                0.638
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Param (k)</td><td rowspan=\"2\">AP50</td><td colspan=\"2\">Inference</td></tr><tr><td>Power (W)</td><td>FPS</td></tr><tr><td>YOLOX</td><td>70.39</td><td>30.60</td><td>1.41</td><td>38.04</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>38.44</td><td>1.37</td><td>47.80</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>46.31</td><td>1.11</td><td>64.47</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.651,
+                0.848,
+                0.668
+            ],
+            "angle": 0,
+            "content": "4.2. Validating the Effectiveness of FemtoDet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We verify the effectiveness of FemtoDet on three datasets: PASCAL VOC, COCO, and TJU-DHD, while resizing inputs to \\(640 \\times 640\\) for training and resizing inputs to \\(416 \\times 416\\) for validating. Two datasets, PASCAL VOC and TJU-DHD two datasets are converted to the COCO data types for evaluation. In addition, we extract campus data from the TJU-DHD dataset to evaluate the pedestrian detection performance of our proposed extremely light detector, i.e., FemtoDet. Considering extremely light-weight detectors are challenging to fit the complex COCO dataset with poor detection performance, we pull the corresponding results to Appendix E. Also, we compare the detection performance of FemtoDet with YOLOX, and NanoDet Plus [28], in which they are at the same parameter level to ensure fairness. All the detector backbones are pretrained on the Ima"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13324"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.123
+            ],
+            "angle": 0,
+            "content": "geNet for 100 epochs, and the metric of mEPT presented in this section is calculated between AP50 and Power."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.137,
+                0.313,
+                0.151
+            ],
+            "angle": 0,
+            "content": "4.2.1 Results on PASCAL VOC"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.162,
+                0.473,
+                0.419
+            ],
+            "angle": 0,
+            "content": "Experimental results are presented in Table 4, which shows light-weight detectors with eight metrics: parameter (Param), energy cost (Power), AP50, factors of mean energy versus performance tradeoffs (mEPT), mAP, mAP of small size objects (mAP-s), mAP of medium size objects (mAP-m), and mAP of large size of objects (mAP-1) respectively. We can see that although YOLOX has a large number of parameters, it is much lower than FemtoDet in many metrics. NanoDet Plus has the parameter comparable to that of FemtoDet, but only outperforming FemtoDet in the metrics of mAP-s. We believe that for such extremely light-weight detectors, their performances on large-scale objects are the most critical. FemtoDet also presented better results than YOLOX and NanoDet Plus on the metrics of mAP-1. Although the metrics i.e. mEPT, used to evaluate performance and energy balance, FemtoDet achieves the best balance compared to the other two models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.42,
+                0.471,
+                0.496
+            ],
+            "angle": 0,
+            "content": "In addition, we evaluated the inference speed (FPS) and power of trained detectors on Qualcomm Snapdragon 865 CPU platforms. As shown in Tab. 5, our FemtoDet also achieves the smallest energy costs and inference speed on edge devices."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.503,
+                0.47,
+                0.534
+            ],
+            "angle": 0,
+            "content": "Table 6: TJU-DHD pedestrian detection results with YOLOX, and FemtoDet."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.109,
+                0.545,
+                0.437,
+                0.654
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>59.40</td><td>6.03</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>66.90</td><td>9.67</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>29.00</td><td>11.50</td><td>37.60</td><td>54.20</td></tr><tr><td>FemtoDet</td><td>33.10</td><td>17.60</td><td>50.20</td><td>61.50</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.671,
+                0.47,
+                0.701
+            ],
+            "angle": 0,
+            "content": "Table 7: Loose metric on TJU-DHD pedestrian detection with YOLOX, and FemtoDet."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.097,
+                0.712,
+                0.449,
+                0.822
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AR20</td><td>AP20</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>90.40</td><td>42.10</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>85.80</td><td>76.30</td></tr><tr><td>Methods</td><td>AR20-m</td><td>AP20-m</td><td>AR20-1</td><td>AP20-1</td></tr><tr><td>YOLOX</td><td>83.70</td><td>34.80</td><td>96.10</td><td>55.60</td></tr><tr><td>FemtoDet</td><td>94.10</td><td>88.80</td><td>98.60</td><td>95.30</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.846,
+                0.281,
+                0.86
+            ],
+            "angle": 0,
+            "content": "4.2.2 Results on TJU-DHD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Extremely light-weight detectors like FemtoDet have broad application prospects in surveillance scenarios. Hence, we"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "evaluate the performance of FemtoDet in pedestrian detection using the campus dataset of TJU-DHD, and show the performance of the detectors on the less stringent metric AP20. Table 6 and 7 demonstrate that FemtoDet is competent for pedestrian detection in common surveillance scenarios: 1) FemtoDet has lower energy costs in deployment, which is \\(29.74\\%\\) lower than YOLOX; 2) FemtoDet obtains \\(76.3\\%\\) AP20, while YOLOX with the same parameters only obtain \\(71.80\\%\\) AP20."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.234,
+                0.894,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Table 8: Ablation study on the effectiveness of our IBE modules and RecWR training strategy. Where FemtoDet* denotes FemtoDet consists of pure DSC without the enhancement of IBE, 300e and 1200e mean the detector training with the same data augmentation with 300 or 1200 epochs."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.516,
+                0.336,
+                0.875,
+                0.438
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>\\</td><td>IBE</td><td>RecWR</td><td>300e</td><td>1200e</td><td>AP50</td></tr><tr><td rowspan=\"5\">FemtoDet*</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>42.50</td></tr><tr><td>X</td><td>X</td><td>X</td><td>✓</td><td>42.11</td></tr><tr><td>X</td><td>✓</td><td>X</td><td>X</td><td>45.13</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>X</td><td>45.78</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>46.31</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.469,
+                0.671,
+                0.484
+            ],
+            "angle": 0,
+            "content": "4.2.3 Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.495,
+                0.892,
+                0.678
+            ],
+            "angle": 0,
+            "content": "We conduct a series of ablation studies on PASCAL VOC to demonstrate the effectiveness and efficiency of our IBE modules and RecWR training strategy. As shown in Table 8: 1) The second and third rows present that by training with 300 and 1200 epochs for FemtoDet*, such a longer epochs do not yield better gains. 2) The fourth and fifth rows present FemtoDet* was trained with RecWR and 300 epochs with the enhancement of IBE, respectively. Results show that independently equipping IBE and RecWR can improve model performance. 3) The six rows demonstrate that jointly using IBE and RecWR enables FemtoDet to achieve the best performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.694,
+                0.619,
+                0.71
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "This paper presented a baseline to encourage the research on energy and performance balance detectors. Our experimental results clearly showed that boosting performance can also cause problem of growth in energy consumption. Conversely, the simple components like ReLU are suitable for building energy-oriented detectors. In addition, we also proposed a novel IBE module and RecWR training strategy to overcome the optimization problem of extremely lightweight detectors. Compared to other state-of-the-art methods under the same parameters setting, IBE and RecWR support these baselines achieving the best performance on VOC, COCO, and TJU-DHD datasets, while consuming the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13325"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.123
+            ],
+            "angle": 0,
+            "content": "least energy. In the future, we will continue improving the detectors on the balance of energy and performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.136,
+                0.173,
+                0.151
+            ],
+            "angle": 0,
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+# FemtoDet: An Object Detection Baseline for Energy Versus Performance Tradeoffs
+
+Peng Tu $^{1}$ , Xu Xie $^{1}$ , GUO AI $^{1}$ , Yuexiang Li $^{2}$ , Yawen Huang $^{2*}$ , Yefeng Zheng $^{2}$ $^{1}$  MicroBT Inc.  
+ $^{2}$  Jarvis Lab, Tencent
+
+# Abstract
+
+Efficient detectors for edge devices are often optimized for parameters or speed count metrics, which remain in weak correlation with the energy of detectors. However, some vision applications of convolutional neural networks, such as always-on surveillance cameras, are critical for energy constraints. This paper aims to serve as a baseline by designing detectors to reach tradeoffs between energy and performance from two perspectives: 1) We extensively analyze various CNNs to identify low-energy architectures, including selecting activation functions, convolutions operators, and feature fusion structures on necks. These underappreciated details in past work seriously affect the energy consumption of detectors; 2) To break through the dilemmacatic energy-performance problem, we propose a balanced detector driven by energy using discovered low-energy components named FemtoDet. In addition to the novel construction, we improve FemtoDet by considering convolutions and training strategy optimizations. Specifically, we develop a new instance boundary enhancement (IBE) module for convolution optimization to overcome the contradiction between the limited capacity of CNNs and detection tasks in diverse spatial representations, and propose a recursive warm_restart (RecWR) for optimizing training strategy to escape the sub-optimization of light-weight detectors by considering the data shift produced in popular augmentations. As a result, FemtoDet with only 68.77k parameters achieves a competitive score of 46.3 AP50 on PASCAL VOC and 1.11 W & 64.47 FPS on Qualcomm Snapdragon 865 CPU platforms. Extensive experiments on COCO and TJUDHD datasets indicate that the proposed method achieves competitive results in diverse scenes.
+
+# 1. Introduction
+
+The deployment of efficient convolutional neural networks (CNNs) enabled immense progress [23, 29, 30, 31, 4, 9, 41] in vision detectors for edge devices, in which they
+
+consistently reduce parameters and speed counts for improving accuracy. However, these metrics are not correlated well with the efficiency of the models in terms of energy. Evaluation metrics, such as parameters, do not take into account the energy cost of models, resulting in a nontrivial effect on the energy cost of detectors. Compared with the same architecture, the parameters of models are positively correlated with their energy cost (shown in Table 2). However, in the case of equal model parameters, their energy consumption may be negatively correlated or even irrelevant to the model parameters (shown in Table 1). Considering that various activation functions, convolution operators, and feature fuse structures may not increase model parameters, but generate more energy costs. Similarly, the speed count is also not well correlated with energy, as it can be optimized by the degree of parallelism. These disconnections will leave customized efficient detectors unavailable, when they are deployed under severe energy constraints like the always-on surveillance cameras.
+
+This paper aims to reduce the energy costs of efficient object detectors, while improving their performances by achieving energy versus performance tradeoffs. Specifically, these bottlenecks fall into several categories:
+
+1) Detector components with unknown energy. Most current object detection methods focus either on latency-oriented [5, 34, 44] or accuracy-oriented [9, 38, 32, 36] works. There are very limited works toward the energy cost of the detector components, which is the first obstacle to designing energy-performance-balanced detectors. To identify energy-efficient components of detectors, we followed [42] to benchmark their energy metrics from three types of structures, i.e., activation functions, convolution operators, and necks of detectors. The following finding is acquired: Firstly, some activation functions have been widely used, because of their ability to improve models without adding more parameters. They have increased costs, yet received very limited attention. As shown in Table 1, we set ReLU [1] based models as a baseline. When replacing the ReLU with the GELU [16],  $4.40\%$  performance is gained, while  $12.50\%$  energy cost is increased, and the corresponding factor of the mean energy versus the perfor
+
+mance tradeoffs (Eq. 1) drops  $7.16\%$ . In addition, although large kernel convolutions [25] can improve models (Table 2), the increased energy cost is unacceptable. As seen in Table 2, the large kernel convolutions are equipped to enable the model to rise by around  $1.87\%$  in performance, but with more energy costs  $(16.20\%)$  than in the small kernel size of convolutions (shown in the second row of Table 2). Finally, the standard FPN [21, 22, 39, 10, 37] in the detectors also causes significant energy costs. We observe that this situation is happened due to multi-feature fusion paths following either bottom-to-up or top-to-down way, resulting in frequent data reading in memory for data coverage. However, it is shown that the up-down fusion between multi-features may not necessary. As shown in Table 3, we propose a simple SharedNeck for replacing FPN to reduce around  $5.77\%$  energy costs, while obtaining  $6.25\%$  performance gains. SharedNeck uses an adaptive fusion between multi-features by learning convolution, instead of feature-by-feature bottom-to-up or top-to-down fusions, as operated in FPN. Based on these analyses, we further build upon a low-energy detector, named FemtoDet. Surprisingly, FemtoDet just has  $68.77\mathrm{k}$  parameters and  $1.1\mathrm{W}$  power on the platform. 2) Optimization for CNN is another bottleneck, since obtaining a favorable detector is very challenging, especially for a small number of parameters. Light-weight detectors are restricted by their limited capacities [6], which will cause obfuscation on feature maps of the instances' boundaries of interesting objects, as shown in Figure 2 (b). Ambiguous instance boundaries on the features may raise the risk of false detection in the models. For this problem, we propose a novel instance boundary enhancement module (IBE), which emphasizes the potential of the object boundary information: The parameter reuse mechanism is first applied to integrate local descriptors with convolution operation to make robust and diverse instance boundary feature representation. But this operation would cause feature un-alignment between normal features and integrated features. Then, in order to sufficiently exploit these two types of features, we design dual-normalization in IBE, as to realign the features (Fig. 4 of the Appendix). IBE employs a shared convolution yet an independent batch normalization layer for separate normalization is also adopted. Finally, we add normal and integrated features together behind the dual-normalization layer. IBE provides a novel form of parameter reuse to generate new local descriptors from shared convolution operators. This method can capture object boundary information by integrating gradient cues around the learned convolution. After trained, IBE modules can be folded into simple convolution operators, thus requiring no extra computations anymore; In addition, data augmentation is a common approach for efficient detector training. Using well-designed strong augmentations is conducive to improving the generalization of mod
+
+els [31, 9]. However, how to prevent data shifts between training and validation images has not been explored, while training data suffers strong augmentations. It is found that the produced data shifts by strong augmentations would prevent light-weight detectors from moving toward global optimization. A common view is that strong image augmentations can effectively encourage networks to learn diverse features [11]. But for light-weight detectors, these diverse features cannot assist the models in making better generalizations in the validation set. In other words, light-weight detectors are more susceptible to these ignored data shifts because of their limited capacities. Furthermore, we propose an effective training strategy, namely recursive warm-start (RecWR), to adapt these diverse features to improve the model's generalization. RecWR works based on multistage training while gradually weakening data augmentation strength. This method can help the limited-capacity detectors jump out of local optima under the assistance of high-dimension & diverse features. The effectiveness of the IBE and RecWR has been evaluated on PASCAL VOC dataset. And the experimental results show that IBE can improve FemtoDet  $\sim 7.72\%$  performance, while incurring no extra parameter burdens, as compared to the original architecture; RecWR can improve FemtoDet  $\sim 6.19\%$  performance by gradually weakening the data augmentation strength in multi-stage learning. By jointly training FemtoDet with IBE and RecWR, our proposed methodology can go over the YOLOX [9] by  $51.34\%$  in performance when using the same-level parameters.
+
+Something worth mentioning is that FemtoDet is specially designed for hierarchical intelligent chips to enable always-on alerts: the always-on low power, high-recall, and decent accuracy - it achieved 85.8 AR20 & 76.3 AP20 (Table 7) while performing pedestrian detection on TJU-DHD. In addition, FemtoDet is poor in detecting small objects but is excellent in detecting medium and large objects, which they are more interested in, with 88.8 AR20-m & 94.1 AP20-m / 95.3 AR20-1 & 98.6 AP20-1 (Table 7) on TJU-DHD. Information can be passed to other models after identifying possible objects of interest, and high-precision robust models are then initiated for accurate recognition. The always-on smart products have a wide range of applications, e.g., in-home monitoring or robots. Hence, the loose metric (e.g., AP50 or AP20) and data scenario with moderate difficulty (e.g., VOC) can well reflect the application ability of FemtoDet. Further, the experiments on COCO datasets have verified that the proposed method is suitable for diverse scenarios resulting in competitive results.
+
+# 2. Related Works
+
+# 2.1. Object Detection
+
+Object detection is a classic computer vision task for identifying the category and location of object in pictures
+
+or videos. The existing object detectors can be divided into two categories: two-stage detectors and one-stage detectors. Two-stage detectors [32, 36, 14, 21] are anchor-based devices that generate region proposals from the image and then produce the final prediction boxes from these proposals. Further, FPN [21] improves the two-stage detectors by fusing multi-level features. Despite their higher accuracy compared to the one-stage detectors, two-stage detectors are still difficult to achieve low latency when deployed on edge devices.
+
+Specifically, there are two types of one-stage detectors: anchor-based and anchor-free, which depends on anchor priors injecting into whole images to enable box regression. SSD [23], as a classical anchor-based one-stage detector, discretizes the output space of bounding boxes into a set of default anchors with different aspect ratios and scales per feature map location. This operation helps detecting tiny objects. Another typical anchor-based detector is the YOLO series [30, 31, 4]. YOLOv2 [30] explores bag of freebies to improve the performances of one-stage detectors. YOLOv3 [31] proposes cross-scale features and novel nms (Non-Maximum Suppression) to obtain more confident predictions. YOLOv4 [4] finds that the repeated gradient of network optimization aggravates detector latency, and thus designs Cross-Stage-Partial-connection modules to reduce the latency of detectors while maintaining detection performance. Anchor-free detectors [29, 9, 19, 38] aim to eliminate the pre-defined set of anchor boxes. YOLO [29], as an anchor-free one-stage detector, divides an image into multiple grids and predict boxes at grids near the object's center. CornerNet [19] detects an object as a pair of key points (through the top-left corner and bottom-right corner of the bounding box). A single convolutional network was leveraged in CornerNet to predict a heatmap for all top-left corners of instances of the same object category, a heatmap for all bottom-right corners, and an embedding vector for each detected corner. Indeed, CornerNet is a new pipeline for object detection. FCOS [38] eliminates the anchor setting by proposing a fully convolutional one-stage object detector, which can solve object detection in a per-pixel prediction manner. The anchor-free detectors solve the problem happened in anchor-based detectors, which reduce the memory cost and increase accuracy of the bounding box.
+
+Both one-stage and two-stage object detection methods have obtained high performance on many challenging public datasets, i.e., COCO and TJU-DHD [27]. These methods provide the accuracy-oriented detectors. However, the critical problem for detectors serving edge devices is detection latency and its power. In other words, detectors obtain higher performance in challenging scenes, which is not a necessary option for detectors deployed on edge devices. For the detection latency, a lot of effort [5, 34, 44] have been devoted to achieving the balance between accuracy
+
+and efficiency. FastYOLO [34] is an optimized architecture extended from YOLOv2 with fewer parameters and  $2\%$  performance drop, which makes FastYOLO run at an average of  $\sim 18$  FPS on an Nvidia Jetson TX1 embedded system. YOLObite [5] focuses on pruning redundancy object detectors to be real-time by designing in a compression- compilation way. NanoDet uses ShuffleNetV2 [26] as its backbone to make the model lighter, and further uses ATSS [47] and GFL [20] to improve its accuracy. It is worth noting that NanoDet also reached  $\sim 60$  FPS on an ARM CPU. These light-weight detectors are latency-oriented. Actually, neither accuracy-oriented nor latency-oriented detectors take their energy cost into account. High energy cost detectors are unfriendly to devices deployed at edges.
+
+This paper aims to develop a light-weight detector that can achieve tradeoffs between energy and performance.
+
+# 2.2. Energy-Oriented Convolutional Neural Networks
+
+Besides the manual design of deep neural networks, a great deal of work has been done to improve the effectiveness and efficiency of deep neural networks via network pruning [45], quantization [13, 2], architecture search [12, 40]. ECC [42] proposes the end-to-end classifier training framework, which provides quantitative energy consumption guarantees by using weighted sparse projection and input masking. Zhang et al. [46] specialized in video broadcast and leveraged distillation techniques to reduce memory consumption by approximating the video frame data. MIME [3] is an algorithm-hardware co-design approach that reuses the weight parameters of a trained parent task and learns task-specific threshold parameters for inferring on multiple child tasks. However, the above works are all in service for image classification, and we can observe that fewer parameters represent lower energy costs in the same architecture. Object detection on edge devices is still a challenging topic, considering that the conflict between the limited capacity of CNNs and diverse spatial representations. This paper is the first work to provide a systematized solution for energy-oriented light-weight detectors.
+
+# 3. FemtoDet
+
+This section will be divided into two subsections to describe how FemtoDet achieves energy versus performance tradeoffs. 1) Benchmarks for Low-energy Detectors: We provide benchmarks for designing low-energy detectors, including the exploring of activation functions, convolution operators, and neck of detectors. 2) Energy-Oriented FemtoDet: Based on the benchmarks for designing low-energy detectors, an energy-oriented light-weight detector named FemtoDet is provided, which stacks layers from depthwise separable convolutions (DSC), BN and ReLU. FemtoDet involves only  $68.77\mathrm{k}$  parameters and power of  $1.11\mathrm{W}$  on
+
+the Qualcomm Snapdragon 865 CPU platform. Moreover, FemtoDet can be optimized with two designs: Firstly, instance boundary enhancement (IBE) modules are used to improve the DSC in FemtoDet, overcoming the bottleneck of light-weight models' representation optimization (i.e., models will learn obfuscation features because of their limited capacity, as shown in Fig. 2(b)). Second, the recursive warm_restart (RecWR) training strategy is a multi-stage recursive warm_restart learning procedure, which can surmount data shifts produced from strong data augmentations.
+
+# 3.1. Benchmarks for Low-energy Detectors' Designing
+
+# 3.1.1 Evaluation Metrics
+
+Top1-Acc (top1 accuracy, for image classification), and AP (average precision, for object detection) are widely used measures to evaluate the performance of CNN. In addition to the commonly used metrics top1 - Acc and AP, we propose the Power (energy costs) and mEPT (mean energy versus performance tradeoffs) to comprehensively evaluate the energy costs of the models and their ability to achieve energy versus performance tradeoffs. Specifically, Power and mEPT are represented by
+
+$$
+\mathrm {m E P T} = \left(\frac {1}{\mathrm {N}} \sum_ {\mathrm {i}} ^ {\mathrm {N}} \mathrm {P}\right) / (\text {P o w e r}), \tag {1}
+$$
+
+$$
+\text {s . t .} \quad \operatorname {P o w e r} = \frac {1}{\mathrm {T} _ {\text {t i m e}}} \sum_ {\mathrm {i}} ^ {\mathrm {N}} \left(\varepsilon \left(\mathbf {W}, \mathrm {x} _ {\mathrm {i}}\right) - \varepsilon \left(\hat {\mathbf {W}}, \mathrm {x} _ {\mathrm {i}}\right)\right), \tag {2}
+$$
+
+where  $\mathrm{T}_{\mathrm{time}}$  indicates the total times required to evaluate  $\mathbf{N}$  images,  $\varepsilon(\mathbf{W}, \mathrm{x_i})$  represents the energy costs while models evaluate i-th image  $\mathrm{x_i}$  with trained parameters  $\mathbf{W}$ .  $\varepsilon(\hat{\mathbf{W}}, \mathrm{x_i})$  is similar to  $\varepsilon(\mathbf{W}, \mathrm{x_i})$ . The difference is that we set a value of 1 for each layer of channels, where the model parameter is  $\hat{\mathbf{W}}$ .  $\varepsilon(\hat{\mathbf{W}}, \mathrm{x_i})$  indicates that the model is an empty state. P denotes the model performance (top1-Acc for image classification while evaluating activation functions and convolution operators, AP50 for object detection while evaluating necks of detectors in Sec. 3.1.2) in image  $\mathrm{x_i}$ . For the power metric, the value is expected to be as small as possible. For the mEPT metric, the result is expected as greater as possible.
+
+# 3.1.2 Components to Be Evaluated
+
+To identify low-energy components of detectors, we followed [42] to benchmark their energy costs from three types of structures: activation functions, convolution operators and necks of detectors:
+
+Activation Functions. Rectified Linear Unit (ReLU) [29, 23], GELU [16], Swish [9], SiLU [8], and etc. are widely used for object detection because they have fewer
+
+parameters and flops. We calculate the energy costs of different activation functions in the same architecture to explore which activation function is more friendly for designing an energy-oriented detector.
+
+Convolution Operators can automatically learn fiber weights while CNNs are trained to summarize helpful information, including horizontal, vertical, edged, diagonal, and etc. features from images. Vanilla convolutions (van-Conv) [18], depthwise separable convolutions (DSC) [17] and their large kernel size versions [25] are widely used. Ding et al. [7] pointed out that when CNNs are constructed based on enough large convolution kernels, results can be comparable to the transformer [24]. Here, we set up energy consumption comparison experiments with different convolutions (vanCon and DSC) and multi-scale convolution kernel sizes  $(3\times 3$ , and  $5\times 5)$  on different network structures (ResNet and MobileNetV2). It is important that for each experiment case, the convolution operator type or kernel size would be the only variable.
+
+Necks of Detectors: Feature pyramid networks (FPN) are essential components for two-stage or one-stage detectors. FPN-based necks of detectors fuse multiple low-resolution and high-resolution feature inputs for better representations, leading to a series of studies for designing manually complex fusion methods [21, 22, 39]. However, they only presented favorable results brought by FPN but ignored its energy costs. We form a series of experiments on Fem-toDet by using different neck types, e.g. FPN [21], PAN [22], and our proposed SharedNeck (details can be found in Sec. 3.2.1) to study corresponding metrics (including energy costs, parameters, and detection precision on PASCAL VOC) changes.
+
+All related experiments can be found in Sec. 4.1. We can observe that DSC and ReLU are more energy friendly than vanCon and other activation functions. In addition, by comparing with the necks of detectors such as FPN and PAN, the proposed SharedNeck is more suitable for light-weight detectors.
+
+# 3.2. Energy-Oriented FemtoDet
+
+# 3.2.1 Building FemtoDet
+
+Backbone: The backbone of FemtoDet contains an initial full convolution layer with 8 filters. We use ReLU as the non-linearity and BN as the batch normalization. From the second layer beginning, all the convolution operators use DSC. The reason is that we follow the results of our benchmarks (the results can be seen in Sec. 4.1) to select the energy friendly components. The whole backbone is described in Appendix Table 9; Neck: We customize a neck for FemtoDet to achieve better tradeoffs between energy and performance. In detail, SharedNeck first aligns the scale information of inputs from backbones, and then merges these alignment features with elements addition. Fi
+
+![](images/06bd57ad96ee3fdfb9f4c4a448b04f286cf71feda743b5d60b754ee4e418c9d1.jpg)  
+(a) FPN
+
+![](images/2a041fe89340f182df35050ee1988fbade5fdcb721cbf6e643b8df719853de2c.jpg)  
+(c) PAN
+
+nally, a DSC performs adaptive multi-scale information fusion between merged features. The implementation details of SharedNeck, and how it differs from other necks are shown in Fig. 1; Head and Training Loss: Here, we use the decouple head of YOLOX as the head of our proposed detector with the same training loss as YOLOX.
+
+# 3.2.2 Instance Boundary Enhancement Module
+
+Optimizing light-weight detectors is a notoriously challenging problem. The reason for this is that limited by their representation, features learned by detectors are diffuse, as shown in Fig. 2 (b). Instance boundary enhancement (IBE) modules are designed to improve the DSC in FemtoDet, thus overcoming the bottleneck of light-weight models' representation optimization. IBE is similar to modules introduced in [45, 35, 43], except that our modules are designed for convolutional layers that are factorized into depthwise and pointwise layers. We further introduce a dual-normalization mechanism, such that the IBE modules can be used for object detection, while the modules in [45, 35, 43] just working for low-level tasks. Based on the DSC block, the basic block of IBE includes  $3 \times 3$  depthwise convolution followed by  $1 \times 1$  convolution. IBE enhances DSC by designing a new local descriptor, semantic projector, and dual-normalization layer. Specifically, the  $1 \times 1$  local descriptor is a parameter reusing mechanism generated by the linear transformation of the integrating gradient cues around shared depthwise convolution. Therefore, the object boundary information can be found in the local descriptors. Previously, the local descriptor is known as the difference convolution [45, 35, 43] used for low-level tasks. Although the idea is easy to get that using these object boundary information to enhance the noisy feature representation (shown in Fig. 2 (b)) of the above standard operators, such
+
+![](images/fcf69e34563b1b3e2a5de60829647774e13d0902ebb962e64621507947b17096.jpg)
+
+![](images/4a40781574cf975f9538a17c2b3f8b338ef4ffaf0d77bcfda671881f8d718966.jpg)
+
+![](images/36bae9606241a317307a361f0de81a1ccf9aac9c38bf99830ca97d4b30aaa54f.jpg)  
+Figure 1: (a) FPN: A top-down multi-scale feature fusion architecture that outputs multiple predictions; (b) Shared-Neck: Simple adaptive multi-scale feature fusion architecture with single prediction, enabling tradeoffs between energy and performance; (c) PAN [22]: Exploring extra bottom-to-up multi-scale feature fusions with many predictions based on FPN.  
+(a) Inputs  
+Figure 2: Feature visualization of the trained light-weight detector. (a) Inputs: RGB images from PASCAL VOC; (b) FemtoDet*: Trained FemtoDet detector consisting of pure depthwise separable convolution; (c) FemtoDet: Trained FemtoDet detector, which was trained with the IBE modules.
+
+![](images/6cd4b946411753c56682ccdd4f60d324676cab9766785ade88838c8683998264.jpg)
+
+![](images/cda1b05584e5331fa31ba682af0dbf853d08d22eeb433f9421ee29700a0ca7cd.jpg)
+
+![](images/2c28f1ff0570646fa2facb343fdfb93d880a450cfcce1099843a7a7f3b545367.jpg)  
+(b) FemtoDet\*
+
+![](images/b4aef114acfc5290183754d239b9ef6411fa3a4f870034ec4d472e18e7d38946.jpg)
+
+![](images/d40514d11bf29b56f94aed71445c3185d980d0d2acad8d4edabc7163baf7bbb2.jpg)
+
+![](images/a83e98d1cce1b288ffafb328523c9f0425b2f9d41e6c28c6d5b2e159ec9b7ae4.jpg)  
+(c) FemtoDet
+
+as depthwise convolution, in practice, the original difference convolution architecture cannot serve for high-level semantic tasks. We observe that features obtained by the difference convolution are unaligned with the features obtained by standard convolution (the figure shown in Fig. 4 of the Appendix). On the one hand, the difference convolution captures diverse information about object boundaries by integrating gradient cues around  $3 \times 3$  or with larger convolution. On the other hand, high-level tasks encourage standard convolution to summarize the abstract semantic information of images. That is the reason that the classical difference convolution cannot serve high-level tasks. To simultaneously solve this problem, we propose a semantic projector and a dual-normalization layer. The semantic projector is the linear transformation of depthwise convolution to transfer operators related to semantic information extraction; The dual-normalization layer consists of two independent batch normalization modules specifically designed for aligning the unaligned features. After that, we incorporate the object boundary cues from the feature addition between the local descriptor and depthwise convolution to guide the model in learning an effective representation of the instance (refined results can be seen in Fig. 2 (c)).
+
+The description of IBE modules is given in Fig. 3 of the Appendix. For the depthwise convolution of kernel size  $3$ ,  $\mathbf{C}_{\mathrm{in}}$  denotes the input channel dimension,  $\mathbf{C}_{\mathrm{out}}$  represents the output channel dimension, the weight matrix can be denoted as  $\mathbf{W}_{\mathrm{conv}} \in \mathbb{R}^{1 \times \mathbf{C}_{\mathrm{in}} \times 3 \times 3}$ , and the bias is represented as  $\mathbf{b} \in \mathbb{R}^{\mathrm{D}}$ . The local descriptor of kernel size 1 can be
+
+generated from the depthwise convolution by reusing parameters. Its weight matric is denoted as  $\mathbf{W}_{\mathrm{des}}$ , which is integrating the gradient cues around  $\mathbf{W}_{\mathrm{conv}}$ :
+
+$$
+\mathbf {W} _ {\text {d e s}} = - \theta_ {1}. \sum_ {\mathrm {p} _ {\mathrm {n}} \in \mathbf {R}} \mathbf {W} _ {\text {c o n v}} \left(\mathrm {p} _ {\mathrm {n}}\right), \tag {3}
+$$
+
+where  $\mathbf{W}_{\mathrm{des}} \in \mathbb{R}^{C_{\mathrm{out}} \times C_{\mathrm{in}}}$ ,  $\theta_1 \in [0,1], \in \mathbb{R}^{1 \times 1}$  is a learnable parameter projection factor.  $\mathbf{R}$  represents the  $3 \times 3$  convolution in  $\mathbf{W}_{\mathrm{conv}}$ , and  $\mathfrak{p}_{\mathrm{n}}$  is the n-the weight value. Integrating the gradient cues around  $\mathbf{W}_{\mathrm{conv}}$  can help the local descriptors capture the object boundary information effectively. The semantic projector is generated from the depthwise convolution, while diverse semantic presentations can be obtained through a learnable linear transformation, shown as follows:
+
+$$
+\mathbf {W} _ {\text {p r o}} = \theta_ {2}. \mathbf {W} _ {\text {c o n v}}, \mathbf {W} _ {\text {p r o}} \in \mathbb {R} ^ {C _ {\text {o u t}} \times C _ {\text {i n}} \times 3 \times 3}, \tag {4}
+$$
+
+where  $\theta_{2} \in [0,1], \mathbb{R}^{1 \times 1}$  is another learnable parameter as the projection factor. Subsequently, the IBE modules perform four steps to refine the feature representation under the guidance of object boundary information. 1) inputs  $\mathrm{x}_{\mathrm{in}}$  will be convolved with the obtained three convolution operators, and the corresponding results are denoted as  $\mathrm{x}_{22}, \mathrm{x}_{21}$ , and  $\mathrm{x}_{23}$ , respectively; 2) elements addition are conducted between  $\mathrm{x}_{22}$  and  $\mathrm{x}_{21}$ ; 3) the dual-normalization layer enables feature distribution normalization on  $\mathrm{x}_{21}$  and  $\mathrm{x}_{23}$ ; 4) the two outputs from the dual-normalization layer can be added together; As a result, the aforementioned added features are convolved through pointwise convolution as the final output of the IBE module.
+
+In addition, we leverage the homogeneity and additivity of the convolutions to fold IBM modules into the simpler depthwise separable convolution in the inference stage without performance degradation. The details can be seen in Appendix C.
+
+# 3.3. Recursive Warm-restart Training Strategy
+
+Strong augmentations (SA) are widely used for object detection, and [9, 31] shows well-designed SA effectively improves detectors. However, we find that well-designed SA does not always benefit light-weight detectors, because the current training strategies cannot sufficiently exploit diverse training representations to boost the generalization ability on real validation data. For example, YOLOX [9] points out MixUp reduces YOLOX-nano's performance by about  $5\%$ . We argue that the limited capacity detectors fit the diverse data generated by SA as much as possible during training, such that the modules have no surplus capacity to adjust learned features to boost the generalization ability of modules on real validation data. In other words, SA produces diverse representations that are equal to the data
+
+shifts, thus breaking the generalization ability of the module. We also propose an effective training strategy to adjust these diverse features to improve the generalization ability, namely recursive warm_restart (RecWR).
+
+As shown in Fig. 5 of the Appendix, the whole training procedure can be divided into four stages. Starting from the 1-st stage to 4-th stage training, the intensity of image augmentations gradually decreases. Specifically, in the 1-st training stage, some SA types will be combined, such as MixUp, Mosaic, and RandomAffine. Starting from the 2-nd training stage, the above SA types are gradually unloaded in each training stage, until the 4-th training stage. For the last training stage, only the random flip and random scales are performed on the training data. In addition, before starting each training stage, the waiting training detectors load the trained weights of the previous training stage as the initialization.
+
+We can see that in Appendix D, after training FemtoDet with RecWR, MixUp also help such extremely small detectors obtain better performance. In other words, RecWR takes advantage of diversity features learned from SA to get FemtoDet out of sub-optimization.
+
+# 4. Experiments
+
+We used VOC, COCO, TJU, and ImageNet datasets to conduct experiments and validate the proposed method. Specifically, whole experiments can be divided into two sections, i.e., identifying low-energy components of detectors mentioned in Sec. 3.1.2, and validating the effectiveness of our designed FemtoDet, where the Power metric was measured in GTX 3090.
+
+Table 1: Comparisons of energy-related metrics in MobileNetV2 0.25 (MBV2) [33] used different activation functions. We trained a classifier on ImageNet to evaluate relevant metrics.
+
+<table><tr><td>Activation Functions</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td>ReLU [1]</td><td></td><td>5.04</td><td>45.22</td><td>8.97</td></tr><tr><td>GELU [16]</td><td></td><td>5.67</td><td>47.21</td><td>8.33</td></tr><tr><td>Swish [9]</td><td>1.48</td><td>5.47</td><td>47.45</td><td>8.67</td></tr><tr><td>HSwish [44]</td><td></td><td>5.33</td><td>47.60</td><td>8.93</td></tr><tr><td>SiLU [8]</td><td></td><td>5.73</td><td>47.25</td><td>8.25</td></tr></table>
+
+# 4.1. Benchmark to Find Low-energy Components
+
+# 4.1.1 Activation Functions
+
+Table 1 shows the energy-related metric results using different activation functions under the same architecture (MobileNetV2 0.25). We observe that the activation functions can significantly improve models without extra parameters (Param). On the other hand, such activation functions incur
+
+unacceptable overhead on some metrics which are inconvenient to measure. For example, Swish improves ReLU-based models performance by  $4.93\%$ , but produces more than  $8.53\%$  more energy cost. The mEPT metric also demonstrate that ReLU results in the best energy versus performance tradeoffs.
+
+Table 2: Comparisons of energy-related metrics in MobileNetV2 0.75 and ResNet18 [15]. The two CNNs can present the two typical convolution operators: vanilla convolutions and depthwise separable convolutions. We compare different convolution operators with different kernel sizes on the same convolution operators. Here,  $\clubsuit$ , and  $\diamond$  indicate two kernel sizes of  $3 \times 3$ , and  $5 \times 5$ . In this experiment, we also evaluate models by training them on ImageNet.
+
+<table><tr><td>CNNs</td><td>Convolution Operators</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td rowspan="2">Res18</td><td>vanConv♣</td><td>12.46</td><td>170.64</td><td>69.93</td><td>0.41</td></tr><tr><td>vanConv◇</td><td>31.99</td><td>198.28</td><td>71.24</td><td>0.36</td></tr><tr><td rowspan="2">MBV2</td><td>DSC♣</td><td>2.29</td><td>5.56</td><td>69.51</td><td>12.50</td></tr><tr><td>DSC◇</td><td>2.35</td><td>6.07</td><td>70.96</td><td>11.69</td></tr></table>
+
+# 4.1.2 Convolution Operators
+
+This sub-section compares energy-related metrics while training an image classifier on the ImageNet dataset based on the different convolution operators (vanCon and DSC), and the different kernel sizes  $(3\times 3$ , and  $5\times 5)$  on the same convolution operator. Experimental results in Table 2 show that: 1) When CNNs were constructed with the same kernel size, mobilenetv2 generated much lower energy costs than resnet18, as shown in Table 2 of vanConv and DSC. In other words, DSC is more energy friendly than vanConv while achieving similar performance; 2) When CNNs were constructed with different kernel sizes and the same types of operators, the smaller kernel generated much lower energy costs than the larger kernel, as shown in Table 2 of vanConv and vanConv. However, the performance gain from the large kernels is not so impressive.
+
+# 4.1.3 Necks of Detectors
+
+Here we evaluated the effects of different necks (including FPN, PAN, and SharedNeck) in FemtoDet. Experimental results are shown in Table 3, and some observation are summarized as follow: 1) Although FPN enables FemtoDet to achieve preferable results, it not only consumes more energy but also has a large parameter overhead; 2) Due to the limited representation of light-weight models, the top-down and bottom-up feature fusion of PAN is poor; 3) SharedNeck achieves the best results in the metrics of parameter, energy cost, object detection performance, and factors of
+
+mean energy versus performance tradeoffs by performing adaptive feature fusion.
+
+Table 3: Comparisons of energy-related metrics in Fem-toDet with different necks: FPN, PAN, and our proposed SharedNeck, respectively. The detector was trained on the PASCAL VOC.  
+
+<table><tr><td>Necks of Detectors</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>FPN</td><td>176.31</td><td>8.31</td><td>40.04</td><td>4.82</td></tr><tr><td>PAN</td><td>79.83</td><td>7.97</td><td>39.91</td><td>5.01</td></tr><tr><td>SharedNeck</td><td>69.77</td><td>7.83</td><td>42.50</td><td>5.43</td></tr></table>
+
+Table 4: PASCAL VOC object detection results with YOLOX, NanoDet Plus, and FemtoDet.  
+
+<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>70.39</td><td>10.42</td><td>30.60</td><td>2.94</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>11.29</td><td>38.44</td><td>3.40</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>7.83</td><td>46.31</td><td>5.91</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>13.60</td><td>3.00</td><td>5.10</td><td>16.60</td></tr><tr><td>NanoDet Plus</td><td>20.78</td><td>4.02</td><td>8.07</td><td>25.48</td></tr><tr><td>FemtoDet</td><td>22.90</td><td>1.10</td><td>8.40</td><td>28.50</td></tr></table>
+
+Table 5: Inference speed (FPS) and power of trained detectors (YOLOX, NanoDet Plus, and FemtoDet were trained on PASCAL VOC) on Qualcomm Snapdragon 865 CPU platforms.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Param (k)</td><td rowspan="2">AP50</td><td colspan="2">Inference</td></tr><tr><td>Power (W)</td><td>FPS</td></tr><tr><td>YOLOX</td><td>70.39</td><td>30.60</td><td>1.41</td><td>38.04</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>38.44</td><td>1.37</td><td>47.80</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>46.31</td><td>1.11</td><td>64.47</td></tr></table>
+
+# 4.2. Validating the Effectiveness of FemtoDet
+
+We verify the effectiveness of FemtoDet on three datasets: PASCAL VOC, COCO, and TJU-DHD, while resizing inputs to  $640 \times 640$  for training and resizing inputs to  $416 \times 416$  for validating. Two datasets, PASCAL VOC and TJU-DHD two datasets are converted to the COCO data types for evaluation. In addition, we extract campus data from the TJU-DHD dataset to evaluate the pedestrian detection performance of our proposed extremely light detector, i.e., FemtoDet. Considering extremely light-weight detectors are challenging to fit the complex COCO dataset with poor detection performance, we pull the corresponding results to Appendix E. Also, we compare the detection performance of FemtoDet with YOLOX, and NanoDet Plus [28], in which they are at the same parameter level to ensure fairness. All the detector backbones are pretrained on the Ima
+
+geNet for 100 epochs, and the metric of mEPT presented in this section is calculated between AP50 and Power.
+
+# 4.2.1 Results on PASCAL VOC
+
+Experimental results are presented in Table 4, which shows light-weight detectors with eight metrics: parameter (Param), energy cost (Power), AP50, factors of mean energy versus performance tradeoffs (mEPT), mAP, mAP of small size objects (mAP-s), mAP of medium size objects (mAP-m), and mAP of large size of objects (mAP-1) respectively. We can see that although YOLOX has a large number of parameters, it is much lower than FemtoDet in many metrics. NanoDet Plus has the parameter comparable to that of FemtoDet, but only outperforming FemtoDet in the metrics of mAP-s. We believe that for such extremely light-weight detectors, their performances on large-scale objects are the most critical. FemtoDet also presented better results than YOLOX and NanoDet Plus on the metrics of mAP-1. Although the metrics i.e. mEPT, used to evaluate performance and energy balance, FemtoDet achieves the best balance compared to the other two models.
+
+In addition, we evaluated the inference speed (FPS) and power of trained detectors on Qualcomm Snapdragon 865 CPU platforms. As shown in Tab. 5, our FemtoDet also achieves the smallest energy costs and inference speed on edge devices.
+
+Table 6: TJU-DHD pedestrian detection results with YOLOX, and FemtoDet.  
+
+<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>59.40</td><td>6.03</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>66.90</td><td>9.67</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>29.00</td><td>11.50</td><td>37.60</td><td>54.20</td></tr><tr><td>FemtoDet</td><td>33.10</td><td>17.60</td><td>50.20</td><td>61.50</td></tr></table>
+
+Table 7: Loose metric on TJU-DHD pedestrian detection with YOLOX, and FemtoDet.  
+
+<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AR20</td><td>AP20</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>90.40</td><td>42.10</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>85.80</td><td>76.30</td></tr><tr><td>Methods</td><td>AR20-m</td><td>AP20-m</td><td>AR20-1</td><td>AP20-1</td></tr><tr><td>YOLOX</td><td>83.70</td><td>34.80</td><td>96.10</td><td>55.60</td></tr><tr><td>FemtoDet</td><td>94.10</td><td>88.80</td><td>98.60</td><td>95.30</td></tr></table>
+
+# 4.2.2 Results on TJU-DHD
+
+Extremely light-weight detectors like FemtoDet have broad application prospects in surveillance scenarios. Hence, we
+
+evaluate the performance of FemtoDet in pedestrian detection using the campus dataset of TJU-DHD, and show the performance of the detectors on the less stringent metric AP20. Table 6 and 7 demonstrate that FemtoDet is competent for pedestrian detection in common surveillance scenarios: 1) FemtoDet has lower energy costs in deployment, which is  $29.74\%$  lower than YOLOX; 2) FemtoDet obtains  $76.3\%$  AP20, while YOLOX with the same parameters only obtain  $71.80\%$  AP20.
+
+Table 8: Ablation study on the effectiveness of our IBE modules and RecWR training strategy. Where FemtoDet* denotes FemtoDet consists of pure DSC without the enhancement of IBE, 300e and 1200e mean the detector training with the same data augmentation with 300 or 1200 epochs.  
+
+<table><tr><td>\</td><td>IBE</td><td>RecWR</td><td>300e</td><td>1200e</td><td>AP50</td></tr><tr><td rowspan="5">FemtoDet*</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>42.50</td></tr><tr><td>X</td><td>X</td><td>X</td><td>✓</td><td>42.11</td></tr><tr><td>X</td><td>✓</td><td>X</td><td>X</td><td>45.13</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>X</td><td>45.78</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>46.31</td></tr></table>
+
+# 4.2.3 Ablation Studies
+
+We conduct a series of ablation studies on PASCAL VOC to demonstrate the effectiveness and efficiency of our IBE modules and RecWR training strategy. As shown in Table 8: 1) The second and third rows present that by training with 300 and 1200 epochs for FemtoDet*, such a longer epochs do not yield better gains. 2) The fourth and fifth rows present FemtoDet* was trained with RecWR and 300 epochs with the enhancement of IBE, respectively. Results show that independently equipping IBE and RecWR can improve model performance. 3) The six rows demonstrate that jointly using IBE and RecWR enables FemtoDet to achieve the best performance.
+
+# 5. Conclusion
+
+This paper presented a baseline to encourage the research on energy and performance balance detectors. Our experimental results clearly showed that boosting performance can also cause problem of growth in energy consumption. Conversely, the simple components like ReLU are suitable for building energy-oriented detectors. In addition, we also proposed a novel IBE module and RecWR training strategy to overcome the optimization problem of extremely lightweight detectors. Compared to other state-of-the-art methods under the same parameters setting, IBE and RecWR support these baselines achieving the best performance on VOC, COCO, and TJU-DHD datasets, while consuming the
+
+least energy. In the future, we will continue improving the detectors on the balance of energy and performance.
+
+# References
+
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\ No newline at end of file
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+                                    "content": "Efficient detectors for edge devices are often optimized for parameters or speed count metrics, which remain in weak correlation with the energy of detectors. However, some vision applications of convolutional neural networks, such as always-on surveillance cameras, are critical for energy constraints. This paper aims to serve as a baseline by designing detectors to reach tradeoffs between energy and performance from two perspectives: 1) We extensively analyze various CNNs to identify low-energy architectures, including selecting activation functions, convolutions operators, and feature fusion structures on necks. These underappreciated details in past work seriously affect the energy consumption of detectors; 2) To break through the dilemmacatic energy-performance problem, we propose a balanced detector driven by energy using discovered low-energy components named FemtoDet. In addition to the novel construction, we improve FemtoDet by considering convolutions and training strategy optimizations. Specifically, we develop a new instance boundary enhancement (IBE) module for convolution optimization to overcome the contradiction between the limited capacity of CNNs and detection tasks in diverse spatial representations, and propose a recursive warm_restart (RecWR) for optimizing training strategy to escape the sub-optimization of light-weight detectors by considering the data shift produced in popular augmentations. As a result, FemtoDet with only 68.77k parameters achieves a competitive score of 46.3 AP50 on PASCAL VOC and 1.11 W & 64.47 FPS on Qualcomm Snapdragon 865 CPU platforms. Extensive experiments on COCO and TJUDHD datasets indicate that the proposed method achieves competitive results in diverse scenes."
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+                                    "content": "consistently reduce parameters and speed counts for improving accuracy. However, these metrics are not correlated well with the efficiency of the models in terms of energy. Evaluation metrics, such as parameters, do not take into account the energy cost of models, resulting in a nontrivial effect on the energy cost of detectors. Compared with the same architecture, the parameters of models are positively correlated with their energy cost (shown in Table 2). However, in the case of equal model parameters, their energy consumption may be negatively correlated or even irrelevant to the model parameters (shown in Table 1). Considering that various activation functions, convolution operators, and feature fuse structures may not increase model parameters, but generate more energy costs. Similarly, the speed count is also not well correlated with energy, as it can be optimized by the degree of parallelism. These disconnections will leave customized efficient detectors unavailable, when they are deployed under severe energy constraints like the always-on surveillance cameras."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "This paper aims to reduce the energy costs of efficient object detectors, while improving their performances by achieving energy versus performance tradeoffs. Specifically, these bottlenecks fall into several categories:"
+                                }
+                            ]
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+                                    "content": "1) Detector components with unknown energy. Most current object detection methods focus either on latency-oriented [5, 34, 44] or accuracy-oriented [9, 38, 32, 36] works. There are very limited works toward the energy cost of the detector components, which is the first obstacle to designing energy-performance-balanced detectors. To identify energy-efficient components of detectors, we followed [42] to benchmark their energy metrics from three types of structures, i.e., activation functions, convolution operators, and necks of detectors. The following finding is acquired: Firstly, some activation functions have been widely used, because of their ability to improve models without adding more parameters. They have increased costs, yet received very limited attention. As shown in Table 1, we set ReLU [1] based models as a baseline. When replacing the ReLU with the GELU [16], "
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+                                    "content": " performance is gained, while "
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+                                    "content": " energy cost is increased, and the corresponding factor of the mean energy versus the perfor"
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+                                    "type": "text",
+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "*Corresponding author; First author's Email: yh.peng.tu@gmail.com"
+                                }
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+                                    "type": "text",
+                                    "content": "mance tradeoffs (Eq. 1) drops "
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+                                    "content": ". In addition, although large kernel convolutions [25] can improve models (Table 2), the increased energy cost is unacceptable. As seen in Table 2, the large kernel convolutions are equipped to enable the model to rise by around "
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+                                    "content": " in performance, but with more energy costs "
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+                                    "content": " than in the small kernel size of convolutions (shown in the second row of Table 2). Finally, the standard FPN [21, 22, 39, 10, 37] in the detectors also causes significant energy costs. We observe that this situation is happened due to multi-feature fusion paths following either bottom-to-up or top-to-down way, resulting in frequent data reading in memory for data coverage. However, it is shown that the up-down fusion between multi-features may not necessary. As shown in Table 3, we propose a simple SharedNeck for replacing FPN to reduce around "
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+                                    "type": "text",
+                                    "content": " energy costs, while obtaining "
+                                },
+                                {
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+                                    "content": " performance gains. SharedNeck uses an adaptive fusion between multi-features by learning convolution, instead of feature-by-feature bottom-to-up or top-to-down fusions, as operated in FPN. Based on these analyses, we further build upon a low-energy detector, named FemtoDet. Surprisingly, FemtoDet just has "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "68.77\\mathrm{k}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " parameters and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "1.1\\mathrm{W}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " power on the platform. 2) Optimization for CNN is another bottleneck, since obtaining a favorable detector is very challenging, especially for a small number of parameters. Light-weight detectors are restricted by their limited capacities [6], which will cause obfuscation on feature maps of the instances' boundaries of interesting objects, as shown in Figure 2 (b). Ambiguous instance boundaries on the features may raise the risk of false detection in the models. For this problem, we propose a novel instance boundary enhancement module (IBE), which emphasizes the potential of the object boundary information: The parameter reuse mechanism is first applied to integrate local descriptors with convolution operation to make robust and diverse instance boundary feature representation. But this operation would cause feature un-alignment between normal features and integrated features. Then, in order to sufficiently exploit these two types of features, we design dual-normalization in IBE, as to realign the features (Fig. 4 of the Appendix). IBE employs a shared convolution yet an independent batch normalization layer for separate normalization is also adopted. Finally, we add normal and integrated features together behind the dual-normalization layer. IBE provides a novel form of parameter reuse to generate new local descriptors from shared convolution operators. This method can capture object boundary information by integrating gradient cues around the learned convolution. After trained, IBE modules can be folded into simple convolution operators, thus requiring no extra computations anymore; In addition, data augmentation is a common approach for efficient detector training. Using well-designed strong augmentations is conducive to improving the generalization of mod"
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+                                    "content": "els [31, 9]. However, how to prevent data shifts between training and validation images has not been explored, while training data suffers strong augmentations. It is found that the produced data shifts by strong augmentations would prevent light-weight detectors from moving toward global optimization. A common view is that strong image augmentations can effectively encourage networks to learn diverse features [11]. But for light-weight detectors, these diverse features cannot assist the models in making better generalizations in the validation set. In other words, light-weight detectors are more susceptible to these ignored data shifts because of their limited capacities. Furthermore, we propose an effective training strategy, namely recursive warm-start (RecWR), to adapt these diverse features to improve the model's generalization. RecWR works based on multistage training while gradually weakening data augmentation strength. This method can help the limited-capacity detectors jump out of local optima under the assistance of high-dimension & diverse features. The effectiveness of the IBE and RecWR has been evaluated on PASCAL VOC dataset. And the experimental results show that IBE can improve FemtoDet "
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+                                    "type": "text",
+                                    "content": " performance, while incurring no extra parameter burdens, as compared to the original architecture; RecWR can improve FemtoDet "
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+                                    "type": "text",
+                                    "content": " performance by gradually weakening the data augmentation strength in multi-stage learning. By jointly training FemtoDet with IBE and RecWR, our proposed methodology can go over the YOLOX [9] by "
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+                                    "type": "text",
+                                    "content": " in performance when using the same-level parameters."
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+                    ],
+                    "index": 1
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+                                    "type": "text",
+                                    "content": "Something worth mentioning is that FemtoDet is specially designed for hierarchical intelligent chips to enable always-on alerts: the always-on low power, high-recall, and decent accuracy - it achieved 85.8 AR20 & 76.3 AP20 (Table 7) while performing pedestrian detection on TJU-DHD. In addition, FemtoDet is poor in detecting small objects but is excellent in detecting medium and large objects, which they are more interested in, with 88.8 AR20-m & 94.1 AP20-m / 95.3 AR20-1 & 98.6 AP20-1 (Table 7) on TJU-DHD. Information can be passed to other models after identifying possible objects of interest, and high-precision robust models are then initiated for accurate recognition. The always-on smart products have a wide range of applications, e.g., in-home monitoring or robots. Hence, the loose metric (e.g., AP50 or AP20) and data scenario with moderate difficulty (e.g., VOC) can well reflect the application ability of FemtoDet. Further, the experiments on COCO datasets have verified that the proposed method is suitable for diverse scenarios resulting in competitive results."
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+                                    "content": "2. Related Works"
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+                                    "content": "2.1. Object Detection"
+                                }
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+                                    "type": "text",
+                                    "content": "Object detection is a classic computer vision task for identifying the category and location of object in pictures"
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+                                    "type": "text",
+                                    "content": "or videos. The existing object detectors can be divided into two categories: two-stage detectors and one-stage detectors. Two-stage detectors [32, 36, 14, 21] are anchor-based devices that generate region proposals from the image and then produce the final prediction boxes from these proposals. Further, FPN [21] improves the two-stage detectors by fusing multi-level features. Despite their higher accuracy compared to the one-stage detectors, two-stage detectors are still difficult to achieve low latency when deployed on edge devices."
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+                                    "type": "text",
+                                    "content": "Specifically, there are two types of one-stage detectors: anchor-based and anchor-free, which depends on anchor priors injecting into whole images to enable box regression. SSD [23], as a classical anchor-based one-stage detector, discretizes the output space of bounding boxes into a set of default anchors with different aspect ratios and scales per feature map location. This operation helps detecting tiny objects. Another typical anchor-based detector is the YOLO series [30, 31, 4]. YOLOv2 [30] explores bag of freebies to improve the performances of one-stage detectors. YOLOv3 [31] proposes cross-scale features and novel nms (Non-Maximum Suppression) to obtain more confident predictions. YOLOv4 [4] finds that the repeated gradient of network optimization aggravates detector latency, and thus designs Cross-Stage-Partial-connection modules to reduce the latency of detectors while maintaining detection performance. Anchor-free detectors [29, 9, 19, 38] aim to eliminate the pre-defined set of anchor boxes. YOLO [29], as an anchor-free one-stage detector, divides an image into multiple grids and predict boxes at grids near the object's center. CornerNet [19] detects an object as a pair of key points (through the top-left corner and bottom-right corner of the bounding box). A single convolutional network was leveraged in CornerNet to predict a heatmap for all top-left corners of instances of the same object category, a heatmap for all bottom-right corners, and an embedding vector for each detected corner. Indeed, CornerNet is a new pipeline for object detection. FCOS [38] eliminates the anchor setting by proposing a fully convolutional one-stage object detector, which can solve object detection in a per-pixel prediction manner. The anchor-free detectors solve the problem happened in anchor-based detectors, which reduce the memory cost and increase accuracy of the bounding box."
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+                                    "type": "text",
+                                    "content": "Both one-stage and two-stage object detection methods have obtained high performance on many challenging public datasets, i.e., COCO and TJU-DHD [27]. These methods provide the accuracy-oriented detectors. However, the critical problem for detectors serving edge devices is detection latency and its power. In other words, detectors obtain higher performance in challenging scenes, which is not a necessary option for detectors deployed on edge devices. For the detection latency, a lot of effort [5, 34, 44] have been devoted to achieving the balance between accuracy"
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+                                    "type": "text",
+                                    "content": "and efficiency. FastYOLO [34] is an optimized architecture extended from YOLOv2 with fewer parameters and "
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+                                    "type": "text",
+                                    "content": " performance drop, which makes FastYOLO run at an average of "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 18"
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+                                    "type": "text",
+                                    "content": " FPS on an Nvidia Jetson TX1 embedded system. YOLObite [5] focuses on pruning redundancy object detectors to be real-time by designing in a compression- compilation way. NanoDet uses ShuffleNetV2 [26] as its backbone to make the model lighter, and further uses ATSS [47] and GFL [20] to improve its accuracy. It is worth noting that NanoDet also reached "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 60"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " FPS on an ARM CPU. These light-weight detectors are latency-oriented. Actually, neither accuracy-oriented nor latency-oriented detectors take their energy cost into account. High energy cost detectors are unfriendly to devices deployed at edges."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "This paper aims to develop a light-weight detector that can achieve tradeoffs between energy and performance."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "2.2. Energy-Oriented Convolutional Neural Networks"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Besides the manual design of deep neural networks, a great deal of work has been done to improve the effectiveness and efficiency of deep neural networks via network pruning [45], quantization [13, 2], architecture search [12, 40]. ECC [42] proposes the end-to-end classifier training framework, which provides quantitative energy consumption guarantees by using weighted sparse projection and input masking. Zhang et al. [46] specialized in video broadcast and leveraged distillation techniques to reduce memory consumption by approximating the video frame data. MIME [3] is an algorithm-hardware co-design approach that reuses the weight parameters of a trained parent task and learns task-specific threshold parameters for inferring on multiple child tasks. However, the above works are all in service for image classification, and we can observe that fewer parameters represent lower energy costs in the same architecture. Object detection on edge devices is still a challenging topic, considering that the conflict between the limited capacity of CNNs and diverse spatial representations. This paper is the first work to provide a systematized solution for energy-oriented light-weight detectors."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. FemtoDet"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "This section will be divided into two subsections to describe how FemtoDet achieves energy versus performance tradeoffs. 1) Benchmarks for Low-energy Detectors: We provide benchmarks for designing low-energy detectors, including the exploring of activation functions, convolution operators, and neck of detectors. 2) Energy-Oriented FemtoDet: Based on the benchmarks for designing low-energy detectors, an energy-oriented light-weight detector named FemtoDet is provided, which stacks layers from depthwise separable convolutions (DSC), BN and ReLU. FemtoDet involves only "
+                                },
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+                                    "content": "68.77\\mathrm{k}"
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+                                    "type": "text",
+                                    "content": " parameters and power of "
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+                                    "type": "inline_equation",
+                                    "content": "1.11\\mathrm{W}"
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+                                {
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+                                    "type": "text",
+                                    "content": " on"
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+                                    "type": "text",
+                                    "content": "the Qualcomm Snapdragon 865 CPU platform. Moreover, FemtoDet can be optimized with two designs: Firstly, instance boundary enhancement (IBE) modules are used to improve the DSC in FemtoDet, overcoming the bottleneck of light-weight models' representation optimization (i.e., models will learn obfuscation features because of their limited capacity, as shown in Fig. 2(b)). Second, the recursive warm_restart (RecWR) training strategy is a multi-stage recursive warm_restart learning procedure, which can surmount data shifts produced from strong data augmentations."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "3.1. Benchmarks for Low-energy Detectors' Designing"
+                                }
+                            ]
+                        }
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+                                    "content": "3.1.1 Evaluation Metrics"
+                                }
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+                                    "type": "text",
+                                    "content": "Top1-Acc (top1 accuracy, for image classification), and AP (average precision, for object detection) are widely used measures to evaluate the performance of CNN. In addition to the commonly used metrics top1 - Acc and AP, we propose the Power (energy costs) and mEPT (mean energy versus performance tradeoffs) to comprehensively evaluate the energy costs of the models and their ability to achieve energy versus performance tradeoffs. Specifically, Power and mEPT are represented by"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {m E P T} = \\left(\\frac {1}{\\mathrm {N}} \\sum_ {\\mathrm {i}} ^ {\\mathrm {N}} \\mathrm {P}\\right) / (\\text {P o w e r}), \\tag {1}",
+                                    "image_path": "5ee9a09d0fd995cdfae45fc42e7e3e70d642fbb9f9601b1f24c7b950fdf19409.jpg"
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\text {s . t .} \\quad \\operatorname {P o w e r} = \\frac {1}{\\mathrm {T} _ {\\text {t i m e}}} \\sum_ {\\mathrm {i}} ^ {\\mathrm {N}} \\left(\\varepsilon \\left(\\mathbf {W}, \\mathrm {x} _ {\\mathrm {i}}\\right) - \\varepsilon \\left(\\hat {\\mathbf {W}}, \\mathrm {x} _ {\\mathrm {i}}\\right)\\right), \\tag {2}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{T}_{\\mathrm{time}}"
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+                                    "type": "text",
+                                    "content": " indicates the total times required to evaluate "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{N}"
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+                                    "type": "text",
+                                    "content": " images, "
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+                                    "type": "inline_equation",
+                                    "content": "\\varepsilon(\\mathbf{W}, \\mathrm{x_i})"
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+                                {
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+                                    "type": "text",
+                                    "content": " represents the energy costs while models evaluate i-th image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{x_i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with trained parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\varepsilon(\\hat{\\mathbf{W}}, \\mathrm{x_i})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is similar to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\varepsilon(\\mathbf{W}, \\mathrm{x_i})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The difference is that we set a value of 1 for each layer of channels, where the model parameter is "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{W}}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
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+                                        289,
+                                        596
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\varepsilon(\\hat{\\mathbf{W}}, \\mathrm{x_i})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " indicates that the model is an empty state. P denotes the model performance (top1-Acc for image classification while evaluating activation functions and convolution operators, AP50 for object detection while evaluating necks of detectors in Sec. 3.1.2) in image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{x_i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". For the power metric, the value is expected to be as small as possible. For the mEPT metric, the result is expected as greater as possible."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "content": "3.1.2 Components to Be Evaluated"
+                                }
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+                    "index": 7
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+                {
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+                                    "type": "text",
+                                    "content": "To identify low-energy components of detectors, we followed [42] to benchmark their energy costs from three types of structures: activation functions, convolution operators and necks of detectors:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Activation Functions. Rectified Linear Unit (ReLU) [29, 23], GELU [16], Swish [9], SiLU [8], and etc. are widely used for object detection because they have fewer"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                {
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+                                    "type": "text",
+                                    "content": "parameters and flops. We calculate the energy costs of different activation functions in the same architecture to explore which activation function is more friendly for designing an energy-oriented detector."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Convolution Operators can automatically learn fiber weights while CNNs are trained to summarize helpful information, including horizontal, vertical, edged, diagonal, and etc. features from images. Vanilla convolutions (van-Conv) [18], depthwise separable convolutions (DSC) [17] and their large kernel size versions [25] are widely used. Ding et al. [7] pointed out that when CNNs are constructed based on enough large convolution kernels, results can be comparable to the transformer [24]. Here, we set up energy consumption comparison experiments with different convolutions (vanCon and DSC) and multi-scale convolution kernel sizes "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(3\\times 3"
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "5\\times 5)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " on different network structures (ResNet and MobileNetV2). It is important that for each experiment case, the convolution operator type or kernel size would be the only variable."
+                                }
+                            ]
+                        }
+                    ],
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+                                            "content": "(c) FemtoDet"
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+                                    "type": "text",
+                                    "content": "as depthwise convolution, in practice, the original difference convolution architecture cannot serve for high-level semantic tasks. We observe that features obtained by the difference convolution are unaligned with the features obtained by standard convolution (the figure shown in Fig. 4 of the Appendix). On the one hand, the difference convolution captures diverse information about object boundaries by integrating gradient cues around "
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+                                    "content": " or with larger convolution. On the other hand, high-level tasks encourage standard convolution to summarize the abstract semantic information of images. That is the reason that the classical difference convolution cannot serve high-level tasks. To simultaneously solve this problem, we propose a semantic projector and a dual-normalization layer. The semantic projector is the linear transformation of depthwise convolution to transfer operators related to semantic information extraction; The dual-normalization layer consists of two independent batch normalization modules specifically designed for aligning the unaligned features. After that, we incorporate the object boundary cues from the feature addition between the local descriptor and depthwise convolution to guide the model in learning an effective representation of the instance (refined results can be seen in Fig. 2 (c))."
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+                                    "content": " represents the output channel dimension, the weight matrix can be denoted as "
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+                                    "content": "\\mathbf {W} _ {\\text {d e s}} = - \\theta_ {1}. \\sum_ {\\mathrm {p} _ {\\mathrm {n}} \\in \\mathbf {R}} \\mathbf {W} _ {\\text {c o n v}} \\left(\\mathrm {p} _ {\\mathrm {n}}\\right), \\tag {3}",
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+                                    "type": "text",
+                                    "content": " is the n-the weight value. Integrating the gradient cues around "
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+                                    "content": " can help the local descriptors capture the object boundary information effectively. The semantic projector is generated from the depthwise convolution, while diverse semantic presentations can be obtained through a learnable linear transformation, shown as follows:"
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+                                    "content": "\\mathbf {W} _ {\\text {p r o}} = \\theta_ {2}. \\mathbf {W} _ {\\text {c o n v}}, \\mathbf {W} _ {\\text {p r o}} \\in \\mathbb {R} ^ {C _ {\\text {o u t}} \\times C _ {\\text {i n}} \\times 3 \\times 3}, \\tag {4}",
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+                                    "type": "text",
+                                    "content": " is another learnable parameter as the projection factor. Subsequently, the IBE modules perform four steps to refine the feature representation under the guidance of object boundary information. 1) inputs "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", respectively; 2) elements addition are conducted between "
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+                                    "type": "text",
+                                    "content": "; 3) the dual-normalization layer enables feature distribution normalization on "
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+                                {
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+                                    "type": "inline_equation",
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": "; 4) the two outputs from the dual-normalization layer can be added together; As a result, the aforementioned added features are convolved through pointwise convolution as the final output of the IBE module."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In addition, we leverage the homogeneity and additivity of the convolutions to fold IBM modules into the simpler depthwise separable convolution in the inference stage without performance degradation. The details can be seen in Appendix C."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.3. Recursive Warm-restart Training Strategy"
+                                }
+                            ]
+                        }
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+                                    "content": "Strong augmentations (SA) are widely used for object detection, and [9, 31] shows well-designed SA effectively improves detectors. However, we find that well-designed SA does not always benefit light-weight detectors, because the current training strategies cannot sufficiently exploit diverse training representations to boost the generalization ability on real validation data. For example, YOLOX [9] points out MixUp reduces YOLOX-nano's performance by about "
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+                                    "content": ". We argue that the limited capacity detectors fit the diverse data generated by SA as much as possible during training, such that the modules have no surplus capacity to adjust learned features to boost the generalization ability of modules on real validation data. In other words, SA produces diverse representations that are equal to the data"
+                                }
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+                                    "type": "text",
+                                    "content": "shifts, thus breaking the generalization ability of the module. We also propose an effective training strategy to adjust these diverse features to improve the generalization ability, namely recursive warm_restart (RecWR)."
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+                                    "content": "As shown in Fig. 5 of the Appendix, the whole training procedure can be divided into four stages. Starting from the 1-st stage to 4-th stage training, the intensity of image augmentations gradually decreases. Specifically, in the 1-st training stage, some SA types will be combined, such as MixUp, Mosaic, and RandomAffine. Starting from the 2-nd training stage, the above SA types are gradually unloaded in each training stage, until the 4-th training stage. For the last training stage, only the random flip and random scales are performed on the training data. In addition, before starting each training stage, the waiting training detectors load the trained weights of the previous training stage as the initialization."
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+                                    "content": "We can see that in Appendix D, after training FemtoDet with RecWR, MixUp also help such extremely small detectors obtain better performance. In other words, RecWR takes advantage of diversity features learned from SA to get FemtoDet out of sub-optimization."
+                                }
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+                                    "content": "4. Experiments"
+                                }
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+                                    "content": "We used VOC, COCO, TJU, and ImageNet datasets to conduct experiments and validate the proposed method. Specifically, whole experiments can be divided into two sections, i.e., identifying low-energy components of detectors mentioned in Sec. 3.1.2, and validating the effectiveness of our designed FemtoDet, where the Power metric was measured in GTX 3090."
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+                                    "type": "text",
+                                    "content": "Table 1: Comparisons of energy-related metrics in MobileNetV2 0.25 (MBV2) [33] used different activation functions. We trained a classifier on ImageNet to evaluate relevant metrics."
+                                }
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+                                            "html": "<table><tr><td>Activation Functions</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td>ReLU [1]</td><td></td><td>5.04</td><td>45.22</td><td>8.97</td></tr><tr><td>GELU [16]</td><td></td><td>5.67</td><td>47.21</td><td>8.33</td></tr><tr><td>Swish [9]</td><td>1.48</td><td>5.47</td><td>47.45</td><td>8.67</td></tr><tr><td>HSwish [44]</td><td></td><td>5.33</td><td>47.60</td><td>8.93</td></tr><tr><td>SiLU [8]</td><td></td><td>5.73</td><td>47.25</td><td>8.25</td></tr></table>",
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+                                    "content": "4.1. Benchmark to Find Low-energy Components"
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+                                    "content": "4.1.1 Activation Functions"
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+                                    "type": "text",
+                                    "content": "Table 1 shows the energy-related metric results using different activation functions under the same architecture (MobileNetV2 0.25). We observe that the activation functions can significantly improve models without extra parameters (Param). On the other hand, such activation functions incur"
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+                                    "type": "text",
+                                    "content": "unacceptable overhead on some metrics which are inconvenient to measure. For example, Swish improves ReLU-based models performance by "
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+                                    "content": " more energy cost. The mEPT metric also demonstrate that ReLU results in the best energy versus performance tradeoffs."
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+                                    "type": "text",
+                                    "content": "Table 2: Comparisons of energy-related metrics in MobileNetV2 0.75 and ResNet18 [15]. The two CNNs can present the two typical convolution operators: vanilla convolutions and depthwise separable convolutions. We compare different convolution operators with different kernel sizes on the same convolution operators. Here, "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " indicate two kernel sizes of "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "content": "5 \\times 5"
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+                                    ],
+                                    "type": "text",
+                                    "content": ". In this experiment, we also evaluate models by training them on ImageNet."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                            "html": "<table><tr><td>CNNs</td><td>Convolution Operators</td><td>Param (M)</td><td>Power (W)</td><td>Top1 (Acc)</td><td>mEPT</td></tr><tr><td rowspan=\"2\">Res18</td><td>vanConv♣</td><td>12.46</td><td>170.64</td><td>69.93</td><td>0.41</td></tr><tr><td>vanConv◇</td><td>31.99</td><td>198.28</td><td>71.24</td><td>0.36</td></tr><tr><td rowspan=\"2\">MBV2</td><td>DSC♣</td><td>2.29</td><td>5.56</td><td>69.51</td><td>12.50</td></tr><tr><td>DSC◇</td><td>2.35</td><td>6.07</td><td>70.96</td><td>11.69</td></tr></table>",
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+                                    "content": "4.1.2 Convolution Operators"
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+                                    "type": "text",
+                                    "content": "This sub-section compares energy-related metrics while training an image classifier on the ImageNet dataset based on the different convolution operators (vanCon and DSC), and the different kernel sizes "
+                                },
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " on the same convolution operator. Experimental results in Table 2 show that: 1) When CNNs were constructed with the same kernel size, mobilenetv2 generated much lower energy costs than resnet18, as shown in Table 2 of vanConv and DSC. In other words, DSC is more energy friendly than vanConv while achieving similar performance; 2) When CNNs were constructed with different kernel sizes and the same types of operators, the smaller kernel generated much lower energy costs than the larger kernel, as shown in Table 2 of vanConv and vanConv. However, the performance gain from the large kernels is not so impressive."
+                                }
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+                                    "type": "text",
+                                    "content": "4.1.3 Necks of Detectors"
+                                }
+                            ]
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+                    "index": 5
+                },
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+                                    "type": "text",
+                                    "content": "Here we evaluated the effects of different necks (including FPN, PAN, and SharedNeck) in FemtoDet. Experimental results are shown in Table 3, and some observation are summarized as follow: 1) Although FPN enables FemtoDet to achieve preferable results, it not only consumes more energy but also has a large parameter overhead; 2) Due to the limited representation of light-weight models, the top-down and bottom-up feature fusion of PAN is poor; 3) SharedNeck achieves the best results in the metrics of parameter, energy cost, object detection performance, and factors of"
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+                                    "type": "text",
+                                    "content": "mean energy versus performance tradeoffs by performing adaptive feature fusion."
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+                                            "content": "Table 4: PASCAL VOC object detection results with YOLOX, NanoDet Plus, and FemtoDet."
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+                                            "content": "Table 5: Inference speed (FPS) and power of trained detectors (YOLOX, NanoDet Plus, and FemtoDet were trained on PASCAL VOC) on Qualcomm Snapdragon 865 CPU platforms."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Param (k)</td><td rowspan=\"2\">AP50</td><td colspan=\"2\">Inference</td></tr><tr><td>Power (W)</td><td>FPS</td></tr><tr><td>YOLOX</td><td>70.39</td><td>30.60</td><td>1.41</td><td>38.04</td></tr><tr><td>NanoDet Plus</td><td>69.60</td><td>38.44</td><td>1.37</td><td>47.80</td></tr><tr><td>FemtoDet</td><td>68.77</td><td>46.31</td><td>1.11</td><td>64.47</td></tr></table>",
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+                                    "content": "4.2. Validating the Effectiveness of FemtoDet"
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+                                    "content": "We verify the effectiveness of FemtoDet on three datasets: PASCAL VOC, COCO, and TJU-DHD, while resizing inputs to "
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+                                    "content": " for training and resizing inputs to "
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+                                    "content": " for validating. Two datasets, PASCAL VOC and TJU-DHD two datasets are converted to the COCO data types for evaluation. In addition, we extract campus data from the TJU-DHD dataset to evaluate the pedestrian detection performance of our proposed extremely light detector, i.e., FemtoDet. Considering extremely light-weight detectors are challenging to fit the complex COCO dataset with poor detection performance, we pull the corresponding results to Appendix E. Also, we compare the detection performance of FemtoDet with YOLOX, and NanoDet Plus [28], in which they are at the same parameter level to ensure fairness. All the detector backbones are pretrained on the Ima"
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+                                    "content": "geNet for 100 epochs, and the metric of mEPT presented in this section is calculated between AP50 and Power."
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+                                    "content": "Experimental results are presented in Table 4, which shows light-weight detectors with eight metrics: parameter (Param), energy cost (Power), AP50, factors of mean energy versus performance tradeoffs (mEPT), mAP, mAP of small size objects (mAP-s), mAP of medium size objects (mAP-m), and mAP of large size of objects (mAP-1) respectively. We can see that although YOLOX has a large number of parameters, it is much lower than FemtoDet in many metrics. NanoDet Plus has the parameter comparable to that of FemtoDet, but only outperforming FemtoDet in the metrics of mAP-s. We believe that for such extremely light-weight detectors, their performances on large-scale objects are the most critical. FemtoDet also presented better results than YOLOX and NanoDet Plus on the metrics of mAP-1. Although the metrics i.e. mEPT, used to evaluate performance and energy balance, FemtoDet achieves the best balance compared to the other two models."
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+                                    "content": "In addition, we evaluated the inference speed (FPS) and power of trained detectors on Qualcomm Snapdragon 865 CPU platforms. As shown in Tab. 5, our FemtoDet also achieves the smallest energy costs and inference speed on edge devices."
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+                                            "content": "Table 6: TJU-DHD pedestrian detection results with YOLOX, and FemtoDet."
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+                                            "html": "<table><tr><td>Methods</td><td>Param (k)</td><td>Power (W)</td><td>AP50</td><td>mEPT</td></tr><tr><td>YOLOX</td><td>67.37</td><td>9.85</td><td>59.40</td><td>6.03</td></tr><tr><td>FemtoDet</td><td>67.54</td><td>6.92</td><td>66.90</td><td>9.67</td></tr><tr><td>Methods</td><td>mAP</td><td>mAP-s</td><td>mAP-m</td><td>mAP-l</td></tr><tr><td>YOLOX</td><td>29.00</td><td>11.50</td><td>37.60</td><td>54.20</td></tr><tr><td>FemtoDet</td><td>33.10</td><td>17.60</td><td>50.20</td><td>61.50</td></tr></table>",
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+                                    "content": "Extremely light-weight detectors like FemtoDet have broad application prospects in surveillance scenarios. Hence, we"
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+                                    "content": " AP20."
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+                                            "content": "Table 8: Ablation study on the effectiveness of our IBE modules and RecWR training strategy. Where FemtoDet* denotes FemtoDet consists of pure DSC without the enhancement of IBE, 300e and 1200e mean the detector training with the same data augmentation with 300 or 1200 epochs."
+                                        }
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+                                            "html": "<table><tr><td>\\</td><td>IBE</td><td>RecWR</td><td>300e</td><td>1200e</td><td>AP50</td></tr><tr><td rowspan=\"5\">FemtoDet*</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>42.50</td></tr><tr><td>X</td><td>X</td><td>X</td><td>✓</td><td>42.11</td></tr><tr><td>X</td><td>✓</td><td>X</td><td>X</td><td>45.13</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>X</td><td>45.78</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>X</td><td>46.31</td></tr></table>",
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+                                    "content": "4.2.3 Ablation Studies"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We conduct a series of ablation studies on PASCAL VOC to demonstrate the effectiveness and efficiency of our IBE modules and RecWR training strategy. As shown in Table 8: 1) The second and third rows present that by training with 300 and 1200 epochs for FemtoDet*, such a longer epochs do not yield better gains. 2) The fourth and fifth rows present FemtoDet* was trained with RecWR and 300 epochs with the enhancement of IBE, respectively. Results show that independently equipping IBE and RecWR can improve model performance. 3) The six rows demonstrate that jointly using IBE and RecWR enables FemtoDet to achieve the best performance."
+                                }
+                            ]
+                        }
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+                                    "content": "5. Conclusion"
+                                }
+                            ]
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "This paper presented a baseline to encourage the research on energy and performance balance detectors. Our experimental results clearly showed that boosting performance can also cause problem of growth in energy consumption. Conversely, the simple components like ReLU are suitable for building energy-oriented detectors. In addition, we also proposed a novel IBE module and RecWR training strategy to overcome the optimization problem of extremely lightweight detectors. Compared to other state-of-the-art methods under the same parameters setting, IBE and RecWR support these baselines achieving the best performance on VOC, COCO, and TJU-DHD datasets, while consuming the"
+                                }
+                            ]
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+                    ],
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+                                    "content": "least energy. In the future, we will continue improving the detectors on the balance of energy and performance."
+                                }
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+                                    "type": "text",
+                                    "content": "References"
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+                                        }
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+                                        }
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+                                            "content": "[47] Shifeng Zhang, Cheng Chi, Yongqiang Yao, Zhen Lei, and Stan Z Li. Bridging the gap between anchor-based and anchor-free detection via adaptive training sample selection. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9759-9768, 2020. 3"
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diff --git a/2023/FerKD_ Surgical Label Adaptation for Efficient Distillation/37537680-ebe0-4e37-b920-5de9f0458feb_content_list.json b/2023/FerKD_ Surgical Label Adaptation for Efficient Distillation/37537680-ebe0-4e37-b920-5de9f0458feb_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..3216cd1cf7d4467db888d35bddb01c13ab507a27
--- /dev/null
+++ b/2023/FerKD_ Surgical Label Adaptation for Efficient Distillation/37537680-ebe0-4e37-b920-5de9f0458feb_content_list.json	
@@ -0,0 +1,1743 @@
+[
+    {
+        "type": "text",
+        "text": "FerKD: Surgical Label Adaptation for Efficient Distillation",
+        "text_level": 1,
+        "bbox": [
+            184,
+            130,
+            782,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zhiqiang Shen  \nMohamed bin Zayed University of AI",
+        "text_level": 1,
+        "bbox": [
+            334,
+            181,
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+            215
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zhiqiang.Shen@mbzuai.ac.ae",
+        "bbox": [
+            367,
+            219,
+            599,
+            232
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            268,
+            313,
+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present FerKD, a novel efficient knowledge distillation framework that incorporates partial soft-hard label adaptation coupled with a region-calibration mechanism. Our approach stems from the observation and intuition that standard data augmentations, such as RandomResized-Crop, tend to transform inputs into diverse conditions: easy positives, hard positives, or hard negatives. In traditional distillation frameworks, these transformed samples are utilized equally through their predictive probabilities derived from pretrained teacher models. However, merely relying on prediction values from a pretrained teacher, a common practice in prior studies, neglects the reliability of these soft label predictions. To address this, we propose a new scheme that calibrates the less-confident regions to be the context using softened hard groundtruth labels. Our approach involves the processes of hard regions mining + calibration. We demonstrate empirically that this method can dramatically improve the convergence speed and final accuracy. Additionally, we find that a consistent mixing strategy can stabilize the distributions of soft supervision, taking advantage of the soft labels. As a result, we introduce a stabilized SelfMix augmentation that weakens the variation of the mixed images and corresponding soft labels through mixing similar regions within the same image. FerKD is an intuitive and well-designed learning system that eliminates several heuristics and hyperparameters in former FKD solution [37]. More importantly, it achieves remarkable improvement on ImageNet-1K and downstream tasks. For instance, FerKD achieves  $81.2\\%$  on ImageNet-1K with ResNet-50, outperforming FKD and FunMatch by remarkable margins. Leveraging better pre-trained weights and larger architectures, our finetuned ViT-G14 even achieves  $89.9\\%$ . Our code is available at https://github.com/szq0214/FKD/tree/main/FerKD.",
+        "bbox": [
+            75,
+            300,
+            473,
+            815
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            209,
+            859
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Knowledge Distillation (KD) [13] has achieved impressive results in various visual domains, including image clas",
+        "bbox": [
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+            468,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/2dc141956ee2cdcd7eb9e2066301851c8715beab6781c64d501b796eeebfaed5.jpg",
+        "image_caption": [
+            "Input",
+            "Center points of RandomResizedCrop"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            268,
+            638,
+            354
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/0e6289ac43ed195e159541c09e247303993711d5e89ec14074bd58c254e161b0.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/0d7c3b965a52e8c9e0c5072206e522f9a58641e5ae845ee6db9a427f9332d914.jpg",
+        "image_caption": [
+            "$\\pmb{p} <   \\mathbf{0}$  25",
+            "Figure 1: Illustration of motivation for FerKD. The left figure depicts the original input, and the middle figure shows the center points of bounding boxes generated using RandomResizedCrop. The radius of each circle corresponds to the area of the bounding box. It can be observed that the center points of the bounding boxes are concentrated in the center of the image, and their area increases as they approach the center. The right figure displays several top and bottom confident bounding boxes and their corresponding predictive probabilities from a pre-trained teacher or teachers ensemble. The proposed hard region calibration strategy is established based on these predictions."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            756,
+            286,
+            890,
+            357
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "sification [52, 36, 5, 37], object detection [6, 46, 11, 8, 53] and semantic segmentation [22, 15, 16]. However, KD methods are often computationally expensive and inefficient due to the additional computational burden imposed by the teacher models. The primary advantage of KD that motivates its usage is its ability to generate precise soft labels that convey more informative details about the input examples. It differs from other label softening techniques, such as label smoothing [43], Mixup [58], and CutMix [56], mainly in two aspects: (1) KD generates soft labels dynamically in each iteration, which is more informative than fixed smoothing patterns used in label smoothing; (2) Mixup and CutMix techniques essentially combine hard labels with coefficients, while KD produces soft labels that are highly correlated with the input sample. This allows KD's soft labels to become more accurate when different data augmentations, such as RandomResizedCrop, flipping and rotation, color jittering, etc., are applied. In general, mixing-based label softening methods cannot monitor such changes in input content, but KD can address them effortlessly.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "1666",
+        "bbox": [
+            483,
+            945,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/3ad367eb627b6e0aca1e378e94285b5a70cf3dc79f4ada56e6b260619bd0af21.jpg",
+        "image_caption": [
+            "Figure 2: Statistics of soft label max-probability for crops on ImageNet-1K. The soft label is from FKD [37]. In each image, 500 regions are randomly cropped."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            90,
+            470,
+            196
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To overcome the computational inefficiency of traditional knowledge distillation, FKD [37] was developed to generate region-level soft labels in advance and reuse them across multiple training cycles to eliminate redundant computation. This approach only requires the preparation of soft labels once at the beginning and they can be reused indefinitely. However, this approach overlooks certain critical issues. One is the quality of the soft labels. When using RandomResizedCrop to generate regions, some may be cropped from background areas, and the teacher model will still produce a soft label for them based on their similarity to the dataset classes. However, in some cases, these areas may contain irrelevant noise, compensatory information, or context information for the class, and the soft labels may not accurately reflect the context of information they carry. To address this problem, this work proposes to recalibrate these soft labels by incorporating context information from hard ground-truth labels with smoothing.",
+        "bbox": [
+            75,
+            258,
+            472,
+            530
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, due to the random nature of the sampling process, a certain proportion of crops that are either excessively easy or difficult do not contribute to the model's learning capacity. As demonstrated in Fig. 2 and Table 1, these samples can be discarded to expedite the convergence process. The pre-generated soft labels can be utilized as useful indicators to select these specific samples. In our adaptation of surgical soft labeling, we categorize the soft labels into four distinct groups: extreme hard (negative), moderate hard (background or context), hard positive (partial object), and easy positive. Each of these categories is subject to different treatment methodologies.",
+        "bbox": [
+            75,
+            532,
+            468,
+            715
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The Role of Background. The role of the background in images is essential, as it provides critical context and spatial information that aids the model in accurately identifying objects of interest within the scene. Backgrounds can vary in complexity and structure, ranging from simple monochromatic backgrounds to highly cluttered and detailed ones. Soft labels in background areas are typically low, and therefore, it is crucial to handle the background carefully with precise supervision to achieve higher model capability within our surgical label calibration framework.",
+        "bbox": [
+            75,
+            715,
+            468,
+            867
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Hard Regions Mining and Calibration. Hard Regions Mining involves the identification and isolation of chal",
+        "bbox": [
+            76,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "table",
+        "img_path": "images/7f36f22caff6a4c0096dd81b5c3fad8f7674d684e454a6b04b28c030c50ebd1a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>range (P)</td><td>ratio</td><td>range (P)</td><td>agg. ratio</td></tr><tr><td>[0.0, 0.1)</td><td>0.43%</td><td>[0, 0.1)</td><td>0.43%</td></tr><tr><td>[0.1, 0.2)</td><td>0.89%</td><td>[0, 0.2)</td><td>1.32%</td></tr><tr><td>[0.2, 0.3)</td><td>1.29%</td><td>[0, 0.3)</td><td>2.61%</td></tr><tr><td>[0.3, 0.4)</td><td>2.03%</td><td>[0, 0.4)</td><td>4.64%</td></tr><tr><td>[0.4, 0.5)</td><td>3.66%</td><td>[0, 0.5)</td><td>8.31%</td></tr><tr><td>[0.5, 0.6)</td><td>4.35%</td><td>[0, 0.6)</td><td>12.65%</td></tr><tr><td>[0.6, 0.7)</td><td>5.04%</td><td>[0, 0.7)</td><td>17.69%</td></tr><tr><td>[0.7, 0.8)</td><td>7.76%</td><td>[0, 0.8)</td><td>25.45%</td></tr><tr><td>[0.8, 0.85)</td><td>8.14%</td><td>[0, 0.85)</td><td>33.59%</td></tr><tr><td>[0.85, 0.9)</td><td>28.73%</td><td>[0, 0.9)</td><td>62.32%</td></tr><tr><td>[0.9, 0.95)</td><td>37.34%</td><td>[0, 0.95)</td><td>99.67%</td></tr><tr><td>[0.95, 1.0)</td><td>0.33%</td><td>[0, 1.0)</td><td>100%</td></tr></table>",
+        "bbox": [
+            544,
+            87,
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+            279
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Detailed statistics of soft labels. \"range\" indicates max-probability of crops, \"ratio\" indicates the percentage in the whole crops. \"agg. ratio\" is the aggregated ratio.",
+        "bbox": [
+            498,
+            280,
+            890,
+            325
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "lenging or complex regions within an image that the model struggles to identify accurately. These regions can include objects with complex shapes, occlusions, or those with low contrast. By identifying these regions, the model can focus on learning the features and characteristics of these regions, resulting in improved performance. Calibration, on the other hand, involves adjusting the confidence levels of the model's predictions in challenging regions. The model's predictions may be less reliable in hard regions, leading to lower confidence scores. Calibrating the predictions can improve the model's accuracy in these regions by adjusting the confidence levels of the predictions. We found that carefully discarding a portion of negative crops and selecting those hard positive crops by calibrating their labels, can force the training process more efficient and effective.",
+        "bbox": [
+            496,
+            340,
+            890,
+            566
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Stable Training on Soft Labels. Mixture-based augmentations, such as Mixup and CutMix have seen widespread use for training models under hard supervision, where each image is labeled with a single class label. However, in the soft label scenario, we have made a different observation: when employed together with pre-generated soft labels on a typical ResNet, Mixup and CutMix tend to be overly strong, which, conversely, leads to decreased performance. To mitigate label fluctuations and achieve more stable training, we propose a SelfMix scheme, which is particularly suitable for cases where data augmentation should not be so strong, such as in finetuning distillation, where mixture-based augmentation is usually disabled. On the other hand, when training ViT models from scratch, stronger data augmentation can yield better results [45, 42], which is consistent with the larger capacity perspective of this type of network.",
+        "bbox": [
+            496,
+            566,
+            892,
+            809
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, our contributions of this work are:",
+        "bbox": [
+            517,
+            810,
+            831,
+            823
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We present FerKD, a sample-calibration framework for Faster Knowledge Distillation that achieves state-of-the-art performance. We conduct extensive analysis, ablation, and discussion on the impact of hard and easy samples.",
+        "bbox": [
+            498,
+            824,
+            890,
+            883
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We make two key observations in the pre-generated soft",
+        "bbox": [
+            508,
+            885,
+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "1667",
+        "bbox": [
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+            944,
+            514,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "label training framework. Firstly, we observe that the few most challenging and simplest crops obtained through the RandomResizedCrop operation do not contribute significantly to the model's learning and can therefore be removed. Secondly, we find that moderately hard crops can provide crucial contextual information that improves the model's ability to learn robust representations.",
+        "bbox": [
+            78,
+            90,
+            467,
+            195
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "- We perform extensive experiments on ImageNet-1K and downstream tasks. On ImageNet-1K, FerKD achieves an accuracy of  $81.2\\%$  using the ResNet-50. When leveraging self-supervised pre-trained weights, our larger model finetuned using ViT-G/14 achieves an accuracy of  $89.9\\%$ .",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Knowledge Distillation and Fast Knowledge Distillation. Knowledge Distillation [13] is a learning method in which a \"student\" model is trained to imitate the predictions of a larger, more complex \"teacher\" model. A key advantage of this approach is that the teacher model can provide soft supervision that contains more information regarding the input data than traditional one-hot human annotated labels, particularly when the input data is subject to data augmentation. There have been many recent variants and extensions of knowledge distillation [31, 26, 47, 59, 25, 27, 35, 7, 41, 50, 45, 18, 51], including approaches that use internal feature representations [7], adversarial training with discriminators [33], transfer learning techniques [54], fast distillation [37] via instance label preparation, and methods that prioritize patient and consistent learning [5].",
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+    },
+    {
+        "type": "text",
+        "text": "Hard Sample Mining. The aim of hard sample mining [23, 38] is to enhance the performance of learning models by selectively focusing on challenging examples that are typically difficult to classify. By prioritizing hard samples during training, models can be trained to better handle a wider range of real-world scenarios and improve their overall performance. One approach [38] to achieve this for object detection is to use Online Hard Example Mining (OHEM) which employs a strategy of selecting challenging examples during training of region-based ConvNet detectors. The motivation behind this approach is that detection datasets typically comprise an overwhelming number of easy examples and a small number of hard examples. Automatic selection of these hard examples can make training more effective and efficient.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Some other techniques that are close to hard sample mining: (1) Curriculum learning [3, 48, 40]: it trains a model on easy examples first and then gradually increasing the difficulty of the examples over time. (2) Active learning [32, 24, 28]: it selects the most informative or uncertain samples for labeling by a human annotator. By focusing on the samples that the model is most uncertain about, the model can learn to better generalize and improve its performance on difficult samples. (3) Loss functions: Attentive",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "loss functions can be used to emphasize the importance of hard samples during training. For example, focal loss [20] places more weight on the difficult examples during training, helping the model to learn to handle them better.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Data Augmentations. Several studies have incorporated data augmentations into distillation frameworks to improve performance. For instance, FunMatch [5] employed Mixup, and FKD [37] utilized CutMix. Both techniques achieved competitive accuracy on large-scale ImageNet-1K dataset. In this work, we investigate the impact of data augmentation intensity on soft labels. We discover that different network architectures require unique data augmentation levels. Specifically, ResNet necessitates mild data augmentation, while ViTs require stronger data augmentation. However, even for ViTs, finetuning distillation requires a reduction in the intensity of data augmentation, especially for mixture-based methods. Motivated by this observation, we propose a mild SelfMix approach for ResNet and finetuning distillation scenarios.",
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+    {
+        "type": "text",
+        "text": "3. Approach",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The proposed FerKD is a soft label calibration framework for fast and efficient knowledge distillation training. In this section, we aim to provide an elaborated overview of our method, starting with an in-depth analysis of the roles of hard and soft labels in the distillation process. We then present the key components of our approach, which include a region selection strategy and a soft label calibration scheme. Additionally, we explore the data augmentation requirements for soft labels and introduce a simple label ensemble technique to enhance the quality of the soft labels.",
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+    {
+        "type": "text",
+        "text": "3.1. Revisiting Hard and Soft Label in Distillation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The utilization of hard and soft labels is dependent on the comprehension, problem scenarios, and underlying objectives. Various arguments exist regarding their effectiveness. The vanilla knowledge distillation method [13] employs both hard and soft labels to maximize the benefits of both. However, recent researches [36, 35, 57, 37] suggest that the use of hard labels is not necessary in distillation on large-scale datasets as strong teachers can provide more precise soft supervision. Incorporating hard labels may introduce erroneous supervisory signals, ultimately hampering student performance. Other than the above views, this work presents a novel perspective beyond them by acknowledging that both hard and soft labels offer unique advantages, highlights the proper practice of usage that is necessary, and finally proposes an elegant solution to reap benefits derived from both sources of hard and soft labels.",
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+        "type": "text",
+        "text": "Combination of Soft and Hard Labels. In vanilla KD design [13], for each training example, it will minimize two loss terms for both hard and soft labels. The final objective",
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+    {
+        "type": "page_number",
+        "text": "1668",
+        "bbox": [
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+        "type": "image",
+        "img_path": "images/19db774ac9b1aa5e4b925859aa41ef47ba26e8a01996047ff244985c509165af.jpg",
+        "image_caption": [
+            "Figure 3: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Bounding box is with high probability and bounding box is with low probability."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "$\\mathcal{L}_{VKD}$  can be formulated as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {V K D} = \\frac {1}{N} \\sum_ {x} (\\alpha * \\underbrace {\\mathcal {L} _ {h} \\left(p _ {\\theta} (x) , y _ {h} (x)\\right)} _ {\\text {C E l o s s w i t h h a r d l a b e l}} + (1 - \\alpha) * \\underbrace {\\mathcal {L} _ {s} \\left(p _ {\\theta} (x) , y _ {s} (x)\\right)} _ {\\text {K L l o s s w i t h s o f t l a b e l}}) \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\alpha$  is the coefficient to balance the loss signal intensity from soft and hard labels.  $p_{\\theta}(x)$  is the logits prediction from the student model and  $\\theta$  is its parameters.  $y_{h}$  is the hard label and  $y_{s}$  is the soft label from a pre-trained teacher.  $N$  is the total number of training samples  $x$ .",
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+    {
+        "type": "text",
+        "text": "Full Soft Label Training. Fast KD [37] proposes to use the soft label solely since the prediction from strong teachers is precise enough. Thus, the loss objective  $\\mathcal{L}_{FKD}$  is:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {F K D} = \\frac {1}{N} \\sum_ {x} \\underbrace {\\hat {\\mathcal {L}} _ {s} \\left(p _ {\\theta} (x) , y _ {s} (x)\\right)} _ {\\text {S C E l o s s w i t h s o f t l a b e l}} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where \"SCE\" is the soft version of cross-entropy loss.",
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+    {
+        "type": "text",
+        "text": "3.2. FerKD: Surgical Label Calibration Distillation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Surgical/Partial Soft and Hard Label Adaptive Training. Different from VKD, the proposed FerKD strategy will only involve one loss term but also unlike FKD, FerKD will employ both hard and soft labels in a single objective term and exploit the additional information derived from both sources. The solution is that we only keep their original soft labels for positive regions since they contain fine-grained information regarding the crops, for those background or context regions, we will re-calibrate them by the human-annotated ground-truth labels to avoid misinformation from the soft labels. Hence, the loss function will be:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {F e r K D}} = \\frac {1}{N} \\sum_ {x} \\underbrace {\\mathcal {L} _ {\\text {a d a p : h o r s ?}} \\left(p _ {\\theta} (x) , y _ {a} (x)\\right)} _ {\\text {S C E l o s s w i t h h a r d / s o f t l a b e l}} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where \"adap:\" indicates  $\\{hard\\}$  or  $\\{soft\\}$  used for individual training samples.  $y_{a}$  is the calibrated soft labels. As illustrated in Fig. 3, we will calibrate regions' soft labels  $y_{a}$  using the following rule:",
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+    {
+        "type": "equation",
+        "text": "\n$$\ny _ {a} = \\left\\{ \\begin{array}{l l} \\mathbf {U R}: \\text {d i s c a r d e d} & \\text {i f} y _ {s} <   \\mathcal {T} _ {L} \\text {o r} y _ {s} > \\mathcal {T} _ {T} \\\\ \\mathbf {H R}: \\mathbf {1 . 0} - \\varepsilon & \\text {i f} \\mathcal {T} _ {L} <   y _ {s} <   \\theta_ {M} \\\\ \\mathbf {I R}: y _ {s} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{T}_L$ ,  $\\mathcal{T}_M$ , and  $\\mathcal{T}_T$  are thresholds at low, middle, and top boundaries. \"UR\" represents the uninformative regions such as black or white blocks in an image that will be discarded during training. As shown in Fig. 4, \"HR\" represents the hard regions with a smoothing value  $\\varepsilon$  and \"IR\" represents the important regions. Thus, the key goal in FerKD becomes to identify the positive or background regions. Thanks to FKD [37], we can have access to all crops' individual predictions. A quick exploration is performed for verification and the result is shown in Fig. 5. It is clear that by discarding a certain ratio of samples (hardest and easiest), the performance is consistently improved.",
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+    {
+        "type": "image",
+        "img_path": "images/ea4777d789c346ce630f7283c271486c39c398b365ea5198bbc00b333e6f40f9.jpg",
+        "image_caption": [
+            "Figure 4: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Right is the rule for calibrating the probabilities of regions."
+        ],
+        "image_footnote": [],
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+        "type": "image",
+        "img_path": "images/27dea78b149d51d6ee790a3c30b350739bf2307a3d3bf59d97575a9bf9ee970a.jpg",
+        "image_caption": [
+            "Figure 5: Minimal and maximal probability. The upper figure indicates that only regions having the max probability in [minimal, 1.0] will be trained, and baseline indicates that the model is trained with all randomly sampled regions. The bottom figure indicates that only regions having the max probability in [0.3, maximal] will be trained, and baseline indicates that the model is trained with regions in [0.3, 1.0]."
+        ],
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+    {
+        "type": "text",
+        "text": "3.3. Training Speed of FerKD",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "When training a model, easy examples allow the model to quickly learn the patterns in the data and update its parameters in a way that minimizes the loss function. This means that the model will converge faster and require fewer",
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+    {
+        "type": "page_number",
+        "text": "1669",
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+    {
+        "type": "text",
+        "text": "iterations to reach a satisfactory level of accuracy. On the other hand, hard examples can slow down the convergence speed but they can force models to learn more robust classify boundaries. The speed of model convergence can be impacted significantly by the sampling strategy of hard and easy examples. In our FerKD framework, \"hard\" and \"easy\" examples refer to the level of difficulty a particular sample presents to a model. This difficulty can be quantified by the probability assigned to the correct label by the teacher. An \"easy\" sample is one where the probability assigned to the correct label is high, indicating that the teacher is confident in its prediction. On the other hand, a \"hard\" sample is one where the probability assigned to the correct label is low, indicating that the teacher is uncertain about its prediction. The threshold for what constitutes an \"easy\" or \"hard\" sample can vary depending on the specific task and model being used, which is the key for exploring in FerKD.",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/08059131b74600089eb2e341e472ac1e7f9ffca1da42a31845729928cc2db414.jpg",
+        "image_caption": [
+            "Figure 6: Illustration of the testing accuracy curves. \"300\" represents the training with the full budget. \"50, 100, 150, 200\" are the training with reduced budgets."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our sampling strategy involves the removal of the easiest and hardest training examples to reduce computational costs incurred during uninformative training steps. This strategy offers a clear benefit, as shown in Fig. 6, which presents the test accuracy curves for different training budgets. The results show that, with a training budget reduced by  $\\frac{2}{3}$  (200 epochs), the achieved accuracy is comparable to that of full-budget training. Although further reducing the budget slightly affects accuracy, our proposed FerKD method is shown to be robust across different training budgets. Moreover, our calibration process will not involve additional training cost since it can be done offline in advance.",
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+        "type": "text",
+        "text": "3.4. SelfMix: A Mild and Stable Data Augmentation for Soft Labels",
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+        "type": "text",
+        "text": "Soft label Calibration with SelfMix. The current prevailing data augmentation techniques are designed for hard labels or smoothed hard labels. However, in the dynamic soft label scenario, a different approach is necessary to meet the unique attributes of pre-generated soft labels. Soft labels themselves can mitigate overfitting, making it imperative to develop tailored data augmentation techniques that account for soft labels to achieve improved accuracy. The proposed SelfMix is based on the empirical observations",
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+        "img_path": "images/800e556b723cf1b0c20cb794cdf25a34b23881339299fed710c99ed06219305e.jpg",
+        "image_caption": [
+            "Figure 7: Illustration of the high-level outline for SelfMix to make mixed soft label consistent, reducing the variance. Practically, each label will be a soft distribution for the input instead of the hard label as illustrated, thus it is more moderate on supervision in training. Empirically, it is observed that this strategy is crucial for ConvNet like ResNet but ViT needs intense data augmentations as introduced in [45]."
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+        "type": "image",
+        "img_path": "images/3e36f3d394b3573bd8d74b3be316365c9012200cfbacfb7b6c7b29120969fa67.jpg",
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+    {
+        "type": "text",
+        "text": "presented in Table 2, which indicate that strong data augmentation does not necessarily improve accuracy if the network is already saturated and may even hurt performance. Consequently, we aim to reduce the intensity of data augmentation while still benefiting from its effects. To achieve this goal, we redesign the data augmentation using a self-mixing approach, as illustrated in Fig. 7.",
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+    {
+        "type": "text",
+        "text": "The specific steps involved in the SelfMix process are illustrated in Fig. 8. Mixing operations are exclusively conducted within each individual image to minimize variations between mixed images and their corresponding mixed soft labels. This straightforward constraint yields significant improvements in the performance of the ResNet backbone and in finetuning distillation.",
+        "bbox": [
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+        "image_caption": [
+            "Figure 8: Illustration of the detailed SelfMix augmentation for FerKD. In this strategy, mixture operation only happens within the same image in a mini-batch and cross-image mixing is disabled to preserve stability of soft labels."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ensemble Supervisions. It has been demonstrated that assembling more teachers [13, 33] can enhance the performance of distilled students. In this work, we apply this approach to improve the quality of pre-existing soft labels. As",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Mixup</td><td>CutMix</td><td>SelfMix (Ours)</td><td>ResNet50</td><td>ViT-S/16</td></tr><tr><td>✓</td><td></td><td></td><td>78.94</td><td>80.32</td></tr><tr><td></td><td>✓</td><td></td><td>79.52</td><td>80.95</td></tr><tr><td></td><td></td><td>✓</td><td>80.47</td><td>79.29</td></tr><tr><td>✓</td><td>✓</td><td></td><td>79.92</td><td>81.16</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>80.26</td><td>80.69</td></tr></table>",
+        "bbox": [
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+            82,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/3cbed58a022f8775abd40eec73c1a5b3c95ce19c22365ccb2777b51888516b8d.jpg",
+        "table_caption": [
+            "Table 2: Top-1 accuracy of data augmentations on different backbones. On ViT, the soft label can benefit from combinations of more mixture operations. The backbones are ResNet-50 and ViT-S/16 and the teacher model is Efficient-Net_L2_475. We run three trials and report the means."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Teacher</td><td>\\( {\\mathrm{T}}_{\\text{Top-1 }}\\left( \\% \\right) \\)</td><td>\\( {\\mathrm{S}}_{\\text{ResNet50 }}\\left( \\% \\right) \\)</td><td>\\( {\\mathrm{S}}_{\\text{ViT-S/16 }}\\left( \\% \\right) \\)</td></tr><tr><td>Effi_L2_475 [52]</td><td>88.14</td><td>80.23</td><td>81.16</td></tr><tr><td>Effi_L2_800 [52]</td><td>88.39</td><td>80.16</td><td>81.30</td></tr><tr><td>RegY_128GF_384 [39]</td><td>88.24</td><td>80.34</td><td>81.42</td></tr><tr><td>ViT_L16_512 [39]</td><td>88.07</td><td>80.29</td><td>81.43</td></tr><tr><td>ViT_H14_518 [39]</td><td>88.55</td><td>80.18</td><td>81.41</td></tr><tr><td>BEIT_L_224 [2]</td><td>87.52</td><td>80.03</td><td>81.16</td></tr><tr><td>BEIT_L_384 [2]</td><td>88.40</td><td>80.06</td><td>81.11</td></tr><tr><td>BEIT_L_512 [2]</td><td>88.60</td><td>80.09</td><td>81.07</td></tr><tr><td>ViT_G14_336_30M [10]</td><td>89.59</td><td>79.03</td><td>79.62</td></tr><tr><td>ViT_G14_336_CLAMP [10]</td><td>89.38</td><td>79.59</td><td>79.48</td></tr></table>",
+        "bbox": [
+            81,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "these soft labels are quantized for efficient storage [37], they must be recovered to their full dimension prior to calibration and averaging for final supervision. Specifically, we define the ensemble soft labels  $y_{en} = \\frac{1}{M}\\sum_{t\\in \\text{teachers}}\\hat{y}_a^t (x)$ , where  $\\hat{y}_a^t$  represents the recovered soft label with calibration from teacher  $t$ ,  $x$  is the input and  $M$  is the number of teachers.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. ImageNet Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            585,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct training on the ImageNet-1K (IN1K) [9] training set. We report top-1 validation accuracy of a single  $224 \\times 224$  crop. The default training budget is 300 epochs, and the temperature for both teacher and student is 1.0. The finetuning distillation settings follow their individual designs. All our soft label generation and model training are performed on the A100-GPU High-Flyer cluster with 80GB on each. More details are provided in Appendix.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baselines: FKD [37] and FunMatch [5]. Regions are randomly sampled in these two approaches. We use ResNet-50 and ViT-S/16 as the backbones for the ablation study. FKD + Curriculum Sampling: (i) we sample regions for training from easier ones and gradually increase the level of difficulty. (ii) In contrast, we sample regions from hard ones and gradually decrease the level of difficulty.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Soft Label from Different Teachers",
+        "text_level": 1,
+        "bbox": [
+            76,
+            847,
+            382,
+            862
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The soft labels produced by distinct teacher models for the same input image may vary owing to differences in their",
+        "bbox": [
+            76,
+            869,
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+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/e45a5f4270a91c3e8e69a1626b3b4c72118d6848ddf3a213a0b9af561df380d9.jpg",
+        "table_caption": [
+            "Table 3: Top-1 accuracy of distillation on ImageNet-1K using a single ConvNet or Vision Transformer teacher. Note that Mixup [58] and CutMix [56] are used for training ViTs/16. We run three trials and report the means."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>calibr. range</td><td>[0, 0.2]</td><td>[0, 0.3]</td><td>[0, 0.4]</td><td>[0, 0.5]</td><td>[0,0.6]</td></tr><tr><td>Top-1</td><td>80.31</td><td>80.42</td><td>80.14</td><td>79.84</td><td>79.66</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/faf7e91464eb3c3efae16d6bb8eec643ea931123b99d2fa83fb61e3c523d2169.jpg",
+        "table_caption": [
+            "Table 4: Ablation of calibration for different probability ranges. The base model is the single teacher FerKD using ResNet-50 without SelfMix data augmentation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Pre-train</td><td>Top-1</td></tr><tr><td>vanilla</td><td>80.23</td></tr><tr><td>+calibration&amp;selfmix</td><td>80.68+0.45</td></tr><tr><td>+multi-teacher ensemble</td><td>81.15+0.47</td></tr><tr><td>+more epochs</td><td>81.44+0.29</td></tr></table>",
+        "bbox": [
+            542,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Ablation results using ResNet-50 on ImageNet-1K.",
+        "bbox": [
+            500,
+            257,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "distinctive features, architectures, and training strategies. In this section, our objective is to determine which teacher model has the greatest capacity to distill a student. We evaluate two types of student models: ResNet-50 and ViT-S/16. The results are shown in Table 3, where RegY_128GF_384 and ViT_L16_512 achieve the highest student accuracy individually, despite not being the best on their own.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablation on Calibration. The results for different calibration ranges are shown in Table 4, it can be observed that [0, 0.3] achieves the best accuracy. In practice, we discard examples in [0, 0.15) and (0.95, 1.0], meanwhile, calibrate examples in [0.15, 0.3] for the final strategy. More visualization of the hardest and easiest regions is shown in Fig. 9.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablation on teacher ensemble and training budget. The results are in Table 5, showing that each design has the consistent improvement. Our final results are shown in Table 8, FerKD performs the best over other SOTA methods.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Curriculum Distillation",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In curriculum distillation, the student model learns from the teachers' knowledge in a sequential manner, starting from easier examples (high probability regions) and gradually increasing the level of difficulty. This allows the student model to learn from easier to more complex regions. By presenting samples in a curriculum, the student model can learn from the easier samples and build a strong foundation before being exposed to more challenging samples. However, our experimental results, as shown in Table 7, demonstrate that this curriculum learning approach is inferior to our surgical label adaptation strategy, FerKD. Our approach outperforms curriculum distillation by  $0.8\\%$ . We attribute this performance improvement to the strong ability of soft labels to mitigate overfitting and improve generalization in the initial stages of training. As a result, the advantage of the curriculum learning approach is not as apparent in this scenario. We also notice that \"e-to-h\" performs slightly better than \"h-to-e\" demonstrating the effectiveness of curriculum strategy, while both of them are",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "1671",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4316567e60e795926f0ac97481261391898a814f171d2d501fd78266032415d9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Effi.L2_475</td><td>Effi.L2_800</td><td>RegY_128GF_384</td><td>ViT_L16_512</td><td>ViT_H14_518</td><td>BEIT_224</td><td>BEIT_384</td><td>BEIT_512</td><td>Student Acc.</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>80.23</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.49</td></tr><tr><td></td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>80.29</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>80.53</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>80.48</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>80.35</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.35</td></tr><tr><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.38</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.53</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.62</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.74</td></tr></table>",
+        "bbox": [
+            86,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/551ea0ea12897ca81c91009a22dbdeddf8470adf7909cfaf1cdb5fca6e4dec76.jpg",
+        "table_caption": [
+            "Table 6: Ablation top-1 accuracy of teacher ensemble on ImageNet-1K with ConvNet, Vision Transformer or hybrid teachers. The left group is ConvNet teachers, the middle is the ViT teachers and the right group is the corresponding student ResNet-50 accuracy. Note that surgical calibration and SelfMix are not used here."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>sampling</td><td>Top-1</td></tr><tr><td>Random (FKD [37])</td><td>random</td><td>80.2</td></tr><tr><td>curriculum distillation</td><td>h-to-e</td><td>79.7</td></tr><tr><td>curriculum distillation</td><td>e-to-h</td><td>79.9</td></tr><tr><td>FerKD (Ours)</td><td>surgical</td><td>80.7</td></tr></table>",
+        "bbox": [
+            119,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/8296435bf3650fc0d3794039fe08cc3f6824ae025761753fb8add10445f64007.jpg",
+        "table_caption": [
+            "Table 7: Curriculum and surgical (no ensemble) distillation. \"e-to-h\" refers to curriculum sampling from easy to hard regions. \"h-to-e\" refers to sampling from hard to easy."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Epoch</td><td>Label</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>600</td><td>HardLS</td><td>80.4</td></tr><tr><td>Pytorch (advanced) [44]</td><td>600</td><td>HardLS</td><td>80.9</td></tr><tr><td>MEAL [33]</td><td>100‡</td><td>Soft</td><td>78.2</td></tr><tr><td>MEAL V2 [36]</td><td>180‡</td><td>Soft</td><td>80.7</td></tr><tr><td>MEAL V2 [36]w/CutMix</td><td>180‡</td><td>Soft</td><td>81.0</td></tr><tr><td>ReLU [57]w/CutMix</td><td>300</td><td>Soft</td><td>80.2</td></tr><tr><td>FunMatch [5]w/Mixup</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FKD [37]</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FerKD (Ours)</td><td>300</td><td>Adap</td><td>81.2+0.7</td></tr><tr><td>FerKD (Ours)</td><td>600</td><td>Adap</td><td>81.4+0.9</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "inferior to the random sampling baseline.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Finetuning Distillation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            756,
+            287,
+            772
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Finetuning distillation [36] has been demonstrated as an effective approach to improve the accuracy of knowledge distillation (KD) frameworks. In the case of hard labels, multiple finetuning schemes have been proposed to adapt the model parameters to fit the target dataset, including partial finetuning on selected intermediate layers with varying learning rates [34, 1, 17, 30] or on the last few layers [55]. In this work, we adopt the MEAL V2 [36] protocol by fine",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/729ae3582021df4224a3fa37edee82359a7ac667aa7e9d0b5e697f97ba4bd6b4.jpg",
+        "table_caption": [
+            "Table 8: Top-1 accuracy on ImageNet-1K dataset. The backbone network in this table is ResNet-50.  $\\ddagger$  indicates that the model was fine-tuned from hard-label pre-trained weights, resulting in a total training epoch of  $300 + \\times$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Pre-train</td><td>FT</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>HardLS</td><td>80.38</td></tr><tr><td>Timm [49]</td><td>FKD [37]*</td><td>80.62</td></tr><tr><td>Timm [49]</td><td>FerKD* (Ours)</td><td>81.06</td></tr><tr><td>SWAG [39]</td><td>HardLS</td><td>87.22</td></tr><tr><td>SWAG [39]</td><td>FKD [37]†</td><td>87.42</td></tr><tr><td>SWAG [39]</td><td>FerKD† (Ours)</td><td>87.76</td></tr><tr><td>EVA_MIM [10]</td><td>HardLS</td><td>89.59</td></tr><tr><td>EVA_MIM [10]</td><td>FKD [37]</td><td>89.67</td></tr><tr><td>EVA_MIM [10]</td><td>FerKD (Ours)</td><td>89.86</td></tr></table>",
+        "bbox": [
+            562,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 9: Fine-tuning distillation results using pre-trained ResNet-50 (Timm), RegNetY-128GF (SWAG) and ViT-G14 (EVA) on ImageNet-1K. We use the same recipe of EVA for SWAG finetuning since SWAG did not provide the complete fine-tuning details. * On ResNet-50, we finetune with 150 epochs for both FKD and FerKD.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tuning the entire network from the pre-trained weights to evaluate the effectiveness of distillation with surgical soft label calibration as the objective. Specifically, we employ three types of pre-trained models:",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(1) Supervised pre-train: ResNet-50 on Timm [49];",
+            "(2) Weakly-supervised pre-train: RegNetY-128GF from SWAG [39];",
+            "(3) Self-supervised pre-train: ViT-G14 from EVA [10];"
+        ],
+        "bbox": [
+            500,
+            664,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We verify whether FerKD can continue improving finetuning distillation. As shown in Table 9, FerKD achieves consistent improvement across different architectures.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Single Teacher vs. Teacher Ensemble",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The soft labels generated by different teachers for the same input image can be different due to their unique features, architectures, and training strategies. By combining these soft labels from different teachers, the resulting label becomes more informative and can help the student model learn better representations. This approach can be",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "1672",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/89600f3326a0f5f362e5ce06100d93bb05ac6d516c7fe09c14aeac37a3d9afe8.jpg",
+        "image_caption": [
+            "Figure 9: Illustration of the location points from RandomResizedCrop and the identified crops by teacher model for hard and easy samples. Note that we do not involve any localization information, but teacher's probability can reflect it automatically."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
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+    {
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+    {
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+        "img_path": "images/bc4be51cdc9c60820ce90b1f0c62721b39bfbb3e166875f6f61bea826727f2b0.jpg",
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+        "table_body": "<table><tr><td>Method</td><td>Label</td><td>APbox</td><td>APmask</td></tr><tr><td>ReLU [57]</td><td>LM</td><td>39.1</td><td>35.2</td></tr><tr><td>FKD [37]</td><td>Soft</td><td>39.7</td><td>35.9</td></tr><tr><td>FerKD (Ours)</td><td>Adap</td><td>40.2</td><td>36.3</td></tr></table>",
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+            "Table 10: COCO object detection and segmentation using a Mask-RCNN with FPN baseline. \"LM\" represents label map during pretraining. The backbone is ResNet-50-300ep."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>iNat 2019224</td><td>iNat 2019336</td><td>Places365224</td></tr><tr><td>EVA_MIM [10]</td><td>79.9</td><td>86.6</td><td>61.0</td></tr><tr><td>FerKD (Ours)</td><td>80.3+0.4</td><td>87.1+0.5</td><td>61.4+0.4</td></tr></table>",
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+        "text": "particularly useful in scenarios where the teacher models have complementary strengths or when the input data is challenging and requires multiple perspectives to be accurately labeled. Furthermore, the use of multiple teachers can also help mitigate the effects of overfitting and improve the generalization performance of the student model. The results are shown in Table 6, assembling four hybrid teachers of Effi_L2_475, RegY_128GF_384, ViT_L16_512, and ViT_H14_518 achieves the best accuracy.",
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+        "text": "5. Transfer Learning Experiments",
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+        "text": "Object detection and segmentation. We conducted evaluations to investigate whether the improvement achieved by FerKD on ImageNet-1K can be transferred to various downstream tasks. Specifically, Table 10 presents the results of object detection and segmentation on COCO dataset [21] using models pre-trained on ImageNet-1K with FerKD. We utilize Mask RCNN [12] with FPN [19] following FKD for the experiment. Our FerKD pre-trained weight consistently outperforms both the baselines ReLabel and FKD on the downstream tasks.",
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+        "type": "text",
+        "text": "Classification tasks. Table 11 shows the transfer learning result on iNaturalists [14] and Places [60] datasets. On both of these two datasets, our results surpass the baseline EVA pretrained model by significant margins.",
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+        "table_caption": [
+            "Table 11: Transfer learning accuracy on various classification datasets. The input sizes are  $224 \\times 224$  and  $336 \\times 336$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>IN1K</td><td>ReAL</td><td>ImageNetV2 Top-images</td><td>ImageNetV2 Matched-freq</td><td>ImageNetV2 Threshold-0.7</td></tr><tr><td colspan=\"6\">ResNet-50:</td></tr><tr><td>ReLU [57]</td><td>78.9</td><td>85.0</td><td>80.5</td><td>67.3</td><td>76.0</td></tr><tr><td>FKD [37]</td><td>80.1</td><td>85.8</td><td>81.2</td><td>68.2</td><td>76.9</td></tr><tr><td>FerKD</td><td>81.2</td><td>86.4+0.6</td><td>82.1+0.9</td><td>69.5+1.3</td><td>77.8+0.9</td></tr><tr><td colspan=\"6\">ViT-G14-336:</td></tr><tr><td>EVA [10]</td><td>89.6</td><td>90.8</td><td>89.0</td><td>81.9</td><td>86.7</td></tr><tr><td>FerKD</td><td>89.9</td><td>91.3+0.5</td><td>89.4+0.4</td><td>82.4+0.5</td><td>87.1+0.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 12: Results of FerKD on ImageNet RealL [4] and ImageNetV2 [29] with ResNet-50 and ViT-G14 backbones.",
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+    {
+        "type": "text",
+        "text": "6. Robustness",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We provide comparisons on ImageNet Real [4] and ImageNetV2 [29] datasets to examine the robustness of FerKD trained models. On ImageNetV2 [29], we verify our FerKD models on three metrics \"Top-Images\", \"Matched Frequency\", and \"Threshold 0.7\" following FKD [37]. We perform experiments on two network structures: ResNet-50 and ViT-G14. The results are shown in Table 12, we achieve consistent improvement over ReLabel and FKD on ResNet-50  $(224\\times 224)$  and better accuracy than EVA on ViT-G14  $(336\\times 336)$ .",
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+        "text": "7. Conclusion",
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+        "text": "In this work, we have presented a new paradigm of faster knowledge distillation (FerKD), which employs label adaptation on randomly cropped regions. The proposed method outperforms existing state-of-the-art distillation approaches in terms of both training speed and convergence. Additionally, we make two key observations that could be leveraged in future studies. Firstly, we notice that the most challenging and easiest few crops obtained through the RandomResizedCrop operation do not contribute to the model's learning and can thus be discarded. Secondly, we find that moderate hardness crops can provide crucial context information that helps calibrate the model to learn more robust representations, which in turn benefit downstream tasks.",
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+    {
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+        "text": "References",
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diff --git a/2023/FerKD_ Surgical Label Adaptation for Efficient Distillation/37537680-ebe0-4e37-b920-5de9f0458feb_model.json b/2023/FerKD_ Surgical Label Adaptation for Efficient Distillation/37537680-ebe0-4e37-b920-5de9f0458feb_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..18789eebc560cd4b226595d3347b091c7075e2f1
--- /dev/null
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+            "content": "We present FerKD, a novel efficient knowledge distillation framework that incorporates partial soft-hard label adaptation coupled with a region-calibration mechanism. Our approach stems from the observation and intuition that standard data augmentations, such as RandomResized-Crop, tend to transform inputs into diverse conditions: easy positives, hard positives, or hard negatives. In traditional distillation frameworks, these transformed samples are utilized equally through their predictive probabilities derived from pretrained teacher models. However, merely relying on prediction values from a pretrained teacher, a common practice in prior studies, neglects the reliability of these soft label predictions. To address this, we propose a new scheme that calibrates the less-confident regions to be the context using softened hard groundtruth labels. Our approach involves the processes of hard regions mining + calibration. We demonstrate empirically that this method can dramatically improve the convergence speed and final accuracy. Additionally, we find that a consistent mixing strategy can stabilize the distributions of soft supervision, taking advantage of the soft labels. As a result, we introduce a stabilized SelfMix augmentation that weakens the variation of the mixed images and corresponding soft labels through mixing similar regions within the same image. FerKD is an intuitive and well-designed learning system that eliminates several heuristics and hyperparameters in former FKD solution [37]. More importantly, it achieves remarkable improvement on ImageNet-1K and downstream tasks. For instance, FerKD achieves \\(81.2\\%\\) on ImageNet-1K with ResNet-50, outperforming FKD and FunMatch by remarkable margins. Leveraging better pre-trained weights and larger architectures, our finetuned ViT-G14 even achieves \\(89.9\\%\\). Our code is available at https://github.com/szq0214/FKD/tree/main/FerKD."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.845,
+                0.21,
+                0.86
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Knowledge Distillation (KD) [13] has achieved impressive results in various visual domains, including image clas"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.27,
+                0.639,
+                0.356
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.558,
+                0.362,
+                0.586,
+                0.372
+            ],
+            "angle": 0,
+            "content": "Input"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.64,
+                0.287,
+                0.757,
+                0.356
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.645,
+                0.358,
+                0.751,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Center points of RandomResizedCrop"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.758,
+                0.287,
+                0.892,
+                0.358
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.814,
+                0.365,
+                0.866,
+                0.375
+            ],
+            "angle": 0,
+            "content": "\\(\\pmb{p} <   \\mathbf{0}\\) 25"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.388,
+                0.895,
+                0.57
+            ],
+            "angle": 0,
+            "content": "Figure 1: Illustration of motivation for FerKD. The left figure depicts the original input, and the middle figure shows the center points of bounding boxes generated using RandomResizedCrop. The radius of each circle corresponds to the area of the bounding box. It can be observed that the center points of the bounding boxes are concentrated in the center of the image, and their area increases as they approach the center. The right figure displays several top and bottom confident bounding boxes and their corresponding predictive probabilities from a pre-trained teacher or teachers ensemble. The proposed hard region calibration strategy is established based on these predictions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "sification [52, 36, 5, 37], object detection [6, 46, 11, 8, 53] and semantic segmentation [22, 15, 16]. However, KD methods are often computationally expensive and inefficient due to the additional computational burden imposed by the teacher models. The primary advantage of KD that motivates its usage is its ability to generate precise soft labels that convey more informative details about the input examples. It differs from other label softening techniques, such as label smoothing [43], Mixup [58], and CutMix [56], mainly in two aspects: (1) KD generates soft labels dynamically in each iteration, which is more informative than fixed smoothing patterns used in label smoothing; (2) Mixup and CutMix techniques essentially combine hard labels with coefficients, while KD produces soft labels that are highly correlated with the input sample. This allows KD's soft labels to become more accurate when different data augmentations, such as RandomResizedCrop, flipping and rotation, color jittering, etc., are applied. In general, mixing-based label softening methods cannot monitor such changes in input content, but KD can address them effortlessly."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1666"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.091,
+                0.472,
+                0.197
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.2,
+                0.47,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Figure 2: Statistics of soft label max-probability for crops on ImageNet-1K. The soft label is from FKD [37]. In each image, 500 regions are randomly cropped."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.259,
+                0.473,
+                0.531
+            ],
+            "angle": 0,
+            "content": "To overcome the computational inefficiency of traditional knowledge distillation, FKD [37] was developed to generate region-level soft labels in advance and reuse them across multiple training cycles to eliminate redundant computation. This approach only requires the preparation of soft labels once at the beginning and they can be reused indefinitely. However, this approach overlooks certain critical issues. One is the quality of the soft labels. When using RandomResizedCrop to generate regions, some may be cropped from background areas, and the teacher model will still produce a soft label for them based on their similarity to the dataset classes. However, in some cases, these areas may contain irrelevant noise, compensatory information, or context information for the class, and the soft labels may not accurately reflect the context of information they carry. To address this problem, this work proposes to recalibrate these soft labels by incorporating context information from hard ground-truth labels with smoothing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.534,
+                0.47,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Furthermore, due to the random nature of the sampling process, a certain proportion of crops that are either excessively easy or difficult do not contribute to the model's learning capacity. As demonstrated in Fig. 2 and Table 1, these samples can be discarded to expedite the convergence process. The pre-generated soft labels can be utilized as useful indicators to select these specific samples. In our adaptation of surgical soft labeling, we categorize the soft labels into four distinct groups: extreme hard (negative), moderate hard (background or context), hard positive (partial object), and easy positive. Each of these categories is subject to different treatment methodologies."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.717,
+                0.47,
+                0.868
+            ],
+            "angle": 0,
+            "content": "The Role of Background. The role of the background in images is essential, as it provides critical context and spatial information that aids the model in accurately identifying objects of interest within the scene. Backgrounds can vary in complexity and structure, ranging from simple monochromatic backgrounds to highly cluttered and detailed ones. Soft labels in background areas are typically low, and therefore, it is crucial to handle the background carefully with precise supervision to achieve higher model capability within our surgical label calibration framework."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Hard Regions Mining and Calibration. Hard Regions Mining involves the identification and isolation of chal"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.545,
+                0.088,
+                0.848,
+                0.28
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>range (P)</td><td>ratio</td><td>range (P)</td><td>agg. ratio</td></tr><tr><td>[0.0, 0.1)</td><td>0.43%</td><td>[0, 0.1)</td><td>0.43%</td></tr><tr><td>[0.1, 0.2)</td><td>0.89%</td><td>[0, 0.2)</td><td>1.32%</td></tr><tr><td>[0.2, 0.3)</td><td>1.29%</td><td>[0, 0.3)</td><td>2.61%</td></tr><tr><td>[0.3, 0.4)</td><td>2.03%</td><td>[0, 0.4)</td><td>4.64%</td></tr><tr><td>[0.4, 0.5)</td><td>3.66%</td><td>[0, 0.5)</td><td>8.31%</td></tr><tr><td>[0.5, 0.6)</td><td>4.35%</td><td>[0, 0.6)</td><td>12.65%</td></tr><tr><td>[0.6, 0.7)</td><td>5.04%</td><td>[0, 0.7)</td><td>17.69%</td></tr><tr><td>[0.7, 0.8)</td><td>7.76%</td><td>[0, 0.8)</td><td>25.45%</td></tr><tr><td>[0.8, 0.85)</td><td>8.14%</td><td>[0, 0.85)</td><td>33.59%</td></tr><tr><td>[0.85, 0.9)</td><td>28.73%</td><td>[0, 0.9)</td><td>62.32%</td></tr><tr><td>[0.9, 0.95)</td><td>37.34%</td><td>[0, 0.95)</td><td>99.67%</td></tr><tr><td>[0.95, 1.0)</td><td>0.33%</td><td>[0, 1.0)</td><td>100%</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.281,
+                0.892,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Table 1: Detailed statistics of soft labels. \"range\" indicates max-probability of crops, \"ratio\" indicates the percentage in the whole crops. \"agg. ratio\" is the aggregated ratio."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.341,
+                0.892,
+                0.567
+            ],
+            "angle": 0,
+            "content": "lenging or complex regions within an image that the model struggles to identify accurately. These regions can include objects with complex shapes, occlusions, or those with low contrast. By identifying these regions, the model can focus on learning the features and characteristics of these regions, resulting in improved performance. Calibration, on the other hand, involves adjusting the confidence levels of the model's predictions in challenging regions. The model's predictions may be less reliable in hard regions, leading to lower confidence scores. Calibrating the predictions can improve the model's accuracy in these regions by adjusting the confidence levels of the predictions. We found that carefully discarding a portion of negative crops and selecting those hard positive crops by calibrating their labels, can force the training process more efficient and effective."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.568,
+                0.893,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Stable Training on Soft Labels. Mixture-based augmentations, such as Mixup and CutMix have seen widespread use for training models under hard supervision, where each image is labeled with a single class label. However, in the soft label scenario, we have made a different observation: when employed together with pre-generated soft labels on a typical ResNet, Mixup and CutMix tend to be overly strong, which, conversely, leads to decreased performance. To mitigate label fluctuations and achieve more stable training, we propose a SelfMix scheme, which is particularly suitable for cases where data augmentation should not be so strong, such as in finetuning distillation, where mixture-based augmentation is usually disabled. On the other hand, when training ViT models from scratch, stronger data augmentation can yield better results [45, 42], which is consistent with the larger capacity perspective of this type of network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.811,
+                0.833,
+                0.824
+            ],
+            "angle": 0,
+            "content": "In summary, our contributions of this work are:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.825,
+                0.892,
+                0.885
+            ],
+            "angle": 0,
+            "content": "- We present FerKD, a sample-calibration framework for Faster Knowledge Distillation that achieves state-of-the-art performance. We conduct extensive analysis, ablation, and discussion on the impact of hard and easy samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.886,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- We make two key observations in the pre-generated soft"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "1667"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.468,
+                0.196
+            ],
+            "angle": 0,
+            "content": "label training framework. Firstly, we observe that the few most challenging and simplest crops obtained through the RandomResizedCrop operation do not contribute significantly to the model's learning and can therefore be removed. Secondly, we find that moderately hard crops can provide crucial contextual information that improves the model's ability to learn robust representations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.197,
+                0.468,
+                0.273
+            ],
+            "angle": 0,
+            "content": "- We perform extensive experiments on ImageNet-1K and downstream tasks. On ImageNet-1K, FerKD achieves an accuracy of \\(81.2\\%\\) using the ResNet-50. When leveraging self-supervised pre-trained weights, our larger model finetuned using ViT-G/14 achieves an accuracy of \\(89.9\\%\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.287,
+                0.218,
+                0.302
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.312,
+                0.468,
+                0.538
+            ],
+            "angle": 0,
+            "content": "Knowledge Distillation and Fast Knowledge Distillation. Knowledge Distillation [13] is a learning method in which a \"student\" model is trained to imitate the predictions of a larger, more complex \"teacher\" model. A key advantage of this approach is that the teacher model can provide soft supervision that contains more information regarding the input data than traditional one-hot human annotated labels, particularly when the input data is subject to data augmentation. There have been many recent variants and extensions of knowledge distillation [31, 26, 47, 59, 25, 27, 35, 7, 41, 50, 45, 18, 51], including approaches that use internal feature representations [7], adversarial training with discriminators [33], transfer learning techniques [54], fast distillation [37] via instance label preparation, and methods that prioritize patient and consistent learning [5]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.539,
+                0.468,
+                0.764
+            ],
+            "angle": 0,
+            "content": "Hard Sample Mining. The aim of hard sample mining [23, 38] is to enhance the performance of learning models by selectively focusing on challenging examples that are typically difficult to classify. By prioritizing hard samples during training, models can be trained to better handle a wider range of real-world scenarios and improve their overall performance. One approach [38] to achieve this for object detection is to use Online Hard Example Mining (OHEM) which employs a strategy of selecting challenging examples during training of region-based ConvNet detectors. The motivation behind this approach is that detection datasets typically comprise an overwhelming number of easy examples and a small number of hard examples. Automatic selection of these hard examples can make training more effective and efficient."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.765,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Some other techniques that are close to hard sample mining: (1) Curriculum learning [3, 48, 40]: it trains a model on easy examples first and then gradually increasing the difficulty of the examples over time. (2) Active learning [32, 24, 28]: it selects the most informative or uncertain samples for labeling by a human annotator. By focusing on the samples that the model is most uncertain about, the model can learn to better generalize and improve its performance on difficult samples. (3) Loss functions: Attentive"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.892,
+                0.151
+            ],
+            "angle": 0,
+            "content": "loss functions can be used to emphasize the importance of hard samples during training. For example, focal loss [20] places more weight on the difficult examples during training, helping the model to learn to handle them better."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.153,
+                0.892,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Data Augmentations. Several studies have incorporated data augmentations into distillation frameworks to improve performance. For instance, FunMatch [5] employed Mixup, and FKD [37] utilized CutMix. Both techniques achieved competitive accuracy on large-scale ImageNet-1K dataset. In this work, we investigate the impact of data augmentation intensity on soft labels. We discover that different network architectures require unique data augmentation levels. Specifically, ResNet necessitates mild data augmentation, while ViTs require stronger data augmentation. However, even for ViTs, finetuning distillation requires a reduction in the intensity of data augmentation, especially for mixture-based methods. Motivated by this observation, we propose a mild SelfMix approach for ResNet and finetuning distillation scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.397,
+                0.607,
+                0.414
+            ],
+            "angle": 0,
+            "content": "3. Approach"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.424,
+                0.891,
+                0.575
+            ],
+            "angle": 0,
+            "content": "The proposed FerKD is a soft label calibration framework for fast and efficient knowledge distillation training. In this section, we aim to provide an elaborated overview of our method, starting with an in-depth analysis of the roles of hard and soft labels in the distillation process. We then present the key components of our approach, which include a region selection strategy and a soft label calibration scheme. Additionally, we explore the data augmentation requirements for soft labels and introduce a simple label ensemble technique to enhance the quality of the soft labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.588,
+                0.882,
+                0.604
+            ],
+            "angle": 0,
+            "content": "3.1. Revisiting Hard and Soft Label in Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.613,
+                0.891,
+                0.852
+            ],
+            "angle": 0,
+            "content": "The utilization of hard and soft labels is dependent on the comprehension, problem scenarios, and underlying objectives. Various arguments exist regarding their effectiveness. The vanilla knowledge distillation method [13] employs both hard and soft labels to maximize the benefits of both. However, recent researches [36, 35, 57, 37] suggest that the use of hard labels is not necessary in distillation on large-scale datasets as strong teachers can provide more precise soft supervision. Incorporating hard labels may introduce erroneous supervisory signals, ultimately hampering student performance. Other than the above views, this work presents a novel perspective beyond them by acknowledging that both hard and soft labels offer unique advantages, highlights the proper practice of usage that is necessary, and finally proposes an elegant solution to reap benefits derived from both sources of hard and soft labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.856,
+                0.891,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Combination of Soft and Hard Labels. In vanilla KD design [13], for each training example, it will minimize two loss terms for both hard and soft labels. The final objective"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.947,
+                0.515,
+                0.956
+            ],
+            "angle": 0,
+            "content": "1668"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.107,
+                0.092,
+                0.443,
+                0.196
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.202,
+                0.471,
+                0.263
+            ],
+            "angle": 0,
+            "content": "Figure 3: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Bounding box is with high probability and bounding box is with low probability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.274,
+                0.262,
+                0.289
+            ],
+            "angle": 0,
+            "content": "\\(\\mathcal{L}_{VKD}\\) can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.078,
+                0.294,
+                0.474,
+                0.343
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {V K D} = \\frac {1}{N} \\sum_ {x} (\\alpha * \\underbrace {\\mathcal {L} _ {h} \\left(p _ {\\theta} (x) , y _ {h} (x)\\right)} _ {\\text {C E l o s s w i t h h a r d l a b e l}} + (1 - \\alpha) * \\underbrace {\\mathcal {L} _ {s} \\left(p _ {\\theta} (x) , y _ {s} (x)\\right)} _ {\\text {K L l o s s w i t h s o f t l a b e l}}) \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.344,
+                0.469,
+                0.419
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) is the coefficient to balance the loss signal intensity from soft and hard labels. \\(p_{\\theta}(x)\\) is the logits prediction from the student model and \\(\\theta\\) is its parameters. \\(y_{h}\\) is the hard label and \\(y_{s}\\) is the soft label from a pre-trained teacher. \\(N\\) is the total number of training samples \\(x\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.42,
+                0.469,
+                0.465
+            ],
+            "angle": 0,
+            "content": "Full Soft Label Training. Fast KD [37] proposes to use the soft label solely since the prediction from strong teachers is precise enough. Thus, the loss objective \\(\\mathcal{L}_{FKD}\\) is:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.16,
+                0.472,
+                0.469,
+                0.514
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {F K D} = \\frac {1}{N} \\sum_ {x} \\underbrace {\\hat {\\mathcal {L}} _ {s} \\left(p _ {\\theta} (x) , y _ {s} (x)\\right)} _ {\\text {S C E l o s s w i t h s o f t l a b e l}} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.521,
+                0.433,
+                0.536
+            ],
+            "angle": 0,
+            "content": "where \"SCE\" is the soft version of cross-entropy loss."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.543,
+                0.468,
+                0.559
+            ],
+            "angle": 0,
+            "content": "3.2. FerKD: Surgical Label Calibration Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.567,
+                0.469,
+                0.732
+            ],
+            "angle": 0,
+            "content": "Surgical/Partial Soft and Hard Label Adaptive Training. Different from VKD, the proposed FerKD strategy will only involve one loss term but also unlike FKD, FerKD will employ both hard and soft labels in a single objective term and exploit the additional information derived from both sources. The solution is that we only keep their original soft labels for positive regions since they contain fine-grained information regarding the crops, for those background or context regions, we will re-calibrate them by the human-annotated ground-truth labels to avoid misinformation from the soft labels. Hence, the loss function will be:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.126,
+                0.74,
+                0.469,
+                0.781
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {F e r K D}} = \\frac {1}{N} \\sum_ {x} \\underbrace {\\mathcal {L} _ {\\text {a d a p : h o r s ?}} \\left(p _ {\\theta} (x) , y _ {a} (x)\\right)} _ {\\text {S C E l o s s w i t h h a r d / s o f t l a b e l}} \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.788,
+                0.469,
+                0.849
+            ],
+            "angle": 0,
+            "content": "where \"adap:\" indicates \\(\\{hard\\}\\) or \\(\\{soft\\}\\) used for individual training samples. \\(y_{a}\\) is the calibrated soft labels. As illustrated in Fig. 3, we will calibrate regions' soft labels \\(y_{a}\\) using the following rule:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.856,
+                0.469,
+                0.905
+            ],
+            "angle": 0,
+            "content": "\\[\ny _ {a} = \\left\\{ \\begin{array}{l l} \\mathbf {U R}: \\text {d i s c a r d e d} & \\text {i f} y _ {s} <   \\mathcal {T} _ {L} \\text {o r} y _ {s} > \\mathcal {T} _ {T} \\\\ \\mathbf {H R}: \\mathbf {1 . 0} - \\varepsilon & \\text {i f} \\mathcal {T} _ {L} <   y _ {s} <   \\theta_ {M} \\\\ \\mathbf {I R}: y _ {s} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.273
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{T}_L\\), \\(\\mathcal{T}_M\\), and \\(\\mathcal{T}_T\\) are thresholds at low, middle, and top boundaries. \"UR\" represents the uninformative regions such as black or white blocks in an image that will be discarded during training. As shown in Fig. 4, \"HR\" represents the hard regions with a smoothing value \\(\\varepsilon\\) and \"IR\" represents the important regions. Thus, the key goal in FerKD becomes to identify the positive or background regions. Thanks to FKD [37], we can have access to all crops' individual predictions. A quick exploration is performed for verification and the result is shown in Fig. 5. It is clear that by discarding a certain ratio of samples (hardest and easiest), the performance is consistently improved."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.275,
+                0.892,
+                0.342
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.347,
+                0.892,
+                0.408
+            ],
+            "angle": 0,
+            "content": "Figure 4: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Right is the rule for calibrating the probabilities of regions."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.517,
+                0.414,
+                0.877,
+                0.55
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.517,
+                0.556,
+                0.877,
+                0.689
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.694,
+                0.892,
+                0.801
+            ],
+            "angle": 0,
+            "content": "Figure 5: Minimal and maximal probability. The upper figure indicates that only regions having the max probability in [minimal, 1.0] will be trained, and baseline indicates that the model is trained with all randomly sampled regions. The bottom figure indicates that only regions having the max probability in [0.3, maximal] will be trained, and baseline indicates that the model is trained with regions in [0.3, 1.0]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.817,
+                0.727,
+                0.833
+            ],
+            "angle": 0,
+            "content": "3.3. Training Speed of FerKD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "When training a model, easy examples allow the model to quickly learn the patterns in the data and update its parameters in a way that minimizes the loss function. This means that the model will converge faster and require fewer"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1669"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.348
+            ],
+            "angle": 0,
+            "content": "iterations to reach a satisfactory level of accuracy. On the other hand, hard examples can slow down the convergence speed but they can force models to learn more robust classify boundaries. The speed of model convergence can be impacted significantly by the sampling strategy of hard and easy examples. In our FerKD framework, \"hard\" and \"easy\" examples refer to the level of difficulty a particular sample presents to a model. This difficulty can be quantified by the probability assigned to the correct label by the teacher. An \"easy\" sample is one where the probability assigned to the correct label is high, indicating that the teacher is confident in its prediction. On the other hand, a \"hard\" sample is one where the probability assigned to the correct label is low, indicating that the teacher is uncertain about its prediction. The threshold for what constitutes an \"easy\" or \"hard\" sample can vary depending on the specific task and model being used, which is the key for exploring in FerKD."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.142,
+                0.35,
+                0.406,
+                0.485
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.487,
+                0.47,
+                0.532
+            ],
+            "angle": 0,
+            "content": "Figure 6: Illustration of the testing accuracy curves. \"300\" represents the training with the full budget. \"50, 100, 150, 200\" are the training with reduced budgets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.536,
+                0.47,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Our sampling strategy involves the removal of the easiest and hardest training examples to reduce computational costs incurred during uninformative training steps. This strategy offers a clear benefit, as shown in Fig. 6, which presents the test accuracy curves for different training budgets. The results show that, with a training budget reduced by \\(\\frac{2}{3}\\) (200 epochs), the achieved accuracy is comparable to that of full-budget training. Although further reducing the budget slightly affects accuracy, our proposed FerKD method is shown to be robust across different training budgets. Moreover, our calibration process will not involve additional training cost since it can be done offline in advance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.727,
+                0.47,
+                0.756
+            ],
+            "angle": 0,
+            "content": "3.4. SelfMix: A Mild and Stable Data Augmentation for Soft Labels"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.765,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Soft label Calibration with SelfMix. The current prevailing data augmentation techniques are designed for hard labels or smoothed hard labels. However, in the dynamic soft label scenario, a different approach is necessary to meet the unique attributes of pre-generated soft labels. Soft labels themselves can mitigate overfitting, making it imperative to develop tailored data augmentation techniques that account for soft labels to achieve improved accuracy. The proposed SelfMix is based on the empirical observations"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.523,
+                0.093,
+                0.603,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.618,
+                0.096,
+                0.699,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.096,
+                0.788,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.792,
+                0.096,
+                0.871,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.523,
+                0.164,
+                0.603,
+                0.247
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.617,
+                0.164,
+                0.698,
+                0.255
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.719,
+                0.164,
+                0.787,
+                0.255
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.792,
+                0.164,
+                0.866,
+                0.255
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.258,
+                0.892,
+                0.364
+            ],
+            "angle": 0,
+            "content": "Figure 7: Illustration of the high-level outline for SelfMix to make mixed soft label consistent, reducing the variance. Practically, each label will be a soft distribution for the input instead of the hard label as illustrated, thus it is more moderate on supervision in training. Empirically, it is observed that this strategy is crucial for ConvNet like ResNet but ViT needs intense data augmentations as introduced in [45]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.382,
+                0.892,
+                0.488
+            ],
+            "angle": 0,
+            "content": "presented in Table 2, which indicate that strong data augmentation does not necessarily improve accuracy if the network is already saturated and may even hurt performance. Consequently, we aim to reduce the intensity of data augmentation while still benefiting from its effects. To achieve this goal, we redesign the data augmentation using a self-mixing approach, as illustrated in Fig. 7."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.488,
+                0.892,
+                0.593
+            ],
+            "angle": 0,
+            "content": "The specific steps involved in the SelfMix process are illustrated in Fig. 8. Mixing operations are exclusively conducted within each individual image to minimize variations between mixed images and their corresponding mixed soft labels. This straightforward constraint yields significant improvements in the performance of the ResNet backbone and in finetuning distillation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.517,
+                0.594,
+                0.88,
+                0.771
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.775,
+                0.892,
+                0.835
+            ],
+            "angle": 0,
+            "content": "Figure 8: Illustration of the detailed SelfMix augmentation for FerKD. In this strategy, mixture operation only happens within the same image in a mini-batch and cross-image mixing is disabled to preserve stability of soft labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.841,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Ensemble Supervisions. It has been demonstrated that assembling more teachers [13, 33] can enhance the performance of distilled students. In this work, we apply this approach to improve the quality of pre-existing soft labels. As"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1670"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.092,
+                0.083,
+                0.454,
+                0.176
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Mixup</td><td>CutMix</td><td>SelfMix (Ours)</td><td>ResNet50</td><td>ViT-S/16</td></tr><tr><td>✓</td><td></td><td></td><td>78.94</td><td>80.32</td></tr><tr><td></td><td>✓</td><td></td><td>79.52</td><td>80.95</td></tr><tr><td></td><td></td><td>✓</td><td>80.47</td><td>79.29</td></tr><tr><td>✓</td><td>✓</td><td></td><td>79.92</td><td>81.16</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>80.26</td><td>80.69</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.178,
+                0.471,
+                0.253
+            ],
+            "angle": 0,
+            "content": "Table 2: Top-1 accuracy of data augmentations on different backbones. On ViT, the soft label can benefit from combinations of more mixture operations. The backbones are ResNet-50 and ViT-S/16 and the teacher model is Efficient-Net_L2_475. We run three trials and report the means."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.253,
+                0.477,
+                0.402
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Teacher</td><td>\\( {\\mathrm{T}}_{\\text{Top-1 }}\\left( \\% \\right) \\)</td><td>\\( {\\mathrm{S}}_{\\text{ResNet50 }}\\left( \\% \\right) \\)</td><td>\\( {\\mathrm{S}}_{\\text{ViT-S/16 }}\\left( \\% \\right) \\)</td></tr><tr><td>Effi_L2_475 [52]</td><td>88.14</td><td>80.23</td><td>81.16</td></tr><tr><td>Effi_L2_800 [52]</td><td>88.39</td><td>80.16</td><td>81.30</td></tr><tr><td>RegY_128GF_384 [39]</td><td>88.24</td><td>80.34</td><td>81.42</td></tr><tr><td>ViT_L16_512 [39]</td><td>88.07</td><td>80.29</td><td>81.43</td></tr><tr><td>ViT_H14_518 [39]</td><td>88.55</td><td>80.18</td><td>81.41</td></tr><tr><td>BEIT_L_224 [2]</td><td>87.52</td><td>80.03</td><td>81.16</td></tr><tr><td>BEIT_L_384 [2]</td><td>88.40</td><td>80.06</td><td>81.11</td></tr><tr><td>BEIT_L_512 [2]</td><td>88.60</td><td>80.09</td><td>81.07</td></tr><tr><td>ViT_G14_336_30M [10]</td><td>89.59</td><td>79.03</td><td>79.62</td></tr><tr><td>ViT_G14_336_CLAMP [10]</td><td>89.38</td><td>79.59</td><td>79.48</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.405,
+                0.471,
+                0.466
+            ],
+            "angle": 0,
+            "content": "Table 3: Top-1 accuracy of distillation on ImageNet-1K using a single ConvNet or Vision Transformer teacher. Note that Mixup [58] and CutMix [56] are used for training ViTs/16. We run three trials and report the means."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.482,
+                0.47,
+                0.574
+            ],
+            "angle": 0,
+            "content": "these soft labels are quantized for efficient storage [37], they must be recovered to their full dimension prior to calibration and averaging for final supervision. Specifically, we define the ensemble soft labels \\( y_{en} = \\frac{1}{M}\\sum_{t\\in \\text{teachers}}\\hat{y}_a^t (x) \\), where \\( \\hat{y}_a^t \\) represents the recovered soft label with calibration from teacher \\( t \\), \\( x \\) is the input and \\( M \\) is the number of teachers."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.587,
+                0.295,
+                0.604
+            ],
+            "angle": 0,
+            "content": "4. ImageNet Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.612,
+                0.47,
+                0.732
+            ],
+            "angle": 0,
+            "content": "We conduct training on the ImageNet-1K (IN1K) [9] training set. We report top-1 validation accuracy of a single \\(224 \\times 224\\) crop. The default training budget is 300 epochs, and the temperature for both teacher and student is 1.0. The finetuning distillation settings follow their individual designs. All our soft label generation and model training are performed on the A100-GPU High-Flyer cluster with 80GB on each. More details are provided in Appendix."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.733,
+                0.47,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Baselines: FKD [37] and FunMatch [5]. Regions are randomly sampled in these two approaches. We use ResNet-50 and ViT-S/16 as the backbones for the ablation study. FKD + Curriculum Sampling: (i) we sample regions for training from easier ones and gradually increase the level of difficulty. (ii) In contrast, we sample regions from hard ones and gradually decrease the level of difficulty."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.383,
+                0.863
+            ],
+            "angle": 0,
+            "content": "4.1. Soft Label from Different Teachers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The soft labels produced by distinct teacher models for the same input image may vary owing to differences in their"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.895,
+                0.125
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>calibr. range</td><td>[0, 0.2]</td><td>[0, 0.3]</td><td>[0, 0.4]</td><td>[0, 0.5]</td><td>[0,0.6]</td></tr><tr><td>Top-1</td><td>80.31</td><td>80.42</td><td>80.14</td><td>79.84</td><td>79.66</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.128,
+                0.892,
+                0.173
+            ],
+            "angle": 0,
+            "content": "Table 4: Ablation of calibration for different probability ranges. The base model is the single teacher FerKD using ResNet-50 without SelfMix data augmentation."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.543,
+                0.175,
+                0.843,
+                0.256
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Pre-train</td><td>Top-1</td></tr><tr><td>vanilla</td><td>80.23</td></tr><tr><td>+calibration&amp;selfmix</td><td>80.68+0.45</td></tr><tr><td>+multi-teacher ensemble</td><td>81.15+0.47</td></tr><tr><td>+more epochs</td><td>81.44+0.29</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.258,
+                0.891,
+                0.273
+            ],
+            "angle": 0,
+            "content": "Table 5: Ablation results using ResNet-50 on ImageNet-1K."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.288,
+                0.892,
+                0.394
+            ],
+            "angle": 0,
+            "content": "distinctive features, architectures, and training strategies. In this section, our objective is to determine which teacher model has the greatest capacity to distill a student. We evaluate two types of student models: ResNet-50 and ViT-S/16. The results are shown in Table 3, where RegY_128GF_384 and ViT_L16_512 achieve the highest student accuracy individually, despite not being the best on their own."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.405,
+                0.611,
+                0.42
+            ],
+            "angle": 0,
+            "content": "4.2. Ablations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.429,
+                0.892,
+                0.52
+            ],
+            "angle": 0,
+            "content": "Ablation on Calibration. The results for different calibration ranges are shown in Table 4, it can be observed that [0, 0.3] achieves the best accuracy. In practice, we discard examples in [0, 0.15) and (0.95, 1.0], meanwhile, calibrate examples in [0.15, 0.3] for the final strategy. More visualization of the hardest and easiest regions is shown in Fig. 9."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.521,
+                0.892,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Ablation on teacher ensemble and training budget. The results are in Table 5, showing that each design has the consistent improvement. Our final results are shown in Table 8, FerKD performs the best over other SOTA methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.59,
+                0.719,
+                0.605
+            ],
+            "angle": 0,
+            "content": "4.3. Curriculum Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In curriculum distillation, the student model learns from the teachers' knowledge in a sequential manner, starting from easier examples (high probability regions) and gradually increasing the level of difficulty. This allows the student model to learn from easier to more complex regions. By presenting samples in a curriculum, the student model can learn from the easier samples and build a strong foundation before being exposed to more challenging samples. However, our experimental results, as shown in Table 7, demonstrate that this curriculum learning approach is inferior to our surgical label adaptation strategy, FerKD. Our approach outperforms curriculum distillation by \\(0.8\\%\\). We attribute this performance improvement to the strong ability of soft labels to mitigate overfitting and improve generalization in the initial stages of training. As a result, the advantage of the curriculum learning approach is not as apparent in this scenario. We also notice that \"e-to-h\" performs slightly better than \"h-to-e\" demonstrating the effectiveness of curriculum strategy, while both of them are"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1671"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.087,
+                0.881,
+                0.299
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Effi.L2_475</td><td>Effi.L2_800</td><td>RegY_128GF_384</td><td>ViT_L16_512</td><td>ViT_H14_518</td><td>BEIT_224</td><td>BEIT_384</td><td>BEIT_512</td><td>Student Acc.</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>80.23</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.49</td></tr><tr><td></td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>80.29</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>80.53</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>80.48</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>80.35</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.35</td></tr><tr><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.38</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.53</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.62</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.74</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.302,
+                0.894,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Table 6: Ablation top-1 accuracy of teacher ensemble on ImageNet-1K with ConvNet, Vision Transformer or hybrid teachers. The left group is ConvNet teachers, the middle is the ViT teachers and the right group is the corresponding student ResNet-50 accuracy. Note that surgical calibration and SelfMix are not used here."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.12,
+                0.351,
+                0.426,
+                0.436
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>sampling</td><td>Top-1</td></tr><tr><td>Random (FKD [37])</td><td>random</td><td>80.2</td></tr><tr><td>curriculum distillation</td><td>h-to-e</td><td>79.7</td></tr><tr><td>curriculum distillation</td><td>e-to-h</td><td>79.9</td></tr><tr><td>FerKD (Ours)</td><td>surgical</td><td>80.7</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.439,
+                0.47,
+                0.485
+            ],
+            "angle": 0,
+            "content": "Table 7: Curriculum and surgical (no ensemble) distillation. \"e-to-h\" refers to curriculum sampling from easy to hard regions. \"h-to-e\" refers to sampling from hard to easy."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.489,
+                0.468,
+                0.655
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Epoch</td><td>Label</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>600</td><td>HardLS</td><td>80.4</td></tr><tr><td>Pytorch (advanced) [44]</td><td>600</td><td>HardLS</td><td>80.9</td></tr><tr><td>MEAL [33]</td><td>100‡</td><td>Soft</td><td>78.2</td></tr><tr><td>MEAL V2 [36]</td><td>180‡</td><td>Soft</td><td>80.7</td></tr><tr><td>MEAL V2 [36]w/CutMix</td><td>180‡</td><td>Soft</td><td>81.0</td></tr><tr><td>ReLU [57]w/CutMix</td><td>300</td><td>Soft</td><td>80.2</td></tr><tr><td>FunMatch [5]w/Mixup</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FKD [37]</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FerKD (Ours)</td><td>300</td><td>Adap</td><td>81.2+0.7</td></tr><tr><td>FerKD (Ours)</td><td>600</td><td>Adap</td><td>81.4+0.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.659,
+                0.47,
+                0.719
+            ],
+            "angle": 0,
+            "content": "Table 8: Top-1 accuracy on ImageNet-1K dataset. The backbone network in this table is ResNet-50. \\(\\ddagger\\) indicates that the model was fine-tuned from hard-label pre-trained weights, resulting in a total training epoch of \\(300 + \\times\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.732,
+                0.351,
+                0.748
+            ],
+            "angle": 0,
+            "content": "inferior to the random sampling baseline."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.757,
+                0.288,
+                0.773
+            ],
+            "angle": 0,
+            "content": "4.4. Finetuning Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Finetuning distillation [36] has been demonstrated as an effective approach to improve the accuracy of knowledge distillation (KD) frameworks. In the case of hard labels, multiple finetuning schemes have been proposed to adapt the model parameters to fit the target dataset, including partial finetuning on selected intermediate layers with varying learning rates [34, 1, 17, 30] or on the last few layers [55]. In this work, we adopt the MEAL V2 [36] protocol by fine"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.563,
+                0.351,
+                0.825,
+                0.488
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Pre-train</td><td>FT</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>HardLS</td><td>80.38</td></tr><tr><td>Timm [49]</td><td>FKD [37]*</td><td>80.62</td></tr><tr><td>Timm [49]</td><td>FerKD* (Ours)</td><td>81.06</td></tr><tr><td>SWAG [39]</td><td>HardLS</td><td>87.22</td></tr><tr><td>SWAG [39]</td><td>FKD [37]†</td><td>87.42</td></tr><tr><td>SWAG [39]</td><td>FerKD† (Ours)</td><td>87.76</td></tr><tr><td>EVA_MIM [10]</td><td>HardLS</td><td>89.59</td></tr><tr><td>EVA_MIM [10]</td><td>FKD [37]</td><td>89.67</td></tr><tr><td>EVA_MIM [10]</td><td>FerKD (Ours)</td><td>89.86</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.493,
+                0.894,
+                0.584
+            ],
+            "angle": 0,
+            "content": "Table 9: Fine-tuning distillation results using pre-trained ResNet-50 (Timm), RegNetY-128GF (SWAG) and ViT-G14 (EVA) on ImageNet-1K. We use the same recipe of EVA for SWAG finetuning since SWAG did not provide the complete fine-tuning details. * On ResNet-50, we finetune with 150 epochs for both FKD and FerKD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.604,
+                0.892,
+                0.663
+            ],
+            "angle": 0,
+            "content": "tuning the entire network from the pre-trained weights to evaluate the effectiveness of distillation with surgical soft label calibration as the objective. Specifically, we employ three types of pre-trained models:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.665,
+                0.86,
+                0.68
+            ],
+            "angle": 0,
+            "content": "(1) Supervised pre-train: ResNet-50 on Timm [49];"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.681,
+                0.891,
+                0.711
+            ],
+            "angle": 0,
+            "content": "(2) Weakly-supervised pre-train: RegNetY-128GF from SWAG [39];"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.712,
+                0.884,
+                0.727
+            ],
+            "angle": 0,
+            "content": "(3) Self-supervised pre-train: ViT-G14 from EVA [10];"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.5,
+                0.665,
+                0.891,
+                0.727
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.729,
+                0.892,
+                0.774
+            ],
+            "angle": 0,
+            "content": "We verify whether FerKD can continue improving finetuning distillation. As shown in Table 9, FerKD achieves consistent improvement across different architectures."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.786,
+                0.82,
+                0.802
+            ],
+            "angle": 0,
+            "content": "4.5. Single Teacher vs. Teacher Ensemble"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The soft labels generated by different teachers for the same input image can be different due to their unique features, architectures, and training strategies. By combining these soft labels from different teachers, the resulting label becomes more informative and can help the student model learn better representations. This approach can be"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1672"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.099,
+                0.091,
+                0.222,
+                0.277
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.223,
+                0.091,
+                0.346,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.347,
+                0.091,
+                0.453,
+                0.275
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.453,
+                0.091,
+                0.56,
+                0.275
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.561,
+                0.091,
+                0.641,
+                0.275
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.641,
+                0.092,
+                0.714,
+                0.274
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.715,
+                0.092,
+                0.793,
+                0.274
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.794,
+                0.092,
+                0.871,
+                0.274
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.28,
+                0.893,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Figure 9: Illustration of the location points from RandomResizedCrop and the identified crops by teacher model for hard and easy samples. Note that we do not involve any localization information, but teacher's probability can reflect it automatically."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.14,
+                0.315,
+                0.404,
+                0.378
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Label</td><td>APbox</td><td>APmask</td></tr><tr><td>ReLU [57]</td><td>LM</td><td>39.1</td><td>35.2</td></tr><tr><td>FKD [37]</td><td>Soft</td><td>39.7</td><td>35.9</td></tr><tr><td>FerKD (Ours)</td><td>Adap</td><td>40.2</td><td>36.3</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.38,
+                0.47,
+                0.425
+            ],
+            "angle": 0,
+            "content": "Table 10: COCO object detection and segmentation using a Mask-RCNN with FPN baseline. \"LM\" represents label map during pretraining. The backbone is ResNet-50-300ep."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.43,
+                0.469,
+                0.478
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>iNat 2019224</td><td>iNat 2019336</td><td>Places365224</td></tr><tr><td>EVA_MIM [10]</td><td>79.9</td><td>86.6</td><td>61.0</td></tr><tr><td>FerKD (Ours)</td><td>80.3+0.4</td><td>87.1+0.5</td><td>61.4+0.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.481,
+                0.469,
+                0.512
+            ],
+            "angle": 0,
+            "content": "Table 11: Transfer learning accuracy on various classification datasets. The input sizes are \\(224 \\times 224\\) and \\(336 \\times 336\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.525,
+                0.47,
+                0.661
+            ],
+            "angle": 0,
+            "content": "particularly useful in scenarios where the teacher models have complementary strengths or when the input data is challenging and requires multiple perspectives to be accurately labeled. Furthermore, the use of multiple teachers can also help mitigate the effects of overfitting and improve the generalization performance of the student model. The results are shown in Table 6, assembling four hybrid teachers of Effi_L2_475, RegY_128GF_384, ViT_L16_512, and ViT_H14_518 achieves the best accuracy."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.669,
+                0.37,
+                0.686
+            ],
+            "angle": 0,
+            "content": "5. Transfer Learning Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.469,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Object detection and segmentation. We conducted evaluations to investigate whether the improvement achieved by FerKD on ImageNet-1K can be transferred to various downstream tasks. Specifically, Table 10 presents the results of object detection and segmentation on COCO dataset [21] using models pre-trained on ImageNet-1K with FerKD. We utilize Mask RCNN [12] with FPN [19] following FKD for the experiment. Our FerKD pre-trained weight consistently outperforms both the baselines ReLabel and FKD on the downstream tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Classification tasks. Table 11 shows the transfer learning result on iNaturalists [14] and Places [60] datasets. On both of these two datasets, our results surpass the baseline EVA pretrained model by significant margins."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.501,
+                0.315,
+                0.896,
+                0.427
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>IN1K</td><td>ReAL</td><td>ImageNetV2 Top-images</td><td>ImageNetV2 Matched-freq</td><td>ImageNetV2 Threshold-0.7</td></tr><tr><td colspan=\"6\">ResNet-50:</td></tr><tr><td>ReLU [57]</td><td>78.9</td><td>85.0</td><td>80.5</td><td>67.3</td><td>76.0</td></tr><tr><td>FKD [37]</td><td>80.1</td><td>85.8</td><td>81.2</td><td>68.2</td><td>76.9</td></tr><tr><td>FerKD</td><td>81.2</td><td>86.4+0.6</td><td>82.1+0.9</td><td>69.5+1.3</td><td>77.8+0.9</td></tr><tr><td colspan=\"6\">ViT-G14-336:</td></tr><tr><td>EVA [10]</td><td>89.6</td><td>90.8</td><td>89.0</td><td>81.9</td><td>86.7</td></tr><tr><td>FerKD</td><td>89.9</td><td>91.3+0.5</td><td>89.4+0.4</td><td>82.4+0.5</td><td>87.1+0.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.436,
+                0.893,
+                0.467
+            ],
+            "angle": 0,
+            "content": "Table 12: Results of FerKD on ImageNet RealL [4] and ImageNetV2 [29] with ResNet-50 and ViT-G14 backbones."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.485,
+                0.62,
+                0.5
+            ],
+            "angle": 0,
+            "content": "6. Robustness"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.511,
+                0.893,
+                0.661
+            ],
+            "angle": 0,
+            "content": "We provide comparisons on ImageNet Real [4] and ImageNetV2 [29] datasets to examine the robustness of FerKD trained models. On ImageNetV2 [29], we verify our FerKD models on three metrics \"Top-Images\", \"Matched Frequency\", and \"Threshold 0.7\" following FKD [37]. We perform experiments on two network structures: ResNet-50 and ViT-G14. The results are shown in Table 12, we achieve consistent improvement over ReLabel and FKD on ResNet-50 \\((224\\times 224)\\) and better accuracy than EVA on ViT-G14 \\((336\\times 336)\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.679,
+                0.619,
+                0.694
+            ],
+            "angle": 0,
+            "content": "7. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.893,
+                0.9
+            ],
+            "angle": 0,
+            "content": "In this work, we have presented a new paradigm of faster knowledge distillation (FerKD), which employs label adaptation on randomly cropped regions. The proposed method outperforms existing state-of-the-art distillation approaches in terms of both training speed and convergence. Additionally, we make two key observations that could be leveraged in future studies. Firstly, we notice that the most challenging and easiest few crops obtained through the RandomResizedCrop operation do not contribute to the model's learning and can thus be discarded. Secondly, we find that moderate hardness crops can provide crucial context information that helps calibrate the model to learn more robust representations, which in turn benefit downstream tasks."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1673"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.175,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.117,
+                0.47,
+                0.171
+            ],
+            "angle": 0,
+            "content": "[1] Armen Aghajanyan, Akshat Shrivastava, Anchit Gupta, Naman Goyal, Luke Zettlemoyer, and Sonal Gupta. Better fine-tuning by reducing representational collapse. arXiv preprint arXiv:2008.03156, 2020. 7"
+        },
+        {
+            "type": "ref_text",
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+        {
+            "type": "ref_text",
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+# FerKD: Surgical Label Adaptation for Efficient Distillation
+
+# Zhiqiang Shen  
+Mohamed bin Zayed University of AI
+
+Zhiqiang.Shen@mbzuai.ac.ae
+
+# Abstract
+
+We present FerKD, a novel efficient knowledge distillation framework that incorporates partial soft-hard label adaptation coupled with a region-calibration mechanism. Our approach stems from the observation and intuition that standard data augmentations, such as RandomResized-Crop, tend to transform inputs into diverse conditions: easy positives, hard positives, or hard negatives. In traditional distillation frameworks, these transformed samples are utilized equally through their predictive probabilities derived from pretrained teacher models. However, merely relying on prediction values from a pretrained teacher, a common practice in prior studies, neglects the reliability of these soft label predictions. To address this, we propose a new scheme that calibrates the less-confident regions to be the context using softened hard groundtruth labels. Our approach involves the processes of hard regions mining + calibration. We demonstrate empirically that this method can dramatically improve the convergence speed and final accuracy. Additionally, we find that a consistent mixing strategy can stabilize the distributions of soft supervision, taking advantage of the soft labels. As a result, we introduce a stabilized SelfMix augmentation that weakens the variation of the mixed images and corresponding soft labels through mixing similar regions within the same image. FerKD is an intuitive and well-designed learning system that eliminates several heuristics and hyperparameters in former FKD solution [37]. More importantly, it achieves remarkable improvement on ImageNet-1K and downstream tasks. For instance, FerKD achieves  $81.2\%$  on ImageNet-1K with ResNet-50, outperforming FKD and FunMatch by remarkable margins. Leveraging better pre-trained weights and larger architectures, our finetuned ViT-G14 even achieves  $89.9\%$ . Our code is available at https://github.com/szq0214/FKD/tree/main/FerKD.
+
+# 1. Introduction
+
+Knowledge Distillation (KD) [13] has achieved impressive results in various visual domains, including image clas
+
+![](images/2dc141956ee2cdcd7eb9e2066301851c8715beab6781c64d501b796eeebfaed5.jpg)  
+Input  
+Center points of RandomResizedCrop
+
+![](images/0e6289ac43ed195e159541c09e247303993711d5e89ec14074bd58c254e161b0.jpg)
+
+![](images/0d7c3b965a52e8c9e0c5072206e522f9a58641e5ae845ee6db9a427f9332d914.jpg)  
+$\pmb{p} <   \mathbf{0}$  25  
+Figure 1: Illustration of motivation for FerKD. The left figure depicts the original input, and the middle figure shows the center points of bounding boxes generated using RandomResizedCrop. The radius of each circle corresponds to the area of the bounding box. It can be observed that the center points of the bounding boxes are concentrated in the center of the image, and their area increases as they approach the center. The right figure displays several top and bottom confident bounding boxes and their corresponding predictive probabilities from a pre-trained teacher or teachers ensemble. The proposed hard region calibration strategy is established based on these predictions.
+
+sification [52, 36, 5, 37], object detection [6, 46, 11, 8, 53] and semantic segmentation [22, 15, 16]. However, KD methods are often computationally expensive and inefficient due to the additional computational burden imposed by the teacher models. The primary advantage of KD that motivates its usage is its ability to generate precise soft labels that convey more informative details about the input examples. It differs from other label softening techniques, such as label smoothing [43], Mixup [58], and CutMix [56], mainly in two aspects: (1) KD generates soft labels dynamically in each iteration, which is more informative than fixed smoothing patterns used in label smoothing; (2) Mixup and CutMix techniques essentially combine hard labels with coefficients, while KD produces soft labels that are highly correlated with the input sample. This allows KD's soft labels to become more accurate when different data augmentations, such as RandomResizedCrop, flipping and rotation, color jittering, etc., are applied. In general, mixing-based label softening methods cannot monitor such changes in input content, but KD can address them effortlessly.
+
+![](images/3ad367eb627b6e0aca1e378e94285b5a70cf3dc79f4ada56e6b260619bd0af21.jpg)  
+Figure 2: Statistics of soft label max-probability for crops on ImageNet-1K. The soft label is from FKD [37]. In each image, 500 regions are randomly cropped.
+
+To overcome the computational inefficiency of traditional knowledge distillation, FKD [37] was developed to generate region-level soft labels in advance and reuse them across multiple training cycles to eliminate redundant computation. This approach only requires the preparation of soft labels once at the beginning and they can be reused indefinitely. However, this approach overlooks certain critical issues. One is the quality of the soft labels. When using RandomResizedCrop to generate regions, some may be cropped from background areas, and the teacher model will still produce a soft label for them based on their similarity to the dataset classes. However, in some cases, these areas may contain irrelevant noise, compensatory information, or context information for the class, and the soft labels may not accurately reflect the context of information they carry. To address this problem, this work proposes to recalibrate these soft labels by incorporating context information from hard ground-truth labels with smoothing.
+
+Furthermore, due to the random nature of the sampling process, a certain proportion of crops that are either excessively easy or difficult do not contribute to the model's learning capacity. As demonstrated in Fig. 2 and Table 1, these samples can be discarded to expedite the convergence process. The pre-generated soft labels can be utilized as useful indicators to select these specific samples. In our adaptation of surgical soft labeling, we categorize the soft labels into four distinct groups: extreme hard (negative), moderate hard (background or context), hard positive (partial object), and easy positive. Each of these categories is subject to different treatment methodologies.
+
+The Role of Background. The role of the background in images is essential, as it provides critical context and spatial information that aids the model in accurately identifying objects of interest within the scene. Backgrounds can vary in complexity and structure, ranging from simple monochromatic backgrounds to highly cluttered and detailed ones. Soft labels in background areas are typically low, and therefore, it is crucial to handle the background carefully with precise supervision to achieve higher model capability within our surgical label calibration framework.
+
+Hard Regions Mining and Calibration. Hard Regions Mining involves the identification and isolation of chal
+
+<table><tr><td>range (P)</td><td>ratio</td><td>range (P)</td><td>agg. ratio</td></tr><tr><td>[0.0, 0.1)</td><td>0.43%</td><td>[0, 0.1)</td><td>0.43%</td></tr><tr><td>[0.1, 0.2)</td><td>0.89%</td><td>[0, 0.2)</td><td>1.32%</td></tr><tr><td>[0.2, 0.3)</td><td>1.29%</td><td>[0, 0.3)</td><td>2.61%</td></tr><tr><td>[0.3, 0.4)</td><td>2.03%</td><td>[0, 0.4)</td><td>4.64%</td></tr><tr><td>[0.4, 0.5)</td><td>3.66%</td><td>[0, 0.5)</td><td>8.31%</td></tr><tr><td>[0.5, 0.6)</td><td>4.35%</td><td>[0, 0.6)</td><td>12.65%</td></tr><tr><td>[0.6, 0.7)</td><td>5.04%</td><td>[0, 0.7)</td><td>17.69%</td></tr><tr><td>[0.7, 0.8)</td><td>7.76%</td><td>[0, 0.8)</td><td>25.45%</td></tr><tr><td>[0.8, 0.85)</td><td>8.14%</td><td>[0, 0.85)</td><td>33.59%</td></tr><tr><td>[0.85, 0.9)</td><td>28.73%</td><td>[0, 0.9)</td><td>62.32%</td></tr><tr><td>[0.9, 0.95)</td><td>37.34%</td><td>[0, 0.95)</td><td>99.67%</td></tr><tr><td>[0.95, 1.0)</td><td>0.33%</td><td>[0, 1.0)</td><td>100%</td></tr></table>
+
+Table 1: Detailed statistics of soft labels. "range" indicates max-probability of crops, "ratio" indicates the percentage in the whole crops. "agg. ratio" is the aggregated ratio.
+
+lenging or complex regions within an image that the model struggles to identify accurately. These regions can include objects with complex shapes, occlusions, or those with low contrast. By identifying these regions, the model can focus on learning the features and characteristics of these regions, resulting in improved performance. Calibration, on the other hand, involves adjusting the confidence levels of the model's predictions in challenging regions. The model's predictions may be less reliable in hard regions, leading to lower confidence scores. Calibrating the predictions can improve the model's accuracy in these regions by adjusting the confidence levels of the predictions. We found that carefully discarding a portion of negative crops and selecting those hard positive crops by calibrating their labels, can force the training process more efficient and effective.
+
+Stable Training on Soft Labels. Mixture-based augmentations, such as Mixup and CutMix have seen widespread use for training models under hard supervision, where each image is labeled with a single class label. However, in the soft label scenario, we have made a different observation: when employed together with pre-generated soft labels on a typical ResNet, Mixup and CutMix tend to be overly strong, which, conversely, leads to decreased performance. To mitigate label fluctuations and achieve more stable training, we propose a SelfMix scheme, which is particularly suitable for cases where data augmentation should not be so strong, such as in finetuning distillation, where mixture-based augmentation is usually disabled. On the other hand, when training ViT models from scratch, stronger data augmentation can yield better results [45, 42], which is consistent with the larger capacity perspective of this type of network.
+
+In summary, our contributions of this work are:
+
+- We present FerKD, a sample-calibration framework for Faster Knowledge Distillation that achieves state-of-the-art performance. We conduct extensive analysis, ablation, and discussion on the impact of hard and easy samples.
+
+- We make two key observations in the pre-generated soft
+
+label training framework. Firstly, we observe that the few most challenging and simplest crops obtained through the RandomResizedCrop operation do not contribute significantly to the model's learning and can therefore be removed. Secondly, we find that moderately hard crops can provide crucial contextual information that improves the model's ability to learn robust representations.
+
+- We perform extensive experiments on ImageNet-1K and downstream tasks. On ImageNet-1K, FerKD achieves an accuracy of  $81.2\%$  using the ResNet-50. When leveraging self-supervised pre-trained weights, our larger model finetuned using ViT-G/14 achieves an accuracy of  $89.9\%$ .
+
+# 2. Related Work
+
+Knowledge Distillation and Fast Knowledge Distillation. Knowledge Distillation [13] is a learning method in which a "student" model is trained to imitate the predictions of a larger, more complex "teacher" model. A key advantage of this approach is that the teacher model can provide soft supervision that contains more information regarding the input data than traditional one-hot human annotated labels, particularly when the input data is subject to data augmentation. There have been many recent variants and extensions of knowledge distillation [31, 26, 47, 59, 25, 27, 35, 7, 41, 50, 45, 18, 51], including approaches that use internal feature representations [7], adversarial training with discriminators [33], transfer learning techniques [54], fast distillation [37] via instance label preparation, and methods that prioritize patient and consistent learning [5].
+
+Hard Sample Mining. The aim of hard sample mining [23, 38] is to enhance the performance of learning models by selectively focusing on challenging examples that are typically difficult to classify. By prioritizing hard samples during training, models can be trained to better handle a wider range of real-world scenarios and improve their overall performance. One approach [38] to achieve this for object detection is to use Online Hard Example Mining (OHEM) which employs a strategy of selecting challenging examples during training of region-based ConvNet detectors. The motivation behind this approach is that detection datasets typically comprise an overwhelming number of easy examples and a small number of hard examples. Automatic selection of these hard examples can make training more effective and efficient.
+
+Some other techniques that are close to hard sample mining: (1) Curriculum learning [3, 48, 40]: it trains a model on easy examples first and then gradually increasing the difficulty of the examples over time. (2) Active learning [32, 24, 28]: it selects the most informative or uncertain samples for labeling by a human annotator. By focusing on the samples that the model is most uncertain about, the model can learn to better generalize and improve its performance on difficult samples. (3) Loss functions: Attentive
+
+loss functions can be used to emphasize the importance of hard samples during training. For example, focal loss [20] places more weight on the difficult examples during training, helping the model to learn to handle them better.
+
+Data Augmentations. Several studies have incorporated data augmentations into distillation frameworks to improve performance. For instance, FunMatch [5] employed Mixup, and FKD [37] utilized CutMix. Both techniques achieved competitive accuracy on large-scale ImageNet-1K dataset. In this work, we investigate the impact of data augmentation intensity on soft labels. We discover that different network architectures require unique data augmentation levels. Specifically, ResNet necessitates mild data augmentation, while ViTs require stronger data augmentation. However, even for ViTs, finetuning distillation requires a reduction in the intensity of data augmentation, especially for mixture-based methods. Motivated by this observation, we propose a mild SelfMix approach for ResNet and finetuning distillation scenarios.
+
+# 3. Approach
+
+The proposed FerKD is a soft label calibration framework for fast and efficient knowledge distillation training. In this section, we aim to provide an elaborated overview of our method, starting with an in-depth analysis of the roles of hard and soft labels in the distillation process. We then present the key components of our approach, which include a region selection strategy and a soft label calibration scheme. Additionally, we explore the data augmentation requirements for soft labels and introduce a simple label ensemble technique to enhance the quality of the soft labels.
+
+# 3.1. Revisiting Hard and Soft Label in Distillation
+
+The utilization of hard and soft labels is dependent on the comprehension, problem scenarios, and underlying objectives. Various arguments exist regarding their effectiveness. The vanilla knowledge distillation method [13] employs both hard and soft labels to maximize the benefits of both. However, recent researches [36, 35, 57, 37] suggest that the use of hard labels is not necessary in distillation on large-scale datasets as strong teachers can provide more precise soft supervision. Incorporating hard labels may introduce erroneous supervisory signals, ultimately hampering student performance. Other than the above views, this work presents a novel perspective beyond them by acknowledging that both hard and soft labels offer unique advantages, highlights the proper practice of usage that is necessary, and finally proposes an elegant solution to reap benefits derived from both sources of hard and soft labels.
+
+Combination of Soft and Hard Labels. In vanilla KD design [13], for each training example, it will minimize two loss terms for both hard and soft labels. The final objective
+
+![](images/19db774ac9b1aa5e4b925859aa41ef47ba26e8a01996047ff244985c509165af.jpg)  
+Figure 3: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Bounding box is with high probability and bounding box is with low probability.
+
+$\mathcal{L}_{VKD}$  can be formulated as:
+
+$$
+\mathcal {L} _ {V K D} = \frac {1}{N} \sum_ {x} (\alpha * \underbrace {\mathcal {L} _ {h} \left(p _ {\theta} (x) , y _ {h} (x)\right)} _ {\text {C E l o s s w i t h h a r d l a b e l}} + (1 - \alpha) * \underbrace {\mathcal {L} _ {s} \left(p _ {\theta} (x) , y _ {s} (x)\right)} _ {\text {K L l o s s w i t h s o f t l a b e l}}) \tag {1}
+$$
+
+where  $\alpha$  is the coefficient to balance the loss signal intensity from soft and hard labels.  $p_{\theta}(x)$  is the logits prediction from the student model and  $\theta$  is its parameters.  $y_{h}$  is the hard label and  $y_{s}$  is the soft label from a pre-trained teacher.  $N$  is the total number of training samples  $x$ .
+
+Full Soft Label Training. Fast KD [37] proposes to use the soft label solely since the prediction from strong teachers is precise enough. Thus, the loss objective  $\mathcal{L}_{FKD}$  is:
+
+$$
+\mathcal {L} _ {F K D} = \frac {1}{N} \sum_ {x} \underbrace {\hat {\mathcal {L}} _ {s} \left(p _ {\theta} (x) , y _ {s} (x)\right)} _ {\text {S C E l o s s w i t h s o f t l a b e l}} \tag {2}
+$$
+
+where "SCE" is the soft version of cross-entropy loss.
+
+# 3.2. FerKD: Surgical Label Calibration Distillation
+
+Surgical/Partial Soft and Hard Label Adaptive Training. Different from VKD, the proposed FerKD strategy will only involve one loss term but also unlike FKD, FerKD will employ both hard and soft labels in a single objective term and exploit the additional information derived from both sources. The solution is that we only keep their original soft labels for positive regions since they contain fine-grained information regarding the crops, for those background or context regions, we will re-calibrate them by the human-annotated ground-truth labels to avoid misinformation from the soft labels. Hence, the loss function will be:
+
+$$
+\mathcal {L} _ {\text {F e r K D}} = \frac {1}{N} \sum_ {x} \underbrace {\mathcal {L} _ {\text {a d a p : h o r s ?}} \left(p _ {\theta} (x) , y _ {a} (x)\right)} _ {\text {S C E l o s s w i t h h a r d / s o f t l a b e l}} \tag {3}
+$$
+
+where "adap:" indicates  $\{hard\}$  or  $\{soft\}$  used for individual training samples.  $y_{a}$  is the calibrated soft labels. As illustrated in Fig. 3, we will calibrate regions' soft labels  $y_{a}$  using the following rule:
+
+$$
+y _ {a} = \left\{ \begin{array}{l l} \mathbf {U R}: \text {d i s c a r d e d} & \text {i f} y _ {s} <   \mathcal {T} _ {L} \text {o r} y _ {s} > \mathcal {T} _ {T} \\ \mathbf {H R}: \mathbf {1 . 0} - \varepsilon & \text {i f} \mathcal {T} _ {L} <   y _ {s} <   \theta_ {M} \\ \mathbf {I R}: y _ {s} & \text {o t h e r w i s e} \end{array} \right. \tag {4}
+$$
+
+where  $\mathcal{T}_L$ ,  $\mathcal{T}_M$ , and  $\mathcal{T}_T$  are thresholds at low, middle, and top boundaries. "UR" represents the uninformative regions such as black or white blocks in an image that will be discarded during training. As shown in Fig. 4, "HR" represents the hard regions with a smoothing value  $\varepsilon$  and "IR" represents the important regions. Thus, the key goal in FerKD becomes to identify the positive or background regions. Thanks to FKD [37], we can have access to all crops' individual predictions. A quick exploration is performed for verification and the result is shown in Fig. 5. It is clear that by discarding a certain ratio of samples (hardest and easiest), the performance is consistently improved.
+
+![](images/ea4777d789c346ce630f7283c271486c39c398b365ea5198bbc00b333e6f40f9.jpg)  
+Figure 4: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Right is the rule for calibrating the probabilities of regions.
+
+![](images/0a3efa6bc1417cc14040dd68621830d676baf260061b26f452bc2b2c76609a24.jpg)
+
+![](images/27dea78b149d51d6ee790a3c30b350739bf2307a3d3bf59d97575a9bf9ee970a.jpg)  
+Figure 5: Minimal and maximal probability. The upper figure indicates that only regions having the max probability in [minimal, 1.0] will be trained, and baseline indicates that the model is trained with all randomly sampled regions. The bottom figure indicates that only regions having the max probability in [0.3, maximal] will be trained, and baseline indicates that the model is trained with regions in [0.3, 1.0].
+
+# 3.3. Training Speed of FerKD
+
+When training a model, easy examples allow the model to quickly learn the patterns in the data and update its parameters in a way that minimizes the loss function. This means that the model will converge faster and require fewer
+
+iterations to reach a satisfactory level of accuracy. On the other hand, hard examples can slow down the convergence speed but they can force models to learn more robust classify boundaries. The speed of model convergence can be impacted significantly by the sampling strategy of hard and easy examples. In our FerKD framework, "hard" and "easy" examples refer to the level of difficulty a particular sample presents to a model. This difficulty can be quantified by the probability assigned to the correct label by the teacher. An "easy" sample is one where the probability assigned to the correct label is high, indicating that the teacher is confident in its prediction. On the other hand, a "hard" sample is one where the probability assigned to the correct label is low, indicating that the teacher is uncertain about its prediction. The threshold for what constitutes an "easy" or "hard" sample can vary depending on the specific task and model being used, which is the key for exploring in FerKD.
+
+![](images/08059131b74600089eb2e341e472ac1e7f9ffca1da42a31845729928cc2db414.jpg)  
+Figure 6: Illustration of the testing accuracy curves. "300" represents the training with the full budget. "50, 100, 150, 200" are the training with reduced budgets.
+
+Our sampling strategy involves the removal of the easiest and hardest training examples to reduce computational costs incurred during uninformative training steps. This strategy offers a clear benefit, as shown in Fig. 6, which presents the test accuracy curves for different training budgets. The results show that, with a training budget reduced by  $\frac{2}{3}$  (200 epochs), the achieved accuracy is comparable to that of full-budget training. Although further reducing the budget slightly affects accuracy, our proposed FerKD method is shown to be robust across different training budgets. Moreover, our calibration process will not involve additional training cost since it can be done offline in advance.
+
+# 3.4. SelfMix: A Mild and Stable Data Augmentation for Soft Labels
+
+Soft label Calibration with SelfMix. The current prevailing data augmentation techniques are designed for hard labels or smoothed hard labels. However, in the dynamic soft label scenario, a different approach is necessary to meet the unique attributes of pre-generated soft labels. Soft labels themselves can mitigate overfitting, making it imperative to develop tailored data augmentation techniques that account for soft labels to achieve improved accuracy. The proposed SelfMix is based on the empirical observations
+
+![](images/9a37e7877e023934295fb8892211f6a663b61ae2302e2c76b14100ff25dc7563.jpg)
+
+![](images/41997b7f6460c272016cf38635d14835963cba0110d81079bce7d86c6e622442.jpg)
+
+![](images/b1b0cf437d14723118e01ad855a101b5258e75fdac531939ae57531a531a88c6.jpg)
+
+![](images/3a629e2594ea24cb91d405d01261a4c39f436875f1ce249f10460c0827ca0a24.jpg)
+
+![](images/06271efbd6dec4aa9257de839a68ec674e02679afdc5f08c824cb5687ec9bb84.jpg)
+
+![](images/800e556b723cf1b0c20cb794cdf25a34b23881339299fed710c99ed06219305e.jpg)  
+Figure 7: Illustration of the high-level outline for SelfMix to make mixed soft label consistent, reducing the variance. Practically, each label will be a soft distribution for the input instead of the hard label as illustrated, thus it is more moderate on supervision in training. Empirically, it is observed that this strategy is crucial for ConvNet like ResNet but ViT needs intense data augmentations as introduced in [45].
+
+![](images/7b534e01caa9e059686119e4feaeb6b8b95af44f5ef9c607242b3831d11d303f.jpg)
+
+![](images/3e36f3d394b3573bd8d74b3be316365c9012200cfbacfb7b6c7b29120969fa67.jpg)
+
+presented in Table 2, which indicate that strong data augmentation does not necessarily improve accuracy if the network is already saturated and may even hurt performance. Consequently, we aim to reduce the intensity of data augmentation while still benefiting from its effects. To achieve this goal, we redesign the data augmentation using a self-mixing approach, as illustrated in Fig. 7.
+
+The specific steps involved in the SelfMix process are illustrated in Fig. 8. Mixing operations are exclusively conducted within each individual image to minimize variations between mixed images and their corresponding mixed soft labels. This straightforward constraint yields significant improvements in the performance of the ResNet backbone and in finetuning distillation.
+
+![](images/45a096ba7c78718ec83bd7a778279c1e315d74979cc137af8ad6330d3d78b362.jpg)  
+Figure 8: Illustration of the detailed SelfMix augmentation for FerKD. In this strategy, mixture operation only happens within the same image in a mini-batch and cross-image mixing is disabled to preserve stability of soft labels.
+
+Ensemble Supervisions. It has been demonstrated that assembling more teachers [13, 33] can enhance the performance of distilled students. In this work, we apply this approach to improve the quality of pre-existing soft labels. As
+
+<table><tr><td>Mixup</td><td>CutMix</td><td>SelfMix (Ours)</td><td>ResNet50</td><td>ViT-S/16</td></tr><tr><td>✓</td><td></td><td></td><td>78.94</td><td>80.32</td></tr><tr><td></td><td>✓</td><td></td><td>79.52</td><td>80.95</td></tr><tr><td></td><td></td><td>✓</td><td>80.47</td><td>79.29</td></tr><tr><td>✓</td><td>✓</td><td></td><td>79.92</td><td>81.16</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>80.26</td><td>80.69</td></tr></table>
+
+Table 2: Top-1 accuracy of data augmentations on different backbones. On ViT, the soft label can benefit from combinations of more mixture operations. The backbones are ResNet-50 and ViT-S/16 and the teacher model is Efficient-Net_L2_475. We run three trials and report the means.  
+
+<table><tr><td>Teacher</td><td>\( {\mathrm{T}}_{\text{Top-1 }}\left( \% \right) \)</td><td>\( {\mathrm{S}}_{\text{ResNet50 }}\left( \% \right) \)</td><td>\( {\mathrm{S}}_{\text{ViT-S/16 }}\left( \% \right) \)</td></tr><tr><td>Effi_L2_475 [52]</td><td>88.14</td><td>80.23</td><td>81.16</td></tr><tr><td>Effi_L2_800 [52]</td><td>88.39</td><td>80.16</td><td>81.30</td></tr><tr><td>RegY_128GF_384 [39]</td><td>88.24</td><td>80.34</td><td>81.42</td></tr><tr><td>ViT_L16_512 [39]</td><td>88.07</td><td>80.29</td><td>81.43</td></tr><tr><td>ViT_H14_518 [39]</td><td>88.55</td><td>80.18</td><td>81.41</td></tr><tr><td>BEIT_L_224 [2]</td><td>87.52</td><td>80.03</td><td>81.16</td></tr><tr><td>BEIT_L_384 [2]</td><td>88.40</td><td>80.06</td><td>81.11</td></tr><tr><td>BEIT_L_512 [2]</td><td>88.60</td><td>80.09</td><td>81.07</td></tr><tr><td>ViT_G14_336_30M [10]</td><td>89.59</td><td>79.03</td><td>79.62</td></tr><tr><td>ViT_G14_336_CLAMP [10]</td><td>89.38</td><td>79.59</td><td>79.48</td></tr></table>
+
+these soft labels are quantized for efficient storage [37], they must be recovered to their full dimension prior to calibration and averaging for final supervision. Specifically, we define the ensemble soft labels  $y_{en} = \frac{1}{M}\sum_{t\in \text{teachers}}\hat{y}_a^t (x)$ , where  $\hat{y}_a^t$  represents the recovered soft label with calibration from teacher  $t$ ,  $x$  is the input and  $M$  is the number of teachers.
+
+# 4. ImageNet Experiments
+
+We conduct training on the ImageNet-1K (IN1K) [9] training set. We report top-1 validation accuracy of a single  $224 \times 224$  crop. The default training budget is 300 epochs, and the temperature for both teacher and student is 1.0. The finetuning distillation settings follow their individual designs. All our soft label generation and model training are performed on the A100-GPU High-Flyer cluster with 80GB on each. More details are provided in Appendix.
+
+Baselines: FKD [37] and FunMatch [5]. Regions are randomly sampled in these two approaches. We use ResNet-50 and ViT-S/16 as the backbones for the ablation study. FKD + Curriculum Sampling: (i) we sample regions for training from easier ones and gradually increase the level of difficulty. (ii) In contrast, we sample regions from hard ones and gradually decrease the level of difficulty.
+
+# 4.1. Soft Label from Different Teachers
+
+The soft labels produced by distinct teacher models for the same input image may vary owing to differences in their
+
+Table 3: Top-1 accuracy of distillation on ImageNet-1K using a single ConvNet or Vision Transformer teacher. Note that Mixup [58] and CutMix [56] are used for training ViTs/16. We run three trials and report the means.  
+
+<table><tr><td>calibr. range</td><td>[0, 0.2]</td><td>[0, 0.3]</td><td>[0, 0.4]</td><td>[0, 0.5]</td><td>[0,0.6]</td></tr><tr><td>Top-1</td><td>80.31</td><td>80.42</td><td>80.14</td><td>79.84</td><td>79.66</td></tr></table>
+
+Table 4: Ablation of calibration for different probability ranges. The base model is the single teacher FerKD using ResNet-50 without SelfMix data augmentation.  
+
+<table><tr><td>Pre-train</td><td>Top-1</td></tr><tr><td>vanilla</td><td>80.23</td></tr><tr><td>+calibration&amp;selfmix</td><td>80.68+0.45</td></tr><tr><td>+multi-teacher ensemble</td><td>81.15+0.47</td></tr><tr><td>+more epochs</td><td>81.44+0.29</td></tr></table>
+
+Table 5: Ablation results using ResNet-50 on ImageNet-1K.
+
+distinctive features, architectures, and training strategies. In this section, our objective is to determine which teacher model has the greatest capacity to distill a student. We evaluate two types of student models: ResNet-50 and ViT-S/16. The results are shown in Table 3, where RegY_128GF_384 and ViT_L16_512 achieve the highest student accuracy individually, despite not being the best on their own.
+
+# 4.2. Ablations
+
+Ablation on Calibration. The results for different calibration ranges are shown in Table 4, it can be observed that [0, 0.3] achieves the best accuracy. In practice, we discard examples in [0, 0.15) and (0.95, 1.0], meanwhile, calibrate examples in [0.15, 0.3] for the final strategy. More visualization of the hardest and easiest regions is shown in Fig. 9.
+
+Ablation on teacher ensemble and training budget. The results are in Table 5, showing that each design has the consistent improvement. Our final results are shown in Table 8, FerKD performs the best over other SOTA methods.
+
+# 4.3. Curriculum Distillation
+
+In curriculum distillation, the student model learns from the teachers' knowledge in a sequential manner, starting from easier examples (high probability regions) and gradually increasing the level of difficulty. This allows the student model to learn from easier to more complex regions. By presenting samples in a curriculum, the student model can learn from the easier samples and build a strong foundation before being exposed to more challenging samples. However, our experimental results, as shown in Table 7, demonstrate that this curriculum learning approach is inferior to our surgical label adaptation strategy, FerKD. Our approach outperforms curriculum distillation by  $0.8\%$ . We attribute this performance improvement to the strong ability of soft labels to mitigate overfitting and improve generalization in the initial stages of training. As a result, the advantage of the curriculum learning approach is not as apparent in this scenario. We also notice that "e-to-h" performs slightly better than "h-to-e" demonstrating the effectiveness of curriculum strategy, while both of them are
+
+<table><tr><td>Effi.L2_475</td><td>Effi.L2_800</td><td>RegY_128GF_384</td><td>ViT_L16_512</td><td>ViT_H14_518</td><td>BEIT_224</td><td>BEIT_384</td><td>BEIT_512</td><td>Student Acc.</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>80.23</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.49</td></tr><tr><td></td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>80.29</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>80.53</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>80.48</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>80.35</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.35</td></tr><tr><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.38</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.53</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.62</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.74</td></tr></table>
+
+Table 6: Ablation top-1 accuracy of teacher ensemble on ImageNet-1K with ConvNet, Vision Transformer or hybrid teachers. The left group is ConvNet teachers, the middle is the ViT teachers and the right group is the corresponding student ResNet-50 accuracy. Note that surgical calibration and SelfMix are not used here.  
+
+<table><tr><td>Method</td><td>sampling</td><td>Top-1</td></tr><tr><td>Random (FKD [37])</td><td>random</td><td>80.2</td></tr><tr><td>curriculum distillation</td><td>h-to-e</td><td>79.7</td></tr><tr><td>curriculum distillation</td><td>e-to-h</td><td>79.9</td></tr><tr><td>FerKD (Ours)</td><td>surgical</td><td>80.7</td></tr></table>
+
+Table 7: Curriculum and surgical (no ensemble) distillation. "e-to-h" refers to curriculum sampling from easy to hard regions. "h-to-e" refers to sampling from hard to easy.  
+
+<table><tr><td>Model</td><td>Epoch</td><td>Label</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>600</td><td>HardLS</td><td>80.4</td></tr><tr><td>Pytorch (advanced) [44]</td><td>600</td><td>HardLS</td><td>80.9</td></tr><tr><td>MEAL [33]</td><td>100‡</td><td>Soft</td><td>78.2</td></tr><tr><td>MEAL V2 [36]</td><td>180‡</td><td>Soft</td><td>80.7</td></tr><tr><td>MEAL V2 [36]w/CutMix</td><td>180‡</td><td>Soft</td><td>81.0</td></tr><tr><td>ReLU [57]w/CutMix</td><td>300</td><td>Soft</td><td>80.2</td></tr><tr><td>FunMatch [5]w/Mixup</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FKD [37]</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FerKD (Ours)</td><td>300</td><td>Adap</td><td>81.2+0.7</td></tr><tr><td>FerKD (Ours)</td><td>600</td><td>Adap</td><td>81.4+0.9</td></tr></table>
+
+inferior to the random sampling baseline.
+
+# 4.4. Finetuning Distillation
+
+Finetuning distillation [36] has been demonstrated as an effective approach to improve the accuracy of knowledge distillation (KD) frameworks. In the case of hard labels, multiple finetuning schemes have been proposed to adapt the model parameters to fit the target dataset, including partial finetuning on selected intermediate layers with varying learning rates [34, 1, 17, 30] or on the last few layers [55]. In this work, we adopt the MEAL V2 [36] protocol by fine
+
+Table 8: Top-1 accuracy on ImageNet-1K dataset. The backbone network in this table is ResNet-50.  $\ddagger$  indicates that the model was fine-tuned from hard-label pre-trained weights, resulting in a total training epoch of  $300 + \times$ .  
+
+<table><tr><td>Pre-train</td><td>FT</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>HardLS</td><td>80.38</td></tr><tr><td>Timm [49]</td><td>FKD [37]*</td><td>80.62</td></tr><tr><td>Timm [49]</td><td>FerKD* (Ours)</td><td>81.06</td></tr><tr><td>SWAG [39]</td><td>HardLS</td><td>87.22</td></tr><tr><td>SWAG [39]</td><td>FKD [37]†</td><td>87.42</td></tr><tr><td>SWAG [39]</td><td>FerKD† (Ours)</td><td>87.76</td></tr><tr><td>EVA_MIM [10]</td><td>HardLS</td><td>89.59</td></tr><tr><td>EVA_MIM [10]</td><td>FKD [37]</td><td>89.67</td></tr><tr><td>EVA_MIM [10]</td><td>FerKD (Ours)</td><td>89.86</td></tr></table>
+
+Table 9: Fine-tuning distillation results using pre-trained ResNet-50 (Timm), RegNetY-128GF (SWAG) and ViT-G14 (EVA) on ImageNet-1K. We use the same recipe of EVA for SWAG finetuning since SWAG did not provide the complete fine-tuning details. * On ResNet-50, we finetune with 150 epochs for both FKD and FerKD.
+
+tuning the entire network from the pre-trained weights to evaluate the effectiveness of distillation with surgical soft label calibration as the objective. Specifically, we employ three types of pre-trained models:
+
+(1) Supervised pre-train: ResNet-50 on Timm [49];  
+(2) Weakly-supervised pre-train: RegNetY-128GF from SWAG [39];  
+(3) Self-supervised pre-train: ViT-G14 from EVA [10];
+
+We verify whether FerKD can continue improving finetuning distillation. As shown in Table 9, FerKD achieves consistent improvement across different architectures.
+
+# 4.5. Single Teacher vs. Teacher Ensemble
+
+The soft labels generated by different teachers for the same input image can be different due to their unique features, architectures, and training strategies. By combining these soft labels from different teachers, the resulting label becomes more informative and can help the student model learn better representations. This approach can be
+
+![](images/89600f3326a0f5f362e5ce06100d93bb05ac6d516c7fe09c14aeac37a3d9afe8.jpg)  
+Figure 9: Illustration of the location points from RandomResizedCrop and the identified crops by teacher model for hard and easy samples. Note that we do not involve any localization information, but teacher's probability can reflect it automatically.
+
+![](images/7c1b3c6c5e42b667a6ed879799443a828ad872e5999748083157d38ab7b8eb3a.jpg)
+
+![](images/21e6cd583df93bcc84aa6b87be885000e43b50c2590516e402f48f2fcfaba27e.jpg)
+
+![](images/bc4be51cdc9c60820ce90b1f0c62721b39bfbb3e166875f6f61bea826727f2b0.jpg)
+
+![](images/8d698a158e19f969131b447f12bd830b1a42fc80aec056e74a5f304e7462afab.jpg)
+
+![](images/a8fd7759b85ced8dba181b121ef1a9db8313ab4263461e0f7db44f2491b906c4.jpg)
+
+![](images/8257b3649d46b8fff20f73be98120652b916321021538c9d20173d16975921bb.jpg)
+
+![](images/855a5776c531d30fe45b95083f3d1fbe192be7f530ab75eda610a1e7ac338eb9.jpg)
+
+<table><tr><td>Method</td><td>Label</td><td>APbox</td><td>APmask</td></tr><tr><td>ReLU [57]</td><td>LM</td><td>39.1</td><td>35.2</td></tr><tr><td>FKD [37]</td><td>Soft</td><td>39.7</td><td>35.9</td></tr><tr><td>FerKD (Ours)</td><td>Adap</td><td>40.2</td><td>36.3</td></tr></table>
+
+Table 10: COCO object detection and segmentation using a Mask-RCNN with FPN baseline. "LM" represents label map during pretraining. The backbone is ResNet-50-300ep.  
+
+<table><tr><td>Method</td><td>iNat 2019224</td><td>iNat 2019336</td><td>Places365224</td></tr><tr><td>EVA_MIM [10]</td><td>79.9</td><td>86.6</td><td>61.0</td></tr><tr><td>FerKD (Ours)</td><td>80.3+0.4</td><td>87.1+0.5</td><td>61.4+0.4</td></tr></table>
+
+particularly useful in scenarios where the teacher models have complementary strengths or when the input data is challenging and requires multiple perspectives to be accurately labeled. Furthermore, the use of multiple teachers can also help mitigate the effects of overfitting and improve the generalization performance of the student model. The results are shown in Table 6, assembling four hybrid teachers of Effi_L2_475, RegY_128GF_384, ViT_L16_512, and ViT_H14_518 achieves the best accuracy.
+
+# 5. Transfer Learning Experiments
+
+Object detection and segmentation. We conducted evaluations to investigate whether the improvement achieved by FerKD on ImageNet-1K can be transferred to various downstream tasks. Specifically, Table 10 presents the results of object detection and segmentation on COCO dataset [21] using models pre-trained on ImageNet-1K with FerKD. We utilize Mask RCNN [12] with FPN [19] following FKD for the experiment. Our FerKD pre-trained weight consistently outperforms both the baselines ReLabel and FKD on the downstream tasks.
+
+Classification tasks. Table 11 shows the transfer learning result on iNaturalists [14] and Places [60] datasets. On both of these two datasets, our results surpass the baseline EVA pretrained model by significant margins.
+
+Table 11: Transfer learning accuracy on various classification datasets. The input sizes are  $224 \times 224$  and  $336 \times 336$ .  
+
+<table><tr><td>Method</td><td>IN1K</td><td>ReAL</td><td>ImageNetV2 Top-images</td><td>ImageNetV2 Matched-freq</td><td>ImageNetV2 Threshold-0.7</td></tr><tr><td colspan="6">ResNet-50:</td></tr><tr><td>ReLU [57]</td><td>78.9</td><td>85.0</td><td>80.5</td><td>67.3</td><td>76.0</td></tr><tr><td>FKD [37]</td><td>80.1</td><td>85.8</td><td>81.2</td><td>68.2</td><td>76.9</td></tr><tr><td>FerKD</td><td>81.2</td><td>86.4+0.6</td><td>82.1+0.9</td><td>69.5+1.3</td><td>77.8+0.9</td></tr><tr><td colspan="6">ViT-G14-336:</td></tr><tr><td>EVA [10]</td><td>89.6</td><td>90.8</td><td>89.0</td><td>81.9</td><td>86.7</td></tr><tr><td>FerKD</td><td>89.9</td><td>91.3+0.5</td><td>89.4+0.4</td><td>82.4+0.5</td><td>87.1+0.4</td></tr></table>
+
+Table 12: Results of FerKD on ImageNet RealL [4] and ImageNetV2 [29] with ResNet-50 and ViT-G14 backbones.
+
+# 6. Robustness
+
+We provide comparisons on ImageNet Real [4] and ImageNetV2 [29] datasets to examine the robustness of FerKD trained models. On ImageNetV2 [29], we verify our FerKD models on three metrics "Top-Images", "Matched Frequency", and "Threshold 0.7" following FKD [37]. We perform experiments on two network structures: ResNet-50 and ViT-G14. The results are shown in Table 12, we achieve consistent improvement over ReLabel and FKD on ResNet-50  $(224\times 224)$  and better accuracy than EVA on ViT-G14  $(336\times 336)$ .
+
+# 7. Conclusion
+
+In this work, we have presented a new paradigm of faster knowledge distillation (FerKD), which employs label adaptation on randomly cropped regions. The proposed method outperforms existing state-of-the-art distillation approaches in terms of both training speed and convergence. Additionally, we make two key observations that could be leveraged in future studies. Firstly, we notice that the most challenging and easiest few crops obtained through the RandomResizedCrop operation do not contribute to the model's learning and can thus be discarded. Secondly, we find that moderate hardness crops can provide crucial context information that helps calibrate the model to learn more robust representations, which in turn benefit downstream tasks.
+
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+[55] Jason Yosinski, Jeff Clune, Yoshua Bengio, and Hod Lipson. How transferable are features in deep neural networks? NeurIPS, 27, 2014. 7  
+[56] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In ICCV, 2019. 1, 6  
+[57] Sangdoo Yun, Seong Joon Oh, Byeongho Heo, Dongyoon Han, Junsuk Choe, and Sanghyuk Chun. Re-labeling image: from single to multi-labels, from global to localized labels. In CVPR, 2021. 3, 7, 8  
+[58] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In ICLR, 2018. 1, 6  
+[59] Linfeng Zhang, Jiebo Song, Anni Gao, Jingwei Chen, Chenglong Bao, and Kaisheng Ma. Be your own teacher: Improve the performance of convolutional neural networks via self distillation. In ICCV, 2019. 3  
+[60] Bolei Zhou, Agata Lapedriza, Jianxiong Xiao, Antonio Torralba, and Aude Oliva. Learning deep features for scene recognition using places database. NeurIPS, 2014. 8
\ No newline at end of file
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+                                    "content": " on ImageNet-1K with ResNet-50, outperforming FKD and FunMatch by remarkable margins. Leveraging better pre-trained weights and larger architectures, our finetuned ViT-G14 even achieves "
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+                                            "content": "Figure 1: Illustration of motivation for FerKD. The left figure depicts the original input, and the middle figure shows the center points of bounding boxes generated using RandomResizedCrop. The radius of each circle corresponds to the area of the bounding box. It can be observed that the center points of the bounding boxes are concentrated in the center of the image, and their area increases as they approach the center. The right figure displays several top and bottom confident bounding boxes and their corresponding predictive probabilities from a pre-trained teacher or teachers ensemble. The proposed hard region calibration strategy is established based on these predictions."
+                                        }
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+                                    "content": "sification [52, 36, 5, 37], object detection [6, 46, 11, 8, 53] and semantic segmentation [22, 15, 16]. However, KD methods are often computationally expensive and inefficient due to the additional computational burden imposed by the teacher models. The primary advantage of KD that motivates its usage is its ability to generate precise soft labels that convey more informative details about the input examples. It differs from other label softening techniques, such as label smoothing [43], Mixup [58], and CutMix [56], mainly in two aspects: (1) KD generates soft labels dynamically in each iteration, which is more informative than fixed smoothing patterns used in label smoothing; (2) Mixup and CutMix techniques essentially combine hard labels with coefficients, while KD produces soft labels that are highly correlated with the input sample. This allows KD's soft labels to become more accurate when different data augmentations, such as RandomResizedCrop, flipping and rotation, color jittering, etc., are applied. In general, mixing-based label softening methods cannot monitor such changes in input content, but KD can address them effortlessly."
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+                                            "content": "Figure 2: Statistics of soft label max-probability for crops on ImageNet-1K. The soft label is from FKD [37]. In each image, 500 regions are randomly cropped."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "content": "To overcome the computational inefficiency of traditional knowledge distillation, FKD [37] was developed to generate region-level soft labels in advance and reuse them across multiple training cycles to eliminate redundant computation. This approach only requires the preparation of soft labels once at the beginning and they can be reused indefinitely. However, this approach overlooks certain critical issues. One is the quality of the soft labels. When using RandomResizedCrop to generate regions, some may be cropped from background areas, and the teacher model will still produce a soft label for them based on their similarity to the dataset classes. However, in some cases, these areas may contain irrelevant noise, compensatory information, or context information for the class, and the soft labels may not accurately reflect the context of information they carry. To address this problem, this work proposes to recalibrate these soft labels by incorporating context information from hard ground-truth labels with smoothing."
+                                }
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+                    ],
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+                                    "content": "Furthermore, due to the random nature of the sampling process, a certain proportion of crops that are either excessively easy or difficult do not contribute to the model's learning capacity. As demonstrated in Fig. 2 and Table 1, these samples can be discarded to expedite the convergence process. The pre-generated soft labels can be utilized as useful indicators to select these specific samples. In our adaptation of surgical soft labeling, we categorize the soft labels into four distinct groups: extreme hard (negative), moderate hard (background or context), hard positive (partial object), and easy positive. Each of these categories is subject to different treatment methodologies."
+                                }
+                            ]
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+                                    "content": "The Role of Background. The role of the background in images is essential, as it provides critical context and spatial information that aids the model in accurately identifying objects of interest within the scene. Backgrounds can vary in complexity and structure, ranging from simple monochromatic backgrounds to highly cluttered and detailed ones. Soft labels in background areas are typically low, and therefore, it is crucial to handle the background carefully with precise supervision to achieve higher model capability within our surgical label calibration framework."
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+                                    "content": "Hard Regions Mining and Calibration. Hard Regions Mining involves the identification and isolation of chal"
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+                                            "html": "<table><tr><td>range (P)</td><td>ratio</td><td>range (P)</td><td>agg. ratio</td></tr><tr><td>[0.0, 0.1)</td><td>0.43%</td><td>[0, 0.1)</td><td>0.43%</td></tr><tr><td>[0.1, 0.2)</td><td>0.89%</td><td>[0, 0.2)</td><td>1.32%</td></tr><tr><td>[0.2, 0.3)</td><td>1.29%</td><td>[0, 0.3)</td><td>2.61%</td></tr><tr><td>[0.3, 0.4)</td><td>2.03%</td><td>[0, 0.4)</td><td>4.64%</td></tr><tr><td>[0.4, 0.5)</td><td>3.66%</td><td>[0, 0.5)</td><td>8.31%</td></tr><tr><td>[0.5, 0.6)</td><td>4.35%</td><td>[0, 0.6)</td><td>12.65%</td></tr><tr><td>[0.6, 0.7)</td><td>5.04%</td><td>[0, 0.7)</td><td>17.69%</td></tr><tr><td>[0.7, 0.8)</td><td>7.76%</td><td>[0, 0.8)</td><td>25.45%</td></tr><tr><td>[0.8, 0.85)</td><td>8.14%</td><td>[0, 0.85)</td><td>33.59%</td></tr><tr><td>[0.85, 0.9)</td><td>28.73%</td><td>[0, 0.9)</td><td>62.32%</td></tr><tr><td>[0.9, 0.95)</td><td>37.34%</td><td>[0, 0.95)</td><td>99.67%</td></tr><tr><td>[0.95, 1.0)</td><td>0.33%</td><td>[0, 1.0)</td><td>100%</td></tr></table>",
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+                                    "content": "Table 1: Detailed statistics of soft labels. \"range\" indicates max-probability of crops, \"ratio\" indicates the percentage in the whole crops. \"agg. ratio\" is the aggregated ratio."
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+                                    "content": "lenging or complex regions within an image that the model struggles to identify accurately. These regions can include objects with complex shapes, occlusions, or those with low contrast. By identifying these regions, the model can focus on learning the features and characteristics of these regions, resulting in improved performance. Calibration, on the other hand, involves adjusting the confidence levels of the model's predictions in challenging regions. The model's predictions may be less reliable in hard regions, leading to lower confidence scores. Calibrating the predictions can improve the model's accuracy in these regions by adjusting the confidence levels of the predictions. We found that carefully discarding a portion of negative crops and selecting those hard positive crops by calibrating their labels, can force the training process more efficient and effective."
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+                                    "content": "Stable Training on Soft Labels. Mixture-based augmentations, such as Mixup and CutMix have seen widespread use for training models under hard supervision, where each image is labeled with a single class label. However, in the soft label scenario, we have made a different observation: when employed together with pre-generated soft labels on a typical ResNet, Mixup and CutMix tend to be overly strong, which, conversely, leads to decreased performance. To mitigate label fluctuations and achieve more stable training, we propose a SelfMix scheme, which is particularly suitable for cases where data augmentation should not be so strong, such as in finetuning distillation, where mixture-based augmentation is usually disabled. On the other hand, when training ViT models from scratch, stronger data augmentation can yield better results [45, 42], which is consistent with the larger capacity perspective of this type of network."
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+                                    "content": "In summary, our contributions of this work are:"
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+                                    "type": "text",
+                                    "content": "- We present FerKD, a sample-calibration framework for Faster Knowledge Distillation that achieves state-of-the-art performance. We conduct extensive analysis, ablation, and discussion on the impact of hard and easy samples."
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+                                    "content": "- We make two key observations in the pre-generated soft"
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+                                    "content": "label training framework. Firstly, we observe that the few most challenging and simplest crops obtained through the RandomResizedCrop operation do not contribute significantly to the model's learning and can therefore be removed. Secondly, we find that moderately hard crops can provide crucial contextual information that improves the model's ability to learn robust representations."
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+                                    "content": "- We perform extensive experiments on ImageNet-1K and downstream tasks. On ImageNet-1K, FerKD achieves an accuracy of "
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+                                    "content": " using the ResNet-50. When leveraging self-supervised pre-trained weights, our larger model finetuned using ViT-G/14 achieves an accuracy of "
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+                                    "content": "."
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+                                    "content": "2. Related Work"
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+                                    "type": "text",
+                                    "content": "Knowledge Distillation and Fast Knowledge Distillation. Knowledge Distillation [13] is a learning method in which a \"student\" model is trained to imitate the predictions of a larger, more complex \"teacher\" model. A key advantage of this approach is that the teacher model can provide soft supervision that contains more information regarding the input data than traditional one-hot human annotated labels, particularly when the input data is subject to data augmentation. There have been many recent variants and extensions of knowledge distillation [31, 26, 47, 59, 25, 27, 35, 7, 41, 50, 45, 18, 51], including approaches that use internal feature representations [7], adversarial training with discriminators [33], transfer learning techniques [54], fast distillation [37] via instance label preparation, and methods that prioritize patient and consistent learning [5]."
+                                }
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+                                    "type": "text",
+                                    "content": "Hard Sample Mining. The aim of hard sample mining [23, 38] is to enhance the performance of learning models by selectively focusing on challenging examples that are typically difficult to classify. By prioritizing hard samples during training, models can be trained to better handle a wider range of real-world scenarios and improve their overall performance. One approach [38] to achieve this for object detection is to use Online Hard Example Mining (OHEM) which employs a strategy of selecting challenging examples during training of region-based ConvNet detectors. The motivation behind this approach is that detection datasets typically comprise an overwhelming number of easy examples and a small number of hard examples. Automatic selection of these hard examples can make training more effective and efficient."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "type": "text",
+                                    "content": "Some other techniques that are close to hard sample mining: (1) Curriculum learning [3, 48, 40]: it trains a model on easy examples first and then gradually increasing the difficulty of the examples over time. (2) Active learning [32, 24, 28]: it selects the most informative or uncertain samples for labeling by a human annotator. By focusing on the samples that the model is most uncertain about, the model can learn to better generalize and improve its performance on difficult samples. (3) Loss functions: Attentive"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "loss functions can be used to emphasize the importance of hard samples during training. For example, focal loss [20] places more weight on the difficult examples during training, helping the model to learn to handle them better."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Data Augmentations. Several studies have incorporated data augmentations into distillation frameworks to improve performance. For instance, FunMatch [5] employed Mixup, and FKD [37] utilized CutMix. Both techniques achieved competitive accuracy on large-scale ImageNet-1K dataset. In this work, we investigate the impact of data augmentation intensity on soft labels. We discover that different network architectures require unique data augmentation levels. Specifically, ResNet necessitates mild data augmentation, while ViTs require stronger data augmentation. However, even for ViTs, finetuning distillation requires a reduction in the intensity of data augmentation, especially for mixture-based methods. Motivated by this observation, we propose a mild SelfMix approach for ResNet and finetuning distillation scenarios."
+                                }
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+                                    "content": "3. Approach"
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+                                    "content": "The proposed FerKD is a soft label calibration framework for fast and efficient knowledge distillation training. In this section, we aim to provide an elaborated overview of our method, starting with an in-depth analysis of the roles of hard and soft labels in the distillation process. We then present the key components of our approach, which include a region selection strategy and a soft label calibration scheme. Additionally, we explore the data augmentation requirements for soft labels and introduce a simple label ensemble technique to enhance the quality of the soft labels."
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+                                    "content": "3.1. Revisiting Hard and Soft Label in Distillation"
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+                                    "content": "The utilization of hard and soft labels is dependent on the comprehension, problem scenarios, and underlying objectives. Various arguments exist regarding their effectiveness. The vanilla knowledge distillation method [13] employs both hard and soft labels to maximize the benefits of both. However, recent researches [36, 35, 57, 37] suggest that the use of hard labels is not necessary in distillation on large-scale datasets as strong teachers can provide more precise soft supervision. Incorporating hard labels may introduce erroneous supervisory signals, ultimately hampering student performance. Other than the above views, this work presents a novel perspective beyond them by acknowledging that both hard and soft labels offer unique advantages, highlights the proper practice of usage that is necessary, and finally proposes an elegant solution to reap benefits derived from both sources of hard and soft labels."
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+                                    "content": "Combination of Soft and Hard Labels. In vanilla KD design [13], for each training example, it will minimize two loss terms for both hard and soft labels. The final objective"
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+                                            "content": "Figure 3: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Bounding box is with high probability and bounding box is with low probability."
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+                                    "content": " can be formulated as:"
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+                                    "content": "\\mathcal {L} _ {V K D} = \\frac {1}{N} \\sum_ {x} (\\alpha * \\underbrace {\\mathcal {L} _ {h} \\left(p _ {\\theta} (x) , y _ {h} (x)\\right)} _ {\\text {C E l o s s w i t h h a r d l a b e l}} + (1 - \\alpha) * \\underbrace {\\mathcal {L} _ {s} \\left(p _ {\\theta} (x) , y _ {s} (x)\\right)} _ {\\text {K L l o s s w i t h s o f t l a b e l}}) \\tag {1}",
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+                                    "content": " is the coefficient to balance the loss signal intensity from soft and hard labels. "
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+                                    "content": " is the logits prediction from the student model and "
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+                                    "type": "text",
+                                    "content": " is the hard label and "
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+                                    "content": " is the soft label from a pre-trained teacher. "
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+                                    "type": "text",
+                                    "content": " is the total number of training samples "
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+                                    "type": "text",
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+                                    "content": "Full Soft Label Training. Fast KD [37] proposes to use the soft label solely since the prediction from strong teachers is precise enough. Thus, the loss objective "
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {F K D} = \\frac {1}{N} \\sum_ {x} \\underbrace {\\hat {\\mathcal {L}} _ {s} \\left(p _ {\\theta} (x) , y _ {s} (x)\\right)} _ {\\text {S C E l o s s w i t h s o f t l a b e l}} \\tag {2}",
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+                                    "type": "text",
+                                    "content": "where \"SCE\" is the soft version of cross-entropy loss."
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+                                    "content": "3.2. FerKD: Surgical Label Calibration Distillation"
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+                                    "type": "text",
+                                    "content": "Surgical/Partial Soft and Hard Label Adaptive Training. Different from VKD, the proposed FerKD strategy will only involve one loss term but also unlike FKD, FerKD will employ both hard and soft labels in a single objective term and exploit the additional information derived from both sources. The solution is that we only keep their original soft labels for positive regions since they contain fine-grained information regarding the crops, for those background or context regions, we will re-calibrate them by the human-annotated ground-truth labels to avoid misinformation from the soft labels. Hence, the loss function will be:"
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+                                    "content": "\\mathcal {L} _ {\\text {F e r K D}} = \\frac {1}{N} \\sum_ {x} \\underbrace {\\mathcal {L} _ {\\text {a d a p : h o r s ?}} \\left(p _ {\\theta} (x) , y _ {a} (x)\\right)} _ {\\text {S C E l o s s w i t h h a r d / s o f t l a b e l}} \\tag {3}",
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+                                    "type": "text",
+                                    "content": "where \"adap:\" indicates "
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+                                    "content": " used for individual training samples. "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the calibrated soft labels. As illustrated in Fig. 3, we will calibrate regions' soft labels "
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+                                    "type": "text",
+                                    "content": " using the following rule:"
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+                                    "content": "y _ {a} = \\left\\{ \\begin{array}{l l} \\mathbf {U R}: \\text {d i s c a r d e d} & \\text {i f} y _ {s} <   \\mathcal {T} _ {L} \\text {o r} y _ {s} > \\mathcal {T} _ {T} \\\\ \\mathbf {H R}: \\mathbf {1 . 0} - \\varepsilon & \\text {i f} \\mathcal {T} _ {L} <   y _ {s} <   \\theta_ {M} \\\\ \\mathbf {I R}: y _ {s} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}",
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are thresholds at low, middle, and top boundaries. \"UR\" represents the uninformative regions such as black or white blocks in an image that will be discarded during training. As shown in Fig. 4, \"HR\" represents the hard regions with a smoothing value "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\varepsilon"
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+                                    "type": "text",
+                                    "content": " and \"IR\" represents the important regions. Thus, the key goal in FerKD becomes to identify the positive or background regions. Thanks to FKD [37], we can have access to all crops' individual predictions. A quick exploration is performed for verification and the result is shown in Fig. 5. It is clear that by discarding a certain ratio of samples (hardest and easiest), the performance is consistently improved."
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 4: Illustration of region calibration according to their predictive probabilities in FerKD. Left is the input image with RandomResizedCrop. Right is the rule for calibrating the probabilities of regions."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "content": "Figure 5: Minimal and maximal probability. The upper figure indicates that only regions having the max probability in [minimal, 1.0] will be trained, and baseline indicates that the model is trained with all randomly sampled regions. The bottom figure indicates that only regions having the max probability in [0.3, maximal] will be trained, and baseline indicates that the model is trained with regions in [0.3, 1.0]."
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+                                    "content": "3.3. Training Speed of FerKD"
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+                                    "content": "When training a model, easy examples allow the model to quickly learn the patterns in the data and update its parameters in a way that minimizes the loss function. This means that the model will converge faster and require fewer"
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+                                    "content": "iterations to reach a satisfactory level of accuracy. On the other hand, hard examples can slow down the convergence speed but they can force models to learn more robust classify boundaries. The speed of model convergence can be impacted significantly by the sampling strategy of hard and easy examples. In our FerKD framework, \"hard\" and \"easy\" examples refer to the level of difficulty a particular sample presents to a model. This difficulty can be quantified by the probability assigned to the correct label by the teacher. An \"easy\" sample is one where the probability assigned to the correct label is high, indicating that the teacher is confident in its prediction. On the other hand, a \"hard\" sample is one where the probability assigned to the correct label is low, indicating that the teacher is uncertain about its prediction. The threshold for what constitutes an \"easy\" or \"hard\" sample can vary depending on the specific task and model being used, which is the key for exploring in FerKD."
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+                                            "content": "Figure 6: Illustration of the testing accuracy curves. \"300\" represents the training with the full budget. \"50, 100, 150, 200\" are the training with reduced budgets."
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+                                    "content": "Our sampling strategy involves the removal of the easiest and hardest training examples to reduce computational costs incurred during uninformative training steps. This strategy offers a clear benefit, as shown in Fig. 6, which presents the test accuracy curves for different training budgets. The results show that, with a training budget reduced by "
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+                                    "content": " (200 epochs), the achieved accuracy is comparable to that of full-budget training. Although further reducing the budget slightly affects accuracy, our proposed FerKD method is shown to be robust across different training budgets. Moreover, our calibration process will not involve additional training cost since it can be done offline in advance."
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+                                    "content": "Soft label Calibration with SelfMix. The current prevailing data augmentation techniques are designed for hard labels or smoothed hard labels. However, in the dynamic soft label scenario, a different approach is necessary to meet the unique attributes of pre-generated soft labels. Soft labels themselves can mitigate overfitting, making it imperative to develop tailored data augmentation techniques that account for soft labels to achieve improved accuracy. The proposed SelfMix is based on the empirical observations"
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+                                    "content": "presented in Table 2, which indicate that strong data augmentation does not necessarily improve accuracy if the network is already saturated and may even hurt performance. Consequently, we aim to reduce the intensity of data augmentation while still benefiting from its effects. To achieve this goal, we redesign the data augmentation using a self-mixing approach, as illustrated in Fig. 7."
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+                                            "content": "Figure 8: Illustration of the detailed SelfMix augmentation for FerKD. In this strategy, mixture operation only happens within the same image in a mini-batch and cross-image mixing is disabled to preserve stability of soft labels."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "Ensemble Supervisions. It has been demonstrated that assembling more teachers [13, 33] can enhance the performance of distilled students. In this work, we apply this approach to improve the quality of pre-existing soft labels. As"
+                                }
+                            ]
+                        }
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+                                            "html": "<table><tr><td>Mixup</td><td>CutMix</td><td>SelfMix (Ours)</td><td>ResNet50</td><td>ViT-S/16</td></tr><tr><td>✓</td><td></td><td></td><td>78.94</td><td>80.32</td></tr><tr><td></td><td>✓</td><td></td><td>79.52</td><td>80.95</td></tr><tr><td></td><td></td><td>✓</td><td>80.47</td><td>79.29</td></tr><tr><td>✓</td><td>✓</td><td></td><td>79.92</td><td>81.16</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>80.26</td><td>80.69</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 2: Top-1 accuracy of data augmentations on different backbones. On ViT, the soft label can benefit from combinations of more mixture operations. The backbones are ResNet-50 and ViT-S/16 and the teacher model is Efficient-Net_L2_475. We run three trials and report the means."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "html": "<table><tr><td>Teacher</td><td>\\( {\\mathrm{T}}_{\\text{Top-1 }}\\left( \\% \\right) \\)</td><td>\\( {\\mathrm{S}}_{\\text{ResNet50 }}\\left( \\% \\right) \\)</td><td>\\( {\\mathrm{S}}_{\\text{ViT-S/16 }}\\left( \\% \\right) \\)</td></tr><tr><td>Effi_L2_475 [52]</td><td>88.14</td><td>80.23</td><td>81.16</td></tr><tr><td>Effi_L2_800 [52]</td><td>88.39</td><td>80.16</td><td>81.30</td></tr><tr><td>RegY_128GF_384 [39]</td><td>88.24</td><td>80.34</td><td>81.42</td></tr><tr><td>ViT_L16_512 [39]</td><td>88.07</td><td>80.29</td><td>81.43</td></tr><tr><td>ViT_H14_518 [39]</td><td>88.55</td><td>80.18</td><td>81.41</td></tr><tr><td>BEIT_L_224 [2]</td><td>87.52</td><td>80.03</td><td>81.16</td></tr><tr><td>BEIT_L_384 [2]</td><td>88.40</td><td>80.06</td><td>81.11</td></tr><tr><td>BEIT_L_512 [2]</td><td>88.60</td><td>80.09</td><td>81.07</td></tr><tr><td>ViT_G14_336_30M [10]</td><td>89.59</td><td>79.03</td><td>79.62</td></tr><tr><td>ViT_G14_336_CLAMP [10]</td><td>89.38</td><td>79.59</td><td>79.48</td></tr></table>",
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+                                        }
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+                                }
+                            ],
+                            "index": 2,
+                            "angle": 0,
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+                    ],
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+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "these soft labels are quantized for efficient storage [37], they must be recovered to their full dimension prior to calibration and averaging for final supervision. Specifically, we define the ensemble soft labels "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "y_{en} = \\frac{1}{M}\\sum_{t\\in \\text{teachers}}\\hat{y}_a^t (x)"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{y}_a^t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the recovered soft label with calibration from teacher "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the input and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of teachers."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4. ImageNet Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We conduct training on the ImageNet-1K (IN1K) [9] training set. We report top-1 validation accuracy of a single "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "224 \\times 224"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " crop. The default training budget is 300 epochs, and the temperature for both teacher and student is 1.0. The finetuning distillation settings follow their individual designs. All our soft label generation and model training are performed on the A100-GPU High-Flyer cluster with 80GB on each. More details are provided in Appendix."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Baselines: FKD [37] and FunMatch [5]. Regions are randomly sampled in these two approaches. We use ResNet-50 and ViT-S/16 as the backbones for the ablation study. FKD + Curriculum Sampling: (i) we sample regions for training from easier ones and gradually increase the level of difficulty. (ii) In contrast, we sample regions from hard ones and gradually decrease the level of difficulty."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.1. Soft Label from Different Teachers"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The soft labels produced by distinct teacher models for the same input image may vary owing to differences in their"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "type": "table",
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+                                            "type": "text",
+                                            "content": "Table 3: Top-1 accuracy of distillation on ImageNet-1K using a single ConvNet or Vision Transformer teacher. Note that Mixup [58] and CutMix [56] are used for training ViTs/16. We run three trials and report the means."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
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+                                            "html": "<table><tr><td>calibr. range</td><td>[0, 0.2]</td><td>[0, 0.3]</td><td>[0, 0.4]</td><td>[0, 0.5]</td><td>[0,0.6]</td></tr><tr><td>Top-1</td><td>80.31</td><td>80.42</td><td>80.14</td><td>79.84</td><td>79.66</td></tr></table>",
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+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Table 4: Ablation of calibration for different probability ranges. The base model is the single teacher FerKD using ResNet-50 without SelfMix data augmentation."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
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+                                            "html": "<table><tr><td>Pre-train</td><td>Top-1</td></tr><tr><td>vanilla</td><td>80.23</td></tr><tr><td>+calibration&amp;selfmix</td><td>80.68+0.45</td></tr><tr><td>+multi-teacher ensemble</td><td>81.15+0.47</td></tr><tr><td>+more epochs</td><td>81.44+0.29</td></tr></table>",
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+                            "index": 12,
+                            "angle": 0,
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+                    ],
+                    "index": 12
+                },
+                {
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+                    ],
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+                                    "type": "text",
+                                    "content": "Table 5: Ablation results using ResNet-50 on ImageNet-1K."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13,
+                    "angle": 0,
+                    "type": "text"
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "distinctive features, architectures, and training strategies. In this section, our objective is to determine which teacher model has the greatest capacity to distill a student. We evaluate two types of student models: ResNet-50 and ViT-S/16. The results are shown in Table 3, where RegY_128GF_384 and ViT_L16_512 achieve the highest student accuracy individually, despite not being the best on their own."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.2. Ablations"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Ablation on Calibration. The results for different calibration ranges are shown in Table 4, it can be observed that [0, 0.3] achieves the best accuracy. In practice, we discard examples in [0, 0.15) and (0.95, 1.0], meanwhile, calibrate examples in [0.15, 0.3] for the final strategy. More visualization of the hardest and easiest regions is shown in Fig. 9."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Ablation on teacher ensemble and training budget. The results are in Table 5, showing that each design has the consistent improvement. Our final results are shown in Table 8, FerKD performs the best over other SOTA methods."
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+                                    "content": "4.3. Curriculum Distillation"
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+                                    "content": "In curriculum distillation, the student model learns from the teachers' knowledge in a sequential manner, starting from easier examples (high probability regions) and gradually increasing the level of difficulty. This allows the student model to learn from easier to more complex regions. By presenting samples in a curriculum, the student model can learn from the easier samples and build a strong foundation before being exposed to more challenging samples. However, our experimental results, as shown in Table 7, demonstrate that this curriculum learning approach is inferior to our surgical label adaptation strategy, FerKD. Our approach outperforms curriculum distillation by "
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+                                    "content": ". We attribute this performance improvement to the strong ability of soft labels to mitigate overfitting and improve generalization in the initial stages of training. As a result, the advantage of the curriculum learning approach is not as apparent in this scenario. We also notice that \"e-to-h\" performs slightly better than \"h-to-e\" demonstrating the effectiveness of curriculum strategy, while both of them are"
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+                                            "html": "<table><tr><td>Effi.L2_475</td><td>Effi.L2_800</td><td>RegY_128GF_384</td><td>ViT_L16_512</td><td>ViT_H14_518</td><td>BEIT_224</td><td>BEIT_384</td><td>BEIT_512</td><td>Student Acc.</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>80.23</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>80.49</td></tr><tr><td></td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>80.29</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>80.53</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>80.48</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>80.35</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td>✓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.35</td></tr><tr><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>80.38</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td>80.51</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.53</td></tr><tr><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.52</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>80.62</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>80.74</td></tr></table>",
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+                                            "content": "Table 6: Ablation top-1 accuracy of teacher ensemble on ImageNet-1K with ConvNet, Vision Transformer or hybrid teachers. The left group is ConvNet teachers, the middle is the ViT teachers and the right group is the corresponding student ResNet-50 accuracy. Note that surgical calibration and SelfMix are not used here."
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+                                            "html": "<table><tr><td>Method</td><td>sampling</td><td>Top-1</td></tr><tr><td>Random (FKD [37])</td><td>random</td><td>80.2</td></tr><tr><td>curriculum distillation</td><td>h-to-e</td><td>79.7</td></tr><tr><td>curriculum distillation</td><td>e-to-h</td><td>79.9</td></tr><tr><td>FerKD (Ours)</td><td>surgical</td><td>80.7</td></tr></table>",
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+                                            "content": "Table 7: Curriculum and surgical (no ensemble) distillation. \"e-to-h\" refers to curriculum sampling from easy to hard regions. \"h-to-e\" refers to sampling from hard to easy."
+                                        }
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+                                            "html": "<table><tr><td>Model</td><td>Epoch</td><td>Label</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>600</td><td>HardLS</td><td>80.4</td></tr><tr><td>Pytorch (advanced) [44]</td><td>600</td><td>HardLS</td><td>80.9</td></tr><tr><td>MEAL [33]</td><td>100‡</td><td>Soft</td><td>78.2</td></tr><tr><td>MEAL V2 [36]</td><td>180‡</td><td>Soft</td><td>80.7</td></tr><tr><td>MEAL V2 [36]w/CutMix</td><td>180‡</td><td>Soft</td><td>81.0</td></tr><tr><td>ReLU [57]w/CutMix</td><td>300</td><td>Soft</td><td>80.2</td></tr><tr><td>FunMatch [5]w/Mixup</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FKD [37]</td><td>300</td><td>Soft</td><td>80.5</td></tr><tr><td>FerKD (Ours)</td><td>300</td><td>Adap</td><td>81.2+0.7</td></tr><tr><td>FerKD (Ours)</td><td>600</td><td>Adap</td><td>81.4+0.9</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "inferior to the random sampling baseline."
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+                                    "type": "text",
+                                    "content": "4.4. Finetuning Distillation"
+                                }
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+                    "index": 7
+                },
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+                                    "type": "text",
+                                    "content": "Finetuning distillation [36] has been demonstrated as an effective approach to improve the accuracy of knowledge distillation (KD) frameworks. In the case of hard labels, multiple finetuning schemes have been proposed to adapt the model parameters to fit the target dataset, including partial finetuning on selected intermediate layers with varying learning rates [34, 1, 17, 30] or on the last few layers [55]. In this work, we adopt the MEAL V2 [36] protocol by fine"
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+                                            "type": "text",
+                                            "content": "Table 8: Top-1 accuracy on ImageNet-1K dataset. The backbone network in this table is ResNet-50. "
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+                                            "type": "text",
+                                            "content": " indicates that the model was fine-tuned from hard-label pre-trained weights, resulting in a total training epoch of "
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+                                            "type": "inline_equation",
+                                            "content": "300 + \\times"
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+                                            "type": "text",
+                                            "content": "."
+                                        }
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+                            "type": "table_caption"
+                        },
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Pre-train</td><td>FT</td><td>Top-1</td></tr><tr><td>Timm [49]</td><td>HardLS</td><td>80.38</td></tr><tr><td>Timm [49]</td><td>FKD [37]*</td><td>80.62</td></tr><tr><td>Timm [49]</td><td>FerKD* (Ours)</td><td>81.06</td></tr><tr><td>SWAG [39]</td><td>HardLS</td><td>87.22</td></tr><tr><td>SWAG [39]</td><td>FKD [37]†</td><td>87.42</td></tr><tr><td>SWAG [39]</td><td>FerKD† (Ours)</td><td>87.76</td></tr><tr><td>EVA_MIM [10]</td><td>HardLS</td><td>89.59</td></tr><tr><td>EVA_MIM [10]</td><td>FKD [37]</td><td>89.67</td></tr><tr><td>EVA_MIM [10]</td><td>FerKD (Ours)</td><td>89.86</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 9: Fine-tuning distillation results using pre-trained ResNet-50 (Timm), RegNetY-128GF (SWAG) and ViT-G14 (EVA) on ImageNet-1K. We use the same recipe of EVA for SWAG finetuning since SWAG did not provide the complete fine-tuning details. * On ResNet-50, we finetune with 150 epochs for both FKD and FerKD."
+                                }
+                            ]
+                        }
+                    ],
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+                    "angle": 0,
+                    "type": "text"
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "tuning the entire network from the pre-trained weights to evaluate the effectiveness of distillation with surgical soft label calibration as the objective. Specifically, we employ three types of pre-trained models:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
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+                                            "type": "text",
+                                            "content": "(1) Supervised pre-train: ResNet-50 on Timm [49];"
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+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "(2) Weakly-supervised pre-train: RegNetY-128GF from SWAG [39];"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
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+                            "type": "text",
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+                                            "type": "text",
+                                            "content": "(3) Self-supervised pre-train: ViT-G14 from EVA [10];"
+                                        }
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+                                    "content": "We verify whether FerKD can continue improving finetuning distillation. As shown in Table 9, FerKD achieves consistent improvement across different architectures."
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+                                            "content": "Table 10: COCO object detection and segmentation using a Mask-RCNN with FPN baseline. \"LM\" represents label map during pretraining. The backbone is ResNet-50-300ep."
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+                                            "html": "<table><tr><td>Method</td><td>iNat 2019224</td><td>iNat 2019336</td><td>Places365224</td></tr><tr><td>EVA_MIM [10]</td><td>79.9</td><td>86.6</td><td>61.0</td></tr><tr><td>FerKD (Ours)</td><td>80.3+0.4</td><td>87.1+0.5</td><td>61.4+0.4</td></tr></table>",
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+                                    "content": "particularly useful in scenarios where the teacher models have complementary strengths or when the input data is challenging and requires multiple perspectives to be accurately labeled. Furthermore, the use of multiple teachers can also help mitigate the effects of overfitting and improve the generalization performance of the student model. The results are shown in Table 6, assembling four hybrid teachers of Effi_L2_475, RegY_128GF_384, ViT_L16_512, and ViT_H14_518 achieves the best accuracy."
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+                                    "content": "Object detection and segmentation. We conducted evaluations to investigate whether the improvement achieved by FerKD on ImageNet-1K can be transferred to various downstream tasks. Specifically, Table 10 presents the results of object detection and segmentation on COCO dataset [21] using models pre-trained on ImageNet-1K with FerKD. We utilize Mask RCNN [12] with FPN [19] following FKD for the experiment. Our FerKD pre-trained weight consistently outperforms both the baselines ReLabel and FKD on the downstream tasks."
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+                                    "content": "Classification tasks. Table 11 shows the transfer learning result on iNaturalists [14] and Places [60] datasets. On both of these two datasets, our results surpass the baseline EVA pretrained model by significant margins."
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+                                            "content": "Table 11: Transfer learning accuracy on various classification datasets. The input sizes are "
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Method</td><td>IN1K</td><td>ReAL</td><td>ImageNetV2 Top-images</td><td>ImageNetV2 Matched-freq</td><td>ImageNetV2 Threshold-0.7</td></tr><tr><td colspan=\"6\">ResNet-50:</td></tr><tr><td>ReLU [57]</td><td>78.9</td><td>85.0</td><td>80.5</td><td>67.3</td><td>76.0</td></tr><tr><td>FKD [37]</td><td>80.1</td><td>85.8</td><td>81.2</td><td>68.2</td><td>76.9</td></tr><tr><td>FerKD</td><td>81.2</td><td>86.4+0.6</td><td>82.1+0.9</td><td>69.5+1.3</td><td>77.8+0.9</td></tr><tr><td colspan=\"6\">ViT-G14-336:</td></tr><tr><td>EVA [10]</td><td>89.6</td><td>90.8</td><td>89.0</td><td>81.9</td><td>86.7</td></tr><tr><td>FerKD</td><td>89.9</td><td>91.3+0.5</td><td>89.4+0.4</td><td>82.4+0.5</td><td>87.1+0.4</td></tr></table>",
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+                                    "content": "Table 12: Results of FerKD on ImageNet RealL [4] and ImageNetV2 [29] with ResNet-50 and ViT-G14 backbones."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "6. Robustness"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
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+                                    "type": "text",
+                                    "content": "We provide comparisons on ImageNet Real [4] and ImageNetV2 [29] datasets to examine the robustness of FerKD trained models. On ImageNetV2 [29], we verify our FerKD models on three metrics \"Top-Images\", \"Matched Frequency\", and \"Threshold 0.7\" following FKD [37]. We perform experiments on two network structures: ResNet-50 and ViT-G14. The results are shown in Table 12, we achieve consistent improvement over ReLabel and FKD on ResNet-50 "
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+                                    "type": "text",
+                                    "content": " and better accuracy than EVA on ViT-G14 "
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "7. Conclusion"
+                                }
+                            ]
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+                },
+                {
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+                                    "content": "In this work, we have presented a new paradigm of faster knowledge distillation (FerKD), which employs label adaptation on randomly cropped regions. The proposed method outperforms existing state-of-the-art distillation approaches in terms of both training speed and convergence. Additionally, we make two key observations that could be leveraged in future studies. Firstly, we notice that the most challenging and easiest few crops obtained through the RandomResizedCrop operation do not contribute to the model's learning and can thus be discarded. Secondly, we find that moderate hardness crops can provide crucial context information that helps calibrate the model to learn more robust representations, which in turn benefit downstream tasks."
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+                                    "content": "References"
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diff --git a/2023/Few Shot Font Generation Via Transferring Similarity Guided Global Style and Quantization Local Style/d538f1f0-c61f-4b9f-8a6c-8946cb533534_content_list.json b/2023/Few Shot Font Generation Via Transferring Similarity Guided Global Style and Quantization Local Style/d538f1f0-c61f-4b9f-8a6c-8946cb533534_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..8f378e86c65a8be1f0f01b280390d7ff3b9865d1
--- /dev/null
+++ b/2023/Few Shot Font Generation Via Transferring Similarity Guided Global Style and Quantization Local Style/d538f1f0-c61f-4b9f-8a6c-8946cb533534_content_list.json	
@@ -0,0 +1,1802 @@
+[
+    {
+        "type": "text",
+        "text": "Few shot font generation via transferring similarity guided global style and quantization local style",
+        "text_level": 1,
+        "bbox": [
+            109,
+            128,
+            861,
+            175
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Wei Pan<sup>1</sup> Anna Zhu<sup>1*</sup> Xinyu Zhou<sup>1</sup> Brian Kenji Iwana<sup>2</sup> Shilin Li<sup>1</sup>  \n<sup>1</sup> School of Computer Science and Artificial Intelligence, Wuhan University of Technology  \n<sup>2</sup> Human Interface Laboratory, Kyushu University",
+        "bbox": [
+            125,
+            202,
+            843,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{aaawei, annazhu, 297932, shilinli}@whut.edu.cn iwana@ait.kyushu-u.ac.jp",
+        "bbox": [
+            156,
+            258,
+            810,
+            273
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            308,
+            313,
+            325
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Automatic few-shot font generation (AFFFG), aiming at generating new fonts with only a few glyph references, reduces the labor cost of manually designing fonts. However, the traditional AFFFG paradigm of style-content disentanglement cannot capture the diverse local details of different fonts. So, many component-based approaches are proposed to tackle this problem. The issue with component-based approaches is that they usually require special pre-defined glyph components, e.g., strokes and radicals, which is infeasible for AFFFG of different languages. In this paper, we present a novel font generation approach by aggregating styles from character similarity-guided global features and stylized component-level representations. We calculate the similarity scores of the target character and the referenced samples by measuring the distance along the corresponding channels from the content features, and assigning them as the weights for aggregating the global style features. To better capture the local styles, a cross-attention-based style transfer module is adopted to transfer the styles of reference glyphs to the components, where the components are self-learned discrete latent codes through vector quantization without manual definition. With these designs, our AFFFG method could obtain a complete set of component-level style representations, and also control the global glyph characteristics. The experimental results reflect the effectiveness and generalization of the proposed method on different linguistic scripts, and also show its superiority when compared with other state-of-the-art methods. The source code can be found at https://github.com/awei669/VQ-Font.",
+        "bbox": [
+            75,
+            340,
+            472,
+            779
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            806,
+            209,
+            821
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Font design techniques can benefit many critical applications, such as logo designs, data augmentation for text-related tasks, handwriting imitation and identification, etc.",
+        "bbox": [
+            75,
+            832,
+            468,
+            878
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However, traditional font design heavily depends on expert designers rendering the glyph styles for each character manually, making the creation of fonts extremely expensive and labor-intensive, especially for glyph-rich scripts.",
+        "bbox": [
+            500,
+            310,
+            890,
+            369
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, with the development of deep learning techniques, many automatic few-shot font generation (AFFFG) methods have been proposed. They have been created using Convolution Neural Networks (CNNs) [22], Generative Adversarial Networks (GANs) [27], Transformers [32], etc. The AFFFG methods use only a few reference font images for generating different glyphs automatically. The typical strategy follows the style and content disentangle-ment and combination paradigm [38, 23], and either adopts global style representation or component-wise style representation. The global style representation [13, 38] is learned and extracted from all the references of each style, which could capture the global characteristics, such as character size and stroke space. However, it lacks the representation of diverse local details, such as the shape and length of local strokes and serif size. On the contrary, the componentwise style representation category [11, 6, 20] generally decomposes each reference sample sharing the same font into pre-defined components and radicals. It either conditions the style encoders jointly on the glyph image and the corresponding component labels or adopts component-label classification losses to train the style encoder. This can be infeasible because each character should be manually associated with a certain set of components, which requires more preparation when applying for new scripts. Additionally, for different content images, their local relations with reference samples can vary. That means the local style representations for different content characters are required to be recomputed when given fixed reference samples, which increases the computational cost.",
+        "bbox": [
+            496,
+            371,
+            892,
+            824
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To tackle the above issue, we propose a hybrid global and local style transferring approach for AFFG in this paper. Since the global style representation of fonts controls more intra-style consistent properties, e.g., the locations, sizes, stroke thickness, and spaces of characters, while the lo",
+        "bbox": [
+            496,
+            824,
+            890,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            805,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author",
+        "bbox": [
+            94,
+            886,
+            220,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "19506",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "cal style representation focuses on capturing inter-style inconsistent component details, e.g., stroke shape, serif-ness, stroke deformation. Therefore, we leverage both the global and local styles for feature complementation. In order to obtain the global style feature representation, we calculate the similarity scores of the target glyph and the referenced samples by measuring their content feature distances, and then assign them as the weights for aggregating the style features. For local style feature representation, the glyph components are first learned automatically, which are discrete latent codes decomposed from a set of glyphs by vector quantization. Then, a cross-attention transformer is employed to transfer component-wise styles, with the representation of the learned components as the queries and the style representations of the reference glyphs as the keys and values. Contrastive learning is used to learn the local styles in an unsupervised way. For each forward pass, the styles from the reference samples can be transferred onto all the components. So, this local style extraction process is independent of the content glyph, avoiding multiple component-wise representation calculations for different inputs. Finally, the global and local style representations are combined with content features, and then decoded into the target glyph. Moreover, we adopt GAN and a self-reconstruction strategy for training the model without strong supervision. Therefore, it can be easily applied for different script font generation.",
+        "bbox": [
+            76,
+            90,
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+            498
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We demonstrate the effectiveness of the proposed method on the Chinese mainly. The experimental results reflect the necessity of combing global and local representations, and also tell that our method outperforms other state-of-the-art (SOTA) AFFG methods given very limited reference examples.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, the contributions of this paper are as follows:",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel AFFG method leveraging complementary global and local representations, which is able to capture intra-style consistent properties and intra-style inconsistent structures of reference glyphs.",
+            "- Similarity of content is used to obtain global styles. It takes a similar degree of glyph structures into consideration. This strategy can better transfer styles for glyphs owning the same components with reference.",
+            "- Pre-trained Vector Quantization-based Variational Autoencoder (VQ-VAE) is adopted to extract components automatically, component labels are not required. The local styles can be transferred to all the components via cross-attention in one-forward pass. It is efficient for font library creation because it is content irrelevant. A style contrastive loss is proposed to unsupervised transfer the component-level styles."
+        ],
+        "bbox": [
+            94,
+            632,
+            470,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- Experimental results show great generalizability of our model for unseen fonts, unseen characters, and different scripts. It achieves SOTA performance for font generation even with very limited reference samples. Additionally, it can transfer styles onto cross-linguistic in the zero-shot manner.",
+        "bbox": [
+            517,
+            90,
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+            181
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            500,
+            195,
+            650,
+            210
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image-to-Image Translation. Image-to-image (I2I) translation aims to learn a mapping between source and target domains while retaining the content of the source. GAN-based methods [12, 7, 16] were widely used in this field. Pix2pix [12] first adopted conditional GAN into the I2I task with paired data. CycleGAN [39] introduced circular consistency loss for unsupervised I2I translation [5, 39]. Recently, several I2I methods [2, 4] were proposed to tackle multi-class unsupervised I2I translation problems, aiming to simultaneously generate multiple style outputs given the same input.",
+        "bbox": [
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+            220,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Font generation belongs to the typical I2I translation task, so the generic I2I translation approaches could be adaptively modified for font generation [17, 9].",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Character Style Transfer. Character style transfer mainly focused on typography transfer. Traditional methods constructed the transformation through shape modeling [31] and statistical modeling [30]. Recent approaches applied deep learning techniques for character synthesis [3]. Some methods were able to synthesize glyphs as well as the textural effects [1, 36, 8]. However, the font generation task emphasizes more on the consistency of character shape instead of text effects.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Global Style-content Disentanglement for Font Generation. Global style-content disentanglement and recombination is a popular strategy for font generation. It models each font style as a universal representation. EMD [35] proposed a network architecture with two encoders, one for content and the other for style. They generated arbitrary fonts by mixing the content and style features, followed by decoding the mixed features. MDM [37] built a framework to disentangle the text images into three factors: text content, font, and style features, and then remixed the factors of different images to transfer a new style. ELDF [15] utilized new consistency losses that forced any combination of encoded features of the stacked inputs to own the consistent features of text contents and font styles.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "However, the local details for the font are more diverse and are hard to capture only by global style representation.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Component-based Font Generation. Since characters such as Chinese characters can be decomposed, some component-based font generation methods [6, 19, 20] have emerged recently. They do not encode the entire image to extract style information, but instead extract style information for each component that makes up a syllable and use it",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "19507",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/5088cd9b0657f4b9451190df2f29e2a0b448c6adae154a31d867ac8c21be1e46.jpg",
+        "image_caption": [
+            "Figure 1. The architecture of our model. The generator consists of five parts: a pre-trained content encoder, a reference style encoder (marked in dark green), a local style aggregator via CAM (marked in yellow), a global style aggregator with content similarity guidance (marked in pink), and a decoder combining content and style features and style features for font generation (marked in gray). A discriminator (marking green) is followed to distinguish the real and fake images, and it simultaneously classifies the content and style category of the generated character."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            94,
+            870,
+            378
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "to generate fonts. For instance, CalliGAN [28] decomposed characters into components and offered low-level structure information, including the order of strokes, to guide the generation process. SA-VAE [24] disentangled the style and content as two irrelevant domains with encoding Chinese characters into high-frequency character structure configurations and radicals. Tang et al. [25] proposed FS-Font model that adopted a cross-attention mechanism to aggregate the reference styles into a fine-grained style representation. XMP-Font [18] proposed a self-supervised cross-modality pre-training cross-modality transformer network to model style representations of stroke-level, component-level, and character-level.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The component-based font generation methods significantly improve the generated glyphs' quality with few-shot references. However, most of them require you to predefine the radicals or components manually.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce the overall framework, different modules and the training strategy in details.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overall Pipeline",
+        "text_level": 1,
+        "bbox": [
+            76,
+            816,
+            238,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a content image  $x_{c}$  and a set of reference character images  $y = \\{y_{1},y_{2},\\ldots ,y_{K}\\}$  sharing the same font, our model aims to generate the character  $y_{c}$  owning the same content with  $x_{c}$  and the font style of the reference images.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The overall framework is displayed in Fig. 1. It consists of a generator  $G$  and a multi-task discriminator  $D$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The generator  $G$  contains five parts as illustrated in Fig. 1. The content-encoder  $E_{c}$  takes the content image as input to extract its structural representation  $f_{c}$ . It is pretrained via VQ-VAE to obtain the component-wise latent codes  $e_{c}$ . The style encoder is designed to learn the style representations from reference images  $y$ . Specifically, it inputs each reference image independently to map them to the style latent vector  $f_{s} = \\{f_{1}, f_{2}, \\ldots, f_{K}\\}$ . A Local Style Aggregator (LSA) is followed afterward to transfer the styles onto the learned components. It works through a cross-attention module (CAM) with all the component-wise latent codes  $e_{c}$  as queries and the representations of the reference characters  $f_{s}$  as the keys and values. After the stylization of components, the content-related local styles  $f_{sr-L}$  can be obtained by searching the most similar codes in  $e_{c} = \\{e_{c}^{1}, e_{c}^{2}, \\ldots, e_{c}^{N}\\}$  with its representation  $f_{c}$  spatially. The Global Style Aggregator (GSA) re-weights the style representations  $f_{s}$  and sums up all of them channel-wisely to get the global representation  $f_{sr-G}$ . The weight is the normalized distance of the content representations between each reference character and the input character, as shown  $f_{r}^{c} = \\{f_{1}^{c}, f_{2}^{c}, \\ldots, f_{K}^{c}\\}$  and  $f_{c}$  in Fig. 1, respectively. Afterwards, a decoder is employed to generate target image  $y_{c}$  with the concatenation features of the content features  $f_{c}$ , local style representation  $f_{sr-L}$  and global style representation",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "19508",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/9bc3111b4bb251e156c6db09a23a02bc9fc1981952ff206f513b75ec0bacf6f6.jpg",
+        "image_caption": [
+            "Figure 2. The glyph feature decomposing network for pre-training the content encoder and obtaining component representation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            95,
+            472,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tation  $f_{sr - G}$  as input.",
+        "bbox": [
+            76,
+            315,
+            225,
+            330
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "During training, a multi-task discriminator is adapted to play the min-max game with the generator for distinguishing the real  $\\hat{y}_c$  from a fake  $y_c$ . To make sure the generated glyph has the correct style with reference samples and still retains the structure of the input content character, the discriminator outputs a binary classification of each character's style and content category.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Glyph Encoders and Component Decomposition",
+        "text_level": 1,
+        "bbox": [
+            76,
+            450,
+            468,
+            479
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The content encoder is pre-trained on the feature decomposing network and kept frozen for the font generation task. In the pre-training step, it is used to decompose the glyph images into component-wise latent codes, and trained on a certain set of character templates for reconstruction. The overview of the feature decomposing network is shown in Fig. 2. It contains a content encoder and a reconstruction decoder, connected by a discrete latent space using a latent codebook  $e_c \\in R^{N \\times d}$ .",
+        "bbox": [
+            75,
+            491,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The encoder is built on CNNs and maps an input glyph image into latent representations,  $z_{e} \\in R^{w \\times h \\times d}$ , where  $d$  is the number of channels, and  $h$  and  $w$  represent the height and width of the feature maps, respectively. Subsequently, vector quantization [26] is used to discrete  $z_{e}$  as follows:",
+        "bbox": [
+            75,
+            628,
+            468,
+            705
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {e} ^ {i} = e _ {c} ^ {n}, \\quad \\text {s . t .} \\quad n = \\underset {n \\in \\{1, 2, \\dots , N \\}} {\\arg \\min } \\| z _ {e} ^ {i} - e _ {c} ^ {n} \\| _ {2} ^ {2}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            116,
+            718,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where each spatial-wise elemental vector  $z_{e}^{i} \\in R^{d}$  in  $z_{e}$  is replaced with the closest code vector by executing a nearest-neighbor lookup on codebook  $e_{c}$ , comprised of  $d$ -dimensional  $n$  code vectors. Finally, the reconstruction decoder uses the matched codes  $z_{q} \\in R^{w \\times h \\times d}$  as an input and outputs a reconstructed glyph.",
+        "bbox": [
+            75,
+            762,
+            468,
+            853
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To optimize this process, the encoder and codebooks are updated to minimize an objective  $L_{pre}$  in Eq. (2), which refers to  $L_{1}$ -based reconstruction loss and latent loss  $L_{lat}$",
+        "bbox": [
+            75,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "as follows:",
+        "bbox": [
+            500,
+            92,
+            576,
+            104
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {p r e} = L _ {1} + L _ {l a t} \\\\ = \\| x _ {c} - \\hat {x} _ {c} \\| _ {1} + \\alpha \\| \\operatorname {s g} [ z _ {e} ] - e _ {c} \\| _ {2} ^ {2} + \\beta \\| z _ {e} - \\operatorname {s g} [ e _ {c} ] \\| _ {2} ^ {2}, \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            113,
+            890,
+            162
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where sg is a stop-gradient operator that is defined as an identity at forward computation time and has zero partial derivatives.  $\\alpha$  and  $\\beta$  are the balancing hyperparameters. Experimentally, we set them as 1 and 0.1, respectively. The first term in Eq. (2) makes sure no information gets lost in the forward pass. The second term updates the codebook variables by moving the embedding vectors  $e_c$  towards the encoder outputs  $z_e$ . Meanwhile, the third term encourages the encoder output to match the targeted code vectors. There are no bypass connections between the encoder and decoder, so all the component-wise information of the glyph set processed by the encoder can be compressed in the latent space [21].",
+        "bbox": [
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+            164,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After this pre-training task, we fix the content encoder  $E_{c}$  as well as the component codebook  $e_{c}$  to build the font generation model. The style encoder  $E_{s}$  has the same architecture as  $E_{c}$ , but it is trained from scratch.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Local Style Aggregator",
+        "text_level": 1,
+        "bbox": [
+            500,
+            429,
+            714,
+            445
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Most recently proposed methods [18, 19] extract local style representation of characters by gaining attention from input content and reference styles. It is inefficient, especially for creating a new font library that contains a large number of glyphs. Since each of the glyphs must go through the attention model for feature aggregation once. However, most of them actually share some local representation if they have the same strokes or radicals. Starting from this point, we design an LSA module, the core is a CAM block to transfer the styles onto all the component-wise codes  $e_{c}$  instead of the input glyph.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The CAM block is built upon stacked multi-head transformers with component codes  $e_{c}$  as queries and reference style vectors  $f_{r}$  as keys and values. Formally, the feature maps  $f_{k} \\in R^{w \\times h \\times d}$  of  $k$ -th reference samples are reshaped along the channel axis, respectively, forming the sequential reference tokens  $\\tilde{f}_{r} \\in R^{k \\cdot w \\cdot h \\times d}$ . For  $i^{th}$  head, two linear projections  $W_{k}^{i} \\in R^{c \\times d}$  and  $W_{v}^{i} \\in R^{c \\times d}$  are applied on it to get the keys  $K_{i} = \\tilde{f}_{r}W_{k}^{iT}$  and values  $V_{i} = \\tilde{f}_{r}W_{v}^{iT}$ , respectively. Meanwhile, we acquire the query matrix  $Q_{i}$  by linear projecting  $e_{c}$  with a learning weight  $W_{e}^{i} \\in R^{c \\times d}$ .",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The attention module operates on the queries  $Q_{i}$ , keys  $K_{i}$ , and values  $V_{i}$  and generates weighted average vectors  $\\hat{V}_{i}$ , which can be formulated as:",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {V} = \\operatorname {A t t e n t i o n} \\left(Q _ {i}, K _ {i}, V _ {i}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {c}}\\right) V _ {i}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            823,
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+            869
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After obtaining the representations in each head, we concatenate all  $\\hat{V}_i$  along the channel dimension, and employ a",
+        "bbox": [
+            500,
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+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19509",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "linear projection to get the multi-head attention result  $e_{s}$ , as follows:",
+        "bbox": [
+            76,
+            90,
+            468,
+            119
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ne _ {s} = \\text {M u l t i - h e a d} (Q, K, V) = \\operatorname {c o n c a t} \\left(\\hat {V} _ {1}, \\hat {V} _ {2},; \\hat {V} _ {m}\\right) W _ {o}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            130,
+            468,
+            167
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $m$  is the number of total attention head, and  $W_{o}$  is the learning weight.",
+        "bbox": [
+            76,
+            167,
+            468,
+            198
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After we get the stylized component-wise codes  $e_s = \\{e_s^1, e_s^2, \\ldots, e_s^N\\}$ . For each input glyph, its local representation  $f_{sr-L}$  can be aggregated from  $e_s$  by searching for the closest label  $n$  in  $e_c$  for each spatial element in  $f_c$  as expressed in Eq. (1), and then selecting the corresponding style representation  $e_s^n$  for replacement.",
+        "bbox": [
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+            199,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Global Style Aggregator",
+        "text_level": 1,
+        "bbox": [
+            76,
+            301,
+            299,
+            316
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The original style representation  $f_{k}$  for each reference sample is able to provide more global information for the font generation, which can control the size, the stroke space, etc. So, we aggregate their features directly as the global representation.",
+        "bbox": [
+            76,
+            324,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in [36], the style features and content features of references are not entirely independent. From a human's perceptual observation, there are some correlations that exist between different characters. If the input glyph has exactly the same radical or structure with some references, their style representations should be highly referred to during the transfer process. Therefore, we re-weight the individual style features  $f_{k}$  of each reference glyph based on the content feature similarity. We extract the content features  $f_{r}^{c} = \\{f_{1}^{c}, f_{2}^{c}, \\ldots, f_{K}^{c}\\} \\in R^{w \\times h \\times d}$  of each reference and reshape them to  $\\tilde{f}_{k}^{c} \\in R^{w \\cdot h \\times d}$ , meanwhile, the content features  $f_{c} \\in R^{w \\times h \\times d}$  of content image are reshaped into  $\\tilde{f}_{c} \\in R^{w \\cdot h \\times d}$ . The glyph similarity is determined by the normalized cross-correlation measurement as:",
+        "bbox": [
+            76,
+            401,
+            468,
+            613
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {k j} = \\frac {\\tilde {f} _ {k} ^ {c} \\cdot \\tilde {f} _ {c}}{\\left\\| \\tilde {f} _ {k} ^ {c} \\right\\| * \\left\\| \\tilde {f} _ {c} \\right\\|}, j \\in \\{1, 2, \\dots , d \\}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            622,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$W_{kj}$  is a scalar that represents the similarity between  $k_{th}$  reference and the input glyph on  $j_{th}$  channel. Then, we normalize it by considering  $k$  samples on each channel as:",
+        "bbox": [
+            76,
+            678,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\overline {{W}} _ {k j} = \\operatorname {s o f t m a x} \\left(\\frac {\\exp (a W _ {k j})}{\\sum_ {k = 1} ^ {K} \\exp (W _ {k j})}\\right). \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This weight is then applied to the reference style representations  $f_{r}$ , where  $j_{t}h$  channel feature  $f_{k}^{j}$  is weighted by  $\\overline{W}_{kj}$ , to aggregate the global representation  $f_{sr - G}$  as expressed in:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf _ {s r - G} = \\operatorname {c o n c a t} _ {j} \\left(\\sum_ {k = 1} ^ {K} \\bar {W} _ {k j} f _ {k} ^ {j}\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This global style representation  $f_{sr - G}$  is concatenated with the content features  $f_{c}$  and local style representation  $f_{sr - L}$ , and then input to the decoder to generate the target font.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Training",
+        "text_level": 1,
+        "bbox": [
+            500,
+            143,
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+            160
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We train our model to generate the image  $y_{c}$  from an input content image  $x_{c}$  and a set of reference glyph images  $y = \\{y_{1},y_{2},\\ldots ,y_{K}\\}$ . The content encoder is pretrained and kept fixed during this period. The losses consist of three parts, an adversarial loss, a matching loss, and a style contrast loss. The adversarial loss and matching loss are used between the generated results  $y_{c}$  and the ground truth  $\\hat{y}_c$ . While the style contrast loss is designed to learn distinguished styles for components.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adversarial loss. To make the model generate plausible images, we employ a multi-head projection discriminator  $D_{s,c}$  for style label  $s$  and character label  $c$  in our framework. The loss function is implemented as the hinge GAN loss [33]:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {a d v} ^ {D} = - \\mathbb {E} _ {\\hat {y} _ {c} \\sim p _ {d a t a}} \\min  (0, - 1 + D _ {s, c} (\\hat {y} _ {c})) \\\\ - \\mathbb {E} _ {y _ {c} \\sim p _ {G}} \\min  (0, - 1 - D _ {s, c} (y _ {c})) \\tag {8} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            545,
+            386,
+            890,
+            424
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {a d v} ^ {G} = - \\mathbb {E} _ {y _ {c} \\sim p _ {G}} D _ {s, c} (y _ {c}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            549,
+            426,
+            733,
+            445
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $p_G$  denotes the set of generated images, and  $p_{data}$  denotes the set of real glyph images.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Matching loss. To make the generated character  $y_{c}$  learn pixel-level and feature-level consistency with ground truth  $\\hat{y}_{c}$ , we employ an  $L_{1}$  loss on both image and image features as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {i m g} = \\mathbb {E} [ \\| y _ {c} - \\hat {y} _ {c} \\| _ {1} ] \\\\ \\mathcal {L} _ {\\text {f e a t}} = \\mathbb {E} \\left[ \\sum_ {l = 1} ^ {L} \\left\\| f ^ {(l)} \\left(y _ {c}\\right) - f ^ {(l)} \\left(\\hat {y} _ {c}\\right) \\right\\| _ {1} \\right], \\tag {9} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            562,
+            549,
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+            609
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $f_{l}(y_{c})$  and  $f_{l}(\\hat{y}_{c})$  represent the intermediate features in the  $l_{t}h$  layer of  $D$ .",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Style contrast loss. Given two different reference sets but sharing the same font style, the associated stylized components for these sets should be the same. However, if the reference character sets have different font styles, the component styles should be distinguished. So, we formulate our style contrastive loss as follows:",
+        "bbox": [
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+            648,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {c s t} = \\\\ - \\log \\left(\\frac {\\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\\right)}{\\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\\right) + \\sum_ {N _ {s} ^ {-}} \\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s -} ^ {n}\\right)}\\right). \\tag {10} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            501,
+            750,
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+            859
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In detail, for each certain font style  $s$  and is corresponding codebook  $e_s$ , where  $e_{s+}$  is the positive codebook pair of",
+        "bbox": [
+            498,
+            869,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "19510",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$e_s$  whose references have the same font style but different content, and  $e_{s-}$  is the negative codebook pair share different font style.  $N_s^-$  is the number of negative style samples, for  $n$ -th codebook entries  $e_s^n$  in codebook  $e_s \\in R^{N \\times d}$ . We can always find the positive pair  $e_{s+}^n$  and negative pair set  $\\{e_{s_1-}^n, e_{s_2-}^n, \\ldots, e_{s_{neg}-}^n\\}$  in the corresponding position.",
+        "bbox": [
+            76,
+            90,
+            468,
+            183
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Overall objective loss. Finally, we optimize the whole model by the following full objective function:",
+        "bbox": [
+            76,
+            184,
+            468,
+            215
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {E _ {s}, G} \\max  _ {D} \\mathcal {L} _ {a d v} ^ {D} + \\mathcal {L} _ {a d v} ^ {G} + \\lambda_ {1} \\mathcal {L} _ {i m g} + \\lambda_ {2} \\mathcal {L} _ {f e a t} + \\lambda_ {3} \\mathcal {L} _ {c s t}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            231,
+            468,
+            255
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The  $\\lambda_{1},\\lambda_{2}$  and  $\\lambda_3$  is weighting hyperparameter. We set them to 1, 1, and 0.1, respectively.",
+        "bbox": [
+            76,
+            272,
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+            303
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experimental Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            324,
+            281,
+            340
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experiment Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            352,
+            253,
+            368
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Dataset. We collected 386 Chinese fonts and generated 3,500 Chinese characters for each font according to the first-level Chinese Character Table. All character pictures are normalized to  $128 \\times 128$ . A font template is randomly selected from the 386 fonts for extracting the glyph content features and kept fixed throughout the training and test [1]. This font set is also used for pre-training the VQ-VAE to get a set of common parts codebooks.",
+        "bbox": [
+            75,
+            378,
+            468,
+            500
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The Chinese training set contains 370 fonts and 3,000 Chinese characters, denoted as the seen font seen character (SFSC) set. To verify our method, we evaluate the font generation ability on two test sets: One is the rest of the 15 unseen fonts with 3,000 seen characters per font, denoted as the seen font unseen character (UFSC) set; the other is the remaining 15 unseen fonts with 500 unseen characters per font, denoted as the unseen font unseen character (UFUC) set.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. The main training process of our method is divided into two parts. First, a component-wise codebook is trained with 3,000 Chinese characters sharing the same font. We set the embedding dimension  $d$  to 256, the batch size to 256, and the iteration steps to 50,000. Then, for training the whole font generation model, we set the batch size to 48, the number of attention heads to 8 in three stacked transformer layers, and iteration steps to 500,000.",
+        "bbox": [
+            75,
+            641,
+            468,
+            775
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. To evaluate the font generation quality, we use the following five metrics [14], root-meansquare deviation (RMSE), structural similarity (SSIM), learned perceptual image patch similarity (LPIPS) [34], Fréchet inception distance (FID) [10], and User Study. The User Study is conducted by 10 volunteers, who observe the reference samples and vote for the best generation result from all the comparison methods.",
+        "bbox": [
+            75,
+            779,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/7f8df2120cecfb53d2dcc5bd294b28809cb31d1583184bbfd73bdcd0d8834b97.jpg",
+        "table_caption": [
+            "Table 1. Ablation study of component codebooks."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Codebook size</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td></tr><tr><td>50</td><td>0.512</td><td>0.422</td><td>0.343</td><td>144.2</td></tr><tr><td>80</td><td>0.546</td><td>0.407</td><td>0.296</td><td>120.7</td></tr><tr><td>100</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td></tr><tr><td>120</td><td>0.568</td><td>0.392</td><td>0.278</td><td>109.5</td></tr><tr><td>150</td><td>0.567</td><td>0.388</td><td>0.282</td><td>112.4</td></tr></table>",
+        "bbox": [
+            504,
+            99,
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+            178
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/52325c1b46668a23552b9777d8318525192360c3683c9cc360ca7a292eee2a6f.jpg",
+        "image_caption": [
+            "Figure 3. The visualization of latent codes."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            542,
+            196,
+            844,
+            248
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
+            500,
+            300,
+            663,
+            315
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We perform three ablation studies to evaluate the effectiveness of our proposed models on the few-shot Chinese font generation task. These experiments are conducted on the UFUC dataset.",
+        "bbox": [
+            498,
+            324,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2.1 The effect of component codebook size",
+        "text_level": 1,
+        "bbox": [
+            498,
+            406,
+            820,
+            421
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The component codebook size reflects the complexity of the script. We set it as different values for training the content encoder and acquiring component-wise representation in VQ-VAE. Then, they are fixed for font generation. The results are displayed in Tab. 1. We can see that when the codebook size exceeds 100, the performance on each metric has limited improvement. That illustrates using 100 components is sufficient to depict the Chinese characters. When we train the model on English script, we find that by only using 15 codes, the model can generate very good results. Therefore, the size of the component codebook has a relationship with the scripts. More complex scripts require larger codebook sizes. In the following experiments, We set the Chinese component codebook size to 100.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We select a certain code from the codebook to compute its similarity with features of different glyphs spatially. The visualization results of the  $32_{th}$  code and  $44_{th}$  code are present in Fig. 3. We can see the  $32_{th}$  code mainly extracts vertical components and  $44_{th}$  extracts horizontal components. It demonstrates the VQ-VAE strategy can generate \"components\" automatically.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2.2 The effect of each module",
+        "text_level": 1,
+        "bbox": [
+            500,
+            768,
+            732,
+            784
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To illustrate the influence of the GSA and LSA modules of our method, we conduct the ablation study with and without it in the model. By removing the LSA, the component-wise representation is not required. The model degrades to a global content-style disentanglement architecture, with the aggregated style representation only conditioned on content similarity. When removing the GSA part, the model focuses",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "19511",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/9175816a1e3cc876887c5debdfd8745336b16f6cf1ce61221887dce49d790f3b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Reference</td><td>雳枪嫌</td><td>惧聂蔬</td><td>鼠韧贻</td></tr><tr><td>w/o GSA</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>w/o LSA</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>Full model</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>GT</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr></table>",
+        "bbox": [
+            106,
+            90,
+            444,
+            200
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "more on the details of the stroke but loses the global style control.",
+        "bbox": [
+            75,
+            304,
+            468,
+            333
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the two models and the proposed full model on our collected UFUC dataset. Fig. 4 displays some comparison results. The results with and without these modules have obvious differences. The model with LSA could better capture the details of reference strokes, while the sizes of generated characters and the inner spaces are not always consistent with the given references. The model with only GSA has the opposite functions. Most strokes are not generated well. The full model combines LSA and GSA, which achieves better performance (see the details in red dash boxes of Fig. 4). Quantitative results in Tab. 3 further confirm the importance of the two modules. The LSA model assists more than GSA, which demonstrates that the style of glyphs mainly lies in the local details. From these results, we conclude that LSA and GSA are both essential in our model and they enable the model to capture diverse local styles and also control the global styles.",
+        "bbox": [
+            75,
+            334,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2.3 The effect of reference numbers",
+        "text_level": 1,
+        "bbox": [
+            76,
+            613,
+            352,
+            627
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, given more reference samples, the generated font better resembles a realistic one. Fig. 5 shows the effect of reference numbers. We can see that when the number of references increases from 1 to 8, the generated characters have an incremental performance improvement. The figure shows that it becomes stable when given more references. However, there are diminishing returns after the first few references. More details can be found in Appendix.",
+        "bbox": [
+            75,
+            638,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Comparing with SOTA Methods",
+        "text_level": 1,
+        "bbox": [
+            76,
+            770,
+            362,
+            786
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare our method with five SOTA AFFG methods. 1) FUNIT [17] used two different encoders with the AdaIN module to generate a new image with mixed content and style. It belongs to the global style-content disentanglement FFG method. 2) MX-Font [20] extracts multiple style features not explicitly conditioned on component labels, but is automatically by designed multiple experts to",
+        "bbox": [
+            75,
+            794,
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+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/835546ecbcaaef061e427238db12978e4fafbf50174376619d9a9597ad60aecd.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative font generation results with and without LSA and GSA modules. The first and last rows are the three references and the ground truth per font, respectively. The middle rows are generated results correspondingly. The red dashed boxes point out details that were better generated by our full proposed model.",
+            "Figure 5. Performance changes of our model by varying numbers of the reference samples."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            545,
+            99,
+            848,
+            238
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "represent different local concepts, e.g., left-side sub-glyph. It shows good generalization ability to unseen languages. 3) LF-Font [19] proposed localized style representation inspired by low-rank matrix factorization, which also extracts component-wise features. 4) DG-Font [29] is an unsupervised network that used a Deformable Convolution in the Generator to deform and transform the character of one font to another. It achieved a good effect on cursive characters. 5) AGIS-net [8] used two different decoders to generate images with character shapes and then the texture information successively. It can transfer the font as well as the text effects. 6) FS-Font [25] requires fixed content-reference mapping to transfer Fine-Grained local styles. We retrain all the models by our dataset using their original training hyperparameters and strategies. The reference samples are set to 3 in the training and test phases for all the methods. The qualitative and quantitative comparison results are shown in Fig. 6 and Tab. 2, respectively.",
+        "bbox": [
+            496,
+            306,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Tab. 2 shows that our method outperforms previous SOTA methods with significant gaps in all the metrics. We can observe that FUNIT fails to capture diverse styles. Only when the content and reference styles are visually close, it can generate a structured character. That illustrates the universal style representation strategy is not a good choice for AFFG. LF-Font generates fonts with worse visual quality since the reference numbers are very limited. Its performance is unstable as they are prone to loss of strokes or distortion of components for certain styles. DG-Font may fail to perform style transfer especially when the reference style significantly differs from that of the content. Additionally, it generates glyphs containing characteristic artifacts. AGIS-Net is more stable to generate the font of different styles and complement structures. It could better transfer the global features such as the size and the thickness of strokes. MX-Font generates better stylized characters than other methods, but it has a higher probability of failing to generate fine-grained style features compared with our method. The generation results of FS-Font are also unsatisfactory, especially on unseen references, due to the randomly selected",
+        "bbox": [
+            496,
+            583,
+            892,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "19512",
+        "bbox": [
+            480,
+            944,
+            517,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/aa1377c5f002587d7236aa0d0a3ca8473313bb95d5a40eec1cf9ad8823cc34c7.jpg",
+        "table_caption": [
+            "Table 2. Quantitative comparison results on UFSC and UFUC datasets"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Method</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td><td>User Study↑</td></tr><tr><td rowspan=\"7\">UFSC</td><td>FUNIT [17]</td><td>0.512</td><td>0.426</td><td>0.361</td><td>161.8</td><td>1.2%</td></tr><tr><td>LF-FONT [19]</td><td>0.548</td><td>0.406</td><td>0.334</td><td>123.9</td><td>3.9%</td></tr><tr><td>AGIS-NET [8]</td><td>0.529</td><td>0.409</td><td>0.302</td><td>145.0</td><td>10.3%</td></tr><tr><td>DG-FONT [29]</td><td>0.517</td><td>0.419</td><td>0.312</td><td>149.0</td><td>11.6%</td></tr><tr><td>MX-FONT [20]</td><td>0.523</td><td>0.407</td><td>0.297</td><td>94.5</td><td>14.4%</td></tr><tr><td>FS-FONT [25]</td><td>0.570</td><td>0.379</td><td>0.327</td><td>172.6</td><td>21.5%</td></tr><tr><td>Ours</td><td>0.636</td><td>0.341</td><td>0.225</td><td>93.7</td><td>58.6%</td></tr><tr><td rowspan=\"7\">UFUC</td><td>FUNIT [17]</td><td>0.468</td><td>0.472</td><td>0.379</td><td>153.4</td><td>3.4%</td></tr><tr><td>LF-FONT [19]</td><td>0.481</td><td>0.462</td><td>0.377</td><td>136.7</td><td>4.8%</td></tr><tr><td>AGIS-NET [8]</td><td>0.550</td><td>0.400</td><td>0.310</td><td>137.2</td><td>11.5%</td></tr><tr><td>DG-FONT [29]</td><td>0.493</td><td>0.397</td><td>0.312</td><td>136.7</td><td>10.8%</td></tr><tr><td>MX-FONT [20]</td><td>0.478</td><td>0.447</td><td>0.333</td><td>114.8</td><td>15.2%</td></tr><tr><td>FS-FONT [25]</td><td>0.418</td><td>0.474</td><td>0.377</td><td>173.7</td><td>19.5%</td></tr><tr><td>Ours</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td><td>54.3%</td></tr></table>",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td colspan=\"6\">UFUC</td><td colspan=\"6\">UFSC</td></tr><tr><td>Reference</td><td>嘉明主</td><td>泛懂隘</td><td>腰也携</td><td>铸符挂</td><td>寒晴宝</td><td>原初忍</td><td>香贬刷</td><td>矩财需</td><td>爷雏仇</td><td>猫悲捕</td><td></td><td></td></tr><tr><td>FUNIT</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>柴火</td><td>此方石</td><td>轧倍沉</td><td>生?学</td><td>灭</td><td>乳吮游</td><td></td><td></td></tr><tr><td>LF-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄搁蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>DG-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>AGIS-Net</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>MX-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>FS-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>Ours</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>GT</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>改善避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr></table>",
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+        "table_caption": [
+            "Figure 6. FFG results of each method on UFUC and UFSC dataset. We represent the generated samples of five different kinds of fonts, given three references and three content images per font. The red boxes represent the better generation details.",
+            "Table 3. Ablation study of different models on UFUC dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td><td>User Study↑</td></tr><tr><td>w/o LSA</td><td>0.496</td><td>0.422</td><td>0.318</td><td>145.0</td><td>7.3%</td></tr><tr><td>w/o GSA</td><td>0.532</td><td>0.402</td><td>0.293</td><td>132.1</td><td>20.3%</td></tr><tr><td>Full model</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td><td>72.4%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "content-reference pairs.",
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+    {
+        "type": "text",
+        "text": "4.4. Applying to Other Languages",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To verify the generalization of our method for other languages, we collected 60 fonts of 125 Japanese characters. 50 fonts with 100 glyphs per font are randomly selected for training, and the rest for test. Some results are displayed in Fig. 7. Since the character structures of the Japanese are much simpler than Chinese, the generated results approach the ground truth more. Additionally, our method can transfer styles onto unseen content, including cross-linguistic glyphs as shown in Fig. 8.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We present a novel AFFG approach in this paper, which could aggregate global and local styles of limited refer",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/f47f76b0a485d9caa19500b29369a70e7e40616aaf710ece3aae94a68dfb77f3.jpg",
+        "image_caption": [
+            "Figure 7. FFG results of Japanese scripts. For each style, the upper and lower rows respectively represent the model generation results and GT."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ences. The designed LSA and GSA modules were assigned different tasks to capture the local details and global structures of the font, respectively. The LSA adopted a cross-attention mechanism for transferring styles onto all of the self-learned components without manual definition. While the GSA utilized the similarity of different glyphs, and then used it to guide the global styles combination of all references. Experiments demonstrated the effectiveness of both modules, and also showed our proposed method significantly outperformed other methods quantitatively and qual",
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+    },
+    {
+        "type": "page_number",
+        "text": "19513",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Content\nReference</td><td>アウマガがせん不の</td></tr><tr><td>别福混伏桔快</td><td>アウマガがせん不の</td></tr></table>",
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+        "img_path": "images/d47be1994973261a67aa5d243cec43851c75e348f43211717e4976f31d1ff2ab.jpg",
+        "table_caption": [
+            "(a)"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Content\nReference</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr><tr><td>痴佳体</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr><tr><td>版贾句</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/fcc1129daf26f7c23ed38b40d245eceefcedf67efc3169ca6a11248bdc1d303d.jpg",
+        "table_caption": [
+            "(b)"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Reference</td><td colspan=\"4\">Generated Chinese samples</td><td colspan=\"4\">Generated Japanese samples</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>宣 呢 除 医 脸 另 追 播 筏 槽 预 缺 街 登 和 旁 骨 板 释 旅 课 急 放 智 蒙 弹</td><td>絹 聘 黔 黎 黎 潘 與 輛 與 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 廣 桃 篡 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻</td><td>絹 渠 槟 懒 懒 穰 橘 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 嘴 嘴 褚 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深</td><td>捻陵 傍管 喷 嘴 鞍 黔 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚</td><td>工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 巠 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 巳</td><td>大 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 甲 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙方 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td></td></tr></table>",
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+        "text": "Figure 8. Cross-language inference on (a) Japanese glyphs and (b) Korean glyphs. (c) Chinese results generated under few-shot and Japanese generated results under zero-shot manner.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "itatively. However, our method is limited to two aspects. If given only one reference or very fancy font, e.g., decoration, or shadow, the generated results are unsatisfactory.",
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+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This work is supported by the Open Project Program of the National Laboratory of Pattern Recognition(NLPR) (No.20220004). We thank all anonymous reviewers for their constructive comments on this paper.",
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+        "text": "Appendix",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Besides the results and discussions presented in the original paper, we provide more experiments and results in this appendix, which further explain the effectiveness and generality of our method.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The effect of different reference characters on the generated results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            801,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The font style is an aesthetic concept and has nothing to do with specific characters. In the process of few shot font generation, given reference characters with different content, the provided style representation should be the same.",
+        "bbox": [
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+        "img_path": "images/a5ef78299cd99a67c752e0dbea9cd832c51a0fe016f8553f69529607e5434a15.jpg",
+        "table_caption": [
+            "(c)"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Reference\\GT</td><td>鞠肖剥频裙翔祥凝挨</td></tr><tr><td>搗冊被海梗畅\\GT</td><td>鞠肖剥频裙翔祥凝挨</td></tr><tr><td>Reference\\GT</td><td>揍煽寝漂菊镜筏壁德</td></tr><tr><td>榆膛蔡燥稀魁</td><td>揍煽寝漂菊镜筏壁德</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Figure 9. Generating the same target character, referring to characters with different contents from the same style font.",
+        "bbox": [
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+        "page_idx": 8
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ref sets</td><td>苏1</td><td>横2</td><td>笑3</td><td>陈4</td><td>洁5</td><td>伟6</td><td>豪7</td><td>科8</td><td>腺9</td></tr><tr><td>Ref1</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-3</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-5</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-7</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-9</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>责</td><td>度</td><td>层</td><td>宇</td></tr><tr><td>GT</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>责</td><td>度</td><td>层</td><td>宇</td></tr></table>",
+        "bbox": [
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+            295,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Figure 10. Generated samples by varying reference set size. Each middle row shows the samples generated by given different number (1, 3, 5, 7, 9) of references. The number (1 to 9) represents the order of each character to be used. The target glyphs are displayed in the bottom row.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In our training process, we randomly select  $k$  style reference characters for generating characters each time. During the inference phase, we select characters with different content in the same style as the reference set. The generated results are shown in Fig. 9. There is a subtle difference between the overall style and the local style of the generated results.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The qualitative results using different numbers of references",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, the larger the number of given reference characters, the richer and more accurate the extracted style features should be. In the inference stage, we change the number of reference characters and observe the impact on the generated results. It can be observed from Fig. 10 that the overall and local quality of generated characters is roughly positively correlated with the number of reference characters. The quality improvement is more obvious when the number increases from 1 to 5, and the improvement beyond this number is limited. In our paper, the number of reference images is set to 3, and the model training and qualitative and quantitative comparisons with other methods are completed with this setting.",
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+        "text": "19514",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+    }
+]
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diff --git a/2023/Few Shot Font Generation Via Transferring Similarity Guided Global Style and Quantization Local Style/d538f1f0-c61f-4b9f-8a6c-8946cb533534_model.json b/2023/Few Shot Font Generation Via Transferring Similarity Guided Global Style and Quantization Local Style/d538f1f0-c61f-4b9f-8a6c-8946cb533534_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..563197602c5ffc1d4dd356a9e8e1669f82bf8924
--- /dev/null
+++ b/2023/Few Shot Font Generation Via Transferring Similarity Guided Global Style and Quantization Local Style/d538f1f0-c61f-4b9f-8a6c-8946cb533534_model.json	
@@ -0,0 +1,2279 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.807,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.11,
+                0.13,
+                0.862,
+                0.176
+            ],
+            "angle": 0,
+            "content": "Few shot font generation via transferring similarity guided global style and quantization local style"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.126,
+                0.203,
+                0.844,
+                0.257
+            ],
+            "angle": 0,
+            "content": "Wei Pan<sup>1</sup> Anna Zhu<sup>1*</sup> Xinyu Zhou<sup>1</sup> Brian Kenji Iwana<sup>2</sup> Shilin Li<sup>1</sup>  \n<sup>1</sup> School of Computer Science and Artificial Intelligence, Wuhan University of Technology  \n<sup>2</sup> Human Interface Laboratory, Kyushu University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.158,
+                0.26,
+                0.812,
+                0.275
+            ],
+            "angle": 0,
+            "content": "{aaawei, annazhu, 297932, shilinli}@whut.edu.cn iwana@ait.kyushu-u.ac.jp"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.309,
+                0.314,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.342,
+                0.473,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Automatic few-shot font generation (AFFFG), aiming at generating new fonts with only a few glyph references, reduces the labor cost of manually designing fonts. However, the traditional AFFFG paradigm of style-content disentanglement cannot capture the diverse local details of different fonts. So, many component-based approaches are proposed to tackle this problem. The issue with component-based approaches is that they usually require special pre-defined glyph components, e.g., strokes and radicals, which is infeasible for AFFFG of different languages. In this paper, we present a novel font generation approach by aggregating styles from character similarity-guided global features and stylized component-level representations. We calculate the similarity scores of the target character and the referenced samples by measuring the distance along the corresponding channels from the content features, and assigning them as the weights for aggregating the global style features. To better capture the local styles, a cross-attention-based style transfer module is adopted to transfer the styles of reference glyphs to the components, where the components are self-learned discrete latent codes through vector quantization without manual definition. With these designs, our AFFFG method could obtain a complete set of component-level style representations, and also control the global glyph characteristics. The experimental results reflect the effectiveness and generalization of the proposed method on different linguistic scripts, and also show its superiority when compared with other state-of-the-art methods. The source code can be found at https://github.com/awei669/VQ-Font."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.808,
+                0.21,
+                0.823
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.833,
+                0.47,
+                0.879
+            ],
+            "angle": 0,
+            "content": "Font design techniques can benefit many critical applications, such as logo designs, data augmentation for text-related tasks, handwriting imitation and identification, etc."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.311,
+                0.892,
+                0.371
+            ],
+            "angle": 0,
+            "content": "However, traditional font design heavily depends on expert designers rendering the glyph styles for each character manually, making the creation of fonts extremely expensive and labor-intensive, especially for glyph-rich scripts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+                0.893,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Recently, with the development of deep learning techniques, many automatic few-shot font generation (AFFFG) methods have been proposed. They have been created using Convolution Neural Networks (CNNs) [22], Generative Adversarial Networks (GANs) [27], Transformers [32], etc. The AFFFG methods use only a few reference font images for generating different glyphs automatically. The typical strategy follows the style and content disentangle-ment and combination paradigm [38, 23], and either adopts global style representation or component-wise style representation. The global style representation [13, 38] is learned and extracted from all the references of each style, which could capture the global characteristics, such as character size and stroke space. However, it lacks the representation of diverse local details, such as the shape and length of local strokes and serif size. On the contrary, the componentwise style representation category [11, 6, 20] generally decomposes each reference sample sharing the same font into pre-defined components and radicals. It either conditions the style encoders jointly on the glyph image and the corresponding component labels or adopts component-label classification losses to train the style encoder. This can be infeasible because each character should be manually associated with a certain set of components, which requires more preparation when applying for new scripts. Additionally, for different content images, their local relations with reference samples can vary. That means the local style representations for different content characters are required to be recomputed when given fixed reference samples, which increases the computational cost."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To tackle the above issue, we propose a hybrid global and local style transferring approach for AFFG in this paper. Since the global style representation of fonts controls more intra-style consistent properties, e.g., the locations, sizes, stroke thickness, and spaces of characters, while the lo"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "*Corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
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+                0.52,
+                0.958
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+            "angle": 0,
+            "content": "19506"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.499
+            ],
+            "angle": 0,
+            "content": "cal style representation focuses on capturing inter-style inconsistent component details, e.g., stroke shape, serif-ness, stroke deformation. Therefore, we leverage both the global and local styles for feature complementation. In order to obtain the global style feature representation, we calculate the similarity scores of the target glyph and the referenced samples by measuring their content feature distances, and then assign them as the weights for aggregating the style features. For local style feature representation, the glyph components are first learned automatically, which are discrete latent codes decomposed from a set of glyphs by vector quantization. Then, a cross-attention transformer is employed to transfer component-wise styles, with the representation of the learned components as the queries and the style representations of the reference glyphs as the keys and values. Contrastive learning is used to learn the local styles in an unsupervised way. For each forward pass, the styles from the reference samples can be transferred onto all the components. So, this local style extraction process is independent of the content glyph, avoiding multiple component-wise representation calculations for different inputs. Finally, the global and local style representations are combined with content features, and then decoded into the target glyph. Moreover, we adopt GAN and a self-reconstruction strategy for training the model without strong supervision. Therefore, it can be easily applied for different script font generation."
+        },
+        {
+            "type": "text",
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+                0.077,
+                0.5,
+                0.472,
+                0.59
+            ],
+            "angle": 0,
+            "content": "We demonstrate the effectiveness of the proposed method on the Chinese mainly. The experimental results reflect the necessity of combing global and local representations, and also tell that our method outperforms other state-of-the-art (SOTA) AFFG methods given very limited reference examples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.591,
+                0.472,
+                0.621
+            ],
+            "angle": 0,
+            "content": "In summary, the contributions of this paper are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.633,
+                0.47,
+                0.695
+            ],
+            "angle": 0,
+            "content": "- We propose a novel AFFG method leveraging complementary global and local representations, which is able to capture intra-style consistent properties and intra-style inconsistent structures of reference glyphs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.707,
+                0.47,
+                0.768
+            ],
+            "angle": 0,
+            "content": "- Similarity of content is used to obtain global styles. It takes a similar degree of glyph structures into consideration. This strategy can better transfer styles for glyphs owning the same components with reference."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.78,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "- Pre-trained Vector Quantization-based Variational Autoencoder (VQ-VAE) is adopted to extract components automatically, component labels are not required. The local styles can be transferred to all the components via cross-attention in one-forward pass. It is efficient for font library creation because it is content irrelevant. A style contrastive loss is proposed to unsupervised transfer the component-level styles."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.633,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.092,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "- Experimental results show great generalizability of our model for unseen fonts, unseen characters, and different scripts. It achieves SOTA performance for font generation even with very limited reference samples. Additionally, it can transfer styles onto cross-linguistic in the zero-shot manner."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.196,
+                0.651,
+                0.212
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.221,
+                0.892,
+                0.386
+            ],
+            "angle": 0,
+            "content": "Image-to-Image Translation. Image-to-image (I2I) translation aims to learn a mapping between source and target domains while retaining the content of the source. GAN-based methods [12, 7, 16] were widely used in this field. Pix2pix [12] first adopted conditional GAN into the I2I task with paired data. CycleGAN [39] introduced circular consistency loss for unsupervised I2I translation [5, 39]. Recently, several I2I methods [2, 4] were proposed to tackle multi-class unsupervised I2I translation problems, aiming to simultaneously generate multiple style outputs given the same input."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.388,
+                0.892,
+                0.432
+            ],
+            "angle": 0,
+            "content": "Font generation belongs to the typical I2I translation task, so the generic I2I translation approaches could be adaptively modified for font generation [17, 9]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.433,
+                0.892,
+                0.568
+            ],
+            "angle": 0,
+            "content": "Character Style Transfer. Character style transfer mainly focused on typography transfer. Traditional methods constructed the transformation through shape modeling [31] and statistical modeling [30]. Recent approaches applied deep learning techniques for character synthesis [3]. Some methods were able to synthesize glyphs as well as the textural effects [1, 36, 8]. However, the font generation task emphasizes more on the consistency of character shape instead of text effects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Global Style-content Disentanglement for Font Generation. Global style-content disentanglement and recombination is a popular strategy for font generation. It models each font style as a universal representation. EMD [35] proposed a network architecture with two encoders, one for content and the other for style. They generated arbitrary fonts by mixing the content and style features, followed by decoding the mixed features. MDM [37] built a framework to disentangle the text images into three factors: text content, font, and style features, and then remixed the factors of different images to transfer a new style. ELDF [15] utilized new consistency losses that forced any combination of encoded features of the stacked inputs to own the consistent features of text contents and font styles."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.811
+            ],
+            "angle": 0,
+            "content": "However, the local details for the font are more diverse and are hard to capture only by global style representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Component-based Font Generation. Since characters such as Chinese characters can be decomposed, some component-based font generation methods [6, 19, 20] have emerged recently. They do not encode the entire image to extract style information, but instead extract style information for each component that makes up a syllable and use it"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19507"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.087,
+                0.095,
+                0.872,
+                0.38
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.389,
+                0.895,
+                0.459
+            ],
+            "angle": 0,
+            "content": "Figure 1. The architecture of our model. The generator consists of five parts: a pre-trained content encoder, a reference style encoder (marked in dark green), a local style aggregator via CAM (marked in yellow), a global style aggregator with content similarity guidance (marked in pink), and a decoder combining content and style features and style features for font generation (marked in gray). A discriminator (marking green) is followed to distinguish the real and fake images, and it simultaneously classifies the content and style category of the generated character."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.484,
+                0.47,
+                0.679
+            ],
+            "angle": 0,
+            "content": "to generate fonts. For instance, CalliGAN [28] decomposed characters into components and offered low-level structure information, including the order of strokes, to guide the generation process. SA-VAE [24] disentangled the style and content as two irrelevant domains with encoding Chinese characters into high-frequency character structure configurations and radicals. Tang et al. [25] proposed FS-Font model that adopted a cross-attention mechanism to aggregate the reference styles into a fine-grained style representation. XMP-Font [18] proposed a self-supervised cross-modality pre-training cross-modality transformer network to model style representations of stroke-level, component-level, and character-level."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.68,
+                0.47,
+                0.741
+            ],
+            "angle": 0,
+            "content": "The component-based font generation methods significantly improve the generated glyphs' quality with few-shot references. However, most of them require you to predefine the radicals or components manually."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.753,
+                0.169,
+                0.768
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.779,
+                0.469,
+                0.81
+            ],
+            "angle": 0,
+            "content": "In this section, we introduce the overall framework, different modules and the training strategy in details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.818,
+                0.239,
+                0.833
+            ],
+            "angle": 0,
+            "content": "3.1. Overall Pipeline"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.841,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Given a content image \\( x_{c} \\) and a set of reference character images \\( y = \\{y_{1},y_{2},\\ldots ,y_{K}\\} \\) sharing the same font, our model aims to generate the character \\( y_{c} \\) owning the same content with \\( x_{c} \\) and the font style of the reference images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.484,
+                0.892,
+                0.514
+            ],
+            "angle": 0,
+            "content": "The overall framework is displayed in Fig. 1. It consists of a generator \\( G \\) and a multi-task discriminator \\( D \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.524,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The generator \\(G\\) contains five parts as illustrated in Fig. 1. The content-encoder \\(E_{c}\\) takes the content image as input to extract its structural representation \\(f_{c}\\). It is pretrained via VQ-VAE to obtain the component-wise latent codes \\(e_{c}\\). The style encoder is designed to learn the style representations from reference images \\(y\\). Specifically, it inputs each reference image independently to map them to the style latent vector \\(f_{s} = \\{f_{1}, f_{2}, \\ldots, f_{K}\\}\\). A Local Style Aggregator (LSA) is followed afterward to transfer the styles onto the learned components. It works through a cross-attention module (CAM) with all the component-wise latent codes \\(e_{c}\\) as queries and the representations of the reference characters \\(f_{s}\\) as the keys and values. After the stylization of components, the content-related local styles \\(f_{sr-L}\\) can be obtained by searching the most similar codes in \\(e_{c} = \\{e_{c}^{1}, e_{c}^{2}, \\ldots, e_{c}^{N}\\}\\) with its representation \\(f_{c}\\) spatially. The Global Style Aggregator (GSA) re-weights the style representations \\(f_{s}\\) and sums up all of them channel-wisely to get the global representation \\(f_{sr-G}\\). The weight is the normalized distance of the content representations between each reference character and the input character, as shown \\(f_{r}^{c} = \\{f_{1}^{c}, f_{2}^{c}, \\ldots, f_{K}^{c}\\}\\) and \\(f_{c}\\) in Fig. 1, respectively. Afterwards, a decoder is employed to generate target image \\(y_{c}\\) with the concatenation features of the content features \\(f_{c}\\), local style representation \\(f_{sr-L}\\) and global style representation"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19508"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.096,
+                0.473,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.259,
+                0.47,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Figure 2. The glyph feature decomposing network for pre-training the content encoder and obtaining component representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.316,
+                0.226,
+                0.331
+            ],
+            "angle": 0,
+            "content": "tation \\(f_{sr - G}\\) as input."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.332,
+                0.47,
+                0.439
+            ],
+            "angle": 0,
+            "content": "During training, a multi-task discriminator is adapted to play the min-max game with the generator for distinguishing the real \\(\\hat{y}_c\\) from a fake \\(y_c\\). To make sure the generated glyph has the correct style with reference samples and still retains the structure of the input content character, the discriminator outputs a binary classification of each character's style and content category."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.452,
+                0.47,
+                0.481
+            ],
+            "angle": 0,
+            "content": "3.2. Glyph Encoders and Component Decomposition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.47,
+                0.627
+            ],
+            "angle": 0,
+            "content": "The content encoder is pre-trained on the feature decomposing network and kept frozen for the font generation task. In the pre-training step, it is used to decompose the glyph images into component-wise latent codes, and trained on a certain set of character templates for reconstruction. The overview of the feature decomposing network is shown in Fig. 2. It contains a content encoder and a reconstruction decoder, connected by a discrete latent space using a latent codebook \\( e_c \\in R^{N \\times d} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.63,
+                0.47,
+                0.706
+            ],
+            "angle": 0,
+            "content": "The encoder is built on CNNs and maps an input glyph image into latent representations, \\( z_{e} \\in R^{w \\times h \\times d} \\), where \\( d \\) is the number of channels, and \\( h \\) and \\( w \\) represent the height and width of the feature maps, respectively. Subsequently, vector quantization [26] is used to discrete \\( z_{e} \\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.117,
+                0.719,
+                0.47,
+                0.749
+            ],
+            "angle": 0,
+            "content": "\\[\nz _ {e} ^ {i} = e _ {c} ^ {n}, \\quad \\text {s . t .} \\quad n = \\underset {n \\in \\{1, 2, \\dots , N \\}} {\\arg \\min } \\| z _ {e} ^ {i} - e _ {c} ^ {n} \\| _ {2} ^ {2}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.763,
+                0.47,
+                0.854
+            ],
+            "angle": 0,
+            "content": "where each spatial-wise elemental vector \\( z_{e}^{i} \\in R^{d} \\) in \\( z_{e} \\) is replaced with the closest code vector by executing a nearest-neighbor lookup on codebook \\( e_{c} \\), comprised of \\( d \\)-dimensional \\( n \\) code vectors. Finally, the reconstruction decoder uses the matched codes \\( z_{q} \\in R^{w \\times h \\times d} \\) as an input and outputs a reconstructed glyph."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To optimize this process, the encoder and codebooks are updated to minimize an objective \\( L_{pre} \\) in Eq. (2), which refers to \\( L_{1} \\)-based reconstruction loss and latent loss \\( L_{lat} \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.093,
+                0.578,
+                0.106
+            ],
+            "angle": 0,
+            "content": "as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.501,
+                0.114,
+                0.892,
+                0.163
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {p r e} = L _ {1} + L _ {l a t} \\\\ = \\| x _ {c} - \\hat {x} _ {c} \\| _ {1} + \\alpha \\| \\operatorname {s g} [ z _ {e} ] - e _ {c} \\| _ {2} ^ {2} + \\beta \\| z _ {e} - \\operatorname {s g} [ e _ {c} ] \\| _ {2} ^ {2}, \\tag {2} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.165,
+                0.892,
+                0.359
+            ],
+            "angle": 0,
+            "content": "where sg is a stop-gradient operator that is defined as an identity at forward computation time and has zero partial derivatives. \\(\\alpha\\) and \\(\\beta\\) are the balancing hyperparameters. Experimentally, we set them as 1 and 0.1, respectively. The first term in Eq. (2) makes sure no information gets lost in the forward pass. The second term updates the codebook variables by moving the embedding vectors \\(e_c\\) towards the encoder outputs \\(z_e\\). Meanwhile, the third term encourages the encoder output to match the targeted code vectors. There are no bypass connections between the encoder and decoder, so all the component-wise information of the glyph set processed by the encoder can be compressed in the latent space [21]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.361,
+                0.892,
+                0.42
+            ],
+            "angle": 0,
+            "content": "After this pre-training task, we fix the content encoder \\( E_{c} \\) as well as the component codebook \\( e_{c} \\) to build the font generation model. The style encoder \\( E_{s} \\) has the same architecture as \\( E_{c} \\), but it is trained from scratch."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.43,
+                0.715,
+                0.446
+            ],
+            "angle": 0,
+            "content": "3.3. Local Style Aggregator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.453,
+                0.892,
+                0.619
+            ],
+            "angle": 0,
+            "content": "Most recently proposed methods [18, 19] extract local style representation of characters by gaining attention from input content and reference styles. It is inefficient, especially for creating a new font library that contains a large number of glyphs. Since each of the glyphs must go through the attention model for feature aggregation once. However, most of them actually share some local representation if they have the same strokes or radicals. Starting from this point, we design an LSA module, the core is a CAM block to transfer the styles onto all the component-wise codes \\( e_{c} \\) instead of the input glyph."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.619,
+                0.892,
+                0.771
+            ],
+            "angle": 0,
+            "content": "The CAM block is built upon stacked multi-head transformers with component codes \\( e_{c} \\) as queries and reference style vectors \\( f_{r} \\) as keys and values. Formally, the feature maps \\( f_{k} \\in R^{w \\times h \\times d} \\) of \\( k \\)-th reference samples are reshaped along the channel axis, respectively, forming the sequential reference tokens \\( \\tilde{f}_{r} \\in R^{k \\cdot w \\cdot h \\times d} \\). For \\( i^{th} \\) head, two linear projections \\( W_{k}^{i} \\in R^{c \\times d} \\) and \\( W_{v}^{i} \\in R^{c \\times d} \\) are applied on it to get the keys \\( K_{i} = \\tilde{f}_{r}W_{k}^{iT} \\) and values \\( V_{i} = \\tilde{f}_{r}W_{v}^{iT} \\), respectively. Meanwhile, we acquire the query matrix \\( Q_{i} \\) by linear projecting \\( e_{c} \\) with a learning weight \\( W_{e}^{i} \\in R^{c \\times d} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.772,
+                0.892,
+                0.816
+            ],
+            "angle": 0,
+            "content": "The attention module operates on the queries \\( Q_{i} \\), keys \\( K_{i} \\), and values \\( V_{i} \\) and generates weighted average vectors \\( \\hat{V}_{i} \\), which can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.512,
+                0.824,
+                0.892,
+                0.87
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {V} = \\operatorname {A t t e n t i o n} \\left(Q _ {i}, K _ {i}, V _ {i}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {c}}\\right) V _ {i}. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "After obtaining the representations in each head, we concatenate all \\(\\hat{V}_i\\) along the channel dimension, and employ a"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19509"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.12
+            ],
+            "angle": 0,
+            "content": "linear projection to get the multi-head attention result \\( e_{s} \\), as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.077,
+                0.131,
+                0.47,
+                0.168
+            ],
+            "angle": 0,
+            "content": "\\[\ne _ {s} = \\text {M u l t i - h e a d} (Q, K, V) = \\operatorname {c o n c a t} \\left(\\hat {V} _ {1}, \\hat {V} _ {2},; \\hat {V} _ {m}\\right) W _ {o}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.169,
+                0.47,
+                0.199
+            ],
+            "angle": 0,
+            "content": "where \\( m \\) is the number of total attention head, and \\( W_{o} \\) is the learning weight."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.2,
+                0.469,
+                0.291
+            ],
+            "angle": 0,
+            "content": "After we get the stylized component-wise codes \\( e_s = \\{e_s^1, e_s^2, \\ldots, e_s^N\\} \\). For each input glyph, its local representation \\( f_{sr-L} \\) can be aggregated from \\( e_s \\) by searching for the closest label \\( n \\) in \\( e_c \\) for each spatial element in \\( f_c \\) as expressed in Eq. (1), and then selecting the corresponding style representation \\( e_s^n \\) for replacement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.302,
+                0.3,
+                0.318
+            ],
+            "angle": 0,
+            "content": "3.4. Global Style Aggregator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.325,
+                0.469,
+                0.4
+            ],
+            "angle": 0,
+            "content": "The original style representation \\( f_{k} \\) for each reference sample is able to provide more global information for the font generation, which can control the size, the stroke space, etc. So, we aggregate their features directly as the global representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.402,
+                0.47,
+                0.614
+            ],
+            "angle": 0,
+            "content": "As illustrated in [36], the style features and content features of references are not entirely independent. From a human's perceptual observation, there are some correlations that exist between different characters. If the input glyph has exactly the same radical or structure with some references, their style representations should be highly referred to during the transfer process. Therefore, we re-weight the individual style features \\( f_{k} \\) of each reference glyph based on the content feature similarity. We extract the content features \\( f_{r}^{c} = \\{f_{1}^{c}, f_{2}^{c}, \\ldots, f_{K}^{c}\\} \\in R^{w \\times h \\times d} \\) of each reference and reshape them to \\( \\tilde{f}_{k}^{c} \\in R^{w \\cdot h \\times d} \\), meanwhile, the content features \\( f_{c} \\in R^{w \\times h \\times d} \\) of content image are reshaped into \\( \\tilde{f}_{c} \\in R^{w \\cdot h \\times d} \\). The glyph similarity is determined by the normalized cross-correlation measurement as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.623,
+                0.469,
+                0.669
+            ],
+            "angle": 0,
+            "content": "\\[\nW _ {k j} = \\frac {\\tilde {f} _ {k} ^ {c} \\cdot \\tilde {f} _ {c}}{\\left\\| \\tilde {f} _ {k} ^ {c} \\right\\| * \\left\\| \\tilde {f} _ {c} \\right\\|}, j \\in \\{1, 2, \\dots , d \\}. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.679,
+                0.469,
+                0.725
+            ],
+            "angle": 0,
+            "content": "\\(W_{kj}\\) is a scalar that represents the similarity between \\(k_{th}\\) reference and the input glyph on \\(j_{th}\\) channel. Then, we normalize it by considering \\(k\\) samples on each channel as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.737,
+                0.469,
+                0.779
+            ],
+            "angle": 0,
+            "content": "\\[\n\\overline {{W}} _ {k j} = \\operatorname {s o f t m a x} \\left(\\frac {\\exp (a W _ {k j})}{\\sum_ {k = 1} ^ {K} \\exp (W _ {k j})}\\right). \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.79,
+                0.469,
+                0.85
+            ],
+            "angle": 0,
+            "content": "This weight is then applied to the reference style representations \\( f_{r} \\), where \\( j_{t}h \\) channel feature \\( f_{k}^{j} \\) is weighted by \\( \\overline{W}_{kj} \\), to aggregate the global representation \\( f_{sr - G} \\) as expressed in:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.157,
+                0.863,
+                0.469,
+                0.905
+            ],
+            "angle": 0,
+            "content": "\\[\nf _ {s r - G} = \\operatorname {c o n c a t} _ {j} \\left(\\sum_ {k = 1} ^ {K} \\bar {W} _ {k j} f _ {k} ^ {j}\\right). \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.137
+            ],
+            "angle": 0,
+            "content": "This global style representation \\( f_{sr - G} \\) is concatenated with the content features \\( f_{c} \\) and local style representation \\( f_{sr - L} \\), and then input to the decoder to generate the target font."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.145,
+                0.605,
+                0.161
+            ],
+            "angle": 0,
+            "content": "3.5. Training"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.169,
+                0.892,
+                0.304
+            ],
+            "angle": 0,
+            "content": "We train our model to generate the image \\( y_{c} \\) from an input content image \\( x_{c} \\) and a set of reference glyph images \\( y = \\{y_{1},y_{2},\\ldots ,y_{K}\\} \\). The content encoder is pretrained and kept fixed during this period. The losses consist of three parts, an adversarial loss, a matching loss, and a style contrast loss. The adversarial loss and matching loss are used between the generated results \\( y_{c} \\) and the ground truth \\( \\hat{y}_c \\). While the style contrast loss is designed to learn distinguished styles for components."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.305,
+                0.892,
+                0.38
+            ],
+            "angle": 0,
+            "content": "Adversarial loss. To make the model generate plausible images, we employ a multi-head projection discriminator \\( D_{s,c} \\) for style label \\( s \\) and character label \\( c \\) in our framework. The loss function is implemented as the hinge GAN loss [33]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.547,
+                0.387,
+                0.891,
+                0.425
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {a d v} ^ {D} = - \\mathbb {E} _ {\\hat {y} _ {c} \\sim p _ {d a t a}} \\min  (0, - 1 + D _ {s, c} (\\hat {y} _ {c})) \\\\ - \\mathbb {E} _ {y _ {c} \\sim p _ {G}} \\min  (0, - 1 - D _ {s, c} (y _ {c})) \\tag {8} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.55,
+                0.427,
+                0.735,
+                0.446
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {a d v} ^ {G} = - \\mathbb {E} _ {y _ {c} \\sim p _ {G}} D _ {s, c} (y _ {c}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.454,
+                0.89,
+                0.483
+            ],
+            "angle": 0,
+            "content": "where \\( p_G \\) denotes the set of generated images, and \\( p_{data} \\) denotes the set of real glyph images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.484,
+                0.892,
+                0.543
+            ],
+            "angle": 0,
+            "content": "Matching loss. To make the generated character \\( y_{c} \\) learn pixel-level and feature-level consistency with ground truth \\( \\hat{y}_{c} \\), we employ an \\( L_{1} \\) loss on both image and image features as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.563,
+                0.55,
+                0.891,
+                0.611
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {i m g} = \\mathbb {E} [ \\| y _ {c} - \\hat {y} _ {c} \\| _ {1} ] \\\\ \\mathcal {L} _ {\\text {f e a t}} = \\mathbb {E} \\left[ \\sum_ {l = 1} ^ {L} \\left\\| f ^ {(l)} \\left(y _ {c}\\right) - f ^ {(l)} \\left(\\hat {y} _ {c}\\right) \\right\\| _ {1} \\right], \\tag {9} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.62,
+                0.89,
+                0.649
+            ],
+            "angle": 0,
+            "content": "where \\( f_{l}(y_{c}) \\) and \\( f_{l}(\\hat{y}_{c}) \\) represent the intermediate features in the \\( l_{t}h \\) layer of \\( D \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.65,
+                0.892,
+                0.74
+            ],
+            "angle": 0,
+            "content": "Style contrast loss. Given two different reference sets but sharing the same font style, the associated stylized components for these sets should be the same. However, if the reference character sets have different font styles, the component styles should be distinguished. So, we formulate our style contrastive loss as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.502,
+                0.75,
+                0.892,
+                0.861
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {c s t} = \\\\ - \\log \\left(\\frac {\\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\\right)}{\\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\\right) + \\sum_ {N _ {s} ^ {-}} \\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s -} ^ {n}\\right)}\\right). \\tag {10} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In detail, for each certain font style \\(s\\) and is corresponding codebook \\(e_s\\), where \\(e_{s+}\\) is the positive codebook pair of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19510"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.184
+            ],
+            "angle": 0,
+            "content": "\\(e_s\\) whose references have the same font style but different content, and \\(e_{s-}\\) is the negative codebook pair share different font style. \\(N_s^-\\) is the number of negative style samples, for \\(n\\)-th codebook entries \\(e_s^n\\) in codebook \\(e_s \\in R^{N \\times d}\\). We can always find the positive pair \\(e_{s+}^n\\) and negative pair set \\(\\{e_{s_1-}^n, e_{s_2-}^n, \\ldots, e_{s_{neg}-}^n\\}\\) in the corresponding position."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.185,
+                0.469,
+                0.216
+            ],
+            "angle": 0,
+            "content": "Overall objective loss. Finally, we optimize the whole model by the following full objective function:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.232,
+                0.469,
+                0.256
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {E _ {s}, G} \\max  _ {D} \\mathcal {L} _ {a d v} ^ {D} + \\mathcal {L} _ {a d v} ^ {G} + \\lambda_ {1} \\mathcal {L} _ {i m g} + \\lambda_ {2} \\mathcal {L} _ {f e a t} + \\lambda_ {3} \\mathcal {L} _ {c s t}. \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.273,
+                0.469,
+                0.304
+            ],
+            "angle": 0,
+            "content": "The \\(\\lambda_{1},\\lambda_{2}\\) and \\(\\lambda_3\\) is weighting hyperparameter. We set them to 1, 1, and 0.1, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.325,
+                0.282,
+                0.342
+            ],
+            "angle": 0,
+            "content": "4. Experimental Results"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.353,
+                0.254,
+                0.369
+            ],
+            "angle": 0,
+            "content": "4.1. Experiment Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.379,
+                0.469,
+                0.501
+            ],
+            "angle": 0,
+            "content": "Dataset. We collected 386 Chinese fonts and generated 3,500 Chinese characters for each font according to the first-level Chinese Character Table. All character pictures are normalized to \\(128 \\times 128\\). A font template is randomly selected from the 386 fonts for extracting the glyph content features and kept fixed throughout the training and test [1]. This font set is also used for pre-training the VQ-VAE to get a set of common parts codebooks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.502,
+                0.469,
+                0.638
+            ],
+            "angle": 0,
+            "content": "The Chinese training set contains 370 fonts and 3,000 Chinese characters, denoted as the seen font seen character (SFSC) set. To verify our method, we evaluate the font generation ability on two test sets: One is the rest of the 15 unseen fonts with 3,000 seen characters per font, denoted as the seen font unseen character (UFSC) set; the other is the remaining 15 unseen fonts with 500 unseen characters per font, denoted as the unseen font unseen character (UFUC) set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.642,
+                0.469,
+                0.776
+            ],
+            "angle": 0,
+            "content": "Implementation details. The main training process of our method is divided into two parts. First, a component-wise codebook is trained with 3,000 Chinese characters sharing the same font. We set the embedding dimension \\(d\\) to 256, the batch size to 256, and the iteration steps to 50,000. Then, for training the whole font generation model, we set the batch size to 48, the number of attention heads to 8 in three stacked transformer layers, and iteration steps to 500,000."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Evaluation metrics. To evaluate the font generation quality, we use the following five metrics [14], root-meansquare deviation (RMSE), structural similarity (SSIM), learned perceptual image patch similarity (LPIPS) [34], Fréchet inception distance (FID) [10], and User Study. The User Study is conducted by 10 volunteers, who observe the reference samples and vote for the best generation result from all the comparison methods."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.547,
+                0.088,
+                0.843,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Table 1. Ablation study of component codebooks."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.1,
+                0.892,
+                0.179
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Codebook size</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td></tr><tr><td>50</td><td>0.512</td><td>0.422</td><td>0.343</td><td>144.2</td></tr><tr><td>80</td><td>0.546</td><td>0.407</td><td>0.296</td><td>120.7</td></tr><tr><td>100</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td></tr><tr><td>120</td><td>0.568</td><td>0.392</td><td>0.278</td><td>109.5</td></tr><tr><td>150</td><td>0.567</td><td>0.388</td><td>0.282</td><td>112.4</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.543,
+                0.197,
+                0.846,
+                0.249
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.567,
+                0.262,
+                0.822,
+                0.275
+            ],
+            "angle": 0,
+            "content": "Figure 3. The visualization of latent codes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.301,
+                0.664,
+                0.316
+            ],
+            "angle": 0,
+            "content": "4.2. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.325,
+                0.892,
+                0.384
+            ],
+            "angle": 0,
+            "content": "We perform three ablation studies to evaluate the effectiveness of our proposed models on the few-shot Chinese font generation task. These experiments are conducted on the UFUC dataset."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.407,
+                0.821,
+                0.422
+            ],
+            "angle": 0,
+            "content": "4.2.1 The effect of component codebook size"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.431,
+                0.892,
+                0.643
+            ],
+            "angle": 0,
+            "content": "The component codebook size reflects the complexity of the script. We set it as different values for training the content encoder and acquiring component-wise representation in VQ-VAE. Then, they are fixed for font generation. The results are displayed in Tab. 1. We can see that when the codebook size exceeds 100, the performance on each metric has limited improvement. That illustrates using 100 components is sufficient to depict the Chinese characters. When we train the model on English script, we find that by only using 15 codes, the model can generate very good results. Therefore, the size of the component codebook has a relationship with the scripts. More complex scripts require larger codebook sizes. In the following experiments, We set the Chinese component codebook size to 100."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.892,
+                0.75
+            ],
+            "angle": 0,
+            "content": "We select a certain code from the codebook to compute its similarity with features of different glyphs spatially. The visualization results of the \\(32_{th}\\) code and \\(44_{th}\\) code are present in Fig. 3. We can see the \\(32_{th}\\) code mainly extracts vertical components and \\(44_{th}\\) extracts horizontal components. It demonstrates the VQ-VAE strategy can generate \"components\" automatically."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.77,
+                0.733,
+                0.785
+            ],
+            "angle": 0,
+            "content": "4.2.2 The effect of each module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To illustrate the influence of the GSA and LSA modules of our method, we conduct the ablation study with and without it in the model. By removing the LSA, the component-wise representation is not required. The model degrades to a global content-style disentanglement architecture, with the aggregated style representation only conditioned on content similarity. When removing the GSA part, the model focuses"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19511"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.107,
+                0.092,
+                0.445,
+                0.201
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Reference</td><td>雳枪嫌</td><td>惧聂蔬</td><td>鼠韧贻</td></tr><tr><td>w/o GSA</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>w/o LSA</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>Full model</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>GT</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr></table>"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.209,
+                0.471,
+                0.279
+            ],
+            "angle": 0,
+            "content": "Figure 4. Qualitative font generation results with and without LSA and GSA modules. The first and last rows are the three references and the ground truth per font, respectively. The middle rows are generated results correspondingly. The red dashed boxes point out details that were better generated by our full proposed model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.305,
+                0.469,
+                0.334
+            ],
+            "angle": 0,
+            "content": "more on the details of the stroke but loses the global style control."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.335,
+                0.47,
+                0.593
+            ],
+            "angle": 0,
+            "content": "We evaluate the two models and the proposed full model on our collected UFUC dataset. Fig. 4 displays some comparison results. The results with and without these modules have obvious differences. The model with LSA could better capture the details of reference strokes, while the sizes of generated characters and the inner spaces are not always consistent with the given references. The model with only GSA has the opposite functions. Most strokes are not generated well. The full model combines LSA and GSA, which achieves better performance (see the details in red dash boxes of Fig. 4). Quantitative results in Tab. 3 further confirm the importance of the two modules. The LSA model assists more than GSA, which demonstrates that the style of glyphs mainly lies in the local details. From these results, we conclude that LSA and GSA are both essential in our model and they enable the model to capture diverse local styles and also control the global styles."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.614,
+                0.353,
+                0.628
+            ],
+            "angle": 0,
+            "content": "4.2.3 The effect of reference numbers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.639,
+                0.469,
+                0.76
+            ],
+            "angle": 0,
+            "content": "Intuitively, given more reference samples, the generated font better resembles a realistic one. Fig. 5 shows the effect of reference numbers. We can see that when the number of references increases from 1 to 8, the generated characters have an incremental performance improvement. The figure shows that it becomes stable when given more references. However, there are diminishing returns after the first few references. More details can be found in Appendix."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.771,
+                0.363,
+                0.787
+            ],
+            "angle": 0,
+            "content": "4.3. Comparing with SOTA Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We compare our method with five SOTA AFFG methods. 1) FUNIT [17] used two different encoders with the AdaIN module to generate a new image with mixed content and style. It belongs to the global style-content disentanglement FFG method. 2) MX-Font [20] extracts multiple style features not explicitly conditioned on component labels, but is automatically by designed multiple experts to"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.547,
+                0.1,
+                0.849,
+                0.239
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.247,
+                0.892,
+                0.275
+            ],
+            "angle": 0,
+            "content": "Figure 5. Performance changes of our model by varying numbers of the reference samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.308,
+                0.893,
+                0.581
+            ],
+            "angle": 0,
+            "content": "represent different local concepts, e.g., left-side sub-glyph. It shows good generalization ability to unseen languages. 3) LF-Font [19] proposed localized style representation inspired by low-rank matrix factorization, which also extracts component-wise features. 4) DG-Font [29] is an unsupervised network that used a Deformable Convolution in the Generator to deform and transform the character of one font to another. It achieved a good effect on cursive characters. 5) AGIS-net [8] used two different decoders to generate images with character shapes and then the texture information successively. It can transfer the font as well as the text effects. 6) FS-Font [25] requires fixed content-reference mapping to transfer Fine-Grained local styles. We retrain all the models by our dataset using their original training hyperparameters and strategies. The reference samples are set to 3 in the training and test phases for all the methods. The qualitative and quantitative comparison results are shown in Fig. 6 and Tab. 2, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
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+                0.901
+            ],
+            "angle": 0,
+            "content": "Tab. 2 shows that our method outperforms previous SOTA methods with significant gaps in all the metrics. We can observe that FUNIT fails to capture diverse styles. Only when the content and reference styles are visually close, it can generate a structured character. That illustrates the universal style representation strategy is not a good choice for AFFG. LF-Font generates fonts with worse visual quality since the reference numbers are very limited. Its performance is unstable as they are prone to loss of strokes or distortion of components for certain styles. DG-Font may fail to perform style transfer especially when the reference style significantly differs from that of the content. Additionally, it generates glyphs containing characteristic artifacts. AGIS-Net is more stable to generate the font of different styles and complement structures. It could better transfer the global features such as the size and the thickness of strokes. MX-Font generates better stylized characters than other methods, but it has a higher probability of failing to generate fine-grained style features compared with our method. The generation results of FS-Font are also unsatisfactory, especially on unseen references, due to the randomly selected"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19512"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.277,
+                0.088,
+                0.694,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Table 2. Quantitative comparison results on UFSC and UFUC datasets"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.184,
+                0.101,
+                0.792,
+                0.298
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>Method</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td><td>User Study↑</td></tr><tr><td rowspan=\"7\">UFSC</td><td>FUNIT [17]</td><td>0.512</td><td>0.426</td><td>0.361</td><td>161.8</td><td>1.2%</td></tr><tr><td>LF-FONT [19]</td><td>0.548</td><td>0.406</td><td>0.334</td><td>123.9</td><td>3.9%</td></tr><tr><td>AGIS-NET [8]</td><td>0.529</td><td>0.409</td><td>0.302</td><td>145.0</td><td>10.3%</td></tr><tr><td>DG-FONT [29]</td><td>0.517</td><td>0.419</td><td>0.312</td><td>149.0</td><td>11.6%</td></tr><tr><td>MX-FONT [20]</td><td>0.523</td><td>0.407</td><td>0.297</td><td>94.5</td><td>14.4%</td></tr><tr><td>FS-FONT [25]</td><td>0.570</td><td>0.379</td><td>0.327</td><td>172.6</td><td>21.5%</td></tr><tr><td>Ours</td><td>0.636</td><td>0.341</td><td>0.225</td><td>93.7</td><td>58.6%</td></tr><tr><td rowspan=\"7\">UFUC</td><td>FUNIT [17]</td><td>0.468</td><td>0.472</td><td>0.379</td><td>153.4</td><td>3.4%</td></tr><tr><td>LF-FONT [19]</td><td>0.481</td><td>0.462</td><td>0.377</td><td>136.7</td><td>4.8%</td></tr><tr><td>AGIS-NET [8]</td><td>0.550</td><td>0.400</td><td>0.310</td><td>137.2</td><td>11.5%</td></tr><tr><td>DG-FONT [29]</td><td>0.493</td><td>0.397</td><td>0.312</td><td>136.7</td><td>10.8%</td></tr><tr><td>MX-FONT [20]</td><td>0.478</td><td>0.447</td><td>0.333</td><td>114.8</td><td>15.2%</td></tr><tr><td>FS-FONT [25]</td><td>0.418</td><td>0.474</td><td>0.377</td><td>173.7</td><td>19.5%</td></tr><tr><td>Ours</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td><td>54.3%</td></tr></table>"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.317,
+                0.891,
+                0.499
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td colspan=\"6\">UFUC</td><td colspan=\"6\">UFSC</td></tr><tr><td>Reference</td><td>嘉明主</td><td>泛懂隘</td><td>腰也携</td><td>铸符挂</td><td>寒晴宝</td><td>原初忍</td><td>香贬刷</td><td>矩财需</td><td>爷雏仇</td><td>猫悲捕</td><td></td><td></td></tr><tr><td>FUNIT</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>柴火</td><td>此方石</td><td>轧倍沉</td><td>生?学</td><td>灭</td><td>乳吮游</td><td></td><td></td></tr><tr><td>LF-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄搁蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>DG-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>AGIS-Net</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>MX-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>FS-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>Ours</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>GT</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>改善避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.505,
+                0.893,
+                0.534
+            ],
+            "angle": 0,
+            "content": "Figure 6. FFG results of each method on UFUC and UFSC dataset. We represent the generated samples of five different kinds of fonts, given three references and three content images per font. The red boxes represent the better generation details."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.555,
+                0.444,
+                0.567
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation study of different models on UFUC dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.567,
+                0.47,
+                0.624
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td><td>User Study↑</td></tr><tr><td>w/o LSA</td><td>0.496</td><td>0.422</td><td>0.318</td><td>145.0</td><td>7.3%</td></tr><tr><td>w/o GSA</td><td>0.532</td><td>0.402</td><td>0.293</td><td>132.1</td><td>20.3%</td></tr><tr><td>Full model</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td><td>72.4%</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.648,
+                0.236,
+                0.663
+            ],
+            "angle": 0,
+            "content": "content-reference pairs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.673,
+                0.342,
+                0.69
+            ],
+            "angle": 0,
+            "content": "4.4. Applying to Other Languages"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.696,
+                0.47,
+                0.833
+            ],
+            "angle": 0,
+            "content": "To verify the generalization of our method for other languages, we collected 60 fonts of 125 Japanese characters. 50 fonts with 100 glyphs per font are randomly selected for training, and the rest for test. Some results are displayed in Fig. 7. Since the character structures of the Japanese are much simpler than Chinese, the generated results approach the ground truth more. Additionally, our method can transfer styles onto unseen content, including cross-linguistic glyphs as shown in Fig. 8."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.846,
+                0.196,
+                0.861
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We present a novel AFFG approach in this paper, which could aggregate global and local styles of limited refer"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.51,
+                0.561,
+                0.888,
+                0.673
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.68,
+                0.892,
+                0.721
+            ],
+            "angle": 0,
+            "content": "Figure 7. FFG results of Japanese scripts. For each style, the upper and lower rows respectively represent the model generation results and GT."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "ences. The designed LSA and GSA modules were assigned different tasks to capture the local details and global structures of the font, respectively. The LSA adopted a cross-attention mechanism for transferring styles onto all of the self-learned components without manual definition. While the GSA utilized the similarity of different glyphs, and then used it to guide the global styles combination of all references. Experiments demonstrated the effectiveness of both modules, and also showed our proposed method significantly outperformed other methods quantitatively and qual"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19513"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
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+                0.462,
+                0.159
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Content\nReference</td><td>アウマガがせん不の</td></tr><tr><td>别福混伏桔快</td><td>アウマガがせん不の</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.266,
+                0.162,
+                0.284,
+                0.174
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.177,
+                0.46,
+                0.241
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Content\nReference</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr><tr><td>痴佳体</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr><tr><td>版贾句</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.267,
+                0.242,
+                0.285,
+                0.254
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.256,
+                0.462,
+                0.457
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Reference</td><td colspan=\"4\">Generated Chinese samples</td><td colspan=\"4\">Generated Japanese samples</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>宣 呢 除 医 脸 另 追 播 筏 槽 预 缺 街 登 和 旁 骨 板 释 旅 课 急 放 智 蒙 弹</td><td>絹 聘 黔 黎 黎 潘 與 輛 與 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 廣 桃 篡 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻</td><td>絹 渠 槟 懒 懒 穰 橘 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 嘴 嘴 褚 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深</td><td>捻陵 傍管 喷 嘴 鞍 黔 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚</td><td>工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 巠 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 巳</td><td>大 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 甲 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙方 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td></td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.266,
+                0.46,
+                0.284,
+                0.472
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.483,
+                0.47,
+                0.525
+            ],
+            "angle": 0,
+            "content": "Figure 8. Cross-language inference on (a) Japanese glyphs and (b) Korean glyphs. (c) Chinese results generated under few-shot and Japanese generated results under zero-shot manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.549,
+                0.47,
+                0.596
+            ],
+            "angle": 0,
+            "content": "itatively. However, our method is limited to two aspects. If given only one reference or very fancy font, e.g., decoration, or shadow, the generated results are unsatisfactory."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.609,
+                0.236,
+                0.626
+            ],
+            "angle": 0,
+            "content": "Acknowledgments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.634,
+                0.469,
+                0.695
+            ],
+            "angle": 0,
+            "content": "This work is supported by the Open Project Program of the National Laboratory of Pattern Recognition(NLPR) (No.20220004). We thank all anonymous reviewers for their constructive comments on this paper."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.708,
+                0.164,
+                0.725
+            ],
+            "angle": 0,
+            "content": "Appendix"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.733,
+                0.469,
+                0.793
+            ],
+            "angle": 0,
+            "content": "Besides the results and discussions presented in the original paper, we provide more experiments and results in this appendix, which further explain the effectiveness and generality of our method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.802,
+                0.469,
+                0.833
+            ],
+            "angle": 0,
+            "content": "The effect of different reference characters on the generated results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.84,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The font style is an aesthetic concept and has nothing to do with specific characters. In the process of few shot font generation, given reference characters with different content, the provided style representation should be the same."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.515,
+                0.095,
+                0.88,
+                0.24
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Reference\\GT</td><td>鞠肖剥频裙翔祥凝挨</td></tr><tr><td>搗冊被海梗畅\\GT</td><td>鞠肖剥频裙翔祥凝挨</td></tr><tr><td>Reference\\GT</td><td>揍煽寝漂菊镜筏壁德</td></tr><tr><td>榆膛蔡燥稀魁</td><td>揍煽寝漂菊镜筏壁德</td></tr></table>"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.247,
+                0.892,
+                0.275
+            ],
+            "angle": 0,
+            "content": "Figure 9. Generating the same target character, referring to characters with different contents from the same style font."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.51,
+                0.296,
+                0.88,
+                0.459
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Ref sets</td><td>苏1</td><td>横2</td><td>笑3</td><td>陈4</td><td>洁5</td><td>伟6</td><td>豪7</td><td>科8</td><td>腺9</td></tr><tr><td>Ref1</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-3</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-5</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-7</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-9</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>责</td><td>度</td><td>层</td><td>宇</td></tr><tr><td>GT</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>责</td><td>度</td><td>层</td><td>宇</td></tr></table>"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.467,
+                0.892,
+                0.536
+            ],
+            "angle": 0,
+            "content": "Figure 10. Generated samples by varying reference set size. Each middle row shows the samples generated by given different number (1, 3, 5, 7, 9) of references. The number (1 to 9) represents the order of each character to be used. The target glyphs are displayed in the bottom row."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.562,
+                0.892,
+                0.653
+            ],
+            "angle": 0,
+            "content": "In our training process, we randomly select \\( k \\) style reference characters for generating characters each time. During the inference phase, we select characters with different content in the same style as the reference set. The generated results are shown in Fig. 9. There is a subtle difference between the overall style and the local style of the generated results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.665,
+                0.892,
+                0.695
+            ],
+            "angle": 0,
+            "content": "The qualitative results using different numbers of references"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.705,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Intuitively, the larger the number of given reference characters, the richer and more accurate the extracted style features should be. In the inference stage, we change the number of reference characters and observe the impact on the generated results. It can be observed from Fig. 10 that the overall and local quality of generated characters is roughly positively correlated with the number of reference characters. The quality improvement is more obvious when the number increases from 1 to 5, and the improvement beyond this number is limited. In our paper, the number of reference images is set to 3, and the model training and qualitative and quantitative comparisons with other methods are completed with this setting."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19514"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+# Few shot font generation via transferring similarity guided global style and quantization local style
+
+Wei Pan<sup>1</sup> Anna Zhu<sup>1*</sup> Xinyu Zhou<sup>1</sup> Brian Kenji Iwana<sup>2</sup> Shilin Li<sup>1</sup>  
+<sup>1</sup> School of Computer Science and Artificial Intelligence, Wuhan University of Technology  
+<sup>2</sup> Human Interface Laboratory, Kyushu University
+
+{aaawei, annazhu, 297932, shilinli}@whut.edu.cn iwana@ait.kyushu-u.ac.jp
+
+# Abstract
+
+Automatic few-shot font generation (AFFFG), aiming at generating new fonts with only a few glyph references, reduces the labor cost of manually designing fonts. However, the traditional AFFFG paradigm of style-content disentanglement cannot capture the diverse local details of different fonts. So, many component-based approaches are proposed to tackle this problem. The issue with component-based approaches is that they usually require special pre-defined glyph components, e.g., strokes and radicals, which is infeasible for AFFFG of different languages. In this paper, we present a novel font generation approach by aggregating styles from character similarity-guided global features and stylized component-level representations. We calculate the similarity scores of the target character and the referenced samples by measuring the distance along the corresponding channels from the content features, and assigning them as the weights for aggregating the global style features. To better capture the local styles, a cross-attention-based style transfer module is adopted to transfer the styles of reference glyphs to the components, where the components are self-learned discrete latent codes through vector quantization without manual definition. With these designs, our AFFFG method could obtain a complete set of component-level style representations, and also control the global glyph characteristics. The experimental results reflect the effectiveness and generalization of the proposed method on different linguistic scripts, and also show its superiority when compared with other state-of-the-art methods. The source code can be found at https://github.com/awei669/VQ-Font.
+
+# 1. Introduction
+
+Font design techniques can benefit many critical applications, such as logo designs, data augmentation for text-related tasks, handwriting imitation and identification, etc.
+
+However, traditional font design heavily depends on expert designers rendering the glyph styles for each character manually, making the creation of fonts extremely expensive and labor-intensive, especially for glyph-rich scripts.
+
+Recently, with the development of deep learning techniques, many automatic few-shot font generation (AFFFG) methods have been proposed. They have been created using Convolution Neural Networks (CNNs) [22], Generative Adversarial Networks (GANs) [27], Transformers [32], etc. The AFFFG methods use only a few reference font images for generating different glyphs automatically. The typical strategy follows the style and content disentangle-ment and combination paradigm [38, 23], and either adopts global style representation or component-wise style representation. The global style representation [13, 38] is learned and extracted from all the references of each style, which could capture the global characteristics, such as character size and stroke space. However, it lacks the representation of diverse local details, such as the shape and length of local strokes and serif size. On the contrary, the componentwise style representation category [11, 6, 20] generally decomposes each reference sample sharing the same font into pre-defined components and radicals. It either conditions the style encoders jointly on the glyph image and the corresponding component labels or adopts component-label classification losses to train the style encoder. This can be infeasible because each character should be manually associated with a certain set of components, which requires more preparation when applying for new scripts. Additionally, for different content images, their local relations with reference samples can vary. That means the local style representations for different content characters are required to be recomputed when given fixed reference samples, which increases the computational cost.
+
+To tackle the above issue, we propose a hybrid global and local style transferring approach for AFFG in this paper. Since the global style representation of fonts controls more intra-style consistent properties, e.g., the locations, sizes, stroke thickness, and spaces of characters, while the lo
+
+cal style representation focuses on capturing inter-style inconsistent component details, e.g., stroke shape, serif-ness, stroke deformation. Therefore, we leverage both the global and local styles for feature complementation. In order to obtain the global style feature representation, we calculate the similarity scores of the target glyph and the referenced samples by measuring their content feature distances, and then assign them as the weights for aggregating the style features. For local style feature representation, the glyph components are first learned automatically, which are discrete latent codes decomposed from a set of glyphs by vector quantization. Then, a cross-attention transformer is employed to transfer component-wise styles, with the representation of the learned components as the queries and the style representations of the reference glyphs as the keys and values. Contrastive learning is used to learn the local styles in an unsupervised way. For each forward pass, the styles from the reference samples can be transferred onto all the components. So, this local style extraction process is independent of the content glyph, avoiding multiple component-wise representation calculations for different inputs. Finally, the global and local style representations are combined with content features, and then decoded into the target glyph. Moreover, we adopt GAN and a self-reconstruction strategy for training the model without strong supervision. Therefore, it can be easily applied for different script font generation.
+
+We demonstrate the effectiveness of the proposed method on the Chinese mainly. The experimental results reflect the necessity of combing global and local representations, and also tell that our method outperforms other state-of-the-art (SOTA) AFFG methods given very limited reference examples.
+
+In summary, the contributions of this paper are as follows:
+
+- We propose a novel AFFG method leveraging complementary global and local representations, which is able to capture intra-style consistent properties and intra-style inconsistent structures of reference glyphs.  
+- Similarity of content is used to obtain global styles. It takes a similar degree of glyph structures into consideration. This strategy can better transfer styles for glyphs owning the same components with reference.  
+- Pre-trained Vector Quantization-based Variational Autoencoder (VQ-VAE) is adopted to extract components automatically, component labels are not required. The local styles can be transferred to all the components via cross-attention in one-forward pass. It is efficient for font library creation because it is content irrelevant. A style contrastive loss is proposed to unsupervised transfer the component-level styles.
+
+- Experimental results show great generalizability of our model for unseen fonts, unseen characters, and different scripts. It achieves SOTA performance for font generation even with very limited reference samples. Additionally, it can transfer styles onto cross-linguistic in the zero-shot manner.
+
+# 2. Related Works
+
+Image-to-Image Translation. Image-to-image (I2I) translation aims to learn a mapping between source and target domains while retaining the content of the source. GAN-based methods [12, 7, 16] were widely used in this field. Pix2pix [12] first adopted conditional GAN into the I2I task with paired data. CycleGAN [39] introduced circular consistency loss for unsupervised I2I translation [5, 39]. Recently, several I2I methods [2, 4] were proposed to tackle multi-class unsupervised I2I translation problems, aiming to simultaneously generate multiple style outputs given the same input.
+
+Font generation belongs to the typical I2I translation task, so the generic I2I translation approaches could be adaptively modified for font generation [17, 9].
+
+Character Style Transfer. Character style transfer mainly focused on typography transfer. Traditional methods constructed the transformation through shape modeling [31] and statistical modeling [30]. Recent approaches applied deep learning techniques for character synthesis [3]. Some methods were able to synthesize glyphs as well as the textural effects [1, 36, 8]. However, the font generation task emphasizes more on the consistency of character shape instead of text effects.
+
+Global Style-content Disentanglement for Font Generation. Global style-content disentanglement and recombination is a popular strategy for font generation. It models each font style as a universal representation. EMD [35] proposed a network architecture with two encoders, one for content and the other for style. They generated arbitrary fonts by mixing the content and style features, followed by decoding the mixed features. MDM [37] built a framework to disentangle the text images into three factors: text content, font, and style features, and then remixed the factors of different images to transfer a new style. ELDF [15] utilized new consistency losses that forced any combination of encoded features of the stacked inputs to own the consistent features of text contents and font styles.
+
+However, the local details for the font are more diverse and are hard to capture only by global style representation.
+
+Component-based Font Generation. Since characters such as Chinese characters can be decomposed, some component-based font generation methods [6, 19, 20] have emerged recently. They do not encode the entire image to extract style information, but instead extract style information for each component that makes up a syllable and use it
+
+![](images/5088cd9b0657f4b9451190df2f29e2a0b448c6adae154a31d867ac8c21be1e46.jpg)  
+Figure 1. The architecture of our model. The generator consists of five parts: a pre-trained content encoder, a reference style encoder (marked in dark green), a local style aggregator via CAM (marked in yellow), a global style aggregator with content similarity guidance (marked in pink), and a decoder combining content and style features and style features for font generation (marked in gray). A discriminator (marking green) is followed to distinguish the real and fake images, and it simultaneously classifies the content and style category of the generated character.
+
+to generate fonts. For instance, CalliGAN [28] decomposed characters into components and offered low-level structure information, including the order of strokes, to guide the generation process. SA-VAE [24] disentangled the style and content as two irrelevant domains with encoding Chinese characters into high-frequency character structure configurations and radicals. Tang et al. [25] proposed FS-Font model that adopted a cross-attention mechanism to aggregate the reference styles into a fine-grained style representation. XMP-Font [18] proposed a self-supervised cross-modality pre-training cross-modality transformer network to model style representations of stroke-level, component-level, and character-level.
+
+The component-based font generation methods significantly improve the generated glyphs' quality with few-shot references. However, most of them require you to predefine the radicals or components manually.
+
+# 3. Method
+
+In this section, we introduce the overall framework, different modules and the training strategy in details.
+
+# 3.1. Overall Pipeline
+
+Given a content image  $x_{c}$  and a set of reference character images  $y = \{y_{1},y_{2},\ldots ,y_{K}\}$  sharing the same font, our model aims to generate the character  $y_{c}$  owning the same content with  $x_{c}$  and the font style of the reference images.
+
+The overall framework is displayed in Fig. 1. It consists of a generator  $G$  and a multi-task discriminator  $D$ .
+
+The generator  $G$  contains five parts as illustrated in Fig. 1. The content-encoder  $E_{c}$  takes the content image as input to extract its structural representation  $f_{c}$ . It is pretrained via VQ-VAE to obtain the component-wise latent codes  $e_{c}$ . The style encoder is designed to learn the style representations from reference images  $y$ . Specifically, it inputs each reference image independently to map them to the style latent vector  $f_{s} = \{f_{1}, f_{2}, \ldots, f_{K}\}$ . A Local Style Aggregator (LSA) is followed afterward to transfer the styles onto the learned components. It works through a cross-attention module (CAM) with all the component-wise latent codes  $e_{c}$  as queries and the representations of the reference characters  $f_{s}$  as the keys and values. After the stylization of components, the content-related local styles  $f_{sr-L}$  can be obtained by searching the most similar codes in  $e_{c} = \{e_{c}^{1}, e_{c}^{2}, \ldots, e_{c}^{N}\}$  with its representation  $f_{c}$  spatially. The Global Style Aggregator (GSA) re-weights the style representations  $f_{s}$  and sums up all of them channel-wisely to get the global representation  $f_{sr-G}$ . The weight is the normalized distance of the content representations between each reference character and the input character, as shown  $f_{r}^{c} = \{f_{1}^{c}, f_{2}^{c}, \ldots, f_{K}^{c}\}$  and  $f_{c}$  in Fig. 1, respectively. Afterwards, a decoder is employed to generate target image  $y_{c}$  with the concatenation features of the content features  $f_{c}$ , local style representation  $f_{sr-L}$  and global style representation
+
+![](images/9bc3111b4bb251e156c6db09a23a02bc9fc1981952ff206f513b75ec0bacf6f6.jpg)  
+Figure 2. The glyph feature decomposing network for pre-training the content encoder and obtaining component representation.
+
+tation  $f_{sr - G}$  as input.
+
+During training, a multi-task discriminator is adapted to play the min-max game with the generator for distinguishing the real  $\hat{y}_c$  from a fake  $y_c$ . To make sure the generated glyph has the correct style with reference samples and still retains the structure of the input content character, the discriminator outputs a binary classification of each character's style and content category.
+
+# 3.2. Glyph Encoders and Component Decomposition
+
+The content encoder is pre-trained on the feature decomposing network and kept frozen for the font generation task. In the pre-training step, it is used to decompose the glyph images into component-wise latent codes, and trained on a certain set of character templates for reconstruction. The overview of the feature decomposing network is shown in Fig. 2. It contains a content encoder and a reconstruction decoder, connected by a discrete latent space using a latent codebook  $e_c \in R^{N \times d}$ .
+
+The encoder is built on CNNs and maps an input glyph image into latent representations,  $z_{e} \in R^{w \times h \times d}$ , where  $d$  is the number of channels, and  $h$  and  $w$  represent the height and width of the feature maps, respectively. Subsequently, vector quantization [26] is used to discrete  $z_{e}$  as follows:
+
+$$
+z _ {e} ^ {i} = e _ {c} ^ {n}, \quad \text {s . t .} \quad n = \underset {n \in \{1, 2, \dots , N \}} {\arg \min } \| z _ {e} ^ {i} - e _ {c} ^ {n} \| _ {2} ^ {2}, \tag {1}
+$$
+
+where each spatial-wise elemental vector  $z_{e}^{i} \in R^{d}$  in  $z_{e}$  is replaced with the closest code vector by executing a nearest-neighbor lookup on codebook  $e_{c}$ , comprised of  $d$ -dimensional  $n$  code vectors. Finally, the reconstruction decoder uses the matched codes  $z_{q} \in R^{w \times h \times d}$  as an input and outputs a reconstructed glyph.
+
+To optimize this process, the encoder and codebooks are updated to minimize an objective  $L_{pre}$  in Eq. (2), which refers to  $L_{1}$ -based reconstruction loss and latent loss  $L_{lat}$
+
+as follows:
+
+$$
+\begin{array}{l} L _ {p r e} = L _ {1} + L _ {l a t} \\ = \| x _ {c} - \hat {x} _ {c} \| _ {1} + \alpha \| \operatorname {s g} [ z _ {e} ] - e _ {c} \| _ {2} ^ {2} + \beta \| z _ {e} - \operatorname {s g} [ e _ {c} ] \| _ {2} ^ {2}, \tag {2} \\ \end{array}
+$$
+
+where sg is a stop-gradient operator that is defined as an identity at forward computation time and has zero partial derivatives.  $\alpha$  and  $\beta$  are the balancing hyperparameters. Experimentally, we set them as 1 and 0.1, respectively. The first term in Eq. (2) makes sure no information gets lost in the forward pass. The second term updates the codebook variables by moving the embedding vectors  $e_c$  towards the encoder outputs  $z_e$ . Meanwhile, the third term encourages the encoder output to match the targeted code vectors. There are no bypass connections between the encoder and decoder, so all the component-wise information of the glyph set processed by the encoder can be compressed in the latent space [21].
+
+After this pre-training task, we fix the content encoder  $E_{c}$  as well as the component codebook  $e_{c}$  to build the font generation model. The style encoder  $E_{s}$  has the same architecture as  $E_{c}$ , but it is trained from scratch.
+
+# 3.3. Local Style Aggregator
+
+Most recently proposed methods [18, 19] extract local style representation of characters by gaining attention from input content and reference styles. It is inefficient, especially for creating a new font library that contains a large number of glyphs. Since each of the glyphs must go through the attention model for feature aggregation once. However, most of them actually share some local representation if they have the same strokes or radicals. Starting from this point, we design an LSA module, the core is a CAM block to transfer the styles onto all the component-wise codes  $e_{c}$  instead of the input glyph.
+
+The CAM block is built upon stacked multi-head transformers with component codes  $e_{c}$  as queries and reference style vectors  $f_{r}$  as keys and values. Formally, the feature maps  $f_{k} \in R^{w \times h \times d}$  of  $k$ -th reference samples are reshaped along the channel axis, respectively, forming the sequential reference tokens  $\tilde{f}_{r} \in R^{k \cdot w \cdot h \times d}$ . For  $i^{th}$  head, two linear projections  $W_{k}^{i} \in R^{c \times d}$  and  $W_{v}^{i} \in R^{c \times d}$  are applied on it to get the keys  $K_{i} = \tilde{f}_{r}W_{k}^{iT}$  and values  $V_{i} = \tilde{f}_{r}W_{v}^{iT}$ , respectively. Meanwhile, we acquire the query matrix  $Q_{i}$  by linear projecting  $e_{c}$  with a learning weight  $W_{e}^{i} \in R^{c \times d}$ .
+
+The attention module operates on the queries  $Q_{i}$ , keys  $K_{i}$ , and values  $V_{i}$  and generates weighted average vectors  $\hat{V}_{i}$ , which can be formulated as:
+
+$$
+\hat {V} = \operatorname {A t t e n t i o n} \left(Q _ {i}, K _ {i}, V _ {i}\right) = \operatorname {s o f t m a x} \left(\frac {Q _ {i} K _ {i} ^ {T}}{\sqrt {c}}\right) V _ {i}. \tag {3}
+$$
+
+After obtaining the representations in each head, we concatenate all  $\hat{V}_i$  along the channel dimension, and employ a
+
+linear projection to get the multi-head attention result  $e_{s}$ , as follows:
+
+$$
+e _ {s} = \text {M u l t i - h e a d} (Q, K, V) = \operatorname {c o n c a t} \left(\hat {V} _ {1}, \hat {V} _ {2},; \hat {V} _ {m}\right) W _ {o}, \tag {4}
+$$
+
+where  $m$  is the number of total attention head, and  $W_{o}$  is the learning weight.
+
+After we get the stylized component-wise codes  $e_s = \{e_s^1, e_s^2, \ldots, e_s^N\}$ . For each input glyph, its local representation  $f_{sr-L}$  can be aggregated from  $e_s$  by searching for the closest label  $n$  in  $e_c$  for each spatial element in  $f_c$  as expressed in Eq. (1), and then selecting the corresponding style representation  $e_s^n$  for replacement.
+
+# 3.4. Global Style Aggregator
+
+The original style representation  $f_{k}$  for each reference sample is able to provide more global information for the font generation, which can control the size, the stroke space, etc. So, we aggregate their features directly as the global representation.
+
+As illustrated in [36], the style features and content features of references are not entirely independent. From a human's perceptual observation, there are some correlations that exist between different characters. If the input glyph has exactly the same radical or structure with some references, their style representations should be highly referred to during the transfer process. Therefore, we re-weight the individual style features  $f_{k}$  of each reference glyph based on the content feature similarity. We extract the content features  $f_{r}^{c} = \{f_{1}^{c}, f_{2}^{c}, \ldots, f_{K}^{c}\} \in R^{w \times h \times d}$  of each reference and reshape them to  $\tilde{f}_{k}^{c} \in R^{w \cdot h \times d}$ , meanwhile, the content features  $f_{c} \in R^{w \times h \times d}$  of content image are reshaped into  $\tilde{f}_{c} \in R^{w \cdot h \times d}$ . The glyph similarity is determined by the normalized cross-correlation measurement as:
+
+$$
+W _ {k j} = \frac {\tilde {f} _ {k} ^ {c} \cdot \tilde {f} _ {c}}{\left\| \tilde {f} _ {k} ^ {c} \right\| * \left\| \tilde {f} _ {c} \right\|}, j \in \{1, 2, \dots , d \}. \tag {5}
+$$
+
+$W_{kj}$  is a scalar that represents the similarity between  $k_{th}$  reference and the input glyph on  $j_{th}$  channel. Then, we normalize it by considering  $k$  samples on each channel as:
+
+$$
+\overline {{W}} _ {k j} = \operatorname {s o f t m a x} \left(\frac {\exp (a W _ {k j})}{\sum_ {k = 1} ^ {K} \exp (W _ {k j})}\right). \tag {6}
+$$
+
+This weight is then applied to the reference style representations  $f_{r}$ , where  $j_{t}h$  channel feature  $f_{k}^{j}$  is weighted by  $\overline{W}_{kj}$ , to aggregate the global representation  $f_{sr - G}$  as expressed in:
+
+$$
+f _ {s r - G} = \operatorname {c o n c a t} _ {j} \left(\sum_ {k = 1} ^ {K} \bar {W} _ {k j} f _ {k} ^ {j}\right). \tag {7}
+$$
+
+This global style representation  $f_{sr - G}$  is concatenated with the content features  $f_{c}$  and local style representation  $f_{sr - L}$ , and then input to the decoder to generate the target font.
+
+# 3.5. Training
+
+We train our model to generate the image  $y_{c}$  from an input content image  $x_{c}$  and a set of reference glyph images  $y = \{y_{1},y_{2},\ldots ,y_{K}\}$ . The content encoder is pretrained and kept fixed during this period. The losses consist of three parts, an adversarial loss, a matching loss, and a style contrast loss. The adversarial loss and matching loss are used between the generated results  $y_{c}$  and the ground truth  $\hat{y}_c$ . While the style contrast loss is designed to learn distinguished styles for components.
+
+Adversarial loss. To make the model generate plausible images, we employ a multi-head projection discriminator  $D_{s,c}$  for style label  $s$  and character label  $c$  in our framework. The loss function is implemented as the hinge GAN loss [33]:
+
+$$
+\begin{array}{l} \mathcal {L} _ {a d v} ^ {D} = - \mathbb {E} _ {\hat {y} _ {c} \sim p _ {d a t a}} \min  (0, - 1 + D _ {s, c} (\hat {y} _ {c})) \\ - \mathbb {E} _ {y _ {c} \sim p _ {G}} \min  (0, - 1 - D _ {s, c} (y _ {c})) \tag {8} \\ \end{array}
+$$
+
+$$
+\mathcal {L} _ {a d v} ^ {G} = - \mathbb {E} _ {y _ {c} \sim p _ {G}} D _ {s, c} (y _ {c}),
+$$
+
+where  $p_G$  denotes the set of generated images, and  $p_{data}$  denotes the set of real glyph images.
+
+Matching loss. To make the generated character  $y_{c}$  learn pixel-level and feature-level consistency with ground truth  $\hat{y}_{c}$ , we employ an  $L_{1}$  loss on both image and image features as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {i m g} = \mathbb {E} [ \| y _ {c} - \hat {y} _ {c} \| _ {1} ] \\ \mathcal {L} _ {\text {f e a t}} = \mathbb {E} \left[ \sum_ {l = 1} ^ {L} \left\| f ^ {(l)} \left(y _ {c}\right) - f ^ {(l)} \left(\hat {y} _ {c}\right) \right\| _ {1} \right], \tag {9} \\ \end{array}
+$$
+
+where  $f_{l}(y_{c})$  and  $f_{l}(\hat{y}_{c})$  represent the intermediate features in the  $l_{t}h$  layer of  $D$ .
+
+Style contrast loss. Given two different reference sets but sharing the same font style, the associated stylized components for these sets should be the same. However, if the reference character sets have different font styles, the component styles should be distinguished. So, we formulate our style contrastive loss as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {c s t} = \\ - \log \left(\frac {\exp \left(\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\right)}{\exp \left(\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\right) + \sum_ {N _ {s} ^ {-}} \exp \left(\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s -} ^ {n}\right)}\right). \tag {10} \\ \end{array}
+$$
+
+In detail, for each certain font style  $s$  and is corresponding codebook  $e_s$ , where  $e_{s+}$  is the positive codebook pair of
+
+$e_s$  whose references have the same font style but different content, and  $e_{s-}$  is the negative codebook pair share different font style.  $N_s^-$  is the number of negative style samples, for  $n$ -th codebook entries  $e_s^n$  in codebook  $e_s \in R^{N \times d}$ . We can always find the positive pair  $e_{s+}^n$  and negative pair set  $\{e_{s_1-}^n, e_{s_2-}^n, \ldots, e_{s_{neg}-}^n\}$  in the corresponding position.
+
+Overall objective loss. Finally, we optimize the whole model by the following full objective function:
+
+$$
+\min  _ {E _ {s}, G} \max  _ {D} \mathcal {L} _ {a d v} ^ {D} + \mathcal {L} _ {a d v} ^ {G} + \lambda_ {1} \mathcal {L} _ {i m g} + \lambda_ {2} \mathcal {L} _ {f e a t} + \lambda_ {3} \mathcal {L} _ {c s t}. \tag {11}
+$$
+
+The  $\lambda_{1},\lambda_{2}$  and  $\lambda_3$  is weighting hyperparameter. We set them to 1, 1, and 0.1, respectively.
+
+# 4. Experimental Results
+
+# 4.1. Experiment Setup
+
+Dataset. We collected 386 Chinese fonts and generated 3,500 Chinese characters for each font according to the first-level Chinese Character Table. All character pictures are normalized to  $128 \times 128$ . A font template is randomly selected from the 386 fonts for extracting the glyph content features and kept fixed throughout the training and test [1]. This font set is also used for pre-training the VQ-VAE to get a set of common parts codebooks.
+
+The Chinese training set contains 370 fonts and 3,000 Chinese characters, denoted as the seen font seen character (SFSC) set. To verify our method, we evaluate the font generation ability on two test sets: One is the rest of the 15 unseen fonts with 3,000 seen characters per font, denoted as the seen font unseen character (UFSC) set; the other is the remaining 15 unseen fonts with 500 unseen characters per font, denoted as the unseen font unseen character (UFUC) set.
+
+Implementation details. The main training process of our method is divided into two parts. First, a component-wise codebook is trained with 3,000 Chinese characters sharing the same font. We set the embedding dimension  $d$  to 256, the batch size to 256, and the iteration steps to 50,000. Then, for training the whole font generation model, we set the batch size to 48, the number of attention heads to 8 in three stacked transformer layers, and iteration steps to 500,000.
+
+Evaluation metrics. To evaluate the font generation quality, we use the following five metrics [14], root-meansquare deviation (RMSE), structural similarity (SSIM), learned perceptual image patch similarity (LPIPS) [34], Fréchet inception distance (FID) [10], and User Study. The User Study is conducted by 10 volunteers, who observe the reference samples and vote for the best generation result from all the comparison methods.
+
+Table 1. Ablation study of component codebooks.  
+
+<table><tr><td>Codebook size</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td></tr><tr><td>50</td><td>0.512</td><td>0.422</td><td>0.343</td><td>144.2</td></tr><tr><td>80</td><td>0.546</td><td>0.407</td><td>0.296</td><td>120.7</td></tr><tr><td>100</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td></tr><tr><td>120</td><td>0.568</td><td>0.392</td><td>0.278</td><td>109.5</td></tr><tr><td>150</td><td>0.567</td><td>0.388</td><td>0.282</td><td>112.4</td></tr></table>
+
+![](images/52325c1b46668a23552b9777d8318525192360c3683c9cc360ca7a292eee2a6f.jpg)  
+Figure 3. The visualization of latent codes.
+
+# 4.2. Ablation Studies
+
+We perform three ablation studies to evaluate the effectiveness of our proposed models on the few-shot Chinese font generation task. These experiments are conducted on the UFUC dataset.
+
+# 4.2.1 The effect of component codebook size
+
+The component codebook size reflects the complexity of the script. We set it as different values for training the content encoder and acquiring component-wise representation in VQ-VAE. Then, they are fixed for font generation. The results are displayed in Tab. 1. We can see that when the codebook size exceeds 100, the performance on each metric has limited improvement. That illustrates using 100 components is sufficient to depict the Chinese characters. When we train the model on English script, we find that by only using 15 codes, the model can generate very good results. Therefore, the size of the component codebook has a relationship with the scripts. More complex scripts require larger codebook sizes. In the following experiments, We set the Chinese component codebook size to 100.
+
+We select a certain code from the codebook to compute its similarity with features of different glyphs spatially. The visualization results of the  $32_{th}$  code and  $44_{th}$  code are present in Fig. 3. We can see the  $32_{th}$  code mainly extracts vertical components and  $44_{th}$  extracts horizontal components. It demonstrates the VQ-VAE strategy can generate "components" automatically.
+
+# 4.2.2 The effect of each module
+
+To illustrate the influence of the GSA and LSA modules of our method, we conduct the ablation study with and without it in the model. By removing the LSA, the component-wise representation is not required. The model degrades to a global content-style disentanglement architecture, with the aggregated style representation only conditioned on content similarity. When removing the GSA part, the model focuses
+
+<table><tr><td>Reference</td><td>雳枪嫌</td><td>惧聂蔬</td><td>鼠韧贻</td></tr><tr><td>w/o GSA</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>w/o LSA</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>Full model</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr><tr><td>GT</td><td>盈内弗</td><td>情息锐</td><td>厕奸纠</td></tr></table>
+
+more on the details of the stroke but loses the global style control.
+
+We evaluate the two models and the proposed full model on our collected UFUC dataset. Fig. 4 displays some comparison results. The results with and without these modules have obvious differences. The model with LSA could better capture the details of reference strokes, while the sizes of generated characters and the inner spaces are not always consistent with the given references. The model with only GSA has the opposite functions. Most strokes are not generated well. The full model combines LSA and GSA, which achieves better performance (see the details in red dash boxes of Fig. 4). Quantitative results in Tab. 3 further confirm the importance of the two modules. The LSA model assists more than GSA, which demonstrates that the style of glyphs mainly lies in the local details. From these results, we conclude that LSA and GSA are both essential in our model and they enable the model to capture diverse local styles and also control the global styles.
+
+# 4.2.3 The effect of reference numbers
+
+Intuitively, given more reference samples, the generated font better resembles a realistic one. Fig. 5 shows the effect of reference numbers. We can see that when the number of references increases from 1 to 8, the generated characters have an incremental performance improvement. The figure shows that it becomes stable when given more references. However, there are diminishing returns after the first few references. More details can be found in Appendix.
+
+# 4.3. Comparing with SOTA Methods
+
+We compare our method with five SOTA AFFG methods. 1) FUNIT [17] used two different encoders with the AdaIN module to generate a new image with mixed content and style. It belongs to the global style-content disentanglement FFG method. 2) MX-Font [20] extracts multiple style features not explicitly conditioned on component labels, but is automatically by designed multiple experts to
+
+![](images/835546ecbcaaef061e427238db12978e4fafbf50174376619d9a9597ad60aecd.jpg)  
+Figure 4. Qualitative font generation results with and without LSA and GSA modules. The first and last rows are the three references and the ground truth per font, respectively. The middle rows are generated results correspondingly. The red dashed boxes point out details that were better generated by our full proposed model.  
+Figure 5. Performance changes of our model by varying numbers of the reference samples.
+
+represent different local concepts, e.g., left-side sub-glyph. It shows good generalization ability to unseen languages. 3) LF-Font [19] proposed localized style representation inspired by low-rank matrix factorization, which also extracts component-wise features. 4) DG-Font [29] is an unsupervised network that used a Deformable Convolution in the Generator to deform and transform the character of one font to another. It achieved a good effect on cursive characters. 5) AGIS-net [8] used two different decoders to generate images with character shapes and then the texture information successively. It can transfer the font as well as the text effects. 6) FS-Font [25] requires fixed content-reference mapping to transfer Fine-Grained local styles. We retrain all the models by our dataset using their original training hyperparameters and strategies. The reference samples are set to 3 in the training and test phases for all the methods. The qualitative and quantitative comparison results are shown in Fig. 6 and Tab. 2, respectively.
+
+Tab. 2 shows that our method outperforms previous SOTA methods with significant gaps in all the metrics. We can observe that FUNIT fails to capture diverse styles. Only when the content and reference styles are visually close, it can generate a structured character. That illustrates the universal style representation strategy is not a good choice for AFFG. LF-Font generates fonts with worse visual quality since the reference numbers are very limited. Its performance is unstable as they are prone to loss of strokes or distortion of components for certain styles. DG-Font may fail to perform style transfer especially when the reference style significantly differs from that of the content. Additionally, it generates glyphs containing characteristic artifacts. AGIS-Net is more stable to generate the font of different styles and complement structures. It could better transfer the global features such as the size and the thickness of strokes. MX-Font generates better stylized characters than other methods, but it has a higher probability of failing to generate fine-grained style features compared with our method. The generation results of FS-Font are also unsatisfactory, especially on unseen references, due to the randomly selected
+
+Table 2. Quantitative comparison results on UFSC and UFUC datasets  
+
+<table><tr><td>Dataset</td><td>Method</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td><td>User Study↑</td></tr><tr><td rowspan="7">UFSC</td><td>FUNIT [17]</td><td>0.512</td><td>0.426</td><td>0.361</td><td>161.8</td><td>1.2%</td></tr><tr><td>LF-FONT [19]</td><td>0.548</td><td>0.406</td><td>0.334</td><td>123.9</td><td>3.9%</td></tr><tr><td>AGIS-NET [8]</td><td>0.529</td><td>0.409</td><td>0.302</td><td>145.0</td><td>10.3%</td></tr><tr><td>DG-FONT [29]</td><td>0.517</td><td>0.419</td><td>0.312</td><td>149.0</td><td>11.6%</td></tr><tr><td>MX-FONT [20]</td><td>0.523</td><td>0.407</td><td>0.297</td><td>94.5</td><td>14.4%</td></tr><tr><td>FS-FONT [25]</td><td>0.570</td><td>0.379</td><td>0.327</td><td>172.6</td><td>21.5%</td></tr><tr><td>Ours</td><td>0.636</td><td>0.341</td><td>0.225</td><td>93.7</td><td>58.6%</td></tr><tr><td rowspan="7">UFUC</td><td>FUNIT [17]</td><td>0.468</td><td>0.472</td><td>0.379</td><td>153.4</td><td>3.4%</td></tr><tr><td>LF-FONT [19]</td><td>0.481</td><td>0.462</td><td>0.377</td><td>136.7</td><td>4.8%</td></tr><tr><td>AGIS-NET [8]</td><td>0.550</td><td>0.400</td><td>0.310</td><td>137.2</td><td>11.5%</td></tr><tr><td>DG-FONT [29]</td><td>0.493</td><td>0.397</td><td>0.312</td><td>136.7</td><td>10.8%</td></tr><tr><td>MX-FONT [20]</td><td>0.478</td><td>0.447</td><td>0.333</td><td>114.8</td><td>15.2%</td></tr><tr><td>FS-FONT [25]</td><td>0.418</td><td>0.474</td><td>0.377</td><td>173.7</td><td>19.5%</td></tr><tr><td>Ours</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td><td>54.3%</td></tr></table>
+
+<table><tr><td>Dataset</td><td colspan="6">UFUC</td><td colspan="6">UFSC</td></tr><tr><td>Reference</td><td>嘉明主</td><td>泛懂隘</td><td>腰也携</td><td>铸符挂</td><td>寒晴宝</td><td>原初忍</td><td>香贬刷</td><td>矩财需</td><td>爷雏仇</td><td>猫悲捕</td><td></td><td></td></tr><tr><td>FUNIT</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>柴火</td><td>此方石</td><td>轧倍沉</td><td>生?学</td><td>灭</td><td>乳吮游</td><td></td><td></td></tr><tr><td>LF-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄搁蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>DG-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>AGIS-Net</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>MX-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>FS-Font</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>Ours</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>政姜避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr><tr><td>GT</td><td>想奠舱</td><td>御僻拌</td><td>牲蚂耿</td><td>拘舟净</td><td>凄捣蜜</td><td>改善避</td><td>轧倍沉</td><td>维洪洪</td><td>英查页</td><td>乳吮游</td><td></td><td></td></tr></table>
+
+Figure 6. FFG results of each method on UFUC and UFSC dataset. We represent the generated samples of five different kinds of fonts, given three references and three content images per font. The red boxes represent the better generation details.  
+Table 3. Ablation study of different models on UFUC dataset.  
+
+<table><tr><td>Methods</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td><td>User Study↑</td></tr><tr><td>w/o LSA</td><td>0.496</td><td>0.422</td><td>0.318</td><td>145.0</td><td>7.3%</td></tr><tr><td>w/o GSA</td><td>0.532</td><td>0.402</td><td>0.293</td><td>132.1</td><td>20.3%</td></tr><tr><td>Full model</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td><td>72.4%</td></tr></table>
+
+content-reference pairs.
+
+# 4.4. Applying to Other Languages
+
+To verify the generalization of our method for other languages, we collected 60 fonts of 125 Japanese characters. 50 fonts with 100 glyphs per font are randomly selected for training, and the rest for test. Some results are displayed in Fig. 7. Since the character structures of the Japanese are much simpler than Chinese, the generated results approach the ground truth more. Additionally, our method can transfer styles onto unseen content, including cross-linguistic glyphs as shown in Fig. 8.
+
+# 5. Conclusion
+
+We present a novel AFFG approach in this paper, which could aggregate global and local styles of limited refer
+
+![](images/f47f76b0a485d9caa19500b29369a70e7e40616aaf710ece3aae94a68dfb77f3.jpg)  
+Figure 7. FFG results of Japanese scripts. For each style, the upper and lower rows respectively represent the model generation results and GT.
+
+ences. The designed LSA and GSA modules were assigned different tasks to capture the local details and global structures of the font, respectively. The LSA adopted a cross-attention mechanism for transferring styles onto all of the self-learned components without manual definition. While the GSA utilized the similarity of different glyphs, and then used it to guide the global styles combination of all references. Experiments demonstrated the effectiveness of both modules, and also showed our proposed method significantly outperformed other methods quantitatively and qual
+
+<table><tr><td>Content
+Reference</td><td>アウマガがせん不の</td></tr><tr><td>别福混伏桔快</td><td>アウマガがせん不の</td></tr></table>
+
+(a)  
+
+<table><tr><td>Content
+Reference</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr><tr><td>痴佳体</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr><tr><td>版贾句</td><td>上</td><td>乙</td><td>乙</td><td>LΔ</td><td>乙</td><td>乙</td><td>E</td><td>山</td><td>山</td></tr></table>
+
+(b)  
+
+<table><tr><td>Reference</td><td colspan="4">Generated Chinese samples</td><td colspan="4">Generated Japanese samples</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>宣 呢 除 医 脸 另 追 播 筏 槽 预 缺 街 登 和 旁 骨 板 释 旅 课 急 放 智 蒙 弹</td><td>絹 聘 黔 黎 黎 潘 與 輛 與 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 畅 廣 桃 篡 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻 藻</td><td>絹 渠 槟 懒 懒 穰 橘 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 覆 嘴 嘴 褚 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深 深</td><td>捻陵 傍管 喷 嘴 鞍 黔 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚 褚</td><td>工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 工 巠 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 巾 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 差 巳</td><td>大 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 田 甲 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙方 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 丁 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 二 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 丙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 亿 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 乙 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 甲 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td>小</td><td>中</td><td>大</td><td></td></tr></table>
+
+Figure 8. Cross-language inference on (a) Japanese glyphs and (b) Korean glyphs. (c) Chinese results generated under few-shot and Japanese generated results under zero-shot manner.
+
+itatively. However, our method is limited to two aspects. If given only one reference or very fancy font, e.g., decoration, or shadow, the generated results are unsatisfactory.
+
+# Acknowledgments
+
+This work is supported by the Open Project Program of the National Laboratory of Pattern Recognition(NLPR) (No.20220004). We thank all anonymous reviewers for their constructive comments on this paper.
+
+# Appendix
+
+Besides the results and discussions presented in the original paper, we provide more experiments and results in this appendix, which further explain the effectiveness and generality of our method.
+
+# The effect of different reference characters on the generated results
+
+The font style is an aesthetic concept and has nothing to do with specific characters. In the process of few shot font generation, given reference characters with different content, the provided style representation should be the same.
+
+(c)  
+
+<table><tr><td>Reference\GT</td><td>鞠肖剥频裙翔祥凝挨</td></tr><tr><td>搗冊被海梗畅\GT</td><td>鞠肖剥频裙翔祥凝挨</td></tr><tr><td>Reference\GT</td><td>揍煽寝漂菊镜筏壁德</td></tr><tr><td>榆膛蔡燥稀魁</td><td>揍煽寝漂菊镜筏壁德</td></tr></table>
+
+Figure 9. Generating the same target character, referring to characters with different contents from the same style font.
+
+<table><tr><td>Ref sets</td><td>苏1</td><td>横2</td><td>笑3</td><td>陈4</td><td>洁5</td><td>伟6</td><td>豪7</td><td>科8</td><td>腺9</td></tr><tr><td>Ref1</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-3</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-5</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>责</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-7</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>度</td><td>昔</td><td>层</td><td>宇</td></tr><tr><td>Ref1-9</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>责</td><td>度</td><td>层</td><td>宇</td></tr><tr><td>GT</td><td>床</td><td>亚</td><td>哇</td><td>泵</td><td>泵</td><td>责</td><td>度</td><td>层</td><td>宇</td></tr></table>
+
+Figure 10. Generated samples by varying reference set size. Each middle row shows the samples generated by given different number (1, 3, 5, 7, 9) of references. The number (1 to 9) represents the order of each character to be used. The target glyphs are displayed in the bottom row.
+
+In our training process, we randomly select  $k$  style reference characters for generating characters each time. During the inference phase, we select characters with different content in the same style as the reference set. The generated results are shown in Fig. 9. There is a subtle difference between the overall style and the local style of the generated results.
+
+# The qualitative results using different numbers of references
+
+Intuitively, the larger the number of given reference characters, the richer and more accurate the extracted style features should be. In the inference stage, we change the number of reference characters and observe the impact on the generated results. It can be observed from Fig. 10 that the overall and local quality of generated characters is roughly positively correlated with the number of reference characters. The quality improvement is more obvious when the number increases from 1 to 5, and the improvement beyond this number is limited. In our paper, the number of reference images is set to 3, and the model training and qualitative and quantitative comparisons with other methods are completed with this setting.
+
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\ No newline at end of file
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+                                    "content": "Wei Pan<sup>1</sup> Anna Zhu<sup>1*</sup> Xinyu Zhou<sup>1</sup> Brian Kenji Iwana<sup>2</sup> Shilin Li<sup>1</sup>  \n<sup>1</sup> School of Computer Science and Artificial Intelligence, Wuhan University of Technology  \n<sup>2</sup> Human Interface Laboratory, Kyushu University"
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+                                    "content": "{aaawei, annazhu, 297932, shilinli}@whut.edu.cn iwana@ait.kyushu-u.ac.jp"
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+                                    "content": "Automatic few-shot font generation (AFFFG), aiming at generating new fonts with only a few glyph references, reduces the labor cost of manually designing fonts. However, the traditional AFFFG paradigm of style-content disentanglement cannot capture the diverse local details of different fonts. So, many component-based approaches are proposed to tackle this problem. The issue with component-based approaches is that they usually require special pre-defined glyph components, e.g., strokes and radicals, which is infeasible for AFFFG of different languages. In this paper, we present a novel font generation approach by aggregating styles from character similarity-guided global features and stylized component-level representations. We calculate the similarity scores of the target character and the referenced samples by measuring the distance along the corresponding channels from the content features, and assigning them as the weights for aggregating the global style features. To better capture the local styles, a cross-attention-based style transfer module is adopted to transfer the styles of reference glyphs to the components, where the components are self-learned discrete latent codes through vector quantization without manual definition. With these designs, our AFFFG method could obtain a complete set of component-level style representations, and also control the global glyph characteristics. The experimental results reflect the effectiveness and generalization of the proposed method on different linguistic scripts, and also show its superiority when compared with other state-of-the-art methods. The source code can be found at https://github.com/awei669/VQ-Font."
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+                                    "content": "Font design techniques can benefit many critical applications, such as logo designs, data augmentation for text-related tasks, handwriting imitation and identification, etc."
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+                                }
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+                                    "content": "Recently, with the development of deep learning techniques, many automatic few-shot font generation (AFFFG) methods have been proposed. They have been created using Convolution Neural Networks (CNNs) [22], Generative Adversarial Networks (GANs) [27], Transformers [32], etc. The AFFFG methods use only a few reference font images for generating different glyphs automatically. The typical strategy follows the style and content disentangle-ment and combination paradigm [38, 23], and either adopts global style representation or component-wise style representation. The global style representation [13, 38] is learned and extracted from all the references of each style, which could capture the global characteristics, such as character size and stroke space. However, it lacks the representation of diverse local details, such as the shape and length of local strokes and serif size. On the contrary, the componentwise style representation category [11, 6, 20] generally decomposes each reference sample sharing the same font into pre-defined components and radicals. It either conditions the style encoders jointly on the glyph image and the corresponding component labels or adopts component-label classification losses to train the style encoder. This can be infeasible because each character should be manually associated with a certain set of components, which requires more preparation when applying for new scripts. Additionally, for different content images, their local relations with reference samples can vary. That means the local style representations for different content characters are required to be recomputed when given fixed reference samples, which increases the computational cost."
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+                                    "content": "To tackle the above issue, we propose a hybrid global and local style transferring approach for AFFG in this paper. Since the global style representation of fonts controls more intra-style consistent properties, e.g., the locations, sizes, stroke thickness, and spaces of characters, while the lo"
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+                                    "content": "cal style representation focuses on capturing inter-style inconsistent component details, e.g., stroke shape, serif-ness, stroke deformation. Therefore, we leverage both the global and local styles for feature complementation. In order to obtain the global style feature representation, we calculate the similarity scores of the target glyph and the referenced samples by measuring their content feature distances, and then assign them as the weights for aggregating the style features. For local style feature representation, the glyph components are first learned automatically, which are discrete latent codes decomposed from a set of glyphs by vector quantization. Then, a cross-attention transformer is employed to transfer component-wise styles, with the representation of the learned components as the queries and the style representations of the reference glyphs as the keys and values. Contrastive learning is used to learn the local styles in an unsupervised way. For each forward pass, the styles from the reference samples can be transferred onto all the components. So, this local style extraction process is independent of the content glyph, avoiding multiple component-wise representation calculations for different inputs. Finally, the global and local style representations are combined with content features, and then decoded into the target glyph. Moreover, we adopt GAN and a self-reconstruction strategy for training the model without strong supervision. Therefore, it can be easily applied for different script font generation."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "We demonstrate the effectiveness of the proposed method on the Chinese mainly. The experimental results reflect the necessity of combing global and local representations, and also tell that our method outperforms other state-of-the-art (SOTA) AFFG methods given very limited reference examples."
+                                }
+                            ]
+                        }
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+                                    "content": "In summary, the contributions of this paper are as follows:"
+                                }
+                            ]
+                        }
+                    ],
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+                                            "type": "text",
+                                            "content": "- We propose a novel AFFG method leveraging complementary global and local representations, which is able to capture intra-style consistent properties and intra-style inconsistent structures of reference glyphs."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Similarity of content is used to obtain global styles. It takes a similar degree of glyph structures into consideration. This strategy can better transfer styles for glyphs owning the same components with reference."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Pre-trained Vector Quantization-based Variational Autoencoder (VQ-VAE) is adopted to extract components automatically, component labels are not required. The local styles can be transferred to all the components via cross-attention in one-forward pass. It is efficient for font library creation because it is content irrelevant. A style contrastive loss is proposed to unsupervised transfer the component-level styles."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        }
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+                                    "content": "- Experimental results show great generalizability of our model for unseen fonts, unseen characters, and different scripts. It achieves SOTA performance for font generation even with very limited reference samples. Additionally, it can transfer styles onto cross-linguistic in the zero-shot manner."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "2. Related Works"
+                                }
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+                                    "type": "text",
+                                    "content": "Image-to-Image Translation. Image-to-image (I2I) translation aims to learn a mapping between source and target domains while retaining the content of the source. GAN-based methods [12, 7, 16] were widely used in this field. Pix2pix [12] first adopted conditional GAN into the I2I task with paired data. CycleGAN [39] introduced circular consistency loss for unsupervised I2I translation [5, 39]. Recently, several I2I methods [2, 4] were proposed to tackle multi-class unsupervised I2I translation problems, aiming to simultaneously generate multiple style outputs given the same input."
+                                }
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+                                    "type": "text",
+                                    "content": "Font generation belongs to the typical I2I translation task, so the generic I2I translation approaches could be adaptively modified for font generation [17, 9]."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Character Style Transfer. Character style transfer mainly focused on typography transfer. Traditional methods constructed the transformation through shape modeling [31] and statistical modeling [30]. Recent approaches applied deep learning techniques for character synthesis [3]. Some methods were able to synthesize glyphs as well as the textural effects [1, 36, 8]. However, the font generation task emphasizes more on the consistency of character shape instead of text effects."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Global Style-content Disentanglement for Font Generation. Global style-content disentanglement and recombination is a popular strategy for font generation. It models each font style as a universal representation. EMD [35] proposed a network architecture with two encoders, one for content and the other for style. They generated arbitrary fonts by mixing the content and style features, followed by decoding the mixed features. MDM [37] built a framework to disentangle the text images into three factors: text content, font, and style features, and then remixed the factors of different images to transfer a new style. ELDF [15] utilized new consistency losses that forced any combination of encoded features of the stacked inputs to own the consistent features of text contents and font styles."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "However, the local details for the font are more diverse and are hard to capture only by global style representation."
+                                }
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+                        }
+                    ],
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+                                    "content": "Component-based Font Generation. Since characters such as Chinese characters can be decomposed, some component-based font generation methods [6, 19, 20] have emerged recently. They do not encode the entire image to extract style information, but instead extract style information for each component that makes up a syllable and use it"
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 1. The architecture of our model. The generator consists of five parts: a pre-trained content encoder, a reference style encoder (marked in dark green), a local style aggregator via CAM (marked in yellow), a global style aggregator with content similarity guidance (marked in pink), and a decoder combining content and style features and style features for font generation (marked in gray). A discriminator (marking green) is followed to distinguish the real and fake images, and it simultaneously classifies the content and style category of the generated character."
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+                                    "type": "text",
+                                    "content": "to generate fonts. For instance, CalliGAN [28] decomposed characters into components and offered low-level structure information, including the order of strokes, to guide the generation process. SA-VAE [24] disentangled the style and content as two irrelevant domains with encoding Chinese characters into high-frequency character structure configurations and radicals. Tang et al. [25] proposed FS-Font model that adopted a cross-attention mechanism to aggregate the reference styles into a fine-grained style representation. XMP-Font [18] proposed a self-supervised cross-modality pre-training cross-modality transformer network to model style representations of stroke-level, component-level, and character-level."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "The component-based font generation methods significantly improve the generated glyphs' quality with few-shot references. However, most of them require you to predefine the radicals or components manually."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
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+                                    "content": "In this section, we introduce the overall framework, different modules and the training strategy in details."
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+                                    "content": "3.1. Overall Pipeline"
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+                                    "type": "text",
+                                    "content": "Given a content image "
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+                                    "type": "inline_equation",
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+                                    "content": " and a set of reference character images "
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+                                    "content": "y = \\{y_{1},y_{2},\\ldots ,y_{K}\\}"
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+                                    "content": " sharing the same font, our model aims to generate the character "
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+                                    "content": " owning the same content with "
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+                                    "content": " and the font style of the reference images."
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+                                    "content": "The overall framework is displayed in Fig. 1. It consists of a generator "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " contains five parts as illustrated in Fig. 1. The content-encoder "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " takes the content image as input to extract its structural representation "
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". It is pretrained via VQ-VAE to obtain the component-wise latent codes "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". The style encoder is designed to learn the style representations from reference images "
+                                },
+                                {
+                                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Specifically, it inputs each reference image independently to map them to the style latent vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{s} = \\{f_{1}, f_{2}, \\ldots, f_{K}\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". A Local Style Aggregator (LSA) is followed afterward to transfer the styles onto the learned components. It works through a cross-attention module (CAM) with all the component-wise latent codes "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": " as queries and the representations of the reference characters "
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+                                    "type": "text",
+                                    "content": " as the keys and values. After the stylization of components, the content-related local styles "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " can be obtained by searching the most similar codes in "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "e_{c} = \\{e_{c}^{1}, e_{c}^{2}, \\ldots, e_{c}^{N}\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with its representation "
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+                                    "content": " spatially. The Global Style Aggregator (GSA) re-weights the style representations "
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+                                    "content": ". To make sure the generated glyph has the correct style with reference samples and still retains the structure of the input content character, the discriminator outputs a binary classification of each character's style and content category."
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+                                    "type": "text",
+                                    "content": "where sg is a stop-gradient operator that is defined as an identity at forward computation time and has zero partial derivatives. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\beta"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        130,
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+                                        284
+                                    ],
+                                    "type": "text",
+                                    "content": " are the balancing hyperparameters. Experimentally, we set them as 1 and 0.1, respectively. The first term in Eq. (2) makes sure no information gets lost in the forward pass. The second term updates the codebook variables by moving the embedding vectors "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        130,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        130,
+                                        545,
+                                        284
+                                    ],
+                                    "type": "text",
+                                    "content": " towards the encoder outputs "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        130,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "z_e"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        130,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Meanwhile, the third term encourages the encoder output to match the targeted code vectors. There are no bypass connections between the encoder and decoder, so all the component-wise information of the glyph set processed by the encoder can be compressed in the latent space [21]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "After this pre-training task, we fix the content encoder "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as well as the component codebook "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        285,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": " to build the font generation model. The style encoder "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        285,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E_{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        285,
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+                                    ],
+                                    "type": "text",
+                                    "content": " has the same architecture as "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        285,
+                                        545,
+                                        332
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        285,
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+                                        332
+                                    ],
+                                    "type": "text",
+                                    "content": ", but it is trained from scratch."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Local Style Aggregator"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Most recently proposed methods [18, 19] extract local style representation of characters by gaining attention from input content and reference styles. It is inefficient, especially for creating a new font library that contains a large number of glyphs. Since each of the glyphs must go through the attention model for feature aggregation once. However, most of them actually share some local representation if they have the same strokes or radicals. Starting from this point, we design an LSA module, the core is a CAM block to transfer the styles onto all the component-wise codes "
+                                },
+                                {
+                                    "bbox": [
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " instead of the input glyph."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The CAM block is built upon stacked multi-head transformers with component codes "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as queries and reference style vectors "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{r}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as keys and values. Formally, the feature maps "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k} \\in R^{w \\times h \\times d}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of "
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th reference samples are reshaped along the channel axis, respectively, forming the sequential reference tokens "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{f}_{r} \\in R^{k \\cdot w \\cdot h \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". For "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i^{th}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " head, two linear projections "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{k}^{i} \\in R^{c \\times d}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{v}^{i} \\in R^{c \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are applied on it to get the keys "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K_{i} = \\tilde{f}_{r}W_{k}^{iT}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        490,
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+                                        610
+                                    ],
+                                    "type": "text",
+                                    "content": " and values "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        490,
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+                                        610
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_{i} = \\tilde{f}_{r}W_{v}^{iT}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        490,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. Meanwhile, we acquire the query matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " by linear projecting "
+                                },
+                                {
+                                    "bbox": [
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+                                        610
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_{c}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with a learning weight "
+                                },
+                                {
+                                    "bbox": [
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+                                        610
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{e}^{i} \\in R^{c \\times d}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The attention module operates on the queries "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", keys "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and values "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and generates weighted average vectors "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{V}_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {V} = \\operatorname {A t t e n t i o n} \\left(Q _ {i}, K _ {i}, V _ {i}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {c}}\\right) V _ {i}. \\tag {3}",
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+                                    "type": "text",
+                                    "content": "After obtaining the representations in each head, we concatenate all "
+                                },
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " along the channel dimension, and employ a"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "linear projection to get the multi-head attention result "
+                                },
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+                                    "type": "interline_equation",
+                                    "content": "e _ {s} = \\text {M u l t i - h e a d} (Q, K, V) = \\operatorname {c o n c a t} \\left(\\hat {V} _ {1}, \\hat {V} _ {2},; \\hat {V} _ {m}\\right) W _ {o}, \\tag {4}",
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+                                        157
+                                    ],
+                                    "type": "text",
+                                    "content": " is the learning weight."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        47,
+                        158,
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+                        230
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": "After we get the stylized component-wise codes "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_s = \\{e_s^1, e_s^2, \\ldots, e_s^N\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": ". For each input glyph, its local representation "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{sr-L}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
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+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": " can be aggregated from "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_s"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": " by searching for the closest label "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
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+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": " in "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_c"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": " for each spatial element in "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_c"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": " as expressed in Eq. (1), and then selecting the corresponding style representation "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_s^n"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        158,
+                                        287,
+                                        230
+                                    ],
+                                    "type": "text",
+                                    "content": " for replacement."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        47,
+                        239,
+                        183,
+                        251
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                            ],
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+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.4. Global Style Aggregator"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
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+                        316
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        257,
+                                        287,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": "The original style representation "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        257,
+                                        287,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        257,
+                                        287,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " for each reference sample is able to provide more global information for the font generation, which can control the size, the stroke space, etc. So, we aggregate their features directly as the global representation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        47,
+                        318,
+                        287,
+                        486
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                318,
+                                287,
+                                486
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "text",
+                                    "content": "As illustrated in [36], the style features and content features of references are not entirely independent. From a human's perceptual observation, there are some correlations that exist between different characters. If the input glyph has exactly the same radical or structure with some references, their style representations should be highly referred to during the transfer process. Therefore, we re-weight the individual style features "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "text",
+                                    "content": " of each reference glyph based on the content feature similarity. We extract the content features "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{r}^{c} = \\{f_{1}^{c}, f_{2}^{c}, \\ldots, f_{K}^{c}\\} \\in R^{w \\times h \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "text",
+                                    "content": " of each reference and reshape them to "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{f}_{k}^{c} \\in R^{w \\cdot h \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "text",
+                                    "content": ", meanwhile, the content features "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{c} \\in R^{w \\times h \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "text",
+                                    "content": " of content image are reshaped into "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{f}_{c} \\in R^{w \\cdot h \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        318,
+                                        287,
+                                        486
+                                    ],
+                                    "type": "text",
+                                    "content": ". The glyph similarity is determined by the normalized cross-correlation measurement as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        85,
+                        493,
+                        287,
+                        529
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                85,
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+                                529
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        85,
+                                        493,
+                                        287,
+                                        529
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "W _ {k j} = \\frac {\\tilde {f} _ {k} ^ {c} \\cdot \\tilde {f} _ {c}}{\\left\\| \\tilde {f} _ {k} ^ {c} \\right\\| * \\left\\| \\tilde {f} _ {c} \\right\\|}, j \\in \\{1, 2, \\dots , d \\}. \\tag {5}",
+                                    "image_path": "2b623a9ef031b7421cf0e1cd09d98e8e93fa134ae64bde33a766d84b588631b0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        47,
+                        537,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                537,
+                                287,
+                                574
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{kj}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " is a scalar that represents the similarity between "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{th}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " reference and the input glyph on "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j_{th}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " channel. Then, we normalize it by considering "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        537,
+                                        287,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " samples on each channel as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        85,
+                        583,
+                        287,
+                        616
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                85,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        85,
+                                        583,
+                                        287,
+                                        616
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\overline {{W}} _ {k j} = \\operatorname {s o f t m a x} \\left(\\frac {\\exp (a W _ {k j})}{\\sum_ {k = 1} ^ {K} \\exp (W _ {k j})}\\right). \\tag {6}",
+                                    "image_path": "f7eede24ff02630c0e26614bc018e563f3ec0619f483e4dc2c8e6cdacf136097.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                        673
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                                287,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "text",
+                                    "content": "This weight is then applied to the reference style representations "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{r}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j_{t}h"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "text",
+                                    "content": " channel feature "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{k}^{j}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "text",
+                                    "content": " is weighted by "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{W}_{kj}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "text",
+                                    "content": ", to aggregate the global representation "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{sr - G}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        625,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "text",
+                                    "content": " as expressed in:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        96,
+                        683,
+                        287,
+                        716
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                96,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        96,
+                                        683,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "f _ {s r - G} = \\operatorname {c o n c a t} _ {j} \\left(\\sum_ {k = 1} ^ {K} \\bar {W} _ {k j} f _ {k} ^ {j}\\right). \\tag {7}",
+                                    "image_path": "01e886c8771f362cc478517dbbb886475bd5897ee6bd13c4bf6de85c39e54d4d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "text",
+                                    "content": "This global style representation "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{sr - G}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "text",
+                                    "content": " is concatenated with the content features "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "text",
+                                    "content": " and local style representation "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{sr - L}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        108
+                                    ],
+                                    "type": "text",
+                                    "content": ", and then input to the decoder to generate the target font."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        306,
+                        114,
+                        370,
+                        127
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                114,
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+                                127
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
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+                                        127
+                                    ],
+                                    "type": "text",
+                                    "content": "3.5. Training"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        304,
+                        133,
+                        545,
+                        240
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                133,
+                                545,
+                                240
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": "We train our model to generate the image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " from an input content image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " and a set of reference glyph images "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y = \\{y_{1},y_{2},\\ldots ,y_{K}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": ". The content encoder is pretrained and kept fixed during this period. The losses consist of three parts, an adversarial loss, a matching loss, and a style contrast loss. The adversarial loss and matching loss are used between the generated results "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        133,
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+                                        240
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+                                    "type": "text",
+                                    "content": " and the ground truth "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{y}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". While the style contrast loss is designed to learn distinguished styles for components."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Adversarial loss. To make the model generate plausible images, we employ a multi-head projection discriminator "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "inline_equation",
+                                    "content": "D_{s,c}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for style label "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        241,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        241,
+                                        545,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and character label "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        241,
+                                        545,
+                                        300
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        241,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in our framework. The loss function is implemented as the hinge GAN loss [33]:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {a d v} ^ {D} = - \\mathbb {E} _ {\\hat {y} _ {c} \\sim p _ {d a t a}} \\min  (0, - 1 + D _ {s, c} (\\hat {y} _ {c})) \\\\ - \\mathbb {E} _ {y _ {c} \\sim p _ {G}} \\min  (0, - 1 - D _ {s, c} (y _ {c})) \\tag {8} \\\\ \\end{array}",
+                                    "image_path": "75b55da3b9719ad1b6afdd280f5a9b6b37742c2528a1623e12b64294683640f3.jpg"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {a d v} ^ {G} = - \\mathbb {E} _ {y _ {c} \\sim p _ {G}} D _ {s, c} (y _ {c}),",
+                                    "image_path": "a1a6fbc98aa7f0bb8786463ae6ac8b49dfe2247a1fd6c3bc415c6b67e121e5ab.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the set of generated images, and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "p_{data}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the set of real glyph images."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Matching loss. To make the generated character "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        383,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " learn pixel-level and feature-level consistency with ground truth "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        383,
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+                                        430
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{y}_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        383,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we employ an "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        383,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " loss on both image and image features as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {i m g} = \\mathbb {E} [ \\| y _ {c} - \\hat {y} _ {c} \\| _ {1} ] \\\\ \\mathcal {L} _ {\\text {f e a t}} = \\mathbb {E} \\left[ \\sum_ {l = 1} ^ {L} \\left\\| f ^ {(l)} \\left(y _ {c}\\right) - f ^ {(l)} \\left(\\hat {y} _ {c}\\right) \\right\\| _ {1} \\right], \\tag {9} \\\\ \\end{array}",
+                                    "image_path": "1ae0f1460c6d7ad8fae36cdef906f47a52924aa3dd1d12e9cfea6ac155db21e1.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{l}(y_{c})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{l}(\\hat{y}_{c})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        491,
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+                                        514
+                                    ],
+                                    "type": "text",
+                                    "content": " represent the intermediate features in the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l_{t}h"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " layer of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Style contrast loss. Given two different reference sets but sharing the same font style, the associated stylized components for these sets should be the same. However, if the reference character sets have different font styles, the component styles should be distinguished. So, we formulate our style contrastive loss as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {c s t} = \\\\ - \\log \\left(\\frac {\\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\\right)}{\\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s +} ^ {n}\\right) + \\sum_ {N _ {s} ^ {-}} \\exp \\left(\\sum_ {n = 1} ^ {N} e _ {s} ^ {n T} e _ {s -} ^ {n}\\right)}\\right). \\tag {10} \\\\ \\end{array}",
+                                    "image_path": "04baadd4a5d26ce24468bc817ba3392d2f3428712f0b3da17a6c3efeb2891470.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "In detail, for each certain font style "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and is corresponding codebook "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_{s+}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the positive codebook pair of"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                }
+            ],
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+                    "lines": [
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+                            "bbox": [
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " whose references have the same font style but different content, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "e_{s-}"
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+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the negative codebook pair share different font style. "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "N_s^-"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of negative style samples, for "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th codebook entries "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_s^n"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in codebook "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_s \\in R^{N \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ". We can always find the positive pair "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        287,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_{s+}^n"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " and negative pair set "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{e_{s_1-}^n, e_{s_2-}^n, \\ldots, e_{s_{neg}-}^n\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in the corresponding position."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Overall objective loss. Finally, we optimize the whole model by the following full objective function:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
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+                                    "content": "\\min  _ {E _ {s}, G} \\max  _ {D} \\mathcal {L} _ {a d v} ^ {D} + \\mathcal {L} _ {a d v} ^ {G} + \\lambda_ {1} \\mathcal {L} _ {i m g} + \\lambda_ {2} \\mathcal {L} _ {f e a t} + \\lambda_ {3} \\mathcal {L} _ {c s t}. \\tag {11}",
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+                                    "type": "text",
+                                    "content": "The "
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+                                    "content": "\\lambda_{1},\\lambda_{2}"
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+                                    "type": "text",
+                                    "content": " is weighting hyperparameter. We set them to 1, 1, and 0.1, respectively."
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+                                    "type": "text",
+                                    "content": "4. Experimental Results"
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+                                    "content": "4.1. Experiment Setup"
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+                                    "type": "text",
+                                    "content": "Dataset. We collected 386 Chinese fonts and generated 3,500 Chinese characters for each font according to the first-level Chinese Character Table. All character pictures are normalized to "
+                                },
+                                {
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+                                    "content": "128 \\times 128"
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+                                    "type": "text",
+                                    "content": ". A font template is randomly selected from the 386 fonts for extracting the glyph content features and kept fixed throughout the training and test [1]. This font set is also used for pre-training the VQ-VAE to get a set of common parts codebooks."
+                                }
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+                                    "content": "The Chinese training set contains 370 fonts and 3,000 Chinese characters, denoted as the seen font seen character (SFSC) set. To verify our method, we evaluate the font generation ability on two test sets: One is the rest of the 15 unseen fonts with 3,000 seen characters per font, denoted as the seen font unseen character (UFSC) set; the other is the remaining 15 unseen fonts with 500 unseen characters per font, denoted as the unseen font unseen character (UFUC) set."
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+                                    "content": "Implementation details. The main training process of our method is divided into two parts. First, a component-wise codebook is trained with 3,000 Chinese characters sharing the same font. We set the embedding dimension "
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+                                    "type": "text",
+                                    "content": " to 256, the batch size to 256, and the iteration steps to 50,000. Then, for training the whole font generation model, we set the batch size to 48, the number of attention heads to 8 in three stacked transformer layers, and iteration steps to 500,000."
+                                }
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+                                    "type": "text",
+                                    "content": "Evaluation metrics. To evaluate the font generation quality, we use the following five metrics [14], root-meansquare deviation (RMSE), structural similarity (SSIM), learned perceptual image patch similarity (LPIPS) [34], Fréchet inception distance (FID) [10], and User Study. The User Study is conducted by 10 volunteers, who observe the reference samples and vote for the best generation result from all the comparison methods."
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+                                            "content": "Table 1. Ablation study of component codebooks."
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+                                            "html": "<table><tr><td>Codebook size</td><td>SSIM↑</td><td>RMSE↓</td><td>LPIPS↓</td><td>FID↓</td></tr><tr><td>50</td><td>0.512</td><td>0.422</td><td>0.343</td><td>144.2</td></tr><tr><td>80</td><td>0.546</td><td>0.407</td><td>0.296</td><td>120.7</td></tr><tr><td>100</td><td>0.566</td><td>0.390</td><td>0.282</td><td>110.1</td></tr><tr><td>120</td><td>0.568</td><td>0.392</td><td>0.278</td><td>109.5</td></tr><tr><td>150</td><td>0.567</td><td>0.388</td><td>0.282</td><td>112.4</td></tr></table>",
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+                                            "content": "Figure 3. The visualization of latent codes."
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+                                    "content": "4.2. Ablation Studies"
+                                }
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+                                    "type": "text",
+                                    "content": "We perform three ablation studies to evaluate the effectiveness of our proposed models on the few-shot Chinese font generation task. These experiments are conducted on the UFUC dataset."
+                                }
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+                                    "content": "4.2.1 The effect of component codebook size"
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+                                    "type": "text",
+                                    "content": "The component codebook size reflects the complexity of the script. We set it as different values for training the content encoder and acquiring component-wise representation in VQ-VAE. Then, they are fixed for font generation. The results are displayed in Tab. 1. We can see that when the codebook size exceeds 100, the performance on each metric has limited improvement. That illustrates using 100 components is sufficient to depict the Chinese characters. When we train the model on English script, we find that by only using 15 codes, the model can generate very good results. Therefore, the size of the component codebook has a relationship with the scripts. More complex scripts require larger codebook sizes. In the following experiments, We set the Chinese component codebook size to 100."
+                                }
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+                                    "type": "text",
+                                    "content": "We select a certain code from the codebook to compute its similarity with features of different glyphs spatially. The visualization results of the "
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+                                    "content": "32_{th}"
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+                                    "type": "text",
+                                    "content": " code and "
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+                                    "type": "inline_equation",
+                                    "content": "44_{th}"
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+                                    "type": "text",
+                                    "content": " code are present in Fig. 3. We can see the "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "32_{th}"
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+                                    "type": "text",
+                                    "content": " code mainly extracts vertical components and "
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+                                    "type": "text",
+                                    "content": " extracts horizontal components. It demonstrates the VQ-VAE strategy can generate \"components\" automatically."
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+                                    "content": "4.2.2 The effect of each module"
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+                                    "content": "To illustrate the influence of the GSA and LSA modules of our method, we conduct the ablation study with and without it in the model. By removing the LSA, the component-wise representation is not required. The model degrades to a global content-style disentanglement architecture, with the aggregated style representation only conditioned on content similarity. When removing the GSA part, the model focuses"
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+                                    "type": "text",
+                                    "content": "We evaluate the two models and the proposed full model on our collected UFUC dataset. Fig. 4 displays some comparison results. The results with and without these modules have obvious differences. The model with LSA could better capture the details of reference strokes, while the sizes of generated characters and the inner spaces are not always consistent with the given references. The model with only GSA has the opposite functions. Most strokes are not generated well. The full model combines LSA and GSA, which achieves better performance (see the details in red dash boxes of Fig. 4). Quantitative results in Tab. 3 further confirm the importance of the two modules. The LSA model assists more than GSA, which demonstrates that the style of glyphs mainly lies in the local details. From these results, we conclude that LSA and GSA are both essential in our model and they enable the model to capture diverse local styles and also control the global styles."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "4.2.3 The effect of reference numbers"
+                                }
+                            ]
+                        }
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+                    "index": 4
+                },
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+                                    "type": "text",
+                                    "content": "Intuitively, given more reference samples, the generated font better resembles a realistic one. Fig. 5 shows the effect of reference numbers. We can see that when the number of references increases from 1 to 8, the generated characters have an incremental performance improvement. The figure shows that it becomes stable when given more references. However, there are diminishing returns after the first few references. More details can be found in Appendix."
+                                }
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+                                    "content": "4.3. Comparing with SOTA Methods"
+                                }
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+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "We compare our method with five SOTA AFFG methods. 1) FUNIT [17] used two different encoders with the AdaIN module to generate a new image with mixed content and style. It belongs to the global style-content disentanglement FFG method. 2) MX-Font [20] extracts multiple style features not explicitly conditioned on component labels, but is automatically by designed multiple experts to"
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+                                            "type": "text",
+                                            "content": "Figure 4. Qualitative font generation results with and without LSA and GSA modules. The first and last rows are the three references and the ground truth per font, respectively. The middle rows are generated results correspondingly. The red dashed boxes point out details that were better generated by our full proposed model."
+                                        }
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+                                            "type": "text",
+                                            "content": "Figure 5. Performance changes of our model by varying numbers of the reference samples."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9,
+                            "angle": 0,
+                            "type": "image_caption"
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+                                    "type": "text",
+                                    "content": "represent different local concepts, e.g., left-side sub-glyph. It shows good generalization ability to unseen languages. 3) LF-Font [19] proposed localized style representation inspired by low-rank matrix factorization, which also extracts component-wise features. 4) DG-Font [29] is an unsupervised network that used a Deformable Convolution in the Generator to deform and transform the character of one font to another. It achieved a good effect on cursive characters. 5) AGIS-net [8] used two different decoders to generate images with character shapes and then the texture information successively. It can transfer the font as well as the text effects. 6) FS-Font [25] requires fixed content-reference mapping to transfer Fine-Grained local styles. We retrain all the models by our dataset using their original training hyperparameters and strategies. The reference samples are set to 3 in the training and test phases for all the methods. The qualitative and quantitative comparison results are shown in Fig. 6 and Tab. 2, respectively."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Tab. 2 shows that our method outperforms previous SOTA methods with significant gaps in all the metrics. We can observe that FUNIT fails to capture diverse styles. Only when the content and reference styles are visually close, it can generate a structured character. That illustrates the universal style representation strategy is not a good choice for AFFG. LF-Font generates fonts with worse visual quality since the reference numbers are very limited. Its performance is unstable as they are prone to loss of strokes or distortion of components for certain styles. DG-Font may fail to perform style transfer especially when the reference style significantly differs from that of the content. Additionally, it generates glyphs containing characteristic artifacts. AGIS-Net is more stable to generate the font of different styles and complement structures. It could better transfer the global features such as the size and the thickness of strokes. MX-Font generates better stylized characters than other methods, but it has a higher probability of failing to generate fine-grained style features compared with our method. The generation results of FS-Font are also unsatisfactory, especially on unseen references, due to the randomly selected"
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+                                            "content": "Table 2. Quantitative comparison results on UFSC and UFUC datasets"
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+                                            "content": "Figure 6. FFG results of each method on UFUC and UFSC dataset. We represent the generated samples of five different kinds of fonts, given three references and three content images per font. The red boxes represent the better generation details."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
+                                            "content": "Table 3. Ablation study of different models on UFUC dataset."
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+                                    ]
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+                            ],
+                            "index": 4,
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+                            "type": "table_caption"
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+                                    "content": "To verify the generalization of our method for other languages, we collected 60 fonts of 125 Japanese characters. 50 fonts with 100 glyphs per font are randomly selected for training, and the rest for test. Some results are displayed in Fig. 7. Since the character structures of the Japanese are much simpler than Chinese, the generated results approach the ground truth more. Additionally, our method can transfer styles onto unseen content, including cross-linguistic glyphs as shown in Fig. 8."
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+                                    "content": "We present a novel AFFG approach in this paper, which could aggregate global and local styles of limited refer"
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+                                    "content": "Figure 8. Cross-language inference on (a) Japanese glyphs and (b) Korean glyphs. (c) Chinese results generated under few-shot and Japanese generated results under zero-shot manner."
+                                }
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+                                    "type": "text",
+                                    "content": "itatively. However, our method is limited to two aspects. If given only one reference or very fancy font, e.g., decoration, or shadow, the generated results are unsatisfactory."
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+                                    "content": "This work is supported by the Open Project Program of the National Laboratory of Pattern Recognition(NLPR) (No.20220004). We thank all anonymous reviewers for their constructive comments on this paper."
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+                                    "content": "Besides the results and discussions presented in the original paper, we provide more experiments and results in this appendix, which further explain the effectiveness and generality of our method."
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+                                    "content": "The effect of different reference characters on the generated results"
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+                                    "content": "Figure 10. Generated samples by varying reference set size. Each middle row shows the samples generated by given different number (1, 3, 5, 7, 9) of references. The number (1 to 9) represents the order of each character to be used. The target glyphs are displayed in the bottom row."
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+                                    "content": " style reference characters for generating characters each time. During the inference phase, we select characters with different content in the same style as the reference set. The generated results are shown in Fig. 9. There is a subtle difference between the overall style and the local style of the generated results."
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+                                        }
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+                                        }
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
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+                                            "content": "[35] Yexun Zhang, Ya Zhang, and Wenbin Cai. Separating style and content for generalized style transfer. In CVPR, 2018. 2"
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+                                            "content": "[37] Anna Zhu, Zhanhui Yin, Brian Kenji Iwana, Xinyu Zhou, and Shengwu Xiong. Text style transfer based on multifactor disentanglement and mixture. In ACMM, 2022. 2"
+                                        }
+                                    ]
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+                            "index": 2
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diff --git a/2023/Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics/4021ee8f-1629-4cd1-8f02-6d3ae43c664d_content_list.json b/2023/Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics/4021ee8f-1629-4cd1-8f02-6d3ae43c664d_content_list.json
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index 0000000000000000000000000000000000000000..490743092c123729cadaadfb5b305f205d8b6ebc
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+++ b/2023/Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics/4021ee8f-1629-4cd1-8f02-6d3ae43c664d_content_list.json	
@@ -0,0 +1,1483 @@
+[
+    {
+        "type": "text",
+        "text": "Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Juntae Lee<sup>1</sup>, Mihir Jain<sup>* *</sup> and Sungrack Yun<sup>1</sup>  \n<sup>1</sup>Qualcomm AI Research†",
+        "bbox": [
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+            202,
+            673,
+            238
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{juntlee, sungrack}@qti=qualcomm.com",
+        "bbox": [
+            325,
+            241,
+            643,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The goal of this paper is to localize action instances in a long untrimmed query video using just meager trimmed support videos representing a common action whose class information is not given. In this task, it is crucial to mine reliable temporal cues representing a common action from handful support videos. In our work, we develop an attention mechanism using cross-correlation. Based on this cross-attention, we first transform the support videos into query video's context to emphasize query-relevant important frames, and suppress less relevant ones. Next, we summarize sub-sequences of support video frames to represent temporal dynamics in coarse temporal granularity, which is then propagated to the fine-grained support video features through the cross-attention. In each case, the cross-attentions are applied to each support video in the individual-to-all strategy to balance heterogeneity and compatibility of the support videos. In contrast, the candidate instances in the query video are lastly attended by the resulting support video features, at once. In addition, we also develop a relational classifier head based on the query and support video representations. We show the effectiveness of our work with the state-of-the-art (SOTA) performance in benchmark datasets (ActivityNet1.3 and THUMOS14), and analyze each component extensively.",
+        "bbox": [
+            75,
+            324,
+            473,
+            686
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            718,
+            209,
+            734
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Temporal action localization [2, 4, 33, 23, 31, 18, 15, 16, 20] have been widely studied in fully or weakly-supervised manner. However, they require collecting massive videos labeled by action classes, and also only detect the action classes observed in training. Whereas, we aim to temporally localize action instances in a long untrimmed query",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/fdb41024b72ec7c3acdc74a7fb4c5f59178909a59a0305c09b8f0b8adf6b3602.jpg",
+        "image_caption": [
+            "Figure 1: Attention represents the relationship between a moment of query and support videos. (a) Vanilla: attention of a query proposal is obtained simultaneously for the frames of all the support videos. (b) Ours: the attention is computed for the frames of one support video, at a time. While important frames of support video #2 cannot be attended by the related query proposal in (a), they are appropriately transformed to the context of the query in (b)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            290,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "video based on the few trimmed support videos describing a common action class. As the testing action class is unseen in training and no ground-truth class cue is given, the only cue is the commonality of the few support videos.",
+        "bbox": [
+            496,
+            643,
+            893,
+            703
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this task, the alignment between query and support videos is important, which can be attained by representing the common action cues of interest from the support videos considering the query video's context. For better alignment, we divide this problem into two points: re-calibrating support video features under query video's context, and enhancing temporal dynamics and compatibility of the recalibrated support video features.",
+        "bbox": [
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+            704,
+            893,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing methods [39, 22, 7, 3] have mainly focused on the former point, handling the multiple support videos as a whole. However, as exemplified in Fig. 1, though the support videos represent a common action class, their context (e.g background, camera angle) can be different. Hence,",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Work completed during employment at Qualcomm Technologies, Inc.",
+        "bbox": [
+            75,
+            845,
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+            872
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{\\dagger}$ Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "10214",
+        "bbox": [
+            480,
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+            519,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/77a2d82c13d23e804783190f9f69609b95208e0678cee80b4ba27ed08efc0c94.jpg",
+        "image_caption": [
+            "Figure 2: Overall process of few-shot common action localization in our work."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            90,
+            467,
+            166
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "when all the support videos are transformed to query context simultaneously, the support videos cluttered by background are overly suppressed although they include useful information (Fig. 1(a)). Whereas, in Fig. 1(b), we can leverage the support videos by attending each individually.",
+        "bbox": [
+            75,
+            215,
+            467,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Regarding the latter point, we pay attention to that the temporal dynamics can be enriched from multiple temporal granularities. Hence, we try to collaboratively fuse the support video features in different temporal granularities, considering the compatibility of different support videos as well. Based on the insight for each point, we propose a novel few-shot common action localization method. The overall process is briefly outlined in Fig. 2. First, the long untrimmed query video is split to query proposals, and they are aligned with the support videos through our three-stage cross-attention. Then, the proposals representing the common action class are detected with temporal location refinement.",
+        "bbox": [
+            75,
+            292,
+            467,
+            487
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For the query-support alignment, we develop a three-stage cross-attention (CA) mechanism. In each stage, cross-correlation between two different features (e.g. support and query, supports in different temporal granularity) is exploited with a learnable weight matrix. The 1st stage, query-to-support Context-CA transforms the support videos into the query video's context by cross-correlating them with the query proposal features. Each support video is individually attended to emphasize its most informative features. In 2nd stage of Dynamics-CA, low-temporal granularity features summarize the tuples of snippets of each support video, and they attend the fine-grained snippet-level features. Here, each support video is attended by the entire support videos in low-temporal granularity. It helps the complementary use of all the individually attended support video features as well as enhancing temporal dynamics. Finally, in the last stage (support-to-query Context-CA), the query video features are simultaneously attended with all the resulting support video features. We call this CA process (Context, Dynamics, Context-CAs) CDC-CA.",
+        "bbox": [
+            75,
+            489,
+            467,
+            791
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Also, for the commonality prediction and refinement, we design a relational classifier with an action classifier and an auxiliary relational module. To prevent overfitting and boost performance, the latter matches the support and query video features using pseudo-label cues as we avoid the use of class labels. In testing, this module is not used.",
+        "bbox": [
+            75,
+            792,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Major contributions: (i) We suggest a three-stage CA to",
+        "bbox": [
+            96,
+            885,
+            467,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "enhance the representation of query video by support videos and vice versa. (ii) We attend each support video individually to increase its discriminative ability in the first two stages. (iii) We develop a relational classifier including an action classifier and an auxiliary relational module. The latter is only needed during training. (iv) Extensive experimental analyses are done on two benchmark datasets, where we achieve SOTA performance.",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            224,
+            635,
+            239
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Temporal action localization The goal is to predict the temporal boundary and the label of action instances in untrimmed videos. In the fully-supervised case where temporal annotations are given during training, several works tried to obtain better temporal proposals [5, 4, 19], while others improved temporal searching [41, 42] or classifiers [29]. R-C3D [35] proposed an end-to-end trainable activity detector based on Faster-RCNN [27]. GNNs [45, 37] are recently used to capture the temporal relationship among proposals/snippets. In the weakly-supervised setting, as only video-level annotations are given, most methods have aimed to obtain discriminative snippet-level activations and conduct post-processing to localize action instances. A co-activity similarity loss to enforce the feature similarity for video pairs with a common class was introduced in [25], and videos are segmented into interpretable fragments in [10]. Some works focused on distinguishing action and near-action/background snippets exploiting variational auto-encoder [28], entropy maximization [20], and an additional class-agnostic model [21]. Also, to better localize difficult snippets, multi-modal (audio-visual) fusion [14] or a contrastive loss with easy foreground/background snippets [43] are devised. Although those fully- and weakly-supervised methods attained large progress in this field, the learned models can only localize activity categories observed in the training dataset.",
+        "bbox": [
+            496,
+            251,
+            890,
+            643
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot temporal action localization [38] pioneered few-shot action localization, where a few (or only one) positive and several negative labeled videos steer the localization via an end-to-end meta-learning strategy. [36] also temporally localized an action from a few positive labeled and several negative labeled videos. They adopted a region proposal network [27] to produce proposals with flexible boundaries. [44] performed few-shot action localization where video-level annotations are needed. They constructed a multi-scale feature pyramid to directly produce temporal features at variable scales. Unlike those works, few-shot common action localization is less tied up with the need for labels. It localizes the action instances in a long untrimmed query video according to the commonality between the query and support inputs. Assuming a query with only one common action instance, [3] computed the probabilities for starting, ending, inside, or outside of ac",
+        "bbox": [
+            496,
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+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "10215",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "tion instances at every time-step, and decided the window with the highest joint probability as the action instance. Extending to the query videos with multiple action instances of the same action class, [39] generated action proposals, and then classified the proposals and regressed their temporal locations. [22] set a linear classifier itself as a prototype, which needs fine-tuning by support videos for every target action, then the prototype is cross-attended by query proposals using multiple self-attention. [7] boosted [39] adding a single-head transformer where two different affinity matrices are used for the cross-attention weight between query and support videos.",
+        "bbox": [
+            75,
+            90,
+            472,
+            272
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Cross-attention To leverage the relationship between two heterogeneous representations, diverse cross-attention schemes have been devised. Inspired by self-attention (scaled dot-product of key, query, and value), [34] applied the scaled dot-product operation for the concatenation of image and text features for VQA. Also, [12] attended student using key and value of teacher for knowledge propagation. Several works exploited the cross-correlation between the heterogeneous representation as the attention weights for image and sentence matching in visual question answering (VQA) [17, 13], query and prototype matching in prototypical few-shot learning [6], and audio-visual fusion [26]. Here, we exploit the cross-attention to improve the matching between query and support video clips as well as to better utilize multiple support videos in the context of few-shot action localization.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            536,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first describe the three-stage cross-attention, CDC-CA, which consists of query-to-support Context, support-to-support (in different temporal granularity) temporal Dynamics, support-to-query Context CAs. Then, we explain the relational classifier.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Problem statement Given an untrimmed query video  $V_{Q}$  and  $L$  trimmed support videos  $\\{V_{S}^{1}, V_{S}^{2}, \\ldots, V_{S}^{L}\\}$ , the goal is to train a network (which consists of backbone  $g$ , proposal-net  $h$ , CDC-CA and relational classifier  $f$ ) to temporally localize action instances in the query video based on the commonality of the support videos whose action classes are same and unseen during training. Note that any ground-truth class cues are not given even during training.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In training, we resort to a meta-learning strategy. Here, the action classes in the training set  $(C_{\\mathrm{train}})$  and those of the testing set  $(C_{\\mathrm{test}})$  have no overlapping. Also, to simulate the few-shot configuration of support and query videos that will be encountered at the testing phase, we exploit episode-based training. Specifically, in a training iteration, we compose an episode as a set of a query and  $L$  support videos  $\\{(V_Q,V_S^1,V_S^2,\\dots ,V_S^L)\\}$  from a randomly selected class of  $C_{\\mathrm{train}}$ . In our work, we set  $L$  to 1 or 5. Formally, the objec",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "tive function is represented by",
+        "bbox": [
+            498,
+            90,
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+            106
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\operatorname *{arg  min}_{g,h,f}\\mathbb{E}_{(V_{Q},\\{V_{S}^{l}\\}_{l = 1}^{L})\\sim C_{\\text{train}}}\\left[\\mathcal{L}(\\mathcal{Y},f(h(g(V_{Q}))\\right), \\\\ \\left. g \\left(\\left\\{V _ {S} ^ {l} \\right\\} _ {l = 1} ^ {L}\\right)\\right), \\tag {1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{V}$  denotes the set of temporal positions for the ground-truth action segments of the interest in  $V_{Q}$ .  $\\mathcal{L}$  is the loss function.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overall framework",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Fig. 3 depicts the overall framework of our method. To obtain the initial representations of the input query and support videos, we follow the preprocessing of [39]. The backbone network  $g$  [32] generates video representations for each input. Then, for the query video, the proposal subnet  $h$  [35] yields potential temporal action instances  $Q = \\{q_i\\}_{i=1}^{N_Q}$ , called action proposals, with diverse temporal lengths (details are in Sec. S-4 of supplementary materials).  $N_Q$  is the number of the proposals, and  $q_i$  denotes  $i$ th action proposal representation. For every  $l$ th support video, we uniformly split each support video into  $N_S$  fine-grained temporal snippets by  $S^{(l)} = \\{s_i^{(l)}\\}_{i=1}^{N_S}$ . Then, CDC-CA aligns  $Q$  and  $\\{S^{(l)}\\}_{l=1}^L$ . Next, in the relational classifier, the action classifier detects the action proposals with the target common action, and yields their temporal offsets to refine the start and end times of the proposals. In training, learning an auxiliary relational module in parallel with the action classifier is beneficial. In testing, the auxiliary relational module is discarded, and the localization head suppresses redundant proposals which is explained in Sec. 4.1.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2.CDC-CA",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The green box of Fig. 3 illustrates three stages of CDC-CA. We first introduce the cross-attention mechanism to individually attend the fine-grained (snippet-level) support video features by the query's context (QtoS Context-CA). Next, we explain the cross-attention to enhance the temporal dynamics of each support video from all the support videos in different temporal granularity (Dynamics-CA). Then, we present the way to attend the features of query proposals via the cross-attention with all the resulting support features (StoQ Context-CA). These enhanced features serve as crucial inputs to the following relational classifier.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "QtoS Context-CA: We first enhance the support features in consideration of the context of the query video (i.e. query to support, dubbed QtoS). To this end, we develop a cross-attention mechanism. When we suppose a vanilla approach such as Fig. 1(a), the attention weight is obtained at once based on the relationship between the query proposals and all the support videos. In this case, a support video, which is relatively less relevant to the query video than the other support videos, gets tiny attention weights and cannot",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "10216",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/4693b4af0f1ceb0627ec38575c20d65c5a853ff22e803262e888fc6d88abeff8.jpg",
+        "image_caption": [
+            "Figure 3: An overview of the proposed method.  $l$ th support video,  $X_{S}^{(l)}$ , is attended by query proposals  $X_{Q}$ , individually. Next, the temporal dynamics of all  $L$  the support videos are propagated to each support video. The resulting support videos  $\\{\\hat{Y}_S^{(l)}\\}_{l=1}^L$  give attention to the query proposals.  $\\hat{X}_{Q}$  is the resulting attended query proposals. Then, the relational classifier predicts the commonality scores of the proposals for the action of support videos, and the localization head finalizes action localization removing redundant proposals."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            87,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/0e0d6b02c87b620e4acb977a49089d46f139236723c2c61770eab892ee32cb3b.jpg",
+        "image_caption": [
+            "(a)",
+            "(b)",
+            "(c)",
+            "Figure 4: Cross-attention (best view in color). (a) QtoS Context-CA for  $l$ th support video by the query proposals. (b) Dynamics-CA for  $l$ th support video by  $L$  support videos in different temporal granularity. (c) StoQ Context-CA of all the query proposals by the attended support videos, at once."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            311,
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+            376
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "represent its action information in the context of the query video. As depicted in Fig. 4(a), to utilize the query video's context faithfully, we individually attend the support videos.",
+        "bbox": [
+            75,
+            479,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In specific, for  $l$ th support video, we first encode the backbone features of the query proposals  $Q$  to  $X_{Q} \\in \\mathbb{R}^{d \\times N_{Q}}$  and the support snippets  $S^{(l)}$  to  $X_{S}^{(l)} \\in \\mathbb{R}^{d \\times N_{S}}$ , with a linear layer. The columns of  $X_{Q}$  and  $X_{S}^{(l)}$  represent the encoded  $d$ -dimensional features of the query proposal and support snippets, respectively. After that, we compute the cross-correlation of  $X_{Q}$  and  $X_{S}^{(l)}$  to measure their relevance. To reduce the gap of the heterogeneity between the query and support videos, we use a learnable weight matrix  $W_{Q \\to S} \\in \\mathbb{R}^{d \\times d}$  and compute the cross-correlation as",
+        "bbox": [
+            75,
+            525,
+            468,
+            685
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Lambda_ {Q \\rightarrow S} ^ {(l)} = X _ {Q} ^ {T} W _ {Q \\rightarrow S} X _ {S} ^ {(l)} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            696,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Lambda_{Q\\to S}^{(l)}\\in \\mathbb{R}^{N_Q\\times N_S}$ . Note that each column of  $X_{Q}$  and  $X_{S}^{(l)}$  are  $l_{2}$ -normalized before the cross-correlation computation, and the learnable weight  $W_{Q\\rightarrow S}$  and the linear layer are shared across all  $l$  i.e. all the support videos.",
+        "bbox": [
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+            732,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the cross-correlation matrix, a high correlation coefficient means that the corresponding proposal and snippet features are highly relevant. Accordingly,  $i$ th row of  $\\Lambda_{Q\\to S}^{(l)}$  corresponds to the relevance of  $i$ th query proposal to the  $N_{S}$  support snippets. Then, from row-wise soft-max of  $\\Lambda_{Q\\to S}^{(l)}$ , we can obtain cross-attention weights  $A_{Q\\to S}^{(l)}$  where each",
+        "bbox": [
+            75,
+            801,
+            468,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "row represents the relative relevance of a query proposal to the support snippets.",
+        "bbox": [
+            496,
+            479,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The attention-weighted proposal features are summed to the corresponding support snippet feature. This is to ensure that the meaningful action information of the support video is well-preserved while applying the cross-attention. Formally, the attended support snippet features  $\\tilde{X}_S^{(l)}$  are obtained by",
+        "bbox": [
+            496,
+            508,
+            892,
+            601
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {X} _ {S} ^ {(l)} = X _ {Q} A _ {Q \\rightarrow S} ^ {(l)} + X _ {S} ^ {(l)}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            599,
+            890,
+            621
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that, through the attention weights, the query proposal injects its context to the support snippets proportionally to their relevance i.e. more to the highly relevant support snippets. With this, the support snippet features are enhanced to better guide the information about the target action to the query proposals in the later stage of attending queries of Fig. 4(a).",
+        "bbox": [
+            496,
+            623,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Dynamics-CA: Temporal dynamics is important to understand the actions, which is well-represented in consecutive snippets (tuple) rather than a single snippet. Hence, as illustrated in Fig. 4(b), to extract temporal dynamics of the attended support video features, we apply 1-dimensional temporal convolution on each  $\\tilde{X}_S^{(l)}$  as",
+        "bbox": [
+            496,
+            729,
+            893,
+            821
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {X} _ {S ^ {\\prime}} ^ {(l)} = \\tilde {X} _ {S} ^ {(l)} \\odot \\mathbf {w} _ {k} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            630,
+            827,
+            890,
+            848
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\odot$  denotes the convolution operation along temporal axis,  $\\mathbf{w}_k$  denotes the weight of 1D-conv layer.  $k$  is the kernel size of  $\\mathbf{w}_k$  ( $k < L$ ). The resulting  $\\tilde{X}_{S'}^{(l)}$  is in different",
+        "bbox": [
+            496,
+            853,
+            892,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "10217",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "temporal granularity with  $\\tilde{X}_S^{(l)}$ , and its components are the temporally-summaramized features for the tuples of  $k$  neighboring snippets, respectively.",
+        "bbox": [
+            75,
+            89,
+            468,
+            136
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Next, we propagate the temporal dynamics from tuple-level features to the fine-grained snippet features. Here, we also consider the compatible use of  $L$  support videos. In other words, as the support videos represent a common action, the support segment features should be closely located in a latent feature space. However, since the QtoS Context-CA are applied individually for each support video, the heterogeneity may be overly increased, which can degenerate the effect of attention on query videos in the following last stage. To compensate this, we attend the snippet-level features of  $l$ th support video  $\\tilde{X}_S^{(l)}$  from the tuple-level features of all  $L$  support videos, i.e.,  $\\tilde{X}_{S'} = \\{\\tilde{X}_{S'}^{(l)}\\}_{l=1}^L$ .",
+        "bbox": [
+            75,
+            137,
+            468,
+            323
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Concretely, like eq. (2), we first compute cross-correlation between  $\\tilde{X}_{S'}$  and  $\\tilde{X}_S^{(l)}$  by",
+        "bbox": [
+            76,
+            323,
+            468,
+            356
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Lambda_ {S ^ {\\prime} \\rightarrow S} ^ {(l)} = \\tilde {X} _ {S ^ {\\prime}} ^ {T} W _ {S ^ {\\prime} \\rightarrow S} \\tilde {X} _ {S} ^ {(l)} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            366,
+            468,
+            387
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then, the temporal dynamics-attended support video feature  $\\tilde{Y}_S^{(l)}$  is generated by",
+        "bbox": [
+            76,
+            412,
+            468,
+            446
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {Y} _ {S} ^ {(l)} = \\tilde {X} _ {S ^ {\\prime}} A _ {S ^ {\\prime} \\rightarrow S} ^ {(l)} + \\tilde {X} _ {S} ^ {\\prime (l)}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            178,
+            455,
+            468,
+            477
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $A_{S' \\to S}^{(l)}$  is the cross-attention weight from  $\\Lambda_{S' \\to S}^{(l)}$ .",
+        "bbox": [
+            76,
+            488,
+            450,
+            507
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "StoQ Context-CA: In this stage, we attend query videos with the support videos using the cross-attention. This support-to-query context attention is called StoQ Context-CA described in Fig. 4(c). To mine the richer information for target action from all the support videos, we attend query proposal features using the entire stabilized support segment features  $\\tilde{Y}_S = \\{\\tilde{Y}_S^{(1)},\\tilde{Y}_S^{(2)},\\dots ,\\tilde{Y}_S^{(L)}\\} \\in \\mathbb{R}^{d\\times LN_S}$ . Similar to attending support features, we exploit the cross-attention to obtain the attended query proposals  $\\tilde{X}_Q$  with a learnable weight matrix  $W_{S\\rightarrow Q}\\in \\mathbb{R}^{d\\times d}$  by",
+        "bbox": [
+            75,
+            507,
+            468,
+            659
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {X} _ {Q} = \\tilde {Y} _ {S} A _ {S \\rightarrow Q} + X _ {Q} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            192,
+            670,
+            468,
+            689
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $A_{S\\rightarrow Q}$  is attention weight computed by row-wise soft-max of cross-correlation,  $\\Lambda_{S\\rightarrow Q} = \\tilde{Y}_S^T W_{S\\rightarrow Q}X_Q$ . From this cross-attention, the query proposals, which have high relevance to crucial support segments, better delineate the target action.",
+        "bbox": [
+            75,
+            700,
+            468,
+            777
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Relational classifier",
+        "text_level": 1,
+        "bbox": [
+            76,
+            786,
+            263,
+            801
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Up to this point, we described how CDC-CA generates better representations of query proposals and support videos. Here, we explain the way to obtain the final decision from the attended representations. Fig. 5 depicts our relational classifier including an action classifier and an auxiliary relational module. The auxiliary module facilitates",
+        "bbox": [
+            75,
+            809,
+            468,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/4162009708de82d1917d37b3123b1b130bc0a0872f81a39ff9b832a1c9b0f715.jpg",
+        "image_caption": [
+            "Figure 5: Relational classifier consists of auxiliary relational module and action classifier."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            88,
+            895,
+            175
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "learning how to understand the relationship between query proposals and a target action with pseudo action class cues. As the auxiliary relational module is discarded in the deployed network, no action class label is required in testing.",
+        "bbox": [
+            496,
+            248,
+            890,
+            309
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Auxiliary relational module: In episodic few-shot learning, an auxiliary classifier can be co-trained to categorize an input into one of the ground-truth classes rather than the target classes of an episode. This is beneficial for feature extractors to prevent overfitting, stabilize the training, and boost the performance [24, 11].",
+        "bbox": [
+            496,
+            309,
+            890,
+            398
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However, since the ground-truth action classes are not available in our task, we utilize pseudo action classes. As in Fig. 5, we develop the auxiliary relational module which takes as an input the concatenation of the attended query proposal (green), support prototype (purple), and a pseudoclass identifier (white). The support prototype is the average of all the attended support segments. The pseudo-class identifier is a multi-hot vector with 1 for the pseudo action classes present in the support videos and 0 otherwise. As action class annotations are unavailable, the pseudo action classes are simply obtained by  $k$ -means clustering of the pre-trained backbone features extracted from all the ground-truth positive action instances in the training set. Then, these pseudo action classes can provide the cue to capture the commonality of the support videos with the same action across episodes. Hence, joint training with the auxiliary module assists the action classifier to learn to more correctly find the common actions in the query video without getting distracted by the non-target actions. The auxiliary relational module predicts whether the query proposal and the prototype are similar or not. Note that this module is only needed for training and discarded in the testing phase as the training and testing classes are mutually exclusive.",
+        "bbox": [
+            496,
+            400,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Action classifier: The action classifier consists of two parallel linear layers. Taking only the query proposal features  $\\tilde{X}_Q$  as inputs, the action classifier computes two outputs. The first is soft-max activated and decides if a query proposal contains target action or not. The second regresses the temporal offsets from the corresponding ground-truth.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Loss functions",
+        "text_level": 1,
+        "bbox": [
+            500,
+            847,
+            645,
+            861
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To optimize the entire network, as in [39], we use loss terms for both support-agnostic and -conditioned parts. In",
+        "bbox": [
+            500,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "10218",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the support-agnostic part, the binary cross-entropy loss  $\\mathcal{L}_{\\mathrm{cls}}^{\\mathrm{ag}}$  predicts if the proposal contains any activity or not, and the smooth  $l_{1}$  regression loss  $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{ag}}$  optimizes the relative displacement between proposals and ground-truths.",
+        "bbox": [
+            75,
+            90,
+            467,
+            151
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the auxiliary relational module of the support-conditioned part, we simply use the binary cross-entropy loss  $\\mathcal{L}_{\\mathrm{aux}}$  to predict if the proposal and support videos are similar or not. In the action classifier of the support-conditioned part, similar to the support-agnostic part, the classification loss  $\\mathcal{L}_{\\mathrm{cls}}^{\\mathrm{co}}$  predicts if the proposal includes the same common action of support videos, and the regression loss  $\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{co}}$  optimizes the relative displacement between the proposals and the ground-truths. Also, we design a pairwise ranking loss to add constraints to the action classifier. Considering a pair of proposals  $q_{i}$  and  $q_{j}$ , where at least one of them is a positive query proposal, we let the proposal with the larger IoU (intersection over union) for the ground-truth action instance have a higher soft-max score for the action class. Formally, the pairwise ranking loss  $\\mathcal{L}_{\\mathrm{rank}}$  is represented by",
+        "bbox": [
+            75,
+            152,
+            472,
+            393
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {r a n k}} = \\frac {1}{N _ {\\text {p a i r}}} \\sum_ {(i, j)} \\left(\\Delta \\mathrm {I o U} _ {i j} - \\Delta p _ {i j} ^ {\\text {a c t i o n}}\\right) ^ {2} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            132,
+            406,
+            468,
+            444
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $N_{\\mathrm{pair}}$  is the number of considered proposal pairs.  $\\Delta \\mathrm{IoU}_{ij}$  is the difference between IoUs of  $q_{i}$  and  $q_{j}$  with their corresponding ground-truths, and  $\\Delta p_{ij}^{\\mathrm{action}}$  is the difference of soft-max predictions for the proposals on the action class from the action classifier. Note that to relax the relationship between IoU and soft-max prediction, we give temperature to the soft-max predictions in  $\\mathcal{L}_{\\mathrm{rank}}$ . Finally, total loss (more details in Sec. S-1 of supplementary materials) is given by",
+        "bbox": [
+            75,
+            457,
+            468,
+            592
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL = L _ {\\mathrm {c l s}} ^ {\\mathrm {a g}} + L _ {\\mathrm {r e g}} ^ {\\mathrm {a g}} + L _ {\\mathrm {c l s}} ^ {\\mathrm {c o}} + L _ {\\mathrm {r e g}} ^ {\\mathrm {c o}} + L _ {\\mathrm {a u x}} + \\lambda L _ {\\mathrm {r a n k}}. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
+            606,
+            468,
+            625
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            638,
+            209,
+            655
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and evaluation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            664,
+            295,
+            679
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To evaluate few-shot common action localization, we use the revised versions [3, 39] of ActivityNet1.3 [1] and THU-MOS14 [9]. In the revised, there are two cases depending on queries: single-instance and multi-instance. We address 1- or 5-shot settings in both cases. For meta-learning strategy, the entire action classes of each dataset are split into  $80\\%$  for training,  $10\\%$  for validation, and  $10\\%$  for testing. For a fair comparison, we follow the data configuration of [39], which will be described in the following paragraphs. Further details are in Sec. S-4 of supplementary material.",
+        "bbox": [
+            75,
+            688,
+            467,
+            852
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Common single-instance: For both datasets, videos with multiple actions are divided into independent videos where each video contains just one action instance and",
+        "bbox": [
+            76,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "background. Then, videos longer than 768 frames are discarded. If a video is selected as a support video, its foreground action instance is only used as the support input. For ActivityNet1.3, there are 10,035 and 2,483 videos for training and validation+testing, each. The average video length is 89.0s. For THUMOS14, there are 3,580 and 775 training and validation+testing videos, respectively. The average length is 11.4s.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Common multi-instance: In real-world scenarios, the lengths of query videos are usually not constrained, and the query videos may contain multiple action instances. Hence, we exploit the original videos of ActivityNet1.3 and THUMOS14 without any processing for query videos. Support videos are still trimmed ones. For ActivityNet1.3, the numbers of videos are 6,747 and 1,545 for training and validation+testing, respectively. The average video length is 148.2s. For THUMOS14, there are 1,664 training videos and 323 validation+testing videos. The average video length is 230.6s.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Inference: In testing, the backbone-generated query proposals are refined by non-maximum suppression (NMS) with a threshold 0.7. Also, following [39], if the query video is longer than 768 frames, we generate the multi-scale segments [30]. We slide windows with sizes of 512 and 768 frames along the temporal axis with  $75\\%$  overlap. The generated proposals of the windows go through the NMS to remove redundant proposals. Then, the selected proposals are fed into our CDC-CA and relational classifier. Finally, we perform NMS (threshold 0.3) for the regressed proposals based on the outputs of the relational classifier to remove redundant ones.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation: We measure the temporal action localization performance with mean Average Precision (mAP). A prediction is correct when it has the correct foreground/background classification and has IoU with its ground-truth larger than a threshold. The threshold is set to 0.5 unless specified.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparative assessment",
+        "text_level": 1,
+        "bbox": [
+            500,
+            664,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We report the performance of compared methods from the literature. Due to the variance of  $k$ -means clustering of the pseudo label generation, we report the average of three runs for our method.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For AcitivityNet1.3, the left of Table 1 demonstrates the comparative results on both common single- and multi-instance cases when  $L = 1$  or 5. [3, 39, 22, 7] were developed for the common temporal action localization (our task) in videos, and [8] was for the common object detection in images. Compared to them, our method shows notably higher performance for all the settings ([3] was designed to use one support video). Specifically, in the single-instance case, we outperform those methods by at least  $1.4\\%$  and  $5.1\\%$  in the 1- and 5-shot settings, respec",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "10219",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4ca44bed5f9444b9bd173882f9ee4e794b14e1c0e13cb25a14c459db4661fb82.jpg",
+        "table_caption": [
+            "Table 1: Comparison with state-of-the-arts in terms of mAP@0.5."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">ActivityNet1.3</td><td colspan=\"4\">THUMOS14</td></tr><tr><td colspan=\"2\">Single-instance</td><td colspan=\"2\">Multi-instance</td><td colspan=\"2\">Single-instance</td><td colspan=\"2\">Multi-instance</td></tr><tr><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>Feng et al. [3]</td><td>43.5</td><td>n/a</td><td>31.4</td><td>n/a</td><td>34.1</td><td>n/a</td><td>4.3</td><td>n/a</td></tr><tr><td>Hu et al. [8]</td><td>41.0</td><td>45.4</td><td>29.6</td><td>38.9</td><td>-</td><td>42.2</td><td>-</td><td>6.8</td></tr><tr><td>Yang et al. [39]</td><td>53.1</td><td>56.5</td><td>42.1</td><td>43.9</td><td>48.7</td><td>51.9</td><td>7.5</td><td>8.6</td></tr><tr><td>Yang et al. [40]</td><td>57.5</td><td>60.6</td><td>47.8</td><td>48.7</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Nag et al. [22]</td><td>55.1</td><td>63.0</td><td>44.1</td><td>48.2</td><td>49.2</td><td>54.3</td><td>7.3</td><td>10.4</td></tr><tr><td>Hsieh et al. [7]</td><td>60.7</td><td>61.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>62.1 ± 1.0</td><td>66.3 ± 1.2</td><td>48.2 ± 1.2</td><td>53.5 ± 1.1</td><td>53.8 ± 1.2</td><td>59.2 ± 1.3</td><td>9.8 ± 0.4</td><td>15.7 ± 0.5</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7cbb61850cbcee140d294387a7a6680cc962d49a6436fe47accffca46c4f8e97.jpg",
+        "table_caption": [
+            "Table 2: Ablation study on CDC-CA for the single-instance setting."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">QtoS Context-CA</td><td rowspan=\"2\">Dynamics-CA</td><td colspan=\"2\">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>C-0</td><td></td><td></td><td>52.0</td><td>54.3</td></tr><tr><td>C-1</td><td>✓</td><td></td><td>61.5</td><td>65.4</td></tr><tr><td>C-2</td><td></td><td>✓</td><td>61.3</td><td>65.1</td></tr><tr><td>C-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tively. In the multi-instance, the margins are at least  $4.1\\%$  and  $5.3\\%$  for 1- and 5-shot, each. Note that [40] was developed for object-level common temporal action localization. Although object-level localization is more challenging, it requires further information to learn their model such as the coordinates of foreground object bounding boxes. Hence, they have advantages in the frame-level localization task. Even so, our method yields better results than [40] in all the settings. Also, in the 5-shot setting, the score margins to the existing works are larger than those of 1-shot in both single- and multi-instance. This means that enhancing the temporal dynamics of a support video by the entire support video in Dynamics-CA and aligning individually each support video to the query video's context in QtoS Context-CA are helpful to mine the knowledge for a common action from multiple support videos. Unlike ActivityNet1.3, THUMOS14 includes shorter action instances which make correct localization more difficult. Nevertheless, we outperform the compared methods over all the settings.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Component analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We analyze our method on ActivitNet1.3. More studies are in supplementary materials.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Impact of cross-attention: First, to see the component-wise impact of our cross-attention, we ablate QtoS Context-CA and Dynamics-CA in Table 2, we can see that without any of them (C-0), the performance is severely degraded.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/56b705c2e4370c09c6388b0c0a9e073ccf7bd9f4bc42207adea317009ebf00e0.jpg",
+        "table_caption": [
+            "Table 3: Ablation study on the relational classifier on the single-instance setting."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Lrank</td><td rowspan=\"2\">Auxiliary rel. module</td><td colspan=\"2\">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>R-0</td><td></td><td></td><td>61.8</td><td>65.8</td></tr><tr><td>R-1</td><td>✓</td><td></td><td>61.9</td><td>66.0</td></tr><tr><td>R-2</td><td></td><td>✓</td><td>61.9</td><td>66.1</td></tr><tr><td>R-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7643e761ea2b07b88ab5c4cac01014427b09c3980a46c72398136678795ad658.jpg",
+        "table_caption": [
+            "Table 4: Analysis of the individual cross-attention strategy on QtoS Context-CA and Dynamics-CA, comparing with the aggregated cross-attention on the 5-shot setting."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>Single-inst.</td><td>Multi-inst.</td></tr><tr><td rowspan=\"2\">QtoS Context-CA</td><td>Aggregated</td><td>65.7</td><td>52.8</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr><tr><td rowspan=\"2\">Dynamics-CA</td><td>Aggregated</td><td>65.8</td><td>52.9</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr></table>",
+        "bbox": [
+            500,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Also, when comparing C-1 and C-2, both cross-attentions show meaningful improvements on C-0, but QtoS Context-CA is slightly more important. Using both shows the best performance in our final method C-3.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We can also consider changing the order of QtoS Context-CA and Dynamics-CA. In this case, we observed that the performance is slightly lowered (62.1%→61.7% in 1-shot, 66.3%→65.6% in 5-shot). Hence, the temporal dynamics extracted under the query video's context is more useful in our task.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Further, we evaluate the efficacy of our cross-attention, comparing it with other cross-attention mechanisms. To this end, we compare our CDC-CA itself (corresponding to R-0 in Table 3) to the progressive cross-attention [39], and the multi-head cross-attention with fine-tuned (50-100 iterations) prototype [22], light-weight transformer-based booster [7]. For a fair comparison, the pairwise ranking",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "10220",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/98fb624fa7d290c372d3121e6f9b4556c10a6e57930c97220ded82427c5e35df.jpg",
+        "table_caption": [
+            "Table 5: Cosine similarity between support videos and between support and query videos in embedding space before/after passing through Dynamics-CA."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Support-Support</td><td colspan=\"3\">Support-Query</td></tr><tr><td>Pos. query</td><td>Neg. query</td><td>Δ</td></tr><tr><td>Cos. Sim. (before)</td><td>0.49</td><td>0.41</td><td>0.38</td><td>0.05</td></tr><tr><td>Cos. Sim. (after)</td><td>0.61</td><td>0.43</td><td>0.34</td><td>0.13</td></tr></table>",
+        "bbox": [
+            76,
+            142,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "loss and auxiliary relational module are not used in R-0. CDC-CA yields mAP gain of at least  $+1.1\\%$  and  $+2.8\\%$  in 1-shot (60.7% [7] in Table 1 vs 61.8% R-0) and 5-shot (63.0% [22] in Table 1 vs 65.8% R-0), each. Hence, we conclude our cross-attention more effectively enhances the query and support videos in this task.",
+        "bbox": [
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+            229,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Individual vs aggregated: To study the effectiveness of the individual cross-attention on QtoS Context-CA and Dynamics-CA for multiple support videos, we compare our individual cross-attention approach with the aggregated cross-attention ('Aggregated') in Table 4. In 'Aggregated' of QtoS Context-CA, we concatenate all the support snippets of the entire support videos, and simultaneously attend them via query proposals. We see that 'Aggregated' degrades the localization performance. This result shows the benefit of individual cross-attention in QtoS Context-CA. Also, in Dynamics-CA, we identified a similar tendency. Accordingly, mining the commonality of temporal dynamics in multiple support videos is more beneficial when it is propagated to each support video, individually.",
+        "bbox": [
+            75,
+            321,
+            470,
+            532
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Compatibility in support videos: In Dynamics-CA, a snippet-level support video feature is attended by tuple-level features from all the support videos to promote compatibility among multiple support videos. To identify this, at two points (before or after passing through Dynamics-CA), we measure the cosine similarities 1) between two support videos, and 2) between a support video and a (positive or negative) query proposal. Table 5 reports the average of cosine similarities. The increased support-support similarity  $(0.49\\% \\rightarrow 0.61\\%)$  indicates that the support videos get closer to each other in the embedding space. Also, we can see that the discriminative ability is improved as seen by the increased difference  $(\\Delta)$  in the similarity of the support to positive and negative query proposals.",
+        "bbox": [
+            75,
+            536,
+            468,
+            748
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Further, to more clearly show the effect of individual-to-all cross-attention in Dynamics-CA, we also identified individual-to-individual Dynamacmis-CA where the snippet-level features are attended by the corresponding temporally-convolutioned features for each support video. Comparison of ours with this variant is  $66.3\\%$  vs  $65.9\\%$  in 5-shot single instance, and  $53.5\\%$  vs  $53.2\\%$  in 5-shot multiple instances. Hence, we can see that our approach (individual-to-all) is more beneficial for the collaborative use of a few support videos.",
+        "bbox": [
+            75,
+            750,
+            470,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2cdc8f0cc87c9bf9b7c5b0959a7016ff489d132e7f8c0a4784a4f31478af8449.jpg",
+        "table_caption": [
+            "Table 6: Effect of the multi-hot pseudo action indicator by varying the number of pseudo action classes or removing it."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>w/o Indicator</td><td colspan=\"4\">k</td></tr><tr><td></td><td></td><td></td><td>80</td><td>160</td><td>240</td><td>320</td></tr><tr><td rowspan=\"2\">Single Inst.</td><td>1-shot</td><td>61.9</td><td>61.9</td><td>62.1</td><td>62.1</td><td>62.3</td></tr><tr><td>5-shot</td><td>66.0</td><td>66.2</td><td>66.3</td><td>66.5</td><td>66.4</td></tr><tr><td rowspan=\"2\">Multiple Inst.</td><td>1-shot</td><td>47.8</td><td>48.0</td><td>48.2</td><td>48.4</td><td>48.4</td></tr><tr><td>5-shot</td><td>53.3</td><td>53.4</td><td>53.5</td><td>53.4</td><td>53.5</td></tr></table>",
+        "bbox": [
+            517,
+            122,
+            874,
+            227
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Relational classifier: Here, we verify the auxiliary relational module and the pairwise ranking loss by ablating each. To show their effect, we compare each ablated version to the baseline R-0 without any of them in Table 3. The pairwise ranking loss gives performance improvement by  $0.1\\%$  and  $0.2\\%$  for 1- and 5-shot, respectively (R-1). Hence, this loss lets the proposals with larger IoUs to ground-truths get higher action scores. From the result of R-2, we also see that learning the auxiliary module in parallel to the action classifier is useful to boost performance in both settings. And, combining both works the best (R-3).",
+        "bbox": [
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+            243,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Adequacy to no. of pseudo action label: In the auxiliary relational module, we use the multi-hot indicator as the pseudo-action cue in consideration that no true label is available. To see its effectiveness, in Table 6, we report the mAP scores by varying the number of pseudo action classes  $(k)$  and w/o the indicator as well. In the single instance case, compared to the R-1 of Table 3, the auxiliary relational module did not show an effect without the multi-hot indicator. Also, for all other settings, as  $k$  gets larger, the multi-hot indicator yields larger performance gains overall. Though the support videos represent a common action, there is diversity in background or action details. Hence, it is beneficial to distinguish the support videos with more pseudo labels. Considering the computational cost, we set  $k$  to 160 as the default value.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusions",
+        "text_level": 1,
+        "bbox": [
+            500,
+            654,
+            627,
+            669
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For few-shot common action localization, we proposed the three-stage cross-attention (CDC-CA) and the relational classifier. CDC-CA increases the effect of the cross-attention by individually attending each support video, enhancing the temporal dynamics of each and the compatibility of multiple support videos, and then attending the query video via all the enhanced support videos. In the relational classifier, we designed the pairwise ranking loss which makes more precise action localization of the action classifier. Learned in parallel with the action classifier, the auxiliary relational module with the pseudo-class labels prevents the network from overfitting to each training episode. This module is discarded in testing. Extensive experiments analyzed and validated each component. Finally, we achieved SOTA on ActivityNet1.3 and THUMOS14.",
+        "bbox": [
+            496,
+            674,
+            890,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "10221",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            174,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[2] Victor Escorcia, Fabian Caba Heilbron, Juan Carlos Niebles, and Bernard Ghanem. Daps: Deep action proposals for action understanding. In ECCV, 2016. 1",
+            "[3] Yang Feng, Lin Ma, Wei Liu, Tong Zhang, and Jiebo Luo. Video re-localization. In ECCV, 2018. 1, 2, 6, 7",
+            "[4] Jiyang Gao, Zhenheng Yang, Kan Chen, Chen Sun, and Ram Nevatia. Turn tap: Temporal unit regression network for temporal action proposals. In ICCV, 2017. 1, 2",
+            "[5] Fabian Caba Heilbron, Juan Carlos Niebles, and Bernard Ghanem. Fast temporal activity proposals for efficient detection of human actions in untrimmed videos. In CVPR, 2016. 2",
+            "[6] Ruibing Hou, Hong Chang, Bingpeng Ma, Shiguang Shan, and Xilin Chen. Cross attention network for few-shot classification. In NeurIPS, 2019. 3",
+            "[7] He-Yen Hsieh, Ding-Jie Chen, Cheng-Wei Chang, and Tyng-Luh Liu. Aggregating bilateral attention for few-shot instance localization. In WACV, 2023. 1, 3, 6, 7, 8",
+            "[8] Tao Hu, Pascal Mettes, Jia-Hong Huang, and Cees GM Snoek. Silco: Show a few images, localize the common object. In ICCV, 2019. 6, 7",
+            "[9] Haroon Idrees, Amir R Zamir, Yu-Gang Jiang, Alex Gorban, Ivan Laptev, Rahul Sukthankar, and Mubarak Shah. The thumos challenge on action recognition for videos “in the wild”. Computer Vision and Image Understanding, 155:1-23, 2017. 6",
+            "[10] Mihir Jain, Amir Ghodrati, and Cees G. M. Snoek. Action-Bytes: Learning from trimmed videos to localize actions. In CVPR. 2020. 2",
+            "[11] Dahiyun Kang, Heeseung Kwon, Juhong Min, and Minsu Cho. Relational embedding for few-shot classification. 2021. 5",
+            "[12] Hanul Kim, Mihir Jain, Jun-Tae Lee, Sungrack Yun, and Fatih Porikli. Efficient action recognition via dynamic knowledge propagation. In ICCV, 2021. 3",
+            "[13] Jin-Hwa Kim, Kyoung-Woon On, Woosang Lim, Jeonghee Kim, Jung-Woo Ha, and Byoung-Tak Zhang. Hadamard product for low-rank bilinear pooling. In ICLR, 2017. 3",
+            "[14] Jun-Tae Lee, Mihir Jain, Hyoungwoo Park, and Sungrack Yun. Cross-attentional audio-visual fusion for weakly-supervised action localization. In ICLR. 2021. 2",
+            "[15] Jun-Tae Lee, Hyunsin Park, Sungrack Yun, and Simyung Chang. Multi-head modularization to leverage generalization capability in multi-modal networks. AAAI, 36(7), 2022. 1",
+            "[16] Jun-Tae Lee, Sungrack Yun, and Mihir Jain. Leaky gated cross-attention for weakly supervised multi-modal temporal action localization. In WACV, 2022. 1",
+            "[17] Kuang-Huei Lee, Xi Chen, Gang Hua, Houdong Hu, and Xiaodong He. Stacked cross attention for image-text matching. In ECCV, 2018. 3"
+        ],
+        "bbox": [
+            78,
+            114,
+            468,
+            898
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[18] Pilhyeon Lee, Jinglu Wang, Yan Lu, and Hyeran Byun. Weakly-supervised temporal action localization by uncertainty modeling. In AAAI. 2021. 1",
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+            "[21] Junwei Ma, Satya Krishna Gorti, Maksims Volkovs, and Guangwei Yu. Weakly supervised action selection learning in video. In CVPR. 2021. 2",
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+            "[26] R Gnana Praveen, Wheidima Carneiro de Melo, Nasib Ullah, Haseeb Aslam, Osama Zeeshan, Théo Denorme, Marco Pedersoli, Alessandro L Koerich, Simon Bacon, Patrick Cardinal, et al. A joint cross-attention model for audio-visual fusion in dimensional emotion recognition. In CVPR. 2022. 3",
+            "[27] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. In NeurIPS, 2015. 2",
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+            "[29] Zheng Shou, Jonathan Chan, Alireza Zareian, Kazuyuki Miyazawa, and Shih-Fu Chang. Cdc: Convolutional-deconvolutional networks for precise temporal action localization in untrimmed videos. In CVPR, 2017. 2",
+            "[30] Zheng Shou, Dongang Wang, and Shih-Fu Chang. Temporal action localization in untrimmed videos via multi-stage cnns. In CVPR, 2016. 6",
+            "[31] Krishna Kumar Singh and Yong Jae Lee. Hide-and-seek: Forcing a network to be meticulous for weakly-supervised object and action localization. In ICCV. 2017. 1",
+            "[32] Du Tran, Lubomir Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. Learning spatiotemporal features with 3d convolutional networks. In ICCV, 2015. 3",
+            "[33] Limin Wang, Yuanjun Xiong, Dahua Lin, and Luc Van Gool. UntrimmedNets for weakly supervised action recognition and detection. In CVPR. 2017. 1",
+            "[34] Xi Wei, Tianzhu Zhang, Yan Li, Yongdong Zhang, and Feng Wu. Multi-modality cross attention network for image and sentence matching. In CVPR, 2020. 3"
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            898
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "10222",
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[35] Huijuan Xu, Abir Das, and Kate Saenko. R-c3d: Region convolutional 3d network for temporal activity detection. In ICCV, 2017. 2, 3",
+            "[36] Huijuan Xu, Xineng Sun, Eric Tzeng, Abir Das, Kate Saenko, and Trevor Darrell. Revisiting few-shot activity detection with class similarity control. In arXiv preprint arXiv:2004.00137, 2020. 2",
+            "[37] Mengmeng Xu, Chen Zhao, David S Rojas, Ali Thabet, and Bernard Ghanem. G-tad: Sub-graph localization for temporal action detection. In CVPR, 2020. 2",
+            "[38] Hongtao Yang, Xuming He, and Fatih Porikli. One-shot action localization by learning sequence matching network. In CVPR, 2018. 2",
+            "[39] Pengwan Yang, Vincent Tao Hu, Pascal Mettes, and Cees GM Snoek. Localizing the common action among a few videos. In ECCV, 2020. 1, 3, 5, 6, 7",
+            "[40] Pengwan Yang, Pascal Mettes, and Cees GM Snoek. Few-shot transformation of common actions into time and space. In CVPR, 2021. 7",
+            "[41] Serena Yeung, Olga Russakovsky, Greg Mori, and Li Fei-Fei. End-to-end learning of action detection from frame glimpses in videos. In CVPR, 2016. 2",
+            "[42] Gang Yu and Junsong Yuan. Fast action proposals for human action detection and search. In CVPR, 2015. 2",
+            "[43] Can Zhang, Meng Cao, Dongming Yang, Jie Chen, and Yuexian Zou. Cola: Weakly-supervised temporal action localization with snippet contrastive learning. In CVPR, 2021. 2",
+            "[44] Da Zhang, Xiyang Dai, and Yuan-Fang Wang. Metal: Minimum effort temporal activity localization in untrimmed videos. In CVPR, 2020. 2",
+            "[45] Chen Zhao, Ali K Thabet, and Bernard Ghanem. Video self-stitching graph network for temporal action localization. In ICCV, 2021. 2"
+        ],
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+]
\ No newline at end of file
diff --git a/2023/Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics/4021ee8f-1629-4cd1-8f02-6d3ae43c664d_model.json b/2023/Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics/4021ee8f-1629-4cd1-8f02-6d3ae43c664d_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..252c497a9b837ccd9450dc83e31c107d0d4df4ee
--- /dev/null
+++ b/2023/Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics/4021ee8f-1629-4cd1-8f02-6d3ae43c664d_model.json	
@@ -0,0 +1,2035 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+                0.003,
+                0.182,
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+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.158,
+                0.131,
+                0.815,
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+            ],
+            "angle": 0,
+            "content": "Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.295,
+                0.203,
+                0.674,
+                0.239
+            ],
+            "angle": 0,
+            "content": "Juntae Lee<sup>1</sup>, Mihir Jain<sup>* *</sup> and Sungrack Yun<sup>1</sup>  \n<sup>1</sup>Qualcomm AI Research†"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.326,
+                0.242,
+                0.644,
+                0.257
+            ],
+            "angle": 0,
+            "content": "{juntlee, sungrack}@qti=qualcomm.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.325,
+                0.474,
+                0.688
+            ],
+            "angle": 0,
+            "content": "The goal of this paper is to localize action instances in a long untrimmed query video using just meager trimmed support videos representing a common action whose class information is not given. In this task, it is crucial to mine reliable temporal cues representing a common action from handful support videos. In our work, we develop an attention mechanism using cross-correlation. Based on this cross-attention, we first transform the support videos into query video's context to emphasize query-relevant important frames, and suppress less relevant ones. Next, we summarize sub-sequences of support video frames to represent temporal dynamics in coarse temporal granularity, which is then propagated to the fine-grained support video features through the cross-attention. In each case, the cross-attentions are applied to each support video in the individual-to-all strategy to balance heterogeneity and compatibility of the support videos. In contrast, the candidate instances in the query video are lastly attended by the resulting support video features, at once. In addition, we also develop a relational classifier head based on the query and support video representations. We show the effectiveness of our work with the state-of-the-art (SOTA) performance in benchmark datasets (ActivityNet1.3 and THUMOS14), and analyze each component extensively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.719,
+                0.21,
+                0.735
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.743,
+                0.47,
+                0.835
+            ],
+            "angle": 0,
+            "content": "Temporal action localization [2, 4, 33, 23, 31, 18, 15, 16, 20] have been widely studied in fully or weakly-supervised manner. However, they require collecting massive videos labeled by action classes, and also only detect the action classes observed in training. Whereas, we aim to temporally localize action instances in a long untrimmed query"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.076,
+                0.846,
+                0.47,
+                0.873
+            ],
+            "angle": 0,
+            "content": "*Work completed during employment at Qualcomm Technologies, Inc."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.873,
+                0.469,
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+            ],
+            "angle": 0,
+            "content": "\\(^{\\dagger}\\)Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.846,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.51,
+                0.291,
+                0.891,
+                0.507
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.516,
+                0.893,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Figure 1: Attention represents the relationship between a moment of query and support videos. (a) Vanilla: attention of a query proposal is obtained simultaneously for the frames of all the support videos. (b) Ours: the attention is computed for the frames of one support video, at a time. While important frames of support video #2 cannot be attended by the related query proposal in (a), they are appropriately transformed to the context of the query in (b)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.894,
+                0.704
+            ],
+            "angle": 0,
+            "content": "video based on the few trimmed support videos describing a common action class. As the testing action class is unseen in training and no ground-truth class cue is given, the only cue is the commonality of the few support videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.895,
+                0.825
+            ],
+            "angle": 0,
+            "content": "In this task, the alignment between query and support videos is important, which can be attained by representing the common action cues of interest from the support videos considering the query video's context. For better alignment, we divide this problem into two points: re-calibrating support video features under query video's context, and enhancing temporal dynamics and compatibility of the recalibrated support video features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Existing methods [39, 22, 7, 3] have mainly focused on the former point, handling the multiple support videos as a whole. However, as exemplified in Fig. 1, though the support videos represent a common action class, their context (e.g background, camera angle) can be different. Hence,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "10214"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.091,
+                0.468,
+                0.167
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.174,
+                0.47,
+                0.203
+            ],
+            "angle": 0,
+            "content": "Figure 2: Overall process of few-shot common action localization in our work."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.216,
+                0.468,
+                0.292
+            ],
+            "angle": 0,
+            "content": "when all the support videos are transformed to query context simultaneously, the support videos cluttered by background are overly suppressed although they include useful information (Fig. 1(a)). Whereas, in Fig. 1(b), we can leverage the support videos by attending each individually."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.293,
+                0.468,
+                0.488
+            ],
+            "angle": 0,
+            "content": "Regarding the latter point, we pay attention to that the temporal dynamics can be enriched from multiple temporal granularities. Hence, we try to collaboratively fuse the support video features in different temporal granularities, considering the compatibility of different support videos as well. Based on the insight for each point, we propose a novel few-shot common action localization method. The overall process is briefly outlined in Fig. 2. First, the long untrimmed query video is split to query proposals, and they are aligned with the support videos through our three-stage cross-attention. Then, the proposals representing the common action class are detected with temporal location refinement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.491,
+                0.468,
+                0.792
+            ],
+            "angle": 0,
+            "content": "For the query-support alignment, we develop a three-stage cross-attention (CA) mechanism. In each stage, cross-correlation between two different features (e.g. support and query, supports in different temporal granularity) is exploited with a learnable weight matrix. The 1st stage, query-to-support Context-CA transforms the support videos into the query video's context by cross-correlating them with the query proposal features. Each support video is individually attended to emphasize its most informative features. In 2nd stage of Dynamics-CA, low-temporal granularity features summarize the tuples of snippets of each support video, and they attend the fine-grained snippet-level features. Here, each support video is attended by the entire support videos in low-temporal granularity. It helps the complementary use of all the individually attended support video features as well as enhancing temporal dynamics. Finally, in the last stage (support-to-query Context-CA), the query video features are simultaneously attended with all the resulting support video features. We call this CA process (Context, Dynamics, Context-CAs) CDC-CA."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.794,
+                0.468,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Also, for the commonality prediction and refinement, we design a relational classifier with an action classifier and an auxiliary relational module. To prevent overfitting and boost performance, the latter matches the support and query video features using pseudo-label cues as we avoid the use of class labels. In testing, this module is not used."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Major contributions: (i) We suggest a three-stage CA to"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.213
+            ],
+            "angle": 0,
+            "content": "enhance the representation of query video by support videos and vice versa. (ii) We attend each support video individually to increase its discriminative ability in the first two stages. (iii) We develop a relational classifier including an action classifier and an auxiliary relational module. The latter is only needed during training. (iv) Extensive experimental analyses are done on two benchmark datasets, where we achieve SOTA performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.226,
+                0.637,
+                0.241
+            ],
+            "angle": 0,
+            "content": "2. Related work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.252,
+                0.892,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Temporal action localization The goal is to predict the temporal boundary and the label of action instances in untrimmed videos. In the fully-supervised case where temporal annotations are given during training, several works tried to obtain better temporal proposals [5, 4, 19], while others improved temporal searching [41, 42] or classifiers [29]. R-C3D [35] proposed an end-to-end trainable activity detector based on Faster-RCNN [27]. GNNs [45, 37] are recently used to capture the temporal relationship among proposals/snippets. In the weakly-supervised setting, as only video-level annotations are given, most methods have aimed to obtain discriminative snippet-level activations and conduct post-processing to localize action instances. A co-activity similarity loss to enforce the feature similarity for video pairs with a common class was introduced in [25], and videos are segmented into interpretable fragments in [10]. Some works focused on distinguishing action and near-action/background snippets exploiting variational auto-encoder [28], entropy maximization [20], and an additional class-agnostic model [21]. Also, to better localize difficult snippets, multi-modal (audio-visual) fusion [14] or a contrastive loss with easy foreground/background snippets [43] are devised. Although those fully- and weakly-supervised methods attained large progress in this field, the learned models can only localize activity categories observed in the training dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.645,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Few-shot temporal action localization [38] pioneered few-shot action localization, where a few (or only one) positive and several negative labeled videos steer the localization via an end-to-end meta-learning strategy. [36] also temporally localized an action from a few positive labeled and several negative labeled videos. They adopted a region proposal network [27] to produce proposals with flexible boundaries. [44] performed few-shot action localization where video-level annotations are needed. They constructed a multi-scale feature pyramid to directly produce temporal features at variable scales. Unlike those works, few-shot common action localization is less tied up with the need for labels. It localizes the action instances in a long untrimmed query video according to the commonality between the query and support inputs. Assuming a query with only one common action instance, [3] computed the probabilities for starting, ending, inside, or outside of ac"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10215"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "tion instances at every time-step, and decided the window with the highest joint probability as the action instance. Extending to the query videos with multiple action instances of the same action class, [39] generated action proposals, and then classified the proposals and regressed their temporal locations. [22] set a linear classifier itself as a prototype, which needs fine-tuning by support videos for every target action, then the prototype is cross-attended by query proposals using multiple self-attention. [7] boosted [39] adding a single-head transformer where two different affinity matrices are used for the cross-attention weight between query and support videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.275,
+                0.473,
+                0.518
+            ],
+            "angle": 0,
+            "content": "Cross-attention To leverage the relationship between two heterogeneous representations, diverse cross-attention schemes have been devised. Inspired by self-attention (scaled dot-product of key, query, and value), [34] applied the scaled dot-product operation for the concatenation of image and text features for VQA. Also, [12] attended student using key and value of teacher for knowledge propagation. Several works exploited the cross-correlation between the heterogeneous representation as the attention weights for image and sentence matching in visual question answering (VQA) [17, 13], query and prototype matching in prototypical few-shot learning [6], and audio-visual fusion [26]. Here, we exploit the cross-attention to improve the matching between query and support video clips as well as to better utilize multiple support videos in the context of few-shot action localization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.537,
+                0.17,
+                0.552
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.565,
+                0.47,
+                0.64
+            ],
+            "angle": 0,
+            "content": "In this section, we first describe the three-stage cross-attention, CDC-CA, which consists of query-to-support Context, support-to-support (in different temporal granularity) temporal Dynamics, support-to-query Context CAs. Then, we explain the relational classifier."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.642,
+                0.47,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Problem statement Given an untrimmed query video \\( V_{Q} \\) and \\( L \\) trimmed support videos \\( \\{V_{S}^{1}, V_{S}^{2}, \\ldots, V_{S}^{L}\\} \\), the goal is to train a network (which consists of backbone \\( g \\), proposal-net \\( h \\), CDC-CA and relational classifier \\( f \\)) to temporally localize action instances in the query video based on the commonality of the support videos whose action classes are same and unseen during training. Note that any ground-truth class cues are not given even during training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In training, we resort to a meta-learning strategy. Here, the action classes in the training set \\((C_{\\mathrm{train}})\\) and those of the testing set \\((C_{\\mathrm{test}})\\) have no overlapping. Also, to simulate the few-shot configuration of support and query videos that will be encountered at the testing phase, we exploit episode-based training. Specifically, in a training iteration, we compose an episode as a set of a query and \\(L\\) support videos \\(\\{(V_Q,V_S^1,V_S^2,\\dots ,V_S^L)\\}\\) from a randomly selected class of \\(C_{\\mathrm{train}}\\). In our work, we set \\(L\\) to 1 or 5. Formally, the objec"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.704,
+                0.107
+            ],
+            "angle": 0,
+            "content": "tive function is represented by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.509,
+                0.115,
+                0.892,
+                0.175
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\operatorname *{arg  min}_{g,h,f}\\mathbb{E}_{(V_{Q},\\{V_{S}^{l}\\}_{l = 1}^{L})\\sim C_{\\text{train}}}\\left[\\mathcal{L}(\\mathcal{Y},f(h(g(V_{Q}))\\right), \\\\ \\left. g \\left(\\left\\{V _ {S} ^ {l} \\right\\} _ {l = 1} ^ {L}\\right)\\right), \\tag {1} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.184,
+                0.892,
+                0.23
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{V}\\) denotes the set of temporal positions for the ground-truth action segments of the interest in \\(V_{Q}\\). \\(\\mathcal{L}\\) is the loss function."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.238,
+                0.686,
+                0.253
+            ],
+            "angle": 0,
+            "content": "3.1. Overall framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.261,
+                0.892,
+                0.568
+            ],
+            "angle": 0,
+            "content": "Fig. 3 depicts the overall framework of our method. To obtain the initial representations of the input query and support videos, we follow the preprocessing of [39]. The backbone network \\( g \\) [32] generates video representations for each input. Then, for the query video, the proposal subnet \\( h \\) [35] yields potential temporal action instances \\( Q = \\{q_i\\}_{i=1}^{N_Q} \\), called action proposals, with diverse temporal lengths (details are in Sec. S-4 of supplementary materials). \\( N_Q \\) is the number of the proposals, and \\( q_i \\) denotes \\( i \\)th action proposal representation. For every \\( l \\)th support video, we uniformly split each support video into \\( N_S \\) fine-grained temporal snippets by \\( S^{(l)} = \\{s_i^{(l)}\\}_{i=1}^{N_S} \\). Then, CDC-CA aligns \\( Q \\) and \\( \\{S^{(l)}\\}_{l=1}^L \\). Next, in the relational classifier, the action classifier detects the action proposals with the target common action, and yields their temporal offsets to refine the start and end times of the proposals. In training, learning an auxiliary relational module in parallel with the action classifier is beneficial. In testing, the auxiliary relational module is discarded, and the localization head suppresses redundant proposals which is explained in Sec. 4.1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.575,
+                0.608,
+                0.59
+            ],
+            "angle": 0,
+            "content": "3.2.CDC-CA"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.765
+            ],
+            "angle": 0,
+            "content": "The green box of Fig. 3 illustrates three stages of CDC-CA. We first introduce the cross-attention mechanism to individually attend the fine-grained (snippet-level) support video features by the query's context (QtoS Context-CA). Next, we explain the cross-attention to enhance the temporal dynamics of each support video from all the support videos in different temporal granularity (Dynamics-CA). Then, we present the way to attend the features of query proposals via the cross-attention with all the resulting support features (StoQ Context-CA). These enhanced features serve as crucial inputs to the following relational classifier."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "QtoS Context-CA: We first enhance the support features in consideration of the context of the query video (i.e. query to support, dubbed QtoS). To this end, we develop a cross-attention mechanism. When we suppose a vanilla approach such as Fig. 1(a), the attention weight is obtained at once based on the relationship between the query proposals and all the support videos. In this case, a support video, which is relatively less relevant to the query video than the other support videos, gets tiny attention weights and cannot"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10216"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.088,
+                0.895,
+                0.21
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.219,
+                0.895,
+                0.3
+            ],
+            "angle": 0,
+            "content": "Figure 3: An overview of the proposed method. \\(l\\)th support video, \\(X_{S}^{(l)}\\), is attended by query proposals \\(X_{Q}\\), individually. Next, the temporal dynamics of all \\(L\\) the support videos are propagated to each support video. The resulting support videos \\(\\{\\hat{Y}_S^{(l)}\\}_{l=1}^L\\) give attention to the query proposals. \\(\\hat{X}_{Q}\\) is the resulting attended query proposals. Then, the relational classifier predicts the commonality scores of the proposals for the action of support videos, and the localization head finalizes action localization removing redundant proposals."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.312,
+                0.896,
+                0.377
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.191,
+                0.378,
+                0.21,
+                0.389
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.452,
+                0.378,
+                0.472,
+                0.389
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.761,
+                0.378,
+                0.78,
+                0.389
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.407,
+                0.893,
+                0.455
+            ],
+            "angle": 0,
+            "content": "Figure 4: Cross-attention (best view in color). (a) QtoS Context-CA for \\( l \\)th support video by the query proposals. (b) Dynamics-CA for \\( l \\)th support video by \\( L \\) support videos in different temporal granularity. (c) StoQ Context-CA of all the query proposals by the attended support videos, at once."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.48,
+                0.469,
+                0.525
+            ],
+            "angle": 0,
+            "content": "represent its action information in the context of the query video. As depicted in Fig. 4(a), to utilize the query video's context faithfully, we individually attend the support videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.526,
+                0.47,
+                0.686
+            ],
+            "angle": 0,
+            "content": "In specific, for \\(l\\)th support video, we first encode the backbone features of the query proposals \\(Q\\) to \\(X_{Q} \\in \\mathbb{R}^{d \\times N_{Q}}\\) and the support snippets \\(S^{(l)}\\) to \\(X_{S}^{(l)} \\in \\mathbb{R}^{d \\times N_{S}}\\), with a linear layer. The columns of \\(X_{Q}\\) and \\(X_{S}^{(l)}\\) represent the encoded \\(d\\)-dimensional features of the query proposal and support snippets, respectively. After that, we compute the cross-correlation of \\(X_{Q}\\) and \\(X_{S}^{(l)}\\) to measure their relevance. To reduce the gap of the heterogeneity between the query and support videos, we use a learnable weight matrix \\(W_{Q \\to S} \\in \\mathbb{R}^{d \\times d}\\) and compute the cross-correlation as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.186,
+                0.698,
+                0.469,
+                0.72
+            ],
+            "angle": 0,
+            "content": "\\[\n\\Lambda_ {Q \\rightarrow S} ^ {(l)} = X _ {Q} ^ {T} W _ {Q \\rightarrow S} X _ {S} ^ {(l)} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.733,
+                0.469,
+                0.801
+            ],
+            "angle": 0,
+            "content": "where \\(\\Lambda_{Q\\to S}^{(l)}\\in \\mathbb{R}^{N_Q\\times N_S}\\). Note that each column of \\(X_{Q}\\) and \\(X_{S}^{(l)}\\) are \\(l_{2}\\)-normalized before the cross-correlation computation, and the learnable weight \\(W_{Q\\rightarrow S}\\) and the linear layer are shared across all \\(l\\) i.e. all the support videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.802,
+                0.47,
+                0.904
+            ],
+            "angle": 0,
+            "content": "In the cross-correlation matrix, a high correlation coefficient means that the corresponding proposal and snippet features are highly relevant. Accordingly, \\(i\\)th row of \\(\\Lambda_{Q\\to S}^{(l)}\\) corresponds to the relevance of \\(i\\)th query proposal to the \\(N_{S}\\) support snippets. Then, from row-wise soft-max of \\(\\Lambda_{Q\\to S}^{(l)}\\), we can obtain cross-attention weights \\(A_{Q\\to S}^{(l)}\\) where each"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.48,
+                0.892,
+                0.51
+            ],
+            "angle": 0,
+            "content": "row represents the relative relevance of a query proposal to the support snippets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.51,
+                0.893,
+                0.602
+            ],
+            "angle": 0,
+            "content": "The attention-weighted proposal features are summed to the corresponding support snippet feature. This is to ensure that the meaningful action information of the support video is well-preserved while applying the cross-attention. Formally, the attended support snippet features \\(\\tilde{X}_S^{(l)}\\) are obtained by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.606,
+                0.601,
+                0.892,
+                0.622
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {X} _ {S} ^ {(l)} = X _ {Q} A _ {Q \\rightarrow S} ^ {(l)} + X _ {S} ^ {(l)}. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.624,
+                0.894,
+                0.729
+            ],
+            "angle": 0,
+            "content": "Note that, through the attention weights, the query proposal injects its context to the support snippets proportionally to their relevance i.e. more to the highly relevant support snippets. With this, the support snippet features are enhanced to better guide the information about the target action to the query proposals in the later stage of attending queries of Fig. 4(a)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.73,
+                0.894,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Dynamics-CA: Temporal dynamics is important to understand the actions, which is well-represented in consecutive snippets (tuple) rather than a single snippet. Hence, as illustrated in Fig. 4(b), to extract temporal dynamics of the attended support video features, we apply 1-dimensional temporal convolution on each \\(\\tilde{X}_S^{(l)}\\) as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.632,
+                0.828,
+                0.892,
+                0.849
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {X} _ {S ^ {\\prime}} ^ {(l)} = \\tilde {X} _ {S} ^ {(l)} \\odot \\mathbf {w} _ {k} \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.854,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where \\(\\odot\\) denotes the convolution operation along temporal axis, \\(\\mathbf{w}_k\\) denotes the weight of 1D-conv layer. \\(k\\) is the kernel size of \\(\\mathbf{w}_k\\) (\\(k < L\\)). The resulting \\(\\tilde{X}_{S'}^{(l)}\\) is in different"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10217"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.09,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "temporal granularity with \\(\\tilde{X}_S^{(l)}\\), and its components are the temporally-summaramized features for the tuples of \\(k\\) neighboring snippets, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.138,
+                0.47,
+                0.324
+            ],
+            "angle": 0,
+            "content": "Next, we propagate the temporal dynamics from tuple-level features to the fine-grained snippet features. Here, we also consider the compatible use of \\( L \\) support videos. In other words, as the support videos represent a common action, the support segment features should be closely located in a latent feature space. However, since the QtoS Context-CA are applied individually for each support video, the heterogeneity may be overly increased, which can degenerate the effect of attention on query videos in the following last stage. To compensate this, we attend the snippet-level features of \\( l \\)th support video \\( \\tilde{X}_S^{(l)} \\) from the tuple-level features of all \\( L \\) support videos, i.e., \\( \\tilde{X}_{S'} = \\{\\tilde{X}_{S'}^{(l)}\\}_{l=1}^L \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.324,
+                0.469,
+                0.357
+            ],
+            "angle": 0,
+            "content": "Concretely, like eq. (2), we first compute cross-correlation between \\(\\tilde{X}_{S'}\\) and \\(\\tilde{X}_S^{(l)}\\) by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.367,
+                0.469,
+                0.388
+            ],
+            "angle": 0,
+            "content": "\\[\n\\Lambda_ {S ^ {\\prime} \\rightarrow S} ^ {(l)} = \\tilde {X} _ {S ^ {\\prime}} ^ {T} W _ {S ^ {\\prime} \\rightarrow S} \\tilde {X} _ {S} ^ {(l)} \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.414,
+                0.469,
+                0.448
+            ],
+            "angle": 0,
+            "content": "Then, the temporal dynamics-attended support video feature \\(\\tilde{Y}_S^{(l)}\\) is generated by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.179,
+                0.457,
+                0.469,
+                0.478
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {Y} _ {S} ^ {(l)} = \\tilde {X} _ {S ^ {\\prime}} A _ {S ^ {\\prime} \\rightarrow S} ^ {(l)} + \\tilde {X} _ {S} ^ {\\prime (l)}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.489,
+                0.452,
+                0.508
+            ],
+            "angle": 0,
+            "content": "where \\(A_{S' \\to S}^{(l)}\\) is the cross-attention weight from \\(\\Lambda_{S' \\to S}^{(l)}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.508,
+                0.469,
+                0.66
+            ],
+            "angle": 0,
+            "content": "StoQ Context-CA: In this stage, we attend query videos with the support videos using the cross-attention. This support-to-query context attention is called StoQ Context-CA described in Fig. 4(c). To mine the richer information for target action from all the support videos, we attend query proposal features using the entire stabilized support segment features \\(\\tilde{Y}_S = \\{\\tilde{Y}_S^{(1)},\\tilde{Y}_S^{(2)},\\dots ,\\tilde{Y}_S^{(L)}\\} \\in \\mathbb{R}^{d\\times LN_S}\\). Similar to attending support features, we exploit the cross-attention to obtain the attended query proposals \\(\\tilde{X}_Q\\) with a learnable weight matrix \\(W_{S\\rightarrow Q}\\in \\mathbb{R}^{d\\times d}\\) by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.194,
+                0.671,
+                0.469,
+                0.69
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {X} _ {Q} = \\tilde {Y} _ {S} A _ {S \\rightarrow Q} + X _ {Q} \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.701,
+                0.469,
+                0.778
+            ],
+            "angle": 0,
+            "content": "where \\(A_{S\\rightarrow Q}\\) is attention weight computed by row-wise soft-max of cross-correlation, \\(\\Lambda_{S\\rightarrow Q} = \\tilde{Y}_S^T W_{S\\rightarrow Q}X_Q\\). From this cross-attention, the query proposals, which have high relevance to crucial support segments, better delineate the target action."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.787,
+                0.264,
+                0.802
+            ],
+            "angle": 0,
+            "content": "3.3. Relational classifier"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Up to this point, we described how CDC-CA generates better representations of query proposals and support videos. Here, we explain the way to obtain the final decision from the attended representations. Fig. 5 depicts our relational classifier including an action classifier and an auxiliary relational module. The auxiliary module facilitates"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.089,
+                0.897,
+                0.176
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.192,
+                0.892,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Figure 5: Relational classifier consists of auxiliary relational module and action classifier."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.249,
+                0.892,
+                0.31
+            ],
+            "angle": 0,
+            "content": "learning how to understand the relationship between query proposals and a target action with pseudo action class cues. As the auxiliary relational module is discarded in the deployed network, no action class label is required in testing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.31,
+                0.892,
+                0.4
+            ],
+            "angle": 0,
+            "content": "Auxiliary relational module: In episodic few-shot learning, an auxiliary classifier can be co-trained to categorize an input into one of the ground-truth classes rather than the target classes of an episode. This is beneficial for feature extractors to prevent overfitting, stabilize the training, and boost the performance [24, 11]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.401,
+                0.893,
+                0.747
+            ],
+            "angle": 0,
+            "content": "However, since the ground-truth action classes are not available in our task, we utilize pseudo action classes. As in Fig. 5, we develop the auxiliary relational module which takes as an input the concatenation of the attended query proposal (green), support prototype (purple), and a pseudoclass identifier (white). The support prototype is the average of all the attended support segments. The pseudo-class identifier is a multi-hot vector with 1 for the pseudo action classes present in the support videos and 0 otherwise. As action class annotations are unavailable, the pseudo action classes are simply obtained by \\( k \\)-means clustering of the pre-trained backbone features extracted from all the ground-truth positive action instances in the training set. Then, these pseudo action classes can provide the cue to capture the commonality of the support videos with the same action across episodes. Hence, joint training with the auxiliary module assists the action classifier to learn to more correctly find the common actions in the query video without getting distracted by the non-target actions. The auxiliary relational module predicts whether the query proposal and the prototype are similar or not. Note that this module is only needed for training and discarded in the testing phase as the training and testing classes are mutually exclusive."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.748,
+                0.892,
+                0.838
+            ],
+            "angle": 0,
+            "content": "Action classifier: The action classifier consists of two parallel linear layers. Taking only the query proposal features \\(\\tilde{X}_Q\\) as inputs, the action classifier computes two outputs. The first is soft-max activated and decides if a query proposal contains target action or not. The second regresses the temporal offsets from the corresponding ground-truth."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.647,
+                0.862
+            ],
+            "angle": 0,
+            "content": "3.4. Loss functions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To optimize the entire network, as in [39], we use loss terms for both support-agnostic and -conditioned parts. In"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10218"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.468,
+                0.152
+            ],
+            "angle": 0,
+            "content": "the support-agnostic part, the binary cross-entropy loss \\(\\mathcal{L}_{\\mathrm{cls}}^{\\mathrm{ag}}\\) predicts if the proposal contains any activity or not, and the smooth \\(l_{1}\\) regression loss \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{ag}}\\) optimizes the relative displacement between proposals and ground-truths."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.153,
+                0.473,
+                0.395
+            ],
+            "angle": 0,
+            "content": "In the auxiliary relational module of the support-conditioned part, we simply use the binary cross-entropy loss \\(\\mathcal{L}_{\\mathrm{aux}}\\) to predict if the proposal and support videos are similar or not. In the action classifier of the support-conditioned part, similar to the support-agnostic part, the classification loss \\(\\mathcal{L}_{\\mathrm{cls}}^{\\mathrm{co}}\\) predicts if the proposal includes the same common action of support videos, and the regression loss \\(\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{co}}\\) optimizes the relative displacement between the proposals and the ground-truths. Also, we design a pairwise ranking loss to add constraints to the action classifier. Considering a pair of proposals \\(q_{i}\\) and \\(q_{j}\\), where at least one of them is a positive query proposal, we let the proposal with the larger IoU (intersection over union) for the ground-truth action instance have a higher soft-max score for the action class. Formally, the pairwise ranking loss \\(\\mathcal{L}_{\\mathrm{rank}}\\) is represented by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.133,
+                0.407,
+                0.47,
+                0.445
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {r a n k}} = \\frac {1}{N _ {\\text {p a i r}}} \\sum_ {(i, j)} \\left(\\Delta \\mathrm {I o U} _ {i j} - \\Delta p _ {i j} ^ {\\text {a c t i o n}}\\right) ^ {2} \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.458,
+                0.47,
+                0.593
+            ],
+            "angle": 0,
+            "content": "where \\(N_{\\mathrm{pair}}\\) is the number of considered proposal pairs. \\(\\Delta \\mathrm{IoU}_{ij}\\) is the difference between IoUs of \\(q_{i}\\) and \\(q_{j}\\) with their corresponding ground-truths, and \\(\\Delta p_{ij}^{\\mathrm{action}}\\) is the difference of soft-max predictions for the proposals on the action class from the action classifier. Note that to relax the relationship between IoU and soft-max prediction, we give temperature to the soft-max predictions in \\(\\mathcal{L}_{\\mathrm{rank}}\\). Finally, total loss (more details in Sec. S-1 of supplementary materials) is given by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.097,
+                0.607,
+                0.47,
+                0.626
+            ],
+            "angle": 0,
+            "content": "\\[\nL = L _ {\\mathrm {c l s}} ^ {\\mathrm {a g}} + L _ {\\mathrm {r e g}} ^ {\\mathrm {a g}} + L _ {\\mathrm {c l s}} ^ {\\mathrm {c o}} + L _ {\\mathrm {r e g}} ^ {\\mathrm {c o}} + L _ {\\mathrm {a u x}} + \\lambda L _ {\\mathrm {r a n k}}. \\tag {9}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.639,
+                0.21,
+                0.656
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.665,
+                0.296,
+                0.68
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.468,
+                0.853
+            ],
+            "angle": 0,
+            "content": "To evaluate few-shot common action localization, we use the revised versions [3, 39] of ActivityNet1.3 [1] and THU-MOS14 [9]. In the revised, there are two cases depending on queries: single-instance and multi-instance. We address 1- or 5-shot settings in both cases. For meta-learning strategy, the entire action classes of each dataset are split into \\(80\\%\\) for training, \\(10\\%\\) for validation, and \\(10\\%\\) for testing. For a fair comparison, we follow the data configuration of [39], which will be described in the following paragraphs. Further details are in Sec. S-4 of supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Common single-instance: For both datasets, videos with multiple actions are divided into independent videos where each video contains just one action instance and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "background. Then, videos longer than 768 frames are discarded. If a video is selected as a support video, its foreground action instance is only used as the support input. For ActivityNet1.3, there are 10,035 and 2,483 videos for training and validation+testing, each. The average video length is 89.0s. For THUMOS14, there are 3,580 and 775 training and validation+testing videos, respectively. The average length is 11.4s."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.213,
+                0.893,
+                0.379
+            ],
+            "angle": 0,
+            "content": "Common multi-instance: In real-world scenarios, the lengths of query videos are usually not constrained, and the query videos may contain multiple action instances. Hence, we exploit the original videos of ActivityNet1.3 and THUMOS14 without any processing for query videos. Support videos are still trimmed ones. For ActivityNet1.3, the numbers of videos are 6,747 and 1,545 for training and validation+testing, respectively. The average video length is 148.2s. For THUMOS14, there are 1,664 training videos and 323 validation+testing videos. The average video length is 230.6s."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.38,
+                0.893,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Inference: In testing, the backbone-generated query proposals are refined by non-maximum suppression (NMS) with a threshold 0.7. Also, following [39], if the query video is longer than 768 frames, we generate the multi-scale segments [30]. We slide windows with sizes of 512 and 768 frames along the temporal axis with \\(75\\%\\) overlap. The generated proposals of the windows go through the NMS to remove redundant proposals. Then, the selected proposals are fed into our CDC-CA and relational classifier. Finally, we perform NMS (threshold 0.3) for the regressed proposals based on the outputs of the relational classifier to remove redundant ones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.562,
+                0.892,
+                0.654
+            ],
+            "angle": 0,
+            "content": "Evaluation: We measure the temporal action localization performance with mean Average Precision (mAP). A prediction is correct when it has the correct foreground/background classification and has IoU with its ground-truth larger than a threshold. The threshold is set to 0.5 unless specified."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.665,
+                0.725,
+                0.681
+            ],
+            "angle": 0,
+            "content": "4.2. Comparative assessment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.748
+            ],
+            "angle": 0,
+            "content": "We report the performance of compared methods from the literature. Due to the variance of \\( k \\)-means clustering of the pseudo label generation, we report the average of three runs for our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For AcitivityNet1.3, the left of Table 1 demonstrates the comparative results on both common single- and multi-instance cases when \\( L = 1 \\) or 5. [3, 39, 22, 7] were developed for the common temporal action localization (our task) in videos, and [8] was for the common object detection in images. Compared to them, our method shows notably higher performance for all the settings ([3] was designed to use one support video). Specifically, in the single-instance case, we outperform those methods by at least \\( 1.4\\% \\) and \\( 5.1\\% \\) in the 1- and 5-shot settings, respec"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10219"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.268,
+                0.089,
+                0.701,
+                0.104
+            ],
+            "angle": 0,
+            "content": "Table 1: Comparison with state-of-the-arts in terms of mAP@0.5."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.116,
+                0.894,
+                0.284
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">ActivityNet1.3</td><td colspan=\"4\">THUMOS14</td></tr><tr><td colspan=\"2\">Single-instance</td><td colspan=\"2\">Multi-instance</td><td colspan=\"2\">Single-instance</td><td colspan=\"2\">Multi-instance</td></tr><tr><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>Feng et al. [3]</td><td>43.5</td><td>n/a</td><td>31.4</td><td>n/a</td><td>34.1</td><td>n/a</td><td>4.3</td><td>n/a</td></tr><tr><td>Hu et al. [8]</td><td>41.0</td><td>45.4</td><td>29.6</td><td>38.9</td><td>-</td><td>42.2</td><td>-</td><td>6.8</td></tr><tr><td>Yang et al. [39]</td><td>53.1</td><td>56.5</td><td>42.1</td><td>43.9</td><td>48.7</td><td>51.9</td><td>7.5</td><td>8.6</td></tr><tr><td>Yang et al. [40]</td><td>57.5</td><td>60.6</td><td>47.8</td><td>48.7</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Nag et al. [22]</td><td>55.1</td><td>63.0</td><td>44.1</td><td>48.2</td><td>49.2</td><td>54.3</td><td>7.3</td><td>10.4</td></tr><tr><td>Hsieh et al. [7]</td><td>60.7</td><td>61.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>62.1 ± 1.0</td><td>66.3 ± 1.2</td><td>48.2 ± 1.2</td><td>53.5 ± 1.1</td><td>53.8 ± 1.2</td><td>59.2 ± 1.3</td><td>9.8 ± 0.4</td><td>15.7 ± 0.5</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.308,
+                0.47,
+                0.339
+            ],
+            "angle": 0,
+            "content": "Table 2: Ablation study on CDC-CA for the single-instance setting."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.35,
+                0.472,
+                0.473
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">QtoS Context-CA</td><td rowspan=\"2\">Dynamics-CA</td><td colspan=\"2\">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>C-0</td><td></td><td></td><td>52.0</td><td>54.3</td></tr><tr><td>C-1</td><td>✓</td><td></td><td>61.5</td><td>65.4</td></tr><tr><td>C-2</td><td></td><td>✓</td><td>61.3</td><td>65.1</td></tr><tr><td>C-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.49,
+                0.47,
+                0.778
+            ],
+            "angle": 0,
+            "content": "tively. In the multi-instance, the margins are at least \\(4.1\\%\\) and \\(5.3\\%\\) for 1- and 5-shot, each. Note that [40] was developed for object-level common temporal action localization. Although object-level localization is more challenging, it requires further information to learn their model such as the coordinates of foreground object bounding boxes. Hence, they have advantages in the frame-level localization task. Even so, our method yields better results than [40] in all the settings. Also, in the 5-shot setting, the score margins to the existing works are larger than those of 1-shot in both single- and multi-instance. This means that enhancing the temporal dynamics of a support video by the entire support video in Dynamics-CA and aligning individually each support video to the query video's context in QtoS Context-CA are helpful to mine the knowledge for a common action from multiple support videos. Unlike ActivityNet1.3, THUMOS14 includes shorter action instances which make correct localization more difficult. Nevertheless, we outperform the compared methods over all the settings."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.789,
+                0.27,
+                0.805
+            ],
+            "angle": 0,
+            "content": "4.3. Component analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.81,
+                0.469,
+                0.84
+            ],
+            "angle": 0,
+            "content": "We analyze our method on ActivitNet1.3. More studies are in supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.841,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Impact of cross-attention: First, to see the component-wise impact of our cross-attention, we ablate QtoS Context-CA and Dynamics-CA in Table 2, we can see that without any of them (C-0), the performance is severely degraded."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.308,
+                0.892,
+                0.34
+            ],
+            "angle": 0,
+            "content": "Table 3: Ablation study on the relational classifier on the single-instance setting."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.507,
+                0.344,
+                0.885,
+                0.472
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Lrank</td><td rowspan=\"2\">Auxiliary rel. module</td><td colspan=\"2\">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>R-0</td><td></td><td></td><td>61.8</td><td>65.8</td></tr><tr><td>R-1</td><td>✓</td><td></td><td>61.9</td><td>66.0</td></tr><tr><td>R-2</td><td></td><td>✓</td><td>61.9</td><td>66.1</td></tr><tr><td>R-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.485,
+                0.892,
+                0.532
+            ],
+            "angle": 0,
+            "content": "Table 4: Analysis of the individual cross-attention strategy on QtoS Context-CA and Dynamics-CA, comparing with the aggregated cross-attention on the 5-shot setting."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.501,
+                0.542,
+                0.892,
+                0.629
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td></td><td>Single-inst.</td><td>Multi-inst.</td></tr><tr><td rowspan=\"2\">QtoS Context-CA</td><td>Aggregated</td><td>65.7</td><td>52.8</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr><tr><td rowspan=\"2\">Dynamics-CA</td><td>Aggregated</td><td>65.8</td><td>52.9</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.892,
+                0.703
+            ],
+            "angle": 0,
+            "content": "Also, when comparing C-1 and C-2, both cross-attentions show meaningful improvements on C-0, but QtoS Context-CA is slightly more important. Using both shows the best performance in our final method C-3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "We can also consider changing the order of QtoS Context-CA and Dynamics-CA. In this case, we observed that the performance is slightly lowered (62.1%→61.7% in 1-shot, 66.3%→65.6% in 5-shot). Hence, the temporal dynamics extracted under the query video's context is more useful in our task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Further, we evaluate the efficacy of our cross-attention, comparing it with other cross-attention mechanisms. To this end, we compare our CDC-CA itself (corresponding to R-0 in Table 3) to the progressive cross-attention [39], and the multi-head cross-attention with fine-tuned (50-100 iterations) prototype [22], light-weight transformer-based booster [7]. For a fair comparison, the pairwise ranking"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10220"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.089,
+                0.472,
+                0.136
+            ],
+            "angle": 0,
+            "content": "Table 5: Cosine similarity between support videos and between support and query videos in embedding space before/after passing through Dynamics-CA."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.143,
+                0.472,
+                0.212
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Support-Support</td><td colspan=\"3\">Support-Query</td></tr><tr><td>Pos. query</td><td>Neg. query</td><td>Δ</td></tr><tr><td>Cos. Sim. (before)</td><td>0.49</td><td>0.41</td><td>0.38</td><td>0.05</td></tr><tr><td>Cos. Sim. (after)</td><td>0.61</td><td>0.43</td><td>0.34</td><td>0.13</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.23,
+                0.47,
+                0.321
+            ],
+            "angle": 0,
+            "content": "loss and auxiliary relational module are not used in R-0. CDC-CA yields mAP gain of at least \\(+1.1\\%\\) and \\(+2.8\\%\\) in 1-shot (60.7% [7] in Table 1 vs 61.8% R-0) and 5-shot (63.0% [22] in Table 1 vs 65.8% R-0), each. Hence, we conclude our cross-attention more effectively enhances the query and support videos in this task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.471,
+                0.534
+            ],
+            "angle": 0,
+            "content": "Individual vs aggregated: To study the effectiveness of the individual cross-attention on QtoS Context-CA and Dynamics-CA for multiple support videos, we compare our individual cross-attention approach with the aggregated cross-attention ('Aggregated') in Table 4. In 'Aggregated' of QtoS Context-CA, we concatenate all the support snippets of the entire support videos, and simultaneously attend them via query proposals. We see that 'Aggregated' degrades the localization performance. This result shows the benefit of individual cross-attention in QtoS Context-CA. Also, in Dynamics-CA, we identified a similar tendency. Accordingly, mining the commonality of temporal dynamics in multiple support videos is more beneficial when it is propagated to each support video, individually."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.537,
+                0.47,
+                0.749
+            ],
+            "angle": 0,
+            "content": "Compatibility in support videos: In Dynamics-CA, a snippet-level support video feature is attended by tuple-level features from all the support videos to promote compatibility among multiple support videos. To identify this, at two points (before or after passing through Dynamics-CA), we measure the cosine similarities 1) between two support videos, and 2) between a support video and a (positive or negative) query proposal. Table 5 reports the average of cosine similarities. The increased support-support similarity \\((0.49\\% \\rightarrow 0.61\\%)\\) indicates that the support videos get closer to each other in the embedding space. Also, we can see that the discriminative ability is improved as seen by the increased difference \\((\\Delta)\\) in the similarity of the support to positive and negative query proposals."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Further, to more clearly show the effect of individual-to-all cross-attention in Dynamics-CA, we also identified individual-to-individual Dynamacmis-CA where the snippet-level features are attended by the corresponding temporally-convolutioned features for each support video. Comparison of ours with this variant is \\(66.3\\%\\) vs \\(65.9\\%\\) in 5-shot single instance, and \\(53.5\\%\\) vs \\(53.2\\%\\) in 5-shot multiple instances. Hence, we can see that our approach (individual-to-all) is more beneficial for the collaborative use of a few support videos."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.089,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "Table 6: Effect of the multi-hot pseudo action indicator by varying the number of pseudo action classes or removing it."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.123,
+                0.875,
+                0.228
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td></td><td>w/o Indicator</td><td colspan=\"4\">k</td></tr><tr><td></td><td></td><td></td><td>80</td><td>160</td><td>240</td><td>320</td></tr><tr><td rowspan=\"2\">Single Inst.</td><td>1-shot</td><td>61.9</td><td>61.9</td><td>62.1</td><td>62.1</td><td>62.3</td></tr><tr><td>5-shot</td><td>66.0</td><td>66.2</td><td>66.3</td><td>66.5</td><td>66.4</td></tr><tr><td rowspan=\"2\">Multiple Inst.</td><td>1-shot</td><td>47.8</td><td>48.0</td><td>48.2</td><td>48.4</td><td>48.4</td></tr><tr><td>5-shot</td><td>53.3</td><td>53.4</td><td>53.5</td><td>53.4</td><td>53.5</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.244,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Relational classifier: Here, we verify the auxiliary relational module and the pairwise ranking loss by ablating each. To show their effect, we compare each ablated version to the baseline R-0 without any of them in Table 3. The pairwise ranking loss gives performance improvement by \\(0.1\\%\\) and \\(0.2\\%\\) for 1- and 5-shot, respectively (R-1). Hence, this loss lets the proposals with larger IoUs to ground-truths get higher action scores. From the result of R-2, we also see that learning the auxiliary module in parallel to the action classifier is useful to boost performance in both settings. And, combining both works the best (R-3)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.411,
+                0.893,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Adequacy to no. of pseudo action label: In the auxiliary relational module, we use the multi-hot indicator as the pseudo-action cue in consideration that no true label is available. To see its effectiveness, in Table 6, we report the mAP scores by varying the number of pseudo action classes \\((k)\\) and w/o the indicator as well. In the single instance case, compared to the R-1 of Table 3, the auxiliary relational module did not show an effect without the multi-hot indicator. Also, for all other settings, as \\(k\\) gets larger, the multi-hot indicator yields larger performance gains overall. Though the support videos represent a common action, there is diversity in background or action details. Hence, it is beneficial to distinguish the support videos with more pseudo labels. Considering the computational cost, we set \\(k\\) to 160 as the default value."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.655,
+                0.628,
+                0.67
+            ],
+            "angle": 0,
+            "content": "5. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For few-shot common action localization, we proposed the three-stage cross-attention (CDC-CA) and the relational classifier. CDC-CA increases the effect of the cross-attention by individually attending each support video, enhancing the temporal dynamics of each and the compatibility of multiple support videos, and then attending the query video via all the enhanced support videos. In the relational classifier, we designed the pairwise ranking loss which makes more precise action localization of the action classifier. Learned in parallel with the action classifier, the auxiliary relational module with the pseudo-class labels prevents the network from overfitting to each training episode. This module is discarded in testing. Extensive experiments analyzed and validated each component. Finally, we achieved SOTA on ActivityNet1.3 and THUMOS14."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10221"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.175,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.116,
+                0.47,
+                0.169
+            ],
+            "angle": 0,
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+# Few-Shot Common Action Localization via Cross-Attentional Fusion of Context and Temporal Dynamics
+
+Juntae Lee<sup>1</sup>, Mihir Jain<sup>* *</sup> and Sungrack Yun<sup>1</sup>  
+<sup>1</sup>Qualcomm AI Research†
+
+{juntlee, sungrack}@qti=qualcomm.com
+
+# Abstract
+
+The goal of this paper is to localize action instances in a long untrimmed query video using just meager trimmed support videos representing a common action whose class information is not given. In this task, it is crucial to mine reliable temporal cues representing a common action from handful support videos. In our work, we develop an attention mechanism using cross-correlation. Based on this cross-attention, we first transform the support videos into query video's context to emphasize query-relevant important frames, and suppress less relevant ones. Next, we summarize sub-sequences of support video frames to represent temporal dynamics in coarse temporal granularity, which is then propagated to the fine-grained support video features through the cross-attention. In each case, the cross-attentions are applied to each support video in the individual-to-all strategy to balance heterogeneity and compatibility of the support videos. In contrast, the candidate instances in the query video are lastly attended by the resulting support video features, at once. In addition, we also develop a relational classifier head based on the query and support video representations. We show the effectiveness of our work with the state-of-the-art (SOTA) performance in benchmark datasets (ActivityNet1.3 and THUMOS14), and analyze each component extensively.
+
+# 1. Introduction
+
+Temporal action localization [2, 4, 33, 23, 31, 18, 15, 16, 20] have been widely studied in fully or weakly-supervised manner. However, they require collecting massive videos labeled by action classes, and also only detect the action classes observed in training. Whereas, we aim to temporally localize action instances in a long untrimmed query
+
+![](images/fdb41024b72ec7c3acdc74a7fb4c5f59178909a59a0305c09b8f0b8adf6b3602.jpg)  
+Figure 1: Attention represents the relationship between a moment of query and support videos. (a) Vanilla: attention of a query proposal is obtained simultaneously for the frames of all the support videos. (b) Ours: the attention is computed for the frames of one support video, at a time. While important frames of support video #2 cannot be attended by the related query proposal in (a), they are appropriately transformed to the context of the query in (b).
+
+video based on the few trimmed support videos describing a common action class. As the testing action class is unseen in training and no ground-truth class cue is given, the only cue is the commonality of the few support videos.
+
+In this task, the alignment between query and support videos is important, which can be attained by representing the common action cues of interest from the support videos considering the query video's context. For better alignment, we divide this problem into two points: re-calibrating support video features under query video's context, and enhancing temporal dynamics and compatibility of the recalibrated support video features.
+
+Existing methods [39, 22, 7, 3] have mainly focused on the former point, handling the multiple support videos as a whole. However, as exemplified in Fig. 1, though the support videos represent a common action class, their context (e.g background, camera angle) can be different. Hence,
+
+![](images/77a2d82c13d23e804783190f9f69609b95208e0678cee80b4ba27ed08efc0c94.jpg)  
+Figure 2: Overall process of few-shot common action localization in our work.
+
+when all the support videos are transformed to query context simultaneously, the support videos cluttered by background are overly suppressed although they include useful information (Fig. 1(a)). Whereas, in Fig. 1(b), we can leverage the support videos by attending each individually.
+
+Regarding the latter point, we pay attention to that the temporal dynamics can be enriched from multiple temporal granularities. Hence, we try to collaboratively fuse the support video features in different temporal granularities, considering the compatibility of different support videos as well. Based on the insight for each point, we propose a novel few-shot common action localization method. The overall process is briefly outlined in Fig. 2. First, the long untrimmed query video is split to query proposals, and they are aligned with the support videos through our three-stage cross-attention. Then, the proposals representing the common action class are detected with temporal location refinement.
+
+For the query-support alignment, we develop a three-stage cross-attention (CA) mechanism. In each stage, cross-correlation between two different features (e.g. support and query, supports in different temporal granularity) is exploited with a learnable weight matrix. The 1st stage, query-to-support Context-CA transforms the support videos into the query video's context by cross-correlating them with the query proposal features. Each support video is individually attended to emphasize its most informative features. In 2nd stage of Dynamics-CA, low-temporal granularity features summarize the tuples of snippets of each support video, and they attend the fine-grained snippet-level features. Here, each support video is attended by the entire support videos in low-temporal granularity. It helps the complementary use of all the individually attended support video features as well as enhancing temporal dynamics. Finally, in the last stage (support-to-query Context-CA), the query video features are simultaneously attended with all the resulting support video features. We call this CA process (Context, Dynamics, Context-CAs) CDC-CA.
+
+Also, for the commonality prediction and refinement, we design a relational classifier with an action classifier and an auxiliary relational module. To prevent overfitting and boost performance, the latter matches the support and query video features using pseudo-label cues as we avoid the use of class labels. In testing, this module is not used.
+
+Major contributions: (i) We suggest a three-stage CA to
+
+enhance the representation of query video by support videos and vice versa. (ii) We attend each support video individually to increase its discriminative ability in the first two stages. (iii) We develop a relational classifier including an action classifier and an auxiliary relational module. The latter is only needed during training. (iv) Extensive experimental analyses are done on two benchmark datasets, where we achieve SOTA performance.
+
+# 2. Related work
+
+Temporal action localization The goal is to predict the temporal boundary and the label of action instances in untrimmed videos. In the fully-supervised case where temporal annotations are given during training, several works tried to obtain better temporal proposals [5, 4, 19], while others improved temporal searching [41, 42] or classifiers [29]. R-C3D [35] proposed an end-to-end trainable activity detector based on Faster-RCNN [27]. GNNs [45, 37] are recently used to capture the temporal relationship among proposals/snippets. In the weakly-supervised setting, as only video-level annotations are given, most methods have aimed to obtain discriminative snippet-level activations and conduct post-processing to localize action instances. A co-activity similarity loss to enforce the feature similarity for video pairs with a common class was introduced in [25], and videos are segmented into interpretable fragments in [10]. Some works focused on distinguishing action and near-action/background snippets exploiting variational auto-encoder [28], entropy maximization [20], and an additional class-agnostic model [21]. Also, to better localize difficult snippets, multi-modal (audio-visual) fusion [14] or a contrastive loss with easy foreground/background snippets [43] are devised. Although those fully- and weakly-supervised methods attained large progress in this field, the learned models can only localize activity categories observed in the training dataset.
+
+Few-shot temporal action localization [38] pioneered few-shot action localization, where a few (or only one) positive and several negative labeled videos steer the localization via an end-to-end meta-learning strategy. [36] also temporally localized an action from a few positive labeled and several negative labeled videos. They adopted a region proposal network [27] to produce proposals with flexible boundaries. [44] performed few-shot action localization where video-level annotations are needed. They constructed a multi-scale feature pyramid to directly produce temporal features at variable scales. Unlike those works, few-shot common action localization is less tied up with the need for labels. It localizes the action instances in a long untrimmed query video according to the commonality between the query and support inputs. Assuming a query with only one common action instance, [3] computed the probabilities for starting, ending, inside, or outside of ac
+
+tion instances at every time-step, and decided the window with the highest joint probability as the action instance. Extending to the query videos with multiple action instances of the same action class, [39] generated action proposals, and then classified the proposals and regressed their temporal locations. [22] set a linear classifier itself as a prototype, which needs fine-tuning by support videos for every target action, then the prototype is cross-attended by query proposals using multiple self-attention. [7] boosted [39] adding a single-head transformer where two different affinity matrices are used for the cross-attention weight between query and support videos.
+
+Cross-attention To leverage the relationship between two heterogeneous representations, diverse cross-attention schemes have been devised. Inspired by self-attention (scaled dot-product of key, query, and value), [34] applied the scaled dot-product operation for the concatenation of image and text features for VQA. Also, [12] attended student using key and value of teacher for knowledge propagation. Several works exploited the cross-correlation between the heterogeneous representation as the attention weights for image and sentence matching in visual question answering (VQA) [17, 13], query and prototype matching in prototypical few-shot learning [6], and audio-visual fusion [26]. Here, we exploit the cross-attention to improve the matching between query and support video clips as well as to better utilize multiple support videos in the context of few-shot action localization.
+
+# 3. Method
+
+In this section, we first describe the three-stage cross-attention, CDC-CA, which consists of query-to-support Context, support-to-support (in different temporal granularity) temporal Dynamics, support-to-query Context CAs. Then, we explain the relational classifier.
+
+Problem statement Given an untrimmed query video  $V_{Q}$  and  $L$  trimmed support videos  $\{V_{S}^{1}, V_{S}^{2}, \ldots, V_{S}^{L}\}$ , the goal is to train a network (which consists of backbone  $g$ , proposal-net  $h$ , CDC-CA and relational classifier  $f$ ) to temporally localize action instances in the query video based on the commonality of the support videos whose action classes are same and unseen during training. Note that any ground-truth class cues are not given even during training.
+
+In training, we resort to a meta-learning strategy. Here, the action classes in the training set  $(C_{\mathrm{train}})$  and those of the testing set  $(C_{\mathrm{test}})$  have no overlapping. Also, to simulate the few-shot configuration of support and query videos that will be encountered at the testing phase, we exploit episode-based training. Specifically, in a training iteration, we compose an episode as a set of a query and  $L$  support videos  $\{(V_Q,V_S^1,V_S^2,\dots ,V_S^L)\}$  from a randomly selected class of  $C_{\mathrm{train}}$ . In our work, we set  $L$  to 1 or 5. Formally, the objec
+
+tive function is represented by
+
+$$
+\begin{array}{l} \operatorname *{arg  min}_{g,h,f}\mathbb{E}_{(V_{Q},\{V_{S}^{l}\}_{l = 1}^{L})\sim C_{\text{train}}}\left[\mathcal{L}(\mathcal{Y},f(h(g(V_{Q}))\right), \\ \left. g \left(\left\{V _ {S} ^ {l} \right\} _ {l = 1} ^ {L}\right)\right), \tag {1} \\ \end{array}
+$$
+
+where  $\mathcal{V}$  denotes the set of temporal positions for the ground-truth action segments of the interest in  $V_{Q}$ .  $\mathcal{L}$  is the loss function.
+
+# 3.1. Overall framework
+
+Fig. 3 depicts the overall framework of our method. To obtain the initial representations of the input query and support videos, we follow the preprocessing of [39]. The backbone network  $g$  [32] generates video representations for each input. Then, for the query video, the proposal subnet  $h$  [35] yields potential temporal action instances  $Q = \{q_i\}_{i=1}^{N_Q}$ , called action proposals, with diverse temporal lengths (details are in Sec. S-4 of supplementary materials).  $N_Q$  is the number of the proposals, and  $q_i$  denotes  $i$ th action proposal representation. For every  $l$ th support video, we uniformly split each support video into  $N_S$  fine-grained temporal snippets by  $S^{(l)} = \{s_i^{(l)}\}_{i=1}^{N_S}$ . Then, CDC-CA aligns  $Q$  and  $\{S^{(l)}\}_{l=1}^L$ . Next, in the relational classifier, the action classifier detects the action proposals with the target common action, and yields their temporal offsets to refine the start and end times of the proposals. In training, learning an auxiliary relational module in parallel with the action classifier is beneficial. In testing, the auxiliary relational module is discarded, and the localization head suppresses redundant proposals which is explained in Sec. 4.1.
+
+# 3.2.CDC-CA
+
+The green box of Fig. 3 illustrates three stages of CDC-CA. We first introduce the cross-attention mechanism to individually attend the fine-grained (snippet-level) support video features by the query's context (QtoS Context-CA). Next, we explain the cross-attention to enhance the temporal dynamics of each support video from all the support videos in different temporal granularity (Dynamics-CA). Then, we present the way to attend the features of query proposals via the cross-attention with all the resulting support features (StoQ Context-CA). These enhanced features serve as crucial inputs to the following relational classifier.
+
+QtoS Context-CA: We first enhance the support features in consideration of the context of the query video (i.e. query to support, dubbed QtoS). To this end, we develop a cross-attention mechanism. When we suppose a vanilla approach such as Fig. 1(a), the attention weight is obtained at once based on the relationship between the query proposals and all the support videos. In this case, a support video, which is relatively less relevant to the query video than the other support videos, gets tiny attention weights and cannot
+
+![](images/4693b4af0f1ceb0627ec38575c20d65c5a853ff22e803262e888fc6d88abeff8.jpg)  
+Figure 3: An overview of the proposed method.  $l$ th support video,  $X_{S}^{(l)}$ , is attended by query proposals  $X_{Q}$ , individually. Next, the temporal dynamics of all  $L$  the support videos are propagated to each support video. The resulting support videos  $\{\hat{Y}_S^{(l)}\}_{l=1}^L$  give attention to the query proposals.  $\hat{X}_{Q}$  is the resulting attended query proposals. Then, the relational classifier predicts the commonality scores of the proposals for the action of support videos, and the localization head finalizes action localization removing redundant proposals.
+
+![](images/0e0d6b02c87b620e4acb977a49089d46f139236723c2c61770eab892ee32cb3b.jpg)  
+(a)  
+(b)  
+(c)  
+Figure 4: Cross-attention (best view in color). (a) QtoS Context-CA for  $l$ th support video by the query proposals. (b) Dynamics-CA for  $l$ th support video by  $L$  support videos in different temporal granularity. (c) StoQ Context-CA of all the query proposals by the attended support videos, at once.
+
+represent its action information in the context of the query video. As depicted in Fig. 4(a), to utilize the query video's context faithfully, we individually attend the support videos.
+
+In specific, for  $l$ th support video, we first encode the backbone features of the query proposals  $Q$  to  $X_{Q} \in \mathbb{R}^{d \times N_{Q}}$  and the support snippets  $S^{(l)}$  to  $X_{S}^{(l)} \in \mathbb{R}^{d \times N_{S}}$ , with a linear layer. The columns of  $X_{Q}$  and  $X_{S}^{(l)}$  represent the encoded  $d$ -dimensional features of the query proposal and support snippets, respectively. After that, we compute the cross-correlation of  $X_{Q}$  and  $X_{S}^{(l)}$  to measure their relevance. To reduce the gap of the heterogeneity between the query and support videos, we use a learnable weight matrix  $W_{Q \to S} \in \mathbb{R}^{d \times d}$  and compute the cross-correlation as
+
+$$
+\Lambda_ {Q \rightarrow S} ^ {(l)} = X _ {Q} ^ {T} W _ {Q \rightarrow S} X _ {S} ^ {(l)} \tag {2}
+$$
+
+where  $\Lambda_{Q\to S}^{(l)}\in \mathbb{R}^{N_Q\times N_S}$ . Note that each column of  $X_{Q}$  and  $X_{S}^{(l)}$  are  $l_{2}$ -normalized before the cross-correlation computation, and the learnable weight  $W_{Q\rightarrow S}$  and the linear layer are shared across all  $l$  i.e. all the support videos.
+
+In the cross-correlation matrix, a high correlation coefficient means that the corresponding proposal and snippet features are highly relevant. Accordingly,  $i$ th row of  $\Lambda_{Q\to S}^{(l)}$  corresponds to the relevance of  $i$ th query proposal to the  $N_{S}$  support snippets. Then, from row-wise soft-max of  $\Lambda_{Q\to S}^{(l)}$ , we can obtain cross-attention weights  $A_{Q\to S}^{(l)}$  where each
+
+row represents the relative relevance of a query proposal to the support snippets.
+
+The attention-weighted proposal features are summed to the corresponding support snippet feature. This is to ensure that the meaningful action information of the support video is well-preserved while applying the cross-attention. Formally, the attended support snippet features  $\tilde{X}_S^{(l)}$  are obtained by
+
+$$
+\tilde {X} _ {S} ^ {(l)} = X _ {Q} A _ {Q \rightarrow S} ^ {(l)} + X _ {S} ^ {(l)}. \tag {3}
+$$
+
+Note that, through the attention weights, the query proposal injects its context to the support snippets proportionally to their relevance i.e. more to the highly relevant support snippets. With this, the support snippet features are enhanced to better guide the information about the target action to the query proposals in the later stage of attending queries of Fig. 4(a).
+
+Dynamics-CA: Temporal dynamics is important to understand the actions, which is well-represented in consecutive snippets (tuple) rather than a single snippet. Hence, as illustrated in Fig. 4(b), to extract temporal dynamics of the attended support video features, we apply 1-dimensional temporal convolution on each  $\tilde{X}_S^{(l)}$  as
+
+$$
+\tilde {X} _ {S ^ {\prime}} ^ {(l)} = \tilde {X} _ {S} ^ {(l)} \odot \mathbf {w} _ {k} \tag {4}
+$$
+
+where  $\odot$  denotes the convolution operation along temporal axis,  $\mathbf{w}_k$  denotes the weight of 1D-conv layer.  $k$  is the kernel size of  $\mathbf{w}_k$  ( $k < L$ ). The resulting  $\tilde{X}_{S'}^{(l)}$  is in different
+
+temporal granularity with  $\tilde{X}_S^{(l)}$ , and its components are the temporally-summaramized features for the tuples of  $k$  neighboring snippets, respectively.
+
+Next, we propagate the temporal dynamics from tuple-level features to the fine-grained snippet features. Here, we also consider the compatible use of  $L$  support videos. In other words, as the support videos represent a common action, the support segment features should be closely located in a latent feature space. However, since the QtoS Context-CA are applied individually for each support video, the heterogeneity may be overly increased, which can degenerate the effect of attention on query videos in the following last stage. To compensate this, we attend the snippet-level features of  $l$ th support video  $\tilde{X}_S^{(l)}$  from the tuple-level features of all  $L$  support videos, i.e.,  $\tilde{X}_{S'} = \{\tilde{X}_{S'}^{(l)}\}_{l=1}^L$ .
+
+Concretely, like eq. (2), we first compute cross-correlation between  $\tilde{X}_{S'}$  and  $\tilde{X}_S^{(l)}$  by
+
+$$
+\Lambda_ {S ^ {\prime} \rightarrow S} ^ {(l)} = \tilde {X} _ {S ^ {\prime}} ^ {T} W _ {S ^ {\prime} \rightarrow S} \tilde {X} _ {S} ^ {(l)} \tag {5}
+$$
+
+Then, the temporal dynamics-attended support video feature  $\tilde{Y}_S^{(l)}$  is generated by
+
+$$
+\tilde {Y} _ {S} ^ {(l)} = \tilde {X} _ {S ^ {\prime}} A _ {S ^ {\prime} \rightarrow S} ^ {(l)} + \tilde {X} _ {S} ^ {\prime (l)}, \tag {6}
+$$
+
+where  $A_{S' \to S}^{(l)}$  is the cross-attention weight from  $\Lambda_{S' \to S}^{(l)}$ .
+
+StoQ Context-CA: In this stage, we attend query videos with the support videos using the cross-attention. This support-to-query context attention is called StoQ Context-CA described in Fig. 4(c). To mine the richer information for target action from all the support videos, we attend query proposal features using the entire stabilized support segment features  $\tilde{Y}_S = \{\tilde{Y}_S^{(1)},\tilde{Y}_S^{(2)},\dots ,\tilde{Y}_S^{(L)}\} \in \mathbb{R}^{d\times LN_S}$ . Similar to attending support features, we exploit the cross-attention to obtain the attended query proposals  $\tilde{X}_Q$  with a learnable weight matrix  $W_{S\rightarrow Q}\in \mathbb{R}^{d\times d}$  by
+
+$$
+\tilde {X} _ {Q} = \tilde {Y} _ {S} A _ {S \rightarrow Q} + X _ {Q} \tag {7}
+$$
+
+where  $A_{S\rightarrow Q}$  is attention weight computed by row-wise soft-max of cross-correlation,  $\Lambda_{S\rightarrow Q} = \tilde{Y}_S^T W_{S\rightarrow Q}X_Q$ . From this cross-attention, the query proposals, which have high relevance to crucial support segments, better delineate the target action.
+
+# 3.3. Relational classifier
+
+Up to this point, we described how CDC-CA generates better representations of query proposals and support videos. Here, we explain the way to obtain the final decision from the attended representations. Fig. 5 depicts our relational classifier including an action classifier and an auxiliary relational module. The auxiliary module facilitates
+
+![](images/4162009708de82d1917d37b3123b1b130bc0a0872f81a39ff9b832a1c9b0f715.jpg)  
+Figure 5: Relational classifier consists of auxiliary relational module and action classifier.
+
+learning how to understand the relationship between query proposals and a target action with pseudo action class cues. As the auxiliary relational module is discarded in the deployed network, no action class label is required in testing.
+
+Auxiliary relational module: In episodic few-shot learning, an auxiliary classifier can be co-trained to categorize an input into one of the ground-truth classes rather than the target classes of an episode. This is beneficial for feature extractors to prevent overfitting, stabilize the training, and boost the performance [24, 11].
+
+However, since the ground-truth action classes are not available in our task, we utilize pseudo action classes. As in Fig. 5, we develop the auxiliary relational module which takes as an input the concatenation of the attended query proposal (green), support prototype (purple), and a pseudoclass identifier (white). The support prototype is the average of all the attended support segments. The pseudo-class identifier is a multi-hot vector with 1 for the pseudo action classes present in the support videos and 0 otherwise. As action class annotations are unavailable, the pseudo action classes are simply obtained by  $k$ -means clustering of the pre-trained backbone features extracted from all the ground-truth positive action instances in the training set. Then, these pseudo action classes can provide the cue to capture the commonality of the support videos with the same action across episodes. Hence, joint training with the auxiliary module assists the action classifier to learn to more correctly find the common actions in the query video without getting distracted by the non-target actions. The auxiliary relational module predicts whether the query proposal and the prototype are similar or not. Note that this module is only needed for training and discarded in the testing phase as the training and testing classes are mutually exclusive.
+
+Action classifier: The action classifier consists of two parallel linear layers. Taking only the query proposal features  $\tilde{X}_Q$  as inputs, the action classifier computes two outputs. The first is soft-max activated and decides if a query proposal contains target action or not. The second regresses the temporal offsets from the corresponding ground-truth.
+
+# 3.4. Loss functions
+
+To optimize the entire network, as in [39], we use loss terms for both support-agnostic and -conditioned parts. In
+
+the support-agnostic part, the binary cross-entropy loss  $\mathcal{L}_{\mathrm{cls}}^{\mathrm{ag}}$  predicts if the proposal contains any activity or not, and the smooth  $l_{1}$  regression loss  $\mathcal{L}_{\mathrm{reg}}^{\mathrm{ag}}$  optimizes the relative displacement between proposals and ground-truths.
+
+In the auxiliary relational module of the support-conditioned part, we simply use the binary cross-entropy loss  $\mathcal{L}_{\mathrm{aux}}$  to predict if the proposal and support videos are similar or not. In the action classifier of the support-conditioned part, similar to the support-agnostic part, the classification loss  $\mathcal{L}_{\mathrm{cls}}^{\mathrm{co}}$  predicts if the proposal includes the same common action of support videos, and the regression loss  $\mathcal{L}_{\mathrm{reg}}^{\mathrm{co}}$  optimizes the relative displacement between the proposals and the ground-truths. Also, we design a pairwise ranking loss to add constraints to the action classifier. Considering a pair of proposals  $q_{i}$  and  $q_{j}$ , where at least one of them is a positive query proposal, we let the proposal with the larger IoU (intersection over union) for the ground-truth action instance have a higher soft-max score for the action class. Formally, the pairwise ranking loss  $\mathcal{L}_{\mathrm{rank}}$  is represented by
+
+$$
+\mathcal {L} _ {\text {r a n k}} = \frac {1}{N _ {\text {p a i r}}} \sum_ {(i, j)} \left(\Delta \mathrm {I o U} _ {i j} - \Delta p _ {i j} ^ {\text {a c t i o n}}\right) ^ {2} \tag {8}
+$$
+
+where  $N_{\mathrm{pair}}$  is the number of considered proposal pairs.  $\Delta \mathrm{IoU}_{ij}$  is the difference between IoUs of  $q_{i}$  and  $q_{j}$  with their corresponding ground-truths, and  $\Delta p_{ij}^{\mathrm{action}}$  is the difference of soft-max predictions for the proposals on the action class from the action classifier. Note that to relax the relationship between IoU and soft-max prediction, we give temperature to the soft-max predictions in  $\mathcal{L}_{\mathrm{rank}}$ . Finally, total loss (more details in Sec. S-1 of supplementary materials) is given by
+
+$$
+L = L _ {\mathrm {c l s}} ^ {\mathrm {a g}} + L _ {\mathrm {r e g}} ^ {\mathrm {a g}} + L _ {\mathrm {c l s}} ^ {\mathrm {c o}} + L _ {\mathrm {r e g}} ^ {\mathrm {c o}} + L _ {\mathrm {a u x}} + \lambda L _ {\mathrm {r a n k}}. \tag {9}
+$$
+
+# 4. Experiments
+
+# 4.1. Datasets and evaluation
+
+To evaluate few-shot common action localization, we use the revised versions [3, 39] of ActivityNet1.3 [1] and THU-MOS14 [9]. In the revised, there are two cases depending on queries: single-instance and multi-instance. We address 1- or 5-shot settings in both cases. For meta-learning strategy, the entire action classes of each dataset are split into  $80\%$  for training,  $10\%$  for validation, and  $10\%$  for testing. For a fair comparison, we follow the data configuration of [39], which will be described in the following paragraphs. Further details are in Sec. S-4 of supplementary material.
+
+Common single-instance: For both datasets, videos with multiple actions are divided into independent videos where each video contains just one action instance and
+
+background. Then, videos longer than 768 frames are discarded. If a video is selected as a support video, its foreground action instance is only used as the support input. For ActivityNet1.3, there are 10,035 and 2,483 videos for training and validation+testing, each. The average video length is 89.0s. For THUMOS14, there are 3,580 and 775 training and validation+testing videos, respectively. The average length is 11.4s.
+
+Common multi-instance: In real-world scenarios, the lengths of query videos are usually not constrained, and the query videos may contain multiple action instances. Hence, we exploit the original videos of ActivityNet1.3 and THUMOS14 without any processing for query videos. Support videos are still trimmed ones. For ActivityNet1.3, the numbers of videos are 6,747 and 1,545 for training and validation+testing, respectively. The average video length is 148.2s. For THUMOS14, there are 1,664 training videos and 323 validation+testing videos. The average video length is 230.6s.
+
+Inference: In testing, the backbone-generated query proposals are refined by non-maximum suppression (NMS) with a threshold 0.7. Also, following [39], if the query video is longer than 768 frames, we generate the multi-scale segments [30]. We slide windows with sizes of 512 and 768 frames along the temporal axis with  $75\%$  overlap. The generated proposals of the windows go through the NMS to remove redundant proposals. Then, the selected proposals are fed into our CDC-CA and relational classifier. Finally, we perform NMS (threshold 0.3) for the regressed proposals based on the outputs of the relational classifier to remove redundant ones.
+
+Evaluation: We measure the temporal action localization performance with mean Average Precision (mAP). A prediction is correct when it has the correct foreground/background classification and has IoU with its ground-truth larger than a threshold. The threshold is set to 0.5 unless specified.
+
+# 4.2. Comparative assessment
+
+We report the performance of compared methods from the literature. Due to the variance of  $k$ -means clustering of the pseudo label generation, we report the average of three runs for our method.
+
+For AcitivityNet1.3, the left of Table 1 demonstrates the comparative results on both common single- and multi-instance cases when  $L = 1$  or 5. [3, 39, 22, 7] were developed for the common temporal action localization (our task) in videos, and [8] was for the common object detection in images. Compared to them, our method shows notably higher performance for all the settings ([3] was designed to use one support video). Specifically, in the single-instance case, we outperform those methods by at least  $1.4\%$  and  $5.1\%$  in the 1- and 5-shot settings, respec
+
+Table 1: Comparison with state-of-the-arts in terms of mAP@0.5.  
+
+<table><tr><td rowspan="3">Method</td><td colspan="4">ActivityNet1.3</td><td colspan="4">THUMOS14</td></tr><tr><td colspan="2">Single-instance</td><td colspan="2">Multi-instance</td><td colspan="2">Single-instance</td><td colspan="2">Multi-instance</td></tr><tr><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>Feng et al. [3]</td><td>43.5</td><td>n/a</td><td>31.4</td><td>n/a</td><td>34.1</td><td>n/a</td><td>4.3</td><td>n/a</td></tr><tr><td>Hu et al. [8]</td><td>41.0</td><td>45.4</td><td>29.6</td><td>38.9</td><td>-</td><td>42.2</td><td>-</td><td>6.8</td></tr><tr><td>Yang et al. [39]</td><td>53.1</td><td>56.5</td><td>42.1</td><td>43.9</td><td>48.7</td><td>51.9</td><td>7.5</td><td>8.6</td></tr><tr><td>Yang et al. [40]</td><td>57.5</td><td>60.6</td><td>47.8</td><td>48.7</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Nag et al. [22]</td><td>55.1</td><td>63.0</td><td>44.1</td><td>48.2</td><td>49.2</td><td>54.3</td><td>7.3</td><td>10.4</td></tr><tr><td>Hsieh et al. [7]</td><td>60.7</td><td>61.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>62.1 ± 1.0</td><td>66.3 ± 1.2</td><td>48.2 ± 1.2</td><td>53.5 ± 1.1</td><td>53.8 ± 1.2</td><td>59.2 ± 1.3</td><td>9.8 ± 0.4</td><td>15.7 ± 0.5</td></tr></table>
+
+Table 2: Ablation study on CDC-CA for the single-instance setting.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">QtoS Context-CA</td><td rowspan="2">Dynamics-CA</td><td colspan="2">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>C-0</td><td></td><td></td><td>52.0</td><td>54.3</td></tr><tr><td>C-1</td><td>✓</td><td></td><td>61.5</td><td>65.4</td></tr><tr><td>C-2</td><td></td><td>✓</td><td>61.3</td><td>65.1</td></tr><tr><td>C-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>
+
+tively. In the multi-instance, the margins are at least  $4.1\%$  and  $5.3\%$  for 1- and 5-shot, each. Note that [40] was developed for object-level common temporal action localization. Although object-level localization is more challenging, it requires further information to learn their model such as the coordinates of foreground object bounding boxes. Hence, they have advantages in the frame-level localization task. Even so, our method yields better results than [40] in all the settings. Also, in the 5-shot setting, the score margins to the existing works are larger than those of 1-shot in both single- and multi-instance. This means that enhancing the temporal dynamics of a support video by the entire support video in Dynamics-CA and aligning individually each support video to the query video's context in QtoS Context-CA are helpful to mine the knowledge for a common action from multiple support videos. Unlike ActivityNet1.3, THUMOS14 includes shorter action instances which make correct localization more difficult. Nevertheless, we outperform the compared methods over all the settings.
+
+# 4.3. Component analysis
+
+We analyze our method on ActivitNet1.3. More studies are in supplementary materials.
+
+Impact of cross-attention: First, to see the component-wise impact of our cross-attention, we ablate QtoS Context-CA and Dynamics-CA in Table 2, we can see that without any of them (C-0), the performance is severely degraded.
+
+Table 3: Ablation study on the relational classifier on the single-instance setting.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Lrank</td><td rowspan="2">Auxiliary rel. module</td><td colspan="2">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>R-0</td><td></td><td></td><td>61.8</td><td>65.8</td></tr><tr><td>R-1</td><td>✓</td><td></td><td>61.9</td><td>66.0</td></tr><tr><td>R-2</td><td></td><td>✓</td><td>61.9</td><td>66.1</td></tr><tr><td>R-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>
+
+Table 4: Analysis of the individual cross-attention strategy on QtoS Context-CA and Dynamics-CA, comparing with the aggregated cross-attention on the 5-shot setting.  
+
+<table><tr><td></td><td></td><td>Single-inst.</td><td>Multi-inst.</td></tr><tr><td rowspan="2">QtoS Context-CA</td><td>Aggregated</td><td>65.7</td><td>52.8</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr><tr><td rowspan="2">Dynamics-CA</td><td>Aggregated</td><td>65.8</td><td>52.9</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr></table>
+
+Also, when comparing C-1 and C-2, both cross-attentions show meaningful improvements on C-0, but QtoS Context-CA is slightly more important. Using both shows the best performance in our final method C-3.
+
+We can also consider changing the order of QtoS Context-CA and Dynamics-CA. In this case, we observed that the performance is slightly lowered (62.1%→61.7% in 1-shot, 66.3%→65.6% in 5-shot). Hence, the temporal dynamics extracted under the query video's context is more useful in our task.
+
+Further, we evaluate the efficacy of our cross-attention, comparing it with other cross-attention mechanisms. To this end, we compare our CDC-CA itself (corresponding to R-0 in Table 3) to the progressive cross-attention [39], and the multi-head cross-attention with fine-tuned (50-100 iterations) prototype [22], light-weight transformer-based booster [7]. For a fair comparison, the pairwise ranking
+
+Table 5: Cosine similarity between support videos and between support and query videos in embedding space before/after passing through Dynamics-CA.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Support-Support</td><td colspan="3">Support-Query</td></tr><tr><td>Pos. query</td><td>Neg. query</td><td>Δ</td></tr><tr><td>Cos. Sim. (before)</td><td>0.49</td><td>0.41</td><td>0.38</td><td>0.05</td></tr><tr><td>Cos. Sim. (after)</td><td>0.61</td><td>0.43</td><td>0.34</td><td>0.13</td></tr></table>
+
+loss and auxiliary relational module are not used in R-0. CDC-CA yields mAP gain of at least  $+1.1\%$  and  $+2.8\%$  in 1-shot (60.7% [7] in Table 1 vs 61.8% R-0) and 5-shot (63.0% [22] in Table 1 vs 65.8% R-0), each. Hence, we conclude our cross-attention more effectively enhances the query and support videos in this task.
+
+Individual vs aggregated: To study the effectiveness of the individual cross-attention on QtoS Context-CA and Dynamics-CA for multiple support videos, we compare our individual cross-attention approach with the aggregated cross-attention ('Aggregated') in Table 4. In 'Aggregated' of QtoS Context-CA, we concatenate all the support snippets of the entire support videos, and simultaneously attend them via query proposals. We see that 'Aggregated' degrades the localization performance. This result shows the benefit of individual cross-attention in QtoS Context-CA. Also, in Dynamics-CA, we identified a similar tendency. Accordingly, mining the commonality of temporal dynamics in multiple support videos is more beneficial when it is propagated to each support video, individually.
+
+Compatibility in support videos: In Dynamics-CA, a snippet-level support video feature is attended by tuple-level features from all the support videos to promote compatibility among multiple support videos. To identify this, at two points (before or after passing through Dynamics-CA), we measure the cosine similarities 1) between two support videos, and 2) between a support video and a (positive or negative) query proposal. Table 5 reports the average of cosine similarities. The increased support-support similarity  $(0.49\% \rightarrow 0.61\%)$  indicates that the support videos get closer to each other in the embedding space. Also, we can see that the discriminative ability is improved as seen by the increased difference  $(\Delta)$  in the similarity of the support to positive and negative query proposals.
+
+Further, to more clearly show the effect of individual-to-all cross-attention in Dynamics-CA, we also identified individual-to-individual Dynamacmis-CA where the snippet-level features are attended by the corresponding temporally-convolutioned features for each support video. Comparison of ours with this variant is  $66.3\%$  vs  $65.9\%$  in 5-shot single instance, and  $53.5\%$  vs  $53.2\%$  in 5-shot multiple instances. Hence, we can see that our approach (individual-to-all) is more beneficial for the collaborative use of a few support videos.
+
+Table 6: Effect of the multi-hot pseudo action indicator by varying the number of pseudo action classes or removing it.  
+
+<table><tr><td></td><td></td><td>w/o Indicator</td><td colspan="4">k</td></tr><tr><td></td><td></td><td></td><td>80</td><td>160</td><td>240</td><td>320</td></tr><tr><td rowspan="2">Single Inst.</td><td>1-shot</td><td>61.9</td><td>61.9</td><td>62.1</td><td>62.1</td><td>62.3</td></tr><tr><td>5-shot</td><td>66.0</td><td>66.2</td><td>66.3</td><td>66.5</td><td>66.4</td></tr><tr><td rowspan="2">Multiple Inst.</td><td>1-shot</td><td>47.8</td><td>48.0</td><td>48.2</td><td>48.4</td><td>48.4</td></tr><tr><td>5-shot</td><td>53.3</td><td>53.4</td><td>53.5</td><td>53.4</td><td>53.5</td></tr></table>
+
+Relational classifier: Here, we verify the auxiliary relational module and the pairwise ranking loss by ablating each. To show their effect, we compare each ablated version to the baseline R-0 without any of them in Table 3. The pairwise ranking loss gives performance improvement by  $0.1\%$  and  $0.2\%$  for 1- and 5-shot, respectively (R-1). Hence, this loss lets the proposals with larger IoUs to ground-truths get higher action scores. From the result of R-2, we also see that learning the auxiliary module in parallel to the action classifier is useful to boost performance in both settings. And, combining both works the best (R-3).
+
+Adequacy to no. of pseudo action label: In the auxiliary relational module, we use the multi-hot indicator as the pseudo-action cue in consideration that no true label is available. To see its effectiveness, in Table 6, we report the mAP scores by varying the number of pseudo action classes  $(k)$  and w/o the indicator as well. In the single instance case, compared to the R-1 of Table 3, the auxiliary relational module did not show an effect without the multi-hot indicator. Also, for all other settings, as  $k$  gets larger, the multi-hot indicator yields larger performance gains overall. Though the support videos represent a common action, there is diversity in background or action details. Hence, it is beneficial to distinguish the support videos with more pseudo labels. Considering the computational cost, we set  $k$  to 160 as the default value.
+
+# 5. Conclusions
+
+For few-shot common action localization, we proposed the three-stage cross-attention (CDC-CA) and the relational classifier. CDC-CA increases the effect of the cross-attention by individually attending each support video, enhancing the temporal dynamics of each and the compatibility of multiple support videos, and then attending the query video via all the enhanced support videos. In the relational classifier, we designed the pairwise ranking loss which makes more precise action localization of the action classifier. Learned in parallel with the action classifier, the auxiliary relational module with the pseudo-class labels prevents the network from overfitting to each training episode. This module is discarded in testing. Extensive experiments analyzed and validated each component. Finally, we achieved SOTA on ActivityNet1.3 and THUMOS14.
+
+# References
+
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+[25] Sujoy Paul, Sourya Roy, and Amit K. Roy-Chowdhury. W-TALC: Weakly-supervised temporal activity localization and classification. In ECCV. 2018. 2  
+[26] R Gnana Praveen, Wheidima Carneiro de Melo, Nasib Ullah, Haseeb Aslam, Osama Zeeshan, Théo Denorme, Marco Pedersoli, Alessandro L Koerich, Simon Bacon, Patrick Cardinal, et al. A joint cross-attention model for audio-visual fusion in dimensional emotion recognition. In CVPR. 2022. 3  
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+[31] Krishna Kumar Singh and Yong Jae Lee. Hide-and-seek: Forcing a network to be meticulous for weakly-supervised object and action localization. In ICCV. 2017. 1  
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+
+[35] Huijuan Xu, Abir Das, and Kate Saenko. R-c3d: Region convolutional 3d network for temporal activity detection. In ICCV, 2017. 2, 3  
+[36] Huijuan Xu, Xineng Sun, Eric Tzeng, Abir Das, Kate Saenko, and Trevor Darrell. Revisiting few-shot activity detection with class similarity control. In arXiv preprint arXiv:2004.00137, 2020. 2  
+[37] Mengmeng Xu, Chen Zhao, David S Rojas, Ali Thabet, and Bernard Ghanem. G-tad: Sub-graph localization for temporal action detection. In CVPR, 2020. 2  
+[38] Hongtao Yang, Xuming He, and Fatih Porikli. One-shot action localization by learning sequence matching network. In CVPR, 2018. 2  
+[39] Pengwan Yang, Vincent Tao Hu, Pascal Mettes, and Cees GM Snoek. Localizing the common action among a few videos. In ECCV, 2020. 1, 3, 5, 6, 7  
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\ No newline at end of file
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+                                    "content": "Juntae Lee<sup>1</sup>, Mihir Jain<sup>* *</sup> and Sungrack Yun<sup>1</sup>  \n<sup>1</sup>Qualcomm AI Research†"
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+                                    "content": "The goal of this paper is to localize action instances in a long untrimmed query video using just meager trimmed support videos representing a common action whose class information is not given. In this task, it is crucial to mine reliable temporal cues representing a common action from handful support videos. In our work, we develop an attention mechanism using cross-correlation. Based on this cross-attention, we first transform the support videos into query video's context to emphasize query-relevant important frames, and suppress less relevant ones. Next, we summarize sub-sequences of support video frames to represent temporal dynamics in coarse temporal granularity, which is then propagated to the fine-grained support video features through the cross-attention. In each case, the cross-attentions are applied to each support video in the individual-to-all strategy to balance heterogeneity and compatibility of the support videos. In contrast, the candidate instances in the query video are lastly attended by the resulting support video features, at once. In addition, we also develop a relational classifier head based on the query and support video representations. We show the effectiveness of our work with the state-of-the-art (SOTA) performance in benchmark datasets (ActivityNet1.3 and THUMOS14), and analyze each component extensively."
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+                                    "content": "video based on the few trimmed support videos describing a common action class. As the testing action class is unseen in training and no ground-truth class cue is given, the only cue is the commonality of the few support videos."
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+                                    "content": "Existing methods [39, 22, 7, 3] have mainly focused on the former point, handling the multiple support videos as a whole. However, as exemplified in Fig. 1, though the support videos represent a common action class, their context (e.g background, camera angle) can be different. Hence,"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                            "content": "Figure 2: Overall process of few-shot common action localization in our work."
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+                                    "content": "when all the support videos are transformed to query context simultaneously, the support videos cluttered by background are overly suppressed although they include useful information (Fig. 1(a)). Whereas, in Fig. 1(b), we can leverage the support videos by attending each individually."
+                                }
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+                                    "content": "Regarding the latter point, we pay attention to that the temporal dynamics can be enriched from multiple temporal granularities. Hence, we try to collaboratively fuse the support video features in different temporal granularities, considering the compatibility of different support videos as well. Based on the insight for each point, we propose a novel few-shot common action localization method. The overall process is briefly outlined in Fig. 2. First, the long untrimmed query video is split to query proposals, and they are aligned with the support videos through our three-stage cross-attention. Then, the proposals representing the common action class are detected with temporal location refinement."
+                                }
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+                                    "content": "For the query-support alignment, we develop a three-stage cross-attention (CA) mechanism. In each stage, cross-correlation between two different features (e.g. support and query, supports in different temporal granularity) is exploited with a learnable weight matrix. The 1st stage, query-to-support Context-CA transforms the support videos into the query video's context by cross-correlating them with the query proposal features. Each support video is individually attended to emphasize its most informative features. In 2nd stage of Dynamics-CA, low-temporal granularity features summarize the tuples of snippets of each support video, and they attend the fine-grained snippet-level features. Here, each support video is attended by the entire support videos in low-temporal granularity. It helps the complementary use of all the individually attended support video features as well as enhancing temporal dynamics. Finally, in the last stage (support-to-query Context-CA), the query video features are simultaneously attended with all the resulting support video features. We call this CA process (Context, Dynamics, Context-CAs) CDC-CA."
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+                                    "content": "Also, for the commonality prediction and refinement, we design a relational classifier with an action classifier and an auxiliary relational module. To prevent overfitting and boost performance, the latter matches the support and query video features using pseudo-label cues as we avoid the use of class labels. In testing, this module is not used."
+                                }
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+                                    "type": "text",
+                                    "content": "Major contributions: (i) We suggest a three-stage CA to"
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+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "enhance the representation of query video by support videos and vice versa. (ii) We attend each support video individually to increase its discriminative ability in the first two stages. (iii) We develop a relational classifier including an action classifier and an auxiliary relational module. The latter is only needed during training. (iv) Extensive experimental analyses are done on two benchmark datasets, where we achieve SOTA performance."
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+                                    "content": "2. Related work"
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+                                    "type": "text",
+                                    "content": "Temporal action localization The goal is to predict the temporal boundary and the label of action instances in untrimmed videos. In the fully-supervised case where temporal annotations are given during training, several works tried to obtain better temporal proposals [5, 4, 19], while others improved temporal searching [41, 42] or classifiers [29]. R-C3D [35] proposed an end-to-end trainable activity detector based on Faster-RCNN [27]. GNNs [45, 37] are recently used to capture the temporal relationship among proposals/snippets. In the weakly-supervised setting, as only video-level annotations are given, most methods have aimed to obtain discriminative snippet-level activations and conduct post-processing to localize action instances. A co-activity similarity loss to enforce the feature similarity for video pairs with a common class was introduced in [25], and videos are segmented into interpretable fragments in [10]. Some works focused on distinguishing action and near-action/background snippets exploiting variational auto-encoder [28], entropy maximization [20], and an additional class-agnostic model [21]. Also, to better localize difficult snippets, multi-modal (audio-visual) fusion [14] or a contrastive loss with easy foreground/background snippets [43] are devised. Although those fully- and weakly-supervised methods attained large progress in this field, the learned models can only localize activity categories observed in the training dataset."
+                                }
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+                    "index": 9
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+                                    "type": "text",
+                                    "content": "Few-shot temporal action localization [38] pioneered few-shot action localization, where a few (or only one) positive and several negative labeled videos steer the localization via an end-to-end meta-learning strategy. [36] also temporally localized an action from a few positive labeled and several negative labeled videos. They adopted a region proposal network [27] to produce proposals with flexible boundaries. [44] performed few-shot action localization where video-level annotations are needed. They constructed a multi-scale feature pyramid to directly produce temporal features at variable scales. Unlike those works, few-shot common action localization is less tied up with the need for labels. It localizes the action instances in a long untrimmed query video according to the commonality between the query and support inputs. Assuming a query with only one common action instance, [3] computed the probabilities for starting, ending, inside, or outside of ac"
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+                                    "type": "text",
+                                    "content": "tion instances at every time-step, and decided the window with the highest joint probability as the action instance. Extending to the query videos with multiple action instances of the same action class, [39] generated action proposals, and then classified the proposals and regressed their temporal locations. [22] set a linear classifier itself as a prototype, which needs fine-tuning by support videos for every target action, then the prototype is cross-attended by query proposals using multiple self-attention. [7] boosted [39] adding a single-head transformer where two different affinity matrices are used for the cross-attention weight between query and support videos."
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+                                    "content": "Cross-attention To leverage the relationship between two heterogeneous representations, diverse cross-attention schemes have been devised. Inspired by self-attention (scaled dot-product of key, query, and value), [34] applied the scaled dot-product operation for the concatenation of image and text features for VQA. Also, [12] attended student using key and value of teacher for knowledge propagation. Several works exploited the cross-correlation between the heterogeneous representation as the attention weights for image and sentence matching in visual question answering (VQA) [17, 13], query and prototype matching in prototypical few-shot learning [6], and audio-visual fusion [26]. Here, we exploit the cross-attention to improve the matching between query and support video clips as well as to better utilize multiple support videos in the context of few-shot action localization."
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+                                    "content": "3. Method"
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+                                    "content": "In this section, we first describe the three-stage cross-attention, CDC-CA, which consists of query-to-support Context, support-to-support (in different temporal granularity) temporal Dynamics, support-to-query Context CAs. Then, we explain the relational classifier."
+                                }
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+                                    "content": "Problem statement Given an untrimmed query video "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " trimmed support videos "
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+                                    "type": "inline_equation",
+                                    "content": "\\{V_{S}^{1}, V_{S}^{2}, \\ldots, V_{S}^{L}\\}"
+                                },
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+                                    "type": "text",
+                                    "content": ", the goal is to train a network (which consists of backbone "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", proposal-net "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "h"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", CDC-CA and relational classifier "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ") to temporally localize action instances in the query video based on the commonality of the support videos whose action classes are same and unseen during training. Note that any ground-truth class cues are not given even during training."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "In training, we resort to a meta-learning strategy. Here, the action classes in the training set "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(C_{\\mathrm{train}})"
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+                                    "type": "text",
+                                    "content": " and those of the testing set "
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+                                    "type": "inline_equation",
+                                    "content": "(C_{\\mathrm{test}})"
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+                                    "type": "text",
+                                    "content": " have no overlapping. Also, to simulate the few-shot configuration of support and query videos that will be encountered at the testing phase, we exploit episode-based training. Specifically, in a training iteration, we compose an episode as a set of a query and "
+                                },
+                                {
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+                                    "content": " support videos "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\{(V_Q,V_S^1,V_S^2,\\dots ,V_S^L)\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " from a randomly selected class of "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". In our work, we set "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to 1 or 5. Formally, the objec"
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+                            ]
+                        }
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+                    "index": 5
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+                                    "type": "text",
+                                    "content": "tive function is represented by"
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\operatorname *{arg  min}_{g,h,f}\\mathbb{E}_{(V_{Q},\\{V_{S}^{l}\\}_{l = 1}^{L})\\sim C_{\\text{train}}}\\left[\\mathcal{L}(\\mathcal{Y},f(h(g(V_{Q}))\\right), \\\\ \\left. g \\left(\\left\\{V _ {S} ^ {l} \\right\\} _ {l = 1} ^ {L}\\right)\\right), \\tag {1} \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " denotes the set of temporal positions for the ground-truth action segments of the interest in "
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " is the loss function."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                {
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+                                    "type": "text",
+                                    "content": "3.1. Overall framework"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Fig. 3 depicts the overall framework of our method. To obtain the initial representations of the input query and support videos, we follow the preprocessing of [39]. The backbone network "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " [32] generates video representations for each input. Then, for the query video, the proposal subnet "
+                                },
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+                                    "type": "text",
+                                    "content": " [35] yields potential temporal action instances "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "Q = \\{q_i\\}_{i=1}^{N_Q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", called action proposals, with diverse temporal lengths (details are in Sec. S-4 of supplementary materials). "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the number of the proposals, and "
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+                                    "type": "text",
+                                    "content": " denotes "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "th action proposal representation. For every "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "th support video, we uniformly split each support video into "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " fine-grained temporal snippets by "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "S^{(l)} = \\{s_i^{(l)}\\}_{i=1}^{N_S}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Then, CDC-CA aligns "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\{S^{(l)}\\}_{l=1}^L"
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+                                    "type": "text",
+                                    "content": ". Next, in the relational classifier, the action classifier detects the action proposals with the target common action, and yields their temporal offsets to refine the start and end times of the proposals. In training, learning an auxiliary relational module in parallel with the action classifier is beneficial. In testing, the auxiliary relational module is discarded, and the localization head suppresses redundant proposals which is explained in Sec. 4.1."
+                                }
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+                                    "content": "The green box of Fig. 3 illustrates three stages of CDC-CA. We first introduce the cross-attention mechanism to individually attend the fine-grained (snippet-level) support video features by the query's context (QtoS Context-CA). Next, we explain the cross-attention to enhance the temporal dynamics of each support video from all the support videos in different temporal granularity (Dynamics-CA). Then, we present the way to attend the features of query proposals via the cross-attention with all the resulting support features (StoQ Context-CA). These enhanced features serve as crucial inputs to the following relational classifier."
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+                                    "type": "text",
+                                    "content": "QtoS Context-CA: We first enhance the support features in consideration of the context of the query video (i.e. query to support, dubbed QtoS). To this end, we develop a cross-attention mechanism. When we suppose a vanilla approach such as Fig. 1(a), the attention weight is obtained at once based on the relationship between the query proposals and all the support videos. In this case, a support video, which is relatively less relevant to the query video than the other support videos, gets tiny attention weights and cannot"
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+                                            ],
+                                            "type": "text",
+                                            "content": " the support videos are propagated to each support video. The resulting support videos "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\hat{Y}_S^{(l)}\\}_{l=1}^L"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                173,
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+                                            ],
+                                            "type": "text",
+                                            "content": " give attention to the query proposals. "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\hat{X}_{Q}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                173,
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+                                            ],
+                                            "type": "text",
+                                            "content": " is the resulting attended query proposals. Then, the relational classifier predicts the commonality scores of the proposals for the action of support videos, and the localization head finalizes action localization removing redundant proposals."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
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+                            "type": "image_caption"
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+                                            "type": "text",
+                                            "content": "(a)"
+                                        }
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+                            "angle": 0,
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+                        },
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+                                            "type": "text",
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+                                        }
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+                                }
+                            ],
+                            "index": 4,
+                            "angle": 0,
+                            "type": "image_caption"
+                        },
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+                                            "type": "text",
+                                            "content": "(c)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "angle": 0,
+                            "type": "image_caption"
+                        },
+                        {
+                            "bbox": [
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+                            "lines": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 4: Cross-attention (best view in color). (a) QtoS Context-CA for "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                                360
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "l"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "th support video by the query proposals. (b) Dynamics-CA for "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
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+                                        {
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+                                            "type": "text",
+                                            "content": "th support video by "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                322,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "L"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                322,
+                                                546,
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+                                            ],
+                                            "type": "text",
+                                            "content": " support videos in different temporal granularity. (c) StoQ Context-CA of all the query proposals by the attended support videos, at once."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        380,
+                        287,
+                        415
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                380,
+                                287,
+                                415
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "represent its action information in the context of the query video. As depicted in Fig. 4(a), to utilize the query video's context faithfully, we individually attend the support videos."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": "In specific, for "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": "th support video, we first encode the backbone features of the query proposals "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{Q} \\in \\mathbb{R}^{d \\times N_{Q}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " and the support snippets "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{S}^{(l)} \\in \\mathbb{R}^{d \\times N_{S}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": ", with a linear layer. The columns of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{Q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{S}^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " represent the encoded "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": "-dimensional features of the query proposal and support snippets, respectively. After that, we compute the cross-correlation of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{Q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{S}^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " to measure their relevance. To reduce the gap of the heterogeneity between the query and support videos, we use a learnable weight matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{Q \\to S} \\in \\mathbb{R}^{d \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        416,
+                                        287,
+                                        543
+                                    ],
+                                    "type": "text",
+                                    "content": " and compute the cross-correlation as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        552,
+                                        287,
+                                        570
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\Lambda_ {Q \\rightarrow S} ^ {(l)} = X _ {Q} ^ {T} W _ {Q \\rightarrow S} X _ {S} ^ {(l)} \\tag {2}",
+                                    "image_path": "46c78facdc6c2aac33766d05320a250e860302cc83bab327620dde1bfc43c1a4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Lambda_{Q\\to S}^{(l)}\\in \\mathbb{R}^{N_Q\\times N_S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that each column of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{Q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{S}^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
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+                                        634
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "text",
+                                    "content": "-normalized before the cross-correlation computation, and the learnable weight "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{Q\\rightarrow S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "text",
+                                    "content": " and the linear layer are shared across all "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        580,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "text",
+                                    "content": " i.e. all the support videos."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        46,
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+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In the cross-correlation matrix, a high correlation coefficient means that the corresponding proposal and snippet features are highly relevant. Accordingly, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "th row of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Lambda_{Q\\to S}^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " corresponds to the relevance of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "th query proposal to the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " support snippets. Then, from row-wise soft-max of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Lambda_{Q\\to S}^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can obtain cross-attention weights "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{Q\\to S}^{(l)}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        635,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " where each"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
+                        380,
+                        545,
+                        403
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "row represents the relative relevance of a query proposal to the support snippets."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        403,
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+                                    ],
+                                    "type": "text",
+                                    "content": "The attention-weighted proposal features are summed to the corresponding support snippet feature. This is to ensure that the meaningful action information of the support video is well-preserved while applying the cross-attention. Formally, the attended support snippet features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        403,
+                                        546,
+                                        476
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{X}_S^{(l)}"
+                                },
+                                {
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+                                    "content": "Dynamics-CA: Temporal dynamics is important to understand the actions, which is well-represented in consecutive snippets (tuple) rather than a single snippet. Hence, as illustrated in Fig. 4(b), to extract temporal dynamics of the attended support video features, we apply 1-dimensional temporal convolution on each "
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+                                    "content": " support videos. In other words, as the support videos represent a common action, the support segment features should be closely located in a latent feature space. However, since the QtoS Context-CA are applied individually for each support video, the heterogeneity may be overly increased, which can degenerate the effect of attention on query videos in the following last stage. To compensate this, we attend the snippet-level features of "
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+                                    "content": " from the tuple-level features of all "
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{X}_{S'} = \\{\\tilde{X}_{S'}^{(l)}\\}_{l=1}^L"
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+                                    "content": "\\Lambda_ {S ^ {\\prime} \\rightarrow S} ^ {(l)} = \\tilde {X} _ {S ^ {\\prime}} ^ {T} W _ {S ^ {\\prime} \\rightarrow S} \\tilde {X} _ {S} ^ {(l)} \\tag {5}",
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+                                    "type": "interline_equation",
+                                    "content": "\\tilde {Y} _ {S} ^ {(l)} = \\tilde {X} _ {S ^ {\\prime}} A _ {S ^ {\\prime} \\rightarrow S} ^ {(l)} + \\tilde {X} _ {S} ^ {\\prime (l)}, \\tag {6}",
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+                                    "content": " is the cross-attention weight from "
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+                                    "type": "text",
+                                    "content": "StoQ Context-CA: In this stage, we attend query videos with the support videos using the cross-attention. This support-to-query context attention is called StoQ Context-CA described in Fig. 4(c). To mine the richer information for target action from all the support videos, we attend query proposal features using the entire stabilized support segment features "
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{Y}_S = \\{\\tilde{Y}_S^{(1)},\\tilde{Y}_S^{(2)},\\dots ,\\tilde{Y}_S^{(L)}\\} \\in \\mathbb{R}^{d\\times LN_S}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Similar to attending support features, we exploit the cross-attention to obtain the attended query proposals "
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+                                    "content": "\\tilde{X}_Q"
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+                                    "type": "text",
+                                    "content": " with a learnable weight matrix "
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+                                    "type": "inline_equation",
+                                    "content": "W_{S\\rightarrow Q}\\in \\mathbb{R}^{d\\times d}"
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\tilde {X} _ {Q} = \\tilde {Y} _ {S} A _ {S \\rightarrow Q} + X _ {Q} \\tag {7}",
+                                    "image_path": "4589e5f54814daf584fd35a2e5489f3d5f09efa2e7b36c3db8d7ade7d77b49ee.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{S\\rightarrow Q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        555,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is attention weight computed by row-wise soft-max of cross-correlation, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        555,
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+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Lambda_{S\\rightarrow Q} = \\tilde{Y}_S^T W_{S\\rightarrow Q}X_Q"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        555,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". From this cross-attention, the query proposals, which have high relevance to crucial support segments, better delineate the target action."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "3.3. Relational classifier"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Up to this point, we described how CDC-CA generates better representations of query proposals and support videos. Here, we explain the way to obtain the final decision from the attended representations. Fig. 5 depicts our relational classifier including an action classifier and an auxiliary relational module. The auxiliary module facilitates"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Figure 5: Relational classifier consists of auxiliary relational module and action classifier."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "learning how to understand the relationship between query proposals and a target action with pseudo action class cues. As the auxiliary relational module is discarded in the deployed network, no action class label is required in testing."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Auxiliary relational module: In episodic few-shot learning, an auxiliary classifier can be co-trained to categorize an input into one of the ground-truth classes rather than the target classes of an episode. This is beneficial for feature extractors to prevent overfitting, stabilize the training, and boost the performance [24, 11]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "However, since the ground-truth action classes are not available in our task, we utilize pseudo action classes. As in Fig. 5, we develop the auxiliary relational module which takes as an input the concatenation of the attended query proposal (green), support prototype (purple), and a pseudoclass identifier (white). The support prototype is the average of all the attended support segments. The pseudo-class identifier is a multi-hot vector with 1 for the pseudo action classes present in the support videos and 0 otherwise. As action class annotations are unavailable, the pseudo action classes are simply obtained by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        317,
+                                        546,
+                                        591
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        317,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-means clustering of the pre-trained backbone features extracted from all the ground-truth positive action instances in the training set. Then, these pseudo action classes can provide the cue to capture the commonality of the support videos with the same action across episodes. Hence, joint training with the auxiliary module assists the action classifier to learn to more correctly find the common actions in the query video without getting distracted by the non-target actions. The auxiliary relational module predicts whether the query proposal and the prototype are similar or not. Note that this module is only needed for training and discarded in the testing phase as the training and testing classes are mutually exclusive."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Action classifier: The action classifier consists of two parallel linear layers. Taking only the query proposal features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{X}_Q"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as inputs, the action classifier computes two outputs. The first is soft-max activated and decides if a query proposal contains target action or not. The second regresses the temporal offsets from the corresponding ground-truth."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.4. Loss functions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "type": "text",
+                                    "content": "To optimize the entire network, as in [39], we use loss terms for both support-agnostic and -conditioned parts. In"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                }
+            ],
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+                                    "content": "10218"
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+                                    "type": "text",
+                                    "content": "the support-agnostic part, the binary cross-entropy loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{cls}}^{\\mathrm{ag}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " predicts if the proposal contains any activity or not, and the smooth "
+                                },
+                                {
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+                                        72,
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+                                    "type": "inline_equation",
+                                    "content": "l_{1}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " regression loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{ag}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": " optimizes the relative displacement between proposals and ground-truths."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "In the auxiliary relational module of the support-conditioned part, we simply use the binary cross-entropy loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{aux}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to predict if the proposal and support videos are similar or not. In the action classifier of the support-conditioned part, similar to the support-agnostic part, the classification loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{cls}}^{\\mathrm{co}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " predicts if the proposal includes the same common action of support videos, and the regression loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{reg}}^{\\mathrm{co}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " optimizes the relative displacement between the proposals and the ground-truths. Also, we design a pairwise ranking loss to add constraints to the action classifier. Considering a pair of proposals "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{j}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": ", where at least one of them is a positive query proposal, we let the proposal with the larger IoU (intersection over union) for the ground-truth action instance have a higher soft-max score for the action class. Formally, the pairwise ranking loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{rank}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        121,
+                                        289,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " is represented by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {r a n k}} = \\frac {1}{N _ {\\text {p a i r}}} \\sum_ {(i, j)} \\left(\\Delta \\mathrm {I o U} _ {i j} - \\Delta p _ {i j} ^ {\\text {a c t i o n}}\\right) ^ {2} \\tag {8}",
+                                    "image_path": "56885d0653b0ef480aa952f16b21017ae704a95a7d886163db430916c175276c.jpg"
+                                }
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+                {
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{\\mathrm{pair}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of considered proposal pairs. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Delta \\mathrm{IoU}_{ij}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": " is the difference between IoUs of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{j}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": " with their corresponding ground-truths, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Delta p_{ij}^{\\mathrm{action}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": " is the difference of soft-max predictions for the proposals on the action class from the action classifier. Note that to relax the relationship between IoU and soft-max prediction, we give temperature to the soft-max predictions in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{rank}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        362,
+                                        287,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": ". Finally, total loss (more details in Sec. S-1 of supplementary materials) is given by"
+                                }
+                            ]
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+                    ],
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+                                    "content": "4.1. Datasets and evaluation"
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+                                    "content": "To evaluate few-shot common action localization, we use the revised versions [3, 39] of ActivityNet1.3 [1] and THU-MOS14 [9]. In the revised, there are two cases depending on queries: single-instance and multi-instance. We address 1- or 5-shot settings in both cases. For meta-learning strategy, the entire action classes of each dataset are split into "
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+                                    "content": " for training, "
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+                                    "content": " for validation, and "
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+                                    "content": " for testing. For a fair comparison, we follow the data configuration of [39], which will be described in the following paragraphs. Further details are in Sec. S-4 of supplementary material."
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+                                    "content": "Common single-instance: For both datasets, videos with multiple actions are divided into independent videos where each video contains just one action instance and"
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+                                    "type": "text",
+                                    "content": "background. Then, videos longer than 768 frames are discarded. If a video is selected as a support video, its foreground action instance is only used as the support input. For ActivityNet1.3, there are 10,035 and 2,483 videos for training and validation+testing, each. The average video length is 89.0s. For THUMOS14, there are 3,580 and 775 training and validation+testing videos, respectively. The average length is 11.4s."
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+                                    "type": "text",
+                                    "content": "Common multi-instance: In real-world scenarios, the lengths of query videos are usually not constrained, and the query videos may contain multiple action instances. Hence, we exploit the original videos of ActivityNet1.3 and THUMOS14 without any processing for query videos. Support videos are still trimmed ones. For ActivityNet1.3, the numbers of videos are 6,747 and 1,545 for training and validation+testing, respectively. The average video length is 148.2s. For THUMOS14, there are 1,664 training videos and 323 validation+testing videos. The average video length is 230.6s."
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+                                    "content": "Inference: In testing, the backbone-generated query proposals are refined by non-maximum suppression (NMS) with a threshold 0.7. Also, following [39], if the query video is longer than 768 frames, we generate the multi-scale segments [30]. We slide windows with sizes of 512 and 768 frames along the temporal axis with "
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+                                    "content": " overlap. The generated proposals of the windows go through the NMS to remove redundant proposals. Then, the selected proposals are fed into our CDC-CA and relational classifier. Finally, we perform NMS (threshold 0.3) for the regressed proposals based on the outputs of the relational classifier to remove redundant ones."
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+                                    "content": "Evaluation: We measure the temporal action localization performance with mean Average Precision (mAP). A prediction is correct when it has the correct foreground/background classification and has IoU with its ground-truth larger than a threshold. The threshold is set to 0.5 unless specified."
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+                                    "content": "4.2. Comparative assessment"
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+                                    "content": "We report the performance of compared methods from the literature. Due to the variance of "
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+                                    "content": "-means clustering of the pseudo label generation, we report the average of three runs for our method."
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+                                    "type": "text",
+                                    "content": "For AcitivityNet1.3, the left of Table 1 demonstrates the comparative results on both common single- and multi-instance cases when "
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+                                    "content": " or 5. [3, 39, 22, 7] were developed for the common temporal action localization (our task) in videos, and [8] was for the common object detection in images. Compared to them, our method shows notably higher performance for all the settings ([3] was designed to use one support video). Specifically, in the single-instance case, we outperform those methods by at least "
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+                                            "html": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">ActivityNet1.3</td><td colspan=\"4\">THUMOS14</td></tr><tr><td colspan=\"2\">Single-instance</td><td colspan=\"2\">Multi-instance</td><td colspan=\"2\">Single-instance</td><td colspan=\"2\">Multi-instance</td></tr><tr><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>Feng et al. [3]</td><td>43.5</td><td>n/a</td><td>31.4</td><td>n/a</td><td>34.1</td><td>n/a</td><td>4.3</td><td>n/a</td></tr><tr><td>Hu et al. [8]</td><td>41.0</td><td>45.4</td><td>29.6</td><td>38.9</td><td>-</td><td>42.2</td><td>-</td><td>6.8</td></tr><tr><td>Yang et al. [39]</td><td>53.1</td><td>56.5</td><td>42.1</td><td>43.9</td><td>48.7</td><td>51.9</td><td>7.5</td><td>8.6</td></tr><tr><td>Yang et al. [40]</td><td>57.5</td><td>60.6</td><td>47.8</td><td>48.7</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Nag et al. [22]</td><td>55.1</td><td>63.0</td><td>44.1</td><td>48.2</td><td>49.2</td><td>54.3</td><td>7.3</td><td>10.4</td></tr><tr><td>Hsieh et al. [7]</td><td>60.7</td><td>61.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>62.1 ± 1.0</td><td>66.3 ± 1.2</td><td>48.2 ± 1.2</td><td>53.5 ± 1.1</td><td>53.8 ± 1.2</td><td>59.2 ± 1.3</td><td>9.8 ± 0.4</td><td>15.7 ± 0.5</td></tr></table>",
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+                                    "content": " for 1- and 5-shot, each. Note that [40] was developed for object-level common temporal action localization. Although object-level localization is more challenging, it requires further information to learn their model such as the coordinates of foreground object bounding boxes. Hence, they have advantages in the frame-level localization task. Even so, our method yields better results than [40] in all the settings. Also, in the 5-shot setting, the score margins to the existing works are larger than those of 1-shot in both single- and multi-instance. This means that enhancing the temporal dynamics of a support video by the entire support video in Dynamics-CA and aligning individually each support video to the query video's context in QtoS Context-CA are helpful to mine the knowledge for a common action from multiple support videos. Unlike ActivityNet1.3, THUMOS14 includes shorter action instances which make correct localization more difficult. Nevertheless, we outperform the compared methods over all the settings."
+                                }
+                            ]
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+                    ],
+                    "index": 4
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+                                    "content": "4.3. Component analysis"
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+                                    "content": "We analyze our method on ActivitNet1.3. More studies are in supplementary materials."
+                                }
+                            ]
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+                                    "content": "Impact of cross-attention: First, to see the component-wise impact of our cross-attention, we ablate QtoS Context-CA and Dynamics-CA in Table 2, we can see that without any of them (C-0), the performance is severely degraded."
+                                }
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+                                            "type": "text",
+                                            "content": "Table 3: Ablation study on the relational classifier on the single-instance setting."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Lrank</td><td rowspan=\"2\">Auxiliary rel. module</td><td colspan=\"2\">mAP (%)</td></tr><tr><td>1-shot</td><td>5-shot</td></tr><tr><td>R-0</td><td></td><td></td><td>61.8</td><td>65.8</td></tr><tr><td>R-1</td><td>✓</td><td></td><td>61.9</td><td>66.0</td></tr><tr><td>R-2</td><td></td><td>✓</td><td>61.9</td><td>66.1</td></tr><tr><td>R-3</td><td>✓</td><td>✓</td><td>62.1</td><td>66.3</td></tr></table>",
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+                                            "content": "Table 4: Analysis of the individual cross-attention strategy on QtoS Context-CA and Dynamics-CA, comparing with the aggregated cross-attention on the 5-shot setting."
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+                                            "html": "<table><tr><td></td><td></td><td>Single-inst.</td><td>Multi-inst.</td></tr><tr><td rowspan=\"2\">QtoS Context-CA</td><td>Aggregated</td><td>65.7</td><td>52.8</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr><tr><td rowspan=\"2\">Dynamics-CA</td><td>Aggregated</td><td>65.8</td><td>52.9</td></tr><tr><td>Individual (Ours)</td><td>66.3</td><td>53.5</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Also, when comparing C-1 and C-2, both cross-attentions show meaningful improvements on C-0, but QtoS Context-CA is slightly more important. Using both shows the best performance in our final method C-3."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We can also consider changing the order of QtoS Context-CA and Dynamics-CA. In this case, we observed that the performance is slightly lowered (62.1%→61.7% in 1-shot, 66.3%→65.6% in 5-shot). Hence, the temporal dynamics extracted under the query video's context is more useful in our task."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Further, we evaluate the efficacy of our cross-attention, comparing it with other cross-attention mechanisms. To this end, we compare our CDC-CA itself (corresponding to R-0 in Table 3) to the progressive cross-attention [39], and the multi-head cross-attention with fine-tuned (50-100 iterations) prototype [22], light-weight transformer-based booster [7]. For a fair comparison, the pairwise ranking"
+                                }
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+                                            "type": "text",
+                                            "content": "Table 5: Cosine similarity between support videos and between support and query videos in embedding space before/after passing through Dynamics-CA."
+                                        }
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Support-Support</td><td colspan=\"3\">Support-Query</td></tr><tr><td>Pos. query</td><td>Neg. query</td><td>Δ</td></tr><tr><td>Cos. Sim. (before)</td><td>0.49</td><td>0.41</td><td>0.38</td><td>0.05</td></tr><tr><td>Cos. Sim. (after)</td><td>0.61</td><td>0.43</td><td>0.34</td><td>0.13</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "loss and auxiliary relational module are not used in R-0. CDC-CA yields mAP gain of at least "
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+                                    "type": "text",
+                                    "content": " in 1-shot (60.7% [7] in Table 1 vs 61.8% R-0) and 5-shot (63.0% [22] in Table 1 vs 65.8% R-0), each. Hence, we conclude our cross-attention more effectively enhances the query and support videos in this task."
+                                }
+                            ]
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+                    ],
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+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Individual vs aggregated: To study the effectiveness of the individual cross-attention on QtoS Context-CA and Dynamics-CA for multiple support videos, we compare our individual cross-attention approach with the aggregated cross-attention ('Aggregated') in Table 4. In 'Aggregated' of QtoS Context-CA, we concatenate all the support snippets of the entire support videos, and simultaneously attend them via query proposals. We see that 'Aggregated' degrades the localization performance. This result shows the benefit of individual cross-attention in QtoS Context-CA. Also, in Dynamics-CA, we identified a similar tendency. Accordingly, mining the commonality of temporal dynamics in multiple support videos is more beneficial when it is propagated to each support video, individually."
+                                }
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+                                    "type": "text",
+                                    "content": "Compatibility in support videos: In Dynamics-CA, a snippet-level support video feature is attended by tuple-level features from all the support videos to promote compatibility among multiple support videos. To identify this, at two points (before or after passing through Dynamics-CA), we measure the cosine similarities 1) between two support videos, and 2) between a support video and a (positive or negative) query proposal. Table 5 reports the average of cosine similarities. The increased support-support similarity "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(0.49\\% \\rightarrow 0.61\\%)"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates that the support videos get closer to each other in the embedding space. Also, we can see that the discriminative ability is improved as seen by the increased difference "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(\\Delta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in the similarity of the support to positive and negative query proposals."
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+                                    "type": "text",
+                                    "content": "Further, to more clearly show the effect of individual-to-all cross-attention in Dynamics-CA, we also identified individual-to-individual Dynamacmis-CA where the snippet-level features are attended by the corresponding temporally-convolutioned features for each support video. Comparison of ours with this variant is "
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+                                    "content": "66.3\\%"
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+                                    "type": "text",
+                                    "content": " vs "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "65.9\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " in 5-shot single instance, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "53.5\\%"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " vs "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "53.2\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in 5-shot multiple instances. Hence, we can see that our approach (individual-to-all) is more beneficial for the collaborative use of a few support videos."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "table",
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+                                            "type": "text",
+                                            "content": "Table 6: Effect of the multi-hot pseudo action indicator by varying the number of pseudo action classes or removing it."
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+                                            "html": "<table><tr><td></td><td></td><td>w/o Indicator</td><td colspan=\"4\">k</td></tr><tr><td></td><td></td><td></td><td>80</td><td>160</td><td>240</td><td>320</td></tr><tr><td rowspan=\"2\">Single Inst.</td><td>1-shot</td><td>61.9</td><td>61.9</td><td>62.1</td><td>62.1</td><td>62.3</td></tr><tr><td>5-shot</td><td>66.0</td><td>66.2</td><td>66.3</td><td>66.5</td><td>66.4</td></tr><tr><td rowspan=\"2\">Multiple Inst.</td><td>1-shot</td><td>47.8</td><td>48.0</td><td>48.2</td><td>48.4</td><td>48.4</td></tr><tr><td>5-shot</td><td>53.3</td><td>53.4</td><td>53.5</td><td>53.4</td><td>53.5</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Relational classifier: Here, we verify the auxiliary relational module and the pairwise ranking loss by ablating each. To show their effect, we compare each ablated version to the baseline R-0 without any of them in Table 3. The pairwise ranking loss gives performance improvement by "
+                                },
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+                                    "type": "text",
+                                    "content": " and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "0.2\\%"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " for 1- and 5-shot, respectively (R-1). Hence, this loss lets the proposals with larger IoUs to ground-truths get higher action scores. From the result of R-2, we also see that learning the auxiliary module in parallel to the action classifier is useful to boost performance in both settings. And, combining both works the best (R-3)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                {
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+                                    "type": "text",
+                                    "content": "Adequacy to no. of pseudo action label: In the auxiliary relational module, we use the multi-hot indicator as the pseudo-action cue in consideration that no true label is available. To see its effectiveness, in Table 6, we report the mAP scores by varying the number of pseudo action classes "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(k)"
+                                },
+                                {
+                                    "bbox": [
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+                                        325,
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+                                    "type": "text",
+                                    "content": " and w/o the indicator as well. In the single instance case, compared to the R-1 of Table 3, the auxiliary relational module did not show an effect without the multi-hot indicator. Also, for all other settings, as "
+                                },
+                                {
+                                    "bbox": [
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+                                        325,
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+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " gets larger, the multi-hot indicator yields larger performance gains overall. Though the support videos represent a common action, there is diversity in background or action details. Hence, it is beneficial to distinguish the support videos with more pseudo labels. Considering the computational cost, we set "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " to 160 as the default value."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Conclusions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "For few-shot common action localization, we proposed the three-stage cross-attention (CDC-CA) and the relational classifier. CDC-CA increases the effect of the cross-attention by individually attending each support video, enhancing the temporal dynamics of each and the compatibility of multiple support videos, and then attending the query video via all the enhanced support videos. In the relational classifier, we designed the pairwise ranking loss which makes more precise action localization of the action classifier. Learned in parallel with the action classifier, the auxiliary relational module with the pseudo-class labels prevents the network from overfitting to each training episode. This module is discarded in testing. Extensive experiments analyzed and validated each component. Finally, we achieved SOTA on ActivityNet1.3 and THUMOS14."
+                                }
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    "blocks": [
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+                                        {
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+                                        }
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+                                }
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+                        },
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+                            ],
+                            "type": "ref_text",
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+                                {
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+                                        {
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+                                        }
+                                    ]
+                                }
+                            ],
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+                        },
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+                            "bbox": [
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+                            ],
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+                                        }
+                                    ]
+                                }
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+                        },
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+                            ],
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                            "bbox": [
+                                48,
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+                            ],
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
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+                                48,
+                                499,
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                {
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+                                        {
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+                                            ],
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+                                        }
+                                    ]
+                                }
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+                            ],
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+                                        {
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
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+                                567,
+                                286,
+                                599
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                {
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                            ],
+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
+                                                48,
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+                                                286,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[15] Jun-Tae Lee, Hyunsin Park, Sungrack Yun, and Simyung Chang. Multi-head modularization to leverage generalization capability in multi-modal networks. AAAI, 36(7), 2022. 1"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                48,
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+                            ],
+                            "type": "ref_text",
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+                                                48,
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+                                            "type": "text",
+                                            "content": "[16] Jun-Tae Lee, Sungrack Yun, and Mihir Jain. Leaky gated cross-attention for weakly supervised multi-modal temporal action localization. In WACV, 2022. 1"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 16
+                        },
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+                                            "type": "text",
+                                            "content": "[43] Can Zhang, Meng Cao, Dongming Yang, Jie Chen, and Yuexian Zou. Cola: Weakly-supervised temporal action localization with snippet contrastive learning. In CVPR, 2021. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                49,
+                                389,
+                                286,
+                                420
+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
+                                                49,
+                                                389,
+                                                286,
+                                                420
+                                            ],
+                                            "type": "text",
+                                            "content": "[44] Da Zhang, Xiyang Dai, and Yuan-Fang Wang. Metal: Minimum effort temporal activity localization in untrimmed videos. In CVPR, 2020. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                49,
+                                422,
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+                                            "bbox": [
+                                                49,
+                                                422,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[45] Chen Zhao, Ali K Thabet, and Bernard Ghanem. Video self-stitching graph network for temporal action localization. In ICCV, 2021. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10
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diff --git a/2023/Few-Shot Dataset Distillation via Translative Pre-Training/72b4828a-ff69-4894-aad7-b57f445d822d_content_list.json b/2023/Few-Shot Dataset Distillation via Translative Pre-Training/72b4828a-ff69-4894-aad7-b57f445d822d_content_list.json
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+++ b/2023/Few-Shot Dataset Distillation via Translative Pre-Training/72b4828a-ff69-4894-aad7-b57f445d822d_content_list.json	
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+[
+    {
+        "type": "text",
+        "text": "Few-Shot Dataset Distillation via Translative Pre-Training",
+        "text_level": 1,
+        "bbox": [
+            191,
+            130,
+            779,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Songhua Liu Xinchao Wang*",
+        "bbox": [
+            361,
+            181,
+            614,
+            199
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "National University of Singapore",
+        "bbox": [
+            352,
+            200,
+            614,
+            217
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "songhua.liu@u.nus.edu，xinchao@nus.edu.sg",
+        "bbox": [
+            303,
+            219,
+            666,
+            233
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            268,
+            313,
+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Dataset distillation aims at a small synthetic dataset to mimic the training performance on neural networks of a given large dataset. Existing approaches heavily rely on an iterative optimization to update synthetic data and multiple forward-backward passes over thousands of neural network spaces, which introduce significant overhead for computation and are inconvenient in scenarios requiring high efficiency. In this paper, we focus on few-shot dataset distillation, where a distilled dataset is synthesized with only a few or even a single network. To this end, we introduce the notion of distillation space, such that synthetic data optimized only in this specific space can achieve the effect of those optimized through numerous neural networks, with dramatically accelerated training and reduced computational cost. To learn such a distillation space, we first formulate the problem as a quad-level optimization framework and propose a bi-level algorithm. Nevertheless, the algorithm in its original form has a large memory footprint in practice due to the back-propagation through an unrolled computational graph. We then convert the problem of learning the distillation space to a first-order one based on image translation. Specifically, the synthetic images are optimized in an arbitrary but fixed neural space and then translated to those in the targeted distillation space. We pre-train the translator on some large datasets like ImageNet so that it requires only a limited number of adaptation steps on the target dataset. Extensive experiments demonstrate that the translator after pre-training and a limited number of adaptation steps achieves comparable distillation performance with state of the arts, with  $\\sim 15\\times$  acceleration. It also exerts satisfactory generalization performance across different datasets, storage budgets, and numbers of classes.",
+        "bbox": [
+            75,
+            301,
+            473,
+            785
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            816,
+            209,
+            832
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Given an original dataset  $\\mathcal{T}$ , Dataset distillation (DD) [41, 51, 35, 18, 47, 20, 22] aims at a much smaller",
+        "bbox": [
+            76,
+            843,
+            468,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/f35aa61de0ec9bde9b018b332fdeaa5d18cd4eee1bdc9c5a7fe6237e834bcfda.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            271,
+            702,
+            362
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/5dee38db11fc60c5bd81e7259cbb68b98a941eca5c9abb1aa06ab54d9ff30a99.jpg",
+        "image_caption": [
+            "(b)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            888,
+            364
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/88d42e8adb3c171ad3ad6b2414e7ae72006defaf97725a4c244d439b9f736d53.jpg",
+        "image_caption": [
+            "(c)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            382,
+            691,
+            472
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7093a48621a4dadf7f691bc994256bc5b4d6741ded1a6a8a95e43d2076378bdd.jpg",
+        "image_caption": [
+            "(d)",
+            "Figure 1. (a) Existing DD methods heavily rely on forward-backward processes through enormous neural networks. (b) More neural networks used in dataset distillation would result in more floating point operations (FLOPs) and higher latency. (c) We introduce the notation of distillation space for few-shot dataset distillation in this paper and aim to learn a neural network such that distilled data only optimized in this specific space can approximate the performance by multiple networks. (d) Given only a few or even a single network, our method achieves comparable performance with state-of-the-art baselines requiring enormous networks. Results in this figure are concerning models trained with 1 image per class distilled from CIFAR100 dataset. OS denotes one-shot DD using only one network, FS denotes few-shot DD with a limited number of adaptation steps, and DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            705,
+            380,
+            890,
+            476
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "synthetic dataset  $S$ , such that the training effect of  $S$  on neural networks can match that of  $\\mathcal{T}$ . Such techniques have received considerable attention to alleviate the heavy burden on storage, transmission, and training of deep learning models brought by large-scale datasets. Recent advances on DD have revealed that models trained with only a few synthetic samples, even 1 image per class in some cases, can retain most of the performance of those trained with real data [49, 50, 2, 28, 29, 40, 13, 52, 23, 21]. Thus, it becomes a research area receiving increasing attention from the aca",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding Author.",
+        "bbox": [
+            94,
+            886,
+            225,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "18654",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "demic and industrial community recently as a potential solution to alleviate the concerns on the storage, transmission, pre-processing, and training effort for large datasets.",
+        "bbox": [
+            75,
+            90,
+            468,
+            136
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Nevertheless, as shown in Fig. 1(a), all existing methods on DD work iteratively: the synthetic dataset is optimized in an outer loop, and real and synthetic data are sent to a newly-initialized neural network in each iteration. Although they have achieved remarkable performance, such forward-backward passes in multiple neural networks can introduce extensive computational overhead to generate a distilled dataset, as illustrated in Fig. 1(b). As a result, the burdensome distillation procedure in existing methods brings significant latency. For instance, one of the state-of-the-art works by Deng et al. [5] requires  $\\sim 18$  days to distill only 1 image per class for CIFAR100 dataset [15] as shown in Fig. 1(d) and [47]. Even FRePo [52], with the most satisfactory efficiency, takes over 3 hours in the same setting requiring 500,000 neural network steps. The long training process in current DD makes it inconvenient for scenarios requiring high efficiency, e.g., processing streaming data.",
+        "bbox": [
+            75,
+            138,
+            468,
+            396
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Focusing on these drawbacks, in this paper, we propose few-shot dataset distillation and are interested in the performance of DD if only a few or even a single neural network is available for training. We first try a naive solution by merely adopting one neural network for the existing method FRePo [52] and visualize the accuracy and efficiency. As shown in Fig. 1(d), although the simple strategy improves the efficiency, the performance gap with the original version based on thousands of networks is significant, which suggests a trade-off between performance and the number of networks. A similar effect is also revealed by Cazenavette et al. [2], where the number of teacher training trajectories would affect the performance substantially. Thus, how to boost the performance by only a limited number of networks becomes an interesting question in few-shot DD.",
+        "bbox": [
+            73,
+            397,
+            468,
+            625
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Currently, the networks used in Fig. 1(d) are randomly and independently initialized, which makes us curious: whether there exists a dedicated neural network, such that the synthetic dataset distilled in it can achieve similar performance to those distilled in multiple ones. In this paper, we describe this concept through a quad-level definition termed as distillation space, as shown in Fig. 1(c), and propose a bi-level algorithm to find it, to optimize the error on real data, for networks trained with the synthetic dataset, distilled in this space.",
+        "bbox": [
+            75,
+            626,
+            468,
+            777
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "However, the bi-level optimization requires backpropagating through an unrolled computational graph over multiple steps of gradient descent, which imposes an intensive GPU footprint. Due to the bottleneck on GPU memory, the number of steps for inner optimization is limited, which further limits the performance in practice. To reduce the complexity, we free the dependency of higher-order gradients via casting the problem as image translation, to make",
+        "bbox": [
+            75,
+            779,
+            468,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "sure that the iterative optimization process is not nested in the computational graph: the synthetic dataset is distilled in a random but fixed neural network space and then translated to the desired space via a translator network.",
+        "bbox": [
+            496,
+            90,
+            890,
+            150
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Specifically, the translator is pre-trained on some large datasets like ImageNet [4]. In each iteration, a random subset is sampled. Distilled results after being translated from the original space are evaluated in some random networks, and the distillation loss is back-propagated to the translator to update its parameters. We find that the distillation space translator after pre-training can generalize well across different datasets, storage budgets, and numbers of classes. With only a few adaptation steps on the target dataset, the performance of distilled data after translation achieves can be on par with those distilled by multiple neural networks at  $\\sim 15\\times$  faster, as shown in Fig. 1(d).",
+        "bbox": [
+            496,
+            152,
+            890,
+            332
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, our contributions are listed as follows:",
+        "bbox": [
+            517,
+            333,
+            857,
+            347
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Tailoring for scenarios requiring high efficiency, we are the first to study the problem of few-shot dataset distillation, where only a limited number of neural networks are available for DD, and introduce the quad-level definition of distillation space for it.",
+            "- An efficient translative modeling approach with a pretraining algorithm is proposed to learn an effective distillation space;",
+            "- Extensive experiments demonstrate that our method is capable of generating dataset distillation results with  $\\sim 15\\times$  acceleration."
+        ],
+        "bbox": [
+            517,
+            359,
+            890,
+            546
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            500,
+            571,
+            648,
+            588
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Dataset distillation (DD) refers to distilling a small synthetic dataset  $S$  from a given large dataset  $T$ , where  $S$  is optimized to have similar downstream training performance to  $T$ . Unlike most existing techniques that focus on reducing the size of a model [6, 25, 45, 44, 7, 46, 12, 11, 10, 33], DD concentrates on learning compressed data to enhance learning efficiency. Wang et al. [41] firstly introduce the task and propose a meta-learning method to minimize the loss of meta-test on  $T$  for models meta-trained on  $S$ . This scheme aligns with the evaluation protocol of DD: to pursue higher accuracy on the real test data for networks optimized by the synthetic ones. However, restricted by the GPU memory, the steps of meta-training in this framework are limited, which bottlenecks the performance [5]. The bilevel loop with a large number of inner steps also affects the efficiency negatively.",
+        "bbox": [
+            496,
+            598,
+            890,
+            840
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address this issue, a series of works consider mapping real and synthetic samples to a feature space with some kernels, e.g., NTK [28, 29], NNGP [23], and non-linear network [52, 24], and then perform kernel ridge regression",
+        "bbox": [
+            496,
+            840,
+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "18655",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/3b890c544f14088c7a66a95b902dc199de9596af28929141ca04fb06c5db09e9.jpg",
+        "image_caption": [
+            "(a)",
+            "Figure 2. (a) Existing DD methods rely on an iterative training process, where a new network has to be initialized for forward and backward passes of the real dataset  $\\mathcal{T}$  and the synthetic dataset  $S$ . (b) We desire to learn a specific distillation space, where  $\\mathcal{S}$  optimized only in such a space can minimize the error of neural feature regression in an arbitrary random network. The loop for optimizing  $\\mathcal{S}$  is nested in the computational graph for optimizing the distillation space. (c) We detach the loop for optimizing  $\\mathcal{S}$  for computational efficiency and convert the problem to a transitive model, where  $\\mathcal{S}$  is distilled in an arbitrary but fixed neural space first and then translated to the desired space."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            88,
+            354,
+            299
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/b544e6607d0a9c1f466794b3285971bc8e190ac713ff642550a4cfc8aba2a023.jpg",
+        "image_caption": [
+            "(b)",
+            "(c)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            359,
+            88,
+            893,
+            299
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "(KRR). Benefiting from the analytical solution of KRR, these methods can access the optimal parameters trained by synthetic datasets via direct computation without the necessity of higher-order gradients, which achieves favorable efficiency and accuracy at the same time. In this paper, the KRR-based formulation is also adopted as the main objective to reduce the complexity of meta-learning, thanks to its satisfactory efficiency.",
+        "bbox": [
+            75,
+            416,
+            468,
+            537
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the literature of DD, matching-based methods are another major branch. For example, Zhao et al. [51] and a lot of following works [49, 13, 17, 9, 48] adopt gradient matching. Cazenavette et al. [2] propose MTT, which optimizes the distance between network parameters trained by  $S$  and  $T$  respectively from some cached initialization. Their insights lie in that gradients in networks or trained model parameters can represent the training effects of different datasets. Some works also consider matching the statistics of  $S$  and  $T$  in some neural networks [50, 40], which get rid of computing gradients of training networks via  $S$  and  $T$  and thus improves the efficiency.",
+        "bbox": [
+            75,
+            537,
+            470,
+            718
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "No matter what objectives existing methods adopt, they all rely on an extensive outer optimization loop to update synthetic data, where  $S$  and  $\\mathcal{T}$  have to undergo forward-backward passes through thousands of networks. To make things worse, a series of works considering synthetic dataset parameterization, which tries to increase the number of images with the same storage budget, require even more such iterations [5, 19]. Motivated by these facts, we focus on the problem of few-shot dataset distillation in this paper where a synthetic dataset is distilled given only a few or even a single neural network. Given that naively adopting only a few random networks results in inferior performance as",
+        "bbox": [
+            75,
+            719,
+            470,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "shown in Fig. 1(d), we introduce the concept of distillation space, such that the performance of synthetic data distilled in this space can match those in enormous networks. Dedicated to finding such a space to benefit dataset distillation to reduce the number of networks required for acceleration while retaining the performance as much as possible, a novel translative model with a pre-training approach is proposed to this end. To our best knowledge, this is the first work focusing on few-shot learning and pre-training in DD.",
+        "bbox": [
+            496,
+            416,
+            893,
+            551
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methods",
+        "text_level": 1,
+        "bbox": [
+            500,
+            566,
+            598,
+            583
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we delve into details about our methods for few-shot dataset distillation, where real and synthetic datasets can be processed by only a few neural networks. We first provide a brief introduction of current mainstream solutions for DD, based on which we propose the quad-level definition of distillation space in formal and a basic bi-level algorithm to learn the space. For computational efficiency, we then convert the original formulation of learning the distillation space to a transitive problem and propose an alternative algorithm, backed up by theoretical analysis. Finally, we explain the paradigm of pre-training for few-shot learning to increase the transferability of the learned distillation space across various datasets, the number of classes, and the storage budgets of synthetic datasets.",
+        "bbox": [
+            496,
+            593,
+            893,
+            805
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminary",
+        "text_level": 1,
+        "bbox": [
+            500,
+            816,
+            629,
+            832
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Dataset distillation (DD) targets a small synthetic dataset  $S$  such that the performance on downstream training with  $S$  can match that with the original dataset  $\\mathcal{T}$ . The seminal work by Wang et al. [41] proposes a meta-learning ap",
+        "bbox": [
+            496,
+            839,
+            893,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "18656",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Bi-Level Optimization for Distillation Space.",
+        "bbox": [
+            78,
+            90,
+            465,
+            104
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Input:  $\\mathcal{T}$ : Target Dataset;  $\\Theta$ : Distribution for Initializing Neural Networks;  $T$ : Number of Inner Update Steps;  $\\alpha$ : Learning Rate for Inner Optimization;  $\\eta$ : Learning Rate for Outer Optimization.",
+        "bbox": [
+            78,
+            107,
+            468,
+            167
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Output:  $\\theta$ : Distillation Space after Optimization.",
+        "bbox": [
+            78,
+            167,
+            406,
+            183
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Initialize  $\\theta \\sim \\Theta$",
+            "2: for  $i = 1,2,3,\\ldots$  do",
+            "3: Initialize  $S$  with random samples from  $\\mathcal{T}$ ;",
+            "4:  $X_{\\mathcal{T}}^{\\theta}\\gets f_{\\theta}(X_{\\mathcal{T}});$",
+            "5: for  $1\\leq t\\leq T$  do",
+            "6:  $w_{\\mathcal{S},\\theta}^* \\gets f_\\theta(X_\\mathcal{S})^\\top (f_\\theta(X_\\mathcal{S})f_\\theta(X_\\mathcal{S})^\\top)^{-1}Y_\\mathcal{S};$",
+            "7:  $X_{\\mathcal{S}} \\gets X_{\\mathcal{S}} - \\alpha \\nabla_{X_{\\mathcal{S}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}}^{2}$ ;",
+            "8:  $Y_{\\mathcal{S}} \\gets Y_{\\mathcal{S}} - \\alpha \\nabla_{Y_{\\mathcal{S}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}$ ;",
+            "9: end for",
+            "10: Randomly sample  $\\theta^{\\prime}\\sim \\Theta$",
+            "11:  $X_{\\mathcal{T}}^{\\theta^{\\prime}}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{T}});$",
+            "12:  $w_{\\mathcal{S},\\theta^{\\prime}}^{*}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top}(f_{\\theta^{\\prime}}(X_{\\mathcal{S}})f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top})^{-1}Y_{\\mathcal{S}};$",
+            "13:  $\\theta \\gets \\theta -\\eta \\nabla_{\\theta}\\| X_{\\mathcal{T}}^{\\theta '}w_{\\mathcal{S},\\theta '}^{*} - Y_{\\mathcal{T}}\\|^{2};$",
+            "14: end for"
+        ],
+        "bbox": [
+            81,
+            184,
+            444,
+            400
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "proach, which optimizes the loss on  $\\mathcal{T}$  for models trained with  $S$  and backpropagates the gradients through multiple training steps to update  $S$ :",
+        "bbox": [
+            75,
+            429,
+            468,
+            474
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} ^ {*} = \\underset {\\mathcal {S}} {\\arg \\min } \\mathbb {E} _ {\\theta^ {(0)} \\sim \\Theta} [ l (\\mathcal {T}; \\theta^ {(T)}) ], \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
+            484,
+            468,
+            516
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\theta^ {(t)} = \\theta^ {(t - 1)} - \\alpha \\nabla l (\\mathcal {S}; \\theta^ {(t - 1)}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            513,
+            367,
+            532
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Theta$  denotes a distribution for initialization,  $T$  is the number of training steps with  $S$  and  $1 \\leq t \\leq T$ ,  $\\alpha$  is the learning rate, and  $l$  is the loss function, e.g., cross-entropy loss for classification problems.",
+        "bbox": [
+            75,
+            542,
+            468,
+            602
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The bi-level optimization algorithm indicated in Eq. 1 relies on backpropagating through an unrolled computational graph of inner optimization steps, which makes it inefficient in both time and memory. Nguyen et al. [28, 29] thus consider the problem of kernel ridge regression (KRR), where the analytical optimal solution gets rid of the necessity to optimize the model with  $S$  for multiple nested steps. For more satisfactory accuracy and efficiency, the spirit is further extended by following works [52, 23], which map a batch of  $n$  samples  $X$  to a feature space with a random neural network and then perform KRR. Denote the function of neural network parameterized by  $\\theta$  as  $f_{\\theta}$  and the label matrix corresponding to  $X \\in \\mathbb{R}^{n \\times d}$  as  $Y \\in \\mathcal{R}^{n \\times c}$ , where  $d$  and  $c$  are the dimensions of sample and label respectively, i.e.,  $h \\times w \\times 3$  and the number of classes in the RGB image classification problem, the objective can be formulated as:",
+        "bbox": [
+            75,
+            603,
+            468,
+            845
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} X _ {\\mathcal {S}} ^ {*}, Y _ {\\mathcal {S}} ^ {*} = \\underset {X _ {\\mathcal {S}}, Y _ {\\mathcal {S}}} {\\arg \\min } \\mathbb {E} _ {\\theta \\sim \\Theta} [ \\| f _ {\\theta} (X _ {\\mathcal {T}}) w _ {\\mathcal {S}, \\theta} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2} ], \\tag {2} \\\\ w _ {S, \\theta} ^ {*} = f _ {\\theta} (X _ {S}) ^ {\\top} \\left(f _ {\\theta} (X _ {S}) f _ {\\theta} (X _ {S}) ^ {\\top}\\right) ^ {- 1} Y _ {S}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
+            854,
+            467,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This technique is known as neural feature regression (NFR) [52]. In each training iteration, a new random neural network is initialized for solving the problem in Eq. 2, as shown in Fig. 2(a).",
+        "bbox": [
+            496,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Learning a Distillation Space",
+        "text_level": 1,
+        "bbox": [
+            500,
+            160,
+            759,
+            176
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Fig. 1(a), the iterative optimization framework shown in Fig. 2(a) involves forward and backward processes through thousands of networks and introduces significant computational overhead. In this work, we thus focus on the problem of DD using only a few or even one network. Given the results in Fig. 1(b) that simply adopting a random network yields limited performance, we are interested in learning a specific network such that  $S$  distilled in it can achieve performance on par with that distilled in multiple networks, i.e., minimize the error on  $\\mathcal{T}$  for an arbitrary model trained with  $S$ . Formally, we term such a network as distillation space in the following definition.",
+        "bbox": [
+            496,
+            183,
+            890,
+            364
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Definition 1 (Distillation Space). A distillation space for a distribution of network  $\\Theta$  and a target dataset  $\\mathcal{T}$  is a neural network function  $f$  parameterized by  $\\theta^{*}$  which satisfies:",
+        "bbox": [
+            496,
+            375,
+            892,
+            420
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\theta^{*} = \\operatorname *{arg  min}_{\\theta^{(0)}}\\mathbb{E}_{\\theta^{(0)^{\\prime}}\\sim \\Theta}[l(\\mathcal{T};\\theta^{(T)^{\\prime}})], \\\\ \\theta^ {(t) ^ {\\prime}} = \\theta^ {(t - 1) ^ {\\prime}} - \\alpha^ {\\prime} \\nabla l \\left(\\mathcal {S} ^ {*}; \\theta^ {(t - 1) ^ {\\prime}}\\right), \\tag {3} \\\\ \\mathcal {S} ^ {*} = \\underset {\\mathcal {S}} {\\arg \\min } l (\\mathcal {T}; \\theta^ {(T)}), \\\\ \\theta^ {(t)} = \\theta^ {(t - 1)} - \\alpha \\nabla l (\\mathcal {T}; \\theta^ {(t - 1)}). \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            570,
+            430,
+            890,
+            529
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In practice, to find an effective distillation space, we first simplify the quad-level definition via NFR in Eq. 2, which derives a bi-level optimization problem:",
+        "bbox": [
+            496,
+            540,
+            890,
+            585
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\theta^ {*} = \\underset {\\theta} {\\arg \\min } \\mathbb {E} _ {\\theta^ {\\prime} \\sim \\Theta} [ \\| f _ {\\theta^ {\\prime}} (X _ {\\mathcal {T}}) w _ {\\mathcal {S} ^ {*}, \\theta^ {\\prime}} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2} ], \\\\ w _ {\\mathcal {S} ^ {*}, \\theta^ {\\prime}} ^ {*} = f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) ^ {\\top} \\left(f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) ^ {\\top}\\right) ^ {- 1} Y _ {\\mathcal {S}} ^ {*}, \\tag {4} \\\\ X _ {\\mathcal {S}} ^ {*}, Y _ {\\mathcal {S}} ^ {*} = \\underset {X _ {\\mathcal {S}}, Y _ {\\mathcal {S}}} {\\arg \\min} \\| f _ {\\theta} (X _ {\\mathcal {T}}) w _ {\\mathcal {S}, \\theta} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2}, \\\\ w _ {S, \\theta} ^ {*} = f _ {\\theta} (X _ {S}) ^ {\\top} \\left(f _ {\\theta} (X _ {S}) f _ {\\theta} (X _ {S}) ^ {\\top}\\right) ^ {- 1} Y _ {S}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            595,
+            890,
+            691
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Eq. 4 indicates a bi-level meta-learning algorithm as shown in Fig. 2(b) and Alg. 1. In each inner iteration,  $S$  is metatrained via NFR in the current neural space  $f_{\\theta}$ .  $S$  after a whole inner loop is meta-tested in a random neural network  $f_{\\theta'}$  and the loss of NFR is back-propagated to update  $\\theta$ .",
+        "bbox": [
+            496,
+            702,
+            890,
+            777
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Learning a Translation to a Distillation Space",
+        "text_level": 1,
+        "bbox": [
+            500,
+            786,
+            883,
+            803
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Although Alg. 1 can be an effective algorithm to learn a valid distillation space, the back-propagation process through a nested computational graph is inefficient in GPU memory. The memory complexity is proportionate to the number of inner optimization steps  $T$  to obtain the optimal synthetic dataset in the current space, which is crucial",
+        "bbox": [
+            496,
+            809,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18657",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "for the final performance [5] but withheld by the limited GPU memory. For instance, in a 40G A100 GPU,  $T$  in Alg. 1 can be set as 16 at most, which is too small to get convergence for inner optimization. To alleviate this drawback, we consider an alternative approach to learn a distillation space. Specifically, we detach the inner optimization from the computational graph by converting the problem to a transitive model, based on the following proposition.",
+        "bbox": [
+            75,
+            90,
+            472,
+            212
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Proposition 1. For a target dataset  $X_{\\mathcal{T}} \\in \\mathbb{R}^{n_{\\mathcal{T}} \\times d}$  and  $Y_{\\mathcal{T}} \\in \\mathbb{R}^{n_{\\mathcal{T}} \\times c}$  with  $n_{\\mathcal{T}} \\geq d$ , assume that  $X_{\\mathcal{S},0}^{*}$  and  $Y_{\\mathcal{S},0}^{*}$  satisfy  $\\| f_{\\theta}(X_{\\mathcal{T}})w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}}\\|^{2} = 0$ , where  $w_{\\mathcal{S},\\theta}^{*} = f_{\\theta}(X_{\\mathcal{S},0}^{*})^{\\top}(f_{\\theta}(X_{\\mathcal{S},0}^{*})f_{\\theta}(X_{\\mathcal{S},0}^{*})^{\\top})^{-1}Y_{\\mathcal{S},0}^{*}$  and  $f_{\\theta}$  is a known linear transformation parameterized by a full-rank matrix  $\\theta \\in \\mathbb{R}^{d \\times d'}$ ,  $d \\leq d'$ . Similarly, let  $f_{\\theta^{*}}$  be a desired linear distillation space and  $\\theta^{*} \\in \\mathbb{R}^{d \\times d''}$ ,  $d \\leq d'' \\leq n_{\\mathcal{T}}$ . The distilled dataset  $X_{\\mathcal{S},*}^{*}$  and  $Y_{\\mathcal{S},*}^{*}$  in this space satisfy  $\\| f_{\\theta^{*}}(X_{\\mathcal{T}})w_{\\mathcal{S},\\theta^{*}}^{*} - Y_{\\mathcal{T}}\\|^{2} = 0$ , where  $w_{\\mathcal{S},\\theta^{*}}^{*} = f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})^{\\top}(f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})^{\\top})^{-1}Y_{\\mathcal{S},*}^{*}$ . There exists a translation function  $G$  for  $X_{\\mathcal{S},0}^{*}$  and  $Y_{\\mathcal{S},0}^{*}$  such that  $X_{\\mathcal{S},*}^{*}, Y_{\\mathcal{S},*}^{*} = G(X_{\\mathcal{S},0}^{*}, Y_{\\mathcal{S},0}^{*})$ , whose parameters are not dependent on the target dataset  $X_{\\mathcal{T}}$  and  $Y_{\\mathcal{T}}$ .",
+        "bbox": [
+            76,
+            218,
+            472,
+            425
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Proof. Due to the linearity of  $f_{\\theta}$  and  $f_{\\theta^{*}}$ , we can rewrite the given conditions as:",
+        "bbox": [
+            75,
+            431,
+            470,
+            460
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {\\mathcal {T}} \\theta w _ {S, \\theta} ^ {*} - Y _ {\\mathcal {T}} = 0, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
+            470,
+            468,
+            488
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {\\mathcal {T}} \\theta^ {*} w _ {S, \\theta^ {*}} ^ {*} - Y _ {\\mathcal {T}} = \\mathbf {0}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            491,
+            468,
+            508
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since  $n_{\\mathcal{T}} \\geq d$  for  $X_{\\mathcal{T}}$ , pre-multiplying terms in Eq. 5 by the Moore-Penrose inverse  $X_{\\mathcal{T}}^{\\dagger}$ , we have",
+        "bbox": [
+            75,
+            517,
+            468,
+            549
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {\\mathcal {T}} ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta w _ {\\mathcal {S}, \\theta} ^ {*}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            215,
+            556,
+            468,
+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Similarly, through Eq. 6, we have",
+        "bbox": [
+            76,
+            584,
+            303,
+            599
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {\\mathcal {S}, \\theta^ {*}} ^ {*} = (X _ {\\mathcal {T}} \\theta^ {*}) ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta^ {* \\dagger} X _ {\\mathcal {T}} ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta^ {* \\dagger} \\theta w _ {\\mathcal {S}, \\theta} ^ {*}, \\quad (8)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            101,
+            606,
+            468,
+            627
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the first, second, and third equalities are due to  $n_{\\mathcal{T}} \\geq d''$ ,  $d'' \\geq d$ , and Eq. 7 respectively. We can observe in Eq. 8 that  $w_{S,\\theta^*}^*$  in the desired distillation space is not dependent on  $\\mathcal{T}$ . Thus, the optimal  $X_{S,*}^*$  and  $Y_{S,*}^*$  resulting the optimal KRR parameter can be obtained given only  $X_{S,0}^*$  and  $Y_{S,0}^*$  by some translation function  $G$ , which implicitly includes the knowledge of the distillation space.",
+        "bbox": [
+            75,
+            633,
+            468,
+            741
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Prop. 1 indicates that it is possible to approach the distillation space by translating samples from some space rather than learning  $\\theta^{*}$  directly, motivated by which we propose to learn a translation from one another space to the distillation space. The main workflow is similar to Alg. 1: synthetic data are first distilled in a random but fixed network in an inner loop and then translated to final results, as shown in Fig. 2(c). The translator is optimized so that results after translation are equipped with the property of those produced in a distillation space: to minimize the NFR error in",
+        "bbox": [
+            75,
+            750,
+            470,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 2 Pre-training a Distillation Space Translator.",
+        "bbox": [
+            500,
+            90,
+            877,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Input:  $\\mathcal{Z}$ : A Large Dataset;  $\\Theta$ : Distribution for Initializing Neural Networks;  $\\theta$ : An Arbitrary Random Neural Network;  $T$ : Number of Update Steps for Synthetic Data;  $\\alpha$ : Learning Rate for Synthetic Data;  $\\eta$ : Learning Rate for Translator.",
+        "bbox": [
+            500,
+            107,
+            890,
+            181
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Output:  $\\omega$ : A Pre-trained Translator.",
+        "bbox": [
+            500,
+            183,
+            750,
+            196
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Initialize  $\\omega$  randomly;",
+            "2: for  $i = 1,2,3,\\ldots$  do",
+            "3: Randomly choose a subset of data  $\\mathcal{T}$  from  $\\mathcal{Z}$ ;",
+            "4: Initialize  $S^{\\prime}$  with random samples from  $\\mathcal{T}$",
+            "5:  $X_{\\mathcal{T}}^{\\theta}\\gets f_{\\theta}(X_{\\mathcal{T}});$",
+            "6: for  $1 \\leq t \\leq T$  do",
+            "7:  $w_{\\mathcal{S}^{\\prime},\\theta}^{*}\\gets f_{\\theta}(X_{\\mathcal{S}^{\\prime}})^{\\top}(f_{\\theta}(X_{\\mathcal{S}^{\\prime}})f_{\\theta}(X_{\\mathcal{S}^{\\prime}})^{\\top})^{-1}Y_{\\mathcal{S}^{\\prime}};$",
+            "8:  $X_{\\mathcal{S}^{\\prime}} \\gets X_{\\mathcal{S}^{\\prime}} - \\alpha \\nabla_{X_{\\mathcal{S}^{\\prime}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S}^{\\prime},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}$ ;",
+            "9:  $Y_{\\mathcal{S}^{\\prime}} \\gets Y_{\\mathcal{S}^{\\prime}} - \\alpha \\nabla_{Y_{\\mathcal{S}^{\\prime}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S}^{\\prime},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}$ ;",
+            "10: end for",
+            "11:  $X_{\\mathcal{S}},Y_{\\mathcal{S}} = G_{\\omega}(X_{\\mathcal{S}^{\\prime}},Y_{\\mathcal{S}^{\\prime}});$",
+            "12: Randomly sample  $\\theta^{\\prime}\\sim \\Theta$",
+            "13:  $X_{\\mathcal{T}}^{\\theta^{\\prime}}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{T}});$",
+            "14:  $w_{\\mathcal{S},\\theta^{\\prime}}^{*}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top}(f_{\\theta^{\\prime}}(X_{\\mathcal{S}})f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top})^{-1}Y_{\\mathcal{S}};$",
+            "15:  $\\omega \\gets \\omega -\\eta \\nabla_{\\omega}\\| X_{\\mathcal{T}}^{\\theta '}w_{S,\\theta '}^{*} - Y_{\\mathcal{T}}\\|^{2};$",
+            "16: end for"
+        ],
+        "bbox": [
+            506,
+            198,
+            888,
+            445
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "any random network. Since gradients are only required to back propagated to the translator rather than the whole inner loop, the memory complexity is irrelevant to the number of inner optimization steps. Thus, the translative model is a memory-efficient algorithm where only first-order gradients are necessary.",
+        "bbox": [
+            496,
+            476,
+            890,
+            566
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Pre-training a Distillation Space Translator",
+        "text_level": 1,
+        "bbox": [
+            500,
+            578,
+            867,
+            594
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We expect that the distillation space optimized in a dataset is transferable across different datasets, storage budgets for synthetic data, and the number of classes. To tackle these challenges on transferability, in this paper, we consider pre-train a translator on some large dataset like ImageNet [4], so that it provides a satisfactory initialization and only requires a small number of adaptation steps for a target dataset, like the typical few-shot learning [42, 39, 38, 30]. The algorithm is shown in Alg. 2. In each training iteration  $i$ , we sample a subset from the large dataset and perform a gradient-decent step with the strategy mentioned in Sec. 3.3. Upon a translator is pre-trained, it can serve as a strong initialization for the adaptation process to a new dataset, which behaves identically to Line 11 to 15 of Alg. 2.",
+        "bbox": [
+            496,
+            602,
+            890,
+            814
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            829,
+            632,
+            845
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct experiments to validate the effectiveness of the proposed method for few-shot DD. We first introduce our experiment settings and implement de",
+        "bbox": [
+            496,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18658",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/d6e2d385c9aaee15b803c429bcb1d60bf42b4c2a9d97267c355fc315f9394e0b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyper-Parameter</td><td>Denotation</td><td>Value</td></tr><tr><td>T</td><td>Number of Update Steps for Synthetic Data</td><td>3,000</td></tr><tr><td>α</td><td>Learning Rate for Synthetic Data</td><td>1e-3</td></tr><tr><td>η</td><td>Learning Rate for Translator in Pre-Training</td><td>1e-5</td></tr><tr><td>N</td><td>Number of Cached Subsets in Pre-Training</td><td>5,000</td></tr><tr><td>Cmax</td><td>Maximal Number of Classes in a Subset in Pre-Training</td><td>100</td></tr><tr><td>Cmin</td><td>Minimal Number of Classes in a Subset in Pre-Training</td><td>10</td></tr><tr><td>M</td><td>Maximal Number of Images in a Subset in Pre-Training</td><td>4,000</td></tr><tr><td>Imax</td><td>Maximal Number of Images in a Synthetic Dataset in Pre-Training</td><td>1,000</td></tr><tr><td>B</td><td>Batch Size in Pre-Training</td><td>4</td></tr><tr><td>S</td><td>Number of Pre-Training Steps</td><td>200,000</td></tr><tr><td>S&#x27;</td><td>Number of Adaptation Steps for Translator</td><td>1,000</td></tr><tr><td>η&#x27;</td><td>Learning Rate for Translator in Adaptation</td><td>1e-4</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1. List of hyper-parameters and their values.",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "tails of the method. Then, we compare our method with state-of-the-art solutions of DD in terms of both accuracy and efficiency. To illustrate how the proposed method works, we also provide an in-depth analysis of the method with a variety of baselines. Finally, we conduct experiments on continual learning, an important use case for DD, to further demonstrate the practical value of our method.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Settings and Implementing Details",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In few-shot dataset distillation, a real dataset  $\\mathcal{T}$  can be processed by only a few neural networks to generate a synthetic dataset  $S$ . In our method,  $S$  is firstly optimized in an arbitrary but fixed neural network by  $T$  steps, with the learning rate  $\\alpha$ . The results are then processed by a translator to generate the final synthetic dataset. The translator adopts an auto-encoder architecture with 3 Conv-BatchNorm-ReLU blocks, and the detailed configuration can be found in the supplement. Notably, due to the fully-convolutional structure, the pre-trained translator can also be adapted to datasets with different resolutions beyond the one used during pre-training. Please refer to the supplement for details. The translator is pre-trained on the ImageNet dataset by  $S$  steps with the learning rate  $\\eta$  and then adapted on the target dataset by a small number of iterations  $S'$ , with a learning rate  $\\eta'$ . Some hyper-parameters are summarized in Tab. 1. Other hyper-parameters follow the default setting in the PyTorch [31] implementation of FRePo [52].",
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+    },
+    {
+        "type": "text",
+        "text": "Pre-Training: The key design of the translative pretraining pipeline lies in the separation of two stages: dataset distillation in an arbitrary but fixed neural network and the translation to the desired space. In practice, instead of directly following the pipeline in Alg. 2 that nests the two steps in one loop, the two stages are conducted independently in the interest of better training efficiency. Results distilled in the pre-defined network are cached for multiple random subsets so that they can be loaded directly and used",
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+    },
+    {
+        "type": "text",
+        "text": "repeatedly in the pre-training stage, which improves the training efficiency. The detailed algorithms for the caching stage and the pre-training stage can be found in the supplement.",
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+    {
+        "type": "text",
+        "text": "The caching stage aims to generate distilled results for multiple subsets. For sampling a subset, we first randomly choose the number of classes ranging from  $C_{\\text{min}}$  to  $C_{\\text{max}}$  and then randomly select the corresponding number of classes from the 1,000 ImageNet classes. For each select class, a certain number of random real images are sampled uniformly for each selected class such that the total number of images is  $M$  at most. The data augmentation technique DSA [49] is applied in the caching stage to mimic the cases of larger datasets. The maximal number of synthetic images is  $I_{\\text{max}}$  and they are initialized with the selected real data. After distillation, indices of selected real samples and the distilled dataset are cached in the disk for future use in the pre-training stage. This process can be deployed to multiple GPUs in parallel, since the distillation for each subset is independent.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In the pre-training stage, cached results in the previous stage are loaded. The NFR loss is calculated in a randomly initialized networks over a distribution in each iteration. Like the caching stage, pre-cached subsets in a batch can also be distributed to multiple GPUs in parallel. In this work, the pre-training is conducted on a single 40G A100 GPU, which takes roughly 2 days for the 200,000 steps.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Adaptation: Given a pre-trained translator, it requires a small number of adaptation steps in general for the target dataset. The detailed adaptation algorithm can be found in the supplement. Intuitively, the procedure is consistent with the two-stage process in pre-training: to generate distilled results in a pre-defined network and then use the translator for the final results. The only difference with the pretraining stage is that real data come from the target dataset. By default, the set of IPC for adaptation only contains the target IPC. More IPCs can also be included in this set to",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "18659",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f572aad2b01b994d9dc5927e6979596add2f9995f696e529fd60567593bd6120.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>IPC</td><td>Metric</td><td>DD</td><td>RTP</td><td>DC</td><td>DSA</td><td>IDC</td><td>MTT</td><td>DM</td><td>FRePo</td><td>Ours</td><td>Ours-DS</td></tr><tr><td rowspan=\"6\">CIFAR 10</td><td rowspan=\"2\">1</td><td>Acc. (%)</td><td>40.5±0.8</td><td>49.1±0.6</td><td>28.3±0.5</td><td>28.8±0.7</td><td>36.7±0.4</td><td>46.3±0.8</td><td>26.0±0.8</td><td>46.8±0.7</td><td>44.0±0.2</td><td>51.4±0.4</td></tr><tr><td>Time (h)</td><td>363.9</td><td>363.9</td><td>0.1</td><td>0.1</td><td>10.6</td><td>0.8</td><td>0.3</td><td>2.4</td><td>0.02×120.0</td><td>0.1×24.0</td></tr><tr><td rowspan=\"2\">10</td><td>Acc. (%)</td><td>50.0±0.5</td><td>62.4±0.4</td><td>44.9±0.5</td><td>52.1±0.5</td><td>58.3±0.4</td><td>65.3±0.7</td><td>48.9±0.6</td><td>65.5±0.6</td><td>59.2±0.3</td><td>66.0±0.3</td></tr><tr><td>Time (h)</td><td>447.2</td><td>447.2</td><td>1.0</td><td>1.3</td><td>11.1</td><td>2.4</td><td>0.3</td><td>3.1</td><td>0.04×77.5</td><td>0.2×15.5</td></tr><tr><td rowspan=\"2\">50</td><td>Acc. (%)</td><td>-</td><td>70.5±0.4</td><td>53.9±0.5</td><td>60.6±0.5</td><td>69.5±0.3</td><td>71.6±0.2</td><td>63.0±0.4</td><td>71.7±0.2</td><td>66.7±0.2</td><td>71.8±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>1377.8</td><td>4.4</td><td>5.3</td><td>12.8</td><td>3.8</td><td>0.4</td><td>8.1</td><td>0.12×67.5</td><td>1.3×6.2</td></tr><tr><td rowspan=\"4\">CIFAR 100</td><td rowspan=\"2\">1</td><td>Acc. (%)</td><td>-</td><td>21.3±0.6</td><td>12.8±0.3</td><td>13.9±0.3</td><td>17.9±0.2</td><td>24.3±0.3</td><td>11.4±0.3</td><td>28.7±0.1</td><td>22.8±0.4</td><td>29.1±0.4</td></tr><tr><td>Time (h)</td><td>-</td><td>447.2</td><td>0.4</td><td>0.5</td><td>50.0</td><td>3.5</td><td>3.1</td><td>3.1</td><td>0.08×38.8</td><td>0.1×31.0</td></tr><tr><td rowspan=\"2\">10</td><td>Acc. (%)</td><td>-</td><td>34.7±0.5</td><td>25.2±0.3</td><td>32.3±0.3</td><td>36.1±0.4</td><td>40.1±0.4</td><td>29.7±0.3</td><td>42.5±0.2</td><td>35.1±0.2</td><td>38.4±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>2520.8</td><td>10.6</td><td>11.4</td><td>68.9</td><td>4.2</td><td>3.1</td><td>10.4</td><td>0.32×32.5</td><td>1.0×10.4</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Comparisons with state-of-the-art methods of DD on test accuracy and training efficiency. DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget. The black subscript indicates the standard deviation over multiple evaluations. The red subscript denotes the times of acceleration compared with the baseline method FRePo [52]. The best and second best results in each setting are marked by bold and underline respectively.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "increase the generalization ability of the translator across other unseen IPCs during adaptation, as shown in Sec. 4.3 and the supplement.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we consider the widely-adopted benchmarks of CIFAR10 and CIFAR100 [15] with a resolution of  $32 \\times 32$  for the main evaluation. Results on datasets with higher resolutions and larger sizes can be found in the supplement. Following previous works [52, 5], we evaluate the proposed method on storage budgets of 1, 10, and 50 images per class (IPC) for CIFAR10 and 1 and 10 IPC for CIFAR100. Synthetic datasets are trained with 3-layer convolutional networks and evaluated on the same architecture. The cross-architecture performance will also be studied in Sec. 4.3. We report the average result and the standard deviation over 3 replicate evaluations for each setting.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparisons with State of the Arts",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Here, we compare the proposed method for few-shot dataset distillation with state-of-the-art methods, including meta-learning-based methods in the seminal  $DD$  [41] and remember-the-past (RTP) [5], gradient-matching based methods in  $DC$ ,  $DSA$ , and  $IDC$ , trajectory-matching based  $MTT$ , distribution-matching based  $DM$ , and KRR-based  $FRePo$  [52]. The accuracy and training efficiency results are shown in Tab. 2. The accuracy results are from original papers while the training time is estimated based on the time-per-iteration results evaluated on the same hardware and the total number of iterations in the official codes. The shape/format of synthetic images in all methods except \"Ours-DS\" is consistent with that of real images in original datasets. For the running time of our method, we report the total time required for distilling using one network and the adaptation. Time for pre-training is not included since it is only conducted once, and once pre-trained, the trans",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "lator can be adapted for an infinite number of downstream datasets.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Through the results, we find that in the default parameterization, the proposed method within 1k adaptation steps falls about  $3 \\sim 7$  points behind the FRePo baseline but with  $30 \\sim 120 \\times$  acceleration due to the few-shot setting. Even compared with the currently most efficient algorithm, the speed of our method is still considerable. And the performance is at least comparable with other methods in terms of accuracy, with even dramatic acceleration, e.g., the meta-learning-based DD and RTP. The superior efficiency makes our method applicable in scenarios where data cannot be held for a long time, like streaming data.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Additionally, in \"Ours-DS\", down-sampled synthetic images are alternatively stored with the same number of stored parameters, which is a simple yet effective method to improve the performance especially when the storage budget is small. This parameterization typically requires more iterations for the adaptation stages. For small synthetic datasets like 1 and 10 IPC, the number of steps is  $6\\mathrm{k}$ , and for 50 IPC, the number is  $15\\mathrm{k}$ . Nevertheless, our method can still result in  $6 \\sim 31 \\times$  acceleration compared with the FRePo baseline with even better performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.3. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baselines: To demonstrate the effectiveness of the translative pre-training and target adaptation strategies proposed in this paper, we consider a series of baselines for ablation studies, including:",
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+    },
+    {
+        "type": "text",
+        "text": "- Baseline: a new neural network is sampled for each training iteration to process the real dataset and update synthetic data, which can be viewed as a benchmark given a sufficient number of networks;",
+        "bbox": [
+            517,
+            839,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "18660",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/06154ccaad20797bedc8e0ce0bcd27deca15f6c303011d9b10c7ecd6f3f9a5ec.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>IPC</td><td>Baseline</td><td>1 Net</td><td>Bi-Level</td><td>w/o Pre-Train</td><td>w AE</td><td>w/o Ada</td><td>w Ada</td></tr><tr><td rowspan=\"3\">CIFAR10</td><td>1</td><td>41.2±0.7</td><td>35.3±0.6</td><td>40.8±0.5</td><td>36.1±0.5</td><td>40.6±0.6</td><td>39.5±0.8</td><td>44.0±0.2</td></tr><tr><td>10</td><td>57.9±0.7</td><td>50.5±0.8</td><td>52.1±0.5</td><td>53.8±0.1</td><td>57.6±0.3</td><td>54.7±0.8</td><td>59.2±0.3</td></tr><tr><td>50</td><td>65.2±0.3</td><td>65.1±0.1</td><td>60.7±0.1</td><td>59.7±0.4</td><td>63.5±0.1</td><td>65.8±0.2</td><td>66.7±0.2</td></tr><tr><td rowspan=\"2\">CIFAR100</td><td>1</td><td>21.6±0.6</td><td>18.7±0.1</td><td>19.1±0.1</td><td>20.5±0.2</td><td>21.8±0.3</td><td>20.9±0.7</td><td>22.8±0.4</td></tr><tr><td>10</td><td>33.8±0.3</td><td>31.7±0.1</td><td>31.0±0.2</td><td>30.7±0.2</td><td>27.0±0.2</td><td>33.0±0.2</td><td>35.1±0.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Ablation studies of our method in different settings. The black subscript indicates the standard deviation over multiple evaluations.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3692b6d2a49b6d991829918028cdf46ca53d08d6b6bcaab143e39133c2b68db.jpg",
+        "image_caption": [
+            "An Arbitrary Net Acc.  $50.5\\%$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/db61bf443b8da7f4b3d355553d4e771e779e51d5a9e98bd2799fe191524f59b4.jpg",
+        "image_caption": [
+            "Translated Results w/o Ada Acc.  $54.7\\%$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c12843e0cd14f2c523e00dbaebca9a65f70c50fbab78f0afb1814ac205ef933f.jpg",
+        "image_caption": [
+            "Translated Results w Ada Acc.  $59.2\\%$",
+            "Figure 3. Qualitative analysis of results produced by our method for IPC 10 on CIFAR10. Zoom in for details."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/8db3621f92bf0aa6f2599bcc1a4233de2c96f623825ce7316bea5afd8a98da58.jpg",
+        "image_caption": [
+            "FRePo Acc.  $65.5\\%$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            691,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- 1 Net: synthetic data are distilled in a single network, which can be treated as a lower bound;",
+            "- Bi-Level: the bi-level algorithm described in Alg. 1;",
+            "-  $w / o$  Pre-Train: the target adaptation stage starts from a randomly initialized translator;",
+            "-  $wAE$ : the target adaptation stage starts from an autoencoder trained with a reconstruction objective;",
+            "-  $w/o$  Ada: directly using the pre-trained translator without the adaptation stage;",
+            "-  $w$  Ada: the default method."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "All the candidates are trained with 4k iterations. For those requiring adaptation, i.e., w/o Pre-Train, w AE, and w Ada, we first distill a synthetic dataset using 1 network with 3k iterations and adapt the translator for another 1k steps. Note that distilling with a single network only requires one forward propagation pass of the real dataset. Thus, the running time of our method is less than that of the baseline given the same number of iterations. Results are shown in Tab. 3.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For one thing, it turns out that the default method in this paper consistently surpasses the benchmark baseline requiring enormous networks in most cases. The reason is that with the number of networks for NFR increasing, it would be more difficult for the training convergence of distilled datasets, especially in the few-shot case. Please refer to the supplement for details.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For another, the consistent improvement comparing results of 1 Net and w/o Ada indicates that the pre-trained translator is capable of generating distilled results in a more favorable space. We visualize their results in the first two plots of Fig. 3, where the global tone is refined towards higher brightness contrast. Moreover, as shown in the 3rd plot, the adaptation stage injects more local details, which tries to improve the performance in a similar way performed by the state-of-the-art FRePo [52].",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Further, as shown in both Tab. 3 and Fig. 4(a-b), the pretrained model offers a more satisfactory initialization for the following adaptation stage, with lower initial loss, faster convergence, and higher accuracy.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "At last, the bi-level algorithm often leads to inferior performance, which may be partially attributed to the insufficient number of inner steps restricted by GPU memory.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Generalization: We observe that one benefit of adapting the translator in a target dataset is that it is generalizable across different storage budgets for synthetic datasets. For instance, as shown in Fig. 4(c), the translator adapted on IPC 1 and 50 can also behave well on IPC 10.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Following previous works [51, 49, 50], we also evaluate the cross-architecture performance in Tab. 4 over AlexNet [16], VGG11 [37], and ResNet18 [8]. The conclusion is consistent with the above analysis.",
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+        "text": "4.4. Application: Continual Learning",
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+        "text": "Continual learning (CL) aims to learn a sequence of tasks where the training data of past tasks are unavailable when",
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+        "table_body": "<table><tr><td>Setting</td><td>ConvNet</td><td>AlexNet</td><td>VGG</td><td>ResNet</td></tr><tr><td>Baseline</td><td>58.8±0.2</td><td>57.1±0.5</td><td>41.1±0.3</td><td>38.1±0.9</td></tr><tr><td>1 Net</td><td>50.5±0.8</td><td>50.9±0.6</td><td>34.2±0.3</td><td>35.3±0.3</td></tr><tr><td>Bi-Level</td><td>52.1±0.5</td><td>50.0±0.4</td><td>37.4±0.5</td><td>34.7±0.5</td></tr><tr><td>w/o Pre-Train</td><td>53.8±0.1</td><td>56.2±0.3</td><td>39.3±0.7</td><td>38.2±0.7</td></tr><tr><td>w/o Ada</td><td>54.7±0.8</td><td>52.8±0.3</td><td>35.7±0.7</td><td>34.8±1.2</td></tr><tr><td>w Ada</td><td>59.2±0.3</td><td>56.8±0.2</td><td>43.0±0.7</td><td>40.8±0.5</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4. Cross-architecture performance of our method in different settings. Results on CIFAR10 with 10 IPC are shown here.",
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+    {
+        "type": "text",
+        "text": "learning the current one. To overcome the problem of catastrophic forgetting [14], many works use a small buffer to store some valuable data of past tasks for future use [32, 1]. Dataset distillation can thus benefit this area by synthesizing informative samples [27, 34, 36, 43, 3, 26] to prevent forgetting as much as possible.",
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+        "type": "text",
+        "text": "In this paper, we evaluate the proposed method on CIFAR100-CL following the same 5-step protocol of [52, 50] with 20 classes for each task and 20 IPC. The results in Fig. 5 suggest a consistent conclusion with the ablation studies shown in Sec. 4.3 and indicate that the few-shot dataset distillation proposed in this paper can further facilitate the practical use when tasks come fast like a stream, which provides limited time for processing and learning.",
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+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we focus on the setting of few-shot dataset distillation to improve its efficiency, where data can only be processed by a limited number of neural networks. We introduce the concept of distillation space to optimize the performance of synthetic data distilled by only one network. Regarding that the complexity of the quad-level definition and the bi-level algorithm for distillation space, we convert the problem to a transitive model. The synthetic dataset is first distilled in a random but fixed neural network and then translated to the desired space. For transferability, we train the translator with a pre-training algorithm, so that a pre",
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+        "image_caption": [
+            "Figure 4. (a-b) NFR loss and test accuracy during adaption for CIFAR10 IPC 10 starting with the pre-trained translator by our algorithm, an auto-encoder, and a randomly initialized model. (c) Generalization performance of the translator on unseen IPC during adaptation.",
+            "Figure 5. Performance of continual learning on CIFAR100 with 5 steps and 20 IPC for different settings."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "trained translator can be adapted for a new dataset within a limited number of steps. Experiments demonstrate that our method achieves  $\\sim 15\\times$  acceleration and comparable performance with the state-of-the-art baselines relying on thousands of networks. Even in some cases, the translator without adaptation yields competitive performance.",
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+    {
+        "type": "text",
+        "text": "One limitation of our method is that in the adaptation stage, errors of translated synthetic datasets have to be further back-propagated through the translator, which introduces additional GPU memory consumption compared with the baseline method, e.g., 3946 v.s. 3456 MB on CIFAR10 with 10 IPC. Nevertheless, as shown in Fig. 4(c), the translator adapted for small sizes can conduct inference for larger sizes, thereby breaking the limitation on GPU memory. Future works may focus on further improving the transferability of the distillation space translator by dedicated architectural designs or objective functions.",
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+        "text": "Acknowledgement",
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+        "type": "text",
+        "text": "This work is supported by the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2), and the Singapore Ministry of Education Academic Research Fund Tier 1 (WBS: A0009440-01-00).",
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+        "type": "text",
+        "text": "References",
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+        "bbox": [
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+    },
+    {
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+        ],
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+            "content": "CVF"
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+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
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+            "content": "Songhua Liu Xinchao Wang*"
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+            "angle": 0,
+            "content": "National University of Singapore"
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+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "songhua.liu@u.nus.edu，xinchao@nus.edu.sg"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "Abstract"
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+            "type": "text",
+            "bbox": [
+                0.076,
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+            ],
+            "angle": 0,
+            "content": "Dataset distillation aims at a small synthetic dataset to mimic the training performance on neural networks of a given large dataset. Existing approaches heavily rely on an iterative optimization to update synthetic data and multiple forward-backward passes over thousands of neural network spaces, which introduce significant overhead for computation and are inconvenient in scenarios requiring high efficiency. In this paper, we focus on few-shot dataset distillation, where a distilled dataset is synthesized with only a few or even a single network. To this end, we introduce the notion of distillation space, such that synthetic data optimized only in this specific space can achieve the effect of those optimized through numerous neural networks, with dramatically accelerated training and reduced computational cost. To learn such a distillation space, we first formulate the problem as a quad-level optimization framework and propose a bi-level algorithm. Nevertheless, the algorithm in its original form has a large memory footprint in practice due to the back-propagation through an unrolled computational graph. We then convert the problem of learning the distillation space to a first-order one based on image translation. Specifically, the synthetic images are optimized in an arbitrary but fixed neural space and then translated to those in the targeted distillation space. We pre-train the translator on some large datasets like ImageNet so that it requires only a limited number of adaptation steps on the target dataset. Extensive experiments demonstrate that the translator after pre-training and a limited number of adaptation steps achieves comparable distillation performance with state of the arts, with \\(\\sim 15\\times\\) acceleration. It also exerts satisfactory generalization performance across different datasets, storage budgets, and numbers of classes."
+        },
+        {
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.844,
+                0.47,
+                0.875
+            ],
+            "angle": 0,
+            "content": "Given an original dataset \\(\\mathcal{T}\\), Dataset distillation (DD) [41, 51, 35, 18, 47, 20, 22] aims at a much smaller"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.703,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.592,
+                0.366,
+                0.609,
+                0.378
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.705,
+                0.268,
+                0.89,
+                0.366
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.798,
+                0.367,
+                0.815,
+                0.377
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.383,
+                0.692,
+                0.473
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.593,
+                0.479,
+                0.61,
+                0.49
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.707,
+                0.381,
+                0.892,
+                0.477
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.797,
+                0.479,
+                0.815,
+                0.49
+            ],
+            "angle": 0,
+            "content": "(d)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.5,
+                0.895,
+                0.724
+            ],
+            "angle": 0,
+            "content": "Figure 1. (a) Existing DD methods heavily rely on forward-backward processes through enormous neural networks. (b) More neural networks used in dataset distillation would result in more floating point operations (FLOPs) and higher latency. (c) We introduce the notation of distillation space for few-shot dataset distillation in this paper and aim to learn a neural network such that distilled data only optimized in this specific space can approximate the performance by multiple networks. (d) Given only a few or even a single network, our method achieves comparable performance with state-of-the-art baselines requiring enormous networks. Results in this figure are concerning models trained with 1 image per class distilled from CIFAR100 dataset. OS denotes one-shot DD using only one network, FS denotes few-shot DD with a limited number of adaptation steps, and DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "synthetic dataset \\(S\\), such that the training effect of \\(S\\) on neural networks can match that of \\(\\mathcal{T}\\). Such techniques have received considerable attention to alleviate the heavy burden on storage, transmission, and training of deep learning models brought by large-scale datasets. Recent advances on DD have revealed that models trained with only a few synthetic samples, even 1 image per class in some cases, can retain most of the performance of those trained with real data [49, 50, 2, 28, 29, 40, 13, 52, 23, 21]. Thus, it becomes a research area receiving increasing attention from the aca"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.227,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding Author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18654"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "demic and industrial community recently as a potential solution to alleviate the concerns on the storage, transmission, pre-processing, and training effort for large datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.139,
+                0.47,
+                0.397
+            ],
+            "angle": 0,
+            "content": "Nevertheless, as shown in Fig. 1(a), all existing methods on DD work iteratively: the synthetic dataset is optimized in an outer loop, and real and synthetic data are sent to a newly-initialized neural network in each iteration. Although they have achieved remarkable performance, such forward-backward passes in multiple neural networks can introduce extensive computational overhead to generate a distilled dataset, as illustrated in Fig. 1(b). As a result, the burdensome distillation procedure in existing methods brings significant latency. For instance, one of the state-of-the-art works by Deng et al. [5] requires \\(\\sim 18\\) days to distill only 1 image per class for CIFAR100 dataset [15] as shown in Fig. 1(d) and [47]. Even FRePo [52], with the most satisfactory efficiency, takes over 3 hours in the same setting requiring 500,000 neural network steps. The long training process in current DD makes it inconvenient for scenarios requiring high efficiency, e.g., processing streaming data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.398,
+                0.47,
+                0.625
+            ],
+            "angle": 0,
+            "content": "Focusing on these drawbacks, in this paper, we propose few-shot dataset distillation and are interested in the performance of DD if only a few or even a single neural network is available for training. We first try a naive solution by merely adopting one neural network for the existing method FRePo [52] and visualize the accuracy and efficiency. As shown in Fig. 1(d), although the simple strategy improves the efficiency, the performance gap with the original version based on thousands of networks is significant, which suggests a trade-off between performance and the number of networks. A similar effect is also revealed by Cazenavette et al. [2], where the number of teacher training trajectories would affect the performance substantially. Thus, how to boost the performance by only a limited number of networks becomes an interesting question in few-shot DD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.627,
+                0.469,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Currently, the networks used in Fig. 1(d) are randomly and independently initialized, which makes us curious: whether there exists a dedicated neural network, such that the synthetic dataset distilled in it can achieve similar performance to those distilled in multiple ones. In this paper, we describe this concept through a quad-level definition termed as distillation space, as shown in Fig. 1(c), and propose a bi-level algorithm to find it, to optimize the error on real data, for networks trained with the synthetic dataset, distilled in this space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "However, the bi-level optimization requires backpropagating through an unrolled computational graph over multiple steps of gradient descent, which imposes an intensive GPU footprint. Due to the bottleneck on GPU memory, the number of steps for inner optimization is limited, which further limits the performance in practice. To reduce the complexity, we free the dependency of higher-order gradients via casting the problem as image translation, to make"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.151
+            ],
+            "angle": 0,
+            "content": "sure that the iterative optimization process is not nested in the computational graph: the synthetic dataset is distilled in a random but fixed neural network space and then translated to the desired space via a translator network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.153,
+                0.892,
+                0.333
+            ],
+            "angle": 0,
+            "content": "Specifically, the translator is pre-trained on some large datasets like ImageNet [4]. In each iteration, a random subset is sampled. Distilled results after being translated from the original space are evaluated in some random networks, and the distillation loss is back-propagated to the translator to update its parameters. We find that the distillation space translator after pre-training can generalize well across different datasets, storage budgets, and numbers of classes. With only a few adaptation steps on the target dataset, the performance of distilled data after translation achieves can be on par with those distilled by multiple neural networks at \\(\\sim 15\\times\\) faster, as shown in Fig. 1(d)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.334,
+                0.858,
+                0.348
+            ],
+            "angle": 0,
+            "content": "In summary, our contributions are listed as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.36,
+                0.892,
+                0.435
+            ],
+            "angle": 0,
+            "content": "- Tailoring for scenarios requiring high efficiency, we are the first to study the problem of few-shot dataset distillation, where only a limited number of neural networks are available for DD, and introduce the quad-level definition of distillation space for it."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.447,
+                0.891,
+                0.491
+            ],
+            "angle": 0,
+            "content": "- An efficient translative modeling approach with a pretraining algorithm is proposed to learn an effective distillation space;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.503,
+                0.892,
+                0.547
+            ],
+            "angle": 0,
+            "content": "- Extensive experiments demonstrate that our method is capable of generating dataset distillation results with \\(\\sim 15\\times\\) acceleration."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.36,
+                0.892,
+                0.547
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.573,
+                0.65,
+                0.589
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.841
+            ],
+            "angle": 0,
+            "content": "Dataset distillation (DD) refers to distilling a small synthetic dataset \\( S \\) from a given large dataset \\( T \\), where \\( S \\) is optimized to have similar downstream training performance to \\( T \\). Unlike most existing techniques that focus on reducing the size of a model [6, 25, 45, 44, 7, 46, 12, 11, 10, 33], DD concentrates on learning compressed data to enhance learning efficiency. Wang et al. [41] firstly introduce the task and propose a meta-learning method to minimize the loss of meta-test on \\( T \\) for models meta-trained on \\( S \\). This scheme aligns with the evaluation protocol of DD: to pursue higher accuracy on the real test data for networks optimized by the synthetic ones. However, restricted by the GPU memory, the steps of meta-training in this framework are limited, which bottlenecks the performance [5]. The bilevel loop with a large number of inner steps also affects the efficiency negatively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.841,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To address this issue, a series of works consider mapping real and synthetic samples to a feature space with some kernels, e.g., NTK [28, 29], NNGP [23], and non-linear network [52, 24], and then perform kernel ridge regression"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18655"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.077,
+                0.089,
+                0.355,
+                0.3
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.219,
+                0.305,
+                0.241,
+                0.319
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.361,
+                0.089,
+                0.895,
+                0.3
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.486,
+                0.304,
+                0.51,
+                0.319
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.759,
+                0.304,
+                0.781,
+                0.319
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.329,
+                0.895,
+                0.4
+            ],
+            "angle": 0,
+            "content": "Figure 2. (a) Existing DD methods rely on an iterative training process, where a new network has to be initialized for forward and backward passes of the real dataset \\(\\mathcal{T}\\) and the synthetic dataset \\(S\\). (b) We desire to learn a specific distillation space, where \\(\\mathcal{S}\\) optimized only in such a space can minimize the error of neural feature regression in an arbitrary random network. The loop for optimizing \\(\\mathcal{S}\\) is nested in the computational graph for optimizing the distillation space. (c) We detach the loop for optimizing \\(\\mathcal{S}\\) for computational efficiency and convert the problem to a transitive model, where \\(\\mathcal{S}\\) is distilled in an arbitrary but fixed neural space first and then translated to the desired space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.417,
+                0.47,
+                0.538
+            ],
+            "angle": 0,
+            "content": "(KRR). Benefiting from the analytical solution of KRR, these methods can access the optimal parameters trained by synthetic datasets via direct computation without the necessity of higher-order gradients, which achieves favorable efficiency and accuracy at the same time. In this paper, the KRR-based formulation is also adopted as the main objective to reduce the complexity of meta-learning, thanks to its satisfactory efficiency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.539,
+                0.471,
+                0.719
+            ],
+            "angle": 0,
+            "content": "In the literature of DD, matching-based methods are another major branch. For example, Zhao et al. [51] and a lot of following works [49, 13, 17, 9, 48] adopt gradient matching. Cazenavette et al. [2] propose MTT, which optimizes the distance between network parameters trained by \\( S \\) and \\( T \\) respectively from some cached initialization. Their insights lie in that gradients in networks or trained model parameters can represent the training effects of different datasets. Some works also consider matching the statistics of \\( S \\) and \\( T \\) in some neural networks [50, 40], which get rid of computing gradients of training networks via \\( S \\) and \\( T \\) and thus improves the efficiency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "No matter what objectives existing methods adopt, they all rely on an extensive outer optimization loop to update synthetic data, where \\( S \\) and \\( \\mathcal{T} \\) have to undergo forward-backward passes through thousands of networks. To make things worse, a series of works considering synthetic dataset parameterization, which tries to increase the number of images with the same storage budget, require even more such iterations [5, 19]. Motivated by these facts, we focus on the problem of few-shot dataset distillation in this paper where a synthetic dataset is distilled given only a few or even a single neural network. Given that naively adopting only a few random networks results in inferior performance as"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.417,
+                0.895,
+                0.553
+            ],
+            "angle": 0,
+            "content": "shown in Fig. 1(d), we introduce the concept of distillation space, such that the performance of synthetic data distilled in this space can match those in enormous networks. Dedicated to finding such a space to benefit dataset distillation to reduce the number of networks required for acceleration while retaining the performance as much as possible, a novel translative model with a pre-training approach is proposed to this end. To our best knowledge, this is the first work focusing on few-shot learning and pre-training in DD."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.568,
+                0.599,
+                0.584
+            ],
+            "angle": 0,
+            "content": "3. Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.594,
+                0.895,
+                0.806
+            ],
+            "angle": 0,
+            "content": "In this section, we delve into details about our methods for few-shot dataset distillation, where real and synthetic datasets can be processed by only a few neural networks. We first provide a brief introduction of current mainstream solutions for DD, based on which we propose the quad-level definition of distillation space in formal and a basic bi-level algorithm to learn the space. For computational efficiency, we then convert the original formulation of learning the distillation space to a transitive problem and propose an alternative algorithm, backed up by theoretical analysis. Finally, we explain the paradigm of pre-training for few-shot learning to increase the transferability of the learned distillation space across various datasets, the number of classes, and the storage budgets of synthetic datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.817,
+                0.63,
+                0.833
+            ],
+            "angle": 0,
+            "content": "3.1. Preliminary"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Dataset distillation (DD) targets a small synthetic dataset \\( S \\) such that the performance on downstream training with \\( S \\) can match that with the original dataset \\( \\mathcal{T} \\). The seminal work by Wang et al. [41] proposes a meta-learning ap"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18656"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.466,
+                0.106
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Bi-Level Optimization for Distillation Space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.108,
+                0.469,
+                0.168
+            ],
+            "angle": 0,
+            "content": "Input: \\(\\mathcal{T}\\): Target Dataset; \\(\\Theta\\): Distribution for Initializing Neural Networks; \\(T\\): Number of Inner Update Steps; \\(\\alpha\\): Learning Rate for Inner Optimization; \\(\\eta\\): Learning Rate for Outer Optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.169,
+                0.408,
+                0.184
+            ],
+            "angle": 0,
+            "content": "Output: \\(\\theta\\): Distillation Space after Optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.185,
+                0.22,
+                0.198
+            ],
+            "angle": 0,
+            "content": "1: Initialize \\(\\theta \\sim \\Theta\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.2,
+                0.251,
+                0.213
+            ],
+            "angle": 0,
+            "content": "2: for \\( i = 1,2,3,\\ldots \\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.214,
+                0.408,
+                0.228
+            ],
+            "angle": 0,
+            "content": "3: Initialize \\( S \\) with random samples from \\( \\mathcal{T} \\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.229,
+                0.242,
+                0.244
+            ],
+            "angle": 0,
+            "content": "4: \\(X_{\\mathcal{T}}^{\\theta}\\gets f_{\\theta}(X_{\\mathcal{T}});\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.245,
+                0.25,
+                0.258
+            ],
+            "angle": 0,
+            "content": "5: for \\(1\\leq t\\leq T\\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.259,
+                0.445,
+                0.275
+            ],
+            "angle": 0,
+            "content": "6: \\(w_{\\mathcal{S},\\theta}^* \\gets f_\\theta(X_\\mathcal{S})^\\top (f_\\theta(X_\\mathcal{S})f_\\theta(X_\\mathcal{S})^\\top)^{-1}Y_\\mathcal{S};\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.276,
+                0.42,
+                0.292
+            ],
+            "angle": 0,
+            "content": "7: \\(X_{\\mathcal{S}} \\gets X_{\\mathcal{S}} - \\alpha \\nabla_{X_{\\mathcal{S}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}}^{2}\\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.293,
+                0.408,
+                0.31
+            ],
+            "angle": 0,
+            "content": "8: \\(Y_{\\mathcal{S}} \\gets Y_{\\mathcal{S}} - \\alpha \\nabla_{Y_{\\mathcal{S}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}\\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.311,
+                0.184,
+                0.322
+            ],
+            "angle": 0,
+            "content": "9: end for"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.082,
+                0.324,
+                0.308,
+                0.338
+            ],
+            "angle": 0,
+            "content": "10: Randomly sample \\(\\theta^{\\prime}\\sim \\Theta\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.084,
+                0.338,
+                0.248,
+                0.354
+            ],
+            "angle": 0,
+            "content": "11: \\(X_{\\mathcal{T}}^{\\theta^{\\prime}}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{T}});\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.084,
+                0.354,
+                0.438,
+                0.371
+            ],
+            "angle": 0,
+            "content": "12: \\(w_{\\mathcal{S},\\theta^{\\prime}}^{*}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top}(f_{\\theta^{\\prime}}(X_{\\mathcal{S}})f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top})^{-1}Y_{\\mathcal{S}};\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.084,
+                0.372,
+                0.357,
+                0.389
+            ],
+            "angle": 0,
+            "content": "13: \\(\\theta \\gets \\theta -\\eta \\nabla_{\\theta}\\| X_{\\mathcal{T}}^{\\theta '}w_{\\mathcal{S},\\theta '}^{*} - Y_{\\mathcal{T}}\\|^{2};\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.084,
+                0.389,
+                0.16,
+                0.401
+            ],
+            "angle": 0,
+            "content": "14: end for"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.082,
+                0.185,
+                0.445,
+                0.401
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.43,
+                0.47,
+                0.476
+            ],
+            "angle": 0,
+            "content": "proach, which optimizes the loss on \\(\\mathcal{T}\\) for models trained with \\(S\\) and backpropagates the gradients through multiple training steps to update \\(S\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.158,
+                0.486,
+                0.469,
+                0.517
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {S} ^ {*} = \\underset {\\mathcal {S}} {\\arg \\min } \\mathbb {E} _ {\\theta^ {(0)} \\sim \\Theta} [ l (\\mathcal {T}; \\theta^ {(T)}) ], \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.155,
+                0.515,
+                0.369,
+                0.533
+            ],
+            "angle": 0,
+            "content": "\\[\n\\theta^ {(t)} = \\theta^ {(t - 1)} - \\alpha \\nabla l (\\mathcal {S}; \\theta^ {(t - 1)}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.543,
+                0.469,
+                0.603
+            ],
+            "angle": 0,
+            "content": "where \\(\\Theta\\) denotes a distribution for initialization, \\(T\\) is the number of training steps with \\(S\\) and \\(1 \\leq t \\leq T\\), \\(\\alpha\\) is the learning rate, and \\(l\\) is the loss function, e.g., cross-entropy loss for classification problems."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.604,
+                0.47,
+                0.846
+            ],
+            "angle": 0,
+            "content": "The bi-level optimization algorithm indicated in Eq. 1 relies on backpropagating through an unrolled computational graph of inner optimization steps, which makes it inefficient in both time and memory. Nguyen et al. [28, 29] thus consider the problem of kernel ridge regression (KRR), where the analytical optimal solution gets rid of the necessity to optimize the model with \\( S \\) for multiple nested steps. For more satisfactory accuracy and efficiency, the spirit is further extended by following works [52, 23], which map a batch of \\( n \\) samples \\( X \\) to a feature space with a random neural network and then perform KRR. Denote the function of neural network parameterized by \\( \\theta \\) as \\( f_{\\theta} \\) and the label matrix corresponding to \\( X \\in \\mathbb{R}^{n \\times d} \\) as \\( Y \\in \\mathcal{R}^{n \\times c} \\), where \\( d \\) and \\( c \\) are the dimensions of sample and label respectively, i.e., \\( h \\times w \\times 3 \\) and the number of classes in the RGB image classification problem, the objective can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.097,
+                0.856,
+                0.468,
+                0.904
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} X _ {\\mathcal {S}} ^ {*}, Y _ {\\mathcal {S}} ^ {*} = \\underset {X _ {\\mathcal {S}}, Y _ {\\mathcal {S}}} {\\arg \\min } \\mathbb {E} _ {\\theta \\sim \\Theta} [ \\| f _ {\\theta} (X _ {\\mathcal {T}}) w _ {\\mathcal {S}, \\theta} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2} ], \\tag {2} \\\\ w _ {S, \\theta} ^ {*} = f _ {\\theta} (X _ {S}) ^ {\\top} \\left(f _ {\\theta} (X _ {S}) f _ {\\theta} (X _ {S}) ^ {\\top}\\right) ^ {- 1} Y _ {S}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "This technique is known as neural feature regression (NFR) [52]. In each training iteration, a new random neural network is initialized for solving the problem in Eq. 2, as shown in Fig. 2(a)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.161,
+                0.76,
+                0.178
+            ],
+            "angle": 0,
+            "content": "3.2. Learning a Distillation Space"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.184,
+                0.892,
+                0.366
+            ],
+            "angle": 0,
+            "content": "As illustrated in Fig. 1(a), the iterative optimization framework shown in Fig. 2(a) involves forward and backward processes through thousands of networks and introduces significant computational overhead. In this work, we thus focus on the problem of DD using only a few or even one network. Given the results in Fig. 1(b) that simply adopting a random network yields limited performance, we are interested in learning a specific network such that \\( S \\) distilled in it can achieve performance on par with that distilled in multiple networks, i.e., minimize the error on \\( \\mathcal{T} \\) for an arbitrary model trained with \\( S \\). Formally, we term such a network as distillation space in the following definition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.375,
+                0.893,
+                0.421
+            ],
+            "angle": 0,
+            "content": "Definition 1 (Distillation Space). A distillation space for a distribution of network \\(\\Theta\\) and a target dataset \\(\\mathcal{T}\\) is a neural network function \\(f\\) parameterized by \\(\\theta^{*}\\) which satisfies:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.571,
+                0.431,
+                0.891,
+                0.53
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\theta^{*} = \\operatorname *{arg  min}_{\\theta^{(0)}}\\mathbb{E}_{\\theta^{(0)^{\\prime}}\\sim \\Theta}[l(\\mathcal{T};\\theta^{(T)^{\\prime}})], \\\\ \\theta^ {(t) ^ {\\prime}} = \\theta^ {(t - 1) ^ {\\prime}} - \\alpha^ {\\prime} \\nabla l \\left(\\mathcal {S} ^ {*}; \\theta^ {(t - 1) ^ {\\prime}}\\right), \\tag {3} \\\\ \\mathcal {S} ^ {*} = \\underset {\\mathcal {S}} {\\arg \\min } l (\\mathcal {T}; \\theta^ {(T)}), \\\\ \\theta^ {(t)} = \\theta^ {(t - 1)} - \\alpha \\nabla l (\\mathcal {T}; \\theta^ {(t - 1)}). \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.541,
+                0.892,
+                0.586
+            ],
+            "angle": 0,
+            "content": "In practice, to find an effective distillation space, we first simplify the quad-level definition via NFR in Eq. 2, which derives a bi-level optimization problem:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.513,
+                0.596,
+                0.891,
+                0.692
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\theta^ {*} = \\underset {\\theta} {\\arg \\min } \\mathbb {E} _ {\\theta^ {\\prime} \\sim \\Theta} [ \\| f _ {\\theta^ {\\prime}} (X _ {\\mathcal {T}}) w _ {\\mathcal {S} ^ {*}, \\theta^ {\\prime}} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2} ], \\\\ w _ {\\mathcal {S} ^ {*}, \\theta^ {\\prime}} ^ {*} = f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) ^ {\\top} \\left(f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) ^ {\\top}\\right) ^ {- 1} Y _ {\\mathcal {S}} ^ {*}, \\tag {4} \\\\ X _ {\\mathcal {S}} ^ {*}, Y _ {\\mathcal {S}} ^ {*} = \\underset {X _ {\\mathcal {S}}, Y _ {\\mathcal {S}}} {\\arg \\min} \\| f _ {\\theta} (X _ {\\mathcal {T}}) w _ {\\mathcal {S}, \\theta} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2}, \\\\ w _ {S, \\theta} ^ {*} = f _ {\\theta} (X _ {S}) ^ {\\top} \\left(f _ {\\theta} (X _ {S}) f _ {\\theta} (X _ {S}) ^ {\\top}\\right) ^ {- 1} Y _ {S}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.703,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Eq. 4 indicates a bi-level meta-learning algorithm as shown in Fig. 2(b) and Alg. 1. In each inner iteration, \\( S \\) is metatrained via NFR in the current neural space \\( f_{\\theta} \\). \\( S \\) after a whole inner loop is meta-tested in a random neural network \\( f_{\\theta'} \\) and the loss of NFR is back-propagated to update \\( \\theta \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.885,
+                0.804
+            ],
+            "angle": 0,
+            "content": "3.3. Learning a Translation to a Distillation Space"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Although Alg. 1 can be an effective algorithm to learn a valid distillation space, the back-propagation process through a nested computational graph is inefficient in GPU memory. The memory complexity is proportionate to the number of inner optimization steps \\( T \\) to obtain the optimal synthetic dataset in the current space, which is crucial"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18657"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.473,
+                0.213
+            ],
+            "angle": 0,
+            "content": "for the final performance [5] but withheld by the limited GPU memory. For instance, in a 40G A100 GPU, \\( T \\) in Alg. 1 can be set as 16 at most, which is too small to get convergence for inner optimization. To alleviate this drawback, we consider an alternative approach to learn a distillation space. Specifically, we detach the inner optimization from the computational graph by converting the problem to a transitive model, based on the following proposition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.219,
+                0.473,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Proposition 1. For a target dataset \\(X_{\\mathcal{T}} \\in \\mathbb{R}^{n_{\\mathcal{T}} \\times d}\\) and \\(Y_{\\mathcal{T}} \\in \\mathbb{R}^{n_{\\mathcal{T}} \\times c}\\) with \\(n_{\\mathcal{T}} \\geq d\\), assume that \\(X_{\\mathcal{S},0}^{*}\\) and \\(Y_{\\mathcal{S},0}^{*}\\) satisfy \\(\\| f_{\\theta}(X_{\\mathcal{T}})w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}}\\|^{2} = 0\\), where \\(w_{\\mathcal{S},\\theta}^{*} = f_{\\theta}(X_{\\mathcal{S},0}^{*})^{\\top}(f_{\\theta}(X_{\\mathcal{S},0}^{*})f_{\\theta}(X_{\\mathcal{S},0}^{*})^{\\top})^{-1}Y_{\\mathcal{S},0}^{*}\\) and \\(f_{\\theta}\\) is a known linear transformation parameterized by a full-rank matrix \\(\\theta \\in \\mathbb{R}^{d \\times d'}\\), \\(d \\leq d'\\). Similarly, let \\(f_{\\theta^{*}}\\) be a desired linear distillation space and \\(\\theta^{*} \\in \\mathbb{R}^{d \\times d''}\\), \\(d \\leq d'' \\leq n_{\\mathcal{T}}\\). The distilled dataset \\(X_{\\mathcal{S},*}^{*}\\) and \\(Y_{\\mathcal{S},*}^{*}\\) in this space satisfy \\(\\| f_{\\theta^{*}}(X_{\\mathcal{T}})w_{\\mathcal{S},\\theta^{*}}^{*} - Y_{\\mathcal{T}}\\|^{2} = 0\\), where \\(w_{\\mathcal{S},\\theta^{*}}^{*} = f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})^{\\top}(f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})^{\\top})^{-1}Y_{\\mathcal{S},*}^{*}\\). There exists a translation function \\(G\\) for \\(X_{\\mathcal{S},0}^{*}\\) and \\(Y_{\\mathcal{S},0}^{*}\\) such that \\(X_{\\mathcal{S},*}^{*}, Y_{\\mathcal{S},*}^{*} = G(X_{\\mathcal{S},0}^{*}, Y_{\\mathcal{S},0}^{*})\\), whose parameters are not dependent on the target dataset \\(X_{\\mathcal{T}}\\) and \\(Y_{\\mathcal{T}}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.432,
+                0.471,
+                0.462
+            ],
+            "angle": 0,
+            "content": "Proof. Due to the linearity of \\( f_{\\theta} \\) and \\( f_{\\theta^{*}} \\), we can rewrite the given conditions as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.201,
+                0.472,
+                0.469,
+                0.489
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {\\mathcal {T}} \\theta w _ {S, \\theta} ^ {*} - Y _ {\\mathcal {T}} = 0, \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.195,
+                0.492,
+                0.469,
+                0.51
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {\\mathcal {T}} \\theta^ {*} w _ {S, \\theta^ {*}} ^ {*} - Y _ {\\mathcal {T}} = \\mathbf {0}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.518,
+                0.47,
+                0.55
+            ],
+            "angle": 0,
+            "content": "Since \\( n_{\\mathcal{T}} \\geq d \\) for \\( X_{\\mathcal{T}} \\), pre-multiplying terms in Eq. 5 by the Moore-Penrose inverse \\( X_{\\mathcal{T}}^{\\dagger} \\), we have"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.216,
+                0.557,
+                0.47,
+                0.577
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {\\mathcal {T}} ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta w _ {\\mathcal {S}, \\theta} ^ {*}. \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.585,
+                0.304,
+                0.6
+            ],
+            "angle": 0,
+            "content": "Similarly, through Eq. 6, we have"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.102,
+                0.607,
+                0.47,
+                0.628
+            ],
+            "angle": 0,
+            "content": "\\[\nw _ {\\mathcal {S}, \\theta^ {*}} ^ {*} = (X _ {\\mathcal {T}} \\theta^ {*}) ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta^ {* \\dagger} X _ {\\mathcal {T}} ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta^ {* \\dagger} \\theta w _ {\\mathcal {S}, \\theta} ^ {*}, \\quad (8)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.635,
+                0.47,
+                0.742
+            ],
+            "angle": 0,
+            "content": "where the first, second, and third equalities are due to \\( n_{\\mathcal{T}} \\geq d'' \\), \\( d'' \\geq d \\), and Eq. 7 respectively. We can observe in Eq. 8 that \\( w_{S,\\theta^*}^* \\) in the desired distillation space is not dependent on \\( \\mathcal{T} \\). Thus, the optimal \\( X_{S,*}^* \\) and \\( Y_{S,*}^* \\) resulting the optimal KRR parameter can be obtained given only \\( X_{S,0}^* \\) and \\( Y_{S,0}^* \\) by some translation function \\( G \\), which implicitly includes the knowledge of the distillation space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Prop. 1 indicates that it is possible to approach the distillation space by translating samples from some space rather than learning \\(\\theta^{*}\\) directly, motivated by which we propose to learn a translation from one another space to the distillation space. The main workflow is similar to Alg. 1: synthetic data are first distilled in a random but fixed network in an inner loop and then translated to final results, as shown in Fig. 2(c). The translator is optimized so that results after translation are equipped with the property of those produced in a distillation space: to minimize the NFR error in"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.091,
+                0.878,
+                0.107
+            ],
+            "angle": 0,
+            "content": "Algorithm 2 Pre-training a Distillation Space Translator."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.108,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "Input: \\(\\mathcal{Z}\\): A Large Dataset; \\(\\Theta\\): Distribution for Initializing Neural Networks; \\(\\theta\\): An Arbitrary Random Neural Network; \\(T\\): Number of Update Steps for Synthetic Data; \\(\\alpha\\): Learning Rate for Synthetic Data; \\(\\eta\\): Learning Rate for Translator."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.184,
+                0.751,
+                0.198
+            ],
+            "angle": 0,
+            "content": "Output: \\(\\omega\\): A Pre-trained Translator."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.199,
+                0.678,
+                0.213
+            ],
+            "angle": 0,
+            "content": "1: Initialize \\(\\omega\\) randomly;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.214,
+                0.675,
+                0.228
+            ],
+            "angle": 0,
+            "content": "2: for \\( i = 1,2,3,\\ldots \\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.229,
+                0.854,
+                0.244
+            ],
+            "angle": 0,
+            "content": "3: Randomly choose a subset of data \\(\\mathcal{T}\\) from \\(\\mathcal{Z}\\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.245,
+                0.836,
+                0.259
+            ],
+            "angle": 0,
+            "content": "4: Initialize \\(S^{\\prime}\\) with random samples from \\(\\mathcal{T}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.259,
+                0.665,
+                0.275
+            ],
+            "angle": 0,
+            "content": "5: \\(X_{\\mathcal{T}}^{\\theta}\\gets f_{\\theta}(X_{\\mathcal{T}});\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.276,
+                0.673,
+                0.288
+            ],
+            "angle": 0,
+            "content": "6: for \\(1 \\leq t \\leq T\\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.289,
+                0.89,
+                0.305
+            ],
+            "angle": 0,
+            "content": "7: \\(w_{\\mathcal{S}^{\\prime},\\theta}^{*}\\gets f_{\\theta}(X_{\\mathcal{S}^{\\prime}})^{\\top}(f_{\\theta}(X_{\\mathcal{S}^{\\prime}})f_{\\theta}(X_{\\mathcal{S}^{\\prime}})^{\\top})^{-1}Y_{\\mathcal{S}^{\\prime}};\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.306,
+                0.86,
+                0.323
+            ],
+            "angle": 0,
+            "content": "8: \\(X_{\\mathcal{S}^{\\prime}} \\gets X_{\\mathcal{S}^{\\prime}} - \\alpha \\nabla_{X_{\\mathcal{S}^{\\prime}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S}^{\\prime},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}\\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.323,
+                0.849,
+                0.34
+            ],
+            "angle": 0,
+            "content": "9: \\(Y_{\\mathcal{S}^{\\prime}} \\gets Y_{\\mathcal{S}^{\\prime}} - \\alpha \\nabla_{Y_{\\mathcal{S}^{\\prime}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S}^{\\prime},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}\\);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.341,
+                0.608,
+                0.353
+            ],
+            "angle": 0,
+            "content": "10: end for"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.354,
+                0.727,
+                0.37
+            ],
+            "angle": 0,
+            "content": "11: \\(X_{\\mathcal{S}},Y_{\\mathcal{S}} = G_{\\omega}(X_{\\mathcal{S}^{\\prime}},Y_{\\mathcal{S}^{\\prime}});\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.37,
+                0.731,
+                0.384
+            ],
+            "angle": 0,
+            "content": "12: Randomly sample \\(\\theta^{\\prime}\\sim \\Theta\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.384,
+                0.671,
+                0.399
+            ],
+            "angle": 0,
+            "content": "13: \\(X_{\\mathcal{T}}^{\\theta^{\\prime}}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{T}});\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.399,
+                0.861,
+                0.416
+            ],
+            "angle": 0,
+            "content": "14: \\(w_{\\mathcal{S},\\theta^{\\prime}}^{*}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top}(f_{\\theta^{\\prime}}(X_{\\mathcal{S}})f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top})^{-1}Y_{\\mathcal{S}};\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.416,
+                0.787,
+                0.434
+            ],
+            "angle": 0,
+            "content": "15: \\(\\omega \\gets \\omega -\\eta \\nabla_{\\omega}\\| X_{\\mathcal{T}}^{\\theta '}w_{S,\\theta '}^{*} - Y_{\\mathcal{T}}\\|^{2};\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.434,
+                0.584,
+                0.446
+            ],
+            "angle": 0,
+            "content": "16: end for"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.508,
+                0.199,
+                0.89,
+                0.446
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.477,
+                0.892,
+                0.568
+            ],
+            "angle": 0,
+            "content": "any random network. Since gradients are only required to back propagated to the translator rather than the whole inner loop, the memory complexity is irrelevant to the number of inner optimization steps. Thus, the translative model is a memory-efficient algorithm where only first-order gradients are necessary."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.579,
+                0.869,
+                0.595
+            ],
+            "angle": 0,
+            "content": "3.4. Pre-training a Distillation Space Translator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.603,
+                0.892,
+                0.815
+            ],
+            "angle": 0,
+            "content": "We expect that the distillation space optimized in a dataset is transferable across different datasets, storage budgets for synthetic data, and the number of classes. To tackle these challenges on transferability, in this paper, we consider pre-train a translator on some large dataset like ImageNet [4], so that it provides a satisfactory initialization and only requires a small number of adaptation steps for a target dataset, like the typical few-shot learning [42, 39, 38, 30]. The algorithm is shown in Alg. 2. In each training iteration \\( i \\), we sample a subset from the large dataset and perform a gradient-decent step with the strategy mentioned in Sec. 3.3. Upon a translator is pre-trained, it can serve as a strong initialization for the adaptation process to a new dataset, which behaves identically to Line 11 to 15 of Alg. 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.83,
+                0.633,
+                0.847
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we conduct experiments to validate the effectiveness of the proposed method for few-shot DD. We first introduce our experiment settings and implement de"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18658"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.153,
+                0.089,
+                0.817,
+                0.302
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Hyper-Parameter</td><td>Denotation</td><td>Value</td></tr><tr><td>T</td><td>Number of Update Steps for Synthetic Data</td><td>3,000</td></tr><tr><td>α</td><td>Learning Rate for Synthetic Data</td><td>1e-3</td></tr><tr><td>η</td><td>Learning Rate for Translator in Pre-Training</td><td>1e-5</td></tr><tr><td>N</td><td>Number of Cached Subsets in Pre-Training</td><td>5,000</td></tr><tr><td>Cmax</td><td>Maximal Number of Classes in a Subset in Pre-Training</td><td>100</td></tr><tr><td>Cmin</td><td>Minimal Number of Classes in a Subset in Pre-Training</td><td>10</td></tr><tr><td>M</td><td>Maximal Number of Images in a Subset in Pre-Training</td><td>4,000</td></tr><tr><td>Imax</td><td>Maximal Number of Images in a Synthetic Dataset in Pre-Training</td><td>1,000</td></tr><tr><td>B</td><td>Batch Size in Pre-Training</td><td>4</td></tr><tr><td>S</td><td>Number of Pre-Training Steps</td><td>200,000</td></tr><tr><td>S&#x27;</td><td>Number of Adaptation Steps for Translator</td><td>1,000</td></tr><tr><td>η&#x27;</td><td>Learning Rate for Translator in Adaptation</td><td>1e-4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.335,
+                0.303,
+                0.634,
+                0.317
+            ],
+            "angle": 0,
+            "content": "Table 1. List of hyper-parameters and their values."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.342,
+                0.471,
+                0.448
+            ],
+            "angle": 0,
+            "content": "tails of the method. Then, we compare our method with state-of-the-art solutions of DD in terms of both accuracy and efficiency. To illustrate how the proposed method works, we also provide an in-depth analysis of the method with a variety of baselines. Finally, we conduct experiments on continual learning, an important use case for DD, to further demonstrate the practical value of our method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.455,
+                0.379,
+                0.472
+            ],
+            "angle": 0,
+            "content": "4.1. Settings and Implementing Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.478,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "In few-shot dataset distillation, a real dataset \\(\\mathcal{T}\\) can be processed by only a few neural networks to generate a synthetic dataset \\(S\\). In our method, \\(S\\) is firstly optimized in an arbitrary but fixed neural network by \\(T\\) steps, with the learning rate \\(\\alpha\\). The results are then processed by a translator to generate the final synthetic dataset. The translator adopts an auto-encoder architecture with 3 Conv-BatchNorm-ReLU blocks, and the detailed configuration can be found in the supplement. Notably, due to the fully-convolutional structure, the pre-trained translator can also be adapted to datasets with different resolutions beyond the one used during pre-training. Please refer to the supplement for details. The translator is pre-trained on the ImageNet dataset by \\(S\\) steps with the learning rate \\(\\eta\\) and then adapted on the target dataset by a small number of iterations \\(S'\\), with a learning rate \\(\\eta'\\). Some hyper-parameters are summarized in Tab. 1. Other hyper-parameters follow the default setting in the PyTorch [31] implementation of FRePo [52]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.766,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Pre-Training: The key design of the translative pretraining pipeline lies in the separation of two stages: dataset distillation in an arbitrary but fixed neural network and the translation to the desired space. In practice, instead of directly following the pipeline in Alg. 2 that nests the two steps in one loop, the two stages are conducted independently in the interest of better training efficiency. Results distilled in the pre-defined network are cached for multiple random subsets so that they can be loaded directly and used"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.342,
+                0.892,
+                0.401
+            ],
+            "angle": 0,
+            "content": "repeatedly in the pre-training stage, which improves the training efficiency. The detailed algorithms for the caching stage and the pre-training stage can be found in the supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.403,
+                0.893,
+                0.644
+            ],
+            "angle": 0,
+            "content": "The caching stage aims to generate distilled results for multiple subsets. For sampling a subset, we first randomly choose the number of classes ranging from \\( C_{\\text{min}} \\) to \\( C_{\\text{max}} \\) and then randomly select the corresponding number of classes from the 1,000 ImageNet classes. For each select class, a certain number of random real images are sampled uniformly for each selected class such that the total number of images is \\( M \\) at most. The data augmentation technique DSA [49] is applied in the caching stage to mimic the cases of larger datasets. The maximal number of synthetic images is \\( I_{\\text{max}} \\) and they are initialized with the selected real data. After distillation, indices of selected real samples and the distilled dataset are cached in the disk for future use in the pre-training stage. This process can be deployed to multiple GPUs in parallel, since the distillation for each subset is independent."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.892,
+                0.75
+            ],
+            "angle": 0,
+            "content": "In the pre-training stage, cached results in the previous stage are loaded. The NFR loss is calculated in a randomly initialized networks over a distribution in each iteration. Like the caching stage, pre-cached subsets in a batch can also be distributed to multiple GPUs in parallel. In this work, the pre-training is conducted on a single 40G A100 GPU, which takes roughly 2 days for the 200,000 steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Adaptation: Given a pre-trained translator, it requires a small number of adaptation steps in general for the target dataset. The detailed adaptation algorithm can be found in the supplement. Intuitively, the procedure is consistent with the two-stage process in pre-training: to generate distilled results in a pre-defined network and then use the translator for the final results. The only difference with the pretraining stage is that real data come from the target dataset. By default, the set of IPC for adaptation only contains the target IPC. More IPCs can also be included in this set to"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18659"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.089,
+                0.895,
+                0.296
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>IPC</td><td>Metric</td><td>DD</td><td>RTP</td><td>DC</td><td>DSA</td><td>IDC</td><td>MTT</td><td>DM</td><td>FRePo</td><td>Ours</td><td>Ours-DS</td></tr><tr><td rowspan=\"6\">CIFAR 10</td><td rowspan=\"2\">1</td><td>Acc. (%)</td><td>40.5±0.8</td><td>49.1±0.6</td><td>28.3±0.5</td><td>28.8±0.7</td><td>36.7±0.4</td><td>46.3±0.8</td><td>26.0±0.8</td><td>46.8±0.7</td><td>44.0±0.2</td><td>51.4±0.4</td></tr><tr><td>Time (h)</td><td>363.9</td><td>363.9</td><td>0.1</td><td>0.1</td><td>10.6</td><td>0.8</td><td>0.3</td><td>2.4</td><td>0.02×120.0</td><td>0.1×24.0</td></tr><tr><td rowspan=\"2\">10</td><td>Acc. (%)</td><td>50.0±0.5</td><td>62.4±0.4</td><td>44.9±0.5</td><td>52.1±0.5</td><td>58.3±0.4</td><td>65.3±0.7</td><td>48.9±0.6</td><td>65.5±0.6</td><td>59.2±0.3</td><td>66.0±0.3</td></tr><tr><td>Time (h)</td><td>447.2</td><td>447.2</td><td>1.0</td><td>1.3</td><td>11.1</td><td>2.4</td><td>0.3</td><td>3.1</td><td>0.04×77.5</td><td>0.2×15.5</td></tr><tr><td rowspan=\"2\">50</td><td>Acc. (%)</td><td>-</td><td>70.5±0.4</td><td>53.9±0.5</td><td>60.6±0.5</td><td>69.5±0.3</td><td>71.6±0.2</td><td>63.0±0.4</td><td>71.7±0.2</td><td>66.7±0.2</td><td>71.8±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>1377.8</td><td>4.4</td><td>5.3</td><td>12.8</td><td>3.8</td><td>0.4</td><td>8.1</td><td>0.12×67.5</td><td>1.3×6.2</td></tr><tr><td rowspan=\"4\">CIFAR 100</td><td rowspan=\"2\">1</td><td>Acc. (%)</td><td>-</td><td>21.3±0.6</td><td>12.8±0.3</td><td>13.9±0.3</td><td>17.9±0.2</td><td>24.3±0.3</td><td>11.4±0.3</td><td>28.7±0.1</td><td>22.8±0.4</td><td>29.1±0.4</td></tr><tr><td>Time (h)</td><td>-</td><td>447.2</td><td>0.4</td><td>0.5</td><td>50.0</td><td>3.5</td><td>3.1</td><td>3.1</td><td>0.08×38.8</td><td>0.1×31.0</td></tr><tr><td rowspan=\"2\">10</td><td>Acc. (%)</td><td>-</td><td>34.7±0.5</td><td>25.2±0.3</td><td>32.3±0.3</td><td>36.1±0.4</td><td>40.1±0.4</td><td>29.7±0.3</td><td>42.5±0.2</td><td>35.1±0.2</td><td>38.4±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>2520.8</td><td>10.6</td><td>11.4</td><td>68.9</td><td>4.2</td><td>3.1</td><td>10.4</td><td>0.32×32.5</td><td>1.0×10.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.303,
+                0.895,
+                0.361
+            ],
+            "angle": 0,
+            "content": "Table 2. Comparisons with state-of-the-art methods of DD on test accuracy and training efficiency. DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget. The black subscript indicates the standard deviation over multiple evaluations. The red subscript denotes the times of acceleration compared with the baseline method FRePo [52]. The best and second best results in each setting are marked by bold and underline respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.377,
+                0.47,
+                0.422
+            ],
+            "angle": 0,
+            "content": "increase the generalization ability of the translator across other unseen IPCs during adaptation, as shown in Sec. 4.3 and the supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.424,
+                0.471,
+                0.606
+            ],
+            "angle": 0,
+            "content": "In this paper, we consider the widely-adopted benchmarks of CIFAR10 and CIFAR100 [15] with a resolution of \\(32 \\times 32\\) for the main evaluation. Results on datasets with higher resolutions and larger sizes can be found in the supplement. Following previous works [52, 5], we evaluate the proposed method on storage budgets of 1, 10, and 50 images per class (IPC) for CIFAR10 and 1 and 10 IPC for CIFAR100. Synthetic datasets are trained with 3-layer convolutional networks and evaluated on the same architecture. The cross-architecture performance will also be studied in Sec. 4.3. We report the average result and the standard deviation over 3 replicate evaluations for each setting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.62,
+                0.385,
+                0.636
+            ],
+            "angle": 0,
+            "content": "4.2. Comparisons with State of the Arts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Here, we compare the proposed method for few-shot dataset distillation with state-of-the-art methods, including meta-learning-based methods in the seminal \\(DD\\) [41] and remember-the-past (RTP) [5], gradient-matching based methods in \\(DC\\), \\(DSA\\), and \\(IDC\\), trajectory-matching based \\(MTT\\), distribution-matching based \\(DM\\), and KRR-based \\(FRePo\\) [52]. The accuracy and training efficiency results are shown in Tab. 2. The accuracy results are from original papers while the training time is estimated based on the time-per-iteration results evaluated on the same hardware and the total number of iterations in the official codes. The shape/format of synthetic images in all methods except \"Ours-DS\" is consistent with that of real images in original datasets. For the running time of our method, we report the total time required for distilling using one network and the adaptation. Time for pre-training is not included since it is only conducted once, and once pre-trained, the trans"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.377,
+                0.892,
+                0.406
+            ],
+            "angle": 0,
+            "content": "lator can be adapted for an infinite number of downstream datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.409,
+                0.893,
+                0.575
+            ],
+            "angle": 0,
+            "content": "Through the results, we find that in the default parameterization, the proposed method within 1k adaptation steps falls about \\(3 \\sim 7\\) points behind the FRePo baseline but with \\(30 \\sim 120 \\times\\) acceleration due to the few-shot setting. Even compared with the currently most efficient algorithm, the speed of our method is still considerable. And the performance is at least comparable with other methods in terms of accuracy, with even dramatic acceleration, e.g., the meta-learning-based DD and RTP. The superior efficiency makes our method applicable in scenarios where data cannot be held for a long time, like streaming data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.576,
+                0.894,
+                0.728
+            ],
+            "angle": 0,
+            "content": "Additionally, in \"Ours-DS\", down-sampled synthetic images are alternatively stored with the same number of stored parameters, which is a simple yet effective method to improve the performance especially when the storage budget is small. This parameterization typically requires more iterations for the adaptation stages. For small synthetic datasets like 1 and 10 IPC, the number of steps is \\(6\\mathrm{k}\\), and for 50 IPC, the number is \\(15\\mathrm{k}\\). Nevertheless, our method can still result in \\(6 \\sim 31 \\times\\) acceleration compared with the FRePo baseline with even better performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.741,
+                0.665,
+                0.756
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.766,
+                0.892,
+                0.827
+            ],
+            "angle": 0,
+            "content": "Baselines: To demonstrate the effectiveness of the translative pre-training and target adaptation strategies proposed in this paper, we consider a series of baselines for ablation studies, including:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.84,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- Baseline: a new neural network is sampled for each training iteration to process the real dataset and update synthetic data, which can be viewed as a benchmark given a sufficient number of networks;"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18660"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.137,
+                0.089,
+                0.833,
+                0.202
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>IPC</td><td>Baseline</td><td>1 Net</td><td>Bi-Level</td><td>w/o Pre-Train</td><td>w AE</td><td>w/o Ada</td><td>w Ada</td></tr><tr><td rowspan=\"3\">CIFAR10</td><td>1</td><td>41.2±0.7</td><td>35.3±0.6</td><td>40.8±0.5</td><td>36.1±0.5</td><td>40.6±0.6</td><td>39.5±0.8</td><td>44.0±0.2</td></tr><tr><td>10</td><td>57.9±0.7</td><td>50.5±0.8</td><td>52.1±0.5</td><td>53.8±0.1</td><td>57.6±0.3</td><td>54.7±0.8</td><td>59.2±0.3</td></tr><tr><td>50</td><td>65.2±0.3</td><td>65.1±0.1</td><td>60.7±0.1</td><td>59.7±0.4</td><td>63.5±0.1</td><td>65.8±0.2</td><td>66.7±0.2</td></tr><tr><td rowspan=\"2\">CIFAR100</td><td>1</td><td>21.6±0.6</td><td>18.7±0.1</td><td>19.1±0.1</td><td>20.5±0.2</td><td>21.8±0.3</td><td>20.9±0.7</td><td>22.8±0.4</td></tr><tr><td>10</td><td>33.8±0.3</td><td>31.7±0.1</td><td>31.0±0.2</td><td>30.7±0.2</td><td>27.0±0.2</td><td>33.0±0.2</td><td>35.1±0.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.203,
+                0.892,
+                0.218
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation studies of our method in different settings. The black subscript indicates the standard deviation over multiple evaluations."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.231,
+                0.28,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.126,
+                0.388,
+                0.236,
+                0.415
+            ],
+            "angle": 0,
+            "content": "An Arbitrary Net Acc. \\(50.5\\%\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.284,
+                0.23,
+                0.484,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.297,
+                0.388,
+                0.472,
+                0.415
+            ],
+            "angle": 0,
+            "content": "Translated Results w/o Ada Acc. \\(54.7\\%\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.487,
+                0.23,
+                0.688,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.506,
+                0.388,
+                0.669,
+                0.415
+            ],
+            "angle": 0,
+            "content": "Translated Results w Ada Acc. \\(59.2\\%\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.692,
+                0.23,
+                0.892,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.753,
+                0.388,
+                0.829,
+                0.415
+            ],
+            "angle": 0,
+            "content": "FRePo Acc. \\(65.5\\%\\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.158,
+                0.426,
+                0.812,
+                0.441
+            ],
+            "angle": 0,
+            "content": "Figure 3. Qualitative analysis of results produced by our method for IPC 10 on CIFAR10. Zoom in for details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.455,
+                0.468,
+                0.484
+            ],
+            "angle": 0,
+            "content": "- 1 Net: synthetic data are distilled in a single network, which can be treated as a lower bound;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.497,
+                0.454,
+                0.512
+            ],
+            "angle": 0,
+            "content": "- Bi-Level: the bi-level algorithm described in Alg. 1;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.524,
+                0.469,
+                0.554
+            ],
+            "angle": 0,
+            "content": "- \\( w / o \\) Pre-Train: the target adaptation stage starts from a randomly initialized translator;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.565,
+                0.469,
+                0.595
+            ],
+            "angle": 0,
+            "content": "- \\(wAE\\): the target adaptation stage starts from an autoencoder trained with a reconstruction objective;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.607,
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+                0.636
+            ],
+            "angle": 0,
+            "content": "- \\( w/o \\) Ada: directly using the pre-trained translator without the adaptation stage;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.649,
+                0.292,
+                0.662
+            ],
+            "angle": 0,
+            "content": "- \\(w\\) Ada: the default method."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.455,
+                0.469,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.469,
+                0.794
+            ],
+            "angle": 0,
+            "content": "All the candidates are trained with 4k iterations. For those requiring adaptation, i.e., w/o Pre-Train, w AE, and w Ada, we first distill a synthetic dataset using 1 network with 3k iterations and adapt the translator for another 1k steps. Note that distilling with a single network only requires one forward propagation pass of the real dataset. Thus, the running time of our method is less than that of the baseline given the same number of iterations. Results are shown in Tab. 3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
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+                0.901
+            ],
+            "angle": 0,
+            "content": "For one thing, it turns out that the default method in this paper consistently surpasses the benchmark baseline requiring enormous networks in most cases. The reason is that with the number of networks for NFR increasing, it would be more difficult for the training convergence of distilled datasets, especially in the few-shot case. Please refer to the supplement for details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.455,
+                0.892,
+                0.59
+            ],
+            "angle": 0,
+            "content": "For another, the consistent improvement comparing results of 1 Net and w/o Ada indicates that the pre-trained translator is capable of generating distilled results in a more favorable space. We visualize their results in the first two plots of Fig. 3, where the global tone is refined towards higher brightness contrast. Moreover, as shown in the 3rd plot, the adaptation stage injects more local details, which tries to improve the performance in a similar way performed by the state-of-the-art FRePo [52]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.591,
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+                0.652
+            ],
+            "angle": 0,
+            "content": "Further, as shown in both Tab. 3 and Fig. 4(a-b), the pretrained model offers a more satisfactory initialization for the following adaptation stage, with lower initial loss, faster convergence, and higher accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "At last, the bi-level algorithm often leads to inferior performance, which may be partially attributed to the insufficient number of inner steps restricted by GPU memory."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "Generalization: We observe that one benefit of adapting the translator in a target dataset is that it is generalizable across different storage budgets for synthetic datasets. For instance, as shown in Fig. 4(c), the translator adapted on IPC 1 and 50 can also behave well on IPC 10."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Following previous works [51, 49, 50], we also evaluate the cross-architecture performance in Tab. 4 over AlexNet [16], VGG11 [37], and ResNet18 [8]. The conclusion is consistent with the above analysis."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4.4. Application: Continual Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Continual learning (CL) aims to learn a sequence of tasks where the training data of past tasks are unavailable when"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "(a)"
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+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.258,
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+            "angle": 0,
+            "content": "Figure 4. (a-b) NFR loss and test accuracy during adaption for CIFAR10 IPC 10 starting with the pre-trained translator by our algorithm, an auto-encoder, and a randomly initialized model. (c) Generalization performance of the translator on unseen IPC during adaptation."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Setting</td><td>ConvNet</td><td>AlexNet</td><td>VGG</td><td>ResNet</td></tr><tr><td>Baseline</td><td>58.8±0.2</td><td>57.1±0.5</td><td>41.1±0.3</td><td>38.1±0.9</td></tr><tr><td>1 Net</td><td>50.5±0.8</td><td>50.9±0.6</td><td>34.2±0.3</td><td>35.3±0.3</td></tr><tr><td>Bi-Level</td><td>52.1±0.5</td><td>50.0±0.4</td><td>37.4±0.5</td><td>34.7±0.5</td></tr><tr><td>w/o Pre-Train</td><td>53.8±0.1</td><td>56.2±0.3</td><td>39.3±0.7</td><td>38.2±0.7</td></tr><tr><td>w/o Ada</td><td>54.7±0.8</td><td>52.8±0.3</td><td>35.7±0.7</td><td>34.8±1.2</td></tr><tr><td>w Ada</td><td>59.2±0.3</td><td>56.8±0.2</td><td>43.0±0.7</td><td>40.8±0.5</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.431,
+                0.47,
+                0.459
+            ],
+            "angle": 0,
+            "content": "Table 4. Cross-architecture performance of our method in different settings. Results on CIFAR10 with 10 IPC are shown here."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.479,
+                0.469,
+                0.57
+            ],
+            "angle": 0,
+            "content": "learning the current one. To overcome the problem of catastrophic forgetting [14], many works use a small buffer to store some valuable data of past tasks for future use [32, 1]. Dataset distillation can thus benefit this area by synthesizing informative samples [27, 34, 36, 43, 3, 26] to prevent forgetting as much as possible."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.571,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "In this paper, we evaluate the proposed method on CIFAR100-CL following the same 5-step protocol of [52, 50] with 20 classes for each task and 20 IPC. The results in Fig. 5 suggest a consistent conclusion with the ablation studies shown in Sec. 4.3 and indicate that the few-shot dataset distillation proposed in this paper can further facilitate the practical use when tasks come fast like a stream, which provides limited time for processing and learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this paper, we focus on the setting of few-shot dataset distillation to improve its efficiency, where data can only be processed by a limited number of neural networks. We introduce the concept of distillation space to optimize the performance of synthetic data distilled by only one network. Regarding that the complexity of the quad-level definition and the bi-level algorithm for distillation space, we convert the problem to a transitive model. The synthetic dataset is first distilled in a random but fixed neural network and then translated to the desired space. For transferability, we train the translator with a pre-training algorithm, so that a pre"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.545,
+                0.304,
+                0.851,
+                0.466
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.474,
+                0.892,
+                0.503
+            ],
+            "angle": 0,
+            "content": "Figure 5. Performance of continual learning on CIFAR100 with 5 steps and 20 IPC for different settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.515,
+                0.893,
+                0.606
+            ],
+            "angle": 0,
+            "content": "trained translator can be adapted for a new dataset within a limited number of steps. Experiments demonstrate that our method achieves \\(\\sim 15\\times\\) acceleration and comparable performance with the state-of-the-art baselines relying on thousands of networks. Even in some cases, the translator without adaptation yields competitive performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.606,
+                0.894,
+                0.773
+            ],
+            "angle": 0,
+            "content": "One limitation of our method is that in the adaptation stage, errors of translated synthetic datasets have to be further back-propagated through the translator, which introduces additional GPU memory consumption compared with the baseline method, e.g., 3946 v.s. 3456 MB on CIFAR10 with 10 IPC. Nevertheless, as shown in Fig. 4(c), the translator adapted for small sizes can conduct inference for larger sizes, thereby breaking the limitation on GPU memory. Future works may focus on further improving the transferability of the distillation space translator by dedicated architectural designs or objective functions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.785,
+                0.661,
+                0.803
+            ],
+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This work is supported by the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2), and the Singapore Ministry of Education Academic Research Fund Tier 1 (WBS: A0009440-01-00)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18662"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "References"
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+# Few-Shot Dataset Distillation via Translative Pre-Training
+
+Songhua Liu Xinchao Wang*
+
+National University of Singapore
+
+songhua.liu@u.nus.edu，xinchao@nus.edu.sg
+
+# Abstract
+
+Dataset distillation aims at a small synthetic dataset to mimic the training performance on neural networks of a given large dataset. Existing approaches heavily rely on an iterative optimization to update synthetic data and multiple forward-backward passes over thousands of neural network spaces, which introduce significant overhead for computation and are inconvenient in scenarios requiring high efficiency. In this paper, we focus on few-shot dataset distillation, where a distilled dataset is synthesized with only a few or even a single network. To this end, we introduce the notion of distillation space, such that synthetic data optimized only in this specific space can achieve the effect of those optimized through numerous neural networks, with dramatically accelerated training and reduced computational cost. To learn such a distillation space, we first formulate the problem as a quad-level optimization framework and propose a bi-level algorithm. Nevertheless, the algorithm in its original form has a large memory footprint in practice due to the back-propagation through an unrolled computational graph. We then convert the problem of learning the distillation space to a first-order one based on image translation. Specifically, the synthetic images are optimized in an arbitrary but fixed neural space and then translated to those in the targeted distillation space. We pre-train the translator on some large datasets like ImageNet so that it requires only a limited number of adaptation steps on the target dataset. Extensive experiments demonstrate that the translator after pre-training and a limited number of adaptation steps achieves comparable distillation performance with state of the arts, with  $\sim 15\times$  acceleration. It also exerts satisfactory generalization performance across different datasets, storage budgets, and numbers of classes.
+
+# 1. Introduction
+
+Given an original dataset  $\mathcal{T}$ , Dataset distillation (DD) [41, 51, 35, 18, 47, 20, 22] aims at a much smaller
+
+![](images/f35aa61de0ec9bde9b018b332fdeaa5d18cd4eee1bdc9c5a7fe6237e834bcfda.jpg)  
+(a)
+
+![](images/5dee38db11fc60c5bd81e7259cbb68b98a941eca5c9abb1aa06ab54d9ff30a99.jpg)  
+(b)
+
+![](images/88d42e8adb3c171ad3ad6b2414e7ae72006defaf97725a4c244d439b9f736d53.jpg)  
+(c)
+
+![](images/7093a48621a4dadf7f691bc994256bc5b4d6741ded1a6a8a95e43d2076378bdd.jpg)  
+(d)  
+Figure 1. (a) Existing DD methods heavily rely on forward-backward processes through enormous neural networks. (b) More neural networks used in dataset distillation would result in more floating point operations (FLOPs) and higher latency. (c) We introduce the notation of distillation space for few-shot dataset distillation in this paper and aim to learn a neural network such that distilled data only optimized in this specific space can approximate the performance by multiple networks. (d) Given only a few or even a single network, our method achieves comparable performance with state-of-the-art baselines requiring enormous networks. Results in this figure are concerning models trained with 1 image per class distilled from CIFAR100 dataset. OS denotes one-shot DD using only one network, FS denotes few-shot DD with a limited number of adaptation steps, and DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget.
+
+synthetic dataset  $S$ , such that the training effect of  $S$  on neural networks can match that of  $\mathcal{T}$ . Such techniques have received considerable attention to alleviate the heavy burden on storage, transmission, and training of deep learning models brought by large-scale datasets. Recent advances on DD have revealed that models trained with only a few synthetic samples, even 1 image per class in some cases, can retain most of the performance of those trained with real data [49, 50, 2, 28, 29, 40, 13, 52, 23, 21]. Thus, it becomes a research area receiving increasing attention from the aca
+
+demic and industrial community recently as a potential solution to alleviate the concerns on the storage, transmission, pre-processing, and training effort for large datasets.
+
+Nevertheless, as shown in Fig. 1(a), all existing methods on DD work iteratively: the synthetic dataset is optimized in an outer loop, and real and synthetic data are sent to a newly-initialized neural network in each iteration. Although they have achieved remarkable performance, such forward-backward passes in multiple neural networks can introduce extensive computational overhead to generate a distilled dataset, as illustrated in Fig. 1(b). As a result, the burdensome distillation procedure in existing methods brings significant latency. For instance, one of the state-of-the-art works by Deng et al. [5] requires  $\sim 18$  days to distill only 1 image per class for CIFAR100 dataset [15] as shown in Fig. 1(d) and [47]. Even FRePo [52], with the most satisfactory efficiency, takes over 3 hours in the same setting requiring 500,000 neural network steps. The long training process in current DD makes it inconvenient for scenarios requiring high efficiency, e.g., processing streaming data.
+
+Focusing on these drawbacks, in this paper, we propose few-shot dataset distillation and are interested in the performance of DD if only a few or even a single neural network is available for training. We first try a naive solution by merely adopting one neural network for the existing method FRePo [52] and visualize the accuracy and efficiency. As shown in Fig. 1(d), although the simple strategy improves the efficiency, the performance gap with the original version based on thousands of networks is significant, which suggests a trade-off between performance and the number of networks. A similar effect is also revealed by Cazenavette et al. [2], where the number of teacher training trajectories would affect the performance substantially. Thus, how to boost the performance by only a limited number of networks becomes an interesting question in few-shot DD.
+
+Currently, the networks used in Fig. 1(d) are randomly and independently initialized, which makes us curious: whether there exists a dedicated neural network, such that the synthetic dataset distilled in it can achieve similar performance to those distilled in multiple ones. In this paper, we describe this concept through a quad-level definition termed as distillation space, as shown in Fig. 1(c), and propose a bi-level algorithm to find it, to optimize the error on real data, for networks trained with the synthetic dataset, distilled in this space.
+
+However, the bi-level optimization requires backpropagating through an unrolled computational graph over multiple steps of gradient descent, which imposes an intensive GPU footprint. Due to the bottleneck on GPU memory, the number of steps for inner optimization is limited, which further limits the performance in practice. To reduce the complexity, we free the dependency of higher-order gradients via casting the problem as image translation, to make
+
+sure that the iterative optimization process is not nested in the computational graph: the synthetic dataset is distilled in a random but fixed neural network space and then translated to the desired space via a translator network.
+
+Specifically, the translator is pre-trained on some large datasets like ImageNet [4]. In each iteration, a random subset is sampled. Distilled results after being translated from the original space are evaluated in some random networks, and the distillation loss is back-propagated to the translator to update its parameters. We find that the distillation space translator after pre-training can generalize well across different datasets, storage budgets, and numbers of classes. With only a few adaptation steps on the target dataset, the performance of distilled data after translation achieves can be on par with those distilled by multiple neural networks at  $\sim 15\times$  faster, as shown in Fig. 1(d).
+
+In summary, our contributions are listed as follows:
+
+- Tailoring for scenarios requiring high efficiency, we are the first to study the problem of few-shot dataset distillation, where only a limited number of neural networks are available for DD, and introduce the quad-level definition of distillation space for it.  
+- An efficient translative modeling approach with a pretraining algorithm is proposed to learn an effective distillation space;  
+- Extensive experiments demonstrate that our method is capable of generating dataset distillation results with  $\sim 15\times$  acceleration.
+
+# 2. Related Works
+
+Dataset distillation (DD) refers to distilling a small synthetic dataset  $S$  from a given large dataset  $T$ , where  $S$  is optimized to have similar downstream training performance to  $T$ . Unlike most existing techniques that focus on reducing the size of a model [6, 25, 45, 44, 7, 46, 12, 11, 10, 33], DD concentrates on learning compressed data to enhance learning efficiency. Wang et al. [41] firstly introduce the task and propose a meta-learning method to minimize the loss of meta-test on  $T$  for models meta-trained on  $S$ . This scheme aligns with the evaluation protocol of DD: to pursue higher accuracy on the real test data for networks optimized by the synthetic ones. However, restricted by the GPU memory, the steps of meta-training in this framework are limited, which bottlenecks the performance [5]. The bilevel loop with a large number of inner steps also affects the efficiency negatively.
+
+To address this issue, a series of works consider mapping real and synthetic samples to a feature space with some kernels, e.g., NTK [28, 29], NNGP [23], and non-linear network [52, 24], and then perform kernel ridge regression
+
+![](images/3b890c544f14088c7a66a95b902dc199de9596af28929141ca04fb06c5db09e9.jpg)  
+(a)  
+Figure 2. (a) Existing DD methods rely on an iterative training process, where a new network has to be initialized for forward and backward passes of the real dataset  $\mathcal{T}$  and the synthetic dataset  $S$ . (b) We desire to learn a specific distillation space, where  $\mathcal{S}$  optimized only in such a space can minimize the error of neural feature regression in an arbitrary random network. The loop for optimizing  $\mathcal{S}$  is nested in the computational graph for optimizing the distillation space. (c) We detach the loop for optimizing  $\mathcal{S}$  for computational efficiency and convert the problem to a transitive model, where  $\mathcal{S}$  is distilled in an arbitrary but fixed neural space first and then translated to the desired space.
+
+![](images/b544e6607d0a9c1f466794b3285971bc8e190ac713ff642550a4cfc8aba2a023.jpg)  
+(b)  
+(c)
+
+(KRR). Benefiting from the analytical solution of KRR, these methods can access the optimal parameters trained by synthetic datasets via direct computation without the necessity of higher-order gradients, which achieves favorable efficiency and accuracy at the same time. In this paper, the KRR-based formulation is also adopted as the main objective to reduce the complexity of meta-learning, thanks to its satisfactory efficiency.
+
+In the literature of DD, matching-based methods are another major branch. For example, Zhao et al. [51] and a lot of following works [49, 13, 17, 9, 48] adopt gradient matching. Cazenavette et al. [2] propose MTT, which optimizes the distance between network parameters trained by  $S$  and  $T$  respectively from some cached initialization. Their insights lie in that gradients in networks or trained model parameters can represent the training effects of different datasets. Some works also consider matching the statistics of  $S$  and  $T$  in some neural networks [50, 40], which get rid of computing gradients of training networks via  $S$  and  $T$  and thus improves the efficiency.
+
+No matter what objectives existing methods adopt, they all rely on an extensive outer optimization loop to update synthetic data, where  $S$  and  $\mathcal{T}$  have to undergo forward-backward passes through thousands of networks. To make things worse, a series of works considering synthetic dataset parameterization, which tries to increase the number of images with the same storage budget, require even more such iterations [5, 19]. Motivated by these facts, we focus on the problem of few-shot dataset distillation in this paper where a synthetic dataset is distilled given only a few or even a single neural network. Given that naively adopting only a few random networks results in inferior performance as
+
+shown in Fig. 1(d), we introduce the concept of distillation space, such that the performance of synthetic data distilled in this space can match those in enormous networks. Dedicated to finding such a space to benefit dataset distillation to reduce the number of networks required for acceleration while retaining the performance as much as possible, a novel translative model with a pre-training approach is proposed to this end. To our best knowledge, this is the first work focusing on few-shot learning and pre-training in DD.
+
+# 3. Methods
+
+In this section, we delve into details about our methods for few-shot dataset distillation, where real and synthetic datasets can be processed by only a few neural networks. We first provide a brief introduction of current mainstream solutions for DD, based on which we propose the quad-level definition of distillation space in formal and a basic bi-level algorithm to learn the space. For computational efficiency, we then convert the original formulation of learning the distillation space to a transitive problem and propose an alternative algorithm, backed up by theoretical analysis. Finally, we explain the paradigm of pre-training for few-shot learning to increase the transferability of the learned distillation space across various datasets, the number of classes, and the storage budgets of synthetic datasets.
+
+# 3.1. Preliminary
+
+Dataset distillation (DD) targets a small synthetic dataset  $S$  such that the performance on downstream training with  $S$  can match that with the original dataset  $\mathcal{T}$ . The seminal work by Wang et al. [41] proposes a meta-learning ap
+
+Algorithm 1 Bi-Level Optimization for Distillation Space.
+
+Input:  $\mathcal{T}$ : Target Dataset;  $\Theta$ : Distribution for Initializing Neural Networks;  $T$ : Number of Inner Update Steps;  $\alpha$ : Learning Rate for Inner Optimization;  $\eta$ : Learning Rate for Outer Optimization.
+
+Output:  $\theta$ : Distillation Space after Optimization.
+
+1: Initialize  $\theta \sim \Theta$  
+2: for  $i = 1,2,3,\ldots$  do  
+3: Initialize  $S$  with random samples from  $\mathcal{T}$ ;  
+4:  $X_{\mathcal{T}}^{\theta}\gets f_{\theta}(X_{\mathcal{T}});$  
+5: for  $1\leq t\leq T$  do  
+6:  $w_{\mathcal{S},\theta}^* \gets f_\theta(X_\mathcal{S})^\top (f_\theta(X_\mathcal{S})f_\theta(X_\mathcal{S})^\top)^{-1}Y_\mathcal{S};$  
+7:  $X_{\mathcal{S}} \gets X_{\mathcal{S}} - \alpha \nabla_{X_{\mathcal{S}}} \| X_{\mathcal{T}}^{\theta} w_{\mathcal{S},\theta}^{*} - Y_{\mathcal{T}}^{2}$ ;  
+8:  $Y_{\mathcal{S}} \gets Y_{\mathcal{S}} - \alpha \nabla_{Y_{\mathcal{S}}} \| X_{\mathcal{T}}^{\theta} w_{\mathcal{S},\theta}^{*} - Y_{\mathcal{T}} \|^{2}$ ;  
+9: end for  
+10: Randomly sample  $\theta^{\prime}\sim \Theta$  
+11:  $X_{\mathcal{T}}^{\theta^{\prime}}\gets f_{\theta^{\prime}}(X_{\mathcal{T}});$  
+12:  $w_{\mathcal{S},\theta^{\prime}}^{*}\gets f_{\theta^{\prime}}(X_{\mathcal{S}})^{\top}(f_{\theta^{\prime}}(X_{\mathcal{S}})f_{\theta^{\prime}}(X_{\mathcal{S}})^{\top})^{-1}Y_{\mathcal{S}};$  
+13:  $\theta \gets \theta -\eta \nabla_{\theta}\| X_{\mathcal{T}}^{\theta '}w_{\mathcal{S},\theta '}^{*} - Y_{\mathcal{T}}\|^{2};$  
+14: end for
+
+proach, which optimizes the loss on  $\mathcal{T}$  for models trained with  $S$  and backpropagates the gradients through multiple training steps to update  $S$ :
+
+$$
+\mathcal {S} ^ {*} = \underset {\mathcal {S}} {\arg \min } \mathbb {E} _ {\theta^ {(0)} \sim \Theta} [ l (\mathcal {T}; \theta^ {(T)}) ], \tag {1}
+$$
+
+$$
+\theta^ {(t)} = \theta^ {(t - 1)} - \alpha \nabla l (\mathcal {S}; \theta^ {(t - 1)}),
+$$
+
+where  $\Theta$  denotes a distribution for initialization,  $T$  is the number of training steps with  $S$  and  $1 \leq t \leq T$ ,  $\alpha$  is the learning rate, and  $l$  is the loss function, e.g., cross-entropy loss for classification problems.
+
+The bi-level optimization algorithm indicated in Eq. 1 relies on backpropagating through an unrolled computational graph of inner optimization steps, which makes it inefficient in both time and memory. Nguyen et al. [28, 29] thus consider the problem of kernel ridge regression (KRR), where the analytical optimal solution gets rid of the necessity to optimize the model with  $S$  for multiple nested steps. For more satisfactory accuracy and efficiency, the spirit is further extended by following works [52, 23], which map a batch of  $n$  samples  $X$  to a feature space with a random neural network and then perform KRR. Denote the function of neural network parameterized by  $\theta$  as  $f_{\theta}$  and the label matrix corresponding to  $X \in \mathbb{R}^{n \times d}$  as  $Y \in \mathcal{R}^{n \times c}$ , where  $d$  and  $c$  are the dimensions of sample and label respectively, i.e.,  $h \times w \times 3$  and the number of classes in the RGB image classification problem, the objective can be formulated as:
+
+$$
+\begin{array}{l} X _ {\mathcal {S}} ^ {*}, Y _ {\mathcal {S}} ^ {*} = \underset {X _ {\mathcal {S}}, Y _ {\mathcal {S}}} {\arg \min } \mathbb {E} _ {\theta \sim \Theta} [ \| f _ {\theta} (X _ {\mathcal {T}}) w _ {\mathcal {S}, \theta} ^ {*} - Y _ {\mathcal {T}} \| ^ {2} ], \tag {2} \\ w _ {S, \theta} ^ {*} = f _ {\theta} (X _ {S}) ^ {\top} \left(f _ {\theta} (X _ {S}) f _ {\theta} (X _ {S}) ^ {\top}\right) ^ {- 1} Y _ {S}. \\ \end{array}
+$$
+
+This technique is known as neural feature regression (NFR) [52]. In each training iteration, a new random neural network is initialized for solving the problem in Eq. 2, as shown in Fig. 2(a).
+
+# 3.2. Learning a Distillation Space
+
+As illustrated in Fig. 1(a), the iterative optimization framework shown in Fig. 2(a) involves forward and backward processes through thousands of networks and introduces significant computational overhead. In this work, we thus focus on the problem of DD using only a few or even one network. Given the results in Fig. 1(b) that simply adopting a random network yields limited performance, we are interested in learning a specific network such that  $S$  distilled in it can achieve performance on par with that distilled in multiple networks, i.e., minimize the error on  $\mathcal{T}$  for an arbitrary model trained with  $S$ . Formally, we term such a network as distillation space in the following definition.
+
+Definition 1 (Distillation Space). A distillation space for a distribution of network  $\Theta$  and a target dataset  $\mathcal{T}$  is a neural network function  $f$  parameterized by  $\theta^{*}$  which satisfies:
+
+$$
+\begin{array}{l} \theta^{*} = \operatorname *{arg  min}_{\theta^{(0)}}\mathbb{E}_{\theta^{(0)^{\prime}}\sim \Theta}[l(\mathcal{T};\theta^{(T)^{\prime}})], \\ \theta^ {(t) ^ {\prime}} = \theta^ {(t - 1) ^ {\prime}} - \alpha^ {\prime} \nabla l \left(\mathcal {S} ^ {*}; \theta^ {(t - 1) ^ {\prime}}\right), \tag {3} \\ \mathcal {S} ^ {*} = \underset {\mathcal {S}} {\arg \min } l (\mathcal {T}; \theta^ {(T)}), \\ \theta^ {(t)} = \theta^ {(t - 1)} - \alpha \nabla l (\mathcal {T}; \theta^ {(t - 1)}). \\ \end{array}
+$$
+
+In practice, to find an effective distillation space, we first simplify the quad-level definition via NFR in Eq. 2, which derives a bi-level optimization problem:
+
+$$
+\begin{array}{l} \theta^ {*} = \underset {\theta} {\arg \min } \mathbb {E} _ {\theta^ {\prime} \sim \Theta} [ \| f _ {\theta^ {\prime}} (X _ {\mathcal {T}}) w _ {\mathcal {S} ^ {*}, \theta^ {\prime}} ^ {*} - Y _ {\mathcal {T}} \| ^ {2} ], \\ w _ {\mathcal {S} ^ {*}, \theta^ {\prime}} ^ {*} = f _ {\theta^ {\prime}} \left(X _ {\mathcal {S}} ^ {*}\right) ^ {\top} \left(f _ {\theta^ {\prime}} \left(X _ {\mathcal {S}} ^ {*}\right) f _ {\theta^ {\prime}} \left(X _ {\mathcal {S}} ^ {*}\right) ^ {\top}\right) ^ {- 1} Y _ {\mathcal {S}} ^ {*}, \tag {4} \\ X _ {\mathcal {S}} ^ {*}, Y _ {\mathcal {S}} ^ {*} = \underset {X _ {\mathcal {S}}, Y _ {\mathcal {S}}} {\arg \min} \| f _ {\theta} (X _ {\mathcal {T}}) w _ {\mathcal {S}, \theta} ^ {*} - Y _ {\mathcal {T}} \| ^ {2}, \\ w _ {S, \theta} ^ {*} = f _ {\theta} (X _ {S}) ^ {\top} \left(f _ {\theta} (X _ {S}) f _ {\theta} (X _ {S}) ^ {\top}\right) ^ {- 1} Y _ {S}. \\ \end{array}
+$$
+
+Eq. 4 indicates a bi-level meta-learning algorithm as shown in Fig. 2(b) and Alg. 1. In each inner iteration,  $S$  is metatrained via NFR in the current neural space  $f_{\theta}$ .  $S$  after a whole inner loop is meta-tested in a random neural network  $f_{\theta'}$  and the loss of NFR is back-propagated to update  $\theta$ .
+
+# 3.3. Learning a Translation to a Distillation Space
+
+Although Alg. 1 can be an effective algorithm to learn a valid distillation space, the back-propagation process through a nested computational graph is inefficient in GPU memory. The memory complexity is proportionate to the number of inner optimization steps  $T$  to obtain the optimal synthetic dataset in the current space, which is crucial
+
+for the final performance [5] but withheld by the limited GPU memory. For instance, in a 40G A100 GPU,  $T$  in Alg. 1 can be set as 16 at most, which is too small to get convergence for inner optimization. To alleviate this drawback, we consider an alternative approach to learn a distillation space. Specifically, we detach the inner optimization from the computational graph by converting the problem to a transitive model, based on the following proposition.
+
+Proposition 1. For a target dataset  $X_{\mathcal{T}} \in \mathbb{R}^{n_{\mathcal{T}} \times d}$  and  $Y_{\mathcal{T}} \in \mathbb{R}^{n_{\mathcal{T}} \times c}$  with  $n_{\mathcal{T}} \geq d$ , assume that  $X_{\mathcal{S},0}^{*}$  and  $Y_{\mathcal{S},0}^{*}$  satisfy  $\| f_{\theta}(X_{\mathcal{T}})w_{\mathcal{S},\theta}^{*} - Y_{\mathcal{T}}\|^{2} = 0$ , where  $w_{\mathcal{S},\theta}^{*} = f_{\theta}(X_{\mathcal{S},0}^{*})^{\top}(f_{\theta}(X_{\mathcal{S},0}^{*})f_{\theta}(X_{\mathcal{S},0}^{*})^{\top})^{-1}Y_{\mathcal{S},0}^{*}$  and  $f_{\theta}$  is a known linear transformation parameterized by a full-rank matrix  $\theta \in \mathbb{R}^{d \times d'}$ ,  $d \leq d'$ . Similarly, let  $f_{\theta^{*}}$  be a desired linear distillation space and  $\theta^{*} \in \mathbb{R}^{d \times d''}$ ,  $d \leq d'' \leq n_{\mathcal{T}}$ . The distilled dataset  $X_{\mathcal{S},*}^{*}$  and  $Y_{\mathcal{S},*}^{*}$  in this space satisfy  $\| f_{\theta^{*}}(X_{\mathcal{T}})w_{\mathcal{S},\theta^{*}}^{*} - Y_{\mathcal{T}}\|^{2} = 0$ , where  $w_{\mathcal{S},\theta^{*}}^{*} = f_{\theta^{*}}(X_{\mathcal{S},*}^{*})^{\top}(f_{\theta^{*}}(X_{\mathcal{S},*}^{*})f_{\theta^{*}}(X_{\mathcal{S},*}^{*})^{\top})^{-1}Y_{\mathcal{S},*}^{*}$ . There exists a translation function  $G$  for  $X_{\mathcal{S},0}^{*}$  and  $Y_{\mathcal{S},0}^{*}$  such that  $X_{\mathcal{S},*}^{*}, Y_{\mathcal{S},*}^{*} = G(X_{\mathcal{S},0}^{*}, Y_{\mathcal{S},0}^{*})$ , whose parameters are not dependent on the target dataset  $X_{\mathcal{T}}$  and  $Y_{\mathcal{T}}$ .
+
+Proof. Due to the linearity of  $f_{\theta}$  and  $f_{\theta^{*}}$ , we can rewrite the given conditions as:
+
+$$
+X _ {\mathcal {T}} \theta w _ {S, \theta} ^ {*} - Y _ {\mathcal {T}} = 0, \tag {5}
+$$
+
+$$
+X _ {\mathcal {T}} \theta^ {*} w _ {S, \theta^ {*}} ^ {*} - Y _ {\mathcal {T}} = \mathbf {0}, \tag {6}
+$$
+
+Since  $n_{\mathcal{T}} \geq d$  for  $X_{\mathcal{T}}$ , pre-multiplying terms in Eq. 5 by the Moore-Penrose inverse  $X_{\mathcal{T}}^{\dagger}$ , we have
+
+$$
+X _ {\mathcal {T}} ^ {\dagger} Y _ {\mathcal {T}} = \theta w _ {\mathcal {S}, \theta} ^ {*}. \tag {7}
+$$
+
+Similarly, through Eq. 6, we have
+
+$$
+w _ {\mathcal {S}, \theta^ {*}} ^ {*} = (X _ {\mathcal {T}} \theta^ {*}) ^ {\dagger} Y _ {\mathcal {T}} = \theta^ {* \dagger} X _ {\mathcal {T}} ^ {\dagger} Y _ {\mathcal {T}} = \theta^ {* \dagger} \theta w _ {\mathcal {S}, \theta} ^ {*}, \quad (8)
+$$
+
+where the first, second, and third equalities are due to  $n_{\mathcal{T}} \geq d''$ ,  $d'' \geq d$ , and Eq. 7 respectively. We can observe in Eq. 8 that  $w_{S,\theta^*}^*$  in the desired distillation space is not dependent on  $\mathcal{T}$ . Thus, the optimal  $X_{S,*}^*$  and  $Y_{S,*}^*$  resulting the optimal KRR parameter can be obtained given only  $X_{S,0}^*$  and  $Y_{S,0}^*$  by some translation function  $G$ , which implicitly includes the knowledge of the distillation space.
+
+Prop. 1 indicates that it is possible to approach the distillation space by translating samples from some space rather than learning  $\theta^{*}$  directly, motivated by which we propose to learn a translation from one another space to the distillation space. The main workflow is similar to Alg. 1: synthetic data are first distilled in a random but fixed network in an inner loop and then translated to final results, as shown in Fig. 2(c). The translator is optimized so that results after translation are equipped with the property of those produced in a distillation space: to minimize the NFR error in
+
+Algorithm 2 Pre-training a Distillation Space Translator.
+
+Input:  $\mathcal{Z}$ : A Large Dataset;  $\Theta$ : Distribution for Initializing Neural Networks;  $\theta$ : An Arbitrary Random Neural Network;  $T$ : Number of Update Steps for Synthetic Data;  $\alpha$ : Learning Rate for Synthetic Data;  $\eta$ : Learning Rate for Translator.
+
+Output:  $\omega$ : A Pre-trained Translator.
+
+1: Initialize  $\omega$  randomly;  
+2: for  $i = 1,2,3,\ldots$  do  
+3: Randomly choose a subset of data  $\mathcal{T}$  from  $\mathcal{Z}$ ;  
+4: Initialize  $S^{\prime}$  with random samples from  $\mathcal{T}$  
+5:  $X_{\mathcal{T}}^{\theta}\gets f_{\theta}(X_{\mathcal{T}});$  
+6: for  $1 \leq t \leq T$  do  
+7:  $w_{\mathcal{S}^{\prime},\theta}^{*}\gets f_{\theta}(X_{\mathcal{S}^{\prime}})^{\top}(f_{\theta}(X_{\mathcal{S}^{\prime}})f_{\theta}(X_{\mathcal{S}^{\prime}})^{\top})^{-1}Y_{\mathcal{S}^{\prime}};$  
+8:  $X_{\mathcal{S}^{\prime}} \gets X_{\mathcal{S}^{\prime}} - \alpha \nabla_{X_{\mathcal{S}^{\prime}}} \| X_{\mathcal{T}}^{\theta} w_{\mathcal{S}^{\prime},\theta}^{*} - Y_{\mathcal{T}} \|^{2}$ ;  
+9:  $Y_{\mathcal{S}^{\prime}} \gets Y_{\mathcal{S}^{\prime}} - \alpha \nabla_{Y_{\mathcal{S}^{\prime}}} \| X_{\mathcal{T}}^{\theta} w_{\mathcal{S}^{\prime},\theta}^{*} - Y_{\mathcal{T}} \|^{2}$ ;  
+10: end for  
+11:  $X_{\mathcal{S}},Y_{\mathcal{S}} = G_{\omega}(X_{\mathcal{S}^{\prime}},Y_{\mathcal{S}^{\prime}});$  
+12: Randomly sample  $\theta^{\prime}\sim \Theta$  
+13:  $X_{\mathcal{T}}^{\theta^{\prime}}\gets f_{\theta^{\prime}}(X_{\mathcal{T}});$  
+14:  $w_{\mathcal{S},\theta^{\prime}}^{*}\gets f_{\theta^{\prime}}(X_{\mathcal{S}})^{\top}(f_{\theta^{\prime}}(X_{\mathcal{S}})f_{\theta^{\prime}}(X_{\mathcal{S}})^{\top})^{-1}Y_{\mathcal{S}};$  
+15:  $\omega \gets \omega -\eta \nabla_{\omega}\| X_{\mathcal{T}}^{\theta '}w_{S,\theta '}^{*} - Y_{\mathcal{T}}\|^{2};$  
+16: end for
+
+any random network. Since gradients are only required to back propagated to the translator rather than the whole inner loop, the memory complexity is irrelevant to the number of inner optimization steps. Thus, the translative model is a memory-efficient algorithm where only first-order gradients are necessary.
+
+# 3.4. Pre-training a Distillation Space Translator
+
+We expect that the distillation space optimized in a dataset is transferable across different datasets, storage budgets for synthetic data, and the number of classes. To tackle these challenges on transferability, in this paper, we consider pre-train a translator on some large dataset like ImageNet [4], so that it provides a satisfactory initialization and only requires a small number of adaptation steps for a target dataset, like the typical few-shot learning [42, 39, 38, 30]. The algorithm is shown in Alg. 2. In each training iteration  $i$ , we sample a subset from the large dataset and perform a gradient-decent step with the strategy mentioned in Sec. 3.3. Upon a translator is pre-trained, it can serve as a strong initialization for the adaptation process to a new dataset, which behaves identically to Line 11 to 15 of Alg. 2.
+
+# 4. Experiments
+
+In this section, we conduct experiments to validate the effectiveness of the proposed method for few-shot DD. We first introduce our experiment settings and implement de
+
+<table><tr><td>Hyper-Parameter</td><td>Denotation</td><td>Value</td></tr><tr><td>T</td><td>Number of Update Steps for Synthetic Data</td><td>3,000</td></tr><tr><td>α</td><td>Learning Rate for Synthetic Data</td><td>1e-3</td></tr><tr><td>η</td><td>Learning Rate for Translator in Pre-Training</td><td>1e-5</td></tr><tr><td>N</td><td>Number of Cached Subsets in Pre-Training</td><td>5,000</td></tr><tr><td>Cmax</td><td>Maximal Number of Classes in a Subset in Pre-Training</td><td>100</td></tr><tr><td>Cmin</td><td>Minimal Number of Classes in a Subset in Pre-Training</td><td>10</td></tr><tr><td>M</td><td>Maximal Number of Images in a Subset in Pre-Training</td><td>4,000</td></tr><tr><td>Imax</td><td>Maximal Number of Images in a Synthetic Dataset in Pre-Training</td><td>1,000</td></tr><tr><td>B</td><td>Batch Size in Pre-Training</td><td>4</td></tr><tr><td>S</td><td>Number of Pre-Training Steps</td><td>200,000</td></tr><tr><td>S&#x27;</td><td>Number of Adaptation Steps for Translator</td><td>1,000</td></tr><tr><td>η&#x27;</td><td>Learning Rate for Translator in Adaptation</td><td>1e-4</td></tr></table>
+
+Table 1. List of hyper-parameters and their values.
+
+tails of the method. Then, we compare our method with state-of-the-art solutions of DD in terms of both accuracy and efficiency. To illustrate how the proposed method works, we also provide an in-depth analysis of the method with a variety of baselines. Finally, we conduct experiments on continual learning, an important use case for DD, to further demonstrate the practical value of our method.
+
+# 4.1. Settings and Implementing Details
+
+In few-shot dataset distillation, a real dataset  $\mathcal{T}$  can be processed by only a few neural networks to generate a synthetic dataset  $S$ . In our method,  $S$  is firstly optimized in an arbitrary but fixed neural network by  $T$  steps, with the learning rate  $\alpha$ . The results are then processed by a translator to generate the final synthetic dataset. The translator adopts an auto-encoder architecture with 3 Conv-BatchNorm-ReLU blocks, and the detailed configuration can be found in the supplement. Notably, due to the fully-convolutional structure, the pre-trained translator can also be adapted to datasets with different resolutions beyond the one used during pre-training. Please refer to the supplement for details. The translator is pre-trained on the ImageNet dataset by  $S$  steps with the learning rate  $\eta$  and then adapted on the target dataset by a small number of iterations  $S'$ , with a learning rate  $\eta'$ . Some hyper-parameters are summarized in Tab. 1. Other hyper-parameters follow the default setting in the PyTorch [31] implementation of FRePo [52].
+
+Pre-Training: The key design of the translative pretraining pipeline lies in the separation of two stages: dataset distillation in an arbitrary but fixed neural network and the translation to the desired space. In practice, instead of directly following the pipeline in Alg. 2 that nests the two steps in one loop, the two stages are conducted independently in the interest of better training efficiency. Results distilled in the pre-defined network are cached for multiple random subsets so that they can be loaded directly and used
+
+repeatedly in the pre-training stage, which improves the training efficiency. The detailed algorithms for the caching stage and the pre-training stage can be found in the supplement.
+
+The caching stage aims to generate distilled results for multiple subsets. For sampling a subset, we first randomly choose the number of classes ranging from  $C_{\text{min}}$  to  $C_{\text{max}}$  and then randomly select the corresponding number of classes from the 1,000 ImageNet classes. For each select class, a certain number of random real images are sampled uniformly for each selected class such that the total number of images is  $M$  at most. The data augmentation technique DSA [49] is applied in the caching stage to mimic the cases of larger datasets. The maximal number of synthetic images is  $I_{\text{max}}$  and they are initialized with the selected real data. After distillation, indices of selected real samples and the distilled dataset are cached in the disk for future use in the pre-training stage. This process can be deployed to multiple GPUs in parallel, since the distillation for each subset is independent.
+
+In the pre-training stage, cached results in the previous stage are loaded. The NFR loss is calculated in a randomly initialized networks over a distribution in each iteration. Like the caching stage, pre-cached subsets in a batch can also be distributed to multiple GPUs in parallel. In this work, the pre-training is conducted on a single 40G A100 GPU, which takes roughly 2 days for the 200,000 steps.
+
+Adaptation: Given a pre-trained translator, it requires a small number of adaptation steps in general for the target dataset. The detailed adaptation algorithm can be found in the supplement. Intuitively, the procedure is consistent with the two-stage process in pre-training: to generate distilled results in a pre-defined network and then use the translator for the final results. The only difference with the pretraining stage is that real data come from the target dataset. By default, the set of IPC for adaptation only contains the target IPC. More IPCs can also be included in this set to
+
+<table><tr><td>Dataset</td><td>IPC</td><td>Metric</td><td>DD</td><td>RTP</td><td>DC</td><td>DSA</td><td>IDC</td><td>MTT</td><td>DM</td><td>FRePo</td><td>Ours</td><td>Ours-DS</td></tr><tr><td rowspan="6">CIFAR 10</td><td rowspan="2">1</td><td>Acc. (%)</td><td>40.5±0.8</td><td>49.1±0.6</td><td>28.3±0.5</td><td>28.8±0.7</td><td>36.7±0.4</td><td>46.3±0.8</td><td>26.0±0.8</td><td>46.8±0.7</td><td>44.0±0.2</td><td>51.4±0.4</td></tr><tr><td>Time (h)</td><td>363.9</td><td>363.9</td><td>0.1</td><td>0.1</td><td>10.6</td><td>0.8</td><td>0.3</td><td>2.4</td><td>0.02×120.0</td><td>0.1×24.0</td></tr><tr><td rowspan="2">10</td><td>Acc. (%)</td><td>50.0±0.5</td><td>62.4±0.4</td><td>44.9±0.5</td><td>52.1±0.5</td><td>58.3±0.4</td><td>65.3±0.7</td><td>48.9±0.6</td><td>65.5±0.6</td><td>59.2±0.3</td><td>66.0±0.3</td></tr><tr><td>Time (h)</td><td>447.2</td><td>447.2</td><td>1.0</td><td>1.3</td><td>11.1</td><td>2.4</td><td>0.3</td><td>3.1</td><td>0.04×77.5</td><td>0.2×15.5</td></tr><tr><td rowspan="2">50</td><td>Acc. (%)</td><td>-</td><td>70.5±0.4</td><td>53.9±0.5</td><td>60.6±0.5</td><td>69.5±0.3</td><td>71.6±0.2</td><td>63.0±0.4</td><td>71.7±0.2</td><td>66.7±0.2</td><td>71.8±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>1377.8</td><td>4.4</td><td>5.3</td><td>12.8</td><td>3.8</td><td>0.4</td><td>8.1</td><td>0.12×67.5</td><td>1.3×6.2</td></tr><tr><td rowspan="4">CIFAR 100</td><td rowspan="2">1</td><td>Acc. (%)</td><td>-</td><td>21.3±0.6</td><td>12.8±0.3</td><td>13.9±0.3</td><td>17.9±0.2</td><td>24.3±0.3</td><td>11.4±0.3</td><td>28.7±0.1</td><td>22.8±0.4</td><td>29.1±0.4</td></tr><tr><td>Time (h)</td><td>-</td><td>447.2</td><td>0.4</td><td>0.5</td><td>50.0</td><td>3.5</td><td>3.1</td><td>3.1</td><td>0.08×38.8</td><td>0.1×31.0</td></tr><tr><td rowspan="2">10</td><td>Acc. (%)</td><td>-</td><td>34.7±0.5</td><td>25.2±0.3</td><td>32.3±0.3</td><td>36.1±0.4</td><td>40.1±0.4</td><td>29.7±0.3</td><td>42.5±0.2</td><td>35.1±0.2</td><td>38.4±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>2520.8</td><td>10.6</td><td>11.4</td><td>68.9</td><td>4.2</td><td>3.1</td><td>10.4</td><td>0.32×32.5</td><td>1.0×10.4</td></tr></table>
+
+Table 2. Comparisons with state-of-the-art methods of DD on test accuracy and training efficiency. DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget. The black subscript indicates the standard deviation over multiple evaluations. The red subscript denotes the times of acceleration compared with the baseline method FRePo [52]. The best and second best results in each setting are marked by bold and underline respectively.
+
+increase the generalization ability of the translator across other unseen IPCs during adaptation, as shown in Sec. 4.3 and the supplement.
+
+In this paper, we consider the widely-adopted benchmarks of CIFAR10 and CIFAR100 [15] with a resolution of  $32 \times 32$  for the main evaluation. Results on datasets with higher resolutions and larger sizes can be found in the supplement. Following previous works [52, 5], we evaluate the proposed method on storage budgets of 1, 10, and 50 images per class (IPC) for CIFAR10 and 1 and 10 IPC for CIFAR100. Synthetic datasets are trained with 3-layer convolutional networks and evaluated on the same architecture. The cross-architecture performance will also be studied in Sec. 4.3. We report the average result and the standard deviation over 3 replicate evaluations for each setting.
+
+# 4.2. Comparisons with State of the Arts
+
+Here, we compare the proposed method for few-shot dataset distillation with state-of-the-art methods, including meta-learning-based methods in the seminal  $DD$  [41] and remember-the-past (RTP) [5], gradient-matching based methods in  $DC$ ,  $DSA$ , and  $IDC$ , trajectory-matching based  $MTT$ , distribution-matching based  $DM$ , and KRR-based  $FRePo$  [52]. The accuracy and training efficiency results are shown in Tab. 2. The accuracy results are from original papers while the training time is estimated based on the time-per-iteration results evaluated on the same hardware and the total number of iterations in the official codes. The shape/format of synthetic images in all methods except "Ours-DS" is consistent with that of real images in original datasets. For the running time of our method, we report the total time required for distilling using one network and the adaptation. Time for pre-training is not included since it is only conducted once, and once pre-trained, the trans
+
+lator can be adapted for an infinite number of downstream datasets.
+
+Through the results, we find that in the default parameterization, the proposed method within 1k adaptation steps falls about  $3 \sim 7$  points behind the FRePo baseline but with  $30 \sim 120 \times$  acceleration due to the few-shot setting. Even compared with the currently most efficient algorithm, the speed of our method is still considerable. And the performance is at least comparable with other methods in terms of accuracy, with even dramatic acceleration, e.g., the meta-learning-based DD and RTP. The superior efficiency makes our method applicable in scenarios where data cannot be held for a long time, like streaming data.
+
+Additionally, in "Ours-DS", down-sampled synthetic images are alternatively stored with the same number of stored parameters, which is a simple yet effective method to improve the performance especially when the storage budget is small. This parameterization typically requires more iterations for the adaptation stages. For small synthetic datasets like 1 and 10 IPC, the number of steps is  $6\mathrm{k}$ , and for 50 IPC, the number is  $15\mathrm{k}$ . Nevertheless, our method can still result in  $6 \sim 31 \times$  acceleration compared with the FRePo baseline with even better performance.
+
+# 4.3. Ablation Studies
+
+Baselines: To demonstrate the effectiveness of the translative pre-training and target adaptation strategies proposed in this paper, we consider a series of baselines for ablation studies, including:
+
+- Baseline: a new neural network is sampled for each training iteration to process the real dataset and update synthetic data, which can be viewed as a benchmark given a sufficient number of networks;
+
+<table><tr><td>Dataset</td><td>IPC</td><td>Baseline</td><td>1 Net</td><td>Bi-Level</td><td>w/o Pre-Train</td><td>w AE</td><td>w/o Ada</td><td>w Ada</td></tr><tr><td rowspan="3">CIFAR10</td><td>1</td><td>41.2±0.7</td><td>35.3±0.6</td><td>40.8±0.5</td><td>36.1±0.5</td><td>40.6±0.6</td><td>39.5±0.8</td><td>44.0±0.2</td></tr><tr><td>10</td><td>57.9±0.7</td><td>50.5±0.8</td><td>52.1±0.5</td><td>53.8±0.1</td><td>57.6±0.3</td><td>54.7±0.8</td><td>59.2±0.3</td></tr><tr><td>50</td><td>65.2±0.3</td><td>65.1±0.1</td><td>60.7±0.1</td><td>59.7±0.4</td><td>63.5±0.1</td><td>65.8±0.2</td><td>66.7±0.2</td></tr><tr><td rowspan="2">CIFAR100</td><td>1</td><td>21.6±0.6</td><td>18.7±0.1</td><td>19.1±0.1</td><td>20.5±0.2</td><td>21.8±0.3</td><td>20.9±0.7</td><td>22.8±0.4</td></tr><tr><td>10</td><td>33.8±0.3</td><td>31.7±0.1</td><td>31.0±0.2</td><td>30.7±0.2</td><td>27.0±0.2</td><td>33.0±0.2</td><td>35.1±0.2</td></tr></table>
+
+Table 3. Ablation studies of our method in different settings. The black subscript indicates the standard deviation over multiple evaluations.
+
+![](images/a3692b6d2a49b6d991829918028cdf46ca53d08d6b6bcaab143e39133c2b68db.jpg)  
+An Arbitrary Net Acc.  $50.5\%$
+
+![](images/db61bf443b8da7f4b3d355553d4e771e779e51d5a9e98bd2799fe191524f59b4.jpg)  
+Translated Results w/o Ada Acc.  $54.7\%$
+
+![](images/c12843e0cd14f2c523e00dbaebca9a65f70c50fbab78f0afb1814ac205ef933f.jpg)  
+Translated Results w Ada Acc.  $59.2\%$  
+Figure 3. Qualitative analysis of results produced by our method for IPC 10 on CIFAR10. Zoom in for details.
+
+![](images/8db3621f92bf0aa6f2599bcc1a4233de2c96f623825ce7316bea5afd8a98da58.jpg)  
+FRePo Acc.  $65.5\%$
+
+- 1 Net: synthetic data are distilled in a single network, which can be treated as a lower bound;  
+- Bi-Level: the bi-level algorithm described in Alg. 1;  
+-  $w / o$  Pre-Train: the target adaptation stage starts from a randomly initialized translator;  
+-  $wAE$ : the target adaptation stage starts from an autoencoder trained with a reconstruction objective;  
+-  $w/o$  Ada: directly using the pre-trained translator without the adaptation stage;  
+-  $w$  Ada: the default method.
+
+All the candidates are trained with 4k iterations. For those requiring adaptation, i.e., w/o Pre-Train, w AE, and w Ada, we first distill a synthetic dataset using 1 network with 3k iterations and adapt the translator for another 1k steps. Note that distilling with a single network only requires one forward propagation pass of the real dataset. Thus, the running time of our method is less than that of the baseline given the same number of iterations. Results are shown in Tab. 3.
+
+For one thing, it turns out that the default method in this paper consistently surpasses the benchmark baseline requiring enormous networks in most cases. The reason is that with the number of networks for NFR increasing, it would be more difficult for the training convergence of distilled datasets, especially in the few-shot case. Please refer to the supplement for details.
+
+For another, the consistent improvement comparing results of 1 Net and w/o Ada indicates that the pre-trained translator is capable of generating distilled results in a more favorable space. We visualize their results in the first two plots of Fig. 3, where the global tone is refined towards higher brightness contrast. Moreover, as shown in the 3rd plot, the adaptation stage injects more local details, which tries to improve the performance in a similar way performed by the state-of-the-art FRePo [52].
+
+Further, as shown in both Tab. 3 and Fig. 4(a-b), the pretrained model offers a more satisfactory initialization for the following adaptation stage, with lower initial loss, faster convergence, and higher accuracy.
+
+At last, the bi-level algorithm often leads to inferior performance, which may be partially attributed to the insufficient number of inner steps restricted by GPU memory.
+
+Generalization: We observe that one benefit of adapting the translator in a target dataset is that it is generalizable across different storage budgets for synthetic datasets. For instance, as shown in Fig. 4(c), the translator adapted on IPC 1 and 50 can also behave well on IPC 10.
+
+Following previous works [51, 49, 50], we also evaluate the cross-architecture performance in Tab. 4 over AlexNet [16], VGG11 [37], and ResNet18 [8]. The conclusion is consistent with the above analysis.
+
+# 4.4. Application: Continual Learning
+
+Continual learning (CL) aims to learn a sequence of tasks where the training data of past tasks are unavailable when
+
+![](images/2881ebb18b6d290024be64ab8692f2c2afbe91c7bf531555d509bd3a7d024a33.jpg)  
+(a)
+
+![](images/0d65f7c1b062e51e1abc85966a98fa51587b11d31a0098aa49e59dcc300b63d8.jpg)  
+(b)
+
+![](images/14ff90bc248989898e23e8868e7ee49f82c962dc2448ee28a65546b4bb0158be.jpg)  
+(c)
+
+<table><tr><td>Setting</td><td>ConvNet</td><td>AlexNet</td><td>VGG</td><td>ResNet</td></tr><tr><td>Baseline</td><td>58.8±0.2</td><td>57.1±0.5</td><td>41.1±0.3</td><td>38.1±0.9</td></tr><tr><td>1 Net</td><td>50.5±0.8</td><td>50.9±0.6</td><td>34.2±0.3</td><td>35.3±0.3</td></tr><tr><td>Bi-Level</td><td>52.1±0.5</td><td>50.0±0.4</td><td>37.4±0.5</td><td>34.7±0.5</td></tr><tr><td>w/o Pre-Train</td><td>53.8±0.1</td><td>56.2±0.3</td><td>39.3±0.7</td><td>38.2±0.7</td></tr><tr><td>w/o Ada</td><td>54.7±0.8</td><td>52.8±0.3</td><td>35.7±0.7</td><td>34.8±1.2</td></tr><tr><td>w Ada</td><td>59.2±0.3</td><td>56.8±0.2</td><td>43.0±0.7</td><td>40.8±0.5</td></tr></table>
+
+Table 4. Cross-architecture performance of our method in different settings. Results on CIFAR10 with 10 IPC are shown here.
+
+learning the current one. To overcome the problem of catastrophic forgetting [14], many works use a small buffer to store some valuable data of past tasks for future use [32, 1]. Dataset distillation can thus benefit this area by synthesizing informative samples [27, 34, 36, 43, 3, 26] to prevent forgetting as much as possible.
+
+In this paper, we evaluate the proposed method on CIFAR100-CL following the same 5-step protocol of [52, 50] with 20 classes for each task and 20 IPC. The results in Fig. 5 suggest a consistent conclusion with the ablation studies shown in Sec. 4.3 and indicate that the few-shot dataset distillation proposed in this paper can further facilitate the practical use when tasks come fast like a stream, which provides limited time for processing and learning.
+
+# 5. Conclusion
+
+In this paper, we focus on the setting of few-shot dataset distillation to improve its efficiency, where data can only be processed by a limited number of neural networks. We introduce the concept of distillation space to optimize the performance of synthetic data distilled by only one network. Regarding that the complexity of the quad-level definition and the bi-level algorithm for distillation space, we convert the problem to a transitive model. The synthetic dataset is first distilled in a random but fixed neural network and then translated to the desired space. For transferability, we train the translator with a pre-training algorithm, so that a pre
+
+![](images/861e3a30de6630c4316ef3664abb0c0a8763c47b949a9a1161356d9fda57738d.jpg)  
+Figure 4. (a-b) NFR loss and test accuracy during adaption for CIFAR10 IPC 10 starting with the pre-trained translator by our algorithm, an auto-encoder, and a randomly initialized model. (c) Generalization performance of the translator on unseen IPC during adaptation.  
+Figure 5. Performance of continual learning on CIFAR100 with 5 steps and 20 IPC for different settings.
+
+trained translator can be adapted for a new dataset within a limited number of steps. Experiments demonstrate that our method achieves  $\sim 15\times$  acceleration and comparable performance with the state-of-the-art baselines relying on thousands of networks. Even in some cases, the translator without adaptation yields competitive performance.
+
+One limitation of our method is that in the adaptation stage, errors of translated synthetic datasets have to be further back-propagated through the translator, which introduces additional GPU memory consumption compared with the baseline method, e.g., 3946 v.s. 3456 MB on CIFAR10 with 10 IPC. Nevertheless, as shown in Fig. 4(c), the translator adapted for small sizes can conduct inference for larger sizes, thereby breaking the limitation on GPU memory. Future works may focus on further improving the transferability of the distillation space translator by dedicated architectural designs or objective functions.
+
+# Acknowledgement
+
+This work is supported by the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2), and the Singapore Ministry of Education Academic Research Fund Tier 1 (WBS: A0009440-01-00).
+
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+                                    "content": "Dataset distillation aims at a small synthetic dataset to mimic the training performance on neural networks of a given large dataset. Existing approaches heavily rely on an iterative optimization to update synthetic data and multiple forward-backward passes over thousands of neural network spaces, which introduce significant overhead for computation and are inconvenient in scenarios requiring high efficiency. In this paper, we focus on few-shot dataset distillation, where a distilled dataset is synthesized with only a few or even a single network. To this end, we introduce the notion of distillation space, such that synthetic data optimized only in this specific space can achieve the effect of those optimized through numerous neural networks, with dramatically accelerated training and reduced computational cost. To learn such a distillation space, we first formulate the problem as a quad-level optimization framework and propose a bi-level algorithm. Nevertheless, the algorithm in its original form has a large memory footprint in practice due to the back-propagation through an unrolled computational graph. We then convert the problem of learning the distillation space to a first-order one based on image translation. Specifically, the synthetic images are optimized in an arbitrary but fixed neural space and then translated to those in the targeted distillation space. We pre-train the translator on some large datasets like ImageNet so that it requires only a limited number of adaptation steps on the target dataset. Extensive experiments demonstrate that the translator after pre-training and a limited number of adaptation steps achieves comparable distillation performance with state of the arts, with "
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+                                    "content": "1. Introduction"
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+                                            "content": "Figure 1. (a) Existing DD methods heavily rely on forward-backward processes through enormous neural networks. (b) More neural networks used in dataset distillation would result in more floating point operations (FLOPs) and higher latency. (c) We introduce the notation of distillation space for few-shot dataset distillation in this paper and aim to learn a neural network such that distilled data only optimized in this specific space can approximate the performance by multiple networks. (d) Given only a few or even a single network, our method achieves comparable performance with state-of-the-art baselines requiring enormous networks. Results in this figure are concerning models trained with 1 image per class distilled from CIFAR100 dataset. OS denotes one-shot DD using only one network, FS denotes few-shot DD with a limited number of adaptation steps, and DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget."
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+                                    "content": ". Such techniques have received considerable attention to alleviate the heavy burden on storage, transmission, and training of deep learning models brought by large-scale datasets. Recent advances on DD have revealed that models trained with only a few synthetic samples, even 1 image per class in some cases, can retain most of the performance of those trained with real data [49, 50, 2, 28, 29, 40, 13, 52, 23, 21]. Thus, it becomes a research area receiving increasing attention from the aca"
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+                                    "content": "demic and industrial community recently as a potential solution to alleviate the concerns on the storage, transmission, pre-processing, and training effort for large datasets."
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+                                    "content": "Nevertheless, as shown in Fig. 1(a), all existing methods on DD work iteratively: the synthetic dataset is optimized in an outer loop, and real and synthetic data are sent to a newly-initialized neural network in each iteration. Although they have achieved remarkable performance, such forward-backward passes in multiple neural networks can introduce extensive computational overhead to generate a distilled dataset, as illustrated in Fig. 1(b). As a result, the burdensome distillation procedure in existing methods brings significant latency. For instance, one of the state-of-the-art works by Deng et al. [5] requires "
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+                                    "type": "text",
+                                    "content": " days to distill only 1 image per class for CIFAR100 dataset [15] as shown in Fig. 1(d) and [47]. Even FRePo [52], with the most satisfactory efficiency, takes over 3 hours in the same setting requiring 500,000 neural network steps. The long training process in current DD makes it inconvenient for scenarios requiring high efficiency, e.g., processing streaming data."
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+                                    "content": "Focusing on these drawbacks, in this paper, we propose few-shot dataset distillation and are interested in the performance of DD if only a few or even a single neural network is available for training. We first try a naive solution by merely adopting one neural network for the existing method FRePo [52] and visualize the accuracy and efficiency. As shown in Fig. 1(d), although the simple strategy improves the efficiency, the performance gap with the original version based on thousands of networks is significant, which suggests a trade-off between performance and the number of networks. A similar effect is also revealed by Cazenavette et al. [2], where the number of teacher training trajectories would affect the performance substantially. Thus, how to boost the performance by only a limited number of networks becomes an interesting question in few-shot DD."
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+                                    "content": "Currently, the networks used in Fig. 1(d) are randomly and independently initialized, which makes us curious: whether there exists a dedicated neural network, such that the synthetic dataset distilled in it can achieve similar performance to those distilled in multiple ones. In this paper, we describe this concept through a quad-level definition termed as distillation space, as shown in Fig. 1(c), and propose a bi-level algorithm to find it, to optimize the error on real data, for networks trained with the synthetic dataset, distilled in this space."
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+                                    "content": "sure that the iterative optimization process is not nested in the computational graph: the synthetic dataset is distilled in a random but fixed neural network space and then translated to the desired space via a translator network."
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+                                    "content": "Specifically, the translator is pre-trained on some large datasets like ImageNet [4]. In each iteration, a random subset is sampled. Distilled results after being translated from the original space are evaluated in some random networks, and the distillation loss is back-propagated to the translator to update its parameters. We find that the distillation space translator after pre-training can generalize well across different datasets, storage budgets, and numbers of classes. With only a few adaptation steps on the target dataset, the performance of distilled data after translation achieves can be on par with those distilled by multiple neural networks at "
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+                                    "content": " faster, as shown in Fig. 1(d)."
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+                                    "content": "In summary, our contributions are listed as follows:"
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+                                            "content": "- Tailoring for scenarios requiring high efficiency, we are the first to study the problem of few-shot dataset distillation, where only a limited number of neural networks are available for DD, and introduce the quad-level definition of distillation space for it."
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+                                            "content": "- An efficient translative modeling approach with a pretraining algorithm is proposed to learn an effective distillation space;"
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+                                            "content": "- Extensive experiments demonstrate that our method is capable of generating dataset distillation results with "
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+                                    "content": "2. Related Works"
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+                                    "content": "Dataset distillation (DD) refers to distilling a small synthetic dataset "
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+                                    "content": " is optimized to have similar downstream training performance to "
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+                                    "content": ". Unlike most existing techniques that focus on reducing the size of a model [6, 25, 45, 44, 7, 46, 12, 11, 10, 33], DD concentrates on learning compressed data to enhance learning efficiency. Wang et al. [41] firstly introduce the task and propose a meta-learning method to minimize the loss of meta-test on "
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+                                    "content": ". This scheme aligns with the evaluation protocol of DD: to pursue higher accuracy on the real test data for networks optimized by the synthetic ones. However, restricted by the GPU memory, the steps of meta-training in this framework are limited, which bottlenecks the performance [5]. The bilevel loop with a large number of inner steps also affects the efficiency negatively."
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+                                    "content": "To address this issue, a series of works consider mapping real and synthetic samples to a feature space with some kernels, e.g., NTK [28, 29], NNGP [23], and non-linear network [52, 24], and then perform kernel ridge regression"
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+                                            "content": "Figure 2. (a) Existing DD methods rely on an iterative training process, where a new network has to be initialized for forward and backward passes of the real dataset "
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+                                            "content": " optimized only in such a space can minimize the error of neural feature regression in an arbitrary random network. The loop for optimizing "
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+                                    "content": "(KRR). Benefiting from the analytical solution of KRR, these methods can access the optimal parameters trained by synthetic datasets via direct computation without the necessity of higher-order gradients, which achieves favorable efficiency and accuracy at the same time. In this paper, the KRR-based formulation is also adopted as the main objective to reduce the complexity of meta-learning, thanks to its satisfactory efficiency."
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+                                    "content": "In the literature of DD, matching-based methods are another major branch. For example, Zhao et al. [51] and a lot of following works [49, 13, 17, 9, 48] adopt gradient matching. Cazenavette et al. [2] propose MTT, which optimizes the distance between network parameters trained by "
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+                                    "content": " respectively from some cached initialization. Their insights lie in that gradients in networks or trained model parameters can represent the training effects of different datasets. Some works also consider matching the statistics of "
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+                                    "type": "text",
+                                    "content": " and thus improves the efficiency."
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+                                    "content": "No matter what objectives existing methods adopt, they all rely on an extensive outer optimization loop to update synthetic data, where "
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+                                    "content": " have to undergo forward-backward passes through thousands of networks. To make things worse, a series of works considering synthetic dataset parameterization, which tries to increase the number of images with the same storage budget, require even more such iterations [5, 19]. Motivated by these facts, we focus on the problem of few-shot dataset distillation in this paper where a synthetic dataset is distilled given only a few or even a single neural network. Given that naively adopting only a few random networks results in inferior performance as"
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+                                    "type": "text",
+                                    "content": "shown in Fig. 1(d), we introduce the concept of distillation space, such that the performance of synthetic data distilled in this space can match those in enormous networks. Dedicated to finding such a space to benefit dataset distillation to reduce the number of networks required for acceleration while retaining the performance as much as possible, a novel translative model with a pre-training approach is proposed to this end. To our best knowledge, this is the first work focusing on few-shot learning and pre-training in DD."
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+                                    "content": "3. Methods"
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+                                    "content": "In this section, we delve into details about our methods for few-shot dataset distillation, where real and synthetic datasets can be processed by only a few neural networks. We first provide a brief introduction of current mainstream solutions for DD, based on which we propose the quad-level definition of distillation space in formal and a basic bi-level algorithm to learn the space. For computational efficiency, we then convert the original formulation of learning the distillation space to a transitive problem and propose an alternative algorithm, backed up by theoretical analysis. Finally, we explain the paradigm of pre-training for few-shot learning to increase the transferability of the learned distillation space across various datasets, the number of classes, and the storage budgets of synthetic datasets."
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+                                    "content": "3.1. Preliminary"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "Dataset distillation (DD) targets a small synthetic dataset "
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+                                    "type": "text",
+                                    "content": " such that the performance on downstream training with "
+                                },
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+                                    "type": "text",
+                                    "content": " can match that with the original dataset "
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+                                    "type": "text",
+                                    "content": ". The seminal work by Wang et al. [41] proposes a meta-learning ap"
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+                                    "content": "Algorithm 1 Bi-Level Optimization for Distillation Space."
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ": Target Dataset; "
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+                                    "type": "text",
+                                    "content": ": Distribution for Initializing Neural Networks; "
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+                                    "type": "inline_equation",
+                                    "content": "T"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ": Number of Inner Update Steps; "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ": Learning Rate for Inner Optimization; "
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+                                    "content": "\\eta"
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+                                    "type": "text",
+                                    "content": ": Learning Rate for Outer Optimization."
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+                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ": Distillation Space after Optimization."
+                                }
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+                                            "content": "1: Initialize "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " do"
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " with random samples from "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
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+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{T}}^{\\theta}\\gets f_{\\theta}(X_{\\mathcal{T}});"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
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+                                            "type": "inline_equation",
+                                            "content": "1\\leq t\\leq T"
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+                                            "type": "text",
+                                            "content": " do"
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+                                            "content": "6: "
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "w_{\\mathcal{S},\\theta}^* \\gets f_\\theta(X_\\mathcal{S})^\\top (f_\\theta(X_\\mathcal{S})f_\\theta(X_\\mathcal{S})^\\top)^{-1}Y_\\mathcal{S};"
+                                        }
+                                    ]
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+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{S}} \\gets X_{\\mathcal{S}} - \\alpha \\nabla_{X_{\\mathcal{S}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}}^{2}"
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "Y_{\\mathcal{S}} \\gets Y_{\\mathcal{S}} - \\alpha \\nabla_{Y_{\\mathcal{S}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}"
+                                        },
+                                        {
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+                                            "type": "text",
+                                            "content": ";"
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+                            "index": 10
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+                                            "type": "text",
+                                            "content": "9: end for"
+                                        }
+                                    ]
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+                            ],
+                            "index": 11
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+                                            "type": "text",
+                                            "content": "10: Randomly sample "
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+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{T}}^{\\theta^{\\prime}}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{T}});"
+                                        }
+                                    ]
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+                                            "type": "inline_equation",
+                                            "content": "w_{\\mathcal{S},\\theta^{\\prime}}^{*}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top}(f_{\\theta^{\\prime}}(X_{\\mathcal{S}})f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top})^{-1}Y_{\\mathcal{S}};"
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+                                            "content": "\\theta \\gets \\theta -\\eta \\nabla_{\\theta}\\| X_{\\mathcal{T}}^{\\theta '}w_{\\mathcal{S},\\theta '}^{*} - Y_{\\mathcal{T}}\\|^{2};"
+                                        }
+                                    ]
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+                                    "content": "\\mathcal {S} ^ {*} = \\underset {\\mathcal {S}} {\\arg \\min } \\mathbb {E} _ {\\theta^ {(0)} \\sim \\Theta} [ l (\\mathcal {T}; \\theta^ {(T)}) ], \\tag {1}",
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+                                    "type": "inline_equation",
+                                    "content": "1 \\leq t \\leq T"
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " is the learning rate, and "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the loss function, e.g., cross-entropy loss for classification problems."
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "content": "The bi-level optimization algorithm indicated in Eq. 1 relies on backpropagating through an unrolled computational graph of inner optimization steps, which makes it inefficient in both time and memory. Nguyen et al. [28, 29] thus consider the problem of kernel ridge regression (KRR), where the analytical optimal solution gets rid of the necessity to optimize the model with "
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+                                    "type": "text",
+                                    "content": " for multiple nested steps. For more satisfactory accuracy and efficiency, the spirit is further extended by following works [52, 23], which map a batch of "
+                                },
+                                {
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+                                    "content": " samples "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to a feature space with a random neural network and then perform KRR. Denote the function of neural network parameterized by "
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+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " and the label matrix corresponding to "
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+                                    "type": "inline_equation",
+                                    "content": "X \\in \\mathbb{R}^{n \\times d}"
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+                                {
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "Y \\in \\mathcal{R}^{n \\times c}"
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+                                {
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are the dimensions of sample and label respectively, i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "h \\times w \\times 3"
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+                                {
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+                                    "type": "text",
+                                    "content": " and the number of classes in the RGB image classification problem, the objective can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
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+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} X _ {\\mathcal {S}} ^ {*}, Y _ {\\mathcal {S}} ^ {*} = \\underset {X _ {\\mathcal {S}}, Y _ {\\mathcal {S}}} {\\arg \\min } \\mathbb {E} _ {\\theta \\sim \\Theta} [ \\| f _ {\\theta} (X _ {\\mathcal {T}}) w _ {\\mathcal {S}, \\theta} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2} ], \\tag {2} \\\\ w _ {S, \\theta} ^ {*} = f _ {\\theta} (X _ {S}) ^ {\\top} \\left(f _ {\\theta} (X _ {S}) f _ {\\theta} (X _ {S}) ^ {\\top}\\right) ^ {- 1} Y _ {S}. \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": "This technique is known as neural feature regression (NFR) [52]. In each training iteration, a new random neural network is initialized for solving the problem in Eq. 2, as shown in Fig. 2(a)."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.2. Learning a Distillation Space"
+                                }
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+                    "index": 25
+                },
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+                                    "type": "text",
+                                    "content": "As illustrated in Fig. 1(a), the iterative optimization framework shown in Fig. 2(a) involves forward and backward processes through thousands of networks and introduces significant computational overhead. In this work, we thus focus on the problem of DD using only a few or even one network. Given the results in Fig. 1(b) that simply adopting a random network yields limited performance, we are interested in learning a specific network such that "
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+                                    "type": "text",
+                                    "content": " distilled in it can achieve performance on par with that distilled in multiple networks, i.e., minimize the error on "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for an arbitrary model trained with "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". Formally, we term such a network as distillation space in the following definition."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
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+                                    "type": "text",
+                                    "content": "Definition 1 (Distillation Space). A distillation space for a distribution of network "
+                                },
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+                                    "type": "text",
+                                    "content": " is a neural network function "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "f"
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+                                    "type": "text",
+                                    "content": " parameterized by "
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+                                    "type": "inline_equation",
+                                    "content": "\\theta^{*}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " which satisfies:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\theta^{*} = \\operatorname *{arg  min}_{\\theta^{(0)}}\\mathbb{E}_{\\theta^{(0)^{\\prime}}\\sim \\Theta}[l(\\mathcal{T};\\theta^{(T)^{\\prime}})], \\\\ \\theta^ {(t) ^ {\\prime}} = \\theta^ {(t - 1) ^ {\\prime}} - \\alpha^ {\\prime} \\nabla l \\left(\\mathcal {S} ^ {*}; \\theta^ {(t - 1) ^ {\\prime}}\\right), \\tag {3} \\\\ \\mathcal {S} ^ {*} = \\underset {\\mathcal {S}} {\\arg \\min } l (\\mathcal {T}; \\theta^ {(T)}), \\\\ \\theta^ {(t)} = \\theta^ {(t - 1)} - \\alpha \\nabla l (\\mathcal {T}; \\theta^ {(t - 1)}). \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": "In practice, to find an effective distillation space, we first simplify the quad-level definition via NFR in Eq. 2, which derives a bi-level optimization problem:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\theta^ {*} = \\underset {\\theta} {\\arg \\min } \\mathbb {E} _ {\\theta^ {\\prime} \\sim \\Theta} [ \\| f _ {\\theta^ {\\prime}} (X _ {\\mathcal {T}}) w _ {\\mathcal {S} ^ {*}, \\theta^ {\\prime}} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2} ], \\\\ w _ {\\mathcal {S} ^ {*}, \\theta^ {\\prime}} ^ {*} = f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) ^ {\\top} \\left(f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) f _ {\\theta^ {\\prime}} \\left(X _ {\\mathcal {S}} ^ {*}\\right) ^ {\\top}\\right) ^ {- 1} Y _ {\\mathcal {S}} ^ {*}, \\tag {4} \\\\ X _ {\\mathcal {S}} ^ {*}, Y _ {\\mathcal {S}} ^ {*} = \\underset {X _ {\\mathcal {S}}, Y _ {\\mathcal {S}}} {\\arg \\min} \\| f _ {\\theta} (X _ {\\mathcal {T}}) w _ {\\mathcal {S}, \\theta} ^ {*} - Y _ {\\mathcal {T}} \\| ^ {2}, \\\\ w _ {S, \\theta} ^ {*} = f _ {\\theta} (X _ {S}) ^ {\\top} \\left(f _ {\\theta} (X _ {S}) f _ {\\theta} (X _ {S}) ^ {\\top}\\right) ^ {- 1} Y _ {S}. \\\\ \\end{array}",
+                                    "image_path": "656832fc3db5b3dd98faedbe6f3701c7f803278540a1fa6d0162bdd00040618b.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Eq. 4 indicates a bi-level meta-learning algorithm as shown in Fig. 2(b) and Alg. 1. In each inner iteration, "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is metatrained via NFR in the current neural space "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " after a whole inner loop is meta-tested in a random neural network "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta'}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and the loss of NFR is back-propagated to update "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "\\theta"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.3. Learning a Translation to a Distillation Space"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 32
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Although Alg. 1 can be an effective algorithm to learn a valid distillation space, the back-propagation process through a nested computational graph is inefficient in GPU memory. The memory complexity is proportionate to the number of inner optimization steps "
+                                },
+                                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to obtain the optimal synthetic dataset in the current space, which is crucial"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33
+                }
+            ],
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+                                    "content": "18657"
+                                }
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+                    ],
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+                }
+            ],
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+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                        72,
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+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": "for the final performance [5] but withheld by the limited GPU memory. For instance, in a 40G A100 GPU, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in Alg. 1 can be set as 16 at most, which is too small to get convergence for inner optimization. To alleviate this drawback, we consider an alternative approach to learn a distillation space. Specifically, we detach the inner optimization from the computational graph by converting the problem to a transitive model, based on the following proposition."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Proposition 1. For a target dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{T}} \\in \\mathbb{R}^{n_{\\mathcal{T}} \\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{\\mathcal{T}} \\in \\mathbb{R}^{n_{\\mathcal{T}} \\times c}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
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+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_{\\mathcal{T}} \\geq d"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", assume that "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{S},0}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{\\mathcal{S},0}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " satisfy "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| f_{\\theta}(X_{\\mathcal{T}})w_{\\mathcal{S},\\theta}^{*} - Y_{\\mathcal{T}}\\|^{2} = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{\\mathcal{S},\\theta}^{*} = f_{\\theta}(X_{\\mathcal{S},0}^{*})^{\\top}(f_{\\theta}(X_{\\mathcal{S},0}^{*})f_{\\theta}(X_{\\mathcal{S},0}^{*})^{\\top})^{-1}Y_{\\mathcal{S},0}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " is a known linear transformation parameterized by a full-rank matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta \\in \\mathbb{R}^{d \\times d'}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d \\leq d'"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ". Similarly, let "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta^{*}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " be a desired linear distillation space and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta^{*} \\in \\mathbb{R}^{d \\times d''}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d \\leq d'' \\leq n_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ". The distilled dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{S},*}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
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+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{\\mathcal{S},*}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " in this space satisfy "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| f_{\\theta^{*}}(X_{\\mathcal{T}})w_{\\mathcal{S},\\theta^{*}}^{*} - Y_{\\mathcal{T}}\\|^{2} = 0"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{\\mathcal{S},\\theta^{*}}^{*} = f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})^{\\top}(f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})f_{\\theta^{*}}(X_{\\mathcal{S},*}^{*})^{\\top})^{-1}Y_{\\mathcal{S},*}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ". There exists a translation function "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " for "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{S},0}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{\\mathcal{S},0}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " such that "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{S},*}^{*}, Y_{\\mathcal{S},*}^{*} = G(X_{\\mathcal{S},0}^{*}, Y_{\\mathcal{S},0}^{*})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", whose parameters are not dependent on the target dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        46,
+                        342,
+                        288,
+                        365
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                342,
+                                288,
+                                365
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        342,
+                                        288,
+                                        365
+                                    ],
+                                    "type": "text",
+                                    "content": "Proof. Due to the linearity of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        342,
+                                        288,
+                                        365
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        342,
+                                        288,
+                                        365
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        342,
+                                        288,
+                                        365
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta^{*}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        342,
+                                        288,
+                                        365
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can rewrite the given conditions as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        123,
+                        373,
+                        287,
+                        387
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                373,
+                                287,
+                                387
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        123,
+                                        373,
+                                        287,
+                                        387
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "X _ {\\mathcal {T}} \\theta w _ {S, \\theta} ^ {*} - Y _ {\\mathcal {T}} = 0, \\tag {5}",
+                                    "image_path": "8cbc9cba49fd2cb22dbf87f53a8128db2c0d9ed998cf6de3c117f14876ab2329.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        119,
+                        389,
+                        287,
+                        403
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                119,
+                                389,
+                                287,
+                                403
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        119,
+                                        389,
+                                        287,
+                                        403
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "X _ {\\mathcal {T}} \\theta^ {*} w _ {S, \\theta^ {*}} ^ {*} - Y _ {\\mathcal {T}} = \\mathbf {0}, \\tag {6}",
+                                    "image_path": "c677d85ee1e8d9e1a9164091f8316b36ea6dd76de12f72b33a5e5ebbd8b11004.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        46,
+                        410,
+                        287,
+                        435
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                410,
+                                287,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "text",
+                                    "content": "Since "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_{\\mathcal{T}} \\geq d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "text",
+                                    "content": " for "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "text",
+                                    "content": ", pre-multiplying terms in Eq. 5 by the Moore-Penrose inverse "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\mathcal{T}}^{\\dagger}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        410,
+                                        287,
+                                        435
+                                    ],
+                                    "type": "text",
+                                    "content": ", we have"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        132,
+                        441,
+                        287,
+                        456
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                132,
+                                441,
+                                287,
+                                456
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        132,
+                                        441,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "X _ {\\mathcal {T}} ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta w _ {\\mathcal {S}, \\theta} ^ {*}. \\tag {7}",
+                                    "image_path": "fc381bb584ef1c628c5294fb56ae4d62a163bc468637dbe3796faaaed1b72e8b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        47,
+                        463,
+                        186,
+                        475
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                463,
+                                186,
+                                475
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        463,
+                                        186,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": "Similarly, through Eq. 6, we have"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        62,
+                        480,
+                        287,
+                        497
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                62,
+                                480,
+                                287,
+                                497
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        62,
+                                        480,
+                                        287,
+                                        497
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "w _ {\\mathcal {S}, \\theta^ {*}} ^ {*} = (X _ {\\mathcal {T}} \\theta^ {*}) ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta^ {* \\dagger} X _ {\\mathcal {T}} ^ {\\dagger} Y _ {\\mathcal {T}} = \\theta^ {* \\dagger} \\theta w _ {\\mathcal {S}, \\theta} ^ {*}, \\quad (8)",
+                                    "image_path": "731e40d30cc5c436a8e7bff70eec010abd0221a311a3b1b7e963d547f46f6480.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        46,
+                        502,
+                        287,
+                        587
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                502,
+                                287,
+                                587
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": "where the first, second, and third equalities are due to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_{\\mathcal{T}} \\geq d''"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d'' \\geq d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": ", and Eq. 7 respectively. We can observe in Eq. 8 that "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{S,\\theta^*}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": " in the desired distillation space is not dependent on "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": ". Thus, the optimal "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{S,*}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{S,*}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": " resulting the optimal KRR parameter can be obtained given only "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{S,0}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{S,0}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": " by some translation function "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        502,
+                                        287,
+                                        587
+                                    ],
+                                    "type": "text",
+                                    "content": ", which implicitly includes the knowledge of the distillation space."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        46,
+                        594,
+                        288,
+                        713
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                594,
+                                288,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "Prop. 1 indicates that it is possible to approach the distillation space by translating samples from some space rather than learning "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
+                                        288,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " directly, motivated by which we propose to learn a translation from one another space to the distillation space. The main workflow is similar to Alg. 1: synthetic data are first distilled in a random but fixed network in an inner loop and then translated to final results, as shown in Fig. 2(c). The translator is optimized so that results after translation are equipped with the property of those produced in a distillation space: to minimize the NFR error in"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        306,
+                        72,
+                        537,
+                        84
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        537,
+                                        84
+                                    ],
+                                    "type": "text",
+                                    "content": "Algorithm 2 Pre-training a Distillation Space Translator."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        306,
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+                        545,
+                        144
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                85,
+                                545,
+                                144
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": "Input: "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Z}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ": A Large Dataset; "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ": Distribution for Initializing Neural Networks; "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ": An Arbitrary Random Neural Network; "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ": Number of Update Steps for Synthetic Data; "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ": Learning Rate for Synthetic Data; "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        85,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ": Learning Rate for Translator."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        306,
+                        145,
+                        459,
+                        156
+                    ],
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+                                    "type": "text",
+                                    "content": "Output: "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ": A Pre-trained Translator."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "1: Initialize "
+                                        },
+                                        {
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+                                            "type": "inline_equation",
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+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " randomly;"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14
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+                                        },
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "i = 1,2,3,\\ldots"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                180
+                                            ],
+                                            "type": "text",
+                                            "content": " do"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "3: Randomly choose a subset of data "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                181,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{T}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                181,
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+                                            ],
+                                            "type": "text",
+                                            "content": " from "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                181,
+                                                522,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{Z}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ";"
+                                        }
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+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "4: Initialize "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "S^{\\prime}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " with random samples from "
+                                        },
+                                        {
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{T}"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
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+                                205,
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "type": "text",
+                                            "content": "5: "
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{T}}^{\\theta}\\gets f_{\\theta}(X_{\\mathcal{T}});"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                228
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "type": "text",
+                                            "content": "6: for "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "1 \\leq t \\leq T"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " do"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 19
+                        },
+                        {
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+                            ],
+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "7: "
+                                        },
+                                        {
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "w_{\\mathcal{S}^{\\prime},\\theta}^{*}\\gets f_{\\theta}(X_{\\mathcal{S}^{\\prime}})^{\\top}(f_{\\theta}(X_{\\mathcal{S}^{\\prime}})f_{\\theta}(X_{\\mathcal{S}^{\\prime}})^{\\top})^{-1}Y_{\\mathcal{S}^{\\prime}};"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 20
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                        },
+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{S}^{\\prime}} \\gets X_{\\mathcal{S}^{\\prime}} - \\alpha \\nabla_{X_{\\mathcal{S}^{\\prime}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S}^{\\prime},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": ";"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
+                                312,
+                                255,
+                                519,
+                                269
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "9: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                312,
+                                                255,
+                                                519,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "Y_{\\mathcal{S}^{\\prime}} \\gets Y_{\\mathcal{S}^{\\prime}} - \\alpha \\nabla_{Y_{\\mathcal{S}^{\\prime}}} \\| X_{\\mathcal{T}}^{\\theta} w_{\\mathcal{S}^{\\prime},\\theta}^{*} - Y_{\\mathcal{T}} \\|^{2}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                312,
+                                                255,
+                                                519,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": ";"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
+                                312,
+                                270,
+                                372,
+                                279
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "type": "text",
+                                            "content": "10: end for"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 23
+                        },
+                        {
+                            "bbox": [
+                                311,
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+                                293
+                            ],
+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "11: "
+                                        },
+                                        {
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{S}},Y_{\\mathcal{S}} = G_{\\omega}(X_{\\mathcal{S}^{\\prime}},Y_{\\mathcal{S}^{\\prime}});"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 24
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "12: Randomly sample "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\theta^{\\prime}\\sim \\Theta"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 25
+                        },
+                        {
+                            "bbox": [
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+                                316
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "13: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                304,
+                                                410,
+                                                316
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "X_{\\mathcal{T}}^{\\theta^{\\prime}}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{T}});"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 26
+                        },
+                        {
+                            "bbox": [
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+                                329
+                            ],
+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "14: "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                316,
+                                                526,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "w_{\\mathcal{S},\\theta^{\\prime}}^{*}\\gets f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top}(f_{\\theta^{\\prime}}(X_{\\mathcal{S}})f_{\\theta^{\\prime}}(X_{\\mathcal{S}})^{\\top})^{-1}Y_{\\mathcal{S}};"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "type": "text",
+                                            "content": "15: "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "\\omega \\gets \\omega -\\eta \\nabla_{\\omega}\\| X_{\\mathcal{T}}^{\\theta '}w_{S,\\theta '}^{*} - Y_{\\mathcal{T}}\\|^{2};"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "16: end for"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "any random network. Since gradients are only required to back propagated to the translator rather than the whole inner loop, the memory complexity is irrelevant to the number of inner optimization steps. Thus, the translative model is a memory-efficient algorithm where only first-order gradients are necessary."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 31
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.4. Pre-training a Distillation Space Translator"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 32
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We expect that the distillation space optimized in a dataset is transferable across different datasets, storage budgets for synthetic data, and the number of classes. To tackle these challenges on transferability, in this paper, we consider pre-train a translator on some large dataset like ImageNet [4], so that it provides a satisfactory initialization and only requires a small number of adaptation steps for a target dataset, like the typical few-shot learning [42, 39, 38, 30]. The algorithm is shown in Alg. 2. In each training iteration "
+                                },
+                                {
+                                    "bbox": [
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+                                        645
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we sample a subset from the large dataset and perform a gradient-decent step with the strategy mentioned in Sec. 3.3. Upon a translator is pre-trained, it can serve as a strong initialization for the adaptation process to a new dataset, which behaves identically to Line 11 to 15 of Alg. 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 33
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 34
+                },
+                {
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+                                    "content": "In this section, we conduct experiments to validate the effectiveness of the proposed method for few-shot DD. We first introduce our experiment settings and implement de"
+                                }
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+                                            "html": "<table><tr><td>Hyper-Parameter</td><td>Denotation</td><td>Value</td></tr><tr><td>T</td><td>Number of Update Steps for Synthetic Data</td><td>3,000</td></tr><tr><td>α</td><td>Learning Rate for Synthetic Data</td><td>1e-3</td></tr><tr><td>η</td><td>Learning Rate for Translator in Pre-Training</td><td>1e-5</td></tr><tr><td>N</td><td>Number of Cached Subsets in Pre-Training</td><td>5,000</td></tr><tr><td>Cmax</td><td>Maximal Number of Classes in a Subset in Pre-Training</td><td>100</td></tr><tr><td>Cmin</td><td>Minimal Number of Classes in a Subset in Pre-Training</td><td>10</td></tr><tr><td>M</td><td>Maximal Number of Images in a Subset in Pre-Training</td><td>4,000</td></tr><tr><td>Imax</td><td>Maximal Number of Images in a Synthetic Dataset in Pre-Training</td><td>1,000</td></tr><tr><td>B</td><td>Batch Size in Pre-Training</td><td>4</td></tr><tr><td>S</td><td>Number of Pre-Training Steps</td><td>200,000</td></tr><tr><td>S&#x27;</td><td>Number of Adaptation Steps for Translator</td><td>1,000</td></tr><tr><td>η&#x27;</td><td>Learning Rate for Translator in Adaptation</td><td>1e-4</td></tr></table>",
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+                                }
+                            ],
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+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                    ],
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+                                    "type": "text",
+                                    "content": "Table 1. List of hyper-parameters and their values."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1,
+                    "angle": 0,
+                    "type": "text"
+                },
+                {
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+                                    "type": "text",
+                                    "content": "tails of the method. Then, we compare our method with state-of-the-art solutions of DD in terms of both accuracy and efficiency. To illustrate how the proposed method works, we also provide an in-depth analysis of the method with a variety of baselines. Finally, we conduct experiments on continual learning, an important use case for DD, to further demonstrate the practical value of our method."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "4.1. Settings and Implementing Details"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "In few-shot dataset distillation, a real dataset "
+                                },
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+                                    "type": "text",
+                                    "content": " can be processed by only a few neural networks to generate a synthetic dataset "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". In our method, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is firstly optimized in an arbitrary but fixed neural network by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " steps, with the learning rate "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". The results are then processed by a translator to generate the final synthetic dataset. The translator adopts an auto-encoder architecture with 3 Conv-BatchNorm-ReLU blocks, and the detailed configuration can be found in the supplement. Notably, due to the fully-convolutional structure, the pre-trained translator can also be adapted to datasets with different resolutions beyond the one used during pre-training. Please refer to the supplement for details. The translator is pre-trained on the ImageNet dataset by "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " steps with the learning rate "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and then adapted on the target dataset by a small number of iterations "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", with a learning rate "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\eta'"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Some hyper-parameters are summarized in Tab. 1. Other hyper-parameters follow the default setting in the PyTorch [31] implementation of FRePo [52]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Pre-Training: The key design of the translative pretraining pipeline lies in the separation of two stages: dataset distillation in an arbitrary but fixed neural network and the translation to the desired space. In practice, instead of directly following the pipeline in Alg. 2 that nests the two steps in one loop, the two stages are conducted independently in the interest of better training efficiency. Results distilled in the pre-defined network are cached for multiple random subsets so that they can be loaded directly and used"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "repeatedly in the pre-training stage, which improves the training efficiency. The detailed algorithms for the caching stage and the pre-training stage can be found in the supplement."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The caching stage aims to generate distilled results for multiple subsets. For sampling a subset, we first randomly choose the number of classes ranging from "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "C_{\\text{min}}"
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+                                    "type": "text",
+                                    "content": " to "
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+                                    "type": "text",
+                                    "content": " and then randomly select the corresponding number of classes from the 1,000 ImageNet classes. For each select class, a certain number of random real images are sampled uniformly for each selected class such that the total number of images is "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " at most. The data augmentation technique DSA [49] is applied in the caching stage to mimic the cases of larger datasets. The maximal number of synthetic images is "
+                                },
+                                {
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+                                    "content": "I_{\\text{max}}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and they are initialized with the selected real data. After distillation, indices of selected real samples and the distilled dataset are cached in the disk for future use in the pre-training stage. This process can be deployed to multiple GPUs in parallel, since the distillation for each subset is independent."
+                                }
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+                                    "type": "text",
+                                    "content": "In the pre-training stage, cached results in the previous stage are loaded. The NFR loss is calculated in a randomly initialized networks over a distribution in each iteration. Like the caching stage, pre-cached subsets in a batch can also be distributed to multiple GPUs in parallel. In this work, the pre-training is conducted on a single 40G A100 GPU, which takes roughly 2 days for the 200,000 steps."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Adaptation: Given a pre-trained translator, it requires a small number of adaptation steps in general for the target dataset. The detailed adaptation algorithm can be found in the supplement. Intuitively, the procedure is consistent with the two-stage process in pre-training: to generate distilled results in a pre-defined network and then use the translator for the final results. The only difference with the pretraining stage is that real data come from the target dataset. By default, the set of IPC for adaptation only contains the target IPC. More IPCs can also be included in this set to"
+                                }
+                            ]
+                        }
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+                                            "html": "<table><tr><td>Dataset</td><td>IPC</td><td>Metric</td><td>DD</td><td>RTP</td><td>DC</td><td>DSA</td><td>IDC</td><td>MTT</td><td>DM</td><td>FRePo</td><td>Ours</td><td>Ours-DS</td></tr><tr><td rowspan=\"6\">CIFAR 10</td><td rowspan=\"2\">1</td><td>Acc. (%)</td><td>40.5±0.8</td><td>49.1±0.6</td><td>28.3±0.5</td><td>28.8±0.7</td><td>36.7±0.4</td><td>46.3±0.8</td><td>26.0±0.8</td><td>46.8±0.7</td><td>44.0±0.2</td><td>51.4±0.4</td></tr><tr><td>Time (h)</td><td>363.9</td><td>363.9</td><td>0.1</td><td>0.1</td><td>10.6</td><td>0.8</td><td>0.3</td><td>2.4</td><td>0.02×120.0</td><td>0.1×24.0</td></tr><tr><td rowspan=\"2\">10</td><td>Acc. (%)</td><td>50.0±0.5</td><td>62.4±0.4</td><td>44.9±0.5</td><td>52.1±0.5</td><td>58.3±0.4</td><td>65.3±0.7</td><td>48.9±0.6</td><td>65.5±0.6</td><td>59.2±0.3</td><td>66.0±0.3</td></tr><tr><td>Time (h)</td><td>447.2</td><td>447.2</td><td>1.0</td><td>1.3</td><td>11.1</td><td>2.4</td><td>0.3</td><td>3.1</td><td>0.04×77.5</td><td>0.2×15.5</td></tr><tr><td rowspan=\"2\">50</td><td>Acc. (%)</td><td>-</td><td>70.5±0.4</td><td>53.9±0.5</td><td>60.6±0.5</td><td>69.5±0.3</td><td>71.6±0.2</td><td>63.0±0.4</td><td>71.7±0.2</td><td>66.7±0.2</td><td>71.8±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>1377.8</td><td>4.4</td><td>5.3</td><td>12.8</td><td>3.8</td><td>0.4</td><td>8.1</td><td>0.12×67.5</td><td>1.3×6.2</td></tr><tr><td rowspan=\"4\">CIFAR 100</td><td rowspan=\"2\">1</td><td>Acc. (%)</td><td>-</td><td>21.3±0.6</td><td>12.8±0.3</td><td>13.9±0.3</td><td>17.9±0.2</td><td>24.3±0.3</td><td>11.4±0.3</td><td>28.7±0.1</td><td>22.8±0.4</td><td>29.1±0.4</td></tr><tr><td>Time (h)</td><td>-</td><td>447.2</td><td>0.4</td><td>0.5</td><td>50.0</td><td>3.5</td><td>3.1</td><td>3.1</td><td>0.08×38.8</td><td>0.1×31.0</td></tr><tr><td rowspan=\"2\">10</td><td>Acc. (%)</td><td>-</td><td>34.7±0.5</td><td>25.2±0.3</td><td>32.3±0.3</td><td>36.1±0.4</td><td>40.1±0.4</td><td>29.7±0.3</td><td>42.5±0.2</td><td>35.1±0.2</td><td>38.4±0.1</td></tr><tr><td>Time (h)</td><td>-</td><td>2520.8</td><td>10.6</td><td>11.4</td><td>68.9</td><td>4.2</td><td>3.1</td><td>10.4</td><td>0.32×32.5</td><td>1.0×10.4</td></tr></table>",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Table 2. Comparisons with state-of-the-art methods of DD on test accuracy and training efficiency. DS denotes using down-sampled parameterization, i.e., storing down-sampled distilled images with the same storage budget. The black subscript indicates the standard deviation over multiple evaluations. The red subscript denotes the times of acceleration compared with the baseline method FRePo [52]. The best and second best results in each setting are marked by bold and underline respectively."
+                                }
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+                                    "type": "text",
+                                    "content": "increase the generalization ability of the translator across other unseen IPCs during adaptation, as shown in Sec. 4.3 and the supplement."
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+                            ]
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+                                    "type": "text",
+                                    "content": "In this paper, we consider the widely-adopted benchmarks of CIFAR10 and CIFAR100 [15] with a resolution of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "32 \\times 32"
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+                                    "type": "text",
+                                    "content": " for the main evaluation. Results on datasets with higher resolutions and larger sizes can be found in the supplement. Following previous works [52, 5], we evaluate the proposed method on storage budgets of 1, 10, and 50 images per class (IPC) for CIFAR10 and 1 and 10 IPC for CIFAR100. Synthetic datasets are trained with 3-layer convolutional networks and evaluated on the same architecture. The cross-architecture performance will also be studied in Sec. 4.3. We report the average result and the standard deviation over 3 replicate evaluations for each setting."
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+                                    "content": "4.2. Comparisons with State of the Arts"
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+                                    "type": "text",
+                                    "content": "Here, we compare the proposed method for few-shot dataset distillation with state-of-the-art methods, including meta-learning-based methods in the seminal "
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+                                    "type": "text",
+                                    "content": " [41] and remember-the-past (RTP) [5], gradient-matching based methods in "
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+                                    "type": "text",
+                                    "content": ", "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "IDC"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        510,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ", trajectory-matching based "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        510,
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+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "MTT"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        510,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", distribution-matching based "
+                                },
+                                {
+                                    "bbox": [
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+                                        510,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "DM"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        510,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and KRR-based "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "FRePo"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " [52]. The accuracy and training efficiency results are shown in Tab. 2. The accuracy results are from original papers while the training time is estimated based on the time-per-iteration results evaluated on the same hardware and the total number of iterations in the official codes. The shape/format of synthetic images in all methods except \"Ours-DS\" is consistent with that of real images in original datasets. For the running time of our method, we report the total time required for distilling using one network and the adaptation. Time for pre-training is not included since it is only conducted once, and once pre-trained, the trans"
+                                }
+                            ]
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+                    ],
+                    "index": 5
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+                {
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+                                    "type": "text",
+                                    "content": "lator can be adapted for an infinite number of downstream datasets."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Through the results, we find that in the default parameterization, the proposed method within 1k adaptation steps falls about "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "3 \\sim 7"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " points behind the FRePo baseline but with "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "30 \\sim 120 \\times"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " acceleration due to the few-shot setting. Even compared with the currently most efficient algorithm, the speed of our method is still considerable. And the performance is at least comparable with other methods in terms of accuracy, with even dramatic acceleration, e.g., the meta-learning-based DD and RTP. The superior efficiency makes our method applicable in scenarios where data cannot be held for a long time, like streaming data."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Additionally, in \"Ours-DS\", down-sampled synthetic images are alternatively stored with the same number of stored parameters, which is a simple yet effective method to improve the performance especially when the storage budget is small. This parameterization typically requires more iterations for the adaptation stages. For small synthetic datasets like 1 and 10 IPC, the number of steps is "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "6\\mathrm{k}"
+                                },
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+                                    "type": "text",
+                                    "content": ", and for 50 IPC, the number is "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "15\\mathrm{k}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Nevertheless, our method can still result in "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "6 \\sim 31 \\times"
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+                                    "type": "text",
+                                    "content": " acceleration compared with the FRePo baseline with even better performance."
+                                }
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+                                    "content": "4.3. Ablation Studies"
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+                                    "content": "Baselines: To demonstrate the effectiveness of the translative pre-training and target adaptation strategies proposed in this paper, we consider a series of baselines for ablation studies, including:"
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+                                    "type": "text",
+                                    "content": "- Baseline: a new neural network is sampled for each training iteration to process the real dataset and update synthetic data, which can be viewed as a benchmark given a sufficient number of networks;"
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+                                            "html": "<table><tr><td>Dataset</td><td>IPC</td><td>Baseline</td><td>1 Net</td><td>Bi-Level</td><td>w/o Pre-Train</td><td>w AE</td><td>w/o Ada</td><td>w Ada</td></tr><tr><td rowspan=\"3\">CIFAR10</td><td>1</td><td>41.2±0.7</td><td>35.3±0.6</td><td>40.8±0.5</td><td>36.1±0.5</td><td>40.6±0.6</td><td>39.5±0.8</td><td>44.0±0.2</td></tr><tr><td>10</td><td>57.9±0.7</td><td>50.5±0.8</td><td>52.1±0.5</td><td>53.8±0.1</td><td>57.6±0.3</td><td>54.7±0.8</td><td>59.2±0.3</td></tr><tr><td>50</td><td>65.2±0.3</td><td>65.1±0.1</td><td>60.7±0.1</td><td>59.7±0.4</td><td>63.5±0.1</td><td>65.8±0.2</td><td>66.7±0.2</td></tr><tr><td rowspan=\"2\">CIFAR100</td><td>1</td><td>21.6±0.6</td><td>18.7±0.1</td><td>19.1±0.1</td><td>20.5±0.2</td><td>21.8±0.3</td><td>20.9±0.7</td><td>22.8±0.4</td></tr><tr><td>10</td><td>33.8±0.3</td><td>31.7±0.1</td><td>31.0±0.2</td><td>30.7±0.2</td><td>27.0±0.2</td><td>33.0±0.2</td><td>35.1±0.2</td></tr></table>",
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+                                            "content": "- 1 Net: synthetic data are distilled in a single network, which can be treated as a lower bound;"
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+                                            "content": "- Bi-Level: the bi-level algorithm described in Alg. 1;"
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+                                            "content": " Pre-Train: the target adaptation stage starts from a randomly initialized translator;"
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+                                            "content": ": the target adaptation stage starts from an autoencoder trained with a reconstruction objective;"
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+                                            "content": " Ada: directly using the pre-trained translator without the adaptation stage;"
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+                                            "content": " Ada: the default method."
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+                                    "type": "text",
+                                    "content": "All the candidates are trained with 4k iterations. For those requiring adaptation, i.e., w/o Pre-Train, w AE, and w Ada, we first distill a synthetic dataset using 1 network with 3k iterations and adapt the translator for another 1k steps. Note that distilling with a single network only requires one forward propagation pass of the real dataset. Thus, the running time of our method is less than that of the baseline given the same number of iterations. Results are shown in Tab. 3."
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+                                    "type": "text",
+                                    "content": "For one thing, it turns out that the default method in this paper consistently surpasses the benchmark baseline requiring enormous networks in most cases. The reason is that with the number of networks for NFR increasing, it would be more difficult for the training convergence of distilled datasets, especially in the few-shot case. Please refer to the supplement for details."
+                                }
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+                                    "type": "text",
+                                    "content": "For another, the consistent improvement comparing results of 1 Net and w/o Ada indicates that the pre-trained translator is capable of generating distilled results in a more favorable space. We visualize their results in the first two plots of Fig. 3, where the global tone is refined towards higher brightness contrast. Moreover, as shown in the 3rd plot, the adaptation stage injects more local details, which tries to improve the performance in a similar way performed by the state-of-the-art FRePo [52]."
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+                                    "content": "Further, as shown in both Tab. 3 and Fig. 4(a-b), the pretrained model offers a more satisfactory initialization for the following adaptation stage, with lower initial loss, faster convergence, and higher accuracy."
+                                }
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+                                    "content": "At last, the bi-level algorithm often leads to inferior performance, which may be partially attributed to the insufficient number of inner steps restricted by GPU memory."
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+                                    "content": "Generalization: We observe that one benefit of adapting the translator in a target dataset is that it is generalizable across different storage budgets for synthetic datasets. For instance, as shown in Fig. 4(c), the translator adapted on IPC 1 and 50 can also behave well on IPC 10."
+                                }
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+                                    "type": "text",
+                                    "content": "Following previous works [51, 49, 50], we also evaluate the cross-architecture performance in Tab. 4 over AlexNet [16], VGG11 [37], and ResNet18 [8]. The conclusion is consistent with the above analysis."
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+                                    "content": "4.4. Application: Continual Learning"
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+                                            "html": "<table><tr><td>Setting</td><td>ConvNet</td><td>AlexNet</td><td>VGG</td><td>ResNet</td></tr><tr><td>Baseline</td><td>58.8±0.2</td><td>57.1±0.5</td><td>41.1±0.3</td><td>38.1±0.9</td></tr><tr><td>1 Net</td><td>50.5±0.8</td><td>50.9±0.6</td><td>34.2±0.3</td><td>35.3±0.3</td></tr><tr><td>Bi-Level</td><td>52.1±0.5</td><td>50.0±0.4</td><td>37.4±0.5</td><td>34.7±0.5</td></tr><tr><td>w/o Pre-Train</td><td>53.8±0.1</td><td>56.2±0.3</td><td>39.3±0.7</td><td>38.2±0.7</td></tr><tr><td>w/o Ada</td><td>54.7±0.8</td><td>52.8±0.3</td><td>35.7±0.7</td><td>34.8±1.2</td></tr><tr><td>w Ada</td><td>59.2±0.3</td><td>56.8±0.2</td><td>43.0±0.7</td><td>40.8±0.5</td></tr></table>",
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+                                    "content": "Table 4. Cross-architecture performance of our method in different settings. Results on CIFAR10 with 10 IPC are shown here."
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+                                    "type": "text",
+                                    "content": "learning the current one. To overcome the problem of catastrophic forgetting [14], many works use a small buffer to store some valuable data of past tasks for future use [32, 1]. Dataset distillation can thus benefit this area by synthesizing informative samples [27, 34, 36, 43, 3, 26] to prevent forgetting as much as possible."
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+                                    "content": "In this paper, we evaluate the proposed method on CIFAR100-CL following the same 5-step protocol of [52, 50] with 20 classes for each task and 20 IPC. The results in Fig. 5 suggest a consistent conclusion with the ablation studies shown in Sec. 4.3 and indicate that the few-shot dataset distillation proposed in this paper can further facilitate the practical use when tasks come fast like a stream, which provides limited time for processing and learning."
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "type": "text",
+                                    "content": "In this paper, we focus on the setting of few-shot dataset distillation to improve its efficiency, where data can only be processed by a limited number of neural networks. We introduce the concept of distillation space to optimize the performance of synthetic data distilled by only one network. Regarding that the complexity of the quad-level definition and the bi-level algorithm for distillation space, we convert the problem to a transitive model. The synthetic dataset is first distilled in a random but fixed neural network and then translated to the desired space. For transferability, we train the translator with a pre-training algorithm, so that a pre"
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+                                            "content": "Figure 4. (a-b) NFR loss and test accuracy during adaption for CIFAR10 IPC 10 starting with the pre-trained translator by our algorithm, an auto-encoder, and a randomly initialized model. (c) Generalization performance of the translator on unseen IPC during adaptation."
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+                                            "content": "Figure 5. Performance of continual learning on CIFAR100 with 5 steps and 20 IPC for different settings."
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+                                    "type": "text",
+                                    "content": "trained translator can be adapted for a new dataset within a limited number of steps. Experiments demonstrate that our method achieves "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 15\\times"
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+                                    "type": "text",
+                                    "content": " acceleration and comparable performance with the state-of-the-art baselines relying on thousands of networks. Even in some cases, the translator without adaptation yields competitive performance."
+                                }
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+                                    "type": "text",
+                                    "content": "One limitation of our method is that in the adaptation stage, errors of translated synthetic datasets have to be further back-propagated through the translator, which introduces additional GPU memory consumption compared with the baseline method, e.g., 3946 v.s. 3456 MB on CIFAR10 with 10 IPC. Nevertheless, as shown in Fig. 4(c), the translator adapted for small sizes can conduct inference for larger sizes, thereby breaking the limitation on GPU memory. Future works may focus on further improving the transferability of the distillation space translator by dedicated architectural designs or objective functions."
+                                }
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+                                    "type": "text",
+                                    "content": "Acknowledgement"
+                                }
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+                    "index": 17
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+                                    "content": "This work is supported by the Advanced Research and Technology Innovation Centre (ARTIC), the National University of Singapore under Grant (project number: A0005947-21-00, project reference: ECT-RP2), and the Singapore Ministry of Education Academic Research Fund Tier 1 (WBS: A0009440-01-00)."
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+                                }
+                            ]
+                        }
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diff --git a/2023/Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation/557cad77-3efc-4a93-9f6c-1ad645fa6bd4_content_list.json b/2023/Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation/557cad77-3efc-4a93-9f6c-1ad645fa6bd4_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..196a8465c1cb4d51183fc89d6de36edbdd3ee3ae
--- /dev/null
+++ b/2023/Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation/557cad77-3efc-4a93-9f6c-1ad645fa6bd4_content_list.json	
@@ -0,0 +1,1405 @@
+[
+    {
+        "type": "text",
+        "text": "Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation",
+        "text_level": 1,
+        "bbox": [
+            196,
+            130,
+            776,
+            174
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xueyi Liu $^{1,5}$ , Bin Wang $^{2}$ , He Wang $^{3}$ , Li Yi $^{1,4,5}$ $^{1}$ Tsinghua University  $^{2}$ Beijing Institute for General Artificial Intelligence  $^{3}$ Peking University  $^{4}$ Shanghai Artificial Intelligence Laboratory  $^{5}$ Shanghai Qi Zhi Institute",
+        "bbox": [
+            104,
+            202,
+            854,
+            257
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We study the problem of few-shot physically-aware articulated mesh generation. By observing an articulated object dataset containing only a few examples, we wish to learn a model that can generate diverse meshes with high visual fidelity and physical validity. Previous mesh generative models either have difficulties in depicting a diverse data space from only a few examples or fail to ensure physical validity of their samples. Regarding the above challenges, we propose two key innovations, including 1) a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy to alleviate the few-shot challenge by borrowing transferrable deformation patterns from large scale rigid meshes and 2) a physics-aware deformation correction scheme to encourage physically plausible generations. We conduct extensive experiments on 6 articulated categories to demonstrate the superiority of our method in generating articulated meshes with better diversity, higher visual fidelity, and better physical validity over previous methods in the few-shot setting. Further, we validate solid contributions of our two innovations in the ablation study. Project page with code is available at meowuu7.github.io/few-arti-object-gen.",
+        "bbox": [
+            75,
+            325,
+            473,
+            657
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            691,
+            209,
+            708
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generative models have aroused a wide spectrum of interests in recent years for their creativity and broad downstream application scenarios [29, 30, 34, 17, 8, 26]. Specific to 3D generation, a variety of techniques such as denoising diffusion [23, 42, 6, 39] have also been discussed for a while. Among them, mesh generation is indeed important since the mesh representation can support a wider range of downstream applications such as rendering and physical simulation compared to other representations such as point clouds. Existing works mainly focus on generating meshes for whole objects [8, 26, 6, 19, 30] considering without modeling object functionalities at all. Besides, they",
+        "bbox": [
+            75,
+            719,
+            470,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/d27d6e24dc041b1cc8763128cff191cda9cb6f8f5c5f2244cccac707976f8e10.jpg",
+        "image_caption": [
+            "Figure 1. Overview. We present a hierarchical mesh deformation-based generative model to solve the challenging yet important few-shot physically-aware articulated mesh generation problem. It tackles the few-shot challenge by borrowing shared convex level deformation patterns from large-scale rigid meshes and incorporates a deformation correction scheme to further enhance the model's ability to generate physically realistic meshes."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            517,
+            292,
+            879,
+            424
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "mainly rely on reconstructing meshes from other kinds of representations such as implicit fields [8, 6, 19] instead of generating meshes directly. In this work, we go one step further and consider mesh generation for articulated objects that can support physically realistic articulations. This not only helps understand the object distribution in real-world assets, but also allows an intelligent agent to learn segmenting [20, 22], tracking [36], reasoning [10] and manipulating [38] articulated objects through a simulation environment. We focus on the articulated mesh generative model that can generate object meshes with diverse geometry, high visual fidelity, and correct physics.",
+        "bbox": [
+            496,
+            518,
+            893,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Training a generative model on publicly available articulated mesh datasets to depict a diverse physically-plausible data space not limited to training assets presents two main challenges to the methodology. First, existing articulated object datasets are usually very restricted in scale. For example, the PartNet-Mobility Dataset [37] contains an average of 51 meshes per category. This naturally requires a few-shot generative model to learn from a very limited number of meshes. Adapting previous approaches immediately without carefully considering the few-shot nature would lead to models suffering from poor generative ability. Second, we need to pursue physically plausible generation to ensure the generated meshes are not only visu-",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "854",
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+    {
+        "type": "text",
+        "text": "ally appealing but also functionally sound to support correction articulation functions, i.e., attached parts without self-penetrations in the full articulation range.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Despite recent advancements in mesh generation community such as a wide variety of models proposed in existing works [8, 41, 6, 33, 19], they are typically challenged by the following difficulties and always fail to solve our problem: 1) Lack of the ability to learn a wide data space not limited to training shapes in the few-shot setting. 2) Difficulty in modeling crucial object-level shape constraints imposed by the functionality of articulated objects. Failure to consider these requirements would result in physically unrealistic samples [8, 6, 26]. Modeling such physical constraints for articulated meshes is a non-trivial task, as it requires accounting for diverse penetration phenomena caused by different types of articulation motions. To our best knowledge, we are the first that presents a valid framework to address such two difficulties for articulated mesh generation.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our work designs a hierarchical mesh deformation-based generative model that tackles the aforementioned challenges using two key innovations: (1) Hierarchical mesh deformation with transfer learning. We introduce an object-convex shape hierarchy and learn the hierarchical articulated mesh generative model. The model is trained by first learning the deformation-based generative model at the leaf convex level and then synchronizing individual convex-level deformation spaces at the root level. We identify that different categories tend to share convex-level deformation patterns and leverage this insight to learn and transfer rich deformation prior from large-scale rigid datasets to expand the model's generative capacity. (2) Physics-aware deformation correction. To address self-penetrations of deformed articulated meshes during mesh articulation, we further introduce a deformation correction scheme. It is composed of an auxiliary loss penalizing self-penetrations during mesh articulation and a collision response-based shape optimization strategy. By integrating this scheme into the hierarchical mesh deformation model, we successfully guide the model to generate more physically realistic deformations, resulting in physically correct articulated meshes finally.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We conduct extensive experiments on 6 categories from the PartNet-Mobility dataset [37] for evaluation. As demonstrated by both the quantitative and qualitative results, we can consistently outperform all baseline methods regarding the fidelity, diversity and physical plausibility of generated meshes, e.g., an average of  $10.4\\%$  higher coverage ratio,  $43.7\\%$  lower minimum matching distance score, and  $26.5\\%$  lower collision score. Ablation studies further validate the value of our design in deformation pattern transfer learning, the hierarchical mesh generation approach, and the effectiveness as well as the versatility of our physics-aware correction scheme.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our key contributions are as follows: (1) We present the first solution, to our best knowledge, for the challenging yet important few-shot physically-aware articulated mesh generation problem with two effective and non-trivial technical innovations. (2) We propose a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy. This design allows us to learn a diverse data space by borrowing shared deformation patterns from large-scale rigid object datasets. (3) We propose a physics-aware deformation correction scheme to encourage the hierarchical generative model to produce physically realistic deformations, resulting in improved physical validity of the generated samples. This scheme can also be effectively integrated into other deformation-based mesh generative models, thereby enhancing the physical validity of their samples as well.",
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+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Mesh generative models. There have been vast and long efforts in devising 3D mesh generative models [26, 8, 41, 6, 21, 35]. Their techniques can be mainly categorized into three genres: 1) direct surface generation [26], 2) deformation-based mesh generation [21, 35], and 3) hybrid representation-based generation [8, 41]. Though methods of the first type exhibit obvious merits such as synthesizing high-quality n-gon meshes, they always suffer from limited generative ability and cannot scale for complex objects. In contrast, deformation-style mesh generation models deform source shapes for new samples which naturally spares the efforts for mesh structure generation, while restricted by poor flexibility. The third strategy separates the mesh surface structure generation problem from the content generation, which offers them with powerful generative ability. However, the quality of their samples is coupled with the power of their surface reconstruction techniques [27, 31]. In this work, we leverage mesh deformation as our generation technique for articulated mesh synthesis, taking advantages of its ability to produce high-quality samples. Instead of deforming whole objects or parts directly, we design a hierarchical deformation strategy to enhance the deformation flexibility and to enrich the data space by borrowing deformation patterns shared across categories from large scale rigid meshes.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot generation. Along with the flourishing image generative models emerged in recent years, the few-shot image generation has been widely explored as well [12, 9, 11, 13, 2]. It wishes to create more data given only a few examples from a novel category that is both diverse in content and semantically consistent with the target category. At the high level, their basic philosophy is to design proper approaches such that the model can benefit from large base datasets for generation, like local fusion [9], latent vari-",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "855",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "ables matching [11, 3]. adversarial delta matching [12]. In this work, we leverage transfer learning to adapt shape patterns from large-scale rigid datasets to target articulated categories. Devising methods in this way requires us to find correct intermediates on which shape patterns are cross-category transferrable. Instead of directly using whole objects or articulated parts, we choose convexes as such intermediates. Transferring knowledge at this level presents further difficulties in fusing them together in a geometrically consistent way and in synthesizing physically realistic meshes while maintaining visual diversity at the same time.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Physics-aware machine learning. Our work is also related to physics-aware machine learning [28, 10, 14, 24, 32, 25, 18], and mostly relevant to physically-aware generative models. To ensure physical validity of generated shapes, typical solutions choose either offline simulations for training data filtering [32] or online simulations leveraging the development of differentiable simulators [7, 15, 16] or by designing online simulation layers [24]. Generating physically-plausible articulated objects presents new challenges considering self-penetrations during mesh articulation that are more complex than stability issues caused by gravity for rigid objects. Our method integrates the physical supervision and a shape optimization strategy. The optimization transforms part shapes to resolve self-penetration issues. High-dimensional and complex shape deformations are involved in the process, different from linear fixing operations considered in [10].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The problem we are targeting is the few-shot physically-aware articulated mesh generation. Given a set of articulated meshes from the category of interest, we would like to learn a conditional generative model which could deform an articulated mesh from the same category into a wide variety of shapes. This conditional generation setup allows generating a large number of physically-plausible articulated meshes from a few examples while avoiding the need to generate the mesh structure. However, it leaves several challenges to address including how to accurately represent complex shape deformation spaces from a few examples and how to ensure that the generated meshes support physically-realistic articulations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Regarding the first challenge, our idea is to learn the deformation space via borrowing knowledge from other object categories. This seemingly simple idea is not trivial to realize though since we need to figure out what knowledge is transferrable. We present a hierarchical mesh deformation strategy to allow deformation prior to transfer at a local convex segment level while still maintaining the deformation consistency at the global shape level. Regarding the second challenge, we introduce a physics-aware deforma",
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+    {
+        "type": "text",
+        "text": "tion correction scheme to avoid unwanted artifacts such as self-penetrations during mesh articulation.",
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+    {
+        "type": "text",
+        "text": "In the following, we will provide a pipeline overview in Section 3.1. Then we will explain our hierarchical mesh deformation strategy and our physics-aware deformation correction scheme in Section 3.2 and Section 3.3 respectively.",
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+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Given a small set of articulated meshes  $\\mathcal{A}$  from a certain category of interest with the same number of parts and joints, sharing a known kinematic chain, our method wishes to learn a conditional generative model depicting a diverse and plausible articulated shape space. We adopt the divide-and-conquer philosophy and develop a hierarchical deformation scheme with transfer learning to tackle the difficulty of few-shot generation. Instead of learning at the whole shape level, we structure each articulated shape into an object-convex hierarchy and solve the generation problem via two steps. We first learn a generative model depicting a diverse shape space at the lowest convex level by borrowing common shape patterns from large rigid mesh datasets, denoted as  $\\mathcal{B}$ . Convexes, with small cross-category distribution gap, serve as good intermediates for transferring common shape prior. After that, we devise a synchronization strategy that composes convex deformations consistently to form valid object shapes. Besides, a physics-aware correction scheme is developed to avoid physically-unnatural phenomena such as self-penetrations. Our overall pipeline is shown in Figure 2.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Specifically, we first decompose the conditional mesh  $a$  into approximately convex segments  $\\mathcal{C}_a$ , forming an object-convex hierarchy. Then, on the leaf level, we learn to deform each convex  $c \\in \\mathcal{C}_a$  through a convex-level conditional generative model  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  where  $\\mathbf{z}_c$  is the noise parameter corresponding to convex  $c$ . Finally, on the root level, we synchronize the convex deformations by replacing the convex-dependent noise parameter  $\\mathbf{z}_c$  with  $S_c\\mathbf{z}$ , where  $S_c$  is a linear transformation and  $\\mathbf{z}$  is a synchronized noise parameter shared among all convexes. This aligns the noise space of different convexes to form a coherent deformation for the whole mesh. The above hierarchical deformation strategy can be mathematically represented as  $g(\\mathbf{z}|a) = \\{g_{\\mathcal{C}}(S_c\\mathbf{z}|c)|c \\in \\mathcal{C}_a\\}$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "During the training time, we first leverage existing unsupervised shape segmentation tools BSP-Net [5] to decompose meshes in both  $\\mathcal{A}$  and  $\\mathcal{B}$  into approximately convex segments  $\\mathcal{C}_{\\mathcal{A}}$  and  $\\mathcal{C}_{\\mathcal{B}}$ . Since BSP-Net decomposes shapes consistently for each category, we can naturally identify corresponding convexes within  $\\mathcal{C}_{\\mathcal{A}}$  or  $\\mathcal{C}_{\\mathcal{B}}$ . We can then pretrain a convex-level conditional generative model  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  on  $\\mathcal{C}_{\\mathcal{B}}$  modeling how corresponding convexes could deform into each other among the large-scale rigid meshes. We then fine-tune the pre-trained model  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  on convexes",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "856",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/64d4c1ef1c5bb34c7b522513594b93a023e121e8daf6e36356f2ef138e6dee81.jpg",
+        "image_caption": [
+            "Figure 2. Framework overview for our few-shot physically-aware articulated mesh generation. In this figure, yellow blocks represent modules with learnable weights optimized during pre-training. Orange blocks contain weights optimized during fine-tuning. Gray blocks contain no learnable weights. Convexes of the same color are of the same type. Our framework consists of a hierarchical mesh deformation scheme that learns and transfers diverse shared deformation patterns from large-scale rigid datasets at the convex level. We also propose a convex deformation synchronization strategy to combine individual convex-level deformation spaces into the object-level space. Furthermore, we introduce a physics-aware deformation correction strategy to address self-penetrations in synthesized articulated meshes."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "in  $\\mathcal{C}_A$  and at the same time estimate the noise synchronization transformation  $S_{c}$ . We further exploit an additional physics-aware deformation correction scheme to improve the physical validity of generated articulated shapes. It consists of 1) an auxiliary loss penalizing self-penetrations to provide physical supervision and 2) a collision response-based shape optimization strategy to encourage the model to generate physically realistic meshes. The auxiliary loss is incorporated into the training pipeline. While the shape optimization scheme functions at both the training time and the test time.",
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+    {
+        "type": "text",
+        "text": "3.2. Hierarchical Mesh Deformation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Given an input articulated mesh  $a$  and its corresponding approximately convex segments  $C_a$ , our hierarchical mesh deformation model  $g(\\mathbf{z}|a) = \\{g_{\\mathcal{C}}(S_c\\mathbf{z}|c)|c \\in C_a\\}$  consists of a convex-level conditional generative model  $g_{\\mathcal{C}}$  as well as a series of synchronization transformations  $\\{S_c\\}$ . We propose to learn the model at the lowest convex level  $g_C$  following a transfer learning paradigm so that convex-level shape patterns can easily transfer across different categories. Given a reference mesh  $a$ , the hierarchical deformation first synthesizes new convex shapes via  $g_C$ . A deformation synchronization strategy is developed to handle the resulting deformation inconsistency issue across different convexes to form a valid object shape.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Convex-level conditional generative model. We propose to leverage mesh deformation to characterize the convex-level conditional generative model. For a convex mesh segment  $c$  containing  $N_{c}$  vertices, the conditional generative model  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  should be able to produce diverse and realistic vertex-level deformation offset  $\\mathbf{d}_c \\in \\mathbb{R}^{N_c \\times 3}$  when we sample different noise parameters  $\\mathbf{z}_c$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The convex deformation  $\\mathbf{d}_c$  lies in a high-dimensional space which varies from convex to convex, prohibiting the knowledge transfer across different convexes. We therefore reparametrize  $\\mathbf{d}_c$  using two tricks inspired by [40, 21]: 1) using cages to control per-vertex deformation; 2) using dic",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tionaries to record the common deformation modes.",
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+    },
+    {
+        "type": "text",
+        "text": "In particular, for each convex  $c$ , we use a coarse triangle mesh (a cage)  $t_c$  enclosing  $c$  to control the deformation of convex  $c$  [40]. The cage  $t_c$  usually contains much less vertices compared with the convex  $c$  so that its distribution is easier to be modeled. The deformation  $\\mathbf{d}_c$  of the convex  $c$  can be easily computed as a linear transformation of the deformation  $\\mathbf{d}_{t_c}$  of cage  $t_c$ :  $\\mathbf{d}_c = \\Phi_c\\mathbf{d}_{t_c}$ . Here  $\\Phi_c$  is an interpolation matrix based upon the generalized barycentric coordinates of convex  $c$  with respect to cage  $t_c$ . We deform a template mesh based upon the shape of each convex to form the cages which we defer the details to supp.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To further reduce the deformation parametrization, we represent the cage deformation  $\\mathbf{d}_{t_c}$  as a linear combination of  $K$  deformation bases  $B_{c} = [\\mathbf{b}_{c}^{1}\\dots \\mathbf{b}_{c}^{K}]$  as  $\\mathbf{d}_{t_c} = B_c\\mathbf{z}_c$  where  $\\mathbf{z}_c$  is a  $K$ -dimensional deformation coefficient. Here each deformation basis  $\\mathbf{b}_c$  represents a common deformation pattern and all the bases span the deformation space of cage  $t_c$  and therefore convex  $c$ . Representing deformation spaces via deformation bases can effectively reduce the dimension of shape space compared to other alternatively such as utilizing latent vectors.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A few-shot deformation learning paradigm. Given the above deformation reparametrizations, learning the convex-level conditional generative model for each convex  $c$  boils down to learning the deformation bases  $B_{c}$  as well as the distribution of deformation coefficient  $\\mathbf{z}_c$ . For deformation bases, we employ a neural network  $\\psi_{\\theta}(\\cdot)$  to predict from convex shapes. It takes a given convex  $c$  as input and outputs its deformation bases, i.e.,  $B_{c} = \\psi_{\\theta}(c)$ . We then optimize the deformation coefficient  $\\mathbf{z}_c^{\\hat{c}}$  for each convex  $\\hat{c}$  in correspondence to  $c$  from the current available dataset. The distribution of  $\\mathbf{z}_c$  is then a mixture of Gaussian fit by the resulting deformation coefficients  $\\{\\mathbf{z}_c^{\\hat{c}}\\}$ . We further leverage a transfer learning approach that transfers deformation priors learned in large-scale rigid dataset to target datasets at the convex level based on the observation that the convex-level deformations usually show similar patterns across cat-",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "857",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "egories, e.g., a slab gets thicker or a strip gets elongated. Therefore we can learn a diverse deformation space from a few examples.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We pre-train  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  on the large-scale rigid mesh dataset  $\\mathcal{B}$  and fine-tune it on each target articulated dataset  $\\mathcal{A}$ . In particular, at the pre-training time, given a set of rigid meshes  $\\mathcal{B}$  from large-scale online repositories as well as the corresponding convexes  $\\mathcal{C}_{\\mathcal{B}}$ , we first identify pairs of convexes in correspondence  $\\{(c,\\hat{c})|c,\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}$  from the same-category shapes, e.g., the noses of two different airplanes. These correspondences come as a result of some off-the-shelf unsupervised co-segmentation algorithms [5]. We then optimize  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  by alternatively optimizing the deformation coefficient set  $\\{\\mathbf{z}_c^{\\hat{c}}|c,\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}$ , and the neural network  $\\psi_{\\theta}(\\cdot)$ . To optimize  $\\{\\mathbf{z}_c^{\\hat{c}}\\}$ , we fix  $\\{B_c\\}$  and optimize each  $\\mathbf{z}_c^{\\hat{c}}$  by minimizing the Chamfer Distance (CD), also denoted as  $d_{\\mathrm{CD}}(\\cdot ,\\cdot)$ , between the deformed convex  $c$  and the target  $\\hat{c}$ . Then we optimize  $\\{B_c\\}$  by fixing deformation coefficients  $\\{\\mathbf{z}_c^{\\hat{c}}\\}$  and minimizing average CD between deformed  $c$  and the target  $\\hat{c}$  for each pair  $(c,\\hat{c})$ , which leads to the convex deformation loss  $\\mathcal{L}_C$  at the training time:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {C} = \\frac {1}{| \\mathcal {C} _ {\\mathcal {B}} |} \\sum_ {c, \\hat {c} \\in \\mathcal {C} _ {\\mathcal {B}}} d _ {\\mathrm {C D}} \\left(g _ {\\mathcal {C}} \\left(\\mathbf {z} _ {c} \\mid c, \\mathbf {z} _ {c} = \\mathbf {z} _ {c} ^ {\\hat {c}}\\right), \\hat {c}\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After the above alternative optimization, the distribution of  $\\mathbf{z}_c$  for each convex  $c$  is modeled by a mixture of Gaussian distribution fit to the final coefficient set  $\\{z_c^{\\hat{c}}|\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}$ . At the fine-tuning time,  $g_{\\mathcal{C}}(\\mathbf{z}|c)$  is further optimized via the same procedure by the convex correspondence set  $\\mathcal{C}_{\\mathcal{A}}$  of the target dataset  $\\mathcal{A}$ .",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/05412a227ef880efe135697a9e178cad3fce5369d2069792d669832f5bb6c3ae.jpg",
+        "image_caption": [
+            "Figure 3. Synchronization Process. The left part illustrates the decomposed convexes and source cages of the input eyeglass frame. The right part visualize synchronization matrices (a  $4 \\times 4$  matrix here for each cage), cages deformed by bases before synchronization (left two columns), and cages deformed by synchronized bases (right two columns)."
+        ],
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+    {
+        "type": "text",
+        "text": "Convex deformation synchronization. After learning the conditional generative model for each convex  $c$ , the next step is to compose all the deformation spaces for the whole mesh  $a$ . Since for each convex  $c$ ,  $g_{\\mathcal{C}}(\\mathbf{z}_c|c)$  exploits a separate set of deformation bases  $B_{c}$ , the noise parameter  $\\mathbf{z}_c$  varies its meaning from convex to convex. As a result, if we draw independent noise parameters for each convex, the",
+        "bbox": [
+            75,
+            796,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "outcoming deformations could easily contradict with each other, failing the whole mesh-level deformation. To tackle this issue, we synchronize different deformation bases  $B_{c}$  with linear transformations  $S_{c}$  so that a single noise parameter  $\\mathbf{z}$  can be shared across all convexes.",
+        "bbox": [
+            496,
+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Formally speaking, given a set of articulated object meshes  $\\mathcal{A}$  from a certain category and an articulated mesh  $a\\in \\mathcal{A}$ , assuming the mesh is segmented into  $M$  convexes  $\\{c_m\\}_{m = 1}^M$  and each convex is equipped with a deformation model  $g_{\\mathcal{C}}(\\mathbf{z}_{c_m}|c_m)$ , our goal is to replace  $\\mathbf{z}_{c_m}$  with  $S_{c_m}\\mathbf{z}$  so that sampling the shared noise parameter  $\\mathbf{z}$  results in a globally consistent mesh deformation. To compute the synchronization transformation  $S_{c_m}$ , we consider the deformation from  $a$  to other articulated meshes  $a^i\\in \\mathcal{A}$ . In particular, for each  $a^i$ , we optimize for a set of deformation coefficients  $\\{\\mathbf{y}_m^i\\}$  so that each convex  $c_m$  in mesh  $a$  could deform into the corresponding convex  $c_m^i$  in mesh  $a^i$  following the deformation model  $g_{\\mathcal{C}}(\\mathbf{z}_{c_m}|c_m,\\mathbf{z}_{c_m} = \\mathbf{y}_m^i)$ . We can then estimate the synchronization transformations  $\\{S_{c_m}\\}$  by solving the following optimization problem:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\underset {\\{S _ {c _ {m}} \\}, \\{\\mathbf {z} ^ {i} \\}} {\\text {m i n i m i z e}} \\sum_ {i = 1} ^ {| \\mathcal {A} |} \\sum_ {m = 1} ^ {M} \\| B _ {c _ {m}} S _ {c _ {m}} \\mathbf {z} ^ {i} - B _ {c _ {m}} \\mathbf {y} _ {m} ^ {i} \\| _ {2}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            544,
+            435,
+            890,
+            479
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $B_{c_m}$  is the deformation bases of convex  $c_{m}$  and  $\\mathbf{z}^i$  is a global deformation coefficient from mesh  $a$  to  $a^i$  shared across all convexes. We solve the above optimization problem via alternatively optimizing the synchronization transformations  $\\{S_{c_m}\\}$  and the global deformation coefficients  $\\{\\mathbf{z}^i\\}$ :",
+        "bbox": [
+            496,
+            511,
+            892,
+            603
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "Fix  $\\{S_{c_m}\\}$ , optimize each global deformation coefficient  $\\mathbf{z}^i$  from  $a$  to  $a^i$  via Algorithm 2. It takes the convex deformation bases  $\\{B_{c_m}\\}$ , current synchronization transformations  $\\{S_{c_m}\\}$ , convex deformation coefficients  $\\{\\mathbf{y}_m^i\\}$  as input, and outputs the optimized  $\\mathbf{z}^i$ .",
+            "Fix  $\\{\\mathbf{z}^i\\}$ , optimize each synchronization transformation  $S_{c_m}$  for each convex  $c_m$  via Algorithm 1. It takes the convex deformation bases  $\\{B_{c_m}\\}$ , current global deformation coefficients  $\\{\\mathbf{z}^i\\}$ , convex deformation coefficients  $\\{\\mathbf{y}_m^i\\}$  as input, and outputs the optimized  $S_{c_m}$ ."
+        ],
+        "bbox": [
+            517,
+            612,
+            890,
+            779
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "w/ Sync.",
+        "bbox": [
+            506,
+            803,
+            550,
+            813
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/91033a5ed731146971c8e20b5b53de04f3c0d7786d7d6d5646a2aeee7148df44.jpg",
+        "image_caption": [
+            "Source Shape"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            815,
+            550,
+            838
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8900be0928c55ade71a9f8a1f63c339cd32bf53e3e53beeac038b7e6350ac0dc.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            558,
+            800,
+            614,
+            840
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/b914669c7401cafc5c60ac03a07461365ccc94b0cd2fb5d5325db4ed980b7983.jpg",
+        "image_caption": [
+            "Figure 4. Synchronization's Effectiveness. The synchronized deformation bases can consistently transform each convex for a valid part shape (upper row), while those before the synchronization fail (bottom row)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            630,
+            799,
+            694,
+            840
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/7b779c2cc937e6b93647baa24b91cc58b04e2127633a469dbe45c8a53da5549a.jpg",
+        "image_caption": [
+            "Convex Cages"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            707,
+            800,
+            763,
+            840
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/f9150b0bd2362bd6dacc22611a97298fcebee89ca2a7f8d3c1d4d4770aed680e.jpg",
+        "image_caption": [
+            "Deformed Cages",
+            "Deformed Part"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            785,
+            801,
+            864,
+            840
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "858",
+        "bbox": [
+            485,
+            945,
+            511,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Synchronization transformation matrices optimization.",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            467,
+            119
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Input: Deformation bases for each convex  $\\{B_{c_m}\\}$ . Global deformation coefficients  $\\{\\mathbf{z}^i\\}$  from  $a$  to other articulated meshes  $\\{a^i\\}$ . Deformation coefficients  $\\{\\mathbf{y}_m^i\\}$  from each convex  $c_m$  to the corresponding convex of the articulated mesh  $a^i$ .",
+            "Output: Synchronization transformation matrix  $S_{c_m}$  of the convex  $c_{m}$ .",
+            "1:  $\\mathbf{Z} \\gets \\operatorname{Stack}(\\{\\mathbf{z}^i\\})$",
+            "2:  $\\mathbf{Y}_m\\gets \\mathrm{Stack}(\\{\\mathbf{y}_m^i\\})$",
+            "3:  $[\\mathbf{U},\\pmb {\\Sigma},\\mathbf{V}^T ]\\gets \\mathrm{SVD}(\\mathbf{Z})$",
+            "4:  $[\\mathbf{U}_m, \\mathbf{\\Sigma}_m, \\mathbf{V}_m^T] \\gets \\mathrm{SVD}(\\mathbf{Y}_m)$",
+            "5:  $S_{c_m}\\gets \\mathbf{U}_m\\Sigma_m\\mathbf{V}_m^T\\mathbf{V}\\Sigma^+ \\mathbf{U}^T$",
+            "6: return  $S_{c_m}$"
+        ],
+        "bbox": [
+            76,
+            122,
+            467,
+            255
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 2 Global deformation coefficients optimization. \"lsq\" denotes the least square solver.",
+        "text_level": 1,
+        "bbox": [
+            76,
+            287,
+            467,
+            316
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Input: Deformation bases for each convex  $\\{B_{c_m}\\}$ . Synchronization transformations  $\\{S_{c_m}\\}$ . Deformation coefficients  $\\mathbf{y}_m^i$  from each convex  $c_m$  to the corresponding convex of the articulated mesh  $a^i$ .",
+            "Output: Global deformation coefficients  $\\mathbf{z}^i$  from  $a$  to  $a^i$ .",
+            "1:  $\\mathcal{S}_{\\mathbf{z}^i}\\gets \\emptyset$",
+            "2: for  $m = 1$  to  $M$  do",
+            "3:  $\\hat{\\mathbf{z}}_m^i\\gets \\mathrm{lsq}(S_{c_m},\\mathbf{z}_m^i)$",
+            "4:  $\\mathcal{S}_{\\mathbf{z}^i}\\gets \\mathcal{S}_{\\mathbf{z}^i}\\cup \\{\\hat{\\mathbf{z}}_m^i\\}$",
+            "5:  $\\mathbf{z}^i = \\mathrm{Average}(S_{\\mathbf{Z}^i})$",
+            "6: return  $\\mathbf{z}^i$"
+        ],
+        "bbox": [
+            76,
+            320,
+            467,
+            441
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As an intuitive illustration of the synchronization process, we select the example of synchronizing the eyeglass frame's convex deformations (with 2 convexes and 4 deformation bases for each convex) and visualize the process (detailed to the cage level) in Figure 3. The synchronized deformation bases can transform two convexes more consistently and symmetrically than those before synchronization (an example on deformed part shapes is shown in Figure 4).",
+        "bbox": [
+            75,
+            462,
+            467,
+            582
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "After deformation synchronization, the distribution of the shared noise parameter  $\\mathbf{z}$  can be simply set as a mixture of Gaussian fit to the optimized global deformation coefficients  $\\{\\mathbf{z}^i\\}$ .",
+        "bbox": [
+            75,
+            583,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3. Physics-Aware Deformation Correction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            650,
+            413,
+            666
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Based upon the above design, our hierarchical deformation model can then synthesize a deformed mesh  $a$  via the noise parameter  $\\mathbf{z}$  by taking a source articulated mesh as input. However, we may frequently observe physically unnatural self-penetrations when articulating  $a$ . To encourage the model to produce physically valid articulated meshes, we further propose a physics-aware deformation correction scheme, which serves two purposes: 1) to optimize the weights of the generative model to produce deformations that are more physically realistic and 2) to optimize the shape  $a$  to improve its physical validity. To accomplish this, we draw inspiration from previous works on stable rigid object generation [24, 25] and develop an online articulation simulation process that places  $a$  into  $K$  different articulation states sequentially, denoted as  $\\operatorname{Sim}(a) = \\{a_k\\}_{k=1}^K$ . The",
+        "bbox": [
+            75,
+            674,
+            467,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "articulation state sequence is designed by hand particularly for each category. We then utilize the physical supervision and a shape optimization strategy to guide the network to generate physically realistic articulated meshes. We will elaborate them in the following text.",
+        "bbox": [
+            496,
+            90,
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+            167
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Physical supervision. To provide physical supervision for articulated mesh generative models requires us to design stability signals to measure physically unstable phenomena, for which we mainly consider self-penetrations during mesh articulation. We therefore devise a metric named average penetration depth (APD) measuring the magnitude of each vertex penetrating through other parts during the articulation simulation process. It is also referred as  $\\mathcal{L}_{phy}$  when we treat it as a loss. Formally,  $\\mathcal{L}_{phy} = \\frac{1}{K}\\sum_{k=1}^{K}\\mathrm{PeneD}(a_k)$ , where  $\\mathrm{PeneD}(a_k)$  measures self-penetrations in a single articulation state. We defer details of  $\\mathcal{L}_{phy}$  to the supp.",
+        "bbox": [
+            496,
+            190,
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+            359
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "One way to provide physical guidance for the network is to utilize the physical stability signal  $\\mathcal{L}_{phy}$  as an auxiliary loss to supervise the network training. However, physically unnatural phenomena of articulated meshes during mesh articulation are more diverse and complex than that of rigid objects caused by diverse part geometric appearance and wide articulation variations. Directly exploring physical supervision to guide the network optimization is not sufficient to regularize the network to produce physically realistic deformations. Therefore we further develop a collision response-based shape optimization strategy to improve the physical realism of the generated mesh  $a$ . Then we first optimize  $a$  for several times to reduce self-penetrations and then use it to calculate  $\\mathcal{L}_{phy}$  for network optimization.",
+        "bbox": [
+            496,
+            376,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Collision response-based shape optimization. To realize the vision of resolving self-penetrations via optimizing shapes, we draw inspirations from collision response strategies and devise a heuristic penetration resolving strategy that projects penetrated vertices onto the surface of the mesh. To guide such projection, we devise an algorithm that calculates  $\\mathrm{ProjD}(a)$  whose gradient over each penetrated vertex in  $a$  informs how to project it to resolve penetrations. Then averaging the  $\\mathrm{ProjD}(a_k)$  over each articulation state  $\\{a_k\\}$  yields the projection loss, i.e.,  $\\mathcal{L}_{proj} = \\frac{1}{K}\\sum_{k=1}^{K}\\mathrm{ProjD}(\\mathrm{sim}_k(a))$ . By iteratively using  $\\mathcal{L}_{proj}$  to update the global deformation coefficient  $\\mathbf{z}$  of the mesh, we can optimize the shape  $a$  to mitigate self-penetrations. At the training time,  $\\mathcal{L}_{proj}$  is used to optimize deformation coefficients  $\\mathbf{z}$  for several iterations at first (i.e., 5 iterations), followed by leveraging  $\\mathcal{L}_{phy}$  calculated on the optimized shape to update network weights. Test-Time Adaptation (TTA). During the test time, only  $\\mathcal{L}_{proj}$  is iteratively applied to refine the result (i.e., for 10 iterations).",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "859",
+        "bbox": [
+            485,
+            944,
+            509,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8a234d3cabed37f2c2f4229d437d066b068c75a3a8bfa06e51f7b993d3e0668c.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative evaluation on few-shot articulated mesh generation. For every four shapes, the leftmost one (highlighted by blue rectangles) is the reference shape from the training dataset, while the remaining three are conditionally generated samples. Object categories from top to down are Eyeglasses, Scissors, TrashCan, and Lamp respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            90,
+            885,
+            290
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/14d342b9615b66e4c21c1dd6691787665fde3885f36ca01dcfecf3958baed369.jpg",
+        "image_caption": [
+            "Figure 6. Visual evaluation on the effectiveness of the physics-aware projection strategy. For every two lines, the upper line draws shapes without such correction while the second line draws corrected shapes."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            343,
+            460,
+            750
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            800,
+            209,
+            816
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our model on 6 articulated object categories to test its few-shot generation ability for articulated objects.",
+        "bbox": [
+            76,
+            829,
+            468,
+            861
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate our method on 6 categories selected from PartNet-Mobility [37] dataset following previous stan-",
+        "bbox": [
+            76,
+            869,
+            468,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7a75397d421206be4ce7412584fd8688d96a54c2c79250ee71acdcd4a498dcd3.jpg",
+        "image_caption": [
+            "Figure 7. Visual comparison on model's target-driven deformation ability."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            509,
+            340,
+            890,
+            441
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/5f5944b61fc513dc88e3cd5126891cc20223c07ab183a5c6f5079c52657a2ae9.jpg",
+        "image_caption": [
+            "Figure 8. Visual evaluation on synchronized convex-level deformation bases. The first line draws the template shape with deformation directions of synchronized deformation bases, while the following two lines are deformed shapes by their corresponding bases. Arrows are drawn to highlight the deformation direction."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            503,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "dard [20], namely Storage Furniture, Eyeglasses, Scissors, Oven, Lamp, and TrashCan. We select 9947 instances from ShapeNet [4] dataset, covering four categories: Table, Chair, Lamp, and Airplane for convex-level deformation pre-training. For each test category, we split it into a few-shot training set with 5 instances and a test set containing the remaining instances. For more details, please refer to the supplementary material.",
+        "bbox": [
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+            630,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare our method to PolyGen [26], an auto-regressive style mesh generative model and DeepMetaHandles [21], a deformation-based mesh generative model. To further adapt them for articulated object generation, we design a part-by-part generation approach for each of them and we defer details to the supp.",
+        "bbox": [
+            496,
+            757,
+            890,
+            849
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Metrics. We employ two kinds of metrics for evaluation: 1) metrics for mesh generative models following previsou literature [21, 23, 1], that is the minimum matching dis",
+        "bbox": [
+            500,
+            854,
+            892,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "860",
+        "bbox": [
+            486,
+            945,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tance (MMD), coverage (COV), 1-NN classifier accuracy (1-NNA), and Jenson-Shannon divergence (JSD) [39]; and 2) average penetration depth (APD) for physical validity evaluation. The MMD score evaluates the fidelity of the generated samples and COV detects mode collapse and measures the diversity of generated samples. The 1-NNA score is computed by testing the generated samples and the reference instances by a 1-NN classifier. We introduce it following [23]. The classifier is not a network but classifies shapes into \"reference\" or \"training\" class based on the Nearest Neighbour. The JSD score computes the similarity between generated samples and reference samples. The APD score calculates the per-vertex average penetration depth averaged over all articulation simulation steps. We defer its details to the supp.",
+        "bbox": [
+            75,
+            90,
+            472,
+            318
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Experimental settings. The number of projections are set to 5 and 10 at the training time and the test time respectively. The number of decomposed convexes may vary across categories and is detailed in the supp.",
+        "bbox": [
+            76,
+            325,
+            468,
+            387
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Quantitative experimental evaluation: Few-shot articulated mesh generation. We summarize the quantitative evaluation results and comparisons to baseline methods on each articulated object category in Table 1. We can make the following observations: 1) We can achieve better average performance on every metric than the baseline models. It demonstrates the power of our model to generate samples with better diversity, higher visual fidelity, and better physical validity than previous models from a small number of examples. 2) On relatively rich categories (containing more than 30 instances) such as Scissors and Eyeglasses, our model can always outperform baseline methods by a large margin. It indicates that our model can cover a wider distribution space than baseline methods by only training on a few examples. 3) Our method can produce shapes with higher visual fidelity and better physical validity but not as a trade for diversity. By contrast, PolyGen generate samples that are more physically correct but exhibits very limited generative ability, i.e., poor COV and MMD scores.",
+        "bbox": [
+            75,
+            393,
+            472,
+            681
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Qualitative evaluation: Free deformation. In the free deformation setting, our model generates articulated meshes by deforming an input reference shape. It draws samples from the optimized object-level deformation coefficient distribution to deform input shapes. We draw deformed shapes from four representative categories, including Eyeglasses, Scissors, TrashCan, and Lamp in Figure 5. It demonstrates the ability of our model to create diverse variations by deforming input reference shapes. Compared with previous mesh deformation literature where the model always struggles to depict large geometry variations in the learned deformation space, our model mitigates this issue and is able to encode such deformations as observed in deformations of TrachCan bodies (line 3 of Figure 5). It mainly credits",
+        "bbox": [
+            75,
+            688,
+            472,
+            902
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "to our deformation coefficient distribution parameterization strategy, which is fit by discrete deformation coefficients, other than the uniform range adopted in [21].",
+        "bbox": [
+            496,
+            90,
+            890,
+            137
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Qualitative results: Target-driven deformation. We also conduct the target-driven experiments to demonstrate the superiority of our hierarchical deformation strategy over previous deformation literature, i.e., DeepMetaHandles [21], and Neural Cages [40]. As shown in Figure 7, our model can deform shapes to be more similar to their corresponding target shapes. It demonstrates the enhanced flexibility of our deformation strategy.",
+        "bbox": [
+            496,
+            142,
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+            265
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Convex deformation synchronization. We visualize the effectiveness of our convex deformation synchronization design by showing how synchronized deformation bases change shapes to produce plausible global mesh-level deformations in Figure 8. Besides, though not imposed directly, we do observe cross-instance similar deformation patterns, as also observed in [21].",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Physics-aware projection. We compare objects synthesized by the network directly without and with physics-aware shape optimization in Figure 6. Our shape optimization design can improve the physical validity of sampled shapes by resolving penetrations caused by either part translation (example 1 in Figure 6) or revolution (example 2,3,4), in either the body part (example 1,2) or around the joint (example 3,4).",
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+        "text": "5. Ablation Study",
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+        "text": "Transfer learning and fine-tuning for the convex-level deformation module. In the few-shot generation design, the transfer learning technique plays an important role in enriching deformation space of the target category. Meanwhile, the fine-tuning process benefits the quality and diversity by learning category-specific deformation patterns. Our further analysis demonstrates that 1) The transfer learning's power can be boosted by increasing the amount of source data and is related to the affinity between source and target categories; 2) The fine-tuning process is crucial for us to maintain high quality while achieving high diversity. We create three ablated models by ablating the transferring learning (\"Ours w/o Transfer\"), using half amount of the original data for transferring (\"Ours w/ Transfer (Half Data)\"), and ablating the fine-tuning process (\"Ours w/o Fine-tuning\") and test their performance. Observations in Table 2 can validate the importance of the transfer learning and the fine-tuning process.",
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+        "text": "Hierarchical mesh deformation. We adopt the divide-and-conquer philosophy and design a hierarchical mesh deformation strategy to learn a diverse mesh deformation space. To demonstrate its superiority over simple part-level deformation and composition, we ablate such design and treat",
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+        "text": "861",
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+        "img_path": "images/0f9a4461d5bc6690cc0fb7c9f33273aeb7fd150be402e4c98f355ee32f25b29d.jpg",
+        "table_caption": [
+            "Table 1. Quantitative evaluation. Comparison between our method and baseline models on the few-shot articulated mesh generation task. MMD is multiplied by  ${10}^{3}$  and APD is multiplied by  ${10}^{2}$  . Bold numbers for best values. \"Avg.\" means \"Average Performance\"."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Method</td><td>Storage Furniture</td><td>Scissors</td><td>Eyeglasses</td><td>Oven</td><td>Lamp</td><td>TrashCan</td><td>Avg.</td></tr><tr><td rowspan=\"3\">MMD (↓)</td><td>PolyGen [26]</td><td>4.447</td><td>3.020</td><td>8.426</td><td>7.477</td><td>12.478</td><td>9.817</td><td>7.611</td></tr><tr><td>DeepMetaHandles [21]</td><td>1.031</td><td>1.854</td><td>6.414</td><td>7.730</td><td>8.560</td><td>9.213</td><td>5.800</td></tr><tr><td>Ours</td><td>1.058</td><td>1.495</td><td>6.062</td><td>7.009</td><td>7.133</td><td>8.430</td><td>5.198</td></tr><tr><td rowspan=\"3\">COV (%, ↑)</td><td>PolyGen [26]</td><td>19.23</td><td>9.76</td><td>8.33</td><td>60.00</td><td>37.50</td><td>14.29</td><td>24.85</td></tr><tr><td>DeepMetaHandles [21]</td><td>43.93</td><td>24.63</td><td>15.00</td><td>60.00</td><td>50.00</td><td>17.14</td><td>35.12</td></tr><tr><td>Ours</td><td>75.33</td><td>57.89</td><td>29.82</td><td>60.00</td><td>62.50</td><td>17.14</td><td>50.45</td></tr><tr><td rowspan=\"3\">1-NNA (%, ↓)</td><td>PolyGen [26]</td><td>99.46</td><td>98.28</td><td>98.71</td><td>98.04</td><td>99.22</td><td>92.68</td><td>97.73</td></tr><tr><td>DeepMetaHandles [21]</td><td>97.72</td><td>98.07</td><td>98.33</td><td>98.50</td><td>94.65</td><td>86.05</td><td>95.55</td></tr><tr><td>Ours</td><td>97.76</td><td>97.02</td><td>98.26</td><td>96.59</td><td>92.44</td><td>72.09</td><td>92.36</td></tr><tr><td rowspan=\"3\">JSD (↓)</td><td>PolyGen [26]</td><td>0.0791</td><td>0.2317</td><td>0.1350</td><td>0.2044</td><td>0.2761</td><td>0.2269</td><td>0.1922</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.0697</td><td>0.2277</td><td>0.0960</td><td>0.1768</td><td>0.2172</td><td>0.1881</td><td>0.1626</td></tr><tr><td>Ours</td><td>0.0290</td><td>0.1274</td><td>0.0681</td><td>0.1597</td><td>0.1874</td><td>0.0994</td><td>0.1118</td></tr><tr><td rowspan=\"3\">APD (↓)</td><td>PolyGen [26]</td><td>0.1305</td><td>0.2592</td><td>0.0479</td><td>0.2548</td><td>5.323</td><td>0.0256</td><td>1.0068</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.2990</td><td>1.6670</td><td>0.3682</td><td>0.4408</td><td>6.3020</td><td>1.6961</td><td>1.7955</td></tr><tr><td>Ours</td><td>0.1700</td><td>1.3520</td><td>0.1707</td><td>0.1602</td><td>5.993</td><td>0.0693</td><td>1.3192</td></tr></table>",
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+        "img_path": "images/b81e262c90f39ab543fce34e817455e15262c9118ef7949e6c201efbb8b15edd.jpg",
+        "table_caption": [
+            "Table 2. Ablation study w.r.t. convex-level deformation transfer learning, hierarchical mesh generation, and physics-aware deformation correction. For metrics of each ablated version, we report their average value over all categories. MMD is multiplied by  $10^{3}$  and APD is multiplied by  $10^{2}$ . Bold numbers for best values. Italics numbers for the second-best one."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ablation Type</td><td>Method</td><td>MMD (↓)</td><td>COV (%, ↑)</td><td>1-NNA (%, ↓)</td><td>JSD (↓)</td><td>APD (↓)</td></tr><tr><td>Hierarchical deformation</td><td>Ours w/o Hier.</td><td>7.170</td><td>36.41</td><td>95.43</td><td>0.1492</td><td>1.4964</td></tr><tr><td rowspan=\"3\">Transfer learning &amp; Fine-tuning</td><td>Ours w/o Transfer</td><td>5.424</td><td>46.64</td><td>93.01</td><td>0.1159</td><td>1.3822</td></tr><tr><td>Ours w/ Transfer (Half Data)</td><td>5.201</td><td>49.43</td><td>92.81</td><td>0.1130</td><td>1.3365</td></tr><tr><td>Ours w/o Fine-tuning</td><td>6.538</td><td>43.20</td><td>94.70</td><td>0.1437</td><td>1.4530</td></tr><tr><td rowspan=\"3\">Physics-aware deformation correction</td><td>DeepMetaHandles w/ Phy.</td><td>6.980</td><td>37.20</td><td>95.69</td><td>0.1587</td><td>1.5705</td></tr><tr><td>Ours w/o Phy.</td><td>5.211</td><td>50.83</td><td>92.57</td><td>0.1060</td><td>1.8079</td></tr><tr><td>Ours w/o TTA</td><td>5.214</td><td>50.71</td><td>92.31</td><td>0.0992</td><td>1.6443</td></tr><tr><td>N/A</td><td>Ours</td><td>5.198</td><td>50.45</td><td>92.36</td><td>0.1118</td><td>1.3192</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "parts as the leaf deformation units (denoted as “Ours w/o Hier.”). As shown in Table 2, this way we observe immediate dropping of the performance on all metrics measuring the generative ability. This further evidence the value of our fine-grained decomposition and the hierarchical deformation space learning.",
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+    {
+        "type": "text",
+        "text": "Physics-aware deformation correction. We design  $\\mathcal{L}_{phy}$  and  $\\mathcal{L}_{proj}$  to provide physical supervision and perform collision response-based shape optimization respectively. This way we are able to improve the physical validity of shapes deformed by our framework. To further validate them as solid contributions and versatile strategies not only work for our method, we create the following variants and test their performance: 1) \"Ours w/o Phy\" by ablating both the shape optimization and the physical supervision, 2) \"Ours w/o TTA\" by only ablating the shape optimization strategy at the test time, and 3) \"DeepMetaHandles w/ Phy\" by integrating such two designs into the baseline DeepMetaHandles's framework. From Table 2, we can make the following observations: 1) Our physics-aware correction strategy is a versatile design that can be easily integrated into another deformation-based mesh generative model, improving its performance effectively; 2)",
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+    {
+        "type": "text",
+        "text": "Only training-time physics-aware corrections can improve physical-related performance by guiding the convex-level deformation module stably and effectively; 3) Further imposing test time optimizations is important for us to arrive at high-quality samples finally.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion and Limitations",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We tackle the few-shot articulated mesh generation problem with 1) a hierarchical deformation model with transfer learning; and 2) a deformation correction scheme.",
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+    {
+        "type": "text",
+        "text": "Limitations. Currently, our work is limited to a category-level setting with the articulation chain and the range of articulation states assumed known. Developing a generation method without such assumption would increase its practical value and is an interesting future research direction. Besides, the deformation correction scheme relies on handcrafted chain of articulation states to detect self-penetrations and optimize shapes based on that. A natural alternative can be detecting articulation states from real-world images. Moreover, the quality of our generated results are restricted by that of the training data. A smart self-correction strategy, beyond mitigating self-penetrations only, may be designed to improve the validity.",
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+    {
+        "type": "text",
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.197,
+                0.131,
+                0.777,
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+            "angle": 0,
+            "content": "Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.203,
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+            "angle": 0,
+            "content": "Xueyi Liu\\(^{1,5}\\), Bin Wang\\(^{2}\\), He Wang\\(^{3}\\), Li Yi\\(^{1,4,5}\\)  \n\\(^{1}\\)Tsinghua University \\(^{2}\\)Beijing Institute for General Artificial Intelligence \\(^{3}\\)Peking University \\(^{4}\\)Shanghai Artificial Intelligence Laboratory \\(^{5}\\)Shanghai Qi Zhi Institute"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.326,
+                0.474,
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+            ],
+            "angle": 0,
+            "content": "We study the problem of few-shot physically-aware articulated mesh generation. By observing an articulated object dataset containing only a few examples, we wish to learn a model that can generate diverse meshes with high visual fidelity and physical validity. Previous mesh generative models either have difficulties in depicting a diverse data space from only a few examples or fail to ensure physical validity of their samples. Regarding the above challenges, we propose two key innovations, including 1) a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy to alleviate the few-shot challenge by borrowing transferrable deformation patterns from large scale rigid meshes and 2) a physics-aware deformation correction scheme to encourage physically plausible generations. We conduct extensive experiments on 6 articulated categories to demonstrate the superiority of our method in generating articulated meshes with better diversity, higher visual fidelity, and better physical validity over previous methods in the few-shot setting. Further, we validate solid contributions of our two innovations in the ablation study. Project page with code is available at meowuu7.github.io/few-arti-object-gen."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.692,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
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+            ],
+            "angle": 0,
+            "content": "Generative models have aroused a wide spectrum of interests in recent years for their creativity and broad downstream application scenarios [29, 30, 34, 17, 8, 26]. Specific to 3D generation, a variety of techniques such as denoising diffusion [23, 42, 6, 39] have also been discussed for a while. Among them, mesh generation is indeed important since the mesh representation can support a wider range of downstream applications such as rendering and physical simulation compared to other representations such as point clouds. Existing works mainly focus on generating meshes for whole objects [8, 26, 6, 19, 30] considering without modeling object functionalities at all. Besides, they"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.519,
+                0.294,
+                0.88,
+                0.425
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.43,
+                0.895,
+                0.515
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview. We present a hierarchical mesh deformation-based generative model to solve the challenging yet important few-shot physically-aware articulated mesh generation problem. It tackles the few-shot challenge by borrowing shared convex level deformation patterns from large-scale rigid meshes and incorporates a deformation correction scheme to further enhance the model's ability to generate physically realistic meshes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.52,
+                0.895,
+                0.702
+            ],
+            "angle": 0,
+            "content": "mainly rely on reconstructing meshes from other kinds of representations such as implicit fields [8, 6, 19] instead of generating meshes directly. In this work, we go one step further and consider mesh generation for articulated objects that can support physically realistic articulations. This not only helps understand the object distribution in real-world assets, but also allows an intelligent agent to learn segmenting [20, 22], tracking [36], reasoning [10] and manipulating [38] articulated objects through a simulation environment. We focus on the articulated mesh generative model that can generate object meshes with diverse geometry, high visual fidelity, and correct physics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.896,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Training a generative model on publicly available articulated mesh datasets to depict a diverse physically-plausible data space not limited to training assets presents two main challenges to the methodology. First, existing articulated object datasets are usually very restricted in scale. For example, the PartNet-Mobility Dataset [37] contains an average of 51 meshes per category. This naturally requires a few-shot generative model to learn from a very limited number of meshes. Adapting previous approaches immediately without carefully considering the few-shot nature would lead to models suffering from poor generative ability. Second, we need to pursue physically plausible generation to ensure the generated meshes are not only visu-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.945,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "854"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.092,
+                0.468,
+                0.137
+            ],
+            "angle": 0,
+            "content": "ally appealing but also functionally sound to support correction articulation functions, i.e., attached parts without self-penetrations in the full articulation range."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.14,
+                0.468,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Despite recent advancements in mesh generation community such as a wide variety of models proposed in existing works [8, 41, 6, 33, 19], they are typically challenged by the following difficulties and always fail to solve our problem: 1) Lack of the ability to learn a wide data space not limited to training shapes in the few-shot setting. 2) Difficulty in modeling crucial object-level shape constraints imposed by the functionality of articulated objects. Failure to consider these requirements would result in physically unrealistic samples [8, 6, 26]. Modeling such physical constraints for articulated meshes is a non-trivial task, as it requires accounting for diverse penetration phenomena caused by different types of articulation motions. To our best knowledge, we are the first that presents a valid framework to address such two difficulties for articulated mesh generation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.385,
+                0.468,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Our work designs a hierarchical mesh deformation-based generative model that tackles the aforementioned challenges using two key innovations: (1) Hierarchical mesh deformation with transfer learning. We introduce an object-convex shape hierarchy and learn the hierarchical articulated mesh generative model. The model is trained by first learning the deformation-based generative model at the leaf convex level and then synchronizing individual convex-level deformation spaces at the root level. We identify that different categories tend to share convex-level deformation patterns and leverage this insight to learn and transfer rich deformation prior from large-scale rigid datasets to expand the model's generative capacity. (2) Physics-aware deformation correction. To address self-penetrations of deformed articulated meshes during mesh articulation, we further introduce a deformation correction scheme. It is composed of an auxiliary loss penalizing self-penetrations during mesh articulation and a collision response-based shape optimization strategy. By integrating this scheme into the hierarchical mesh deformation model, we successfully guide the model to generate more physically realistic deformations, resulting in physically correct articulated meshes finally."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.72,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "We conduct extensive experiments on 6 categories from the PartNet-Mobility dataset [37] for evaluation. As demonstrated by both the quantitative and qualitative results, we can consistently outperform all baseline methods regarding the fidelity, diversity and physical plausibility of generated meshes, e.g., an average of \\(10.4\\%\\) higher coverage ratio, \\(43.7\\%\\) lower minimum matching distance score, and \\(26.5\\%\\) lower collision score. Ablation studies further validate the value of our design in deformation pattern transfer learning, the hierarchical mesh generation approach, and the effectiveness as well as the versatility of our physics-aware correction scheme."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.891,
+                0.332
+            ],
+            "angle": 0,
+            "content": "Our key contributions are as follows: (1) We present the first solution, to our best knowledge, for the challenging yet important few-shot physically-aware articulated mesh generation problem with two effective and non-trivial technical innovations. (2) We propose a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy. This design allows us to learn a diverse data space by borrowing shared deformation patterns from large-scale rigid object datasets. (3) We propose a physics-aware deformation correction scheme to encourage the hierarchical generative model to produce physically realistic deformations, resulting in improved physical validity of the generated samples. This scheme can also be effectively integrated into other deformation-based mesh generative models, thereby enhancing the physical validity of their samples as well."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.348,
+                0.647,
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+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.381,
+                0.891,
+                0.758
+            ],
+            "angle": 0,
+            "content": "Mesh generative models. There have been vast and long efforts in devising 3D mesh generative models [26, 8, 41, 6, 21, 35]. Their techniques can be mainly categorized into three genres: 1) direct surface generation [26], 2) deformation-based mesh generation [21, 35], and 3) hybrid representation-based generation [8, 41]. Though methods of the first type exhibit obvious merits such as synthesizing high-quality n-gon meshes, they always suffer from limited generative ability and cannot scale for complex objects. In contrast, deformation-style mesh generation models deform source shapes for new samples which naturally spares the efforts for mesh structure generation, while restricted by poor flexibility. The third strategy separates the mesh surface structure generation problem from the content generation, which offers them with powerful generative ability. However, the quality of their samples is coupled with the power of their surface reconstruction techniques [27, 31]. In this work, we leverage mesh deformation as our generation technique for articulated mesh synthesis, taking advantages of its ability to produce high-quality samples. Instead of deforming whole objects or parts directly, we design a hierarchical deformation strategy to enhance the deformation flexibility and to enrich the data space by borrowing deformation patterns shared across categories from large scale rigid meshes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.765,
+                0.891,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Few-shot generation. Along with the flourishing image generative models emerged in recent years, the few-shot image generation has been widely explored as well [12, 9, 11, 13, 2]. It wishes to create more data given only a few examples from a novel category that is both diverse in content and semantically consistent with the target category. At the high level, their basic philosophy is to design proper approaches such that the model can benefit from large base datasets for generation, like local fusion [9], latent vari-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.488,
+                0.947,
+                0.51,
+                0.957
+            ],
+            "angle": 0,
+            "content": "855"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.259
+            ],
+            "angle": 0,
+            "content": "ables matching [11, 3]. adversarial delta matching [12]. In this work, we leverage transfer learning to adapt shape patterns from large-scale rigid datasets to target articulated categories. Devising methods in this way requires us to find correct intermediates on which shape patterns are cross-category transferrable. Instead of directly using whole objects or articulated parts, we choose convexes as such intermediates. Transferring knowledge at this level presents further difficulties in fusing them together in a geometrically consistent way and in synthesizing physically realistic meshes while maintaining visual diversity at the same time."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.266,
+                0.473,
+                0.524
+            ],
+            "angle": 0,
+            "content": "Physics-aware machine learning. Our work is also related to physics-aware machine learning [28, 10, 14, 24, 32, 25, 18], and mostly relevant to physically-aware generative models. To ensure physical validity of generated shapes, typical solutions choose either offline simulations for training data filtering [32] or online simulations leveraging the development of differentiable simulators [7, 15, 16] or by designing online simulation layers [24]. Generating physically-plausible articulated objects presents new challenges considering self-penetrations during mesh articulation that are more complex than stability issues caused by gravity for rigid objects. Our method integrates the physical supervision and a shape optimization strategy. The optimization transforms part shapes to resolve self-penetration issues. High-dimensional and complex shape deformations are involved in the process, different from linear fixing operations considered in [10]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.541,
+                0.17,
+                0.556
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.567,
+                0.47,
+                0.764
+            ],
+            "angle": 0,
+            "content": "The problem we are targeting is the few-shot physically-aware articulated mesh generation. Given a set of articulated meshes from the category of interest, we would like to learn a conditional generative model which could deform an articulated mesh from the same category into a wide variety of shapes. This conditional generation setup allows generating a large number of physically-plausible articulated meshes from a few examples while avoiding the need to generate the mesh structure. However, it leaves several challenges to address including how to accurately represent complex shape deformation spaces from a few examples and how to ensure that the generated meshes support physically-realistic articulations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Regarding the first challenge, our idea is to learn the deformation space via borrowing knowledge from other object categories. This seemingly simple idea is not trivial to realize though since we need to figure out what knowledge is transferrable. We present a hierarchical mesh deformation strategy to allow deformation prior to transfer at a local convex segment level while still maintaining the deformation consistency at the global shape level. Regarding the second challenge, we introduce a physics-aware deforma"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "tion correction scheme to avoid unwanted artifacts such as self-penetrations during mesh articulation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.123,
+                0.894,
+                0.185
+            ],
+            "angle": 0,
+            "content": "In the following, we will provide a pipeline overview in Section 3.1. Then we will explain our hierarchical mesh deformation strategy and our physics-aware deformation correction scheme in Section 3.2 and Section 3.3 respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.196,
+                0.611,
+                0.211
+            ],
+            "angle": 0,
+            "content": "3.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.22,
+                0.895,
+                0.536
+            ],
+            "angle": 0,
+            "content": "Given a small set of articulated meshes \\(\\mathcal{A}\\) from a certain category of interest with the same number of parts and joints, sharing a known kinematic chain, our method wishes to learn a conditional generative model depicting a diverse and plausible articulated shape space. We adopt the divide-and-conquer philosophy and develop a hierarchical deformation scheme with transfer learning to tackle the difficulty of few-shot generation. Instead of learning at the whole shape level, we structure each articulated shape into an object-convex hierarchy and solve the generation problem via two steps. We first learn a generative model depicting a diverse shape space at the lowest convex level by borrowing common shape patterns from large rigid mesh datasets, denoted as \\(\\mathcal{B}\\). Convexes, with small cross-category distribution gap, serve as good intermediates for transferring common shape prior. After that, we devise a synchronization strategy that composes convex deformations consistently to form valid object shapes. Besides, a physics-aware correction scheme is developed to avoid physically-unnatural phenomena such as self-penetrations. Our overall pipeline is shown in Figure 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.538,
+                0.895,
+                0.75
+            ],
+            "angle": 0,
+            "content": "Specifically, we first decompose the conditional mesh \\(a\\) into approximately convex segments \\(\\mathcal{C}_a\\), forming an object-convex hierarchy. Then, on the leaf level, we learn to deform each convex \\(c \\in \\mathcal{C}_a\\) through a convex-level conditional generative model \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) where \\(\\mathbf{z}_c\\) is the noise parameter corresponding to convex \\(c\\). Finally, on the root level, we synchronize the convex deformations by replacing the convex-dependent noise parameter \\(\\mathbf{z}_c\\) with \\(S_c\\mathbf{z}\\), where \\(S_c\\) is a linear transformation and \\(\\mathbf{z}\\) is a synchronized noise parameter shared among all convexes. This aligns the noise space of different convexes to form a coherent deformation for the whole mesh. The above hierarchical deformation strategy can be mathematically represented as \\(g(\\mathbf{z}|a) = \\{g_{\\mathcal{C}}(S_c\\mathbf{z}|c)|c \\in \\mathcal{C}_a\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.751,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "During the training time, we first leverage existing unsupervised shape segmentation tools BSP-Net [5] to decompose meshes in both \\(\\mathcal{A}\\) and \\(\\mathcal{B}\\) into approximately convex segments \\(\\mathcal{C}_{\\mathcal{A}}\\) and \\(\\mathcal{C}_{\\mathcal{B}}\\). Since BSP-Net decomposes shapes consistently for each category, we can naturally identify corresponding convexes within \\(\\mathcal{C}_{\\mathcal{A}}\\) or \\(\\mathcal{C}_{\\mathcal{B}}\\). We can then pretrain a convex-level conditional generative model \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) on \\(\\mathcal{C}_{\\mathcal{B}}\\) modeling how corresponding convexes could deform into each other among the large-scale rigid meshes. We then fine-tune the pre-trained model \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) on convexes"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "856"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.09,
+                0.891,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.222,
+                0.894,
+                0.296
+            ],
+            "angle": 0,
+            "content": "Figure 2. Framework overview for our few-shot physically-aware articulated mesh generation. In this figure, yellow blocks represent modules with learnable weights optimized during pre-training. Orange blocks contain weights optimized during fine-tuning. Gray blocks contain no learnable weights. Convexes of the same color are of the same type. Our framework consists of a hierarchical mesh deformation scheme that learns and transfers diverse shared deformation patterns from large-scale rigid datasets at the convex level. We also propose a convex deformation synchronization strategy to combine individual convex-level deformation spaces into the object-level space. Furthermore, we introduce a physics-aware deformation correction strategy to address self-penetrations in synthesized articulated meshes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.319,
+                0.473,
+                0.485
+            ],
+            "angle": 0,
+            "content": "in \\(\\mathcal{C}_A\\) and at the same time estimate the noise synchronization transformation \\(S_{c}\\). We further exploit an additional physics-aware deformation correction scheme to improve the physical validity of generated articulated shapes. It consists of 1) an auxiliary loss penalizing self-penetrations to provide physical supervision and 2) a collision response-based shape optimization strategy to encourage the model to generate physically realistic meshes. The auxiliary loss is incorporated into the training pipeline. While the shape optimization scheme functions at both the training time and the test time."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.494,
+                0.358,
+                0.509
+            ],
+            "angle": 0,
+            "content": "3.2. Hierarchical Mesh Deformation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.517,
+                0.47,
+                0.715
+            ],
+            "angle": 0,
+            "content": "Given an input articulated mesh \\( a \\) and its corresponding approximately convex segments \\( C_a \\), our hierarchical mesh deformation model \\( g(\\mathbf{z}|a) = \\{g_{\\mathcal{C}}(S_c\\mathbf{z}|c)|c \\in C_a\\} \\) consists of a convex-level conditional generative model \\( g_{\\mathcal{C}} \\) as well as a series of synchronization transformations \\( \\{S_c\\} \\). We propose to learn the model at the lowest convex level \\( g_C \\) following a transfer learning paradigm so that convex-level shape patterns can easily transfer across different categories. Given a reference mesh \\( a \\), the hierarchical deformation first synthesizes new convex shapes via \\( g_C \\). A deformation synchronization strategy is developed to handle the resulting deformation inconsistency issue across different convexes to form a valid object shape."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.469,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Convex-level conditional generative model. We propose to leverage mesh deformation to characterize the convex-level conditional generative model. For a convex mesh segment \\(c\\) containing \\(N_{c}\\) vertices, the conditional generative model \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) should be able to produce diverse and realistic vertex-level deformation offset \\(\\mathbf{d}_c \\in \\mathbb{R}^{N_c \\times 3}\\) when we sample different noise parameters \\(\\mathbf{z}_c\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The convex deformation \\(\\mathbf{d}_c\\) lies in a high-dimensional space which varies from convex to convex, prohibiting the knowledge transfer across different convexes. We therefore reparametrize \\(\\mathbf{d}_c\\) using two tricks inspired by [40, 21]: 1) using cages to control per-vertex deformation; 2) using dic"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.32,
+                0.843,
+                0.334
+            ],
+            "angle": 0,
+            "content": "tionaries to record the common deformation modes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.336,
+                0.892,
+                0.501
+            ],
+            "angle": 0,
+            "content": "In particular, for each convex \\( c \\), we use a coarse triangle mesh (a cage) \\( t_c \\) enclosing \\( c \\) to control the deformation of convex \\( c \\) [40]. The cage \\( t_c \\) usually contains much less vertices compared with the convex \\( c \\) so that its distribution is easier to be modeled. The deformation \\( \\mathbf{d}_c \\) of the convex \\( c \\) can be easily computed as a linear transformation of the deformation \\( \\mathbf{d}_{t_c} \\) of cage \\( t_c \\): \\( \\mathbf{d}_c = \\Phi_c\\mathbf{d}_{t_c} \\). Here \\( \\Phi_c \\) is an interpolation matrix based upon the generalized barycentric coordinates of convex \\( c \\) with respect to cage \\( t_c \\). We deform a template mesh based upon the shape of each convex to form the cages which we defer the details to supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.502,
+                0.893,
+                0.653
+            ],
+            "angle": 0,
+            "content": "To further reduce the deformation parametrization, we represent the cage deformation \\(\\mathbf{d}_{t_c}\\) as a linear combination of \\(K\\) deformation bases \\(B_{c} = [\\mathbf{b}_{c}^{1}\\dots \\mathbf{b}_{c}^{K}]\\) as \\(\\mathbf{d}_{t_c} = B_c\\mathbf{z}_c\\) where \\(\\mathbf{z}_c\\) is a \\(K\\)-dimensional deformation coefficient. Here each deformation basis \\(\\mathbf{b}_c\\) represents a common deformation pattern and all the bases span the deformation space of cage \\(t_c\\) and therefore convex \\(c\\). Representing deformation spaces via deformation bases can effectively reduce the dimension of shape space compared to other alternatively such as utilizing latent vectors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "A few-shot deformation learning paradigm. Given the above deformation reparametrizations, learning the convex-level conditional generative model for each convex \\(c\\) boils down to learning the deformation bases \\(B_{c}\\) as well as the distribution of deformation coefficient \\(\\mathbf{z}_c\\). For deformation bases, we employ a neural network \\(\\psi_{\\theta}(\\cdot)\\) to predict from convex shapes. It takes a given convex \\(c\\) as input and outputs its deformation bases, i.e., \\(B_{c} = \\psi_{\\theta}(c)\\). We then optimize the deformation coefficient \\(\\mathbf{z}_c^{\\hat{c}}\\) for each convex \\(\\hat{c}\\) in correspondence to \\(c\\) from the current available dataset. The distribution of \\(\\mathbf{z}_c\\) is then a mixture of Gaussian fit by the resulting deformation coefficients \\(\\{\\mathbf{z}_c^{\\hat{c}}\\}\\). We further leverage a transfer learning approach that transfers deformation priors learned in large-scale rigid dataset to target datasets at the convex level based on the observation that the convex-level deformations usually show similar patterns across cat-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.945,
+                0.511,
+                0.956
+            ],
+            "angle": 0,
+            "content": "857"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "egories, e.g., a slab gets thicker or a strip gets elongated. Therefore we can learn a diverse deformation space from a few examples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.137,
+                0.474,
+                0.41
+            ],
+            "angle": 0,
+            "content": "We pre-train \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) on the large-scale rigid mesh dataset \\(\\mathcal{B}\\) and fine-tune it on each target articulated dataset \\(\\mathcal{A}\\). In particular, at the pre-training time, given a set of rigid meshes \\(\\mathcal{B}\\) from large-scale online repositories as well as the corresponding convexes \\(\\mathcal{C}_{\\mathcal{B}}\\), we first identify pairs of convexes in correspondence \\(\\{(c,\\hat{c})|c,\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}\\) from the same-category shapes, e.g., the noses of two different airplanes. These correspondences come as a result of some off-the-shelf unsupervised co-segmentation algorithms [5]. We then optimize \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) by alternatively optimizing the deformation coefficient set \\(\\{\\mathbf{z}_c^{\\hat{c}}|c,\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}\\), and the neural network \\(\\psi_{\\theta}(\\cdot)\\). To optimize \\(\\{\\mathbf{z}_c^{\\hat{c}}\\}\\), we fix \\(\\{B_c\\}\\) and optimize each \\(\\mathbf{z}_c^{\\hat{c}}\\) by minimizing the Chamfer Distance (CD), also denoted as \\(d_{\\mathrm{CD}}(\\cdot ,\\cdot)\\), between the deformed convex \\(c\\) and the target \\(\\hat{c}\\). Then we optimize \\(\\{B_c\\}\\) by fixing deformation coefficients \\(\\{\\mathbf{z}_c^{\\hat{c}}\\}\\) and minimizing average CD between deformed \\(c\\) and the target \\(\\hat{c}\\) for each pair \\((c,\\hat{c})\\), which leads to the convex deformation loss \\(\\mathcal{L}_C\\) at the training time:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.124,
+                0.417,
+                0.47,
+                0.455
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {C} = \\frac {1}{| \\mathcal {C} _ {\\mathcal {B}} |} \\sum_ {c, \\hat {c} \\in \\mathcal {C} _ {\\mathcal {B}}} d _ {\\mathrm {C D}} \\left(g _ {\\mathcal {C}} \\left(\\mathbf {z} _ {c} \\mid c, \\mathbf {z} _ {c} = \\mathbf {z} _ {c} ^ {\\hat {c}}\\right), \\hat {c}\\right). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.464,
+                0.471,
+                0.555
+            ],
+            "angle": 0,
+            "content": "After the above alternative optimization, the distribution of \\(\\mathbf{z}_c\\) for each convex \\(c\\) is modeled by a mixture of Gaussian distribution fit to the final coefficient set \\(\\{z_c^{\\hat{c}}|\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}\\). At the fine-tuning time, \\(g_{\\mathcal{C}}(\\mathbf{z}|c)\\) is further optimized via the same procedure by the convex correspondence set \\(\\mathcal{C}_{\\mathcal{A}}\\) of the target dataset \\(\\mathcal{A}\\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.568,
+                0.451,
+                0.734
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.739,
+                0.47,
+                0.798
+            ],
+            "angle": 0,
+            "content": "Figure 3. Synchronization Process. The left part illustrates the decomposed convexes and source cages of the input eyeglass frame. The right part visualize synchronization matrices (a \\(4 \\times 4\\) matrix here for each cage), cages deformed by bases before synchronization (left two columns), and cages deformed by synchronized bases (right two columns)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.797,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Convex deformation synchronization. After learning the conditional generative model for each convex \\(c\\), the next step is to compose all the deformation spaces for the whole mesh \\(a\\). Since for each convex \\(c\\), \\(g_{\\mathcal{C}}(\\mathbf{z}_c|c)\\) exploits a separate set of deformation bases \\(B_{c}\\), the noise parameter \\(\\mathbf{z}_c\\) varies its meaning from convex to convex. As a result, if we draw independent noise parameters for each convex, the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.893,
+                0.168
+            ],
+            "angle": 0,
+            "content": "outcoming deformations could easily contradict with each other, failing the whole mesh-level deformation. To tackle this issue, we synchronize different deformation bases \\( B_{c} \\) with linear transformations \\( S_{c} \\) so that a single noise parameter \\( \\mathbf{z} \\) can be shared across all convexes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.178,
+                0.895,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Formally speaking, given a set of articulated object meshes \\(\\mathcal{A}\\) from a certain category and an articulated mesh \\(a\\in \\mathcal{A}\\), assuming the mesh is segmented into \\(M\\) convexes \\(\\{c_m\\}_{m = 1}^M\\) and each convex is equipped with a deformation model \\(g_{\\mathcal{C}}(\\mathbf{z}_{c_m}|c_m)\\), our goal is to replace \\(\\mathbf{z}_{c_m}\\) with \\(S_{c_m}\\mathbf{z}\\) so that sampling the shared noise parameter \\(\\mathbf{z}\\) results in a globally consistent mesh deformation. To compute the synchronization transformation \\(S_{c_m}\\), we consider the deformation from \\(a\\) to other articulated meshes \\(a^i\\in \\mathcal{A}\\). In particular, for each \\(a^i\\), we optimize for a set of deformation coefficients \\(\\{\\mathbf{y}_m^i\\}\\) so that each convex \\(c_m\\) in mesh \\(a\\) could deform into the corresponding convex \\(c_m^i\\) in mesh \\(a^i\\) following the deformation model \\(g_{\\mathcal{C}}(\\mathbf{z}_{c_m}|c_m,\\mathbf{z}_{c_m} = \\mathbf{y}_m^i)\\). We can then estimate the synchronization transformations \\(\\{S_{c_m}\\}\\) by solving the following optimization problem:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.545,
+                0.436,
+                0.892,
+                0.48
+            ],
+            "angle": 0,
+            "content": "\\[\n\\underset {\\{S _ {c _ {m}} \\}, \\{\\mathbf {z} ^ {i} \\}} {\\text {m i n i m i z e}} \\sum_ {i = 1} ^ {| \\mathcal {A} |} \\sum_ {m = 1} ^ {M} \\| B _ {c _ {m}} S _ {c _ {m}} \\mathbf {z} ^ {i} - B _ {c _ {m}} \\mathbf {y} _ {m} ^ {i} \\| _ {2}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.512,
+                0.893,
+                0.604
+            ],
+            "angle": 0,
+            "content": "where \\(B_{c_m}\\) is the deformation bases of convex \\(c_{m}\\) and \\(\\mathbf{z}^i\\) is a global deformation coefficient from mesh \\(a\\) to \\(a^i\\) shared across all convexes. We solve the above optimization problem via alternatively optimizing the synchronization transformations \\(\\{S_{c_m}\\}\\) and the global deformation coefficients \\(\\{\\mathbf{z}^i\\}\\):"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.613,
+                0.892,
+                0.689
+            ],
+            "angle": 0,
+            "content": "Fix \\(\\{S_{c_m}\\}\\), optimize each global deformation coefficient \\(\\mathbf{z}^i\\) from \\(a\\) to \\(a^i\\) via Algorithm 2. It takes the convex deformation bases \\(\\{B_{c_m}\\}\\), current synchronization transformations \\(\\{S_{c_m}\\}\\), convex deformation coefficients \\(\\{\\mathbf{y}_m^i\\}\\) as input, and outputs the optimized \\(\\mathbf{z}^i\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.689,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Fix \\(\\{\\mathbf{z}^i\\}\\), optimize each synchronization transformation \\(S_{c_m}\\) for each convex \\(c_m\\) via Algorithm 1. It takes the convex deformation bases \\(\\{B_{c_m}\\}\\), current global deformation coefficients \\(\\{\\mathbf{z}^i\\}\\), convex deformation coefficients \\(\\{\\mathbf{y}_m^i\\}\\) as input, and outputs the optimized \\(S_{c_m}\\)."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.613,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.508,
+                0.804,
+                0.551,
+                0.814
+            ],
+            "angle": 0,
+            "content": "w/ Sync."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.816,
+                0.552,
+                0.839
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.559,
+                0.801,
+                0.616,
+                0.842
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.56,
+                0.845,
+                0.62,
+                0.855
+            ],
+            "angle": 0,
+            "content": "Source Shape"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.632,
+                0.8,
+                0.695,
+                0.842
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.635,
+                0.845,
+                0.697,
+                0.855
+            ],
+            "angle": 0,
+            "content": "Convex Cages"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.801,
+                0.764,
+                0.842
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.709,
+                0.845,
+                0.781,
+                0.855
+            ],
+            "angle": 0,
+            "content": "Deformed Cages"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.786,
+                0.802,
+                0.866,
+                0.842
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.791,
+                0.845,
+                0.854,
+                0.855
+            ],
+            "angle": 0,
+            "content": "Deformed Part"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.861,
+                0.892,
+                0.899
+            ],
+            "angle": 0,
+            "content": "Figure 4. Synchronization's Effectiveness. The synchronized deformation bases can consistently transform each convex for a valid part shape (upper row), while those before the synchronization fail (bottom row)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "858"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.468,
+                0.12
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Synchronization transformation matrices optimization."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.078,
+                0.123,
+                0.468,
+                0.171
+            ],
+            "angle": 0,
+            "content": "Input: Deformation bases for each convex \\(\\{B_{c_m}\\}\\). Global deformation coefficients \\(\\{\\mathbf{z}^i\\}\\) from \\(a\\) to other articulated meshes \\(\\{a^i\\}\\). Deformation coefficients \\(\\{\\mathbf{y}_m^i\\}\\) from each convex \\(c_m\\) to the corresponding convex of the articulated mesh \\(a^i\\)."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.078,
+                0.172,
+                0.463,
+                0.184
+            ],
+            "angle": 0,
+            "content": "Output: Synchronization transformation matrix \\(S_{c_m}\\) of the convex \\(c_{m}\\)."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.085,
+                0.184,
+                0.203,
+                0.197
+            ],
+            "angle": 0,
+            "content": "1: \\(\\mathbf{Z} \\gets \\operatorname{Stack}(\\{\\mathbf{z}^i\\})\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.085,
+                0.197,
+                0.223,
+                0.209
+            ],
+            "angle": 0,
+            "content": "2: \\(\\mathbf{Y}_m\\gets \\mathrm{Stack}(\\{\\mathbf{y}_m^i\\})\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.208,
+                0.236,
+                0.22
+            ],
+            "angle": 0,
+            "content": "3: \\([\\mathbf{U},\\pmb {\\Sigma},\\mathbf{V}^T ]\\gets \\mathrm{SVD}(\\mathbf{Z})\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.22,
+                0.276,
+                0.233
+            ],
+            "angle": 0,
+            "content": "4: \\([\\mathbf{U}_m, \\mathbf{\\Sigma}_m, \\mathbf{V}_m^T] \\gets \\mathrm{SVD}(\\mathbf{Y}_m)\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.232,
+                0.276,
+                0.245
+            ],
+            "angle": 0,
+            "content": "5: \\(S_{c_m}\\gets \\mathbf{U}_m\\Sigma_m\\mathbf{V}_m^T\\mathbf{V}\\Sigma^+ \\mathbf{U}^T\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.245,
+                0.167,
+                0.256
+            ],
+            "angle": 0,
+            "content": "6: return \\( S_{c_m} \\)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.078,
+                0.123,
+                0.468,
+                0.256
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.288,
+                0.468,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Algorithm 2 Global deformation coefficients optimization. \"lsq\" denotes the least square solver."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.078,
+                0.321,
+                0.468,
+                0.357
+            ],
+            "angle": 0,
+            "content": "Input: Deformation bases for each convex \\(\\{B_{c_m}\\}\\). Synchronization transformations \\(\\{S_{c_m}\\}\\). Deformation coefficients \\(\\mathbf{y}_m^i\\) from each convex \\(c_m\\) to the corresponding convex of the articulated mesh \\(a^i\\)."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.079,
+                0.358,
+                0.385,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Output: Global deformation coefficients \\(\\mathbf{z}^i\\) from \\(a\\) to \\(a^i\\)."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.369,
+                0.153,
+                0.383
+            ],
+            "angle": 0,
+            "content": "1: \\(\\mathcal{S}_{\\mathbf{z}^i}\\gets \\emptyset\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.382,
+                0.21,
+                0.393
+            ],
+            "angle": 0,
+            "content": "2: for \\(m = 1\\) to \\(M\\) do"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.393,
+                0.239,
+                0.406
+            ],
+            "angle": 0,
+            "content": "3: \\(\\hat{\\mathbf{z}}_m^i\\gets \\mathrm{lsq}(S_{c_m},\\mathbf{z}_m^i)\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.406,
+                0.233,
+                0.419
+            ],
+            "angle": 0,
+            "content": "4: \\(\\mathcal{S}_{\\mathbf{z}^i}\\gets \\mathcal{S}_{\\mathbf{z}^i}\\cup \\{\\hat{\\mathbf{z}}_m^i\\}\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.419,
+                0.208,
+                0.433
+            ],
+            "angle": 0,
+            "content": "5: \\(\\mathbf{z}^i = \\mathrm{Average}(S_{\\mathbf{Z}^i})\\)"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.086,
+                0.433,
+                0.155,
+                0.443
+            ],
+            "angle": 0,
+            "content": "6: return \\(\\mathbf{z}^i\\)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.078,
+                0.321,
+                0.468,
+                0.443
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.463,
+                0.468,
+                0.583
+            ],
+            "angle": 0,
+            "content": "As an intuitive illustration of the synchronization process, we select the example of synchronizing the eyeglass frame's convex deformations (with 2 convexes and 4 deformation bases for each convex) and visualize the process (detailed to the cage level) in Figure 3. The synchronized deformation bases can transform two convexes more consistently and symmetrically than those before synchronization (an example on deformed part shapes is shown in Figure 4)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.584,
+                0.468,
+                0.644
+            ],
+            "angle": 0,
+            "content": "After deformation synchronization, the distribution of the shared noise parameter \\(\\mathbf{z}\\) can be simply set as a mixture of Gaussian fit to the optimized global deformation coefficients \\(\\{\\mathbf{z}^i\\}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.651,
+                0.415,
+                0.667
+            ],
+            "angle": 0,
+            "content": "3.3. Physics-Aware Deformation Correction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Based upon the above design, our hierarchical deformation model can then synthesize a deformed mesh \\(a\\) via the noise parameter \\(\\mathbf{z}\\) by taking a source articulated mesh as input. However, we may frequently observe physically unnatural self-penetrations when articulating \\(a\\). To encourage the model to produce physically valid articulated meshes, we further propose a physics-aware deformation correction scheme, which serves two purposes: 1) to optimize the weights of the generative model to produce deformations that are more physically realistic and 2) to optimize the shape \\(a\\) to improve its physical validity. To accomplish this, we draw inspiration from previous works on stable rigid object generation [24, 25] and develop an online articulation simulation process that places \\(a\\) into \\(K\\) different articulation states sequentially, denoted as \\(\\operatorname{Sim}(a) = \\{a_k\\}_{k=1}^K\\). The"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "articulation state sequence is designed by hand particularly for each category. We then utilize the physical supervision and a shape optimization strategy to guide the network to generate physically realistic articulated meshes. We will elaborate them in the following text."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.191,
+                0.892,
+                0.36
+            ],
+            "angle": 0,
+            "content": "Physical supervision. To provide physical supervision for articulated mesh generative models requires us to design stability signals to measure physically unstable phenomena, for which we mainly consider self-penetrations during mesh articulation. We therefore devise a metric named average penetration depth (APD) measuring the magnitude of each vertex penetrating through other parts during the articulation simulation process. It is also referred as \\(\\mathcal{L}_{phy}\\) when we treat it as a loss. Formally, \\(\\mathcal{L}_{phy} = \\frac{1}{K}\\sum_{k=1}^{K}\\mathrm{PeneD}(a_k)\\), where \\(\\mathrm{PeneD}(a_k)\\) measures self-penetrations in a single articulation state. We defer details of \\(\\mathcal{L}_{phy}\\) to the supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.377,
+                0.892,
+                0.59
+            ],
+            "angle": 0,
+            "content": "One way to provide physical guidance for the network is to utilize the physical stability signal \\(\\mathcal{L}_{phy}\\) as an auxiliary loss to supervise the network training. However, physically unnatural phenomena of articulated meshes during mesh articulation are more diverse and complex than that of rigid objects caused by diverse part geometric appearance and wide articulation variations. Directly exploring physical supervision to guide the network optimization is not sufficient to regularize the network to produce physically realistic deformations. Therefore we further develop a collision response-based shape optimization strategy to improve the physical realism of the generated mesh \\(a\\). Then we first optimize \\(a\\) for several times to reduce self-penetrations and then use it to calculate \\(\\mathcal{L}_{phy}\\) for network optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.612,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Collision response-based shape optimization. To realize the vision of resolving self-penetrations via optimizing shapes, we draw inspirations from collision response strategies and devise a heuristic penetration resolving strategy that projects penetrated vertices onto the surface of the mesh. To guide such projection, we devise an algorithm that calculates \\(\\mathrm{ProjD}(a)\\) whose gradient over each penetrated vertex in \\(a\\) informs how to project it to resolve penetrations. Then averaging the \\(\\mathrm{ProjD}(a_k)\\) over each articulation state \\(\\{a_k\\}\\) yields the projection loss, i.e., \\(\\mathcal{L}_{proj} = \\frac{1}{K}\\sum_{k=1}^{K}\\mathrm{ProjD}(\\mathrm{sim}_k(a))\\). By iteratively using \\(\\mathcal{L}_{proj}\\) to update the global deformation coefficient \\(\\mathbf{z}\\) of the mesh, we can optimize the shape \\(a\\) to mitigate self-penetrations. At the training time, \\(\\mathcal{L}_{proj}\\) is used to optimize deformation coefficients \\(\\mathbf{z}\\) for several iterations at first (i.e., 5 iterations), followed by leveraging \\(\\mathcal{L}_{phy}\\) calculated on the optimized shape to update network weights. Test-Time Adaptation (TTA). During the test time, only \\(\\mathcal{L}_{proj}\\) is iteratively applied to refine the result (i.e., for 10 iterations)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.945,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "859"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.092,
+                0.887,
+                0.291
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.294,
+                0.893,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative evaluation on few-shot articulated mesh generation. For every four shapes, the leftmost one (highlighted by blue rectangles) is the reference shape from the training dataset, while the remaining three are conditionally generated samples. Object categories from top to down are Eyeglasses, Scissors, TrashCan, and Lamp respectively."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.085,
+                0.344,
+                0.462,
+                0.75
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.753,
+                0.47,
+                0.793
+            ],
+            "angle": 0,
+            "content": "Figure 6. Visual evaluation on the effectiveness of the physics-aware projection strategy. For every two lines, the upper line draws shapes without such correction while the second line draws corrected shapes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.801,
+                0.21,
+                0.818
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.83,
+                0.47,
+                0.862
+            ],
+            "angle": 0,
+            "content": "We evaluate our model on 6 articulated object categories to test its few-shot generation ability for articulated objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Datasets. We evaluate our method on 6 categories selected from PartNet-Mobility [37] dataset following previous stan-"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.51,
+                0.342,
+                0.891,
+                0.442
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.447,
+                0.893,
+                0.472
+            ],
+            "angle": 0,
+            "content": "Figure 7. Visual comparison on model's target-driven deformation ability."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.474,
+                0.885,
+                0.554
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.564,
+                0.892,
+                0.626
+            ],
+            "angle": 0,
+            "content": "Figure 8. Visual evaluation on synchronized convex-level deformation bases. The first line draws the template shape with deformation directions of synchronized deformation bases, while the following two lines are deformed shapes by their corresponding bases. Arrows are drawn to highlight the deformation direction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.631,
+                0.893,
+                0.752
+            ],
+            "angle": 0,
+            "content": "dard [20], namely Storage Furniture, Eyeglasses, Scissors, Oven, Lamp, and TrashCan. We select 9947 instances from ShapeNet [4] dataset, covering four categories: Table, Chair, Lamp, and Airplane for convex-level deformation pre-training. For each test category, we split it into a few-shot training set with 5 instances and a test set containing the remaining instances. For more details, please refer to the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.758,
+                0.892,
+                0.85
+            ],
+            "angle": 0,
+            "content": "Baselines. We compare our method to PolyGen [26], an auto-regressive style mesh generative model and DeepMetaHandles [21], a deformation-based mesh generative model. To further adapt them for articulated object generation, we design a part-by-part generation approach for each of them and we defer details to the supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.856,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Metrics. We employ two kinds of metrics for evaluation: 1) metrics for mesh generative models following previsou literature [21, 23, 1], that is the minimum matching dis"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.487,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "860"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.319
+            ],
+            "angle": 0,
+            "content": "tance (MMD), coverage (COV), 1-NN classifier accuracy (1-NNA), and Jenson-Shannon divergence (JSD) [39]; and 2) average penetration depth (APD) for physical validity evaluation. The MMD score evaluates the fidelity of the generated samples and COV detects mode collapse and measures the diversity of generated samples. The 1-NNA score is computed by testing the generated samples and the reference instances by a 1-NN classifier. We introduce it following [23]. The classifier is not a network but classifies shapes into \"reference\" or \"training\" class based on the Nearest Neighbour. The JSD score computes the similarity between generated samples and reference samples. The APD score calculates the per-vertex average penetration depth averaged over all articulation simulation steps. We defer its details to the supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.327,
+                0.47,
+                0.388
+            ],
+            "angle": 0,
+            "content": "Experimental settings. The number of projections are set to 5 and 10 at the training time and the test time respectively. The number of decomposed convexes may vary across categories and is detailed in the supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.395,
+                0.473,
+                0.683
+            ],
+            "angle": 0,
+            "content": "Quantitative experimental evaluation: Few-shot articulated mesh generation. We summarize the quantitative evaluation results and comparisons to baseline methods on each articulated object category in Table 1. We can make the following observations: 1) We can achieve better average performance on every metric than the baseline models. It demonstrates the power of our model to generate samples with better diversity, higher visual fidelity, and better physical validity than previous models from a small number of examples. 2) On relatively rich categories (containing more than 30 instances) such as Scissors and Eyeglasses, our model can always outperform baseline methods by a large margin. It indicates that our model can cover a wider distribution space than baseline methods by only training on a few examples. 3) Our method can produce shapes with higher visual fidelity and better physical validity but not as a trade for diversity. By contrast, PolyGen generate samples that are more physically correct but exhibits very limited generative ability, i.e., poor COV and MMD scores."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Qualitative evaluation: Free deformation. In the free deformation setting, our model generates articulated meshes by deforming an input reference shape. It draws samples from the optimized object-level deformation coefficient distribution to deform input shapes. We draw deformed shapes from four representative categories, including Eyeglasses, Scissors, TrashCan, and Lamp in Figure 5. It demonstrates the ability of our model to create diverse variations by deforming input reference shapes. Compared with previous mesh deformation literature where the model always struggles to depict large geometry variations in the learned deformation space, our model mitigates this issue and is able to encode such deformations as observed in deformations of TrachCan bodies (line 3 of Figure 5). It mainly credits"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.138
+            ],
+            "angle": 0,
+            "content": "to our deformation coefficient distribution parameterization strategy, which is fit by discrete deformation coefficients, other than the uniform range adopted in [21]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.143,
+                0.895,
+                0.266
+            ],
+            "angle": 0,
+            "content": "Qualitative results: Target-driven deformation. We also conduct the target-driven experiments to demonstrate the superiority of our hierarchical deformation strategy over previous deformation literature, i.e., DeepMetaHandles [21], and Neural Cages [40]. As shown in Figure 7, our model can deform shapes to be more similar to their corresponding target shapes. It demonstrates the enhanced flexibility of our deformation strategy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.27,
+                0.895,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Convex deformation synchronization. We visualize the effectiveness of our convex deformation synchronization design by showing how synchronized deformation bases change shapes to produce plausible global mesh-level deformations in Figure 8. Besides, though not imposed directly, we do observe cross-instance similar deformation patterns, as also observed in [21]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.382,
+                0.895,
+                0.504
+            ],
+            "angle": 0,
+            "content": "Physics-aware projection. We compare objects synthesized by the network directly without and with physics-aware shape optimization in Figure 6. Our shape optimization design can improve the physical validity of sampled shapes by resolving penetrations caused by either part translation (example 1 in Figure 6) or revolution (example 2,3,4), in either the body part (example 1,2) or around the joint (example 3,4)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.516,
+                0.652,
+                0.533
+            ],
+            "angle": 0,
+            "content": "5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.547,
+                0.895,
+                0.821
+            ],
+            "angle": 0,
+            "content": "Transfer learning and fine-tuning for the convex-level deformation module. In the few-shot generation design, the transfer learning technique plays an important role in enriching deformation space of the target category. Meanwhile, the fine-tuning process benefits the quality and diversity by learning category-specific deformation patterns. Our further analysis demonstrates that 1) The transfer learning's power can be boosted by increasing the amount of source data and is related to the affinity between source and target categories; 2) The fine-tuning process is crucial for us to maintain high quality while achieving high diversity. We create three ablated models by ablating the transferring learning (\"Ours w/o Transfer\"), using half amount of the original data for transferring (\"Ours w/ Transfer (Half Data)\"), and ablating the fine-tuning process (\"Ours w/o Fine-tuning\") and test their performance. Observations in Table 2 can validate the importance of the transfer learning and the fine-tuning process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Hierarchical mesh deformation. We adopt the divide-and-conquer philosophy and design a hierarchical mesh deformation strategy to learn a diverse mesh deformation space. To demonstrate its superiority over simple part-level deformation and composition, we ablate such design and treat"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "861"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.088,
+                0.894,
+                0.113
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative evaluation. Comparison between our method and baseline models on the few-shot articulated mesh generation task. MMD is multiplied by \\( {10}^{3} \\) and APD is multiplied by \\( {10}^{2} \\) . Bold numbers for best values. \"Avg.\" means \"Average Performance\"."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.157,
+                0.115,
+                0.807,
+                0.346
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Method</td><td>Storage Furniture</td><td>Scissors</td><td>Eyeglasses</td><td>Oven</td><td>Lamp</td><td>TrashCan</td><td>Avg.</td></tr><tr><td rowspan=\"3\">MMD (↓)</td><td>PolyGen [26]</td><td>4.447</td><td>3.020</td><td>8.426</td><td>7.477</td><td>12.478</td><td>9.817</td><td>7.611</td></tr><tr><td>DeepMetaHandles [21]</td><td>1.031</td><td>1.854</td><td>6.414</td><td>7.730</td><td>8.560</td><td>9.213</td><td>5.800</td></tr><tr><td>Ours</td><td>1.058</td><td>1.495</td><td>6.062</td><td>7.009</td><td>7.133</td><td>8.430</td><td>5.198</td></tr><tr><td rowspan=\"3\">COV (%, ↑)</td><td>PolyGen [26]</td><td>19.23</td><td>9.76</td><td>8.33</td><td>60.00</td><td>37.50</td><td>14.29</td><td>24.85</td></tr><tr><td>DeepMetaHandles [21]</td><td>43.93</td><td>24.63</td><td>15.00</td><td>60.00</td><td>50.00</td><td>17.14</td><td>35.12</td></tr><tr><td>Ours</td><td>75.33</td><td>57.89</td><td>29.82</td><td>60.00</td><td>62.50</td><td>17.14</td><td>50.45</td></tr><tr><td rowspan=\"3\">1-NNA (%, ↓)</td><td>PolyGen [26]</td><td>99.46</td><td>98.28</td><td>98.71</td><td>98.04</td><td>99.22</td><td>92.68</td><td>97.73</td></tr><tr><td>DeepMetaHandles [21]</td><td>97.72</td><td>98.07</td><td>98.33</td><td>98.50</td><td>94.65</td><td>86.05</td><td>95.55</td></tr><tr><td>Ours</td><td>97.76</td><td>97.02</td><td>98.26</td><td>96.59</td><td>92.44</td><td>72.09</td><td>92.36</td></tr><tr><td rowspan=\"3\">JSD (↓)</td><td>PolyGen [26]</td><td>0.0791</td><td>0.2317</td><td>0.1350</td><td>0.2044</td><td>0.2761</td><td>0.2269</td><td>0.1922</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.0697</td><td>0.2277</td><td>0.0960</td><td>0.1768</td><td>0.2172</td><td>0.1881</td><td>0.1626</td></tr><tr><td>Ours</td><td>0.0290</td><td>0.1274</td><td>0.0681</td><td>0.1597</td><td>0.1874</td><td>0.0994</td><td>0.1118</td></tr><tr><td rowspan=\"3\">APD (↓)</td><td>PolyGen [26]</td><td>0.1305</td><td>0.2592</td><td>0.0479</td><td>0.2548</td><td>5.323</td><td>0.0256</td><td>1.0068</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.2990</td><td>1.6670</td><td>0.3682</td><td>0.4408</td><td>6.3020</td><td>1.6961</td><td>1.7955</td></tr><tr><td>Ours</td><td>0.1700</td><td>1.3520</td><td>0.1707</td><td>0.1602</td><td>5.993</td><td>0.0693</td><td>1.3192</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.358,
+                0.895,
+                0.394
+            ],
+            "angle": 0,
+            "content": "Table 2. Ablation study w.r.t. convex-level deformation transfer learning, hierarchical mesh generation, and physics-aware deformation correction. For metrics of each ablated version, we report their average value over all categories. MMD is multiplied by \\(10^{3}\\) and APD is multiplied by \\(10^{2}\\). Bold numbers for best values. Italics numbers for the second-best one."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.137,
+                0.395,
+                0.828,
+                0.523
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Ablation Type</td><td>Method</td><td>MMD (↓)</td><td>COV (%, ↑)</td><td>1-NNA (%, ↓)</td><td>JSD (↓)</td><td>APD (↓)</td></tr><tr><td>Hierarchical deformation</td><td>Ours w/o Hier.</td><td>7.170</td><td>36.41</td><td>95.43</td><td>0.1492</td><td>1.4964</td></tr><tr><td rowspan=\"3\">Transfer learning &amp; Fine-tuning</td><td>Ours w/o Transfer</td><td>5.424</td><td>46.64</td><td>93.01</td><td>0.1159</td><td>1.3822</td></tr><tr><td>Ours w/ Transfer (Half Data)</td><td>5.201</td><td>49.43</td><td>92.81</td><td>0.1130</td><td>1.3365</td></tr><tr><td>Ours w/o Fine-tuning</td><td>6.538</td><td>43.20</td><td>94.70</td><td>0.1437</td><td>1.4530</td></tr><tr><td rowspan=\"3\">Physics-aware deformation correction</td><td>DeepMetaHandles w/ Phy.</td><td>6.980</td><td>37.20</td><td>95.69</td><td>0.1587</td><td>1.5705</td></tr><tr><td>Ours w/o Phy.</td><td>5.211</td><td>50.83</td><td>92.57</td><td>0.1060</td><td>1.8079</td></tr><tr><td>Ours w/o TTA</td><td>5.214</td><td>50.71</td><td>92.31</td><td>0.0992</td><td>1.6443</td></tr><tr><td>N/A</td><td>Ours</td><td>5.198</td><td>50.45</td><td>92.36</td><td>0.1118</td><td>1.3192</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.537,
+                0.471,
+                0.628
+            ],
+            "angle": 0,
+            "content": "parts as the leaf deformation units (denoted as “Ours w/o Hier.”). As shown in Table 2, this way we observe immediate dropping of the performance on all metrics measuring the generative ability. This further evidence the value of our fine-grained decomposition and the hierarchical deformation space learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Physics-aware deformation correction. We design \\(\\mathcal{L}_{phy}\\) and \\(\\mathcal{L}_{proj}\\) to provide physical supervision and perform collision response-based shape optimization respectively. This way we are able to improve the physical validity of shapes deformed by our framework. To further validate them as solid contributions and versatile strategies not only work for our method, we create the following variants and test their performance: 1) \"Ours w/o Phy\" by ablating both the shape optimization and the physical supervision, 2) \"Ours w/o TTA\" by only ablating the shape optimization strategy at the test time, and 3) \"DeepMetaHandles w/ Phy\" by integrating such two designs into the baseline DeepMetaHandles's framework. From Table 2, we can make the following observations: 1) Our physics-aware correction strategy is a versatile design that can be easily integrated into another deformation-based mesh generative model, improving its performance effectively; 2)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.537,
+                0.892,
+                0.613
+            ],
+            "angle": 0,
+            "content": "Only training-time physics-aware corrections can improve physical-related performance by guiding the convex-level deformation module stably and effectively; 3) Further imposing test time optimizations is important for us to arrive at high-quality samples finally."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.625,
+                0.757,
+                0.642
+            ],
+            "angle": 0,
+            "content": "6. Conclusion and Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.651,
+                0.892,
+                0.696
+            ],
+            "angle": 0,
+            "content": "We tackle the few-shot articulated mesh generation problem with 1) a hierarchical deformation model with transfer learning; and 2) a deformation correction scheme."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.697,
+                0.892,
+                0.893
+            ],
+            "angle": 0,
+            "content": "Limitations. Currently, our work is limited to a category-level setting with the articulation chain and the range of articulation states assumed known. Developing a generation method without such assumption would increase its practical value and is an interesting future research direction. Besides, the deformation correction scheme relies on handcrafted chain of articulation states to detect self-penetrations and optimize shapes based on that. A natural alternative can be detecting articulation states from real-world images. Moreover, the quality of our generated results are restricted by that of the training data. A smart self-correction strategy, beyond mitigating self-penetrations only, may be designed to improve the validity."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "862"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.087,
+                0.116,
+                0.47,
+                0.171
+            ],
+            "angle": 0,
+            "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. PMLR, 2018. 7"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "[2] Antreas Antoniou, Amos Storkey, and Harrison Edwards. Data augmentation generative adversarial networks. arXiv preprint arXiv:1711.04340, 2017. 2"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "[3] Sergey Bartunov and Dmitry Vetrov. Few-shot generative modelling with generative matching networks. In International Conference on Artificial Intelligence and Statistics, pages 670-678. PMLR, 2018. 3"
+        },
+        {
+            "type": "ref_text",
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+# Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation
+
+Xueyi Liu $^{1,5}$ , Bin Wang $^{2}$ , He Wang $^{3}$ , Li Yi $^{1,4,5}$ $^{1}$ Tsinghua University  $^{2}$ Beijing Institute for General Artificial Intelligence  $^{3}$ Peking University  $^{4}$ Shanghai Artificial Intelligence Laboratory  $^{5}$ Shanghai Qi Zhi Institute
+
+# Abstract
+
+We study the problem of few-shot physically-aware articulated mesh generation. By observing an articulated object dataset containing only a few examples, we wish to learn a model that can generate diverse meshes with high visual fidelity and physical validity. Previous mesh generative models either have difficulties in depicting a diverse data space from only a few examples or fail to ensure physical validity of their samples. Regarding the above challenges, we propose two key innovations, including 1) a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy to alleviate the few-shot challenge by borrowing transferrable deformation patterns from large scale rigid meshes and 2) a physics-aware deformation correction scheme to encourage physically plausible generations. We conduct extensive experiments on 6 articulated categories to demonstrate the superiority of our method in generating articulated meshes with better diversity, higher visual fidelity, and better physical validity over previous methods in the few-shot setting. Further, we validate solid contributions of our two innovations in the ablation study. Project page with code is available at meowuu7.github.io/few-arti-object-gen.
+
+# 1. Introduction
+
+Generative models have aroused a wide spectrum of interests in recent years for their creativity and broad downstream application scenarios [29, 30, 34, 17, 8, 26]. Specific to 3D generation, a variety of techniques such as denoising diffusion [23, 42, 6, 39] have also been discussed for a while. Among them, mesh generation is indeed important since the mesh representation can support a wider range of downstream applications such as rendering and physical simulation compared to other representations such as point clouds. Existing works mainly focus on generating meshes for whole objects [8, 26, 6, 19, 30] considering without modeling object functionalities at all. Besides, they
+
+![](images/d27d6e24dc041b1cc8763128cff191cda9cb6f8f5c5f2244cccac707976f8e10.jpg)  
+Figure 1. Overview. We present a hierarchical mesh deformation-based generative model to solve the challenging yet important few-shot physically-aware articulated mesh generation problem. It tackles the few-shot challenge by borrowing shared convex level deformation patterns from large-scale rigid meshes and incorporates a deformation correction scheme to further enhance the model's ability to generate physically realistic meshes.
+
+mainly rely on reconstructing meshes from other kinds of representations such as implicit fields [8, 6, 19] instead of generating meshes directly. In this work, we go one step further and consider mesh generation for articulated objects that can support physically realistic articulations. This not only helps understand the object distribution in real-world assets, but also allows an intelligent agent to learn segmenting [20, 22], tracking [36], reasoning [10] and manipulating [38] articulated objects through a simulation environment. We focus on the articulated mesh generative model that can generate object meshes with diverse geometry, high visual fidelity, and correct physics.
+
+Training a generative model on publicly available articulated mesh datasets to depict a diverse physically-plausible data space not limited to training assets presents two main challenges to the methodology. First, existing articulated object datasets are usually very restricted in scale. For example, the PartNet-Mobility Dataset [37] contains an average of 51 meshes per category. This naturally requires a few-shot generative model to learn from a very limited number of meshes. Adapting previous approaches immediately without carefully considering the few-shot nature would lead to models suffering from poor generative ability. Second, we need to pursue physically plausible generation to ensure the generated meshes are not only visu-
+
+ally appealing but also functionally sound to support correction articulation functions, i.e., attached parts without self-penetrations in the full articulation range.
+
+Despite recent advancements in mesh generation community such as a wide variety of models proposed in existing works [8, 41, 6, 33, 19], they are typically challenged by the following difficulties and always fail to solve our problem: 1) Lack of the ability to learn a wide data space not limited to training shapes in the few-shot setting. 2) Difficulty in modeling crucial object-level shape constraints imposed by the functionality of articulated objects. Failure to consider these requirements would result in physically unrealistic samples [8, 6, 26]. Modeling such physical constraints for articulated meshes is a non-trivial task, as it requires accounting for diverse penetration phenomena caused by different types of articulation motions. To our best knowledge, we are the first that presents a valid framework to address such two difficulties for articulated mesh generation.
+
+Our work designs a hierarchical mesh deformation-based generative model that tackles the aforementioned challenges using two key innovations: (1) Hierarchical mesh deformation with transfer learning. We introduce an object-convex shape hierarchy and learn the hierarchical articulated mesh generative model. The model is trained by first learning the deformation-based generative model at the leaf convex level and then synchronizing individual convex-level deformation spaces at the root level. We identify that different categories tend to share convex-level deformation patterns and leverage this insight to learn and transfer rich deformation prior from large-scale rigid datasets to expand the model's generative capacity. (2) Physics-aware deformation correction. To address self-penetrations of deformed articulated meshes during mesh articulation, we further introduce a deformation correction scheme. It is composed of an auxiliary loss penalizing self-penetrations during mesh articulation and a collision response-based shape optimization strategy. By integrating this scheme into the hierarchical mesh deformation model, we successfully guide the model to generate more physically realistic deformations, resulting in physically correct articulated meshes finally.
+
+We conduct extensive experiments on 6 categories from the PartNet-Mobility dataset [37] for evaluation. As demonstrated by both the quantitative and qualitative results, we can consistently outperform all baseline methods regarding the fidelity, diversity and physical plausibility of generated meshes, e.g., an average of  $10.4\%$  higher coverage ratio,  $43.7\%$  lower minimum matching distance score, and  $26.5\%$  lower collision score. Ablation studies further validate the value of our design in deformation pattern transfer learning, the hierarchical mesh generation approach, and the effectiveness as well as the versatility of our physics-aware correction scheme.
+
+Our key contributions are as follows: (1) We present the first solution, to our best knowledge, for the challenging yet important few-shot physically-aware articulated mesh generation problem with two effective and non-trivial technical innovations. (2) We propose a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy. This design allows us to learn a diverse data space by borrowing shared deformation patterns from large-scale rigid object datasets. (3) We propose a physics-aware deformation correction scheme to encourage the hierarchical generative model to produce physically realistic deformations, resulting in improved physical validity of the generated samples. This scheme can also be effectively integrated into other deformation-based mesh generative models, thereby enhancing the physical validity of their samples as well.
+
+# 2. Related Works
+
+Mesh generative models. There have been vast and long efforts in devising 3D mesh generative models [26, 8, 41, 6, 21, 35]. Their techniques can be mainly categorized into three genres: 1) direct surface generation [26], 2) deformation-based mesh generation [21, 35], and 3) hybrid representation-based generation [8, 41]. Though methods of the first type exhibit obvious merits such as synthesizing high-quality n-gon meshes, they always suffer from limited generative ability and cannot scale for complex objects. In contrast, deformation-style mesh generation models deform source shapes for new samples which naturally spares the efforts for mesh structure generation, while restricted by poor flexibility. The third strategy separates the mesh surface structure generation problem from the content generation, which offers them with powerful generative ability. However, the quality of their samples is coupled with the power of their surface reconstruction techniques [27, 31]. In this work, we leverage mesh deformation as our generation technique for articulated mesh synthesis, taking advantages of its ability to produce high-quality samples. Instead of deforming whole objects or parts directly, we design a hierarchical deformation strategy to enhance the deformation flexibility and to enrich the data space by borrowing deformation patterns shared across categories from large scale rigid meshes.
+
+Few-shot generation. Along with the flourishing image generative models emerged in recent years, the few-shot image generation has been widely explored as well [12, 9, 11, 13, 2]. It wishes to create more data given only a few examples from a novel category that is both diverse in content and semantically consistent with the target category. At the high level, their basic philosophy is to design proper approaches such that the model can benefit from large base datasets for generation, like local fusion [9], latent vari-
+
+ables matching [11, 3]. adversarial delta matching [12]. In this work, we leverage transfer learning to adapt shape patterns from large-scale rigid datasets to target articulated categories. Devising methods in this way requires us to find correct intermediates on which shape patterns are cross-category transferrable. Instead of directly using whole objects or articulated parts, we choose convexes as such intermediates. Transferring knowledge at this level presents further difficulties in fusing them together in a geometrically consistent way and in synthesizing physically realistic meshes while maintaining visual diversity at the same time.
+
+Physics-aware machine learning. Our work is also related to physics-aware machine learning [28, 10, 14, 24, 32, 25, 18], and mostly relevant to physically-aware generative models. To ensure physical validity of generated shapes, typical solutions choose either offline simulations for training data filtering [32] or online simulations leveraging the development of differentiable simulators [7, 15, 16] or by designing online simulation layers [24]. Generating physically-plausible articulated objects presents new challenges considering self-penetrations during mesh articulation that are more complex than stability issues caused by gravity for rigid objects. Our method integrates the physical supervision and a shape optimization strategy. The optimization transforms part shapes to resolve self-penetration issues. High-dimensional and complex shape deformations are involved in the process, different from linear fixing operations considered in [10].
+
+# 3. Method
+
+The problem we are targeting is the few-shot physically-aware articulated mesh generation. Given a set of articulated meshes from the category of interest, we would like to learn a conditional generative model which could deform an articulated mesh from the same category into a wide variety of shapes. This conditional generation setup allows generating a large number of physically-plausible articulated meshes from a few examples while avoiding the need to generate the mesh structure. However, it leaves several challenges to address including how to accurately represent complex shape deformation spaces from a few examples and how to ensure that the generated meshes support physically-realistic articulations.
+
+Regarding the first challenge, our idea is to learn the deformation space via borrowing knowledge from other object categories. This seemingly simple idea is not trivial to realize though since we need to figure out what knowledge is transferrable. We present a hierarchical mesh deformation strategy to allow deformation prior to transfer at a local convex segment level while still maintaining the deformation consistency at the global shape level. Regarding the second challenge, we introduce a physics-aware deforma
+
+tion correction scheme to avoid unwanted artifacts such as self-penetrations during mesh articulation.
+
+In the following, we will provide a pipeline overview in Section 3.1. Then we will explain our hierarchical mesh deformation strategy and our physics-aware deformation correction scheme in Section 3.2 and Section 3.3 respectively.
+
+# 3.1. Overview
+
+Given a small set of articulated meshes  $\mathcal{A}$  from a certain category of interest with the same number of parts and joints, sharing a known kinematic chain, our method wishes to learn a conditional generative model depicting a diverse and plausible articulated shape space. We adopt the divide-and-conquer philosophy and develop a hierarchical deformation scheme with transfer learning to tackle the difficulty of few-shot generation. Instead of learning at the whole shape level, we structure each articulated shape into an object-convex hierarchy and solve the generation problem via two steps. We first learn a generative model depicting a diverse shape space at the lowest convex level by borrowing common shape patterns from large rigid mesh datasets, denoted as  $\mathcal{B}$ . Convexes, with small cross-category distribution gap, serve as good intermediates for transferring common shape prior. After that, we devise a synchronization strategy that composes convex deformations consistently to form valid object shapes. Besides, a physics-aware correction scheme is developed to avoid physically-unnatural phenomena such as self-penetrations. Our overall pipeline is shown in Figure 2.
+
+Specifically, we first decompose the conditional mesh  $a$  into approximately convex segments  $\mathcal{C}_a$ , forming an object-convex hierarchy. Then, on the leaf level, we learn to deform each convex  $c \in \mathcal{C}_a$  through a convex-level conditional generative model  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  where  $\mathbf{z}_c$  is the noise parameter corresponding to convex  $c$ . Finally, on the root level, we synchronize the convex deformations by replacing the convex-dependent noise parameter  $\mathbf{z}_c$  with  $S_c\mathbf{z}$ , where  $S_c$  is a linear transformation and  $\mathbf{z}$  is a synchronized noise parameter shared among all convexes. This aligns the noise space of different convexes to form a coherent deformation for the whole mesh. The above hierarchical deformation strategy can be mathematically represented as  $g(\mathbf{z}|a) = \{g_{\mathcal{C}}(S_c\mathbf{z}|c)|c \in \mathcal{C}_a\}$ .
+
+During the training time, we first leverage existing unsupervised shape segmentation tools BSP-Net [5] to decompose meshes in both  $\mathcal{A}$  and  $\mathcal{B}$  into approximately convex segments  $\mathcal{C}_{\mathcal{A}}$  and  $\mathcal{C}_{\mathcal{B}}$ . Since BSP-Net decomposes shapes consistently for each category, we can naturally identify corresponding convexes within  $\mathcal{C}_{\mathcal{A}}$  or  $\mathcal{C}_{\mathcal{B}}$ . We can then pretrain a convex-level conditional generative model  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  on  $\mathcal{C}_{\mathcal{B}}$  modeling how corresponding convexes could deform into each other among the large-scale rigid meshes. We then fine-tune the pre-trained model  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  on convexes
+
+![](images/64d4c1ef1c5bb34c7b522513594b93a023e121e8daf6e36356f2ef138e6dee81.jpg)  
+Figure 2. Framework overview for our few-shot physically-aware articulated mesh generation. In this figure, yellow blocks represent modules with learnable weights optimized during pre-training. Orange blocks contain weights optimized during fine-tuning. Gray blocks contain no learnable weights. Convexes of the same color are of the same type. Our framework consists of a hierarchical mesh deformation scheme that learns and transfers diverse shared deformation patterns from large-scale rigid datasets at the convex level. We also propose a convex deformation synchronization strategy to combine individual convex-level deformation spaces into the object-level space. Furthermore, we introduce a physics-aware deformation correction strategy to address self-penetrations in synthesized articulated meshes.
+
+in  $\mathcal{C}_A$  and at the same time estimate the noise synchronization transformation  $S_{c}$ . We further exploit an additional physics-aware deformation correction scheme to improve the physical validity of generated articulated shapes. It consists of 1) an auxiliary loss penalizing self-penetrations to provide physical supervision and 2) a collision response-based shape optimization strategy to encourage the model to generate physically realistic meshes. The auxiliary loss is incorporated into the training pipeline. While the shape optimization scheme functions at both the training time and the test time.
+
+# 3.2. Hierarchical Mesh Deformation
+
+Given an input articulated mesh  $a$  and its corresponding approximately convex segments  $C_a$ , our hierarchical mesh deformation model  $g(\mathbf{z}|a) = \{g_{\mathcal{C}}(S_c\mathbf{z}|c)|c \in C_a\}$  consists of a convex-level conditional generative model  $g_{\mathcal{C}}$  as well as a series of synchronization transformations  $\{S_c\}$ . We propose to learn the model at the lowest convex level  $g_C$  following a transfer learning paradigm so that convex-level shape patterns can easily transfer across different categories. Given a reference mesh  $a$ , the hierarchical deformation first synthesizes new convex shapes via  $g_C$ . A deformation synchronization strategy is developed to handle the resulting deformation inconsistency issue across different convexes to form a valid object shape.
+
+Convex-level conditional generative model. We propose to leverage mesh deformation to characterize the convex-level conditional generative model. For a convex mesh segment  $c$  containing  $N_{c}$  vertices, the conditional generative model  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  should be able to produce diverse and realistic vertex-level deformation offset  $\mathbf{d}_c \in \mathbb{R}^{N_c \times 3}$  when we sample different noise parameters  $\mathbf{z}_c$ .
+
+The convex deformation  $\mathbf{d}_c$  lies in a high-dimensional space which varies from convex to convex, prohibiting the knowledge transfer across different convexes. We therefore reparametrize  $\mathbf{d}_c$  using two tricks inspired by [40, 21]: 1) using cages to control per-vertex deformation; 2) using dic
+
+tionaries to record the common deformation modes.
+
+In particular, for each convex  $c$ , we use a coarse triangle mesh (a cage)  $t_c$  enclosing  $c$  to control the deformation of convex  $c$  [40]. The cage  $t_c$  usually contains much less vertices compared with the convex  $c$  so that its distribution is easier to be modeled. The deformation  $\mathbf{d}_c$  of the convex  $c$  can be easily computed as a linear transformation of the deformation  $\mathbf{d}_{t_c}$  of cage  $t_c$ :  $\mathbf{d}_c = \Phi_c\mathbf{d}_{t_c}$ . Here  $\Phi_c$  is an interpolation matrix based upon the generalized barycentric coordinates of convex  $c$  with respect to cage  $t_c$ . We deform a template mesh based upon the shape of each convex to form the cages which we defer the details to supp.
+
+To further reduce the deformation parametrization, we represent the cage deformation  $\mathbf{d}_{t_c}$  as a linear combination of  $K$  deformation bases  $B_{c} = [\mathbf{b}_{c}^{1}\dots \mathbf{b}_{c}^{K}]$  as  $\mathbf{d}_{t_c} = B_c\mathbf{z}_c$  where  $\mathbf{z}_c$  is a  $K$ -dimensional deformation coefficient. Here each deformation basis  $\mathbf{b}_c$  represents a common deformation pattern and all the bases span the deformation space of cage  $t_c$  and therefore convex  $c$ . Representing deformation spaces via deformation bases can effectively reduce the dimension of shape space compared to other alternatively such as utilizing latent vectors.
+
+A few-shot deformation learning paradigm. Given the above deformation reparametrizations, learning the convex-level conditional generative model for each convex  $c$  boils down to learning the deformation bases  $B_{c}$  as well as the distribution of deformation coefficient  $\mathbf{z}_c$ . For deformation bases, we employ a neural network  $\psi_{\theta}(\cdot)$  to predict from convex shapes. It takes a given convex  $c$  as input and outputs its deformation bases, i.e.,  $B_{c} = \psi_{\theta}(c)$ . We then optimize the deformation coefficient  $\mathbf{z}_c^{\hat{c}}$  for each convex  $\hat{c}$  in correspondence to  $c$  from the current available dataset. The distribution of  $\mathbf{z}_c$  is then a mixture of Gaussian fit by the resulting deformation coefficients  $\{\mathbf{z}_c^{\hat{c}}\}$ . We further leverage a transfer learning approach that transfers deformation priors learned in large-scale rigid dataset to target datasets at the convex level based on the observation that the convex-level deformations usually show similar patterns across cat-
+
+egories, e.g., a slab gets thicker or a strip gets elongated. Therefore we can learn a diverse deformation space from a few examples.
+
+We pre-train  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  on the large-scale rigid mesh dataset  $\mathcal{B}$  and fine-tune it on each target articulated dataset  $\mathcal{A}$ . In particular, at the pre-training time, given a set of rigid meshes  $\mathcal{B}$  from large-scale online repositories as well as the corresponding convexes  $\mathcal{C}_{\mathcal{B}}$ , we first identify pairs of convexes in correspondence  $\{(c,\hat{c})|c,\hat{c}\in \mathcal{C}_{\mathcal{B}}\}$  from the same-category shapes, e.g., the noses of two different airplanes. These correspondences come as a result of some off-the-shelf unsupervised co-segmentation algorithms [5]. We then optimize  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  by alternatively optimizing the deformation coefficient set  $\{\mathbf{z}_c^{\hat{c}}|c,\hat{c}\in \mathcal{C}_{\mathcal{B}}\}$ , and the neural network  $\psi_{\theta}(\cdot)$ . To optimize  $\{\mathbf{z}_c^{\hat{c}}\}$ , we fix  $\{B_c\}$  and optimize each  $\mathbf{z}_c^{\hat{c}}$  by minimizing the Chamfer Distance (CD), also denoted as  $d_{\mathrm{CD}}(\cdot ,\cdot)$ , between the deformed convex  $c$  and the target  $\hat{c}$ . Then we optimize  $\{B_c\}$  by fixing deformation coefficients  $\{\mathbf{z}_c^{\hat{c}}\}$  and minimizing average CD between deformed  $c$  and the target  $\hat{c}$  for each pair  $(c,\hat{c})$ , which leads to the convex deformation loss  $\mathcal{L}_C$  at the training time:
+
+$$
+\mathcal {L} _ {C} = \frac {1}{| \mathcal {C} _ {\mathcal {B}} |} \sum_ {c, \hat {c} \in \mathcal {C} _ {\mathcal {B}}} d _ {\mathrm {C D}} \left(g _ {\mathcal {C}} \left(\mathbf {z} _ {c} \mid c, \mathbf {z} _ {c} = \mathbf {z} _ {c} ^ {\hat {c}}\right), \hat {c}\right). \tag {1}
+$$
+
+After the above alternative optimization, the distribution of  $\mathbf{z}_c$  for each convex  $c$  is modeled by a mixture of Gaussian distribution fit to the final coefficient set  $\{z_c^{\hat{c}}|\hat{c}\in \mathcal{C}_{\mathcal{B}}\}$ . At the fine-tuning time,  $g_{\mathcal{C}}(\mathbf{z}|c)$  is further optimized via the same procedure by the convex correspondence set  $\mathcal{C}_{\mathcal{A}}$  of the target dataset  $\mathcal{A}$ .
+
+![](images/05412a227ef880efe135697a9e178cad3fce5369d2069792d669832f5bb6c3ae.jpg)  
+Figure 3. Synchronization Process. The left part illustrates the decomposed convexes and source cages of the input eyeglass frame. The right part visualize synchronization matrices (a  $4 \times 4$  matrix here for each cage), cages deformed by bases before synchronization (left two columns), and cages deformed by synchronized bases (right two columns).
+
+Convex deformation synchronization. After learning the conditional generative model for each convex  $c$ , the next step is to compose all the deformation spaces for the whole mesh  $a$ . Since for each convex  $c$ ,  $g_{\mathcal{C}}(\mathbf{z}_c|c)$  exploits a separate set of deformation bases  $B_{c}$ , the noise parameter  $\mathbf{z}_c$  varies its meaning from convex to convex. As a result, if we draw independent noise parameters for each convex, the
+
+outcoming deformations could easily contradict with each other, failing the whole mesh-level deformation. To tackle this issue, we synchronize different deformation bases  $B_{c}$  with linear transformations  $S_{c}$  so that a single noise parameter  $\mathbf{z}$  can be shared across all convexes.
+
+Formally speaking, given a set of articulated object meshes  $\mathcal{A}$  from a certain category and an articulated mesh  $a\in \mathcal{A}$ , assuming the mesh is segmented into  $M$  convexes  $\{c_m\}_{m = 1}^M$  and each convex is equipped with a deformation model  $g_{\mathcal{C}}(\mathbf{z}_{c_m}|c_m)$ , our goal is to replace  $\mathbf{z}_{c_m}$  with  $S_{c_m}\mathbf{z}$  so that sampling the shared noise parameter  $\mathbf{z}$  results in a globally consistent mesh deformation. To compute the synchronization transformation  $S_{c_m}$ , we consider the deformation from  $a$  to other articulated meshes  $a^i\in \mathcal{A}$ . In particular, for each  $a^i$ , we optimize for a set of deformation coefficients  $\{\mathbf{y}_m^i\}$  so that each convex  $c_m$  in mesh  $a$  could deform into the corresponding convex  $c_m^i$  in mesh  $a^i$  following the deformation model  $g_{\mathcal{C}}(\mathbf{z}_{c_m}|c_m,\mathbf{z}_{c_m} = \mathbf{y}_m^i)$ . We can then estimate the synchronization transformations  $\{S_{c_m}\}$  by solving the following optimization problem:
+
+$$
+\underset {\{S _ {c _ {m}} \}, \{\mathbf {z} ^ {i} \}} {\text {m i n i m i z e}} \sum_ {i = 1} ^ {| \mathcal {A} |} \sum_ {m = 1} ^ {M} \| B _ {c _ {m}} S _ {c _ {m}} \mathbf {z} ^ {i} - B _ {c _ {m}} \mathbf {y} _ {m} ^ {i} \| _ {2}, \tag {2}
+$$
+
+where  $B_{c_m}$  is the deformation bases of convex  $c_{m}$  and  $\mathbf{z}^i$  is a global deformation coefficient from mesh  $a$  to  $a^i$  shared across all convexes. We solve the above optimization problem via alternatively optimizing the synchronization transformations  $\{S_{c_m}\}$  and the global deformation coefficients  $\{\mathbf{z}^i\}$ :
+
+Fix  $\{S_{c_m}\}$ , optimize each global deformation coefficient  $\mathbf{z}^i$  from  $a$  to  $a^i$  via Algorithm 2. It takes the convex deformation bases  $\{B_{c_m}\}$ , current synchronization transformations  $\{S_{c_m}\}$ , convex deformation coefficients  $\{\mathbf{y}_m^i\}$  as input, and outputs the optimized  $\mathbf{z}^i$ .  
+Fix  $\{\mathbf{z}^i\}$ , optimize each synchronization transformation  $S_{c_m}$  for each convex  $c_m$  via Algorithm 1. It takes the convex deformation bases  $\{B_{c_m}\}$ , current global deformation coefficients  $\{\mathbf{z}^i\}$ , convex deformation coefficients  $\{\mathbf{y}_m^i\}$  as input, and outputs the optimized  $S_{c_m}$ .
+
+w/ Sync.
+
+![](images/91033a5ed731146971c8e20b5b53de04f3c0d7786d7d6d5646a2aeee7148df44.jpg)  
+Source Shape
+
+![](images/8900be0928c55ade71a9f8a1f63c339cd32bf53e3e53beeac038b7e6350ac0dc.jpg)
+
+![](images/b914669c7401cafc5c60ac03a07461365ccc94b0cd2fb5d5325db4ed980b7983.jpg)  
+Figure 4. Synchronization's Effectiveness. The synchronized deformation bases can consistently transform each convex for a valid part shape (upper row), while those before the synchronization fail (bottom row).
+
+![](images/7b779c2cc937e6b93647baa24b91cc58b04e2127633a469dbe45c8a53da5549a.jpg)  
+Convex Cages
+
+![](images/f9150b0bd2362bd6dacc22611a97298fcebee89ca2a7f8d3c1d4d4770aed680e.jpg)  
+Deformed Cages  
+Deformed Part
+
+# Algorithm 1 Synchronization transformation matrices optimization.
+
+Input: Deformation bases for each convex  $\{B_{c_m}\}$ . Global deformation coefficients  $\{\mathbf{z}^i\}$  from  $a$  to other articulated meshes  $\{a^i\}$ . Deformation coefficients  $\{\mathbf{y}_m^i\}$  from each convex  $c_m$  to the corresponding convex of the articulated mesh  $a^i$ .  
+Output: Synchronization transformation matrix  $S_{c_m}$  of the convex  $c_{m}$ .  
+1:  $\mathbf{Z} \gets \operatorname{Stack}(\{\mathbf{z}^i\})$  
+2:  $\mathbf{Y}_m\gets \mathrm{Stack}(\{\mathbf{y}_m^i\})$  
+3:  $[\mathbf{U},\pmb {\Sigma},\mathbf{V}^T ]\gets \mathrm{SVD}(\mathbf{Z})$  
+4:  $[\mathbf{U}_m, \mathbf{\Sigma}_m, \mathbf{V}_m^T] \gets \mathrm{SVD}(\mathbf{Y}_m)$  
+5:  $S_{c_m}\gets \mathbf{U}_m\Sigma_m\mathbf{V}_m^T\mathbf{V}\Sigma^+ \mathbf{U}^T$  
+6: return  $S_{c_m}$
+
+# Algorithm 2 Global deformation coefficients optimization. "lsq" denotes the least square solver.
+
+Input: Deformation bases for each convex  $\{B_{c_m}\}$ . Synchronization transformations  $\{S_{c_m}\}$ . Deformation coefficients  $\mathbf{y}_m^i$  from each convex  $c_m$  to the corresponding convex of the articulated mesh  $a^i$ .  
+Output: Global deformation coefficients  $\mathbf{z}^i$  from  $a$  to  $a^i$ .  
+1:  $\mathcal{S}_{\mathbf{z}^i}\gets \emptyset$  
+2: for  $m = 1$  to  $M$  do  
+3:  $\hat{\mathbf{z}}_m^i\gets \mathrm{lsq}(S_{c_m},\mathbf{z}_m^i)$  
+4:  $\mathcal{S}_{\mathbf{z}^i}\gets \mathcal{S}_{\mathbf{z}^i}\cup \{\hat{\mathbf{z}}_m^i\}$  
+5:  $\mathbf{z}^i = \mathrm{Average}(S_{\mathbf{Z}^i})$  
+6: return  $\mathbf{z}^i$
+
+As an intuitive illustration of the synchronization process, we select the example of synchronizing the eyeglass frame's convex deformations (with 2 convexes and 4 deformation bases for each convex) and visualize the process (detailed to the cage level) in Figure 3. The synchronized deformation bases can transform two convexes more consistently and symmetrically than those before synchronization (an example on deformed part shapes is shown in Figure 4).
+
+After deformation synchronization, the distribution of the shared noise parameter  $\mathbf{z}$  can be simply set as a mixture of Gaussian fit to the optimized global deformation coefficients  $\{\mathbf{z}^i\}$ .
+
+# 3.3. Physics-Aware Deformation Correction
+
+Based upon the above design, our hierarchical deformation model can then synthesize a deformed mesh  $a$  via the noise parameter  $\mathbf{z}$  by taking a source articulated mesh as input. However, we may frequently observe physically unnatural self-penetrations when articulating  $a$ . To encourage the model to produce physically valid articulated meshes, we further propose a physics-aware deformation correction scheme, which serves two purposes: 1) to optimize the weights of the generative model to produce deformations that are more physically realistic and 2) to optimize the shape  $a$  to improve its physical validity. To accomplish this, we draw inspiration from previous works on stable rigid object generation [24, 25] and develop an online articulation simulation process that places  $a$  into  $K$  different articulation states sequentially, denoted as  $\operatorname{Sim}(a) = \{a_k\}_{k=1}^K$ . The
+
+articulation state sequence is designed by hand particularly for each category. We then utilize the physical supervision and a shape optimization strategy to guide the network to generate physically realistic articulated meshes. We will elaborate them in the following text.
+
+Physical supervision. To provide physical supervision for articulated mesh generative models requires us to design stability signals to measure physically unstable phenomena, for which we mainly consider self-penetrations during mesh articulation. We therefore devise a metric named average penetration depth (APD) measuring the magnitude of each vertex penetrating through other parts during the articulation simulation process. It is also referred as  $\mathcal{L}_{phy}$  when we treat it as a loss. Formally,  $\mathcal{L}_{phy} = \frac{1}{K}\sum_{k=1}^{K}\mathrm{PeneD}(a_k)$ , where  $\mathrm{PeneD}(a_k)$  measures self-penetrations in a single articulation state. We defer details of  $\mathcal{L}_{phy}$  to the supp.
+
+One way to provide physical guidance for the network is to utilize the physical stability signal  $\mathcal{L}_{phy}$  as an auxiliary loss to supervise the network training. However, physically unnatural phenomena of articulated meshes during mesh articulation are more diverse and complex than that of rigid objects caused by diverse part geometric appearance and wide articulation variations. Directly exploring physical supervision to guide the network optimization is not sufficient to regularize the network to produce physically realistic deformations. Therefore we further develop a collision response-based shape optimization strategy to improve the physical realism of the generated mesh  $a$ . Then we first optimize  $a$  for several times to reduce self-penetrations and then use it to calculate  $\mathcal{L}_{phy}$  for network optimization.
+
+Collision response-based shape optimization. To realize the vision of resolving self-penetrations via optimizing shapes, we draw inspirations from collision response strategies and devise a heuristic penetration resolving strategy that projects penetrated vertices onto the surface of the mesh. To guide such projection, we devise an algorithm that calculates  $\mathrm{ProjD}(a)$  whose gradient over each penetrated vertex in  $a$  informs how to project it to resolve penetrations. Then averaging the  $\mathrm{ProjD}(a_k)$  over each articulation state  $\{a_k\}$  yields the projection loss, i.e.,  $\mathcal{L}_{proj} = \frac{1}{K}\sum_{k=1}^{K}\mathrm{ProjD}(\mathrm{sim}_k(a))$ . By iteratively using  $\mathcal{L}_{proj}$  to update the global deformation coefficient  $\mathbf{z}$  of the mesh, we can optimize the shape  $a$  to mitigate self-penetrations. At the training time,  $\mathcal{L}_{proj}$  is used to optimize deformation coefficients  $\mathbf{z}$  for several iterations at first (i.e., 5 iterations), followed by leveraging  $\mathcal{L}_{phy}$  calculated on the optimized shape to update network weights. Test-Time Adaptation (TTA). During the test time, only  $\mathcal{L}_{proj}$  is iteratively applied to refine the result (i.e., for 10 iterations).
+
+![](images/8a234d3cabed37f2c2f4229d437d066b068c75a3a8bfa06e51f7b993d3e0668c.jpg)  
+Figure 5. Qualitative evaluation on few-shot articulated mesh generation. For every four shapes, the leftmost one (highlighted by blue rectangles) is the reference shape from the training dataset, while the remaining three are conditionally generated samples. Object categories from top to down are Eyeglasses, Scissors, TrashCan, and Lamp respectively.
+
+![](images/14d342b9615b66e4c21c1dd6691787665fde3885f36ca01dcfecf3958baed369.jpg)  
+Figure 6. Visual evaluation on the effectiveness of the physics-aware projection strategy. For every two lines, the upper line draws shapes without such correction while the second line draws corrected shapes.
+
+# 4. Experiments
+
+We evaluate our model on 6 articulated object categories to test its few-shot generation ability for articulated objects.
+
+Datasets. We evaluate our method on 6 categories selected from PartNet-Mobility [37] dataset following previous stan-
+
+![](images/7a75397d421206be4ce7412584fd8688d96a54c2c79250ee71acdcd4a498dcd3.jpg)  
+Figure 7. Visual comparison on model's target-driven deformation ability.
+
+![](images/5f5944b61fc513dc88e3cd5126891cc20223c07ab183a5c6f5079c52657a2ae9.jpg)  
+Figure 8. Visual evaluation on synchronized convex-level deformation bases. The first line draws the template shape with deformation directions of synchronized deformation bases, while the following two lines are deformed shapes by their corresponding bases. Arrows are drawn to highlight the deformation direction.
+
+dard [20], namely Storage Furniture, Eyeglasses, Scissors, Oven, Lamp, and TrashCan. We select 9947 instances from ShapeNet [4] dataset, covering four categories: Table, Chair, Lamp, and Airplane for convex-level deformation pre-training. For each test category, we split it into a few-shot training set with 5 instances and a test set containing the remaining instances. For more details, please refer to the supplementary material.
+
+Baselines. We compare our method to PolyGen [26], an auto-regressive style mesh generative model and DeepMetaHandles [21], a deformation-based mesh generative model. To further adapt them for articulated object generation, we design a part-by-part generation approach for each of them and we defer details to the supp.
+
+Metrics. We employ two kinds of metrics for evaluation: 1) metrics for mesh generative models following previsou literature [21, 23, 1], that is the minimum matching dis
+
+tance (MMD), coverage (COV), 1-NN classifier accuracy (1-NNA), and Jenson-Shannon divergence (JSD) [39]; and 2) average penetration depth (APD) for physical validity evaluation. The MMD score evaluates the fidelity of the generated samples and COV detects mode collapse and measures the diversity of generated samples. The 1-NNA score is computed by testing the generated samples and the reference instances by a 1-NN classifier. We introduce it following [23]. The classifier is not a network but classifies shapes into "reference" or "training" class based on the Nearest Neighbour. The JSD score computes the similarity between generated samples and reference samples. The APD score calculates the per-vertex average penetration depth averaged over all articulation simulation steps. We defer its details to the supp.
+
+Experimental settings. The number of projections are set to 5 and 10 at the training time and the test time respectively. The number of decomposed convexes may vary across categories and is detailed in the supp.
+
+Quantitative experimental evaluation: Few-shot articulated mesh generation. We summarize the quantitative evaluation results and comparisons to baseline methods on each articulated object category in Table 1. We can make the following observations: 1) We can achieve better average performance on every metric than the baseline models. It demonstrates the power of our model to generate samples with better diversity, higher visual fidelity, and better physical validity than previous models from a small number of examples. 2) On relatively rich categories (containing more than 30 instances) such as Scissors and Eyeglasses, our model can always outperform baseline methods by a large margin. It indicates that our model can cover a wider distribution space than baseline methods by only training on a few examples. 3) Our method can produce shapes with higher visual fidelity and better physical validity but not as a trade for diversity. By contrast, PolyGen generate samples that are more physically correct but exhibits very limited generative ability, i.e., poor COV and MMD scores.
+
+Qualitative evaluation: Free deformation. In the free deformation setting, our model generates articulated meshes by deforming an input reference shape. It draws samples from the optimized object-level deformation coefficient distribution to deform input shapes. We draw deformed shapes from four representative categories, including Eyeglasses, Scissors, TrashCan, and Lamp in Figure 5. It demonstrates the ability of our model to create diverse variations by deforming input reference shapes. Compared with previous mesh deformation literature where the model always struggles to depict large geometry variations in the learned deformation space, our model mitigates this issue and is able to encode such deformations as observed in deformations of TrachCan bodies (line 3 of Figure 5). It mainly credits
+
+to our deformation coefficient distribution parameterization strategy, which is fit by discrete deformation coefficients, other than the uniform range adopted in [21].
+
+Qualitative results: Target-driven deformation. We also conduct the target-driven experiments to demonstrate the superiority of our hierarchical deformation strategy over previous deformation literature, i.e., DeepMetaHandles [21], and Neural Cages [40]. As shown in Figure 7, our model can deform shapes to be more similar to their corresponding target shapes. It demonstrates the enhanced flexibility of our deformation strategy.
+
+Convex deformation synchronization. We visualize the effectiveness of our convex deformation synchronization design by showing how synchronized deformation bases change shapes to produce plausible global mesh-level deformations in Figure 8. Besides, though not imposed directly, we do observe cross-instance similar deformation patterns, as also observed in [21].
+
+Physics-aware projection. We compare objects synthesized by the network directly without and with physics-aware shape optimization in Figure 6. Our shape optimization design can improve the physical validity of sampled shapes by resolving penetrations caused by either part translation (example 1 in Figure 6) or revolution (example 2,3,4), in either the body part (example 1,2) or around the joint (example 3,4).
+
+# 5. Ablation Study
+
+Transfer learning and fine-tuning for the convex-level deformation module. In the few-shot generation design, the transfer learning technique plays an important role in enriching deformation space of the target category. Meanwhile, the fine-tuning process benefits the quality and diversity by learning category-specific deformation patterns. Our further analysis demonstrates that 1) The transfer learning's power can be boosted by increasing the amount of source data and is related to the affinity between source and target categories; 2) The fine-tuning process is crucial for us to maintain high quality while achieving high diversity. We create three ablated models by ablating the transferring learning ("Ours w/o Transfer"), using half amount of the original data for transferring ("Ours w/ Transfer (Half Data)"), and ablating the fine-tuning process ("Ours w/o Fine-tuning") and test their performance. Observations in Table 2 can validate the importance of the transfer learning and the fine-tuning process.
+
+Hierarchical mesh deformation. We adopt the divide-and-conquer philosophy and design a hierarchical mesh deformation strategy to learn a diverse mesh deformation space. To demonstrate its superiority over simple part-level deformation and composition, we ablate such design and treat
+
+Table 1. Quantitative evaluation. Comparison between our method and baseline models on the few-shot articulated mesh generation task. MMD is multiplied by  ${10}^{3}$  and APD is multiplied by  ${10}^{2}$  . Bold numbers for best values. "Avg." means "Average Performance".  
+
+<table><tr><td></td><td>Method</td><td>Storage Furniture</td><td>Scissors</td><td>Eyeglasses</td><td>Oven</td><td>Lamp</td><td>TrashCan</td><td>Avg.</td></tr><tr><td rowspan="3">MMD (↓)</td><td>PolyGen [26]</td><td>4.447</td><td>3.020</td><td>8.426</td><td>7.477</td><td>12.478</td><td>9.817</td><td>7.611</td></tr><tr><td>DeepMetaHandles [21]</td><td>1.031</td><td>1.854</td><td>6.414</td><td>7.730</td><td>8.560</td><td>9.213</td><td>5.800</td></tr><tr><td>Ours</td><td>1.058</td><td>1.495</td><td>6.062</td><td>7.009</td><td>7.133</td><td>8.430</td><td>5.198</td></tr><tr><td rowspan="3">COV (%, ↑)</td><td>PolyGen [26]</td><td>19.23</td><td>9.76</td><td>8.33</td><td>60.00</td><td>37.50</td><td>14.29</td><td>24.85</td></tr><tr><td>DeepMetaHandles [21]</td><td>43.93</td><td>24.63</td><td>15.00</td><td>60.00</td><td>50.00</td><td>17.14</td><td>35.12</td></tr><tr><td>Ours</td><td>75.33</td><td>57.89</td><td>29.82</td><td>60.00</td><td>62.50</td><td>17.14</td><td>50.45</td></tr><tr><td rowspan="3">1-NNA (%, ↓)</td><td>PolyGen [26]</td><td>99.46</td><td>98.28</td><td>98.71</td><td>98.04</td><td>99.22</td><td>92.68</td><td>97.73</td></tr><tr><td>DeepMetaHandles [21]</td><td>97.72</td><td>98.07</td><td>98.33</td><td>98.50</td><td>94.65</td><td>86.05</td><td>95.55</td></tr><tr><td>Ours</td><td>97.76</td><td>97.02</td><td>98.26</td><td>96.59</td><td>92.44</td><td>72.09</td><td>92.36</td></tr><tr><td rowspan="3">JSD (↓)</td><td>PolyGen [26]</td><td>0.0791</td><td>0.2317</td><td>0.1350</td><td>0.2044</td><td>0.2761</td><td>0.2269</td><td>0.1922</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.0697</td><td>0.2277</td><td>0.0960</td><td>0.1768</td><td>0.2172</td><td>0.1881</td><td>0.1626</td></tr><tr><td>Ours</td><td>0.0290</td><td>0.1274</td><td>0.0681</td><td>0.1597</td><td>0.1874</td><td>0.0994</td><td>0.1118</td></tr><tr><td rowspan="3">APD (↓)</td><td>PolyGen [26]</td><td>0.1305</td><td>0.2592</td><td>0.0479</td><td>0.2548</td><td>5.323</td><td>0.0256</td><td>1.0068</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.2990</td><td>1.6670</td><td>0.3682</td><td>0.4408</td><td>6.3020</td><td>1.6961</td><td>1.7955</td></tr><tr><td>Ours</td><td>0.1700</td><td>1.3520</td><td>0.1707</td><td>0.1602</td><td>5.993</td><td>0.0693</td><td>1.3192</td></tr></table>
+
+Table 2. Ablation study w.r.t. convex-level deformation transfer learning, hierarchical mesh generation, and physics-aware deformation correction. For metrics of each ablated version, we report their average value over all categories. MMD is multiplied by  $10^{3}$  and APD is multiplied by  $10^{2}$ . Bold numbers for best values. Italics numbers for the second-best one.  
+
+<table><tr><td>Ablation Type</td><td>Method</td><td>MMD (↓)</td><td>COV (%, ↑)</td><td>1-NNA (%, ↓)</td><td>JSD (↓)</td><td>APD (↓)</td></tr><tr><td>Hierarchical deformation</td><td>Ours w/o Hier.</td><td>7.170</td><td>36.41</td><td>95.43</td><td>0.1492</td><td>1.4964</td></tr><tr><td rowspan="3">Transfer learning &amp; Fine-tuning</td><td>Ours w/o Transfer</td><td>5.424</td><td>46.64</td><td>93.01</td><td>0.1159</td><td>1.3822</td></tr><tr><td>Ours w/ Transfer (Half Data)</td><td>5.201</td><td>49.43</td><td>92.81</td><td>0.1130</td><td>1.3365</td></tr><tr><td>Ours w/o Fine-tuning</td><td>6.538</td><td>43.20</td><td>94.70</td><td>0.1437</td><td>1.4530</td></tr><tr><td rowspan="3">Physics-aware deformation correction</td><td>DeepMetaHandles w/ Phy.</td><td>6.980</td><td>37.20</td><td>95.69</td><td>0.1587</td><td>1.5705</td></tr><tr><td>Ours w/o Phy.</td><td>5.211</td><td>50.83</td><td>92.57</td><td>0.1060</td><td>1.8079</td></tr><tr><td>Ours w/o TTA</td><td>5.214</td><td>50.71</td><td>92.31</td><td>0.0992</td><td>1.6443</td></tr><tr><td>N/A</td><td>Ours</td><td>5.198</td><td>50.45</td><td>92.36</td><td>0.1118</td><td>1.3192</td></tr></table>
+
+parts as the leaf deformation units (denoted as “Ours w/o Hier.”). As shown in Table 2, this way we observe immediate dropping of the performance on all metrics measuring the generative ability. This further evidence the value of our fine-grained decomposition and the hierarchical deformation space learning.
+
+Physics-aware deformation correction. We design  $\mathcal{L}_{phy}$  and  $\mathcal{L}_{proj}$  to provide physical supervision and perform collision response-based shape optimization respectively. This way we are able to improve the physical validity of shapes deformed by our framework. To further validate them as solid contributions and versatile strategies not only work for our method, we create the following variants and test their performance: 1) "Ours w/o Phy" by ablating both the shape optimization and the physical supervision, 2) "Ours w/o TTA" by only ablating the shape optimization strategy at the test time, and 3) "DeepMetaHandles w/ Phy" by integrating such two designs into the baseline DeepMetaHandles's framework. From Table 2, we can make the following observations: 1) Our physics-aware correction strategy is a versatile design that can be easily integrated into another deformation-based mesh generative model, improving its performance effectively; 2)
+
+Only training-time physics-aware corrections can improve physical-related performance by guiding the convex-level deformation module stably and effectively; 3) Further imposing test time optimizations is important for us to arrive at high-quality samples finally.
+
+# 6. Conclusion and Limitations
+
+We tackle the few-shot articulated mesh generation problem with 1) a hierarchical deformation model with transfer learning; and 2) a deformation correction scheme.
+
+Limitations. Currently, our work is limited to a category-level setting with the articulation chain and the range of articulation states assumed known. Developing a generation method without such assumption would increase its practical value and is an interesting future research direction. Besides, the deformation correction scheme relies on handcrafted chain of articulation states to detect self-penetrations and optimize shapes based on that. A natural alternative can be detecting articulation states from real-world images. Moreover, the quality of our generated results are restricted by that of the training data. A smart self-correction strategy, beyond mitigating self-penetrations only, may be designed to improve the validity.
+
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+                                    "content": "We study the problem of few-shot physically-aware articulated mesh generation. By observing an articulated object dataset containing only a few examples, we wish to learn a model that can generate diverse meshes with high visual fidelity and physical validity. Previous mesh generative models either have difficulties in depicting a diverse data space from only a few examples or fail to ensure physical validity of their samples. Regarding the above challenges, we propose two key innovations, including 1) a hierarchical mesh deformation-based generative model based upon the divide-and-conquer philosophy to alleviate the few-shot challenge by borrowing transferrable deformation patterns from large scale rigid meshes and 2) a physics-aware deformation correction scheme to encourage physically plausible generations. We conduct extensive experiments on 6 articulated categories to demonstrate the superiority of our method in generating articulated meshes with better diversity, higher visual fidelity, and better physical validity over previous methods in the few-shot setting. Further, we validate solid contributions of our two innovations in the ablation study. Project page with code is available at meowuu7.github.io/few-arti-object-gen."
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+                                    "content": "Generative models have aroused a wide spectrum of interests in recent years for their creativity and broad downstream application scenarios [29, 30, 34, 17, 8, 26]. Specific to 3D generation, a variety of techniques such as denoising diffusion [23, 42, 6, 39] have also been discussed for a while. Among them, mesh generation is indeed important since the mesh representation can support a wider range of downstream applications such as rendering and physical simulation compared to other representations such as point clouds. Existing works mainly focus on generating meshes for whole objects [8, 26, 6, 19, 30] considering without modeling object functionalities at all. Besides, they"
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+                                            "content": "Figure 1. Overview. We present a hierarchical mesh deformation-based generative model to solve the challenging yet important few-shot physically-aware articulated mesh generation problem. It tackles the few-shot challenge by borrowing shared convex level deformation patterns from large-scale rigid meshes and incorporates a deformation correction scheme to further enhance the model's ability to generate physically realistic meshes."
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+                                    "content": "mainly rely on reconstructing meshes from other kinds of representations such as implicit fields [8, 6, 19] instead of generating meshes directly. In this work, we go one step further and consider mesh generation for articulated objects that can support physically realistic articulations. This not only helps understand the object distribution in real-world assets, but also allows an intelligent agent to learn segmenting [20, 22], tracking [36], reasoning [10] and manipulating [38] articulated objects through a simulation environment. We focus on the articulated mesh generative model that can generate object meshes with diverse geometry, high visual fidelity, and correct physics."
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+                                    "content": " lower collision score. Ablation studies further validate the value of our design in deformation pattern transfer learning, the hierarchical mesh generation approach, and the effectiveness as well as the versatility of our physics-aware correction scheme."
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+                                    "content": "Mesh generative models. There have been vast and long efforts in devising 3D mesh generative models [26, 8, 41, 6, 21, 35]. Their techniques can be mainly categorized into three genres: 1) direct surface generation [26], 2) deformation-based mesh generation [21, 35], and 3) hybrid representation-based generation [8, 41]. Though methods of the first type exhibit obvious merits such as synthesizing high-quality n-gon meshes, they always suffer from limited generative ability and cannot scale for complex objects. In contrast, deformation-style mesh generation models deform source shapes for new samples which naturally spares the efforts for mesh structure generation, while restricted by poor flexibility. The third strategy separates the mesh surface structure generation problem from the content generation, which offers them with powerful generative ability. However, the quality of their samples is coupled with the power of their surface reconstruction techniques [27, 31]. In this work, we leverage mesh deformation as our generation technique for articulated mesh synthesis, taking advantages of its ability to produce high-quality samples. Instead of deforming whole objects or parts directly, we design a hierarchical deformation strategy to enhance the deformation flexibility and to enrich the data space by borrowing deformation patterns shared across categories from large scale rigid meshes."
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+                                    "content": "855"
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+                                    "type": "text",
+                                    "content": "ables matching [11, 3]. adversarial delta matching [12]. In this work, we leverage transfer learning to adapt shape patterns from large-scale rigid datasets to target articulated categories. Devising methods in this way requires us to find correct intermediates on which shape patterns are cross-category transferrable. Instead of directly using whole objects or articulated parts, we choose convexes as such intermediates. Transferring knowledge at this level presents further difficulties in fusing them together in a geometrically consistent way and in synthesizing physically realistic meshes while maintaining visual diversity at the same time."
+                                }
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+                                    "type": "text",
+                                    "content": "Physics-aware machine learning. Our work is also related to physics-aware machine learning [28, 10, 14, 24, 32, 25, 18], and mostly relevant to physically-aware generative models. To ensure physical validity of generated shapes, typical solutions choose either offline simulations for training data filtering [32] or online simulations leveraging the development of differentiable simulators [7, 15, 16] or by designing online simulation layers [24]. Generating physically-plausible articulated objects presents new challenges considering self-penetrations during mesh articulation that are more complex than stability issues caused by gravity for rigid objects. Our method integrates the physical supervision and a shape optimization strategy. The optimization transforms part shapes to resolve self-penetration issues. High-dimensional and complex shape deformations are involved in the process, different from linear fixing operations considered in [10]."
+                                }
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+                                    "type": "text",
+                                    "content": "3. Method"
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+                                    "type": "text",
+                                    "content": "The problem we are targeting is the few-shot physically-aware articulated mesh generation. Given a set of articulated meshes from the category of interest, we would like to learn a conditional generative model which could deform an articulated mesh from the same category into a wide variety of shapes. This conditional generation setup allows generating a large number of physically-plausible articulated meshes from a few examples while avoiding the need to generate the mesh structure. However, it leaves several challenges to address including how to accurately represent complex shape deformation spaces from a few examples and how to ensure that the generated meshes support physically-realistic articulations."
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+                                    "content": "Regarding the first challenge, our idea is to learn the deformation space via borrowing knowledge from other object categories. This seemingly simple idea is not trivial to realize though since we need to figure out what knowledge is transferrable. We present a hierarchical mesh deformation strategy to allow deformation prior to transfer at a local convex segment level while still maintaining the deformation consistency at the global shape level. Regarding the second challenge, we introduce a physics-aware deforma"
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+                                    "type": "text",
+                                    "content": "tion correction scheme to avoid unwanted artifacts such as self-penetrations during mesh articulation."
+                                }
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+                                    "content": "In the following, we will provide a pipeline overview in Section 3.1. Then we will explain our hierarchical mesh deformation strategy and our physics-aware deformation correction scheme in Section 3.2 and Section 3.3 respectively."
+                                }
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+                                    "content": "3.1. Overview"
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+                                    "type": "text",
+                                    "content": "Given a small set of articulated meshes "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}"
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+                                {
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+                                    "type": "text",
+                                    "content": " from a certain category of interest with the same number of parts and joints, sharing a known kinematic chain, our method wishes to learn a conditional generative model depicting a diverse and plausible articulated shape space. We adopt the divide-and-conquer philosophy and develop a hierarchical deformation scheme with transfer learning to tackle the difficulty of few-shot generation. Instead of learning at the whole shape level, we structure each articulated shape into an object-convex hierarchy and solve the generation problem via two steps. We first learn a generative model depicting a diverse shape space at the lowest convex level by borrowing common shape patterns from large rigid mesh datasets, denoted as "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". Convexes, with small cross-category distribution gap, serve as good intermediates for transferring common shape prior. After that, we devise a synchronization strategy that composes convex deformations consistently to form valid object shapes. Besides, a physics-aware correction scheme is developed to avoid physically-unnatural phenomena such as self-penetrations. Our overall pipeline is shown in Figure 2."
+                                }
+                            ]
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+                                    "content": "Specifically, we first decompose the conditional mesh "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " into approximately convex segments "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", forming an object-convex hierarchy. Then, on the leaf level, we learn to deform each convex "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "c \\in \\mathcal{C}_a"
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+                                    "type": "text",
+                                    "content": " through a convex-level conditional generative model "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_c|c)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " where "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        426,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the noise parameter corresponding to convex "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". Finally, on the root level, we synchronize the convex deformations by replacing the convex-dependent noise parameter "
+                                },
+                                {
+                                    "bbox": [
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+                                {
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "S_c\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is a linear transformation and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a synchronized noise parameter shared among all convexes. This aligns the noise space of different convexes to form a coherent deformation for the whole mesh. The above hierarchical deformation strategy can be mathematically represented as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "g(\\mathbf{z}|a) = \\{g_{\\mathcal{C}}(S_c\\mathbf{z}|c)|c \\in \\mathcal{C}_a\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "During the training time, we first leverage existing unsupervised shape segmentation tools BSP-Net [5] to decompose meshes in both "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " into approximately convex segments "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{\\mathcal{B}}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Since BSP-Net decomposes shapes consistently for each category, we can naturally identify corresponding convexes within "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". We can then pretrain a convex-level conditional generative model "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " modeling how corresponding convexes could deform into each other among the large-scale rigid meshes. We then fine-tune the pre-trained model "
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+                                    "type": "text",
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+                                            "content": "Figure 2. Framework overview for our few-shot physically-aware articulated mesh generation. In this figure, yellow blocks represent modules with learnable weights optimized during pre-training. Orange blocks contain weights optimized during fine-tuning. Gray blocks contain no learnable weights. Convexes of the same color are of the same type. Our framework consists of a hierarchical mesh deformation scheme that learns and transfers diverse shared deformation patterns from large-scale rigid datasets at the convex level. We also propose a convex deformation synchronization strategy to combine individual convex-level deformation spaces into the object-level space. Furthermore, we introduce a physics-aware deformation correction strategy to address self-penetrations in synthesized articulated meshes."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "in "
+                                },
+                                {
+                                    "bbox": [
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+                                        252,
+                                        289,
+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        252,
+                                        289,
+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": " and at the same time estimate the noise synchronization transformation "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        252,
+                                        289,
+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        252,
+                                        289,
+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": ". We further exploit an additional physics-aware deformation correction scheme to improve the physical validity of generated articulated shapes. It consists of 1) an auxiliary loss penalizing self-penetrations to provide physical supervision and 2) a collision response-based shape optimization strategy to encourage the model to generate physically realistic meshes. The auxiliary loss is incorporated into the training pipeline. While the shape optimization scheme functions at both the training time and the test time."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Hierarchical Mesh Deformation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Given an input articulated mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and its corresponding approximately convex segments "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ", our hierarchical mesh deformation model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g(\\mathbf{z}|a) = \\{g_{\\mathcal{C}}(S_c\\mathbf{z}|c)|c \\in C_a\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " consists of a convex-level conditional generative model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " as well as a series of synchronization transformations "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{S_c\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ". We propose to learn the model at the lowest convex level "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_C"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " following a transfer learning paradigm so that convex-level shape patterns can easily transfer across different categories. Given a reference mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ", the hierarchical deformation first synthesizes new convex shapes via "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_C"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        409,
+                                        287,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ". A deformation synchronization strategy is developed to handle the resulting deformation inconsistency issue across different convexes to form a valid object shape."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Convex-level conditional generative model. We propose to leverage mesh deformation to characterize the convex-level conditional generative model. For a convex mesh segment "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " containing "
+                                },
+                                {
+                                    "bbox": [
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+                                        653
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "text",
+                                    "content": " vertices, the conditional generative model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_c|c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "text",
+                                    "content": " should be able to produce diverse and realistic vertex-level deformation offset "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_c \\in \\mathbb{R}^{N_c \\times 3}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "text",
+                                    "content": " when we sample different noise parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        46,
+                        653,
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+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        653,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": "The convex deformation "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        653,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        653,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " lies in a high-dimensional space which varies from convex to convex, prohibiting the knowledge transfer across different convexes. We therefore reparametrize "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        653,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        653,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " using two tricks inspired by [40, 21]: 1) using cages to control per-vertex deformation; 2) using dic"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        305,
+                        253,
+                        515,
+                        264
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        253,
+                                        515,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": "tionaries to record the common deformation modes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        304,
+                        266,
+                        545,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                266,
+                                545,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": "In particular, for each convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": ", we use a coarse triangle mesh (a cage) "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " enclosing "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " to control the deformation of convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " [40]. The cage "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " usually contains much less vertices compared with the convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " so that its distribution is easier to be modeled. The deformation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " of the convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " can be easily computed as a linear transformation of the deformation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_{t_c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " of cage "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": ": "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_c = \\Phi_c\\mathbf{d}_{t_c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": ". Here "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Phi_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " is an interpolation matrix based upon the generalized barycentric coordinates of convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " with respect to cage "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        266,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": ". We deform a template mesh based upon the shape of each convex to form the cages which we defer the details to supp."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
+                        397,
+                        546,
+                        517
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                397,
+                                546,
+                                517
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": "To further reduce the deformation parametrization, we represent the cage deformation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_{t_c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " as a linear combination of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " deformation bases "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B_{c} = [\\mathbf{b}_{c}^{1}\\dots \\mathbf{b}_{c}^{K}]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_{t_c} = B_c\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " is a "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": "-dimensional deformation coefficient. Here each deformation basis "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " represents a common deformation pattern and all the bases span the deformation space of cage "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": " and therefore convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
+                                        546,
+                                        517
+                                    ],
+                                    "type": "text",
+                                    "content": ". Representing deformation spaces via deformation bases can effectively reduce the dimension of shape space compared to other alternatively such as utilizing latent vectors."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
+                        521,
+                        546,
+                        713
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                521,
+                                546,
+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "A few-shot deformation learning paradigm. Given the above deformation reparametrizations, learning the convex-level conditional generative model for each convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " boils down to learning the deformation bases "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " as well as the distribution of deformation coefficient "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". For deformation bases, we employ a neural network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\psi_{\\theta}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " to predict from convex shapes. It takes a given convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " as input and outputs its deformation bases, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B_{c} = \\psi_{\\theta}(c)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then optimize the deformation coefficient "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c^{\\hat{c}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " for each convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " in correspondence to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " from the current available dataset. The distribution of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " is then a mixture of Gaussian fit by the resulting deformation coefficients "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{z}_c^{\\hat{c}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        521,
+                                        546,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". We further leverage a transfer learning approach that transfers deformation priors learned in large-scale rigid dataset to target datasets at the convex level based on the observation that the convex-level deformations usually show similar patterns across cat-"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                }
+            ],
+            "discarded_blocks": [
+                {
+                    "bbox": [
+                        297,
+                        748,
+                        312,
+                        757
+                    ],
+                    "type": "page_number",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                297,
+                                748,
+                                312,
+                                757
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        297,
+                                        748,
+                                        312,
+                                        757
+                                    ],
+                                    "type": "text",
+                                    "content": "857"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
+            "page_size": [
+                612,
+                792
+            ],
+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
+                        46,
+                        72,
+                        287,
+                        108
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                72,
+                                287,
+                                108
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        287,
+                                        108
+                                    ],
+                                    "type": "text",
+                                    "content": "egories, e.g., a slab gets thicker or a strip gets elongated. Therefore we can learn a diverse deformation space from a few examples."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
+                        108,
+                        290,
+                        324
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                108,
+                                290,
+                                324
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": "We pre-train "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_c|c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " on the large-scale rigid mesh dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " and fine-tune it on each target articulated dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ". In particular, at the pre-training time, given a set of rigid meshes "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " from large-scale online repositories as well as the corresponding convexes "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{\\mathcal{B}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ", we first identify pairs of convexes in correspondence "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{(c,\\hat{c})|c,\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " from the same-category shapes, e.g., the noses of two different airplanes. These correspondences come as a result of some off-the-shelf unsupervised co-segmentation algorithms [5]. We then optimize "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_c|c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " by alternatively optimizing the deformation coefficient set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{z}_c^{\\hat{c}}|c,\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the neural network "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\psi_{\\theta}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ". To optimize "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{z}_c^{\\hat{c}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ", we fix "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{B_c\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " and optimize each "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c^{\\hat{c}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " by minimizing the Chamfer Distance (CD), also denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d_{\\mathrm{CD}}(\\cdot ,\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ", between the deformed convex "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " and the target "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we optimize "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{B_c\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " by fixing deformation coefficients "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{z}_c^{\\hat{c}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " and minimizing average CD between deformed "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " and the target "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " for each pair "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(c,\\hat{c})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": ", which leads to the convex deformation loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_C"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        108,
+                                        290,
+                                        324
+                                    ],
+                                    "type": "text",
+                                    "content": " at the training time:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        75,
+                        330,
+                        287,
+                        360
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                75,
+                                330,
+                                287,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        75,
+                                        330,
+                                        287,
+                                        360
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {C} = \\frac {1}{| \\mathcal {C} _ {\\mathcal {B}} |} \\sum_ {c, \\hat {c} \\in \\mathcal {C} _ {\\mathcal {B}}} d _ {\\mathrm {C D}} \\left(g _ {\\mathcal {C}} \\left(\\mathbf {z} _ {c} \\mid c, \\mathbf {z} _ {c} = \\mathbf {z} _ {c} ^ {\\hat {c}}\\right), \\hat {c}\\right). \\tag {1}",
+                                    "image_path": "3e95ad43ba232a20ac346a0247e89a55f3a77ca4717a832b7857f4dd8556a755.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        367,
+                        288,
+                        439
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                367,
+                                288,
+                                439
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": "After the above alternative optimization, the distribution of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": " for each convex "
+                                },
+                                {
+                                    "bbox": [
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+                                        367,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": " is modeled by a mixture of Gaussian distribution fit to the final coefficient set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{z_c^{\\hat{c}}|\\hat{c}\\in \\mathcal{C}_{\\mathcal{B}}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": ". At the fine-tuning time, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}|c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": " is further optimized via the same procedure by the convex correspondence set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{\\mathcal{A}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": " of the target dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        288,
+                                        439
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "type": "image",
+                    "bbox": [
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+                    ],
+                    "blocks": [
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+                            "bbox": [
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 3. Synchronization Process. The left part illustrates the decomposed convexes and source cages of the input eyeglass frame. The right part visualize synchronization matrices (a "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                585,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "4 \\times 4"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "text",
+                                            "content": " matrix here for each cage), cages deformed by bases before synchronization (left two columns), and cages deformed by synchronized bases (right two columns)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        46,
+                        631,
+                        288,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
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+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "Convex deformation synchronization. After learning the conditional generative model for each convex "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", the next step is to compose all the deformation spaces for the whole mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since for each convex "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_c|c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " exploits a separate set of deformation bases "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", the noise parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        631,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " varies its meaning from convex to convex. As a result, if we draw independent noise parameters for each convex, the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        546,
+                        133
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                72,
+                                546,
+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": "outcoming deformations could easily contradict with each other, failing the whole mesh-level deformation. To tackle this issue, we synchronize different deformation bases "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " with linear transformations "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " so that a single noise parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " can be shared across all convexes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        304,
+                        140,
+                        547,
+                        321
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                140,
+                                547,
+                                321
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": "Formally speaking, given a set of articulated object meshes "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " from a certain category and an articulated mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a\\in \\mathcal{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", assuming the mesh is segmented into "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " convexes "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{c_m\\}_{m = 1}^M"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " and each convex is equipped with a deformation model "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_{c_m}|c_m)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", our goal is to replace "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_{c_m}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{c_m}\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " so that sampling the shared noise parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " results in a globally consistent mesh deformation. To compute the synchronization transformation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{c_m}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", we consider the deformation from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " to other articulated meshes "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a^i\\in \\mathcal{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ". In particular, for each "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a^i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ", we optimize for a set of deformation coefficients "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{y}_m^i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " so that each convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c_m"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " in mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " could deform into the corresponding convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c_m^i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " in mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a^i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " following the deformation model "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{\\mathcal{C}}(\\mathbf{z}_{c_m}|c_m,\\mathbf{z}_{c_m} = \\mathbf{y}_m^i)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": ". We can then estimate the synchronization transformations "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{S_{c_m}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        140,
+                                        547,
+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": " by solving the following optimization problem:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        333,
+                        345,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        333,
+                                        345,
+                                        545,
+                                        380
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\underset {\\{S _ {c _ {m}} \\}, \\{\\mathbf {z} ^ {i} \\}} {\\text {m i n i m i z e}} \\sum_ {i = 1} ^ {| \\mathcal {A} |} \\sum_ {m = 1} ^ {M} \\| B _ {c _ {m}} S _ {c _ {m}} \\mathbf {z} ^ {i} - B _ {c _ {m}} \\mathbf {y} _ {m} ^ {i} \\| _ {2}, \\tag {2}",
+                                    "image_path": "dde3c0c661adde57f7ae12a581807c07aa9224b67f33e53130c0fb88c7dc89eb.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                405,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B_{c_m}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": " is the deformation bases of convex "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        546,
+                                        478
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c_{m}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        478
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}^i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": " is a global deformation coefficient from mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a^i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": " shared across all convexes. We solve the above optimization problem via alternatively optimizing the synchronization transformations "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{S_{c_m}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": " and the global deformation coefficients "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{z}^i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        405,
+                                        546,
+                                        478
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        317,
+                        485,
+                        545,
+                        617
+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 13,
+                    "blocks": [
+                        {
+                            "bbox": [
+                                317,
+                                485,
+                                545,
+                                545
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        317,
+                                        485,
+                                        545,
+                                        545
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": "Fix "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{S_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": ", optimize each global deformation coefficient "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{z}^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": " from "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": " to "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": " via Algorithm 2. It takes the convex deformation bases "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{B_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": ", current synchronization transformations "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{S_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": ", convex deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{y}_m^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": " as input, and outputs the optimized "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{z}^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                485,
+                                                545,
+                                                545
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                317,
+                                545,
+                                545,
+                                617
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        317,
+                                        545,
+                                        545,
+                                        617
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": "Fix "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{z}^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": ", optimize each synchronization transformation "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "S_{c_m}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": " for each convex "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "c_m"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": " via Algorithm 1. It takes the convex deformation bases "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{B_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": ", current global deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{z}^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": ", convex deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{y}_m^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": " as input, and outputs the optimized "
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "S_{c_m}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                317,
+                                                545,
+                                                545,
+                                                617
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "w/ Sync."
+                                }
+                            ]
+                        }
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+                    "index": 14
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+                    "bbox": [
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+                                        }
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+                                }
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+                            "index": 15,
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+                                            "type": "text",
+                                            "content": "Source Shape"
+                                        }
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+                                }
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+                            "index": 17,
+                            "angle": 0,
+                            "type": "image_caption"
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+                                            "type": "text",
+                                            "content": "Figure 4. Synchronization's Effectiveness. The synchronized deformation bases can consistently transform each convex for a valid part shape (upper row), while those before the synchronization fail (bottom row)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 24,
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+                                            "content": "Convex Cages"
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+                                            "type": "text",
+                                            "content": "Deformed Part"
+                                        }
+                                    ]
+                                }
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+                            "index": 23,
+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "Algorithm 1 Synchronization transformation matrices optimization."
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+                                            "type": "text",
+                                            "content": "Input: Deformation bases for each convex "
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{B_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": ". Global deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{z}^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": " from "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": " to other articulated meshes "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{a^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": ". Deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{y}_m^i\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": " from each convex "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "c_m"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": " to the corresponding convex of the articulated mesh "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                97,
+                                                286,
+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                47,
+                                136,
+                                283,
+                                145
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        136,
+                                        283,
+                                        145
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                47,
+                                                136,
+                                                283,
+                                                145
+                                            ],
+                                            "type": "text",
+                                            "content": "Output: Synchronization transformation matrix "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                136,
+                                                283,
+                                                145
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "S_{c_m}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                136,
+                                                283,
+                                                145
+                                            ],
+                                            "type": "text",
+                                            "content": " of the convex "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                136,
+                                                283,
+                                                145
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "c_{m}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                136,
+                                                283,
+                                                145
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                145,
+                                124,
+                                156
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        52,
+                                        145,
+                                        124,
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+                                    ],
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+                                        {
+                                            "bbox": [
+                                                52,
+                                                145,
+                                                124,
+                                                156
+                                            ],
+                                            "type": "text",
+                                            "content": "1: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                145,
+                                                124,
+                                                156
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{Z} \\gets \\operatorname{Stack}(\\{\\mathbf{z}^i\\})"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                156,
+                                136,
+                                165
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                        {
+                                            "bbox": [
+                                                52,
+                                                156,
+                                                136,
+                                                165
+                                            ],
+                                            "type": "text",
+                                            "content": "2: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                156,
+                                                136,
+                                                165
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{Y}_m\\gets \\mathrm{Stack}(\\{\\mathbf{y}_m^i\\})"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                164,
+                                144,
+                                174
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        52,
+                                        164,
+                                        144,
+                                        174
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                52,
+                                                164,
+                                                144,
+                                                174
+                                            ],
+                                            "type": "text",
+                                            "content": "3: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                164,
+                                                144,
+                                                174
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "[\\mathbf{U},\\pmb {\\Sigma},\\mathbf{V}^T ]\\gets \\mathrm{SVD}(\\mathbf{Z})"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                174,
+                                168,
+                                184
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        52,
+                                        174,
+                                        168,
+                                        184
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                52,
+                                                174,
+                                                168,
+                                                184
+                                            ],
+                                            "type": "text",
+                                            "content": "4: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                174,
+                                                168,
+                                                184
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "[\\mathbf{U}_m, \\mathbf{\\Sigma}_m, \\mathbf{V}_m^T] \\gets \\mathrm{SVD}(\\mathbf{Y}_m)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                183,
+                                168,
+                                194
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        52,
+                                        183,
+                                        168,
+                                        194
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                52,
+                                                183,
+                                                168,
+                                                194
+                                            ],
+                                            "type": "text",
+                                            "content": "5: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                183,
+                                                168,
+                                                194
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "S_{c_m}\\gets \\mathbf{U}_m\\Sigma_m\\mathbf{V}_m^T\\mathbf{V}\\Sigma^+ \\mathbf{U}^T"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                194,
+                                102,
+                                202
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        52,
+                                        194,
+                                        102,
+                                        202
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                52,
+                                                194,
+                                                102,
+                                                202
+                                            ],
+                                            "type": "text",
+                                            "content": "6: return "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                194,
+                                                102,
+                                                202
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "S_{c_m}"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "sub_type": "ref_text"
+                },
+                {
+                    "bbox": [
+                        47,
+                        228,
+                        286,
+                        251
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                228,
+                                286,
+                                251
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        228,
+                                        286,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": "Algorithm 2 Global deformation coefficients optimization. \"lsq\" denotes the least square solver."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        47,
+                        254,
+                        286,
+                        350
+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 19,
+                    "blocks": [
+                        {
+                            "bbox": [
+                                47,
+                                254,
+                                286,
+                                282
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        254,
+                                        286,
+                                        282
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "text",
+                                            "content": "Input: Deformation bases for each convex "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{B_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "text",
+                                            "content": ". Synchronization transformations "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{S_{c_m}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "text",
+                                            "content": ". Deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{y}_m^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "text",
+                                            "content": " from each convex "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "c_m"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "text",
+                                            "content": " to the corresponding convex of the articulated mesh "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
+                                                254,
+                                                286,
+                                                282
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                48,
+                                283,
+                                235,
+                                291
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        48,
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+                                    ],
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+                                        {
+                                            "bbox": [
+                                                48,
+                                                283,
+                                                235,
+                                                291
+                                            ],
+                                            "type": "text",
+                                            "content": "Output: Global deformation coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                283,
+                                                235,
+                                                291
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{z}^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                283,
+                                                235,
+                                                291
+                                            ],
+                                            "type": "text",
+                                            "content": " from "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
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+                                                235,
+                                                291
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a"
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+                                            "bbox": [
+                                                48,
+                                                283,
+                                                235,
+                                                291
+                                            ],
+                                            "type": "text",
+                                            "content": " to "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                283,
+                                                235,
+                                                291
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a^i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                283,
+                                                235,
+                                                291
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                292,
+                                93,
+                                303
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                    ],
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "1: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                292,
+                                                93,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{S}_{\\mathbf{z}^i}\\gets \\emptyset"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                302,
+                                128,
+                                311
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "2: for "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                302,
+                                                128,
+                                                311
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "m = 1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                302,
+                                                128,
+                                                311
+                                            ],
+                                            "type": "text",
+                                            "content": " to "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                302,
+                                                128,
+                                                311
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "M"
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                302,
+                                                128,
+                                                311
+                                            ],
+                                            "type": "text",
+                                            "content": " do"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                311,
+                                146,
+                                321
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                        {
+                                            "bbox": [
+                                                52,
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+                                            ],
+                                            "type": "text",
+                                            "content": "3: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                311,
+                                                146,
+                                                321
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\hat{\\mathbf{z}}_m^i\\gets \\mathrm{lsq}(S_{c_m},\\mathbf{z}_m^i)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                321,
+                                142,
+                                331
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
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+                                            "bbox": [
+                                                52,
+                                                321,
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+                                                331
+                                            ],
+                                            "type": "text",
+                                            "content": "4: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
+                                                321,
+                                                142,
+                                                331
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{S}_{\\mathbf{z}^i}\\gets \\mathcal{S}_{\\mathbf{z}^i}\\cup \\{\\hat{\\mathbf{z}}_m^i\\}"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 16
+                        },
+                        {
+                            "bbox": [
+                                52,
+                                331,
+                                127,
+                                342
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                            "bbox": [
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+                                            ],
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+                                            "content": "5: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                52,
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+                                                127,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{z}^i = \\mathrm{Average}(S_{\\mathbf{Z}^i})"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
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+                                350
+                            ],
+                            "type": "ref_text",
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+                                            "type": "text",
+                                            "content": "6: return "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{z}^i"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        }
+                    ],
+                    "sub_type": "ref_text"
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "As an intuitive illustration of the synchronization process, we select the example of synchronizing the eyeglass frame's convex deformations (with 2 convexes and 4 deformation bases for each convex) and visualize the process (detailed to the cage level) in Figure 3. The synchronized deformation bases can transform two convexes more consistently and symmetrically than those before synchronization (an example on deformed part shapes is shown in Figure 4)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
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+                                    "bbox": [
+                                        46,
+                                        462,
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+                                    ],
+                                    "type": "text",
+                                    "content": "After deformation synchronization, the distribution of the shared noise parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        462,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        462,
+                                        286,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be simply set as a mixture of Gaussian fit to the optimized global deformation coefficients "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{z}^i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "3.3. Physics-Aware Deformation Correction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Based upon the above design, our hierarchical deformation model can then synthesize a deformed mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " via the noise parameter "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " by taking a source articulated mesh as input. However, we may frequently observe physically unnatural self-penetrations when articulating "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". To encourage the model to produce physically valid articulated meshes, we further propose a physics-aware deformation correction scheme, which serves two purposes: 1) to optimize the weights of the generative model to produce deformations that are more physically realistic and 2) to optimize the shape "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " to improve its physical validity. To accomplish this, we draw inspiration from previous works on stable rigid object generation [24, 25] and develop an online articulation simulation process that places "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
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+                                    ],
+                                    "type": "text",
+                                    "content": " into "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " different articulation states sequentially, denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\operatorname{Sim}(a) = \\{a_k\\}_{k=1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". The"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        545,
+                        133
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": "articulation state sequence is designed by hand particularly for each category. We then utilize the physical supervision and a shape optimization strategy to guide the network to generate physically realistic articulated meshes. We will elaborate them in the following text."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
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+                                        285
+                                    ],
+                                    "type": "text",
+                                    "content": "Physical supervision. To provide physical supervision for articulated mesh generative models requires us to design stability signals to measure physically unstable phenomena, for which we mainly consider self-penetrations during mesh articulation. We therefore devise a metric named average penetration depth (APD) measuring the magnitude of each vertex penetrating through other parts during the articulation simulation process. It is also referred as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "text",
+                                    "content": " when we treat it as a loss. Formally, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy} = \\frac{1}{K}\\sum_{k=1}^{K}\\mathrm{PeneD}(a_k)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{PeneD}(a_k)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "text",
+                                    "content": " measures self-penetrations in a single articulation state. We defer details of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        151,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "text",
+                                    "content": " to the supp."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
+                {
+                    "bbox": [
+                        304,
+                        298,
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+                        467
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "text",
+                                    "content": "One way to provide physical guidance for the network is to utilize the physical stability signal "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "text",
+                                    "content": " as an auxiliary loss to supervise the network training. However, physically unnatural phenomena of articulated meshes during mesh articulation are more diverse and complex than that of rigid objects caused by diverse part geometric appearance and wide articulation variations. Directly exploring physical supervision to guide the network optimization is not sufficient to regularize the network to produce physically realistic deformations. Therefore we further develop a collision response-based shape optimization strategy to improve the physical realism of the generated mesh "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we first optimize "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "text",
+                                    "content": " for several times to reduce self-penetrations and then use it to calculate "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        298,
+                                        545,
+                                        467
+                                    ],
+                                    "type": "text",
+                                    "content": " for network optimization."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
+                {
+                    "bbox": [
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+                        484,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "Collision response-based shape optimization. To realize the vision of resolving self-penetrations via optimizing shapes, we draw inspirations from collision response strategies and devise a heuristic penetration resolving strategy that projects penetrated vertices onto the surface of the mesh. To guide such projection, we devise an algorithm that calculates "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{ProjD}(a)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " whose gradient over each penetrated vertex in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " informs how to project it to resolve penetrations. Then averaging the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{ProjD}(a_k)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " over each articulation state "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{a_k\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
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+                                    ],
+                                    "type": "text",
+                                    "content": " yields the projection loss, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{proj} = \\frac{1}{K}\\sum_{k=1}^{K}\\mathrm{ProjD}(\\mathrm{sim}_k(a))"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". By iteratively using "
+                                },
+                                {
+                                    "bbox": [
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{proj}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " to update the global deformation coefficient "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the mesh, we can optimize the shape "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to mitigate self-penetrations. At the training time, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{proj}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is used to optimize deformation coefficients "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for several iterations at first (i.e., 5 iterations), followed by leveraging "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " calculated on the optimized shape to update network weights. Test-Time Adaptation (TTA). During the test time, only "
+                                },
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+                                    "type": "inline_equation",
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+                                },
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+                                    "type": "text",
+                                    "content": " is iteratively applied to refine the result (i.e., for 10 iterations)."
+                                }
+                            ]
+                        }
+                    ],
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+                                            "content": "Figure 6. Visual evaluation on the effectiveness of the physics-aware projection strategy. For every two lines, the upper line draws shapes without such correction while the second line draws corrected shapes."
+                                        }
+                                    ]
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+                            ],
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+                                    "content": "4. Experiments"
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+                                    "content": "We evaluate our model on 6 articulated object categories to test its few-shot generation ability for articulated objects."
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+                                    "content": "Datasets. We evaluate our method on 6 categories selected from PartNet-Mobility [37] dataset following previous stan-"
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+                                            "content": "Figure 7. Visual comparison on model's target-driven deformation ability."
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+                                            "content": "Figure 8. Visual evaluation on synchronized convex-level deformation bases. The first line draws the template shape with deformation directions of synchronized deformation bases, while the following two lines are deformed shapes by their corresponding bases. Arrows are drawn to highlight the deformation direction."
+                                        }
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+                                    "type": "text",
+                                    "content": "dard [20], namely Storage Furniture, Eyeglasses, Scissors, Oven, Lamp, and TrashCan. We select 9947 instances from ShapeNet [4] dataset, covering four categories: Table, Chair, Lamp, and Airplane for convex-level deformation pre-training. For each test category, we split it into a few-shot training set with 5 instances and a test set containing the remaining instances. For more details, please refer to the supplementary material."
+                                }
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+                                    "content": "Baselines. We compare our method to PolyGen [26], an auto-regressive style mesh generative model and DeepMetaHandles [21], a deformation-based mesh generative model. To further adapt them for articulated object generation, we design a part-by-part generation approach for each of them and we defer details to the supp."
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+                                    "content": "Metrics. We employ two kinds of metrics for evaluation: 1) metrics for mesh generative models following previsou literature [21, 23, 1], that is the minimum matching dis"
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+                                    "type": "text",
+                                    "content": "tance (MMD), coverage (COV), 1-NN classifier accuracy (1-NNA), and Jenson-Shannon divergence (JSD) [39]; and 2) average penetration depth (APD) for physical validity evaluation. The MMD score evaluates the fidelity of the generated samples and COV detects mode collapse and measures the diversity of generated samples. The 1-NNA score is computed by testing the generated samples and the reference instances by a 1-NN classifier. We introduce it following [23]. The classifier is not a network but classifies shapes into \"reference\" or \"training\" class based on the Nearest Neighbour. The JSD score computes the similarity between generated samples and reference samples. The APD score calculates the per-vertex average penetration depth averaged over all articulation simulation steps. We defer its details to the supp."
+                                }
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+                                    "content": "Experimental settings. The number of projections are set to 5 and 10 at the training time and the test time respectively. The number of decomposed convexes may vary across categories and is detailed in the supp."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Quantitative experimental evaluation: Few-shot articulated mesh generation. We summarize the quantitative evaluation results and comparisons to baseline methods on each articulated object category in Table 1. We can make the following observations: 1) We can achieve better average performance on every metric than the baseline models. It demonstrates the power of our model to generate samples with better diversity, higher visual fidelity, and better physical validity than previous models from a small number of examples. 2) On relatively rich categories (containing more than 30 instances) such as Scissors and Eyeglasses, our model can always outperform baseline methods by a large margin. It indicates that our model can cover a wider distribution space than baseline methods by only training on a few examples. 3) Our method can produce shapes with higher visual fidelity and better physical validity but not as a trade for diversity. By contrast, PolyGen generate samples that are more physically correct but exhibits very limited generative ability, i.e., poor COV and MMD scores."
+                                }
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+                                    "type": "text",
+                                    "content": "Qualitative evaluation: Free deformation. In the free deformation setting, our model generates articulated meshes by deforming an input reference shape. It draws samples from the optimized object-level deformation coefficient distribution to deform input shapes. We draw deformed shapes from four representative categories, including Eyeglasses, Scissors, TrashCan, and Lamp in Figure 5. It demonstrates the ability of our model to create diverse variations by deforming input reference shapes. Compared with previous mesh deformation literature where the model always struggles to depict large geometry variations in the learned deformation space, our model mitigates this issue and is able to encode such deformations as observed in deformations of TrachCan bodies (line 3 of Figure 5). It mainly credits"
+                                }
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+                                    "type": "text",
+                                    "content": "to our deformation coefficient distribution parameterization strategy, which is fit by discrete deformation coefficients, other than the uniform range adopted in [21]."
+                                }
+                            ]
+                        }
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+                                    "content": "Qualitative results: Target-driven deformation. We also conduct the target-driven experiments to demonstrate the superiority of our hierarchical deformation strategy over previous deformation literature, i.e., DeepMetaHandles [21], and Neural Cages [40]. As shown in Figure 7, our model can deform shapes to be more similar to their corresponding target shapes. It demonstrates the enhanced flexibility of our deformation strategy."
+                                }
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+                                    "content": "Convex deformation synchronization. We visualize the effectiveness of our convex deformation synchronization design by showing how synchronized deformation bases change shapes to produce plausible global mesh-level deformations in Figure 8. Besides, though not imposed directly, we do observe cross-instance similar deformation patterns, as also observed in [21]."
+                                }
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+                                    "content": "Physics-aware projection. We compare objects synthesized by the network directly without and with physics-aware shape optimization in Figure 6. Our shape optimization design can improve the physical validity of sampled shapes by resolving penetrations caused by either part translation (example 1 in Figure 6) or revolution (example 2,3,4), in either the body part (example 1,2) or around the joint (example 3,4)."
+                                }
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+                                    "content": "5. Ablation Study"
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+                                    "content": "Transfer learning and fine-tuning for the convex-level deformation module. In the few-shot generation design, the transfer learning technique plays an important role in enriching deformation space of the target category. Meanwhile, the fine-tuning process benefits the quality and diversity by learning category-specific deformation patterns. Our further analysis demonstrates that 1) The transfer learning's power can be boosted by increasing the amount of source data and is related to the affinity between source and target categories; 2) The fine-tuning process is crucial for us to maintain high quality while achieving high diversity. We create three ablated models by ablating the transferring learning (\"Ours w/o Transfer\"), using half amount of the original data for transferring (\"Ours w/ Transfer (Half Data)\"), and ablating the fine-tuning process (\"Ours w/o Fine-tuning\") and test their performance. Observations in Table 2 can validate the importance of the transfer learning and the fine-tuning process."
+                                }
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+                                    "content": "Hierarchical mesh deformation. We adopt the divide-and-conquer philosophy and design a hierarchical mesh deformation strategy to learn a diverse mesh deformation space. To demonstrate its superiority over simple part-level deformation and composition, we ablate such design and treat"
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+                                            "content": "Table 1. Quantitative evaluation. Comparison between our method and baseline models on the few-shot articulated mesh generation task. MMD is multiplied by "
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+                                            "content": " . Bold numbers for best values. \"Avg.\" means \"Average Performance\"."
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+                                            "html": "<table><tr><td></td><td>Method</td><td>Storage Furniture</td><td>Scissors</td><td>Eyeglasses</td><td>Oven</td><td>Lamp</td><td>TrashCan</td><td>Avg.</td></tr><tr><td rowspan=\"3\">MMD (↓)</td><td>PolyGen [26]</td><td>4.447</td><td>3.020</td><td>8.426</td><td>7.477</td><td>12.478</td><td>9.817</td><td>7.611</td></tr><tr><td>DeepMetaHandles [21]</td><td>1.031</td><td>1.854</td><td>6.414</td><td>7.730</td><td>8.560</td><td>9.213</td><td>5.800</td></tr><tr><td>Ours</td><td>1.058</td><td>1.495</td><td>6.062</td><td>7.009</td><td>7.133</td><td>8.430</td><td>5.198</td></tr><tr><td rowspan=\"3\">COV (%, ↑)</td><td>PolyGen [26]</td><td>19.23</td><td>9.76</td><td>8.33</td><td>60.00</td><td>37.50</td><td>14.29</td><td>24.85</td></tr><tr><td>DeepMetaHandles [21]</td><td>43.93</td><td>24.63</td><td>15.00</td><td>60.00</td><td>50.00</td><td>17.14</td><td>35.12</td></tr><tr><td>Ours</td><td>75.33</td><td>57.89</td><td>29.82</td><td>60.00</td><td>62.50</td><td>17.14</td><td>50.45</td></tr><tr><td rowspan=\"3\">1-NNA (%, ↓)</td><td>PolyGen [26]</td><td>99.46</td><td>98.28</td><td>98.71</td><td>98.04</td><td>99.22</td><td>92.68</td><td>97.73</td></tr><tr><td>DeepMetaHandles [21]</td><td>97.72</td><td>98.07</td><td>98.33</td><td>98.50</td><td>94.65</td><td>86.05</td><td>95.55</td></tr><tr><td>Ours</td><td>97.76</td><td>97.02</td><td>98.26</td><td>96.59</td><td>92.44</td><td>72.09</td><td>92.36</td></tr><tr><td rowspan=\"3\">JSD (↓)</td><td>PolyGen [26]</td><td>0.0791</td><td>0.2317</td><td>0.1350</td><td>0.2044</td><td>0.2761</td><td>0.2269</td><td>0.1922</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.0697</td><td>0.2277</td><td>0.0960</td><td>0.1768</td><td>0.2172</td><td>0.1881</td><td>0.1626</td></tr><tr><td>Ours</td><td>0.0290</td><td>0.1274</td><td>0.0681</td><td>0.1597</td><td>0.1874</td><td>0.0994</td><td>0.1118</td></tr><tr><td rowspan=\"3\">APD (↓)</td><td>PolyGen [26]</td><td>0.1305</td><td>0.2592</td><td>0.0479</td><td>0.2548</td><td>5.323</td><td>0.0256</td><td>1.0068</td></tr><tr><td>DeepMetaHandles [21]</td><td>0.2990</td><td>1.6670</td><td>0.3682</td><td>0.4408</td><td>6.3020</td><td>1.6961</td><td>1.7955</td></tr><tr><td>Ours</td><td>0.1700</td><td>1.3520</td><td>0.1707</td><td>0.1602</td><td>5.993</td><td>0.0693</td><td>1.3192</td></tr></table>",
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+                                            "content": "Table 2. Ablation study w.r.t. convex-level deformation transfer learning, hierarchical mesh generation, and physics-aware deformation correction. For metrics of each ablated version, we report their average value over all categories. MMD is multiplied by "
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+                                            "content": " and APD is multiplied by "
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+                                            "type": "text",
+                                            "content": ". Bold numbers for best values. Italics numbers for the second-best one."
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+                                            "html": "<table><tr><td>Ablation Type</td><td>Method</td><td>MMD (↓)</td><td>COV (%, ↑)</td><td>1-NNA (%, ↓)</td><td>JSD (↓)</td><td>APD (↓)</td></tr><tr><td>Hierarchical deformation</td><td>Ours w/o Hier.</td><td>7.170</td><td>36.41</td><td>95.43</td><td>0.1492</td><td>1.4964</td></tr><tr><td rowspan=\"3\">Transfer learning &amp; Fine-tuning</td><td>Ours w/o Transfer</td><td>5.424</td><td>46.64</td><td>93.01</td><td>0.1159</td><td>1.3822</td></tr><tr><td>Ours w/ Transfer (Half Data)</td><td>5.201</td><td>49.43</td><td>92.81</td><td>0.1130</td><td>1.3365</td></tr><tr><td>Ours w/o Fine-tuning</td><td>6.538</td><td>43.20</td><td>94.70</td><td>0.1437</td><td>1.4530</td></tr><tr><td rowspan=\"3\">Physics-aware deformation correction</td><td>DeepMetaHandles w/ Phy.</td><td>6.980</td><td>37.20</td><td>95.69</td><td>0.1587</td><td>1.5705</td></tr><tr><td>Ours w/o Phy.</td><td>5.211</td><td>50.83</td><td>92.57</td><td>0.1060</td><td>1.8079</td></tr><tr><td>Ours w/o TTA</td><td>5.214</td><td>50.71</td><td>92.31</td><td>0.0992</td><td>1.6443</td></tr><tr><td>N/A</td><td>Ours</td><td>5.198</td><td>50.45</td><td>92.36</td><td>0.1118</td><td>1.3192</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "parts as the leaf deformation units (denoted as “Ours w/o Hier.”). As shown in Table 2, this way we observe immediate dropping of the performance on all metrics measuring the generative ability. This further evidence the value of our fine-grained decomposition and the hierarchical deformation space learning."
+                                }
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+                                    "content": "Physics-aware deformation correction. We design "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{phy}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{proj}"
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+                                    "type": "text",
+                                    "content": " to provide physical supervision and perform collision response-based shape optimization respectively. This way we are able to improve the physical validity of shapes deformed by our framework. To further validate them as solid contributions and versatile strategies not only work for our method, we create the following variants and test their performance: 1) \"Ours w/o Phy\" by ablating both the shape optimization and the physical supervision, 2) \"Ours w/o TTA\" by only ablating the shape optimization strategy at the test time, and 3) \"DeepMetaHandles w/ Phy\" by integrating such two designs into the baseline DeepMetaHandles's framework. From Table 2, we can make the following observations: 1) Our physics-aware correction strategy is a versatile design that can be easily integrated into another deformation-based mesh generative model, improving its performance effectively; 2)"
+                                }
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+                                    "type": "text",
+                                    "content": "Only training-time physics-aware corrections can improve physical-related performance by guiding the convex-level deformation module stably and effectively; 3) Further imposing test time optimizations is important for us to arrive at high-quality samples finally."
+                                }
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+                                    "type": "text",
+                                    "content": "6. Conclusion and Limitations"
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+                                    "content": "We tackle the few-shot articulated mesh generation problem with 1) a hierarchical deformation model with transfer learning; and 2) a deformation correction scheme."
+                                }
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+                                    "content": "Limitations. Currently, our work is limited to a category-level setting with the articulation chain and the range of articulation states assumed known. Developing a generation method without such assumption would increase its practical value and is an interesting future research direction. Besides, the deformation correction scheme relies on handcrafted chain of articulation states to detect self-penetrations and optimize shapes based on that. A natural alternative can be detecting articulation states from real-world images. Moreover, the quality of our generated results are restricted by that of the training data. A smart self-correction strategy, beyond mitigating self-penetrations only, may be designed to improve the validity."
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+                                }
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+                    ],
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+                                    ]
+                                }
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+                            "index": 5
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+                        {
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diff --git a/2023/Few-Shot Video Classification via Representation Fusion and Promotion Learning/8b77d936-d037-44d1-977f-aa19f41ff071_content_list.json b/2023/Few-Shot Video Classification via Representation Fusion and Promotion Learning/8b77d936-d037-44d1-977f-aa19f41ff071_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..a6bd3d9eb34f3b29ebec83f98151e320d178278a
--- /dev/null
+++ b/2023/Few-Shot Video Classification via Representation Fusion and Promotion Learning/8b77d936-d037-44d1-977f-aa19f41ff071_content_list.json	
@@ -0,0 +1,1283 @@
+[
+    {
+        "type": "text",
+        "text": "Few-Shot Video Classification via Representation Fusion and Promotion Learning",
+        "text_level": 1,
+        "bbox": [
+            179,
+            130,
+            794,
+            176
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Haifeng Xia $^{1*}$ , Kai Li $^{2}$ , Martin Renqiang Min $^{2}$ , Zhengming Ding $^{1}$ $^{1}$ Department of Computer Science, Tulane University,  $^{2}$ NEC Labs, America  \n{hxia, zdingl}@tulane.edu, {kaili, renqiang}@nec-labs.com",
+        "bbox": [
+            184,
+            202,
+            785,
+            257
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent few-shot video classification (FSVC) works achieve promising performance by capturing similarity across support and query samples with different temporal alignment strategies or learning discriminative features via Transformer block within each episode. However, they ignore two important issues: a) It is difficult to capture rich intrinsic action semantics from a limited number of support instances within each task. b) Redundant or irrelevant frames in videos easily weaken the positive influence of discriminative frames. To address these two issues, this paper proposes a novel Representation Fusion and Promotion Learning (RFPL) mechanism with two sub-modules: meta-action learning (MAL) and reinforced image representation (RIR). Concretely, during training stage, we perform online learning for seeking a task-shared meta-action bank to enrich task-specific action representation by injecting global knowledge. Besides, we exploit reinforcement learning to obtain the importance of each frame and refine the representation. This operation maximizes the contribution of discriminative frames to further capture the similarity of support and query samples from the same category. Our RFPL framework is highly flexible that it can be integrated with many existing FSVC methods. Extensive experiments show that RFPL significantly enhances the performance of existing FSVC models when integrated with them.",
+        "bbox": [
+            75,
+            323,
+            472,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            729,
+            209,
+            744
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Due to the emergence of deep learning [43, 18, 15], video action recognition has obtained impressive improvement by learning informative semantics from raw videos [23, 38]. These achievements heavily rely on the powerful supervision of considerable well-labeled videos to optimize deep neural networks [32, 41]. However, the collection and annotation of training samples become laborious and expensive, especially for video sequences. Hence, such a learning",
+        "bbox": [
+            75,
+            755,
+            468,
+            878
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "paradigm does not always feasible for many practical applications [7, 29]. This conflict motivates investigations on few-shot video classification (FSVC) which aims to learn a model of good generalization performance from a few labeled video samples [4, 35, 37].",
+        "bbox": [
+            500,
+            292,
+            890,
+            368
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The mainstream solutions to FSVC typically adopt metric-based meta-learning [30, 12] fashion by training model across multiple episodes where each includes one support set with a few annotated videos and the other query set with unlabeled instances. For inference, the well-trained model measures the similarities across support and query videos within each episode to determine which categories the query samples come from [17]. However, it is difficult to precisely assess frame-wise relationships within video sequences, since their temporal information has significant divergence or even mismatch. To overcome such a challenge, the intuitive strategy is to achieve temporal alignment among cross-video frames. For example, OTAM [4] develops a variant of dynamic time wrapping (DTW) [27] to find the optimal alignment path via the frame-level cumulative distance function. Similarly, ITANet [45] explores implicit temporal alignment via a traversal strategy. Moreover, TRX [28] develops multiple tuples of sub-sequence to achieve action matching. And STRM [35] studies self-attention mechanisms to emphasize channel representation in a single video. HyRSM [37] presents a set matching concept to explore temporal alignment without frame-level ordering across various videos.",
+        "bbox": [
+            496,
+            369,
+            892,
+            715
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Although these existing works have achieved appealing results, they tend to encounter performance bottlenecks due to ignorance of the following two issues. First, the limited number of labeled samples within each individual task hardly provides sufficient support to assist model learning the essential action semantics for the recognition task. Second, there are redundant or irrelevant frames in videos; treating these less informative frames in the same way as the other informative ones likely weakens the discriminability of the learned video representations, and thus triggers a negative effect on solving the FSVC task.",
+        "bbox": [
+            496,
+            717,
+            893,
+            883
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel Representation Fusion",
+        "bbox": [
+            517,
+            885,
+            890,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Work done during the internship at NEC Laboratories America.",
+        "bbox": [
+            94,
+            886,
+            437,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "19311",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "and Promotion Learning (RFPL) framework to address the two issues, by two novel modules, respectively. To address the deficiency of semantic information within each individual task, we propose the meta-action learning (MAL) module which introduces external knowledge learned globally to enrich video representations learned locally within each individual task. Specifically, MAL maintains a global meta-action bank storing representations of atomic action snippets that can be used to compose various action categories of higher complexity. The global meta-action bank is shared by all action types and all individual FSVC tasks. We explore it to enrich the video feature representations learned locally in each individual task via a novel Single Value Decomposition (SVD) technique.",
+        "bbox": [
+            75,
+            90,
+            472,
+            301
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address the redundant/irrelevant frame issue, we propose the reinforced image representation (RIR) module which explores reinforcement learning to discover the importance of each frame to the FSVC task. We train the reinforcement learning agent by exploiting the relationship between support and query video pairs, striving to emphasize the influence of discriminative frames to help the model accurately capture sample-wise similarity. Our MAL and RIR can be easily plugged into the existing FSVC methods to promote their performance. Our main contributions in this work are summarized in three folds as:",
+        "bbox": [
+            75,
+            301,
+            472,
+            467
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose the meta-action learning module which learns a global meta-action bank to enrich video representation learned locally in individual tasks, via a novel SVD technique.",
+            "- We address the negative effect of task-irrelevant frames on capturing cross-video relationships and develop a reinforced image representation module that promotes the contribution of discriminative frames.",
+            "- Our RFPL framework is highly flexible such that it can be integrated with various FSVC methods and gets improved performance."
+        ],
+        "bbox": [
+            96,
+            470,
+            467,
+            643
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            76,
+            656,
+            225,
+            671
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Few-Shot Video Classification (FSVC)",
+        "text_level": 1,
+        "bbox": [
+            76,
+            680,
+            405,
+            696
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "When using meta-learning manner [8, 9], FSVC scenario assumes that each episode includes a few labeled support videos and query ones without annotations and aims to learn and generalize a model to identify unseen classes [3, 50]. The current solutions are based on metric learning. Concretely, raw video sequences are first converted into corresponding high-level feature representations with DNN. The prediction of the query sample is determined by the matching support instance with the highest similarity [48]. However, video data with temporal dimension content is extremely complicated so it is difficult to precisely measure sample-wise relationships. To eliminate such a drawback, the current works generally calculate the similarity",
+        "bbox": [
+            75,
+            704,
+            472,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "after temporal alignment. For instance, OTAM [4] assumes that frame orderings across various videos are consistent and utilizes dynamic time wrapping to find the frame-level alignment path with a cumulative distance matrix. ITANet [45] adopts a traversal manner to match frames across different videos. TRX [28] first builds tuples of sub-sequence and exploits them to match action. STRM [35] advances TRX by considering spatial information within each video. HyRSM [38] explores set matching [13, 46] metric to efficiently compute cross-video connection. Differently, our proposed RFPL focuses on video representation enhancement by injecting meta-action knowledge and precise similarity measurement via the importance-aware refinement of discriminative frames with reinforcement learning.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Reinforcement Learning (RL)",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Reinforcement Learning (RL) arises from the neuroscientific and psychological study that which actions humans can do to gain more benefits from the environment [16, 33]. In other words, RL is utilizing the interaction of agent and environment to learn a policy that brings the most reward [14]. In fact, such a sequential decision-making procedure can be formulated as a Markov Decision Process (MDP) [6]. Recently, due to the powerful learning ability of DNN, the advanced RL works typically deploy a trainable DNN to approximate the value function or policy function as Deep Q-Network (DQN) [26] and Deep Deterministic Policy Gradient (DDPG) [22]. In addition, many real-world applications also consider using RL to improve model performance such as object tracking [42], protein analysis [20], video summarization [21] and action recognition [34]. Unlike them, our deployment of RL is solving the few-shot video action scenario by producing frame-wise weight to promote the effect of discriminative frames. Moreover, we also conduct delicate designs on DQN to be suitable for FSVC.",
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+    {
+        "type": "text",
+        "text": "3. Proposed Method",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Problem Setup",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In few-shot video classification (FSVC), the main task is to learn a high-generalization model to identify novel action categories of video with only a few annotated video instances. To make model training and test environment consistent, the mainstream learning strategy is meta-learning fashion [28]. Concretely, we can access a label-sufficient meta-training set  $\\mathcal{D}_{train}$  and another meta-testing set  $\\mathcal{D}_{test}$  and there is no category overlap across these two sets. During the training stage, videos of each episodic are collected from  $\\mathcal{D}_{train}$  and further divided into a support set and a query set. The support set includes  $k$ -samples in each of  $n$  classes, which is typically defined as  $n$ -way- $k$ -shot scenario. Under this condition, the relationship across support and query samples will be explored to identify which cate",
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+    },
+    {
+        "type": "page_number",
+        "text": "19312",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/9a784b4a5050c1d99ab3789bcfa3cdea6d1972af255da61d5a9a38b5ffa16139.jpg",
+        "image_caption": [
+            "Figure 1. Overview of our representation fusion and promotion learning (RFPL) framework. RFPL involves two sub-modules: meta-action learning (MAL) fusing task-shared action semantics to enrich video representation and reinforced image representation (RIR) highlighting the effect of discriminative frames to precisely learn sample-wise similarity."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "gory each query video belongs to. In terms of the test stage, each episodic also consists of support and query set which are derived from  $\\mathcal{D}_{test}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Framework Overview",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The key to solving FSVC problem lies in how to effectively learn the pattern of discriminative action semantics from a few labeled support videos. Motivated by this, we propose a flexible Representation Fusion & Promotion Learning (RFPL) framework to enrich semantic information of video features via two novel sub-modules, as Fig.1 shows. One meta-action learning module utilizes episodes of meta-training set to build a task-shared action bank further refining feature embedding via knowledge fusion. Another reinforced image representation module adjusts the importance of frames to achieve the enhancement of discriminative semantics with reinforcement learning.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Meta-Action Learning",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It is acknowledged that a video can be decomposed into multiple image frames corresponding to sub-actions, i.e.,  $\\mathbf{X}_i = \\{\\mathbf{x}_{ij}\\}_{j=1}^m$  where  $m$  is the number of frames in the  $i$ -th video. For example, a long jump video records some sub-actions: running, jumping and landing. In addition, we also observe that several videos come from different categories but they do share similar sub-actions such as jumping in long jump and playing basketball videos. When these two categories appear in different episodes, the transfer of similar patterns across them will facilitate the model to easily and accurately discover the similarity between support and query samples.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To achieve such a goal, the intuitive manner is to construct a task-shared action bank  $\\mathbf{D}$  to store representations of considerable sub-actions. Hence, the similar sub-actions in the long jump and playing basketball videos can be represented by the same atoms of this bank. Specifically, the widely-used backbone (e.g., ResNet-50) is first utilized to extract high-level feature of each frame, resulting in one video being transformed into the corresponding feature set  $\\mathbf{F}_i = \\{\\mathbf{f}_{ij} | \\mathbf{f}_{ij} = \\Phi(x_{ij})\\}_{j=1}^m$ , where  $\\Phi$  is the feature generator. And support videos within each episode are also converted into a feature matrix  $\\mathbf{F}^s \\in \\mathbb{R}^{d \\times nk_m}$  where each column denotes the feature of one frame with the dimension as  $d$ . To this end, we can gradually build and refine the memory bank  $\\mathbf{D} \\in \\mathbb{R}^{d \\times \\kappa}$  across different training episodes:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {D}, \\mathbf {A}} \\| \\mathbf {F} ^ {s} - \\mathbf {D A} \\| _ {\\mathrm {F}} ^ {2} + \\| \\mathbf {A} \\| _ {\\ell_ {1}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
+            316,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{D}$  is the learnable dictionary and  $\\mathbf{A}$  is sparse coefficient with  $\\ell_1$ -norm, which controls the sparseness of coefficient to achieve better reconstruction by using as fewer atoms as possible and efficiently avoids information redundancy in  $\\mathbf{D}$ . Since the current fruitful solutions to FSVC generally adopt episodic training fashion without repeatedly accessing the previous task, we expect to gradually involve action semantics per episode into task-shared bank  $\\mathbf{D}$ , thus, the online gradient update manner [25, 24] is adopted to optimize  $\\mathbf{D}$  and  $\\mathbf{A}$  instead of closed-form solution.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "After obtaining the task-shared meta-action bank, another consideration is how to adaptively fuse such semantics into each specific episode. Consequently, we rethink the meaning of learned action bank. In fact, it constitutes an action space where each atom represents a basis vector. But not all are needed for the current episode due to the assumption that the number of action categories in  $\\mathbf{D}$  is much larger than that in this episode. Therefore, a reasonable adaptation operation is to highlight the episode-relevant basis vectors from  $\\mathbf{D}$ . Fortunately, the classical single value decomposition (SVD) [40, 1] helps us achieve this expectation. Specifically, we adopts SVD to decompose support feature matrix  $\\mathbf{F}^s$  and action memory bank  $\\mathbf{D}$  as:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {S V D} \\left(\\mathbf {F} ^ {s}\\right) \\Rightarrow \\mathbf {U} ^ {s} \\boldsymbol {\\Sigma} ^ {s} \\mathbf {V} ^ {\\mathbf {s}} ^ {\\top}, \\quad \\operatorname {S V D} (\\mathbf {D}) \\Rightarrow \\mathbf {U} \\boldsymbol {\\Sigma} \\mathbf {V} ^ {\\top}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            703,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where single values  $\\Sigma$  or  $\\Sigma^s$  control the contribution of corresponding basis vectors. So far, it is intuitive to obtain two observations from the decomposition. First, the information of feature space basis in  $\\mathbf{U}$  is more robust and generic than that of  $\\mathbf{U}^s$ , since action bank refers to sufficient videos. Second, compared with  $\\Sigma$ ,  $\\Sigma^s$  can better estimate the intrinsic importance of basis vectors due to the fact that it is directly captured from the current episode. Based on these points, we consider fusing the advantage of each component to form the episode-adaptive action bank as  $\\mathbf{D}^e = \\mathbf{U}\\Sigma^s\\mathbf{V}^{s^\\top}$ . Note that  $\\mathbf{D}^e = \\mathbf{U}(\\mathbf{U}^{s^\\top}\\mathbf{U}^s)\\Sigma^s\\mathbf{V}^{s^\\top} =$",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "19313",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf{U}\\mathbf{U}^{s^{\\top}}\\mathbf{F}^{s}$ , which is exactly a rotation of  $\\mathbf{F}^{s}$  using the feature basis correlation between  $\\mathbf{U}$  and  $\\mathbf{U}^{s}$ . This rotation matrix brings more robust and generic semantic knowledge from  $\\mathbf{D}$  to  $\\mathbf{F}^{s}$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The next task is fusing the robust action semantics  $\\mathbf{D}^e$  into video representations. Meanwhile, we discover that the inner product between frame feature  $\\mathbf{f}_{*j}^{s/q}$  and  $\\mathbf{d}_l^e \\in \\mathbf{D}^e$  actually reflects the projection coefficient on each space basis, which supports us to re-express video features via  $\\mathbf{D}^e$ . The adaptive updating strategy is formalized as:",
+        "bbox": [
+            75,
+            151,
+            467,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathbf {f}} _ {* j} ^ {s / q} = (1 - \\rho) \\mathbf {f} _ {* j} ^ {s / q} + \\rho \\sum_ {l = 1} ^ {\\kappa} \\alpha_ {j l} \\mathbf {d} _ {l} ^ {e}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            248,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha_{jl} = \\cos (\\mathbf{f}_{*j}^{s / q},\\mathbf{d}_l^e)$  denotes the cosine similarity,  $\\rho$  balances accepting external knowledge and keeping original representations, and  $\\mathbf{d}_l^e$  is the  $l$ -th column basis vector of  $\\mathbf{D}^e$ . Since support and query samples both undergo re-expression via  $\\mathbf{D}^e$ , their similar or dissimilar associations will be further adjusted and promoted.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Reinforced Image Representation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            391,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our meta-action learning module enriches their latent features via the captured generic dictionary. However, not all frames in a video contain discriminative action semantics. In other words, they belong to two types: action-relevant frames and action-irrelevant ones. Promoting the contribution of the former and minimizing influence of the latter benefits the precise estimation of similarity between support and query videos. The keys to this expectation are automatically distinguish these two types and adjust their ratios in the fused representation  $\\widetilde{\\mathbf{f}}_j^{s/q}$ . Without manual annotations on the importance of frames, it is difficult for the model to learn the distinction ability. To overcome this challenge, we can break it down into a simple situation. Given the paired support and query videos from the same action, the action-relevant frames are likely to be similar or even the same, while the remaining ones tend to be different. Calculating frame-wise similarity across two videos easily discovers the discriminative frames. Their representation enhancement obviously narrows cross-video distance. For the paired samples in various classes, the weight adjustment on frames results in the reduction of cross-video similarity. In summary, these two cases indicate that frame-wise comparison and weight modification trigger the corresponding effects. This is an analogy to the basic logic of reinforcement learning adopting an action and receiving its reward.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With the analogy, we develop a reinforced image representation (RIR) module within the reinforcement learning (RL) framework to fulfill our goal. Specifically, in FSVC, the basic concepts of RL are redefined:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "- State: the video feature at  $t$  time, i.e.,  $s_t = \\{w_j \\widetilde{\\mathbf{f}}_{*j}\\}_{j=1}^m$  where  $w_j$  initialized as 1 is the importance of the corresponding  $j$ -th frame;",
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+        ],
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Action:  $a_{t}$  depends on the output of agent  $(p \\in [0,1])$  with the Sigmoid function applied. When  $p < 0.5$ , the action  $a_{t} = 0$  with  $\\mathrm{p}(a_t) = 2p$  and  $w_{j} = w_{j} - \\mathrm{p}(a_{t})$ , otherwise,  $a_{t} = 1$  with  $\\mathrm{p}(a_t) = 2(p - 0.5)$  and  $w_{j} = w_{j} + \\mathrm{p}(a_{t})$ . The agent in Figure 1 is implemented as one deep neural network.",
+            "- Reward:  $r_t$  of  $t$  time includes positive type and negative one. For the paired videos in the same class,  $r_t$  is positive with cross-video similarity improvement, while the reduction results in the negative one. The operation is inverse for paired videos in different classes. The reward is considered as the supervision to instruct the learning of the agent. Note that we ignore superscript  $s / q$  in three concepts, since they are suitable for all videos."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In reinforcement learning, the interaction procedure between agent and environment actually is a Markov decision process [20]. Concretely, given the estimated action value, the state is transferred from  $s_t^{s/q}$  to  $s_{t+1}^{s/q}$  according to an implicit probability distribution. During the state transition stage, the main challenge is how to decide the optimal action at the current state. In fact, the action  $a_t^{s/q}$  exists in a hidden probability space which is effectively estimated by Q-learning [26, 39] strategy. Under this condition, the expectation value of actions  $a_t^{s/q}$  is formally defined as  $Q_t$  and the current action modifies the importance  $w_j^{s/q}$  of frame  $\\widetilde{\\mathbf{f}}_{*j}^{s/q}$  and affects the final reward. The formulation of  $Q_t$  is:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ _ {t} \\left(s _ {t} ^ {s / q}, a _ {t} ^ {s / q}\\right) = \\max  _ {\\pi} \\mathbb {E} \\left[ r _ {t} + \\gamma r _ {t + 1} + \\gamma^ {2} r _ {t + 2} \\dots | \\pi \\right], \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            503,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\gamma$  denotes the discount factor balancing the immediate reward and the future ones, and  $\\pi = \\arg \\min_{a_t^{s/q}} Q_t$  is our desired probability distribution policy of action. To estimate such a policy, the Deep-Q network (DQN) [26] as an effective tool is generally utilized to approximate  $Q_t$ . In a nutshell, DQN typically constructs the learnable function taking the state as input to produce the probabilities  $p$  of action space. The function is always instantiated as a parameterized network.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "However, such a straightforward input design of DQN fails to observe the relationship of video pairs and embed this pivotal knowledge into action selection. For FSVC, the appropriate input of DQN is supposed to involve three different valuable contents. The first part is the feature of the chosen frame  $\\widetilde{\\mathbf{f}}_{*j}^{s / q}$  on which the estimated action is to be conducted. Emphasizing the current frame representation significantly upgrades its contribution to the prediction. The second one is the fused feature of the remaining frames, i.e.,  $\\frac{1}{m - 1}\\sum_{l = 1,l\\neq j}^{m}w_{l}^{s / q}\\widetilde{\\mathbf{f}}_{*l}^{s / q}$ . This information tends to affect the computation of future rewards. The third special point lies in measuring the cosine similarities across this frame and other frames in another video, written as  $\\mathbf{v}_j\\in \\mathbb{R}^m$  with its element  $\\mathbf{v}_{jl} = \\cos (\\widetilde{\\mathbf{f}}_j^{s / q},\\widetilde{\\mathbf{f}}_l^{q / s})$ .  $\\mathbf{v}_j$  reflects its potentiality to promote the cross-video similarity.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19314",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In terms of the output of DQN,  $a_{t}^{s / q} = 0$  suggests that the importance of this frame should be reduced via  $w_{j}^{s / q} = w_{j}^{s / q} - \\mathrm{p}(a_{t}^{s / q})$ , where  $\\mathrm{p}(a_t^{s / q}) = 2p$  and  $p$  is the probability of action. For the other situation, weight update of frame is  $w_{j}^{s / q} = w_{j}^{s / q} + \\mathrm{p}(a_{t}^{s / q})$  with  $\\mathrm{p}(a_t^{s / q}) = 2(p - 0.5)$ . After conducting actions, we have  $w_{j}^{s / q}\\in (0,2)$  and it is simple to attain the corresponding reward by calculating the change of similarity of video representations  $r = \\mathrm{sign}\\left(\\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)|s_{t + 1} - \\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)|s_t\\right)$ , where  $\\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)$  means  $\\cos (\\sum_{j = 1}^{m}w_{j}^{s}\\widetilde{\\mathbf{f}}_{*j}^{s},\\sum_{j = 1}^{m}w_{j}^{q}\\widetilde{\\mathbf{f}}_{*j}^{q})$ , and  $\\mathrm{sign}(\\cdot)$  denotes a sign function. Finally, with the Bellman theorem [2], the Deep-Q network is optimized with:",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\underset {\\Theta} {\\min} \\mathbb {E} \\left[ r + \\gamma \\max _ {a _ {i + 1} ^ {s / q}} Q (s _ {i + 1} ^ {s / q}, a _ {i + 1} ^ {s / q}) - Q (s _ {i} ^ {s / q}, a _ {i} ^ {s / q}) \\right] ^ {2}, \\quad (5)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            300,
+            470,
+            347
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Theta$  includes all the trainable network parameters of DQN. For the training stage, the snapshot of state, action, and reward at any time is stored and divided into several mini-batches with random sampling, and we adopt  $\\epsilon$ -greedy strategy to determine action using  $\\pi$  with probability  $\\epsilon$  and use random actions with  $1 - \\epsilon$ . For the inference stage, the well-trained DQN is frozen and infers the weight for each frame given the paired videos. To this end, video representations are further advanced with frame-wise importance.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Module Deployment",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our developed Representation Fusion & Promotion Learning (RFPL) framework includes two components. Meta-action learning (MAL) stores abundant action semantics via  $\\mathcal{D}_{train}$  and is adapted into each specific episode to enhance video representations, while Reinforced image representation (RIR) exploits deep Q-learning theory of RL to increase the representation of informative frame. Actually, it is straightforward and convenient to plug our REM into various FSVC methods to boost the model performance. In this paper, we choose three state-of-the-art FSVC models, e.g., OTAM [4], TRX [28] and STRM [35].",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Concretely, original OTAM first extracts frame-level features across all support and query samples per episode, and then calculate frame-wise similarity from support and query video pair. It finally utilizes a dynamic time wrapping algorithm (DTW) to obtain the similarity of videos and uses a metric manner to optimize or deduce the category of the query. When embedding RFPL into OTAM, our MAL module is combined with the outputs of the feature extractor, and our RIR is performed before the calculation of frame-wise similarity of video pairs. Similarly, for TRX, the average-pooling features of ResNet-50 are regarded as the inputs for MAL, and the refined representations further help in the selection of discriminative frames. Different from OTAM, RIR in TRX compares the given",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "query instances with all support ones, determines an optimal weighted query representation with the highest similarity, and feeds it into the following modules. Compared with OTAM and TRX, STRM utilizes the feature maps before the average pooling of ResNet-50 as inputs for a Transformer block and finally compresses them into frame-level vector representation as  $\\mathbf{F}_i^{s/q}$  where our RFPL is conducted.",
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Datasets. Three popular few-shot benchmarks are evaluated including UCF101 [31], Kinetics [5] and SSv2-Full [10]. For Kinetics and SSv2-Full, we follow the data split protocol of [4, 28, 37] to build meta-training set  $\\mathcal{D}_{train}$ , meta-validation set  $\\mathcal{D}_{val}$  and meta-testing set  $\\mathcal{D}_{test}$ , which consists 64, 12 and 24 categories, respectively. For UCF101, we adopt the split and sampling manners in [44].",
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+    {
+        "type": "text",
+        "text": "Implementation Details. Following the existing works [4, 28, 35], 8 image frames per video are randomly and uniformly selected as its raw representations and the pretrained ResNet-50 [11] is considered as the backbone to extract high-level features from frame-level images. For the task-shared bank, we regard  $\\mathbf{D}$  as one learnable tensor randomly initialized and optimized by Eq. (1) with SGD optimizer (learning rate:  $10^{-3} \\rightarrow 10^{-5}$ ) in each episode during training stage and it is frozen for the test procedure. In addition, the DQN in our RIR module includes three fully-connected (FC) layers mapping the input to the number of actions, whose training is independent of other parts. Concretely, we first train DQN with several episodes by freezing the remaining networks (ResNet-50, task-shared Bank, and Transformer block), and then update the remains with the fixed DQN by other episodes. The iterative process is repeated by many times. Other training regulations are preserved as each specific method. For inference, 10,000 episodes are randomly selected from  $\\mathcal{D}_{test}$  to evaluate the performance of the model.",
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+        "type": "text",
+        "text": "Baselines. Currently, HyRSM [37] and STRM [35] achieve the state-of-the-art results on most FSVC tasks, which are considered as important baselines. Besides, other excellent works such as TRN [47], CMN [48], CMN-J [49], TARN [3], OTAM [4], TTAN [19], TRX [28], ITANet [45], ARN [44], MAML [8] and MatchingNet [36] also serve as strong competitors.",
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+    {
+        "type": "text",
+        "text": "4.2. Result Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Table 1 summarizes the results of our method and other competitors on three datasets (UCF101, Kinetics, SSv2-Full) when solving various few-shot video classification tasks. According to the results, it is straightforward to achieve several important conclusions.",
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+    {
+        "type": "page_number",
+        "text": "19315",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/859d370655fed85d298466f162f874808a589ef977e3c1d5b8451dbc65797e61.jpg",
+        "table_caption": [
+            "Table 1. Result comparison of multiple methods on few-shot video classification problem. Evaluations are conducted on the meta-testing set of UCF101, Kinetics, and SSv2-Full under 5-way scenario. The number of support videos per class varies from 1 to 5 within each episode. The highest and second results are highlighted by **bold** and **underline**."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Source</td><td>Dataset</td><td>1-shot</td><td>2-shot</td><td>3-shot</td><td>4-shot</td><td>5-shot</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td rowspan=\"6\">UCF101</td><td>66.3</td><td>-</td><td>-</td><td>-</td><td>83.1</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>80.9</td><td>-</td><td>-</td><td>-</td><td>93.2</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>79.9</td><td>85.5</td><td>87.0</td><td>88.3</td><td>88.9</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>78.2</td><td>88.9</td><td>92.4</td><td>94.1</td><td>96.1</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>78.3</td><td>88.9</td><td>91.9</td><td>93.5</td><td>96.9</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>83.9</td><td>-</td><td>93.0</td><td>-</td><td>94.7</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>84.3↑4.4</td><td>88.9↑3.4</td><td>90.2↑3.2</td><td>91.9↑3.6</td><td>92.1↑3.2</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>82.5↑4.2</td><td>91.1↑2.2</td><td>94.1↑1.7</td><td>95.6↑1.5</td><td>96.3↑0.2</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>79.7↑1.4</td><td>90.1↑1.2</td><td>93.8↑1.9</td><td>95.8↑2.3</td><td>96.7↓0.2</td></tr><tr><td>MatchNet [36]</td><td>NeuIPS-16</td><td rowspan=\"11\">Kinetics</td><td>53.3</td><td>64.3</td><td>69.2</td><td>71.8</td><td>74.6</td></tr><tr><td>MAML [8]</td><td>ICML-17</td><td>54.2</td><td>65.5</td><td>70.0</td><td>72.1</td><td>75.3</td></tr><tr><td>Plain CMN [48]</td><td>ECCV-18</td><td>57.3</td><td>67.5</td><td>72.5</td><td>74.7</td><td>76.0</td></tr><tr><td>CMN-J [49]</td><td>TPAMI-20</td><td>60.5</td><td>70.0</td><td>75.6</td><td>77.3</td><td>78.9</td></tr><tr><td>TARN [3]</td><td>BMVC-19</td><td>64.8</td><td>-</td><td>-</td><td>-</td><td>78.5</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td>63.7</td><td>-</td><td>-</td><td>-</td><td>82.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>73.6</td><td>-</td><td>-</td><td>-</td><td>84.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>73.0</td><td>75.9</td><td>78.7</td><td>81.9</td><td>85.8</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>63.6</td><td>76.2</td><td>81.8</td><td>83.4</td><td>85.9</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>62.1</td><td>78.6</td><td>82.2</td><td>82.8</td><td>86.7</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>73.7</td><td>80.0</td><td>83.5</td><td>84.6</td><td>86.1</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>74.6↑1.6</td><td>80.0↑4.1</td><td>82.1↑3.4</td><td>84.1↑2.2</td><td>86.8↑1.0</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>66.2↑2.6</td><td>77.5↑1.3</td><td>83.8↑2.0</td><td>85.1↑1.7</td><td>87.3↑1.4</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>64.9↑2.8</td><td>80.3↑1.7</td><td>84.3↑2.1</td><td>84.8↑2.0</td><td>87.7↑1.0</td></tr><tr><td>CMN++ [48]</td><td>ECCV-18</td><td rowspan=\"8\">SSv2-Full</td><td>34.4</td><td>-</td><td>-</td><td>-</td><td>43.8</td></tr><tr><td>TRN++ [47]</td><td>ECCV-18</td><td>38.6</td><td>-</td><td>-</td><td>-</td><td>48.9</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>46.3</td><td>52.5</td><td>57.3</td><td>59.3</td><td>60.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>49.2</td><td>55.5</td><td>59.1</td><td>61.0</td><td>62.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>42.6</td><td>49.1</td><td>51.5</td><td>52.0</td><td>52.3</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>42.0</td><td>53.1</td><td>57.6</td><td>61.1</td><td>64.6</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>42.1</td><td>53.8</td><td>59.3</td><td>64.2</td><td>68.1</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>54.3</td><td>62.2</td><td>65.1</td><td>67.9</td><td>69.0</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>47.0↑4.2</td><td>54.6↑5.5</td><td>58.3↑6.8</td><td>60.3↑8.3</td><td>61.0↑8.7</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>44.6↑2.6</td><td>54.2↑1.1</td><td>59.9↑2.3</td><td>63.1↑2.1</td><td>64.6↑2.3</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>45.7↑3.6</td><td>55.8↑2.0</td><td>61.7↑2.4</td><td>66.8↑2.6</td><td>69.5↑1.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "First, when plugging our proposed modules into the existing FSVC works such as OTAM, its performance gains significant improvement. Concretely, for 5-way-5-shot task on SSv2-Full, the classification accuracy of OTAM using our module attains  $61.0\\%$  which is much higher than its original  $52.3\\%$ . In addition, the integration of our designed modules and OTAM exceeds the original one by  $4.4\\%$  on 1-shot task of UCF101. These phenomenons illustrate that our method effectively facilitates OTAM to conduct more accurate temporal alignment across support and query videos by refining video representations with task-shared knowledge and discriminative frame selection. Second, compared with OTAM, original TRX and STRM not only consider learning temporal relationships but also draw assistance from Transformer block to achieve information complementary within each episode. Although their methods seem to be perfect",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "and promising, our RFPL still facilitates them to boost  $2\\%$  on most tasks. The main reason for success lies in that our method further helps them enrich the representations of action semantics by introducing meta-action semantics and accurately capture the intrinsic similarity across support and query instances via the increasing effect of important image frames. Finally, injecting our RFPL into other baselines achieves comparable performance with HyRSM on most tasks. Especially, STRM with our RFPL surpasses HyRSM by an obvious gain margin, i.e.,  $1.6\\%$  on 5-shot task of Kinetics, validating that our proposed method is an efficient auxiliary tool for addressing the FSVC problem.",
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+    {
+        "type": "text",
+        "text": "4.3. Performance Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Path Visualization & Confusion Matrix. From Table 1, we conclude that our RFPL effectively promotes the perfor",
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+        "page_idx": 5
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+    {
+        "type": "page_number",
+        "text": "19316",
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+    {
+        "type": "image",
+        "img_path": "images/acdeabb33169ff5f7c68f5c4d36d3ef17767bcdbf3976682b70562788bb6e0bd.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/02ec62c45ed906fa2f2fc0700492204773be1479054c87a5fcc3978708166e0c.jpg",
+        "image_caption": [
+            "Figure 2. Comparison between plain OTAM and Ours+OTAM on action recognition result and temporal alignment path. This episode is randomly selected from the meta-testing set of Kinetics. The query video belongs to dancing ballet. Our+OTAM successfully matches it with the support sample from the same category, while plain OTAM matches into a dancing charleston video."
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/a3a3a33cf4fe18be4df5bef7f5321b218537cdb53e98520ef20572c4c0e30f75.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/38d249175e3d57ebd182b0b731dae63d40f00028e0976121c1ab840072d7c332.jpg",
+        "image_caption": [
+            "(a) OTAM @ Kinetics"
+        ],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/56c547e13fa4b8b3fa596c1a7bb21a58b1cad351d6ef6b619cfb607caf6c7e96.jpg",
+        "image_caption": [
+            "(b) Ours+OTAM @ Kinetics"
+        ],
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+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9b0e1e2f1e755c4711c53a1382ab65add1dff9f5c2b7a85a513d77e51c49f52a.jpg",
+        "image_caption": [
+            "(c) OTAM @ SSV-Full"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/82706303d712a9377ff699b01121b9f8278a823bce170bfd0081eba4e6dccf58.jpg",
+        "image_caption": [
+            "(d) Ours+OTAM @ SSV-Full",
+            "Figure 3. Comparison of confusion matrix deduced from the model prediction of plain OTAM and Ours+OTAM. These two episodes are collected from the meta-testing set of Kinetics (2-shot) and SSv2-Full (5-shot)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "mance of OTAM by a large margin. To explicitly explain the reason for improvement, we randomly select an episode from meta-testing set  $\\mathcal{D}_{test}$  and visualize the frame-level cumulative distance across query video and the selected support ones as Fig. 2 shows. This visualization indicates that OTAM is sensitive to image background and its temporal alignment becomes invalid. Thus, it considers that this query video from the dancing ballet class has the highest similarity with the support sample from dancing charleston. Differently, our method assists OTAM to focus on the similarity of action semantics, especially on distinguishing body posture. Hence, Ours+OTAM accurately matches the query sample with the support video from the identical category and achieves better temporal alignment.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In addition, we draw the confusion matrix of two specific episodes to further discuss their differences. Concretely, during the inference stage, for 2-shot of Kinetics or 5-shot of SSv2-Full, we randomly choose an episode with 200 query samples uniformly distributed in five categories and compare model prediction and ground-truth to form Fig. 3. For the task of Kinetics, with the help of our RFPL, the recognition abilities of OTAM in five categories are all strengthened. With respect to the more challenging task of SSv2-Full, OTAM with our method learns more discrimina",
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+    {
+        "type": "text",
+        "text": "tive action semantics and achieves significant performance improvement on several categories without reduction on the remaining ones.",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Reinforced Image Frames. In our RFPL, reinforced image representation as one important module aims to discover the discriminative image frames via the comparison of the paired videos. To analyze its effect, we record the frame-wise weights deduced from the agent as Fig. 4 in one test episode. From two \"folding paper\" videos, several image frames without any \"folding\" action are provided with lower weights such as frames in the red box. For action-relevant images, the learned network produces higher weights for them as the blue box shows. From the other example \"cutting watermelon\", we have an interesting finding. The well-trained network does not give larger weights for frames including \"cutting\" action, while highlighting images with two halves of the red pulp of a watermelon as the green box shows. It suggests that the network considers that these image contents are useful for the improvement of cross-video similarity.",
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+    {
+        "type": "text",
+        "text": "Parameter Analysis. There is one hyper-parameter  $\\rho$  in our RFPL, which serves as a trade-off between accepting external global knowledge and preserving current feature representations. In practical experiments, this parameter is",
+        "bbox": [
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+    {
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+        "text": "19317",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4465409d8c43c95a65d36d35b73b44a2442676f72216700d68107a894f14ba07.jpg",
+        "image_caption": [
+            "Figure 4. Importance of frames produced by reinforced image representation module. Videos of the first and second rows belong to folding paper, while the remaining videos are from cutting watermelon. Images in the red box are regarded as key action semantics by the network, while the effect of others in the blue box is reduced. Similarly, the representations of images in the green box are also enhanced."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/1ccdc6da05c5d9dc13e7ccc42aa0ea5d1a0acbbb683b10d93f5ce7dc356ab7a8.jpg",
+        "image_caption": [
+            "Figure 5. Parameter analysis of  $\\rho$  with different selections."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            412,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "tuned for different tasks, i.e.,  $\\rho \\in \\{0.001, 0.01, 0.1, 0.5\\}$ . Definitely, the optimal parameter is determined by the performance of the learned model on the meta-validation set. Concretely, Fig. 5 shows the change of model classification ability on the validation set of SSv2-Full with the varying  $\\rho$ . Based on this parameter analysis, we find that when  $\\rho = 0.5$ , the video classification accuracy is lower than that of smaller  $\\rho$  on many tasks. Therefore, it is reasonable to infer that while introducing global knowledge to enhance semantics information, the protection of current information is very necessary and stabilizes the model training.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Ablation Study. Our RFPL consists of two modules: meta-action learning and reinforced image representation. The first one aims to enrich video representation by fusing global knowledge of the meta-action bank to each specific episode, while the second one expects to emphasize the representation of informative image frames via reinforcement learning selection. In fact, we also separately plug each module into the existing baseline, named as Ours-v1 (adding MAL) and Ours-v2 (adding RIR). These variants",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/65dc24487e5579c0b1b1565e50d8bb8842c77e4b0a96f165120b9c861f2d1a0a.jpg",
+        "image_caption": [
+            "Figure 6. Ablation study. Ours-v1 and Ours-v2 mean that meta-action learning and reinforced image representation modules are plugged into the existing FSVC works, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "are combined with OTAM and evaluated on three tasks of Kinetics with results in Fig. 6. The comparisons with plain OTAM mean that each module can independently make positive contributions on advancing it. And the collaboration of MAL and RIR will bring more benefits to OTAM than each independent module. Thus, using the complete RFPL is the optimal strategy.",
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+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a flexible representation fusion and enhancement learning (RFPL) mechanism with two sub-modules to solve few-shot video classification. The meta-action learning module builds a generic action bank and fuses the adapted one to enrich video features, while the reinforced image representation module identifies important frames via an agent and promotes their positive effect to precisely capture cross-video similarity. Considerable experimental results and analysis verify that our RFPL effectively advances the existing FSVC methods.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+    {
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+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
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+            "[41] Haifeng Xia, Pu Wang, and Zhengming Ding. Incomplete multi-view domain adaptation via channel enhancement and"
+        ],
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "knowledge transfer. In European Conference on Computer Vision, pages 200-217. Springer, 2022. 1",
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+            "[48] Linchao Zhu and Yi Yang. Compound memory networks for few-shot video classification. In Proceedings of the European Conference on Computer Vision (ECCV), pages 751-766, 2018. 2, 5, 6",
+            "[49] Linchao Zhu and Yi Yang. Label independent memory for semi-supervised few-shot video classification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(1):273-285, 2020. 5, 6",
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+        ],
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+        ],
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+    },
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+        "page_idx": 9
+    }
+]
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diff --git a/2023/Few-Shot Video Classification via Representation Fusion and Promotion Learning/8b77d936-d037-44d1-977f-aa19f41ff071_model.json b/2023/Few-Shot Video Classification via Representation Fusion and Promotion Learning/8b77d936-d037-44d1-977f-aa19f41ff071_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..3bce474f5985947995db78d80fb6e1be86a9c99f
--- /dev/null
+++ b/2023/Few-Shot Video Classification via Representation Fusion and Promotion Learning/8b77d936-d037-44d1-977f-aa19f41ff071_model.json	
@@ -0,0 +1,1903 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.18,
+                0.131,
+                0.795,
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+            ],
+            "angle": 0,
+            "content": "Few-Shot Video Classification via Representation Fusion and Promotion Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.186,
+                0.203,
+                0.787,
+                0.258
+            ],
+            "angle": 0,
+            "content": "Haifeng Xia\\(^{1*}\\), Kai Li\\(^{2}\\), Martin Renqiang Min\\(^{2}\\), Zhengming Ding\\(^{1}\\)  \n\\(^{1}\\)Department of Computer Science, Tulane University, \\(^{2}\\)NEC Labs, America  \n{hxia, zdingl}@tulane.edu, {kaili, renqiang}@nec-labs.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.324,
+                0.473,
+                0.702
+            ],
+            "angle": 0,
+            "content": "Recent few-shot video classification (FSVC) works achieve promising performance by capturing similarity across support and query samples with different temporal alignment strategies or learning discriminative features via Transformer block within each episode. However, they ignore two important issues: a) It is difficult to capture rich intrinsic action semantics from a limited number of support instances within each task. b) Redundant or irrelevant frames in videos easily weaken the positive influence of discriminative frames. To address these two issues, this paper proposes a novel Representation Fusion and Promotion Learning (RFPL) mechanism with two sub-modules: meta-action learning (MAL) and reinforced image representation (RIR). Concretely, during training stage, we perform online learning for seeking a task-shared meta-action bank to enrich task-specific action representation by injecting global knowledge. Besides, we exploit reinforcement learning to obtain the importance of each frame and refine the representation. This operation maximizes the contribution of discriminative frames to further capture the similarity of support and query samples from the same category. Our RFPL framework is highly flexible that it can be integrated with many existing FSVC methods. Extensive experiments show that RFPL significantly enhances the performance of existing FSVC models when integrated with them."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.731,
+                0.21,
+                0.746
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.756,
+                0.47,
+                0.879
+            ],
+            "angle": 0,
+            "content": "Due to the emergence of deep learning [43, 18, 15], video action recognition has obtained impressive improvement by learning informative semantics from raw videos [23, 38]. These achievements heavily rely on the powerful supervision of considerable well-labeled videos to optimize deep neural networks [32, 41]. However, the collection and annotation of training samples become laborious and expensive, especially for video sequences. Hence, such a learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.293,
+                0.892,
+                0.369
+            ],
+            "angle": 0,
+            "content": "paradigm does not always feasible for many practical applications [7, 29]. This conflict motivates investigations on few-shot video classification (FSVC) which aims to learn a model of good generalization performance from a few labeled video samples [4, 35, 37]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.37,
+                0.893,
+                0.717
+            ],
+            "angle": 0,
+            "content": "The mainstream solutions to FSVC typically adopt metric-based meta-learning [30, 12] fashion by training model across multiple episodes where each includes one support set with a few annotated videos and the other query set with unlabeled instances. For inference, the well-trained model measures the similarities across support and query videos within each episode to determine which categories the query samples come from [17]. However, it is difficult to precisely assess frame-wise relationships within video sequences, since their temporal information has significant divergence or even mismatch. To overcome such a challenge, the intuitive strategy is to achieve temporal alignment among cross-video frames. For example, OTAM [4] develops a variant of dynamic time wrapping (DTW) [27] to find the optimal alignment path via the frame-level cumulative distance function. Similarly, ITANet [45] explores implicit temporal alignment via a traversal strategy. Moreover, TRX [28] develops multiple tuples of sub-sequence to achieve action matching. And STRM [35] studies self-attention mechanisms to emphasize channel representation in a single video. HyRSM [37] presents a set matching concept to explore temporal alignment without frame-level ordering across various videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.718,
+                0.895,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Although these existing works have achieved appealing results, they tend to encounter performance bottlenecks due to ignorance of the following two issues. First, the limited number of labeled samples within each individual task hardly provides sufficient support to assist model learning the essential action semantics for the recognition task. Second, there are redundant or irrelevant frames in videos; treating these less informative frames in the same way as the other informative ones likely weakens the discriminability of the learned video representations, and thus triggers a negative effect on solving the FSVC task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a novel Representation Fusion"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.438,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Work done during the internship at NEC Laboratories America."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
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+            "angle": 0,
+            "content": "19311"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.302
+            ],
+            "angle": 0,
+            "content": "and Promotion Learning (RFPL) framework to address the two issues, by two novel modules, respectively. To address the deficiency of semantic information within each individual task, we propose the meta-action learning (MAL) module which introduces external knowledge learned globally to enrich video representations learned locally within each individual task. Specifically, MAL maintains a global meta-action bank storing representations of atomic action snippets that can be used to compose various action categories of higher complexity. The global meta-action bank is shared by all action types and all individual FSVC tasks. We explore it to enrich the video feature representations learned locally in each individual task via a novel Single Value Decomposition (SVD) technique."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.303,
+                0.473,
+                0.468
+            ],
+            "angle": 0,
+            "content": "To address the redundant/irrelevant frame issue, we propose the reinforced image representation (RIR) module which explores reinforcement learning to discover the importance of each frame to the FSVC task. We train the reinforcement learning agent by exploiting the relationship between support and query video pairs, striving to emphasize the influence of discriminative frames to help the model accurately capture sample-wise similarity. Our MAL and RIR can be easily plugged into the existing FSVC methods to promote their performance. Our main contributions in this work are summarized in three folds as:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.471,
+                0.468,
+                0.531
+            ],
+            "angle": 0,
+            "content": "- We propose the meta-action learning module which learns a global meta-action bank to enrich video representation learned locally in individual tasks, via a novel SVD technique."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.536,
+                0.468,
+                0.595
+            ],
+            "angle": 0,
+            "content": "- We address the negative effect of task-irrelevant frames on capturing cross-video relationships and develop a reinforced image representation module that promotes the contribution of discriminative frames."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.6,
+                0.468,
+                0.645
+            ],
+            "angle": 0,
+            "content": "- Our RFPL framework is highly flexible such that it can be integrated with various FSVC methods and gets improved performance."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.097,
+                0.471,
+                0.468,
+                0.645
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
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+                0.227,
+                0.672
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.681,
+                0.406,
+                0.697
+            ],
+            "angle": 0,
+            "content": "2.1. Few-Shot Video Classification (FSVC)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "When using meta-learning manner [8, 9], FSVC scenario assumes that each episode includes a few labeled support videos and query ones without annotations and aims to learn and generalize a model to identify unseen classes [3, 50]. The current solutions are based on metric learning. Concretely, raw video sequences are first converted into corresponding high-level feature representations with DNN. The prediction of the query sample is determined by the matching support instance with the highest similarity [48]. However, video data with temporal dimension content is extremely complicated so it is difficult to precisely measure sample-wise relationships. To eliminate such a drawback, the current works generally calculate the similarity"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.304
+            ],
+            "angle": 0,
+            "content": "after temporal alignment. For instance, OTAM [4] assumes that frame orderings across various videos are consistent and utilizes dynamic time wrapping to find the frame-level alignment path with a cumulative distance matrix. ITANet [45] adopts a traversal manner to match frames across different videos. TRX [28] first builds tuples of sub-sequence and exploits them to match action. STRM [35] advances TRX by considering spatial information within each video. HyRSM [38] explores set matching [13, 46] metric to efficiently compute cross-video connection. Differently, our proposed RFPL focuses on video representation enhancement by injecting meta-action knowledge and precise similarity measurement via the importance-aware refinement of discriminative frames with reinforcement learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.314,
+                0.766,
+                0.331
+            ],
+            "angle": 0,
+            "content": "2.2. Reinforcement Learning (RL)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.338,
+                0.895,
+                0.626
+            ],
+            "angle": 0,
+            "content": "Reinforcement Learning (RL) arises from the neuroscientific and psychological study that which actions humans can do to gain more benefits from the environment [16, 33]. In other words, RL is utilizing the interaction of agent and environment to learn a policy that brings the most reward [14]. In fact, such a sequential decision-making procedure can be formulated as a Markov Decision Process (MDP) [6]. Recently, due to the powerful learning ability of DNN, the advanced RL works typically deploy a trainable DNN to approximate the value function or policy function as Deep Q-Network (DQN) [26] and Deep Deterministic Policy Gradient (DDPG) [22]. In addition, many real-world applications also consider using RL to improve model performance such as object tracking [42], protein analysis [20], video summarization [21] and action recognition [34]. Unlike them, our deployment of RL is solving the few-shot video action scenario by producing frame-wise weight to promote the effect of discriminative frames. Moreover, we also conduct delicate designs on DQN to be suitable for FSVC."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.64,
+                0.673,
+                0.657
+            ],
+            "angle": 0,
+            "content": "3. Proposed Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.666,
+                0.652,
+                0.683
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In few-shot video classification (FSVC), the main task is to learn a high-generalization model to identify novel action categories of video with only a few annotated video instances. To make model training and test environment consistent, the mainstream learning strategy is meta-learning fashion [28]. Concretely, we can access a label-sufficient meta-training set \\(\\mathcal{D}_{train}\\) and another meta-testing set \\(\\mathcal{D}_{test}\\) and there is no category overlap across these two sets. During the training stage, videos of each episodic are collected from \\(\\mathcal{D}_{train}\\) and further divided into a support set and a query set. The support set includes \\(k\\)-samples in each of \\(n\\) classes, which is typically defined as \\(n\\)-way-\\(k\\)-shot scenario. Under this condition, the relationship across support and query samples will be explored to identify which cate"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19312"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.092,
+                0.468,
+                0.302
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.307,
+                0.471,
+                0.391
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview of our representation fusion and promotion learning (RFPL) framework. RFPL involves two sub-modules: meta-action learning (MAL) fusing task-shared action semantics to enrich video representation and reinforced image representation (RIR) highlighting the effect of discriminative frames to precisely learn sample-wise similarity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.407,
+                0.47,
+                0.453
+            ],
+            "angle": 0,
+            "content": "gory each query video belongs to. In terms of the test stage, each episodic also consists of support and query set which are derived from \\(\\mathcal{D}_{test}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.465,
+                0.283,
+                0.48
+            ],
+            "angle": 0,
+            "content": "3.2. Framework Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.489,
+                0.471,
+                0.673
+            ],
+            "angle": 0,
+            "content": "The key to solving FSVC problem lies in how to effectively learn the pattern of discriminative action semantics from a few labeled support videos. Motivated by this, we propose a flexible Representation Fusion & Promotion Learning (RFPL) framework to enrich semantic information of video features via two novel sub-modules, as Fig.1 shows. One meta-action learning module utilizes episodes of meta-training set to build a task-shared action bank further refining feature embedding via knowledge fusion. Another reinforced image representation module adjusts the importance of frames to achieve the enhancement of discriminative semantics with reinforcement learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.694,
+                0.289,
+                0.71
+            ],
+            "angle": 0,
+            "content": "3.2.1 Meta-Action Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "It is acknowledged that a video can be decomposed into multiple image frames corresponding to sub-actions, i.e., \\(\\mathbf{X}_i = \\{\\mathbf{x}_{ij}\\}_{j=1}^m\\) where \\(m\\) is the number of frames in the \\(i\\)-th video. For example, a long jump video records some sub-actions: running, jumping and landing. In addition, we also observe that several videos come from different categories but they do share similar sub-actions such as jumping in long jump and playing basketball videos. When these two categories appear in different episodes, the transfer of similar patterns across them will facilitate the model to easily and accurately discover the similarity between support and query samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.304
+            ],
+            "angle": 0,
+            "content": "To achieve such a goal, the intuitive manner is to construct a task-shared action bank \\(\\mathbf{D}\\) to store representations of considerable sub-actions. Hence, the similar sub-actions in the long jump and playing basketball videos can be represented by the same atoms of this bank. Specifically, the widely-used backbone (e.g., ResNet-50) is first utilized to extract high-level feature of each frame, resulting in one video being transformed into the corresponding feature set \\(\\mathbf{F}_i = \\{\\mathbf{f}_{ij} | \\mathbf{f}_{ij} = \\Phi(x_{ij})\\}_{j=1}^m\\), where \\(\\Phi\\) is the feature generator. And support videos within each episode are also converted into a feature matrix \\(\\mathbf{F}^s \\in \\mathbb{R}^{d \\times nk_m}\\) where each column denotes the feature of one frame with the dimension as \\(d\\). To this end, we can gradually build and refine the memory bank \\(\\mathbf{D} \\in \\mathbb{R}^{d \\times \\kappa}\\) across different training episodes:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.598,
+                0.317,
+                0.892,
+                0.34
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\mathbf {D}, \\mathbf {A}} \\| \\mathbf {F} ^ {s} - \\mathbf {D A} \\| _ {\\mathrm {F}} ^ {2} + \\| \\mathbf {A} \\| _ {\\ell_ {1}}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.347,
+                0.892,
+                0.497
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{D}\\) is the learnable dictionary and \\(\\mathbf{A}\\) is sparse coefficient with \\(\\ell_1\\)-norm, which controls the sparseness of coefficient to achieve better reconstruction by using as fewer atoms as possible and efficiently avoids information redundancy in \\(\\mathbf{D}\\). Since the current fruitful solutions to FSVC generally adopt episodic training fashion without repeatedly accessing the previous task, we expect to gradually involve action semantics per episode into task-shared bank \\(\\mathbf{D}\\), thus, the online gradient update manner [25, 24] is adopted to optimize \\(\\mathbf{D}\\) and \\(\\mathbf{A}\\) instead of closed-form solution."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.499,
+                0.893,
+                0.694
+            ],
+            "angle": 0,
+            "content": "After obtaining the task-shared meta-action bank, another consideration is how to adaptively fuse such semantics into each specific episode. Consequently, we rethink the meaning of learned action bank. In fact, it constitutes an action space where each atom represents a basis vector. But not all are needed for the current episode due to the assumption that the number of action categories in \\(\\mathbf{D}\\) is much larger than that in this episode. Therefore, a reasonable adaptation operation is to highlight the episode-relevant basis vectors from \\(\\mathbf{D}\\). Fortunately, the classical single value decomposition (SVD) [40, 1] helps us achieve this expectation. Specifically, we adopts SVD to decompose support feature matrix \\(\\mathbf{F}^s\\) and action memory bank \\(\\mathbf{D}\\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.704,
+                0.892,
+                0.723
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {S V D} \\left(\\mathbf {F} ^ {s}\\right) \\Rightarrow \\mathbf {U} ^ {s} \\boldsymbol {\\Sigma} ^ {s} \\mathbf {V} ^ {\\mathbf {s}} ^ {\\top}, \\quad \\operatorname {S V D} (\\mathbf {D}) \\Rightarrow \\mathbf {U} \\boldsymbol {\\Sigma} \\mathbf {V} ^ {\\top}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where single values \\(\\Sigma\\) or \\(\\Sigma^s\\) control the contribution of corresponding basis vectors. So far, it is intuitive to obtain two observations from the decomposition. First, the information of feature space basis in \\(\\mathbf{U}\\) is more robust and generic than that of \\(\\mathbf{U}^s\\), since action bank refers to sufficient videos. Second, compared with \\(\\Sigma\\), \\(\\Sigma^s\\) can better estimate the intrinsic importance of basis vectors due to the fact that it is directly captured from the current episode. Based on these points, we consider fusing the advantage of each component to form the episode-adaptive action bank as \\(\\mathbf{D}^e = \\mathbf{U}\\Sigma^s\\mathbf{V}^{s^\\top}\\). Note that \\(\\mathbf{D}^e = \\mathbf{U}(\\mathbf{U}^{s^\\top}\\mathbf{U}^s)\\Sigma^s\\mathbf{V}^{s^\\top} =\\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19313"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.09,
+                0.47,
+                0.151
+            ],
+            "angle": 0,
+            "content": "\\(\\mathbf{U}\\mathbf{U}^{s^{\\top}}\\mathbf{F}^{s}\\), which is exactly a rotation of \\(\\mathbf{F}^{s}\\) using the feature basis correlation between \\(\\mathbf{U}\\) and \\(\\mathbf{U}^{s}\\). This rotation matrix brings more robust and generic semantic knowledge from \\(\\mathbf{D}\\) to \\(\\mathbf{F}^{s}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.152,
+                0.468,
+                0.244
+            ],
+            "angle": 0,
+            "content": "The next task is fusing the robust action semantics \\(\\mathbf{D}^e\\) into video representations. Meanwhile, we discover that the inner product between frame feature \\(\\mathbf{f}_{*j}^{s/q}\\) and \\(\\mathbf{d}_l^e \\in \\mathbf{D}^e\\) actually reflects the projection coefficient on each space basis, which supports us to re-express video features via \\(\\mathbf{D}^e\\). The adaptive updating strategy is formalized as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.129,
+                0.249,
+                0.468,
+                0.273
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\mathbf {f}} _ {* j} ^ {s / q} = (1 - \\rho) \\mathbf {f} _ {* j} ^ {s / q} + \\rho \\sum_ {l = 1} ^ {\\kappa} \\alpha_ {j l} \\mathbf {d} _ {l} ^ {e}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.283,
+                0.468,
+                0.374
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha_{jl} = \\cos (\\mathbf{f}_{*j}^{s / q},\\mathbf{d}_l^e)\\) denotes the cosine similarity, \\(\\rho\\) balances accepting external knowledge and keeping original representations, and \\(\\mathbf{d}_l^e\\) is the \\(l\\)-th column basis vector of \\(\\mathbf{D}^e\\). Since support and query samples both undergo re-expression via \\(\\mathbf{D}^e\\), their similar or dissimilar associations will be further adjusted and promoted."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.392,
+                0.365,
+                0.407
+            ],
+            "angle": 0,
+            "content": "3.2.2 Reinforced Image Representation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.416,
+                0.468,
+                0.795
+            ],
+            "angle": 0,
+            "content": "Our meta-action learning module enriches their latent features via the captured generic dictionary. However, not all frames in a video contain discriminative action semantics. In other words, they belong to two types: action-relevant frames and action-irrelevant ones. Promoting the contribution of the former and minimizing influence of the latter benefits the precise estimation of similarity between support and query videos. The keys to this expectation are automatically distinguish these two types and adjust their ratios in the fused representation \\(\\widetilde{\\mathbf{f}}_j^{s/q}\\). Without manual annotations on the importance of frames, it is difficult for the model to learn the distinction ability. To overcome this challenge, we can break it down into a simple situation. Given the paired support and query videos from the same action, the action-relevant frames are likely to be similar or even the same, while the remaining ones tend to be different. Calculating frame-wise similarity across two videos easily discovers the discriminative frames. Their representation enhancement obviously narrows cross-video distance. For the paired samples in various classes, the weight adjustment on frames results in the reduction of cross-video similarity. In summary, these two cases indicate that frame-wise comparison and weight modification trigger the corresponding effects. This is an analogy to the basic logic of reinforcement learning adopting an action and receiving its reward."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.468,
+                0.855
+            ],
+            "angle": 0,
+            "content": "With the analogy, we develop a reinforced image representation (RIR) module within the reinforcement learning (RL) framework to fulfill our goal. Specifically, in FSVC, the basic concepts of RL are redefined:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.857,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- State: the video feature at \\( t \\) time, i.e., \\( s_t = \\{w_j \\widetilde{\\mathbf{f}}_{*j}\\}_{j=1}^m \\) where \\( w_j \\) initialized as 1 is the importance of the corresponding \\( j \\)-th frame;"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.181
+            ],
+            "angle": 0,
+            "content": "- Action: \\( a_{t} \\) depends on the output of agent \\( (p \\in [0,1]) \\) with the Sigmoid function applied. When \\( p < 0.5 \\), the action \\( a_{t} = 0 \\) with \\( \\mathrm{p}(a_t) = 2p \\) and \\( w_{j} = w_{j} - \\mathrm{p}(a_{t}) \\), otherwise, \\( a_{t} = 1 \\) with \\( \\mathrm{p}(a_t) = 2(p - 0.5) \\) and \\( w_{j} = w_{j} + \\mathrm{p}(a_{t}) \\). The agent in Figure 1 is implemented as one deep neural network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.182,
+                0.892,
+                0.302
+            ],
+            "angle": 0,
+            "content": "- Reward: \\( r_t \\) of \\( t \\) time includes positive type and negative one. For the paired videos in the same class, \\( r_t \\) is positive with cross-video similarity improvement, while the reduction results in the negative one. The operation is inverse for paired videos in different classes. The reward is considered as the supervision to instruct the learning of the agent. Note that we ignore superscript \\( s / q \\) in three concepts, since they are suitable for all videos."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.302
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.303,
+                0.892,
+                0.499
+            ],
+            "angle": 0,
+            "content": "In reinforcement learning, the interaction procedure between agent and environment actually is a Markov decision process [20]. Concretely, given the estimated action value, the state is transferred from \\( s_t^{s/q} \\) to \\( s_{t+1}^{s/q} \\) according to an implicit probability distribution. During the state transition stage, the main challenge is how to decide the optimal action at the current state. In fact, the action \\( a_t^{s/q} \\) exists in a hidden probability space which is effectively estimated by Q-learning [26, 39] strategy. Under this condition, the expectation value of actions \\( a_t^{s/q} \\) is formally defined as \\( Q_t \\) and the current action modifies the importance \\( w_j^{s/q} \\) of frame \\( \\widetilde{\\mathbf{f}}_{*j}^{s/q} \\) and affects the final reward. The formulation of \\( Q_t \\) is:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.502,
+                0.505,
+                0.892,
+                0.529
+            ],
+            "angle": 0,
+            "content": "\\[\nQ _ {t} \\left(s _ {t} ^ {s / q}, a _ {t} ^ {s / q}\\right) = \\max  _ {\\pi} \\mathbb {E} \\left[ r _ {t} + \\gamma r _ {t + 1} + \\gamma^ {2} r _ {t + 2} \\dots | \\pi \\right], \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.535,
+                0.892,
+                0.672
+            ],
+            "angle": 0,
+            "content": "where \\(\\gamma\\) denotes the discount factor balancing the immediate reward and the future ones, and \\(\\pi = \\arg \\min_{a_t^{s/q}} Q_t\\) is our desired probability distribution policy of action. To estimate such a policy, the Deep-Q network (DQN) [26] as an effective tool is generally utilized to approximate \\(Q_t\\). In a nutshell, DQN typically constructs the learnable function taking the state as input to produce the probabilities \\(p\\) of action space. The function is always instantiated as a parameterized network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.673,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "However, such a straightforward input design of DQN fails to observe the relationship of video pairs and embed this pivotal knowledge into action selection. For FSVC, the appropriate input of DQN is supposed to involve three different valuable contents. The first part is the feature of the chosen frame \\(\\widetilde{\\mathbf{f}}_{*j}^{s / q}\\) on which the estimated action is to be conducted. Emphasizing the current frame representation significantly upgrades its contribution to the prediction. The second one is the fused feature of the remaining frames, i.e., \\(\\frac{1}{m - 1}\\sum_{l = 1,l\\neq j}^{m}w_{l}^{s / q}\\widetilde{\\mathbf{f}}_{*l}^{s / q}\\). This information tends to affect the computation of future rewards. The third special point lies in measuring the cosine similarities across this frame and other frames in another video, written as \\(\\mathbf{v}_j\\in \\mathbb{R}^m\\) with its element \\(\\mathbf{v}_{jl} = \\cos (\\widetilde{\\mathbf{f}}_j^{s / q},\\widetilde{\\mathbf{f}}_l^{q / s})\\). \\(\\mathbf{v}_j\\) reflects its potentiality to promote the cross-video similarity."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19314"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.091,
+                0.473,
+                0.298
+            ],
+            "angle": 0,
+            "content": "In terms of the output of DQN, \\(a_{t}^{s / q} = 0\\) suggests that the importance of this frame should be reduced via \\(w_{j}^{s / q} = w_{j}^{s / q} - \\mathrm{p}(a_{t}^{s / q})\\), where \\(\\mathrm{p}(a_t^{s / q}) = 2p\\) and \\(p\\) is the probability of action. For the other situation, weight update of frame is \\(w_{j}^{s / q} = w_{j}^{s / q} + \\mathrm{p}(a_{t}^{s / q})\\) with \\(\\mathrm{p}(a_t^{s / q}) = 2(p - 0.5)\\). After conducting actions, we have \\(w_{j}^{s / q}\\in (0,2)\\) and it is simple to attain the corresponding reward by calculating the change of similarity of video representations \\(r = \\mathrm{sign}\\left(\\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)|s_{t + 1} - \\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)|s_t\\right)\\), where \\(\\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)\\) means \\(\\cos (\\sum_{j = 1}^{m}w_{j}^{s}\\widetilde{\\mathbf{f}}_{*j}^{s},\\sum_{j = 1}^{m}w_{j}^{q}\\widetilde{\\mathbf{f}}_{*j}^{q})\\), and \\(\\mathrm{sign}(\\cdot)\\) denotes a sign function. Finally, with the Bellman theorem [2], the Deep-Q network is optimized with:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.078,
+                0.301,
+                0.472,
+                0.348
+            ],
+            "angle": 0,
+            "content": "\\[\n\\underset {\\Theta} {\\min} \\mathbb {E} \\left[ r + \\gamma \\max _ {a _ {i + 1} ^ {s / q}} Q (s _ {i + 1} ^ {s / q}, a _ {i + 1} ^ {s / q}) - Q (s _ {i} ^ {s / q}, a _ {i} ^ {s / q}) \\right] ^ {2}, \\quad (5)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.355,
+                0.473,
+                0.492
+            ],
+            "angle": 0,
+            "content": "where \\(\\Theta\\) includes all the trainable network parameters of DQN. For the training stage, the snapshot of state, action, and reward at any time is stored and divided into several mini-batches with random sampling, and we adopt \\(\\epsilon\\)-greedy strategy to determine action using \\(\\pi\\) with probability \\(\\epsilon\\) and use random actions with \\(1 - \\epsilon\\). For the inference stage, the well-trained DQN is frozen and infers the weight for each frame given the paired videos. To this end, video representations are further advanced with frame-wise importance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.5,
+                0.272,
+                0.517
+            ],
+            "angle": 0,
+            "content": "3.3. Module Deployment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.524,
+                0.47,
+                0.689
+            ],
+            "angle": 0,
+            "content": "Our developed Representation Fusion & Promotion Learning (RFPL) framework includes two components. Meta-action learning (MAL) stores abundant action semantics via \\( \\mathcal{D}_{train} \\) and is adapted into each specific episode to enhance video representations, while Reinforced image representation (RIR) exploits deep Q-learning theory of RL to increase the representation of informative frame. Actually, it is straightforward and convenient to plug our REM into various FSVC methods to boost the model performance. In this paper, we choose three state-of-the-art FSVC models, e.g., OTAM [4], TRX [28] and STRM [35]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Concretely, original OTAM first extracts frame-level features across all support and query samples per episode, and then calculate frame-wise similarity from support and query video pair. It finally utilizes a dynamic time wrapping algorithm (DTW) to obtain the similarity of videos and uses a metric manner to optimize or deduce the category of the query. When embedding RFPL into OTAM, our MAL module is combined with the outputs of the feature extractor, and our RIR is performed before the calculation of frame-wise similarity of video pairs. Similarly, for TRX, the average-pooling features of ResNet-50 are regarded as the inputs for MAL, and the refined representations further help in the selection of discriminative frames. Different from OTAM, RIR in TRX compares the given"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.202
+            ],
+            "angle": 0,
+            "content": "query instances with all support ones, determines an optimal weighted query representation with the highest similarity, and feeds it into the following modules. Compared with OTAM and TRX, STRM utilizes the feature maps before the average pooling of ResNet-50 as inputs for a Transformer block and finally compresses them into frame-level vector representation as \\(\\mathbf{F}_i^{s/q}\\) where our RFPL is conducted."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.216,
+                0.634,
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+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.242,
+                0.709,
+                0.259
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.267,
+                0.895,
+                0.373
+            ],
+            "angle": 0,
+            "content": "Datasets. Three popular few-shot benchmarks are evaluated including UCF101 [31], Kinetics [5] and SSv2-Full [10]. For Kinetics and SSv2-Full, we follow the data split protocol of [4, 28, 37] to build meta-training set \\( \\mathcal{D}_{train} \\), meta-validation set \\( \\mathcal{D}_{val} \\) and meta-testing set \\( \\mathcal{D}_{test} \\), which consists 64, 12 and 24 categories, respectively. For UCF101, we adopt the split and sampling manners in [44]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.376,
+                0.895,
+                0.679
+            ],
+            "angle": 0,
+            "content": "Implementation Details. Following the existing works [4, 28, 35], 8 image frames per video are randomly and uniformly selected as its raw representations and the pretrained ResNet-50 [11] is considered as the backbone to extract high-level features from frame-level images. For the task-shared bank, we regard \\(\\mathbf{D}\\) as one learnable tensor randomly initialized and optimized by Eq. (1) with SGD optimizer (learning rate: \\(10^{-3} \\rightarrow 10^{-5}\\)) in each episode during training stage and it is frozen for the test procedure. In addition, the DQN in our RIR module includes three fully-connected (FC) layers mapping the input to the number of actions, whose training is independent of other parts. Concretely, we first train DQN with several episodes by freezing the remaining networks (ResNet-50, task-shared Bank, and Transformer block), and then update the remains with the fixed DQN by other episodes. The iterative process is repeated by many times. Other training regulations are preserved as each specific method. For inference, 10,000 episodes are randomly selected from \\(\\mathcal{D}_{test}\\) to evaluate the performance of the model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.683,
+                0.895,
+                0.79
+            ],
+            "angle": 0,
+            "content": "Baselines. Currently, HyRSM [37] and STRM [35] achieve the state-of-the-art results on most FSVC tasks, which are considered as important baselines. Besides, other excellent works such as TRN [47], CMN [48], CMN-J [49], TARN [3], OTAM [4], TTAN [19], TRX [28], ITANet [45], ARN [44], MAML [8] and MatchingNet [36] also serve as strong competitors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.801,
+                0.658,
+                0.817
+            ],
+            "angle": 0,
+            "content": "4.2. Result Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Table 1 summarizes the results of our method and other competitors on three datasets (UCF101, Kinetics, SSv2-Full) when solving various few-shot video classification tasks. According to the results, it is straightforward to achieve several important conclusions."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.52,
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+            ],
+            "angle": 0,
+            "content": "19315"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.088,
+                0.894,
+                0.129
+            ],
+            "angle": 0,
+            "content": "Table 1. Result comparison of multiple methods on few-shot video classification problem. Evaluations are conducted on the meta-testing set of UCF101, Kinetics, and SSv2-Full under 5-way scenario. The number of support videos per class varies from 1 to 5 within each episode. The highest and second results are highlighted by **bold** and **underline**."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.094,
+                0.129,
+                0.875,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Source</td><td>Dataset</td><td>1-shot</td><td>2-shot</td><td>3-shot</td><td>4-shot</td><td>5-shot</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td rowspan=\"6\">UCF101</td><td>66.3</td><td>-</td><td>-</td><td>-</td><td>83.1</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>80.9</td><td>-</td><td>-</td><td>-</td><td>93.2</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>79.9</td><td>85.5</td><td>87.0</td><td>88.3</td><td>88.9</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>78.2</td><td>88.9</td><td>92.4</td><td>94.1</td><td>96.1</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>78.3</td><td>88.9</td><td>91.9</td><td>93.5</td><td>96.9</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>83.9</td><td>-</td><td>93.0</td><td>-</td><td>94.7</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>84.3↑4.4</td><td>88.9↑3.4</td><td>90.2↑3.2</td><td>91.9↑3.6</td><td>92.1↑3.2</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>82.5↑4.2</td><td>91.1↑2.2</td><td>94.1↑1.7</td><td>95.6↑1.5</td><td>96.3↑0.2</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>79.7↑1.4</td><td>90.1↑1.2</td><td>93.8↑1.9</td><td>95.8↑2.3</td><td>96.7↓0.2</td></tr><tr><td>MatchNet [36]</td><td>NeuIPS-16</td><td rowspan=\"11\">Kinetics</td><td>53.3</td><td>64.3</td><td>69.2</td><td>71.8</td><td>74.6</td></tr><tr><td>MAML [8]</td><td>ICML-17</td><td>54.2</td><td>65.5</td><td>70.0</td><td>72.1</td><td>75.3</td></tr><tr><td>Plain CMN [48]</td><td>ECCV-18</td><td>57.3</td><td>67.5</td><td>72.5</td><td>74.7</td><td>76.0</td></tr><tr><td>CMN-J [49]</td><td>TPAMI-20</td><td>60.5</td><td>70.0</td><td>75.6</td><td>77.3</td><td>78.9</td></tr><tr><td>TARN [3]</td><td>BMVC-19</td><td>64.8</td><td>-</td><td>-</td><td>-</td><td>78.5</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td>63.7</td><td>-</td><td>-</td><td>-</td><td>82.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>73.6</td><td>-</td><td>-</td><td>-</td><td>84.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>73.0</td><td>75.9</td><td>78.7</td><td>81.9</td><td>85.8</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>63.6</td><td>76.2</td><td>81.8</td><td>83.4</td><td>85.9</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>62.1</td><td>78.6</td><td>82.2</td><td>82.8</td><td>86.7</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>73.7</td><td>80.0</td><td>83.5</td><td>84.6</td><td>86.1</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>74.6↑1.6</td><td>80.0↑4.1</td><td>82.1↑3.4</td><td>84.1↑2.2</td><td>86.8↑1.0</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>66.2↑2.6</td><td>77.5↑1.3</td><td>83.8↑2.0</td><td>85.1↑1.7</td><td>87.3↑1.4</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>64.9↑2.8</td><td>80.3↑1.7</td><td>84.3↑2.1</td><td>84.8↑2.0</td><td>87.7↑1.0</td></tr><tr><td>CMN++ [48]</td><td>ECCV-18</td><td rowspan=\"8\">SSv2-Full</td><td>34.4</td><td>-</td><td>-</td><td>-</td><td>43.8</td></tr><tr><td>TRN++ [47]</td><td>ECCV-18</td><td>38.6</td><td>-</td><td>-</td><td>-</td><td>48.9</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>46.3</td><td>52.5</td><td>57.3</td><td>59.3</td><td>60.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>49.2</td><td>55.5</td><td>59.1</td><td>61.0</td><td>62.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>42.6</td><td>49.1</td><td>51.5</td><td>52.0</td><td>52.3</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>42.0</td><td>53.1</td><td>57.6</td><td>61.1</td><td>64.6</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>42.1</td><td>53.8</td><td>59.3</td><td>64.2</td><td>68.1</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>54.3</td><td>62.2</td><td>65.1</td><td>67.9</td><td>69.0</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>47.0↑4.2</td><td>54.6↑5.5</td><td>58.3↑6.8</td><td>60.3↑8.3</td><td>61.0↑8.7</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>44.6↑2.6</td><td>54.2↑1.1</td><td>59.9↑2.3</td><td>63.1↑2.1</td><td>64.6↑2.3</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>45.7↑3.6</td><td>55.8↑2.0</td><td>61.7↑2.4</td><td>66.8↑2.6</td><td>69.5↑1.4</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.648,
+                0.473,
+                0.89
+            ],
+            "angle": 0,
+            "content": "First, when plugging our proposed modules into the existing FSVC works such as OTAM, its performance gains significant improvement. Concretely, for 5-way-5-shot task on SSv2-Full, the classification accuracy of OTAM using our module attains \\(61.0\\%\\) which is much higher than its original \\(52.3\\%\\). In addition, the integration of our designed modules and OTAM exceeds the original one by \\(4.4\\%\\) on 1-shot task of UCF101. These phenomenons illustrate that our method effectively facilitates OTAM to conduct more accurate temporal alignment across support and query videos by refining video representations with task-shared knowledge and discriminative frame selection. Second, compared with OTAM, original TRX and STRM not only consider learning temporal relationships but also draw assistance from Transformer block to achieve information complementary within each episode. Although their methods seem to be perfect"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.648,
+                0.892,
+                0.83
+            ],
+            "angle": 0,
+            "content": "and promising, our RFPL still facilitates them to boost \\(2\\%\\) on most tasks. The main reason for success lies in that our method further helps them enrich the representations of action semantics by introducing meta-action semantics and accurately capture the intrinsic similarity across support and query instances via the increasing effect of important image frames. Finally, injecting our RFPL into other baselines achieves comparable performance with HyRSM on most tasks. Especially, STRM with our RFPL surpasses HyRSM by an obvious gain margin, i.e., \\(1.6\\%\\) on 5-shot task of Kinetics, validating that our proposed method is an efficient auxiliary tool for addressing the FSVC problem."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.845,
+                0.686,
+                0.862
+            ],
+            "angle": 0,
+            "content": "4.3. Performance Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Path Visualization & Confusion Matrix. From Table 1, we conclude that our RFPL effectively promotes the perfor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19316"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.083,
+                0.089,
+                0.379,
+                0.27
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.384,
+                0.091,
+                0.635,
+                0.272
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.636,
+                0.092,
+                0.89,
+                0.272
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.273,
+                0.893,
+                0.316
+            ],
+            "angle": 0,
+            "content": "Figure 2. Comparison between plain OTAM and Ours+OTAM on action recognition result and temporal alignment path. This episode is randomly selected from the meta-testing set of Kinetics. The query video belongs to dancing ballet. Our+OTAM successfully matches it with the support sample from the same category, while plain OTAM matches into a dancing charleston video."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.32,
+                0.29,
+                0.484
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.133,
+                0.487,
+                0.26,
+                0.499
+            ],
+            "angle": 0,
+            "content": "(a) OTAM @ Kinetics"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.291,
+                0.32,
+                0.481,
+                0.484
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.305,
+                0.487,
+                0.466,
+                0.5
+            ],
+            "angle": 0,
+            "content": "(b) Ours+OTAM @ Kinetics"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.481,
+                0.32,
+                0.671,
+                0.484
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.488,
+                0.643,
+                0.5
+            ],
+            "angle": 0,
+            "content": "(c) OTAM @ SSV-Full"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.671,
+                0.32,
+                0.89,
+                0.484
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.696,
+                0.488,
+                0.862,
+                0.5
+            ],
+            "angle": 0,
+            "content": "(d) Ours+OTAM @ SSV-Full"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.503,
+                0.893,
+                0.531
+            ],
+            "angle": 0,
+            "content": "Figure 3. Comparison of confusion matrix deduced from the model prediction of plain OTAM and Ours+OTAM. These two episodes are collected from the meta-testing set of Kinetics (2-shot) and SSv2-Full (5-shot)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.538,
+                0.47,
+                0.749
+            ],
+            "angle": 0,
+            "content": "mance of OTAM by a large margin. To explicitly explain the reason for improvement, we randomly select an episode from meta-testing set \\( \\mathcal{D}_{test} \\) and visualize the frame-level cumulative distance across query video and the selected support ones as Fig. 2 shows. This visualization indicates that OTAM is sensitive to image background and its temporal alignment becomes invalid. Thus, it considers that this query video from the dancing ballet class has the highest similarity with the support sample from dancing charleston. Differently, our method assists OTAM to focus on the similarity of action semantics, especially on distinguishing body posture. Hence, Ours+OTAM accurately matches the query sample with the support video from the identical category and achieves better temporal alignment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In addition, we draw the confusion matrix of two specific episodes to further discuss their differences. Concretely, during the inference stage, for 2-shot of Kinetics or 5-shot of SSv2-Full, we randomly choose an episode with 200 query samples uniformly distributed in five categories and compare model prediction and ground-truth to form Fig. 3. For the task of Kinetics, with the help of our RFPL, the recognition abilities of OTAM in five categories are all strengthened. With respect to the more challenging task of SSv2-Full, OTAM with our method learns more discrimina"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.538,
+                0.892,
+                0.583
+            ],
+            "angle": 0,
+            "content": "tive action semantics and achieves significant performance improvement on several categories without reduction on the remaining ones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.893,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Reinforced Image Frames. In our RFPL, reinforced image representation as one important module aims to discover the discriminative image frames via the comparison of the paired videos. To analyze its effect, we record the frame-wise weights deduced from the agent as Fig. 4 in one test episode. From two \"folding paper\" videos, several image frames without any \"folding\" action are provided with lower weights such as frames in the red box. For action-relevant images, the learned network produces higher weights for them as the blue box shows. From the other example \"cutting watermelon\", we have an interesting finding. The well-trained network does not give larger weights for frames including \"cutting\" action, while highlighting images with two halves of the red pulp of a watermelon as the green box shows. It suggests that the network considers that these image contents are useful for the improvement of cross-video similarity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Parameter Analysis. There is one hyper-parameter \\(\\rho\\) in our RFPL, which serves as a trade-off between accepting external global knowledge and preserving current feature representations. In practical experiments, this parameter is"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19317"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.093,
+                0.87,
+                0.363
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.365,
+                0.895,
+                0.407
+            ],
+            "angle": 0,
+            "content": "Figure 4. Importance of frames produced by reinforced image representation module. Videos of the first and second rows belong to folding paper, while the remaining videos are from cutting watermelon. Images in the red box are regarded as key action semantics by the network, while the effect of others in the blue box is reduced. Similarly, the representations of images in the green box are also enhanced."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.119,
+                0.414,
+                0.422,
+                0.58
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.098,
+                0.58,
+                0.446,
+                0.594
+            ],
+            "angle": 0,
+            "content": "Figure 5. Parameter analysis of \\(\\rho\\) with different selections."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "tuned for different tasks, i.e., \\(\\rho \\in \\{0.001, 0.01, 0.1, 0.5\\}\\). Definitely, the optimal parameter is determined by the performance of the learned model on the meta-validation set. Concretely, Fig. 5 shows the change of model classification ability on the validation set of SSv2-Full with the varying \\(\\rho\\). Based on this parameter analysis, we find that when \\(\\rho = 0.5\\), the video classification accuracy is lower than that of smaller \\(\\rho\\) on many tasks. Therefore, it is reasonable to infer that while introducing global knowledge to enhance semantics information, the protection of current information is very necessary and stabilizes the model training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Ablation Study. Our RFPL consists of two modules: meta-action learning and reinforced image representation. The first one aims to enrich video representation by fusing global knowledge of the meta-action bank to each specific episode, while the second one expects to emphasize the representation of informative image frames via reinforcement learning selection. In fact, we also separately plug each module into the existing baseline, named as Ours-v1 (adding MAL) and Ours-v2 (adding RIR). These variants"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.53,
+                0.41,
+                0.861,
+                0.546
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.546,
+                0.892,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Figure 6. Ablation study. Ours-v1 and Ours-v2 mean that meta-action learning and reinforced image representation modules are plugged into the existing FSVC works, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.597,
+                0.892,
+                0.704
+            ],
+            "angle": 0,
+            "content": "are combined with OTAM and evaluated on three tasks of Kinetics with results in Fig. 6. The comparisons with plain OTAM mean that each module can independently make positive contributions on advancing it. And the collaboration of MAL and RIR will bring more benefits to OTAM than each independent module. Thus, using the complete RFPL is the optimal strategy."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.742,
+                0.892,
+                0.893
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a flexible representation fusion and enhancement learning (RFPL) mechanism with two sub-modules to solve few-shot video classification. The meta-action learning module builds a generic action bank and fuses the adapted one to enrich video features, while the reinforced image representation module identifies important frames via an agent and promotes their positive effect to precisely capture cross-video similarity. Considerable experimental results and analysis verify that our RFPL effectively advances the existing FSVC methods."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "19318"
+        }
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+            "type": "title",
+            "bbox": [
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+            "angle": 0,
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+# Few-Shot Video Classification via Representation Fusion and Promotion Learning
+
+Haifeng Xia $^{1*}$ , Kai Li $^{2}$ , Martin Renqiang Min $^{2}$ , Zhengming Ding $^{1}$ $^{1}$ Department of Computer Science, Tulane University,  $^{2}$ NEC Labs, America  
+{hxia, zdingl}@tulane.edu, {kaili, renqiang}@nec-labs.com
+
+# Abstract
+
+Recent few-shot video classification (FSVC) works achieve promising performance by capturing similarity across support and query samples with different temporal alignment strategies or learning discriminative features via Transformer block within each episode. However, they ignore two important issues: a) It is difficult to capture rich intrinsic action semantics from a limited number of support instances within each task. b) Redundant or irrelevant frames in videos easily weaken the positive influence of discriminative frames. To address these two issues, this paper proposes a novel Representation Fusion and Promotion Learning (RFPL) mechanism with two sub-modules: meta-action learning (MAL) and reinforced image representation (RIR). Concretely, during training stage, we perform online learning for seeking a task-shared meta-action bank to enrich task-specific action representation by injecting global knowledge. Besides, we exploit reinforcement learning to obtain the importance of each frame and refine the representation. This operation maximizes the contribution of discriminative frames to further capture the similarity of support and query samples from the same category. Our RFPL framework is highly flexible that it can be integrated with many existing FSVC methods. Extensive experiments show that RFPL significantly enhances the performance of existing FSVC models when integrated with them.
+
+# 1. Introduction
+
+Due to the emergence of deep learning [43, 18, 15], video action recognition has obtained impressive improvement by learning informative semantics from raw videos [23, 38]. These achievements heavily rely on the powerful supervision of considerable well-labeled videos to optimize deep neural networks [32, 41]. However, the collection and annotation of training samples become laborious and expensive, especially for video sequences. Hence, such a learning
+
+paradigm does not always feasible for many practical applications [7, 29]. This conflict motivates investigations on few-shot video classification (FSVC) which aims to learn a model of good generalization performance from a few labeled video samples [4, 35, 37].
+
+The mainstream solutions to FSVC typically adopt metric-based meta-learning [30, 12] fashion by training model across multiple episodes where each includes one support set with a few annotated videos and the other query set with unlabeled instances. For inference, the well-trained model measures the similarities across support and query videos within each episode to determine which categories the query samples come from [17]. However, it is difficult to precisely assess frame-wise relationships within video sequences, since their temporal information has significant divergence or even mismatch. To overcome such a challenge, the intuitive strategy is to achieve temporal alignment among cross-video frames. For example, OTAM [4] develops a variant of dynamic time wrapping (DTW) [27] to find the optimal alignment path via the frame-level cumulative distance function. Similarly, ITANet [45] explores implicit temporal alignment via a traversal strategy. Moreover, TRX [28] develops multiple tuples of sub-sequence to achieve action matching. And STRM [35] studies self-attention mechanisms to emphasize channel representation in a single video. HyRSM [37] presents a set matching concept to explore temporal alignment without frame-level ordering across various videos.
+
+Although these existing works have achieved appealing results, they tend to encounter performance bottlenecks due to ignorance of the following two issues. First, the limited number of labeled samples within each individual task hardly provides sufficient support to assist model learning the essential action semantics for the recognition task. Second, there are redundant or irrelevant frames in videos; treating these less informative frames in the same way as the other informative ones likely weakens the discriminability of the learned video representations, and thus triggers a negative effect on solving the FSVC task.
+
+In this paper, we propose a novel Representation Fusion
+
+and Promotion Learning (RFPL) framework to address the two issues, by two novel modules, respectively. To address the deficiency of semantic information within each individual task, we propose the meta-action learning (MAL) module which introduces external knowledge learned globally to enrich video representations learned locally within each individual task. Specifically, MAL maintains a global meta-action bank storing representations of atomic action snippets that can be used to compose various action categories of higher complexity. The global meta-action bank is shared by all action types and all individual FSVC tasks. We explore it to enrich the video feature representations learned locally in each individual task via a novel Single Value Decomposition (SVD) technique.
+
+To address the redundant/irrelevant frame issue, we propose the reinforced image representation (RIR) module which explores reinforcement learning to discover the importance of each frame to the FSVC task. We train the reinforcement learning agent by exploiting the relationship between support and query video pairs, striving to emphasize the influence of discriminative frames to help the model accurately capture sample-wise similarity. Our MAL and RIR can be easily plugged into the existing FSVC methods to promote their performance. Our main contributions in this work are summarized in three folds as:
+
+- We propose the meta-action learning module which learns a global meta-action bank to enrich video representation learned locally in individual tasks, via a novel SVD technique.  
+- We address the negative effect of task-irrelevant frames on capturing cross-video relationships and develop a reinforced image representation module that promotes the contribution of discriminative frames.  
+- Our RFPL framework is highly flexible such that it can be integrated with various FSVC methods and gets improved performance.
+
+# 2. Related Works
+
+# 2.1. Few-Shot Video Classification (FSVC)
+
+When using meta-learning manner [8, 9], FSVC scenario assumes that each episode includes a few labeled support videos and query ones without annotations and aims to learn and generalize a model to identify unseen classes [3, 50]. The current solutions are based on metric learning. Concretely, raw video sequences are first converted into corresponding high-level feature representations with DNN. The prediction of the query sample is determined by the matching support instance with the highest similarity [48]. However, video data with temporal dimension content is extremely complicated so it is difficult to precisely measure sample-wise relationships. To eliminate such a drawback, the current works generally calculate the similarity
+
+after temporal alignment. For instance, OTAM [4] assumes that frame orderings across various videos are consistent and utilizes dynamic time wrapping to find the frame-level alignment path with a cumulative distance matrix. ITANet [45] adopts a traversal manner to match frames across different videos. TRX [28] first builds tuples of sub-sequence and exploits them to match action. STRM [35] advances TRX by considering spatial information within each video. HyRSM [38] explores set matching [13, 46] metric to efficiently compute cross-video connection. Differently, our proposed RFPL focuses on video representation enhancement by injecting meta-action knowledge and precise similarity measurement via the importance-aware refinement of discriminative frames with reinforcement learning.
+
+# 2.2. Reinforcement Learning (RL)
+
+Reinforcement Learning (RL) arises from the neuroscientific and psychological study that which actions humans can do to gain more benefits from the environment [16, 33]. In other words, RL is utilizing the interaction of agent and environment to learn a policy that brings the most reward [14]. In fact, such a sequential decision-making procedure can be formulated as a Markov Decision Process (MDP) [6]. Recently, due to the powerful learning ability of DNN, the advanced RL works typically deploy a trainable DNN to approximate the value function or policy function as Deep Q-Network (DQN) [26] and Deep Deterministic Policy Gradient (DDPG) [22]. In addition, many real-world applications also consider using RL to improve model performance such as object tracking [42], protein analysis [20], video summarization [21] and action recognition [34]. Unlike them, our deployment of RL is solving the few-shot video action scenario by producing frame-wise weight to promote the effect of discriminative frames. Moreover, we also conduct delicate designs on DQN to be suitable for FSVC.
+
+# 3. Proposed Method
+
+# 3.1. Problem Setup
+
+In few-shot video classification (FSVC), the main task is to learn a high-generalization model to identify novel action categories of video with only a few annotated video instances. To make model training and test environment consistent, the mainstream learning strategy is meta-learning fashion [28]. Concretely, we can access a label-sufficient meta-training set  $\mathcal{D}_{train}$  and another meta-testing set  $\mathcal{D}_{test}$  and there is no category overlap across these two sets. During the training stage, videos of each episodic are collected from  $\mathcal{D}_{train}$  and further divided into a support set and a query set. The support set includes  $k$ -samples in each of  $n$  classes, which is typically defined as  $n$ -way- $k$ -shot scenario. Under this condition, the relationship across support and query samples will be explored to identify which cate
+
+![](images/9a784b4a5050c1d99ab3789bcfa3cdea6d1972af255da61d5a9a38b5ffa16139.jpg)  
+Figure 1. Overview of our representation fusion and promotion learning (RFPL) framework. RFPL involves two sub-modules: meta-action learning (MAL) fusing task-shared action semantics to enrich video representation and reinforced image representation (RIR) highlighting the effect of discriminative frames to precisely learn sample-wise similarity.
+
+gory each query video belongs to. In terms of the test stage, each episodic also consists of support and query set which are derived from  $\mathcal{D}_{test}$ .
+
+# 3.2. Framework Overview
+
+The key to solving FSVC problem lies in how to effectively learn the pattern of discriminative action semantics from a few labeled support videos. Motivated by this, we propose a flexible Representation Fusion & Promotion Learning (RFPL) framework to enrich semantic information of video features via two novel sub-modules, as Fig.1 shows. One meta-action learning module utilizes episodes of meta-training set to build a task-shared action bank further refining feature embedding via knowledge fusion. Another reinforced image representation module adjusts the importance of frames to achieve the enhancement of discriminative semantics with reinforcement learning.
+
+# 3.2.1 Meta-Action Learning
+
+It is acknowledged that a video can be decomposed into multiple image frames corresponding to sub-actions, i.e.,  $\mathbf{X}_i = \{\mathbf{x}_{ij}\}_{j=1}^m$  where  $m$  is the number of frames in the  $i$ -th video. For example, a long jump video records some sub-actions: running, jumping and landing. In addition, we also observe that several videos come from different categories but they do share similar sub-actions such as jumping in long jump and playing basketball videos. When these two categories appear in different episodes, the transfer of similar patterns across them will facilitate the model to easily and accurately discover the similarity between support and query samples.
+
+To achieve such a goal, the intuitive manner is to construct a task-shared action bank  $\mathbf{D}$  to store representations of considerable sub-actions. Hence, the similar sub-actions in the long jump and playing basketball videos can be represented by the same atoms of this bank. Specifically, the widely-used backbone (e.g., ResNet-50) is first utilized to extract high-level feature of each frame, resulting in one video being transformed into the corresponding feature set  $\mathbf{F}_i = \{\mathbf{f}_{ij} | \mathbf{f}_{ij} = \Phi(x_{ij})\}_{j=1}^m$ , where  $\Phi$  is the feature generator. And support videos within each episode are also converted into a feature matrix  $\mathbf{F}^s \in \mathbb{R}^{d \times nk_m}$  where each column denotes the feature of one frame with the dimension as  $d$ . To this end, we can gradually build and refine the memory bank  $\mathbf{D} \in \mathbb{R}^{d \times \kappa}$  across different training episodes:
+
+$$
+\min  _ {\mathbf {D}, \mathbf {A}} \| \mathbf {F} ^ {s} - \mathbf {D A} \| _ {\mathrm {F}} ^ {2} + \| \mathbf {A} \| _ {\ell_ {1}}, \tag {1}
+$$
+
+where  $\mathbf{D}$  is the learnable dictionary and  $\mathbf{A}$  is sparse coefficient with  $\ell_1$ -norm, which controls the sparseness of coefficient to achieve better reconstruction by using as fewer atoms as possible and efficiently avoids information redundancy in  $\mathbf{D}$ . Since the current fruitful solutions to FSVC generally adopt episodic training fashion without repeatedly accessing the previous task, we expect to gradually involve action semantics per episode into task-shared bank  $\mathbf{D}$ , thus, the online gradient update manner [25, 24] is adopted to optimize  $\mathbf{D}$  and  $\mathbf{A}$  instead of closed-form solution.
+
+After obtaining the task-shared meta-action bank, another consideration is how to adaptively fuse such semantics into each specific episode. Consequently, we rethink the meaning of learned action bank. In fact, it constitutes an action space where each atom represents a basis vector. But not all are needed for the current episode due to the assumption that the number of action categories in  $\mathbf{D}$  is much larger than that in this episode. Therefore, a reasonable adaptation operation is to highlight the episode-relevant basis vectors from  $\mathbf{D}$ . Fortunately, the classical single value decomposition (SVD) [40, 1] helps us achieve this expectation. Specifically, we adopts SVD to decompose support feature matrix  $\mathbf{F}^s$  and action memory bank  $\mathbf{D}$  as:
+
+$$
+\operatorname {S V D} \left(\mathbf {F} ^ {s}\right) \Rightarrow \mathbf {U} ^ {s} \boldsymbol {\Sigma} ^ {s} \mathbf {V} ^ {\mathbf {s}} ^ {\top}, \quad \operatorname {S V D} (\mathbf {D}) \Rightarrow \mathbf {U} \boldsymbol {\Sigma} \mathbf {V} ^ {\top}, \tag {2}
+$$
+
+where single values  $\Sigma$  or  $\Sigma^s$  control the contribution of corresponding basis vectors. So far, it is intuitive to obtain two observations from the decomposition. First, the information of feature space basis in  $\mathbf{U}$  is more robust and generic than that of  $\mathbf{U}^s$ , since action bank refers to sufficient videos. Second, compared with  $\Sigma$ ,  $\Sigma^s$  can better estimate the intrinsic importance of basis vectors due to the fact that it is directly captured from the current episode. Based on these points, we consider fusing the advantage of each component to form the episode-adaptive action bank as  $\mathbf{D}^e = \mathbf{U}\Sigma^s\mathbf{V}^{s^\top}$ . Note that  $\mathbf{D}^e = \mathbf{U}(\mathbf{U}^{s^\top}\mathbf{U}^s)\Sigma^s\mathbf{V}^{s^\top} =$
+
+$\mathbf{U}\mathbf{U}^{s^{\top}}\mathbf{F}^{s}$ , which is exactly a rotation of  $\mathbf{F}^{s}$  using the feature basis correlation between  $\mathbf{U}$  and  $\mathbf{U}^{s}$ . This rotation matrix brings more robust and generic semantic knowledge from  $\mathbf{D}$  to  $\mathbf{F}^{s}$ .
+
+The next task is fusing the robust action semantics  $\mathbf{D}^e$  into video representations. Meanwhile, we discover that the inner product between frame feature  $\mathbf{f}_{*j}^{s/q}$  and  $\mathbf{d}_l^e \in \mathbf{D}^e$  actually reflects the projection coefficient on each space basis, which supports us to re-express video features via  $\mathbf{D}^e$ . The adaptive updating strategy is formalized as:
+
+$$
+\widetilde {\mathbf {f}} _ {* j} ^ {s / q} = (1 - \rho) \mathbf {f} _ {* j} ^ {s / q} + \rho \sum_ {l = 1} ^ {\kappa} \alpha_ {j l} \mathbf {d} _ {l} ^ {e}, \tag {3}
+$$
+
+where  $\alpha_{jl} = \cos (\mathbf{f}_{*j}^{s / q},\mathbf{d}_l^e)$  denotes the cosine similarity,  $\rho$  balances accepting external knowledge and keeping original representations, and  $\mathbf{d}_l^e$  is the  $l$ -th column basis vector of  $\mathbf{D}^e$ . Since support and query samples both undergo re-expression via  $\mathbf{D}^e$ , their similar or dissimilar associations will be further adjusted and promoted.
+
+# 3.2.2 Reinforced Image Representation
+
+Our meta-action learning module enriches their latent features via the captured generic dictionary. However, not all frames in a video contain discriminative action semantics. In other words, they belong to two types: action-relevant frames and action-irrelevant ones. Promoting the contribution of the former and minimizing influence of the latter benefits the precise estimation of similarity between support and query videos. The keys to this expectation are automatically distinguish these two types and adjust their ratios in the fused representation  $\widetilde{\mathbf{f}}_j^{s/q}$ . Without manual annotations on the importance of frames, it is difficult for the model to learn the distinction ability. To overcome this challenge, we can break it down into a simple situation. Given the paired support and query videos from the same action, the action-relevant frames are likely to be similar or even the same, while the remaining ones tend to be different. Calculating frame-wise similarity across two videos easily discovers the discriminative frames. Their representation enhancement obviously narrows cross-video distance. For the paired samples in various classes, the weight adjustment on frames results in the reduction of cross-video similarity. In summary, these two cases indicate that frame-wise comparison and weight modification trigger the corresponding effects. This is an analogy to the basic logic of reinforcement learning adopting an action and receiving its reward.
+
+With the analogy, we develop a reinforced image representation (RIR) module within the reinforcement learning (RL) framework to fulfill our goal. Specifically, in FSVC, the basic concepts of RL are redefined:
+
+- State: the video feature at  $t$  time, i.e.,  $s_t = \{w_j \widetilde{\mathbf{f}}_{*j}\}_{j=1}^m$  where  $w_j$  initialized as 1 is the importance of the corresponding  $j$ -th frame;
+
+- Action:  $a_{t}$  depends on the output of agent  $(p \in [0,1])$  with the Sigmoid function applied. When  $p < 0.5$ , the action  $a_{t} = 0$  with  $\mathrm{p}(a_t) = 2p$  and  $w_{j} = w_{j} - \mathrm{p}(a_{t})$ , otherwise,  $a_{t} = 1$  with  $\mathrm{p}(a_t) = 2(p - 0.5)$  and  $w_{j} = w_{j} + \mathrm{p}(a_{t})$ . The agent in Figure 1 is implemented as one deep neural network.  
+- Reward:  $r_t$  of  $t$  time includes positive type and negative one. For the paired videos in the same class,  $r_t$  is positive with cross-video similarity improvement, while the reduction results in the negative one. The operation is inverse for paired videos in different classes. The reward is considered as the supervision to instruct the learning of the agent. Note that we ignore superscript  $s / q$  in three concepts, since they are suitable for all videos.
+
+In reinforcement learning, the interaction procedure between agent and environment actually is a Markov decision process [20]. Concretely, given the estimated action value, the state is transferred from  $s_t^{s/q}$  to  $s_{t+1}^{s/q}$  according to an implicit probability distribution. During the state transition stage, the main challenge is how to decide the optimal action at the current state. In fact, the action  $a_t^{s/q}$  exists in a hidden probability space which is effectively estimated by Q-learning [26, 39] strategy. Under this condition, the expectation value of actions  $a_t^{s/q}$  is formally defined as  $Q_t$  and the current action modifies the importance  $w_j^{s/q}$  of frame  $\widetilde{\mathbf{f}}_{*j}^{s/q}$  and affects the final reward. The formulation of  $Q_t$  is:
+
+$$
+Q _ {t} \left(s _ {t} ^ {s / q}, a _ {t} ^ {s / q}\right) = \max  _ {\pi} \mathbb {E} \left[ r _ {t} + \gamma r _ {t + 1} + \gamma^ {2} r _ {t + 2} \dots | \pi \right], \tag {4}
+$$
+
+where  $\gamma$  denotes the discount factor balancing the immediate reward and the future ones, and  $\pi = \arg \min_{a_t^{s/q}} Q_t$  is our desired probability distribution policy of action. To estimate such a policy, the Deep-Q network (DQN) [26] as an effective tool is generally utilized to approximate  $Q_t$ . In a nutshell, DQN typically constructs the learnable function taking the state as input to produce the probabilities  $p$  of action space. The function is always instantiated as a parameterized network.
+
+However, such a straightforward input design of DQN fails to observe the relationship of video pairs and embed this pivotal knowledge into action selection. For FSVC, the appropriate input of DQN is supposed to involve three different valuable contents. The first part is the feature of the chosen frame  $\widetilde{\mathbf{f}}_{*j}^{s / q}$  on which the estimated action is to be conducted. Emphasizing the current frame representation significantly upgrades its contribution to the prediction. The second one is the fused feature of the remaining frames, i.e.,  $\frac{1}{m - 1}\sum_{l = 1,l\neq j}^{m}w_{l}^{s / q}\widetilde{\mathbf{f}}_{*l}^{s / q}$ . This information tends to affect the computation of future rewards. The third special point lies in measuring the cosine similarities across this frame and other frames in another video, written as  $\mathbf{v}_j\in \mathbb{R}^m$  with its element  $\mathbf{v}_{jl} = \cos (\widetilde{\mathbf{f}}_j^{s / q},\widetilde{\mathbf{f}}_l^{q / s})$ .  $\mathbf{v}_j$  reflects its potentiality to promote the cross-video similarity.
+
+In terms of the output of DQN,  $a_{t}^{s / q} = 0$  suggests that the importance of this frame should be reduced via  $w_{j}^{s / q} = w_{j}^{s / q} - \mathrm{p}(a_{t}^{s / q})$ , where  $\mathrm{p}(a_t^{s / q}) = 2p$  and  $p$  is the probability of action. For the other situation, weight update of frame is  $w_{j}^{s / q} = w_{j}^{s / q} + \mathrm{p}(a_{t}^{s / q})$  with  $\mathrm{p}(a_t^{s / q}) = 2(p - 0.5)$ . After conducting actions, we have  $w_{j}^{s / q}\in (0,2)$  and it is simple to attain the corresponding reward by calculating the change of similarity of video representations  $r = \mathrm{sign}\left(\mathbf{d}(\widetilde{\mathbf{f}}^s,\widetilde{\mathbf{f}}^q)|s_{t + 1} - \mathbf{d}(\widetilde{\mathbf{f}}^s,\widetilde{\mathbf{f}}^q)|s_t\right)$ , where  $\mathbf{d}(\widetilde{\mathbf{f}}^s,\widetilde{\mathbf{f}}^q)$  means  $\cos (\sum_{j = 1}^{m}w_{j}^{s}\widetilde{\mathbf{f}}_{*j}^{s},\sum_{j = 1}^{m}w_{j}^{q}\widetilde{\mathbf{f}}_{*j}^{q})$ , and  $\mathrm{sign}(\cdot)$  denotes a sign function. Finally, with the Bellman theorem [2], the Deep-Q network is optimized with:
+
+$$
+\underset {\Theta} {\min} \mathbb {E} \left[ r + \gamma \max _ {a _ {i + 1} ^ {s / q}} Q (s _ {i + 1} ^ {s / q}, a _ {i + 1} ^ {s / q}) - Q (s _ {i} ^ {s / q}, a _ {i} ^ {s / q}) \right] ^ {2}, \quad (5)
+$$
+
+where  $\Theta$  includes all the trainable network parameters of DQN. For the training stage, the snapshot of state, action, and reward at any time is stored and divided into several mini-batches with random sampling, and we adopt  $\epsilon$ -greedy strategy to determine action using  $\pi$  with probability  $\epsilon$  and use random actions with  $1 - \epsilon$ . For the inference stage, the well-trained DQN is frozen and infers the weight for each frame given the paired videos. To this end, video representations are further advanced with frame-wise importance.
+
+# 3.3. Module Deployment
+
+Our developed Representation Fusion & Promotion Learning (RFPL) framework includes two components. Meta-action learning (MAL) stores abundant action semantics via  $\mathcal{D}_{train}$  and is adapted into each specific episode to enhance video representations, while Reinforced image representation (RIR) exploits deep Q-learning theory of RL to increase the representation of informative frame. Actually, it is straightforward and convenient to plug our REM into various FSVC methods to boost the model performance. In this paper, we choose three state-of-the-art FSVC models, e.g., OTAM [4], TRX [28] and STRM [35].
+
+Concretely, original OTAM first extracts frame-level features across all support and query samples per episode, and then calculate frame-wise similarity from support and query video pair. It finally utilizes a dynamic time wrapping algorithm (DTW) to obtain the similarity of videos and uses a metric manner to optimize or deduce the category of the query. When embedding RFPL into OTAM, our MAL module is combined with the outputs of the feature extractor, and our RIR is performed before the calculation of frame-wise similarity of video pairs. Similarly, for TRX, the average-pooling features of ResNet-50 are regarded as the inputs for MAL, and the refined representations further help in the selection of discriminative frames. Different from OTAM, RIR in TRX compares the given
+
+query instances with all support ones, determines an optimal weighted query representation with the highest similarity, and feeds it into the following modules. Compared with OTAM and TRX, STRM utilizes the feature maps before the average pooling of ResNet-50 as inputs for a Transformer block and finally compresses them into frame-level vector representation as  $\mathbf{F}_i^{s/q}$  where our RFPL is conducted.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Datasets. Three popular few-shot benchmarks are evaluated including UCF101 [31], Kinetics [5] and SSv2-Full [10]. For Kinetics and SSv2-Full, we follow the data split protocol of [4, 28, 37] to build meta-training set  $\mathcal{D}_{train}$ , meta-validation set  $\mathcal{D}_{val}$  and meta-testing set  $\mathcal{D}_{test}$ , which consists 64, 12 and 24 categories, respectively. For UCF101, we adopt the split and sampling manners in [44].
+
+Implementation Details. Following the existing works [4, 28, 35], 8 image frames per video are randomly and uniformly selected as its raw representations and the pretrained ResNet-50 [11] is considered as the backbone to extract high-level features from frame-level images. For the task-shared bank, we regard  $\mathbf{D}$  as one learnable tensor randomly initialized and optimized by Eq. (1) with SGD optimizer (learning rate:  $10^{-3} \rightarrow 10^{-5}$ ) in each episode during training stage and it is frozen for the test procedure. In addition, the DQN in our RIR module includes three fully-connected (FC) layers mapping the input to the number of actions, whose training is independent of other parts. Concretely, we first train DQN with several episodes by freezing the remaining networks (ResNet-50, task-shared Bank, and Transformer block), and then update the remains with the fixed DQN by other episodes. The iterative process is repeated by many times. Other training regulations are preserved as each specific method. For inference, 10,000 episodes are randomly selected from  $\mathcal{D}_{test}$  to evaluate the performance of the model.
+
+Baselines. Currently, HyRSM [37] and STRM [35] achieve the state-of-the-art results on most FSVC tasks, which are considered as important baselines. Besides, other excellent works such as TRN [47], CMN [48], CMN-J [49], TARN [3], OTAM [4], TTAN [19], TRX [28], ITANet [45], ARN [44], MAML [8] and MatchingNet [36] also serve as strong competitors.
+
+# 4.2. Result Analysis
+
+Table 1 summarizes the results of our method and other competitors on three datasets (UCF101, Kinetics, SSv2-Full) when solving various few-shot video classification tasks. According to the results, it is straightforward to achieve several important conclusions.
+
+Table 1. Result comparison of multiple methods on few-shot video classification problem. Evaluations are conducted on the meta-testing set of UCF101, Kinetics, and SSv2-Full under 5-way scenario. The number of support videos per class varies from 1 to 5 within each episode. The highest and second results are highlighted by **bold** and **underline**.  
+
+<table><tr><td>Methods</td><td>Source</td><td>Dataset</td><td>1-shot</td><td>2-shot</td><td>3-shot</td><td>4-shot</td><td>5-shot</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td rowspan="6">UCF101</td><td>66.3</td><td>-</td><td>-</td><td>-</td><td>83.1</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>80.9</td><td>-</td><td>-</td><td>-</td><td>93.2</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>79.9</td><td>85.5</td><td>87.0</td><td>88.3</td><td>88.9</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>78.2</td><td>88.9</td><td>92.4</td><td>94.1</td><td>96.1</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>78.3</td><td>88.9</td><td>91.9</td><td>93.5</td><td>96.9</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>83.9</td><td>-</td><td>93.0</td><td>-</td><td>94.7</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>84.3↑4.4</td><td>88.9↑3.4</td><td>90.2↑3.2</td><td>91.9↑3.6</td><td>92.1↑3.2</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>82.5↑4.2</td><td>91.1↑2.2</td><td>94.1↑1.7</td><td>95.6↑1.5</td><td>96.3↑0.2</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>79.7↑1.4</td><td>90.1↑1.2</td><td>93.8↑1.9</td><td>95.8↑2.3</td><td>96.7↓0.2</td></tr><tr><td>MatchNet [36]</td><td>NeuIPS-16</td><td rowspan="11">Kinetics</td><td>53.3</td><td>64.3</td><td>69.2</td><td>71.8</td><td>74.6</td></tr><tr><td>MAML [8]</td><td>ICML-17</td><td>54.2</td><td>65.5</td><td>70.0</td><td>72.1</td><td>75.3</td></tr><tr><td>Plain CMN [48]</td><td>ECCV-18</td><td>57.3</td><td>67.5</td><td>72.5</td><td>74.7</td><td>76.0</td></tr><tr><td>CMN-J [49]</td><td>TPAMI-20</td><td>60.5</td><td>70.0</td><td>75.6</td><td>77.3</td><td>78.9</td></tr><tr><td>TARN [3]</td><td>BMVC-19</td><td>64.8</td><td>-</td><td>-</td><td>-</td><td>78.5</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td>63.7</td><td>-</td><td>-</td><td>-</td><td>82.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>73.6</td><td>-</td><td>-</td><td>-</td><td>84.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>73.0</td><td>75.9</td><td>78.7</td><td>81.9</td><td>85.8</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>63.6</td><td>76.2</td><td>81.8</td><td>83.4</td><td>85.9</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>62.1</td><td>78.6</td><td>82.2</td><td>82.8</td><td>86.7</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>73.7</td><td>80.0</td><td>83.5</td><td>84.6</td><td>86.1</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>74.6↑1.6</td><td>80.0↑4.1</td><td>82.1↑3.4</td><td>84.1↑2.2</td><td>86.8↑1.0</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>66.2↑2.6</td><td>77.5↑1.3</td><td>83.8↑2.0</td><td>85.1↑1.7</td><td>87.3↑1.4</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>64.9↑2.8</td><td>80.3↑1.7</td><td>84.3↑2.1</td><td>84.8↑2.0</td><td>87.7↑1.0</td></tr><tr><td>CMN++ [48]</td><td>ECCV-18</td><td rowspan="8">SSv2-Full</td><td>34.4</td><td>-</td><td>-</td><td>-</td><td>43.8</td></tr><tr><td>TRN++ [47]</td><td>ECCV-18</td><td>38.6</td><td>-</td><td>-</td><td>-</td><td>48.9</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>46.3</td><td>52.5</td><td>57.3</td><td>59.3</td><td>60.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>49.2</td><td>55.5</td><td>59.1</td><td>61.0</td><td>62.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>42.6</td><td>49.1</td><td>51.5</td><td>52.0</td><td>52.3</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>42.0</td><td>53.1</td><td>57.6</td><td>61.1</td><td>64.6</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>42.1</td><td>53.8</td><td>59.3</td><td>64.2</td><td>68.1</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>54.3</td><td>62.2</td><td>65.1</td><td>67.9</td><td>69.0</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>47.0↑4.2</td><td>54.6↑5.5</td><td>58.3↑6.8</td><td>60.3↑8.3</td><td>61.0↑8.7</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>44.6↑2.6</td><td>54.2↑1.1</td><td>59.9↑2.3</td><td>63.1↑2.1</td><td>64.6↑2.3</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>45.7↑3.6</td><td>55.8↑2.0</td><td>61.7↑2.4</td><td>66.8↑2.6</td><td>69.5↑1.4</td></tr></table>
+
+First, when plugging our proposed modules into the existing FSVC works such as OTAM, its performance gains significant improvement. Concretely, for 5-way-5-shot task on SSv2-Full, the classification accuracy of OTAM using our module attains  $61.0\%$  which is much higher than its original  $52.3\%$ . In addition, the integration of our designed modules and OTAM exceeds the original one by  $4.4\%$  on 1-shot task of UCF101. These phenomenons illustrate that our method effectively facilitates OTAM to conduct more accurate temporal alignment across support and query videos by refining video representations with task-shared knowledge and discriminative frame selection. Second, compared with OTAM, original TRX and STRM not only consider learning temporal relationships but also draw assistance from Transformer block to achieve information complementary within each episode. Although their methods seem to be perfect
+
+and promising, our RFPL still facilitates them to boost  $2\%$  on most tasks. The main reason for success lies in that our method further helps them enrich the representations of action semantics by introducing meta-action semantics and accurately capture the intrinsic similarity across support and query instances via the increasing effect of important image frames. Finally, injecting our RFPL into other baselines achieves comparable performance with HyRSM on most tasks. Especially, STRM with our RFPL surpasses HyRSM by an obvious gain margin, i.e.,  $1.6\%$  on 5-shot task of Kinetics, validating that our proposed method is an efficient auxiliary tool for addressing the FSVC problem.
+
+# 4.3. Performance Study
+
+Path Visualization & Confusion Matrix. From Table 1, we conclude that our RFPL effectively promotes the perfor
+
+![](images/acdeabb33169ff5f7c68f5c4d36d3ef17767bcdbf3976682b70562788bb6e0bd.jpg)
+
+![](images/02ec62c45ed906fa2f2fc0700492204773be1479054c87a5fcc3978708166e0c.jpg)  
+Figure 2. Comparison between plain OTAM and Ours+OTAM on action recognition result and temporal alignment path. This episode is randomly selected from the meta-testing set of Kinetics. The query video belongs to dancing ballet. Our+OTAM successfully matches it with the support sample from the same category, while plain OTAM matches into a dancing charleston video.
+
+![](images/a3a3a33cf4fe18be4df5bef7f5321b218537cdb53e98520ef20572c4c0e30f75.jpg)
+
+![](images/38d249175e3d57ebd182b0b731dae63d40f00028e0976121c1ab840072d7c332.jpg)  
+(a) OTAM @ Kinetics
+
+![](images/56c547e13fa4b8b3fa596c1a7bb21a58b1cad351d6ef6b619cfb607caf6c7e96.jpg)  
+(b) Ours+OTAM @ Kinetics
+
+![](images/9b0e1e2f1e755c4711c53a1382ab65add1dff9f5c2b7a85a513d77e51c49f52a.jpg)  
+(c) OTAM @ SSV-Full
+
+![](images/82706303d712a9377ff699b01121b9f8278a823bce170bfd0081eba4e6dccf58.jpg)  
+(d) Ours+OTAM @ SSV-Full  
+Figure 3. Comparison of confusion matrix deduced from the model prediction of plain OTAM and Ours+OTAM. These two episodes are collected from the meta-testing set of Kinetics (2-shot) and SSv2-Full (5-shot).
+
+mance of OTAM by a large margin. To explicitly explain the reason for improvement, we randomly select an episode from meta-testing set  $\mathcal{D}_{test}$  and visualize the frame-level cumulative distance across query video and the selected support ones as Fig. 2 shows. This visualization indicates that OTAM is sensitive to image background and its temporal alignment becomes invalid. Thus, it considers that this query video from the dancing ballet class has the highest similarity with the support sample from dancing charleston. Differently, our method assists OTAM to focus on the similarity of action semantics, especially on distinguishing body posture. Hence, Ours+OTAM accurately matches the query sample with the support video from the identical category and achieves better temporal alignment.
+
+In addition, we draw the confusion matrix of two specific episodes to further discuss their differences. Concretely, during the inference stage, for 2-shot of Kinetics or 5-shot of SSv2-Full, we randomly choose an episode with 200 query samples uniformly distributed in five categories and compare model prediction and ground-truth to form Fig. 3. For the task of Kinetics, with the help of our RFPL, the recognition abilities of OTAM in five categories are all strengthened. With respect to the more challenging task of SSv2-Full, OTAM with our method learns more discrimina
+
+tive action semantics and achieves significant performance improvement on several categories without reduction on the remaining ones.
+
+Reinforced Image Frames. In our RFPL, reinforced image representation as one important module aims to discover the discriminative image frames via the comparison of the paired videos. To analyze its effect, we record the frame-wise weights deduced from the agent as Fig. 4 in one test episode. From two "folding paper" videos, several image frames without any "folding" action are provided with lower weights such as frames in the red box. For action-relevant images, the learned network produces higher weights for them as the blue box shows. From the other example "cutting watermelon", we have an interesting finding. The well-trained network does not give larger weights for frames including "cutting" action, while highlighting images with two halves of the red pulp of a watermelon as the green box shows. It suggests that the network considers that these image contents are useful for the improvement of cross-video similarity.
+
+Parameter Analysis. There is one hyper-parameter  $\rho$  in our RFPL, which serves as a trade-off between accepting external global knowledge and preserving current feature representations. In practical experiments, this parameter is
+
+![](images/4465409d8c43c95a65d36d35b73b44a2442676f72216700d68107a894f14ba07.jpg)  
+Figure 4. Importance of frames produced by reinforced image representation module. Videos of the first and second rows belong to folding paper, while the remaining videos are from cutting watermelon. Images in the red box are regarded as key action semantics by the network, while the effect of others in the blue box is reduced. Similarly, the representations of images in the green box are also enhanced.
+
+![](images/1ccdc6da05c5d9dc13e7ccc42aa0ea5d1a0acbbb683b10d93f5ce7dc356ab7a8.jpg)  
+Figure 5. Parameter analysis of  $\rho$  with different selections.
+
+tuned for different tasks, i.e.,  $\rho \in \{0.001, 0.01, 0.1, 0.5\}$ . Definitely, the optimal parameter is determined by the performance of the learned model on the meta-validation set. Concretely, Fig. 5 shows the change of model classification ability on the validation set of SSv2-Full with the varying  $\rho$ . Based on this parameter analysis, we find that when  $\rho = 0.5$ , the video classification accuracy is lower than that of smaller  $\rho$  on many tasks. Therefore, it is reasonable to infer that while introducing global knowledge to enhance semantics information, the protection of current information is very necessary and stabilizes the model training.
+
+Ablation Study. Our RFPL consists of two modules: meta-action learning and reinforced image representation. The first one aims to enrich video representation by fusing global knowledge of the meta-action bank to each specific episode, while the second one expects to emphasize the representation of informative image frames via reinforcement learning selection. In fact, we also separately plug each module into the existing baseline, named as Ours-v1 (adding MAL) and Ours-v2 (adding RIR). These variants
+
+![](images/65dc24487e5579c0b1b1565e50d8bb8842c77e4b0a96f165120b9c861f2d1a0a.jpg)  
+Figure 6. Ablation study. Ours-v1 and Ours-v2 mean that meta-action learning and reinforced image representation modules are plugged into the existing FSVC works, respectively.
+
+are combined with OTAM and evaluated on three tasks of Kinetics with results in Fig. 6. The comparisons with plain OTAM mean that each module can independently make positive contributions on advancing it. And the collaboration of MAL and RIR will bring more benefits to OTAM than each independent module. Thus, using the complete RFPL is the optimal strategy.
+
+# 5. Conclusion
+
+In this paper, we propose a flexible representation fusion and enhancement learning (RFPL) mechanism with two sub-modules to solve few-shot video classification. The meta-action learning module builds a generic action bank and fuses the adapted one to enrich video features, while the reinforced image representation module identifies important frames via an agent and promotes their positive effect to precisely capture cross-video similarity. Considerable experimental results and analysis verify that our RFPL effectively advances the existing FSVC methods.
+
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+                                    "content": "Department of Computer Science, Tulane University, "
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+                                    "content": "Abstract"
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+                                    "content": "Recent few-shot video classification (FSVC) works achieve promising performance by capturing similarity across support and query samples with different temporal alignment strategies or learning discriminative features via Transformer block within each episode. However, they ignore two important issues: a) It is difficult to capture rich intrinsic action semantics from a limited number of support instances within each task. b) Redundant or irrelevant frames in videos easily weaken the positive influence of discriminative frames. To address these two issues, this paper proposes a novel Representation Fusion and Promotion Learning (RFPL) mechanism with two sub-modules: meta-action learning (MAL) and reinforced image representation (RIR). Concretely, during training stage, we perform online learning for seeking a task-shared meta-action bank to enrich task-specific action representation by injecting global knowledge. Besides, we exploit reinforcement learning to obtain the importance of each frame and refine the representation. This operation maximizes the contribution of discriminative frames to further capture the similarity of support and query samples from the same category. Our RFPL framework is highly flexible that it can be integrated with many existing FSVC methods. Extensive experiments show that RFPL significantly enhances the performance of existing FSVC models when integrated with them."
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+                                    "content": "1. Introduction"
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+                                    "content": "Due to the emergence of deep learning [43, 18, 15], video action recognition has obtained impressive improvement by learning informative semantics from raw videos [23, 38]. These achievements heavily rely on the powerful supervision of considerable well-labeled videos to optimize deep neural networks [32, 41]. However, the collection and annotation of training samples become laborious and expensive, especially for video sequences. Hence, such a learning"
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+                                    "content": "paradigm does not always feasible for many practical applications [7, 29]. This conflict motivates investigations on few-shot video classification (FSVC) which aims to learn a model of good generalization performance from a few labeled video samples [4, 35, 37]."
+                                }
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+                                    "content": "The mainstream solutions to FSVC typically adopt metric-based meta-learning [30, 12] fashion by training model across multiple episodes where each includes one support set with a few annotated videos and the other query set with unlabeled instances. For inference, the well-trained model measures the similarities across support and query videos within each episode to determine which categories the query samples come from [17]. However, it is difficult to precisely assess frame-wise relationships within video sequences, since their temporal information has significant divergence or even mismatch. To overcome such a challenge, the intuitive strategy is to achieve temporal alignment among cross-video frames. For example, OTAM [4] develops a variant of dynamic time wrapping (DTW) [27] to find the optimal alignment path via the frame-level cumulative distance function. Similarly, ITANet [45] explores implicit temporal alignment via a traversal strategy. Moreover, TRX [28] develops multiple tuples of sub-sequence to achieve action matching. And STRM [35] studies self-attention mechanisms to emphasize channel representation in a single video. HyRSM [37] presents a set matching concept to explore temporal alignment without frame-level ordering across various videos."
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+                                    "content": "Although these existing works have achieved appealing results, they tend to encounter performance bottlenecks due to ignorance of the following two issues. First, the limited number of labeled samples within each individual task hardly provides sufficient support to assist model learning the essential action semantics for the recognition task. Second, there are redundant or irrelevant frames in videos; treating these less informative frames in the same way as the other informative ones likely weakens the discriminability of the learned video representations, and thus triggers a negative effect on solving the FSVC task."
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+                                    "content": "In this paper, we propose a novel Representation Fusion"
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+                                    "content": "and Promotion Learning (RFPL) framework to address the two issues, by two novel modules, respectively. To address the deficiency of semantic information within each individual task, we propose the meta-action learning (MAL) module which introduces external knowledge learned globally to enrich video representations learned locally within each individual task. Specifically, MAL maintains a global meta-action bank storing representations of atomic action snippets that can be used to compose various action categories of higher complexity. The global meta-action bank is shared by all action types and all individual FSVC tasks. We explore it to enrich the video feature representations learned locally in each individual task via a novel Single Value Decomposition (SVD) technique."
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+                                    "content": "To address the redundant/irrelevant frame issue, we propose the reinforced image representation (RIR) module which explores reinforcement learning to discover the importance of each frame to the FSVC task. We train the reinforcement learning agent by exploiting the relationship between support and query video pairs, striving to emphasize the influence of discriminative frames to help the model accurately capture sample-wise similarity. Our MAL and RIR can be easily plugged into the existing FSVC methods to promote their performance. Our main contributions in this work are summarized in three folds as:"
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+                                            "type": "text",
+                                            "content": "- We propose the meta-action learning module which learns a global meta-action bank to enrich video representation learned locally in individual tasks, via a novel SVD technique."
+                                        }
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+                                            "content": "- We address the negative effect of task-irrelevant frames on capturing cross-video relationships and develop a reinforced image representation module that promotes the contribution of discriminative frames."
+                                        }
+                                    ]
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+                                            "content": "- Our RFPL framework is highly flexible such that it can be integrated with various FSVC methods and gets improved performance."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "content": "2. Related Works"
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+                                    "content": "2.1. Few-Shot Video Classification (FSVC)"
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+                                    "content": "When using meta-learning manner [8, 9], FSVC scenario assumes that each episode includes a few labeled support videos and query ones without annotations and aims to learn and generalize a model to identify unseen classes [3, 50]. The current solutions are based on metric learning. Concretely, raw video sequences are first converted into corresponding high-level feature representations with DNN. The prediction of the query sample is determined by the matching support instance with the highest similarity [48]. However, video data with temporal dimension content is extremely complicated so it is difficult to precisely measure sample-wise relationships. To eliminate such a drawback, the current works generally calculate the similarity"
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+                                    "content": "after temporal alignment. For instance, OTAM [4] assumes that frame orderings across various videos are consistent and utilizes dynamic time wrapping to find the frame-level alignment path with a cumulative distance matrix. ITANet [45] adopts a traversal manner to match frames across different videos. TRX [28] first builds tuples of sub-sequence and exploits them to match action. STRM [35] advances TRX by considering spatial information within each video. HyRSM [38] explores set matching [13, 46] metric to efficiently compute cross-video connection. Differently, our proposed RFPL focuses on video representation enhancement by injecting meta-action knowledge and precise similarity measurement via the importance-aware refinement of discriminative frames with reinforcement learning."
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+                                    "content": "2.2. Reinforcement Learning (RL)"
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+                                    "content": "Reinforcement Learning (RL) arises from the neuroscientific and psychological study that which actions humans can do to gain more benefits from the environment [16, 33]. In other words, RL is utilizing the interaction of agent and environment to learn a policy that brings the most reward [14]. In fact, such a sequential decision-making procedure can be formulated as a Markov Decision Process (MDP) [6]. Recently, due to the powerful learning ability of DNN, the advanced RL works typically deploy a trainable DNN to approximate the value function or policy function as Deep Q-Network (DQN) [26] and Deep Deterministic Policy Gradient (DDPG) [22]. In addition, many real-world applications also consider using RL to improve model performance such as object tracking [42], protein analysis [20], video summarization [21] and action recognition [34]. Unlike them, our deployment of RL is solving the few-shot video action scenario by producing frame-wise weight to promote the effect of discriminative frames. Moreover, we also conduct delicate designs on DQN to be suitable for FSVC."
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+                                            "content": "Figure 1. Overview of our representation fusion and promotion learning (RFPL) framework. RFPL involves two sub-modules: meta-action learning (MAL) fusing task-shared action semantics to enrich video representation and reinforced image representation (RIR) highlighting the effect of discriminative frames to precisely learn sample-wise similarity."
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+                                    "content": "gory each query video belongs to. In terms of the test stage, each episodic also consists of support and query set which are derived from "
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+                                    "content": "The key to solving FSVC problem lies in how to effectively learn the pattern of discriminative action semantics from a few labeled support videos. Motivated by this, we propose a flexible Representation Fusion & Promotion Learning (RFPL) framework to enrich semantic information of video features via two novel sub-modules, as Fig.1 shows. One meta-action learning module utilizes episodes of meta-training set to build a task-shared action bank further refining feature embedding via knowledge fusion. Another reinforced image representation module adjusts the importance of frames to achieve the enhancement of discriminative semantics with reinforcement learning."
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+                                    "content": "\\mathbf{X}_i = \\{\\mathbf{x}_{ij}\\}_{j=1}^m"
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+                                    "content": "-th video. For example, a long jump video records some sub-actions: running, jumping and landing. In addition, we also observe that several videos come from different categories but they do share similar sub-actions such as jumping in long jump and playing basketball videos. When these two categories appear in different episodes, the transfer of similar patterns across them will facilitate the model to easily and accurately discover the similarity between support and query samples."
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+                                    "content": " to store representations of considerable sub-actions. Hence, the similar sub-actions in the long jump and playing basketball videos can be represented by the same atoms of this bank. Specifically, the widely-used backbone (e.g., ResNet-50) is first utilized to extract high-level feature of each frame, resulting in one video being transformed into the corresponding feature set "
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+                                    "content": "\\mathbf{F}^s \\in \\mathbb{R}^{d \\times nk_m}"
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+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Since the current fruitful solutions to FSVC generally adopt episodic training fashion without repeatedly accessing the previous task, we expect to gradually involve action semantics per episode into task-shared bank "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", thus, the online gradient update manner [25, 24] is adopted to optimize "
+                                },
+                                {
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+                                        393
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        274,
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+                                        393
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        274,
+                                        545,
+                                        393
+                                    ],
+                                    "type": "text",
+                                    "content": " instead of closed-form solution."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
+                        395,
+                        546,
+                        549
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "After obtaining the task-shared meta-action bank, another consideration is how to adaptively fuse such semantics into each specific episode. Consequently, we rethink the meaning of learned action bank. In fact, it constitutes an action space where each atom represents a basis vector. But not all are needed for the current episode due to the assumption that the number of action categories in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
+                                        546,
+                                        549
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
+                                        546,
+                                        549
+                                    ],
+                                    "type": "text",
+                                    "content": " is much larger than that in this episode. Therefore, a reasonable adaptation operation is to highlight the episode-relevant basis vectors from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
+                                        546,
+                                        549
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
+                                        546,
+                                        549
+                                    ],
+                                    "type": "text",
+                                    "content": ". Fortunately, the classical single value decomposition (SVD) [40, 1] helps us achieve this expectation. Specifically, we adopts SVD to decompose support feature matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
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+                                        549
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
+                                        546,
+                                        549
+                                    ],
+                                    "type": "text",
+                                    "content": " and action memory bank "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
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+                                        549
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        395,
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+                                        549
+                                    ],
+                                    "type": "text",
+                                    "content": " as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
+                                        317,
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+                                        545,
+                                        572
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {S V D} \\left(\\mathbf {F} ^ {s}\\right) \\Rightarrow \\mathbf {U} ^ {s} \\boldsymbol {\\Sigma} ^ {s} \\mathbf {V} ^ {\\mathbf {s}} ^ {\\top}, \\quad \\operatorname {S V D} (\\mathbf {D}) \\Rightarrow \\mathbf {U} \\boldsymbol {\\Sigma} \\mathbf {V} ^ {\\top}, \\tag {2}",
+                                    "image_path": "76d5c958ab9d25b5fcff69ebce59097dcea6046305cd12abb9f8288eb377f9e6.jpg"
+                                }
+                            ]
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+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where single values "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Sigma"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " or "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Sigma^s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " control the contribution of corresponding basis vectors. So far, it is intuitive to obtain two observations from the decomposition. First, the information of feature space basis in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is more robust and generic than that of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{U}^s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", since action bank refers to sufficient videos. Second, compared with "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Sigma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Sigma^s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " can better estimate the intrinsic importance of basis vectors due to the fact that it is directly captured from the current episode. Based on these points, we consider fusing the advantage of each component to form the episode-adaptive action bank as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}^e = \\mathbf{U}\\Sigma^s\\mathbf{V}^{s^\\top}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}^e = \\mathbf{U}(\\mathbf{U}^{s^\\top}\\mathbf{U}^s)\\Sigma^s\\mathbf{V}^{s^\\top} ="
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "19313"
+                                }
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+            ],
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+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                        287,
+                                        119
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{U}\\mathbf{U}^{s^{\\top}}\\mathbf{F}^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which is exactly a rotation of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        119
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
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+                                        119
+                                    ],
+                                    "type": "text",
+                                    "content": " using the feature basis correlation between "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
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+                                        119
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{U}^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "text",
+                                    "content": ". This rotation matrix brings more robust and generic semantic knowledge from "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        119
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
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+                                        286,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": "The next task is fusing the robust action semantics "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}^e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " into video representations. Meanwhile, we discover that the inner product between frame feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_{*j}^{s/q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_l^e \\in \\mathbf{D}^e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": " actually reflects the projection coefficient on each space basis, which supports us to re-express video features via "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}^e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        120,
+                                        286,
+                                        193
+                                    ],
+                                    "type": "text",
+                                    "content": ". The adaptive updating strategy is formalized as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        78,
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+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
+                                        78,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\mathbf {f}} _ {* j} ^ {s / q} = (1 - \\rho) \\mathbf {f} _ {* j} ^ {s / q} + \\rho \\sum_ {l = 1} ^ {\\kappa} \\alpha_ {j l} \\mathbf {d} _ {l} ^ {e}, \\tag {3}",
+                                    "image_path": "1f372a940cb035b7699a2e7cc0d4d1ed8524b820c86896c061fdb1167394c893.jpg"
+                                }
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+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{jl} = \\cos (\\mathbf{f}_{*j}^{s / q},\\mathbf{d}_l^e)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the cosine similarity, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
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+                                    ],
+                                    "type": "text",
+                                    "content": " balances accepting external knowledge and keeping original representations, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        286,
+                                        296
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}_l^e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th column basis vector of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}^e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Since support and query samples both undergo re-expression via "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}^e"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", their similar or dissimilar associations will be further adjusted and promoted."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.2.2 Reinforced Image Representation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "type": "text",
+                                    "content": "Our meta-action learning module enriches their latent features via the captured generic dictionary. However, not all frames in a video contain discriminative action semantics. In other words, they belong to two types: action-relevant frames and action-irrelevant ones. Promoting the contribution of the former and minimizing influence of the latter benefits the precise estimation of similarity between support and query videos. The keys to this expectation are automatically distinguish these two types and adjust their ratios in the fused representation "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        286,
+                                        629
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{f}}_j^{s/q}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        329,
+                                        286,
+                                        629
+                                    ],
+                                    "type": "text",
+                                    "content": ". Without manual annotations on the importance of frames, it is difficult for the model to learn the distinction ability. To overcome this challenge, we can break it down into a simple situation. Given the paired support and query videos from the same action, the action-relevant frames are likely to be similar or even the same, while the remaining ones tend to be different. Calculating frame-wise similarity across two videos easily discovers the discriminative frames. Their representation enhancement obviously narrows cross-video distance. For the paired samples in various classes, the weight adjustment on frames results in the reduction of cross-video similarity. In summary, these two cases indicate that frame-wise comparison and weight modification trigger the corresponding effects. This is an analogy to the basic logic of reinforcement learning adopting an action and receiving its reward."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        46,
+                        630,
+                        286,
+                        677
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                630,
+                                286,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        630,
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+                                    ],
+                                    "type": "text",
+                                    "content": "With the analogy, we develop a reinforced image representation (RIR) module within the reinforcement learning (RL) framework to fulfill our goal. Specifically, in FSVC, the basic concepts of RL are redefined:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "- State: the video feature at "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " time, i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                        678,
+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s_t = \\{w_j \\widetilde{\\mathbf{f}}_{*j}\\}_{j=1}^m"
+                                },
+                                {
+                                    "bbox": [
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+                                        678,
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+                                    ],
+                                    "type": "text",
+                                    "content": " where "
+                                },
+                                {
+                                    "bbox": [
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+                                        678,
+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_j"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        678,
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+                                    ],
+                                    "type": "text",
+                                    "content": " initialized as 1 is the importance of the corresponding "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        678,
+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        678,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th frame;"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 10,
+                    "blocks": [
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+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "- Action: "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                72,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a_{t}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " depends on the output of agent "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "(p \\in [0,1])"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": " with the Sigmoid function applied. When "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "p < 0.5"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ", the action "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a_{t} = 0"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": " with "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{p}(a_t) = 2p"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
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+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "w_{j} = w_{j} - \\mathrm{p}(a_{t})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": ", otherwise, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "a_{t} = 1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": " with "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{p}(a_t) = 2(p - 0.5)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "w_{j} = w_{j} + \\mathrm{p}(a_{t})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                72,
+                                                545,
+                                                143
+                                            ],
+                                            "type": "text",
+                                            "content": ". The agent in Figure 1 is implemented as one deep neural network."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                304,
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+                                239
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "- Reward: "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "r_t"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                144,
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+                                            ],
+                                            "type": "text",
+                                            "content": " of "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                239
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "t"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " time includes positive type and negative one. For the paired videos in the same class, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                144,
+                                                545,
+                                                239
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "r_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
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+                                            ],
+                                            "type": "text",
+                                            "content": " is positive with cross-video similarity improvement, while the reduction results in the negative one. The operation is inverse for paired videos in different classes. The reward is considered as the supervision to instruct the learning of the agent. Note that we ignore superscript "
+                                        },
+                                        {
+                                            "bbox": [
+                                                304,
+                                                144,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "s / q"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " in three concepts, since they are suitable for all videos."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "In reinforcement learning, the interaction procedure between agent and environment actually is a Markov decision process [20]. Concretely, given the estimated action value, the state is transferred from "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "s_t^{s/q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s_{t+1}^{s/q}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " according to an implicit probability distribution. During the state transition stage, the main challenge is how to decide the optimal action at the current state. In fact, the action "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "a_t^{s/q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " exists in a hidden probability space which is effectively estimated by Q-learning [26, 39] strategy. Under this condition, the expectation value of actions "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is formally defined as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "Q_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the current action modifies the importance "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_j^{s/q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of frame "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{f}}_{*j}^{s/q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and affects the final reward. The formulation of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "Q _ {t} \\left(s _ {t} ^ {s / q}, a _ {t} ^ {s / q}\\right) = \\max  _ {\\pi} \\mathbb {E} \\left[ r _ {t} + \\gamma r _ {t + 1} + \\gamma^ {2} r _ {t + 2} \\dots | \\pi \\right], \\tag {4}",
+                                    "image_path": "7a3486a110da3325967bff53bce810550db889508ed7459d7523188e2cb3fc7a.jpg"
+                                }
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+                        }
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "where "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the discount factor balancing the immediate reward and the future ones, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pi = \\arg \\min_{a_t^{s/q}} Q_t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is our desired probability distribution policy of action. To estimate such a policy, the Deep-Q network (DQN) [26] as an effective tool is generally utilized to approximate "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "Q_t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". In a nutshell, DQN typically constructs the learnable function taking the state as input to produce the probabilities "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of action space. The function is always instantiated as a parameterized network."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "However, such a straightforward input design of DQN fails to observe the relationship of video pairs and embed this pivotal knowledge into action selection. For FSVC, the appropriate input of DQN is supposed to involve three different valuable contents. The first part is the feature of the chosen frame "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{f}}_{*j}^{s / q}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
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+                                    ],
+                                    "type": "text",
+                                    "content": " on which the estimated action is to be conducted. Emphasizing the current frame representation significantly upgrades its contribution to the prediction. The second one is the fused feature of the remaining frames, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        533,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{1}{m - 1}\\sum_{l = 1,l\\neq j}^{m}w_{l}^{s / q}\\widetilde{\\mathbf{f}}_{*l}^{s / q}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This information tends to affect the computation of future rewards. The third special point lies in measuring the cosine similarities across this frame and other frames in another video, written as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_j\\in \\mathbb{R}^m"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with its element "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_{jl} = \\cos (\\widetilde{\\mathbf{f}}_j^{s / q},\\widetilde{\\mathbf{f}}_l^{q / s})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_j"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " reflects its potentiality to promote the cross-video similarity."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "19314"
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+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "In terms of the output of DQN, "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{t}^{s / q} = 0"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " suggests that the importance of this frame should be reduced via "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{j}^{s / q} = w_{j}^{s / q} - \\mathrm{p}(a_{t}^{s / q})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{p}(a_t^{s / q}) = 2p"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " is the probability of action. For the other situation, weight update of frame is "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{j}^{s / q} = w_{j}^{s / q} + \\mathrm{p}(a_{t}^{s / q})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
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+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{p}(a_t^{s / q}) = 2(p - 0.5)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": ". After conducting actions, we have "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{j}^{s / q}\\in (0,2)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " and it is simple to attain the corresponding reward by calculating the change of similarity of video representations "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r = \\mathrm{sign}\\left(\\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)|s_{t + 1} - \\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)|s_t\\right)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}(\\widetilde{\\mathbf{f}}^s,\\widetilde{\\mathbf{f}}^q)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " means "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\cos (\\sum_{j = 1}^{m}w_{j}^{s}\\widetilde{\\mathbf{f}}_{*j}^{s},\\sum_{j = 1}^{m}w_{j}^{q}\\widetilde{\\mathbf{f}}_{*j}^{q})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{sign}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes a sign function. Finally, with the Bellman theorem [2], the Deep-Q network is optimized with:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        47,
+                                        238,
+                                        288,
+                                        275
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\underset {\\Theta} {\\min} \\mathbb {E} \\left[ r + \\gamma \\max _ {a _ {i + 1} ^ {s / q}} Q (s _ {i + 1} ^ {s / q}, a _ {i + 1} ^ {s / q}) - Q (s _ {i} ^ {s / q}, a _ {i} ^ {s / q}) \\right] ^ {2}, \\quad (5)",
+                                    "image_path": "fc73ac231277f582fd21486d0787df345e475f43f15752527a1785dd6a4548e5.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "text",
+                                    "content": " includes all the trainable network parameters of DQN. For the training stage, the snapshot of state, action, and reward at any time is stored and divided into several mini-batches with random sampling, and we adopt "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "text",
+                                    "content": "-greedy strategy to determine action using "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pi"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "text",
+                                    "content": " with probability "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "text",
+                                    "content": " and use random actions with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1 - \\epsilon"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        281,
+                                        289,
+                                        389
+                                    ],
+                                    "type": "text",
+                                    "content": ". For the inference stage, the well-trained DQN is frozen and infers the weight for each frame given the paired videos. To this end, video representations are further advanced with frame-wise importance."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                        166,
+                        409
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Module Deployment"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Our developed Representation Fusion & Promotion Learning (RFPL) framework includes two components. Meta-action learning (MAL) stores abundant action semantics via "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        415,
+                                        287,
+                                        545
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{train}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        415,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and is adapted into each specific episode to enhance video representations, while Reinforced image representation (RIR) exploits deep Q-learning theory of RL to increase the representation of informative frame. Actually, it is straightforward and convenient to plug our REM into various FSVC methods to boost the model performance. In this paper, we choose three state-of-the-art FSVC models, e.g., OTAM [4], TRX [28] and STRM [35]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                        288,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        545,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "Concretely, original OTAM first extracts frame-level features across all support and query samples per episode, and then calculate frame-wise similarity from support and query video pair. It finally utilizes a dynamic time wrapping algorithm (DTW) to obtain the similarity of videos and uses a metric manner to optimize or deduce the category of the query. When embedding RFPL into OTAM, our MAL module is combined with the outputs of the feature extractor, and our RIR is performed before the calculation of frame-wise similarity of video pairs. Similarly, for TRX, the average-pooling features of ResNet-50 are regarded as the inputs for MAL, and the refined representations further help in the selection of discriminative frames. Different from OTAM, RIR in TRX compares the given"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        304,
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+                        159
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        159
+                                    ],
+                                    "type": "text",
+                                    "content": "query instances with all support ones, determines an optimal weighted query representation with the highest similarity, and feeds it into the following modules. Compared with OTAM and TRX, STRM utilizes the feature maps before the average pooling of ResNet-50 as inputs for a Transformer block and finally compresses them into frame-level vector representation as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        159
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i^{s/q}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        159
+                                    ],
+                                    "type": "text",
+                                    "content": " where our RFPL is conducted."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4.1. Experimental Settings"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                        295
+                                    ],
+                                    "type": "text",
+                                    "content": "Datasets. Three popular few-shot benchmarks are evaluated including UCF101 [31], Kinetics [5] and SSv2-Full [10]. For Kinetics and SSv2-Full, we follow the data split protocol of [4, 28, 37] to build meta-training set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        547,
+                                        295
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{train}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        547,
+                                        295
+                                    ],
+                                    "type": "text",
+                                    "content": ", meta-validation set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        547,
+                                        295
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{val}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        547,
+                                        295
+                                    ],
+                                    "type": "text",
+                                    "content": " and meta-testing set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        547,
+                                        295
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{test}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        547,
+                                        295
+                                    ],
+                                    "type": "text",
+                                    "content": ", which consists 64, 12 and 24 categories, respectively. For UCF101, we adopt the split and sampling manners in [44]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Implementation Details. Following the existing works [4, 28, 35], 8 image frames per video are randomly and uniformly selected as its raw representations and the pretrained ResNet-50 [11] is considered as the backbone to extract high-level features from frame-level images. For the task-shared bank, we regard "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
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+                                        537
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        547,
+                                        537
+                                    ],
+                                    "type": "text",
+                                    "content": " as one learnable tensor randomly initialized and optimized by Eq. (1) with SGD optimizer (learning rate: "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        547,
+                                        537
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "10^{-3} \\rightarrow 10^{-5}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ") in each episode during training stage and it is frozen for the test procedure. In addition, the DQN in our RIR module includes three fully-connected (FC) layers mapping the input to the number of actions, whose training is independent of other parts. Concretely, we first train DQN with several episodes by freezing the remaining networks (ResNet-50, task-shared Bank, and Transformer block), and then update the remains with the fixed DQN by other episodes. The iterative process is repeated by many times. Other training regulations are preserved as each specific method. For inference, 10,000 episodes are randomly selected from "
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+                                    "content": "\\mathcal{D}_{test}"
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+                                    "type": "text",
+                                    "content": " to evaluate the performance of the model."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Baselines. Currently, HyRSM [37] and STRM [35] achieve the state-of-the-art results on most FSVC tasks, which are considered as important baselines. Besides, other excellent works such as TRN [47], CMN [48], CMN-J [49], TARN [3], OTAM [4], TTAN [19], TRX [28], ITANet [45], ARN [44], MAML [8] and MatchingNet [36] also serve as strong competitors."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "4.2. Result Analysis"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "content": "Table 1 summarizes the results of our method and other competitors on three datasets (UCF101, Kinetics, SSv2-Full) when solving various few-shot video classification tasks. According to the results, it is straightforward to achieve several important conclusions."
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+                                            "content": "Table 1. Result comparison of multiple methods on few-shot video classification problem. Evaluations are conducted on the meta-testing set of UCF101, Kinetics, and SSv2-Full under 5-way scenario. The number of support videos per class varies from 1 to 5 within each episode. The highest and second results are highlighted by **bold** and **underline**."
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+                                            "html": "<table><tr><td>Methods</td><td>Source</td><td>Dataset</td><td>1-shot</td><td>2-shot</td><td>3-shot</td><td>4-shot</td><td>5-shot</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td rowspan=\"6\">UCF101</td><td>66.3</td><td>-</td><td>-</td><td>-</td><td>83.1</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>80.9</td><td>-</td><td>-</td><td>-</td><td>93.2</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>79.9</td><td>85.5</td><td>87.0</td><td>88.3</td><td>88.9</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>78.2</td><td>88.9</td><td>92.4</td><td>94.1</td><td>96.1</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>78.3</td><td>88.9</td><td>91.9</td><td>93.5</td><td>96.9</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>83.9</td><td>-</td><td>93.0</td><td>-</td><td>94.7</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>84.3↑4.4</td><td>88.9↑3.4</td><td>90.2↑3.2</td><td>91.9↑3.6</td><td>92.1↑3.2</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>82.5↑4.2</td><td>91.1↑2.2</td><td>94.1↑1.7</td><td>95.6↑1.5</td><td>96.3↑0.2</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>79.7↑1.4</td><td>90.1↑1.2</td><td>93.8↑1.9</td><td>95.8↑2.3</td><td>96.7↓0.2</td></tr><tr><td>MatchNet [36]</td><td>NeuIPS-16</td><td rowspan=\"11\">Kinetics</td><td>53.3</td><td>64.3</td><td>69.2</td><td>71.8</td><td>74.6</td></tr><tr><td>MAML [8]</td><td>ICML-17</td><td>54.2</td><td>65.5</td><td>70.0</td><td>72.1</td><td>75.3</td></tr><tr><td>Plain CMN [48]</td><td>ECCV-18</td><td>57.3</td><td>67.5</td><td>72.5</td><td>74.7</td><td>76.0</td></tr><tr><td>CMN-J [49]</td><td>TPAMI-20</td><td>60.5</td><td>70.0</td><td>75.6</td><td>77.3</td><td>78.9</td></tr><tr><td>TARN [3]</td><td>BMVC-19</td><td>64.8</td><td>-</td><td>-</td><td>-</td><td>78.5</td></tr><tr><td>ARN [44]</td><td>ECCV-20</td><td>63.7</td><td>-</td><td>-</td><td>-</td><td>82.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>73.6</td><td>-</td><td>-</td><td>-</td><td>84.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>73.0</td><td>75.9</td><td>78.7</td><td>81.9</td><td>85.8</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>63.6</td><td>76.2</td><td>81.8</td><td>83.4</td><td>85.9</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>62.1</td><td>78.6</td><td>82.2</td><td>82.8</td><td>86.7</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>73.7</td><td>80.0</td><td>83.5</td><td>84.6</td><td>86.1</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>74.6↑1.6</td><td>80.0↑4.1</td><td>82.1↑3.4</td><td>84.1↑2.2</td><td>86.8↑1.0</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>66.2↑2.6</td><td>77.5↑1.3</td><td>83.8↑2.0</td><td>85.1↑1.7</td><td>87.3↑1.4</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>64.9↑2.8</td><td>80.3↑1.7</td><td>84.3↑2.1</td><td>84.8↑2.0</td><td>87.7↑1.0</td></tr><tr><td>CMN++ [48]</td><td>ECCV-18</td><td rowspan=\"8\">SSv2-Full</td><td>34.4</td><td>-</td><td>-</td><td>-</td><td>43.8</td></tr><tr><td>TRN++ [47]</td><td>ECCV-18</td><td>38.6</td><td>-</td><td>-</td><td>-</td><td>48.9</td></tr><tr><td>TTAN [19]</td><td>ArXiv-21</td><td>46.3</td><td>52.5</td><td>57.3</td><td>59.3</td><td>60.4</td></tr><tr><td>ITANet [45]</td><td>IJCAI-21</td><td>49.2</td><td>55.5</td><td>59.1</td><td>61.0</td><td>62.3</td></tr><tr><td>OTAM [4]</td><td>CVPR-20</td><td>42.6</td><td>49.1</td><td>51.5</td><td>52.0</td><td>52.3</td></tr><tr><td>TRX [28]</td><td>CVPR-21</td><td>42.0</td><td>53.1</td><td>57.6</td><td>61.1</td><td>64.6</td></tr><tr><td>STRM [35]</td><td>CVPR-22</td><td>42.1</td><td>53.8</td><td>59.3</td><td>64.2</td><td>68.1</td></tr><tr><td>HyRSM [37]</td><td>CVPR-22</td><td>54.3</td><td>62.2</td><td>65.1</td><td>67.9</td><td>69.0</td></tr><tr><td>Ours+OTAM</td><td>-</td><td></td><td>47.0↑4.2</td><td>54.6↑5.5</td><td>58.3↑6.8</td><td>60.3↑8.3</td><td>61.0↑8.7</td></tr><tr><td>Ours+TRX</td><td>-</td><td></td><td>44.6↑2.6</td><td>54.2↑1.1</td><td>59.9↑2.3</td><td>63.1↑2.1</td><td>64.6↑2.3</td></tr><tr><td>Ours+STRM</td><td>-</td><td></td><td>45.7↑3.6</td><td>55.8↑2.0</td><td>61.7↑2.4</td><td>66.8↑2.6</td><td>69.5↑1.4</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "First, when plugging our proposed modules into the existing FSVC works such as OTAM, its performance gains significant improvement. Concretely, for 5-way-5-shot task on SSv2-Full, the classification accuracy of OTAM using our module attains "
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+                                    "type": "text",
+                                    "content": " which is much higher than its original "
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+                                    "content": ". In addition, the integration of our designed modules and OTAM exceeds the original one by "
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+                                    "content": " on 1-shot task of UCF101. These phenomenons illustrate that our method effectively facilitates OTAM to conduct more accurate temporal alignment across support and query videos by refining video representations with task-shared knowledge and discriminative frame selection. Second, compared with OTAM, original TRX and STRM not only consider learning temporal relationships but also draw assistance from Transformer block to achieve information complementary within each episode. Although their methods seem to be perfect"
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+                                    "type": "text",
+                                    "content": "and promising, our RFPL still facilitates them to boost "
+                                },
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+                                    "type": "text",
+                                    "content": " on most tasks. The main reason for success lies in that our method further helps them enrich the representations of action semantics by introducing meta-action semantics and accurately capture the intrinsic similarity across support and query instances via the increasing effect of important image frames. Finally, injecting our RFPL into other baselines achieves comparable performance with HyRSM on most tasks. Especially, STRM with our RFPL surpasses HyRSM by an obvious gain margin, i.e., "
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+                                    "content": " on 5-shot task of Kinetics, validating that our proposed method is an efficient auxiliary tool for addressing the FSVC problem."
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+                                    "content": "4.3. Performance Study"
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+                                    "content": "Path Visualization & Confusion Matrix. From Table 1, we conclude that our RFPL effectively promotes the perfor"
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+                                            "content": "Figure 2. Comparison between plain OTAM and Ours+OTAM on action recognition result and temporal alignment path. This episode is randomly selected from the meta-testing set of Kinetics. The query video belongs to dancing ballet. Our+OTAM successfully matches it with the support sample from the same category, while plain OTAM matches into a dancing charleston video."
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+                                            "content": "(c) OTAM @ SSV-Full"
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+                                            "content": "(d) Ours+OTAM @ SSV-Full"
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+                                            "content": "Figure 3. Comparison of confusion matrix deduced from the model prediction of plain OTAM and Ours+OTAM. These two episodes are collected from the meta-testing set of Kinetics (2-shot) and SSv2-Full (5-shot)."
+                                        }
+                                    ]
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+                                    "type": "text",
+                                    "content": "mance of OTAM by a large margin. To explicitly explain the reason for improvement, we randomly select an episode from meta-testing set "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{test}"
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+                                    "type": "text",
+                                    "content": " and visualize the frame-level cumulative distance across query video and the selected support ones as Fig. 2 shows. This visualization indicates that OTAM is sensitive to image background and its temporal alignment becomes invalid. Thus, it considers that this query video from the dancing ballet class has the highest similarity with the support sample from dancing charleston. Differently, our method assists OTAM to focus on the similarity of action semantics, especially on distinguishing body posture. Hence, Ours+OTAM accurately matches the query sample with the support video from the identical category and achieves better temporal alignment."
+                                }
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+                                    "type": "text",
+                                    "content": "In addition, we draw the confusion matrix of two specific episodes to further discuss their differences. Concretely, during the inference stage, for 2-shot of Kinetics or 5-shot of SSv2-Full, we randomly choose an episode with 200 query samples uniformly distributed in five categories and compare model prediction and ground-truth to form Fig. 3. For the task of Kinetics, with the help of our RFPL, the recognition abilities of OTAM in five categories are all strengthened. With respect to the more challenging task of SSv2-Full, OTAM with our method learns more discrimina"
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+                                    "type": "text",
+                                    "content": "tive action semantics and achieves significant performance improvement on several categories without reduction on the remaining ones."
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+                                    "type": "text",
+                                    "content": "Reinforced Image Frames. In our RFPL, reinforced image representation as one important module aims to discover the discriminative image frames via the comparison of the paired videos. To analyze its effect, we record the frame-wise weights deduced from the agent as Fig. 4 in one test episode. From two \"folding paper\" videos, several image frames without any \"folding\" action are provided with lower weights such as frames in the red box. For action-relevant images, the learned network produces higher weights for them as the blue box shows. From the other example \"cutting watermelon\", we have an interesting finding. The well-trained network does not give larger weights for frames including \"cutting\" action, while highlighting images with two halves of the red pulp of a watermelon as the green box shows. It suggests that the network considers that these image contents are useful for the improvement of cross-video similarity."
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+                                    "content": "Parameter Analysis. There is one hyper-parameter "
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+                                    "content": " in our RFPL, which serves as a trade-off between accepting external global knowledge and preserving current feature representations. In practical experiments, this parameter is"
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+                                    "content": "\\rho \\in \\{0.001, 0.01, 0.1, 0.5\\}"
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+                                    "type": "text",
+                                    "content": ". Definitely, the optimal parameter is determined by the performance of the learned model on the meta-validation set. Concretely, Fig. 5 shows the change of model classification ability on the validation set of SSv2-Full with the varying "
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+                                    "content": ". Based on this parameter analysis, we find that when "
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+                                    "content": " on many tasks. Therefore, it is reasonable to infer that while introducing global knowledge to enhance semantics information, the protection of current information is very necessary and stabilizes the model training."
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+                                    "type": "text",
+                                    "content": "Ablation Study. Our RFPL consists of two modules: meta-action learning and reinforced image representation. The first one aims to enrich video representation by fusing global knowledge of the meta-action bank to each specific episode, while the second one expects to emphasize the representation of informative image frames via reinforcement learning selection. In fact, we also separately plug each module into the existing baseline, named as Ours-v1 (adding MAL) and Ours-v2 (adding RIR). These variants"
+                                }
+                            ]
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+                                            "content": "Figure 6. Ablation study. Ours-v1 and Ours-v2 mean that meta-action learning and reinforced image representation modules are plugged into the existing FSVC works, respectively."
+                                        }
+                                    ]
+                                }
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+                                    "content": "are combined with OTAM and evaluated on three tasks of Kinetics with results in Fig. 6. The comparisons with plain OTAM mean that each module can independently make positive contributions on advancing it. And the collaboration of MAL and RIR will bring more benefits to OTAM than each independent module. Thus, using the complete RFPL is the optimal strategy."
+                                }
+                            ]
+                        }
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+                                    "content": "5. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "content": "In this paper, we propose a flexible representation fusion and enhancement learning (RFPL) mechanism with two sub-modules to solve few-shot video classification. The meta-action learning module builds a generic action bank and fuses the adapted one to enrich video features, while the reinforced image representation module identifies important frames via an agent and promotes their positive effect to precisely capture cross-video similarity. Considerable experimental results and analysis verify that our RFPL effectively advances the existing FSVC methods."
+                                }
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[45] Songyang Zhang, Jiale Zhou, and Xuming He. Learning implicit temporal alignment for few-shot video classification. arXiv preprint arXiv:2105.04823, 2021. 1, 2, 5, 6"
+                                        }
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+                            "index": 19
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+                                        }
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+                                        }
+                                    ]
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+                        },
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+                                        }
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diff --git a/2023/Few-shot Continual Infomax Learning/4bda674e-273c-4a6b-8394-b466c9dde520_content_list.json b/2023/Few-shot Continual Infomax Learning/4bda674e-273c-4a6b-8394-b466c9dde520_content_list.json
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+[
+    {
+        "type": "text",
+        "text": "Few-shot Continual Infomax Learning",
+        "text_level": 1,
+        "bbox": [
+            289,
+            130,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ziqi Gu#, Chunyan Xu#, Jian Yang, Zhen Cui*  \nPCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{ziqigu, cyx, csjyang, zhen.cui}@njust.edu.cn",
+        "bbox": [
+            285,
+            253,
+            683,
+            268
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            304,
+            313,
+            320
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Few-shot continual learning is the ability to continually train a neural network from a sequential stream of few-shot data. In this paper, we propose a Few-shot Continua! Infomax Learning (FCIL) framework that makes a deep model to continually/incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting of past knowledge. Specifically, inspired by the theoretical definition of transfer entropy, we introduce a feature embedding infomax to effectively perform the few-shot learning, which can transfer the strong encoding capability of the base network to learn the feature embedding of these novel classes by maximizing the mutual information of different-level feature distributions. Further, considering that the learned knowledge in the human brain is a generalization of actual information and exists in a certain relational structure, we perform continual structure infomax learning to relieve the catastrophic forgetting problem in the continual learning process. The information structure of this learned knowledge can be preserved through maximizing the mutual information across these continual-changing relations of inter-classes. Comprehensive evaluations on CIFAR100, miniImageNet, and CUB200 datasets demonstrate the superiority of our FCIL when compared against state-of-the-art methods on the few-shot continual learning task.",
+        "bbox": [
+            75,
+            335,
+            473,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            729,
+            209,
+            744
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent deep learning technologies [23, 30, 13] have made great progress in many computer vision tasks. The success of deep neural networks is achieved by employing a large number of labeled training data. However, it is difficult to collect large-scale supervised data in advance, while we would encounter a sequential data stream with unknown new classes in many realistic situations. This would require",
+        "bbox": [
+            75,
+            756,
+            468,
+            863
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "a neural network with continual learning ability, especially when some new classes with very few labeled samples often appear. Therefore, this work focuses on dealing with the few-shot continual/incremental learning task [28, 26]. They are two critical challenges in a few-shot continual learning task: i) how to learn new knowledge with few-shot instances, and ii) how to avoid catastrophic forgetting of the preceding learned knowledge.",
+        "bbox": [
+            500,
+            305,
+            892,
+            426
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, numerous previous works [31] have been devoted to few-shot continual learning from various perspectives. In [31, 35, 8], the topological structure of the knowledge space formed by different classes has been considered to perform few-shot continual learning by using a neural gas network or graph model. Cheraghian et al. [8] have proposed a semantic-aware knowledge distillation method to solve few-shot class incremental learning by making use of word embeddings. Several meta-learning based methods [7, 18] have been also proposed to enable the model to preserve old knowledge and adapt to the new classes for continual learning. By assigning virtual prototypes to squeeze the embedding of known classes and reserve for new ones, the forward compatible training method [37] has efficiently incorporated new classes with forward compatibility and meanwhile resists forgetting old ones. Similarly, the mixture of subspaces and synthesized features [6] have been used to alleviate the forgetting and over-fitting problem in the few-shot continual learning process. In [38], the self-promoted prototype learning scheme has been proposed to explicitly learn the feature representation under the few-shot learning situation and thus facilitated subsequent incremental tasks. The self-supervised strategy has been also used to enhance the feature extraction ability of the model by adding self-supervised loss function assistance during the training process [20, 26]. Moreover, to minimize over-fitting and the catastrophic forgetting problem, Mazumder et al. [26] have selected very few unimportant model parameters to perform few-shot learning on new classes. In [11], mutual information (MI) maximization has been first used as a solution method to deal with the catas",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "Equal Contribution.",
+        "bbox": [
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+            875,
+            222,
+            887
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "* Corresponding Author.",
+        "bbox": [
+            102,
+            887,
+            238,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "19224",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "trophic forgetting problem in the online continual learning task, but it cannot well consider how to perform continual infomax learning from the perspective of information entropy, especially in the few-shot regime.",
+        "bbox": [
+            75,
+            90,
+            468,
+            151
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a novel Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to continually learn from a stream of few-shot labeled data. In general, the continual learning model would be trained with a large amount of labeled data in the initial learning stage, while few-shot samples of some unknown classes would be encountered in the continual learning process. Here we attempt to address the few-shot continual learning task from two aspects. First, inspired by the theoretical definition of transfer entropy, we attempt to transfer the strong encoding capability of the base network to promote few-shot continual learning. Specifically, we propose a feature embedding infomax learning to new concepts from a few labeled samples through maximizing the mutual information between different level feature distributions, where the convolutional representations and the feature embedding of new classes are encoded with these fixed convolution layers of the base network and newly increased parameters of fully-connected layer, respectively. Second, considering that the learned knowledge in the human brain is a generalization or abstraction of the actual information learned from these seen samples [10], we wish the continual learning model with a stable information structure that can be updated incrementally. Thus we propose a continual structure infomax learning mechanism to alleviate the catastrophic forgetting problem during the continual learning process. The structure relation of this learned information can be preserved through maximizing the mutual information across these continual-changing structure relations of inter-classes.",
+        "bbox": [
+            75,
+            151,
+            472,
+            604
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, our primary contributions can be summarized as follows: i) We propose a Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting problem of previously learned ones. ii) Two specially-designed infomax learning mechanisms are proposed to address the few-shot continual learning problem with the help of mutual information maximization, including feature embedding infomax and continual structure infomax. iii) We validate the effectiveness of our proposed FCIL on three benchmarks (including CIFAR100, CUB200, and miniImageNet), and also demonstrate the superiority of our proposed FCIL when compared with existing state-of-the-art methods.",
+        "bbox": [
+            75,
+            604,
+            472,
+            816
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            830,
+            215,
+            845
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot continual learning: Few-shot continual learning, which has recently attracted growing attention, aims to enable a model to perform continual/incremental",
+        "bbox": [
+            75,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "learning with a stream of few-shot labeled data. A number of related works have been proposed to address the few-shot continual learning task. For example, Tao et al. [31] employed neural gas networks to perform incrementally learning for a series of new classes with few-shot data, with the goal of avoiding forgetting previously learned classes. Zhang et al. [35] proposed an evolving classifier based on graph attention networks that propagated information between classifiers by adding graph models. Also, pseudo-incremental training was proposed to optimize the graph module. The forward compatible training (FACT) [37] was proposed to effectively incorporate novel classes into forward compatible by generating virtual classes, where knowledge of old classes can be also maintained to reduce the catastrophic forgetting problem. A bi-level meta-learning-based optimization [7] was proposed to directly optimize the model towards forgetting alleviation of learned knowledge and adaptation of the new classes. In [20], a self-supervised stochastic classifier was proposed to deal with the few-shot class incremental learning task with the help of a self-supervision mechanism. Zhu et al. [38] proposed an incremental prototype learning scheme to perform continual learning, which was used to constrain the prototypes of new classes through the dynamic model and then achieved a reduction in catastrophic forgetting of knowledge. In order to offer a trade-off between accuracy and compute-memory cost of learning novel classes, the hyper-dimensional embedding was used to continually learn many more classes than the fixed dimensions in the feature space [14]. Further, few-shot lifelong learning was proposed to perform continual learning with only updating very few parameters of the model [26] or semantic-aware knowledge distillation [5].",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Mutual information: Mutual Information as a quantity is used to measure the degree of interdependence between two random variables [21]. As it is difficult to exactly compute the mutual information between second-dimensional random variables, mutual information neural estimator (MINE) [2] can be achieved by employing the dual representations of the Kullback-Leibler divergence (KL) [9]. Subsequently, the Jensen-Shannon divergence (JSD) [27] and noise-contrastive estimation (NCE) [12] were used to estimate the mutual information with a learned network [16], and then the mutual information maximization method was used to improve the deep representation in an unsupervised learning way. The second-order deep multiplex infomax method [19] further extended the mutual information estimation to a three-variable calculation and was applied across multiple networks. The deep mutual information maximin method [25] was used to address the cross-modal clustering task by maximally preserving the shared information of multiple modalities and eliminating the superfluous information of individual modalities. In [1], mutual information networks are applied to unsupervised",
+        "bbox": [
+            496,
+            584,
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+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "19225",
+        "bbox": [
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+            944,
+            517,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "classification tasks with excellent results. In the online continual learning task, Guo et al. [11] first used mutual information estimation to learn more robust features and preserve the past model learned from the previous task. Different from these previous methods, we perform continual infomax learning from the perspective of information entropy in the few-shot setting.",
+        "bbox": [
+            75,
+            90,
+            472,
+            196
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. The Proposed Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            214,
+            287,
+            231
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Definition",
+        "text_level": 1,
+        "bbox": [
+            76,
+            241,
+            261,
+            255
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Few-shot continual learning aims to train a model for new tasks sequentially from a stream of few-shot labeled data, relieving the forgetting of knowledge learned from the old tasks, where the data in the old tasks are not available anymore during learning a new set of few-shot tasks. Formally, we define  $X$ ,  $Y$ , and  $Z$  as the training set, label set, and test set, respectively. Our task is to train the model with a continuous stream of labeled training sets  $X_{1}, X_{2}, \\ldots, X_{T}$ , where  $X_{t}$  denotes the  $t$ -th training set,  $Y_{t}$  is the corresponding label set, and  $T$  refers to the number of continual learning sessions. In the continual learning process, each training set is with no repetition of class labels, i.e.,  $\\forall i, j$  and  $i \\neq j$ ,  $Y_{i} \\cap Y_{j} = \\emptyset$ . Usually, when  $t = 1$ , the training set  $X_{1}$  is with large-scale samples for training the base network; when  $t > 1$ ,  $X_{t}$  refers to the few-shot training set of new classes in the incremental learning stage (i.e.,  $|X_{1}| \\gg |X_{t}|, t = 2, 3, \\ldots, T$ ). For example, under the 5-way 10-shot setting, each incremental/continual process (i.e.,  $t > 1$ ) contains five new classes, each of which has only ten training samples. The test set  $Z$  is used to evaluate the classification performance at each stage  $t$ , and its corresponding classes may be from all training label sets, i.e.,  $\\{Y_{1} \\cup Y_{2} \\dots \\cup Y_{T}\\}$ .",
+        "bbox": [
+            75,
+            265,
+            472,
+            613
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the few-shot continual learning task, there are two critical problems we need to consider: i) New classes are with a small amount of training data, which makes it hard to learn the feature embeddings for these new classes. ii) Catastrophic forgetting should be well relieved to preserve this learned knowledge in the continual learning process. In this work, we attempt to address them from two aspects. First, we start from the transfer entropy perspective [3] to obtain new knowledge from few-shot samples, where the strong encoding capability of the base network can be transferred to learn feature embeddings of these new classes. Second, considering that the learned knowledge in the human brain is not isolated, but exists in a certain relational structure [10], we wish to preserve the structure information of this learned knowledge to relieve the catastrophic forgetting problem during the continual learning process. With the help of the recently-developed mutual information estimation method [2, 16, 36], we achieve these above goals by performing continual infomax learning.",
+        "bbox": [
+            75,
+            613,
+            472,
+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/aa7adcb9237bd04db99ee4e6d59b5c1ecb9cd4af010f6a820d077c75450eb06b.jpg",
+        "image_caption": [
+            "Figure 1. The pipeline of our few-shot continual infomax learning, where  $t$  refers to the  $t$ -th session in the continual learning process ( $t \\geqslant 1$ ). To transfer the strong encoding capability of the base network into the subsequent continual learning sessions, we first propose the feature embedding infomax to learn new knowledge with few-shot labeled data in the  $t$ -th session. Here we maximize the mutual information between multi-level convolutional representations  $F_{conv}(x_i)$  and full-connected feature embedding  $F_{fc}(x_i)$  of each input sample, which are encoded with these fixed convolution layers of the base network  $\\Theta_{conv}^{base}$  and updated fully-connected layer  $\\Theta_{fc}^{t}$ , respectively. To address the catastrophic forgetting problem in the continual learning process, we further perform the continual structure infomax learning by maximizing the mutual information between current and previous inter-class knowledge structures (i.e.,  $S(A^t, R^t)$  and  $S(A^{t-1}, R^{t-1})$ )."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            90,
+            890,
+            324
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. FCIL Paradigm",
+        "text_level": 1,
+        "bbox": [
+            500,
+            540,
+            660,
+            556
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The proposed few-shot continual infomax learning (FCIL) framework is shown in Fig. 1. Generally, the base network  $\\Theta^{base}$ , which is a large-scale set of training samples  $X_{1}$ , can optimize with the classic cross-entropy loss. For further improving the deep representation capability of the base network, we also employ self-supervised mutual information mechanism. Here the mutual information estimated network  $\\vartheta^{MI}$  can be well optimized in the initial stage (i.e.,  $t = 1$ ), which contributes to the subsequent continual learning sessions. In the next continual learning sessions (i.e.,  $t > 1$ ), a stream of few-shot labeled data with new classes would be gradually fed into the network, and we would perform few-shot continual infomax learning for capturing new knowledge, without forgetting these learned ones. To improve the feature embedding capability of these new classes, we attempt to transfer the strong representation capability of the base network  $\\Theta^{base}$  into the next continual learning sessions. Specifically, we introduce the feature embedding infomax learning to optimize these fully-connected parameters  $\\Theta_{fc}^{t}$  of new classes. Given an input image  $x_{i}$  from the few-shot set  $D_{t}$ , we use the convolutional net optimized in the base stage to extract multi-level convolutional",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "19226",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "features  $F_{conv}(x_i)$ , and get the feature embeddings from new full-connected layer  $F_{fc}(x_i)$ . We maximize the mutual information between the convolutional and full-connected feature distributions for each input sample (i.e.,  $F_{conv}(x_i)$  and  $F_{fc}(x_i)$ ), and thus the feature embedding of the novel classes can well inherit the powerful feature representation capability of the base network (i.e.,  $\\max \\mathcal{T}_{\\Theta^{base} \\to \\Theta_{fc}^t}$ ). Further, to alleviate the catastrophic forgetting problem of this learned knowledge during the subsequent continual learning sessions, we introduce a continual structure infomax learning (i.e.,  $\\max \\mathcal{D}_S$ ) to maintain/preserve the relations of intra-classes across one or more learning sessions. At each learning session  $t$ , we can obtain the first-order attributes and the second-order structure information of this learned knowledge, which refer to the class-wise feature embeddings and the relations among different classes, respectively. We then maximize the mutual information between the current information structure  $S(A^t, R^t)$  and this previous information  $S(A^{t'}, R^{t'})$  ( $t' = t - 1, t - 2, \\ldots, t - K$  and  $t - K \\geqslant 1$ ) of these old classes. With the help of feature embedding infomax and continual structure infomax, the deep model can be well worked in the few-shot continual learning process. See the supplementary materia for more details.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Feature Embedding Infomax",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "When the base network  $\\Theta^{base}$  faces unknown new classes, it is difficult to learn new concepts with only few-shot labeled samples. Inspired by the classic transfer entropy method which is a non-parametric measure of directed, asymmetric information transfer between two processes [3], we attempt to migrate the powerful feature representation capability of the base network to capture the feature embedding of the novel classes. Given few-shot training samples of new classes in the  $t$ -continual learning stage (i.e.,  $t > 1$ ), the transfer entropy from the base network  $\\Theta^{base}$  to the feature embedding layer of novel classes  $\\Theta_{fc}^{t}$  (i.e., fully-connected model parameters) can be formulated as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {T} _ {\\Theta^ {b a s e} \\rightarrow \\Theta_ {f c} ^ {t}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\left(H \\left(\\mathbf {Z} _ {f c}\\right) - H \\left(\\mathbf {Z} _ {f c} \\mid \\mathbf {Z} _ {c o n v}\\right)\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            681,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $X_{t} = \\{x_{1},x_{2},\\dots,x_{|X_{t}|}\\}$  is the training set of few-shot data in the  $t$  -th continual learning session;  $F_{conv}(x_i)$  is the convolution representations of the training sample  $x_{i}$  with the base encoding network  $\\Theta^{base}$ .  $F_{fc}(x_{i})$  is the feature embedding of  $x_{i}$  with the fully-connected parameters  $\\Theta_{fc}^t$  of the  $t$  -th continual learning stage. Let  $\\mathbf{Z}_{conv} = F_{conv}(x_i)$  and  $\\mathbf{Z}_{fc} = F_{fc}(x_i)$ ,  $H(\\mathbf{Z}_{fc})$  refers to the Shannon entropy information of fully-connected feature of  $x_{i}$  and the conditional entropy  $H(\\mathbf{Z}_{fc}|\\mathbf{Z}_{conv})$  is the entropy of  $\\mathbf{Z}_{conv}$  conditioned on  $\\mathbf{Z}_{fc}$ . To facilitate the calculation of Eqn. (1), the transfer entropy  $\\mathcal{T}_{\\Theta^{base}\\to \\Theta_{fc}^t}$  can be further",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "expressed as the conditional mutual information of different level features with the corresponding network parameters in the condition:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {T} _ {\\Theta^ {b a s e} \\rightarrow \\Theta_ {f c} ^ {t}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} I ((\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l})), \\\\ \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} \\hat {I} \\left(\\left(\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}\\right), \\vartheta^ {M I}\\right), \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "here, we directly maximize the mutual information between multi-level convolutional features and fully-connected feature embedding, which can better transfer the strong encoding capability of the base network  $\\Theta^{base}$  to the fully-connected layer  $\\Theta_{fc}^{t}$ . With the support of the Kullback-Leibler divergence [9] and the learned mutual information estimation network  $\\vartheta^{MI}$ , the transfer entropy process can be approximately formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathcal {T}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}\\right), \\vartheta^ {M I}\\right)\\right) \\tag {3} \\\\ - \\log \\mathbb {E} (e ^ {\\mathcal {F} ((\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}), \\vartheta^ {M I})}). \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{F}(\\cdot)$  is a discriminant function between features of different layers. Here this transfer entropy process can help to capture the feature embeddings of these few-shot training samples in the continual learning stages, thus we name it as \"feature embedding infomax\" learning process. The final learning objective to optimize the  $t$ -th continual fully-connected layer  $\\Theta_{fc}^{t}$  is defined as:  $\\mathcal{L}_{FEI} = \\mathcal{L}_{CE} - \\alpha \\mathcal{L}_{\\mathcal{T}}$  where  $\\mathcal{L}_{CE}$  is the classic cross-entropy loss and  $\\alpha$  is a hyper-parameter.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Continual Structure Infomax",
+        "text_level": 1,
+        "bbox": [
+            500,
+            590,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Another critical problem for a continual learning model is exiting the catastrophic forgetting this learned knowledge when discarding old samples. An obvious solution is that continual learning must have a strategy to preserve the information related to these old training samples. Usually, the information preserved in a continual learning system is a generalization or abstraction of the actual information embedded in the learned samples. The knowledge we learn in the human brain [10] does not exist in isolation; there is some kind of relational structure between different pieces of knowledge that maintains the connection between knowledge. In order to possess an information structure that would be updated incrementally along the continual learning process, we can preserve useful information from learned samples as much as possible so that the subsequent continual learning process can be guided by this information. Therefore, we propose a continual structure infomax learning to conserve both first-order and second-order information in the continual learning process, which can be",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19227",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "related to class-wise individual attributions and intra-class relations, respectively. In the  $t$ -th continual learning session, the continual structure infomax can be performed under the guidance of these previous information structures:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {S} = \\sum_ {k = 1} ^ {K} \\underbrace {H \\left(A _ {t}\\right) - H \\left(A _ {t} \\mid A _ {t - k}\\right)} _ {\\text {f i r s t - o r d e r}} + \\underbrace {H \\left(R _ {t}\\right) - H \\left(R _ {t} \\mid R _ {t - k}\\right)} _ {\\text {s e c o n d - o r d e r}} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            156,
+            472,
+            213
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $K$  is the number of previous sessions with  $t - K \\geq 1$ .  $A_{t}$  and  $A_{t - k}$  refer to the feature embeddings of all learned classes  $c_{t}$ , e.g.,  $A_{t} = [e_{1}, e_{2}, \\ldots, e_{c}, \\ldots, e_{c_{t}}]$ . Due to the fact that the mean value of each class is approximate to the parameter weights of the last fully-connected layer,  $e_{c}$  is achieved by the weight parameters of the last classification layer corresponding to the  $c$ -th class. Their corresponding information entropy  $A_{t}$  and  $A_{t - k}$  are represented as  $H(A_{t})$  and  $H(A_{t}|A_{t - k})$ .  $R_{t} \\in \\mathbb{R}^{c_{t} \\times c_{t}}$  and  $R_{t - k} \\in \\mathbb{R}^{c_{t - k} \\times c_{t - k}}$  refer to the inter-class relation matrices of all learned classes in the  $t$ -th and  $(t - k)$ -th stages.  $H(R_{t})$  and  $H(R_{t}|R_{t - k})$  represent the second-order information entropy concerning the relation among different classes. Through maximizing the first-order and second-order mutual information between different learning stages, the network parameters of the last fully-connected layer  $\\Theta_{fc}$  can be incrementally updated along the continual learning process, formally,",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {D} _ {S} = \\sum_ {k = 1} ^ {K} \\underbrace {I (A _ {t} ; A _ {t - k})} _ {\\text {f i r s t - o r d e r}} + \\underbrace {I (R _ {t} ; R _ {t - k})} _ {\\text {s e c o n d - o r d e r}}, \\\\ \\geq \\sum_ {k = 1} ^ {K} \\underbrace {\\hat {I} \\left(\\left(A _ {t} ; A _ {t - k}\\right) , \\vartheta^ {M I}\\right)} _ {\\text {f i r s t - o r d e r}} + \\underbrace {\\hat {I} \\left(\\left(R _ {t} ; R _ {t - k}\\right) , \\vartheta^ {M I}\\right)} _ {\\text {s e c o n d - o r d e r}}, \\tag {5} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Similar to the feature embedding infomax, we also use mutual information to measure the amount of information shared by different sessions, and this continual structure infomax process can be further formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {S} = \\sum_ {k = 1} ^ {K} \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(A _ {t}; A _ {t - k}\\right), \\vartheta^ {M I}\\right)\\right) - \\log \\mathbb {E} \\left(e ^ {\\mathcal {F} \\left(\\left(A _ {t}; A _ {t - k}\\right), \\vartheta^ {M I}\\right)}\\right) \\\\ + \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(R _ {t}; R _ {t - k}\\right), \\vartheta^ {M I}\\right)\\right) - \\log \\mathbb {E} \\left(e ^ {\\mathcal {F} \\left(\\left(R _ {t}; R _ {t - k}\\right), \\vartheta^ {M I}\\right)}\\right), \\tag {6} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            643,
+            488,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $k$  refers to the  $k$ -th session with  $1 \\leqslant k \\leqslant K$ . We employ both  $\\mathcal{L}_S$  and  $\\mathcal{L}_{CE}$  to optimize the fully-connected parameters  $\\Theta_{fc}^t$  to adapt new classes without forgetting these learned ones. In the structure continual infomax process, the corresponding loss is defined as  $\\mathcal{L}_{CSI} = \\mathcal{L}_{CE} - \\gamma \\mathcal{L}_S$ , where  $\\gamma$  is a balance factor.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            821,
+            209,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            847,
+            266,
+            863
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets: We evaluate our FCIL on three public datasets, including CIFAR100 [22], miniImageNet [29],",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and CUB200 [33]. For CIFAR100 [22] and miniImageNet [29], we use all the training data of the 60 base classes to train a base network, and the 40 new classes are used to perform eight 5-way 5-shot continual learning tasks. We divide the 200 classes of CUB200 [33] into 100 base classes and 100 new classes. The 100 new classes are used to perform ten 10-way 5-shot continual learning tasks. We follow the same split setting of FSCIL [31] as other methods in the three datasets for a fair comparison. See the supplementary materia for more details.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details: Following FSCIL [31], we use ResNet20 as the backbone on CIFAR100 [22] and ResNet18 is used as the backbone on miniImageNet [29] and CUB200 [33]. The network  $\\vartheta^{MI}$  consists of a convolution branch and a linear branch, where the former consists of three convolution layers whose kernel sizes are 1, 5, and 7, and the latter is one linear layer. In the CSI module, the convolution branch and the linear branch separately take  $F_{conv}^{l}(x_{i})$  and  $F_{fc}(x_{i})$  as inputs, and their outputs are used to compute  $\\mathcal{L}_{\\mathcal{T}}$ . In the CSI module, the linear layer of  $\\vartheta^{MI}$  separately take  $A_{t}$  and  $A_{t - k}$  as inputs, and we use the outputs to compute  $\\mathcal{L}_s$ . In the base learning stage, we train the base network and the mutual information network with the first training set. The parameters of the convolutional layers  $\\Theta^{base}$  and the mutual information network  $\\vartheta^{MI}$  are frozen in the continual learning sessions to perform mutual information estimation in both the proposed feature embedding infomax. For all datasets, we set  $\\alpha$  and  $\\gamma$  as 0.015 and 0.03, respectively. Random cropping, random scaling, and random horizontal flipping are used for training data. We use to evaluate our proposed method from different perspectives. \"Acc_t\" represents to the Top-1 accuracy in the t-th continual session. \"Avg\" represents for an average score, i.e.,  $\\sum_{t=1}^{T} \\mathrm{Acc}_t / T$ . \"ΔFinal\" represents the difference value of  $\\mathrm{Acc}_t$  between our method and the compared method in the final state. \"KR\" is the knowledge retention rate, i.e.,  $\\mathrm{Acc}_T / \\mathrm{Acc}_1$ . All the experiments are conducted with the Pytorch framework on one Geforce 2080Ti GPU.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison with state-of-the-art methods",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We first compare our proposed FCIL with other state-of-the-art methods on the challenging miniImageNet dataset [29]. The detailed results have been listed in Table 1, and the accuracy changing curves with growing continual sessions are plotted in Fig. 2 (a). Our proposed FCIL outperforms all other compared methods by a great margin and sets new state-of-the-art. In particular, our FCIL achieves the best score among all the methods. Considering that in the first continual session, very little data are available and it requires borrowing the learning capability of the base stage into this session to promote the classifier accuracy. In addition, as to the overall performance in the final continual session, our FCIL also surpasses the second best method C-",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "19228",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/430ed91f927b2c2e640e3eef190a37984f3a50f754369381e6c099dd34ff1479.jpg",
+        "table_caption": [
+            "Table 1. Few-shot continual classification performance of state-of-the-art methods and our FCIL on the miniImageNet dataset [29]. The results with * are obtained from the authors' published code. See the supplementary materia for results of other datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"10\">Accuracy in each session (%)↑</td><td>KR↑</td><td>ΔFinal↑</td><td>Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>Ft-CNN</td><td>61.31</td><td>27.22</td><td>16.37</td><td>6.08</td><td>2.54</td><td>1.56</td><td>1.93</td><td>2.60</td><td>1.40</td><td>2.28</td><td>+51.36</td><td>13.44</td><td></td></tr><tr><td>iCaRL [28]</td><td>61.31</td><td>46.32</td><td>42.94</td><td>37.63</td><td>30.49</td><td>24.00</td><td>20.89</td><td>18.80</td><td>17.21</td><td>28.07</td><td>+35.55</td><td>33.29</td><td></td></tr><tr><td>EEIL [4]</td><td>61.31</td><td>46.58</td><td>44.00</td><td>37.29</td><td>33.14</td><td>27.12</td><td>24.10</td><td>21.57</td><td>19.58</td><td>31.93</td><td>+33.18</td><td>34.97</td><td></td></tr><tr><td>TOPIC [31]</td><td>61.31</td><td>50.09</td><td>45.17</td><td>41.16</td><td>37.48</td><td>35.52</td><td>32.19</td><td>29.46</td><td>24.42</td><td>39.83</td><td>+28.34</td><td>39.65</td><td></td></tr><tr><td>NCM [17]</td><td>61.31</td><td>47.80</td><td>39.31</td><td>31.91</td><td>25.68</td><td>21.35</td><td>18.67</td><td>17.24</td><td>14.17</td><td>23.11</td><td>+38.59</td><td>30.83</td><td></td></tr><tr><td>Decoupled-NegCosine [24]</td><td>71.68</td><td>66.64</td><td>62.57</td><td>58.82</td><td>55.91</td><td>52.88</td><td>49.41</td><td>47.50</td><td>45.81</td><td>63.90</td><td>+6.95</td><td>56.80</td><td></td></tr><tr><td>Decoupled-Cosine [32]</td><td>70.37</td><td>65.45</td><td>61.41</td><td>58.00</td><td>54.81</td><td>51.89</td><td>49.10</td><td>47.27</td><td>45.63</td><td>64.84</td><td>+7.13</td><td>55.99</td><td></td></tr><tr><td>Decoupled-DeepEMD [34]</td><td>69.77</td><td>64.59</td><td>60.21</td><td>56.63</td><td>53.16</td><td>50.13</td><td>47.79</td><td>45.42</td><td>43.41</td><td>62.21</td><td>+9.35</td><td>54.57</td><td></td></tr><tr><td>MateFSCIL [7]</td><td>72.04</td><td>67.94</td><td>63.77</td><td>60.29</td><td>57.58</td><td>55.16</td><td>52.90</td><td>50.79</td><td>49.19</td><td>68.28</td><td>+3.57</td><td>58.85</td><td></td></tr><tr><td>C-FSCIL Model1 (d=512) [15]</td><td>76.37</td><td>70.94</td><td>66.36</td><td>62.64</td><td>59.31</td><td>56.02</td><td>53.14</td><td>51.04</td><td>48.87</td><td>63.99</td><td>+3.89</td><td>60.52</td><td></td></tr><tr><td>C-FSCIL Mode2 (d=512) [15]</td><td>76.45</td><td>71.23</td><td>66.71</td><td>63.01</td><td>60.09</td><td>56.73</td><td>53.94</td><td>52.01</td><td>50.08</td><td>65.50</td><td>+2.68</td><td>61.14</td><td></td></tr><tr><td>C-FSCIL Mode3 (d=512) [15]</td><td>76.40</td><td>71.14</td><td>66.46</td><td>63.29</td><td>60.42</td><td>57.46</td><td>54.78</td><td>53.11</td><td>51.41</td><td>67.29</td><td>+1.35</td><td>61.61</td><td></td></tr><tr><td>FACT* [37]</td><td>75.68</td><td>70.65</td><td>66.53</td><td>62.75</td><td>59.39</td><td>56.19</td><td>53.26</td><td>51.10</td><td>49.48</td><td>65.38</td><td>+3.28</td><td>60.56</td><td></td></tr><tr><td>FACT* + FCIL</td><td>76.21</td><td>70.92</td><td>66.69</td><td>63.23</td><td>60.73</td><td>57.88</td><td>54.08</td><td>52.17</td><td>50.34</td><td>66.05</td><td>+2.42</td><td>61.36</td><td></td></tr><tr><td>CEC [35]</td><td>72.00</td><td>66.83</td><td>62.97</td><td>59.43</td><td>56.70</td><td>53.73</td><td>51.19</td><td>49.24</td><td>47.63</td><td>66.15</td><td>+5.13</td><td>57.75</td><td></td></tr><tr><td>CEC + FCIL</td><td>72.87</td><td>68.23</td><td>64.46</td><td>60.64</td><td>57.71</td><td>55.12</td><td>52.79</td><td>50.65</td><td>48.62</td><td>66.72</td><td>+4.14</td><td>59.01</td><td></td></tr><tr><td>FCIL (Ours)</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>-</td><td>62.37</td><td></td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/6e8806132b03c841dfed725047ec8a1436b8d20f927a90f58960bb6b05ec74e8.jpg",
+        "image_caption": [
+            "(a) miniImageNet"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/1041a4c22f7293580cdb28b0e24fa9930a961d824b12690011981568873517d1.jpg",
+        "image_caption": [
+            "(b) CIFAR100"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/445125f576ff6154d6ad92a3c5937145ab7e2b500541aaf57937e6b17558baad.jpg",
+        "image_caption": [
+            "(c) CUB200",
+            "Figure 2. The accuracy changing curves with growing continual sessions of different methods on the three datasets."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            629,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "FSCIL Mode3 (d=512) [15] by a non-trivial gap of  $1.35\\%$ . It shows that our FCIL could keep great learning capability when performing the continual learning process, and we owe the superiority to the strong capability borrowed from the base network by the proposed feature embedding infomax module. Further, our method also achieves the best performance on Avg, outperforming the compared methods by at least  $0.76\\%$ . It indicates that our FCIL could always obtain better performance during all the continual sessions, further demonstrating the strong learning capability borrowed from the base network. Overall, the superior performances of our FCIL in terms of Avg and  $\\Delta$ Final sufficiently verify the effectiveness of our proposed feature embedding infomax module on enhancing the learning capability of new classes. Besides, we integrate our proposed FCIL mechanisms into the FACT [37] and CEC [35] frameworks (i.e., FACT+FCIL and CEC+FCIL), and the compared results show that we can lead to significant improvements of  $0.99\\%$  and  $0.86\\%$  on the  $\\Delta$ Final metric. It further verifies the superiority of our FCIL framework in learning new knowledge and alleviating catastrophic forgetting.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our FCIL achieves the best performance on the KR met-",
+        "bbox": [
+            96,
+            885,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ric, with a promotion of at least  $0.83\\%$ . Since KR represents the accuracy ratio of the final continual session and the base stage, a larger KR value means that less learned knowledge is forgotten. Compared with previous methods such as CEC [35], FACT [37], C-FSCIL [15] which also freeze the base classifier as our FCIL to avoid catastrophic forgetting, our FCIL still outperforms them by a considerable margin. It means that the relationship preserving capability brought by the proposed continual structure infomax module could better preserve the previously learned knowledge. It clearly validates the effectiveness of our proposed continual structure infomax module in mitigating the catastrophic forgetting problem. As a whole, the superior performance clearly verifies the superiority of our proposed FCIL in learning novel class knowledge as well as mitigating the catastrophic forgetting problem. The accuracy changing curves with growing continual sessions in Fig. 2(a) further visually show the superiority of our FCIL. We further plot the accuracy changing curves on the CIFAR100 [22] and CUB200 [33] datasets separately in Fig. 2(b) and Fig. 2(c). It could be observed that our proposed FCIL also achieves the best performances on the two datasets, and it further ver",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "19229",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/e5ee9f58545025c8c26790d6a079bde375bf4b83523b8ae9803da77ff5ade9bc.jpg",
+        "table_caption": [
+            "Table 2. Overall ablation study of the proposed method on the miniImageNet dataset. Feature embedding infomax (FEI) and continual structure infomax (CSI) are the two functional modules we proposed."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Base</td><td rowspan=\"2\">FEI</td><td rowspan=\"2\">CSI</td><td colspan=\"9\">Accuracy in each session (%)↑</td><td rowspan=\"2\">KR</td><td rowspan=\"2\">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>✓</td><td></td><td></td><td>75.87</td><td>70.22</td><td>65.92</td><td>62.64</td><td>59.96</td><td>57.11</td><td>54.58</td><td>52.66</td><td>51.49</td><td>67.86</td><td>61.16</td></tr><tr><td>✓</td><td>✓</td><td></td><td>76.34</td><td>71.18</td><td>67.16</td><td>63.85</td><td>61.05</td><td>58.23</td><td>55.33</td><td>53.67</td><td>52.32</td><td>68.54</td><td>62.13</td></tr><tr><td>✓</td><td></td><td>✓</td><td>75.87</td><td>70.16</td><td>65.76</td><td>63.76</td><td>60.34</td><td>57.52</td><td>54.96</td><td>53.06</td><td>52.06</td><td>68.61</td><td>61.39</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/5004f46cf58c92f4446f76cf061949bc04d11bebd8148b1d6bb8a7e53263645f.jpg",
+        "image_caption": [
+            "Figure 3. Confusion matrix of the final classification results on the miniImageNet dataset [29]. (a) Baseline. (b) Our FCIL. We used red lines to partition the region of the base class and the new class. Our method improves the predictive power of the network which reduces the scattered confusion matrix."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/44856d4fa325af491f7405dd1ab770f5ae2b34b734325c25a284954ebc341c3d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "ifies the superiority of our proposed feature embedding infomax and continual structure infomax modules in learning novel class knowledge and meantime mitigating the catastrophic forgetting problem.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation study",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "All ablation studies are performed on the miniImageNet dataset [29] to evaluate the effectiveness of our proposed modules as well as some experimental settings.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of the proposed modules: We first conduct experiments to analyze the effectiveness of our proposed feature embedding infomax (FEI) and continual structure infomax (CSI) modules. The detailed results are listed in Table 2. In continual learning sessions  $(t > 1)$ , the feature embedding infomax module is added to maximize the mutual information between the convolutional features produced by the fixed base backbone and the embedding features from the newly updated classifier. The performance improves over the baseline by  $0.97\\%$  and  $0.68\\%$  on Avg and KR, demonstrating that the proposed feature embedding infomax module could well transfer the strong learning capability of the base network into the following continual sessions to enhance the learning capability of the model on novel classes. It verifies the effectiveness of our proposed feature embedding the infomax module. The continual structure infomax learning module is conducted to maximize the mutual information between the current information structure and the previous ones. The performance promotion of the CSI model seems not significant in the early stages, since CSI is designed to alleviate catastrophic",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "forgetting, and in the early stages (i.e.,  $t = 2,3,4$ ) the few new classes only pose limited influence on the learned knowledge. Further, with new classes increased in the later stages, the performance gain of CSI greatly increases. It achieves performance promotions of  $0.75\\%$  and  $0.23\\%$  separately on KR and Avg, which are clearly non-trivial. It shows that our proposed continual structure infomax module could well preserve the learned knowledge of the previous classes to mitigate the catastrophic forgetting issue. We believe it is because the attributes and class relationships could be well preserved during the continual sessions, and it verifies the effectiveness of the proposed continual structure infomax module. Finally, when both modules are applied, the performances could be further boosted to form a new state-of-the-art performance, quantitatively verifying the effectiveness of our proposed FCIL framework.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We further plot the confusion matrix of the baseline and our FCIL in Fig. 3. It could be observed that in the new classes, the diagonal of our FCIL has a darker color than the baseline model, vividly showing that the proposed FCIL is more powerful at learning new classes. In addition, it also indicates that the prediction distribution of FCIL on new classes is more concentrated than the baseline model, and it visually demonstrates the superiority of our FCIL in preserving learned knowledge.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Different methods for MI estimation and relation construction: The mutual information (MI) estimation ways can be adopted with the support of JSD [27] or KL [9], i.e., \"MIJSD\" and \"MIKL\". We achieve the information related in the continual structure infomax module with KNN or Cosine distance, named:  $\\mathrm{R_{KNN}}$  and  $\\mathrm{R_{Cos}}$ . The FCIL results with the above different methods are listed in Table 3, and it could be observed that the performance of the four variants changes little. It means that it is the proposed structure preserve mechanism rather than the specifically chosen functions that mitigate the catastrophic forgetting problem. Therefore, we adopt KL to estimate the mutual information and use the Cosine distance to build the relationship between different classes in our work.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The level of convolutional Feature  $L$ : When performing the feature embedding infomax learning, we can estimate mutual information by using more layers of convolutional features  $F_{conv}^{l}(x_{i})$ . To study the effect of different level sets, we construct three variants of FCIL by separately setting  $L$  as  $\\{1,2\\}, \\{1,3\\}$ , and  $\\{1,2,3\\}$ . The correspond",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "19230",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/83da8a1be880ecae4d060d90972fa87d05a3ec45cd526ea6642c886672b669be.jpg",
+        "table_caption": [
+            "Table 3. The results with different methods for MI estimation and relation construction on the miniImageNet dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"9\">Accuracy in each session (%)↑</td><td rowspan=\"2\">KR</td><td rowspan=\"2\">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>MI_KL + R_KNN</td><td>76.34</td><td>71.40</td><td>67.07</td><td>64.05</td><td>61.29</td><td>58.51</td><td>55.73</td><td>54.07</td><td>52.74</td><td>68.08</td><td>62.35</td></tr><tr><td>MI_KL + R_Cos</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr><tr><td>MI_JSD + R_KNN</td><td>76.34</td><td>71.34</td><td>67.03</td><td>64.0</td><td>61.28</td><td>58.52</td><td>55.7</td><td>54.03</td><td>52.7</td><td>69.03</td><td>62.32</td></tr><tr><td>MI_JSD + R_Cos</td><td>76.34</td><td>71.26</td><td>66.99</td><td>64.03</td><td>61.24</td><td>58.46</td><td>55.65</td><td>53.98</td><td>52.63</td><td>68.94</td><td>62.28</td></tr></table>",
+        "bbox": [
+            161,
+            99,
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+            175
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/30532322dce2d0e7158c6232162542d71a46bbd25a81ba9f23b1a366f72b03db.jpg",
+        "table_caption": [
+            "Table 4. The comparison results between our FCIL and the open-source methods FACT [37] and CEC [35] by fixing the performance of the base classes on the miniImageNet dataset [29]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"9\">Accuracy in each session (%) ↑</td><td rowspan=\"2\">KR↑</td><td rowspan=\"2\">ΔFinal↑</td><td rowspan=\"2\">Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>CEC [35]</td><td>72.57</td><td>66.48</td><td>62.74</td><td>59.46</td><td>56.67</td><td>53.68</td><td>51.12</td><td>49.23</td><td>47.58</td><td>65.56</td><td>+1.16</td><td>57.73</td></tr><tr><td>FACT [37]</td><td>72.73</td><td>67.73</td><td>63.77</td><td>60.29</td><td>57.25</td><td>54.07</td><td>51.17</td><td>49.31</td><td>47.91</td><td>65.87</td><td>+0.83</td><td>58.25</td></tr><tr><td>FCIL(Ours)</td><td>72.63</td><td>67.71</td><td>63.70</td><td>60.67</td><td>57.61</td><td>54.73</td><td>52.09</td><td>50.26</td><td>48.74</td><td>66.94</td><td></td><td>58.71</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/fc9322d50340dfd4e6e41ba8d4a378ddf969d7595266e223225c2922590e152a.jpg",
+        "image_caption": [
+            "Figure 4. Performance comparison bars with different levels of convolutional features."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/bade0378c4af3331e236474d4b9cadf5f1514f0666354e53088b33aea2609251.jpg",
+        "image_caption": [
+            "Figure 5. Performance comparison with the different shot numbers."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            364,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/4d0f758d259406eca5d8b49f3d06a812496f007bfc9b6c400fea1528dddbb0b1.jpg",
+        "image_caption": [
+            "Figure 6. Performance comparison with different number of  $K$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            627,
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+        ],
+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "ing accuracy changing bars are plotted in Fig. 4. It can be observed that the three variants change make little performance change. Further, it is worth noting that when employing all the levels of features (i.e.,  $L = \\{1,2,3\\}$ ), it could obtain better results than the other two variants, and all three convolutional features have been used. It means that our proposed feature embedding infomax module is able to continually transfer more useful encoding capabilities from multi-level convolutional features. It sufficiently validates the strong power of the feature embedding infomax module on transferring the encoding capability of the base network to the newly learned classifiers.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The shot number in the continual learning: We plot the accuracy changing curves with different shot numbers in Fig. 5. It shows that more sample shots could result in better few-shot continual classification performance. The reason is more shots could bring better class attribute distribution as well as more accurate class relations to benefit the learned new knowledge. Further, when the shot number is more than 15, the performance promotion becomes trivial. It shows that we only need a proper number of newly labeled samples to achieve satisfactory performances, verifying the effectiveness of our FCIL framework in addressing the few-shot continual classification task.",
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+    {
+        "type": "text",
+        "text": "Different number of  $K$ : In the continual structure infomax learning module, we can use the different number of these previous information structures  $K$  to constrain the structure of learned knowledge in the continual stage. As",
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+    {
+        "type": "text",
+        "text": "$K$  increases, there is a slight but smaller growth in the KR results, indicating that the structural information of the adjacent stages is adequately constrained for the current stage. This result can clearly show that it is possible to better mitigate catastrophic forgetting by imposing structural constraints on learned knowledge, but the demand for computational complexity and memory would increase significantly. Therefore, considering the performance and complexity of our method, we set  $K$  equal to 2 in our work.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Different methods with similar starting performance: As shown in Table 4, we give the comparison results of the FCIL, FACT [37], and CEC [35] methods with similar performance in the initial/base stage. We can observe that the three metrics of the FCIL framework are superior to the other methods, which indicates that the FCIL framework can retain the learned knowledge better, and the improvement is not because of the base model performance but our introduced FCIL. It clearly verifies the superiority of the proposed FCIL framework in effectively learning new knowledge and mitigating catastrophic forgetting.",
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+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a Few-show Continual Informal Learning (FCIL) framework to address the few-shot class continual learning task. Our FCIL enables a deep model to continually/incrementally learn new concepts from a few labeled samples and meantime prevent the model from forgetting the previously learned knowl-",
+        "bbox": [
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+        "type": "page_number",
+        "text": "19231",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "edge. Inspired by the transfer entropy concept, a feature embedding infomax module is proposed by maximizing the mutual information between different level feature distributions and then grants the model to transfer the strong encoding capability of the base network into the new classes. Further, a continual structure infomax module is proposed to maximize the mutual information across these continually changing relations of the classes to resemble the continual learning progress, so that catastrophic forgetting could be well mitigated.",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Acknowledgement",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work was supported by the National Natural Science Foundation of China (Grants Nos. 61972204, 62072244), the fundamental research funds for the central universities under Grant 30919011232, the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020LZH008, ZR2022LZH003), and in part by State Key Laboratory of High-end Server & Storage Technology.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            405,
+            174,
+            420
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+    {
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+        "bbox": [
+            480,
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+        "page_idx": 8
+    },
+    {
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+            "[32] Oriol Vinyals, Charles Blundell, Timothy Lillicrap, Daan Wierstra, et al. Matching networks for one shot learning. Advances in neural information processing systems, 29, 2016. 6",
+            "[33] Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltech-ucsd birds-200-2011 dataset. 2011. 5, 6",
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+            "[36] Wenting Zhao, Gongping Xu, Zhen Cui, Siqiang Luo, Cheng Long, and Tong Zhang. Deep graph structural infomax."
+        ],
+        "bbox": [
+            78,
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+            900
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 4920-4928, 2023. 3",
+            "[37] Da-Wei Zhou, Fu-Yun Wang, Han-Jia Ye, Liang Ma, Shiliang Pu, and De-Chuan Zhan. Forward compatible few-shot class-incremental learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 9046–9056, 2022. 1, 2, 6, 8",
+            "[38] Kai Zhu, Yang Cao, Wei Zhai, Jie Cheng, and Zheng-Jun Zha. Self-promoted prototype refinement for few-shot class incremental learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 6801-6810, 2021. 1, 2"
+        ],
+        "bbox": [
+            501,
+            92,
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+        "type": "page_number",
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+    }
+]
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diff --git a/2023/Few-shot Continual Infomax Learning/4bda674e-273c-4a6b-8394-b466c9dde520_model.json b/2023/Few-shot Continual Infomax Learning/4bda674e-273c-4a6b-8394-b466c9dde520_model.json
new file mode 100644
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Few-shot Continual Infomax Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.15,
+                0.181,
+                0.82,
+                0.252
+            ],
+            "angle": 0,
+            "content": "Ziqi Gu#, Chunyan Xu#, Jian Yang, Zhen Cui*  \nPCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.286,
+                0.255,
+                0.684,
+                0.27
+            ],
+            "angle": 0,
+            "content": "{ziqigu, cyx, csjyang, zhen.cui}@njust.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.305,
+                0.314,
+                0.321
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.337,
+                0.474,
+                0.701
+            ],
+            "angle": 0,
+            "content": "Few-shot continual learning is the ability to continually train a neural network from a sequential stream of few-shot data. In this paper, we propose a Few-shot Continua! Infomax Learning (FCIL) framework that makes a deep model to continually/incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting of past knowledge. Specifically, inspired by the theoretical definition of transfer entropy, we introduce a feature embedding infomax to effectively perform the few-shot learning, which can transfer the strong encoding capability of the base network to learn the feature embedding of these novel classes by maximizing the mutual information of different-level feature distributions. Further, considering that the learned knowledge in the human brain is a generalization of actual information and exists in a certain relational structure, we perform continual structure infomax learning to relieve the catastrophic forgetting problem in the continual learning process. The information structure of this learned knowledge can be preserved through maximizing the mutual information across these continual-changing relations of inter-classes. Comprehensive evaluations on CIFAR100, miniImageNet, and CUB200 datasets demonstrate the superiority of our FCIL when compared against state-of-the-art methods on the few-shot continual learning task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
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+                0.21,
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.757,
+                0.47,
+                0.864
+            ],
+            "angle": 0,
+            "content": "Recent deep learning technologies [23, 30, 13] have made great progress in many computer vision tasks. The success of deep neural networks is achieved by employing a large number of labeled training data. However, it is difficult to collect large-scale supervised data in advance, while we would encounter a sequential data stream with unknown new classes in many realistic situations. This would require"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "a neural network with continual learning ability, especially when some new classes with very few labeled samples often appear. Therefore, this work focuses on dealing with the few-shot continual/incremental learning task [28, 26]. They are two critical challenges in a few-shot continual learning task: i) how to learn new knowledge with few-shot instances, and ii) how to avoid catastrophic forgetting of the preceding learned knowledge."
+        },
+        {
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+            "bbox": [
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+            "content": "Recently, numerous previous works [31] have been devoted to few-shot continual learning from various perspectives. In [31, 35, 8], the topological structure of the knowledge space formed by different classes has been considered to perform few-shot continual learning by using a neural gas network or graph model. Cheraghian et al. [8] have proposed a semantic-aware knowledge distillation method to solve few-shot class incremental learning by making use of word embeddings. Several meta-learning based methods [7, 18] have been also proposed to enable the model to preserve old knowledge and adapt to the new classes for continual learning. By assigning virtual prototypes to squeeze the embedding of known classes and reserve for new ones, the forward compatible training method [37] has efficiently incorporated new classes with forward compatibility and meanwhile resists forgetting old ones. Similarly, the mixture of subspaces and synthesized features [6] have been used to alleviate the forgetting and over-fitting problem in the few-shot continual learning process. In [38], the self-promoted prototype learning scheme has been proposed to explicitly learn the feature representation under the few-shot learning situation and thus facilitated subsequent incremental tasks. The self-supervised strategy has been also used to enhance the feature extraction ability of the model by adding self-supervised loss function assistance during the training process [20, 26]. Moreover, to minimize over-fitting and the catastrophic forgetting problem, Mazumder et al. [26] have selected very few unimportant model parameters to perform few-shot learning on new classes. In [11], mutual information (MI) maximization has been first used as a solution method to deal with the catas"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Equal Contribution."
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+            "bbox": [
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+            "angle": 0,
+            "content": "* Corresponding Author."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+        }
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+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
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+                0.152
+            ],
+            "angle": 0,
+            "content": "trophic forgetting problem in the online continual learning task, but it cannot well consider how to perform continual infomax learning from the perspective of information entropy, especially in the few-shot regime."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.152,
+                0.473,
+                0.605
+            ],
+            "angle": 0,
+            "content": "In this work, we propose a novel Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to continually learn from a stream of few-shot labeled data. In general, the continual learning model would be trained with a large amount of labeled data in the initial learning stage, while few-shot samples of some unknown classes would be encountered in the continual learning process. Here we attempt to address the few-shot continual learning task from two aspects. First, inspired by the theoretical definition of transfer entropy, we attempt to transfer the strong encoding capability of the base network to promote few-shot continual learning. Specifically, we propose a feature embedding infomax learning to new concepts from a few labeled samples through maximizing the mutual information between different level feature distributions, where the convolutional representations and the feature embedding of new classes are encoded with these fixed convolution layers of the base network and newly increased parameters of fully-connected layer, respectively. Second, considering that the learned knowledge in the human brain is a generalization or abstraction of the actual information learned from these seen samples [10], we wish the continual learning model with a stable information structure that can be updated incrementally. Thus we propose a continual structure infomax learning mechanism to alleviate the catastrophic forgetting problem during the continual learning process. The structure relation of this learned information can be preserved through maximizing the mutual information across these continual-changing structure relations of inter-classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.606,
+                0.473,
+                0.818
+            ],
+            "angle": 0,
+            "content": "In summary, our primary contributions can be summarized as follows: i) We propose a Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting problem of previously learned ones. ii) Two specially-designed infomax learning mechanisms are proposed to address the few-shot continual learning problem with the help of mutual information maximization, including feature embedding infomax and continual structure infomax. iii) We validate the effectiveness of our proposed FCIL on three benchmarks (including CIFAR100, CUB200, and miniImageNet), and also demonstrate the superiority of our proposed FCIL when compared with existing state-of-the-art methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Related work"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "Few-shot continual learning: Few-shot continual learning, which has recently attracted growing attention, aims to enable a model to perform continual/incremental"
+        },
+        {
+            "type": "text",
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+            ],
+            "angle": 0,
+            "content": "learning with a stream of few-shot labeled data. A number of related works have been proposed to address the few-shot continual learning task. For example, Tao et al. [31] employed neural gas networks to perform incrementally learning for a series of new classes with few-shot data, with the goal of avoiding forgetting previously learned classes. Zhang et al. [35] proposed an evolving classifier based on graph attention networks that propagated information between classifiers by adding graph models. Also, pseudo-incremental training was proposed to optimize the graph module. The forward compatible training (FACT) [37] was proposed to effectively incorporate novel classes into forward compatible by generating virtual classes, where knowledge of old classes can be also maintained to reduce the catastrophic forgetting problem. A bi-level meta-learning-based optimization [7] was proposed to directly optimize the model towards forgetting alleviation of learned knowledge and adaptation of the new classes. In [20], a self-supervised stochastic classifier was proposed to deal with the few-shot class incremental learning task with the help of a self-supervision mechanism. Zhu et al. [38] proposed an incremental prototype learning scheme to perform continual learning, which was used to constrain the prototypes of new classes through the dynamic model and then achieved a reduction in catastrophic forgetting of knowledge. In order to offer a trade-off between accuracy and compute-memory cost of learning novel classes, the hyper-dimensional embedding was used to continually learn many more classes than the fixed dimensions in the feature space [14]. Further, few-shot lifelong learning was proposed to perform continual learning with only updating very few parameters of the model [26] or semantic-aware knowledge distillation [5]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.585,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Mutual information: Mutual Information as a quantity is used to measure the degree of interdependence between two random variables [21]. As it is difficult to exactly compute the mutual information between second-dimensional random variables, mutual information neural estimator (MINE) [2] can be achieved by employing the dual representations of the Kullback-Leibler divergence (KL) [9]. Subsequently, the Jensen-Shannon divergence (JSD) [27] and noise-contrastive estimation (NCE) [12] were used to estimate the mutual information with a learned network [16], and then the mutual information maximization method was used to improve the deep representation in an unsupervised learning way. The second-order deep multiplex infomax method [19] further extended the mutual information estimation to a three-variable calculation and was applied across multiple networks. The deep mutual information maximin method [25] was used to address the cross-modal clustering task by maximally preserving the shared information of multiple modalities and eliminating the superfluous information of individual modalities. In [1], mutual information networks are applied to unsupervised"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19225"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.198
+            ],
+            "angle": 0,
+            "content": "classification tasks with excellent results. In the online continual learning task, Guo et al. [11] first used mutual information estimation to learn more robust features and preserve the past model learned from the previous task. Different from these previous methods, we perform continual infomax learning from the perspective of information entropy in the few-shot setting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.215,
+                0.289,
+                0.232
+            ],
+            "angle": 0,
+            "content": "3. The Proposed Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.242,
+                0.262,
+                0.256
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Definition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.266,
+                0.473,
+                0.614
+            ],
+            "angle": 0,
+            "content": "Few-shot continual learning aims to train a model for new tasks sequentially from a stream of few-shot labeled data, relieving the forgetting of knowledge learned from the old tasks, where the data in the old tasks are not available anymore during learning a new set of few-shot tasks. Formally, we define \\(X\\), \\(Y\\), and \\(Z\\) as the training set, label set, and test set, respectively. Our task is to train the model with a continuous stream of labeled training sets \\(X_{1}, X_{2}, \\ldots, X_{T}\\), where \\(X_{t}\\) denotes the \\(t\\)-th training set, \\(Y_{t}\\) is the corresponding label set, and \\(T\\) refers to the number of continual learning sessions. In the continual learning process, each training set is with no repetition of class labels, i.e., \\(\\forall i, j\\) and \\(i \\neq j\\), \\(Y_{i} \\cap Y_{j} = \\emptyset\\). Usually, when \\(t = 1\\), the training set \\(X_{1}\\) is with large-scale samples for training the base network; when \\(t > 1\\), \\(X_{t}\\) refers to the few-shot training set of new classes in the incremental learning stage (i.e., \\(|X_{1}| \\gg |X_{t}|, t = 2, 3, \\ldots, T\\)). For example, under the 5-way 10-shot setting, each incremental/continual process (i.e., \\(t > 1\\)) contains five new classes, each of which has only ten training samples. The test set \\(Z\\) is used to evaluate the classification performance at each stage \\(t\\), and its corresponding classes may be from all training label sets, i.e., \\(\\{Y_{1} \\cup Y_{2} \\dots \\cup Y_{T}\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.614,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In the few-shot continual learning task, there are two critical problems we need to consider: i) New classes are with a small amount of training data, which makes it hard to learn the feature embeddings for these new classes. ii) Catastrophic forgetting should be well relieved to preserve this learned knowledge in the continual learning process. In this work, we attempt to address them from two aspects. First, we start from the transfer entropy perspective [3] to obtain new knowledge from few-shot samples, where the strong encoding capability of the base network can be transferred to learn feature embeddings of these new classes. Second, considering that the learned knowledge in the human brain is not isolated, but exists in a certain relational structure [10], we wish to preserve the structure information of this learned knowledge to relieve the catastrophic forgetting problem during the continual learning process. With the help of the recently-developed mutual information estimation method [2, 16, 36], we achieve these above goals by performing continual infomax learning."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.48,
+                0.091,
+                0.891,
+                0.325
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.325,
+                0.895,
+                0.532
+            ],
+            "angle": 0,
+            "content": "Figure 1. The pipeline of our few-shot continual infomax learning, where \\( t \\) refers to the \\( t \\)-th session in the continual learning process (\\( t \\geqslant 1 \\)). To transfer the strong encoding capability of the base network into the subsequent continual learning sessions, we first propose the feature embedding infomax to learn new knowledge with few-shot labeled data in the \\( t \\)-th session. Here we maximize the mutual information between multi-level convolutional representations \\( F_{conv}(x_i) \\) and full-connected feature embedding \\( F_{fc}(x_i) \\) of each input sample, which are encoded with these fixed convolution layers of the base network \\( \\Theta_{conv}^{base} \\) and updated fully-connected layer \\( \\Theta_{fc}^{t} \\), respectively. To address the catastrophic forgetting problem in the continual learning process, we further perform the continual structure infomax learning by maximizing the mutual information between current and previous inter-class knowledge structures (i.e., \\( S(A^t, R^t) \\) and \\( S(A^{t-1}, R^{t-1}) \\))."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.541,
+                0.661,
+                0.557
+            ],
+            "angle": 0,
+            "content": "3.2. FCIL Paradigm"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The proposed few-shot continual infomax learning (FCIL) framework is shown in Fig. 1. Generally, the base network \\(\\Theta^{base}\\), which is a large-scale set of training samples \\(X_{1}\\), can optimize with the classic cross-entropy loss. For further improving the deep representation capability of the base network, we also employ self-supervised mutual information mechanism. Here the mutual information estimated network \\(\\vartheta^{MI}\\) can be well optimized in the initial stage (i.e., \\(t = 1\\)), which contributes to the subsequent continual learning sessions. In the next continual learning sessions (i.e., \\(t > 1\\)), a stream of few-shot labeled data with new classes would be gradually fed into the network, and we would perform few-shot continual infomax learning for capturing new knowledge, without forgetting these learned ones. To improve the feature embedding capability of these new classes, we attempt to transfer the strong representation capability of the base network \\(\\Theta^{base}\\) into the next continual learning sessions. Specifically, we introduce the feature embedding infomax learning to optimize these fully-connected parameters \\(\\Theta_{fc}^{t}\\) of new classes. Given an input image \\(x_{i}\\) from the few-shot set \\(D_{t}\\), we use the convolutional net optimized in the base stage to extract multi-level convolutional"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19226"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.456
+            ],
+            "angle": 0,
+            "content": "features \\( F_{conv}(x_i) \\), and get the feature embeddings from new full-connected layer \\( F_{fc}(x_i) \\). We maximize the mutual information between the convolutional and full-connected feature distributions for each input sample (i.e., \\( F_{conv}(x_i) \\) and \\( F_{fc}(x_i) \\)), and thus the feature embedding of the novel classes can well inherit the powerful feature representation capability of the base network (i.e., \\( \\max \\mathcal{T}_{\\Theta^{base} \\to \\Theta_{fc}^t} \\)). Further, to alleviate the catastrophic forgetting problem of this learned knowledge during the subsequent continual learning sessions, we introduce a continual structure infomax learning (i.e., \\( \\max \\mathcal{D}_S \\)) to maintain/preserve the relations of intra-classes across one or more learning sessions. At each learning session \\( t \\), we can obtain the first-order attributes and the second-order structure information of this learned knowledge, which refer to the class-wise feature embeddings and the relations among different classes, respectively. We then maximize the mutual information between the current information structure \\( S(A^t, R^t) \\) and this previous information \\( S(A^{t'}, R^{t'}) \\) (\\( t' = t - 1, t - 2, \\ldots, t - K \\) and \\( t - K \\geqslant 1 \\)) of these old classes. With the help of feature embedding infomax and continual structure infomax, the deep model can be well worked in the few-shot continual learning process. See the supplementary materia for more details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.473,
+                0.333,
+                0.489
+            ],
+            "angle": 0,
+            "content": "3.2.1 Feature Embedding Infomax"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.497,
+                0.471,
+                0.679
+            ],
+            "angle": 0,
+            "content": "When the base network \\(\\Theta^{base}\\) faces unknown new classes, it is difficult to learn new concepts with only few-shot labeled samples. Inspired by the classic transfer entropy method which is a non-parametric measure of directed, asymmetric information transfer between two processes [3], we attempt to migrate the powerful feature representation capability of the base network to capture the feature embedding of the novel classes. Given few-shot training samples of new classes in the \\(t\\)-continual learning stage (i.e., \\(t > 1\\)), the transfer entropy from the base network \\(\\Theta^{base}\\) to the feature embedding layer of novel classes \\(\\Theta_{fc}^{t}\\) (i.e., fully-connected model parameters) can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.105,
+                0.682,
+                0.47,
+                0.725
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {T} _ {\\Theta^ {b a s e} \\rightarrow \\Theta_ {f c} ^ {t}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\left(H \\left(\\mathbf {Z} _ {f c}\\right) - H \\left(\\mathbf {Z} _ {f c} \\mid \\mathbf {Z} _ {c o n v}\\right)\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.734,
+                0.473,
+                0.906
+            ],
+            "angle": 0,
+            "content": "where \\(X_{t} = \\{x_{1},x_{2},\\dots,x_{|X_{t}|}\\}\\) is the training set of few-shot data in the \\(t\\) -th continual learning session; \\(F_{conv}(x_i)\\) is the convolution representations of the training sample \\(x_{i}\\) with the base encoding network \\(\\Theta^{base}\\). \\(F_{fc}(x_{i})\\) is the feature embedding of \\(x_{i}\\) with the fully-connected parameters \\(\\Theta_{fc}^t\\) of the \\(t\\) -th continual learning stage. Let \\(\\mathbf{Z}_{conv} = F_{conv}(x_i)\\) and \\(\\mathbf{Z}_{fc} = F_{fc}(x_i)\\), \\(H(\\mathbf{Z}_{fc})\\) refers to the Shannon entropy information of fully-connected feature of \\(x_{i}\\) and the conditional entropy \\(H(\\mathbf{Z}_{fc}|\\mathbf{Z}_{conv})\\) is the entropy of \\(\\mathbf{Z}_{conv}\\) conditioned on \\(\\mathbf{Z}_{fc}\\). To facilitate the calculation of Eqn. (1), the transfer entropy \\(\\mathcal{T}_{\\Theta^{base}\\to \\Theta_{fc}^t}\\) can be further"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.136
+            ],
+            "angle": 0,
+            "content": "expressed as the conditional mutual information of different level features with the corresponding network parameters in the condition:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.542,
+                0.138,
+                0.891,
+                0.227
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {T} _ {\\Theta^ {b a s e} \\rightarrow \\Theta_ {f c} ^ {t}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} I ((\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l})), \\\\ \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} \\hat {I} \\left(\\left(\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}\\right), \\vartheta^ {M I}\\right), \\tag {2} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.236,
+                0.892,
+                0.357
+            ],
+            "angle": 0,
+            "content": "here, we directly maximize the mutual information between multi-level convolutional features and fully-connected feature embedding, which can better transfer the strong encoding capability of the base network \\(\\Theta^{base}\\) to the fully-connected layer \\(\\Theta_{fc}^{t}\\). With the support of the Kullback-Leibler divergence [9] and the learned mutual information estimation network \\(\\vartheta^{MI}\\), the transfer entropy process can be approximately formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.552,
+                0.361,
+                0.892,
+                0.426
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathcal {T}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}\\right), \\vartheta^ {M I}\\right)\\right) \\tag {3} \\\\ - \\log \\mathbb {E} (e ^ {\\mathcal {F} ((\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}), \\vartheta^ {M I})}). \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.436,
+                0.892,
+                0.573
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{F}(\\cdot)\\) is a discriminant function between features of different layers. Here this transfer entropy process can help to capture the feature embeddings of these few-shot training samples in the continual learning stages, thus we name it as \"feature embedding infomax\" learning process. The final learning objective to optimize the \\(t\\)-th continual fully-connected layer \\(\\Theta_{fc}^{t}\\) is defined as: \\(\\mathcal{L}_{FEI} = \\mathcal{L}_{CE} - \\alpha \\mathcal{L}_{\\mathcal{T}}\\) where \\(\\mathcal{L}_{CE}\\) is the classic cross-entropy loss and \\(\\alpha\\) is a hyper-parameter."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.591,
+                0.757,
+                0.605
+            ],
+            "angle": 0,
+            "content": "3.2.2 Continual Structure Infomax"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Another critical problem for a continual learning model is exiting the catastrophic forgetting this learned knowledge when discarding old samples. An obvious solution is that continual learning must have a strategy to preserve the information related to these old training samples. Usually, the information preserved in a continual learning system is a generalization or abstraction of the actual information embedded in the learned samples. The knowledge we learn in the human brain [10] does not exist in isolation; there is some kind of relational structure between different pieces of knowledge that maintains the connection between knowledge. In order to possess an information structure that would be updated incrementally along the continual learning process, we can preserve useful information from learned samples as much as possible so that the subsequent continual learning process can be guided by this information. Therefore, we propose a continual structure infomax learning to conserve both first-order and second-order information in the continual learning process, which can be"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19227"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.152
+            ],
+            "angle": 0,
+            "content": "related to class-wise individual attributions and intra-class relations, respectively. In the \\(t\\)-th continual learning session, the continual structure infomax can be performed under the guidance of these previous information structures:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.078,
+                0.157,
+                0.473,
+                0.214
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {S} = \\sum_ {k = 1} ^ {K} \\underbrace {H \\left(A _ {t}\\right) - H \\left(A _ {t} \\mid A _ {t - k}\\right)} _ {\\text {f i r s t - o r d e r}} + \\underbrace {H \\left(R _ {t}\\right) - H \\left(R _ {t} \\mid R _ {t - k}\\right)} _ {\\text {s e c o n d - o r d e r}} \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.216,
+                0.473,
+                0.473
+            ],
+            "angle": 0,
+            "content": "where \\(K\\) is the number of previous sessions with \\(t - K \\geq 1\\). \\(A_{t}\\) and \\(A_{t - k}\\) refer to the feature embeddings of all learned classes \\(c_{t}\\), e.g., \\(A_{t} = [e_{1}, e_{2}, \\ldots, e_{c}, \\ldots, e_{c_{t}}]\\). Due to the fact that the mean value of each class is approximate to the parameter weights of the last fully-connected layer, \\(e_{c}\\) is achieved by the weight parameters of the last classification layer corresponding to the \\(c\\)-th class. Their corresponding information entropy \\(A_{t}\\) and \\(A_{t - k}\\) are represented as \\(H(A_{t})\\) and \\(H(A_{t}|A_{t - k})\\). \\(R_{t} \\in \\mathbb{R}^{c_{t} \\times c_{t}}\\) and \\(R_{t - k} \\in \\mathbb{R}^{c_{t - k} \\times c_{t - k}}\\) refer to the inter-class relation matrices of all learned classes in the \\(t\\)-th and \\((t - k)\\)-th stages. \\(H(R_{t})\\) and \\(H(R_{t}|R_{t - k})\\) represent the second-order information entropy concerning the relation among different classes. Through maximizing the first-order and second-order mutual information between different learning stages, the network parameters of the last fully-connected layer \\(\\Theta_{fc}\\) can be incrementally updated along the continual learning process, formally,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.474,
+                0.469,
+                0.58
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {D} _ {S} = \\sum_ {k = 1} ^ {K} \\underbrace {I (A _ {t} ; A _ {t - k})} _ {\\text {f i r s t - o r d e r}} + \\underbrace {I (R _ {t} ; R _ {t - k})} _ {\\text {s e c o n d - o r d e r}}, \\\\ \\geq \\sum_ {k = 1} ^ {K} \\underbrace {\\hat {I} \\left(\\left(A _ {t} ; A _ {t - k}\\right) , \\vartheta^ {M I}\\right)} _ {\\text {f i r s t - o r d e r}} + \\underbrace {\\hat {I} \\left(\\left(R _ {t} ; R _ {t - k}\\right) , \\vartheta^ {M I}\\right)} _ {\\text {s e c o n d - o r d e r}}, \\tag {5} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.583,
+                0.47,
+                0.642
+            ],
+            "angle": 0,
+            "content": "Similar to the feature embedding infomax, we also use mutual information to measure the amount of information shared by different sessions, and this continual structure infomax process can be further formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.078,
+                0.644,
+                0.49,
+                0.719
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {S} = \\sum_ {k = 1} ^ {K} \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(A _ {t}; A _ {t - k}\\right), \\vartheta^ {M I}\\right)\\right) - \\log \\mathbb {E} \\left(e ^ {\\mathcal {F} \\left(\\left(A _ {t}; A _ {t - k}\\right), \\vartheta^ {M I}\\right)}\\right) \\\\ + \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(R _ {t}; R _ {t - k}\\right), \\vartheta^ {M I}\\right)\\right) - \\log \\mathbb {E} \\left(e ^ {\\mathcal {F} \\left(\\left(R _ {t}; R _ {t - k}\\right), \\vartheta^ {M I}\\right)}\\right), \\tag {6} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.47,
+                0.81
+            ],
+            "angle": 0,
+            "content": "where \\(k\\) refers to the \\(k\\)-th session with \\(1 \\leqslant k \\leqslant K\\). We employ both \\(\\mathcal{L}_S\\) and \\(\\mathcal{L}_{CE}\\) to optimize the fully-connected parameters \\(\\Theta_{fc}^t\\) to adapt new classes without forgetting these learned ones. In the structure continual infomax process, the corresponding loss is defined as \\(\\mathcal{L}_{CSI} = \\mathcal{L}_{CE} - \\gamma \\mathcal{L}_S\\), where \\(\\gamma\\) is a balance factor."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.822,
+                0.21,
+                0.839
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.267,
+                0.864
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Datasets: We evaluate our FCIL on three public datasets, including CIFAR100 [22], miniImageNet [29],"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.242
+            ],
+            "angle": 0,
+            "content": "and CUB200 [33]. For CIFAR100 [22] and miniImageNet [29], we use all the training data of the 60 base classes to train a base network, and the 40 new classes are used to perform eight 5-way 5-shot continual learning tasks. We divide the 200 classes of CUB200 [33] into 100 base classes and 100 new classes. The 100 new classes are used to perform ten 10-way 5-shot continual learning tasks. We follow the same split setting of FSCIL [31] as other methods in the three datasets for a fair comparison. See the supplementary materia for more details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.244,
+                0.893,
+                0.668
+            ],
+            "angle": 0,
+            "content": "Implementation Details: Following FSCIL [31], we use ResNet20 as the backbone on CIFAR100 [22] and ResNet18 is used as the backbone on miniImageNet [29] and CUB200 [33]. The network \\(\\vartheta^{MI}\\) consists of a convolution branch and a linear branch, where the former consists of three convolution layers whose kernel sizes are 1, 5, and 7, and the latter is one linear layer. In the CSI module, the convolution branch and the linear branch separately take \\(F_{conv}^{l}(x_{i})\\) and \\(F_{fc}(x_{i})\\) as inputs, and their outputs are used to compute \\(\\mathcal{L}_{\\mathcal{T}}\\). In the CSI module, the linear layer of \\(\\vartheta^{MI}\\) separately take \\(A_{t}\\) and \\(A_{t - k}\\) as inputs, and we use the outputs to compute \\(\\mathcal{L}_s\\). In the base learning stage, we train the base network and the mutual information network with the first training set. The parameters of the convolutional layers \\(\\Theta^{base}\\) and the mutual information network \\(\\vartheta^{MI}\\) are frozen in the continual learning sessions to perform mutual information estimation in both the proposed feature embedding infomax. For all datasets, we set \\(\\alpha\\) and \\(\\gamma\\) as 0.015 and 0.03, respectively. Random cropping, random scaling, and random horizontal flipping are used for training data. We use to evaluate our proposed method from different perspectives. \"Acc_t\" represents to the Top-1 accuracy in the t-th continual session. \"Avg\" represents for an average score, i.e., \\(\\sum_{t=1}^{T} \\mathrm{Acc}_t / T\\). \"ΔFinal\" represents the difference value of \\(\\mathrm{Acc}_t\\) between our method and the compared method in the final state. \"KR\" is the knowledge retention rate, i.e., \\(\\mathrm{Acc}_T / \\mathrm{Acc}_1\\). All the experiments are conducted with the Pytorch framework on one Geforce 2080Ti GPU."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.68,
+                0.859,
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+            ],
+            "angle": 0,
+            "content": "4.2. Comparison with state-of-the-art methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We first compare our proposed FCIL with other state-of-the-art methods on the challenging miniImageNet dataset [29]. The detailed results have been listed in Table 1, and the accuracy changing curves with growing continual sessions are plotted in Fig. 2 (a). Our proposed FCIL outperforms all other compared methods by a great margin and sets new state-of-the-art. In particular, our FCIL achieves the best score among all the methods. Considering that in the first continual session, very little data are available and it requires borrowing the learning capability of the base stage into this session to promote the classifier accuracy. In addition, as to the overall performance in the final continual session, our FCIL also surpasses the second best method C-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19228"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.116
+            ],
+            "angle": 0,
+            "content": "Table 1. Few-shot continual classification performance of state-of-the-art methods and our FCIL on the miniImageNet dataset [29]. The results with * are obtained from the authors' published code. See the supplementary materia for results of other datasets."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.091,
+                0.117,
+                0.88,
+                0.351
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"10\">Accuracy in each session (%)↑</td><td>KR↑</td><td>ΔFinal↑</td><td>Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>Ft-CNN</td><td>61.31</td><td>27.22</td><td>16.37</td><td>6.08</td><td>2.54</td><td>1.56</td><td>1.93</td><td>2.60</td><td>1.40</td><td>2.28</td><td>+51.36</td><td>13.44</td><td></td></tr><tr><td>iCaRL [28]</td><td>61.31</td><td>46.32</td><td>42.94</td><td>37.63</td><td>30.49</td><td>24.00</td><td>20.89</td><td>18.80</td><td>17.21</td><td>28.07</td><td>+35.55</td><td>33.29</td><td></td></tr><tr><td>EEIL [4]</td><td>61.31</td><td>46.58</td><td>44.00</td><td>37.29</td><td>33.14</td><td>27.12</td><td>24.10</td><td>21.57</td><td>19.58</td><td>31.93</td><td>+33.18</td><td>34.97</td><td></td></tr><tr><td>TOPIC [31]</td><td>61.31</td><td>50.09</td><td>45.17</td><td>41.16</td><td>37.48</td><td>35.52</td><td>32.19</td><td>29.46</td><td>24.42</td><td>39.83</td><td>+28.34</td><td>39.65</td><td></td></tr><tr><td>NCM [17]</td><td>61.31</td><td>47.80</td><td>39.31</td><td>31.91</td><td>25.68</td><td>21.35</td><td>18.67</td><td>17.24</td><td>14.17</td><td>23.11</td><td>+38.59</td><td>30.83</td><td></td></tr><tr><td>Decoupled-NegCosine [24]</td><td>71.68</td><td>66.64</td><td>62.57</td><td>58.82</td><td>55.91</td><td>52.88</td><td>49.41</td><td>47.50</td><td>45.81</td><td>63.90</td><td>+6.95</td><td>56.80</td><td></td></tr><tr><td>Decoupled-Cosine [32]</td><td>70.37</td><td>65.45</td><td>61.41</td><td>58.00</td><td>54.81</td><td>51.89</td><td>49.10</td><td>47.27</td><td>45.63</td><td>64.84</td><td>+7.13</td><td>55.99</td><td></td></tr><tr><td>Decoupled-DeepEMD [34]</td><td>69.77</td><td>64.59</td><td>60.21</td><td>56.63</td><td>53.16</td><td>50.13</td><td>47.79</td><td>45.42</td><td>43.41</td><td>62.21</td><td>+9.35</td><td>54.57</td><td></td></tr><tr><td>MateFSCIL [7]</td><td>72.04</td><td>67.94</td><td>63.77</td><td>60.29</td><td>57.58</td><td>55.16</td><td>52.90</td><td>50.79</td><td>49.19</td><td>68.28</td><td>+3.57</td><td>58.85</td><td></td></tr><tr><td>C-FSCIL Model1 (d=512) [15]</td><td>76.37</td><td>70.94</td><td>66.36</td><td>62.64</td><td>59.31</td><td>56.02</td><td>53.14</td><td>51.04</td><td>48.87</td><td>63.99</td><td>+3.89</td><td>60.52</td><td></td></tr><tr><td>C-FSCIL Mode2 (d=512) [15]</td><td>76.45</td><td>71.23</td><td>66.71</td><td>63.01</td><td>60.09</td><td>56.73</td><td>53.94</td><td>52.01</td><td>50.08</td><td>65.50</td><td>+2.68</td><td>61.14</td><td></td></tr><tr><td>C-FSCIL Mode3 (d=512) [15]</td><td>76.40</td><td>71.14</td><td>66.46</td><td>63.29</td><td>60.42</td><td>57.46</td><td>54.78</td><td>53.11</td><td>51.41</td><td>67.29</td><td>+1.35</td><td>61.61</td><td></td></tr><tr><td>FACT* [37]</td><td>75.68</td><td>70.65</td><td>66.53</td><td>62.75</td><td>59.39</td><td>56.19</td><td>53.26</td><td>51.10</td><td>49.48</td><td>65.38</td><td>+3.28</td><td>60.56</td><td></td></tr><tr><td>FACT* + FCIL</td><td>76.21</td><td>70.92</td><td>66.69</td><td>63.23</td><td>60.73</td><td>57.88</td><td>54.08</td><td>52.17</td><td>50.34</td><td>66.05</td><td>+2.42</td><td>61.36</td><td></td></tr><tr><td>CEC [35]</td><td>72.00</td><td>66.83</td><td>62.97</td><td>59.43</td><td>56.70</td><td>53.73</td><td>51.19</td><td>49.24</td><td>47.63</td><td>66.15</td><td>+5.13</td><td>57.75</td><td></td></tr><tr><td>CEC + FCIL</td><td>72.87</td><td>68.23</td><td>64.46</td><td>60.64</td><td>57.71</td><td>55.12</td><td>52.79</td><td>50.65</td><td>48.62</td><td>66.72</td><td>+4.14</td><td>59.01</td><td></td></tr><tr><td>FCIL (Ours)</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>-</td><td>62.37</td><td></td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.362,
+                0.35,
+                0.53
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.176,
+                0.532,
+                0.268,
+                0.544
+            ],
+            "angle": 0,
+            "content": "(a) miniImageNet"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.346,
+                0.361,
+                0.622,
+                0.53
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.463,
+                0.532,
+                0.538,
+                0.543
+            ],
+            "angle": 0,
+            "content": "(b) CIFAR100"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.63,
+                0.363,
+                0.891,
+                0.529
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.754,
+                0.532,
+                0.818,
+                0.543
+            ],
+            "angle": 0,
+            "content": "(c) CUB200"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.141,
+                0.544,
+                0.822,
+                0.558
+            ],
+            "angle": 0,
+            "content": "Figure 2. The accuracy changing curves with growing continual sessions of different methods on the three datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.561,
+                0.473,
+                0.88
+            ],
+            "angle": 0,
+            "content": "FSCIL Mode3 (d=512) [15] by a non-trivial gap of \\(1.35\\%\\). It shows that our FCIL could keep great learning capability when performing the continual learning process, and we owe the superiority to the strong capability borrowed from the base network by the proposed feature embedding infomax module. Further, our method also achieves the best performance on Avg, outperforming the compared methods by at least \\(0.76\\%\\). It indicates that our FCIL could always obtain better performance during all the continual sessions, further demonstrating the strong learning capability borrowed from the base network. Overall, the superior performances of our FCIL in terms of Avg and \\(\\Delta\\)Final sufficiently verify the effectiveness of our proposed feature embedding infomax module on enhancing the learning capability of new classes. Besides, we integrate our proposed FCIL mechanisms into the FACT [37] and CEC [35] frameworks (i.e., FACT+FCIL and CEC+FCIL), and the compared results show that we can lead to significant improvements of \\(0.99\\%\\) and \\(0.86\\%\\) on the \\(\\Delta\\)Final metric. It further verifies the superiority of our FCIL framework in learning new knowledge and alleviating catastrophic forgetting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our FCIL achieves the best performance on the KR met-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.561,
+                0.892,
+                0.895
+            ],
+            "angle": 0,
+            "content": "ric, with a promotion of at least \\(0.83\\%\\). Since KR represents the accuracy ratio of the final continual session and the base stage, a larger KR value means that less learned knowledge is forgotten. Compared with previous methods such as CEC [35], FACT [37], C-FSCIL [15] which also freeze the base classifier as our FCIL to avoid catastrophic forgetting, our FCIL still outperforms them by a considerable margin. It means that the relationship preserving capability brought by the proposed continual structure infomax module could better preserve the previously learned knowledge. It clearly validates the effectiveness of our proposed continual structure infomax module in mitigating the catastrophic forgetting problem. As a whole, the superior performance clearly verifies the superiority of our proposed FCIL in learning novel class knowledge as well as mitigating the catastrophic forgetting problem. The accuracy changing curves with growing continual sessions in Fig. 2(a) further visually show the superiority of our FCIL. We further plot the accuracy changing curves on the CIFAR100 [22] and CUB200 [33] datasets separately in Fig. 2(b) and Fig. 2(c). It could be observed that our proposed FCIL also achieves the best performances on the two datasets, and it further ver"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19229"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.088,
+                0.895,
+                0.119
+            ],
+            "angle": 0,
+            "content": "Table 2. Overall ablation study of the proposed method on the miniImageNet dataset. Feature embedding infomax (FEI) and continual structure infomax (CSI) are the two functional modules we proposed."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.159,
+                0.121,
+                0.808,
+                0.196
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Base</td><td rowspan=\"2\">FEI</td><td rowspan=\"2\">CSI</td><td colspan=\"9\">Accuracy in each session (%)↑</td><td rowspan=\"2\">KR</td><td rowspan=\"2\">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>✓</td><td></td><td></td><td>75.87</td><td>70.22</td><td>65.92</td><td>62.64</td><td>59.96</td><td>57.11</td><td>54.58</td><td>52.66</td><td>51.49</td><td>67.86</td><td>61.16</td></tr><tr><td>✓</td><td>✓</td><td></td><td>76.34</td><td>71.18</td><td>67.16</td><td>63.85</td><td>61.05</td><td>58.23</td><td>55.33</td><td>53.67</td><td>52.32</td><td>68.54</td><td>62.13</td></tr><tr><td>✓</td><td></td><td>✓</td><td>75.87</td><td>70.16</td><td>65.76</td><td>63.76</td><td>60.34</td><td>57.52</td><td>54.96</td><td>53.06</td><td>52.06</td><td>68.61</td><td>61.39</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.219,
+                0.282,
+                0.368
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.284,
+                0.219,
+                0.479,
+                0.367
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.369,
+                0.471,
+                0.438
+            ],
+            "angle": 0,
+            "content": "Figure 3. Confusion matrix of the final classification results on the miniImageNet dataset [29]. (a) Baseline. (b) Our FCIL. We used red lines to partition the region of the base class and the new class. Our method improves the predictive power of the network which reduces the scattered confusion matrix."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.443,
+                0.47,
+                0.506
+            ],
+            "angle": 0,
+            "content": "ifies the superiority of our proposed feature embedding infomax and continual structure infomax modules in learning novel class knowledge and meantime mitigating the catastrophic forgetting problem."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.515,
+                0.228,
+                0.53
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.538,
+                0.47,
+                0.584
+            ],
+            "angle": 0,
+            "content": "All ablation studies are performed on the miniImageNet dataset [29] to evaluate the effectiveness of our proposed modules as well as some experimental settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.585,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Effectiveness of the proposed modules: We first conduct experiments to analyze the effectiveness of our proposed feature embedding infomax (FEI) and continual structure infomax (CSI) modules. The detailed results are listed in Table 2. In continual learning sessions \\((t > 1)\\), the feature embedding infomax module is added to maximize the mutual information between the convolutional features produced by the fixed base backbone and the embedding features from the newly updated classifier. The performance improves over the baseline by \\(0.97\\%\\) and \\(0.68\\%\\) on Avg and KR, demonstrating that the proposed feature embedding infomax module could well transfer the strong learning capability of the base network into the following continual sessions to enhance the learning capability of the model on novel classes. It verifies the effectiveness of our proposed feature embedding the infomax module. The continual structure infomax learning module is conducted to maximize the mutual information between the current information structure and the previous ones. The performance promotion of the CSI model seems not significant in the early stages, since CSI is designed to alleviate catastrophic"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.219,
+                0.895,
+                0.461
+            ],
+            "angle": 0,
+            "content": "forgetting, and in the early stages (i.e., \\( t = 2,3,4 \\)) the few new classes only pose limited influence on the learned knowledge. Further, with new classes increased in the later stages, the performance gain of CSI greatly increases. It achieves performance promotions of \\( 0.75\\% \\) and \\( 0.23\\% \\) separately on KR and Avg, which are clearly non-trivial. It shows that our proposed continual structure infomax module could well preserve the learned knowledge of the previous classes to mitigate the catastrophic forgetting issue. We believe it is because the attributes and class relationships could be well preserved during the continual sessions, and it verifies the effectiveness of the proposed continual structure infomax module. Finally, when both modules are applied, the performances could be further boosted to form a new state-of-the-art performance, quantitatively verifying the effectiveness of our proposed FCIL framework."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.462,
+                0.895,
+                0.598
+            ],
+            "angle": 0,
+            "content": "We further plot the confusion matrix of the baseline and our FCIL in Fig. 3. It could be observed that in the new classes, the diagonal of our FCIL has a darker color than the baseline model, vividly showing that the proposed FCIL is more powerful at learning new classes. In addition, it also indicates that the prediction distribution of FCIL on new classes is more concentrated than the baseline model, and it visually demonstrates the superiority of our FCIL in preserving learned knowledge."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.895,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Different methods for MI estimation and relation construction: The mutual information (MI) estimation ways can be adopted with the support of JSD [27] or KL [9], i.e., \"MIJSD\" and \"MIKL\". We achieve the information related in the continual structure infomax module with KNN or Cosine distance, named: \\( \\mathrm{R_{KNN}} \\) and \\( \\mathrm{R_{Cos}} \\). The FCIL results with the above different methods are listed in Table 3, and it could be observed that the performance of the four variants changes little. It means that it is the proposed structure preserve mechanism rather than the specifically chosen functions that mitigate the catastrophic forgetting problem. Therefore, we adopt KL to estimate the mutual information and use the Cosine distance to build the relationship between different classes in our work."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The level of convolutional Feature \\(L\\): When performing the feature embedding infomax learning, we can estimate mutual information by using more layers of convolutional features \\(F_{conv}^{l}(x_{i})\\). To study the effect of different level sets, we construct three variants of FCIL by separately setting \\(L\\) as \\(\\{1,2\\}, \\{1,3\\}\\), and \\(\\{1,2,3\\}\\). The correspond"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19230"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.138,
+                0.088,
+                0.826,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Table 3. The results with different methods for MI estimation and relation construction on the miniImageNet dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.162,
+                0.101,
+                0.805,
+                0.176
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td colspan=\"9\">Accuracy in each session (%)↑</td><td rowspan=\"2\">KR</td><td rowspan=\"2\">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>MI_KL + R_KNN</td><td>76.34</td><td>71.40</td><td>67.07</td><td>64.05</td><td>61.29</td><td>58.51</td><td>55.73</td><td>54.07</td><td>52.74</td><td>68.08</td><td>62.35</td></tr><tr><td>MI_KL + R_Cos</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr><tr><td>MI_JSD + R_KNN</td><td>76.34</td><td>71.34</td><td>67.03</td><td>64.0</td><td>61.28</td><td>58.52</td><td>55.7</td><td>54.03</td><td>52.7</td><td>69.03</td><td>62.32</td></tr><tr><td>MI_JSD + R_Cos</td><td>76.34</td><td>71.26</td><td>66.99</td><td>64.03</td><td>61.24</td><td>58.46</td><td>55.65</td><td>53.98</td><td>52.63</td><td>68.94</td><td>62.28</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.179,
+                0.894,
+                0.204
+            ],
+            "angle": 0,
+            "content": "Table 4. The comparison results between our FCIL and the open-source methods FACT [37] and CEC [35] by fixing the performance of the base classes on the miniImageNet dataset [29]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.141,
+                0.204,
+                0.83,
+                0.268
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"9\">Accuracy in each session (%) ↑</td><td rowspan=\"2\">KR↑</td><td rowspan=\"2\">ΔFinal↑</td><td rowspan=\"2\">Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>CEC [35]</td><td>72.57</td><td>66.48</td><td>62.74</td><td>59.46</td><td>56.67</td><td>53.68</td><td>51.12</td><td>49.23</td><td>47.58</td><td>65.56</td><td>+1.16</td><td>57.73</td></tr><tr><td>FACT [37]</td><td>72.73</td><td>67.73</td><td>63.77</td><td>60.29</td><td>57.25</td><td>54.07</td><td>51.17</td><td>49.31</td><td>47.91</td><td>65.87</td><td>+0.83</td><td>58.25</td></tr><tr><td>FCIL(Ours)</td><td>72.63</td><td>67.71</td><td>63.70</td><td>60.67</td><td>57.61</td><td>54.73</td><td>52.09</td><td>50.26</td><td>48.74</td><td>66.94</td><td></td><td>58.71</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.281,
+                0.348,
+                0.438
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.438,
+                0.349,
+                0.464
+            ],
+            "angle": 0,
+            "content": "Figure 4. Performance comparison bars with different levels of convolutional features."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.366,
+                0.288,
+                0.613,
+                0.44
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.365,
+                0.44,
+                0.612,
+                0.464
+            ],
+            "angle": 0,
+            "content": "Figure 5. Performance comparison with the different shot numbers."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.629,
+                0.306,
+                0.871,
+                0.44
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.628,
+                0.44,
+                0.875,
+                0.464
+            ],
+            "angle": 0,
+            "content": "Figure 6. Performance comparison with different number of \\( K \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.47,
+                0.47,
+                0.651
+            ],
+            "angle": 0,
+            "content": "ing accuracy changing bars are plotted in Fig. 4. It can be observed that the three variants change make little performance change. Further, it is worth noting that when employing all the levels of features (i.e., \\( L = \\{1,2,3\\} \\)), it could obtain better results than the other two variants, and all three convolutional features have been used. It means that our proposed feature embedding infomax module is able to continually transfer more useful encoding capabilities from multi-level convolutional features. It sufficiently validates the strong power of the feature embedding infomax module on transferring the encoding capability of the base network to the newly learned classifiers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.656,
+                0.47,
+                0.837
+            ],
+            "angle": 0,
+            "content": "The shot number in the continual learning: We plot the accuracy changing curves with different shot numbers in Fig. 5. It shows that more sample shots could result in better few-shot continual classification performance. The reason is more shots could bring better class attribute distribution as well as more accurate class relations to benefit the learned new knowledge. Further, when the shot number is more than 15, the performance promotion becomes trivial. It shows that we only need a proper number of newly labeled samples to achieve satisfactory performances, verifying the effectiveness of our FCIL framework in addressing the few-shot continual classification task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Different number of \\(K\\): In the continual structure infomax learning module, we can use the different number of these previous information structures \\(K\\) to constrain the structure of learned knowledge in the continual stage. As"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.47,
+                0.892,
+                0.606
+            ],
+            "angle": 0,
+            "content": "\\(K\\) increases, there is a slight but smaller growth in the KR results, indicating that the structural information of the adjacent stages is adequately constrained for the current stage. This result can clearly show that it is possible to better mitigate catastrophic forgetting by imposing structural constraints on learned knowledge, but the demand for computational complexity and memory would increase significantly. Therefore, considering the performance and complexity of our method, we set \\(K\\) equal to 2 in our work."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.607,
+                0.892,
+                0.773
+            ],
+            "angle": 0,
+            "content": "Different methods with similar starting performance: As shown in Table 4, we give the comparison results of the FCIL, FACT [37], and CEC [35] methods with similar performance in the initial/base stage. We can observe that the three metrics of the FCIL framework are superior to the other methods, which indicates that the FCIL framework can retain the learned knowledge better, and the improvement is not because of the base model performance but our introduced FCIL. It clearly verifies the superiority of the proposed FCIL framework in effectively learning new knowledge and mitigating catastrophic forgetting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.785,
+                0.619,
+                0.801
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a Few-show Continual Informal Learning (FCIL) framework to address the few-shot class continual learning task. Our FCIL enables a deep model to continually/incrementally learn new concepts from a few labeled samples and meantime prevent the model from forgetting the previously learned knowl-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19231"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.244
+            ],
+            "angle": 0,
+            "content": "edge. Inspired by the transfer entropy concept, a feature embedding infomax module is proposed by maximizing the mutual information between different level feature distributions and then grants the model to transfer the strong encoding capability of the base network into the new classes. Further, a continual structure infomax module is proposed to maximize the mutual information across these continually changing relations of the classes to resemble the continual learning progress, so that catastrophic forgetting could be well mitigated."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.259,
+                0.258,
+                0.276
+            ],
+            "angle": 0,
+            "content": "6. Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.285,
+                0.473,
+                0.392
+            ],
+            "angle": 0,
+            "content": "This work was supported by the National Natural Science Foundation of China (Grants Nos. 61972204, 62072244), the fundamental research funds for the central universities under Grant 30919011232, the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020LZH008, ZR2022LZH003), and in part by State Key Laboratory of High-end Server & Storage Technology."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
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+                0.175,
+                0.421
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+            "angle": 0,
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+        },
+        {
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+            ],
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+        },
+        {
+            "type": "page_number",
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+# Few-shot Continual Infomax Learning
+
+Ziqi Gu#, Chunyan Xu#, Jian Yang, Zhen Cui*  
+PCA Lab, Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China.
+
+{ziqigu, cyx, csjyang, zhen.cui}@njust.edu.cn
+
+# Abstract
+
+Few-shot continual learning is the ability to continually train a neural network from a sequential stream of few-shot data. In this paper, we propose a Few-shot Continua! Infomax Learning (FCIL) framework that makes a deep model to continually/incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting of past knowledge. Specifically, inspired by the theoretical definition of transfer entropy, we introduce a feature embedding infomax to effectively perform the few-shot learning, which can transfer the strong encoding capability of the base network to learn the feature embedding of these novel classes by maximizing the mutual information of different-level feature distributions. Further, considering that the learned knowledge in the human brain is a generalization of actual information and exists in a certain relational structure, we perform continual structure infomax learning to relieve the catastrophic forgetting problem in the continual learning process. The information structure of this learned knowledge can be preserved through maximizing the mutual information across these continual-changing relations of inter-classes. Comprehensive evaluations on CIFAR100, miniImageNet, and CUB200 datasets demonstrate the superiority of our FCIL when compared against state-of-the-art methods on the few-shot continual learning task.
+
+# 1. Introduction
+
+Recent deep learning technologies [23, 30, 13] have made great progress in many computer vision tasks. The success of deep neural networks is achieved by employing a large number of labeled training data. However, it is difficult to collect large-scale supervised data in advance, while we would encounter a sequential data stream with unknown new classes in many realistic situations. This would require
+
+a neural network with continual learning ability, especially when some new classes with very few labeled samples often appear. Therefore, this work focuses on dealing with the few-shot continual/incremental learning task [28, 26]. They are two critical challenges in a few-shot continual learning task: i) how to learn new knowledge with few-shot instances, and ii) how to avoid catastrophic forgetting of the preceding learned knowledge.
+
+Recently, numerous previous works [31] have been devoted to few-shot continual learning from various perspectives. In [31, 35, 8], the topological structure of the knowledge space formed by different classes has been considered to perform few-shot continual learning by using a neural gas network or graph model. Cheraghian et al. [8] have proposed a semantic-aware knowledge distillation method to solve few-shot class incremental learning by making use of word embeddings. Several meta-learning based methods [7, 18] have been also proposed to enable the model to preserve old knowledge and adapt to the new classes for continual learning. By assigning virtual prototypes to squeeze the embedding of known classes and reserve for new ones, the forward compatible training method [37] has efficiently incorporated new classes with forward compatibility and meanwhile resists forgetting old ones. Similarly, the mixture of subspaces and synthesized features [6] have been used to alleviate the forgetting and over-fitting problem in the few-shot continual learning process. In [38], the self-promoted prototype learning scheme has been proposed to explicitly learn the feature representation under the few-shot learning situation and thus facilitated subsequent incremental tasks. The self-supervised strategy has been also used to enhance the feature extraction ability of the model by adding self-supervised loss function assistance during the training process [20, 26]. Moreover, to minimize over-fitting and the catastrophic forgetting problem, Mazumder et al. [26] have selected very few unimportant model parameters to perform few-shot learning on new classes. In [11], mutual information (MI) maximization has been first used as a solution method to deal with the catas
+
+trophic forgetting problem in the online continual learning task, but it cannot well consider how to perform continual infomax learning from the perspective of information entropy, especially in the few-shot regime.
+
+In this work, we propose a novel Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to continually learn from a stream of few-shot labeled data. In general, the continual learning model would be trained with a large amount of labeled data in the initial learning stage, while few-shot samples of some unknown classes would be encountered in the continual learning process. Here we attempt to address the few-shot continual learning task from two aspects. First, inspired by the theoretical definition of transfer entropy, we attempt to transfer the strong encoding capability of the base network to promote few-shot continual learning. Specifically, we propose a feature embedding infomax learning to new concepts from a few labeled samples through maximizing the mutual information between different level feature distributions, where the convolutional representations and the feature embedding of new classes are encoded with these fixed convolution layers of the base network and newly increased parameters of fully-connected layer, respectively. Second, considering that the learned knowledge in the human brain is a generalization or abstraction of the actual information learned from these seen samples [10], we wish the continual learning model with a stable information structure that can be updated incrementally. Thus we propose a continual structure infomax learning mechanism to alleviate the catastrophic forgetting problem during the continual learning process. The structure relation of this learned information can be preserved through maximizing the mutual information across these continual-changing structure relations of inter-classes.
+
+In summary, our primary contributions can be summarized as follows: i) We propose a Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting problem of previously learned ones. ii) Two specially-designed infomax learning mechanisms are proposed to address the few-shot continual learning problem with the help of mutual information maximization, including feature embedding infomax and continual structure infomax. iii) We validate the effectiveness of our proposed FCIL on three benchmarks (including CIFAR100, CUB200, and miniImageNet), and also demonstrate the superiority of our proposed FCIL when compared with existing state-of-the-art methods.
+
+# 2. Related work
+
+Few-shot continual learning: Few-shot continual learning, which has recently attracted growing attention, aims to enable a model to perform continual/incremental
+
+learning with a stream of few-shot labeled data. A number of related works have been proposed to address the few-shot continual learning task. For example, Tao et al. [31] employed neural gas networks to perform incrementally learning for a series of new classes with few-shot data, with the goal of avoiding forgetting previously learned classes. Zhang et al. [35] proposed an evolving classifier based on graph attention networks that propagated information between classifiers by adding graph models. Also, pseudo-incremental training was proposed to optimize the graph module. The forward compatible training (FACT) [37] was proposed to effectively incorporate novel classes into forward compatible by generating virtual classes, where knowledge of old classes can be also maintained to reduce the catastrophic forgetting problem. A bi-level meta-learning-based optimization [7] was proposed to directly optimize the model towards forgetting alleviation of learned knowledge and adaptation of the new classes. In [20], a self-supervised stochastic classifier was proposed to deal with the few-shot class incremental learning task with the help of a self-supervision mechanism. Zhu et al. [38] proposed an incremental prototype learning scheme to perform continual learning, which was used to constrain the prototypes of new classes through the dynamic model and then achieved a reduction in catastrophic forgetting of knowledge. In order to offer a trade-off between accuracy and compute-memory cost of learning novel classes, the hyper-dimensional embedding was used to continually learn many more classes than the fixed dimensions in the feature space [14]. Further, few-shot lifelong learning was proposed to perform continual learning with only updating very few parameters of the model [26] or semantic-aware knowledge distillation [5].
+
+Mutual information: Mutual Information as a quantity is used to measure the degree of interdependence between two random variables [21]. As it is difficult to exactly compute the mutual information between second-dimensional random variables, mutual information neural estimator (MINE) [2] can be achieved by employing the dual representations of the Kullback-Leibler divergence (KL) [9]. Subsequently, the Jensen-Shannon divergence (JSD) [27] and noise-contrastive estimation (NCE) [12] were used to estimate the mutual information with a learned network [16], and then the mutual information maximization method was used to improve the deep representation in an unsupervised learning way. The second-order deep multiplex infomax method [19] further extended the mutual information estimation to a three-variable calculation and was applied across multiple networks. The deep mutual information maximin method [25] was used to address the cross-modal clustering task by maximally preserving the shared information of multiple modalities and eliminating the superfluous information of individual modalities. In [1], mutual information networks are applied to unsupervised
+
+classification tasks with excellent results. In the online continual learning task, Guo et al. [11] first used mutual information estimation to learn more robust features and preserve the past model learned from the previous task. Different from these previous methods, we perform continual infomax learning from the perspective of information entropy in the few-shot setting.
+
+# 3. The Proposed Method
+
+# 3.1. Problem Definition
+
+Few-shot continual learning aims to train a model for new tasks sequentially from a stream of few-shot labeled data, relieving the forgetting of knowledge learned from the old tasks, where the data in the old tasks are not available anymore during learning a new set of few-shot tasks. Formally, we define  $X$ ,  $Y$ , and  $Z$  as the training set, label set, and test set, respectively. Our task is to train the model with a continuous stream of labeled training sets  $X_{1}, X_{2}, \ldots, X_{T}$ , where  $X_{t}$  denotes the  $t$ -th training set,  $Y_{t}$  is the corresponding label set, and  $T$  refers to the number of continual learning sessions. In the continual learning process, each training set is with no repetition of class labels, i.e.,  $\forall i, j$  and  $i \neq j$ ,  $Y_{i} \cap Y_{j} = \emptyset$ . Usually, when  $t = 1$ , the training set  $X_{1}$  is with large-scale samples for training the base network; when  $t > 1$ ,  $X_{t}$  refers to the few-shot training set of new classes in the incremental learning stage (i.e.,  $|X_{1}| \gg |X_{t}|, t = 2, 3, \ldots, T$ ). For example, under the 5-way 10-shot setting, each incremental/continual process (i.e.,  $t > 1$ ) contains five new classes, each of which has only ten training samples. The test set  $Z$  is used to evaluate the classification performance at each stage  $t$ , and its corresponding classes may be from all training label sets, i.e.,  $\{Y_{1} \cup Y_{2} \dots \cup Y_{T}\}$ .
+
+In the few-shot continual learning task, there are two critical problems we need to consider: i) New classes are with a small amount of training data, which makes it hard to learn the feature embeddings for these new classes. ii) Catastrophic forgetting should be well relieved to preserve this learned knowledge in the continual learning process. In this work, we attempt to address them from two aspects. First, we start from the transfer entropy perspective [3] to obtain new knowledge from few-shot samples, where the strong encoding capability of the base network can be transferred to learn feature embeddings of these new classes. Second, considering that the learned knowledge in the human brain is not isolated, but exists in a certain relational structure [10], we wish to preserve the structure information of this learned knowledge to relieve the catastrophic forgetting problem during the continual learning process. With the help of the recently-developed mutual information estimation method [2, 16, 36], we achieve these above goals by performing continual infomax learning.
+
+![](images/aa7adcb9237bd04db99ee4e6d59b5c1ecb9cd4af010f6a820d077c75450eb06b.jpg)  
+Figure 1. The pipeline of our few-shot continual infomax learning, where  $t$  refers to the  $t$ -th session in the continual learning process ( $t \geqslant 1$ ). To transfer the strong encoding capability of the base network into the subsequent continual learning sessions, we first propose the feature embedding infomax to learn new knowledge with few-shot labeled data in the  $t$ -th session. Here we maximize the mutual information between multi-level convolutional representations  $F_{conv}(x_i)$  and full-connected feature embedding  $F_{fc}(x_i)$  of each input sample, which are encoded with these fixed convolution layers of the base network  $\Theta_{conv}^{base}$  and updated fully-connected layer  $\Theta_{fc}^{t}$ , respectively. To address the catastrophic forgetting problem in the continual learning process, we further perform the continual structure infomax learning by maximizing the mutual information between current and previous inter-class knowledge structures (i.e.,  $S(A^t, R^t)$  and  $S(A^{t-1}, R^{t-1})$ ).
+
+# 3.2. FCIL Paradigm
+
+The proposed few-shot continual infomax learning (FCIL) framework is shown in Fig. 1. Generally, the base network  $\Theta^{base}$ , which is a large-scale set of training samples  $X_{1}$ , can optimize with the classic cross-entropy loss. For further improving the deep representation capability of the base network, we also employ self-supervised mutual information mechanism. Here the mutual information estimated network  $\vartheta^{MI}$  can be well optimized in the initial stage (i.e.,  $t = 1$ ), which contributes to the subsequent continual learning sessions. In the next continual learning sessions (i.e.,  $t > 1$ ), a stream of few-shot labeled data with new classes would be gradually fed into the network, and we would perform few-shot continual infomax learning for capturing new knowledge, without forgetting these learned ones. To improve the feature embedding capability of these new classes, we attempt to transfer the strong representation capability of the base network  $\Theta^{base}$  into the next continual learning sessions. Specifically, we introduce the feature embedding infomax learning to optimize these fully-connected parameters  $\Theta_{fc}^{t}$  of new classes. Given an input image  $x_{i}$  from the few-shot set  $D_{t}$ , we use the convolutional net optimized in the base stage to extract multi-level convolutional
+
+features  $F_{conv}(x_i)$ , and get the feature embeddings from new full-connected layer  $F_{fc}(x_i)$ . We maximize the mutual information between the convolutional and full-connected feature distributions for each input sample (i.e.,  $F_{conv}(x_i)$  and  $F_{fc}(x_i)$ ), and thus the feature embedding of the novel classes can well inherit the powerful feature representation capability of the base network (i.e.,  $\max \mathcal{T}_{\Theta^{base} \to \Theta_{fc}^t}$ ). Further, to alleviate the catastrophic forgetting problem of this learned knowledge during the subsequent continual learning sessions, we introduce a continual structure infomax learning (i.e.,  $\max \mathcal{D}_S$ ) to maintain/preserve the relations of intra-classes across one or more learning sessions. At each learning session  $t$ , we can obtain the first-order attributes and the second-order structure information of this learned knowledge, which refer to the class-wise feature embeddings and the relations among different classes, respectively. We then maximize the mutual information between the current information structure  $S(A^t, R^t)$  and this previous information  $S(A^{t'}, R^{t'})$  ( $t' = t - 1, t - 2, \ldots, t - K$  and  $t - K \geqslant 1$ ) of these old classes. With the help of feature embedding infomax and continual structure infomax, the deep model can be well worked in the few-shot continual learning process. See the supplementary materia for more details.
+
+# 3.2.1 Feature Embedding Infomax
+
+When the base network  $\Theta^{base}$  faces unknown new classes, it is difficult to learn new concepts with only few-shot labeled samples. Inspired by the classic transfer entropy method which is a non-parametric measure of directed, asymmetric information transfer between two processes [3], we attempt to migrate the powerful feature representation capability of the base network to capture the feature embedding of the novel classes. Given few-shot training samples of new classes in the  $t$ -continual learning stage (i.e.,  $t > 1$ ), the transfer entropy from the base network  $\Theta^{base}$  to the feature embedding layer of novel classes  $\Theta_{fc}^{t}$  (i.e., fully-connected model parameters) can be formulated as:
+
+$$
+\mathcal {T} _ {\Theta^ {b a s e} \rightarrow \Theta_ {f c} ^ {t}} = \sum_ {i = 1} ^ {| X _ {t} |} \left(H \left(\mathbf {Z} _ {f c}\right) - H \left(\mathbf {Z} _ {f c} \mid \mathbf {Z} _ {c o n v}\right)\right), \tag {1}
+$$
+
+where  $X_{t} = \{x_{1},x_{2},\dots,x_{|X_{t}|}\}$  is the training set of few-shot data in the  $t$  -th continual learning session;  $F_{conv}(x_i)$  is the convolution representations of the training sample  $x_{i}$  with the base encoding network  $\Theta^{base}$ .  $F_{fc}(x_{i})$  is the feature embedding of  $x_{i}$  with the fully-connected parameters  $\Theta_{fc}^t$  of the  $t$  -th continual learning stage. Let  $\mathbf{Z}_{conv} = F_{conv}(x_i)$  and  $\mathbf{Z}_{fc} = F_{fc}(x_i)$ ,  $H(\mathbf{Z}_{fc})$  refers to the Shannon entropy information of fully-connected feature of  $x_{i}$  and the conditional entropy  $H(\mathbf{Z}_{fc}|\mathbf{Z}_{conv})$  is the entropy of  $\mathbf{Z}_{conv}$  conditioned on  $\mathbf{Z}_{fc}$ . To facilitate the calculation of Eqn. (1), the transfer entropy  $\mathcal{T}_{\Theta^{base}\to \Theta_{fc}^t}$  can be further
+
+expressed as the conditional mutual information of different level features with the corresponding network parameters in the condition:
+
+$$
+\begin{array}{l} \mathcal {T} _ {\Theta^ {b a s e} \rightarrow \Theta_ {f c} ^ {t}} = \sum_ {i = 1} ^ {| X _ {t} |} \sum_ {l = 1} ^ {L} I ((\mathbf {Z} _ {f c}; \mathbf {Z} _ {c o n v} ^ {l})), \\ \sum_ {i = 1} ^ {| X _ {t} |} \sum_ {l = 1} ^ {L} \hat {I} \left(\left(\mathbf {Z} _ {f c}; \mathbf {Z} _ {c o n v} ^ {l}\right), \vartheta^ {M I}\right), \tag {2} \\ \end{array}
+$$
+
+here, we directly maximize the mutual information between multi-level convolutional features and fully-connected feature embedding, which can better transfer the strong encoding capability of the base network  $\Theta^{base}$  to the fully-connected layer  $\Theta_{fc}^{t}$ . With the support of the Kullback-Leibler divergence [9] and the learned mutual information estimation network  $\vartheta^{MI}$ , the transfer entropy process can be approximately formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathcal {T}} = \sum_ {i = 1} ^ {| X _ {t} |} \sum_ {l = 1} ^ {L} \mathbb {E} \left(\mathcal {F} \left(\left(\mathbf {Z} _ {f c}; \mathbf {Z} _ {c o n v} ^ {l}\right), \vartheta^ {M I}\right)\right) \tag {3} \\ - \log \mathbb {E} (e ^ {\mathcal {F} ((\mathbf {Z} _ {f c}; \mathbf {Z} _ {c o n v} ^ {l}), \vartheta^ {M I})}). \\ \end{array}
+$$
+
+where  $\mathcal{F}(\cdot)$  is a discriminant function between features of different layers. Here this transfer entropy process can help to capture the feature embeddings of these few-shot training samples in the continual learning stages, thus we name it as "feature embedding infomax" learning process. The final learning objective to optimize the  $t$ -th continual fully-connected layer  $\Theta_{fc}^{t}$  is defined as:  $\mathcal{L}_{FEI} = \mathcal{L}_{CE} - \alpha \mathcal{L}_{\mathcal{T}}$  where  $\mathcal{L}_{CE}$  is the classic cross-entropy loss and  $\alpha$  is a hyper-parameter.
+
+# 3.2.2 Continual Structure Infomax
+
+Another critical problem for a continual learning model is exiting the catastrophic forgetting this learned knowledge when discarding old samples. An obvious solution is that continual learning must have a strategy to preserve the information related to these old training samples. Usually, the information preserved in a continual learning system is a generalization or abstraction of the actual information embedded in the learned samples. The knowledge we learn in the human brain [10] does not exist in isolation; there is some kind of relational structure between different pieces of knowledge that maintains the connection between knowledge. In order to possess an information structure that would be updated incrementally along the continual learning process, we can preserve useful information from learned samples as much as possible so that the subsequent continual learning process can be guided by this information. Therefore, we propose a continual structure infomax learning to conserve both first-order and second-order information in the continual learning process, which can be
+
+related to class-wise individual attributions and intra-class relations, respectively. In the  $t$ -th continual learning session, the continual structure infomax can be performed under the guidance of these previous information structures:
+
+$$
+\mathcal {D} _ {S} = \sum_ {k = 1} ^ {K} \underbrace {H \left(A _ {t}\right) - H \left(A _ {t} \mid A _ {t - k}\right)} _ {\text {f i r s t - o r d e r}} + \underbrace {H \left(R _ {t}\right) - H \left(R _ {t} \mid R _ {t - k}\right)} _ {\text {s e c o n d - o r d e r}} \tag {4}
+$$
+
+where  $K$  is the number of previous sessions with  $t - K \geq 1$ .  $A_{t}$  and  $A_{t - k}$  refer to the feature embeddings of all learned classes  $c_{t}$ , e.g.,  $A_{t} = [e_{1}, e_{2}, \ldots, e_{c}, \ldots, e_{c_{t}}]$ . Due to the fact that the mean value of each class is approximate to the parameter weights of the last fully-connected layer,  $e_{c}$  is achieved by the weight parameters of the last classification layer corresponding to the  $c$ -th class. Their corresponding information entropy  $A_{t}$  and  $A_{t - k}$  are represented as  $H(A_{t})$  and  $H(A_{t}|A_{t - k})$ .  $R_{t} \in \mathbb{R}^{c_{t} \times c_{t}}$  and  $R_{t - k} \in \mathbb{R}^{c_{t - k} \times c_{t - k}}$  refer to the inter-class relation matrices of all learned classes in the  $t$ -th and  $(t - k)$ -th stages.  $H(R_{t})$  and  $H(R_{t}|R_{t - k})$  represent the second-order information entropy concerning the relation among different classes. Through maximizing the first-order and second-order mutual information between different learning stages, the network parameters of the last fully-connected layer  $\Theta_{fc}$  can be incrementally updated along the continual learning process, formally,
+
+$$
+\begin{array}{l} \mathcal {D} _ {S} = \sum_ {k = 1} ^ {K} \underbrace {I (A _ {t} ; A _ {t - k})} _ {\text {f i r s t - o r d e r}} + \underbrace {I (R _ {t} ; R _ {t - k})} _ {\text {s e c o n d - o r d e r}}, \\ \geq \sum_ {k = 1} ^ {K} \underbrace {\hat {I} \left(\left(A _ {t} ; A _ {t - k}\right) , \vartheta^ {M I}\right)} _ {\text {f i r s t - o r d e r}} + \underbrace {\hat {I} \left(\left(R _ {t} ; R _ {t - k}\right) , \vartheta^ {M I}\right)} _ {\text {s e c o n d - o r d e r}}, \tag {5} \\ \end{array}
+$$
+
+Similar to the feature embedding infomax, we also use mutual information to measure the amount of information shared by different sessions, and this continual structure infomax process can be further formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {S} = \sum_ {k = 1} ^ {K} \mathbb {E} \left(\mathcal {F} \left(\left(A _ {t}; A _ {t - k}\right), \vartheta^ {M I}\right)\right) - \log \mathbb {E} \left(e ^ {\mathcal {F} \left(\left(A _ {t}; A _ {t - k}\right), \vartheta^ {M I}\right)}\right) \\ + \mathbb {E} \left(\mathcal {F} \left(\left(R _ {t}; R _ {t - k}\right), \vartheta^ {M I}\right)\right) - \log \mathbb {E} \left(e ^ {\mathcal {F} \left(\left(R _ {t}; R _ {t - k}\right), \vartheta^ {M I}\right)}\right), \tag {6} \\ \end{array}
+$$
+
+where  $k$  refers to the  $k$ -th session with  $1 \leqslant k \leqslant K$ . We employ both  $\mathcal{L}_S$  and  $\mathcal{L}_{CE}$  to optimize the fully-connected parameters  $\Theta_{fc}^t$  to adapt new classes without forgetting these learned ones. In the structure continual infomax process, the corresponding loss is defined as  $\mathcal{L}_{CSI} = \mathcal{L}_{CE} - \gamma \mathcal{L}_S$ , where  $\gamma$  is a balance factor.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets: We evaluate our FCIL on three public datasets, including CIFAR100 [22], miniImageNet [29],
+
+and CUB200 [33]. For CIFAR100 [22] and miniImageNet [29], we use all the training data of the 60 base classes to train a base network, and the 40 new classes are used to perform eight 5-way 5-shot continual learning tasks. We divide the 200 classes of CUB200 [33] into 100 base classes and 100 new classes. The 100 new classes are used to perform ten 10-way 5-shot continual learning tasks. We follow the same split setting of FSCIL [31] as other methods in the three datasets for a fair comparison. See the supplementary materia for more details.
+
+Implementation Details: Following FSCIL [31], we use ResNet20 as the backbone on CIFAR100 [22] and ResNet18 is used as the backbone on miniImageNet [29] and CUB200 [33]. The network  $\vartheta^{MI}$  consists of a convolution branch and a linear branch, where the former consists of three convolution layers whose kernel sizes are 1, 5, and 7, and the latter is one linear layer. In the CSI module, the convolution branch and the linear branch separately take  $F_{conv}^{l}(x_{i})$  and  $F_{fc}(x_{i})$  as inputs, and their outputs are used to compute  $\mathcal{L}_{\mathcal{T}}$ . In the CSI module, the linear layer of  $\vartheta^{MI}$  separately take  $A_{t}$  and  $A_{t - k}$  as inputs, and we use the outputs to compute  $\mathcal{L}_s$ . In the base learning stage, we train the base network and the mutual information network with the first training set. The parameters of the convolutional layers  $\Theta^{base}$  and the mutual information network  $\vartheta^{MI}$  are frozen in the continual learning sessions to perform mutual information estimation in both the proposed feature embedding infomax. For all datasets, we set  $\alpha$  and  $\gamma$  as 0.015 and 0.03, respectively. Random cropping, random scaling, and random horizontal flipping are used for training data. We use to evaluate our proposed method from different perspectives. "Acc_t" represents to the Top-1 accuracy in the t-th continual session. "Avg" represents for an average score, i.e.,  $\sum_{t=1}^{T} \mathrm{Acc}_t / T$ . "ΔFinal" represents the difference value of  $\mathrm{Acc}_t$  between our method and the compared method in the final state. "KR" is the knowledge retention rate, i.e.,  $\mathrm{Acc}_T / \mathrm{Acc}_1$ . All the experiments are conducted with the Pytorch framework on one Geforce 2080Ti GPU.
+
+# 4.2. Comparison with state-of-the-art methods
+
+We first compare our proposed FCIL with other state-of-the-art methods on the challenging miniImageNet dataset [29]. The detailed results have been listed in Table 1, and the accuracy changing curves with growing continual sessions are plotted in Fig. 2 (a). Our proposed FCIL outperforms all other compared methods by a great margin and sets new state-of-the-art. In particular, our FCIL achieves the best score among all the methods. Considering that in the first continual session, very little data are available and it requires borrowing the learning capability of the base stage into this session to promote the classifier accuracy. In addition, as to the overall performance in the final continual session, our FCIL also surpasses the second best method C-
+
+Table 1. Few-shot continual classification performance of state-of-the-art methods and our FCIL on the miniImageNet dataset [29]. The results with * are obtained from the authors' published code. See the supplementary materia for results of other datasets.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="10">Accuracy in each session (%)↑</td><td>KR↑</td><td>ΔFinal↑</td><td>Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>Ft-CNN</td><td>61.31</td><td>27.22</td><td>16.37</td><td>6.08</td><td>2.54</td><td>1.56</td><td>1.93</td><td>2.60</td><td>1.40</td><td>2.28</td><td>+51.36</td><td>13.44</td><td></td></tr><tr><td>iCaRL [28]</td><td>61.31</td><td>46.32</td><td>42.94</td><td>37.63</td><td>30.49</td><td>24.00</td><td>20.89</td><td>18.80</td><td>17.21</td><td>28.07</td><td>+35.55</td><td>33.29</td><td></td></tr><tr><td>EEIL [4]</td><td>61.31</td><td>46.58</td><td>44.00</td><td>37.29</td><td>33.14</td><td>27.12</td><td>24.10</td><td>21.57</td><td>19.58</td><td>31.93</td><td>+33.18</td><td>34.97</td><td></td></tr><tr><td>TOPIC [31]</td><td>61.31</td><td>50.09</td><td>45.17</td><td>41.16</td><td>37.48</td><td>35.52</td><td>32.19</td><td>29.46</td><td>24.42</td><td>39.83</td><td>+28.34</td><td>39.65</td><td></td></tr><tr><td>NCM [17]</td><td>61.31</td><td>47.80</td><td>39.31</td><td>31.91</td><td>25.68</td><td>21.35</td><td>18.67</td><td>17.24</td><td>14.17</td><td>23.11</td><td>+38.59</td><td>30.83</td><td></td></tr><tr><td>Decoupled-NegCosine [24]</td><td>71.68</td><td>66.64</td><td>62.57</td><td>58.82</td><td>55.91</td><td>52.88</td><td>49.41</td><td>47.50</td><td>45.81</td><td>63.90</td><td>+6.95</td><td>56.80</td><td></td></tr><tr><td>Decoupled-Cosine [32]</td><td>70.37</td><td>65.45</td><td>61.41</td><td>58.00</td><td>54.81</td><td>51.89</td><td>49.10</td><td>47.27</td><td>45.63</td><td>64.84</td><td>+7.13</td><td>55.99</td><td></td></tr><tr><td>Decoupled-DeepEMD [34]</td><td>69.77</td><td>64.59</td><td>60.21</td><td>56.63</td><td>53.16</td><td>50.13</td><td>47.79</td><td>45.42</td><td>43.41</td><td>62.21</td><td>+9.35</td><td>54.57</td><td></td></tr><tr><td>MateFSCIL [7]</td><td>72.04</td><td>67.94</td><td>63.77</td><td>60.29</td><td>57.58</td><td>55.16</td><td>52.90</td><td>50.79</td><td>49.19</td><td>68.28</td><td>+3.57</td><td>58.85</td><td></td></tr><tr><td>C-FSCIL Model1 (d=512) [15]</td><td>76.37</td><td>70.94</td><td>66.36</td><td>62.64</td><td>59.31</td><td>56.02</td><td>53.14</td><td>51.04</td><td>48.87</td><td>63.99</td><td>+3.89</td><td>60.52</td><td></td></tr><tr><td>C-FSCIL Mode2 (d=512) [15]</td><td>76.45</td><td>71.23</td><td>66.71</td><td>63.01</td><td>60.09</td><td>56.73</td><td>53.94</td><td>52.01</td><td>50.08</td><td>65.50</td><td>+2.68</td><td>61.14</td><td></td></tr><tr><td>C-FSCIL Mode3 (d=512) [15]</td><td>76.40</td><td>71.14</td><td>66.46</td><td>63.29</td><td>60.42</td><td>57.46</td><td>54.78</td><td>53.11</td><td>51.41</td><td>67.29</td><td>+1.35</td><td>61.61</td><td></td></tr><tr><td>FACT* [37]</td><td>75.68</td><td>70.65</td><td>66.53</td><td>62.75</td><td>59.39</td><td>56.19</td><td>53.26</td><td>51.10</td><td>49.48</td><td>65.38</td><td>+3.28</td><td>60.56</td><td></td></tr><tr><td>FACT* + FCIL</td><td>76.21</td><td>70.92</td><td>66.69</td><td>63.23</td><td>60.73</td><td>57.88</td><td>54.08</td><td>52.17</td><td>50.34</td><td>66.05</td><td>+2.42</td><td>61.36</td><td></td></tr><tr><td>CEC [35]</td><td>72.00</td><td>66.83</td><td>62.97</td><td>59.43</td><td>56.70</td><td>53.73</td><td>51.19</td><td>49.24</td><td>47.63</td><td>66.15</td><td>+5.13</td><td>57.75</td><td></td></tr><tr><td>CEC + FCIL</td><td>72.87</td><td>68.23</td><td>64.46</td><td>60.64</td><td>57.71</td><td>55.12</td><td>52.79</td><td>50.65</td><td>48.62</td><td>66.72</td><td>+4.14</td><td>59.01</td><td></td></tr><tr><td>FCIL (Ours)</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>-</td><td>62.37</td><td></td></tr></table>
+
+![](images/6e8806132b03c841dfed725047ec8a1436b8d20f927a90f58960bb6b05ec74e8.jpg)  
+(a) miniImageNet
+
+![](images/1041a4c22f7293580cdb28b0e24fa9930a961d824b12690011981568873517d1.jpg)  
+(b) CIFAR100
+
+![](images/445125f576ff6154d6ad92a3c5937145ab7e2b500541aaf57937e6b17558baad.jpg)  
+(c) CUB200  
+Figure 2. The accuracy changing curves with growing continual sessions of different methods on the three datasets.
+
+FSCIL Mode3 (d=512) [15] by a non-trivial gap of  $1.35\%$ . It shows that our FCIL could keep great learning capability when performing the continual learning process, and we owe the superiority to the strong capability borrowed from the base network by the proposed feature embedding infomax module. Further, our method also achieves the best performance on Avg, outperforming the compared methods by at least  $0.76\%$ . It indicates that our FCIL could always obtain better performance during all the continual sessions, further demonstrating the strong learning capability borrowed from the base network. Overall, the superior performances of our FCIL in terms of Avg and  $\Delta$ Final sufficiently verify the effectiveness of our proposed feature embedding infomax module on enhancing the learning capability of new classes. Besides, we integrate our proposed FCIL mechanisms into the FACT [37] and CEC [35] frameworks (i.e., FACT+FCIL and CEC+FCIL), and the compared results show that we can lead to significant improvements of  $0.99\%$  and  $0.86\%$  on the  $\Delta$ Final metric. It further verifies the superiority of our FCIL framework in learning new knowledge and alleviating catastrophic forgetting.
+
+Our FCIL achieves the best performance on the KR met-
+
+ric, with a promotion of at least  $0.83\%$ . Since KR represents the accuracy ratio of the final continual session and the base stage, a larger KR value means that less learned knowledge is forgotten. Compared with previous methods such as CEC [35], FACT [37], C-FSCIL [15] which also freeze the base classifier as our FCIL to avoid catastrophic forgetting, our FCIL still outperforms them by a considerable margin. It means that the relationship preserving capability brought by the proposed continual structure infomax module could better preserve the previously learned knowledge. It clearly validates the effectiveness of our proposed continual structure infomax module in mitigating the catastrophic forgetting problem. As a whole, the superior performance clearly verifies the superiority of our proposed FCIL in learning novel class knowledge as well as mitigating the catastrophic forgetting problem. The accuracy changing curves with growing continual sessions in Fig. 2(a) further visually show the superiority of our FCIL. We further plot the accuracy changing curves on the CIFAR100 [22] and CUB200 [33] datasets separately in Fig. 2(b) and Fig. 2(c). It could be observed that our proposed FCIL also achieves the best performances on the two datasets, and it further ver
+
+Table 2. Overall ablation study of the proposed method on the miniImageNet dataset. Feature embedding infomax (FEI) and continual structure infomax (CSI) are the two functional modules we proposed.  
+
+<table><tr><td rowspan="2">Base</td><td rowspan="2">FEI</td><td rowspan="2">CSI</td><td colspan="9">Accuracy in each session (%)↑</td><td rowspan="2">KR</td><td rowspan="2">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>✓</td><td></td><td></td><td>75.87</td><td>70.22</td><td>65.92</td><td>62.64</td><td>59.96</td><td>57.11</td><td>54.58</td><td>52.66</td><td>51.49</td><td>67.86</td><td>61.16</td></tr><tr><td>✓</td><td>✓</td><td></td><td>76.34</td><td>71.18</td><td>67.16</td><td>63.85</td><td>61.05</td><td>58.23</td><td>55.33</td><td>53.67</td><td>52.32</td><td>68.54</td><td>62.13</td></tr><tr><td>✓</td><td></td><td>✓</td><td>75.87</td><td>70.16</td><td>65.76</td><td>63.76</td><td>60.34</td><td>57.52</td><td>54.96</td><td>53.06</td><td>52.06</td><td>68.61</td><td>61.39</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr></table>
+
+![](images/5004f46cf58c92f4446f76cf061949bc04d11bebd8148b1d6bb8a7e53263645f.jpg)  
+Figure 3. Confusion matrix of the final classification results on the miniImageNet dataset [29]. (a) Baseline. (b) Our FCIL. We used red lines to partition the region of the base class and the new class. Our method improves the predictive power of the network which reduces the scattered confusion matrix.
+
+![](images/44856d4fa325af491f7405dd1ab770f5ae2b34b734325c25a284954ebc341c3d.jpg)
+
+ifies the superiority of our proposed feature embedding infomax and continual structure infomax modules in learning novel class knowledge and meantime mitigating the catastrophic forgetting problem.
+
+# 4.3. Ablation study
+
+All ablation studies are performed on the miniImageNet dataset [29] to evaluate the effectiveness of our proposed modules as well as some experimental settings.
+
+Effectiveness of the proposed modules: We first conduct experiments to analyze the effectiveness of our proposed feature embedding infomax (FEI) and continual structure infomax (CSI) modules. The detailed results are listed in Table 2. In continual learning sessions  $(t > 1)$ , the feature embedding infomax module is added to maximize the mutual information between the convolutional features produced by the fixed base backbone and the embedding features from the newly updated classifier. The performance improves over the baseline by  $0.97\%$  and  $0.68\%$  on Avg and KR, demonstrating that the proposed feature embedding infomax module could well transfer the strong learning capability of the base network into the following continual sessions to enhance the learning capability of the model on novel classes. It verifies the effectiveness of our proposed feature embedding the infomax module. The continual structure infomax learning module is conducted to maximize the mutual information between the current information structure and the previous ones. The performance promotion of the CSI model seems not significant in the early stages, since CSI is designed to alleviate catastrophic
+
+forgetting, and in the early stages (i.e.,  $t = 2,3,4$ ) the few new classes only pose limited influence on the learned knowledge. Further, with new classes increased in the later stages, the performance gain of CSI greatly increases. It achieves performance promotions of  $0.75\%$  and  $0.23\%$  separately on KR and Avg, which are clearly non-trivial. It shows that our proposed continual structure infomax module could well preserve the learned knowledge of the previous classes to mitigate the catastrophic forgetting issue. We believe it is because the attributes and class relationships could be well preserved during the continual sessions, and it verifies the effectiveness of the proposed continual structure infomax module. Finally, when both modules are applied, the performances could be further boosted to form a new state-of-the-art performance, quantitatively verifying the effectiveness of our proposed FCIL framework.
+
+We further plot the confusion matrix of the baseline and our FCIL in Fig. 3. It could be observed that in the new classes, the diagonal of our FCIL has a darker color than the baseline model, vividly showing that the proposed FCIL is more powerful at learning new classes. In addition, it also indicates that the prediction distribution of FCIL on new classes is more concentrated than the baseline model, and it visually demonstrates the superiority of our FCIL in preserving learned knowledge.
+
+Different methods for MI estimation and relation construction: The mutual information (MI) estimation ways can be adopted with the support of JSD [27] or KL [9], i.e., "MIJSD" and "MIKL". We achieve the information related in the continual structure infomax module with KNN or Cosine distance, named:  $\mathrm{R_{KNN}}$  and  $\mathrm{R_{Cos}}$ . The FCIL results with the above different methods are listed in Table 3, and it could be observed that the performance of the four variants changes little. It means that it is the proposed structure preserve mechanism rather than the specifically chosen functions that mitigate the catastrophic forgetting problem. Therefore, we adopt KL to estimate the mutual information and use the Cosine distance to build the relationship between different classes in our work.
+
+The level of convolutional Feature  $L$ : When performing the feature embedding infomax learning, we can estimate mutual information by using more layers of convolutional features  $F_{conv}^{l}(x_{i})$ . To study the effect of different level sets, we construct three variants of FCIL by separately setting  $L$  as  $\{1,2\}, \{1,3\}$ , and  $\{1,2,3\}$ . The correspond
+
+Table 3. The results with different methods for MI estimation and relation construction on the miniImageNet dataset.  
+
+<table><tr><td rowspan="2"></td><td colspan="9">Accuracy in each session (%)↑</td><td rowspan="2">KR</td><td rowspan="2">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>MI_KL + R_KNN</td><td>76.34</td><td>71.40</td><td>67.07</td><td>64.05</td><td>61.29</td><td>58.51</td><td>55.73</td><td>54.07</td><td>52.74</td><td>68.08</td><td>62.35</td></tr><tr><td>MI_KL + R_Cos</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr><tr><td>MI_JSD + R_KNN</td><td>76.34</td><td>71.34</td><td>67.03</td><td>64.0</td><td>61.28</td><td>58.52</td><td>55.7</td><td>54.03</td><td>52.7</td><td>69.03</td><td>62.32</td></tr><tr><td>MI_JSD + R_Cos</td><td>76.34</td><td>71.26</td><td>66.99</td><td>64.03</td><td>61.24</td><td>58.46</td><td>55.65</td><td>53.98</td><td>52.63</td><td>68.94</td><td>62.28</td></tr></table>
+
+Table 4. The comparison results between our FCIL and the open-source methods FACT [37] and CEC [35] by fixing the performance of the base classes on the miniImageNet dataset [29].  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="9">Accuracy in each session (%) ↑</td><td rowspan="2">KR↑</td><td rowspan="2">ΔFinal↑</td><td rowspan="2">Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>CEC [35]</td><td>72.57</td><td>66.48</td><td>62.74</td><td>59.46</td><td>56.67</td><td>53.68</td><td>51.12</td><td>49.23</td><td>47.58</td><td>65.56</td><td>+1.16</td><td>57.73</td></tr><tr><td>FACT [37]</td><td>72.73</td><td>67.73</td><td>63.77</td><td>60.29</td><td>57.25</td><td>54.07</td><td>51.17</td><td>49.31</td><td>47.91</td><td>65.87</td><td>+0.83</td><td>58.25</td></tr><tr><td>FCIL(Ours)</td><td>72.63</td><td>67.71</td><td>63.70</td><td>60.67</td><td>57.61</td><td>54.73</td><td>52.09</td><td>50.26</td><td>48.74</td><td>66.94</td><td></td><td>58.71</td></tr></table>
+
+![](images/fc9322d50340dfd4e6e41ba8d4a378ddf969d7595266e223225c2922590e152a.jpg)  
+Figure 4. Performance comparison bars with different levels of convolutional features.
+
+![](images/bade0378c4af3331e236474d4b9cadf5f1514f0666354e53088b33aea2609251.jpg)  
+Figure 5. Performance comparison with the different shot numbers.
+
+![](images/4d0f758d259406eca5d8b49f3d06a812496f007bfc9b6c400fea1528dddbb0b1.jpg)  
+Figure 6. Performance comparison with different number of  $K$ .
+
+ing accuracy changing bars are plotted in Fig. 4. It can be observed that the three variants change make little performance change. Further, it is worth noting that when employing all the levels of features (i.e.,  $L = \{1,2,3\}$ ), it could obtain better results than the other two variants, and all three convolutional features have been used. It means that our proposed feature embedding infomax module is able to continually transfer more useful encoding capabilities from multi-level convolutional features. It sufficiently validates the strong power of the feature embedding infomax module on transferring the encoding capability of the base network to the newly learned classifiers.
+
+The shot number in the continual learning: We plot the accuracy changing curves with different shot numbers in Fig. 5. It shows that more sample shots could result in better few-shot continual classification performance. The reason is more shots could bring better class attribute distribution as well as more accurate class relations to benefit the learned new knowledge. Further, when the shot number is more than 15, the performance promotion becomes trivial. It shows that we only need a proper number of newly labeled samples to achieve satisfactory performances, verifying the effectiveness of our FCIL framework in addressing the few-shot continual classification task.
+
+Different number of  $K$ : In the continual structure infomax learning module, we can use the different number of these previous information structures  $K$  to constrain the structure of learned knowledge in the continual stage. As
+
+$K$  increases, there is a slight but smaller growth in the KR results, indicating that the structural information of the adjacent stages is adequately constrained for the current stage. This result can clearly show that it is possible to better mitigate catastrophic forgetting by imposing structural constraints on learned knowledge, but the demand for computational complexity and memory would increase significantly. Therefore, considering the performance and complexity of our method, we set  $K$  equal to 2 in our work.
+
+Different methods with similar starting performance: As shown in Table 4, we give the comparison results of the FCIL, FACT [37], and CEC [35] methods with similar performance in the initial/base stage. We can observe that the three metrics of the FCIL framework are superior to the other methods, which indicates that the FCIL framework can retain the learned knowledge better, and the improvement is not because of the base model performance but our introduced FCIL. It clearly verifies the superiority of the proposed FCIL framework in effectively learning new knowledge and mitigating catastrophic forgetting.
+
+# 5. Conclusion
+
+In this paper, we propose a Few-show Continual Informal Learning (FCIL) framework to address the few-shot class continual learning task. Our FCIL enables a deep model to continually/incrementally learn new concepts from a few labeled samples and meantime prevent the model from forgetting the previously learned knowl-
+
+edge. Inspired by the transfer entropy concept, a feature embedding infomax module is proposed by maximizing the mutual information between different level feature distributions and then grants the model to transfer the strong encoding capability of the base network into the new classes. Further, a continual structure infomax module is proposed to maximize the mutual information across these continually changing relations of the classes to resemble the continual learning progress, so that catastrophic forgetting could be well mitigated.
+
+# 6. Acknowledgement
+
+This work was supported by the National Natural Science Foundation of China (Grants Nos. 61972204, 62072244), the fundamental research funds for the central universities under Grant 30919011232, the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020LZH008, ZR2022LZH003), and in part by State Key Laboratory of High-end Server & Storage Technology.
+
+# References
+
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+[2] Mohamed Ishmael Belghazi, Aristide Baratin, Sai Rajeshwar, Sherjil Ozair, Yoshua Bengio, Aaron Courville, and Devon Hjelm. Mutual information neural estimation. In International Conference on Machine Learning, pages 531-540. PMLR, 2018. 2, 3  
+[3] Terry Bossomaier, Lionel Barnett, Michael Harre, and Joseph T Lizier. Transfer entropy. In An introduction to transfer entropy, pages 65-95. 2016. 3, 4  
+[4] Francisco M Castro, Manuel J Marín-Jiménez, Nicolas Guil, Cordelia Schmid, and Karteek Alahari. End-to-end incremental learning. In Proceedings of the European Conference on Computer Vision, pages 233-248, 2018. 6  
+[5] Ali Cheraghian, Shafin Rahman, Pengfei Fang, Soumava Kumar Roy, Lars Petersson, and Mehrtash Harandi. Semantic-aware knowledge distillation for few-shot class-incremental learning. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2021. 2  
+[6] Ali Cheraghian, Shafin Rahman, Sameera Ramasinghe, Pengfei Fang, Christian Simon, Lars Petersson, and Mehrtash Harandi. Synthesized feature based few-shot class incremental learning on a mixture of subspaces. In IEEE International Conference on Computer Vision, pages 8661-8670, 2021. 1  
+[7] Zhixiang Chi, Li Gu, Huan Liu, Yang Wang, Yuanhao Yu, and Jin Tang. Metastructuring: A meta-learning approach for few-shot class incremental learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 14166-14175, 2022. 1, 2, 6
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+[8] Songlin Dong, Xiaopeng Hong, Xiaoyu Tao, Xinyuan Chang, Xing Wei, and Yihong Gong. Few-shot class-incremental learning via relation knowledge distillation. 2021. 1  
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+[31] Xiaoyu Tao, Xiaopeng Hong, Xinyuan Chang, Songlin Dong, Xing Wei, and Yihong Gong. Few-shot class incremental learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 12183-12192, 2020. 1, 2, 5, 6  
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+[36] Wenting Zhao, Gongping Xu, Zhen Cui, Siqiang Luo, Cheng Long, and Tong Zhang. Deep graph structural infomax.
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+In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 4920-4928, 2023. 3  
+[37] Da-Wei Zhou, Fu-Yun Wang, Han-Jia Ye, Liang Ma, Shiliang Pu, and De-Chuan Zhan. Forward compatible few-shot class-incremental learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 9046–9056, 2022. 1, 2, 6, 8  
+[38] Kai Zhu, Yang Cao, Wei Zhai, Jie Cheng, and Zheng-Jun Zha. Self-promoted prototype refinement for few-shot class incremental learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 6801-6810, 2021. 1, 2
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+                                    "content": "In this work, we propose a novel Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to continually learn from a stream of few-shot labeled data. In general, the continual learning model would be trained with a large amount of labeled data in the initial learning stage, while few-shot samples of some unknown classes would be encountered in the continual learning process. Here we attempt to address the few-shot continual learning task from two aspects. First, inspired by the theoretical definition of transfer entropy, we attempt to transfer the strong encoding capability of the base network to promote few-shot continual learning. Specifically, we propose a feature embedding infomax learning to new concepts from a few labeled samples through maximizing the mutual information between different level feature distributions, where the convolutional representations and the feature embedding of new classes are encoded with these fixed convolution layers of the base network and newly increased parameters of fully-connected layer, respectively. Second, considering that the learned knowledge in the human brain is a generalization or abstraction of the actual information learned from these seen samples [10], we wish the continual learning model with a stable information structure that can be updated incrementally. Thus we propose a continual structure infomax learning mechanism to alleviate the catastrophic forgetting problem during the continual learning process. The structure relation of this learned information can be preserved through maximizing the mutual information across these continual-changing structure relations of inter-classes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
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+                                    "content": "In summary, our primary contributions can be summarized as follows: i) We propose a Few-shot Continual Infomax Learning (FCIL) framework that makes a deep model to incrementally learn new concepts from few labeled samples, relieving the catastrophic forgetting problem of previously learned ones. ii) Two specially-designed infomax learning mechanisms are proposed to address the few-shot continual learning problem with the help of mutual information maximization, including feature embedding infomax and continual structure infomax. iii) We validate the effectiveness of our proposed FCIL on three benchmarks (including CIFAR100, CUB200, and miniImageNet), and also demonstrate the superiority of our proposed FCIL when compared with existing state-of-the-art methods."
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+                                    "content": "learning with a stream of few-shot labeled data. A number of related works have been proposed to address the few-shot continual learning task. For example, Tao et al. [31] employed neural gas networks to perform incrementally learning for a series of new classes with few-shot data, with the goal of avoiding forgetting previously learned classes. Zhang et al. [35] proposed an evolving classifier based on graph attention networks that propagated information between classifiers by adding graph models. Also, pseudo-incremental training was proposed to optimize the graph module. The forward compatible training (FACT) [37] was proposed to effectively incorporate novel classes into forward compatible by generating virtual classes, where knowledge of old classes can be also maintained to reduce the catastrophic forgetting problem. A bi-level meta-learning-based optimization [7] was proposed to directly optimize the model towards forgetting alleviation of learned knowledge and adaptation of the new classes. In [20], a self-supervised stochastic classifier was proposed to deal with the few-shot class incremental learning task with the help of a self-supervision mechanism. Zhu et al. [38] proposed an incremental prototype learning scheme to perform continual learning, which was used to constrain the prototypes of new classes through the dynamic model and then achieved a reduction in catastrophic forgetting of knowledge. In order to offer a trade-off between accuracy and compute-memory cost of learning novel classes, the hyper-dimensional embedding was used to continually learn many more classes than the fixed dimensions in the feature space [14]. Further, few-shot lifelong learning was proposed to perform continual learning with only updating very few parameters of the model [26] or semantic-aware knowledge distillation [5]."
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+                                    "content": "Mutual information: Mutual Information as a quantity is used to measure the degree of interdependence between two random variables [21]. As it is difficult to exactly compute the mutual information between second-dimensional random variables, mutual information neural estimator (MINE) [2] can be achieved by employing the dual representations of the Kullback-Leibler divergence (KL) [9]. Subsequently, the Jensen-Shannon divergence (JSD) [27] and noise-contrastive estimation (NCE) [12] were used to estimate the mutual information with a learned network [16], and then the mutual information maximization method was used to improve the deep representation in an unsupervised learning way. The second-order deep multiplex infomax method [19] further extended the mutual information estimation to a three-variable calculation and was applied across multiple networks. The deep mutual information maximin method [25] was used to address the cross-modal clustering task by maximally preserving the shared information of multiple modalities and eliminating the superfluous information of individual modalities. In [1], mutual information networks are applied to unsupervised"
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+                                    "content": "classification tasks with excellent results. In the online continual learning task, Guo et al. [11] first used mutual information estimation to learn more robust features and preserve the past model learned from the previous task. Different from these previous methods, we perform continual infomax learning from the perspective of information entropy in the few-shot setting."
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+                                    "content": "3. The Proposed Method"
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+                                    "content": " as the training set, label set, and test set, respectively. Our task is to train the model with a continuous stream of labeled training sets "
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+                                    "content": " refers to the number of continual learning sessions. In the continual learning process, each training set is with no repetition of class labels, i.e., "
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+                                    "content": "In the few-shot continual learning task, there are two critical problems we need to consider: i) New classes are with a small amount of training data, which makes it hard to learn the feature embeddings for these new classes. ii) Catastrophic forgetting should be well relieved to preserve this learned knowledge in the continual learning process. In this work, we attempt to address them from two aspects. First, we start from the transfer entropy perspective [3] to obtain new knowledge from few-shot samples, where the strong encoding capability of the base network can be transferred to learn feature embeddings of these new classes. Second, considering that the learned knowledge in the human brain is not isolated, but exists in a certain relational structure [10], we wish to preserve the structure information of this learned knowledge to relieve the catastrophic forgetting problem during the continual learning process. With the help of the recently-developed mutual information estimation method [2, 16, 36], we achieve these above goals by performing continual infomax learning."
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+                                            "content": "). To transfer the strong encoding capability of the base network into the subsequent continual learning sessions, we first propose the feature embedding infomax to learn new knowledge with few-shot labeled data in the "
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+                                            "content": "-th session. Here we maximize the mutual information between multi-level convolutional representations "
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+                                            "type": "text",
+                                            "content": " of each input sample, which are encoded with these fixed convolution layers of the base network "
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+                                            "content": " and updated fully-connected layer "
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+                                            "type": "text",
+                                            "content": ", respectively. To address the catastrophic forgetting problem in the continual learning process, we further perform the continual structure infomax learning by maximizing the mutual information between current and previous inter-class knowledge structures (i.e., "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": ")."
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+                                    ]
+                                }
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+                            "index": 6,
+                            "angle": 0,
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+                    ],
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+                                    "content": "3.2. FCIL Paradigm"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "The proposed few-shot continual infomax learning (FCIL) framework is shown in Fig. 1. Generally, the base network "
+                                },
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+                                    "type": "text",
+                                    "content": ", which is a large-scale set of training samples "
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+                                    "type": "text",
+                                    "content": ", can optimize with the classic cross-entropy loss. For further improving the deep representation capability of the base network, we also employ self-supervised mutual information mechanism. Here the mutual information estimated network "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " can be well optimized in the initial stage (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "t = 1"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "), which contributes to the subsequent continual learning sessions. In the next continual learning sessions (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "), a stream of few-shot labeled data with new classes would be gradually fed into the network, and we would perform few-shot continual infomax learning for capturing new knowledge, without forgetting these learned ones. To improve the feature embedding capability of these new classes, we attempt to transfer the strong representation capability of the base network "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\Theta^{base}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " into the next continual learning sessions. Specifically, we introduce the feature embedding infomax learning to optimize these fully-connected parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}^{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of new classes. Given an input image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " from the few-shot set "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "D_{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we use the convolutional net optimized in the base stage to extract multi-level convolutional"
+                                }
+                            ]
+                        }
+                    ],
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+            ],
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+                                    "content": "features "
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+                                    "type": "inline_equation",
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+                                {
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+                                    "content": ", and get the feature embeddings from new full-connected layer "
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+                                {
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+                                    "type": "text",
+                                    "content": ". We maximize the mutual information between the convolutional and full-connected feature distributions for each input sample (i.e., "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "F_{fc}(x_i)"
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+                                {
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+                                    "type": "text",
+                                    "content": "), and thus the feature embedding of the novel classes can well inherit the powerful feature representation capability of the base network (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\max \\mathcal{T}_{\\Theta^{base} \\to \\Theta_{fc}^t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "). Further, to alleviate the catastrophic forgetting problem of this learned knowledge during the subsequent continual learning sessions, we introduce a continual structure infomax learning (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\max \\mathcal{D}_S"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ") to maintain/preserve the relations of intra-classes across one or more learning sessions. At each learning session "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "t"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we can obtain the first-order attributes and the second-order structure information of this learned knowledge, which refer to the class-wise feature embeddings and the relations among different classes, respectively. We then maximize the mutual information between the current information structure "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S(A^t, R^t)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and this previous information "
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+                                    "type": "inline_equation",
+                                    "content": "S(A^{t'}, R^{t'})"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " ("
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "t' = t - 1, t - 2, \\ldots, t - K"
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+                                {
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "t - K \\geqslant 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ") of these old classes. With the help of feature embedding infomax and continual structure infomax, the deep model can be well worked in the few-shot continual learning process. See the supplementary materia for more details."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.2.1 Feature Embedding Infomax"
+                                }
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+                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "When the base network "
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+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " faces unknown new classes, it is difficult to learn new concepts with only few-shot labeled samples. Inspired by the classic transfer entropy method which is a non-parametric measure of directed, asymmetric information transfer between two processes [3], we attempt to migrate the powerful feature representation capability of the base network to capture the feature embedding of the novel classes. Given few-shot training samples of new classes in the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "t"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-continual learning stage (i.e., "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "t > 1"
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+                                {
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+                                    "type": "text",
+                                    "content": "), the transfer entropy from the base network "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to the feature embedding layer of novel classes "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}^{t}"
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+                                {
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+                                    "type": "text",
+                                    "content": " (i.e., fully-connected model parameters) can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {T} _ {\\Theta^ {b a s e} \\rightarrow \\Theta_ {f c} ^ {t}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\left(H \\left(\\mathbf {Z} _ {f c}\\right) - H \\left(\\mathbf {Z} _ {f c} \\mid \\mathbf {Z} _ {c o n v}\\right)\\right), \\tag {1}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "X_{t} = \\{x_{1},x_{2},\\dots,x_{|X_{t}|}\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the training set of few-shot data in the "
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+                                {
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+                                    "type": "text",
+                                    "content": " -th continual learning session; "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{conv}(x_i)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the convolution representations of the training sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with the base encoding network "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "F_{fc}(x_{i})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the feature embedding of "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    ],
+                                    "type": "text",
+                                    "content": " with the fully-connected parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}^t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
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+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " of the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " -th continual learning stage. Let "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Z}_{conv} = F_{conv}(x_i)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Z}_{fc} = F_{fc}(x_i)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H(\\mathbf{Z}_{fc})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " refers to the Shannon entropy information of fully-connected feature of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " and the conditional entropy "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H(\\mathbf{Z}_{fc}|\\mathbf{Z}_{conv})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " is the entropy of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Z}_{conv}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " conditioned on "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Z}_{fc}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": ". To facilitate the calculation of Eqn. (1), the transfer entropy "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
+                                        289,
+                                        717
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{\\Theta^{base}\\to \\Theta_{fc}^t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        581,
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+                                        717
+                                    ],
+                                    "type": "text",
+                                    "content": " can be further"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
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+                        107
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "expressed as the conditional mutual information of different level features with the corresponding network parameters in the condition:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {T} _ {\\Theta^ {b a s e} \\rightarrow \\Theta_ {f c} ^ {t}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} I ((\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l})), \\\\ \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} \\hat {I} \\left(\\left(\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}\\right), \\vartheta^ {M I}\\right), \\tag {2} \\\\ \\end{array}",
+                                    "image_path": "b3b088fb070c202f442e48a0428ab508e2abe7e2a2f76376708a84a4e461b371.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                282
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                        282
+                                    ],
+                                    "type": "text",
+                                    "content": "here, we directly maximize the mutual information between multi-level convolutional features and fully-connected feature embedding, which can better transfer the strong encoding capability of the base network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        186,
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+                                        282
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta^{base}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        186,
+                                        545,
+                                        282
+                                    ],
+                                    "type": "text",
+                                    "content": " to the fully-connected layer "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        186,
+                                        545,
+                                        282
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        186,
+                                        545,
+                                        282
+                                    ],
+                                    "type": "text",
+                                    "content": ". With the support of the Kullback-Leibler divergence [9] and the learned mutual information estimation network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        186,
+                                        545,
+                                        282
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\vartheta^{MI}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        186,
+                                        545,
+                                        282
+                                    ],
+                                    "type": "text",
+                                    "content": ", the transfer entropy process can be approximately formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathcal {T}} = \\sum_ {i = 1} ^ {| X _ {t} |} \\sum_ {l = 1} ^ {L} \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}\\right), \\vartheta^ {M I}\\right)\\right) \\tag {3} \\\\ - \\log \\mathbb {E} (e ^ {\\mathcal {F} ((\\mathbf {Z} _ {f c}; \\mathbf {Z} _ {c o n v} ^ {l}), \\vartheta^ {M I})}). \\\\ \\end{array}",
+                                    "image_path": "b86802bb245b05e4c78b47c8a9258ea92978beea037837b23271a93c52b902ba.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "text",
+                                    "content": " is a discriminant function between features of different layers. Here this transfer entropy process can help to capture the feature embeddings of these few-shot training samples in the continual learning stages, thus we name it as \"feature embedding infomax\" learning process. The final learning objective to optimize the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th continual fully-connected layer "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is defined as: "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{FEI} = \\mathcal{L}_{CE} - \\alpha \\mathcal{L}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "text",
+                                    "content": " where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{CE}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
+                                        545,
+                                        453
+                                    ],
+                                    "type": "text",
+                                    "content": " is the classic cross-entropy loss and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
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+                                        453
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        345,
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+                                        453
+                                    ],
+                                    "type": "text",
+                                    "content": " is a hyper-parameter."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2.2 Continual Structure Infomax"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Another critical problem for a continual learning model is exiting the catastrophic forgetting this learned knowledge when discarding old samples. An obvious solution is that continual learning must have a strategy to preserve the information related to these old training samples. Usually, the information preserved in a continual learning system is a generalization or abstraction of the actual information embedded in the learned samples. The knowledge we learn in the human brain [10] does not exist in isolation; there is some kind of relational structure between different pieces of knowledge that maintains the connection between knowledge. In order to possess an information structure that would be updated incrementally along the continual learning process, we can preserve useful information from learned samples as much as possible so that the subsequent continual learning process can be guided by this information. Therefore, we propose a continual structure infomax learning to conserve both first-order and second-order information in the continual learning process, which can be"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "19227"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
+            "page_size": [
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+            ],
+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "related to class-wise individual attributions and intra-class relations, respectively. In the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th continual learning session, the continual structure infomax can be performed under the guidance of these previous information structures:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {D} _ {S} = \\sum_ {k = 1} ^ {K} \\underbrace {H \\left(A _ {t}\\right) - H \\left(A _ {t} \\mid A _ {t - k}\\right)} _ {\\text {f i r s t - o r d e r}} + \\underbrace {H \\left(R _ {t}\\right) - H \\left(R _ {t} \\mid R _ {t - k}\\right)} _ {\\text {s e c o n d - o r d e r}} \\tag {4}",
+                                    "image_path": "caa68a92829d8c30aefe13e558d0973577a6bc068278d7c38f571959db632a12.jpg"
+                                }
+                            ]
+                        }
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+                    "index": 1
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+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of previous sessions with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t - K \\geq 1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
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+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t - k}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " refer to the feature embeddings of all learned classes "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", e.g., "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t} = [e_{1}, e_{2}, \\ldots, e_{c}, \\ldots, e_{c_{t}}]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": ". Due to the fact that the mean value of each class is approximate to the parameter weights of the last fully-connected layer, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " is achieved by the weight parameters of the last classification layer corresponding to the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th class. Their corresponding information entropy "
+                                },
+                                {
+                                    "bbox": [
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+                                        171,
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+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                        171,
+                                        289,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t - k}"
+                                },
+                                {
+                                    "bbox": [
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+                                        171,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are represented as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H(A_{t})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H(A_{t}|A_{t - k})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
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+                                        171,
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+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{t} \\in \\mathbb{R}^{c_{t} \\times c_{t}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{t - k} \\in \\mathbb{R}^{c_{t - k} \\times c_{t - k}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " refer to the inter-class relation matrices of all learned classes in the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(t - k)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": "-th stages. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H(R_{t})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H(R_{t}|R_{t - k})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "text",
+                                    "content": " represent the second-order information entropy concerning the relation among different classes. Through maximizing the first-order and second-order mutual information between different learning stages, the network parameters of the last fully-connected layer "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
+                                        289,
+                                        374
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        171,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be incrementally updated along the continual learning process, formally,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {D} _ {S} = \\sum_ {k = 1} ^ {K} \\underbrace {I (A _ {t} ; A _ {t - k})} _ {\\text {f i r s t - o r d e r}} + \\underbrace {I (R _ {t} ; R _ {t - k})} _ {\\text {s e c o n d - o r d e r}}, \\\\ \\geq \\sum_ {k = 1} ^ {K} \\underbrace {\\hat {I} \\left(\\left(A _ {t} ; A _ {t - k}\\right) , \\vartheta^ {M I}\\right)} _ {\\text {f i r s t - o r d e r}} + \\underbrace {\\hat {I} \\left(\\left(R _ {t} ; R _ {t - k}\\right) , \\vartheta^ {M I}\\right)} _ {\\text {s e c o n d - o r d e r}}, \\tag {5} \\\\ \\end{array}",
+                                    "image_path": "517bf616594b3bc8cd577dc71d3738f087d57b239d063abf3c270369e10aa731.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Similar to the feature embedding infomax, we also use mutual information to measure the amount of information shared by different sessions, and this continual structure infomax process can be further formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "bbox": [
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+                                        510,
+                                        299,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {S} = \\sum_ {k = 1} ^ {K} \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(A _ {t}; A _ {t - k}\\right), \\vartheta^ {M I}\\right)\\right) - \\log \\mathbb {E} \\left(e ^ {\\mathcal {F} \\left(\\left(A _ {t}; A _ {t - k}\\right), \\vartheta^ {M I}\\right)}\\right) \\\\ + \\mathbb {E} \\left(\\mathcal {F} \\left(\\left(R _ {t}; R _ {t - k}\\right), \\vartheta^ {M I}\\right)\\right) - \\log \\mathbb {E} \\left(e ^ {\\mathcal {F} \\left(\\left(R _ {t}; R _ {t - k}\\right), \\vartheta^ {M I}\\right)}\\right), \\tag {6} \\\\ \\end{array}",
+                                    "image_path": "91d796654109e7f0f31b5410368817d6427ade8180e500669fa398ead64ac850.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                        570,
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+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " refers to the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th session with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1 \\leqslant k \\leqslant K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We employ both "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_S"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{CE}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " to optimize the fully-connected parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta_{fc}^t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " to adapt new classes without forgetting these learned ones. In the structure continual infomax process, the corresponding loss is defined as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{CSI} = \\mathcal{L}_{CE} - \\gamma \\mathcal{L}_S"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                        641
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                        641
+                                    ],
+                                    "type": "text",
+                                    "content": " is a balance factor."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.1. Experimental Setup"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Datasets: We evaluate our FCIL on three public datasets, including CIFAR100 [22], miniImageNet [29],"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "and CUB200 [33]. For CIFAR100 [22] and miniImageNet [29], we use all the training data of the 60 base classes to train a base network, and the 40 new classes are used to perform eight 5-way 5-shot continual learning tasks. We divide the 200 classes of CUB200 [33] into 100 base classes and 100 new classes. The 100 new classes are used to perform ten 10-way 5-shot continual learning tasks. We follow the same split setting of FSCIL [31] as other methods in the three datasets for a fair comparison. See the supplementary materia for more details."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        193,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Implementation Details: Following FSCIL [31], we use ResNet20 as the backbone on CIFAR100 [22] and ResNet18 is used as the backbone on miniImageNet [29] and CUB200 [33]. The network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
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+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\vartheta^{MI}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
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+                                    ],
+                                    "type": "text",
+                                    "content": " consists of a convolution branch and a linear branch, where the former consists of three convolution layers whose kernel sizes are 1, 5, and 7, and the latter is one linear layer. In the CSI module, the convolution branch and the linear branch separately take "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{conv}^{l}(x_{i})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
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+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{fc}(x_{i})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " as inputs, and their outputs are used to compute "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ". In the CSI module, the linear layer of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\vartheta^{MI}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " separately take "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{t - k}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " as inputs, and we use the outputs to compute "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": ". In the base learning stage, we train the base network and the mutual information network with the first training set. The parameters of the convolutional layers "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta^{base}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " and the mutual information network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\vartheta^{MI}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "text",
+                                    "content": " are frozen in the continual learning sessions to perform mutual information estimation in both the proposed feature embedding infomax. For all datasets, we set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        193,
+                                        546,
+                                        529
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as 0.015 and 0.03, respectively. Random cropping, random scaling, and random horizontal flipping are used for training data. We use to evaluate our proposed method from different perspectives. \"Acc_t\" represents to the Top-1 accuracy in the t-th continual session. \"Avg\" represents for an average score, i.e., "
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+                                    "type": "text",
+                                    "content": ". \"ΔFinal\" represents the difference value of "
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+                                    "type": "text",
+                                    "content": " between our method and the compared method in the final state. \"KR\" is the knowledge retention rate, i.e., "
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+                                    "content": "\\mathrm{Acc}_T / \\mathrm{Acc}_1"
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+                                    "type": "text",
+                                    "content": ". All the experiments are conducted with the Pytorch framework on one Geforce 2080Ti GPU."
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+                                    "content": "4.2. Comparison with state-of-the-art methods"
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+                                    "content": "We first compare our proposed FCIL with other state-of-the-art methods on the challenging miniImageNet dataset [29]. The detailed results have been listed in Table 1, and the accuracy changing curves with growing continual sessions are plotted in Fig. 2 (a). Our proposed FCIL outperforms all other compared methods by a great margin and sets new state-of-the-art. In particular, our FCIL achieves the best score among all the methods. Considering that in the first continual session, very little data are available and it requires borrowing the learning capability of the base stage into this session to promote the classifier accuracy. In addition, as to the overall performance in the final continual session, our FCIL also surpasses the second best method C-"
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+                                            "content": "Table 1. Few-shot continual classification performance of state-of-the-art methods and our FCIL on the miniImageNet dataset [29]. The results with * are obtained from the authors' published code. See the supplementary materia for results of other datasets."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"10\">Accuracy in each session (%)↑</td><td>KR↑</td><td>ΔFinal↑</td><td>Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>Ft-CNN</td><td>61.31</td><td>27.22</td><td>16.37</td><td>6.08</td><td>2.54</td><td>1.56</td><td>1.93</td><td>2.60</td><td>1.40</td><td>2.28</td><td>+51.36</td><td>13.44</td><td></td></tr><tr><td>iCaRL [28]</td><td>61.31</td><td>46.32</td><td>42.94</td><td>37.63</td><td>30.49</td><td>24.00</td><td>20.89</td><td>18.80</td><td>17.21</td><td>28.07</td><td>+35.55</td><td>33.29</td><td></td></tr><tr><td>EEIL [4]</td><td>61.31</td><td>46.58</td><td>44.00</td><td>37.29</td><td>33.14</td><td>27.12</td><td>24.10</td><td>21.57</td><td>19.58</td><td>31.93</td><td>+33.18</td><td>34.97</td><td></td></tr><tr><td>TOPIC [31]</td><td>61.31</td><td>50.09</td><td>45.17</td><td>41.16</td><td>37.48</td><td>35.52</td><td>32.19</td><td>29.46</td><td>24.42</td><td>39.83</td><td>+28.34</td><td>39.65</td><td></td></tr><tr><td>NCM [17]</td><td>61.31</td><td>47.80</td><td>39.31</td><td>31.91</td><td>25.68</td><td>21.35</td><td>18.67</td><td>17.24</td><td>14.17</td><td>23.11</td><td>+38.59</td><td>30.83</td><td></td></tr><tr><td>Decoupled-NegCosine [24]</td><td>71.68</td><td>66.64</td><td>62.57</td><td>58.82</td><td>55.91</td><td>52.88</td><td>49.41</td><td>47.50</td><td>45.81</td><td>63.90</td><td>+6.95</td><td>56.80</td><td></td></tr><tr><td>Decoupled-Cosine [32]</td><td>70.37</td><td>65.45</td><td>61.41</td><td>58.00</td><td>54.81</td><td>51.89</td><td>49.10</td><td>47.27</td><td>45.63</td><td>64.84</td><td>+7.13</td><td>55.99</td><td></td></tr><tr><td>Decoupled-DeepEMD [34]</td><td>69.77</td><td>64.59</td><td>60.21</td><td>56.63</td><td>53.16</td><td>50.13</td><td>47.79</td><td>45.42</td><td>43.41</td><td>62.21</td><td>+9.35</td><td>54.57</td><td></td></tr><tr><td>MateFSCIL [7]</td><td>72.04</td><td>67.94</td><td>63.77</td><td>60.29</td><td>57.58</td><td>55.16</td><td>52.90</td><td>50.79</td><td>49.19</td><td>68.28</td><td>+3.57</td><td>58.85</td><td></td></tr><tr><td>C-FSCIL Model1 (d=512) [15]</td><td>76.37</td><td>70.94</td><td>66.36</td><td>62.64</td><td>59.31</td><td>56.02</td><td>53.14</td><td>51.04</td><td>48.87</td><td>63.99</td><td>+3.89</td><td>60.52</td><td></td></tr><tr><td>C-FSCIL Mode2 (d=512) [15]</td><td>76.45</td><td>71.23</td><td>66.71</td><td>63.01</td><td>60.09</td><td>56.73</td><td>53.94</td><td>52.01</td><td>50.08</td><td>65.50</td><td>+2.68</td><td>61.14</td><td></td></tr><tr><td>C-FSCIL Mode3 (d=512) [15]</td><td>76.40</td><td>71.14</td><td>66.46</td><td>63.29</td><td>60.42</td><td>57.46</td><td>54.78</td><td>53.11</td><td>51.41</td><td>67.29</td><td>+1.35</td><td>61.61</td><td></td></tr><tr><td>FACT* [37]</td><td>75.68</td><td>70.65</td><td>66.53</td><td>62.75</td><td>59.39</td><td>56.19</td><td>53.26</td><td>51.10</td><td>49.48</td><td>65.38</td><td>+3.28</td><td>60.56</td><td></td></tr><tr><td>FACT* + FCIL</td><td>76.21</td><td>70.92</td><td>66.69</td><td>63.23</td><td>60.73</td><td>57.88</td><td>54.08</td><td>52.17</td><td>50.34</td><td>66.05</td><td>+2.42</td><td>61.36</td><td></td></tr><tr><td>CEC [35]</td><td>72.00</td><td>66.83</td><td>62.97</td><td>59.43</td><td>56.70</td><td>53.73</td><td>51.19</td><td>49.24</td><td>47.63</td><td>66.15</td><td>+5.13</td><td>57.75</td><td></td></tr><tr><td>CEC + FCIL</td><td>72.87</td><td>68.23</td><td>64.46</td><td>60.64</td><td>57.71</td><td>55.12</td><td>52.79</td><td>50.65</td><td>48.62</td><td>66.72</td><td>+4.14</td><td>59.01</td><td></td></tr><tr><td>FCIL (Ours)</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>-</td><td>62.37</td><td></td></tr></table>",
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+                                    "content": ". It shows that our FCIL could keep great learning capability when performing the continual learning process, and we owe the superiority to the strong capability borrowed from the base network by the proposed feature embedding infomax module. Further, our method also achieves the best performance on Avg, outperforming the compared methods by at least "
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+                                    "content": ". It indicates that our FCIL could always obtain better performance during all the continual sessions, further demonstrating the strong learning capability borrowed from the base network. Overall, the superior performances of our FCIL in terms of Avg and "
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+                                    "content": "Final sufficiently verify the effectiveness of our proposed feature embedding infomax module on enhancing the learning capability of new classes. Besides, we integrate our proposed FCIL mechanisms into the FACT [37] and CEC [35] frameworks (i.e., FACT+FCIL and CEC+FCIL), and the compared results show that we can lead to significant improvements of "
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+                                    "content": ". Since KR represents the accuracy ratio of the final continual session and the base stage, a larger KR value means that less learned knowledge is forgotten. Compared with previous methods such as CEC [35], FACT [37], C-FSCIL [15] which also freeze the base classifier as our FCIL to avoid catastrophic forgetting, our FCIL still outperforms them by a considerable margin. It means that the relationship preserving capability brought by the proposed continual structure infomax module could better preserve the previously learned knowledge. It clearly validates the effectiveness of our proposed continual structure infomax module in mitigating the catastrophic forgetting problem. As a whole, the superior performance clearly verifies the superiority of our proposed FCIL in learning novel class knowledge as well as mitigating the catastrophic forgetting problem. The accuracy changing curves with growing continual sessions in Fig. 2(a) further visually show the superiority of our FCIL. We further plot the accuracy changing curves on the CIFAR100 [22] and CUB200 [33] datasets separately in Fig. 2(b) and Fig. 2(c). It could be observed that our proposed FCIL also achieves the best performances on the two datasets, and it further ver"
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+                                            "content": "Table 2. Overall ablation study of the proposed method on the miniImageNet dataset. Feature embedding infomax (FEI) and continual structure infomax (CSI) are the two functional modules we proposed."
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+                                            "html": "<table><tr><td rowspan=\"2\">Base</td><td rowspan=\"2\">FEI</td><td rowspan=\"2\">CSI</td><td colspan=\"9\">Accuracy in each session (%)↑</td><td rowspan=\"2\">KR</td><td rowspan=\"2\">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>✓</td><td></td><td></td><td>75.87</td><td>70.22</td><td>65.92</td><td>62.64</td><td>59.96</td><td>57.11</td><td>54.58</td><td>52.66</td><td>51.49</td><td>67.86</td><td>61.16</td></tr><tr><td>✓</td><td>✓</td><td></td><td>76.34</td><td>71.18</td><td>67.16</td><td>63.85</td><td>61.05</td><td>58.23</td><td>55.33</td><td>53.67</td><td>52.32</td><td>68.54</td><td>62.13</td></tr><tr><td>✓</td><td></td><td>✓</td><td>75.87</td><td>70.16</td><td>65.76</td><td>63.76</td><td>60.34</td><td>57.52</td><td>54.96</td><td>53.06</td><td>52.06</td><td>68.61</td><td>61.39</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr></table>",
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+                                            "content": "Figure 3. Confusion matrix of the final classification results on the miniImageNet dataset [29]. (a) Baseline. (b) Our FCIL. We used red lines to partition the region of the base class and the new class. Our method improves the predictive power of the network which reduces the scattered confusion matrix."
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+                                    "content": "ifies the superiority of our proposed feature embedding infomax and continual structure infomax modules in learning novel class knowledge and meantime mitigating the catastrophic forgetting problem."
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+                                    "content": "All ablation studies are performed on the miniImageNet dataset [29] to evaluate the effectiveness of our proposed modules as well as some experimental settings."
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+                                    "content": "Effectiveness of the proposed modules: We first conduct experiments to analyze the effectiveness of our proposed feature embedding infomax (FEI) and continual structure infomax (CSI) modules. The detailed results are listed in Table 2. In continual learning sessions "
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+                                    "content": ", the feature embedding infomax module is added to maximize the mutual information between the convolutional features produced by the fixed base backbone and the embedding features from the newly updated classifier. The performance improves over the baseline by "
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+                                    "content": " on Avg and KR, demonstrating that the proposed feature embedding infomax module could well transfer the strong learning capability of the base network into the following continual sessions to enhance the learning capability of the model on novel classes. It verifies the effectiveness of our proposed feature embedding the infomax module. The continual structure infomax learning module is conducted to maximize the mutual information between the current information structure and the previous ones. The performance promotion of the CSI model seems not significant in the early stages, since CSI is designed to alleviate catastrophic"
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+                                    "content": "forgetting, and in the early stages (i.e., "
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+                                    "content": ") the few new classes only pose limited influence on the learned knowledge. Further, with new classes increased in the later stages, the performance gain of CSI greatly increases. It achieves performance promotions of "
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+                                    "content": " separately on KR and Avg, which are clearly non-trivial. It shows that our proposed continual structure infomax module could well preserve the learned knowledge of the previous classes to mitigate the catastrophic forgetting issue. We believe it is because the attributes and class relationships could be well preserved during the continual sessions, and it verifies the effectiveness of the proposed continual structure infomax module. Finally, when both modules are applied, the performances could be further boosted to form a new state-of-the-art performance, quantitatively verifying the effectiveness of our proposed FCIL framework."
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+                                    "content": "We further plot the confusion matrix of the baseline and our FCIL in Fig. 3. It could be observed that in the new classes, the diagonal of our FCIL has a darker color than the baseline model, vividly showing that the proposed FCIL is more powerful at learning new classes. In addition, it also indicates that the prediction distribution of FCIL on new classes is more concentrated than the baseline model, and it visually demonstrates the superiority of our FCIL in preserving learned knowledge."
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+                                    "content": "Different methods for MI estimation and relation construction: The mutual information (MI) estimation ways can be adopted with the support of JSD [27] or KL [9], i.e., \"MIJSD\" and \"MIKL\". We achieve the information related in the continual structure infomax module with KNN or Cosine distance, named: "
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+                                    "content": "\\mathrm{R_{KNN}}"
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+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{R_{Cos}}"
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+                                    "type": "text",
+                                    "content": ". The FCIL results with the above different methods are listed in Table 3, and it could be observed that the performance of the four variants changes little. It means that it is the proposed structure preserve mechanism rather than the specifically chosen functions that mitigate the catastrophic forgetting problem. Therefore, we adopt KL to estimate the mutual information and use the Cosine distance to build the relationship between different classes in our work."
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+                                    "content": "The level of convolutional Feature "
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+                                    "content": ": When performing the feature embedding infomax learning, we can estimate mutual information by using more layers of convolutional features "
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+                                    "content": ". To study the effect of different level sets, we construct three variants of FCIL by separately setting "
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+                                            "content": "Table 3. The results with different methods for MI estimation and relation construction on the miniImageNet dataset."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td colspan=\"9\">Accuracy in each session (%)↑</td><td rowspan=\"2\">KR</td><td rowspan=\"2\">Avg</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>MI_KL + R_KNN</td><td>76.34</td><td>71.40</td><td>67.07</td><td>64.05</td><td>61.29</td><td>58.51</td><td>55.73</td><td>54.07</td><td>52.74</td><td>68.08</td><td>62.35</td></tr><tr><td>MI_KL + R_Cos</td><td>76.34</td><td>71.40</td><td>67.10</td><td>64.08</td><td>61.30</td><td>58.51</td><td>55.72</td><td>54.08</td><td>52.76</td><td>69.11</td><td>62.37</td></tr><tr><td>MI_JSD + R_KNN</td><td>76.34</td><td>71.34</td><td>67.03</td><td>64.0</td><td>61.28</td><td>58.52</td><td>55.7</td><td>54.03</td><td>52.7</td><td>69.03</td><td>62.32</td></tr><tr><td>MI_JSD + R_Cos</td><td>76.34</td><td>71.26</td><td>66.99</td><td>64.03</td><td>61.24</td><td>58.46</td><td>55.65</td><td>53.98</td><td>52.63</td><td>68.94</td><td>62.28</td></tr></table>",
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+                                            "content": "Table 4. The comparison results between our FCIL and the open-source methods FACT [37] and CEC [35] by fixing the performance of the base classes on the miniImageNet dataset [29]."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"9\">Accuracy in each session (%) ↑</td><td rowspan=\"2\">KR↑</td><td rowspan=\"2\">ΔFinal↑</td><td rowspan=\"2\">Avg↑</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td>CEC [35]</td><td>72.57</td><td>66.48</td><td>62.74</td><td>59.46</td><td>56.67</td><td>53.68</td><td>51.12</td><td>49.23</td><td>47.58</td><td>65.56</td><td>+1.16</td><td>57.73</td></tr><tr><td>FACT [37]</td><td>72.73</td><td>67.73</td><td>63.77</td><td>60.29</td><td>57.25</td><td>54.07</td><td>51.17</td><td>49.31</td><td>47.91</td><td>65.87</td><td>+0.83</td><td>58.25</td></tr><tr><td>FCIL(Ours)</td><td>72.63</td><td>67.71</td><td>63.70</td><td>60.67</td><td>57.61</td><td>54.73</td><td>52.09</td><td>50.26</td><td>48.74</td><td>66.94</td><td></td><td>58.71</td></tr></table>",
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+                                            "content": "Figure 6. Performance comparison with different number of "
+                                        },
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+                                    "type": "text",
+                                    "content": "ing accuracy changing bars are plotted in Fig. 4. It can be observed that the three variants change make little performance change. Further, it is worth noting that when employing all the levels of features (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "L = \\{1,2,3\\}"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "), it could obtain better results than the other two variants, and all three convolutional features have been used. It means that our proposed feature embedding infomax module is able to continually transfer more useful encoding capabilities from multi-level convolutional features. It sufficiently validates the strong power of the feature embedding infomax module on transferring the encoding capability of the base network to the newly learned classifiers."
+                                }
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+                                    "type": "text",
+                                    "content": "The shot number in the continual learning: We plot the accuracy changing curves with different shot numbers in Fig. 5. It shows that more sample shots could result in better few-shot continual classification performance. The reason is more shots could bring better class attribute distribution as well as more accurate class relations to benefit the learned new knowledge. Further, when the shot number is more than 15, the performance promotion becomes trivial. It shows that we only need a proper number of newly labeled samples to achieve satisfactory performances, verifying the effectiveness of our FCIL framework in addressing the few-shot continual classification task."
+                                }
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+                                    "type": "text",
+                                    "content": ": In the continual structure infomax learning module, we can use the different number of these previous information structures "
+                                },
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+                                    "type": "text",
+                                    "content": " to constrain the structure of learned knowledge in the continual stage. As"
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+                                    "type": "text",
+                                    "content": " increases, there is a slight but smaller growth in the KR results, indicating that the structural information of the adjacent stages is adequately constrained for the current stage. This result can clearly show that it is possible to better mitigate catastrophic forgetting by imposing structural constraints on learned knowledge, but the demand for computational complexity and memory would increase significantly. Therefore, considering the performance and complexity of our method, we set "
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+                                    "type": "text",
+                                    "content": " equal to 2 in our work."
+                                }
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+                                    "type": "text",
+                                    "content": "Different methods with similar starting performance: As shown in Table 4, we give the comparison results of the FCIL, FACT [37], and CEC [35] methods with similar performance in the initial/base stage. We can observe that the three metrics of the FCIL framework are superior to the other methods, which indicates that the FCIL framework can retain the learned knowledge better, and the improvement is not because of the base model performance but our introduced FCIL. It clearly verifies the superiority of the proposed FCIL framework in effectively learning new knowledge and mitigating catastrophic forgetting."
+                                }
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
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+                                    "type": "text",
+                                    "content": "In this paper, we propose a Few-show Continual Informal Learning (FCIL) framework to address the few-shot class continual learning task. Our FCIL enables a deep model to continually/incrementally learn new concepts from a few labeled samples and meantime prevent the model from forgetting the previously learned knowl-"
+                                }
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+                                    "type": "text",
+                                    "content": "edge. Inspired by the transfer entropy concept, a feature embedding infomax module is proposed by maximizing the mutual information between different level feature distributions and then grants the model to transfer the strong encoding capability of the base network into the new classes. Further, a continual structure infomax module is proposed to maximize the mutual information across these continually changing relations of the classes to resemble the continual learning progress, so that catastrophic forgetting could be well mitigated."
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+                                    "content": "This work was supported by the National Natural Science Foundation of China (Grants Nos. 61972204, 62072244), the fundamental research funds for the central universities under Grant 30919011232, the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020LZH008, ZR2022LZH003), and in part by State Key Laboratory of High-end Server & Storage Technology."
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diff --git a/2023/Fg-T2M_ Fine-Grained Text-Driven Human Motion Generation via Diffusion Model/449cb3f1-1251-409f-b17a-0a1369fa81f7_content_list.json b/2023/Fg-T2M_ Fine-Grained Text-Driven Human Motion Generation via Diffusion Model/449cb3f1-1251-409f-b17a-0a1369fa81f7_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..3c98c3bb90df6c5382c6a164199d3e6b228de431
--- /dev/null
+++ b/2023/Fg-T2M_ Fine-Grained Text-Driven Human Motion Generation via Diffusion Model/449cb3f1-1251-409f-b17a-0a1369fa81f7_content_list.json	
@@ -0,0 +1,1500 @@
+[
+    {
+        "type": "text",
+        "text": "Fg-T2M: Fine-Grained Text-Driven Human Motion Generation via Diffusion Model",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Yin Wang $^{1}$ , Zhiying Leng $^{1,2}$ , Frederick W. B. Li $^{3}$ , Shun-Cheng Wu $^{2}$ , Xiaohui Liang $^{1,4,*}$",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China",
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+        ],
+        "page_idx": 0
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+    {
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+        "text": "$^{2}$ Technical University of Munich, Germany",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{3}$ Department of Computer Science, University of Durham, U.K.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{4}$ Zhongguancun Laboratory, Beijing, China.",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{wang_yin, zhiyingleng, liang_xiaohui}@buaa.edu.cn, frederick.li@durham.ac.uk, shuncheng.wu@tum.de",
+        "bbox": [
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+        "text": "Abstract",
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+    {
+        "type": "text",
+        "text": "Text-driven human motion generation in computer vision is both significant and challenging. However, current methods are limited to producing either deterministic or imprecise motion sequences, failing to effectively control the temporal and spatial relationships required to conform to a given text description. In this work, we propose a fine-grained method for generating high-quality, conditional human motion sequences supporting precise text description. Our approach consists of two key components: 1) a linguistics-structure assisted module that constructs accurate and complete language feature to fully utilize text information; and 2) a context-aware progressive reasoning module that learns neighborhood and overall semantic linguistics features from shallow and deep graph neural networks to achieve a multi-step inference. Experiments show that our approach outperforms text-driven motion generation methods on HumanML3D and KIT test sets and generates better visually confirmed motion to the text conditions.",
+        "bbox": [
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+    {
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+        "text": "1. Introduction",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Human motion generation is a crucial task in computer vision with various applications in animation production, gaming, robot control, and movie script visualization. Obtaining human motion sequences through traditional software is a labor-intensive and tedious process, while motion capture is complex and expensive. Recently, with the advancements in deep learning and computer vision, learning-based human motion generation has emerged as a solution to this problem, leading to the development of associated generation methods based on multimodal data. The input multimodal data include music [12, 15, 25, 27], motion cat",
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+        "page_idx": 0
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+        "img_path": "images/c2a121fb0b5673d6bbb73d2f203b85aec87b6d8592be93acffaaff573ef271cb.jpg",
+        "image_caption": [
+            "Figure 1: Our approach generates human motion sequences that grasp fine-grained details."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
+        "type": "text",
+        "text": "egories [4, 9, 20], text [2, 3, 5, 7, 8, 16, 21, 23, 28, 33], among others. Text-driven human motion generation has been a popular research topic, because of its convenience and human-friendliness. In particular, natural language comprises nouns, verbs, adverbs, etc. The mutual connections among different words in a sentence establish its semantics. Verbs define the action's category, while adverbs control the fineness of the action. The interaction between words in syntax plays a vital role in determining the structure and meaning of a sentence. Failure to fully incorporate these text features may result in inadequate text modeling, causing the generated motion sequence to deviate from the intended meaning of the original text.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing methods can be divided into two branches, including 1) cross-modal alignment of motion and text [2, 3, 5, 7, 8, 16, 21]; 2) conditional diffusion models [28, 33]. In the first methods, text sequences and motion sequences are mapped onto separate feature spaces and forcibly aligned, leading to a loss of original information from both domains. In the second methods, the diffusion model incorporates",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "22035",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "text information as a conditioning factor to learn the probability mapping of human motions. However, the model interacts with only one text feature at each time step of the inference process, lacking a progressive approach. Moreover, text modeling only involves simple manipulation, which ignores the importance of certain fine-grained words and leads to incomplete semantic understanding, making it challenging to learn focus points at each step. Overall, existing methods only use text information to a limited extent, which in turn affects the accuracy of motion generation based on the corresponding text content, especially for the motion in which texts contain fine-grained words. For instance, comprehending the sentence \"A man is walking forward while waving his right hand\" can be a difficult task, and expecting the model to grasp the fine-grained meaning of the terms \"while\" and \"right hand\" is even more demanding.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To tackle the aforementioned issues, we propose a fine-grained text-driven method for generating human motion sequences that precisely align with text prompts in Figure 1. Typically, people initially read a sentence to gain an overall semantic understanding before focusing on the fine-grained details of individual words. To replicate this process, our method includes a linguistics-structure assisted module and a context-aware progressive reasoning module to fully utilize text information. Firstly, we utilize linguistics structure to facilitate information exchange between each text word. We use dependency parsing [19] to analyze the relationships among words in each sentence and construct a dependency tree, allowing each node to effectively communicate based on its dependent nodes and relationships. Then, the dependency tree nodes are passed to multi-layer graph neural networks to learn information aggregation. The multilayer graph neural networks allow shallow network to learn neighborhood features as it can comprehend nearby details, and allow deep network to grasp overall semantic features because it is capable of aggregating information from entire nodes. Additionally, our GAT captures rich inter-word relationships while preserving the text linguistics structure by designing adaptive weights for each part-of-speech and dependency relation due to their distinctive role in the Text to Motion (T2M) task.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Secondly, achieving the purpose of fine-grained interaction, context-aware progressive reasoning module performs a multi-step inference process with the progressive fusion of global and local information between text and motion, which is unprecedented in the T2M task. This involves utilizing hierarchical semantic features to simulate the way humans comprehend sentences. We adopt the diffusion model framework and stack the hierarchical semantic features obtained from deep to shallow networks at each step to capture high-order relationships at different semantic levels. We evaluate our method on HumanML3D dataset [7] and KIT dataset [22]. Experiments show that our approach out",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "performs the state-of-the-art methods and generates better visual motion. Our main contributions include:",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- To the best of our knowledge, we are the first to bring NLP methods into T2M task. Utilizing the structured understanding of the natural language prompts to help T2M models achieve better reasoning skills, which brings new ideas for the text-to-X community from a textual perspective.",
+            "- We propose the Linguistics-Structure Assisted Module (LSAM), which utilizes a dependency parsing tree and graph networks to facilitate effective information exchange and data aggregation. It can obtain both neighborhood and overall semantic linguistic features.",
+            "- We propose a Context-Aware Progressive Reasoning Module (CAPR) that implements a multi-step progressive inference strategy within the diffusion model framework, mimicking the human reading process by moving from global to local relationships.",
+            "- Experimental results demonstrate that our proposed method outperforms previous methods, and achieves competitive performance on the HumanML3D and KIT datasets."
+        ],
+        "bbox": [
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+            131,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            474,
+            640,
+            491
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Motion generation model",
+        "text_level": 1,
+        "bbox": [
+            500,
+            500,
+            728,
+            515
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Generative models play a crucial role in motion synthesis by generating high-quality human motion. Generative Adversarial Nets (GAN) [6] use two sub-models: a generator model that produces new samples, and a discriminator model that attempts to classify samples as either real or fake. These two models compete against each other during training. However, the interpretability of GAN is poor because the learned data distribution lacks an explicit expression, resembling a black box mapping function.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Auto-Encoding Variational Bayes (VAE) [13] is a widely used generative model in motion synthesis. Its primary objective is to generate new samples from the learned distribution of objects by learning latent attributes from the probability distribution of the latent variable space, thereby constructing new examples. Despite its usefulness, the quality of samples generated by VAE can be improved.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently proposed diffusion models [10, 18, 26] have shown immense potential in modeling and present an exciting opportunity to expand into text-driven motion generation. These models utilize the stochastic diffusion process modeled in thermodynamics, which gradually adds noise to the samples of the data distribution. The deep learning model then learns the reverse process of denoising the samples gradually. Diffusion models have the advantage over previous models as they do not make any assumptions about",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "22036",
+        "bbox": [
+            478,
+            945,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "the target distribution, leading to a more diverse generation and better suitability for our task. Therefore, we propose a novel fine-grained human motion generation method that employs the Denoising Diffusion Probability Model [10].",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Text-driven human motion generation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            176,
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+            193
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The task of text-driven human motion generation involves generating 3D human motion sequences that conform to a textual description. Several previous works have tackled this task. Initially, Text2Action [1] proposed short-text conditioned motion generation based on an RNN model. Subsequently, Ahuja et al. [2] and Ghosh et al. [5] focused on creating a joint representation of text and motion by projecting both features into a shared latent space. However, these methods involve a one-to-one mapping between text and motion, implying that given the same text, they can only produce fixed motion sequence results.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To increase generated result diversity, TEMOS [21] introduced a VAE architecture that finds a joint latent space for motion and text under Gaussian distribution constraints. Guo et al. [7] used a temporal VAE to autoregressively generate motion sequences based on text features. However, these methods have a significant drawback of mapping text and motion sequences to separate feature spaces and forcibly align them, leading to a loss of information in both domains. Recently, diffusion models have shown great potential in image generation and have inspired the development of diffusion models for human motion generation. Tevet et al. [28] and Zhang et al. [33] encoded text descriptions using pre-trained models and estimated Gaussian noise or the original motion sequence at each reverse diffusion step. However, their text modeling is often crude and does not fully leverage linguistic structure for sentence semantics. Also, they do not have a progressive process that allows the diffusion model to focus on different content at different time stamps, and they only interact with fixed text features during the inference process.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Preliminaries",
+        "text_level": 1,
+        "bbox": [
+            76,
+            709,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The diffusion process is a Markov process consisting of a forward process and a reverse process. The forward process starts with the real data  $X_0$  at step 0 and proceeds in a Markovian manner by adding Gaussian noise at each step. Over  $t$  steps,  $X_0$  is transformed into  $X_t$ , which is close to the Gaussian distribution  $N(0, I)$ . As a result, the original motion sequence is converted into a complete noise distribution, which can be expressed as:",
+        "bbox": [
+            75,
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+            468,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} I\\right) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            132,
+            883,
+            468,
+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\beta_{t}$  is a hyper-parameter that controls the diffusion rate. The entire diffusion forward process is formulated as:",
+        "bbox": [
+            498,
+            90,
+            890,
+            121
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq \\left(\\mathbf {x} _ {1: T} \\mid \\mathbf {x} _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            132,
+            890,
+            172
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $T$  denotes total steps in diffusion. The diffusion reverse process samples from the Gaussian distribution  $X_{t}$  as the initial input and attempts to gradually remove the noise on a reverse Markov-chain, which can be defined as follows:",
+        "bbox": [
+            498,
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+            244
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            573,
+            255,
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+            296
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\Sigma_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            540,
+            306,
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+            325
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu_{\\theta}$  is the estimated item by model,  $t$  is the timestep indicating where the denoising process has conducted.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To enhance the modeling of fine-grained human motion generation, we present our proposed method in Figure 2. Previous methods [1, 2, 5] have adopted a coarse approach to text modeling, leading to an underutilization of text information. Moreover, they treat all words equally without considering their importance and uniqueness. In contrast, we leverage linguistic structures in sentences to further enhance text encoding and differentiate between overall semantic information and detailed features using a multi-step progressive reasoning strategy.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a text prompt,  $W = \\{w_{1}, w_{2}, \\ldots, w_{n}\\}$ ,  $W \\in \\mathbb{R}^{N \\times L}$  where  $N$  represents the number of words and  $L$  is the dimension of word vector. Our goal is to generate a human motion sequence, denoted as  $M = \\{m_{1}, m_{2}, \\ldots, m_{t}\\}$ , where  $M \\in \\mathbb{R}^{T \\times D}$ . Here,  $T$  refers to the sequence length and  $D$  is the motion representation dimension. To achieve this, we introduce Fg-T2M, a method that generates motion sequences that align well with the corresponding textual content. In the following, we provide an overview of our approach in section 4.1, followed by the introduction of the Linguistics-Structure Assisted Module (LSAM) in section 4.2. Lastly, we present the Context-Aware Progressive Reasoning (CAPR) module in section 4.3.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            500,
+            756,
+            609,
+            771
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Figure 2 shows our pipeline for generating motion sequences. We randomly sample  $\\mathbf{x}_T$  from distribution  $N(0, I)$ , input  $\\mathbf{x}_T$ , current step  $T$ , and text control condition  $c$  to obtain  $\\mathbf{x}_{T-1}$ , iterating  $T$  rounds until we get  $\\mathbf{x}_0$ . In the denoising process, the condition  $c$  is fed into our LSAM text encoder. By leveraging dependency relationships between words, we use graph neural networks to aggregate data and extract hierarchical semantic features. The motion decoder",
+        "bbox": [
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+            780,
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+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "22037",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/e477c781af1c35cf046ce6d58ce5b9333bf5a3b23701381b6a1dc9a14f51c3c0.jpg",
+        "image_caption": [
+            "Figure 2: Overall Pipeline of our proposed method Fg-T2M: (a) the reverse denoising process of the diffusion model from  $X_{T}$  to  $X_{0}$ ; (b) the text encoder with proposed linguistics-structure assisted module with dependency parsing in section 4.2; (c) the motion decoder with introduced context-aware progressive reasoning module in section 4.3."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            92,
+            885,
+            385
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "is stacked with CAPR. Multiple layers of these modules enhance the quality of the generated motion sequence.",
+        "bbox": [
+            75,
+            470,
+            468,
+            501
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To train the motion diffusion model, we optimize the objective to predict the original data, representing as follows:",
+        "bbox": [
+            75,
+            502,
+            468,
+            532
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathrm {E} _ {t \\in [ 1, T ], \\mathbf {x} _ {0} \\sim q (\\mathbf {x} _ {0}), \\epsilon \\sim \\mathcal {N} (0, I)} [ \\| \\mathbf {x} _ {0} - \\hat {\\mathbf {x}} _ {0} (\\mathbf {x} _ {t}, t, c) \\| _ {2} ^ {2} ]. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The regular L2 loss can improve performance for all geometric losses mentioned above.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Linguistics-Structure Assisted Module",
+        "text_level": 1,
+        "bbox": [
+            76,
+            633,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The current text modeling method is limited in its sensitivity to fine-grained words, which hinders the effectiveness of subsequent generations. To address this, we enhance the context modeling of sentences by identifying the phrase structure and syntactic relationships between phrases using dependency parsing, as shown in Figure 3. Linguistic structure, which comprises phrase structure and syntax relationships, helps us better understand the essence of text and the differences and similarities between sentences. Dependency parsing [19] precisely analyzes vocabulary and syntax to identify the dependency relationships between words in a sentence. In this approach, each word is treated as a node, and the dependency relationships between words are represented by edges that indicate syntactic connections. The resulting node and edge features representing the dependency relationships are input into a graph network to",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/7c4fa65f3d484bb86c917adaa5baadd7653ca826dd1b8142618e956a97a5fd8a.jpg",
+        "image_caption": [
+            "Figure 3: Architecture of LSAM. The left panel illustrates the process of obtaining node and edge features for one sentence in dependency analysis feature extraction, while the right panel demonstrates the workflows that utilize multiple layers of Graph Attention Network to extract feature information with varying degrees."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            473,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "obtain multi-level semantics. In summary, given a sentence, the dependency parsing analyses to build a text tree, nodes for words, and links between nodes for their linguistic relationships. The text tree structure as the graph initialization for graph topology and edge features provides GAT a better prior. The GAT aims to capture inter-word relationships while maintaining the linguistic structure of the text.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To extract word associations, we parse the dependency",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22038",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "of phrase and obtain the hierarchical syntactic relationships using Spacy<sup>1</sup> for dependency parsing, as shown in the left panel of Figure 3. Spacy is a natural language processing software library for text processing, including lexical analysis, syntactic analysis, and more. In dependency parsing, each word is treated as a node, and the edges represent the labels of the dependency relationships between words, allowing us to construct a tree of language structure for the given text. We extract features using a graph attention network (GAT) [31]. For the input nodes of the graph network, we use word features obtained from the CLIP [24] model. For the adjacency matrix, we set a value of 1 or 0 to represent the presence or absence of a dependency relationship between nodes. Since the number of dependency relationships is fixed, we use one-hot encoding to obtain a one-hot label for each relationship, which is then fed into an embedding layer. This can be described as:",
+        "bbox": [
+            75,
+            90,
+            472,
+            348
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {v} _ {\\mathbf {e}} = \\beta_ {i} \\left(\\varphi_ {e} \\left(\\mathrm {F} _ {\\text {o n e h o t}} \\left(R _ {i}\\right)\\right)\\right) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            181,
+            356,
+            468,
+            372
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{v}_{\\mathrm{e}} \\in \\mathbb{R}^{D_{e}}$ ,  $D_{e}$  is the dimension of edge feature,  $\\varphi_{e}$  denotes an embedding layer,  $\\beta_{i}$  is adaptive weight parameters to be learned for every  $R_{i}$ , while  $R_{i}$  indicates the edge relation between two nodes. Since each word may be adjacent to multiple nodes, and different nodes contribute differently to semantics, it is necessary to distinguish them during the text feature extraction process. We achieve this by applying GAT [31], which extracts multi-level features from the obtained node information, adjacency matrix, and edge information. GAT [31] considers differences between nodes during information aggregation and handles irregularities between different nodes effectively, which is described as:",
+        "bbox": [
+            75,
+            378,
+            472,
+            561
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {i} ^ {\\prime} = \\alpha_ {i, i} \\Theta x _ {i} + \\sum_ {j \\in N (i)} \\alpha_ {i, j} \\Theta x _ {j} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            166,
+            566,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i, j} = \\frac {\\exp \\left(\\mathrm {F} \\left(\\omega^ {\\top} \\left[ \\Theta \\mathrm {x} _ {\\mathrm {i}} \\right| | \\Theta \\mathrm {x} _ {\\mathrm {j}} | | \\Theta_ {\\mathrm {e}} \\mathrm {e} _ {\\mathrm {i} , \\mathrm {j}} ]\\right)\\right)}{\\sum_ {k \\in N (i) \\cup \\{i \\}} \\exp \\left(\\mathrm {F} \\left(\\omega^ {\\top} \\left[ \\Theta x _ {i} \\right| | \\Theta x _ {k} | | \\Theta_ {e} e _ {i , k} ]\\right)\\right)} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            618,
+            468,
+            656
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We have  $x, \\alpha \\in \\mathbb{R}^{N \\times L}$ , where  $\\alpha_{i,j}$  represents attention coefficients,  $F$  denotes LeakyReLU,  $e$  is edge features,  $\\omega$  and  $\\Theta$  represents the weight parameters to be learned, and  $||$  is the concatenation operation. GAT [31] can model high-order dependency relationships by stacking multiple graph attention layers to capture global and local graph topology effectively. For example, stacking three layers of GAT [31] results in  $x_i^1$ ,  $x_i^2$ , and  $x_i^3$  for each node  $x_i$ , as follows:",
+        "bbox": [
+            75,
+            662,
+            468,
+            785
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {i} ^ {l + 1} = \\alpha_ {i, i} ^ {l} \\Theta x _ {i} ^ {l} + \\sum_ {j \\in N (i)} \\alpha_ {i, j} ^ {l} \\Theta x _ {j} ^ {l} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
+            791,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The shallow network  $x_{i}^{1}$  learns detailed features of the neighborhood as it can only gather information from directly adjacent nodes in the first step of node aggregation.",
+        "bbox": [
+            75,
+            834,
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/5df61e6546ed88fa6034c744544cb5d25a810932e67d9c03c3dfdfa928955d59.jpg",
+        "image_caption": [
+            "Figure 4: Architecture of CAPR. The left panel illustrates inferring  $X_{t-1}$  from  $X_t$ ,  $t$ , and text features. The right panel provides the detailed view of one context-aware progressive reasoning module, which comprises two parts: sentence-level feature fusion and word-level cross-attention."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            224
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This process captures more local and fine-grained information. By comparison, the deep network  $x_{i}^{3}$  can learn overall semantic features by aggregating information from distant nodes after multiple aggregation steps. This enables it to capture more global and holistic information.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.3. Context-Aware Progressive Reasoning Module",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Guided by the Linguistics-Structure Assisted Module (LSAM) in the previous section, we stack Context-Aware Progressive Reasoning Modules to perform multi-step progressive reasoning in a structured manner. Unlike previous methods that learn fixed features [28, 33], our stacked modules grasp features from global to local. Each block receives distinct contextual information, with higher-level blocks utilizing deeper context features from the LSAM, and lower-level blocks utilizing shallower features. This results in the model perceiving hierarchical information during the inference process, which greatly benefits its ability to hierarchically comprehend the meaning of text content and sense its fine-grained words.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The CAPR comprises two parts: Multi-Modal Sentence-level Feature-Fusion and Multi-Head Word-level Cross-Attention. Figure 4 shows that we start with the motion feature  $x_{t} \\in \\mathbb{R}^{T \\times D}$ , text feature  $W \\in \\mathbb{R}^{N \\times L}$ , and timestep  $t$ . To better capture the unique characteristics of each time step in the diffusion model, we first perform sinusoidal time embedding through linear layers to obtain timestep embedding  $emb_{t}$ . We then add the motion and text features to  $emb_{t}$  to incorporate different time information at each timestep.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Multi-Modal Sentence-Level Feature-Fusion module fuses sentence-level text features and motions to obtain multi-modal features, as shown in Figure 5. For the i-th Context-Aware Progressive Reasoning Module block, the text  $W_{i}$  is transformed to a sentence-level feature  $S$  using convolution, which is derived from the i-th LSAM layer:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {i} = \\operatorname {C o n v} _ {1 d} \\left(W _ {i}\\right) \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "1 Spacy: https://spacy.io/",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "footer",
+        "text": "22039",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/c6f89060fc2fc35eca19602713f48f9f15e35890d7d813e93a7d8a204c90bcd0.jpg",
+        "image_caption": [
+            "Figure 5: Illustration of Multi-Modal Sentence-Level Feature-Fusion Module."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            104,
+            90,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $S_{i}\\in \\mathbb{R}^{1\\times D_{s}}$ ,  $W_{i}\\in \\mathbb{R}^{N\\times D_{w}}$ ,  $D_{s}$  and  $D_{w}$  denotes the dimension of sentence feature and words feature, and Conv1d is the 1d convolution. We then perform a matrix multiplication to obtain an attention list  $A$ :",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA = \\mathbf {X} _ {t} S _ {i} ^ {\\mathrm {T}} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{X}_t\\in \\mathbb{R}^{T\\times D}$  and  $A\\in \\mathbb{R}^{T\\times 1}$ . Here,  $\\mathbf{X}_t$  represents the motion feature at timestep  $t$ , and  $A$  calculates the feature relevance between the sentence and each frame on the feature map. The resulting cross-modal feature,  $\\mathbf{X}_t'$ , highlights the sentence-relevant frame feature channels:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {X} _ {t} ^ {\\prime} = \\mathrm {X} _ {t} + \\lambda \\left(\\mathrm {X} _ {t} \\odot (\\sigma (A))\\right) \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  is a hyper-parameter,  $\\odot$  is element-wise multiplication and  $\\sigma$  is a sigmoid activation function. To enhance modeling the correlation between different fused information, a self-attention mechanism [30] is added to strengthen the connection between multiple frames. Multi-head self-attention is conducted on the fusion feature  $X_{t}^{\\prime}$  as follows:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {Q} = W _ {q} \\mathrm {X} _ {t} ^ {\\prime}, \\mathrm {K} = W _ {k} \\mathrm {X} _ {t} ^ {\\prime}, \\text {a n d} \\mathrm {V} = W _ {v} \\mathrm {X} _ {t} ^ {\\prime} \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            109,
+            559,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{q}, W_{k}$  and  $W_{v}$  are trainable weights to generate Q, K and V, respectively. Obtain the attention scores using the formula below, where  $\\otimes$  is the matrix multiplication.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} (\\mathrm {Q}, \\mathrm {K}, \\mathrm {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathrm {Q} \\otimes \\mathrm {K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathrm {V} \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            109,
+            631,
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+            667
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Multi-Head Word-Level Cross-Attention module learns the cross-interaction between motion sequences and multi-level contextual text features. It uses the formulas mentioned in the self-attention module for calculation, but modifies the motion features of K and V to text features. Therefore, on the stacked Context-Aware Progressive Reasoning modules  $B_{1}, B_{2}, \\ldots, B_{i}$ , Block  $B_{i}$  utilizes different word-level semantic features by:",
+        "bbox": [
+            75,
+            672,
+            468,
+            792
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {X}} _ {t} = \\mathbf {X} _ {t} ^ {\\prime} + \\text {A t t e n t i o n} \\left(\\mathbf {X} _ {t} ^ {\\prime}, \\mathbf {W} _ {i}, \\mathbf {W} _ {i}\\right) \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            800,
+            468,
+            816
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{X}_t^\\prime$  is motion features and  $\\mathrm{W}_i$  is the text features.  $\\mathbf{X}_t^\\prime$  forms the query vector  $Q$ ,  $\\mathbf{W}_i$  forms the key vector  $K$  and value vector  $V$ . They pass through the process in Equation 14. Finally, several MLP layers further processes the above features to output the predicted target  $\\mathbf{X}_t\\in \\mathbb{R}^{T\\times D}$",
+        "bbox": [
+            75,
+            824,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/d008a2350f7d405530ec1511215aff21ba7a81e67c60def5d98cc01b767b8fcf.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.511±.003</td><td>0.703±.003</td><td>0.797±.002</td><td>0.002±.000</td><td>2.974±.008</td><td>9.503±.065</td><td>-</td></tr><tr><td>Seq2Seq [16]</td><td>0.180±.002</td><td>0.300±.002</td><td>0.396±.002</td><td>11.75±.035</td><td>5.529±.007</td><td>6.223±.061</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.246±.002</td><td>0.387±.002</td><td>0.486±.002</td><td>11.02±.046</td><td>5.296±.008</td><td>7.676±.058</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.165±.001</td><td>0.267±.002</td><td>0.345±.002</td><td>7.664±.030</td><td>6.030±.008</td><td>6.409±.071</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.301±.002</td><td>0.425±.002</td><td>0.552±.004</td><td>6.532±.024</td><td>5.012±.018</td><td>8.332±.042</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.037±.000</td><td>0.072±.001</td><td>0.106±.001</td><td>94.41±.021</td><td>9.643±.006</td><td>0.462±.008</td><td>0.019±.000</td></tr><tr><td>Dance2Music [14]</td><td>0.033±.000</td><td>0.065±.001</td><td>0.097±.001</td><td>66.98±.016</td><td>8.116±.006</td><td>0.725±.011</td><td>0.043±.001</td></tr><tr><td>TEMOS [21]</td><td>0.424±.002</td><td>0.612±.002</td><td>0.722±.002</td><td>3.734±.028</td><td>3.703±.008</td><td>8.973±.071</td><td>0.368±.018</td></tr><tr><td>Temporal VAE [7]</td><td>0.455±.003</td><td>0.636±.003</td><td>0.740±.003</td><td>1.067±.002</td><td>3.340±.008</td><td>9.188±.002</td><td>2.090±.083</td></tr><tr><td>TM2T [8]</td><td>0.424±.003</td><td>0.618±.003</td><td>0.729±.002</td><td>1.501±.017</td><td>3.467±.011</td><td>8.589±.076</td><td>2.424±.093</td></tr><tr><td>MotionDiffuse [33]</td><td>0.491±.001</td><td>0.681±.001</td><td>0.782±.001</td><td>0.630±.001</td><td>3.113±.001</td><td>9.410±.049</td><td>1.553±.042</td></tr><tr><td>MDM [28]</td><td>0.320±.005</td><td>0.498±.004</td><td>0.611±.007</td><td>0.544±.044</td><td>5.566±.027</td><td>9.559±.086</td><td>2.790±.072</td></tr><tr><td>T2M-GPT [32]</td><td>0.491±.003</td><td>0.680±.003</td><td>0.775±.002</td><td>0.116±.004</td><td>3.118±.011</td><td>9.761±.081</td><td>1.856±.011</td></tr><tr><td>Fg-T2M</td><td>0.492±.002</td><td>0.683±.003</td><td>0.783±.002</td><td>0.243±.019</td><td>3.109±.007</td><td>9.278±.072</td><td>1.614±.049</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/76802043f140b2afea24ff4d38ee29ac1360f2bbc0b6b91686c6f9df189fa086.jpg",
+        "table_caption": [
+            "Table 1: Comparison of text-conditional motion synthesis on HumanML3D [7] dataset. Red and Blue indicate the best and the second best result, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.424±.005</td><td>0.649±.006</td><td>0.779±.006</td><td>0.031±.004</td><td>2.788±.012</td><td>11.08±.097</td><td>-</td></tr><tr><td>Seq2Seq[16]</td><td>0.103±.003</td><td>0.178±.005</td><td>0.241±.006</td><td>24.86±.348</td><td>7.960±.031</td><td>6.741±.106</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.156±.004</td><td>0.255±.004</td><td>0.338±.005</td><td>12.12±.183</td><td>6.964±.029</td><td>9.334±.079</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.221±.005</td><td>0.373±.004</td><td>0.483±.005</td><td>6.545±.072</td><td>5.147±.030</td><td>9.073±.100</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.255±.006</td><td>0.432±.007</td><td>0.531±.007</td><td>5.203±.107</td><td>4.986±.027</td><td>9.563±.072</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.022±.002</td><td>0.042±.003</td><td>0.063±.003</td><td>82.69±.242</td><td>10.47±.012</td><td>3.091±.043</td><td>0.250±.009</td></tr><tr><td>Dance2Music [14]</td><td>0.031±.002</td><td>0.058±.002</td><td>0.086±.003</td><td>115.4±.240</td><td>10.40±.016</td><td>0.241±.004</td><td>0.062±.002</td></tr><tr><td>TEMOS [21]</td><td>0.353±.006</td><td>0.561±.007</td><td>0.687±.005</td><td>3.717±.051</td><td>3.417±.019</td><td>10.84±.100</td><td>0.532±.034</td></tr><tr><td>Temporal VAE [7]</td><td>0.361±.006</td><td>0.559±.007</td><td>0.693±.007</td><td>2.770±.109</td><td>3.401±.008</td><td>10.91±.119</td><td>1.482±.065</td></tr><tr><td>TM2T [8]</td><td>0.280±.005</td><td>0.463±.006</td><td>0.587±.005</td><td>3.599±.153</td><td>4.591±.026</td><td>9.473±.117</td><td>3.292±.081</td></tr><tr><td>MotionDiffuse [33]</td><td>0.417±.004</td><td>0.621±.004</td><td>0.739±.004</td><td>1.954±.062</td><td>2.958±.005</td><td>11.10±.143</td><td>0.730±.013</td></tr><tr><td>MDM [28]</td><td>0.164±.004</td><td>0.291±.004</td><td>0.396±.004</td><td>0.497±.021</td><td>9.19±.022</td><td>10.847±.109</td><td>1.907±.214</td></tr><tr><td>T2M-GPT [32]</td><td>0.416±.006</td><td>0.627±.006</td><td>0.745±.006</td><td>0.514±.029</td><td>3.007±.023</td><td>10.92±.108</td><td>1.570±.039</td></tr><tr><td>Fg-T2M</td><td>0.418±.005</td><td>0.626±.004</td><td>0.745±.004</td><td>0.571±.047</td><td>3.114±.015</td><td>10.93±.083</td><td>1.019±.029</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Comparison of text-conditional motion synthesis on KIT [22] dataset. Red and Blue indicate the best and the second best result, respectively.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our Fg-T2M framework is evaluated on text-driven motion generation task in this section. We first describe the dataset used and the evaluation metrics in section 5.1. In section 5.2, we provide implementation details. We compare our framework with the current state-of-the-art methods in section 5.3. Finally, we present qualitative results and visualization for comparison in section 5.4.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Datasets and Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Several datasets exist for conditional motion generation, such as proposed in [7, 9, 11, 22]. However, datasets such as [9] and [11] are based on action categories and do not provide complete text sentences as conditioning inputs, making them unsuitable for our method. Instead, we use text-driven datasets, specifically, HumanML3D dataset [7] and KIT Motion-Language dataset [22], for our experiments.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The HumanML3D dataset [7] is a combination of the HumanAct12 [9] and AMASS [17] datasets, comprising 14,616 motions and 44,970 text descriptions across various human activities, such as daily activities, sports, acrobatics, etc., with a total duration of about 28.59 hours. The KIT Motion-Language dataset [22] consists of 3,911 motion sequences and 6,353 natural language descriptions, with a total duration of around 10.33 hours.",
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+    {
+        "type": "page_number",
+        "text": "22040",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/e27eca9015b40291b92c44117de2e9566800c5d208ff7768de5d0943acd8832c.jpg",
+        "image_caption": [
+            "Figure 6: Qualitative results: Our method is compared with two state-of-the-art methods: MotionDiffuse [33] and Temporal VAE [7]. Motion frames are ordered from left to right. Those not matching with text prompt are marked with a box."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics are followed [7]. (1)  $R$ -precision. For each inferred text-motion pair, 31 mismatched descriptions are randomly selected from the test set. The average top-k precision is obtained by calculating and ranking the Euclidean distance between the motion and each of the 32 descriptions. (2) Frechet Inception Distance (FID). FID measures the similarity between the feature distributions extracted from the generated motions and ground truth motions. (3) Multi-Modal Distance. The multimodal distance is computed between the text feature and the relevant generated motion feature, concerning the given description. (4) Diversity. Diversity evaluates the dissimilarities among all generated motions across all descriptions by computing the mean pairwise Euclidean distance between randomly partitioned groups of motions. (5) Multimodality. For a given text description, 32 motion sequences are generated randomly, and multimodality quantifies the dissimilarities among these generated motion sequences. We primarily value R-precision and FID as pivotal performance metrics, which serve as important measures for evaluating the overall quality of generated motions.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
+            738,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The diffusion model uses 1000 diffusion steps and a linearly varying variance  $\\beta_{t}$  ranging from 0.0001 to 0.02. LSAM employs a 3-layer GAT network with a corresponding CAPR layer also set to 3. Hyper-parameter  $\\lambda$  in CAPR is 0.1. Training is performed with the Adam optimizer using a fixed learning rate of 5e-5, a batch size of 128, and NVIDIA GeForce RTX 3090 hardware. The KIT dataset is trained for approximately 40K iterations, while the HumanML3D dataset is trained for about 80K iterations.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Comparison with State-of-the-arts",
+        "text_level": 1,
+        "bbox": [
+            500,
+            400,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compared our method with several state-of-the-art models, including Lin et al. [16], Language2Pose [2], Ghosh et al. [5], MoCoGAN [29], Dance2Music [14], TEMOS [21], TM2T [8], Text2Gesture [3], Guo et al. [7], MotionDiffuse [33], and MDM [28]. Quantitative comparisons of our method with these models on the HumanML3D [7] and KIT [22] datasets are shown in Tables 1 and 2, respectively.",
+        "bbox": [
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+        "type": "text",
+        "text": "Our method achieves competitive performance between text and motion features, as measured by MM Dist, to state-of-the-art methods, while exhibiting significantly higher scores in R-precision and FID. This demonstrates the ability of our method to generate high-quality motions that align with the text prompts. On the other hand, other approaches showcase remarkable competitiveness in diversity and multimodality. However, these aspects should be grounded in accuracy (R-precision) and precision (FID, MMDist) to strengthen their persuasiveness. Otherwise, the diversity or multimodality would be rendered meaningless if the generated motion fails to align with the desired outcome. Therefore, based on our experiments, our method has achieved advanced experimental results and demonstrates robustness in terms of model performance on the two datasets.",
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+        "text": "Meanwhile, we design two experiments to evaluate fine-grained control. The first one is conducted on a Harder-HumanML3D dataset. We compress the HumanML3D test set of 4382 data into a Harder-HumanML3D set with 2582 data, by searching for sentences that contain more fine-grained words, like \"left\", \"right\", and so on. The comparison results are shown in Table 3. Our method exhibits significantly higher scores, indicating a better ability to capture",
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+        "image_caption": [
+            "Figure 7: The result of user study."
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+        "table_caption": [],
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+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"3\">R-Precision ↑</td><td rowspan=\"2\">FID ↓</td></tr><tr><td>Top-1</td><td>Top-2</td><td>Top-3</td></tr><tr><td>MotionDiffuse [33]</td><td>0.439±.006</td><td>0.614±.004</td><td>0.725±.005</td><td>0.732±.021</td></tr><tr><td>Fg-T2M</td><td>0.460±.005</td><td>0.660±.004</td><td>0.763±.004</td><td>0.421±.013</td></tr></table>",
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+        "type": "text",
+        "text": "fine-grained details. The second one is a user study in which we collect user preferences with T2M-GPT [32] and MotionDiffuse [33]. The statistics of the user study are shown in Figure 7. Compared with others, our method achieves superior performance in R-Precision, MM Dist, and yields competitive results in FID, which generates motions with comparable quality. Furthermore, for both questions, especially in the fine-grained aspect, ours is preferred over others and even competitive to the ground truth motions.",
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+        "type": "text",
+        "text": "We present ablation results in Table 4 to further understand the role of LSAM and CAPR in our method. The results demonstrate that models without the CAPR and LSAM modules exhibit performance degradation. And we also show the comparison of some qualitative examples on the ablation study of this two modules. Additionally, we experiment with the impact of different GAT semantic layers of text information. Since a common dependency tree of motion-text prompt often has three or four depths, a three-layer GAT is sufficient to capture overall nodes information. Hence, a shallow or deep GAT layer hinders the global or local semantic comprehension, resulting in diminished results. We further evaluate the proposed two parts in CAPR. The results show that without CAPR-2 part remarkably reduces the results, which also reflects the importance of fine-grained words for T2M tasks. Finally, the hyper-parameter  $\\lambda$  in CAPR controls the degree of text information fusion. A larger  $\\lambda$  dilutes the inherent properties of the motion features, leading to a decrease in precision.",
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+        "text": "5.4. Qualitative Results",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Visual results on the HumanML3D [7] dataset are presented in Figure 6, where our method is compared with the state-of-the-art models of MotionDiffuse [33] and Temporal VAE [7]. As can be seen from the examples in the figure, our method generates human motions that more accurately reflect the text prompts. In contrast, the methods of MotionDiffuse [33] and Temporal VAE [7] often result in unrealistic movements. Specifically, these methods tend to",
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+        "table_caption": [
+            "Table 3: Experiment results on Harder-HumanML3D split from the HumanML3D [7] test set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>R-TOP3↑</td><td>FID↓</td></tr><tr><td>Fg-T2M</td><td>0.745±.004</td><td>0.571±.047</td></tr><tr><td>Fg-T2M (w/o LSAM)</td><td>0.722±.005</td><td>1.077±.101</td></tr><tr><td>Fg-T2M (w/o CAPR)</td><td>0.727±.007</td><td>0.943±.089</td></tr><tr><td>Fg-T2M (one layer)</td><td>0.729±.006</td><td>0.951±.092</td></tr><tr><td>Fg-T2M (two layers)</td><td>0.738±.003</td><td>0.692±.086</td></tr><tr><td>Fg-T2M (four layers)</td><td>0.740±.004</td><td>0.636±.102</td></tr><tr><td>Fg-T2M(w/o CAPR-1)</td><td>0.739±.006</td><td>0.652±.035</td></tr><tr><td>Fg-T2M(w/o CAPR-2)</td><td>0.732±.004</td><td>0.764±.039</td></tr><tr><td>Fg-T2M (λ = 0.2)</td><td>0.738±.008</td><td>0.686±.062</td></tr><tr><td>Fg-T2M (λ = 0.3)</td><td>0.732±.006</td><td>0.830±.074</td></tr><tr><td>Fg-T2M (λ = 0.5)</td><td>0.729±.011</td><td>1.086±.104</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 4: Ablation analysis on KIT [22]. \"layers\" indicates the number of layers of GAT in LSAM. \"(w/o) CAPR-1\" means without multi-modal sentence-level feature-fusion. \"(w/o) CAPR-2\" means without multi-head word-level cross-attention. \"λ\" is the hyper-parameter of Multi-Modal Sentence-Level Feature-Fusion module in CAPR.",
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+    {
+        "type": "text",
+        "text": "only understand one motion within a long text prompt and are not sensitive to specific numerical values, such as 'one' or 'two'. As depicted in example one, MotionDiffuse [33] only performed a backward motion without considering the required number of steps. On the other hand, Temporal VAE [7] successfully achieved the desired effect of walking forward and then backward, but its backward motion step count did not meet the expected requirement. Moreover, They also make errors in spatial orientation, such as 'left' or 'right', and lack a thorough understanding of temporal issues, such as 'while' and 'then', related to movement. Overall, our proposed method outperforms these models, especially in terms of the issues mentioned above. More diverse samples are presented in the supplementary material.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We present a novel method for text-driven human motion generation using the diffusion model, which offers several advantages over existing techniques. Specifically, our method leverages two key modules - a linguistics-structure assisted module and a context-aware progressive reasoning module - to effectively model fine-grained words in the text. The former module extracts dependency parsing relationships in the text, while the latter performs hierarchical effective information feature fusion based on graph neural networks. Our quantitative and qualitative results demonstrate that our method outperforms existing techniques in text-driven motion generation tasks.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by the National Natural Science Foundation of China (Project Number: 62272019).",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
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+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+    {
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.098,
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+            "angle": 0,
+            "content": "Fg-T2M: Fine-Grained Text-Driven Human Motion Generation via Diffusion Model"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.203,
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+            "angle": 0,
+            "content": "Yin Wang\\(^{1}\\), Zhiying Leng\\(^{1,2}\\), Frederick W. B. Li\\(^{3}\\), Shun-Cheng Wu\\(^{2}\\), Xiaohui Liang\\(^{1,4,*}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.203,
+                0.23,
+                0.812,
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+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.378,
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+                0.638,
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+            "angle": 0,
+            "content": "\\(^{2}\\)Technical University of Munich, Germany"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{3}\\)Department of Computer Science, University of Durham, U.K."
+        },
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+            "type": "text",
+            "bbox": [
+                0.377,
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+                0.64,
+                0.3
+            ],
+            "angle": 0,
+            "content": "\\(^{4}\\)Zhongguancun Laboratory, Beijing, China."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.302,
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+                0.317
+            ],
+            "angle": 0,
+            "content": "{wang_yin, zhiyingleng, liang_xiaohui}@buaa.edu.cn, frederick.li@durham.ac.uk, shuncheng.wu@tum.de"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "Abstract"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Text-driven human motion generation in computer vision is both significant and challenging. However, current methods are limited to producing either deterministic or imprecise motion sequences, failing to effectively control the temporal and spatial relationships required to conform to a given text description. In this work, we propose a fine-grained method for generating high-quality, conditional human motion sequences supporting precise text description. Our approach consists of two key components: 1) a linguistics-structure assisted module that constructs accurate and complete language feature to fully utilize text information; and 2) a context-aware progressive reasoning module that learns neighborhood and overall semantic linguistics features from shallow and deep graph neural networks to achieve a multi-step inference. Experiments show that our approach outperforms text-driven motion generation methods on HumanML3D and KIT test sets and generates better visually confirmed motion to the text conditions."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "1. Introduction"
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+            "content": "Human motion generation is a crucial task in computer vision with various applications in animation production, gaming, robot control, and movie script visualization. Obtaining human motion sequences through traditional software is a labor-intensive and tedious process, while motion capture is complex and expensive. Recently, with the advancements in deep learning and computer vision, learning-based human motion generation has emerged as a solution to this problem, leading to the development of associated generation methods based on multimodal data. The input multimodal data include music [12, 15, 25, 27], motion cat"
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+        {
+            "type": "image",
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+                0.532,
+                0.894,
+                0.563
+            ],
+            "angle": 0,
+            "content": "Figure 1: Our approach generates human motion sequences that grasp fine-grained details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.595,
+                0.895,
+                0.793
+            ],
+            "angle": 0,
+            "content": "egories [4, 9, 20], text [2, 3, 5, 7, 8, 16, 21, 23, 28, 33], among others. Text-driven human motion generation has been a popular research topic, because of its convenience and human-friendliness. In particular, natural language comprises nouns, verbs, adverbs, etc. The mutual connections among different words in a sentence establish its semantics. Verbs define the action's category, while adverbs control the fineness of the action. The interaction between words in syntax plays a vital role in determining the structure and meaning of a sentence. Failure to fully incorporate these text features may result in inadequate text modeling, causing the generated motion sequence to deviate from the intended meaning of the original text."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Existing methods can be divided into two branches, including 1) cross-modal alignment of motion and text [2, 3, 5, 7, 8, 16, 21]; 2) conditional diffusion models [28, 33]. In the first methods, text sequences and motion sequences are mapped onto separate feature spaces and forcibly aligned, leading to a loss of original information from both domains. In the second methods, the diffusion model incorporates"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.224,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Corresponding author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22035"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.334
+            ],
+            "angle": 0,
+            "content": "text information as a conditioning factor to learn the probability mapping of human motions. However, the model interacts with only one text feature at each time step of the inference process, lacking a progressive approach. Moreover, text modeling only involves simple manipulation, which ignores the importance of certain fine-grained words and leads to incomplete semantic understanding, making it challenging to learn focus points at each step. Overall, existing methods only use text information to a limited extent, which in turn affects the accuracy of motion generation based on the corresponding text content, especially for the motion in which texts contain fine-grained words. For instance, comprehending the sentence \"A man is walking forward while waving his right hand\" can be a difficult task, and expecting the model to grasp the fine-grained meaning of the terms \"while\" and \"right hand\" is even more demanding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.338,
+                0.473,
+                0.716
+            ],
+            "angle": 0,
+            "content": "To tackle the aforementioned issues, we propose a fine-grained text-driven method for generating human motion sequences that precisely align with text prompts in Figure 1. Typically, people initially read a sentence to gain an overall semantic understanding before focusing on the fine-grained details of individual words. To replicate this process, our method includes a linguistics-structure assisted module and a context-aware progressive reasoning module to fully utilize text information. Firstly, we utilize linguistics structure to facilitate information exchange between each text word. We use dependency parsing [19] to analyze the relationships among words in each sentence and construct a dependency tree, allowing each node to effectively communicate based on its dependent nodes and relationships. Then, the dependency tree nodes are passed to multi-layer graph neural networks to learn information aggregation. The multilayer graph neural networks allow shallow network to learn neighborhood features as it can comprehend nearby details, and allow deep network to grasp overall semantic features because it is capable of aggregating information from entire nodes. Additionally, our GAT captures rich inter-word relationships while preserving the text linguistics structure by designing adaptive weights for each part-of-speech and dependency relation due to their distinctive role in the Text to Motion (T2M) task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Secondly, achieving the purpose of fine-grained interaction, context-aware progressive reasoning module performs a multi-step inference process with the progressive fusion of global and local information between text and motion, which is unprecedented in the T2M task. This involves utilizing hierarchical semantic features to simulate the way humans comprehend sentences. We adopt the diffusion model framework and stack the hierarchical semantic features obtained from deep to shallow networks at each step to capture high-order relationships at different semantic levels. We evaluate our method on HumanML3D dataset [7] and KIT dataset [22]. Experiments show that our approach out"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "performs the state-of-the-art methods and generates better visual motion. Our main contributions include:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.132,
+                0.892,
+                0.222
+            ],
+            "angle": 0,
+            "content": "- To the best of our knowledge, we are the first to bring NLP methods into T2M task. Utilizing the structured understanding of the natural language prompts to help T2M models achieve better reasoning skills, which brings new ideas for the text-to-X community from a textual perspective."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.232,
+                0.892,
+                0.307
+            ],
+            "angle": 0,
+            "content": "- We propose the Linguistics-Structure Assisted Module (LSAM), which utilizes a dependency parsing tree and graph networks to facilitate effective information exchange and data aggregation. It can obtain both neighborhood and overall semantic linguistic features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.317,
+                0.892,
+                0.393
+            ],
+            "angle": 0,
+            "content": "- We propose a Context-Aware Progressive Reasoning Module (CAPR) that implements a multi-step progressive inference strategy within the diffusion model framework, mimicking the human reading process by moving from global to local relationships."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.402,
+                0.892,
+                0.461
+            ],
+            "angle": 0,
+            "content": "- Experimental results demonstrate that our proposed method outperforms previous methods, and achieves competitive performance on the HumanML3D and KIT datasets."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.132,
+                0.892,
+                0.461
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.476,
+                0.642,
+                0.492
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.5,
+                0.73,
+                0.516
+            ],
+            "angle": 0,
+            "content": "2.1. Motion generation model"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.524,
+                0.892,
+                0.659
+            ],
+            "angle": 0,
+            "content": "Generative models play a crucial role in motion synthesis by generating high-quality human motion. Generative Adversarial Nets (GAN) [6] use two sub-models: a generator model that produces new samples, and a discriminator model that attempts to classify samples as either real or fake. These two models compete against each other during training. However, the interpretability of GAN is poor because the learned data distribution lacks an explicit expression, resembling a black box mapping function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Auto-Encoding Variational Bayes (VAE) [13] is a widely used generative model in motion synthesis. Its primary objective is to generate new samples from the learned distribution of objects by learning latent attributes from the probability distribution of the latent variable space, thereby constructing new examples. Despite its usefulness, the quality of samples generated by VAE can be improved."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.766,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Recently proposed diffusion models [10, 18, 26] have shown immense potential in modeling and present an exciting opportunity to expand into text-driven motion generation. These models utilize the stochastic diffusion process modeled in thermodynamics, which gradually adds noise to the samples of the data distribution. The deep learning model then learns the reverse process of denoising the samples gradually. Diffusion models have the advantage over previous models as they do not make any assumptions about"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.946,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22036"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.152
+            ],
+            "angle": 0,
+            "content": "the target distribution, leading to a more diverse generation and better suitability for our task. Therefore, we propose a novel fine-grained human motion generation method that employs the Denoising Diffusion Probability Model [10]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.178,
+                0.406,
+                0.194
+            ],
+            "angle": 0,
+            "content": "2.2. Text-driven human motion generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.206,
+                0.47,
+                0.372
+            ],
+            "angle": 0,
+            "content": "The task of text-driven human motion generation involves generating 3D human motion sequences that conform to a textual description. Several previous works have tackled this task. Initially, Text2Action [1] proposed short-text conditioned motion generation based on an RNN model. Subsequently, Ahuja et al. [2] and Ghosh et al. [5] focused on creating a joint representation of text and motion by projecting both features into a shared latent space. However, these methods involve a one-to-one mapping between text and motion, implying that given the same text, they can only produce fixed motion sequence results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.377,
+                0.473,
+                0.681
+            ],
+            "angle": 0,
+            "content": "To increase generated result diversity, TEMOS [21] introduced a VAE architecture that finds a joint latent space for motion and text under Gaussian distribution constraints. Guo et al. [7] used a temporal VAE to autoregressively generate motion sequences based on text features. However, these methods have a significant drawback of mapping text and motion sequences to separate feature spaces and forcibly align them, leading to a loss of information in both domains. Recently, diffusion models have shown great potential in image generation and have inspired the development of diffusion models for human motion generation. Tevet et al. [28] and Zhang et al. [33] encoded text descriptions using pre-trained models and estimated Gaussian noise or the original motion sequence at each reverse diffusion step. However, their text modeling is often crude and does not fully leverage linguistic structure for sentence semantics. Also, they do not have a progressive process that allows the diffusion model to focus on different content at different time stamps, and they only interact with fixed text features during the inference process."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.71,
+                0.216,
+                0.725
+            ],
+            "angle": 0,
+            "content": "3. Preliminaries"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.74,
+                0.47,
+                0.862
+            ],
+            "angle": 0,
+            "content": "The diffusion process is a Markov process consisting of a forward process and a reverse process. The forward process starts with the real data \\( X_0 \\) at step 0 and proceeds in a Markovian manner by adding Gaussian noise at each step. Over \\( t \\) steps, \\( X_0 \\) is transformed into \\( X_t \\), which is close to the Gaussian distribution \\( N(0, I) \\). As a result, the original motion sequence is converted into a complete noise distribution, which can be expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.133,
+                0.884,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} I\\right) \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "where \\(\\beta_{t}\\) is a hyper-parameter that controls the diffusion rate. The entire diffusion forward process is formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.595,
+                0.133,
+                0.892,
+                0.174
+            ],
+            "angle": 0,
+            "content": "\\[\nq \\left(\\mathbf {x} _ {1: T} \\mid \\mathbf {x} _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.184,
+                0.892,
+                0.245
+            ],
+            "angle": 0,
+            "content": "where \\(T\\) denotes total steps in diffusion. The diffusion reverse process samples from the Gaussian distribution \\(X_{t}\\) as the initial input and attempts to gradually remove the noise on a reverse Markov-chain, which can be defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.575,
+                0.256,
+                0.892,
+                0.297
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.542,
+                0.308,
+                0.892,
+                0.326
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\mu_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right), \\Sigma_ {\\theta} \\left(\\mathbf {x} _ {t}, t\\right)\\right) \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.332,
+                0.892,
+                0.362
+            ],
+            "angle": 0,
+            "content": "where \\(\\mu_{\\theta}\\) is the estimated item by model, \\(t\\) is the timestep indicating where the denoising process has conducted."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.375,
+                0.591,
+                0.39
+            ],
+            "angle": 0,
+            "content": "4. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.4,
+                0.892,
+                0.551
+            ],
+            "angle": 0,
+            "content": "To enhance the modeling of fine-grained human motion generation, we present our proposed method in Figure 2. Previous methods [1, 2, 5] have adopted a coarse approach to text modeling, leading to an underutilization of text information. Moreover, they treat all words equally without considering their importance and uniqueness. In contrast, we leverage linguistic structures in sentences to further enhance text encoding and differentiate between overall semantic information and detailed features using a multi-step progressive reasoning strategy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.552,
+                0.892,
+                0.749
+            ],
+            "angle": 0,
+            "content": "Given a text prompt, \\( W = \\{w_{1}, w_{2}, \\ldots, w_{n}\\} \\), \\( W \\in \\mathbb{R}^{N \\times L} \\) where \\( N \\) represents the number of words and \\( L \\) is the dimension of word vector. Our goal is to generate a human motion sequence, denoted as \\( M = \\{m_{1}, m_{2}, \\ldots, m_{t}\\} \\), where \\( M \\in \\mathbb{R}^{T \\times D} \\). Here, \\( T \\) refers to the sequence length and \\( D \\) is the motion representation dimension. To achieve this, we introduce Fg-T2M, a method that generates motion sequences that align well with the corresponding textual content. In the following, we provide an overview of our approach in section 4.1, followed by the introduction of the Linguistics-Structure Assisted Module (LSAM) in section 4.2. Lastly, we present the Context-Aware Progressive Reasoning (CAPR) module in section 4.3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.757,
+                0.611,
+                0.772
+            ],
+            "angle": 0,
+            "content": "4.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Figure 2 shows our pipeline for generating motion sequences. We randomly sample \\(\\mathbf{x}_T\\) from distribution \\(N(0, I)\\), input \\(\\mathbf{x}_T\\), current step \\(T\\), and text control condition \\(c\\) to obtain \\(\\mathbf{x}_{T-1}\\), iterating \\(T\\) rounds until we get \\(\\mathbf{x}_0\\). In the denoising process, the condition \\(c\\) is fed into our LSAM text encoder. By leveraging dependency relationships between words, we use graph neural networks to aggregate data and extract hierarchical semantic features. The motion decoder"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22037"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.093,
+                0.887,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.399,
+                0.893,
+                0.446
+            ],
+            "angle": 0,
+            "content": "Figure 2: Overall Pipeline of our proposed method Fg-T2M: (a) the reverse denoising process of the diffusion model from \\( X_{T} \\) to \\( X_{0} \\); (b) the text encoder with proposed linguistics-structure assisted module with dependency parsing in section 4.2; (c) the motion decoder with introduced context-aware progressive reasoning module in section 4.3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.471,
+                0.469,
+                0.502
+            ],
+            "angle": 0,
+            "content": "is stacked with CAPR. Multiple layers of these modules enhance the quality of the generated motion sequence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.503,
+                0.469,
+                0.534
+            ],
+            "angle": 0,
+            "content": "To train the motion diffusion model, we optimize the objective to predict the original data, representing as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.561,
+                0.469,
+                0.592
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathrm {E} _ {t \\in [ 1, T ], \\mathbf {x} _ {0} \\sim q (\\mathbf {x} _ {0}), \\epsilon \\sim \\mathcal {N} (0, I)} [ \\| \\mathbf {x} _ {0} - \\hat {\\mathbf {x}} _ {0} (\\mathbf {x} _ {t}, t, c) \\| _ {2} ^ {2} ]. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.593,
+                0.469,
+                0.622
+            ],
+            "angle": 0,
+            "content": "The regular L2 loss can improve performance for all geometric losses mentioned above."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.635,
+                0.408,
+                0.651
+            ],
+            "angle": 0,
+            "content": "4.2. Linguistics-Structure Assisted Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The current text modeling method is limited in its sensitivity to fine-grained words, which hinders the effectiveness of subsequent generations. To address this, we enhance the context modeling of sentences by identifying the phrase structure and syntactic relationships between phrases using dependency parsing, as shown in Figure 3. Linguistic structure, which comprises phrase structure and syntax relationships, helps us better understand the essence of text and the differences and similarities between sentences. Dependency parsing [19] precisely analyzes vocabulary and syntax to identify the dependency relationships between words in a sentence. In this approach, each word is treated as a node, and the dependency relationships between words are represented by edges that indicate syntactic connections. The resulting node and edge features representing the dependency relationships are input into a graph network to"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.526,
+                0.474,
+                0.871,
+                0.637
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.65,
+                0.892,
+                0.742
+            ],
+            "angle": 0,
+            "content": "Figure 3: Architecture of LSAM. The left panel illustrates the process of obtaining node and edge features for one sentence in dependency analysis feature extraction, while the right panel demonstrates the workflows that utilize multiple layers of Graph Attention Network to extract feature information with varying degrees."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.776,
+                0.892,
+                0.882
+            ],
+            "angle": 0,
+            "content": "obtain multi-level semantics. In summary, given a sentence, the dependency parsing analyses to build a text tree, nodes for words, and links between nodes for their linguistic relationships. The text tree structure as the graph initialization for graph topology and edge features provides GAT a better prior. The GAT aims to capture inter-word relationships while maintaining the linguistic structure of the text."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "To extract word associations, we parse the dependency"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22038"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.349
+            ],
+            "angle": 0,
+            "content": "of phrase and obtain the hierarchical syntactic relationships using Spacy<sup>1</sup> for dependency parsing, as shown in the left panel of Figure 3. Spacy is a natural language processing software library for text processing, including lexical analysis, syntactic analysis, and more. In dependency parsing, each word is treated as a node, and the edges represent the labels of the dependency relationships between words, allowing us to construct a tree of language structure for the given text. We extract features using a graph attention network (GAT) [31]. For the input nodes of the graph network, we use word features obtained from the CLIP [24] model. For the adjacency matrix, we set a value of 1 or 0 to represent the presence or absence of a dependency relationship between nodes. Since the number of dependency relationships is fixed, we use one-hot encoding to obtain a one-hot label for each relationship, which is then fed into an embedding layer. This can be described as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.357,
+                0.47,
+                0.373
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {v} _ {\\mathbf {e}} = \\beta_ {i} \\left(\\varphi_ {e} \\left(\\mathrm {F} _ {\\text {o n e h o t}} \\left(R _ {i}\\right)\\right)\\right) \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.38,
+                0.473,
+                0.562
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{v}_{\\mathrm{e}} \\in \\mathbb{R}^{D_{e}}\\), \\(D_{e}\\) is the dimension of edge feature, \\(\\varphi_{e}\\) denotes an embedding layer, \\(\\beta_{i}\\) is adaptive weight parameters to be learned for every \\(R_{i}\\), while \\(R_{i}\\) indicates the edge relation between two nodes. Since each word may be adjacent to multiple nodes, and different nodes contribute differently to semantics, it is necessary to distinguish them during the text feature extraction process. We achieve this by applying GAT [31], which extracts multi-level features from the obtained node information, adjacency matrix, and edge information. GAT [31] considers differences between nodes during information aggregation and handles irregularities between different nodes effectively, which is described as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.167,
+                0.568,
+                0.47,
+                0.602
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {i} ^ {\\prime} = \\alpha_ {i, i} \\Theta x _ {i} + \\sum_ {j \\in N (i)} \\alpha_ {i, j} \\Theta x _ {j} \\tag {7}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.619,
+                0.47,
+                0.657
+            ],
+            "angle": 0,
+            "content": "\\[\n\\alpha_ {i, j} = \\frac {\\exp \\left(\\mathrm {F} \\left(\\omega^ {\\top} \\left[ \\Theta \\mathrm {x} _ {\\mathrm {i}} \\right| | \\Theta \\mathrm {x} _ {\\mathrm {j}} | | \\Theta_ {\\mathrm {e}} \\mathrm {e} _ {\\mathrm {i} , \\mathrm {j}} ]\\right)\\right)}{\\sum_ {k \\in N (i) \\cup \\{i \\}} \\exp \\left(\\mathrm {F} \\left(\\omega^ {\\top} \\left[ \\Theta x _ {i} \\right| | \\Theta x _ {k} | | \\Theta_ {e} e _ {i , k} ]\\right)\\right)} \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.664,
+                0.47,
+                0.786
+            ],
+            "angle": 0,
+            "content": "We have \\(x, \\alpha \\in \\mathbb{R}^{N \\times L}\\), where \\(\\alpha_{i,j}\\) represents attention coefficients, \\(F\\) denotes LeakyReLU, \\(e\\) is edge features, \\(\\omega\\) and \\(\\Theta\\) represents the weight parameters to be learned, and \\(||\\) is the concatenation operation. GAT [31] can model high-order dependency relationships by stacking multiple graph attention layers to capture global and local graph topology effectively. For example, stacking three layers of GAT [31] results in \\(x_i^1\\), \\(x_i^2\\), and \\(x_i^3\\) for each node \\(x_i\\), as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.158,
+                0.792,
+                0.47,
+                0.827
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {i} ^ {l + 1} = \\alpha_ {i, i} ^ {l} \\Theta x _ {i} ^ {l} + \\sum_ {j \\in N (i)} \\alpha_ {i, j} ^ {l} \\Theta x _ {j} ^ {l} \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.835,
+                0.47,
+                0.881
+            ],
+            "angle": 0,
+            "content": "The shallow network \\( x_{i}^{1} \\) learns detailed features of the neighborhood as it can only gather information from directly adjacent nodes in the first step of node aggregation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.522,
+                0.091,
+                0.875,
+                0.226
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.235,
+                0.894,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Figure 4: Architecture of CAPR. The left panel illustrates inferring \\( X_{t-1} \\) from \\( X_t \\), \\( t \\), and text features. The right panel provides the detailed view of one context-aware progressive reasoning module, which comprises two parts: sentence-level feature fusion and word-level cross-attention."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.339,
+                0.893,
+                0.415
+            ],
+            "angle": 0,
+            "content": "This process captures more local and fine-grained information. By comparison, the deep network \\( x_{i}^{3} \\) can learn overall semantic features by aggregating information from distant nodes after multiple aggregation steps. This enables it to capture more global and holistic information."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.424,
+                0.892,
+                0.44
+            ],
+            "angle": 0,
+            "content": "4.3. Context-Aware Progressive Reasoning Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.447,
+                0.893,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Guided by the Linguistics-Structure Assisted Module (LSAM) in the previous section, we stack Context-Aware Progressive Reasoning Modules to perform multi-step progressive reasoning in a structured manner. Unlike previous methods that learn fixed features [28, 33], our stacked modules grasp features from global to local. Each block receives distinct contextual information, with higher-level blocks utilizing deeper context features from the LSAM, and lower-level blocks utilizing shallower features. This results in the model perceiving hierarchical information during the inference process, which greatly benefits its ability to hierarchically comprehend the meaning of text content and sense its fine-grained words."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.644,
+                0.894,
+                0.78
+            ],
+            "angle": 0,
+            "content": "The CAPR comprises two parts: Multi-Modal Sentence-level Feature-Fusion and Multi-Head Word-level Cross-Attention. Figure 4 shows that we start with the motion feature \\( x_{t} \\in \\mathbb{R}^{T \\times D} \\), text feature \\( W \\in \\mathbb{R}^{N \\times L} \\), and timestep \\( t \\). To better capture the unique characteristics of each time step in the diffusion model, we first perform sinusoidal time embedding through linear layers to obtain timestep embedding \\( emb_{t} \\). We then add the motion and text features to \\( emb_{t} \\) to incorporate different time information at each timestep."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.78,
+                0.894,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Multi-Modal Sentence-Level Feature-Fusion module fuses sentence-level text features and motions to obtain multi-modal features, as shown in Figure 5. For the i-th Context-Aware Progressive Reasoning Module block, the text \\( W_{i} \\) is transformed to a sentence-level feature \\( S \\) using convolution, which is derived from the i-th LSAM layer:"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.277,
+                0.902
+            ],
+            "angle": 0,
+            "content": "1 Spacy: https://spacy.io/"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.632,
+                0.886,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\nS _ {i} = \\operatorname {C o n v} _ {1 d} \\left(W _ {i}\\right) \\tag {10}\n\\]"
+        },
+        {
+            "type": "footer",
+            "bbox": [
+                0.479,
+                0.946,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22039"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.105,
+                0.092,
+                0.443,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.202,
+                0.471,
+                0.231
+            ],
+            "angle": 0,
+            "content": "Figure 5: Illustration of Multi-Modal Sentence-Level Feature-Fusion Module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.254,
+                0.47,
+                0.316
+            ],
+            "angle": 0,
+            "content": "where \\(S_{i}\\in \\mathbb{R}^{1\\times D_{s}}\\), \\(W_{i}\\in \\mathbb{R}^{N\\times D_{w}}\\), \\(D_{s}\\) and \\(D_{w}\\) denotes the dimension of sentence feature and words feature, and Conv1d is the 1d convolution. We then perform a matrix multiplication to obtain an attention list \\(A\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.235,
+                0.322,
+                0.469,
+                0.34
+            ],
+            "angle": 0,
+            "content": "\\[\nA = \\mathbf {X} _ {t} S _ {i} ^ {\\mathrm {T}} \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.347,
+                0.469,
+                0.422
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{X}_t\\in \\mathbb{R}^{T\\times D}\\) and \\(A\\in \\mathbb{R}^{T\\times 1}\\). Here, \\(\\mathbf{X}_t\\) represents the motion feature at timestep \\(t\\), and \\(A\\) calculates the feature relevance between the sentence and each frame on the feature map. The resulting cross-modal feature, \\(\\mathbf{X}_t'\\), highlights the sentence-relevant frame feature channels:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.176,
+                0.431,
+                0.469,
+                0.448
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {X} _ {t} ^ {\\prime} = \\mathrm {X} _ {t} + \\lambda \\left(\\mathrm {X} _ {t} \\odot (\\sigma (A))\\right) \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.455,
+                0.469,
+                0.546
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) is a hyper-parameter, \\(\\odot\\) is element-wise multiplication and \\(\\sigma\\) is a sigmoid activation function. To enhance modeling the correlation between different fused information, a self-attention mechanism [30] is added to strengthen the connection between multiple frames. Multi-head self-attention is conducted on the fusion feature \\(X_{t}^{\\prime}\\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.11,
+                0.56,
+                0.469,
+                0.577
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {Q} = W _ {q} \\mathrm {X} _ {t} ^ {\\prime}, \\mathrm {K} = W _ {k} \\mathrm {X} _ {t} ^ {\\prime}, \\text {a n d} \\mathrm {V} = W _ {v} \\mathrm {X} _ {t} ^ {\\prime} \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.58,
+                0.469,
+                0.626
+            ],
+            "angle": 0,
+            "content": "where \\( W_{q}, W_{k} \\) and \\( W_{v} \\) are trainable weights to generate Q, K and V, respectively. Obtain the attention scores using the formula below, where \\( \\otimes \\) is the matrix multiplication."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.11,
+                0.632,
+                0.469,
+                0.668
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A t t e n t i o n} (\\mathrm {Q}, \\mathrm {K}, \\mathrm {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathrm {Q} \\otimes \\mathrm {K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathrm {V} \\tag {14}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.673,
+                0.469,
+                0.793
+            ],
+            "angle": 0,
+            "content": "Multi-Head Word-Level Cross-Attention module learns the cross-interaction between motion sequences and multi-level contextual text features. It uses the formulas mentioned in the self-attention module for calculation, but modifies the motion features of K and V to text features. Therefore, on the stacked Context-Aware Progressive Reasoning modules \\( B_{1}, B_{2}, \\ldots, B_{i} \\), Block \\( B_{i} \\) utilizes different word-level semantic features by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.154,
+                0.801,
+                0.469,
+                0.818
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathbf {X}} _ {t} = \\mathbf {X} _ {t} ^ {\\prime} + \\text {A t t e n t i o n} \\left(\\mathbf {X} _ {t} ^ {\\prime}, \\mathbf {W} _ {i}, \\mathbf {W} _ {i}\\right) \\tag {15}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{X}_t^\\prime\\) is motion features and \\(\\mathrm{W}_i\\) is the text features. \\(\\mathbf{X}_t^\\prime\\) forms the query vector \\(Q\\), \\(\\mathbf{W}_i\\) forms the key vector \\(K\\) and value vector \\(V\\). They pass through the process in Equation 14. Finally, several MLP layers further processes the above features to output the predicted target \\(\\mathbf{X}_t\\in \\mathbb{R}^{T\\times D}\\)"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.511±.003</td><td>0.703±.003</td><td>0.797±.002</td><td>0.002±.000</td><td>2.974±.008</td><td>9.503±.065</td><td>-</td></tr><tr><td>Seq2Seq [16]</td><td>0.180±.002</td><td>0.300±.002</td><td>0.396±.002</td><td>11.75±.035</td><td>5.529±.007</td><td>6.223±.061</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.246±.002</td><td>0.387±.002</td><td>0.486±.002</td><td>11.02±.046</td><td>5.296±.008</td><td>7.676±.058</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.165±.001</td><td>0.267±.002</td><td>0.345±.002</td><td>7.664±.030</td><td>6.030±.008</td><td>6.409±.071</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.301±.002</td><td>0.425±.002</td><td>0.552±.004</td><td>6.532±.024</td><td>5.012±.018</td><td>8.332±.042</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.037±.000</td><td>0.072±.001</td><td>0.106±.001</td><td>94.41±.021</td><td>9.643±.006</td><td>0.462±.008</td><td>0.019±.000</td></tr><tr><td>Dance2Music [14]</td><td>0.033±.000</td><td>0.065±.001</td><td>0.097±.001</td><td>66.98±.016</td><td>8.116±.006</td><td>0.725±.011</td><td>0.043±.001</td></tr><tr><td>TEMOS [21]</td><td>0.424±.002</td><td>0.612±.002</td><td>0.722±.002</td><td>3.734±.028</td><td>3.703±.008</td><td>8.973±.071</td><td>0.368±.018</td></tr><tr><td>Temporal VAE [7]</td><td>0.455±.003</td><td>0.636±.003</td><td>0.740±.003</td><td>1.067±.002</td><td>3.340±.008</td><td>9.188±.002</td><td>2.090±.083</td></tr><tr><td>TM2T [8]</td><td>0.424±.003</td><td>0.618±.003</td><td>0.729±.002</td><td>1.501±.017</td><td>3.467±.011</td><td>8.589±.076</td><td>2.424±.093</td></tr><tr><td>MotionDiffuse [33]</td><td>0.491±.001</td><td>0.681±.001</td><td>0.782±.001</td><td>0.630±.001</td><td>3.113±.001</td><td>9.410±.049</td><td>1.553±.042</td></tr><tr><td>MDM [28]</td><td>0.320±.005</td><td>0.498±.004</td><td>0.611±.007</td><td>0.544±.044</td><td>5.566±.027</td><td>9.559±.086</td><td>2.790±.072</td></tr><tr><td>T2M-GPT [32]</td><td>0.491±.003</td><td>0.680±.003</td><td>0.775±.002</td><td>0.116±.004</td><td>3.118±.011</td><td>9.761±.081</td><td>1.856±.011</td></tr><tr><td>Fg-T2M</td><td>0.492±.002</td><td>0.683±.003</td><td>0.783±.002</td><td>0.243±.019</td><td>3.109±.007</td><td>9.278±.072</td><td>1.614±.049</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.234,
+                0.892,
+                0.279
+            ],
+            "angle": 0,
+            "content": "Table 1: Comparison of text-conditional motion synthesis on HumanML3D [7] dataset. Red and Blue indicate the best and the second best result, respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.5,
+                0.297,
+                0.892,
+                0.432
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.424±.005</td><td>0.649±.006</td><td>0.779±.006</td><td>0.031±.004</td><td>2.788±.012</td><td>11.08±.097</td><td>-</td></tr><tr><td>Seq2Seq[16]</td><td>0.103±.003</td><td>0.178±.005</td><td>0.241±.006</td><td>24.86±.348</td><td>7.960±.031</td><td>6.741±.106</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.156±.004</td><td>0.255±.004</td><td>0.338±.005</td><td>12.12±.183</td><td>6.964±.029</td><td>9.334±.079</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.221±.005</td><td>0.373±.004</td><td>0.483±.005</td><td>6.545±.072</td><td>5.147±.030</td><td>9.073±.100</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.255±.006</td><td>0.432±.007</td><td>0.531±.007</td><td>5.203±.107</td><td>4.986±.027</td><td>9.563±.072</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.022±.002</td><td>0.042±.003</td><td>0.063±.003</td><td>82.69±.242</td><td>10.47±.012</td><td>3.091±.043</td><td>0.250±.009</td></tr><tr><td>Dance2Music [14]</td><td>0.031±.002</td><td>0.058±.002</td><td>0.086±.003</td><td>115.4±.240</td><td>10.40±.016</td><td>0.241±.004</td><td>0.062±.002</td></tr><tr><td>TEMOS [21]</td><td>0.353±.006</td><td>0.561±.007</td><td>0.687±.005</td><td>3.717±.051</td><td>3.417±.019</td><td>10.84±.100</td><td>0.532±.034</td></tr><tr><td>Temporal VAE [7]</td><td>0.361±.006</td><td>0.559±.007</td><td>0.693±.007</td><td>2.770±.109</td><td>3.401±.008</td><td>10.91±.119</td><td>1.482±.065</td></tr><tr><td>TM2T [8]</td><td>0.280±.005</td><td>0.463±.006</td><td>0.587±.005</td><td>3.599±.153</td><td>4.591±.026</td><td>9.473±.117</td><td>3.292±.081</td></tr><tr><td>MotionDiffuse [33]</td><td>0.417±.004</td><td>0.621±.004</td><td>0.739±.004</td><td>1.954±.062</td><td>2.958±.005</td><td>11.10±.143</td><td>0.730±.013</td></tr><tr><td>MDM [28]</td><td>0.164±.004</td><td>0.291±.004</td><td>0.396±.004</td><td>0.497±.021</td><td>9.19±.022</td><td>10.847±.109</td><td>1.907±.214</td></tr><tr><td>T2M-GPT [32]</td><td>0.416±.006</td><td>0.627±.006</td><td>0.745±.006</td><td>0.514±.029</td><td>3.007±.023</td><td>10.92±.108</td><td>1.570±.039</td></tr><tr><td>Fg-T2M</td><td>0.418±.005</td><td>0.626±.004</td><td>0.745±.004</td><td>0.571±.047</td><td>3.114±.015</td><td>10.93±.083</td><td>1.019±.029</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.438,
+                0.892,
+                0.483
+            ],
+            "angle": 0,
+            "content": "Table 2: Comparison of text-conditional motion synthesis on KIT [22] dataset. Red and Blue indicate the best and the second best result, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.509,
+                0.633,
+                0.527
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.535,
+                0.892,
+                0.64
+            ],
+            "angle": 0,
+            "content": "Our Fg-T2M framework is evaluated on text-driven motion generation task in this section. We first describe the dataset used and the evaluation metrics in section 5.1. In section 5.2, we provide implementation details. We compare our framework with the current state-of-the-art methods in section 5.3. Finally, we present qualitative results and visualization for comparison in section 5.4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.651,
+                0.787,
+                0.667
+            ],
+            "angle": 0,
+            "content": "5.1. Datasets and Evaluation Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.674,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Several datasets exist for conditional motion generation, such as proposed in [7, 9, 11, 22]. However, datasets such as [9] and [11] are based on action categories and do not provide complete text sentences as conditioning inputs, making them unsuitable for our method. Instead, we use text-driven datasets, specifically, HumanML3D dataset [7] and KIT Motion-Language dataset [22], for our experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "The HumanML3D dataset [7] is a combination of the HumanAct12 [9] and AMASS [17] datasets, comprising 14,616 motions and 44,970 text descriptions across various human activities, such as daily activities, sports, acrobatics, etc., with a total duration of about 28.59 hours. The KIT Motion-Language dataset [22] consists of 3,911 motion sequences and 6,353 natural language descriptions, with a total duration of around 10.33 hours."
+        },
+        {
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+            "content": "22040"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.343,
+                0.895,
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+            "angle": 0,
+            "content": "Figure 6: Qualitative results: Our method is compared with two state-of-the-art methods: MotionDiffuse [33] and Temporal VAE [7]. Motion frames are ordered from left to right. Those not matching with text prompt are marked with a box."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.401,
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+            "angle": 0,
+            "content": "Evaluation Metrics are followed [7]. (1) \\( R \\)-precision. For each inferred text-motion pair, 31 mismatched descriptions are randomly selected from the test set. The average top-k precision is obtained by calculating and ranking the Euclidean distance between the motion and each of the 32 descriptions. (2) Frechet Inception Distance (FID). FID measures the similarity between the feature distributions extracted from the generated motions and ground truth motions. (3) Multi-Modal Distance. The multimodal distance is computed between the text feature and the relevant generated motion feature, concerning the given description. (4) Diversity. Diversity evaluates the dissimilarities among all generated motions across all descriptions by computing the mean pairwise Euclidean distance between randomly partitioned groups of motions. (5) Multimodality. For a given text description, 32 motion sequences are generated randomly, and multimodality quantifies the dissimilarities among these generated motion sequences. We primarily value R-precision and FID as pivotal performance metrics, which serve as important measures for evaluating the overall quality of generated motions."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+            "angle": 0,
+            "content": "The diffusion model uses 1000 diffusion steps and a linearly varying variance \\(\\beta_{t}\\) ranging from 0.0001 to 0.02. LSAM employs a 3-layer GAT network with a corresponding CAPR layer also set to 3. Hyper-parameter \\(\\lambda\\) in CAPR is 0.1. Training is performed with the Adam optimizer using a fixed learning rate of 5e-5, a batch size of 128, and NVIDIA GeForce RTX 3090 hardware. The KIT dataset is trained for approximately 40K iterations, while the HumanML3D dataset is trained for about 80K iterations."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5.3. Comparison with State-of-the-arts"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "We compared our method with several state-of-the-art models, including Lin et al. [16], Language2Pose [2], Ghosh et al. [5], MoCoGAN [29], Dance2Music [14], TEMOS [21], TM2T [8], Text2Gesture [3], Guo et al. [7], MotionDiffuse [33], and MDM [28]. Quantitative comparisons of our method with these models on the HumanML3D [7] and KIT [22] datasets are shown in Tables 1 and 2, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "Our method achieves competitive performance between text and motion features, as measured by MM Dist, to state-of-the-art methods, while exhibiting significantly higher scores in R-precision and FID. This demonstrates the ability of our method to generate high-quality motions that align with the text prompts. On the other hand, other approaches showcase remarkable competitiveness in diversity and multimodality. However, these aspects should be grounded in accuracy (R-precision) and precision (FID, MMDist) to strengthen their persuasiveness. Otherwise, the diversity or multimodality would be rendered meaningless if the generated motion fails to align with the desired outcome. Therefore, based on our experiments, our method has achieved advanced experimental results and demonstrates robustness in terms of model performance on the two datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Meanwhile, we design two experiments to evaluate fine-grained control. The first one is conducted on a Harder-HumanML3D dataset. We compress the HumanML3D test set of 4382 data into a Harder-HumanML3D set with 2582 data, by searching for sentences that contain more fine-grained words, like \"left\", \"right\", and so on. The comparison results are shown in Table 3. Our method exhibits significantly higher scores, indicating a better ability to capture"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "22041"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.447,
+                0.151
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.16,
+                0.164,
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+            ],
+            "angle": 0,
+            "content": "Figure 7: The result of user study."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"3\">R-Precision ↑</td><td rowspan=\"2\">FID ↓</td></tr><tr><td>Top-1</td><td>Top-2</td><td>Top-3</td></tr><tr><td>MotionDiffuse [33]</td><td>0.439±.006</td><td>0.614±.004</td><td>0.725±.005</td><td>0.732±.021</td></tr><tr><td>Fg-T2M</td><td>0.460±.005</td><td>0.660±.004</td><td>0.763±.004</td><td>0.421±.013</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.258,
+                0.47,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Table 3: Experiment results on Harder-HumanML3D split from the HumanML3D [7] test set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.318,
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+            "angle": 0,
+            "content": "fine-grained details. The second one is a user study in which we collect user preferences with T2M-GPT [32] and MotionDiffuse [33]. The statistics of the user study are shown in Figure 7. Compared with others, our method achieves superior performance in R-Precision, MM Dist, and yields competitive results in FID, which generates motions with comparable quality. Furthermore, for both questions, especially in the fine-grained aspect, ours is preferred over others and even competitive to the ground truth motions."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "We present ablation results in Table 4 to further understand the role of LSAM and CAPR in our method. The results demonstrate that models without the CAPR and LSAM modules exhibit performance degradation. And we also show the comparison of some qualitative examples on the ablation study of this two modules. Additionally, we experiment with the impact of different GAT semantic layers of text information. Since a common dependency tree of motion-text prompt often has three or four depths, a three-layer GAT is sufficient to capture overall nodes information. Hence, a shallow or deep GAT layer hinders the global or local semantic comprehension, resulting in diminished results. We further evaluate the proposed two parts in CAPR. The results show that without CAPR-2 part remarkably reduces the results, which also reflects the importance of fine-grained words for T2M tasks. Finally, the hyper-parameter \\(\\lambda\\) in CAPR controls the degree of text information fusion. A larger \\(\\lambda\\) dilutes the inherent properties of the motion features, leading to a decrease in precision."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "5.4. Qualitative Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visual results on the HumanML3D [7] dataset are presented in Figure 6, where our method is compared with the state-of-the-art models of MotionDiffuse [33] and Temporal VAE [7]. As can be seen from the examples in the figure, our method generates human motions that more accurately reflect the text prompts. In contrast, the methods of MotionDiffuse [33] and Temporal VAE [7] often result in unrealistic movements. Specifically, these methods tend to"
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>R-TOP3↑</td><td>FID↓</td></tr><tr><td>Fg-T2M</td><td>0.745±.004</td><td>0.571±.047</td></tr><tr><td>Fg-T2M (w/o LSAM)</td><td>0.722±.005</td><td>1.077±.101</td></tr><tr><td>Fg-T2M (w/o CAPR)</td><td>0.727±.007</td><td>0.943±.089</td></tr><tr><td>Fg-T2M (one layer)</td><td>0.729±.006</td><td>0.951±.092</td></tr><tr><td>Fg-T2M (two layers)</td><td>0.738±.003</td><td>0.692±.086</td></tr><tr><td>Fg-T2M (four layers)</td><td>0.740±.004</td><td>0.636±.102</td></tr><tr><td>Fg-T2M(w/o CAPR-1)</td><td>0.739±.006</td><td>0.652±.035</td></tr><tr><td>Fg-T2M(w/o CAPR-2)</td><td>0.732±.004</td><td>0.764±.039</td></tr><tr><td>Fg-T2M (λ = 0.2)</td><td>0.738±.008</td><td>0.686±.062</td></tr><tr><td>Fg-T2M (λ = 0.3)</td><td>0.732±.006</td><td>0.830±.074</td></tr><tr><td>Fg-T2M (λ = 0.5)</td><td>0.729±.011</td><td>1.086±.104</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.297,
+                0.892,
+                0.387
+            ],
+            "angle": 0,
+            "content": "Table 4: Ablation analysis on KIT [22]. \"layers\" indicates the number of layers of GAT in LSAM. \"(w/o) CAPR-1\" means without multi-modal sentence-level feature-fusion. \"(w/o) CAPR-2\" means without multi-head word-level cross-attention. \"λ\" is the hyper-parameter of Multi-Modal Sentence-Level Feature-Fusion module in CAPR."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.418,
+                0.892,
+                0.63
+            ],
+            "angle": 0,
+            "content": "only understand one motion within a long text prompt and are not sensitive to specific numerical values, such as 'one' or 'two'. As depicted in example one, MotionDiffuse [33] only performed a backward motion without considering the required number of steps. On the other hand, Temporal VAE [7] successfully achieved the desired effect of walking forward and then backward, but its backward motion step count did not meet the expected requirement. Moreover, They also make errors in spatial orientation, such as 'left' or 'right', and lack a thorough understanding of temporal issues, such as 'while' and 'then', related to movement. Overall, our proposed method outperforms these models, especially in terms of the issues mentioned above. More diverse samples are presented in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.647,
+                0.618,
+                0.662
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.673,
+                0.892,
+                0.854
+            ],
+            "angle": 0,
+            "content": "We present a novel method for text-driven human motion generation using the diffusion model, which offers several advantages over existing techniques. Specifically, our method leverages two key modules - a linguistics-structure assisted module and a context-aware progressive reasoning module - to effectively model fine-grained words in the text. The former module extracts dependency parsing relationships in the text, while the latter performs hierarchical effective information feature fusion based on graph neural networks. Our quantitative and qualitative results demonstrate that our method outperforms existing techniques in text-driven motion generation tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work was supported by the National Natural Science Foundation of China (Project Number: 62272019)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "22042"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
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+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+        },
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+                0.47,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.957
+            ],
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+        }
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+]
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+# Fg-T2M: Fine-Grained Text-Driven Human Motion Generation via Diffusion Model
+
+Yin Wang $^{1}$ , Zhiying Leng $^{1,2}$ , Frederick W. B. Li $^{3}$ , Shun-Cheng Wu $^{2}$ , Xiaohui Liang $^{1,4,*}$
+
+$^{1}$ State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China
+
+$^{2}$ Technical University of Munich, Germany
+
+$^{3}$ Department of Computer Science, University of Durham, U.K.
+
+$^{4}$ Zhongguancun Laboratory, Beijing, China.
+
+{wang_yin, zhiyingleng, liang_xiaohui}@buaa.edu.cn, frederick.li@durham.ac.uk, shuncheng.wu@tum.de
+
+# Abstract
+
+Text-driven human motion generation in computer vision is both significant and challenging. However, current methods are limited to producing either deterministic or imprecise motion sequences, failing to effectively control the temporal and spatial relationships required to conform to a given text description. In this work, we propose a fine-grained method for generating high-quality, conditional human motion sequences supporting precise text description. Our approach consists of two key components: 1) a linguistics-structure assisted module that constructs accurate and complete language feature to fully utilize text information; and 2) a context-aware progressive reasoning module that learns neighborhood and overall semantic linguistics features from shallow and deep graph neural networks to achieve a multi-step inference. Experiments show that our approach outperforms text-driven motion generation methods on HumanML3D and KIT test sets and generates better visually confirmed motion to the text conditions.
+
+# 1. Introduction
+
+Human motion generation is a crucial task in computer vision with various applications in animation production, gaming, robot control, and movie script visualization. Obtaining human motion sequences through traditional software is a labor-intensive and tedious process, while motion capture is complex and expensive. Recently, with the advancements in deep learning and computer vision, learning-based human motion generation has emerged as a solution to this problem, leading to the development of associated generation methods based on multimodal data. The input multimodal data include music [12, 15, 25, 27], motion cat
+
+![](images/c2a121fb0b5673d6bbb73d2f203b85aec87b6d8592be93acffaaff573ef271cb.jpg)  
+Figure 1: Our approach generates human motion sequences that grasp fine-grained details.
+
+egories [4, 9, 20], text [2, 3, 5, 7, 8, 16, 21, 23, 28, 33], among others. Text-driven human motion generation has been a popular research topic, because of its convenience and human-friendliness. In particular, natural language comprises nouns, verbs, adverbs, etc. The mutual connections among different words in a sentence establish its semantics. Verbs define the action's category, while adverbs control the fineness of the action. The interaction between words in syntax plays a vital role in determining the structure and meaning of a sentence. Failure to fully incorporate these text features may result in inadequate text modeling, causing the generated motion sequence to deviate from the intended meaning of the original text.
+
+Existing methods can be divided into two branches, including 1) cross-modal alignment of motion and text [2, 3, 5, 7, 8, 16, 21]; 2) conditional diffusion models [28, 33]. In the first methods, text sequences and motion sequences are mapped onto separate feature spaces and forcibly aligned, leading to a loss of original information from both domains. In the second methods, the diffusion model incorporates
+
+text information as a conditioning factor to learn the probability mapping of human motions. However, the model interacts with only one text feature at each time step of the inference process, lacking a progressive approach. Moreover, text modeling only involves simple manipulation, which ignores the importance of certain fine-grained words and leads to incomplete semantic understanding, making it challenging to learn focus points at each step. Overall, existing methods only use text information to a limited extent, which in turn affects the accuracy of motion generation based on the corresponding text content, especially for the motion in which texts contain fine-grained words. For instance, comprehending the sentence "A man is walking forward while waving his right hand" can be a difficult task, and expecting the model to grasp the fine-grained meaning of the terms "while" and "right hand" is even more demanding.
+
+To tackle the aforementioned issues, we propose a fine-grained text-driven method for generating human motion sequences that precisely align with text prompts in Figure 1. Typically, people initially read a sentence to gain an overall semantic understanding before focusing on the fine-grained details of individual words. To replicate this process, our method includes a linguistics-structure assisted module and a context-aware progressive reasoning module to fully utilize text information. Firstly, we utilize linguistics structure to facilitate information exchange between each text word. We use dependency parsing [19] to analyze the relationships among words in each sentence and construct a dependency tree, allowing each node to effectively communicate based on its dependent nodes and relationships. Then, the dependency tree nodes are passed to multi-layer graph neural networks to learn information aggregation. The multilayer graph neural networks allow shallow network to learn neighborhood features as it can comprehend nearby details, and allow deep network to grasp overall semantic features because it is capable of aggregating information from entire nodes. Additionally, our GAT captures rich inter-word relationships while preserving the text linguistics structure by designing adaptive weights for each part-of-speech and dependency relation due to their distinctive role in the Text to Motion (T2M) task.
+
+Secondly, achieving the purpose of fine-grained interaction, context-aware progressive reasoning module performs a multi-step inference process with the progressive fusion of global and local information between text and motion, which is unprecedented in the T2M task. This involves utilizing hierarchical semantic features to simulate the way humans comprehend sentences. We adopt the diffusion model framework and stack the hierarchical semantic features obtained from deep to shallow networks at each step to capture high-order relationships at different semantic levels. We evaluate our method on HumanML3D dataset [7] and KIT dataset [22]. Experiments show that our approach out
+
+performs the state-of-the-art methods and generates better visual motion. Our main contributions include:
+
+- To the best of our knowledge, we are the first to bring NLP methods into T2M task. Utilizing the structured understanding of the natural language prompts to help T2M models achieve better reasoning skills, which brings new ideas for the text-to-X community from a textual perspective.  
+- We propose the Linguistics-Structure Assisted Module (LSAM), which utilizes a dependency parsing tree and graph networks to facilitate effective information exchange and data aggregation. It can obtain both neighborhood and overall semantic linguistic features.  
+- We propose a Context-Aware Progressive Reasoning Module (CAPR) that implements a multi-step progressive inference strategy within the diffusion model framework, mimicking the human reading process by moving from global to local relationships.  
+- Experimental results demonstrate that our proposed method outperforms previous methods, and achieves competitive performance on the HumanML3D and KIT datasets.
+
+# 2. Related Work
+
+# 2.1. Motion generation model
+
+Generative models play a crucial role in motion synthesis by generating high-quality human motion. Generative Adversarial Nets (GAN) [6] use two sub-models: a generator model that produces new samples, and a discriminator model that attempts to classify samples as either real or fake. These two models compete against each other during training. However, the interpretability of GAN is poor because the learned data distribution lacks an explicit expression, resembling a black box mapping function.
+
+Auto-Encoding Variational Bayes (VAE) [13] is a widely used generative model in motion synthesis. Its primary objective is to generate new samples from the learned distribution of objects by learning latent attributes from the probability distribution of the latent variable space, thereby constructing new examples. Despite its usefulness, the quality of samples generated by VAE can be improved.
+
+Recently proposed diffusion models [10, 18, 26] have shown immense potential in modeling and present an exciting opportunity to expand into text-driven motion generation. These models utilize the stochastic diffusion process modeled in thermodynamics, which gradually adds noise to the samples of the data distribution. The deep learning model then learns the reverse process of denoising the samples gradually. Diffusion models have the advantage over previous models as they do not make any assumptions about
+
+the target distribution, leading to a more diverse generation and better suitability for our task. Therefore, we propose a novel fine-grained human motion generation method that employs the Denoising Diffusion Probability Model [10].
+
+# 2.2. Text-driven human motion generation
+
+The task of text-driven human motion generation involves generating 3D human motion sequences that conform to a textual description. Several previous works have tackled this task. Initially, Text2Action [1] proposed short-text conditioned motion generation based on an RNN model. Subsequently, Ahuja et al. [2] and Ghosh et al. [5] focused on creating a joint representation of text and motion by projecting both features into a shared latent space. However, these methods involve a one-to-one mapping between text and motion, implying that given the same text, they can only produce fixed motion sequence results.
+
+To increase generated result diversity, TEMOS [21] introduced a VAE architecture that finds a joint latent space for motion and text under Gaussian distribution constraints. Guo et al. [7] used a temporal VAE to autoregressively generate motion sequences based on text features. However, these methods have a significant drawback of mapping text and motion sequences to separate feature spaces and forcibly align them, leading to a loss of information in both domains. Recently, diffusion models have shown great potential in image generation and have inspired the development of diffusion models for human motion generation. Tevet et al. [28] and Zhang et al. [33] encoded text descriptions using pre-trained models and estimated Gaussian noise or the original motion sequence at each reverse diffusion step. However, their text modeling is often crude and does not fully leverage linguistic structure for sentence semantics. Also, they do not have a progressive process that allows the diffusion model to focus on different content at different time stamps, and they only interact with fixed text features during the inference process.
+
+# 3. Preliminaries
+
+The diffusion process is a Markov process consisting of a forward process and a reverse process. The forward process starts with the real data  $X_0$  at step 0 and proceeds in a Markovian manner by adding Gaussian noise at each step. Over  $t$  steps,  $X_0$  is transformed into  $X_t$ , which is close to the Gaussian distribution  $N(0, I)$ . As a result, the original motion sequence is converted into a complete noise distribution, which can be expressed as:
+
+$$
+q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1}, \beta_ {t} I\right) \tag {1}
+$$
+
+where  $\beta_{t}$  is a hyper-parameter that controls the diffusion rate. The entire diffusion forward process is formulated as:
+
+$$
+q \left(\mathbf {x} _ {1: T} \mid \mathbf {x} _ {0}\right) = \prod_ {t = 1} ^ {T} q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) \tag {2}
+$$
+
+where  $T$  denotes total steps in diffusion. The diffusion reverse process samples from the Gaussian distribution  $X_{t}$  as the initial input and attempts to gradually remove the noise on a reverse Markov-chain, which can be defined as follows:
+
+$$
+p _ {\theta} \left(\mathbf {x} _ {0: T}\right) = p \left(\mathbf {x} _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) \tag {3}
+$$
+
+$$
+p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) = \mathcal {N} \left(\mathbf {x} _ {t - 1}; \mu_ {\theta} \left(\mathbf {x} _ {t}, t\right), \Sigma_ {\theta} \left(\mathbf {x} _ {t}, t\right)\right) \tag {4}
+$$
+
+where  $\mu_{\theta}$  is the estimated item by model,  $t$  is the timestep indicating where the denoising process has conducted.
+
+# 4. Method
+
+To enhance the modeling of fine-grained human motion generation, we present our proposed method in Figure 2. Previous methods [1, 2, 5] have adopted a coarse approach to text modeling, leading to an underutilization of text information. Moreover, they treat all words equally without considering their importance and uniqueness. In contrast, we leverage linguistic structures in sentences to further enhance text encoding and differentiate between overall semantic information and detailed features using a multi-step progressive reasoning strategy.
+
+Given a text prompt,  $W = \{w_{1}, w_{2}, \ldots, w_{n}\}$ ,  $W \in \mathbb{R}^{N \times L}$  where  $N$  represents the number of words and  $L$  is the dimension of word vector. Our goal is to generate a human motion sequence, denoted as  $M = \{m_{1}, m_{2}, \ldots, m_{t}\}$ , where  $M \in \mathbb{R}^{T \times D}$ . Here,  $T$  refers to the sequence length and  $D$  is the motion representation dimension. To achieve this, we introduce Fg-T2M, a method that generates motion sequences that align well with the corresponding textual content. In the following, we provide an overview of our approach in section 4.1, followed by the introduction of the Linguistics-Structure Assisted Module (LSAM) in section 4.2. Lastly, we present the Context-Aware Progressive Reasoning (CAPR) module in section 4.3.
+
+# 4.1. Overview
+
+Figure 2 shows our pipeline for generating motion sequences. We randomly sample  $\mathbf{x}_T$  from distribution  $N(0, I)$ , input  $\mathbf{x}_T$ , current step  $T$ , and text control condition  $c$  to obtain  $\mathbf{x}_{T-1}$ , iterating  $T$  rounds until we get  $\mathbf{x}_0$ . In the denoising process, the condition  $c$  is fed into our LSAM text encoder. By leveraging dependency relationships between words, we use graph neural networks to aggregate data and extract hierarchical semantic features. The motion decoder
+
+![](images/e477c781af1c35cf046ce6d58ce5b9333bf5a3b23701381b6a1dc9a14f51c3c0.jpg)  
+Figure 2: Overall Pipeline of our proposed method Fg-T2M: (a) the reverse denoising process of the diffusion model from  $X_{T}$  to  $X_{0}$ ; (b) the text encoder with proposed linguistics-structure assisted module with dependency parsing in section 4.2; (c) the motion decoder with introduced context-aware progressive reasoning module in section 4.3.
+
+is stacked with CAPR. Multiple layers of these modules enhance the quality of the generated motion sequence.
+
+To train the motion diffusion model, we optimize the objective to predict the original data, representing as follows:
+
+$$
+\mathcal {L} = \mathrm {E} _ {t \in [ 1, T ], \mathbf {x} _ {0} \sim q (\mathbf {x} _ {0}), \epsilon \sim \mathcal {N} (0, I)} [ \| \mathbf {x} _ {0} - \hat {\mathbf {x}} _ {0} (\mathbf {x} _ {t}, t, c) \| _ {2} ^ {2} ]. \tag {5}
+$$
+
+The regular L2 loss can improve performance for all geometric losses mentioned above.
+
+# 4.2. Linguistics-Structure Assisted Module
+
+The current text modeling method is limited in its sensitivity to fine-grained words, which hinders the effectiveness of subsequent generations. To address this, we enhance the context modeling of sentences by identifying the phrase structure and syntactic relationships between phrases using dependency parsing, as shown in Figure 3. Linguistic structure, which comprises phrase structure and syntax relationships, helps us better understand the essence of text and the differences and similarities between sentences. Dependency parsing [19] precisely analyzes vocabulary and syntax to identify the dependency relationships between words in a sentence. In this approach, each word is treated as a node, and the dependency relationships between words are represented by edges that indicate syntactic connections. The resulting node and edge features representing the dependency relationships are input into a graph network to
+
+![](images/7c4fa65f3d484bb86c917adaa5baadd7653ca826dd1b8142618e956a97a5fd8a.jpg)  
+Figure 3: Architecture of LSAM. The left panel illustrates the process of obtaining node and edge features for one sentence in dependency analysis feature extraction, while the right panel demonstrates the workflows that utilize multiple layers of Graph Attention Network to extract feature information with varying degrees.
+
+obtain multi-level semantics. In summary, given a sentence, the dependency parsing analyses to build a text tree, nodes for words, and links between nodes for their linguistic relationships. The text tree structure as the graph initialization for graph topology and edge features provides GAT a better prior. The GAT aims to capture inter-word relationships while maintaining the linguistic structure of the text.
+
+To extract word associations, we parse the dependency
+
+of phrase and obtain the hierarchical syntactic relationships using Spacy<sup>1</sup> for dependency parsing, as shown in the left panel of Figure 3. Spacy is a natural language processing software library for text processing, including lexical analysis, syntactic analysis, and more. In dependency parsing, each word is treated as a node, and the edges represent the labels of the dependency relationships between words, allowing us to construct a tree of language structure for the given text. We extract features using a graph attention network (GAT) [31]. For the input nodes of the graph network, we use word features obtained from the CLIP [24] model. For the adjacency matrix, we set a value of 1 or 0 to represent the presence or absence of a dependency relationship between nodes. Since the number of dependency relationships is fixed, we use one-hot encoding to obtain a one-hot label for each relationship, which is then fed into an embedding layer. This can be described as:
+
+$$
+\mathbf {v} _ {\mathbf {e}} = \beta_ {i} \left(\varphi_ {e} \left(\mathrm {F} _ {\text {o n e h o t}} \left(R _ {i}\right)\right)\right) \tag {6}
+$$
+
+where  $\mathbf{v}_{\mathrm{e}} \in \mathbb{R}^{D_{e}}$ ,  $D_{e}$  is the dimension of edge feature,  $\varphi_{e}$  denotes an embedding layer,  $\beta_{i}$  is adaptive weight parameters to be learned for every  $R_{i}$ , while  $R_{i}$  indicates the edge relation between two nodes. Since each word may be adjacent to multiple nodes, and different nodes contribute differently to semantics, it is necessary to distinguish them during the text feature extraction process. We achieve this by applying GAT [31], which extracts multi-level features from the obtained node information, adjacency matrix, and edge information. GAT [31] considers differences between nodes during information aggregation and handles irregularities between different nodes effectively, which is described as:
+
+$$
+x _ {i} ^ {\prime} = \alpha_ {i, i} \Theta x _ {i} + \sum_ {j \in N (i)} \alpha_ {i, j} \Theta x _ {j} \tag {7}
+$$
+
+$$
+\alpha_ {i, j} = \frac {\exp \left(\mathrm {F} \left(\omega^ {\top} \left[ \Theta \mathrm {x} _ {\mathrm {i}} \right| | \Theta \mathrm {x} _ {\mathrm {j}} | | \Theta_ {\mathrm {e}} \mathrm {e} _ {\mathrm {i} , \mathrm {j}} ]\right)\right)}{\sum_ {k \in N (i) \cup \{i \}} \exp \left(\mathrm {F} \left(\omega^ {\top} \left[ \Theta x _ {i} \right| | \Theta x _ {k} | | \Theta_ {e} e _ {i , k} ]\right)\right)} \tag {8}
+$$
+
+We have  $x, \alpha \in \mathbb{R}^{N \times L}$ , where  $\alpha_{i,j}$  represents attention coefficients,  $F$  denotes LeakyReLU,  $e$  is edge features,  $\omega$  and  $\Theta$  represents the weight parameters to be learned, and  $||$  is the concatenation operation. GAT [31] can model high-order dependency relationships by stacking multiple graph attention layers to capture global and local graph topology effectively. For example, stacking three layers of GAT [31] results in  $x_i^1$ ,  $x_i^2$ , and  $x_i^3$  for each node  $x_i$ , as follows:
+
+$$
+x _ {i} ^ {l + 1} = \alpha_ {i, i} ^ {l} \Theta x _ {i} ^ {l} + \sum_ {j \in N (i)} \alpha_ {i, j} ^ {l} \Theta x _ {j} ^ {l} \tag {9}
+$$
+
+The shallow network  $x_{i}^{1}$  learns detailed features of the neighborhood as it can only gather information from directly adjacent nodes in the first step of node aggregation.
+
+![](images/5df61e6546ed88fa6034c744544cb5d25a810932e67d9c03c3dfdfa928955d59.jpg)  
+Figure 4: Architecture of CAPR. The left panel illustrates inferring  $X_{t-1}$  from  $X_t$ ,  $t$ , and text features. The right panel provides the detailed view of one context-aware progressive reasoning module, which comprises two parts: sentence-level feature fusion and word-level cross-attention.
+
+This process captures more local and fine-grained information. By comparison, the deep network  $x_{i}^{3}$  can learn overall semantic features by aggregating information from distant nodes after multiple aggregation steps. This enables it to capture more global and holistic information.
+
+# 4.3. Context-Aware Progressive Reasoning Module
+
+Guided by the Linguistics-Structure Assisted Module (LSAM) in the previous section, we stack Context-Aware Progressive Reasoning Modules to perform multi-step progressive reasoning in a structured manner. Unlike previous methods that learn fixed features [28, 33], our stacked modules grasp features from global to local. Each block receives distinct contextual information, with higher-level blocks utilizing deeper context features from the LSAM, and lower-level blocks utilizing shallower features. This results in the model perceiving hierarchical information during the inference process, which greatly benefits its ability to hierarchically comprehend the meaning of text content and sense its fine-grained words.
+
+The CAPR comprises two parts: Multi-Modal Sentence-level Feature-Fusion and Multi-Head Word-level Cross-Attention. Figure 4 shows that we start with the motion feature  $x_{t} \in \mathbb{R}^{T \times D}$ , text feature  $W \in \mathbb{R}^{N \times L}$ , and timestep  $t$ . To better capture the unique characteristics of each time step in the diffusion model, we first perform sinusoidal time embedding through linear layers to obtain timestep embedding  $emb_{t}$ . We then add the motion and text features to  $emb_{t}$  to incorporate different time information at each timestep.
+
+Multi-Modal Sentence-Level Feature-Fusion module fuses sentence-level text features and motions to obtain multi-modal features, as shown in Figure 5. For the i-th Context-Aware Progressive Reasoning Module block, the text  $W_{i}$  is transformed to a sentence-level feature  $S$  using convolution, which is derived from the i-th LSAM layer:
+
+$$
+S _ {i} = \operatorname {C o n v} _ {1 d} \left(W _ {i}\right) \tag {10}
+$$
+
+![](images/c6f89060fc2fc35eca19602713f48f9f15e35890d7d813e93a7d8a204c90bcd0.jpg)  
+Figure 5: Illustration of Multi-Modal Sentence-Level Feature-Fusion Module.
+
+where  $S_{i}\in \mathbb{R}^{1\times D_{s}}$ ,  $W_{i}\in \mathbb{R}^{N\times D_{w}}$ ,  $D_{s}$  and  $D_{w}$  denotes the dimension of sentence feature and words feature, and Conv1d is the 1d convolution. We then perform a matrix multiplication to obtain an attention list  $A$ :
+
+$$
+A = \mathbf {X} _ {t} S _ {i} ^ {\mathrm {T}} \tag {11}
+$$
+
+where  $\mathbf{X}_t\in \mathbb{R}^{T\times D}$  and  $A\in \mathbb{R}^{T\times 1}$ . Here,  $\mathbf{X}_t$  represents the motion feature at timestep  $t$ , and  $A$  calculates the feature relevance between the sentence and each frame on the feature map. The resulting cross-modal feature,  $\mathbf{X}_t'$ , highlights the sentence-relevant frame feature channels:
+
+$$
+\mathrm {X} _ {t} ^ {\prime} = \mathrm {X} _ {t} + \lambda \left(\mathrm {X} _ {t} \odot (\sigma (A))\right) \tag {12}
+$$
+
+where  $\lambda$  is a hyper-parameter,  $\odot$  is element-wise multiplication and  $\sigma$  is a sigmoid activation function. To enhance modeling the correlation between different fused information, a self-attention mechanism [30] is added to strengthen the connection between multiple frames. Multi-head self-attention is conducted on the fusion feature  $X_{t}^{\prime}$  as follows:
+
+$$
+\mathrm {Q} = W _ {q} \mathrm {X} _ {t} ^ {\prime}, \mathrm {K} = W _ {k} \mathrm {X} _ {t} ^ {\prime}, \text {a n d} \mathrm {V} = W _ {v} \mathrm {X} _ {t} ^ {\prime} \tag {13}
+$$
+
+where  $W_{q}, W_{k}$  and  $W_{v}$  are trainable weights to generate Q, K and V, respectively. Obtain the attention scores using the formula below, where  $\otimes$  is the matrix multiplication.
+
+$$
+\operatorname {A t t e n t i o n} (\mathrm {Q}, \mathrm {K}, \mathrm {V}) = \operatorname {s o f t m a x} \left(\frac {\mathrm {Q} \otimes \mathrm {K} ^ {\top}}{\sqrt {d}}\right) \mathrm {V} \tag {14}
+$$
+
+Multi-Head Word-Level Cross-Attention module learns the cross-interaction between motion sequences and multi-level contextual text features. It uses the formulas mentioned in the self-attention module for calculation, but modifies the motion features of K and V to text features. Therefore, on the stacked Context-Aware Progressive Reasoning modules  $B_{1}, B_{2}, \ldots, B_{i}$ , Block  $B_{i}$  utilizes different word-level semantic features by:
+
+$$
+\hat {\mathbf {X}} _ {t} = \mathbf {X} _ {t} ^ {\prime} + \text {A t t e n t i o n} \left(\mathbf {X} _ {t} ^ {\prime}, \mathbf {W} _ {i}, \mathbf {W} _ {i}\right) \tag {15}
+$$
+
+where  $\mathbf{X}_t^\prime$  is motion features and  $\mathrm{W}_i$  is the text features.  $\mathbf{X}_t^\prime$  forms the query vector  $Q$ ,  $\mathbf{W}_i$  forms the key vector  $K$  and value vector  $V$ . They pass through the process in Equation 14. Finally, several MLP layers further processes the above features to output the predicted target  $\mathbf{X}_t\in \mathbb{R}^{T\times D}$
+
+<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.511±.003</td><td>0.703±.003</td><td>0.797±.002</td><td>0.002±.000</td><td>2.974±.008</td><td>9.503±.065</td><td>-</td></tr><tr><td>Seq2Seq [16]</td><td>0.180±.002</td><td>0.300±.002</td><td>0.396±.002</td><td>11.75±.035</td><td>5.529±.007</td><td>6.223±.061</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.246±.002</td><td>0.387±.002</td><td>0.486±.002</td><td>11.02±.046</td><td>5.296±.008</td><td>7.676±.058</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.165±.001</td><td>0.267±.002</td><td>0.345±.002</td><td>7.664±.030</td><td>6.030±.008</td><td>6.409±.071</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.301±.002</td><td>0.425±.002</td><td>0.552±.004</td><td>6.532±.024</td><td>5.012±.018</td><td>8.332±.042</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.037±.000</td><td>0.072±.001</td><td>0.106±.001</td><td>94.41±.021</td><td>9.643±.006</td><td>0.462±.008</td><td>0.019±.000</td></tr><tr><td>Dance2Music [14]</td><td>0.033±.000</td><td>0.065±.001</td><td>0.097±.001</td><td>66.98±.016</td><td>8.116±.006</td><td>0.725±.011</td><td>0.043±.001</td></tr><tr><td>TEMOS [21]</td><td>0.424±.002</td><td>0.612±.002</td><td>0.722±.002</td><td>3.734±.028</td><td>3.703±.008</td><td>8.973±.071</td><td>0.368±.018</td></tr><tr><td>Temporal VAE [7]</td><td>0.455±.003</td><td>0.636±.003</td><td>0.740±.003</td><td>1.067±.002</td><td>3.340±.008</td><td>9.188±.002</td><td>2.090±.083</td></tr><tr><td>TM2T [8]</td><td>0.424±.003</td><td>0.618±.003</td><td>0.729±.002</td><td>1.501±.017</td><td>3.467±.011</td><td>8.589±.076</td><td>2.424±.093</td></tr><tr><td>MotionDiffuse [33]</td><td>0.491±.001</td><td>0.681±.001</td><td>0.782±.001</td><td>0.630±.001</td><td>3.113±.001</td><td>9.410±.049</td><td>1.553±.042</td></tr><tr><td>MDM [28]</td><td>0.320±.005</td><td>0.498±.004</td><td>0.611±.007</td><td>0.544±.044</td><td>5.566±.027</td><td>9.559±.086</td><td>2.790±.072</td></tr><tr><td>T2M-GPT [32]</td><td>0.491±.003</td><td>0.680±.003</td><td>0.775±.002</td><td>0.116±.004</td><td>3.118±.011</td><td>9.761±.081</td><td>1.856±.011</td></tr><tr><td>Fg-T2M</td><td>0.492±.002</td><td>0.683±.003</td><td>0.783±.002</td><td>0.243±.019</td><td>3.109±.007</td><td>9.278±.072</td><td>1.614±.049</td></tr></table>
+
+Table 1: Comparison of text-conditional motion synthesis on HumanML3D [7] dataset. Red and Blue indicate the best and the second best result, respectively.  
+
+<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.424±.005</td><td>0.649±.006</td><td>0.779±.006</td><td>0.031±.004</td><td>2.788±.012</td><td>11.08±.097</td><td>-</td></tr><tr><td>Seq2Seq[16]</td><td>0.103±.003</td><td>0.178±.005</td><td>0.241±.006</td><td>24.86±.348</td><td>7.960±.031</td><td>6.741±.106</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.156±.004</td><td>0.255±.004</td><td>0.338±.005</td><td>12.12±.183</td><td>6.964±.029</td><td>9.334±.079</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.221±.005</td><td>0.373±.004</td><td>0.483±.005</td><td>6.545±.072</td><td>5.147±.030</td><td>9.073±.100</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.255±.006</td><td>0.432±.007</td><td>0.531±.007</td><td>5.203±.107</td><td>4.986±.027</td><td>9.563±.072</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.022±.002</td><td>0.042±.003</td><td>0.063±.003</td><td>82.69±.242</td><td>10.47±.012</td><td>3.091±.043</td><td>0.250±.009</td></tr><tr><td>Dance2Music [14]</td><td>0.031±.002</td><td>0.058±.002</td><td>0.086±.003</td><td>115.4±.240</td><td>10.40±.016</td><td>0.241±.004</td><td>0.062±.002</td></tr><tr><td>TEMOS [21]</td><td>0.353±.006</td><td>0.561±.007</td><td>0.687±.005</td><td>3.717±.051</td><td>3.417±.019</td><td>10.84±.100</td><td>0.532±.034</td></tr><tr><td>Temporal VAE [7]</td><td>0.361±.006</td><td>0.559±.007</td><td>0.693±.007</td><td>2.770±.109</td><td>3.401±.008</td><td>10.91±.119</td><td>1.482±.065</td></tr><tr><td>TM2T [8]</td><td>0.280±.005</td><td>0.463±.006</td><td>0.587±.005</td><td>3.599±.153</td><td>4.591±.026</td><td>9.473±.117</td><td>3.292±.081</td></tr><tr><td>MotionDiffuse [33]</td><td>0.417±.004</td><td>0.621±.004</td><td>0.739±.004</td><td>1.954±.062</td><td>2.958±.005</td><td>11.10±.143</td><td>0.730±.013</td></tr><tr><td>MDM [28]</td><td>0.164±.004</td><td>0.291±.004</td><td>0.396±.004</td><td>0.497±.021</td><td>9.19±.022</td><td>10.847±.109</td><td>1.907±.214</td></tr><tr><td>T2M-GPT [32]</td><td>0.416±.006</td><td>0.627±.006</td><td>0.745±.006</td><td>0.514±.029</td><td>3.007±.023</td><td>10.92±.108</td><td>1.570±.039</td></tr><tr><td>Fg-T2M</td><td>0.418±.005</td><td>0.626±.004</td><td>0.745±.004</td><td>0.571±.047</td><td>3.114±.015</td><td>10.93±.083</td><td>1.019±.029</td></tr></table>
+
+Table 2: Comparison of text-conditional motion synthesis on KIT [22] dataset. Red and Blue indicate the best and the second best result, respectively.
+
+# 5. Experiments
+
+Our Fg-T2M framework is evaluated on text-driven motion generation task in this section. We first describe the dataset used and the evaluation metrics in section 5.1. In section 5.2, we provide implementation details. We compare our framework with the current state-of-the-art methods in section 5.3. Finally, we present qualitative results and visualization for comparison in section 5.4.
+
+# 5.1. Datasets and Evaluation Metrics
+
+Several datasets exist for conditional motion generation, such as proposed in [7, 9, 11, 22]. However, datasets such as [9] and [11] are based on action categories and do not provide complete text sentences as conditioning inputs, making them unsuitable for our method. Instead, we use text-driven datasets, specifically, HumanML3D dataset [7] and KIT Motion-Language dataset [22], for our experiments.
+
+The HumanML3D dataset [7] is a combination of the HumanAct12 [9] and AMASS [17] datasets, comprising 14,616 motions and 44,970 text descriptions across various human activities, such as daily activities, sports, acrobatics, etc., with a total duration of about 28.59 hours. The KIT Motion-Language dataset [22] consists of 3,911 motion sequences and 6,353 natural language descriptions, with a total duration of around 10.33 hours.
+
+![](images/e27eca9015b40291b92c44117de2e9566800c5d208ff7768de5d0943acd8832c.jpg)  
+Figure 6: Qualitative results: Our method is compared with two state-of-the-art methods: MotionDiffuse [33] and Temporal VAE [7]. Motion frames are ordered from left to right. Those not matching with text prompt are marked with a box.
+
+Evaluation Metrics are followed [7]. (1)  $R$ -precision. For each inferred text-motion pair, 31 mismatched descriptions are randomly selected from the test set. The average top-k precision is obtained by calculating and ranking the Euclidean distance between the motion and each of the 32 descriptions. (2) Frechet Inception Distance (FID). FID measures the similarity between the feature distributions extracted from the generated motions and ground truth motions. (3) Multi-Modal Distance. The multimodal distance is computed between the text feature and the relevant generated motion feature, concerning the given description. (4) Diversity. Diversity evaluates the dissimilarities among all generated motions across all descriptions by computing the mean pairwise Euclidean distance between randomly partitioned groups of motions. (5) Multimodality. For a given text description, 32 motion sequences are generated randomly, and multimodality quantifies the dissimilarities among these generated motion sequences. We primarily value R-precision and FID as pivotal performance metrics, which serve as important measures for evaluating the overall quality of generated motions.
+
+# 5.2. Implementation Details
+
+The diffusion model uses 1000 diffusion steps and a linearly varying variance  $\beta_{t}$  ranging from 0.0001 to 0.02. LSAM employs a 3-layer GAT network with a corresponding CAPR layer also set to 3. Hyper-parameter  $\lambda$  in CAPR is 0.1. Training is performed with the Adam optimizer using a fixed learning rate of 5e-5, a batch size of 128, and NVIDIA GeForce RTX 3090 hardware. The KIT dataset is trained for approximately 40K iterations, while the HumanML3D dataset is trained for about 80K iterations.
+
+# 5.3. Comparison with State-of-the-arts
+
+We compared our method with several state-of-the-art models, including Lin et al. [16], Language2Pose [2], Ghosh et al. [5], MoCoGAN [29], Dance2Music [14], TEMOS [21], TM2T [8], Text2Gesture [3], Guo et al. [7], MotionDiffuse [33], and MDM [28]. Quantitative comparisons of our method with these models on the HumanML3D [7] and KIT [22] datasets are shown in Tables 1 and 2, respectively.
+
+Our method achieves competitive performance between text and motion features, as measured by MM Dist, to state-of-the-art methods, while exhibiting significantly higher scores in R-precision and FID. This demonstrates the ability of our method to generate high-quality motions that align with the text prompts. On the other hand, other approaches showcase remarkable competitiveness in diversity and multimodality. However, these aspects should be grounded in accuracy (R-precision) and precision (FID, MMDist) to strengthen their persuasiveness. Otherwise, the diversity or multimodality would be rendered meaningless if the generated motion fails to align with the desired outcome. Therefore, based on our experiments, our method has achieved advanced experimental results and demonstrates robustness in terms of model performance on the two datasets.
+
+Meanwhile, we design two experiments to evaluate fine-grained control. The first one is conducted on a Harder-HumanML3D dataset. We compress the HumanML3D test set of 4382 data into a Harder-HumanML3D set with 2582 data, by searching for sentences that contain more fine-grained words, like "left", "right", and so on. The comparison results are shown in Table 3. Our method exhibits significantly higher scores, indicating a better ability to capture
+
+![](images/19b44330938222eca3c66947c0a77bf5ce983539665a0e7cefc30345c06d4583.jpg)  
+Figure 7: The result of user study.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="3">R-Precision ↑</td><td rowspan="2">FID ↓</td></tr><tr><td>Top-1</td><td>Top-2</td><td>Top-3</td></tr><tr><td>MotionDiffuse [33]</td><td>0.439±.006</td><td>0.614±.004</td><td>0.725±.005</td><td>0.732±.021</td></tr><tr><td>Fg-T2M</td><td>0.460±.005</td><td>0.660±.004</td><td>0.763±.004</td><td>0.421±.013</td></tr></table>
+
+fine-grained details. The second one is a user study in which we collect user preferences with T2M-GPT [32] and MotionDiffuse [33]. The statistics of the user study are shown in Figure 7. Compared with others, our method achieves superior performance in R-Precision, MM Dist, and yields competitive results in FID, which generates motions with comparable quality. Furthermore, for both questions, especially in the fine-grained aspect, ours is preferred over others and even competitive to the ground truth motions.
+
+We present ablation results in Table 4 to further understand the role of LSAM and CAPR in our method. The results demonstrate that models without the CAPR and LSAM modules exhibit performance degradation. And we also show the comparison of some qualitative examples on the ablation study of this two modules. Additionally, we experiment with the impact of different GAT semantic layers of text information. Since a common dependency tree of motion-text prompt often has three or four depths, a three-layer GAT is sufficient to capture overall nodes information. Hence, a shallow or deep GAT layer hinders the global or local semantic comprehension, resulting in diminished results. We further evaluate the proposed two parts in CAPR. The results show that without CAPR-2 part remarkably reduces the results, which also reflects the importance of fine-grained words for T2M tasks. Finally, the hyper-parameter  $\lambda$  in CAPR controls the degree of text information fusion. A larger  $\lambda$  dilutes the inherent properties of the motion features, leading to a decrease in precision.
+
+# 5.4. Qualitative Results
+
+Visual results on the HumanML3D [7] dataset are presented in Figure 6, where our method is compared with the state-of-the-art models of MotionDiffuse [33] and Temporal VAE [7]. As can be seen from the examples in the figure, our method generates human motions that more accurately reflect the text prompts. In contrast, the methods of MotionDiffuse [33] and Temporal VAE [7] often result in unrealistic movements. Specifically, these methods tend to
+
+Table 3: Experiment results on Harder-HumanML3D split from the HumanML3D [7] test set.  
+
+<table><tr><td>Methods</td><td>R-TOP3↑</td><td>FID↓</td></tr><tr><td>Fg-T2M</td><td>0.745±.004</td><td>0.571±.047</td></tr><tr><td>Fg-T2M (w/o LSAM)</td><td>0.722±.005</td><td>1.077±.101</td></tr><tr><td>Fg-T2M (w/o CAPR)</td><td>0.727±.007</td><td>0.943±.089</td></tr><tr><td>Fg-T2M (one layer)</td><td>0.729±.006</td><td>0.951±.092</td></tr><tr><td>Fg-T2M (two layers)</td><td>0.738±.003</td><td>0.692±.086</td></tr><tr><td>Fg-T2M (four layers)</td><td>0.740±.004</td><td>0.636±.102</td></tr><tr><td>Fg-T2M(w/o CAPR-1)</td><td>0.739±.006</td><td>0.652±.035</td></tr><tr><td>Fg-T2M(w/o CAPR-2)</td><td>0.732±.004</td><td>0.764±.039</td></tr><tr><td>Fg-T2M (λ = 0.2)</td><td>0.738±.008</td><td>0.686±.062</td></tr><tr><td>Fg-T2M (λ = 0.3)</td><td>0.732±.006</td><td>0.830±.074</td></tr><tr><td>Fg-T2M (λ = 0.5)</td><td>0.729±.011</td><td>1.086±.104</td></tr></table>
+
+Table 4: Ablation analysis on KIT [22]. "layers" indicates the number of layers of GAT in LSAM. "(w/o) CAPR-1" means without multi-modal sentence-level feature-fusion. "(w/o) CAPR-2" means without multi-head word-level cross-attention. "λ" is the hyper-parameter of Multi-Modal Sentence-Level Feature-Fusion module in CAPR.
+
+only understand one motion within a long text prompt and are not sensitive to specific numerical values, such as 'one' or 'two'. As depicted in example one, MotionDiffuse [33] only performed a backward motion without considering the required number of steps. On the other hand, Temporal VAE [7] successfully achieved the desired effect of walking forward and then backward, but its backward motion step count did not meet the expected requirement. Moreover, They also make errors in spatial orientation, such as 'left' or 'right', and lack a thorough understanding of temporal issues, such as 'while' and 'then', related to movement. Overall, our proposed method outperforms these models, especially in terms of the issues mentioned above. More diverse samples are presented in the supplementary material.
+
+# 6. Conclusion
+
+We present a novel method for text-driven human motion generation using the diffusion model, which offers several advantages over existing techniques. Specifically, our method leverages two key modules - a linguistics-structure assisted module and a context-aware progressive reasoning module - to effectively model fine-grained words in the text. The former module extracts dependency parsing relationships in the text, while the latter performs hierarchical effective information feature fusion based on graph neural networks. Our quantitative and qualitative results demonstrate that our method outperforms existing techniques in text-driven motion generation tasks.
+
+Acknowledgements. This work was supported by the National Natural Science Foundation of China (Project Number: 62272019).
+
+# References
+
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+                                    "content": "Human motion generation is a crucial task in computer vision with various applications in animation production, gaming, robot control, and movie script visualization. Obtaining human motion sequences through traditional software is a labor-intensive and tedious process, while motion capture is complex and expensive. Recently, with the advancements in deep learning and computer vision, learning-based human motion generation has emerged as a solution to this problem, leading to the development of associated generation methods based on multimodal data. The input multimodal data include music [12, 15, 25, 27], motion cat"
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+                                    "content": "egories [4, 9, 20], text [2, 3, 5, 7, 8, 16, 21, 23, 28, 33], among others. Text-driven human motion generation has been a popular research topic, because of its convenience and human-friendliness. In particular, natural language comprises nouns, verbs, adverbs, etc. The mutual connections among different words in a sentence establish its semantics. Verbs define the action's category, while adverbs control the fineness of the action. The interaction between words in syntax plays a vital role in determining the structure and meaning of a sentence. Failure to fully incorporate these text features may result in inadequate text modeling, causing the generated motion sequence to deviate from the intended meaning of the original text."
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+                                    "content": "text information as a conditioning factor to learn the probability mapping of human motions. However, the model interacts with only one text feature at each time step of the inference process, lacking a progressive approach. Moreover, text modeling only involves simple manipulation, which ignores the importance of certain fine-grained words and leads to incomplete semantic understanding, making it challenging to learn focus points at each step. Overall, existing methods only use text information to a limited extent, which in turn affects the accuracy of motion generation based on the corresponding text content, especially for the motion in which texts contain fine-grained words. For instance, comprehending the sentence \"A man is walking forward while waving his right hand\" can be a difficult task, and expecting the model to grasp the fine-grained meaning of the terms \"while\" and \"right hand\" is even more demanding."
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+                                    "content": "To tackle the aforementioned issues, we propose a fine-grained text-driven method for generating human motion sequences that precisely align with text prompts in Figure 1. Typically, people initially read a sentence to gain an overall semantic understanding before focusing on the fine-grained details of individual words. To replicate this process, our method includes a linguistics-structure assisted module and a context-aware progressive reasoning module to fully utilize text information. Firstly, we utilize linguistics structure to facilitate information exchange between each text word. We use dependency parsing [19] to analyze the relationships among words in each sentence and construct a dependency tree, allowing each node to effectively communicate based on its dependent nodes and relationships. Then, the dependency tree nodes are passed to multi-layer graph neural networks to learn information aggregation. The multilayer graph neural networks allow shallow network to learn neighborhood features as it can comprehend nearby details, and allow deep network to grasp overall semantic features because it is capable of aggregating information from entire nodes. Additionally, our GAT captures rich inter-word relationships while preserving the text linguistics structure by designing adaptive weights for each part-of-speech and dependency relation due to their distinctive role in the Text to Motion (T2M) task."
+                                }
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+                                    "content": "Secondly, achieving the purpose of fine-grained interaction, context-aware progressive reasoning module performs a multi-step inference process with the progressive fusion of global and local information between text and motion, which is unprecedented in the T2M task. This involves utilizing hierarchical semantic features to simulate the way humans comprehend sentences. We adopt the diffusion model framework and stack the hierarchical semantic features obtained from deep to shallow networks at each step to capture high-order relationships at different semantic levels. We evaluate our method on HumanML3D dataset [7] and KIT dataset [22]. Experiments show that our approach out"
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+                                    "content": "performs the state-of-the-art methods and generates better visual motion. Our main contributions include:"
+                                }
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+                        }
+                    ],
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+                                            "content": "- To the best of our knowledge, we are the first to bring NLP methods into T2M task. Utilizing the structured understanding of the natural language prompts to help T2M models achieve better reasoning skills, which brings new ideas for the text-to-X community from a textual perspective."
+                                        }
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+                                            "content": "- We propose the Linguistics-Structure Assisted Module (LSAM), which utilizes a dependency parsing tree and graph networks to facilitate effective information exchange and data aggregation. It can obtain both neighborhood and overall semantic linguistic features."
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+                                            "content": "- We propose a Context-Aware Progressive Reasoning Module (CAPR) that implements a multi-step progressive inference strategy within the diffusion model framework, mimicking the human reading process by moving from global to local relationships."
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+                                            "content": "- Experimental results demonstrate that our proposed method outperforms previous methods, and achieves competitive performance on the HumanML3D and KIT datasets."
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+                                    "content": "2. Related Work"
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+                                    "content": "2.1. Motion generation model"
+                                }
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+                                    "type": "text",
+                                    "content": "Generative models play a crucial role in motion synthesis by generating high-quality human motion. Generative Adversarial Nets (GAN) [6] use two sub-models: a generator model that produces new samples, and a discriminator model that attempts to classify samples as either real or fake. These two models compete against each other during training. However, the interpretability of GAN is poor because the learned data distribution lacks an explicit expression, resembling a black box mapping function."
+                                }
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+                                    "type": "text",
+                                    "content": "Auto-Encoding Variational Bayes (VAE) [13] is a widely used generative model in motion synthesis. Its primary objective is to generate new samples from the learned distribution of objects by learning latent attributes from the probability distribution of the latent variable space, thereby constructing new examples. Despite its usefulness, the quality of samples generated by VAE can be improved."
+                                }
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+                                    "content": "Recently proposed diffusion models [10, 18, 26] have shown immense potential in modeling and present an exciting opportunity to expand into text-driven motion generation. These models utilize the stochastic diffusion process modeled in thermodynamics, which gradually adds noise to the samples of the data distribution. The deep learning model then learns the reverse process of denoising the samples gradually. Diffusion models have the advantage over previous models as they do not make any assumptions about"
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+                                    "content": "the target distribution, leading to a more diverse generation and better suitability for our task. Therefore, we propose a novel fine-grained human motion generation method that employs the Denoising Diffusion Probability Model [10]."
+                                }
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+                                    "content": "2.2. Text-driven human motion generation"
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+                                    "content": "The task of text-driven human motion generation involves generating 3D human motion sequences that conform to a textual description. Several previous works have tackled this task. Initially, Text2Action [1] proposed short-text conditioned motion generation based on an RNN model. Subsequently, Ahuja et al. [2] and Ghosh et al. [5] focused on creating a joint representation of text and motion by projecting both features into a shared latent space. However, these methods involve a one-to-one mapping between text and motion, implying that given the same text, they can only produce fixed motion sequence results."
+                                }
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+                                    "type": "text",
+                                    "content": "To increase generated result diversity, TEMOS [21] introduced a VAE architecture that finds a joint latent space for motion and text under Gaussian distribution constraints. Guo et al. [7] used a temporal VAE to autoregressively generate motion sequences based on text features. However, these methods have a significant drawback of mapping text and motion sequences to separate feature spaces and forcibly align them, leading to a loss of information in both domains. Recently, diffusion models have shown great potential in image generation and have inspired the development of diffusion models for human motion generation. Tevet et al. [28] and Zhang et al. [33] encoded text descriptions using pre-trained models and estimated Gaussian noise or the original motion sequence at each reverse diffusion step. However, their text modeling is often crude and does not fully leverage linguistic structure for sentence semantics. Also, they do not have a progressive process that allows the diffusion model to focus on different content at different time stamps, and they only interact with fixed text features during the inference process."
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+                                    "content": "3. Preliminaries"
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+                                    "content": "The diffusion process is a Markov process consisting of a forward process and a reverse process. The forward process starts with the real data "
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+                                    "content": " at step 0 and proceeds in a Markovian manner by adding Gaussian noise at each step. Over "
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+                                    "type": "text",
+                                    "content": ", which is close to the Gaussian distribution "
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+                                    "type": "inline_equation",
+                                    "content": "N(0, I)"
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+                                    "type": "text",
+                                    "content": ". As a result, the original motion sequence is converted into a complete noise distribution, which can be expressed as:"
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+                                    "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} I\\right) \\tag {1}",
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+                                    "content": "p _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) \\tag {3}",
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+                                    "content": "4. Method"
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+                                    "content": "To enhance the modeling of fine-grained human motion generation, we present our proposed method in Figure 2. Previous methods [1, 2, 5] have adopted a coarse approach to text modeling, leading to an underutilization of text information. Moreover, they treat all words equally without considering their importance and uniqueness. In contrast, we leverage linguistic structures in sentences to further enhance text encoding and differentiate between overall semantic information and detailed features using a multi-step progressive reasoning strategy."
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+                                    "content": "W = \\{w_{1}, w_{2}, \\ldots, w_{n}\\}"
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+                                    "content": " represents the number of words and "
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+                                    "type": "text",
+                                    "content": " is the dimension of word vector. Our goal is to generate a human motion sequence, denoted as "
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+                                    "type": "text",
+                                    "content": ". Here, "
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+                                    "content": " refers to the sequence length and "
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+                                    "type": "text",
+                                    "content": " is the motion representation dimension. To achieve this, we introduce Fg-T2M, a method that generates motion sequences that align well with the corresponding textual content. In the following, we provide an overview of our approach in section 4.1, followed by the introduction of the Linguistics-Structure Assisted Module (LSAM) in section 4.2. Lastly, we present the Context-Aware Progressive Reasoning (CAPR) module in section 4.3."
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+                                    "content": "Figure 2 shows our pipeline for generating motion sequences. We randomly sample "
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+                                    "content": "To train the motion diffusion model, we optimize the objective to predict the original data, representing as follows:"
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+                                    "content": "\\mathcal {L} = \\mathrm {E} _ {t \\in [ 1, T ], \\mathbf {x} _ {0} \\sim q (\\mathbf {x} _ {0}), \\epsilon \\sim \\mathcal {N} (0, I)} [ \\| \\mathbf {x} _ {0} - \\hat {\\mathbf {x}} _ {0} (\\mathbf {x} _ {t}, t, c) \\| _ {2} ^ {2} ]. \\tag {5}",
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+                                    "content": "The regular L2 loss can improve performance for all geometric losses mentioned above."
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+                                    "content": "4.2. Linguistics-Structure Assisted Module"
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+                                    "content": "The current text modeling method is limited in its sensitivity to fine-grained words, which hinders the effectiveness of subsequent generations. To address this, we enhance the context modeling of sentences by identifying the phrase structure and syntactic relationships between phrases using dependency parsing, as shown in Figure 3. Linguistic structure, which comprises phrase structure and syntax relationships, helps us better understand the essence of text and the differences and similarities between sentences. Dependency parsing [19] precisely analyzes vocabulary and syntax to identify the dependency relationships between words in a sentence. In this approach, each word is treated as a node, and the dependency relationships between words are represented by edges that indicate syntactic connections. The resulting node and edge features representing the dependency relationships are input into a graph network to"
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+                                            "type": "text",
+                                            "content": "Figure 3: Architecture of LSAM. The left panel illustrates the process of obtaining node and edge features for one sentence in dependency analysis feature extraction, while the right panel demonstrates the workflows that utilize multiple layers of Graph Attention Network to extract feature information with varying degrees."
+                                        }
+                                    ]
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+                                    "content": "obtain multi-level semantics. In summary, given a sentence, the dependency parsing analyses to build a text tree, nodes for words, and links between nodes for their linguistic relationships. The text tree structure as the graph initialization for graph topology and edge features provides GAT a better prior. The GAT aims to capture inter-word relationships while maintaining the linguistic structure of the text."
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+                                    "content": "To extract word associations, we parse the dependency"
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+                                    "type": "text",
+                                    "content": "of phrase and obtain the hierarchical syntactic relationships using Spacy<sup>1</sup> for dependency parsing, as shown in the left panel of Figure 3. Spacy is a natural language processing software library for text processing, including lexical analysis, syntactic analysis, and more. In dependency parsing, each word is treated as a node, and the edges represent the labels of the dependency relationships between words, allowing us to construct a tree of language structure for the given text. We extract features using a graph attention network (GAT) [31]. For the input nodes of the graph network, we use word features obtained from the CLIP [24] model. For the adjacency matrix, we set a value of 1 or 0 to represent the presence or absence of a dependency relationship between nodes. Since the number of dependency relationships is fixed, we use one-hot encoding to obtain a one-hot label for each relationship, which is then fed into an embedding layer. This can be described as:"
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+                                    "content": "\\mathbf {v} _ {\\mathbf {e}} = \\beta_ {i} \\left(\\varphi_ {e} \\left(\\mathrm {F} _ {\\text {o n e h o t}} \\left(R _ {i}\\right)\\right)\\right) \\tag {6}",
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+                                    "content": "\\mathbf{v}_{\\mathrm{e}} \\in \\mathbb{R}^{D_{e}}"
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+                                    "type": "text",
+                                    "content": " is the dimension of edge feature, "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is adaptive weight parameters to be learned for every "
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+                                    "type": "text",
+                                    "content": " indicates the edge relation between two nodes. Since each word may be adjacent to multiple nodes, and different nodes contribute differently to semantics, it is necessary to distinguish them during the text feature extraction process. We achieve this by applying GAT [31], which extracts multi-level features from the obtained node information, adjacency matrix, and edge information. GAT [31] considers differences between nodes during information aggregation and handles irregularities between different nodes effectively, which is described as:"
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+                                    "content": "x _ {i} ^ {\\prime} = \\alpha_ {i, i} \\Theta x _ {i} + \\sum_ {j \\in N (i)} \\alpha_ {i, j} \\Theta x _ {j} \\tag {7}",
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+                                    "content": "\\alpha_ {i, j} = \\frac {\\exp \\left(\\mathrm {F} \\left(\\omega^ {\\top} \\left[ \\Theta \\mathrm {x} _ {\\mathrm {i}} \\right| | \\Theta \\mathrm {x} _ {\\mathrm {j}} | | \\Theta_ {\\mathrm {e}} \\mathrm {e} _ {\\mathrm {i} , \\mathrm {j}} ]\\right)\\right)}{\\sum_ {k \\in N (i) \\cup \\{i \\}} \\exp \\left(\\mathrm {F} \\left(\\omega^ {\\top} \\left[ \\Theta x _ {i} \\right| | \\Theta x _ {k} | | \\Theta_ {e} e _ {i , k} ]\\right)\\right)} \\tag {8}",
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+                                    "content": "We have "
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+                                    "type": "inline_equation",
+                                    "content": "x, \\alpha \\in \\mathbb{R}^{N \\times L}"
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " denotes LeakyReLU, "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " represents the weight parameters to be learned, and "
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+                                    "type": "text",
+                                    "content": " is the concatenation operation. GAT [31] can model high-order dependency relationships by stacking multiple graph attention layers to capture global and local graph topology effectively. For example, stacking three layers of GAT [31] results in "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for each node "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", as follows:"
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " calculates the feature relevance between the sentence and each frame on the feature map. The resulting cross-modal feature, "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", highlights the sentence-relevant frame feature channels:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {X} _ {t} ^ {\\prime} = \\mathrm {X} _ {t} + \\lambda \\left(\\mathrm {X} _ {t} \\odot (\\sigma (A))\\right) \\tag {12}",
+                                    "image_path": "4dcef45e47425d2e0ad8b1bd8fa7ad0cb89405b66a0a846a08240fdb62bb91c4.jpg"
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+                                    "content": " is a sigmoid activation function. To enhance modeling the correlation between different fused information, a self-attention mechanism [30] is added to strengthen the connection between multiple frames. Multi-head self-attention is conducted on the fusion feature "
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+                                    "content": "\\mathrm {Q} = W _ {q} \\mathrm {X} _ {t} ^ {\\prime}, \\mathrm {K} = W _ {k} \\mathrm {X} _ {t} ^ {\\prime}, \\text {a n d} \\mathrm {V} = W _ {v} \\mathrm {X} _ {t} ^ {\\prime} \\tag {13}",
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+                                    "type": "text",
+                                    "content": " are trainable weights to generate Q, K and V, respectively. Obtain the attention scores using the formula below, where "
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+                                {
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+                                    "type": "text",
+                                    "content": " is the matrix multiplication."
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+                                    "content": "\\operatorname {A t t e n t i o n} (\\mathrm {Q}, \\mathrm {K}, \\mathrm {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathrm {Q} \\otimes \\mathrm {K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathrm {V} \\tag {14}",
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+                                    "type": "text",
+                                    "content": "Multi-Head Word-Level Cross-Attention module learns the cross-interaction between motion sequences and multi-level contextual text features. It uses the formulas mentioned in the self-attention module for calculation, but modifies the motion features of K and V to text features. Therefore, on the stacked Context-Aware Progressive Reasoning modules "
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+                                    "type": "inline_equation",
+                                    "content": "B_{1}, B_{2}, \\ldots, B_{i}"
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+                                    "type": "text",
+                                    "content": ", Block "
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+                                    "type": "text",
+                                    "content": " utilizes different word-level semantic features by:"
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {\\mathbf {X}} _ {t} = \\mathbf {X} _ {t} ^ {\\prime} + \\text {A t t e n t i o n} \\left(\\mathbf {X} _ {t} ^ {\\prime}, \\mathbf {W} _ {i}, \\mathbf {W} _ {i}\\right) \\tag {15}",
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+                                    "content": " is motion features and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{W}_i"
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+                                    "type": "text",
+                                    "content": " is the text features. "
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+                                    "type": "inline_equation",
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+                                    "content": " forms the query vector "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " forms the key vector "
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+                                    "type": "text",
+                                    "content": " and value vector "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". They pass through the process in Equation 14. Finally, several MLP layers further processes the above features to output the predicted target "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}_t\\in \\mathbb{R}^{T\\times D}"
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+                                            "html": "<table><tr><td>Methods</td><td>R-TOP1 ↑</td><td>R-TOP2 ↑</td><td>R-TOP3 ↑</td><td>FID↓</td><td>MM Dist↓</td><td>Diversity↑</td><td>MModality↑</td></tr><tr><td>Real</td><td>0.511±.003</td><td>0.703±.003</td><td>0.797±.002</td><td>0.002±.000</td><td>2.974±.008</td><td>9.503±.065</td><td>-</td></tr><tr><td>Seq2Seq [16]</td><td>0.180±.002</td><td>0.300±.002</td><td>0.396±.002</td><td>11.75±.035</td><td>5.529±.007</td><td>6.223±.061</td><td>-</td></tr><tr><td>L2P [2]</td><td>0.246±.002</td><td>0.387±.002</td><td>0.486±.002</td><td>11.02±.046</td><td>5.296±.008</td><td>7.676±.058</td><td>-</td></tr><tr><td>T2G[3]</td><td>0.165±.001</td><td>0.267±.002</td><td>0.345±.002</td><td>7.664±.030</td><td>6.030±.008</td><td>6.409±.071</td><td>-</td></tr><tr><td>Hier [5]</td><td>0.301±.002</td><td>0.425±.002</td><td>0.552±.004</td><td>6.532±.024</td><td>5.012±.018</td><td>8.332±.042</td><td>-</td></tr><tr><td>MoCoGAN [29]</td><td>0.037±.000</td><td>0.072±.001</td><td>0.106±.001</td><td>94.41±.021</td><td>9.643±.006</td><td>0.462±.008</td><td>0.019±.000</td></tr><tr><td>Dance2Music [14]</td><td>0.033±.000</td><td>0.065±.001</td><td>0.097±.001</td><td>66.98±.016</td><td>8.116±.006</td><td>0.725±.011</td><td>0.043±.001</td></tr><tr><td>TEMOS [21]</td><td>0.424±.002</td><td>0.612±.002</td><td>0.722±.002</td><td>3.734±.028</td><td>3.703±.008</td><td>8.973±.071</td><td>0.368±.018</td></tr><tr><td>Temporal VAE [7]</td><td>0.455±.003</td><td>0.636±.003</td><td>0.740±.003</td><td>1.067±.002</td><td>3.340±.008</td><td>9.188±.002</td><td>2.090±.083</td></tr><tr><td>TM2T [8]</td><td>0.424±.003</td><td>0.618±.003</td><td>0.729±.002</td><td>1.501±.017</td><td>3.467±.011</td><td>8.589±.076</td><td>2.424±.093</td></tr><tr><td>MotionDiffuse [33]</td><td>0.491±.001</td><td>0.681±.001</td><td>0.782±.001</td><td>0.630±.001</td><td>3.113±.001</td><td>9.410±.049</td><td>1.553±.042</td></tr><tr><td>MDM [28]</td><td>0.320±.005</td><td>0.498±.004</td><td>0.611±.007</td><td>0.544±.044</td><td>5.566±.027</td><td>9.559±.086</td><td>2.790±.072</td></tr><tr><td>T2M-GPT [32]</td><td>0.491±.003</td><td>0.680±.003</td><td>0.775±.002</td><td>0.116±.004</td><td>3.118±.011</td><td>9.761±.081</td><td>1.856±.011</td></tr><tr><td>Fg-T2M</td><td>0.492±.002</td><td>0.683±.003</td><td>0.783±.002</td><td>0.243±.019</td><td>3.109±.007</td><td>9.278±.072</td><td>1.614±.049</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1: Comparison of text-conditional motion synthesis on HumanML3D [7] dataset. Red and Blue indicate the best and the second best result, respectively."
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+                                    "content": "Table 2: Comparison of text-conditional motion synthesis on KIT [22] dataset. Red and Blue indicate the best and the second best result, respectively."
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+                                    "content": "5. Experiments"
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+                                    "content": "Our Fg-T2M framework is evaluated on text-driven motion generation task in this section. We first describe the dataset used and the evaluation metrics in section 5.1. In section 5.2, we provide implementation details. We compare our framework with the current state-of-the-art methods in section 5.3. Finally, we present qualitative results and visualization for comparison in section 5.4."
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+                                    "content": "5.1. Datasets and Evaluation Metrics"
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+                                    "content": "Several datasets exist for conditional motion generation, such as proposed in [7, 9, 11, 22]. However, datasets such as [9] and [11] are based on action categories and do not provide complete text sentences as conditioning inputs, making them unsuitable for our method. Instead, we use text-driven datasets, specifically, HumanML3D dataset [7] and KIT Motion-Language dataset [22], for our experiments."
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+                                    "content": "The HumanML3D dataset [7] is a combination of the HumanAct12 [9] and AMASS [17] datasets, comprising 14,616 motions and 44,970 text descriptions across various human activities, such as daily activities, sports, acrobatics, etc., with a total duration of about 28.59 hours. The KIT Motion-Language dataset [22] consists of 3,911 motion sequences and 6,353 natural language descriptions, with a total duration of around 10.33 hours."
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+                                            "content": "Figure 6: Qualitative results: Our method is compared with two state-of-the-art methods: MotionDiffuse [33] and Temporal VAE [7]. Motion frames are ordered from left to right. Those not matching with text prompt are marked with a box."
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+                                    "content": "-precision. For each inferred text-motion pair, 31 mismatched descriptions are randomly selected from the test set. The average top-k precision is obtained by calculating and ranking the Euclidean distance between the motion and each of the 32 descriptions. (2) Frechet Inception Distance (FID). FID measures the similarity between the feature distributions extracted from the generated motions and ground truth motions. (3) Multi-Modal Distance. The multimodal distance is computed between the text feature and the relevant generated motion feature, concerning the given description. (4) Diversity. Diversity evaluates the dissimilarities among all generated motions across all descriptions by computing the mean pairwise Euclidean distance between randomly partitioned groups of motions. (5) Multimodality. For a given text description, 32 motion sequences are generated randomly, and multimodality quantifies the dissimilarities among these generated motion sequences. We primarily value R-precision and FID as pivotal performance metrics, which serve as important measures for evaluating the overall quality of generated motions."
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+                                    "content": "The diffusion model uses 1000 diffusion steps and a linearly varying variance "
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+                                    "content": " ranging from 0.0001 to 0.02. LSAM employs a 3-layer GAT network with a corresponding CAPR layer also set to 3. Hyper-parameter "
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+                                    "content": " in CAPR is 0.1. Training is performed with the Adam optimizer using a fixed learning rate of 5e-5, a batch size of 128, and NVIDIA GeForce RTX 3090 hardware. The KIT dataset is trained for approximately 40K iterations, while the HumanML3D dataset is trained for about 80K iterations."
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+                                    "content": "We compared our method with several state-of-the-art models, including Lin et al. [16], Language2Pose [2], Ghosh et al. [5], MoCoGAN [29], Dance2Music [14], TEMOS [21], TM2T [8], Text2Gesture [3], Guo et al. [7], MotionDiffuse [33], and MDM [28]. Quantitative comparisons of our method with these models on the HumanML3D [7] and KIT [22] datasets are shown in Tables 1 and 2, respectively."
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+                                    "content": "Our method achieves competitive performance between text and motion features, as measured by MM Dist, to state-of-the-art methods, while exhibiting significantly higher scores in R-precision and FID. This demonstrates the ability of our method to generate high-quality motions that align with the text prompts. On the other hand, other approaches showcase remarkable competitiveness in diversity and multimodality. However, these aspects should be grounded in accuracy (R-precision) and precision (FID, MMDist) to strengthen their persuasiveness. Otherwise, the diversity or multimodality would be rendered meaningless if the generated motion fails to align with the desired outcome. Therefore, based on our experiments, our method has achieved advanced experimental results and demonstrates robustness in terms of model performance on the two datasets."
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+                                    "content": "Meanwhile, we design two experiments to evaluate fine-grained control. The first one is conducted on a Harder-HumanML3D dataset. We compress the HumanML3D test set of 4382 data into a Harder-HumanML3D set with 2582 data, by searching for sentences that contain more fine-grained words, like \"left\", \"right\", and so on. The comparison results are shown in Table 3. Our method exhibits significantly higher scores, indicating a better ability to capture"
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+                                    "content": "fine-grained details. The second one is a user study in which we collect user preferences with T2M-GPT [32] and MotionDiffuse [33]. The statistics of the user study are shown in Figure 7. Compared with others, our method achieves superior performance in R-Precision, MM Dist, and yields competitive results in FID, which generates motions with comparable quality. Furthermore, for both questions, especially in the fine-grained aspect, ours is preferred over others and even competitive to the ground truth motions."
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+                                    "content": "We present ablation results in Table 4 to further understand the role of LSAM and CAPR in our method. The results demonstrate that models without the CAPR and LSAM modules exhibit performance degradation. And we also show the comparison of some qualitative examples on the ablation study of this two modules. Additionally, we experiment with the impact of different GAT semantic layers of text information. Since a common dependency tree of motion-text prompt often has three or four depths, a three-layer GAT is sufficient to capture overall nodes information. Hence, a shallow or deep GAT layer hinders the global or local semantic comprehension, resulting in diminished results. We further evaluate the proposed two parts in CAPR. The results show that without CAPR-2 part remarkably reduces the results, which also reflects the importance of fine-grained words for T2M tasks. Finally, the hyper-parameter "
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+                                    "content": " in CAPR controls the degree of text information fusion. A larger "
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+                                    "content": " dilutes the inherent properties of the motion features, leading to a decrease in precision."
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+                                    "content": "5.4. Qualitative Results"
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+                                    "content": "Visual results on the HumanML3D [7] dataset are presented in Figure 6, where our method is compared with the state-of-the-art models of MotionDiffuse [33] and Temporal VAE [7]. As can be seen from the examples in the figure, our method generates human motions that more accurately reflect the text prompts. In contrast, the methods of MotionDiffuse [33] and Temporal VAE [7] often result in unrealistic movements. Specifically, these methods tend to"
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+                                            "content": "Table 3: Experiment results on Harder-HumanML3D split from the HumanML3D [7] test set."
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+                                            "html": "<table><tr><td>Methods</td><td>R-TOP3↑</td><td>FID↓</td></tr><tr><td>Fg-T2M</td><td>0.745±.004</td><td>0.571±.047</td></tr><tr><td>Fg-T2M (w/o LSAM)</td><td>0.722±.005</td><td>1.077±.101</td></tr><tr><td>Fg-T2M (w/o CAPR)</td><td>0.727±.007</td><td>0.943±.089</td></tr><tr><td>Fg-T2M (one layer)</td><td>0.729±.006</td><td>0.951±.092</td></tr><tr><td>Fg-T2M (two layers)</td><td>0.738±.003</td><td>0.692±.086</td></tr><tr><td>Fg-T2M (four layers)</td><td>0.740±.004</td><td>0.636±.102</td></tr><tr><td>Fg-T2M(w/o CAPR-1)</td><td>0.739±.006</td><td>0.652±.035</td></tr><tr><td>Fg-T2M(w/o CAPR-2)</td><td>0.732±.004</td><td>0.764±.039</td></tr><tr><td>Fg-T2M (λ = 0.2)</td><td>0.738±.008</td><td>0.686±.062</td></tr><tr><td>Fg-T2M (λ = 0.3)</td><td>0.732±.006</td><td>0.830±.074</td></tr><tr><td>Fg-T2M (λ = 0.5)</td><td>0.729±.011</td><td>1.086±.104</td></tr></table>",
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+                                    "content": "Table 4: Ablation analysis on KIT [22]. \"layers\" indicates the number of layers of GAT in LSAM. \"(w/o) CAPR-1\" means without multi-modal sentence-level feature-fusion. \"(w/o) CAPR-2\" means without multi-head word-level cross-attention. \"λ\" is the hyper-parameter of Multi-Modal Sentence-Level Feature-Fusion module in CAPR."
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+                                    "content": "only understand one motion within a long text prompt and are not sensitive to specific numerical values, such as 'one' or 'two'. As depicted in example one, MotionDiffuse [33] only performed a backward motion without considering the required number of steps. On the other hand, Temporal VAE [7] successfully achieved the desired effect of walking forward and then backward, but its backward motion step count did not meet the expected requirement. Moreover, They also make errors in spatial orientation, such as 'left' or 'right', and lack a thorough understanding of temporal issues, such as 'while' and 'then', related to movement. Overall, our proposed method outperforms these models, especially in terms of the issues mentioned above. More diverse samples are presented in the supplementary material."
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+                                    "content": "6. Conclusion"
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+                                    "content": "We present a novel method for text-driven human motion generation using the diffusion model, which offers several advantages over existing techniques. Specifically, our method leverages two key modules - a linguistics-structure assisted module and a context-aware progressive reasoning module - to effectively model fine-grained words in the text. The former module extracts dependency parsing relationships in the text, while the latter performs hierarchical effective information feature fusion based on graph neural networks. Our quantitative and qualitative results demonstrate that our method outperforms existing techniques in text-driven motion generation tasks."
+                                }
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+                    "index": 12
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work was supported by the National Natural Science Foundation of China (Project Number: 62272019)."
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
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+                                        {
+                                            "bbox": [
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+                                        }
+                                    ]
+                                }
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+                            "index": 2
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
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+                        {
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+                                    ]
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+                                        }
+                                    ]
+                                }
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+                                        }
+                                    ]
+                                }
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+                                        }
+                                    ]
+                                }
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+                                            "type": "text",
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+                                            "content": "[33] Mingyuan Zhang, Zhongang Cai, Liang Pan, Fangzhou Hong, Xinying Guo, Lei Yang, and Ziwei Liu. Motiondiffuse: Text-driven human motion generation with diffusion model. arXiv preprint arXiv:2208.15001, 2022. 1, 3, 5, 6, 7, 8"
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+[
+    {
+        "type": "text",
+        "text": "Fine-grained Unsupervised Domain Adaptation for Gait Recognition",
+        "text_level": 1,
+        "bbox": [
+            138,
+            130,
+            831,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Kang Ma $^{1}$ , Ying Fu $^{1*}$ , Dezhi Zheng $^{1*}$ , Yunjie Peng $^{2}$ , Chunshui Cao $^{3}$ , Yongzhen Huang $^{3,4*}$ ,  $^{1}$ Beijing Institute of Technology,  $^{2}$ Beihang University,  $^{3}$ WATRIX.AI,  $^{4}$ Beijing Normal University",
+        "bbox": [
+            102,
+            179,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "kangx.ma@gmail.com, {fuying, zhengdezhi}@bit.edu.cn, YunjiePeng@buaa.edu.cn",
+        "bbox": [
+            151,
+            219,
+            815,
+            233
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "chunshui.cao@watrix.ai, huangyongzhen@bnu.edu.cn",
+        "bbox": [
+            271,
+            237,
+            697,
+            250
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            286,
+            313,
+            301
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Gait recognition has emerged as a promising technique for the long-range retrieval of pedestrians, providing numerous advantages such as accurate identification in challenging conditions and non-intrusiveness, making it highly desirable for improving public safety and security. However, the high cost of labeling datasets, which is a prerequisite for most existing fully supervised approaches, poses a significant obstacle to the development of gait recognition. Recently, some unsupervised methods for gait recognition have shown promising results. However, these methods mainly rely on a fine-tuning approach that does not sufficiently consider the relationship between source and target domains, leading to the catastrophic forgetting of source domain knowledge. This paper presents a novel perspective that adjacent-view sequences exhibit overlapping views, which can be leveraged by the network to gradually attain cross-view and cross-dressing capabilities without pre-training on the labeled source domain. Specifically, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that iteratively alternates between two stages. The initial stage involves offline clustering, which transfers knowledge from the labeled source domain to the unlabeled target domain and adaptively generates pseudo-labels according to the expressiveness of each part. Subsequently, the second stage encompasses online training, which further achieves cross-dressing capabilities by continuously learning to distinguish numerous features of source and target domains. The effectiveness of the proposed method is demonstrated through extensive experiments conducted on widely-used public gait datasets.",
+        "bbox": [
+            75,
+            318,
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+            773
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            803,
+            209,
+            819
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Gait recognition, a biometric technology [37, 41, 15] that identifies individuals based on their unique walking patterns, has gained significant attention for its ability to recog",
+        "bbox": [
+            76,
+            829,
+            468,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/a24c59214fea4947d2bf7d74c945d27dbb0d896ee0c73276b508d044a20cfaa6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
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+    {
+        "type": "image",
+        "img_path": "images/df2f43d8601eb6db4b14d184352372e6779218b1e0904b5faca7634ba82dfe9c.jpg",
+        "image_caption": [
+            "(b) The Fine-grained UDA Framework",
+            "Figure 1. (a) The prior knowledge of the existence of angle overlap between adjacent-view. (b) The proposed Fine-grained Unsupervised Domain Adaptation (UDA) framework for gait recognition."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "nize people at long distances, regardless of their attire. The applications [6, 31, 12] of gait recognition have been greatly facilitated by advances in deep learning and the availability of vast amounts of labeled data. However, accurately annotating large amounts of data remains a daunting challenge, especially under long-distance cameras, where critical information such as the human face is often blurred, making it difficult to label gait sequences of the same person in different clothing, views, and carrying conditions. As a solution, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that transfers knowledge from a labeled source domain to an unlabeled target domain.",
+        "bbox": [
+            496,
+            568,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In the gait recognition task, an essential prior knowledge is the existence of overlapping angles in adjacent-view sequences as shown in Fig. 1 (a), which enables networks to build cross-view capabilities through a chain-like approach. Leveraging this premise, the UDA framework for gait recognition can gradually learn cross-dressing capabilities in the target domain through knowledge transfer and clustering, without the need for pre-training the network. We aim to reveal it by addressing the following aspects:",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(i) Offline clustering stage. In the offline clustering phase,",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding Authors",
+        "bbox": [
+            94,
+            886,
+            228,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "11313",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "as shown in Fig. 1, the primary goal is to assign accurate pseudo-labels to unlabeled data by leveraging cross-view chaining relationships. To achieve this, the network extracts essential insights for gait from a labeled source domain and subsequently transfers this acquired knowledge to the unlabeled target domain. Following this knowledge transfer, the precise pseudo-label is assigned to the cross-view and cross-dressing data present within the target domain. This assignment hinges on the observed global feature space distribution within the aforementioned target domain. Furthermore, previous methods [3, 10, 16, 25, 19, 28] demonstrate that part-based methods outperform other approaches. To this end, we leverage the varied expressive capabilities of different body parts and adaptively generate a global feature space, which results in a more accurate assignment of pseudo-labels to unlabeled data.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "(ii) Online training stage. During the online training stage, the core objective is to continually learn the gait features in both the source and target domains. As depicted in Fig. 1 (a), the angles of the sequences vary continuously during human walking, with identical angles and actions appearing in sequences from adjacent viewpoints (indicated by the blue and red arrows). Consequently, the network can establish associations of neighboring perspectives by focusing on temporal features and gain cross-view capabilities through the association of all perspectives. Moreover, as shown in Fig. 1 (b), the network is trained by continuously selecting features from the unlabelled target domain that have been assigned the same pseudo-label as the training set. By continually adding data to the target domain in this way, the network focuses on more robust motion patterns to distinguish features from different domains. Prior methods [25, 26, 28] have demonstrated the criticality of motion pattern extraction in cross-dressing recognition. Consequently, the network gradually develops the cross-dressing capability, even in cases where it is absent from the source domain data.",
+        "bbox": [
+            75,
+            335,
+            472,
+            638
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Driven by this analysis, we propose a simple yet effective fine-grained UDA framework, wherein knowledge learned from the labeled source domain is transferred to obtain pseudo-labels for the unlabeled target domain. Subsequently, we utilize both labeled source and target domain data to extract fine-grained spatio-temporal motion patterns. As illustrated in Fig. 3, the offline clustering stage calculates the confidence scores for each part-based feature. These confidence scores are employed to derive the global feature space and assign pseudo-labels for unlabeled data. And the hybrid memory is initialized based on these pseudolabels. Additionally, information scores are utilized to supervise the hybrid memory and facilitate the computation of the part-based contrastive loss. Furthermore, the online training stage is shown in Fig. 2, we propose a novel Spatio-Temporal Aggregation Network (STANet) for learning global motion patterns, which contains spatial designed",
+        "bbox": [
+            75,
+            643,
+            472,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Cycle Temporal Shift convolution (CTS-Conv) and Global context block. At each iteration, the hybrid memory is dynamically updated using the global motion patterns.",
+        "bbox": [
+            496,
+            90,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions can be summarized in three aspects.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a unified UDA framework structure based on the prior knowledge of the existence of an overlap between adjacent-view sequences, which enables our network to gradually acquire cross-view and cross-dressing capabilities without pre-training.",
+            "- We present an innovative STANet that effectively captures fine-grained motion patterns while enabling the acquisition of cross-view and cross-dressing capabilities. Our approach demonstrates superior performance than current state-of-the-art methods, particularly under the cross-dressing condition.",
+            "- The effectiveness of the proposed UDA framework is demonstrated through experimental results, which show superior performance on the CASIA-B [41], OUMVLP [32], and GREW [48] datasets. Moreover, comprehensive ablation experiments performed on the CASIA-B dataset further corroborate the efficacy of the proposed method within the UDA framework."
+        ],
+        "bbox": [
+            517,
+            164,
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+            460
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            476,
+            640,
+            492
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we review the most relevant research in the area of unsupervised domain adaptation, part-based approaches, and spatial-temporal modeling.",
+        "bbox": [
+            496,
+            502,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Unsupervised Domain Adaptation Approaches",
+        "text_level": 1,
+        "bbox": [
+            498,
+            559,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The Unsupervised Domain Adaptation (UDA) methods [30, 11, 44, 42, 14, 40, 8, 13, 7] for person re-identification (re-ID) have made significant progress. Advanced UDA methods for re-ID tasks often employ clustering algorithms, such as K-means [47], DBSCAN [9, 18], and InfoMAP [5], to generate pseudo-labels for unlabeled data from global features. For instance, MMT [13] used mutual mean-teaching to softly refine the pseudo labels in the target domain, AD-Cluster [42] incorporated style-translated images using a novel discriminative clustering method, and SpCL [14] employed a self-paced approach to create more reliable clusters gradually and refine the hybrid memory and the targets. Despite significant progress in recent years, adapting these methods for gait recognition tasks remains challenging due to inherent differences between gait and re-ID data. Specifically, re-ID data typically contains informative features such as texture and color, which enable the association of individuals without explicit labels. In contrast, the silhouette sequence in gait lacks such information, which poses a significant challenge for unsupervised tasks. Recent pioneering UDA methods for gait recognition [36, 45]",
+        "bbox": [
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+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "11314",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/724cf58913e15774f3a8b3be378ad0ca298a526a8cc1e95f2680506dfd84b0b1.jpg",
+        "image_caption": [
+            "Figure 2. The overview of the online training stage in the proposed UDA framework, where \"HP\" represent the Horizontal Pooling, and \"GC\" represents the Global Context block. (a) The fine-grained motion patterns are extracted by Spatio-Temporal Aggregation Network (STANet). (b) The hybrid memory is used to supervise the training data and dynamically updated based on these features. (c) The features extracted by GC are used to calculate triplet loss, and the normalized features are used to calculate cross-entropy and contrastive losses."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            93,
+            92,
+            883,
+            256
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "have made some achievements on unlabeled datasets. However, these methods do not sufficiently consider the relationship between source and target domains, which ultimately restricts their performance and practical applications. As a solution, we propose a novel UDA framework that transfers valuable knowledge from a labeled source domain to an unlabeled target domain. By leveraging UDA, gait can be applied in more challenging real-world situations.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Part-based Approaches",
+        "text_level": 1,
+        "bbox": [
+            76,
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+            478
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The extraction of fine-grained features of body parts in gait recognition is a critical insight that plays a pivotal role to distinguish different individuals. Extensive research [3, 10, 16, 26, 19] has emphasized the significance of horizontally dividing these features into distinct parts. For example, GaitSet [3] introduced the Horizontal Pyramid Mapping (HPM) module, which partitions gait features into 62 strips along the height dimension. Since then, most gait recognition algorithms [16, 17, 25, 2] have adopted a part-based approach, training features with distinct parts separately. GaitPart [10] divided gait features horizontally into 16 strips, while GaitGL [26] separated global and local features into 32 strips, respectively. 3DLocal [19] proposed a localization module to learn the adaptive spatial and temporal scales. Therefore, gait recognition relies on the representation of multiple motion patterns with critical parts. However, the clustering algorithms typically assign pseudolabels based on the global feature. To this end, we develop a fine-grained UDA framework for gait recognition that leverages the part-based features. Specifically, we evaluate the expressiveness of different parts to calculate confidence scores and then adaptively obtain the pseudo-labels.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Spatio-temporal Modeling",
+        "text_level": 1,
+        "bbox": [
+            76,
+            830,
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+            847
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Gait recognition approaches can be broadly categorized into two primary domains: model-based [20, 34, 23, 24, 22] and appearance-based [39, 15, 29, 33, 34]. The appearance-",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "based approaches have become the mainstream for gait recognition, which can be broadly classified into two categories, including silhouette-based methods [43, 3, 16, 10, 17] and video-based methods [25, 26, 2, 19, 38]. The silhouette-based methods generally employ 2D convolution (2D-Conv) neural networks to extract spatial features on either a single Gait Energy Image (GEI) or a collection of randomly arranged silhouette sets. For example, CNN-LB [39] introduced a CNN-based technique for gait feature learning from Gait Energy Images (GEI), while GaitSet [3] employed 2D convolution for feature extraction, assuming that the silhouette's appearance contained its positional information. However, these methods neglect temporal features which is the robust information in gait sequences. On the other hand, video-based techniques [10, 25, 26, 19] strive to acquire spatio-temporal features, which have been established as advantageous for enhancing gait recognition. For example, GaitGL [26] employed a 3D convolution (3D-Conv) neural network to extract spatio-temporal features. However, these methods use 3D-Conv to extract temporal features with a high amount of parameters. Different from these methods, we propose a more efficient solution named Cycle-Temporal Shit Convolution (CTS-Conv) that enables both low-level and high-level spatio-temporal features with a low computational cost. Further, we refined a global context modeling to extract robust motion patterns.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we begin by introducing the overarching structure of fine-grained UDA framework in Sec. 3.1. Following that, we outline the offline clustering stage in Sec. 3.2, and subsequently detail the online training stage in Sec. 3.3. Finally, we present the joint loss in Sec. 3.4.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The UDA framework for gait recognition aims to transfer knowledge gained from labeled source domains to un",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "11315",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/09cb614533d99e535f6ecbbea692fc5837b8d29a9405e1f4a75424854c5f18cd.jpg",
+        "image_caption": [
+            "Figure 3. The offline clustering stage in the proposed UDA framework. (a) Calculating the confidence scores using a  $k$ -nearest neighbor search algorithm. (b) Generating pseudo labels using a clustering algorithm in the global space. (c) Initializing the hybrid memory using class-level features. (d) Using the confidence scores to further optimize contrastive loss."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "labeled target domains, enabling accurate identification of individuals in unlabeled data. Following the previous UDA methods [50, 35, 4, 46, 21], as shown in Fig. 1 (b), we divide the training of the UDA framework into two stages, including the stage of offline clustering and online training.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the offline clustering stage, we first assign pseudolabels to unlabeled data. Then, we extract class-level central features from both source and target domains, which are used to initialize the hybrid memory module. Formally, Let  $\\mathcal{D}_s = \\{(x_s,y_s)|x_s\\in \\mathbb{R}^{N_S\\times T\\times H\\times W},y_s\\in \\mathbb{R}^{N_S}\\}$  and  $\\mathcal{D}_t = \\{x_t|x_t\\in \\mathbb{R}^{N_T\\times T\\times H\\times W}\\}$  denote the labeled and unlabeled data, where  $N_{S}$  and  $N_{T}$  are the numbers of sequences. The generation of pseudo-labels  $y_{t}$  can be expressed as",
+        "bbox": [
+            76,
+            381,
+            470,
+            501
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ny _ {t} = \\mathcal {C} \\left(\\left\\langle \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right), \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right) \\right\\rangle\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{C}$  represents the clustering algorithm,  $\\langle \\cdot ,\\cdot \\rangle$  denotes the operation to measure the similarity between gait features space,  $\\mathcal{F}_{\\theta}$  is a learnable network parameterized by  $\\theta$ . During the online training stage, the pseudo-labeled data can be sampled with the labeled data. The gait features  $(f_{s},f_{t})$  extraction can be expressed as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(f _ {s}, f _ {t}\\right) = \\left(\\mathcal {F} _ {\\theta} \\left(x _ {s}\\right), \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right)\\right). \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "To perform gait recognition on unlabeled sequences, TranND [45] utilizes a fine-tuning approach, which may lead to catastrophic forgetting of the knowledge learned in the source domain when trained on the target domain. In this paper, the proposed UDA framework is an end-to-end approach that utilizes alternating \"offline clustering stage\" and \"online training stage\" to simultaneously train the data in both source and target domains.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Offline Clustering Stage",
+        "text_level": 1,
+        "bbox": [
+            76,
+            786,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This part provides a comprehensive overview of the offline clustering stage, which generates the pseudo-labels for unlabeled data and initializes the hybrid memory.",
+        "bbox": [
+            75,
+            810,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Generating pseudo-labels. The offline clustering stage, as shown in Fig. 3, plays a crucial role in UDA tasks by generating pseudo-labels for unlabeled data. The effectiveness",
+        "bbox": [
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+            854,
+            470,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "of the UDA algorithm relies on the distribution that features with the same label cluster densely in feature space, while those with different labels are scattered. However, one of the main challenges in the UDA framework is generating accurate pseudo-labels by effectively utilizing the relationships between the part-level features, given that features are comprised of multiple spatio-temporal motion patterns.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To accurately distribute unlabeled data, we take into account the expressive capabilities of different body parts and calculate the confidence score for each part feature accordingly. Formally, let  $f_{t} \\in \\mathbb{R}^{N_{T} \\times P \\times C}$  denote the target domain part-level features, where  $P$  is the number of horizontally sliced parts, and  $C$  is the feature channels. Specifically, we perform the  $k$ -nearest neighbor search algorithm on both the global feature space and each part feature space to generate ranked lists  $\\{\\mathcal{R}_g, \\mathcal{R}_1, \\dots, \\mathcal{R}_P\\}$  for each unlabeled feature. The  $\\mathcal{R}_g$  represents the sets of global feature indices for the top-  $k$  samples in the ranked list, while  $\\mathcal{R}_p$  denotes the sets of  $p$ -th part feature indices. We then compute the confidence scores  $S_{p}$  between the global feature indices  $\\mathcal{R}_g$  and the  $p$ -th part feature indices  $\\mathcal{R}_p$  as follows,",
+        "bbox": [
+            496,
+            411,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} _ {p} = \\frac {\\left| \\mathcal {R} _ {g} \\cap \\mathcal {R} _ {p} \\right|}{\\left| \\mathcal {R} _ {g} \\cup \\mathcal {R} _ {p} \\right|} \\in [ 0, 1 ], \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            606,
+            631,
+            890,
+            666
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $|\\cdot|$  is a non-negative real number denoting the cardinality of a set. The confidence scores are further used to refine the part-based space to global feature space. We then use a clustering algorithm  $\\mathcal{C}$  (e.g., DBSCAN [9]) to assign pseudo-labels on the global feature space, i.e.,",
+        "bbox": [
+            496,
+            672,
+            893,
+            750
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ny _ {t} = \\mathcal {C} \\left\\{\\mathcal {J} \\left(\\frac {1}{P} \\sum_ {p = 1} ^ {P} \\left[ \\langle f _ {t} ^ {p}, f _ {t} ^ {p} \\rangle * \\frac {\\mathcal {S} _ {p}}{\\sum_ {p = 1} ^ {P} \\mathcal {S} _ {p}} \\right]\\right) \\right\\}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            758,
+            890,
+            801
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{I}$  is the Jaccard distance [49] computed in global feature space and  $*$  denotes the Hadamard product.",
+        "bbox": [
+            496,
+            809,
+            890,
+            840
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Initializing Hybrid Memory. To initialize the part-based hybrid memory, we utilize the class-level features of both source and target domains. It is worth illustrating that in the target domain, we only retain samples assigned with pseudo",
+        "bbox": [
+            496,
+            840,
+            893,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "11316",
+        "bbox": [
+            478,
+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "labels, and exclude those with discrete labels from the subsequent online training stage, i.e.,",
+        "bbox": [
+            76,
+            90,
+            468,
+            122
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{c _ {s}, c _ {t} \\right\\} = \\left\\{\\frac {1}{| \\mathcal {N} _ {s} |} \\sum_ {f _ {s} \\in \\mathcal {N} _ {s}} f _ {s}, \\frac {1}{| \\mathcal {N} _ {t} |} \\sum_ {f _ {t} \\in \\mathcal {N} _ {t}} f _ {t} \\right\\}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            145,
+            468,
+            193
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\{c_s, c_t\\}$  denotes the source and target domain class-level features,  $(\\mathcal{N}_s, \\mathcal{N}_t)$  is the same label set or cluster set.",
+        "bbox": [
+            76,
+            205,
+            468,
+            236
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Online Training Stage",
+        "text_level": 1,
+        "bbox": [
+            76,
+            246,
+            282,
+            262
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This part provides a detailed explanation of the Cycle Temporal Shift Convolution (CTS-Conv) and Global Context Block. Then, we introduce the utilization of class-level momentum updating for the part-based hybrid memory.",
+        "bbox": [
+            75,
+            268,
+            468,
+            330
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Cycle Temporal Shift Convolution. Gait recognition is a challenging task due to the impact of various external factors, including carrying conditions, wearing coats, and varying viewing angles, leading to a much higher intra-class variance than inter-class. Previous studies [25, 26] proposed to use 3D convolution (3D-Conv) neural network to capture temporal information in gait sequences and extract robust features. However, when applied to part-based UDA tasks, 3D-Conv is limited by its high computational cost and parameter-rich structure, increasing the risk of over-fitting. To address this, we propose a novel CTS-Conv, which separates temporal feature learning from spatial feature learning based on the well-designed temporal shift convolution (TS-Conv) [27]. In CTS-Conv, the input features are denoted as  $\\Upsilon = \\{v_{1}, v_{2}, \\ldots, v_{E}\\} \\in \\mathbb{R}^{C \\times T \\times H \\times W}$ , where  $v_{i}$  represents the input features divided equally into  $E$  pieces, and  $T$  denotes the number of frames. As shown in Fig. 2, the CTS-Conv operation can be expressed as",
+        "bbox": [
+            75,
+            330,
+            468,
+            602
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\overrightarrow {v} _ {1} ^ {t} = v _ {1} ^ {t - 1}, \\overrightarrow {v} _ {1} ^ {0} = v _ {1} ^ {T}, \\overleftarrow {v} _ {2} ^ {t} = v _ {2} ^ {t + 1}, \\overleftarrow {v} _ {2} ^ {T} = v _ {2} ^ {0}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            612,
+            468,
+            632
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\overrightarrow{v}_1$  and  $\\overleftarrow{v}_2$  denote the first two pieces which are shifted to the right and left along the temporal dimension, respectively. The remaining pieces  $[v_3,v_4,\\dots ,v_E]$  are unshifted. The CTS-Conv operation in STANet learns temporal features by exchanging the features of adjacent frames, without introducing any additional parameters.",
+        "bbox": [
+            75,
+            642,
+            468,
+            733
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Global Context Block. After extracting the spatiotemporal features using the CTS-Conv, we further refine the global context modeling technique called global context (GC) block base on [1, 28]. The GC block employs multiple heads to map features during context modeling, thereby facilitating the comprehensive extraction of global motion patterns. To generate the output feature, a horizontal pooling method (HP) is first utilized, resulting in horizontally sliced features denoted as  $H = \\{h^1, h^2, \\dots, h^P\\} \\in \\mathbb{R}^{P \\times T \\times C}$ , where  $P$  represents the number of horizontally sliced parts. Then, the global motion patterns  $g^p$  are derived",
+        "bbox": [
+            75,
+            734,
+            468,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1: The training process of UDA for Gait"
+        ],
+        "code_body": "Require: Labeled data  $\\mathcal{D}_s$  and Unlabeled data  $\\mathcal{D}_t$ ;  \nRequire: Random initialize pipeline  $\\mathcal{F}_{\\theta}$ ;  \nRequire:  $m$  for Eq. (9) and  $\\tau$  of Eq. (10);  \nfor  $i \\leq N_e$  do  \nOffline Clustering Stage,  $N_e$  is the total iterations; Assign pseudo-label for  $\\mathcal{D}_t$  with Eq. (4); Initialize the hybrid memory with Eq. (5);  \nfor  $j \\leq T_e$  do  \nOnline Training Stage,  $T_e$  is the train iterations; Sample mini-batch data  $(x_s, x_t)$ ; Encoder part-based features  $(f_s, f_t)$ ; Compute the joint loss with Eq. (11); Update part-based hybrid memory with Eq. (9);  \nend  \nend",
+        "bbox": [
+            519,
+            113,
+            859,
+            324
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "using the subsequent expression:",
+        "bbox": [
+            500,
+            357,
+            718,
+            372
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {g} ^ {p} = \\frac {\\exp \\left(W _ {k} W _ {v 1} h _ {t} ^ {p}\\right)}{\\sum_ {t = 1} ^ {T} \\exp \\left(W _ {k} W _ {v 1} h _ {t} ^ {p}\\right)} \\otimes W _ {v 1} h ^ {p}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            558,
+            380,
+            890,
+            417
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ng ^ {p} = \\delta \\left(W _ {v 2} \\tilde {g} ^ {p}\\right) \\oplus h ^ {p}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            617,
+            420,
+            890,
+            436
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{g}^p$  represents the context modeling,  $W_{k}$ ,  $W_{v1}$ , and  $W_{v2}$  are learnable parameters,  $\\delta$  denotes the activation function,  $\\otimes$  signifies matrix multiplication, and  $\\oplus$  indicates the broadcast element-wise addition.",
+        "bbox": [
+            500,
+            446,
+            890,
+            505
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Updating Hybrid Memory. Each mini-batch of the sampled data is passed through a pipeline that extracts part-based features  $(f_s, f_t)$ . It is worth noting that our proposed UDA framework is highly versatile and can be readily applied to other network architectures [3, 26], as illustrated in Fig. 2, where STANet can be replaced by any of the existing popular networks. At each iteration, the extracted features in each mini-batch would be involved in part-based hybrid memory momentum updating, i.e.,",
+        "bbox": [
+            496,
+            507,
+            890,
+            643
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l} c _ {s} \\leftarrow m \\cdot f _ {s} + (1 - m) \\cdot \\frac {1}{| \\mathcal {B} _ {s} |} \\sum_ {f _ {s} \\in \\mathcal {B} _ {s}} f _ {s} \\\\ c _ {t} \\leftarrow m \\cdot f _ {t} + (1 - m) \\cdot \\frac {1}{| \\mathcal {B} _ {t} |} \\sum_ {f _ {t} \\in \\mathcal {B} _ {t}} f _ {t} \\end{array} \\right\\}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            542,
+            652,
+            890,
+            693
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $(c_s, c_t)$  denotes the class-level features,  $(\\mathcal{B}_s, \\mathcal{B}_t)$  represents the set of features belonging to the source or target domain class and  $m \\in [0,1]$  is a momentum coefficient.",
+        "bbox": [
+            496,
+            700,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Joint Loss Function",
+        "text_level": 1,
+        "bbox": [
+            500,
+            756,
+            687,
+            771
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this work, three types of part-based loss functions are employed, namely, the triplet loss  $\\mathcal{L}_{tp}$ , the cross-entropy loss  $\\mathcal{L}_{ce}$ , and the contrastive loss  $\\mathcal{L}_{cl}$ . These loss functions are used to constrain the features of each part individually. As shown in Fig. 2, the output features  $(o_s,o_t)$  are used to calculate  $\\mathcal{L}_{tp}$ , while the normalized output features  $(f_s,f_t)$  are used to calculate  $\\mathcal{L}_{ce}$  and  $\\mathcal{L}_{cl}$ . Additionally, we consider the varying expressiveness of different body parts and",
+        "bbox": [
+            496,
+            779,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "11317",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/eef92c86b1ce5bddefb6921d1486d25160e4b08036e6ac66aee1d212f2a20b47.jpg",
+        "table_caption": [
+            "Table 1. The Rank-1 (\\%) performance comparison of fully supervised and unsupervised domain adaptation methods on CASIA-B. Where “OUMVLP→CASIA-B” denotes the use of OUMVLP as the source domain and CASIA-B as the target domain."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"11\">Probe View</td><td rowspan=\"2\">Mean</td></tr><tr><td>0°</td><td>18°</td><td>36°</td><td>54°</td><td>72°</td><td>90°</td><td>108°</td><td>126°</td><td>134°</td><td>162°</td><td>180°</td></tr><tr><td colspan=\"14\">Fully supervised methods with all labels on CASIA-B</td></tr><tr><td rowspan=\"4\">NM</td><td>CNN-LB [39]</td><td>82.6</td><td>90.3</td><td>96.1</td><td>94.3</td><td>90.1</td><td>87.4</td><td>89.9</td><td>94.0</td><td>94.7</td><td>91.3</td><td>78.5</td><td>89.9</td></tr><tr><td>GaitSet [3]</td><td>90.8</td><td>97.9</td><td>99.4</td><td>96.9</td><td>93.6</td><td>91.7</td><td>95.0</td><td>97.8</td><td>98.9</td><td>96.8</td><td>85.8</td><td>95.0</td></tr><tr><td>GaitGL [26]</td><td>96.0</td><td>98.3</td><td>99.0</td><td>97.9</td><td>96.9</td><td>95.4</td><td>97.0</td><td>98.9</td><td>99.3</td><td>98.8</td><td>94.0</td><td>97.4</td></tr><tr><td>STANet(ours)</td><td>96.4</td><td>99.4</td><td>99.3</td><td>98.9</td><td>97.0</td><td>95.8</td><td>98.2</td><td>99.2</td><td>99.6</td><td>99.2</td><td>96.0</td><td>98.1</td></tr><tr><td rowspan=\"4\">BG</td><td>CNN-LB [39]</td><td>64.2</td><td>80.6</td><td>82.7</td><td>76.9</td><td>64.8</td><td>63.1</td><td>68.0</td><td>76.9</td><td>82.2</td><td>75.4</td><td>61.3</td><td>72.4</td></tr><tr><td>GaitSet [3]</td><td>83.8</td><td>91.2</td><td>91.8</td><td>88.8</td><td>83.3</td><td>81.0</td><td>84.1</td><td>90.0</td><td>92.2</td><td>94.4</td><td>79.0</td><td>87.2</td></tr><tr><td>GaitGL [26]</td><td>92.6</td><td>96.6</td><td>96.8</td><td>95.5</td><td>93.5</td><td>89.3</td><td>92.2</td><td>96.5</td><td>98.2</td><td>96.9</td><td>91.5</td><td>94.5</td></tr><tr><td>STANet(ours)</td><td>94.4</td><td>98.2</td><td>98.9</td><td>97.5</td><td>94.1</td><td>91.2</td><td>93.9</td><td>97.4</td><td>98.5</td><td>97.8</td><td>94.0</td><td>96.0</td></tr><tr><td rowspan=\"4\">CL</td><td>CNN-LB [39]</td><td>37.7</td><td>57.2</td><td>66.6</td><td>61.1</td><td>55.2</td><td>54.6</td><td>55.2</td><td>59.1</td><td>58.9</td><td>48.8</td><td>39.4</td><td>54.0</td></tr><tr><td>GaitSet [3]</td><td>61.4</td><td>75.4</td><td>80.7</td><td>77.3</td><td>72.1</td><td>70.1</td><td>71.5</td><td>73.5</td><td>73.5</td><td>68.4</td><td>50.0</td><td>70.4</td></tr><tr><td>GaitGL [26]</td><td>76.6</td><td>90.0</td><td>90.3</td><td>87.1</td><td>84.5</td><td>79.0</td><td>84.1</td><td>87.0</td><td>87.3</td><td>84.4</td><td>69.5</td><td>83.6</td></tr><tr><td>STANet(ours)</td><td>83.4</td><td>94.6</td><td>96.8</td><td>93.9</td><td>89.6</td><td>86.0</td><td>88.2</td><td>92.1</td><td>93.9</td><td>90.2</td><td>78.1</td><td>89.7</td></tr><tr><td colspan=\"14\">Unsupervised Domain Adaptation methods without any labels on CASIA-B (OUMVLP→CASIA-B)</td></tr><tr><td rowspan=\"4\">NM</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>63.4</td></tr><tr><td>UDA(GaitSet)</td><td>84.7</td><td>95.8</td><td>97.2</td><td>95.8</td><td>95.1</td><td>92.9</td><td>94.8</td><td>96.1</td><td>97.3</td><td>96.6</td><td>79.2</td><td>93.2</td></tr><tr><td>UDA(GaitGL)</td><td>76.7</td><td>88.3</td><td>88.8</td><td>87.1</td><td>88.4</td><td>82.9</td><td>85.9</td><td>90.6</td><td>93.1</td><td>93.9</td><td>73.0</td><td>86.2</td></tr><tr><td>UDA(STANet)</td><td>84.3</td><td>95.2</td><td>95.5</td><td>91.1</td><td>90.7</td><td>85.9</td><td>89.4</td><td>93.3</td><td>94.9</td><td>93.7</td><td>82.4</td><td>90.6</td></tr><tr><td rowspan=\"4\">BG</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>42.7</td></tr><tr><td>UDA(GaitSet)</td><td>77.5</td><td>87.5</td><td>90.0</td><td>89.2</td><td>86.2</td><td>81.2</td><td>87.1</td><td>89.9</td><td>94.0</td><td>91.1</td><td>70.9</td><td>85.9</td></tr><tr><td>UDA(GaitGL)</td><td>69.1</td><td>85.3</td><td>84.7</td><td>83.6</td><td>82.9</td><td>76.1</td><td>79.9</td><td>86.8</td><td>89.1</td><td>88.0</td><td>63.6</td><td>80.8</td></tr><tr><td>UDA(STANet)</td><td>75.4</td><td>88.7</td><td>86.6</td><td>83.6</td><td>82.9</td><td>76.2</td><td>82.6</td><td>86.9</td><td>89.3</td><td>87.5</td><td>73.7</td><td>83.0</td></tr><tr><td rowspan=\"4\">CL</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>15.8</td></tr><tr><td>UDA(GaitSet)</td><td>24.2</td><td>38.9</td><td>42.3</td><td>39.6</td><td>41.1</td><td>38.1</td><td>37.9</td><td>43.3</td><td>43.4</td><td>29.6</td><td>25.4</td><td>36.7</td></tr><tr><td>UDA(GaitGL)</td><td>43.9</td><td>65.3</td><td>66.5</td><td>66.9</td><td>68.8</td><td>60.0</td><td>66.4</td><td>71.2</td><td>69.3</td><td>61.8</td><td>42.2</td><td>62.0</td></tr><tr><td>UDA(STANet)</td><td>54.0</td><td>73.2</td><td>75.7</td><td>72.0</td><td>71.4</td><td>64.4</td><td>70.1</td><td>74.6</td><td>73.7</td><td>69.2</td><td>51.4</td><td>68.2</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "use the confidence scores to accurately constrain the features by constraining the contrastive loss for each part. The contrastive loss  $\\mathcal{L}_{cl}$  can be formulated as follows:",
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {c l} = - \\sum_ {p = 1} ^ {P} \\frac {\\mathcal {S} _ {p}}{N _ {c s}} \\left\\{- \\log \\frac {\\exp \\left(f ^ {p} \\cdot c _ {s} ^ {p , +} / \\tau\\right)}{\\sum_ {k = 1} ^ {| \\mathcal {N} _ {s} |} \\exp \\left(f ^ {p} \\cdot c _ {s} ^ {p , k} / \\tau\\right)} \\right\\} \\tag {10} \\\\ - \\sum_ {p = 1} ^ {P} \\frac {\\mathcal {S} _ {p}}{N _ {c t}} \\left\\{- \\log \\frac {\\exp (f ^ {p} \\cdot c _ {t} ^ {p , +} / \\tau)}{\\sum_ {k = 1} ^ {| \\mathcal {N} _ {t} |} \\exp (f ^ {p} \\cdot c _ {t} ^ {p , k} / \\tau)} \\right\\}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $N_{cs}, N_{ct}$  is a positive integer obtained by multiplying the mini-batch with parts,  $\\tau$  is a hyper-parameter,  $c_s, c_t$  denote the class-level features of source and target domains, and  $c_s^{p, + }, c_t^{p, + }$  indicate the positive class prototype corresponding to  $f^p$ . The combined loss  $\\mathcal{L}_c$  can be expressed as",
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {c} = \\mathcal {L} _ {t p} + \\alpha \\mathcal {L} _ {c e} + \\beta \\mathcal {L} _ {c l}, \\tag {11}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\alpha$  and  $\\beta$  are the hyper-parameters to balance the combined loss and are empirically set to 0.3.",
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we evaluate the proposed method on three large-scale gait recognition benchmarks, including two widely adopted datasets (i.e., CASIA-B and OUMVLP) and one real-world dataset (i.e., GREW). Then, we compare our method to state-of-the-art methods. Finally, comprehensive ablation studies are conducted to substantiate the effectiveness of our proposed method.",
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+    {
+        "type": "text",
+        "text": "4.1. Datasets and Implementation Details",
+        "text_level": 1,
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+        "text": "CASIA-B [41] is a well-established dataset widely used in the field of gait recognition research. It comprises 124 subjects and encompasses 3 distinct walking conditions: normal walking (NM), walking while wearing a coat (CL), and walking with bags (BG). The dataset is captured by 11 cameras positioned uniformly between  $0^{\\circ}$  and  $180^{\\circ}$ , providing a diverse range of viewpoints. Each subject has a total of 110 sequences. The first 74 subjects are used for training, while the remaining 50 subjects are reserved for testing. During",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "11318",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b2b4b26f5f460a877ec81ceb43f822bbc2b861211fe8ec310dcf29c2dc897825.jpg",
+        "table_caption": [
+            "Table 2. Rank-1 accuracy of fully supervised and unsupervised domain adaptation methods on OUMVLP under all view angles. Where \"CASIA-B→OUMVLP\" represents the use of CASIA-B as the labeled source domain and OUMVLP as the unlabeled target domain."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"14\">Probe View</td><td rowspan=\"2\">Mean</td></tr><tr><td>0°</td><td>15°</td><td>30°</td><td>45°</td><td>60°</td><td>75°</td><td>90°</td><td>180°</td><td>195°</td><td>210°</td><td>225°</td><td>240°</td><td>255°</td><td>270°</td></tr><tr><td colspan=\"16\">Fully supervised methods with all labels on OUMVLP</td></tr><tr><td>GaitSet [3]</td><td>79.5</td><td>87.9</td><td>89.9</td><td>90.2</td><td>88.1</td><td>88.7</td><td>87.8</td><td>81.7</td><td>86.7</td><td>89.0</td><td>89.3</td><td>87.2</td><td>87.8</td><td>86.2</td><td>87.1</td></tr><tr><td>GaitGL [26]</td><td>84.9</td><td>90.2</td><td>91.1</td><td>91.5</td><td>91.1</td><td>90.8</td><td>90.3</td><td>88.5</td><td>88.6</td><td>90.3</td><td>90.4</td><td>89.6</td><td>89.5</td><td>88.8</td><td>89.7</td></tr><tr><td>STANet(ours)</td><td>87.7</td><td>91.4</td><td>91.6</td><td>91.9</td><td>91.6</td><td>91.4</td><td>91.2</td><td>90.4</td><td>90.3</td><td>90.8</td><td>91.0</td><td>90.5</td><td>90.3</td><td>90.1</td><td>90.7</td></tr><tr><td colspan=\"16\">Unsupervised Domain Adaptation methods without any labels on OUMVLP (CASIA-B→OUMVLP)</td></tr><tr><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>75.6</td></tr><tr><td>UDA(GaitSet)</td><td>45.6</td><td>60.1</td><td>75.3</td><td>80.7</td><td>75.5</td><td>73.9</td><td>73.9</td><td>49.9</td><td>59.9</td><td>75.5</td><td>81.7</td><td>74.9</td><td>73.2</td><td>72.9</td><td>69.5</td></tr><tr><td>UDA(GaitGL)</td><td>23.6</td><td>50.5</td><td>79.5</td><td>78.5</td><td>75.3</td><td>74.6</td><td>74.5</td><td>28.7</td><td>50.9</td><td>77.5</td><td>77.5</td><td>74.3</td><td>73.3</td><td>73.0</td><td>65.1</td></tr><tr><td>UDA(STANet)</td><td>42.8</td><td>85.1</td><td>92.1</td><td>91.2</td><td>88.9</td><td>89.2</td><td>89.5</td><td>50.4</td><td>86.6</td><td>90.8</td><td>90.1</td><td>88.0</td><td>87.9</td><td>88.0</td><td>82.9</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "testing, the first four \"NM\" conditions are utilized as the gallery, while the remaining conditions serve as the probe.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "OUMVLP [32] is a prominent public gait dataset that comprises 10,307 subjects, two distinct walking sequences (labeled as “00” and “01”), and 14 cameras positioned uniformly between  $(0^{\\circ} \\rightarrow 90^{\\circ})$  and  $(180^{\\circ} \\rightarrow 270^{\\circ})$ . To ensure fair data volume in comparison to CASIA-B, we select the first 1,000 subjects from OUMVLP for our UDA experiments without any specific instructions. In the UDA experiment, we followed the official data split and used 500 individuals for training and the remaining 500 for testing. During the test phase, the “00” sequences serve as the probe, while the remaining “01” sequences serve as the gallery.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "GREW [48] is a comprehensive and extensive dataset designed for gait recognition, encompassing silhouettes and 2D/3D human body pose. In contrast to CASIA-B and OUMVLP, GREW was collected in diverse and complex scenes in the wild, making it a more challenging task for gait recognition. The GREW dataset comprises 26345 subjects, 128671 sequences, and 882 camera viewpoints. To ensure fairness in data volume with respect to CASIA-B, we use the first 4000 subjects from GREW for UDA experiments without any special instructions. During testing, we make full use of the official query and gallery set.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. The training process of UDA is shown in Algorithm 1, and all datasets are uniformly resized to  $64 \\times 44$  [3]. The model is trained end-to-end using the SGD optimizer, starting with an initial learning rate of 0.1, which is then decreased by a factor of 10 iteratively until convergence. The training mini-batch size for CASIA-B and OUMVLP is set to (8, 16), while for GREW dataset, it is set to (4, 32). Data augmentation techniques are utilized to preserve both the original and augmented data in real-world datasets. The convolutional channels in the STANet are set to (64, 128, 256). The network is trained for a total of  $N_{e} = 100\\mathrm{K}$  iterations, and offline clustering is performed every  $T_{e} = 5\\mathrm{K}$  iteration to assign pseudo-labels to unlabeled data and reinitialize the hybrid memory dictionary.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison with State-of-the-art Methods",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the effectiveness of the proposed approach, we compared it with both existing fully supervised methods [39, 3, 26] and Unsupervised Domain Adaptation (UDA) method [45] for gait recognition.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Evaluation on CASIA-B. The performance of both fully supervised [39, 3, 26] and UDA methods [45] on CASIA-B is presented in Tab. 1. (1) The proposed STANet algorithm outperforms the fully supervised algorithm [39, 3, 26], especially in the cross-dressing condition. Experimental results show that our method has the ability to learn more robust motion patterns compared to others. (2) The proposed UDA framework outperforms the existing UDA algorithm [45] under all conditions. The experimental results demonstrate that our UDA framework can effectively utilize fine-grained part-based features to generate pseudo-labels that supervise network learning, leading to a significant improvement in recognition accuracy. (3) We conducted experiments by substituting STANet with various state-of-the-art algorithms, such as GaitSet [3] and GaitGL [26]. In the UDA framework, the GaitSet method outperforms other methods in \"NM\" and \"BG\" but has lower performance in \"CL\". The experimental results demonstrate that GaitSet emphasizes learning cross-view information from the OUMVLP but struggles to capture robust motion patterns.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on OUMVLP. To provide additional evidence of the effectiveness of our proposed method, we evaluated the proposed approach with some state-of-the-art fully supervised [3, 26] and UDA [45] methods on OUMVLP. (1) The proposed STANet outperforms other methods, including GaitSet [3] and GaitGL [26], under both the whole dataset and fully supervised conditions. Our experimental results demonstrate the critical importance of effectively utilizing fine-grained spatio-temporal motion patterns for achieving high performance on large-scale gait datasets. (2) Our proposed UDA framework outperforms the existing UDA algorithm [45]. The experimental results demon",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "11319",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "strate that our framework can effectively transfer the norm walking information from CASIA-B to OUMVLP. (3) We conducted experiments to compare STANet with other algorithms, including GaitSet [3] and GaitGL [26]. The results showed that the proposed STANet in the UDA framework effectively utilized fine-grained part-based features, even in the presence of cross-dressing influence in CASIA-B.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on GREW. We evaluated the proposed method on a wild dataset, i.e., GREW, to provide additional evidence for the effectiveness of our method. (1) The experimental results presented in Tab. 3 demonstrate the effectiveness of the fine-grained motion patterns extracted by our method on real datasets. (2) The UDA experimental results confirm that knowledge gained from accurately labeled data in a laboratory setting can be transferred to real-world scenarios. This validation also confirms the efficacy of our proposed approach in extracting fine-grained motion patterns.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this section, an ablation study is performed on the proposed UDA framework to improve the understanding of the effects of different configurations.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The effectiveness of STANet. To comprehensively evaluate the impact of STANet in the UDA framework, we conducted a thorough comparative experiment in Tab. 4. Specifically, (1) The \"w/o CTS-Conv\" represents replacing the CTS-Conv with 2D convolution. The experiment demonstrates a decrease in the performance of the \"CL\", thereby confirming the ability of CTS-Conv to acquire resilient temporal features in the UDA framework. (2) Furthermore, we conducted additional experiments to remove the GC block, denoted as \"w/o GC block\", in which the GC block was replaced with Max Pooling along the temporal dimension. The experiment results showed that STANet exhibited performance comparable to that of GaitGL [26].",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The effectiveness of confidence scores. To explore the impact of confidence scores on the offline clustering stage, we completely remove the process of generating confidence scores and generate the global feature space directly averaged over the part-based feature space. The experimental results \"w/o Confidence scores\" from the Tab. 4 show that removing the confidence score decreased the performance.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Analysis of the number of spatial slices parts. We conducted an in-depth analysis to assess the influence of different spatial bin numbers of the UDA framework in Tab. 4. (1) The experimental results indicate that the performance improves as the number of  $N_{\\text{part}}$  increases. (2) In the field of gait recognition, many popular approaches [10, 26] have confirmed that the number of parts has a significant impact on the recognition results. Specifically, increasing the number of parts requires the network to focus more on fine-grained parts. Experimental results show that  $N_{\\text{part}}$  also has a significant impact on unlabeled feature learning.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fd1b3588626910a31e4160a4e0063d56a25e72b389cff0289b7ad9706e1069ac.jpg",
+        "table_caption": [
+            "Table 3. Rank-1  $(\\%)$  performance comparison of fully supervised and unsupervised domain adaptation methods on GREW."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Source</td><td>Rank-1 (%)</td></tr><tr><td colspan=\"3\">Fully supervised methods on GREW</td></tr><tr><td>CNN-LB [39]</td><td>TPAMI 2017</td><td>12.2</td></tr><tr><td>GaitSet [3]</td><td>AAAI 2019</td><td>33.5</td></tr><tr><td>GaitGL [26]</td><td>ICCV 2021</td><td>32.7</td></tr><tr><td>STANet(ours)</td><td>-</td><td>41.3</td></tr><tr><td colspan=\"3\">UDA methods without any labels (OUMVLP→GREW)</td></tr><tr><td>UDA(Gaitset)</td><td>-</td><td>15.3</td></tr><tr><td>UDA(GaitGL)</td><td>-</td><td>13.7</td></tr><tr><td>UDA(STANet)</td><td>-</td><td>26.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/539e86ae1882b8f74b99bc164984259ff20573676ee133356832ff8a9540e01f.jpg",
+        "table_caption": [
+            "Table 4. The ablation study on CASIA-B with rank-1 accuracy."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">OUMVLP→CASIA-B</td></tr><tr><td>NM</td><td>BG</td><td>CL</td><td>Mean</td></tr><tr><td colspan=\"5\">Analysis of the UDA framework</td></tr><tr><td>Baseline</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr><tr><td>- w/o CTS-Conv</td><td>91.7</td><td>84.7</td><td>62.5</td><td>79.6</td></tr><tr><td>- w/o GC block</td><td>86.3</td><td>79.9</td><td>62.3</td><td>76.1</td></tr><tr><td>- w/o Confidence scores</td><td>88.6</td><td>81.3</td><td>66.8</td><td>78.9</td></tr><tr><td colspan=\"5\">Analysis of the number spatial bins Npart</td></tr><tr><td>Npart = 2</td><td>85.2</td><td>72.3</td><td>25.7</td><td>61.1</td></tr><tr><td>Npart = 4</td><td>83.5</td><td>76.2</td><td>51.3</td><td>70.3</td></tr><tr><td>Npart = 8</td><td>84.7</td><td>76.4</td><td>54.8</td><td>72.0</td></tr><tr><td>Npart = 16</td><td>84.2</td><td>77.1</td><td>59.4</td><td>73.6</td></tr><tr><td>Npart = 32</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
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+        "text": "In this paper, we present a novel part-based Unsupervised Domain Adaptation (UDA) framework for gait recognition. Our framework consists of an offline clustering stage and an online training stage, which facilitate the knowledge transformation from a labeled source domain to an unlabeled target domain. Our method enhances the reliability of spatio-temporal features and extracts robust gait features for further knowledge transfer. We evaluate the proposed method on three popular gait datasets: CASIA-B, OUMVLP, and GREW, and our experimental results demonstrate the effectiveness of the UDA framework and its potential for practical applications. In future work, we plan to conduct more extensive investigations of UDA methods for gait recognition to accelerate network training and improve the accuracy of pseudo-labels.",
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+        "text": "6. Acknowledgement",
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+        "text": "This work was supported by the National Key R&D Program of China (2022YFC3300700), the National Natural Science Foundation of China (62171038, 62088101, 62276031 and 62276025), and the Fundamental Research Funds for the Central Universities.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
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+        "type": "list",
+        "sub_type": "ref_text",
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+        ],
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diff --git a/2023/Fine-grained Unsupervised Domain Adaptation for Gait Recognition/4500f2e6-687c-4c2c-b586-2f14ced6ff0b_model.json b/2023/Fine-grained Unsupervised Domain Adaptation for Gait Recognition/4500f2e6-687c-4c2c-b586-2f14ced6ff0b_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..ec68ac0982c40012605c48c6211c1cf702c3e7d6
--- /dev/null
+++ b/2023/Fine-grained Unsupervised Domain Adaptation for Gait Recognition/4500f2e6-687c-4c2c-b586-2f14ced6ff0b_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
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+                0.808,
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Fine-grained Unsupervised Domain Adaptation for Gait Recognition"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Kang Ma\\(^{1}\\), Ying Fu\\(^{1*}\\), Dezhi Zheng\\(^{1*}\\), Yunjie Peng\\(^{2}\\), Chunshui Cao\\(^{3}\\), Yongzhen Huang\\(^{3,4*}\\), \\(^{1}\\)Beijing Institute of Technology, \\(^{2}\\)Beihang University, \\(^{3}\\)WATRIX.AI, \\(^{4}\\)Beijing Normal University"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "kangx.ma@gmail.com, {fuying, zhengdezhi}@bit.edu.cn, YunjiePeng@buaa.edu.cn"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.698,
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+            ],
+            "angle": 0,
+            "content": "chunshui.cao@watrix.ai, huangyongzhen@bnu.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.287,
+                0.314,
+                0.303
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.319,
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+            "angle": 0,
+            "content": "Gait recognition has emerged as a promising technique for the long-range retrieval of pedestrians, providing numerous advantages such as accurate identification in challenging conditions and non-intrusiveness, making it highly desirable for improving public safety and security. However, the high cost of labeling datasets, which is a prerequisite for most existing fully supervised approaches, poses a significant obstacle to the development of gait recognition. Recently, some unsupervised methods for gait recognition have shown promising results. However, these methods mainly rely on a fine-tuning approach that does not sufficiently consider the relationship between source and target domains, leading to the catastrophic forgetting of source domain knowledge. This paper presents a novel perspective that adjacent-view sequences exhibit overlapping views, which can be leveraged by the network to gradually attain cross-view and cross-dressing capabilities without pre-training on the labeled source domain. Specifically, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that iteratively alternates between two stages. The initial stage involves offline clustering, which transfers knowledge from the labeled source domain to the unlabeled target domain and adaptively generates pseudo-labels according to the expressiveness of each part. Subsequently, the second stage encompasses online training, which further achieves cross-dressing capabilities by continuously learning to distinguish numerous features of source and target domains. The effectiveness of the proposed method is demonstrated through extensive experiments conducted on widely-used public gait datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.804,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Gait recognition, a biometric technology [37, 41, 15] that identifies individuals based on their unique walking patterns, has gained significant attention for its ability to recog"
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+            "angle": 0,
+            "content": "(b) The Fine-grained UDA Framework"
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+        {
+            "type": "image",
+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1. (a) The prior knowledge of the existence of angle overlap between adjacent-view. (b) The proposed Fine-grained Unsupervised Domain Adaptation (UDA) framework for gait recognition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "nize people at long distances, regardless of their attire. The applications [6, 31, 12] of gait recognition have been greatly facilitated by advances in deep learning and the availability of vast amounts of labeled data. However, accurately annotating large amounts of data remains a daunting challenge, especially under long-distance cameras, where critical information such as the human face is often blurred, making it difficult to label gait sequences of the same person in different clothing, views, and carrying conditions. As a solution, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that transfers knowledge from a labeled source domain to an unlabeled target domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In the gait recognition task, an essential prior knowledge is the existence of overlapping angles in adjacent-view sequences as shown in Fig. 1 (a), which enables networks to build cross-view capabilities through a chain-like approach. Leveraging this premise, the UDA framework for gait recognition can gradually learn cross-dressing capabilities in the target domain through knowledge transfer and clustering, without the need for pre-training the network. We aim to reveal it by addressing the following aspects:"
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+            "bbox": [
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+            "angle": 0,
+            "content": "(i) Offline clustering stage. In the offline clustering phase,"
+        },
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+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "*Corresponding Authors"
+        },
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+            "type": "page_number",
+            "bbox": [
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+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "as shown in Fig. 1, the primary goal is to assign accurate pseudo-labels to unlabeled data by leveraging cross-view chaining relationships. To achieve this, the network extracts essential insights for gait from a labeled source domain and subsequently transfers this acquired knowledge to the unlabeled target domain. Following this knowledge transfer, the precise pseudo-label is assigned to the cross-view and cross-dressing data present within the target domain. This assignment hinges on the observed global feature space distribution within the aforementioned target domain. Furthermore, previous methods [3, 10, 16, 25, 19, 28] demonstrate that part-based methods outperform other approaches. To this end, we leverage the varied expressive capabilities of different body parts and adaptively generate a global feature space, which results in a more accurate assignment of pseudo-labels to unlabeled data."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "(ii) Online training stage. During the online training stage, the core objective is to continually learn the gait features in both the source and target domains. As depicted in Fig. 1 (a), the angles of the sequences vary continuously during human walking, with identical angles and actions appearing in sequences from adjacent viewpoints (indicated by the blue and red arrows). Consequently, the network can establish associations of neighboring perspectives by focusing on temporal features and gain cross-view capabilities through the association of all perspectives. Moreover, as shown in Fig. 1 (b), the network is trained by continuously selecting features from the unlabelled target domain that have been assigned the same pseudo-label as the training set. By continually adding data to the target domain in this way, the network focuses on more robust motion patterns to distinguish features from different domains. Prior methods [25, 26, 28] have demonstrated the criticality of motion pattern extraction in cross-dressing recognition. Consequently, the network gradually develops the cross-dressing capability, even in cases where it is absent from the source domain data."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Driven by this analysis, we propose a simple yet effective fine-grained UDA framework, wherein knowledge learned from the labeled source domain is transferred to obtain pseudo-labels for the unlabeled target domain. Subsequently, we utilize both labeled source and target domain data to extract fine-grained spatio-temporal motion patterns. As illustrated in Fig. 3, the offline clustering stage calculates the confidence scores for each part-based feature. These confidence scores are employed to derive the global feature space and assign pseudo-labels for unlabeled data. And the hybrid memory is initialized based on these pseudolabels. Additionally, information scores are utilized to supervise the hybrid memory and facilitate the computation of the part-based contrastive loss. Furthermore, the online training stage is shown in Fig. 2, we propose a novel Spatio-Temporal Aggregation Network (STANet) for learning global motion patterns, which contains spatial designed"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Cycle Temporal Shift convolution (CTS-Conv) and Global context block. At each iteration, the hybrid memory is dynamically updated using the global motion patterns."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.138,
+                0.878,
+                0.153
+            ],
+            "angle": 0,
+            "content": "Our contributions can be summarized in three aspects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.165,
+                0.892,
+                0.24
+            ],
+            "angle": 0,
+            "content": "- We propose a unified UDA framework structure based on the prior knowledge of the existence of an overlap between adjacent-view sequences, which enables our network to gradually acquire cross-view and cross-dressing capabilities without pre-training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.253,
+                0.892,
+                0.343
+            ],
+            "angle": 0,
+            "content": "- We present an innovative STANet that effectively captures fine-grained motion patterns while enabling the acquisition of cross-view and cross-dressing capabilities. Our approach demonstrates superior performance than current state-of-the-art methods, particularly under the cross-dressing condition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.356,
+                0.892,
+                0.462
+            ],
+            "angle": 0,
+            "content": "- The effectiveness of the proposed UDA framework is demonstrated through experimental results, which show superior performance on the CASIA-B [41], OUMVLP [32], and GREW [48] datasets. Moreover, comprehensive ablation experiments performed on the CASIA-B dataset further corroborate the efficacy of the proposed method within the UDA framework."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.477,
+                0.642,
+                0.493
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.503,
+                0.892,
+                0.55
+            ],
+            "angle": 0,
+            "content": "In this section, we review the most relevant research in the area of unsupervised domain adaptation, part-based approaches, and spatial-temporal modeling."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.56,
+                0.892,
+                0.577
+            ],
+            "angle": 0,
+            "content": "2.1. Unsupervised Domain Adaptation Approaches"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The Unsupervised Domain Adaptation (UDA) methods [30, 11, 44, 42, 14, 40, 8, 13, 7] for person re-identification (re-ID) have made significant progress. Advanced UDA methods for re-ID tasks often employ clustering algorithms, such as K-means [47], DBSCAN [9, 18], and InfoMAP [5], to generate pseudo-labels for unlabeled data from global features. For instance, MMT [13] used mutual mean-teaching to softly refine the pseudo labels in the target domain, AD-Cluster [42] incorporated style-translated images using a novel discriminative clustering method, and SpCL [14] employed a self-paced approach to create more reliable clusters gradually and refine the hybrid memory and the targets. Despite significant progress in recent years, adapting these methods for gait recognition tasks remains challenging due to inherent differences between gait and re-ID data. Specifically, re-ID data typically contains informative features such as texture and color, which enable the association of individuals without explicit labels. In contrast, the silhouette sequence in gait lacks such information, which poses a significant challenge for unsupervised tasks. Recent pioneering UDA methods for gait recognition [36, 45]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11314"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.094,
+                0.093,
+                0.885,
+                0.257
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.262,
+                0.895,
+                0.32
+            ],
+            "angle": 0,
+            "content": "Figure 2. The overview of the online training stage in the proposed UDA framework, where \"HP\" represent the Horizontal Pooling, and \"GC\" represents the Global Context block. (a) The fine-grained motion patterns are extracted by Spatio-Temporal Aggregation Network (STANet). (b) The hybrid memory is used to supervise the training data and dynamically updated based on these features. (c) The features extracted by GC are used to calculate triplet loss, and the normalized features are used to calculate cross-entropy and contrastive losses."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.328,
+                0.473,
+                0.451
+            ],
+            "angle": 0,
+            "content": "have made some achievements on unlabeled datasets. However, these methods do not sufficiently consider the relationship between source and target domains, which ultimately restricts their performance and practical applications. As a solution, we propose a novel UDA framework that transfers valuable knowledge from a labeled source domain to an unlabeled target domain. By leveraging UDA, gait can be applied in more challenging real-world situations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.462,
+                0.295,
+                0.479
+            ],
+            "angle": 0,
+            "content": "2.2. Part-based Approaches"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.486,
+                0.473,
+                0.82
+            ],
+            "angle": 0,
+            "content": "The extraction of fine-grained features of body parts in gait recognition is a critical insight that plays a pivotal role to distinguish different individuals. Extensive research [3, 10, 16, 26, 19] has emphasized the significance of horizontally dividing these features into distinct parts. For example, GaitSet [3] introduced the Horizontal Pyramid Mapping (HPM) module, which partitions gait features into 62 strips along the height dimension. Since then, most gait recognition algorithms [16, 17, 25, 2] have adopted a part-based approach, training features with distinct parts separately. GaitPart [10] divided gait features horizontally into 16 strips, while GaitGL [26] separated global and local features into 32 strips, respectively. 3DLocal [19] proposed a localization module to learn the adaptive spatial and temporal scales. Therefore, gait recognition relies on the representation of multiple motion patterns with critical parts. However, the clustering algorithms typically assign pseudolabels based on the global feature. To this end, we develop a fine-grained UDA framework for gait recognition that leverages the part-based features. Specifically, we evaluate the expressiveness of different parts to calculate confidence scores and then adaptively obtain the pseudo-labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.831,
+                0.318,
+                0.848
+            ],
+            "angle": 0,
+            "content": "2.3. Spatio-temporal Modeling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Gait recognition approaches can be broadly categorized into two primary domains: model-based [20, 34, 23, 24, 22] and appearance-based [39, 15, 29, 33, 34]. The appearance-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.328,
+                0.895,
+                0.722
+            ],
+            "angle": 0,
+            "content": "based approaches have become the mainstream for gait recognition, which can be broadly classified into two categories, including silhouette-based methods [43, 3, 16, 10, 17] and video-based methods [25, 26, 2, 19, 38]. The silhouette-based methods generally employ 2D convolution (2D-Conv) neural networks to extract spatial features on either a single Gait Energy Image (GEI) or a collection of randomly arranged silhouette sets. For example, CNN-LB [39] introduced a CNN-based technique for gait feature learning from Gait Energy Images (GEI), while GaitSet [3] employed 2D convolution for feature extraction, assuming that the silhouette's appearance contained its positional information. However, these methods neglect temporal features which is the robust information in gait sequences. On the other hand, video-based techniques [10, 25, 26, 19] strive to acquire spatio-temporal features, which have been established as advantageous for enhancing gait recognition. For example, GaitGL [26] employed a 3D convolution (3D-Conv) neural network to extract spatio-temporal features. However, these methods use 3D-Conv to extract temporal features with a high amount of parameters. Different from these methods, we propose a more efficient solution named Cycle-Temporal Shit Convolution (CTS-Conv) that enables both low-level and high-level spatio-temporal features with a low computational cost. Further, we refined a global context modeling to extract robust motion patterns."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.735,
+                0.593,
+                0.751
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.761,
+                0.894,
+                0.839
+            ],
+            "angle": 0,
+            "content": "In this section, we begin by introducing the overarching structure of fine-grained UDA framework in Sec. 3.1. Following that, we outline the offline clustering stage in Sec. 3.2, and subsequently detail the online training stage in Sec. 3.3. Finally, we present the joint loss in Sec. 3.4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.847,
+                0.611,
+                0.862
+            ],
+            "angle": 0,
+            "content": "3.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The UDA framework for gait recognition aims to transfer knowledge gained from labeled source domains to un"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11315"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.094,
+                0.093,
+                0.878,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.254,
+                0.895,
+                0.298
+            ],
+            "angle": 0,
+            "content": "Figure 3. The offline clustering stage in the proposed UDA framework. (a) Calculating the confidence scores using a \\(k\\)-nearest neighbor search algorithm. (b) Generating pseudo labels using a clustering algorithm in the global space. (c) Initializing the hybrid memory using class-level features. (d) Using the confidence scores to further optimize contrastive loss."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.306,
+                0.47,
+                0.382
+            ],
+            "angle": 0,
+            "content": "labeled target domains, enabling accurate identification of individuals in unlabeled data. Following the previous UDA methods [50, 35, 4, 46, 21], as shown in Fig. 1 (b), we divide the training of the UDA framework into two stages, including the stage of offline clustering and online training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.382,
+                0.471,
+                0.502
+            ],
+            "angle": 0,
+            "content": "In the offline clustering stage, we first assign pseudolabels to unlabeled data. Then, we extract class-level central features from both source and target domains, which are used to initialize the hybrid memory module. Formally, Let \\(\\mathcal{D}_s = \\{(x_s,y_s)|x_s\\in \\mathbb{R}^{N_S\\times T\\times H\\times W},y_s\\in \\mathbb{R}^{N_S}\\}\\) and \\(\\mathcal{D}_t = \\{x_t|x_t\\in \\mathbb{R}^{N_T\\times T\\times H\\times W}\\}\\) denote the labeled and unlabeled data, where \\(N_{S}\\) and \\(N_{T}\\) are the numbers of sequences. The generation of pseudo-labels \\(y_{t}\\) can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.51,
+                0.47,
+                0.528
+            ],
+            "angle": 0,
+            "content": "\\[\ny _ {t} = \\mathcal {C} \\left(\\left\\langle \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right), \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right) \\right\\rangle\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.535,
+                0.47,
+                0.626
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{C}\\) represents the clustering algorithm, \\(\\langle \\cdot ,\\cdot \\rangle\\) denotes the operation to measure the similarity between gait features space, \\(\\mathcal{F}_{\\theta}\\) is a learnable network parameterized by \\(\\theta\\). During the online training stage, the pseudo-labeled data can be sampled with the labeled data. The gait features \\((f_{s},f_{t})\\) extraction can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.176,
+                0.634,
+                0.47,
+                0.651
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(f _ {s}, f _ {t}\\right) = \\left(\\mathcal {F} _ {\\theta} \\left(x _ {s}\\right), \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right)\\right). \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.659,
+                0.47,
+                0.78
+            ],
+            "angle": 0,
+            "content": "To perform gait recognition on unlabeled sequences, TranND [45] utilizes a fine-tuning approach, which may lead to catastrophic forgetting of the knowledge learned in the source domain when trained on the target domain. In this paper, the proposed UDA framework is an end-to-end approach that utilizes alternating \"offline clustering stage\" and \"online training stage\" to simultaneously train the data in both source and target domains."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.787,
+                0.3,
+                0.804
+            ],
+            "angle": 0,
+            "content": "3.2. Offline Clustering Stage"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.47,
+                0.856
+            ],
+            "angle": 0,
+            "content": "This part provides a comprehensive overview of the offline clustering stage, which generates the pseudo-labels for unlabeled data and initializes the hybrid memory."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Generating pseudo-labels. The offline clustering stage, as shown in Fig. 3, plays a crucial role in UDA tasks by generating pseudo-labels for unlabeled data. The effectiveness"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.306,
+                0.895,
+                0.412
+            ],
+            "angle": 0,
+            "content": "of the UDA algorithm relies on the distribution that features with the same label cluster densely in feature space, while those with different labels are scattered. However, one of the main challenges in the UDA framework is generating accurate pseudo-labels by effectively utilizing the relationships between the part-level features, given that features are comprised of multiple spatio-temporal motion patterns."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.412,
+                0.895,
+                0.625
+            ],
+            "angle": 0,
+            "content": "To accurately distribute unlabeled data, we take into account the expressive capabilities of different body parts and calculate the confidence score for each part feature accordingly. Formally, let \\( f_{t} \\in \\mathbb{R}^{N_{T} \\times P \\times C} \\) denote the target domain part-level features, where \\( P \\) is the number of horizontally sliced parts, and \\( C \\) is the feature channels. Specifically, we perform the \\( k \\)-nearest neighbor search algorithm on both the global feature space and each part feature space to generate ranked lists \\( \\{\\mathcal{R}_g, \\mathcal{R}_1, \\dots, \\mathcal{R}_P\\} \\) for each unlabeled feature. The \\( \\mathcal{R}_g \\) represents the sets of global feature indices for the top- \\( k \\) samples in the ranked list, while \\( \\mathcal{R}_p \\) denotes the sets of \\( p \\)-th part feature indices. We then compute the confidence scores \\( S_{p} \\) between the global feature indices \\( \\mathcal{R}_g \\) and the \\( p \\)-th part feature indices \\( \\mathcal{R}_p \\) as follows,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.607,
+                0.632,
+                0.892,
+                0.667
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {S} _ {p} = \\frac {\\left| \\mathcal {R} _ {g} \\cap \\mathcal {R} _ {p} \\right|}{\\left| \\mathcal {R} _ {g} \\cup \\mathcal {R} _ {p} \\right|} \\in [ 0, 1 ], \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.674,
+                0.894,
+                0.751
+            ],
+            "angle": 0,
+            "content": "where \\(|\\cdot|\\) is a non-negative real number denoting the cardinality of a set. The confidence scores are further used to refine the part-based space to global feature space. We then use a clustering algorithm \\(\\mathcal{C}\\) (e.g., DBSCAN [9]) to assign pseudo-labels on the global feature space, i.e.,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.521,
+                0.759,
+                0.892,
+                0.802
+            ],
+            "angle": 0,
+            "content": "\\[\ny _ {t} = \\mathcal {C} \\left\\{\\mathcal {J} \\left(\\frac {1}{P} \\sum_ {p = 1} ^ {P} \\left[ \\langle f _ {t} ^ {p}, f _ {t} ^ {p} \\rangle * \\frac {\\mathcal {S} _ {p}}{\\sum_ {p = 1} ^ {P} \\mathcal {S} _ {p}} \\right]\\right) \\right\\}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.841
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{I}\\) is the Jaccard distance [49] computed in global feature space and \\(*\\) denotes the Hadamard product."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.841,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Initializing Hybrid Memory. To initialize the part-based hybrid memory, we utilize the class-level features of both source and target domains. It is worth illustrating that in the target domain, we only retain samples assigned with pseudo"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11316"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.123
+            ],
+            "angle": 0,
+            "content": "labels, and exclude those with discrete labels from the subsequent online training stage, i.e.,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.123,
+                0.146,
+                0.47,
+                0.194
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\{c _ {s}, c _ {t} \\right\\} = \\left\\{\\frac {1}{| \\mathcal {N} _ {s} |} \\sum_ {f _ {s} \\in \\mathcal {N} _ {s}} f _ {s}, \\frac {1}{| \\mathcal {N} _ {t} |} \\sum_ {f _ {t} \\in \\mathcal {N} _ {t}} f _ {t} \\right\\}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.206,
+                0.469,
+                0.237
+            ],
+            "angle": 0,
+            "content": "where \\(\\{c_s, c_t\\}\\) denotes the source and target domain class-level features, \\((\\mathcal{N}_s, \\mathcal{N}_t)\\) is the same label set or cluster set."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.247,
+                0.283,
+                0.263
+            ],
+            "angle": 0,
+            "content": "3.3. Online Training Stage"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.27,
+                0.469,
+                0.331
+            ],
+            "angle": 0,
+            "content": "This part provides a detailed explanation of the Cycle Temporal Shift Convolution (CTS-Conv) and Global Context Block. Then, we introduce the utilization of class-level momentum updating for the part-based hybrid memory."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.331,
+                0.47,
+                0.603
+            ],
+            "angle": 0,
+            "content": "Cycle Temporal Shift Convolution. Gait recognition is a challenging task due to the impact of various external factors, including carrying conditions, wearing coats, and varying viewing angles, leading to a much higher intra-class variance than inter-class. Previous studies [25, 26] proposed to use 3D convolution (3D-Conv) neural network to capture temporal information in gait sequences and extract robust features. However, when applied to part-based UDA tasks, 3D-Conv is limited by its high computational cost and parameter-rich structure, increasing the risk of over-fitting. To address this, we propose a novel CTS-Conv, which separates temporal feature learning from spatial feature learning based on the well-designed temporal shift convolution (TS-Conv) [27]. In CTS-Conv, the input features are denoted as \\(\\Upsilon = \\{v_{1}, v_{2}, \\ldots, v_{E}\\} \\in \\mathbb{R}^{C \\times T \\times H \\times W}\\), where \\(v_{i}\\) represents the input features divided equally into \\(E\\) pieces, and \\(T\\) denotes the number of frames. As shown in Fig. 2, the CTS-Conv operation can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.116,
+                0.613,
+                0.469,
+                0.633
+            ],
+            "angle": 0,
+            "content": "\\[\n\\overrightarrow {v} _ {1} ^ {t} = v _ {1} ^ {t - 1}, \\overrightarrow {v} _ {1} ^ {0} = v _ {1} ^ {T}, \\overleftarrow {v} _ {2} ^ {t} = v _ {2} ^ {t + 1}, \\overleftarrow {v} _ {2} ^ {T} = v _ {2} ^ {0}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.643,
+                0.469,
+                0.734
+            ],
+            "angle": 0,
+            "content": "where \\(\\overrightarrow{v}_1\\) and \\(\\overleftarrow{v}_2\\) denote the first two pieces which are shifted to the right and left along the temporal dimension, respectively. The remaining pieces \\([v_3,v_4,\\dots ,v_E]\\) are unshifted. The CTS-Conv operation in STANet learns temporal features by exchanging the features of adjacent frames, without introducing any additional parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Global Context Block. After extracting the spatiotemporal features using the CTS-Conv, we further refine the global context modeling technique called global context (GC) block base on [1, 28]. The GC block employs multiple heads to map features during context modeling, thereby facilitating the comprehensive extraction of global motion patterns. To generate the output feature, a horizontal pooling method (HP) is first utilized, resulting in horizontally sliced features denoted as \\( H = \\{h^1, h^2, \\dots, h^P\\} \\in \\mathbb{R}^{P \\times T \\times C} \\), where \\( P \\) represents the number of horizontally sliced parts. Then, the global motion patterns \\( g^p \\) are derived"
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.51,
+                0.095,
+                0.85,
+                0.11
+            ],
+            "angle": 0,
+            "content": "Algorithm 1: The training process of UDA for Gait"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.52,
+                0.114,
+                0.86,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Require: Labeled data \\(\\mathcal{D}_s\\) and Unlabeled data \\(\\mathcal{D}_t\\);  \nRequire: Random initialize pipeline \\(\\mathcal{F}_{\\theta}\\);  \nRequire: \\(m\\) for Eq. (9) and \\(\\tau\\) of Eq. (10);  \nfor \\(i \\leq N_e\\) do  \nOffline Clustering Stage, \\(N_e\\) is the total iterations; Assign pseudo-label for \\(\\mathcal{D}_t\\) with Eq. (4); Initialize the hybrid memory with Eq. (5);  \nfor \\(j \\leq T_e\\) do  \nOnline Training Stage, \\(T_e\\) is the train iterations; Sample mini-batch data \\((x_s, x_t)\\); Encoder part-based features \\((f_s, f_t)\\); Compute the joint loss with Eq. (11); Update part-based hybrid memory with Eq. (9);  \nend  \nend"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.358,
+                0.719,
+                0.373
+            ],
+            "angle": 0,
+            "content": "using the subsequent expression:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.56,
+                0.381,
+                0.892,
+                0.418
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {g} ^ {p} = \\frac {\\exp \\left(W _ {k} W _ {v 1} h _ {t} ^ {p}\\right)}{\\sum_ {t = 1} ^ {T} \\exp \\left(W _ {k} W _ {v 1} h _ {t} ^ {p}\\right)} \\otimes W _ {v 1} h ^ {p}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.619,
+                0.421,
+                0.891,
+                0.437
+            ],
+            "angle": 0,
+            "content": "\\[\ng ^ {p} = \\delta \\left(W _ {v 2} \\tilde {g} ^ {p}\\right) \\oplus h ^ {p}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.447,
+                0.892,
+                0.506
+            ],
+            "angle": 0,
+            "content": "where \\(\\tilde{g}^p\\) represents the context modeling, \\(W_{k}\\), \\(W_{v1}\\), and \\(W_{v2}\\) are learnable parameters, \\(\\delta\\) denotes the activation function, \\(\\otimes\\) signifies matrix multiplication, and \\(\\oplus\\) indicates the broadcast element-wise addition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.508,
+                0.892,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Updating Hybrid Memory. Each mini-batch of the sampled data is passed through a pipeline that extracts part-based features \\((f_s, f_t)\\). It is worth noting that our proposed UDA framework is highly versatile and can be readily applied to other network architectures [3, 26], as illustrated in Fig. 2, where STANet can be replaced by any of the existing popular networks. At each iteration, the extracted features in each mini-batch would be involved in part-based hybrid memory momentum updating, i.e.,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.544,
+                0.653,
+                0.891,
+                0.694
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\{ \\begin{array}{l} c _ {s} \\leftarrow m \\cdot f _ {s} + (1 - m) \\cdot \\frac {1}{| \\mathcal {B} _ {s} |} \\sum_ {f _ {s} \\in \\mathcal {B} _ {s}} f _ {s} \\\\ c _ {t} \\leftarrow m \\cdot f _ {t} + (1 - m) \\cdot \\frac {1}{| \\mathcal {B} _ {t} |} \\sum_ {f _ {t} \\in \\mathcal {B} _ {t}} f _ {t} \\end{array} \\right\\}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.702,
+                0.892,
+                0.749
+            ],
+            "angle": 0,
+            "content": "where \\((c_s, c_t)\\) denotes the class-level features, \\((\\mathcal{B}_s, \\mathcal{B}_t)\\) represents the set of features belonging to the source or target domain class and \\(m \\in [0,1]\\) is a momentum coefficient."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.757,
+                0.688,
+                0.772
+            ],
+            "angle": 0,
+            "content": "3.4. Joint Loss Function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, three types of part-based loss functions are employed, namely, the triplet loss \\(\\mathcal{L}_{tp}\\), the cross-entropy loss \\(\\mathcal{L}_{ce}\\), and the contrastive loss \\(\\mathcal{L}_{cl}\\). These loss functions are used to constrain the features of each part individually. As shown in Fig. 2, the output features \\((o_s,o_t)\\) are used to calculate \\(\\mathcal{L}_{tp}\\), while the normalized output features \\((f_s,f_t)\\) are used to calculate \\(\\mathcal{L}_{ce}\\) and \\(\\mathcal{L}_{cl}\\). Additionally, we consider the varying expressiveness of different body parts and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11317"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.116
+            ],
+            "angle": 0,
+            "content": "Table 1. The Rank-1 (\\%) performance comparison of fully supervised and unsupervised domain adaptation methods on CASIA-B. Where “OUMVLP→CASIA-B” denotes the use of OUMVLP as the source domain and CASIA-B as the target domain."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.099,
+                0.127,
+                0.869,
+                0.581
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"11\">Probe View</td><td rowspan=\"2\">Mean</td></tr><tr><td>0°</td><td>18°</td><td>36°</td><td>54°</td><td>72°</td><td>90°</td><td>108°</td><td>126°</td><td>134°</td><td>162°</td><td>180°</td></tr><tr><td colspan=\"14\">Fully supervised methods with all labels on CASIA-B</td></tr><tr><td rowspan=\"4\">NM</td><td>CNN-LB [39]</td><td>82.6</td><td>90.3</td><td>96.1</td><td>94.3</td><td>90.1</td><td>87.4</td><td>89.9</td><td>94.0</td><td>94.7</td><td>91.3</td><td>78.5</td><td>89.9</td></tr><tr><td>GaitSet [3]</td><td>90.8</td><td>97.9</td><td>99.4</td><td>96.9</td><td>93.6</td><td>91.7</td><td>95.0</td><td>97.8</td><td>98.9</td><td>96.8</td><td>85.8</td><td>95.0</td></tr><tr><td>GaitGL [26]</td><td>96.0</td><td>98.3</td><td>99.0</td><td>97.9</td><td>96.9</td><td>95.4</td><td>97.0</td><td>98.9</td><td>99.3</td><td>98.8</td><td>94.0</td><td>97.4</td></tr><tr><td>STANet(ours)</td><td>96.4</td><td>99.4</td><td>99.3</td><td>98.9</td><td>97.0</td><td>95.8</td><td>98.2</td><td>99.2</td><td>99.6</td><td>99.2</td><td>96.0</td><td>98.1</td></tr><tr><td rowspan=\"4\">BG</td><td>CNN-LB [39]</td><td>64.2</td><td>80.6</td><td>82.7</td><td>76.9</td><td>64.8</td><td>63.1</td><td>68.0</td><td>76.9</td><td>82.2</td><td>75.4</td><td>61.3</td><td>72.4</td></tr><tr><td>GaitSet [3]</td><td>83.8</td><td>91.2</td><td>91.8</td><td>88.8</td><td>83.3</td><td>81.0</td><td>84.1</td><td>90.0</td><td>92.2</td><td>94.4</td><td>79.0</td><td>87.2</td></tr><tr><td>GaitGL [26]</td><td>92.6</td><td>96.6</td><td>96.8</td><td>95.5</td><td>93.5</td><td>89.3</td><td>92.2</td><td>96.5</td><td>98.2</td><td>96.9</td><td>91.5</td><td>94.5</td></tr><tr><td>STANet(ours)</td><td>94.4</td><td>98.2</td><td>98.9</td><td>97.5</td><td>94.1</td><td>91.2</td><td>93.9</td><td>97.4</td><td>98.5</td><td>97.8</td><td>94.0</td><td>96.0</td></tr><tr><td rowspan=\"4\">CL</td><td>CNN-LB [39]</td><td>37.7</td><td>57.2</td><td>66.6</td><td>61.1</td><td>55.2</td><td>54.6</td><td>55.2</td><td>59.1</td><td>58.9</td><td>48.8</td><td>39.4</td><td>54.0</td></tr><tr><td>GaitSet [3]</td><td>61.4</td><td>75.4</td><td>80.7</td><td>77.3</td><td>72.1</td><td>70.1</td><td>71.5</td><td>73.5</td><td>73.5</td><td>68.4</td><td>50.0</td><td>70.4</td></tr><tr><td>GaitGL [26]</td><td>76.6</td><td>90.0</td><td>90.3</td><td>87.1</td><td>84.5</td><td>79.0</td><td>84.1</td><td>87.0</td><td>87.3</td><td>84.4</td><td>69.5</td><td>83.6</td></tr><tr><td>STANet(ours)</td><td>83.4</td><td>94.6</td><td>96.8</td><td>93.9</td><td>89.6</td><td>86.0</td><td>88.2</td><td>92.1</td><td>93.9</td><td>90.2</td><td>78.1</td><td>89.7</td></tr><tr><td colspan=\"14\">Unsupervised Domain Adaptation methods without any labels on CASIA-B (OUMVLP→CASIA-B)</td></tr><tr><td rowspan=\"4\">NM</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>63.4</td></tr><tr><td>UDA(GaitSet)</td><td>84.7</td><td>95.8</td><td>97.2</td><td>95.8</td><td>95.1</td><td>92.9</td><td>94.8</td><td>96.1</td><td>97.3</td><td>96.6</td><td>79.2</td><td>93.2</td></tr><tr><td>UDA(GaitGL)</td><td>76.7</td><td>88.3</td><td>88.8</td><td>87.1</td><td>88.4</td><td>82.9</td><td>85.9</td><td>90.6</td><td>93.1</td><td>93.9</td><td>73.0</td><td>86.2</td></tr><tr><td>UDA(STANet)</td><td>84.3</td><td>95.2</td><td>95.5</td><td>91.1</td><td>90.7</td><td>85.9</td><td>89.4</td><td>93.3</td><td>94.9</td><td>93.7</td><td>82.4</td><td>90.6</td></tr><tr><td rowspan=\"4\">BG</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>42.7</td></tr><tr><td>UDA(GaitSet)</td><td>77.5</td><td>87.5</td><td>90.0</td><td>89.2</td><td>86.2</td><td>81.2</td><td>87.1</td><td>89.9</td><td>94.0</td><td>91.1</td><td>70.9</td><td>85.9</td></tr><tr><td>UDA(GaitGL)</td><td>69.1</td><td>85.3</td><td>84.7</td><td>83.6</td><td>82.9</td><td>76.1</td><td>79.9</td><td>86.8</td><td>89.1</td><td>88.0</td><td>63.6</td><td>80.8</td></tr><tr><td>UDA(STANet)</td><td>75.4</td><td>88.7</td><td>86.6</td><td>83.6</td><td>82.9</td><td>76.2</td><td>82.6</td><td>86.9</td><td>89.3</td><td>87.5</td><td>73.7</td><td>83.0</td></tr><tr><td rowspan=\"4\">CL</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>15.8</td></tr><tr><td>UDA(GaitSet)</td><td>24.2</td><td>38.9</td><td>42.3</td><td>39.6</td><td>41.1</td><td>38.1</td><td>37.9</td><td>43.3</td><td>43.4</td><td>29.6</td><td>25.4</td><td>36.7</td></tr><tr><td>UDA(GaitGL)</td><td>43.9</td><td>65.3</td><td>66.5</td><td>66.9</td><td>68.8</td><td>60.0</td><td>66.4</td><td>71.2</td><td>69.3</td><td>61.8</td><td>42.2</td><td>62.0</td></tr><tr><td>UDA(STANet)</td><td>54.0</td><td>73.2</td><td>75.7</td><td>72.0</td><td>71.4</td><td>64.4</td><td>70.1</td><td>74.6</td><td>73.7</td><td>69.2</td><td>51.4</td><td>68.2</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.604,
+                0.47,
+                0.65
+            ],
+            "angle": 0,
+            "content": "use the confidence scores to accurately constrain the features by constraining the contrastive loss for each part. The contrastive loss \\(\\mathcal{L}_{cl}\\) can be formulated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.084,
+                0.655,
+                0.469,
+                0.743
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {c l} = - \\sum_ {p = 1} ^ {P} \\frac {\\mathcal {S} _ {p}}{N _ {c s}} \\left\\{- \\log \\frac {\\exp \\left(f ^ {p} \\cdot c _ {s} ^ {p , +} / \\tau\\right)}{\\sum_ {k = 1} ^ {| \\mathcal {N} _ {s} |} \\exp \\left(f ^ {p} \\cdot c _ {s} ^ {p , k} / \\tau\\right)} \\right\\} \\tag {10} \\\\ - \\sum_ {p = 1} ^ {P} \\frac {\\mathcal {S} _ {p}}{N _ {c t}} \\left\\{- \\log \\frac {\\exp (f ^ {p} \\cdot c _ {t} ^ {p , +} / \\tau)}{\\sum_ {k = 1} ^ {| \\mathcal {N} _ {t} |} \\exp (f ^ {p} \\cdot c _ {t} ^ {p , k} / \\tau)} \\right\\}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.75,
+                0.47,
+                0.827
+            ],
+            "angle": 0,
+            "content": "where \\(N_{cs}, N_{ct}\\) is a positive integer obtained by multiplying the mini-batch with parts, \\(\\tau\\) is a hyper-parameter, \\(c_s, c_t\\) denote the class-level features of source and target domains, and \\(c_s^{p, + }, c_t^{p, + }\\) indicate the positive class prototype corresponding to \\(f^p\\). The combined loss \\(\\mathcal{L}_c\\) can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.183,
+                0.848,
+                0.469,
+                0.865
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {c} = \\mathcal {L} _ {t p} + \\alpha \\mathcal {L} _ {c e} + \\beta \\mathcal {L} _ {c l}, \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) and \\(\\beta\\) are the hyper-parameters to balance the combined loss and are empirically set to 0.3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.603,
+                0.633,
+                0.62
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "In this section, we evaluate the proposed method on three large-scale gait recognition benchmarks, including two widely adopted datasets (i.e., CASIA-B and OUMVLP) and one real-world dataset (i.e., GREW). Then, we compare our method to state-of-the-art methods. Finally, comprehensive ablation studies are conducted to substantiate the effectiveness of our proposed method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.742,
+                0.82,
+                0.758
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "CASIA-B [41] is a well-established dataset widely used in the field of gait recognition research. It comprises 124 subjects and encompasses 3 distinct walking conditions: normal walking (NM), walking while wearing a coat (CL), and walking with bags (BG). The dataset is captured by 11 cameras positioned uniformly between \\(0^{\\circ}\\) and \\(180^{\\circ}\\), providing a diverse range of viewpoints. Each subject has a total of 110 sequences. The first 74 subjects are used for training, while the remaining 50 subjects are reserved for testing. During"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11318"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.116
+            ],
+            "angle": 0,
+            "content": "Table 2. Rank-1 accuracy of fully supervised and unsupervised domain adaptation methods on OUMVLP under all view angles. Where \"CASIA-B→OUMVLP\" represents the use of CASIA-B as the labeled source domain and OUMVLP as the unlabeled target domain."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.102,
+                0.127,
+                0.875,
+                0.304
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"14\">Probe View</td><td rowspan=\"2\">Mean</td></tr><tr><td>0°</td><td>15°</td><td>30°</td><td>45°</td><td>60°</td><td>75°</td><td>90°</td><td>180°</td><td>195°</td><td>210°</td><td>225°</td><td>240°</td><td>255°</td><td>270°</td></tr><tr><td colspan=\"16\">Fully supervised methods with all labels on OUMVLP</td></tr><tr><td>GaitSet [3]</td><td>79.5</td><td>87.9</td><td>89.9</td><td>90.2</td><td>88.1</td><td>88.7</td><td>87.8</td><td>81.7</td><td>86.7</td><td>89.0</td><td>89.3</td><td>87.2</td><td>87.8</td><td>86.2</td><td>87.1</td></tr><tr><td>GaitGL [26]</td><td>84.9</td><td>90.2</td><td>91.1</td><td>91.5</td><td>91.1</td><td>90.8</td><td>90.3</td><td>88.5</td><td>88.6</td><td>90.3</td><td>90.4</td><td>89.6</td><td>89.5</td><td>88.8</td><td>89.7</td></tr><tr><td>STANet(ours)</td><td>87.7</td><td>91.4</td><td>91.6</td><td>91.9</td><td>91.6</td><td>91.4</td><td>91.2</td><td>90.4</td><td>90.3</td><td>90.8</td><td>91.0</td><td>90.5</td><td>90.3</td><td>90.1</td><td>90.7</td></tr><tr><td colspan=\"16\">Unsupervised Domain Adaptation methods without any labels on OUMVLP (CASIA-B→OUMVLP)</td></tr><tr><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>75.6</td></tr><tr><td>UDA(GaitSet)</td><td>45.6</td><td>60.1</td><td>75.3</td><td>80.7</td><td>75.5</td><td>73.9</td><td>73.9</td><td>49.9</td><td>59.9</td><td>75.5</td><td>81.7</td><td>74.9</td><td>73.2</td><td>72.9</td><td>69.5</td></tr><tr><td>UDA(GaitGL)</td><td>23.6</td><td>50.5</td><td>79.5</td><td>78.5</td><td>75.3</td><td>74.6</td><td>74.5</td><td>28.7</td><td>50.9</td><td>77.5</td><td>77.5</td><td>74.3</td><td>73.3</td><td>73.0</td><td>65.1</td></tr><tr><td>UDA(STANet)</td><td>42.8</td><td>85.1</td><td>92.1</td><td>91.2</td><td>88.9</td><td>89.2</td><td>89.5</td><td>50.4</td><td>86.6</td><td>90.8</td><td>90.1</td><td>88.0</td><td>87.9</td><td>88.0</td><td>82.9</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.325,
+                0.468,
+                0.355
+            ],
+            "angle": 0,
+            "content": "testing, the first four \"NM\" conditions are utilized as the gallery, while the remaining conditions serve as the probe."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.356,
+                0.468,
+                0.522
+            ],
+            "angle": 0,
+            "content": "OUMVLP [32] is a prominent public gait dataset that comprises 10,307 subjects, two distinct walking sequences (labeled as “00” and “01”), and 14 cameras positioned uniformly between \\((0^{\\circ} \\rightarrow 90^{\\circ})\\) and \\((180^{\\circ} \\rightarrow 270^{\\circ})\\). To ensure fair data volume in comparison to CASIA-B, we select the first 1,000 subjects from OUMVLP for our UDA experiments without any specific instructions. In the UDA experiment, we followed the official data split and used 500 individuals for training and the remaining 500 for testing. During the test phase, the “00” sequences serve as the probe, while the remaining “01” sequences serve as the gallery."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.523,
+                0.468,
+                0.688
+            ],
+            "angle": 0,
+            "content": "GREW [48] is a comprehensive and extensive dataset designed for gait recognition, encompassing silhouettes and 2D/3D human body pose. In contrast to CASIA-B and OUMVLP, GREW was collected in diverse and complex scenes in the wild, making it a more challenging task for gait recognition. The GREW dataset comprises 26345 subjects, 128671 sequences, and 882 camera viewpoints. To ensure fairness in data volume with respect to CASIA-B, we use the first 4000 subjects from GREW for UDA experiments without any special instructions. During testing, we make full use of the official query and gallery set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Implementation Details. The training process of UDA is shown in Algorithm 1, and all datasets are uniformly resized to \\(64 \\times 44\\) [3]. The model is trained end-to-end using the SGD optimizer, starting with an initial learning rate of 0.1, which is then decreased by a factor of 10 iteratively until convergence. The training mini-batch size for CASIA-B and OUMVLP is set to (8, 16), while for GREW dataset, it is set to (4, 32). Data augmentation techniques are utilized to preserve both the original and augmented data in real-world datasets. The convolutional channels in the STANet are set to (64, 128, 256). The network is trained for a total of \\(N_{e} = 100\\mathrm{K}\\) iterations, and offline clustering is performed every \\(T_{e} = 5\\mathrm{K}\\) iteration to assign pseudo-labels to unlabeled data and reinitialize the hybrid memory dictionary."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.324,
+                0.866,
+                0.34
+            ],
+            "angle": 0,
+            "content": "4.2. Comparison with State-of-the-art Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.351,
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+            ],
+            "angle": 0,
+            "content": "To evaluate the effectiveness of the proposed approach, we compared it with both existing fully supervised methods [39, 3, 26] and Unsupervised Domain Adaptation (UDA) method [45] for gait recognition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.414,
+                0.892,
+                0.717
+            ],
+            "angle": 0,
+            "content": "Evaluation on CASIA-B. The performance of both fully supervised [39, 3, 26] and UDA methods [45] on CASIA-B is presented in Tab. 1. (1) The proposed STANet algorithm outperforms the fully supervised algorithm [39, 3, 26], especially in the cross-dressing condition. Experimental results show that our method has the ability to learn more robust motion patterns compared to others. (2) The proposed UDA framework outperforms the existing UDA algorithm [45] under all conditions. The experimental results demonstrate that our UDA framework can effectively utilize fine-grained part-based features to generate pseudo-labels that supervise network learning, leading to a significant improvement in recognition accuracy. (3) We conducted experiments by substituting STANet with various state-of-the-art algorithms, such as GaitSet [3] and GaitGL [26]. In the UDA framework, the GaitSet method outperforms other methods in \"NM\" and \"BG\" but has lower performance in \"CL\". The experimental results demonstrate that GaitSet emphasizes learning cross-view information from the OUMVLP but struggles to capture robust motion patterns."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Evaluation on OUMVLP. To provide additional evidence of the effectiveness of our proposed method, we evaluated the proposed approach with some state-of-the-art fully supervised [3, 26] and UDA [45] methods on OUMVLP. (1) The proposed STANet outperforms other methods, including GaitSet [3] and GaitGL [26], under both the whole dataset and fully supervised conditions. Our experimental results demonstrate the critical importance of effectively utilizing fine-grained spatio-temporal motion patterns for achieving high performance on large-scale gait datasets. (2) Our proposed UDA framework outperforms the existing UDA algorithm [45]. The experimental results demon"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.957
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+            "angle": 0,
+            "content": "11319"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "strate that our framework can effectively transfer the norm walking information from CASIA-B to OUMVLP. (3) We conducted experiments to compare STANet with other algorithms, including GaitSet [3] and GaitGL [26]. The results showed that the proposed STANet in the UDA framework effectively utilized fine-grained part-based features, even in the presence of cross-dressing influence in CASIA-B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.198,
+                0.471,
+                0.351
+            ],
+            "angle": 0,
+            "content": "Evaluation on GREW. We evaluated the proposed method on a wild dataset, i.e., GREW, to provide additional evidence for the effectiveness of our method. (1) The experimental results presented in Tab. 3 demonstrate the effectiveness of the fine-grained motion patterns extracted by our method on real datasets. (2) The UDA experimental results confirm that knowledge gained from accurately labeled data in a laboratory setting can be transferred to real-world scenarios. This validation also confirms the efficacy of our proposed approach in extracting fine-grained motion patterns."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+                0.47,
+                0.43
+            ],
+            "angle": 0,
+            "content": "In this section, an ablation study is performed on the proposed UDA framework to improve the understanding of the effects of different configurations."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "The effectiveness of STANet. To comprehensively evaluate the impact of STANet in the UDA framework, we conducted a thorough comparative experiment in Tab. 4. Specifically, (1) The \"w/o CTS-Conv\" represents replacing the CTS-Conv with 2D convolution. The experiment demonstrates a decrease in the performance of the \"CL\", thereby confirming the ability of CTS-Conv to acquire resilient temporal features in the UDA framework. (2) Furthermore, we conducted additional experiments to remove the GC block, denoted as \"w/o GC block\", in which the GC block was replaced with Max Pooling along the temporal dimension. The experiment results showed that STANet exhibited performance comparable to that of GaitGL [26]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.629,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "The effectiveness of confidence scores. To explore the impact of confidence scores on the offline clustering stage, we completely remove the process of generating confidence scores and generate the global feature space directly averaged over the part-based feature space. The experimental results \"w/o Confidence scores\" from the Tab. 4 show that removing the confidence score decreased the performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Analysis of the number of spatial slices parts. We conducted an in-depth analysis to assess the influence of different spatial bin numbers of the UDA framework in Tab. 4. (1) The experimental results indicate that the performance improves as the number of \\( N_{\\text{part}} \\) increases. (2) In the field of gait recognition, many popular approaches [10, 26] have confirmed that the number of parts has a significant impact on the recognition results. Specifically, increasing the number of parts requires the network to focus more on fine-grained parts. Experimental results show that \\( N_{\\text{part}} \\) also has a significant impact on unlabeled feature learning."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
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+                0.114
+            ],
+            "angle": 0,
+            "content": "Table 3. Rank-1 \\((\\%)\\) performance comparison of fully supervised and unsupervised domain adaptation methods on GREW."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "content": "<table><tr><td>Method</td><td>Source</td><td>Rank-1 (%)</td></tr><tr><td colspan=\"3\">Fully supervised methods on GREW</td></tr><tr><td>CNN-LB [39]</td><td>TPAMI 2017</td><td>12.2</td></tr><tr><td>GaitSet [3]</td><td>AAAI 2019</td><td>33.5</td></tr><tr><td>GaitGL [26]</td><td>ICCV 2021</td><td>32.7</td></tr><tr><td>STANet(ours)</td><td>-</td><td>41.3</td></tr><tr><td colspan=\"3\">UDA methods without any labels (OUMVLP→GREW)</td></tr><tr><td>UDA(Gaitset)</td><td>-</td><td>15.3</td></tr><tr><td>UDA(GaitGL)</td><td>-</td><td>13.7</td></tr><tr><td>UDA(STANet)</td><td>-</td><td>26.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.501,
+                0.295,
+                0.875,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Table 4. The ablation study on CASIA-B with rank-1 accuracy."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.517,
+                0.308,
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+                0.523
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">OUMVLP→CASIA-B</td></tr><tr><td>NM</td><td>BG</td><td>CL</td><td>Mean</td></tr><tr><td colspan=\"5\">Analysis of the UDA framework</td></tr><tr><td>Baseline</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr><tr><td>- w/o CTS-Conv</td><td>91.7</td><td>84.7</td><td>62.5</td><td>79.6</td></tr><tr><td>- w/o GC block</td><td>86.3</td><td>79.9</td><td>62.3</td><td>76.1</td></tr><tr><td>- w/o Confidence scores</td><td>88.6</td><td>81.3</td><td>66.8</td><td>78.9</td></tr><tr><td colspan=\"5\">Analysis of the number spatial bins Npart</td></tr><tr><td>Npart = 2</td><td>85.2</td><td>72.3</td><td>25.7</td><td>61.1</td></tr><tr><td>Npart = 4</td><td>83.5</td><td>76.2</td><td>51.3</td><td>70.3</td></tr><tr><td>Npart = 8</td><td>84.7</td><td>76.4</td><td>54.8</td><td>72.0</td></tr><tr><td>Npart = 16</td><td>84.2</td><td>77.1</td><td>59.4</td><td>73.6</td></tr><tr><td>Npart = 32</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.533,
+                0.62,
+                0.549
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.559,
+                0.892,
+                0.786
+            ],
+            "angle": 0,
+            "content": "In this paper, we present a novel part-based Unsupervised Domain Adaptation (UDA) framework for gait recognition. Our framework consists of an offline clustering stage and an online training stage, which facilitate the knowledge transformation from a labeled source domain to an unlabeled target domain. Our method enhances the reliability of spatio-temporal features and extracts robust gait features for further knowledge transfer. We evaluate the proposed method on three popular gait datasets: CASIA-B, OUMVLP, and GREW, and our experimental results demonstrate the effectiveness of the UDA framework and its potential for practical applications. In future work, we plan to conduct more extensive investigations of UDA methods for gait recognition to accelerate network training and improve the accuracy of pseudo-labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.8,
+                0.681,
+                0.817
+            ],
+            "angle": 0,
+            "content": "6. Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "This work was supported by the National Key R&D Program of China (2022YFC3300700), the National Natural Science Foundation of China (62171038, 62088101, 62276031 and 62276025), and the Fundamental Research Funds for the Central Universities."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11320"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+# Fine-grained Unsupervised Domain Adaptation for Gait Recognition
+
+Kang Ma $^{1}$ , Ying Fu $^{1*}$ , Dezhi Zheng $^{1*}$ , Yunjie Peng $^{2}$ , Chunshui Cao $^{3}$ , Yongzhen Huang $^{3,4*}$ ,  $^{1}$ Beijing Institute of Technology,  $^{2}$ Beihang University,  $^{3}$ WATRIX.AI,  $^{4}$ Beijing Normal University
+
+kangx.ma@gmail.com, {fuying, zhengdezhi}@bit.edu.cn, YunjiePeng@buaa.edu.cn
+
+chunshui.cao@watrix.ai, huangyongzhen@bnu.edu.cn
+
+# Abstract
+
+Gait recognition has emerged as a promising technique for the long-range retrieval of pedestrians, providing numerous advantages such as accurate identification in challenging conditions and non-intrusiveness, making it highly desirable for improving public safety and security. However, the high cost of labeling datasets, which is a prerequisite for most existing fully supervised approaches, poses a significant obstacle to the development of gait recognition. Recently, some unsupervised methods for gait recognition have shown promising results. However, these methods mainly rely on a fine-tuning approach that does not sufficiently consider the relationship between source and target domains, leading to the catastrophic forgetting of source domain knowledge. This paper presents a novel perspective that adjacent-view sequences exhibit overlapping views, which can be leveraged by the network to gradually attain cross-view and cross-dressing capabilities without pre-training on the labeled source domain. Specifically, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that iteratively alternates between two stages. The initial stage involves offline clustering, which transfers knowledge from the labeled source domain to the unlabeled target domain and adaptively generates pseudo-labels according to the expressiveness of each part. Subsequently, the second stage encompasses online training, which further achieves cross-dressing capabilities by continuously learning to distinguish numerous features of source and target domains. The effectiveness of the proposed method is demonstrated through extensive experiments conducted on widely-used public gait datasets.
+
+# 1. Introduction
+
+Gait recognition, a biometric technology [37, 41, 15] that identifies individuals based on their unique walking patterns, has gained significant attention for its ability to recog
+
+![](images/a24c59214fea4947d2bf7d74c945d27dbb0d896ee0c73276b508d044a20cfaa6.jpg)
+
+![](images/df2f43d8601eb6db4b14d184352372e6779218b1e0904b5faca7634ba82dfe9c.jpg)  
+(b) The Fine-grained UDA Framework  
+Figure 1. (a) The prior knowledge of the existence of angle overlap between adjacent-view. (b) The proposed Fine-grained Unsupervised Domain Adaptation (UDA) framework for gait recognition.
+
+nize people at long distances, regardless of their attire. The applications [6, 31, 12] of gait recognition have been greatly facilitated by advances in deep learning and the availability of vast amounts of labeled data. However, accurately annotating large amounts of data remains a daunting challenge, especially under long-distance cameras, where critical information such as the human face is often blurred, making it difficult to label gait sequences of the same person in different clothing, views, and carrying conditions. As a solution, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that transfers knowledge from a labeled source domain to an unlabeled target domain.
+
+In the gait recognition task, an essential prior knowledge is the existence of overlapping angles in adjacent-view sequences as shown in Fig. 1 (a), which enables networks to build cross-view capabilities through a chain-like approach. Leveraging this premise, the UDA framework for gait recognition can gradually learn cross-dressing capabilities in the target domain through knowledge transfer and clustering, without the need for pre-training the network. We aim to reveal it by addressing the following aspects:
+
+(i) Offline clustering stage. In the offline clustering phase,
+
+as shown in Fig. 1, the primary goal is to assign accurate pseudo-labels to unlabeled data by leveraging cross-view chaining relationships. To achieve this, the network extracts essential insights for gait from a labeled source domain and subsequently transfers this acquired knowledge to the unlabeled target domain. Following this knowledge transfer, the precise pseudo-label is assigned to the cross-view and cross-dressing data present within the target domain. This assignment hinges on the observed global feature space distribution within the aforementioned target domain. Furthermore, previous methods [3, 10, 16, 25, 19, 28] demonstrate that part-based methods outperform other approaches. To this end, we leverage the varied expressive capabilities of different body parts and adaptively generate a global feature space, which results in a more accurate assignment of pseudo-labels to unlabeled data.
+
+(ii) Online training stage. During the online training stage, the core objective is to continually learn the gait features in both the source and target domains. As depicted in Fig. 1 (a), the angles of the sequences vary continuously during human walking, with identical angles and actions appearing in sequences from adjacent viewpoints (indicated by the blue and red arrows). Consequently, the network can establish associations of neighboring perspectives by focusing on temporal features and gain cross-view capabilities through the association of all perspectives. Moreover, as shown in Fig. 1 (b), the network is trained by continuously selecting features from the unlabelled target domain that have been assigned the same pseudo-label as the training set. By continually adding data to the target domain in this way, the network focuses on more robust motion patterns to distinguish features from different domains. Prior methods [25, 26, 28] have demonstrated the criticality of motion pattern extraction in cross-dressing recognition. Consequently, the network gradually develops the cross-dressing capability, even in cases where it is absent from the source domain data.
+
+Driven by this analysis, we propose a simple yet effective fine-grained UDA framework, wherein knowledge learned from the labeled source domain is transferred to obtain pseudo-labels for the unlabeled target domain. Subsequently, we utilize both labeled source and target domain data to extract fine-grained spatio-temporal motion patterns. As illustrated in Fig. 3, the offline clustering stage calculates the confidence scores for each part-based feature. These confidence scores are employed to derive the global feature space and assign pseudo-labels for unlabeled data. And the hybrid memory is initialized based on these pseudolabels. Additionally, information scores are utilized to supervise the hybrid memory and facilitate the computation of the part-based contrastive loss. Furthermore, the online training stage is shown in Fig. 2, we propose a novel Spatio-Temporal Aggregation Network (STANet) for learning global motion patterns, which contains spatial designed
+
+Cycle Temporal Shift convolution (CTS-Conv) and Global context block. At each iteration, the hybrid memory is dynamically updated using the global motion patterns.
+
+Our contributions can be summarized in three aspects.
+
+- We propose a unified UDA framework structure based on the prior knowledge of the existence of an overlap between adjacent-view sequences, which enables our network to gradually acquire cross-view and cross-dressing capabilities without pre-training.  
+- We present an innovative STANet that effectively captures fine-grained motion patterns while enabling the acquisition of cross-view and cross-dressing capabilities. Our approach demonstrates superior performance than current state-of-the-art methods, particularly under the cross-dressing condition.  
+- The effectiveness of the proposed UDA framework is demonstrated through experimental results, which show superior performance on the CASIA-B [41], OUMVLP [32], and GREW [48] datasets. Moreover, comprehensive ablation experiments performed on the CASIA-B dataset further corroborate the efficacy of the proposed method within the UDA framework.
+
+# 2. Related Work
+
+In this section, we review the most relevant research in the area of unsupervised domain adaptation, part-based approaches, and spatial-temporal modeling.
+
+# 2.1. Unsupervised Domain Adaptation Approaches
+
+The Unsupervised Domain Adaptation (UDA) methods [30, 11, 44, 42, 14, 40, 8, 13, 7] for person re-identification (re-ID) have made significant progress. Advanced UDA methods for re-ID tasks often employ clustering algorithms, such as K-means [47], DBSCAN [9, 18], and InfoMAP [5], to generate pseudo-labels for unlabeled data from global features. For instance, MMT [13] used mutual mean-teaching to softly refine the pseudo labels in the target domain, AD-Cluster [42] incorporated style-translated images using a novel discriminative clustering method, and SpCL [14] employed a self-paced approach to create more reliable clusters gradually and refine the hybrid memory and the targets. Despite significant progress in recent years, adapting these methods for gait recognition tasks remains challenging due to inherent differences between gait and re-ID data. Specifically, re-ID data typically contains informative features such as texture and color, which enable the association of individuals without explicit labels. In contrast, the silhouette sequence in gait lacks such information, which poses a significant challenge for unsupervised tasks. Recent pioneering UDA methods for gait recognition [36, 45]
+
+![](images/724cf58913e15774f3a8b3be378ad0ca298a526a8cc1e95f2680506dfd84b0b1.jpg)  
+Figure 2. The overview of the online training stage in the proposed UDA framework, where "HP" represent the Horizontal Pooling, and "GC" represents the Global Context block. (a) The fine-grained motion patterns are extracted by Spatio-Temporal Aggregation Network (STANet). (b) The hybrid memory is used to supervise the training data and dynamically updated based on these features. (c) The features extracted by GC are used to calculate triplet loss, and the normalized features are used to calculate cross-entropy and contrastive losses.
+
+have made some achievements on unlabeled datasets. However, these methods do not sufficiently consider the relationship between source and target domains, which ultimately restricts their performance and practical applications. As a solution, we propose a novel UDA framework that transfers valuable knowledge from a labeled source domain to an unlabeled target domain. By leveraging UDA, gait can be applied in more challenging real-world situations.
+
+# 2.2. Part-based Approaches
+
+The extraction of fine-grained features of body parts in gait recognition is a critical insight that plays a pivotal role to distinguish different individuals. Extensive research [3, 10, 16, 26, 19] has emphasized the significance of horizontally dividing these features into distinct parts. For example, GaitSet [3] introduced the Horizontal Pyramid Mapping (HPM) module, which partitions gait features into 62 strips along the height dimension. Since then, most gait recognition algorithms [16, 17, 25, 2] have adopted a part-based approach, training features with distinct parts separately. GaitPart [10] divided gait features horizontally into 16 strips, while GaitGL [26] separated global and local features into 32 strips, respectively. 3DLocal [19] proposed a localization module to learn the adaptive spatial and temporal scales. Therefore, gait recognition relies on the representation of multiple motion patterns with critical parts. However, the clustering algorithms typically assign pseudolabels based on the global feature. To this end, we develop a fine-grained UDA framework for gait recognition that leverages the part-based features. Specifically, we evaluate the expressiveness of different parts to calculate confidence scores and then adaptively obtain the pseudo-labels.
+
+# 2.3. Spatio-temporal Modeling
+
+Gait recognition approaches can be broadly categorized into two primary domains: model-based [20, 34, 23, 24, 22] and appearance-based [39, 15, 29, 33, 34]. The appearance-
+
+based approaches have become the mainstream for gait recognition, which can be broadly classified into two categories, including silhouette-based methods [43, 3, 16, 10, 17] and video-based methods [25, 26, 2, 19, 38]. The silhouette-based methods generally employ 2D convolution (2D-Conv) neural networks to extract spatial features on either a single Gait Energy Image (GEI) or a collection of randomly arranged silhouette sets. For example, CNN-LB [39] introduced a CNN-based technique for gait feature learning from Gait Energy Images (GEI), while GaitSet [3] employed 2D convolution for feature extraction, assuming that the silhouette's appearance contained its positional information. However, these methods neglect temporal features which is the robust information in gait sequences. On the other hand, video-based techniques [10, 25, 26, 19] strive to acquire spatio-temporal features, which have been established as advantageous for enhancing gait recognition. For example, GaitGL [26] employed a 3D convolution (3D-Conv) neural network to extract spatio-temporal features. However, these methods use 3D-Conv to extract temporal features with a high amount of parameters. Different from these methods, we propose a more efficient solution named Cycle-Temporal Shit Convolution (CTS-Conv) that enables both low-level and high-level spatio-temporal features with a low computational cost. Further, we refined a global context modeling to extract robust motion patterns.
+
+# 3. Method
+
+In this section, we begin by introducing the overarching structure of fine-grained UDA framework in Sec. 3.1. Following that, we outline the offline clustering stage in Sec. 3.2, and subsequently detail the online training stage in Sec. 3.3. Finally, we present the joint loss in Sec. 3.4.
+
+# 3.1. Overview
+
+The UDA framework for gait recognition aims to transfer knowledge gained from labeled source domains to un
+
+![](images/09cb614533d99e535f6ecbbea692fc5837b8d29a9405e1f4a75424854c5f18cd.jpg)  
+Figure 3. The offline clustering stage in the proposed UDA framework. (a) Calculating the confidence scores using a  $k$ -nearest neighbor search algorithm. (b) Generating pseudo labels using a clustering algorithm in the global space. (c) Initializing the hybrid memory using class-level features. (d) Using the confidence scores to further optimize contrastive loss.
+
+labeled target domains, enabling accurate identification of individuals in unlabeled data. Following the previous UDA methods [50, 35, 4, 46, 21], as shown in Fig. 1 (b), we divide the training of the UDA framework into two stages, including the stage of offline clustering and online training.
+
+In the offline clustering stage, we first assign pseudolabels to unlabeled data. Then, we extract class-level central features from both source and target domains, which are used to initialize the hybrid memory module. Formally, Let  $\mathcal{D}_s = \{(x_s,y_s)|x_s\in \mathbb{R}^{N_S\times T\times H\times W},y_s\in \mathbb{R}^{N_S}\}$  and  $\mathcal{D}_t = \{x_t|x_t\in \mathbb{R}^{N_T\times T\times H\times W}\}$  denote the labeled and unlabeled data, where  $N_{S}$  and  $N_{T}$  are the numbers of sequences. The generation of pseudo-labels  $y_{t}$  can be expressed as
+
+$$
+y _ {t} = \mathcal {C} \left(\left\langle \mathcal {F} _ {\theta} \left(x _ {t}\right), \mathcal {F} _ {\theta} \left(x _ {t}\right) \right\rangle\right), \tag {1}
+$$
+
+where  $\mathcal{C}$  represents the clustering algorithm,  $\langle \cdot ,\cdot \rangle$  denotes the operation to measure the similarity between gait features space,  $\mathcal{F}_{\theta}$  is a learnable network parameterized by  $\theta$ . During the online training stage, the pseudo-labeled data can be sampled with the labeled data. The gait features  $(f_{s},f_{t})$  extraction can be expressed as
+
+$$
+\left(f _ {s}, f _ {t}\right) = \left(\mathcal {F} _ {\theta} \left(x _ {s}\right), \mathcal {F} _ {\theta} \left(x _ {t}\right)\right). \tag {2}
+$$
+
+To perform gait recognition on unlabeled sequences, TranND [45] utilizes a fine-tuning approach, which may lead to catastrophic forgetting of the knowledge learned in the source domain when trained on the target domain. In this paper, the proposed UDA framework is an end-to-end approach that utilizes alternating "offline clustering stage" and "online training stage" to simultaneously train the data in both source and target domains.
+
+# 3.2. Offline Clustering Stage
+
+This part provides a comprehensive overview of the offline clustering stage, which generates the pseudo-labels for unlabeled data and initializes the hybrid memory.
+
+Generating pseudo-labels. The offline clustering stage, as shown in Fig. 3, plays a crucial role in UDA tasks by generating pseudo-labels for unlabeled data. The effectiveness
+
+of the UDA algorithm relies on the distribution that features with the same label cluster densely in feature space, while those with different labels are scattered. However, one of the main challenges in the UDA framework is generating accurate pseudo-labels by effectively utilizing the relationships between the part-level features, given that features are comprised of multiple spatio-temporal motion patterns.
+
+To accurately distribute unlabeled data, we take into account the expressive capabilities of different body parts and calculate the confidence score for each part feature accordingly. Formally, let  $f_{t} \in \mathbb{R}^{N_{T} \times P \times C}$  denote the target domain part-level features, where  $P$  is the number of horizontally sliced parts, and  $C$  is the feature channels. Specifically, we perform the  $k$ -nearest neighbor search algorithm on both the global feature space and each part feature space to generate ranked lists  $\{\mathcal{R}_g, \mathcal{R}_1, \dots, \mathcal{R}_P\}$  for each unlabeled feature. The  $\mathcal{R}_g$  represents the sets of global feature indices for the top-  $k$  samples in the ranked list, while  $\mathcal{R}_p$  denotes the sets of  $p$ -th part feature indices. We then compute the confidence scores  $S_{p}$  between the global feature indices  $\mathcal{R}_g$  and the  $p$ -th part feature indices  $\mathcal{R}_p$  as follows,
+
+$$
+\mathcal {S} _ {p} = \frac {\left| \mathcal {R} _ {g} \cap \mathcal {R} _ {p} \right|}{\left| \mathcal {R} _ {g} \cup \mathcal {R} _ {p} \right|} \in [ 0, 1 ], \tag {3}
+$$
+
+where  $|\cdot|$  is a non-negative real number denoting the cardinality of a set. The confidence scores are further used to refine the part-based space to global feature space. We then use a clustering algorithm  $\mathcal{C}$  (e.g., DBSCAN [9]) to assign pseudo-labels on the global feature space, i.e.,
+
+$$
+y _ {t} = \mathcal {C} \left\{\mathcal {J} \left(\frac {1}{P} \sum_ {p = 1} ^ {P} \left[ \langle f _ {t} ^ {p}, f _ {t} ^ {p} \rangle * \frac {\mathcal {S} _ {p}}{\sum_ {p = 1} ^ {P} \mathcal {S} _ {p}} \right]\right) \right\}, \tag {4}
+$$
+
+where  $\mathcal{I}$  is the Jaccard distance [49] computed in global feature space and  $*$  denotes the Hadamard product.
+
+Initializing Hybrid Memory. To initialize the part-based hybrid memory, we utilize the class-level features of both source and target domains. It is worth illustrating that in the target domain, we only retain samples assigned with pseudo
+
+labels, and exclude those with discrete labels from the subsequent online training stage, i.e.,
+
+$$
+\left\{c _ {s}, c _ {t} \right\} = \left\{\frac {1}{| \mathcal {N} _ {s} |} \sum_ {f _ {s} \in \mathcal {N} _ {s}} f _ {s}, \frac {1}{| \mathcal {N} _ {t} |} \sum_ {f _ {t} \in \mathcal {N} _ {t}} f _ {t} \right\}, \tag {5}
+$$
+
+where  $\{c_s, c_t\}$  denotes the source and target domain class-level features,  $(\mathcal{N}_s, \mathcal{N}_t)$  is the same label set or cluster set.
+
+# 3.3. Online Training Stage
+
+This part provides a detailed explanation of the Cycle Temporal Shift Convolution (CTS-Conv) and Global Context Block. Then, we introduce the utilization of class-level momentum updating for the part-based hybrid memory.
+
+Cycle Temporal Shift Convolution. Gait recognition is a challenging task due to the impact of various external factors, including carrying conditions, wearing coats, and varying viewing angles, leading to a much higher intra-class variance than inter-class. Previous studies [25, 26] proposed to use 3D convolution (3D-Conv) neural network to capture temporal information in gait sequences and extract robust features. However, when applied to part-based UDA tasks, 3D-Conv is limited by its high computational cost and parameter-rich structure, increasing the risk of over-fitting. To address this, we propose a novel CTS-Conv, which separates temporal feature learning from spatial feature learning based on the well-designed temporal shift convolution (TS-Conv) [27]. In CTS-Conv, the input features are denoted as  $\Upsilon = \{v_{1}, v_{2}, \ldots, v_{E}\} \in \mathbb{R}^{C \times T \times H \times W}$ , where  $v_{i}$  represents the input features divided equally into  $E$  pieces, and  $T$  denotes the number of frames. As shown in Fig. 2, the CTS-Conv operation can be expressed as
+
+$$
+\overrightarrow {v} _ {1} ^ {t} = v _ {1} ^ {t - 1}, \overrightarrow {v} _ {1} ^ {0} = v _ {1} ^ {T}, \overleftarrow {v} _ {2} ^ {t} = v _ {2} ^ {t + 1}, \overleftarrow {v} _ {2} ^ {T} = v _ {2} ^ {0}, \tag {6}
+$$
+
+where  $\overrightarrow{v}_1$  and  $\overleftarrow{v}_2$  denote the first two pieces which are shifted to the right and left along the temporal dimension, respectively. The remaining pieces  $[v_3,v_4,\dots ,v_E]$  are unshifted. The CTS-Conv operation in STANet learns temporal features by exchanging the features of adjacent frames, without introducing any additional parameters.
+
+Global Context Block. After extracting the spatiotemporal features using the CTS-Conv, we further refine the global context modeling technique called global context (GC) block base on [1, 28]. The GC block employs multiple heads to map features during context modeling, thereby facilitating the comprehensive extraction of global motion patterns. To generate the output feature, a horizontal pooling method (HP) is first utilized, resulting in horizontally sliced features denoted as  $H = \{h^1, h^2, \dots, h^P\} \in \mathbb{R}^{P \times T \times C}$ , where  $P$  represents the number of horizontally sliced parts. Then, the global motion patterns  $g^p$  are derived
+
+Algorithm 1: The training process of UDA for Gait  
+Require: Labeled data  $\mathcal{D}_s$  and Unlabeled data  $\mathcal{D}_t$ ;  
+Require: Random initialize pipeline  $\mathcal{F}_{\theta}$ ;  
+Require:  $m$  for Eq. (9) and  $\tau$  of Eq. (10);  
+for  $i \leq N_e$  do  
+Offline Clustering Stage,  $N_e$  is the total iterations; Assign pseudo-label for  $\mathcal{D}_t$  with Eq. (4); Initialize the hybrid memory with Eq. (5);  
+for  $j \leq T_e$  do  
+Online Training Stage,  $T_e$  is the train iterations; Sample mini-batch data  $(x_s, x_t)$ ; Encoder part-based features  $(f_s, f_t)$ ; Compute the joint loss with Eq. (11); Update part-based hybrid memory with Eq. (9);  
+end  
+end
+
+using the subsequent expression:
+
+$$
+\tilde {g} ^ {p} = \frac {\exp \left(W _ {k} W _ {v 1} h _ {t} ^ {p}\right)}{\sum_ {t = 1} ^ {T} \exp \left(W _ {k} W _ {v 1} h _ {t} ^ {p}\right)} \otimes W _ {v 1} h ^ {p}, \tag {7}
+$$
+
+$$
+g ^ {p} = \delta \left(W _ {v 2} \tilde {g} ^ {p}\right) \oplus h ^ {p}, \tag {8}
+$$
+
+where  $\tilde{g}^p$  represents the context modeling,  $W_{k}$ ,  $W_{v1}$ , and  $W_{v2}$  are learnable parameters,  $\delta$  denotes the activation function,  $\otimes$  signifies matrix multiplication, and  $\oplus$  indicates the broadcast element-wise addition.
+
+Updating Hybrid Memory. Each mini-batch of the sampled data is passed through a pipeline that extracts part-based features  $(f_s, f_t)$ . It is worth noting that our proposed UDA framework is highly versatile and can be readily applied to other network architectures [3, 26], as illustrated in Fig. 2, where STANet can be replaced by any of the existing popular networks. At each iteration, the extracted features in each mini-batch would be involved in part-based hybrid memory momentum updating, i.e.,
+
+$$
+\left\{ \begin{array}{l} c _ {s} \leftarrow m \cdot f _ {s} + (1 - m) \cdot \frac {1}{| \mathcal {B} _ {s} |} \sum_ {f _ {s} \in \mathcal {B} _ {s}} f _ {s} \\ c _ {t} \leftarrow m \cdot f _ {t} + (1 - m) \cdot \frac {1}{| \mathcal {B} _ {t} |} \sum_ {f _ {t} \in \mathcal {B} _ {t}} f _ {t} \end{array} \right\}, \tag {9}
+$$
+
+where  $(c_s, c_t)$  denotes the class-level features,  $(\mathcal{B}_s, \mathcal{B}_t)$  represents the set of features belonging to the source or target domain class and  $m \in [0,1]$  is a momentum coefficient.
+
+# 3.4. Joint Loss Function
+
+In this work, three types of part-based loss functions are employed, namely, the triplet loss  $\mathcal{L}_{tp}$ , the cross-entropy loss  $\mathcal{L}_{ce}$ , and the contrastive loss  $\mathcal{L}_{cl}$ . These loss functions are used to constrain the features of each part individually. As shown in Fig. 2, the output features  $(o_s,o_t)$  are used to calculate  $\mathcal{L}_{tp}$ , while the normalized output features  $(f_s,f_t)$  are used to calculate  $\mathcal{L}_{ce}$  and  $\mathcal{L}_{cl}$ . Additionally, we consider the varying expressiveness of different body parts and
+
+Table 1. The Rank-1 (\%) performance comparison of fully supervised and unsupervised domain adaptation methods on CASIA-B. Where “OUMVLP→CASIA-B” denotes the use of OUMVLP as the source domain and CASIA-B as the target domain.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Method</td><td colspan="11">Probe View</td><td rowspan="2">Mean</td></tr><tr><td>0°</td><td>18°</td><td>36°</td><td>54°</td><td>72°</td><td>90°</td><td>108°</td><td>126°</td><td>134°</td><td>162°</td><td>180°</td></tr><tr><td colspan="14">Fully supervised methods with all labels on CASIA-B</td></tr><tr><td rowspan="4">NM</td><td>CNN-LB [39]</td><td>82.6</td><td>90.3</td><td>96.1</td><td>94.3</td><td>90.1</td><td>87.4</td><td>89.9</td><td>94.0</td><td>94.7</td><td>91.3</td><td>78.5</td><td>89.9</td></tr><tr><td>GaitSet [3]</td><td>90.8</td><td>97.9</td><td>99.4</td><td>96.9</td><td>93.6</td><td>91.7</td><td>95.0</td><td>97.8</td><td>98.9</td><td>96.8</td><td>85.8</td><td>95.0</td></tr><tr><td>GaitGL [26]</td><td>96.0</td><td>98.3</td><td>99.0</td><td>97.9</td><td>96.9</td><td>95.4</td><td>97.0</td><td>98.9</td><td>99.3</td><td>98.8</td><td>94.0</td><td>97.4</td></tr><tr><td>STANet(ours)</td><td>96.4</td><td>99.4</td><td>99.3</td><td>98.9</td><td>97.0</td><td>95.8</td><td>98.2</td><td>99.2</td><td>99.6</td><td>99.2</td><td>96.0</td><td>98.1</td></tr><tr><td rowspan="4">BG</td><td>CNN-LB [39]</td><td>64.2</td><td>80.6</td><td>82.7</td><td>76.9</td><td>64.8</td><td>63.1</td><td>68.0</td><td>76.9</td><td>82.2</td><td>75.4</td><td>61.3</td><td>72.4</td></tr><tr><td>GaitSet [3]</td><td>83.8</td><td>91.2</td><td>91.8</td><td>88.8</td><td>83.3</td><td>81.0</td><td>84.1</td><td>90.0</td><td>92.2</td><td>94.4</td><td>79.0</td><td>87.2</td></tr><tr><td>GaitGL [26]</td><td>92.6</td><td>96.6</td><td>96.8</td><td>95.5</td><td>93.5</td><td>89.3</td><td>92.2</td><td>96.5</td><td>98.2</td><td>96.9</td><td>91.5</td><td>94.5</td></tr><tr><td>STANet(ours)</td><td>94.4</td><td>98.2</td><td>98.9</td><td>97.5</td><td>94.1</td><td>91.2</td><td>93.9</td><td>97.4</td><td>98.5</td><td>97.8</td><td>94.0</td><td>96.0</td></tr><tr><td rowspan="4">CL</td><td>CNN-LB [39]</td><td>37.7</td><td>57.2</td><td>66.6</td><td>61.1</td><td>55.2</td><td>54.6</td><td>55.2</td><td>59.1</td><td>58.9</td><td>48.8</td><td>39.4</td><td>54.0</td></tr><tr><td>GaitSet [3]</td><td>61.4</td><td>75.4</td><td>80.7</td><td>77.3</td><td>72.1</td><td>70.1</td><td>71.5</td><td>73.5</td><td>73.5</td><td>68.4</td><td>50.0</td><td>70.4</td></tr><tr><td>GaitGL [26]</td><td>76.6</td><td>90.0</td><td>90.3</td><td>87.1</td><td>84.5</td><td>79.0</td><td>84.1</td><td>87.0</td><td>87.3</td><td>84.4</td><td>69.5</td><td>83.6</td></tr><tr><td>STANet(ours)</td><td>83.4</td><td>94.6</td><td>96.8</td><td>93.9</td><td>89.6</td><td>86.0</td><td>88.2</td><td>92.1</td><td>93.9</td><td>90.2</td><td>78.1</td><td>89.7</td></tr><tr><td colspan="14">Unsupervised Domain Adaptation methods without any labels on CASIA-B (OUMVLP→CASIA-B)</td></tr><tr><td rowspan="4">NM</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>63.4</td></tr><tr><td>UDA(GaitSet)</td><td>84.7</td><td>95.8</td><td>97.2</td><td>95.8</td><td>95.1</td><td>92.9</td><td>94.8</td><td>96.1</td><td>97.3</td><td>96.6</td><td>79.2</td><td>93.2</td></tr><tr><td>UDA(GaitGL)</td><td>76.7</td><td>88.3</td><td>88.8</td><td>87.1</td><td>88.4</td><td>82.9</td><td>85.9</td><td>90.6</td><td>93.1</td><td>93.9</td><td>73.0</td><td>86.2</td></tr><tr><td>UDA(STANet)</td><td>84.3</td><td>95.2</td><td>95.5</td><td>91.1</td><td>90.7</td><td>85.9</td><td>89.4</td><td>93.3</td><td>94.9</td><td>93.7</td><td>82.4</td><td>90.6</td></tr><tr><td rowspan="4">BG</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>42.7</td></tr><tr><td>UDA(GaitSet)</td><td>77.5</td><td>87.5</td><td>90.0</td><td>89.2</td><td>86.2</td><td>81.2</td><td>87.1</td><td>89.9</td><td>94.0</td><td>91.1</td><td>70.9</td><td>85.9</td></tr><tr><td>UDA(GaitGL)</td><td>69.1</td><td>85.3</td><td>84.7</td><td>83.6</td><td>82.9</td><td>76.1</td><td>79.9</td><td>86.8</td><td>89.1</td><td>88.0</td><td>63.6</td><td>80.8</td></tr><tr><td>UDA(STANet)</td><td>75.4</td><td>88.7</td><td>86.6</td><td>83.6</td><td>82.9</td><td>76.2</td><td>82.6</td><td>86.9</td><td>89.3</td><td>87.5</td><td>73.7</td><td>83.0</td></tr><tr><td rowspan="4">CL</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>15.8</td></tr><tr><td>UDA(GaitSet)</td><td>24.2</td><td>38.9</td><td>42.3</td><td>39.6</td><td>41.1</td><td>38.1</td><td>37.9</td><td>43.3</td><td>43.4</td><td>29.6</td><td>25.4</td><td>36.7</td></tr><tr><td>UDA(GaitGL)</td><td>43.9</td><td>65.3</td><td>66.5</td><td>66.9</td><td>68.8</td><td>60.0</td><td>66.4</td><td>71.2</td><td>69.3</td><td>61.8</td><td>42.2</td><td>62.0</td></tr><tr><td>UDA(STANet)</td><td>54.0</td><td>73.2</td><td>75.7</td><td>72.0</td><td>71.4</td><td>64.4</td><td>70.1</td><td>74.6</td><td>73.7</td><td>69.2</td><td>51.4</td><td>68.2</td></tr></table>
+
+use the confidence scores to accurately constrain the features by constraining the contrastive loss for each part. The contrastive loss  $\mathcal{L}_{cl}$  can be formulated as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {c l} = - \sum_ {p = 1} ^ {P} \frac {\mathcal {S} _ {p}}{N _ {c s}} \left\{- \log \frac {\exp \left(f ^ {p} \cdot c _ {s} ^ {p , +} / \tau\right)}{\sum_ {k = 1} ^ {| \mathcal {N} _ {s} |} \exp \left(f ^ {p} \cdot c _ {s} ^ {p , k} / \tau\right)} \right\} \tag {10} \\ - \sum_ {p = 1} ^ {P} \frac {\mathcal {S} _ {p}}{N _ {c t}} \left\{- \log \frac {\exp (f ^ {p} \cdot c _ {t} ^ {p , +} / \tau)}{\sum_ {k = 1} ^ {| \mathcal {N} _ {t} |} \exp (f ^ {p} \cdot c _ {t} ^ {p , k} / \tau)} \right\}, \\ \end{array}
+$$
+
+where  $N_{cs}, N_{ct}$  is a positive integer obtained by multiplying the mini-batch with parts,  $\tau$  is a hyper-parameter,  $c_s, c_t$  denote the class-level features of source and target domains, and  $c_s^{p, + }, c_t^{p, + }$  indicate the positive class prototype corresponding to  $f^p$ . The combined loss  $\mathcal{L}_c$  can be expressed as
+
+$$
+\mathcal {L} _ {c} = \mathcal {L} _ {t p} + \alpha \mathcal {L} _ {c e} + \beta \mathcal {L} _ {c l}, \tag {11}
+$$
+
+where  $\alpha$  and  $\beta$  are the hyper-parameters to balance the combined loss and are empirically set to 0.3.
+
+# 4. Experiments
+
+In this section, we evaluate the proposed method on three large-scale gait recognition benchmarks, including two widely adopted datasets (i.e., CASIA-B and OUMVLP) and one real-world dataset (i.e., GREW). Then, we compare our method to state-of-the-art methods. Finally, comprehensive ablation studies are conducted to substantiate the effectiveness of our proposed method.
+
+# 4.1. Datasets and Implementation Details
+
+CASIA-B [41] is a well-established dataset widely used in the field of gait recognition research. It comprises 124 subjects and encompasses 3 distinct walking conditions: normal walking (NM), walking while wearing a coat (CL), and walking with bags (BG). The dataset is captured by 11 cameras positioned uniformly between  $0^{\circ}$  and  $180^{\circ}$ , providing a diverse range of viewpoints. Each subject has a total of 110 sequences. The first 74 subjects are used for training, while the remaining 50 subjects are reserved for testing. During
+
+Table 2. Rank-1 accuracy of fully supervised and unsupervised domain adaptation methods on OUMVLP under all view angles. Where "CASIA-B→OUMVLP" represents the use of CASIA-B as the labeled source domain and OUMVLP as the unlabeled target domain.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="14">Probe View</td><td rowspan="2">Mean</td></tr><tr><td>0°</td><td>15°</td><td>30°</td><td>45°</td><td>60°</td><td>75°</td><td>90°</td><td>180°</td><td>195°</td><td>210°</td><td>225°</td><td>240°</td><td>255°</td><td>270°</td></tr><tr><td colspan="16">Fully supervised methods with all labels on OUMVLP</td></tr><tr><td>GaitSet [3]</td><td>79.5</td><td>87.9</td><td>89.9</td><td>90.2</td><td>88.1</td><td>88.7</td><td>87.8</td><td>81.7</td><td>86.7</td><td>89.0</td><td>89.3</td><td>87.2</td><td>87.8</td><td>86.2</td><td>87.1</td></tr><tr><td>GaitGL [26]</td><td>84.9</td><td>90.2</td><td>91.1</td><td>91.5</td><td>91.1</td><td>90.8</td><td>90.3</td><td>88.5</td><td>88.6</td><td>90.3</td><td>90.4</td><td>89.6</td><td>89.5</td><td>88.8</td><td>89.7</td></tr><tr><td>STANet(ours)</td><td>87.7</td><td>91.4</td><td>91.6</td><td>91.9</td><td>91.6</td><td>91.4</td><td>91.2</td><td>90.4</td><td>90.3</td><td>90.8</td><td>91.0</td><td>90.5</td><td>90.3</td><td>90.1</td><td>90.7</td></tr><tr><td colspan="16">Unsupervised Domain Adaptation methods without any labels on OUMVLP (CASIA-B→OUMVLP)</td></tr><tr><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>75.6</td></tr><tr><td>UDA(GaitSet)</td><td>45.6</td><td>60.1</td><td>75.3</td><td>80.7</td><td>75.5</td><td>73.9</td><td>73.9</td><td>49.9</td><td>59.9</td><td>75.5</td><td>81.7</td><td>74.9</td><td>73.2</td><td>72.9</td><td>69.5</td></tr><tr><td>UDA(GaitGL)</td><td>23.6</td><td>50.5</td><td>79.5</td><td>78.5</td><td>75.3</td><td>74.6</td><td>74.5</td><td>28.7</td><td>50.9</td><td>77.5</td><td>77.5</td><td>74.3</td><td>73.3</td><td>73.0</td><td>65.1</td></tr><tr><td>UDA(STANet)</td><td>42.8</td><td>85.1</td><td>92.1</td><td>91.2</td><td>88.9</td><td>89.2</td><td>89.5</td><td>50.4</td><td>86.6</td><td>90.8</td><td>90.1</td><td>88.0</td><td>87.9</td><td>88.0</td><td>82.9</td></tr></table>
+
+testing, the first four "NM" conditions are utilized as the gallery, while the remaining conditions serve as the probe.
+
+OUMVLP [32] is a prominent public gait dataset that comprises 10,307 subjects, two distinct walking sequences (labeled as “00” and “01”), and 14 cameras positioned uniformly between  $(0^{\circ} \rightarrow 90^{\circ})$  and  $(180^{\circ} \rightarrow 270^{\circ})$ . To ensure fair data volume in comparison to CASIA-B, we select the first 1,000 subjects from OUMVLP for our UDA experiments without any specific instructions. In the UDA experiment, we followed the official data split and used 500 individuals for training and the remaining 500 for testing. During the test phase, the “00” sequences serve as the probe, while the remaining “01” sequences serve as the gallery.
+
+GREW [48] is a comprehensive and extensive dataset designed for gait recognition, encompassing silhouettes and 2D/3D human body pose. In contrast to CASIA-B and OUMVLP, GREW was collected in diverse and complex scenes in the wild, making it a more challenging task for gait recognition. The GREW dataset comprises 26345 subjects, 128671 sequences, and 882 camera viewpoints. To ensure fairness in data volume with respect to CASIA-B, we use the first 4000 subjects from GREW for UDA experiments without any special instructions. During testing, we make full use of the official query and gallery set.
+
+Implementation Details. The training process of UDA is shown in Algorithm 1, and all datasets are uniformly resized to  $64 \times 44$  [3]. The model is trained end-to-end using the SGD optimizer, starting with an initial learning rate of 0.1, which is then decreased by a factor of 10 iteratively until convergence. The training mini-batch size for CASIA-B and OUMVLP is set to (8, 16), while for GREW dataset, it is set to (4, 32). Data augmentation techniques are utilized to preserve both the original and augmented data in real-world datasets. The convolutional channels in the STANet are set to (64, 128, 256). The network is trained for a total of  $N_{e} = 100\mathrm{K}$  iterations, and offline clustering is performed every  $T_{e} = 5\mathrm{K}$  iteration to assign pseudo-labels to unlabeled data and reinitialize the hybrid memory dictionary.
+
+# 4.2. Comparison with State-of-the-art Methods
+
+To evaluate the effectiveness of the proposed approach, we compared it with both existing fully supervised methods [39, 3, 26] and Unsupervised Domain Adaptation (UDA) method [45] for gait recognition.
+
+Evaluation on CASIA-B. The performance of both fully supervised [39, 3, 26] and UDA methods [45] on CASIA-B is presented in Tab. 1. (1) The proposed STANet algorithm outperforms the fully supervised algorithm [39, 3, 26], especially in the cross-dressing condition. Experimental results show that our method has the ability to learn more robust motion patterns compared to others. (2) The proposed UDA framework outperforms the existing UDA algorithm [45] under all conditions. The experimental results demonstrate that our UDA framework can effectively utilize fine-grained part-based features to generate pseudo-labels that supervise network learning, leading to a significant improvement in recognition accuracy. (3) We conducted experiments by substituting STANet with various state-of-the-art algorithms, such as GaitSet [3] and GaitGL [26]. In the UDA framework, the GaitSet method outperforms other methods in "NM" and "BG" but has lower performance in "CL". The experimental results demonstrate that GaitSet emphasizes learning cross-view information from the OUMVLP but struggles to capture robust motion patterns.
+
+Evaluation on OUMVLP. To provide additional evidence of the effectiveness of our proposed method, we evaluated the proposed approach with some state-of-the-art fully supervised [3, 26] and UDA [45] methods on OUMVLP. (1) The proposed STANet outperforms other methods, including GaitSet [3] and GaitGL [26], under both the whole dataset and fully supervised conditions. Our experimental results demonstrate the critical importance of effectively utilizing fine-grained spatio-temporal motion patterns for achieving high performance on large-scale gait datasets. (2) Our proposed UDA framework outperforms the existing UDA algorithm [45]. The experimental results demon
+
+strate that our framework can effectively transfer the norm walking information from CASIA-B to OUMVLP. (3) We conducted experiments to compare STANet with other algorithms, including GaitSet [3] and GaitGL [26]. The results showed that the proposed STANet in the UDA framework effectively utilized fine-grained part-based features, even in the presence of cross-dressing influence in CASIA-B.
+
+Evaluation on GREW. We evaluated the proposed method on a wild dataset, i.e., GREW, to provide additional evidence for the effectiveness of our method. (1) The experimental results presented in Tab. 3 demonstrate the effectiveness of the fine-grained motion patterns extracted by our method on real datasets. (2) The UDA experimental results confirm that knowledge gained from accurately labeled data in a laboratory setting can be transferred to real-world scenarios. This validation also confirms the efficacy of our proposed approach in extracting fine-grained motion patterns.
+
+# 4.3. Ablation Study
+
+In this section, an ablation study is performed on the proposed UDA framework to improve the understanding of the effects of different configurations.
+
+The effectiveness of STANet. To comprehensively evaluate the impact of STANet in the UDA framework, we conducted a thorough comparative experiment in Tab. 4. Specifically, (1) The "w/o CTS-Conv" represents replacing the CTS-Conv with 2D convolution. The experiment demonstrates a decrease in the performance of the "CL", thereby confirming the ability of CTS-Conv to acquire resilient temporal features in the UDA framework. (2) Furthermore, we conducted additional experiments to remove the GC block, denoted as "w/o GC block", in which the GC block was replaced with Max Pooling along the temporal dimension. The experiment results showed that STANet exhibited performance comparable to that of GaitGL [26].
+
+The effectiveness of confidence scores. To explore the impact of confidence scores on the offline clustering stage, we completely remove the process of generating confidence scores and generate the global feature space directly averaged over the part-based feature space. The experimental results "w/o Confidence scores" from the Tab. 4 show that removing the confidence score decreased the performance.
+
+Analysis of the number of spatial slices parts. We conducted an in-depth analysis to assess the influence of different spatial bin numbers of the UDA framework in Tab. 4. (1) The experimental results indicate that the performance improves as the number of  $N_{\text{part}}$  increases. (2) In the field of gait recognition, many popular approaches [10, 26] have confirmed that the number of parts has a significant impact on the recognition results. Specifically, increasing the number of parts requires the network to focus more on fine-grained parts. Experimental results show that  $N_{\text{part}}$  also has a significant impact on unlabeled feature learning.
+
+Table 3. Rank-1  $(\%)$  performance comparison of fully supervised and unsupervised domain adaptation methods on GREW.  
+
+<table><tr><td>Method</td><td>Source</td><td>Rank-1 (%)</td></tr><tr><td colspan="3">Fully supervised methods on GREW</td></tr><tr><td>CNN-LB [39]</td><td>TPAMI 2017</td><td>12.2</td></tr><tr><td>GaitSet [3]</td><td>AAAI 2019</td><td>33.5</td></tr><tr><td>GaitGL [26]</td><td>ICCV 2021</td><td>32.7</td></tr><tr><td>STANet(ours)</td><td>-</td><td>41.3</td></tr><tr><td colspan="3">UDA methods without any labels (OUMVLP→GREW)</td></tr><tr><td>UDA(Gaitset)</td><td>-</td><td>15.3</td></tr><tr><td>UDA(GaitGL)</td><td>-</td><td>13.7</td></tr><tr><td>UDA(STANet)</td><td>-</td><td>26.2</td></tr></table>
+
+Table 4. The ablation study on CASIA-B with rank-1 accuracy.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">OUMVLP→CASIA-B</td></tr><tr><td>NM</td><td>BG</td><td>CL</td><td>Mean</td></tr><tr><td colspan="5">Analysis of the UDA framework</td></tr><tr><td>Baseline</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr><tr><td>- w/o CTS-Conv</td><td>91.7</td><td>84.7</td><td>62.5</td><td>79.6</td></tr><tr><td>- w/o GC block</td><td>86.3</td><td>79.9</td><td>62.3</td><td>76.1</td></tr><tr><td>- w/o Confidence scores</td><td>88.6</td><td>81.3</td><td>66.8</td><td>78.9</td></tr><tr><td colspan="5">Analysis of the number spatial bins Npart</td></tr><tr><td>Npart = 2</td><td>85.2</td><td>72.3</td><td>25.7</td><td>61.1</td></tr><tr><td>Npart = 4</td><td>83.5</td><td>76.2</td><td>51.3</td><td>70.3</td></tr><tr><td>Npart = 8</td><td>84.7</td><td>76.4</td><td>54.8</td><td>72.0</td></tr><tr><td>Npart = 16</td><td>84.2</td><td>77.1</td><td>59.4</td><td>73.6</td></tr><tr><td>Npart = 32</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr></table>
+
+# 5. Conclusion
+
+In this paper, we present a novel part-based Unsupervised Domain Adaptation (UDA) framework for gait recognition. Our framework consists of an offline clustering stage and an online training stage, which facilitate the knowledge transformation from a labeled source domain to an unlabeled target domain. Our method enhances the reliability of spatio-temporal features and extracts robust gait features for further knowledge transfer. We evaluate the proposed method on three popular gait datasets: CASIA-B, OUMVLP, and GREW, and our experimental results demonstrate the effectiveness of the UDA framework and its potential for practical applications. In future work, we plan to conduct more extensive investigations of UDA methods for gait recognition to accelerate network training and improve the accuracy of pseudo-labels.
+
+# 6. Acknowledgement
+
+This work was supported by the National Key R&D Program of China (2022YFC3300700), the National Natural Science Foundation of China (62171038, 62088101, 62276031 and 62276025), and the Fundamental Research Funds for the Central Universities.
+
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\ No newline at end of file
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+                                    "content": "1. Introduction"
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+                                    "content": "Gait recognition, a biometric technology [37, 41, 15] that identifies individuals based on their unique walking patterns, has gained significant attention for its ability to recog"
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+                                            "content": "(b) The Fine-grained UDA Framework"
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+                                            "content": "Figure 1. (a) The prior knowledge of the existence of angle overlap between adjacent-view. (b) The proposed Fine-grained Unsupervised Domain Adaptation (UDA) framework for gait recognition."
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+                                    "content": "nize people at long distances, regardless of their attire. The applications [6, 31, 12] of gait recognition have been greatly facilitated by advances in deep learning and the availability of vast amounts of labeled data. However, accurately annotating large amounts of data remains a daunting challenge, especially under long-distance cameras, where critical information such as the human face is often blurred, making it difficult to label gait sequences of the same person in different clothing, views, and carrying conditions. As a solution, we propose a fine-grained Unsupervised Domain Adaptation (UDA) framework that transfers knowledge from a labeled source domain to an unlabeled target domain."
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+                                    "content": "In the gait recognition task, an essential prior knowledge is the existence of overlapping angles in adjacent-view sequences as shown in Fig. 1 (a), which enables networks to build cross-view capabilities through a chain-like approach. Leveraging this premise, the UDA framework for gait recognition can gradually learn cross-dressing capabilities in the target domain through knowledge transfer and clustering, without the need for pre-training the network. We aim to reveal it by addressing the following aspects:"
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+                                    "content": "(i) Offline clustering stage. In the offline clustering phase,"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "type": "text",
+                                    "content": "as shown in Fig. 1, the primary goal is to assign accurate pseudo-labels to unlabeled data by leveraging cross-view chaining relationships. To achieve this, the network extracts essential insights for gait from a labeled source domain and subsequently transfers this acquired knowledge to the unlabeled target domain. Following this knowledge transfer, the precise pseudo-label is assigned to the cross-view and cross-dressing data present within the target domain. This assignment hinges on the observed global feature space distribution within the aforementioned target domain. Furthermore, previous methods [3, 10, 16, 25, 19, 28] demonstrate that part-based methods outperform other approaches. To this end, we leverage the varied expressive capabilities of different body parts and adaptively generate a global feature space, which results in a more accurate assignment of pseudo-labels to unlabeled data."
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+                                    "content": "(ii) Online training stage. During the online training stage, the core objective is to continually learn the gait features in both the source and target domains. As depicted in Fig. 1 (a), the angles of the sequences vary continuously during human walking, with identical angles and actions appearing in sequences from adjacent viewpoints (indicated by the blue and red arrows). Consequently, the network can establish associations of neighboring perspectives by focusing on temporal features and gain cross-view capabilities through the association of all perspectives. Moreover, as shown in Fig. 1 (b), the network is trained by continuously selecting features from the unlabelled target domain that have been assigned the same pseudo-label as the training set. By continually adding data to the target domain in this way, the network focuses on more robust motion patterns to distinguish features from different domains. Prior methods [25, 26, 28] have demonstrated the criticality of motion pattern extraction in cross-dressing recognition. Consequently, the network gradually develops the cross-dressing capability, even in cases where it is absent from the source domain data."
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+                                    "content": "Driven by this analysis, we propose a simple yet effective fine-grained UDA framework, wherein knowledge learned from the labeled source domain is transferred to obtain pseudo-labels for the unlabeled target domain. Subsequently, we utilize both labeled source and target domain data to extract fine-grained spatio-temporal motion patterns. As illustrated in Fig. 3, the offline clustering stage calculates the confidence scores for each part-based feature. These confidence scores are employed to derive the global feature space and assign pseudo-labels for unlabeled data. And the hybrid memory is initialized based on these pseudolabels. Additionally, information scores are utilized to supervise the hybrid memory and facilitate the computation of the part-based contrastive loss. Furthermore, the online training stage is shown in Fig. 2, we propose a novel Spatio-Temporal Aggregation Network (STANet) for learning global motion patterns, which contains spatial designed"
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+                                    "content": "Cycle Temporal Shift convolution (CTS-Conv) and Global context block. At each iteration, the hybrid memory is dynamically updated using the global motion patterns."
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+                                    "content": "Our contributions can be summarized in three aspects."
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+                                            "content": "- We propose a unified UDA framework structure based on the prior knowledge of the existence of an overlap between adjacent-view sequences, which enables our network to gradually acquire cross-view and cross-dressing capabilities without pre-training."
+                                        }
+                                    ]
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+                                            "type": "text",
+                                            "content": "- We present an innovative STANet that effectively captures fine-grained motion patterns while enabling the acquisition of cross-view and cross-dressing capabilities. Our approach demonstrates superior performance than current state-of-the-art methods, particularly under the cross-dressing condition."
+                                        }
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+                                            "type": "text",
+                                            "content": "- The effectiveness of the proposed UDA framework is demonstrated through experimental results, which show superior performance on the CASIA-B [41], OUMVLP [32], and GREW [48] datasets. Moreover, comprehensive ablation experiments performed on the CASIA-B dataset further corroborate the efficacy of the proposed method within the UDA framework."
+                                        }
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+                                    "content": "2. Related Work"
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+                                    "content": "In this section, we review the most relevant research in the area of unsupervised domain adaptation, part-based approaches, and spatial-temporal modeling."
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+                                    "content": "2.1. Unsupervised Domain Adaptation Approaches"
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+                                    "content": "The Unsupervised Domain Adaptation (UDA) methods [30, 11, 44, 42, 14, 40, 8, 13, 7] for person re-identification (re-ID) have made significant progress. Advanced UDA methods for re-ID tasks often employ clustering algorithms, such as K-means [47], DBSCAN [9, 18], and InfoMAP [5], to generate pseudo-labels for unlabeled data from global features. For instance, MMT [13] used mutual mean-teaching to softly refine the pseudo labels in the target domain, AD-Cluster [42] incorporated style-translated images using a novel discriminative clustering method, and SpCL [14] employed a self-paced approach to create more reliable clusters gradually and refine the hybrid memory and the targets. Despite significant progress in recent years, adapting these methods for gait recognition tasks remains challenging due to inherent differences between gait and re-ID data. Specifically, re-ID data typically contains informative features such as texture and color, which enable the association of individuals without explicit labels. In contrast, the silhouette sequence in gait lacks such information, which poses a significant challenge for unsupervised tasks. Recent pioneering UDA methods for gait recognition [36, 45]"
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+                                            "content": "Figure 2. The overview of the online training stage in the proposed UDA framework, where \"HP\" represent the Horizontal Pooling, and \"GC\" represents the Global Context block. (a) The fine-grained motion patterns are extracted by Spatio-Temporal Aggregation Network (STANet). (b) The hybrid memory is used to supervise the training data and dynamically updated based on these features. (c) The features extracted by GC are used to calculate triplet loss, and the normalized features are used to calculate cross-entropy and contrastive losses."
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+                                    "content": "have made some achievements on unlabeled datasets. However, these methods do not sufficiently consider the relationship between source and target domains, which ultimately restricts their performance and practical applications. As a solution, we propose a novel UDA framework that transfers valuable knowledge from a labeled source domain to an unlabeled target domain. By leveraging UDA, gait can be applied in more challenging real-world situations."
+                                }
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+                                    "content": "2.2. Part-based Approaches"
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+                                    "content": "The extraction of fine-grained features of body parts in gait recognition is a critical insight that plays a pivotal role to distinguish different individuals. Extensive research [3, 10, 16, 26, 19] has emphasized the significance of horizontally dividing these features into distinct parts. For example, GaitSet [3] introduced the Horizontal Pyramid Mapping (HPM) module, which partitions gait features into 62 strips along the height dimension. Since then, most gait recognition algorithms [16, 17, 25, 2] have adopted a part-based approach, training features with distinct parts separately. GaitPart [10] divided gait features horizontally into 16 strips, while GaitGL [26] separated global and local features into 32 strips, respectively. 3DLocal [19] proposed a localization module to learn the adaptive spatial and temporal scales. Therefore, gait recognition relies on the representation of multiple motion patterns with critical parts. However, the clustering algorithms typically assign pseudolabels based on the global feature. To this end, we develop a fine-grained UDA framework for gait recognition that leverages the part-based features. Specifically, we evaluate the expressiveness of different parts to calculate confidence scores and then adaptively obtain the pseudo-labels."
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+                                    "content": "2.3. Spatio-temporal Modeling"
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+                                    "content": "Gait recognition approaches can be broadly categorized into two primary domains: model-based [20, 34, 23, 24, 22] and appearance-based [39, 15, 29, 33, 34]. The appearance-"
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+                                    "content": "based approaches have become the mainstream for gait recognition, which can be broadly classified into two categories, including silhouette-based methods [43, 3, 16, 10, 17] and video-based methods [25, 26, 2, 19, 38]. The silhouette-based methods generally employ 2D convolution (2D-Conv) neural networks to extract spatial features on either a single Gait Energy Image (GEI) or a collection of randomly arranged silhouette sets. For example, CNN-LB [39] introduced a CNN-based technique for gait feature learning from Gait Energy Images (GEI), while GaitSet [3] employed 2D convolution for feature extraction, assuming that the silhouette's appearance contained its positional information. However, these methods neglect temporal features which is the robust information in gait sequences. On the other hand, video-based techniques [10, 25, 26, 19] strive to acquire spatio-temporal features, which have been established as advantageous for enhancing gait recognition. For example, GaitGL [26] employed a 3D convolution (3D-Conv) neural network to extract spatio-temporal features. However, these methods use 3D-Conv to extract temporal features with a high amount of parameters. Different from these methods, we propose a more efficient solution named Cycle-Temporal Shit Convolution (CTS-Conv) that enables both low-level and high-level spatio-temporal features with a low computational cost. Further, we refined a global context modeling to extract robust motion patterns."
+                                }
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+                                    "content": "3. Method"
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+                                    "content": "In this section, we begin by introducing the overarching structure of fine-grained UDA framework in Sec. 3.1. Following that, we outline the offline clustering stage in Sec. 3.2, and subsequently detail the online training stage in Sec. 3.3. Finally, we present the joint loss in Sec. 3.4."
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+                                    "content": "3.1. Overview"
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+                                    "content": "The UDA framework for gait recognition aims to transfer knowledge gained from labeled source domains to un"
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+                                            "content": "Figure 3. The offline clustering stage in the proposed UDA framework. (a) Calculating the confidence scores using a "
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+                                            "content": "-nearest neighbor search algorithm. (b) Generating pseudo labels using a clustering algorithm in the global space. (c) Initializing the hybrid memory using class-level features. (d) Using the confidence scores to further optimize contrastive loss."
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+                                    "content": "labeled target domains, enabling accurate identification of individuals in unlabeled data. Following the previous UDA methods [50, 35, 4, 46, 21], as shown in Fig. 1 (b), we divide the training of the UDA framework into two stages, including the stage of offline clustering and online training."
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+                                    "content": "In the offline clustering stage, we first assign pseudolabels to unlabeled data. Then, we extract class-level central features from both source and target domains, which are used to initialize the hybrid memory module. Formally, Let "
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+                                    "content": "\\mathcal{D}_s = \\{(x_s,y_s)|x_s\\in \\mathbb{R}^{N_S\\times T\\times H\\times W},y_s\\in \\mathbb{R}^{N_S}\\}"
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+                                    "content": " denote the labeled and unlabeled data, where "
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+                                    "type": "text",
+                                    "content": " are the numbers of sequences. The generation of pseudo-labels "
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+                                    "content": " can be expressed as"
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+                                    "content": "y _ {t} = \\mathcal {C} \\left(\\left\\langle \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right), \\mathcal {F} _ {\\theta} \\left(x _ {t}\\right) \\right\\rangle\\right), \\tag {1}",
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+                                    "content": " denotes the operation to measure the similarity between gait features space, "
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+                                    "type": "text",
+                                    "content": ". During the online training stage, the pseudo-labeled data can be sampled with the labeled data. The gait features "
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+                                    "type": "text",
+                                    "content": "To perform gait recognition on unlabeled sequences, TranND [45] utilizes a fine-tuning approach, which may lead to catastrophic forgetting of the knowledge learned in the source domain when trained on the target domain. In this paper, the proposed UDA framework is an end-to-end approach that utilizes alternating \"offline clustering stage\" and \"online training stage\" to simultaneously train the data in both source and target domains."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "3.2. Offline Clustering Stage"
+                                }
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+                },
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+                                    "content": "This part provides a comprehensive overview of the offline clustering stage, which generates the pseudo-labels for unlabeled data and initializes the hybrid memory."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Generating pseudo-labels. The offline clustering stage, as shown in Fig. 3, plays a crucial role in UDA tasks by generating pseudo-labels for unlabeled data. The effectiveness"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "of the UDA algorithm relies on the distribution that features with the same label cluster densely in feature space, while those with different labels are scattered. However, one of the main challenges in the UDA framework is generating accurate pseudo-labels by effectively utilizing the relationships between the part-level features, given that features are comprised of multiple spatio-temporal motion patterns."
+                                }
+                            ]
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+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "To accurately distribute unlabeled data, we take into account the expressive capabilities of different body parts and calculate the confidence score for each part feature accordingly. Formally, let "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{t} \\in \\mathbb{R}^{N_{T} \\times P \\times C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denote the target domain part-level features, where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of horizontally sliced parts, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "C"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the feature channels. Specifically, we perform the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-nearest neighbor search algorithm on both the global feature space and each part feature space to generate ranked lists "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{R}_g, \\mathcal{R}_1, \\dots, \\mathcal{R}_P\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " for each unlabeled feature. The "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}_g"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the sets of global feature indices for the top- "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " samples in the ranked list, while "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}_p"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the sets of "
+                                },
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th part feature indices. We then compute the confidence scores "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{p}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " between the global feature indices "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}_g"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and the "
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th part feature indices "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}_p"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as follows,"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {S} _ {p} = \\frac {\\left| \\mathcal {R} _ {g} \\cap \\mathcal {R} _ {p} \\right|}{\\left| \\mathcal {R} _ {g} \\cup \\mathcal {R} _ {p} \\right|} \\in [ 0, 1 ], \\tag {3}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "|\\cdot|"
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+                                    "type": "text",
+                                    "content": " is a non-negative real number denoting the cardinality of a set. The confidence scores are further used to refine the part-based space to global feature space. We then use a clustering algorithm "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " (e.g., DBSCAN [9]) to assign pseudo-labels on the global feature space, i.e.,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "y _ {t} = \\mathcal {C} \\left\\{\\mathcal {J} \\left(\\frac {1}{P} \\sum_ {p = 1} ^ {P} \\left[ \\langle f _ {t} ^ {p}, f _ {t} ^ {p} \\rangle * \\frac {\\mathcal {S} _ {p}}{\\sum_ {p = 1} ^ {P} \\mathcal {S} _ {p}} \\right]\\right) \\right\\}, \\tag {4}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the Jaccard distance [49] computed in global feature space and "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " denotes the Hadamard product."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Initializing Hybrid Memory. To initialize the part-based hybrid memory, we utilize the class-level features of both source and target domains. It is worth illustrating that in the target domain, we only retain samples assigned with pseudo"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "labels, and exclude those with discrete labels from the subsequent online training stage, i.e.,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\left\\{c _ {s}, c _ {t} \\right\\} = \\left\\{\\frac {1}{| \\mathcal {N} _ {s} |} \\sum_ {f _ {s} \\in \\mathcal {N} _ {s}} f _ {s}, \\frac {1}{| \\mathcal {N} _ {t} |} \\sum_ {f _ {t} \\in \\mathcal {N} _ {t}} f _ {t} \\right\\}, \\tag {5}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{c_s, c_t\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the source and target domain class-level features, "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{N}_s, \\mathcal{N}_t)"
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+                                {
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+                                    "type": "text",
+                                    "content": " is the same label set or cluster set."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.3. Online Training Stage"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "This part provides a detailed explanation of the Cycle Temporal Shift Convolution (CTS-Conv) and Global Context Block. Then, we introduce the utilization of class-level momentum updating for the part-based hybrid memory."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Cycle Temporal Shift Convolution. Gait recognition is a challenging task due to the impact of various external factors, including carrying conditions, wearing coats, and varying viewing angles, leading to a much higher intra-class variance than inter-class. Previous studies [25, 26] proposed to use 3D convolution (3D-Conv) neural network to capture temporal information in gait sequences and extract robust features. However, when applied to part-based UDA tasks, 3D-Conv is limited by its high computational cost and parameter-rich structure, increasing the risk of over-fitting. To address this, we propose a novel CTS-Conv, which separates temporal feature learning from spatial feature learning based on the well-designed temporal shift convolution (TS-Conv) [27]. In CTS-Conv, the input features are denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Upsilon = \\{v_{1}, v_{2}, \\ldots, v_{E}\\} \\in \\mathbb{R}^{C \\times T \\times H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "v_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the input features divided equally into "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "text",
+                                    "content": " pieces, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        262,
+                                        287,
+                                        477
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the number of frames. As shown in Fig. 2, the CTS-Conv operation can be expressed as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        70,
+                        485,
+                        287,
+                        501
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                70,
+                                485,
+                                287,
+                                501
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        70,
+                                        485,
+                                        287,
+                                        501
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\overrightarrow {v} _ {1} ^ {t} = v _ {1} ^ {t - 1}, \\overrightarrow {v} _ {1} ^ {0} = v _ {1} ^ {T}, \\overleftarrow {v} _ {2} ^ {t} = v _ {2} ^ {t + 1}, \\overleftarrow {v} _ {2} ^ {T} = v _ {2} ^ {0}, \\tag {6}",
+                                    "image_path": "a0ead9e8ab93695167aefcfa1ca82fa965cd8b682ef1ae1dc111f3ac45ff7bad.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        46,
+                        509,
+                        287,
+                        581
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                509,
+                                287,
+                                581
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overrightarrow{v}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overleftarrow{v}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the first two pieces which are shifted to the right and left along the temporal dimension, respectively. The remaining pieces "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[v_3,v_4,\\dots ,v_E]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        509,
+                                        287,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " are unshifted. The CTS-Conv operation in STANet learns temporal features by exchanging the features of adjacent frames, without introducing any additional parameters."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        46,
+                        582,
+                        287,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Global Context Block. After extracting the spatiotemporal features using the CTS-Conv, we further refine the global context modeling technique called global context (GC) block base on [1, 28]. The GC block employs multiple heads to map features during context modeling, thereby facilitating the comprehensive extraction of global motion patterns. To generate the output feature, a horizontal pooling method (HP) is first utilized, resulting in horizontally sliced features denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H = \\{h^1, h^2, \\dots, h^P\\} \\in \\mathbb{R}^{P \\times T \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the number of horizontally sliced parts. Then, the global motion patterns "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g^p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " are derived"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "code",
+                    "bbox": [
+                        318,
+                        90,
+                        526,
+                        257
+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
+                                312,
+                                75,
+                                520,
+                                87
+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        75,
+                                        520,
+                                        87
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                312,
+                                                75,
+                                                520,
+                                                87
+                                            ],
+                                            "type": "text",
+                                            "content": "Algorithm 1: The training process of UDA for Gait"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9,
+                            "angle": 0,
+                            "type": "code_caption"
+                        },
+                        {
+                            "bbox": [
+                                318,
+                                90,
+                                526,
+                                257
+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        318,
+                                        90,
+                                        526,
+                                        257
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": "Require: Labeled data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{D}_s"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " and Unlabeled data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{D}_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \nRequire: Random initialize pipeline "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{F}_{\\theta}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \nRequire: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "m"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " for Eq. (9) and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tau"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " of Eq. (10);  \nfor "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "i \\leq N_e"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " do  \nOffline Clustering Stage, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "N_e"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " is the total iterations; Assign pseudo-label for "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{D}_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " with Eq. (4); Initialize the hybrid memory with Eq. (5);  \nfor "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "j \\leq T_e"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " do  \nOnline Training Stage, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "T_e"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": " is the train iterations; Sample mini-batch data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "(x_s, x_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": "; Encoder part-based features "
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "(f_s, f_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                318,
+                                                90,
+                                                526,
+                                                257
+                                            ],
+                                            "type": "text",
+                                            "content": "; Compute the joint loss with Eq. (11); Update part-based hybrid memory with Eq. (9);  \nend  \nend"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
+                            "type": "code_body"
+                        }
+                    ],
+                    "index": 10,
+                    "sub_type": "algorithm"
+                },
+                {
+                    "bbox": [
+                        306,
+                        283,
+                        440,
+                        295
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        283,
+                                        440,
+                                        295
+                                    ],
+                                    "type": "text",
+                                    "content": "using the subsequent expression:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                        301,
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+                                    "bbox": [
+                                        342,
+                                        301,
+                                        545,
+                                        331
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\tilde {g} ^ {p} = \\frac {\\exp \\left(W _ {k} W _ {v 1} h _ {t} ^ {p}\\right)}{\\sum_ {t = 1} ^ {T} \\exp \\left(W _ {k} W _ {v 1} h _ {t} ^ {p}\\right)} \\otimes W _ {v 1} h ^ {p}, \\tag {7}",
+                                    "image_path": "368fe7fb32cd56cfde4fc000a2d9e4ea733b2cda0e1ad55317d30411162a6672.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        378,
+                                        333,
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+                                        346
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "g ^ {p} = \\delta \\left(W _ {v 2} \\tilde {g} ^ {p}\\right) \\oplus h ^ {p}, \\tag {8}",
+                                    "image_path": "1cc89637714220f08b92d59e1f24364c5946463a1f93e50dbff99130a0514893.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
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+                                        400
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                        354,
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+                                        400
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{g}^p"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
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+                                        400
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the context modeling, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{k}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                        354,
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+                                        400
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{v1}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                        400
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{v2}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
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+                                        400
+                                    ],
+                                    "type": "text",
+                                    "content": " are learnable parameters, "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
+                                        545,
+                                        400
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
+                                        545,
+                                        400
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the activation function, "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
+                                        545,
+                                        400
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\otimes"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
+                                        545,
+                                        400
+                                    ],
+                                    "type": "text",
+                                    "content": " signifies matrix multiplication, and "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
+                                        545,
+                                        400
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\oplus"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        354,
+                                        545,
+                                        400
+                                    ],
+                                    "type": "text",
+                                    "content": " indicates the broadcast element-wise addition."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        304,
+                        402,
+                        545,
+                        510
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        510
+                                    ],
+                                    "type": "text",
+                                    "content": "Updating Hybrid Memory. Each mini-batch of the sampled data is passed through a pipeline that extracts part-based features "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "(f_s, f_t)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". It is worth noting that our proposed UDA framework is highly versatile and can be readily applied to other network architectures [3, 26], as illustrated in Fig. 2, where STANet can be replaced by any of the existing popular networks. At each iteration, the extracted features in each mini-batch would be involved in part-based hybrid memory momentum updating, i.e.,"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\left\\{ \\begin{array}{l} c _ {s} \\leftarrow m \\cdot f _ {s} + (1 - m) \\cdot \\frac {1}{| \\mathcal {B} _ {s} |} \\sum_ {f _ {s} \\in \\mathcal {B} _ {s}} f _ {s} \\\\ c _ {t} \\leftarrow m \\cdot f _ {t} + (1 - m) \\cdot \\frac {1}{| \\mathcal {B} _ {t} |} \\sum_ {f _ {t} \\in \\mathcal {B} _ {t}} f _ {t} \\end{array} \\right\\}, \\tag {9}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "text",
+                                    "content": " denotes the class-level features, "
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+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{B}_s, \\mathcal{B}_t)"
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+                                    "content": " represents the set of features belonging to the source or target domain class and "
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+                                    "content": "m \\in [0,1]"
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+                                    "type": "text",
+                                    "content": " is a momentum coefficient."
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+                                    "content": "3.4. Joint Loss Function"
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+                                    "content": "In this work, three types of part-based loss functions are employed, namely, the triplet loss "
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+                                    "content": ", the cross-entropy loss "
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+                                    "type": "text",
+                                    "content": ". These loss functions are used to constrain the features of each part individually. As shown in Fig. 2, the output features "
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+                                    "content": "(o_s,o_t)"
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+                                    "type": "text",
+                                    "content": " are used to calculate "
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+                                    "type": "text",
+                                    "content": ", while the normalized output features "
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+                                    "content": " and "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Additionally, we consider the varying expressiveness of different body parts and"
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+                                            "type": "text",
+                                            "content": "Table 1. The Rank-1 (\\%) performance comparison of fully supervised and unsupervised domain adaptation methods on CASIA-B. Where “OUMVLP→CASIA-B” denotes the use of OUMVLP as the source domain and CASIA-B as the target domain."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"11\">Probe View</td><td rowspan=\"2\">Mean</td></tr><tr><td>0°</td><td>18°</td><td>36°</td><td>54°</td><td>72°</td><td>90°</td><td>108°</td><td>126°</td><td>134°</td><td>162°</td><td>180°</td></tr><tr><td colspan=\"14\">Fully supervised methods with all labels on CASIA-B</td></tr><tr><td rowspan=\"4\">NM</td><td>CNN-LB [39]</td><td>82.6</td><td>90.3</td><td>96.1</td><td>94.3</td><td>90.1</td><td>87.4</td><td>89.9</td><td>94.0</td><td>94.7</td><td>91.3</td><td>78.5</td><td>89.9</td></tr><tr><td>GaitSet [3]</td><td>90.8</td><td>97.9</td><td>99.4</td><td>96.9</td><td>93.6</td><td>91.7</td><td>95.0</td><td>97.8</td><td>98.9</td><td>96.8</td><td>85.8</td><td>95.0</td></tr><tr><td>GaitGL [26]</td><td>96.0</td><td>98.3</td><td>99.0</td><td>97.9</td><td>96.9</td><td>95.4</td><td>97.0</td><td>98.9</td><td>99.3</td><td>98.8</td><td>94.0</td><td>97.4</td></tr><tr><td>STANet(ours)</td><td>96.4</td><td>99.4</td><td>99.3</td><td>98.9</td><td>97.0</td><td>95.8</td><td>98.2</td><td>99.2</td><td>99.6</td><td>99.2</td><td>96.0</td><td>98.1</td></tr><tr><td rowspan=\"4\">BG</td><td>CNN-LB [39]</td><td>64.2</td><td>80.6</td><td>82.7</td><td>76.9</td><td>64.8</td><td>63.1</td><td>68.0</td><td>76.9</td><td>82.2</td><td>75.4</td><td>61.3</td><td>72.4</td></tr><tr><td>GaitSet [3]</td><td>83.8</td><td>91.2</td><td>91.8</td><td>88.8</td><td>83.3</td><td>81.0</td><td>84.1</td><td>90.0</td><td>92.2</td><td>94.4</td><td>79.0</td><td>87.2</td></tr><tr><td>GaitGL [26]</td><td>92.6</td><td>96.6</td><td>96.8</td><td>95.5</td><td>93.5</td><td>89.3</td><td>92.2</td><td>96.5</td><td>98.2</td><td>96.9</td><td>91.5</td><td>94.5</td></tr><tr><td>STANet(ours)</td><td>94.4</td><td>98.2</td><td>98.9</td><td>97.5</td><td>94.1</td><td>91.2</td><td>93.9</td><td>97.4</td><td>98.5</td><td>97.8</td><td>94.0</td><td>96.0</td></tr><tr><td rowspan=\"4\">CL</td><td>CNN-LB [39]</td><td>37.7</td><td>57.2</td><td>66.6</td><td>61.1</td><td>55.2</td><td>54.6</td><td>55.2</td><td>59.1</td><td>58.9</td><td>48.8</td><td>39.4</td><td>54.0</td></tr><tr><td>GaitSet [3]</td><td>61.4</td><td>75.4</td><td>80.7</td><td>77.3</td><td>72.1</td><td>70.1</td><td>71.5</td><td>73.5</td><td>73.5</td><td>68.4</td><td>50.0</td><td>70.4</td></tr><tr><td>GaitGL [26]</td><td>76.6</td><td>90.0</td><td>90.3</td><td>87.1</td><td>84.5</td><td>79.0</td><td>84.1</td><td>87.0</td><td>87.3</td><td>84.4</td><td>69.5</td><td>83.6</td></tr><tr><td>STANet(ours)</td><td>83.4</td><td>94.6</td><td>96.8</td><td>93.9</td><td>89.6</td><td>86.0</td><td>88.2</td><td>92.1</td><td>93.9</td><td>90.2</td><td>78.1</td><td>89.7</td></tr><tr><td colspan=\"14\">Unsupervised Domain Adaptation methods without any labels on CASIA-B (OUMVLP→CASIA-B)</td></tr><tr><td rowspan=\"4\">NM</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>63.4</td></tr><tr><td>UDA(GaitSet)</td><td>84.7</td><td>95.8</td><td>97.2</td><td>95.8</td><td>95.1</td><td>92.9</td><td>94.8</td><td>96.1</td><td>97.3</td><td>96.6</td><td>79.2</td><td>93.2</td></tr><tr><td>UDA(GaitGL)</td><td>76.7</td><td>88.3</td><td>88.8</td><td>87.1</td><td>88.4</td><td>82.9</td><td>85.9</td><td>90.6</td><td>93.1</td><td>93.9</td><td>73.0</td><td>86.2</td></tr><tr><td>UDA(STANet)</td><td>84.3</td><td>95.2</td><td>95.5</td><td>91.1</td><td>90.7</td><td>85.9</td><td>89.4</td><td>93.3</td><td>94.9</td><td>93.7</td><td>82.4</td><td>90.6</td></tr><tr><td rowspan=\"4\">BG</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>42.7</td></tr><tr><td>UDA(GaitSet)</td><td>77.5</td><td>87.5</td><td>90.0</td><td>89.2</td><td>86.2</td><td>81.2</td><td>87.1</td><td>89.9</td><td>94.0</td><td>91.1</td><td>70.9</td><td>85.9</td></tr><tr><td>UDA(GaitGL)</td><td>69.1</td><td>85.3</td><td>84.7</td><td>83.6</td><td>82.9</td><td>76.1</td><td>79.9</td><td>86.8</td><td>89.1</td><td>88.0</td><td>63.6</td><td>80.8</td></tr><tr><td>UDA(STANet)</td><td>75.4</td><td>88.7</td><td>86.6</td><td>83.6</td><td>82.9</td><td>76.2</td><td>82.6</td><td>86.9</td><td>89.3</td><td>87.5</td><td>73.7</td><td>83.0</td></tr><tr><td rowspan=\"4\">CL</td><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>15.8</td></tr><tr><td>UDA(GaitSet)</td><td>24.2</td><td>38.9</td><td>42.3</td><td>39.6</td><td>41.1</td><td>38.1</td><td>37.9</td><td>43.3</td><td>43.4</td><td>29.6</td><td>25.4</td><td>36.7</td></tr><tr><td>UDA(GaitGL)</td><td>43.9</td><td>65.3</td><td>66.5</td><td>66.9</td><td>68.8</td><td>60.0</td><td>66.4</td><td>71.2</td><td>69.3</td><td>61.8</td><td>42.2</td><td>62.0</td></tr><tr><td>UDA(STANet)</td><td>54.0</td><td>73.2</td><td>75.7</td><td>72.0</td><td>71.4</td><td>64.4</td><td>70.1</td><td>74.6</td><td>73.7</td><td>69.2</td><td>51.4</td><td>68.2</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "use the confidence scores to accurately constrain the features by constraining the contrastive loss for each part. The contrastive loss "
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+                                    "type": "text",
+                                    "content": " can be formulated as follows:"
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {c l} = - \\sum_ {p = 1} ^ {P} \\frac {\\mathcal {S} _ {p}}{N _ {c s}} \\left\\{- \\log \\frac {\\exp \\left(f ^ {p} \\cdot c _ {s} ^ {p , +} / \\tau\\right)}{\\sum_ {k = 1} ^ {| \\mathcal {N} _ {s} |} \\exp \\left(f ^ {p} \\cdot c _ {s} ^ {p , k} / \\tau\\right)} \\right\\} \\tag {10} \\\\ - \\sum_ {p = 1} ^ {P} \\frac {\\mathcal {S} _ {p}}{N _ {c t}} \\left\\{- \\log \\frac {\\exp (f ^ {p} \\cdot c _ {t} ^ {p , +} / \\tau)}{\\sum_ {k = 1} ^ {| \\mathcal {N} _ {t} |} \\exp (f ^ {p} \\cdot c _ {t} ^ {p , k} / \\tau)} \\right\\}, \\\\ \\end{array}",
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+                                    "content": "N_{cs}, N_{ct}"
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+                                    "content": " is a positive integer obtained by multiplying the mini-batch with parts, "
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+                                    "content": " denote the class-level features of source and target domains, and "
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+                                    "content": "c_s^{p, + }, c_t^{p, + }"
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+                                    "type": "text",
+                                    "content": " indicate the positive class prototype corresponding to "
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+                                    "content": ". The combined loss "
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+                                    "content": " can be expressed as"
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+                                    "content": " are the hyper-parameters to balance the combined loss and are empirically set to 0.3."
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
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+                                    "type": "text",
+                                    "content": "In this section, we evaluate the proposed method on three large-scale gait recognition benchmarks, including two widely adopted datasets (i.e., CASIA-B and OUMVLP) and one real-world dataset (i.e., GREW). Then, we compare our method to state-of-the-art methods. Finally, comprehensive ablation studies are conducted to substantiate the effectiveness of our proposed method."
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+                                    "content": "4.1. Datasets and Implementation Details"
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+                                    "content": "CASIA-B [41] is a well-established dataset widely used in the field of gait recognition research. It comprises 124 subjects and encompasses 3 distinct walking conditions: normal walking (NM), walking while wearing a coat (CL), and walking with bags (BG). The dataset is captured by 11 cameras positioned uniformly between "
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+                                    "type": "text",
+                                    "content": ", providing a diverse range of viewpoints. Each subject has a total of 110 sequences. The first 74 subjects are used for training, while the remaining 50 subjects are reserved for testing. During"
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+                                            "type": "text",
+                                            "content": "Table 2. Rank-1 accuracy of fully supervised and unsupervised domain adaptation methods on OUMVLP under all view angles. Where \"CASIA-B→OUMVLP\" represents the use of CASIA-B as the labeled source domain and OUMVLP as the unlabeled target domain."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"14\">Probe View</td><td rowspan=\"2\">Mean</td></tr><tr><td>0°</td><td>15°</td><td>30°</td><td>45°</td><td>60°</td><td>75°</td><td>90°</td><td>180°</td><td>195°</td><td>210°</td><td>225°</td><td>240°</td><td>255°</td><td>270°</td></tr><tr><td colspan=\"16\">Fully supervised methods with all labels on OUMVLP</td></tr><tr><td>GaitSet [3]</td><td>79.5</td><td>87.9</td><td>89.9</td><td>90.2</td><td>88.1</td><td>88.7</td><td>87.8</td><td>81.7</td><td>86.7</td><td>89.0</td><td>89.3</td><td>87.2</td><td>87.8</td><td>86.2</td><td>87.1</td></tr><tr><td>GaitGL [26]</td><td>84.9</td><td>90.2</td><td>91.1</td><td>91.5</td><td>91.1</td><td>90.8</td><td>90.3</td><td>88.5</td><td>88.6</td><td>90.3</td><td>90.4</td><td>89.6</td><td>89.5</td><td>88.8</td><td>89.7</td></tr><tr><td>STANet(ours)</td><td>87.7</td><td>91.4</td><td>91.6</td><td>91.9</td><td>91.6</td><td>91.4</td><td>91.2</td><td>90.4</td><td>90.3</td><td>90.8</td><td>91.0</td><td>90.5</td><td>90.3</td><td>90.1</td><td>90.7</td></tr><tr><td colspan=\"16\">Unsupervised Domain Adaptation methods without any labels on OUMVLP (CASIA-B→OUMVLP)</td></tr><tr><td>TranND [45]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>75.6</td></tr><tr><td>UDA(GaitSet)</td><td>45.6</td><td>60.1</td><td>75.3</td><td>80.7</td><td>75.5</td><td>73.9</td><td>73.9</td><td>49.9</td><td>59.9</td><td>75.5</td><td>81.7</td><td>74.9</td><td>73.2</td><td>72.9</td><td>69.5</td></tr><tr><td>UDA(GaitGL)</td><td>23.6</td><td>50.5</td><td>79.5</td><td>78.5</td><td>75.3</td><td>74.6</td><td>74.5</td><td>28.7</td><td>50.9</td><td>77.5</td><td>77.5</td><td>74.3</td><td>73.3</td><td>73.0</td><td>65.1</td></tr><tr><td>UDA(STANet)</td><td>42.8</td><td>85.1</td><td>92.1</td><td>91.2</td><td>88.9</td><td>89.2</td><td>89.5</td><td>50.4</td><td>86.6</td><td>90.8</td><td>90.1</td><td>88.0</td><td>87.9</td><td>88.0</td><td>82.9</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "testing, the first four \"NM\" conditions are utilized as the gallery, while the remaining conditions serve as the probe."
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+                },
+                {
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+                                    "content": "OUMVLP [32] is a prominent public gait dataset that comprises 10,307 subjects, two distinct walking sequences (labeled as “00” and “01”), and 14 cameras positioned uniformly between "
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+                                    "type": "inline_equation",
+                                    "content": "(0^{\\circ} \\rightarrow 90^{\\circ})"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "(180^{\\circ} \\rightarrow 270^{\\circ})"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". To ensure fair data volume in comparison to CASIA-B, we select the first 1,000 subjects from OUMVLP for our UDA experiments without any specific instructions. In the UDA experiment, we followed the official data split and used 500 individuals for training and the remaining 500 for testing. During the test phase, the “00” sequences serve as the probe, while the remaining “01” sequences serve as the gallery."
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+                                    "type": "text",
+                                    "content": "GREW [48] is a comprehensive and extensive dataset designed for gait recognition, encompassing silhouettes and 2D/3D human body pose. In contrast to CASIA-B and OUMVLP, GREW was collected in diverse and complex scenes in the wild, making it a more challenging task for gait recognition. The GREW dataset comprises 26345 subjects, 128671 sequences, and 882 camera viewpoints. To ensure fairness in data volume with respect to CASIA-B, we use the first 4000 subjects from GREW for UDA experiments without any special instructions. During testing, we make full use of the official query and gallery set."
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+                                    "type": "text",
+                                    "content": "Implementation Details. The training process of UDA is shown in Algorithm 1, and all datasets are uniformly resized to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "64 \\times 44"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " [3]. The model is trained end-to-end using the SGD optimizer, starting with an initial learning rate of 0.1, which is then decreased by a factor of 10 iteratively until convergence. The training mini-batch size for CASIA-B and OUMVLP is set to (8, 16), while for GREW dataset, it is set to (4, 32). Data augmentation techniques are utilized to preserve both the original and augmented data in real-world datasets. The convolutional channels in the STANet are set to (64, 128, 256). The network is trained for a total of "
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+                                    "type": "inline_equation",
+                                    "content": "N_{e} = 100\\mathrm{K}"
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+                                    "type": "text",
+                                    "content": " iterations, and offline clustering is performed every "
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+                                    "type": "inline_equation",
+                                    "content": "T_{e} = 5\\mathrm{K}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " iteration to assign pseudo-labels to unlabeled data and reinitialize the hybrid memory dictionary."
+                                }
+                            ]
+                        }
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+                                    "content": "4.2. Comparison with State-of-the-art Methods"
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+                                    "type": "text",
+                                    "content": "To evaluate the effectiveness of the proposed approach, we compared it with both existing fully supervised methods [39, 3, 26] and Unsupervised Domain Adaptation (UDA) method [45] for gait recognition."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
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+                                    "type": "text",
+                                    "content": "Evaluation on CASIA-B. The performance of both fully supervised [39, 3, 26] and UDA methods [45] on CASIA-B is presented in Tab. 1. (1) The proposed STANet algorithm outperforms the fully supervised algorithm [39, 3, 26], especially in the cross-dressing condition. Experimental results show that our method has the ability to learn more robust motion patterns compared to others. (2) The proposed UDA framework outperforms the existing UDA algorithm [45] under all conditions. The experimental results demonstrate that our UDA framework can effectively utilize fine-grained part-based features to generate pseudo-labels that supervise network learning, leading to a significant improvement in recognition accuracy. (3) We conducted experiments by substituting STANet with various state-of-the-art algorithms, such as GaitSet [3] and GaitGL [26]. In the UDA framework, the GaitSet method outperforms other methods in \"NM\" and \"BG\" but has lower performance in \"CL\". The experimental results demonstrate that GaitSet emphasizes learning cross-view information from the OUMVLP but struggles to capture robust motion patterns."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                                    "content": "Evaluation on OUMVLP. To provide additional evidence of the effectiveness of our proposed method, we evaluated the proposed approach with some state-of-the-art fully supervised [3, 26] and UDA [45] methods on OUMVLP. (1) The proposed STANet outperforms other methods, including GaitSet [3] and GaitGL [26], under both the whole dataset and fully supervised conditions. Our experimental results demonstrate the critical importance of effectively utilizing fine-grained spatio-temporal motion patterns for achieving high performance on large-scale gait datasets. (2) Our proposed UDA framework outperforms the existing UDA algorithm [45]. The experimental results demon"
+                                }
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+                                    "content": "strate that our framework can effectively transfer the norm walking information from CASIA-B to OUMVLP. (3) We conducted experiments to compare STANet with other algorithms, including GaitSet [3] and GaitGL [26]. The results showed that the proposed STANet in the UDA framework effectively utilized fine-grained part-based features, even in the presence of cross-dressing influence in CASIA-B."
+                                }
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+                                    "content": "Evaluation on GREW. We evaluated the proposed method on a wild dataset, i.e., GREW, to provide additional evidence for the effectiveness of our method. (1) The experimental results presented in Tab. 3 demonstrate the effectiveness of the fine-grained motion patterns extracted by our method on real datasets. (2) The UDA experimental results confirm that knowledge gained from accurately labeled data in a laboratory setting can be transferred to real-world scenarios. This validation also confirms the efficacy of our proposed approach in extracting fine-grained motion patterns."
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+                                    "type": "text",
+                                    "content": "4.3. Ablation Study"
+                                }
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+                                    "content": "In this section, an ablation study is performed on the proposed UDA framework to improve the understanding of the effects of different configurations."
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+                                    "content": "The effectiveness of STANet. To comprehensively evaluate the impact of STANet in the UDA framework, we conducted a thorough comparative experiment in Tab. 4. Specifically, (1) The \"w/o CTS-Conv\" represents replacing the CTS-Conv with 2D convolution. The experiment demonstrates a decrease in the performance of the \"CL\", thereby confirming the ability of CTS-Conv to acquire resilient temporal features in the UDA framework. (2) Furthermore, we conducted additional experiments to remove the GC block, denoted as \"w/o GC block\", in which the GC block was replaced with Max Pooling along the temporal dimension. The experiment results showed that STANet exhibited performance comparable to that of GaitGL [26]."
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "The effectiveness of confidence scores. To explore the impact of confidence scores on the offline clustering stage, we completely remove the process of generating confidence scores and generate the global feature space directly averaged over the part-based feature space. The experimental results \"w/o Confidence scores\" from the Tab. 4 show that removing the confidence score decreased the performance."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Analysis of the number of spatial slices parts. We conducted an in-depth analysis to assess the influence of different spatial bin numbers of the UDA framework in Tab. 4. (1) The experimental results indicate that the performance improves as the number of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "N_{\\text{part}}"
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+                                    "type": "text",
+                                    "content": " increases. (2) In the field of gait recognition, many popular approaches [10, 26] have confirmed that the number of parts has a significant impact on the recognition results. Specifically, increasing the number of parts requires the network to focus more on fine-grained parts. Experimental results show that "
+                                },
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+                                    "type": "text",
+                                    "content": " also has a significant impact on unlabeled feature learning."
+                                }
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+                                            "type": "text",
+                                            "content": "Table 3. Rank-1 "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " performance comparison of fully supervised and unsupervised domain adaptation methods on GREW."
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+                            "type": "table_caption"
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Method</td><td>Source</td><td>Rank-1 (%)</td></tr><tr><td colspan=\"3\">Fully supervised methods on GREW</td></tr><tr><td>CNN-LB [39]</td><td>TPAMI 2017</td><td>12.2</td></tr><tr><td>GaitSet [3]</td><td>AAAI 2019</td><td>33.5</td></tr><tr><td>GaitGL [26]</td><td>ICCV 2021</td><td>32.7</td></tr><tr><td>STANet(ours)</td><td>-</td><td>41.3</td></tr><tr><td colspan=\"3\">UDA methods without any labels (OUMVLP→GREW)</td></tr><tr><td>UDA(Gaitset)</td><td>-</td><td>15.3</td></tr><tr><td>UDA(GaitGL)</td><td>-</td><td>13.7</td></tr><tr><td>UDA(STANet)</td><td>-</td><td>26.2</td></tr></table>",
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+                                            "content": "Table 4. The ablation study on CASIA-B with rank-1 accuracy."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">OUMVLP→CASIA-B</td></tr><tr><td>NM</td><td>BG</td><td>CL</td><td>Mean</td></tr><tr><td colspan=\"5\">Analysis of the UDA framework</td></tr><tr><td>Baseline</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr><tr><td>- w/o CTS-Conv</td><td>91.7</td><td>84.7</td><td>62.5</td><td>79.6</td></tr><tr><td>- w/o GC block</td><td>86.3</td><td>79.9</td><td>62.3</td><td>76.1</td></tr><tr><td>- w/o Confidence scores</td><td>88.6</td><td>81.3</td><td>66.8</td><td>78.9</td></tr><tr><td colspan=\"5\">Analysis of the number spatial bins Npart</td></tr><tr><td>Npart = 2</td><td>85.2</td><td>72.3</td><td>25.7</td><td>61.1</td></tr><tr><td>Npart = 4</td><td>83.5</td><td>76.2</td><td>51.3</td><td>70.3</td></tr><tr><td>Npart = 8</td><td>84.7</td><td>76.4</td><td>54.8</td><td>72.0</td></tr><tr><td>Npart = 16</td><td>84.2</td><td>77.1</td><td>59.4</td><td>73.6</td></tr><tr><td>Npart = 32</td><td>90.6</td><td>83.0</td><td>68.2</td><td>80.6</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "In this paper, we present a novel part-based Unsupervised Domain Adaptation (UDA) framework for gait recognition. Our framework consists of an offline clustering stage and an online training stage, which facilitate the knowledge transformation from a labeled source domain to an unlabeled target domain. Our method enhances the reliability of spatio-temporal features and extracts robust gait features for further knowledge transfer. We evaluate the proposed method on three popular gait datasets: CASIA-B, OUMVLP, and GREW, and our experimental results demonstrate the effectiveness of the UDA framework and its potential for practical applications. In future work, we plan to conduct more extensive investigations of UDA methods for gait recognition to accelerate network training and improve the accuracy of pseudo-labels."
+                                }
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+                                    "type": "text",
+                                    "content": "6. Acknowledgement"
+                                }
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+                                    "content": "This work was supported by the National Key R&D Program of China (2022YFC3300700), the National Natural Science Foundation of China (62171038, 62088101, 62276031 and 62276025), and the Fundamental Research Funds for the Central Universities."
+                                }
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[1] Yue Cao, Jiarui Xu, Stephen Lin, Fangyun Wei, and Han Hu. Gcnet: Non-local networks meet squeeze-excitation networks and beyond. In ICCV, 2019. 5"
+                                        }
+                                    ]
+                                }
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+                                }
+                            ],
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+}
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diff --git a/2023/Fine-grained Visible Watermark Removal/3abb59a8-32e1-4765-b180-3a381113d9b8_content_list.json b/2023/Fine-grained Visible Watermark Removal/3abb59a8-32e1-4765-b180-3a381113d9b8_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..3541d95a0353871b78cb498e7532359d8c093507
--- /dev/null
+++ b/2023/Fine-grained Visible Watermark Removal/3abb59a8-32e1-4765-b180-3a381113d9b8_content_list.json	
@@ -0,0 +1,1449 @@
+[
+    {
+        "type": "text",
+        "text": "Fine-grained Visible Watermark Removal",
+        "text_level": 1,
+        "bbox": [
+            272,
+            130,
+            697,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Li Niu*, Xing Zhao, Bo Zhang, Liqing Zhang  \nDepartment of Computer Science and Engineering, MoE Key Lab of Artificial Intelligence, Shanghai Jiao Tong University",
+        "bbox": [
+            124,
+            180,
+            843,
+            233
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{ustcnewly,1033874657,bo-zhang}@sjtu.edu.cn,zhang-lq@cs.sjtu.edu.cn",
+        "bbox": [
+            184,
+            236,
+            784,
+            252
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            286,
+            313,
+            301
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Visible watermark removal aims to erase the watermark from watermarked image and recover the background image, which is a challenging task due to the diverse watermarks. Previous works have designed dynamic network to handle various types of watermarks adaptively, but they ignore that even the watermarked region in a single image can be divided into multiple local parts with distinct visual appearances. In this work, we advance image-specific dynamic network towards part-specific dynamic network, which discovers multiple local parts within the watermarked region and handle them adaptively. Specifically, we propose a query-based multi-task framework, in which part query embeddings are jointly used in two branches to predict part masks and restore watermarked parts. Extensive experiments demonstrate the effectiveness of our fine-grained watermark removal network.",
+        "bbox": [
+            73,
+            318,
+            473,
+            561
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "text": "Overlaying visible watermark on a digital image has been a prevalent way to claim copyright and declare ownership. As its reverse process, visual watermark removal [33, 56] has attracted more and more research interest, which can verify and promote the resilience of overlaid watermarks. Specifically, visible watermark removal aims to erase the watermark and reconstruct the watermark-free (background) image. One major challenge of watermark removal task is that the watermarks are very diversified, in terms of different locations, patterns, transparencies, and so on. Recent works [33, 56] realize this issue and develop dynamic networks to cope with diversified watermarks adaptively. For example, [33] extracts the feature of watermarked region and appends it to original feature map as extra guidance. [56] also extracts the feature of watermarked region, but uses it to generate dynamic convolution kernel to manipulate the original feature map. Although [33, 56] have",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/d33de13b9b956846192a906f95317c67ab484c57a2cbd9fc48262d36da3ca36b.jpg",
+        "image_caption": [
+            "Figure 1. Two examples of watermarked images associated with their background images, watermark masks, and watermarks. Visible watermark removal aims to erase the watermark and reconstruct the background image."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "achieved significant improvement over previous methods by adaptively coping with various types of watermarks, they still treat the watermarked region in an image as a whole, disregarding the fact that even the watermarked region in a single image could be divided into multiple parts with vastly distinct appearances. For example, the watermarked region in Figure 1(a) consists of one pattern and two lines of texts, and the watermarked region in Figure 1(b) consists of one symbol, one line of text, and extra curves. Moreover, when a watermark is overlaid on a background image with certain transparency, one part (e.g., one line of text) in the watermarked region could also exhibit diverse colors due to the colorful background, which makes the appearance of watermarked region even more complicated.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, inheriting the spirit of previous works [33, 56], we take a further step along the path of dynamic network. Specifically, we not only cope with the watermarked regions in different images adaptively, but also cope with different watermarked parts in one image adaptively, which advances image-specific dynamic network towards part-specific dynamic network. We adopt the multi-task framework used in previous works [33, 56], which contains one encoder and two encoders. The mask decoder accounts",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            2,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "12770",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "for localizing the watermark and the background decoder accounts for recovering the watermarked region. Following previous works [33, 56], we also add skip connections [42] linking one encoder with two decoders. To cope with different watermarked parts adaptively, we need to localize them in the mask decoder and repair them in the background decoder. Inspired by query-based network structures in previous works [3, 6], we introduce query embeddings into our multi-task framework, which establishes a connection between mask decoder and background decoder.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In particular, assuming that there are in total  $K$  fine-grained categories of watermarked parts,  $K$  part query embeddings and one watermark-free query embedding interact with the encoder feature map through a transformer [45] block to produce adapted query embeddings.  $K + 1$  adapted query embeddings are expected to contain the part-relevant information and watermark-free information of one specific image. Then, we apply  $K + 1$  adapted query embeddings to mask decoder and background decoder. In the mask decoder, similar to [6], we calculate the similarity between  $K + 1$  adapted query embeddings with the last feature map in the mask decoder to generate  $K$  part masks corresponding to  $K$  part categories and one watermark-free mask. Different from [6], we do not have ground-truth masks for  $K$  part categories. Hence, we enforce the union of  $K$  predicted part masks to approach the ground-truth watermark mask and employ low-entropy loss [17] to push apart  $K$  predicted part masks. In the background decoder, we use  $K$  adapted part query embeddings to produce  $K$  modulated convolution kernels for  $K$  part categories, which act upon  $K$  local parts specified by  $K$  predicted part masks. In this way, we can restore different watermarked parts adaptively and achieve better restoration effect.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on two benchmark watermark removal datasets: CLWD [38] and LOGO30K [8], to verify the effectiveness of our proposed method. Our contributions can be summarized as follows. 1) We are the first to consider fine-grained part categories in the visible watermark removal task, which advances image-specific dynamic network towards part-specific dynamic network; 2) We design a query-based multi-task framework, in which the adapted query embeddings are jointly used to localize different part categories in the mask decoder and restore the corresponding local parts in the background decoder; 3) Extensive experiments on two benchmark datasets demonstrate the effectiveness of our proposed network.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Visible Watermark Removal",
+        "text_level": 1,
+        "bbox": [
+            76,
+            830,
+            333,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Visual watermarking prevails in protecting the digital image copyright, by superimposing a watermark on the background image. As its adversarial task, visible wa",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "termark removal can enhance the resilience of watermark. Early methods [31, 2] proposed GAN [16]-based network structures for watermark removal. [38, 23] formulated watermark removal under a multi-task framework, which predicts watermark-free image, watermark mask, and watermark pattern collaboratively. [8] designed a two-stage multi-task framework with attention mechanism and refinement stage. [33] designed self-calibrated mask refinement for adaptive mask prediction and mask-guided background enhancement. [56] used semantic similarity to propagate useful information and applied dynamic convolution to handle diverse watermarks. [14] designed a novel architecture for better information extraction in the long range. [37] proposed watermark vaccine, which adds invisible perturbation to the watermarked images to attack against the existing watermark removal methods.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "However, the above methods are still struggling to tackle diversified and complicated watermarked regions. Moreover, they ignore that even the watermarked region in a single watermarked image could be decomposed into multiple parts. In this work, we consider fine-grained part categories by localizing and restoring different local parts adaptively.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Image Content Removal",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image content removal or image restoration includes myriads of tasks such as image deraining [46, 51], image dehazing [7, 12, 55], shadow removal [9, 11], and so on. Besides the research works in each field, there are also some general methods [49, 20, 54, 53, 57, 40, 32] for universal image content removal or image restoration. To name a few, [49] proposed a transformer block with locally enhanced window and a learnable multi-scale restoration modulator. In [20], they proposed a general blind image decomposition network. In [54], they proposed a multi-stage progressive image restoration architecture. In visible watermark removal task, the removal target is watermark with diverse colors, patterns, locations, transparencies, etc, making it a challenging and unique task.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3. Vision Transformer",
+        "text_level": 1,
+        "bbox": [
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+            707,
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+            722
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Transformer has been applied to a wide range of computer vision tasks like detection [3, 58], segmentation [48, 47, 6], and pose estimation [24, 35]. Transformer has also been used in some low-level computer vision tasks like image super-resolution [50, 34, 52, 1], image denoising and image deraining [4, 49], image harmonization [18], style transfer [10]. Our mask decoder is similar to [6], but we do not have ground-truth part masks. More importantly, our network is query-based multi-task framework, in which the adapted query embeddings are jointly used in the mask decoder and the background decoder.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "12771",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.4. Dynamic Network",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
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+            106
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Dynamic networks have been widely used in deep learning image processing tasks, which has been discussed and categorized in [21]. According to [21], dynamic parameters can be classified into parameter adjustment [22, 15], weight prediction [43, 25, 39, 19], and dynamic features [30, 5]. Our model uses adapted query embeddings to control the kernel weights, which belongs to weight prediction. This is the first work to handle different watermarked parts dynamically.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Our Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overall Network Structure",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "When superimposing one watermark on a watermark-free (background) image  $I^{bg}$ , we can obtain the watermarked image  $I^{wm}$  and its corresponding watermark mask  $M$ . Visible watermark removal task aims to localize and recover the watermarked region in  $I^{wm}$ , producing the watermark-free image  $I^{bg}$ . Since visible watermark removal task needs to handle two tasks simultaneously: watermark mask prediction and background image restoration, which falls into the realm of multi-task learning. Thus, previous works [33, 56] usually adopt the multi-task framework with one encoder shared by different tasks and multiple decoders accounting for different tasks. In this work, we also employ one encoder  $E$  and two decoders  $\\{D^{ms}, D^{bg}\\}$ , in which  $D^{ms}$  is the mask decoder used to predict the watermark mask  $M$  and  $D^{bg}$  is the background decoder used to recover the background image  $I^{bg}$ . The encoder  $E$  consists of five encoder blocks. The decoder  $D^{bg}/D^{ms}$  consists of four decoder blocks, in which the first decoder block is shared by two decoders. The structures of encoder and decoder blocks are inherited from [23, 33]. Following previous works [33, 56], we also add skip connections [42] to link one encoder with two decoders.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To cope with diversified watermarked parts, we learn part query embeddings corresponding to different part categories, which are jointly used by mask decoder and background decoder. For the mask decoder, we calculate the similarity between query embeddings and mask decoder feature map, yielding part masks for different part categories. For the background decoder, the query embeddings are used to modulate convolution weights for different part categories, which act upon the background decoder feature map within the corresponding local parts specified by part masks. Next, we will introduce the details of part query embeddings in Section 3.2 and describe their usage in the mask (resp., background) decoder in Section 3.3 (resp., 3.4).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Part Query Embeddings",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Assuming that the local parts of watermarked regions can be classified into  $K$  part categories based on dis",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "tinct visual appearances, we use  $K$  part query embeddings  $\\{q_k|_{k = 1}^K\\}$  to represent the prior knowledge (e.g., color, scale, pattern) of  $K$  part categories. Additionally, we introduce a watermark-free query embedding  $q_{K + 1}$  for the watermark-free category. These  $K + 1$  query embeddings can be used to predict the watermark mask and restore the watermarked region, establishing the connection between the mask decoder and the background decoder.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Even for the same part category, the local parts in different images are likely to have different visual appearances. Similarly, the watermark-free regions in different images also vary dramatically. To better cope with diverse images, we further adapt query embeddings to each specific image. Specifically, we use encoder  $E$  to extract the feature map  $\\pmb{F}^{en}$  from watermarked image  $\\pmb{I}^{wm}$ . Each query embedding  $\\pmb{q}_k$  interacts with the encoder feature map  $\\pmb{F}^{en}$  through a transformer [45] block  $T$ , during which  $\\pmb{q}_k$  serves as key and the pixel-wise feature vectors in  $\\pmb{F}^{en}$  serve as keys/values, producing an adapted query embedding  $\\pmb{q}_k^{\\prime}$ . The adapted query embeddings are supposed to incorporate the relevant information from  $\\pmb{I}^{wm}$  and become well-tailored to this image. Next, we will introduce how the adapted query embeddings  $\\{\\pmb{q}_k^{\\prime}|_{k = 1}^{K + 1}\\}$  are used to predict fine-grained watermark part masks and restore local parts accordingly.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Part Mask Prediction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The mask decoder  $D^{ms}$  targets at predicting the masks for different part categories and watermark-free category. We denote the last feature map in  $D^{ms}$  as  $F^{ms}$ . Analogous to [6], we obtain the masks for different part categories and watermark-free category by calculating the similarity between each adapted query embedding and pixel-wise feature vectors in  $F^{ms}$ . Specifically, for the  $k$ -th adapted query embedding  $q_{k}^{\\prime}$ , we project it to the same space as  $F^{ms}$  using a fully-connected (FC) layer and calculate its dot product with all pixel-wise feature vectors in  $F^{ms}$ . We perform softmax normalization on the dot product results over  $K + 1$  query embeddings, leading to  $K$  part masks  $\\{\\hat{M}_{k}^{pt}|_{k = 1}^{K}\\}$  and one watermark-free mask  $\\hat{M}_{K + 1}^{pt}$ . Note that we only have the ground-truth mask  $M$  for the entire watermark region, and there is no ground-truth supervision for each part mask. Thus, we calculate the sum of  $K$  part masks as  $\\hat{M}^{wm} = \\sum_{k = 1}^{K}\\hat{M}_{k}^{pt}$ , which is equivalent to  $1 - \\hat{M}_{K + 1}^{pt}$ .  $\\hat{M}^{wm}$  is enforced to be close to  $M$  using binary cross-entropy loss:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {m s} = - \\sum_ {i, j} [ M (i, j) \\log \\hat {M} ^ {w m} (i, j) \\tag {1} \\\\ + (1 - M (i, j)) \\log (1 - \\hat {M} ^ {w m} (i, j)) ], \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "in which  $M(i,j)$  (resp.,  $\\hat{M}^{wm}(i,j)$ ) is the  $(i,j)$ -th entry in  $M$  (resp.,  $\\hat{M}^{wm}$ ).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "When only using  $\\mathcal{L}_{ms}$ , we observe that the predicted",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "12772",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/fbf226241c792e5bcc121b117d867427ffe245aa94a8af22cb6b9a1a93f403e8.jpg",
+        "image_caption": [
+            "Figure 2. Our network consists of one encoder  $E$  and two decoders  $\\{D^{ms}, D^{bg}\\}$ . We omit the skip connections in this figure for brevity. The transformer block  $T$  outputs the adapted query embeddings, which interact with mask decoder feature to produce part masks and interact with background decoder feature through our PFM block to restore the background image. The detailed architecture of PFM block is shown in the right subfigure."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+    {
+        "type": "text",
+        "text": "$K$  part masks are all close to each other, failing to distinguish different parts. To address this issue, we additionally employ low-entropy loss [17] for the predicted part masks, which ensures that each watermarked pixel is classified into certain part categories instead of uniformly distributed over all part categories. Formally, we apply low-entropy loss to the watermarked pixels:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {l e} = - \\sum_ {i, j} M (i, j) \\sum_ {k = 1} ^ {K + 1} \\hat {M} _ {k} ^ {p t} (i, j) \\log \\hat {M} _ {k} ^ {p t} (i, j), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "in which  $M(i,j) = 1$  (resp.,  $M(i,j) = 0$ ) indicates the watermarked (resp., watermark-free) pixels and  $\\hat{M}_k^{pt}(i,j)$  is the  $(i,j)$ -th entry in  $\\hat{M}_k^{pt}$ . Note that lower entropy implies higher concentration. In addition, the probabilities that watermarked pixels belong to watermark-free category have been suppressed to zero based on Eqn. 1. Therefore, the probabilities that watermarked pixels belong to different part categories are pushed to be concentrated based on Eqn. 2.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Although the procedure of our query-based mask prediction resembles that in [6] to some extent, our method has several major differences: 1) [6] has ground-truth masks, which are inaccessible in our task. Hence, we design  $\\mathcal{L}_{ms}$  and  $\\mathcal{L}_{le}$  to supervise the predicted masks; 2) Our predicted part masks and watermark-free mask are also used in the background decoder to help restore the background, rendering a novel query-based multi-task framework in which two tasks jointly use the adapted query embeddings.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Part-aware Background Restoration",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The background decoder  $D^{bg}$  targets at predicting the background image. Because different part categories have",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "quite distinct visual appearances, we conjecture that restoring different local parts in the watermarked region adaptively could achieve better restoration effect. Therefore, we design a novel Part-aware Feature Modulation (PFM) block, which utilizes the adapted query embeddings and the masks predicted by mask decoder to restore different local parts adaptively. The adapted query embeddings and predicted masks solve the problem of how and where to restore, respectively.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We denote the last feature map in  $D^{bg}$  as  $\\pmb{F}^{bg}$ . We expect to transform the feature map in the watermarked region while keeping the watermark-free region unchanged, since only the watermarked region needs to be restored. To transform different local parts in the watermarked region adaptively, we opt for the dynamic feature transformation technique proposed in [28], which dynamically modulates convolution weights. In our work, we use  $K$  adapted part query embeddings to produce  $K$  modulated convolution weights, which are applied to  $\\pmb{F}^{bg}$  separately to acquire  $K$  transformed feature maps  $\\{\\hat{\\pmb{F}}_k^{bg}|_{k = 1}^K\\}$ .",
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+    {
+        "type": "text",
+        "text": "Specifically, we have learnable base convolution weights  $\\bar{W}$ , in which  $\\bar{W}(m,n,l)$  is the weight for the  $m$ -th input channel,  $n$ -th output channel, and the  $l$ -th spatial location. Then, we pass each adapted query embedding  $\\pmb{q}_k^{\\prime}$  through one FC layer to predict the scale vector  $\\pmb{s}_k$  corresponding to input channels, which are used to modulate the base convolution weights:",
+        "bbox": [
+            496,
+            707,
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+            813
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {W} _ {k} ^ {\\prime} (m, n, l) = \\bar {W} (m, n, l) \\cdot s _ {k} (m), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            558,
+            832,
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+            849
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $s_k(m)$  is the  $m$ -th entry in  $s_k$  (scale for the  $m$ -th input channel) and  $\\tilde{W}_k'(m,n,l)$  is the modulated weight.",
+        "bbox": [
+            498,
+            869,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12773",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we normalize the modulated weights following [28]:",
+        "bbox": [
+            76,
+            90,
+            464,
+            107
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {W} _ {k} ^ {\\prime \\prime} (m, n, l) = \\frac {\\bar {W} _ {k} ^ {\\prime} (m , n , l)}{\\sqrt {\\sum_ {m , l} \\bar {W} _ {k} ^ {\\prime} (m , n , l) ^ {2} + \\epsilon}}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            112,
+            114,
+            468,
+            159
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "in which  $\\epsilon$  is a small constant to avoid numerical error. For more details of convolution weights modulation, please refer to [28]. We apply the modulated convolution weights  $\\bar{W}_k^{\\prime \\prime}$  to  $F^{bg}$  and produce the transformed feature map  $\\hat{F}_k^{bg}$ . Then, we combine  $K$  transformed feature maps and the original feature map based on the predicted  $K$  part masks and one watermark-free mask, giving rise to the final feature map  $\\hat{F}^{bg}$ :",
+        "bbox": [
+            76,
+            167,
+            468,
+            287
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\boldsymbol {F}} ^ {b g} = \\sum_ {k = 1} ^ {K} \\hat {\\boldsymbol {M}} _ {k} ^ {p t} \\circ \\hat {\\boldsymbol {F}} _ {k} ^ {b g} + \\hat {\\boldsymbol {M}} _ {K + 1} ^ {p t} \\circ \\boldsymbol {F} ^ {b g}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            120,
+            297,
+            468,
+            339
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "in which  $\\circ$  means element-wise product. Although similar dynamic kernel has been used in [56], our method is vastly different from theirs in the following aspects: 1) [56] uses the pooled watermark feature to predict the entire convolution kernel, while we use adapted query embeddings to modulate the base convolution weights; 2) [56] only predicts a single convolution kernel for the entire watermarked region, whereas we use  $K$  modulated convolution weights to cope with  $K$  part categories adaptively.",
+        "bbox": [
+            75,
+            348,
+            468,
+            484
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The final feature map  $\\hat{F}^{bg}$  is used to predict the background image  $\\hat{I}^{bg}$ . We combine  $\\hat{I}^{bg}$  with the input watermarked image  $I^{wm}$  using the predicted watermark mask  $\\hat{M}^{wm}$ , yielding the final output  $\\hat{I}^{bg} = \\hat{M}^{wm} \\circ \\hat{I}^{bg} + (1 - \\hat{M}^{wm}) \\circ I^{wm}$ . Following [33, 56], we regularize the final output with  $\\mathcal{L}_1$  loss and perceptual loss [26]:",
+        "bbox": [
+            76,
+            484,
+            468,
+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {b g} = \\| \\tilde {\\boldsymbol {I}} ^ {b g} - \\boldsymbol {I} ^ {b g} \\| _ {1} + \\sum_ {d = 1} ^ {3} \\| \\Phi_ {d} (\\tilde {\\boldsymbol {I}} ^ {b g}) - \\Phi_ {d} (\\boldsymbol {I} ^ {b g}) \\| _ {1}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            83,
+            585,
+            468,
+            626
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Phi_d(\\cdot)$  represents the activation map of  $d$ -th layer in VGG16 [44].",
+        "bbox": [
+            76,
+            636,
+            468,
+            665
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "So far, all the losses can be summarized as",
+        "bbox": [
+            96,
+            667,
+            379,
+            680
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {a l l} = \\mathcal {L} _ {m s} + \\mathcal {L} _ {l e} + \\lambda \\mathcal {L} _ {b g}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            691,
+            468,
+            709
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "in which  $\\lambda$  is a hyper-parameter.",
+        "bbox": [
+            76,
+            719,
+            290,
+            733
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            746,
+            207,
+            762
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
+            771,
+            395,
+            787
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on two benchmark datasets: Colored Large-scale Watermark Dataset (CLWD) [38] and LOGO30K Dataset [8]. Both datasets are constructed with colored complex watermarks, which are challenging for watermark removal task.",
+        "bbox": [
+            75,
+            795,
+            468,
+            868
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "CLWD [38]: In CLWD, the training set has 60,000 images with 160 different watermarks and the test set has 10,000",
+        "bbox": [
+            76,
+            869,
+            468,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "images with 40 different watermarks. The watermarks are collected from public image websites. The background images in the training (resp., test) set are randomly chosen from the training (resp., test) set of PASCAL VOC2012 [13]. When superimposing the collected watermarks on the background images, the location, scale, rotation, and transparency of watermarks are randomly determined, with the watermark transparency in the range of [0.3, 0.7].",
+        "bbox": [
+            496,
+            90,
+            890,
+            210
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "LOGO30K [8]: In LOGO30K, the training set has 28, 352 images and the test set has 4, 051 images. The watermarks collected from Internet include more than 1k famous logos. The background images come from the VAL2014 subset of MSCOCO [36] dataset. When creating watermarked images, the watermark transparency is set in the range of [0.35, 0.85].",
+        "bbox": [
+            496,
+            212,
+            890,
+            316
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following previous methods [38, 33], we use PSNR, SSIM, RMSE, and  $\\mathrm{RMSE}_w$  to evaluate the restored background, in which  $\\mathrm{RMSE}_w$  means RMSE calculated within the watermarked region. We use IoU and  $\\mathbf{F}_1$  to evaluate the predicted watermark mask.",
+        "bbox": [
+            496,
+            318,
+            890,
+            393
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our method is implemented with Pytorch [41]. The input image size is set to  $256 \\times 256$ . During training, we choose Adam [29] optimizer with the initial learning rate being 0.001. All methods are trained and evaluated on Ubuntu 4.18.0, with 512GB memory, Intel(R) Xeon(R) Platinum 8358 CPU, and one A100 SXM4 40GB GPU. The encoder  $E$  has five encoder blocks and the decoder  $D^{ms} / D^{bg}$  has four decoder blocks, in which the encoder and decoder block structures are borrowed from [33]. The transformer block  $T$  has two transformer layers [45]. We set  $K = 8$  and  $\\lambda = 10$  by default.",
+        "bbox": [
+            496,
+            395,
+            890,
+            561
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison with Baselines",
+        "text_level": 1,
+        "bbox": [
+            500,
+            573,
+            743,
+            588
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We compare with two groups of baselines: 1) the general methods for image content removal; 2) the watermark removal methods.",
+        "bbox": [
+            496,
+            597,
+            890,
+            641
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For the first group of methods, we compare with recent methods MPRNet [54], UFormer [49], and BIDNet [20]. We also include UNet [42] for general image-to-image translation as a baseline. For the second group of methods, we compare with the following watermark removal methods: Li et al. [31], Cao et al. [2], WDNet [38], BVMR [23], SplitNet [8], SLBR [33], DKSP [56].",
+        "bbox": [
+            496,
+            643,
+            890,
+            748
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We first evaluate the restored backgrounds from different methods, which are summarized in Table 1. We observe that the methods specifically designed for watermark removal are generally better than general content removal methods [54, 49, 20]. Among the watermark removal methods, [8, 33, 56] achieve competitive performance due to the multi-task framework. Our method significantly outperforms the existing methods, including [56] which uses additional semantic information. The superiority of our method is attributed to the fined-grained watermark removal ability",
+        "bbox": [
+            496,
+            750,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12774",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/174d074ca1b67a7ff2b188083b460577623bff4c8497c1325068c093bad4a009.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. The results of restored backgrounds of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [8, 33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">CLWD</td><td colspan=\"4\">LOGO30K</td></tr><tr><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td></tr><tr><td>U-Net [42]</td><td>23.21*</td><td>0.8567*</td><td>19.35*</td><td>48.43*</td><td>24.64*</td><td>0.8816</td><td>17.84</td><td>43.29*</td></tr><tr><td>MPRNet [54]</td><td>35.19</td><td>0.9725</td><td>5.52</td><td>20.76</td><td>37.81</td><td>0.9866</td><td>4.26</td><td>20.67</td></tr><tr><td>UFormer [49]</td><td>34.07</td><td>0.9784</td><td>6.29</td><td>25.66</td><td>39.84</td><td>0.9936</td><td>3.34</td><td>18.68</td></tr><tr><td>BIDNet [20]</td><td>35.02</td><td>0.9709</td><td>5.66</td><td>21.75</td><td>36.63</td><td>0.9829</td><td>4.83</td><td>24.29</td></tr><tr><td>Li et al. [31]</td><td>27.96*</td><td>0.9161*</td><td>12.63*</td><td>46.80*</td><td>30.51*</td><td>0.9312</td><td>10.51</td><td>39.11*</td></tr><tr><td>Cao et al. [2]</td><td>29.04*</td><td>0.9363*</td><td>10.36*</td><td>41.21*</td><td>32.18*</td><td>0.9654</td><td>8.20</td><td>35.16*</td></tr><tr><td>WDNet [38]</td><td>35.53*</td><td>0.9738*</td><td>5.11*</td><td>17.27*</td><td>39.15*</td><td>0.9874</td><td>3.49</td><td>15.94*</td></tr><tr><td>BVMR [23]</td><td>35.89*</td><td>0.9734*</td><td>5.02*</td><td>18.71*</td><td>38.28*</td><td>0.9852*</td><td>3.52</td><td>16.72*</td></tr><tr><td>SplitNet [8]</td><td>37.41*</td><td>0.9787*</td><td>4.23*</td><td>15.25*</td><td>41.27*</td><td>0.9910*</td><td>3.12</td><td>14.85*</td></tr><tr><td>SLBR [33]</td><td>38.28*</td><td>0.9814*</td><td>3.76*</td><td>14.07*</td><td>41.50*</td><td>0.9914</td><td>2.98</td><td>14.69*</td></tr><tr><td>DKSP† [56]</td><td>38.84*</td><td>0.9813</td><td>3.53</td><td>12.16*</td><td>42.16*</td><td>0.9921</td><td>2.77</td><td>13.78*</td></tr><tr><td>Ours</td><td>39.45</td><td>0.9823</td><td>3.19</td><td>11.28</td><td>42.57</td><td>0.9923</td><td>2.46</td><td>12.44</td></tr></table>",
+        "bbox": [
+            127,
+            88,
+            841,
+            303
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4e686e4997e9be6f0d5b62d894e3c64ff09ce8f03015ff5cf38432ca5afb2a49.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 2. The results of predicted watermark masks of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CLWD</td><td colspan=\"2\">LOGO30K</td></tr><tr><td>IoU↑</td><td>F1↑</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>WDNet [38]</td><td>0.6120*</td><td>0.7240*</td><td>0.6821*</td><td>0.8010*</td></tr><tr><td>BVMR [23]</td><td>0.7021*</td><td>0.7871*</td><td>0.7287*</td><td>0.8305*</td></tr><tr><td>SplitNet [8]</td><td>0.7196*</td><td>0.8027*</td><td>0.7414*</td><td>0.8411*</td></tr><tr><td>SLBR [33]</td><td>0.7463*</td><td>0.8234*</td><td>0.7858*</td><td>0.8647*</td></tr><tr><td>DKSP†[56]</td><td>0.7730*</td><td>0.8480*</td><td>0.8016*</td><td>0.8770*</td></tr><tr><td>Ours</td><td>0.7909</td><td>0.8634</td><td>0.8185</td><td>0.8898</td></tr></table>",
+        "bbox": [
+            76,
+            363,
+            470,
+            487
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "by considering fine-grained part categories.",
+        "bbox": [
+            75,
+            580,
+            364,
+            595
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We also compare the quality of watermark masks predicted by different methods in Table 2. We only compare with those methods [38, 23, 8, 33, 56] which predict watermark masks. Again, our method achieves the best results on both datasets.",
+        "bbox": [
+            75,
+            597,
+            468,
+            672
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We show the visual comparison between different methods in Figure 3. We compare with the competitive baselines WDNet [38], SplitNet [8], SLBR [33], DKSP [56]. We show both predicted watermark masks and restored backgrounds. Our method can predict accurate and complete watermark masks, while the baseline methods could only predict incomplete mask, when the watermark is composed of multiple parts. This is because we use adapted query embeddings corresponding to different part categories to produce multiple part masks, which can cover the complete watermarked region. For background restoration, since baselines fail to predict complete watermark masks, they cannot erase the whole watermark and the recovered backgrounds are far below expectation. With the predicted complete watermark masks, our method can successfully repair the en",
+        "bbox": [
+            75,
+            674,
+            470,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/6abb48e782f95d7afbcb4649329958dc4d91b64de5e7b4052969a2669cb320ed.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3. The ablation study results on LOGO30K [8]. \"SB\" is short for scale/bias, \"DK\" is short for dynamic kernel, and \"q\" stands for query embeddings."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">#</td><td rowspan=\"2\">T</td><td rowspan=\"2\">Dms</td><td rowspan=\"2\">Dbg</td><td colspan=\"4\">Evaluation Metrics</td></tr><tr><td>PSNR↑</td><td>RMSEw↓</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>1</td><td></td><td>-q</td><td>- PFM</td><td>40.08</td><td>16.60</td><td>0.7474</td><td>0.8325</td></tr><tr><td>2</td><td></td><td>- Lle</td><td>- PFM</td><td>40.20</td><td>16.54</td><td>0.7576</td><td>0.8409</td></tr><tr><td>3</td><td></td><td>+</td><td>-PFM</td><td>40.23</td><td>16.48</td><td>0.7893</td><td>0.8674</td></tr><tr><td>4</td><td></td><td>+</td><td>+</td><td>41.67</td><td>13.85</td><td>0.8023</td><td>0.8772</td></tr><tr><td>5</td><td></td><td>+</td><td>SB</td><td>41.04</td><td>14.84</td><td>0.7928</td><td>0.8699</td></tr><tr><td>6</td><td></td><td>+</td><td>DK</td><td>40.82</td><td>15.51</td><td>0.7896</td><td>0.8679</td></tr><tr><td>7</td><td></td><td>+</td><td>-g</td><td>40.47</td><td>16.43</td><td>0.7895</td><td>0.8672</td></tr><tr><td>8</td><td>+</td><td>+</td><td>+</td><td>42.57</td><td>12.44</td><td>0.8185</td><td>0.8898</td></tr></table>",
+        "bbox": [
+            501,
+            363,
+            888,
+            520
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "tire watermarked region by handling different local parts adaptively, producing visually pleasant backgrounds closer to the ground-truth.",
+        "bbox": [
+            498,
+            590,
+            890,
+            635
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
+            500,
+            648,
+            663,
+            664
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct ablation studies to analyze the effectiveness of each component and loss term, which are summarized in Table 3. We first build a basic model without using query embeddings or PFM module in row 1, in which case  $\\pmb{F}^{ms}$  directly outputs the watermark mask and  $\\pmb{F}^{bg}$  directly outputs the restored background. Then, we use  $K + 1$  query embedding to interact with  $\\pmb{F}^{ms}$  to predict mask without low-entropy loss  $\\mathcal{L}_{le}$ . The obtained mask results in row 2 are better than those in row 1, which proves the effectiveness of query-based mask prediction. However, we observe that the predicted masks for different part categories are prone to resemble each other. Thus, we add  $\\mathcal{L}_{le}$  to enforce  $K$  part masks to be different from each other. By comparing row 3 with row 2, we observe that the mask results are significantly improved by discovering multiple part",
+        "bbox": [
+            496,
+            674,
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+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "12775",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "watermarked image",
+        "bbox": [
+            135,
+            95,
+            232,
+            127
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "WDNet",
+        "bbox": [
+            258,
+            104,
+            315,
+            118
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "SplitNet",
+        "bbox": [
+            352,
+            104,
+            415,
+            119
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "SLBR",
+        "bbox": [
+            460,
+            104,
+            506,
+            117
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "DKSP",
+        "bbox": [
+            558,
+            104,
+            604,
+            116
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ours",
+        "bbox": [
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+            104,
+            700,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ground-truth",
+        "bbox": [
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+            104,
+            831,
+            116
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/aa389343a6d1017c71f7832c819e7438ba2756ea6d6402d7612459182ff482af.jpg",
+        "image_caption": [
+            "Figure 3. From left to right, we show the watermarked image, the results of WDNet [38], SplitNet [8], SLBR [33], DKSP [56], our method, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask. The top two examples are from LOGO30K [8] and the bottom two examples are from CLWD [38]."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            133,
+            135,
+            838,
+            763
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "categories. Based on row 3, we insert our PFM block into the background decoder, leading to row 4. We observe that the background results are greatly improved. In the mean",
+        "bbox": [
+            75,
+            844,
+            468,
+            888
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "while, the mask results are also improved, which might benefit from the information sharing between two tasks.",
+        "bbox": [
+            500,
+            844,
+            888,
+            873
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Based on row 4, we explore several variants of our PFM",
+        "bbox": [
+            519,
+            885,
+            890,
+            898
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "12776",
+        "bbox": [
+            480,
+            945,
+            517,
+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c6306fa28550a4d7b5270110b05c5095533eb73fdb6449ef07fbda1689158494.jpg",
+        "image_caption": [
+            "Figure 4. From left to right, we show the watermarked image, the results of row 1, 2, 3, 4, 8 in Table 3, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            89,
+            854,
+            429
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "block. Recall that we use the dynamic strategy proposed in [28]. We also try some alternative ways of dynamic feature transformation. One alternative is dynamic convolution similar to [33]. Specifically, we use adapted query embeddings to predict dynamic convolution kernels for different part categories, which are applied to the corresponding regions in the feature map. Another alternative is predicting scales and biases similar to [27]. Specifically, we use adapted query embeddings to predict channel-wise scales and biases for different part categories, which are applied to the corresponding local regions in the feature map. The comparison among row 4, row 5, and row 6 shows that our choice in the method is the optimal one. Moreover, we remove the guidance from query embeddings and treat the input channel scales as learnable parameters. Without the guidance of query embeddings, the learnt dynamic convolution weights are less effective and thus the performance (row 7) becomes worse than those with guidance (row 4-6).",
+        "bbox": [
+            75,
+            496,
+            472,
+            770
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "At last, we add the transformer block  $T$  to adapt query embeddings to each specific image. The obtained results in row 8 verify the validity of adapted query embeddings, because the local parts from different images belonging to the same part category may still have highly contrastive visual appearances.",
+        "bbox": [
+            75,
+            773,
+            468,
+            864
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Figure 4, we show the results of row 1, 2, 3, 4, 8 in Table 3. From row 1 to row 4, although the quality of",
+        "bbox": [
+            76,
+            869,
+            470,
+            902
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "restored backgrounds are getting better, the watermarks are not completely erased and residual watermark traces can be obviously seen. When using our full method equipped with all modules, row 8 achieves the best results that are close to the ground-truth backgrounds.",
+        "bbox": [
+            496,
+            496,
+            892,
+            573
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            599,
+            619,
+            616
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we have proposed a query-based multi-task framework for visible watermark removal, in which query embeddings corresponding to different part categories are jointly used for fine-grained mask prediction and background reconstruction. Our network can split one watermarked region into multiple local parts and restore different local parts adaptively. By considering fine-grained watermarked parts, our network surpasses the existing methods on two benchmark datasets.",
+        "bbox": [
+            496,
+            631,
+            893,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            500,
+            795,
+            660,
+            811
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300).",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "12777",
+        "bbox": [
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+            944,
+            517,
+            957
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+        ],
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+        "page_idx": 9
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+    {
+        "type": "list",
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+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            402
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "12779",
+        "bbox": [
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+        "page_idx": 9
+    }
+]
\ No newline at end of file
diff --git a/2023/Fine-grained Visible Watermark Removal/3abb59a8-32e1-4765-b180-3a381113d9b8_model.json b/2023/Fine-grained Visible Watermark Removal/3abb59a8-32e1-4765-b180-3a381113d9b8_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..70409971e2b396271e1f5ffb7d5a28c8736db53e
--- /dev/null
+++ b/2023/Fine-grained Visible Watermark Removal/3abb59a8-32e1-4765-b180-3a381113d9b8_model.json	
@@ -0,0 +1,2068 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.273,
+                0.131,
+                0.699,
+                0.154
+            ],
+            "angle": 0,
+            "content": "Fine-grained Visible Watermark Removal"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.125,
+                0.181,
+                0.844,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Li Niu*, Xing Zhao, Bo Zhang, Liqing Zhang  \nDepartment of Computer Science and Engineering, MoE Key Lab of Artificial Intelligence, Shanghai Jiao Tong University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.185,
+                0.237,
+                0.785,
+                0.253
+            ],
+            "angle": 0,
+            "content": "{ustcnewly,1033874657,bo-zhang}@sjtu.edu.cn,zhang-lq@cs.sjtu.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.287,
+                0.314,
+                0.303
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.319,
+                0.474,
+                0.562
+            ],
+            "angle": 0,
+            "content": "Visible watermark removal aims to erase the watermark from watermarked image and recover the background image, which is a challenging task due to the diverse watermarks. Previous works have designed dynamic network to handle various types of watermarks adaptively, but they ignore that even the watermarked region in a single image can be divided into multiple local parts with distinct visual appearances. In this work, we advance image-specific dynamic network towards part-specific dynamic network, which discovers multiple local parts within the watermarked region and handle them adaptively. Specifically, we propose a query-based multi-task framework, in which part query embeddings are jointly used in two branches to predict part masks and restore watermarked parts. Extensive experiments demonstrate the effectiveness of our fine-grained watermark removal network."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.592,
+                0.21,
+                0.608
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.618,
+                0.471,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Overlaying visible watermark on a digital image has been a prevalent way to claim copyright and declare ownership. As its reverse process, visual watermark removal [33, 56] has attracted more and more research interest, which can verify and promote the resilience of overlaid watermarks. Specifically, visible watermark removal aims to erase the watermark and reconstruct the watermark-free (background) image. One major challenge of watermark removal task is that the watermarks are very diversified, in terms of different locations, patterns, transparencies, and so on. Recent works [33, 56] realize this issue and develop dynamic networks to cope with diversified watermarks adaptively. For example, [33] extracts the feature of watermarked region and appends it to original feature map as extra guidance. [56] also extracts the feature of watermarked region, but uses it to generate dynamic convolution kernel to manipulate the original feature map. Although [33, 56] have"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.526,
+                0.288,
+                0.874,
+                0.461
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.468,
+                0.893,
+                0.524
+            ],
+            "angle": 0,
+            "content": "Figure 1. Two examples of watermarked images associated with their background images, watermark masks, and watermarks. Visible watermark removal aims to erase the watermark and reconstruct the background image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.552,
+                0.893,
+                0.763
+            ],
+            "angle": 0,
+            "content": "achieved significant improvement over previous methods by adaptively coping with various types of watermarks, they still treat the watermarked region in an image as a whole, disregarding the fact that even the watermarked region in a single image could be divided into multiple parts with vastly distinct appearances. For example, the watermarked region in Figure 1(a) consists of one pattern and two lines of texts, and the watermarked region in Figure 1(b) consists of one symbol, one line of text, and extra curves. Moreover, when a watermark is overlaid on a background image with certain transparency, one part (e.g., one line of text) in the watermarked region could also exhibit diverse colors due to the colorful background, which makes the appearance of watermarked region even more complicated."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, inheriting the spirit of previous works [33, 56], we take a further step along the path of dynamic network. Specifically, we not only cope with the watermarked regions in different images adaptively, but also cope with different watermarked parts in one image adaptively, which advances image-specific dynamic network towards part-specific dynamic network. We adopt the multi-task framework used in previous works [33, 56], which contains one encoder and two encoders. The mask decoder accounts"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.222,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "12770"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.242
+            ],
+            "angle": 0,
+            "content": "for localizing the watermark and the background decoder accounts for recovering the watermarked region. Following previous works [33, 56], we also add skip connections [42] linking one encoder with two decoders. To cope with different watermarked parts adaptively, we need to localize them in the mask decoder and repair them in the background decoder. Inspired by query-based network structures in previous works [3, 6], we introduce query embeddings into our multi-task framework, which establishes a connection between mask decoder and background decoder."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.244,
+                0.471,
+                0.59
+            ],
+            "angle": 0,
+            "content": "In particular, assuming that there are in total \\( K \\) fine-grained categories of watermarked parts, \\( K \\) part query embeddings and one watermark-free query embedding interact with the encoder feature map through a transformer [45] block to produce adapted query embeddings. \\( K + 1 \\) adapted query embeddings are expected to contain the part-relevant information and watermark-free information of one specific image. Then, we apply \\( K + 1 \\) adapted query embeddings to mask decoder and background decoder. In the mask decoder, similar to [6], we calculate the similarity between \\( K + 1 \\) adapted query embeddings with the last feature map in the mask decoder to generate \\( K \\) part masks corresponding to \\( K \\) part categories and one watermark-free mask. Different from [6], we do not have ground-truth masks for \\( K \\) part categories. Hence, we enforce the union of \\( K \\) predicted part masks to approach the ground-truth watermark mask and employ low-entropy loss [17] to push apart \\( K \\) predicted part masks. In the background decoder, we use \\( K \\) adapted part query embeddings to produce \\( K \\) modulated convolution kernels for \\( K \\) part categories, which act upon \\( K \\) local parts specified by \\( K \\) predicted part masks. In this way, we can restore different watermarked parts adaptively and achieve better restoration effect."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.592,
+                0.47,
+                0.789
+            ],
+            "angle": 0,
+            "content": "We conduct experiments on two benchmark watermark removal datasets: CLWD [38] and LOGO30K [8], to verify the effectiveness of our proposed method. Our contributions can be summarized as follows. 1) We are the first to consider fine-grained part categories in the visible watermark removal task, which advances image-specific dynamic network towards part-specific dynamic network; 2) We design a query-based multi-task framework, in which the adapted query embeddings are jointly used to localize different part categories in the mask decoder and restore the corresponding local parts in the background decoder; 3) Extensive experiments on two benchmark datasets demonstrate the effectiveness of our proposed network."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.806,
+                0.22,
+                0.821
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.831,
+                0.334,
+                0.847
+            ],
+            "angle": 0,
+            "content": "2.1. Visible Watermark Removal"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visual watermarking prevails in protecting the digital image copyright, by superimposing a watermark on the background image. As its adversarial task, visible wa"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.332
+            ],
+            "angle": 0,
+            "content": "termark removal can enhance the resilience of watermark. Early methods [31, 2] proposed GAN [16]-based network structures for watermark removal. [38, 23] formulated watermark removal under a multi-task framework, which predicts watermark-free image, watermark mask, and watermark pattern collaboratively. [8] designed a two-stage multi-task framework with attention mechanism and refinement stage. [33] designed self-calibrated mask refinement for adaptive mask prediction and mask-guided background enhancement. [56] used semantic similarity to propagate useful information and applied dynamic convolution to handle diverse watermarks. [14] designed a novel architecture for better information extraction in the long range. [37] proposed watermark vaccine, which adds invisible perturbation to the watermarked images to attack against the existing watermark removal methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.337,
+                0.892,
+                0.429
+            ],
+            "angle": 0,
+            "content": "However, the above methods are still struggling to tackle diversified and complicated watermarked regions. Moreover, they ignore that even the watermarked region in a single watermarked image could be decomposed into multiple parts. In this work, we consider fine-grained part categories by localizing and restoring different local parts adaptively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.449,
+                0.724,
+                0.464
+            ],
+            "angle": 0,
+            "content": "2.2. Image Content Removal"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.476,
+                0.892,
+                0.688
+            ],
+            "angle": 0,
+            "content": "Image content removal or image restoration includes myriads of tasks such as image deraining [46, 51], image dehazing [7, 12, 55], shadow removal [9, 11], and so on. Besides the research works in each field, there are also some general methods [49, 20, 54, 53, 57, 40, 32] for universal image content removal or image restoration. To name a few, [49] proposed a transformer block with locally enhanced window and a learnable multi-scale restoration modulator. In [20], they proposed a general blind image decomposition network. In [54], they proposed a multi-stage progressive image restoration architecture. In visible watermark removal task, the removal target is watermark with diverse colors, patterns, locations, transparencies, etc, making it a challenging and unique task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.708,
+                0.688,
+                0.723
+            ],
+            "angle": 0,
+            "content": "2.3. Vision Transformer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Transformer has been applied to a wide range of computer vision tasks like detection [3, 58], segmentation [48, 47, 6], and pose estimation [24, 35]. Transformer has also been used in some low-level computer vision tasks like image super-resolution [50, 34, 52, 1], image denoising and image deraining [4, 49], image harmonization [18], style transfer [10]. Our mask decoder is similar to [6], but we do not have ground-truth part masks. More importantly, our network is query-based multi-task framework, in which the adapted query embeddings are jointly used in the mask decoder and the background decoder."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12771"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.254,
+                0.107
+            ],
+            "angle": 0,
+            "content": "2.4. Dynamic Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.114,
+                0.47,
+                0.25
+            ],
+            "angle": 0,
+            "content": "Dynamic networks have been widely used in deep learning image processing tasks, which has been discussed and categorized in [21]. According to [21], dynamic parameters can be classified into parameter adjustment [22, 15], weight prediction [43, 25, 39, 19], and dynamic features [30, 5]. Our model uses adapted query embeddings to control the kernel weights, which belongs to weight prediction. This is the first work to handle different watermarked parts dynamically."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.263,
+                0.208,
+                0.278
+            ],
+            "angle": 0,
+            "content": "3. Our Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.288,
+                0.32,
+                0.303
+            ],
+            "angle": 0,
+            "content": "3.1. Overall Network Structure"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.311,
+                0.471,
+                0.642
+            ],
+            "angle": 0,
+            "content": "When superimposing one watermark on a watermark-free (background) image \\( I^{bg} \\), we can obtain the watermarked image \\( I^{wm} \\) and its corresponding watermark mask \\( M \\). Visible watermark removal task aims to localize and recover the watermarked region in \\( I^{wm} \\), producing the watermark-free image \\( I^{bg} \\). Since visible watermark removal task needs to handle two tasks simultaneously: watermark mask prediction and background image restoration, which falls into the realm of multi-task learning. Thus, previous works [33, 56] usually adopt the multi-task framework with one encoder shared by different tasks and multiple decoders accounting for different tasks. In this work, we also employ one encoder \\( E \\) and two decoders \\( \\{D^{ms}, D^{bg}\\} \\), in which \\( D^{ms} \\) is the mask decoder used to predict the watermark mask \\( M \\) and \\( D^{bg} \\) is the background decoder used to recover the background image \\( I^{bg} \\). The encoder \\( E \\) consists of five encoder blocks. The decoder \\( D^{bg}/D^{ms} \\) consists of four decoder blocks, in which the first decoder block is shared by two decoders. The structures of encoder and decoder blocks are inherited from [23, 33]. Following previous works [33, 56], we also add skip connections [42] to link one encoder with two decoders."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.643,
+                0.47,
+                0.84
+            ],
+            "angle": 0,
+            "content": "To cope with diversified watermarked parts, we learn part query embeddings corresponding to different part categories, which are jointly used by mask decoder and background decoder. For the mask decoder, we calculate the similarity between query embeddings and mask decoder feature map, yielding part masks for different part categories. For the background decoder, the query embeddings are used to modulate convolution weights for different part categories, which act upon the background decoder feature map within the corresponding local parts specified by part masks. Next, we will introduce the details of part query embeddings in Section 3.2 and describe their usage in the mask (resp., background) decoder in Section 3.3 (resp., 3.4)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.848,
+                0.303,
+                0.864
+            ],
+            "angle": 0,
+            "content": "3.2. Part Query Embeddings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Assuming that the local parts of watermarked regions can be classified into \\(K\\) part categories based on dis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "tinct visual appearances, we use \\(K\\) part query embeddings \\(\\{q_k|_{k = 1}^K\\}\\) to represent the prior knowledge (e.g., color, scale, pattern) of \\(K\\) part categories. Additionally, we introduce a watermark-free query embedding \\(q_{K + 1}\\) for the watermark-free category. These \\(K + 1\\) query embeddings can be used to predict the watermark mask and restore the watermarked region, establishing the connection between the mask decoder and the background decoder."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.213,
+                0.893,
+                0.455
+            ],
+            "angle": 0,
+            "content": "Even for the same part category, the local parts in different images are likely to have different visual appearances. Similarly, the watermark-free regions in different images also vary dramatically. To better cope with diverse images, we further adapt query embeddings to each specific image. Specifically, we use encoder \\(E\\) to extract the feature map \\(\\pmb{F}^{en}\\) from watermarked image \\(\\pmb{I}^{wm}\\). Each query embedding \\(\\pmb{q}_k\\) interacts with the encoder feature map \\(\\pmb{F}^{en}\\) through a transformer [45] block \\(T\\), during which \\(\\pmb{q}_k\\) serves as key and the pixel-wise feature vectors in \\(\\pmb{F}^{en}\\) serve as keys/values, producing an adapted query embedding \\(\\pmb{q}_k^{\\prime}\\). The adapted query embeddings are supposed to incorporate the relevant information from \\(\\pmb{I}^{wm}\\) and become well-tailored to this image. Next, we will introduce how the adapted query embeddings \\(\\{\\pmb{q}_k^{\\prime}|_{k = 1}^{K + 1}\\}\\) are used to predict fine-grained watermark part masks and restore local parts accordingly."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.464,
+                0.702,
+                0.478
+            ],
+            "angle": 0,
+            "content": "3.3. Part Mask Prediction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.486,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": "The mask decoder \\( D^{ms} \\) targets at predicting the masks for different part categories and watermark-free category. We denote the last feature map in \\( D^{ms} \\) as \\( F^{ms} \\). Analogous to [6], we obtain the masks for different part categories and watermark-free category by calculating the similarity between each adapted query embedding and pixel-wise feature vectors in \\( F^{ms} \\). Specifically, for the \\( k \\)-th adapted query embedding \\( q_{k}^{\\prime} \\), we project it to the same space as \\( F^{ms} \\) using a fully-connected (FC) layer and calculate its dot product with all pixel-wise feature vectors in \\( F^{ms} \\). We perform softmax normalization on the dot product results over \\( K + 1 \\) query embeddings, leading to \\( K \\) part masks \\( \\{\\hat{M}_{k}^{pt}|_{k = 1}^{K}\\} \\) and one watermark-free mask \\( \\hat{M}_{K + 1}^{pt} \\). Note that we only have the ground-truth mask \\( M \\) for the entire watermark region, and there is no ground-truth supervision for each part mask. Thus, we calculate the sum of \\( K \\) part masks as \\( \\hat{M}^{wm} = \\sum_{k = 1}^{K}\\hat{M}_{k}^{pt} \\), which is equivalent to \\( 1 - \\hat{M}_{K + 1}^{pt} \\). \\( \\hat{M}^{wm} \\) is enforced to be close to \\( M \\) using binary cross-entropy loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.538,
+                0.789,
+                0.892,
+                0.844
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {m s} = - \\sum_ {i, j} [ M (i, j) \\log \\hat {M} ^ {w m} (i, j) \\tag {1} \\\\ + (1 - M (i, j)) \\log (1 - \\hat {M} ^ {w m} (i, j)) ], \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.853,
+                0.892,
+                0.885
+            ],
+            "angle": 0,
+            "content": "in which \\( M(i,j) \\) (resp., \\( \\hat{M}^{wm}(i,j) \\)) is the \\( (i,j) \\)-th entry in \\( M \\) (resp., \\( \\hat{M}^{wm} \\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.886,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "When only using \\(\\mathcal{L}_{ms}\\), we observe that the predicted"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12772"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.117,
+                0.087,
+                0.51,
+                0.301
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.53,
+                0.087,
+                0.858,
+                0.301
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.317,
+                0.894,
+                0.375
+            ],
+            "angle": 0,
+            "content": "Figure 2. Our network consists of one encoder \\( E \\) and two decoders \\( \\{D^{ms}, D^{bg}\\} \\). We omit the skip connections in this figure for brevity. The transformer block \\( T \\) outputs the adapted query embeddings, which interact with mask decoder feature to produce part masks and interact with background decoder feature through our PFM block to restore the background image. The detailed architecture of PFM block is shown in the right subfigure."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.398,
+                0.471,
+                0.504
+            ],
+            "angle": 0,
+            "content": "\\(K\\) part masks are all close to each other, failing to distinguish different parts. To address this issue, we additionally employ low-entropy loss [17] for the predicted part masks, which ensures that each watermarked pixel is classified into certain part categories instead of uniformly distributed over all part categories. Formally, we apply low-entropy loss to the watermarked pixels:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.088,
+                0.513,
+                0.47,
+                0.556
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {l e} = - \\sum_ {i, j} M (i, j) \\sum_ {k = 1} ^ {K + 1} \\hat {M} _ {k} ^ {p t} (i, j) \\log \\hat {M} _ {k} ^ {p t} (i, j), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.565,
+                0.47,
+                0.702
+            ],
+            "angle": 0,
+            "content": "in which \\( M(i,j) = 1 \\) (resp., \\( M(i,j) = 0 \\)) indicates the watermarked (resp., watermark-free) pixels and \\( \\hat{M}_k^{pt}(i,j) \\) is the \\( (i,j) \\)-th entry in \\( \\hat{M}_k^{pt} \\). Note that lower entropy implies higher concentration. In addition, the probabilities that watermarked pixels belong to watermark-free category have been suppressed to zero based on Eqn. 1. Therefore, the probabilities that watermarked pixels belong to different part categories are pushed to be concentrated based on Eqn. 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.704,
+                0.47,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Although the procedure of our query-based mask prediction resembles that in [6] to some extent, our method has several major differences: 1) [6] has ground-truth masks, which are inaccessible in our task. Hence, we design \\(\\mathcal{L}_{ms}\\) and \\(\\mathcal{L}_{le}\\) to supervise the predicted masks; 2) Our predicted part masks and watermark-free mask are also used in the background decoder to help restore the background, rendering a novel query-based multi-task framework in which two tasks jointly use the adapted query embeddings."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.848,
+                0.394,
+                0.864
+            ],
+            "angle": 0,
+            "content": "3.4. Part-aware Background Restoration"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The background decoder \\( D^{bg} \\) targets at predicting the background image. Because different part categories have"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.398,
+                0.892,
+                0.534
+            ],
+            "angle": 0,
+            "content": "quite distinct visual appearances, we conjecture that restoring different local parts in the watermarked region adaptively could achieve better restoration effect. Therefore, we design a novel Part-aware Feature Modulation (PFM) block, which utilizes the adapted query embeddings and the masks predicted by mask decoder to restore different local parts adaptively. The adapted query embeddings and predicted masks solve the problem of how and where to restore, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.537,
+                0.893,
+                0.706
+            ],
+            "angle": 0,
+            "content": "We denote the last feature map in \\(D^{bg}\\) as \\(\\pmb{F}^{bg}\\). We expect to transform the feature map in the watermarked region while keeping the watermark-free region unchanged, since only the watermarked region needs to be restored. To transform different local parts in the watermarked region adaptively, we opt for the dynamic feature transformation technique proposed in [28], which dynamically modulates convolution weights. In our work, we use \\(K\\) adapted part query embeddings to produce \\(K\\) modulated convolution weights, which are applied to \\(\\pmb{F}^{bg}\\) separately to acquire \\(K\\) transformed feature maps \\(\\{\\hat{\\pmb{F}}_k^{bg}|_{k = 1}^K\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.708,
+                0.892,
+                0.814
+            ],
+            "angle": 0,
+            "content": "Specifically, we have learnable base convolution weights \\(\\bar{W}\\), in which \\(\\bar{W}(m,n,l)\\) is the weight for the \\(m\\)-th input channel, \\(n\\)-th output channel, and the \\(l\\)-th spatial location. Then, we pass each adapted query embedding \\(\\pmb{q}_k^{\\prime}\\) through one FC layer to predict the scale vector \\(\\pmb{s}_k\\) corresponding to input channels, which are used to modulate the base convolution weights:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.559,
+                0.833,
+                0.892,
+                0.851
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {W} _ {k} ^ {\\prime} (m, n, l) = \\bar {W} (m, n, l) \\cdot s _ {k} (m), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\( s_k(m) \\) is the \\( m \\)-th entry in \\( s_k \\) (scale for the \\( m \\)-th input channel) and \\( \\tilde{W}_k'(m,n,l) \\) is the modulated weight."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12773"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.465,
+                0.108
+            ],
+            "angle": 0,
+            "content": "Next, we normalize the modulated weights following [28]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.113,
+                0.115,
+                0.47,
+                0.16
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {W} _ {k} ^ {\\prime \\prime} (m, n, l) = \\frac {\\bar {W} _ {k} ^ {\\prime} (m , n , l)}{\\sqrt {\\sum_ {m , l} \\bar {W} _ {k} ^ {\\prime} (m , n , l) ^ {2} + \\epsilon}}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.168,
+                0.47,
+                0.289
+            ],
+            "angle": 0,
+            "content": "in which \\(\\epsilon\\) is a small constant to avoid numerical error. For more details of convolution weights modulation, please refer to [28]. We apply the modulated convolution weights \\(\\bar{W}_k^{\\prime \\prime}\\) to \\(F^{bg}\\) and produce the transformed feature map \\(\\hat{F}_k^{bg}\\). Then, we combine \\(K\\) transformed feature maps and the original feature map based on the predicted \\(K\\) part masks and one watermark-free mask, giving rise to the final feature map \\(\\hat{F}^{bg}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.122,
+                0.298,
+                0.469,
+                0.34
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\boldsymbol {F}} ^ {b g} = \\sum_ {k = 1} ^ {K} \\hat {\\boldsymbol {M}} _ {k} ^ {p t} \\circ \\hat {\\boldsymbol {F}} _ {k} ^ {b g} + \\hat {\\boldsymbol {M}} _ {K + 1} ^ {p t} \\circ \\boldsymbol {F} ^ {b g}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.349,
+                0.469,
+                0.485
+            ],
+            "angle": 0,
+            "content": "in which \\(\\circ\\) means element-wise product. Although similar dynamic kernel has been used in [56], our method is vastly different from theirs in the following aspects: 1) [56] uses the pooled watermark feature to predict the entire convolution kernel, while we use adapted query embeddings to modulate the base convolution weights; 2) [56] only predicts a single convolution kernel for the entire watermarked region, whereas we use \\(K\\) modulated convolution weights to cope with \\(K\\) part categories adaptively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.485,
+                0.469,
+                0.577
+            ],
+            "angle": 0,
+            "content": "The final feature map \\(\\hat{F}^{bg}\\) is used to predict the background image \\(\\hat{I}^{bg}\\). We combine \\(\\hat{I}^{bg}\\) with the input watermarked image \\(I^{wm}\\) using the predicted watermark mask \\(\\hat{M}^{wm}\\), yielding the final output \\(\\hat{I}^{bg} = \\hat{M}^{wm} \\circ \\hat{I}^{bg} + (1 - \\hat{M}^{wm}) \\circ I^{wm}\\). Following [33, 56], we regularize the final output with \\(\\mathcal{L}_1\\) loss and perceptual loss [26]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.084,
+                0.586,
+                0.469,
+                0.627
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {b g} = \\| \\tilde {\\boldsymbol {I}} ^ {b g} - \\boldsymbol {I} ^ {b g} \\| _ {1} + \\sum_ {d = 1} ^ {3} \\| \\Phi_ {d} (\\tilde {\\boldsymbol {I}} ^ {b g}) - \\Phi_ {d} (\\boldsymbol {I} ^ {b g}) \\| _ {1}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.637,
+                0.469,
+                0.666
+            ],
+            "angle": 0,
+            "content": "where \\(\\Phi_d(\\cdot)\\) represents the activation map of \\(d\\)-th layer in VGG16 [44]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.668,
+                0.38,
+                0.681
+            ],
+            "angle": 0,
+            "content": "So far, all the losses can be summarized as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.165,
+                0.693,
+                0.469,
+                0.71
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {a l l} = \\mathcal {L} _ {m s} + \\mathcal {L} _ {l e} + \\lambda \\mathcal {L} _ {b g}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.72,
+                0.292,
+                0.734
+            ],
+            "angle": 0,
+            "content": "in which \\(\\lambda\\) is a hyper-parameter."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.747,
+                0.208,
+                0.763
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.772,
+                0.396,
+                0.788
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.469,
+                0.869
+            ],
+            "angle": 0,
+            "content": "We conduct experiments on two benchmark datasets: Colored Large-scale Watermark Dataset (CLWD) [38] and LOGO30K Dataset [8]. Both datasets are constructed with colored complex watermarks, which are challenging for watermark removal task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.899
+            ],
+            "angle": 0,
+            "content": "CLWD [38]: In CLWD, the training set has 60,000 images with 160 different watermarks and the test set has 10,000"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "images with 40 different watermarks. The watermarks are collected from public image websites. The background images in the training (resp., test) set are randomly chosen from the training (resp., test) set of PASCAL VOC2012 [13]. When superimposing the collected watermarks on the background images, the location, scale, rotation, and transparency of watermarks are randomly determined, with the watermark transparency in the range of [0.3, 0.7]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.213,
+                0.892,
+                0.318
+            ],
+            "angle": 0,
+            "content": "LOGO30K [8]: In LOGO30K, the training set has 28, 352 images and the test set has 4, 051 images. The watermarks collected from Internet include more than 1k famous logos. The background images come from the VAL2014 subset of MSCOCO [36] dataset. When creating watermarked images, the watermark transparency is set in the range of [0.35, 0.85]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.319,
+                0.892,
+                0.394
+            ],
+            "angle": 0,
+            "content": "Following previous methods [38, 33], we use PSNR, SSIM, RMSE, and \\(\\mathrm{RMSE}_w\\) to evaluate the restored background, in which \\(\\mathrm{RMSE}_w\\) means RMSE calculated within the watermarked region. We use IoU and \\(\\mathbf{F}_1\\) to evaluate the predicted watermark mask."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.396,
+                0.892,
+                0.562
+            ],
+            "angle": 0,
+            "content": "Our method is implemented with Pytorch [41]. The input image size is set to \\(256 \\times 256\\). During training, we choose Adam [29] optimizer with the initial learning rate being 0.001. All methods are trained and evaluated on Ubuntu 4.18.0, with 512GB memory, Intel(R) Xeon(R) Platinum 8358 CPU, and one A100 SXM4 40GB GPU. The encoder \\(E\\) has five encoder blocks and the decoder \\(D^{ms} / D^{bg}\\) has four decoder blocks, in which the encoder and decoder block structures are borrowed from [33]. The transformer block \\(T\\) has two transformer layers [45]. We set \\(K = 8\\) and \\(\\lambda = 10\\) by default."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.574,
+                0.744,
+                0.589
+            ],
+            "angle": 0,
+            "content": "4.2. Comparison with Baselines"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.598,
+                0.891,
+                0.642
+            ],
+            "angle": 0,
+            "content": "We compare with two groups of baselines: 1) the general methods for image content removal; 2) the watermark removal methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.892,
+                0.749
+            ],
+            "angle": 0,
+            "content": "For the first group of methods, we compare with recent methods MPRNet [54], UFormer [49], and BIDNet [20]. We also include UNet [42] for general image-to-image translation as a baseline. For the second group of methods, we compare with the following watermark removal methods: Li et al. [31], Cao et al. [2], WDNet [38], BVMR [23], SplitNet [8], SLBR [33], DKSP [56]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We first evaluate the restored backgrounds from different methods, which are summarized in Table 1. We observe that the methods specifically designed for watermark removal are generally better than general content removal methods [54, 49, 20]. Among the watermark removal methods, [8, 33, 56] achieve competitive performance due to the multi-task framework. Our method significantly outperforms the existing methods, including [56] which uses additional semantic information. The superiority of our method is attributed to the fined-grained watermark removal ability"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12774"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.129,
+                0.089,
+                0.843,
+                0.304
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">CLWD</td><td colspan=\"4\">LOGO30K</td></tr><tr><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td></tr><tr><td>U-Net [42]</td><td>23.21*</td><td>0.8567*</td><td>19.35*</td><td>48.43*</td><td>24.64*</td><td>0.8816</td><td>17.84</td><td>43.29*</td></tr><tr><td>MPRNet [54]</td><td>35.19</td><td>0.9725</td><td>5.52</td><td>20.76</td><td>37.81</td><td>0.9866</td><td>4.26</td><td>20.67</td></tr><tr><td>UFormer [49]</td><td>34.07</td><td>0.9784</td><td>6.29</td><td>25.66</td><td>39.84</td><td>0.9936</td><td>3.34</td><td>18.68</td></tr><tr><td>BIDNet [20]</td><td>35.02</td><td>0.9709</td><td>5.66</td><td>21.75</td><td>36.63</td><td>0.9829</td><td>4.83</td><td>24.29</td></tr><tr><td>Li et al. [31]</td><td>27.96*</td><td>0.9161*</td><td>12.63*</td><td>46.80*</td><td>30.51*</td><td>0.9312</td><td>10.51</td><td>39.11*</td></tr><tr><td>Cao et al. [2]</td><td>29.04*</td><td>0.9363*</td><td>10.36*</td><td>41.21*</td><td>32.18*</td><td>0.9654</td><td>8.20</td><td>35.16*</td></tr><tr><td>WDNet [38]</td><td>35.53*</td><td>0.9738*</td><td>5.11*</td><td>17.27*</td><td>39.15*</td><td>0.9874</td><td>3.49</td><td>15.94*</td></tr><tr><td>BVMR [23]</td><td>35.89*</td><td>0.9734*</td><td>5.02*</td><td>18.71*</td><td>38.28*</td><td>0.9852*</td><td>3.52</td><td>16.72*</td></tr><tr><td>SplitNet [8]</td><td>37.41*</td><td>0.9787*</td><td>4.23*</td><td>15.25*</td><td>41.27*</td><td>0.9910*</td><td>3.12</td><td>14.85*</td></tr><tr><td>SLBR [33]</td><td>38.28*</td><td>0.9814*</td><td>3.76*</td><td>14.07*</td><td>41.50*</td><td>0.9914</td><td>2.98</td><td>14.69*</td></tr><tr><td>DKSP† [56]</td><td>38.84*</td><td>0.9813</td><td>3.53</td><td>12.16*</td><td>42.16*</td><td>0.9921</td><td>2.77</td><td>13.78*</td></tr><tr><td>Ours</td><td>39.45</td><td>0.9823</td><td>3.19</td><td>11.28</td><td>42.57</td><td>0.9923</td><td>2.46</td><td>12.44</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.304,
+                0.893,
+                0.345
+            ],
+            "angle": 0,
+            "content": "Table 1. The results of restored backgrounds of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [8, 33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.364,
+                0.472,
+                0.488
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CLWD</td><td colspan=\"2\">LOGO30K</td></tr><tr><td>IoU↑</td><td>F1↑</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>WDNet [38]</td><td>0.6120*</td><td>0.7240*</td><td>0.6821*</td><td>0.8010*</td></tr><tr><td>BVMR [23]</td><td>0.7021*</td><td>0.7871*</td><td>0.7287*</td><td>0.8305*</td></tr><tr><td>SplitNet [8]</td><td>0.7196*</td><td>0.8027*</td><td>0.7414*</td><td>0.8411*</td></tr><tr><td>SLBR [33]</td><td>0.7463*</td><td>0.8234*</td><td>0.7858*</td><td>0.8647*</td></tr><tr><td>DKSP†[56]</td><td>0.7730*</td><td>0.8480*</td><td>0.8016*</td><td>0.8770*</td></tr><tr><td>Ours</td><td>0.7909</td><td>0.8634</td><td>0.8185</td><td>0.8898</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.488,
+                0.472,
+                0.556
+            ],
+            "angle": 0,
+            "content": "Table 2. The results of predicted watermark masks of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.582,
+                0.365,
+                0.597
+            ],
+            "angle": 0,
+            "content": "by considering fine-grained part categories."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.47,
+                0.673
+            ],
+            "angle": 0,
+            "content": "We also compare the quality of watermark masks predicted by different methods in Table 2. We only compare with those methods [38, 23, 8, 33, 56] which predict watermark masks. Again, our method achieves the best results on both datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We show the visual comparison between different methods in Figure 3. We compare with the competitive baselines WDNet [38], SplitNet [8], SLBR [33], DKSP [56]. We show both predicted watermark masks and restored backgrounds. Our method can predict accurate and complete watermark masks, while the baseline methods could only predict incomplete mask, when the watermark is composed of multiple parts. This is because we use adapted query embeddings corresponding to different part categories to produce multiple part masks, which can cover the complete watermarked region. For background restoration, since baselines fail to predict complete watermark masks, they cannot erase the whole watermark and the recovered backgrounds are far below expectation. With the predicted complete watermark masks, our method can successfully repair the en"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.503,
+                0.364,
+                0.89,
+                0.521
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">#</td><td rowspan=\"2\">T</td><td rowspan=\"2\">Dms</td><td rowspan=\"2\">Dbg</td><td colspan=\"4\">Evaluation Metrics</td></tr><tr><td>PSNR↑</td><td>RMSEw↓</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>1</td><td></td><td>-q</td><td>- PFM</td><td>40.08</td><td>16.60</td><td>0.7474</td><td>0.8325</td></tr><tr><td>2</td><td></td><td>- Lle</td><td>- PFM</td><td>40.20</td><td>16.54</td><td>0.7576</td><td>0.8409</td></tr><tr><td>3</td><td></td><td>+</td><td>-PFM</td><td>40.23</td><td>16.48</td><td>0.7893</td><td>0.8674</td></tr><tr><td>4</td><td></td><td>+</td><td>+</td><td>41.67</td><td>13.85</td><td>0.8023</td><td>0.8772</td></tr><tr><td>5</td><td></td><td>+</td><td>SB</td><td>41.04</td><td>14.84</td><td>0.7928</td><td>0.8699</td></tr><tr><td>6</td><td></td><td>+</td><td>DK</td><td>40.82</td><td>15.51</td><td>0.7896</td><td>0.8679</td></tr><tr><td>7</td><td></td><td>+</td><td>-g</td><td>40.47</td><td>16.43</td><td>0.7895</td><td>0.8672</td></tr><tr><td>8</td><td>+</td><td>+</td><td>+</td><td>42.57</td><td>12.44</td><td>0.8185</td><td>0.8898</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.522,
+                0.892,
+                0.563
+            ],
+            "angle": 0,
+            "content": "Table 3. The ablation study results on LOGO30K [8]. \"SB\" is short for scale/bias, \"DK\" is short for dynamic kernel, and \"q\" stands for query embeddings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.591,
+                0.892,
+                0.636
+            ],
+            "angle": 0,
+            "content": "tire watermarked region by handling different local parts adaptively, producing visually pleasant backgrounds closer to the ground-truth."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.65,
+                0.665,
+                0.665
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We conduct ablation studies to analyze the effectiveness of each component and loss term, which are summarized in Table 3. We first build a basic model without using query embeddings or PFM module in row 1, in which case \\( \\pmb{F}^{ms} \\) directly outputs the watermark mask and \\( \\pmb{F}^{bg} \\) directly outputs the restored background. Then, we use \\( K + 1 \\) query embedding to interact with \\( \\pmb{F}^{ms} \\) to predict mask without low-entropy loss \\( \\mathcal{L}_{le} \\). The obtained mask results in row 2 are better than those in row 1, which proves the effectiveness of query-based mask prediction. However, we observe that the predicted masks for different part categories are prone to resemble each other. Thus, we add \\( \\mathcal{L}_{le} \\) to enforce \\( K \\) part masks to be different from each other. By comparing row 3 with row 2, we observe that the mask results are significantly improved by discovering multiple part"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12775"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.137,
+                0.096,
+                0.233,
+                0.128
+            ],
+            "angle": 0,
+            "content": "watermarked image"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.259,
+                0.105,
+                0.316,
+                0.119
+            ],
+            "angle": 0,
+            "content": "WDNet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.354,
+                0.105,
+                0.416,
+                0.12
+            ],
+            "angle": 0,
+            "content": "SplitNet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.461,
+                0.105,
+                0.507,
+                0.118
+            ],
+            "angle": 0,
+            "content": "SLBR"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.559,
+                0.105,
+                0.605,
+                0.117
+            ],
+            "angle": 0,
+            "content": "DKSP"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.666,
+                0.105,
+                0.702,
+                0.117
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.738,
+                0.105,
+                0.832,
+                0.117
+            ],
+            "angle": 0,
+            "content": "Ground-truth"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.134,
+                0.136,
+                0.839,
+                0.764
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.778,
+                0.892,
+                0.82
+            ],
+            "angle": 0,
+            "content": "Figure 3. From left to right, we show the watermarked image, the results of WDNet [38], SplitNet [8], SLBR [33], DKSP [56], our method, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask. The top two examples are from LOGO30K [8] and the bottom two examples are from CLWD [38]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.845,
+                0.47,
+                0.89
+            ],
+            "angle": 0,
+            "content": "categories. Based on row 3, we insert our PFM block into the background decoder, leading to row 4. We observe that the background results are greatly improved. In the mean"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.845,
+                0.89,
+                0.874
+            ],
+            "angle": 0,
+            "content": "while, the mask results are also improved, which might benefit from the information sharing between two tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.886,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Based on row 4, we explore several variants of our PFM"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12776"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.119,
+                0.09,
+                0.855,
+                0.43
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.444,
+                0.893,
+                0.472
+            ],
+            "angle": 0,
+            "content": "Figure 4. From left to right, we show the watermarked image, the results of row 1, 2, 3, 4, 8 in Table 3, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.497,
+                0.473,
+                0.771
+            ],
+            "angle": 0,
+            "content": "block. Recall that we use the dynamic strategy proposed in [28]. We also try some alternative ways of dynamic feature transformation. One alternative is dynamic convolution similar to [33]. Specifically, we use adapted query embeddings to predict dynamic convolution kernels for different part categories, which are applied to the corresponding regions in the feature map. Another alternative is predicting scales and biases similar to [27]. Specifically, we use adapted query embeddings to predict channel-wise scales and biases for different part categories, which are applied to the corresponding local regions in the feature map. The comparison among row 4, row 5, and row 6 shows that our choice in the method is the optimal one. Moreover, we remove the guidance from query embeddings and treat the input channel scales as learnable parameters. Without the guidance of query embeddings, the learnt dynamic convolution weights are less effective and thus the performance (row 7) becomes worse than those with guidance (row 4-6)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.775,
+                0.47,
+                0.866
+            ],
+            "angle": 0,
+            "content": "At last, we add the transformer block \\( T \\) to adapt query embeddings to each specific image. The obtained results in row 8 verify the validity of adapted query embeddings, because the local parts from different images belonging to the same part category may still have highly contrastive visual appearances."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In Figure 4, we show the results of row 1, 2, 3, 4, 8 in Table 3. From row 1 to row 4, although the quality of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.497,
+                0.893,
+                0.574
+            ],
+            "angle": 0,
+            "content": "restored backgrounds are getting better, the watermarks are not completely erased and residual watermark traces can be obviously seen. When using our full method equipped with all modules, row 8 achieves the best results that are close to the ground-truth backgrounds."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.601,
+                0.62,
+                0.617
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.632,
+                0.895,
+                0.768
+            ],
+            "angle": 0,
+            "content": "In this work, we have proposed a query-based multi-task framework for visible watermark removal, in which query embeddings corresponding to different part categories are jointly used for fine-grained mask prediction and background reconstruction. Our network can split one watermarked region into multiple local parts and restore different local parts adaptively. By considering fine-grained watermarked parts, our network surpasses the existing methods on two benchmark datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.796,
+                0.661,
+                0.813
+            ],
+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300)."
+        },
+        {
+            "type": "page_number",
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+            "angle": 0,
+            "content": "12777"
+        }
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+            "angle": 0,
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+# Fine-grained Visible Watermark Removal
+
+Li Niu*, Xing Zhao, Bo Zhang, Liqing Zhang  
+Department of Computer Science and Engineering, MoE Key Lab of Artificial Intelligence, Shanghai Jiao Tong University
+
+{ustcnewly,1033874657,bo-zhang}@sjtu.edu.cn,zhang-lq@cs.sjtu.edu.cn
+
+# Abstract
+
+Visible watermark removal aims to erase the watermark from watermarked image and recover the background image, which is a challenging task due to the diverse watermarks. Previous works have designed dynamic network to handle various types of watermarks adaptively, but they ignore that even the watermarked region in a single image can be divided into multiple local parts with distinct visual appearances. In this work, we advance image-specific dynamic network towards part-specific dynamic network, which discovers multiple local parts within the watermarked region and handle them adaptively. Specifically, we propose a query-based multi-task framework, in which part query embeddings are jointly used in two branches to predict part masks and restore watermarked parts. Extensive experiments demonstrate the effectiveness of our fine-grained watermark removal network.
+
+# 1. Introduction
+
+Overlaying visible watermark on a digital image has been a prevalent way to claim copyright and declare ownership. As its reverse process, visual watermark removal [33, 56] has attracted more and more research interest, which can verify and promote the resilience of overlaid watermarks. Specifically, visible watermark removal aims to erase the watermark and reconstruct the watermark-free (background) image. One major challenge of watermark removal task is that the watermarks are very diversified, in terms of different locations, patterns, transparencies, and so on. Recent works [33, 56] realize this issue and develop dynamic networks to cope with diversified watermarks adaptively. For example, [33] extracts the feature of watermarked region and appends it to original feature map as extra guidance. [56] also extracts the feature of watermarked region, but uses it to generate dynamic convolution kernel to manipulate the original feature map. Although [33, 56] have
+
+![](images/d33de13b9b956846192a906f95317c67ab484c57a2cbd9fc48262d36da3ca36b.jpg)  
+Figure 1. Two examples of watermarked images associated with their background images, watermark masks, and watermarks. Visible watermark removal aims to erase the watermark and reconstruct the background image.
+
+achieved significant improvement over previous methods by adaptively coping with various types of watermarks, they still treat the watermarked region in an image as a whole, disregarding the fact that even the watermarked region in a single image could be divided into multiple parts with vastly distinct appearances. For example, the watermarked region in Figure 1(a) consists of one pattern and two lines of texts, and the watermarked region in Figure 1(b) consists of one symbol, one line of text, and extra curves. Moreover, when a watermark is overlaid on a background image with certain transparency, one part (e.g., one line of text) in the watermarked region could also exhibit diverse colors due to the colorful background, which makes the appearance of watermarked region even more complicated.
+
+In this work, inheriting the spirit of previous works [33, 56], we take a further step along the path of dynamic network. Specifically, we not only cope with the watermarked regions in different images adaptively, but also cope with different watermarked parts in one image adaptively, which advances image-specific dynamic network towards part-specific dynamic network. We adopt the multi-task framework used in previous works [33, 56], which contains one encoder and two encoders. The mask decoder accounts
+
+for localizing the watermark and the background decoder accounts for recovering the watermarked region. Following previous works [33, 56], we also add skip connections [42] linking one encoder with two decoders. To cope with different watermarked parts adaptively, we need to localize them in the mask decoder and repair them in the background decoder. Inspired by query-based network structures in previous works [3, 6], we introduce query embeddings into our multi-task framework, which establishes a connection between mask decoder and background decoder.
+
+In particular, assuming that there are in total  $K$  fine-grained categories of watermarked parts,  $K$  part query embeddings and one watermark-free query embedding interact with the encoder feature map through a transformer [45] block to produce adapted query embeddings.  $K + 1$  adapted query embeddings are expected to contain the part-relevant information and watermark-free information of one specific image. Then, we apply  $K + 1$  adapted query embeddings to mask decoder and background decoder. In the mask decoder, similar to [6], we calculate the similarity between  $K + 1$  adapted query embeddings with the last feature map in the mask decoder to generate  $K$  part masks corresponding to  $K$  part categories and one watermark-free mask. Different from [6], we do not have ground-truth masks for  $K$  part categories. Hence, we enforce the union of  $K$  predicted part masks to approach the ground-truth watermark mask and employ low-entropy loss [17] to push apart  $K$  predicted part masks. In the background decoder, we use  $K$  adapted part query embeddings to produce  $K$  modulated convolution kernels for  $K$  part categories, which act upon  $K$  local parts specified by  $K$  predicted part masks. In this way, we can restore different watermarked parts adaptively and achieve better restoration effect.
+
+We conduct experiments on two benchmark watermark removal datasets: CLWD [38] and LOGO30K [8], to verify the effectiveness of our proposed method. Our contributions can be summarized as follows. 1) We are the first to consider fine-grained part categories in the visible watermark removal task, which advances image-specific dynamic network towards part-specific dynamic network; 2) We design a query-based multi-task framework, in which the adapted query embeddings are jointly used to localize different part categories in the mask decoder and restore the corresponding local parts in the background decoder; 3) Extensive experiments on two benchmark datasets demonstrate the effectiveness of our proposed network.
+
+# 2. Related Work
+
+# 2.1. Visible Watermark Removal
+
+Visual watermarking prevails in protecting the digital image copyright, by superimposing a watermark on the background image. As its adversarial task, visible wa
+
+termark removal can enhance the resilience of watermark. Early methods [31, 2] proposed GAN [16]-based network structures for watermark removal. [38, 23] formulated watermark removal under a multi-task framework, which predicts watermark-free image, watermark mask, and watermark pattern collaboratively. [8] designed a two-stage multi-task framework with attention mechanism and refinement stage. [33] designed self-calibrated mask refinement for adaptive mask prediction and mask-guided background enhancement. [56] used semantic similarity to propagate useful information and applied dynamic convolution to handle diverse watermarks. [14] designed a novel architecture for better information extraction in the long range. [37] proposed watermark vaccine, which adds invisible perturbation to the watermarked images to attack against the existing watermark removal methods.
+
+However, the above methods are still struggling to tackle diversified and complicated watermarked regions. Moreover, they ignore that even the watermarked region in a single watermarked image could be decomposed into multiple parts. In this work, we consider fine-grained part categories by localizing and restoring different local parts adaptively.
+
+# 2.2. Image Content Removal
+
+Image content removal or image restoration includes myriads of tasks such as image deraining [46, 51], image dehazing [7, 12, 55], shadow removal [9, 11], and so on. Besides the research works in each field, there are also some general methods [49, 20, 54, 53, 57, 40, 32] for universal image content removal or image restoration. To name a few, [49] proposed a transformer block with locally enhanced window and a learnable multi-scale restoration modulator. In [20], they proposed a general blind image decomposition network. In [54], they proposed a multi-stage progressive image restoration architecture. In visible watermark removal task, the removal target is watermark with diverse colors, patterns, locations, transparencies, etc, making it a challenging and unique task.
+
+# 2.3. Vision Transformer
+
+Transformer has been applied to a wide range of computer vision tasks like detection [3, 58], segmentation [48, 47, 6], and pose estimation [24, 35]. Transformer has also been used in some low-level computer vision tasks like image super-resolution [50, 34, 52, 1], image denoising and image deraining [4, 49], image harmonization [18], style transfer [10]. Our mask decoder is similar to [6], but we do not have ground-truth part masks. More importantly, our network is query-based multi-task framework, in which the adapted query embeddings are jointly used in the mask decoder and the background decoder.
+
+# 2.4. Dynamic Network
+
+Dynamic networks have been widely used in deep learning image processing tasks, which has been discussed and categorized in [21]. According to [21], dynamic parameters can be classified into parameter adjustment [22, 15], weight prediction [43, 25, 39, 19], and dynamic features [30, 5]. Our model uses adapted query embeddings to control the kernel weights, which belongs to weight prediction. This is the first work to handle different watermarked parts dynamically.
+
+# 3. Our Method
+
+# 3.1. Overall Network Structure
+
+When superimposing one watermark on a watermark-free (background) image  $I^{bg}$ , we can obtain the watermarked image  $I^{wm}$  and its corresponding watermark mask  $M$ . Visible watermark removal task aims to localize and recover the watermarked region in  $I^{wm}$ , producing the watermark-free image  $I^{bg}$ . Since visible watermark removal task needs to handle two tasks simultaneously: watermark mask prediction and background image restoration, which falls into the realm of multi-task learning. Thus, previous works [33, 56] usually adopt the multi-task framework with one encoder shared by different tasks and multiple decoders accounting for different tasks. In this work, we also employ one encoder  $E$  and two decoders  $\{D^{ms}, D^{bg}\}$ , in which  $D^{ms}$  is the mask decoder used to predict the watermark mask  $M$  and  $D^{bg}$  is the background decoder used to recover the background image  $I^{bg}$ . The encoder  $E$  consists of five encoder blocks. The decoder  $D^{bg}/D^{ms}$  consists of four decoder blocks, in which the first decoder block is shared by two decoders. The structures of encoder and decoder blocks are inherited from [23, 33]. Following previous works [33, 56], we also add skip connections [42] to link one encoder with two decoders.
+
+To cope with diversified watermarked parts, we learn part query embeddings corresponding to different part categories, which are jointly used by mask decoder and background decoder. For the mask decoder, we calculate the similarity between query embeddings and mask decoder feature map, yielding part masks for different part categories. For the background decoder, the query embeddings are used to modulate convolution weights for different part categories, which act upon the background decoder feature map within the corresponding local parts specified by part masks. Next, we will introduce the details of part query embeddings in Section 3.2 and describe their usage in the mask (resp., background) decoder in Section 3.3 (resp., 3.4).
+
+# 3.2. Part Query Embeddings
+
+Assuming that the local parts of watermarked regions can be classified into  $K$  part categories based on dis
+
+tinct visual appearances, we use  $K$  part query embeddings  $\{q_k|_{k = 1}^K\}$  to represent the prior knowledge (e.g., color, scale, pattern) of  $K$  part categories. Additionally, we introduce a watermark-free query embedding  $q_{K + 1}$  for the watermark-free category. These  $K + 1$  query embeddings can be used to predict the watermark mask and restore the watermarked region, establishing the connection between the mask decoder and the background decoder.
+
+Even for the same part category, the local parts in different images are likely to have different visual appearances. Similarly, the watermark-free regions in different images also vary dramatically. To better cope with diverse images, we further adapt query embeddings to each specific image. Specifically, we use encoder  $E$  to extract the feature map  $\pmb{F}^{en}$  from watermarked image  $\pmb{I}^{wm}$ . Each query embedding  $\pmb{q}_k$  interacts with the encoder feature map  $\pmb{F}^{en}$  through a transformer [45] block  $T$ , during which  $\pmb{q}_k$  serves as key and the pixel-wise feature vectors in  $\pmb{F}^{en}$  serve as keys/values, producing an adapted query embedding  $\pmb{q}_k^{\prime}$ . The adapted query embeddings are supposed to incorporate the relevant information from  $\pmb{I}^{wm}$  and become well-tailored to this image. Next, we will introduce how the adapted query embeddings  $\{\pmb{q}_k^{\prime}|_{k = 1}^{K + 1}\}$  are used to predict fine-grained watermark part masks and restore local parts accordingly.
+
+# 3.3. Part Mask Prediction
+
+The mask decoder  $D^{ms}$  targets at predicting the masks for different part categories and watermark-free category. We denote the last feature map in  $D^{ms}$  as  $F^{ms}$ . Analogous to [6], we obtain the masks for different part categories and watermark-free category by calculating the similarity between each adapted query embedding and pixel-wise feature vectors in  $F^{ms}$ . Specifically, for the  $k$ -th adapted query embedding  $q_{k}^{\prime}$ , we project it to the same space as  $F^{ms}$  using a fully-connected (FC) layer and calculate its dot product with all pixel-wise feature vectors in  $F^{ms}$ . We perform softmax normalization on the dot product results over  $K + 1$  query embeddings, leading to  $K$  part masks  $\{\hat{M}_{k}^{pt}|_{k = 1}^{K}\}$  and one watermark-free mask  $\hat{M}_{K + 1}^{pt}$ . Note that we only have the ground-truth mask  $M$  for the entire watermark region, and there is no ground-truth supervision for each part mask. Thus, we calculate the sum of  $K$  part masks as  $\hat{M}^{wm} = \sum_{k = 1}^{K}\hat{M}_{k}^{pt}$ , which is equivalent to  $1 - \hat{M}_{K + 1}^{pt}$ .  $\hat{M}^{wm}$  is enforced to be close to  $M$  using binary cross-entropy loss:
+
+$$
+\begin{array}{l} \mathcal {L} _ {m s} = - \sum_ {i, j} [ M (i, j) \log \hat {M} ^ {w m} (i, j) \tag {1} \\ + (1 - M (i, j)) \log (1 - \hat {M} ^ {w m} (i, j)) ], \\ \end{array}
+$$
+
+in which  $M(i,j)$  (resp.,  $\hat{M}^{wm}(i,j)$ ) is the  $(i,j)$ -th entry in  $M$  (resp.,  $\hat{M}^{wm}$ ).
+
+When only using  $\mathcal{L}_{ms}$ , we observe that the predicted
+
+![](images/fbf226241c792e5bcc121b117d867427ffe245aa94a8af22cb6b9a1a93f403e8.jpg)  
+Figure 2. Our network consists of one encoder  $E$  and two decoders  $\{D^{ms}, D^{bg}\}$ . We omit the skip connections in this figure for brevity. The transformer block  $T$  outputs the adapted query embeddings, which interact with mask decoder feature to produce part masks and interact with background decoder feature through our PFM block to restore the background image. The detailed architecture of PFM block is shown in the right subfigure.
+
+![](images/6d182755d040f96bf00b4992364eb80065a12bf20ec6aa5d69e7c669efa930a0.jpg)
+
+$K$  part masks are all close to each other, failing to distinguish different parts. To address this issue, we additionally employ low-entropy loss [17] for the predicted part masks, which ensures that each watermarked pixel is classified into certain part categories instead of uniformly distributed over all part categories. Formally, we apply low-entropy loss to the watermarked pixels:
+
+$$
+\mathcal {L} _ {l e} = - \sum_ {i, j} M (i, j) \sum_ {k = 1} ^ {K + 1} \hat {M} _ {k} ^ {p t} (i, j) \log \hat {M} _ {k} ^ {p t} (i, j), \tag {2}
+$$
+
+in which  $M(i,j) = 1$  (resp.,  $M(i,j) = 0$ ) indicates the watermarked (resp., watermark-free) pixels and  $\hat{M}_k^{pt}(i,j)$  is the  $(i,j)$ -th entry in  $\hat{M}_k^{pt}$ . Note that lower entropy implies higher concentration. In addition, the probabilities that watermarked pixels belong to watermark-free category have been suppressed to zero based on Eqn. 1. Therefore, the probabilities that watermarked pixels belong to different part categories are pushed to be concentrated based on Eqn. 2.
+
+Although the procedure of our query-based mask prediction resembles that in [6] to some extent, our method has several major differences: 1) [6] has ground-truth masks, which are inaccessible in our task. Hence, we design  $\mathcal{L}_{ms}$  and  $\mathcal{L}_{le}$  to supervise the predicted masks; 2) Our predicted part masks and watermark-free mask are also used in the background decoder to help restore the background, rendering a novel query-based multi-task framework in which two tasks jointly use the adapted query embeddings.
+
+# 3.4. Part-aware Background Restoration
+
+The background decoder  $D^{bg}$  targets at predicting the background image. Because different part categories have
+
+quite distinct visual appearances, we conjecture that restoring different local parts in the watermarked region adaptively could achieve better restoration effect. Therefore, we design a novel Part-aware Feature Modulation (PFM) block, which utilizes the adapted query embeddings and the masks predicted by mask decoder to restore different local parts adaptively. The adapted query embeddings and predicted masks solve the problem of how and where to restore, respectively.
+
+We denote the last feature map in  $D^{bg}$  as  $\pmb{F}^{bg}$ . We expect to transform the feature map in the watermarked region while keeping the watermark-free region unchanged, since only the watermarked region needs to be restored. To transform different local parts in the watermarked region adaptively, we opt for the dynamic feature transformation technique proposed in [28], which dynamically modulates convolution weights. In our work, we use  $K$  adapted part query embeddings to produce  $K$  modulated convolution weights, which are applied to  $\pmb{F}^{bg}$  separately to acquire  $K$  transformed feature maps  $\{\hat{\pmb{F}}_k^{bg}|_{k = 1}^K\}$ .
+
+Specifically, we have learnable base convolution weights  $\bar{W}$ , in which  $\bar{W}(m,n,l)$  is the weight for the  $m$ -th input channel,  $n$ -th output channel, and the  $l$ -th spatial location. Then, we pass each adapted query embedding  $\pmb{q}_k^{\prime}$  through one FC layer to predict the scale vector  $\pmb{s}_k$  corresponding to input channels, which are used to modulate the base convolution weights:
+
+$$
+\bar {W} _ {k} ^ {\prime} (m, n, l) = \bar {W} (m, n, l) \cdot s _ {k} (m), \tag {3}
+$$
+
+where  $s_k(m)$  is the  $m$ -th entry in  $s_k$  (scale for the  $m$ -th input channel) and  $\tilde{W}_k'(m,n,l)$  is the modulated weight.
+
+Next, we normalize the modulated weights following [28]:
+
+$$
+\bar {W} _ {k} ^ {\prime \prime} (m, n, l) = \frac {\bar {W} _ {k} ^ {\prime} (m , n , l)}{\sqrt {\sum_ {m , l} \bar {W} _ {k} ^ {\prime} (m , n , l) ^ {2} + \epsilon}}, \tag {4}
+$$
+
+in which  $\epsilon$  is a small constant to avoid numerical error. For more details of convolution weights modulation, please refer to [28]. We apply the modulated convolution weights  $\bar{W}_k^{\prime \prime}$  to  $F^{bg}$  and produce the transformed feature map  $\hat{F}_k^{bg}$ . Then, we combine  $K$  transformed feature maps and the original feature map based on the predicted  $K$  part masks and one watermark-free mask, giving rise to the final feature map  $\hat{F}^{bg}$ :
+
+$$
+\hat {\boldsymbol {F}} ^ {b g} = \sum_ {k = 1} ^ {K} \hat {\boldsymbol {M}} _ {k} ^ {p t} \circ \hat {\boldsymbol {F}} _ {k} ^ {b g} + \hat {\boldsymbol {M}} _ {K + 1} ^ {p t} \circ \boldsymbol {F} ^ {b g}, \tag {5}
+$$
+
+in which  $\circ$  means element-wise product. Although similar dynamic kernel has been used in [56], our method is vastly different from theirs in the following aspects: 1) [56] uses the pooled watermark feature to predict the entire convolution kernel, while we use adapted query embeddings to modulate the base convolution weights; 2) [56] only predicts a single convolution kernel for the entire watermarked region, whereas we use  $K$  modulated convolution weights to cope with  $K$  part categories adaptively.
+
+The final feature map  $\hat{F}^{bg}$  is used to predict the background image  $\hat{I}^{bg}$ . We combine  $\hat{I}^{bg}$  with the input watermarked image  $I^{wm}$  using the predicted watermark mask  $\hat{M}^{wm}$ , yielding the final output  $\hat{I}^{bg} = \hat{M}^{wm} \circ \hat{I}^{bg} + (1 - \hat{M}^{wm}) \circ I^{wm}$ . Following [33, 56], we regularize the final output with  $\mathcal{L}_1$  loss and perceptual loss [26]:
+
+$$
+\mathcal {L} _ {b g} = \| \tilde {\boldsymbol {I}} ^ {b g} - \boldsymbol {I} ^ {b g} \| _ {1} + \sum_ {d = 1} ^ {3} \| \Phi_ {d} (\tilde {\boldsymbol {I}} ^ {b g}) - \Phi_ {d} (\boldsymbol {I} ^ {b g}) \| _ {1}, \tag {6}
+$$
+
+where  $\Phi_d(\cdot)$  represents the activation map of  $d$ -th layer in VGG16 [44].
+
+So far, all the losses can be summarized as
+
+$$
+\mathcal {L} _ {a l l} = \mathcal {L} _ {m s} + \mathcal {L} _ {l e} + \lambda \mathcal {L} _ {b g}, \tag {7}
+$$
+
+in which  $\lambda$  is a hyper-parameter.
+
+# 4. Experiments
+
+# 4.1. Datasets and Implementation Details
+
+We conduct experiments on two benchmark datasets: Colored Large-scale Watermark Dataset (CLWD) [38] and LOGO30K Dataset [8]. Both datasets are constructed with colored complex watermarks, which are challenging for watermark removal task.
+
+CLWD [38]: In CLWD, the training set has 60,000 images with 160 different watermarks and the test set has 10,000
+
+images with 40 different watermarks. The watermarks are collected from public image websites. The background images in the training (resp., test) set are randomly chosen from the training (resp., test) set of PASCAL VOC2012 [13]. When superimposing the collected watermarks on the background images, the location, scale, rotation, and transparency of watermarks are randomly determined, with the watermark transparency in the range of [0.3, 0.7].
+
+LOGO30K [8]: In LOGO30K, the training set has 28, 352 images and the test set has 4, 051 images. The watermarks collected from Internet include more than 1k famous logos. The background images come from the VAL2014 subset of MSCOCO [36] dataset. When creating watermarked images, the watermark transparency is set in the range of [0.35, 0.85].
+
+Following previous methods [38, 33], we use PSNR, SSIM, RMSE, and  $\mathrm{RMSE}_w$  to evaluate the restored background, in which  $\mathrm{RMSE}_w$  means RMSE calculated within the watermarked region. We use IoU and  $\mathbf{F}_1$  to evaluate the predicted watermark mask.
+
+Our method is implemented with Pytorch [41]. The input image size is set to  $256 \times 256$ . During training, we choose Adam [29] optimizer with the initial learning rate being 0.001. All methods are trained and evaluated on Ubuntu 4.18.0, with 512GB memory, Intel(R) Xeon(R) Platinum 8358 CPU, and one A100 SXM4 40GB GPU. The encoder  $E$  has five encoder blocks and the decoder  $D^{ms} / D^{bg}$  has four decoder blocks, in which the encoder and decoder block structures are borrowed from [33]. The transformer block  $T$  has two transformer layers [45]. We set  $K = 8$  and  $\lambda = 10$  by default.
+
+# 4.2. Comparison with Baselines
+
+We compare with two groups of baselines: 1) the general methods for image content removal; 2) the watermark removal methods.
+
+For the first group of methods, we compare with recent methods MPRNet [54], UFormer [49], and BIDNet [20]. We also include UNet [42] for general image-to-image translation as a baseline. For the second group of methods, we compare with the following watermark removal methods: Li et al. [31], Cao et al. [2], WDNet [38], BVMR [23], SplitNet [8], SLBR [33], DKSP [56].
+
+We first evaluate the restored backgrounds from different methods, which are summarized in Table 1. We observe that the methods specifically designed for watermark removal are generally better than general content removal methods [54, 49, 20]. Among the watermark removal methods, [8, 33, 56] achieve competitive performance due to the multi-task framework. Our method significantly outperforms the existing methods, including [56] which uses additional semantic information. The superiority of our method is attributed to the fined-grained watermark removal ability
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">CLWD</td><td colspan="4">LOGO30K</td></tr><tr><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td></tr><tr><td>U-Net [42]</td><td>23.21*</td><td>0.8567*</td><td>19.35*</td><td>48.43*</td><td>24.64*</td><td>0.8816</td><td>17.84</td><td>43.29*</td></tr><tr><td>MPRNet [54]</td><td>35.19</td><td>0.9725</td><td>5.52</td><td>20.76</td><td>37.81</td><td>0.9866</td><td>4.26</td><td>20.67</td></tr><tr><td>UFormer [49]</td><td>34.07</td><td>0.9784</td><td>6.29</td><td>25.66</td><td>39.84</td><td>0.9936</td><td>3.34</td><td>18.68</td></tr><tr><td>BIDNet [20]</td><td>35.02</td><td>0.9709</td><td>5.66</td><td>21.75</td><td>36.63</td><td>0.9829</td><td>4.83</td><td>24.29</td></tr><tr><td>Li et al. [31]</td><td>27.96*</td><td>0.9161*</td><td>12.63*</td><td>46.80*</td><td>30.51*</td><td>0.9312</td><td>10.51</td><td>39.11*</td></tr><tr><td>Cao et al. [2]</td><td>29.04*</td><td>0.9363*</td><td>10.36*</td><td>41.21*</td><td>32.18*</td><td>0.9654</td><td>8.20</td><td>35.16*</td></tr><tr><td>WDNet [38]</td><td>35.53*</td><td>0.9738*</td><td>5.11*</td><td>17.27*</td><td>39.15*</td><td>0.9874</td><td>3.49</td><td>15.94*</td></tr><tr><td>BVMR [23]</td><td>35.89*</td><td>0.9734*</td><td>5.02*</td><td>18.71*</td><td>38.28*</td><td>0.9852*</td><td>3.52</td><td>16.72*</td></tr><tr><td>SplitNet [8]</td><td>37.41*</td><td>0.9787*</td><td>4.23*</td><td>15.25*</td><td>41.27*</td><td>0.9910*</td><td>3.12</td><td>14.85*</td></tr><tr><td>SLBR [33]</td><td>38.28*</td><td>0.9814*</td><td>3.76*</td><td>14.07*</td><td>41.50*</td><td>0.9914</td><td>2.98</td><td>14.69*</td></tr><tr><td>DKSP† [56]</td><td>38.84*</td><td>0.9813</td><td>3.53</td><td>12.16*</td><td>42.16*</td><td>0.9921</td><td>2.77</td><td>13.78*</td></tr><tr><td>Ours</td><td>39.45</td><td>0.9823</td><td>3.19</td><td>11.28</td><td>42.57</td><td>0.9923</td><td>2.46</td><td>12.44</td></tr></table>
+
+Table 1. The results of restored backgrounds of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [8, 33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface.
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">CLWD</td><td colspan="2">LOGO30K</td></tr><tr><td>IoU↑</td><td>F1↑</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>WDNet [38]</td><td>0.6120*</td><td>0.7240*</td><td>0.6821*</td><td>0.8010*</td></tr><tr><td>BVMR [23]</td><td>0.7021*</td><td>0.7871*</td><td>0.7287*</td><td>0.8305*</td></tr><tr><td>SplitNet [8]</td><td>0.7196*</td><td>0.8027*</td><td>0.7414*</td><td>0.8411*</td></tr><tr><td>SLBR [33]</td><td>0.7463*</td><td>0.8234*</td><td>0.7858*</td><td>0.8647*</td></tr><tr><td>DKSP†[56]</td><td>0.7730*</td><td>0.8480*</td><td>0.8016*</td><td>0.8770*</td></tr><tr><td>Ours</td><td>0.7909</td><td>0.8634</td><td>0.8185</td><td>0.8898</td></tr></table>
+
+Table 2. The results of predicted watermark masks of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface.
+
+by considering fine-grained part categories.
+
+We also compare the quality of watermark masks predicted by different methods in Table 2. We only compare with those methods [38, 23, 8, 33, 56] which predict watermark masks. Again, our method achieves the best results on both datasets.
+
+We show the visual comparison between different methods in Figure 3. We compare with the competitive baselines WDNet [38], SplitNet [8], SLBR [33], DKSP [56]. We show both predicted watermark masks and restored backgrounds. Our method can predict accurate and complete watermark masks, while the baseline methods could only predict incomplete mask, when the watermark is composed of multiple parts. This is because we use adapted query embeddings corresponding to different part categories to produce multiple part masks, which can cover the complete watermarked region. For background restoration, since baselines fail to predict complete watermark masks, they cannot erase the whole watermark and the recovered backgrounds are far below expectation. With the predicted complete watermark masks, our method can successfully repair the en
+
+<table><tr><td rowspan="2">#</td><td rowspan="2">T</td><td rowspan="2">Dms</td><td rowspan="2">Dbg</td><td colspan="4">Evaluation Metrics</td></tr><tr><td>PSNR↑</td><td>RMSEw↓</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>1</td><td></td><td>-q</td><td>- PFM</td><td>40.08</td><td>16.60</td><td>0.7474</td><td>0.8325</td></tr><tr><td>2</td><td></td><td>- Lle</td><td>- PFM</td><td>40.20</td><td>16.54</td><td>0.7576</td><td>0.8409</td></tr><tr><td>3</td><td></td><td>+</td><td>-PFM</td><td>40.23</td><td>16.48</td><td>0.7893</td><td>0.8674</td></tr><tr><td>4</td><td></td><td>+</td><td>+</td><td>41.67</td><td>13.85</td><td>0.8023</td><td>0.8772</td></tr><tr><td>5</td><td></td><td>+</td><td>SB</td><td>41.04</td><td>14.84</td><td>0.7928</td><td>0.8699</td></tr><tr><td>6</td><td></td><td>+</td><td>DK</td><td>40.82</td><td>15.51</td><td>0.7896</td><td>0.8679</td></tr><tr><td>7</td><td></td><td>+</td><td>-g</td><td>40.47</td><td>16.43</td><td>0.7895</td><td>0.8672</td></tr><tr><td>8</td><td>+</td><td>+</td><td>+</td><td>42.57</td><td>12.44</td><td>0.8185</td><td>0.8898</td></tr></table>
+
+Table 3. The ablation study results on LOGO30K [8]. "SB" is short for scale/bias, "DK" is short for dynamic kernel, and "q" stands for query embeddings.
+
+tire watermarked region by handling different local parts adaptively, producing visually pleasant backgrounds closer to the ground-truth.
+
+# 4.3. Ablation Studies
+
+We conduct ablation studies to analyze the effectiveness of each component and loss term, which are summarized in Table 3. We first build a basic model without using query embeddings or PFM module in row 1, in which case  $\pmb{F}^{ms}$  directly outputs the watermark mask and  $\pmb{F}^{bg}$  directly outputs the restored background. Then, we use  $K + 1$  query embedding to interact with  $\pmb{F}^{ms}$  to predict mask without low-entropy loss  $\mathcal{L}_{le}$ . The obtained mask results in row 2 are better than those in row 1, which proves the effectiveness of query-based mask prediction. However, we observe that the predicted masks for different part categories are prone to resemble each other. Thus, we add  $\mathcal{L}_{le}$  to enforce  $K$  part masks to be different from each other. By comparing row 3 with row 2, we observe that the mask results are significantly improved by discovering multiple part
+
+watermarked image
+
+WDNet
+
+SplitNet
+
+SLBR
+
+DKSP
+
+Ours
+
+Ground-truth
+
+![](images/aa389343a6d1017c71f7832c819e7438ba2756ea6d6402d7612459182ff482af.jpg)  
+Figure 3. From left to right, we show the watermarked image, the results of WDNet [38], SplitNet [8], SLBR [33], DKSP [56], our method, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask. The top two examples are from LOGO30K [8] and the bottom two examples are from CLWD [38].
+
+categories. Based on row 3, we insert our PFM block into the background decoder, leading to row 4. We observe that the background results are greatly improved. In the mean
+
+while, the mask results are also improved, which might benefit from the information sharing between two tasks.
+
+Based on row 4, we explore several variants of our PFM
+
+![](images/c6306fa28550a4d7b5270110b05c5095533eb73fdb6449ef07fbda1689158494.jpg)  
+Figure 4. From left to right, we show the watermarked image, the results of row 1, 2, 3, 4, 8 in Table 3, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask.
+
+block. Recall that we use the dynamic strategy proposed in [28]. We also try some alternative ways of dynamic feature transformation. One alternative is dynamic convolution similar to [33]. Specifically, we use adapted query embeddings to predict dynamic convolution kernels for different part categories, which are applied to the corresponding regions in the feature map. Another alternative is predicting scales and biases similar to [27]. Specifically, we use adapted query embeddings to predict channel-wise scales and biases for different part categories, which are applied to the corresponding local regions in the feature map. The comparison among row 4, row 5, and row 6 shows that our choice in the method is the optimal one. Moreover, we remove the guidance from query embeddings and treat the input channel scales as learnable parameters. Without the guidance of query embeddings, the learnt dynamic convolution weights are less effective and thus the performance (row 7) becomes worse than those with guidance (row 4-6).
+
+At last, we add the transformer block  $T$  to adapt query embeddings to each specific image. The obtained results in row 8 verify the validity of adapted query embeddings, because the local parts from different images belonging to the same part category may still have highly contrastive visual appearances.
+
+In Figure 4, we show the results of row 1, 2, 3, 4, 8 in Table 3. From row 1 to row 4, although the quality of
+
+restored backgrounds are getting better, the watermarks are not completely erased and residual watermark traces can be obviously seen. When using our full method equipped with all modules, row 8 achieves the best results that are close to the ground-truth backgrounds.
+
+# 5. Conclusion
+
+In this work, we have proposed a query-based multi-task framework for visible watermark removal, in which query embeddings corresponding to different part categories are jointly used for fine-grained mask prediction and background reconstruction. Our network can split one watermarked region into multiple local parts and restore different local parts adaptively. By considering fine-grained watermarked parts, our network surpasses the existing methods on two benchmark datasets.
+
+# Acknowledgement
+
+The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300).
+
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+                                    "content": "Li Niu*, Xing Zhao, Bo Zhang, Liqing Zhang  \nDepartment of Computer Science and Engineering, MoE Key Lab of Artificial Intelligence, Shanghai Jiao Tong University"
+                                }
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+                                    "content": "{ustcnewly,1033874657,bo-zhang}@sjtu.edu.cn,zhang-lq@cs.sjtu.edu.cn"
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+                                }
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+                                    "type": "text",
+                                    "content": "Visible watermark removal aims to erase the watermark from watermarked image and recover the background image, which is a challenging task due to the diverse watermarks. Previous works have designed dynamic network to handle various types of watermarks adaptively, but they ignore that even the watermarked region in a single image can be divided into multiple local parts with distinct visual appearances. In this work, we advance image-specific dynamic network towards part-specific dynamic network, which discovers multiple local parts within the watermarked region and handle them adaptively. Specifically, we propose a query-based multi-task framework, in which part query embeddings are jointly used in two branches to predict part masks and restore watermarked parts. Extensive experiments demonstrate the effectiveness of our fine-grained watermark removal network."
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+                                    "content": "1. Introduction"
+                                }
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+                                    "content": "Overlaying visible watermark on a digital image has been a prevalent way to claim copyright and declare ownership. As its reverse process, visual watermark removal [33, 56] has attracted more and more research interest, which can verify and promote the resilience of overlaid watermarks. Specifically, visible watermark removal aims to erase the watermark and reconstruct the watermark-free (background) image. One major challenge of watermark removal task is that the watermarks are very diversified, in terms of different locations, patterns, transparencies, and so on. Recent works [33, 56] realize this issue and develop dynamic networks to cope with diversified watermarks adaptively. For example, [33] extracts the feature of watermarked region and appends it to original feature map as extra guidance. [56] also extracts the feature of watermarked region, but uses it to generate dynamic convolution kernel to manipulate the original feature map. Although [33, 56] have"
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+                                            "content": "Figure 1. Two examples of watermarked images associated with their background images, watermark masks, and watermarks. Visible watermark removal aims to erase the watermark and reconstruct the background image."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "achieved significant improvement over previous methods by adaptively coping with various types of watermarks, they still treat the watermarked region in an image as a whole, disregarding the fact that even the watermarked region in a single image could be divided into multiple parts with vastly distinct appearances. For example, the watermarked region in Figure 1(a) consists of one pattern and two lines of texts, and the watermarked region in Figure 1(b) consists of one symbol, one line of text, and extra curves. Moreover, when a watermark is overlaid on a background image with certain transparency, one part (e.g., one line of text) in the watermarked region could also exhibit diverse colors due to the colorful background, which makes the appearance of watermarked region even more complicated."
+                                }
+                            ]
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+                                    "content": "In this work, inheriting the spirit of previous works [33, 56], we take a further step along the path of dynamic network. Specifically, we not only cope with the watermarked regions in different images adaptively, but also cope with different watermarked parts in one image adaptively, which advances image-specific dynamic network towards part-specific dynamic network. We adopt the multi-task framework used in previous works [33, 56], which contains one encoder and two encoders. The mask decoder accounts"
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+                                    "type": "text",
+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+                                }
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+                                    "type": "text",
+                                    "content": "*Corresponding author."
+                                }
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+                                    "type": "text",
+                                    "content": "for localizing the watermark and the background decoder accounts for recovering the watermarked region. Following previous works [33, 56], we also add skip connections [42] linking one encoder with two decoders. To cope with different watermarked parts adaptively, we need to localize them in the mask decoder and repair them in the background decoder. Inspired by query-based network structures in previous works [3, 6], we introduce query embeddings into our multi-task framework, which establishes a connection between mask decoder and background decoder."
+                                }
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+                                    "type": "text",
+                                    "content": "In particular, assuming that there are in total "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " fine-grained categories of watermarked parts, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " part query embeddings and one watermark-free query embedding interact with the encoder feature map through a transformer [45] block to produce adapted query embeddings. "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K + 1"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " adapted query embeddings are expected to contain the part-relevant information and watermark-free information of one specific image. Then, we apply "
+                                },
+                                {
+                                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " adapted query embeddings to mask decoder and background decoder. In the mask decoder, similar to [6], we calculate the similarity between "
+                                },
+                                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " adapted query embeddings with the last feature map in the mask decoder to generate "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " part masks corresponding to "
+                                },
+                                {
+                                    "bbox": [
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+                                        193,
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+                                    "type": "inline_equation",
+                                    "content": "K"
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+                                {
+                                    "bbox": [
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+                                        193,
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+                                    "type": "text",
+                                    "content": " part categories and one watermark-free mask. Different from [6], we do not have ground-truth masks for "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K"
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " part categories. Hence, we enforce the union of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " predicted part masks to approach the ground-truth watermark mask and employ low-entropy loss [17] to push apart "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " predicted part masks. In the background decoder, we use "
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " adapted part query embeddings to produce "
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+                                    "content": " modulated convolution kernels for "
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+                                    "type": "text",
+                                    "content": " part categories, which act upon "
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+                                    "content": " predicted part masks. In this way, we can restore different watermarked parts adaptively and achieve better restoration effect."
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+                                    "content": "We conduct experiments on two benchmark watermark removal datasets: CLWD [38] and LOGO30K [8], to verify the effectiveness of our proposed method. Our contributions can be summarized as follows. 1) We are the first to consider fine-grained part categories in the visible watermark removal task, which advances image-specific dynamic network towards part-specific dynamic network; 2) We design a query-based multi-task framework, in which the adapted query embeddings are jointly used to localize different part categories in the mask decoder and restore the corresponding local parts in the background decoder; 3) Extensive experiments on two benchmark datasets demonstrate the effectiveness of our proposed network."
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+                                    "content": "2. Related Work"
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+                                    "content": "2.1. Visible Watermark Removal"
+                                }
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+                },
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+                                    "content": "Visual watermarking prevails in protecting the digital image copyright, by superimposing a watermark on the background image. As its adversarial task, visible wa"
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+                            ]
+                        }
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+                                    "content": "termark removal can enhance the resilience of watermark. Early methods [31, 2] proposed GAN [16]-based network structures for watermark removal. [38, 23] formulated watermark removal under a multi-task framework, which predicts watermark-free image, watermark mask, and watermark pattern collaboratively. [8] designed a two-stage multi-task framework with attention mechanism and refinement stage. [33] designed self-calibrated mask refinement for adaptive mask prediction and mask-guided background enhancement. [56] used semantic similarity to propagate useful information and applied dynamic convolution to handle diverse watermarks. [14] designed a novel architecture for better information extraction in the long range. [37] proposed watermark vaccine, which adds invisible perturbation to the watermarked images to attack against the existing watermark removal methods."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "However, the above methods are still struggling to tackle diversified and complicated watermarked regions. Moreover, they ignore that even the watermarked region in a single watermarked image could be decomposed into multiple parts. In this work, we consider fine-grained part categories by localizing and restoring different local parts adaptively."
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+                            ]
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+                                    "content": "2.2. Image Content Removal"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "Image content removal or image restoration includes myriads of tasks such as image deraining [46, 51], image dehazing [7, 12, 55], shadow removal [9, 11], and so on. Besides the research works in each field, there are also some general methods [49, 20, 54, 53, 57, 40, 32] for universal image content removal or image restoration. To name a few, [49] proposed a transformer block with locally enhanced window and a learnable multi-scale restoration modulator. In [20], they proposed a general blind image decomposition network. In [54], they proposed a multi-stage progressive image restoration architecture. In visible watermark removal task, the removal target is watermark with diverse colors, patterns, locations, transparencies, etc, making it a challenging and unique task."
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+                                    "content": "2.3. Vision Transformer"
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+                                    "type": "text",
+                                    "content": "Transformer has been applied to a wide range of computer vision tasks like detection [3, 58], segmentation [48, 47, 6], and pose estimation [24, 35]. Transformer has also been used in some low-level computer vision tasks like image super-resolution [50, 34, 52, 1], image denoising and image deraining [4, 49], image harmonization [18], style transfer [10]. Our mask decoder is similar to [6], but we do not have ground-truth part masks. More importantly, our network is query-based multi-task framework, in which the adapted query embeddings are jointly used in the mask decoder and the background decoder."
+                                }
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+                                    "content": "2.4. Dynamic Network"
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+                                    "content": "Dynamic networks have been widely used in deep learning image processing tasks, which has been discussed and categorized in [21]. According to [21], dynamic parameters can be classified into parameter adjustment [22, 15], weight prediction [43, 25, 39, 19], and dynamic features [30, 5]. Our model uses adapted query embeddings to control the kernel weights, which belongs to weight prediction. This is the first work to handle different watermarked parts dynamically."
+                                }
+                            ]
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+                    ],
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+                                    "content": "3. Our Method"
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+                                    "content": "3.1. Overall Network Structure"
+                                }
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+                                    "type": "text",
+                                    "content": "When superimposing one watermark on a watermark-free (background) image "
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+                                    "content": ", we can obtain the watermarked image "
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+                                    "type": "text",
+                                    "content": " and its corresponding watermark mask "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". Visible watermark removal task aims to localize and recover the watermarked region in "
+                                },
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+                                    "type": "text",
+                                    "content": ". Since visible watermark removal task needs to handle two tasks simultaneously: watermark mask prediction and background image restoration, which falls into the realm of multi-task learning. Thus, previous works [33, 56] usually adopt the multi-task framework with one encoder shared by different tasks and multiple decoders accounting for different tasks. In this work, we also employ one encoder "
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+                                    "content": "\\{D^{ms}, D^{bg}\\}"
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+                                    "type": "text",
+                                    "content": ". The encoder "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E"
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+                                    "type": "text",
+                                    "content": " consists of five encoder blocks. The decoder "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "D^{bg}/D^{ms}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " consists of four decoder blocks, in which the first decoder block is shared by two decoders. The structures of encoder and decoder blocks are inherited from [23, 33]. Following previous works [33, 56], we also add skip connections [42] to link one encoder with two decoders."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "To cope with diversified watermarked parts, we learn part query embeddings corresponding to different part categories, which are jointly used by mask decoder and background decoder. For the mask decoder, we calculate the similarity between query embeddings and mask decoder feature map, yielding part masks for different part categories. For the background decoder, the query embeddings are used to modulate convolution weights for different part categories, which act upon the background decoder feature map within the corresponding local parts specified by part masks. Next, we will introduce the details of part query embeddings in Section 3.2 and describe their usage in the mask (resp., background) decoder in Section 3.3 (resp., 3.4)."
+                                }
+                            ]
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+                    ],
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+                                    "content": "3.2. Part Query Embeddings"
+                                }
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+                                    "type": "text",
+                                    "content": "Assuming that the local parts of watermarked regions can be classified into "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " part categories based on dis"
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+                                    "type": "text",
+                                    "content": "tinct visual appearances, we use "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " part query embeddings "
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+                                        167
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{q_k|_{k = 1}^K\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "text",
+                                    "content": " to represent the prior knowledge (e.g., color, scale, pattern) of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "text",
+                                    "content": " part categories. Additionally, we introduce a watermark-free query embedding "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{K + 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "text",
+                                    "content": " for the watermark-free category. These "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K + 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "text",
+                                    "content": " query embeddings can be used to predict the watermark mask and restore the watermarked region, establishing the connection between the mask decoder and the background decoder."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
+                        168,
+                        546,
+                        360
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                168,
+                                546,
+                                360
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": "Even for the same part category, the local parts in different images are likely to have different visual appearances. Similarly, the watermark-free regions in different images also vary dramatically. To better cope with diverse images, we further adapt query embeddings to each specific image. Specifically, we use encoder "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " to extract the feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{en}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " from watermarked image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{I}^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": ". Each query embedding "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{q}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " interacts with the encoder feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{en}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " through a transformer [45] block "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": ", during which "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{q}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " serves as key and the pixel-wise feature vectors in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{en}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " serve as keys/values, producing an adapted query embedding "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{q}_k^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": ". The adapted query embeddings are supposed to incorporate the relevant information from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{I}^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " and become well-tailored to this image. Next, we will introduce how the adapted query embeddings "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\pmb{q}_k^{\\prime}|_{k = 1}^{K + 1}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        168,
+                                        546,
+                                        360
+                                    ],
+                                    "type": "text",
+                                    "content": " are used to predict fine-grained watermark part masks and restore local parts accordingly."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        306,
+                        367,
+                        429,
+                        378
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                367,
+                                429,
+                                378
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        367,
+                                        429,
+                                        378
+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Part Mask Prediction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        384,
+                        545,
+                        616
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                384,
+                                545,
+                                616
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": "The mask decoder "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " targets at predicting the masks for different part categories and watermark-free category. We denote the last feature map in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ". Analogous to [6], we obtain the masks for different part categories and watermark-free category by calculating the similarity between each adapted query embedding and pixel-wise feature vectors in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ". Specifically, for the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": "-th adapted query embedding "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{k}^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ", we project it to the same space as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " using a fully-connected (FC) layer and calculate its dot product with all pixel-wise feature vectors in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ". We perform softmax normalization on the dot product results over "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K + 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " query embeddings, leading to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " part masks "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{M}_{k}^{pt}|_{k = 1}^{K}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " and one watermark-free mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}_{K + 1}^{pt}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that we only have the ground-truth mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " for the entire watermark region, and there is no ground-truth supervision for each part mask. Thus, we calculate the sum of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " part masks as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}^{wm} = \\sum_{k = 1}^{K}\\hat{M}_{k}^{pt}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ", which is equivalent to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1 - \\hat{M}_{K + 1}^{pt}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " is enforced to be close to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
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+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        384,
+                                        545,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " using binary cross-entropy loss:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        329,
+                        624,
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+                        668
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        329,
+                                        624,
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+                                        668
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {m s} = - \\sum_ {i, j} [ M (i, j) \\log \\hat {M} ^ {w m} (i, j) \\tag {1} \\\\ + (1 - M (i, j)) \\log (1 - \\hat {M} ^ {w m} (i, j)) ], \\\\ \\end{array}",
+                                    "image_path": "1507ef58d084bdeaf85f4536370ca387b297d2cac19b090c1da7b00ae1e2ea46.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        306,
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+                        700
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                675,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
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+                                        700
+                                    ],
+                                    "type": "text",
+                                    "content": "in which "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M(i,j)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "text",
+                                    "content": " (resp., "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}^{wm}(i,j)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "text",
+                                    "content": ") is the "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(i,j)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "text",
+                                    "content": "-th entry in "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "text",
+                                    "content": " (resp., "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        675,
+                                        545,
+                                        700
+                                    ],
+                                    "type": "text",
+                                    "content": ")."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        318,
+                                        701,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "When only using "
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        701,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        318,
+                                        701,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ", we observe that the predicted"
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 2. Our network consists of one encoder "
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+                                            "type": "text",
+                                            "content": ". We omit the skip connections in this figure for brevity. The transformer block "
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+                                            "type": "text",
+                                            "content": " outputs the adapted query embeddings, which interact with mask decoder feature to produce part masks and interact with background decoder feature through our PFM block to restore the background image. The detailed architecture of PFM block is shown in the right subfigure."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": " part masks are all close to each other, failing to distinguish different parts. To address this issue, we additionally employ low-entropy loss [17] for the predicted part masks, which ensures that each watermarked pixel is classified into certain part categories instead of uniformly distributed over all part categories. Formally, we apply low-entropy loss to the watermarked pixels:"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {l e} = - \\sum_ {i, j} M (i, j) \\sum_ {k = 1} ^ {K + 1} \\hat {M} _ {k} ^ {p t} (i, j) \\log \\hat {M} _ {k} ^ {p t} (i, j), \\tag {2}",
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+                                    "type": "text",
+                                    "content": "in which "
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+                                    "type": "inline_equation",
+                                    "content": "M(i,j) = 1"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (resp., "
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+                                    "type": "inline_equation",
+                                    "content": "M(i,j) = 0"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ") indicates the watermarked (resp., watermark-free) pixels and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}_k^{pt}(i,j)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "(i,j)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th entry in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}_k^{pt}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that lower entropy implies higher concentration. In addition, the probabilities that watermarked pixels belong to watermark-free category have been suppressed to zero based on Eqn. 1. Therefore, the probabilities that watermarked pixels belong to different part categories are pushed to be concentrated based on Eqn. 2."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Although the procedure of our query-based mask prediction resembles that in [6] to some extent, our method has several major differences: 1) [6] has ground-truth masks, which are inaccessible in our task. Hence, we design "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{ms}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{le}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " to supervise the predicted masks; 2) Our predicted part masks and watermark-free mask are also used in the background decoder to help restore the background, rendering a novel query-based multi-task framework in which two tasks jointly use the adapted query embeddings."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.4. Part-aware Background Restoration"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The background decoder "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "D^{bg}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " targets at predicting the background image. Because different part categories have"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "quite distinct visual appearances, we conjecture that restoring different local parts in the watermarked region adaptively could achieve better restoration effect. Therefore, we design a novel Part-aware Feature Modulation (PFM) block, which utilizes the adapted query embeddings and the masks predicted by mask decoder to restore different local parts adaptively. The adapted query embeddings and predicted masks solve the problem of how and where to restore, respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We denote the last feature map in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D^{bg}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We expect to transform the feature map in the watermarked region while keeping the watermark-free region unchanged, since only the watermarked region needs to be restored. To transform different local parts in the watermarked region adaptively, we opt for the dynamic feature transformation technique proposed in [28], which dynamically modulates convolution weights. In our work, we use "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " adapted part query embeddings to produce "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " modulated convolution weights, which are applied to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{bg}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " separately to acquire "
+                                },
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " transformed feature maps "
+                                },
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{\\pmb{F}}_k^{bg}|_{k = 1}^K\\}"
+                                },
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+                                    "type": "text",
+                                    "content": "."
+                                }
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+                                    "type": "text",
+                                    "content": "Specifically, we have learnable base convolution weights "
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+                                {
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+                                    "type": "text",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{W}(m,n,l)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the weight for the "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th input channel, "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th output channel, and the "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th spatial location. Then, we pass each adapted query embedding "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{q}_k^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " through one FC layer to predict the scale vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{s}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " corresponding to input channels, which are used to modulate the base convolution weights:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\bar {W} _ {k} ^ {\\prime} (m, n, l) = \\bar {W} (m, n, l) \\cdot s _ {k} (m), \\tag {3}",
+                                    "image_path": "49700886c71f753a7febc5a79d8ae4896faf651fd2b5df3dd156d2a8c98cb6ae.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "s_k(m)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        689,
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+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " is the "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "m"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th entry in "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        689,
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+                                    "type": "inline_equation",
+                                    "content": "s_k"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (scale for the "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        689,
+                                        545,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        689,
+                                        545,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th input channel) and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        689,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{W}_k'(m,n,l)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        689,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " is the modulated weight."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
+            "discarded_blocks": [
+                {
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+                                    "type": "text",
+                                    "content": "12773"
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+                {
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": "Next, we normalize the modulated weights following [28]:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\bar {W} _ {k} ^ {\\prime \\prime} (m, n, l) = \\frac {\\bar {W} _ {k} ^ {\\prime} (m , n , l)}{\\sqrt {\\sum_ {m , l} \\bar {W} _ {k} ^ {\\prime} (m , n , l) ^ {2} + \\epsilon}}, \\tag {4}",
+                                    "image_path": "6a27ac2dd94cb43f40cfe2b8932b9bb660168e7c4a8991c83c751403e8f823ad.jpg"
+                                }
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+                {
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+                    "angle": 0,
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+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
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+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": "in which "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " is a small constant to avoid numerical error. For more details of convolution weights modulation, please refer to [28]. We apply the modulated convolution weights "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{W}_k^{\\prime \\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
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+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
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+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " and produce the transformed feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{F}_k^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, we combine "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " transformed feature maps and the original feature map based on the predicted "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": " part masks and one watermark-free mask, giving rise to the final feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
+                                        287,
+                                        228
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{F}^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        228
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                    "bbox": [
+                                        74,
+                                        236,
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+                                        269
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {\\boldsymbol {F}} ^ {b g} = \\sum_ {k = 1} ^ {K} \\hat {\\boldsymbol {M}} _ {k} ^ {p t} \\circ \\hat {\\boldsymbol {F}} _ {k} ^ {b g} + \\hat {\\boldsymbol {M}} _ {K + 1} ^ {p t} \\circ \\boldsymbol {F} ^ {b g}, \\tag {5}",
+                                    "image_path": "1273e77176458471cfe540beb363a4e3922ab9b86de19fdba86e6a1fae133506.jpg"
+                                }
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+                    ],
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+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "in which "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\circ"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " means element-wise product. Although similar dynamic kernel has been used in [56], our method is vastly different from theirs in the following aspects: 1) [56] uses the pooled watermark feature to predict the entire convolution kernel, while we use adapted query embeddings to modulate the base convolution weights; 2) [56] only predicts a single convolution kernel for the entire watermarked region, whereas we use "
+                                },
+                                {
+                                    "bbox": [
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+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        276,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": " modulated convolution weights to cope with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        276,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        276,
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+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": " part categories adaptively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": "The final feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{F}^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": " is used to predict the background image "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{I}^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": ". We combine "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{I}^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": " with the input watermarked image "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": " using the predicted watermark mask "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": ", yielding the final output "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{I}^{bg} = \\hat{M}^{wm} \\circ \\hat{I}^{bg} + (1 - \\hat{M}^{wm}) \\circ I^{wm}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": ". Following [33, 56], we regularize the final output with "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        384,
+                                        287,
+                                        456
+                                    ],
+                                    "type": "text",
+                                    "content": " loss and perceptual loss [26]:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {b g} = \\| \\tilde {\\boldsymbol {I}} ^ {b g} - \\boldsymbol {I} ^ {b g} \\| _ {1} + \\sum_ {d = 1} ^ {3} \\| \\Phi_ {d} (\\tilde {\\boldsymbol {I}} ^ {b g}) - \\Phi_ {d} (\\boldsymbol {I} ^ {b g}) \\| _ {1}, \\tag {6}",
+                                    "image_path": "fc43a78c1470f071e15d53bce69688c074ffc8862f6c1661ee7707d9ed8cc976.jpg"
+                                }
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+                    "lines": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Phi_d(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        504,
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the activation map of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th layer in VGG16 [44]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "So far, all the losses can be summarized as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {a l l} = \\mathcal {L} _ {m s} + \\mathcal {L} _ {l e} + \\lambda \\mathcal {L} _ {b g}, \\tag {7}",
+                                    "image_path": "83cd0d8a6d7745283380fd790b2978d97dbf645433a7d072a1e12537151f178b.jpg"
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+                                    "type": "text",
+                                    "content": "in which "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        570,
+                                        178,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " is a hyper-parameter."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4.1. Datasets and Implementation Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        46,
+                        630,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We conduct experiments on two benchmark datasets: Colored Large-scale Watermark Dataset (CLWD) [38] and LOGO30K Dataset [8]. Both datasets are constructed with colored complex watermarks, which are challenging for watermark removal task."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "CLWD [38]: In CLWD, the training set has 60,000 images with 160 different watermarks and the test set has 10,000"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        545,
+                        167
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        167
+                                    ],
+                                    "type": "text",
+                                    "content": "images with 40 different watermarks. The watermarks are collected from public image websites. The background images in the training (resp., test) set are randomly chosen from the training (resp., test) set of PASCAL VOC2012 [13]. When superimposing the collected watermarks on the background images, the location, scale, rotation, and transparency of watermarks are randomly determined, with the watermark transparency in the range of [0.3, 0.7]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        304,
+                        168,
+                        545,
+                        251
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        304,
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+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": "LOGO30K [8]: In LOGO30K, the training set has 28, 352 images and the test set has 4, 051 images. The watermarks collected from Internet include more than 1k famous logos. The background images come from the VAL2014 subset of MSCOCO [36] dataset. When creating watermarked images, the watermark transparency is set in the range of [0.35, 0.85]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        304,
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+                        545,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
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+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": "Following previous methods [38, 33], we use PSNR, SSIM, RMSE, and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{RMSE}_w"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " to evaluate the restored background, in which "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{RMSE}_w"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " means RMSE calculated within the watermarked region. We use IoU and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        252,
+                                        545,
+                                        312
+                                    ],
+                                    "type": "text",
+                                    "content": " to evaluate the predicted watermark mask."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        304,
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+                        545,
+                        445
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
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+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": "Our method is implemented with Pytorch [41]. The input image size is set to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "256 \\times 256"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": ". During training, we choose Adam [29] optimizer with the initial learning rate being 0.001. All methods are trained and evaluated on Ubuntu 4.18.0, with 512GB memory, Intel(R) Xeon(R) Platinum 8358 CPU, and one A100 SXM4 40GB GPU. The encoder "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": " has five encoder blocks and the decoder "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D^{ms} / D^{bg}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": " has four decoder blocks, in which the encoder and decoder block structures are borrowed from [33]. The transformer block "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        545,
+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": " has two transformer layers [45]. We set "
+                                },
+                                {
+                                    "bbox": [
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+                                        313,
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+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 8"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
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+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        313,
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+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda = 10"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": " by default."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. Comparison with Baselines"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We compare with two groups of baselines: 1) the general methods for image content removal; 2) the watermark removal methods."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "For the first group of methods, we compare with recent methods MPRNet [54], UFormer [49], and BIDNet [20]. We also include UNet [42] for general image-to-image translation as a baseline. For the second group of methods, we compare with the following watermark removal methods: Li et al. [31], Cao et al. [2], WDNet [38], BVMR [23], SplitNet [8], SLBR [33], DKSP [56]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We first evaluate the restored backgrounds from different methods, which are summarized in Table 1. We observe that the methods specifically designed for watermark removal are generally better than general content removal methods [54, 49, 20]. Among the watermark removal methods, [8, 33, 56] achieve competitive performance due to the multi-task framework. Our method significantly outperforms the existing methods, including [56] which uses additional semantic information. The superiority of our method is attributed to the fined-grained watermark removal ability"
+                                }
+                            ]
+                        }
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">CLWD</td><td colspan=\"4\">LOGO30K</td></tr><tr><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td><td>PSNR↑</td><td>SSIM ↑</td><td>RMSE↓</td><td>RMSEw ↓</td></tr><tr><td>U-Net [42]</td><td>23.21*</td><td>0.8567*</td><td>19.35*</td><td>48.43*</td><td>24.64*</td><td>0.8816</td><td>17.84</td><td>43.29*</td></tr><tr><td>MPRNet [54]</td><td>35.19</td><td>0.9725</td><td>5.52</td><td>20.76</td><td>37.81</td><td>0.9866</td><td>4.26</td><td>20.67</td></tr><tr><td>UFormer [49]</td><td>34.07</td><td>0.9784</td><td>6.29</td><td>25.66</td><td>39.84</td><td>0.9936</td><td>3.34</td><td>18.68</td></tr><tr><td>BIDNet [20]</td><td>35.02</td><td>0.9709</td><td>5.66</td><td>21.75</td><td>36.63</td><td>0.9829</td><td>4.83</td><td>24.29</td></tr><tr><td>Li et al. [31]</td><td>27.96*</td><td>0.9161*</td><td>12.63*</td><td>46.80*</td><td>30.51*</td><td>0.9312</td><td>10.51</td><td>39.11*</td></tr><tr><td>Cao et al. [2]</td><td>29.04*</td><td>0.9363*</td><td>10.36*</td><td>41.21*</td><td>32.18*</td><td>0.9654</td><td>8.20</td><td>35.16*</td></tr><tr><td>WDNet [38]</td><td>35.53*</td><td>0.9738*</td><td>5.11*</td><td>17.27*</td><td>39.15*</td><td>0.9874</td><td>3.49</td><td>15.94*</td></tr><tr><td>BVMR [23]</td><td>35.89*</td><td>0.9734*</td><td>5.02*</td><td>18.71*</td><td>38.28*</td><td>0.9852*</td><td>3.52</td><td>16.72*</td></tr><tr><td>SplitNet [8]</td><td>37.41*</td><td>0.9787*</td><td>4.23*</td><td>15.25*</td><td>41.27*</td><td>0.9910*</td><td>3.12</td><td>14.85*</td></tr><tr><td>SLBR [33]</td><td>38.28*</td><td>0.9814*</td><td>3.76*</td><td>14.07*</td><td>41.50*</td><td>0.9914</td><td>2.98</td><td>14.69*</td></tr><tr><td>DKSP† [56]</td><td>38.84*</td><td>0.9813</td><td>3.53</td><td>12.16*</td><td>42.16*</td><td>0.9921</td><td>2.77</td><td>13.78*</td></tr><tr><td>Ours</td><td>39.45</td><td>0.9823</td><td>3.19</td><td>11.28</td><td>42.57</td><td>0.9923</td><td>2.46</td><td>12.44</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. The results of restored backgrounds of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [8, 33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface."
+                                        }
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+                            "angle": 0,
+                            "type": "table_footnote"
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CLWD</td><td colspan=\"2\">LOGO30K</td></tr><tr><td>IoU↑</td><td>F1↑</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>WDNet [38]</td><td>0.6120*</td><td>0.7240*</td><td>0.6821*</td><td>0.8010*</td></tr><tr><td>BVMR [23]</td><td>0.7021*</td><td>0.7871*</td><td>0.7287*</td><td>0.8305*</td></tr><tr><td>SplitNet [8]</td><td>0.7196*</td><td>0.8027*</td><td>0.7414*</td><td>0.8411*</td></tr><tr><td>SLBR [33]</td><td>0.7463*</td><td>0.8234*</td><td>0.7858*</td><td>0.8647*</td></tr><tr><td>DKSP†[56]</td><td>0.7730*</td><td>0.8480*</td><td>0.8016*</td><td>0.8770*</td></tr><tr><td>Ours</td><td>0.7909</td><td>0.8634</td><td>0.8185</td><td>0.8898</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 2. The results of predicted watermark masks of different methods on CLWD [38] and LOGO30K [8]. The results marked with * are directly copied from previous papers [33, 56]. The method marked with † uses additional semantic information. The best results are denoted in boldface."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "table_footnote"
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "by considering fine-grained part categories."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We also compare the quality of watermark masks predicted by different methods in Table 2. We only compare with those methods [38, 23, 8, 33, 56] which predict watermark masks. Again, our method achieves the best results on both datasets."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                        46,
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+                                    "type": "text",
+                                    "content": "We show the visual comparison between different methods in Figure 3. We compare with the competitive baselines WDNet [38], SplitNet [8], SLBR [33], DKSP [56]. We show both predicted watermark masks and restored backgrounds. Our method can predict accurate and complete watermark masks, while the baseline methods could only predict incomplete mask, when the watermark is composed of multiple parts. This is because we use adapted query embeddings corresponding to different part categories to produce multiple part masks, which can cover the complete watermarked region. For background restoration, since baselines fail to predict complete watermark masks, they cannot erase the whole watermark and the recovered backgrounds are far below expectation. With the predicted complete watermark masks, our method can successfully repair the en"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "type": "table",
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">#</td><td rowspan=\"2\">T</td><td rowspan=\"2\">Dms</td><td rowspan=\"2\">Dbg</td><td colspan=\"4\">Evaluation Metrics</td></tr><tr><td>PSNR↑</td><td>RMSEw↓</td><td>IoU↑</td><td>F1↑</td></tr><tr><td>1</td><td></td><td>-q</td><td>- PFM</td><td>40.08</td><td>16.60</td><td>0.7474</td><td>0.8325</td></tr><tr><td>2</td><td></td><td>- Lle</td><td>- PFM</td><td>40.20</td><td>16.54</td><td>0.7576</td><td>0.8409</td></tr><tr><td>3</td><td></td><td>+</td><td>-PFM</td><td>40.23</td><td>16.48</td><td>0.7893</td><td>0.8674</td></tr><tr><td>4</td><td></td><td>+</td><td>+</td><td>41.67</td><td>13.85</td><td>0.8023</td><td>0.8772</td></tr><tr><td>5</td><td></td><td>+</td><td>SB</td><td>41.04</td><td>14.84</td><td>0.7928</td><td>0.8699</td></tr><tr><td>6</td><td></td><td>+</td><td>DK</td><td>40.82</td><td>15.51</td><td>0.7896</td><td>0.8679</td></tr><tr><td>7</td><td></td><td>+</td><td>-g</td><td>40.47</td><td>16.43</td><td>0.7895</td><td>0.8672</td></tr><tr><td>8</td><td>+</td><td>+</td><td>+</td><td>42.57</td><td>12.44</td><td>0.8185</td><td>0.8898</td></tr></table>",
+                                            "image_path": "6abb48e782f95d7afbcb4649329958dc4d91b64de5e7b4052969a2669cb320ed.jpg"
+                                        }
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+                                }
+                            ],
+                            "index": 7,
+                            "angle": 0,
+                            "type": "table_body"
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Table 3. The ablation study results on LOGO30K [8]. \"SB\" is short for scale/bias, \"DK\" is short for dynamic kernel, and \"q\" stands for query embeddings."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "angle": 0,
+                            "type": "table_footnote"
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "tire watermarked region by handling different local parts adaptively, producing visually pleasant backgrounds closer to the ground-truth."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.3. Ablation Studies"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We conduct ablation studies to analyze the effectiveness of each component and loss term, which are summarized in Table 3. We first build a basic model without using query embeddings or PFM module in row 1, in which case "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " directly outputs the watermark mask and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{bg}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " directly outputs the restored background. Then, we use "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K + 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " query embedding to interact with "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{F}^{ms}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to predict mask without low-entropy loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{le}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ". The obtained mask results in row 2 are better than those in row 1, which proves the effectiveness of query-based mask prediction. However, we observe that the predicted masks for different part categories are prone to resemble each other. Thus, we add "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{le}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to enforce "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " part masks to be different from each other. By comparing row 3 with row 2, we observe that the mask results are significantly improved by discovering multiple part"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "watermarked image"
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+                                    "content": "Ground-truth"
+                                }
+                            ]
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+                            "index": 7,
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+                            "type": "image_body"
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+                                            "type": "text",
+                                            "content": "Figure 3. From left to right, we show the watermarked image, the results of WDNet [38], SplitNet [8], SLBR [33], DKSP [56], our method, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask. The top two examples are from LOGO30K [8] and the bottom two examples are from CLWD [38]."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
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+                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "categories. Based on row 3, we insert our PFM block into the background decoder, leading to row 4. We observe that the background results are greatly improved. In the mean"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
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+                                    "type": "text",
+                                    "content": "while, the mask results are also improved, which might benefit from the information sharing between two tasks."
+                                }
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+                                    "type": "text",
+                                    "content": "Based on row 4, we explore several variants of our PFM"
+                                }
+                            ]
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+                }
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+                                            "bbox": [
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+                                            "type": "image",
+                                            "image_path": "c6306fa28550a4d7b5270110b05c5095533eb73fdb6449ef07fbda1689158494.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 0,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
+                                                46,
+                                                351,
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+                                            "type": "text",
+                                            "content": "Figure 4. From left to right, we show the watermarked image, the results of row 1, 2, 3, 4, 8 in Table 3, and the ground-truth. In each group, the top row shows the restored background image and the bottom row shows the predicted watermark mask."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
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+                        610
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                393,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        393,
+                                        289,
+                                        610
+                                    ],
+                                    "type": "text",
+                                    "content": "block. Recall that we use the dynamic strategy proposed in [28]. We also try some alternative ways of dynamic feature transformation. One alternative is dynamic convolution similar to [33]. Specifically, we use adapted query embeddings to predict dynamic convolution kernels for different part categories, which are applied to the corresponding regions in the feature map. Another alternative is predicting scales and biases similar to [27]. Specifically, we use adapted query embeddings to predict channel-wise scales and biases for different part categories, which are applied to the corresponding local regions in the feature map. The comparison among row 4, row 5, and row 6 shows that our choice in the method is the optimal one. Moreover, we remove the guidance from query embeddings and treat the input channel scales as learnable parameters. Without the guidance of query embeddings, the learnt dynamic convolution weights are less effective and thus the performance (row 7) becomes worse than those with guidance (row 4-6)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        613,
+                        287,
+                        685
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        613,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": "At last, we add the transformer block "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        613,
+                                        287,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        613,
+                                        287,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " to adapt query embeddings to each specific image. The obtained results in row 8 verify the validity of adapted query embeddings, because the local parts from different images belonging to the same part category may still have highly contrastive visual appearances."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        47,
+                        689,
+                        288,
+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                689,
+                                288,
+                                715
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        689,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "In Figure 4, we show the results of row 1, 2, 3, 4, 8 in Table 3. From row 1 to row 4, although the quality of"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        304,
+                        393,
+                        546,
+                        454
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "text",
+                                    "content": "restored backgrounds are getting better, the watermarks are not completely erased and residual watermark traces can be obviously seen. When using our full method equipped with all modules, row 8 achieves the best results that are close to the ground-truth backgrounds."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        306,
+                        475,
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+                        488
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        304,
+                        500,
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In this work, we have proposed a query-based multi-task framework for visible watermark removal, in which query embeddings corresponding to different part categories are jointly used for fine-grained mask prediction and background reconstruction. Our network can split one watermarked region into multiple local parts and restore different local parts adaptively. By considering fine-grained watermarked parts, our network surpasses the existing methods on two benchmark datasets."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        306,
+                        630,
+                        404,
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Acknowledgement"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
+                        654,
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+            ],
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+                                83
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+                                    "type": "text",
+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        48,
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+                    "type": "list",
+                    "angle": 0,
+                    "index": 18,
+                    "blocks": [
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+                                        }
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+                                    ],
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+                                        {
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+                                        }
+                                    ]
+                                }
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+                                        }
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
+                        },
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diff --git a/2023/FineDance_ A Fine-grained Choreography Dataset for 3D Full Body Dance Generation/dfc4e0d1-1a1e-402c-8793-12d9907332cb_content_list.json b/2023/FineDance_ A Fine-grained Choreography Dataset for 3D Full Body Dance Generation/dfc4e0d1-1a1e-402c-8793-12d9907332cb_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc4b70ea6468ccacb7d467462f23129140ecc4b1
--- /dev/null
+++ b/2023/FineDance_ A Fine-grained Choreography Dataset for 3D Full Body Dance Generation/dfc4e0d1-1a1e-402c-8793-12d9907332cb_content_list.json	
@@ -0,0 +1,1552 @@
+[
+    {
+        "type": "text",
+        "text": "FineDance: A Fine-grained Choreography Dataset for 3D Full Body Dance Generation",
+        "text_level": 1,
+        "bbox": [
+            228,
+            130,
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+            176
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ronghui Li $^{1*}$ , Junfan Zhao $^{1*}$ , Yachao Zhang $^{1}$ , Mingyang Su $^{1}$ , Zeping Ren $^{1}$ , Han Zhang $^{2}$ , Yansong Tang $^{1}$ , Xiu Li $^{1\\dagger}$ $^{1}$ Tsinghua Shenzhen International Graduate School, Tsinghua University  \n $^{2}$ Northwestern Polytechnical University  \n{lrh22, yf-zhao21}  $@$  mails.tsinghua.edu.cn, {yachaozhang, tang.yansong, li.xiu}  $@$  sz.tsinghua.edu.cn",
+        "bbox": [
+            184,
+            202,
+            784,
+            292
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/73d28fdca6082e86312f978b7a2a3bdf35c364951e15891397e6b3315bdd9b06.jpg",
+        "image_caption": [
+            "Figure 1. A conceptual overview. We release a large-scale professional 3D motion capture dance dataset FineDance, and propose a choreography network FineNet. Training with FineDance, FineNet can generate multi-genre dances with expressive hand movements."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            594,
+            313,
+            609
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generating full-body and multi-genre dance sequences from given music is a challenging task, due to the limitations of existing datasets and the inherent complexity of the fine-grained hand motion and dance genres. To address these problems, we propose FineDance, which contains 14.6 hours of music-dance paired data, with fine-grained hand motions, fine-grained genres (22 dance genres), and accurate posture. To the best of our knowledge, FineDance is the largest music-dance paired dataset with the most dance genres. Additionally, to address monotonous and unnatural hand movements existing in previous methods, we propose a full-body dance generation network, which utilizes the diverse generation capabilities of the diffusion model to solve monotonous problems, and use expert nets to solve unreal problems. To further enhance the genrematching and long-term stability of generated dances, we",
+        "bbox": [
+            73,
+            628,
+            473,
+            872
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "propose a Genre&Coherent aware Retrieval Module. Besides, we propose a novel metric named Genre Matching Score to evaluate the genre-matching degree between dance and music. Quantitative and qualitative experiments demonstrate the quality of FineDance, and the state-of-the-art performance of FineNet. The FineDance Dataset and more qualitative samples can be found at website.",
+        "bbox": [
+            500,
+            595,
+            893,
+            703
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            500,
+            737,
+            632,
+            752
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Music and dance are two enduring art forms that can express a wide range of human emotions, and they have become essential elements in modern entertainment industries such as concerts, movies, and games[11]. However, creating high-quality 3D dance animations can be a costly and complex process that often involves skilled dancers, engineers, and expensive motion-capture equipment[5]. As a result, there is growing interest in using artificial intelligence (AI) to generate 3D dance animations from music, which",
+        "bbox": [
+            496,
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+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "* equal contribution, † corresponding author",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "10234",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "has become a rapidly developing research topic.",
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Despite the wide range of research in this field [19, 14, 22, 21, 2, 49, 35, 5, 44, 36, 25, 46, 47], enetering high-quality dances is still limited by the existing datasets: (1) Full-body expressiveness: Existing dance datasets contain few hand movements, and only 1.5 hours of full body dance data is available. The previous methods in motion generation, treating body and hand as the same, lead to unnatural or monotonous hand motions, because the body and hand are in different feature spaces. However, uncoordinated body and hand motions can destroy the expressiveness of the overall dance. (2) Multi-genre: Existing datasets contain a limited number of dance genres, so the generated dances are not sufficient to match various music styles. Previous methods struggle with limited coarse dance genres and have no suitable objective metric to measure the genrematching degree between music and generated dances.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To address the limitations of existing datasets, we introduce a Fine-grained Choreography Dance dataset (FineDance). It comprises over 14.6 hours of data collected from 346 paired songs and dances, was created by professional dancers and a motion capture system, which has accurate body and hand motions. The fine-grained 22 dance genres of FineDance spanning traditional and modern styles, which make the genre-matching of generated dance sequences and given music become more challenging. FineDance includes music, dance sequences, FilmBox (fbx) files, SMPL[23, 29], and multi-view videos.",
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+        "text": "Early music-driven dance synthesis methods [3, 16, 24, 32, 15, 35, 2, 48] often rely on motion graph-based algorithms where the dance fragments from a pre-existing music-dance database are stitched together to synthesize one dance. While such methods can synthesize long-term dances, they do not produce new dance fragments. Recently methods have employed generative networks such as VAE[33], GAN[30], Normalization Flow Network[40], Diffusion[38]. But they focus solely on body part, while neglecting hand movements, resulting in unnatural or monotonous hand motions even trained with well-annotated body and hand labels. Additionally, the generative-based methods are limited by the long-term modeling ability of the networks, making them difficult to generate long-term dance sequences.",
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+        "text": "Therefore, we propose FineNet, a two-stage generative-synthesis network that addresses the limitations of previous dance generation methods. In the first stage, we propose a diffusion-based Full-body dance generation network (FDGN). The key of FDGN is to design two expert networks, which are dedicated to the generation of body and hand motions, and use a Refine Net to assemble them coordinately. In the second stage, we propose a Genre&Coherence aware Retrieval Module (GCRM), which ensures the coherence of dance fragments and",
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+    {
+        "type": "text",
+        "text": "matches the genre between the music and the dances. Based on the suitable dance fragments retrieved by GCRM, we can produce genre-matching and long-term dances. A conceptual overview of the dataset and method is shown in Figure1. Finally, to objectively evaluate the genre-matching degree between generated dances and given music, we propose a novel metric, named Genre-matching Score (GS).",
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+        "type": "text",
+        "text": "Overall, our contributions can be summarized as follows:",
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+        "list_items": [
+            "- We release FineDance, which is the largest 3D motion capture music-dance paired dataset with accurate full-body posture, containing 22 fine-grained genres. FineDance encourages the development of AI choreography, motion prior, and full-body reconstruction methods.",
+            "- We present FineNet, which leverages expert networks and refine network to generate expressive full-body dances, and employs a cross-modal retrieval network to improve genre-matching scores.",
+            "- Extensive quantitative experiments and user studies demonstrate that our approach can generate multiple different genre-matched dances from arbitrary music with natural and flexible hand movements."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Choreography Dataset",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Currently, the most popular 3D choreography dataset is AIST++ [22], which provides 5 hours of dance but does not have hand motions. AIST++ is reconstructed through multi-view video. Therefore, there is inevitably a deviation between the generated 3D dance motions and the real motions because of the reconstruction error. Li et al. [21] provided another major type of 3D dance dataset: modeling in software, which is obtained by experienced animators. However, this type of dataset lacks the authenticity of the dance. At present, the most accurate datasets are obtained from motion capture systems. GrooveNet dataset [2] only contains the electronic dance genre in 23 minutes sequence. Dance with Melody [35] further constructed a 94-minute 3D dance dataset with 4 genres. Music2Dance [49] is a dataset with only one hour and 2 genres (modern and curtailage dance). Chen et al. [5] built a 9 hours dataset, but it only has four different dance genres. This genre partition does not match the discernment of professional dance artists. For example, Anime and K-pop do not count as specific dance genres. In conclusion, these datasets have limitations in hand motion, duration, and the diversity of genres and dancers. Our dataset contains 14.6 hours with 22 genres, and is collected by 27 dancers.",
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+    },
+    {
+        "type": "page_number",
+        "text": "10235",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.2. AI Choreography",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Synthesis based approach. Early works[28, 26, 4, 43, 20] usually synthesis dances based on motion graphs and databases, which share one core idea: retrieving the most matching dance fragment for the given music clip, and splicing multiple fragments into a complete dance. In computer graphics, motion synthesis has long attracted a lot of attention as it can synthesize 3D actions from existing motion databases. Lamouret et al. [18] first delivered this idea and proposed a prototype system to create new actions by cutting and pasting action fragments from an action database. Arikan et al. [3] formally introduced the concept of graph-based motion synthesis, transforming this problem into finding paths in a pre-built motion graph. Under such a framework, the task of synthesizing actions is usually regarded as finding the optimal path in a constructed motion graph. Similar utilizing this graph-based scheme, Kim et al. [16] made the first attempt to synthesize rhythmic movements by adding constraints connecting action beats and rhythmic patterns. Shiratori et al. [32] and Kim et al. [15] formally pointed the music-driven dance movement synthesis problem and further developed more complex rules to associate dance movement segments with input music segments. This type of method can synthesize dances that match the music style well. However, as it is unable to learn the internal connections between music and dance, the synthesized dances cannot match the rhythm well. In addition, because the dance fragments are all from the database, such methods have no ability to create new dance motions. In this paper, we introduce the diversity generated technology into the synthesis method to maintain the advantages of synthesis and avoid the above problems.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Generation based approach. Generative Adversarial Network (GAN) [10] and Variational Auto Encoder (VAE) [17] have been successfully applied to generate various data modalities, including image, motion, music, etc. As a result, researchers also propose music-driven dance generation algorithms based on the general deep generation paradigm[7, 22, 34, 1, 21, 8, 42, 13, 12]. Such methods can be divided into 2D and 3D solutions according to the dimension of the generated dance data. Lee et al. [19] proposed the first music-driven 2D dance generative network, which uses VAE to model dance units and GAN to loop to generate dance sequences. Since the human skeleton is a natural graph data, Ren et al. [30] and Ferreira et al. [6] adopted a Graph Convolutional Network to improve the spatial naturalness of the generated 2D dance movements. Both music and dance belong to sequence data. Therefore, Li et al. [22] used the Transformer [41] network with strong sequence modeling ability to design a music-driven 3D dance action generation network. Recently, diffusion-based networks succeed in text2motion generation[37, 45]. Although these generative networks have the advantages, such as rhythm-",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/439cc5f5ab9543f591ca3c06ba882a93c2e8ca9b97e764388c0b40905a6f8c27.jpg",
+        "image_caption": [
+            "Figure 2. FineDance acquisition process. We capture the dancers' motions with the Vicon optical motion capture system. Then engineers retarget it to a standard skeleton in MotionBuilder. Dancers manually align the music with the dance motions and extract the skeletal information of the dance in Blender."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "matched and diversity, they neglect the quality of generated hand motions, and only generate motion fragments within several seconds. Our method can generate expressive full-body dances due to our diffusion based expert nets, and use a retrieval based modal to enhance the genre-matching score and take the advantages of synthetic methods such as genrematching, long-term stability.",
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+    {
+        "type": "text",
+        "text": "3. FineDance Dataset",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The review of the choreography dataset is shown in Section 2.1, there are still few accessible large-scale motion capture choreography datasets even though many papers reported their choreography datasets. Meanwhile, most of these datasets are insufficient to train a diversified and generalized-well choreography model due to the limiting of dance genres, and poor music-dance pairings. Our FineDance can fill these gaps.",
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Data Acquisition and Analysis",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For the fine-grained dataset, we take the following regulations into account for our dataset acquisition. We give the flowchart of the process shown in Figure 2. We summarized the comparison of FineDance and existing 3D dance datasets in Table 1.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Fine-grained motions. So far, there are only 2 datasets containing finger motion, and the available data is less than 1.5 hours. Fine-grained motions are ignored in existing methods. For example, GrooveNet[2] only contains 30 body joints, and Dance with Melody[35] has only 21 body joints, while EA-MUD[34], PhantomDance[21] and AIST++[22] all use 24 body joints of the SMPL[23] model.",
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+    {
+        "type": "text",
+        "text": "Our data store the information of the skeleton joints in 3D space in each frame including fingers, which can help to improve the artistry and reality of the dance motion. For easy to utilize, we use the standard 52 joints to represent the dance data.",
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+    {
+        "type": "text",
+        "text": "Fine-grained dance genres. Previous literature focuses on a few dance genres, such as GrooveNet[2],",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "10236",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/86231ede2d63c7eb8444f0fce8d72e94cdf7a5f97af6223ee4749dec7c055e5e.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. Comparisons of 3D Dance Datasets. Pos and Ros means 3D position and Rotation information respectively. Fbx (FilmBox) is one of the main 3D exchange formats as used by many 3D tools. \"avg Sec per Seq\" means the average seconds per sequence."
+        ],
+        "table_body": "<table><tr><td>Dataset</td><td>Pos/Rot</td><td>Joints num</td><td>Hand joint</td><td>Genres</td><td>Mocap</td><td>RGB Views</td><td>Fbx</td><td>SMPL</td><td>Dancers</td><td>Total hours</td><td>avg Sec per Seq</td></tr><tr><td>GrooveNet[2]</td><td>✓/X</td><td>30</td><td>X</td><td>1</td><td>✓</td><td>1</td><td>X</td><td>X</td><td>1</td><td>0.38</td><td>690</td></tr><tr><td>Dance w/Melody[35]</td><td>✓/X</td><td>21</td><td>X</td><td>4</td><td>✓</td><td>4</td><td>X</td><td>X</td><td>-</td><td>1.6</td><td>92.5</td></tr><tr><td>Music2Dance[49]</td><td>✓/X</td><td>55</td><td>✓</td><td>2</td><td>✓</td><td>2</td><td>X</td><td>X</td><td>2</td><td>0.96</td><td>-</td></tr><tr><td>EA-MUD[34]</td><td>✓/✓</td><td>24</td><td>X</td><td>4</td><td>X</td><td>4</td><td>X</td><td>X</td><td>-</td><td>0.35</td><td>73.8</td></tr><tr><td>PhantomDance[21]</td><td>✓/X</td><td>24</td><td>X</td><td>13</td><td>X</td><td>0</td><td>X</td><td>X</td><td>-</td><td>9.6</td><td>133.3</td></tr><tr><td>AIST++[22]</td><td>✓/✓</td><td>17/24</td><td>X</td><td>10</td><td>X</td><td>10</td><td>X</td><td>✓</td><td>-</td><td>5.2</td><td>13.3</td></tr><tr><td>MMD[5]</td><td>✓/✓</td><td>52</td><td>✓</td><td>4</td><td>✓</td><td>0</td><td>✓</td><td>X</td><td>-</td><td>9.9</td><td>-</td></tr><tr><td>FineDance (Ours)</td><td>✓/✓</td><td>52</td><td>✓</td><td>22</td><td>✓</td><td>2</td><td>✓</td><td>✓</td><td>27</td><td>14.6</td><td>152.3</td></tr></table>",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Music2Dance[49], MMD[5] and Dance with Melody[35]. This dataset uses a rough genre classification strategy, which is a non-standardized dance division.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We improve the diversity of our dataset from two aspects: more genres and more dancers. Our FineDance is reasonably classified under the advice of dance artists, covering hip-hop and Chinese classical dance more completely. To the best of our knowledge, it also includes folk dance motions for the first time, expanding the dance genres of the choreography dataset. Totally, FineDance has up to 22 genres of dance defined by professional dance artists. And we obtained more than 14 hours of data. It is worth noting that FineDance contains the most genres. Details are given in the supplementary materials.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Accurate posture. Currently, the largest available dataset is AIST++[22], which is collected by reconstructing 3D poses in multi-view videos. But the dance data is not real due to the reconstructing errors. Instead of reconstruction from the videos, ours is collected by a motion capture system, and all dance motions and music are well paired.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In FineDance, all motions are captured by the Vicon optical motion capture system and retargeted to a standard skeleton in MotionBuilder by engineers. Therefore, FineDance can donate accurate postures. Moreover, FineDance will be the largest fully available 3D music-dance paired dataset, and it will be available.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Well-paired dance and music. Dance fragments are strongly associated with the rhythm and style of music. However, due to the lack of enough well-paired data, the generative model is hard to fit the relevance of the motion rhythm and music rhythm. Therefore, we asked the professional dancers to pay attention to the matching of rhythm and style when dancing.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Professional dancer. We invited 27 professional dancers, and each dancer was asked to dance to the music while his/her motions were captured utilizing the capture system.",
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+    },
+    {
+        "type": "text",
+        "text": "4. FineNet",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Overall Framework",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Given music of unknown style and arbitrary duration, our goal is to generate multiple different full-body dances. This task presents challenges in three areas: (1) Full-body: Body and two hands motions in different spaces have different grains, using a single network to generate full-body motions like the previous method can lead to unreal and monotonous hand gestures. (2) Genre-matching: Making the generated dances consistent with the fine-grained genre is also challenging due to the modal gap between music and dance. (3) Long-term: Generating long-term novel motion is challenging because neural networks tend to accumulate errors over time. To address these issues, we propose FineNet, which comprises a Diffusion-based Full-body Diverse Dance Generation Network (FDGN) and a Genre & Coherent aware Retrieval Module (GCRM). The FDGN focuses on creating detailed dances with expressive movements, while the GCRM considers the overall choreography of the dance. FineNet cleverly combines generative and synthetic methods, making them complementary, much like the process of human choreography. Furthermore, FineNet allows for the generation of multiple different dances by selecting distinct dance segments at the initial time step. This capability offers users a wide range of creative possibilities.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The overall framework of our method is shown in Figure 3. First, the input music  $X$  is split into 4-second clips  $\\{X^t\\}_{t=1}^N$  without overlapping, and  $N$  is the number of clips of the given music. For each  $X^t$ , we use the Librosa toolbox [27] to extract the temporal feature  $\\bar{X}^t \\in \\mathbb{R}^{T \\times C^m}$ , and the mel-spectrogram image  $\\tilde{\\bar{X}}^t \\in \\mathbb{R}^{W \\times H \\times 3}$ , where  $T$  is the time length of a clip and  $C^m$  is the channel dimension.  $W$  and  $H$  are the width and height of the image respectively, and 3 means the number of RGB channels. FineNet generates and retrieves the best dance fragment at each time step,",
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+    {
+        "type": "page_number",
+        "text": "10237",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/d058aea2b7f4f67160b063f265639553b9edcd16541bf4723de7f9bca72864f6.jpg",
+        "image_caption": [
+            "Figure 3. An overview of our framework. FineNet can iteratively generate and choreograph different dance fragments based on the mel-spectrogram and temporal features of music. FineNet consists of a diffusion-based Full body Dance Generation Network (FDGN) and a Genre&Coherence retrieval module. The former is utilized to generate expressive and diverse full-body dance fragments; the latter is designed to retrieve the best matching dance fragments from the generated multiple dance fragments and synthesis them smoothly."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and this process can be formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {Y} ^ {1} = \\text {F i n e N e t} (\\bar {X} ^ {1}, \\tilde {X} ^ {1}) \\\\ \\hat {\\mathrm {V}} ^ {t} = \\text {F i n e N e t} (\\tilde {X} ^ {t}, \\tilde {X} ^ {t}, \\hat {\\mathrm {V}} ^ {t - 1}) \\end{array} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {Y} ^ {t} = F i n e N e t (\\bar {X} ^ {t}, \\widetilde {X} ^ {t}, \\hat {Y} ^ {t - 1}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $t \\in \\{2,3,\\dots ,N\\}$  is the current time step.  $\\hat{Y}^t \\in \\mathbb{R}^{V \\times (T \\times 3)}$  is the dance action fragment obtained by FineNet at time step t, and  $V$  is the number of body and hand joints, \"3\" represents 3-dimensional axis angle and position of joints.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Diverse Dance Generation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The previous generative models such as VAE[33] and GAN[30], mostly directly link music embedding to dance embedding method, which results in the limited diversity of the generated dances. This is because high-level condensed features of music usually contain insufficient details to guide the network to generate different dances [45].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To generate novel and diverse dances, we employ a diffusion-based model, FDGN. To make the network perceive the music rhythm better, we feed the music temporal feature to FDGN  $\\bar{X}^t$  instead of  $X^t$ . Given  $\\bar{X}^t$  and different noise sampled from  $\\mathcal{N}(0,I)$ , FDGN can generate  $M$  distinctive dance fragments, represented as  $\\{\\hat{Y}_i^t\\}_{i=1}^M$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. FDGN: Full-body Dance Generation Network",
+        "text_level": 1,
+        "bbox": [
+            76,
+            739,
+            465,
+            757
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We propose FDGN, a network for generating full body dance motions. Compared to previous models, FDGN can produce more realistic, natural, and expressive hand motions that coordinate well with body motion and music styles. As shown in Figure 4, we use two expert networks to generate body and hand motion separately. This is based on two observations: (1) The range of motion of the body and hand is obviously different and belongs to different feature spaces. Therefore, using a single network to generate",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8d0236ccb183e2c4c347115c387f8620ea27c42d39f4e907ec57240f32425f48.jpg",
+        "image_caption": [
+            "Figure 4. Full-body Dance Generation Network.\"  $\\bigoplus$  \" means add."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
+            361,
+            893,
+            584
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "full-body dances can result in unnatural hand motions. (2) In dance generation, music rhythm mainly coordinates with the limbs, and hand motion should be consistent with the body and music style. The structure of body/hand expert net is modified by MDM[37] and EDGE[39]. The training process of body expert net can be formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {d} = \\mathrm {E} _ {s \\in [ 1, S ], Y b _ {0} \\sim q (Y b _ {0})} \\left[ \\left\\| Y b _ {0} - B E N \\left(Y b _ {s}, s, \\bar {X}\\right) \\right\\| _ {2} ^ {2} \\right], \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            503,
+            699,
+            890,
+            731
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $Yb_{0}$  is the label dance data,  $BEN(\\cdot)$  means Body Expert Net,  $s$  is the number of diffusion steps. The refine net is consisted of a spatial convolution network and a refine gate unit, which is used to assemble two parts naturally.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.4. Genre&Coherent aware Retrieval Module",
+        "text_level": 1,
+        "bbox": [
+            500,
+            801,
+            856,
+            816
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Thanks to FDGN's diverse generative capabilities, we can generate  $M$  candidate dance fragments  $\\{\\bar{Y}_i^t\\}_{i=1}^M$  for the  $t-th$  music clip  $\\{\\bar{X}^t\\}$ . To search the genre-matched candidate dance fragment and synthesis them coherently, we propose Genre&Coherent aware Retrieval Module (GCRM),",
+        "bbox": [
+            496,
+            824,
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+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "10238",
+        "bbox": [
+            480,
+            924,
+            517,
+            935
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "which calculates the Genre Matching Score (GS) of the current music clip and the candidate dance fragments, and the coherent score of the previous selected dance fragment and the current candidate dance fragments. Finally, we choreograph the complete dance by combining the two scores.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Genre matching score. We use GS to evaluate the matching degree of the style of music clip  $\\widetilde{X^t}$  and the genres of generated candidate dance fragments  $\\{\\hat{Y}_i^t\\}_{i=1}^M$ . However, music and dance are different data modalities, and it is difficult to calculate the genre similarity directly. To cover this problem, we propose a cross-modal retrieval network.",
+        "bbox": [
+            75,
+            167,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We utilize two models (one music style encoder  $\\mathcal{F}_{\\theta}^{m}(\\cdot)$  and one dance genre encoder  $\\mathcal{F}_{\\theta}^{d}(\\cdot))$  to encode different modalities into one embedding space. The music style encoder is the backbone of AST [9] and the dance genre encoder is the backbone of AGCN [31]. We extract the mel-spectrogram features  $\\widetilde{X^t}$  of music  $X^t$  and send it to the music encoder. For each  $\\{\\widetilde{X^t}\\}_{t = 1}^N$ , we compute its genre-matching score with candidate dance fragments generated by FDGN. We utilize the cosine similarity as the genre matching score. So the genre matching score between  $\\widetilde{X^t}$  and  $\\{\\hat{Y}_i^{t}\\}_{i = 1}^M$  can be formulated as:",
+        "bbox": [
+            75,
+            258,
+            467,
+            428
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nG S _ {i} ^ {t} = s \\left(\\widetilde {X ^ {t}}, \\hat {Y} _ {i} ^ {t}\\right) = \\frac {\\mathcal {F} _ {\\theta} ^ {m} \\left(\\widetilde {X ^ {t}}\\right) ^ {T} \\mathcal {F} _ {\\theta} ^ {d} \\left(Y _ {i} ^ {t}\\right)}{\\left| \\left| \\mathcal {F} _ {\\theta} ^ {m} \\left(\\widetilde {X ^ {t}}\\right) \\right| \\right| \\times \\left| \\left| \\mathcal {F} _ {\\theta} ^ {d} \\left(Y _ {i} ^ {t}\\right) \\right| \\right|}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            102,
+            429,
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+            467
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We train the above two models by a cosine loss  $\\mathcal{L}_{cos}$  as a retrieval task, which can be formulated as:",
+        "bbox": [
+            76,
+            474,
+            467,
+            503
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {c o s}} = y \\left(1 - s \\left(\\widetilde {X _ {i}}, Y _ {j}\\right)\\right) + (1 - y) \\left(\\max  \\left(0, s \\left(\\widetilde {X _ {i}}, Y _ {j}\\right)\\right), \\right. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            518,
+            467,
+            553
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\widetilde{X_i}$  is the MFCCs feature of music clip,  $Y_{j}$  is a dance fragment.  $y = 1$  when  $\\widetilde{X_i}$  and  $Y_{j}$  are genre-matched, otherwise  $y = 0$ .",
+        "bbox": [
+            76,
+            565,
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+            613
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Coherent score. We take the L2 distance of the start and end states of the two dance segments as the coherence score. To make the transition smoother, we cut 5 frames of the last temporal clip  $(t - 1)$  best matching fragment  $\\hat{Y}_b^{t - 1}$  on the tail and cut the start 5 frames of the  $M$  candidate dance fragments  $\\{\\hat{Y}_i^t\\}_{i = 1}^M$  at the current time step  $t$ . These cut frames are finally filled with a linear interpolation algorithm.",
+        "bbox": [
+            75,
+            614,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nC S _ {i} ^ {1} = 0 \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
+            727,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nC S _ {i} ^ {\\ell} = - | | Y _ {b} ^ {t - 1} [ - 5, : ] - Y _ {i} ^ {t} [ 5, : ] | | _ {2},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            739,
+            393,
+            758
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $t\\in \\{2,3,\\dots ,N\\}$  is the time step.",
+        "bbox": [
+            76,
+            768,
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+            784
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Combining GS and CS, GCRM can find the best  $\\hat{Y}^t$  from the candidate dance segments  $\\{Y_i^t\\}_{i=1}^M$  as the output at time step  $t$ :",
+        "bbox": [
+            75,
+            784,
+            467,
+            828
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ni d x ^ {t} = \\operatorname {a r g m a x} _ {i} \\left(\\alpha G S _ {i} ^ {t} + \\beta C S _ {i} ^ {t}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            155,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {Y} ^ {t} := \\hat {Y} _ {i d x ^ {t}} ^ {t}, \\hat {Y} _ {i d x ^ {t}} ^ {t} \\in \\left\\{Y _ {i} ^ {t} \\right\\} _ {i = 1} ^ {M},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
+            843,
+            362,
+            862
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha$  and  $\\beta$  are weight parameters. For complete music  $X$ , FineNet outputs the dance fragments step by step, and",
+        "bbox": [
+            76,
+            869,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/cf0a80540606a7aeab1d5dcf69d45374c7ff7c6d14eda01e17e77c277deb0da6.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative result comparisons for a Jazz song."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            99,
+            885,
+            325
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the final result is:  $\\hat{Y} = [\\hat{Y}^1, \\hat{Y}^2, \\dots, \\hat{Y}^T]$ . Furthermore, by choosing different  $\\hat{Y}^1$  at step 1, FineNet can generate multiple dances with excellent diversity.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Data Preprocessing. We spilt FineDance dataset into train, val and test sets in two ways: FineDance@Genre and FineDance@Dancer. The test set of FineDance@Genre includes a broader range of dance genres, but the same dancer appear in train/val/test set. FineDance@Dancer means the train/val/test set divided by different dancers, which test set contains fewer dance genres, yet the same dancer won't appear in different sets. We only reported the results of test set on FineDance@Genre in this paper, the details of dataset split can be found in our supplementary materials. Each music and paired dance are only present in one set. For all the dance fragments, we combine the 3-dim axis angle vector representation for all 52 joints, along with a 3-dim global position vector, resulting in 159-dim motion features. For all the music clips, we use Librosa [27] to extract the 35-dim music temporal features. We also extract the mel-spectrogram of the music clips with Librosa and resized it to  $224 \\times 224 \\times 3$ . During extracting audio features, the sampling rate is  $76,800\\mathrm{Hz}$  and hop size is 512.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. In FDGN, we build 3 MLP layers to encode the music and body features. We use the transformer layer as the backbone of the body/hand expert net. The refine net consists of a 1-D convolution layer and a learnable weight parameter. The total epoch, learning rate, and batch size are set as 200,  $2e^{-4}$ , 2048. In the GCRM, the  $\\alpha$ ,  $\\beta$  are set as 1.0 and 0.5 respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. (1) FID score. Fréchet inception distance (FID) is widely used to measure how close the distribution of the generated dances is to that of the ground truth.",
+        "bbox": [
+            498,
+            854,
+            890,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "10239",
+        "bbox": [
+            480,
+            924,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/36d8561d5acba3b6bcb9c8226a6a134104c4c8a9eaa9ee3abbb16b44e78b4373.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"6\">FineDance Dataset</td><td colspan=\"6\">AIST++ Dataset</td></tr><tr><td>FID↓</td><td>FIDh↓</td><td>Div↑</td><td>Divh↑</td><td>MM↑</td><td>GS↑</td><td>FID↓</td><td>FIDh↓</td><td>Div↑</td><td>Divh↑</td><td>MM↑</td><td>GS↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>/</td><td>6.28</td><td>3.48</td><td>/</td><td>0.71</td><td>/</td><td>/</td><td>9.07</td><td>/</td><td>/</td><td>0.77</td></tr><tr><td>ChoreoMaster#</td><td>1.92</td><td>0.61</td><td>6.18</td><td>3.33</td><td>12.20</td><td>0.39</td><td>2.21</td><td>/</td><td>9.38</td><td>/</td><td>30.71</td><td>0.71</td></tr><tr><td>DanceRevolution*</td><td>7.44</td><td>3.21</td><td>3.92</td><td>1.80</td><td>4.22</td><td>0.30</td><td>6.05</td><td>/</td><td>7.67</td><td>/</td><td>12.88</td><td>0.75</td></tr><tr><td>DeepDance*</td><td>5.77</td><td>1.95</td><td>5.07</td><td>3.50</td><td>0.73</td><td>0.36</td><td>25.78</td><td>/</td><td>8.98</td><td>/</td><td>3.08</td><td>0.73</td></tr><tr><td>Bailando*</td><td>4.77</td><td>2.24</td><td>3.09</td><td>1.12</td><td>2.33</td><td>0.29</td><td>17.45</td><td>/</td><td>9.44</td><td>/</td><td>2.58</td><td>0.74</td></tr><tr><td>FineNet (w/o. FDGN)</td><td>1.90</td><td>1.20</td><td>5.87</td><td>3.40</td><td>12.86</td><td>0.62</td><td>2.11</td><td>/</td><td>9.13</td><td>/</td><td>31.09</td><td>0.79</td></tr><tr><td>FineNet</td><td>1.66</td><td>0.48</td><td>5.99</td><td>3.59</td><td>16.72</td><td>0.74</td><td>2.05</td><td>/</td><td>9.94</td><td>/</td><td>33.67</td><td>0.80</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Similar to Lee et al.[19], we trained a style classifier in our dataset to extract motion features, and then use the features to calculate FID. (2) Diversity. We follow Lee et al. [19] to evaluate the average feature distance between generated dances for different input music. The same feature extractor used in FID is used again. (3) Hand FID score and Hand Diversity. Similarly, we extract hand motion features and calculate the FID and diversity for hand motion. (4) Multi-modality. We follow Lee et al.[19] to evaluate the average feature distance between the 10 choreography versions of every music. This metric measures the model's ability to generate different dances for the same music. (5) Genre Matching Score. We evaluate the average genre matching score between generated dance and the input music using the genre matching score calculation network mentioned in section 4.4. The genre matching score is defined as Eq. (3).",
+        "bbox": [
+            75,
+            296,
+            472,
+            541
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Quantitative and Qualitative Evaluation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            555,
+            421,
+            571
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Compared methods. We compare our method with several generation-based methods and one synthesis-based method. ChoreoMaster [5] is a dance synthesis method with style embedding network and graph-based motion synthesis. Since the code is not available, we reproduced the code according to the paper. DanceRevolution [14] is a generation method using Transformer to generate long-term dances. DeepDance [10] is a generation method with a GAN-based cross-modal association framework. Bailando [33] is a generation method with VAE and an actor-critic generative pre-trained transformer model. All the methods are tested on FineDance and AIST++ to evaluate the comprehensive choreography ability of FineNet.",
+        "bbox": [
+            75,
+            580,
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+            777
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results and analysis. For all methods, we generate 10 versions of the dance for each song in the test set, and take the paired real dance as the Ground Truth. As shown in Table 2, our method gets the best performance in all evaluation metrics except Diversity on both datasets. Choreo-Master gets better on Diversity because it must retrieve all the fragments in the whole training set but no new motion is created. Specifically, on Multimodality (MM), FineNet",
+        "bbox": [
+            75,
+            779,
+            470,
+            901
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "gains 4.52 improvements compared to ChoreoMaster. On GS, FineNet is 0.03 higher than the ground truth. These two metrics show FineNet can generate diverse and genrematched dance. Besides, FineNet gets the highest Hand FID and Hand Diversity which shows our method can generate real and diverse hand motion.",
+        "bbox": [
+            496,
+            296,
+            890,
+            386
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Qualitative results are shown in Figure 5. DanceRevelation, DeepDance and Bailando generated almost identical stiff motions (refer to row 1 and row 2). ChoreoMaster generates classical dance motions in the last two images that do not match the Jazz music. But the generated dance motions of FineNet are diverse and in line with the Jazz style. The hand motion generated by FineNet W/ FDGN is more real. The corresponding videos refer to supplementary material.",
+        "bbox": [
+            496,
+            388,
+            892,
+            510
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
+            521,
+            653,
+            537
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We replace different components of our method, and conduct experiments to demonstrate the effectiveness of each component on the test set of FineDance.",
+        "bbox": [
+            496,
+            546,
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+            590
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Infulence of the FDGN. In order to verify whether FDGN can make hand movements more natural and flexible. We modified FDGN as a single network that generates body and hand motion simultaneously. We then employed  $FID_{h}$  and  $DIV_{h}$  metrics to evaluate the realism and diversity of the resulting hand motion. As shown in Table2, all the quantitative metrics for FineNet w/o. FDGN becomes worse on both datasets. Specifically, on Hand Fid and Hand Diversity, FineNet w/o. FDGN drops by 0.72 and 0.14. The huge increase in  $FID_{h}$  is mainly because FDGN generates hand movements with complete body information, making the hand motions more coordinated with the body.",
+        "bbox": [
+            496,
+            592,
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+            773
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/4dde1f73360c0444eb12eac32d99d9490ae84c57b69f015e8661b4d263b19ea9.jpg",
+        "table_caption": [
+            "Table 2. Compared with SOTAs. # means we reproduce the code, * means we use the published code."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Strategy</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>6.28</td><td>/</td><td>0.71</td></tr><tr><td>FDGN-G</td><td>2.85</td><td>6.22</td><td>12.02</td><td>0.27</td></tr><tr><td>FDGN-C</td><td>1.68</td><td>6.34</td><td>11.51</td><td>0.46</td></tr><tr><td>FineNet</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>",
+        "bbox": [
+            500,
+            787,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Ablation study on different choreography strategies.",
+        "bbox": [
+            500,
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+            859,
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+        ],
+        "page_idx": 6
+    },
+    {
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+        "text": "10240",
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+        "text": "Choreography Strategy. To verify the proposed generative-synthesis strategy, we use the following strategies to generate 3D dances: directly generating long-term 3D dances by FDGN (FDGN-G); generating 4s dance fragments according to the music clip by FDGN and concatenating these fragments together (FDGN-C), as Table 3 shows.",
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+        "text": "FineNet performs better than others in FID, MM, and GS. For FDGN-G, a long music clip will cause the FID and GS to drop dramatically. FineNet achieves a lower Diversity score than FDGN-C because while retrieving the GCRM gives up some dances whose genre doesn't match. For MM and GS, FineNet increases by 5.21 and 0.28 compared to FDGN-C, which demonstrates that GCRM can increase the ability to generate diverse and genre-matched dance for the same song.",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Generation Model</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>DeepDance</td><td>4.91</td><td>4.47</td><td>1.15</td><td>0.32</td></tr><tr><td>DanceRevolution</td><td>6.99</td><td>3.51</td><td>6.64</td><td>0.37</td></tr><tr><td>FDGN</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Influence of the generation model. We choose DanceRevolution, DeepDance as the backbone of the generative model, and get the whole 3D dances through our GCRM. All the results are shown in Table 4. Our FDGN performs best, which shows excellent dance generation ability. Besides, compared the results of Table 2 and Table 4, where DeepDance and DanceRevolution are inserted into our method in Table 4, and their performances can be improved on MM, FID and GS. These results show our GCRM is scalable.",
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+        "text": "5.4. User Study",
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+        "type": "text",
+        "text": "We invite 30 participants, including 15 dancers. Everyone watches 5 dances with a duration of 32 seconds. They are asked to evaluate the dances in 2 aspects: Effective duration and Artistry.",
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+        "type": "text",
+        "text": "Effective duration. Each participant has to judge the time interval from the beginning until abnormal actions occur, such as abnormal shaking, motion freezing, or excessive joint distortion. As Table 5 shows, synthesis methods generally performs better than generation methods, generation methods can only generate effective dances for less than 10 seconds. These results show that generation methods are limited in effective duration. But, ours is a generative-synthesis method, and achieves the best performance.",
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+        "type": "text",
+        "text": "Artistry. We measure the artistry of the dances from the following dimensions: genre matching (GM), rhythm matching (RM), diversity (Div.), and comprehensive artistry (CA). The full score of every dimension is 100. As shown in Table 6, synthesis methods generally perform better than generation methods, and our method gets a 77.0 average score",
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+        "table_caption": [
+            "Table 4. Ablation study on different generation networks."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Duration ↑</td><td>Type</td></tr><tr><td>Ground Truth</td><td>30.7s</td><td>/</td></tr><tr><td>ChoreoMaster</td><td>26.9s</td><td>synthesis</td></tr><tr><td>DanceRevolution</td><td>5.4s</td><td>generation</td></tr><tr><td>DeepDance</td><td>2.2s</td><td>generation</td></tr><tr><td>Baildando</td><td>3.1s</td><td>generation</td></tr><tr><td>FineNet (Ours)</td><td>28.2s</td><td>generation&amp;synthesis</td></tr></table>",
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+        "type": "table",
+        "img_path": "images/1e622584ef66efff2b1f59931ce34c447c3aa9f2c7837f799caa3dba678b723c.jpg",
+        "table_caption": [
+            "Table 5. User study on effective duration."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>GM</td><td>RM</td><td>Div.</td><td>CA</td><td>Avg</td></tr><tr><td>Ground Truth</td><td>94.1</td><td>96.3</td><td>95.5</td><td>97.9</td><td>96.0</td></tr><tr><td>ChoreoMaster</td><td>64.2</td><td>59.7</td><td>77.2</td><td>69.8</td><td>67.7</td></tr><tr><td>DanceRevolution</td><td>33.2</td><td>30.7</td><td>47.4</td><td>31.4</td><td>36.7</td></tr><tr><td>DeepDance</td><td>17.2</td><td>22.1</td><td>24.4</td><td>25.6</td><td>22.3</td></tr><tr><td>Bailando</td><td>23.2</td><td>33.5</td><td>39.4</td><td>21.6</td><td>30.1</td></tr><tr><td>FineNet (Ours)</td><td>79.9</td><td>70.3</td><td>81.2</td><td>76.4</td><td>77.0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 6. Result of the user study. Avg denotes the average score.",
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+    },
+    {
+        "type": "text",
+        "text": "which clearly surpasses the baselines. However, compared to the ground truth, all the methods still need to improve especially in rhythm matching and Comprehensive artistry.",
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+    {
+        "type": "text",
+        "text": "6. Conclusions",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a large-scale, high-quality 3D dance dataset (FineDance) for music-driven dance generation, which records professional and abundant dance genres with accurate and fine-grained hand motions. Meanwhile, we also propose a choreography Network (FineNet), which can generate multiple diverse genre-matched dances with flexible hand movements. Furthermore, we propose a new metric to evaluate the genre matching degree between music and dance. Quantitative and qualitative results show that FineNet can generate long-term, diverse, and genrematched dances from given music.",
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+        "type": "text",
+        "text": "Acknowledgment",
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+        "type": "text",
+        "text": "We would like to express our sincere gratitude to Yan Zhang (https://yz-cnsdqz.github.io/) and Yulun Zhang (https://yulunzhang.com/) for their invaluable guidance and insights during the course of our research.",
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+        "type": "text",
+        "text": "This work was supported in part by the Shenzhen Key Laboratory of next generation interactive media innovative technology (No.ZDSYS20210623092001004), in part by the China Postdoctoral Science Foundation (No.2023M731957), in part by the National Natural Science Foundation of China under Grant 62206153, Young Elite Scientists Sponsorship Program by CAST (No. 2023QNRC002)",
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+    {
+        "type": "text",
+        "text": "References",
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+    },
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diff --git a/2023/FineDance_ A Fine-grained Choreography Dataset for 3D Full Body Dance Generation/dfc4e0d1-1a1e-402c-8793-12d9907332cb_model.json b/2023/FineDance_ A Fine-grained Choreography Dataset for 3D Full Body Dance Generation/dfc4e0d1-1a1e-402c-8793-12d9907332cb_model.json
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+            "angle": 0,
+            "content": "Figure 1. A conceptual overview. We release a large-scale professional 3D motion capture dance dataset FineDance, and propose a choreography network FineNet. Training with FineDance, FineNet can generate multi-genre dances with expressive hand movements."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.595,
+                0.314,
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+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.629,
+                0.474,
+                0.873
+            ],
+            "angle": 0,
+            "content": "Generating full-body and multi-genre dance sequences from given music is a challenging task, due to the limitations of existing datasets and the inherent complexity of the fine-grained hand motion and dance genres. To address these problems, we propose FineDance, which contains 14.6 hours of music-dance paired data, with fine-grained hand motions, fine-grained genres (22 dance genres), and accurate posture. To the best of our knowledge, FineDance is the largest music-dance paired dataset with the most dance genres. Additionally, to address monotonous and unnatural hand movements existing in previous methods, we propose a full-body dance generation network, which utilizes the diverse generation capabilities of the diffusion model to solve monotonous problems, and use expert nets to solve unreal problems. To further enhance the genrematching and long-term stability of generated dances, we"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.597,
+                0.895,
+                0.704
+            ],
+            "angle": 0,
+            "content": "propose a Genre&Coherent aware Retrieval Module. Besides, we propose a novel metric named Genre Matching Score to evaluate the genre-matching degree between dance and music. Quantitative and qualitative experiments demonstrate the quality of FineDance, and the state-of-the-art performance of FineNet. The FineDance Dataset and more qualitative samples can be found at website."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.738,
+                0.633,
+                0.753
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Music and dance are two enduring art forms that can express a wide range of human emotions, and they have become essential elements in modern entertainment industries such as concerts, movies, and games[11]. However, creating high-quality 3D dance animations can be a costly and complex process that often involves skilled dancers, engineers, and expensive motion-capture equipment[5]. As a result, there is growing interest in using artificial intelligence (AI) to generate 3D dance animations from music, which"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.102,
+                0.888,
+                0.341,
+                0.901
+            ],
+            "angle": 0,
+            "content": "* equal contribution, † corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.52,
+                0.937
+            ],
+            "angle": 0,
+            "content": "10234"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.395,
+                0.106
+            ],
+            "angle": 0,
+            "content": "has become a rapidly developing research topic."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.109,
+                0.468,
+                0.35
+            ],
+            "angle": 0,
+            "content": "Despite the wide range of research in this field [19, 14, 22, 21, 2, 49, 35, 5, 44, 36, 25, 46, 47], enetering high-quality dances is still limited by the existing datasets: (1) Full-body expressiveness: Existing dance datasets contain few hand movements, and only 1.5 hours of full body dance data is available. The previous methods in motion generation, treating body and hand as the same, lead to unnatural or monotonous hand motions, because the body and hand are in different feature spaces. However, uncoordinated body and hand motions can destroy the expressiveness of the overall dance. (2) Multi-genre: Existing datasets contain a limited number of dance genres, so the generated dances are not sufficient to match various music styles. Previous methods struggle with limited coarse dance genres and have no suitable objective metric to measure the genrematching degree between music and generated dances."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.353,
+                0.468,
+                0.518
+            ],
+            "angle": 0,
+            "content": "To address the limitations of existing datasets, we introduce a Fine-grained Choreography Dance dataset (FineDance). It comprises over 14.6 hours of data collected from 346 paired songs and dances, was created by professional dancers and a motion capture system, which has accurate body and hand motions. The fine-grained 22 dance genres of FineDance spanning traditional and modern styles, which make the genre-matching of generated dance sequences and given music become more challenging. FineDance includes music, dance sequences, FilmBox (fbx) files, SMPL[23, 29], and multi-view videos."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.521,
+                0.468,
+                0.747
+            ],
+            "angle": 0,
+            "content": "Early music-driven dance synthesis methods [3, 16, 24, 32, 15, 35, 2, 48] often rely on motion graph-based algorithms where the dance fragments from a pre-existing music-dance database are stitched together to synthesize one dance. While such methods can synthesize long-term dances, they do not produce new dance fragments. Recently methods have employed generative networks such as VAE[33], GAN[30], Normalization Flow Network[40], Diffusion[38]. But they focus solely on body part, while neglecting hand movements, resulting in unnatural or monotonous hand motions even trained with well-annotated body and hand labels. Additionally, the generative-based methods are limited by the long-term modeling ability of the networks, making them difficult to generate long-term dance sequences."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Therefore, we propose FineNet, a two-stage generative-synthesis network that addresses the limitations of previous dance generation methods. In the first stage, we propose a diffusion-based Full-body dance generation network (FDGN). The key of FDGN is to design two expert networks, which are dedicated to the generation of body and hand motions, and use a Refine Net to assemble them coordinately. In the second stage, we propose a Genre&Coherence aware Retrieval Module (GCRM), which ensures the coherence of dance fragments and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.198
+            ],
+            "angle": 0,
+            "content": "matches the genre between the music and the dances. Based on the suitable dance fragments retrieved by GCRM, we can produce genre-matching and long-term dances. A conceptual overview of the dataset and method is shown in Figure1. Finally, to objectively evaluate the genre-matching degree between generated dances and given music, we propose a novel metric, named Genre-matching Score (GS)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.2,
+                0.892,
+                0.214
+            ],
+            "angle": 0,
+            "content": "Overall, our contributions can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.231,
+                0.892,
+                0.321
+            ],
+            "angle": 0,
+            "content": "- We release FineDance, which is the largest 3D motion capture music-dance paired dataset with accurate full-body posture, containing 22 fine-grained genres. FineDance encourages the development of AI choreography, motion prior, and full-body reconstruction methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.341,
+                0.892,
+                0.402
+            ],
+            "angle": 0,
+            "content": "- We present FineNet, which leverages expert networks and refine network to generate expressive full-body dances, and employs a cross-modal retrieval network to improve genre-matching scores."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.421,
+                0.892,
+                0.48
+            ],
+            "angle": 0,
+            "content": "- Extensive quantitative experiments and user studies demonstrate that our approach can generate multiple different genre-matched dances from arbitrary music with natural and flexible hand movements."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.519,
+                0.231,
+                0.892,
+                0.48
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.501,
+                0.65,
+                0.517
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.528,
+                0.71,
+                0.544
+            ],
+            "angle": 0,
+            "content": "2.1. Choreography Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.554,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Currently, the most popular 3D choreography dataset is AIST++ [22], which provides 5 hours of dance but does not have hand motions. AIST++ is reconstructed through multi-view video. Therefore, there is inevitably a deviation between the generated 3D dance motions and the real motions because of the reconstruction error. Li et al. [21] provided another major type of 3D dance dataset: modeling in software, which is obtained by experienced animators. However, this type of dataset lacks the authenticity of the dance. At present, the most accurate datasets are obtained from motion capture systems. GrooveNet dataset [2] only contains the electronic dance genre in 23 minutes sequence. Dance with Melody [35] further constructed a 94-minute 3D dance dataset with 4 genres. Music2Dance [49] is a dataset with only one hour and 2 genres (modern and curtailage dance). Chen et al. [5] built a 9 hours dataset, but it only has four different dance genres. This genre partition does not match the discernment of professional dance artists. For example, Anime and K-pop do not count as specific dance genres. In conclusion, these datasets have limitations in hand motion, duration, and the diversity of genres and dancers. Our dataset contains 14.6 hours with 22 genres, and is collected by 27 dancers."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "10235"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.091,
+                0.25,
+                0.108
+            ],
+            "angle": 0,
+            "content": "2.2. AI Choreography"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.115,
+                0.473,
+                0.584
+            ],
+            "angle": 0,
+            "content": "Synthesis based approach. Early works[28, 26, 4, 43, 20] usually synthesis dances based on motion graphs and databases, which share one core idea: retrieving the most matching dance fragment for the given music clip, and splicing multiple fragments into a complete dance. In computer graphics, motion synthesis has long attracted a lot of attention as it can synthesize 3D actions from existing motion databases. Lamouret et al. [18] first delivered this idea and proposed a prototype system to create new actions by cutting and pasting action fragments from an action database. Arikan et al. [3] formally introduced the concept of graph-based motion synthesis, transforming this problem into finding paths in a pre-built motion graph. Under such a framework, the task of synthesizing actions is usually regarded as finding the optimal path in a constructed motion graph. Similar utilizing this graph-based scheme, Kim et al. [16] made the first attempt to synthesize rhythmic movements by adding constraints connecting action beats and rhythmic patterns. Shiratori et al. [32] and Kim et al. [15] formally pointed the music-driven dance movement synthesis problem and further developed more complex rules to associate dance movement segments with input music segments. This type of method can synthesize dances that match the music style well. However, as it is unable to learn the internal connections between music and dance, the synthesized dances cannot match the rhythm well. In addition, because the dance fragments are all from the database, such methods have no ability to create new dance motions. In this paper, we introduce the diversity generated technology into the synthesis method to maintain the advantages of synthesis and avoid the above problems."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.585,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Generation based approach. Generative Adversarial Network (GAN) [10] and Variational Auto Encoder (VAE) [17] have been successfully applied to generate various data modalities, including image, motion, music, etc. As a result, researchers also propose music-driven dance generation algorithms based on the general deep generation paradigm[7, 22, 34, 1, 21, 8, 42, 13, 12]. Such methods can be divided into 2D and 3D solutions according to the dimension of the generated dance data. Lee et al. [19] proposed the first music-driven 2D dance generative network, which uses VAE to model dance units and GAN to loop to generate dance sequences. Since the human skeleton is a natural graph data, Ren et al. [30] and Ferreira et al. [6] adopted a Graph Convolutional Network to improve the spatial naturalness of the generated 2D dance movements. Both music and dance belong to sequence data. Therefore, Li et al. [22] used the Transformer [41] network with strong sequence modeling ability to design a music-driven 3D dance action generation network. Recently, diffusion-based networks succeed in text2motion generation[37, 45]. Although these generative networks have the advantages, such as rhythm-"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.089,
+                0.909,
+                0.234
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.239,
+                0.895,
+                0.309
+            ],
+            "angle": 0,
+            "content": "Figure 2. FineDance acquisition process. We capture the dancers' motions with the Vicon optical motion capture system. Then engineers retarget it to a standard skeleton in MotionBuilder. Dancers manually align the music with the dance motions and extract the skeletal information of the dance in Blender."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.318,
+                0.895,
+                0.427
+            ],
+            "angle": 0,
+            "content": "matched and diversity, they neglect the quality of generated hand motions, and only generate motion fragments within several seconds. Our method can generate expressive full-body dances due to our diffusion based expert nets, and use a retrieval based modal to enhance the genre-matching score and take the advantages of synthetic methods such as genrematching, long-term stability."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.437,
+                0.684,
+                0.453
+            ],
+            "angle": 0,
+            "content": "3. FineDance Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.462,
+                0.895,
+                0.584
+            ],
+            "angle": 0,
+            "content": "The review of the choreography dataset is shown in Section 2.1, there are still few accessible large-scale motion capture choreography datasets even though many papers reported their choreography datasets. Meanwhile, most of these datasets are insufficient to train a diversified and generalized-well choreography model due to the limiting of dance genres, and poor music-dance pairings. Our FineDance can fill these gaps."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.591,
+                0.771,
+                0.607
+            ],
+            "angle": 0,
+            "content": "3.1. Data Acquisition and Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.894,
+                0.688
+            ],
+            "angle": 0,
+            "content": "For the fine-grained dataset, we take the following regulations into account for our dataset acquisition. We give the flowchart of the process shown in Figure 2. We summarized the comparison of FineDance and existing 3D dance datasets in Table 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.69,
+                0.895,
+                0.796
+            ],
+            "angle": 0,
+            "content": "Fine-grained motions. So far, there are only 2 datasets containing finger motion, and the available data is less than 1.5 hours. Fine-grained motions are ignored in existing methods. For example, GrooveNet[2] only contains 30 body joints, and Dance with Melody[35] has only 21 body joints, while EA-MUD[34], PhantomDance[21] and AIST++[22] all use 24 body joints of the SMPL[23] model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.797,
+                0.895,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Our data store the information of the skeleton joints in 3D space in each frame including fingers, which can help to improve the artistry and reality of the dance motion. For easy to utilize, we use the standard 52 joints to represent the dance data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Fine-grained dance genres. Previous literature focuses on a few dance genres, such as GrooveNet[2],"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.52,
+                0.937
+            ],
+            "angle": 0,
+            "content": "10236"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.891,
+                0.31
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>Pos/Rot</td><td>Joints num</td><td>Hand joint</td><td>Genres</td><td>Mocap</td><td>RGB Views</td><td>Fbx</td><td>SMPL</td><td>Dancers</td><td>Total hours</td><td>avg Sec per Seq</td></tr><tr><td>GrooveNet[2]</td><td>✓/X</td><td>30</td><td>X</td><td>1</td><td>✓</td><td>1</td><td>X</td><td>X</td><td>1</td><td>0.38</td><td>690</td></tr><tr><td>Dance w/Melody[35]</td><td>✓/X</td><td>21</td><td>X</td><td>4</td><td>✓</td><td>4</td><td>X</td><td>X</td><td>-</td><td>1.6</td><td>92.5</td></tr><tr><td>Music2Dance[49]</td><td>✓/X</td><td>55</td><td>✓</td><td>2</td><td>✓</td><td>2</td><td>X</td><td>X</td><td>2</td><td>0.96</td><td>-</td></tr><tr><td>EA-MUD[34]</td><td>✓/✓</td><td>24</td><td>X</td><td>4</td><td>X</td><td>4</td><td>X</td><td>X</td><td>-</td><td>0.35</td><td>73.8</td></tr><tr><td>PhantomDance[21]</td><td>✓/X</td><td>24</td><td>X</td><td>13</td><td>X</td><td>0</td><td>X</td><td>X</td><td>-</td><td>9.6</td><td>133.3</td></tr><tr><td>AIST++[22]</td><td>✓/✓</td><td>17/24</td><td>X</td><td>10</td><td>X</td><td>10</td><td>X</td><td>✓</td><td>-</td><td>5.2</td><td>13.3</td></tr><tr><td>MMD[5]</td><td>✓/✓</td><td>52</td><td>✓</td><td>4</td><td>✓</td><td>0</td><td>✓</td><td>X</td><td>-</td><td>9.9</td><td>-</td></tr><tr><td>FineDance (Ours)</td><td>✓/✓</td><td>52</td><td>✓</td><td>22</td><td>✓</td><td>2</td><td>✓</td><td>✓</td><td>27</td><td>14.6</td><td>152.3</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.313,
+                0.893,
+                0.343
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparisons of 3D Dance Datasets. Pos and Ros means 3D position and Rotation information respectively. Fbx (FilmBox) is one of the main 3D exchange formats as used by many 3D tools. \"avg Sec per Seq\" means the average seconds per sequence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.354,
+                0.469,
+                0.399
+            ],
+            "angle": 0,
+            "content": "Music2Dance[49], MMD[5] and Dance with Melody[35]. This dataset uses a rough genre classification strategy, which is a non-standardized dance division."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.401,
+                0.469,
+                0.566
+            ],
+            "angle": 0,
+            "content": "We improve the diversity of our dataset from two aspects: more genres and more dancers. Our FineDance is reasonably classified under the advice of dance artists, covering hip-hop and Chinese classical dance more completely. To the best of our knowledge, it also includes folk dance motions for the first time, expanding the dance genres of the choreography dataset. Totally, FineDance has up to 22 genres of dance defined by professional dance artists. And we obtained more than 14 hours of data. It is worth noting that FineDance contains the most genres. Details are given in the supplementary materials."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.567,
+                0.47,
+                0.657
+            ],
+            "angle": 0,
+            "content": "Accurate posture. Currently, the largest available dataset is AIST++[22], which is collected by reconstructing 3D poses in multi-view videos. But the dance data is not real due to the reconstructing errors. Instead of reconstruction from the videos, ours is collected by a motion capture system, and all dance motions and music are well paired."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.658,
+                0.469,
+                0.748
+            ],
+            "angle": 0,
+            "content": "In FineDance, all motions are captured by the Vicon optical motion capture system and retargeted to a standard skeleton in MotionBuilder by engineers. Therefore, FineDance can donate accurate postures. Moreover, FineDance will be the largest fully available 3D music-dance paired dataset, and it will be available."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.469,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Well-paired dance and music. Dance fragments are strongly associated with the rhythm and style of music. However, due to the lack of enough well-paired data, the generative model is hard to fit the relevance of the motion rhythm and music rhythm. Therefore, we asked the professional dancers to pay attention to the matching of rhythm and style when dancing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Professional dancer. We invited 27 professional dancers, and each dancer was asked to dance to the music while his/her motions were captured utilizing the capture system."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.353,
+                0.593,
+                0.369
+            ],
+            "angle": 0,
+            "content": "4. FineNet"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.378,
+                0.691,
+                0.393
+            ],
+            "angle": 0,
+            "content": "4.1. Overall Framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.402,
+                0.892,
+                0.749
+            ],
+            "angle": 0,
+            "content": "Given music of unknown style and arbitrary duration, our goal is to generate multiple different full-body dances. This task presents challenges in three areas: (1) Full-body: Body and two hands motions in different spaces have different grains, using a single network to generate full-body motions like the previous method can lead to unreal and monotonous hand gestures. (2) Genre-matching: Making the generated dances consistent with the fine-grained genre is also challenging due to the modal gap between music and dance. (3) Long-term: Generating long-term novel motion is challenging because neural networks tend to accumulate errors over time. To address these issues, we propose FineNet, which comprises a Diffusion-based Full-body Diverse Dance Generation Network (FDGN) and a Genre & Coherent aware Retrieval Module (GCRM). The FDGN focuses on creating detailed dances with expressive movements, while the GCRM considers the overall choreography of the dance. FineNet cleverly combines generative and synthetic methods, making them complementary, much like the process of human choreography. Furthermore, FineNet allows for the generation of multiple different dances by selecting distinct dance segments at the initial time step. This capability offers users a wide range of creative possibilities."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The overall framework of our method is shown in Figure 3. First, the input music \\(X\\) is split into 4-second clips \\(\\{X^t\\}_{t=1}^N\\) without overlapping, and \\(N\\) is the number of clips of the given music. For each \\(X^t\\), we use the Librosa toolbox [27] to extract the temporal feature \\(\\bar{X}^t \\in \\mathbb{R}^{T \\times C^m}\\), and the mel-spectrogram image \\(\\tilde{\\bar{X}}^t \\in \\mathbb{R}^{W \\times H \\times 3}\\), where \\(T\\) is the time length of a clip and \\(C^m\\) is the channel dimension. \\(W\\) and \\(H\\) are the width and height of the image respectively, and 3 means the number of RGB channels. FineNet generates and retrieves the best dance fragment at each time step,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "10237"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.089,
+                0.887,
+                0.293
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.295,
+                0.895,
+                0.352
+            ],
+            "angle": 0,
+            "content": "Figure 3. An overview of our framework. FineNet can iteratively generate and choreograph different dance fragments based on the mel-spectrogram and temporal features of music. FineNet consists of a diffusion-based Full body Dance Generation Network (FDGN) and a Genre&Coherence retrieval module. The former is utilized to generate expressive and diverse full-body dance fragments; the latter is designed to retrieve the best matching dance fragments from the generated multiple dance fragments and synthesis them smoothly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.365,
+                0.332,
+                0.38
+            ],
+            "angle": 0,
+            "content": "and this process can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.155,
+                0.388,
+                0.47,
+                0.413
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\hat {Y} ^ {1} = \\text {F i n e N e t} (\\bar {X} ^ {1}, \\tilde {X} ^ {1}) \\\\ \\hat {\\mathrm {V}} ^ {t} = \\text {F i n e N e t} (\\tilde {X} ^ {t}, \\tilde {X} ^ {t}, \\hat {\\mathrm {V}} ^ {t - 1}) \\end{array} \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.158,
+                0.402,
+                0.374,
+                0.423
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {Y} ^ {t} = F i n e N e t (\\bar {X} ^ {t}, \\widetilde {X} ^ {t}, \\hat {Y} ^ {t - 1}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.436,
+                0.47,
+                0.511
+            ],
+            "angle": 0,
+            "content": "where \\(t \\in \\{2,3,\\dots ,N\\}\\) is the current time step. \\(\\hat{Y}^t \\in \\mathbb{R}^{V \\times (T \\times 3)}\\) is the dance action fragment obtained by FineNet at time step t, and \\(V\\) is the number of body and hand joints, \"3\" represents 3-dimensional axis angle and position of joints."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.522,
+                0.315,
+                0.536
+            ],
+            "angle": 0,
+            "content": "4.2. Diverse Dance Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.546,
+                0.469,
+                0.636
+            ],
+            "angle": 0,
+            "content": "The previous generative models such as VAE[33] and GAN[30], mostly directly link music embedding to dance embedding method, which results in the limited diversity of the generated dances. This is because high-level condensed features of music usually contain insufficient details to guide the network to generate different dances [45]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.637,
+                0.469,
+                0.733
+            ],
+            "angle": 0,
+            "content": "To generate novel and diverse dances, we employ a diffusion-based model, FDGN. To make the network perceive the music rhythm better, we feed the music temporal feature to FDGN \\(\\bar{X}^t\\) instead of \\(X^t\\). Given \\(\\bar{X}^t\\) and different noise sampled from \\(\\mathcal{N}(0,I)\\), FDGN can generate \\(M\\) distinctive dance fragments, represented as \\(\\{\\hat{Y}_i^t\\}_{i=1}^M\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.741,
+                0.466,
+                0.758
+            ],
+            "angle": 0,
+            "content": "4.3. FDGN: Full-body Dance Generation Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We propose FDGN, a network for generating full body dance motions. Compared to previous models, FDGN can produce more realistic, natural, and expressive hand motions that coordinate well with body motion and music styles. As shown in Figure 4, we use two expert networks to generate body and hand motion separately. This is based on two observations: (1) The range of motion of the body and hand is obviously different and belongs to different feature spaces. Therefore, using a single network to generate"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.362,
+                0.895,
+                0.585
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.585,
+                0.885,
+                0.6
+            ],
+            "angle": 0,
+            "content": "Figure 4. Full-body Dance Generation Network.\" \\(\\bigoplus\\) \" means add."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.612,
+                0.892,
+                0.701
+            ],
+            "angle": 0,
+            "content": "full-body dances can result in unnatural hand motions. (2) In dance generation, music rhythm mainly coordinates with the limbs, and hand motion should be consistent with the body and music style. The structure of body/hand expert net is modified by MDM[37] and EDGE[39]. The training process of body expert net can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.504,
+                0.7,
+                0.891,
+                0.732
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {d} = \\mathrm {E} _ {s \\in [ 1, S ], Y b _ {0} \\sim q (Y b _ {0})} \\left[ \\left\\| Y b _ {0} - B E N \\left(Y b _ {s}, s, \\bar {X}\\right) \\right\\| _ {2} ^ {2} \\right], \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.733,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "where \\( Yb_{0} \\) is the label dance data, \\( BEN(\\cdot) \\) means Body Expert Net, \\( s \\) is the number of diffusion steps. The refine net is consisted of a spatial convolution network and a refine gate unit, which is used to assemble two parts naturally."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.802,
+                0.857,
+                0.817
+            ],
+            "angle": 0,
+            "content": "4.4. Genre&Coherent aware Retrieval Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Thanks to FDGN's diverse generative capabilities, we can generate \\(M\\) candidate dance fragments \\(\\{\\bar{Y}_i^t\\}_{i=1}^M\\) for the \\(t-th\\) music clip \\(\\{\\bar{X}^t\\}\\). To search the genre-matched candidate dance fragment and synthesis them coherently, we propose Genre&Coherent aware Retrieval Module (GCRM),"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.519,
+                0.936
+            ],
+            "angle": 0,
+            "content": "10238"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.167
+            ],
+            "angle": 0,
+            "content": "which calculates the Genre Matching Score (GS) of the current music clip and the candidate dance fragments, and the coherent score of the previous selected dance fragment and the current candidate dance fragments. Finally, we choreograph the complete dance by combining the two scores."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.168,
+                0.468,
+                0.259
+            ],
+            "angle": 0,
+            "content": "Genre matching score. We use GS to evaluate the matching degree of the style of music clip \\(\\widetilde{X^t}\\) and the genres of generated candidate dance fragments \\(\\{\\hat{Y}_i^t\\}_{i=1}^M\\). However, music and dance are different data modalities, and it is difficult to calculate the genre similarity directly. To cover this problem, we propose a cross-modal retrieval network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.259,
+                0.468,
+                0.429
+            ],
+            "angle": 0,
+            "content": "We utilize two models (one music style encoder \\(\\mathcal{F}_{\\theta}^{m}(\\cdot)\\) and one dance genre encoder \\(\\mathcal{F}_{\\theta}^{d}(\\cdot))\\) to encode different modalities into one embedding space. The music style encoder is the backbone of AST [9] and the dance genre encoder is the backbone of AGCN [31]. We extract the mel-spectrogram features \\(\\widetilde{X^t}\\) of music \\(X^t\\) and send it to the music encoder. For each \\(\\{\\widetilde{X^t}\\}_{t = 1}^N\\), we compute its genre-matching score with candidate dance fragments generated by FDGN. We utilize the cosine similarity as the genre matching score. So the genre matching score between \\(\\widetilde{X^t}\\) and \\(\\{\\hat{Y}_i^{t}\\}_{i = 1}^M\\) can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.103,
+                0.43,
+                0.468,
+                0.468
+            ],
+            "angle": 0,
+            "content": "\\[\nG S _ {i} ^ {t} = s \\left(\\widetilde {X ^ {t}}, \\hat {Y} _ {i} ^ {t}\\right) = \\frac {\\mathcal {F} _ {\\theta} ^ {m} \\left(\\widetilde {X ^ {t}}\\right) ^ {T} \\mathcal {F} _ {\\theta} ^ {d} \\left(Y _ {i} ^ {t}\\right)}{\\left| \\left| \\mathcal {F} _ {\\theta} ^ {m} \\left(\\widetilde {X ^ {t}}\\right) \\right| \\right| \\times \\left| \\left| \\mathcal {F} _ {\\theta} ^ {d} \\left(Y _ {i} ^ {t}\\right) \\right| \\right|}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.476,
+                0.468,
+                0.505
+            ],
+            "angle": 0,
+            "content": "We train the above two models by a cosine loss \\(\\mathcal{L}_{cos}\\) as a retrieval task, which can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.086,
+                0.519,
+                0.468,
+                0.554
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {c o s}} = y \\left(1 - s \\left(\\widetilde {X _ {i}}, Y _ {j}\\right)\\right) + (1 - y) \\left(\\max  \\left(0, s \\left(\\widetilde {X _ {i}}, Y _ {j}\\right)\\right), \\right. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.566,
+                0.468,
+                0.614
+            ],
+            "angle": 0,
+            "content": "where \\(\\widetilde{X_i}\\) is the MFCCs feature of music clip, \\(Y_{j}\\) is a dance fragment. \\(y = 1\\) when \\(\\widetilde{X_i}\\) and \\(Y_{j}\\) are genre-matched, otherwise \\(y = 0\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.616,
+                0.468,
+                0.725
+            ],
+            "angle": 0,
+            "content": "Coherent score. We take the L2 distance of the start and end states of the two dance segments as the coherence score. To make the transition smoother, we cut 5 frames of the last temporal clip \\((t - 1)\\) best matching fragment \\(\\hat{Y}_b^{t - 1}\\) on the tail and cut the start 5 frames of the \\(M\\) candidate dance fragments \\(\\{\\hat{Y}_i^t\\}_{i = 1}^M\\) at the current time step \\(t\\). These cut frames are finally filled with a linear interpolation algorithm."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.728,
+                0.468,
+                0.746
+            ],
+            "angle": 0,
+            "content": "\\[\nC S _ {i} ^ {1} = 0 \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.154,
+                0.741,
+                0.394,
+                0.76
+            ],
+            "angle": 0,
+            "content": "\\[\nC S _ {i} ^ {\\ell} = - | | Y _ {b} ^ {t - 1} [ - 5, : ] - Y _ {i} ^ {t} [ 5, : ] | | _ {2},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.77,
+                0.352,
+                0.785
+            ],
+            "angle": 0,
+            "content": "where \\(t\\in \\{2,3,\\dots ,N\\}\\) is the time step."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.785,
+                0.468,
+                0.829
+            ],
+            "angle": 0,
+            "content": "Combining GS and CS, GCRM can find the best \\(\\hat{Y}^t\\) from the candidate dance segments \\(\\{Y_i^t\\}_{i=1}^M\\) as the output at time step \\(t\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.156,
+                0.828,
+                0.468,
+                0.847
+            ],
+            "angle": 0,
+            "content": "\\[\ni d x ^ {t} = \\operatorname {a r g m a x} _ {i} \\left(\\alpha G S _ {i} ^ {t} + \\beta C S _ {i} ^ {t}\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.159,
+                0.844,
+                0.363,
+                0.863
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {Y} ^ {t} := \\hat {Y} _ {i d x ^ {t}} ^ {t}, \\hat {Y} _ {i d x ^ {t}} ^ {t} \\in \\left\\{Y _ {i} ^ {t} \\right\\} _ {i = 1} ^ {M},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.871,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) and \\(\\beta\\) are weight parameters. For complete music \\(X\\), FineNet outputs the dance fragments step by step, and"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.1,
+                0.887,
+                0.327
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.527,
+                0.332,
+                0.862,
+                0.345
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative result comparisons for a Jazz song."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.347,
+                0.89,
+                0.395
+            ],
+            "angle": 0,
+            "content": "the final result is: \\(\\hat{Y} = [\\hat{Y}^1, \\hat{Y}^2, \\dots, \\hat{Y}^T]\\). Furthermore, by choosing different \\(\\hat{Y}^1\\) at step 1, FineNet can generate multiple dances with excellent diversity."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.412,
+                0.632,
+                0.428
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.437,
+                0.69,
+                0.453
+            ],
+            "angle": 0,
+            "content": "5.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.461,
+                0.892,
+                0.747
+            ],
+            "angle": 0,
+            "content": "Data Preprocessing. We spilt FineDance dataset into train, val and test sets in two ways: FineDance@Genre and FineDance@Dancer. The test set of FineDance@Genre includes a broader range of dance genres, but the same dancer appear in train/val/test set. FineDance@Dancer means the train/val/test set divided by different dancers, which test set contains fewer dance genres, yet the same dancer won't appear in different sets. We only reported the results of test set on FineDance@Genre in this paper, the details of dataset split can be found in our supplementary materials. Each music and paired dance are only present in one set. For all the dance fragments, we combine the 3-dim axis angle vector representation for all 52 joints, along with a 3-dim global position vector, resulting in 159-dim motion features. For all the music clips, we use Librosa [27] to extract the 35-dim music temporal features. We also extract the mel-spectrogram of the music clips with Librosa and resized it to \\(224 \\times 224 \\times 3\\). During extracting audio features, the sampling rate is \\(76,800\\mathrm{Hz}\\) and hop size is 512."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.749,
+                0.892,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Implementation Details. In FDGN, we build 3 MLP layers to encode the music and body features. We use the transformer layer as the backbone of the body/hand expert net. The refine net consists of a 1-D convolution layer and a learnable weight parameter. The total epoch, learning rate, and batch size are set as 200, \\(2e^{-4}\\), 2048. In the GCRM, the \\(\\alpha\\), \\(\\beta\\) are set as 1.0 and 0.5 respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Evaluation Metrics. (1) FID score. Fréchet inception distance (FID) is widely used to measure how close the distribution of the generated dances is to that of the ground truth."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.519,
+                0.936
+            ],
+            "angle": 0,
+            "content": "10239"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.894,
+                0.27
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"6\">FineDance Dataset</td><td colspan=\"6\">AIST++ Dataset</td></tr><tr><td>FID↓</td><td>FIDh↓</td><td>Div↑</td><td>Divh↑</td><td>MM↑</td><td>GS↑</td><td>FID↓</td><td>FIDh↓</td><td>Div↑</td><td>Divh↑</td><td>MM↑</td><td>GS↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>/</td><td>6.28</td><td>3.48</td><td>/</td><td>0.71</td><td>/</td><td>/</td><td>9.07</td><td>/</td><td>/</td><td>0.77</td></tr><tr><td>ChoreoMaster#</td><td>1.92</td><td>0.61</td><td>6.18</td><td>3.33</td><td>12.20</td><td>0.39</td><td>2.21</td><td>/</td><td>9.38</td><td>/</td><td>30.71</td><td>0.71</td></tr><tr><td>DanceRevolution*</td><td>7.44</td><td>3.21</td><td>3.92</td><td>1.80</td><td>4.22</td><td>0.30</td><td>6.05</td><td>/</td><td>7.67</td><td>/</td><td>12.88</td><td>0.75</td></tr><tr><td>DeepDance*</td><td>5.77</td><td>1.95</td><td>5.07</td><td>3.50</td><td>0.73</td><td>0.36</td><td>25.78</td><td>/</td><td>8.98</td><td>/</td><td>3.08</td><td>0.73</td></tr><tr><td>Bailando*</td><td>4.77</td><td>2.24</td><td>3.09</td><td>1.12</td><td>2.33</td><td>0.29</td><td>17.45</td><td>/</td><td>9.44</td><td>/</td><td>2.58</td><td>0.74</td></tr><tr><td>FineNet (w/o. FDGN)</td><td>1.90</td><td>1.20</td><td>5.87</td><td>3.40</td><td>12.86</td><td>0.62</td><td>2.11</td><td>/</td><td>9.13</td><td>/</td><td>31.09</td><td>0.79</td></tr><tr><td>FineNet</td><td>1.66</td><td>0.48</td><td>5.99</td><td>3.59</td><td>16.72</td><td>0.74</td><td>2.05</td><td>/</td><td>9.94</td><td>/</td><td>33.67</td><td>0.80</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.183,
+                0.271,
+                0.785,
+                0.285
+            ],
+            "angle": 0,
+            "content": "Table 2. Compared with SOTAs. # means we reproduce the code, * means we use the published code."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.297,
+                0.473,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Similar to Lee et al.[19], we trained a style classifier in our dataset to extract motion features, and then use the features to calculate FID. (2) Diversity. We follow Lee et al. [19] to evaluate the average feature distance between generated dances for different input music. The same feature extractor used in FID is used again. (3) Hand FID score and Hand Diversity. Similarly, we extract hand motion features and calculate the FID and diversity for hand motion. (4) Multi-modality. We follow Lee et al.[19] to evaluate the average feature distance between the 10 choreography versions of every music. This metric measures the model's ability to generate different dances for the same music. (5) Genre Matching Score. We evaluate the average genre matching score between generated dance and the input music using the genre matching score calculation network mentioned in section 4.4. The genre matching score is defined as Eq. (3)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.556,
+                0.422,
+                0.572
+            ],
+            "angle": 0,
+            "content": "5.2. Quantitative and Qualitative Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.581,
+                0.47,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Compared methods. We compare our method with several generation-based methods and one synthesis-based method. ChoreoMaster [5] is a dance synthesis method with style embedding network and graph-based motion synthesis. Since the code is not available, we reproduced the code according to the paper. DanceRevolution [14] is a generation method using Transformer to generate long-term dances. DeepDance [10] is a generation method with a GAN-based cross-modal association framework. Bailando [33] is a generation method with VAE and an actor-critic generative pre-trained transformer model. All the methods are tested on FineDance and AIST++ to evaluate the comprehensive choreography ability of FineNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Results and analysis. For all methods, we generate 10 versions of the dance for each song in the test set, and take the paired real dance as the Ground Truth. As shown in Table 2, our method gets the best performance in all evaluation metrics except Diversity on both datasets. Choreo-Master gets better on Diversity because it must retrieve all the fragments in the whole training set but no new motion is created. Specifically, on Multimodality (MM), FineNet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.297,
+                0.892,
+                0.387
+            ],
+            "angle": 0,
+            "content": "gains 4.52 improvements compared to ChoreoMaster. On GS, FineNet is 0.03 higher than the ground truth. These two metrics show FineNet can generate diverse and genrematched dance. Besides, FineNet gets the highest Hand FID and Hand Diversity which shows our method can generate real and diverse hand motion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.389,
+                0.893,
+                0.511
+            ],
+            "angle": 0,
+            "content": "Qualitative results are shown in Figure 5. DanceRevelation, DeepDance and Bailando generated almost identical stiff motions (refer to row 1 and row 2). ChoreoMaster generates classical dance motions in the last two images that do not match the Jazz music. But the generated dance motions of FineNet are diverse and in line with the Jazz style. The hand motion generated by FineNet W/ FDGN is more real. The corresponding videos refer to supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.522,
+                0.655,
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+            ],
+            "angle": 0,
+            "content": "5.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.547,
+                0.894,
+                0.592
+            ],
+            "angle": 0,
+            "content": "We replace different components of our method, and conduct experiments to demonstrate the effectiveness of each component on the test set of FineDance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.593,
+                0.892,
+                0.775
+            ],
+            "angle": 0,
+            "content": "Infulence of the FDGN. In order to verify whether FDGN can make hand movements more natural and flexible. We modified FDGN as a single network that generates body and hand motion simultaneously. We then employed \\( FID_{h} \\) and \\( DIV_{h} \\) metrics to evaluate the realism and diversity of the resulting hand motion. As shown in Table2, all the quantitative metrics for FineNet w/o. FDGN becomes worse on both datasets. Specifically, on Hand Fid and Hand Diversity, FineNet w/o. FDGN drops by 0.72 and 0.14. The huge increase in \\( FID_{h} \\) is mainly because FDGN generates hand movements with complete body information, making the hand motions more coordinated with the body."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.501,
+                0.789,
+                0.879,
+                0.896
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Strategy</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>6.28</td><td>/</td><td>0.71</td></tr><tr><td>FDGN-G</td><td>2.85</td><td>6.22</td><td>12.02</td><td>0.27</td></tr><tr><td>FDGN-C</td><td>1.68</td><td>6.34</td><td>11.51</td><td>0.46</td></tr><tr><td>FineNet</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.501,
+                0.897,
+                0.861,
+                0.912
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation study on different choreography strategies."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.52,
+                0.937
+            ],
+            "angle": 0,
+            "content": "10240"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.182
+            ],
+            "angle": 0,
+            "content": "Choreography Strategy. To verify the proposed generative-synthesis strategy, we use the following strategies to generate 3D dances: directly generating long-term 3D dances by FDGN (FDGN-G); generating 4s dance fragments according to the music clip by FDGN and concatenating these fragments together (FDGN-C), as Table 3 shows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.183,
+                0.468,
+                0.318
+            ],
+            "angle": 0,
+            "content": "FineNet performs better than others in FID, MM, and GS. For FDGN-G, a long music clip will cause the FID and GS to drop dramatically. FineNet achieves a lower Diversity score than FDGN-C because while retrieving the GCRM gives up some dances whose genre doesn't match. For MM and GS, FineNet increases by 5.21 and 0.28 compared to FDGN-C, which demonstrates that GCRM can increase the ability to generate diverse and genre-matched dance for the same song."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.332,
+                0.482,
+                0.409
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Generation Model</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>DeepDance</td><td>4.91</td><td>4.47</td><td>1.15</td><td>0.32</td></tr><tr><td>DanceRevolution</td><td>6.99</td><td>3.51</td><td>6.64</td><td>0.37</td></tr><tr><td>FDGN</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.102,
+                0.411,
+                0.443,
+                0.425
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation study on different generation networks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.429,
+                0.468,
+                0.579
+            ],
+            "angle": 0,
+            "content": "Influence of the generation model. We choose DanceRevolution, DeepDance as the backbone of the generative model, and get the whole 3D dances through our GCRM. All the results are shown in Table 4. Our FDGN performs best, which shows excellent dance generation ability. Besides, compared the results of Table 2 and Table 4, where DeepDance and DanceRevolution are inserted into our method in Table 4, and their performances can be improved on MM, FID and GS. These results show our GCRM is scalable."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.59,
+                0.199,
+                0.607
+            ],
+            "angle": 0,
+            "content": "5.4. User Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.613,
+                0.468,
+                0.674
+            ],
+            "angle": 0,
+            "content": "We invite 30 participants, including 15 dancers. Everyone watches 5 dances with a duration of 32 seconds. They are asked to evaluate the dances in 2 aspects: Effective duration and Artistry."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.468,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Effective duration. Each participant has to judge the time interval from the beginning until abnormal actions occur, such as abnormal shaking, motion freezing, or excessive joint distortion. As Table 5 shows, synthesis methods generally performs better than generation methods, generation methods can only generate effective dances for less than 10 seconds. These results show that generation methods are limited in effective duration. But, ours is a generative-synthesis method, and achieves the best performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Artistry. We measure the artistry of the dances from the following dimensions: genre matching (GM), rhythm matching (RM), diversity (Div.), and comprehensive artistry (CA). The full score of every dimension is 100. As shown in Table 6, synthesis methods generally perform better than generation methods, and our method gets a 77.0 average score"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.09,
+                0.89,
+                0.226
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Duration ↑</td><td>Type</td></tr><tr><td>Ground Truth</td><td>30.7s</td><td>/</td></tr><tr><td>ChoreoMaster</td><td>26.9s</td><td>synthesis</td></tr><tr><td>DanceRevolution</td><td>5.4s</td><td>generation</td></tr><tr><td>DeepDance</td><td>2.2s</td><td>generation</td></tr><tr><td>Baildando</td><td>3.1s</td><td>generation</td></tr><tr><td>FineNet (Ours)</td><td>28.2s</td><td>generation&amp;synthesis</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.573,
+                0.227,
+                0.819,
+                0.241
+            ],
+            "angle": 0,
+            "content": "Table 5. User study on effective duration."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.255,
+                0.885,
+                0.392
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>GM</td><td>RM</td><td>Div.</td><td>CA</td><td>Avg</td></tr><tr><td>Ground Truth</td><td>94.1</td><td>96.3</td><td>95.5</td><td>97.9</td><td>96.0</td></tr><tr><td>ChoreoMaster</td><td>64.2</td><td>59.7</td><td>77.2</td><td>69.8</td><td>67.7</td></tr><tr><td>DanceRevolution</td><td>33.2</td><td>30.7</td><td>47.4</td><td>31.4</td><td>36.7</td></tr><tr><td>DeepDance</td><td>17.2</td><td>22.1</td><td>24.4</td><td>25.6</td><td>22.3</td></tr><tr><td>Bailando</td><td>23.2</td><td>33.5</td><td>39.4</td><td>21.6</td><td>30.1</td></tr><tr><td>FineNet (Ours)</td><td>79.9</td><td>70.3</td><td>81.2</td><td>76.4</td><td>77.0</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.394,
+                0.882,
+                0.408
+            ],
+            "angle": 0,
+            "content": "Table 6. Result of the user study. Avg denotes the average score."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.424,
+                0.892,
+                0.469
+            ],
+            "angle": 0,
+            "content": "which clearly surpasses the baselines. However, compared to the ground truth, all the methods still need to improve especially in rhythm matching and Comprehensive artistry."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.485,
+                0.627,
+                0.5
+            ],
+            "angle": 0,
+            "content": "6. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.511,
+                0.892,
+                0.677
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a large-scale, high-quality 3D dance dataset (FineDance) for music-driven dance generation, which records professional and abundant dance genres with accurate and fine-grained hand motions. Meanwhile, we also propose a choreography Network (FineNet), which can generate multiple diverse genre-matched dances with flexible hand movements. Furthermore, we propose a new metric to evaluate the genre matching degree between music and dance. Quantitative and qualitative results show that FineNet can generate long-term, diverse, and genrematched dances from given music."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.693,
+                0.652,
+                0.71
+            ],
+            "angle": 0,
+            "content": "Acknowledgment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.719,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "We would like to express our sincere gratitude to Yan Zhang (https://yz-cnsdqz.github.io/) and Yulun Zhang (https://yulunzhang.com/) for their invaluable guidance and insights during the course of our research."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This work was supported in part by the Shenzhen Key Laboratory of next generation interactive media innovative technology (No.ZDSYS20210623092001004), in part by the China Postdoctoral Science Foundation (No.2023M731957), in part by the National Natural Science Foundation of China under Grant 62206153, Young Elite Scientists Sponsorship Program by CAST (No. 2023QNRC002)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.518,
+                0.937
+            ],
+            "angle": 0,
+            "content": "10241"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+# FineDance: A Fine-grained Choreography Dataset for 3D Full Body Dance Generation
+
+Ronghui Li $^{1*}$ , Junfan Zhao $^{1*}$ , Yachao Zhang $^{1}$ , Mingyang Su $^{1}$ , Zeping Ren $^{1}$ , Han Zhang $^{2}$ , Yansong Tang $^{1}$ , Xiu Li $^{1\dagger}$ $^{1}$ Tsinghua Shenzhen International Graduate School, Tsinghua University  
+ $^{2}$ Northwestern Polytechnical University  
+{lrh22, yf-zhao21}  $@$  mails.tsinghua.edu.cn, {yachaozhang, tang.yansong, li.xiu}  $@$  sz.tsinghua.edu.cn
+
+![](images/73d28fdca6082e86312f978b7a2a3bdf35c364951e15891397e6b3315bdd9b06.jpg)  
+Figure 1. A conceptual overview. We release a large-scale professional 3D motion capture dance dataset FineDance, and propose a choreography network FineNet. Training with FineDance, FineNet can generate multi-genre dances with expressive hand movements.
+
+![](images/b0989db44a6f6d559da137f0fd5925f62d1666a59adae4bd23fb206fa2900462.jpg)
+
+# Abstract
+
+Generating full-body and multi-genre dance sequences from given music is a challenging task, due to the limitations of existing datasets and the inherent complexity of the fine-grained hand motion and dance genres. To address these problems, we propose FineDance, which contains 14.6 hours of music-dance paired data, with fine-grained hand motions, fine-grained genres (22 dance genres), and accurate posture. To the best of our knowledge, FineDance is the largest music-dance paired dataset with the most dance genres. Additionally, to address monotonous and unnatural hand movements existing in previous methods, we propose a full-body dance generation network, which utilizes the diverse generation capabilities of the diffusion model to solve monotonous problems, and use expert nets to solve unreal problems. To further enhance the genrematching and long-term stability of generated dances, we
+
+propose a Genre&Coherent aware Retrieval Module. Besides, we propose a novel metric named Genre Matching Score to evaluate the genre-matching degree between dance and music. Quantitative and qualitative experiments demonstrate the quality of FineDance, and the state-of-the-art performance of FineNet. The FineDance Dataset and more qualitative samples can be found at website.
+
+# 1. Introduction
+
+Music and dance are two enduring art forms that can express a wide range of human emotions, and they have become essential elements in modern entertainment industries such as concerts, movies, and games[11]. However, creating high-quality 3D dance animations can be a costly and complex process that often involves skilled dancers, engineers, and expensive motion-capture equipment[5]. As a result, there is growing interest in using artificial intelligence (AI) to generate 3D dance animations from music, which
+
+has become a rapidly developing research topic.
+
+Despite the wide range of research in this field [19, 14, 22, 21, 2, 49, 35, 5, 44, 36, 25, 46, 47], enetering high-quality dances is still limited by the existing datasets: (1) Full-body expressiveness: Existing dance datasets contain few hand movements, and only 1.5 hours of full body dance data is available. The previous methods in motion generation, treating body and hand as the same, lead to unnatural or monotonous hand motions, because the body and hand are in different feature spaces. However, uncoordinated body and hand motions can destroy the expressiveness of the overall dance. (2) Multi-genre: Existing datasets contain a limited number of dance genres, so the generated dances are not sufficient to match various music styles. Previous methods struggle with limited coarse dance genres and have no suitable objective metric to measure the genrematching degree between music and generated dances.
+
+To address the limitations of existing datasets, we introduce a Fine-grained Choreography Dance dataset (FineDance). It comprises over 14.6 hours of data collected from 346 paired songs and dances, was created by professional dancers and a motion capture system, which has accurate body and hand motions. The fine-grained 22 dance genres of FineDance spanning traditional and modern styles, which make the genre-matching of generated dance sequences and given music become more challenging. FineDance includes music, dance sequences, FilmBox (fbx) files, SMPL[23, 29], and multi-view videos.
+
+Early music-driven dance synthesis methods [3, 16, 24, 32, 15, 35, 2, 48] often rely on motion graph-based algorithms where the dance fragments from a pre-existing music-dance database are stitched together to synthesize one dance. While such methods can synthesize long-term dances, they do not produce new dance fragments. Recently methods have employed generative networks such as VAE[33], GAN[30], Normalization Flow Network[40], Diffusion[38]. But they focus solely on body part, while neglecting hand movements, resulting in unnatural or monotonous hand motions even trained with well-annotated body and hand labels. Additionally, the generative-based methods are limited by the long-term modeling ability of the networks, making them difficult to generate long-term dance sequences.
+
+Therefore, we propose FineNet, a two-stage generative-synthesis network that addresses the limitations of previous dance generation methods. In the first stage, we propose a diffusion-based Full-body dance generation network (FDGN). The key of FDGN is to design two expert networks, which are dedicated to the generation of body and hand motions, and use a Refine Net to assemble them coordinately. In the second stage, we propose a Genre&Coherence aware Retrieval Module (GCRM), which ensures the coherence of dance fragments and
+
+matches the genre between the music and the dances. Based on the suitable dance fragments retrieved by GCRM, we can produce genre-matching and long-term dances. A conceptual overview of the dataset and method is shown in Figure1. Finally, to objectively evaluate the genre-matching degree between generated dances and given music, we propose a novel metric, named Genre-matching Score (GS).
+
+Overall, our contributions can be summarized as follows:
+
+- We release FineDance, which is the largest 3D motion capture music-dance paired dataset with accurate full-body posture, containing 22 fine-grained genres. FineDance encourages the development of AI choreography, motion prior, and full-body reconstruction methods.  
+- We present FineNet, which leverages expert networks and refine network to generate expressive full-body dances, and employs a cross-modal retrieval network to improve genre-matching scores.  
+- Extensive quantitative experiments and user studies demonstrate that our approach can generate multiple different genre-matched dances from arbitrary music with natural and flexible hand movements.
+
+# 2. Related Works
+
+# 2.1. Choreography Dataset
+
+Currently, the most popular 3D choreography dataset is AIST++ [22], which provides 5 hours of dance but does not have hand motions. AIST++ is reconstructed through multi-view video. Therefore, there is inevitably a deviation between the generated 3D dance motions and the real motions because of the reconstruction error. Li et al. [21] provided another major type of 3D dance dataset: modeling in software, which is obtained by experienced animators. However, this type of dataset lacks the authenticity of the dance. At present, the most accurate datasets are obtained from motion capture systems. GrooveNet dataset [2] only contains the electronic dance genre in 23 minutes sequence. Dance with Melody [35] further constructed a 94-minute 3D dance dataset with 4 genres. Music2Dance [49] is a dataset with only one hour and 2 genres (modern and curtailage dance). Chen et al. [5] built a 9 hours dataset, but it only has four different dance genres. This genre partition does not match the discernment of professional dance artists. For example, Anime and K-pop do not count as specific dance genres. In conclusion, these datasets have limitations in hand motion, duration, and the diversity of genres and dancers. Our dataset contains 14.6 hours with 22 genres, and is collected by 27 dancers.
+
+# 2.2. AI Choreography
+
+Synthesis based approach. Early works[28, 26, 4, 43, 20] usually synthesis dances based on motion graphs and databases, which share one core idea: retrieving the most matching dance fragment for the given music clip, and splicing multiple fragments into a complete dance. In computer graphics, motion synthesis has long attracted a lot of attention as it can synthesize 3D actions from existing motion databases. Lamouret et al. [18] first delivered this idea and proposed a prototype system to create new actions by cutting and pasting action fragments from an action database. Arikan et al. [3] formally introduced the concept of graph-based motion synthesis, transforming this problem into finding paths in a pre-built motion graph. Under such a framework, the task of synthesizing actions is usually regarded as finding the optimal path in a constructed motion graph. Similar utilizing this graph-based scheme, Kim et al. [16] made the first attempt to synthesize rhythmic movements by adding constraints connecting action beats and rhythmic patterns. Shiratori et al. [32] and Kim et al. [15] formally pointed the music-driven dance movement synthesis problem and further developed more complex rules to associate dance movement segments with input music segments. This type of method can synthesize dances that match the music style well. However, as it is unable to learn the internal connections between music and dance, the synthesized dances cannot match the rhythm well. In addition, because the dance fragments are all from the database, such methods have no ability to create new dance motions. In this paper, we introduce the diversity generated technology into the synthesis method to maintain the advantages of synthesis and avoid the above problems.
+
+Generation based approach. Generative Adversarial Network (GAN) [10] and Variational Auto Encoder (VAE) [17] have been successfully applied to generate various data modalities, including image, motion, music, etc. As a result, researchers also propose music-driven dance generation algorithms based on the general deep generation paradigm[7, 22, 34, 1, 21, 8, 42, 13, 12]. Such methods can be divided into 2D and 3D solutions according to the dimension of the generated dance data. Lee et al. [19] proposed the first music-driven 2D dance generative network, which uses VAE to model dance units and GAN to loop to generate dance sequences. Since the human skeleton is a natural graph data, Ren et al. [30] and Ferreira et al. [6] adopted a Graph Convolutional Network to improve the spatial naturalness of the generated 2D dance movements. Both music and dance belong to sequence data. Therefore, Li et al. [22] used the Transformer [41] network with strong sequence modeling ability to design a music-driven 3D dance action generation network. Recently, diffusion-based networks succeed in text2motion generation[37, 45]. Although these generative networks have the advantages, such as rhythm-
+
+![](images/439cc5f5ab9543f591ca3c06ba882a93c2e8ca9b97e764388c0b40905a6f8c27.jpg)  
+Figure 2. FineDance acquisition process. We capture the dancers' motions with the Vicon optical motion capture system. Then engineers retarget it to a standard skeleton in MotionBuilder. Dancers manually align the music with the dance motions and extract the skeletal information of the dance in Blender.
+
+matched and diversity, they neglect the quality of generated hand motions, and only generate motion fragments within several seconds. Our method can generate expressive full-body dances due to our diffusion based expert nets, and use a retrieval based modal to enhance the genre-matching score and take the advantages of synthetic methods such as genrematching, long-term stability.
+
+# 3. FineDance Dataset
+
+The review of the choreography dataset is shown in Section 2.1, there are still few accessible large-scale motion capture choreography datasets even though many papers reported their choreography datasets. Meanwhile, most of these datasets are insufficient to train a diversified and generalized-well choreography model due to the limiting of dance genres, and poor music-dance pairings. Our FineDance can fill these gaps.
+
+# 3.1. Data Acquisition and Analysis
+
+For the fine-grained dataset, we take the following regulations into account for our dataset acquisition. We give the flowchart of the process shown in Figure 2. We summarized the comparison of FineDance and existing 3D dance datasets in Table 1.
+
+Fine-grained motions. So far, there are only 2 datasets containing finger motion, and the available data is less than 1.5 hours. Fine-grained motions are ignored in existing methods. For example, GrooveNet[2] only contains 30 body joints, and Dance with Melody[35] has only 21 body joints, while EA-MUD[34], PhantomDance[21] and AIST++[22] all use 24 body joints of the SMPL[23] model.
+
+Our data store the information of the skeleton joints in 3D space in each frame including fingers, which can help to improve the artistry and reality of the dance motion. For easy to utilize, we use the standard 52 joints to represent the dance data.
+
+Fine-grained dance genres. Previous literature focuses on a few dance genres, such as GrooveNet[2],
+
+<table><tr><td>Dataset</td><td>Pos/Rot</td><td>Joints num</td><td>Hand joint</td><td>Genres</td><td>Mocap</td><td>RGB Views</td><td>Fbx</td><td>SMPL</td><td>Dancers</td><td>Total hours</td><td>avg Sec per Seq</td></tr><tr><td>GrooveNet[2]</td><td>✓/X</td><td>30</td><td>X</td><td>1</td><td>✓</td><td>1</td><td>X</td><td>X</td><td>1</td><td>0.38</td><td>690</td></tr><tr><td>Dance w/Melody[35]</td><td>✓/X</td><td>21</td><td>X</td><td>4</td><td>✓</td><td>4</td><td>X</td><td>X</td><td>-</td><td>1.6</td><td>92.5</td></tr><tr><td>Music2Dance[49]</td><td>✓/X</td><td>55</td><td>✓</td><td>2</td><td>✓</td><td>2</td><td>X</td><td>X</td><td>2</td><td>0.96</td><td>-</td></tr><tr><td>EA-MUD[34]</td><td>✓/✓</td><td>24</td><td>X</td><td>4</td><td>X</td><td>4</td><td>X</td><td>X</td><td>-</td><td>0.35</td><td>73.8</td></tr><tr><td>PhantomDance[21]</td><td>✓/X</td><td>24</td><td>X</td><td>13</td><td>X</td><td>0</td><td>X</td><td>X</td><td>-</td><td>9.6</td><td>133.3</td></tr><tr><td>AIST++[22]</td><td>✓/✓</td><td>17/24</td><td>X</td><td>10</td><td>X</td><td>10</td><td>X</td><td>✓</td><td>-</td><td>5.2</td><td>13.3</td></tr><tr><td>MMD[5]</td><td>✓/✓</td><td>52</td><td>✓</td><td>4</td><td>✓</td><td>0</td><td>✓</td><td>X</td><td>-</td><td>9.9</td><td>-</td></tr><tr><td>FineDance (Ours)</td><td>✓/✓</td><td>52</td><td>✓</td><td>22</td><td>✓</td><td>2</td><td>✓</td><td>✓</td><td>27</td><td>14.6</td><td>152.3</td></tr></table>
+
+Table 1. Comparisons of 3D Dance Datasets. Pos and Ros means 3D position and Rotation information respectively. Fbx (FilmBox) is one of the main 3D exchange formats as used by many 3D tools. "avg Sec per Seq" means the average seconds per sequence.
+
+Music2Dance[49], MMD[5] and Dance with Melody[35]. This dataset uses a rough genre classification strategy, which is a non-standardized dance division.
+
+We improve the diversity of our dataset from two aspects: more genres and more dancers. Our FineDance is reasonably classified under the advice of dance artists, covering hip-hop and Chinese classical dance more completely. To the best of our knowledge, it also includes folk dance motions for the first time, expanding the dance genres of the choreography dataset. Totally, FineDance has up to 22 genres of dance defined by professional dance artists. And we obtained more than 14 hours of data. It is worth noting that FineDance contains the most genres. Details are given in the supplementary materials.
+
+Accurate posture. Currently, the largest available dataset is AIST++[22], which is collected by reconstructing 3D poses in multi-view videos. But the dance data is not real due to the reconstructing errors. Instead of reconstruction from the videos, ours is collected by a motion capture system, and all dance motions and music are well paired.
+
+In FineDance, all motions are captured by the Vicon optical motion capture system and retargeted to a standard skeleton in MotionBuilder by engineers. Therefore, FineDance can donate accurate postures. Moreover, FineDance will be the largest fully available 3D music-dance paired dataset, and it will be available.
+
+Well-paired dance and music. Dance fragments are strongly associated with the rhythm and style of music. However, due to the lack of enough well-paired data, the generative model is hard to fit the relevance of the motion rhythm and music rhythm. Therefore, we asked the professional dancers to pay attention to the matching of rhythm and style when dancing.
+
+Professional dancer. We invited 27 professional dancers, and each dancer was asked to dance to the music while his/her motions were captured utilizing the capture system.
+
+# 4. FineNet
+
+# 4.1. Overall Framework
+
+Given music of unknown style and arbitrary duration, our goal is to generate multiple different full-body dances. This task presents challenges in three areas: (1) Full-body: Body and two hands motions in different spaces have different grains, using a single network to generate full-body motions like the previous method can lead to unreal and monotonous hand gestures. (2) Genre-matching: Making the generated dances consistent with the fine-grained genre is also challenging due to the modal gap between music and dance. (3) Long-term: Generating long-term novel motion is challenging because neural networks tend to accumulate errors over time. To address these issues, we propose FineNet, which comprises a Diffusion-based Full-body Diverse Dance Generation Network (FDGN) and a Genre & Coherent aware Retrieval Module (GCRM). The FDGN focuses on creating detailed dances with expressive movements, while the GCRM considers the overall choreography of the dance. FineNet cleverly combines generative and synthetic methods, making them complementary, much like the process of human choreography. Furthermore, FineNet allows for the generation of multiple different dances by selecting distinct dance segments at the initial time step. This capability offers users a wide range of creative possibilities.
+
+The overall framework of our method is shown in Figure 3. First, the input music  $X$  is split into 4-second clips  $\{X^t\}_{t=1}^N$  without overlapping, and  $N$  is the number of clips of the given music. For each  $X^t$ , we use the Librosa toolbox [27] to extract the temporal feature  $\bar{X}^t \in \mathbb{R}^{T \times C^m}$ , and the mel-spectrogram image  $\tilde{\bar{X}}^t \in \mathbb{R}^{W \times H \times 3}$ , where  $T$  is the time length of a clip and  $C^m$  is the channel dimension.  $W$  and  $H$  are the width and height of the image respectively, and 3 means the number of RGB channels. FineNet generates and retrieves the best dance fragment at each time step,
+
+![](images/d058aea2b7f4f67160b063f265639553b9edcd16541bf4723de7f9bca72864f6.jpg)  
+Figure 3. An overview of our framework. FineNet can iteratively generate and choreograph different dance fragments based on the mel-spectrogram and temporal features of music. FineNet consists of a diffusion-based Full body Dance Generation Network (FDGN) and a Genre&Coherence retrieval module. The former is utilized to generate expressive and diverse full-body dance fragments; the latter is designed to retrieve the best matching dance fragments from the generated multiple dance fragments and synthesis them smoothly.
+
+and this process can be formulated as:
+
+$$
+\begin{array}{l} \hat {Y} ^ {1} = \text {F i n e N e t} (\bar {X} ^ {1}, \tilde {X} ^ {1}) \\ \hat {\mathrm {V}} ^ {t} = \text {F i n e N e t} (\tilde {X} ^ {t}, \tilde {X} ^ {t}, \hat {\mathrm {V}} ^ {t - 1}) \end{array} \tag {1}
+$$
+
+$$
+\hat {Y} ^ {t} = F i n e N e t (\bar {X} ^ {t}, \widetilde {X} ^ {t}, \hat {Y} ^ {t - 1}),
+$$
+
+where  $t \in \{2,3,\dots ,N\}$  is the current time step.  $\hat{Y}^t \in \mathbb{R}^{V \times (T \times 3)}$  is the dance action fragment obtained by FineNet at time step t, and  $V$  is the number of body and hand joints, "3" represents 3-dimensional axis angle and position of joints.
+
+# 4.2. Diverse Dance Generation
+
+The previous generative models such as VAE[33] and GAN[30], mostly directly link music embedding to dance embedding method, which results in the limited diversity of the generated dances. This is because high-level condensed features of music usually contain insufficient details to guide the network to generate different dances [45].
+
+To generate novel and diverse dances, we employ a diffusion-based model, FDGN. To make the network perceive the music rhythm better, we feed the music temporal feature to FDGN  $\bar{X}^t$  instead of  $X^t$ . Given  $\bar{X}^t$  and different noise sampled from  $\mathcal{N}(0,I)$ , FDGN can generate  $M$  distinctive dance fragments, represented as  $\{\hat{Y}_i^t\}_{i=1}^M$ .
+
+# 4.3. FDGN: Full-body Dance Generation Network
+
+We propose FDGN, a network for generating full body dance motions. Compared to previous models, FDGN can produce more realistic, natural, and expressive hand motions that coordinate well with body motion and music styles. As shown in Figure 4, we use two expert networks to generate body and hand motion separately. This is based on two observations: (1) The range of motion of the body and hand is obviously different and belongs to different feature spaces. Therefore, using a single network to generate
+
+![](images/8d0236ccb183e2c4c347115c387f8620ea27c42d39f4e907ec57240f32425f48.jpg)  
+Figure 4. Full-body Dance Generation Network."  $\bigoplus$  " means add.
+
+full-body dances can result in unnatural hand motions. (2) In dance generation, music rhythm mainly coordinates with the limbs, and hand motion should be consistent with the body and music style. The structure of body/hand expert net is modified by MDM[37] and EDGE[39]. The training process of body expert net can be formulated as:
+
+$$
+\mathcal {L} _ {d} = \mathrm {E} _ {s \in [ 1, S ], Y b _ {0} \sim q (Y b _ {0})} \left[ \left\| Y b _ {0} - B E N \left(Y b _ {s}, s, \bar {X}\right) \right\| _ {2} ^ {2} \right], \tag {2}
+$$
+
+where  $Yb_{0}$  is the label dance data,  $BEN(\cdot)$  means Body Expert Net,  $s$  is the number of diffusion steps. The refine net is consisted of a spatial convolution network and a refine gate unit, which is used to assemble two parts naturally.
+
+# 4.4. Genre&Coherent aware Retrieval Module
+
+Thanks to FDGN's diverse generative capabilities, we can generate  $M$  candidate dance fragments  $\{\bar{Y}_i^t\}_{i=1}^M$  for the  $t-th$  music clip  $\{\bar{X}^t\}$ . To search the genre-matched candidate dance fragment and synthesis them coherently, we propose Genre&Coherent aware Retrieval Module (GCRM),
+
+which calculates the Genre Matching Score (GS) of the current music clip and the candidate dance fragments, and the coherent score of the previous selected dance fragment and the current candidate dance fragments. Finally, we choreograph the complete dance by combining the two scores.
+
+Genre matching score. We use GS to evaluate the matching degree of the style of music clip  $\widetilde{X^t}$  and the genres of generated candidate dance fragments  $\{\hat{Y}_i^t\}_{i=1}^M$ . However, music and dance are different data modalities, and it is difficult to calculate the genre similarity directly. To cover this problem, we propose a cross-modal retrieval network.
+
+We utilize two models (one music style encoder  $\mathcal{F}_{\theta}^{m}(\cdot)$  and one dance genre encoder  $\mathcal{F}_{\theta}^{d}(\cdot))$  to encode different modalities into one embedding space. The music style encoder is the backbone of AST [9] and the dance genre encoder is the backbone of AGCN [31]. We extract the mel-spectrogram features  $\widetilde{X^t}$  of music  $X^t$  and send it to the music encoder. For each  $\{\widetilde{X^t}\}_{t = 1}^N$ , we compute its genre-matching score with candidate dance fragments generated by FDGN. We utilize the cosine similarity as the genre matching score. So the genre matching score between  $\widetilde{X^t}$  and  $\{\hat{Y}_i^{t}\}_{i = 1}^M$  can be formulated as:
+
+$$
+G S _ {i} ^ {t} = s \left(\widetilde {X ^ {t}}, \hat {Y} _ {i} ^ {t}\right) = \frac {\mathcal {F} _ {\theta} ^ {m} \left(\widetilde {X ^ {t}}\right) ^ {T} \mathcal {F} _ {\theta} ^ {d} \left(Y _ {i} ^ {t}\right)}{\left| \left| \mathcal {F} _ {\theta} ^ {m} \left(\widetilde {X ^ {t}}\right) \right| \right| \times \left| \left| \mathcal {F} _ {\theta} ^ {d} \left(Y _ {i} ^ {t}\right) \right| \right|}, \tag {3}
+$$
+
+We train the above two models by a cosine loss  $\mathcal{L}_{cos}$  as a retrieval task, which can be formulated as:
+
+$$
+\mathcal {L} _ {\text {c o s}} = y \left(1 - s \left(\widetilde {X _ {i}}, Y _ {j}\right)\right) + (1 - y) \left(\max  \left(0, s \left(\widetilde {X _ {i}}, Y _ {j}\right)\right), \right. \tag {4}
+$$
+
+where  $\widetilde{X_i}$  is the MFCCs feature of music clip,  $Y_{j}$  is a dance fragment.  $y = 1$  when  $\widetilde{X_i}$  and  $Y_{j}$  are genre-matched, otherwise  $y = 0$ .
+
+Coherent score. We take the L2 distance of the start and end states of the two dance segments as the coherence score. To make the transition smoother, we cut 5 frames of the last temporal clip  $(t - 1)$  best matching fragment  $\hat{Y}_b^{t - 1}$  on the tail and cut the start 5 frames of the  $M$  candidate dance fragments  $\{\hat{Y}_i^t\}_{i = 1}^M$  at the current time step  $t$ . These cut frames are finally filled with a linear interpolation algorithm.
+
+$$
+C S _ {i} ^ {1} = 0 \tag {5}
+$$
+
+$$
+C S _ {i} ^ {\ell} = - | | Y _ {b} ^ {t - 1} [ - 5, : ] - Y _ {i} ^ {t} [ 5, : ] | | _ {2},
+$$
+
+where  $t\in \{2,3,\dots ,N\}$  is the time step.
+
+Combining GS and CS, GCRM can find the best  $\hat{Y}^t$  from the candidate dance segments  $\{Y_i^t\}_{i=1}^M$  as the output at time step  $t$ :
+
+$$
+i d x ^ {t} = \operatorname {a r g m a x} _ {i} \left(\alpha G S _ {i} ^ {t} + \beta C S _ {i} ^ {t}\right), \tag {6}
+$$
+
+$$
+\hat {Y} ^ {t} := \hat {Y} _ {i d x ^ {t}} ^ {t}, \hat {Y} _ {i d x ^ {t}} ^ {t} \in \left\{Y _ {i} ^ {t} \right\} _ {i = 1} ^ {M},
+$$
+
+where  $\alpha$  and  $\beta$  are weight parameters. For complete music  $X$ , FineNet outputs the dance fragments step by step, and
+
+![](images/cf0a80540606a7aeab1d5dcf69d45374c7ff7c6d14eda01e17e77c277deb0da6.jpg)  
+Figure 5. Qualitative result comparisons for a Jazz song.
+
+the final result is:  $\hat{Y} = [\hat{Y}^1, \hat{Y}^2, \dots, \hat{Y}^T]$ . Furthermore, by choosing different  $\hat{Y}^1$  at step 1, FineNet can generate multiple dances with excellent diversity.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+Data Preprocessing. We spilt FineDance dataset into train, val and test sets in two ways: FineDance@Genre and FineDance@Dancer. The test set of FineDance@Genre includes a broader range of dance genres, but the same dancer appear in train/val/test set. FineDance@Dancer means the train/val/test set divided by different dancers, which test set contains fewer dance genres, yet the same dancer won't appear in different sets. We only reported the results of test set on FineDance@Genre in this paper, the details of dataset split can be found in our supplementary materials. Each music and paired dance are only present in one set. For all the dance fragments, we combine the 3-dim axis angle vector representation for all 52 joints, along with a 3-dim global position vector, resulting in 159-dim motion features. For all the music clips, we use Librosa [27] to extract the 35-dim music temporal features. We also extract the mel-spectrogram of the music clips with Librosa and resized it to  $224 \times 224 \times 3$ . During extracting audio features, the sampling rate is  $76,800\mathrm{Hz}$  and hop size is 512.
+
+Implementation Details. In FDGN, we build 3 MLP layers to encode the music and body features. We use the transformer layer as the backbone of the body/hand expert net. The refine net consists of a 1-D convolution layer and a learnable weight parameter. The total epoch, learning rate, and batch size are set as 200,  $2e^{-4}$ , 2048. In the GCRM, the  $\alpha$ ,  $\beta$  are set as 1.0 and 0.5 respectively.
+
+Evaluation Metrics. (1) FID score. Fréchet inception distance (FID) is widely used to measure how close the distribution of the generated dances is to that of the ground truth.
+
+<table><tr><td rowspan="2">Method</td><td colspan="6">FineDance Dataset</td><td colspan="6">AIST++ Dataset</td></tr><tr><td>FID↓</td><td>FIDh↓</td><td>Div↑</td><td>Divh↑</td><td>MM↑</td><td>GS↑</td><td>FID↓</td><td>FIDh↓</td><td>Div↑</td><td>Divh↑</td><td>MM↑</td><td>GS↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>/</td><td>6.28</td><td>3.48</td><td>/</td><td>0.71</td><td>/</td><td>/</td><td>9.07</td><td>/</td><td>/</td><td>0.77</td></tr><tr><td>ChoreoMaster#</td><td>1.92</td><td>0.61</td><td>6.18</td><td>3.33</td><td>12.20</td><td>0.39</td><td>2.21</td><td>/</td><td>9.38</td><td>/</td><td>30.71</td><td>0.71</td></tr><tr><td>DanceRevolution*</td><td>7.44</td><td>3.21</td><td>3.92</td><td>1.80</td><td>4.22</td><td>0.30</td><td>6.05</td><td>/</td><td>7.67</td><td>/</td><td>12.88</td><td>0.75</td></tr><tr><td>DeepDance*</td><td>5.77</td><td>1.95</td><td>5.07</td><td>3.50</td><td>0.73</td><td>0.36</td><td>25.78</td><td>/</td><td>8.98</td><td>/</td><td>3.08</td><td>0.73</td></tr><tr><td>Bailando*</td><td>4.77</td><td>2.24</td><td>3.09</td><td>1.12</td><td>2.33</td><td>0.29</td><td>17.45</td><td>/</td><td>9.44</td><td>/</td><td>2.58</td><td>0.74</td></tr><tr><td>FineNet (w/o. FDGN)</td><td>1.90</td><td>1.20</td><td>5.87</td><td>3.40</td><td>12.86</td><td>0.62</td><td>2.11</td><td>/</td><td>9.13</td><td>/</td><td>31.09</td><td>0.79</td></tr><tr><td>FineNet</td><td>1.66</td><td>0.48</td><td>5.99</td><td>3.59</td><td>16.72</td><td>0.74</td><td>2.05</td><td>/</td><td>9.94</td><td>/</td><td>33.67</td><td>0.80</td></tr></table>
+
+Similar to Lee et al.[19], we trained a style classifier in our dataset to extract motion features, and then use the features to calculate FID. (2) Diversity. We follow Lee et al. [19] to evaluate the average feature distance between generated dances for different input music. The same feature extractor used in FID is used again. (3) Hand FID score and Hand Diversity. Similarly, we extract hand motion features and calculate the FID and diversity for hand motion. (4) Multi-modality. We follow Lee et al.[19] to evaluate the average feature distance between the 10 choreography versions of every music. This metric measures the model's ability to generate different dances for the same music. (5) Genre Matching Score. We evaluate the average genre matching score between generated dance and the input music using the genre matching score calculation network mentioned in section 4.4. The genre matching score is defined as Eq. (3).
+
+# 5.2. Quantitative and Qualitative Evaluation
+
+Compared methods. We compare our method with several generation-based methods and one synthesis-based method. ChoreoMaster [5] is a dance synthesis method with style embedding network and graph-based motion synthesis. Since the code is not available, we reproduced the code according to the paper. DanceRevolution [14] is a generation method using Transformer to generate long-term dances. DeepDance [10] is a generation method with a GAN-based cross-modal association framework. Bailando [33] is a generation method with VAE and an actor-critic generative pre-trained transformer model. All the methods are tested on FineDance and AIST++ to evaluate the comprehensive choreography ability of FineNet.
+
+Results and analysis. For all methods, we generate 10 versions of the dance for each song in the test set, and take the paired real dance as the Ground Truth. As shown in Table 2, our method gets the best performance in all evaluation metrics except Diversity on both datasets. Choreo-Master gets better on Diversity because it must retrieve all the fragments in the whole training set but no new motion is created. Specifically, on Multimodality (MM), FineNet
+
+gains 4.52 improvements compared to ChoreoMaster. On GS, FineNet is 0.03 higher than the ground truth. These two metrics show FineNet can generate diverse and genrematched dance. Besides, FineNet gets the highest Hand FID and Hand Diversity which shows our method can generate real and diverse hand motion.
+
+Qualitative results are shown in Figure 5. DanceRevelation, DeepDance and Bailando generated almost identical stiff motions (refer to row 1 and row 2). ChoreoMaster generates classical dance motions in the last two images that do not match the Jazz music. But the generated dance motions of FineNet are diverse and in line with the Jazz style. The hand motion generated by FineNet W/ FDGN is more real. The corresponding videos refer to supplementary material.
+
+# 5.3. Ablation Study
+
+We replace different components of our method, and conduct experiments to demonstrate the effectiveness of each component on the test set of FineDance.
+
+Infulence of the FDGN. In order to verify whether FDGN can make hand movements more natural and flexible. We modified FDGN as a single network that generates body and hand motion simultaneously. We then employed  $FID_{h}$  and  $DIV_{h}$  metrics to evaluate the realism and diversity of the resulting hand motion. As shown in Table2, all the quantitative metrics for FineNet w/o. FDGN becomes worse on both datasets. Specifically, on Hand Fid and Hand Diversity, FineNet w/o. FDGN drops by 0.72 and 0.14. The huge increase in  $FID_{h}$  is mainly because FDGN generates hand movements with complete body information, making the hand motions more coordinated with the body.
+
+Table 2. Compared with SOTAs. # means we reproduce the code, * means we use the published code.  
+
+<table><tr><td>Strategy</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>6.28</td><td>/</td><td>0.71</td></tr><tr><td>FDGN-G</td><td>2.85</td><td>6.22</td><td>12.02</td><td>0.27</td></tr><tr><td>FDGN-C</td><td>1.68</td><td>6.34</td><td>11.51</td><td>0.46</td></tr><tr><td>FineNet</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>
+
+Table 3. Ablation study on different choreography strategies.
+
+Choreography Strategy. To verify the proposed generative-synthesis strategy, we use the following strategies to generate 3D dances: directly generating long-term 3D dances by FDGN (FDGN-G); generating 4s dance fragments according to the music clip by FDGN and concatenating these fragments together (FDGN-C), as Table 3 shows.
+
+FineNet performs better than others in FID, MM, and GS. For FDGN-G, a long music clip will cause the FID and GS to drop dramatically. FineNet achieves a lower Diversity score than FDGN-C because while retrieving the GCRM gives up some dances whose genre doesn't match. For MM and GS, FineNet increases by 5.21 and 0.28 compared to FDGN-C, which demonstrates that GCRM can increase the ability to generate diverse and genre-matched dance for the same song.
+
+<table><tr><td>Generation Model</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>DeepDance</td><td>4.91</td><td>4.47</td><td>1.15</td><td>0.32</td></tr><tr><td>DanceRevolution</td><td>6.99</td><td>3.51</td><td>6.64</td><td>0.37</td></tr><tr><td>FDGN</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>
+
+Influence of the generation model. We choose DanceRevolution, DeepDance as the backbone of the generative model, and get the whole 3D dances through our GCRM. All the results are shown in Table 4. Our FDGN performs best, which shows excellent dance generation ability. Besides, compared the results of Table 2 and Table 4, where DeepDance and DanceRevolution are inserted into our method in Table 4, and their performances can be improved on MM, FID and GS. These results show our GCRM is scalable.
+
+# 5.4. User Study
+
+We invite 30 participants, including 15 dancers. Everyone watches 5 dances with a duration of 32 seconds. They are asked to evaluate the dances in 2 aspects: Effective duration and Artistry.
+
+Effective duration. Each participant has to judge the time interval from the beginning until abnormal actions occur, such as abnormal shaking, motion freezing, or excessive joint distortion. As Table 5 shows, synthesis methods generally performs better than generation methods, generation methods can only generate effective dances for less than 10 seconds. These results show that generation methods are limited in effective duration. But, ours is a generative-synthesis method, and achieves the best performance.
+
+Artistry. We measure the artistry of the dances from the following dimensions: genre matching (GM), rhythm matching (RM), diversity (Div.), and comprehensive artistry (CA). The full score of every dimension is 100. As shown in Table 6, synthesis methods generally perform better than generation methods, and our method gets a 77.0 average score
+
+Table 4. Ablation study on different generation networks.  
+
+<table><tr><td>Method</td><td>Duration ↑</td><td>Type</td></tr><tr><td>Ground Truth</td><td>30.7s</td><td>/</td></tr><tr><td>ChoreoMaster</td><td>26.9s</td><td>synthesis</td></tr><tr><td>DanceRevolution</td><td>5.4s</td><td>generation</td></tr><tr><td>DeepDance</td><td>2.2s</td><td>generation</td></tr><tr><td>Baildando</td><td>3.1s</td><td>generation</td></tr><tr><td>FineNet (Ours)</td><td>28.2s</td><td>generation&amp;synthesis</td></tr></table>
+
+Table 5. User study on effective duration.  
+
+<table><tr><td>Method</td><td>GM</td><td>RM</td><td>Div.</td><td>CA</td><td>Avg</td></tr><tr><td>Ground Truth</td><td>94.1</td><td>96.3</td><td>95.5</td><td>97.9</td><td>96.0</td></tr><tr><td>ChoreoMaster</td><td>64.2</td><td>59.7</td><td>77.2</td><td>69.8</td><td>67.7</td></tr><tr><td>DanceRevolution</td><td>33.2</td><td>30.7</td><td>47.4</td><td>31.4</td><td>36.7</td></tr><tr><td>DeepDance</td><td>17.2</td><td>22.1</td><td>24.4</td><td>25.6</td><td>22.3</td></tr><tr><td>Bailando</td><td>23.2</td><td>33.5</td><td>39.4</td><td>21.6</td><td>30.1</td></tr><tr><td>FineNet (Ours)</td><td>79.9</td><td>70.3</td><td>81.2</td><td>76.4</td><td>77.0</td></tr></table>
+
+Table 6. Result of the user study. Avg denotes the average score.
+
+which clearly surpasses the baselines. However, compared to the ground truth, all the methods still need to improve especially in rhythm matching and Comprehensive artistry.
+
+# 6. Conclusions
+
+In this paper, we propose a large-scale, high-quality 3D dance dataset (FineDance) for music-driven dance generation, which records professional and abundant dance genres with accurate and fine-grained hand motions. Meanwhile, we also propose a choreography Network (FineNet), which can generate multiple diverse genre-matched dances with flexible hand movements. Furthermore, we propose a new metric to evaluate the genre matching degree between music and dance. Quantitative and qualitative results show that FineNet can generate long-term, diverse, and genrematched dances from given music.
+
+# Acknowledgment
+
+We would like to express our sincere gratitude to Yan Zhang (https://yz-cnsdqz.github.io/) and Yulun Zhang (https://yulunzhang.com/) for their invaluable guidance and insights during the course of our research.
+
+This work was supported in part by the Shenzhen Key Laboratory of next generation interactive media innovative technology (No.ZDSYS20210623092001004), in part by the China Postdoctoral Science Foundation (No.2023M731957), in part by the National Natural Science Foundation of China under Grant 62206153, Young Elite Scientists Sponsorship Program by CAST (No. 2023QNRC002)
+
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+                                    "content": "Generating full-body and multi-genre dance sequences from given music is a challenging task, due to the limitations of existing datasets and the inherent complexity of the fine-grained hand motion and dance genres. To address these problems, we propose FineDance, which contains 14.6 hours of music-dance paired data, with fine-grained hand motions, fine-grained genres (22 dance genres), and accurate posture. To the best of our knowledge, FineDance is the largest music-dance paired dataset with the most dance genres. Additionally, to address monotonous and unnatural hand movements existing in previous methods, we propose a full-body dance generation network, which utilizes the diverse generation capabilities of the diffusion model to solve monotonous problems, and use expert nets to solve unreal problems. To further enhance the genrematching and long-term stability of generated dances, we"
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+                                    "content": "propose a Genre&Coherent aware Retrieval Module. Besides, we propose a novel metric named Genre Matching Score to evaluate the genre-matching degree between dance and music. Quantitative and qualitative experiments demonstrate the quality of FineDance, and the state-of-the-art performance of FineNet. The FineDance Dataset and more qualitative samples can be found at website."
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+                                    "content": "1. Introduction"
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+                                    "content": "Music and dance are two enduring art forms that can express a wide range of human emotions, and they have become essential elements in modern entertainment industries such as concerts, movies, and games[11]. However, creating high-quality 3D dance animations can be a costly and complex process that often involves skilled dancers, engineers, and expensive motion-capture equipment[5]. As a result, there is growing interest in using artificial intelligence (AI) to generate 3D dance animations from music, which"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "type": "text",
+                                    "content": "* equal contribution, † corresponding author"
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+                                    "type": "text",
+                                    "content": "has become a rapidly developing research topic."
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+                                    "content": "Despite the wide range of research in this field [19, 14, 22, 21, 2, 49, 35, 5, 44, 36, 25, 46, 47], enetering high-quality dances is still limited by the existing datasets: (1) Full-body expressiveness: Existing dance datasets contain few hand movements, and only 1.5 hours of full body dance data is available. The previous methods in motion generation, treating body and hand as the same, lead to unnatural or monotonous hand motions, because the body and hand are in different feature spaces. However, uncoordinated body and hand motions can destroy the expressiveness of the overall dance. (2) Multi-genre: Existing datasets contain a limited number of dance genres, so the generated dances are not sufficient to match various music styles. Previous methods struggle with limited coarse dance genres and have no suitable objective metric to measure the genrematching degree between music and generated dances."
+                                }
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+                                    "content": "To address the limitations of existing datasets, we introduce a Fine-grained Choreography Dance dataset (FineDance). It comprises over 14.6 hours of data collected from 346 paired songs and dances, was created by professional dancers and a motion capture system, which has accurate body and hand motions. The fine-grained 22 dance genres of FineDance spanning traditional and modern styles, which make the genre-matching of generated dance sequences and given music become more challenging. FineDance includes music, dance sequences, FilmBox (fbx) files, SMPL[23, 29], and multi-view videos."
+                                }
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+                                    "content": "Early music-driven dance synthesis methods [3, 16, 24, 32, 15, 35, 2, 48] often rely on motion graph-based algorithms where the dance fragments from a pre-existing music-dance database are stitched together to synthesize one dance. While such methods can synthesize long-term dances, they do not produce new dance fragments. Recently methods have employed generative networks such as VAE[33], GAN[30], Normalization Flow Network[40], Diffusion[38]. But they focus solely on body part, while neglecting hand movements, resulting in unnatural or monotonous hand motions even trained with well-annotated body and hand labels. Additionally, the generative-based methods are limited by the long-term modeling ability of the networks, making them difficult to generate long-term dance sequences."
+                                }
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+                                    "content": "Therefore, we propose FineNet, a two-stage generative-synthesis network that addresses the limitations of previous dance generation methods. In the first stage, we propose a diffusion-based Full-body dance generation network (FDGN). The key of FDGN is to design two expert networks, which are dedicated to the generation of body and hand motions, and use a Refine Net to assemble them coordinately. In the second stage, we propose a Genre&Coherence aware Retrieval Module (GCRM), which ensures the coherence of dance fragments and"
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+                },
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+                                    "type": "text",
+                                    "content": "matches the genre between the music and the dances. Based on the suitable dance fragments retrieved by GCRM, we can produce genre-matching and long-term dances. A conceptual overview of the dataset and method is shown in Figure1. Finally, to objectively evaluate the genre-matching degree between generated dances and given music, we propose a novel metric, named Genre-matching Score (GS)."
+                                }
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+                    ],
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+                                    "content": "Overall, our contributions can be summarized as follows:"
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+                                            "content": "- We release FineDance, which is the largest 3D motion capture music-dance paired dataset with accurate full-body posture, containing 22 fine-grained genres. FineDance encourages the development of AI choreography, motion prior, and full-body reconstruction methods."
+                                        }
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+                                            "content": "- We present FineNet, which leverages expert networks and refine network to generate expressive full-body dances, and employs a cross-modal retrieval network to improve genre-matching scores."
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+                                            "content": "- Extensive quantitative experiments and user studies demonstrate that our approach can generate multiple different genre-matched dances from arbitrary music with natural and flexible hand movements."
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+                            "index": 9
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+                                    "content": "2. Related Works"
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+                                    "content": "2.1. Choreography Dataset"
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+                                    "content": "Currently, the most popular 3D choreography dataset is AIST++ [22], which provides 5 hours of dance but does not have hand motions. AIST++ is reconstructed through multi-view video. Therefore, there is inevitably a deviation between the generated 3D dance motions and the real motions because of the reconstruction error. Li et al. [21] provided another major type of 3D dance dataset: modeling in software, which is obtained by experienced animators. However, this type of dataset lacks the authenticity of the dance. At present, the most accurate datasets are obtained from motion capture systems. GrooveNet dataset [2] only contains the electronic dance genre in 23 minutes sequence. Dance with Melody [35] further constructed a 94-minute 3D dance dataset with 4 genres. Music2Dance [49] is a dataset with only one hour and 2 genres (modern and curtailage dance). Chen et al. [5] built a 9 hours dataset, but it only has four different dance genres. This genre partition does not match the discernment of professional dance artists. For example, Anime and K-pop do not count as specific dance genres. In conclusion, these datasets have limitations in hand motion, duration, and the diversity of genres and dancers. Our dataset contains 14.6 hours with 22 genres, and is collected by 27 dancers."
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+                                    "content": "Synthesis based approach. Early works[28, 26, 4, 43, 20] usually synthesis dances based on motion graphs and databases, which share one core idea: retrieving the most matching dance fragment for the given music clip, and splicing multiple fragments into a complete dance. In computer graphics, motion synthesis has long attracted a lot of attention as it can synthesize 3D actions from existing motion databases. Lamouret et al. [18] first delivered this idea and proposed a prototype system to create new actions by cutting and pasting action fragments from an action database. Arikan et al. [3] formally introduced the concept of graph-based motion synthesis, transforming this problem into finding paths in a pre-built motion graph. Under such a framework, the task of synthesizing actions is usually regarded as finding the optimal path in a constructed motion graph. Similar utilizing this graph-based scheme, Kim et al. [16] made the first attempt to synthesize rhythmic movements by adding constraints connecting action beats and rhythmic patterns. Shiratori et al. [32] and Kim et al. [15] formally pointed the music-driven dance movement synthesis problem and further developed more complex rules to associate dance movement segments with input music segments. This type of method can synthesize dances that match the music style well. However, as it is unable to learn the internal connections between music and dance, the synthesized dances cannot match the rhythm well. In addition, because the dance fragments are all from the database, such methods have no ability to create new dance motions. In this paper, we introduce the diversity generated technology into the synthesis method to maintain the advantages of synthesis and avoid the above problems."
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+                                    "content": "Generation based approach. Generative Adversarial Network (GAN) [10] and Variational Auto Encoder (VAE) [17] have been successfully applied to generate various data modalities, including image, motion, music, etc. As a result, researchers also propose music-driven dance generation algorithms based on the general deep generation paradigm[7, 22, 34, 1, 21, 8, 42, 13, 12]. Such methods can be divided into 2D and 3D solutions according to the dimension of the generated dance data. Lee et al. [19] proposed the first music-driven 2D dance generative network, which uses VAE to model dance units and GAN to loop to generate dance sequences. Since the human skeleton is a natural graph data, Ren et al. [30] and Ferreira et al. [6] adopted a Graph Convolutional Network to improve the spatial naturalness of the generated 2D dance movements. Both music and dance belong to sequence data. Therefore, Li et al. [22] used the Transformer [41] network with strong sequence modeling ability to design a music-driven 3D dance action generation network. Recently, diffusion-based networks succeed in text2motion generation[37, 45]. Although these generative networks have the advantages, such as rhythm-"
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+                                            "type": "text",
+                                            "content": "Figure 2. FineDance acquisition process. We capture the dancers' motions with the Vicon optical motion capture system. Then engineers retarget it to a standard skeleton in MotionBuilder. Dancers manually align the music with the dance motions and extract the skeletal information of the dance in Blender."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
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+                                    "type": "text",
+                                    "content": "matched and diversity, they neglect the quality of generated hand motions, and only generate motion fragments within several seconds. Our method can generate expressive full-body dances due to our diffusion based expert nets, and use a retrieval based modal to enhance the genre-matching score and take the advantages of synthetic methods such as genrematching, long-term stability."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "3. FineDance Dataset"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "The review of the choreography dataset is shown in Section 2.1, there are still few accessible large-scale motion capture choreography datasets even though many papers reported their choreography datasets. Meanwhile, most of these datasets are insufficient to train a diversified and generalized-well choreography model due to the limiting of dance genres, and poor music-dance pairings. Our FineDance can fill these gaps."
+                                }
+                            ]
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+                                    "content": "3.1. Data Acquisition and Analysis"
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+                                    "type": "text",
+                                    "content": "For the fine-grained dataset, we take the following regulations into account for our dataset acquisition. We give the flowchart of the process shown in Figure 2. We summarized the comparison of FineDance and existing 3D dance datasets in Table 1."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Fine-grained motions. So far, there are only 2 datasets containing finger motion, and the available data is less than 1.5 hours. Fine-grained motions are ignored in existing methods. For example, GrooveNet[2] only contains 30 body joints, and Dance with Melody[35] has only 21 body joints, while EA-MUD[34], PhantomDance[21] and AIST++[22] all use 24 body joints of the SMPL[23] model."
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+                                    "type": "text",
+                                    "content": "Our data store the information of the skeleton joints in 3D space in each frame including fingers, which can help to improve the artistry and reality of the dance motion. For easy to utilize, we use the standard 52 joints to represent the dance data."
+                                }
+                            ]
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+                                    "content": "Fine-grained dance genres. Previous literature focuses on a few dance genres, such as GrooveNet[2],"
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+                                            "html": "<table><tr><td>Dataset</td><td>Pos/Rot</td><td>Joints num</td><td>Hand joint</td><td>Genres</td><td>Mocap</td><td>RGB Views</td><td>Fbx</td><td>SMPL</td><td>Dancers</td><td>Total hours</td><td>avg Sec per Seq</td></tr><tr><td>GrooveNet[2]</td><td>✓/X</td><td>30</td><td>X</td><td>1</td><td>✓</td><td>1</td><td>X</td><td>X</td><td>1</td><td>0.38</td><td>690</td></tr><tr><td>Dance w/Melody[35]</td><td>✓/X</td><td>21</td><td>X</td><td>4</td><td>✓</td><td>4</td><td>X</td><td>X</td><td>-</td><td>1.6</td><td>92.5</td></tr><tr><td>Music2Dance[49]</td><td>✓/X</td><td>55</td><td>✓</td><td>2</td><td>✓</td><td>2</td><td>X</td><td>X</td><td>2</td><td>0.96</td><td>-</td></tr><tr><td>EA-MUD[34]</td><td>✓/✓</td><td>24</td><td>X</td><td>4</td><td>X</td><td>4</td><td>X</td><td>X</td><td>-</td><td>0.35</td><td>73.8</td></tr><tr><td>PhantomDance[21]</td><td>✓/X</td><td>24</td><td>X</td><td>13</td><td>X</td><td>0</td><td>X</td><td>X</td><td>-</td><td>9.6</td><td>133.3</td></tr><tr><td>AIST++[22]</td><td>✓/✓</td><td>17/24</td><td>X</td><td>10</td><td>X</td><td>10</td><td>X</td><td>✓</td><td>-</td><td>5.2</td><td>13.3</td></tr><tr><td>MMD[5]</td><td>✓/✓</td><td>52</td><td>✓</td><td>4</td><td>✓</td><td>0</td><td>✓</td><td>X</td><td>-</td><td>9.9</td><td>-</td></tr><tr><td>FineDance (Ours)</td><td>✓/✓</td><td>52</td><td>✓</td><td>22</td><td>✓</td><td>2</td><td>✓</td><td>✓</td><td>27</td><td>14.6</td><td>152.3</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. Comparisons of 3D Dance Datasets. Pos and Ros means 3D position and Rotation information respectively. Fbx (FilmBox) is one of the main 3D exchange formats as used by many 3D tools. \"avg Sec per Seq\" means the average seconds per sequence."
+                                        }
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+                                    "type": "text",
+                                    "content": "Music2Dance[49], MMD[5] and Dance with Melody[35]. This dataset uses a rough genre classification strategy, which is a non-standardized dance division."
+                                }
+                            ]
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+                    ],
+                    "index": 2
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+                                    "type": "text",
+                                    "content": "We improve the diversity of our dataset from two aspects: more genres and more dancers. Our FineDance is reasonably classified under the advice of dance artists, covering hip-hop and Chinese classical dance more completely. To the best of our knowledge, it also includes folk dance motions for the first time, expanding the dance genres of the choreography dataset. Totally, FineDance has up to 22 genres of dance defined by professional dance artists. And we obtained more than 14 hours of data. It is worth noting that FineDance contains the most genres. Details are given in the supplementary materials."
+                                }
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+                                    "type": "text",
+                                    "content": "Accurate posture. Currently, the largest available dataset is AIST++[22], which is collected by reconstructing 3D poses in multi-view videos. But the dance data is not real due to the reconstructing errors. Instead of reconstruction from the videos, ours is collected by a motion capture system, and all dance motions and music are well paired."
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+                                    "content": "In FineDance, all motions are captured by the Vicon optical motion capture system and retargeted to a standard skeleton in MotionBuilder by engineers. Therefore, FineDance can donate accurate postures. Moreover, FineDance will be the largest fully available 3D music-dance paired dataset, and it will be available."
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+                                    "type": "text",
+                                    "content": "Well-paired dance and music. Dance fragments are strongly associated with the rhythm and style of music. However, due to the lack of enough well-paired data, the generative model is hard to fit the relevance of the motion rhythm and music rhythm. Therefore, we asked the professional dancers to pay attention to the matching of rhythm and style when dancing."
+                                }
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+                                    "content": "Professional dancer. We invited 27 professional dancers, and each dancer was asked to dance to the music while his/her motions were captured utilizing the capture system."
+                                }
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+                                    "content": "4. FineNet"
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+                                    "content": "4.1. Overall Framework"
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+                                    "content": "Given music of unknown style and arbitrary duration, our goal is to generate multiple different full-body dances. This task presents challenges in three areas: (1) Full-body: Body and two hands motions in different spaces have different grains, using a single network to generate full-body motions like the previous method can lead to unreal and monotonous hand gestures. (2) Genre-matching: Making the generated dances consistent with the fine-grained genre is also challenging due to the modal gap between music and dance. (3) Long-term: Generating long-term novel motion is challenging because neural networks tend to accumulate errors over time. To address these issues, we propose FineNet, which comprises a Diffusion-based Full-body Diverse Dance Generation Network (FDGN) and a Genre & Coherent aware Retrieval Module (GCRM). The FDGN focuses on creating detailed dances with expressive movements, while the GCRM considers the overall choreography of the dance. FineNet cleverly combines generative and synthetic methods, making them complementary, much like the process of human choreography. Furthermore, FineNet allows for the generation of multiple different dances by selecting distinct dance segments at the initial time step. This capability offers users a wide range of creative possibilities."
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+                                    "content": "The overall framework of our method is shown in Figure 3. First, the input music "
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+                                    "content": " is split into 4-second clips "
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+                                    "content": " without overlapping, and "
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+                                    "content": " is the number of clips of the given music. For each "
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+                                    "content": " is the dance action fragment obtained by FineNet at time step t, and "
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+                                    "content": " is the number of body and hand joints, \"3\" represents 3-dimensional axis angle and position of joints."
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+                                    "type": "inline_equation",
+                                    "content": "BEN(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " means Body Expert Net, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the number of diffusion steps. The refine net is consisted of a spatial convolution network and a refine gate unit, which is used to assemble two parts naturally."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
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+                                    "type": "text",
+                                    "content": "4.4. Genre&Coherent aware Retrieval Module"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Thanks to FDGN's diverse generative capabilities, we can generate "
+                                },
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+                                    "type": "text",
+                                    "content": " candidate dance fragments "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\bar{Y}_i^t\\}_{i=1}^M"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for the "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " music clip "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\bar{X}^t\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". To search the genre-matched candidate dance fragment and synthesis them coherently, we propose Genre&Coherent aware Retrieval Module (GCRM),"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                }
+            ],
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "which calculates the Genre Matching Score (GS) of the current music clip and the candidate dance fragments, and the coherent score of the previous selected dance fragment and the current candidate dance fragments. Finally, we choreograph the complete dance by combining the two scores."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Genre matching score. We use GS to evaluate the matching degree of the style of music clip "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{X^t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the genres of generated candidate dance fragments "
+                                },
+                                {
+                                    "bbox": [
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+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{Y}_i^t\\}_{i=1}^M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". However, music and dance are different data modalities, and it is difficult to calculate the genre similarity directly. To cover this problem, we propose a cross-modal retrieval network."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
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+                                    "type": "text",
+                                    "content": "We utilize two models (one music style encoder "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}_{\\theta}^{m}(\\cdot)"
+                                },
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+                                    ],
+                                    "type": "text",
+                                    "content": " and one dance genre encoder "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}_{\\theta}^{d}(\\cdot))"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to encode different modalities into one embedding space. The music style encoder is the backbone of AST [9] and the dance genre encoder is the backbone of AGCN [31]. We extract the mel-spectrogram features "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{X^t}"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of music "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X^t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        205,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and send it to the music encoder. For each "
+                                },
+                                {
+                                    "bbox": [
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+                                        339
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\widetilde{X^t}\\}_{t = 1}^N"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we compute its genre-matching score with candidate dance fragments generated by FDGN. We utilize the cosine similarity as the genre matching score. So the genre matching score between "
+                                },
+                                {
+                                    "bbox": [
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+                                        339
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{X^t}"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{Y}_i^{t}\\}_{i = 1}^M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be formulated as:"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "G S _ {i} ^ {t} = s \\left(\\widetilde {X ^ {t}}, \\hat {Y} _ {i} ^ {t}\\right) = \\frac {\\mathcal {F} _ {\\theta} ^ {m} \\left(\\widetilde {X ^ {t}}\\right) ^ {T} \\mathcal {F} _ {\\theta} ^ {d} \\left(Y _ {i} ^ {t}\\right)}{\\left| \\left| \\mathcal {F} _ {\\theta} ^ {m} \\left(\\widetilde {X ^ {t}}\\right) \\right| \\right| \\times \\left| \\left| \\mathcal {F} _ {\\theta} ^ {d} \\left(Y _ {i} ^ {t}\\right) \\right| \\right|}, \\tag {3}",
+                                    "image_path": "d642e7acd8f4b9e79ab186176922a7e8f9fbbdad62979518a5170dfa2361e0d3.jpg"
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+                                    "type": "text",
+                                    "content": "We train the above two models by a cosine loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{cos}"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " as a retrieval task, which can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {c o s}} = y \\left(1 - s \\left(\\widetilde {X _ {i}}, Y _ {j}\\right)\\right) + (1 - y) \\left(\\max  \\left(0, s \\left(\\widetilde {X _ {i}}, Y _ {j}\\right)\\right), \\right. \\tag {4}",
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+                                    "content": "where "
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the MFCCs feature of music clip, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "Y_{j}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a dance fragment. "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "y = 1"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " when "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{X_i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "Y_{j}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are genre-matched, otherwise "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "y = 0"
+                                },
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Coherent score. We take the L2 distance of the start and end states of the two dance segments as the coherence score. To make the transition smoother, we cut 5 frames of the last temporal clip "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(t - 1)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " best matching fragment "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{Y}_b^{t - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        487,
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+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " on the tail and cut the start 5 frames of the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " candidate dance fragments "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        487,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{Y}_i^t\\}_{i = 1}^M"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " at the current time step "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". These cut frames are finally filled with a linear interpolation algorithm."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
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+                                    "type": "interline_equation",
+                                    "content": "C S _ {i} ^ {1} = 0 \\tag {5}",
+                                    "image_path": "d4ca956b8f5165d01ca1313c6e30f59d27791fe149e2e29b5b05d77f2da0304f.jpg"
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+                                    "content": " are weight parameters. For complete music "
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+                                    "content": ", FineNet outputs the dance fragments step by step, and"
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+                                            "content": "Figure 5. Qualitative result comparisons for a Jazz song."
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+                                    "content": "Data Preprocessing. We spilt FineDance dataset into train, val and test sets in two ways: FineDance@Genre and FineDance@Dancer. The test set of FineDance@Genre includes a broader range of dance genres, but the same dancer appear in train/val/test set. FineDance@Dancer means the train/val/test set divided by different dancers, which test set contains fewer dance genres, yet the same dancer won't appear in different sets. We only reported the results of test set on FineDance@Genre in this paper, the details of dataset split can be found in our supplementary materials. Each music and paired dance are only present in one set. For all the dance fragments, we combine the 3-dim axis angle vector representation for all 52 joints, along with a 3-dim global position vector, resulting in 159-dim motion features. For all the music clips, we use Librosa [27] to extract the 35-dim music temporal features. We also extract the mel-spectrogram of the music clips with Librosa and resized it to "
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+                                    "content": "224 \\times 224 \\times 3"
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+                                    "type": "text",
+                                    "content": ". During extracting audio features, the sampling rate is "
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+                                    "content": "76,800\\mathrm{Hz}"
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+                                    "content": " and hop size is 512."
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+                                    "content": "Implementation Details. In FDGN, we build 3 MLP layers to encode the music and body features. We use the transformer layer as the backbone of the body/hand expert net. The refine net consists of a 1-D convolution layer and a learnable weight parameter. The total epoch, learning rate, and batch size are set as 200, "
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+                                    "type": "text",
+                                    "content": ", 2048. In the GCRM, the "
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+                                    "content": " are set as 1.0 and 0.5 respectively."
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+                                    "content": "Evaluation Metrics. (1) FID score. Fréchet inception distance (FID) is widely used to measure how close the distribution of the generated dances is to that of the ground truth."
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+                                    "type": "text",
+                                    "content": "Similar to Lee et al.[19], we trained a style classifier in our dataset to extract motion features, and then use the features to calculate FID. (2) Diversity. We follow Lee et al. [19] to evaluate the average feature distance between generated dances for different input music. The same feature extractor used in FID is used again. (3) Hand FID score and Hand Diversity. Similarly, we extract hand motion features and calculate the FID and diversity for hand motion. (4) Multi-modality. We follow Lee et al.[19] to evaluate the average feature distance between the 10 choreography versions of every music. This metric measures the model's ability to generate different dances for the same music. (5) Genre Matching Score. We evaluate the average genre matching score between generated dance and the input music using the genre matching score calculation network mentioned in section 4.4. The genre matching score is defined as Eq. (3)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
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+                                    "type": "text",
+                                    "content": "5.2. Quantitative and Qualitative Evaluation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
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+                                    "type": "text",
+                                    "content": "Compared methods. We compare our method with several generation-based methods and one synthesis-based method. ChoreoMaster [5] is a dance synthesis method with style embedding network and graph-based motion synthesis. Since the code is not available, we reproduced the code according to the paper. DanceRevolution [14] is a generation method using Transformer to generate long-term dances. DeepDance [10] is a generation method with a GAN-based cross-modal association framework. Bailando [33] is a generation method with VAE and an actor-critic generative pre-trained transformer model. All the methods are tested on FineDance and AIST++ to evaluate the comprehensive choreography ability of FineNet."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Results and analysis. For all methods, we generate 10 versions of the dance for each song in the test set, and take the paired real dance as the Ground Truth. As shown in Table 2, our method gets the best performance in all evaluation metrics except Diversity on both datasets. Choreo-Master gets better on Diversity because it must retrieve all the fragments in the whole training set but no new motion is created. Specifically, on Multimodality (MM), FineNet"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                                    "type": "text",
+                                    "content": "gains 4.52 improvements compared to ChoreoMaster. On GS, FineNet is 0.03 higher than the ground truth. These two metrics show FineNet can generate diverse and genrematched dance. Besides, FineNet gets the highest Hand FID and Hand Diversity which shows our method can generate real and diverse hand motion."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Qualitative results are shown in Figure 5. DanceRevelation, DeepDance and Bailando generated almost identical stiff motions (refer to row 1 and row 2). ChoreoMaster generates classical dance motions in the last two images that do not match the Jazz music. But the generated dance motions of FineNet are diverse and in line with the Jazz style. The hand motion generated by FineNet W/ FDGN is more real. The corresponding videos refer to supplementary material."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
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+                                    "type": "text",
+                                    "content": "5.3. Ablation Study"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We replace different components of our method, and conduct experiments to demonstrate the effectiveness of each component on the test set of FineDance."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Infulence of the FDGN. In order to verify whether FDGN can make hand movements more natural and flexible. We modified FDGN as a single network that generates body and hand motion simultaneously. We then employed "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "FID_{h}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "DIV_{h}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " metrics to evaluate the realism and diversity of the resulting hand motion. As shown in Table2, all the quantitative metrics for FineNet w/o. FDGN becomes worse on both datasets. Specifically, on Hand Fid and Hand Diversity, FineNet w/o. FDGN drops by 0.72 and 0.14. The huge increase in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "FID_{h}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is mainly because FDGN generates hand movements with complete body information, making the hand motions more coordinated with the body."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                            "type": "text",
+                                            "content": "Table 2. Compared with SOTAs. # means we reproduce the code, * means we use the published code."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Strategy</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>Ground Truth</td><td>/</td><td>6.28</td><td>/</td><td>0.71</td></tr><tr><td>FDGN-G</td><td>2.85</td><td>6.22</td><td>12.02</td><td>0.27</td></tr><tr><td>FDGN-C</td><td>1.68</td><td>6.34</td><td>11.51</td><td>0.46</td></tr><tr><td>FineNet</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>",
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+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "Table 3. Ablation study on different choreography strategies."
+                                }
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+                                    "type": "text",
+                                    "content": "Choreography Strategy. To verify the proposed generative-synthesis strategy, we use the following strategies to generate 3D dances: directly generating long-term 3D dances by FDGN (FDGN-G); generating 4s dance fragments according to the music clip by FDGN and concatenating these fragments together (FDGN-C), as Table 3 shows."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "FineNet performs better than others in FID, MM, and GS. For FDGN-G, a long music clip will cause the FID and GS to drop dramatically. FineNet achieves a lower Diversity score than FDGN-C because while retrieving the GCRM gives up some dances whose genre doesn't match. For MM and GS, FineNet increases by 5.21 and 0.28 compared to FDGN-C, which demonstrates that GCRM can increase the ability to generate diverse and genre-matched dance for the same song."
+                                }
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+                                            "html": "<table><tr><td>Generation Model</td><td>FID ↓</td><td>Diversity ↑</td><td>MM ↑</td><td>GS ↑</td></tr><tr><td>DeepDance</td><td>4.91</td><td>4.47</td><td>1.15</td><td>0.32</td></tr><tr><td>DanceRevolution</td><td>6.99</td><td>3.51</td><td>6.64</td><td>0.37</td></tr><tr><td>FDGN</td><td>1.66</td><td>5.99</td><td>16.72</td><td>0.74</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Influence of the generation model. We choose DanceRevolution, DeepDance as the backbone of the generative model, and get the whole 3D dances through our GCRM. All the results are shown in Table 4. Our FDGN performs best, which shows excellent dance generation ability. Besides, compared the results of Table 2 and Table 4, where DeepDance and DanceRevolution are inserted into our method in Table 4, and their performances can be improved on MM, FID and GS. These results show our GCRM is scalable."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
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+                                    "content": "5.4. User Study"
+                                }
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+                    "index": 5
+                },
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+                                    "type": "text",
+                                    "content": "We invite 30 participants, including 15 dancers. Everyone watches 5 dances with a duration of 32 seconds. They are asked to evaluate the dances in 2 aspects: Effective duration and Artistry."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "type": "text",
+                                    "content": "Effective duration. Each participant has to judge the time interval from the beginning until abnormal actions occur, such as abnormal shaking, motion freezing, or excessive joint distortion. As Table 5 shows, synthesis methods generally performs better than generation methods, generation methods can only generate effective dances for less than 10 seconds. These results show that generation methods are limited in effective duration. But, ours is a generative-synthesis method, and achieves the best performance."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Artistry. We measure the artistry of the dances from the following dimensions: genre matching (GM), rhythm matching (RM), diversity (Div.), and comprehensive artistry (CA). The full score of every dimension is 100. As shown in Table 6, synthesis methods generally perform better than generation methods, and our method gets a 77.0 average score"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                            "type": "text",
+                                            "content": "Table 4. Ablation study on different generation networks."
+                                        }
+                                    ]
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+                            "index": 3,
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+                            "type": "table_caption"
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+                                            "html": "<table><tr><td>Method</td><td>Duration ↑</td><td>Type</td></tr><tr><td>Ground Truth</td><td>30.7s</td><td>/</td></tr><tr><td>ChoreoMaster</td><td>26.9s</td><td>synthesis</td></tr><tr><td>DanceRevolution</td><td>5.4s</td><td>generation</td></tr><tr><td>DeepDance</td><td>2.2s</td><td>generation</td></tr><tr><td>Baildando</td><td>3.1s</td><td>generation</td></tr><tr><td>FineNet (Ours)</td><td>28.2s</td><td>generation&amp;synthesis</td></tr></table>",
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+                                            "content": "Table 5. User study on effective duration."
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+                                            "html": "<table><tr><td>Method</td><td>GM</td><td>RM</td><td>Div.</td><td>CA</td><td>Avg</td></tr><tr><td>Ground Truth</td><td>94.1</td><td>96.3</td><td>95.5</td><td>97.9</td><td>96.0</td></tr><tr><td>ChoreoMaster</td><td>64.2</td><td>59.7</td><td>77.2</td><td>69.8</td><td>67.7</td></tr><tr><td>DanceRevolution</td><td>33.2</td><td>30.7</td><td>47.4</td><td>31.4</td><td>36.7</td></tr><tr><td>DeepDance</td><td>17.2</td><td>22.1</td><td>24.4</td><td>25.6</td><td>22.3</td></tr><tr><td>Bailando</td><td>23.2</td><td>33.5</td><td>39.4</td><td>21.6</td><td>30.1</td></tr><tr><td>FineNet (Ours)</td><td>79.9</td><td>70.3</td><td>81.2</td><td>76.4</td><td>77.0</td></tr></table>",
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+                                    "content": "Table 6. Result of the user study. Avg denotes the average score."
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+                                    "content": "which clearly surpasses the baselines. However, compared to the ground truth, all the methods still need to improve especially in rhythm matching and Comprehensive artistry."
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+                                    "type": "text",
+                                    "content": "6. Conclusions"
+                                }
+                            ]
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+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "In this paper, we propose a large-scale, high-quality 3D dance dataset (FineDance) for music-driven dance generation, which records professional and abundant dance genres with accurate and fine-grained hand motions. Meanwhile, we also propose a choreography Network (FineNet), which can generate multiple diverse genre-matched dances with flexible hand movements. Furthermore, we propose a new metric to evaluate the genre matching degree between music and dance. Quantitative and qualitative results show that FineNet can generate long-term, diverse, and genrematched dances from given music."
+                                }
+                            ]
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+                                    "content": "Acknowledgment"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We would like to express our sincere gratitude to Yan Zhang (https://yz-cnsdqz.github.io/) and Yulun Zhang (https://yulunzhang.com/) for their invaluable guidance and insights during the course of our research."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "This work was supported in part by the Shenzhen Key Laboratory of next generation interactive media innovative technology (No.ZDSYS20210623092001004), in part by the China Postdoctoral Science Foundation (No.2023M731957), in part by the National Natural Science Foundation of China under Grant 62206153, Young Elite Scientists Sponsorship Program by CAST (No. 2023QNRC002)"
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+                                    "content": "References"
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+                                        }
+                                    ]
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+                            ],
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diff --git a/2023/FineRecon_ Depth-aware Feed-forward Network for Detailed 3D Reconstruction/6c51d26e-268b-4ab2-8995-1d2780bb8d14_content_list.json b/2023/FineRecon_ Depth-aware Feed-forward Network for Detailed 3D Reconstruction/6c51d26e-268b-4ab2-8995-1d2780bb8d14_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..6ecc20ac376881f1733e8cff89a1dd1ddf0074a3
--- /dev/null
+++ b/2023/FineRecon_ Depth-aware Feed-forward Network for Detailed 3D Reconstruction/6c51d26e-268b-4ab2-8995-1d2780bb8d14_content_list.json	
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+    {
+        "type": "text",
+        "text": "FineRecon: Depth-aware Feed-forward Network for Detailed 3D Reconstruction",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Noah Stier $^{1,2}$  Anurag Ranjan $^{1}$  Alex Colburn $^{1}$  Yajie Yan $^{1}$  Liang Yang $^{1}$  Fangchang Ma $^{1}$  Baptiste Angles $^{1}$",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ Apple  $^{2}$ University of California, Santa Barbara",
+        "bbox": [
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+            250
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent works on 3D reconstruction from posed images [17, 23, 24] have demonstrated that direct inference of scene-level 3D geometry without test-time optimization is feasible using deep neural networks, showing remarkable promise and high efficiency. However, the reconstructed geometry, typically represented as a 3D truncated signed distance function (TSDF), is often coarse without fine geometric details. To address this problem, we propose three effective solutions for improving the fidelity of inference-based 3D reconstructions. We first present a resolution-agnostic TSDF supervision strategy to provide the network with a more accurate learning signal during training, avoiding the pitfalls of TSDF interpolation seen in previous work. We then introduce a depth guidance strategy using multiview depth estimates to enhance the scene representation and recover more accurate surfaces. Finally, we develop a novel architecture for the final layers of the network, conditioning the output TSDF prediction on high-resolution image features in addition to coarse voxel features, enabling sharper reconstruction of fine details. Our method, FineRecon<sup>1</sup>, produces smooth and highly accurate reconstructions, showing significant improvements across multiple depth and 3D reconstruction metrics.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            710
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Reconstruction of 3D scenes from posed images is a long-standing problem in computer vision, with many applications such as autonomous driving, robotic navigation, and digital 3D asset creation. The traditional approach is to estimate depth maps over the input images using multiview stereo (MVS), and then fuse them together to form a unified 3D model [9, 10, 22]. However, the fusion process commonly results in missing geometry or artifacts in areas where the depth maps do not agree, due to effects such as occlusion, specularity, and transparent or low-texture sur",
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+        "image_caption": [
+            "Figure 1. Our method, FineRecon, recovers highly detailed and coherent geometry relative to state-of-the-art methods. Our contributions of lossless ground truth sampling, depth-aware feature volume, and point backprojection result in smooth surfaces that preserve high-frequency structures without creating strong artifacts."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
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+    {
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+        "img_path": "images/b449b2eaa5e3beea9a812f1b0f2a0b13d737df4ed2a631f78934d5a55d72d015.jpg",
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+    {
+        "type": "text",
+        "text": "faces. Recently, an alternative method has been proposed to address this issue in Atlas [17], which back-projects learned image features onto a voxel grid and directly predicts the scene's truncated signed distance function (TSDF) using a 3D convolutional neural network (CNN). The main advantage is that the CNN can learn to produce smooth, consistent surfaces, and to fill in holes that would otherwise result from low-texture regions and occlusion. Several methods have proposed improvements to this framework [1, 2, 23, 24], consistently pushing the state of the art in reconstruction accuracy. However, despite these efforts, the reconstructions produced by these methods remain coarse. We identify three key factors restricting the accuracy and level of detail in prior works, and we introduce solutions to address them, demonstrating their effectiveness within a new system: FineRecon.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "First, existing works use tri-linear interpolation to resample the ground-truth TSDF to align with the model's voxel grid during training [17, 23, 24]. This allows su",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>https://github.com/apple/ml-finerecon",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "18423",
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+    },
+    {
+        "type": "text",
+        "text": "pervision of the model's TSDF predictions at each voxel center, even when the voxel centers do not coincide with the pre-computed ground-truth TSDF points. However, resampling via tri-linear interpolation corrupts detail in the training data, because distance fields are not linear when non-planar geometry such a corner is present, as shown in Fig. 3. We avoid this issue by making supervised predictions only at the exact points where the ground-truth TSDF is known. This supervision change comes at no extra cost, and it results in greatly improved visual detail as well as a relative reduction in average chamfer distance between reconstruction and ground truth of over  $10\\%$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Second, prior work [1, 2, 17, 23, 24] uses dense back-projection, sampling a feature from each input image in each voxel. This causes blurring in the back-projection volume, which increases the difficulty of extracting accurate surface locations. To address this, our method uses an initial multi-view stereo depth estimation step, after which the depth estimates are used to enhance the feature volume and guide the 3D CNN toward areas of high surface likelihood. We show that this step significantly increases the quality of the reconstructions produced by our system.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Third, because of the high computational cost of 3D CNNs, it is expensive to increase the voxel resolution. Existing works use voxel sizes of  $4\\mathrm{cm}$  or larger [1, 2, 17, 23, 24], which is not enough to resolve the level of geometric detail visible in natural images at ranges of a few meters. To remedy this, we propose a new method to query the TSDF prediction at any point in  $\\mathbb{R}^3$ , conditioned on the CNN grid features and image features projected directly to the query point. This reduces aliasing and allows our model to resolve sub-voxel detail. Furthermore, this enables reconstruction at arbitrary resolution without re-training.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "FineRecon achieves state-of-the-art performance on the challenging ScanNet dataset, as measured by 3D mesh metrics and rendered 2D depth metrics. We further show that it produces substantially improved visual detail with reduced artifacts relative to prior work.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Contributions. The main contributions of this paper are:",
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+        "page_idx": 1
+    },
+    {
+        "type": "list",
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+        "list_items": [
+            "- We increase the accuracy of the training data using resolution-agnostic TSDF supervision, allowing FineRecon to reconstruct details with higher fidelity.",
+            "- We improve reconstruction accuracy using a novel MVS depth-guidance strategy, augmenting the backprojection volume with an estimated TSDF fusion channel.",
+            "- We enable the reconstruction of sub-voxel detail with a novel TSDF prediction architecture that can be queried at any 3D point, using point back-projected fine-grained image features."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Multi-view stereo. 3D reconstruction is traditionally posed as per-pixel depth estimation [9, 10, 22]. While recent works have shown strong results [12, 21], a known drawback is that the estimation of each depth map is independent, so continuity across frustum boundaries is not enforced, and this often leads to artifacts. Solutions have been proposed [7, 11, 18], but it is still an open problem.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Feed-forward 3D reconstruction. An effective recent strategy is to perform volumetric reconstruction directly in scene space using feed-forward neural networks [1, 2, 17, 23, 24]. In this line of research, image features are encoded by a 2D CNN and densely back-projected into a global feature volume, then a 3D CNN predicts the scene TSDF. These models can generalize to new scenes at inference time without computationally-demanding test-time optimization, and they can produce smooth and complete reconstructions. However, they tend to blur out surface details and omit thin structures. In contrast, ours is the first of these volumetric TSDF methods to reconstruct accurate sub-voxel detail. 3D-Former [30], a concurrent work, replaces the 3D CNN with a transformer, an orthogonal direction that could potentially be combined with our method.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Geometric priors in neural radiance fields. Recent novel-view synthesis methods based on neural radiance fields [16] have shown remarkable 2D rendering quality, typically relying on time-consuming per-scene optimization to obtain good results. These methods have also been extended to predict surface geometry [26, 28], and it has been shown that geometric priors, such as depth and normal maps, can boost performance. For instance, multiple works [13, 19, 27] use depth estimates to improve ray sampling efficiency. MonoSDF [29] uses monocular depth and normal estimation as pseudo-ground truth to supervise its predicted SDF. Similarly, our method uses guidance from a depth-prediction network, but with a focus on interactive reconstruction speed and generalization to new scenes.",
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+    {
+        "type": "text",
+        "text": "Geometric priors in feed-forward networks. Only a few previous methods based on feed-forward networks have incorporated geometric priors. MonoNeuralFusion [31] uses monocular normal estimates but does not explore depth priors. Similar to our approach, VolumeFusion [2] uses depth as an additional feature by fusing it into a density volume and concatenating it with the image feature volume. However, density does not encode the difference between occluded space and observed free space, and it omits crucial information about inward vs. outward surface orientation. In contrast, we explore multiple forms of depth guidance, finding that guidance by TSDF fusion outperforms the density-based variant and others (Table 5). CVRecon [8], a concurrent work, uses frustum-aligned cost volumes in addition to global features, which is related to our work but does not explicitly predict depth.",
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+    {
+        "type": "page_number",
+        "text": "18424",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/59caf10cbda106479a296791be0f095cdc23f83fdf7568519a4c83f19784c36f.jpg",
+        "image_caption": [
+            "Figure 2. Model overview. Given a monocular RGB image sequence, we use a pre-trained depth network to estimate depth images  $\\hat{\\mathcal{D}}$ . In the meantime we also extract image features  $\\mathcal{F}^c$  for global volume fusion and  $\\mathcal{F}^f$  for point back-projection. The depth  $\\hat{\\mathcal{D}}$  is then fused into an initial, approximate TSDF volume  $\\nu^d$ , and  $\\mathcal{F}^c$  is back-projected into a feature volume  $\\nu^c$  using the camera parameters. The two volumes are then concatenated and fed to a 3D CNN  $\\Psi$  to produce the global feature volume  $\\nu^{\\Psi}$  and the coarse occupancy grid  $\\hat{\\mathcal{O}}$  (used to accelerate inference). Finally, at any query point  $x \\in \\mathbb{R}^3$ , we sample high-resolution image features  $\\mathcal{F}^f$  and concatenate with the interpolated voxel feature  $\\nu^{\\Psi}(x)$ . This is passed to an MLP to predict the final TSDF value."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/5a313e9d5441150dbed3ddf19ad4b694a7ffc1f3085615689a4d1a574df1e4d7.jpg",
+        "image_caption": [
+            "Figure 3. Illustration of our improved, resolution-agnostic TSDF supervision. With rotational augmentation during training, the model's voxel grid (gray) does not align with the points (blue) where the ground-truth TSDF is known. Previous work uses linear interpolation (a) to estimate the TSDF at the voxel centers for supervision, but this leads to errors: the ground-truth geometry (yellow) is intersected by the interpolated TSDF values (red circles). In contrast, our model can be supervised at any 3D point. Therefore, regardless of the feature grid orientation, we can supervise the model at the exact points where the ground-truth is known (b). This reduces noise during training and increases reconstruction accuracy (see Table 6)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+            720,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a set of input images  $\\{I_i\\}$  along with their camera poses  $\\{P_i\\}$  and intrinsics  $\\{K_i\\}$ , we seek to compute an estimate  $\\hat{S}$  of the true scene TSDF  $S$ . We train a deep-learning model  $\\Phi$  to perform this mapping,  $\\hat{S} = \\Phi (\\{I_i\\}, \\{P_i\\}, \\{K_i\\})$ .",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Model overview",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our model (illustrated in Fig. 2) extracts a set of 2D features  $\\{\\mathcal{F}_i^c\\}$  from each input image using a convolutional neural network (CNN),  $\\Omega^c$ . We then use the camera pa",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "rameters to back-project  $\\{\\mathcal{F}_i^c\\}$  onto a 3D voxel grid. The back-projection process is augmented using depth estimates  $\\{\\hat{D}_i\\}$  to produce the depth-guided feature volume  $\\nu^g$ , as described in Section 3.2.2. We process  $\\nu^g$  using a 3D CNN  $\\Psi$  to produce a new feature volume  $\\nu^{\\Psi}$ , which we can query for  $\\hat{S}(q)$  at any 3D point  $q \\in \\mathbb{R}^3$  using the interpolation strategy defined in Section 3.2.3. To extract a surface mesh, we query the reconstruction on a grid of arbitrary resolution to produce a TSDF volume, from which a mesh can be extracted with Marching cubes [15].",
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Key improvements",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Resolution-agnostic TSDF supervision",
+        "text_level": 1,
+        "bbox": [
+            500,
+            556,
+            820,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "During training, as in previous works [17, 23, 24] we randomly orient the coordinate system of the feature volume relative to  $S$  using  $\\pm 3^{\\circ}$  rotations about the horizontal axis and  $\\pm 180^{\\circ}$  rotations about the gravitational axis. Thus, the voxel centers may not coincide with the points  $\\{x\\}$  where  $S$  is known. This is typically addressed using linear interpolation on  $S$  to estimate the ground-truth TSDF at the voxel centers. However, this process is not accurate, since with non-planar geometry the TSDF is a non-linear function of space. Interpolation therefore corrupts the ground-truth TSDF, as shown in Fig. 3. In theory this effect can be minimized by sampling the ground truth on a very high-resolution grid, but this greatly increases training cost. To preserve the accuracy of the ground truth with no added cost, we instead supervise only at the points  $\\{x\\}$  where the ground truth is known, so that no interpolation is required. This decouples the accuracy of our ground truth from its sampling rate, rendering it resolution-agnostic. To support this, our model must be able to estimate the TSDF at any point in  $\\mathbb{R}^3$ , which we achieve using the strategy outlined in Section 3.2.3. This simple supervision change enables our",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "18425",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "model to reconstruct significantly more visual detail (see Fig. 6).",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Depth guidance",
+        "text_level": 1,
+        "bbox": [
+            76,
+            126,
+            240,
+            142
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In order to localize image features in 3D space, we sample a pixel feature at each voxel from each available input image:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\mathcal {V}} _ {i} ^ {c} (q) = \\alpha \\left(\\mathcal {F} _ {i} ^ {c}, K _ {i} P _ {i} q _ {h}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            193,
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+            212
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha(F, u)$  represents sampling a feature from 2D map  $F$  at pixel location  $u$ , and  $q_h$  is the voxel center in homogeneous coordinates. We then reduce using a per-channel mean across views to form one feature vector per-voxel:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {V} ^ {c} (q) = \\frac {1}{| \\{I _ {i} \\} |} \\sum_ {i} \\tilde {\\mathcal {V}} _ {i} ^ {c} (q) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As an additional signal in recovering the scene surfaces, we propose to inject a multi-view depth prior using depth estimates from an MVS system  $M$ . As MVS is a well-studied problem, we treat  $M$  as an off-the-shelf component, and in the Supplementary we study the sensitivity of our system to depth noise and choice of  $M$ . We fuse  $\\hat{\\mathcal{D}}$  into scene space using the standard TSDF fusion [4] to form  $\\mathcal{V}^d$ . We then concatenate  $\\mathcal{V}^d$  as an extra channel in the back-projection volume. Our depth-guided back-projection volume is thus defined as",
+        "bbox": [
+            75,
+            335,
+            468,
+            484
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {V} ^ {g} = \\left[ \\mathcal {V} ^ {c}, \\mathcal {V} ^ {d} \\right]. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our experiments (see Table 5), the depth-guided feature volume  $\\mathcal{V}^g$  shows significantly improved results with respect to image features alone  $(\\mathcal{V}^c)$ , or depth inputs alone  $(\\mathcal{V}^d)$ . With naive application of the depth guidance, we find that this additional signal increases our network's propensity to over-fit to the training data, relying too heavily on the depth guidance which is often inaccurate. To address this, we scale each predicted depth map by a factor sampled uniformly in the range [0.9, 1.1] as a data augmentation during training. This reduces over-fitting and encourages the network to learn to use the image features in regions where the depth maps are unreliable.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We additionally experiment with several strategies for using the depth estimate to directly modulate the image feature back-projection. However, as shown in our experiments, our TSDF fusion approach outperforms these methods by a large margin (see Table 5).",
+        "bbox": [
+            75,
+            691,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.3 Point back-projection TSDF inference",
+        "text_level": 1,
+        "bbox": [
+            76,
+            770,
+            397,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use tri-linear interpolation to sample the 3D CNN's output feature volume  $\\mathcal{V}^{\\Psi}$  at any query point  $q$ . This results in a continuous-valued feature  $\\tilde{\\mathcal{V}}^{\\Psi} = \\Lambda (\\mathcal{V}^{\\Psi}, q)$  where  $\\Lambda$  represents tri-linear interpolation. Directly estimating  $\\hat{S}$  from this feature is severely limited in its ability to reconstruct sub-voxel detail, since the effective resolution of  $\\tilde{\\mathcal{V}}^{\\Psi}$  is still constrained to the size of the voxels.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We improve on this paradigm using an additional point back-projection step to directly sample image features  $\\mathcal{W}(q)$  at the point  $q$ . This step is identical to the depth-guided back-projection outlined in Section 3.2.2, except that the point  $q$  is no longer constrained to be a voxel center. The effective resolution of this new continuous-valued feature is thus determined by the resolution of the 2D image feature grid rather than the 3D voxel size. Assuming high-enough 2D feature resolution,  $\\mathcal{W}(q)$  thus carries much finer-grained information than the linearly-interpolated voxel feature  $\\tilde{\\mathcal{V}}^{\\Psi}(q)$ , complementing the 3D CNN's ability to produce smooth and context-informed features. We concatenate  $\\mathcal{W}$  with  $\\tilde{\\mathcal{V}}^{\\Psi}$  as the input to a multilayer perceptron (MLP)  $\\theta_{S}$ :",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {S} = \\theta_ {S} ([ \\mathcal {W}, \\tilde {\\mathcal {V}} ^ {\\Psi} ]). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            630,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "At a given 3D sampling rate, our point back-projection inference strategy adds a small but non-negligible cost relative to using only  $\\tilde{\\mathcal{V}}^{\\Psi}$ : we must run an additional round of feature extraction and back-projection using  $\\Omega^{f}$ , and the input dimension of  $\\theta_{S}$  must be doubled in order to receive the extra input features. We show in our experiments that this cost is tractable (see Section 4.4).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We observe that the fine-grained features  $\\mathcal{W}$  can contain spurious high-frequency content, particularly near the borders of the 2D features where the CNN output is unreliable due to edge effects. To reduce artifacts, we downweight  $\\{F_i^f\\}$  near the borders prior to back-projection using a weight  $w = \\sigma (l\\cdot (min(\\frac{d}{m},1)\\cdot 2 - 1))$  ,where  $d$  is the distance to the nearest border in pixels;  $m = 20$  is a margin distance;  $l = 6$  controls the falloff rate; and  $\\sigma (x) = \\frac{1}{1 + e^{-x}}$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.4 Output resolution & occupancy filtering",
+        "text_level": 1,
+        "bbox": [
+            500,
+            573,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our model can be sampled at any point in  $\\mathbb{R}^3$ , and we choose to sample it on a regular grid at test time in order to support meshing with marching cubes [15]. The resolution of this grid can be determined arbitrarily without retraining, and we experiment with several output grid resolutions (see Fig. 5). Naively, the cost of our point back-projection inference strategy grows cubically with the sampling rate. At high resolutions, it thus becomes expensive due to the cost of running the additional back-projection and  $\\theta_S$  densely over the full volume. To mitigate this, we predict the per-voxel occupancy  $\\hat{O}$  with an additional MLP:  $\\hat{O} = \\theta_O(\\mathcal{V})$ . Then at test time we sample  $\\hat{S}$  only within voxels that are predicted to be occupied. While the asymptotic complexity is still cubic, in practice this greatly reduces the cost due to the prevalence of empty space.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Training",
+        "text_level": 1,
+        "bbox": [
+            500,
+            832,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "At training time, we require a ground-truth TSDF  $S$  to supervise  $\\hat{S}$ . For training on real scans, we use TSDF fusion [4] to generate  $S$  on a discrete grid of points  $X$  with",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18426",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3bc971014a15f970179f41ffba0683d888603cb30d77952b4842e4b14cb84a96.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative results. Comparison of our method with NeuralRecon [24], VoRTX [23], and SimpleRecon [21]. NeuralRecon and VoRTX capture consistent global structure but lose many details, whereas SimpleRecon recovers details but fails to keep geometry consistent across views, leading to duplicate surfaces after TSDF fusion. Our method produces the most complete, consistent reconstruction while preserving details."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            83,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "resolution  $\\delta$ ,  $X = \\{x \\in [i \\cdot \\delta, j \\cdot \\delta, k \\cdot \\delta]\\}$ , assuming the existence of a set of ground-truth depth maps  $\\{D_i\\}$  corresponding to  $\\{I_i\\}$ . While ground truth depth can be noisy when acquired by sensors such as structured-light infrared scanners, we minimize artifacts by 1) using a large number of views to generate the ground-truth, 2) using an appropriate TSDF truncation distance following previous work [17, 23, 24], and 3) discarding depths beyond the range where the accuracy starts to visibly degrade.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Loss function. We define the TSDF loss  $\\mathcal{L}_{\\mathcal{S}}$  following SG-NN [6] as",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {S} = \\frac {1}{| X |} \\sum_ {x \\in X} | t (\\hat {S} (x)) - t (S (x) |, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            775,
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+            813
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $t(x) = \\mathrm{sign}(x)\\cdot \\ln (|x| + 1)$ . We define occupancy loss  $\\mathcal{L}_O$  using the standard binary cross-entropy, abbreviated  $BCE$ :",
+        "bbox": [
+            75,
+            818,
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+            862
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {O} = \\frac {1}{| X |} \\sum_ {x \\in X} B C E (O (x), \\hat {O} (x)) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            867,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following VoRTX [23] we compute the ground-truth occupancy as",
+        "bbox": [
+            498,
+            604,
+            890,
+            635
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nO (x) = \\oplus (\\tilde {O} (x)); \\quad \\tilde {O} (x) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} | S (x) | <   1 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            522,
+            643,
+            890,
+            684
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\oplus$  represents morphological dilation with a  $3\\times 3\\times 3$  structuring element. Note, this definition of occupancy describes space near a surface [6, 23, 24], rather than space interior to an object. Our training loss  $\\mathcal{L}$  is then defined as",
+        "bbox": [
+            498,
+            691,
+            890,
+            752
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {S} + \\mathcal {L} _ {O}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            642,
+            761,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "CNN backbone architectures. Our 2D CNN architecture is a feature pyramid network [14] using EfficientNetV2-S [25] as a backbone. This structure is shared for both  $\\Omega^c$  and  $\\Omega^f$ , but the weights are duplicated and then trained independently. Despite their identical architectures, these networks learn strikingly different features (see Supp.). Our 3D CNN  $\\Psi$  is inspired by U-Net [3, 20], see Supp. for details.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18427",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. As the depth predictor  $M$  we use our re-implementation of the MVS network SimpleRecon [21]. We use a voxel size of 4cm in our model, and we train on volumetric scene chunks of size  $(3.84\\mathrm{m} \\times 3.84\\mathrm{m} \\times 2.24\\mathrm{m})$ . During training we select views by uniform random sampling over all views that at least partially observe the training chunk. At test time we fuse only keyframes, using the view selection strategy from DeepVideoMVS [7]. Training takes 36 hours on eight Nvidia V100 GPUs.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Dataset, baselines, and metrics",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Dataset. We validate our method by training and evaluating our model on the popular ScanNet dataset [5], which is composed of 1,613 indoor scans. We report all our metrics on the official test set containing 100 scans.",
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+    {
+        "type": "text",
+        "text": "Baselines. We compare our model with several previous works. For end-to-end 3D reconstruction methods we select Atlas [17], NeuralRecon [24], VoRTX [23], and TransformerFusion [1]. We also compare to MVS depth-prediction, selecting SimpleRecon [21], which we re-implement. In order to compare to SimpleRecon, we apply TSDF fusion [4] on the predicted depth maps to produce a 3D mesh.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Metrics. We compute 3D metrics directly on the mesh reconstructions, and we compute depth metrics by rendering the meshes to generate predicted depth maps. Relative to prior works on depth estimation such as SimpleRecon [21], this is a slight change from the typical protocol of computing depth metrics directly on the raw depth maps. We believe our strategy is more indicative of performance in real-world applications that rely on the unified 3D reconstruction. Our definition for all metrics is the same as in Atlas [17] (see Supp. for details).",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For computing 3D metrics we use the evaluation code from TransformerFusion [1], which includes a trimming protocol to avoid penalizing reconstructions for in-painting surfaces in unobserved regions. As noted in previous work [1, 23], precision or recall can easily be optimized individually at the expense of the other, as with accuracy and completeness. We thus emphasize Chamfer distance and F1 (i.e. F-score) as the most important 3D metrics, capturing this trade-off.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            816,
+            171,
+            830
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Qualitative Results. In Fig. 4, we show qualitative results of our method compared to baselines and ground truth. We observe that our method preserves more details while minimizing high-frequency artifacts. The surfaces",
+        "bbox": [
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+            839,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/2e3e86ef278d9cee3b97839578753b103b53e70f85b6d7e4710b09061ae617a7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Acc ↓</td><td>Comp ↓</td><td>Cham ↓</td><td>Prec ↑</td><td>Rec ↑</td><td>F1 ↑</td></tr><tr><td>Atlas [17]</td><td>7.09</td><td>7.52</td><td>7.30</td><td>68.4</td><td>61.1</td><td>64.3</td></tr><tr><td>NeuralRecon [24]</td><td>5.04</td><td>10.68</td><td>7.86</td><td>62.7</td><td>59.1</td><td>60.7</td></tr><tr><td>3DVNet [18]</td><td>6.73</td><td>7.72</td><td>7.22</td><td>65.5</td><td>59.6</td><td>62.1</td></tr><tr><td>Transf. Fusion [1]</td><td>5.52</td><td>8.27</td><td>6.89</td><td>72.8</td><td>60.0</td><td>65.5</td></tr><tr><td>VoRTX [23]</td><td>4.32</td><td>7.52</td><td>5.92</td><td>76.3</td><td>64.0</td><td>69.5</td></tr><tr><td>SimpleRecon [21]</td><td>6.43</td><td>5.18</td><td>5.80</td><td>66.0</td><td>69.7</td><td>67.6</td></tr><tr><td>Ours</td><td>5.25</td><td>5.11</td><td>5.18</td><td>78.0</td><td>73.4</td><td>75.5</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/125f5f50b9faaa5124315f7e74261fdd7ba7e413fef336ff8e7d4adc8a601b5a.jpg",
+        "table_caption": [
+            "Table 1. 3D reconstruction metrics for ScanNet. We compare with recent work on mesh metrics defined in Atlas [17]. Best and Second -best are highlighted."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>L1 ↓</td><td>AbsRel ↓</td><td>SqRel ↓</td><td>δ1.05 ↑</td><td>δ1.25 ↑</td><td>Comp. ↑</td></tr><tr><td>Atlas [17]</td><td>11.96</td><td>6.26</td><td>4.22</td><td>75.2</td><td>93.8</td><td>98.8</td></tr><tr><td>NeuralRecon [24]</td><td>9.84</td><td>6.54</td><td>3.79</td><td>75.0</td><td>94.6</td><td>90.8</td></tr><tr><td>VoRTX [23]</td><td>9.32</td><td>5.92</td><td>3.65</td><td>79.0</td><td>94.9</td><td>96.1</td></tr><tr><td>SimpleRecon [21]</td><td>8.23</td><td>4.83</td><td>2.66</td><td>81.0</td><td>96.8</td><td>97.4</td></tr><tr><td>Ours</td><td>6.91</td><td>4.24</td><td>2.57</td><td>86.6</td><td>97.1</td><td>97.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. 2D metrics for ScanNet. The 2D depth is rendered and metrics are computed in the same way as with Atlas [17]. We highlight the Best and Second best with colors respectively.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "in our reconstructions are smooth and consistent, gracefully unifying information from all views without the depth-disagreement artifacts or noticeable discontinuities visible in SimpleRecon. VoRTX suffers from blurry reconstructions where fine details such as chair legs are completely lost, whereas our approach reconstructs these elements faithfully.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Fig. 5 we show qualitative results at three output resolutions:  $4\\mathrm{cm}$ ,  $1\\mathrm{cm}$  and  $0.5\\mathrm{cm}$ . VoRTX is not tractable at high resolutions, so we upsample VoRTX's  $4\\mathrm{cm}$  TSDF with linear interpolation, which does not increase the effective level of detail. For SimpleRecon, we can generate reconstructions at any desired resolution by decreasing the voxel size during TSDF fusion, and we note that artifacts and noise increase greatly at high resolution. In contrast, our results consistently preserve a high level of detail while avoiding noisy surfaces.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Results. Table 1 shows our 3D reconstruction metrics on the ScanNet dataset. We report metrics for our method and SimpleRecon at the relatively high resolution of  $1\\mathrm{cm}$  because it is tractable to do so. We report metrics for the other baselines at their native resolution of  $4\\mathrm{cm}$ , because increasing this resolution would add significant compute cost and engineering effort. For fairness, metrics for our method at  $4\\mathrm{cm}$  are shown in Table 3, and we note that the quantitative differences from  $1\\mathrm{cm}$  are negligible. Our method achieves the best result in most metrics. In particular, it achieves the lowest Chamfer distance and highest F-score by large margins.",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "18428",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/a08bf72229c7ec96094e349515ed4958b710dedf8477eb2cd38d0597b1e12ef5.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative results at various output resolutions. With our method, we observe increased sub-voxel detail when increasing the output sampling rate from  $4\\mathrm{cm}$  to  $1\\mathrm{cm}$ , as well as the occasional appearance of small artifacts near view frustum boundaries. Beyond  $1\\mathrm{cm}$  we observe no significant changes, suggesting we have reached our system's limit of detail given the 2D feature resolution. In contrast, upsampling the VoRTX outputs from  $4\\mathrm{cm}$  slightly increases smoothness but adds no extra detail, and SimpleRecon shows the appearance of significant frustum boundary artifacts starting at  $1\\mathrm{cm}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ac90c8831987e08e6ebe46cc3fdb9c07996b83ee49a593597124c4d016a69b7c.jpg",
+        "image_caption": [
+            "Figure 6. Ablation of our contributions. Compared to the baseline result (same as Table 4, row (i)), our improved supervision signal provides an overall increase in detail and accuracy at negligible added cost. Inconsistent areas (e.g. right side of couch, towels) are further refined by adding depth guidance. Finally, point back-projection provides higher effective resolution for capturing high-frequency and sub-voxel structures."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation studies",
+        "text_level": 1,
+        "bbox": [
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+            643,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In Table 4 we compare ablations of the main novel components of our method. We note that resolution-agnostic TSDF supervision (RTS) and depth guidance (DG) both result in significant improvement across all metrics. Interestingly, point back-projection (PB) improves all metrics when DG is used ((v) vs. (iv)) but degrades them in the absence of DG ((iii) vs. (ii)). We interpret this as follows: the high-frequency content recovered by PB is locally accurate, but if the coarse alignment relative to ground truth is incorrect, then the added details actually reduce overall accuracy. DG helps to correctly localize the large structures, interacting constructively with PB to achieve the best performance.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Depth guidance strategies In Table 5 we compare different ways to leverage the predicted depth maps to improve our reconstruction. In row (b) we use the density fusion",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "strategy introduced by VolumeFusion [2], and we observe that it does not perform as well as our method using TSDF fusion. We hypothesize that this is because the density does not encode free space information or inward vs. outward surface orientation. In row (c) we test using the depth to directly modulate the image feature projection, using a Gaussian window to down-weight the image features far from the estimated depth. Our experiments show that this manual weighting is an improvement relative to using no depth guidance at all, but that our TSDF fusion guidance yields the best results overall. To explore the relative importance of the image features and the depth guidance, we ablate each one individually in rows (e) and (f), noting worse results in each case.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "18429",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/78f87bbf125016eb1c64a21be0849c2cbb258f5eabe96b7b4d381b7b91956d81.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Resolution</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham↓</td><td>F1 ↑</td><td>L1↓</td><td>δ1.05 ↑</td></tr><tr><td rowspan=\"3\">VoRTX [23]</td><td>4 cm</td><td>5.92</td><td>69.5</td><td>9.32</td><td>79.0</td></tr><tr><td>1 cm</td><td>5.91</td><td>69.6</td><td>9.27</td><td>79.0</td></tr><tr><td>.5 cm</td><td>5.91</td><td>69.5</td><td>9.29</td><td>79.0</td></tr><tr><td rowspan=\"3\">SimpleRecon [21]</td><td>4 cm</td><td>5.51</td><td>68.6</td><td>8.40</td><td>80.4</td></tr><tr><td>1 cm</td><td>5.80</td><td>67.6</td><td>8.23</td><td>81.0</td></tr><tr><td>.5 cm</td><td>5.94</td><td>66.9</td><td>8.67</td><td>80.7</td></tr><tr><td rowspan=\"3\">Ours</td><td>4 cm</td><td>5.15</td><td>75.6</td><td>7.11</td><td>86.2</td></tr><tr><td>1 cm</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>.5 cm</td><td>5.19</td><td>75.4</td><td>6.70</td><td>84.4</td></tr></table>",
+        "bbox": [
+            78,
+            89,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/56f90cca14d7db09ed8b280e03d5bff6d2d69b0f7518608674c182489a2f65da.jpg",
+        "table_caption": [
+            "Table 3. Reconstruction metrics as a function of output resolution. The 2D and 3D metrics show very little sensitivity to the output resolution, despite clear visual differences (see Figure 5). This suggests that future work may require additional metrics to distinguish among high-quality reconstructions."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">DG</td><td rowspan=\"2\">PB</td><td rowspan=\"2\">RTS</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(i)</td><td>□</td><td>□</td><td>□</td><td>6.40</td><td>71.0</td><td>9.38</td><td>81.7</td></tr><tr><td>(ii)</td><td>□</td><td>□</td><td>√</td><td>5.58</td><td>73.8</td><td>7.63</td><td>84.5</td></tr><tr><td>(iii)</td><td>□</td><td>√</td><td>√</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(iv)</td><td>√</td><td>□</td><td>√</td><td>5.25</td><td>75.1</td><td>7.20</td><td>86.1</td></tr><tr><td>(v)</td><td>√</td><td>√</td><td>√</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr></table>",
+        "bbox": [
+            89,
+            340,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/89461d77947267a0bbe40ff9d68bc85f641f59a65159428658a2b9af1889e315.jpg",
+        "table_caption": [
+            "Table 4. Ablation study. We examine the quantitative improvement from the novel components of our method – depth guidance (DG), point pack-projection (PB) and resolution-agnostic TSDF supervision (RTS). Relative to baseline (i), the largest gains come from RTS (ii). PB is helpful with DG enabled (v) but hurts metrics in the absence of DG (iii)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(a)</td><td>Ours - TSDF (main)</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>(b)</td><td>Ours - Density volume [2]</td><td>5.29</td><td>74.3</td><td>7.31</td><td>85.7</td></tr><tr><td>(c)</td><td>Ours - Gaussian weight</td><td>5.47</td><td>73.2</td><td>7.48</td><td>85.1</td></tr><tr><td>(d)</td><td>Ours - TSDF &amp; gaussian weight</td><td>5.52</td><td>73.8</td><td>7.24</td><td>85.8</td></tr><tr><td>(e)</td><td>Ours - No depth guidance</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(f)</td><td>Ours - TSDF (no image features)</td><td>5.66</td><td>71.9</td><td>7.74</td><td>83.8</td></tr></table>",
+        "bbox": [
+            81,
+            549,
+            465,
+            654
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5. Ablation of depth guidance strategies. We compare our depth guidance strategy (a) to other forms of depth guidance: (b) a density fusion volume similar to VolumeFusion [2]; (c) weighting the features using a Gaussian window centered on the predicted depth along each camera ray; (d) combination of (b) and (c); (e) no depth guidance; and (f) TSDF depth guidance with no image features. We find that our TSDF guidance (a) achieves the best performance on all metrics.",
+        "bbox": [
+            75,
+            662,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4. Inference time",
+        "text_level": 1,
+        "bbox": [
+            76,
+            801,
+            223,
+            816
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "FineRecon reconstructs the ScanNet test scenes at 4cm resolution in an average of 18s per scene using an Nvidia V100 GPU. This is composed of a per-frame time of 87ms for 2D feature extraction, depth estimation, and backprojection, plus a one-time TSDF extraction time of 1.1s",
+        "bbox": [
+            75,
+            824,
+            470,
+            902
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "including running the 3D CNN and output layers. Because we use a fixed voxel size, we can increase the output sampling rate with no increase to the per-frame time or 3D CNN time. As we apply higher spatial sampling rates, the cost of high-resolution inference increases proportionally to the number of occupied voxels due to back-projection and MLP execution at each sample point. Our average full-scene reconstruction time is 18s at 4cm, 21s at 2cm, 43s at 1cm. At the limit we test 0.5cm resolution which takes 3.6 minutes per scene on average. For faster inference times, the point back-projection can be disabled, resulting in an average time of 17s per scene at 1cm or 20s per scene at 0.5cm.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            287,
+            617,
+            304
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We have presented an end-to-end network producing detailed 3D reconstructions from posed images. We have demonstrated that our novel supervision (RTS) is key in enabling the network to learn fine details. We have also introduced large improvements by using a depth-prediction network to guide the back-projection (DG). Lastly, we have developed a novel architecture (PB) to allow the free selection of output resolution at test time without requiring additional training or 3D convolution levels. PB opens interesting future avenues in which the TSDF is not predicted on a regular grid, such as adaptive sampling rates or alternative polygonization algorithms beyond marching cubes.",
+        "bbox": [
+            496,
+            313,
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+            494
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Limitations. While FineRecon produces more accurate geometric details than prior work, limitations remain. Despite an improvement over the state-of-the-art, our approach still misses certain local fine structures. One reason is the limitation of the training data, in a large capture setting with pose noise and imperfect depth sensors. Another is that the forward-inference setting does not guarantee consistency with the input observations: to close this gap, future work may explore the hybridization of the techniques presented here with iterative optimization and differentiable rendering. Finally, despite our favorable inference times, running a 3D CNN over a dense feature volume is costly in terms of power and memory, which may be prohibitive for certain applications (sparse convolution may help, but it adds to implementation complexity and is not implemented on all platforms); increased efficiency is thus an important future goal.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            500,
+            775,
+            596,
+            791
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Aljaž Božić, Pablo Palafox, Justus Thies, Angela Dai, and Matthias Nießner. Transformerfusion: Monocular rgb scene reconstruction using transformers. Proc. Neural Information Processing Systems (NeurIPS), 2021. 1, 2, 6",
+            "[2] Jaesung Choe, Sunghoon Im, Francois Rameau, Minjun Kang, and In So Kweon. Volumefusion: Deep depth fusion for 3d scene reconstruction. In Proceedings of the IEEE/CVF"
+        ],
+        "bbox": [
+            506,
+            800,
+            893,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "18430",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "International Conference on Computer Vision, pages 16086-16095, 2021. 1, 2, 7, 8",
+            "[3] Özgün Çiçek, Ahmed Abdulkadir, Soeren S Lienkamp, Thomas Brox, and Olaf Ronneberger. 3d u-net: learning dense volumetric segmentation from sparse annotation. In Medical Image Computing and Computer-Assisted Intervention-MICCAI 2016: 19th International Conference, Athens, Greece, October 17-21, 2016, Proceedings, Part II 19, pages 424-432. Springer, 2016. 5",
+            "[4] Brian Curless and Marc Levoy. A volumetric method for building complex models from range images. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 303-312, 1996. 4, 6",
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+            "[12] Sunghoon Im, Hae-Gon Jeon, Stephen Lin, and In So Kweon. Dpsnet: End-to-end deep plane sweep stereo. arXiv preprint arXiv:1905.00538, 2019. 2",
+            "[13] Haotong Lin, Sida Peng, Zhen Xu, Yunzhi Yan, Qing Shuai, Hujun Bao, and Xiaowei Zhou. Efficient neural radiance fields for interactive free-viewpoint video. In SIGGRAPH Asia 2022 Conference Papers, pages 1-9, 2022. 2",
+            "[14] Tsung-Yi Lin, Piotr Dólar, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2117-2125, 2017. 5"
+        ],
+        "bbox": [
+            78,
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+            898
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[15] William E Lorensen and Harvey E Cline. Marching cubes: A high resolution 3d surface construction algorithm. ACM siggraph computer graphics, 21(4):163-169, 1987. 3, 4",
+            "[16] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. Communications of the ACM, 65(1):99-106, 2021. 2",
+            "[17] Zak Murez, Tarrence van As, James Bartolozzi, Ayan Sinha, Vijay Badrinarayanan, and Andrew Rabinovich. Atlas: End-to-end 3d scene reconstruction from posed images. In European conference on computer vision, pages 414-431. Springer, 2020. 1, 2, 3, 5, 6",
+            "[18] Alexander Rich, Noah Stier, Pradeep Sen, and Tobias Höllerer. 3dvnet: Multi-view depth prediction and volumetric refinement. In 2021 International Conference on 3D Vision (3DV), pages 700-709. IEEE, 2021. 2, 6",
+            "[19] Barbara Roessle, Jonathan T Barron, Ben Mildenhall, Pratul P Srinivasan, and Matthias Nießner. Dense depth priors for neural radiance fields from sparse input views. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12892-12901, 2022. 2",
+            "[20] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention-MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pages 234-241. Springer, 2015. 5",
+            "[21] Mohamed Sayed, John Gibson, Jamie Watson, Victor Prisacariu, Michael Firman, and Clément Godard. Simplerecon: 3d reconstruction without 3d convolutions. In Proceedings of the European Conference on Computer Vision (ECCV), 2022. 2, 5, 6, 8",
+            "[22] Johannes L Schonberger, Enliang Zheng, Jan-Michael Frahm, and Marc Pollefeys. Pixelwise view selection for unstructured multi-view stereo. In European conference on computer vision, pages 501-518. Springer, 2016. 1, 2",
+            "[23] Noah Stier, Alexander Rich, Pradeep Sen, and Tobias Höllerer. Vortex: Volumetric 3d reconstruction with transformers for voxelwise view selection and fusion. In 2021 International Conference on 3D Vision (3DV), pages 320-330. IEEE, 2021. 1, 2, 3, 5, 6, 8",
+            "[24] Jiaming Sun, Yiming Xie, Linghao Chen, Xiaowei Zhou, and Hujun Bao. Neuralrecon: Real-time coherent 3d reconstruction from monocular video. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15598-15607, 2021. 1, 2, 3, 5, 6",
+            "[25] Mingxing Tan and Quoc Le. Efficientnetv2: Smaller models and faster training. In International conference on machine learning, pages 10096-10106. PMLR, 2021. 5",
+            "[26] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Advances in Neural Information Processing Systems, 34:27171-27183, 2021. 2",
+            "[27] Yi Wei, Shaohui Liu, Yongming Rao, Wang Zhao, Jiwen Lu, and Jie Zhou. Nerfingmvs: Guided optimization of neural"
+        ],
+        "bbox": [
+            501,
+            92,
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+        ],
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+    },
+    {
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+        "sub_type": "ref_text",
+        "list_items": [
+            "radiance fields for indoor multi-view stereo. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5610-5619, 2021. 2",
+            "[28] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. Advances in Neural Information Processing Systems, 34:4805-4815, 2021. 2",
+            "[29] Zehao Yu, Songyou Peng, Michael Niemeyer, Torsten Sattler, and Andreas Geiger. Monosdf: Exploring monocular geometric cues for neural implicit surface reconstruction. arXiv preprint arXiv:2206.00665, 2022. 2",
+            "[30] Weihao Yuan, Xiaodong Gu, Heng Li, Zilong Dong, and Siyu Zhu. 3d-former: Monocular scene reconstruction with 3d sdf transformers. In Proceedings of the International Conference on Learning Representations, 2023. 2",
+            "[31] Zi-Xin Zou, Shi-Sheng Huang, Yan-Pei Cao, Tai-Jiang Mu, Ying Shan, and Hongbo Fu. Mononeuralfusion: Online monocular neural 3d reconstruction with geometric priors. arXiv preprint arXiv:2209.15153, 2022. 2"
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diff --git a/2023/FineRecon_ Depth-aware Feed-forward Network for Detailed 3D Reconstruction/6c51d26e-268b-4ab2-8995-1d2780bb8d14_model.json b/2023/FineRecon_ Depth-aware Feed-forward Network for Detailed 3D Reconstruction/6c51d26e-268b-4ab2-8995-1d2780bb8d14_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..08938a3fa00dc3aaefca3701347adf20e549373f
--- /dev/null
+++ b/2023/FineRecon_ Depth-aware Feed-forward Network for Detailed 3D Reconstruction/6c51d26e-268b-4ab2-8995-1d2780bb8d14_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "FineRecon: Depth-aware Feed-forward Network for Detailed 3D Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Noah Stier\\(^{1,2}\\) Anurag Ranjan\\(^{1}\\) Alex Colburn\\(^{1}\\) Yajie Yan\\(^{1}\\) Liang Yang\\(^{1}\\) Fangchang Ma\\(^{1}\\) Baptiste Angles\\(^{1}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{1}\\)Apple \\(^{2}\\)University of California, Santa Barbara"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "Abstract"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Recent works on 3D reconstruction from posed images [17, 23, 24] have demonstrated that direct inference of scene-level 3D geometry without test-time optimization is feasible using deep neural networks, showing remarkable promise and high efficiency. However, the reconstructed geometry, typically represented as a 3D truncated signed distance function (TSDF), is often coarse without fine geometric details. To address this problem, we propose three effective solutions for improving the fidelity of inference-based 3D reconstructions. We first present a resolution-agnostic TSDF supervision strategy to provide the network with a more accurate learning signal during training, avoiding the pitfalls of TSDF interpolation seen in previous work. We then introduce a depth guidance strategy using multiview depth estimates to enhance the scene representation and recover more accurate surfaces. Finally, we develop a novel architecture for the final layers of the network, conditioning the output TSDF prediction on high-resolution image features in addition to coarse voxel features, enabling sharper reconstruction of fine details. Our method, FineRecon<sup>1</sup>, produces smooth and highly accurate reconstructions, showing significant improvements across multiple depth and 3D reconstruction metrics."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "1. Introduction"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Reconstruction of 3D scenes from posed images is a long-standing problem in computer vision, with many applications such as autonomous driving, robotic navigation, and digital 3D asset creation. The traditional approach is to estimate depth maps over the input images using multiview stereo (MVS), and then fuse them together to form a unified 3D model [9, 10, 22]. However, the fusion process commonly results in missing geometry or artifacts in areas where the depth maps do not agree, due to effects such as occlusion, specularity, and transparent or low-texture sur"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1. Our method, FineRecon, recovers highly detailed and coherent geometry relative to state-of-the-art methods. Our contributions of lossless ground truth sampling, depth-aware feature volume, and point backprojection result in smooth surfaces that preserve high-frequency structures without creating strong artifacts."
+        },
+        {
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+            "bbox": [
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+            "content": "faces. Recently, an alternative method has been proposed to address this issue in Atlas [17], which back-projects learned image features onto a voxel grid and directly predicts the scene's truncated signed distance function (TSDF) using a 3D convolutional neural network (CNN). The main advantage is that the CNN can learn to produce smooth, consistent surfaces, and to fill in holes that would otherwise result from low-texture regions and occlusion. Several methods have proposed improvements to this framework [1, 2, 23, 24], consistently pushing the state of the art in reconstruction accuracy. However, despite these efforts, the reconstructions produced by these methods remain coarse. We identify three key factors restricting the accuracy and level of detail in prior works, and we introduce solutions to address them, demonstrating their effectiveness within a new system: FineRecon."
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+            "bbox": [
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+            "content": "First, existing works use tri-linear interpolation to resample the ground-truth TSDF to align with the model's voxel grid during training [17, 23, 24]. This allows su"
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+            "content": "<sup>1</sup>https://github.com/apple/ml-finerecon"
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+        {
+            "type": "page_number",
+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "pervision of the model's TSDF predictions at each voxel center, even when the voxel centers do not coincide with the pre-computed ground-truth TSDF points. However, resampling via tri-linear interpolation corrupts detail in the training data, because distance fields are not linear when non-planar geometry such a corner is present, as shown in Fig. 3. We avoid this issue by making supervised predictions only at the exact points where the ground-truth TSDF is known. This supervision change comes at no extra cost, and it results in greatly improved visual detail as well as a relative reduction in average chamfer distance between reconstruction and ground truth of over \\(10\\%\\)."
+        },
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+            "type": "text",
+            "bbox": [
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+            "content": "Second, prior work [1, 2, 17, 23, 24] uses dense back-projection, sampling a feature from each input image in each voxel. This causes blurring in the back-projection volume, which increases the difficulty of extracting accurate surface locations. To address this, our method uses an initial multi-view stereo depth estimation step, after which the depth estimates are used to enhance the feature volume and guide the 3D CNN toward areas of high surface likelihood. We show that this step significantly increases the quality of the reconstructions produced by our system."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Third, because of the high computational cost of 3D CNNs, it is expensive to increase the voxel resolution. Existing works use voxel sizes of \\(4\\mathrm{cm}\\) or larger [1, 2, 17, 23, 24], which is not enough to resolve the level of geometric detail visible in natural images at ranges of a few meters. To remedy this, we propose a new method to query the TSDF prediction at any point in \\(\\mathbb{R}^3\\), conditioned on the CNN grid features and image features projected directly to the query point. This reduces aliasing and allows our model to resolve sub-voxel detail. Furthermore, this enables reconstruction at arbitrary resolution without re-training."
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "FineRecon achieves state-of-the-art performance on the challenging ScanNet dataset, as measured by 3D mesh metrics and rendered 2D depth metrics. We further show that it produces substantially improved visual detail with reduced artifacts relative to prior work."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Contributions. The main contributions of this paper are:"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- We increase the accuracy of the training data using resolution-agnostic TSDF supervision, allowing FineRecon to reconstruct details with higher fidelity."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- We improve reconstruction accuracy using a novel MVS depth-guidance strategy, augmenting the backprojection volume with an estimated TSDF fusion channel."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- We enable the reconstruction of sub-voxel detail with a novel TSDF prediction architecture that can be queried at any 3D point, using point back-projected fine-grained image features."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "Multi-view stereo. 3D reconstruction is traditionally posed as per-pixel depth estimation [9, 10, 22]. While recent works have shown strong results [12, 21], a known drawback is that the estimation of each depth map is independent, so continuity across frustum boundaries is not enforced, and this often leads to artifacts. Solutions have been proposed [7, 11, 18], but it is still an open problem."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.222,
+                0.893,
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+            "angle": 0,
+            "content": "Feed-forward 3D reconstruction. An effective recent strategy is to perform volumetric reconstruction directly in scene space using feed-forward neural networks [1, 2, 17, 23, 24]. In this line of research, image features are encoded by a 2D CNN and densely back-projected into a global feature volume, then a 3D CNN predicts the scene TSDF. These models can generalize to new scenes at inference time without computationally-demanding test-time optimization, and they can produce smooth and complete reconstructions. However, they tend to blur out surface details and omit thin structures. In contrast, ours is the first of these volumetric TSDF methods to reconstruct accurate sub-voxel detail. 3D-Former [30], a concurrent work, replaces the 3D CNN with a transformer, an orthogonal direction that could potentially be combined with our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.449,
+                0.893,
+                0.659
+            ],
+            "angle": 0,
+            "content": "Geometric priors in neural radiance fields. Recent novel-view synthesis methods based on neural radiance fields [16] have shown remarkable 2D rendering quality, typically relying on time-consuming per-scene optimization to obtain good results. These methods have also been extended to predict surface geometry [26, 28], and it has been shown that geometric priors, such as depth and normal maps, can boost performance. For instance, multiple works [13, 19, 27] use depth estimates to improve ray sampling efficiency. MonoSDF [29] uses monocular depth and normal estimation as pseudo-ground truth to supervise its predicted SDF. Similarly, our method uses guidance from a depth-prediction network, but with a focus on interactive reconstruction speed and generalization to new scenes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Geometric priors in feed-forward networks. Only a few previous methods based on feed-forward networks have incorporated geometric priors. MonoNeuralFusion [31] uses monocular normal estimates but does not explore depth priors. Similar to our approach, VolumeFusion [2] uses depth as an additional feature by fusing it into a density volume and concatenating it with the image feature volume. However, density does not encode the difference between occluded space and observed free space, and it omits crucial information about inward vs. outward surface orientation. In contrast, we explore multiple forms of depth guidance, finding that guidance by TSDF fusion outperforms the density-based variant and others (Table 5). CVRecon [8], a concurrent work, uses frustum-aligned cost volumes in addition to global features, which is related to our work but does not explicitly predict depth."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+    [
+        {
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+            "bbox": [
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+            "angle": 0,
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+        {
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+            "bbox": [
+                0.076,
+                0.256,
+                0.895,
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+            ],
+            "angle": 0,
+            "content": "Figure 2. Model overview. Given a monocular RGB image sequence, we use a pre-trained depth network to estimate depth images \\(\\hat{\\mathcal{D}}\\). In the meantime we also extract image features \\(\\mathcal{F}^c\\) for global volume fusion and \\(\\mathcal{F}^f\\) for point back-projection. The depth \\(\\hat{\\mathcal{D}}\\) is then fused into an initial, approximate TSDF volume \\(\\nu^d\\), and \\(\\mathcal{F}^c\\) is back-projected into a feature volume \\(\\nu^c\\) using the camera parameters. The two volumes are then concatenated and fed to a 3D CNN \\(\\Psi\\) to produce the global feature volume \\(\\nu^{\\Psi}\\) and the coarse occupancy grid \\(\\hat{\\mathcal{O}}\\) (used to accelerate inference). Finally, at any query point \\(x \\in \\mathbb{R}^3\\), we sample high-resolution image features \\(\\mathcal{F}^f\\) and concatenate with the interpolated voxel feature \\(\\nu^{\\Psi}(x)\\). This is passed to an MLP to predict the final TSDF value."
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+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.544,
+                0.47,
+                0.71
+            ],
+            "angle": 0,
+            "content": "Figure 3. Illustration of our improved, resolution-agnostic TSDF supervision. With rotational augmentation during training, the model's voxel grid (gray) does not align with the points (blue) where the ground-truth TSDF is known. Previous work uses linear interpolation (a) to estimate the TSDF at the voxel centers for supervision, but this leads to errors: the ground-truth geometry (yellow) is intersected by the interpolated TSDF values (red circles). In contrast, our model can be supervised at any 3D point. Therefore, regardless of the feature grid orientation, we can supervise the model at the exact points where the ground-truth is known (b). This reduces noise during training and increases reconstruction accuracy (see Table 6)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.722,
+                0.168,
+                0.737
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.747,
+                0.47,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Given a set of input images \\(\\{I_i\\}\\) along with their camera poses \\(\\{P_i\\}\\) and intrinsics \\(\\{K_i\\}\\), we seek to compute an estimate \\(\\hat{S}\\) of the true scene TSDF \\(S\\). We train a deep-learning model \\(\\Phi\\) to perform this mapping, \\(\\hat{S} = \\Phi (\\{I_i\\}, \\{P_i\\}, \\{K_i\\})\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.833,
+                0.236,
+                0.847
+            ],
+            "angle": 0,
+            "content": "3.1. Model overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our model (illustrated in Fig. 2) extracts a set of 2D features \\(\\{\\mathcal{F}_i^c\\}\\) from each input image using a convolutional neural network (CNN), \\(\\Omega^c\\). We then use the camera pa"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.365,
+                0.892,
+                0.516
+            ],
+            "angle": 0,
+            "content": "rameters to back-project \\(\\{\\mathcal{F}_i^c\\}\\) onto a 3D voxel grid. The back-projection process is augmented using depth estimates \\(\\{\\hat{D}_i\\}\\) to produce the depth-guided feature volume \\(\\nu^g\\), as described in Section 3.2.2. We process \\(\\nu^g\\) using a 3D CNN \\(\\Psi\\) to produce a new feature volume \\(\\nu^{\\Psi}\\), which we can query for \\(\\hat{S}(q)\\) at any 3D point \\(q \\in \\mathbb{R}^3\\) using the interpolation strategy defined in Section 3.2.3. To extract a surface mesh, we query the reconstruction on a grid of arbitrary resolution to produce a TSDF volume, from which a mesh can be extracted with Marching cubes [15]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.532,
+                0.681,
+                0.547
+            ],
+            "angle": 0,
+            "content": "3.2. Key improvements"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.557,
+                0.821,
+                0.572
+            ],
+            "angle": 0,
+            "content": "3.2.1 Resolution-agnostic TSDF supervision"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "During training, as in previous works [17, 23, 24] we randomly orient the coordinate system of the feature volume relative to \\(S\\) using \\(\\pm 3^{\\circ}\\) rotations about the horizontal axis and \\(\\pm 180^{\\circ}\\) rotations about the gravitational axis. Thus, the voxel centers may not coincide with the points \\(\\{x\\}\\) where \\(S\\) is known. This is typically addressed using linear interpolation on \\(S\\) to estimate the ground-truth TSDF at the voxel centers. However, this process is not accurate, since with non-planar geometry the TSDF is a non-linear function of space. Interpolation therefore corrupts the ground-truth TSDF, as shown in Fig. 3. In theory this effect can be minimized by sampling the ground truth on a very high-resolution grid, but this greatly increases training cost. To preserve the accuracy of the ground truth with no added cost, we instead supervise only at the points \\(\\{x\\}\\) where the ground truth is known, so that no interpolation is required. This decouples the accuracy of our ground truth from its sampling rate, rendering it resolution-agnostic. To support this, our model must be able to estimate the TSDF at any point in \\(\\mathbb{R}^3\\), which we achieve using the strategy outlined in Section 3.2.3. This simple supervision change enables our"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18425"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.122
+            ],
+            "angle": 0,
+            "content": "model to reconstruct significantly more visual detail (see Fig. 6)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.127,
+                0.241,
+                0.143
+            ],
+            "angle": 0,
+            "content": "3.2.2 Depth guidance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.15,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "In order to localize image features in 3D space, we sample a pixel feature at each voxel from each available input image:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.194,
+                0.47,
+                0.213
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {\\mathcal {V}} _ {i} ^ {c} (q) = \\alpha \\left(\\mathcal {F} _ {i} ^ {c}, K _ {i} P _ {i} q _ {h}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.219,
+                0.469,
+                0.28
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha(F, u)\\) represents sampling a feature from 2D map \\(F\\) at pixel location \\(u\\), and \\(q_h\\) is the voxel center in homogeneous coordinates. We then reduce using a per-channel mean across views to form one feature vector per-voxel:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.185,
+                0.29,
+                0.469,
+                0.326
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {V} ^ {c} (q) = \\frac {1}{| \\{I _ {i} \\} |} \\sum_ {i} \\tilde {\\mathcal {V}} _ {i} ^ {c} (q) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.336,
+                0.469,
+                0.485
+            ],
+            "angle": 0,
+            "content": "As an additional signal in recovering the scene surfaces, we propose to inject a multi-view depth prior using depth estimates from an MVS system \\(M\\). As MVS is a well-studied problem, we treat \\(M\\) as an off-the-shelf component, and in the Supplementary we study the sensitivity of our system to depth noise and choice of \\(M\\). We fuse \\(\\hat{\\mathcal{D}}\\) into scene space using the standard TSDF fusion [4] to form \\(\\mathcal{V}^d\\). We then concatenate \\(\\mathcal{V}^d\\) as an extra channel in the back-projection volume. Our depth-guided back-projection volume is thus defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.221,
+                0.486,
+                0.469,
+                0.504
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {V} ^ {g} = \\left[ \\mathcal {V} ^ {c}, \\mathcal {V} ^ {d} \\right]. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.51,
+                0.469,
+                0.691
+            ],
+            "angle": 0,
+            "content": "In our experiments (see Table 5), the depth-guided feature volume \\(\\mathcal{V}^g\\) shows significantly improved results with respect to image features alone \\((\\mathcal{V}^c)\\), or depth inputs alone \\((\\mathcal{V}^d)\\). With naive application of the depth guidance, we find that this additional signal increases our network's propensity to over-fit to the training data, relying too heavily on the depth guidance which is often inaccurate. To address this, we scale each predicted depth map by a factor sampled uniformly in the range [0.9, 1.1] as a data augmentation during training. This reduces over-fitting and encourages the network to learn to use the image features in regions where the depth maps are unreliable."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.692,
+                0.469,
+                0.767
+            ],
+            "angle": 0,
+            "content": "We additionally experiment with several strategies for using the depth estimate to directly modulate the image feature back-projection. However, as shown in our experiments, our TSDF fusion approach outperforms these methods by a large margin (see Table 5)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.771,
+                0.398,
+                0.787
+            ],
+            "angle": 0,
+            "content": "3.2.3 Point back-projection TSDF inference"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "We use tri-linear interpolation to sample the 3D CNN's output feature volume \\(\\mathcal{V}^{\\Psi}\\) at any query point \\(q\\). This results in a continuous-valued feature \\(\\tilde{\\mathcal{V}}^{\\Psi} = \\Lambda (\\mathcal{V}^{\\Psi}, q)\\) where \\(\\Lambda\\) represents tri-linear interpolation. Directly estimating \\(\\hat{S}\\) from this feature is severely limited in its ability to reconstruct sub-voxel detail, since the effective resolution of \\(\\tilde{\\mathcal{V}}^{\\Psi}\\) is still constrained to the size of the voxels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.304
+            ],
+            "angle": 0,
+            "content": "We improve on this paradigm using an additional point back-projection step to directly sample image features \\(\\mathcal{W}(q)\\) at the point \\(q\\). This step is identical to the depth-guided back-projection outlined in Section 3.2.2, except that the point \\(q\\) is no longer constrained to be a voxel center. The effective resolution of this new continuous-valued feature is thus determined by the resolution of the 2D image feature grid rather than the 3D voxel size. Assuming high-enough 2D feature resolution, \\(\\mathcal{W}(q)\\) thus carries much finer-grained information than the linearly-interpolated voxel feature \\(\\tilde{\\mathcal{V}}^{\\Psi}(q)\\), complementing the 3D CNN's ability to produce smooth and context-informed features. We concatenate \\(\\mathcal{W}\\) with \\(\\tilde{\\mathcal{V}}^{\\Psi}\\) as the input to a multilayer perceptron (MLP) \\(\\theta_{S}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.632,
+                0.313,
+                0.892,
+                0.332
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {S} = \\theta_ {S} ([ \\mathcal {W}, \\tilde {\\mathcal {V}} ^ {\\Psi} ]). \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.343,
+                0.892,
+                0.447
+            ],
+            "angle": 0,
+            "content": "At a given 3D sampling rate, our point back-projection inference strategy adds a small but non-negligible cost relative to using only \\(\\tilde{\\mathcal{V}}^{\\Psi}\\): we must run an additional round of feature extraction and back-projection using \\(\\Omega^{f}\\), and the input dimension of \\(\\theta_{S}\\) must be doubled in order to receive the extra input features. We show in our experiments that this cost is tractable (see Section 4.4)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.449,
+                0.892,
+                0.571
+            ],
+            "angle": 0,
+            "content": "We observe that the fine-grained features \\(\\mathcal{W}\\) can contain spurious high-frequency content, particularly near the borders of the 2D features where the CNN output is unreliable due to edge effects. To reduce artifacts, we downweight \\(\\{F_i^f\\}\\) near the borders prior to back-projection using a weight \\(w = \\sigma (l\\cdot (min(\\frac{d}{m},1)\\cdot 2 - 1))\\) ,where \\(d\\) is the distance to the nearest border in pixels; \\(m = 20\\) is a margin distance; \\(l = 6\\) controls the falloff rate; and \\(\\sigma (x) = \\frac{1}{1 + e^{-x}}\\)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.574,
+                0.834,
+                0.589
+            ],
+            "angle": 0,
+            "content": "3.2.4 Output resolution & occupancy filtering"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.597,
+                0.892,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Our model can be sampled at any point in \\(\\mathbb{R}^3\\), and we choose to sample it on a regular grid at test time in order to support meshing with marching cubes [15]. The resolution of this grid can be determined arbitrarily without retraining, and we experiment with several output grid resolutions (see Fig. 5). Naively, the cost of our point back-projection inference strategy grows cubically with the sampling rate. At high resolutions, it thus becomes expensive due to the cost of running the additional back-projection and \\(\\theta_S\\) densely over the full volume. To mitigate this, we predict the per-voxel occupancy \\(\\hat{O}\\) with an additional MLP: \\(\\hat{O} = \\theta_O(\\mathcal{V})\\). Then at test time we sample \\(\\hat{S}\\) only within voxels that are predicted to be occupied. While the asymptotic complexity is still cubic, in practice this greatly reduces the cost due to the prevalence of empty space."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.833,
+                0.605,
+                0.849
+            ],
+            "angle": 0,
+            "content": "3.3. Training"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "At training time, we require a ground-truth TSDF \\( S \\) to supervise \\( \\hat{S} \\). For training on real scans, we use TSDF fusion [4] to generate \\( S \\) on a discrete grid of points \\( X \\) with"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18426"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.084,
+                0.891,
+                0.528
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.531,
+                0.895,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Figure 4. Qualitative results. Comparison of our method with NeuralRecon [24], VoRTX [23], and SimpleRecon [21]. NeuralRecon and VoRTX capture consistent global structure but lose many details, whereas SimpleRecon recovers details but fails to keep geometry consistent across views, leading to duplicate surfaces after TSDF fusion. Our method produces the most complete, consistent reconstruction while preserving details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.605,
+                0.47,
+                0.741
+            ],
+            "angle": 0,
+            "content": "resolution \\(\\delta\\), \\(X = \\{x \\in [i \\cdot \\delta, j \\cdot \\delta, k \\cdot \\delta]\\}\\), assuming the existence of a set of ground-truth depth maps \\(\\{D_i\\}\\) corresponding to \\(\\{I_i\\}\\). While ground truth depth can be noisy when acquired by sensors such as structured-light infrared scanners, we minimize artifacts by 1) using a large number of views to generate the ground-truth, 2) using an appropriate TSDF truncation distance following previous work [17, 23, 24], and 3) discarding depths beyond the range where the accuracy starts to visibly degrade."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.741,
+                0.47,
+                0.772
+            ],
+            "angle": 0,
+            "content": "Loss function. We define the TSDF loss \\(\\mathcal{L}_{\\mathcal{S}}\\) following SG-NN [6] as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.154,
+                0.776,
+                0.47,
+                0.814
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {S} = \\frac {1}{| X |} \\sum_ {x \\in X} | t (\\hat {S} (x)) - t (S (x) |, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.819,
+                0.469,
+                0.863
+            ],
+            "angle": 0,
+            "content": "where \\(t(x) = \\mathrm{sign}(x)\\cdot \\ln (|x| + 1)\\). We define occupancy loss \\(\\mathcal{L}_O\\) using the standard binary cross-entropy, abbreviated \\(BCE\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.153,
+                0.868,
+                0.47,
+                0.905
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {O} = \\frac {1}{| X |} \\sum_ {x \\in X} B C E (O (x), \\hat {O} (x)) \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.606,
+                0.892,
+                0.636
+            ],
+            "angle": 0,
+            "content": "Following VoRTX [23] we compute the ground-truth occupancy as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.524,
+                0.644,
+                0.892,
+                0.685
+            ],
+            "angle": 0,
+            "content": "\\[\nO (x) = \\oplus (\\tilde {O} (x)); \\quad \\tilde {O} (x) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} | S (x) | <   1 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.692,
+                0.892,
+                0.753
+            ],
+            "angle": 0,
+            "content": "where \\(\\oplus\\) represents morphological dilation with a \\(3\\times 3\\times 3\\) structuring element. Note, this definition of occupancy describes space near a surface [6, 23, 24], rather than space interior to an object. Our training loss \\(\\mathcal{L}\\) is then defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.643,
+                0.762,
+                0.891,
+                0.778
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {S} + \\mathcal {L} _ {O}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "CNN backbone architectures. Our 2D CNN architecture is a feature pyramid network [14] using EfficientNetV2-S [25] as a backbone. This structure is shared for both \\(\\Omega^c\\) and \\(\\Omega^f\\), but the weights are duplicated and then trained independently. Despite their identical architectures, these networks learn strikingly different features (see Supp.). Our 3D CNN \\(\\Psi\\) is inspired by U-Net [3, 20], see Supp. for details."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18427"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.242
+            ],
+            "angle": 0,
+            "content": "Implementation details. As the depth predictor \\( M \\) we use our re-implementation of the MVS network SimpleRecon [21]. We use a voxel size of 4cm in our model, and we train on volumetric scene chunks of size \\( (3.84\\mathrm{m} \\times 3.84\\mathrm{m} \\times 2.24\\mathrm{m}) \\). During training we select views by uniform random sampling over all views that at least partially observe the training chunk. At test time we fuse only keyframes, using the view selection strategy from DeepVideoMVS [7]. Training takes 36 hours on eight Nvidia V100 GPUs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.258,
+                0.21,
+                0.276
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.284,
+                0.35,
+                0.3
+            ],
+            "angle": 0,
+            "content": "4.1. Dataset, baselines, and metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.307,
+                0.471,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Dataset. We validate our method by training and evaluating our model on the popular ScanNet dataset [5], which is composed of 1,613 indoor scans. We report all our metrics on the official test set containing 100 scans."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.382,
+                0.47,
+                0.503
+            ],
+            "angle": 0,
+            "content": "Baselines. We compare our model with several previous works. For end-to-end 3D reconstruction methods we select Atlas [17], NeuralRecon [24], VoRTX [23], and TransformerFusion [1]. We also compare to MVS depth-prediction, selecting SimpleRecon [21], which we re-implement. In order to compare to SimpleRecon, we apply TSDF fusion [4] on the predicted depth maps to produce a 3D mesh."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.518,
+                0.47,
+                0.669
+            ],
+            "angle": 0,
+            "content": "Metrics. We compute 3D metrics directly on the mesh reconstructions, and we compute depth metrics by rendering the meshes to generate predicted depth maps. Relative to prior works on depth estimation such as SimpleRecon [21], this is a slight change from the typical protocol of computing depth metrics directly on the raw depth maps. We believe our strategy is more indicative of performance in real-world applications that rely on the unified 3D reconstruction. Our definition for all metrics is the same as in Atlas [17] (see Supp. for details)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.67,
+                0.471,
+                0.806
+            ],
+            "angle": 0,
+            "content": "For computing 3D metrics we use the evaluation code from TransformerFusion [1], which includes a trimming protocol to avoid penalizing reconstructions for in-painting surfaces in unobserved regions. As noted in previous work [1, 23], precision or recall can easily be optimized individually at the expense of the other, as with accuracy and completeness. We thus emphasize Chamfer distance and F1 (i.e. F-score) as the most important 3D metrics, capturing this trade-off."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.817,
+                0.172,
+                0.832
+            ],
+            "angle": 0,
+            "content": "4.2. Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Qualitative Results. In Fig. 4, we show qualitative results of our method compared to baselines and ground truth. We observe that our method preserves more details while minimizing high-frequency artifacts. The surfaces"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.09,
+                0.891,
+                0.194
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Acc ↓</td><td>Comp ↓</td><td>Cham ↓</td><td>Prec ↑</td><td>Rec ↑</td><td>F1 ↑</td></tr><tr><td>Atlas [17]</td><td>7.09</td><td>7.52</td><td>7.30</td><td>68.4</td><td>61.1</td><td>64.3</td></tr><tr><td>NeuralRecon [24]</td><td>5.04</td><td>10.68</td><td>7.86</td><td>62.7</td><td>59.1</td><td>60.7</td></tr><tr><td>3DVNet [18]</td><td>6.73</td><td>7.72</td><td>7.22</td><td>65.5</td><td>59.6</td><td>62.1</td></tr><tr><td>Transf. Fusion [1]</td><td>5.52</td><td>8.27</td><td>6.89</td><td>72.8</td><td>60.0</td><td>65.5</td></tr><tr><td>VoRTX [23]</td><td>4.32</td><td>7.52</td><td>5.92</td><td>76.3</td><td>64.0</td><td>69.5</td></tr><tr><td>SimpleRecon [21]</td><td>6.43</td><td>5.18</td><td>5.80</td><td>66.0</td><td>69.7</td><td>67.6</td></tr><tr><td>Ours</td><td>5.25</td><td>5.11</td><td>5.18</td><td>78.0</td><td>73.4</td><td>75.5</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.204,
+                0.894,
+                0.249
+            ],
+            "angle": 0,
+            "content": "Table 1. 3D reconstruction metrics for ScanNet. We compare with recent work on mesh metrics defined in Atlas [17]. Best and Second -best are highlighted."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.269,
+                0.891,
+                0.345
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>L1 ↓</td><td>AbsRel ↓</td><td>SqRel ↓</td><td>δ1.05 ↑</td><td>δ1.25 ↑</td><td>Comp. ↑</td></tr><tr><td>Atlas [17]</td><td>11.96</td><td>6.26</td><td>4.22</td><td>75.2</td><td>93.8</td><td>98.8</td></tr><tr><td>NeuralRecon [24]</td><td>9.84</td><td>6.54</td><td>3.79</td><td>75.0</td><td>94.6</td><td>90.8</td></tr><tr><td>VoRTX [23]</td><td>9.32</td><td>5.92</td><td>3.65</td><td>79.0</td><td>94.9</td><td>96.1</td></tr><tr><td>SimpleRecon [21]</td><td>8.23</td><td>4.83</td><td>2.66</td><td>81.0</td><td>96.8</td><td>97.4</td></tr><tr><td>Ours</td><td>6.91</td><td>4.24</td><td>2.57</td><td>86.6</td><td>97.1</td><td>97.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.354,
+                0.893,
+                0.399
+            ],
+            "angle": 0,
+            "content": "Table 2. 2D metrics for ScanNet. The 2D depth is rendered and metrics are computed in the same way as with Atlas [17]. We highlight the Best and Second best with colors respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.42,
+                0.892,
+                0.526
+            ],
+            "angle": 0,
+            "content": "in our reconstructions are smooth and consistent, gracefully unifying information from all views without the depth-disagreement artifacts or noticeable discontinuities visible in SimpleRecon. VoRTX suffers from blurry reconstructions where fine details such as chair legs are completely lost, whereas our approach reconstructs these elements faithfully."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.529,
+                0.894,
+                0.682
+            ],
+            "angle": 0,
+            "content": "In Fig. 5 we show qualitative results at three output resolutions: \\(4\\mathrm{cm}\\), \\(1\\mathrm{cm}\\) and \\(0.5\\mathrm{cm}\\). VoRTX is not tractable at high resolutions, so we upsample VoRTX's \\(4\\mathrm{cm}\\) TSDF with linear interpolation, which does not increase the effective level of detail. For SimpleRecon, we can generate reconstructions at any desired resolution by decreasing the voxel size during TSDF fusion, and we note that artifacts and noise increase greatly at high resolution. In contrast, our results consistently preserve a high level of detail while avoiding noisy surfaces."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Quantitative Results. Table 1 shows our 3D reconstruction metrics on the ScanNet dataset. We report metrics for our method and SimpleRecon at the relatively high resolution of \\(1\\mathrm{cm}\\) because it is tractable to do so. We report metrics for the other baselines at their native resolution of \\(4\\mathrm{cm}\\), because increasing this resolution would add significant compute cost and engineering effort. For fairness, metrics for our method at \\(4\\mathrm{cm}\\) are shown in Table 3, and we note that the quantitative differences from \\(1\\mathrm{cm}\\) are negligible. Our method achieves the best result in most metrics. In particular, it achieves the lowest Chamfer distance and highest F-score by large margins."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18428"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.12,
+                0.085,
+                0.852,
+                0.332
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.336,
+                0.895,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative results at various output resolutions. With our method, we observe increased sub-voxel detail when increasing the output sampling rate from \\(4\\mathrm{cm}\\) to \\(1\\mathrm{cm}\\), as well as the occasional appearance of small artifacts near view frustum boundaries. Beyond \\(1\\mathrm{cm}\\) we observe no significant changes, suggesting we have reached our system's limit of detail given the 2D feature resolution. In contrast, upsampling the VoRTX outputs from \\(4\\mathrm{cm}\\) slightly increases smoothness but adds no extra detail, and SimpleRecon shows the appearance of significant frustum boundary artifacts starting at \\(1\\mathrm{cm}\\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.414,
+                0.891,
+                0.569
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.572,
+                0.895,
+                0.629
+            ],
+            "angle": 0,
+            "content": "Figure 6. Ablation of our contributions. Compared to the baseline result (same as Table 4, row (i)), our improved supervision signal provides an overall increase in detail and accuracy at negligible added cost. Inconsistent areas (e.g. right side of couch, towels) are further refined by adding depth guidance. Finally, point back-projection provides higher effective resolution for capturing high-frequency and sub-voxel structures."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.644,
+                0.24,
+                0.658
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.668,
+                0.471,
+                0.851
+            ],
+            "angle": 0,
+            "content": "In Table 4 we compare ablations of the main novel components of our method. We note that resolution-agnostic TSDF supervision (RTS) and depth guidance (DG) both result in significant improvement across all metrics. Interestingly, point back-projection (PB) improves all metrics when DG is used ((v) vs. (iv)) but degrades them in the absence of DG ((iii) vs. (ii)). We interpret this as follows: the high-frequency content recovered by PB is locally accurate, but if the coarse alignment relative to ground truth is incorrect, then the added details actually reduce overall accuracy. DG helps to correctly localize the large structures, interacting constructively with PB to achieve the best performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Depth guidance strategies In Table 5 we compare different ways to leverage the predicted depth maps to improve our reconstruction. In row (b) we use the density fusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.895,
+                0.856
+            ],
+            "angle": 0,
+            "content": "strategy introduced by VolumeFusion [2], and we observe that it does not perform as well as our method using TSDF fusion. We hypothesize that this is because the density does not encode free space information or inward vs. outward surface orientation. In row (c) we test using the depth to directly modulate the image feature projection, using a Gaussian window to down-weight the image features far from the estimated depth. Our experiments show that this manual weighting is an improvement relative to using no depth guidance at all, but that our TSDF fusion guidance yields the best results overall. To explore the relative importance of the image features and the depth guidance, we ablate each one individually in rows (e) and (f), noting worse results in each case."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "18429"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.09,
+                0.477,
+                0.25
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Resolution</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham↓</td><td>F1 ↑</td><td>L1↓</td><td>δ1.05 ↑</td></tr><tr><td rowspan=\"3\">VoRTX [23]</td><td>4 cm</td><td>5.92</td><td>69.5</td><td>9.32</td><td>79.0</td></tr><tr><td>1 cm</td><td>5.91</td><td>69.6</td><td>9.27</td><td>79.0</td></tr><tr><td>.5 cm</td><td>5.91</td><td>69.5</td><td>9.29</td><td>79.0</td></tr><tr><td rowspan=\"3\">SimpleRecon [21]</td><td>4 cm</td><td>5.51</td><td>68.6</td><td>8.40</td><td>80.4</td></tr><tr><td>1 cm</td><td>5.80</td><td>67.6</td><td>8.23</td><td>81.0</td></tr><tr><td>.5 cm</td><td>5.94</td><td>66.9</td><td>8.67</td><td>80.7</td></tr><tr><td rowspan=\"3\">Ours</td><td>4 cm</td><td>5.15</td><td>75.6</td><td>7.11</td><td>86.2</td></tr><tr><td>1 cm</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>.5 cm</td><td>5.19</td><td>75.4</td><td>6.70</td><td>84.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.259,
+                0.471,
+                0.331
+            ],
+            "angle": 0,
+            "content": "Table 3. Reconstruction metrics as a function of output resolution. The 2D and 3D metrics show very little sensitivity to the output resolution, despite clear visual differences (see Figure 5). This suggests that future work may require additional metrics to distinguish among high-quality reconstructions."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.09,
+                0.342,
+                0.458,
+                0.442
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">DG</td><td rowspan=\"2\">PB</td><td rowspan=\"2\">RTS</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(i)</td><td>□</td><td>□</td><td>□</td><td>6.40</td><td>71.0</td><td>9.38</td><td>81.7</td></tr><tr><td>(ii)</td><td>□</td><td>□</td><td>√</td><td>5.58</td><td>73.8</td><td>7.63</td><td>84.5</td></tr><tr><td>(iii)</td><td>□</td><td>√</td><td>√</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(iv)</td><td>√</td><td>□</td><td>√</td><td>5.25</td><td>75.1</td><td>7.20</td><td>86.1</td></tr><tr><td>(v)</td><td>√</td><td>√</td><td>√</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.453,
+                0.471,
+                0.537
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation study. We examine the quantitative improvement from the novel components of our method – depth guidance (DG), point pack-projection (PB) and resolution-agnostic TSDF supervision (RTS). Relative to baseline (i), the largest gains come from RTS (ii). PB is helpful with DG enabled (v) but hurts metrics in the absence of DG (iii)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.55,
+                0.466,
+                0.655
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(a)</td><td>Ours - TSDF (main)</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>(b)</td><td>Ours - Density volume [2]</td><td>5.29</td><td>74.3</td><td>7.31</td><td>85.7</td></tr><tr><td>(c)</td><td>Ours - Gaussian weight</td><td>5.47</td><td>73.2</td><td>7.48</td><td>85.1</td></tr><tr><td>(d)</td><td>Ours - TSDF &amp; gaussian weight</td><td>5.52</td><td>73.8</td><td>7.24</td><td>85.8</td></tr><tr><td>(e)</td><td>Ours - No depth guidance</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(f)</td><td>Ours - TSDF (no image features)</td><td>5.66</td><td>71.9</td><td>7.74</td><td>83.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.664,
+                0.47,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Table 5. Ablation of depth guidance strategies. We compare our depth guidance strategy (a) to other forms of depth guidance: (b) a density fusion volume similar to VolumeFusion [2]; (c) weighting the features using a Gaussian window centered on the predicted depth along each camera ray; (d) combination of (b) and (c); (e) no depth guidance; and (f) TSDF depth guidance with no image features. We find that our TSDF guidance (a) achieves the best performance on all metrics."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.802,
+                0.225,
+                0.817
+            ],
+            "angle": 0,
+            "content": "4.4. Inference time"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "FineRecon reconstructs the ScanNet test scenes at 4cm resolution in an average of 18s per scene using an Nvidia V100 GPU. This is composed of a per-frame time of 87ms for 2D feature extraction, depth estimation, and backprojection, plus a one-time TSDF extraction time of 1.1s"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.273
+            ],
+            "angle": 0,
+            "content": "including running the 3D CNN and output layers. Because we use a fixed voxel size, we can increase the output sampling rate with no increase to the per-frame time or 3D CNN time. As we apply higher spatial sampling rates, the cost of high-resolution inference increases proportionally to the number of occupied voxels due to back-projection and MLP execution at each sample point. Our average full-scene reconstruction time is 18s at 4cm, 21s at 2cm, 43s at 1cm. At the limit we test 0.5cm resolution which takes 3.6 minutes per scene on average. For faster inference times, the point back-projection can be disabled, resulting in an average time of 17s per scene at 1cm or 20s per scene at 0.5cm."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.289,
+                0.619,
+                0.305
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.314,
+                0.892,
+                0.496
+            ],
+            "angle": 0,
+            "content": "We have presented an end-to-end network producing detailed 3D reconstructions from posed images. We have demonstrated that our novel supervision (RTS) is key in enabling the network to learn fine details. We have also introduced large improvements by using a depth-prediction network to guide the back-projection (DG). Lastly, we have developed a novel architecture (PB) to allow the free selection of output resolution at test time without requiring additional training or 3D convolution levels. PB opens interesting future avenues in which the TSDF is not predicted on a regular grid, such as adaptive sampling rates or alternative polygonization algorithms beyond marching cubes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.504,
+                0.892,
+                0.761
+            ],
+            "angle": 0,
+            "content": "Limitations. While FineRecon produces more accurate geometric details than prior work, limitations remain. Despite an improvement over the state-of-the-art, our approach still misses certain local fine structures. One reason is the limitation of the training data, in a large capture setting with pose noise and imperfect depth sensors. Another is that the forward-inference setting does not guarantee consistency with the input observations: to close this gap, future work may explore the hybridization of the techniques presented here with iterative optimization and differentiable rendering. Finally, despite our favorable inference times, running a 3D CNN over a dense feature volume is costly in terms of power and memory, which may be prohibitive for certain applications (sparse convolution may help, but it adds to implementation complexity and is not implemented on all platforms); increased efficiency is thus an important future goal."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.776,
+                0.597,
+                0.792
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
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+            ],
+            "angle": 0,
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+# FineRecon: Depth-aware Feed-forward Network for Detailed 3D Reconstruction
+
+Noah Stier $^{1,2}$  Anurag Ranjan $^{1}$  Alex Colburn $^{1}$  Yajie Yan $^{1}$  Liang Yang $^{1}$  Fangchang Ma $^{1}$  Baptiste Angles $^{1}$
+
+$^{1}$ Apple  $^{2}$ University of California, Santa Barbara
+
+# Abstract
+
+Recent works on 3D reconstruction from posed images [17, 23, 24] have demonstrated that direct inference of scene-level 3D geometry without test-time optimization is feasible using deep neural networks, showing remarkable promise and high efficiency. However, the reconstructed geometry, typically represented as a 3D truncated signed distance function (TSDF), is often coarse without fine geometric details. To address this problem, we propose three effective solutions for improving the fidelity of inference-based 3D reconstructions. We first present a resolution-agnostic TSDF supervision strategy to provide the network with a more accurate learning signal during training, avoiding the pitfalls of TSDF interpolation seen in previous work. We then introduce a depth guidance strategy using multiview depth estimates to enhance the scene representation and recover more accurate surfaces. Finally, we develop a novel architecture for the final layers of the network, conditioning the output TSDF prediction on high-resolution image features in addition to coarse voxel features, enabling sharper reconstruction of fine details. Our method, FineRecon<sup>1</sup>, produces smooth and highly accurate reconstructions, showing significant improvements across multiple depth and 3D reconstruction metrics.
+
+# 1. Introduction
+
+Reconstruction of 3D scenes from posed images is a long-standing problem in computer vision, with many applications such as autonomous driving, robotic navigation, and digital 3D asset creation. The traditional approach is to estimate depth maps over the input images using multiview stereo (MVS), and then fuse them together to form a unified 3D model [9, 10, 22]. However, the fusion process commonly results in missing geometry or artifacts in areas where the depth maps do not agree, due to effects such as occlusion, specularity, and transparent or low-texture sur
+
+![](images/897dd5dd37a04b682c00c8e84d2c43208b9773a57bfc50d6f0bc97d6a755937f.jpg)
+
+![](images/384cd23d7fdd78dc62dff7c72c1916a7c675073b5dd2d02154e3e1c6412f18e5.jpg)
+
+![](images/27e84ba0fa81ed9dce8e447ba5483e86bf8090262973d2362768d0025ef07500.jpg)
+
+![](images/e4380467fbbd02ad1d3ea3a3e7b2cd749154b03fbaba197d2e1601e771ee96c7.jpg)
+
+![](images/7a256b8e12f761b0b5b4f44b9a5891916d3f7cb8b5a764df3229ed40d3ae4329.jpg)  
+Figure 1. Our method, FineRecon, recovers highly detailed and coherent geometry relative to state-of-the-art methods. Our contributions of lossless ground truth sampling, depth-aware feature volume, and point backprojection result in smooth surfaces that preserve high-frequency structures without creating strong artifacts.
+
+![](images/b449b2eaa5e3beea9a812f1b0f2a0b13d737df4ed2a631f78934d5a55d72d015.jpg)
+
+faces. Recently, an alternative method has been proposed to address this issue in Atlas [17], which back-projects learned image features onto a voxel grid and directly predicts the scene's truncated signed distance function (TSDF) using a 3D convolutional neural network (CNN). The main advantage is that the CNN can learn to produce smooth, consistent surfaces, and to fill in holes that would otherwise result from low-texture regions and occlusion. Several methods have proposed improvements to this framework [1, 2, 23, 24], consistently pushing the state of the art in reconstruction accuracy. However, despite these efforts, the reconstructions produced by these methods remain coarse. We identify three key factors restricting the accuracy and level of detail in prior works, and we introduce solutions to address them, demonstrating their effectiveness within a new system: FineRecon.
+
+First, existing works use tri-linear interpolation to resample the ground-truth TSDF to align with the model's voxel grid during training [17, 23, 24]. This allows su
+
+pervision of the model's TSDF predictions at each voxel center, even when the voxel centers do not coincide with the pre-computed ground-truth TSDF points. However, resampling via tri-linear interpolation corrupts detail in the training data, because distance fields are not linear when non-planar geometry such a corner is present, as shown in Fig. 3. We avoid this issue by making supervised predictions only at the exact points where the ground-truth TSDF is known. This supervision change comes at no extra cost, and it results in greatly improved visual detail as well as a relative reduction in average chamfer distance between reconstruction and ground truth of over  $10\%$ .
+
+Second, prior work [1, 2, 17, 23, 24] uses dense back-projection, sampling a feature from each input image in each voxel. This causes blurring in the back-projection volume, which increases the difficulty of extracting accurate surface locations. To address this, our method uses an initial multi-view stereo depth estimation step, after which the depth estimates are used to enhance the feature volume and guide the 3D CNN toward areas of high surface likelihood. We show that this step significantly increases the quality of the reconstructions produced by our system.
+
+Third, because of the high computational cost of 3D CNNs, it is expensive to increase the voxel resolution. Existing works use voxel sizes of  $4\mathrm{cm}$  or larger [1, 2, 17, 23, 24], which is not enough to resolve the level of geometric detail visible in natural images at ranges of a few meters. To remedy this, we propose a new method to query the TSDF prediction at any point in  $\mathbb{R}^3$ , conditioned on the CNN grid features and image features projected directly to the query point. This reduces aliasing and allows our model to resolve sub-voxel detail. Furthermore, this enables reconstruction at arbitrary resolution without re-training.
+
+FineRecon achieves state-of-the-art performance on the challenging ScanNet dataset, as measured by 3D mesh metrics and rendered 2D depth metrics. We further show that it produces substantially improved visual detail with reduced artifacts relative to prior work.
+
+Contributions. The main contributions of this paper are:
+
+- We increase the accuracy of the training data using resolution-agnostic TSDF supervision, allowing FineRecon to reconstruct details with higher fidelity.  
+- We improve reconstruction accuracy using a novel MVS depth-guidance strategy, augmenting the backprojection volume with an estimated TSDF fusion channel.  
+- We enable the reconstruction of sub-voxel detail with a novel TSDF prediction architecture that can be queried at any 3D point, using point back-projected fine-grained image features.
+
+# 2. Related Work
+
+Multi-view stereo. 3D reconstruction is traditionally posed as per-pixel depth estimation [9, 10, 22]. While recent works have shown strong results [12, 21], a known drawback is that the estimation of each depth map is independent, so continuity across frustum boundaries is not enforced, and this often leads to artifacts. Solutions have been proposed [7, 11, 18], but it is still an open problem.
+
+Feed-forward 3D reconstruction. An effective recent strategy is to perform volumetric reconstruction directly in scene space using feed-forward neural networks [1, 2, 17, 23, 24]. In this line of research, image features are encoded by a 2D CNN and densely back-projected into a global feature volume, then a 3D CNN predicts the scene TSDF. These models can generalize to new scenes at inference time without computationally-demanding test-time optimization, and they can produce smooth and complete reconstructions. However, they tend to blur out surface details and omit thin structures. In contrast, ours is the first of these volumetric TSDF methods to reconstruct accurate sub-voxel detail. 3D-Former [30], a concurrent work, replaces the 3D CNN with a transformer, an orthogonal direction that could potentially be combined with our method.
+
+Geometric priors in neural radiance fields. Recent novel-view synthesis methods based on neural radiance fields [16] have shown remarkable 2D rendering quality, typically relying on time-consuming per-scene optimization to obtain good results. These methods have also been extended to predict surface geometry [26, 28], and it has been shown that geometric priors, such as depth and normal maps, can boost performance. For instance, multiple works [13, 19, 27] use depth estimates to improve ray sampling efficiency. MonoSDF [29] uses monocular depth and normal estimation as pseudo-ground truth to supervise its predicted SDF. Similarly, our method uses guidance from a depth-prediction network, but with a focus on interactive reconstruction speed and generalization to new scenes.
+
+Geometric priors in feed-forward networks. Only a few previous methods based on feed-forward networks have incorporated geometric priors. MonoNeuralFusion [31] uses monocular normal estimates but does not explore depth priors. Similar to our approach, VolumeFusion [2] uses depth as an additional feature by fusing it into a density volume and concatenating it with the image feature volume. However, density does not encode the difference between occluded space and observed free space, and it omits crucial information about inward vs. outward surface orientation. In contrast, we explore multiple forms of depth guidance, finding that guidance by TSDF fusion outperforms the density-based variant and others (Table 5). CVRecon [8], a concurrent work, uses frustum-aligned cost volumes in addition to global features, which is related to our work but does not explicitly predict depth.
+
+![](images/59caf10cbda106479a296791be0f095cdc23f83fdf7568519a4c83f19784c36f.jpg)  
+Figure 2. Model overview. Given a monocular RGB image sequence, we use a pre-trained depth network to estimate depth images  $\hat{\mathcal{D}}$ . In the meantime we also extract image features  $\mathcal{F}^c$  for global volume fusion and  $\mathcal{F}^f$  for point back-projection. The depth  $\hat{\mathcal{D}}$  is then fused into an initial, approximate TSDF volume  $\nu^d$ , and  $\mathcal{F}^c$  is back-projected into a feature volume  $\nu^c$  using the camera parameters. The two volumes are then concatenated and fed to a 3D CNN  $\Psi$  to produce the global feature volume  $\nu^{\Psi}$  and the coarse occupancy grid  $\hat{\mathcal{O}}$  (used to accelerate inference). Finally, at any query point  $x \in \mathbb{R}^3$ , we sample high-resolution image features  $\mathcal{F}^f$  and concatenate with the interpolated voxel feature  $\nu^{\Psi}(x)$ . This is passed to an MLP to predict the final TSDF value.
+
+![](images/5a313e9d5441150dbed3ddf19ad4b694a7ffc1f3085615689a4d1a574df1e4d7.jpg)  
+Figure 3. Illustration of our improved, resolution-agnostic TSDF supervision. With rotational augmentation during training, the model's voxel grid (gray) does not align with the points (blue) where the ground-truth TSDF is known. Previous work uses linear interpolation (a) to estimate the TSDF at the voxel centers for supervision, but this leads to errors: the ground-truth geometry (yellow) is intersected by the interpolated TSDF values (red circles). In contrast, our model can be supervised at any 3D point. Therefore, regardless of the feature grid orientation, we can supervise the model at the exact points where the ground-truth is known (b). This reduces noise during training and increases reconstruction accuracy (see Table 6).
+
+# 3. Method
+
+Given a set of input images  $\{I_i\}$  along with their camera poses  $\{P_i\}$  and intrinsics  $\{K_i\}$ , we seek to compute an estimate  $\hat{S}$  of the true scene TSDF  $S$ . We train a deep-learning model  $\Phi$  to perform this mapping,  $\hat{S} = \Phi (\{I_i\}, \{P_i\}, \{K_i\})$ .
+
+# 3.1. Model overview
+
+Our model (illustrated in Fig. 2) extracts a set of 2D features  $\{\mathcal{F}_i^c\}$  from each input image using a convolutional neural network (CNN),  $\Omega^c$ . We then use the camera pa
+
+rameters to back-project  $\{\mathcal{F}_i^c\}$  onto a 3D voxel grid. The back-projection process is augmented using depth estimates  $\{\hat{D}_i\}$  to produce the depth-guided feature volume  $\nu^g$ , as described in Section 3.2.2. We process  $\nu^g$  using a 3D CNN  $\Psi$  to produce a new feature volume  $\nu^{\Psi}$ , which we can query for  $\hat{S}(q)$  at any 3D point  $q \in \mathbb{R}^3$  using the interpolation strategy defined in Section 3.2.3. To extract a surface mesh, we query the reconstruction on a grid of arbitrary resolution to produce a TSDF volume, from which a mesh can be extracted with Marching cubes [15].
+
+# 3.2. Key improvements
+
+# 3.2.1 Resolution-agnostic TSDF supervision
+
+During training, as in previous works [17, 23, 24] we randomly orient the coordinate system of the feature volume relative to  $S$  using  $\pm 3^{\circ}$  rotations about the horizontal axis and  $\pm 180^{\circ}$  rotations about the gravitational axis. Thus, the voxel centers may not coincide with the points  $\{x\}$  where  $S$  is known. This is typically addressed using linear interpolation on  $S$  to estimate the ground-truth TSDF at the voxel centers. However, this process is not accurate, since with non-planar geometry the TSDF is a non-linear function of space. Interpolation therefore corrupts the ground-truth TSDF, as shown in Fig. 3. In theory this effect can be minimized by sampling the ground truth on a very high-resolution grid, but this greatly increases training cost. To preserve the accuracy of the ground truth with no added cost, we instead supervise only at the points  $\{x\}$  where the ground truth is known, so that no interpolation is required. This decouples the accuracy of our ground truth from its sampling rate, rendering it resolution-agnostic. To support this, our model must be able to estimate the TSDF at any point in  $\mathbb{R}^3$ , which we achieve using the strategy outlined in Section 3.2.3. This simple supervision change enables our
+
+model to reconstruct significantly more visual detail (see Fig. 6).
+
+# 3.2.2 Depth guidance
+
+In order to localize image features in 3D space, we sample a pixel feature at each voxel from each available input image:
+
+$$
+\tilde {\mathcal {V}} _ {i} ^ {c} (q) = \alpha \left(\mathcal {F} _ {i} ^ {c}, K _ {i} P _ {i} q _ {h}\right), \tag {1}
+$$
+
+where  $\alpha(F, u)$  represents sampling a feature from 2D map  $F$  at pixel location  $u$ , and  $q_h$  is the voxel center in homogeneous coordinates. We then reduce using a per-channel mean across views to form one feature vector per-voxel:
+
+$$
+\mathcal {V} ^ {c} (q) = \frac {1}{| \{I _ {i} \} |} \sum_ {i} \tilde {\mathcal {V}} _ {i} ^ {c} (q) \tag {2}
+$$
+
+As an additional signal in recovering the scene surfaces, we propose to inject a multi-view depth prior using depth estimates from an MVS system  $M$ . As MVS is a well-studied problem, we treat  $M$  as an off-the-shelf component, and in the Supplementary we study the sensitivity of our system to depth noise and choice of  $M$ . We fuse  $\hat{\mathcal{D}}$  into scene space using the standard TSDF fusion [4] to form  $\mathcal{V}^d$ . We then concatenate  $\mathcal{V}^d$  as an extra channel in the back-projection volume. Our depth-guided back-projection volume is thus defined as
+
+$$
+\mathcal {V} ^ {g} = \left[ \mathcal {V} ^ {c}, \mathcal {V} ^ {d} \right]. \tag {3}
+$$
+
+In our experiments (see Table 5), the depth-guided feature volume  $\mathcal{V}^g$  shows significantly improved results with respect to image features alone  $(\mathcal{V}^c)$ , or depth inputs alone  $(\mathcal{V}^d)$ . With naive application of the depth guidance, we find that this additional signal increases our network's propensity to over-fit to the training data, relying too heavily on the depth guidance which is often inaccurate. To address this, we scale each predicted depth map by a factor sampled uniformly in the range [0.9, 1.1] as a data augmentation during training. This reduces over-fitting and encourages the network to learn to use the image features in regions where the depth maps are unreliable.
+
+We additionally experiment with several strategies for using the depth estimate to directly modulate the image feature back-projection. However, as shown in our experiments, our TSDF fusion approach outperforms these methods by a large margin (see Table 5).
+
+# 3.2.3 Point back-projection TSDF inference
+
+We use tri-linear interpolation to sample the 3D CNN's output feature volume  $\mathcal{V}^{\Psi}$  at any query point  $q$ . This results in a continuous-valued feature  $\tilde{\mathcal{V}}^{\Psi} = \Lambda (\mathcal{V}^{\Psi}, q)$  where  $\Lambda$  represents tri-linear interpolation. Directly estimating  $\hat{S}$  from this feature is severely limited in its ability to reconstruct sub-voxel detail, since the effective resolution of  $\tilde{\mathcal{V}}^{\Psi}$  is still constrained to the size of the voxels.
+
+We improve on this paradigm using an additional point back-projection step to directly sample image features  $\mathcal{W}(q)$  at the point  $q$ . This step is identical to the depth-guided back-projection outlined in Section 3.2.2, except that the point  $q$  is no longer constrained to be a voxel center. The effective resolution of this new continuous-valued feature is thus determined by the resolution of the 2D image feature grid rather than the 3D voxel size. Assuming high-enough 2D feature resolution,  $\mathcal{W}(q)$  thus carries much finer-grained information than the linearly-interpolated voxel feature  $\tilde{\mathcal{V}}^{\Psi}(q)$ , complementing the 3D CNN's ability to produce smooth and context-informed features. We concatenate  $\mathcal{W}$  with  $\tilde{\mathcal{V}}^{\Psi}$  as the input to a multilayer perceptron (MLP)  $\theta_{S}$ :
+
+$$
+\hat {S} = \theta_ {S} ([ \mathcal {W}, \tilde {\mathcal {V}} ^ {\Psi} ]). \tag {4}
+$$
+
+At a given 3D sampling rate, our point back-projection inference strategy adds a small but non-negligible cost relative to using only  $\tilde{\mathcal{V}}^{\Psi}$ : we must run an additional round of feature extraction and back-projection using  $\Omega^{f}$ , and the input dimension of  $\theta_{S}$  must be doubled in order to receive the extra input features. We show in our experiments that this cost is tractable (see Section 4.4).
+
+We observe that the fine-grained features  $\mathcal{W}$  can contain spurious high-frequency content, particularly near the borders of the 2D features where the CNN output is unreliable due to edge effects. To reduce artifacts, we downweight  $\{F_i^f\}$  near the borders prior to back-projection using a weight  $w = \sigma (l\cdot (min(\frac{d}{m},1)\cdot 2 - 1))$  ,where  $d$  is the distance to the nearest border in pixels;  $m = 20$  is a margin distance;  $l = 6$  controls the falloff rate; and  $\sigma (x) = \frac{1}{1 + e^{-x}}$
+
+# 3.2.4 Output resolution & occupancy filtering
+
+Our model can be sampled at any point in  $\mathbb{R}^3$ , and we choose to sample it on a regular grid at test time in order to support meshing with marching cubes [15]. The resolution of this grid can be determined arbitrarily without retraining, and we experiment with several output grid resolutions (see Fig. 5). Naively, the cost of our point back-projection inference strategy grows cubically with the sampling rate. At high resolutions, it thus becomes expensive due to the cost of running the additional back-projection and  $\theta_S$  densely over the full volume. To mitigate this, we predict the per-voxel occupancy  $\hat{O}$  with an additional MLP:  $\hat{O} = \theta_O(\mathcal{V})$ . Then at test time we sample  $\hat{S}$  only within voxels that are predicted to be occupied. While the asymptotic complexity is still cubic, in practice this greatly reduces the cost due to the prevalence of empty space.
+
+# 3.3. Training
+
+At training time, we require a ground-truth TSDF  $S$  to supervise  $\hat{S}$ . For training on real scans, we use TSDF fusion [4] to generate  $S$  on a discrete grid of points  $X$  with
+
+![](images/3bc971014a15f970179f41ffba0683d888603cb30d77952b4842e4b14cb84a96.jpg)  
+Figure 4. Qualitative results. Comparison of our method with NeuralRecon [24], VoRTX [23], and SimpleRecon [21]. NeuralRecon and VoRTX capture consistent global structure but lose many details, whereas SimpleRecon recovers details but fails to keep geometry consistent across views, leading to duplicate surfaces after TSDF fusion. Our method produces the most complete, consistent reconstruction while preserving details.
+
+resolution  $\delta$ ,  $X = \{x \in [i \cdot \delta, j \cdot \delta, k \cdot \delta]\}$ , assuming the existence of a set of ground-truth depth maps  $\{D_i\}$  corresponding to  $\{I_i\}$ . While ground truth depth can be noisy when acquired by sensors such as structured-light infrared scanners, we minimize artifacts by 1) using a large number of views to generate the ground-truth, 2) using an appropriate TSDF truncation distance following previous work [17, 23, 24], and 3) discarding depths beyond the range where the accuracy starts to visibly degrade.
+
+Loss function. We define the TSDF loss  $\mathcal{L}_{\mathcal{S}}$  following SG-NN [6] as
+
+$$
+\mathcal {L} _ {S} = \frac {1}{| X |} \sum_ {x \in X} | t (\hat {S} (x)) - t (S (x) |, \tag {5}
+$$
+
+where  $t(x) = \mathrm{sign}(x)\cdot \ln (|x| + 1)$ . We define occupancy loss  $\mathcal{L}_O$  using the standard binary cross-entropy, abbreviated  $BCE$ :
+
+$$
+\mathcal {L} _ {O} = \frac {1}{| X |} \sum_ {x \in X} B C E (O (x), \hat {O} (x)) \tag {6}
+$$
+
+Following VoRTX [23] we compute the ground-truth occupancy as
+
+$$
+O (x) = \oplus (\tilde {O} (x)); \quad \tilde {O} (x) = \left\{ \begin{array}{l l} 1, & \text {i f} | S (x) | <   1 \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {7}
+$$
+
+where  $\oplus$  represents morphological dilation with a  $3\times 3\times 3$  structuring element. Note, this definition of occupancy describes space near a surface [6, 23, 24], rather than space interior to an object. Our training loss  $\mathcal{L}$  is then defined as
+
+$$
+\mathcal {L} = \mathcal {L} _ {S} + \mathcal {L} _ {O}. \tag {8}
+$$
+
+CNN backbone architectures. Our 2D CNN architecture is a feature pyramid network [14] using EfficientNetV2-S [25] as a backbone. This structure is shared for both  $\Omega^c$  and  $\Omega^f$ , but the weights are duplicated and then trained independently. Despite their identical architectures, these networks learn strikingly different features (see Supp.). Our 3D CNN  $\Psi$  is inspired by U-Net [3, 20], see Supp. for details.
+
+Implementation details. As the depth predictor  $M$  we use our re-implementation of the MVS network SimpleRecon [21]. We use a voxel size of 4cm in our model, and we train on volumetric scene chunks of size  $(3.84\mathrm{m} \times 3.84\mathrm{m} \times 2.24\mathrm{m})$ . During training we select views by uniform random sampling over all views that at least partially observe the training chunk. At test time we fuse only keyframes, using the view selection strategy from DeepVideoMVS [7]. Training takes 36 hours on eight Nvidia V100 GPUs.
+
+# 4. Experiments
+
+# 4.1. Dataset, baselines, and metrics
+
+Dataset. We validate our method by training and evaluating our model on the popular ScanNet dataset [5], which is composed of 1,613 indoor scans. We report all our metrics on the official test set containing 100 scans.
+
+Baselines. We compare our model with several previous works. For end-to-end 3D reconstruction methods we select Atlas [17], NeuralRecon [24], VoRTX [23], and TransformerFusion [1]. We also compare to MVS depth-prediction, selecting SimpleRecon [21], which we re-implement. In order to compare to SimpleRecon, we apply TSDF fusion [4] on the predicted depth maps to produce a 3D mesh.
+
+Metrics. We compute 3D metrics directly on the mesh reconstructions, and we compute depth metrics by rendering the meshes to generate predicted depth maps. Relative to prior works on depth estimation such as SimpleRecon [21], this is a slight change from the typical protocol of computing depth metrics directly on the raw depth maps. We believe our strategy is more indicative of performance in real-world applications that rely on the unified 3D reconstruction. Our definition for all metrics is the same as in Atlas [17] (see Supp. for details).
+
+For computing 3D metrics we use the evaluation code from TransformerFusion [1], which includes a trimming protocol to avoid penalizing reconstructions for in-painting surfaces in unobserved regions. As noted in previous work [1, 23], precision or recall can easily be optimized individually at the expense of the other, as with accuracy and completeness. We thus emphasize Chamfer distance and F1 (i.e. F-score) as the most important 3D metrics, capturing this trade-off.
+
+# 4.2. Results
+
+Qualitative Results. In Fig. 4, we show qualitative results of our method compared to baselines and ground truth. We observe that our method preserves more details while minimizing high-frequency artifacts. The surfaces
+
+<table><tr><td>Method</td><td>Acc ↓</td><td>Comp ↓</td><td>Cham ↓</td><td>Prec ↑</td><td>Rec ↑</td><td>F1 ↑</td></tr><tr><td>Atlas [17]</td><td>7.09</td><td>7.52</td><td>7.30</td><td>68.4</td><td>61.1</td><td>64.3</td></tr><tr><td>NeuralRecon [24]</td><td>5.04</td><td>10.68</td><td>7.86</td><td>62.7</td><td>59.1</td><td>60.7</td></tr><tr><td>3DVNet [18]</td><td>6.73</td><td>7.72</td><td>7.22</td><td>65.5</td><td>59.6</td><td>62.1</td></tr><tr><td>Transf. Fusion [1]</td><td>5.52</td><td>8.27</td><td>6.89</td><td>72.8</td><td>60.0</td><td>65.5</td></tr><tr><td>VoRTX [23]</td><td>4.32</td><td>7.52</td><td>5.92</td><td>76.3</td><td>64.0</td><td>69.5</td></tr><tr><td>SimpleRecon [21]</td><td>6.43</td><td>5.18</td><td>5.80</td><td>66.0</td><td>69.7</td><td>67.6</td></tr><tr><td>Ours</td><td>5.25</td><td>5.11</td><td>5.18</td><td>78.0</td><td>73.4</td><td>75.5</td></tr></table>
+
+Table 1. 3D reconstruction metrics for ScanNet. We compare with recent work on mesh metrics defined in Atlas [17]. Best and Second -best are highlighted.  
+
+<table><tr><td>Method</td><td>L1 ↓</td><td>AbsRel ↓</td><td>SqRel ↓</td><td>δ1.05 ↑</td><td>δ1.25 ↑</td><td>Comp. ↑</td></tr><tr><td>Atlas [17]</td><td>11.96</td><td>6.26</td><td>4.22</td><td>75.2</td><td>93.8</td><td>98.8</td></tr><tr><td>NeuralRecon [24]</td><td>9.84</td><td>6.54</td><td>3.79</td><td>75.0</td><td>94.6</td><td>90.8</td></tr><tr><td>VoRTX [23]</td><td>9.32</td><td>5.92</td><td>3.65</td><td>79.0</td><td>94.9</td><td>96.1</td></tr><tr><td>SimpleRecon [21]</td><td>8.23</td><td>4.83</td><td>2.66</td><td>81.0</td><td>96.8</td><td>97.4</td></tr><tr><td>Ours</td><td>6.91</td><td>4.24</td><td>2.57</td><td>86.6</td><td>97.1</td><td>97.2</td></tr></table>
+
+Table 2. 2D metrics for ScanNet. The 2D depth is rendered and metrics are computed in the same way as with Atlas [17]. We highlight the Best and Second best with colors respectively.
+
+in our reconstructions are smooth and consistent, gracefully unifying information from all views without the depth-disagreement artifacts or noticeable discontinuities visible in SimpleRecon. VoRTX suffers from blurry reconstructions where fine details such as chair legs are completely lost, whereas our approach reconstructs these elements faithfully.
+
+In Fig. 5 we show qualitative results at three output resolutions:  $4\mathrm{cm}$ ,  $1\mathrm{cm}$  and  $0.5\mathrm{cm}$ . VoRTX is not tractable at high resolutions, so we upsample VoRTX's  $4\mathrm{cm}$  TSDF with linear interpolation, which does not increase the effective level of detail. For SimpleRecon, we can generate reconstructions at any desired resolution by decreasing the voxel size during TSDF fusion, and we note that artifacts and noise increase greatly at high resolution. In contrast, our results consistently preserve a high level of detail while avoiding noisy surfaces.
+
+Quantitative Results. Table 1 shows our 3D reconstruction metrics on the ScanNet dataset. We report metrics for our method and SimpleRecon at the relatively high resolution of  $1\mathrm{cm}$  because it is tractable to do so. We report metrics for the other baselines at their native resolution of  $4\mathrm{cm}$ , because increasing this resolution would add significant compute cost and engineering effort. For fairness, metrics for our method at  $4\mathrm{cm}$  are shown in Table 3, and we note that the quantitative differences from  $1\mathrm{cm}$  are negligible. Our method achieves the best result in most metrics. In particular, it achieves the lowest Chamfer distance and highest F-score by large margins.
+
+![](images/a08bf72229c7ec96094e349515ed4958b710dedf8477eb2cd38d0597b1e12ef5.jpg)  
+Figure 5. Qualitative results at various output resolutions. With our method, we observe increased sub-voxel detail when increasing the output sampling rate from  $4\mathrm{cm}$  to  $1\mathrm{cm}$ , as well as the occasional appearance of small artifacts near view frustum boundaries. Beyond  $1\mathrm{cm}$  we observe no significant changes, suggesting we have reached our system's limit of detail given the 2D feature resolution. In contrast, upsampling the VoRTX outputs from  $4\mathrm{cm}$  slightly increases smoothness but adds no extra detail, and SimpleRecon shows the appearance of significant frustum boundary artifacts starting at  $1\mathrm{cm}$ .
+
+![](images/ac90c8831987e08e6ebe46cc3fdb9c07996b83ee49a593597124c4d016a69b7c.jpg)  
+Figure 6. Ablation of our contributions. Compared to the baseline result (same as Table 4, row (i)), our improved supervision signal provides an overall increase in detail and accuracy at negligible added cost. Inconsistent areas (e.g. right side of couch, towels) are further refined by adding depth guidance. Finally, point back-projection provides higher effective resolution for capturing high-frequency and sub-voxel structures.
+
+# 4.3. Ablation studies
+
+In Table 4 we compare ablations of the main novel components of our method. We note that resolution-agnostic TSDF supervision (RTS) and depth guidance (DG) both result in significant improvement across all metrics. Interestingly, point back-projection (PB) improves all metrics when DG is used ((v) vs. (iv)) but degrades them in the absence of DG ((iii) vs. (ii)). We interpret this as follows: the high-frequency content recovered by PB is locally accurate, but if the coarse alignment relative to ground truth is incorrect, then the added details actually reduce overall accuracy. DG helps to correctly localize the large structures, interacting constructively with PB to achieve the best performance.
+
+Depth guidance strategies In Table 5 we compare different ways to leverage the predicted depth maps to improve our reconstruction. In row (b) we use the density fusion
+
+strategy introduced by VolumeFusion [2], and we observe that it does not perform as well as our method using TSDF fusion. We hypothesize that this is because the density does not encode free space information or inward vs. outward surface orientation. In row (c) we test using the depth to directly modulate the image feature projection, using a Gaussian window to down-weight the image features far from the estimated depth. Our experiments show that this manual weighting is an improvement relative to using no depth guidance at all, but that our TSDF fusion guidance yields the best results overall. To explore the relative importance of the image features and the depth guidance, we ablate each one individually in rows (e) and (f), noting worse results in each case.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Resolution</td><td colspan="2">3D metrics</td><td colspan="2">2D metrics</td></tr><tr><td>Cham↓</td><td>F1 ↑</td><td>L1↓</td><td>δ1.05 ↑</td></tr><tr><td rowspan="3">VoRTX [23]</td><td>4 cm</td><td>5.92</td><td>69.5</td><td>9.32</td><td>79.0</td></tr><tr><td>1 cm</td><td>5.91</td><td>69.6</td><td>9.27</td><td>79.0</td></tr><tr><td>.5 cm</td><td>5.91</td><td>69.5</td><td>9.29</td><td>79.0</td></tr><tr><td rowspan="3">SimpleRecon [21]</td><td>4 cm</td><td>5.51</td><td>68.6</td><td>8.40</td><td>80.4</td></tr><tr><td>1 cm</td><td>5.80</td><td>67.6</td><td>8.23</td><td>81.0</td></tr><tr><td>.5 cm</td><td>5.94</td><td>66.9</td><td>8.67</td><td>80.7</td></tr><tr><td rowspan="3">Ours</td><td>4 cm</td><td>5.15</td><td>75.6</td><td>7.11</td><td>86.2</td></tr><tr><td>1 cm</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>.5 cm</td><td>5.19</td><td>75.4</td><td>6.70</td><td>84.4</td></tr></table>
+
+Table 3. Reconstruction metrics as a function of output resolution. The 2D and 3D metrics show very little sensitivity to the output resolution, despite clear visual differences (see Figure 5). This suggests that future work may require additional metrics to distinguish among high-quality reconstructions.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">DG</td><td rowspan="2">PB</td><td rowspan="2">RTS</td><td colspan="2">3D metrics</td><td colspan="2">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(i)</td><td>□</td><td>□</td><td>□</td><td>6.40</td><td>71.0</td><td>9.38</td><td>81.7</td></tr><tr><td>(ii)</td><td>□</td><td>□</td><td>√</td><td>5.58</td><td>73.8</td><td>7.63</td><td>84.5</td></tr><tr><td>(iii)</td><td>□</td><td>√</td><td>√</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(iv)</td><td>√</td><td>□</td><td>√</td><td>5.25</td><td>75.1</td><td>7.20</td><td>86.1</td></tr><tr><td>(v)</td><td>√</td><td>√</td><td>√</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr></table>
+
+Table 4. Ablation study. We examine the quantitative improvement from the novel components of our method – depth guidance (DG), point pack-projection (PB) and resolution-agnostic TSDF supervision (RTS). Relative to baseline (i), the largest gains come from RTS (ii). PB is helpful with DG enabled (v) but hurts metrics in the absence of DG (iii).  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Method</td><td colspan="2">3D metrics</td><td colspan="2">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(a)</td><td>Ours - TSDF (main)</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>(b)</td><td>Ours - Density volume [2]</td><td>5.29</td><td>74.3</td><td>7.31</td><td>85.7</td></tr><tr><td>(c)</td><td>Ours - Gaussian weight</td><td>5.47</td><td>73.2</td><td>7.48</td><td>85.1</td></tr><tr><td>(d)</td><td>Ours - TSDF &amp; gaussian weight</td><td>5.52</td><td>73.8</td><td>7.24</td><td>85.8</td></tr><tr><td>(e)</td><td>Ours - No depth guidance</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(f)</td><td>Ours - TSDF (no image features)</td><td>5.66</td><td>71.9</td><td>7.74</td><td>83.8</td></tr></table>
+
+Table 5. Ablation of depth guidance strategies. We compare our depth guidance strategy (a) to other forms of depth guidance: (b) a density fusion volume similar to VolumeFusion [2]; (c) weighting the features using a Gaussian window centered on the predicted depth along each camera ray; (d) combination of (b) and (c); (e) no depth guidance; and (f) TSDF depth guidance with no image features. We find that our TSDF guidance (a) achieves the best performance on all metrics.
+
+# 4.4. Inference time
+
+FineRecon reconstructs the ScanNet test scenes at 4cm resolution in an average of 18s per scene using an Nvidia V100 GPU. This is composed of a per-frame time of 87ms for 2D feature extraction, depth estimation, and backprojection, plus a one-time TSDF extraction time of 1.1s
+
+including running the 3D CNN and output layers. Because we use a fixed voxel size, we can increase the output sampling rate with no increase to the per-frame time or 3D CNN time. As we apply higher spatial sampling rates, the cost of high-resolution inference increases proportionally to the number of occupied voxels due to back-projection and MLP execution at each sample point. Our average full-scene reconstruction time is 18s at 4cm, 21s at 2cm, 43s at 1cm. At the limit we test 0.5cm resolution which takes 3.6 minutes per scene on average. For faster inference times, the point back-projection can be disabled, resulting in an average time of 17s per scene at 1cm or 20s per scene at 0.5cm.
+
+# 5. Conclusion
+
+We have presented an end-to-end network producing detailed 3D reconstructions from posed images. We have demonstrated that our novel supervision (RTS) is key in enabling the network to learn fine details. We have also introduced large improvements by using a depth-prediction network to guide the back-projection (DG). Lastly, we have developed a novel architecture (PB) to allow the free selection of output resolution at test time without requiring additional training or 3D convolution levels. PB opens interesting future avenues in which the TSDF is not predicted on a regular grid, such as adaptive sampling rates or alternative polygonization algorithms beyond marching cubes.
+
+Limitations. While FineRecon produces more accurate geometric details than prior work, limitations remain. Despite an improvement over the state-of-the-art, our approach still misses certain local fine structures. One reason is the limitation of the training data, in a large capture setting with pose noise and imperfect depth sensors. Another is that the forward-inference setting does not guarantee consistency with the input observations: to close this gap, future work may explore the hybridization of the techniques presented here with iterative optimization and differentiable rendering. Finally, despite our favorable inference times, running a 3D CNN over a dense feature volume is costly in terms of power and memory, which may be prohibitive for certain applications (sparse convolution may help, but it adds to implementation complexity and is not implemented on all platforms); increased efficiency is thus an important future goal.
+
+# References
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+radiance fields for indoor multi-view stereo. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5610-5619, 2021. 2  
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+                                    "content": "faces. Recently, an alternative method has been proposed to address this issue in Atlas [17], which back-projects learned image features onto a voxel grid and directly predicts the scene's truncated signed distance function (TSDF) using a 3D convolutional neural network (CNN). The main advantage is that the CNN can learn to produce smooth, consistent surfaces, and to fill in holes that would otherwise result from low-texture regions and occlusion. Several methods have proposed improvements to this framework [1, 2, 23, 24], consistently pushing the state of the art in reconstruction accuracy. However, despite these efforts, the reconstructions produced by these methods remain coarse. We identify three key factors restricting the accuracy and level of detail in prior works, and we introduce solutions to address them, demonstrating their effectiveness within a new system: FineRecon."
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "<sup>1</sup>https://github.com/apple/ml-finerecon"
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+                                    "content": "pervision of the model's TSDF predictions at each voxel center, even when the voxel centers do not coincide with the pre-computed ground-truth TSDF points. However, resampling via tri-linear interpolation corrupts detail in the training data, because distance fields are not linear when non-planar geometry such a corner is present, as shown in Fig. 3. We avoid this issue by making supervised predictions only at the exact points where the ground-truth TSDF is known. This supervision change comes at no extra cost, and it results in greatly improved visual detail as well as a relative reduction in average chamfer distance between reconstruction and ground truth of over "
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+                                    "content": "Second, prior work [1, 2, 17, 23, 24] uses dense back-projection, sampling a feature from each input image in each voxel. This causes blurring in the back-projection volume, which increases the difficulty of extracting accurate surface locations. To address this, our method uses an initial multi-view stereo depth estimation step, after which the depth estimates are used to enhance the feature volume and guide the 3D CNN toward areas of high surface likelihood. We show that this step significantly increases the quality of the reconstructions produced by our system."
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+                                    "content": " or larger [1, 2, 17, 23, 24], which is not enough to resolve the level of geometric detail visible in natural images at ranges of a few meters. To remedy this, we propose a new method to query the TSDF prediction at any point in "
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+                                    "content": ", conditioned on the CNN grid features and image features projected directly to the query point. This reduces aliasing and allows our model to resolve sub-voxel detail. Furthermore, this enables reconstruction at arbitrary resolution without re-training."
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+                                    "content": "Contributions. The main contributions of this paper are:"
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+                                            "content": "- We increase the accuracy of the training data using resolution-agnostic TSDF supervision, allowing FineRecon to reconstruct details with higher fidelity."
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+                                            "content": "- We improve reconstruction accuracy using a novel MVS depth-guidance strategy, augmenting the backprojection volume with an estimated TSDF fusion channel."
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+                                            "content": "- We enable the reconstruction of sub-voxel detail with a novel TSDF prediction architecture that can be queried at any 3D point, using point back-projected fine-grained image features."
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+                                    "content": "2. Related Work"
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+                                    "content": "Feed-forward 3D reconstruction. An effective recent strategy is to perform volumetric reconstruction directly in scene space using feed-forward neural networks [1, 2, 17, 23, 24]. In this line of research, image features are encoded by a 2D CNN and densely back-projected into a global feature volume, then a 3D CNN predicts the scene TSDF. These models can generalize to new scenes at inference time without computationally-demanding test-time optimization, and they can produce smooth and complete reconstructions. However, they tend to blur out surface details and omit thin structures. In contrast, ours is the first of these volumetric TSDF methods to reconstruct accurate sub-voxel detail. 3D-Former [30], a concurrent work, replaces the 3D CNN with a transformer, an orthogonal direction that could potentially be combined with our method."
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+                                    "type": "text",
+                                    "content": "Geometric priors in neural radiance fields. Recent novel-view synthesis methods based on neural radiance fields [16] have shown remarkable 2D rendering quality, typically relying on time-consuming per-scene optimization to obtain good results. These methods have also been extended to predict surface geometry [26, 28], and it has been shown that geometric priors, such as depth and normal maps, can boost performance. For instance, multiple works [13, 19, 27] use depth estimates to improve ray sampling efficiency. MonoSDF [29] uses monocular depth and normal estimation as pseudo-ground truth to supervise its predicted SDF. Similarly, our method uses guidance from a depth-prediction network, but with a focus on interactive reconstruction speed and generalization to new scenes."
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+                                    "content": "Geometric priors in feed-forward networks. Only a few previous methods based on feed-forward networks have incorporated geometric priors. MonoNeuralFusion [31] uses monocular normal estimates but does not explore depth priors. Similar to our approach, VolumeFusion [2] uses depth as an additional feature by fusing it into a density volume and concatenating it with the image feature volume. However, density does not encode the difference between occluded space and observed free space, and it omits crucial information about inward vs. outward surface orientation. In contrast, we explore multiple forms of depth guidance, finding that guidance by TSDF fusion outperforms the density-based variant and others (Table 5). CVRecon [8], a concurrent work, uses frustum-aligned cost volumes in addition to global features, which is related to our work but does not explicitly predict depth."
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+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": " is back-projected into a feature volume "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\nu^c"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": " using the camera parameters. The two volumes are then concatenated and fed to a 3D CNN "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\Psi"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": " to produce the global feature volume "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\nu^{\\Psi}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": " and the coarse occupancy grid "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\hat{\\mathcal{O}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": " (used to accelerate inference). Finally, at any query point "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "x \\in \\mathbb{R}^3"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": ", we sample high-resolution image features "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{F}^f"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": " and concatenate with the interpolated voxel feature "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\nu^{\\Psi}(x)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                202,
+                                                547,
+                                                269
+                                            ],
+                                            "type": "text",
+                                            "content": ". This is passed to an MLP to predict the final TSDF value."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "type": "image",
+                    "bbox": [
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+                    ],
+                    "blocks": [
+                        {
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+                            ],
+                            "lines": [
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+                                    "spans": [
+                                        {
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+                                            "type": "image",
+                                            "image_path": "5a313e9d5441150dbed3ddf19ad4b694a7ffc1f3085615689a4d1a574df1e4d7.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        {
+                                            "bbox": [
+                                                46,
+                                                430,
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 3. Illustration of our improved, resolution-agnostic TSDF supervision. With rotational augmentation during training, the model's voxel grid (gray) does not align with the points (blue) where the ground-truth TSDF is known. Previous work uses linear interpolation (a) to estimate the TSDF at the voxel centers for supervision, but this leads to errors: the ground-truth geometry (yellow) is intersected by the interpolated TSDF values (red circles). In contrast, our model can be supervised at any 3D point. Therefore, regardless of the feature grid orientation, we can supervise the model at the exact points where the ground-truth is known (b). This reduces noise during training and increases reconstruction accuracy (see Table 6)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        46,
+                        591,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": "Given a set of input images "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{I_i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": " along with their camera poses "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{P_i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": " and intrinsics "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{K_i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": ", we seek to compute an estimate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": " of the true scene TSDF "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": ". We train a deep-learning model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Phi"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": " to perform this mapping, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{S} = \\Phi (\\{I_i\\}, \\{P_i\\}, \\{K_i\\})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        591,
+                                        287,
+                                        652
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                        659,
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+                        670
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                659,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.1. Model overview"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "Our model (illustrated in Fig. 2) extracts a set of 2D features "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{F}_i^c\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " from each input image using a convolutional neural network (CNN), "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Omega^c"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then use the camera pa"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "rameters to back-project "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{F}_i^c\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": " onto a 3D voxel grid. The back-projection process is augmented using depth estimates "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\hat{D}_i\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": " to produce the depth-guided feature volume "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nu^g"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": ", as described in Section 3.2.2. We process "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nu^g"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": " using a 3D CNN "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Psi"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": " to produce a new feature volume "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nu^{\\Psi}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": ", which we can query for "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{S}(q)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": " at any 3D point "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q \\in \\mathbb{R}^3"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        289,
+                                        545,
+                                        408
+                                    ],
+                                    "type": "text",
+                                    "content": " using the interpolation strategy defined in Section 3.2.3. To extract a surface mesh, we query the reconstruction on a grid of arbitrary resolution to produce a TSDF volume, from which a mesh can be extracted with Marching cubes [15]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                        433
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Key improvements"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2.1 Resolution-agnostic TSDF supervision"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "During training, as in previous works [17, 23, 24] we randomly orient the coordinate system of the feature volume relative to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
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+                                    ],
+                                    "type": "text",
+                                    "content": " using "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pm 3^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " rotations about the horizontal axis and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pm 180^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " rotations about the gravitational axis. Thus, the voxel centers may not coincide with the points "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{x\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " is known. This is typically addressed using linear interpolation on "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " to estimate the ground-truth TSDF at the voxel centers. However, this process is not accurate, since with non-planar geometry the TSDF is a non-linear function of space. Interpolation therefore corrupts the ground-truth TSDF, as shown in Fig. 3. In theory this effect can be minimized by sampling the ground truth on a very high-resolution grid, but this greatly increases training cost. To preserve the accuracy of the ground truth with no added cost, we instead supervise only at the points "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        462,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{x\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " where the ground truth is known, so that no interpolation is required. This decouples the accuracy of our ground truth from its sampling rate, rendering it resolution-agnostic. To support this, our model must be able to estimate the TSDF at any point in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^3"
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which we achieve using the strategy outlined in Section 3.2.3. This simple supervision change enables our"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "model to reconstruct significantly more visual detail (see Fig. 6)."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "3.2.2 Depth guidance"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
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+                                    "type": "text",
+                                    "content": "In order to localize image features in 3D space, we sample a pixel feature at each voxel from each available input image:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\tilde {\\mathcal {V}} _ {i} ^ {c} (q) = \\alpha \\left(\\mathcal {F} _ {i} ^ {c}, K _ {i} P _ {i} q _ {h}\\right), \\tag {1}",
+                                    "image_path": "6bea9a1a491dd6af78373a124c34c83fbf1bd447694e966b231bf2559a84a5fe.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha(F, u)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents sampling a feature from 2D map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " at pixel location "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u"
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+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_h"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        173,
+                                        287,
+                                        221
+                                    ],
+                                    "type": "text",
+                                    "content": " is the voxel center in homogeneous coordinates. We then reduce using a per-channel mean across views to form one feature vector per-voxel:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {V} ^ {c} (q) = \\frac {1}{| \\{I _ {i} \\} |} \\sum_ {i} \\tilde {\\mathcal {V}} _ {i} ^ {c} (q) \\tag {2}",
+                                    "image_path": "38bc560f55d4908a7600a57c500f6a029fc6dd10c81f080fb8d558b1e37012cd.jpg"
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "As an additional signal in recovering the scene surfaces, we propose to inject a multi-view depth prior using depth estimates from an MVS system "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
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+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". As MVS is a well-studied problem, we treat "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": " as an off-the-shelf component, and in the Supplementary we study the sensitivity of our system to depth noise and choice of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We fuse "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": " into scene space using the standard TSDF fusion [4] to form "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}^d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then concatenate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}^d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        266,
+                                        287,
+                                        384
+                                    ],
+                                    "type": "text",
+                                    "content": " as an extra channel in the back-projection volume. Our depth-guided back-projection volume is thus defined as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {V} ^ {g} = \\left[ \\mathcal {V} ^ {c}, \\mathcal {V} ^ {d} \\right]. \\tag {3}",
+                                    "image_path": "7aec0e5a98466b35b31bdb5f4fc0ae2589c372971f7e80e3880c81a894ae74ee.jpg"
+                                }
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+                {
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+                    "angle": 0,
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+                        {
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "In our experiments (see Table 5), the depth-guided feature volume "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        403,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}^g"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " shows significantly improved results with respect to image features alone "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        403,
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+                                        547
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{V}^c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        403,
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+                                        547
+                                    ],
+                                    "type": "text",
+                                    "content": ", or depth inputs alone "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        403,
+                                        287,
+                                        547
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{V}^d)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        403,
+                                        287,
+                                        547
+                                    ],
+                                    "type": "text",
+                                    "content": ". With naive application of the depth guidance, we find that this additional signal increases our network's propensity to over-fit to the training data, relying too heavily on the depth guidance which is often inaccurate. To address this, we scale each predicted depth map by a factor sampled uniformly in the range [0.9, 1.1] as a data augmentation during training. This reduces over-fitting and encourages the network to learn to use the image features in regions where the depth maps are unreliable."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                        607
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        548,
+                                        287,
+                                        607
+                                    ],
+                                    "type": "text",
+                                    "content": "We additionally experiment with several strategies for using the depth estimate to directly modulate the image feature back-projection. However, as shown in our experiments, our TSDF fusion approach outperforms these methods by a large margin (see Table 5)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "3.2.3 Point back-projection TSDF inference"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
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+                                    ],
+                                    "type": "text",
+                                    "content": "We use tri-linear interpolation to sample the 3D CNN's output feature volume "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}^{\\Psi}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
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+                                    ],
+                                    "type": "text",
+                                    "content": " at any query point "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": ". This results in a continuous-valued feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{V}}^{\\Psi} = \\Lambda (\\mathcal{V}^{\\Psi}, q)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": " where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": " represents tri-linear interpolation. Directly estimating "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
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+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from this feature is severely limited in its ability to reconstruct sub-voxel detail, since the effective resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{V}}^{\\Psi}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        629,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": " is still constrained to the size of the voxels."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": "We improve on this paradigm using an additional point back-projection step to directly sample image features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{W}(q)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " at the point "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": ". This step is identical to the depth-guided back-projection outlined in Section 3.2.2, except that the point "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " is no longer constrained to be a voxel center. The effective resolution of this new continuous-valued feature is thus determined by the resolution of the 2D image feature grid rather than the 3D voxel size. Assuming high-enough 2D feature resolution, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{W}(q)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " thus carries much finer-grained information than the linearly-interpolated voxel feature "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{V}}^{\\Psi}(q)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": ", complementing the 3D CNN's ability to produce smooth and context-informed features. We concatenate "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{W}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
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+                                        545,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{V}}^{\\Psi}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " as the input to a multilayer perceptron (MLP) "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta_{S}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                    "type": "interline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {S} = \\theta_ {S} ([ \\mathcal {W}, \\tilde {\\mathcal {V}} ^ {\\Psi} ]). \\tag {4}",
+                                    "image_path": "4a73576da5ca074b70ae73bd5feed12b49d91ef50f45168a0468ec037df2fe2f.jpg"
+                                }
+                            ]
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "At a given 3D sampling rate, our point back-projection inference strategy adds a small but non-negligible cost relative to using only "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        271,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{V}}^{\\Psi}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ": we must run an additional round of feature extraction and back-projection using "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Omega^{f}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and the input dimension of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        271,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta_{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " must be doubled in order to receive the extra input features. We show in our experiments that this cost is tractable (see Section 4.4)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We observe that the fine-grained features "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{W}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can contain spurious high-frequency content, particularly near the borders of the 2D features where the CNN output is unreliable due to edge effects. To reduce artifacts, we downweight "
+                                },
+                                {
+                                    "bbox": [
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+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{F_i^f\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        355,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " near the borders prior to back-projection using a weight "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        355,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w = \\sigma (l\\cdot (min(\\frac{d}{m},1)\\cdot 2 - 1))"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " ,where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the distance to the nearest border in pixels; "
+                                },
+                                {
+                                    "bbox": [
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+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m = 20"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        452
+                                    ],
+                                    "type": "text",
+                                    "content": " is a margin distance; "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        355,
+                                        545,
+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l = 6"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        355,
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+                                    ],
+                                    "type": "text",
+                                    "content": " controls the falloff rate; and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma (x) = \\frac{1}{1 + e^{-x}}"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
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+                                    "type": "text",
+                                    "content": "3.2.4 Output resolution & occupancy filtering"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Our model can be sampled at any point in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^3"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and we choose to sample it on a regular grid at test time in order to support meshing with marching cubes [15]. The resolution of this grid can be determined arbitrarily without retraining, and we experiment with several output grid resolutions (see Fig. 5). Naively, the cost of our point back-projection inference strategy grows cubically with the sampling rate. At high resolutions, it thus becomes expensive due to the cost of running the additional back-projection and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta_S"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " densely over the full volume. To mitigate this, we predict the per-voxel occupancy "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{O}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " with an additional MLP: "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{O} = \\theta_O(\\mathcal{V})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Then at test time we sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{S}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " only within voxels that are predicted to be occupied. While the asymptotic complexity is still cubic, in practice this greatly reduces the cost due to the prevalence of empty space."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
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+                                    "type": "text",
+                                    "content": "3.3. Training"
+                                }
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+                                    "type": "text",
+                                    "content": "At training time, we require a ground-truth TSDF "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "S"
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+                                    "content": " to supervise "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". For training on real scans, we use TSDF fusion [4] to generate "
+                                },
+                                {
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+                                    "type": "text",
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+                                            "content": "Figure 4. Qualitative results. Comparison of our method with NeuralRecon [24], VoRTX [23], and SimpleRecon [21]. NeuralRecon and VoRTX capture consistent global structure but lose many details, whereas SimpleRecon recovers details but fails to keep geometry consistent across views, leading to duplicate surfaces after TSDF fusion. Our method produces the most complete, consistent reconstruction while preserving details."
+                                        }
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+                                    "content": "X = \\{x \\in [i \\cdot \\delta, j \\cdot \\delta, k \\cdot \\delta]\\}"
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+                                    "type": "text",
+                                    "content": ", assuming the existence of a set of ground-truth depth maps "
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+                                    "content": "\\{D_i\\}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " corresponding to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{I_i\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". While ground truth depth can be noisy when acquired by sensors such as structured-light infrared scanners, we minimize artifacts by 1) using a large number of views to generate the ground-truth, 2) using an appropriate TSDF truncation distance following previous work [17, 23, 24], and 3) discarding depths beyond the range where the accuracy starts to visibly degrade."
+                                }
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+                                    "content": "Loss function. We define the TSDF loss "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathcal{S}}"
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+                                    "type": "text",
+                                    "content": " following SG-NN [6] as"
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+                                    "content": " represents morphological dilation with a "
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+                                    "type": "text",
+                                    "content": " structuring element. Note, this definition of occupancy describes space near a surface [6, 23, 24], rather than space interior to an object. Our training loss "
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+                                    "content": "CNN backbone architectures. Our 2D CNN architecture is a feature pyramid network [14] using EfficientNetV2-S [25] as a backbone. This structure is shared for both "
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+                                    "type": "text",
+                                    "content": ", but the weights are duplicated and then trained independently. Despite their identical architectures, these networks learn strikingly different features (see Supp.). Our 3D CNN "
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+                                    "content": " is inspired by U-Net [3, 20], see Supp. for details."
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+                                    "type": "text",
+                                    "content": " we use our re-implementation of the MVS network SimpleRecon [21]. We use a voxel size of 4cm in our model, and we train on volumetric scene chunks of size "
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+                                    "content": "(3.84\\mathrm{m} \\times 3.84\\mathrm{m} \\times 2.24\\mathrm{m})"
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+                                    "content": ". During training we select views by uniform random sampling over all views that at least partially observe the training chunk. At test time we fuse only keyframes, using the view selection strategy from DeepVideoMVS [7]. Training takes 36 hours on eight Nvidia V100 GPUs."
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+                                    "content": "4. Experiments"
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+                                    "content": "4.1. Dataset, baselines, and metrics"
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+                                    "type": "text",
+                                    "content": "Dataset. We validate our method by training and evaluating our model on the popular ScanNet dataset [5], which is composed of 1,613 indoor scans. We report all our metrics on the official test set containing 100 scans."
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+                                    "content": "Baselines. We compare our model with several previous works. For end-to-end 3D reconstruction methods we select Atlas [17], NeuralRecon [24], VoRTX [23], and TransformerFusion [1]. We also compare to MVS depth-prediction, selecting SimpleRecon [21], which we re-implement. In order to compare to SimpleRecon, we apply TSDF fusion [4] on the predicted depth maps to produce a 3D mesh."
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+                                    "content": "Metrics. We compute 3D metrics directly on the mesh reconstructions, and we compute depth metrics by rendering the meshes to generate predicted depth maps. Relative to prior works on depth estimation such as SimpleRecon [21], this is a slight change from the typical protocol of computing depth metrics directly on the raw depth maps. We believe our strategy is more indicative of performance in real-world applications that rely on the unified 3D reconstruction. Our definition for all metrics is the same as in Atlas [17] (see Supp. for details)."
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+                                    "content": "For computing 3D metrics we use the evaluation code from TransformerFusion [1], which includes a trimming protocol to avoid penalizing reconstructions for in-painting surfaces in unobserved regions. As noted in previous work [1, 23], precision or recall can easily be optimized individually at the expense of the other, as with accuracy and completeness. We thus emphasize Chamfer distance and F1 (i.e. F-score) as the most important 3D metrics, capturing this trade-off."
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+                                    "content": "Qualitative Results. In Fig. 4, we show qualitative results of our method compared to baselines and ground truth. We observe that our method preserves more details while minimizing high-frequency artifacts. The surfaces"
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+                                            "html": "<table><tr><td>Method</td><td>Acc ↓</td><td>Comp ↓</td><td>Cham ↓</td><td>Prec ↑</td><td>Rec ↑</td><td>F1 ↑</td></tr><tr><td>Atlas [17]</td><td>7.09</td><td>7.52</td><td>7.30</td><td>68.4</td><td>61.1</td><td>64.3</td></tr><tr><td>NeuralRecon [24]</td><td>5.04</td><td>10.68</td><td>7.86</td><td>62.7</td><td>59.1</td><td>60.7</td></tr><tr><td>3DVNet [18]</td><td>6.73</td><td>7.72</td><td>7.22</td><td>65.5</td><td>59.6</td><td>62.1</td></tr><tr><td>Transf. Fusion [1]</td><td>5.52</td><td>8.27</td><td>6.89</td><td>72.8</td><td>60.0</td><td>65.5</td></tr><tr><td>VoRTX [23]</td><td>4.32</td><td>7.52</td><td>5.92</td><td>76.3</td><td>64.0</td><td>69.5</td></tr><tr><td>SimpleRecon [21]</td><td>6.43</td><td>5.18</td><td>5.80</td><td>66.0</td><td>69.7</td><td>67.6</td></tr><tr><td>Ours</td><td>5.25</td><td>5.11</td><td>5.18</td><td>78.0</td><td>73.4</td><td>75.5</td></tr></table>",
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+                                            "content": "Table 1. 3D reconstruction metrics for ScanNet. We compare with recent work on mesh metrics defined in Atlas [17]. Best and Second -best are highlighted."
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+                                            "html": "<table><tr><td>Method</td><td>L1 ↓</td><td>AbsRel ↓</td><td>SqRel ↓</td><td>δ1.05 ↑</td><td>δ1.25 ↑</td><td>Comp. ↑</td></tr><tr><td>Atlas [17]</td><td>11.96</td><td>6.26</td><td>4.22</td><td>75.2</td><td>93.8</td><td>98.8</td></tr><tr><td>NeuralRecon [24]</td><td>9.84</td><td>6.54</td><td>3.79</td><td>75.0</td><td>94.6</td><td>90.8</td></tr><tr><td>VoRTX [23]</td><td>9.32</td><td>5.92</td><td>3.65</td><td>79.0</td><td>94.9</td><td>96.1</td></tr><tr><td>SimpleRecon [21]</td><td>8.23</td><td>4.83</td><td>2.66</td><td>81.0</td><td>96.8</td><td>97.4</td></tr><tr><td>Ours</td><td>6.91</td><td>4.24</td><td>2.57</td><td>86.6</td><td>97.1</td><td>97.2</td></tr></table>",
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+                                    "content": "Table 2. 2D metrics for ScanNet. The 2D depth is rendered and metrics are computed in the same way as with Atlas [17]. We highlight the Best and Second best with colors respectively."
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+                    ],
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+                                    "content": "in our reconstructions are smooth and consistent, gracefully unifying information from all views without the depth-disagreement artifacts or noticeable discontinuities visible in SimpleRecon. VoRTX suffers from blurry reconstructions where fine details such as chair legs are completely lost, whereas our approach reconstructs these elements faithfully."
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+                                    "type": "text",
+                                    "content": "In Fig. 5 we show qualitative results at three output resolutions: "
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+                                    "type": "text",
+                                    "content": ". VoRTX is not tractable at high resolutions, so we upsample VoRTX's "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " TSDF with linear interpolation, which does not increase the effective level of detail. For SimpleRecon, we can generate reconstructions at any desired resolution by decreasing the voxel size during TSDF fusion, and we note that artifacts and noise increase greatly at high resolution. In contrast, our results consistently preserve a high level of detail while avoiding noisy surfaces."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Quantitative Results. Table 1 shows our 3D reconstruction metrics on the ScanNet dataset. We report metrics for our method and SimpleRecon at the relatively high resolution of "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " because it is tractable to do so. We report metrics for the other baselines at their native resolution of "
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+                                    "type": "text",
+                                    "content": ", because increasing this resolution would add significant compute cost and engineering effort. For fairness, metrics for our method at "
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+                                    "type": "text",
+                                    "content": " are shown in Table 3, and we note that the quantitative differences from "
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+                                    "content": " are negligible. Our method achieves the best result in most metrics. In particular, it achieves the lowest Chamfer distance and highest F-score by large margins."
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+                                            "content": "Figure 5. Qualitative results at various output resolutions. With our method, we observe increased sub-voxel detail when increasing the output sampling rate from "
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+                                            "type": "text",
+                                            "content": ", as well as the occasional appearance of small artifacts near view frustum boundaries. Beyond "
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+                                            "content": " we observe no significant changes, suggesting we have reached our system's limit of detail given the 2D feature resolution. In contrast, upsampling the VoRTX outputs from "
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+                                            "content": " slightly increases smoothness but adds no extra detail, and SimpleRecon shows the appearance of significant frustum boundary artifacts starting at "
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+                                            "type": "text",
+                                            "content": "Figure 6. Ablation of our contributions. Compared to the baseline result (same as Table 4, row (i)), our improved supervision signal provides an overall increase in detail and accuracy at negligible added cost. Inconsistent areas (e.g. right side of couch, towels) are further refined by adding depth guidance. Finally, point back-projection provides higher effective resolution for capturing high-frequency and sub-voxel structures."
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+                                    "content": "4.3. Ablation studies"
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+                                    "content": "In Table 4 we compare ablations of the main novel components of our method. We note that resolution-agnostic TSDF supervision (RTS) and depth guidance (DG) both result in significant improvement across all metrics. Interestingly, point back-projection (PB) improves all metrics when DG is used ((v) vs. (iv)) but degrades them in the absence of DG ((iii) vs. (ii)). We interpret this as follows: the high-frequency content recovered by PB is locally accurate, but if the coarse alignment relative to ground truth is incorrect, then the added details actually reduce overall accuracy. DG helps to correctly localize the large structures, interacting constructively with PB to achieve the best performance."
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+                                    "content": "Depth guidance strategies In Table 5 we compare different ways to leverage the predicted depth maps to improve our reconstruction. In row (b) we use the density fusion"
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+                                    "content": "strategy introduced by VolumeFusion [2], and we observe that it does not perform as well as our method using TSDF fusion. We hypothesize that this is because the density does not encode free space information or inward vs. outward surface orientation. In row (c) we test using the depth to directly modulate the image feature projection, using a Gaussian window to down-weight the image features far from the estimated depth. Our experiments show that this manual weighting is an improvement relative to using no depth guidance at all, but that our TSDF fusion guidance yields the best results overall. To explore the relative importance of the image features and the depth guidance, we ablate each one individually in rows (e) and (f), noting worse results in each case."
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+                                            "content": "Table 3. Reconstruction metrics as a function of output resolution. The 2D and 3D metrics show very little sensitivity to the output resolution, despite clear visual differences (see Figure 5). This suggests that future work may require additional metrics to distinguish among high-quality reconstructions."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">DG</td><td rowspan=\"2\">PB</td><td rowspan=\"2\">RTS</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(i)</td><td>□</td><td>□</td><td>□</td><td>6.40</td><td>71.0</td><td>9.38</td><td>81.7</td></tr><tr><td>(ii)</td><td>□</td><td>□</td><td>√</td><td>5.58</td><td>73.8</td><td>7.63</td><td>84.5</td></tr><tr><td>(iii)</td><td>□</td><td>√</td><td>√</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(iv)</td><td>√</td><td>□</td><td>√</td><td>5.25</td><td>75.1</td><td>7.20</td><td>86.1</td></tr><tr><td>(v)</td><td>√</td><td>√</td><td>√</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr></table>",
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+                                            "content": "Table 4. Ablation study. We examine the quantitative improvement from the novel components of our method – depth guidance (DG), point pack-projection (PB) and resolution-agnostic TSDF supervision (RTS). Relative to baseline (i), the largest gains come from RTS (ii). PB is helpful with DG enabled (v) but hurts metrics in the absence of DG (iii)."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"2\">3D metrics</td><td colspan=\"2\">2D metrics</td></tr><tr><td>Cham ↓</td><td>F1 ↑</td><td>L1 ↓</td><td>δ1.05 ↑</td></tr><tr><td>(a)</td><td>Ours - TSDF (main)</td><td>5.18</td><td>75.5</td><td>6.91</td><td>86.6</td></tr><tr><td>(b)</td><td>Ours - Density volume [2]</td><td>5.29</td><td>74.3</td><td>7.31</td><td>85.7</td></tr><tr><td>(c)</td><td>Ours - Gaussian weight</td><td>5.47</td><td>73.2</td><td>7.48</td><td>85.1</td></tr><tr><td>(d)</td><td>Ours - TSDF &amp; gaussian weight</td><td>5.52</td><td>73.8</td><td>7.24</td><td>85.8</td></tr><tr><td>(e)</td><td>Ours - No depth guidance</td><td>5.80</td><td>72.4</td><td>8.26</td><td>83.0</td></tr><tr><td>(f)</td><td>Ours - TSDF (no image features)</td><td>5.66</td><td>71.9</td><td>7.74</td><td>83.8</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 5. Ablation of depth guidance strategies. We compare our depth guidance strategy (a) to other forms of depth guidance: (b) a density fusion volume similar to VolumeFusion [2]; (c) weighting the features using a Gaussian window centered on the predicted depth along each camera ray; (d) combination of (b) and (c); (e) no depth guidance; and (f) TSDF depth guidance with no image features. We find that our TSDF guidance (a) achieves the best performance on all metrics."
+                                }
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+                                    "type": "text",
+                                    "content": "4.4. Inference time"
+                                }
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+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "FineRecon reconstructs the ScanNet test scenes at 4cm resolution in an average of 18s per scene using an Nvidia V100 GPU. This is composed of a per-frame time of 87ms for 2D feature extraction, depth estimation, and backprojection, plus a one-time TSDF extraction time of 1.1s"
+                                }
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+                                    "type": "text",
+                                    "content": "including running the 3D CNN and output layers. Because we use a fixed voxel size, we can increase the output sampling rate with no increase to the per-frame time or 3D CNN time. As we apply higher spatial sampling rates, the cost of high-resolution inference increases proportionally to the number of occupied voxels due to back-projection and MLP execution at each sample point. Our average full-scene reconstruction time is 18s at 4cm, 21s at 2cm, 43s at 1cm. At the limit we test 0.5cm resolution which takes 3.6 minutes per scene on average. For faster inference times, the point back-projection can be disabled, resulting in an average time of 17s per scene at 1cm or 20s per scene at 0.5cm."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
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+                                    "type": "text",
+                                    "content": "We have presented an end-to-end network producing detailed 3D reconstructions from posed images. We have demonstrated that our novel supervision (RTS) is key in enabling the network to learn fine details. We have also introduced large improvements by using a depth-prediction network to guide the back-projection (DG). Lastly, we have developed a novel architecture (PB) to allow the free selection of output resolution at test time without requiring additional training or 3D convolution levels. PB opens interesting future avenues in which the TSDF is not predicted on a regular grid, such as adaptive sampling rates or alternative polygonization algorithms beyond marching cubes."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Limitations. While FineRecon produces more accurate geometric details than prior work, limitations remain. Despite an improvement over the state-of-the-art, our approach still misses certain local fine structures. One reason is the limitation of the training data, in a large capture setting with pose noise and imperfect depth sensors. Another is that the forward-inference setting does not guarantee consistency with the input observations: to close this gap, future work may explore the hybridization of the techniques presented here with iterative optimization and differentiable rendering. Finally, despite our favorable inference times, running a 3D CNN over a dense feature volume is costly in terms of power and memory, which may be prohibitive for certain applications (sparse convolution may help, but it adds to implementation complexity and is not implemented on all platforms); increased efficiency is thus an important future goal."
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                        }
+                                    ]
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+                                        }
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+                                            "type": "text",
+                                            "content": "International Conference on Computer Vision, pages 16086-16095, 2021. 1, 2, 7, 8"
+                                        }
+                                    ]
+                                }
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+                            "index": 0
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+                                        }
+                                    ]
+                                }
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+                                            "bbox": [
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+                                        }
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+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
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+[
+    {
+        "type": "text",
+        "text": "Fingerprinting Deep Image Restoration Models",
+        "text_level": 1,
+        "bbox": [
+            243,
+            130,
+            725,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yuhui Quan $^{1,2}$",
+        "bbox": [
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+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Huan Teng<sup>1,3</sup>",
+        "bbox": [
+            315,
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+            421,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ruotao  $\\mathbf{X}\\mathbf{u}^{1,2}$",
+        "bbox": [
+            464,
+            180,
+            581,
+            196
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Jun Huang<sup>3</sup>",
+        "bbox": [
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+            180,
+            710,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Hui Ji",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China",
+        "bbox": [
+            109,
+            199,
+            861,
+            215
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{2}$ Pazhou Lab, Guangzhou 510335, China",
+        "bbox": [
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+            410,
+            233
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>3</sup>Platform of AI, Alibaba Group, Hangzhou 311121, China",
+        "bbox": [
+            442,
+            218,
+            830,
+            233
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{4}$ Department of Mathematics, National University of Singapore, Singapore 119076",
+        "bbox": [
+            214,
+            234,
+            756,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            286,
+            313,
+            301
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Fingerprinting is a promising non-invasive method for protecting the intellectual property rights (IPR) of deep neural network (DNN) models. It extracts a feature called a fingerprint from a DNN model to identify its ownership. Existing fingerprinting methods focus only on classification-related models that map images to labels, while inapplicable to models for image restoration that map images to images. This paper proposes a fingerprinting framework for DNN models of image restoration. The proposed framework defines the fingerprint using a critical image, which exhibits strongly discriminative patterns and is robust to modest model modifications. Model ownership is then verified by comparing the distance of color histograms and local gradient pattern histograms of critical images between the suspect and source models. We apply the proposed framework to two representative tasks, denoising and super-resolution. It outperforms the baselines of fingerprinting and competes against existing invasive model watermarking methods.",
+        "bbox": [
+            75,
+            316,
+            472,
+            590
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            616,
+            209,
+            632
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep learning has become a prominent tool for solving problems in computer vision, ranging from high-level image classification problems to low-level image restoration problems. However, the cost of designing and training a DNN model for specific applications has grown exponentially, leading to expenses in many areas such as hardware resources, data collection and labeling, and paying for engineers and researchers. Although sharing pre-trained DNN models has become a common practice in the community, many companies and institutes charge for the commercial usage of pre-trained models. This creates a strong incentive",
+        "bbox": [
+            75,
+            642,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "for adversaries to plagiarize/steal the models, using methods such as malware infection or internal leaks, to bypass the expensive training process. Consequently, both the community and companies have a strong motivation to protect the IPR of their DNN models.",
+        "bbox": [
+            500,
+            287,
+            890,
+            362
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "One popular approach for protecting the IPR of DNN models is model watermarking (e.g. [44, 1, 10, 7, 53, 8, 39, 20, 54, 21]), which invasively embeds specific information called watermark into the source model and examines its existence in the suspect model for ownership verification. However, modifying model weights can potentially affect the model's utility, making it less desirable in practice.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, a non-invasive approach called model fingerprinting has gained attention. Unlike watermarking, fingerprinting keeps the model intact and creates a unique feature called fingerprint from the model for identifying ownership. The ownership of a model is verified by comparing the fingerprint of the source model with that of the suspect model. While fingerprinting is still in its early stages with few existing works [3, 24, 11, 60, 33], it is gaining popularity as a non-invasive alternative to model watermarking.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1.1. Motivation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we focus on protecting the IPR of DNN models used for low-level image restoration tasks. These types of models map degraded images or measurements to high-quality target images. Deep learning has proven to be a powerful tool for solving a variety of image restoration problems, e.g., image denoising [57, 35, 36, 32], superresolution (SR) [22, 47, 59, 43, 15], deblurring [58, 29, 40, 17, 41], and bad weather removal [34, 45, 37, 50, 51, 38].",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Most existing works on IPR protection for DNN models focus on high-level vision tasks such as image classification, where the DNN outputs a label in a finite discrete set. In contrast, DNN models for image restoration output an image in a very high-dimensional space. Though there are a few works on watermarking DNN models for various image restoration tasks (e.g.[53, 39, 54]), these image restoration models can be vulnerable to modifications of DNN weights required in watermarking, resulting in the loss of important",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author: Ruotao Xu (xrt@scut.edu.cn). This work is supported by the Natural Science Foundation of Guangdong Province (Grant No. 2023A1515012841, 2022A1515011755, 2022A1515011087); National Natural Science Foundation of China (Grant No. 62106077); Postdoctoral Special Foundation of China (Grant No. 2022T150219); Postdoctoral Foundation of China (Grant No. 2020M682705); and Singapore MOE AcRF Tier 1 (Grant No. A-8000981-00-00).",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "13285",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/ba00baf838899bb59f472da73d8ab3fd4fbcc5c3a9c2b9b10ec8eb2888fa508a.jpg",
+        "image_caption": [
+            "Figure 1: Main idea of our model fingerprinting approach for an image recovery DNN. We aim to find a critical image (blue point) around the DNN's performance border zone."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            89,
+            88,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "image details and the addition of undesired artifacts.",
+        "bbox": [
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+            338
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Fingerprinting is a more attractive option for image restoration DNNs, as it does not require any modification to model weights. However, to the best of our knowledge, no existing study has explored fingerprinting for DNN models used in image restoration tasks. The existing fingerprinting methods are designed for classification DNNs which can be fully characterized by their decision boundaries. These methods use adversarial examples to characterize the decision boundaries and generate a fingerprint for the model. In contrast, image restoration generates an image in a high-dimensional space, and its accuracy is measured by a continuous metric such as mean squared error to the ground truth. Therefore, the concept of \"decision boundary\" is not well-defined for image restoration models.",
+        "bbox": [
+            73,
+            338,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Due to the significant differences between image restoration and image classification, the existing fingerprinting methods for classification DNNs cannot be easily extended to image restoration DNNs. As a result, we were motivated to develop a new fingerprinting framework specifically designed for image restoration DNN models.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "1.2. Main Idea",
+        "text_level": 1,
+        "bbox": [
+            76,
+            650,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "An image restoration task (e.g. denoising and SR) is to predict a latent image  $\\mathbf{X}$  from its degraded or partial measurements  $\\mathbf{Y} = \\mathcal{D}(\\mathbf{X})$ , where  $\\mathcal{D}$  denotes the degrading/measuring process. In deep learning, a DNN model  $\\mathcal{M}: \\mathbb{R}^{n \\times m} \\to \\mathbb{R}^{N \\times M}$  is trained to accurately predict  $\\mathbf{X}$  from the input  $\\mathcal{D}(\\mathbf{X})$  in some task-related domain  $\\mathbb{D}$ . While the prediction error for most images in  $\\mathbb{D}$ , measured by  $\\| \\mathbf{X} - \\mathcal{M}(\\mathcal{D}(\\mathbf{X})) \\|_2^2$ , is small, there exists a complementary set  $\\overline{\\mathbb{D}}$  where the DNN has large prediction errors.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Indeed, an image restoration DNN usually works well only for target images that lie within a low-dimensional manifold in  $\\mathbb{R}^{N\\times M}$ . It is not expected that a DNN will perform well for all points in  $\\mathbb{R}^{N\\times M}$ . For instance, consider image denoising where  $\\mathbf{Y} = \\mathcal{D}(\\mathbf{X}) = \\mathbf{X} + \\mathbf{N}$ , with  $\\mathbf{N}$  representing Gaussian white noise. Let  $\\mathbf{X}_1$  be a constant matrix",
+        "bbox": [
+            75,
+            810,
+            467,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "and  $\\mathbf{X}_2$  be a random matrix with entries randomly sampled from a normal distribution. Since adding two independent Gaussian random variables results in a new Gaussian random variable [18],  $\\mathbf{Y}_2$  also corresponds to a constant image corrupted by larger Gaussian white noise. Suppose a denoising model performs well on predicting  $\\mathbf{X}_1$  (a constant matrix) from its noisy version  $\\mathbf{Y}_1$ . Then, the denoiser will consistently take  $\\mathbf{Y}_2$  as the noisy version of a constant matrix and output a constant matrix, which is far away from the ground-truth matrix  $\\mathbf{X}_2$  (a random matrix). In other words, a denoising model designed to work well for constant matrices may not work well for random matrices.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To summarize, just like the decision boundary in classification, there exists a \"performance border zone\" that separates the set of images that the restoration model can accurately restore and the set of images that it cannot. This zone encodes essential characteristics of the model, and the points close to it can be used for its characterization. Particularly, these points can be the images in the complementary set  $\\overline{\\mathbb{D}}$  that are close to the set  $\\mathbb{D}$  of images that the DNN can restore accurately (i.e., their prediction errors by the DNN are small). See Figure 1 for an illustration of this concept.",
+        "bbox": [
+            496,
+            272,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we define the term \"critical images\" to refer to the points near the performance border zone. Suppose that the target images in  $\\mathbb{D}$  follow some prior, such as the sparsity prior of gradients. Then, a critical image for the model  $\\mathcal{M}$  is an image  $\\mathbf{X}$  that minimizes the prediction error  $\\| \\mathbf{X} - \\mathcal{M}(\\mathcal{D}(\\mathbf{X}))\\|_2^2$  (i.e.,  $\\mathbf{X}$  is close to  $\\mathbb{D}$ ) while also maximizing a penalty that reflects the prior on the images in  $\\mathbb{D}$  (i.e.,  $\\mathbf{X}$  is close to  $\\bar{\\mathbb{D}}$ ). This ensures that  $\\mathbf{X}$  is simultaneously close to both  $\\mathbb{D}$  and  $\\bar{\\mathbb{D}}$ , i.e., it lies near their border zone.",
+        "bbox": [
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+            425,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Empirical observations suggest that the critical images obtained from independently-trained DNNs using the proposed approach consist of strong spatial patterns that not only convey discriminative information, but are also robust to moderate modifications in model weights. Therefore, these critical images can serve as the fingerprints of a model. For model verification, we measure the distances between the fingerprints using two standard image descriptors: color histograms and local gradient patterns (LGP) [13].",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "1.3. Contributions",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The construction of a critical image forms the foundation of our proposed fingerprinting approach for image restoration models. Our approach is applied to two representative image restoration tasks: denoising and SR. Denoising is a core problem in many image restoration tasks, and SR is one of the most successful applications of deep learning in image restoration. Extensive experiments on these two tasks have demonstrated that our proposed approach is more robust than the baseline fingerprinting methods and competitive with recent intrusive watermarking methods. See below for a summary of the main contributions:",
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "13286",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- A fingerprinting framework is proposed for protecting the IPR of image restoration DNN models. To the best of our knowledge, this is the first study on fingerprinting DNN models of image restoration.",
+            "- Analogous to decision boundaries in classification, the concept of performance border zone is introduced to characterize image restoration DNN models.",
+            "- The concept of critical images, points in proximity to the performance border zone, is introduced to showcase discriminative and robust patterns that can serve as effective fingerprints for image restoration DNN models."
+        ],
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            76,
+            277,
+            225,
+            294
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.1. Model Fingerprinting",
+        "text_level": 1,
+        "bbox": [
+            76,
+            303,
+            281,
+            319
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Model fingerprinting shares a similar spirit with the zerowatermarking for digital images (e.g. [48]), where discriminative yet robust features are extracted from an image to represent its ownership. While it is possible to extract features directly from the weights of a DNN by treating them as digital media, this method is not robust to modifications of the model. To improve robustness, existing works [3, 24, 11, 60, 60, 33] extract features from the decision boundaries of a classification DNN, as these features are often transferable for plagiarism models but not for independently-trained models.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Cao et al. [3] proposed to fingerprint decision boundaries via using nearby data points defined by adversarial examples. The ownership is verified by checking whether the suspect model predicts the same labels as the source model on those data points. Lukas et al. [24] proposed to fingerprint the overlap of adversarial subspaces around decision boundaries between the source model and its surrogates. They synthesized conferrable adversarial examples that transfer exclusively with a target label from the source model to its surrogates. Zhao et al. [60] proposed to improve adversarial examples for fingerprinting by encouraging them to mimic the logits vector of a target sample randomly chosen from the target category. Peng et al. [33] proposed to profile decision boundaries by characterizing the universal adversarial perturbations [26]. Additionally, they trained an encoder via contrastive learning to map fingerprints from two models to a similarity score for ownership verification. Chen et al. [5] proposed to quantify the similarity between two models using a diverse set of testing metrics and test case generation algorithms to produce a chain of evidence for verification. This method can include many existing fingerprinting algorithms as test metrics.",
+        "bbox": [
+            76,
+            492,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "All the methods discussed above are limited to classification DNNs. Our approach, however, is specifically designed for fingerprinting models of image restoration by using critical images instead of adversarial examples. It is noted that while the aforementioned methods aim to detect",
+        "bbox": [
+            76,
+            825,
+            467,
+            898
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "model plagiarism, He et al. [11] proposed a fingerprinting method to examine model integrity. This method identifies a small set of human-unnoticeable transformed inputs that make a model's outputs sensitive to its parameters.",
+        "bbox": [
+            498,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Model Watermarking",
+        "text_level": 1,
+        "bbox": [
+            500,
+            162,
+            702,
+            178
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Model watermarking serves a similar purpose as model fingerprinting; however, it involves embedding a code or opening a backdoor inside a DNN that could potentially harm the DNN's performance. Most existing watermarking methods are designed for classification DNNs (e.g. [44, 42, 56, 1, 10, 27, 4, 28, 7, 16, 53, 8, 20, 54, 21, 19, 23]), but there are also a few works that target image restoration DNN models (e.g. [53, 39, 31, 54]). Zhang et al. [53, 54] proposed to train the DNN to automatically embed an invisible watermark in its output image. The model ownership is verified by detecting the presence of watermarks in the output images of the suspect DNN. Quan et al. [39] proposed to train the DNN to map a random image to its naive recovered version that is unlikely to be generated by other independently well-trained DNNs. The model ownership is verified by checking whether such a mapping holds for the suspect DNN. Ong et al. [31] proposed to train the DNN so that an input image embedded with a visible key can lead to an output image with a visible logo. The model ownership is verified by attempting to trigger the logo via the key.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Statement and Overview",
+        "text_level": 1,
+        "bbox": [
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+            527,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Threat model In a typical attack-defense scenario, an owner has trained a source model using private resources. An adversary attempts to plagiarize or steal the model. The owner is both a victim and a defender, with the goal of determining whether the suspect model is a plagiarized one. This involves verifying ownership in a white-box setting. An adversary or attacker who steals a model may modify it to avoid detection of ownership while maintaining its functionality and performance, but the access to the original training data is not given. Under this setting, we consider often-seen attacks that modify model weights, e.g., pruning, finetuning, and quantization.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Principles Discriminability is a fundamental property of model fingerprinting. A model fingerprint is trustworthy for protecting IPR only if it is distinguishable for different models. Given the importance of training data and open sources of DNN architecture, two models with the same architecture but trained independently using different data are considered as independent models, and their fingerprints should be distinguishable from each other. Robustness is another critical property of model fingerprinting. A model fingerprint is expected to remain nearly unchanged under various modifications (attacks) on the model. However, these two",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "13287",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/c5a51db681c35b4638d9c4af9b996a5388457866de6276e7cb80cafa8fb37a00.jpg",
+        "image_caption": [
+            "Figure 2: Proposed model fingerprinting framework."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            88,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "properties often conflict with each other, and an ideal model fingerprinter should balance them carefully. It is worth noting that the fidelity of model performance, a desirable property for model watermarking, is not necessary for a non-invasive method like fingerprinting.",
+        "bbox": [
+            75,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "**Framework** The proposed fingerprinting method for image restoration DNN models is outlined in Figure 2, involving 3 steps. First, a fingerprint defined over critical images is extracted from the source model and registered. Second, the fingerprint of a suspect model is computed for notarization. Finally, ownership is verified by comparing the features of the two fingerprints. The remaining issues are (i) how to extract a discriminative yet robust fingerprint from a model, and (ii) how to efficiently compare two fingerprints.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Fingerprint Extraction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            527,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As discussed in Section 1.2, we use critical images to fingerprint a model. These critical images are located near the performance border zone of an image restoration DNN. Now we focus on the restoration problems for natural images which are assumed to follow a Laplacian prior. Such a prior is generally true for natural images. Specifically, the total variation (TV)  $|\\nabla \\mathbf{X}|_1$  of an image  $\\mathbf{X}$  in the domain  $\\mathbb{D}$  is small, while an image  $\\overline{\\mathbf{X}}$  in  $\\overline{\\mathbb{D}}$  has a large value of  $|\\nabla \\overline{\\mathbf{X}}|_1$ . Our proposed approach is also applicable to images in other domains, provided that there is some prior knowledge available for latent images.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Given a DNN model  $\\mathcal{M}$  trained for an image restoration task  $\\mathcal{T}$ , we define the critical image  $\\mathbf{S}$  by solving the following optimization problem:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {S} := \\underset {\\overline {{\\mathbf {X}}} \\in [ 0, 1 ] ^ {M \\times N}} {\\arg \\min } \\| \\overline {{\\mathbf {X}}} - \\mathcal {M} \\left(\\mathcal {D} _ {\\mathcal {T}} (\\overline {{\\mathbf {X}}})\\right) \\| _ {2} ^ {2} - \\lambda \\| \\nabla \\overline {{\\mathbf {X}}} \\| _ {1}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
+            771,
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+            800
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{D}_{\\mathcal{T}}$  denotes a degradation operator associated with the task  $\\mathcal{T}$ , and  $\\lambda \\in \\mathbb{R}^{+}$  is a weight. The objective of the first term in (1) is to find an image close to the set  $\\mathbb{D}$ . The second term encourages the image to be close to  $\\overline{\\mathbb{D}}$ . This is achieved by maximizing the value of  $\\| \\nabla \\overline{\\mathbf{X}} \\|_1$ , which is a necessary condition for images in  $\\overline{\\mathbb{D}}$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The operator  $\\mathcal{D}_{\\mathcal{T}}$  varies depending on the specific image restoration task. For instance, it corresponds to noise corruption for image denoising, downsampling for image SR, and blurring for image deblurring. For image denoising and SR, we adopt the following construction schemes for  $\\mathcal{D}_{\\mathcal{T}}$ :",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} + \\mathbf {N}, \\quad \\mathbf {N} \\sim \\mathcal {N} (\\mathbf {0}, \\sigma^ {2} \\mathbf {I}), \\quad [ \\text {D e n o i s i n g} ] \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} \\downarrow_ {4}, \\quad [ \\text {I m a g e S R} ] \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            194,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{N}$  denotes normal distribution and  $\\downarrow_4$  denotes dyadic downsampling that reduces the image size by half. The definition of  $\\mathcal{D}_{\\mathcal{T}}$  can be adapted to other restoration tasks.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To solve (1), we use the Adam solver [14]. However, since the problem involves a DNN, it is highly non-convex, and the output of an iterative solver depends on the initialization of  $\\mathbf{X}$ . We use random initialization for solving (1), i.e., we set  $\\mathbf{S}^{(0)}$ , the initial point of  $\\mathbf{S}$ , as follows:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {S} ^ {(0)} \\sim \\mathcal {N} (\\mathbf {0}, \\beta^ {2} \\mathbf {I}), \\quad \\beta \\in \\mathbb {R}. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            349,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 illustrates the critical images calculated using different instances of  $\\mathbf{S}^{(0)}$  generated via (4). We observe that critical images from the same model with different  $\\mathbf{S}^{(0)}$  exhibit similar (homogeneous) patterns, while those from different models differ significantly from each other.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we construct the fingerprint denoted by  $\\mathcal{F}$  via (1). To form a fingerprint of arbitrary length, one can solve (1) for multiple times using different  $\\mathbf{S}^{(0)}$ :",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} = \\left\\{\\left(\\mathbf {S} _ {1} ^ {(0)}, \\mathbf {S} _ {1}\\right), \\dots , \\left(\\mathbf {S} _ {K} ^ {(0)}, \\mathbf {S} _ {K}\\right) \\right\\}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            505,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{S}_k$  is the critical image calculated using  $\\mathbf{S}_k^{(0)}$  as the initial point for solving (1). Note that different  $\\mathbf{S}_k$  of the same model contain the same patterns (see Figure 3) and image restoration models usually allow input (output) images of varying sizes. To obtain a similar amount of fingerprint information while avoiding multiple extractions, we can set  $K = 1$  and use a single large  $\\mathbf{S}$  to approximate multiple  $\\mathbf{S}_k$  of smaller sizes. It is worth noting that solving  $\\mathbf{S}_k$  from (1) does not require accessing the model weights of  $\\mathcal{M}$ , but only the gradients of  $\\mathcal{M}(\\mathcal{D}_{\\mathcal{T}}(\\overline{\\mathbf{X}}))$  w.r.t.  $\\overline{\\mathbf{X}}$ , in a similar spirit to federated learning.",
+        "bbox": [
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+            535,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Verification of Ownership",
+        "text_level": 1,
+        "bbox": [
+            500,
+            710,
+            733,
+            727
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Verification of ownership is accomplished by comparing fingerprints between the source and suspect models. While critical images can be visually compared, automated verification is often desirable in practice. Because critical images display distinct patterns in terms of color distribution and texture, we characterize them using color histograms (a standard color descriptor) and an improved version of LGP histograms [13] (a classic texture descriptor) based on the idea of [30]. Further details can be found in the supplemental material. Our approach is learning-free and does not require collecting training data for a learning-based verifier.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "13288",
+        "bbox": [
+            480,
+            944,
+            517,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/dce37dc5e76889fbf48b831acbf218a43ad82b9b28f767bed8aaec631c29f479.jpg",
+        "image_caption": [
+            "Figure 3: Critical images of DBSN [49] (upper) and EDSR [22] (bottom) calculated by using  $\\mathbf{S}^{(0)}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$  while fixing all other hyper-parameters."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            87,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let  $h_{\\mathrm{su}}$ ,  $h_{\\mathrm{sus}} \\in \\mathbb{R}^L$  be the features. i.e., the concatenation of normalized color and LGP histograms, computed from the fingerprints of the source model and the suspect model, respectively. When  $K > 1$ , the features from multiple  $\\mathbf{S}_k$  are averaged. In essence, these features serve as a refined version of the fingerprints. Then the suspect model will be identified as plagiarism if",
+        "bbox": [
+            75,
+            316,
+            472,
+            425
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nd = \\left\\| \\boldsymbol {h} _ {\\text {s o u}} - \\boldsymbol {h} _ {\\text {s u s}} \\right\\| _ {2} ^ {2} / L <   \\eta , \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            179,
+            435,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\eta$  is a threshold (the bound of negligible error) determined by a probabilistic scheme with the same spirit of [39]. Suppose that the error  $e(j) = h_{\\mathrm{su}}(j) - h_{\\mathrm{sus}}(j)\\sim \\mathcal{N}(0,\\sigma^2),\\forall j$  , where  $\\sigma = 0.015$  (see supplemental material for our idea to determine this value). Then, the random variable  $Z = \\frac{\\|e\\|_2^2}{\\sigma^2}$  follows a Chi-squared distribution  $\\mathcal{X}_L^2$  . By applying the  $p$  -value approach with  $p <   0.05$  , we can find a value of  $\\gamma$  such that  $P[Z\\leq \\gamma ] <   0.05$  , or equivalently,  $P[d\\leq \\eta ] <   0.05$  . This allows us to safely reject the null hypothesis that  $h_\\mathrm{su}$  and  $h_\\mathrm{sus}$  are similar.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            631,
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+            648
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We assess the effectiveness of the proposed approach for two restoration tasks, namely image denoising and image SR, by measuring their discriminability and robustness.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Source models We choose six DNNs from existing literature as the source models for each task, respectively. (a) Image denoising: DnCNN [57], DBSN [49], Nei2Nei [12], Restormer [50], SimBase [6], and NAFNet [6]; (b) Image SR: EDSR [22], RRDBNet [47], RNAN [59], MobileSR [43], RFLN [15], and DRLN [2]. To comprehensively evaluate the effectiveness of fingerprinting, we consider models with varying structures, training data, and training strategies, for both tasks. We either use the pretrained models or train them using their released codes. See more details in the supplemental material.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation details In fingerprint extraction, we use a single critical image of size  $128 \\times 128$ , for all models in both tasks. We set  $\\beta = 1$  in (4) for initializing  $\\mathbf{X}$ . The learning rate of Adam for solving (1) is set to 0.1. A total number of 5000 iterations is used. In ownership verification, we form a 30-dimensional RGB+LGP histogram. The resulting threshold is  $\\eta = 1.39 \\times 10^{-4}$ . For denoising DNNs, we set  $\\sigma = 1$  for constructing  $\\mathcal{D}_{\\mathcal{T}}$  in (2). For both denoising and SR, we set  $\\lambda = 0.001$ . The seeds involved in our approach are fixed to make the whole process deterministic and reproducible.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Discriminability Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We begin by a visual inspection on the fingerprints extracted via our approach. See Figure 4 for the critical images extracted from various source models, all of which contain unique and distinguishable patterns that vary in scale, appearance, local shape, regularity and color, across different images. For instance, larger-scale patterns are visible for SimBase while the smaller-scale ones for DnCNN. The fingerprint of DnCNN exhibits random patterns, while that of NAFNet shows regular ones. Moreover, the red tone of fingerprint of NAFNet differs from the chromatic tone of SimBase. These significant visual differences demonstrate the strong discriminability of the extracted fingerprints.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The discriminability is further quantitatively assessed by computing the feature distances (6) between critical images for every pair of source models. The distance matrices in Figure 5(a) and (b) show the ratios between the resulting distances and the threshold  $\\eta$ , for denoising DNNs and SR DNNs, respectively. In both tasks, all off-diagonal elements, i.e., distances between every model pair, exceed the threshold, indicating no confusion among the models. The results indicate excellent discriminability of our extracted critical images, and the simple RGB+LGP histograms are able to effectively capture their patterns for verification.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We also test whether our approach can differentiate models with the same architecture but trained on different datasets. The Restormer model [50] is retrained on six different datasets; see the details in the supplemental material. Figure 4(c) visually compares the fingerprints of each model, and Figure 5(c) shows the resulting distance matrix. Our approach effectively differentiates the models, even those with the same architecture, with many large off-diagonal values observed in the distance matrix.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Robustness Analysis",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conduct robustness analysis using three common attacks: model pruning, model finetuning, and model quantization. A meaningful attack should only have a minor effect on the original function of a model. For analysis, we quantify the impact of an attack on the model's performance based on the resulting average PSNR gap on the recovered",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "13289",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/de6fd3a3fb36b75487d0eda110f971fe5e85430f9b3c7c76ea5eaff11de72651.jpg",
+        "image_caption": [
+            "(a) Fingerprints of denoising models"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            90,
+            343,
+            256
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/58f98caa857974b120de8b0811ebfc2f3b36b21d365e4ad7640c38c6c283db2d.jpg",
+        "image_caption": [
+            "(b) Fingerprints of SR models"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            351,
+            90,
+            614,
+            255
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/099a124dda0c58fde2e1d27db955b42b8adc0c5fdbabcdbc293a195a86eee1af.jpg",
+        "image_caption": [
+            "(c) Fingerprints of independent Restormer models"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            620,
+            90,
+            885,
+            256
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/72e1c3e45c2aea7906471fd87ba5207b554a5e0d0a23dc9dbc08e9903a8040c8.jpg",
+        "image_caption": [
+            "(a) Denoising models"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            303,
+            343,
+            467
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/41b1c7c8a123b9add3a22d4cb095c8787c8a5b1bfc31d485b43ef65738728cb0.jpg",
+        "image_caption": [
+            "Figure 4: Fingerprints (critical images) extracted from different source models.",
+            "(b) SR models"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            348,
+            303,
+            614,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/7051fe07be19387140c2a00a79d3814b85e5ee4a99f65e02951e83149a9484ce.jpg",
+        "image_caption": [
+            "(c) Restomers trained with different datasets.",
+            "Figure 5: Visualization of pairwise feature distance of fingerprints between source models. The ratios between the distance and the threshold are shown. For better illustration, all the color bars are set as follows. The color goes from purple to blue when the value decreases from 1, while the color goes from orange to yellow when the value increases from 1."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            620,
+            303,
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+            467
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "images. Each attack has its strength controlled such that it only leads to  $\\leq 1\\mathrm{dB}$  change in the average PSNR value for all the models on a test set. This ensures that all attacks are not meaningless. The robustness is measured by the times of successful ownership verification under an attack.",
+        "bbox": [
+            75,
+            560,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baselines So far, no fingerprinting method is available that is specifically designed for image restoration DNNs, making our work the first in this area. For experimental comparison, we construct two baselines by adapting existing fingerprint methods designed for classification DNNs:",
+        "bbox": [
+            75,
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+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. ProjCL: Each image restoration source model is converted to a classification DNN by adding a random projection layer with softmax activation in the end, so as to output a 100-dimensional label vector. Then, the well-known fingerprinting method IPGuard [3] is applied for the classification DNNs.",
+            "2. PoolCL: The output of each source model is downsampled to form a  $10 \\times 10$  image, which is then vectorized and subjected to a Softmax function, producing a 100-dimensional label vector. This converts each source model into a classification DNN, and then we fingerprint it using the IPGuard [3]."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We tune the baselines' hyper-parameters, including label vector dimensions, for their discriminability. We set their verification thresholds to the minimum values that ensure all tested models pass the discrimination test. These threshold values optimize the robustness metrics, as reducing the verification threshold improves robustness.",
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+    {
+        "type": "text",
+        "text": "Furthermore, we present three watermarking methods specifically designed for image restoration DNNs to compare the performance gap between non-invasive fingerprinting and invasive watermarking:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "1. Zhang et al. [55]: The source model is retrained to embed an invisible watermark in each output.",
+            "2. Ong et al. [31]: The source model is retrained to composite a visible watermark region into the output when the input is composed of a specific trigger region.",
+            "3. Quan et al. [39]: The source model is retrained to produce a copyright image for a specific input noise."
+        ],
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We tune the hyper-parameters for the watermark embedding in these methods to maintain high fidelity on the PSNR performance of the source models on test data. To facilitate a more informative comparison between fingerprinting and watermarking, we create a baseline called \"WeakWM\" by",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "13290",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3c06cbc07de75f51b57f13b171f05c7085f69238f6d3f23cb910d7c1ae966b1.jpg",
+        "image_caption": [
+            "(a) Fingerprints on denoising models."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3de919d8f1ffc3587441769169242941227192444ca559e6ab4f33570e8da932.jpg",
+        "image_caption": [
+            "(b) Fingerprints on SR models.",
+            "Figure 6: Fingerprints (critical images) calculated from different models under three attacks."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/6285aa037a6bc165e9c44027b7c9ac11d5f8c6e112dfab79b8345556b2fe8a67.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"8\">Image Denoising</td><td colspan=\"8\">Image SR</td></tr><tr><td></td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td></tr><tr><td rowspan=\"6\">Pruning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RNAN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan=\"6\">Finetuning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan=\"6\">Quantization</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>DRLN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>√</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td colspan=\"2\">Success Rate</td><td>67%</td><td>78%</td><td>100%</td><td>100%</td><td>100%</td><td>28%</td><td>100%</td><td>Success Rate</td><td>0%</td><td>61%</td><td>100%</td><td>100%</td><td>100%</td><td>22%</td><td>100%</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Verification under attacks. Blue: fingerprinting; Purple: watermarking; X: failure;  $\\checkmark$  : success.",
+        "bbox": [
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+            712,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "reducing the watermark embedding strength of Quan et al.'s method [39] to a sufficiently low value where no significant loss in fidelity is observed. The fingerprints extracted by our approach for both tasks are shown in Figure 6, under various attacks. Verification results for different methods are listed in Table 1.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Model pruning We prune the source models by zeroing the top  $p\\%$  of smallest weights in the DNN's layers, where  $p = 10$  for denoising and  $p = 5$  for SR. The pat",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "terns are nearly the same for both tasks under model pruning. Our approach achieves successful verification on all models under all pruning ratios for both tasks, outperforming the two baselines that fails in nearly half the cases. Notably, the baselines perform much worse for SR models than for denoising models. The baseline ProjCL fails in all SR cases, suggesting that the methods designed for classification DNNs are ineffective when applied to image restoration DNNs. The watermarking methods succeed for all mod",
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "13291",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "els, which is expected due to their invasive manner. However, when the watermark embedding strength is very weak, WeakWM fails in most cases during watermark verification.",
+        "bbox": [
+            75,
+            90,
+            468,
+            136
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Model finetuning We fine-tune the source models with their original tasks on the BSD68 dataset [25] for 500 iterations (steps). Little change can be observed in the patterns of the resulting critical images. Our fingerprinting approach and the three watermarking methods successfully verify all models. However, among the baselines, PoolCL fails in one denoising and one SR case, ProjCL fails in two denoising and all SR cases, and WeakWM succeeds only once in each task due to weak watermark strength.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Model quantization When Int8 quantization with simple rounding is applied to the source models, our approach still produces robust yet discriminative fingerprints. It successfully verifies all models, like the three watermarking methods. WeakWM only succeeds in one half cases. ProjCL fails in two denoising cases and all SR cases. PoolCL performs acceptably on denoising models but fails in a half of the SR cases.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
+            407,
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+            422
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We form additional two baselines of our approach for further study, which are as follows:",
+        "bbox": [
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+            460
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. w/o TV: Removing the TV (second term) in (1) for calculating the critical image.",
+            "2. MaxObj: Replacing the critical image in our approach with an image generated by maximizing the objective function in (1) instead of minimizing it. The resulting image is expected to be as smooth as possible while hard to recover, which can be seen as an adversarial sample."
+        ],
+        "bbox": [
+            80,
+            464,
+            468,
+            577
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For the \"w/o TV\" case, we observe that the resulting critical images tend to degenerate into a constant image easily for some models, meaning that its discriminability could not be guaranteed. Therefore, we only compare the success rates of MaxObj and our approach in terms of robustness. See Table 2 for the results, where our approach outperforms MaxObj. This may be because the fingerprints generated by MaxObj are not as close to the performance border zone as those generated by our approach.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/7875f6f18c1534a264831f5cd48b02fb11855cf117ac3ec9fa3b8c5afb1a024b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Compression</td><td colspan=\"2\">Finetuning</td><td colspan=\"2\">Quantization</td></tr><tr><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td></tr><tr><td>MaxObj</td><td>5/6</td><td>4/6</td><td>6/6</td><td>4/6</td><td>6/6</td><td>3/6</td></tr><tr><td>Ours</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td></tr></table>",
+        "bbox": [
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+            729,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Success rates of baselines in ablation study.",
+        "bbox": [
+            99,
+            803,
+            444,
+            816
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5. Demos Beyond Denoising and SR",
+        "text_level": 1,
+        "bbox": [
+            76,
+            845,
+            367,
+            863
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To further examine the applicability of our approach to other image restoration tasks, we provide demos on addi",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/cdf8b9febb02e0e6d52710f2bffa2b12753f9b7d7ee4352daef13b05512bf498.jpg",
+        "image_caption": [
+            "Figure 7: Fingerprints calculated from different pre-trained and attacked DNN models on other tasks. See supplemental material for the results on deraining."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            87,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "tional tasks: deblurring (including motion deblurring and defocus deblurring), deraining, and low-light enhancement. The operator  $\\mathcal{D}_{\\mathcal{T}}$ s are defined as follows:",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {K} \\otimes \\mathbf {X} + \\mathbf {N}, \\quad [ \\text {D e b l u r r i n g} ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            387,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\operatorname {N o r m} \\left(\\mathbf {X} ^ {3}\\right), \\quad [ \\text {L o w - l i g h t E n h a n c e m e n t} ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            407,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} + \\mathbf {R}, \\quad [ \\text {D e r a i n i n g} ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            517,
+            426,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{K}$  is a blur kernel,  $\\mathrm{Norm}(\\cdot)$  denotes min-max normalization, and  $\\mathbf{R}$  is a synthetic rain layer; see supplemental material for details. We select three DNNs with published pre-trained models for each task: IFAN [17], GKMNet [40] and NRKNet [41] for defocus deblurring; Restormer [50], SimBase [6] and NAFNet [6] for motion deblurring; Restormer [50], MPRNet [51] and VRGNet [45] for deraining; and MIRNetv2 [52], DLN [46] and ZeroDCE [9] for low-light enhancement. The results in Figure 7 (for defocus deblurring and low-light enhancement) and supplemental material (for motion deblurring and deraining) show that, the extracted fingerprints exhibit discriminative patterns, and meanwhile they remain similar under pruning and quantization attacks.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion and Discussion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Given the prevalence of DNN models used in image restoration, protecting their IPR has become increasingly important. Toward this end, we proposed a non-intrusive fingerprinting framework for verifying the model ownership of image restoration DNNs, with its effectiveness demonstrated in two important tasks: image denoising and SR. Similar to existing white-box methods, ours requires the access to model weights. One possible future direction is exploring online model encryption techniques to extend our approach to the black-box setting. In addition, the theoretical aspects of the critical image such as uniqueness, as well as the extensions to other low-level vision DNNs, will be investigated in our future work.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "13292",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Yossi Adi, Carsten Baum, Moustapha Cisse, Benny Pinkas, and Joseph Keshet. Turning your weakness into a strength: Watermarking deep neural networks by backdooring. In USENIX Security Symposium, pages 1615-1631, Baltimore, MD, 2018. USENIX Association. 1, 3",
+            "[2] Saeed Anwar and Nick Barnes. Densely Residual Laplacian Super-Resolution. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(3):1192–1204, Mar. 2022. 5",
+            "[3] Xiaoyu Cao, Jinyuan Jia, and Neil Zhenqiang Gong. Ipguard: Protecting intellectual property of deep neural networks via fingerprinting the classification boundary. In Proceedings of ACM Asia Conference on Computer and Communications Security, pages 14-25, 2021. 1, 3, 6",
+            "[4] Huili Chen, Bita Darvish Rouhani, Cheng Fu, Jishen Zhao, and Farinaz Koushanfar. Deepmarks: A secure fingerprinting framework for digital rights management of deep learning models. In Proceedings of International Conference on Multimedia Retrieval, pages 105-113, 2019. 3",
+            "[5] Jialuo Chen, Jingyi Wang, Tinglan Peng, Youcheng Sun, Peng Cheng, Shouling Ji, Xingjun Ma, Bo Li, and Dawn Song. Copy, right? a testing framework for copyright protection of deep learning models. In IEEE Symposium on Security and Privacy, pages 824-841. IEEE, 2022. 3",
+            "[6] Liangyu Chen, Xiaojie Chu, Xiangyu Zhang, and Jian Sun. Simple Baselines for Image Restoration, Aug. 2022. 5, 8",
+            "[7] Lixin Fan, Kam Woh Ng, and Chee Seng Chan. Rethinking deep neural network ownership verification: Embedding passports to defeat ambiguity attacks. Advances in Neural Information Processing Systems, 32, 2019. 1, 3",
+            "[8] Xiquan Guan, Huamin Feng, Weiming Zhang, Hang Zhou, Jie Zhang, and Nenghai Yu. Reversible watermarking in deep convolutional neural networks for integrity authentication. In Proceedings of ACM International Conference on Multimedia, pages 2273-2280, 2020. 1, 3",
+            "[9] Chunle Guo, Chongyi Li, Jichang Guo, Chen Change Loy, Junhui Hou, Sam Kwong, and Runmin Cong. Zero-reference deep curve estimation for low-light image enhancement. In Proceedings of IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1780-1789, 2020. 8",
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+        ],
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diff --git a/2023/Fingerprinting Deep Image Restoration Models/2d0eb633-eeca-41e3-8998-eafb5489c443_model.json b/2023/Fingerprinting Deep Image Restoration Models/2d0eb633-eeca-41e3-8998-eafb5489c443_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..72487409cbca49845d48acbfb854ef7a637f7833
--- /dev/null
+++ b/2023/Fingerprinting Deep Image Restoration Models/2d0eb633-eeca-41e3-8998-eafb5489c443_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "content": "CVF"
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Fingerprinting Deep Image Restoration Models"
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+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Yuhui Quan\\(^{1,2}\\)"
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+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Huan Teng<sup>1,3</sup>"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.583,
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+            ],
+            "angle": 0,
+            "content": "Ruotao \\(\\mathbf{X}\\mathbf{u}^{1,2}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Jun Huang<sup>3</sup>"
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+            "type": "text",
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+            "angle": 0,
+            "content": "Hui Ji"
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+            "angle": 0,
+            "content": "\\(^{1}\\)School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "\\(^{2}\\)Pazhou Lab, Guangzhou 510335, China"
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+            "content": "<sup>3</sup>Platform of AI, Alibaba Group, Hangzhou 311121, China"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "\\(^{4}\\)Department of Mathematics, National University of Singapore, Singapore 119076"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.287,
+                0.314,
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.318,
+                0.473,
+                0.591
+            ],
+            "angle": 0,
+            "content": "Fingerprinting is a promising non-invasive method for protecting the intellectual property rights (IPR) of deep neural network (DNN) models. It extracts a feature called a fingerprint from a DNN model to identify its ownership. Existing fingerprinting methods focus only on classification-related models that map images to labels, while inapplicable to models for image restoration that map images to images. This paper proposes a fingerprinting framework for DNN models of image restoration. The proposed framework defines the fingerprint using a critical image, which exhibits strongly discriminative patterns and is robust to modest model modifications. Model ownership is then verified by comparing the distance of color histograms and local gradient pattern histograms of critical images between the suspect and source models. We apply the proposed framework to two representative tasks, denoising and super-resolution. It outperforms the baselines of fingerprinting and competes against existing invasive model watermarking methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.617,
+                0.21,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.643,
+                0.47,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Deep learning has become a prominent tool for solving problems in computer vision, ranging from high-level image classification problems to low-level image restoration problems. However, the cost of designing and training a DNN model for specific applications has grown exponentially, leading to expenses in many areas such as hardware resources, data collection and labeling, and paying for engineers and researchers. Although sharing pre-trained DNN models has become a common practice in the community, many companies and institutes charge for the commercial usage of pre-trained models. This creates a strong incentive"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.288,
+                0.892,
+                0.363
+            ],
+            "angle": 0,
+            "content": "for adversaries to plagiarize/steal the models, using methods such as malware infection or internal leaks, to bypass the expensive training process. Consequently, both the community and companies have a strong motivation to protect the IPR of their DNN models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.365,
+                0.893,
+                0.47
+            ],
+            "angle": 0,
+            "content": "One popular approach for protecting the IPR of DNN models is model watermarking (e.g. [44, 1, 10, 7, 53, 8, 39, 20, 54, 21]), which invasively embeds specific information called watermark into the source model and examines its existence in the suspect model for ownership verification. However, modifying model weights can potentially affect the model's utility, making it less desirable in practice."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.472,
+                0.893,
+                0.608
+            ],
+            "angle": 0,
+            "content": "Recently, a non-invasive approach called model fingerprinting has gained attention. Unlike watermarking, fingerprinting keeps the model intact and creates a unique feature called fingerprint from the model for identifying ownership. The ownership of a model is verified by comparing the fingerprint of the source model with that of the suspect model. While fingerprinting is still in its early stages with few existing works [3, 24, 11, 60, 33], it is gaining popularity as a non-invasive alternative to model watermarking."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.619,
+                0.622,
+                0.634
+            ],
+            "angle": 0,
+            "content": "1.1. Motivation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.892,
+                0.764
+            ],
+            "angle": 0,
+            "content": "In this paper, we focus on protecting the IPR of DNN models used for low-level image restoration tasks. These types of models map degraded images or measurements to high-quality target images. Deep learning has proven to be a powerful tool for solving a variety of image restoration problems, e.g., image denoising [57, 35, 36, 32], superresolution (SR) [22, 47, 59, 43, 15], deblurring [58, 29, 40, 17, 41], and bad weather removal [34, 45, 37, 50, 51, 38]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Most existing works on IPR protection for DNN models focus on high-level vision tasks such as image classification, where the DNN outputs a label in a finite discrete set. In contrast, DNN models for image restoration output an image in a very high-dimensional space. Though there are a few works on watermarking DNN models for various image restoration tasks (e.g.[53, 39, 54]), these image restoration models can be vulnerable to modifications of DNN weights required in watermarking, resulting in the loss of important"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "*Corresponding author: Ruotao Xu (xrt@scut.edu.cn). This work is supported by the Natural Science Foundation of Guangdong Province (Grant No. 2023A1515012841, 2022A1515011755, 2022A1515011087); National Natural Science Foundation of China (Grant No. 62106077); Postdoctoral Special Foundation of China (Grant No. 2022T150219); Postdoctoral Foundation of China (Grant No. 2020M682705); and Singapore MOE AcRF Tier 1 (Grant No. A-8000981-00-00)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "13285"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.089,
+                0.46,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.249,
+                0.47,
+                0.294
+            ],
+            "angle": 0,
+            "content": "Figure 1: Main idea of our model fingerprinting approach for an image recovery DNN. We aim to find a critical image (blue point) around the DNN's performance border zone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.324,
+                0.423,
+                0.339
+            ],
+            "angle": 0,
+            "content": "image details and the addition of undesired artifacts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.339,
+                0.47,
+                0.549
+            ],
+            "angle": 0,
+            "content": "Fingerprinting is a more attractive option for image restoration DNNs, as it does not require any modification to model weights. However, to the best of our knowledge, no existing study has explored fingerprinting for DNN models used in image restoration tasks. The existing fingerprinting methods are designed for classification DNNs which can be fully characterized by their decision boundaries. These methods use adversarial examples to characterize the decision boundaries and generate a fingerprint for the model. In contrast, image restoration generates an image in a high-dimensional space, and its accuracy is measured by a continuous metric such as mean squared error to the ground truth. Therefore, the concept of \"decision boundary\" is not well-defined for image restoration models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.551,
+                0.47,
+                0.641
+            ],
+            "angle": 0,
+            "content": "Due to the significant differences between image restoration and image classification, the existing fingerprinting methods for classification DNNs cannot be easily extended to image restoration DNNs. As a result, we were motivated to develop a new fingerprinting framework specifically designed for image restoration DNN models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.651,
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+            ],
+            "angle": 0,
+            "content": "1.2. Main Idea"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.468,
+                0.809
+            ],
+            "angle": 0,
+            "content": "An image restoration task (e.g. denoising and SR) is to predict a latent image \\(\\mathbf{X}\\) from its degraded or partial measurements \\(\\mathbf{Y} = \\mathcal{D}(\\mathbf{X})\\), where \\(\\mathcal{D}\\) denotes the degrading/measuring process. In deep learning, a DNN model \\(\\mathcal{M}: \\mathbb{R}^{n \\times m} \\to \\mathbb{R}^{N \\times M}\\) is trained to accurately predict \\(\\mathbf{X}\\) from the input \\(\\mathcal{D}(\\mathbf{X})\\) in some task-related domain \\(\\mathbb{D}\\). While the prediction error for most images in \\(\\mathbb{D}\\), measured by \\(\\| \\mathbf{X} - \\mathcal{M}(\\mathcal{D}(\\mathbf{X})) \\|_2^2\\), is small, there exists a complementary set \\(\\overline{\\mathbb{D}}\\) where the DNN has large prediction errors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Indeed, an image restoration DNN usually works well only for target images that lie within a low-dimensional manifold in \\(\\mathbb{R}^{N\\times M}\\). It is not expected that a DNN will perform well for all points in \\(\\mathbb{R}^{N\\times M}\\). For instance, consider image denoising where \\(\\mathbf{Y} = \\mathcal{D}(\\mathbf{X}) = \\mathbf{X} + \\mathbf{N}\\), with \\(\\mathbf{N}\\) representing Gaussian white noise. Let \\(\\mathbf{X}_1\\) be a constant matrix"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.272
+            ],
+            "angle": 0,
+            "content": "and \\(\\mathbf{X}_2\\) be a random matrix with entries randomly sampled from a normal distribution. Since adding two independent Gaussian random variables results in a new Gaussian random variable [18], \\(\\mathbf{Y}_2\\) also corresponds to a constant image corrupted by larger Gaussian white noise. Suppose a denoising model performs well on predicting \\(\\mathbf{X}_1\\) (a constant matrix) from its noisy version \\(\\mathbf{Y}_1\\). Then, the denoiser will consistently take \\(\\mathbf{Y}_2\\) as the noisy version of a constant matrix and output a constant matrix, which is far away from the ground-truth matrix \\(\\mathbf{X}_2\\) (a random matrix). In other words, a denoising model designed to work well for constant matrices may not work well for random matrices."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.273,
+                0.892,
+                0.426
+            ],
+            "angle": 0,
+            "content": "To summarize, just like the decision boundary in classification, there exists a \"performance border zone\" that separates the set of images that the restoration model can accurately restore and the set of images that it cannot. This zone encodes essential characteristics of the model, and the points close to it can be used for its characterization. Particularly, these points can be the images in the complementary set \\(\\overline{\\mathbb{D}}\\) that are close to the set \\(\\mathbb{D}\\) of images that the DNN can restore accurately (i.e., their prediction errors by the DNN are small). See Figure 1 for an illustration of this concept."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.426,
+                0.892,
+                0.56
+            ],
+            "angle": 0,
+            "content": "In this paper, we define the term \"critical images\" to refer to the points near the performance border zone. Suppose that the target images in \\(\\mathbb{D}\\) follow some prior, such as the sparsity prior of gradients. Then, a critical image for the model \\(\\mathcal{M}\\) is an image \\(\\mathbf{X}\\) that minimizes the prediction error \\(\\| \\mathbf{X} - \\mathcal{M}(\\mathcal{D}(\\mathbf{X}))\\|_2^2\\) (i.e., \\(\\mathbf{X}\\) is close to \\(\\mathbb{D}\\)) while also maximizing a penalty that reflects the prior on the images in \\(\\mathbb{D}\\) (i.e., \\(\\mathbf{X}\\) is close to \\(\\bar{\\mathbb{D}}\\)). This ensures that \\(\\mathbf{X}\\) is simultaneously close to both \\(\\mathbb{D}\\) and \\(\\bar{\\mathbb{D}}\\), i.e., it lies near their border zone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.563,
+                0.892,
+                0.7
+            ],
+            "angle": 0,
+            "content": "Empirical observations suggest that the critical images obtained from independently-trained DNNs using the proposed approach consist of strong spatial patterns that not only convey discriminative information, but are also robust to moderate modifications in model weights. Therefore, these critical images can serve as the fingerprints of a model. For model verification, we measure the distances between the fingerprints using two standard image descriptors: color histograms and local gradient patterns (LGP) [13]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.71,
+                0.644,
+                0.726
+            ],
+            "angle": 0,
+            "content": "1.3. Contributions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The construction of a critical image forms the foundation of our proposed fingerprinting approach for image restoration models. Our approach is applied to two representative image restoration tasks: denoising and SR. Denoising is a core problem in many image restoration tasks, and SR is one of the most successful applications of deep learning in image restoration. Extensive experiments on these two tasks have demonstrated that our proposed approach is more robust than the baseline fingerprinting methods and competitive with recent intrusive watermarking methods. See below for a summary of the main contributions:"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13286"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.092,
+                0.468,
+                0.152
+            ],
+            "angle": 0,
+            "content": "- A fingerprinting framework is proposed for protecting the IPR of image restoration DNN models. To the best of our knowledge, this is the first study on fingerprinting DNN models of image restoration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.156,
+                0.468,
+                0.201
+            ],
+            "angle": 0,
+            "content": "- Analogous to decision boundaries in classification, the concept of performance border zone is introduced to characterize image restoration DNN models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.205,
+                0.468,
+                0.265
+            ],
+            "angle": 0,
+            "content": "- The concept of critical images, points in proximity to the performance border zone, is introduced to showcase discriminative and robust patterns that can serve as effective fingerprints for image restoration DNN models."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.088,
+                0.092,
+                0.468,
+                0.265
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.279,
+                0.227,
+                0.295
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.304,
+                0.282,
+                0.32
+            ],
+            "angle": 0,
+            "content": "2.1. Model Fingerprinting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.327,
+                0.468,
+                0.492
+            ],
+            "angle": 0,
+            "content": "Model fingerprinting shares a similar spirit with the zerowatermarking for digital images (e.g. [48]), where discriminative yet robust features are extracted from an image to represent its ownership. While it is possible to extract features directly from the weights of a DNN by treating them as digital media, this method is not robust to modifications of the model. To improve robustness, existing works [3, 24, 11, 60, 60, 33] extract features from the decision boundaries of a classification DNN, as these features are often transferable for plagiarism models but not for independently-trained models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.493,
+                0.468,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Cao et al. [3] proposed to fingerprint decision boundaries via using nearby data points defined by adversarial examples. The ownership is verified by checking whether the suspect model predicts the same labels as the source model on those data points. Lukas et al. [24] proposed to fingerprint the overlap of adversarial subspaces around decision boundaries between the source model and its surrogates. They synthesized conferrable adversarial examples that transfer exclusively with a target label from the source model to its surrogates. Zhao et al. [60] proposed to improve adversarial examples for fingerprinting by encouraging them to mimic the logits vector of a target sample randomly chosen from the target category. Peng et al. [33] proposed to profile decision boundaries by characterizing the universal adversarial perturbations [26]. Additionally, they trained an encoder via contrastive learning to map fingerprints from two models to a similarity score for ownership verification. Chen et al. [5] proposed to quantify the similarity between two models using a diverse set of testing metrics and test case generation algorithms to produce a chain of evidence for verification. This method can include many existing fingerprinting algorithms as test metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.826,
+                0.468,
+                0.899
+            ],
+            "angle": 0,
+            "content": "All the methods discussed above are limited to classification DNNs. Our approach, however, is specifically designed for fingerprinting models of image restoration by using critical images instead of adversarial examples. It is noted that while the aforementioned methods aim to detect"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "model plagiarism, He et al. [11] proposed a fingerprinting method to examine model integrity. This method identifies a small set of human-unnoticeable transformed inputs that make a model's outputs sensitive to its parameters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.163,
+                0.704,
+                0.179
+            ],
+            "angle": 0,
+            "content": "2.2. Model Watermarking"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.186,
+                0.892,
+                0.488
+            ],
+            "angle": 0,
+            "content": "Model watermarking serves a similar purpose as model fingerprinting; however, it involves embedding a code or opening a backdoor inside a DNN that could potentially harm the DNN's performance. Most existing watermarking methods are designed for classification DNNs (e.g. [44, 42, 56, 1, 10, 27, 4, 28, 7, 16, 53, 8, 20, 54, 21, 19, 23]), but there are also a few works that target image restoration DNN models (e.g. [53, 39, 31, 54]). Zhang et al. [53, 54] proposed to train the DNN to automatically embed an invisible watermark in its output image. The model ownership is verified by detecting the presence of watermarks in the output images of the suspect DNN. Quan et al. [39] proposed to train the DNN to map a random image to its naive recovered version that is unlikely to be generated by other independently well-trained DNNs. The model ownership is verified by checking whether such a mapping holds for the suspect DNN. Ong et al. [31] proposed to train the DNN so that an input image embedded with a visible key can lead to an output image with a visible logo. The model ownership is verified by attempting to trigger the logo via the key."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.502,
+                0.635,
+                0.519
+            ],
+            "angle": 0,
+            "content": "3. Methodology"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.528,
+                0.795,
+                0.542
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Statement and Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.551,
+                0.892,
+                0.732
+            ],
+            "angle": 0,
+            "content": "Threat model In a typical attack-defense scenario, an owner has trained a source model using private resources. An adversary attempts to plagiarize or steal the model. The owner is both a victim and a defender, with the goal of determining whether the suspect model is a plagiarized one. This involves verifying ownership in a white-box setting. An adversary or attacker who steals a model may modify it to avoid detection of ownership while maintaining its functionality and performance, but the access to the original training data is not given. Under this setting, we consider often-seen attacks that modify model weights, e.g., pruning, finetuning, and quantization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Principles Discriminability is a fundamental property of model fingerprinting. A model fingerprint is trustworthy for protecting IPR only if it is distinguishable for different models. Given the importance of training data and open sources of DNN architecture, two models with the same architecture but trained independently using different data are considered as independent models, and their fingerprints should be distinguishable from each other. Robustness is another critical property of model fingerprinting. A model fingerprint is expected to remain nearly unchanged under various modifications (attacks) on the model. However, these two"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13287"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.089,
+                0.468,
+                0.26
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.099,
+                0.263,
+                0.446,
+                0.278
+            ],
+            "angle": 0,
+            "content": "Figure 2: Proposed model fingerprinting framework."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.306,
+                0.47,
+                0.382
+            ],
+            "angle": 0,
+            "content": "properties often conflict with each other, and an ideal model fingerprinter should balance them carefully. It is worth noting that the fidelity of model performance, a desirable property for model watermarking, is not necessary for a non-invasive method like fingerprinting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.384,
+                0.469,
+                0.52
+            ],
+            "angle": 0,
+            "content": "**Framework** The proposed fingerprinting method for image restoration DNN models is outlined in Figure 2, involving 3 steps. First, a fingerprint defined over critical images is extracted from the source model and registered. Second, the fingerprint of a suspect model is computed for notarization. Finally, ownership is verified by comparing the features of the two fingerprints. The remaining issues are (i) how to extract a discriminative yet robust fingerprint from a model, and (ii) how to efficiently compare two fingerprints."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.528,
+                0.291,
+                0.544
+            ],
+            "angle": 0,
+            "content": "3.2. Fingerprint Extraction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.552,
+                0.469,
+                0.717
+            ],
+            "angle": 0,
+            "content": "As discussed in Section 1.2, we use critical images to fingerprint a model. These critical images are located near the performance border zone of an image restoration DNN. Now we focus on the restoration problems for natural images which are assumed to follow a Laplacian prior. Such a prior is generally true for natural images. Specifically, the total variation (TV) \\( |\\nabla \\mathbf{X}|_1 \\) of an image \\( \\mathbf{X} \\) in the domain \\( \\mathbb{D} \\) is small, while an image \\( \\overline{\\mathbf{X}} \\) in \\( \\overline{\\mathbb{D}} \\) has a large value of \\( |\\nabla \\overline{\\mathbf{X}}|_1 \\). Our proposed approach is also applicable to images in other domains, provided that there is some prior knowledge available for latent images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.718,
+                0.469,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Given a DNN model \\(\\mathcal{M}\\) trained for an image restoration task \\(\\mathcal{T}\\), we define the critical image \\(\\mathbf{S}\\) by solving the following optimization problem:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.772,
+                0.469,
+                0.801
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {S} := \\underset {\\overline {{\\mathbf {X}}} \\in [ 0, 1 ] ^ {M \\times N}} {\\arg \\min } \\| \\overline {{\\mathbf {X}}} - \\mathcal {M} \\left(\\mathcal {D} _ {\\mathcal {T}} (\\overline {{\\mathbf {X}}})\\right) \\| _ {2} ^ {2} - \\lambda \\| \\nabla \\overline {{\\mathbf {X}}} \\| _ {1}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{D}_{\\mathcal{T}}\\) denotes a degradation operator associated with the task \\(\\mathcal{T}\\), and \\(\\lambda \\in \\mathbb{R}^{+}\\) is a weight. The objective of the first term in (1) is to find an image close to the set \\(\\mathbb{D}\\). The second term encourages the image to be close to \\(\\overline{\\mathbb{D}}\\). This is achieved by maximizing the value of \\(\\| \\nabla \\overline{\\mathbf{X}} \\|_1\\), which is a necessary condition for images in \\(\\overline{\\mathbb{D}}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "The operator \\(\\mathcal{D}_{\\mathcal{T}}\\) varies depending on the specific image restoration task. For instance, it corresponds to noise corruption for image denoising, downsampling for image SR, and blurring for image deblurring. For image denoising and SR, we adopt the following construction schemes for \\(\\mathcal{D}_{\\mathcal{T}}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.511,
+                0.175,
+                0.892,
+                0.193
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} + \\mathbf {N}, \\quad \\mathbf {N} \\sim \\mathcal {N} (\\mathbf {0}, \\sigma^ {2} \\mathbf {I}), \\quad [ \\text {D e n o i s i n g} ] \\tag {2}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.513,
+                0.195,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} \\downarrow_ {4}, \\quad [ \\text {I m a g e S R} ] \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.221,
+                0.891,
+                0.266
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{N}\\) denotes normal distribution and \\(\\downarrow_4\\) denotes dyadic downsampling that reduces the image size by half. The definition of \\(\\mathcal{D}_{\\mathcal{T}}\\) can be adapted to other restoration tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.267,
+                0.892,
+                0.341
+            ],
+            "angle": 0,
+            "content": "To solve (1), we use the Adam solver [14]. However, since the problem involves a DNN, it is highly non-convex, and the output of an iterative solver depends on the initialization of \\(\\mathbf{X}\\). We use random initialization for solving (1), i.e., we set \\(\\mathbf{S}^{(0)}\\), the initial point of \\(\\mathbf{S}\\), as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.602,
+                0.35,
+                0.892,
+                0.367
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {S} ^ {(0)} \\sim \\mathcal {N} (\\mathbf {0}, \\beta^ {2} \\mathbf {I}), \\quad \\beta \\in \\mathbb {R}. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.376,
+                0.892,
+                0.451
+            ],
+            "angle": 0,
+            "content": "Figure 3 illustrates the critical images calculated using different instances of \\(\\mathbf{S}^{(0)}\\) generated via (4). We observe that critical images from the same model with different \\(\\mathbf{S}^{(0)}\\) exhibit similar (homogeneous) patterns, while those from different models differ significantly from each other."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.453,
+                0.892,
+                0.497
+            ],
+            "angle": 0,
+            "content": "Next, we construct the fingerprint denoted by \\(\\mathcal{F}\\) via (1). To form a fingerprint of arbitrary length, one can solve (1) for multiple times using different \\(\\mathbf{S}^{(0)}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.587,
+                0.506,
+                0.891,
+                0.526
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {F} = \\left\\{\\left(\\mathbf {S} _ {1} ^ {(0)}, \\mathbf {S} _ {1}\\right), \\dots , \\left(\\mathbf {S} _ {K} ^ {(0)}, \\mathbf {S} _ {K}\\right) \\right\\}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.536,
+                0.892,
+                0.703
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{S}_k\\) is the critical image calculated using \\(\\mathbf{S}_k^{(0)}\\) as the initial point for solving (1). Note that different \\(\\mathbf{S}_k\\) of the same model contain the same patterns (see Figure 3) and image restoration models usually allow input (output) images of varying sizes. To obtain a similar amount of fingerprint information while avoiding multiple extractions, we can set \\(K = 1\\) and use a single large \\(\\mathbf{S}\\) to approximate multiple \\(\\mathbf{S}_k\\) of smaller sizes. It is worth noting that solving \\(\\mathbf{S}_k\\) from (1) does not require accessing the model weights of \\(\\mathcal{M}\\), but only the gradients of \\(\\mathcal{M}(\\mathcal{D}_{\\mathcal{T}}(\\overline{\\mathbf{X}}))\\) w.r.t. \\(\\overline{\\mathbf{X}}\\), in a similar spirit to federated learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.712,
+                0.734,
+                0.728
+            ],
+            "angle": 0,
+            "content": "3.3. Verification of Ownership"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Verification of ownership is accomplished by comparing fingerprints between the source and suspect models. While critical images can be visually compared, automated verification is often desirable in practice. Because critical images display distinct patterns in terms of color distribution and texture, we characterize them using color histograms (a standard color descriptor) and an improved version of LGP histograms [13] (a classic texture descriptor) based on the idea of [30]. Further details can be found in the supplemental material. Our approach is learning-free and does not require collecting training data for a learning-based verifier."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.956
+            ],
+            "angle": 0,
+            "content": "13288"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.088,
+                0.468,
+                0.24
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.243,
+                0.472,
+                0.292
+            ],
+            "angle": 0,
+            "content": "Figure 3: Critical images of DBSN [49] (upper) and EDSR [22] (bottom) calculated by using \\(\\mathbf{S}^{(0)}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) while fixing all other hyper-parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.318,
+                0.473,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Let \\( h_{\\mathrm{su}} \\), \\( h_{\\mathrm{sus}} \\in \\mathbb{R}^L \\) be the features. i.e., the concatenation of normalized color and LGP histograms, computed from the fingerprints of the source model and the suspect model, respectively. When \\( K > 1 \\), the features from multiple \\( \\mathbf{S}_k \\) are averaged. In essence, these features serve as a refined version of the fingerprints. Then the suspect model will be identified as plagiarism if"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.436,
+                0.47,
+                0.457
+            ],
+            "angle": 0,
+            "content": "\\[\nd = \\left\\| \\boldsymbol {h} _ {\\text {s o u}} - \\boldsymbol {h} _ {\\text {s u s}} \\right\\| _ {2} ^ {2} / L <   \\eta , \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.464,
+                0.473,
+                0.62
+            ],
+            "angle": 0,
+            "content": "where \\(\\eta\\) is a threshold (the bound of negligible error) determined by a probabilistic scheme with the same spirit of [39]. Suppose that the error \\(e(j) = h_{\\mathrm{su}}(j) - h_{\\mathrm{sus}}(j)\\sim \\mathcal{N}(0,\\sigma^2),\\forall j\\) , where \\(\\sigma = 0.015\\) (see supplemental material for our idea to determine this value). Then, the random variable \\(Z = \\frac{\\|e\\|_2^2}{\\sigma^2}\\) follows a Chi-squared distribution \\(\\mathcal{X}_L^2\\) . By applying the \\(p\\) -value approach with \\(p <   0.05\\) , we can find a value of \\(\\gamma\\) such that \\(P[Z\\leq \\gamma ] <   0.05\\) , or equivalently, \\(P[d\\leq \\eta ] <   0.05\\) . This allows us to safely reject the null hypothesis that \\(h_\\mathrm{su}\\) and \\(h_\\mathrm{sus}\\) are similar."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.632,
+                0.212,
+                0.649
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.657,
+                0.47,
+                0.703
+            ],
+            "angle": 0,
+            "content": "We assess the effectiveness of the proposed approach for two restoration tasks, namely image denoising and image SR, by measuring their discriminability and robustness."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.712,
+                0.268,
+                0.729
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Source models We choose six DNNs from existing literature as the source models for each task, respectively. (a) Image denoising: DnCNN [57], DBSN [49], Nei2Nei [12], Restormer [50], SimBase [6], and NAFNet [6]; (b) Image SR: EDSR [22], RRDBNet [47], RNAN [59], MobileSR [43], RFLN [15], and DRLN [2]. To comprehensively evaluate the effectiveness of fingerprinting, we consider models with varying structures, training data, and training strategies, for both tasks. We either use the pretrained models or train them using their released codes. See more details in the supplemental material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.26
+            ],
+            "angle": 0,
+            "content": "Implementation details In fingerprint extraction, we use a single critical image of size \\(128 \\times 128\\), for all models in both tasks. We set \\(\\beta = 1\\) in (4) for initializing \\(\\mathbf{X}\\). The learning rate of Adam for solving (1) is set to 0.1. A total number of 5000 iterations is used. In ownership verification, we form a 30-dimensional RGB+LGP histogram. The resulting threshold is \\(\\eta = 1.39 \\times 10^{-4}\\). For denoising DNNs, we set \\(\\sigma = 1\\) for constructing \\(\\mathcal{D}_{\\mathcal{T}}\\) in (2). For both denoising and SR, we set \\(\\lambda = 0.001\\). The seeds involved in our approach are fixed to make the whole process deterministic and reproducible."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.268,
+                0.733,
+                0.285
+            ],
+            "angle": 0,
+            "content": "4.2. Discriminability Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.292,
+                0.892,
+                0.474
+            ],
+            "angle": 0,
+            "content": "We begin by a visual inspection on the fingerprints extracted via our approach. See Figure 4 for the critical images extracted from various source models, all of which contain unique and distinguishable patterns that vary in scale, appearance, local shape, regularity and color, across different images. For instance, larger-scale patterns are visible for SimBase while the smaller-scale ones for DnCNN. The fingerprint of DnCNN exhibits random patterns, while that of NAFNet shows regular ones. Moreover, the red tone of fingerprint of NAFNet differs from the chromatic tone of SimBase. These significant visual differences demonstrate the strong discriminability of the extracted fingerprints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.474,
+                0.893,
+                0.639
+            ],
+            "angle": 0,
+            "content": "The discriminability is further quantitatively assessed by computing the feature distances (6) between critical images for every pair of source models. The distance matrices in Figure 5(a) and (b) show the ratios between the resulting distances and the threshold \\(\\eta\\), for denoising DNNs and SR DNNs, respectively. In both tasks, all off-diagonal elements, i.e., distances between every model pair, exceed the threshold, indicating no confusion among the models. The results indicate excellent discriminability of our extracted critical images, and the simple RGB+LGP histograms are able to effectively capture their patterns for verification."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.64,
+                0.895,
+                0.777
+            ],
+            "angle": 0,
+            "content": "We also test whether our approach can differentiate models with the same architecture but trained on different datasets. The Restormer model [50] is retrained on six different datasets; see the details in the supplemental material. Figure 4(c) visually compares the fingerprints of each model, and Figure 5(c) shows the resulting distance matrix. Our approach effectively differentiates the models, even those with the same architecture, with many large off-diagonal values observed in the distance matrix."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.694,
+                0.803
+            ],
+            "angle": 0,
+            "content": "4.3. Robustness Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We conduct robustness analysis using three common attacks: model pruning, model finetuning, and model quantization. A meaningful attack should only have a minor effect on the original function of a model. For analysis, we quantify the impact of an attack on the model's performance based on the resulting average PSNR gap on the recovered"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "13289"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.092,
+                0.344,
+                0.257
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.117,
+                0.26,
+                0.309,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(a) Fingerprints of denoising models"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.352,
+                0.092,
+                0.615,
+                0.256
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.405,
+                0.26,
+                0.562,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(b) Fingerprints of SR models"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.622,
+                0.092,
+                0.887,
+                0.257
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.623,
+                0.26,
+                0.884,
+                0.27
+            ],
+            "angle": 0,
+            "content": "(c) Fingerprints of independent Restormer models"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.224,
+                0.273,
+                0.744,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Figure 4: Fingerprints (critical images) extracted from different source models."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.079,
+                0.304,
+                0.344,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.156,
+                0.471,
+                0.27,
+                0.482
+            ],
+            "angle": 0,
+            "content": "(a) Denoising models"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.349,
+                0.304,
+                0.616,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.447,
+                0.471,
+                0.524,
+                0.482
+            ],
+            "angle": 0,
+            "content": "(b) SR models"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.622,
+                0.304,
+                0.889,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.64,
+                0.471,
+                0.875,
+                0.482
+            ],
+            "angle": 0,
+            "content": "(c) Restomers trained with different datasets."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.486,
+                0.893,
+                0.532
+            ],
+            "angle": 0,
+            "content": "Figure 5: Visualization of pairwise feature distance of fingerprints between source models. The ratios between the distance and the threshold are shown. For better illustration, all the color bars are set as follows. The color goes from purple to blue when the value decreases from 1, while the color goes from orange to yellow when the value increases from 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.561,
+                0.47,
+                0.636
+            ],
+            "angle": 0,
+            "content": "images. Each attack has its strength controlled such that it only leads to \\(\\leq 1\\mathrm{dB}\\) change in the average PSNR value for all the models on a test set. This ensures that all attacks are not meaningless. The robustness is measured by the times of successful ownership verification under an attack."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.64,
+                0.47,
+                0.715
+            ],
+            "angle": 0,
+            "content": "Baselines So far, no fingerprinting method is available that is specifically designed for image restoration DNNs, making our work the first in this area. For experimental comparison, we construct two baselines by adapting existing fingerprint methods designed for classification DNNs:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.082,
+                0.72,
+                0.47,
+                0.809
+            ],
+            "angle": 0,
+            "content": "1. ProjCL: Each image restoration source model is converted to a classification DNN by adding a random projection layer with softmax activation in the end, so as to output a 100-dimensional label vector. Then, the well-known fingerprinting method IPGuard [3] is applied for the classification DNNs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.082,
+                0.811,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "2. PoolCL: The output of each source model is downsampled to form a \\(10 \\times 10\\) image, which is then vectorized and subjected to a Softmax function, producing a 100-dimensional label vector. This converts each source model into a classification DNN, and then we fingerprint it using the IPGuard [3]."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.082,
+                0.72,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.561,
+                0.892,
+                0.652
+            ],
+            "angle": 0,
+            "content": "We tune the baselines' hyper-parameters, including label vector dimensions, for their discriminability. We set their verification thresholds to the minimum values that ensure all tested models pass the discrimination test. These threshold values optimize the robustness metrics, as reducing the verification threshold improves robustness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.653,
+                0.892,
+                0.713
+            ],
+            "angle": 0,
+            "content": "Furthermore, we present three watermarking methods specifically designed for image restoration DNNs to compare the performance gap between non-invasive fingerprinting and invasive watermarking:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.716,
+                0.891,
+                0.746
+            ],
+            "angle": 0,
+            "content": "1. Zhang et al. [55]: The source model is retrained to embed an invisible watermark in each output."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.747,
+                0.892,
+                0.791
+            ],
+            "angle": 0,
+            "content": "2. Ong et al. [31]: The source model is retrained to composite a visible watermark region into the output when the input is composed of a specific trigger region."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.792,
+                0.891,
+                0.822
+            ],
+            "angle": 0,
+            "content": "3. Quan et al. [39]: The source model is retrained to produce a copyright image for a specific input noise."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.504,
+                0.716,
+                0.892,
+                0.822
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We tune the hyper-parameters for the watermark embedding in these methods to maintain high fidelity on the PSNR performance of the source models on test data. To facilitate a more informative comparison between fingerprinting and watermarking, we create a baseline called \"WeakWM\" by"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13290"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.086,
+                0.482,
+                0.339
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.185,
+                0.34,
+                0.382,
+                0.351
+            ],
+            "angle": 0,
+            "content": "(a) Fingerprints on denoising models."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.493,
+                0.087,
+                0.885,
+                0.34
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.606,
+                0.34,
+                0.769,
+                0.351
+            ],
+            "angle": 0,
+            "content": "(b) Fingerprints on SR models."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.18,
+                0.354,
+                0.788,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Figure 6: Fingerprints (critical images) calculated from different models under three attacks."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.385,
+                0.889,
+                0.71
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td colspan=\"8\">Image Denoising</td><td colspan=\"8\">Image SR</td></tr><tr><td></td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td></tr><tr><td rowspan=\"6\">Pruning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RNAN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan=\"6\">Finetuning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan=\"6\">Quantization</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>DRLN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>√</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td colspan=\"2\">Success Rate</td><td>67%</td><td>78%</td><td>100%</td><td>100%</td><td>100%</td><td>28%</td><td>100%</td><td>Success Rate</td><td>0%</td><td>61%</td><td>100%</td><td>100%</td><td>100%</td><td>22%</td><td>100%</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.142,
+                0.713,
+                0.825,
+                0.729
+            ],
+            "angle": 0,
+            "content": "Table 1: Verification under attacks. Blue: fingerprinting; Purple: watermarking; X: failure; \\( \\checkmark \\) : success."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.758,
+                0.47,
+                0.849
+            ],
+            "angle": 0,
+            "content": "reducing the watermark embedding strength of Quan et al.'s method [39] to a sufficiently low value where no significant loss in fidelity is observed. The fingerprints extracted by our approach for both tasks are shown in Figure 6, under various attacks. Verification results for different methods are listed in Table 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Model pruning We prune the source models by zeroing the top \\( p\\% \\) of smallest weights in the DNN's layers, where \\( p = 10 \\) for denoising and \\( p = 5 \\) for SR. The pat"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.758,
+                0.892,
+                0.895
+            ],
+            "angle": 0,
+            "content": "terns are nearly the same for both tasks under model pruning. Our approach achieves successful verification on all models under all pruning ratios for both tasks, outperforming the two baselines that fails in nearly half the cases. Notably, the baselines perform much worse for SR models than for denoising models. The baseline ProjCL fails in all SR cases, suggesting that the methods designed for classification DNNs are ineffective when applied to image restoration DNNs. The watermarking methods succeed for all mod"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13291"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "els, which is expected due to their invasive manner. However, when the watermark embedding strength is very weak, WeakWM fails in most cases during watermark verification."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.139,
+                0.468,
+                0.275
+            ],
+            "angle": 0,
+            "content": "Model finetuning We fine-tune the source models with their original tasks on the BSD68 dataset [25] for 500 iterations (steps). Little change can be observed in the patterns of the resulting critical images. Our fingerprinting approach and the three watermarking methods successfully verify all models. However, among the baselines, PoolCL fails in one denoising and one SR case, ProjCL fails in two denoising and all SR cases, and WeakWM succeeds only once in each task due to weak watermark strength."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.278,
+                0.468,
+                0.398
+            ],
+            "angle": 0,
+            "content": "Model quantization When Int8 quantization with simple rounding is applied to the source models, our approach still produces robust yet discriminative fingerprints. It successfully verifies all models, like the three watermarking methods. WeakWM only succeeds in one half cases. ProjCL fails in two denoising cases and all SR cases. PoolCL performs acceptably on denoising models but fails in a half of the SR cases."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.408,
+                0.229,
+                0.424
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.432,
+                0.469,
+                0.461
+            ],
+            "angle": 0,
+            "content": "We form additional two baselines of our approach for further study, which are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.082,
+                0.465,
+                0.469,
+                0.497
+            ],
+            "angle": 0,
+            "content": "1. w/o TV: Removing the TV (second term) in (1) for calculating the critical image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.502,
+                0.469,
+                0.578
+            ],
+            "angle": 0,
+            "content": "2. MaxObj: Replacing the critical image in our approach with an image generated by maximizing the objective function in (1) instead of minimizing it. The resulting image is expected to be as smooth as possible while hard to recover, which can be seen as an adversarial sample."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.081,
+                0.465,
+                0.469,
+                0.578
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.581,
+                0.469,
+                0.717
+            ],
+            "angle": 0,
+            "content": "For the \"w/o TV\" case, we observe that the resulting critical images tend to degenerate into a constant image easily for some models, meaning that its discriminability could not be guaranteed. Therefore, we only compare the success rates of MaxObj and our approach in terms of robustness. See Table 2 for the results, where our approach outperforms MaxObj. This may be because the fingerprints generated by MaxObj are not as close to the performance border zone as those generated by our approach."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.73,
+                0.462,
+                0.802
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Compression</td><td colspan=\"2\">Finetuning</td><td colspan=\"2\">Quantization</td></tr><tr><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td></tr><tr><td>MaxObj</td><td>5/6</td><td>4/6</td><td>6/6</td><td>4/6</td><td>6/6</td><td>3/6</td></tr><tr><td>Ours</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.1,
+                0.804,
+                0.445,
+                0.818
+            ],
+            "angle": 0,
+            "content": "Table 2: Success rates of baselines in ablation study."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.847,
+                0.369,
+                0.864
+            ],
+            "angle": 0,
+            "content": "4.5. Demos Beyond Denoising and SR"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To further examine the applicability of our approach to other image restoration tasks, we provide demos on addi"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.088,
+                0.885,
+                0.253
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.257,
+                0.892,
+                0.302
+            ],
+            "angle": 0,
+            "content": "Figure 7: Fingerprints calculated from different pre-trained and attacked DNN models on other tasks. See supplemental material for the results on deraining."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.331,
+                0.892,
+                0.377
+            ],
+            "angle": 0,
+            "content": "tional tasks: deblurring (including motion deblurring and defocus deblurring), deraining, and low-light enhancement. The operator \\(\\mathcal{D}_{\\mathcal{T}}\\)s are defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.388,
+                0.871,
+                0.405
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {K} \\otimes \\mathbf {X} + \\mathbf {N}, \\quad [ \\text {D e b l u r r i n g} ]\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.408,
+                0.872,
+                0.425
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\operatorname {N o r m} \\left(\\mathbf {X} ^ {3}\\right), \\quad [ \\text {L o w - l i g h t E n h a n c e m e n t} ]\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.428,
+                0.872,
+                0.444
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} + \\mathbf {R}, \\quad [ \\text {D e r a i n i n g} ]\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.454,
+                0.892,
+                0.666
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{K}\\) is a blur kernel, \\(\\mathrm{Norm}(\\cdot)\\) denotes min-max normalization, and \\(\\mathbf{R}\\) is a synthetic rain layer; see supplemental material for details. We select three DNNs with published pre-trained models for each task: IFAN [17], GKMNet [40] and NRKNet [41] for defocus deblurring; Restormer [50], SimBase [6] and NAFNet [6] for motion deblurring; Restormer [50], MPRNet [51] and VRGNet [45] for deraining; and MIRNetv2 [52], DLN [46] and ZeroDCE [9] for low-light enhancement. The results in Figure 7 (for defocus deblurring and low-light enhancement) and supplemental material (for motion deblurring and deraining) show that, the extracted fingerprints exhibit discriminative patterns, and meanwhile they remain similar under pruning and quantization attacks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.68,
+                0.747,
+                0.695
+            ],
+            "angle": 0,
+            "content": "5. Conclusion and Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Given the prevalence of DNN models used in image restoration, protecting their IPR has become increasingly important. Toward this end, we proposed a non-intrusive fingerprinting framework for verifying the model ownership of image restoration DNNs, with its effectiveness demonstrated in two important tasks: image denoising and SR. Similar to existing white-box methods, ours requires the access to model weights. One possible future direction is exploring online model encryption techniques to extend our approach to the black-box setting. In addition, the theoretical aspects of the critical image such as uniqueness, as well as the extensions to other low-level vision DNNs, will be investigated in our future work."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13292"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+            ],
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+# Fingerprinting Deep Image Restoration Models
+
+Yuhui Quan $^{1,2}$
+
+Huan Teng<sup>1,3</sup>
+
+Ruotao  $\mathbf{X}\mathbf{u}^{1,2}$
+
+Jun Huang<sup>3</sup>
+
+Hui Ji
+
+$^{1}$ School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China
+
+$^{2}$ Pazhou Lab, Guangzhou 510335, China
+
+<sup>3</sup>Platform of AI, Alibaba Group, Hangzhou 311121, China
+
+$^{4}$ Department of Mathematics, National University of Singapore, Singapore 119076
+
+# Abstract
+
+Fingerprinting is a promising non-invasive method for protecting the intellectual property rights (IPR) of deep neural network (DNN) models. It extracts a feature called a fingerprint from a DNN model to identify its ownership. Existing fingerprinting methods focus only on classification-related models that map images to labels, while inapplicable to models for image restoration that map images to images. This paper proposes a fingerprinting framework for DNN models of image restoration. The proposed framework defines the fingerprint using a critical image, which exhibits strongly discriminative patterns and is robust to modest model modifications. Model ownership is then verified by comparing the distance of color histograms and local gradient pattern histograms of critical images between the suspect and source models. We apply the proposed framework to two representative tasks, denoising and super-resolution. It outperforms the baselines of fingerprinting and competes against existing invasive model watermarking methods.
+
+# 1. Introduction
+
+Deep learning has become a prominent tool for solving problems in computer vision, ranging from high-level image classification problems to low-level image restoration problems. However, the cost of designing and training a DNN model for specific applications has grown exponentially, leading to expenses in many areas such as hardware resources, data collection and labeling, and paying for engineers and researchers. Although sharing pre-trained DNN models has become a common practice in the community, many companies and institutes charge for the commercial usage of pre-trained models. This creates a strong incentive
+
+for adversaries to plagiarize/steal the models, using methods such as malware infection or internal leaks, to bypass the expensive training process. Consequently, both the community and companies have a strong motivation to protect the IPR of their DNN models.
+
+One popular approach for protecting the IPR of DNN models is model watermarking (e.g. [44, 1, 10, 7, 53, 8, 39, 20, 54, 21]), which invasively embeds specific information called watermark into the source model and examines its existence in the suspect model for ownership verification. However, modifying model weights can potentially affect the model's utility, making it less desirable in practice.
+
+Recently, a non-invasive approach called model fingerprinting has gained attention. Unlike watermarking, fingerprinting keeps the model intact and creates a unique feature called fingerprint from the model for identifying ownership. The ownership of a model is verified by comparing the fingerprint of the source model with that of the suspect model. While fingerprinting is still in its early stages with few existing works [3, 24, 11, 60, 33], it is gaining popularity as a non-invasive alternative to model watermarking.
+
+# 1.1. Motivation
+
+In this paper, we focus on protecting the IPR of DNN models used for low-level image restoration tasks. These types of models map degraded images or measurements to high-quality target images. Deep learning has proven to be a powerful tool for solving a variety of image restoration problems, e.g., image denoising [57, 35, 36, 32], superresolution (SR) [22, 47, 59, 43, 15], deblurring [58, 29, 40, 17, 41], and bad weather removal [34, 45, 37, 50, 51, 38].
+
+Most existing works on IPR protection for DNN models focus on high-level vision tasks such as image classification, where the DNN outputs a label in a finite discrete set. In contrast, DNN models for image restoration output an image in a very high-dimensional space. Though there are a few works on watermarking DNN models for various image restoration tasks (e.g.[53, 39, 54]), these image restoration models can be vulnerable to modifications of DNN weights required in watermarking, resulting in the loss of important
+
+![](images/ba00baf838899bb59f472da73d8ab3fd4fbcc5c3a9c2b9b10ec8eb2888fa508a.jpg)  
+Figure 1: Main idea of our model fingerprinting approach for an image recovery DNN. We aim to find a critical image (blue point) around the DNN's performance border zone.
+
+image details and the addition of undesired artifacts.
+
+Fingerprinting is a more attractive option for image restoration DNNs, as it does not require any modification to model weights. However, to the best of our knowledge, no existing study has explored fingerprinting for DNN models used in image restoration tasks. The existing fingerprinting methods are designed for classification DNNs which can be fully characterized by their decision boundaries. These methods use adversarial examples to characterize the decision boundaries and generate a fingerprint for the model. In contrast, image restoration generates an image in a high-dimensional space, and its accuracy is measured by a continuous metric such as mean squared error to the ground truth. Therefore, the concept of "decision boundary" is not well-defined for image restoration models.
+
+Due to the significant differences between image restoration and image classification, the existing fingerprinting methods for classification DNNs cannot be easily extended to image restoration DNNs. As a result, we were motivated to develop a new fingerprinting framework specifically designed for image restoration DNN models.
+
+# 1.2. Main Idea
+
+An image restoration task (e.g. denoising and SR) is to predict a latent image  $\mathbf{X}$  from its degraded or partial measurements  $\mathbf{Y} = \mathcal{D}(\mathbf{X})$ , where  $\mathcal{D}$  denotes the degrading/measuring process. In deep learning, a DNN model  $\mathcal{M}: \mathbb{R}^{n \times m} \to \mathbb{R}^{N \times M}$  is trained to accurately predict  $\mathbf{X}$  from the input  $\mathcal{D}(\mathbf{X})$  in some task-related domain  $\mathbb{D}$ . While the prediction error for most images in  $\mathbb{D}$ , measured by  $\| \mathbf{X} - \mathcal{M}(\mathcal{D}(\mathbf{X})) \|_2^2$ , is small, there exists a complementary set  $\overline{\mathbb{D}}$  where the DNN has large prediction errors.
+
+Indeed, an image restoration DNN usually works well only for target images that lie within a low-dimensional manifold in  $\mathbb{R}^{N\times M}$ . It is not expected that a DNN will perform well for all points in  $\mathbb{R}^{N\times M}$ . For instance, consider image denoising where  $\mathbf{Y} = \mathcal{D}(\mathbf{X}) = \mathbf{X} + \mathbf{N}$ , with  $\mathbf{N}$  representing Gaussian white noise. Let  $\mathbf{X}_1$  be a constant matrix
+
+and  $\mathbf{X}_2$  be a random matrix with entries randomly sampled from a normal distribution. Since adding two independent Gaussian random variables results in a new Gaussian random variable [18],  $\mathbf{Y}_2$  also corresponds to a constant image corrupted by larger Gaussian white noise. Suppose a denoising model performs well on predicting  $\mathbf{X}_1$  (a constant matrix) from its noisy version  $\mathbf{Y}_1$ . Then, the denoiser will consistently take  $\mathbf{Y}_2$  as the noisy version of a constant matrix and output a constant matrix, which is far away from the ground-truth matrix  $\mathbf{X}_2$  (a random matrix). In other words, a denoising model designed to work well for constant matrices may not work well for random matrices.
+
+To summarize, just like the decision boundary in classification, there exists a "performance border zone" that separates the set of images that the restoration model can accurately restore and the set of images that it cannot. This zone encodes essential characteristics of the model, and the points close to it can be used for its characterization. Particularly, these points can be the images in the complementary set  $\overline{\mathbb{D}}$  that are close to the set  $\mathbb{D}$  of images that the DNN can restore accurately (i.e., their prediction errors by the DNN are small). See Figure 1 for an illustration of this concept.
+
+In this paper, we define the term "critical images" to refer to the points near the performance border zone. Suppose that the target images in  $\mathbb{D}$  follow some prior, such as the sparsity prior of gradients. Then, a critical image for the model  $\mathcal{M}$  is an image  $\mathbf{X}$  that minimizes the prediction error  $\| \mathbf{X} - \mathcal{M}(\mathcal{D}(\mathbf{X}))\|_2^2$  (i.e.,  $\mathbf{X}$  is close to  $\mathbb{D}$ ) while also maximizing a penalty that reflects the prior on the images in  $\mathbb{D}$  (i.e.,  $\mathbf{X}$  is close to  $\bar{\mathbb{D}}$ ). This ensures that  $\mathbf{X}$  is simultaneously close to both  $\mathbb{D}$  and  $\bar{\mathbb{D}}$ , i.e., it lies near their border zone.
+
+Empirical observations suggest that the critical images obtained from independently-trained DNNs using the proposed approach consist of strong spatial patterns that not only convey discriminative information, but are also robust to moderate modifications in model weights. Therefore, these critical images can serve as the fingerprints of a model. For model verification, we measure the distances between the fingerprints using two standard image descriptors: color histograms and local gradient patterns (LGP) [13].
+
+# 1.3. Contributions
+
+The construction of a critical image forms the foundation of our proposed fingerprinting approach for image restoration models. Our approach is applied to two representative image restoration tasks: denoising and SR. Denoising is a core problem in many image restoration tasks, and SR is one of the most successful applications of deep learning in image restoration. Extensive experiments on these two tasks have demonstrated that our proposed approach is more robust than the baseline fingerprinting methods and competitive with recent intrusive watermarking methods. See below for a summary of the main contributions:
+
+- A fingerprinting framework is proposed for protecting the IPR of image restoration DNN models. To the best of our knowledge, this is the first study on fingerprinting DNN models of image restoration.  
+- Analogous to decision boundaries in classification, the concept of performance border zone is introduced to characterize image restoration DNN models.  
+- The concept of critical images, points in proximity to the performance border zone, is introduced to showcase discriminative and robust patterns that can serve as effective fingerprints for image restoration DNN models.
+
+# 2. Related Works
+
+# 2.1. Model Fingerprinting
+
+Model fingerprinting shares a similar spirit with the zerowatermarking for digital images (e.g. [48]), where discriminative yet robust features are extracted from an image to represent its ownership. While it is possible to extract features directly from the weights of a DNN by treating them as digital media, this method is not robust to modifications of the model. To improve robustness, existing works [3, 24, 11, 60, 60, 33] extract features from the decision boundaries of a classification DNN, as these features are often transferable for plagiarism models but not for independently-trained models.
+
+Cao et al. [3] proposed to fingerprint decision boundaries via using nearby data points defined by adversarial examples. The ownership is verified by checking whether the suspect model predicts the same labels as the source model on those data points. Lukas et al. [24] proposed to fingerprint the overlap of adversarial subspaces around decision boundaries between the source model and its surrogates. They synthesized conferrable adversarial examples that transfer exclusively with a target label from the source model to its surrogates. Zhao et al. [60] proposed to improve adversarial examples for fingerprinting by encouraging them to mimic the logits vector of a target sample randomly chosen from the target category. Peng et al. [33] proposed to profile decision boundaries by characterizing the universal adversarial perturbations [26]. Additionally, they trained an encoder via contrastive learning to map fingerprints from two models to a similarity score for ownership verification. Chen et al. [5] proposed to quantify the similarity between two models using a diverse set of testing metrics and test case generation algorithms to produce a chain of evidence for verification. This method can include many existing fingerprinting algorithms as test metrics.
+
+All the methods discussed above are limited to classification DNNs. Our approach, however, is specifically designed for fingerprinting models of image restoration by using critical images instead of adversarial examples. It is noted that while the aforementioned methods aim to detect
+
+model plagiarism, He et al. [11] proposed a fingerprinting method to examine model integrity. This method identifies a small set of human-unnoticeable transformed inputs that make a model's outputs sensitive to its parameters.
+
+# 2.2. Model Watermarking
+
+Model watermarking serves a similar purpose as model fingerprinting; however, it involves embedding a code or opening a backdoor inside a DNN that could potentially harm the DNN's performance. Most existing watermarking methods are designed for classification DNNs (e.g. [44, 42, 56, 1, 10, 27, 4, 28, 7, 16, 53, 8, 20, 54, 21, 19, 23]), but there are also a few works that target image restoration DNN models (e.g. [53, 39, 31, 54]). Zhang et al. [53, 54] proposed to train the DNN to automatically embed an invisible watermark in its output image. The model ownership is verified by detecting the presence of watermarks in the output images of the suspect DNN. Quan et al. [39] proposed to train the DNN to map a random image to its naive recovered version that is unlikely to be generated by other independently well-trained DNNs. The model ownership is verified by checking whether such a mapping holds for the suspect DNN. Ong et al. [31] proposed to train the DNN so that an input image embedded with a visible key can lead to an output image with a visible logo. The model ownership is verified by attempting to trigger the logo via the key.
+
+# 3. Methodology
+
+# 3.1. Problem Statement and Overview
+
+Threat model In a typical attack-defense scenario, an owner has trained a source model using private resources. An adversary attempts to plagiarize or steal the model. The owner is both a victim and a defender, with the goal of determining whether the suspect model is a plagiarized one. This involves verifying ownership in a white-box setting. An adversary or attacker who steals a model may modify it to avoid detection of ownership while maintaining its functionality and performance, but the access to the original training data is not given. Under this setting, we consider often-seen attacks that modify model weights, e.g., pruning, finetuning, and quantization.
+
+Principles Discriminability is a fundamental property of model fingerprinting. A model fingerprint is trustworthy for protecting IPR only if it is distinguishable for different models. Given the importance of training data and open sources of DNN architecture, two models with the same architecture but trained independently using different data are considered as independent models, and their fingerprints should be distinguishable from each other. Robustness is another critical property of model fingerprinting. A model fingerprint is expected to remain nearly unchanged under various modifications (attacks) on the model. However, these two
+
+![](images/c5a51db681c35b4638d9c4af9b996a5388457866de6276e7cb80cafa8fb37a00.jpg)  
+Figure 2: Proposed model fingerprinting framework.
+
+properties often conflict with each other, and an ideal model fingerprinter should balance them carefully. It is worth noting that the fidelity of model performance, a desirable property for model watermarking, is not necessary for a non-invasive method like fingerprinting.
+
+**Framework** The proposed fingerprinting method for image restoration DNN models is outlined in Figure 2, involving 3 steps. First, a fingerprint defined over critical images is extracted from the source model and registered. Second, the fingerprint of a suspect model is computed for notarization. Finally, ownership is verified by comparing the features of the two fingerprints. The remaining issues are (i) how to extract a discriminative yet robust fingerprint from a model, and (ii) how to efficiently compare two fingerprints.
+
+# 3.2. Fingerprint Extraction
+
+As discussed in Section 1.2, we use critical images to fingerprint a model. These critical images are located near the performance border zone of an image restoration DNN. Now we focus on the restoration problems for natural images which are assumed to follow a Laplacian prior. Such a prior is generally true for natural images. Specifically, the total variation (TV)  $|\nabla \mathbf{X}|_1$  of an image  $\mathbf{X}$  in the domain  $\mathbb{D}$  is small, while an image  $\overline{\mathbf{X}}$  in  $\overline{\mathbb{D}}$  has a large value of  $|\nabla \overline{\mathbf{X}}|_1$ . Our proposed approach is also applicable to images in other domains, provided that there is some prior knowledge available for latent images.
+
+Given a DNN model  $\mathcal{M}$  trained for an image restoration task  $\mathcal{T}$ , we define the critical image  $\mathbf{S}$  by solving the following optimization problem:
+
+$$
+\mathbf {S} := \underset {\overline {{\mathbf {X}}} \in [ 0, 1 ] ^ {M \times N}} {\arg \min } \| \overline {{\mathbf {X}}} - \mathcal {M} \left(\mathcal {D} _ {\mathcal {T}} (\overline {{\mathbf {X}}})\right) \| _ {2} ^ {2} - \lambda \| \nabla \overline {{\mathbf {X}}} \| _ {1}, \tag {1}
+$$
+
+where  $\mathcal{D}_{\mathcal{T}}$  denotes a degradation operator associated with the task  $\mathcal{T}$ , and  $\lambda \in \mathbb{R}^{+}$  is a weight. The objective of the first term in (1) is to find an image close to the set  $\mathbb{D}$ . The second term encourages the image to be close to  $\overline{\mathbb{D}}$ . This is achieved by maximizing the value of  $\| \nabla \overline{\mathbf{X}} \|_1$ , which is a necessary condition for images in  $\overline{\mathbb{D}}$ .
+
+The operator  $\mathcal{D}_{\mathcal{T}}$  varies depending on the specific image restoration task. For instance, it corresponds to noise corruption for image denoising, downsampling for image SR, and blurring for image deblurring. For image denoising and SR, we adopt the following construction schemes for  $\mathcal{D}_{\mathcal{T}}$ :
+
+$$
+\mathcal {D} _ {\mathcal {T}} (\mathbf {X}) := \mathbf {X} + \mathbf {N}, \quad \mathbf {N} \sim \mathcal {N} (\mathbf {0}, \sigma^ {2} \mathbf {I}), \quad [ \text {D e n o i s i n g} ] \tag {2}
+$$
+
+$$
+\mathcal {D} _ {\mathcal {T}} (\mathbf {X}) := \mathbf {X} \downarrow_ {4}, \quad [ \text {I m a g e S R} ] \tag {3}
+$$
+
+where  $\mathcal{N}$  denotes normal distribution and  $\downarrow_4$  denotes dyadic downsampling that reduces the image size by half. The definition of  $\mathcal{D}_{\mathcal{T}}$  can be adapted to other restoration tasks.
+
+To solve (1), we use the Adam solver [14]. However, since the problem involves a DNN, it is highly non-convex, and the output of an iterative solver depends on the initialization of  $\mathbf{X}$ . We use random initialization for solving (1), i.e., we set  $\mathbf{S}^{(0)}$ , the initial point of  $\mathbf{S}$ , as follows:
+
+$$
+\mathbf {S} ^ {(0)} \sim \mathcal {N} (\mathbf {0}, \beta^ {2} \mathbf {I}), \quad \beta \in \mathbb {R}. \tag {4}
+$$
+
+Figure 3 illustrates the critical images calculated using different instances of  $\mathbf{S}^{(0)}$  generated via (4). We observe that critical images from the same model with different  $\mathbf{S}^{(0)}$  exhibit similar (homogeneous) patterns, while those from different models differ significantly from each other.
+
+Next, we construct the fingerprint denoted by  $\mathcal{F}$  via (1). To form a fingerprint of arbitrary length, one can solve (1) for multiple times using different  $\mathbf{S}^{(0)}$ :
+
+$$
+\mathcal {F} = \left\{\left(\mathbf {S} _ {1} ^ {(0)}, \mathbf {S} _ {1}\right), \dots , \left(\mathbf {S} _ {K} ^ {(0)}, \mathbf {S} _ {K}\right) \right\}, \tag {5}
+$$
+
+where  $\mathbf{S}_k$  is the critical image calculated using  $\mathbf{S}_k^{(0)}$  as the initial point for solving (1). Note that different  $\mathbf{S}_k$  of the same model contain the same patterns (see Figure 3) and image restoration models usually allow input (output) images of varying sizes. To obtain a similar amount of fingerprint information while avoiding multiple extractions, we can set  $K = 1$  and use a single large  $\mathbf{S}$  to approximate multiple  $\mathbf{S}_k$  of smaller sizes. It is worth noting that solving  $\mathbf{S}_k$  from (1) does not require accessing the model weights of  $\mathcal{M}$ , but only the gradients of  $\mathcal{M}(\mathcal{D}_{\mathcal{T}}(\overline{\mathbf{X}}))$  w.r.t.  $\overline{\mathbf{X}}$ , in a similar spirit to federated learning.
+
+# 3.3. Verification of Ownership
+
+Verification of ownership is accomplished by comparing fingerprints between the source and suspect models. While critical images can be visually compared, automated verification is often desirable in practice. Because critical images display distinct patterns in terms of color distribution and texture, we characterize them using color histograms (a standard color descriptor) and an improved version of LGP histograms [13] (a classic texture descriptor) based on the idea of [30]. Further details can be found in the supplemental material. Our approach is learning-free and does not require collecting training data for a learning-based verifier.
+
+![](images/dce37dc5e76889fbf48b831acbf218a43ad82b9b28f767bed8aaec631c29f479.jpg)  
+Figure 3: Critical images of DBSN [49] (upper) and EDSR [22] (bottom) calculated by using  $\mathbf{S}^{(0)}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$  while fixing all other hyper-parameters.
+
+Let  $h_{\mathrm{su}}$ ,  $h_{\mathrm{sus}} \in \mathbb{R}^L$  be the features. i.e., the concatenation of normalized color and LGP histograms, computed from the fingerprints of the source model and the suspect model, respectively. When  $K > 1$ , the features from multiple  $\mathbf{S}_k$  are averaged. In essence, these features serve as a refined version of the fingerprints. Then the suspect model will be identified as plagiarism if
+
+$$
+d = \left\| \boldsymbol {h} _ {\text {s o u}} - \boldsymbol {h} _ {\text {s u s}} \right\| _ {2} ^ {2} / L <   \eta , \tag {6}
+$$
+
+where  $\eta$  is a threshold (the bound of negligible error) determined by a probabilistic scheme with the same spirit of [39]. Suppose that the error  $e(j) = h_{\mathrm{su}}(j) - h_{\mathrm{sus}}(j)\sim \mathcal{N}(0,\sigma^2),\forall j$  , where  $\sigma = 0.015$  (see supplemental material for our idea to determine this value). Then, the random variable  $Z = \frac{\|e\|_2^2}{\sigma^2}$  follows a Chi-squared distribution  $\mathcal{X}_L^2$  . By applying the  $p$  -value approach with  $p <   0.05$  , we can find a value of  $\gamma$  such that  $P[Z\leq \gamma ] <   0.05$  , or equivalently,  $P[d\leq \eta ] <   0.05$  . This allows us to safely reject the null hypothesis that  $h_\mathrm{su}$  and  $h_\mathrm{sus}$  are similar.
+
+# 4. Experiments
+
+We assess the effectiveness of the proposed approach for two restoration tasks, namely image denoising and image SR, by measuring their discriminability and robustness.
+
+# 4.1. Experimental Setup
+
+Source models We choose six DNNs from existing literature as the source models for each task, respectively. (a) Image denoising: DnCNN [57], DBSN [49], Nei2Nei [12], Restormer [50], SimBase [6], and NAFNet [6]; (b) Image SR: EDSR [22], RRDBNet [47], RNAN [59], MobileSR [43], RFLN [15], and DRLN [2]. To comprehensively evaluate the effectiveness of fingerprinting, we consider models with varying structures, training data, and training strategies, for both tasks. We either use the pretrained models or train them using their released codes. See more details in the supplemental material.
+
+Implementation details In fingerprint extraction, we use a single critical image of size  $128 \times 128$ , for all models in both tasks. We set  $\beta = 1$  in (4) for initializing  $\mathbf{X}$ . The learning rate of Adam for solving (1) is set to 0.1. A total number of 5000 iterations is used. In ownership verification, we form a 30-dimensional RGB+LGP histogram. The resulting threshold is  $\eta = 1.39 \times 10^{-4}$ . For denoising DNNs, we set  $\sigma = 1$  for constructing  $\mathcal{D}_{\mathcal{T}}$  in (2). For both denoising and SR, we set  $\lambda = 0.001$ . The seeds involved in our approach are fixed to make the whole process deterministic and reproducible.
+
+# 4.2. Discriminability Analysis
+
+We begin by a visual inspection on the fingerprints extracted via our approach. See Figure 4 for the critical images extracted from various source models, all of which contain unique and distinguishable patterns that vary in scale, appearance, local shape, regularity and color, across different images. For instance, larger-scale patterns are visible for SimBase while the smaller-scale ones for DnCNN. The fingerprint of DnCNN exhibits random patterns, while that of NAFNet shows regular ones. Moreover, the red tone of fingerprint of NAFNet differs from the chromatic tone of SimBase. These significant visual differences demonstrate the strong discriminability of the extracted fingerprints.
+
+The discriminability is further quantitatively assessed by computing the feature distances (6) between critical images for every pair of source models. The distance matrices in Figure 5(a) and (b) show the ratios between the resulting distances and the threshold  $\eta$ , for denoising DNNs and SR DNNs, respectively. In both tasks, all off-diagonal elements, i.e., distances between every model pair, exceed the threshold, indicating no confusion among the models. The results indicate excellent discriminability of our extracted critical images, and the simple RGB+LGP histograms are able to effectively capture their patterns for verification.
+
+We also test whether our approach can differentiate models with the same architecture but trained on different datasets. The Restormer model [50] is retrained on six different datasets; see the details in the supplemental material. Figure 4(c) visually compares the fingerprints of each model, and Figure 5(c) shows the resulting distance matrix. Our approach effectively differentiates the models, even those with the same architecture, with many large off-diagonal values observed in the distance matrix.
+
+# 4.3. Robustness Analysis
+
+We conduct robustness analysis using three common attacks: model pruning, model finetuning, and model quantization. A meaningful attack should only have a minor effect on the original function of a model. For analysis, we quantify the impact of an attack on the model's performance based on the resulting average PSNR gap on the recovered
+
+![](images/de6fd3a3fb36b75487d0eda110f971fe5e85430f9b3c7c76ea5eaff11de72651.jpg)  
+(a) Fingerprints of denoising models
+
+![](images/58f98caa857974b120de8b0811ebfc2f3b36b21d365e4ad7640c38c6c283db2d.jpg)  
+(b) Fingerprints of SR models
+
+![](images/099a124dda0c58fde2e1d27db955b42b8adc0c5fdbabcdbc293a195a86eee1af.jpg)  
+(c) Fingerprints of independent Restormer models
+
+![](images/72e1c3e45c2aea7906471fd87ba5207b554a5e0d0a23dc9dbc08e9903a8040c8.jpg)  
+(a) Denoising models
+
+![](images/41b1c7c8a123b9add3a22d4cb095c8787c8a5b1bfc31d485b43ef65738728cb0.jpg)  
+Figure 4: Fingerprints (critical images) extracted from different source models.  
+(b) SR models
+
+![](images/7051fe07be19387140c2a00a79d3814b85e5ee4a99f65e02951e83149a9484ce.jpg)  
+(c) Restomers trained with different datasets.  
+Figure 5: Visualization of pairwise feature distance of fingerprints between source models. The ratios between the distance and the threshold are shown. For better illustration, all the color bars are set as follows. The color goes from purple to blue when the value decreases from 1, while the color goes from orange to yellow when the value increases from 1.
+
+images. Each attack has its strength controlled such that it only leads to  $\leq 1\mathrm{dB}$  change in the average PSNR value for all the models on a test set. This ensures that all attacks are not meaningless. The robustness is measured by the times of successful ownership verification under an attack.
+
+Baselines So far, no fingerprinting method is available that is specifically designed for image restoration DNNs, making our work the first in this area. For experimental comparison, we construct two baselines by adapting existing fingerprint methods designed for classification DNNs:
+
+1. ProjCL: Each image restoration source model is converted to a classification DNN by adding a random projection layer with softmax activation in the end, so as to output a 100-dimensional label vector. Then, the well-known fingerprinting method IPGuard [3] is applied for the classification DNNs.  
+2. PoolCL: The output of each source model is downsampled to form a  $10 \times 10$  image, which is then vectorized and subjected to a Softmax function, producing a 100-dimensional label vector. This converts each source model into a classification DNN, and then we fingerprint it using the IPGuard [3].
+
+We tune the baselines' hyper-parameters, including label vector dimensions, for their discriminability. We set their verification thresholds to the minimum values that ensure all tested models pass the discrimination test. These threshold values optimize the robustness metrics, as reducing the verification threshold improves robustness.
+
+Furthermore, we present three watermarking methods specifically designed for image restoration DNNs to compare the performance gap between non-invasive fingerprinting and invasive watermarking:
+
+1. Zhang et al. [55]: The source model is retrained to embed an invisible watermark in each output.  
+2. Ong et al. [31]: The source model is retrained to composite a visible watermark region into the output when the input is composed of a specific trigger region.  
+3. Quan et al. [39]: The source model is retrained to produce a copyright image for a specific input noise.
+
+We tune the hyper-parameters for the watermark embedding in these methods to maintain high fidelity on the PSNR performance of the source models on test data. To facilitate a more informative comparison between fingerprinting and watermarking, we create a baseline called "WeakWM" by
+
+![](images/a3c06cbc07de75f51b57f13b171f05c7085f69238f6d3f23cb910d7c1ae966b1.jpg)  
+(a) Fingerprints on denoising models.
+
+![](images/3de919d8f1ffc3587441769169242941227192444ca559e6ab4f33570e8da932.jpg)  
+(b) Fingerprints on SR models.  
+Figure 6: Fingerprints (critical images) calculated from different models under three attacks.
+
+<table><tr><td></td><td colspan="8">Image Denoising</td><td colspan="8">Image SR</td></tr><tr><td></td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td></tr><tr><td rowspan="6">Pruning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RNAN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan="6">Finetuning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan="6">Quantization</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>DRLN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>√</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td colspan="2">Success Rate</td><td>67%</td><td>78%</td><td>100%</td><td>100%</td><td>100%</td><td>28%</td><td>100%</td><td>Success Rate</td><td>0%</td><td>61%</td><td>100%</td><td>100%</td><td>100%</td><td>22%</td><td>100%</td></tr></table>
+
+Table 1: Verification under attacks. Blue: fingerprinting; Purple: watermarking; X: failure;  $\checkmark$  : success.
+
+reducing the watermark embedding strength of Quan et al.'s method [39] to a sufficiently low value where no significant loss in fidelity is observed. The fingerprints extracted by our approach for both tasks are shown in Figure 6, under various attacks. Verification results for different methods are listed in Table 1.
+
+Model pruning We prune the source models by zeroing the top  $p\%$  of smallest weights in the DNN's layers, where  $p = 10$  for denoising and  $p = 5$  for SR. The pat
+
+terns are nearly the same for both tasks under model pruning. Our approach achieves successful verification on all models under all pruning ratios for both tasks, outperforming the two baselines that fails in nearly half the cases. Notably, the baselines perform much worse for SR models than for denoising models. The baseline ProjCL fails in all SR cases, suggesting that the methods designed for classification DNNs are ineffective when applied to image restoration DNNs. The watermarking methods succeed for all mod
+
+els, which is expected due to their invasive manner. However, when the watermark embedding strength is very weak, WeakWM fails in most cases during watermark verification.
+
+Model finetuning We fine-tune the source models with their original tasks on the BSD68 dataset [25] for 500 iterations (steps). Little change can be observed in the patterns of the resulting critical images. Our fingerprinting approach and the three watermarking methods successfully verify all models. However, among the baselines, PoolCL fails in one denoising and one SR case, ProjCL fails in two denoising and all SR cases, and WeakWM succeeds only once in each task due to weak watermark strength.
+
+Model quantization When Int8 quantization with simple rounding is applied to the source models, our approach still produces robust yet discriminative fingerprints. It successfully verifies all models, like the three watermarking methods. WeakWM only succeeds in one half cases. ProjCL fails in two denoising cases and all SR cases. PoolCL performs acceptably on denoising models but fails in a half of the SR cases.
+
+# 4.4. Ablation Study
+
+We form additional two baselines of our approach for further study, which are as follows:
+
+1. w/o TV: Removing the TV (second term) in (1) for calculating the critical image.  
+2. MaxObj: Replacing the critical image in our approach with an image generated by maximizing the objective function in (1) instead of minimizing it. The resulting image is expected to be as smooth as possible while hard to recover, which can be seen as an adversarial sample.
+
+For the "w/o TV" case, we observe that the resulting critical images tend to degenerate into a constant image easily for some models, meaning that its discriminability could not be guaranteed. Therefore, we only compare the success rates of MaxObj and our approach in terms of robustness. See Table 2 for the results, where our approach outperforms MaxObj. This may be because the fingerprints generated by MaxObj are not as close to the performance border zone as those generated by our approach.
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Compression</td><td colspan="2">Finetuning</td><td colspan="2">Quantization</td></tr><tr><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td></tr><tr><td>MaxObj</td><td>5/6</td><td>4/6</td><td>6/6</td><td>4/6</td><td>6/6</td><td>3/6</td></tr><tr><td>Ours</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td></tr></table>
+
+Table 2: Success rates of baselines in ablation study.
+
+# 4.5. Demos Beyond Denoising and SR
+
+To further examine the applicability of our approach to other image restoration tasks, we provide demos on addi
+
+![](images/cdf8b9febb02e0e6d52710f2bffa2b12753f9b7d7ee4352daef13b05512bf498.jpg)  
+Figure 7: Fingerprints calculated from different pre-trained and attacked DNN models on other tasks. See supplemental material for the results on deraining.
+
+tional tasks: deblurring (including motion deblurring and defocus deblurring), deraining, and low-light enhancement. The operator  $\mathcal{D}_{\mathcal{T}}$ s are defined as follows:
+
+$$
+\mathcal {D} _ {\mathcal {T}} (\mathbf {X}) := \mathbf {K} \otimes \mathbf {X} + \mathbf {N}, \quad [ \text {D e b l u r r i n g} ]
+$$
+
+$$
+\mathcal {D} _ {\mathcal {T}} (\mathbf {X}) := \operatorname {N o r m} \left(\mathbf {X} ^ {3}\right), \quad [ \text {L o w - l i g h t E n h a n c e m e n t} ]
+$$
+
+$$
+\mathcal {D} _ {\mathcal {T}} (\mathbf {X}) := \mathbf {X} + \mathbf {R}, \quad [ \text {D e r a i n i n g} ]
+$$
+
+where  $\mathbf{K}$  is a blur kernel,  $\mathrm{Norm}(\cdot)$  denotes min-max normalization, and  $\mathbf{R}$  is a synthetic rain layer; see supplemental material for details. We select three DNNs with published pre-trained models for each task: IFAN [17], GKMNet [40] and NRKNet [41] for defocus deblurring; Restormer [50], SimBase [6] and NAFNet [6] for motion deblurring; Restormer [50], MPRNet [51] and VRGNet [45] for deraining; and MIRNetv2 [52], DLN [46] and ZeroDCE [9] for low-light enhancement. The results in Figure 7 (for defocus deblurring and low-light enhancement) and supplemental material (for motion deblurring and deraining) show that, the extracted fingerprints exhibit discriminative patterns, and meanwhile they remain similar under pruning and quantization attacks.
+
+# 5. Conclusion and Discussion
+
+Given the prevalence of DNN models used in image restoration, protecting their IPR has become increasingly important. Toward this end, we proposed a non-intrusive fingerprinting framework for verifying the model ownership of image restoration DNNs, with its effectiveness demonstrated in two important tasks: image denoising and SR. Similar to existing white-box methods, ours requires the access to model weights. One possible future direction is exploring online model encryption techniques to extend our approach to the black-box setting. In addition, the theoretical aspects of the critical image such as uniqueness, as well as the extensions to other low-level vision DNNs, will be investigated in our future work.
+
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\ No newline at end of file
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+                                    "content": "Fingerprinting is a promising non-invasive method for protecting the intellectual property rights (IPR) of deep neural network (DNN) models. It extracts a feature called a fingerprint from a DNN model to identify its ownership. Existing fingerprinting methods focus only on classification-related models that map images to labels, while inapplicable to models for image restoration that map images to images. This paper proposes a fingerprinting framework for DNN models of image restoration. The proposed framework defines the fingerprint using a critical image, which exhibits strongly discriminative patterns and is robust to modest model modifications. Model ownership is then verified by comparing the distance of color histograms and local gradient pattern histograms of critical images between the suspect and source models. We apply the proposed framework to two representative tasks, denoising and super-resolution. It outperforms the baselines of fingerprinting and competes against existing invasive model watermarking methods."
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+                            ]
+                        }
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+                },
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+                                    "content": "Deep learning has become a prominent tool for solving problems in computer vision, ranging from high-level image classification problems to low-level image restoration problems. However, the cost of designing and training a DNN model for specific applications has grown exponentially, leading to expenses in many areas such as hardware resources, data collection and labeling, and paying for engineers and researchers. Although sharing pre-trained DNN models has become a common practice in the community, many companies and institutes charge for the commercial usage of pre-trained models. This creates a strong incentive"
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+                            ]
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+                    "index": 15
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+                {
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+                                    "type": "text",
+                                    "content": "for adversaries to plagiarize/steal the models, using methods such as malware infection or internal leaks, to bypass the expensive training process. Consequently, both the community and companies have a strong motivation to protect the IPR of their DNN models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                                    "type": "text",
+                                    "content": "One popular approach for protecting the IPR of DNN models is model watermarking (e.g. [44, 1, 10, 7, 53, 8, 39, 20, 54, 21]), which invasively embeds specific information called watermark into the source model and examines its existence in the suspect model for ownership verification. However, modifying model weights can potentially affect the model's utility, making it less desirable in practice."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        304,
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+                                    "type": "text",
+                                    "content": "Recently, a non-invasive approach called model fingerprinting has gained attention. Unlike watermarking, fingerprinting keeps the model intact and creates a unique feature called fingerprint from the model for identifying ownership. The ownership of a model is verified by comparing the fingerprint of the source model with that of the suspect model. While fingerprinting is still in its early stages with few existing works [3, 24, 11, 60, 33], it is gaining popularity as a non-invasive alternative to model watermarking."
+                                }
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+                                    "content": "Most existing works on IPR protection for DNN models focus on high-level vision tasks such as image classification, where the DNN outputs a label in a finite discrete set. In contrast, DNN models for image restoration output an image in a very high-dimensional space. Though there are a few works on watermarking DNN models for various image restoration tasks (e.g.[53, 39, 54]), these image restoration models can be vulnerable to modifications of DNN weights required in watermarking, resulting in the loss of important"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "*Corresponding author: Ruotao Xu (xrt@scut.edu.cn). This work is supported by the Natural Science Foundation of Guangdong Province (Grant No. 2023A1515012841, 2022A1515011755, 2022A1515011087); National Natural Science Foundation of China (Grant No. 62106077); Postdoctoral Special Foundation of China (Grant No. 2022T150219); Postdoctoral Foundation of China (Grant No. 2020M682705); and Singapore MOE AcRF Tier 1 (Grant No. A-8000981-00-00)."
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+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "image details and the addition of undesired artifacts."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Fingerprinting is a more attractive option for image restoration DNNs, as it does not require any modification to model weights. However, to the best of our knowledge, no existing study has explored fingerprinting for DNN models used in image restoration tasks. The existing fingerprinting methods are designed for classification DNNs which can be fully characterized by their decision boundaries. These methods use adversarial examples to characterize the decision boundaries and generate a fingerprint for the model. In contrast, image restoration generates an image in a high-dimensional space, and its accuracy is measured by a continuous metric such as mean squared error to the ground truth. Therefore, the concept of \"decision boundary\" is not well-defined for image restoration models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Due to the significant differences between image restoration and image classification, the existing fingerprinting methods for classification DNNs cannot be easily extended to image restoration DNNs. As a result, we were motivated to develop a new fingerprinting framework specifically designed for image restoration DNN models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "1.2. Main Idea"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "An image restoration task (e.g. denoising and SR) is to predict a latent image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from its degraded or partial measurements "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y} = \\mathcal{D}(\\mathbf{X})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the degrading/measuring process. In deep learning, a DNN model "
+                                },
+                                {
+                                    "bbox": [
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+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}: \\mathbb{R}^{n \\times m} \\to \\mathbb{R}^{N \\times M}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is trained to accurately predict "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " from the input "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}(\\mathbf{X})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in some task-related domain "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ". While the prediction error for most images in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", measured by "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{X} - \\mathcal{M}(\\mathcal{D}(\\mathbf{X})) \\|_2^2"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ", is small, there exists a complementary set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        534,
+                                        286,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": " where the DNN has large prediction errors."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Indeed, an image restoration DNN usually works well only for target images that lie within a low-dimensional manifold in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{N\\times M}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". It is not expected that a DNN will perform well for all points in "
+                                },
+                                {
+                                    "bbox": [
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{N\\times M}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". For instance, consider image denoising where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y} = \\mathcal{D}(\\mathbf{X}) = \\mathbf{X} + \\mathbf{N}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        286,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{N}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " representing Gaussian white noise. Let "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " be a constant matrix"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        215
+                                    ],
+                                    "type": "text",
+                                    "content": " be a random matrix with entries randomly sampled from a normal distribution. Since adding two independent Gaussian random variables results in a new Gaussian random variable [18], "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        215
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        215
+                                    ],
+                                    "type": "text",
+                                    "content": " also corresponds to a constant image corrupted by larger Gaussian white noise. Suppose a denoising model performs well on predicting "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        215
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (a constant matrix) from its noisy version "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        215
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        215
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, the denoiser will consistently take "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        215
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        215
+                                    ],
+                                    "type": "text",
+                                    "content": " as the noisy version of a constant matrix and output a constant matrix, which is far away from the ground-truth matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        215
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}_2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        215
+                                    ],
+                                    "type": "text",
+                                    "content": " (a random matrix). In other words, a denoising model designed to work well for constant matrices may not work well for random matrices."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                        216,
+                        545,
+                        337
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "To summarize, just like the decision boundary in classification, there exists a \"performance border zone\" that separates the set of images that the restoration model can accurately restore and the set of images that it cannot. This zone encodes essential characteristics of the model, and the points close to it can be used for its characterization. Particularly, these points can be the images in the complementary set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        216,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        216,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " that are close to the set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        216,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        216,
+                                        545,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " of images that the DNN can restore accurately (i.e., their prediction errors by the DNN are small). See Figure 1 for an illustration of this concept."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": "In this paper, we define the term \"critical images\" to refer to the points near the performance border zone. Suppose that the target images in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " follow some prior, such as the sparsity prior of gradients. Then, a critical image for the model "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": " is an image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                    ],
+                                    "type": "text",
+                                    "content": " that minimizes the prediction error "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{X} - \\mathcal{M}(\\mathcal{D}(\\mathbf{X}))\\|_2^2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is close to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": ") while also maximizing a penalty that reflects the prior on the images in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is close to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "). This ensures that "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is simultaneously close to both "
+                                },
+                                {
+                                    "bbox": [
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+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
+                                        545,
+                                        443
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        337,
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+                                        443
+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e., it lies near their border zone."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Empirical observations suggest that the critical images obtained from independently-trained DNNs using the proposed approach consist of strong spatial patterns that not only convey discriminative information, but are also robust to moderate modifications in model weights. Therefore, these critical images can serve as the fingerprints of a model. For model verification, we measure the distances between the fingerprints using two standard image descriptors: color histograms and local gradient patterns (LGP) [13]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                        574
+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "1.3. Contributions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The construction of a critical image forms the foundation of our proposed fingerprinting approach for image restoration models. Our approach is applied to two representative image restoration tasks: denoising and SR. Denoising is a core problem in many image restoration tasks, and SR is one of the most successful applications of deep learning in image restoration. Extensive experiments on these two tasks have demonstrated that our proposed approach is more robust than the baseline fingerprinting methods and competitive with recent intrusive watermarking methods. See below for a summary of the main contributions:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
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+                        }
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+                }
+            ],
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- A fingerprinting framework is proposed for protecting the IPR of image restoration DNN models. To the best of our knowledge, this is the first study on fingerprinting DNN models of image restoration."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 0
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Analogous to decision boundaries in classification, the concept of performance border zone is introduced to characterize image restoration DNN models."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
+                            "bbox": [
+                                53,
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                            "type": "text",
+                                            "content": "- The concept of critical images, points in proximity to the performance border zone, is introduced to showcase discriminative and robust patterns that can serve as effective fingerprints for image restoration DNN models."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
+                        }
+                    ],
+                    "sub_type": "text"
+                },
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+                                    "type": "text",
+                                    "content": "2. Related Works"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "2.1. Model Fingerprinting"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Model fingerprinting shares a similar spirit with the zerowatermarking for digital images (e.g. [48]), where discriminative yet robust features are extracted from an image to represent its ownership. While it is possible to extract features directly from the weights of a DNN by treating them as digital media, this method is not robust to modifications of the model. To improve robustness, existing works [3, 24, 11, 60, 60, 33] extract features from the decision boundaries of a classification DNN, as these features are often transferable for plagiarism models but not for independently-trained models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Cao et al. [3] proposed to fingerprint decision boundaries via using nearby data points defined by adversarial examples. The ownership is verified by checking whether the suspect model predicts the same labels as the source model on those data points. Lukas et al. [24] proposed to fingerprint the overlap of adversarial subspaces around decision boundaries between the source model and its surrogates. They synthesized conferrable adversarial examples that transfer exclusively with a target label from the source model to its surrogates. Zhao et al. [60] proposed to improve adversarial examples for fingerprinting by encouraging them to mimic the logits vector of a target sample randomly chosen from the target category. Peng et al. [33] proposed to profile decision boundaries by characterizing the universal adversarial perturbations [26]. Additionally, they trained an encoder via contrastive learning to map fingerprints from two models to a similarity score for ownership verification. Chen et al. [5] proposed to quantify the similarity between two models using a diverse set of testing metrics and test case generation algorithms to produce a chain of evidence for verification. This method can include many existing fingerprinting algorithms as test metrics."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "All the methods discussed above are limited to classification DNNs. Our approach, however, is specifically designed for fingerprinting models of image restoration by using critical images instead of adversarial examples. It is noted that while the aforementioned methods aim to detect"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "model plagiarism, He et al. [11] proposed a fingerprinting method to examine model integrity. This method identifies a small set of human-unnoticeable transformed inputs that make a model's outputs sensitive to its parameters."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "type": "text",
+                                    "content": "2.2. Model Watermarking"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Model watermarking serves a similar purpose as model fingerprinting; however, it involves embedding a code or opening a backdoor inside a DNN that could potentially harm the DNN's performance. Most existing watermarking methods are designed for classification DNNs (e.g. [44, 42, 56, 1, 10, 27, 4, 28, 7, 16, 53, 8, 20, 54, 21, 19, 23]), but there are also a few works that target image restoration DNN models (e.g. [53, 39, 31, 54]). Zhang et al. [53, 54] proposed to train the DNN to automatically embed an invisible watermark in its output image. The model ownership is verified by detecting the presence of watermarks in the output images of the suspect DNN. Quan et al. [39] proposed to train the DNN to map a random image to its naive recovered version that is unlikely to be generated by other independently well-trained DNNs. The model ownership is verified by checking whether such a mapping holds for the suspect DNN. Ong et al. [31] proposed to train the DNN so that an input image embedded with a visible key can lead to an output image with a visible logo. The model ownership is verified by attempting to trigger the logo via the key."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3. Methodology"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.1. Problem Statement and Overview"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Threat model In a typical attack-defense scenario, an owner has trained a source model using private resources. An adversary attempts to plagiarize or steal the model. The owner is both a victim and a defender, with the goal of determining whether the suspect model is a plagiarized one. This involves verifying ownership in a white-box setting. An adversary or attacker who steals a model may modify it to avoid detection of ownership while maintaining its functionality and performance, but the access to the original training data is not given. Under this setting, we consider often-seen attacks that modify model weights, e.g., pruning, finetuning, and quantization."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Principles Discriminability is a fundamental property of model fingerprinting. A model fingerprint is trustworthy for protecting IPR only if it is distinguishable for different models. Given the importance of training data and open sources of DNN architecture, two models with the same architecture but trained independently using different data are considered as independent models, and their fingerprints should be distinguishable from each other. Robustness is another critical property of model fingerprinting. A model fingerprint is expected to remain nearly unchanged under various modifications (attacks) on the model. However, these two"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                }
+            ],
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+                                    "content": "13287"
+                                }
+                            ]
+                        }
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+            ],
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+                            ],
+                            "index": 0,
+                            "angle": 0,
+                            "type": "image_body"
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+                                            "type": "text",
+                                            "content": "Figure 2: Proposed model fingerprinting framework."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "type": "text",
+                                    "content": "properties often conflict with each other, and an ideal model fingerprinter should balance them carefully. It is worth noting that the fidelity of model performance, a desirable property for model watermarking, is not necessary for a non-invasive method like fingerprinting."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "**Framework** The proposed fingerprinting method for image restoration DNN models is outlined in Figure 2, involving 3 steps. First, a fingerprint defined over critical images is extracted from the source model and registered. Second, the fingerprint of a suspect model is computed for notarization. Finally, ownership is verified by comparing the features of the two fingerprints. The remaining issues are (i) how to extract a discriminative yet robust fingerprint from a model, and (ii) how to efficiently compare two fingerprints."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.2. Fingerprint Extraction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": "As discussed in Section 1.2, we use critical images to fingerprint a model. These critical images are located near the performance border zone of an image restoration DNN. Now we focus on the restoration problems for natural images which are assumed to follow a Laplacian prior. Such a prior is generally true for natural images. Specifically, the total variation (TV) "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|\\nabla \\mathbf{X}|_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": " of an image "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": " in the domain "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": " is small, while an image "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{X}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": " in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": " has a large value of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|\\nabla \\overline{\\mathbf{X}}|_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        437,
+                                        287,
+                                        567
+                                    ],
+                                    "type": "text",
+                                    "content": ". Our proposed approach is also applicable to images in other domains, provided that there is some prior knowledge available for latent images."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        46,
+                        568,
+                        287,
+                        604
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
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+                                604
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": "Given a DNN model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " trained for an image restoration task "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": ", we define the critical image "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        568,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " by solving the following optimization problem:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                        611,
+                        287,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        55,
+                                        611,
+                                        287,
+                                        634
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {S} := \\underset {\\overline {{\\mathbf {X}}} \\in [ 0, 1 ] ^ {M \\times N}} {\\arg \\min } \\| \\overline {{\\mathbf {X}}} - \\mathcal {M} \\left(\\mathcal {D} _ {\\mathcal {T}} (\\overline {{\\mathbf {X}}})\\right) \\| _ {2} ^ {2} - \\lambda \\| \\nabla \\overline {{\\mathbf {X}}} \\| _ {1}, \\tag {1}",
+                                    "image_path": "495cf750f3f40775a023382bfcaf4c15c3ebc6cb69072b94e8a51bea26c98ebf.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes a degradation operator associated with the task "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda \\in \\mathbb{R}^{+}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": " is a weight. The objective of the first term in (1) is to find an image close to the set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": ". The second term encourages the image to be close to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": ". This is achieved by maximizing the value of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\nabla \\overline{\\mathbf{X}} \\|_1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": ", which is a necessary condition for images in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbb{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        641,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
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+                        133
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": "The operator "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " varies depending on the specific image restoration task. For instance, it corresponds to noise corruption for image denoising, downsampling for image SR, and blurring for image deblurring. For image denoising and SR, we adopt the following construction schemes for "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                        152
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        312,
+                                        138,
+                                        545,
+                                        152
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} + \\mathbf {N}, \\quad \\mathbf {N} \\sim \\mathcal {N} (\\mathbf {0}, \\sigma^ {2} \\mathbf {I}), \\quad [ \\text {D e n o i s i n g} ] \\tag {2}",
+                                    "image_path": "14c9dc20fe44d41d0494ae8895d9e50f9b72cfcb87e2a224896a3b62aa06f221.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                        545,
+                        167
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                313,
+                                154,
+                                545,
+                                167
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        313,
+                                        154,
+                                        545,
+                                        167
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} \\downarrow_ {4}, \\quad [ \\text {I m a g e S R} ] \\tag {3}",
+                                    "image_path": "94a5ceab38c4957060c57974f046c06742556415a57f867b88d46d5c72de550b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                        175,
+                        545,
+                        210
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                175,
+                                545,
+                                210
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes normal distribution and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\downarrow_4"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes dyadic downsampling that reduces the image size by half. The definition of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        175,
+                                        545,
+                                        210
+                                    ],
+                                    "type": "text",
+                                    "content": " can be adapted to other restoration tasks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        304,
+                        211,
+                        545,
+                        270
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                211,
+                                545,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": "To solve (1), we use the Adam solver [14]. However, since the problem involves a DNN, it is highly non-convex, and the output of an iterative solver depends on the initialization of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ". We use random initialization for solving (1), i.e., we set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}^{(0)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ", the initial point of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        211,
+                                        545,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ", as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        368,
+                        277,
+                        545,
+                        290
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                368,
+                                277,
+                                545,
+                                290
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        368,
+                                        277,
+                                        545,
+                                        290
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {S} ^ {(0)} \\sim \\mathcal {N} (\\mathbf {0}, \\beta^ {2} \\mathbf {I}), \\quad \\beta \\in \\mathbb {R}. \\tag {4}",
+                                    "image_path": "c3acdef22470dd4a8f27e42f4b1e448365aa8ba7ca110734bc49a152b6b8036c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                        357
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                297,
+                                545,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        357
+                                    ],
+                                    "type": "text",
+                                    "content": "Figure 3 illustrates the critical images calculated using different instances of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        357
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}^{(0)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        357
+                                    ],
+                                    "type": "text",
+                                    "content": " generated via (4). We observe that critical images from the same model with different "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        357
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}^{(0)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        297,
+                                        545,
+                                        357
+                                    ],
+                                    "type": "text",
+                                    "content": " exhibit similar (homogeneous) patterns, while those from different models differ significantly from each other."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        304,
+                        358,
+                        545,
+                        393
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                358,
+                                545,
+                                393
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        358,
+                                        545,
+                                        393
+                                    ],
+                                    "type": "text",
+                                    "content": "Next, we construct the fingerprint denoted by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        358,
+                                        545,
+                                        393
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        358,
+                                        545,
+                                        393
+                                    ],
+                                    "type": "text",
+                                    "content": " via (1). To form a fingerprint of arbitrary length, one can solve (1) for multiple times using different "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        358,
+                                        545,
+                                        393
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}^{(0)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        358,
+                                        545,
+                                        393
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        359,
+                        400,
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+                        416
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                416
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        359,
+                                        400,
+                                        545,
+                                        416
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {F} = \\left\\{\\left(\\mathbf {S} _ {1} ^ {(0)}, \\mathbf {S} _ {1}\\right), \\dots , \\left(\\mathbf {S} _ {K} ^ {(0)}, \\mathbf {S} _ {K}\\right) \\right\\}, \\tag {5}",
+                                    "image_path": "c4af91111c854a42bea3805b5539597d45a6dac118ad6fd76fd510cfd8dc6944.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " is the critical image calculated using "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}_k^{(0)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " as the initial point for solving (1). Note that different "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " of the same model contain the same patterns (see Figure 3) and image restoration models usually allow input (output) images of varying sizes. To obtain a similar amount of fingerprint information while avoiding multiple extractions, we can set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " and use a single large "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " to approximate multiple "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " of smaller sizes. It is worth noting that solving "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " from (1) does not require accessing the model weights of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", but only the gradients of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M}(\\mathcal{D}_{\\mathcal{T}}(\\overline{\\mathbf{X}}))"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
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+                                    ],
+                                    "type": "text",
+                                    "content": " w.r.t. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{X}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", in a similar spirit to federated learning."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.3. Verification of Ownership"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                        582,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Verification of ownership is accomplished by comparing fingerprints between the source and suspect models. While critical images can be visually compared, automated verification is often desirable in practice. Because critical images display distinct patterns in terms of color distribution and texture, we characterize them using color histograms (a standard color descriptor) and an improved version of LGP histograms [13] (a classic texture descriptor) based on the idea of [30]. Further details can be found in the supplemental material. Our approach is learning-free and does not require collecting training data for a learning-based verifier."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "13288"
+                                }
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+                                        }
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+                            "index": 0,
+                            "angle": 0,
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 3: Critical images of DBSN [49] (upper) and EDSR [22] (bottom) calculated by using "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                192,
+                                                288,
+                                                231
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{S}^{(0)}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                192,
+                                                288,
+                                                231
+                                            ],
+                                            "type": "text",
+                                            "content": " while fixing all other hyper-parameters."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": "Let "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_{\\mathrm{su}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_{\\mathrm{sus}} \\in \\mathbb{R}^L"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " be the features. i.e., the concatenation of normalized color and LGP histograms, computed from the fingerprints of the source model and the suspect model, respectively. When "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K > 1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": ", the features from multiple "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{S}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        251,
+                                        289,
+                                        337
+                                    ],
+                                    "type": "text",
+                                    "content": " are averaged. In essence, these features serve as a refined version of the fingerprints. Then the suspect model will be identified as plagiarism if"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        110,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        110,
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+                                        287,
+                                        361
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "d = \\left\\| \\boldsymbol {h} _ {\\text {s o u}} - \\boldsymbol {h} _ {\\text {s u s}} \\right\\| _ {2} ^ {2} / L <   \\eta , \\tag {6}",
+                                    "image_path": "27e5055fed8c23ed4dd8ff14f87f4d57cf4da89424b0297f2a5bd063c2e1708c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " is a threshold (the bound of negligible error) determined by a probabilistic scheme with the same spirit of [39]. Suppose that the error "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e(j) = h_{\\mathrm{su}}(j) - h_{\\mathrm{sus}}(j)\\sim \\mathcal{N}(0,\\sigma^2),\\forall j"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " , where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma = 0.015"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " (see supplemental material for our idea to determine this value). Then, the random variable "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z = \\frac{\\|e\\|_2^2}{\\sigma^2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " follows a Chi-squared distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_L^2"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " . By applying the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " -value approach with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p <   0.05"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " , we can find a value of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " such that "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P[Z\\leq \\gamma ] <   0.05"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " , or equivalently, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P[d\\leq \\eta ] <   0.05"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " . This allows us to safely reject the null hypothesis that "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_\\mathrm{su}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h_\\mathrm{sus}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        367,
+                                        289,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " are similar."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
+                        500,
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+                        514
+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "We assess the effectiveness of the proposed approach for two restoration tasks, namely image denoising and image SR, by measuring their discriminability and robustness."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    ],
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+                                    "type": "text",
+                                    "content": "4.1. Experimental Setup"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Source models We choose six DNNs from existing literature as the source models for each task, respectively. (a) Image denoising: DnCNN [57], DBSN [49], Nei2Nei [12], Restormer [50], SimBase [6], and NAFNet [6]; (b) Image SR: EDSR [22], RRDBNet [47], RNAN [59], MobileSR [43], RFLN [15], and DRLN [2]. To comprehensively evaluate the effectiveness of fingerprinting, we consider models with varying structures, training data, and training strategies, for both tasks. We either use the pretrained models or train them using their released codes. See more details in the supplemental material."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Implementation details In fingerprint extraction, we use a single critical image of size "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "128 \\times 128"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": ", for all models in both tasks. We set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": " in (4) for initializing "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": ". The learning rate of Adam for solving (1) is set to 0.1. A total number of 5000 iterations is used. In ownership verification, we form a 30-dimensional RGB+LGP histogram. The resulting threshold is "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta = 1.39 \\times 10^{-4}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": ". For denoising DNNs, we set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": " for constructing "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathcal{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": " in (2). For both denoising and SR, we set "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda = 0.001"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        205
+                                    ],
+                                    "type": "text",
+                                    "content": ". The seeds involved in our approach are fixed to make the whole process deterministic and reproducible."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                        448,
+                        225
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "4.2. Discriminability Analysis"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We begin by a visual inspection on the fingerprints extracted via our approach. See Figure 4 for the critical images extracted from various source models, all of which contain unique and distinguishable patterns that vary in scale, appearance, local shape, regularity and color, across different images. For instance, larger-scale patterns are visible for SimBase while the smaller-scale ones for DnCNN. The fingerprint of DnCNN exhibits random patterns, while that of NAFNet shows regular ones. Moreover, the red tone of fingerprint of NAFNet differs from the chromatic tone of SimBase. These significant visual differences demonstrate the strong discriminability of the extracted fingerprints."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The discriminability is further quantitatively assessed by computing the feature distances (6) between critical images for every pair of source models. The distance matrices in Figure 5(a) and (b) show the ratios between the resulting distances and the threshold "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        375,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        375,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", for denoising DNNs and SR DNNs, respectively. In both tasks, all off-diagonal elements, i.e., distances between every model pair, exceed the threshold, indicating no confusion among the models. The results indicate excellent discriminability of our extracted critical images, and the simple RGB+LGP histograms are able to effectively capture their patterns for verification."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We also test whether our approach can differentiate models with the same architecture but trained on different datasets. The Restormer model [50] is retrained on six different datasets; see the details in the supplemental material. Figure 4(c) visually compares the fingerprints of each model, and Figure 5(c) shows the resulting distance matrix. Our approach effectively differentiates the models, even those with the same architecture, with many large off-diagonal values observed in the distance matrix."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.3. Robustness Analysis"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We conduct robustness analysis using three common attacks: model pruning, model finetuning, and model quantization. A meaningful attack should only have a minor effect on the original function of a model. For analysis, we quantify the impact of an attack on the model's performance based on the resulting average PSNR gap on the recovered"
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "(a) Fingerprints of denoising models"
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+                                            "content": "(b) Fingerprints of SR models"
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+                                            "type": "text",
+                                            "content": "(c) Fingerprints of independent Restormer models"
+                                        }
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+                            ],
+                            "index": 5,
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+                                            "type": "text",
+                                            "content": "(a) Denoising models"
+                                        }
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+                                            "type": "text",
+                                            "content": "Figure 4: Fingerprints (critical images) extracted from different source models."
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+                                            "type": "text",
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+                                        }
+                                    ]
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+                            "angle": 0,
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+                        }
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+                                            "type": "text",
+                                            "content": "(c) Restomers trained with different datasets."
+                                        }
+                                    ]
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+                                            "type": "text",
+                                            "content": "Figure 5: Visualization of pairwise feature distance of fingerprints between source models. The ratios between the distance and the threshold are shown. For better illustration, all the color bars are set as follows. The color goes from purple to blue when the value decreases from 1, while the color goes from orange to yellow when the value increases from 1."
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+                                    "type": "text",
+                                    "content": "images. Each attack has its strength controlled such that it only leads to "
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+                                    "type": "inline_equation",
+                                    "content": "\\leq 1\\mathrm{dB}"
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+                                    "type": "text",
+                                    "content": " change in the average PSNR value for all the models on a test set. This ensures that all attacks are not meaningless. The robustness is measured by the times of successful ownership verification under an attack."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Baselines So far, no fingerprinting method is available that is specifically designed for image restoration DNNs, making our work the first in this area. For experimental comparison, we construct two baselines by adapting existing fingerprint methods designed for classification DNNs:"
+                                }
+                            ]
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+                                            "type": "text",
+                                            "content": "1. ProjCL: Each image restoration source model is converted to a classification DNN by adding a random projection layer with softmax activation in the end, so as to output a 100-dimensional label vector. Then, the well-known fingerprinting method IPGuard [3] is applied for the classification DNNs."
+                                        }
+                                    ]
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+                                            "type": "text",
+                                            "content": "2. PoolCL: The output of each source model is downsampled to form a "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "10 \\times 10"
+                                        },
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+                                            "type": "text",
+                                            "content": " image, which is then vectorized and subjected to a Softmax function, producing a 100-dimensional label vector. This converts each source model into a classification DNN, and then we fingerprint it using the IPGuard [3]."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "We tune the baselines' hyper-parameters, including label vector dimensions, for their discriminability. We set their verification thresholds to the minimum values that ensure all tested models pass the discrimination test. These threshold values optimize the robustness metrics, as reducing the verification threshold improves robustness."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Furthermore, we present three watermarking methods specifically designed for image restoration DNNs to compare the performance gap between non-invasive fingerprinting and invasive watermarking:"
+                                }
+                            ]
+                        }
+                    ],
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+                                            "type": "text",
+                                            "content": "1. Zhang et al. [55]: The source model is retrained to embed an invisible watermark in each output."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21
+                        },
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+                                            "type": "text",
+                                            "content": "2. Ong et al. [31]: The source model is retrained to composite a visible watermark region into the output when the input is composed of a specific trigger region."
+                                        }
+                                    ]
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+                            ],
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+                                            "type": "text",
+                                            "content": "3. Quan et al. [39]: The source model is retrained to produce a copyright image for a specific input noise."
+                                        }
+                                    ]
+                                }
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+                            "index": 23
+                        }
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+                                    "content": "We tune the hyper-parameters for the watermark embedding in these methods to maintain high fidelity on the PSNR performance of the source models on test data. To facilitate a more informative comparison between fingerprinting and watermarking, we create a baseline called \"WeakWM\" by"
+                                }
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+                                            "content": "(a) Fingerprints on denoising models."
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+                                            "content": "Figure 6: Fingerprints (critical images) calculated from different models under three attacks."
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+                                            "html": "<table><tr><td></td><td colspan=\"8\">Image Denoising</td><td colspan=\"8\">Image SR</td></tr><tr><td></td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td><td>Model</td><td>ProjCL</td><td>PoolCL</td><td>Zhang</td><td>Quan</td><td>Ong</td><td>WeakWM</td><td>Ours</td></tr><tr><td rowspan=\"6\">Pruning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>RNAN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan=\"6\">Finetuning</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>DRLN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td rowspan=\"6\">Quantization</td><td>SimBase</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>DRLN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>DBSN</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>EDSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>DnCNN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>MobileSR</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>NAFNet</td><td>X</td><td>✓</td><td>✓</td><td>√</td><td>✓</td><td>X</td><td>✓</td><td>RLFN</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Nei2Nei</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RNAN</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Restormer</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td><td>RRDBNet</td><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td colspan=\"2\">Success Rate</td><td>67%</td><td>78%</td><td>100%</td><td>100%</td><td>100%</td><td>28%</td><td>100%</td><td>Success Rate</td><td>0%</td><td>61%</td><td>100%</td><td>100%</td><td>100%</td><td>22%</td><td>100%</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1: Verification under attacks. Blue: fingerprinting; Purple: watermarking; X: failure; "
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+                                    "type": "text",
+                                    "content": " : success."
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+                                    "type": "text",
+                                    "content": "reducing the watermark embedding strength of Quan et al.'s method [39] to a sufficiently low value where no significant loss in fidelity is observed. The fingerprints extracted by our approach for both tasks are shown in Figure 6, under various attacks. Verification results for different methods are listed in Table 1."
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+                                    "type": "text",
+                                    "content": "Model pruning We prune the source models by zeroing the top "
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+                                    "type": "text",
+                                    "content": " of smallest weights in the DNN's layers, where "
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+                                    "type": "text",
+                                    "content": " for denoising and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for SR. The pat"
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+                                    "type": "text",
+                                    "content": "terns are nearly the same for both tasks under model pruning. Our approach achieves successful verification on all models under all pruning ratios for both tasks, outperforming the two baselines that fails in nearly half the cases. Notably, the baselines perform much worse for SR models than for denoising models. The baseline ProjCL fails in all SR cases, suggesting that the methods designed for classification DNNs are ineffective when applied to image restoration DNNs. The watermarking methods succeed for all mod"
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+                                    "type": "text",
+                                    "content": "els, which is expected due to their invasive manner. However, when the watermark embedding strength is very weak, WeakWM fails in most cases during watermark verification."
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+                                    "type": "text",
+                                    "content": "Model finetuning We fine-tune the source models with their original tasks on the BSD68 dataset [25] for 500 iterations (steps). Little change can be observed in the patterns of the resulting critical images. Our fingerprinting approach and the three watermarking methods successfully verify all models. However, among the baselines, PoolCL fails in one denoising and one SR case, ProjCL fails in two denoising and all SR cases, and WeakWM succeeds only once in each task due to weak watermark strength."
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+                                    "content": "Model quantization When Int8 quantization with simple rounding is applied to the source models, our approach still produces robust yet discriminative fingerprints. It successfully verifies all models, like the three watermarking methods. WeakWM only succeeds in one half cases. ProjCL fails in two denoising cases and all SR cases. PoolCL performs acceptably on denoising models but fails in a half of the SR cases."
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+                                    "type": "text",
+                                    "content": "4.4. Ablation Study"
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+                                    "content": "We form additional two baselines of our approach for further study, which are as follows:"
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+                                            "content": "1. w/o TV: Removing the TV (second term) in (1) for calculating the critical image."
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+                                            "content": "2. MaxObj: Replacing the critical image in our approach with an image generated by maximizing the objective function in (1) instead of minimizing it. The resulting image is expected to be as smooth as possible while hard to recover, which can be seen as an adversarial sample."
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+                                    "type": "text",
+                                    "content": "For the \"w/o TV\" case, we observe that the resulting critical images tend to degenerate into a constant image easily for some models, meaning that its discriminability could not be guaranteed. Therefore, we only compare the success rates of MaxObj and our approach in terms of robustness. See Table 2 for the results, where our approach outperforms MaxObj. This may be because the fingerprints generated by MaxObj are not as close to the performance border zone as those generated by our approach."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Compression</td><td colspan=\"2\">Finetuning</td><td colspan=\"2\">Quantization</td></tr><tr><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td><td>Denoising</td><td>SR</td></tr><tr><td>MaxObj</td><td>5/6</td><td>4/6</td><td>6/6</td><td>4/6</td><td>6/6</td><td>3/6</td></tr><tr><td>Ours</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td><td>6/6</td></tr></table>",
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+                                    "content": "Table 2: Success rates of baselines in ablation study."
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+                                    "content": "4.5. Demos Beyond Denoising and SR"
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+                                    "content": "To further examine the applicability of our approach to other image restoration tasks, we provide demos on addi"
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+                                            "content": "Figure 7: Fingerprints calculated from different pre-trained and attacked DNN models on other tasks. See supplemental material for the results on deraining."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "tional tasks: deblurring (including motion deblurring and defocus deblurring), deraining, and low-light enhancement. The operator "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathcal{T}}"
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+                                    "type": "text",
+                                    "content": "s are defined as follows:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {K} \\otimes \\mathbf {X} + \\mathbf {N}, \\quad [ \\text {D e b l u r r i n g} ]",
+                                    "image_path": "42dfd591de4acd67a0ffc9cb72931fe6a5854c627550f377cc8d0d10eea01d97.jpg"
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+                                    "content": "\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\operatorname {N o r m} \\left(\\mathbf {X} ^ {3}\\right), \\quad [ \\text {L o w - l i g h t E n h a n c e m e n t} ]",
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {D} _ {\\mathcal {T}} (\\mathbf {X}) := \\mathbf {X} + \\mathbf {R}, \\quad [ \\text {D e r a i n i n g} ]",
+                                    "image_path": "e810134c3cf04f444c1c0d84b2e5360a884c8abcc4bc0c26236bdda261838eca.jpg"
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{K}"
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+                                    "type": "text",
+                                    "content": " is a blur kernel, "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{Norm}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "text",
+                                    "content": " denotes min-max normalization, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{R}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a synthetic rain layer; see supplemental material for details. We select three DNNs with published pre-trained models for each task: IFAN [17], GKMNet [40] and NRKNet [41] for defocus deblurring; Restormer [50], SimBase [6] and NAFNet [6] for motion deblurring; Restormer [50], MPRNet [51] and VRGNet [45] for deraining; and MIRNetv2 [52], DLN [46] and ZeroDCE [9] for low-light enhancement. The results in Figure 7 (for defocus deblurring and low-light enhancement) and supplemental material (for motion deblurring and deraining) show that, the extracted fingerprints exhibit discriminative patterns, and meanwhile they remain similar under pruning and quantization attacks."
+                                }
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+                                    "type": "text",
+                                    "content": "5. Conclusion and Discussion"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Given the prevalence of DNN models used in image restoration, protecting their IPR has become increasingly important. Toward this end, we proposed a non-intrusive fingerprinting framework for verifying the model ownership of image restoration DNNs, with its effectiveness demonstrated in two important tasks: image denoising and SR. Similar to existing white-box methods, ours requires the access to model weights. One possible future direction is exploring online model encryption techniques to extend our approach to the black-box setting. In addition, the theoretical aspects of the critical image such as uniqueness, as well as the extensions to other low-level vision DNNs, will be investigated in our future work."
+                                }
+                            ]
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+                                }
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+                                            "bbox": [
+                                                53,
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
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+                            "index": 1
+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                                    ],
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+                                        {
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+                                        }
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+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                53,
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
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+                                239,
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+                                294
+                            ],
+                            "type": "ref_text",
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+                                {
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+                                        {
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                        },
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+                            ],
+                            "type": "ref_text",
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+                            "lines": [
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+                                        {
+                                            "bbox": [
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+                                            ],
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "ref_text",
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+                            "lines": [
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
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+                        },
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+                            ],
+                            "type": "ref_text",
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+                                            ],
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                            ],
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+                                        }
+                                    ]
+                                }
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+                            "index": 8
+                        },
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+                                        }
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+                        },
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10
+                        },
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                        },
+                        {
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diff --git a/2023/First Session Adaptation_ A Strong Replay-Free Baseline for Class-Incremental Learning/34f3da95-3b97-4ef3-a0db-22b854de2065_content_list.json b/2023/First Session Adaptation_ A Strong Replay-Free Baseline for Class-Incremental Learning/34f3da95-3b97-4ef3-a0db-22b854de2065_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..18eb829432d6a77c8700eff44987915df054e4ac
--- /dev/null
+++ b/2023/First Session Adaptation_ A Strong Replay-Free Baseline for Class-Incremental Learning/34f3da95-3b97-4ef3-a0db-22b854de2065_content_list.json	
@@ -0,0 +1,1486 @@
+[
+    {
+        "type": "text",
+        "text": "First Session Adaptation: A Strong Replay-Free Baseline for Class-Incremental Learning",
+        "text_level": 1,
+        "bbox": [
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+            175
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Aristeidis Panos  \nUniversity of Cambridge",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ap2313@cam.ac.uk",
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+            255
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yuriko Kobe University of Cambridge",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "yk384@cam.ac.uk",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Daniel Olmeda Reino  \nToyota Motor Europe",
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+    },
+    {
+        "type": "text",
+        "text": "daniel.olmeda.reino@toyota-europe.com",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Rahaf Aljundi  \nToyota Motor Europe",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "rahaf.al.jundi@toyota-europe.com",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Richard E. Turner  \nUniversity of Cambridge",
+        "bbox": [
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+            324,
+            583,
+            359
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ret26@cam.ac.uk",
+        "bbox": [
+            416,
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+            375
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            412,
+            312,
+            428
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In Class-Incremental Learning (CIL) an image classification system is exposed to new classes in each learning session and must be updated incrementally. Methods approaching this problem have updated both the classification head and the feature extractor body at each session of CIL. In this work, we develop a baseline method, First Session Adaptation (FSA), that sheds light on the efficacy of existing CIL approaches, and allows us to assess the relative performance contributions from head and body adaption. FSA adapts a pre-trained neural network body only on the first learning session and fixes it thereafter; a head based on linear discriminant analysis (LDA), is then placed on top of the adapted body, allowing exact updates through CIL. FSA is replay-free i.e. it does not memorize examples from previous sessions of continual learning. To empirically motivate FSA, we first consider a diverse selection of 22 image-classification datasets, evaluating different heads and body adaptation techniques in high/low-shot offline settings. We find that the LDA head performs well and supports CIL out-of-the-box. We also find that Featurewise Layer Modulation (FiLM) adapters are highly effective in the few-shot setting, and full-body adaption in the high-shot setting. Second, we empirically investigate various CIL settings including high-shot CIL and few-shot CIL, including settings that have previously been used in the literature. We show that FSA significantly improves over the state-of-the-art in 15 of the 16 settings considered. FSA with FiLM adapters is especially performant in the few-shot setting. These results indicate that current approaches to continuous body adaptation are not working as expected. Finally, we propose a measure",
+        "bbox": [
+            75,
+            446,
+            472,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "that can be applied to a set of unlabelled inputs which is predictive of the benefits of body adaptation.",
+        "bbox": [
+            500,
+            412,
+            890,
+            444
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            501,
+            477,
+            632,
+            493
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Continual learning (CL) is needed to bring machine learning models to many real-life applications. After a model is trained on a given set of data, and once deployed in its test environment, it is likely that new classes will naturally emerge. For example, in an autonomous driving scenario, new types of road transportation and traffic signage can be encountered. The deployed model needs to efficiently acquire this new knowledge with minimal cost (e.g. annotation requirements) without deteriorating the performance on existing classes of objects. The process of efficiently acquiring new knowledge while preserving what is already captured by the model is what continual learning methods target.",
+        "bbox": [
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+            503,
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+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Continual learning can be mainly divided into task incremental learning and class incremental learning. Task incremental learning (TIL) sequentially learns independent sets of heterogeneous tasks and is out of this paper's scope. Class incremental learning (CIL), in contrast, assumes that all classes (already learnt and future ones) form part of a single classification task. In class-incremental learning, data arrive in a sequence of sessions with new classes appearing as the sessions progress. Critically, the data in each session cannot be stored in its entirety and cannot be revisited. The goal is to train a single classification model under these constraints.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In both task incremental and class incremental learning,",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "18820",
+        "bbox": [
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+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "the data distribution will change as the sessions progress. However, these changes tend to be smaller in real-world class incremental learning settings than in the task incremental setting. For, example consider a human support robot learning about new objects in a home in an incremental manner (CIL) vs. the same robot learning to adapt to different homes (TIL).",
+        "bbox": [
+            75,
+            90,
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+            196
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Practically, CIL has two major uses. First, in situations where large amounts of data arrive in each session and so retraining the model is computationally prohibitive. Second, in situations where data are not allowed to be revisited due to privacy reasons such as under General Data Protection Regulation (GDPR). The latter situation is relevant for applications such as personalization where small numbers of data points are available i.e. few-shot continual learning. So-called replay-free methods are necessary for such settings, as samples of previous sessions are not allowed to be memorized, but CIL is known to be challenging in such settings.",
+        "bbox": [
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+            199,
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+            381
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Current SOTA methods for class incremental learning start from a pre-trained backbone [13, 19, 35, 34] and then adapt the features at each session of continual learning. The use of a pre-trained backbone has been shown to lead to strong performance especially in the few-shot CIL setting due to the lack of data [21]. However, it is unclear to what extent continuous adaptation of the features in each session is helpful. In general, in CIL there is a trade-off between adaptation (which helps adapt to the new statistics of the target domain) and catastrophic forgetting (whereby earlier classes are forgotten as the representation changes). When memorization of previous samples is restricted, the benefits from adapting the feature extractor body to learn better features might well be out-weighted by the increase in forgetting of old classes. Moreover, body adaptation in earlier sessions is arguably more critical (e.g. adapting the backbone to the new domain in the first session), whilst it is less essential in later sessions where the changes in the ideal representation between sessions are smaller.",
+        "bbox": [
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+            383,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This work explores under what conditions continuous adaptation of the body is beneficial, both in principle and in current practice. In order to do this, we develop a new replay-free method, inspired by the first encoding method of [2], called First Session Adaptation (FSA). FSA adapts the body of a pre-trained neural network on only the first session of continual learning. We investigate adapting all body parameters and the use of Feature-wise Layer Modulation (FiLM) adapters [23] which learn only a small number of parameters. The head, in contrast, is adapted at each session using an approach that is similar to Linear Discriminate Analysis (LDA), which suffers from no forgetting, and improves over the Nearest Class Mean classifier (NCM) [18] approach. The efficacy of this general approach, including comparisons to a standard linear head, is first motivated",
+        "bbox": [
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+            674,
+            470,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "through experiments in the offline setting (Sec. 4.2). We then carry out experiments under three CIL settings. First, we consider the high-shot setting (high-shot CIL). The other two settings consider few-shot continual learning. Specifically, one setting follows previous approaches that employ an initial session with a large number of data points and few-shot sessions thereafter (few-shot+ CIL) while the other exclusively includes sessions with only a small amount of data (few-shot CIL).",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The contributions of the paper are as follows: (1) We develop a replay-free CIL baseline, namely FSA, that is extremely simple to implement and performs well in many different scenarios. (2) We empirically motivate FSA through a set of offline experiments that evaluate different forms of neural network head and body adaptation; (3) We then compare FSA to a set of strong continual learning baseline methods in a fair way using the same pre-trained backbone for all methods. (4) We show that the FSA-FiLM baseline performs well in the high-shot CIL setting, outperforming the SOTA whilst avoiding data memorization. (5) In the few-shot learning settings, FSA outperforms existing continual learning methods on eight benchmarks, often by a substantial margin, and is statistically tied with the best performing method on the one remaining dataset. (6) Finally, we propose a measure that can be applied to a set of unlabeled inputs which is predictive of the benefits of body adaptation.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+            512,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Class Incremental Learning is more challenging than task-incremental continual learning as a shared output layer is used for the classes of different learning sessions. We refer to [7] for a survey on both class and task incremental learning. While softmax cross entropy loss is considered a standard in classification models, it is shown to be a source of class interference in continual learning [38, 4]. Thus, recent works either focus on fixing the softmax classifier [4, 1, 44] or deploy nearest class mean classifiers (NCM) as an alternative [25, 5, 11]. In this work, we deploy an LDA classifier that uses the mean embedding of each class and an incrementally updated covariance matrix shared across all classes. We show that this approach is comparable to a softmax classifier in the offline setting and that it outperforms NCM.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Due to the challenging nature of class incremental learning, some methods employ a buffer of stored samples from previous sessions [24, 39]. [24] suggests a simple baseline, GDumb, that performs offline training on both buffer data and new session data at each incremental step. GDumb shows strong performance compared to sophisticated continual learning solutions. Here we show that our simple yet effective solution often outperforms variants of GDumb that have a large memory without leveraging any buffer of stored",
+        "bbox": [
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+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "18821",
+        "bbox": [
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+            944,
+            517,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "samples.",
+        "bbox": [
+            76,
+            92,
+            138,
+            104
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In addition to the issues arising from the shared classification layer, learning a feature extractor that can provide representative features of all classes is a key element in continual learning. Some class incremental learning methods leverage large initial training session or start from a pretrained network, e.g., [35, 9, 36] and show improved overall continual learning performance without questioning the role of such pre-training steps and whether the learned representations have in fact improved. Recently, [19] studies continual learning with strong pre-trained models and proposes deploying exemplar-based replay in the latent space using a small multilayer network on top of the fixed pretrained model. The authors show that such latent replay improves performance, especially for tasks that are different from the distribution used to train the initial model. In this work, we show that adaptation of pre-trained models is essential for strong continual learning performance. However, different from all existing continual learning works, we show that adapting the representation only in the first session is sufficient to obtain representative features for the classes being learned and that this forms a strong baseline for future continual learning methods.",
+        "bbox": [
+            76,
+            106,
+            472,
+            436
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In addition to the incremental classification in the full data regime, we focus on the few-shot scenario where only a few labeled examples per class are provided at each training session. [9] utilize a meta-trained network for few-shot classification and explore multiple design choices including a no-adaptation baseline and a method to optimize orthogonal prototypes with the last classification layer only. The method heavily relies on a pre-training and meta-training step on a large subset of classes from the original dataset. In this work, we show that the meta-training step is not essential and that a simple LDA head is sufficient without the reliance on a big initial training stage. In [11] the authors propose a new distillation loss functioning at the feature map level where importance values are estimated per feature map along with replay and consider an NCM classifier at test time. [45] heavily relies on the training of an initial session using a specific loss function that takes into account classes that will be added in future. It further requires the total number of classes to be known a priori which is unrealistic for real applications. Our solution adapts FILM parameters to the first session data and fixes the representation for the remaining training sessions. We show that surprisingly few samples in the first session are sufficient for adaptation and that our solution is more powerful than current few-shot continual learning solutions.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Proposed Algorithm",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, first we discuss the main components of the proposed methods FSA/FSA-FiLM, namely body adaptation techniques and classifier heads. Then we formally",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "introduce the two methods for tackling CIL.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In CIL, we are given a dataset  $\\mathcal{D}_s = \\{\\mathbf{x}_{i,s},y_{i,s}\\}_{i = 1}^{N_s}$  for each session  $s\\in \\{1,\\ldots ,S\\}$ , where  $X_{s} = \\{\\mathbf{x}_{i,s}\\}_{i = 1}^{N_{s}}$  is a set of images and  $Y_{s} = \\{y_{i,s}\\}_{i = 1}^{N_{s}}$  is the set of the corresponding labels with  $y_{i,s}\\in \\mathcal{V}_s$ . Here  $\\mathcal{V}_s$  is the label space of session  $s$ . It is common in CIL that label spaces are mutually exclusive across sessions, i.e.  $\\mathcal{V}_s\\cap \\mathcal{V}_{s'} = \\emptyset$ ,  $\\forall s\\neq s'$  and we only have access to  $\\mathcal{D}_s$  in the current session  $s$  to train our model. The proposed FSA method can naturally handle sessions with overlapping label spaces too, however, we follow the former paradigm in our experiments. Another typical assumption in CIL is that the data in all sessions come from the same dataset. We also adopt this assumption in this work, although our experiments on DomainNet are a step toward considering different datasets in each session.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In session  $s$ , we will use models defined as",
+        "bbox": [
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+            354,
+            805,
+            368
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf _ {s} (\\mathbf {x}) = W _ {s} ^ {\\top} g _ {\\boldsymbol {\\theta} _ {s}} (\\mathbf {x}) + \\mathbf {b} _ {s}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            378,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $g_{\\theta_s}(\\mathbf{x}) \\in \\mathbb{R}^d$  is a feature extractor backbone<sup>1</sup> with session-dependent parameters  $\\theta_s$ . The linear classifier head comprises the class weights  $W_s \\in \\mathbb{R}^{d \\times |\\mathcal{Y}_{1:s}|}$  and biases  $\\mathbf{b}_s \\in \\mathbb{R}^{|\\mathcal{Y}_{1:s}|}$ , and  $\\mathcal{Y}_{1:s} = \\cup_{j=1}^{s} \\mathcal{Y}_j$  is the label space of all distinct classes we have seen up to session  $s$ . Ideally, when a new dataset  $\\mathcal{D}_s$  is available at the  $s$ -th session, the model should be able to update the backbone parameters  $\\theta$  and the linear classifier head  $W_s$  with the minimum computational overhead and without compromising performance over the previously seen classes  $\\mathcal{Y}_{1:s}$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Backbone adaptation. Traditionally, the adaptation of the body at the current session  $s$  requires updating the full set of the network parameters  $\\theta_{s}$  (full-body adaptation). Options include using specifically designed loss functions that mitigate catastrophic forgetting or using a memory buffer that stores a subset of the previously encountered data. See [16] for a review of continual learning techniques. Nevertheless, when training data availability is scarce relative to the size of the model then full-body adaptation ceases to be suitable, and few-shot learning techniques [33], such as meta-learning [10] and transfer learning [40] become favorable.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recent works in few-shot learning [26] showed that a pre-trained backbone can be efficiently adapted by keeping its parameters  $\\theta_{s}$  frozen and introducing Feature-wise Linear Modulation (FiLM) [23] layers with additional parameters  $\\xi_{s}$  which scale and shift the activations produced by a convolutional layer. In [26], these parameters are generated by a meta-trained network when a downstream task is",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>In this paper, we interchangeably use the terms feature extractor, backbone, and body.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "18822",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "given. Alternatively,  $\\xi_{s}$  can be learned (fine-tuned) by the downstream data as in [27]. In this work, we consider both meta-learned (Supplement) and fine-tuned (Sec. 4) FiLM parameters.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Classifier heads. In both offline and CIL settings, (linear) classifier heads can be divided into two groups; parametrized and parameter-free. Parametrized heads require the weights/biases in Eq. (1) to be updated by an iterative gradient-based procedure whilst for parameter-free heads, a closed-form formula is available that directly computes the weights/biases after the update of the backbone. We consider three different heads (for notational simplicity we consider the offline setting, and thus suppress session  $s$  dependence), one parametrized, and two parameter-free.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- The linear (learnable) head where  $W, \\mathbf{b}$  are learned.",
+            "- The Nearest Class Mean (NCM) classifier where the weight and bias of the  $k$ -th class is given by"
+        ],
+        "bbox": [
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+            330,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {w} _ {k} = \\hat {\\boldsymbol {\\mu}} _ {k} \\text {a n d} b _ {k} = \\ln \\frac {| X ^ {(k)} |}{N} - \\frac {1}{2} \\hat {\\boldsymbol {\\mu}} _ {k} ^ {\\top} \\hat {\\boldsymbol {\\mu}} _ {k}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $X^{(k)} = \\{\\mathbf{x}_i:y_i = k\\}$  is the set of images belonging in class  $k$  and  $\\hat{\\pmb{\\mu}}_k = \\frac{1}{|X^{(k)}|}\\sum_{\\mathbf{x}\\in X^{(k)}}g_\\pmb {\\theta}(\\mathbf{x})$  is the mean vector of the embedded images of class  $k$",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "- The Linear Discriminant Analysis (LDA) classifier with weights/biases defined as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {w} _ {k} = \\tilde {S} ^ {- 1} \\hat {\\boldsymbol {\\mu}} _ {k} \\text {a n d} b _ {k} = \\ln \\frac {| X ^ {(k)} |}{N} - \\frac {1}{2} \\hat {\\boldsymbol {\\mu}} _ {k} ^ {\\top} \\tilde {S} ^ {- 1} \\hat {\\boldsymbol {\\mu}} _ {k}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            120,
+            537,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{S} = S + I_d$  is the regularized sample covariance matrix with sample covariance matrix  $S = \\frac{1}{|X| - 1}\\sum_{\\mathbf{x}\\in X}(g_{\\boldsymbol{\\theta}}(\\mathbf{x}) - \\hat{\\boldsymbol{\\mu}})(g_{\\boldsymbol{\\theta}}(\\mathbf{x}) - \\hat{\\boldsymbol{\\mu}})^\\top$ ,  $\\hat{\\boldsymbol{\\mu}} = \\frac{1}{|X|}\\sum_{\\mathbf{x}\\in X}g_{\\boldsymbol{\\theta}}(\\mathbf{x})$ , and identity matrix  $I_d \\in \\mathbb{R}^{d\\times d}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Both NCM and LDA classifiers are suitable for CIL since their closed-form updates in Eq. (2) and Eq. (3) support exact, computationally inexpensive, continual updates (via running averages) that incur no forgetting. Updating the linear head, in contrast, requires more computational effort and machinery when novel classes appear in a new session. Notice that setting  $\\tilde{S} = I_d$  in LDA recovers NCM.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The continuous update of the LDA head is not as straightforward as it is for NCM, since LDA also requires updating the sample covariance  $S$ . We discuss how this can be attained in the next section where we introduce our proposed method FSA/FSA-FiLM.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. First Session Adaptation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Motivated by the efficient adaptation techniques and CIL-friendly classifiers discussed in the previous section,",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "we propose two simple and computationally efficient CIL methods called First Session Adaptation (FSA) and FSA-FiLM. FSA is based on a full-body adaptation while FSA-FiLM uses FiLM layers to adapt the body. Both methods utilize pre-trained backbones. FSA (-FiLM) (i) adapts the backbone only at the first session and then the backbone remains frozen for the rest of the sessions, and (ii) makes use of an LDA classifier which is continuously updated as new data become available. For adapting the body (either full or FiLM-based adaptation) at the first session, we use a linear head and a cross-entropy loss first, and then after the optimization is over, the linear head is removed and an LDA head is deployed instead, based on the optimized parameters  $\\theta^{*}$  and Eq. (3). Updating the LDA head when the data of the next session becomes available, can be done by using Algorithm 1 recursively until the last session  $S$ . Specifically, by having access to the running terms  $\\{A, \\mathbf{b}, \\text{count}\\}$ , the sample covariance matrix is given by",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS = \\frac {1}{\\operatorname {c o u n t} - 1} \\left(A - \\frac {1}{\\operatorname {c o u n t}} \\mathbf {b b} ^ {\\top}\\right). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The time complexity of LDA scales as  $\\mathcal{O}(d^3 + |\\mathcal{Y}_s|d^2)$  and",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Update of sample covariance running terms",
+        "bbox": [
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+            448,
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+            464
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require:  $g(\\cdot) \\equiv a$  feature extractor backbone",
+        "bbox": [
+            501,
+            465,
+            807,
+            481
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require:  $X_{s} = \\{\\mathbf{x}_{i,s}\\}_{i = 1}^{N_{s}}$ : Images of session  $s$",
+        "bbox": [
+            501,
+            481,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require:  $A\\in \\mathbb{R}^{d\\times d}$ $\\mathbf{b}\\in \\mathbb{R}^d$  count  $\\in \\mathbb{N}^*$  if  $s > 1$",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: function INCUPDATE  $(g(\\cdot), X_s, A, b, \\text{count})$",
+            "2: if  $s = 1$  then Initialize  $A, \\mathbf{b}$ , count",
+            "3:  $A\\gets \\mathbf{0}_{d\\times d},\\mathbf{b}\\gets \\mathbf{0}_d,\\mathrm{count}\\gets 0$",
+            "4: end if",
+            "5:  $A\\gets A + \\sum_{\\mathbf{x}\\in X_s}g(\\mathbf{x})g(\\mathbf{x})^\\top$",
+            "6:  $\\mathbf{b}\\gets \\mathbf{b} + \\sum_{\\mathbf{x}\\in X_s}g(\\mathbf{x})$",
+            "7: count  $\\leftarrow$  count  $+N_{s}$",
+            "8: return  $A$ , b, count",
+            "9: end function"
+        ],
+        "bbox": [
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+            512,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "its space complexity is  $\\mathcal{O}(d^2 + |\\mathcal{Y}_{1:s}|d)$  at the  $s$ -th session. This computational burden is negligible compared to taking gradient steps for learning a linear head and as we will see in Sec. 4.2 using covariance information boosts performance significantly against the vanilla NCM head.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present a series of experiments to investigate the performance of FSA (-FiLM) under different CIL settings. First, we detail the datasets used for the experiments and discuss our implementation. Second, we perform a large empirical comparison between LDA, linear, and NCM classifiers, in combination with different body adaptation techniques, in the offline setting. For the CIL settings, the results are compared to the vanilla method,  $N_{o}$",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18823",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Adaptation (NA), where a pretrained backbone is combined with an LDA head and remains frozen across sessions. We also consider how these findings are affected by the number of shots available. Third, we compare FSA (-FiLM) with state-of-the-art continual learning methods and conduct ablation studies. Finally, we investigate the effect of adapting the backbone when the CIL dataset is \"similar\" to ImageNet-1k and discuss a similarity metric that indicates whether body adaptation is required.",
+        "bbox": [
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+            90,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Implementation details",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We employ a diverse collection of 26 image-classification datasets across the offline and CIL experiments. For the offline experiments of Sec. 4.2, we use the 19 datasets of VTAB [42], a low-shot transfer learning benchmark, plus three additional datasets, FGVC-Aircraft [17], Stanford Cars [12], and Letters [6]. We refer to this group of datasets as VTAB+. For the CIL-based experiments, we choose 5 VTAB+ datasets from different domains, having an adequate number of classes to create realistic CIL scenarios. The datasets are CIFAR100, SVHN, dSprites-location, FGVC-Aircraft, Cars, and Letters while also including 4 extra datasets: CUB200 [32], CORE50 [15], iNaturalist [30], and DomainNet [22]. Exact details for each dataset are provided in the Supplement.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training details. All models are implemented with PyTorch [20]. We use a pre-trained EfficientNet-B0 [28] onImagenet-1k as the main backbone for all methods. For the few-shot+ CIL experiment in Sec. 4.3, we also consider two ResNet architectures, ResNet-18 and ResNet-20 [8] to enable direct comparison to the original settings used in [45]. All the deployed backbones (except ResNet-20, due to the unavailability of pre-trained weights on ImageNet-1k), are pre-trained on ImageNet-1k for all methods. We keep the optimization settings the same across all baselines for fairness. Optimization details are given in the Supplement.",
+        "bbox": [
+            75,
+            488,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation protocol. We report the Top-1 accuracy after the last continual learning session evaluated on a test set including instances from all the previously seen classes. In the Supplement, we provide the accuracy after each session. To quantify the forgetting behavior, we use a scaled modification of the performance dropping rate [29], namely percent performance dropping rate (PPDR), defined as  $\\mathrm{PPDR} = 100 \\times \\frac{\\mathcal{A}_1 - \\mathcal{A}_S}{\\mathcal{A}_1}\\%$ , where  $\\mathcal{A}_1$  denotes test accuracy after the first session, and  $\\mathcal{A}_S$  the test accuracy after the last session.",
+        "bbox": [
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+            672,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Head Comparisons",
+        "text_level": 1,
+        "bbox": [
+            76,
+            816,
+            264,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To motivate the choice of the LDA head for FSA (-FiLM), we compare its average accuracy across all VTAB+ datasets with that of the linear and NCM classifiers under the offline setting where all the classes are available and",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "no incremental learning is required. For the body, we use no adaptation (NA) as a baseline (i.e. using the unadapted original backbone), FiLM-based adaptation, and full-body adaptation while ranging the number of shots from 5 to 10, then 50, and finally using all available training data. As Fig. 1 illustrates, LDA consistently outperforms both NCM and linear heads when the number of shots is equal to 5 and 10, regardless of adaptation technique. Notice also that as the number of learnable parameters increases, the choice of the head plays a less significant role in the predictive power of the method. Overall, LDA performs similarly to the linear head in the high-shot settings and performs the best of all heads in the low-shot settings. Finally, the full covariance information of LDA provides a consistent advantage over its isotropic covariance counterpart, i.e. the NCM classifier. This is in agreement with the results presented in [27] for the LDA and NCM classifier. In addition to the results presented here, we have also tested meta-learning based body adaptation methods [3, 26, 2] which support continual learning out of the box. We find these perform poorly compared to the fine-tuning based methods. See next section for more results.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Class-Incremental Learning Comparisons",
+        "text_level": 1,
+        "bbox": [
+            498,
+            433,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We consider three different CIL scenarios: (i) high-shot CIL, (ii) few-shot+ CIL, and (iii) few-shot CIL. We compare our FSA/FSA-FiLM methods with recent state-of-the-art FSCIL methods, including Decoupled-Cosine [31], CEC [43], FACT [45], and ALICE. Additionally, for the high-shot CIL setting, we consider a strong replay-based baseline for CIL, GDumb [24] and a competitive replay-free method, E-EWC+SDC [41]. Finally, we introduce an additional baseline adapter inspired by [37], called FSA-LL (Last Layer). In FSA-LL only the parameters of the backbone's last block are fine-tuned which can be compared to the FSA-FiLM adaption method.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "High-shot CIL. In this setting, we consider all the available training data for each class while keeping the number of novel classes in each session low. We use CIFAR100, CORE50, SVHN, dSprites-loc, FGVC-Aircraft, Cars, and Letters for our experiments. For CIFAR100, CORE50, and FGVC-Aircraft, the first session consists of 10 classes, 4 for dSprites-loc, 16 for Cars, and 12 for letters. The rest of the sessions include 10 classes for CIFAR100, FGVC-Aircraft, 20 for Cars, 5 for CORE50 and Letters, 2 for SVHN and dSprites-loc. Therefore, the total number of incremental sessions for CIFAR100, FGVC-Aircraft, and Cars is 10 while for CORE50 we have 9 sessions. A pre-trained on Imagenet-1k EfficientNet-B0 is deployed as a backbone for all methods. FSA-FiLM outperforms all the competitors by a significant margin on all datasets except dSprites-loc. We attribute the performance gap on dSprites-loc due to the",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18824",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/60d2677741a9d16c98988e84a31a49a3efc26f7383bc46a6087fe4ccb1771f07.jpg",
+        "image_caption": [
+            "Figure 1. Average accuracy across all VTAB+ datasets using no-adaptation (NA), FiLM adaptation (A-FiLM), and full body adaptation (A-FB) for different classifier heads (NCM, LDA, Linear) and number of shots (5, 10, 50, All Data). The results correspond to the offline setting where all classes are available without any incremental learning."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/ccde9c21b8b8f72cd809396554c7006af3c3330cdb4c30446c92ddcb508f3b98.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>CIFAR100</td><td>CORE50</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Cars</td><td>Letters</td><td>Avg Diff</td></tr><tr><td>NA</td><td>68.2 (26.8)</td><td>82.6 (14.2)</td><td>39.9 (51.1)</td><td>20.6 (54.0)</td><td>41.3 (1.7)</td><td>43.3 (40.3)</td><td>68.4 (24.1)</td><td>0.0</td></tr><tr><td>E-EWC+SDC[41]</td><td>32.4 (66.7)</td><td>21.7 (78.1)</td><td>39.5 (60.1)</td><td>18.6 (81.4)</td><td>25.6 (55.8)</td><td>30.0 (62.6)</td><td>33.6 (66.3)</td><td>-23.3</td></tr><tr><td>FACT [45]</td><td>10.2 (89.4)</td><td>22.0 (77.7)</td><td>33.8 (65.9)</td><td>6.4 (93.6)</td><td>4.7 (90.3)</td><td>0.6 (99.3)</td><td>20.9 (79.1)</td><td>-38.0</td></tr><tr><td>ALICE [21]</td><td>52.4 (45.8)</td><td>72.8 (25.8)</td><td>46.1 (53.6)</td><td>68.3 (31.7)</td><td>39.8 (35.0)</td><td>36.4 (56.0)</td><td>75.7 (24.2)</td><td>+3.9</td></tr><tr><td>FSA</td><td>62.8 (34.5)</td><td>82.8 (15.5)</td><td>71.3 (26.6)</td><td>91.5 (8.5)</td><td>50.8 (6.3)</td><td>50.3 (36.6)</td><td>78.4 (21.4)</td><td>+17.7</td></tr><tr><td>FSA-LL</td><td>60.5 (37.2)</td><td>79.0 (19.2)</td><td>64.6 (33.1)</td><td>91.3 (8.5)</td><td>45.4 (21.7)</td><td>45.7 (43.8)</td><td>77.2 (22.7)</td><td>+14.2</td></tr><tr><td>FSA-FiLM</td><td>73.8 (23.4)</td><td>85.4 (13.3)</td><td>75.9 (23.4)</td><td>76.9 (22.8)</td><td>55.9 (-5.7)</td><td>55.9 (30.2)</td><td>79.7 (20.0)</td><td>+19.9</td></tr><tr><td>GDumb [24]</td><td>54.5 (42.2)</td><td>82.4 (15.0)</td><td>78.2 (19.6)</td><td>79.5 (12.9)</td><td>25.3 (56.9)</td><td>14.2 (82.6)</td><td>70.1 (27.0)</td><td>+5.7</td></tr><tr><td>Offline-FiLM</td><td>78.2</td><td>88.4</td><td>93.1</td><td>98.5</td><td>67.5</td><td>67.3</td><td>85.2</td><td>+30.6</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 1. Last session's test accuracy  $(\\%)$ $(\\uparrow)$  and the PPDR  $(\\%)$ $(\\downarrow)$  in parentheses, for the high-shot CIL setting (Sec. 4.3). The last column reports the average accuracy difference  $(\\uparrow)$  across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on Imagenet-1k is used as a backbone for all methods. For reference, we include the replay-based baseline GDumb where 1k images are used for the memory buffer.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "large number of data points (25k) and the portion of the classes  $(25\\%)$  in the first session. It is also apparent the efficiency of fine-tuning FiLM parameters over fine-tuning the parameters of the model's last layer; note the number of FiLM parameters is only 20.5k while the last layer of an EfficientNet-B0 comprises 2.9M parameters. Furthermore, fine-tuning the FiLM parameters offer almost  $20\\%$  accuracy increase on average compared to using a pretrained model without doing any further adaptation. Interestingly, the replay-free FSA-FILM is able to outperform significantly the replay-based method GDumb with a 1k memory buffer on most of the datasets; accuracy and time comparisons between FSA-FiLM and GDumb with varying buffer sizes can be found in Figure 1 of the Supplement. Regarding FACT's performance, although it starts from a pre-trained backbone, it was developed under the assumption that the first session contains lots of data and a high fraction of the classes that will be encountered  $(>50\\%)$  which is not true for the setting treated in Table 1. FACT overfits in this setting and this results in poor performance. It turns out that FACT's assumptions about the first session are a strong requirement",
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "which is not necessary for obtaining good performance as our FSA baseline shows.",
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+    {
+        "type": "text",
+        "text": "Few-shot+ CIL. This setting is the one that has most commonly been used for few-shot CIL (FSCIL) and it involves an initial session that contains a large number of classes (around  $50 - 60\\%$  of the total number of classes in the dataset) and all the available training images of these classes. The remaining sessions comprise a small number of classes and shots (typically 5/10-way 5-shot). Here we follow the exact FSCIL settings as described in [45, 21] for CIFAR100 and CUB200. We use ResNet-18/20 and EfficientNet-B0 as backbones. Table 2 summarizes the performance comparison between baselines. FSA performs on par with FACT on CIFAR100 when we use the original backbone used in [45], and it outperforms FACT by almost  $10\\%$  and ALICE by  $3.4\\%$  when EfficientNet-B0 is utilized while FSA-FiLM exhibits the lowest PPDR score. Notice also that FSA is only marginally worse than its offline counterpart, meaning there is little room for continuous body adaptation to improve things further. For CUB200, FSA",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "18825",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "with an EfficientNet-B0 performs on par with ALICE. Interestingly, we observe that NA performs well on this dataset. This indicates that CUB200 is not far from ImageNet-1k. The current results of FSA set new SOTA performance on CIFAR100 for the FSCIL setting.",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Backbone</td><td colspan=\"2\">Datasets</td></tr><tr><td>CIFAR100</td><td>CUB200</td></tr><tr><td>CEC [43]</td><td></td><td>49.1 (32.7)*</td><td>-</td></tr><tr><td>FACT [45]</td><td>RN-20</td><td>52.1 (30.2)*</td><td>-</td></tr><tr><td>FSA</td><td></td><td>52.0 (30.8)</td><td>-</td></tr><tr><td>NA</td><td></td><td>50.4 (26.8)</td><td>50.0 (29.3)</td></tr><tr><td>CEC [43]</td><td></td><td>-</td><td>52.3 (31.1)*</td></tr><tr><td>FACT [45]</td><td rowspan=\"2\">RN-18</td><td>49.5 (34.8)*</td><td>56.9 (25.0)*</td></tr><tr><td>ALICE [21]</td><td>54.1 (31.5)†</td><td>60.1 (22.4)†</td></tr><tr><td>FSA-FiLM</td><td></td><td>55.2 (24.4)</td><td>52.7 (27.6)</td></tr><tr><td>FSA</td><td></td><td>61.4 (25.1)</td><td>57.6 (24.3)</td></tr><tr><td>NA</td><td></td><td>55.2 (25.8)</td><td>63.2 (19.6)</td></tr><tr><td>FACT [45]</td><td></td><td>56.5 (34.6)</td><td>62.9 (23.3)</td></tr><tr><td>ALICE [21]</td><td rowspan=\"2\">EN-B0</td><td>62.7 (28.4)</td><td>63.5 (22.2)</td></tr><tr><td>FSA-LL</td><td>61.4 (25.7)</td><td>55.9 (22.3)</td></tr><tr><td>FSA-FiLM</td><td></td><td>61.8 (22.4)</td><td>62.9 (20.4)</td></tr><tr><td>FSA</td><td></td><td>66.1 (24.6)</td><td>63.4 (20.9)</td></tr><tr><td>Offline</td><td>EN-B0</td><td>67.0</td><td>65.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Baseline comparison under the few-shot+ CIL setting (Sec. 4.3). We report the accuracy  $(\\%)$  ( $\\uparrow$ ) of the last session and the PPDR  $(\\%)$  ( $\\downarrow$ ) in parentheses. Asterisk  $(*)$  indicates that the reported results are from [45] and  $\\dagger$  indicates results reported in [21]. We use three different backbones, EfficientNet-B0 (EN-B0) and ResNet-18/20 (RN-18/20); EN-B0 and RN-18 are pre-trained onImagenet-1k.",
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+    },
+    {
+        "type": "text",
+        "text": "Few-shot CIL. The final setting, which is firstly introduced in this work, considers an alternative FSCIL setting in which only a small number of data points are available in all sessions, including the first. We use 50 shots per session while the first session includes  $20\\%$  of the total number of classes of the dataset. Each of the remaining sessions includes around  $10\\%$  of the total number of classes; more details are available in the Supplement. We repeat experiments 5 times and we report the mean accuracy and PPDR in Table 3. FSA-FiLM outperforms all the other baselines by a large margin in terms of both accuracy and PPDR, indicating that transfer learning is considerably advantageous for CIL when the data availability is low. Notice that both ALICE and FACT struggle to achieve good performance under this setting due to the limited amount of data in the first session. We find that FGVC-Aircraft exhibits a positive backward transfer behavior that we attribute to a difficult initial session followed by sessions that contain classes that are comparatively easier to distinguish.",
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+    {
+        "type": "text",
+        "text": "Finally, we demonstrate the suitability of the LDA head",
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+    },
+    {
+        "type": "text",
+        "text": "in FSA-FiLM compared to a nearest class mean head, denoted FSA-FiLM-NCM. In the continual learning setting, LDA gives far larger improvements over NCM; e.g.  $10\\%$  on average as presented in Table 3. This highlights the importance of a strong classification layer. Note that the incremental update of LDA does not require any replay buffer as opposed to a linear head.",
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+    {
+        "type": "text",
+        "text": "4.4. Inhomogeneous Class-Incremental Learning",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "FSA adapts the body only on the first session of continual learning and it is therefore likely to be sensitive to the particular classes which are present in this session. To investigate the degree of performance sensitivity for FSA, we devise a setting similar to the few-shot CIL setting of Sec. 4.3, where each session includes classes that share some common attribute. We select CIFAR100 which provides superclass information, and DomainNet which consists of different domains and also has superclass information available. We create three distinct CIL configurations for each dataset, each of which has different types of data in the first session. For CIFAR100, we split the data into 19 sessions. The first session includes 10 classes from super-classes (i) aquatic mammals and fish  $(Aq)$ , (ii) electric devices and furniture  $(DevF)$ , or (iii) Vehicles 1 and Vehicles 2 (Veh). Each of the other 18 sessions include images from the remaining 18 super-classes. Similarly, for DomainNet, we split the data into 6 sessions using 50 shots with 10 classes in each session. The first session includes 10 classes of (i) the \"electricity\" superclass of the real domain  $(El-R)$ , (ii) the \"furniture\" superclass of the clipart domain  $(F-Clp)$ , or (iii) the \"transportation\" superclass of the sketch domain  $(Tr-Sk)$ . In this way, we can vary the content of the first session and analyze the effect this has on performance. Table 4 reveals that FSA-FiLM's performance is similar even if the data in the first session used for the body adaptation appears disparate from that contained in the remaining sessions. Even for DomainNet where the distribution shift of the data across sessions is considerable, performance is only marginally affected in each of the three settings. This provides evidence that adapting the body only on the first session achieves competitive performance regardless of the class order, given the assumption that the data come from a single dataset (albeit a varied one in the case of DomainNet).",
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+    {
+        "type": "text",
+        "text": "4.5. When to adapt the body?",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Despite the strong performance of FSA (-FiLM) in the few-shot settings of Sec. 4.3, there are cases where the NA method achieves very close accuracy to FSA (e.g. see CUB200 results in Table 2). This implies that there may be datasets where adaptation is not required and all we need is the pre-trained backbone. In order to decide whether we require body adaptation or not, we compute the minimum cosine distance in the embedding space of the pre",
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+    },
+    {
+        "type": "page_number",
+        "text": "18826",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/daf836b0d71cdd742920b3f40c42ee43510fa0c9824306bc97fba203f12995ef.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method/Dataset</td><td>CIFAR100</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Letters</td><td>DomainNet</td><td>iNaturalist</td><td>Avg Diff</td></tr><tr><td>NA</td><td>57.4 (28.4)</td><td>28.3 (61.5)</td><td>11.9 (66.6)</td><td>41.0 (-15.5)</td><td>57.6 (29.9)</td><td>69.0 (17.2)</td><td>49.7 (4.3)</td><td>0.0</td></tr><tr><td>FACT [45]</td><td>16.8 (79.7)</td><td>24.1 (66.2)</td><td>11.7 (64.1)</td><td>8.3 (79.9)</td><td>49.8 (40.9)</td><td>20.6 (75.6)</td><td>14.3 (74.0)</td><td>-24.2</td></tr><tr><td>ALICE [21]</td><td>58.0 (33.8)</td><td>23.0 (65.9)</td><td>23.0 (46.0)</td><td>42.0 (27.5)</td><td>66.5 (31.4)</td><td>66.5 (25.1)</td><td>47.9 (13.7)</td><td>+1.7</td></tr><tr><td>FSA</td><td>60.3 (27.0)</td><td>32.9 (53.5)</td><td>33.7 (41.3)</td><td>50.1 (-16.8)</td><td>62.2 (28.5)</td><td>70.3 (17.5)</td><td>51.5 (1.1)</td><td>+6.6</td></tr><tr><td>FSA-LL</td><td>62.0 (25.7)</td><td>43.5 (47.0)</td><td>18.8 (61.7)</td><td>45.8 (-2.1)</td><td>69.4 (26.1)</td><td>67.6 (16.9)</td><td>49.2 (14.1)</td><td>+5.9</td></tr><tr><td>FSA-FiLM-NCM</td><td>66.4 (24.8)</td><td>38.8 (56.5)</td><td>25.1 (59.4)</td><td>42.5 (-7.5)</td><td>57.1 (34.9)</td><td>68.8 (18.5)</td><td>51.5 (12.1)</td><td>+5.0</td></tr><tr><td>FSA-FiLM</td><td>70.9 (20.5)</td><td>51.3 (43.5)</td><td>35.7 (43.1)</td><td>55.8 (-19.8)</td><td>73.4 (22.1)</td><td>74.0 (15.6)</td><td>58.8 (4.8)</td><td>+15.0</td></tr><tr><td>Offline-FiLM</td><td>73.8</td><td>77.2</td><td>83.7</td><td>65.1</td><td>79.7</td><td>75.1</td><td>62.1</td><td>+28.0</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/3251907ddae537d3c1c6efdfb44349f27b14127192efade52d8d5e29fbaab32b.jpg",
+        "table_caption": [
+            "Table 3. Accuracy  $(\\%)$  (↑) of the last session and PPDR  $(\\%)$  (↓) in parentheses for the few-shot CIL setting of Sec. 4.3. The last column reports the average accuracy difference  $(\\uparrow)$  across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone for all methods. FSA-FiLM-NCM utilizes an NCM classifier while NA, FSA (-LL, FiLM) and Offline uses a LDA head."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>NA</td><td>Aq</td><td>DevF</td><td>Veh</td></tr><tr><td>CIFAR100</td><td>57.4±1.0</td><td>66.1±1.6</td><td>66.2±1.9</td><td>67.9±1.2</td></tr><tr><td></td><td>NA</td><td>El-R</td><td>F-Clp</td><td>Tr-Sk</td></tr><tr><td>DomainNet</td><td>69.0±0.4</td><td>70.6±0.6</td><td>71.7±0.6</td><td>72.8±0.5</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/771c64d4340355af9f0022e1ca5c2dd84744c70af8e4647b81e3f3f3fb4da3d1.jpg",
+        "image_caption": [
+            "Figure 2. Scatter plot of the accuracy differences between FSA-FiLM and NA against the minimum cosine distance between a dataset and miniImagenet dataset evaluated using the NA method. We consider the offline setting with 50 shots. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "trained backbone between the downstream dataset and the miniImagenet [31] dataset. We use miniImagenet (60k images) as a proxy ofImagenet-1k (1.3M images) to reduce the computational overhead of evaluating pairwise distances. This allows us to approximately measure the dissimilarity between the downstream dataset andImagenet-1k.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Fig. 2 shows the accuracy difference between FSA-FiLM and NA as a function of the cosine distance for the offline setting with 50 shots whilst Fig. 3 illustrates the same accuracy difference where the datasets are grouped based on the VTAB+ categorization. For this experiment, we use 24",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "datasets (VTAB+, DomainNet, and iNaturalist). We observe that adaptation is more beneficial for datasets in the structured domain, which contain images that are dissimilar to those of ImageNet-1k.",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/5e00bc4d14b3d904cf9115d01ed46201c80caab98f9a04f5b241fcbb0910130d.jpg",
+        "image_caption": [
+            "Figure 3. Bar plot of the accuracy differences between FSA-FiLM and NA for the offline case with 50 shots."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c771ebfde7663b0505cfcca1b19a0ad4e04aa875289ad0ee0279e9b04b90ee8a.jpg",
+        "table_caption": [
+            "Table 4. Last session accuracy  $(\\%)$ $(\\uparrow)$  of FSA-FiLM for three different session splits on CIFAR100 and DomainNet as described in Sec. 4.4. For reference, we also include the accuracy of NA. Results are averaged over 5 runs (mean  $\\pm$  std)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CFR100</td><td>SVHN</td><td>dSp-loc</td><td>FGVC</td><td>Letters</td><td>DNet</td><td>iNat</td></tr><tr><td>EffNet-B0 (FSA-FILM)</td><td>70.9</td><td>51.3</td><td>35.7</td><td>55.8</td><td>73.4</td><td>74.0</td><td>58.8</td></tr><tr><td>ConvNext (NA)</td><td>87.1</td><td>43.6</td><td>13.6</td><td>50.2</td><td>63.1</td><td>82.9</td><td>72.6</td></tr><tr><td>ConvNext-CosD</td><td>0.2</td><td>0.6</td><td>0.6</td><td>0.3</td><td>0.4</td><td>0.3</td><td>0.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5. Accuracy comparison between a pre-trained ConvNext on ImageNet-22k without body adaptation (NA) and a pre-trained EfficientNet-B0 on ImageNet-1k which is adapted on the first session (FSA-FiLM). We use the few-shot CIL setting (Sec. 4.3) and we report the accuracy  $(\\%)$  ( $\\uparrow$ ) after the last session. Results are averaged over 5 runs (mean±std). We also include the minimum cosine distance using the pre-trained ConvNext as in Figure 2.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To stress the importance of adaptation on datasets far from ImageNet, we compare FSA-FiLM with an EfficientNet-B0 backbone to the no-adaptation method with a ConvNext [14] pre-trained onImagenet-22k. The total number of parameters for FSA-FiLM (backbone and FiLM",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "18827",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "parameters) is  $\\sim 4\\mathrm{M}$  while for ConvNext is  $348\\mathrm{M}$ . Table 5 shows that a small adapted backbone can significantly surpass the accuracy of a much larger pre-trained backbone for datasets far from ImageNet. We also compute the cosine distance measure for ConvNext and find that it is predictive of the performance of the unadapted ConvNext model and the benefits of adaptation. We show this in Table 5; note that for CIFAR100 the ConvNext's cosine distance values are small relative to the other datasets (indicating that CIFAR100 is close to the pretraining distribution) whereas for EfficientNet the values in Figure 2 indicate that CIFAR100 is more out-of-distribution.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The main takeaway from these results is that when there is a large cosine distance (e.g. SVHN, dSprites, FGVC, Letters) FiLM adaptation of a light-weight backbone performs well - better even than applying LDA head adaptation to a much larger backbone trained on a much larger dataset. As the community employs ever-larger models and datasets, these results indicate that adapters are likely to continue to bring improvements over simply learning a classifier head (the NA baseline).",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Discussion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We have presented FSA (-FiLM), a simple yet effective replay-free baseline for CIL which adapts a pre-trained backbone via full body adaptation or FiLM layers only at the first session of continual learning and then utilizes a flexible incrementally updated LDA classifier on top of the body. Extensive experiments in several CIL scenarios have shown that FSA outperforms previous SOTA baselines in most cases, thus, questioning the efficacy of current approaches to continuous body adaption. Furthermore, the experiments have revealed that FiLM layers are helpful when the amount of data available in the target domain is relatively low and the number of parameters in the neural network and the size of the source domain data set is large. For very large foundation models trained on very large source domain data sets, it is likely we are often in this situation and FiLM-like layers will be more effective than full-body adaptation, even when the target domain has a fairly large amount of data.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Limitations and future work. The main limitation of this work is inextricably linked with the distributional assumptions of CIL in general. If the data distribution at each session shifts considerably (e.g. the first session includes natural images while the next session includes images of numbers) then first session body adaptation is not suitable. In future work, we plan to combine FSA (-FiLM) with a memory method like GDumb to get the best of both worlds and deal with more challenging CIL scenarios.",
+        "bbox": [
+            75,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            501,
+            90,
+            596,
+            106
+        ],
+        "page_idx": 8
+    },
+    {
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+        "sub_type": "ref_text",
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+        ],
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+            "[36] Guile Wu, Shaogang Gong, and Pan Li. Striking a balance between stability and plasticity for class-incremental learning. In Proceedings of the IEEE/CVF International Confer"
+        ],
+        "bbox": [
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+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "ence on Computer Vision (ICCV), pages 1124-1133, 2021. 3",
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+            "[39] Shipeng Yan, Jiangwei Xie, and Xuming He. Der: Dynamically expandable representation for class incremental learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3014-3023, 2021. 2",
+            "[40] Jason Yosinski, Jeff Clune, Yoshua Bengio, and Hod Lipson. How transferable are features in deep neural networks? Advances in Neural Information Processing Systems, 27, 2014. 3",
+            "[41] Lu Yu, Bartlomiej Twardowski, Xialei Liu, Luis Herranz, Kai Wang, Yongmei Cheng, Shangling Jui, and Joost van de Weijer. Semantic drift compensation for class-incremental learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 6982-6991, 2020. 5, 6",
+            "[42] Xiaohua Zhai, Joan Puigcerver, Alexander Kolesnikov, Pierre Ruyssen, Carlos Riquelme, Mario Lucic, Josip Djolonga, Andre Susano Pinto, Maxim Neumann, Alexey Dosovitskiy, et al. A large-scale study of representation learning with the visual task adaptation benchmark. arXiv preprint arXiv:1910.04867, 2019. 5",
+            "[43] Chi Zhang, Nan Song, Guosheng Lin, Yun Zheng, Pan Pan, and Yinghui Xu. Few-shot incremental learning with continually evolved classifiers. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12455-12464, 2021. 5, 7",
+            "[44] Bowen Zhao, Xi Xiao, Guojun Gan, Bin Zhang, and Shu-Tao Xia. Maintaining discrimination and fairness in class incremental learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13208-13217, 2020. 2",
+            "[45] Da-Wei Zhou, Fu-Yun Wang, Han-Jia Ye, Liang Ma, Shiliang Pu, and De-Chuan Zhan. Forward compatible few-shot class-incremental learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9046-9056, 2022. 3, 5, 6, 7, 8"
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new file mode 100644
index 0000000000000000000000000000000000000000..67b9f8a4f7ea3ec3a37d8d3182e4670666e81aad
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+            "content": "First Session Adaptation: A Strong Replay-Free Baseline for Class-Incremental Learning"
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+            "content": "Aristeidis Panos  \nUniversity of Cambridge"
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+            "content": "Yuriko Kobe University of Cambridge"
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+            "angle": 0,
+            "content": "Daniel Olmeda Reino  \nToyota Motor Europe"
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+            "content": "Richard E. Turner  \nUniversity of Cambridge"
+        },
+        {
+            "type": "text",
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+                0.376
+            ],
+            "angle": 0,
+            "content": "ret26@cam.ac.uk"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.313,
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In Class-Incremental Learning (CIL) an image classification system is exposed to new classes in each learning session and must be updated incrementally. Methods approaching this problem have updated both the classification head and the feature extractor body at each session of CIL. In this work, we develop a baseline method, First Session Adaptation (FSA), that sheds light on the efficacy of existing CIL approaches, and allows us to assess the relative performance contributions from head and body adaption. FSA adapts a pre-trained neural network body only on the first learning session and fixes it thereafter; a head based on linear discriminant analysis (LDA), is then placed on top of the adapted body, allowing exact updates through CIL. FSA is replay-free i.e. it does not memorize examples from previous sessions of continual learning. To empirically motivate FSA, we first consider a diverse selection of 22 image-classification datasets, evaluating different heads and body adaptation techniques in high/low-shot offline settings. We find that the LDA head performs well and supports CIL out-of-the-box. We also find that Featurewise Layer Modulation (FiLM) adapters are highly effective in the few-shot setting, and full-body adaption in the high-shot setting. Second, we empirically investigate various CIL settings including high-shot CIL and few-shot CIL, including settings that have previously been used in the literature. We show that FSA significantly improves over the state-of-the-art in 15 of the 16 settings considered. FSA with FiLM adapters is especially performant in the few-shot setting. These results indicate that current approaches to continuous body adaptation are not working as expected. Finally, we propose a measure"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.414,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "that can be applied to a set of unlabelled inputs which is predictive of the benefits of body adaptation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.502,
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Continual learning (CL) is needed to bring machine learning models to many real-life applications. After a model is trained on a given set of data, and once deployed in its test environment, it is likely that new classes will naturally emerge. For example, in an autonomous driving scenario, new types of road transportation and traffic signage can be encountered. The deployed model needs to efficiently acquire this new knowledge with minimal cost (e.g. annotation requirements) without deteriorating the performance on existing classes of objects. The process of efficiently acquiring new knowledge while preserving what is already captured by the model is what continual learning methods target."
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Continual learning can be mainly divided into task incremental learning and class incremental learning. Task incremental learning (TIL) sequentially learns independent sets of heterogeneous tasks and is out of this paper's scope. Class incremental learning (CIL), in contrast, assumes that all classes (already learnt and future ones) form part of a single classification task. In class-incremental learning, data arrive in a sequence of sessions with new classes appearing as the sessions progress. Critically, the data in each session cannot be stored in its entirety and cannot be revisited. The goal is to train a single classification model under these constraints."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In both task incremental and class incremental learning,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
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+            ],
+            "angle": 0,
+            "content": "the data distribution will change as the sessions progress. However, these changes tend to be smaller in real-world class incremental learning settings than in the task incremental setting. For, example consider a human support robot learning about new objects in a home in an incremental manner (CIL) vs. the same robot learning to adapt to different homes (TIL)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.2,
+                0.47,
+                0.382
+            ],
+            "angle": 0,
+            "content": "Practically, CIL has two major uses. First, in situations where large amounts of data arrive in each session and so retraining the model is computationally prohibitive. Second, in situations where data are not allowed to be revisited due to privacy reasons such as under General Data Protection Regulation (GDPR). The latter situation is relevant for applications such as personalization where small numbers of data points are available i.e. few-shot continual learning. So-called replay-free methods are necessary for such settings, as samples of previous sessions are not allowed to be memorized, but CIL is known to be challenging in such settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+                0.471,
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+            "angle": 0,
+            "content": "Current SOTA methods for class incremental learning start from a pre-trained backbone [13, 19, 35, 34] and then adapt the features at each session of continual learning. The use of a pre-trained backbone has been shown to lead to strong performance especially in the few-shot CIL setting due to the lack of data [21]. However, it is unclear to what extent continuous adaptation of the features in each session is helpful. In general, in CIL there is a trade-off between adaptation (which helps adapt to the new statistics of the target domain) and catastrophic forgetting (whereby earlier classes are forgotten as the representation changes). When memorization of previous samples is restricted, the benefits from adapting the feature extractor body to learn better features might well be out-weighted by the increase in forgetting of old classes. Moreover, body adaptation in earlier sessions is arguably more critical (e.g. adapting the backbone to the new domain in the first session), whilst it is less essential in later sessions where the changes in the ideal representation between sessions are smaller."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "This work explores under what conditions continuous adaptation of the body is beneficial, both in principle and in current practice. In order to do this, we develop a new replay-free method, inspired by the first encoding method of [2], called First Session Adaptation (FSA). FSA adapts the body of a pre-trained neural network on only the first session of continual learning. We investigate adapting all body parameters and the use of Feature-wise Layer Modulation (FiLM) adapters [23] which learn only a small number of parameters. The head, in contrast, is adapted at each session using an approach that is similar to Linear Discriminate Analysis (LDA), which suffers from no forgetting, and improves over the Nearest Class Mean classifier (NCM) [18] approach. The efficacy of this general approach, including comparisons to a standard linear head, is first motivated"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.227
+            ],
+            "angle": 0,
+            "content": "through experiments in the offline setting (Sec. 4.2). We then carry out experiments under three CIL settings. First, we consider the high-shot setting (high-shot CIL). The other two settings consider few-shot continual learning. Specifically, one setting follows previous approaches that employ an initial session with a large number of data points and few-shot sessions thereafter (few-shot+ CIL) while the other exclusively includes sessions with only a small amount of data (few-shot CIL)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.228,
+                0.893,
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+            ],
+            "angle": 0,
+            "content": "The contributions of the paper are as follows: (1) We develop a replay-free CIL baseline, namely FSA, that is extremely simple to implement and performs well in many different scenarios. (2) We empirically motivate FSA through a set of offline experiments that evaluate different forms of neural network head and body adaptation; (3) We then compare FSA to a set of strong continual learning baseline methods in a fair way using the same pre-trained backbone for all methods. (4) We show that the FSA-FiLM baseline performs well in the high-shot CIL setting, outperforming the SOTA whilst avoiding data memorization. (5) In the few-shot learning settings, FSA outperforms existing continual learning methods on eight benchmarks, often by a substantial margin, and is statistically tied with the best performing method on the one remaining dataset. (6) Finally, we propose a measure that can be applied to a set of unlabeled inputs which is predictive of the benefits of body adaptation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.513,
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Class Incremental Learning is more challenging than task-incremental continual learning as a shared output layer is used for the classes of different learning sessions. We refer to [7] for a survey on both class and task incremental learning. While softmax cross entropy loss is considered a standard in classification models, it is shown to be a source of class interference in continual learning [38, 4]. Thus, recent works either focus on fixing the softmax classifier [4, 1, 44] or deploy nearest class mean classifiers (NCM) as an alternative [25, 5, 11]. In this work, we deploy an LDA classifier that uses the mean embedding of each class and an incrementally updated covariance matrix shared across all classes. We show that this approach is comparable to a softmax classifier in the offline setting and that it outperforms NCM."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.766,
+                0.892,
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+            "angle": 0,
+            "content": "Due to the challenging nature of class incremental learning, some methods employ a buffer of stored samples from previous sessions [24, 39]. [24] suggests a simple baseline, GDumb, that performs offline training on both buffer data and new session data at each incremental step. GDumb shows strong performance compared to sophisticated continual learning solutions. Here we show that our simple yet effective solution often outperforms variants of GDumb that have a large memory without leveraging any buffer of stored"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
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+            "angle": 0,
+            "content": "18821"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.093,
+                0.139,
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+            "angle": 0,
+            "content": "samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.107,
+                0.473,
+                0.438
+            ],
+            "angle": 0,
+            "content": "In addition to the issues arising from the shared classification layer, learning a feature extractor that can provide representative features of all classes is a key element in continual learning. Some class incremental learning methods leverage large initial training session or start from a pretrained network, e.g., [35, 9, 36] and show improved overall continual learning performance without questioning the role of such pre-training steps and whether the learned representations have in fact improved. Recently, [19] studies continual learning with strong pre-trained models and proposes deploying exemplar-based replay in the latent space using a small multilayer network on top of the fixed pretrained model. The authors show that such latent replay improves performance, especially for tasks that are different from the distribution used to train the initial model. In this work, we show that adaptation of pre-trained models is essential for strong continual learning performance. However, different from all existing continual learning works, we show that adapting the representation only in the first session is sufficient to obtain representative features for the classes being learned and that this forms a strong baseline for future continual learning methods."
+        },
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+            ],
+            "angle": 0,
+            "content": "In addition to the incremental classification in the full data regime, we focus on the few-shot scenario where only a few labeled examples per class are provided at each training session. [9] utilize a meta-trained network for few-shot classification and explore multiple design choices including a no-adaptation baseline and a method to optimize orthogonal prototypes with the last classification layer only. The method heavily relies on a pre-training and meta-training step on a large subset of classes from the original dataset. In this work, we show that the meta-training step is not essential and that a simple LDA head is sufficient without the reliance on a big initial training stage. In [11] the authors propose a new distillation loss functioning at the feature map level where importance values are estimated per feature map along with replay and consider an NCM classifier at test time. [45] heavily relies on the training of an initial session using a specific loss function that takes into account classes that will be added in future. It further requires the total number of classes to be known a priori which is unrealistic for real applications. Our solution adapts FILM parameters to the first session data and fixes the representation for the remaining training sessions. We show that surprisingly few samples in the first session are sufficient for adaptation and that our solution is more powerful than current few-shot continual learning solutions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.83,
+                0.273,
+                0.848
+            ],
+            "angle": 0,
+            "content": "3. Proposed Algorithm"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, first we discuss the main components of the proposed methods FSA/FSA-FiLM, namely body adaptation techniques and classifier heads. Then we formally"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.792,
+                0.107
+            ],
+            "angle": 0,
+            "content": "introduce the two methods for tackling CIL."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.116,
+                0.704,
+                0.131
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.138,
+                0.895,
+                0.353
+            ],
+            "angle": 0,
+            "content": "In CIL, we are given a dataset \\(\\mathcal{D}_s = \\{\\mathbf{x}_{i,s},y_{i,s}\\}_{i = 1}^{N_s}\\) for each session \\(s\\in \\{1,\\ldots ,S\\}\\), where \\(X_{s} = \\{\\mathbf{x}_{i,s}\\}_{i = 1}^{N_{s}}\\) is a set of images and \\(Y_{s} = \\{y_{i,s}\\}_{i = 1}^{N_{s}}\\) is the set of the corresponding labels with \\(y_{i,s}\\in \\mathcal{V}_s\\). Here \\(\\mathcal{V}_s\\) is the label space of session \\(s\\). It is common in CIL that label spaces are mutually exclusive across sessions, i.e. \\(\\mathcal{V}_s\\cap \\mathcal{V}_{s'} = \\emptyset\\), \\(\\forall s\\neq s'\\) and we only have access to \\(\\mathcal{D}_s\\) in the current session \\(s\\) to train our model. The proposed FSA method can naturally handle sessions with overlapping label spaces too, however, we follow the former paradigm in our experiments. Another typical assumption in CIL is that the data in all sessions come from the same dataset. We also adopt this assumption in this work, although our experiments on DomainNet are a step toward considering different datasets in each session."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.355,
+                0.807,
+                0.369
+            ],
+            "angle": 0,
+            "content": "In session \\(s\\), we will use models defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.605,
+                0.379,
+                0.892,
+                0.4
+            ],
+            "angle": 0,
+            "content": "\\[\nf _ {s} (\\mathbf {x}) = W _ {s} ^ {\\top} g _ {\\boldsymbol {\\theta} _ {s}} (\\mathbf {x}) + \\mathbf {b} _ {s}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.409,
+                0.895,
+                0.562
+            ],
+            "angle": 0,
+            "content": "where \\(g_{\\theta_s}(\\mathbf{x}) \\in \\mathbb{R}^d\\) is a feature extractor backbone<sup>1</sup> with session-dependent parameters \\(\\theta_s\\). The linear classifier head comprises the class weights \\(W_s \\in \\mathbb{R}^{d \\times |\\mathcal{Y}_{1:s}|}\\) and biases \\(\\mathbf{b}_s \\in \\mathbb{R}^{|\\mathcal{Y}_{1:s}|}\\), and \\(\\mathcal{Y}_{1:s} = \\cup_{j=1}^{s} \\mathcal{Y}_j\\) is the label space of all distinct classes we have seen up to session \\(s\\). Ideally, when a new dataset \\(\\mathcal{D}_s\\) is available at the \\(s\\)-th session, the model should be able to update the backbone parameters \\(\\theta\\) and the linear classifier head \\(W_s\\) with the minimum computational overhead and without compromising performance over the previously seen classes \\(\\mathcal{Y}_{1:s}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.579,
+                0.895,
+                0.759
+            ],
+            "angle": 0,
+            "content": "Backbone adaptation. Traditionally, the adaptation of the body at the current session \\(s\\) requires updating the full set of the network parameters \\(\\theta_{s}\\) (full-body adaptation). Options include using specifically designed loss functions that mitigate catastrophic forgetting or using a memory buffer that stores a subset of the previously encountered data. See [16] for a review of continual learning techniques. Nevertheless, when training data availability is scarce relative to the size of the model then full-body adaptation ceases to be suitable, and few-shot learning techniques [33], such as meta-learning [10] and transfer learning [40] become favorable."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.761,
+                0.894,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Recent works in few-shot learning [26] showed that a pre-trained backbone can be efficiently adapted by keeping its parameters \\(\\theta_{s}\\) frozen and introducing Feature-wise Linear Modulation (FiLM) [23] layers with additional parameters \\(\\xi_{s}\\) which scale and shift the activations produced by a convolutional layer. In [26], these parameters are generated by a meta-trained network when a downstream task is"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.875,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>In this paper, we interchangeably use the terms feature extractor, backbone, and body."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "18822"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.152
+            ],
+            "angle": 0,
+            "content": "given. Alternatively, \\(\\xi_{s}\\) can be learned (fine-tuned) by the downstream data as in [27]. In this work, we consider both meta-learned (Supplement) and fine-tuned (Sec. 4) FiLM parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.17,
+                0.473,
+                0.323
+            ],
+            "angle": 0,
+            "content": "Classifier heads. In both offline and CIL settings, (linear) classifier heads can be divided into two groups; parametrized and parameter-free. Parametrized heads require the weights/biases in Eq. (1) to be updated by an iterative gradient-based procedure whilst for parameter-free heads, a closed-form formula is available that directly computes the weights/biases after the update of the backbone. We consider three different heads (for notational simplicity we consider the offline setting, and thus suppress session \\(s\\) dependence), one parametrized, and two parameter-free."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.331,
+                0.454,
+                0.347
+            ],
+            "angle": 0,
+            "content": "- The linear (learnable) head where \\( W, \\mathbf{b} \\) are learned."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.356,
+                0.47,
+                0.387
+            ],
+            "angle": 0,
+            "content": "- The Nearest Class Mean (NCM) classifier where the weight and bias of the \\( k \\)-th class is given by"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.331,
+                0.47,
+                0.387
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.397,
+                0.47,
+                0.43
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {w} _ {k} = \\hat {\\boldsymbol {\\mu}} _ {k} \\text {a n d} b _ {k} = \\ln \\frac {| X ^ {(k)} |}{N} - \\frac {1}{2} \\hat {\\boldsymbol {\\mu}} _ {k} ^ {\\top} \\hat {\\boldsymbol {\\mu}} _ {k}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.109,
+                0.439,
+                0.47,
+                0.488
+            ],
+            "angle": 0,
+            "content": "where \\(X^{(k)} = \\{\\mathbf{x}_i:y_i = k\\}\\) is the set of images belonging in class \\(k\\) and \\(\\hat{\\pmb{\\mu}}_k = \\frac{1}{|X^{(k)}|}\\sum_{\\mathbf{x}\\in X^{(k)}}g_\\pmb {\\theta}(\\mathbf{x})\\) is the mean vector of the embedded images of class \\(k\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.498,
+                0.47,
+                0.528
+            ],
+            "angle": 0,
+            "content": "- The Linear Discriminant Analysis (LDA) classifier with weights/biases defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.122,
+                0.538,
+                0.469,
+                0.582
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {w} _ {k} = \\tilde {S} ^ {- 1} \\hat {\\boldsymbol {\\mu}} _ {k} \\text {a n d} b _ {k} = \\ln \\frac {| X ^ {(k)} |}{N} - \\frac {1}{2} \\hat {\\boldsymbol {\\mu}} _ {k} ^ {\\top} \\tilde {S} ^ {- 1} \\hat {\\boldsymbol {\\mu}} _ {k}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.109,
+                0.582,
+                0.47,
+                0.651
+            ],
+            "angle": 0,
+            "content": "where \\(\\tilde{S} = S + I_d\\) is the regularized sample covariance matrix with sample covariance matrix \\(S = \\frac{1}{|X| - 1}\\sum_{\\mathbf{x}\\in X}(g_{\\boldsymbol{\\theta}}(\\mathbf{x}) - \\hat{\\boldsymbol{\\mu}})(g_{\\boldsymbol{\\theta}}(\\mathbf{x}) - \\hat{\\boldsymbol{\\mu}})^\\top\\), \\(\\hat{\\boldsymbol{\\mu}} = \\frac{1}{|X|}\\sum_{\\mathbf{x}\\in X}g_{\\boldsymbol{\\theta}}(\\mathbf{x})\\), and identity matrix \\(I_d \\in \\mathbb{R}^{d\\times d}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.657,
+                0.47,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Both NCM and LDA classifiers are suitable for CIL since their closed-form updates in Eq. (2) and Eq. (3) support exact, computationally inexpensive, continual updates (via running averages) that incur no forgetting. Updating the linear head, in contrast, requires more computational effort and machinery when novel classes appear in a new session. Notice that setting \\(\\tilde{S} = I_d\\) in LDA recovers NCM."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.763,
+                0.47,
+                0.839
+            ],
+            "angle": 0,
+            "content": "The continuous update of the LDA head is not as straightforward as it is for NCM, since LDA also requires updating the sample covariance \\( S \\). We discuss how this can be attained in the next section where we introduce our proposed method FSA/FSA-FiLM."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.848,
+                0.303,
+                0.864
+            ],
+            "angle": 0,
+            "content": "3.2. First Session Adaptation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Motivated by the efficient adaptation techniques and CIL-friendly classifiers discussed in the previous section,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.365
+            ],
+            "angle": 0,
+            "content": "we propose two simple and computationally efficient CIL methods called First Session Adaptation (FSA) and FSA-FiLM. FSA is based on a full-body adaptation while FSA-FiLM uses FiLM layers to adapt the body. Both methods utilize pre-trained backbones. FSA (-FiLM) (i) adapts the backbone only at the first session and then the backbone remains frozen for the rest of the sessions, and (ii) makes use of an LDA classifier which is continuously updated as new data become available. For adapting the body (either full or FiLM-based adaptation) at the first session, we use a linear head and a cross-entropy loss first, and then after the optimization is over, the linear head is removed and an LDA head is deployed instead, based on the optimized parameters \\(\\theta^{*}\\) and Eq. (3). Updating the LDA head when the data of the next session becomes available, can be done by using Algorithm 1 recursively until the last session \\(S\\). Specifically, by having access to the running terms \\(\\{A, \\mathbf{b}, \\text{count}\\}\\), the sample covariance matrix is given by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.574,
+                0.374,
+                0.892,
+                0.409
+            ],
+            "angle": 0,
+            "content": "\\[\nS = \\frac {1}{\\operatorname {c o u n t} - 1} \\left(A - \\frac {1}{\\operatorname {c o u n t}} \\mathbf {b b} ^ {\\top}\\right). \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.418,
+                0.892,
+                0.435
+            ],
+            "angle": 0,
+            "content": "The time complexity of LDA scales as \\(\\mathcal{O}(d^3 + |\\mathcal{Y}_s|d^2)\\) and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.449,
+                0.88,
+                0.465
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Update of sample covariance running terms"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.502,
+                0.467,
+                0.808,
+                0.482
+            ],
+            "angle": 0,
+            "content": "Require: \\( g(\\cdot) \\equiv a \\) feature extractor backbone"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.482,
+                0.818,
+                0.498
+            ],
+            "angle": 0,
+            "content": "Require: \\(X_{s} = \\{\\mathbf{x}_{i,s}\\}_{i = 1}^{N_{s}}\\): Images of session \\(s\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.498,
+                0.839,
+                0.513
+            ],
+            "angle": 0,
+            "content": "Require: \\(A\\in \\mathbb{R}^{d\\times d}\\) \\(\\mathbf{b}\\in \\mathbb{R}^d\\) count \\(\\in \\mathbb{N}^*\\) if \\(s > 1\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.513,
+                0.824,
+                0.528
+            ],
+            "angle": 0,
+            "content": "1: function INCUPDATE \\((g(\\cdot), X_s, A, b, \\text{count})\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.528,
+                0.892,
+                0.542
+            ],
+            "angle": 0,
+            "content": "2: if \\(s = 1\\) then Initialize \\(A, \\mathbf{b}\\), count"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.543,
+                0.791,
+                0.558
+            ],
+            "angle": 0,
+            "content": "3: \\(A\\gets \\mathbf{0}_{d\\times d},\\mathbf{b}\\gets \\mathbf{0}_d,\\mathrm{count}\\gets 0\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.559,
+                0.598,
+                0.571
+            ],
+            "angle": 0,
+            "content": "4: end if"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.572,
+                0.753,
+                0.589
+            ],
+            "angle": 0,
+            "content": "5: \\(A\\gets A + \\sum_{\\mathbf{x}\\in X_s}g(\\mathbf{x})g(\\mathbf{x})^\\top\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.589,
+                0.707,
+                0.604
+            ],
+            "angle": 0,
+            "content": "6: \\(\\mathbf{b}\\gets \\mathbf{b} + \\sum_{\\mathbf{x}\\in X_s}g(\\mathbf{x})\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.604,
+                0.694,
+                0.617
+            ],
+            "angle": 0,
+            "content": "7: count \\(\\leftarrow\\) count \\(+N_{s}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.619,
+                0.68,
+                0.632
+            ],
+            "angle": 0,
+            "content": "8: return \\(A\\), b, count"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.634,
+                0.62,
+                0.647
+            ],
+            "angle": 0,
+            "content": "9: end function"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.511,
+                0.513,
+                0.892,
+                0.647
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.665,
+                0.892,
+                0.743
+            ],
+            "angle": 0,
+            "content": "its space complexity is \\(\\mathcal{O}(d^2 + |\\mathcal{Y}_{1:s}|d)\\) at the \\(s\\)-th session. This computational burden is negligible compared to taking gradient steps for learning a linear head and as we will see in Sec. 4.2 using covariance information boosts performance significantly against the vanilla NCM head."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.755,
+                0.634,
+                0.772
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this section, we present a series of experiments to investigate the performance of FSA (-FiLM) under different CIL settings. First, we detail the datasets used for the experiments and discuss our implementation. Second, we perform a large empirical comparison between LDA, linear, and NCM classifiers, in combination with different body adaptation techniques, in the offline setting. For the CIL settings, the results are compared to the vanilla method, \\(N_{o}\\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18823"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.228
+            ],
+            "angle": 0,
+            "content": "Adaptation (NA), where a pretrained backbone is combined with an LDA head and remains frozen across sessions. We also consider how these findings are affected by the number of shots available. Third, we compare FSA (-FiLM) with state-of-the-art continual learning methods and conduct ablation studies. Finally, we investigate the effect of adapting the backbone when the CIL dataset is \"similar\" to ImageNet-1k and discuss a similarity metric that indicates whether body adaptation is required."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.236,
+                0.396,
+                0.254
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Implementation details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.259,
+                0.473,
+                0.471
+            ],
+            "angle": 0,
+            "content": "Datasets. We employ a diverse collection of 26 image-classification datasets across the offline and CIL experiments. For the offline experiments of Sec. 4.2, we use the 19 datasets of VTAB [42], a low-shot transfer learning benchmark, plus three additional datasets, FGVC-Aircraft [17], Stanford Cars [12], and Letters [6]. We refer to this group of datasets as VTAB+. For the CIL-based experiments, we choose 5 VTAB+ datasets from different domains, having an adequate number of classes to create realistic CIL scenarios. The datasets are CIFAR100, SVHN, dSprites-location, FGVC-Aircraft, Cars, and Letters while also including 4 extra datasets: CUB200 [32], CORE50 [15], iNaturalist [30], and DomainNet [22]. Exact details for each dataset are provided in the Supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.489,
+                0.473,
+                0.655
+            ],
+            "angle": 0,
+            "content": "Training details. All models are implemented with PyTorch [20]. We use a pre-trained EfficientNet-B0 [28] onImagenet-1k as the main backbone for all methods. For the few-shot+ CIL experiment in Sec. 4.3, we also consider two ResNet architectures, ResNet-18 and ResNet-20 [8] to enable direct comparison to the original settings used in [45]. All the deployed backbones (except ResNet-20, due to the unavailability of pre-trained weights on ImageNet-1k), are pre-trained on ImageNet-1k for all methods. We keep the optimization settings the same across all baselines for fairness. Optimization details are given in the Supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.673,
+                0.473,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Evaluation protocol. We report the Top-1 accuracy after the last continual learning session evaluated on a test set including instances from all the previously seen classes. In the Supplement, we provide the accuracy after each session. To quantify the forgetting behavior, we use a scaled modification of the performance dropping rate [29], namely percent performance dropping rate (PPDR), defined as \\(\\mathrm{PPDR} = 100 \\times \\frac{\\mathcal{A}_1 - \\mathcal{A}_S}{\\mathcal{A}_1}\\%\\), where \\(\\mathcal{A}_1\\) denotes test accuracy after the first session, and \\(\\mathcal{A}_S\\) the test accuracy after the last session."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.818,
+                0.265,
+                0.835
+            ],
+            "angle": 0,
+            "content": "4.2. Head Comparisons"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To motivate the choice of the LDA head for FSA (-FiLM), we compare its average accuracy across all VTAB+ datasets with that of the linear and NCM classifiers under the offline setting where all the classes are available and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.424
+            ],
+            "angle": 0,
+            "content": "no incremental learning is required. For the body, we use no adaptation (NA) as a baseline (i.e. using the unadapted original backbone), FiLM-based adaptation, and full-body adaptation while ranging the number of shots from 5 to 10, then 50, and finally using all available training data. As Fig. 1 illustrates, LDA consistently outperforms both NCM and linear heads when the number of shots is equal to 5 and 10, regardless of adaptation technique. Notice also that as the number of learnable parameters increases, the choice of the head plays a less significant role in the predictive power of the method. Overall, LDA performs similarly to the linear head in the high-shot settings and performs the best of all heads in the low-shot settings. Finally, the full covariance information of LDA provides a consistent advantage over its isotropic covariance counterpart, i.e. the NCM classifier. This is in agreement with the results presented in [27] for the LDA and NCM classifier. In addition to the results presented here, we have also tested meta-learning based body adaptation methods [3, 26, 2] which support continual learning out of the box. We find these perform poorly compared to the fine-tuning based methods. See next section for more results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.434,
+                0.86,
+                0.452
+            ],
+            "angle": 0,
+            "content": "4.3. Class-Incremental Learning Comparisons"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.457,
+                0.895,
+                0.641
+            ],
+            "angle": 0,
+            "content": "We consider three different CIL scenarios: (i) high-shot CIL, (ii) few-shot+ CIL, and (iii) few-shot CIL. We compare our FSA/FSA-FiLM methods with recent state-of-the-art FSCIL methods, including Decoupled-Cosine [31], CEC [43], FACT [45], and ALICE. Additionally, for the high-shot CIL setting, we consider a strong replay-based baseline for CIL, GDumb [24] and a competitive replay-free method, E-EWC+SDC [41]. Finally, we introduce an additional baseline adapter inspired by [37], called FSA-LL (Last Layer). In FSA-LL only the parameters of the backbone's last block are fine-tuned which can be compared to the FSA-FiLM adaption method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "High-shot CIL. In this setting, we consider all the available training data for each class while keeping the number of novel classes in each session low. We use CIFAR100, CORE50, SVHN, dSprites-loc, FGVC-Aircraft, Cars, and Letters for our experiments. For CIFAR100, CORE50, and FGVC-Aircraft, the first session consists of 10 classes, 4 for dSprites-loc, 16 for Cars, and 12 for letters. The rest of the sessions include 10 classes for CIFAR100, FGVC-Aircraft, 20 for Cars, 5 for CORE50 and Letters, 2 for SVHN and dSprites-loc. Therefore, the total number of incremental sessions for CIFAR100, FGVC-Aircraft, and Cars is 10 while for CORE50 we have 9 sessions. A pre-trained on Imagenet-1k EfficientNet-B0 is deployed as a backbone for all methods. FSA-FiLM outperforms all the competitors by a significant margin on all datasets except dSprites-loc. We attribute the performance gap on dSprites-loc due to the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "18824"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.09,
+                0.891,
+                0.254
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.259,
+                0.893,
+                0.302
+            ],
+            "angle": 0,
+            "content": "Figure 1. Average accuracy across all VTAB+ datasets using no-adaptation (NA), FiLM adaptation (A-FiLM), and full body adaptation (A-FB) for different classifier heads (NCM, LDA, Linear) and number of shots (5, 10, 50, All Data). The results correspond to the offline setting where all classes are available without any incremental learning."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.313,
+                0.891,
+                0.481
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>CIFAR100</td><td>CORE50</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Cars</td><td>Letters</td><td>Avg Diff</td></tr><tr><td>NA</td><td>68.2 (26.8)</td><td>82.6 (14.2)</td><td>39.9 (51.1)</td><td>20.6 (54.0)</td><td>41.3 (1.7)</td><td>43.3 (40.3)</td><td>68.4 (24.1)</td><td>0.0</td></tr><tr><td>E-EWC+SDC[41]</td><td>32.4 (66.7)</td><td>21.7 (78.1)</td><td>39.5 (60.1)</td><td>18.6 (81.4)</td><td>25.6 (55.8)</td><td>30.0 (62.6)</td><td>33.6 (66.3)</td><td>-23.3</td></tr><tr><td>FACT [45]</td><td>10.2 (89.4)</td><td>22.0 (77.7)</td><td>33.8 (65.9)</td><td>6.4 (93.6)</td><td>4.7 (90.3)</td><td>0.6 (99.3)</td><td>20.9 (79.1)</td><td>-38.0</td></tr><tr><td>ALICE [21]</td><td>52.4 (45.8)</td><td>72.8 (25.8)</td><td>46.1 (53.6)</td><td>68.3 (31.7)</td><td>39.8 (35.0)</td><td>36.4 (56.0)</td><td>75.7 (24.2)</td><td>+3.9</td></tr><tr><td>FSA</td><td>62.8 (34.5)</td><td>82.8 (15.5)</td><td>71.3 (26.6)</td><td>91.5 (8.5)</td><td>50.8 (6.3)</td><td>50.3 (36.6)</td><td>78.4 (21.4)</td><td>+17.7</td></tr><tr><td>FSA-LL</td><td>60.5 (37.2)</td><td>79.0 (19.2)</td><td>64.6 (33.1)</td><td>91.3 (8.5)</td><td>45.4 (21.7)</td><td>45.7 (43.8)</td><td>77.2 (22.7)</td><td>+14.2</td></tr><tr><td>FSA-FiLM</td><td>73.8 (23.4)</td><td>85.4 (13.3)</td><td>75.9 (23.4)</td><td>76.9 (22.8)</td><td>55.9 (-5.7)</td><td>55.9 (30.2)</td><td>79.7 (20.0)</td><td>+19.9</td></tr><tr><td>GDumb [24]</td><td>54.5 (42.2)</td><td>82.4 (15.0)</td><td>78.2 (19.6)</td><td>79.5 (12.9)</td><td>25.3 (56.9)</td><td>14.2 (82.6)</td><td>70.1 (27.0)</td><td>+5.7</td></tr><tr><td>Offline-FiLM</td><td>78.2</td><td>88.4</td><td>93.1</td><td>98.5</td><td>67.5</td><td>67.3</td><td>85.2</td><td>+30.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.491,
+                0.893,
+                0.545
+            ],
+            "angle": 0,
+            "content": "Table 1. Last session's test accuracy \\((\\%)\\) \\((\\uparrow)\\) and the PPDR \\((\\%)\\) \\((\\downarrow)\\) in parentheses, for the high-shot CIL setting (Sec. 4.3). The last column reports the average accuracy difference \\((\\uparrow)\\) across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on Imagenet-1k is used as a backbone for all methods. For reference, we include the replay-based baseline GDumb where 1k images are used for the memory buffer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.57,
+                0.473,
+                0.888
+            ],
+            "angle": 0,
+            "content": "large number of data points (25k) and the portion of the classes \\((25\\%)\\) in the first session. It is also apparent the efficiency of fine-tuning FiLM parameters over fine-tuning the parameters of the model's last layer; note the number of FiLM parameters is only 20.5k while the last layer of an EfficientNet-B0 comprises 2.9M parameters. Furthermore, fine-tuning the FiLM parameters offer almost \\(20\\%\\) accuracy increase on average compared to using a pretrained model without doing any further adaptation. Interestingly, the replay-free FSA-FILM is able to outperform significantly the replay-based method GDumb with a 1k memory buffer on most of the datasets; accuracy and time comparisons between FSA-FiLM and GDumb with varying buffer sizes can be found in Figure 1 of the Supplement. Regarding FACT's performance, although it starts from a pre-trained backbone, it was developed under the assumption that the first session contains lots of data and a high fraction of the classes that will be encountered \\((>50\\%)\\) which is not true for the setting treated in Table 1. FACT overfits in this setting and this results in poor performance. It turns out that FACT's assumptions about the first session are a strong requirement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.57,
+                0.892,
+                0.599
+            ],
+            "angle": 0,
+            "content": "which is not necessary for obtaining good performance as our FSA baseline shows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Few-shot+ CIL. This setting is the one that has most commonly been used for few-shot CIL (FSCIL) and it involves an initial session that contains a large number of classes (around \\(50 - 60\\%\\) of the total number of classes in the dataset) and all the available training images of these classes. The remaining sessions comprise a small number of classes and shots (typically 5/10-way 5-shot). Here we follow the exact FSCIL settings as described in [45, 21] for CIFAR100 and CUB200. We use ResNet-18/20 and EfficientNet-B0 as backbones. Table 2 summarizes the performance comparison between baselines. FSA performs on par with FACT on CIFAR100 when we use the original backbone used in [45], and it outperforms FACT by almost \\(10\\%\\) and ALICE by \\(3.4\\%\\) when EfficientNet-B0 is utilized while FSA-FiLM exhibits the lowest PPDR score. Notice also that FSA is only marginally worse than its offline counterpart, meaning there is little room for continuous body adaptation to improve things further. For CUB200, FSA"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18825"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.471,
+                0.168
+            ],
+            "angle": 0,
+            "content": "with an EfficientNet-B0 performs on par with ALICE. Interestingly, we observe that NA performs well on this dataset. This indicates that CUB200 is not far from ImageNet-1k. The current results of FSA set new SOTA performance on CIFAR100 for the FSCIL setting."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.18,
+                0.462,
+                0.459
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Backbone</td><td colspan=\"2\">Datasets</td></tr><tr><td>CIFAR100</td><td>CUB200</td></tr><tr><td>CEC [43]</td><td></td><td>49.1 (32.7)*</td><td>-</td></tr><tr><td>FACT [45]</td><td>RN-20</td><td>52.1 (30.2)*</td><td>-</td></tr><tr><td>FSA</td><td></td><td>52.0 (30.8)</td><td>-</td></tr><tr><td>NA</td><td></td><td>50.4 (26.8)</td><td>50.0 (29.3)</td></tr><tr><td>CEC [43]</td><td></td><td>-</td><td>52.3 (31.1)*</td></tr><tr><td>FACT [45]</td><td rowspan=\"2\">RN-18</td><td>49.5 (34.8)*</td><td>56.9 (25.0)*</td></tr><tr><td>ALICE [21]</td><td>54.1 (31.5)†</td><td>60.1 (22.4)†</td></tr><tr><td>FSA-FiLM</td><td></td><td>55.2 (24.4)</td><td>52.7 (27.6)</td></tr><tr><td>FSA</td><td></td><td>61.4 (25.1)</td><td>57.6 (24.3)</td></tr><tr><td>NA</td><td></td><td>55.2 (25.8)</td><td>63.2 (19.6)</td></tr><tr><td>FACT [45]</td><td></td><td>56.5 (34.6)</td><td>62.9 (23.3)</td></tr><tr><td>ALICE [21]</td><td rowspan=\"2\">EN-B0</td><td>62.7 (28.4)</td><td>63.5 (22.2)</td></tr><tr><td>FSA-LL</td><td>61.4 (25.7)</td><td>55.9 (22.3)</td></tr><tr><td>FSA-FiLM</td><td></td><td>61.8 (22.4)</td><td>62.9 (20.4)</td></tr><tr><td>FSA</td><td></td><td>66.1 (24.6)</td><td>63.4 (20.9)</td></tr><tr><td>Offline</td><td>EN-B0</td><td>67.0</td><td>65.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.469,
+                0.47,
+                0.566
+            ],
+            "angle": 0,
+            "content": "Table 2. Baseline comparison under the few-shot+ CIL setting (Sec. 4.3). We report the accuracy \\((\\%)\\) (\\(\\uparrow\\)) of the last session and the PPDR \\((\\%)\\) (\\(\\downarrow\\)) in parentheses. Asterisk \\((*)\\) indicates that the reported results are from [45] and \\(\\dagger\\) indicates results reported in [21]. We use three different backbones, EfficientNet-B0 (EN-B0) and ResNet-18/20 (RN-18/20); EN-B0 and RN-18 are pre-trained onImagenet-1k."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.47,
+                0.885
+            ],
+            "angle": 0,
+            "content": "Few-shot CIL. The final setting, which is firstly introduced in this work, considers an alternative FSCIL setting in which only a small number of data points are available in all sessions, including the first. We use 50 shots per session while the first session includes \\(20\\%\\) of the total number of classes of the dataset. Each of the remaining sessions includes around \\(10\\%\\) of the total number of classes; more details are available in the Supplement. We repeat experiments 5 times and we report the mean accuracy and PPDR in Table 3. FSA-FiLM outperforms all the other baselines by a large margin in terms of both accuracy and PPDR, indicating that transfer learning is considerably advantageous for CIL when the data availability is low. Notice that both ALICE and FACT struggle to achieve good performance under this setting due to the limited amount of data in the first session. We find that FGVC-Aircraft exhibits a positive backward transfer behavior that we attribute to a difficult initial session followed by sessions that contain classes that are comparatively easier to distinguish."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Finally, we demonstrate the suitability of the LDA head"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.198
+            ],
+            "angle": 0,
+            "content": "in FSA-FiLM compared to a nearest class mean head, denoted FSA-FiLM-NCM. In the continual learning setting, LDA gives far larger improvements over NCM; e.g. \\(10\\%\\) on average as presented in Table 3. This highlights the importance of a strong classification layer. Note that the incremental update of LDA does not require any replay buffer as opposed to a linear head."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.209,
+                0.878,
+                0.224
+            ],
+            "angle": 0,
+            "content": "4.4. Inhomogeneous Class-Incremental Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.232,
+                0.892,
+                0.744
+            ],
+            "angle": 0,
+            "content": "FSA adapts the body only on the first session of continual learning and it is therefore likely to be sensitive to the particular classes which are present in this session. To investigate the degree of performance sensitivity for FSA, we devise a setting similar to the few-shot CIL setting of Sec. 4.3, where each session includes classes that share some common attribute. We select CIFAR100 which provides superclass information, and DomainNet which consists of different domains and also has superclass information available. We create three distinct CIL configurations for each dataset, each of which has different types of data in the first session. For CIFAR100, we split the data into 19 sessions. The first session includes 10 classes from super-classes (i) aquatic mammals and fish \\((Aq)\\), (ii) electric devices and furniture \\((DevF)\\), or (iii) Vehicles 1 and Vehicles 2 (Veh). Each of the other 18 sessions include images from the remaining 18 super-classes. Similarly, for DomainNet, we split the data into 6 sessions using 50 shots with 10 classes in each session. The first session includes 10 classes of (i) the \"electricity\" superclass of the real domain \\((El-R)\\), (ii) the \"furniture\" superclass of the clipart domain \\((F-Clp)\\), or (iii) the \"transportation\" superclass of the sketch domain \\((Tr-Sk)\\). In this way, we can vary the content of the first session and analyze the effect this has on performance. Table 4 reveals that FSA-FiLM's performance is similar even if the data in the first session used for the body adaptation appears disparate from that contained in the remaining sessions. Even for DomainNet where the distribution shift of the data across sessions is considerable, performance is only marginally affected in each of the three settings. This provides evidence that adapting the body only on the first session achieves competitive performance regardless of the class order, given the assumption that the data come from a single dataset (albeit a varied one in the case of DomainNet)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.757,
+                0.73,
+                0.773
+            ],
+            "angle": 0,
+            "content": "4.5. When to adapt the body?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Despite the strong performance of FSA (-FiLM) in the few-shot settings of Sec. 4.3, there are cases where the NA method achieves very close accuracy to FSA (e.g. see CUB200 results in Table 2). This implies that there may be datasets where adaptation is not required and all we need is the pre-trained backbone. In order to decide whether we require body adaptation or not, we compute the minimum cosine distance in the embedding space of the pre"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18826"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.089,
+                0.891,
+                0.236
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method/Dataset</td><td>CIFAR100</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Letters</td><td>DomainNet</td><td>iNaturalist</td><td>Avg Diff</td></tr><tr><td>NA</td><td>57.4 (28.4)</td><td>28.3 (61.5)</td><td>11.9 (66.6)</td><td>41.0 (-15.5)</td><td>57.6 (29.9)</td><td>69.0 (17.2)</td><td>49.7 (4.3)</td><td>0.0</td></tr><tr><td>FACT [45]</td><td>16.8 (79.7)</td><td>24.1 (66.2)</td><td>11.7 (64.1)</td><td>8.3 (79.9)</td><td>49.8 (40.9)</td><td>20.6 (75.6)</td><td>14.3 (74.0)</td><td>-24.2</td></tr><tr><td>ALICE [21]</td><td>58.0 (33.8)</td><td>23.0 (65.9)</td><td>23.0 (46.0)</td><td>42.0 (27.5)</td><td>66.5 (31.4)</td><td>66.5 (25.1)</td><td>47.9 (13.7)</td><td>+1.7</td></tr><tr><td>FSA</td><td>60.3 (27.0)</td><td>32.9 (53.5)</td><td>33.7 (41.3)</td><td>50.1 (-16.8)</td><td>62.2 (28.5)</td><td>70.3 (17.5)</td><td>51.5 (1.1)</td><td>+6.6</td></tr><tr><td>FSA-LL</td><td>62.0 (25.7)</td><td>43.5 (47.0)</td><td>18.8 (61.7)</td><td>45.8 (-2.1)</td><td>69.4 (26.1)</td><td>67.6 (16.9)</td><td>49.2 (14.1)</td><td>+5.9</td></tr><tr><td>FSA-FiLM-NCM</td><td>66.4 (24.8)</td><td>38.8 (56.5)</td><td>25.1 (59.4)</td><td>42.5 (-7.5)</td><td>57.1 (34.9)</td><td>68.8 (18.5)</td><td>51.5 (12.1)</td><td>+5.0</td></tr><tr><td>FSA-FiLM</td><td>70.9 (20.5)</td><td>51.3 (43.5)</td><td>35.7 (43.1)</td><td>55.8 (-19.8)</td><td>73.4 (22.1)</td><td>74.0 (15.6)</td><td>58.8 (4.8)</td><td>+15.0</td></tr><tr><td>Offline-FiLM</td><td>73.8</td><td>77.2</td><td>83.7</td><td>65.1</td><td>79.7</td><td>75.1</td><td>62.1</td><td>+28.0</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.247,
+                0.893,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Table 3. Accuracy \\((\\%)\\) (↑) of the last session and PPDR \\((\\%)\\) (↓) in parentheses for the few-shot CIL setting of Sec. 4.3. The last column reports the average accuracy difference \\((\\uparrow)\\) across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone for all methods. FSA-FiLM-NCM utilizes an NCM classifier while NA, FSA (-LL, FiLM) and Offline uses a LDA head."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.322,
+                0.467,
+                0.404
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>NA</td><td>Aq</td><td>DevF</td><td>Veh</td></tr><tr><td>CIFAR100</td><td>57.4±1.0</td><td>66.1±1.6</td><td>66.2±1.9</td><td>67.9±1.2</td></tr><tr><td></td><td>NA</td><td>El-R</td><td>F-Clp</td><td>Tr-Sk</td></tr><tr><td>DomainNet</td><td>69.0±0.4</td><td>70.6±0.6</td><td>71.7±0.6</td><td>72.8±0.5</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.413,
+                0.47,
+                0.469
+            ],
+            "angle": 0,
+            "content": "Table 4. Last session accuracy \\((\\%)\\) \\((\\uparrow)\\) of FSA-FiLM for three different session splits on CIFAR100 and DomainNet as described in Sec. 4.4. For reference, we also include the accuracy of NA. Results are averaged over 5 runs (mean \\(\\pm\\) std)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.486,
+                0.466,
+                0.629
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.634,
+                0.47,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Figure 2. Scatter plot of the accuracy differences between FSA-FiLM and NA against the minimum cosine distance between a dataset and miniImagenet dataset evaluated using the NA method. We consider the offline setting with 50 shots. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.733,
+                0.468,
+                0.824
+            ],
+            "angle": 0,
+            "content": "trained backbone between the downstream dataset and the miniImagenet [31] dataset. We use miniImagenet (60k images) as a proxy ofImagenet-1k (1.3M images) to reduce the computational overhead of evaluating pairwise distances. This allows us to approximately measure the dissimilarity between the downstream dataset andImagenet-1k."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Fig. 2 shows the accuracy difference between FSA-FiLM and NA as a function of the cosine distance for the offline setting with 50 shots whilst Fig. 3 illustrates the same accuracy difference where the datasets are grouped based on the VTAB+ categorization. For this experiment, we use 24"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.325,
+                0.892,
+                0.386
+            ],
+            "angle": 0,
+            "content": "datasets (VTAB+, DomainNet, and iNaturalist). We observe that adaptation is more beneficial for datasets in the structured domain, which contain images that are dissimilar to those of ImageNet-1k."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.399,
+                0.891,
+                0.575
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.578,
+                0.892,
+                0.607
+            ],
+            "angle": 0,
+            "content": "Figure 3. Bar plot of the accuracy differences between FSA-FiLM and NA for the offline case with 50 shots."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.503,
+                0.63,
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+                0.706
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>CFR100</td><td>SVHN</td><td>dSp-loc</td><td>FGVC</td><td>Letters</td><td>DNet</td><td>iNat</td></tr><tr><td>EffNet-B0 (FSA-FILM)</td><td>70.9</td><td>51.3</td><td>35.7</td><td>55.8</td><td>73.4</td><td>74.0</td><td>58.8</td></tr><tr><td>ConvNext (NA)</td><td>87.1</td><td>43.6</td><td>13.6</td><td>50.2</td><td>63.1</td><td>82.9</td><td>72.6</td></tr><tr><td>ConvNext-CosD</td><td>0.2</td><td>0.6</td><td>0.6</td><td>0.3</td><td>0.4</td><td>0.3</td><td>0.1</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.714,
+                0.892,
+                0.812
+            ],
+            "angle": 0,
+            "content": "Table 5. Accuracy comparison between a pre-trained ConvNext on ImageNet-22k without body adaptation (NA) and a pre-trained EfficientNet-B0 on ImageNet-1k which is adapted on the first session (FSA-FiLM). We use the few-shot CIL setting (Sec. 4.3) and we report the accuracy \\((\\%)\\) (\\(\\uparrow\\)) after the last session. Results are averaged over 5 runs (mean±std). We also include the minimum cosine distance using the pre-trained ConvNext as in Figure 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To stress the importance of adaptation on datasets far from ImageNet, we compare FSA-FiLM with an EfficientNet-B0 backbone to the no-adaptation method with a ConvNext [14] pre-trained onImagenet-22k. The total number of parameters for FSA-FiLM (backbone and FiLM"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18827"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "parameters) is \\(\\sim 4\\mathrm{M}\\) while for ConvNext is \\(348\\mathrm{M}\\). Table 5 shows that a small adapted backbone can significantly surpass the accuracy of a much larger pre-trained backbone for datasets far from ImageNet. We also compute the cosine distance measure for ConvNext and find that it is predictive of the performance of the unadapted ConvNext model and the benefits of adaptation. We show this in Table 5; note that for CIFAR100 the ConvNext's cosine distance values are small relative to the other datasets (indicating that CIFAR100 is close to the pretraining distribution) whereas for EfficientNet the values in Figure 2 indicate that CIFAR100 is more out-of-distribution."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.281,
+                0.473,
+                0.417
+            ],
+            "angle": 0,
+            "content": "The main takeaway from these results is that when there is a large cosine distance (e.g. SVHN, dSprites, FGVC, Letters) FiLM adaptation of a light-weight backbone performs well - better even than applying LDA head adaptation to a much larger backbone trained on a much larger dataset. As the community employs ever-larger models and datasets, these results indicate that adapters are likely to continue to bring improvements over simply learning a classifier head (the NA baseline)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.453,
+                0.192,
+                0.469
+            ],
+            "angle": 0,
+            "content": "5. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.486,
+                0.473,
+                0.758
+            ],
+            "angle": 0,
+            "content": "We have presented FSA (-FiLM), a simple yet effective replay-free baseline for CIL which adapts a pre-trained backbone via full body adaptation or FiLM layers only at the first session of continual learning and then utilizes a flexible incrementally updated LDA classifier on top of the body. Extensive experiments in several CIL scenarios have shown that FSA outperforms previous SOTA baselines in most cases, thus, questioning the efficacy of current approaches to continuous body adaption. Furthermore, the experiments have revealed that FiLM layers are helpful when the amount of data available in the target domain is relatively low and the number of parameters in the neural network and the size of the source domain data set is large. For very large foundation models trained on very large source domain data sets, it is likely we are often in this situation and FiLM-like layers will be more effective than full-body adaptation, even when the target domain has a fairly large amount of data."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Limitations and future work. The main limitation of this work is inextricably linked with the distributional assumptions of CIL in general. If the data distribution at each session shifts considerably (e.g. the first session includes natural images while the next session includes images of numbers) then first session body adaptation is not suitable. In future work, we plan to combine FSA (-FiLM) with a memory method like GDumb to get the best of both worlds and deal with more challenging CIL scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.502,
+                0.091,
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+                0.107
+            ],
+            "angle": 0,
+            "content": "References"
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+# First Session Adaptation: A Strong Replay-Free Baseline for Class-Incremental Learning
+
+Aristeidis Panos  
+University of Cambridge
+
+ap2313@cam.ac.uk
+
+Yuriko Kobe University of Cambridge
+
+yk384@cam.ac.uk
+
+Daniel Olmeda Reino  
+Toyota Motor Europe
+
+daniel.olmeda.reino@toyota-europe.com
+
+Rahaf Aljundi  
+Toyota Motor Europe
+
+rahaf.al.jundi@toyota-europe.com
+
+Richard E. Turner  
+University of Cambridge
+
+ret26@cam.ac.uk
+
+# Abstract
+
+In Class-Incremental Learning (CIL) an image classification system is exposed to new classes in each learning session and must be updated incrementally. Methods approaching this problem have updated both the classification head and the feature extractor body at each session of CIL. In this work, we develop a baseline method, First Session Adaptation (FSA), that sheds light on the efficacy of existing CIL approaches, and allows us to assess the relative performance contributions from head and body adaption. FSA adapts a pre-trained neural network body only on the first learning session and fixes it thereafter; a head based on linear discriminant analysis (LDA), is then placed on top of the adapted body, allowing exact updates through CIL. FSA is replay-free i.e. it does not memorize examples from previous sessions of continual learning. To empirically motivate FSA, we first consider a diverse selection of 22 image-classification datasets, evaluating different heads and body adaptation techniques in high/low-shot offline settings. We find that the LDA head performs well and supports CIL out-of-the-box. We also find that Featurewise Layer Modulation (FiLM) adapters are highly effective in the few-shot setting, and full-body adaption in the high-shot setting. Second, we empirically investigate various CIL settings including high-shot CIL and few-shot CIL, including settings that have previously been used in the literature. We show that FSA significantly improves over the state-of-the-art in 15 of the 16 settings considered. FSA with FiLM adapters is especially performant in the few-shot setting. These results indicate that current approaches to continuous body adaptation are not working as expected. Finally, we propose a measure
+
+that can be applied to a set of unlabelled inputs which is predictive of the benefits of body adaptation.
+
+# 1. Introduction
+
+Continual learning (CL) is needed to bring machine learning models to many real-life applications. After a model is trained on a given set of data, and once deployed in its test environment, it is likely that new classes will naturally emerge. For example, in an autonomous driving scenario, new types of road transportation and traffic signage can be encountered. The deployed model needs to efficiently acquire this new knowledge with minimal cost (e.g. annotation requirements) without deteriorating the performance on existing classes of objects. The process of efficiently acquiring new knowledge while preserving what is already captured by the model is what continual learning methods target.
+
+Continual learning can be mainly divided into task incremental learning and class incremental learning. Task incremental learning (TIL) sequentially learns independent sets of heterogeneous tasks and is out of this paper's scope. Class incremental learning (CIL), in contrast, assumes that all classes (already learnt and future ones) form part of a single classification task. In class-incremental learning, data arrive in a sequence of sessions with new classes appearing as the sessions progress. Critically, the data in each session cannot be stored in its entirety and cannot be revisited. The goal is to train a single classification model under these constraints.
+
+In both task incremental and class incremental learning,
+
+the data distribution will change as the sessions progress. However, these changes tend to be smaller in real-world class incremental learning settings than in the task incremental setting. For, example consider a human support robot learning about new objects in a home in an incremental manner (CIL) vs. the same robot learning to adapt to different homes (TIL).
+
+Practically, CIL has two major uses. First, in situations where large amounts of data arrive in each session and so retraining the model is computationally prohibitive. Second, in situations where data are not allowed to be revisited due to privacy reasons such as under General Data Protection Regulation (GDPR). The latter situation is relevant for applications such as personalization where small numbers of data points are available i.e. few-shot continual learning. So-called replay-free methods are necessary for such settings, as samples of previous sessions are not allowed to be memorized, but CIL is known to be challenging in such settings.
+
+Current SOTA methods for class incremental learning start from a pre-trained backbone [13, 19, 35, 34] and then adapt the features at each session of continual learning. The use of a pre-trained backbone has been shown to lead to strong performance especially in the few-shot CIL setting due to the lack of data [21]. However, it is unclear to what extent continuous adaptation of the features in each session is helpful. In general, in CIL there is a trade-off between adaptation (which helps adapt to the new statistics of the target domain) and catastrophic forgetting (whereby earlier classes are forgotten as the representation changes). When memorization of previous samples is restricted, the benefits from adapting the feature extractor body to learn better features might well be out-weighted by the increase in forgetting of old classes. Moreover, body adaptation in earlier sessions is arguably more critical (e.g. adapting the backbone to the new domain in the first session), whilst it is less essential in later sessions where the changes in the ideal representation between sessions are smaller.
+
+This work explores under what conditions continuous adaptation of the body is beneficial, both in principle and in current practice. In order to do this, we develop a new replay-free method, inspired by the first encoding method of [2], called First Session Adaptation (FSA). FSA adapts the body of a pre-trained neural network on only the first session of continual learning. We investigate adapting all body parameters and the use of Feature-wise Layer Modulation (FiLM) adapters [23] which learn only a small number of parameters. The head, in contrast, is adapted at each session using an approach that is similar to Linear Discriminate Analysis (LDA), which suffers from no forgetting, and improves over the Nearest Class Mean classifier (NCM) [18] approach. The efficacy of this general approach, including comparisons to a standard linear head, is first motivated
+
+through experiments in the offline setting (Sec. 4.2). We then carry out experiments under three CIL settings. First, we consider the high-shot setting (high-shot CIL). The other two settings consider few-shot continual learning. Specifically, one setting follows previous approaches that employ an initial session with a large number of data points and few-shot sessions thereafter (few-shot+ CIL) while the other exclusively includes sessions with only a small amount of data (few-shot CIL).
+
+The contributions of the paper are as follows: (1) We develop a replay-free CIL baseline, namely FSA, that is extremely simple to implement and performs well in many different scenarios. (2) We empirically motivate FSA through a set of offline experiments that evaluate different forms of neural network head and body adaptation; (3) We then compare FSA to a set of strong continual learning baseline methods in a fair way using the same pre-trained backbone for all methods. (4) We show that the FSA-FiLM baseline performs well in the high-shot CIL setting, outperforming the SOTA whilst avoiding data memorization. (5) In the few-shot learning settings, FSA outperforms existing continual learning methods on eight benchmarks, often by a substantial margin, and is statistically tied with the best performing method on the one remaining dataset. (6) Finally, we propose a measure that can be applied to a set of unlabeled inputs which is predictive of the benefits of body adaptation.
+
+# 2. Related Work
+
+Class Incremental Learning is more challenging than task-incremental continual learning as a shared output layer is used for the classes of different learning sessions. We refer to [7] for a survey on both class and task incremental learning. While softmax cross entropy loss is considered a standard in classification models, it is shown to be a source of class interference in continual learning [38, 4]. Thus, recent works either focus on fixing the softmax classifier [4, 1, 44] or deploy nearest class mean classifiers (NCM) as an alternative [25, 5, 11]. In this work, we deploy an LDA classifier that uses the mean embedding of each class and an incrementally updated covariance matrix shared across all classes. We show that this approach is comparable to a softmax classifier in the offline setting and that it outperforms NCM.
+
+Due to the challenging nature of class incremental learning, some methods employ a buffer of stored samples from previous sessions [24, 39]. [24] suggests a simple baseline, GDumb, that performs offline training on both buffer data and new session data at each incremental step. GDumb shows strong performance compared to sophisticated continual learning solutions. Here we show that our simple yet effective solution often outperforms variants of GDumb that have a large memory without leveraging any buffer of stored
+
+samples.
+
+In addition to the issues arising from the shared classification layer, learning a feature extractor that can provide representative features of all classes is a key element in continual learning. Some class incremental learning methods leverage large initial training session or start from a pretrained network, e.g., [35, 9, 36] and show improved overall continual learning performance without questioning the role of such pre-training steps and whether the learned representations have in fact improved. Recently, [19] studies continual learning with strong pre-trained models and proposes deploying exemplar-based replay in the latent space using a small multilayer network on top of the fixed pretrained model. The authors show that such latent replay improves performance, especially for tasks that are different from the distribution used to train the initial model. In this work, we show that adaptation of pre-trained models is essential for strong continual learning performance. However, different from all existing continual learning works, we show that adapting the representation only in the first session is sufficient to obtain representative features for the classes being learned and that this forms a strong baseline for future continual learning methods.
+
+In addition to the incremental classification in the full data regime, we focus on the few-shot scenario where only a few labeled examples per class are provided at each training session. [9] utilize a meta-trained network for few-shot classification and explore multiple design choices including a no-adaptation baseline and a method to optimize orthogonal prototypes with the last classification layer only. The method heavily relies on a pre-training and meta-training step on a large subset of classes from the original dataset. In this work, we show that the meta-training step is not essential and that a simple LDA head is sufficient without the reliance on a big initial training stage. In [11] the authors propose a new distillation loss functioning at the feature map level where importance values are estimated per feature map along with replay and consider an NCM classifier at test time. [45] heavily relies on the training of an initial session using a specific loss function that takes into account classes that will be added in future. It further requires the total number of classes to be known a priori which is unrealistic for real applications. Our solution adapts FILM parameters to the first session data and fixes the representation for the remaining training sessions. We show that surprisingly few samples in the first session are sufficient for adaptation and that our solution is more powerful than current few-shot continual learning solutions.
+
+# 3. Proposed Algorithm
+
+In this section, first we discuss the main components of the proposed methods FSA/FSA-FiLM, namely body adaptation techniques and classifier heads. Then we formally
+
+introduce the two methods for tackling CIL.
+
+# 3.1. Problem Formulation
+
+In CIL, we are given a dataset  $\mathcal{D}_s = \{\mathbf{x}_{i,s},y_{i,s}\}_{i = 1}^{N_s}$  for each session  $s\in \{1,\ldots ,S\}$ , where  $X_{s} = \{\mathbf{x}_{i,s}\}_{i = 1}^{N_{s}}$  is a set of images and  $Y_{s} = \{y_{i,s}\}_{i = 1}^{N_{s}}$  is the set of the corresponding labels with  $y_{i,s}\in \mathcal{V}_s$ . Here  $\mathcal{V}_s$  is the label space of session  $s$ . It is common in CIL that label spaces are mutually exclusive across sessions, i.e.  $\mathcal{V}_s\cap \mathcal{V}_{s'} = \emptyset$ ,  $\forall s\neq s'$  and we only have access to  $\mathcal{D}_s$  in the current session  $s$  to train our model. The proposed FSA method can naturally handle sessions with overlapping label spaces too, however, we follow the former paradigm in our experiments. Another typical assumption in CIL is that the data in all sessions come from the same dataset. We also adopt this assumption in this work, although our experiments on DomainNet are a step toward considering different datasets in each session.
+
+In session  $s$ , we will use models defined as
+
+$$
+f _ {s} (\mathbf {x}) = W _ {s} ^ {\top} g _ {\boldsymbol {\theta} _ {s}} (\mathbf {x}) + \mathbf {b} _ {s}, \tag {1}
+$$
+
+where  $g_{\theta_s}(\mathbf{x}) \in \mathbb{R}^d$  is a feature extractor backbone<sup>1</sup> with session-dependent parameters  $\theta_s$ . The linear classifier head comprises the class weights  $W_s \in \mathbb{R}^{d \times |\mathcal{Y}_{1:s}|}$  and biases  $\mathbf{b}_s \in \mathbb{R}^{|\mathcal{Y}_{1:s}|}$ , and  $\mathcal{Y}_{1:s} = \cup_{j=1}^{s} \mathcal{Y}_j$  is the label space of all distinct classes we have seen up to session  $s$ . Ideally, when a new dataset  $\mathcal{D}_s$  is available at the  $s$ -th session, the model should be able to update the backbone parameters  $\theta$  and the linear classifier head  $W_s$  with the minimum computational overhead and without compromising performance over the previously seen classes  $\mathcal{Y}_{1:s}$ .
+
+Backbone adaptation. Traditionally, the adaptation of the body at the current session  $s$  requires updating the full set of the network parameters  $\theta_{s}$  (full-body adaptation). Options include using specifically designed loss functions that mitigate catastrophic forgetting or using a memory buffer that stores a subset of the previously encountered data. See [16] for a review of continual learning techniques. Nevertheless, when training data availability is scarce relative to the size of the model then full-body adaptation ceases to be suitable, and few-shot learning techniques [33], such as meta-learning [10] and transfer learning [40] become favorable.
+
+Recent works in few-shot learning [26] showed that a pre-trained backbone can be efficiently adapted by keeping its parameters  $\theta_{s}$  frozen and introducing Feature-wise Linear Modulation (FiLM) [23] layers with additional parameters  $\xi_{s}$  which scale and shift the activations produced by a convolutional layer. In [26], these parameters are generated by a meta-trained network when a downstream task is
+
+given. Alternatively,  $\xi_{s}$  can be learned (fine-tuned) by the downstream data as in [27]. In this work, we consider both meta-learned (Supplement) and fine-tuned (Sec. 4) FiLM parameters.
+
+Classifier heads. In both offline and CIL settings, (linear) classifier heads can be divided into two groups; parametrized and parameter-free. Parametrized heads require the weights/biases in Eq. (1) to be updated by an iterative gradient-based procedure whilst for parameter-free heads, a closed-form formula is available that directly computes the weights/biases after the update of the backbone. We consider three different heads (for notational simplicity we consider the offline setting, and thus suppress session  $s$  dependence), one parametrized, and two parameter-free.
+
+- The linear (learnable) head where  $W, \mathbf{b}$  are learned.  
+- The Nearest Class Mean (NCM) classifier where the weight and bias of the  $k$ -th class is given by
+
+$$
+\mathbf {w} _ {k} = \hat {\boldsymbol {\mu}} _ {k} \text {a n d} b _ {k} = \ln \frac {| X ^ {(k)} |}{N} - \frac {1}{2} \hat {\boldsymbol {\mu}} _ {k} ^ {\top} \hat {\boldsymbol {\mu}} _ {k}, \tag {2}
+$$
+
+where  $X^{(k)} = \{\mathbf{x}_i:y_i = k\}$  is the set of images belonging in class  $k$  and  $\hat{\pmb{\mu}}_k = \frac{1}{|X^{(k)}|}\sum_{\mathbf{x}\in X^{(k)}}g_\pmb {\theta}(\mathbf{x})$  is the mean vector of the embedded images of class  $k$
+
+- The Linear Discriminant Analysis (LDA) classifier with weights/biases defined as
+
+$$
+\mathbf {w} _ {k} = \tilde {S} ^ {- 1} \hat {\boldsymbol {\mu}} _ {k} \text {a n d} b _ {k} = \ln \frac {| X ^ {(k)} |}{N} - \frac {1}{2} \hat {\boldsymbol {\mu}} _ {k} ^ {\top} \tilde {S} ^ {- 1} \hat {\boldsymbol {\mu}} _ {k}, \tag {3}
+$$
+
+where  $\tilde{S} = S + I_d$  is the regularized sample covariance matrix with sample covariance matrix  $S = \frac{1}{|X| - 1}\sum_{\mathbf{x}\in X}(g_{\boldsymbol{\theta}}(\mathbf{x}) - \hat{\boldsymbol{\mu}})(g_{\boldsymbol{\theta}}(\mathbf{x}) - \hat{\boldsymbol{\mu}})^\top$ ,  $\hat{\boldsymbol{\mu}} = \frac{1}{|X|}\sum_{\mathbf{x}\in X}g_{\boldsymbol{\theta}}(\mathbf{x})$ , and identity matrix  $I_d \in \mathbb{R}^{d\times d}$ .
+
+Both NCM and LDA classifiers are suitable for CIL since their closed-form updates in Eq. (2) and Eq. (3) support exact, computationally inexpensive, continual updates (via running averages) that incur no forgetting. Updating the linear head, in contrast, requires more computational effort and machinery when novel classes appear in a new session. Notice that setting  $\tilde{S} = I_d$  in LDA recovers NCM.
+
+The continuous update of the LDA head is not as straightforward as it is for NCM, since LDA also requires updating the sample covariance  $S$ . We discuss how this can be attained in the next section where we introduce our proposed method FSA/FSA-FiLM.
+
+# 3.2. First Session Adaptation
+
+Motivated by the efficient adaptation techniques and CIL-friendly classifiers discussed in the previous section,
+
+we propose two simple and computationally efficient CIL methods called First Session Adaptation (FSA) and FSA-FiLM. FSA is based on a full-body adaptation while FSA-FiLM uses FiLM layers to adapt the body. Both methods utilize pre-trained backbones. FSA (-FiLM) (i) adapts the backbone only at the first session and then the backbone remains frozen for the rest of the sessions, and (ii) makes use of an LDA classifier which is continuously updated as new data become available. For adapting the body (either full or FiLM-based adaptation) at the first session, we use a linear head and a cross-entropy loss first, and then after the optimization is over, the linear head is removed and an LDA head is deployed instead, based on the optimized parameters  $\theta^{*}$  and Eq. (3). Updating the LDA head when the data of the next session becomes available, can be done by using Algorithm 1 recursively until the last session  $S$ . Specifically, by having access to the running terms  $\{A, \mathbf{b}, \text{count}\}$ , the sample covariance matrix is given by
+
+$$
+S = \frac {1}{\operatorname {c o u n t} - 1} \left(A - \frac {1}{\operatorname {c o u n t}} \mathbf {b b} ^ {\top}\right). \tag {4}
+$$
+
+The time complexity of LDA scales as  $\mathcal{O}(d^3 + |\mathcal{Y}_s|d^2)$  and
+
+Algorithm 1 Update of sample covariance running terms
+
+Require:  $g(\cdot) \equiv a$  feature extractor backbone
+
+Require:  $X_{s} = \{\mathbf{x}_{i,s}\}_{i = 1}^{N_{s}}$ : Images of session  $s$
+
+Require:  $A\in \mathbb{R}^{d\times d}$ $\mathbf{b}\in \mathbb{R}^d$  count  $\in \mathbb{N}^*$  if  $s > 1$
+
+1: function INCUPDATE  $(g(\cdot), X_s, A, b, \text{count})$  
+2: if  $s = 1$  then Initialize  $A, \mathbf{b}$ , count  
+3:  $A\gets \mathbf{0}_{d\times d},\mathbf{b}\gets \mathbf{0}_d,\mathrm{count}\gets 0$  
+4: end if  
+5:  $A\gets A + \sum_{\mathbf{x}\in X_s}g(\mathbf{x})g(\mathbf{x})^\top$  
+6:  $\mathbf{b}\gets \mathbf{b} + \sum_{\mathbf{x}\in X_s}g(\mathbf{x})$  
+7: count  $\leftarrow$  count  $+N_{s}$  
+8: return  $A$ , b, count  
+9: end function
+
+its space complexity is  $\mathcal{O}(d^2 + |\mathcal{Y}_{1:s}|d)$  at the  $s$ -th session. This computational burden is negligible compared to taking gradient steps for learning a linear head and as we will see in Sec. 4.2 using covariance information boosts performance significantly against the vanilla NCM head.
+
+# 4. Experiments
+
+In this section, we present a series of experiments to investigate the performance of FSA (-FiLM) under different CIL settings. First, we detail the datasets used for the experiments and discuss our implementation. Second, we perform a large empirical comparison between LDA, linear, and NCM classifiers, in combination with different body adaptation techniques, in the offline setting. For the CIL settings, the results are compared to the vanilla method,  $N_{o}$
+
+Adaptation (NA), where a pretrained backbone is combined with an LDA head and remains frozen across sessions. We also consider how these findings are affected by the number of shots available. Third, we compare FSA (-FiLM) with state-of-the-art continual learning methods and conduct ablation studies. Finally, we investigate the effect of adapting the backbone when the CIL dataset is "similar" to ImageNet-1k and discuss a similarity metric that indicates whether body adaptation is required.
+
+# 4.1. Datasets and Implementation details
+
+Datasets. We employ a diverse collection of 26 image-classification datasets across the offline and CIL experiments. For the offline experiments of Sec. 4.2, we use the 19 datasets of VTAB [42], a low-shot transfer learning benchmark, plus three additional datasets, FGVC-Aircraft [17], Stanford Cars [12], and Letters [6]. We refer to this group of datasets as VTAB+. For the CIL-based experiments, we choose 5 VTAB+ datasets from different domains, having an adequate number of classes to create realistic CIL scenarios. The datasets are CIFAR100, SVHN, dSprites-location, FGVC-Aircraft, Cars, and Letters while also including 4 extra datasets: CUB200 [32], CORE50 [15], iNaturalist [30], and DomainNet [22]. Exact details for each dataset are provided in the Supplement.
+
+Training details. All models are implemented with PyTorch [20]. We use a pre-trained EfficientNet-B0 [28] onImagenet-1k as the main backbone for all methods. For the few-shot+ CIL experiment in Sec. 4.3, we also consider two ResNet architectures, ResNet-18 and ResNet-20 [8] to enable direct comparison to the original settings used in [45]. All the deployed backbones (except ResNet-20, due to the unavailability of pre-trained weights on ImageNet-1k), are pre-trained on ImageNet-1k for all methods. We keep the optimization settings the same across all baselines for fairness. Optimization details are given in the Supplement.
+
+Evaluation protocol. We report the Top-1 accuracy after the last continual learning session evaluated on a test set including instances from all the previously seen classes. In the Supplement, we provide the accuracy after each session. To quantify the forgetting behavior, we use a scaled modification of the performance dropping rate [29], namely percent performance dropping rate (PPDR), defined as  $\mathrm{PPDR} = 100 \times \frac{\mathcal{A}_1 - \mathcal{A}_S}{\mathcal{A}_1}\%$ , where  $\mathcal{A}_1$  denotes test accuracy after the first session, and  $\mathcal{A}_S$  the test accuracy after the last session.
+
+# 4.2. Head Comparisons
+
+To motivate the choice of the LDA head for FSA (-FiLM), we compare its average accuracy across all VTAB+ datasets with that of the linear and NCM classifiers under the offline setting where all the classes are available and
+
+no incremental learning is required. For the body, we use no adaptation (NA) as a baseline (i.e. using the unadapted original backbone), FiLM-based adaptation, and full-body adaptation while ranging the number of shots from 5 to 10, then 50, and finally using all available training data. As Fig. 1 illustrates, LDA consistently outperforms both NCM and linear heads when the number of shots is equal to 5 and 10, regardless of adaptation technique. Notice also that as the number of learnable parameters increases, the choice of the head plays a less significant role in the predictive power of the method. Overall, LDA performs similarly to the linear head in the high-shot settings and performs the best of all heads in the low-shot settings. Finally, the full covariance information of LDA provides a consistent advantage over its isotropic covariance counterpart, i.e. the NCM classifier. This is in agreement with the results presented in [27] for the LDA and NCM classifier. In addition to the results presented here, we have also tested meta-learning based body adaptation methods [3, 26, 2] which support continual learning out of the box. We find these perform poorly compared to the fine-tuning based methods. See next section for more results.
+
+# 4.3. Class-Incremental Learning Comparisons
+
+We consider three different CIL scenarios: (i) high-shot CIL, (ii) few-shot+ CIL, and (iii) few-shot CIL. We compare our FSA/FSA-FiLM methods with recent state-of-the-art FSCIL methods, including Decoupled-Cosine [31], CEC [43], FACT [45], and ALICE. Additionally, for the high-shot CIL setting, we consider a strong replay-based baseline for CIL, GDumb [24] and a competitive replay-free method, E-EWC+SDC [41]. Finally, we introduce an additional baseline adapter inspired by [37], called FSA-LL (Last Layer). In FSA-LL only the parameters of the backbone's last block are fine-tuned which can be compared to the FSA-FiLM adaption method.
+
+High-shot CIL. In this setting, we consider all the available training data for each class while keeping the number of novel classes in each session low. We use CIFAR100, CORE50, SVHN, dSprites-loc, FGVC-Aircraft, Cars, and Letters for our experiments. For CIFAR100, CORE50, and FGVC-Aircraft, the first session consists of 10 classes, 4 for dSprites-loc, 16 for Cars, and 12 for letters. The rest of the sessions include 10 classes for CIFAR100, FGVC-Aircraft, 20 for Cars, 5 for CORE50 and Letters, 2 for SVHN and dSprites-loc. Therefore, the total number of incremental sessions for CIFAR100, FGVC-Aircraft, and Cars is 10 while for CORE50 we have 9 sessions. A pre-trained on Imagenet-1k EfficientNet-B0 is deployed as a backbone for all methods. FSA-FiLM outperforms all the competitors by a significant margin on all datasets except dSprites-loc. We attribute the performance gap on dSprites-loc due to the
+
+![](images/60d2677741a9d16c98988e84a31a49a3efc26f7383bc46a6087fe4ccb1771f07.jpg)  
+Figure 1. Average accuracy across all VTAB+ datasets using no-adaptation (NA), FiLM adaptation (A-FiLM), and full body adaptation (A-FB) for different classifier heads (NCM, LDA, Linear) and number of shots (5, 10, 50, All Data). The results correspond to the offline setting where all classes are available without any incremental learning.
+
+<table><tr><td>Method</td><td>CIFAR100</td><td>CORE50</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Cars</td><td>Letters</td><td>Avg Diff</td></tr><tr><td>NA</td><td>68.2 (26.8)</td><td>82.6 (14.2)</td><td>39.9 (51.1)</td><td>20.6 (54.0)</td><td>41.3 (1.7)</td><td>43.3 (40.3)</td><td>68.4 (24.1)</td><td>0.0</td></tr><tr><td>E-EWC+SDC[41]</td><td>32.4 (66.7)</td><td>21.7 (78.1)</td><td>39.5 (60.1)</td><td>18.6 (81.4)</td><td>25.6 (55.8)</td><td>30.0 (62.6)</td><td>33.6 (66.3)</td><td>-23.3</td></tr><tr><td>FACT [45]</td><td>10.2 (89.4)</td><td>22.0 (77.7)</td><td>33.8 (65.9)</td><td>6.4 (93.6)</td><td>4.7 (90.3)</td><td>0.6 (99.3)</td><td>20.9 (79.1)</td><td>-38.0</td></tr><tr><td>ALICE [21]</td><td>52.4 (45.8)</td><td>72.8 (25.8)</td><td>46.1 (53.6)</td><td>68.3 (31.7)</td><td>39.8 (35.0)</td><td>36.4 (56.0)</td><td>75.7 (24.2)</td><td>+3.9</td></tr><tr><td>FSA</td><td>62.8 (34.5)</td><td>82.8 (15.5)</td><td>71.3 (26.6)</td><td>91.5 (8.5)</td><td>50.8 (6.3)</td><td>50.3 (36.6)</td><td>78.4 (21.4)</td><td>+17.7</td></tr><tr><td>FSA-LL</td><td>60.5 (37.2)</td><td>79.0 (19.2)</td><td>64.6 (33.1)</td><td>91.3 (8.5)</td><td>45.4 (21.7)</td><td>45.7 (43.8)</td><td>77.2 (22.7)</td><td>+14.2</td></tr><tr><td>FSA-FiLM</td><td>73.8 (23.4)</td><td>85.4 (13.3)</td><td>75.9 (23.4)</td><td>76.9 (22.8)</td><td>55.9 (-5.7)</td><td>55.9 (30.2)</td><td>79.7 (20.0)</td><td>+19.9</td></tr><tr><td>GDumb [24]</td><td>54.5 (42.2)</td><td>82.4 (15.0)</td><td>78.2 (19.6)</td><td>79.5 (12.9)</td><td>25.3 (56.9)</td><td>14.2 (82.6)</td><td>70.1 (27.0)</td><td>+5.7</td></tr><tr><td>Offline-FiLM</td><td>78.2</td><td>88.4</td><td>93.1</td><td>98.5</td><td>67.5</td><td>67.3</td><td>85.2</td><td>+30.6</td></tr></table>
+
+Table 1. Last session's test accuracy  $(\%)$ $(\uparrow)$  and the PPDR  $(\%)$ $(\downarrow)$  in parentheses, for the high-shot CIL setting (Sec. 4.3). The last column reports the average accuracy difference  $(\uparrow)$  across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on Imagenet-1k is used as a backbone for all methods. For reference, we include the replay-based baseline GDumb where 1k images are used for the memory buffer.
+
+large number of data points (25k) and the portion of the classes  $(25\%)$  in the first session. It is also apparent the efficiency of fine-tuning FiLM parameters over fine-tuning the parameters of the model's last layer; note the number of FiLM parameters is only 20.5k while the last layer of an EfficientNet-B0 comprises 2.9M parameters. Furthermore, fine-tuning the FiLM parameters offer almost  $20\%$  accuracy increase on average compared to using a pretrained model without doing any further adaptation. Interestingly, the replay-free FSA-FILM is able to outperform significantly the replay-based method GDumb with a 1k memory buffer on most of the datasets; accuracy and time comparisons between FSA-FiLM and GDumb with varying buffer sizes can be found in Figure 1 of the Supplement. Regarding FACT's performance, although it starts from a pre-trained backbone, it was developed under the assumption that the first session contains lots of data and a high fraction of the classes that will be encountered  $(>50\%)$  which is not true for the setting treated in Table 1. FACT overfits in this setting and this results in poor performance. It turns out that FACT's assumptions about the first session are a strong requirement
+
+which is not necessary for obtaining good performance as our FSA baseline shows.
+
+Few-shot+ CIL. This setting is the one that has most commonly been used for few-shot CIL (FSCIL) and it involves an initial session that contains a large number of classes (around  $50 - 60\%$  of the total number of classes in the dataset) and all the available training images of these classes. The remaining sessions comprise a small number of classes and shots (typically 5/10-way 5-shot). Here we follow the exact FSCIL settings as described in [45, 21] for CIFAR100 and CUB200. We use ResNet-18/20 and EfficientNet-B0 as backbones. Table 2 summarizes the performance comparison between baselines. FSA performs on par with FACT on CIFAR100 when we use the original backbone used in [45], and it outperforms FACT by almost  $10\%$  and ALICE by  $3.4\%$  when EfficientNet-B0 is utilized while FSA-FiLM exhibits the lowest PPDR score. Notice also that FSA is only marginally worse than its offline counterpart, meaning there is little room for continuous body adaptation to improve things further. For CUB200, FSA
+
+with an EfficientNet-B0 performs on par with ALICE. Interestingly, we observe that NA performs well on this dataset. This indicates that CUB200 is not far from ImageNet-1k. The current results of FSA set new SOTA performance on CIFAR100 for the FSCIL setting.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Backbone</td><td colspan="2">Datasets</td></tr><tr><td>CIFAR100</td><td>CUB200</td></tr><tr><td>CEC [43]</td><td></td><td>49.1 (32.7)*</td><td>-</td></tr><tr><td>FACT [45]</td><td>RN-20</td><td>52.1 (30.2)*</td><td>-</td></tr><tr><td>FSA</td><td></td><td>52.0 (30.8)</td><td>-</td></tr><tr><td>NA</td><td></td><td>50.4 (26.8)</td><td>50.0 (29.3)</td></tr><tr><td>CEC [43]</td><td></td><td>-</td><td>52.3 (31.1)*</td></tr><tr><td>FACT [45]</td><td rowspan="2">RN-18</td><td>49.5 (34.8)*</td><td>56.9 (25.0)*</td></tr><tr><td>ALICE [21]</td><td>54.1 (31.5)†</td><td>60.1 (22.4)†</td></tr><tr><td>FSA-FiLM</td><td></td><td>55.2 (24.4)</td><td>52.7 (27.6)</td></tr><tr><td>FSA</td><td></td><td>61.4 (25.1)</td><td>57.6 (24.3)</td></tr><tr><td>NA</td><td></td><td>55.2 (25.8)</td><td>63.2 (19.6)</td></tr><tr><td>FACT [45]</td><td></td><td>56.5 (34.6)</td><td>62.9 (23.3)</td></tr><tr><td>ALICE [21]</td><td rowspan="2">EN-B0</td><td>62.7 (28.4)</td><td>63.5 (22.2)</td></tr><tr><td>FSA-LL</td><td>61.4 (25.7)</td><td>55.9 (22.3)</td></tr><tr><td>FSA-FiLM</td><td></td><td>61.8 (22.4)</td><td>62.9 (20.4)</td></tr><tr><td>FSA</td><td></td><td>66.1 (24.6)</td><td>63.4 (20.9)</td></tr><tr><td>Offline</td><td>EN-B0</td><td>67.0</td><td>65.1</td></tr></table>
+
+Table 2. Baseline comparison under the few-shot+ CIL setting (Sec. 4.3). We report the accuracy  $(\%)$  ( $\uparrow$ ) of the last session and the PPDR  $(\%)$  ( $\downarrow$ ) in parentheses. Asterisk  $(*)$  indicates that the reported results are from [45] and  $\dagger$  indicates results reported in [21]. We use three different backbones, EfficientNet-B0 (EN-B0) and ResNet-18/20 (RN-18/20); EN-B0 and RN-18 are pre-trained onImagenet-1k.
+
+Few-shot CIL. The final setting, which is firstly introduced in this work, considers an alternative FSCIL setting in which only a small number of data points are available in all sessions, including the first. We use 50 shots per session while the first session includes  $20\%$  of the total number of classes of the dataset. Each of the remaining sessions includes around  $10\%$  of the total number of classes; more details are available in the Supplement. We repeat experiments 5 times and we report the mean accuracy and PPDR in Table 3. FSA-FiLM outperforms all the other baselines by a large margin in terms of both accuracy and PPDR, indicating that transfer learning is considerably advantageous for CIL when the data availability is low. Notice that both ALICE and FACT struggle to achieve good performance under this setting due to the limited amount of data in the first session. We find that FGVC-Aircraft exhibits a positive backward transfer behavior that we attribute to a difficult initial session followed by sessions that contain classes that are comparatively easier to distinguish.
+
+Finally, we demonstrate the suitability of the LDA head
+
+in FSA-FiLM compared to a nearest class mean head, denoted FSA-FiLM-NCM. In the continual learning setting, LDA gives far larger improvements over NCM; e.g.  $10\%$  on average as presented in Table 3. This highlights the importance of a strong classification layer. Note that the incremental update of LDA does not require any replay buffer as opposed to a linear head.
+
+# 4.4. Inhomogeneous Class-Incremental Learning
+
+FSA adapts the body only on the first session of continual learning and it is therefore likely to be sensitive to the particular classes which are present in this session. To investigate the degree of performance sensitivity for FSA, we devise a setting similar to the few-shot CIL setting of Sec. 4.3, where each session includes classes that share some common attribute. We select CIFAR100 which provides superclass information, and DomainNet which consists of different domains and also has superclass information available. We create three distinct CIL configurations for each dataset, each of which has different types of data in the first session. For CIFAR100, we split the data into 19 sessions. The first session includes 10 classes from super-classes (i) aquatic mammals and fish  $(Aq)$ , (ii) electric devices and furniture  $(DevF)$ , or (iii) Vehicles 1 and Vehicles 2 (Veh). Each of the other 18 sessions include images from the remaining 18 super-classes. Similarly, for DomainNet, we split the data into 6 sessions using 50 shots with 10 classes in each session. The first session includes 10 classes of (i) the "electricity" superclass of the real domain  $(El-R)$ , (ii) the "furniture" superclass of the clipart domain  $(F-Clp)$ , or (iii) the "transportation" superclass of the sketch domain  $(Tr-Sk)$ . In this way, we can vary the content of the first session and analyze the effect this has on performance. Table 4 reveals that FSA-FiLM's performance is similar even if the data in the first session used for the body adaptation appears disparate from that contained in the remaining sessions. Even for DomainNet where the distribution shift of the data across sessions is considerable, performance is only marginally affected in each of the three settings. This provides evidence that adapting the body only on the first session achieves competitive performance regardless of the class order, given the assumption that the data come from a single dataset (albeit a varied one in the case of DomainNet).
+
+# 4.5. When to adapt the body?
+
+Despite the strong performance of FSA (-FiLM) in the few-shot settings of Sec. 4.3, there are cases where the NA method achieves very close accuracy to FSA (e.g. see CUB200 results in Table 2). This implies that there may be datasets where adaptation is not required and all we need is the pre-trained backbone. In order to decide whether we require body adaptation or not, we compute the minimum cosine distance in the embedding space of the pre
+
+<table><tr><td>Method/Dataset</td><td>CIFAR100</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Letters</td><td>DomainNet</td><td>iNaturalist</td><td>Avg Diff</td></tr><tr><td>NA</td><td>57.4 (28.4)</td><td>28.3 (61.5)</td><td>11.9 (66.6)</td><td>41.0 (-15.5)</td><td>57.6 (29.9)</td><td>69.0 (17.2)</td><td>49.7 (4.3)</td><td>0.0</td></tr><tr><td>FACT [45]</td><td>16.8 (79.7)</td><td>24.1 (66.2)</td><td>11.7 (64.1)</td><td>8.3 (79.9)</td><td>49.8 (40.9)</td><td>20.6 (75.6)</td><td>14.3 (74.0)</td><td>-24.2</td></tr><tr><td>ALICE [21]</td><td>58.0 (33.8)</td><td>23.0 (65.9)</td><td>23.0 (46.0)</td><td>42.0 (27.5)</td><td>66.5 (31.4)</td><td>66.5 (25.1)</td><td>47.9 (13.7)</td><td>+1.7</td></tr><tr><td>FSA</td><td>60.3 (27.0)</td><td>32.9 (53.5)</td><td>33.7 (41.3)</td><td>50.1 (-16.8)</td><td>62.2 (28.5)</td><td>70.3 (17.5)</td><td>51.5 (1.1)</td><td>+6.6</td></tr><tr><td>FSA-LL</td><td>62.0 (25.7)</td><td>43.5 (47.0)</td><td>18.8 (61.7)</td><td>45.8 (-2.1)</td><td>69.4 (26.1)</td><td>67.6 (16.9)</td><td>49.2 (14.1)</td><td>+5.9</td></tr><tr><td>FSA-FiLM-NCM</td><td>66.4 (24.8)</td><td>38.8 (56.5)</td><td>25.1 (59.4)</td><td>42.5 (-7.5)</td><td>57.1 (34.9)</td><td>68.8 (18.5)</td><td>51.5 (12.1)</td><td>+5.0</td></tr><tr><td>FSA-FiLM</td><td>70.9 (20.5)</td><td>51.3 (43.5)</td><td>35.7 (43.1)</td><td>55.8 (-19.8)</td><td>73.4 (22.1)</td><td>74.0 (15.6)</td><td>58.8 (4.8)</td><td>+15.0</td></tr><tr><td>Offline-FiLM</td><td>73.8</td><td>77.2</td><td>83.7</td><td>65.1</td><td>79.7</td><td>75.1</td><td>62.1</td><td>+28.0</td></tr></table>
+
+Table 3. Accuracy  $(\%)$  (↑) of the last session and PPDR  $(\%)$  (↓) in parentheses for the few-shot CIL setting of Sec. 4.3. The last column reports the average accuracy difference  $(\uparrow)$  across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone for all methods. FSA-FiLM-NCM utilizes an NCM classifier while NA, FSA (-LL, FiLM) and Offline uses a LDA head.  
+
+<table><tr><td>Dataset</td><td>NA</td><td>Aq</td><td>DevF</td><td>Veh</td></tr><tr><td>CIFAR100</td><td>57.4±1.0</td><td>66.1±1.6</td><td>66.2±1.9</td><td>67.9±1.2</td></tr><tr><td></td><td>NA</td><td>El-R</td><td>F-Clp</td><td>Tr-Sk</td></tr><tr><td>DomainNet</td><td>69.0±0.4</td><td>70.6±0.6</td><td>71.7±0.6</td><td>72.8±0.5</td></tr></table>
+
+![](images/771c64d4340355af9f0022e1ca5c2dd84744c70af8e4647b81e3f3f3fb4da3d1.jpg)  
+Figure 2. Scatter plot of the accuracy differences between FSA-FiLM and NA against the minimum cosine distance between a dataset and miniImagenet dataset evaluated using the NA method. We consider the offline setting with 50 shots. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone.
+
+trained backbone between the downstream dataset and the miniImagenet [31] dataset. We use miniImagenet (60k images) as a proxy ofImagenet-1k (1.3M images) to reduce the computational overhead of evaluating pairwise distances. This allows us to approximately measure the dissimilarity between the downstream dataset andImagenet-1k.
+
+Fig. 2 shows the accuracy difference between FSA-FiLM and NA as a function of the cosine distance for the offline setting with 50 shots whilst Fig. 3 illustrates the same accuracy difference where the datasets are grouped based on the VTAB+ categorization. For this experiment, we use 24
+
+datasets (VTAB+, DomainNet, and iNaturalist). We observe that adaptation is more beneficial for datasets in the structured domain, which contain images that are dissimilar to those of ImageNet-1k.
+
+![](images/5e00bc4d14b3d904cf9115d01ed46201c80caab98f9a04f5b241fcbb0910130d.jpg)  
+Figure 3. Bar plot of the accuracy differences between FSA-FiLM and NA for the offline case with 50 shots.
+
+Table 4. Last session accuracy  $(\%)$ $(\uparrow)$  of FSA-FiLM for three different session splits on CIFAR100 and DomainNet as described in Sec. 4.4. For reference, we also include the accuracy of NA. Results are averaged over 5 runs (mean  $\pm$  std).  
+
+<table><tr><td></td><td>CFR100</td><td>SVHN</td><td>dSp-loc</td><td>FGVC</td><td>Letters</td><td>DNet</td><td>iNat</td></tr><tr><td>EffNet-B0 (FSA-FILM)</td><td>70.9</td><td>51.3</td><td>35.7</td><td>55.8</td><td>73.4</td><td>74.0</td><td>58.8</td></tr><tr><td>ConvNext (NA)</td><td>87.1</td><td>43.6</td><td>13.6</td><td>50.2</td><td>63.1</td><td>82.9</td><td>72.6</td></tr><tr><td>ConvNext-CosD</td><td>0.2</td><td>0.6</td><td>0.6</td><td>0.3</td><td>0.4</td><td>0.3</td><td>0.1</td></tr></table>
+
+Table 5. Accuracy comparison between a pre-trained ConvNext on ImageNet-22k without body adaptation (NA) and a pre-trained EfficientNet-B0 on ImageNet-1k which is adapted on the first session (FSA-FiLM). We use the few-shot CIL setting (Sec. 4.3) and we report the accuracy  $(\%)$  ( $\uparrow$ ) after the last session. Results are averaged over 5 runs (mean±std). We also include the minimum cosine distance using the pre-trained ConvNext as in Figure 2.
+
+To stress the importance of adaptation on datasets far from ImageNet, we compare FSA-FiLM with an EfficientNet-B0 backbone to the no-adaptation method with a ConvNext [14] pre-trained onImagenet-22k. The total number of parameters for FSA-FiLM (backbone and FiLM
+
+parameters) is  $\sim 4\mathrm{M}$  while for ConvNext is  $348\mathrm{M}$ . Table 5 shows that a small adapted backbone can significantly surpass the accuracy of a much larger pre-trained backbone for datasets far from ImageNet. We also compute the cosine distance measure for ConvNext and find that it is predictive of the performance of the unadapted ConvNext model and the benefits of adaptation. We show this in Table 5; note that for CIFAR100 the ConvNext's cosine distance values are small relative to the other datasets (indicating that CIFAR100 is close to the pretraining distribution) whereas for EfficientNet the values in Figure 2 indicate that CIFAR100 is more out-of-distribution.
+
+The main takeaway from these results is that when there is a large cosine distance (e.g. SVHN, dSprites, FGVC, Letters) FiLM adaptation of a light-weight backbone performs well - better even than applying LDA head adaptation to a much larger backbone trained on a much larger dataset. As the community employs ever-larger models and datasets, these results indicate that adapters are likely to continue to bring improvements over simply learning a classifier head (the NA baseline).
+
+# 5. Discussion
+
+We have presented FSA (-FiLM), a simple yet effective replay-free baseline for CIL which adapts a pre-trained backbone via full body adaptation or FiLM layers only at the first session of continual learning and then utilizes a flexible incrementally updated LDA classifier on top of the body. Extensive experiments in several CIL scenarios have shown that FSA outperforms previous SOTA baselines in most cases, thus, questioning the efficacy of current approaches to continuous body adaption. Furthermore, the experiments have revealed that FiLM layers are helpful when the amount of data available in the target domain is relatively low and the number of parameters in the neural network and the size of the source domain data set is large. For very large foundation models trained on very large source domain data sets, it is likely we are often in this situation and FiLM-like layers will be more effective than full-body adaptation, even when the target domain has a fairly large amount of data.
+
+Limitations and future work. The main limitation of this work is inextricably linked with the distributional assumptions of CIL in general. If the data distribution at each session shifts considerably (e.g. the first session includes natural images while the next session includes images of numbers) then first session body adaptation is not suitable. In future work, we plan to combine FSA (-FiLM) with a memory method like GDumb to get the best of both worlds and deal with more challenging CIL scenarios.
+
+# References
+
+[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. Ss-il: Separated softmax for incremental learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 844-853, October 2021. 2  
+[2] Peyman Bateni, Raghav Goyal, Vaden Masrani, Frank Wood, and Leonid Sigal. Improved few-shot visual classification. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14493-14502, 2020. 2, 5  
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+                                    "content": "In Class-Incremental Learning (CIL) an image classification system is exposed to new classes in each learning session and must be updated incrementally. Methods approaching this problem have updated both the classification head and the feature extractor body at each session of CIL. In this work, we develop a baseline method, First Session Adaptation (FSA), that sheds light on the efficacy of existing CIL approaches, and allows us to assess the relative performance contributions from head and body adaption. FSA adapts a pre-trained neural network body only on the first learning session and fixes it thereafter; a head based on linear discriminant analysis (LDA), is then placed on top of the adapted body, allowing exact updates through CIL. FSA is replay-free i.e. it does not memorize examples from previous sessions of continual learning. To empirically motivate FSA, we first consider a diverse selection of 22 image-classification datasets, evaluating different heads and body adaptation techniques in high/low-shot offline settings. We find that the LDA head performs well and supports CIL out-of-the-box. We also find that Featurewise Layer Modulation (FiLM) adapters are highly effective in the few-shot setting, and full-body adaption in the high-shot setting. Second, we empirically investigate various CIL settings including high-shot CIL and few-shot CIL, including settings that have previously been used in the literature. We show that FSA significantly improves over the state-of-the-art in 15 of the 16 settings considered. FSA with FiLM adapters is especially performant in the few-shot setting. These results indicate that current approaches to continuous body adaptation are not working as expected. Finally, we propose a measure"
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+                                    "content": "that can be applied to a set of unlabelled inputs which is predictive of the benefits of body adaptation."
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+                                    "content": "1. Introduction"
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+                                    "content": "Continual learning (CL) is needed to bring machine learning models to many real-life applications. After a model is trained on a given set of data, and once deployed in its test environment, it is likely that new classes will naturally emerge. For example, in an autonomous driving scenario, new types of road transportation and traffic signage can be encountered. The deployed model needs to efficiently acquire this new knowledge with minimal cost (e.g. annotation requirements) without deteriorating the performance on existing classes of objects. The process of efficiently acquiring new knowledge while preserving what is already captured by the model is what continual learning methods target."
+                                }
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+                },
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+                                    "content": "Continual learning can be mainly divided into task incremental learning and class incremental learning. Task incremental learning (TIL) sequentially learns independent sets of heterogeneous tasks and is out of this paper's scope. Class incremental learning (CIL), in contrast, assumes that all classes (already learnt and future ones) form part of a single classification task. In class-incremental learning, data arrive in a sequence of sessions with new classes appearing as the sessions progress. Critically, the data in each session cannot be stored in its entirety and cannot be revisited. The goal is to train a single classification model under these constraints."
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "the data distribution will change as the sessions progress. However, these changes tend to be smaller in real-world class incremental learning settings than in the task incremental setting. For, example consider a human support robot learning about new objects in a home in an incremental manner (CIL) vs. the same robot learning to adapt to different homes (TIL)."
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+                                    "content": "Practically, CIL has two major uses. First, in situations where large amounts of data arrive in each session and so retraining the model is computationally prohibitive. Second, in situations where data are not allowed to be revisited due to privacy reasons such as under General Data Protection Regulation (GDPR). The latter situation is relevant for applications such as personalization where small numbers of data points are available i.e. few-shot continual learning. So-called replay-free methods are necessary for such settings, as samples of previous sessions are not allowed to be memorized, but CIL is known to be challenging in such settings."
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+                                    "content": "Current SOTA methods for class incremental learning start from a pre-trained backbone [13, 19, 35, 34] and then adapt the features at each session of continual learning. The use of a pre-trained backbone has been shown to lead to strong performance especially in the few-shot CIL setting due to the lack of data [21]. However, it is unclear to what extent continuous adaptation of the features in each session is helpful. In general, in CIL there is a trade-off between adaptation (which helps adapt to the new statistics of the target domain) and catastrophic forgetting (whereby earlier classes are forgotten as the representation changes). When memorization of previous samples is restricted, the benefits from adapting the feature extractor body to learn better features might well be out-weighted by the increase in forgetting of old classes. Moreover, body adaptation in earlier sessions is arguably more critical (e.g. adapting the backbone to the new domain in the first session), whilst it is less essential in later sessions where the changes in the ideal representation between sessions are smaller."
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+                                    "content": "This work explores under what conditions continuous adaptation of the body is beneficial, both in principle and in current practice. In order to do this, we develop a new replay-free method, inspired by the first encoding method of [2], called First Session Adaptation (FSA). FSA adapts the body of a pre-trained neural network on only the first session of continual learning. We investigate adapting all body parameters and the use of Feature-wise Layer Modulation (FiLM) adapters [23] which learn only a small number of parameters. The head, in contrast, is adapted at each session using an approach that is similar to Linear Discriminate Analysis (LDA), which suffers from no forgetting, and improves over the Nearest Class Mean classifier (NCM) [18] approach. The efficacy of this general approach, including comparisons to a standard linear head, is first motivated"
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+                                    "content": "through experiments in the offline setting (Sec. 4.2). We then carry out experiments under three CIL settings. First, we consider the high-shot setting (high-shot CIL). The other two settings consider few-shot continual learning. Specifically, one setting follows previous approaches that employ an initial session with a large number of data points and few-shot sessions thereafter (few-shot+ CIL) while the other exclusively includes sessions with only a small amount of data (few-shot CIL)."
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+                                    "content": "The contributions of the paper are as follows: (1) We develop a replay-free CIL baseline, namely FSA, that is extremely simple to implement and performs well in many different scenarios. (2) We empirically motivate FSA through a set of offline experiments that evaluate different forms of neural network head and body adaptation; (3) We then compare FSA to a set of strong continual learning baseline methods in a fair way using the same pre-trained backbone for all methods. (4) We show that the FSA-FiLM baseline performs well in the high-shot CIL setting, outperforming the SOTA whilst avoiding data memorization. (5) In the few-shot learning settings, FSA outperforms existing continual learning methods on eight benchmarks, often by a substantial margin, and is statistically tied with the best performing method on the one remaining dataset. (6) Finally, we propose a measure that can be applied to a set of unlabeled inputs which is predictive of the benefits of body adaptation."
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+                                    "content": "2. Related Work"
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+                                    "content": "Class Incremental Learning is more challenging than task-incremental continual learning as a shared output layer is used for the classes of different learning sessions. We refer to [7] for a survey on both class and task incremental learning. While softmax cross entropy loss is considered a standard in classification models, it is shown to be a source of class interference in continual learning [38, 4]. Thus, recent works either focus on fixing the softmax classifier [4, 1, 44] or deploy nearest class mean classifiers (NCM) as an alternative [25, 5, 11]. In this work, we deploy an LDA classifier that uses the mean embedding of each class and an incrementally updated covariance matrix shared across all classes. We show that this approach is comparable to a softmax classifier in the offline setting and that it outperforms NCM."
+                                }
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+                                    "content": "Due to the challenging nature of class incremental learning, some methods employ a buffer of stored samples from previous sessions [24, 39]. [24] suggests a simple baseline, GDumb, that performs offline training on both buffer data and new session data at each incremental step. GDumb shows strong performance compared to sophisticated continual learning solutions. Here we show that our simple yet effective solution often outperforms variants of GDumb that have a large memory without leveraging any buffer of stored"
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+                                    "content": "In addition to the issues arising from the shared classification layer, learning a feature extractor that can provide representative features of all classes is a key element in continual learning. Some class incremental learning methods leverage large initial training session or start from a pretrained network, e.g., [35, 9, 36] and show improved overall continual learning performance without questioning the role of such pre-training steps and whether the learned representations have in fact improved. Recently, [19] studies continual learning with strong pre-trained models and proposes deploying exemplar-based replay in the latent space using a small multilayer network on top of the fixed pretrained model. The authors show that such latent replay improves performance, especially for tasks that are different from the distribution used to train the initial model. In this work, we show that adaptation of pre-trained models is essential for strong continual learning performance. However, different from all existing continual learning works, we show that adapting the representation only in the first session is sufficient to obtain representative features for the classes being learned and that this forms a strong baseline for future continual learning methods."
+                                }
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+                                    "content": "In addition to the incremental classification in the full data regime, we focus on the few-shot scenario where only a few labeled examples per class are provided at each training session. [9] utilize a meta-trained network for few-shot classification and explore multiple design choices including a no-adaptation baseline and a method to optimize orthogonal prototypes with the last classification layer only. The method heavily relies on a pre-training and meta-training step on a large subset of classes from the original dataset. In this work, we show that the meta-training step is not essential and that a simple LDA head is sufficient without the reliance on a big initial training stage. In [11] the authors propose a new distillation loss functioning at the feature map level where importance values are estimated per feature map along with replay and consider an NCM classifier at test time. [45] heavily relies on the training of an initial session using a specific loss function that takes into account classes that will be added in future. It further requires the total number of classes to be known a priori which is unrealistic for real applications. Our solution adapts FILM parameters to the first session data and fixes the representation for the remaining training sessions. We show that surprisingly few samples in the first session are sufficient for adaptation and that our solution is more powerful than current few-shot continual learning solutions."
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+                                    "content": "3. Proposed Algorithm"
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+                                    "content": "In this section, first we discuss the main components of the proposed methods FSA/FSA-FiLM, namely body adaptation techniques and classifier heads. Then we formally"
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+                                    "content": "introduce the two methods for tackling CIL."
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+                                    "content": "3.1. Problem Formulation"
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+                                    "content": "In CIL, we are given a dataset "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_s = \\{\\mathbf{x}_{i,s},y_{i,s}\\}_{i = 1}^{N_s}"
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+                                    "type": "inline_equation",
+                                    "content": "s\\in \\{1,\\ldots ,S\\}"
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+                                    "type": "inline_equation",
+                                    "content": "X_{s} = \\{\\mathbf{x}_{i,s}\\}_{i = 1}^{N_{s}}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a set of images and "
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+                                    "type": "inline_equation",
+                                    "content": "Y_{s} = \\{y_{i,s}\\}_{i = 1}^{N_{s}}"
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+                                    "content": " is the set of the corresponding labels with "
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+                                    "type": "text",
+                                    "content": ". Here "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the label space of session "
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+                                    "type": "text",
+                                    "content": ". It is common in CIL that label spaces are mutually exclusive across sessions, i.e. "
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+                                    "content": "\\mathcal{V}_s\\cap \\mathcal{V}_{s'} = \\emptyset"
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+                                    "type": "inline_equation",
+                                    "content": "\\forall s\\neq s'"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and we only have access to "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_s"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in the current session "
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+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " to train our model. The proposed FSA method can naturally handle sessions with overlapping label spaces too, however, we follow the former paradigm in our experiments. Another typical assumption in CIL is that the data in all sessions come from the same dataset. We also adopt this assumption in this work, although our experiments on DomainNet are a step toward considering different datasets in each session."
+                                }
+                            ]
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+                    ],
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+                                    "content": "In session "
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+                                    "type": "text",
+                                    "content": ", we will use models defined as"
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+                                    "type": "interline_equation",
+                                    "content": "f _ {s} (\\mathbf {x}) = W _ {s} ^ {\\top} g _ {\\boldsymbol {\\theta} _ {s}} (\\mathbf {x}) + \\mathbf {b} _ {s}, \\tag {1}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "content": "g_{\\theta_s}(\\mathbf{x}) \\in \\mathbb{R}^d"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is a feature extractor backbone<sup>1</sup> with session-dependent parameters "
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+                                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". The linear classifier head comprises the class weights "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "W_s \\in \\mathbb{R}^{d \\times |\\mathcal{Y}_{1:s}|}"
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+                                    "type": "text",
+                                    "content": " and biases "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}_s \\in \\mathbb{R}^{|\\mathcal{Y}_{1:s}|}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Y}_{1:s} = \\cup_{j=1}^{s} \\mathcal{Y}_j"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the label space of all distinct classes we have seen up to session "
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+                                {
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+                                    "type": "text",
+                                    "content": ". Ideally, when a new dataset "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is available at the "
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+                                {
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+                                    "type": "text",
+                                    "content": "-th session, the model should be able to update the backbone parameters "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\theta"
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+                                {
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+                                    "type": "text",
+                                    "content": " and the linear classifier head "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "W_s"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with the minimum computational overhead and without compromising performance over the previously seen classes "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Y}_{1:s}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                    "index": 10
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+                {
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+                                    "type": "text",
+                                    "content": "Backbone adaptation. Traditionally, the adaptation of the body at the current session "
+                                },
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+                                    "type": "text",
+                                    "content": " requires updating the full set of the network parameters "
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+                                    "type": "text",
+                                    "content": " (full-body adaptation). Options include using specifically designed loss functions that mitigate catastrophic forgetting or using a memory buffer that stores a subset of the previously encountered data. See [16] for a review of continual learning techniques. Nevertheless, when training data availability is scarce relative to the size of the model then full-body adaptation ceases to be suitable, and few-shot learning techniques [33], such as meta-learning [10] and transfer learning [40] become favorable."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Recent works in few-shot learning [26] showed that a pre-trained backbone can be efficiently adapted by keeping its parameters "
+                                },
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+                                    "content": " frozen and introducing Feature-wise Linear Modulation (FiLM) [23] layers with additional parameters "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\xi_{s}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " which scale and shift the activations produced by a convolutional layer. In [26], these parameters are generated by a meta-trained network when a downstream task is"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+            ],
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+                                    "type": "text",
+                                    "content": "<sup>1</sup>In this paper, we interchangeably use the terms feature extractor, backbone, and body."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "given. Alternatively, "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " can be learned (fine-tuned) by the downstream data as in [27]. In this work, we consider both meta-learned (Supplement) and fine-tuned (Sec. 4) FiLM parameters."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Classifier heads. In both offline and CIL settings, (linear) classifier heads can be divided into two groups; parametrized and parameter-free. Parametrized heads require the weights/biases in Eq. (1) to be updated by an iterative gradient-based procedure whilst for parameter-free heads, a closed-form formula is available that directly computes the weights/biases after the update of the backbone. We consider three different heads (for notational simplicity we consider the offline setting, and thus suppress session "
+                                },
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+                                    "type": "text",
+                                    "content": " dependence), one parametrized, and two parameter-free."
+                                }
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+                                            "type": "text",
+                                            "content": "- The linear (learnable) head where "
+                                        },
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+                                            "type": "inline_equation",
+                                            "content": "W, \\mathbf{b}"
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+                                            "type": "text",
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+                            "type": "text",
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+                                            "type": "text",
+                                            "content": "- The Nearest Class Mean (NCM) classifier where the weight and bias of the "
+                                        },
+                                        {
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+                                            "type": "text",
+                                            "content": "-th class is given by"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {w} _ {k} = \\hat {\\boldsymbol {\\mu}} _ {k} \\text {a n d} b _ {k} = \\ln \\frac {| X ^ {(k)} |}{N} - \\frac {1}{2} \\hat {\\boldsymbol {\\mu}} _ {k} ^ {\\top} \\hat {\\boldsymbol {\\mu}} _ {k}, \\tag {2}",
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                        347,
+                                        287,
+                                        386
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X^{(k)} = \\{\\mathbf{x}_i:y_i = k\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        347,
+                                        287,
+                                        386
+                                    ],
+                                    "type": "text",
+                                    "content": " is the set of images belonging in class "
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        347,
+                                        287,
+                                        386
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
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+                                        347,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        347,
+                                        287,
+                                        386
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\pmb{\\mu}}_k = \\frac{1}{|X^{(k)}|}\\sum_{\\mathbf{x}\\in X^{(k)}}g_\\pmb {\\theta}(\\mathbf{x})"
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        347,
+                                        287,
+                                        386
+                                    ],
+                                    "type": "text",
+                                    "content": " is the mean vector of the embedded images of class "
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        347,
+                                        287,
+                                        386
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "- The Linear Discriminant Analysis (LDA) classifier with weights/biases defined as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {w} _ {k} = \\tilde {S} ^ {- 1} \\hat {\\boldsymbol {\\mu}} _ {k} \\text {a n d} b _ {k} = \\ln \\frac {| X ^ {(k)} |}{N} - \\frac {1}{2} \\hat {\\boldsymbol {\\mu}} _ {k} ^ {\\top} \\tilde {S} ^ {- 1} \\hat {\\boldsymbol {\\mu}} _ {k}, \\tag {3}",
+                                    "image_path": "78f1c102a1d9ef9cf03579c87823acd94b273e6717be607634116e2492a43798.jpg"
+                                }
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+                {
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{S} = S + I_d"
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        460,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the regularized sample covariance matrix with sample covariance matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        460,
+                                        287,
+                                        515
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S = \\frac{1}{|X| - 1}\\sum_{\\mathbf{x}\\in X}(g_{\\boldsymbol{\\theta}}(\\mathbf{x}) - \\hat{\\boldsymbol{\\mu}})(g_{\\boldsymbol{\\theta}}(\\mathbf{x}) - \\hat{\\boldsymbol{\\mu}})^\\top"
+                                },
+                                {
+                                    "bbox": [
+                                        66,
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\boldsymbol{\\mu}} = \\frac{1}{|X|}\\sum_{\\mathbf{x}\\in X}g_{\\boldsymbol{\\theta}}(\\mathbf{x})"
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        460,
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+                                        515
+                                    ],
+                                    "type": "text",
+                                    "content": ", and identity matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        460,
+                                        287,
+                                        515
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_d \\in \\mathbb{R}^{d\\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        66,
+                                        460,
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+                                        515
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        46,
+                        520,
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Both NCM and LDA classifiers are suitable for CIL since their closed-form updates in Eq. (2) and Eq. (3) support exact, computationally inexpensive, continual updates (via running averages) that incur no forgetting. Updating the linear head, in contrast, requires more computational effort and machinery when novel classes appear in a new session. Notice that setting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        520,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{S} = I_d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        520,
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+                                        604
+                                    ],
+                                    "type": "text",
+                                    "content": " in LDA recovers NCM."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        46,
+                        604,
+                        287,
+                        664
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The continuous update of the LDA head is not as straightforward as it is for NCM, since LDA also requires updating the sample covariance "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        604,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We discuss how this can be attained in the next section where we introduce our proposed method FSA/FSA-FiLM."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.2. First Session Adaptation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Motivated by the efficient adaptation techniques and CIL-friendly classifiers discussed in the previous section,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                        289
+                                    ],
+                                    "type": "text",
+                                    "content": "we propose two simple and computationally efficient CIL methods called First Session Adaptation (FSA) and FSA-FiLM. FSA is based on a full-body adaptation while FSA-FiLM uses FiLM layers to adapt the body. Both methods utilize pre-trained backbones. FSA (-FiLM) (i) adapts the backbone only at the first session and then the backbone remains frozen for the rest of the sessions, and (ii) makes use of an LDA classifier which is continuously updated as new data become available. For adapting the body (either full or FiLM-based adaptation) at the first session, we use a linear head and a cross-entropy loss first, and then after the optimization is over, the linear head is removed and an LDA head is deployed instead, based on the optimized parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        289
+                                    ],
+                                    "type": "text",
+                                    "content": " and Eq. (3). Updating the LDA head when the data of the next session becomes available, can be done by using Algorithm 1 recursively until the last session "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        289
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Specifically, by having access to the running terms "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        289
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{A, \\mathbf{b}, \\text{count}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        547,
+                                        289
+                                    ],
+                                    "type": "text",
+                                    "content": ", the sample covariance matrix is given by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "interline_equation",
+                                    "content": "S = \\frac {1}{\\operatorname {c o u n t} - 1} \\left(A - \\frac {1}{\\operatorname {c o u n t}} \\mathbf {b b} ^ {\\top}\\right). \\tag {4}",
+                                    "image_path": "c92358249dedb87278318430375eb4796393870319e71b8f3b8e7b2798b66aae.jpg"
+                                }
+                            ]
+                        }
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+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        307,
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+                                    ],
+                                    "type": "text",
+                                    "content": "The time complexity of LDA scales as "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        331,
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+                                        344
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(d^3 + |\\mathcal{Y}_s|d^2)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Algorithm 1 Update of sample covariance running terms"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Require: "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        369,
+                                        494,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g(\\cdot) \\equiv a"
+                                },
+                                {
+                                    "bbox": [
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+                                        369,
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+                                    ],
+                                    "type": "text",
+                                    "content": " feature extractor backbone"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Require: "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        381,
+                                        500,
+                                        394
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{s} = \\{\\mathbf{x}_{i,s}\\}_{i = 1}^{N_{s}}"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        381,
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+                                    ],
+                                    "type": "text",
+                                    "content": ": Images of session "
+                                },
+                                {
+                                    "bbox": [
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+                                        500,
+                                        394
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                }
+                            ]
+                        }
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+                    "index": 19
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Require: "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        394,
+                                        513,
+                                        406
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A\\in \\mathbb{R}^{d\\times d}"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        394,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}\\in \\mathbb{R}^d"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        394,
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+                                    ],
+                                    "type": "text",
+                                    "content": " count "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\in \\mathbb{N}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        394,
+                                        513,
+                                        406
+                                    ],
+                                    "type": "text",
+                                    "content": " if "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        394,
+                                        513,
+                                        406
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s > 1"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                    "type": "list",
+                    "angle": 0,
+                    "index": 30,
+                    "blocks": [
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+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "1: function INCUPDATE "
+                                        },
+                                        {
+                                            "bbox": [
+                                                312,
+                                                406,
+                                                504,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "(g(\\cdot), X_s, A, b, \\text{count})"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "2: if "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "s = 1"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " then Initialize "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "A, \\mathbf{b}"
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+                                            "type": "text",
+                                            "content": ", count"
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+                                            "content": "A\\gets \\mathbf{0}_{d\\times d},\\mathbf{b}\\gets \\mathbf{0}_d,\\mathrm{count}\\gets 0"
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+                                            "content": "4: end if"
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+                                            "content": "A\\gets A + \\sum_{\\mathbf{x}\\in X_s}g(\\mathbf{x})g(\\mathbf{x})^\\top"
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+                                            "content": "\\mathbf{b}\\gets \\mathbf{b} + \\sum_{\\mathbf{x}\\in X_s}g(\\mathbf{x})"
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+                                    ]
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+                                            "content": "8: return "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": ", b, count"
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+                                    ]
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+                                            "content": "9: end function"
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+                                    "type": "text",
+                                    "content": "its space complexity is "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": "-th session. This computational burden is negligible compared to taking gradient steps for learning a linear head and as we will see in Sec. 4.2 using covariance information boosts performance significantly against the vanilla NCM head."
+                                }
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+                                    "type": "text",
+                                    "content": "In this section, we present a series of experiments to investigate the performance of FSA (-FiLM) under different CIL settings. First, we detail the datasets used for the experiments and discuss our implementation. Second, we perform a large empirical comparison between LDA, linear, and NCM classifiers, in combination with different body adaptation techniques, in the offline setting. For the CIL settings, the results are compared to the vanilla method, "
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+                                    "content": "Adaptation (NA), where a pretrained backbone is combined with an LDA head and remains frozen across sessions. We also consider how these findings are affected by the number of shots available. Third, we compare FSA (-FiLM) with state-of-the-art continual learning methods and conduct ablation studies. Finally, we investigate the effect of adapting the backbone when the CIL dataset is \"similar\" to ImageNet-1k and discuss a similarity metric that indicates whether body adaptation is required."
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+                                    "content": "4.1. Datasets and Implementation details"
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+                                    "type": "text",
+                                    "content": "Datasets. We employ a diverse collection of 26 image-classification datasets across the offline and CIL experiments. For the offline experiments of Sec. 4.2, we use the 19 datasets of VTAB [42], a low-shot transfer learning benchmark, plus three additional datasets, FGVC-Aircraft [17], Stanford Cars [12], and Letters [6]. We refer to this group of datasets as VTAB+. For the CIL-based experiments, we choose 5 VTAB+ datasets from different domains, having an adequate number of classes to create realistic CIL scenarios. The datasets are CIFAR100, SVHN, dSprites-location, FGVC-Aircraft, Cars, and Letters while also including 4 extra datasets: CUB200 [32], CORE50 [15], iNaturalist [30], and DomainNet [22]. Exact details for each dataset are provided in the Supplement."
+                                }
+                            ]
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+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "Training details. All models are implemented with PyTorch [20]. We use a pre-trained EfficientNet-B0 [28] onImagenet-1k as the main backbone for all methods. For the few-shot+ CIL experiment in Sec. 4.3, we also consider two ResNet architectures, ResNet-18 and ResNet-20 [8] to enable direct comparison to the original settings used in [45]. All the deployed backbones (except ResNet-20, due to the unavailability of pre-trained weights on ImageNet-1k), are pre-trained on ImageNet-1k for all methods. We keep the optimization settings the same across all baselines for fairness. Optimization details are given in the Supplement."
+                                }
+                            ]
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+                    ],
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+                                    "content": "Evaluation protocol. We report the Top-1 accuracy after the last continual learning session evaluated on a test set including instances from all the previously seen classes. In the Supplement, we provide the accuracy after each session. To quantify the forgetting behavior, we use a scaled modification of the performance dropping rate [29], namely percent performance dropping rate (PPDR), defined as "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{PPDR} = 100 \\times \\frac{\\mathcal{A}_1 - \\mathcal{A}_S}{\\mathcal{A}_1}\\%"
+                                },
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}_1"
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+                                    "bbox": [
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+                                        533,
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+                                    "type": "text",
+                                    "content": " denotes test accuracy after the first session, and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}_S"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " the test accuracy after the last session."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "type": "text",
+                                    "content": "4.2. Head Comparisons"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "To motivate the choice of the LDA head for FSA (-FiLM), we compare its average accuracy across all VTAB+ datasets with that of the linear and NCM classifiers under the offline setting where all the classes are available and"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "no incremental learning is required. For the body, we use no adaptation (NA) as a baseline (i.e. using the unadapted original backbone), FiLM-based adaptation, and full-body adaptation while ranging the number of shots from 5 to 10, then 50, and finally using all available training data. As Fig. 1 illustrates, LDA consistently outperforms both NCM and linear heads when the number of shots is equal to 5 and 10, regardless of adaptation technique. Notice also that as the number of learnable parameters increases, the choice of the head plays a less significant role in the predictive power of the method. Overall, LDA performs similarly to the linear head in the high-shot settings and performs the best of all heads in the low-shot settings. Finally, the full covariance information of LDA provides a consistent advantage over its isotropic covariance counterpart, i.e. the NCM classifier. This is in agreement with the results presented in [27] for the LDA and NCM classifier. In addition to the results presented here, we have also tested meta-learning based body adaptation methods [3, 26, 2] which support continual learning out of the box. We find these perform poorly compared to the fine-tuning based methods. See next section for more results."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.3. Class-Incremental Learning Comparisons"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We consider three different CIL scenarios: (i) high-shot CIL, (ii) few-shot+ CIL, and (iii) few-shot CIL. We compare our FSA/FSA-FiLM methods with recent state-of-the-art FSCIL methods, including Decoupled-Cosine [31], CEC [43], FACT [45], and ALICE. Additionally, for the high-shot CIL setting, we consider a strong replay-based baseline for CIL, GDumb [24] and a competitive replay-free method, E-EWC+SDC [41]. Finally, we introduce an additional baseline adapter inspired by [37], called FSA-LL (Last Layer). In FSA-LL only the parameters of the backbone's last block are fine-tuned which can be compared to the FSA-FiLM adaption method."
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+                            ]
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+                                    "type": "text",
+                                    "content": "High-shot CIL. In this setting, we consider all the available training data for each class while keeping the number of novel classes in each session low. We use CIFAR100, CORE50, SVHN, dSprites-loc, FGVC-Aircraft, Cars, and Letters for our experiments. For CIFAR100, CORE50, and FGVC-Aircraft, the first session consists of 10 classes, 4 for dSprites-loc, 16 for Cars, and 12 for letters. The rest of the sessions include 10 classes for CIFAR100, FGVC-Aircraft, 20 for Cars, 5 for CORE50 and Letters, 2 for SVHN and dSprites-loc. Therefore, the total number of incremental sessions for CIFAR100, FGVC-Aircraft, and Cars is 10 while for CORE50 we have 9 sessions. A pre-trained on Imagenet-1k EfficientNet-B0 is deployed as a backbone for all methods. FSA-FiLM outperforms all the competitors by a significant margin on all datasets except dSprites-loc. We attribute the performance gap on dSprites-loc due to the"
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+                                            "content": "Figure 1. Average accuracy across all VTAB+ datasets using no-adaptation (NA), FiLM adaptation (A-FiLM), and full body adaptation (A-FB) for different classifier heads (NCM, LDA, Linear) and number of shots (5, 10, 50, All Data). The results correspond to the offline setting where all classes are available without any incremental learning."
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+                                            "html": "<table><tr><td>Method</td><td>CIFAR100</td><td>CORE50</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Cars</td><td>Letters</td><td>Avg Diff</td></tr><tr><td>NA</td><td>68.2 (26.8)</td><td>82.6 (14.2)</td><td>39.9 (51.1)</td><td>20.6 (54.0)</td><td>41.3 (1.7)</td><td>43.3 (40.3)</td><td>68.4 (24.1)</td><td>0.0</td></tr><tr><td>E-EWC+SDC[41]</td><td>32.4 (66.7)</td><td>21.7 (78.1)</td><td>39.5 (60.1)</td><td>18.6 (81.4)</td><td>25.6 (55.8)</td><td>30.0 (62.6)</td><td>33.6 (66.3)</td><td>-23.3</td></tr><tr><td>FACT [45]</td><td>10.2 (89.4)</td><td>22.0 (77.7)</td><td>33.8 (65.9)</td><td>6.4 (93.6)</td><td>4.7 (90.3)</td><td>0.6 (99.3)</td><td>20.9 (79.1)</td><td>-38.0</td></tr><tr><td>ALICE [21]</td><td>52.4 (45.8)</td><td>72.8 (25.8)</td><td>46.1 (53.6)</td><td>68.3 (31.7)</td><td>39.8 (35.0)</td><td>36.4 (56.0)</td><td>75.7 (24.2)</td><td>+3.9</td></tr><tr><td>FSA</td><td>62.8 (34.5)</td><td>82.8 (15.5)</td><td>71.3 (26.6)</td><td>91.5 (8.5)</td><td>50.8 (6.3)</td><td>50.3 (36.6)</td><td>78.4 (21.4)</td><td>+17.7</td></tr><tr><td>FSA-LL</td><td>60.5 (37.2)</td><td>79.0 (19.2)</td><td>64.6 (33.1)</td><td>91.3 (8.5)</td><td>45.4 (21.7)</td><td>45.7 (43.8)</td><td>77.2 (22.7)</td><td>+14.2</td></tr><tr><td>FSA-FiLM</td><td>73.8 (23.4)</td><td>85.4 (13.3)</td><td>75.9 (23.4)</td><td>76.9 (22.8)</td><td>55.9 (-5.7)</td><td>55.9 (30.2)</td><td>79.7 (20.0)</td><td>+19.9</td></tr><tr><td>GDumb [24]</td><td>54.5 (42.2)</td><td>82.4 (15.0)</td><td>78.2 (19.6)</td><td>79.5 (12.9)</td><td>25.3 (56.9)</td><td>14.2 (82.6)</td><td>70.1 (27.0)</td><td>+5.7</td></tr><tr><td>Offline-FiLM</td><td>78.2</td><td>88.4</td><td>93.1</td><td>98.5</td><td>67.5</td><td>67.3</td><td>85.2</td><td>+30.6</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1. Last session's test accuracy "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and the PPDR "
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+                                    "type": "inline_equation",
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+                                    "content": "(\\downarrow)"
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+                                    "type": "text",
+                                    "content": " in parentheses, for the high-shot CIL setting (Sec. 4.3). The last column reports the average accuracy difference "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on Imagenet-1k is used as a backbone for all methods. For reference, we include the replay-based baseline GDumb where 1k images are used for the memory buffer."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "large number of data points (25k) and the portion of the classes "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(25\\%)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in the first session. It is also apparent the efficiency of fine-tuning FiLM parameters over fine-tuning the parameters of the model's last layer; note the number of FiLM parameters is only 20.5k while the last layer of an EfficientNet-B0 comprises 2.9M parameters. Furthermore, fine-tuning the FiLM parameters offer almost "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " accuracy increase on average compared to using a pretrained model without doing any further adaptation. Interestingly, the replay-free FSA-FILM is able to outperform significantly the replay-based method GDumb with a 1k memory buffer on most of the datasets; accuracy and time comparisons between FSA-FiLM and GDumb with varying buffer sizes can be found in Figure 1 of the Supplement. Regarding FACT's performance, although it starts from a pre-trained backbone, it was developed under the assumption that the first session contains lots of data and a high fraction of the classes that will be encountered "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "(>50\\%)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " which is not true for the setting treated in Table 1. FACT overfits in this setting and this results in poor performance. It turns out that FACT's assumptions about the first session are a strong requirement"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                {
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+                                    "type": "text",
+                                    "content": "which is not necessary for obtaining good performance as our FSA baseline shows."
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+                                    "type": "text",
+                                    "content": "Few-shot+ CIL. This setting is the one that has most commonly been used for few-shot CIL (FSCIL) and it involves an initial session that contains a large number of classes (around "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "50 - 60\\%"
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+                                    "type": "text",
+                                    "content": " of the total number of classes in the dataset) and all the available training images of these classes. The remaining sessions comprise a small number of classes and shots (typically 5/10-way 5-shot). Here we follow the exact FSCIL settings as described in [45, 21] for CIFAR100 and CUB200. We use ResNet-18/20 and EfficientNet-B0 as backbones. Table 2 summarizes the performance comparison between baselines. FSA performs on par with FACT on CIFAR100 when we use the original backbone used in [45], and it outperforms FACT by almost "
+                                },
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+                                    "type": "text",
+                                    "content": " and ALICE by "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " when EfficientNet-B0 is utilized while FSA-FiLM exhibits the lowest PPDR score. Notice also that FSA is only marginally worse than its offline counterpart, meaning there is little room for continuous body adaptation to improve things further. For CUB200, FSA"
+                                }
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+                                    "content": "with an EfficientNet-B0 performs on par with ALICE. Interestingly, we observe that NA performs well on this dataset. This indicates that CUB200 is not far from ImageNet-1k. The current results of FSA set new SOTA performance on CIFAR100 for the FSCIL setting."
+                                }
+                            ]
+                        }
+                    ],
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Backbone</td><td colspan=\"2\">Datasets</td></tr><tr><td>CIFAR100</td><td>CUB200</td></tr><tr><td>CEC [43]</td><td></td><td>49.1 (32.7)*</td><td>-</td></tr><tr><td>FACT [45]</td><td>RN-20</td><td>52.1 (30.2)*</td><td>-</td></tr><tr><td>FSA</td><td></td><td>52.0 (30.8)</td><td>-</td></tr><tr><td>NA</td><td></td><td>50.4 (26.8)</td><td>50.0 (29.3)</td></tr><tr><td>CEC [43]</td><td></td><td>-</td><td>52.3 (31.1)*</td></tr><tr><td>FACT [45]</td><td rowspan=\"2\">RN-18</td><td>49.5 (34.8)*</td><td>56.9 (25.0)*</td></tr><tr><td>ALICE [21]</td><td>54.1 (31.5)†</td><td>60.1 (22.4)†</td></tr><tr><td>FSA-FiLM</td><td></td><td>55.2 (24.4)</td><td>52.7 (27.6)</td></tr><tr><td>FSA</td><td></td><td>61.4 (25.1)</td><td>57.6 (24.3)</td></tr><tr><td>NA</td><td></td><td>55.2 (25.8)</td><td>63.2 (19.6)</td></tr><tr><td>FACT [45]</td><td></td><td>56.5 (34.6)</td><td>62.9 (23.3)</td></tr><tr><td>ALICE [21]</td><td rowspan=\"2\">EN-B0</td><td>62.7 (28.4)</td><td>63.5 (22.2)</td></tr><tr><td>FSA-LL</td><td>61.4 (25.7)</td><td>55.9 (22.3)</td></tr><tr><td>FSA-FiLM</td><td></td><td>61.8 (22.4)</td><td>62.9 (20.4)</td></tr><tr><td>FSA</td><td></td><td>66.1 (24.6)</td><td>63.4 (20.9)</td></tr><tr><td>Offline</td><td>EN-B0</td><td>67.0</td><td>65.1</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 2. Baseline comparison under the few-shot+ CIL setting (Sec. 4.3). We report the accuracy "
+                                },
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+                                    "type": "text",
+                                    "content": " ("
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+                                    "type": "text",
+                                    "content": ") of the last session and the PPDR "
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+                                    "content": "(\\%)"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " ("
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+                                    "type": "inline_equation",
+                                    "content": "\\downarrow"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ") in parentheses. Asterisk "
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(*)"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " indicates that the reported results are from [45] and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\dagger"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        371,
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+                                        448
+                                    ],
+                                    "type": "text",
+                                    "content": " indicates results reported in [21]. We use three different backbones, EfficientNet-B0 (EN-B0) and ResNet-18/20 (RN-18/20); EN-B0 and RN-18 are pre-trained onImagenet-1k."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2,
+                    "angle": 0,
+                    "type": "text"
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Few-shot CIL. The final setting, which is firstly introduced in this work, considers an alternative FSCIL setting in which only a small number of data points are available in all sessions, including the first. We use 50 shots per session while the first session includes "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "20\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the total number of classes of the dataset. Each of the remaining sessions includes around "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "10\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of the total number of classes; more details are available in the Supplement. We repeat experiments 5 times and we report the mean accuracy and PPDR in Table 3. FSA-FiLM outperforms all the other baselines by a large margin in terms of both accuracy and PPDR, indicating that transfer learning is considerably advantageous for CIL when the data availability is low. Notice that both ALICE and FACT struggle to achieve good performance under this setting due to the limited amount of data in the first session. We find that FGVC-Aircraft exhibits a positive backward transfer behavior that we attribute to a difficult initial session followed by sessions that contain classes that are comparatively easier to distinguish."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Finally, we demonstrate the suitability of the LDA head"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "in FSA-FiLM compared to a nearest class mean head, denoted FSA-FiLM-NCM. In the continual learning setting, LDA gives far larger improvements over NCM; e.g. "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " on average as presented in Table 3. This highlights the importance of a strong classification layer. Note that the incremental update of LDA does not require any replay buffer as opposed to a linear head."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "4.4. Inhomogeneous Class-Incremental Learning"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "FSA adapts the body only on the first session of continual learning and it is therefore likely to be sensitive to the particular classes which are present in this session. To investigate the degree of performance sensitivity for FSA, we devise a setting similar to the few-shot CIL setting of Sec. 4.3, where each session includes classes that share some common attribute. We select CIFAR100 which provides superclass information, and DomainNet which consists of different domains and also has superclass information available. We create three distinct CIL configurations for each dataset, each of which has different types of data in the first session. For CIFAR100, we split the data into 19 sessions. The first session includes 10 classes from super-classes (i) aquatic mammals and fish "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(Aq)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", (ii) electric devices and furniture "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(DevF)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        183,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", or (iii) Vehicles 1 and Vehicles 2 (Veh). Each of the other 18 sessions include images from the remaining 18 super-classes. Similarly, for DomainNet, we split the data into 6 sessions using 50 shots with 10 classes in each session. The first session includes 10 classes of (i) the \"electricity\" superclass of the real domain "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(El-R)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", (ii) the \"furniture\" superclass of the clipart domain "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(F-Clp)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", or (iii) the \"transportation\" superclass of the sketch domain "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(Tr-Sk)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". In this way, we can vary the content of the first session and analyze the effect this has on performance. Table 4 reveals that FSA-FiLM's performance is similar even if the data in the first session used for the body adaptation appears disparate from that contained in the remaining sessions. Even for DomainNet where the distribution shift of the data across sessions is considerable, performance is only marginally affected in each of the three settings. This provides evidence that adapting the body only on the first session achieves competitive performance regardless of the class order, given the assumption that the data come from a single dataset (albeit a varied one in the case of DomainNet)."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.5. When to adapt the body?"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Despite the strong performance of FSA (-FiLM) in the few-shot settings of Sec. 4.3, there are cases where the NA method achieves very close accuracy to FSA (e.g. see CUB200 results in Table 2). This implies that there may be datasets where adaptation is not required and all we need is the pre-trained backbone. In order to decide whether we require body adaptation or not, we compute the minimum cosine distance in the embedding space of the pre"
+                                }
+                            ]
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+                                            "html": "<table><tr><td>Method/Dataset</td><td>CIFAR100</td><td>SVHN</td><td>dSprites-loc</td><td>FGVC-Aircraft</td><td>Letters</td><td>DomainNet</td><td>iNaturalist</td><td>Avg Diff</td></tr><tr><td>NA</td><td>57.4 (28.4)</td><td>28.3 (61.5)</td><td>11.9 (66.6)</td><td>41.0 (-15.5)</td><td>57.6 (29.9)</td><td>69.0 (17.2)</td><td>49.7 (4.3)</td><td>0.0</td></tr><tr><td>FACT [45]</td><td>16.8 (79.7)</td><td>24.1 (66.2)</td><td>11.7 (64.1)</td><td>8.3 (79.9)</td><td>49.8 (40.9)</td><td>20.6 (75.6)</td><td>14.3 (74.0)</td><td>-24.2</td></tr><tr><td>ALICE [21]</td><td>58.0 (33.8)</td><td>23.0 (65.9)</td><td>23.0 (46.0)</td><td>42.0 (27.5)</td><td>66.5 (31.4)</td><td>66.5 (25.1)</td><td>47.9 (13.7)</td><td>+1.7</td></tr><tr><td>FSA</td><td>60.3 (27.0)</td><td>32.9 (53.5)</td><td>33.7 (41.3)</td><td>50.1 (-16.8)</td><td>62.2 (28.5)</td><td>70.3 (17.5)</td><td>51.5 (1.1)</td><td>+6.6</td></tr><tr><td>FSA-LL</td><td>62.0 (25.7)</td><td>43.5 (47.0)</td><td>18.8 (61.7)</td><td>45.8 (-2.1)</td><td>69.4 (26.1)</td><td>67.6 (16.9)</td><td>49.2 (14.1)</td><td>+5.9</td></tr><tr><td>FSA-FiLM-NCM</td><td>66.4 (24.8)</td><td>38.8 (56.5)</td><td>25.1 (59.4)</td><td>42.5 (-7.5)</td><td>57.1 (34.9)</td><td>68.8 (18.5)</td><td>51.5 (12.1)</td><td>+5.0</td></tr><tr><td>FSA-FiLM</td><td>70.9 (20.5)</td><td>51.3 (43.5)</td><td>35.7 (43.1)</td><td>55.8 (-19.8)</td><td>73.4 (22.1)</td><td>74.0 (15.6)</td><td>58.8 (4.8)</td><td>+15.0</td></tr><tr><td>Offline-FiLM</td><td>73.8</td><td>77.2</td><td>83.7</td><td>65.1</td><td>79.7</td><td>75.1</td><td>62.1</td><td>+28.0</td></tr></table>",
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+                                            "content": "Table 3. Accuracy "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " (↑) of the last session and PPDR "
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+                                            "type": "text",
+                                            "content": " (↓) in parentheses for the few-shot CIL setting of Sec. 4.3. The last column reports the average accuracy difference "
+                                        },
+                                        {
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+                                            "type": "text",
+                                            "content": " across all datasets between a baseline and NA. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone for all methods. FSA-FiLM-NCM utilizes an NCM classifier while NA, FSA (-LL, FiLM) and Offline uses a LDA head."
+                                        }
+                                    ]
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+                            ],
+                            "index": 1,
+                            "angle": 0,
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+                                            "html": "<table><tr><td>Dataset</td><td>NA</td><td>Aq</td><td>DevF</td><td>Veh</td></tr><tr><td>CIFAR100</td><td>57.4±1.0</td><td>66.1±1.6</td><td>66.2±1.9</td><td>67.9±1.2</td></tr><tr><td></td><td>NA</td><td>El-R</td><td>F-Clp</td><td>Tr-Sk</td></tr><tr><td>DomainNet</td><td>69.0±0.4</td><td>70.6±0.6</td><td>71.7±0.6</td><td>72.8±0.5</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Figure 2. Scatter plot of the accuracy differences between FSA-FiLM and NA against the minimum cosine distance between a dataset and miniImagenet dataset evaluated using the NA method. We consider the offline setting with 50 shots. A pre-trained EfficientNet-B0 on ImageNet-1k is used as a backbone."
+                                        }
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+                                    "content": "trained backbone between the downstream dataset and the miniImagenet [31] dataset. We use miniImagenet (60k images) as a proxy ofImagenet-1k (1.3M images) to reduce the computational overhead of evaluating pairwise distances. This allows us to approximately measure the dissimilarity between the downstream dataset andImagenet-1k."
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+                                    "content": "Fig. 2 shows the accuracy difference between FSA-FiLM and NA as a function of the cosine distance for the offline setting with 50 shots whilst Fig. 3 illustrates the same accuracy difference where the datasets are grouped based on the VTAB+ categorization. For this experiment, we use 24"
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+                                    "type": "text",
+                                    "content": "datasets (VTAB+, DomainNet, and iNaturalist). We observe that adaptation is more beneficial for datasets in the structured domain, which contain images that are dissimilar to those of ImageNet-1k."
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+                                            "content": "Figure 3. Bar plot of the accuracy differences between FSA-FiLM and NA for the offline case with 50 shots."
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+                                            "type": "text",
+                                            "content": "Table 4. Last session accuracy "
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " of FSA-FiLM for three different session splits on CIFAR100 and DomainNet as described in Sec. 4.4. For reference, we also include the accuracy of NA. Results are averaged over 5 runs (mean "
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+                                            "type": "text",
+                                            "content": " std)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "table_caption"
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+                                            "type": "table",
+                                            "html": "<table><tr><td></td><td>CFR100</td><td>SVHN</td><td>dSp-loc</td><td>FGVC</td><td>Letters</td><td>DNet</td><td>iNat</td></tr><tr><td>EffNet-B0 (FSA-FILM)</td><td>70.9</td><td>51.3</td><td>35.7</td><td>55.8</td><td>73.4</td><td>74.0</td><td>58.8</td></tr><tr><td>ConvNext (NA)</td><td>87.1</td><td>43.6</td><td>13.6</td><td>50.2</td><td>63.1</td><td>82.9</td><td>72.6</td></tr><tr><td>ConvNext-CosD</td><td>0.2</td><td>0.6</td><td>0.6</td><td>0.3</td><td>0.4</td><td>0.3</td><td>0.1</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 5. Accuracy comparison between a pre-trained ConvNext on ImageNet-22k without body adaptation (NA) and a pre-trained EfficientNet-B0 on ImageNet-1k which is adapted on the first session (FSA-FiLM). We use the few-shot CIL setting (Sec. 4.3) and we report the accuracy "
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+                                    "type": "text",
+                                    "content": " ("
+                                },
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+                                    "type": "text",
+                                    "content": ") after the last session. Results are averaged over 5 runs (mean±std). We also include the minimum cosine distance using the pre-trained ConvNext as in Figure 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+                                    "type": "text",
+                                    "content": "To stress the importance of adaptation on datasets far from ImageNet, we compare FSA-FiLM with an EfficientNet-B0 backbone to the no-adaptation method with a ConvNext [14] pre-trained onImagenet-22k. The total number of parameters for FSA-FiLM (backbone and FiLM"
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 4\\mathrm{M}"
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+                                    "type": "text",
+                                    "content": " while for ConvNext is "
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+                                    "type": "text",
+                                    "content": ". Table 5 shows that a small adapted backbone can significantly surpass the accuracy of a much larger pre-trained backbone for datasets far from ImageNet. We also compute the cosine distance measure for ConvNext and find that it is predictive of the performance of the unadapted ConvNext model and the benefits of adaptation. We show this in Table 5; note that for CIFAR100 the ConvNext's cosine distance values are small relative to the other datasets (indicating that CIFAR100 is close to the pretraining distribution) whereas for EfficientNet the values in Figure 2 indicate that CIFAR100 is more out-of-distribution."
+                                }
+                            ]
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+                    "index": 0
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+                {
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+                                    "type": "text",
+                                    "content": "The main takeaway from these results is that when there is a large cosine distance (e.g. SVHN, dSprites, FGVC, Letters) FiLM adaptation of a light-weight backbone performs well - better even than applying LDA head adaptation to a much larger backbone trained on a much larger dataset. As the community employs ever-larger models and datasets, these results indicate that adapters are likely to continue to bring improvements over simply learning a classifier head (the NA baseline)."
+                                }
+                            ]
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+                    ],
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+                                    "content": "5. Discussion"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "We have presented FSA (-FiLM), a simple yet effective replay-free baseline for CIL which adapts a pre-trained backbone via full body adaptation or FiLM layers only at the first session of continual learning and then utilizes a flexible incrementally updated LDA classifier on top of the body. Extensive experiments in several CIL scenarios have shown that FSA outperforms previous SOTA baselines in most cases, thus, questioning the efficacy of current approaches to continuous body adaption. Furthermore, the experiments have revealed that FiLM layers are helpful when the amount of data available in the target domain is relatively low and the number of parameters in the neural network and the size of the source domain data set is large. For very large foundation models trained on very large source domain data sets, it is likely we are often in this situation and FiLM-like layers will be more effective than full-body adaptation, even when the target domain has a fairly large amount of data."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Limitations and future work. The main limitation of this work is inextricably linked with the distributional assumptions of CIL in general. If the data distribution at each session shifts considerably (e.g. the first session includes natural images while the next session includes images of numbers) then first session body adaptation is not suitable. In future work, we plan to combine FSA (-FiLM) with a memory method like GDumb to get the best of both worlds and deal with more challenging CIL scenarios."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                            "bbox": [
+                                                311,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[1] Hongjoon Ahn, Jihwan Kwak, Subin Lim, Hyeonsu Bang, Hyojun Kim, and Taesup Moon. Ss-il: Separated softmax for incremental learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 844-853, October 2021. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                            "lines": [
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+                                            "bbox": [
+                                                311,
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+                                                203
+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                311,
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+                                259
+                            ],
+                            "type": "ref_text",
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+                            "lines": [
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+                                        {
+                                            "bbox": [
+                                                311,
+                                                205,
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+                                                259
+                                            ],
+                                            "type": "text",
+                                            "content": "[3] John Bronskill, Daniela Massiceti, Massimiliano Patacchiola, Katja Hofmann, Sebastian Nowozin, and Richard Turner. Memory efficient meta-learning with large images. Advances in Neural Information Processing Systems, 34:24327-24339, 2021. 5"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                311,
+                                261,
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+                                305
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
+                                                311,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[4] Lucas Caccia, Rahaf Aljundi, Nader Asadi, Tinne Tuyte-laars, Joelle Pineau, and Eugene Belilovsky. New insights on reducing abrupt representation change in online continual learning. arXiv preprint arXiv:2203.03798, 2022. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[5] MohammadReza Davari, Nader Asadi, Sudhir Mudur, Rahaf Aljundi, and Eugene Belilovsky. Probing representation forgetting in supervised and unsupervised continual learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16712-16721, 2022. 2"
+                                        }
+                                    ]
+                                }
+                            ],
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diff --git a/2023/FishNet_ A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction/76ca1838-244d-4142-bae4-84af44e0f40e_content_list.json b/2023/FishNet_ A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction/76ca1838-244d-4142-bae4-84af44e0f40e_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2213d60f0a97628cecc45b6056a0d6ef9d0c2ce8
--- /dev/null
+++ b/2023/FishNet_ A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction/76ca1838-244d-4142-bae4-84af44e0f40e_content_list.json	
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+        "text": "FishNet: A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction",
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+    {
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+    {
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+    {
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+        "text": "* equal contribution",
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "$\\dagger$  project lead",
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+    {
+        "type": "text",
+        "text": "King Abdullah University of Science and Technology (KAUST)",
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+    },
+    {
+        "type": "text",
+        "text": "{faizan.khan, xiang.li.1, andrew.template, mohamed.elhoseiny}@kaust.edu.sa",
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+        "image_caption": [
+            "Figure 1: We present FishNet, a comprehensive benchmark for large-scale aquatic species recognition, detection, and functional trait identification. Our benchmark dataset is based on an aquatic biological taxonomy, consisting of 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, 17,357 species, and 94,532 images. The dataset also includes bounding box annotations for fish detection. Additionally, the dataset encompasses 22 traits, grouped into three categories: habitat, ecological rule, and nutritional value. These traits facilitate the identification of the ecological roles of aquatic species and their interactions with other species."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Aquatic species are essential components of the world's ecosystem, and the preservation of aquatic biodiversity is crucial for maintaining proper ecosystem functioning. Unfortunately, increasing anthropogenic pressures such as overfishing, climate change, and coastal development pose significant threats to aquatic biodiversity. To address this challenge, it is necessary to design an automatic aquatic species monitoring systems that can help researchers and policymakers better understand changes in aquatic ecosystems and take appropriate actions to preserve biodiversity. However, the development of such systems is impeded by a lack of large-scale diverse aquatic species datasets. Existing aquatic species recognition datasets generally have a limited num",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ber of species, nor do they provide functional trait data, and so have only narrow potential for application. To address the need for generalized systems that can recognize, locate, and predict a wide array of species and their functional traits, we present FishNet, a large-scale diverse dataset containing 94,532 meticulously organized images from 17,357 aquatic species, organized according to aquatic biological taxonomy (order, family, genus, and species). We further build three benchmarks, i.e., fish classification, fish detection, and functional trait prediction, inspired by ecological research needs, to facilitate the development of aquatic species recognition systems, and promote further research in the field of aquatic ecology. Our FishNet dataset has the potential to encourage the development of more accurate and effective tools for the monitoring and protection of aquatic ecosystems, and hence",
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+    {
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+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "take effective action toward the conservation of our planet's aquatic biodiversity. Our dataset and code will be released at https://fishnet-2023.github.io/.",
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+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Aquatic biodiversity is of paramount importance in safeguarding the structure, stability, and overall health of aquatic ecosystems. Nonetheless, in recent decades, the escalating anthropogenic pressures from human activities, including fisheries, climate change, and coastal development [22, 24, 29], have made the conservation of aquatic biodiversity increasingly difficult and increasingly prominent in public attention. A key step in aquatic biodiversity protection is the ongoing monitoring, which calls for highly efficient species recognition and functional trait identification [36, 39, 42]. However, this process generally calls for a high level of expert knowledge due to complicated species taxonomy, which makes it time- and labor-consuming.",
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+        "text": "In recent years, deep learning methods have made significant breakthroughs in various computer vision tasks, presenting a promising solution for automatic and efficient species recognition. However, it is well-known that the accuracy of these AI-based models is heavily reliant on the scale and diversity of the training datasets. In the context of safeguarding aquatic biodiversity, there is an urgent need to develop large-scale and diverse datasets to facilitate AI-based aquatic species recognition systems. Several previous works have focused on building such datasets for fish recognition. For example, Fish4Knowledge [15] collected 27,370 fish images from 23 distinct species. WildFish++ [44] collected 103,034 fish images from 2,348 species along with text descriptions. Other works [3,6,16,17,35] have also accumulated fish images from specific regions, primarily focusing on species classification. However, these datasets are limited to a relatively small proportion of the  $>35,000$  described species of fish, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. Therefore, there is an urgent need to develop more extensive and diverse datasets that can enable more robust AI-based systems to accurately identify a broader range of aquatic species, supporting aquatic biodiversity conservation efforts.",
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+        "text": "In this work, we present a large-scale diverse dataset, called FishNet, to foster aquatic species recognition research. FishNet contains 94,532 images of aquatic species from 17,357 species, collected from different regions around the world. Please refer to Table 1 for a detailed comparison of our FishNet dataset with existing datasets. FishNet contains 94,532 images with different sizes, resolutions, and illumination, representing a diverse set of aquatic species. The dataset is meticulously organized based on the scientific classification of aquatic species, including 8 taxonomic",
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+        "type": "text",
+        "text": "classes $^{1}$ , 83 orders, 463 families, 3826 genera, and 17,357 species, and is accompanied by manual-labeled bounding box annotations.",
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+        "text": "Our FishNet dataset also provides traits associated with each species of the dataset, which can facilitate a better understanding of the ecological roles of aquatic species. To the best of our knowledge, we are the first to use deep learning techniques to predict functional traits directly from fish images. The proposed dataset can serve as a valuable resource for training and evaluating deep learning models for aquatic species classification and detection, and can further support research efforts toward the conservation and protection of aquatic ecosystems.",
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+        "text": "Additionally, we establish three benchmarks inspired by ecological research needs - fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition systems, and promote further research in the field of aquatic ecology. We conducted fish recognition and functional trait prediction using state-of-the-art deep learning models on these three benchmarks. The results show that accurate fish recognition and functional trait prediction on our FishNet dataset remains challenging: (1) The best-performing model achieved a classification accuracy of  $61.38\\%$  at the family levels, and the best-performing detection model achieved  $mAP_{50}$  of 56.5 at the order level. (2) For functional trait prediction, the best-performing model achieved a classification accuracy of  $54.80\\%$  and  $18.00\\%$  under supervised and zero-shot settings, respectively.",
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+        "text": "2. Related Work",
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+        "text": "Fish taxonomy has been a longstanding area of scientific inquiry, with early works dating back to Aristotle's taxonomic classification of 117 Mediterranean fish in the 4th century BC [18]. In the 18th century, Linnaeus developed a widely-used system for naming and classifying organisms, and subsequent taxonomists have further built upon his work using both morphological and genetic data [2,32]. Despite the advances made, classifying fish species remains a time-consuming process [30, 43]. In recent decades, computer vision techniques have played a vital role in automating the fish identification process, resulting in faster and more cost-effective identification of fish species [43]. However, computer vision models targeted at fish classification and detection face several challenges, including illumination change, low contrast, frequent occlusion, turbid water, and complex background [4, 43]. To tackle the challenges of fish recognition, a large-scale high-quality dataset is desired to automatically recognize aquatic species for biodiversity monitoring and protection. In this section, we provide a summary of previous aquatic species datasets and delineate",
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+        "text": "<sup>1</sup>We use \"taxonomic class\" to avoid confusion with the term \"class\" in the computer vision field that denotes the categorization of images or objects into groups based on their visual characteristics.",
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+        "text": "20497",
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+    {
+        "type": "table",
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+        "table_body": "<table><tr><td rowspan=\"2\">Datasets</td><td colspan=\"4\">Properties</td><td colspan=\"3\">Tasks</td></tr><tr><td>Images</td><td>Species</td><td>Taxonomy Level</td><td>Functional Traits</td><td>Classification</td><td>Trait Prediction</td><td>Detection</td></tr><tr><td>Fish4-Knowledge-A [15]</td><td>27,370</td><td>23</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>SEAMPD21 [3]</td><td>28,328</td><td>130</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish-gres [35]</td><td>3,248</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Mediterranean Fish Species [16]</td><td>≈40,000</td><td>20</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish Abundance [17]</td><td>4,909</td><td>50</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Image Dataset [12]</td><td>33,805</td><td>30</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>NCFM [6]</td><td>16,915</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>iNaturalistFish 1001[21]</td><td>54,006</td><td>369</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>WildFish++ [44]</td><td>103,034</td><td>2,348</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Ours</td><td>94,778</td><td>17,357</td><td>5-1</td><td>22</td><td>✓</td><td>✓</td><td>✓</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Comparison with existing datasets for fish recognition. FishNet provides annotations following biological taxonomy from class(5) to species(1); while previous datasets only provide species-level annotations. FishNet covers two orders of magnitude more species categories than existing datasets (17k vs 130). More importantly, FishNet provides additional functional traits that enable trait identification.",
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+    {
+        "type": "text",
+        "text": "the limitations that impede their applicability for detailed analysis of aquatic species.",
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+    },
+    {
+        "type": "text",
+        "text": "Lack of species diversity. Fish4Knowledge [15] is one of the pioneering works to build a fish recognition dataset. This dataset comprises a vast collection of approximately 700,000 underwater video clips captured in open sea waters in the Adriatic Sea in Croatia. A subset of 27,370 images was extracted from these video clips and manually annotated with bounding boxes and the corresponding species name. Another work [12] collects 33,805 images of 30 different fish species along with information about the meteorological and oceanographic conditions from the region of Barcelona, Spain. Several other works like [3,6,16,17,35] also collect fish images for classification from specific regions. These datasets are limited to a small number of species, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. In contrast, our FishNet dataset contains more than 17,000 aquatic species which is more suitable for real-world application.",
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+    {
+        "type": "text",
+        "text": "Lack of taxonomic diversity. Taxonomic classification of fishes is a crucial task in ecology and conservation biology [40]. Although several datasets have been previously developed for this task [3, 12], most of them have focused on a narrow taxonomic range (i.e. containing species from a small number of higher-order taxonomic groups), limiting their utility for exploring the wider diversity of fish species. For instance, the SEAMPD-21 [3] dataset comprises over 23,000 images, but only encompasses 130 species, while another dataset [12] containing more than 30,000 images includes merely 30 species. While these datasets serve as valuable resources for studying specific species, they do not provide a comprehensive representation of the diverse range of fish species present, which is crucial for understanding the fish ecosystem and recognizing the unique properties of different fish species.",
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+        "text": "Lack of functional traits. Functional traits are characteristics of an organism that relate to its ecological role [31, 39].",
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+        "text": "Functional traits in fish, such as trophic ecology, swimming modality, habitat use, and reproductive strategies, provide crucial insights into their ecological role and interactions with other species [28]. Understanding these traits can aid in sustainable fisheries management and maintaining ecosystem balance [38]. Monitoring functional diversity, rather than species diversity, is a common method of understanding ecosystem health, and guiding ecosystem management. Moreover, predicting functional traits can facilitate the understanding of probable functions performed by unknown or novel species, which otherwise may take considerable research effort and time to ascertain [9].",
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+    {
+        "type": "text",
+        "text": "Unlike most existing large-scale bio-related datasets (such as iNaturalist [21] and WildFish++ [44]) that primarily focuses on species classification, the Brackish dataset [33] provides underwater images with bounding box annotations of fish, crabs, and starfish. The BrackishMOT [34] dataset focuses on tracking schools of small fish and provides 98 video sequences captured in the wild. The Caltech fish counting dataset [23] consists of sonar videos, which makes it challenging for diverse species recognition. Similar to functional traits in our FishNet dataset, the NEWT dataset [41] offers functional attributes within broader domains such as behavior, age, and health. In contrast, FishNet places its emphasis on habitat-related functional traits, e.g., tropical area suitability. A notable distinction lies in the breadth of species categories covered: our FishNet dataset encompasses a significantly larger spectrum of categories compared to the NEWT dataset (17,000 vs. 183). We compare our FishNet dataset with other existing fish-related datasets and summarize the key differences in Table 1.",
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+        "type": "text",
+        "text": "3. FishNet",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The goal of our FishNet dataset is to provide a large-scale fish image dataset that benchmarks fish recognition, detection, and functional trait predictions. In this section,",
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+        "image_caption": [
+            "Figure 2. Order distribution. We plot the natural logarithm of the number of images per order. We show 42 more frequent orders at the top and 41 less frequent orders at the bottom."
+        ],
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+        "type": "text",
+        "text": "we outline our dataset collection approach, including fish taxonomy construction, image and attribute collection, and detection annotation. To ensure the accuracy and consistency of our annotations, we implemented a quality control process during annotation collection. Finally, we present statistics of FishNet.",
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+        "text": "3.1. Fish taxonomy construction",
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+        "text": "The construction of fish taxonomy represents a critical preliminary step for the development of a fish recognition system. In order to facilitate the scientific and user-friendly utilization of our FishNet dataset, we constructed and organized the dataset in accordance with standard fish taxonomy protocols. To ensure the quality of the data and meet the ecological objectives, aquatic behavioral ecologists actively participated in this project and provided input on the design of the data collection for both taxonomical labels and functional traits. Initially, a comprehensive list of fish, amounting to approximately 35,024 distinct species, was sourced from FishBase [13]. Within FishBase, each individual fish is mapped to its respective position within the taxonomic hierarchy, consisting of taxonomic class, order, family, genus, and species. See Fig. 1 for a detailed structure of fish taxonomy.",
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+        "text": "3.2. Image and Functional Traits Collection",
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+        "text": "For each of the fish species in our taxonomic list, we collected available images from two key online databases, FishBase [13] and iNaturalist [21]. 51,433 images were scraped from FishBase using an updated version of the spiderfish package [37]. After we obtained the fish images from Fishbase [13], to ensure the quality and relevance of the data, we manually reviewed all the images and removed any instances that were not suitable for our analysis. This involved removing images that were not photographs of fish, such as images of fish sketches, coin images, stamp images, larval fish, and images of fish bone structures. By performing this manual filtering process, we were able to ensure that our dataset consisted only of high-quality images that were suitable for our research purposes. This process also helped to reduce the potential for errors or inaccuracies in our analysis, by removing any images that could introduce additional bias or noise into the data. Some of the removed instances are shown in Figure 3.",
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+        "text": "During this phase, 7,634 images were dropped from the dataset and the remaining 43,799 were added to our FishNet dataset. A further 51,006 images were then downloaded from the iNaturalist database. Combined, the compiled im",
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+            "Figure 3. Examples removed from the dataset: The first row shows bone structures, the second row shows larval fish, the third row shows stamps and coins, and the fourth row shows fish sketches. All instances of these were identified and excluded."
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+    },
+    {
+        "type": "text",
+        "text": "age library encompasses 94,805 images from 17,518 species. To facilitate model training and evaluation, we dropped 273 images whose families have less than 5 images. For each species in our dataset, we gathered information on 22 traits (90,147 images have traits), which we believe to be important indicators of ecological roles and nutritional properties. These traits include the true functional traits of trophic level, feeding pathway, and habitat preferences based on temperature and salinity. In addition, we also included nutritional content \"traits\" for calcium, iron, omega-3 fatty acid, protein, selenium, vitamin A, and zinc content [20]. Table 2 provides detailed descriptions of the ten true functional traits.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Fish Detection Annotations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We employed the Amazon Mechanical Turk (AMT) [7] platform to collect bounding box annotations for all images in our dataset. Specifically, three independent annotators were tasked with providing locations for every instance in each image. To ensure accurate and reliable annotation of our image dataset, we have implemented a rigorous process for collecting annotations for object detection. Each image undergoes annotation by three different users on Amazon Mechanical Turk (AMT) [7]. We only accept annotations if all three users provide the same number of bounding boxes and if all the boxes have an Intersection over Union (IOU) value greater than 0.9. In cases where the annotations do not meet these criteria, we collect an additional annotation for the image and repeat the process of comparing the annotations reported by the different AMT users. We continue this process until we have at least three user annotations that agree with the number of bounding boxes and have an IOU greater than 0.9. For image categorization, we have already",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/98ad127d560094a4526ee459e0158e3aeb72ca9f9f4812af7aaf4317bb691945.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Trait</td><td>Value</td><td>Description</td></tr><tr><td>Trophic level</td><td>Real value</td><td>The position in the food chain or food web.</td></tr><tr><td>Feeding path</td><td>Benthic/ Pelagic</td><td>Species feeds primarily from which trophic pathway.</td></tr><tr><td>Tropical</td><td>True/ False</td><td>Whether the fish can live in tropical areas.</td></tr><tr><td>Temperate</td><td>True/ False</td><td>Whether the fish can live in temperate areas.</td></tr><tr><td>Subtropical</td><td>True/ False</td><td>Whether the fish can live in subtropical areas.</td></tr><tr><td>Boreal</td><td>True/ False</td><td>Whether the fish can live in boreal areas.</td></tr><tr><td>Polar</td><td>True/ False</td><td>Whether the fish can live in polar areas.</td></tr><tr><td>Freshwater</td><td>True/ False</td><td>Whether the fish can live in freshwater.</td></tr><tr><td>Saltwater</td><td>True/ False</td><td>Whether the fish can live in saltwater.</td></tr><tr><td>Brackish</td><td>True/ False</td><td>Whether the fish can live in brackish.</td></tr></table>",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Table 2. The explanation for 10 selected functional traits in the FishNet dataset. Please check the supplementary for the rest.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "assigned labels to each image and asked users to select images that belong to a specific family by providing example images of that family. Through this meticulous process, we were able to calculate 114,375 object instances.",
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+    },
+    {
+        "type": "text",
+        "text": "3.4. FishNet Statistics",
+        "text_level": 1,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "The FishNet dataset comprises a total of 94,532 images featuring 17,357 distinct species. The images were compiled",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "20500",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ed0b79d7adcd55a6f4f00de4bdb873739cf8db3be64f02feef3c3220b8cbfc5b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"4\">Family Classification (%)</td><td colspan=\"4\">Order Classification (%)</td></tr><tr><td>Common</td><td>Medium</td><td>Rare</td><td>All</td><td>Common</td><td>Medium</td><td>Rare</td><td>All</td></tr><tr><td>ResNet-34 [19]</td><td>77.16</td><td>69.10</td><td>36.65</td><td>40.82</td><td>83.42</td><td>77.87</td><td>47.36</td><td>52.07</td></tr><tr><td>ResNet-50 [19]</td><td>76.82</td><td>70.27</td><td>35.99</td><td>40.37</td><td>82.46</td><td>75.93</td><td>42.84</td><td>47.94</td></tr><tr><td>ResNet-101 [19]</td><td>75.73</td><td>69.00</td><td>31.61</td><td>36.38</td><td>81.35</td><td>75.01</td><td>42.32</td><td>47.36</td></tr><tr><td>ViT-S [10]</td><td>76.08</td><td>67.02</td><td>33.67</td><td>37.97</td><td>84.14</td><td>74.78</td><td>44.09</td><td>48.79</td></tr><tr><td>ViT-B [10]</td><td>82.93</td><td>74.50</td><td>38.26</td><td>42.91</td><td>88.52</td><td>81.64</td><td>52.44</td><td>56.93</td></tr><tr><td>ViT-L [10]</td><td>85.51</td><td>77.05</td><td>44.18</td><td>48.40</td><td>89.02</td><td>83.89</td><td>55.94</td><td>60.26</td></tr><tr><td>BeiT [1]</td><td>86.09</td><td>77.67</td><td>50.78</td><td>54.26</td><td>91.41</td><td>88.24</td><td>38.16</td><td>45.97</td></tr><tr><td>ConvNeXt* [27]</td><td>42.63</td><td>26.56</td><td>12.57</td><td>14.53</td><td>63.58</td><td>40.67</td><td>17.82</td><td>21.12</td></tr><tr><td>ConvNeXt [27]</td><td>90.32</td><td>85.13</td><td>57.03</td><td>60.61</td><td>94.07</td><td>90.49</td><td>64.84</td><td>68.81</td></tr><tr><td>ConvNeXt [27] + FL [25]</td><td>88.28</td><td>82.02</td><td>51.22</td><td>55.16</td><td>87.60</td><td>81.11</td><td>22.22</td><td>31.37</td></tr><tr><td>ConvNeXt [27] + CB [8]</td><td>90.53</td><td>84.80</td><td>57.94</td><td>61.38</td><td>93.15</td><td>90.56</td><td>71.41</td><td>74.38</td></tr><tr><td>ConvNeXt [27] + FL [25] + CB [8]</td><td>84.89</td><td>77.92</td><td>48.99</td><td>52.71</td><td>85.14</td><td>57.25</td><td>39.28</td><td>41.76</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Fish Family/Order classification accuracy. * denotes training from scratch, 'FL' denotes using focal loss during training, and 'CB' denotes using class-balanced training.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "from 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, and 17,357 species, with each species having at least one image. We present the distribution of Orders within our dataset in Fig. 2. The figure displays the logarithmic frequency of each Order category, and it demonstrates a long-tail distribution within the FishNet dataset with respect to Order categories. We observed similar distribution for other taxonomy levels. In our FishNet dataset, each image in the dataset is accompanied by 22 functional traits. Additionally, the dataset includes instance-level bounding box annotations. In total, the FishNet dataset encompasses 114,375 object instances.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Based on FishNet, we build three main challenges: 1) Fish classification. To identify family/order labels from input images; 2) Fish detection. Identifying the fish locations and family/order labels from input images; 3) Functional trait prediction. Predicting 10 functional traits from input images. For each challenge, we baseline several state-of-the-art models to show the capabilities of automatic fish identification and functional trait prediction using deep learning models. For all experiments, unless otherwise stated, we randomly select  $80\\%$  for training and the remaining  $20\\%$  for performance evaluation.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Fish Classification",
+        "text_level": 1,
+        "bbox": [
+            76,
+            801,
+            253,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Benchmark settings. We conducted Family/Order classification using both ResNet-based and ViT-based architectures, including ResNets (ResNet-34, ResNet-50, ResNet101) [19], ViT (ViT-S, ViT-B, ViT-L) [10], BeiT [1], and ConvNeXt [27]. We replaced the classification head using",
+        "bbox": [
+            75,
+            824,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "two fully connected (FC) layers, with a dropout of 0.5 for the first FC layer. For all comparing methods, the backbone networks were pretrained on ImageNet, and we finetuned the whole model using an Adam optimizer for 100 epochs. The initial learning rate was set to 3e-5, and 3e-4 for backbone networks and classification head, and we divided the learning rate by 2 every 20 epochs. In our experiments, we also explored recent techniques to address the long-tail classification problem. We explored focal loss [25] and class-balanced training [8] to improve the fish recognition performance in less frequent classes. Furthermore, we provided genus-level classification in the supplementary file.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Class split. To capture the effect of the long-tailed nature of the FishNet dataset, the FishNet dataset was partitioned into three distinct subsets, namely common, medium, and rare categories, based on their respective class frequencies. To categorize the classes according to their frequencies, we established a criterion for the Family/Order categories. Specifically, we selected those categories with a proportional representation of  $25\\%$  of the total number of images as the common classes, those categories with subsequent  $50\\%$  as medium classes, and the remaining  $25\\%$  as rare classes. After splitting, we identified a total of 6, 52, and 405 common, medium, and rare family classes, respectively. In our experiments, we reported class-averaged accuracy for each split and also the overall accuracy among all splits.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results. Table 3 shows the fish classification results at the Family and Order levels. From Table 3, it is evident that larger models consistently outperform smaller models in terms of classification accuracy. Specifically, the best-performing ConvNeXt model achieved an average classification accuracy of  $60.61\\%$  and  $68.81\\%$  at the Family and Order levels, respectively. We also observed that the performance",
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+    },
+    {
+        "type": "page_number",
+        "text": "20501",
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+    {
+        "type": "image",
+        "img_path": "images/e262053e822966479bdd851852d2238b04141b2554f3d8c48454128d9dbfcb91.jpg",
+        "image_caption": [
+            "Cls=Centrarchidae, Conf=1.00",
+            "Cls=Acanthuridae, Conf=0.99"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/29a5bcb2cb2fe712028e151eb776fbeafba0bffa924e3e36d7e5f2aec5818040.jpg",
+        "image_caption": [
+            "CIs=Centrarchidae, Conf=1.00",
+            "Cls=Acanthuridae, Conf=1.00"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            189,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a8ed7656f8b5ee908809d48e499fac1a8842ceb52ad780c2bfd5d06e30702cd4.jpg",
+        "image_caption": [
+            "CIs  $=$  Centrarchidae, Conf=1.00",
+            "Cls=Acanthuridae, Conf=1.00"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            290,
+            101,
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/621e53d9219ef476fad11f5def04b9a3066c442aaccad99d72cea7e055b9a89d.jpg",
+        "image_caption": [
+            "CIs  $=$  Centrarchidae, Conf.  $= 1.00$",
+            "Cls= Acanthuridae, Conf  $= {1.00}$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            390,
+            101,
+            478,
+            165
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/bf386dceeff17425c4ef78c0ae757f0d412ae5b6a6eef1dfdd4f227a7059b526.jpg",
+        "image_caption": [
+            "CIs  $=$  Centrarchidae, Conf=1.00",
+            "Cls=Acanthuridae, Conf=1.00"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            101,
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d9db322baeb9ad334bd21dc99f7e0515275623c0ac40a4cc0c8a5de6cf2d29b0.jpg",
+        "image_caption": [
+            "CIs  $=$  Centrarchidae, Conf  $= 1.00$",
+            "Cls= Acanthuridae, Conf  $= {1.00}$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            593,
+            101,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a2a7d9945ab737c2a3723db209acb98acca3be0b705533752ff0cdd9472ec75.jpg",
+        "image_caption": [
+            "CIs=cihilidae, Conf=0.66",
+            "CIs=Girellidae, Conf.  $\\equiv$  0.88"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            101,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ba3ef2c58cc16fd297e9cb1e355267ec9aafaf7c6a5b303512220ecb7814bdd1.jpg",
+        "image_caption": [
+            "Cls=Amiidae, Conf=0.32",
+            "Cls=Percidae, Conf=0.55"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/cb161c99930c6116141f4ef9e2cda5baead3ca9e2daaefa9fa3526687cfa176c.jpg",
+        "image_caption": [
+            "CIs  $=$  Dasyatidae, Conf=1.00"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0a7c5afd770da2b3dca875bbd3662dbe99934810819b56c0c3780fc2ff8a02ab.jpg",
+        "image_caption": [
+            "Figure 4. Selected visualization of FishNet Family classification. For each ground truth class, we showcase six examples in which the ConvNeXt model accurately predicts the correct Family label on the left. Additionally, we display two examples in which the ConvNeXt makes incorrect predictions on the right. For reference, we show the predicted Family class ('Cls') and confidence score ('Conf') above each image."
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/db2c5de10f29f0f768731303e950e3cc62cba29d77650363d4e217fb25c485a6.jpg",
+        "image_caption": [
+            "Cls  $=$  Dasyatidae, Conf=1.00"
+        ],
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+        "bbox": [
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+    {
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+        "img_path": "images/40b3e42a06063dd4cdf4968ef62c3e85857f909a88caaed7c0ea0ab5d156aef9.jpg",
+        "image_caption": [
+            "Cls  $=$  Dasyatidae, Conf  $\\equiv$  0.94"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/3c2bbe60d758a4d14c774c3ee9d45907928ac79e6713b7b6502c92dbef047d88.jpg",
+        "image_caption": [
+            "CIs  $=$  Dasyatidae, Conf  $\\equiv 1.00$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            392,
+            180,
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+            243
+        ],
+        "page_idx": 6
+    },
+    {
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+    {
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+        "img_path": "images/b6be3fe4c2d909a2d49c921289945b66bc6a14b530487cc885b1931d82e6e63e.jpg",
+        "image_caption": [
+            "CIs  $=$  Dasytidae, Conf  $= 1.00$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
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+    {
+        "type": "image",
+        "img_path": "images/10e418d1b874576034b445cad7076a8a6f7d18e6cc4ec9e2f011306066b1d9b2.jpg",
+        "image_caption": [
+            "CIs  $=$  Dasyatidae, Conf  $\\equiv$  0.98"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            180,
+            679,
+            243
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
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+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
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+        "img_path": "images/bb50863f3ab7de6f475fcb478ef3f4f8c303897ca86e1ee727a95f5103511676.jpg",
+        "image_caption": [
+            "Cis=Arhynchobatidae, Conf=0.34"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            180,
+            779,
+            243
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ec154c27a39dac5d52533285eed81850f8dab56728e48347f3be5e08028b3f41.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "type": "image",
+        "img_path": "images/3487ec08bfe094389da20b1e81293e02570d8048122f9613e780fa52d1c76e08.jpg",
+        "image_caption": [
+            "CIs=Uroliophidae, Conf=0.37"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/d73c1a75cdedf5cc90dff1ec99af82617ac13f853a747bc1ab4a63b3ecf3f3e9.jpg",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a14bb7ea187a5a5b32fe4ff71c3c94eb1fbabc3f3f5e22a1a8e8d308a78a9f46.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Level</td><td rowspan=\"2\">Method</td><td colspan=\"5\">Common Classes/Medium Classes/Rare Classes</td><td colspan=\"5\">Average Per Class</td></tr><tr><td>\\( {mAP}_{50} \\)</td><td>\\( {mAP}_{60} \\)</td><td>\\( {mAP}_{70} \\)</td><td>\\( {mAP}_{80} \\)</td><td>\\( {mAP}_{90} \\)</td><td>\\( {mAP}_{50} \\)</td><td>\\( {mAP}_{60} \\)</td><td>\\( {mAP}_{70} \\)</td><td>\\( {mAP}_{80} \\)</td><td>\\( {mAP}_{90} \\)</td></tr><tr><td rowspan=\"2\">Order</td><td>YOLOF [5]</td><td>77.3/65.2/39.2</td><td>72.7/62.1/38.0</td><td>61.6/53.4/34.7</td><td>38.8/34.9/25.4</td><td>11.7/9.6/11.8</td><td>45.0</td><td>43.4</td><td>39.3</td><td>27.8</td><td>11.7</td></tr><tr><td>TOOD [11]</td><td>84.8/76.8/50.3</td><td>80.1/73.2/48.5</td><td>69.4/64.4/43.6</td><td>46.1/42.6/32.7</td><td>15.4/14.3/13.6</td><td>56.5</td><td>54.3</td><td>48.5</td><td>35.4</td><td>14.1</td></tr><tr><td rowspan=\"2\">Family</td><td>YOLOF [5]</td><td>67.2/53.1/27.1</td><td>64.0/50.4/26.6</td><td>54.9/43.3/24.4</td><td>35.5/27.3/18.8</td><td>9.9/7.9/7.7</td><td>30.6</td><td>29.8</td><td>26.9</td><td>20.0</td><td>7.8</td></tr><tr><td>TOOD [11]</td><td>81.1/64.0/22.5</td><td>77.1/60.1/21.9</td><td>66.5/51.2/20.1</td><td>44.0/32.8/15.7</td><td>14.5/10.9/7.7</td><td>27.9</td><td>26.9</td><td>24.2</td><td>18</td><td>8.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Fish detection performance on common, medium, and rare classes at the order and family taxonomic levels.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "for rare classes was significantly worse than that for common classes, with an average classification accuracy of  $57.03\\%$  and  $64.84\\%$  at the Family and Order levels, respectively. This is because these rare classes have insufficient annotations, which poses great challenges for fish classification recognition.",
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+    },
+    {
+        "type": "text",
+        "text": "Fig. 4 visualizes selected classification results on the Family level using the ConvNeXt model. We showed both good cases in the first six columns and bad cases in the last two columns. Based on the results presented in Figure 4, it is evident that the ConvNeXt model is capable of accurately identifying the Family categories of input images, even when they exhibit significant variations in illumination and shape. However, there are some instances where the model failed to perform optimally. These failures are primarily attributed to factors such as low contrast, challenging view-angles, or visual similarities between different families. For example, arhynchobatidae, urolophidae, and dasyatidae belong to cartilaginous fish meaning skeletons are made of cartilage, have flattened bodies, and have a venomous spine on their tail, which can cause confusion for our classification models, as shown in the bottom right of the figure. More examples can",
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+    {
+        "type": "text",
+        "text": "be found in the supplementary file.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Effect of pretraining. We investigated the effect of using pretraining on the ImageNet dataset. By comparing the performance between ConvNeXt and ConvNeXt*, using ImageNet pretraining can significantly improve the fish classification performance on our FishNet dataset.",
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+    {
+        "type": "text",
+        "text": "Effect of balanced loss. From Table 4, using class-balanced loss can significantly improve classification performance, especially in rare classes; while using focal loss harms the performance. Specifically, for Order classification, using class-balanced loss improved the classification accuracy on rare classes from  $64.84\\%$  to  $71.41\\%$ . We emphasize that there exist several other techniques that can be employed to mitigate long-tail classification problems, which may potentially yield superior results. Nonetheless, our focus in this experiment was not to maximize performance but rather to raise awareness of the long-tail issue with our FishNet dataset, thereby encouraging further investigations.",
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+    {
+        "type": "text",
+        "text": "4.2. Fish Detection",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Benchmark settings. We conducted fish detection experiments using two well-known methods, YOLOF [5], and",
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+    {
+        "type": "page_number",
+        "text": "20502",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f9fd7e0b441019e91d882186373b319c9a03d8720536c81e3294051581a07e6c.jpg",
+        "image_caption": [
+            "Figure 5. Visualization of fish detection results using family-level classification labels. We show successful cases in the first 2 rows and failure cases in the last row."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "TOOD [11] on our FishNet dataset. For both methods, the backbone networks are pretrained on MS-COCO [26], and we finetuned the whole model using the stochastic gradient descent (SGD) optimizer with a learning rate of 2.5e-4, a momentum of 0.9, and a weight decay of 0.0001 for 100 epochs. For performance evaluation, we reported performance on two splits according to the Family/Order distribution, including common, medium, and rare classes, that contain  $25\\%$ ,  $50\\%$ , and  $25\\%$  of images.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Results. Table 4 shows the fish detection results at both the Family and Order levels. Our results demonstrated that for order-level classification, TOOD [11] outperformed YOLOF [5] in all the dataset splits. However, we observed that for family-level classification, YOLOF [5] exhibited better performance for Rare classes. Given the significantly higher number of Rare classes (405) as compared to Medium (52) and Common (6) classes, it is not surprising that the average Mean Average Precision (MAP) per class was lower for TOOD [11]. Therefore, we note that the evaluation of model performance can be influenced by the prevalence of different classes in the dataset, as shown in Table 4.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fig. 5 visualizes several examples of fish detection results obtained by the TOOD model [11]. The model has proven successful in detecting fish from various species, with different scales, orientations, and backgrounds. However, the TOOD model may struggle to predict family labels for less frequent classes or those with low contrast. We provide more examples in the supplementary file.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Functional trait Prediction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Benchmark settings. In this section, we explored using deep learning models to predict fish functional traits based on input images. We tried ten functional traits in our experi-",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/fa078f71101f7710d2b1c42195ac3e5a36ada49e587721b74b82ed05cac2fdc4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"2\">Seen (%)</td><td colspan=\"2\">Unseen (%)</td></tr><tr><td>F1/Acc.</td><td>Acc-all</td><td>F1/Acc.</td><td>Acc-all</td></tr><tr><td>ResNet-34 [19]</td><td>74.83 / 87.20</td><td>40.04</td><td>54.38 / 78.48</td><td>15.84</td></tr><tr><td>ResNet-50 [19]</td><td>71.80 / 84.52</td><td>30.85</td><td>53.52 / 76.71</td><td>13.92</td></tr><tr><td>ResNet-101 [19]</td><td>73.80 / 85.67</td><td>34.45</td><td>54.37 / 77.47</td><td>15.12</td></tr><tr><td>ViT-S [10]</td><td>75.25 / 86.86</td><td>38.62</td><td>54.62 / 78.99</td><td>16.94</td></tr><tr><td>ViT-B [10]</td><td>78.65 / 88.94</td><td>46.91</td><td>55.72 / 79.93</td><td>18.44</td></tr><tr><td>ViT-L [10]</td><td>81.72 / 90.45</td><td>54.00</td><td>55.94 / 80.23</td><td>18.80</td></tr><tr><td>BeiT [1]</td><td>78.15 / 88.93</td><td>49.97</td><td>54.60 / 78.82</td><td>17.26</td></tr><tr><td>ConvNeXt [27]</td><td>83.30 / 91.03</td><td>54.80</td><td>56.34 / 79.50</td><td>18.00</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 5. Habitat Classification performance in supervised and zero-shot settings.",
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+    {
+        "type": "text",
+        "text": "ments, namely trophic level, feeding path, and presence or absence in the following temperature and salinity zonations: tropical, temperate, subtropical, boreal, polar, freshwater, saltwater, and brackish. We used the same network architectures and training strategies as Section 4.1. For evaluating trophic level regression, we reported Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). For habitat classification, we used the average F1 score and overall accuracy to evaluate the performance. Additionally, we calculated the classification-all metric, which reflects the model's ability to accurately predict all functional traits simultaneously.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Trophic level Regression. In our experiments, we found that different models showed similar performance for trophic level prediction, with an MAE of 0.45 and an RMSE of 0.60, respectively. We found that trophic level prediction is a challenging task when using common L1 or L2 loss functions. More advanced techniques, such as ordinal regression [14], could potentially remedy this challenge. However, we leave this for further research.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Habitat Classification Results. Table 5 shows the classification results for nine fish functional traits. Overall, the larger models outperformed the smaller ones. Specifically, the ConvNeXt model achieved the best results with an average f1-score of  $81.72\\%$  and a classification accuracy of  $90.45\\%$ . We also reported the classification accuracy when our model correctly predicts all nine functional traits simultaneously, marked as \"Acc-all\". It was surprising that the best-performing ConvNeXt model obtained an accuracy-all of  $54.0\\%$  for correctly predicting all classes simultaneously. Fig. 6 shows selected examples of functional trait classification using the ConvNeXt model. From the figure, we can see that the ConvNeXt model can successfully predict most of the functional traits with large color and structure variations. In addition, Table 6 provides a detailed breakdown of the per-trait classification performance of the ConvNeXt model. The results show that the model achieved an f1-score of over  $90\\%$  for four out of nine functional traits. However, the",
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+        "type": "page_number",
+        "text": "20503",
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+        "img_path": "images/3b41ed33fd13789f6092aaba1767a41ab2675988d694608a566c5dc77cfb1e35.jpg",
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/4e896f1b85bd7ece7e0ea7fe047e07f25914556c410bbc17f80f18a579a1c328.jpg",
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/452d6e82f73a7d9d0f956458cf2ae7b75dcf78caf88c5e6ada765e3a879558e7.jpg",
+        "image_caption": [
+            "Figure 6. Selected visualization of functional trait classification. For each image, we show its species name on the top, and the \"ground truth/predicted\" functional trait labels on the right. The first two columns show success cases and the last two columns show failure cases. Correct predictions are shown in blue color, false predictions are shown in red color."
+        ],
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/4672e0f59f887dbb2023e8b70a536ec00615935975d67794db0bb80477adba26.jpg",
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/8548f8600b22bdd3517dee8460994ffbf969d903d3cdf5008c617cb7624b66bb.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/c1b66ebfd396813146a8f8efc94c5cd7a8beac484367156c56a966974c8bcf9c.jpg",
+        "image_caption": [],
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+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/69100aea9966f59e63f88d2aaff96f4749304ddc58577882ed71a39c94c84e80.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>FeedingPath</td><td>Tropical</td><td>Temperate</td><td>Subtropical</td><td>Boreal</td><td>Polar</td><td>Freshwater</td><td>Saltwater</td><td>Brackish</td><td>Avg.</td></tr><tr><td>Acc.</td><td>84.73</td><td>88.64</td><td>84.41</td><td>90.95</td><td>92.88</td><td>96.88</td><td>91.98</td><td>93.10</td><td>90.51</td><td>90.45</td></tr><tr><td>F1</td><td>68.07</td><td>92.97</td><td>88.03</td><td>94.49</td><td>76.99</td><td>59.91</td><td>91.02</td><td>95.59</td><td>68.40</td><td>81.72</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 6. Per-trait classification performance. For each trait, we report both the F1 score (%) and classification accuracy (%)",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "model obtains less impressive performance for feeding path and polar classification.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot Habitat Classification. We further evaluated the habitat classification performance in a zero-shot setting, where we evaluated habitat classification on unseen classes, which were not never seen during training. To achieve this, we trained the ConvNeXt model on 58 common and medium classes (according to their family classes) and evaluated the performance on 405 rare classes. From Table 5, although zero-shot habitat classification performance is worse than the supervised setting, the best-performed ViT-L model still shows a reasonable performance for zero-shot habitat classification, with a classification accuracy of  $80.23\\%$  and  $18.80\\%$  on accuracy and accuracy-all. This demonstration showcases the capacity of the deep learning model to predict the functional traits of previously unseen species, thereby establishing a valuable tool for the discovery of new species.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5. Conclusions and Future Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work presents FishNet, a large-scale diverse dataset consisting of 94,532 images from 17,357 species organized based on the scientific classification of aquatic species. The dataset is accompanied by 114,375 manually labeled bounding box annotations and 22 functional trait information. Fur",
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "thermore, we establish three benchmarks, namely fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition and promote further research in the field of aquatic ecology. The experimental results demonstrate that accurate fish recognition and functional trait prediction are still challenging due to several factors, such as large species diversity, diverse backgrounds, low contrast, etc.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We release our data and associated code to encourage further research in developing more accurate and effective tools for monitoring and protecting aquatic ecosystems. Our FishNet dataset will also encourage research into evaluating the impact of climate change on aquatic ecosystems and identifying potential solutions to help maintain the health and resilience of aquatic ecosystems and contribute to mitigating the impacts of climate change.",
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+    {
+        "type": "text",
+        "text": "6. Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Jun Chen and Habib Slim for providing their suggestions and Cameron Trotter for updating the spiderfish package to facilitate image collection from FishBase. This work is supported by KAUST, under Award No. BAS/1/1685-01-01. AJT is supported by KAUST Global Fellowship Program under Award No. ORA-2022-5001.",
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+        "text": "20504",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            174,
+            104
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
+        "bbox": [
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+        "list_items": [
+            "Willy Verstraete, and Nico Boon. Integrating abundance and functional traits reveals new global hotspots of fish diversity. Nature, 458, 2009. 2",
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+        ],
+        "bbox": [
+            501,
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diff --git a/2023/FishNet_ A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction/76ca1838-244d-4142-bae4-84af44e0f40e_model.json b/2023/FishNet_ A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction/76ca1838-244d-4142-bae4-84af44e0f40e_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..901988a9769c78f323170b5819fd182093ade5af
--- /dev/null
+++ b/2023/FishNet_ A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction/76ca1838-244d-4142-bae4-84af44e0f40e_model.json	
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+            "content": "FishNet: A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction"
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+            "content": "Faizan Farooq Khan*,†"
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+            "content": "\\(\\dagger\\) project lead"
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+            "content": "King Abdullah University of Science and Technology (KAUST)"
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+            "content": "{faizan.khan, xiang.li.1, andrew.template, mohamed.elhoseiny}@kaust.edu.sa"
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+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1: We present FishNet, a comprehensive benchmark for large-scale aquatic species recognition, detection, and functional trait identification. Our benchmark dataset is based on an aquatic biological taxonomy, consisting of 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, 17,357 species, and 94,532 images. The dataset also includes bounding box annotations for fish detection. Additionally, the dataset encompasses 22 traits, grouped into three categories: habitat, ecological rule, and nutritional value. These traits facilitate the identification of the ecological roles of aquatic species and their interactions with other species."
+        },
+        {
+            "type": "title",
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+            "content": "Abstract"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Aquatic species are essential components of the world's ecosystem, and the preservation of aquatic biodiversity is crucial for maintaining proper ecosystem functioning. Unfortunately, increasing anthropogenic pressures such as overfishing, climate change, and coastal development pose significant threats to aquatic biodiversity. To address this challenge, it is necessary to design an automatic aquatic species monitoring systems that can help researchers and policymakers better understand changes in aquatic ecosystems and take appropriate actions to preserve biodiversity. However, the development of such systems is impeded by a lack of large-scale diverse aquatic species datasets. Existing aquatic species recognition datasets generally have a limited num"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "ber of species, nor do they provide functional trait data, and so have only narrow potential for application. To address the need for generalized systems that can recognize, locate, and predict a wide array of species and their functional traits, we present FishNet, a large-scale diverse dataset containing 94,532 meticulously organized images from 17,357 aquatic species, organized according to aquatic biological taxonomy (order, family, genus, and species). We further build three benchmarks, i.e., fish classification, fish detection, and functional trait prediction, inspired by ecological research needs, to facilitate the development of aquatic species recognition systems, and promote further research in the field of aquatic ecology. Our FishNet dataset has the potential to encourage the development of more accurate and effective tools for the monitoring and protection of aquatic ecosystems, and hence"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "take effective action toward the conservation of our planet's aquatic biodiversity. Our dataset and code will be released at https://fishnet-2023.github.io/."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Aquatic biodiversity is of paramount importance in safeguarding the structure, stability, and overall health of aquatic ecosystems. Nonetheless, in recent decades, the escalating anthropogenic pressures from human activities, including fisheries, climate change, and coastal development [22, 24, 29], have made the conservation of aquatic biodiversity increasingly difficult and increasingly prominent in public attention. A key step in aquatic biodiversity protection is the ongoing monitoring, which calls for highly efficient species recognition and functional trait identification [36, 39, 42]. However, this process generally calls for a high level of expert knowledge due to complicated species taxonomy, which makes it time- and labor-consuming."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.388,
+                0.471,
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+            "angle": 0,
+            "content": "In recent years, deep learning methods have made significant breakthroughs in various computer vision tasks, presenting a promising solution for automatic and efficient species recognition. However, it is well-known that the accuracy of these AI-based models is heavily reliant on the scale and diversity of the training datasets. In the context of safeguarding aquatic biodiversity, there is an urgent need to develop large-scale and diverse datasets to facilitate AI-based aquatic species recognition systems. Several previous works have focused on building such datasets for fish recognition. For example, Fish4Knowledge [15] collected 27,370 fish images from 23 distinct species. WildFish++ [44] collected 103,034 fish images from 2,348 species along with text descriptions. Other works [3,6,16,17,35] have also accumulated fish images from specific regions, primarily focusing on species classification. However, these datasets are limited to a relatively small proportion of the \\(>35,000\\) described species of fish, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. Therefore, there is an urgent need to develop more extensive and diverse datasets that can enable more robust AI-based systems to accurately identify a broader range of aquatic species, supporting aquatic biodiversity conservation efforts."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.472,
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+            "angle": 0,
+            "content": "In this work, we present a large-scale diverse dataset, called FishNet, to foster aquatic species recognition research. FishNet contains 94,532 images of aquatic species from 17,357 species, collected from different regions around the world. Please refer to Table 1 for a detailed comparison of our FishNet dataset with existing datasets. FishNet contains 94,532 images with different sizes, resolutions, and illumination, representing a diverse set of aquatic species. The dataset is meticulously organized based on the scientific classification of aquatic species, including 8 taxonomic"
+        },
+        {
+            "type": "text",
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+            "content": "classes\\(^{1}\\), 83 orders, 463 families, 3826 genera, and 17,357 species, and is accompanied by manual-labeled bounding box annotations."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Our FishNet dataset also provides traits associated with each species of the dataset, which can facilitate a better understanding of the ecological roles of aquatic species. To the best of our knowledge, we are the first to use deep learning techniques to predict functional traits directly from fish images. The proposed dataset can serve as a valuable resource for training and evaluating deep learning models for aquatic species classification and detection, and can further support research efforts toward the conservation and protection of aquatic ecosystems."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Additionally, we establish three benchmarks inspired by ecological research needs - fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition systems, and promote further research in the field of aquatic ecology. We conducted fish recognition and functional trait prediction using state-of-the-art deep learning models on these three benchmarks. The results show that accurate fish recognition and functional trait prediction on our FishNet dataset remains challenging: (1) The best-performing model achieved a classification accuracy of \\(61.38\\%\\) at the family levels, and the best-performing detection model achieved \\(mAP_{50}\\) of 56.5 at the order level. (2) For functional trait prediction, the best-performing model achieved a classification accuracy of \\(54.80\\%\\) and \\(18.00\\%\\) under supervised and zero-shot settings, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Fish taxonomy has been a longstanding area of scientific inquiry, with early works dating back to Aristotle's taxonomic classification of 117 Mediterranean fish in the 4th century BC [18]. In the 18th century, Linnaeus developed a widely-used system for naming and classifying organisms, and subsequent taxonomists have further built upon his work using both morphological and genetic data [2,32]. Despite the advances made, classifying fish species remains a time-consuming process [30, 43]. In recent decades, computer vision techniques have played a vital role in automating the fish identification process, resulting in faster and more cost-effective identification of fish species [43]. However, computer vision models targeted at fish classification and detection face several challenges, including illumination change, low contrast, frequent occlusion, turbid water, and complex background [4, 43]. To tackle the challenges of fish recognition, a large-scale high-quality dataset is desired to automatically recognize aquatic species for biodiversity monitoring and protection. In this section, we provide a summary of previous aquatic species datasets and delineate"
+        },
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+            "content": "<sup>1</sup>We use \"taxonomic class\" to avoid confusion with the term \"class\" in the computer vision field that denotes the categorization of images or objects into groups based on their visual characteristics."
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+            "content": "<table><tr><td rowspan=\"2\">Datasets</td><td colspan=\"4\">Properties</td><td colspan=\"3\">Tasks</td></tr><tr><td>Images</td><td>Species</td><td>Taxonomy Level</td><td>Functional Traits</td><td>Classification</td><td>Trait Prediction</td><td>Detection</td></tr><tr><td>Fish4-Knowledge-A [15]</td><td>27,370</td><td>23</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>SEAMPD21 [3]</td><td>28,328</td><td>130</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish-gres [35]</td><td>3,248</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Mediterranean Fish Species [16]</td><td>≈40,000</td><td>20</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish Abundance [17]</td><td>4,909</td><td>50</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Image Dataset [12]</td><td>33,805</td><td>30</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>NCFM [6]</td><td>16,915</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>iNaturalistFish 1001[21]</td><td>54,006</td><td>369</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>WildFish++ [44]</td><td>103,034</td><td>2,348</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Ours</td><td>94,778</td><td>17,357</td><td>5-1</td><td>22</td><td>✓</td><td>✓</td><td>✓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.272,
+                0.895,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison with existing datasets for fish recognition. FishNet provides annotations following biological taxonomy from class(5) to species(1); while previous datasets only provide species-level annotations. FishNet covers two orders of magnitude more species categories than existing datasets (17k vs 130). More importantly, FishNet provides additional functional traits that enable trait identification."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.34,
+                0.47,
+                0.371
+            ],
+            "angle": 0,
+            "content": "the limitations that impede their applicability for detailed analysis of aquatic species."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.371,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "Lack of species diversity. Fish4Knowledge [15] is one of the pioneering works to build a fish recognition dataset. This dataset comprises a vast collection of approximately 700,000 underwater video clips captured in open sea waters in the Adriatic Sea in Croatia. A subset of 27,370 images was extracted from these video clips and manually annotated with bounding boxes and the corresponding species name. Another work [12] collects 33,805 images of 30 different fish species along with information about the meteorological and oceanographic conditions from the region of Barcelona, Spain. Several other works like [3,6,16,17,35] also collect fish images for classification from specific regions. These datasets are limited to a small number of species, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. In contrast, our FishNet dataset contains more than 17,000 aquatic species which is more suitable for real-world application."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.629,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "Lack of taxonomic diversity. Taxonomic classification of fishes is a crucial task in ecology and conservation biology [40]. Although several datasets have been previously developed for this task [3, 12], most of them have focused on a narrow taxonomic range (i.e. containing species from a small number of higher-order taxonomic groups), limiting their utility for exploring the wider diversity of fish species. For instance, the SEAMPD-21 [3] dataset comprises over 23,000 images, but only encompasses 130 species, while another dataset [12] containing more than 30,000 images includes merely 30 species. While these datasets serve as valuable resources for studying specific species, they do not provide a comprehensive representation of the diverse range of fish species present, which is crucial for understanding the fish ecosystem and recognizing the unique properties of different fish species."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "Lack of functional traits. Functional traits are characteristics of an organism that relate to its ecological role [31, 39]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "content": "Functional traits in fish, such as trophic ecology, swimming modality, habitat use, and reproductive strategies, provide crucial insights into their ecological role and interactions with other species [28]. Understanding these traits can aid in sustainable fisheries management and maintaining ecosystem balance [38]. Monitoring functional diversity, rather than species diversity, is a common method of understanding ecosystem health, and guiding ecosystem management. Moreover, predicting functional traits can facilitate the understanding of probable functions performed by unknown or novel species, which otherwise may take considerable research effort and time to ascertain [9]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.524,
+                0.897,
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+            ],
+            "angle": 0,
+            "content": "Unlike most existing large-scale bio-related datasets (such as iNaturalist [21] and WildFish++ [44]) that primarily focuses on species classification, the Brackish dataset [33] provides underwater images with bounding box annotations of fish, crabs, and starfish. The BrackishMOT [34] dataset focuses on tracking schools of small fish and provides 98 video sequences captured in the wild. The Caltech fish counting dataset [23] consists of sonar videos, which makes it challenging for diverse species recognition. Similar to functional traits in our FishNet dataset, the NEWT dataset [41] offers functional attributes within broader domains such as behavior, age, and health. In contrast, FishNet places its emphasis on habitat-related functional traits, e.g., tropical area suitability. A notable distinction lies in the breadth of species categories covered: our FishNet dataset encompasses a significantly larger spectrum of categories compared to the NEWT dataset (17,000 vs. 183). We compare our FishNet dataset with other existing fish-related datasets and summarize the key differences in Table 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.593,
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+            ],
+            "angle": 0,
+            "content": "3. FishNet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The goal of our FishNet dataset is to provide a large-scale fish image dataset that benchmarks fish recognition, detection, and functional trait predictions. In this section,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "20498"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.094,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.874,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.482,
+                0.893,
+                0.511
+            ],
+            "angle": 0,
+            "content": "Figure 2. Order distribution. We plot the natural logarithm of the number of images per order. We show 42 more frequent orders at the top and 41 less frequent orders at the bottom."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.537,
+                0.471,
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+            ],
+            "angle": 0,
+            "content": "we outline our dataset collection approach, including fish taxonomy construction, image and attribute collection, and detection annotation. To ensure the accuracy and consistency of our annotations, we implemented a quality control process during annotation collection. Finally, we present statistics of FishNet."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.636,
+                0.328,
+                0.652
+            ],
+            "angle": 0,
+            "content": "3.1. Fish taxonomy construction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.472,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The construction of fish taxonomy represents a critical preliminary step for the development of a fish recognition system. In order to facilitate the scientific and user-friendly utilization of our FishNet dataset, we constructed and organized the dataset in accordance with standard fish taxonomy protocols. To ensure the quality of the data and meet the ecological objectives, aquatic behavioral ecologists actively participated in this project and provided input on the design of the data collection for both taxonomical labels and functional traits. Initially, a comprehensive list of fish, amounting to approximately 35,024 distinct species, was sourced from FishBase [13]. Within FishBase, each individual fish is mapped to its respective position within the taxonomic hierarchy, consisting of taxonomic class, order, family, genus, and species. See Fig. 1 for a detailed structure of fish taxonomy."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.537,
+                0.838,
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+            ],
+            "angle": 0,
+            "content": "3.2. Image and Functional Traits Collection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.565,
+                0.895,
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+            ],
+            "angle": 0,
+            "content": "For each of the fish species in our taxonomic list, we collected available images from two key online databases, FishBase [13] and iNaturalist [21]. 51,433 images were scraped from FishBase using an updated version of the spiderfish package [37]. After we obtained the fish images from Fishbase [13], to ensure the quality and relevance of the data, we manually reviewed all the images and removed any instances that were not suitable for our analysis. This involved removing images that were not photographs of fish, such as images of fish sketches, coin images, stamp images, larval fish, and images of fish bone structures. By performing this manual filtering process, we were able to ensure that our dataset consisted only of high-quality images that were suitable for our research purposes. This process also helped to reduce the potential for errors or inaccuracies in our analysis, by removing any images that could introduce additional bias or noise into the data. Some of the removed instances are shown in Figure 3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            ],
+            "angle": 0,
+            "content": "During this phase, 7,634 images were dropped from the dataset and the remaining 43,799 were added to our FishNet dataset. A further 51,006 images were then downloaded from the iNaturalist database. Combined, the compiled im"
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+        {
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+            "bbox": [
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+        {
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+        {
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+        },
+        {
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+            ],
+            "angle": 0,
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+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.851,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.673,
+                0.278,
+                0.856,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.353,
+                0.892,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Figure 3. Examples removed from the dataset: The first row shows bone structures, the second row shows larval fish, the third row shows stamps and coins, and the fourth row shows fish sketches. All instances of these were identified and excluded."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.408,
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+            ],
+            "angle": 0,
+            "content": "age library encompasses 94,805 images from 17,518 species. To facilitate model training and evaluation, we dropped 273 images whose families have less than 5 images. For each species in our dataset, we gathered information on 22 traits (90,147 images have traits), which we believe to be important indicators of ecological roles and nutritional properties. These traits include the true functional traits of trophic level, feeding pathway, and habitat preferences based on temperature and salinity. In addition, we also included nutritional content \"traits\" for calcium, iron, omega-3 fatty acid, protein, selenium, vitamin A, and zinc content [20]. Table 2 provides detailed descriptions of the ten true functional traits."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.604,
+                0.323,
+                0.619
+            ],
+            "angle": 0,
+            "content": "3.3. Fish Detection Annotations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.629,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We employed the Amazon Mechanical Turk (AMT) [7] platform to collect bounding box annotations for all images in our dataset. Specifically, three independent annotators were tasked with providing locations for every instance in each image. To ensure accurate and reliable annotation of our image dataset, we have implemented a rigorous process for collecting annotations for object detection. Each image undergoes annotation by three different users on Amazon Mechanical Turk (AMT) [7]. We only accept annotations if all three users provide the same number of bounding boxes and if all the boxes have an Intersection over Union (IOU) value greater than 0.9. In cases where the annotations do not meet these criteria, we collect an additional annotation for the image and repeat the process of comparing the annotations reported by the different AMT users. We continue this process until we have at least three user annotations that agree with the number of bounding boxes and have an IOU greater than 0.9. For image categorization, we have already"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.507,
+                0.405,
+                0.925,
+                0.713
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Trait</td><td>Value</td><td>Description</td></tr><tr><td>Trophic level</td><td>Real value</td><td>The position in the food chain or food web.</td></tr><tr><td>Feeding path</td><td>Benthic/ Pelagic</td><td>Species feeds primarily from which trophic pathway.</td></tr><tr><td>Tropical</td><td>True/ False</td><td>Whether the fish can live in tropical areas.</td></tr><tr><td>Temperate</td><td>True/ False</td><td>Whether the fish can live in temperate areas.</td></tr><tr><td>Subtropical</td><td>True/ False</td><td>Whether the fish can live in subtropical areas.</td></tr><tr><td>Boreal</td><td>True/ False</td><td>Whether the fish can live in boreal areas.</td></tr><tr><td>Polar</td><td>True/ False</td><td>Whether the fish can live in polar areas.</td></tr><tr><td>Freshwater</td><td>True/ False</td><td>Whether the fish can live in freshwater.</td></tr><tr><td>Saltwater</td><td>True/ False</td><td>Whether the fish can live in saltwater.</td></tr><tr><td>Brackish</td><td>True/ False</td><td>Whether the fish can live in brackish.</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.722,
+                0.892,
+                0.752
+            ],
+            "angle": 0,
+            "content": "Table 2. The explanation for 10 selected functional traits in the FishNet dataset. Please check the supplementary for the rest."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.778,
+                0.895,
+                0.839
+            ],
+            "angle": 0,
+            "content": "assigned labels to each image and asked users to select images that belong to a specific family by providing example images of that family. Through this meticulous process, we were able to calculate 114,375 object instances."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
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+                0.671,
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+            ],
+            "angle": 0,
+            "content": "3.4. FishNet Statistics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The FishNet dataset comprises a total of 94,532 images featuring 17,357 distinct species. The images were compiled"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "20500"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"4\">Family Classification (%)</td><td colspan=\"4\">Order Classification (%)</td></tr><tr><td>Common</td><td>Medium</td><td>Rare</td><td>All</td><td>Common</td><td>Medium</td><td>Rare</td><td>All</td></tr><tr><td>ResNet-34 [19]</td><td>77.16</td><td>69.10</td><td>36.65</td><td>40.82</td><td>83.42</td><td>77.87</td><td>47.36</td><td>52.07</td></tr><tr><td>ResNet-50 [19]</td><td>76.82</td><td>70.27</td><td>35.99</td><td>40.37</td><td>82.46</td><td>75.93</td><td>42.84</td><td>47.94</td></tr><tr><td>ResNet-101 [19]</td><td>75.73</td><td>69.00</td><td>31.61</td><td>36.38</td><td>81.35</td><td>75.01</td><td>42.32</td><td>47.36</td></tr><tr><td>ViT-S [10]</td><td>76.08</td><td>67.02</td><td>33.67</td><td>37.97</td><td>84.14</td><td>74.78</td><td>44.09</td><td>48.79</td></tr><tr><td>ViT-B [10]</td><td>82.93</td><td>74.50</td><td>38.26</td><td>42.91</td><td>88.52</td><td>81.64</td><td>52.44</td><td>56.93</td></tr><tr><td>ViT-L [10]</td><td>85.51</td><td>77.05</td><td>44.18</td><td>48.40</td><td>89.02</td><td>83.89</td><td>55.94</td><td>60.26</td></tr><tr><td>BeiT [1]</td><td>86.09</td><td>77.67</td><td>50.78</td><td>54.26</td><td>91.41</td><td>88.24</td><td>38.16</td><td>45.97</td></tr><tr><td>ConvNeXt* [27]</td><td>42.63</td><td>26.56</td><td>12.57</td><td>14.53</td><td>63.58</td><td>40.67</td><td>17.82</td><td>21.12</td></tr><tr><td>ConvNeXt [27]</td><td>90.32</td><td>85.13</td><td>57.03</td><td>60.61</td><td>94.07</td><td>90.49</td><td>64.84</td><td>68.81</td></tr><tr><td>ConvNeXt [27] + FL [25]</td><td>88.28</td><td>82.02</td><td>51.22</td><td>55.16</td><td>87.60</td><td>81.11</td><td>22.22</td><td>31.37</td></tr><tr><td>ConvNeXt [27] + CB [8]</td><td>90.53</td><td>84.80</td><td>57.94</td><td>61.38</td><td>93.15</td><td>90.56</td><td>71.41</td><td>74.38</td></tr><tr><td>ConvNeXt [27] + FL [25] + CB [8]</td><td>84.89</td><td>77.92</td><td>48.99</td><td>52.71</td><td>85.14</td><td>57.25</td><td>39.28</td><td>41.76</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.348,
+                0.894,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Table 3. Fish Family/Order classification accuracy. * denotes training from scratch, 'FL' denotes using focal loss during training, and 'CB' denotes using class-balanced training."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "from 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, and 17,357 species, with each species having at least one image. We present the distribution of Orders within our dataset in Fig. 2. The figure displays the logarithmic frequency of each Order category, and it demonstrates a long-tail distribution within the FishNet dataset with respect to Order categories. We observed similar distribution for other taxonomy levels. In our FishNet dataset, each image in the dataset is accompanied by 22 functional traits. Additionally, the dataset includes instance-level bounding box annotations. In total, the FishNet dataset encompasses 114,375 object instances."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.625,
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+                0.792
+            ],
+            "angle": 0,
+            "content": "Based on FishNet, we build three main challenges: 1) Fish classification. To identify family/order labels from input images; 2) Fish detection. Identifying the fish locations and family/order labels from input images; 3) Functional trait prediction. Predicting 10 functional traits from input images. For each challenge, we baseline several state-of-the-art models to show the capabilities of automatic fish identification and functional trait prediction using deep learning models. For all experiments, unless otherwise stated, we randomly select \\(80\\%\\) for training and the remaining \\(20\\%\\) for performance evaluation."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.802,
+                0.254,
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+            ],
+            "angle": 0,
+            "content": "4.1. Fish Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Benchmark settings. We conducted Family/Order classification using both ResNet-based and ViT-based architectures, including ResNets (ResNet-34, ResNet-50, ResNet101) [19], ViT (ViT-S, ViT-B, ViT-L) [10], BeiT [1], and ConvNeXt [27]. We replaced the classification head using"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.403,
+                0.895,
+                0.584
+            ],
+            "angle": 0,
+            "content": "two fully connected (FC) layers, with a dropout of 0.5 for the first FC layer. For all comparing methods, the backbone networks were pretrained on ImageNet, and we finetuned the whole model using an Adam optimizer for 100 epochs. The initial learning rate was set to 3e-5, and 3e-4 for backbone networks and classification head, and we divided the learning rate by 2 every 20 epochs. In our experiments, we also explored recent techniques to address the long-tail classification problem. We explored focal loss [25] and class-balanced training [8] to improve the fish recognition performance in less frequent classes. Furthermore, we provided genus-level classification in the supplementary file."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.585,
+                0.896,
+                0.795
+            ],
+            "angle": 0,
+            "content": "Class split. To capture the effect of the long-tailed nature of the FishNet dataset, the FishNet dataset was partitioned into three distinct subsets, namely common, medium, and rare categories, based on their respective class frequencies. To categorize the classes according to their frequencies, we established a criterion for the Family/Order categories. Specifically, we selected those categories with a proportional representation of \\(25\\%\\) of the total number of images as the common classes, those categories with subsequent \\(50\\%\\) as medium classes, and the remaining \\(25\\%\\) as rare classes. After splitting, we identified a total of 6, 52, and 405 common, medium, and rare family classes, respectively. In our experiments, we reported class-averaged accuracy for each split and also the overall accuracy among all splits."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.897,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Results. Table 3 shows the fish classification results at the Family and Order levels. From Table 3, it is evident that larger models consistently outperform smaller models in terms of classification accuracy. Specifically, the best-performing ConvNeXt model achieved an average classification accuracy of \\(60.61\\%\\) and \\(68.81\\%\\) at the Family and Order levels, respectively. We also observed that the performance"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "20501"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Cls=Centrarchidae, Conf=1.00"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
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+            "bbox": [
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+            "angle": 0,
+            "content": "Cls=Acanthuridae, Conf=0.99"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.089,
+                0.272,
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+            "angle": 0,
+            "content": "CIs=Centrarchidae, Conf=1.00"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Cls=Acanthuridae, Conf=1.00"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.089,
+                0.373,
+                0.102
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+            "angle": 0,
+            "content": "CIs \\(=\\) Centrarchidae, Conf=1.00"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
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+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "Cls=Acanthuridae, Conf=1.00"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.474,
+                0.102
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Centrarchidae, Conf. \\(= 1.00\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.392,
+                0.102,
+                0.479,
+                0.166
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.395,
+                0.167,
+                0.473,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Cls= Acanthuridae, Conf \\( = {1.00} \\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.495,
+                0.089,
+                0.574,
+                0.102
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Centrarchidae, Conf=1.00"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.494,
+                0.102,
+                0.579,
+                0.167
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.167,
+                0.573,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Cls=Acanthuridae, Conf=1.00"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.596,
+                0.089,
+                0.676,
+                0.102
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Centrarchidae, Conf \\(= 1.00\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.594,
+                0.102,
+                0.68,
+                0.167
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.597,
+                0.167,
+                0.674,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Cls= Acanthuridae, Conf \\( = {1.00} \\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.707,
+                0.089,
+                0.765,
+                0.102
+            ],
+            "angle": 0,
+            "content": "CIs=cihilidae, Conf=0.66"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.695,
+                0.102,
+                0.781,
+                0.167
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.706,
+                0.167,
+                0.766,
+                0.179
+            ],
+            "angle": 0,
+            "content": "CIs=Girellidae, Conf. \\(\\equiv\\) 0.88"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.81,
+                0.089,
+                0.863,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Cls=Amiidae, Conf=0.32"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.795,
+                0.102,
+                0.881,
+                0.167
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.807,
+                0.167,
+                0.871,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Cls=Percidae, Conf=0.55"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.091,
+                0.181,
+                0.177,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.098,
+                0.244,
+                0.166,
+                0.256
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Dasyatidae, Conf=1.00"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.256,
+                0.177,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.181,
+                0.278,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.244,
+                0.266,
+                0.256
+            ],
+            "angle": 0,
+            "content": "Cls \\(=\\) Dasyatidae, Conf=1.00"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.244,
+                0.367,
+                0.256
+            ],
+            "angle": 0,
+            "content": "Cls \\(=\\) Dasyatidae, Conf \\(\\equiv\\) 0.94"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+                0.479,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.244,
+                0.468,
+                0.256
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Dasyatidae, Conf \\(\\equiv 1.00\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.256,
+                0.479,
+                0.322
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.181,
+                0.579,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.244,
+                0.574,
+                0.256
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Dasytidae, Conf \\(= 1.00\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.256,
+                0.579,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.593,
+                0.181,
+                0.68,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.602,
+                0.244,
+                0.668,
+                0.256
+            ],
+            "angle": 0,
+            "content": "CIs \\(=\\) Dasyatidae, Conf \\(\\equiv\\) 0.98"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.594,
+                0.256,
+                0.68,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.695,
+                0.181,
+                0.781,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.691,
+                0.244,
+                0.781,
+                0.256
+            ],
+            "angle": 0,
+            "content": "Cis=Arhynchobatidae, Conf=0.34"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.695,
+                0.256,
+                0.779,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.795,
+                0.181,
+                0.881,
+                0.244
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.8,
+                0.244,
+                0.872,
+                0.256
+            ],
+            "angle": 0,
+            "content": "CIs=Uroliophidae, Conf=0.37"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.795,
+                0.256,
+                0.881,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.336,
+                0.895,
+                0.392
+            ],
+            "angle": 0,
+            "content": "Figure 4. Selected visualization of FishNet Family classification. For each ground truth class, we showcase six examples in which the ConvNeXt model accurately predicts the correct Family label on the left. Additionally, we display two examples in which the ConvNeXt makes incorrect predictions on the right. For reference, we show the predicted Family class ('Cls') and confidence score ('Conf') above each image."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.407,
+                0.907,
+                0.492
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Level</td><td rowspan=\"2\">Method</td><td colspan=\"5\">Common Classes/Medium Classes/Rare Classes</td><td colspan=\"5\">Average Per Class</td></tr><tr><td>\\( {mAP}_{50} \\)</td><td>\\( {mAP}_{60} \\)</td><td>\\( {mAP}_{70} \\)</td><td>\\( {mAP}_{80} \\)</td><td>\\( {mAP}_{90} \\)</td><td>\\( {mAP}_{50} \\)</td><td>\\( {mAP}_{60} \\)</td><td>\\( {mAP}_{70} \\)</td><td>\\( {mAP}_{80} \\)</td><td>\\( {mAP}_{90} \\)</td></tr><tr><td rowspan=\"2\">Order</td><td>YOLOF [5]</td><td>77.3/65.2/39.2</td><td>72.7/62.1/38.0</td><td>61.6/53.4/34.7</td><td>38.8/34.9/25.4</td><td>11.7/9.6/11.8</td><td>45.0</td><td>43.4</td><td>39.3</td><td>27.8</td><td>11.7</td></tr><tr><td>TOOD [11]</td><td>84.8/76.8/50.3</td><td>80.1/73.2/48.5</td><td>69.4/64.4/43.6</td><td>46.1/42.6/32.7</td><td>15.4/14.3/13.6</td><td>56.5</td><td>54.3</td><td>48.5</td><td>35.4</td><td>14.1</td></tr><tr><td rowspan=\"2\">Family</td><td>YOLOF [5]</td><td>67.2/53.1/27.1</td><td>64.0/50.4/26.6</td><td>54.9/43.3/24.4</td><td>35.5/27.3/18.8</td><td>9.9/7.9/7.7</td><td>30.6</td><td>29.8</td><td>26.9</td><td>20.0</td><td>7.8</td></tr><tr><td>TOOD [11]</td><td>81.1/64.0/22.5</td><td>77.1/60.1/21.9</td><td>66.5/51.2/20.1</td><td>44.0/32.8/15.7</td><td>14.5/10.9/7.7</td><td>27.9</td><td>26.9</td><td>24.2</td><td>18</td><td>8.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.14,
+                0.513,
+                0.828,
+                0.528
+            ],
+            "angle": 0,
+            "content": "Table 4. Fish detection performance on common, medium, and rare classes at the order and family taxonomic levels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.555,
+                0.471,
+                0.646
+            ],
+            "angle": 0,
+            "content": "for rare classes was significantly worse than that for common classes, with an average classification accuracy of \\(57.03\\%\\) and \\(64.84\\%\\) at the Family and Order levels, respectively. This is because these rare classes have insufficient annotations, which poses great challenges for fish classification recognition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Fig. 4 visualizes selected classification results on the Family level using the ConvNeXt model. We showed both good cases in the first six columns and bad cases in the last two columns. Based on the results presented in Figure 4, it is evident that the ConvNeXt model is capable of accurately identifying the Family categories of input images, even when they exhibit significant variations in illumination and shape. However, there are some instances where the model failed to perform optimally. These failures are primarily attributed to factors such as low contrast, challenging view-angles, or visual similarities between different families. For example, arhynchobatidae, urolophidae, and dasyatidae belong to cartilaginous fish meaning skeletons are made of cartilage, have flattened bodies, and have a venomous spine on their tail, which can cause confusion for our classification models, as shown in the bottom right of the figure. More examples can"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.555,
+                0.733,
+                0.571
+            ],
+            "angle": 0,
+            "content": "be found in the supplementary file."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.571,
+                0.895,
+                0.647
+            ],
+            "angle": 0,
+            "content": "Effect of pretraining. We investigated the effect of using pretraining on the ImageNet dataset. By comparing the performance between ConvNeXt and ConvNeXt*, using ImageNet pretraining can significantly improve the fish classification performance on our FishNet dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.649,
+                0.895,
+                0.831
+            ],
+            "angle": 0,
+            "content": "Effect of balanced loss. From Table 4, using class-balanced loss can significantly improve classification performance, especially in rare classes; while using focal loss harms the performance. Specifically, for Order classification, using class-balanced loss improved the classification accuracy on rare classes from \\(64.84\\%\\) to \\(71.41\\%\\). We emphasize that there exist several other techniques that can be employed to mitigate long-tail classification problems, which may potentially yield superior results. Nonetheless, our focus in this experiment was not to maximize performance but rather to raise awareness of the long-tail issue with our FishNet dataset, thereby encouraging further investigations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.846,
+                0.649,
+                0.861
+            ],
+            "angle": 0,
+            "content": "4.2. Fish Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Benchmark settings. We conducted fish detection experiments using two well-known methods, YOLOF [5], and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "20502"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.09,
+                0.46,
+                0.31
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.321,
+                0.472,
+                0.362
+            ],
+            "angle": 0,
+            "content": "Figure 5. Visualization of fish detection results using family-level classification labels. We show successful cases in the first 2 rows and failure cases in the last row."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.392,
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+            ],
+            "angle": 0,
+            "content": "TOOD [11] on our FishNet dataset. For both methods, the backbone networks are pretrained on MS-COCO [26], and we finetuned the whole model using the stochastic gradient descent (SGD) optimizer with a learning rate of 2.5e-4, a momentum of 0.9, and a weight decay of 0.0001 for 100 epochs. For performance evaluation, we reported performance on two splits according to the Family/Order distribution, including common, medium, and rare classes, that contain \\(25\\%\\), \\(50\\%\\), and \\(25\\%\\) of images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.529,
+                0.472,
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+            ],
+            "angle": 0,
+            "content": "Results. Table 4 shows the fish detection results at both the Family and Order levels. Our results demonstrated that for order-level classification, TOOD [11] outperformed YOLOF [5] in all the dataset splits. However, we observed that for family-level classification, YOLOF [5] exhibited better performance for Rare classes. Given the significantly higher number of Rare classes (405) as compared to Medium (52) and Common (6) classes, it is not surprising that the average Mean Average Precision (MAP) per class was lower for TOOD [11]. Therefore, we note that the evaluation of model performance can be influenced by the prevalence of different classes in the dataset, as shown in Table 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.712,
+                0.472,
+                0.818
+            ],
+            "angle": 0,
+            "content": "Fig. 5 visualizes several examples of fish detection results obtained by the TOOD model [11]. The model has proven successful in detecting fish from various species, with different scales, orientations, and backgrounds. However, the TOOD model may struggle to predict family labels for less frequent classes or those with low contrast. We provide more examples in the supplementary file."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "4.3. Functional trait Prediction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+                0.903
+            ],
+            "angle": 0,
+            "content": "Benchmark settings. In this section, we explored using deep learning models to predict fish functional traits based on input images. We tried ten functional traits in our experi-"
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"2\">Seen (%)</td><td colspan=\"2\">Unseen (%)</td></tr><tr><td>F1/Acc.</td><td>Acc-all</td><td>F1/Acc.</td><td>Acc-all</td></tr><tr><td>ResNet-34 [19]</td><td>74.83 / 87.20</td><td>40.04</td><td>54.38 / 78.48</td><td>15.84</td></tr><tr><td>ResNet-50 [19]</td><td>71.80 / 84.52</td><td>30.85</td><td>53.52 / 76.71</td><td>13.92</td></tr><tr><td>ResNet-101 [19]</td><td>73.80 / 85.67</td><td>34.45</td><td>54.37 / 77.47</td><td>15.12</td></tr><tr><td>ViT-S [10]</td><td>75.25 / 86.86</td><td>38.62</td><td>54.62 / 78.99</td><td>16.94</td></tr><tr><td>ViT-B [10]</td><td>78.65 / 88.94</td><td>46.91</td><td>55.72 / 79.93</td><td>18.44</td></tr><tr><td>ViT-L [10]</td><td>81.72 / 90.45</td><td>54.00</td><td>55.94 / 80.23</td><td>18.80</td></tr><tr><td>BeiT [1]</td><td>78.15 / 88.93</td><td>49.97</td><td>54.60 / 78.82</td><td>17.26</td></tr><tr><td>ConvNeXt [27]</td><td>83.30 / 91.03</td><td>54.80</td><td>56.34 / 79.50</td><td>18.00</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.264,
+                0.892,
+                0.293
+            ],
+            "angle": 0,
+            "content": "Table 5. Habitat Classification performance in supervised and zero-shot settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.324,
+                0.895,
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+            ],
+            "angle": 0,
+            "content": "ments, namely trophic level, feeding path, and presence or absence in the following temperature and salinity zonations: tropical, temperate, subtropical, boreal, polar, freshwater, saltwater, and brackish. We used the same network architectures and training strategies as Section 4.1. For evaluating trophic level regression, we reported Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). For habitat classification, we used the average F1 score and overall accuracy to evaluate the performance. Additionally, we calculated the classification-all metric, which reflects the model's ability to accurately predict all functional traits simultaneously."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.506,
+                0.895,
+                0.627
+            ],
+            "angle": 0,
+            "content": "Trophic level Regression. In our experiments, we found that different models showed similar performance for trophic level prediction, with an MAE of 0.45 and an RMSE of 0.60, respectively. We found that trophic level prediction is a challenging task when using common L1 or L2 loss functions. More advanced techniques, such as ordinal regression [14], could potentially remedy this challenge. However, we leave this for further research."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.897,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Habitat Classification Results. Table 5 shows the classification results for nine fish functional traits. Overall, the larger models outperformed the smaller ones. Specifically, the ConvNeXt model achieved the best results with an average f1-score of \\(81.72\\%\\) and a classification accuracy of \\(90.45\\%\\). We also reported the classification accuracy when our model correctly predicts all nine functional traits simultaneously, marked as \"Acc-all\". It was surprising that the best-performing ConvNeXt model obtained an accuracy-all of \\(54.0\\%\\) for correctly predicting all classes simultaneously. Fig. 6 shows selected examples of functional trait classification using the ConvNeXt model. From the figure, we can see that the ConvNeXt model can successfully predict most of the functional traits with large color and structure variations. In addition, Table 6 provides a detailed breakdown of the per-trait classification performance of the ConvNeXt model. The results show that the model achieved an f1-score of over \\(90\\%\\) for four out of nine functional traits. However, the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "content": "20503"
+        }
+    ],
+    [
+        {
+            "type": "image",
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+            "angle": 0,
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+        },
+        {
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+            ],
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+        },
+        {
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.493,
+                0.215,
+                0.681,
+                0.335
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.699,
+                0.215,
+                0.888,
+                0.335
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.344,
+                0.897,
+                0.386
+            ],
+            "angle": 0,
+            "content": "Figure 6. Selected visualization of functional trait classification. For each image, we show its species name on the top, and the \"ground truth/predicted\" functional trait labels on the right. The first two columns show success cases and the last two columns show failure cases. Correct predictions are shown in blue color, false predictions are shown in red color."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.091,
+                0.399,
+                0.882,
+                0.46
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Metric</td><td>FeedingPath</td><td>Tropical</td><td>Temperate</td><td>Subtropical</td><td>Boreal</td><td>Polar</td><td>Freshwater</td><td>Saltwater</td><td>Brackish</td><td>Avg.</td></tr><tr><td>Acc.</td><td>84.73</td><td>88.64</td><td>84.41</td><td>90.95</td><td>92.88</td><td>96.88</td><td>91.98</td><td>93.10</td><td>90.51</td><td>90.45</td></tr><tr><td>F1</td><td>68.07</td><td>92.97</td><td>88.03</td><td>94.49</td><td>76.99</td><td>59.91</td><td>91.02</td><td>95.59</td><td>68.40</td><td>81.72</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.118,
+                0.481,
+                0.851,
+                0.496
+            ],
+            "angle": 0,
+            "content": "Table 6. Per-trait classification performance. For each trait, we report both the F1 score (%) and classification accuracy (%)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.522,
+                0.47,
+                0.553
+            ],
+            "angle": 0,
+            "content": "model obtains less impressive performance for feeding path and polar classification."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.554,
+                0.473,
+                0.782
+            ],
+            "angle": 0,
+            "content": "Zero-shot Habitat Classification. We further evaluated the habitat classification performance in a zero-shot setting, where we evaluated habitat classification on unseen classes, which were not never seen during training. To achieve this, we trained the ConvNeXt model on 58 common and medium classes (according to their family classes) and evaluated the performance on 405 rare classes. From Table 5, although zero-shot habitat classification performance is worse than the supervised setting, the best-performed ViT-L model still shows a reasonable performance for zero-shot habitat classification, with a classification accuracy of \\(80.23\\%\\) and \\(18.80\\%\\) on accuracy and accuracy-all. This demonstration showcases the capacity of the deep learning model to predict the functional traits of previously unseen species, thereby establishing a valuable tool for the discovery of new species."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.799,
+                0.355,
+                0.815
+            ],
+            "angle": 0,
+            "content": "5. Conclusions and Future Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "This work presents FishNet, a large-scale diverse dataset consisting of 94,532 images from 17,357 species organized based on the scientific classification of aquatic species. The dataset is accompanied by 114,375 manually labeled bounding box annotations and 22 functional trait information. Fur"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.522,
+                0.895,
+                0.643
+            ],
+            "angle": 0,
+            "content": "thermore, we establish three benchmarks, namely fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition and promote further research in the field of aquatic ecology. The experimental results demonstrate that accurate fish recognition and functional trait prediction are still challenging due to several factors, such as large species diversity, diverse backgrounds, low contrast, etc."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.895,
+                0.765
+            ],
+            "angle": 0,
+            "content": "We release our data and associated code to encourage further research in developing more accurate and effective tools for monitoring and protecting aquatic ecosystems. Our FishNet dataset will also encourage research into evaluating the impact of climate change on aquatic ecosystems and identifying potential solutions to help maintain the health and resilience of aquatic ecosystems and contribute to mitigating the impacts of climate change."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.778,
+                0.688,
+                0.794
+            ],
+            "angle": 0,
+            "content": "6. Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.803,
+                0.895,
+                0.894
+            ],
+            "angle": 0,
+            "content": "We would like to thank Jun Chen and Habib Slim for providing their suggestions and Cameron Trotter for updating the spiderfish package to facilitate image collection from FishBase. This work is supported by KAUST, under Award No. BAS/1/1685-01-01. AJT is supported by KAUST Global Fellowship Program under Award No. ORA-2022-5001."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.521,
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+            ],
+            "angle": 0,
+            "content": "20504"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.175,
+                0.106
+            ],
+            "angle": 0,
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+# FishNet: A Large-scale Dataset and Benchmark for Fish Recognition, Detection, and Functional Trait Prediction
+
+Faizan Farooq Khan*,†
+
+Xiang Li*
+
+Andrew J. Temple
+
+Mohamed Elhoseiny
+
+* equal contribution
+
+$\dagger$  project lead
+
+King Abdullah University of Science and Technology (KAUST)
+
+{faizan.khan, xiang.li.1, andrew.template, mohamed.elhoseiny}@kaust.edu.sa
+
+![](images/e6d7cf78ff8eee8a0f98388d9a7debf69da0bbaacdf0b58656e11894fa5752df.jpg)  
+Figure 1: We present FishNet, a comprehensive benchmark for large-scale aquatic species recognition, detection, and functional trait identification. Our benchmark dataset is based on an aquatic biological taxonomy, consisting of 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, 17,357 species, and 94,532 images. The dataset also includes bounding box annotations for fish detection. Additionally, the dataset encompasses 22 traits, grouped into three categories: habitat, ecological rule, and nutritional value. These traits facilitate the identification of the ecological roles of aquatic species and their interactions with other species.
+
+# Abstract
+
+Aquatic species are essential components of the world's ecosystem, and the preservation of aquatic biodiversity is crucial for maintaining proper ecosystem functioning. Unfortunately, increasing anthropogenic pressures such as overfishing, climate change, and coastal development pose significant threats to aquatic biodiversity. To address this challenge, it is necessary to design an automatic aquatic species monitoring systems that can help researchers and policymakers better understand changes in aquatic ecosystems and take appropriate actions to preserve biodiversity. However, the development of such systems is impeded by a lack of large-scale diverse aquatic species datasets. Existing aquatic species recognition datasets generally have a limited num
+
+ber of species, nor do they provide functional trait data, and so have only narrow potential for application. To address the need for generalized systems that can recognize, locate, and predict a wide array of species and their functional traits, we present FishNet, a large-scale diverse dataset containing 94,532 meticulously organized images from 17,357 aquatic species, organized according to aquatic biological taxonomy (order, family, genus, and species). We further build three benchmarks, i.e., fish classification, fish detection, and functional trait prediction, inspired by ecological research needs, to facilitate the development of aquatic species recognition systems, and promote further research in the field of aquatic ecology. Our FishNet dataset has the potential to encourage the development of more accurate and effective tools for the monitoring and protection of aquatic ecosystems, and hence
+
+take effective action toward the conservation of our planet's aquatic biodiversity. Our dataset and code will be released at https://fishnet-2023.github.io/.
+
+# 1. Introduction
+
+Aquatic biodiversity is of paramount importance in safeguarding the structure, stability, and overall health of aquatic ecosystems. Nonetheless, in recent decades, the escalating anthropogenic pressures from human activities, including fisheries, climate change, and coastal development [22, 24, 29], have made the conservation of aquatic biodiversity increasingly difficult and increasingly prominent in public attention. A key step in aquatic biodiversity protection is the ongoing monitoring, which calls for highly efficient species recognition and functional trait identification [36, 39, 42]. However, this process generally calls for a high level of expert knowledge due to complicated species taxonomy, which makes it time- and labor-consuming.
+
+In recent years, deep learning methods have made significant breakthroughs in various computer vision tasks, presenting a promising solution for automatic and efficient species recognition. However, it is well-known that the accuracy of these AI-based models is heavily reliant on the scale and diversity of the training datasets. In the context of safeguarding aquatic biodiversity, there is an urgent need to develop large-scale and diverse datasets to facilitate AI-based aquatic species recognition systems. Several previous works have focused on building such datasets for fish recognition. For example, Fish4Knowledge [15] collected 27,370 fish images from 23 distinct species. WildFish++ [44] collected 103,034 fish images from 2,348 species along with text descriptions. Other works [3,6,16,17,35] have also accumulated fish images from specific regions, primarily focusing on species classification. However, these datasets are limited to a relatively small proportion of the  $>35,000$  described species of fish, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. Therefore, there is an urgent need to develop more extensive and diverse datasets that can enable more robust AI-based systems to accurately identify a broader range of aquatic species, supporting aquatic biodiversity conservation efforts.
+
+In this work, we present a large-scale diverse dataset, called FishNet, to foster aquatic species recognition research. FishNet contains 94,532 images of aquatic species from 17,357 species, collected from different regions around the world. Please refer to Table 1 for a detailed comparison of our FishNet dataset with existing datasets. FishNet contains 94,532 images with different sizes, resolutions, and illumination, representing a diverse set of aquatic species. The dataset is meticulously organized based on the scientific classification of aquatic species, including 8 taxonomic
+
+classes $^{1}$ , 83 orders, 463 families, 3826 genera, and 17,357 species, and is accompanied by manual-labeled bounding box annotations.
+
+Our FishNet dataset also provides traits associated with each species of the dataset, which can facilitate a better understanding of the ecological roles of aquatic species. To the best of our knowledge, we are the first to use deep learning techniques to predict functional traits directly from fish images. The proposed dataset can serve as a valuable resource for training and evaluating deep learning models for aquatic species classification and detection, and can further support research efforts toward the conservation and protection of aquatic ecosystems.
+
+Additionally, we establish three benchmarks inspired by ecological research needs - fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition systems, and promote further research in the field of aquatic ecology. We conducted fish recognition and functional trait prediction using state-of-the-art deep learning models on these three benchmarks. The results show that accurate fish recognition and functional trait prediction on our FishNet dataset remains challenging: (1) The best-performing model achieved a classification accuracy of  $61.38\%$  at the family levels, and the best-performing detection model achieved  $mAP_{50}$  of 56.5 at the order level. (2) For functional trait prediction, the best-performing model achieved a classification accuracy of  $54.80\%$  and  $18.00\%$  under supervised and zero-shot settings, respectively.
+
+# 2. Related Work
+
+Fish taxonomy has been a longstanding area of scientific inquiry, with early works dating back to Aristotle's taxonomic classification of 117 Mediterranean fish in the 4th century BC [18]. In the 18th century, Linnaeus developed a widely-used system for naming and classifying organisms, and subsequent taxonomists have further built upon his work using both morphological and genetic data [2,32]. Despite the advances made, classifying fish species remains a time-consuming process [30, 43]. In recent decades, computer vision techniques have played a vital role in automating the fish identification process, resulting in faster and more cost-effective identification of fish species [43]. However, computer vision models targeted at fish classification and detection face several challenges, including illumination change, low contrast, frequent occlusion, turbid water, and complex background [4, 43]. To tackle the challenges of fish recognition, a large-scale high-quality dataset is desired to automatically recognize aquatic species for biodiversity monitoring and protection. In this section, we provide a summary of previous aquatic species datasets and delineate
+
+<table><tr><td rowspan="2">Datasets</td><td colspan="4">Properties</td><td colspan="3">Tasks</td></tr><tr><td>Images</td><td>Species</td><td>Taxonomy Level</td><td>Functional Traits</td><td>Classification</td><td>Trait Prediction</td><td>Detection</td></tr><tr><td>Fish4-Knowledge-A [15]</td><td>27,370</td><td>23</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>SEAMPD21 [3]</td><td>28,328</td><td>130</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish-gres [35]</td><td>3,248</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Mediterranean Fish Species [16]</td><td>≈40,000</td><td>20</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish Abundance [17]</td><td>4,909</td><td>50</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Image Dataset [12]</td><td>33,805</td><td>30</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>NCFM [6]</td><td>16,915</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>iNaturalistFish 1001[21]</td><td>54,006</td><td>369</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>WildFish++ [44]</td><td>103,034</td><td>2,348</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Ours</td><td>94,778</td><td>17,357</td><td>5-1</td><td>22</td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+Table 1. Comparison with existing datasets for fish recognition. FishNet provides annotations following biological taxonomy from class(5) to species(1); while previous datasets only provide species-level annotations. FishNet covers two orders of magnitude more species categories than existing datasets (17k vs 130). More importantly, FishNet provides additional functional traits that enable trait identification.
+
+the limitations that impede their applicability for detailed analysis of aquatic species.
+
+Lack of species diversity. Fish4Knowledge [15] is one of the pioneering works to build a fish recognition dataset. This dataset comprises a vast collection of approximately 700,000 underwater video clips captured in open sea waters in the Adriatic Sea in Croatia. A subset of 27,370 images was extracted from these video clips and manually annotated with bounding boxes and the corresponding species name. Another work [12] collects 33,805 images of 30 different fish species along with information about the meteorological and oceanographic conditions from the region of Barcelona, Spain. Several other works like [3,6,16,17,35] also collect fish images for classification from specific regions. These datasets are limited to a small number of species, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. In contrast, our FishNet dataset contains more than 17,000 aquatic species which is more suitable for real-world application.
+
+Lack of taxonomic diversity. Taxonomic classification of fishes is a crucial task in ecology and conservation biology [40]. Although several datasets have been previously developed for this task [3, 12], most of them have focused on a narrow taxonomic range (i.e. containing species from a small number of higher-order taxonomic groups), limiting their utility for exploring the wider diversity of fish species. For instance, the SEAMPD-21 [3] dataset comprises over 23,000 images, but only encompasses 130 species, while another dataset [12] containing more than 30,000 images includes merely 30 species. While these datasets serve as valuable resources for studying specific species, they do not provide a comprehensive representation of the diverse range of fish species present, which is crucial for understanding the fish ecosystem and recognizing the unique properties of different fish species.
+
+Lack of functional traits. Functional traits are characteristics of an organism that relate to its ecological role [31, 39].
+
+Functional traits in fish, such as trophic ecology, swimming modality, habitat use, and reproductive strategies, provide crucial insights into their ecological role and interactions with other species [28]. Understanding these traits can aid in sustainable fisheries management and maintaining ecosystem balance [38]. Monitoring functional diversity, rather than species diversity, is a common method of understanding ecosystem health, and guiding ecosystem management. Moreover, predicting functional traits can facilitate the understanding of probable functions performed by unknown or novel species, which otherwise may take considerable research effort and time to ascertain [9].
+
+Unlike most existing large-scale bio-related datasets (such as iNaturalist [21] and WildFish++ [44]) that primarily focuses on species classification, the Brackish dataset [33] provides underwater images with bounding box annotations of fish, crabs, and starfish. The BrackishMOT [34] dataset focuses on tracking schools of small fish and provides 98 video sequences captured in the wild. The Caltech fish counting dataset [23] consists of sonar videos, which makes it challenging for diverse species recognition. Similar to functional traits in our FishNet dataset, the NEWT dataset [41] offers functional attributes within broader domains such as behavior, age, and health. In contrast, FishNet places its emphasis on habitat-related functional traits, e.g., tropical area suitability. A notable distinction lies in the breadth of species categories covered: our FishNet dataset encompasses a significantly larger spectrum of categories compared to the NEWT dataset (17,000 vs. 183). We compare our FishNet dataset with other existing fish-related datasets and summarize the key differences in Table 1.
+
+# 3. FishNet
+
+The goal of our FishNet dataset is to provide a large-scale fish image dataset that benchmarks fish recognition, detection, and functional trait predictions. In this section,
+
+![](images/2ac37b06a70a116a331db6744bc15d81e1a9d1cf1242938284be5684784f67f6.jpg)
+
+![](images/d045fba42cd2f736433a7e994a90c5af2abd9eed9af2901b7717c24ca6233a56.jpg)  
+Figure 2. Order distribution. We plot the natural logarithm of the number of images per order. We show 42 more frequent orders at the top and 41 less frequent orders at the bottom.
+
+we outline our dataset collection approach, including fish taxonomy construction, image and attribute collection, and detection annotation. To ensure the accuracy and consistency of our annotations, we implemented a quality control process during annotation collection. Finally, we present statistics of FishNet.
+
+# 3.1. Fish taxonomy construction
+
+The construction of fish taxonomy represents a critical preliminary step for the development of a fish recognition system. In order to facilitate the scientific and user-friendly utilization of our FishNet dataset, we constructed and organized the dataset in accordance with standard fish taxonomy protocols. To ensure the quality of the data and meet the ecological objectives, aquatic behavioral ecologists actively participated in this project and provided input on the design of the data collection for both taxonomical labels and functional traits. Initially, a comprehensive list of fish, amounting to approximately 35,024 distinct species, was sourced from FishBase [13]. Within FishBase, each individual fish is mapped to its respective position within the taxonomic hierarchy, consisting of taxonomic class, order, family, genus, and species. See Fig. 1 for a detailed structure of fish taxonomy.
+
+# 3.2. Image and Functional Traits Collection
+
+For each of the fish species in our taxonomic list, we collected available images from two key online databases, FishBase [13] and iNaturalist [21]. 51,433 images were scraped from FishBase using an updated version of the spiderfish package [37]. After we obtained the fish images from Fishbase [13], to ensure the quality and relevance of the data, we manually reviewed all the images and removed any instances that were not suitable for our analysis. This involved removing images that were not photographs of fish, such as images of fish sketches, coin images, stamp images, larval fish, and images of fish bone structures. By performing this manual filtering process, we were able to ensure that our dataset consisted only of high-quality images that were suitable for our research purposes. This process also helped to reduce the potential for errors or inaccuracies in our analysis, by removing any images that could introduce additional bias or noise into the data. Some of the removed instances are shown in Figure 3.
+
+During this phase, 7,634 images were dropped from the dataset and the remaining 43,799 were added to our FishNet dataset. A further 51,006 images were then downloaded from the iNaturalist database. Combined, the compiled im
+
+![](images/106496639bb1612165f97d852e80aa25be34be0cccbfe096cfb2e98dca36c387.jpg)
+
+![](images/98f2210528f9edbb43043d340d75247f71aa39af4118a2e9423338ccbbf073df.jpg)
+
+![](images/fc17ff2327e8fd9f5a52dd8aabba38c2712929303bbfb95343bbc4134beffd3c.jpg)
+
+![](images/37351570162b1cef2bdf13dba887e49ca753e9942b385931e4e2477339319107.jpg)  
+Figure 3. Examples removed from the dataset: The first row shows bone structures, the second row shows larval fish, the third row shows stamps and coins, and the fourth row shows fish sketches. All instances of these were identified and excluded.
+
+![](images/ed697eede149da99f8c633e9bbb982962a6056fb52553aa0ed53c0ac84d538ec.jpg)
+
+![](images/95bec6b13c7e94249749f37529b7d2da34fbc0e2a8cccfc78ad5992ca29e984a.jpg)
+
+![](images/9dd0dcea1777f6b1f6b17da9a4bbd21b49893b2833bf35058f7a3ba74c4b8346.jpg)
+
+![](images/f2636664e6ea733ad459af9bf2104004f49a57a6cf8cb0bd16f7176e875250ec.jpg)
+
+![](images/bdfc06a2c66be05e86639489672e47726f7a90c369185cb6a13cbb73c53bd165.jpg)
+
+![](images/187805510140e7429fed33aba8595313f7c57accc472483f5f56be177379575c.jpg)
+
+![](images/2906faf894966596007647365ce2c2e24125ccaaaa45f86c50f41da81341540a.jpg)
+
+![](images/3af90b3efde560c5c49674e0d07e496b36928e0026c97085dc1286acbf0116c2.jpg)
+
+![](images/bae24748bec8abf27ab1de6fd3fd4e34933c5f357918b679a170783337facb53.jpg)
+
+![](images/36e9b521b2b6cfc62a869f0bbe11a5730897633b9cb618e7b3654d2aab587d6d.jpg)
+
+![](images/72235e5e91077b33d90844acb7482ac75cd31f6643db224f08316baf52761e19.jpg)
+
+![](images/378b509857bfc3175cdc267e31b0677d80d46aff18cf1fdab96faed82a2071c4.jpg)
+
+age library encompasses 94,805 images from 17,518 species. To facilitate model training and evaluation, we dropped 273 images whose families have less than 5 images. For each species in our dataset, we gathered information on 22 traits (90,147 images have traits), which we believe to be important indicators of ecological roles and nutritional properties. These traits include the true functional traits of trophic level, feeding pathway, and habitat preferences based on temperature and salinity. In addition, we also included nutritional content "traits" for calcium, iron, omega-3 fatty acid, protein, selenium, vitamin A, and zinc content [20]. Table 2 provides detailed descriptions of the ten true functional traits.
+
+# 3.3. Fish Detection Annotations
+
+We employed the Amazon Mechanical Turk (AMT) [7] platform to collect bounding box annotations for all images in our dataset. Specifically, three independent annotators were tasked with providing locations for every instance in each image. To ensure accurate and reliable annotation of our image dataset, we have implemented a rigorous process for collecting annotations for object detection. Each image undergoes annotation by three different users on Amazon Mechanical Turk (AMT) [7]. We only accept annotations if all three users provide the same number of bounding boxes and if all the boxes have an Intersection over Union (IOU) value greater than 0.9. In cases where the annotations do not meet these criteria, we collect an additional annotation for the image and repeat the process of comparing the annotations reported by the different AMT users. We continue this process until we have at least three user annotations that agree with the number of bounding boxes and have an IOU greater than 0.9. For image categorization, we have already
+
+<table><tr><td>Trait</td><td>Value</td><td>Description</td></tr><tr><td>Trophic level</td><td>Real value</td><td>The position in the food chain or food web.</td></tr><tr><td>Feeding path</td><td>Benthic/ Pelagic</td><td>Species feeds primarily from which trophic pathway.</td></tr><tr><td>Tropical</td><td>True/ False</td><td>Whether the fish can live in tropical areas.</td></tr><tr><td>Temperate</td><td>True/ False</td><td>Whether the fish can live in temperate areas.</td></tr><tr><td>Subtropical</td><td>True/ False</td><td>Whether the fish can live in subtropical areas.</td></tr><tr><td>Boreal</td><td>True/ False</td><td>Whether the fish can live in boreal areas.</td></tr><tr><td>Polar</td><td>True/ False</td><td>Whether the fish can live in polar areas.</td></tr><tr><td>Freshwater</td><td>True/ False</td><td>Whether the fish can live in freshwater.</td></tr><tr><td>Saltwater</td><td>True/ False</td><td>Whether the fish can live in saltwater.</td></tr><tr><td>Brackish</td><td>True/ False</td><td>Whether the fish can live in brackish.</td></tr></table>
+
+Table 2. The explanation for 10 selected functional traits in the FishNet dataset. Please check the supplementary for the rest.
+
+assigned labels to each image and asked users to select images that belong to a specific family by providing example images of that family. Through this meticulous process, we were able to calculate 114,375 object instances.
+
+# 3.4. FishNet Statistics
+
+The FishNet dataset comprises a total of 94,532 images featuring 17,357 distinct species. The images were compiled
+
+<table><tr><td rowspan="2">Backbone</td><td colspan="4">Family Classification (%)</td><td colspan="4">Order Classification (%)</td></tr><tr><td>Common</td><td>Medium</td><td>Rare</td><td>All</td><td>Common</td><td>Medium</td><td>Rare</td><td>All</td></tr><tr><td>ResNet-34 [19]</td><td>77.16</td><td>69.10</td><td>36.65</td><td>40.82</td><td>83.42</td><td>77.87</td><td>47.36</td><td>52.07</td></tr><tr><td>ResNet-50 [19]</td><td>76.82</td><td>70.27</td><td>35.99</td><td>40.37</td><td>82.46</td><td>75.93</td><td>42.84</td><td>47.94</td></tr><tr><td>ResNet-101 [19]</td><td>75.73</td><td>69.00</td><td>31.61</td><td>36.38</td><td>81.35</td><td>75.01</td><td>42.32</td><td>47.36</td></tr><tr><td>ViT-S [10]</td><td>76.08</td><td>67.02</td><td>33.67</td><td>37.97</td><td>84.14</td><td>74.78</td><td>44.09</td><td>48.79</td></tr><tr><td>ViT-B [10]</td><td>82.93</td><td>74.50</td><td>38.26</td><td>42.91</td><td>88.52</td><td>81.64</td><td>52.44</td><td>56.93</td></tr><tr><td>ViT-L [10]</td><td>85.51</td><td>77.05</td><td>44.18</td><td>48.40</td><td>89.02</td><td>83.89</td><td>55.94</td><td>60.26</td></tr><tr><td>BeiT [1]</td><td>86.09</td><td>77.67</td><td>50.78</td><td>54.26</td><td>91.41</td><td>88.24</td><td>38.16</td><td>45.97</td></tr><tr><td>ConvNeXt* [27]</td><td>42.63</td><td>26.56</td><td>12.57</td><td>14.53</td><td>63.58</td><td>40.67</td><td>17.82</td><td>21.12</td></tr><tr><td>ConvNeXt [27]</td><td>90.32</td><td>85.13</td><td>57.03</td><td>60.61</td><td>94.07</td><td>90.49</td><td>64.84</td><td>68.81</td></tr><tr><td>ConvNeXt [27] + FL [25]</td><td>88.28</td><td>82.02</td><td>51.22</td><td>55.16</td><td>87.60</td><td>81.11</td><td>22.22</td><td>31.37</td></tr><tr><td>ConvNeXt [27] + CB [8]</td><td>90.53</td><td>84.80</td><td>57.94</td><td>61.38</td><td>93.15</td><td>90.56</td><td>71.41</td><td>74.38</td></tr><tr><td>ConvNeXt [27] + FL [25] + CB [8]</td><td>84.89</td><td>77.92</td><td>48.99</td><td>52.71</td><td>85.14</td><td>57.25</td><td>39.28</td><td>41.76</td></tr></table>
+
+Table 3. Fish Family/Order classification accuracy. * denotes training from scratch, 'FL' denotes using focal loss during training, and 'CB' denotes using class-balanced training.
+
+from 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, and 17,357 species, with each species having at least one image. We present the distribution of Orders within our dataset in Fig. 2. The figure displays the logarithmic frequency of each Order category, and it demonstrates a long-tail distribution within the FishNet dataset with respect to Order categories. We observed similar distribution for other taxonomy levels. In our FishNet dataset, each image in the dataset is accompanied by 22 functional traits. Additionally, the dataset includes instance-level bounding box annotations. In total, the FishNet dataset encompasses 114,375 object instances.
+
+# 4. Experiments
+
+Based on FishNet, we build three main challenges: 1) Fish classification. To identify family/order labels from input images; 2) Fish detection. Identifying the fish locations and family/order labels from input images; 3) Functional trait prediction. Predicting 10 functional traits from input images. For each challenge, we baseline several state-of-the-art models to show the capabilities of automatic fish identification and functional trait prediction using deep learning models. For all experiments, unless otherwise stated, we randomly select  $80\%$  for training and the remaining  $20\%$  for performance evaluation.
+
+# 4.1. Fish Classification
+
+Benchmark settings. We conducted Family/Order classification using both ResNet-based and ViT-based architectures, including ResNets (ResNet-34, ResNet-50, ResNet101) [19], ViT (ViT-S, ViT-B, ViT-L) [10], BeiT [1], and ConvNeXt [27]. We replaced the classification head using
+
+two fully connected (FC) layers, with a dropout of 0.5 for the first FC layer. For all comparing methods, the backbone networks were pretrained on ImageNet, and we finetuned the whole model using an Adam optimizer for 100 epochs. The initial learning rate was set to 3e-5, and 3e-4 for backbone networks and classification head, and we divided the learning rate by 2 every 20 epochs. In our experiments, we also explored recent techniques to address the long-tail classification problem. We explored focal loss [25] and class-balanced training [8] to improve the fish recognition performance in less frequent classes. Furthermore, we provided genus-level classification in the supplementary file.
+
+Class split. To capture the effect of the long-tailed nature of the FishNet dataset, the FishNet dataset was partitioned into three distinct subsets, namely common, medium, and rare categories, based on their respective class frequencies. To categorize the classes according to their frequencies, we established a criterion for the Family/Order categories. Specifically, we selected those categories with a proportional representation of  $25\%$  of the total number of images as the common classes, those categories with subsequent  $50\%$  as medium classes, and the remaining  $25\%$  as rare classes. After splitting, we identified a total of 6, 52, and 405 common, medium, and rare family classes, respectively. In our experiments, we reported class-averaged accuracy for each split and also the overall accuracy among all splits.
+
+Results. Table 3 shows the fish classification results at the Family and Order levels. From Table 3, it is evident that larger models consistently outperform smaller models in terms of classification accuracy. Specifically, the best-performing ConvNeXt model achieved an average classification accuracy of  $60.61\%$  and  $68.81\%$  at the Family and Order levels, respectively. We also observed that the performance
+
+![](images/e262053e822966479bdd851852d2238b04141b2554f3d8c48454128d9dbfcb91.jpg)  
+Cls=Centrarchidae, Conf=1.00  
+Cls=Acanthuridae, Conf=0.99
+
+![](images/29a5bcb2cb2fe712028e151eb776fbeafba0bffa924e3e36d7e5f2aec5818040.jpg)  
+CIs=Centrarchidae, Conf=1.00  
+Cls=Acanthuridae, Conf=1.00
+
+![](images/a8ed7656f8b5ee908809d48e499fac1a8842ceb52ad780c2bfd5d06e30702cd4.jpg)  
+CIs  $=$  Centrarchidae, Conf=1.00  
+Cls=Acanthuridae, Conf=1.00
+
+![](images/621e53d9219ef476fad11f5def04b9a3066c442aaccad99d72cea7e055b9a89d.jpg)  
+CIs  $=$  Centrarchidae, Conf.  $= 1.00$  
+Cls= Acanthuridae, Conf  $= {1.00}$
+
+![](images/bf386dceeff17425c4ef78c0ae757f0d412ae5b6a6eef1dfdd4f227a7059b526.jpg)  
+CIs  $=$  Centrarchidae, Conf=1.00  
+Cls=Acanthuridae, Conf=1.00
+
+![](images/d9db322baeb9ad334bd21dc99f7e0515275623c0ac40a4cc0c8a5de6cf2d29b0.jpg)  
+CIs  $=$  Centrarchidae, Conf  $= 1.00$  
+Cls= Acanthuridae, Conf  $= {1.00}$
+
+![](images/9a2a7d9945ab737c2a3723db209acb98acca3be0b705533752ff0cdd9472ec75.jpg)  
+CIs=cihilidae, Conf=0.66  
+CIs=Girellidae, Conf.  $\equiv$  0.88
+
+![](images/ba3ef2c58cc16fd297e9cb1e355267ec9aafaf7c6a5b303512220ecb7814bdd1.jpg)  
+Cls=Amiidae, Conf=0.32  
+Cls=Percidae, Conf=0.55
+
+![](images/cb161c99930c6116141f4ef9e2cda5baead3ca9e2daaefa9fa3526687cfa176c.jpg)  
+CIs  $=$  Dasyatidae, Conf=1.00
+
+![](images/0a7c5afd770da2b3dca875bbd3662dbe99934810819b56c0c3780fc2ff8a02ab.jpg)  
+Figure 4. Selected visualization of FishNet Family classification. For each ground truth class, we showcase six examples in which the ConvNeXt model accurately predicts the correct Family label on the left. Additionally, we display two examples in which the ConvNeXt makes incorrect predictions on the right. For reference, we show the predicted Family class ('Cls') and confidence score ('Conf') above each image.
+
+![](images/db2c5de10f29f0f768731303e950e3cc62cba29d77650363d4e217fb25c485a6.jpg)  
+Cls  $=$  Dasyatidae, Conf=1.00
+
+![](images/3bff7c738a63e046d4477089c18688446672712bf86701e0863ed98730d3581c.jpg)
+
+![](images/40b3e42a06063dd4cdf4968ef62c3e85857f909a88caaed7c0ea0ab5d156aef9.jpg)  
+Cls  $=$  Dasyatidae, Conf  $\equiv$  0.94
+
+![](images/5db215deaa1d235dfd70c3a55e2e7c49934aaa458524aee4b266d9106754007a.jpg)
+
+![](images/3c2bbe60d758a4d14c774c3ee9d45907928ac79e6713b7b6502c92dbef047d88.jpg)  
+CIs  $=$  Dasyatidae, Conf  $\equiv 1.00$
+
+![](images/55d4fb22a798bc02d56adaacb0d01a0e492c3bbc93f2f581ef9ffee832920658.jpg)
+
+![](images/b6be3fe4c2d909a2d49c921289945b66bc6a14b530487cc885b1931d82e6e63e.jpg)  
+CIs  $=$  Dasytidae, Conf  $= 1.00$
+
+![](images/2a832c1a4fc533ce0aee5eef85bcfd33c4b73e2e677f6c51304d940ecec9ce38.jpg)
+
+![](images/10e418d1b874576034b445cad7076a8a6f7d18e6cc4ec9e2f011306066b1d9b2.jpg)  
+CIs  $=$  Dasyatidae, Conf  $\equiv$  0.98
+
+![](images/95d6f54a07d07904c773025f03197018d7d0ce9e60b7b8b29c88b5586a1399f2.jpg)
+
+![](images/bb50863f3ab7de6f475fcb478ef3f4f8c303897ca86e1ee727a95f5103511676.jpg)  
+Cis=Arhynchobatidae, Conf=0.34
+
+![](images/ec154c27a39dac5d52533285eed81850f8dab56728e48347f3be5e08028b3f41.jpg)
+
+![](images/3487ec08bfe094389da20b1e81293e02570d8048122f9613e780fa52d1c76e08.jpg)  
+CIs=Uroliophidae, Conf=0.37
+
+![](images/d73c1a75cdedf5cc90dff1ec99af82617ac13f853a747bc1ab4a63b3ecf3f3e9.jpg)
+
+<table><tr><td rowspan="2">Level</td><td rowspan="2">Method</td><td colspan="5">Common Classes/Medium Classes/Rare Classes</td><td colspan="5">Average Per Class</td></tr><tr><td>\( {mAP}_{50} \)</td><td>\( {mAP}_{60} \)</td><td>\( {mAP}_{70} \)</td><td>\( {mAP}_{80} \)</td><td>\( {mAP}_{90} \)</td><td>\( {mAP}_{50} \)</td><td>\( {mAP}_{60} \)</td><td>\( {mAP}_{70} \)</td><td>\( {mAP}_{80} \)</td><td>\( {mAP}_{90} \)</td></tr><tr><td rowspan="2">Order</td><td>YOLOF [5]</td><td>77.3/65.2/39.2</td><td>72.7/62.1/38.0</td><td>61.6/53.4/34.7</td><td>38.8/34.9/25.4</td><td>11.7/9.6/11.8</td><td>45.0</td><td>43.4</td><td>39.3</td><td>27.8</td><td>11.7</td></tr><tr><td>TOOD [11]</td><td>84.8/76.8/50.3</td><td>80.1/73.2/48.5</td><td>69.4/64.4/43.6</td><td>46.1/42.6/32.7</td><td>15.4/14.3/13.6</td><td>56.5</td><td>54.3</td><td>48.5</td><td>35.4</td><td>14.1</td></tr><tr><td rowspan="2">Family</td><td>YOLOF [5]</td><td>67.2/53.1/27.1</td><td>64.0/50.4/26.6</td><td>54.9/43.3/24.4</td><td>35.5/27.3/18.8</td><td>9.9/7.9/7.7</td><td>30.6</td><td>29.8</td><td>26.9</td><td>20.0</td><td>7.8</td></tr><tr><td>TOOD [11]</td><td>81.1/64.0/22.5</td><td>77.1/60.1/21.9</td><td>66.5/51.2/20.1</td><td>44.0/32.8/15.7</td><td>14.5/10.9/7.7</td><td>27.9</td><td>26.9</td><td>24.2</td><td>18</td><td>8.2</td></tr></table>
+
+Table 4. Fish detection performance on common, medium, and rare classes at the order and family taxonomic levels.
+
+for rare classes was significantly worse than that for common classes, with an average classification accuracy of  $57.03\%$  and  $64.84\%$  at the Family and Order levels, respectively. This is because these rare classes have insufficient annotations, which poses great challenges for fish classification recognition.
+
+Fig. 4 visualizes selected classification results on the Family level using the ConvNeXt model. We showed both good cases in the first six columns and bad cases in the last two columns. Based on the results presented in Figure 4, it is evident that the ConvNeXt model is capable of accurately identifying the Family categories of input images, even when they exhibit significant variations in illumination and shape. However, there are some instances where the model failed to perform optimally. These failures are primarily attributed to factors such as low contrast, challenging view-angles, or visual similarities between different families. For example, arhynchobatidae, urolophidae, and dasyatidae belong to cartilaginous fish meaning skeletons are made of cartilage, have flattened bodies, and have a venomous spine on their tail, which can cause confusion for our classification models, as shown in the bottom right of the figure. More examples can
+
+be found in the supplementary file.
+
+Effect of pretraining. We investigated the effect of using pretraining on the ImageNet dataset. By comparing the performance between ConvNeXt and ConvNeXt*, using ImageNet pretraining can significantly improve the fish classification performance on our FishNet dataset.
+
+Effect of balanced loss. From Table 4, using class-balanced loss can significantly improve classification performance, especially in rare classes; while using focal loss harms the performance. Specifically, for Order classification, using class-balanced loss improved the classification accuracy on rare classes from  $64.84\%$  to  $71.41\%$ . We emphasize that there exist several other techniques that can be employed to mitigate long-tail classification problems, which may potentially yield superior results. Nonetheless, our focus in this experiment was not to maximize performance but rather to raise awareness of the long-tail issue with our FishNet dataset, thereby encouraging further investigations.
+
+# 4.2. Fish Detection
+
+Benchmark settings. We conducted fish detection experiments using two well-known methods, YOLOF [5], and
+
+![](images/f9fd7e0b441019e91d882186373b319c9a03d8720536c81e3294051581a07e6c.jpg)  
+Figure 5. Visualization of fish detection results using family-level classification labels. We show successful cases in the first 2 rows and failure cases in the last row.
+
+TOOD [11] on our FishNet dataset. For both methods, the backbone networks are pretrained on MS-COCO [26], and we finetuned the whole model using the stochastic gradient descent (SGD) optimizer with a learning rate of 2.5e-4, a momentum of 0.9, and a weight decay of 0.0001 for 100 epochs. For performance evaluation, we reported performance on two splits according to the Family/Order distribution, including common, medium, and rare classes, that contain  $25\%$ ,  $50\%$ , and  $25\%$  of images.
+
+Results. Table 4 shows the fish detection results at both the Family and Order levels. Our results demonstrated that for order-level classification, TOOD [11] outperformed YOLOF [5] in all the dataset splits. However, we observed that for family-level classification, YOLOF [5] exhibited better performance for Rare classes. Given the significantly higher number of Rare classes (405) as compared to Medium (52) and Common (6) classes, it is not surprising that the average Mean Average Precision (MAP) per class was lower for TOOD [11]. Therefore, we note that the evaluation of model performance can be influenced by the prevalence of different classes in the dataset, as shown in Table 4.
+
+Fig. 5 visualizes several examples of fish detection results obtained by the TOOD model [11]. The model has proven successful in detecting fish from various species, with different scales, orientations, and backgrounds. However, the TOOD model may struggle to predict family labels for less frequent classes or those with low contrast. We provide more examples in the supplementary file.
+
+# 4.3. Functional trait Prediction
+
+Benchmark settings. In this section, we explored using deep learning models to predict fish functional traits based on input images. We tried ten functional traits in our experi-
+
+<table><tr><td rowspan="2">Backbone</td><td colspan="2">Seen (%)</td><td colspan="2">Unseen (%)</td></tr><tr><td>F1/Acc.</td><td>Acc-all</td><td>F1/Acc.</td><td>Acc-all</td></tr><tr><td>ResNet-34 [19]</td><td>74.83 / 87.20</td><td>40.04</td><td>54.38 / 78.48</td><td>15.84</td></tr><tr><td>ResNet-50 [19]</td><td>71.80 / 84.52</td><td>30.85</td><td>53.52 / 76.71</td><td>13.92</td></tr><tr><td>ResNet-101 [19]</td><td>73.80 / 85.67</td><td>34.45</td><td>54.37 / 77.47</td><td>15.12</td></tr><tr><td>ViT-S [10]</td><td>75.25 / 86.86</td><td>38.62</td><td>54.62 / 78.99</td><td>16.94</td></tr><tr><td>ViT-B [10]</td><td>78.65 / 88.94</td><td>46.91</td><td>55.72 / 79.93</td><td>18.44</td></tr><tr><td>ViT-L [10]</td><td>81.72 / 90.45</td><td>54.00</td><td>55.94 / 80.23</td><td>18.80</td></tr><tr><td>BeiT [1]</td><td>78.15 / 88.93</td><td>49.97</td><td>54.60 / 78.82</td><td>17.26</td></tr><tr><td>ConvNeXt [27]</td><td>83.30 / 91.03</td><td>54.80</td><td>56.34 / 79.50</td><td>18.00</td></tr></table>
+
+Table 5. Habitat Classification performance in supervised and zero-shot settings.
+
+ments, namely trophic level, feeding path, and presence or absence in the following temperature and salinity zonations: tropical, temperate, subtropical, boreal, polar, freshwater, saltwater, and brackish. We used the same network architectures and training strategies as Section 4.1. For evaluating trophic level regression, we reported Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). For habitat classification, we used the average F1 score and overall accuracy to evaluate the performance. Additionally, we calculated the classification-all metric, which reflects the model's ability to accurately predict all functional traits simultaneously.
+
+Trophic level Regression. In our experiments, we found that different models showed similar performance for trophic level prediction, with an MAE of 0.45 and an RMSE of 0.60, respectively. We found that trophic level prediction is a challenging task when using common L1 or L2 loss functions. More advanced techniques, such as ordinal regression [14], could potentially remedy this challenge. However, we leave this for further research.
+
+Habitat Classification Results. Table 5 shows the classification results for nine fish functional traits. Overall, the larger models outperformed the smaller ones. Specifically, the ConvNeXt model achieved the best results with an average f1-score of  $81.72\%$  and a classification accuracy of  $90.45\%$ . We also reported the classification accuracy when our model correctly predicts all nine functional traits simultaneously, marked as "Acc-all". It was surprising that the best-performing ConvNeXt model obtained an accuracy-all of  $54.0\%$  for correctly predicting all classes simultaneously. Fig. 6 shows selected examples of functional trait classification using the ConvNeXt model. From the figure, we can see that the ConvNeXt model can successfully predict most of the functional traits with large color and structure variations. In addition, Table 6 provides a detailed breakdown of the per-trait classification performance of the ConvNeXt model. The results show that the model achieved an f1-score of over  $90\%$  for four out of nine functional traits. However, the
+
+![](images/eb34d257130bc4a0215b84806f405a82bf76746ef5547b8e219c69e0126f92a6.jpg)
+
+![](images/aa3aaedf0b31961bcd56d6755318f1353fd1cab1c6b777e1463d13093591c52a.jpg)
+
+![](images/3b41ed33fd13789f6092aaba1767a41ab2675988d694608a566c5dc77cfb1e35.jpg)
+
+![](images/4e896f1b85bd7ece7e0ea7fe047e07f25914556c410bbc17f80f18a579a1c328.jpg)
+
+![](images/452d6e82f73a7d9d0f956458cf2ae7b75dcf78caf88c5e6ada765e3a879558e7.jpg)  
+Figure 6. Selected visualization of functional trait classification. For each image, we show its species name on the top, and the "ground truth/predicted" functional trait labels on the right. The first two columns show success cases and the last two columns show failure cases. Correct predictions are shown in blue color, false predictions are shown in red color.
+
+![](images/4672e0f59f887dbb2023e8b70a536ec00615935975d67794db0bb80477adba26.jpg)
+
+![](images/8548f8600b22bdd3517dee8460994ffbf969d903d3cdf5008c617cb7624b66bb.jpg)
+
+![](images/c1b66ebfd396813146a8f8efc94c5cd7a8beac484367156c56a966974c8bcf9c.jpg)
+
+<table><tr><td>Metric</td><td>FeedingPath</td><td>Tropical</td><td>Temperate</td><td>Subtropical</td><td>Boreal</td><td>Polar</td><td>Freshwater</td><td>Saltwater</td><td>Brackish</td><td>Avg.</td></tr><tr><td>Acc.</td><td>84.73</td><td>88.64</td><td>84.41</td><td>90.95</td><td>92.88</td><td>96.88</td><td>91.98</td><td>93.10</td><td>90.51</td><td>90.45</td></tr><tr><td>F1</td><td>68.07</td><td>92.97</td><td>88.03</td><td>94.49</td><td>76.99</td><td>59.91</td><td>91.02</td><td>95.59</td><td>68.40</td><td>81.72</td></tr></table>
+
+Table 6. Per-trait classification performance. For each trait, we report both the F1 score (%) and classification accuracy (%)
+
+model obtains less impressive performance for feeding path and polar classification.
+
+Zero-shot Habitat Classification. We further evaluated the habitat classification performance in a zero-shot setting, where we evaluated habitat classification on unseen classes, which were not never seen during training. To achieve this, we trained the ConvNeXt model on 58 common and medium classes (according to their family classes) and evaluated the performance on 405 rare classes. From Table 5, although zero-shot habitat classification performance is worse than the supervised setting, the best-performed ViT-L model still shows a reasonable performance for zero-shot habitat classification, with a classification accuracy of  $80.23\%$  and  $18.80\%$  on accuracy and accuracy-all. This demonstration showcases the capacity of the deep learning model to predict the functional traits of previously unseen species, thereby establishing a valuable tool for the discovery of new species.
+
+# 5. Conclusions and Future Work
+
+This work presents FishNet, a large-scale diverse dataset consisting of 94,532 images from 17,357 species organized based on the scientific classification of aquatic species. The dataset is accompanied by 114,375 manually labeled bounding box annotations and 22 functional trait information. Fur
+
+thermore, we establish three benchmarks, namely fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition and promote further research in the field of aquatic ecology. The experimental results demonstrate that accurate fish recognition and functional trait prediction are still challenging due to several factors, such as large species diversity, diverse backgrounds, low contrast, etc.
+
+We release our data and associated code to encourage further research in developing more accurate and effective tools for monitoring and protecting aquatic ecosystems. Our FishNet dataset will also encourage research into evaluating the impact of climate change on aquatic ecosystems and identifying potential solutions to help maintain the health and resilience of aquatic ecosystems and contribute to mitigating the impacts of climate change.
+
+# 6. Acknowledgements
+
+We would like to thank Jun Chen and Habib Slim for providing their suggestions and Cameron Trotter for updating the spiderfish package to facilitate image collection from FishBase. This work is supported by KAUST, under Award No. BAS/1/1685-01-01. AJT is supported by KAUST Global Fellowship Program under Award No. ORA-2022-5001.
+
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\ No newline at end of file
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+                                    "content": "Aquatic species are essential components of the world's ecosystem, and the preservation of aquatic biodiversity is crucial for maintaining proper ecosystem functioning. Unfortunately, increasing anthropogenic pressures such as overfishing, climate change, and coastal development pose significant threats to aquatic biodiversity. To address this challenge, it is necessary to design an automatic aquatic species monitoring systems that can help researchers and policymakers better understand changes in aquatic ecosystems and take appropriate actions to preserve biodiversity. However, the development of such systems is impeded by a lack of large-scale diverse aquatic species datasets. Existing aquatic species recognition datasets generally have a limited num"
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+                                    "content": "ber of species, nor do they provide functional trait data, and so have only narrow potential for application. To address the need for generalized systems that can recognize, locate, and predict a wide array of species and their functional traits, we present FishNet, a large-scale diverse dataset containing 94,532 meticulously organized images from 17,357 aquatic species, organized according to aquatic biological taxonomy (order, family, genus, and species). We further build three benchmarks, i.e., fish classification, fish detection, and functional trait prediction, inspired by ecological research needs, to facilitate the development of aquatic species recognition systems, and promote further research in the field of aquatic ecology. Our FishNet dataset has the potential to encourage the development of more accurate and effective tools for the monitoring and protection of aquatic ecosystems, and hence"
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+                                    "content": "take effective action toward the conservation of our planet's aquatic biodiversity. Our dataset and code will be released at https://fishnet-2023.github.io/."
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+                                    "content": "In this work, we present a large-scale diverse dataset, called FishNet, to foster aquatic species recognition research. FishNet contains 94,532 images of aquatic species from 17,357 species, collected from different regions around the world. Please refer to Table 1 for a detailed comparison of our FishNet dataset with existing datasets. FishNet contains 94,532 images with different sizes, resolutions, and illumination, representing a diverse set of aquatic species. The dataset is meticulously organized based on the scientific classification of aquatic species, including 8 taxonomic"
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+                                    "content": "Our FishNet dataset also provides traits associated with each species of the dataset, which can facilitate a better understanding of the ecological roles of aquatic species. To the best of our knowledge, we are the first to use deep learning techniques to predict functional traits directly from fish images. The proposed dataset can serve as a valuable resource for training and evaluating deep learning models for aquatic species classification and detection, and can further support research efforts toward the conservation and protection of aquatic ecosystems."
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+                                    "content": "Additionally, we establish three benchmarks inspired by ecological research needs - fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition systems, and promote further research in the field of aquatic ecology. We conducted fish recognition and functional trait prediction using state-of-the-art deep learning models on these three benchmarks. The results show that accurate fish recognition and functional trait prediction on our FishNet dataset remains challenging: (1) The best-performing model achieved a classification accuracy of "
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+                                    "content": " of 56.5 at the order level. (2) For functional trait prediction, the best-performing model achieved a classification accuracy of "
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+                                    "content": " under supervised and zero-shot settings, respectively."
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+                                    "content": "Fish taxonomy has been a longstanding area of scientific inquiry, with early works dating back to Aristotle's taxonomic classification of 117 Mediterranean fish in the 4th century BC [18]. In the 18th century, Linnaeus developed a widely-used system for naming and classifying organisms, and subsequent taxonomists have further built upon his work using both morphological and genetic data [2,32]. Despite the advances made, classifying fish species remains a time-consuming process [30, 43]. In recent decades, computer vision techniques have played a vital role in automating the fish identification process, resulting in faster and more cost-effective identification of fish species [43]. However, computer vision models targeted at fish classification and detection face several challenges, including illumination change, low contrast, frequent occlusion, turbid water, and complex background [4, 43]. To tackle the challenges of fish recognition, a large-scale high-quality dataset is desired to automatically recognize aquatic species for biodiversity monitoring and protection. In this section, we provide a summary of previous aquatic species datasets and delineate"
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+                                    "content": "<sup>1</sup>We use \"taxonomic class\" to avoid confusion with the term \"class\" in the computer vision field that denotes the categorization of images or objects into groups based on their visual characteristics."
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+                                            "html": "<table><tr><td rowspan=\"2\">Datasets</td><td colspan=\"4\">Properties</td><td colspan=\"3\">Tasks</td></tr><tr><td>Images</td><td>Species</td><td>Taxonomy Level</td><td>Functional Traits</td><td>Classification</td><td>Trait Prediction</td><td>Detection</td></tr><tr><td>Fish4-Knowledge-A [15]</td><td>27,370</td><td>23</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>SEAMPD21 [3]</td><td>28,328</td><td>130</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish-gres [35]</td><td>3,248</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Mediterranean Fish Species [16]</td><td>≈40,000</td><td>20</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Fish Abundance [17]</td><td>4,909</td><td>50</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Image Dataset [12]</td><td>33,805</td><td>30</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>NCFM [6]</td><td>16,915</td><td>8</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>iNaturalistFish 1001[21]</td><td>54,006</td><td>369</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>WildFish++ [44]</td><td>103,034</td><td>2,348</td><td>1</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>Ours</td><td>94,778</td><td>17,357</td><td>5-1</td><td>22</td><td>✓</td><td>✓</td><td>✓</td></tr></table>",
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+                                    "content": "Table 1. Comparison with existing datasets for fish recognition. FishNet provides annotations following biological taxonomy from class(5) to species(1); while previous datasets only provide species-level annotations. FishNet covers two orders of magnitude more species categories than existing datasets (17k vs 130). More importantly, FishNet provides additional functional traits that enable trait identification."
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+                                    "content": "the limitations that impede their applicability for detailed analysis of aquatic species."
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+                                    "content": "Lack of species diversity. Fish4Knowledge [15] is one of the pioneering works to build a fish recognition dataset. This dataset comprises a vast collection of approximately 700,000 underwater video clips captured in open sea waters in the Adriatic Sea in Croatia. A subset of 27,370 images was extracted from these video clips and manually annotated with bounding boxes and the corresponding species name. Another work [12] collects 33,805 images of 30 different fish species along with information about the meteorological and oceanographic conditions from the region of Barcelona, Spain. Several other works like [3,6,16,17,35] also collect fish images for classification from specific regions. These datasets are limited to a small number of species, posing a challenge to their application in real-world scenarios that require the recognition of diverse species. In contrast, our FishNet dataset contains more than 17,000 aquatic species which is more suitable for real-world application."
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+                                    "content": "Lack of taxonomic diversity. Taxonomic classification of fishes is a crucial task in ecology and conservation biology [40]. Although several datasets have been previously developed for this task [3, 12], most of them have focused on a narrow taxonomic range (i.e. containing species from a small number of higher-order taxonomic groups), limiting their utility for exploring the wider diversity of fish species. For instance, the SEAMPD-21 [3] dataset comprises over 23,000 images, but only encompasses 130 species, while another dataset [12] containing more than 30,000 images includes merely 30 species. While these datasets serve as valuable resources for studying specific species, they do not provide a comprehensive representation of the diverse range of fish species present, which is crucial for understanding the fish ecosystem and recognizing the unique properties of different fish species."
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+                                    "content": "Lack of functional traits. Functional traits are characteristics of an organism that relate to its ecological role [31, 39]."
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+                                    "content": "Functional traits in fish, such as trophic ecology, swimming modality, habitat use, and reproductive strategies, provide crucial insights into their ecological role and interactions with other species [28]. Understanding these traits can aid in sustainable fisheries management and maintaining ecosystem balance [38]. Monitoring functional diversity, rather than species diversity, is a common method of understanding ecosystem health, and guiding ecosystem management. Moreover, predicting functional traits can facilitate the understanding of probable functions performed by unknown or novel species, which otherwise may take considerable research effort and time to ascertain [9]."
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+                                    "content": "Unlike most existing large-scale bio-related datasets (such as iNaturalist [21] and WildFish++ [44]) that primarily focuses on species classification, the Brackish dataset [33] provides underwater images with bounding box annotations of fish, crabs, and starfish. The BrackishMOT [34] dataset focuses on tracking schools of small fish and provides 98 video sequences captured in the wild. The Caltech fish counting dataset [23] consists of sonar videos, which makes it challenging for diverse species recognition. Similar to functional traits in our FishNet dataset, the NEWT dataset [41] offers functional attributes within broader domains such as behavior, age, and health. In contrast, FishNet places its emphasis on habitat-related functional traits, e.g., tropical area suitability. A notable distinction lies in the breadth of species categories covered: our FishNet dataset encompasses a significantly larger spectrum of categories compared to the NEWT dataset (17,000 vs. 183). We compare our FishNet dataset with other existing fish-related datasets and summarize the key differences in Table 1."
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+                                    "content": "we outline our dataset collection approach, including fish taxonomy construction, image and attribute collection, and detection annotation. To ensure the accuracy and consistency of our annotations, we implemented a quality control process during annotation collection. Finally, we present statistics of FishNet."
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+                                    "content": "The construction of fish taxonomy represents a critical preliminary step for the development of a fish recognition system. In order to facilitate the scientific and user-friendly utilization of our FishNet dataset, we constructed and organized the dataset in accordance with standard fish taxonomy protocols. To ensure the quality of the data and meet the ecological objectives, aquatic behavioral ecologists actively participated in this project and provided input on the design of the data collection for both taxonomical labels and functional traits. Initially, a comprehensive list of fish, amounting to approximately 35,024 distinct species, was sourced from FishBase [13]. Within FishBase, each individual fish is mapped to its respective position within the taxonomic hierarchy, consisting of taxonomic class, order, family, genus, and species. See Fig. 1 for a detailed structure of fish taxonomy."
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+                                    "content": "For each of the fish species in our taxonomic list, we collected available images from two key online databases, FishBase [13] and iNaturalist [21]. 51,433 images were scraped from FishBase using an updated version of the spiderfish package [37]. After we obtained the fish images from Fishbase [13], to ensure the quality and relevance of the data, we manually reviewed all the images and removed any instances that were not suitable for our analysis. This involved removing images that were not photographs of fish, such as images of fish sketches, coin images, stamp images, larval fish, and images of fish bone structures. By performing this manual filtering process, we were able to ensure that our dataset consisted only of high-quality images that were suitable for our research purposes. This process also helped to reduce the potential for errors or inaccuracies in our analysis, by removing any images that could introduce additional bias or noise into the data. Some of the removed instances are shown in Figure 3."
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+                                    "type": "text",
+                                    "content": "age library encompasses 94,805 images from 17,518 species. To facilitate model training and evaluation, we dropped 273 images whose families have less than 5 images. For each species in our dataset, we gathered information on 22 traits (90,147 images have traits), which we believe to be important indicators of ecological roles and nutritional properties. These traits include the true functional traits of trophic level, feeding pathway, and habitat preferences based on temperature and salinity. In addition, we also included nutritional content \"traits\" for calcium, iron, omega-3 fatty acid, protein, selenium, vitamin A, and zinc content [20]. Table 2 provides detailed descriptions of the ten true functional traits."
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+                                    "content": "3.3. Fish Detection Annotations"
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+                                    "content": "We employed the Amazon Mechanical Turk (AMT) [7] platform to collect bounding box annotations for all images in our dataset. Specifically, three independent annotators were tasked with providing locations for every instance in each image. To ensure accurate and reliable annotation of our image dataset, we have implemented a rigorous process for collecting annotations for object detection. Each image undergoes annotation by three different users on Amazon Mechanical Turk (AMT) [7]. We only accept annotations if all three users provide the same number of bounding boxes and if all the boxes have an Intersection over Union (IOU) value greater than 0.9. In cases where the annotations do not meet these criteria, we collect an additional annotation for the image and repeat the process of comparing the annotations reported by the different AMT users. We continue this process until we have at least three user annotations that agree with the number of bounding boxes and have an IOU greater than 0.9. For image categorization, we have already"
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+                                            "html": "<table><tr><td>Trait</td><td>Value</td><td>Description</td></tr><tr><td>Trophic level</td><td>Real value</td><td>The position in the food chain or food web.</td></tr><tr><td>Feeding path</td><td>Benthic/ Pelagic</td><td>Species feeds primarily from which trophic pathway.</td></tr><tr><td>Tropical</td><td>True/ False</td><td>Whether the fish can live in tropical areas.</td></tr><tr><td>Temperate</td><td>True/ False</td><td>Whether the fish can live in temperate areas.</td></tr><tr><td>Subtropical</td><td>True/ False</td><td>Whether the fish can live in subtropical areas.</td></tr><tr><td>Boreal</td><td>True/ False</td><td>Whether the fish can live in boreal areas.</td></tr><tr><td>Polar</td><td>True/ False</td><td>Whether the fish can live in polar areas.</td></tr><tr><td>Freshwater</td><td>True/ False</td><td>Whether the fish can live in freshwater.</td></tr><tr><td>Saltwater</td><td>True/ False</td><td>Whether the fish can live in saltwater.</td></tr><tr><td>Brackish</td><td>True/ False</td><td>Whether the fish can live in brackish.</td></tr></table>",
+                                            "image_path": "98ad127d560094a4526ee459e0158e3aeb72ca9f9f4812af7aaf4317bb691945.jpg"
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+                                    "type": "text",
+                                    "content": "Table 2. The explanation for 10 selected functional traits in the FishNet dataset. Please check the supplementary for the rest."
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+                                    "type": "text",
+                                    "content": "assigned labels to each image and asked users to select images that belong to a specific family by providing example images of that family. Through this meticulous process, we were able to calculate 114,375 object instances."
+                                }
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+                                    "content": "The FishNet dataset comprises a total of 94,532 images featuring 17,357 distinct species. The images were compiled"
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+                                            "html": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"4\">Family Classification (%)</td><td colspan=\"4\">Order Classification (%)</td></tr><tr><td>Common</td><td>Medium</td><td>Rare</td><td>All</td><td>Common</td><td>Medium</td><td>Rare</td><td>All</td></tr><tr><td>ResNet-34 [19]</td><td>77.16</td><td>69.10</td><td>36.65</td><td>40.82</td><td>83.42</td><td>77.87</td><td>47.36</td><td>52.07</td></tr><tr><td>ResNet-50 [19]</td><td>76.82</td><td>70.27</td><td>35.99</td><td>40.37</td><td>82.46</td><td>75.93</td><td>42.84</td><td>47.94</td></tr><tr><td>ResNet-101 [19]</td><td>75.73</td><td>69.00</td><td>31.61</td><td>36.38</td><td>81.35</td><td>75.01</td><td>42.32</td><td>47.36</td></tr><tr><td>ViT-S [10]</td><td>76.08</td><td>67.02</td><td>33.67</td><td>37.97</td><td>84.14</td><td>74.78</td><td>44.09</td><td>48.79</td></tr><tr><td>ViT-B [10]</td><td>82.93</td><td>74.50</td><td>38.26</td><td>42.91</td><td>88.52</td><td>81.64</td><td>52.44</td><td>56.93</td></tr><tr><td>ViT-L [10]</td><td>85.51</td><td>77.05</td><td>44.18</td><td>48.40</td><td>89.02</td><td>83.89</td><td>55.94</td><td>60.26</td></tr><tr><td>BeiT [1]</td><td>86.09</td><td>77.67</td><td>50.78</td><td>54.26</td><td>91.41</td><td>88.24</td><td>38.16</td><td>45.97</td></tr><tr><td>ConvNeXt* [27]</td><td>42.63</td><td>26.56</td><td>12.57</td><td>14.53</td><td>63.58</td><td>40.67</td><td>17.82</td><td>21.12</td></tr><tr><td>ConvNeXt [27]</td><td>90.32</td><td>85.13</td><td>57.03</td><td>60.61</td><td>94.07</td><td>90.49</td><td>64.84</td><td>68.81</td></tr><tr><td>ConvNeXt [27] + FL [25]</td><td>88.28</td><td>82.02</td><td>51.22</td><td>55.16</td><td>87.60</td><td>81.11</td><td>22.22</td><td>31.37</td></tr><tr><td>ConvNeXt [27] + CB [8]</td><td>90.53</td><td>84.80</td><td>57.94</td><td>61.38</td><td>93.15</td><td>90.56</td><td>71.41</td><td>74.38</td></tr><tr><td>ConvNeXt [27] + FL [25] + CB [8]</td><td>84.89</td><td>77.92</td><td>48.99</td><td>52.71</td><td>85.14</td><td>57.25</td><td>39.28</td><td>41.76</td></tr></table>",
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+                                    "content": "Table 3. Fish Family/Order classification accuracy. * denotes training from scratch, 'FL' denotes using focal loss during training, and 'CB' denotes using class-balanced training."
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+                                    "content": "from 8 taxonomic classes, 83 orders, 463 families, 3,826 genera, and 17,357 species, with each species having at least one image. We present the distribution of Orders within our dataset in Fig. 2. The figure displays the logarithmic frequency of each Order category, and it demonstrates a long-tail distribution within the FishNet dataset with respect to Order categories. We observed similar distribution for other taxonomy levels. In our FishNet dataset, each image in the dataset is accompanied by 22 functional traits. Additionally, the dataset includes instance-level bounding box annotations. In total, the FishNet dataset encompasses 114,375 object instances."
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+                                    "content": "Based on FishNet, we build three main challenges: 1) Fish classification. To identify family/order labels from input images; 2) Fish detection. Identifying the fish locations and family/order labels from input images; 3) Functional trait prediction. Predicting 10 functional traits from input images. For each challenge, we baseline several state-of-the-art models to show the capabilities of automatic fish identification and functional trait prediction using deep learning models. For all experiments, unless otherwise stated, we randomly select "
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+                                    "content": "4.1. Fish Classification"
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+                                    "content": "Benchmark settings. We conducted Family/Order classification using both ResNet-based and ViT-based architectures, including ResNets (ResNet-34, ResNet-50, ResNet101) [19], ViT (ViT-S, ViT-B, ViT-L) [10], BeiT [1], and ConvNeXt [27]. We replaced the classification head using"
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+                                    "content": "two fully connected (FC) layers, with a dropout of 0.5 for the first FC layer. For all comparing methods, the backbone networks were pretrained on ImageNet, and we finetuned the whole model using an Adam optimizer for 100 epochs. The initial learning rate was set to 3e-5, and 3e-4 for backbone networks and classification head, and we divided the learning rate by 2 every 20 epochs. In our experiments, we also explored recent techniques to address the long-tail classification problem. We explored focal loss [25] and class-balanced training [8] to improve the fish recognition performance in less frequent classes. Furthermore, we provided genus-level classification in the supplementary file."
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+                                    "content": "Class split. To capture the effect of the long-tailed nature of the FishNet dataset, the FishNet dataset was partitioned into three distinct subsets, namely common, medium, and rare categories, based on their respective class frequencies. To categorize the classes according to their frequencies, we established a criterion for the Family/Order categories. Specifically, we selected those categories with a proportional representation of "
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+                                    "content": " as rare classes. After splitting, we identified a total of 6, 52, and 405 common, medium, and rare family classes, respectively. In our experiments, we reported class-averaged accuracy for each split and also the overall accuracy among all splits."
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+                                            "html": "<table><tr><td rowspan=\"2\">Level</td><td rowspan=\"2\">Method</td><td colspan=\"5\">Common Classes/Medium Classes/Rare Classes</td><td colspan=\"5\">Average Per Class</td></tr><tr><td>\\( {mAP}_{50} \\)</td><td>\\( {mAP}_{60} \\)</td><td>\\( {mAP}_{70} \\)</td><td>\\( {mAP}_{80} \\)</td><td>\\( {mAP}_{90} \\)</td><td>\\( {mAP}_{50} \\)</td><td>\\( {mAP}_{60} \\)</td><td>\\( {mAP}_{70} \\)</td><td>\\( {mAP}_{80} \\)</td><td>\\( {mAP}_{90} \\)</td></tr><tr><td rowspan=\"2\">Order</td><td>YOLOF [5]</td><td>77.3/65.2/39.2</td><td>72.7/62.1/38.0</td><td>61.6/53.4/34.7</td><td>38.8/34.9/25.4</td><td>11.7/9.6/11.8</td><td>45.0</td><td>43.4</td><td>39.3</td><td>27.8</td><td>11.7</td></tr><tr><td>TOOD [11]</td><td>84.8/76.8/50.3</td><td>80.1/73.2/48.5</td><td>69.4/64.4/43.6</td><td>46.1/42.6/32.7</td><td>15.4/14.3/13.6</td><td>56.5</td><td>54.3</td><td>48.5</td><td>35.4</td><td>14.1</td></tr><tr><td rowspan=\"2\">Family</td><td>YOLOF [5]</td><td>67.2/53.1/27.1</td><td>64.0/50.4/26.6</td><td>54.9/43.3/24.4</td><td>35.5/27.3/18.8</td><td>9.9/7.9/7.7</td><td>30.6</td><td>29.8</td><td>26.9</td><td>20.0</td><td>7.8</td></tr><tr><td>TOOD [11]</td><td>81.1/64.0/22.5</td><td>77.1/60.1/21.9</td><td>66.5/51.2/20.1</td><td>44.0/32.8/15.7</td><td>14.5/10.9/7.7</td><td>27.9</td><td>26.9</td><td>24.2</td><td>18</td><td>8.2</td></tr></table>",
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+                                    "content": "Table 4. Fish detection performance on common, medium, and rare classes at the order and family taxonomic levels."
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+                                    "type": "text",
+                                    "content": "for rare classes was significantly worse than that for common classes, with an average classification accuracy of "
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+                                    "type": "text",
+                                    "content": " at the Family and Order levels, respectively. This is because these rare classes have insufficient annotations, which poses great challenges for fish classification recognition."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 51
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Fig. 4 visualizes selected classification results on the Family level using the ConvNeXt model. We showed both good cases in the first six columns and bad cases in the last two columns. Based on the results presented in Figure 4, it is evident that the ConvNeXt model is capable of accurately identifying the Family categories of input images, even when they exhibit significant variations in illumination and shape. However, there are some instances where the model failed to perform optimally. These failures are primarily attributed to factors such as low contrast, challenging view-angles, or visual similarities between different families. For example, arhynchobatidae, urolophidae, and dasyatidae belong to cartilaginous fish meaning skeletons are made of cartilage, have flattened bodies, and have a venomous spine on their tail, which can cause confusion for our classification models, as shown in the bottom right of the figure. More examples can"
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+                                    "type": "text",
+                                    "content": "be found in the supplementary file."
+                                }
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+                                    "content": "Effect of pretraining. We investigated the effect of using pretraining on the ImageNet dataset. By comparing the performance between ConvNeXt and ConvNeXt*, using ImageNet pretraining can significantly improve the fish classification performance on our FishNet dataset."
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+                                    "content": "Effect of balanced loss. From Table 4, using class-balanced loss can significantly improve classification performance, especially in rare classes; while using focal loss harms the performance. Specifically, for Order classification, using class-balanced loss improved the classification accuracy on rare classes from "
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+                                    "type": "text",
+                                    "content": ". We emphasize that there exist several other techniques that can be employed to mitigate long-tail classification problems, which may potentially yield superior results. Nonetheless, our focus in this experiment was not to maximize performance but rather to raise awareness of the long-tail issue with our FishNet dataset, thereby encouraging further investigations."
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+                                    "content": "4.2. Fish Detection"
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+                                    "content": "Benchmark settings. We conducted fish detection experiments using two well-known methods, YOLOF [5], and"
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+                                    "content": "TOOD [11] on our FishNet dataset. For both methods, the backbone networks are pretrained on MS-COCO [26], and we finetuned the whole model using the stochastic gradient descent (SGD) optimizer with a learning rate of 2.5e-4, a momentum of 0.9, and a weight decay of 0.0001 for 100 epochs. For performance evaluation, we reported performance on two splits according to the Family/Order distribution, including common, medium, and rare classes, that contain "
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+                                    "content": "Results. Table 4 shows the fish detection results at both the Family and Order levels. Our results demonstrated that for order-level classification, TOOD [11] outperformed YOLOF [5] in all the dataset splits. However, we observed that for family-level classification, YOLOF [5] exhibited better performance for Rare classes. Given the significantly higher number of Rare classes (405) as compared to Medium (52) and Common (6) classes, it is not surprising that the average Mean Average Precision (MAP) per class was lower for TOOD [11]. Therefore, we note that the evaluation of model performance can be influenced by the prevalence of different classes in the dataset, as shown in Table 4."
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+                                    "content": "Fig. 5 visualizes several examples of fish detection results obtained by the TOOD model [11]. The model has proven successful in detecting fish from various species, with different scales, orientations, and backgrounds. However, the TOOD model may struggle to predict family labels for less frequent classes or those with low contrast. We provide more examples in the supplementary file."
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+                                    "content": "Benchmark settings. In this section, we explored using deep learning models to predict fish functional traits based on input images. We tried ten functional traits in our experi-"
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+                                            "html": "<table><tr><td rowspan=\"2\">Backbone</td><td colspan=\"2\">Seen (%)</td><td colspan=\"2\">Unseen (%)</td></tr><tr><td>F1/Acc.</td><td>Acc-all</td><td>F1/Acc.</td><td>Acc-all</td></tr><tr><td>ResNet-34 [19]</td><td>74.83 / 87.20</td><td>40.04</td><td>54.38 / 78.48</td><td>15.84</td></tr><tr><td>ResNet-50 [19]</td><td>71.80 / 84.52</td><td>30.85</td><td>53.52 / 76.71</td><td>13.92</td></tr><tr><td>ResNet-101 [19]</td><td>73.80 / 85.67</td><td>34.45</td><td>54.37 / 77.47</td><td>15.12</td></tr><tr><td>ViT-S [10]</td><td>75.25 / 86.86</td><td>38.62</td><td>54.62 / 78.99</td><td>16.94</td></tr><tr><td>ViT-B [10]</td><td>78.65 / 88.94</td><td>46.91</td><td>55.72 / 79.93</td><td>18.44</td></tr><tr><td>ViT-L [10]</td><td>81.72 / 90.45</td><td>54.00</td><td>55.94 / 80.23</td><td>18.80</td></tr><tr><td>BeiT [1]</td><td>78.15 / 88.93</td><td>49.97</td><td>54.60 / 78.82</td><td>17.26</td></tr><tr><td>ConvNeXt [27]</td><td>83.30 / 91.03</td><td>54.80</td><td>56.34 / 79.50</td><td>18.00</td></tr></table>",
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+                                    "content": "Table 5. Habitat Classification performance in supervised and zero-shot settings."
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+                                    "content": "ments, namely trophic level, feeding path, and presence or absence in the following temperature and salinity zonations: tropical, temperate, subtropical, boreal, polar, freshwater, saltwater, and brackish. We used the same network architectures and training strategies as Section 4.1. For evaluating trophic level regression, we reported Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). For habitat classification, we used the average F1 score and overall accuracy to evaluate the performance. Additionally, we calculated the classification-all metric, which reflects the model's ability to accurately predict all functional traits simultaneously."
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+                                    "content": "Trophic level Regression. In our experiments, we found that different models showed similar performance for trophic level prediction, with an MAE of 0.45 and an RMSE of 0.60, respectively. We found that trophic level prediction is a challenging task when using common L1 or L2 loss functions. More advanced techniques, such as ordinal regression [14], could potentially remedy this challenge. However, we leave this for further research."
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+                                    "content": "Habitat Classification Results. Table 5 shows the classification results for nine fish functional traits. Overall, the larger models outperformed the smaller ones. Specifically, the ConvNeXt model achieved the best results with an average f1-score of "
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+                                    "content": ". We also reported the classification accuracy when our model correctly predicts all nine functional traits simultaneously, marked as \"Acc-all\". It was surprising that the best-performing ConvNeXt model obtained an accuracy-all of "
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+                                    "content": " for correctly predicting all classes simultaneously. Fig. 6 shows selected examples of functional trait classification using the ConvNeXt model. From the figure, we can see that the ConvNeXt model can successfully predict most of the functional traits with large color and structure variations. In addition, Table 6 provides a detailed breakdown of the per-trait classification performance of the ConvNeXt model. The results show that the model achieved an f1-score of over "
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+                                    "content": " for four out of nine functional traits. However, the"
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+                                            "html": "<table><tr><td>Metric</td><td>FeedingPath</td><td>Tropical</td><td>Temperate</td><td>Subtropical</td><td>Boreal</td><td>Polar</td><td>Freshwater</td><td>Saltwater</td><td>Brackish</td><td>Avg.</td></tr><tr><td>Acc.</td><td>84.73</td><td>88.64</td><td>84.41</td><td>90.95</td><td>92.88</td><td>96.88</td><td>91.98</td><td>93.10</td><td>90.51</td><td>90.45</td></tr><tr><td>F1</td><td>68.07</td><td>92.97</td><td>88.03</td><td>94.49</td><td>76.99</td><td>59.91</td><td>91.02</td><td>95.59</td><td>68.40</td><td>81.72</td></tr></table>",
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+                                    "content": "Table 6. Per-trait classification performance. For each trait, we report both the F1 score (%) and classification accuracy (%)"
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+                                    "content": "model obtains less impressive performance for feeding path and polar classification."
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+                                    "content": "Zero-shot Habitat Classification. We further evaluated the habitat classification performance in a zero-shot setting, where we evaluated habitat classification on unseen classes, which were not never seen during training. To achieve this, we trained the ConvNeXt model on 58 common and medium classes (according to their family classes) and evaluated the performance on 405 rare classes. From Table 5, although zero-shot habitat classification performance is worse than the supervised setting, the best-performed ViT-L model still shows a reasonable performance for zero-shot habitat classification, with a classification accuracy of "
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+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": " on accuracy and accuracy-all. This demonstration showcases the capacity of the deep learning model to predict the functional traits of previously unseen species, thereby establishing a valuable tool for the discovery of new species."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+                                    "type": "text",
+                                    "content": "5. Conclusions and Future Work"
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+                                    "type": "text",
+                                    "content": "This work presents FishNet, a large-scale diverse dataset consisting of 94,532 images from 17,357 species organized based on the scientific classification of aquatic species. The dataset is accompanied by 114,375 manually labeled bounding box annotations and 22 functional trait information. Fur"
+                                }
+                            ]
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+                    "index": 14
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+                {
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+                                    "type": "text",
+                                    "content": "thermore, we establish three benchmarks, namely fish classification, fish detection, and functional trait prediction, to facilitate the advancement of aquatic species recognition and promote further research in the field of aquatic ecology. The experimental results demonstrate that accurate fish recognition and functional trait prediction are still challenging due to several factors, such as large species diversity, diverse backgrounds, low contrast, etc."
+                                }
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+                                    "content": "We release our data and associated code to encourage further research in developing more accurate and effective tools for monitoring and protecting aquatic ecosystems. Our FishNet dataset will also encourage research into evaluating the impact of climate change on aquatic ecosystems and identifying potential solutions to help maintain the health and resilience of aquatic ecosystems and contribute to mitigating the impacts of climate change."
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+                                    "content": "6. Acknowledgements"
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+                        }
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+                                    "content": "We would like to thank Jun Chen and Habib Slim for providing their suggestions and Cameron Trotter for updating the spiderfish package to facilitate image collection from FishBase. This work is supported by KAUST, under Award No. BAS/1/1685-01-01. AJT is supported by KAUST Global Fellowship Program under Award No. ORA-2022-5001."
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+[
+    {
+        "type": "text",
+        "text": "Flatness-Aware Minimization for Domain Generalization",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Xingxuan Zhang, Renzhe Xu, Han Yu, Yancheng Dong, Pengfei Tian, Peng Cui*  \nDepartment of Computer Science, Tsinghua University",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "xingxuanzhang@hotmail.com, cuip@tsinghua.edu.cn",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
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+            268,
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+            284
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Domain generalization (DG) seeks to learn robust models that generalize well under unknown distribution shifts. As a critical aspect of DG, optimizer selection has not been explored in depth. Currently, most DG methods follow the widely used benchmark, DomainBed, and utilize Adam as the default optimizer for all datasets. However, we reveal that Adam is not necessarily the optimal choice for the majority of current DG methods and datasets. Based on the perspective of loss landscape flatness, we propose a novel approach, Flatness-Aware Minimization for Domain Generalization (FAD), which can efficiently optimize both zeroth-order and first-order flatness simultaneously for DG. We provide theoretical analyses of the FAD's out-of-distribution (OOD) generalization error and convergence. Our experimental results demonstrate the superiority of FAD on various DG datasets.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Current neural networks are expected to generalize to unseen distributions in real-world applications, which can break the independent and identically distributional (I.I.D.) assumption of traditional machine learning algorithms [129, 99]. The distribution shift between training and test data may largely deteriorate most current approaches in practice. Hence, instead of generalization within the training distribution, the ability to generalize under distribution shift, namely domain generalization (DG) [73], has attracted increasing attention [99].",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Various methods have been proposed to address the DG problem recently, many of which have shown promising performance. As a learning problem mainly in the computer vision field, the DG task relies highly on the chosen optimizer, yet the effect of the optimizer in DG has hardly been studied. Most current algorithms, following the well-known benchmark DomainBed [32], default to optimize",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/b3b3023209032dd977e3fc44859670cf2826821717b98e850f898aaa2b370cf0.jpg",
+        "image_caption": [
+            "Figure 1. Test accuracy on PACS and DomainNet of different optimizers. Adam, the default optimizer in popular benchmarks shows no advantage compared with its counterparts, while the proposed FAD achieve better OOD generalization performance compared with current optimizers."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "models with Adam [48] without considering other optimizers. However, the in-distribution generalization ability of popular optimizers has been investigated from the perspective of loss landscape recently [28, 29] and Adam is found to achieve inferior generalization compared with other optimizers such as SGD [76] due to the sharp minima Adam selected. Thus, investigating the impact of optimizers in DG and clarifying whether Adam should be considered as the default optimizer is of significance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we empirically compare the performance of current optimizers, including Adam, SGD, AdaBelief [131], YOGI [117], AdaHessian [116], SAM [28], and GAM[121]. Through extensive experiments on current DG benchmarks, we show that Adam can hardly surpass other optimizers on most DG datasets. The best choice of the optimizer for different DG methods varies across different datasets, and choosing the right optimizer can help exceed the current leaderboards' limitations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recently, the connection between the flatness of the loss landscape and in-distribution generalization ability has been widely studied and verified both theoretically[130] and empirically[25]. Some works [13, 87] show that flatness also leads to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach.",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "5189",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Among flatness-aware optimization methods, sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 126, 47], which optimize the zeroth-order flatness, achieve SOTA performance on various in-distribution image classification tasks [53, 130]. Most recently, Gradient Norm Aware Minimization (GAM) [121] shows that minimizing the first-order flatness provides a more substantial penalty on the sharpness of minima than zeroth-order flatness yet requires more computation overhead. Due to the first-order Taylor expansions adopted to optimize zeroth-order and first-order flatness, both SAM and GAM lose some of their penalty strength, and thus they can be mutually reinforced by each other. To accelerate the optimization of first-order flatness and combine zero-order flatness, we propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), which eliminates the considerable computation overhead for Hessian or Hessian-vector products. We theoretically show that the proposed FAD controls the dominant eigenvalue of Hessian of the training loss, which indicates the sharpness of the loss landscape along its most critical direction [42]. We present an OOD generalization bound to show that the proposed FAD guarantees the generalization error on test data and convergence analysis. Through extensive experiments, we evaluate FAD and other optimizers on various DG benchmarks.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We summarize the main contribution as follows.",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- We propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness simultaneously. Without calculating Hessian and Hessian-vector products, FAD considerably reduces the computation overhead of first-order flatness.",
+            "- We theoretically analyze the OOD generalization error and convergence of FAD. We show that FAD controls the dominant eigenvalue of Hessian and thus the flatness of learned minima.",
+            "- We empirically show that Adam, the default optimizer for most current DG benchmarks, can hardly be the optimal choice for most DG datasets. We present the superiority of FAD compared with current optimizers through extensive experiments.",
+            "- We empirically validate that FAD finds flatter optima with lower Hessian spectra compared with zeroth- and first-order flatness-aware optimization methods."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2.1. Optimizers",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Some works [107, 28] have studied the connection between current optimization approaches, such as SGD [76], Adam [49], AdamW [65] and others [26, 63] and in-distribution generalization. Some literature shows that",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Adam is more vulnerable to sharp minima than SGD [104], which may result in worse generalization [106, 33, 35]. Some follow-ups [66, 16, 107, 117] propose generalizable optimizers to address this problem. However, the generalization ability and convergence speed is often a trade-off [44, 107, 63, 117, 26]. Different optimizers may favor different tasks and network architectures (e.g., SGD is often chosen for ResNet [34] while AdamW [65] for ViTs [21]). Selecting the right optimizer is critical for performance and convergence while the understanding of its relationship to model generalization remains nascent [28]. [74] finds that fine-tuned SGD outperforms Adam on OOD tasks. Yet all the previous works do not consider the effect of optimizers in current DG benchmarks and evaluation protocols. In this paper, we discuss the selection of the default optimizer in DG benchmarks.",
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+    {
+        "type": "text",
+        "text": "2.2. Domain Generalization and Optimization",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Domain generalization (DG) aims to improve the generalization ability to novel domains [31, 45, 50]. A common approach is to learn domain-invariant or causal features over multiple source domains [22, 36, 57, 59, 72, 80, 89, 120, 110, 118, 101, 123] or aggregating domain-specific modules [67, 68]. Some works propose to enlarge the input space by augmentation of training data [12, 98, 81, 91, 127, 128, 109]. Exploit regularization with meta-learning [22, 58] and Invariant Risk Minimization (IRM) framework [2] are also proposed for DG. Recently, several works propose to ensemble model weights for better generalization [13, 4, 84, 105, 86, 62, 18] and achieve outstanding performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.3. Flatness of loss landscape",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recent works study the relationship between flatter minima lead and better generalization on in-distribution data [44, 130, 41, 79]. [42] reviews the literature related to generalization and the sharpness of minima. It highlights the role of maximum Hessian eigenvalue in deciding the sharpness of minima [44, 103]. Some simple strategies are proposed to optimize maximum Hessian eigenvalue, such as choosing a large learning rate [54, 19, 40] and smaller batch size [94, 54, 39]. Sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 24, 64, 25, 71, 126, 47, 46], which are representative training algorithms to seek zeroth-order flatness, show outstanding performance on indistribution generalization. Most recently, several works discuss the relationship between generalization and gradient norm [8, 125]. GAM[121] proposes to optimize first-order flatness for better generalization. [13, 87] show that flatness minima also lead to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach.",
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+    {
+        "type": "page_number",
+        "text": "5190",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In in-distribution generalization tasks, sharpness-aware optimization methods show outstanding performance [28]. We theoretically show that optimizing both zeroth-order and first-order flatness strengthens out-of-distribution performance via a generalization bound. We propose a unified optimization framework to optimize zeroth-order and first-order flatness effectively and efficiently. We present the connection between Hessian spectra and our regularization term and give the convergence analysis of our method.",
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+        "type": "text",
+        "text": "Notations We use  $\\mathcal{X}$  and  $\\mathcal{Y}$  to denote the space of input  $X$  and outcome  $Y$ , respectively. We use  $\\Delta_{\\mathcal{Y}}$  to denote a distribution on  $\\mathcal{Y}$ . Let  $S = \\{(x_i, y_i)\\}_{i=1}^n$  denote the training dataset with  $n$  data-points drawn independently from the training distribution  $\\mathcal{D}_{\\mathrm{tr}}$ . We consider the covariate shift scenario [10, 92, 111] and assume that the conditional probabilities are invariant across training and test distributions (i.e.,  $P_{\\mathrm{tr}}(Y|X) = P_{\\mathrm{te}}(Y|X)$ ). The invariant conditional probability is denoted as  $P(Y|X)$ . A prediction model  $f_{\\theta}: \\mathcal{X} \\to \\Delta_{\\mathcal{Y}}$  parametrized by  $\\theta \\in \\Theta \\subseteq \\mathbb{R}^d$  with dimension  $d$  maps an input to a simplex on  $\\mathcal{Y}$ , which indicates the predicted probability of each class<sup>1</sup>.  $\\Theta$  is the hypothesis set. We further assume that the ground truth model  $\\theta^*$  that characterizes  $P(Y|X)$  is in the hypothesis set  $\\Theta$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Let  $\\ell: \\Delta_{\\mathcal{Y}} \\times \\Delta_{\\mathcal{Y}} \\to \\mathbb{R}_{+}$  define a loss function over  $\\Delta_{\\mathcal{Y}}$ . For any hypotheses  $\\theta_1, \\theta_2 \\in \\Theta$ , the expected loss  $\\mathcal{L}_{\\mathcal{D}}(\\theta_1, \\theta_2)$  for distribution  $\\mathcal{D}$  is given as  $\\mathcal{L}_{\\mathcal{D}}(\\theta_1, \\theta_2) = \\mathbb{E}_{x \\sim \\mathcal{D}}[\\ell(f_{\\theta_1}(x), f_{\\theta_2}(x))]$ . To simplify the notations, we use  $\\mathcal{L}_{\\mathrm{tr}}$  and  $\\mathcal{L}_{\\mathrm{te}}$  to denote the expected loss  $\\mathcal{L}_{\\mathcal{D}_{\\mathrm{tr}}}$  and  $\\mathcal{L}_{\\mathcal{D}_{\\mathrm{te}}}$  in training and test distributions, respectively. In addition, we use  $\\mathcal{E}_{\\mathrm{tr}}(\\pmb{\\theta}) = \\mathcal{L}_{\\mathrm{tr}}(\\pmb{\\theta}, \\pmb{\\theta}^*)$  and  $\\mathcal{E}_{\\mathrm{te}}(\\pmb{\\theta}) = \\mathcal{L}_{\\mathrm{te}}(\\pmb{\\theta}, \\pmb{\\theta}^*)$  to denote the loss of a function  $\\pmb{\\theta} \\in \\Theta$  w.r.t. the true labeling function  $\\pmb{\\theta}^*$  in the two distributions. We use  $\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})$  to denote the empirical loss function w.r.t. the  $n$  samples  $S$  from the training distribution. In addition, we assume that  $\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})$  is twice differentiable throughout the paper and we use  $\\nabla \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})$  and  $\\nabla^2 \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})$  to denote the derivative and Hessian matrix, respectively.",
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+    {
+        "type": "text",
+        "text": "3.1. A General Flatness-Aware Optimization for DG",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In in-distribution generalization tasks, it is shown that the zeroth-order flatness can be not strong enough in cases where  $\\rho$  covers multiple minima or the maximum loss in  $\\rho$  is misaligned with the uptrend of loss and first-order flatness can help improve it [121]. But both zeroth-order and first-order flatness require first-order approximations in practice. Thus optimizing both zeroth-order and first-order flatness together leads to stronger generalization than both of them",
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+    {
+        "type": "text",
+        "text": "[121]. Yet optimizing first-order flatness requires the calculation of Hessian or Hessian-vector products, which introduces heavy computation overhead. As a result, we aim to accelerate the optimization in a Hessian-free way for OOD generalization.",
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+    {
+        "type": "text",
+        "text": "Formally, the zeroth-order and first-order flatness are defined as follows [28, 130, 121].",
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+    {
+        "type": "text",
+        "text": "Definition 3.1 ( $\\rho$ -zeroth-order flatness). For any  $\\rho > 0$ , the  $\\rho$ -zeroth-order flatness  $R_{\\rho}^{(0)}(\\pmb{\\theta})$  of function  $\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})$  at a point  $\\pmb{\\theta}$  is defined as",
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+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {\\rho} ^ {(0)} (\\boldsymbol {\\theta}) \\triangleq \\max  _ {\\boldsymbol {\\theta} ^ {\\prime} \\in B (\\boldsymbol {\\theta}, \\rho)} \\left(\\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {\\prime}\\right) - \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta})\\right), \\quad \\forall \\boldsymbol {\\theta} \\in \\Theta . \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Here  $\\rho$  is the perturbation radius that controls the magnitude of the neighborhood.",
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+    {
+        "type": "text",
+        "text": "Definition 3.2 ( $\\rho$ -first-order flatness). For any  $\\rho > 0$ , the  $\\rho$ -first-order flatness  $R_{\\rho}^{(1)}(\\theta)$  of function  $\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\theta)$  at a point  $\\theta$  is defined as",
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+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {\\rho} ^ {(1)} (\\boldsymbol {\\theta}) \\triangleq \\rho \\cdot \\max  _ {\\boldsymbol {\\theta} ^ {\\prime} \\in B (\\boldsymbol {\\theta}, \\rho)} \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {\\prime}\\right) \\right\\|, \\quad \\forall \\boldsymbol {\\theta} \\in \\Theta . \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Here  $\\rho$  is the perturbation radius similar to Definition 3.1.",
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+    {
+        "type": "text",
+        "text": "Based on these definitions, we propose to jointly optimize zeroth-order and first-order flatness through the following linear combination of the two flatness metrics.",
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+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} (\\boldsymbol {\\theta}) = \\alpha R _ {\\rho} ^ {(0)} (\\boldsymbol {\\theta}) + (1 - \\alpha) R _ {\\rho} ^ {(1)} (\\boldsymbol {\\theta}), \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\alpha$  is a hyper-parameter that controls the trade-off between zeroth-order and first-order flatness. Since both flatness are related to the maximal eigenvalue of the Hessian matrices [130, 121], we can derive that  $R_{\\rho ,\\alpha}^{\\mathrm{FAD}}(\\pmb {\\theta})$  is also related to the maximal eigenvalue. Specifically, when a point  $\\pmb{\\theta}^{*}$  is a local minimum of  $\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta})$  and  $\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta})$  can be second-order Taylor approximated in the neighbourhood of  $\\pmb{\\theta}^{*}$ , then",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\lambda_ {\\max } \\left(\\nabla^ {2} \\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {*}\\right)\\right) = \\frac {R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} \\left(\\boldsymbol {\\theta} ^ {*}\\right)}{\\rho^ {2} \\left(1 - \\frac {\\alpha}{2}\\right)}. \\tag {4}\n$$\n",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "See Appendix A for details. Since the maximal eigenvalue is a proper measure of the curvature of minima [42, 43] and related to generalization abilities [121, 17, 39], optimizing Equation (3) would hopefully improve the DG performances, which we demonstrate in Section 3.2.",
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+        "type": "text",
+        "text": "Then the overall objective of our method, Flatness-Aware minimization for Domain generalization (FAD), is as follows.",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {a l l}} (\\boldsymbol {\\theta}) = \\hat {\\mathcal {E}} _ {\\text {t r}} (\\boldsymbol {\\theta}) + \\beta \\cdot R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} (\\boldsymbol {\\theta}). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            839,
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+            859
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The strength of FAD regularization is controlled by a hyperparameter  $\\beta$ .",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>We use  $\\Delta y$  to denote the non-deterministic function case. This formulation also includes deterministic function cases.",
+        "bbox": [
+            76,
+            875,
+            468,
+            898
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "5191",
+        "bbox": [
+            480,
+            926,
+            513,
+            936
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Flatness Penalty and DG Performance",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            406,
+            107
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We give a generalization bound to demonstrate that FAD controls the generalization error on test distribution as follows.",
+        "bbox": [
+            76,
+            113,
+            468,
+            157
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proposition 3.1. Suppose the per-data-point loss function  $\\ell$  is differentiable, symmetric, bounded by  $M$ , and obeys the triangle inequality. Suppose  $\\pmb{\\theta}^{*}\\in \\Theta$ . Fix  $\\rho >0$  and  $\\pmb {\\theta}\\in \\Theta$ . Then with probability at least  $1 - \\delta$  over training set  $S$  generated from the distribution  $\\mathcal{D}$",
+        "bbox": [
+            76,
+            166,
+            468,
+            242
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\epsilon_ {i} \\sim N (0, \\rho^ {2} / (\\sqrt {d} + \\sqrt {\\log n}) ^ {2})} \\left[ \\mathcal {E} _ {t e} (\\boldsymbol {\\theta} + \\boldsymbol {\\epsilon}) \\right] \\\\ \\leq \\hat {\\mathcal {E}} _ {t r} (\\boldsymbol {\\theta}) + R _ {\\rho , \\alpha} ^ {E A D} (\\boldsymbol {\\theta}) \\\\ + \\sup  _ {\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2} \\in \\Theta} | \\mathcal {L} _ {t r} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}) - \\mathcal {L} _ {t e} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}) | + \\frac {M}{\\sqrt {n}} \\\\ + \\sqrt {\\frac {\\frac {1}{4} d \\log \\left(1 + \\frac {\\| \\theta \\| ^ {2} (\\sqrt {d} + \\sqrt {\\log n}) ^ {2}}{d \\rho^ {2}}\\right) + \\frac {1}{4} + \\log \\frac {n}{\\delta} + 2 \\log (6 n + 3 d)}{n - 1}} \\tag {6} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            80,
+            250,
+            501,
+            383
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Remark. The term  $\\sup_{\\theta_1, \\theta_2 \\in \\Theta} |\\cdot|$  corresponds to the discrepancy distance [69], which measures the covariate shift between the training domain and the unknown test domain. Please note that in DG/OOD generalization tasks, the information on test distribution is unavailable in the optimization phase. Thus one cannot intervene in the third term on RHS. Thus optimizing the regularization of FAD (the second term on RHS) with ERM loss on training data leads to better generalization on test data.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Algorithm Details",
+        "text_level": 1,
+        "bbox": [
+            76,
+            532,
+            251,
+            549
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Although the regularization of FAD controls the OOD generalization error, directly optimizing it suffers from significant computational costs. Previous works [114, 121] propose to calculate second order gradient with Hessian-vector product, yet the cost increases fast as the model dimension grows. Inspired by [93, 125], we approximate second-order gradient with first-order gradients and optimize zeroth-order and first-order flatness simultaneously as follows.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Optimization and acceleration At each round, suppose the perturbation radius is set to  $\\rho_{t}$ , then the gradient of  $\\mathcal{L}_{\\mathrm{all}}(\\pmb{\\theta}_t)$  at the point  $\\pmb{\\theta}_t$  in Equation (5) is approximated as follows.",
+        "bbox": [
+            76,
+            710,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The gradient of  $R_{\\rho_t}^{(0)}(\\pmb {\\theta}_t)$  . Following [28], let",
+        "bbox": [
+            76,
+            768,
+            377,
+            787
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\tilde {\\boldsymbol {\\theta}} _ {t, 1} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\boldsymbol {g} _ {t , 0}}{\\| \\boldsymbol {g} _ {t , 0} \\|} \\quad \\text {w h e r e} \\quad \\boldsymbol {g} _ {t, 0} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}), \\tag {7} \\\\ \\boldsymbol {g} _ {t, 1} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 1}). \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            796,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Then the gradient of  $R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)$  is approximated by",
+        "bbox": [
+            76,
+            858,
+            406,
+            877
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla R _ {\\rho_ {t}} ^ {(0)} \\left(\\boldsymbol {\\theta} _ {t}\\right) \\approx \\boldsymbol {g} _ {t, 1} - \\boldsymbol {g} _ {t, 0}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            883,
+            468,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Flatness-Aware Minimization for Domain Generalization (FAD)"
+        ],
+        "code_body": "1: Input: Batch size  $b$ , Learning rate  $\\eta_t$ , Perturbation radius  $\\rho_t$ , Trade-off coefficients  $\\alpha$ ,  $\\beta$ , Small constant  $\\xi$   \n2:  $t \\gets 0$ ,  $\\theta_0 \\gets$  initial parameters  \n3: while  $\\theta_t$  not converged do  \n4: Sample  $W_t$  from the training data with  $b$  instances  \n5:  $g_{t,0} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\theta_t)$   \n6:  $\\tilde{\\pmb{\\theta}}_{t,1} \\gets \\pmb{\\theta}_t + \\rho_t \\cdot \\pmb{g}_{t,0} / (\\| \\pmb{g}_{t,0} \\| + \\xi)$   \n7:  $g_{t,1} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,1})$   \n8:  $h_{t,0} \\gets g_{t,1} - g_{t,0}$  gradient of  $R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)$   \n9:  $\\tilde{\\pmb{\\theta}}_{t,2} \\gets \\pmb{\\theta}_t + \\rho_t \\cdot h_{t,0} / (\\| h_{t,0} \\| + \\xi)$   \n10:  $g_{t,2} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,2})$   \n11:  $\\tilde{\\pmb{\\theta}}_{t,3} \\gets \\tilde{\\pmb{\\theta}}_{t,2} + \\rho_t \\cdot g_{t,2} / (\\| g_{t,2} \\| + \\xi)$   \n12:  $g_{t,3} = \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,3})$   \n13:  $h_{t,1} \\gets g_{t,3} - g_{t,2}$  gradient of  $R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)$   \n14:  $\\pmb{\\theta}_{t+1} \\gets \\pmb{\\theta}_t - \\eta_t(g_{t,0} + \\beta (\\alpha h_{t,0} + (1 - \\alpha) h_{t,1}))$   \n15:  $t \\gets t + 1$   \n16: end while  \n17: return  $\\pmb{\\theta}_t$",
+        "bbox": [
+            506,
+            123,
+            890,
+            421
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The gradient of  $R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)$ . [121] propose to approximate the gradient through the following procedure",
+        "bbox": [
+            500,
+            448,
+            890,
+            481
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla R _ {\\rho_ {t}} ^ {(1)} (\\boldsymbol {\\theta} _ {t}) \\approx \\rho_ {t} \\cdot \\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t} ^ {\\mathrm {a d v}}) \\right\\|, \\boldsymbol {\\theta} _ {t} ^ {\\mathrm {a d v}} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\right\\|}{\\left\\| \\nabla \\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\| \\right\\|}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            491,
+            905,
+            541
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "One can approximate  $\\nabla \\| \\nabla \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta}_t)\\|$  with first-order gradient as follows.",
+        "bbox": [
+            500,
+            551,
+            890,
+            582
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\right\\| \\approx \\frac {\\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t , 1}) - \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t})}{\\rho_ {t}} = \\frac {\\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0}}{\\rho_ {t}},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            509,
+            593,
+            879,
+            628
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Thus we can approximate the gradient of  $R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)$  efficiently and rewrite the term as follows. The details of the derivation can be found in Appendix A.",
+        "bbox": [
+            498,
+            642,
+            890,
+            690
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla R _ {\\rho_ {t}} ^ {(1)} (\\boldsymbol {\\theta} _ {t}) \\approx \\boldsymbol {g} _ {t, 3} - \\boldsymbol {g} _ {t, 2}, \\quad \\text {w h e r e}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            702,
+            735,
+            722
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\boldsymbol {\\theta}} _ {t, 2} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0}}{\\| \\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0} \\|}, \\quad \\boldsymbol {g} _ {t, 2} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 2}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            547,
+            724,
+            893,
+            756
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\boldsymbol {\\theta}} _ {t, 3} = \\tilde {\\boldsymbol {\\theta}} _ {t, 2} + \\rho_ {t} \\frac {\\boldsymbol {g} _ {t , 2}}{\\| \\boldsymbol {g} _ {t , 2} \\|}, \\quad \\boldsymbol {g} _ {t, 3} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 3}). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            547,
+            758,
+            890,
+            801
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Please note that the terms  $\\pmb{g}_{t,1}$  and  $\\pmb{g}_{t,1}$  for optimizing zeroth-order flatness  $R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)$  are preserved in the approximation of  $R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)$  and thus causes no overhead. Combining the gradient approximation steps as shown in Equations (8) and (9), we can obtain the unified optimization framework as shown in Algorithm 1.",
+        "bbox": [
+            500,
+            803,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5192",
+        "bbox": [
+            480,
+            924,
+            514,
+            936
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Convergence analysis To analyze the convergence property of Algorithm 1, we first introduce the Lipschitz smooth assumption that are adopted commonly in optimization-related literature [1, 112, 130].",
+        "bbox": [
+            75,
+            90,
+            468,
+            151
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Definition 3.3. For a function  $J:\\Theta \\to \\mathbb{R}$ ,  $J$  is  $\\gamma_{2}$ -Lipschitz smooth if",
+        "bbox": [
+            75,
+            157,
+            468,
+            188
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\forall \\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2} \\in \\Theta , \\| \\nabla J (\\boldsymbol {\\theta} _ {1}) - \\nabla J (\\boldsymbol {\\theta} _ {2}) \\| \\leq \\gamma_ {2} \\| \\boldsymbol {\\theta} _ {1} - \\boldsymbol {\\theta} _ {2} \\|. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            83,
+            194,
+            467,
+            212
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\pmb{\\Delta}_{t} = \\pmb{g}_{t,0} + \\beta (\\alpha \\pmb{h}_{t,0} + (1 - \\alpha)\\pmb{h}_{t,1})$  be the estimated gradient at round  $t$  as shown in Line 14 in Algorithm 1. Now we can prove that the algorithm would eventually converge by the following theorem.",
+        "bbox": [
+            75,
+            217,
+            467,
+            277
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Theorem 3.2. Suppose  $\\hat{\\mathcal{E}}_{tr}(\\pmb{\\theta})$  is  $\\gamma$ -Lipschitz smooth and bounded by  $M$ . For any timestamp  $t \\in \\{0,1,\\dots,T\\}$  and any  $\\pmb{\\theta} \\in \\Theta$ , suppose we can obtain noisy and bounded observations  $f_t(\\pmb{\\theta})$  of  $\\nabla \\hat{\\mathcal{E}}_{tr}(\\pmb{\\theta})$  such that",
+        "bbox": [
+            75,
+            282,
+            468,
+            345
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} \\left[ f _ {t} (\\boldsymbol {\\theta}) \\right] = \\nabla \\hat {\\mathcal {E}} _ {t r} (\\boldsymbol {\\theta}), \\| f _ {t} (\\boldsymbol {\\theta}) \\| \\leq G. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            145,
+            349,
+            467,
+            368
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then with learning rate  $\\eta_t = \\eta_0 / \\sqrt{t}$  and perturbation radius  $\\rho_t = \\rho_0 / \\sqrt{t}$ ,",
+        "bbox": [
+            75,
+            375,
+            467,
+            405
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sum_ {t = 1} ^ {T} \\mathbb {E} \\left[ \\| \\boldsymbol {\\Delta} _ {t} \\| ^ {2} \\right] \\leq \\frac {C _ {1} + C _ {2} \\log T}{\\sqrt {T}}, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            155,
+            411,
+            467,
+            452
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "for some constants  $C_1$  and  $C_2$  that only depend on  $\\gamma_1, \\gamma_2, G, M, \\eta_0, \\rho_0, \\alpha, \\beta$ .",
+        "bbox": [
+            73,
+            457,
+            467,
+            488
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Thus, the convergence of FAD is guaranteed, and we show FAD's convergence rate empirically in Section 4.4.",
+        "bbox": [
+            75,
+            493,
+            467,
+            523
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            75,
+            535,
+            207,
+            551
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
+            75,
+            560,
+            282,
+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our optimization method and current optimizers on various DG benchmarks including PACS [55], VLCS [27], OfficeHome [97], TerraIncognita [9], DomainNet [78] and  $\\mathrm{NICO + + }$  [122]. Detailed introductions of these datasets are in Appendix. We consider the generalization accuracy, training time, and hessian spectra of found minima as the evaluation metrics. We show how optimizers contribute when training with ERM and current SOTA DG algorithms. Generally, Adam is hardly the best choice for DG benchmarks.",
+        "bbox": [
+            75,
+            583,
+            467,
+            733
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For a fair comparison, we follow the basic training and evaluation protocol introduced in [32], where the information of test data is unavailable for hyperparameter search. We train all the models on DomainNet for 15,000 iterations as suggested in [13], 10,000 iterations on  $\\mathrm{NICO + + }$  ,and 5,000 iterations on other datasets unless otherwise noted. For datasets except for  $\\mathrm{NICO + + }$  , we follow the leave-oneout protocol in [32] where one domain is chosen as the target domain and the remaining domains as the training domain. For  $\\mathrm{NICO + + }$  , we choose two domains as target domains in each run and train models on the remaining four",
+        "bbox": [
+            75,
+            734,
+            467,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "domains. Following the official combination [122], we select {autumn, rock}, {dim, grass}, {outdoor, water} as the target domain pairs. A detailed description of the split of training and test domains is in Appendix B. For all datasets,  $20\\%$  samples in the training data are used for validation and model selection. ImageNet [20] pretrained ResNet-50 [34] is adopted as the initial model. The search space for the initial learning rate, weight decay, and other hyperparameters is in Appendix B.",
+        "bbox": [
+            496,
+            90,
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+            227
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison of Optimizers on DG",
+        "text_level": 1,
+        "bbox": [
+            498,
+            239,
+            795,
+            255
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Here we investigate how the optimizers affect the generalization under domain shifts. We first conduct experiments with various optimizers following the validation with training data protocol in DomainBed [32] to study the generalization of current optimizers and the robustness of the choice of hyperparameters. The results are shown in Table 1. Detailed results of optimizers on all the splits of reported datasets are in Appendix B.",
+        "bbox": [
+            496,
+            263,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Despite SGD remaining the most popular optimizer for most CNN-based models on in-distribution image recognition benchmarks, such as CIFAR [51], and ImageNet due to its outstanding performance, it fails to show advantages compared with other optimizers on current benchmarks for DG. The previous work [74] shows that SGD with momentum outperforms adaptive-based optimizers such as Adam with an exhaustive hyperparameter search (hundreds of trials for each optimizer on each dataset) to select hyperparameters with good in-distribution performance. Yet for fair comparisons with previous works, we follow the model selection protocol in DomainBed, where only 20 trials of search are conducted for each evaluation, resulting in inadequate searches. In our experiments, SGD fails to outperform adaptive-based optimizers (e.g., AdamW and AdaBelief). This may be because SGD is more sensitive to the choice of hyperparameters [48] and the hyperparameter search space in evaluation protocols for DG is too large to be traversed and fine-tune the hyperparameters within several random runs. The empirical demonstration of the sensitivity of optimizers to hyperparameters is in Appendix B.",
+        "bbox": [
+            496,
+            385,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, it is important to note that different datasets may require different optimization strategies. For example, Adam outperforms SGD considerably on PACS, while the opposite stands for VLCS, OfficeHome, and NICO++. Among none-flatness-aware optimizers, AdaBelief shows the best average performance. AdamW outperforms Adam on 5 out of 6 datasets and achieves higher average accuracy. Thus, Adam is hardly the best choice for DG and choosing the right optimizer can help exceed current leaderboards' limitations.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Among all optimizers, flatness-aware optimizers (e.g., SAM, GAM, and FAD) show promising results across all the datasets. FAD considerably outperforms all its coun",
+        "bbox": [
+            498,
+            854,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5193",
+        "bbox": [
+            480,
+            925,
+            514,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/f4ebbf708fc5216814be70fdd517a36bfd735318d5ed324ba235e8845a9b2417.jpg",
+        "table_caption": [
+            "Table 1. Comparison of current optimizers on DG datasets. The best results for each dataset are highlighted in bold font."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam [48]</td><td>84.2±0.6</td><td>77.3±1.3</td><td>67.6±0.4</td><td>44.4±0.8</td><td>43.0±0.1</td><td>76.9±0.0</td><td>65.6</td></tr><tr><td>AdamW [65]</td><td>83.6±1.5</td><td>77.4±0.8</td><td>68.8±0.6</td><td>45.2±1.4</td><td>43.4±0.1</td><td>77.5±0.1</td><td>66.0</td></tr><tr><td>SGD [76]</td><td>79.9±1.4</td><td>78.1±0.2</td><td>68.5±0.3</td><td>44.9±1.8</td><td>43.2±0.1</td><td>77.2±0.2</td><td>65.3</td></tr><tr><td>YOGI [117]</td><td>81.2±0.4</td><td>77.6±0.6</td><td>68.3±0.3</td><td>45.4±0.5</td><td>43.5±0.0</td><td>77.9±0.2</td><td>65.7</td></tr><tr><td>AdaBelief [131]</td><td>84.6±0.6</td><td>78.4±0.4</td><td>68.0±0.9</td><td>45.2±2.0</td><td>43.5±0.1</td><td>77.4±0.1</td><td>66.2</td></tr><tr><td>AdaHessian [116]</td><td>84.5±1.0</td><td>78.6±0.8</td><td>68.4±0.9</td><td>44.4±0.5</td><td>44.4±0.1</td><td>77.7±0.1</td><td>66.3</td></tr><tr><td>SAM [28]</td><td>85.3±1.0</td><td>78.2±0.5</td><td>68.0±0.8</td><td>45.7±0.9</td><td>43.4±0.1</td><td>77.9±0.1</td><td>66.4</td></tr><tr><td>GAM [121]</td><td>86.1±0.6</td><td>78.5±0.4</td><td>68.2±1.0</td><td>45.2±0.6</td><td>43.8±0.1</td><td>78.0±0.2</td><td>66.6</td></tr><tr><td>FAD (Ours)</td><td>88.2±0.5</td><td>78.9±0.8</td><td>69.2±0.5</td><td>45.7±1.0</td><td>44.4±0.1</td><td>79.0±0.1</td><td>67.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "terparts on all the benchmarks, indicating that optimizing zeroth-order and first-order flatness simultaneously learns flatter minima and better generalization.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ensemble with current DG algorithms",
+        "text_level": 1,
+        "bbox": [
+            76,
+            377,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As a base optimizer, FAD can be combined with current DG methods with various objective functions. The compatibility with DG methods is critical for the choice of optimizers. In this subsection, we investigate the compatibility of GAM with current DG algorithms and compare it with other optimizers. We also report the results of other DG methods for better comparisons.",
+        "bbox": [
+            75,
+            407,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Please note that we only consider a single pretrained model (i.e., ImageNet pretrained ResNet-50) as the initial model for fair comparisons in this paper, so we do not combine optimizers with some SOTA methods, such as SIMPLE [62], MIRO [14] with RegNetY-16GF [83], and CARFT [70] with CLIP [82] which involve the knowledge of pretrained models other than ImageNet pretrained ResNet50. We consider SOTA and representative methods including CORAL [95], SWAD [13], and Fishr [85] as the base approach to compare optimizers and leave more methods, including EoA [4] and RSC [37] in Appendix B.",
+        "bbox": [
+            75,
+            522,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The results are shown in Table 2. Different optimizers seem to favor different DG methods. AdamW achieves the best performance when combined with SWAD and CORAL, while SGD surpasses Adam and AdamW with Fishr. This indicates that fixing a single optimizer in DG benchmarks may be unfair for some methods that are not favored, and choosing the proper optimizer can further improve DG methods' performance.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "FAD consistently outperforms other optimizers with all the methods across various datasets. Compared with the default optimizer Adam, FAD further improves SWAD by  $1.7\\%$  on PACS and  $1.2\\%$  on average and surpasses previous SOTA methods.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/aa30df0a905a191d20c5c1f53c51bab5c28fe3b16d8526716ff51300efe9fe40.jpg",
+        "image_caption": [
+            "Figure 2. Comparison of computation overhead. Red points on folding lines indicate models trained with FAD for various ratios of iterations (From left to right in each figure, the proportions are  $100\\%$ ,  $50\\%$ ,  $10\\%$ ,  $5\\%$ )."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Computation Overhead",
+        "text_level": 1,
+        "bbox": [
+            500,
+            507,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Since flatness-aware optimization methods require more computation overhead than traditional optimizers, we report the comparison of FAD with other optimizers with more training iterations. We train current optimizers on DG benchmarks for 5,000, 10,000, and 15,000 iterations. We report the performance and required average training time in Table 3. Most optimizers achieve noticeable improvements in performance with more training iterations on PACS, VLCS, and OfficeHome. We show that FAD still outperforms current optimizers with fewer training iterations. For example, models trained with FAD for 5,000 iterations on PACS and  $\\mathrm{NICO + + }$  outperform those trained with other optimizers for 15,000 iterations. This indicates the effectiveness and efficiency of FAD.",
+        "bbox": [
+            496,
+            534,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, as discussed in Section 3.3, the FAD gradient can be efficiently calculated via first-order gradient approximation. Yet it still introduces extra computation when calculated in each iteration. Here we investigate optimizing the FAD term only for a subset of iterations in each epoch and optimize the remaining iterations simply with SGD on PACS and  $\\mathrm{NICO + + }$ . We change the ratio of the subset with FAD from  $5\\%$  to  $100\\%$  and report the performance and training speed. We set the batch size to 96  $(32\\times 3)$  for PACS and  $128(32\\times 4)$  for  $\\mathrm{NICO + + }$  for all the methods for a fair",
+        "bbox": [
+            496,
+            750,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "5194",
+        "bbox": [
+            482,
+            926,
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+            936
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0aa2d1da1096b6609dd17dd7003d8cece11df63f568598c412e098f0e8228bd3.jpg",
+        "table_caption": [
+            "Table 2. Ensemble with domain generalization methods. Numbers for methods marked with * and all the combinations of DG methods with optimizers other than Adam are reproduced results. Other results are from the original literature and DomainBed (donated with †)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>Avg.</td></tr><tr><td>MASF [23]</td><td>82.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DMC [15]</td><td>83.4</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>MetaReg [7]</td><td>83.6</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>ER [124]</td><td>85.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>pAdalN [77]</td><td>85.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>EISNet [100]</td><td>85.8</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DSON [90]</td><td>86.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ERM† [96]</td><td>85.5</td><td>77.5</td><td>66.5</td><td>46.1</td><td>40.9</td><td>63.3</td></tr><tr><td>ERM* (with Adam)</td><td>84.2</td><td>77.3</td><td>67.6</td><td>44.4</td><td>43.0</td><td>63.3</td></tr><tr><td>IRM† [3]</td><td>83.5</td><td>78.6</td><td>64.3</td><td>47.6</td><td>33.9</td><td>61.6</td></tr><tr><td>GroupDRO† [88]</td><td>84.4</td><td>76.7</td><td>66.0</td><td>43.2</td><td>33.3</td><td>60.7</td></tr><tr><td>I-Mixup† [108, 113, 102]</td><td>84.6</td><td>77.4</td><td>68.1</td><td>47.9</td><td>39.2</td><td>63.4</td></tr><tr><td>MLDG† [56]</td><td>84.9</td><td>77.2</td><td>66.8</td><td>47.8</td><td>41.2</td><td>63.6</td></tr><tr><td>MMD† [60]</td><td>84.7</td><td>77.5</td><td>66.4</td><td>42.2</td><td>23.4</td><td>58.8</td></tr><tr><td>DANN† [30]</td><td>83.7</td><td>78.6</td><td>65.9</td><td>46.7</td><td>38.3</td><td>62.6</td></tr><tr><td>CDANN† [61]</td><td>82.6</td><td>77.5</td><td>65.7</td><td>45.8</td><td>38.3</td><td>62.0</td></tr><tr><td>MTL† [11]</td><td>84.6</td><td>77.2</td><td>66.4</td><td>45.6</td><td>40.6</td><td>62.9</td></tr><tr><td>SagNet† [75]</td><td>86.3</td><td>77.8</td><td>68.1</td><td>48.6</td><td>40.3</td><td>64.2</td></tr><tr><td>ARM† [119]</td><td>85.1</td><td>77.6</td><td>64.8</td><td>45.5</td><td>35.5</td><td>61.7</td></tr><tr><td>VREx† [52]</td><td>84.9</td><td>78.3</td><td>66.4</td><td>46.4</td><td>33.6</td><td>61.9</td></tr><tr><td>RSC† [38]</td><td>85.2</td><td>77.1</td><td>65.5</td><td>46.6</td><td>38.9</td><td>62.7</td></tr><tr><td>Mixstyle [129]</td><td>85.2</td><td>77.9</td><td>60.4</td><td>44.0</td><td>34.0</td><td>60.3</td></tr><tr><td>MIRO* [14]</td><td>85.4</td><td>78.9</td><td>69.5</td><td>45.4</td><td>44.0</td><td>64.6</td></tr><tr><td>Adam + SWAD* [13]</td><td>86.8</td><td>79.1</td><td>70.1</td><td>46.5</td><td>44.1</td><td>65.3</td></tr><tr><td>AdamW + SWAD</td><td>87.0</td><td>78.5</td><td>70.8</td><td>46.9</td><td>45.0</td><td>65.6</td></tr><tr><td>SGD + SWAD</td><td>85.2</td><td>79.1</td><td>71.0</td><td>46.7</td><td>42.8</td><td>65.0</td></tr><tr><td>FAD (Ours) + SWAD</td><td>88.5</td><td>79.8</td><td>71.8</td><td>47.5</td><td>45.0</td><td>66.5</td></tr><tr><td>Adam + Fishr* [85]</td><td>85.5</td><td>78.0</td><td>68.2</td><td>46.2</td><td>44.7</td><td>64.5</td></tr><tr><td>AdamW + Fishr</td><td>85.7</td><td>77.5</td><td>68.0</td><td>46.7</td><td>43.6</td><td>64.3</td></tr><tr><td>SGD + Fishr</td><td>84.4</td><td>78.5</td><td>69.2</td><td>46.9</td><td>44.4</td><td>64.7</td></tr><tr><td>FAD (Ours) + Fishr</td><td>88.3</td><td>79.6</td><td>69.2</td><td>48.1</td><td>43.8</td><td>65.8</td></tr><tr><td>Adam + CORAL* [95]</td><td>86.0</td><td>78.9</td><td>68.7</td><td>43.7</td><td>44.5</td><td>64.5</td></tr><tr><td>AdamW + CORAL</td><td>86.4</td><td>79.5</td><td>69.8</td><td>45.0</td><td>44.9</td><td>65.1</td></tr><tr><td>SGD + CORAL</td><td>85.6</td><td>78.2</td><td>69.5</td><td>45.8</td><td>44.6</td><td>64.7</td></tr><tr><td>FAD (Ours) + CORAL</td><td>88.5</td><td>78.9</td><td>70.8</td><td>46.1</td><td>44.9</td><td>65.9</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "comparison. As shown in Figure 2, FAD consistently outperforms SGD, Adam, and AdamW by considerable margins and surpasses SAM and GAM with less training time when setting the ratio of FAD to  $10\\%$  and  $50\\%$ . Detailed results are in Appendix B.",
+        "bbox": [
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+            700,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. The Hessian spectra of selected minima",
+        "text_level": 1,
+        "bbox": [
+            76,
+            786,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Sharpness-aware optimization methods are shown to decrease the curvature of loss landscape [28, 121]. We investigate how FAD affects the flatness of minima. We consider the maximum eigenvalue of Hessian, which indicates the sharpness across the most critical direction, and the Hessian trace, which measures the expected loss increase under",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "random perturbations to the weights [42] as the measures of flatness.",
+        "bbox": [
+            498,
+            700,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We show the Hessian spectra of ResNet-50 trained on artpainting, cartoon, and photo domains of PACS for 5,000 iterations with SGD, Adam, AdamW, GAM, SAM, and FAD. Following [121], we adopt power iteration [115] to compute the top eigenvalues of Hessian and Hutchinson's method [6, 5, 114] to compute the Hessian trace. We report the distribution of the top-50 Hessian eigenvalues and Hessian trace for each method at convergence in Figure 3. None-flatness-aware optimizers, including SGD, Adam, and AdamW show high Hessian trace and dominant eigenvalues. In contrast, flatness-aware optimizers find",
+        "bbox": [
+            496,
+            734,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "5195",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/60955eea2019af12c40dd7af7ae31257bcbf3df8c2f818e05dd3f906bcccb4f2.jpg",
+        "table_caption": [
+            "Table 3. The performance and average training time of current optimizers and FAD when training for 5,000, 10,000, 15,000 iterations. Training Time is the average time for finishing each dataset with the given iterations."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Optimizers</td><td>Iterations</td><td>Training Time /s</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam</td><td>5,000</td><td>1613.9</td><td>84.2</td><td>77.3</td><td>67.6</td><td>76.2</td><td>76.3</td></tr><tr><td>Adam</td><td>10,000</td><td>3049.5</td><td>82.9</td><td>77.7</td><td>67.4</td><td>76.9</td><td>76.2</td></tr><tr><td>Adam</td><td>15,000</td><td>4478.6</td><td>84.0</td><td>78.4</td><td>69.6</td><td>77.3</td><td>77.3</td></tr><tr><td>AdamW</td><td>5,000</td><td>2145.2</td><td>83.6</td><td>77.4</td><td>68.8</td><td>76.9</td><td>76.7</td></tr><tr><td>AdamW</td><td>10,000</td><td>4632.8</td><td>83.3</td><td>77.1</td><td>66.9</td><td>77.5</td><td>76.2</td></tr><tr><td>AdamW</td><td>15,000</td><td>6995.3</td><td>83.7</td><td>76.3</td><td>68.0</td><td>77.5</td><td>76.4</td></tr><tr><td>SGD</td><td>5,000</td><td>1864.1</td><td>79.9</td><td>78.1</td><td>68.5</td><td>76.5</td><td>75.8</td></tr><tr><td>SGD</td><td>10,000</td><td>3438.9</td><td>81.4</td><td>78.1</td><td>68.7</td><td>77.2</td><td>76.4</td></tr><tr><td>SGD</td><td>15,000</td><td>4992.0</td><td>82.6</td><td>78.7</td><td>69.6</td><td>77.0</td><td>77.0</td></tr><tr><td>YOGI</td><td>5,000</td><td>1388.9</td><td>81.2</td><td>77.6</td><td>68.3</td><td>77.1</td><td>76.1</td></tr><tr><td>YOGI</td><td>10,000</td><td>2882.9</td><td>81.2</td><td>77.8</td><td>70.2</td><td>77.9</td><td>76.8</td></tr><tr><td>YOGI</td><td>15,000</td><td>4434.2</td><td>83.1</td><td>78.1</td><td>67.9</td><td>77.5</td><td>76.7</td></tr><tr><td>SAM</td><td>5,000</td><td>3325.6</td><td>85.3</td><td>78.2</td><td>68.0</td><td>77.0</td><td>77.1</td></tr><tr><td>SAM</td><td>10,000</td><td>6506.8</td><td>85.6</td><td>78.3</td><td>68.6</td><td>77.9</td><td>77.6</td></tr><tr><td>SAM</td><td>15,000</td><td>9960.2</td><td>86.1</td><td>78.9</td><td>68.8</td><td>78.1</td><td>78.0</td></tr><tr><td>GAM</td><td>5,000</td><td>8073.6</td><td>86.1</td><td>78.5</td><td>68.2</td><td>77.4</td><td>77.6</td></tr><tr><td>GAM</td><td>10,000</td><td>16210.5</td><td>86.0</td><td>79.2</td><td>68.5</td><td>78.0</td><td>78.0</td></tr><tr><td>GAM</td><td>15,000</td><td>23855.1</td><td>86.5</td><td>78.6</td><td>69.0</td><td>77.8</td><td>78.0</td></tr><tr><td>FAD (Ours)</td><td>5,000</td><td>5057.8</td><td>88.2</td><td>78.9</td><td>69.2</td><td>78.5</td><td>78.7</td></tr><tr><td>FAD (Ours)</td><td>10,000</td><td>10450.8</td><td>88.5</td><td>79.5</td><td>69.6</td><td>79.0</td><td>79.1</td></tr><tr><td>FAD (Ours)</td><td>15,000</td><td>16255.2</td><td>88.5</td><td>79.0</td><td>69.0</td><td>79.1</td><td>78.9</td></tr></table>",
+        "bbox": [
+            184,
+            114,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/ee602666417ee6d9610d909e22d01c6dd36ba698aa6da12a4381d2f8fed2f5d9.jpg",
+        "image_caption": [
+            "Figure 3. The distribution of top eigenvalues and the trace of Hessian at convergence on PACS with SGD, Adam, AdamW, GAM, SAM, and FAD. Trace indicates Hessian trace and  $\\lambda_{\\mathrm{max}}$  indicates the maximum eigenvalue of Hessian."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "minima with significantly lower Hessian spectra. FAD leads to both the lowest Hessian maximum eigenvalue and trace and thus the lowest curvature compared with other optimizers. More results are shown in Appendix B.",
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+    {
+        "type": "text",
+        "text": "5. Discussions",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Despite the wide usage in DG benchmarks, Adam is hardly the optimal choice of default optimizer. We show that the best optimizer for different DG methods varies across different datasets. Choosing the right optimizer can help exceed the current benchmarks' limitations. We propose a unified optimization method, flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness efficiently to address the problem. We further show that FAD controls the OOD generalization error and convergences fast. Compared with current optimizers, flatness-aware optimization approaches,",
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+    {
+        "type": "text",
+        "text": "including SAM, GAM, and FAD, leads to flatter minima and better generalization. FAD outperforms its counterparts significantly on most DG datasets.",
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+    {
+        "type": "text",
+        "text": "FAD still has the following limitations which could lead to potential future work. First, the term  $\\sup_{\\pmb{\\theta}_1,\\pmb{\\theta}_2\\in \\Theta}|\\mathcal{L}_{\\mathrm{tr}}(\\pmb{\\theta}_1,\\pmb{\\theta}_2) - \\mathcal{L}_{\\mathrm{te}}(\\pmb{\\theta}_1,\\pmb{\\theta}_2)|$  in Equation (6) indicates the discrepancy between training and test data. Without knowledge of test distribution and extra assumptions, the term cannot be optimized and leads to the optimization of the flatness term. Proper assumptions on the connection between training and test data or the geometry of data may help to learn the connection between flatness and the discrepancy, and thus control the discrepancy for better generalization. Second, We show that Adam is hardly an optimal choice of default optimizer in DG. However, selecting a proper optimizer for each DG method leads to massive overhead. Designing a better DG protocol",
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+    {
+        "type": "page_number",
+        "text": "5196",
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+    },
+    {
+        "type": "text",
+        "text": "or learning an indicator for the fitness of optimizers and methods can significantly contribute.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work was supported in part by National Key R&D Program of China (No. 2018AAA0102004, No. 2020AAA0106300), National Natural Science Foundation of China (No. U1936219, 62141607), Beijing Academy of Artificial Intelligence (BAAI).",
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+            "[130] Juntang Zhuang, Boqing Gong, Liangzhe Yuan, Yin Cui, Hartwig Adam, Nicha C Dvornek, James s Duncan, Ting Liu, et al. Surrogate gap minimization improves sharpness"
+        ],
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+    },
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+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "aware training. In International Conference on Learning Representations, 2022. 1, 2, 3, 5",
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+        ],
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diff --git a/2023/Flatness-Aware Minimization for Domain Generalization/493c4d3d-8eb2-483f-be83-a0524b08186b_model.json b/2023/Flatness-Aware Minimization for Domain Generalization/493c4d3d-8eb2-483f-be83-a0524b08186b_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..2784b1739d4c0a54cceaf0b2635f7ee11b8e2c64
--- /dev/null
+++ b/2023/Flatness-Aware Minimization for Domain Generalization/493c4d3d-8eb2-483f-be83-a0524b08186b_model.json	
@@ -0,0 +1,3242 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.198,
+                0.131,
+                0.773,
+                0.151
+            ],
+            "angle": 0,
+            "content": "Flatness-Aware Minimization for Domain Generalization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.165,
+                0.181,
+                0.804,
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+            ],
+            "angle": 0,
+            "content": "Xingxuan Zhang, Renzhe Xu, Han Yu, Yancheng Dong, Pengfei Tian, Peng Cui*  \nDepartment of Computer Science, Tsinghua University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.275,
+                0.22,
+                0.695,
+                0.234
+            ],
+            "angle": 0,
+            "content": "xingxuanzhang@hotmail.com, cuip@tsinghua.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.269,
+                0.314,
+                0.285
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.302,
+                0.474,
+                0.543
+            ],
+            "angle": 0,
+            "content": "Domain generalization (DG) seeks to learn robust models that generalize well under unknown distribution shifts. As a critical aspect of DG, optimizer selection has not been explored in depth. Currently, most DG methods follow the widely used benchmark, DomainBed, and utilize Adam as the default optimizer for all datasets. However, we reveal that Adam is not necessarily the optimal choice for the majority of current DG methods and datasets. Based on the perspective of loss landscape flatness, we propose a novel approach, Flatness-Aware Minimization for Domain Generalization (FAD), which can efficiently optimize both zeroth-order and first-order flatness simultaneously for DG. We provide theoretical analyses of the FAD's out-of-distribution (OOD) generalization error and convergence. Our experimental results demonstrate the superiority of FAD on various DG datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.591,
+                0.21,
+                0.607
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.617,
+                0.47,
+                0.768
+            ],
+            "angle": 0,
+            "content": "Current neural networks are expected to generalize to unseen distributions in real-world applications, which can break the independent and identically distributional (I.I.D.) assumption of traditional machine learning algorithms [129, 99]. The distribution shift between training and test data may largely deteriorate most current approaches in practice. Hence, instead of generalization within the training distribution, the ability to generalize under distribution shift, namely domain generalization (DG) [73], has attracted increasing attention [99]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.769,
+                0.47,
+                0.875
+            ],
+            "angle": 0,
+            "content": "Various methods have been proposed to address the DG problem recently, many of which have shown promising performance. As a learning problem mainly in the computer vision field, the DG task relies highly on the chosen optimizer, yet the effect of the optimizer in DG has hardly been studied. Most current algorithms, following the well-known benchmark DomainBed [32], default to optimize"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.269,
+                0.891,
+                0.415
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.42,
+                0.895,
+                0.492
+            ],
+            "angle": 0,
+            "content": "Figure 1. Test accuracy on PACS and DomainNet of different optimizers. Adam, the default optimizer in popular benchmarks shows no advantage compared with its counterparts, while the proposed FAD achieve better OOD generalization performance compared with current optimizers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.519,
+                0.895,
+                0.656
+            ],
+            "angle": 0,
+            "content": "models with Adam [48] without considering other optimizers. However, the in-distribution generalization ability of popular optimizers has been investigated from the perspective of loss landscape recently [28, 29] and Adam is found to achieve inferior generalization compared with other optimizers such as SGD [76] due to the sharp minima Adam selected. Thus, investigating the impact of optimizers in DG and clarifying whether Adam should be considered as the default optimizer is of significance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.657,
+                0.895,
+                0.793
+            ],
+            "angle": 0,
+            "content": "In this paper, we empirically compare the performance of current optimizers, including Adam, SGD, AdaBelief [131], YOGI [117], AdaHessian [116], SAM [28], and GAM[121]. Through extensive experiments on current DG benchmarks, we show that Adam can hardly surpass other optimizers on most DG datasets. The best choice of the optimizer for different DG methods varies across different datasets, and choosing the right optimizer can help exceed the current leaderboards' limitations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Recently, the connection between the flatness of the loss landscape and in-distribution generalization ability has been widely studied and verified both theoretically[130] and empirically[25]. Some works [13, 87] show that flatness also leads to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.102,
+                0.888,
+                0.227,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.925,
+                0.516,
+                0.937
+            ],
+            "angle": 0,
+            "content": "5189"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.484
+            ],
+            "angle": 0,
+            "content": "Among flatness-aware optimization methods, sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 126, 47], which optimize the zeroth-order flatness, achieve SOTA performance on various in-distribution image classification tasks [53, 130]. Most recently, Gradient Norm Aware Minimization (GAM) [121] shows that minimizing the first-order flatness provides a more substantial penalty on the sharpness of minima than zeroth-order flatness yet requires more computation overhead. Due to the first-order Taylor expansions adopted to optimize zeroth-order and first-order flatness, both SAM and GAM lose some of their penalty strength, and thus they can be mutually reinforced by each other. To accelerate the optimization of first-order flatness and combine zero-order flatness, we propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), which eliminates the considerable computation overhead for Hessian or Hessian-vector products. We theoretically show that the proposed FAD controls the dominant eigenvalue of Hessian of the training loss, which indicates the sharpness of the loss landscape along its most critical direction [42]. We present an OOD generalization bound to show that the proposed FAD guarantees the generalization error on test data and convergence analysis. Through extensive experiments, we evaluate FAD and other optimizers on various DG benchmarks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.486,
+                0.418,
+                0.499
+            ],
+            "angle": 0,
+            "content": "We summarize the main contribution as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.502,
+                0.469,
+                0.591
+            ],
+            "angle": 0,
+            "content": "- We propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness simultaneously. Without calculating Hessian and Hessian-vector products, FAD considerably reduces the computation overhead of first-order flatness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.593,
+                0.469,
+                0.651
+            ],
+            "angle": 0,
+            "content": "- We theoretically analyze the OOD generalization error and convergence of FAD. We show that FAD controls the dominant eigenvalue of Hessian and thus the flatness of learned minima."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.653,
+                0.469,
+                0.728
+            ],
+            "angle": 0,
+            "content": "- We empirically show that Adam, the default optimizer for most current DG benchmarks, can hardly be the optimal choice for most DG datasets. We present the superiority of FAD compared with current optimizers through extensive experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.729,
+                0.469,
+                0.773
+            ],
+            "angle": 0,
+            "content": "- We empirically validate that FAD finds flatter optima with lower Hessian spectra compared with zeroth- and first-order flatness-aware optimization methods."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.502,
+                0.469,
+                0.773
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.79,
+                0.227,
+                0.807
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.816,
+                0.2,
+                0.832
+            ],
+            "angle": 0,
+            "content": "2.1. Optimizers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Some works [107, 28] have studied the connection between current optimization approaches, such as SGD [76], Adam [49], AdamW [65] and others [26, 63] and in-distribution generalization. Some literature shows that"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.332
+            ],
+            "angle": 0,
+            "content": "Adam is more vulnerable to sharp minima than SGD [104], which may result in worse generalization [106, 33, 35]. Some follow-ups [66, 16, 107, 117] propose generalizable optimizers to address this problem. However, the generalization ability and convergence speed is often a trade-off [44, 107, 63, 117, 26]. Different optimizers may favor different tasks and network architectures (e.g., SGD is often chosen for ResNet [34] while AdamW [65] for ViTs [21]). Selecting the right optimizer is critical for performance and convergence while the understanding of its relationship to model generalization remains nascent [28]. [74] finds that fine-tuned SGD outperforms Adam on OOD tasks. Yet all the previous works do not consider the effect of optimizers in current DG benchmarks and evaluation protocols. In this paper, we discuss the selection of the default optimizer in DG benchmarks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.35,
+                0.855,
+                0.366
+            ],
+            "angle": 0,
+            "content": "2.2. Domain Generalization and Optimization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.376,
+                0.892,
+                0.572
+            ],
+            "angle": 0,
+            "content": "Domain generalization (DG) aims to improve the generalization ability to novel domains [31, 45, 50]. A common approach is to learn domain-invariant or causal features over multiple source domains [22, 36, 57, 59, 72, 80, 89, 120, 110, 118, 101, 123] or aggregating domain-specific modules [67, 68]. Some works propose to enlarge the input space by augmentation of training data [12, 98, 81, 91, 127, 128, 109]. Exploit regularization with meta-learning [22, 58] and Invariant Risk Minimization (IRM) framework [2] are also proposed for DG. Recently, several works propose to ensemble model weights for better generalization [13, 4, 84, 105, 86, 62, 18] and achieve outstanding performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.589,
+                0.733,
+                0.605
+            ],
+            "angle": 0,
+            "content": "2.3. Flatness of loss landscape"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Recent works study the relationship between flatter minima lead and better generalization on in-distribution data [44, 130, 41, 79]. [42] reviews the literature related to generalization and the sharpness of minima. It highlights the role of maximum Hessian eigenvalue in deciding the sharpness of minima [44, 103]. Some simple strategies are proposed to optimize maximum Hessian eigenvalue, such as choosing a large learning rate [54, 19, 40] and smaller batch size [94, 54, 39]. Sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 24, 64, 25, 71, 126, 47, 46], which are representative training algorithms to seek zeroth-order flatness, show outstanding performance on indistribution generalization. Most recently, several works discuss the relationship between generalization and gradient norm [8, 125]. GAM[121] proposes to optimize first-order flatness for better generalization. [13, 87] show that flatness minima also lead to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.925,
+                0.516,
+                0.937
+            ],
+            "angle": 0,
+            "content": "5190"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.09,
+                0.17,
+                0.106
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.117,
+                0.47,
+                0.254
+            ],
+            "angle": 0,
+            "content": "In in-distribution generalization tasks, sharpness-aware optimization methods show outstanding performance [28]. We theoretically show that optimizing both zeroth-order and first-order flatness strengthens out-of-distribution performance via a generalization bound. We propose a unified optimization framework to optimize zeroth-order and first-order flatness effectively and efficiently. We present the connection between Hessian spectra and our regularization term and give the convergence analysis of our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.278,
+                0.47,
+                0.49
+            ],
+            "angle": 0,
+            "content": "Notations We use \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) to denote the space of input \\(X\\) and outcome \\(Y\\), respectively. We use \\(\\Delta_{\\mathcal{Y}}\\) to denote a distribution on \\(\\mathcal{Y}\\). Let \\(S = \\{(x_i, y_i)\\}_{i=1}^n\\) denote the training dataset with \\(n\\) data-points drawn independently from the training distribution \\(\\mathcal{D}_{\\mathrm{tr}}\\). We consider the covariate shift scenario [10, 92, 111] and assume that the conditional probabilities are invariant across training and test distributions (i.e., \\(P_{\\mathrm{tr}}(Y|X) = P_{\\mathrm{te}}(Y|X)\\)). The invariant conditional probability is denoted as \\(P(Y|X)\\). A prediction model \\(f_{\\theta}: \\mathcal{X} \\to \\Delta_{\\mathcal{Y}}\\) parametrized by \\(\\theta \\in \\Theta \\subseteq \\mathbb{R}^d\\) with dimension \\(d\\) maps an input to a simplex on \\(\\mathcal{Y}\\), which indicates the predicted probability of each class<sup>1</sup>. \\(\\Theta\\) is the hypothesis set. We further assume that the ground truth model \\(\\theta^*\\) that characterizes \\(P(Y|X)\\) is in the hypothesis set \\(\\Theta\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.491,
+                0.471,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Let \\(\\ell: \\Delta_{\\mathcal{Y}} \\times \\Delta_{\\mathcal{Y}} \\to \\mathbb{R}_{+}\\) define a loss function over \\(\\Delta_{\\mathcal{Y}}\\). For any hypotheses \\(\\theta_1, \\theta_2 \\in \\Theta\\), the expected loss \\(\\mathcal{L}_{\\mathcal{D}}(\\theta_1, \\theta_2)\\) for distribution \\(\\mathcal{D}\\) is given as \\(\\mathcal{L}_{\\mathcal{D}}(\\theta_1, \\theta_2) = \\mathbb{E}_{x \\sim \\mathcal{D}}[\\ell(f_{\\theta_1}(x), f_{\\theta_2}(x))]\\). To simplify the notations, we use \\(\\mathcal{L}_{\\mathrm{tr}}\\) and \\(\\mathcal{L}_{\\mathrm{te}}\\) to denote the expected loss \\(\\mathcal{L}_{\\mathcal{D}_{\\mathrm{tr}}}\\) and \\(\\mathcal{L}_{\\mathcal{D}_{\\mathrm{te}}}\\) in training and test distributions, respectively. In addition, we use \\(\\mathcal{E}_{\\mathrm{tr}}(\\pmb{\\theta}) = \\mathcal{L}_{\\mathrm{tr}}(\\pmb{\\theta}, \\pmb{\\theta}^*)\\) and \\(\\mathcal{E}_{\\mathrm{te}}(\\pmb{\\theta}) = \\mathcal{L}_{\\mathrm{te}}(\\pmb{\\theta}, \\pmb{\\theta}^*)\\) to denote the loss of a function \\(\\pmb{\\theta} \\in \\Theta\\) w.r.t. the true labeling function \\(\\pmb{\\theta}^*\\) in the two distributions. We use \\(\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})\\) to denote the empirical loss function w.r.t. the \\(n\\) samples \\(S\\) from the training distribution. In addition, we assume that \\(\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})\\) is twice differentiable throughout the paper and we use \\(\\nabla \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})\\) and \\(\\nabla^2 \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})\\) to denote the derivative and Hessian matrix, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.716,
+                0.469,
+                0.733
+            ],
+            "angle": 0,
+            "content": "3.1. A General Flatness-Aware Optimization for DG"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.74,
+                0.469,
+                0.862
+            ],
+            "angle": 0,
+            "content": "In in-distribution generalization tasks, it is shown that the zeroth-order flatness can be not strong enough in cases where \\(\\rho\\) covers multiple minima or the maximum loss in \\(\\rho\\) is misaligned with the uptrend of loss and first-order flatness can help improve it [121]. But both zeroth-order and first-order flatness require first-order approximations in practice. Thus optimizing both zeroth-order and first-order flatness together leads to stronger generalization than both of them"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.892,
+                0.166
+            ],
+            "angle": 0,
+            "content": "[121]. Yet optimizing first-order flatness requires the calculation of Hessian or Hessian-vector products, which introduces heavy computation overhead. As a result, we aim to accelerate the optimization in a Hessian-free way for OOD generalization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.168,
+                0.892,
+                0.197
+            ],
+            "angle": 0,
+            "content": "Formally, the zeroth-order and first-order flatness are defined as follows [28, 130, 121]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.208,
+                0.892,
+                0.255
+            ],
+            "angle": 0,
+            "content": "Definition 3.1 (\\(\\rho\\)-zeroth-order flatness). For any \\(\\rho > 0\\), the \\(\\rho\\)-zeroth-order flatness \\(R_{\\rho}^{(0)}(\\pmb{\\theta})\\) of function \\(\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})\\) at a point \\(\\pmb{\\theta}\\) is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.527,
+                0.262,
+                0.892,
+                0.288
+            ],
+            "angle": 0,
+            "content": "\\[\nR _ {\\rho} ^ {(0)} (\\boldsymbol {\\theta}) \\triangleq \\max  _ {\\boldsymbol {\\theta} ^ {\\prime} \\in B (\\boldsymbol {\\theta}, \\rho)} \\left(\\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {\\prime}\\right) - \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta})\\right), \\quad \\forall \\boldsymbol {\\theta} \\in \\Theta . \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.297,
+                0.892,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Here \\(\\rho\\) is the perturbation radius that controls the magnitude of the neighborhood."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.338,
+                0.892,
+                0.384
+            ],
+            "angle": 0,
+            "content": "Definition 3.2 (\\(\\rho\\)-first-order flatness). For any \\(\\rho > 0\\), the \\(\\rho\\)-first-order flatness \\(R_{\\rho}^{(1)}(\\theta)\\) of function \\(\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\theta)\\) at a point \\(\\theta\\) is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.527,
+                0.393,
+                0.892,
+                0.422
+            ],
+            "angle": 0,
+            "content": "\\[\nR _ {\\rho} ^ {(1)} (\\boldsymbol {\\theta}) \\triangleq \\rho \\cdot \\max  _ {\\boldsymbol {\\theta} ^ {\\prime} \\in B (\\boldsymbol {\\theta}, \\rho)} \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {\\prime}\\right) \\right\\|, \\quad \\forall \\boldsymbol {\\theta} \\in \\Theta . \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.433,
+                0.88,
+                0.449
+            ],
+            "angle": 0,
+            "content": "Here \\(\\rho\\) is the perturbation radius similar to Definition 3.1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.459,
+                0.892,
+                0.504
+            ],
+            "angle": 0,
+            "content": "Based on these definitions, we propose to jointly optimize zeroth-order and first-order flatness through the following linear combination of the two flatness metrics."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.515,
+                0.892,
+                0.535
+            ],
+            "angle": 0,
+            "content": "\\[\nR _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} (\\boldsymbol {\\theta}) = \\alpha R _ {\\rho} ^ {(0)} (\\boldsymbol {\\theta}) + (1 - \\alpha) R _ {\\rho} ^ {(1)} (\\boldsymbol {\\theta}), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.545,
+                0.892,
+                0.651
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) is a hyper-parameter that controls the trade-off between zeroth-order and first-order flatness. Since both flatness are related to the maximal eigenvalue of the Hessian matrices [130, 121], we can derive that \\(R_{\\rho ,\\alpha}^{\\mathrm{FAD}}(\\pmb {\\theta})\\) is also related to the maximal eigenvalue. Specifically, when a point \\(\\pmb{\\theta}^{*}\\) is a local minimum of \\(\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta})\\) and \\(\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta})\\) can be second-order Taylor approximated in the neighbourhood of \\(\\pmb{\\theta}^{*}\\), then"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.579,
+                0.661,
+                0.892,
+                0.7
+            ],
+            "angle": 0,
+            "content": "\\[\n\\lambda_ {\\max } \\left(\\nabla^ {2} \\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {*}\\right)\\right) = \\frac {R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} \\left(\\boldsymbol {\\theta} ^ {*}\\right)}{\\rho^ {2} \\left(1 - \\frac {\\alpha}{2}\\right)}. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.709,
+                0.892,
+                0.784
+            ],
+            "angle": 0,
+            "content": "See Appendix A for details. Since the maximal eigenvalue is a proper measure of the curvature of minima [42, 43] and related to generalization abilities [121, 17, 39], optimizing Equation (3) would hopefully improve the DG performances, which we demonstrate in Section 3.2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.785,
+                0.892,
+                0.829
+            ],
+            "angle": 0,
+            "content": "Then the overall objective of our method, Flatness-Aware minimization for Domain generalization (FAD), is as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.588,
+                0.84,
+                0.892,
+                0.861
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {a l l}} (\\boldsymbol {\\theta}) = \\hat {\\mathcal {E}} _ {\\text {t r}} (\\boldsymbol {\\theta}) + \\beta \\cdot R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} (\\boldsymbol {\\theta}). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The strength of FAD regularization is controlled by a hyperparameter \\(\\beta\\)."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>We use \\(\\Delta y\\) to denote the non-deterministic function case. This formulation also includes deterministic function cases."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.927,
+                0.514,
+                0.938
+            ],
+            "angle": 0,
+            "content": "5191"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.408,
+                0.108
+            ],
+            "angle": 0,
+            "content": "3.2. Flatness Penalty and DG Performance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.114,
+                0.47,
+                0.158
+            ],
+            "angle": 0,
+            "content": "We give a generalization bound to demonstrate that FAD controls the generalization error on test distribution as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.167,
+                0.47,
+                0.243
+            ],
+            "angle": 0,
+            "content": "Proposition 3.1. Suppose the per-data-point loss function \\(\\ell\\) is differentiable, symmetric, bounded by \\(M\\), and obeys the triangle inequality. Suppose \\(\\pmb{\\theta}^{*}\\in \\Theta\\). Fix \\(\\rho >0\\) and \\(\\pmb {\\theta}\\in \\Theta\\). Then with probability at least \\(1 - \\delta\\) over training set \\(S\\) generated from the distribution \\(\\mathcal{D}\\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.081,
+                0.25,
+                0.503,
+                0.385
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\epsilon_ {i} \\sim N (0, \\rho^ {2} / (\\sqrt {d} + \\sqrt {\\log n}) ^ {2})} \\left[ \\mathcal {E} _ {t e} (\\boldsymbol {\\theta} + \\boldsymbol {\\epsilon}) \\right] \\\\ \\leq \\hat {\\mathcal {E}} _ {t r} (\\boldsymbol {\\theta}) + R _ {\\rho , \\alpha} ^ {E A D} (\\boldsymbol {\\theta}) \\\\ + \\sup  _ {\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2} \\in \\Theta} | \\mathcal {L} _ {t r} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}) - \\mathcal {L} _ {t e} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}) | + \\frac {M}{\\sqrt {n}} \\\\ + \\sqrt {\\frac {\\frac {1}{4} d \\log \\left(1 + \\frac {\\| \\theta \\| ^ {2} (\\sqrt {d} + \\sqrt {\\log n}) ^ {2}}{d \\rho^ {2}}\\right) + \\frac {1}{4} + \\log \\frac {n}{\\delta} + 2 \\log (6 n + 3 d)}{n - 1}} \\tag {6} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.392,
+                0.47,
+                0.527
+            ],
+            "angle": 0,
+            "content": "Remark. The term \\(\\sup_{\\theta_1, \\theta_2 \\in \\Theta} |\\cdot|\\) corresponds to the discrepancy distance [69], which measures the covariate shift between the training domain and the unknown test domain. Please note that in DG/OOD generalization tasks, the information on test distribution is unavailable in the optimization phase. Thus one cannot intervene in the third term on RHS. Thus optimizing the regularization of FAD (the second term on RHS) with ERM loss on training data leads to better generalization on test data."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.534,
+                0.252,
+                0.55
+            ],
+            "angle": 0,
+            "content": "3.3. Algorithm Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.557,
+                0.47,
+                0.692
+            ],
+            "angle": 0,
+            "content": "Although the regularization of FAD controls the OOD generalization error, directly optimizing it suffers from significant computational costs. Previous works [114, 121] propose to calculate second order gradient with Hessian-vector product, yet the cost increases fast as the model dimension grows. Inspired by [93, 125], we approximate second-order gradient with first-order gradients and optimize zeroth-order and first-order flatness simultaneously as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.711,
+                0.47,
+                0.769
+            ],
+            "angle": 0,
+            "content": "Optimization and acceleration At each round, suppose the perturbation radius is set to \\(\\rho_{t}\\), then the gradient of \\(\\mathcal{L}_{\\mathrm{all}}(\\pmb{\\theta}_t)\\) at the point \\(\\pmb{\\theta}_t\\) in Equation (5) is approximated as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.77,
+                0.378,
+                0.788
+            ],
+            "angle": 0,
+            "content": "The gradient of \\(R_{\\rho_t}^{(0)}(\\pmb {\\theta}_t)\\) . Following [28], let"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.797,
+                0.469,
+                0.85
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\tilde {\\boldsymbol {\\theta}} _ {t, 1} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\boldsymbol {g} _ {t , 0}}{\\| \\boldsymbol {g} _ {t , 0} \\|} \\quad \\text {w h e r e} \\quad \\boldsymbol {g} _ {t, 0} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}), \\tag {7} \\\\ \\boldsymbol {g} _ {t, 1} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 1}). \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.859,
+                0.407,
+                0.878
+            ],
+            "angle": 0,
+            "content": "Then the gradient of \\(R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)\\) is approximated by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.186,
+                0.884,
+                0.469,
+                0.904
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla R _ {\\rho_ {t}} ^ {(0)} \\left(\\boldsymbol {\\theta} _ {t}\\right) \\approx \\boldsymbol {g} _ {t, 1} - \\boldsymbol {g} _ {t, 0}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.501,
+                0.091,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Flatness-Aware Minimization for Domain Generalization (FAD)"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.507,
+                0.124,
+                0.892,
+                0.422
+            ],
+            "angle": 0,
+            "content": "1: Input: Batch size \\(b\\), Learning rate \\(\\eta_t\\), Perturbation radius \\(\\rho_t\\), Trade-off coefficients \\(\\alpha\\), \\(\\beta\\), Small constant \\(\\xi\\)  \n2: \\(t \\gets 0\\), \\(\\theta_0 \\gets\\) initial parameters  \n3: while \\(\\theta_t\\) not converged do  \n4: Sample \\(W_t\\) from the training data with \\(b\\) instances  \n5: \\(g_{t,0} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\theta_t)\\)  \n6: \\(\\tilde{\\pmb{\\theta}}_{t,1} \\gets \\pmb{\\theta}_t + \\rho_t \\cdot \\pmb{g}_{t,0} / (\\| \\pmb{g}_{t,0} \\| + \\xi)\\)  \n7: \\(g_{t,1} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,1})\\)  \n8: \\(h_{t,0} \\gets g_{t,1} - g_{t,0}\\) gradient of \\(R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)\\)  \n9: \\(\\tilde{\\pmb{\\theta}}_{t,2} \\gets \\pmb{\\theta}_t + \\rho_t \\cdot h_{t,0} / (\\| h_{t,0} \\| + \\xi)\\)  \n10: \\(g_{t,2} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,2})\\)  \n11: \\(\\tilde{\\pmb{\\theta}}_{t,3} \\gets \\tilde{\\pmb{\\theta}}_{t,2} + \\rho_t \\cdot g_{t,2} / (\\| g_{t,2} \\| + \\xi)\\)  \n12: \\(g_{t,3} = \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,3})\\)  \n13: \\(h_{t,1} \\gets g_{t,3} - g_{t,2}\\) gradient of \\(R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)\\)  \n14: \\(\\pmb{\\theta}_{t+1} \\gets \\pmb{\\theta}_t - \\eta_t(g_{t,0} + \\beta (\\alpha h_{t,0} + (1 - \\alpha) h_{t,1}))\\)  \n15: \\(t \\gets t + 1\\)  \n16: end while  \n17: return \\(\\pmb{\\theta}_t\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.449,
+                0.892,
+                0.482
+            ],
+            "angle": 0,
+            "content": "The gradient of \\( R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t) \\). [121] propose to approximate the gradient through the following procedure"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.492,
+                0.906,
+                0.542
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla R _ {\\rho_ {t}} ^ {(1)} (\\boldsymbol {\\theta} _ {t}) \\approx \\rho_ {t} \\cdot \\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t} ^ {\\mathrm {a d v}}) \\right\\|, \\boldsymbol {\\theta} _ {t} ^ {\\mathrm {a d v}} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\right\\|}{\\left\\| \\nabla \\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\| \\right\\|}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.553,
+                0.892,
+                0.583
+            ],
+            "angle": 0,
+            "content": "One can approximate \\(\\nabla \\| \\nabla \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta}_t)\\|\\) with first-order gradient as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.51,
+                0.594,
+                0.88,
+                0.63
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\right\\| \\approx \\frac {\\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t , 1}) - \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t})}{\\rho_ {t}} = \\frac {\\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0}}{\\rho_ {t}},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.643,
+                0.892,
+                0.691
+            ],
+            "angle": 0,
+            "content": "Thus we can approximate the gradient of \\( R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t) \\) efficiently and rewrite the term as follows. The details of the derivation can be found in Appendix A."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.501,
+                0.703,
+                0.736,
+                0.723
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla R _ {\\rho_ {t}} ^ {(1)} (\\boldsymbol {\\theta} _ {t}) \\approx \\boldsymbol {g} _ {t, 3} - \\boldsymbol {g} _ {t, 2}, \\quad \\text {w h e r e}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.548,
+                0.726,
+                0.894,
+                0.757
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {\\boldsymbol {\\theta}} _ {t, 2} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0}}{\\| \\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0} \\|}, \\quad \\boldsymbol {g} _ {t, 2} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 2}),\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.548,
+                0.76,
+                0.892,
+                0.803
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {\\boldsymbol {\\theta}} _ {t, 3} = \\tilde {\\boldsymbol {\\theta}} _ {t, 2} + \\rho_ {t} \\frac {\\boldsymbol {g} _ {t , 2}}{\\| \\boldsymbol {g} _ {t , 2} \\|}, \\quad \\boldsymbol {g} _ {t, 3} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 3}). \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.804,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Please note that the terms \\( \\pmb{g}_{t,1} \\) and \\( \\pmb{g}_{t,1} \\) for optimizing zeroth-order flatness \\( R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t) \\) are preserved in the approximation of \\( R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t) \\) and thus causes no overhead. Combining the gradient approximation steps as shown in Equations (8) and (9), we can obtain the unified optimization framework as shown in Algorithm 1."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.925,
+                0.516,
+                0.937
+            ],
+            "angle": 0,
+            "content": "5192"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.152
+            ],
+            "angle": 0,
+            "content": "Convergence analysis To analyze the convergence property of Algorithm 1, we first introduce the Lipschitz smooth assumption that are adopted commonly in optimization-related literature [1, 112, 130]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.158,
+                0.47,
+                0.189
+            ],
+            "angle": 0,
+            "content": "Definition 3.3. For a function \\(J:\\Theta \\to \\mathbb{R}\\), \\(J\\) is \\(\\gamma_{2}\\)-Lipschitz smooth if"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.084,
+                0.195,
+                0.468,
+                0.213
+            ],
+            "angle": 0,
+            "content": "\\[\n\\forall \\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2} \\in \\Theta , \\| \\nabla J (\\boldsymbol {\\theta} _ {1}) - \\nabla J (\\boldsymbol {\\theta} _ {2}) \\| \\leq \\gamma_ {2} \\| \\boldsymbol {\\theta} _ {1} - \\boldsymbol {\\theta} _ {2} \\|. \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.218,
+                0.468,
+                0.279
+            ],
+            "angle": 0,
+            "content": "Let \\(\\pmb{\\Delta}_{t} = \\pmb{g}_{t,0} + \\beta (\\alpha \\pmb{h}_{t,0} + (1 - \\alpha)\\pmb{h}_{t,1})\\) be the estimated gradient at round \\(t\\) as shown in Line 14 in Algorithm 1. Now we can prove that the algorithm would eventually converge by the following theorem."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.284,
+                0.47,
+                0.346
+            ],
+            "angle": 0,
+            "content": "Theorem 3.2. Suppose \\(\\hat{\\mathcal{E}}_{tr}(\\pmb{\\theta})\\) is \\(\\gamma\\)-Lipschitz smooth and bounded by \\(M\\). For any timestamp \\(t \\in \\{0,1,\\dots,T\\}\\) and any \\(\\pmb{\\theta} \\in \\Theta\\), suppose we can obtain noisy and bounded observations \\(f_t(\\pmb{\\theta})\\) of \\(\\nabla \\hat{\\mathcal{E}}_{tr}(\\pmb{\\theta})\\) such that"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.147,
+                0.351,
+                0.468,
+                0.369
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbb {E} \\left[ f _ {t} (\\boldsymbol {\\theta}) \\right] = \\nabla \\hat {\\mathcal {E}} _ {t r} (\\boldsymbol {\\theta}), \\| f _ {t} (\\boldsymbol {\\theta}) \\| \\leq G. \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.375,
+                0.468,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Then with learning rate \\(\\eta_t = \\eta_0 / \\sqrt{t}\\) and perturbation radius \\(\\rho_t = \\rho_0 / \\sqrt{t}\\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.156,
+                0.412,
+                0.468,
+                0.453
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sum_ {t = 1} ^ {T} \\mathbb {E} \\left[ \\| \\boldsymbol {\\Delta} _ {t} \\| ^ {2} \\right] \\leq \\frac {C _ {1} + C _ {2} \\log T}{\\sqrt {T}}, \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.458,
+                0.468,
+                0.489
+            ],
+            "angle": 0,
+            "content": "for some constants \\(C_1\\) and \\(C_2\\) that only depend on \\(\\gamma_1, \\gamma_2, G, M, \\eta_0, \\rho_0, \\alpha, \\beta\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.494,
+                0.468,
+                0.525
+            ],
+            "angle": 0,
+            "content": "Thus, the convergence of FAD is guaranteed, and we show FAD's convergence rate empirically in Section 4.4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.076,
+                0.536,
+                0.209,
+                0.552
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.076,
+                0.561,
+                0.284,
+                0.577
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.584,
+                0.468,
+                0.734
+            ],
+            "angle": 0,
+            "content": "We evaluate our optimization method and current optimizers on various DG benchmarks including PACS [55], VLCS [27], OfficeHome [97], TerraIncognita [9], DomainNet [78] and \\(\\mathrm{NICO + + }\\) [122]. Detailed introductions of these datasets are in Appendix. We consider the generalization accuracy, training time, and hessian spectra of found minima as the evaluation metrics. We show how optimizers contribute when training with ERM and current SOTA DG algorithms. Generally, Adam is hardly the best choice for DG benchmarks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For a fair comparison, we follow the basic training and evaluation protocol introduced in [32], where the information of test data is unavailable for hyperparameter search. We train all the models on DomainNet for 15,000 iterations as suggested in [13], 10,000 iterations on \\(\\mathrm{NICO + + }\\) ,and 5,000 iterations on other datasets unless otherwise noted. For datasets except for \\(\\mathrm{NICO + + }\\) , we follow the leave-oneout protocol in [32] where one domain is chosen as the target domain and the remaining domains as the training domain. For \\(\\mathrm{NICO + + }\\) , we choose two domains as target domains in each run and train models on the remaining four"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "domains. Following the official combination [122], we select {autumn, rock}, {dim, grass}, {outdoor, water} as the target domain pairs. A detailed description of the split of training and test domains is in Appendix B. For all datasets, \\(20\\%\\) samples in the training data are used for validation and model selection. ImageNet [20] pretrained ResNet-50 [34] is adopted as the initial model. The search space for the initial learning rate, weight decay, and other hyperparameters is in Appendix B."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.24,
+                0.796,
+                0.256
+            ],
+            "angle": 0,
+            "content": "4.2. Comparison of Optimizers on DG"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.264,
+                0.892,
+                0.385
+            ],
+            "angle": 0,
+            "content": "Here we investigate how the optimizers affect the generalization under domain shifts. We first conduct experiments with various optimizers following the validation with training data protocol in DomainBed [32] to study the generalization of current optimizers and the robustness of the choice of hyperparameters. The results are shown in Table 1. Detailed results of optimizers on all the splits of reported datasets are in Appendix B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.386,
+                0.892,
+                0.703
+            ],
+            "angle": 0,
+            "content": "Despite SGD remaining the most popular optimizer for most CNN-based models on in-distribution image recognition benchmarks, such as CIFAR [51], and ImageNet due to its outstanding performance, it fails to show advantages compared with other optimizers on current benchmarks for DG. The previous work [74] shows that SGD with momentum outperforms adaptive-based optimizers such as Adam with an exhaustive hyperparameter search (hundreds of trials for each optimizer on each dataset) to select hyperparameters with good in-distribution performance. Yet for fair comparisons with previous works, we follow the model selection protocol in DomainBed, where only 20 trials of search are conducted for each evaluation, resulting in inadequate searches. In our experiments, SGD fails to outperform adaptive-based optimizers (e.g., AdamW and AdaBelief). This may be because SGD is more sensitive to the choice of hyperparameters [48] and the hyperparameter search space in evaluation protocols for DG is too large to be traversed and fine-tune the hyperparameters within several random runs. The empirical demonstration of the sensitivity of optimizers to hyperparameters is in Appendix B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.853
+            ],
+            "angle": 0,
+            "content": "Furthermore, it is important to note that different datasets may require different optimization strategies. For example, Adam outperforms SGD considerably on PACS, while the opposite stands for VLCS, OfficeHome, and NICO++. Among none-flatness-aware optimizers, AdaBelief shows the best average performance. AdamW outperforms Adam on 5 out of 6 datasets and achieves higher average accuracy. Thus, Adam is hardly the best choice for DG and choosing the right optimizer can help exceed current leaderboards' limitations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Among all optimizers, flatness-aware optimizers (e.g., SAM, GAM, and FAD) show promising results across all the datasets. FAD considerably outperforms all its coun"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.926,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "5193"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.131,
+                0.088,
+                0.839,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison of current optimizers on DG datasets. The best results for each dataset are highlighted in bold font."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.137,
+                0.103,
+                0.83,
+                0.274
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam [48]</td><td>84.2±0.6</td><td>77.3±1.3</td><td>67.6±0.4</td><td>44.4±0.8</td><td>43.0±0.1</td><td>76.9±0.0</td><td>65.6</td></tr><tr><td>AdamW [65]</td><td>83.6±1.5</td><td>77.4±0.8</td><td>68.8±0.6</td><td>45.2±1.4</td><td>43.4±0.1</td><td>77.5±0.1</td><td>66.0</td></tr><tr><td>SGD [76]</td><td>79.9±1.4</td><td>78.1±0.2</td><td>68.5±0.3</td><td>44.9±1.8</td><td>43.2±0.1</td><td>77.2±0.2</td><td>65.3</td></tr><tr><td>YOGI [117]</td><td>81.2±0.4</td><td>77.6±0.6</td><td>68.3±0.3</td><td>45.4±0.5</td><td>43.5±0.0</td><td>77.9±0.2</td><td>65.7</td></tr><tr><td>AdaBelief [131]</td><td>84.6±0.6</td><td>78.4±0.4</td><td>68.0±0.9</td><td>45.2±2.0</td><td>43.5±0.1</td><td>77.4±0.1</td><td>66.2</td></tr><tr><td>AdaHessian [116]</td><td>84.5±1.0</td><td>78.6±0.8</td><td>68.4±0.9</td><td>44.4±0.5</td><td>44.4±0.1</td><td>77.7±0.1</td><td>66.3</td></tr><tr><td>SAM [28]</td><td>85.3±1.0</td><td>78.2±0.5</td><td>68.0±0.8</td><td>45.7±0.9</td><td>43.4±0.1</td><td>77.9±0.1</td><td>66.4</td></tr><tr><td>GAM [121]</td><td>86.1±0.6</td><td>78.5±0.4</td><td>68.2±1.0</td><td>45.2±0.6</td><td>43.8±0.1</td><td>78.0±0.2</td><td>66.6</td></tr><tr><td>FAD (Ours)</td><td>88.2±0.5</td><td>78.9±0.8</td><td>69.2±0.5</td><td>45.7±1.0</td><td>44.4±0.1</td><td>79.0±0.1</td><td>67.6</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.3,
+                0.47,
+                0.346
+            ],
+            "angle": 0,
+            "content": "terparts on all the benchmarks, indicating that optimizing zeroth-order and first-order flatness simultaneously learns flatter minima and better generalization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.378,
+                0.408,
+                0.394
+            ],
+            "angle": 0,
+            "content": "4.3. Ensemble with current DG algorithms"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.409,
+                0.469,
+                0.515
+            ],
+            "angle": 0,
+            "content": "As a base optimizer, FAD can be combined with current DG methods with various objective functions. The compatibility with DG methods is critical for the choice of optimizers. In this subsection, we investigate the compatibility of GAM with current DG algorithms and compare it with other optimizers. We also report the results of other DG methods for better comparisons."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.523,
+                0.469,
+                0.689
+            ],
+            "angle": 0,
+            "content": "Please note that we only consider a single pretrained model (i.e., ImageNet pretrained ResNet-50) as the initial model for fair comparisons in this paper, so we do not combine optimizers with some SOTA methods, such as SIMPLE [62], MIRO [14] with RegNetY-16GF [83], and CARFT [70] with CLIP [82] which involve the knowledge of pretrained models other than ImageNet pretrained ResNet50. We consider SOTA and representative methods including CORAL [95], SWAD [13], and Fishr [85] as the base approach to compare optimizers and leave more methods, including EoA [4] and RSC [37] in Appendix B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.697,
+                0.469,
+                0.818
+            ],
+            "angle": 0,
+            "content": "The results are shown in Table 2. Different optimizers seem to favor different DG methods. AdamW achieves the best performance when combined with SWAD and CORAL, while SGD surpasses Adam and AdamW with Fishr. This indicates that fixing a single optimizer in DG benchmarks may be unfair for some methods that are not favored, and choosing the proper optimizer can further improve DG methods' performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "FAD consistently outperforms other optimizers with all the methods across various datasets. Compared with the default optimizer Adam, FAD further improves SWAD by \\(1.7\\%\\) on PACS and \\(1.2\\%\\) on average and surpasses previous SOTA methods."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.299,
+                0.889,
+                0.433
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.441,
+                0.892,
+                0.496
+            ],
+            "angle": 0,
+            "content": "Figure 2. Comparison of computation overhead. Red points on folding lines indicate models trained with FAD for various ratios of iterations (From left to right in each figure, the proportions are \\(100\\%\\), \\(50\\%\\), \\(10\\%\\), \\(5\\%\\))."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.508,
+                0.719,
+                0.525
+            ],
+            "angle": 0,
+            "content": "4.4. Computation Overhead"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.535,
+                0.892,
+                0.746
+            ],
+            "angle": 0,
+            "content": "Since flatness-aware optimization methods require more computation overhead than traditional optimizers, we report the comparison of FAD with other optimizers with more training iterations. We train current optimizers on DG benchmarks for 5,000, 10,000, and 15,000 iterations. We report the performance and required average training time in Table 3. Most optimizers achieve noticeable improvements in performance with more training iterations on PACS, VLCS, and OfficeHome. We show that FAD still outperforms current optimizers with fewer training iterations. For example, models trained with FAD for 5,000 iterations on PACS and \\(\\mathrm{NICO + + }\\) outperform those trained with other optimizers for 15,000 iterations. This indicates the effectiveness and efficiency of FAD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Furthermore, as discussed in Section 3.3, the FAD gradient can be efficiently calculated via first-order gradient approximation. Yet it still introduces extra computation when calculated in each iteration. Here we investigate optimizing the FAD term only for a subset of iterations in each epoch and optimize the remaining iterations simply with SGD on PACS and \\(\\mathrm{NICO + + }\\). We change the ratio of the subset with FAD from \\(5\\%\\) to \\(100\\%\\) and report the performance and training speed. We set the batch size to 96 \\((32\\times 3)\\) for PACS and \\(128(32\\times 4)\\) for \\(\\mathrm{NICO + + }\\) for all the methods for a fair"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "5194"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.894,
+                0.117
+            ],
+            "angle": 0,
+            "content": "Table 2. Ensemble with domain generalization methods. Numbers for methods marked with * and all the combinations of DG methods with optimizers other than Adam are reproduced results. Other results are from the original literature and DomainBed (donated with †)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.182,
+                0.117,
+                0.79,
+                0.677
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>Avg.</td></tr><tr><td>MASF [23]</td><td>82.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DMC [15]</td><td>83.4</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>MetaReg [7]</td><td>83.6</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>ER [124]</td><td>85.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>pAdalN [77]</td><td>85.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>EISNet [100]</td><td>85.8</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DSON [90]</td><td>86.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ERM† [96]</td><td>85.5</td><td>77.5</td><td>66.5</td><td>46.1</td><td>40.9</td><td>63.3</td></tr><tr><td>ERM* (with Adam)</td><td>84.2</td><td>77.3</td><td>67.6</td><td>44.4</td><td>43.0</td><td>63.3</td></tr><tr><td>IRM† [3]</td><td>83.5</td><td>78.6</td><td>64.3</td><td>47.6</td><td>33.9</td><td>61.6</td></tr><tr><td>GroupDRO† [88]</td><td>84.4</td><td>76.7</td><td>66.0</td><td>43.2</td><td>33.3</td><td>60.7</td></tr><tr><td>I-Mixup† [108, 113, 102]</td><td>84.6</td><td>77.4</td><td>68.1</td><td>47.9</td><td>39.2</td><td>63.4</td></tr><tr><td>MLDG† [56]</td><td>84.9</td><td>77.2</td><td>66.8</td><td>47.8</td><td>41.2</td><td>63.6</td></tr><tr><td>MMD† [60]</td><td>84.7</td><td>77.5</td><td>66.4</td><td>42.2</td><td>23.4</td><td>58.8</td></tr><tr><td>DANN† [30]</td><td>83.7</td><td>78.6</td><td>65.9</td><td>46.7</td><td>38.3</td><td>62.6</td></tr><tr><td>CDANN† [61]</td><td>82.6</td><td>77.5</td><td>65.7</td><td>45.8</td><td>38.3</td><td>62.0</td></tr><tr><td>MTL† [11]</td><td>84.6</td><td>77.2</td><td>66.4</td><td>45.6</td><td>40.6</td><td>62.9</td></tr><tr><td>SagNet† [75]</td><td>86.3</td><td>77.8</td><td>68.1</td><td>48.6</td><td>40.3</td><td>64.2</td></tr><tr><td>ARM† [119]</td><td>85.1</td><td>77.6</td><td>64.8</td><td>45.5</td><td>35.5</td><td>61.7</td></tr><tr><td>VREx† [52]</td><td>84.9</td><td>78.3</td><td>66.4</td><td>46.4</td><td>33.6</td><td>61.9</td></tr><tr><td>RSC† [38]</td><td>85.2</td><td>77.1</td><td>65.5</td><td>46.6</td><td>38.9</td><td>62.7</td></tr><tr><td>Mixstyle [129]</td><td>85.2</td><td>77.9</td><td>60.4</td><td>44.0</td><td>34.0</td><td>60.3</td></tr><tr><td>MIRO* [14]</td><td>85.4</td><td>78.9</td><td>69.5</td><td>45.4</td><td>44.0</td><td>64.6</td></tr><tr><td>Adam + SWAD* [13]</td><td>86.8</td><td>79.1</td><td>70.1</td><td>46.5</td><td>44.1</td><td>65.3</td></tr><tr><td>AdamW + SWAD</td><td>87.0</td><td>78.5</td><td>70.8</td><td>46.9</td><td>45.0</td><td>65.6</td></tr><tr><td>SGD + SWAD</td><td>85.2</td><td>79.1</td><td>71.0</td><td>46.7</td><td>42.8</td><td>65.0</td></tr><tr><td>FAD (Ours) + SWAD</td><td>88.5</td><td>79.8</td><td>71.8</td><td>47.5</td><td>45.0</td><td>66.5</td></tr><tr><td>Adam + Fishr* [85]</td><td>85.5</td><td>78.0</td><td>68.2</td><td>46.2</td><td>44.7</td><td>64.5</td></tr><tr><td>AdamW + Fishr</td><td>85.7</td><td>77.5</td><td>68.0</td><td>46.7</td><td>43.6</td><td>64.3</td></tr><tr><td>SGD + Fishr</td><td>84.4</td><td>78.5</td><td>69.2</td><td>46.9</td><td>44.4</td><td>64.7</td></tr><tr><td>FAD (Ours) + Fishr</td><td>88.3</td><td>79.6</td><td>69.2</td><td>48.1</td><td>43.8</td><td>65.8</td></tr><tr><td>Adam + CORAL* [95]</td><td>86.0</td><td>78.9</td><td>68.7</td><td>43.7</td><td>44.5</td><td>64.5</td></tr><tr><td>AdamW + CORAL</td><td>86.4</td><td>79.5</td><td>69.8</td><td>45.0</td><td>44.9</td><td>65.1</td></tr><tr><td>SGD + CORAL</td><td>85.6</td><td>78.2</td><td>69.5</td><td>45.8</td><td>44.6</td><td>64.7</td></tr><tr><td>FAD (Ours) + CORAL</td><td>88.5</td><td>78.9</td><td>70.8</td><td>46.1</td><td>44.9</td><td>65.9</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.702,
+                0.471,
+                0.779
+            ],
+            "angle": 0,
+            "content": "comparison. As shown in Figure 2, FAD consistently outperforms SGD, Adam, and AdamW by considerable margins and surpasses SAM and GAM with less training time when setting the ratio of FAD to \\(10\\%\\) and \\(50\\%\\). Detailed results are in Appendix B."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.787,
+                0.416,
+                0.803
+            ],
+            "angle": 0,
+            "content": "4.5. The Hessian spectra of selected minima"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Sharpness-aware optimization methods are shown to decrease the curvature of loss landscape [28, 121]. We investigate how FAD affects the flatness of minima. We consider the maximum eigenvalue of Hessian, which indicates the sharpness across the most critical direction, and the Hessian trace, which measures the expected loss increase under"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.702,
+                0.892,
+                0.731
+            ],
+            "angle": 0,
+            "content": "random perturbations to the weights [42] as the measures of flatness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We show the Hessian spectra of ResNet-50 trained on artpainting, cartoon, and photo domains of PACS for 5,000 iterations with SGD, Adam, AdamW, GAM, SAM, and FAD. Following [121], we adopt power iteration [115] to compute the top eigenvalues of Hessian and Hutchinson's method [6, 5, 114] to compute the Hessian trace. We report the distribution of the top-50 Hessian eigenvalues and Hessian trace for each method at convergence in Figure 3. None-flatness-aware optimizers, including SGD, Adam, and AdamW show high Hessian trace and dominant eigenvalues. In contrast, flatness-aware optimizers find"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "5195"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.114
+            ],
+            "angle": 0,
+            "content": "Table 3. The performance and average training time of current optimizers and FAD when training for 5,000, 10,000, 15,000 iterations. Training Time is the average time for finishing each dataset with the given iterations."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.186,
+                0.115,
+                0.785,
+                0.465
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Optimizers</td><td>Iterations</td><td>Training Time /s</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam</td><td>5,000</td><td>1613.9</td><td>84.2</td><td>77.3</td><td>67.6</td><td>76.2</td><td>76.3</td></tr><tr><td>Adam</td><td>10,000</td><td>3049.5</td><td>82.9</td><td>77.7</td><td>67.4</td><td>76.9</td><td>76.2</td></tr><tr><td>Adam</td><td>15,000</td><td>4478.6</td><td>84.0</td><td>78.4</td><td>69.6</td><td>77.3</td><td>77.3</td></tr><tr><td>AdamW</td><td>5,000</td><td>2145.2</td><td>83.6</td><td>77.4</td><td>68.8</td><td>76.9</td><td>76.7</td></tr><tr><td>AdamW</td><td>10,000</td><td>4632.8</td><td>83.3</td><td>77.1</td><td>66.9</td><td>77.5</td><td>76.2</td></tr><tr><td>AdamW</td><td>15,000</td><td>6995.3</td><td>83.7</td><td>76.3</td><td>68.0</td><td>77.5</td><td>76.4</td></tr><tr><td>SGD</td><td>5,000</td><td>1864.1</td><td>79.9</td><td>78.1</td><td>68.5</td><td>76.5</td><td>75.8</td></tr><tr><td>SGD</td><td>10,000</td><td>3438.9</td><td>81.4</td><td>78.1</td><td>68.7</td><td>77.2</td><td>76.4</td></tr><tr><td>SGD</td><td>15,000</td><td>4992.0</td><td>82.6</td><td>78.7</td><td>69.6</td><td>77.0</td><td>77.0</td></tr><tr><td>YOGI</td><td>5,000</td><td>1388.9</td><td>81.2</td><td>77.6</td><td>68.3</td><td>77.1</td><td>76.1</td></tr><tr><td>YOGI</td><td>10,000</td><td>2882.9</td><td>81.2</td><td>77.8</td><td>70.2</td><td>77.9</td><td>76.8</td></tr><tr><td>YOGI</td><td>15,000</td><td>4434.2</td><td>83.1</td><td>78.1</td><td>67.9</td><td>77.5</td><td>76.7</td></tr><tr><td>SAM</td><td>5,000</td><td>3325.6</td><td>85.3</td><td>78.2</td><td>68.0</td><td>77.0</td><td>77.1</td></tr><tr><td>SAM</td><td>10,000</td><td>6506.8</td><td>85.6</td><td>78.3</td><td>68.6</td><td>77.9</td><td>77.6</td></tr><tr><td>SAM</td><td>15,000</td><td>9960.2</td><td>86.1</td><td>78.9</td><td>68.8</td><td>78.1</td><td>78.0</td></tr><tr><td>GAM</td><td>5,000</td><td>8073.6</td><td>86.1</td><td>78.5</td><td>68.2</td><td>77.4</td><td>77.6</td></tr><tr><td>GAM</td><td>10,000</td><td>16210.5</td><td>86.0</td><td>79.2</td><td>68.5</td><td>78.0</td><td>78.0</td></tr><tr><td>GAM</td><td>15,000</td><td>23855.1</td><td>86.5</td><td>78.6</td><td>69.0</td><td>77.8</td><td>78.0</td></tr><tr><td>FAD (Ours)</td><td>5,000</td><td>5057.8</td><td>88.2</td><td>78.9</td><td>69.2</td><td>78.5</td><td>78.7</td></tr><tr><td>FAD (Ours)</td><td>10,000</td><td>10450.8</td><td>88.5</td><td>79.5</td><td>69.6</td><td>79.0</td><td>79.1</td></tr><tr><td>FAD (Ours)</td><td>15,000</td><td>16255.2</td><td>88.5</td><td>79.0</td><td>69.0</td><td>79.1</td><td>78.9</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.479,
+                0.891,
+                0.58
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.584,
+                0.894,
+                0.613
+            ],
+            "angle": 0,
+            "content": "Figure 3. The distribution of top eigenvalues and the trace of Hessian at convergence on PACS with SGD, Adam, AdamW, GAM, SAM, and FAD. Trace indicates Hessian trace and \\(\\lambda_{\\mathrm{max}}\\) indicates the maximum eigenvalue of Hessian."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.637,
+                0.47,
+                0.699
+            ],
+            "angle": 0,
+            "content": "minima with significantly lower Hessian spectra. FAD leads to both the lowest Hessian maximum eigenvalue and trace and thus the lowest curvature compared with other optimizers. More results are shown in Appendix B."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.71,
+                0.2,
+                0.725
+            ],
+            "angle": 0,
+            "content": "5. Discussions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Despite the wide usage in DG benchmarks, Adam is hardly the optimal choice of default optimizer. We show that the best optimizer for different DG methods varies across different datasets. Choosing the right optimizer can help exceed the current benchmarks' limitations. We propose a unified optimization method, flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness efficiently to address the problem. We further show that FAD controls the OOD generalization error and convergences fast. Compared with current optimizers, flatness-aware optimization approaches,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.637,
+                0.892,
+                0.684
+            ],
+            "angle": 0,
+            "content": "including SAM, GAM, and FAD, leads to flatter minima and better generalization. FAD outperforms its counterparts significantly on most DG datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "FAD still has the following limitations which could lead to potential future work. First, the term \\(\\sup_{\\pmb{\\theta}_1,\\pmb{\\theta}_2\\in \\Theta}|\\mathcal{L}_{\\mathrm{tr}}(\\pmb{\\theta}_1,\\pmb{\\theta}_2) - \\mathcal{L}_{\\mathrm{te}}(\\pmb{\\theta}_1,\\pmb{\\theta}_2)|\\) in Equation (6) indicates the discrepancy between training and test data. Without knowledge of test distribution and extra assumptions, the term cannot be optimized and leads to the optimization of the flatness term. Proper assumptions on the connection between training and test data or the geometry of data may help to learn the connection between flatness and the discrepancy, and thus control the discrepancy for better generalization. Second, We show that Adam is hardly an optimal choice of default optimizer in DG. However, selecting a proper optimizer for each DG method leads to massive overhead. Designing a better DG protocol"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.927,
+                0.516,
+                0.938
+            ],
+            "angle": 0,
+            "content": "5196"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.123
+            ],
+            "angle": 0,
+            "content": "or learning an indicator for the fitness of optimizers and methods can significantly contribute."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
+                0.138,
+                0.238,
+                0.156
+            ],
+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.165,
+                0.47,
+                0.241
+            ],
+            "angle": 0,
+            "content": "This work was supported in part by National Key R&D Program of China (No. 2018AAA0102004, No. 2020AAA0106300), National Natural Science Foundation of China (No. U1936219, 62141607), Beijing Academy of Artificial Intelligence (BAAI)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.256,
+                0.174,
+                0.272
+            ],
+            "angle": 0,
+            "content": "References"
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+# Flatness-Aware Minimization for Domain Generalization
+
+Xingxuan Zhang, Renzhe Xu, Han Yu, Yancheng Dong, Pengfei Tian, Peng Cui*  
+Department of Computer Science, Tsinghua University
+
+xingxuanzhang@hotmail.com, cuip@tsinghua.edu.cn
+
+# Abstract
+
+Domain generalization (DG) seeks to learn robust models that generalize well under unknown distribution shifts. As a critical aspect of DG, optimizer selection has not been explored in depth. Currently, most DG methods follow the widely used benchmark, DomainBed, and utilize Adam as the default optimizer for all datasets. However, we reveal that Adam is not necessarily the optimal choice for the majority of current DG methods and datasets. Based on the perspective of loss landscape flatness, we propose a novel approach, Flatness-Aware Minimization for Domain Generalization (FAD), which can efficiently optimize both zeroth-order and first-order flatness simultaneously for DG. We provide theoretical analyses of the FAD's out-of-distribution (OOD) generalization error and convergence. Our experimental results demonstrate the superiority of FAD on various DG datasets.
+
+# 1. Introduction
+
+Current neural networks are expected to generalize to unseen distributions in real-world applications, which can break the independent and identically distributional (I.I.D.) assumption of traditional machine learning algorithms [129, 99]. The distribution shift between training and test data may largely deteriorate most current approaches in practice. Hence, instead of generalization within the training distribution, the ability to generalize under distribution shift, namely domain generalization (DG) [73], has attracted increasing attention [99].
+
+Various methods have been proposed to address the DG problem recently, many of which have shown promising performance. As a learning problem mainly in the computer vision field, the DG task relies highly on the chosen optimizer, yet the effect of the optimizer in DG has hardly been studied. Most current algorithms, following the well-known benchmark DomainBed [32], default to optimize
+
+![](images/b3b3023209032dd977e3fc44859670cf2826821717b98e850f898aaa2b370cf0.jpg)  
+Figure 1. Test accuracy on PACS and DomainNet of different optimizers. Adam, the default optimizer in popular benchmarks shows no advantage compared with its counterparts, while the proposed FAD achieve better OOD generalization performance compared with current optimizers.
+
+models with Adam [48] without considering other optimizers. However, the in-distribution generalization ability of popular optimizers has been investigated from the perspective of loss landscape recently [28, 29] and Adam is found to achieve inferior generalization compared with other optimizers such as SGD [76] due to the sharp minima Adam selected. Thus, investigating the impact of optimizers in DG and clarifying whether Adam should be considered as the default optimizer is of significance.
+
+In this paper, we empirically compare the performance of current optimizers, including Adam, SGD, AdaBelief [131], YOGI [117], AdaHessian [116], SAM [28], and GAM[121]. Through extensive experiments on current DG benchmarks, we show that Adam can hardly surpass other optimizers on most DG datasets. The best choice of the optimizer for different DG methods varies across different datasets, and choosing the right optimizer can help exceed the current leaderboards' limitations.
+
+Recently, the connection between the flatness of the loss landscape and in-distribution generalization ability has been widely studied and verified both theoretically[130] and empirically[25]. Some works [13, 87] show that flatness also leads to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach.
+
+Among flatness-aware optimization methods, sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 126, 47], which optimize the zeroth-order flatness, achieve SOTA performance on various in-distribution image classification tasks [53, 130]. Most recently, Gradient Norm Aware Minimization (GAM) [121] shows that minimizing the first-order flatness provides a more substantial penalty on the sharpness of minima than zeroth-order flatness yet requires more computation overhead. Due to the first-order Taylor expansions adopted to optimize zeroth-order and first-order flatness, both SAM and GAM lose some of their penalty strength, and thus they can be mutually reinforced by each other. To accelerate the optimization of first-order flatness and combine zero-order flatness, we propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), which eliminates the considerable computation overhead for Hessian or Hessian-vector products. We theoretically show that the proposed FAD controls the dominant eigenvalue of Hessian of the training loss, which indicates the sharpness of the loss landscape along its most critical direction [42]. We present an OOD generalization bound to show that the proposed FAD guarantees the generalization error on test data and convergence analysis. Through extensive experiments, we evaluate FAD and other optimizers on various DG benchmarks.
+
+We summarize the main contribution as follows.
+
+- We propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness simultaneously. Without calculating Hessian and Hessian-vector products, FAD considerably reduces the computation overhead of first-order flatness.  
+- We theoretically analyze the OOD generalization error and convergence of FAD. We show that FAD controls the dominant eigenvalue of Hessian and thus the flatness of learned minima.  
+- We empirically show that Adam, the default optimizer for most current DG benchmarks, can hardly be the optimal choice for most DG datasets. We present the superiority of FAD compared with current optimizers through extensive experiments.  
+- We empirically validate that FAD finds flatter optima with lower Hessian spectra compared with zeroth- and first-order flatness-aware optimization methods.
+
+# 2. Related Works
+
+# 2.1. Optimizers
+
+Some works [107, 28] have studied the connection between current optimization approaches, such as SGD [76], Adam [49], AdamW [65] and others [26, 63] and in-distribution generalization. Some literature shows that
+
+Adam is more vulnerable to sharp minima than SGD [104], which may result in worse generalization [106, 33, 35]. Some follow-ups [66, 16, 107, 117] propose generalizable optimizers to address this problem. However, the generalization ability and convergence speed is often a trade-off [44, 107, 63, 117, 26]. Different optimizers may favor different tasks and network architectures (e.g., SGD is often chosen for ResNet [34] while AdamW [65] for ViTs [21]). Selecting the right optimizer is critical for performance and convergence while the understanding of its relationship to model generalization remains nascent [28]. [74] finds that fine-tuned SGD outperforms Adam on OOD tasks. Yet all the previous works do not consider the effect of optimizers in current DG benchmarks and evaluation protocols. In this paper, we discuss the selection of the default optimizer in DG benchmarks.
+
+# 2.2. Domain Generalization and Optimization
+
+Domain generalization (DG) aims to improve the generalization ability to novel domains [31, 45, 50]. A common approach is to learn domain-invariant or causal features over multiple source domains [22, 36, 57, 59, 72, 80, 89, 120, 110, 118, 101, 123] or aggregating domain-specific modules [67, 68]. Some works propose to enlarge the input space by augmentation of training data [12, 98, 81, 91, 127, 128, 109]. Exploit regularization with meta-learning [22, 58] and Invariant Risk Minimization (IRM) framework [2] are also proposed for DG. Recently, several works propose to ensemble model weights for better generalization [13, 4, 84, 105, 86, 62, 18] and achieve outstanding performance.
+
+# 2.3. Flatness of loss landscape
+
+Recent works study the relationship between flatter minima lead and better generalization on in-distribution data [44, 130, 41, 79]. [42] reviews the literature related to generalization and the sharpness of minima. It highlights the role of maximum Hessian eigenvalue in deciding the sharpness of minima [44, 103]. Some simple strategies are proposed to optimize maximum Hessian eigenvalue, such as choosing a large learning rate [54, 19, 40] and smaller batch size [94, 54, 39]. Sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 24, 64, 25, 71, 126, 47, 46], which are representative training algorithms to seek zeroth-order flatness, show outstanding performance on indistribution generalization. Most recently, several works discuss the relationship between generalization and gradient norm [8, 125]. GAM[121] proposes to optimize first-order flatness for better generalization. [13, 87] show that flatness minima also lead to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach.
+
+# 3. Method
+
+In in-distribution generalization tasks, sharpness-aware optimization methods show outstanding performance [28]. We theoretically show that optimizing both zeroth-order and first-order flatness strengthens out-of-distribution performance via a generalization bound. We propose a unified optimization framework to optimize zeroth-order and first-order flatness effectively and efficiently. We present the connection between Hessian spectra and our regularization term and give the convergence analysis of our method.
+
+Notations We use  $\mathcal{X}$  and  $\mathcal{Y}$  to denote the space of input  $X$  and outcome  $Y$ , respectively. We use  $\Delta_{\mathcal{Y}}$  to denote a distribution on  $\mathcal{Y}$ . Let  $S = \{(x_i, y_i)\}_{i=1}^n$  denote the training dataset with  $n$  data-points drawn independently from the training distribution  $\mathcal{D}_{\mathrm{tr}}$ . We consider the covariate shift scenario [10, 92, 111] and assume that the conditional probabilities are invariant across training and test distributions (i.e.,  $P_{\mathrm{tr}}(Y|X) = P_{\mathrm{te}}(Y|X)$ ). The invariant conditional probability is denoted as  $P(Y|X)$ . A prediction model  $f_{\theta}: \mathcal{X} \to \Delta_{\mathcal{Y}}$  parametrized by  $\theta \in \Theta \subseteq \mathbb{R}^d$  with dimension  $d$  maps an input to a simplex on  $\mathcal{Y}$ , which indicates the predicted probability of each class<sup>1</sup>.  $\Theta$  is the hypothesis set. We further assume that the ground truth model  $\theta^*$  that characterizes  $P(Y|X)$  is in the hypothesis set  $\Theta$ .
+
+Let  $\ell: \Delta_{\mathcal{Y}} \times \Delta_{\mathcal{Y}} \to \mathbb{R}_{+}$  define a loss function over  $\Delta_{\mathcal{Y}}$ . For any hypotheses  $\theta_1, \theta_2 \in \Theta$ , the expected loss  $\mathcal{L}_{\mathcal{D}}(\theta_1, \theta_2)$  for distribution  $\mathcal{D}$  is given as  $\mathcal{L}_{\mathcal{D}}(\theta_1, \theta_2) = \mathbb{E}_{x \sim \mathcal{D}}[\ell(f_{\theta_1}(x), f_{\theta_2}(x))]$ . To simplify the notations, we use  $\mathcal{L}_{\mathrm{tr}}$  and  $\mathcal{L}_{\mathrm{te}}$  to denote the expected loss  $\mathcal{L}_{\mathcal{D}_{\mathrm{tr}}}$  and  $\mathcal{L}_{\mathcal{D}_{\mathrm{te}}}$  in training and test distributions, respectively. In addition, we use  $\mathcal{E}_{\mathrm{tr}}(\pmb{\theta}) = \mathcal{L}_{\mathrm{tr}}(\pmb{\theta}, \pmb{\theta}^*)$  and  $\mathcal{E}_{\mathrm{te}}(\pmb{\theta}) = \mathcal{L}_{\mathrm{te}}(\pmb{\theta}, \pmb{\theta}^*)$  to denote the loss of a function  $\pmb{\theta} \in \Theta$  w.r.t. the true labeling function  $\pmb{\theta}^*$  in the two distributions. We use  $\hat{\mathcal{E}}_{\mathrm{tr}}(\pmb{\theta})$  to denote the empirical loss function w.r.t. the  $n$  samples  $S$  from the training distribution. In addition, we assume that  $\hat{\mathcal{E}}_{\mathrm{tr}}(\pmb{\theta})$  is twice differentiable throughout the paper and we use  $\nabla \hat{\mathcal{E}}_{\mathrm{tr}}(\pmb{\theta})$  and  $\nabla^2 \hat{\mathcal{E}}_{\mathrm{tr}}(\pmb{\theta})$  to denote the derivative and Hessian matrix, respectively.
+
+# 3.1. A General Flatness-Aware Optimization for DG
+
+In in-distribution generalization tasks, it is shown that the zeroth-order flatness can be not strong enough in cases where  $\rho$  covers multiple minima or the maximum loss in  $\rho$  is misaligned with the uptrend of loss and first-order flatness can help improve it [121]. But both zeroth-order and first-order flatness require first-order approximations in practice. Thus optimizing both zeroth-order and first-order flatness together leads to stronger generalization than both of them
+
+[121]. Yet optimizing first-order flatness requires the calculation of Hessian or Hessian-vector products, which introduces heavy computation overhead. As a result, we aim to accelerate the optimization in a Hessian-free way for OOD generalization.
+
+Formally, the zeroth-order and first-order flatness are defined as follows [28, 130, 121].
+
+Definition 3.1 ( $\rho$ -zeroth-order flatness). For any  $\rho > 0$ , the  $\rho$ -zeroth-order flatness  $R_{\rho}^{(0)}(\pmb{\theta})$  of function  $\hat{\mathcal{E}}_{\mathrm{tr}}(\pmb{\theta})$  at a point  $\pmb{\theta}$  is defined as
+
+$$
+R _ {\rho} ^ {(0)} (\boldsymbol {\theta}) \triangleq \max  _ {\boldsymbol {\theta} ^ {\prime} \in B (\boldsymbol {\theta}, \rho)} \left(\hat {\mathcal {E}} _ {\mathrm {t r}} \left(\boldsymbol {\theta} ^ {\prime}\right) - \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta})\right), \quad \forall \boldsymbol {\theta} \in \Theta . \tag {1}
+$$
+
+Here  $\rho$  is the perturbation radius that controls the magnitude of the neighborhood.
+
+Definition 3.2 ( $\rho$ -first-order flatness). For any  $\rho > 0$ , the  $\rho$ -first-order flatness  $R_{\rho}^{(1)}(\theta)$  of function  $\hat{\mathcal{E}}_{\mathrm{tr}}(\theta)$  at a point  $\theta$  is defined as
+
+$$
+R _ {\rho} ^ {(1)} (\boldsymbol {\theta}) \triangleq \rho \cdot \max  _ {\boldsymbol {\theta} ^ {\prime} \in B (\boldsymbol {\theta}, \rho)} \left\| \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} \left(\boldsymbol {\theta} ^ {\prime}\right) \right\|, \quad \forall \boldsymbol {\theta} \in \Theta . \tag {2}
+$$
+
+Here  $\rho$  is the perturbation radius similar to Definition 3.1.
+
+Based on these definitions, we propose to jointly optimize zeroth-order and first-order flatness through the following linear combination of the two flatness metrics.
+
+$$
+R _ {\rho , \alpha} ^ {\mathrm {F A D}} (\boldsymbol {\theta}) = \alpha R _ {\rho} ^ {(0)} (\boldsymbol {\theta}) + (1 - \alpha) R _ {\rho} ^ {(1)} (\boldsymbol {\theta}), \tag {3}
+$$
+
+where  $\alpha$  is a hyper-parameter that controls the trade-off between zeroth-order and first-order flatness. Since both flatness are related to the maximal eigenvalue of the Hessian matrices [130, 121], we can derive that  $R_{\rho ,\alpha}^{\mathrm{FAD}}(\pmb {\theta})$  is also related to the maximal eigenvalue. Specifically, when a point  $\pmb{\theta}^{*}$  is a local minimum of  $\hat{\mathcal{E}}_{\mathrm{tr}}(\pmb {\theta})$  and  $\hat{\mathcal{E}}_{\mathrm{tr}}(\pmb {\theta})$  can be second-order Taylor approximated in the neighbourhood of  $\pmb{\theta}^{*}$ , then
+
+$$
+\lambda_ {\max } \left(\nabla^ {2} \hat {\mathcal {E}} _ {\mathrm {t r}} \left(\boldsymbol {\theta} ^ {*}\right)\right) = \frac {R _ {\rho , \alpha} ^ {\mathrm {F A D}} \left(\boldsymbol {\theta} ^ {*}\right)}{\rho^ {2} \left(1 - \frac {\alpha}{2}\right)}. \tag {4}
+$$
+
+See Appendix A for details. Since the maximal eigenvalue is a proper measure of the curvature of minima [42, 43] and related to generalization abilities [121, 17, 39], optimizing Equation (3) would hopefully improve the DG performances, which we demonstrate in Section 3.2.
+
+Then the overall objective of our method, Flatness-Aware minimization for Domain generalization (FAD), is as follows.
+
+$$
+\mathcal {L} _ {\text {a l l}} (\boldsymbol {\theta}) = \hat {\mathcal {E}} _ {\text {t r}} (\boldsymbol {\theta}) + \beta \cdot R _ {\rho , \alpha} ^ {\mathrm {F A D}} (\boldsymbol {\theta}). \tag {5}
+$$
+
+The strength of FAD regularization is controlled by a hyperparameter  $\beta$ .
+
+# 3.2. Flatness Penalty and DG Performance
+
+We give a generalization bound to demonstrate that FAD controls the generalization error on test distribution as follows.
+
+Proposition 3.1. Suppose the per-data-point loss function  $\ell$  is differentiable, symmetric, bounded by  $M$ , and obeys the triangle inequality. Suppose  $\pmb{\theta}^{*}\in \Theta$ . Fix  $\rho >0$  and  $\pmb {\theta}\in \Theta$ . Then with probability at least  $1 - \delta$  over training set  $S$  generated from the distribution  $\mathcal{D}$
+
+$$
+\begin{array}{l} \mathbb {E} _ {\epsilon_ {i} \sim N (0, \rho^ {2} / (\sqrt {d} + \sqrt {\log n}) ^ {2})} \left[ \mathcal {E} _ {t e} (\boldsymbol {\theta} + \boldsymbol {\epsilon}) \right] \\ \leq \hat {\mathcal {E}} _ {t r} (\boldsymbol {\theta}) + R _ {\rho , \alpha} ^ {E A D} (\boldsymbol {\theta}) \\ + \sup  _ {\boldsymbol {\theta} _ {1}, \boldsymbol {\theta} _ {2} \in \Theta} | \mathcal {L} _ {t r} (\boldsymbol {\theta} _ {1}, \boldsymbol {\theta} _ {2}) - \mathcal {L} _ {t e} (\boldsymbol {\theta} _ {1}, \boldsymbol {\theta} _ {2}) | + \frac {M}{\sqrt {n}} \\ + \sqrt {\frac {\frac {1}{4} d \log \left(1 + \frac {\| \theta \| ^ {2} (\sqrt {d} + \sqrt {\log n}) ^ {2}}{d \rho^ {2}}\right) + \frac {1}{4} + \log \frac {n}{\delta} + 2 \log (6 n + 3 d)}{n - 1}} \tag {6} \\ \end{array}
+$$
+
+Remark. The term  $\sup_{\theta_1, \theta_2 \in \Theta} |\cdot|$  corresponds to the discrepancy distance [69], which measures the covariate shift between the training domain and the unknown test domain. Please note that in DG/OOD generalization tasks, the information on test distribution is unavailable in the optimization phase. Thus one cannot intervene in the third term on RHS. Thus optimizing the regularization of FAD (the second term on RHS) with ERM loss on training data leads to better generalization on test data.
+
+# 3.3. Algorithm Details
+
+Although the regularization of FAD controls the OOD generalization error, directly optimizing it suffers from significant computational costs. Previous works [114, 121] propose to calculate second order gradient with Hessian-vector product, yet the cost increases fast as the model dimension grows. Inspired by [93, 125], we approximate second-order gradient with first-order gradients and optimize zeroth-order and first-order flatness simultaneously as follows.
+
+Optimization and acceleration At each round, suppose the perturbation radius is set to  $\rho_{t}$ , then the gradient of  $\mathcal{L}_{\mathrm{all}}(\pmb{\theta}_t)$  at the point  $\pmb{\theta}_t$  in Equation (5) is approximated as follows.
+
+The gradient of  $R_{\rho_t}^{(0)}(\pmb {\theta}_t)$  . Following [28], let
+
+$$
+\begin{array}{l} \tilde {\boldsymbol {\theta}} _ {t, 1} = \boldsymbol {\theta} _ {t} + \rho_ {t} \cdot \frac {\boldsymbol {g} _ {t , 0}}{\| \boldsymbol {g} _ {t , 0} \|} \quad \text {w h e r e} \quad \boldsymbol {g} _ {t, 0} = \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta} _ {t}), \tag {7} \\ \boldsymbol {g} _ {t, 1} = \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\tilde {\boldsymbol {\theta}} _ {t, 1}). \\ \end{array}
+$$
+
+Then the gradient of  $R_{\rho_t}^{(0)}(\pmb{\theta}_t)$  is approximated by
+
+$$
+\nabla R _ {\rho_ {t}} ^ {(0)} \left(\boldsymbol {\theta} _ {t}\right) \approx \boldsymbol {g} _ {t, 1} - \boldsymbol {g} _ {t, 0}. \tag {8}
+$$
+
+Algorithm 1 Flatness-Aware Minimization for Domain Generalization (FAD)  
+1: Input: Batch size  $b$ , Learning rate  $\eta_t$ , Perturbation radius  $\rho_t$ , Trade-off coefficients  $\alpha$ ,  $\beta$ , Small constant  $\xi$   
+2:  $t \gets 0$ ,  $\theta_0 \gets$  initial parameters  
+3: while  $\theta_t$  not converged do  
+4: Sample  $W_t$  from the training data with  $b$  instances  
+5:  $g_{t,0} \gets \nabla \hat{\mathcal{E}}_{W_t}(\theta_t)$   
+6:  $\tilde{\pmb{\theta}}_{t,1} \gets \pmb{\theta}_t + \rho_t \cdot \pmb{g}_{t,0} / (\| \pmb{g}_{t,0} \| + \xi)$   
+7:  $g_{t,1} \gets \nabla \hat{\mathcal{E}}_{W_t}(\tilde{\pmb{\theta}}_{t,1})$   
+8:  $h_{t,0} \gets g_{t,1} - g_{t,0}$  gradient of  $R_{\rho_t}^{(0)}(\pmb{\theta}_t)$   
+9:  $\tilde{\pmb{\theta}}_{t,2} \gets \pmb{\theta}_t + \rho_t \cdot h_{t,0} / (\| h_{t,0} \| + \xi)$   
+10:  $g_{t,2} \gets \nabla \hat{\mathcal{E}}_{W_t}(\tilde{\pmb{\theta}}_{t,2})$   
+11:  $\tilde{\pmb{\theta}}_{t,3} \gets \tilde{\pmb{\theta}}_{t,2} + \rho_t \cdot g_{t,2} / (\| g_{t,2} \| + \xi)$   
+12:  $g_{t,3} = \nabla \hat{\mathcal{E}}_{W_t}(\tilde{\pmb{\theta}}_{t,3})$   
+13:  $h_{t,1} \gets g_{t,3} - g_{t,2}$  gradient of  $R_{\rho_t}^{(1)}(\pmb{\theta}_t)$   
+14:  $\pmb{\theta}_{t+1} \gets \pmb{\theta}_t - \eta_t(g_{t,0} + \beta (\alpha h_{t,0} + (1 - \alpha) h_{t,1}))$   
+15:  $t \gets t + 1$   
+16: end while  
+17: return  $\pmb{\theta}_t$
+
+The gradient of  $R_{\rho_t}^{(1)}(\pmb{\theta}_t)$ . [121] propose to approximate the gradient through the following procedure
+
+$$
+\nabla R _ {\rho_ {t}} ^ {(1)} (\boldsymbol {\theta} _ {t}) \approx \rho_ {t} \cdot \nabla \left\| \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta} _ {t} ^ {\mathrm {a d v}}) \right\|, \boldsymbol {\theta} _ {t} ^ {\mathrm {a d v}} = \boldsymbol {\theta} _ {t} + \rho_ {t} \cdot \frac {\nabla \left\| \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta} _ {t}) \right\|}{\left\| \nabla \| \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta} _ {t}) \| \right\|}.
+$$
+
+One can approximate  $\nabla \| \nabla \hat{\mathcal{E}}_{\mathrm{tr}}(\pmb {\theta}_t)\|$  with first-order gradient as follows.
+
+$$
+\nabla \left\| \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta} _ {t}) \right\| \approx \frac {\nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\tilde {\boldsymbol {\theta}} _ {t , 1}) - \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\boldsymbol {\theta} _ {t})}{\rho_ {t}} = \frac {\boldsymbol {g} _ {t , 1} - \boldsymbol {g} _ {t , 0}}{\rho_ {t}},
+$$
+
+Thus we can approximate the gradient of  $R_{\rho_t}^{(1)}(\pmb{\theta}_t)$  efficiently and rewrite the term as follows. The details of the derivation can be found in Appendix A.
+
+$$
+\nabla R _ {\rho_ {t}} ^ {(1)} (\boldsymbol {\theta} _ {t}) \approx \boldsymbol {g} _ {t, 3} - \boldsymbol {g} _ {t, 2}, \quad \text {w h e r e}
+$$
+
+$$
+\tilde {\boldsymbol {\theta}} _ {t, 2} = \boldsymbol {\theta} _ {t} + \rho_ {t} \cdot \frac {\boldsymbol {g} _ {t , 1} - \boldsymbol {g} _ {t , 0}}{\| \boldsymbol {g} _ {t , 1} - \boldsymbol {g} _ {t , 0} \|}, \quad \boldsymbol {g} _ {t, 2} = \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\tilde {\boldsymbol {\theta}} _ {t, 2}),
+$$
+
+$$
+\tilde {\boldsymbol {\theta}} _ {t, 3} = \tilde {\boldsymbol {\theta}} _ {t, 2} + \rho_ {t} \frac {\boldsymbol {g} _ {t , 2}}{\| \boldsymbol {g} _ {t , 2} \|}, \quad \boldsymbol {g} _ {t, 3} = \nabla \hat {\mathcal {E}} _ {\mathrm {t r}} (\tilde {\boldsymbol {\theta}} _ {t, 3}). \tag {9}
+$$
+
+Please note that the terms  $\pmb{g}_{t,1}$  and  $\pmb{g}_{t,1}$  for optimizing zeroth-order flatness  $R_{\rho_t}^{(0)}(\pmb{\theta}_t)$  are preserved in the approximation of  $R_{\rho_t}^{(1)}(\pmb{\theta}_t)$  and thus causes no overhead. Combining the gradient approximation steps as shown in Equations (8) and (9), we can obtain the unified optimization framework as shown in Algorithm 1.
+
+Convergence analysis To analyze the convergence property of Algorithm 1, we first introduce the Lipschitz smooth assumption that are adopted commonly in optimization-related literature [1, 112, 130].
+
+Definition 3.3. For a function  $J:\Theta \to \mathbb{R}$ ,  $J$  is  $\gamma_{2}$ -Lipschitz smooth if
+
+$$
+\forall \boldsymbol {\theta} _ {1}, \boldsymbol {\theta} _ {2} \in \Theta , \| \nabla J (\boldsymbol {\theta} _ {1}) - \nabla J (\boldsymbol {\theta} _ {2}) \| \leq \gamma_ {2} \| \boldsymbol {\theta} _ {1} - \boldsymbol {\theta} _ {2} \|. \tag {10}
+$$
+
+Let  $\pmb{\Delta}_{t} = \pmb{g}_{t,0} + \beta (\alpha \pmb{h}_{t,0} + (1 - \alpha)\pmb{h}_{t,1})$  be the estimated gradient at round  $t$  as shown in Line 14 in Algorithm 1. Now we can prove that the algorithm would eventually converge by the following theorem.
+
+Theorem 3.2. Suppose  $\hat{\mathcal{E}}_{tr}(\pmb{\theta})$  is  $\gamma$ -Lipschitz smooth and bounded by  $M$ . For any timestamp  $t \in \{0,1,\dots,T\}$  and any  $\pmb{\theta} \in \Theta$ , suppose we can obtain noisy and bounded observations  $f_t(\pmb{\theta})$  of  $\nabla \hat{\mathcal{E}}_{tr}(\pmb{\theta})$  such that
+
+$$
+\mathbb {E} \left[ f _ {t} (\boldsymbol {\theta}) \right] = \nabla \hat {\mathcal {E}} _ {t r} (\boldsymbol {\theta}), \| f _ {t} (\boldsymbol {\theta}) \| \leq G. \tag {11}
+$$
+
+Then with learning rate  $\eta_t = \eta_0 / \sqrt{t}$  and perturbation radius  $\rho_t = \rho_0 / \sqrt{t}$ ,
+
+$$
+\sum_ {t = 1} ^ {T} \mathbb {E} \left[ \| \boldsymbol {\Delta} _ {t} \| ^ {2} \right] \leq \frac {C _ {1} + C _ {2} \log T}{\sqrt {T}}, \tag {12}
+$$
+
+for some constants  $C_1$  and  $C_2$  that only depend on  $\gamma_1, \gamma_2, G, M, \eta_0, \rho_0, \alpha, \beta$ .
+
+Thus, the convergence of FAD is guaranteed, and we show FAD's convergence rate empirically in Section 4.4.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+We evaluate our optimization method and current optimizers on various DG benchmarks including PACS [55], VLCS [27], OfficeHome [97], TerraIncognita [9], DomainNet [78] and  $\mathrm{NICO + + }$  [122]. Detailed introductions of these datasets are in Appendix. We consider the generalization accuracy, training time, and hessian spectra of found minima as the evaluation metrics. We show how optimizers contribute when training with ERM and current SOTA DG algorithms. Generally, Adam is hardly the best choice for DG benchmarks.
+
+For a fair comparison, we follow the basic training and evaluation protocol introduced in [32], where the information of test data is unavailable for hyperparameter search. We train all the models on DomainNet for 15,000 iterations as suggested in [13], 10,000 iterations on  $\mathrm{NICO + + }$  ,and 5,000 iterations on other datasets unless otherwise noted. For datasets except for  $\mathrm{NICO + + }$  , we follow the leave-oneout protocol in [32] where one domain is chosen as the target domain and the remaining domains as the training domain. For  $\mathrm{NICO + + }$  , we choose two domains as target domains in each run and train models on the remaining four
+
+domains. Following the official combination [122], we select {autumn, rock}, {dim, grass}, {outdoor, water} as the target domain pairs. A detailed description of the split of training and test domains is in Appendix B. For all datasets,  $20\%$  samples in the training data are used for validation and model selection. ImageNet [20] pretrained ResNet-50 [34] is adopted as the initial model. The search space for the initial learning rate, weight decay, and other hyperparameters is in Appendix B.
+
+# 4.2. Comparison of Optimizers on DG
+
+Here we investigate how the optimizers affect the generalization under domain shifts. We first conduct experiments with various optimizers following the validation with training data protocol in DomainBed [32] to study the generalization of current optimizers and the robustness of the choice of hyperparameters. The results are shown in Table 1. Detailed results of optimizers on all the splits of reported datasets are in Appendix B.
+
+Despite SGD remaining the most popular optimizer for most CNN-based models on in-distribution image recognition benchmarks, such as CIFAR [51], and ImageNet due to its outstanding performance, it fails to show advantages compared with other optimizers on current benchmarks for DG. The previous work [74] shows that SGD with momentum outperforms adaptive-based optimizers such as Adam with an exhaustive hyperparameter search (hundreds of trials for each optimizer on each dataset) to select hyperparameters with good in-distribution performance. Yet for fair comparisons with previous works, we follow the model selection protocol in DomainBed, where only 20 trials of search are conducted for each evaluation, resulting in inadequate searches. In our experiments, SGD fails to outperform adaptive-based optimizers (e.g., AdamW and AdaBelief). This may be because SGD is more sensitive to the choice of hyperparameters [48] and the hyperparameter search space in evaluation protocols for DG is too large to be traversed and fine-tune the hyperparameters within several random runs. The empirical demonstration of the sensitivity of optimizers to hyperparameters is in Appendix B.
+
+Furthermore, it is important to note that different datasets may require different optimization strategies. For example, Adam outperforms SGD considerably on PACS, while the opposite stands for VLCS, OfficeHome, and NICO++. Among none-flatness-aware optimizers, AdaBelief shows the best average performance. AdamW outperforms Adam on 5 out of 6 datasets and achieves higher average accuracy. Thus, Adam is hardly the best choice for DG and choosing the right optimizer can help exceed current leaderboards' limitations.
+
+Among all optimizers, flatness-aware optimizers (e.g., SAM, GAM, and FAD) show promising results across all the datasets. FAD considerably outperforms all its coun
+
+Table 1. Comparison of current optimizers on DG datasets. The best results for each dataset are highlighted in bold font.  
+
+<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam [48]</td><td>84.2±0.6</td><td>77.3±1.3</td><td>67.6±0.4</td><td>44.4±0.8</td><td>43.0±0.1</td><td>76.9±0.0</td><td>65.6</td></tr><tr><td>AdamW [65]</td><td>83.6±1.5</td><td>77.4±0.8</td><td>68.8±0.6</td><td>45.2±1.4</td><td>43.4±0.1</td><td>77.5±0.1</td><td>66.0</td></tr><tr><td>SGD [76]</td><td>79.9±1.4</td><td>78.1±0.2</td><td>68.5±0.3</td><td>44.9±1.8</td><td>43.2±0.1</td><td>77.2±0.2</td><td>65.3</td></tr><tr><td>YOGI [117]</td><td>81.2±0.4</td><td>77.6±0.6</td><td>68.3±0.3</td><td>45.4±0.5</td><td>43.5±0.0</td><td>77.9±0.2</td><td>65.7</td></tr><tr><td>AdaBelief [131]</td><td>84.6±0.6</td><td>78.4±0.4</td><td>68.0±0.9</td><td>45.2±2.0</td><td>43.5±0.1</td><td>77.4±0.1</td><td>66.2</td></tr><tr><td>AdaHessian [116]</td><td>84.5±1.0</td><td>78.6±0.8</td><td>68.4±0.9</td><td>44.4±0.5</td><td>44.4±0.1</td><td>77.7±0.1</td><td>66.3</td></tr><tr><td>SAM [28]</td><td>85.3±1.0</td><td>78.2±0.5</td><td>68.0±0.8</td><td>45.7±0.9</td><td>43.4±0.1</td><td>77.9±0.1</td><td>66.4</td></tr><tr><td>GAM [121]</td><td>86.1±0.6</td><td>78.5±0.4</td><td>68.2±1.0</td><td>45.2±0.6</td><td>43.8±0.1</td><td>78.0±0.2</td><td>66.6</td></tr><tr><td>FAD (Ours)</td><td>88.2±0.5</td><td>78.9±0.8</td><td>69.2±0.5</td><td>45.7±1.0</td><td>44.4±0.1</td><td>79.0±0.1</td><td>67.6</td></tr></table>
+
+terparts on all the benchmarks, indicating that optimizing zeroth-order and first-order flatness simultaneously learns flatter minima and better generalization.
+
+# 4.3. Ensemble with current DG algorithms
+
+As a base optimizer, FAD can be combined with current DG methods with various objective functions. The compatibility with DG methods is critical for the choice of optimizers. In this subsection, we investigate the compatibility of GAM with current DG algorithms and compare it with other optimizers. We also report the results of other DG methods for better comparisons.
+
+Please note that we only consider a single pretrained model (i.e., ImageNet pretrained ResNet-50) as the initial model for fair comparisons in this paper, so we do not combine optimizers with some SOTA methods, such as SIMPLE [62], MIRO [14] with RegNetY-16GF [83], and CARFT [70] with CLIP [82] which involve the knowledge of pretrained models other than ImageNet pretrained ResNet50. We consider SOTA and representative methods including CORAL [95], SWAD [13], and Fishr [85] as the base approach to compare optimizers and leave more methods, including EoA [4] and RSC [37] in Appendix B.
+
+The results are shown in Table 2. Different optimizers seem to favor different DG methods. AdamW achieves the best performance when combined with SWAD and CORAL, while SGD surpasses Adam and AdamW with Fishr. This indicates that fixing a single optimizer in DG benchmarks may be unfair for some methods that are not favored, and choosing the proper optimizer can further improve DG methods' performance.
+
+FAD consistently outperforms other optimizers with all the methods across various datasets. Compared with the default optimizer Adam, FAD further improves SWAD by  $1.7\%$  on PACS and  $1.2\%$  on average and surpasses previous SOTA methods.
+
+![](images/aa30df0a905a191d20c5c1f53c51bab5c28fe3b16d8526716ff51300efe9fe40.jpg)  
+Figure 2. Comparison of computation overhead. Red points on folding lines indicate models trained with FAD for various ratios of iterations (From left to right in each figure, the proportions are  $100\%$ ,  $50\%$ ,  $10\%$ ,  $5\%$ ).
+
+# 4.4. Computation Overhead
+
+Since flatness-aware optimization methods require more computation overhead than traditional optimizers, we report the comparison of FAD with other optimizers with more training iterations. We train current optimizers on DG benchmarks for 5,000, 10,000, and 15,000 iterations. We report the performance and required average training time in Table 3. Most optimizers achieve noticeable improvements in performance with more training iterations on PACS, VLCS, and OfficeHome. We show that FAD still outperforms current optimizers with fewer training iterations. For example, models trained with FAD for 5,000 iterations on PACS and  $\mathrm{NICO + + }$  outperform those trained with other optimizers for 15,000 iterations. This indicates the effectiveness and efficiency of FAD.
+
+Furthermore, as discussed in Section 3.3, the FAD gradient can be efficiently calculated via first-order gradient approximation. Yet it still introduces extra computation when calculated in each iteration. Here we investigate optimizing the FAD term only for a subset of iterations in each epoch and optimize the remaining iterations simply with SGD on PACS and  $\mathrm{NICO + + }$ . We change the ratio of the subset with FAD from  $5\%$  to  $100\%$  and report the performance and training speed. We set the batch size to 96  $(32\times 3)$  for PACS and  $128(32\times 4)$  for  $\mathrm{NICO + + }$  for all the methods for a fair
+
+Table 2. Ensemble with domain generalization methods. Numbers for methods marked with * and all the combinations of DG methods with optimizers other than Adam are reproduced results. Other results are from the original literature and DomainBed (donated with †).  
+
+<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>Avg.</td></tr><tr><td>MASF [23]</td><td>82.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DMC [15]</td><td>83.4</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>MetaReg [7]</td><td>83.6</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>ER [124]</td><td>85.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>pAdalN [77]</td><td>85.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>EISNet [100]</td><td>85.8</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DSON [90]</td><td>86.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ERM† [96]</td><td>85.5</td><td>77.5</td><td>66.5</td><td>46.1</td><td>40.9</td><td>63.3</td></tr><tr><td>ERM* (with Adam)</td><td>84.2</td><td>77.3</td><td>67.6</td><td>44.4</td><td>43.0</td><td>63.3</td></tr><tr><td>IRM† [3]</td><td>83.5</td><td>78.6</td><td>64.3</td><td>47.6</td><td>33.9</td><td>61.6</td></tr><tr><td>GroupDRO† [88]</td><td>84.4</td><td>76.7</td><td>66.0</td><td>43.2</td><td>33.3</td><td>60.7</td></tr><tr><td>I-Mixup† [108, 113, 102]</td><td>84.6</td><td>77.4</td><td>68.1</td><td>47.9</td><td>39.2</td><td>63.4</td></tr><tr><td>MLDG† [56]</td><td>84.9</td><td>77.2</td><td>66.8</td><td>47.8</td><td>41.2</td><td>63.6</td></tr><tr><td>MMD† [60]</td><td>84.7</td><td>77.5</td><td>66.4</td><td>42.2</td><td>23.4</td><td>58.8</td></tr><tr><td>DANN† [30]</td><td>83.7</td><td>78.6</td><td>65.9</td><td>46.7</td><td>38.3</td><td>62.6</td></tr><tr><td>CDANN† [61]</td><td>82.6</td><td>77.5</td><td>65.7</td><td>45.8</td><td>38.3</td><td>62.0</td></tr><tr><td>MTL† [11]</td><td>84.6</td><td>77.2</td><td>66.4</td><td>45.6</td><td>40.6</td><td>62.9</td></tr><tr><td>SagNet† [75]</td><td>86.3</td><td>77.8</td><td>68.1</td><td>48.6</td><td>40.3</td><td>64.2</td></tr><tr><td>ARM† [119]</td><td>85.1</td><td>77.6</td><td>64.8</td><td>45.5</td><td>35.5</td><td>61.7</td></tr><tr><td>VREx† [52]</td><td>84.9</td><td>78.3</td><td>66.4</td><td>46.4</td><td>33.6</td><td>61.9</td></tr><tr><td>RSC† [38]</td><td>85.2</td><td>77.1</td><td>65.5</td><td>46.6</td><td>38.9</td><td>62.7</td></tr><tr><td>Mixstyle [129]</td><td>85.2</td><td>77.9</td><td>60.4</td><td>44.0</td><td>34.0</td><td>60.3</td></tr><tr><td>MIRO* [14]</td><td>85.4</td><td>78.9</td><td>69.5</td><td>45.4</td><td>44.0</td><td>64.6</td></tr><tr><td>Adam + SWAD* [13]</td><td>86.8</td><td>79.1</td><td>70.1</td><td>46.5</td><td>44.1</td><td>65.3</td></tr><tr><td>AdamW + SWAD</td><td>87.0</td><td>78.5</td><td>70.8</td><td>46.9</td><td>45.0</td><td>65.6</td></tr><tr><td>SGD + SWAD</td><td>85.2</td><td>79.1</td><td>71.0</td><td>46.7</td><td>42.8</td><td>65.0</td></tr><tr><td>FAD (Ours) + SWAD</td><td>88.5</td><td>79.8</td><td>71.8</td><td>47.5</td><td>45.0</td><td>66.5</td></tr><tr><td>Adam + Fishr* [85]</td><td>85.5</td><td>78.0</td><td>68.2</td><td>46.2</td><td>44.7</td><td>64.5</td></tr><tr><td>AdamW + Fishr</td><td>85.7</td><td>77.5</td><td>68.0</td><td>46.7</td><td>43.6</td><td>64.3</td></tr><tr><td>SGD + Fishr</td><td>84.4</td><td>78.5</td><td>69.2</td><td>46.9</td><td>44.4</td><td>64.7</td></tr><tr><td>FAD (Ours) + Fishr</td><td>88.3</td><td>79.6</td><td>69.2</td><td>48.1</td><td>43.8</td><td>65.8</td></tr><tr><td>Adam + CORAL* [95]</td><td>86.0</td><td>78.9</td><td>68.7</td><td>43.7</td><td>44.5</td><td>64.5</td></tr><tr><td>AdamW + CORAL</td><td>86.4</td><td>79.5</td><td>69.8</td><td>45.0</td><td>44.9</td><td>65.1</td></tr><tr><td>SGD + CORAL</td><td>85.6</td><td>78.2</td><td>69.5</td><td>45.8</td><td>44.6</td><td>64.7</td></tr><tr><td>FAD (Ours) + CORAL</td><td>88.5</td><td>78.9</td><td>70.8</td><td>46.1</td><td>44.9</td><td>65.9</td></tr></table>
+
+comparison. As shown in Figure 2, FAD consistently outperforms SGD, Adam, and AdamW by considerable margins and surpasses SAM and GAM with less training time when setting the ratio of FAD to  $10\%$  and  $50\%$ . Detailed results are in Appendix B.
+
+# 4.5. The Hessian spectra of selected minima
+
+Sharpness-aware optimization methods are shown to decrease the curvature of loss landscape [28, 121]. We investigate how FAD affects the flatness of minima. We consider the maximum eigenvalue of Hessian, which indicates the sharpness across the most critical direction, and the Hessian trace, which measures the expected loss increase under
+
+random perturbations to the weights [42] as the measures of flatness.
+
+We show the Hessian spectra of ResNet-50 trained on artpainting, cartoon, and photo domains of PACS for 5,000 iterations with SGD, Adam, AdamW, GAM, SAM, and FAD. Following [121], we adopt power iteration [115] to compute the top eigenvalues of Hessian and Hutchinson's method [6, 5, 114] to compute the Hessian trace. We report the distribution of the top-50 Hessian eigenvalues and Hessian trace for each method at convergence in Figure 3. None-flatness-aware optimizers, including SGD, Adam, and AdamW show high Hessian trace and dominant eigenvalues. In contrast, flatness-aware optimizers find
+
+Table 3. The performance and average training time of current optimizers and FAD when training for 5,000, 10,000, 15,000 iterations. Training Time is the average time for finishing each dataset with the given iterations.  
+
+<table><tr><td>Optimizers</td><td>Iterations</td><td>Training Time /s</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam</td><td>5,000</td><td>1613.9</td><td>84.2</td><td>77.3</td><td>67.6</td><td>76.2</td><td>76.3</td></tr><tr><td>Adam</td><td>10,000</td><td>3049.5</td><td>82.9</td><td>77.7</td><td>67.4</td><td>76.9</td><td>76.2</td></tr><tr><td>Adam</td><td>15,000</td><td>4478.6</td><td>84.0</td><td>78.4</td><td>69.6</td><td>77.3</td><td>77.3</td></tr><tr><td>AdamW</td><td>5,000</td><td>2145.2</td><td>83.6</td><td>77.4</td><td>68.8</td><td>76.9</td><td>76.7</td></tr><tr><td>AdamW</td><td>10,000</td><td>4632.8</td><td>83.3</td><td>77.1</td><td>66.9</td><td>77.5</td><td>76.2</td></tr><tr><td>AdamW</td><td>15,000</td><td>6995.3</td><td>83.7</td><td>76.3</td><td>68.0</td><td>77.5</td><td>76.4</td></tr><tr><td>SGD</td><td>5,000</td><td>1864.1</td><td>79.9</td><td>78.1</td><td>68.5</td><td>76.5</td><td>75.8</td></tr><tr><td>SGD</td><td>10,000</td><td>3438.9</td><td>81.4</td><td>78.1</td><td>68.7</td><td>77.2</td><td>76.4</td></tr><tr><td>SGD</td><td>15,000</td><td>4992.0</td><td>82.6</td><td>78.7</td><td>69.6</td><td>77.0</td><td>77.0</td></tr><tr><td>YOGI</td><td>5,000</td><td>1388.9</td><td>81.2</td><td>77.6</td><td>68.3</td><td>77.1</td><td>76.1</td></tr><tr><td>YOGI</td><td>10,000</td><td>2882.9</td><td>81.2</td><td>77.8</td><td>70.2</td><td>77.9</td><td>76.8</td></tr><tr><td>YOGI</td><td>15,000</td><td>4434.2</td><td>83.1</td><td>78.1</td><td>67.9</td><td>77.5</td><td>76.7</td></tr><tr><td>SAM</td><td>5,000</td><td>3325.6</td><td>85.3</td><td>78.2</td><td>68.0</td><td>77.0</td><td>77.1</td></tr><tr><td>SAM</td><td>10,000</td><td>6506.8</td><td>85.6</td><td>78.3</td><td>68.6</td><td>77.9</td><td>77.6</td></tr><tr><td>SAM</td><td>15,000</td><td>9960.2</td><td>86.1</td><td>78.9</td><td>68.8</td><td>78.1</td><td>78.0</td></tr><tr><td>GAM</td><td>5,000</td><td>8073.6</td><td>86.1</td><td>78.5</td><td>68.2</td><td>77.4</td><td>77.6</td></tr><tr><td>GAM</td><td>10,000</td><td>16210.5</td><td>86.0</td><td>79.2</td><td>68.5</td><td>78.0</td><td>78.0</td></tr><tr><td>GAM</td><td>15,000</td><td>23855.1</td><td>86.5</td><td>78.6</td><td>69.0</td><td>77.8</td><td>78.0</td></tr><tr><td>FAD (Ours)</td><td>5,000</td><td>5057.8</td><td>88.2</td><td>78.9</td><td>69.2</td><td>78.5</td><td>78.7</td></tr><tr><td>FAD (Ours)</td><td>10,000</td><td>10450.8</td><td>88.5</td><td>79.5</td><td>69.6</td><td>79.0</td><td>79.1</td></tr><tr><td>FAD (Ours)</td><td>15,000</td><td>16255.2</td><td>88.5</td><td>79.0</td><td>69.0</td><td>79.1</td><td>78.9</td></tr></table>
+
+![](images/ee602666417ee6d9610d909e22d01c6dd36ba698aa6da12a4381d2f8fed2f5d9.jpg)  
+Figure 3. The distribution of top eigenvalues and the trace of Hessian at convergence on PACS with SGD, Adam, AdamW, GAM, SAM, and FAD. Trace indicates Hessian trace and  $\lambda_{\mathrm{max}}$  indicates the maximum eigenvalue of Hessian.
+
+minima with significantly lower Hessian spectra. FAD leads to both the lowest Hessian maximum eigenvalue and trace and thus the lowest curvature compared with other optimizers. More results are shown in Appendix B.
+
+# 5. Discussions
+
+Despite the wide usage in DG benchmarks, Adam is hardly the optimal choice of default optimizer. We show that the best optimizer for different DG methods varies across different datasets. Choosing the right optimizer can help exceed the current benchmarks' limitations. We propose a unified optimization method, flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness efficiently to address the problem. We further show that FAD controls the OOD generalization error and convergences fast. Compared with current optimizers, flatness-aware optimization approaches,
+
+including SAM, GAM, and FAD, leads to flatter minima and better generalization. FAD outperforms its counterparts significantly on most DG datasets.
+
+FAD still has the following limitations which could lead to potential future work. First, the term  $\sup_{\pmb{\theta}_1,\pmb{\theta}_2\in \Theta}|\mathcal{L}_{\mathrm{tr}}(\pmb{\theta}_1,\pmb{\theta}_2) - \mathcal{L}_{\mathrm{te}}(\pmb{\theta}_1,\pmb{\theta}_2)|$  in Equation (6) indicates the discrepancy between training and test data. Without knowledge of test distribution and extra assumptions, the term cannot be optimized and leads to the optimization of the flatness term. Proper assumptions on the connection between training and test data or the geometry of data may help to learn the connection between flatness and the discrepancy, and thus control the discrepancy for better generalization. Second, We show that Adam is hardly an optimal choice of default optimizer in DG. However, selecting a proper optimizer for each DG method leads to massive overhead. Designing a better DG protocol
+
+or learning an indicator for the fitness of optimizers and methods can significantly contribute.
+
+# Acknowledgement
+
+This work was supported in part by National Key R&D Program of China (No. 2018AAA0102004, No. 2020AAA0106300), National Natural Science Foundation of China (No. U1936219, 62141607), Beijing Academy of Artificial Intelligence (BAAI).
+
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+                                    "content": "Among flatness-aware optimization methods, sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 126, 47], which optimize the zeroth-order flatness, achieve SOTA performance on various in-distribution image classification tasks [53, 130]. Most recently, Gradient Norm Aware Minimization (GAM) [121] shows that minimizing the first-order flatness provides a more substantial penalty on the sharpness of minima than zeroth-order flatness yet requires more computation overhead. Due to the first-order Taylor expansions adopted to optimize zeroth-order and first-order flatness, both SAM and GAM lose some of their penalty strength, and thus they can be mutually reinforced by each other. To accelerate the optimization of first-order flatness and combine zero-order flatness, we propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), which eliminates the considerable computation overhead for Hessian or Hessian-vector products. We theoretically show that the proposed FAD controls the dominant eigenvalue of Hessian of the training loss, which indicates the sharpness of the loss landscape along its most critical direction [42]. We present an OOD generalization bound to show that the proposed FAD guarantees the generalization error on test data and convergence analysis. Through extensive experiments, we evaluate FAD and other optimizers on various DG benchmarks."
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+                                    "type": "text",
+                                    "content": "We summarize the main contribution as follows."
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- We propose a unified optimization framework, Flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness simultaneously. Without calculating Hessian and Hessian-vector products, FAD considerably reduces the computation overhead of first-order flatness."
+                                        }
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+                        {
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+                                            "type": "text",
+                                            "content": "- We theoretically analyze the OOD generalization error and convergence of FAD. We show that FAD controls the dominant eigenvalue of Hessian and thus the flatness of learned minima."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
+                                            "content": "- We empirically show that Adam, the default optimizer for most current DG benchmarks, can hardly be the optimal choice for most DG datasets. We present the superiority of FAD compared with current optimizers through extensive experiments."
+                                        }
+                                    ]
+                                }
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+                            "index": 4
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+                        {
+                            "bbox": [
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+                                            "content": "- We empirically validate that FAD finds flatter optima with lower Hessian spectra compared with zeroth- and first-order flatness-aware optimization methods."
+                                        }
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+                                    "type": "text",
+                                    "content": "2. Related Works"
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+                                    "content": "2.1. Optimizers"
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+                                    "type": "text",
+                                    "content": "Some works [107, 28] have studied the connection between current optimization approaches, such as SGD [76], Adam [49], AdamW [65] and others [26, 63] and in-distribution generalization. Some literature shows that"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Adam is more vulnerable to sharp minima than SGD [104], which may result in worse generalization [106, 33, 35]. Some follow-ups [66, 16, 107, 117] propose generalizable optimizers to address this problem. However, the generalization ability and convergence speed is often a trade-off [44, 107, 63, 117, 26]. Different optimizers may favor different tasks and network architectures (e.g., SGD is often chosen for ResNet [34] while AdamW [65] for ViTs [21]). Selecting the right optimizer is critical for performance and convergence while the understanding of its relationship to model generalization remains nascent [28]. [74] finds that fine-tuned SGD outperforms Adam on OOD tasks. Yet all the previous works do not consider the effect of optimizers in current DG benchmarks and evaluation protocols. In this paper, we discuss the selection of the default optimizer in DG benchmarks."
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+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "2.2. Domain Generalization and Optimization"
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+                            ]
+                        }
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+                    "index": 11
+                },
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+                                    "type": "text",
+                                    "content": "Domain generalization (DG) aims to improve the generalization ability to novel domains [31, 45, 50]. A common approach is to learn domain-invariant or causal features over multiple source domains [22, 36, 57, 59, 72, 80, 89, 120, 110, 118, 101, 123] or aggregating domain-specific modules [67, 68]. Some works propose to enlarge the input space by augmentation of training data [12, 98, 81, 91, 127, 128, 109]. Exploit regularization with meta-learning [22, 58] and Invariant Risk Minimization (IRM) framework [2] are also proposed for DG. Recently, several works propose to ensemble model weights for better generalization [13, 4, 84, 105, 86, 62, 18] and achieve outstanding performance."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "2.3. Flatness of loss landscape"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Recent works study the relationship between flatter minima lead and better generalization on in-distribution data [44, 130, 41, 79]. [42] reviews the literature related to generalization and the sharpness of minima. It highlights the role of maximum Hessian eigenvalue in deciding the sharpness of minima [44, 103]. Some simple strategies are proposed to optimize maximum Hessian eigenvalue, such as choosing a large learning rate [54, 19, 40] and smaller batch size [94, 54, 39]. Sharpness-Aware Minimization (SAM) [28] and its variants [130, 53, 24, 64, 25, 71, 126, 47, 46], which are representative training algorithms to seek zeroth-order flatness, show outstanding performance on indistribution generalization. Most recently, several works discuss the relationship between generalization and gradient norm [8, 125]. GAM[121] proposes to optimize first-order flatness for better generalization. [13, 87] show that flatness minima also lead to superior OOD generalization. However, none of the previous works consider the optimization in DG nor provide theoretical assurance of their approach."
+                                }
+                            ]
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+                                    "content": "3. Method"
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+                                    "content": "In in-distribution generalization tasks, sharpness-aware optimization methods show outstanding performance [28]. We theoretically show that optimizing both zeroth-order and first-order flatness strengthens out-of-distribution performance via a generalization bound. We propose a unified optimization framework to optimize zeroth-order and first-order flatness effectively and efficiently. We present the connection between Hessian spectra and our regularization term and give the convergence analysis of our method."
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+                                    "type": "text",
+                                    "content": "Notations We use "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Y}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the space of input "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and outcome "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "Y"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. We use "
+                                },
+                                {
+                                    "bbox": [
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+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Delta_{\\mathcal{Y}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote a distribution on "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Y}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": ". Let "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S = \\{(x_i, y_i)\\}_{i=1}^n"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the training dataset with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " data-points drawn independently from the training distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\mathrm{tr}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": ". We consider the covariate shift scenario [10, 92, 111] and assume that the conditional probabilities are invariant across training and test distributions (i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{\\mathrm{tr}}(Y|X) = P_{\\mathrm{te}}(Y|X)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                    ],
+                                    "type": "text",
+                                    "content": "). The invariant conditional probability is denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P(Y|X)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". A prediction model "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\theta}: \\mathcal{X} \\to \\Delta_{\\mathcal{Y}}"
+                                },
+                                {
+                                    "bbox": [
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+                                        220,
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+                                    ],
+                                    "type": "text",
+                                    "content": " parametrized by "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta \\in \\Theta \\subseteq \\mathbb{R}^d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
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+                                    ],
+                                    "type": "text",
+                                    "content": " with dimension "
+                                },
+                                {
+                                    "bbox": [
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+                                        220,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " maps an input to a simplex on "
+                                },
+                                {
+                                    "bbox": [
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+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Y}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": ", which indicates the predicted probability of each class<sup>1</sup>. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " is the hypothesis set. We further assume that the ground truth model "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta^*"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " that characterizes "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P(Y|X)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": " is in the hypothesis set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        220,
+                                        287,
+                                        388
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        47,
+                        388,
+                        288,
+                        557
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                388,
+                                288,
+                                557
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": "Let "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell: \\Delta_{\\mathcal{Y}} \\times \\Delta_{\\mathcal{Y}} \\to \\mathbb{R}_{+}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " define a loss function over "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Delta_{\\mathcal{Y}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": ". For any hypotheses "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta_1, \\theta_2 \\in \\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": ", the expected loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathcal{D}}(\\theta_1, \\theta_2)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " for distribution "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " is given as "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathcal{D}}(\\theta_1, \\theta_2) = \\mathbb{E}_{x \\sim \\mathcal{D}}[\\ell(f_{\\theta_1}(x), f_{\\theta_2}(x))]"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": ". To simplify the notations, we use "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{tr}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{te}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the expected loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathcal{D}_{\\mathrm{tr}}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathcal{D}_{\\mathrm{te}}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " in training and test distributions, respectively. In addition, we use "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{E}_{\\mathrm{tr}}(\\pmb{\\theta}) = \\mathcal{L}_{\\mathrm{tr}}(\\pmb{\\theta}, \\pmb{\\theta}^*)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{E}_{\\mathrm{te}}(\\pmb{\\theta}) = \\mathcal{L}_{\\mathrm{te}}(\\pmb{\\theta}, \\pmb{\\theta}^*)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the loss of a function "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta} \\in \\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " w.r.t. the true labeling function "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}^*"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " in the two distributions. We use "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the empirical loss function w.r.t. the "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " samples "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " from the training distribution. In addition, we assume that "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " is twice differentiable throughout the paper and we use "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla^2 \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        388,
+                                        288,
+                                        557
+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the derivative and Hessian matrix, respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        47,
+                        567,
+                        287,
+                        580
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.1. A General Flatness-Aware Optimization for DG"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        586,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": "In in-distribution generalization tasks, it is shown that the zeroth-order flatness can be not strong enough in cases where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        586,
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+                                    ],
+                                    "type": "text",
+                                    "content": " covers multiple minima or the maximum loss in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        586,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        586,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is misaligned with the uptrend of loss and first-order flatness can help improve it [121]. But both zeroth-order and first-order flatness require first-order approximations in practice. Thus optimizing both zeroth-order and first-order flatness together leads to stronger generalization than both of them"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
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+                                        131
+                                    ],
+                                    "type": "text",
+                                    "content": "[121]. Yet optimizing first-order flatness requires the calculation of Hessian or Hessian-vector products, which introduces heavy computation overhead. As a result, we aim to accelerate the optimization in a Hessian-free way for OOD generalization."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Formally, the zeroth-order and first-order flatness are defined as follows [28, 130, 121]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    "type": "text",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Definition 3.1 ("
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-zeroth-order flatness). For any "
+                                },
+                                {
+                                    "bbox": [
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+                                        164,
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+                                        201
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho > 0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        201
+                                    ],
+                                    "type": "text",
+                                    "content": ", the "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        164,
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+                                        201
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        164,
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+                                        201
+                                    ],
+                                    "type": "text",
+                                    "content": "-zeroth-order flatness "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho}^{(0)}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of function "
+                                },
+                                {
+                                    "bbox": [
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+                                        201
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        201
+                                    ],
+                                    "type": "text",
+                                    "content": " at a point "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is defined as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "R _ {\\rho} ^ {(0)} (\\boldsymbol {\\theta}) \\triangleq \\max  _ {\\boldsymbol {\\theta} ^ {\\prime} \\in B (\\boldsymbol {\\theta}, \\rho)} \\left(\\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {\\prime}\\right) - \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta})\\right), \\quad \\forall \\boldsymbol {\\theta} \\in \\Theta . \\tag {1}",
+                                    "image_path": "2054eb9a97475a94f053adaa43d17b96ead197e547985c7a27027a610964680b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Here "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the perturbation radius that controls the magnitude of the neighborhood."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            ],
+                            "spans": [
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+                                    "type": "text",
+                                    "content": "Definition 3.2 ("
+                                },
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+                                    "type": "text",
+                                    "content": "-first-order flatness). For any "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\rho > 0"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", the "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "-first-order flatness "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho}^{(1)}(\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of function "
+                                },
+                                {
+                                    "bbox": [
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+                                        304
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\theta)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " at a point "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is defined as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "interline_equation",
+                                    "content": "R _ {\\rho} ^ {(1)} (\\boldsymbol {\\theta}) \\triangleq \\rho \\cdot \\max  _ {\\boldsymbol {\\theta} ^ {\\prime} \\in B (\\boldsymbol {\\theta}, \\rho)} \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {\\prime}\\right) \\right\\|, \\quad \\forall \\boldsymbol {\\theta} \\in \\Theta . \\tag {2}",
+                                    "image_path": "dcbca580d8f9458a183e511937c32b30e0e8bcf149c161b00e989169e1dea997.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Here "
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+                                    "type": "text",
+                                    "content": " is the perturbation radius similar to Definition 3.1."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Based on these definitions, we propose to jointly optimize zeroth-order and first-order flatness through the following linear combination of the two flatness metrics."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} (\\boldsymbol {\\theta}) = \\alpha R _ {\\rho} ^ {(0)} (\\boldsymbol {\\theta}) + (1 - \\alpha) R _ {\\rho} ^ {(1)} (\\boldsymbol {\\theta}), \\tag {3}",
+                                    "image_path": "b283abe2aaa8aef65a250eb76e6ad56512a4bffdea096212d0eeafaeac468e52.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a hyper-parameter that controls the trade-off between zeroth-order and first-order flatness. Since both flatness are related to the maximal eigenvalue of the Hessian matrices [130, 121], we can derive that "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho ,\\alpha}^{\\mathrm{FAD}}(\\pmb {\\theta})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is also related to the maximal eigenvalue. Specifically, when a point "
+                                },
+                                {
+                                    "bbox": [
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+                                        515
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+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}^{*}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a local minimum of "
+                                },
+                                {
+                                    "bbox": [
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+                                        515
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be second-order Taylor approximated in the neighbourhood of "
+                                },
+                                {
+                                    "bbox": [
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+                                        515
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}^{*}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", then"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\lambda_ {\\max } \\left(\\nabla^ {2} \\hat {\\mathcal {E}} _ {\\mathrm {t r}} \\left(\\boldsymbol {\\theta} ^ {*}\\right)\\right) = \\frac {R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} \\left(\\boldsymbol {\\theta} ^ {*}\\right)}{\\rho^ {2} \\left(1 - \\frac {\\alpha}{2}\\right)}. \\tag {4}",
+                                    "image_path": "b44f0c90bf93e4408647e69cf813eac0bc6179a5b2c2480513b7bed790b07170.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        305,
+                                        561,
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+                                        620
+                                    ],
+                                    "type": "text",
+                                    "content": "See Appendix A for details. Since the maximal eigenvalue is a proper measure of the curvature of minima [42, 43] and related to generalization abilities [121, 17, 39], optimizing Equation (3) would hopefully improve the DG performances, which we demonstrate in Section 3.2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        621,
+                                        545,
+                                        656
+                                    ],
+                                    "type": "text",
+                                    "content": "Then the overall objective of our method, Flatness-Aware minimization for Domain generalization (FAD), is as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        359,
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {a l l}} (\\boldsymbol {\\theta}) = \\hat {\\mathcal {E}} _ {\\text {t r}} (\\boldsymbol {\\theta}) + \\beta \\cdot R _ {\\rho , \\alpha} ^ {\\mathrm {F A D}} (\\boldsymbol {\\theta}). \\tag {5}",
+                                    "image_path": "9693500fb1c28726901512e3ee3c6f99523ca028020b5e5506d4eb530ae978e7.jpg"
+                                }
+                            ]
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The strength of FAD regularization is controlled by a hyperparameter "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\beta"
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "<sup>1</sup>We use "
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+                                    "type": "inline_equation",
+                                    "content": "\\Delta y"
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+                                    "type": "text",
+                                    "content": " to denote the non-deterministic function case. This formulation also includes deterministic function cases."
+                                }
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+                                    "content": "5191"
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+                                    "type": "text",
+                                    "content": "3.2. Flatness Penalty and DG Performance"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We give a generalization bound to demonstrate that FAD controls the generalization error on test distribution as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Proposition 3.1. Suppose the per-data-point loss function "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\ell"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is differentiable, symmetric, bounded by "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and obeys the triangle inequality. Suppose "
+                                },
+                                {
+                                    "bbox": [
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+                                        192
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}^{*}\\in \\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        132,
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+                                        192
+                                    ],
+                                    "type": "text",
+                                    "content": ". Fix "
+                                },
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+                                    "bbox": [
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+                                        192
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho >0"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb {\\theta}\\in \\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Then with probability at least "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1 - \\delta"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " over training set "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " generated from the distribution "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        49,
+                        198,
+                        307,
+                        304
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                49,
+                                198,
+                                307,
+                                304
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        49,
+                                        198,
+                                        307,
+                                        304
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathbb {E} _ {\\epsilon_ {i} \\sim N (0, \\rho^ {2} / (\\sqrt {d} + \\sqrt {\\log n}) ^ {2})} \\left[ \\mathcal {E} _ {t e} (\\boldsymbol {\\theta} + \\boldsymbol {\\epsilon}) \\right] \\\\ \\leq \\hat {\\mathcal {E}} _ {t r} (\\boldsymbol {\\theta}) + R _ {\\rho , \\alpha} ^ {E A D} (\\boldsymbol {\\theta}) \\\\ + \\sup  _ {\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2} \\in \\Theta} | \\mathcal {L} _ {t r} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}) - \\mathcal {L} _ {t e} (\\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2}) | + \\frac {M}{\\sqrt {n}} \\\\ + \\sqrt {\\frac {\\frac {1}{4} d \\log \\left(1 + \\frac {\\| \\theta \\| ^ {2} (\\sqrt {d} + \\sqrt {\\log n}) ^ {2}}{d \\rho^ {2}}\\right) + \\frac {1}{4} + \\log \\frac {n}{\\delta} + 2 \\log (6 n + 3 d)}{n - 1}} \\tag {6} \\\\ \\end{array}",
+                                    "image_path": "65ab61734fad2e11e63bfa48c473fd824e397bbcce6380a26554e99208a89e22.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        47,
+                        310,
+                        287,
+                        417
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                310,
+                                287,
+                                417
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        310,
+                                        287,
+                                        417
+                                    ],
+                                    "type": "text",
+                                    "content": "Remark. The term "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        310,
+                                        287,
+                                        417
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sup_{\\theta_1, \\theta_2 \\in \\Theta} |\\cdot|"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        310,
+                                        287,
+                                        417
+                                    ],
+                                    "type": "text",
+                                    "content": " corresponds to the discrepancy distance [69], which measures the covariate shift between the training domain and the unknown test domain. Please note that in DG/OOD generalization tasks, the information on test distribution is unavailable in the optimization phase. Thus one cannot intervene in the third term on RHS. Thus optimizing the regularization of FAD (the second term on RHS) with ERM loss on training data leads to better generalization on test data."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
+                        422,
+                        154,
+                        435
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                422,
+                                154,
+                                435
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        154,
+                                        435
+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Algorithm Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        47,
+                        441,
+                        287,
+                        548
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                441,
+                                287,
+                                548
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        441,
+                                        287,
+                                        548
+                                    ],
+                                    "type": "text",
+                                    "content": "Although the regularization of FAD controls the OOD generalization error, directly optimizing it suffers from significant computational costs. Previous works [114, 121] propose to calculate second order gradient with Hessian-vector product, yet the cost increases fast as the model dimension grows. Inspired by [93, 125], we approximate second-order gradient with first-order gradients and optimize zeroth-order and first-order flatness simultaneously as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        47,
+                        563,
+                        287,
+                        609
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                563,
+                                287,
+                                609
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "text",
+                                    "content": "Optimization and acceleration At each round, suppose the perturbation radius is set to "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "text",
+                                    "content": ", then the gradient of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{all}}(\\pmb{\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "text",
+                                    "content": " at the point "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        563,
+                                        287,
+                                        609
+                                    ],
+                                    "type": "text",
+                                    "content": " in Equation (5) is approximated as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        47,
+                        609,
+                        231,
+                        624
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                609,
+                                231,
+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        231,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": "The gradient of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        231,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho_t}^{(0)}(\\pmb {\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        231,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " . Following [28], let"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        58,
+                        631,
+                        287,
+                        673
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                58,
+                                631,
+                                287,
+                                673
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        58,
+                                        631,
+                                        287,
+                                        673
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\tilde {\\boldsymbol {\\theta}} _ {t, 1} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\boldsymbol {g} _ {t , 0}}{\\| \\boldsymbol {g} _ {t , 0} \\|} \\quad \\text {w h e r e} \\quad \\boldsymbol {g} _ {t, 0} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}), \\tag {7} \\\\ \\boldsymbol {g} _ {t, 1} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 1}). \\\\ \\end{array}",
+                                    "image_path": "737650e98f77d8c0bbc8cca98b5bcac552223b84b5cf38dad792d9c5d75aa696.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        47,
+                        680,
+                        249,
+                        695
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                680,
+                                249,
+                                695
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        680,
+                                        249,
+                                        695
+                                    ],
+                                    "type": "text",
+                                    "content": "Then the gradient of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        680,
+                                        249,
+                                        695
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        680,
+                                        249,
+                                        695
+                                    ],
+                                    "type": "text",
+                                    "content": " is approximated by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        113,
+                        700,
+                        287,
+                        715
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                113,
+                                700,
+                                287,
+                                715
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        113,
+                                        700,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\nabla R _ {\\rho_ {t}} ^ {(0)} \\left(\\boldsymbol {\\theta} _ {t}\\right) \\approx \\boldsymbol {g} _ {t, 1} - \\boldsymbol {g} _ {t, 0}. \\tag {8}",
+                                    "image_path": "cbb9dbe751810dd23e65bda3620c8ae29fb20d31b39da77959f734cd7510ea9b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "code",
+                    "bbox": [
+                        310,
+                        98,
+                        545,
+                        334
+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
+                                306,
+                                72,
+                                545,
+                                95
+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                306,
+                                                72,
+                                                545,
+                                                95
+                                            ],
+                                            "type": "text",
+                                            "content": "Algorithm 1 Flatness-Aware Minimization for Domain Generalization (FAD)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12,
+                            "angle": 0,
+                            "type": "code_caption"
+                        },
+                        {
+                            "bbox": [
+                                310,
+                                98,
+                                545,
+                                334
+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        310,
+                                        98,
+                                        545,
+                                        334
+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "1: Input: Batch size "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "b"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": ", Learning rate "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\eta_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": ", Perturbation radius "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\rho_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": ", Trade-off coefficients "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\alpha"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": ", "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\beta"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": ", Small constant "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\xi"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n2: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "t \\gets 0"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": ", "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\theta_0 \\gets"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": " initial parameters  \n3: while "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\theta_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": " not converged do  \n4: Sample "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "W_t"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": " from the training data with "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "b"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": " instances  \n5: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "g_{t,0} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\theta_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n6: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tilde{\\pmb{\\theta}}_{t,1} \\gets \\pmb{\\theta}_t + \\rho_t \\cdot \\pmb{g}_{t,0} / (\\| \\pmb{g}_{t,0} \\| + \\xi)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n7: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "g_{t,1} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,1})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n8: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "h_{t,0} \\gets g_{t,1} - g_{t,0}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": " gradient of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n9: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tilde{\\pmb{\\theta}}_{t,2} \\gets \\pmb{\\theta}_t + \\rho_t \\cdot h_{t,0} / (\\| h_{t,0} \\| + \\xi)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n10: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "g_{t,2} \\gets \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,2})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n11: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tilde{\\pmb{\\theta}}_{t,3} \\gets \\tilde{\\pmb{\\theta}}_{t,2} + \\rho_t \\cdot g_{t,2} / (\\| g_{t,2} \\| + \\xi)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n12: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "g_{t,3} = \\nabla \\hat{\\mathcal{E}}_{W_t}(\\tilde{\\pmb{\\theta}}_{t,3})"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n13: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "h_{t,1} \\gets g_{t,3} - g_{t,2}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": " gradient of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n14: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\pmb{\\theta}_{t+1} \\gets \\pmb{\\theta}_t - \\eta_t(g_{t,0} + \\beta (\\alpha h_{t,0} + (1 - \\alpha) h_{t,1}))"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n15: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "t \\gets t + 1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "text",
+                                            "content": "  \n16: end while  \n17: return "
+                                        },
+                                        {
+                                            "bbox": [
+                                                310,
+                                                98,
+                                                545,
+                                                334
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\pmb{\\theta}_t"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13,
+                            "angle": 0,
+                            "type": "code_body"
+                        }
+                    ],
+                    "index": 13,
+                    "sub_type": "algorithm"
+                },
+                {
+                    "bbox": [
+                        306,
+                        355,
+                        545,
+                        381
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                381
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        355,
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+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": "The gradient of "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        355,
+                                        545,
+                                        381
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        355,
+                                        545,
+                                        381
+                                    ],
+                                    "type": "text",
+                                    "content": ". [121] propose to approximate the gradient through the following procedure"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        306,
+                        389,
+                        554,
+                        429
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        389,
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+                                        429
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\nabla R _ {\\rho_ {t}} ^ {(1)} (\\boldsymbol {\\theta} _ {t}) \\approx \\rho_ {t} \\cdot \\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t} ^ {\\mathrm {a d v}}) \\right\\|, \\boldsymbol {\\theta} _ {t} ^ {\\mathrm {a d v}} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\right\\|}{\\left\\| \\nabla \\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\| \\right\\|}.",
+                                    "image_path": "17f4350733331a59bf56090a1210e95b7ee34d8787016df6505ea6977eccebac.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        306,
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+                        461
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        437,
+                                        545,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": "One can approximate "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        437,
+                                        545,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla \\| \\nabla \\hat{\\mathcal{E}}_{\\mathrm{tr}}(\\pmb {\\theta}_t)\\|"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        437,
+                                        545,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": " with first-order gradient as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        312,
+                        470,
+                        538,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                312,
+                                470,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        312,
+                                        470,
+                                        538,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\nabla \\left\\| \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t}) \\right\\| \\approx \\frac {\\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t , 1}) - \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\boldsymbol {\\theta} _ {t})}{\\rho_ {t}} = \\frac {\\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0}}{\\rho_ {t}},",
+                                    "image_path": "2e8a140cb1a934c9b885bbe2da7b05495dffa42b9c27a4bb6903108d0a83ef88.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
+                        305,
+                        509,
+                        545,
+                        547
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        509,
+                                        545,
+                                        547
+                                    ],
+                                    "type": "text",
+                                    "content": "Thus we can approximate the gradient of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        509,
+                                        545,
+                                        547
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        509,
+                                        545,
+                                        547
+                                    ],
+                                    "type": "text",
+                                    "content": " efficiently and rewrite the term as follows. The details of the derivation can be found in Appendix A."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        306,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        556,
+                                        450,
+                                        572
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\nabla R _ {\\rho_ {t}} ^ {(1)} (\\boldsymbol {\\theta} _ {t}) \\approx \\boldsymbol {g} _ {t, 3} - \\boldsymbol {g} _ {t, 2}, \\quad \\text {w h e r e}",
+                                    "image_path": "b47503fc72f99ebb128b213ab74dd767de2e917c7552e0e65ba50f130aeecddc.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                335,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        335,
+                                        574,
+                                        547,
+                                        599
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\tilde {\\boldsymbol {\\theta}} _ {t, 2} = \\boldsymbol {\\theta} _ {t} + \\rho_ {t} \\cdot \\frac {\\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0}}{\\| \\boldsymbol {g} _ {t , 1} - \\boldsymbol {g} _ {t , 0} \\|}, \\quad \\boldsymbol {g} _ {t, 2} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 2}),",
+                                    "image_path": "8bc835653dbd52f2abe53b4d6825e8a19d0af77a2f32b5e45bdf3ff99a67d87d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
+                        335,
+                        601,
+                        545,
+                        635
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                335,
+                                601,
+                                545,
+                                635
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        335,
+                                        601,
+                                        545,
+                                        635
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\tilde {\\boldsymbol {\\theta}} _ {t, 3} = \\tilde {\\boldsymbol {\\theta}} _ {t, 2} + \\rho_ {t} \\frac {\\boldsymbol {g} _ {t , 2}}{\\| \\boldsymbol {g} _ {t , 2} \\|}, \\quad \\boldsymbol {g} _ {t, 3} = \\nabla \\hat {\\mathcal {E}} _ {\\mathrm {t r}} (\\tilde {\\boldsymbol {\\theta}} _ {t, 3}). \\tag {9}",
+                                    "image_path": "642e8a565425ce2c8732e3cfc3b6db53fbe5559e546a255a4354ba7b8a7e938d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
+                        306,
+                        636,
+                        545,
+                        713
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
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+                                713
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "Please note that the terms "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{g}_{t,1}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{g}_{t,1}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " for optimizing zeroth-order flatness "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho_t}^{(0)}(\\pmb{\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " are preserved in the approximation of "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_{\\rho_t}^{(1)}(\\pmb{\\theta}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        636,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " and thus causes no overhead. Combining the gradient approximation steps as shown in Equations (8) and (9), we can obtain the unified optimization framework as shown in Algorithm 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                }
+            ],
+            "discarded_blocks": [
+                {
+                    "bbox": [
+                        294,
+                        732,
+                        315,
+                        742
+                    ],
+                    "type": "page_number",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                294,
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+                                315,
+                                742
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        294,
+                                        732,
+                                        315,
+                                        742
+                                    ],
+                                    "type": "text",
+                                    "content": "5192"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                }
+            ],
+            "page_size": [
+                612,
+                792
+            ],
+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
+                        46,
+                        72,
+                        287,
+                        120
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                72,
+                                287,
+                                120
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": "Convergence analysis To analyze the convergence property of Algorithm 1, we first introduce the Lipschitz smooth assumption that are adopted commonly in optimization-related literature [1, 112, 130]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
+                        125,
+                        287,
+                        149
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
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+                                287,
+                                149
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "text",
+                                    "content": "Definition 3.3. For a function "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "J:\\Theta \\to \\mathbb{R}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "J"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "text",
+                                    "content": " is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        125,
+                                        287,
+                                        149
+                                    ],
+                                    "type": "text",
+                                    "content": "-Lipschitz smooth if"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        51,
+                        154,
+                        286,
+                        168
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                51,
+                                154,
+                                286,
+                                168
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        51,
+                                        154,
+                                        286,
+                                        168
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\forall \\boldsymbol {\\theta} _ {1}, \\boldsymbol {\\theta} _ {2} \\in \\Theta , \\| \\nabla J (\\boldsymbol {\\theta} _ {1}) - \\nabla J (\\boldsymbol {\\theta} _ {2}) \\| \\leq \\gamma_ {2} \\| \\boldsymbol {\\theta} _ {1} - \\boldsymbol {\\theta} _ {2} \\|. \\tag {10}",
+                                    "image_path": "af656f83b4aeb5b8708793d866dff2dc226ed757abfcbbb18dd21275699483aa.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        172,
+                        286,
+                        220
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                172,
+                                286,
+                                220
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        172,
+                                        286,
+                                        220
+                                    ],
+                                    "type": "text",
+                                    "content": "Let "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        172,
+                                        286,
+                                        220
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\Delta}_{t} = \\pmb{g}_{t,0} + \\beta (\\alpha \\pmb{h}_{t,0} + (1 - \\alpha)\\pmb{h}_{t,1})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        172,
+                                        286,
+                                        220
+                                    ],
+                                    "type": "text",
+                                    "content": " be the estimated gradient at round "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        172,
+                                        286,
+                                        220
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        172,
+                                        286,
+                                        220
+                                    ],
+                                    "type": "text",
+                                    "content": " as shown in Line 14 in Algorithm 1. Now we can prove that the algorithm would eventually converge by the following theorem."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        224,
+                        287,
+                        274
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                224,
+                                287,
+                                274
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": "Theorem 3.2. Suppose "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{E}}_{tr}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": "-Lipschitz smooth and bounded by "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        224,
+                                        287,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". For any timestamp "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t \\in \\{0,1,\\dots,T\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and any "
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta} \\in \\Theta"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", suppose we can obtain noisy and bounded observations "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_t(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla \\hat{\\mathcal{E}}_{tr}(\\pmb{\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " such that"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbb {E} \\left[ f _ {t} (\\boldsymbol {\\theta}) \\right] = \\nabla \\hat {\\mathcal {E}} _ {t r} (\\boldsymbol {\\theta}), \\| f _ {t} (\\boldsymbol {\\theta}) \\| \\leq G. \\tag {11}",
+                                    "image_path": "51d0bd77c39ecd10b2d96225c373e6fe769166c8b2f82bd1c6ebe998fee95553.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Then with learning rate "
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+                                    "type": "inline_equation",
+                                    "content": "\\eta_t = \\eta_0 / \\sqrt{t}"
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+                                {
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+                                    "type": "text",
+                                    "content": " and perturbation radius "
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+                                    "type": "inline_equation",
+                                    "content": "\\rho_t = \\rho_0 / \\sqrt{t}"
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+                                    "type": "text",
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+                                    "type": "interline_equation",
+                                    "content": "\\sum_ {t = 1} ^ {T} \\mathbb {E} \\left[ \\| \\boldsymbol {\\Delta} _ {t} \\| ^ {2} \\right] \\leq \\frac {C _ {1} + C _ {2} \\log T}{\\sqrt {T}}, \\tag {12}",
+                                    "image_path": "d2bfca4ea9a0ab51551e1acb9cfdf7487406830b58c6ff39dd4ac5743d684c4c.jpg"
+                                }
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+                                    "content": "for some constants "
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+                                    "type": "inline_equation",
+                                    "content": "C_1"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "C_2"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " that only depend on "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_1, \\gamma_2, G, M, \\eta_0, \\rho_0, \\alpha, \\beta"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Thus, the convergence of FAD is guaranteed, and we show FAD's convergence rate empirically in Section 4.4."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4.1. Experimental Settings"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We evaluate our optimization method and current optimizers on various DG benchmarks including PACS [55], VLCS [27], OfficeHome [97], TerraIncognita [9], DomainNet [78] and "
+                                },
+                                {
+                                    "bbox": [
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+                                        462,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NICO + + }"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        462,
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+                                    ],
+                                    "type": "text",
+                                    "content": " [122]. Detailed introductions of these datasets are in Appendix. We consider the generalization accuracy, training time, and hessian spectra of found minima as the evaluation metrics. We show how optimizers contribute when training with ERM and current SOTA DG algorithms. Generally, Adam is hardly the best choice for DG benchmarks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For a fair comparison, we follow the basic training and evaluation protocol introduced in [32], where the information of test data is unavailable for hyperparameter search. We train all the models on DomainNet for 15,000 iterations as suggested in [13], 10,000 iterations on "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NICO + + }"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
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+                                    ],
+                                    "type": "text",
+                                    "content": " ,and 5,000 iterations on other datasets unless otherwise noted. For datasets except for "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NICO + + }"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " , we follow the leave-oneout protocol in [32] where one domain is chosen as the target domain and the remaining domains as the training domain. For "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NICO + + }"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        582,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " , we choose two domains as target domains in each run and train models on the remaining four"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "domains. Following the official combination [122], we select {autumn, rock}, {dim, grass}, {outdoor, water} as the target domain pairs. A detailed description of the split of training and test domains is in Appendix B. For all datasets, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "20\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " samples in the training data are used for validation and model selection. ImageNet [20] pretrained ResNet-50 [34] is adopted as the initial model. The search space for the initial learning rate, weight decay, and other hyperparameters is in Appendix B."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. Comparison of Optimizers on DG"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Here we investigate how the optimizers affect the generalization under domain shifts. We first conduct experiments with various optimizers following the validation with training data protocol in DomainBed [32] to study the generalization of current optimizers and the robustness of the choice of hyperparameters. The results are shown in Table 1. Detailed results of optimizers on all the splits of reported datasets are in Appendix B."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Despite SGD remaining the most popular optimizer for most CNN-based models on in-distribution image recognition benchmarks, such as CIFAR [51], and ImageNet due to its outstanding performance, it fails to show advantages compared with other optimizers on current benchmarks for DG. The previous work [74] shows that SGD with momentum outperforms adaptive-based optimizers such as Adam with an exhaustive hyperparameter search (hundreds of trials for each optimizer on each dataset) to select hyperparameters with good in-distribution performance. Yet for fair comparisons with previous works, we follow the model selection protocol in DomainBed, where only 20 trials of search are conducted for each evaluation, resulting in inadequate searches. In our experiments, SGD fails to outperform adaptive-based optimizers (e.g., AdamW and AdaBelief). This may be because SGD is more sensitive to the choice of hyperparameters [48] and the hyperparameter search space in evaluation protocols for DG is too large to be traversed and fine-tune the hyperparameters within several random runs. The empirical demonstration of the sensitivity of optimizers to hyperparameters is in Appendix B."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Furthermore, it is important to note that different datasets may require different optimization strategies. For example, Adam outperforms SGD considerably on PACS, while the opposite stands for VLCS, OfficeHome, and NICO++. Among none-flatness-aware optimizers, AdaBelief shows the best average performance. AdamW outperforms Adam on 5 out of 6 datasets and achieves higher average accuracy. Thus, Adam is hardly the best choice for DG and choosing the right optimizer can help exceed current leaderboards' limitations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Among all optimizers, flatness-aware optimizers (e.g., SAM, GAM, and FAD) show promising results across all the datasets. FAD considerably outperforms all its coun"
+                                }
+                            ]
+                        }
+                    ],
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+                                            "content": "Table 1. Comparison of current optimizers on DG datasets. The best results for each dataset are highlighted in bold font."
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+                                            "html": "<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam [48]</td><td>84.2±0.6</td><td>77.3±1.3</td><td>67.6±0.4</td><td>44.4±0.8</td><td>43.0±0.1</td><td>76.9±0.0</td><td>65.6</td></tr><tr><td>AdamW [65]</td><td>83.6±1.5</td><td>77.4±0.8</td><td>68.8±0.6</td><td>45.2±1.4</td><td>43.4±0.1</td><td>77.5±0.1</td><td>66.0</td></tr><tr><td>SGD [76]</td><td>79.9±1.4</td><td>78.1±0.2</td><td>68.5±0.3</td><td>44.9±1.8</td><td>43.2±0.1</td><td>77.2±0.2</td><td>65.3</td></tr><tr><td>YOGI [117]</td><td>81.2±0.4</td><td>77.6±0.6</td><td>68.3±0.3</td><td>45.4±0.5</td><td>43.5±0.0</td><td>77.9±0.2</td><td>65.7</td></tr><tr><td>AdaBelief [131]</td><td>84.6±0.6</td><td>78.4±0.4</td><td>68.0±0.9</td><td>45.2±2.0</td><td>43.5±0.1</td><td>77.4±0.1</td><td>66.2</td></tr><tr><td>AdaHessian [116]</td><td>84.5±1.0</td><td>78.6±0.8</td><td>68.4±0.9</td><td>44.4±0.5</td><td>44.4±0.1</td><td>77.7±0.1</td><td>66.3</td></tr><tr><td>SAM [28]</td><td>85.3±1.0</td><td>78.2±0.5</td><td>68.0±0.8</td><td>45.7±0.9</td><td>43.4±0.1</td><td>77.9±0.1</td><td>66.4</td></tr><tr><td>GAM [121]</td><td>86.1±0.6</td><td>78.5±0.4</td><td>68.2±1.0</td><td>45.2±0.6</td><td>43.8±0.1</td><td>78.0±0.2</td><td>66.6</td></tr><tr><td>FAD (Ours)</td><td>88.2±0.5</td><td>78.9±0.8</td><td>69.2±0.5</td><td>45.7±1.0</td><td>44.4±0.1</td><td>79.0±0.1</td><td>67.6</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "terparts on all the benchmarks, indicating that optimizing zeroth-order and first-order flatness simultaneously learns flatter minima and better generalization."
+                                }
+                            ]
+                        }
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.3. Ensemble with current DG algorithms"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "As a base optimizer, FAD can be combined with current DG methods with various objective functions. The compatibility with DG methods is critical for the choice of optimizers. In this subsection, we investigate the compatibility of GAM with current DG algorithms and compare it with other optimizers. We also report the results of other DG methods for better comparisons."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    "type": "text",
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+                                    "type": "text",
+                                    "content": "Please note that we only consider a single pretrained model (i.e., ImageNet pretrained ResNet-50) as the initial model for fair comparisons in this paper, so we do not combine optimizers with some SOTA methods, such as SIMPLE [62], MIRO [14] with RegNetY-16GF [83], and CARFT [70] with CLIP [82] which involve the knowledge of pretrained models other than ImageNet pretrained ResNet50. We consider SOTA and representative methods including CORAL [95], SWAD [13], and Fishr [85] as the base approach to compare optimizers and leave more methods, including EoA [4] and RSC [37] in Appendix B."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The results are shown in Table 2. Different optimizers seem to favor different DG methods. AdamW achieves the best performance when combined with SWAD and CORAL, while SGD surpasses Adam and AdamW with Fishr. This indicates that fixing a single optimizer in DG benchmarks may be unfair for some methods that are not favored, and choosing the proper optimizer can further improve DG methods' performance."
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+                                    "type": "text",
+                                    "content": "FAD consistently outperforms other optimizers with all the methods across various datasets. Compared with the default optimizer Adam, FAD further improves SWAD by "
+                                },
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+                                    "type": "text",
+                                    "content": " on PACS and "
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+                                    "type": "text",
+                                    "content": " on average and surpasses previous SOTA methods."
+                                }
+                            ]
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+                            "index": 8,
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+                                            "type": "text",
+                                            "content": "Figure 2. Comparison of computation overhead. Red points on folding lines indicate models trained with FAD for various ratios of iterations (From left to right in each figure, the proportions are "
+                                        },
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+                                            "type": "text",
+                                            "content": ")."
+                                        }
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+                                }
+                            ],
+                            "index": 9,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "4.4. Computation Overhead"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Since flatness-aware optimization methods require more computation overhead than traditional optimizers, we report the comparison of FAD with other optimizers with more training iterations. We train current optimizers on DG benchmarks for 5,000, 10,000, and 15,000 iterations. We report the performance and required average training time in Table 3. Most optimizers achieve noticeable improvements in performance with more training iterations on PACS, VLCS, and OfficeHome. We show that FAD still outperforms current optimizers with fewer training iterations. For example, models trained with FAD for 5,000 iterations on PACS and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        423,
+                                        545,
+                                        590
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NICO + + }"
+                                },
+                                {
+                                    "bbox": [
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+                                        423,
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+                                        590
+                                    ],
+                                    "type": "text",
+                                    "content": " outperform those trained with other optimizers for 15,000 iterations. This indicates the effectiveness and efficiency of FAD."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Furthermore, as discussed in Section 3.3, the FAD gradient can be efficiently calculated via first-order gradient approximation. Yet it still introduces extra computation when calculated in each iteration. Here we investigate optimizing the FAD term only for a subset of iterations in each epoch and optimize the remaining iterations simply with SGD on PACS and "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We change the ratio of the subset with FAD from "
+                                },
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+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and report the performance and training speed. We set the batch size to 96 "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for PACS and "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " for "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{NICO + + }"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for all the methods for a fair"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
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+                {
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+            "page_idx": 5
+        },
+        {
+            "para_blocks": [
+                {
+                    "type": "table",
+                    "bbox": [
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+                        92,
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+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
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+                            "lines": [
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+                                            "type": "text",
+                                            "content": "Table 2. Ensemble with domain generalization methods. Numbers for methods marked with * and all the combinations of DG methods with optimizers other than Adam are reproduced results. Other results are from the original literature and DomainBed (donated with †)."
+                                        }
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+                                            "html": "<table><tr><td>Algorithm</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>TerraInc</td><td>DomainNet</td><td>Avg.</td></tr><tr><td>MASF [23]</td><td>82.7</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DMC [15]</td><td>83.4</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>MetaReg [7]</td><td>83.6</td><td>-</td><td>-</td><td>-</td><td>43.6</td><td>-</td></tr><tr><td>ER [124]</td><td>85.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>pAdalN [77]</td><td>85.4</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>EISNet [100]</td><td>85.8</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DSON [90]</td><td>86.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ERM† [96]</td><td>85.5</td><td>77.5</td><td>66.5</td><td>46.1</td><td>40.9</td><td>63.3</td></tr><tr><td>ERM* (with Adam)</td><td>84.2</td><td>77.3</td><td>67.6</td><td>44.4</td><td>43.0</td><td>63.3</td></tr><tr><td>IRM† [3]</td><td>83.5</td><td>78.6</td><td>64.3</td><td>47.6</td><td>33.9</td><td>61.6</td></tr><tr><td>GroupDRO† [88]</td><td>84.4</td><td>76.7</td><td>66.0</td><td>43.2</td><td>33.3</td><td>60.7</td></tr><tr><td>I-Mixup† [108, 113, 102]</td><td>84.6</td><td>77.4</td><td>68.1</td><td>47.9</td><td>39.2</td><td>63.4</td></tr><tr><td>MLDG† [56]</td><td>84.9</td><td>77.2</td><td>66.8</td><td>47.8</td><td>41.2</td><td>63.6</td></tr><tr><td>MMD† [60]</td><td>84.7</td><td>77.5</td><td>66.4</td><td>42.2</td><td>23.4</td><td>58.8</td></tr><tr><td>DANN† [30]</td><td>83.7</td><td>78.6</td><td>65.9</td><td>46.7</td><td>38.3</td><td>62.6</td></tr><tr><td>CDANN† [61]</td><td>82.6</td><td>77.5</td><td>65.7</td><td>45.8</td><td>38.3</td><td>62.0</td></tr><tr><td>MTL† [11]</td><td>84.6</td><td>77.2</td><td>66.4</td><td>45.6</td><td>40.6</td><td>62.9</td></tr><tr><td>SagNet† [75]</td><td>86.3</td><td>77.8</td><td>68.1</td><td>48.6</td><td>40.3</td><td>64.2</td></tr><tr><td>ARM† [119]</td><td>85.1</td><td>77.6</td><td>64.8</td><td>45.5</td><td>35.5</td><td>61.7</td></tr><tr><td>VREx† [52]</td><td>84.9</td><td>78.3</td><td>66.4</td><td>46.4</td><td>33.6</td><td>61.9</td></tr><tr><td>RSC† [38]</td><td>85.2</td><td>77.1</td><td>65.5</td><td>46.6</td><td>38.9</td><td>62.7</td></tr><tr><td>Mixstyle [129]</td><td>85.2</td><td>77.9</td><td>60.4</td><td>44.0</td><td>34.0</td><td>60.3</td></tr><tr><td>MIRO* [14]</td><td>85.4</td><td>78.9</td><td>69.5</td><td>45.4</td><td>44.0</td><td>64.6</td></tr><tr><td>Adam + SWAD* [13]</td><td>86.8</td><td>79.1</td><td>70.1</td><td>46.5</td><td>44.1</td><td>65.3</td></tr><tr><td>AdamW + SWAD</td><td>87.0</td><td>78.5</td><td>70.8</td><td>46.9</td><td>45.0</td><td>65.6</td></tr><tr><td>SGD + SWAD</td><td>85.2</td><td>79.1</td><td>71.0</td><td>46.7</td><td>42.8</td><td>65.0</td></tr><tr><td>FAD (Ours) + SWAD</td><td>88.5</td><td>79.8</td><td>71.8</td><td>47.5</td><td>45.0</td><td>66.5</td></tr><tr><td>Adam + Fishr* [85]</td><td>85.5</td><td>78.0</td><td>68.2</td><td>46.2</td><td>44.7</td><td>64.5</td></tr><tr><td>AdamW + Fishr</td><td>85.7</td><td>77.5</td><td>68.0</td><td>46.7</td><td>43.6</td><td>64.3</td></tr><tr><td>SGD + Fishr</td><td>84.4</td><td>78.5</td><td>69.2</td><td>46.9</td><td>44.4</td><td>64.7</td></tr><tr><td>FAD (Ours) + Fishr</td><td>88.3</td><td>79.6</td><td>69.2</td><td>48.1</td><td>43.8</td><td>65.8</td></tr><tr><td>Adam + CORAL* [95]</td><td>86.0</td><td>78.9</td><td>68.7</td><td>43.7</td><td>44.5</td><td>64.5</td></tr><tr><td>AdamW + CORAL</td><td>86.4</td><td>79.5</td><td>69.8</td><td>45.0</td><td>44.9</td><td>65.1</td></tr><tr><td>SGD + CORAL</td><td>85.6</td><td>78.2</td><td>69.5</td><td>45.8</td><td>44.6</td><td>64.7</td></tr><tr><td>FAD (Ours) + CORAL</td><td>88.5</td><td>78.9</td><td>70.8</td><td>46.1</td><td>44.9</td><td>65.9</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "comparison. As shown in Figure 2, FAD consistently outperforms SGD, Adam, and AdamW by considerable margins and surpasses SAM and GAM with less training time when setting the ratio of FAD to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "10\\%"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "50\\%"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Detailed results are in Appendix B."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
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+                                    "type": "text",
+                                    "content": "4.5. The Hessian spectra of selected minima"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Sharpness-aware optimization methods are shown to decrease the curvature of loss landscape [28, 121]. We investigate how FAD affects the flatness of minima. We consider the maximum eigenvalue of Hessian, which indicates the sharpness across the most critical direction, and the Hessian trace, which measures the expected loss increase under"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "type": "text",
+                                    "content": "random perturbations to the weights [42] as the measures of flatness."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We show the Hessian spectra of ResNet-50 trained on artpainting, cartoon, and photo domains of PACS for 5,000 iterations with SGD, Adam, AdamW, GAM, SAM, and FAD. Following [121], we adopt power iteration [115] to compute the top eigenvalues of Hessian and Hutchinson's method [6, 5, 114] to compute the Hessian trace. We report the distribution of the top-50 Hessian eigenvalues and Hessian trace for each method at convergence in Figure 3. None-flatness-aware optimizers, including SGD, Adam, and AdamW show high Hessian trace and dominant eigenvalues. In contrast, flatness-aware optimizers find"
+                                }
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+                                            "type": "text",
+                                            "content": "Table 3. The performance and average training time of current optimizers and FAD when training for 5,000, 10,000, 15,000 iterations. Training Time is the average time for finishing each dataset with the given iterations."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "html": "<table><tr><td>Optimizers</td><td>Iterations</td><td>Training Time /s</td><td>PACS</td><td>VLCS</td><td>OfficeHome</td><td>NICO++</td><td>Avg.</td></tr><tr><td>Adam</td><td>5,000</td><td>1613.9</td><td>84.2</td><td>77.3</td><td>67.6</td><td>76.2</td><td>76.3</td></tr><tr><td>Adam</td><td>10,000</td><td>3049.5</td><td>82.9</td><td>77.7</td><td>67.4</td><td>76.9</td><td>76.2</td></tr><tr><td>Adam</td><td>15,000</td><td>4478.6</td><td>84.0</td><td>78.4</td><td>69.6</td><td>77.3</td><td>77.3</td></tr><tr><td>AdamW</td><td>5,000</td><td>2145.2</td><td>83.6</td><td>77.4</td><td>68.8</td><td>76.9</td><td>76.7</td></tr><tr><td>AdamW</td><td>10,000</td><td>4632.8</td><td>83.3</td><td>77.1</td><td>66.9</td><td>77.5</td><td>76.2</td></tr><tr><td>AdamW</td><td>15,000</td><td>6995.3</td><td>83.7</td><td>76.3</td><td>68.0</td><td>77.5</td><td>76.4</td></tr><tr><td>SGD</td><td>5,000</td><td>1864.1</td><td>79.9</td><td>78.1</td><td>68.5</td><td>76.5</td><td>75.8</td></tr><tr><td>SGD</td><td>10,000</td><td>3438.9</td><td>81.4</td><td>78.1</td><td>68.7</td><td>77.2</td><td>76.4</td></tr><tr><td>SGD</td><td>15,000</td><td>4992.0</td><td>82.6</td><td>78.7</td><td>69.6</td><td>77.0</td><td>77.0</td></tr><tr><td>YOGI</td><td>5,000</td><td>1388.9</td><td>81.2</td><td>77.6</td><td>68.3</td><td>77.1</td><td>76.1</td></tr><tr><td>YOGI</td><td>10,000</td><td>2882.9</td><td>81.2</td><td>77.8</td><td>70.2</td><td>77.9</td><td>76.8</td></tr><tr><td>YOGI</td><td>15,000</td><td>4434.2</td><td>83.1</td><td>78.1</td><td>67.9</td><td>77.5</td><td>76.7</td></tr><tr><td>SAM</td><td>5,000</td><td>3325.6</td><td>85.3</td><td>78.2</td><td>68.0</td><td>77.0</td><td>77.1</td></tr><tr><td>SAM</td><td>10,000</td><td>6506.8</td><td>85.6</td><td>78.3</td><td>68.6</td><td>77.9</td><td>77.6</td></tr><tr><td>SAM</td><td>15,000</td><td>9960.2</td><td>86.1</td><td>78.9</td><td>68.8</td><td>78.1</td><td>78.0</td></tr><tr><td>GAM</td><td>5,000</td><td>8073.6</td><td>86.1</td><td>78.5</td><td>68.2</td><td>77.4</td><td>77.6</td></tr><tr><td>GAM</td><td>10,000</td><td>16210.5</td><td>86.0</td><td>79.2</td><td>68.5</td><td>78.0</td><td>78.0</td></tr><tr><td>GAM</td><td>15,000</td><td>23855.1</td><td>86.5</td><td>78.6</td><td>69.0</td><td>77.8</td><td>78.0</td></tr><tr><td>FAD (Ours)</td><td>5,000</td><td>5057.8</td><td>88.2</td><td>78.9</td><td>69.2</td><td>78.5</td><td>78.7</td></tr><tr><td>FAD (Ours)</td><td>10,000</td><td>10450.8</td><td>88.5</td><td>79.5</td><td>69.6</td><td>79.0</td><td>79.1</td></tr><tr><td>FAD (Ours)</td><td>15,000</td><td>16255.2</td><td>88.5</td><td>79.0</td><td>69.0</td><td>79.1</td><td>78.9</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Figure 3. The distribution of top eigenvalues and the trace of Hessian at convergence on PACS with SGD, Adam, AdamW, GAM, SAM, and FAD. Trace indicates Hessian trace and "
+                                        },
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+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\lambda_{\\mathrm{max}}"
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+                                            "type": "text",
+                                            "content": " indicates the maximum eigenvalue of Hessian."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "minima with significantly lower Hessian spectra. FAD leads to both the lowest Hessian maximum eigenvalue and trace and thus the lowest curvature compared with other optimizers. More results are shown in Appendix B."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Discussions"
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+                                    "content": "Despite the wide usage in DG benchmarks, Adam is hardly the optimal choice of default optimizer. We show that the best optimizer for different DG methods varies across different datasets. Choosing the right optimizer can help exceed the current benchmarks' limitations. We propose a unified optimization method, flatness-Aware minimization for Domain generalization (FAD), to optimize zeroth-order and first-order flatness efficiently to address the problem. We further show that FAD controls the OOD generalization error and convergences fast. Compared with current optimizers, flatness-aware optimization approaches,"
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+                                    "content": "including SAM, GAM, and FAD, leads to flatter minima and better generalization. FAD outperforms its counterparts significantly on most DG datasets."
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+                                    "content": "FAD still has the following limitations which could lead to potential future work. First, the term "
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+                                    "content": "\\sup_{\\pmb{\\theta}_1,\\pmb{\\theta}_2\\in \\Theta}|\\mathcal{L}_{\\mathrm{tr}}(\\pmb{\\theta}_1,\\pmb{\\theta}_2) - \\mathcal{L}_{\\mathrm{te}}(\\pmb{\\theta}_1,\\pmb{\\theta}_2)|"
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+                                    "content": " in Equation (6) indicates the discrepancy between training and test data. Without knowledge of test distribution and extra assumptions, the term cannot be optimized and leads to the optimization of the flatness term. Proper assumptions on the connection between training and test data or the geometry of data may help to learn the connection between flatness and the discrepancy, and thus control the discrepancy for better generalization. Second, We show that Adam is hardly an optimal choice of default optimizer in DG. However, selecting a proper optimizer for each DG method leads to massive overhead. Designing a better DG protocol"
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+                                    "content": "or learning an indicator for the fitness of optimizers and methods can significantly contribute."
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+                                    "content": "This work was supported in part by National Key R&D Program of China (No. 2018AAA0102004, No. 2020AAA0106300), National Natural Science Foundation of China (No. U1936219, 62141607), Beijing Academy of Artificial Intelligence (BAAI)."
+                                }
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diff --git a/2023/Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance/c13c514a-2666-4045-89a1-55d246dbfa1d_content_list.json b/2023/Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance/c13c514a-2666-4045-89a1-55d246dbfa1d_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..59ce6c47d67cabf127cb59e4d7eeac2565745ff7
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+++ b/2023/Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance/c13c514a-2666-4045-89a1-55d246dbfa1d_content_list.json	
@@ -0,0 +1,1941 @@
+[
+    {
+        "type": "text",
+        "text": "Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance",
+        "text_level": 1,
+        "bbox": [
+            212,
+            130,
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+            175
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Lei Fan $^{1}$ , Bo Liu $^{2}$ , Haoxiang Li $^{2}$ , Ying Wu $^{1}$  and Gang Hua $^{2}$ \\\n $^{1}$ Northwestern University  $^{2}$ Wormpex AI Research",
+        "bbox": [
+            256,
+            202,
+            730,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "leifan@u.northwestern.edu,yingwu@northwestern.edu,{richardboliu,lhxustcer,ganghua}@gmail.com",
+        "bbox": [
+            86,
+            241,
+            898,
+            257
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition.",
+        "bbox": [
+            76,
+            325,
+            473,
+            704
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            737,
+            209,
+            752
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "When employing visual classifiers in open-world conditions, obtaining reliable uncertainty estimations could significantly benefit downstream tasks, including autonomous driving [1, 13, 37], medical diagnosis [36, 49], and embodied intelligence [40, 35]. Recent uncertainty quantification techniques [53, 15, 28, 32, 34, 33, 9, 43] have achieved notable progress toward this goal by saying \"I do not know\" when the testing distributions differ from the training. However, besides directly giving no prediction, a more flexible",
+        "bbox": [
+            76,
+            763,
+            468,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/2922f421db359d998ac498b26044f802c492921817679d0aa3845cf2735706f1.jpg",
+        "image_caption": [
+            "Figure 1: Classification of the proposed approach on images interpolated from a known-known-unknown triplet. Ignorance reflects the lack of evidence, whereas confusion is caused by conflicting evidence, i.e., evidence that fails to provide discrimination between specific classes. A flexible visual recognition system could provide combined predictions when having large confusion and reject making predictions for unknown-class samples. Note the mixup images are for illustrative purposes and are not a requisite in our training."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            290,
+            893,
+            407
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "and informative visual recognition system could also give combined predictions when possible, implying the correct answer is one of its predictions but uncertain. Naturally, the capability of rejecting or providing unspecific predictions demands separately measuring different sources of uncertainties, i.e., ignorance and confusion, if seen from the Subjective Logic [21] perspective. Furthermore, to enable flexible recognition, both uncertainties should possess the virtue of comparability between samples and in-sample additivity.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In evidential deep learning, the training of a recognition model could be regarded as an evidence-collecting process [21, 44]. Unlike ignorance describing a total lack of evidence, confusion is defined as conflicting evidence, which mandates the existence of multiple hypotheses in the frame of discernment. In other words, we cannot assess confusion for a single-class classification problem. The mass of confusion between two classes then reflects shared features that contribute to both classes while not discriminative. Likewise, confusion exists for all combinations of classes larger than two. Unlike typical visual classifiers that only predict",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "1338",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "a single output, flexible predictions could be obtained if we could combine singleton belief derived from class-exclusive evidence with their inter-class confusion.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "With great potential for explicitly estimating confusion and ignorance, this area is still under-explored for deep visual classifiers. Recent methods regard uncertainties as the degree of mismatch between training and testing distributions, which comprise but do not distinguish between confusion and ignorance. Deep Bayesian models, including dropout [15, 22] and ensemble-based approximations [28, 51, 4], require multiple forwards to estimate the posterior predictive distribution. Evidential models [44, 1, 11, 5] predict parameters of the posterior of class distribution directly. However, these models regard uncertainty as a whole term covering both confusion and ignorance, making it infeasible to perform flexible visual recognition further.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Distinct from existing uncertainty quantification methods, the proposed method models confusion and ignorance for each sample separately, which provides valuable information to facilitate various visual tasks, including flexible visual recognition. An illustrative example with the prediction of our method is shown in Fig. 1. Under the theory of Subjective Logic [6, 21], confusion is defined as the shared evidence contributing to multiple categories while not discriminative between them, while ignorance is completely missing evidence.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The contribution of this paper could be summarized as follow: (1) The proposed method could explicitly predict two sources of uncertainties, i.e., confusion and ignorance, simultaneously for each sample. (2) The solution to confusion and ignorance is based on standard architectures, and the training does not rely on external information. (3) The effectiveness of the proposed method is extensively validated across different experiments, including studies on synthetic data, visual recognitions, and open-set detections.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Uncertainty estimation. Typical neural networks can not detect their own failure. However, this ability can be important in several real-world applications, like rejecting unseen samples, and providing prediction confidence, to name a few. Bayesian NN [15, 27, 47, 14, 25] predicts epistemic uncertainty as the mutual information between model parameters and samples. By assuming a probabilistic prior on the network, it approximates prediction variance by sampling weight during inference. Several works [20, 49, 23] choose to model epistemic and aleatoric uncertainties separately. The Subjective Logic on which our method is established falls within the realm of epistemology instead of a frequentist (aleatoric) view. In other words, we focus on further separating epistemic uncertainty into confusion and ignorance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evidential deep learning [44, 1, 5, 11], in contrast, pro",
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+    {
+        "type": "text",
+        "text": "poses to learn the prior of the predictions directly. The prior, known as evidential prior, is interpreted as beliefs in Dempster-Shafer Theory [6]. In [11], they model the first- and second-order uncertainties by introducing an auxiliary uncertainty network to approximate the difference between Dirichlet distributions.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "While uncertainty is provided to describe the variance of model prediction, it is not clear if uncertainty comes from different sources when dealing with in-distribution or out-of-distribution data. Orthogonal to previous approaches, we separate the uncertainty into confusion and ignorance in this work. Confusion depicts the uncertainty between different known classes, while ignorance decides whether the sample is unknown. With this separation, we can make dynamic predictions on known classes and reject unknown classes at the same time.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Open Set Recognition. Machine learning models are usually designed with the closed-set assumption, where testing data shares the same distribution as the training. Open-set recognition (OSR) [8] introduces semantic shifts to the problem. Samples are from the classes that are not in the training set. Out-of-distribution (OOD) [19] detection introduces domain shifts to the testing set. In both of the settings, models should have the ability to reject unknown samples.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In general, OSR and OOD methods reject unknown samples depending on reweighting outputs [8, 16, 24, 19, 30, 50], getting better feature embedding metrics [31, 10, 42, 38], and exploring reconstruction errors [39, 46, 45, 52, 41]. These metrics are all related to the quality of classifier prediction. However, the recognition can fail on closed-set samples because of the existence of confusion. In this work, we show that when the confusion between known classes is adequately modeled, unknown samples can be identified more accurately.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Conformal Prediction. Parallel to our task, conformal prediction is a paradigm that could provide single or multiple predictions by empirically constructing confidence regions [2, 3, 48]. However, conformal prediction is confined to closed scenarios without open samples, as the empirical quantile is established on a labeled validation set sampled from the same testing distribution.",
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+    },
+    {
+        "type": "text",
+        "text": "3. Flexible Recognition",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Flexible recognition aims to provide a classification model  $\\mathcal{M}$  that could deliver adaptive predictive sets. Specifically, the model rejects samples, i.e., making no prediction, when the input is entirely out of the training distribution, like an open-set sample. The model also should cautiously give a set of predictions with the true class contained in it when being unsure.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For a  $K$ -class classification problem, we formalize the flexible recognition system  $\\mathcal{M}(\\cdot)$  as  $\\{y_1,\\ldots ,y_k\\} = \\mathcal{M}(\\mathbf{x})$  where  $\\mathbf{x}$  denotes the input image, and the predictive set",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "1339",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "$\\{y_{1}, \\ldots, y_{k}\\}$  obeys  $0 \\leq k \\leq K$ . Therefore,  $k = 0$  means the recognition system rejects making a prediction, and the true label  $\\mathbf{y}$  is supposed to be contained in the predictive set when  $\\mathbf{x}$  is from known classes.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose to tackle flexible recognition by separately estimating the confusion and ignorance for each sample. Intuitively, confusion denotes conflicting evidence between known classes, which should be additive to single-class beliefs for making reasonable multiple predictions. Ignorance denotes a lack of evidence to support rejecting samples. Most of this section falls into the proposed evidential modeling, which formulates confusion and ignorance in visual recognition under the theory of Subject Logic [21]. The approach to combining evidence and developing opinions follows. The approach to achieve flexible recognition is presented in the final.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Existing learning-based visual recognition models often rely on a softmax layer to give class probabilities. As a point estimation of predictive distribution, the classifier trained with the cross-entropy loss tends to deliver inflating probabilities to a single class and could not provide a reliable estimation of uncertainties [19].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We develop confusion and ignorance based on the Dempster-Shafer Theory of Evidence (DST) [6], which is a generalized scheme towards subjective probabilities [21]. The theory allows plausible reasoning with operations of evidence, namely the combination of evidence. Consider a  $K$ -class recognition task,  $\\Theta = \\{i, 1 \\leq i \\leq K\\}$  would be the frame of discernment containing exclusive propositions, e.g., class labels. Extensively, the general propositions under this frame would be the set of all subsets of  $\\Theta$ , which is",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n2 ^ {\\Theta} = \\{\\emptyset , 1, \\dots , K, \\{1, 2 \\}, \\dots , \\Theta \\}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $2^{\\Theta}$  contains a total of  $2^{K}$  elements.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Supposing  $b_A \\in [0,1]$  as a measure of belief mass contained in proposition  $A$ , the total mass of general propositions satisfies  $\\sum_{A \\in 2^{\\Theta}} b_A = 1$ . The belief for any proposition is then defined as the summation of contained mass, which is formulated as  $b_A = \\sum_{B \\subset A} b_B$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "And it is worth noting that  $B \\subseteq A$  suggests the logical statement that  $B$  implies  $A$ . The total belief in  $A$  is the sum of belief in all propositions that imply  $A$  plus the belief in  $A$  itself. For a more intuitive understanding, considering a binary visual classification task, the belief for predicting both classes is the combination of mass shared between classes and also class-exclusive masses.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We could further define the plausibility of  $A$  as  $p l_{A}$ , which is the total mass of propositions that has a non-empty",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/8c3d2e39cf2a97fa2cc337d73d8ef3a65f2b3d857831c3994edda06090b6e1ec.jpg",
+        "image_caption": [
+            "Figure 2: The relation between different masses constituting the final set of opinions towards a hypothesis."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "union with the current one. Also, the plausibility of a hypothesis could only be larger or equal to its own belief, i.e.,  $p l_{A} \\geq b_{A}$ . We demonstrate the basic probability assignments and their relations in Fig. 2.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.2. Uncertainty, Confusion, and Ignorance",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recent evidential deep learning methods [44] develop uncertainties under multinomial opinions, which model belief for singletons as  $\\{b_i, i = 1, \\dots, K\\}$  and regard the leftover as the total uncertainty  $\\mathcal{U}$ . We, therefore, have  $\\mathcal{U} + \\sum_{i=1}^{K} b_i = 1$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, in our modeling, we argue the uncertainty  $\\mathcal{U}$  for each sample  $\\mathbf{x}$  comes from two distinct sources, i.e., confusion  $\\mathcal{C}$  and ignorance  $\\mathcal{I}$ , which is written as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {U} ^ {\\mathbf {x}} = \\mathcal {C} ^ {\\mathbf {x}} + \\mathcal {I} ^ {\\mathbf {x}}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Intuitively, a large confusion  $\\mathcal{C}^{\\times}$  denotes the model is hard to distinguish  $\\mathbf{x}$  from known classes. For example, the model could have high confusion with a huskie image when the model has known classes of dog and wolf. An image from previously unknown classes, on the other hand, could have high ignorance. The superscript  $\\mathbf{x}$  will be omitted in the following for clarity.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To introduce the separate measurements of confusion and ignorance, our method is formalized with hyper opinions, composing masses of  $2^{K}$  subsets for a  $K$ -class frame of discernment. Therefore, the overall confusion  $\\mathcal{C}$  is the total mass of the non-singleton subsets as  $\\mathcal{C} = \\sum_{A,A\\in 2^{\\ominus},2\\leq |A|\\leq K}b_A$ . In other words, the confusion  $\\mathcal{C}$  is the sum of masses shared between two or more classes. Altogether, following Eq. 2, we have  $2^{K}$  mass values satisfy",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C} + \\mathcal {I} + \\sum_ {i = 1} ^ {K} b _ {i} = \\sum_ {A, A \\in 2 ^ {\\Theta}, 2 \\leq | A | \\leq K} b _ {A} + \\mathcal {I} + \\sum_ {i = 1} ^ {K} b _ {i} = 1, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{I} \\geq 0$  and  $b \\geq 0$  for all singletons and non-singleton subsets. The ignorance  $\\mathcal{I}$ , therefore, could be regarded as the mass placed on the empty set  $\\emptyset$  in the frame, which indicates the level of lacking evidence. Confusion, defined on subsets with cardinalities larger than 1, reflects evidence that fails to discriminate between specific singletons.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To further facilitate our evidence combination process, we group non-singleton confusion terms based on whether they hold evidence for a particular class  $i$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "1340",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/d8e178d890ff3271ec1949c5b85622032c5d2c8519221f7fcfbb45692262cebf.jpg",
+        "image_caption": [
+            "Figure 3: Two graphical demonstrations of evidence combination on 2- and 3-class classification task. We only show ignorance in the 3-class example to avoid overlappings."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/13ad8bc57db7dcc5317b43b3f4b3a951b1cc09391b54877108323215937ad4a1.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Class  $i$ -related confusion mass  $\\mathcal{C}_i$ . It is defined as  $\\mathcal{C}_i = \\sum_{A,A\\in 2^\\Theta, |A| \\geq 2, i \\cap A = i} b_A$ . To be more specific,  $\\mathcal{C}_i$  is the total mass placed on the set of all confusion terms that are supersets of singleton  $i$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Class  $i$ -unrelated confusion mass  $\\mathcal{C}_{\\neg i}$ . Conversely, we have  $\\mathcal{C}_{\\neg i} = \\sum_{A,A\\in 2^{\\Theta},|A|\\geq 2,i\\cap A\\neq i}b_A$ . Accordingly, for any class  $i$ , we have",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C} = \\mathcal {C} _ {i} + \\mathcal {C} _ {- i}. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "And, as shown in Fig. 2, the plausibility of the current sample belonging to class  $i$  is  $p l_{i} = b_{i} + \\mathcal{C}_{i}$ , which stands for a combination of class-exclusive singleton belief mass and class-shared confusion masses.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.3. Evidence Combinations",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The objective of the proposed approach is to predict ignorance and confusion explicitly for each sample. However, unlike ignorance which is a single term, the number of confusion reaches the exponential of classes, which means our model is required to give a comprehensive quantification of  $2^{K}$  estimates. While intimidating, we propose to handle this by decomposing the problem into  $K$  plausibility functions  $f_{i}(\\cdot)$  for  $i = 1,\\dots ,K$  on the same frame. Each plausibility function  $f_{i}(\\cdot)$  is designed to give two predictions only considering class  $i$ , which is written as  $f_{i}(\\mathbf{x}) = (pl_{i},1 - pl_{i})$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Supposing we have obtained the plausibilities for all classes, any propositions, including the singleton class belief, confusion, and ignorance could then be derived by the rule of evidence combinations. In general, for  $K$  plausibility functions, the belief assignment of any proposition  $A$  is combined by computing as",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nb _ {A} = \\sum_ {B, \\cap B = A} \\prod_ {1 \\leq j \\leq K} b _ {B, j} (\\mathbf {x}) = \\sum_ {B, \\cap B = A} \\prod_ {1 \\leq j \\leq K} f _ {j} ^ {B} (\\mathbf {x}). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note we do not have the normalization term in our formulation because we do not exclude the empty set from our frame. We demonstrate the combination process with 2- and 3-class classification examples in Fig. 3. To clarify fur",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ther, the singleton belief for class  $i$  is computed as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nb _ {i} = p l _ {i} \\prod_ {1 \\leq j \\leq K, j \\neq i} (1 - p l _ {j}) = f _ {i} ^ {1} (\\mathbf {x}) \\prod_ {1 \\leq j \\leq K, j \\neq i} f _ {j} ^ {2} (\\mathbf {x}). \\tag {6}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "And we have the total uncertainty  $\\mathcal{U} = 1 - \\sum_{i=1}^{K} b_i$ . As the ignorance  $\\mathcal{I}$  could be calculated similarly as",
+        "bbox": [
+            498,
+            164,
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+            196
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {I} = \\prod_ {1 \\leq j \\leq K} (1 - p l _ {j}) = \\prod_ {1 \\leq j \\leq K} f _ {j} ^ {2} (\\mathbf {x}), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            565,
+            208,
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+            242
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the total confusion between all different class combinations is  $\\mathcal{C} = \\mathcal{U} - \\mathcal{I}$ . The confusion term between specific classes could be further calculated with Eq. 5.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, the belief for each combination could be regarded as the occupation in a unit  $K$ -dim volume. The modeling of confusion becomes feasible by spanning a  $K$ -dim hypothesis space with  $K$  plausibility functions. Moreover, the computation complexity of each combination is  $\\mathcal{O}(n)$ , and for specific conditions, we could only calculate necessary confusion terms.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.4. Developing Opinions",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            431
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we describe how to develop opinions from training data. Each plausibility function  $f_{i}(\\cdot)$  can be constructed as a normalized dual-output linear layer or a single multi-output layer after being activated by a sigmoid function  $\\sigma (\\cdot)$ . In this work, the second is implemented to reduce the network parameters. In particular, the output is regarded as the value of class plausibility. The plausibility function is then formulated as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(p l _ {i}, 1 - p l _ {i}\\right) = f _ {i} (\\mathbf {x}) = \\sigma \\left(w _ {i} ^ {\\top} \\Phi (\\mathbf {x})\\right) \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            570,
+            574,
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+            592
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Phi :\\mathcal{X}\\to \\mathbb{R}^D$  is a feature embedding function.",
+        "bbox": [
+            500,
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+    },
+    {
+        "type": "text",
+        "text": "Typically, only one deterministic label is given for each image in a standard visual recognition dataset. Following EDL [44], the learning of singleton belief is implemented as evidence acquisition on a Dirichlet prior. The loss of EDL is",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {E D L}} = \\sum_ {i = 1} ^ {K} y _ {i} \\left[ \\log \\left(\\sum_ {j = 1} ^ {K} \\alpha_ {j}\\right) - \\log \\left(\\alpha_ {i}\\right) \\right], \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            705,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{y} = [y_1, y_2, \\ldots, y_i, \\ldots, y_K]^T$  is one-hot class label for a sample  $\\mathbf{x}$ , and  $\\boldsymbol{\\alpha} = [\\alpha_1, \\alpha_2, \\ldots, \\alpha_K]^T$  are parameters of a Dirichlet distribution  $Dir(\\cdot|\\boldsymbol{\\alpha})$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Different from EDL, class evidence is replaced with belief. Hence,  $\\alpha$  is directly calculated from singleton beliefs and overall uncertainty. It is derived as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i} = \\frac {K b _ {i}}{\\mathcal {U}} + 1 = \\frac {K b _ {i}}{1 - \\sum_ {j = 1} ^ {K} b _ {j}} + 1, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "1341",
+        "bbox": [
+            483,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $b_{i}$  could be obtained from Eq. 6. During inference, all opinions could be directly predicted by performing combinations on the output of plausibility functions.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To encourage the plausibility function to match our expected behavior, i.e., predicting the plausibility instead of the belief of singleton, we add a regularization term as",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\sum_ {i = 1} ^ {K} y _ {i} \\left[ p l _ {i} - (1 - \\hat {\\mathcal {I}}) \\right] ^ {2}, \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            169,
+            188,
+            468,
+            229
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{\\mathcal{I}}$  is the current estimation of ignorance.",
+        "bbox": [
+            76,
+            238,
+            387,
+            253
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following EDL, a Kullback-Leibler loss is used to minimize evidence on unrelated classes as",
+        "bbox": [
+            76,
+            253,
+            468,
+            282
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K L}} = K L (D i r (\\cdot | \\tilde {\\alpha}) | | D i r (\\cdot | \\langle 1, \\dots , 1 \\rangle)), \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            133,
+            291,
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+            309
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tilde{\\alpha} = \\mathbf{y} + (1 - \\mathbf{y})\\odot \\boldsymbol {\\alpha},$  0 for element-wise multiplication. Combining all terms together yields the final loss as",
+        "bbox": [
+            76,
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+            345
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {E D L}} + \\lambda_ {\\mathrm {r e g}} \\mathcal {L} _ {\\mathrm {r e g}} + \\lambda_ {\\mathrm {K L}} \\mathcal {L} _ {\\mathrm {K L}}. \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Each loss term is accompanied by a balance weight, and we gradually increase the effect of  $\\mathcal{L}_{kl}$  through an additional annealing coefficient.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After developing opinions with the proposed method, a straightforward solution would be setting the belief threshold for outputs to achieve flexible recognition. The sample will be rejected if the ignorance is too large that no combination would exceed the threshold. And the model gives incrementally combined predictions if no singleton belief meets the bar.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            542,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The proposed method could model two sources of uncertainty for each sample to handle the task of flexible recognition. To enable better comparison with existing methods, our experiments are primarily decomposed into three components. (1) Demonstrating the separation of two sources of uncertainty, i.e., confusion and ignorance. (2) Indicating the correct class on misclassified samples with estimated confusion. (3) Applying ignorance to compare with other methods on the task open-set detection. More experiments, including on adversarial-attacked samples and ablation studies, follow to give a more comprehensive evaluation.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. We adopt the ResNet-18 as the backbone for our experiments except on synthetic data and open-set detection. The dimension of extracted feature is set to 512. For the proposed method, we apply the sigmoid activation on the last linear layer to work as our multiple plausibility functions. We empirically find both EDL [44] and our method are more sensitive to the learning rate. Specifically, we set the learning rate for both methods to 0.004 with a momentum of 0.9 for the batch size of 128.  $\\lambda_{\\mathrm{KL}}$  in Eq. 13 anneals to 0 with epochs with the maximum coefficient of 0.05, and  $\\lambda_{\\mathrm{reg}}$  is set to 1.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/bc92dae818ba65c6de8c1e5e1ee2b123ad7305a9252206df33c42e5a5f1d1d67.jpg",
+        "image_caption": [
+            "(a) Class 1"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/72bb460d1a3e71a2ad4f27304f014781b0789cca77b30e4896b1f4481546d34a.jpg",
+        "image_caption": [
+            "(b) Class 2"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            638,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0de752b88ed981990a136d14880638d76ba55939c14b911ed6aeb38327e439d1.jpg",
+        "image_caption": [
+            "(c) Class 3"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            767,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/66f4757e16c036b92f275ffffb102c9a886384fd73083878210e59a97a73af71.jpg",
+        "image_caption": [
+            "(d) Confusion"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/4862dd105dae7aa4395cc9880af829a46464aec7060f1fbe707ee7d2abb41219.jpg",
+        "image_caption": [
+            "(e) Ignorance"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            638,
+            188,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/227d8cebdd5595bc6bd297204c76b594ba0f644108f219d371c45524a392ad9b.jpg",
+        "image_caption": [
+            "(f) Standard Entropy",
+            "Figure 4: A 3-class classification problem. The Gaussian-distributed training data are depicted with dots, while the background color indicates the estimated value of the corresponding location. Our results are plotted from (a) to (e). The entropy over predictions of a standard net trained with cross-entropy loss is shown in (f) for comparison."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            767,
+            186,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Synthetic Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            402,
+            709,
+            419
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we examine the behavior of our approach in Fig. 4 in the 2-dimensional space. A dataset with three isotropic Gaussian distributed classes is created for training. The distances between each Gaussian are equal to 9, and we set  $\\sigma = 4$  for all Gaussian. Each class has 500 training samples which are denoted by colored dots. We discretize the background into 2D locations for testing. The background color denotes corresponding estimated values.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Both our method and the standard entropy are trained with the same multi-layer perceptron. As we can observe in Fig. 4 (a) to (e), the proposed method acts as a density estimator. Confusion happens between class boundaries, while ignorance is high for out-of-distribution data points. The proposed method does not require intricate adoptions to network architectures to achieve the desired properties. In Fig. 4 (f), the entropy of a standard deterministic neural net with the cross-entropy loss is plotted, which shows that using entropy to distinguish out-of-distributions could face multiple downsides due to its sharp boundaries.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.2. Confusion on Misclassified Samples",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this part, the confusion is tested on misclassified samples, checking whether it is correlated with the ground-truth label. That is, the confusion should be high between the misclassified class and the ground-truth class. Besides in-sample comparison on the level of confusion, we argue the between-sample comparability of confusion is also critical for flexible visual recognition. For example, a flexible recognition system would tend to give a second prediction if its confusion is higher than in other samples. To address this concern, we employ the Area Under the Receiver Oper-",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "1342",
+        "bbox": [
+            483,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/f82c106e4401ed2341ec199086544bb0062b1a9e8f49d91e7a207fa42c565b30.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"2\">CIFAR-10</td><td colspan=\"2\">CIFAR-100</td><td colspan=\"2\">Imagenet</td></tr><tr><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td></tr><tr><td>Softmax</td><td>95.2</td><td>63.4</td><td>76.0</td><td>57.3</td><td>54.3</td><td>58.2</td></tr><tr><td>EDL [44]</td><td>94.8</td><td>60.4</td><td>74.5</td><td>54.9</td><td>54.2</td><td>58.3</td></tr><tr><td>Dropout [15]</td><td>94.7</td><td>64.5</td><td>74.5</td><td>58.9</td><td>47.3</td><td>61.8</td></tr><tr><td>OvR</td><td>95.1</td><td>63.2</td><td>72.2</td><td>63.4</td><td>46.3</td><td>60.2</td></tr><tr><td>ASL [7]</td><td>95.2</td><td>70.9</td><td>75.8</td><td>79.9</td><td>54.1</td><td>62.8</td></tr><tr><td>Ours</td><td>95.0</td><td>89.5</td><td>74.9</td><td>90.0</td><td>54.6</td><td>97.6</td></tr></table>",
+        "bbox": [
+            83,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Comparison on whether the confusion indicates the correct class on misclassified samples. Results of classification accuracy and AUROC on misclassified samples are shown on three datasets with different class scales.",
+        "bbox": [
+            75,
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+            470,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ating Characteristic curve (AUROC) as our evaluation metric, which sorts the predicted value along samples in each class. More specifically, the ROC curve is a graph showing the true positive rate against the false positive rate. A random classifier would correspond to a  $50\\%$  AUROC. Moreover, the metric sidesteps the issue of threshold selection.",
+        "bbox": [
+            75,
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+            364
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To be more clear, the confusion terms between all classes and the predicted class are regarded as the input to the metrics, while the target is one-hot class labels. As the groundtruth class could be imbalanced among misclassified samples, the AUROC is weighted by the categorical base rate.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The results on CIFAR-10, CIFAR-100 [26], and ImageNet [12] with 10, 100, and 1000 classes, respectively, are shown in Tab. 1 to demonstrate the comparison with different class scales. TheImagenet used here is an official downsampled version with the resolution of  $64 \\times 64$ . Besides standard Softmax, the Dropout [15] refers to the method using Monte Carlo Dropout (with the dropout rate of 0.2 and 10 dropout iterations) to approximate the distribution of model parameters. Since these methods do not contain explicit outputs of confusion, they are compromised to an intuitive approach, which measures the difference between predicted class probabilities. Two multi-label classification methods, namely, the One-vs-Rest (OvR) and the ASL [7], are included as baselines whose outputs are not normalized between classes. For EDL [44], confusion is defined as the difference between estimated singleton beliefs. In stark contrast to these methods, the proposed method uses explicitly estimated confusion between any classes with the predicted class following the definition in Eq. 5.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As shown in Tab. 1, the performance of the proposed method is significantly higher than all other approaches on three datasets. There are two reasons to support this result. First, the probability produced by softmax should not be viewed as the direct measure of confidence for each class [18], which means there might be no suitable way to derive confusion from softmax probability after training. Second, for the evidential method [44], the difference between predicted beliefs does not capture their shared features. In other words, the confusion in EDL is mixed with ignorance in their one uncertainty estimate. Orthogonal to",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/0faf67e657791a7c334d70a91e8727a0a08d605fcbfcf1bf46ff31a7fcac5356.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/7788a3de198504727e82f63dcee192c5034412f3e91d7172e3e5c80278ee9d56.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2401d3804f9a3452113b131c5645e13812d23414667f8882c320f3b69af7c3cf.jpg",
+        "image_caption": [
+            "(a) Results on CIFAR-10"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            220,
+            694,
+            334
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2a8336da84264525e2cddb71874cdf3babe3f684545533124dd33a9e4c7e1c1a.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            699,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/857a798139849e7b0023f36c91835ee81fa13a759fd2eaa84403366dd3fa0f96.jpg",
+        "image_caption": [
+            "(b) Results on CIFAR-100",
+            "(c) Results on Imagenet"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            354,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2a227159a58801a2f57e39d90f9f25138b6fd382a269c6cafd7c37bd77ad4cff.jpg",
+        "image_caption": [
+            "Figure 5: Precision and recall of delivering multiple predictions on misclassified samples with respect to the average number of predictions. The intention to predict extra classes is dependent on the confusion term between classes."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "these methods, the proposed approach could model the confusion that occurred between classes and could help flexible recognition systems determine when and which class to be predicted next.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3. Flexible Closed-set Recognition",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We turn to the task of flexible visual recognition on the closed CIFAR-10, CIFAR-100, and Imagenet, where methods are supposed to make multiple predictions when they are unsure. And we regard the output as correct as long as the correct answer is included in the prediction set. However, simply increasing the number of predictions for each sample should be penalized. Thus, for a more meaningful comparison, we show precision and recall as the function of the average number of predictions. We only evaluate methods on their misclassified samples, where providing more predictions is urgently demanded. And the indicator for making another prediction is the confusion between the considered and the predicted class, the same as in Section 5.2. The confusion for the first-predicted class itself is intuitively described as 0.",
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+        "table_caption": [],
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+        "table_body": "<table><tr><td>Closed Dataset CIFAR-10</td><td>+ LSUN (crop)</td><td>+ ImageNet (crop)</td></tr><tr><td>Softmax</td><td>64.2</td><td>63.9</td></tr><tr><td>OpenMax [8]</td><td>65.7</td><td>66.0</td></tr><tr><td>OSRCI [38]</td><td>65.0</td><td>63.6</td></tr><tr><td>LadderNet + OpenMax [52]</td><td>65.2</td><td>65.3</td></tr><tr><td>DHRNet + OpenMax [52]</td><td>65.6</td><td>65.5</td></tr><tr><td>CROSR [52]</td><td>72.0</td><td>72.1</td></tr><tr><td>GFROSR [41]</td><td>75.1</td><td>75.7</td></tr><tr><td>Ours</td><td>80.5</td><td>76.8</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Comparison on open-set detection by adding different unknown samples to the test set. The performance is evaluated by Macro-F1, which considers  $K + 1$  classes.",
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+        "type": "text",
+        "text": "The curves of three datasets are drawn in Fig. 5. We incrementally select more predictions for each class, i.e., the samples are deserved to make an extra prediction if its confusion on this considered class is more significant than in other samples. By doing this, we could control the average predictions while being threshold-independent in evaluating flexible visual recognition. A desired precision-average prediction curve would have a near 1 value for the start of making predictions. For the recall-average prediction curve, the closer it adheres to the left-top corner, the earlier it delivers the correct class. When comparing the precision curve, our method could achieve a significantly higher value than other methods when making limited predictions. For example, on the CIFAR-10 dataset, the proposed method reaches the precision of 0.62 for making an average of only one prediction for each sample, while the second highest is 0.33. Note some samples could have no prediction at the beginning as all of their confusion terms are lower than other samples. Besides, we also notice that ASL [7] is better than other baselines in the recall curve. This indicates that for flexible recognition, a multi-label classifier could be a better choice as it prevents the overconfident problem in the softmax probabilities to some extent.",
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+        "text": "5.4. Ignorance for Open-set Detection",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As a crucial part of flexible recognition, we additionally demonstrate the effectiveness of our method on the task of open-set detection in Tab. 2 following standard protocols [52, 18, 29]. The same network architecture, i.e., a 13-layer VGG model, is used to implement the proposed method as in [52].",
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+    {
+        "type": "text",
+        "text": "During the test time of open-set detection, the test images from CIFAR-10 datasets are viewed as closed-set examples. For open-set samples, we consider two natural image datasets, i.e., LSUN (crop) and ImageNet (crop), introduced by Liang et al [29]. The Macro-F1 is therefore evaluated on  $K + 1$  classes by regarding all open samples as an additional class. And the threshold for being detected as open-set is chosen when  $95\\%$  of closed-set images can be correctly classified. Among the compared methods, OS-RCI [38] augments the training set with hard and counterfactual generated images to improve unknown sample de",
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+        "img_path": "images/1bf23e8f3e46ed1915b1dc754ff4d652cedd0b45b3d604a2a59ee28607053b44.jpg",
+        "image_caption": [
+            "Figure 6: Top 1 and 2 accuracies with adversarial perturbations  $\\epsilon$  on CIFAR-10 [26] dataset."
+        ],
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+        "text": "tection during testing. CROSR [52] and GFROSR [41] incorporate reconstruction loss into the procedure of closed-set training to better model the data distribution. For the proposed method, we use ignorance  $\\mathcal{I}$  as the indicator of unknown samples and achieve better performance without additional adversarial training data. The F1 score of the proposed method is higher than other methods on both datasets, which supports the claim that ignorance in the proposed method could effectively handle the lack of evidence in open-set samples. It is worth noting that, besides explicitly delivering ignorance to detect unknown samples, the advantage of the proposed method also lies in the estimate of confusion, which is evaluated in closed-set experiments.",
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+        "text": "5.5. Performance on Adversarial Samples",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We compare the robustness of different classification methods [15, 44] against adversarial attacks. Besides models introduced in the previous experiment, we include the recent multi-label classification method ASL [7] as another baseline. The reason is that multi-label classification methods usually adopt the same sigmoid activation and multiple binary linear layers as our method. For our method, we use the plausibility  $p l_{i}$  for class  $i$  to predict instead of their singleton beliefs, i.e., the confusion for each class that occurred during adding perturbations is involved in the ranking. The reason is that we want to test whether the confusion correctly characterizes the conflicting evidence shared between the correct and other classes.",
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+        "text": "Adversarial samples are generated on CIFAR-10 [26] using the Fast Gradient Sign method [17] with various perturbation parameters  $\\epsilon$ . The adversarial attack method uses the gradient during inference to generate samples that are more challenging to make correct predictions as  $\\epsilon$  increases. Both the top 1 and top 2 results are shown in Fig. 6. The figure indicates that the proposed method could almost achieve both the highest top 1 and top 2 results. That is, the confusion that happened during perturbating is captured by our method, which could still contribute to the corresponding correct class. The proposed method is only slightly worse than the Dropout method when  $\\epsilon = 0.25$ , which is forgivable as its training includes stochastic zeroing on the model parameter to increase its robustness.",
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+        "image_caption": [
+            "(a)"
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+        "image_caption": [
+            "Figure 7: Matrices of confusion of misclassified samples on the CIFAR-10 dataset. The diagonal of each matrix is set to the singleton belief of each class. Notice that the background color for each heatmap is normalized individually. The total ignorance is demonstrated in the caption."
+        ],
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+        "img_path": "images/3b72102ca3360af71e5a061cdd4255d576fbe8ac40b6d90618b5637d743efeed.jpg",
+        "image_caption": [
+            "(c)"
+        ],
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+        "bbox": [
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+    {
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+        "img_path": "images/57db3fc54994ed35078c61fa44dc3d99f8c661d67b71d4ad3bff298e4f8bbffa.jpg",
+        "image_caption": [],
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+    {
+        "type": "table",
+        "img_path": "images/a57ba1019a1b0b16bd54467ede742d3016898bd4d9b7fc24ea550b5eabfcf3c9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"5\">CIFAR-10 + LSUN (crop)</td></tr><tr><td>Acc.</td><td>F1</td><td>AUROC</td><td>AUPR closed</td><td>AUPR open</td></tr><tr><td>Ours w/o Reg.</td><td>72.4</td><td>84.8</td><td>96.2</td><td>96.9</td><td>95.3</td></tr><tr><td>Ours w/ Reg.</td><td>79.9</td><td>86.9</td><td>97.0</td><td>97.5</td><td>96.6</td></tr><tr><td></td><td colspan=\"5\">CIFAR-10 + ImageNet (crop)</td></tr><tr><td>Ours w/o Reg.</td><td>63.9</td><td>82.0</td><td>95.1</td><td>96.1</td><td>93.8</td></tr><tr><td>Ours w/ Reg.</td><td>71.7</td><td>83.9</td><td>95.8</td><td>96.5</td><td>94.7</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 3: Ablation studies about the regularization term  $\\mathcal{L}_{\\mathrm{reg}}$  on the task of open-set detection with two hybrid datasets.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.6. Qualitative Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Furthermore, to provide a more intuitive impression of our results, we demonstrate the matrices of binary confusion estimates in Fig. 7. We take the misclassified images of the proposed method for the CIFAR-10 dataset. The ground truth label, the prediction, the singleton belief, the ignorance, and the highest binary confusion are noted in their captions. Each grid in the confusion matrix denotes the confusion between any two classes, while the diagonal represents the singleton belief.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Fig. 7b, the proposed method wrongly recognizes the image into dog class while maintaining a very high confusion towards the correct class horse. However, as the singleton belief is not significant for the predicted class, the proposed method could predict a combined result, i.e., both dog and horse, if setting a relatively high threshold on the sum of beliefs. Another example in Fig. 7c implies the ability of our method to reject making a prediction. As the image in Fig. 7c is contentless and low-resolution, the proposed failed to collect enough supportive evidence for any known classes, which delivers a very high ignorance value.",
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+    {
+        "type": "text",
+        "text": "5.7. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We investigate how the regularization term  $\\mathcal{L}_{\\mathrm{reg}}$  influences performance. The reason we add the regularization is to avoid the first output of each plausibility function converging to the belief instead of the plausibility. To show its effectiveness, we evaluate the proposed method on the task of open-set detection in Tab. 3. The separation could",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "be deemed to be more sufficient if the ignorance term performs better in detecting open-set samples. Note we use the ResNet-18 as our backbone here to remain consistent with our flexible recognition experiments. For the metric of open-set detection accuracy and AUROC, closed-set samples are regarded as negative samples, while open-set samples constitute positive samples. The other two metrics, AUPR closed and AUPR open, denote the Area Under the Precision-Recall curve where closed-set or open-set images are specified as positives, respectively. The overall improvements in adding the regularization term  $\\mathcal{L}_{\\mathrm{reg}}$ , as demonstrated in Tab. 3, indicate its effectiveness in promoting the separation.",
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+    {
+        "type": "text",
+        "text": "5.8. Discussions and Future works",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In our experiments, we find the scale of confusion and ignorance varies with different backbones and datasets. The correlation behind it could be related to the capabilities of different models and the learning difficulties of different datasets. We leave the investigation for our future work.",
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+    {
+        "type": "text",
+        "text": "6. Conclusions",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we introduce a novel approach to explicitly model two distinct sources of uncertainties, i.e., confusion and ignorance, under the novel task of flexible recognition. The recognition system is expected to reject samples from unknown classes and also make multiple predictions when it is uncertain about a closed-set image. Particularly, in the proposed method, the confusion is modeled as the conflicting evidence, while the ignorance represents the total lack of evidence. The hypothesis space of recognition is then divided and modeled by multiple plausibility functions. The model learns the concentration parameter of Dirichlet prior, which is being placed on the belief for singletons. A complete set of opinions could be generated through evidence combinations. Experiments on different datasets, along with challenging tasks of adversarial disturbance, flexible recognition, and open-set detection, confirm the effectiveness of the proposed method.",
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+        "text": "1345",
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+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
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+        "page_idx": 8
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+            "[30] Shiyu Liang, Yixuan Li, and R Srikant. Enhancing the reliability of out-of-distribution image detection in neural networks. In International Conference on Learning Representations, 2018. 2",
+            "[31] Bo Liu, Hao Kang, Haoxiang Li, Gang Hua, and Nuno Vasconcelos. Few-shot open-set recognition using meta-learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8798-8807, 2020. 2",
+            "[32] Jeremiah Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax Weiss, and Balaji Lakshminarayanan. Simple and principled uncertainty estimation with deterministic deep learning via distance awareness. Advances in Neural Information Processing Systems, 33:7498-7512, 2020. 1",
+            "[33] Andrey Malinin and Mark Gales. Predictive uncertainty estimation via prior networks. Advances in neural information processing systems, 31, 2018. 1",
+            "[34] Andrey Malinin and Mark Gales. Reverse kl-divergence training of prior networks: Improved uncertainty and adversarial robustness. Advances in Neural Information Processing Systems, 32, 2019. 1",
+            "[35] Mateusz Malinowski and Mario Fritz. A multi-world approach to question answering about real-world scenes based on uncertain input. Advances in neural information processing systems, 27, 2014. 1",
+            "[36] Alireza Mehrtash, William M Wells, Clare M Tempany, Purang Abolmaesumi, and Tina Kapur. Confidence calibration and predictive uncertainty estimation for deep medical image segmentation. IEEE transactions on medical imaging, 39(12):3868-3878, 2020. 1",
+            "[37] Rhiannon Michelmore, Marta Kwiatkowska, and Yarin Gal. Evaluating uncertainty quantification in end-to-end autonomous driving control. arXiv preprint arXiv:1811.06817, 2018. 1",
+            "[38] Lawrence Neal, Matthew Olson, Xiaoli Fern, Weng-Keen Wong, and Fuxin Li. Open set learning with counterfactual images. In Proceedings of the European Conference on Computer Vision (ECCV), pages 613–628, 2018. 2, 7",
+            "[39] Poojan Oza and Vishal M Patel. C2ae: Class conditioned auto-encoder for open-set recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2307–2316, 2019. 2",
+            "[40] Badri N Patro, Mayank Lunayach, Shivansh Patel, and Vinay P Namboodiri. U-cam: Visual explanation using uncertainty based class activation maps. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7444-7453, 2019. 1",
+            "[41] Pramuditha Perera, Vlad I Morariu, Rajiv Jain, Varun Manjunatha, Curtis Wigington, Vicente Ordonez, and Vishal M Patel. Generative-discriminative feature representations for"
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "open-set recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11814-11823, 2020. 2, 7",
+            "[42] Chandramouli Shama Sastry and Sageev Oore. Detecting out-of-distribution examples with Gram matrices. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 8491-8501. PMLR, 13-18 Jul 2020. 2",
+            "[43] Murat Sensoy, Lance Kaplan, Federico Cerutti, and Maryam Saleki. Uncertainty-aware deep classifiers using generative models. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34,04, pages 5620-5627, 2020. 1",
+            "[44] Murat Sensoy, Lance Kaplan, and Melih Kandemir. Evidential deep learning to quantify classification uncertainty. Advances in neural information processing systems, 31, 2018. 1, 2, 3, 4, 5, 6, 7",
+            "[45] Rui Shao, Pramuditha Perera, Pong C Yuen, and Vishal M Patel. Open-set adversarial defense. In European Conference on Computer Vision, pages 682-698. Springer, 2020. 2",
+            "[46] Xin Sun, Zhenning Yang, Chi Zhang, Keck-Voon Ling, and Guohao Peng. Conditional gaussian distribution learning for open set recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13480-13489, 2020. 2",
+            "[47] Dustin Tran, Mike Dusenberry, Mark van der Wilk, and Danijar Hafner. Bayesian layers: A module for neural network uncertainty. Advances in neural information processing systems, 32, 2019. 2",
+            "[48] Vladimir Vovk, Alexander Gammerman, and Glenn Shafer. Algorithmic learning in a random world, volume 29. Springer, 2005. 2",
+            "[49] Guotai Wang, Wenqi Li, Michael Aertsen, Jan Deprest, Sébastien Ourselin, and Tom Vercauteren. Aleatoric uncertainty estimation with test-time augmentation for medical image segmentation with convolutional neural networks. Neurocomputing, 338:34-45, 2019. 1, 2",
+            "[50] Haoqi Wang, Zhizhong Li, Litong Feng, and Wayne Zhang. Vim: Out-of-distribution with virtual-logit matching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4921-4930, 2022. 2",
+            "[51] Florian Wenzel, Jasper Snoek, Dustin Tran, and Rodolphe Jenatton. Hyperparameter ensembles for robustness and uncertainty quantification. Advances in Neural Information Processing Systems, 33:6514-6527, 2020. 2",
+            "[52] Ryota Yoshihashi, Wen Shao, Rei Kawakami, Shaodi You, Makoto Iida, and Takeshi Naemura. Classification-reconstruction learning for open-set recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4016-4025, 2019. 2, 7",
+            "[53] Kuang Zhou, Arnaud Martin, and Quan Pan. Evidence combination for a large number of sources. In 2017 20th International Conference on Information Fusion (Fusion), pages 1-8. IEEE, 2017. 1"
+        ],
+        "bbox": [
+            503,
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+            890,
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+    }
+]
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diff --git a/2023/Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance/c13c514a-2666-4045-89a1-55d246dbfa1d_model.json b/2023/Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance/c13c514a-2666-4045-89a1-55d246dbfa1d_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..ff435fe272b407f58bb755df17753e4ae7b67476
--- /dev/null
+++ b/2023/Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance/c13c514a-2666-4045-89a1-55d246dbfa1d_model.json	
@@ -0,0 +1,2585 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.214,
+                0.131,
+                0.761,
+                0.176
+            ],
+            "angle": 0,
+            "content": "Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.257,
+                0.203,
+                0.731,
+                0.24
+            ],
+            "angle": 0,
+            "content": "Lei Fan\\(^{1}\\), Bo Liu\\(^{2}\\), Haoxiang Li\\(^{2}\\), Ying Wu\\(^{1}\\) and Gang Hua\\(^{2}\\)\\\n\\(^{1}\\)Northwestern University \\(^{2}\\)Wormpex AI Research"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.242,
+                0.9,
+                0.258
+            ],
+            "angle": 0,
+            "content": "leifan@u.northwestern.edu,yingwu@northwestern.edu,{richardboliu,lhxustcer,ganghua}@gmail.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.326,
+                0.474,
+                0.705
+            ],
+            "angle": 0,
+            "content": "In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.738,
+                0.21,
+                0.753
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "When employing visual classifiers in open-world conditions, obtaining reliable uncertainty estimations could significantly benefit downstream tasks, including autonomous driving [1, 13, 37], medical diagnosis [36, 49], and embodied intelligence [40, 35]. Recent uncertainty quantification techniques [53, 15, 28, 32, 34, 33, 9, 43] have achieved notable progress toward this goal by saying \"I do not know\" when the testing distributions differ from the training. However, besides directly giving no prediction, a more flexible"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.291,
+                0.895,
+                0.409
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.419,
+                0.895,
+                0.571
+            ],
+            "angle": 0,
+            "content": "Figure 1: Classification of the proposed approach on images interpolated from a known-known-unknown triplet. Ignorance reflects the lack of evidence, whereas confusion is caused by conflicting evidence, i.e., evidence that fails to provide discrimination between specific classes. A flexible visual recognition system could provide combined predictions when having large confusion and reject making predictions for unknown-class samples. Note the mixup images are for illustrative purposes and are not a requisite in our training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.596,
+                0.895,
+                0.734
+            ],
+            "angle": 0,
+            "content": "and informative visual recognition system could also give combined predictions when possible, implying the correct answer is one of its predictions but uncertain. Naturally, the capability of rejecting or providing unspecific predictions demands separately measuring different sources of uncertainties, i.e., ignorance and confusion, if seen from the Subjective Logic [21] perspective. Furthermore, to enable flexible recognition, both uncertainties should possess the virtue of comparability between samples and in-sample additivity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.896,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In evidential deep learning, the training of a recognition model could be regarded as an evidence-collecting process [21, 44]. Unlike ignorance describing a total lack of evidence, confusion is defined as conflicting evidence, which mandates the existence of multiple hypotheses in the frame of discernment. In other words, we cannot assess confusion for a single-class classification problem. The mass of confusion between two classes then reflects shared features that contribute to both classes while not discriminative. Likewise, confusion exists for all combinations of classes larger than two. Unlike typical visual classifiers that only predict"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1338"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.136
+            ],
+            "angle": 0,
+            "content": "a single output, flexible predictions could be obtained if we could combine singleton belief derived from class-exclusive evidence with their inter-class confusion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.137,
+                0.47,
+                0.333
+            ],
+            "angle": 0,
+            "content": "With great potential for explicitly estimating confusion and ignorance, this area is still under-explored for deep visual classifiers. Recent methods regard uncertainties as the degree of mismatch between training and testing distributions, which comprise but do not distinguish between confusion and ignorance. Deep Bayesian models, including dropout [15, 22] and ensemble-based approximations [28, 51, 4], require multiple forwards to estimate the posterior predictive distribution. Evidential models [44, 1, 11, 5] predict parameters of the posterior of class distribution directly. However, these models regard uncertainty as a whole term covering both confusion and ignorance, making it infeasible to perform flexible visual recognition further."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.333,
+                0.47,
+                0.485
+            ],
+            "angle": 0,
+            "content": "Distinct from existing uncertainty quantification methods, the proposed method models confusion and ignorance for each sample separately, which provides valuable information to facilitate various visual tasks, including flexible visual recognition. An illustrative example with the prediction of our method is shown in Fig. 1. Under the theory of Subjective Logic [6, 21], confusion is defined as the shared evidence contributing to multiple categories while not discriminative between them, while ignorance is completely missing evidence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.485,
+                0.47,
+                0.621
+            ],
+            "angle": 0,
+            "content": "The contribution of this paper could be summarized as follow: (1) The proposed method could explicitly predict two sources of uncertainties, i.e., confusion and ignorance, simultaneously for each sample. (2) The solution to confusion and ignorance is based on standard architectures, and the training does not rely on external information. (3) The effectiveness of the proposed method is extensively validated across different experiments, including studies on synthetic data, visual recognitions, and open-set detections."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.634,
+                0.22,
+                0.65
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.47,
+                0.885
+            ],
+            "angle": 0,
+            "content": "Uncertainty estimation. Typical neural networks can not detect their own failure. However, this ability can be important in several real-world applications, like rejecting unseen samples, and providing prediction confidence, to name a few. Bayesian NN [15, 27, 47, 14, 25] predicts epistemic uncertainty as the mutual information between model parameters and samples. By assuming a probabilistic prior on the network, it approximates prediction variance by sampling weight during inference. Several works [20, 49, 23] choose to model epistemic and aleatoric uncertainties separately. The Subjective Logic on which our method is established falls within the realm of epistemology instead of a frequentist (aleatoric) view. In other words, we focus on further separating epistemic uncertainty into confusion and ignorance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Evidential deep learning [44, 1, 5, 11], in contrast, pro"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.181
+            ],
+            "angle": 0,
+            "content": "poses to learn the prior of the predictions directly. The prior, known as evidential prior, is interpreted as beliefs in Dempster-Shafer Theory [6]. In [11], they model the first- and second-order uncertainties by introducing an auxiliary uncertainty network to approximate the difference between Dirichlet distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.183,
+                0.893,
+                0.332
+            ],
+            "angle": 0,
+            "content": "While uncertainty is provided to describe the variance of model prediction, it is not clear if uncertainty comes from different sources when dealing with in-distribution or out-of-distribution data. Orthogonal to previous approaches, we separate the uncertainty into confusion and ignorance in this work. Confusion depicts the uncertainty between different known classes, while ignorance decides whether the sample is unknown. With this separation, we can make dynamic predictions on known classes and reject unknown classes at the same time."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.333,
+                0.892,
+                0.454
+            ],
+            "angle": 0,
+            "content": "Open Set Recognition. Machine learning models are usually designed with the closed-set assumption, where testing data shares the same distribution as the training. Open-set recognition (OSR) [8] introduces semantic shifts to the problem. Samples are from the classes that are not in the training set. Out-of-distribution (OOD) [19] detection introduces domain shifts to the testing set. In both of the settings, models should have the ability to reject unknown samples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.455,
+                0.893,
+                0.605
+            ],
+            "angle": 0,
+            "content": "In general, OSR and OOD methods reject unknown samples depending on reweighting outputs [8, 16, 24, 19, 30, 50], getting better feature embedding metrics [31, 10, 42, 38], and exploring reconstruction errors [39, 46, 45, 52, 41]. These metrics are all related to the quality of classifier prediction. However, the recognition can fail on closed-set samples because of the existence of confusion. In this work, we show that when the confusion between known classes is adequately modeled, unknown samples can be identified more accurately."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.606,
+                0.892,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Conformal Prediction. Parallel to our task, conformal prediction is a paradigm that could provide single or multiple predictions by empirically constructing confidence regions [2, 3, 48]. However, conformal prediction is confined to closed scenarios without open samples, as the empirical quantile is established on a labeled validation set sampled from the same testing distribution."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.725,
+                0.696,
+                0.741
+            ],
+            "angle": 0,
+            "content": "3. Flexible Recognition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.855
+            ],
+            "angle": 0,
+            "content": "Flexible recognition aims to provide a classification model \\(\\mathcal{M}\\) that could deliver adaptive predictive sets. Specifically, the model rejects samples, i.e., making no prediction, when the input is entirely out of the training distribution, like an open-set sample. The model also should cautiously give a set of predictions with the true class contained in it when being unsure."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For a \\(K\\)-class classification problem, we formalize the flexible recognition system \\(\\mathcal{M}(\\cdot)\\) as \\(\\{y_1,\\ldots ,y_k\\} = \\mathcal{M}(\\mathbf{x})\\) where \\(\\mathbf{x}\\) denotes the input image, and the predictive set"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1339"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.091,
+                0.47,
+                0.152
+            ],
+            "angle": 0,
+            "content": "\\(\\{y_{1}, \\ldots, y_{k}\\}\\) obeys \\(0 \\leq k \\leq K\\). Therefore, \\(k = 0\\) means the recognition system rejects making a prediction, and the true label \\(\\mathbf{y}\\) is supposed to be contained in the predictive set when \\(\\mathbf{x}\\) is from known classes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.167,
+                0.168,
+                0.182
+            ],
+            "angle": 0,
+            "content": "4. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.192,
+                0.471,
+                0.373
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose to tackle flexible recognition by separately estimating the confusion and ignorance for each sample. Intuitively, confusion denotes conflicting evidence between known classes, which should be additive to single-class beliefs for making reasonable multiple predictions. Ignorance denotes a lack of evidence to support rejecting samples. Most of this section falls into the proposed evidential modeling, which formulates confusion and ignorance in visual recognition under the theory of Subject Logic [21]. The approach to combining evidence and developing opinions follows. The approach to achieve flexible recognition is presented in the final."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.384,
+                0.218,
+                0.399
+            ],
+            "angle": 0,
+            "content": "4.1. Preliminaries"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.407,
+                0.469,
+                0.497
+            ],
+            "angle": 0,
+            "content": "Existing learning-based visual recognition models often rely on a softmax layer to give class probabilities. As a point estimation of predictive distribution, the classifier trained with the cross-entropy loss tends to deliver inflating probabilities to a single class and could not provide a reliable estimation of uncertainties [19]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.498,
+                0.47,
+                0.634
+            ],
+            "angle": 0,
+            "content": "We develop confusion and ignorance based on the Dempster-Shafer Theory of Evidence (DST) [6], which is a generalized scheme towards subjective probabilities [21]. The theory allows plausible reasoning with operations of evidence, namely the combination of evidence. Consider a \\(K\\)-class recognition task, \\(\\Theta = \\{i, 1 \\leq i \\leq K\\}\\) would be the frame of discernment containing exclusive propositions, e.g., class labels. Extensively, the general propositions under this frame would be the set of all subsets of \\(\\Theta\\), which is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.154,
+                0.649,
+                0.469,
+                0.667
+            ],
+            "angle": 0,
+            "content": "\\[\n2 ^ {\\Theta} = \\{\\emptyset , 1, \\dots , K, \\{1, 2 \\}, \\dots , \\Theta \\}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.673,
+                0.356,
+                0.687
+            ],
+            "angle": 0,
+            "content": "where \\(2^{\\Theta}\\) contains a total of \\(2^{K}\\) elements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.469,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Supposing \\( b_A \\in [0,1] \\) as a measure of belief mass contained in proposition \\( A \\), the total mass of general propositions satisfies \\( \\sum_{A \\in 2^{\\Theta}} b_A = 1 \\). The belief for any proposition is then defined as the summation of contained mass, which is formulated as \\( b_A = \\sum_{B \\subset A} b_B \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.766,
+                0.469,
+                0.869
+            ],
+            "angle": 0,
+            "content": "And it is worth noting that \\( B \\subseteq A \\) suggests the logical statement that \\( B \\) implies \\( A \\). The total belief in \\( A \\) is the sum of belief in all propositions that imply \\( A \\) plus the belief in \\( A \\) itself. For a more intuitive understanding, considering a binary visual classification task, the belief for predicting both classes is the combination of mass shared between classes and also class-exclusive masses."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We could further define the plausibility of \\( A \\) as \\( p l_{A} \\), which is the total mass of propositions that has a non-empty"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.088,
+                0.891,
+                0.131
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.141,
+                0.892,
+                0.171
+            ],
+            "angle": 0,
+            "content": "Figure 2: The relation between different masses constituting the final set of opinions towards a hypothesis."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.196,
+                0.892,
+                0.258
+            ],
+            "angle": 0,
+            "content": "union with the current one. Also, the plausibility of a hypothesis could only be larger or equal to its own belief, i.e., \\( p l_{A} \\geq b_{A} \\). We demonstrate the basic probability assignments and their relations in Fig. 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.268,
+                0.835,
+                0.284
+            ],
+            "angle": 0,
+            "content": "4.2. Uncertainty, Confusion, and Ignorance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.292,
+                0.892,
+                0.367
+            ],
+            "angle": 0,
+            "content": "Recent evidential deep learning methods [44] develop uncertainties under multinomial opinions, which model belief for singletons as \\(\\{b_i, i = 1, \\dots, K\\}\\) and regard the leftover as the total uncertainty \\(\\mathcal{U}\\). We, therefore, have \\(\\mathcal{U} + \\sum_{i=1}^{K} b_i = 1\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.368,
+                0.892,
+                0.413
+            ],
+            "angle": 0,
+            "content": "However, in our modeling, we argue the uncertainty \\(\\mathcal{U}\\) for each sample \\(\\mathbf{x}\\) comes from two distinct sources, i.e., confusion \\(\\mathcal{C}\\) and ignorance \\(\\mathcal{I}\\), which is written as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.64,
+                0.426,
+                0.891,
+                0.442
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {U} ^ {\\mathbf {x}} = \\mathcal {C} ^ {\\mathbf {x}} + \\mathcal {I} ^ {\\mathbf {x}}. \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.892,
+                0.561
+            ],
+            "angle": 0,
+            "content": "Intuitively, a large confusion \\(\\mathcal{C}^{\\times}\\) denotes the model is hard to distinguish \\(\\mathbf{x}\\) from known classes. For example, the model could have high confusion with a huskie image when the model has known classes of dog and wolf. An image from previously unknown classes, on the other hand, could have high ignorance. The superscript \\(\\mathbf{x}\\) will be omitted in the following for clarity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.563,
+                0.892,
+                0.684
+            ],
+            "angle": 0,
+            "content": "To introduce the separate measurements of confusion and ignorance, our method is formalized with hyper opinions, composing masses of \\(2^{K}\\) subsets for a \\(K\\)-class frame of discernment. Therefore, the overall confusion \\(\\mathcal{C}\\) is the total mass of the non-singleton subsets as \\(\\mathcal{C} = \\sum_{A,A\\in 2^{\\ominus},2\\leq |A|\\leq K}b_A\\). In other words, the confusion \\(\\mathcal{C}\\) is the sum of masses shared between two or more classes. Altogether, following Eq. 2, we have \\(2^{K}\\) mass values satisfy"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.507,
+                0.708,
+                0.891,
+                0.752
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {C} + \\mathcal {I} + \\sum_ {i = 1} ^ {K} b _ {i} = \\sum_ {A, A \\in 2 ^ {\\Theta}, 2 \\leq | A | \\leq K} b _ {A} + \\mathcal {I} + \\sum_ {i = 1} ^ {K} b _ {i} = 1, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.764,
+                0.892,
+                0.854
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{I} \\geq 0\\) and \\(b \\geq 0\\) for all singletons and non-singleton subsets. The ignorance \\(\\mathcal{I}\\), therefore, could be regarded as the mass placed on the empty set \\(\\emptyset\\) in the frame, which indicates the level of lacking evidence. Confusion, defined on subsets with cardinalities larger than 1, reflects evidence that fails to discriminate between specific singletons."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To further facilitate our evidence combination process, we group non-singleton confusion terms based on whether they hold evidence for a particular class \\( i \\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1340"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.255,
+                0.233
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.291,
+                0.089,
+                0.468,
+                0.233
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.244,
+                0.47,
+                0.292
+            ],
+            "angle": 0,
+            "content": "Figure 3: Two graphical demonstrations of evidence combination on 2- and 3-class classification task. We only show ignorance in the 3-class example to avoid overlappings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.311,
+                0.469,
+                0.371
+            ],
+            "angle": 0,
+            "content": "Class \\(i\\)-related confusion mass \\(\\mathcal{C}_i\\). It is defined as \\(\\mathcal{C}_i = \\sum_{A,A\\in 2^\\Theta, |A| \\geq 2, i \\cap A = i} b_A\\). To be more specific, \\(\\mathcal{C}_i\\) is the total mass placed on the set of all confusion terms that are supersets of singleton \\(i\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.372,
+                0.469,
+                0.416
+            ],
+            "angle": 0,
+            "content": "Class \\(i\\)-unrelated confusion mass \\(\\mathcal{C}_{\\neg i}\\). Conversely, we have \\(\\mathcal{C}_{\\neg i} = \\sum_{A,A\\in 2^{\\Theta},|A|\\geq 2,i\\cap A\\neq i}b_A\\). Accordingly, for any class \\(i\\), we have"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.223,
+                0.419,
+                0.469,
+                0.435
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {C} = \\mathcal {C} _ {i} + \\mathcal {C} _ {- i}. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.444,
+                0.469,
+                0.504
+            ],
+            "angle": 0,
+            "content": "And, as shown in Fig. 2, the plausibility of the current sample belonging to class \\( i \\) is \\( p l_{i} = b_{i} + \\mathcal{C}_{i} \\), which stands for a combination of class-exclusive singleton belief mass and class-shared confusion masses."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.516,
+                0.296,
+                0.53
+            ],
+            "angle": 0,
+            "content": "4.3. Evidence Combinations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.54,
+                0.469,
+                0.691
+            ],
+            "angle": 0,
+            "content": "The objective of the proposed approach is to predict ignorance and confusion explicitly for each sample. However, unlike ignorance which is a single term, the number of confusion reaches the exponential of classes, which means our model is required to give a comprehensive quantification of \\(2^{K}\\) estimates. While intimidating, we propose to handle this by decomposing the problem into \\(K\\) plausibility functions \\(f_{i}(\\cdot)\\) for \\(i = 1,\\dots ,K\\) on the same frame. Each plausibility function \\(f_{i}(\\cdot)\\) is designed to give two predictions only considering class \\(i\\), which is written as \\(f_{i}(\\mathbf{x}) = (pl_{i},1 - pl_{i})\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.692,
+                0.469,
+                0.782
+            ],
+            "angle": 0,
+            "content": "Supposing we have obtained the plausibilities for all classes, any propositions, including the singleton class belief, confusion, and ignorance could then be derived by the rule of evidence combinations. In general, for \\( K \\) plausibility functions, the belief assignment of any proposition \\( A \\) is combined by computing as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.794,
+                0.469,
+                0.84
+            ],
+            "angle": 0,
+            "content": "\\[\nb _ {A} = \\sum_ {B, \\cap B = A} \\prod_ {1 \\leq j \\leq K} b _ {B, j} (\\mathbf {x}) = \\sum_ {B, \\cap B = A} \\prod_ {1 \\leq j \\leq K} f _ {j} ^ {B} (\\mathbf {x}). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.841,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Note we do not have the normalization term in our formulation because we do not exclude the empty set from our frame. We demonstrate the combination process with 2- and 3-class classification examples in Fig. 3. To clarify fur"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.834,
+                0.107
+            ],
+            "angle": 0,
+            "content": "ther, the singleton belief for class \\(i\\) is computed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.51,
+                0.119,
+                0.89,
+                0.164
+            ],
+            "angle": 0,
+            "content": "\\[\nb _ {i} = p l _ {i} \\prod_ {1 \\leq j \\leq K, j \\neq i} (1 - p l _ {j}) = f _ {i} ^ {1} (\\mathbf {x}) \\prod_ {1 \\leq j \\leq K, j \\neq i} f _ {j} ^ {2} (\\mathbf {x}). \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.165,
+                0.892,
+                0.197
+            ],
+            "angle": 0,
+            "content": "And we have the total uncertainty \\(\\mathcal{U} = 1 - \\sum_{i=1}^{K} b_i\\). As the ignorance \\(\\mathcal{I}\\) could be calculated similarly as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.566,
+                0.209,
+                0.892,
+                0.243
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {I} = \\prod_ {1 \\leq j \\leq K} (1 - p l _ {j}) = \\prod_ {1 \\leq j \\leq K} f _ {j} ^ {2} (\\mathbf {x}), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.254,
+                0.892,
+                0.3
+            ],
+            "angle": 0,
+            "content": "the total confusion between all different class combinations is \\(\\mathcal{C} = \\mathcal{U} - \\mathcal{I}\\). The confusion term between specific classes could be further calculated with Eq. 5."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.3,
+                0.892,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Intuitively, the belief for each combination could be regarded as the occupation in a unit \\( K \\)-dim volume. The modeling of confusion becomes feasible by spanning a \\( K \\)-dim hypothesis space with \\( K \\) plausibility functions. Moreover, the computation complexity of each combination is \\( \\mathcal{O}(n) \\), and for specific conditions, we could only calculate necessary confusion terms."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.418,
+                0.697,
+                0.433
+            ],
+            "angle": 0,
+            "content": "4.4. Developing Opinions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.442,
+                0.892,
+                0.562
+            ],
+            "angle": 0,
+            "content": "In this section, we describe how to develop opinions from training data. Each plausibility function \\( f_{i}(\\cdot) \\) can be constructed as a normalized dual-output linear layer or a single multi-output layer after being activated by a sigmoid function \\( \\sigma (\\cdot) \\). In this work, the second is implemented to reduce the network parameters. In particular, the output is regarded as the value of class plausibility. The plausibility function is then formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.571,
+                0.575,
+                0.891,
+                0.593
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(p l _ {i}, 1 - p l _ {i}\\right) = f _ {i} (\\mathbf {x}) = \\sigma \\left(w _ {i} ^ {\\top} \\Phi (\\mathbf {x})\\right) \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.606,
+                0.852,
+                0.621
+            ],
+            "angle": 0,
+            "content": "where \\(\\Phi :\\mathcal{X}\\to \\mathbb{R}^D\\) is a feature embedding function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.622,
+                0.892,
+                0.696
+            ],
+            "angle": 0,
+            "content": "Typically, only one deterministic label is given for each image in a standard visual recognition dataset. Following EDL [44], the learning of singleton belief is implemented as evidence acquisition on a Dirichlet prior. The loss of EDL is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.565,
+                0.707,
+                0.891,
+                0.75
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {E D L}} = \\sum_ {i = 1} ^ {K} y _ {i} \\left[ \\log \\left(\\sum_ {j = 1} ^ {K} \\alpha_ {j}\\right) - \\log \\left(\\alpha_ {i}\\right) \\right], \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.763,
+                0.891,
+                0.81
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{y} = [y_1, y_2, \\ldots, y_i, \\ldots, y_K]^T\\) is one-hot class label for a sample \\(\\mathbf{x}\\), and \\(\\boldsymbol{\\alpha} = [\\alpha_1, \\alpha_2, \\ldots, \\alpha_K]^T\\) are parameters of a Dirichlet distribution \\(Dir(\\cdot|\\boldsymbol{\\alpha})\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.891,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Different from EDL, class evidence is replaced with belief. Hence, \\(\\alpha\\) is directly calculated from singleton beliefs and overall uncertainty. It is derived as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.571,
+                0.867,
+                0.891,
+                0.905
+            ],
+            "angle": 0,
+            "content": "\\[\n\\alpha_ {i} = \\frac {K b _ {i}}{\\mathcal {U}} + 1 = \\frac {K b _ {i}}{1 - \\sum_ {j = 1} ^ {K} b _ {j}} + 1, \\tag {10}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1341"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "where \\( b_{i} \\) could be obtained from Eq. 6. During inference, all opinions could be directly predicted by performing combinations on the output of plausibility functions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.137,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "To encourage the plausibility function to match our expected behavior, i.e., predicting the plausibility instead of the belief of singleton, we add a regularization term as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.171,
+                0.189,
+                0.469,
+                0.23
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\sum_ {i = 1} ^ {K} y _ {i} \\left[ p l _ {i} - (1 - \\hat {\\mathcal {I}}) \\right] ^ {2}, \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.239,
+                0.388,
+                0.254
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{\\mathcal{I}}\\) is the current estimation of ignorance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.255,
+                0.469,
+                0.283
+            ],
+            "angle": 0,
+            "content": "Following EDL, a Kullback-Leibler loss is used to minimize evidence on unrelated classes as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.135,
+                0.292,
+                0.469,
+                0.31
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {K L}} = K L (D i r (\\cdot | \\tilde {\\alpha}) | | D i r (\\cdot | \\langle 1, \\dots , 1 \\rangle)), \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.315,
+                0.469,
+                0.346
+            ],
+            "angle": 0,
+            "content": "where \\(\\tilde{\\alpha} = \\mathbf{y} + (1 - \\mathbf{y})\\odot \\boldsymbol {\\alpha},\\) 0 for element-wise multiplication. Combining all terms together yields the final loss as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.163,
+                0.361,
+                0.469,
+                0.377
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {E D L}} + \\lambda_ {\\mathrm {r e g}} \\mathcal {L} _ {\\mathrm {r e g}} + \\lambda_ {\\mathrm {K L}} \\mathcal {L} _ {\\mathrm {K L}}. \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.381,
+                0.469,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Each loss term is accompanied by a balance weight, and we gradually increase the effect of \\(\\mathcal{L}_{kl}\\) through an additional annealing coefficient."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.426,
+                0.469,
+                0.531
+            ],
+            "angle": 0,
+            "content": "After developing opinions with the proposed method, a straightforward solution would be setting the belief threshold for outputs to achieve flexible recognition. The sample will be rejected if the ignorance is too large that no combination would exceed the threshold. And the model gives incrementally combined predictions if no singleton belief meets the bar."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.544,
+                0.209,
+                0.56
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.469,
+                0.734
+            ],
+            "angle": 0,
+            "content": "The proposed method could model two sources of uncertainty for each sample to handle the task of flexible recognition. To enable better comparison with existing methods, our experiments are primarily decomposed into three components. (1) Demonstrating the separation of two sources of uncertainty, i.e., confusion and ignorance. (2) Indicating the correct class on misclassified samples with estimated confusion. (3) Applying ignorance to compare with other methods on the task open-set detection. More experiments, including on adversarial-attacked samples and ablation studies, follow to give a more comprehensive evaluation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Implementation details. We adopt the ResNet-18 as the backbone for our experiments except on synthetic data and open-set detection. The dimension of extracted feature is set to 512. For the proposed method, we apply the sigmoid activation on the last linear layer to work as our multiple plausibility functions. We empirically find both EDL [44] and our method are more sensitive to the learning rate. Specifically, we set the learning rate for both methods to 0.004 with a momentum of 0.9 for the batch size of 128. \\(\\lambda_{\\mathrm{KL}}\\) in Eq. 13 anneals to 0 with epochs with the maximum coefficient of 0.05, and \\(\\lambda_{\\mathrm{reg}}\\) is set to 1."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.51,
+                0.093,
+                0.624,
+                0.161
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.534,
+                0.171,
+                0.599,
+                0.183
+            ],
+            "angle": 0,
+            "content": "(a) Class 1"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.639,
+                0.093,
+                0.755,
+                0.16
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.665,
+                0.171,
+                0.73,
+                0.183
+            ],
+            "angle": 0,
+            "content": "(b) Class 2"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.768,
+                0.093,
+                0.884,
+                0.16
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.795,
+                0.171,
+                0.859,
+                0.183
+            ],
+            "angle": 0,
+            "content": "(c) Class 3"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.51,
+                0.189,
+                0.625,
+                0.255
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.525,
+                0.267,
+                0.609,
+                0.279
+            ],
+            "angle": 0,
+            "content": "(d) Confusion"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.64,
+                0.189,
+                0.755,
+                0.256
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.657,
+                0.267,
+                0.737,
+                0.279
+            ],
+            "angle": 0,
+            "content": "(e) Ignorance"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.768,
+                0.188,
+                0.884,
+                0.256
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.765,
+                0.267,
+                0.888,
+                0.28
+            ],
+            "angle": 0,
+            "content": "(f) Standard Entropy"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.292,
+                0.892,
+                0.383
+            ],
+            "angle": 0,
+            "content": "Figure 4: A 3-class classification problem. The Gaussian-distributed training data are depicted with dots, while the background color indicates the estimated value of the corresponding location. Our results are plotted from (a) to (e). The entropy over predictions of a standard net trained with cross-entropy loss is shown in (f) for comparison."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.403,
+                0.71,
+                0.42
+            ],
+            "angle": 0,
+            "content": "5.1. Synthetic Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.427,
+                0.892,
+                0.548
+            ],
+            "angle": 0,
+            "content": "In this section, we examine the behavior of our approach in Fig. 4 in the 2-dimensional space. A dataset with three isotropic Gaussian distributed classes is created for training. The distances between each Gaussian are equal to 9, and we set \\(\\sigma = 4\\) for all Gaussian. Each class has 500 training samples which are denoted by colored dots. We discretize the background into 2D locations for testing. The background color denotes corresponding estimated values."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.549,
+                0.892,
+                0.715
+            ],
+            "angle": 0,
+            "content": "Both our method and the standard entropy are trained with the same multi-layer perceptron. As we can observe in Fig. 4 (a) to (e), the proposed method acts as a density estimator. Confusion happens between class boundaries, while ignorance is high for out-of-distribution data points. The proposed method does not require intricate adoptions to network architectures to achieve the desired properties. In Fig. 4 (f), the entropy of a standard deterministic neural net with the cross-entropy loss is plotted, which shows that using entropy to distinguish out-of-distributions could face multiple downsides due to its sharp boundaries."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.726,
+                0.809,
+                0.743
+            ],
+            "angle": 0,
+            "content": "5.2. Confusion on Misclassified Samples"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this part, the confusion is tested on misclassified samples, checking whether it is correlated with the ground-truth label. That is, the confusion should be high between the misclassified class and the ground-truth class. Besides in-sample comparison on the level of confusion, we argue the between-sample comparability of confusion is also critical for flexible visual recognition. For example, a flexible recognition system would tend to give a second prediction if its confusion is higher than in other samples. To address this concern, we employ the Area Under the Receiver Oper-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1342"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.089,
+                0.465,
+                0.179
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"2\">CIFAR-10</td><td colspan=\"2\">CIFAR-100</td><td colspan=\"2\">Imagenet</td></tr><tr><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td></tr><tr><td>Softmax</td><td>95.2</td><td>63.4</td><td>76.0</td><td>57.3</td><td>54.3</td><td>58.2</td></tr><tr><td>EDL [44]</td><td>94.8</td><td>60.4</td><td>74.5</td><td>54.9</td><td>54.2</td><td>58.3</td></tr><tr><td>Dropout [15]</td><td>94.7</td><td>64.5</td><td>74.5</td><td>58.9</td><td>47.3</td><td>61.8</td></tr><tr><td>OvR</td><td>95.1</td><td>63.2</td><td>72.2</td><td>63.4</td><td>46.3</td><td>60.2</td></tr><tr><td>ASL [7]</td><td>95.2</td><td>70.9</td><td>75.8</td><td>79.9</td><td>54.1</td><td>62.8</td></tr><tr><td>Ours</td><td>95.0</td><td>89.5</td><td>74.9</td><td>90.0</td><td>54.6</td><td>97.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.189,
+                0.471,
+                0.25
+            ],
+            "angle": 0,
+            "content": "Table 1: Comparison on whether the confusion indicates the correct class on misclassified samples. Results of classification accuracy and AUROC on misclassified samples are shown on three datasets with different class scales."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.275,
+                0.469,
+                0.365
+            ],
+            "angle": 0,
+            "content": "ating Characteristic curve (AUROC) as our evaluation metric, which sorts the predicted value along samples in each class. More specifically, the ROC curve is a graph showing the true positive rate against the false positive rate. A random classifier would correspond to a \\(50\\%\\) AUROC. Moreover, the metric sidesteps the issue of threshold selection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.368,
+                0.469,
+                0.444
+            ],
+            "angle": 0,
+            "content": "To be more clear, the confusion terms between all classes and the predicted class are regarded as the input to the metrics, while the target is one-hot class labels. As the groundtruth class could be imbalanced among misclassified samples, the AUROC is weighted by the categorical base rate."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.445,
+                0.47,
+                0.734
+            ],
+            "angle": 0,
+            "content": "The results on CIFAR-10, CIFAR-100 [26], and ImageNet [12] with 10, 100, and 1000 classes, respectively, are shown in Tab. 1 to demonstrate the comparison with different class scales. TheImagenet used here is an official downsampled version with the resolution of \\(64 \\times 64\\). Besides standard Softmax, the Dropout [15] refers to the method using Monte Carlo Dropout (with the dropout rate of 0.2 and 10 dropout iterations) to approximate the distribution of model parameters. Since these methods do not contain explicit outputs of confusion, they are compromised to an intuitive approach, which measures the difference between predicted class probabilities. Two multi-label classification methods, namely, the One-vs-Rest (OvR) and the ASL [7], are included as baselines whose outputs are not normalized between classes. For EDL [44], confusion is defined as the difference between estimated singleton beliefs. In stark contrast to these methods, the proposed method uses explicitly estimated confusion between any classes with the predicted class following the definition in Eq. 5."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "As shown in Tab. 1, the performance of the proposed method is significantly higher than all other approaches on three datasets. There are two reasons to support this result. First, the probability produced by softmax should not be viewed as the direct measure of confidence for each class [18], which means there might be no suitable way to derive confusion from softmax probability after training. Second, for the evidential method [44], the difference between predicted beliefs does not capture their shared features. In other words, the confusion in EDL is mixed with ignorance in their one uncertainty estimate. Orthogonal to"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.089,
+                0.695,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.698,
+                0.089,
+                0.892,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.622,
+                0.208,
+                0.773,
+                0.22
+            ],
+            "angle": 0,
+            "content": "(a) Results on CIFAR-10"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.222,
+                0.695,
+                0.335
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.7,
+                0.222,
+                0.894,
+                0.335
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.619,
+                0.341,
+                0.776,
+                0.353
+            ],
+            "angle": 0,
+            "content": "(b) Results on CIFAR-100"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.355,
+                0.695,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.7,
+                0.355,
+                0.894,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.626,
+                0.474,
+                0.768,
+                0.487
+            ],
+            "angle": 0,
+            "content": "(c) Results on Imagenet"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.499,
+                0.892,
+                0.561
+            ],
+            "angle": 0,
+            "content": "Figure 5: Precision and recall of delivering multiple predictions on misclassified samples with respect to the average number of predictions. The intention to predict extra classes is dependent on the confusion term between classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.58,
+                0.892,
+                0.641
+            ],
+            "angle": 0,
+            "content": "these methods, the proposed approach could model the confusion that occurred between classes and could help flexible recognition systems determine when and which class to be predicted next."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.651,
+                0.776,
+                0.668
+            ],
+            "angle": 0,
+            "content": "5.3. Flexible Closed-set Recognition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We turn to the task of flexible visual recognition on the closed CIFAR-10, CIFAR-100, and Imagenet, where methods are supposed to make multiple predictions when they are unsure. And we regard the output as correct as long as the correct answer is included in the prediction set. However, simply increasing the number of predictions for each sample should be penalized. Thus, for a more meaningful comparison, we show precision and recall as the function of the average number of predictions. We only evaluate methods on their misclassified samples, where providing more predictions is urgently demanded. And the indicator for making another prediction is the confusion between the considered and the predicted class, the same as in Section 5.2. The confusion for the first-predicted class itself is intuitively described as 0."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1343"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.099,
+                0.089,
+                0.451,
+                0.19
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Closed Dataset CIFAR-10</td><td>+ LSUN (crop)</td><td>+ ImageNet (crop)</td></tr><tr><td>Softmax</td><td>64.2</td><td>63.9</td></tr><tr><td>OpenMax [8]</td><td>65.7</td><td>66.0</td></tr><tr><td>OSRCI [38]</td><td>65.0</td><td>63.6</td></tr><tr><td>LadderNet + OpenMax [52]</td><td>65.2</td><td>65.3</td></tr><tr><td>DHRNet + OpenMax [52]</td><td>65.6</td><td>65.5</td></tr><tr><td>CROSR [52]</td><td>72.0</td><td>72.1</td></tr><tr><td>GFROSR [41]</td><td>75.1</td><td>75.7</td></tr><tr><td>Ours</td><td>80.5</td><td>76.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.2,
+                0.47,
+                0.247
+            ],
+            "angle": 0,
+            "content": "Table 2: Comparison on open-set detection by adding different unknown samples to the test set. The performance is evaluated by Macro-F1, which considers \\( K + 1 \\) classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.265,
+                0.473,
+                0.611
+            ],
+            "angle": 0,
+            "content": "The curves of three datasets are drawn in Fig. 5. We incrementally select more predictions for each class, i.e., the samples are deserved to make an extra prediction if its confusion on this considered class is more significant than in other samples. By doing this, we could control the average predictions while being threshold-independent in evaluating flexible visual recognition. A desired precision-average prediction curve would have a near 1 value for the start of making predictions. For the recall-average prediction curve, the closer it adheres to the left-top corner, the earlier it delivers the correct class. When comparing the precision curve, our method could achieve a significantly higher value than other methods when making limited predictions. For example, on the CIFAR-10 dataset, the proposed method reaches the precision of 0.62 for making an average of only one prediction for each sample, while the second highest is 0.33. Note some samples could have no prediction at the beginning as all of their confusion terms are lower than other samples. Besides, we also notice that ASL [7] is better than other baselines in the recall curve. This indicates that for flexible recognition, a multi-label classifier could be a better choice as it prevents the overconfident problem in the softmax probabilities to some extent."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.621,
+                0.371,
+                0.637
+            ],
+            "angle": 0,
+            "content": "5.4. Ignorance for Open-set Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.47,
+                0.734
+            ],
+            "angle": 0,
+            "content": "As a crucial part of flexible recognition, we additionally demonstrate the effectiveness of our method on the task of open-set detection in Tab. 2 following standard protocols [52, 18, 29]. The same network architecture, i.e., a 13-layer VGG model, is used to implement the proposed method as in [52]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "During the test time of open-set detection, the test images from CIFAR-10 datasets are viewed as closed-set examples. For open-set samples, we consider two natural image datasets, i.e., LSUN (crop) and ImageNet (crop), introduced by Liang et al [29]. The Macro-F1 is therefore evaluated on \\( K + 1 \\) classes by regarding all open samples as an additional class. And the threshold for being detected as open-set is chosen when \\( 95\\% \\) of closed-set images can be correctly classified. Among the compared methods, OS-RCI [38] augments the training set with hard and counterfactual generated images to improve unknown sample de"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.089,
+                0.695,
+                0.201
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.699,
+                0.089,
+                0.892,
+                0.201
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.213,
+                0.892,
+                0.243
+            ],
+            "angle": 0,
+            "content": "Figure 6: Top 1 and 2 accuracies with adversarial perturbations \\(\\epsilon\\) on CIFAR-10 [26] dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.263,
+                0.892,
+                0.46
+            ],
+            "angle": 0,
+            "content": "tection during testing. CROSR [52] and GFROSR [41] incorporate reconstruction loss into the procedure of closed-set training to better model the data distribution. For the proposed method, we use ignorance \\(\\mathcal{I}\\) as the indicator of unknown samples and achieve better performance without additional adversarial training data. The F1 score of the proposed method is higher than other methods on both datasets, which supports the claim that ignorance in the proposed method could effectively handle the lack of evidence in open-set samples. It is worth noting that, besides explicitly delivering ignorance to detect unknown samples, the advantage of the proposed method also lies in the estimate of confusion, which is evaluated in closed-set experiments."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.47,
+                0.822,
+                0.485
+            ],
+            "angle": 0,
+            "content": "5.5. Performance on Adversarial Samples"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.493,
+                0.892,
+                0.688
+            ],
+            "angle": 0,
+            "content": "We compare the robustness of different classification methods [15, 44] against adversarial attacks. Besides models introduced in the previous experiment, we include the recent multi-label classification method ASL [7] as another baseline. The reason is that multi-label classification methods usually adopt the same sigmoid activation and multiple binary linear layers as our method. For our method, we use the plausibility \\( p l_{i} \\) for class \\( i \\) to predict instead of their singleton beliefs, i.e., the confusion for each class that occurred during adding perturbations is involved in the ranking. The reason is that we want to test whether the confusion correctly characterizes the conflicting evidence shared between the correct and other classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Adversarial samples are generated on CIFAR-10 [26] using the Fast Gradient Sign method [17] with various perturbation parameters \\(\\epsilon\\). The adversarial attack method uses the gradient during inference to generate samples that are more challenging to make correct predictions as \\(\\epsilon\\) increases. Both the top 1 and top 2 results are shown in Fig. 6. The figure indicates that the proposed method could almost achieve both the highest top 1 and top 2 results. That is, the confusion that happened during perturbating is captured by our method, which could still contribute to the corresponding correct class. The proposed method is only slightly worse than the Dropout method when \\(\\epsilon = 0.25\\), which is forgivable as its training includes stochastic zeroing on the model parameter to increase its robustness."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "1344"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.089,
+                0.197,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.2,
+                0.089,
+                0.352,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.212,
+                0.21,
+                0.233,
+                0.222
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.089,
+                0.459,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.46,
+                0.089,
+                0.614,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.616,
+                0.089,
+                0.722,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.723,
+                0.089,
+                0.88,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.475,
+                0.209,
+                0.496,
+                0.222
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.739,
+                0.21,
+                0.758,
+                0.221
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.234,
+                0.895,
+                0.281
+            ],
+            "angle": 0,
+            "content": "Figure 7: Matrices of confusion of misclassified samples on the CIFAR-10 dataset. The diagonal of each matrix is set to the singleton belief of each class. Notice that the background color for each heatmap is normalized individually. The total ignorance is demonstrated in the caption."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.11,
+                0.297,
+                0.439,
+                0.39
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"5\">CIFAR-10 + LSUN (crop)</td></tr><tr><td>Acc.</td><td>F1</td><td>AUROC</td><td>AUPR closed</td><td>AUPR open</td></tr><tr><td>Ours w/o Reg.</td><td>72.4</td><td>84.8</td><td>96.2</td><td>96.9</td><td>95.3</td></tr><tr><td>Ours w/ Reg.</td><td>79.9</td><td>86.9</td><td>97.0</td><td>97.5</td><td>96.6</td></tr><tr><td></td><td colspan=\"5\">CIFAR-10 + ImageNet (crop)</td></tr><tr><td>Ours w/o Reg.</td><td>63.9</td><td>82.0</td><td>95.1</td><td>96.1</td><td>93.8</td></tr><tr><td>Ours w/ Reg.</td><td>71.7</td><td>83.9</td><td>95.8</td><td>96.5</td><td>94.7</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.4,
+                0.47,
+                0.43
+            ],
+            "angle": 0,
+            "content": "Table 3: Ablation studies about the regularization term \\(\\mathcal{L}_{\\mathrm{reg}}\\) on the task of open-set detection with two hybrid datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.45,
+                0.262,
+                0.466
+            ],
+            "angle": 0,
+            "content": "5.6. Qualitative Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.474,
+                0.47,
+                0.609
+            ],
+            "angle": 0,
+            "content": "Furthermore, to provide a more intuitive impression of our results, we demonstrate the matrices of binary confusion estimates in Fig. 7. We take the misclassified images of the proposed method for the CIFAR-10 dataset. The ground truth label, the prediction, the singleton belief, the ignorance, and the highest binary confusion are noted in their captions. Each grid in the confusion matrix denotes the confusion between any two classes, while the diagonal represents the singleton belief."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.61,
+                0.47,
+                0.777
+            ],
+            "angle": 0,
+            "content": "In Fig. 7b, the proposed method wrongly recognizes the image into dog class while maintaining a very high confusion towards the correct class horse. However, as the singleton belief is not significant for the predicted class, the proposed method could predict a combined result, i.e., both dog and horse, if setting a relatively high threshold on the sum of beliefs. Another example in Fig. 7c implies the ability of our method to reject making a prediction. As the image in Fig. 7c is contentless and low-resolution, the proposed failed to collect enough supportive evidence for any known classes, which delivers a very high ignorance value."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.787,
+                0.242,
+                0.801
+            ],
+            "angle": 0,
+            "content": "5.7. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We investigate how the regularization term \\(\\mathcal{L}_{\\mathrm{reg}}\\) influences performance. The reason we add the regularization is to avoid the first output of each plausibility function converging to the belief instead of the plausibility. To show its effectiveness, we evaluate the proposed method on the task of open-set detection in Tab. 3. The separation could"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.3,
+                0.895,
+                0.497
+            ],
+            "angle": 0,
+            "content": "be deemed to be more sufficient if the ignorance term performs better in detecting open-set samples. Note we use the ResNet-18 as our backbone here to remain consistent with our flexible recognition experiments. For the metric of open-set detection accuracy and AUROC, closed-set samples are regarded as negative samples, while open-set samples constitute positive samples. The other two metrics, AUPR closed and AUPR open, denote the Area Under the Precision-Recall curve where closed-set or open-set images are specified as positives, respectively. The overall improvements in adding the regularization term \\(\\mathcal{L}_{\\mathrm{reg}}\\), as demonstrated in Tab. 3, indicate its effectiveness in promoting the separation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.507,
+                0.768,
+                0.521
+            ],
+            "angle": 0,
+            "content": "5.8. Discussions and Future works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.53,
+                0.894,
+                0.605
+            ],
+            "angle": 0,
+            "content": "In our experiments, we find the scale of confusion and ignorance varies with different backbones and datasets. The correlation behind it could be related to the capabilities of different models and the learning difficulties of different datasets. We leave the investigation for our future work."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.619,
+                0.628,
+                0.635
+            ],
+            "angle": 0,
+            "content": "6. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.645,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this paper, we introduce a novel approach to explicitly model two distinct sources of uncertainties, i.e., confusion and ignorance, under the novel task of flexible recognition. The recognition system is expected to reject samples from unknown classes and also make multiple predictions when it is uncertain about a closed-set image. Particularly, in the proposed method, the confusion is modeled as the conflicting evidence, while the ignorance represents the total lack of evidence. The hypothesis space of recognition is then divided and modeled by multiple plausibility functions. The model learns the concentration parameter of Dirichlet prior, which is being placed on the belief for singletons. A complete set of opinions could be generated through evidence combinations. Experiments on different datasets, along with challenging tasks of adversarial disturbance, flexible recognition, and open-set detection, confirm the effectiveness of the proposed method."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "1345"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
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+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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\ No newline at end of file
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+# Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorance
+
+Lei Fan $^{1}$ , Bo Liu $^{2}$ , Haoxiang Li $^{2}$ , Ying Wu $^{1}$  and Gang Hua $^{2}$ \
+ $^{1}$ Northwestern University  $^{2}$ Wormpex AI Research
+
+leifan@u.northwestern.edu,yingwu@northwestern.edu,{richardboliu,lhxustcer,ganghua}@gmail.com
+
+# Abstract
+
+In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition.
+
+# 1. Introduction
+
+When employing visual classifiers in open-world conditions, obtaining reliable uncertainty estimations could significantly benefit downstream tasks, including autonomous driving [1, 13, 37], medical diagnosis [36, 49], and embodied intelligence [40, 35]. Recent uncertainty quantification techniques [53, 15, 28, 32, 34, 33, 9, 43] have achieved notable progress toward this goal by saying "I do not know" when the testing distributions differ from the training. However, besides directly giving no prediction, a more flexible
+
+![](images/2922f421db359d998ac498b26044f802c492921817679d0aa3845cf2735706f1.jpg)  
+Figure 1: Classification of the proposed approach on images interpolated from a known-known-unknown triplet. Ignorance reflects the lack of evidence, whereas confusion is caused by conflicting evidence, i.e., evidence that fails to provide discrimination between specific classes. A flexible visual recognition system could provide combined predictions when having large confusion and reject making predictions for unknown-class samples. Note the mixup images are for illustrative purposes and are not a requisite in our training.
+
+and informative visual recognition system could also give combined predictions when possible, implying the correct answer is one of its predictions but uncertain. Naturally, the capability of rejecting or providing unspecific predictions demands separately measuring different sources of uncertainties, i.e., ignorance and confusion, if seen from the Subjective Logic [21] perspective. Furthermore, to enable flexible recognition, both uncertainties should possess the virtue of comparability between samples and in-sample additivity.
+
+In evidential deep learning, the training of a recognition model could be regarded as an evidence-collecting process [21, 44]. Unlike ignorance describing a total lack of evidence, confusion is defined as conflicting evidence, which mandates the existence of multiple hypotheses in the frame of discernment. In other words, we cannot assess confusion for a single-class classification problem. The mass of confusion between two classes then reflects shared features that contribute to both classes while not discriminative. Likewise, confusion exists for all combinations of classes larger than two. Unlike typical visual classifiers that only predict
+
+a single output, flexible predictions could be obtained if we could combine singleton belief derived from class-exclusive evidence with their inter-class confusion.
+
+With great potential for explicitly estimating confusion and ignorance, this area is still under-explored for deep visual classifiers. Recent methods regard uncertainties as the degree of mismatch between training and testing distributions, which comprise but do not distinguish between confusion and ignorance. Deep Bayesian models, including dropout [15, 22] and ensemble-based approximations [28, 51, 4], require multiple forwards to estimate the posterior predictive distribution. Evidential models [44, 1, 11, 5] predict parameters of the posterior of class distribution directly. However, these models regard uncertainty as a whole term covering both confusion and ignorance, making it infeasible to perform flexible visual recognition further.
+
+Distinct from existing uncertainty quantification methods, the proposed method models confusion and ignorance for each sample separately, which provides valuable information to facilitate various visual tasks, including flexible visual recognition. An illustrative example with the prediction of our method is shown in Fig. 1. Under the theory of Subjective Logic [6, 21], confusion is defined as the shared evidence contributing to multiple categories while not discriminative between them, while ignorance is completely missing evidence.
+
+The contribution of this paper could be summarized as follow: (1) The proposed method could explicitly predict two sources of uncertainties, i.e., confusion and ignorance, simultaneously for each sample. (2) The solution to confusion and ignorance is based on standard architectures, and the training does not rely on external information. (3) The effectiveness of the proposed method is extensively validated across different experiments, including studies on synthetic data, visual recognitions, and open-set detections.
+
+# 2. Related Work
+
+Uncertainty estimation. Typical neural networks can not detect their own failure. However, this ability can be important in several real-world applications, like rejecting unseen samples, and providing prediction confidence, to name a few. Bayesian NN [15, 27, 47, 14, 25] predicts epistemic uncertainty as the mutual information between model parameters and samples. By assuming a probabilistic prior on the network, it approximates prediction variance by sampling weight during inference. Several works [20, 49, 23] choose to model epistemic and aleatoric uncertainties separately. The Subjective Logic on which our method is established falls within the realm of epistemology instead of a frequentist (aleatoric) view. In other words, we focus on further separating epistemic uncertainty into confusion and ignorance.
+
+Evidential deep learning [44, 1, 5, 11], in contrast, pro
+
+poses to learn the prior of the predictions directly. The prior, known as evidential prior, is interpreted as beliefs in Dempster-Shafer Theory [6]. In [11], they model the first- and second-order uncertainties by introducing an auxiliary uncertainty network to approximate the difference between Dirichlet distributions.
+
+While uncertainty is provided to describe the variance of model prediction, it is not clear if uncertainty comes from different sources when dealing with in-distribution or out-of-distribution data. Orthogonal to previous approaches, we separate the uncertainty into confusion and ignorance in this work. Confusion depicts the uncertainty between different known classes, while ignorance decides whether the sample is unknown. With this separation, we can make dynamic predictions on known classes and reject unknown classes at the same time.
+
+Open Set Recognition. Machine learning models are usually designed with the closed-set assumption, where testing data shares the same distribution as the training. Open-set recognition (OSR) [8] introduces semantic shifts to the problem. Samples are from the classes that are not in the training set. Out-of-distribution (OOD) [19] detection introduces domain shifts to the testing set. In both of the settings, models should have the ability to reject unknown samples.
+
+In general, OSR and OOD methods reject unknown samples depending on reweighting outputs [8, 16, 24, 19, 30, 50], getting better feature embedding metrics [31, 10, 42, 38], and exploring reconstruction errors [39, 46, 45, 52, 41]. These metrics are all related to the quality of classifier prediction. However, the recognition can fail on closed-set samples because of the existence of confusion. In this work, we show that when the confusion between known classes is adequately modeled, unknown samples can be identified more accurately.
+
+Conformal Prediction. Parallel to our task, conformal prediction is a paradigm that could provide single or multiple predictions by empirically constructing confidence regions [2, 3, 48]. However, conformal prediction is confined to closed scenarios without open samples, as the empirical quantile is established on a labeled validation set sampled from the same testing distribution.
+
+# 3. Flexible Recognition
+
+Flexible recognition aims to provide a classification model  $\mathcal{M}$  that could deliver adaptive predictive sets. Specifically, the model rejects samples, i.e., making no prediction, when the input is entirely out of the training distribution, like an open-set sample. The model also should cautiously give a set of predictions with the true class contained in it when being unsure.
+
+For a  $K$ -class classification problem, we formalize the flexible recognition system  $\mathcal{M}(\cdot)$  as  $\{y_1,\ldots ,y_k\} = \mathcal{M}(\mathbf{x})$  where  $\mathbf{x}$  denotes the input image, and the predictive set
+
+$\{y_{1}, \ldots, y_{k}\}$  obeys  $0 \leq k \leq K$ . Therefore,  $k = 0$  means the recognition system rejects making a prediction, and the true label  $\mathbf{y}$  is supposed to be contained in the predictive set when  $\mathbf{x}$  is from known classes.
+
+# 4. Method
+
+In this paper, we propose to tackle flexible recognition by separately estimating the confusion and ignorance for each sample. Intuitively, confusion denotes conflicting evidence between known classes, which should be additive to single-class beliefs for making reasonable multiple predictions. Ignorance denotes a lack of evidence to support rejecting samples. Most of this section falls into the proposed evidential modeling, which formulates confusion and ignorance in visual recognition under the theory of Subject Logic [21]. The approach to combining evidence and developing opinions follows. The approach to achieve flexible recognition is presented in the final.
+
+# 4.1. Preliminaries
+
+Existing learning-based visual recognition models often rely on a softmax layer to give class probabilities. As a point estimation of predictive distribution, the classifier trained with the cross-entropy loss tends to deliver inflating probabilities to a single class and could not provide a reliable estimation of uncertainties [19].
+
+We develop confusion and ignorance based on the Dempster-Shafer Theory of Evidence (DST) [6], which is a generalized scheme towards subjective probabilities [21]. The theory allows plausible reasoning with operations of evidence, namely the combination of evidence. Consider a  $K$ -class recognition task,  $\Theta = \{i, 1 \leq i \leq K\}$  would be the frame of discernment containing exclusive propositions, e.g., class labels. Extensively, the general propositions under this frame would be the set of all subsets of  $\Theta$ , which is
+
+$$
+2 ^ {\Theta} = \{\emptyset , 1, \dots , K, \{1, 2 \}, \dots , \Theta \}, \tag {1}
+$$
+
+where  $2^{\Theta}$  contains a total of  $2^{K}$  elements.
+
+Supposing  $b_A \in [0,1]$  as a measure of belief mass contained in proposition  $A$ , the total mass of general propositions satisfies  $\sum_{A \in 2^{\Theta}} b_A = 1$ . The belief for any proposition is then defined as the summation of contained mass, which is formulated as  $b_A = \sum_{B \subset A} b_B$ .
+
+And it is worth noting that  $B \subseteq A$  suggests the logical statement that  $B$  implies  $A$ . The total belief in  $A$  is the sum of belief in all propositions that imply  $A$  plus the belief in  $A$  itself. For a more intuitive understanding, considering a binary visual classification task, the belief for predicting both classes is the combination of mass shared between classes and also class-exclusive masses.
+
+We could further define the plausibility of  $A$  as  $p l_{A}$ , which is the total mass of propositions that has a non-empty
+
+![](images/8c3d2e39cf2a97fa2cc337d73d8ef3a65f2b3d857831c3994edda06090b6e1ec.jpg)  
+Figure 2: The relation between different masses constituting the final set of opinions towards a hypothesis.
+
+union with the current one. Also, the plausibility of a hypothesis could only be larger or equal to its own belief, i.e.,  $p l_{A} \geq b_{A}$ . We demonstrate the basic probability assignments and their relations in Fig. 2.
+
+# 4.2. Uncertainty, Confusion, and Ignorance
+
+Recent evidential deep learning methods [44] develop uncertainties under multinomial opinions, which model belief for singletons as  $\{b_i, i = 1, \dots, K\}$  and regard the leftover as the total uncertainty  $\mathcal{U}$ . We, therefore, have  $\mathcal{U} + \sum_{i=1}^{K} b_i = 1$ .
+
+However, in our modeling, we argue the uncertainty  $\mathcal{U}$  for each sample  $\mathbf{x}$  comes from two distinct sources, i.e., confusion  $\mathcal{C}$  and ignorance  $\mathcal{I}$ , which is written as
+
+$$
+\mathcal {U} ^ {\mathbf {x}} = \mathcal {C} ^ {\mathbf {x}} + \mathcal {I} ^ {\mathbf {x}}. \tag {2}
+$$
+
+Intuitively, a large confusion  $\mathcal{C}^{\times}$  denotes the model is hard to distinguish  $\mathbf{x}$  from known classes. For example, the model could have high confusion with a huskie image when the model has known classes of dog and wolf. An image from previously unknown classes, on the other hand, could have high ignorance. The superscript  $\mathbf{x}$  will be omitted in the following for clarity.
+
+To introduce the separate measurements of confusion and ignorance, our method is formalized with hyper opinions, composing masses of  $2^{K}$  subsets for a  $K$ -class frame of discernment. Therefore, the overall confusion  $\mathcal{C}$  is the total mass of the non-singleton subsets as  $\mathcal{C} = \sum_{A,A\in 2^{\ominus},2\leq |A|\leq K}b_A$ . In other words, the confusion  $\mathcal{C}$  is the sum of masses shared between two or more classes. Altogether, following Eq. 2, we have  $2^{K}$  mass values satisfy
+
+$$
+\mathcal {C} + \mathcal {I} + \sum_ {i = 1} ^ {K} b _ {i} = \sum_ {A, A \in 2 ^ {\Theta}, 2 \leq | A | \leq K} b _ {A} + \mathcal {I} + \sum_ {i = 1} ^ {K} b _ {i} = 1, \tag {3}
+$$
+
+where  $\mathcal{I} \geq 0$  and  $b \geq 0$  for all singletons and non-singleton subsets. The ignorance  $\mathcal{I}$ , therefore, could be regarded as the mass placed on the empty set  $\emptyset$  in the frame, which indicates the level of lacking evidence. Confusion, defined on subsets with cardinalities larger than 1, reflects evidence that fails to discriminate between specific singletons.
+
+To further facilitate our evidence combination process, we group non-singleton confusion terms based on whether they hold evidence for a particular class  $i$ .
+
+![](images/d8e178d890ff3271ec1949c5b85622032c5d2c8519221f7fcfbb45692262cebf.jpg)  
+Figure 3: Two graphical demonstrations of evidence combination on 2- and 3-class classification task. We only show ignorance in the 3-class example to avoid overlappings.
+
+![](images/13ad8bc57db7dcc5317b43b3f4b3a951b1cc09391b54877108323215937ad4a1.jpg)
+
+Class  $i$ -related confusion mass  $\mathcal{C}_i$ . It is defined as  $\mathcal{C}_i = \sum_{A,A\in 2^\Theta, |A| \geq 2, i \cap A = i} b_A$ . To be more specific,  $\mathcal{C}_i$  is the total mass placed on the set of all confusion terms that are supersets of singleton  $i$ .
+
+Class  $i$ -unrelated confusion mass  $\mathcal{C}_{\neg i}$ . Conversely, we have  $\mathcal{C}_{\neg i} = \sum_{A,A\in 2^{\Theta},|A|\geq 2,i\cap A\neq i}b_A$ . Accordingly, for any class  $i$ , we have
+
+$$
+\mathcal {C} = \mathcal {C} _ {i} + \mathcal {C} _ {- i}. \tag {4}
+$$
+
+And, as shown in Fig. 2, the plausibility of the current sample belonging to class  $i$  is  $p l_{i} = b_{i} + \mathcal{C}_{i}$ , which stands for a combination of class-exclusive singleton belief mass and class-shared confusion masses.
+
+# 4.3. Evidence Combinations
+
+The objective of the proposed approach is to predict ignorance and confusion explicitly for each sample. However, unlike ignorance which is a single term, the number of confusion reaches the exponential of classes, which means our model is required to give a comprehensive quantification of  $2^{K}$  estimates. While intimidating, we propose to handle this by decomposing the problem into  $K$  plausibility functions  $f_{i}(\cdot)$  for  $i = 1,\dots ,K$  on the same frame. Each plausibility function  $f_{i}(\cdot)$  is designed to give two predictions only considering class  $i$ , which is written as  $f_{i}(\mathbf{x}) = (pl_{i},1 - pl_{i})$ .
+
+Supposing we have obtained the plausibilities for all classes, any propositions, including the singleton class belief, confusion, and ignorance could then be derived by the rule of evidence combinations. In general, for  $K$  plausibility functions, the belief assignment of any proposition  $A$  is combined by computing as
+
+$$
+b _ {A} = \sum_ {B, \cap B = A} \prod_ {1 \leq j \leq K} b _ {B, j} (\mathbf {x}) = \sum_ {B, \cap B = A} \prod_ {1 \leq j \leq K} f _ {j} ^ {B} (\mathbf {x}). \tag {5}
+$$
+
+Note we do not have the normalization term in our formulation because we do not exclude the empty set from our frame. We demonstrate the combination process with 2- and 3-class classification examples in Fig. 3. To clarify fur
+
+ther, the singleton belief for class  $i$  is computed as
+
+$$
+b _ {i} = p l _ {i} \prod_ {1 \leq j \leq K, j \neq i} (1 - p l _ {j}) = f _ {i} ^ {1} (\mathbf {x}) \prod_ {1 \leq j \leq K, j \neq i} f _ {j} ^ {2} (\mathbf {x}). \tag {6}
+$$
+
+And we have the total uncertainty  $\mathcal{U} = 1 - \sum_{i=1}^{K} b_i$ . As the ignorance  $\mathcal{I}$  could be calculated similarly as
+
+$$
+\mathcal {I} = \prod_ {1 \leq j \leq K} (1 - p l _ {j}) = \prod_ {1 \leq j \leq K} f _ {j} ^ {2} (\mathbf {x}), \tag {7}
+$$
+
+the total confusion between all different class combinations is  $\mathcal{C} = \mathcal{U} - \mathcal{I}$ . The confusion term between specific classes could be further calculated with Eq. 5.
+
+Intuitively, the belief for each combination could be regarded as the occupation in a unit  $K$ -dim volume. The modeling of confusion becomes feasible by spanning a  $K$ -dim hypothesis space with  $K$  plausibility functions. Moreover, the computation complexity of each combination is  $\mathcal{O}(n)$ , and for specific conditions, we could only calculate necessary confusion terms.
+
+# 4.4. Developing Opinions
+
+In this section, we describe how to develop opinions from training data. Each plausibility function  $f_{i}(\cdot)$  can be constructed as a normalized dual-output linear layer or a single multi-output layer after being activated by a sigmoid function  $\sigma (\cdot)$ . In this work, the second is implemented to reduce the network parameters. In particular, the output is regarded as the value of class plausibility. The plausibility function is then formulated as
+
+$$
+\left(p l _ {i}, 1 - p l _ {i}\right) = f _ {i} (\mathbf {x}) = \sigma \left(w _ {i} ^ {\top} \Phi (\mathbf {x})\right) \tag {8}
+$$
+
+where  $\Phi :\mathcal{X}\to \mathbb{R}^D$  is a feature embedding function.
+
+Typically, only one deterministic label is given for each image in a standard visual recognition dataset. Following EDL [44], the learning of singleton belief is implemented as evidence acquisition on a Dirichlet prior. The loss of EDL is
+
+$$
+\mathcal {L} _ {\mathrm {E D L}} = \sum_ {i = 1} ^ {K} y _ {i} \left[ \log \left(\sum_ {j = 1} ^ {K} \alpha_ {j}\right) - \log \left(\alpha_ {i}\right) \right], \tag {9}
+$$
+
+where  $\mathbf{y} = [y_1, y_2, \ldots, y_i, \ldots, y_K]^T$  is one-hot class label for a sample  $\mathbf{x}$ , and  $\boldsymbol{\alpha} = [\alpha_1, \alpha_2, \ldots, \alpha_K]^T$  are parameters of a Dirichlet distribution  $Dir(\cdot|\boldsymbol{\alpha})$ .
+
+Different from EDL, class evidence is replaced with belief. Hence,  $\alpha$  is directly calculated from singleton beliefs and overall uncertainty. It is derived as
+
+$$
+\alpha_ {i} = \frac {K b _ {i}}{\mathcal {U}} + 1 = \frac {K b _ {i}}{1 - \sum_ {j = 1} ^ {K} b _ {j}} + 1, \tag {10}
+$$
+
+where  $b_{i}$  could be obtained from Eq. 6. During inference, all opinions could be directly predicted by performing combinations on the output of plausibility functions.
+
+To encourage the plausibility function to match our expected behavior, i.e., predicting the plausibility instead of the belief of singleton, we add a regularization term as
+
+$$
+\mathcal {L} _ {\text {r e g}} = \sum_ {i = 1} ^ {K} y _ {i} \left[ p l _ {i} - (1 - \hat {\mathcal {I}}) \right] ^ {2}, \tag {11}
+$$
+
+where  $\hat{\mathcal{I}}$  is the current estimation of ignorance.
+
+Following EDL, a Kullback-Leibler loss is used to minimize evidence on unrelated classes as
+
+$$
+\mathcal {L} _ {\mathrm {K L}} = K L (D i r (\cdot | \tilde {\alpha}) | | D i r (\cdot | \langle 1, \dots , 1 \rangle)), \tag {12}
+$$
+
+where  $\tilde{\alpha} = \mathbf{y} + (1 - \mathbf{y})\odot \boldsymbol {\alpha},$  0 for element-wise multiplication. Combining all terms together yields the final loss as
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {E D L}} + \lambda_ {\mathrm {r e g}} \mathcal {L} _ {\mathrm {r e g}} + \lambda_ {\mathrm {K L}} \mathcal {L} _ {\mathrm {K L}}. \tag {13}
+$$
+
+Each loss term is accompanied by a balance weight, and we gradually increase the effect of  $\mathcal{L}_{kl}$  through an additional annealing coefficient.
+
+After developing opinions with the proposed method, a straightforward solution would be setting the belief threshold for outputs to achieve flexible recognition. The sample will be rejected if the ignorance is too large that no combination would exceed the threshold. And the model gives incrementally combined predictions if no singleton belief meets the bar.
+
+# 5. Experiments
+
+The proposed method could model two sources of uncertainty for each sample to handle the task of flexible recognition. To enable better comparison with existing methods, our experiments are primarily decomposed into three components. (1) Demonstrating the separation of two sources of uncertainty, i.e., confusion and ignorance. (2) Indicating the correct class on misclassified samples with estimated confusion. (3) Applying ignorance to compare with other methods on the task open-set detection. More experiments, including on adversarial-attacked samples and ablation studies, follow to give a more comprehensive evaluation.
+
+Implementation details. We adopt the ResNet-18 as the backbone for our experiments except on synthetic data and open-set detection. The dimension of extracted feature is set to 512. For the proposed method, we apply the sigmoid activation on the last linear layer to work as our multiple plausibility functions. We empirically find both EDL [44] and our method are more sensitive to the learning rate. Specifically, we set the learning rate for both methods to 0.004 with a momentum of 0.9 for the batch size of 128.  $\lambda_{\mathrm{KL}}$  in Eq. 13 anneals to 0 with epochs with the maximum coefficient of 0.05, and  $\lambda_{\mathrm{reg}}$  is set to 1.
+
+![](images/bc92dae818ba65c6de8c1e5e1ee2b123ad7305a9252206df33c42e5a5f1d1d67.jpg)  
+(a) Class 1
+
+![](images/72bb460d1a3e71a2ad4f27304f014781b0789cca77b30e4896b1f4481546d34a.jpg)  
+(b) Class 2
+
+![](images/0de752b88ed981990a136d14880638d76ba55939c14b911ed6aeb38327e439d1.jpg)  
+(c) Class 3
+
+![](images/66f4757e16c036b92f275ffffb102c9a886384fd73083878210e59a97a73af71.jpg)  
+(d) Confusion
+
+![](images/4862dd105dae7aa4395cc9880af829a46464aec7060f1fbe707ee7d2abb41219.jpg)  
+(e) Ignorance
+
+![](images/227d8cebdd5595bc6bd297204c76b594ba0f644108f219d371c45524a392ad9b.jpg)  
+(f) Standard Entropy  
+Figure 4: A 3-class classification problem. The Gaussian-distributed training data are depicted with dots, while the background color indicates the estimated value of the corresponding location. Our results are plotted from (a) to (e). The entropy over predictions of a standard net trained with cross-entropy loss is shown in (f) for comparison.
+
+# 5.1. Synthetic Experiments
+
+In this section, we examine the behavior of our approach in Fig. 4 in the 2-dimensional space. A dataset with three isotropic Gaussian distributed classes is created for training. The distances between each Gaussian are equal to 9, and we set  $\sigma = 4$  for all Gaussian. Each class has 500 training samples which are denoted by colored dots. We discretize the background into 2D locations for testing. The background color denotes corresponding estimated values.
+
+Both our method and the standard entropy are trained with the same multi-layer perceptron. As we can observe in Fig. 4 (a) to (e), the proposed method acts as a density estimator. Confusion happens between class boundaries, while ignorance is high for out-of-distribution data points. The proposed method does not require intricate adoptions to network architectures to achieve the desired properties. In Fig. 4 (f), the entropy of a standard deterministic neural net with the cross-entropy loss is plotted, which shows that using entropy to distinguish out-of-distributions could face multiple downsides due to its sharp boundaries.
+
+# 5.2. Confusion on Misclassified Samples
+
+In this part, the confusion is tested on misclassified samples, checking whether it is correlated with the ground-truth label. That is, the confusion should be high between the misclassified class and the ground-truth class. Besides in-sample comparison on the level of confusion, we argue the between-sample comparability of confusion is also critical for flexible visual recognition. For example, a flexible recognition system would tend to give a second prediction if its confusion is higher than in other samples. To address this concern, we employ the Area Under the Receiver Oper-
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="2">CIFAR-10</td><td colspan="2">CIFAR-100</td><td colspan="2">Imagenet</td></tr><tr><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td></tr><tr><td>Softmax</td><td>95.2</td><td>63.4</td><td>76.0</td><td>57.3</td><td>54.3</td><td>58.2</td></tr><tr><td>EDL [44]</td><td>94.8</td><td>60.4</td><td>74.5</td><td>54.9</td><td>54.2</td><td>58.3</td></tr><tr><td>Dropout [15]</td><td>94.7</td><td>64.5</td><td>74.5</td><td>58.9</td><td>47.3</td><td>61.8</td></tr><tr><td>OvR</td><td>95.1</td><td>63.2</td><td>72.2</td><td>63.4</td><td>46.3</td><td>60.2</td></tr><tr><td>ASL [7]</td><td>95.2</td><td>70.9</td><td>75.8</td><td>79.9</td><td>54.1</td><td>62.8</td></tr><tr><td>Ours</td><td>95.0</td><td>89.5</td><td>74.9</td><td>90.0</td><td>54.6</td><td>97.6</td></tr></table>
+
+Table 1: Comparison on whether the confusion indicates the correct class on misclassified samples. Results of classification accuracy and AUROC on misclassified samples are shown on three datasets with different class scales.
+
+ating Characteristic curve (AUROC) as our evaluation metric, which sorts the predicted value along samples in each class. More specifically, the ROC curve is a graph showing the true positive rate against the false positive rate. A random classifier would correspond to a  $50\%$  AUROC. Moreover, the metric sidesteps the issue of threshold selection.
+
+To be more clear, the confusion terms between all classes and the predicted class are regarded as the input to the metrics, while the target is one-hot class labels. As the groundtruth class could be imbalanced among misclassified samples, the AUROC is weighted by the categorical base rate.
+
+The results on CIFAR-10, CIFAR-100 [26], and ImageNet [12] with 10, 100, and 1000 classes, respectively, are shown in Tab. 1 to demonstrate the comparison with different class scales. TheImagenet used here is an official downsampled version with the resolution of  $64 \times 64$ . Besides standard Softmax, the Dropout [15] refers to the method using Monte Carlo Dropout (with the dropout rate of 0.2 and 10 dropout iterations) to approximate the distribution of model parameters. Since these methods do not contain explicit outputs of confusion, they are compromised to an intuitive approach, which measures the difference between predicted class probabilities. Two multi-label classification methods, namely, the One-vs-Rest (OvR) and the ASL [7], are included as baselines whose outputs are not normalized between classes. For EDL [44], confusion is defined as the difference between estimated singleton beliefs. In stark contrast to these methods, the proposed method uses explicitly estimated confusion between any classes with the predicted class following the definition in Eq. 5.
+
+As shown in Tab. 1, the performance of the proposed method is significantly higher than all other approaches on three datasets. There are two reasons to support this result. First, the probability produced by softmax should not be viewed as the direct measure of confidence for each class [18], which means there might be no suitable way to derive confusion from softmax probability after training. Second, for the evidential method [44], the difference between predicted beliefs does not capture their shared features. In other words, the confusion in EDL is mixed with ignorance in their one uncertainty estimate. Orthogonal to
+
+![](images/0faf67e657791a7c334d70a91e8727a0a08d605fcbfcf1bf46ff31a7fcac5356.jpg)
+
+![](images/7788a3de198504727e82f63dcee192c5034412f3e91d7172e3e5c80278ee9d56.jpg)
+
+![](images/2401d3804f9a3452113b131c5645e13812d23414667f8882c320f3b69af7c3cf.jpg)  
+(a) Results on CIFAR-10
+
+![](images/2a8336da84264525e2cddb71874cdf3babe3f684545533124dd33a9e4c7e1c1a.jpg)
+
+![](images/857a798139849e7b0023f36c91835ee81fa13a759fd2eaa84403366dd3fa0f96.jpg)  
+(b) Results on CIFAR-100  
+(c) Results on Imagenet
+
+![](images/2a227159a58801a2f57e39d90f9f25138b6fd382a269c6cafd7c37bd77ad4cff.jpg)  
+Figure 5: Precision and recall of delivering multiple predictions on misclassified samples with respect to the average number of predictions. The intention to predict extra classes is dependent on the confusion term between classes.
+
+these methods, the proposed approach could model the confusion that occurred between classes and could help flexible recognition systems determine when and which class to be predicted next.
+
+# 5.3. Flexible Closed-set Recognition
+
+We turn to the task of flexible visual recognition on the closed CIFAR-10, CIFAR-100, and Imagenet, where methods are supposed to make multiple predictions when they are unsure. And we regard the output as correct as long as the correct answer is included in the prediction set. However, simply increasing the number of predictions for each sample should be penalized. Thus, for a more meaningful comparison, we show precision and recall as the function of the average number of predictions. We only evaluate methods on their misclassified samples, where providing more predictions is urgently demanded. And the indicator for making another prediction is the confusion between the considered and the predicted class, the same as in Section 5.2. The confusion for the first-predicted class itself is intuitively described as 0.
+
+<table><tr><td>Closed Dataset CIFAR-10</td><td>+ LSUN (crop)</td><td>+ ImageNet (crop)</td></tr><tr><td>Softmax</td><td>64.2</td><td>63.9</td></tr><tr><td>OpenMax [8]</td><td>65.7</td><td>66.0</td></tr><tr><td>OSRCI [38]</td><td>65.0</td><td>63.6</td></tr><tr><td>LadderNet + OpenMax [52]</td><td>65.2</td><td>65.3</td></tr><tr><td>DHRNet + OpenMax [52]</td><td>65.6</td><td>65.5</td></tr><tr><td>CROSR [52]</td><td>72.0</td><td>72.1</td></tr><tr><td>GFROSR [41]</td><td>75.1</td><td>75.7</td></tr><tr><td>Ours</td><td>80.5</td><td>76.8</td></tr></table>
+
+Table 2: Comparison on open-set detection by adding different unknown samples to the test set. The performance is evaluated by Macro-F1, which considers  $K + 1$  classes.
+
+The curves of three datasets are drawn in Fig. 5. We incrementally select more predictions for each class, i.e., the samples are deserved to make an extra prediction if its confusion on this considered class is more significant than in other samples. By doing this, we could control the average predictions while being threshold-independent in evaluating flexible visual recognition. A desired precision-average prediction curve would have a near 1 value for the start of making predictions. For the recall-average prediction curve, the closer it adheres to the left-top corner, the earlier it delivers the correct class. When comparing the precision curve, our method could achieve a significantly higher value than other methods when making limited predictions. For example, on the CIFAR-10 dataset, the proposed method reaches the precision of 0.62 for making an average of only one prediction for each sample, while the second highest is 0.33. Note some samples could have no prediction at the beginning as all of their confusion terms are lower than other samples. Besides, we also notice that ASL [7] is better than other baselines in the recall curve. This indicates that for flexible recognition, a multi-label classifier could be a better choice as it prevents the overconfident problem in the softmax probabilities to some extent.
+
+# 5.4. Ignorance for Open-set Detection
+
+As a crucial part of flexible recognition, we additionally demonstrate the effectiveness of our method on the task of open-set detection in Tab. 2 following standard protocols [52, 18, 29]. The same network architecture, i.e., a 13-layer VGG model, is used to implement the proposed method as in [52].
+
+During the test time of open-set detection, the test images from CIFAR-10 datasets are viewed as closed-set examples. For open-set samples, we consider two natural image datasets, i.e., LSUN (crop) and ImageNet (crop), introduced by Liang et al [29]. The Macro-F1 is therefore evaluated on  $K + 1$  classes by regarding all open samples as an additional class. And the threshold for being detected as open-set is chosen when  $95\%$  of closed-set images can be correctly classified. Among the compared methods, OS-RCI [38] augments the training set with hard and counterfactual generated images to improve unknown sample de
+
+![](images/1bf23e8f3e46ed1915b1dc754ff4d652cedd0b45b3d604a2a59ee28607053b44.jpg)  
+Figure 6: Top 1 and 2 accuracies with adversarial perturbations  $\epsilon$  on CIFAR-10 [26] dataset.
+
+![](images/933c17f3d0598d8351a1cd8dc3376d62edd3da709b42a8cab6c24ea9f7a64c0d.jpg)
+
+tection during testing. CROSR [52] and GFROSR [41] incorporate reconstruction loss into the procedure of closed-set training to better model the data distribution. For the proposed method, we use ignorance  $\mathcal{I}$  as the indicator of unknown samples and achieve better performance without additional adversarial training data. The F1 score of the proposed method is higher than other methods on both datasets, which supports the claim that ignorance in the proposed method could effectively handle the lack of evidence in open-set samples. It is worth noting that, besides explicitly delivering ignorance to detect unknown samples, the advantage of the proposed method also lies in the estimate of confusion, which is evaluated in closed-set experiments.
+
+# 5.5. Performance on Adversarial Samples
+
+We compare the robustness of different classification methods [15, 44] against adversarial attacks. Besides models introduced in the previous experiment, we include the recent multi-label classification method ASL [7] as another baseline. The reason is that multi-label classification methods usually adopt the same sigmoid activation and multiple binary linear layers as our method. For our method, we use the plausibility  $p l_{i}$  for class  $i$  to predict instead of their singleton beliefs, i.e., the confusion for each class that occurred during adding perturbations is involved in the ranking. The reason is that we want to test whether the confusion correctly characterizes the conflicting evidence shared between the correct and other classes.
+
+Adversarial samples are generated on CIFAR-10 [26] using the Fast Gradient Sign method [17] with various perturbation parameters  $\epsilon$ . The adversarial attack method uses the gradient during inference to generate samples that are more challenging to make correct predictions as  $\epsilon$  increases. Both the top 1 and top 2 results are shown in Fig. 6. The figure indicates that the proposed method could almost achieve both the highest top 1 and top 2 results. That is, the confusion that happened during perturbating is captured by our method, which could still contribute to the corresponding correct class. The proposed method is only slightly worse than the Dropout method when  $\epsilon = 0.25$ , which is forgivable as its training includes stochastic zeroing on the model parameter to increase its robustness.
+
+![](images/3077f68af12cb90109fc5cc6ffefcca1501efb5af3b24a141436d277f146bedf.jpg)  
+(a)
+
+![](images/ccccdcd49ffb9b7612022eaf0e6b97801ad6dd5196b46c2778cbaa5b7d7597fc.jpg)  
+Figure 7: Matrices of confusion of misclassified samples on the CIFAR-10 dataset. The diagonal of each matrix is set to the singleton belief of each class. Notice that the background color for each heatmap is normalized individually. The total ignorance is demonstrated in the caption.
+
+![](images/cd8dd643d99fdec3bea296cf3515927e9d89fc61553264cccc2771cf419e4831.jpg)  
+(b)
+
+![](images/9e5fb52998cfe520d70e1acfe4438e006e519a1fdf9798cd9d6686e8709aac22.jpg)
+
+![](images/3b72102ca3360af71e5a061cdd4255d576fbe8ac40b6d90618b5637d743efeed.jpg)  
+(c)
+
+![](images/57db3fc54994ed35078c61fa44dc3d99f8c661d67b71d4ad3bff298e4f8bbffa.jpg)
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">CIFAR-10 + LSUN (crop)</td></tr><tr><td>Acc.</td><td>F1</td><td>AUROC</td><td>AUPR closed</td><td>AUPR open</td></tr><tr><td>Ours w/o Reg.</td><td>72.4</td><td>84.8</td><td>96.2</td><td>96.9</td><td>95.3</td></tr><tr><td>Ours w/ Reg.</td><td>79.9</td><td>86.9</td><td>97.0</td><td>97.5</td><td>96.6</td></tr><tr><td></td><td colspan="5">CIFAR-10 + ImageNet (crop)</td></tr><tr><td>Ours w/o Reg.</td><td>63.9</td><td>82.0</td><td>95.1</td><td>96.1</td><td>93.8</td></tr><tr><td>Ours w/ Reg.</td><td>71.7</td><td>83.9</td><td>95.8</td><td>96.5</td><td>94.7</td></tr></table>
+
+Table 3: Ablation studies about the regularization term  $\mathcal{L}_{\mathrm{reg}}$  on the task of open-set detection with two hybrid datasets.
+
+# 5.6. Qualitative Results
+
+Furthermore, to provide a more intuitive impression of our results, we demonstrate the matrices of binary confusion estimates in Fig. 7. We take the misclassified images of the proposed method for the CIFAR-10 dataset. The ground truth label, the prediction, the singleton belief, the ignorance, and the highest binary confusion are noted in their captions. Each grid in the confusion matrix denotes the confusion between any two classes, while the diagonal represents the singleton belief.
+
+In Fig. 7b, the proposed method wrongly recognizes the image into dog class while maintaining a very high confusion towards the correct class horse. However, as the singleton belief is not significant for the predicted class, the proposed method could predict a combined result, i.e., both dog and horse, if setting a relatively high threshold on the sum of beliefs. Another example in Fig. 7c implies the ability of our method to reject making a prediction. As the image in Fig. 7c is contentless and low-resolution, the proposed failed to collect enough supportive evidence for any known classes, which delivers a very high ignorance value.
+
+# 5.7. Ablation Studies
+
+We investigate how the regularization term  $\mathcal{L}_{\mathrm{reg}}$  influences performance. The reason we add the regularization is to avoid the first output of each plausibility function converging to the belief instead of the plausibility. To show its effectiveness, we evaluate the proposed method on the task of open-set detection in Tab. 3. The separation could
+
+be deemed to be more sufficient if the ignorance term performs better in detecting open-set samples. Note we use the ResNet-18 as our backbone here to remain consistent with our flexible recognition experiments. For the metric of open-set detection accuracy and AUROC, closed-set samples are regarded as negative samples, while open-set samples constitute positive samples. The other two metrics, AUPR closed and AUPR open, denote the Area Under the Precision-Recall curve where closed-set or open-set images are specified as positives, respectively. The overall improvements in adding the regularization term  $\mathcal{L}_{\mathrm{reg}}$ , as demonstrated in Tab. 3, indicate its effectiveness in promoting the separation.
+
+# 5.8. Discussions and Future works
+
+In our experiments, we find the scale of confusion and ignorance varies with different backbones and datasets. The correlation behind it could be related to the capabilities of different models and the learning difficulties of different datasets. We leave the investigation for our future work.
+
+# 6. Conclusions
+
+In this paper, we introduce a novel approach to explicitly model two distinct sources of uncertainties, i.e., confusion and ignorance, under the novel task of flexible recognition. The recognition system is expected to reject samples from unknown classes and also make multiple predictions when it is uncertain about a closed-set image. Particularly, in the proposed method, the confusion is modeled as the conflicting evidence, while the ignorance represents the total lack of evidence. The hypothesis space of recognition is then divided and modeled by multiple plausibility functions. The model learns the concentration parameter of Dirichlet prior, which is being placed on the belief for singletons. A complete set of opinions could be generated through evidence combinations. Experiments on different datasets, along with challenging tasks of adversarial disturbance, flexible recognition, and open-set detection, confirm the effectiveness of the proposed method.
+
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+                                    "content": "and informative visual recognition system could also give combined predictions when possible, implying the correct answer is one of its predictions but uncertain. Naturally, the capability of rejecting or providing unspecific predictions demands separately measuring different sources of uncertainties, i.e., ignorance and confusion, if seen from the Subjective Logic [21] perspective. Furthermore, to enable flexible recognition, both uncertainties should possess the virtue of comparability between samples and in-sample additivity."
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+                                    "content": "The contribution of this paper could be summarized as follow: (1) The proposed method could explicitly predict two sources of uncertainties, i.e., confusion and ignorance, simultaneously for each sample. (2) The solution to confusion and ignorance is based on standard architectures, and the training does not rely on external information. (3) The effectiveness of the proposed method is extensively validated across different experiments, including studies on synthetic data, visual recognitions, and open-set detections."
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+                                    "content": "2. Related Work"
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+                                    "content": "Uncertainty estimation. Typical neural networks can not detect their own failure. However, this ability can be important in several real-world applications, like rejecting unseen samples, and providing prediction confidence, to name a few. Bayesian NN [15, 27, 47, 14, 25] predicts epistemic uncertainty as the mutual information between model parameters and samples. By assuming a probabilistic prior on the network, it approximates prediction variance by sampling weight during inference. Several works [20, 49, 23] choose to model epistemic and aleatoric uncertainties separately. The Subjective Logic on which our method is established falls within the realm of epistemology instead of a frequentist (aleatoric) view. In other words, we focus on further separating epistemic uncertainty into confusion and ignorance."
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+                                    "content": "Evidential deep learning [44, 1, 5, 11], in contrast, pro"
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+                                    "content": "poses to learn the prior of the predictions directly. The prior, known as evidential prior, is interpreted as beliefs in Dempster-Shafer Theory [6]. In [11], they model the first- and second-order uncertainties by introducing an auxiliary uncertainty network to approximate the difference between Dirichlet distributions."
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+                                    "content": "While uncertainty is provided to describe the variance of model prediction, it is not clear if uncertainty comes from different sources when dealing with in-distribution or out-of-distribution data. Orthogonal to previous approaches, we separate the uncertainty into confusion and ignorance in this work. Confusion depicts the uncertainty between different known classes, while ignorance decides whether the sample is unknown. With this separation, we can make dynamic predictions on known classes and reject unknown classes at the same time."
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+                                    "content": "Open Set Recognition. Machine learning models are usually designed with the closed-set assumption, where testing data shares the same distribution as the training. Open-set recognition (OSR) [8] introduces semantic shifts to the problem. Samples are from the classes that are not in the training set. Out-of-distribution (OOD) [19] detection introduces domain shifts to the testing set. In both of the settings, models should have the ability to reject unknown samples."
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+                                    "content": "In general, OSR and OOD methods reject unknown samples depending on reweighting outputs [8, 16, 24, 19, 30, 50], getting better feature embedding metrics [31, 10, 42, 38], and exploring reconstruction errors [39, 46, 45, 52, 41]. These metrics are all related to the quality of classifier prediction. However, the recognition can fail on closed-set samples because of the existence of confusion. In this work, we show that when the confusion between known classes is adequately modeled, unknown samples can be identified more accurately."
+                                }
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+                                    "content": "Conformal Prediction. Parallel to our task, conformal prediction is a paradigm that could provide single or multiple predictions by empirically constructing confidence regions [2, 3, 48]. However, conformal prediction is confined to closed scenarios without open samples, as the empirical quantile is established on a labeled validation set sampled from the same testing distribution."
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+                                    "content": "3. Flexible Recognition"
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+                                    "content": "Flexible recognition aims to provide a classification model "
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+                                    "type": "text",
+                                    "content": " that could deliver adaptive predictive sets. Specifically, the model rejects samples, i.e., making no prediction, when the input is entirely out of the training distribution, like an open-set sample. The model also should cautiously give a set of predictions with the true class contained in it when being unsure."
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+                                    "type": "text",
+                                    "content": " denotes the input image, and the predictive set"
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+                                    "type": "text",
+                                    "content": "In this paper, we propose to tackle flexible recognition by separately estimating the confusion and ignorance for each sample. Intuitively, confusion denotes conflicting evidence between known classes, which should be additive to single-class beliefs for making reasonable multiple predictions. Ignorance denotes a lack of evidence to support rejecting samples. Most of this section falls into the proposed evidential modeling, which formulates confusion and ignorance in visual recognition under the theory of Subject Logic [21]. The approach to combining evidence and developing opinions follows. The approach to achieve flexible recognition is presented in the final."
+                                }
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+                                    "content": "Existing learning-based visual recognition models often rely on a softmax layer to give class probabilities. As a point estimation of predictive distribution, the classifier trained with the cross-entropy loss tends to deliver inflating probabilities to a single class and could not provide a reliable estimation of uncertainties [19]."
+                                }
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " would be the frame of discernment containing exclusive propositions, e.g., class labels. Extensively, the general propositions under this frame would be the set of all subsets of "
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+                                    "type": "text",
+                                    "content": " contains a total of "
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+                                    "type": "inline_equation",
+                                    "content": "2^{K}"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " elements."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Supposing "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "b_A \\in [0,1]"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as a measure of belief mass contained in proposition "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", the total mass of general propositions satisfies "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sum_{A \\in 2^{\\Theta}} b_A = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": ". The belief for any proposition is then defined as the summation of contained mass, which is formulated as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_A = \\sum_{B \\subset A} b_B"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "And it is worth noting that "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "B \\subseteq A"
+                                },
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+                                    "type": "text",
+                                    "content": " suggests the logical statement that "
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+                                    "type": "text",
+                                    "content": " implies "
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The total belief in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the sum of belief in all propositions that imply "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " plus the belief in "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " itself. For a more intuitive understanding, considering a binary visual classification task, the belief for predicting both classes is the combination of mass shared between classes and also class-exclusive masses."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We could further define the plausibility of "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " as "
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+                                    "type": "inline_equation",
+                                    "content": "p l_{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which is the total mass of propositions that has a non-empty"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "type": "image",
+                    "bbox": [
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+                    "blocks": [
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+                            "lines": [
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+                                            "type": "image",
+                                            "image_path": "8c3d2e39cf2a97fa2cc337d73d8ef3a65f2b3d857831c3994edda06090b6e1ec.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                305,
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+                                                135
+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 2: The relation between different masses constituting the final set of opinions towards a hypothesis."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        305,
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+                        204
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        155,
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+                                        204
+                                    ],
+                                    "type": "text",
+                                    "content": "union with the current one. Also, the plausibility of a hypothesis could only be larger or equal to its own belief, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        155,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p l_{A} \\geq b_{A}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        155,
+                                        545,
+                                        204
+                                    ],
+                                    "type": "text",
+                                    "content": ". We demonstrate the basic probability assignments and their relations in Fig. 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.2. Uncertainty, Confusion, and Ignorance"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Recent evidential deep learning methods [44] develop uncertainties under multinomial opinions, which model belief for singletons as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{b_i, i = 1, \\dots, K\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        231,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and regard the leftover as the total uncertainty "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We, therefore, have "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        290
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U} + \\sum_{i=1}^{K} b_i = 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "However, in our modeling, we argue the uncertainty "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " for each sample "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " comes from two distinct sources, i.e., confusion "
+                                },
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and ignorance "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which is written as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {U} ^ {\\mathbf {x}} = \\mathcal {C} ^ {\\mathbf {x}} + \\mathcal {I} ^ {\\mathbf {x}}. \\tag {2}",
+                                    "image_path": "a4a1b5733a6721c96004ba29c746bba13c210480f65533bfe585521c9ab5e116.jpg"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Intuitively, a large confusion "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}^{\\times}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the model is hard to distinguish "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " from known classes. For example, the model could have high confusion with a huskie image when the model has known classes of dog and wolf. An image from previously unknown classes, on the other hand, could have high ignorance. The superscript "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " will be omitted in the following for clarity."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
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+                    "lines": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "To introduce the separate measurements of confusion and ignorance, our method is formalized with hyper opinions, composing masses of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2^{K}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " subsets for a "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-class frame of discernment. Therefore, the overall confusion "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the total mass of the non-singleton subsets as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C} = \\sum_{A,A\\in 2^{\\ominus},2\\leq |A|\\leq K}b_A"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". In other words, the confusion "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the sum of masses shared between two or more classes. Altogether, following Eq. 2, we have "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " mass values satisfy"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {C} + \\mathcal {I} + \\sum_ {i = 1} ^ {K} b _ {i} = \\sum_ {A, A \\in 2 ^ {\\Theta}, 2 \\leq | A | \\leq K} b _ {A} + \\mathcal {I} + \\sum_ {i = 1} ^ {K} b _ {i} = 1, \\tag {3}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I} \\geq 0"
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "b \\geq 0"
+                                },
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+                                    "type": "text",
+                                    "content": " for all singletons and non-singleton subsets. The ignorance "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}"
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+                                    "type": "text",
+                                    "content": ", therefore, could be regarded as the mass placed on the empty set "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\emptyset"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in the frame, which indicates the level of lacking evidence. Confusion, defined on subsets with cardinalities larger than 1, reflects evidence that fails to discriminate between specific singletons."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
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+                                    "type": "text",
+                                    "content": "To further facilitate our evidence combination process, we group non-singleton confusion terms based on whether they hold evidence for a particular class "
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+                                            "type": "text",
+                                            "content": "Figure 3: Two graphical demonstrations of evidence combination on 2- and 3-class classification task. We only show ignorance in the 3-class example to avoid overlappings."
+                                        }
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+                                    "type": "text",
+                                    "content": "Class "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        246,
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+                                        293
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-related confusion mass "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        246,
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+                                        293
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        246,
+                                        287,
+                                        293
+                                    ],
+                                    "type": "text",
+                                    "content": ". It is defined as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        293
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_i = \\sum_{A,A\\in 2^\\Theta, |A| \\geq 2, i \\cap A = i} b_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        293
+                                    ],
+                                    "type": "text",
+                                    "content": ". To be more specific, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        287,
+                                        293
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        246,
+                                        287,
+                                        293
+                                    ],
+                                    "type": "text",
+                                    "content": " is the total mass placed on the set of all confusion terms that are supersets of singleton "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                    "index": 3
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+                {
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+                                    "type": "text",
+                                    "content": "Class "
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+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-unrelated confusion mass "
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{\\neg i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
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+                                        329
+                                    ],
+                                    "type": "text",
+                                    "content": ". Conversely, we have "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}_{\\neg i} = \\sum_{A,A\\in 2^{\\Theta},|A|\\geq 2,i\\cap A\\neq i}b_A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Accordingly, for any class "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we have"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {C} = \\mathcal {C} _ {i} + \\mathcal {C} _ {- i}. \\tag {4}",
+                                    "image_path": "a9525f66db75d24853e185beec983e7deaf1f3e309c4e4f1ea7e69619714e543.jpg"
+                                }
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+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "And, as shown in Fig. 2, the plausibility of the current sample belonging to class "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is "
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p l_{i} = b_{i} + \\mathcal{C}_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        351,
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+                                        399
+                                    ],
+                                    "type": "text",
+                                    "content": ", which stands for a combination of class-exclusive singleton belief mass and class-shared confusion masses."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.3. Evidence Combinations"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "The objective of the proposed approach is to predict ignorance and confusion explicitly for each sample. However, unlike ignorance which is a single term, the number of confusion reaches the exponential of classes, which means our model is required to give a comprehensive quantification of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2^{K}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " estimates. While intimidating, we propose to handle this by decomposing the problem into "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        427,
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+                                    ],
+                                    "type": "text",
+                                    "content": " plausibility functions "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        427,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{i}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "i = 1,\\dots ,K"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " on the same frame. Each plausibility function "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{i}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is designed to give two predictions only considering class "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", which is written as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        427,
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+                                        547
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{i}(\\mathbf{x}) = (pl_{i},1 - pl_{i})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Supposing we have obtained the plausibilities for all classes, any propositions, including the singleton class belief, confusion, and ignorance could then be derived by the rule of evidence combinations. In general, for "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " plausibility functions, the belief assignment of any proposition "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        548,
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+                                        619
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is combined by computing as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "b _ {A} = \\sum_ {B, \\cap B = A} \\prod_ {1 \\leq j \\leq K} b _ {B, j} (\\mathbf {x}) = \\sum_ {B, \\cap B = A} \\prod_ {1 \\leq j \\leq K} f _ {j} ^ {B} (\\mathbf {x}). \\tag {5}",
+                                    "image_path": "abae476f5e36dcc721e843a7b97226bf00741cb49e07399af3c63cbce368e5c3.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Note we do not have the normalization term in our formulation because we do not exclude the empty set from our frame. We demonstrate the combination process with 2- and 3-class classification examples in Fig. 3. To clarify fur"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "ther, the singleton belief for class "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "i"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is computed as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "b _ {i} = p l _ {i} \\prod_ {1 \\leq j \\leq K, j \\neq i} (1 - p l _ {j}) = f _ {i} ^ {1} (\\mathbf {x}) \\prod_ {1 \\leq j \\leq K, j \\neq i} f _ {j} ^ {2} (\\mathbf {x}). \\tag {6}",
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+                    "angle": 0,
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+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": "And we have the total uncertainty "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U} = 1 - \\sum_{i=1}^{K} b_i"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        130,
+                                        545,
+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": ". As the ignorance "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        130,
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+                                        156
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        130,
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+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": " could be calculated similarly as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {I} = \\prod_ {1 \\leq j \\leq K} (1 - p l _ {j}) = \\prod_ {1 \\leq j \\leq K} f _ {j} ^ {2} (\\mathbf {x}), \\tag {7}",
+                                    "image_path": "ed72791174476f65fb2df67e66487bb9331fcc0b173333191652be953e098d57.jpg"
+                                }
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+                    "index": 15
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+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "the total confusion between all different class combinations is "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C} = \\mathcal{U} - \\mathcal{I}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        201,
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+                                        237
+                                    ],
+                                    "type": "text",
+                                    "content": ". The confusion term between specific classes could be further calculated with Eq. 5."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                        321
+                                    ],
+                                    "type": "text",
+                                    "content": "Intuitively, the belief for each combination could be regarded as the occupation in a unit "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-dim volume. The modeling of confusion becomes feasible by spanning a "
+                                },
+                                {
+                                    "bbox": [
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+                                        321
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-dim hypothesis space with "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " plausibility functions. Moreover, the computation complexity of each combination is "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(n)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and for specific conditions, we could only calculate necessary confusion terms."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.4. Developing Opinions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In this section, we describe how to develop opinions from training data. Each plausibility function "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        445
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{i}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        445
+                                    ],
+                                    "type": "text",
+                                    "content": " can be constructed as a normalized dual-output linear layer or a single multi-output layer after being activated by a sigmoid function "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        350,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma (\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". In this work, the second is implemented to reduce the network parameters. In particular, the output is regarded as the value of class plausibility. The plausibility function is then formulated as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\left(p l _ {i}, 1 - p l _ {i}\\right) = f _ {i} (\\mathbf {x}) = \\sigma \\left(w _ {i} ^ {\\top} \\Phi (\\mathbf {x})\\right) \\tag {8}",
+                                    "image_path": "894068c1083188ead57369561a05a8af766e08a218731927ef267daa0b07dc94.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\Phi :\\mathcal{X}\\to \\mathbb{R}^D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a feature embedding function."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Typically, only one deterministic label is given for each image in a standard visual recognition dataset. Following EDL [44], the learning of singleton belief is implemented as evidence acquisition on a Dirichlet prior. The loss of EDL is"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {E D L}} = \\sum_ {i = 1} ^ {K} y _ {i} \\left[ \\log \\left(\\sum_ {j = 1} ^ {K} \\alpha_ {j}\\right) - \\log \\left(\\alpha_ {i}\\right) \\right], \\tag {9}",
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+                                }
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+                                    "type": "text",
+                                    "content": "where "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y} = [y_1, y_2, \\ldots, y_i, \\ldots, y_K]^T"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is one-hot class label for a sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\boldsymbol{\\alpha} = [\\alpha_1, \\alpha_2, \\ldots, \\alpha_K]^T"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are parameters of a Dirichlet distribution "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Dir(\\cdot|\\boldsymbol{\\alpha})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Different from EDL, class evidence is replaced with belief. Hence, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is directly calculated from singleton beliefs and overall uncertainty. It is derived as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\alpha_ {i} = \\frac {K b _ {i}}{\\mathcal {U}} + 1 = \\frac {K b _ {i}}{1 - \\sum_ {j = 1} ^ {K} b _ {j}} + 1, \\tag {10}",
+                                    "image_path": "becb19e4ace223b49acbae22fbbfecf8253dea1eec560334af396b407cf7de04.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "1341"
+                                }
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+                                    "type": "inline_equation",
+                                    "content": "b_{i}"
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+                                    "type": "text",
+                                    "content": " could be obtained from Eq. 6. During inference, all opinions could be directly predicted by performing combinations on the output of plausibility functions."
+                                }
+                            ]
+                        }
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+                },
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+                                    "content": "To encourage the plausibility function to match our expected behavior, i.e., predicting the plausibility instead of the belief of singleton, we add a regularization term as"
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+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {r e g}} = \\sum_ {i = 1} ^ {K} y _ {i} \\left[ p l _ {i} - (1 - \\hat {\\mathcal {I}}) \\right] ^ {2}, \\tag {11}",
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{I}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the current estimation of ignorance."
+                                }
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+                                    "type": "text",
+                                    "content": "Following EDL, a Kullback-Leibler loss is used to minimize evidence on unrelated classes as"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {K L}} = K L (D i r (\\cdot | \\tilde {\\alpha}) | | D i r (\\cdot | \\langle 1, \\dots , 1 \\rangle)), \\tag {12}",
+                                    "image_path": "ae2ecfb104e4b8a9886aeaf37ed8dd6f07b28735d81df53dd4c9274e6377ada8.jpg"
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\alpha} = \\mathbf{y} + (1 - \\mathbf{y})\\odot \\boldsymbol {\\alpha},"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " 0 for element-wise multiplication. Combining all terms together yields the final loss as"
+                                }
+                            ]
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+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {E D L}} + \\lambda_ {\\mathrm {r e g}} \\mathcal {L} _ {\\mathrm {r e g}} + \\lambda_ {\\mathrm {K L}} \\mathcal {L} _ {\\mathrm {K L}}. \\tag {13}",
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+                                    "content": "Each loss term is accompanied by a balance weight, and we gradually increase the effect of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{kl}"
+                                },
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+                                    "type": "text",
+                                    "content": " through an additional annealing coefficient."
+                                }
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+                                    "content": "After developing opinions with the proposed method, a straightforward solution would be setting the belief threshold for outputs to achieve flexible recognition. The sample will be rejected if the ignorance is too large that no combination would exceed the threshold. And the model gives incrementally combined predictions if no singleton belief meets the bar."
+                                }
+                            ]
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+                                    "content": "5. Experiments"
+                                }
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+                                    "content": "The proposed method could model two sources of uncertainty for each sample to handle the task of flexible recognition. To enable better comparison with existing methods, our experiments are primarily decomposed into three components. (1) Demonstrating the separation of two sources of uncertainty, i.e., confusion and ignorance. (2) Indicating the correct class on misclassified samples with estimated confusion. (3) Applying ignorance to compare with other methods on the task open-set detection. More experiments, including on adversarial-attacked samples and ablation studies, follow to give a more comprehensive evaluation."
+                                }
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+                                    "type": "text",
+                                    "content": "Implementation details. We adopt the ResNet-18 as the backbone for our experiments except on synthetic data and open-set detection. The dimension of extracted feature is set to 512. For the proposed method, we apply the sigmoid activation on the last linear layer to work as our multiple plausibility functions. We empirically find both EDL [44] and our method are more sensitive to the learning rate. Specifically, we set the learning rate for both methods to 0.004 with a momentum of 0.9 for the batch size of 128. "
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+                                    "type": "text",
+                                    "content": " in Eq. 13 anneals to 0 with epochs with the maximum coefficient of 0.05, and "
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+                                    "content": "\\lambda_{\\mathrm{reg}}"
+                                },
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+                                    "type": "text",
+                                    "content": " is set to 1."
+                                }
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+                                            "content": "(f) Standard Entropy"
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+                                            "content": "Figure 4: A 3-class classification problem. The Gaussian-distributed training data are depicted with dots, while the background color indicates the estimated value of the corresponding location. Our results are plotted from (a) to (e). The entropy over predictions of a standard net trained with cross-entropy loss is shown in (f) for comparison."
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+                                    "content": "In this section, we examine the behavior of our approach in Fig. 4 in the 2-dimensional space. A dataset with three isotropic Gaussian distributed classes is created for training. The distances between each Gaussian are equal to 9, and we set "
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+                                    "content": " for all Gaussian. Each class has 500 training samples which are denoted by colored dots. We discretize the background into 2D locations for testing. The background color denotes corresponding estimated values."
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+                                    "content": "Both our method and the standard entropy are trained with the same multi-layer perceptron. As we can observe in Fig. 4 (a) to (e), the proposed method acts as a density estimator. Confusion happens between class boundaries, while ignorance is high for out-of-distribution data points. The proposed method does not require intricate adoptions to network architectures to achieve the desired properties. In Fig. 4 (f), the entropy of a standard deterministic neural net with the cross-entropy loss is plotted, which shows that using entropy to distinguish out-of-distributions could face multiple downsides due to its sharp boundaries."
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+                                    "content": "5.2. Confusion on Misclassified Samples"
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+                                    "content": "In this part, the confusion is tested on misclassified samples, checking whether it is correlated with the ground-truth label. That is, the confusion should be high between the misclassified class and the ground-truth class. Besides in-sample comparison on the level of confusion, we argue the between-sample comparability of confusion is also critical for flexible visual recognition. For example, a flexible recognition system would tend to give a second prediction if its confusion is higher than in other samples. To address this concern, we employ the Area Under the Receiver Oper-"
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+                                            "html": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"2\">CIFAR-10</td><td colspan=\"2\">CIFAR-100</td><td colspan=\"2\">Imagenet</td></tr><tr><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td><td>Acc.</td><td>AUROC</td></tr><tr><td>Softmax</td><td>95.2</td><td>63.4</td><td>76.0</td><td>57.3</td><td>54.3</td><td>58.2</td></tr><tr><td>EDL [44]</td><td>94.8</td><td>60.4</td><td>74.5</td><td>54.9</td><td>54.2</td><td>58.3</td></tr><tr><td>Dropout [15]</td><td>94.7</td><td>64.5</td><td>74.5</td><td>58.9</td><td>47.3</td><td>61.8</td></tr><tr><td>OvR</td><td>95.1</td><td>63.2</td><td>72.2</td><td>63.4</td><td>46.3</td><td>60.2</td></tr><tr><td>ASL [7]</td><td>95.2</td><td>70.9</td><td>75.8</td><td>79.9</td><td>54.1</td><td>62.8</td></tr><tr><td>Ours</td><td>95.0</td><td>89.5</td><td>74.9</td><td>90.0</td><td>54.6</td><td>97.6</td></tr></table>",
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+                                    "content": "Table 1: Comparison on whether the confusion indicates the correct class on misclassified samples. Results of classification accuracy and AUROC on misclassified samples are shown on three datasets with different class scales."
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+                                    "type": "text",
+                                    "content": "ating Characteristic curve (AUROC) as our evaluation metric, which sorts the predicted value along samples in each class. More specifically, the ROC curve is a graph showing the true positive rate against the false positive rate. A random classifier would correspond to a "
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+                                    "content": " AUROC. Moreover, the metric sidesteps the issue of threshold selection."
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+                                    "content": "To be more clear, the confusion terms between all classes and the predicted class are regarded as the input to the metrics, while the target is one-hot class labels. As the groundtruth class could be imbalanced among misclassified samples, the AUROC is weighted by the categorical base rate."
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+                                    "content": "The results on CIFAR-10, CIFAR-100 [26], and ImageNet [12] with 10, 100, and 1000 classes, respectively, are shown in Tab. 1 to demonstrate the comparison with different class scales. TheImagenet used here is an official downsampled version with the resolution of "
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+                                    "content": ". Besides standard Softmax, the Dropout [15] refers to the method using Monte Carlo Dropout (with the dropout rate of 0.2 and 10 dropout iterations) to approximate the distribution of model parameters. Since these methods do not contain explicit outputs of confusion, they are compromised to an intuitive approach, which measures the difference between predicted class probabilities. Two multi-label classification methods, namely, the One-vs-Rest (OvR) and the ASL [7], are included as baselines whose outputs are not normalized between classes. For EDL [44], confusion is defined as the difference between estimated singleton beliefs. In stark contrast to these methods, the proposed method uses explicitly estimated confusion between any classes with the predicted class following the definition in Eq. 5."
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+                                            "content": "Figure 5: Precision and recall of delivering multiple predictions on misclassified samples with respect to the average number of predictions. The intention to predict extra classes is dependent on the confusion term between classes."
+                                        }
+                                    ]
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+                            ],
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+                                    "type": "text",
+                                    "content": "these methods, the proposed approach could model the confusion that occurred between classes and could help flexible recognition systems determine when and which class to be predicted next."
+                                }
+                            ]
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+                                    "content": "5.3. Flexible Closed-set Recognition"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We turn to the task of flexible visual recognition on the closed CIFAR-10, CIFAR-100, and Imagenet, where methods are supposed to make multiple predictions when they are unsure. And we regard the output as correct as long as the correct answer is included in the prediction set. However, simply increasing the number of predictions for each sample should be penalized. Thus, for a more meaningful comparison, we show precision and recall as the function of the average number of predictions. We only evaluate methods on their misclassified samples, where providing more predictions is urgently demanded. And the indicator for making another prediction is the confusion between the considered and the predicted class, the same as in Section 5.2. The confusion for the first-predicted class itself is intuitively described as 0."
+                                }
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Closed Dataset CIFAR-10</td><td>+ LSUN (crop)</td><td>+ ImageNet (crop)</td></tr><tr><td>Softmax</td><td>64.2</td><td>63.9</td></tr><tr><td>OpenMax [8]</td><td>65.7</td><td>66.0</td></tr><tr><td>OSRCI [38]</td><td>65.0</td><td>63.6</td></tr><tr><td>LadderNet + OpenMax [52]</td><td>65.2</td><td>65.3</td></tr><tr><td>DHRNet + OpenMax [52]</td><td>65.6</td><td>65.5</td></tr><tr><td>CROSR [52]</td><td>72.0</td><td>72.1</td></tr><tr><td>GFROSR [41]</td><td>75.1</td><td>75.7</td></tr><tr><td>Ours</td><td>80.5</td><td>76.8</td></tr></table>",
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+                                    "content": "Table 2: Comparison on open-set detection by adding different unknown samples to the test set. The performance is evaluated by Macro-F1, which considers "
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+                                    "content": "The curves of three datasets are drawn in Fig. 5. We incrementally select more predictions for each class, i.e., the samples are deserved to make an extra prediction if its confusion on this considered class is more significant than in other samples. By doing this, we could control the average predictions while being threshold-independent in evaluating flexible visual recognition. A desired precision-average prediction curve would have a near 1 value for the start of making predictions. For the recall-average prediction curve, the closer it adheres to the left-top corner, the earlier it delivers the correct class. When comparing the precision curve, our method could achieve a significantly higher value than other methods when making limited predictions. For example, on the CIFAR-10 dataset, the proposed method reaches the precision of 0.62 for making an average of only one prediction for each sample, while the second highest is 0.33. Note some samples could have no prediction at the beginning as all of their confusion terms are lower than other samples. Besides, we also notice that ASL [7] is better than other baselines in the recall curve. This indicates that for flexible recognition, a multi-label classifier could be a better choice as it prevents the overconfident problem in the softmax probabilities to some extent."
+                                }
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+                                    "type": "text",
+                                    "content": "5.4. Ignorance for Open-set Detection"
+                                }
+                            ]
+                        }
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+                                    "content": "As a crucial part of flexible recognition, we additionally demonstrate the effectiveness of our method on the task of open-set detection in Tab. 2 following standard protocols [52, 18, 29]. The same network architecture, i.e., a 13-layer VGG model, is used to implement the proposed method as in [52]."
+                                }
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+                                    "type": "text",
+                                    "content": "During the test time of open-set detection, the test images from CIFAR-10 datasets are viewed as closed-set examples. For open-set samples, we consider two natural image datasets, i.e., LSUN (crop) and ImageNet (crop), introduced by Liang et al [29]. The Macro-F1 is therefore evaluated on "
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+                                    "type": "text",
+                                    "content": " classes by regarding all open samples as an additional class. And the threshold for being detected as open-set is chosen when "
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+                                    "type": "text",
+                                    "content": " of closed-set images can be correctly classified. Among the compared methods, OS-RCI [38] augments the training set with hard and counterfactual generated images to improve unknown sample de"
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 6: Top 1 and 2 accuracies with adversarial perturbations "
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+                                            "content": " on CIFAR-10 [26] dataset."
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+                                    "type": "text",
+                                    "content": "tection during testing. CROSR [52] and GFROSR [41] incorporate reconstruction loss into the procedure of closed-set training to better model the data distribution. For the proposed method, we use ignorance "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}"
+                                },
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+                                    "type": "text",
+                                    "content": " as the indicator of unknown samples and achieve better performance without additional adversarial training data. The F1 score of the proposed method is higher than other methods on both datasets, which supports the claim that ignorance in the proposed method could effectively handle the lack of evidence in open-set samples. It is worth noting that, besides explicitly delivering ignorance to detect unknown samples, the advantage of the proposed method also lies in the estimate of confusion, which is evaluated in closed-set experiments."
+                                }
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+                                    "content": "5.5. Performance on Adversarial Samples"
+                                }
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+                                    "type": "text",
+                                    "content": "We compare the robustness of different classification methods [15, 44] against adversarial attacks. Besides models introduced in the previous experiment, we include the recent multi-label classification method ASL [7] as another baseline. The reason is that multi-label classification methods usually adopt the same sigmoid activation and multiple binary linear layers as our method. For our method, we use the plausibility "
+                                },
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+                                    "type": "text",
+                                    "content": " for class "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "i"
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+                                    "type": "text",
+                                    "content": " to predict instead of their singleton beliefs, i.e., the confusion for each class that occurred during adding perturbations is involved in the ranking. The reason is that we want to test whether the confusion correctly characterizes the conflicting evidence shared between the correct and other classes."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Adversarial samples are generated on CIFAR-10 [26] using the Fast Gradient Sign method [17] with various perturbation parameters "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". The adversarial attack method uses the gradient during inference to generate samples that are more challenging to make correct predictions as "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " increases. Both the top 1 and top 2 results are shown in Fig. 6. The figure indicates that the proposed method could almost achieve both the highest top 1 and top 2 results. That is, the confusion that happened during perturbating is captured by our method, which could still contribute to the corresponding correct class. The proposed method is only slightly worse than the Dropout method when "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\epsilon = 0.25"
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+                                    "type": "text",
+                                    "content": ", which is forgivable as its training includes stochastic zeroing on the model parameter to increase its robustness."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"5\">CIFAR-10 + LSUN (crop)</td></tr><tr><td>Acc.</td><td>F1</td><td>AUROC</td><td>AUPR closed</td><td>AUPR open</td></tr><tr><td>Ours w/o Reg.</td><td>72.4</td><td>84.8</td><td>96.2</td><td>96.9</td><td>95.3</td></tr><tr><td>Ours w/ Reg.</td><td>79.9</td><td>86.9</td><td>97.0</td><td>97.5</td><td>96.6</td></tr><tr><td></td><td colspan=\"5\">CIFAR-10 + ImageNet (crop)</td></tr><tr><td>Ours w/o Reg.</td><td>63.9</td><td>82.0</td><td>95.1</td><td>96.1</td><td>93.8</td></tr><tr><td>Ours w/ Reg.</td><td>71.7</td><td>83.9</td><td>95.8</td><td>96.5</td><td>94.7</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 3: Ablation studies about the regularization term "
+                                },
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+                                    "type": "text",
+                                    "content": " on the task of open-set detection with two hybrid datasets."
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+                                    "content": "5.6. Qualitative Results"
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+                                    "type": "text",
+                                    "content": "Furthermore, to provide a more intuitive impression of our results, we demonstrate the matrices of binary confusion estimates in Fig. 7. We take the misclassified images of the proposed method for the CIFAR-10 dataset. The ground truth label, the prediction, the singleton belief, the ignorance, and the highest binary confusion are noted in their captions. Each grid in the confusion matrix denotes the confusion between any two classes, while the diagonal represents the singleton belief."
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+                                    "type": "text",
+                                    "content": "In Fig. 7b, the proposed method wrongly recognizes the image into dog class while maintaining a very high confusion towards the correct class horse. However, as the singleton belief is not significant for the predicted class, the proposed method could predict a combined result, i.e., both dog and horse, if setting a relatively high threshold on the sum of beliefs. Another example in Fig. 7c implies the ability of our method to reject making a prediction. As the image in Fig. 7c is contentless and low-resolution, the proposed failed to collect enough supportive evidence for any known classes, which delivers a very high ignorance value."
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+                                    "content": "5.7. Ablation Studies"
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+                                    "content": "We investigate how the regularization term "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{reg}}"
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+                                    "type": "text",
+                                    "content": " influences performance. The reason we add the regularization is to avoid the first output of each plausibility function converging to the belief instead of the plausibility. To show its effectiveness, we evaluate the proposed method on the task of open-set detection in Tab. 3. The separation could"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                                    "type": "text",
+                                    "content": "be deemed to be more sufficient if the ignorance term performs better in detecting open-set samples. Note we use the ResNet-18 as our backbone here to remain consistent with our flexible recognition experiments. For the metric of open-set detection accuracy and AUROC, closed-set samples are regarded as negative samples, while open-set samples constitute positive samples. The other two metrics, AUPR closed and AUPR open, denote the Area Under the Precision-Recall curve where closed-set or open-set images are specified as positives, respectively. The overall improvements in adding the regularization term "
+                                },
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+                                    "type": "text",
+                                    "content": ", as demonstrated in Tab. 3, indicate its effectiveness in promoting the separation."
+                                }
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+                                    "content": "5.8. Discussions and Future works"
+                                }
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+                                    "type": "text",
+                                    "content": "In our experiments, we find the scale of confusion and ignorance varies with different backbones and datasets. The correlation behind it could be related to the capabilities of different models and the learning difficulties of different datasets. We leave the investigation for our future work."
+                                }
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+                                    "content": "6. Conclusions"
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+                                    "type": "text",
+                                    "content": "In this paper, we introduce a novel approach to explicitly model two distinct sources of uncertainties, i.e., confusion and ignorance, under the novel task of flexible recognition. The recognition system is expected to reject samples from unknown classes and also make multiple predictions when it is uncertain about a closed-set image. Particularly, in the proposed method, the confusion is modeled as the conflicting evidence, while the ignorance represents the total lack of evidence. The hypothesis space of recognition is then divided and modeled by multiple plausibility functions. The model learns the concentration parameter of Dirichlet prior, which is being placed on the belief for singletons. A complete set of opinions could be generated through evidence combinations. Experiments on different datasets, along with challenging tasks of adversarial disturbance, flexible recognition, and open-set detection, confirm the effectiveness of the proposed method."
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+                                        }
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+                                }
+                            ],
+                            "index": 23
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+                        {
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+                                            "type": "text",
+                                            "content": "[50] Haoqi Wang, Zhizhong Li, Litong Feng, and Wayne Zhang. Vim: Out-of-distribution with virtual-logit matching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4921-4930, 2022. 2"
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
+                                            "content": "[51] Florian Wenzel, Jasper Snoek, Dustin Tran, and Rodolphe Jenatton. Hyperparameter ensembles for robustness and uncertainty quantification. Advances in Neural Information Processing Systems, 33:6514-6527, 2020. 2"
+                                        }
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+                            ],
+                            "index": 25
+                        },
+                        {
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+                                            "type": "text",
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+                                        }
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+                                            "type": "text",
+                                            "content": "[53] Kuang Zhou, Arnaud Martin, and Quan Pan. Evidence combination for a large number of sources. In 2017 20th International Conference on Information Fusion (Fusion), pages 1-8. IEEE, 2017. 1"
+                                        }
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diff --git a/2023/FlipNeRF_ Flipped Reflection Rays for Few-shot Novel View Synthesis/b773a3a0-692f-4508-af4b-b8359e51e763_content_list.json b/2023/FlipNeRF_ Flipped Reflection Rays for Few-shot Novel View Synthesis/b773a3a0-692f-4508-af4b-b8359e51e763_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e8088c81805008d77f0d7ad5353c9b6aa410226
--- /dev/null
+++ b/2023/FlipNeRF_ Flipped Reflection Rays for Few-shot Novel View Synthesis/b773a3a0-692f-4508-af4b-b8359e51e763_content_list.json	
@@ -0,0 +1,1723 @@
+[
+    {
+        "type": "text",
+        "text": "FlipNeRF: Flipped Reflection Rays for Few-shot Novel View Synthesis",
+        "text_level": 1,
+        "bbox": [
+            130,
+            130,
+            839,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Seunghyeon Seo Yeonjin Chang Nojun Kwak Seoul National Univeristy",
+        "bbox": [
+            285,
+            180,
+            679,
+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{zzzzlssh, yjean8315, nojunk}@snu.ac.kr",
+        "bbox": [
+            316,
+            222,
+            653,
+            237
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            272,
+            313,
+            287
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural Radiance Field (NeRF) has been a mainstream in novel view synthesis with its remarkable quality of rendered images and simple architecture. Although NeRF has been developed in various directions improving continuously its performance, the necessity of a dense set of multi-view images still exists as a stumbling block to progress for practical application. In this work, we propose FlipNeRF, a novel regularization method for few-shot novel view synthesis by utilizing our proposed flipped reflection rays. The flipped reflection rays are explicitly derived from the input ray directions and estimated normal vectors, and play a role of effective additional training rays while enabling to estimate more accurate surface normals and learn the 3D geometry effectively. Since the surface normal and the scene depth are both derived from the estimated densities along a ray, the accurate surface normal leads to more exact depth estimation, which is a key factor for few-shot novel view synthesis. Furthermore, with our proposed Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss, FlipNeRF is able to estimate more reliable outputs with reducing floating artifacts effectively across the different scene structures, and enhance the feature-level consistency between the pair of the rays cast toward the photo-consistent pixels without any additional feature extractor, respectively. Our FlipNeRF achieves the SOTA performance on the multiple benchmarks across all the scenarios.",
+        "bbox": [
+            75,
+            303,
+            473,
+            696
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            724,
+            209,
+            739
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural Radiance Field (NeRF) [24] has achieved great success in rendering photo-realistic images from novel viewpoints. However, the necessity of a dense set of training images remains as a practical bottleneck since it suffers from significant performance degradation when trained with sparse views.",
+        "bbox": [
+            75,
+            750,
+            468,
+            839
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There are two main streams for few-shot novel view synthesis: pre-training and regularization methods, both of which focus on learning the 3D geometry efficiently from sparse inputs. The pre-training methods [43, 5, 6, 39, 20,",
+        "bbox": [
+            75,
+            839,
+            470,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/27bc8df263d7f84132970d2f10ae9723e8255e44b240716d2f0a1eea707cdb41.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            266,
+            890,
+            342
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/37fa4ba39e9bd6e9e4d350ca2dbf254da9266aeb58bb89a0e1509046e1cb22cc.jpg",
+        "image_caption": [
+            "(a) Sparse training views",
+            "(b) Synthesized unseen views",
+            "Figure 1: Synthesis results from sparse inputs. Our Flip-NeRF significantly improves rendering quality compared to other baselines. Compared to the vanilla mip-NeRF [1] and MixNeRF [31], which is the state-of-the-art regularization method, ours reduces the noises and floating artifacts noticeably with superior surface normal estimation. Although Ref-NeRF [36] estimates smooth normal vectors, it shows much inferior rendering results to ours with a large chunk of noise under the few-shot setting."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            366,
+            890,
+            618
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "12, 19, 29, 35, 14] require large-scale datasets consisting of different scenes with multi-view images for injecting prior knowledge during the pre-training, while the regularization methods [25, 31, 15, 11, 30, 8, 17] are optimized per scene, exploiting additional training resources, e.g. unseen viewpoints [25, 15, 17], depth map generation [8, 30], off-the",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "22883",
+        "bbox": [
+            478,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "shelf models [11, 25], and so on, for an effective regularization to alleviate overfitting. Although the prior arts achieved promising results in novel view synthesis from sparse inputs, there still exist hurdles to overcome. The large-scale datasets, which are used for pre-training methods, are expensive to collect and the NeRF model is prone to performance degradation for the out-of-distribution dataset. On the other hand, the regularization methods heavily rely on additional training resources which might not always be available and require many heuristic factors, e.g. the choice of off-the-shelf models, the hyperparameters for sampling unseen viewpoints, and so on.",
+        "bbox": [
+            75,
+            90,
+            472,
+            271
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose FlipNeRF, which is an effective regularization method exploiting the flipped reflection rays<sup>1</sup> as additional training resources with filtering the ineffective newly generated rays. We derive a batch of flipped reflection rays from the original ray directions and estimated surface normals so that they are cast toward the same target pixels of the original input ray. Compared to the existing regularization methods which have mainly focused on the accurate depth estimation from limited input views [31, 25, 15, 30, 8], our FlipNeRF is trained to reconstruct surface normals accurately by learning to generate effective reflection rays to be used in training. Since both estimated surface normals and depths are derived from the volume densities representing underlying 3D geometry, accurately estimating the surface normals of an object naturally leads to more accurate depth maps.",
+        "bbox": [
+            75,
+            273,
+            472,
+            513
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), to reduce the floating artifacts effectively while considering the uncertainty of the model's outputs by using the estimated scale parameters for mixture models. Since our FlipNeRF is built upon MixNeRF [31], which is a regularization method achieving promising results by modeling input rays with mixture density models [2], we are able to apply our proposed loss without any modification of the architecture by using the estimated scale parameters of each sample along a ray, which stand for the uncertainty of the samples' estimated probability density distributions.",
+        "bbox": [
+            75,
+            515,
+            472,
+            696
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Additionally, inspired by [6, 11, 15] which address the feature-level consistency of targets under the sparse input setting, we encourage the consistency for the pairs of bottleneck features between the original input rays and flipped reflection rays. We leverage a Jensen-Shannon Divergence, which is based on the similarity between the probability distributions, to make the pairs of bottleneck feature distributions of original and flipped reflection rays more similar to each other improving feature consistency.",
+        "bbox": [
+            75,
+            696,
+            472,
+            833
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We demonstrate the effectiveness of our proposed FlipNeRF through the experiments on the multiple bench",
+        "bbox": [
+            76,
+            833,
+            470,
+            863
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "marks, e.g. Realistic Synthetic  $360^{\\circ}$  [24], DTU [13], and LLFF [23]. Our method achieves state-of-the-art (SOTA) performances compared to other baselines. Especially, ours outperforms other baselines by a large margin with more accurate surface normals under the extremely sparse settings such as 3/4-view setting which are the most challenging ones. Our contributions are summarized as follows:",
+        "bbox": [
+            500,
+            90,
+            893,
+            196
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose an effective training framework for NeRF with sparse training views, called FlipNeRF. It leverages flipped reflection rays to provide additional training resources, resulting in more precise surface normals with our proposed masking strategy to filter the ineffective rays.",
+            "- We also propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), which reduces floating artifacts with considering the uncertainty of outputs, leading to more reliable estimation.",
+            "- We enhance the consistency of bottleneck features between the original input rays and flipped reflection rays by Jensen-Shannon Divergence, coined as Bottleneck Feature Consistency Loss (BFC Loss), improving the robustness for rendering from unseen viewpoints.",
+            "- Our FlipNeRF achieves SOTA performance over the multiple benchmarks. Especially, ours outperforms other baselines by a large margin in more challenging scenarios, e.g. 3/4-view."
+        ],
+        "bbox": [
+            500,
+            196,
+            893,
+            483
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            500,
+            500,
+            650,
+            515
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Neural Radiance Field",
+        "text_level": 1,
+        "bbox": [
+            500,
+            523,
+            710,
+            539
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, Neural Radiance Field (NeRF) [24] has shown impressive performance and potential in the novel view synthesis task. NeRF represents a scene with an MLP, mapping coordinates and viewing directions to its colors and volume density, and then creates a novel view through volume rendering. Subsequent studies have developed NeRF in several directions, e.g. using conical frustums instead of rays [1], reparameterizing an input viewing direction as its reflection direction [36], and so on. These works have made significant progress by addressing the various issues in novel view synthesis, but there still exists a limitation in that NeRF requires a dense set of training images and a lengthy training time. Many studies have addressed these issues [10, 28, 5], including the utilization of various data structures for faster training and inference [9, 42] and attempts to train NeRF with only a few training images. Our work focuses on enhancing the performance of NeRF when a sparse set of views are provided as training images.",
+        "bbox": [
+            496,
+            547,
+            893,
+            821
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Few-Shot Novel View Synthesis",
+        "text_level": 1,
+        "bbox": [
+            500,
+            830,
+            777,
+            847
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There are two main approaches for a few-shot novel view synthesis: the pre-training and the regularization method. The pre-training methods require a large dataset of multi-",
+        "bbox": [
+            500,
+            854,
+            893,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>The term 'flipped' is used because the reflected ray has an opposite direction (from an object to a camera).",
+        "bbox": [
+            76,
+            875,
+            470,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "22884",
+        "bbox": [
+            478,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/e2d805983ce1e59396e6692534e95c4baf4d19df835d969af2247cb5dfead645.jpg",
+        "image_caption": [
+            "Figure 2: Overall framework of FlipNeRF. Our FlipNeRF utilize the newly generated flipped reflection rays with our proposed UE Loss and BFC Loss as well as existing MSE, NLL and Orientation losses. See Sec. 3 and Fig. 3 for more details about generation process of flipped reflection rays and the loss terms."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            127,
+            88,
+            844,
+            210
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "view scenes to provide prior knowledges of 3D geometry to a NeRF model and then optionally finetune on the target scene [5, 6, 12, 19, 29, 35, 39, 43]. On the contrary, the regularization methods [31, 15, 11, 25, 8, 30, 17] are optimized per scene without pre-training process by exploiting additional training resources, e.g. depth maps [8, 30] and semantic consistency [11], as an extra supervision. Among them, [25, 15, 17] adopt an unseen viewpoint sampling strategy to make up for insufficient training views. However, these sampling processes require many hand-designed factors such as the ranges of rotation, translation, jittering, and so on, which can introduce artificial biases. Our work proposes a novel regularization approach to derive a set of flipped reflection rays from estimated surface normals and utilizes these for regularization, which does not require a heuristic factor to be finetuned, resulting in more effective training strategy with limited inputs.",
+        "bbox": [
+            75,
+            284,
+            472,
+            541
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Surface Normal Reconstruction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            558,
+            357,
+            571
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "There is a line of research to recover accurate textures and lighting conditions of objects with NeRF [26, 41, 38, 7, 34, 44, 3]. Although these earlier studies successfully reconstruct the high-quality isosurfaces derived from the scene representations, their rendering quality for novel views is still inferior to the NeRF-like models. Meanwhile, Ref-NeRF [36] achieved superior performance with remarkable quality of surface normals compared to the existing NeRF models. Since the normal vectors utilized in NeRF framework are derived from the negative normalized density gradients [34, 3, 36], which represent the underlying geometry of 3D scenes, learning an accurate density distribution along a ray is a key factor for surface normal reconstruction. However, for the few-shot novel view synthesis, the prior works mostly focus on the accurate depth estimation without attention to the surface normals, both of which are derived from the estimated volume densities. In this work, we approach the few-shot novel view synthesis problem with focusing on the surface normals, which is another critical factor for an effective learning of 3D scene geometry. To the best of our knowledge, our work is the first attempt to focus on the sur",
+        "bbox": [
+            75,
+            583,
+            472,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "face normal estimation for few-shot novel view synthesis.",
+        "bbox": [
+            498,
+            284,
+            880,
+            299
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            311,
+            591,
+            328
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose an effective regularization method for few-shot novel view synthesis with flipped reflection rays. Our FlipNeRF is built upon MixNeRF [31] which leverages a mixture model framework (Sec. 3.1). We derive a batch of flipped reflection rays and cast them toward the identical target pixels as additional training rays (Sec. 3.2). Furthermore, we propose the Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss to alleviate the floating artifacts adaptively based on the uncertainty and enhance the consistency between the bottleneck feature distributions of the original and flipped reflection rays, respectively (Sec. 3.3 and Sec. 3.4). Finally, our FlipNeRF is trained to minimize the MSE and NLL losses as well as the proposed regularization loss terms with their corresponding balancing weights (Sec. 3.5). Fig. 2 shows an overview of our FlipNeRF.",
+        "bbox": [
+            496,
+            337,
+            890,
+            580
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
+            500,
+            588,
+            640,
+            602
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "NeRF. The NeRF [24], which is an MLP-based neural network, represents a 3D scene as a continuous radiance field of RGB color and volume density. For every point sampled along a ray, the 3D coordinates  $\\mathbf{x} = (x,y,z)$  and viewing directions  $(\\theta ,\\phi)$  are mapped to the colors  $\\mathbf{c} = (r,g,b)$  and densities  $\\sigma$  ..",
+        "bbox": [
+            496,
+            609,
+            890,
+            700
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF (\\gamma (\\mathbf {x}), \\gamma (\\hat {\\mathbf {d}})) \\rightarrow (\\mathbf {c}, \\sigma), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            609,
+            710,
+            890,
+            729
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $F(\\cdot), \\gamma(\\cdot)$ , and  $\\hat{\\mathbf{d}}$  indicate an MLP, the positional encoding for the inputs, and the 3D Cartesian unit vector used as an input viewing direction in practice, respectively.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The volumetric radiance field is rendered by alpha composing the RGB values along an input ray  $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}$  [22], where  $\\mathbf{o}$  and  $\\mathbf{d}$  denote the camera origin and unnormalized direction vector, i.e.  $\\mathbf{d} = \\| \\mathbf{d}\\| _2\\cdot \\hat{\\mathbf{d}}$  respectively. The volume rendering integrals are denoted as follows:",
+        "bbox": [
+            496,
+            785,
+            890,
+            859
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {c}} (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) \\mathbf {c} (\\mathbf {r} (t), \\hat {\\mathbf {d}}) d t, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
+            868,
+            890,
+            905
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "22885",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/1c49d188db66f370e6b42b74b935cd959508d01329287f592b38d125f29bc8a4.jpg",
+        "image_caption": [
+            "Figure 3: Flipped reflection ray generation. Our FlipNeRF generates the flipped reflection ray  $\\mathbf{r}'$  from the estimated normal vector  $\\hat{\\mathbf{n}}$  and original input ray direction  $\\mathbf{d}$ . With our masking strategy,  $\\mathbf{r}_2'$  is filtered out since it does not satisfy the photo-consistency condition, i.e.  $\\theta_{2}$  is bigger than  $90^{\\circ}$ . The smaller  $\\theta$  is, the more photo-consistent the target pixel is, where the pair of  $\\mathbf{r}$  and  $\\mathbf{r}'$  are cast."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            116,
+            98,
+            410,
+            349
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $T(t) = \\exp(-\\int_{t_n}^t \\sigma(s) ds)$  indicates the degree of transparency. In practice, it is approximated with numerical quadrature [24] by sampling points along a ray.",
+        "bbox": [
+            76,
+            479,
+            468,
+            527
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The radiance field is trained to minimize the mean squared error (MSE) between rendered and GT pixels:",
+        "bbox": [
+            76,
+            527,
+            468,
+            558
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {M S E}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} | | \\hat {\\mathbf {c}} (\\mathbf {r}) - \\mathbf {c} ^ {\\mathrm {G T}} (\\mathbf {r}) | | _ {2} ^ {2}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            565,
+            468,
+            595
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{R}$  is denoted as a set of rays.",
+        "bbox": [
+            76,
+            604,
+            313,
+            619
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "MixNeRF. Built upon mip-NeRF [1], which leveraged a cone tracing method and proposed an integrated positional encoding to address an aliasing problem, MixNeRF [31] estimates the joint probability distribution of color values and models a ray with a mixture of densities:",
+        "bbox": [
+            76,
+            637,
+            468,
+            713
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (\\mathbf {c} | \\mathbf {r}) = \\sum_ {i = 1} ^ {M} \\pi_ {i} \\mathcal {F} (\\mathbf {c}; \\mu_ {i} ^ {\\mathbf {c}}, \\beta_ {i}), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            174,
+            720,
+            468,
+            762
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $M$  is the number of sampled points,  $\\mathcal{F}(\\mathbf{c};\\mu_i^{\\mathbf{c}},\\beta_i)$  denotes the Laplacian distribution of RGB  $\\mathbf{c}$  with location parameter  $\\mu_i^{\\mathbf{c}}\\in \\{\\mu_i^r,\\mu_i^g,\\mu_i^b\\}$ , i.e. estimated RGB values of sample, and scale parameter  $\\beta_{i}\\in \\{\\beta_{i}^{r},\\beta_{i}^{g},\\beta_{i}^{b}\\}$ . The mixture coefficient  $\\pi_{i}$  is derived from the estimated volume density  $\\sigma_{i}$  as follows:",
+        "bbox": [
+            76,
+            768,
+            468,
+            861
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\pi_ {i} = \\frac {w _ {i}}{\\sum_ {m = 1} ^ {M} w _ {m}} = \\frac {T _ {i} (1 - \\exp (- \\sigma_ {i} \\delta_ {i}))}{\\sum_ {m = 1} ^ {M} T _ {m} (1 - \\exp (- \\sigma_ {m} \\delta_ {m}))}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            86,
+            868,
+            468,
+            905
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $w_{i}$  and  $\\delta_{i}$  indicate the alpha blending weight and sample interval, respectively. Thanks to the mixture model's capacity of representing complex distributions, MixNeRF learns the density distribution effectively with sparse inputs by minimizing the negative log-likelihood (NLL) in Eq. 4.",
+        "bbox": [
+            498,
+            90,
+            890,
+            167
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our FlipNeRF is built upon MixNeRF leveraging the mixture modeling framework while achieving superior rendering quality with noticeably fewer artifacts and more accurate surface normals to MixNeRF.",
+        "bbox": [
+            498,
+            167,
+            890,
+            226
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Auxiliary Flipped Reflection Ray",
+        "text_level": 1,
+        "bbox": [
+            500,
+            234,
+            787,
+            252
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 3, we exploit a batch of flipped reflection rays  $\\mathbf{r}' \\in \\mathcal{R}'$  as extra training resources, which are derived from the original input ray directions  $\\mathbf{d}$  and estimated surface normals  $\\hat{\\mathbf{n}}$ . First, we derive a flipped reflection direction  $\\mathbf{d}'$  from  $\\mathbf{d}$  and  $\\hat{\\mathbf{n}}$ :",
+        "bbox": [
+            498,
+            258,
+            890,
+            333
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {d} ^ {\\prime} = 2 (\\mathbf {d} \\cdot \\hat {\\mathbf {n}}) \\hat {\\mathbf {n}} - \\mathbf {d}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            624,
+            343,
+            890,
+            359
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{\\mathbf{n}}$  denotes the weighted sum of blending weights and estimated normal vectors along a ray, i.e.  $\\hat{\\mathbf{n}} = \\sum_{i=1}^{M} w_i \\mathbf{n}_i$ . Note that we use the gradient of volume density as estimated surface normals following [3, 34, 36].",
+        "bbox": [
+            498,
+            369,
+            890,
+            429
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To generate the additional training rays based on  $\\mathbf{d}'$ , we need a set of imaginary ray origins  $\\mathbf{o}'$  located in a suitable space considering the hitting point and the original input ray origins  $\\mathbf{o}$ . Since the vanilla NeRF models, which are trained with a dense set of images, tend to have the blending weight distribution whose peak is located on the point around the object surface  $\\mathbf{p}_s = \\mathbf{o} + t_s\\mathbf{d}$  [8, 31], i.e. the  $s$ -th sample whose blending weight is the highest along a ray. Therefore, we place  $\\mathbf{o}'$  so that the  $s$ -th sample of  $\\mathbf{r}'$  is  $\\mathbf{p}_s$ :",
+        "bbox": [
+            498,
+            430,
+            890,
+            566
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {o} ^ {\\prime} = \\mathbf {p} _ {s} - t _ {s} \\mathbf {d} ^ {\\prime}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            638,
+            575,
+            890,
+            590
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "resulting in our proposed flipped reflection ray,  $\\mathbf{r}'(t) = \\mathbf{o}' + t\\mathbf{d}'$ . Compared to the previous unseen viewpoint sampling strategies [15, 25, 17], our proposed strategy does not rely on the randomness of unseen viewpoint sampling and reduces the heuristic factors for sampling schemes, e.g. the range of rotation, translation, and so on. Furthermore, since our newly generated  $\\mathbf{r}'$  are cast on the identical object surfaces where the original input rays  $\\mathbf{r}$  are cast, i.e. the target pixels are photo-consistent for the pair of  $\\mathbf{r}$  and  $\\mathbf{r}'$  without any sophisticated viewpoint sampling process, we are able to train  $\\mathbf{r}'$  effectively with the same GT pixels of  $\\mathbf{r}$ .",
+        "bbox": [
+            498,
+            601,
+            890,
+            767
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "However, since  $\\hat{\\mathbf{n}}$ , which are used to derive  $\\mathbf{d}'$ , are not the ground truth but the estimation, there exists a concern that even miscreated  $\\mathbf{r}'$ , which do not satisfy photo-consistency, can be used for training. As a result, it might lead to performance degradation while providing misleading training",
+        "bbox": [
+            498,
+            767,
+            890,
+            843
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "${}^{2}$  Technically,  $\\widehat{\\mathbf{n}}$  is not guaranteed to be a unit vector without an explicit normalization process. However, we empirically found that the normalization rather destabilizes the training and leads to the performance degradation. Kindly refer to our supplementary material for related experiments.",
+        "bbox": [
+            500,
+            849,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22886",
+        "bbox": [
+            478,
+            945,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "cues. To address this problem, we mask the ineffective  $\\mathbf{r}'$  by considering the angle  $\\theta$  between  $\\hat{\\mathbf{n}}$  and  $-\\hat{\\mathbf{d}}$  as follows:",
+        "bbox": [
+            75,
+            90,
+            468,
+            121
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM \\left(\\mathbf {r} ^ {\\prime}\\right) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\arccos  \\left(- (\\hat {\\mathbf {d}} \\cdot \\hat {\\mathbf {n}})\\right) <   \\tau \\\\ 0 & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            132,
+            132,
+            468,
+            174
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $-(\\hat{\\mathbf{d}}\\cdot \\hat{\\mathbf{n}})$  amounts to  $\\cos \\theta$  of original input rays and normal vectors, and  $\\tau$  indicates the threshold for filtering the invalid rays, which we set as  $90^{\\circ}$  unless specified. Through this masking process, only  $\\mathbf{r}'$  which are cast toward the photo-consistent point can be remained as we intend. Finally, our proposed flipped reflection rays are modeled by mixture density like the original input rays:",
+        "bbox": [
+            75,
+            186,
+            468,
+            294
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np \\left(\\mathbf {c} \\mid \\mathbf {r} ^ {\\prime}\\right) = \\sum_ {i = 1} ^ {M} \\pi_ {i} ^ {\\prime} \\mathcal {F} \\left(\\mathbf {c}; \\mu_ {i} ^ {\\mathbf {c} ^ {\\prime}}, \\beta_ {i} ^ {\\prime}\\right). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            169,
+            305,
+            468,
+            347
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Additionally, we leverage the Orientation Loss proposed in Ref-NeRF [36] to penalize the backward-facing normal vectors for learning accurate surface normals:",
+        "bbox": [
+            76,
+            358,
+            468,
+            404
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nl _ {\\text {O r i .}} (\\mathbf {r}) = \\sum_ {i = 1} ^ {M} w _ {i} \\max  (0, \\mathbf {n} _ {i} \\cdot \\hat {\\mathbf {d}}) ^ {2}. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
+            416,
+            468,
+            455
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Unlike Ref-NeRF, we penalize underlying density gradient normal  $\\mathbf{n}_i$  instead of predicted normals.",
+        "bbox": [
+            76,
+            468,
+            468,
+            497
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Note that our FlipNeRF is fundamentally different compared to Ref-NeRF since ours generates additional training rays through the derivation of reflection direction without modification to original representations while Ref-NeRF replaced the input viewing direction with its reflection direction, reparameterizing the outgoing radiance.",
+        "bbox": [
+            75,
+            500,
+            468,
+            590
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Uncertainty-aware Regularization",
+        "text_level": 1,
+        "bbox": [
+            76,
+            599,
+            375,
+            617
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Several regularization techniques have been proposed to reduce the floating artifacts present in synthesized images, which is one of the major problems of NeRF. Among them, we leverage the Emptiness Loss [37] which penalizes the small blending weights along a ray as follows:",
+        "bbox": [
+            75,
+            623,
+            468,
+            700
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nl _ {\\text {E m p .}} (\\mathbf {r}) = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\log (1 + \\eta \\cdot w _ {i}), \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            155,
+            710,
+            468,
+            753
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the bigger  $\\eta$  is, the steeper the loss function becomes around 0.",
+        "bbox": [
+            75,
+            763,
+            468,
+            792
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However, the naive application of existing regularization techniques with limited training views might not be consistently helpful across the different scenes due to the scene-by-scene different structure, resulting in overall performance degradation. To address this problem, we propose Uncertainty-aware Emptiness Loss (UE Loss) developed upon the Emptiness Loss, which reduces the floating",
+        "bbox": [
+            75,
+            795,
+            468,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "artifacts consistently over the different scenes by considering the output uncertainty:",
+        "bbox": [
+            498,
+            90,
+            888,
+            121
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nl _ {\\mathrm {U E}} (\\mathbf {r}) = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\log (1 + \\rho \\cdot \\eta \\cdot w _ {i}), \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            573,
+            136,
+            888,
+            186
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {w h e r e} \\quad \\rho = \\frac {1}{3} \\sum_ {c} ^ {\\{r, g, b \\}} \\sum_ {i = 1} ^ {M} \\beta_ {i} ^ {c}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            622,
+            181,
+            815,
+            223
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$\\rho$  amounts to the average of the summation of estimated scale parameters of RGB color distributions from all samples along a ray, which we use as the uncertainty of a ray. By our proposed UE Loss, we are able to regularize the blending weights adaptively, i.e. the more uncertain a ray is, the more penalized the blending weights along the ray are. It is able to reduce floating artifacts consistently across the scenes with different structures and enables to synthesize more reliable outputs by considering uncertainty.",
+        "bbox": [
+            498,
+            238,
+            890,
+            375
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Bottleneck Feature Consistency",
+        "text_level": 1,
+        "bbox": [
+            500,
+            388,
+            777,
+            405
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Motivated by previous works addressing the feature-level consistency of multiple views for few-shot novel view synthesis [6, 11, 15], we encourage the consistency of bottleneck feature distributions between  $\\mathbf{r}$  and  $\\mathbf{r}'$ , which are intermediate feature vectors, i.e. outputs of the spatial MLP of NeRF, by Jensen-Shannon Divergence (JSD):",
+        "bbox": [
+            498,
+            414,
+            890,
+            505
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nl _ {\\mathrm {B F C}} \\left(\\mathbf {r}, \\mathbf {r} ^ {\\prime}\\right) = J S D \\left(\\psi (\\mathbf {b}), \\psi \\left(\\mathbf {b} ^ {\\prime}\\right)\\right), \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            580,
+            520,
+            888,
+            537
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\psi (\\cdot)$ ,  $\\mathbf{b}$  and  $\\mathbf{b}^{\\prime}$  denote the softmax function, the bottleneck features of  $\\mathbf{r}$  and  $\\mathbf{r}^{\\prime}$ , respectively. While the existing methods [6, 11] rely on off-the-shelf feature extractors like 2D CNN or CLIP [27] to address high-level feature consistency, we regulate the pair of features effectively by enhancing consistency between bottleneck features without depending on additional feature extractors.",
+        "bbox": [
+            498,
+            551,
+            890,
+            657
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Total Loss",
+        "text_level": 1,
+        "bbox": [
+            500,
+            674,
+            614,
+            688
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our FlipNeRF is not only trained to maximize the log-likelihood of the target pixel  $\\mathbf{c}_{\\mathrm{GT}}$  for a set of original input rays  $\\mathcal{R}$ , but also for flipped reflection rays  $\\mathcal{R}_M^\\prime$ , where the ineffective rays are excluded from the total flipped reflection rays  $\\mathcal{R}^\\prime$  by our masking strategy in Eq. 8. Likewise, the UE Losses are applied for both  $\\mathcal{R}$  and  $\\mathcal{R}_M^\\prime$ .",
+        "bbox": [
+            498,
+            699,
+            890,
+            790
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Aggregating all, our total loss over a batch is as follows:",
+        "bbox": [
+            519,
+            792,
+            888,
+            806
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {T o t a l}} = \\mathcal {L} _ {\\text {M S E}} + \\lambda_ {1} \\mathcal {L} _ {\\text {N L L}} + \\lambda_ {2} \\mathcal {L} _ {\\text {N L L}} ^ {\\prime} \\tag {14} \\\\ + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {U E}} + \\lambda_ {4} \\mathcal {L} _ {\\mathrm {U E}} ^ {\\prime} + \\lambda_ {5} \\mathcal {L} _ {\\mathrm {B F C}} + \\lambda_ {6} \\mathcal {L} _ {\\mathrm {O r i}}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            526,
+            835,
+            888,
+            869
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where a set of  $\\lambda$ 's are balancing weight terms for the losses.",
+        "bbox": [
+            500,
+            885,
+            888,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "22887",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/1a443a0677773699f7929878a515265944777d040bbaea2a77789d462f38957c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>τ</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>30°</td><td>18.62</td><td>0.747</td><td>0.206</td><td>0.121</td></tr><tr><td>60°</td><td>18.12</td><td>0.723</td><td>0.237</td><td>0.126</td></tr><tr><td>90°</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr><tr><td>180° (No masking)</td><td>18.76</td><td>0.755</td><td>0.190</td><td>0.111</td></tr></table>",
+        "bbox": [
+            81,
+            89,
+            467,
+            161
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Comparison of masking conditions. Our masking strategy with  $\\tau$  of  $90^{\\circ}$  achieves the best results, filtering out the ineffective flipped reflection rays successfully.",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/7bcdc432db4a80bd7668513f39889200756de9675845cec296540b823c91c78b.jpg",
+        "image_caption": [
+            "(a) Effective  $\\mathbf{r}'$  ratio by  $\\tau$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "img_path": "images/2ed9f0b59d0c0e1bbf7375d42d236a2fef8f035db90d3709ff30b00fafd53cc9.jpg",
+        "image_caption": [
+            "(b) Distribution of  $\\theta$",
+            "Figure 4: Analysis of the masking strategy."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Implementation details. Our FlipNeRF is built upon MixNeRF [31] based on the JAX codebase [4], which is developed upon mip-NeRF [1]. The overall training scheme follows [25, 31]. We adopt a scene space annealing strategy for the early training phase. Also, we apply the exponential decay and warm up for the learning rate. The Adam optimizer [16] and the gradient clippings by value at 0.1 and norm at 0.1 are used. We train our FlipNeRF for 500 pixel epochs with a batch size of 4,096 on 4 NVIDIA RTX 3090. Additionally, since the LLFF dataset [23] consists of scenes with much more static movement of viewpoints compared to other datasets, we set the threshold  $(\\tau)$  of our masking strategy as  $30^{\\circ}$  for the experiments on LLFF. More detailed hyperparameters and our loss balancing terms by the datasets and the number of training views are provided in the supplementary material.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Datasets and metrics. We evaluate the performance of our FlipNeRF and baselines on the representative benchmarks: Realistic Synthetic  $360^{\\circ}$  [24], DTU [13], and LLFF [23]. Realistic Synthetic  $360^{\\circ}$  contains 8 synthetic scenes, each consisting of 400 multi-view rendered images with white background. To compare against other representative baselines [15, 11, 31, 25, 1], we evaluate our FlipNeRF under the scenarios of 4 and 8 views. For a fair comparison, we sample the first  $n$ -image of the training set for the  $n$ -view scenario so that the identical images are provided for training different methods following [31]. We use 200 images of the test set for evaluation. For DTU, which provide various scenes including objects put on a white table with a black background, we conduct experiments on the 15",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "specific scenes under the scenarios of 3, 6, and 9-view, following the experimental protocol of [43]. We also conduct a series of experiments for the analysis of FlipNeRF under 3-view setting as well as comparison against other baselines. Additionally, we compare our FlipNeRF against other baselines on LLFF consisting of real forward-facing scenes, which is often tested as an out-of-distribution dataset for pre-training methods. Following [24], every 8th image of each scene is used for a held-out test set and the training views are evenly selected from the remaining images. Like DTU, we report our results of the 3, 6, and 9-view scenarios, following [43].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For the quantitative evaluation for rendered images, we adopt the mean of PSNR, SSIM [40], LPIPS [45], and the geometric average [1]. Furthermore, we also adopt the mean angular error  $(\\mathrm{MAE}^{\\circ})$  [36] and NLL [33, 32, 21, 18] for evaluating the surface normals and uncertainty, respectively. Specifically, following [33], we compute the NLL by deriving the probability of the GT pixel values given a Gaussian distribution with the estimated RGB values as mean and the uncertainty as variance, which is derived from the weighted sum of the blending weights and estimated scale parameters along a ray in our FlipNeRF. For DTU, we report the results evaluated by masked metrics to prevent background bias, following [25, 31].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baselines. We compare our FlipNeRF against the SOTA regularization methods [11, 15, 25, 31] on Realistic Synthetic  $360^{\\circ}$  as well as the vanilla mip-NeRF [1] and Ref-NeRF [36], which is known for achieving promising results with accurate surface normals. Furthermore, we compare ours against the representative pre-training methods [5, 6, 43] as well as regularization methods on DTU and LLFF. The pre-training baselines exploit the DTU and LLFF as pre-training dataset and out-of-distribution test set, respectively, while the regularization methods, mip-NeRF and Ref-NeRF are optimized per scene. Note that we report the quantitative results of other baselines on DTU and LLFF from [25], which achieved better results than its original papers by the modified training scheme, and those on Realistic Synthetic  $360^{\\circ}$  from [31], which trained the baselines with the identical training views for a fair comparison.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Analysis of FlipNeRF",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Analysis of flipped reflection rays. As shown in Tab. 1, our masking strategy of filtering out the ineffective flipped reflection rays with the threshold  $(\\tau)$  of  $90^{\\circ}$  achieves the best performance among different options. With  $\\tau$  of  $30^{\\circ}$  and  $60^{\\circ}$ , the rendering quality is rather degraded since the newly generated rays are overly-filtered and do not provide enough additional supervision as demonstrated in Fig. 4a. On the other hand, when we exploit all the flipped reflection rays without masking, there exists a little improvement",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "22888",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/803ad8ee3b00a5fd5761d6878aa7e75201a67f8f5f0863f00021dfb8d3f21296.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average ↓</td><td>NLL ↓</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>0.744</td><td>0.203</td><td>0.113</td><td>9.99</td></tr><tr><td>FlipNeRF (Ours)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>w/o LEmp. or LUE</td><td>19.30</td><td>0.758</td><td>0.196</td><td>0.108</td><td>4.88</td></tr><tr><td>w/ LEmptiness</td><td>18.62</td><td>0.749</td><td>0.204</td><td>0.118</td><td>4.92</td></tr><tr><td>w/ LUE</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td><td>2.56</td></tr></table>",
+        "bbox": [
+            81,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/76b16cabab8c3f7355fe9205a6f5a29c4ba1f29f97fec83e6add3d1d3c0fbb97.jpg",
+        "image_caption": [
+            "Figure 5: Comparison of FlipNeRF and MixNeRF. Our FlipNeRF renders the images from novel views with much fewer artifacts and more accurate depth maps than MixNeRF. Considering the standard deviation of RGB and depths, our FlipNeRF is able to estimate more reliable outputs than MixNeRF. For the std. map, the darker the pixel is, the more certain the output is."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "of performance compared to  $30^{\\circ}$  and  $60^{\\circ}$  masking, but it is still much inferior to  $90^{\\circ}$  due to the negative impact from the ineffective rays. Additionally, Fig. 4b shows the distribution of  $\\theta$ , i.e. angles between the input viewing directions and normal vectors. As the smaller  $\\theta$  is, the more photo-consistent the target pixel is, i.e. the more effective the newly generated flipped reflection rays are for training. Since our FlipNeRF is trained to estimate the accurate normal vectors, we are able to exploit a set of more effective flipped reflection rays through the training, which are cast on the more photo-consistent target pixels. Furthermore, at the initial training phase, the invalid additional rays are filtered effectively by our masking strategy, leading to high-quality supervision and stabilizing the training.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Uncertainty-aware regularization. Tab. 2 shows the effectiveness of our proposed UE Loss. Compared to MixNeRF [31] which models a ray with mixture of distributions as our FlipNeRF, ours consistently achieves more reliable rendering results with much lower NLL. Without  $\\mathcal{L}_{\\mathrm{Emp}}$ , [37] or our proposed  $\\mathcal{L}_{\\mathrm{UE}}$ , ours already outperforms MixNeRF by a large margin. However, ours with naively leveraged  $\\mathcal{L}_{\\mathrm{Emp}}$  rather shows inferior results to MixNeRF. It shows that naive application of the existing regularization technique for reducing artifacts under the few-shot setting can lead to overall performance degradation due to the scene",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7b318624c637a815a17f39f199c72492363684dae570079b4bcb4fdc5173125b.jpg",
+        "table_caption": [
+            "Table 2: Effectiveness of  $\\mathcal{L}_{\\mathrm{UE}}$ . Our proposed  $\\mathcal{L}_{\\mathrm{UE}}$  improves the rendering quality consistently across the scenes with considering the uncertainty."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>w/o LBCF</td><td>18.79</td><td>0.755</td><td>0.200</td><td>0.115</td></tr><tr><td>w/ LBCF</td><td></td><td></td><td></td><td></td></tr><tr><td>MSE on b</td><td>18.83</td><td>0.755</td><td>0.197</td><td>0.113</td></tr><tr><td>Cos. Sim. on b</td><td>18.77</td><td>0.755</td><td>0.193</td><td>0.115</td></tr><tr><td>JSD on bhat</td><td>18.43</td><td>0.749</td><td>0.204</td><td>0.120</td></tr><tr><td>JSD on b</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr></table>",
+        "bbox": [
+            504,
+            88,
+            888,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/0fca5b04cf1502378ea4f7c3f411563246242e5e12cd21115a1b6859cbefbc6f.jpg",
+        "table_caption": [
+            "Table 3: Comparison of different strategies for  $\\mathcal{L}_{\\mathrm{BFC}}$ . Our  $\\mathcal{L}_{\\mathrm{BFC}}$  achieves a significant performance gain compared to other regularization schemes for feature consistency."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>\\( \\mathcal{L}_{\\text{NLL}} \\)</td><td>\\( \\mathcal{L}_{\\text{NLL}}^{\\prime} \\)</td><td>\\( \\mathcal{L}_{\\text{UE}}^\\dagger \\)</td><td>\\( \\mathcal{L}_{\\text{BFC}} \\)</td><td>\\( \\mathcal{L}_{\\text{Ori.}} \\)</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average ↓</td></tr><tr><td>(1)</td><td>✓</td><td></td><td></td><td></td><td></td><td>17.44</td><td>0.729</td><td>0.187</td><td>0.130</td></tr><tr><td>(2)</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>16.94</td><td>0.727</td><td>0.217</td><td>0.143</td></tr><tr><td>(3)</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>17.89</td><td>0.736</td><td>0.206</td><td>0.130</td></tr><tr><td>(4)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>19.01</td><td>0.755</td><td>0.181</td><td>0.107</td></tr><tr><td>(5)</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>18.79</td><td>0.755</td><td>0.200</td><td>0.115</td></tr><tr><td>(6)</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>19.30</td><td>0.758</td><td>0.196</td><td>0.108</td></tr><tr><td>(7)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Ablation study.  $\\dagger$  indicate that the losses are applied to both  $\\mathbf{r}$  and  $\\mathbf{r}'$ .",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "by-scene various structures. As illustrated in Fig. 5, with our proposed  $\\mathcal{L}_{\\mathrm{UE}}$ , ours improves both of the rendering quality and the reliability of the model outputs by a large margin compared to MixNeRF.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Bottleneck feature consistency. As shown in Tab. 3, there is no significant impact on the performance with regularizing the bottleneck feature  $\\mathbf{b}$  using MSE or cosine similarity. By our proposed  $\\mathcal{L}_{\\mathrm{BFC}}$  with JSD, we achieve a considerable performance improvement. Interestingly, the performance rather degrades when we apply  $\\mathcal{L}_{\\mathrm{BFC}}$  with JSD to  $\\mathbf{b}_{\\hat{\\mathbf{d}}}$ , i.e. the bottleneck feature conditioned with input viewing direction  $\\hat{\\mathbf{d}}$ . We conjecture that the reduced feature dimension of  $\\mathbf{b}_{\\hat{\\mathbf{d}}}$  reduces the capacity of feature representations and prevents the model from improving robustness.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The quantitative results of our ablation study are reported in Tab. 4. With only additionally exploiting our proposed flipped reflection rays, our FlipNeRF achieves more degenerate results compared to the baseline  $((1) \\rightarrow (2))$ . However, we are able to achieve performance improvement by a large margin with our proposed  $\\mathcal{L}_{\\mathrm{UE}}$  and  $\\mathcal{L}_{\\mathrm{BFC}}$ $((2) \\rightarrow (3) \\rightarrow (4))$ .  $(5) \\rightarrow (7)$  shows that enhancing the consistency of bottleneck features between the pair of original and flipped reflection rays is considerably effective. Additionally, by leveraging  $\\mathcal{L}_{\\mathrm{Ori}}$ , from Ref-NeRF, we are able to estimate more accurate normal vectors, leading to more effective flipped reflection rays and performance gain  $((4) \\rightarrow (7))$ .",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "22889",
+        "bbox": [
+            478,
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/78ea0ec08cec4255f6d432defec80d36b711f78a7f8d3ff6d9ab6d35fa6c25f1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">PSNR ↑</td><td colspan=\"2\">SSIM ↑</td><td colspan=\"2\">LPIPS ↓</td><td colspan=\"2\">Average Err. ↓</td><td colspan=\"2\">MAE° ↓</td></tr><tr><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td></tr><tr><td>mip-NeRF [1]</td><td>14.12</td><td>18.74</td><td>0.722</td><td>0.828</td><td>0.382</td><td>0.238</td><td>0.221</td><td>0.121</td><td>96.05</td><td>101.21</td></tr><tr><td>Ref-NeRF [36]</td><td>18.09</td><td>24.00</td><td>0.764</td><td>0.879</td><td>0.269</td><td>0.106</td><td>0.150</td><td>0.058</td><td>65.62</td><td>57.93</td></tr><tr><td>DietNeRF [11]</td><td>15.42</td><td>21.31</td><td>0.730</td><td>0.847</td><td>0.314</td><td>0.153</td><td>0.201</td><td>0.086</td><td>-</td><td>-</td></tr><tr><td>InfoNeRF [15]</td><td>18.44</td><td>22.01</td><td>0.792</td><td>0.852</td><td>0.223</td><td>0.133</td><td>0.119</td><td>0.073</td><td>-</td><td>-</td></tr><tr><td>RegNeRF [25]</td><td>13.71</td><td>19.11</td><td>0.786</td><td>0.841</td><td>0.346</td><td>0.200</td><td>0.210</td><td>0.122</td><td>62.78</td><td>60.37</td></tr><tr><td>MixNeRF [31]</td><td>18.99</td><td>23.84</td><td>0.807</td><td>0.878</td><td>0.199</td><td>0.103</td><td>0.113</td><td>0.060</td><td>70.90</td><td>62.04</td></tr><tr><td>FlipNeRF (Ours)</td><td>20.60</td><td>24.38</td><td>0.822</td><td>0.883</td><td>0.159</td><td>0.095</td><td>0.091</td><td>0.055</td><td>58.72</td><td>57.17</td></tr></table>",
+        "bbox": [
+            119,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/260a01ead5ef00fd662e3b1a30d0ca291d82d213b18c1568456861207040e8f0.jpg",
+        "table_caption": [
+            "Table 5: Quantitative results on Realistic Synthetic  ${360}^{ \\circ  }$  . Our FlipNeRF achieves the SOTA performance among other baselines across all the scenarios and metrics."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">PSNR ↑ 6-view</td><td rowspan=\"2\">9-view</td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">SSIM ↑ 6-view</td><td rowspan=\"2\">9-view</td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">LPIPS ↓ 6-view</td><td rowspan=\"2\">9-view</td><td colspan=\"3\">Average Error ↓</td></tr><tr><td>3-view</td><td>6-view</td><td>9-view</td></tr><tr><td>mip-NeRF [1]</td><td>8.68</td><td>16.54</td><td>23.58</td><td>0.571</td><td>0.741</td><td>0.879</td><td>0.353</td><td>0.198</td><td>0.092</td><td>0.323</td><td>0.148</td><td>0.056</td></tr><tr><td colspan=\"13\">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>16.82</td><td>19.11</td><td>20.40</td><td>0.695</td><td>0.745</td><td>0.768</td><td>0.270</td><td>0.232</td><td>0.220</td><td>0.147</td><td>0.115</td><td>0.100</td></tr><tr><td>PixelNeRF†[43]</td><td>18.95</td><td>20.56</td><td>21.83</td><td>0.710</td><td>0.753</td><td>0.781</td><td>0.269</td><td>0.223</td><td>0.203</td><td>0.125</td><td>0.104</td><td>0.090</td></tr><tr><td>SRF [6]</td><td>15.32</td><td>17.54</td><td>18.35</td><td>0.671</td><td>0.730</td><td>0.752</td><td>0.304</td><td>0.250</td><td>0.232</td><td>0.171</td><td>0.132</td><td>0.120</td></tr><tr><td>SRF†[6]</td><td>15.68</td><td>18.87</td><td>20.75</td><td>0.698</td><td>0.757</td><td>0.785</td><td>0.281</td><td>0.225</td><td>0.205</td><td>0.162</td><td>0.114</td><td>0.093</td></tr><tr><td>MVSNeRF [5]</td><td>18.63</td><td>20.70</td><td>22.40</td><td>0.769</td><td>0.823</td><td>0.853</td><td>0.197</td><td>0.156</td><td>0.135</td><td>0.113</td><td>0.088</td><td>0.068</td></tr><tr><td>MVSNeRF†[5]</td><td>18.54</td><td>20.49</td><td>22.22</td><td>0.769</td><td>0.822</td><td>0.853</td><td>0.197</td><td>0.155</td><td>0.135</td><td>0.113</td><td>0.089</td><td>0.069</td></tr><tr><td colspan=\"13\">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>11.85</td><td>20.63</td><td>23.83</td><td>0.633</td><td>0.778</td><td>0.823</td><td>0.314</td><td>0.201</td><td>0.173</td><td>0.243</td><td>0.101</td><td>0.068</td></tr><tr><td>RegNeRF [25]</td><td>18.89</td><td>22.20</td><td>24.93</td><td>0.745</td><td>0.841</td><td>0.884</td><td>0.190</td><td>0.117</td><td>0.089</td><td>0.112</td><td>0.071</td><td>0.047</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>22.30</td><td>25.03</td><td>0.744</td><td>0.835</td><td>0.879</td><td>0.203</td><td>0.102</td><td>0.065</td><td>0.113</td><td>0.066</td><td>0.042</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.55</td><td>22.45</td><td>25.12</td><td>0.767</td><td>0.839</td><td>0.882</td><td>0.180</td><td>0.098</td><td>0.062</td><td>0.101</td><td>0.064</td><td>0.041</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/838ee46c6e4435806705b94ab12873ab85fa4ca4968ced862ba93ab1f654552e.jpg",
+        "table_caption": [
+            "Table 6: Comparison with baselines on DTU. Our FlipNeRF outperforms all the pre-training and regularization methods in every scenario, especially by a large margin under the 3-view setting.  $\\dagger$  indicates fine-tuning."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>mip-NeRF [1]</td><td>14.62</td><td>0.351</td><td>0.495</td><td>0.246</td></tr><tr><td colspan=\"5\">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>7.93</td><td>0.272</td><td>0.682</td><td>0.461</td></tr><tr><td>PixelNeRF† [43]</td><td>16.17</td><td>0.438</td><td>0.512</td><td>0.217</td></tr><tr><td>SRF [6]</td><td>12.34</td><td>0.250</td><td>0.591</td><td>0.313</td></tr><tr><td>SRF† [6]</td><td>17.07</td><td>0.436</td><td>0.529</td><td>0.203</td></tr><tr><td>MVSNeRF [5]</td><td>17.25</td><td>0.557</td><td>0.356</td><td>0.171</td></tr><tr><td>MVSNeRF† [5]</td><td>17.88</td><td>0.584</td><td>0.327</td><td>0.157</td></tr><tr><td colspan=\"5\">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>14.94</td><td>0.370</td><td>0.496</td><td>0.240</td></tr><tr><td>RegNeRF [25]</td><td>19.08</td><td>0.587</td><td>0.336</td><td>0.146</td></tr><tr><td>MixNeRF [31]</td><td>19.27</td><td>0.629</td><td>0.236</td><td>0.124</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.34</td><td>0.631</td><td>0.235</td><td>0.123</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 7: Comparison with baselines on LLFF 3-view. † indicates fine-tuning.",
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+    {
+        "type": "text",
+        "text": "4.4. Comparison with other SOTA Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Realistic Synthetic  $360^{\\circ}$ . As demonstrated in Tab. 5, our FlipNeRF achieves the SOTA performance across all the evaluation metrics. Compared to MixNeRF which leverages a mixture model framework as ours, our FlipNeRF",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "improves the performance by a large margin. Noticeably, our FlipNeRF estimates more accurate surface normals than other baselines, leading to the performance gain with better reconstructed fine details from limited input views as shown in Fig. 6a. Additionally, the vanilla Ref-NeRF, which shows great performance with accurate normal vectors, achieves comparable or even better performance than other regularization methods except ours. From this result, we are able to expect that estimating the accurate surface normals is one of the key factors for learning 3D geometry with sparse inputs. Note that the comparable  $\\mathrm{MAE}^{\\circ}$  of RegNeRF results from the overly-smoothed depth estimation, not indicating the high-quality of rendering results, as shown in Fig. 6a.",
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+    {
+        "type": "text",
+        "text": "DTU. Our FlipNeRF achieves the best results across all the scenarios and most of the evaluation metrics on DTU as shown in Tab. 6. Remarkably, ours trained with 6-view outperforms all the pre-training methods trained with 9-view in every metric except SSIM. Furthermore, ours trained with 3-view still outperforms PixelNeRF [43] and SRF [6] trained with 6-view. Similar to the results on Realistic Synthetic  $360^{\\circ}$ , ours outperforms other baselines by a large",
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+    },
+    {
+        "type": "page_number",
+        "text": "22890",
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+    {
+        "type": "image",
+        "img_path": "images/d9a0cc943fffec29d76e0447f76d5d66d7964b6be6e9c319ea98bc020970f699.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/4b90633e79c8847ab9c7aea9648f23c200f093d7677463dd16ab8123b501d088.jpg",
+        "image_caption": [
+            "Figure 6: Qualitative results on Realistic Synthetic  $360^{\\circ}$  and DTU. More results are provided in the supp. material."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "margin especially under the 3-view, which is the most challenging scenario, with reducing the floating artifacts successfully as shown in Fig. 6b. Since the flipped reflection rays are effective training resources for unseen views, the fewer the training views are provided, the more performance gain is expected.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "LLFF. Table 7 compares our FlipNeRF against other baselines on LLFF, which is a real forward-facing dataset. Although ours achieves the SOTA performance among other baselines, it is much more marginal than those on Realistic Synthetic  $360^{\\circ}$  and DTU. We conjecture the reason for the marginal improvement of our proposed method can be the fact that a set of flipped reflection rays, which are able to widely cover the unseen views, are not very useful for the scenes in LLFF, where a set of camera poses are much less dynamic than other datasets. In other words, our FlipNeRF is able to not only achieve a competitive performance for the scenes consisting of a set of simple camera poses, but also render the novel views in much higher quality for more dynamically captured scenes with only a few shots. The rendered images are provided in the supp. material.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we have focused on accurate surface normals, which is another key factor for the few-shot novel view synthesis. Our proposed FlipNeRF utilizes a set of flipped reflection rays as additional training resources, which are simply derived from the estimated normal vectors and the input ray directions. Since it does not require a heuristic factor to be finetuned delicately for unseen view generation, we are able to exploit these additional training resources with much less burden. Furthermore, with our proposed UE Loss, FlipNeRF reduces the floating artifacts consistently across the different scene structures while",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "considering the output uncertainty, leading to more reliable outputs. Also, our proposed BFC Loss enhances the bottleneck feature consistency between the rays cast on the photo-consistent pixels without leveraging the off-the-shelf feature extractor, leading to performance improvement under the few-shot setting. Our FlipNeRF achieves the SOTA performance with limited input views among the other few-shot baselines and vanilla NeRF-like models. We expect that our work is able to open another meaningful direction for the research of few-shot novel view synthesis.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Limitations and future work. Our FlipNeRF exploits the flipped reflection rays as a set of additional training rays, leading to more accurate surface normal estimation. Although Ref-NeRF achieved promising results with the high-quality surface reconstruction, we use mip-NeRF representation instead of Ref-NeRF for a fair comparison with other methods which are based on mip-NeRF. However, as shown in Tab. 6 and Fig. 6a, Ref-NeRF shows promising results without any additional consideration for few-shot setting compared to the vanilla mip-NeRF. Like our FlipNeRF, the accurate surface normal estimation leads to the competitive performance of Ref-NeRF even in the few-shot scenarios. Therefore, a combination of our FlipNeRF training framework with the Ref-NeRF representation or further exploration with regard to the view-dependent appearance for the few-shot novel view synthesis can be interesting directions for future research.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by NRF (2021R1A2C3006659) and IITP (2021-0-01343) both funded by Korean Government. It was also supported by Samsung Electronics (IO201223-08260-01).",
+        "bbox": [
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+        "type": "page_number",
+        "text": "22891",
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+    {
+        "type": "text",
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+            "[41] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. Advances in Neural Information Processing Systems, 34:4805-4815, 2021.",
+            "[42] Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5752-5761, 2021.",
+            "[43] Alex Yu, Vickie Ye, Matthew Tancik, and Angjoo Kanazawa. pixelnerf: Neural radiance fields from one or few images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4578-4587, 2021.",
+            "[44] Kai Zhang, Fujun Luan, Qianqian Wang, Kavita Bala, and Noah Snavely. Physg: Inverse rendering with spherical gaussians for physics-based material editing and relighting. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5453-5462, 2021.",
+            "[45] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018."
+        ],
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+        ],
+        "page_idx": 10
+    },
+    {
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+        "text": "22893",
+        "bbox": [
+            478,
+            944,
+            517,
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+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/FlipNeRF_ Flipped Reflection Rays for Few-shot Novel View Synthesis/b773a3a0-692f-4508-af4b-b8359e51e763_model.json b/2023/FlipNeRF_ Flipped Reflection Rays for Few-shot Novel View Synthesis/b773a3a0-692f-4508-af4b-b8359e51e763_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..d2f29dd37d99b4969d8fa1765e48b69d6f1e97b6
--- /dev/null
+++ b/2023/FlipNeRF_ Flipped Reflection Rays for Few-shot Novel View Synthesis/b773a3a0-692f-4508-af4b-b8359e51e763_model.json	
@@ -0,0 +1,2290 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.132,
+                0.131,
+                0.84,
+                0.154
+            ],
+            "angle": 0,
+            "content": "FlipNeRF: Flipped Reflection Rays for Few-shot Novel View Synthesis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.287,
+                0.181,
+                0.681,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Seunghyeon Seo Yeonjin Chang Nojun Kwak Seoul National Univeristy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.318,
+                0.223,
+                0.654,
+                0.238
+            ],
+            "angle": 0,
+            "content": "{zzzzlssh, yjean8315, nojunk}@snu.ac.kr"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.273,
+                0.314,
+                0.289
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.304,
+                0.474,
+                0.697
+            ],
+            "angle": 0,
+            "content": "Neural Radiance Field (NeRF) has been a mainstream in novel view synthesis with its remarkable quality of rendered images and simple architecture. Although NeRF has been developed in various directions improving continuously its performance, the necessity of a dense set of multi-view images still exists as a stumbling block to progress for practical application. In this work, we propose FlipNeRF, a novel regularization method for few-shot novel view synthesis by utilizing our proposed flipped reflection rays. The flipped reflection rays are explicitly derived from the input ray directions and estimated normal vectors, and play a role of effective additional training rays while enabling to estimate more accurate surface normals and learn the 3D geometry effectively. Since the surface normal and the scene depth are both derived from the estimated densities along a ray, the accurate surface normal leads to more exact depth estimation, which is a key factor for few-shot novel view synthesis. Furthermore, with our proposed Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss, FlipNeRF is able to estimate more reliable outputs with reducing floating artifacts effectively across the different scene structures, and enhance the feature-level consistency between the pair of the rays cast toward the photo-consistent pixels without any additional feature extractor, respectively. Our FlipNeRF achieves the SOTA performance on the multiple benchmarks across all the scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.725,
+                0.21,
+                0.74
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Neural Radiance Field (NeRF) [24] has achieved great success in rendering photo-realistic images from novel viewpoints. However, the necessity of a dense set of training images remains as a practical bottleneck since it suffers from significant performance degradation when trained with sparse views."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "There are two main streams for few-shot novel view synthesis: pre-training and regularization methods, both of which focus on learning the 3D geometry efficiently from sparse inputs. The pre-training methods [43, 5, 6, 39, 20,"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.267,
+                0.892,
+                0.343
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.622,
+                0.35,
+                0.771,
+                0.364
+            ],
+            "angle": 0,
+            "content": "(a) Sparse training views"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.367,
+                0.892,
+                0.619
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.608,
+                0.624,
+                0.786,
+                0.637
+            ],
+            "angle": 0,
+            "content": "(b) Synthesized unseen views"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.643,
+                0.895,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Figure 1: Synthesis results from sparse inputs. Our Flip-NeRF significantly improves rendering quality compared to other baselines. Compared to the vanilla mip-NeRF [1] and MixNeRF [31], which is the state-of-the-art regularization method, ours reduces the noises and floating artifacts noticeably with superior surface normal estimation. Although Ref-NeRF [36] estimates smooth normal vectors, it shows much inferior rendering results to ours with a large chunk of noise under the few-shot setting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "12, 19, 29, 35, 14] require large-scale datasets consisting of different scenes with multi-view images for injecting prior knowledge during the pre-training, while the regularization methods [25, 31, 15, 11, 30, 8, 17] are optimized per scene, exploiting additional training resources, e.g. unseen viewpoints [25, 15, 17], depth map generation [8, 30], off-the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22883"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.272
+            ],
+            "angle": 0,
+            "content": "shelf models [11, 25], and so on, for an effective regularization to alleviate overfitting. Although the prior arts achieved promising results in novel view synthesis from sparse inputs, there still exist hurdles to overcome. The large-scale datasets, which are used for pre-training methods, are expensive to collect and the NeRF model is prone to performance degradation for the out-of-distribution dataset. On the other hand, the regularization methods heavily rely on additional training resources which might not always be available and require many heuristic factors, e.g. the choice of off-the-shelf models, the hyperparameters for sampling unseen viewpoints, and so on."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.274,
+                0.473,
+                0.515
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose FlipNeRF, which is an effective regularization method exploiting the flipped reflection rays<sup>1</sup> as additional training resources with filtering the ineffective newly generated rays. We derive a batch of flipped reflection rays from the original ray directions and estimated surface normals so that they are cast toward the same target pixels of the original input ray. Compared to the existing regularization methods which have mainly focused on the accurate depth estimation from limited input views [31, 25, 15, 30, 8], our FlipNeRF is trained to reconstruct surface normals accurately by learning to generate effective reflection rays to be used in training. Since both estimated surface normals and depths are derived from the volume densities representing underlying 3D geometry, accurately estimating the surface normals of an object naturally leads to more accurate depth maps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.516,
+                0.473,
+                0.697
+            ],
+            "angle": 0,
+            "content": "Furthermore, we propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), to reduce the floating artifacts effectively while considering the uncertainty of the model's outputs by using the estimated scale parameters for mixture models. Since our FlipNeRF is built upon MixNeRF [31], which is a regularization method achieving promising results by modeling input rays with mixture density models [2], we are able to apply our proposed loss without any modification of the architecture by using the estimated scale parameters of each sample along a ray, which stand for the uncertainty of the samples' estimated probability density distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.697,
+                0.473,
+                0.834
+            ],
+            "angle": 0,
+            "content": "Additionally, inspired by [6, 11, 15] which address the feature-level consistency of targets under the sparse input setting, we encourage the consistency for the pairs of bottleneck features between the original input rays and flipped reflection rays. We leverage a Jensen-Shannon Divergence, which is based on the similarity between the probability distributions, to make the pairs of bottleneck feature distributions of original and flipped reflection rays more similar to each other improving feature consistency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.834,
+                0.472,
+                0.864
+            ],
+            "angle": 0,
+            "content": "We demonstrate the effectiveness of our proposed FlipNeRF through the experiments on the multiple bench"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.894,
+                0.197
+            ],
+            "angle": 0,
+            "content": "marks, e.g. Realistic Synthetic \\(360^{\\circ}\\) [24], DTU [13], and LLFF [23]. Our method achieves state-of-the-art (SOTA) performances compared to other baselines. Especially, ours outperforms other baselines by a large margin with more accurate surface normals under the extremely sparse settings such as 3/4-view setting which are the most challenging ones. Our contributions are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.198,
+                0.894,
+                0.288
+            ],
+            "angle": 0,
+            "content": "- We propose an effective training framework for NeRF with sparse training views, called FlipNeRF. It leverages flipped reflection rays to provide additional training resources, resulting in more precise surface normals with our proposed masking strategy to filter the ineffective rays."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.289,
+                0.894,
+                0.348
+            ],
+            "angle": 0,
+            "content": "- We also propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), which reduces floating artifacts with considering the uncertainty of outputs, leading to more reliable estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.349,
+                0.894,
+                0.424
+            ],
+            "angle": 0,
+            "content": "- We enhance the consistency of bottleneck features between the original input rays and flipped reflection rays by Jensen-Shannon Divergence, coined as Bottleneck Feature Consistency Loss (BFC Loss), improving the robustness for rendering from unseen viewpoints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.424,
+                0.894,
+                0.484
+            ],
+            "angle": 0,
+            "content": "- Our FlipNeRF achieves SOTA performance over the multiple benchmarks. Especially, ours outperforms other baselines by a large margin in more challenging scenarios, e.g. 3/4-view."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.501,
+                0.198,
+                0.894,
+                0.484
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.5,
+                0.651,
+                0.516
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.525,
+                0.712,
+                0.54
+            ],
+            "angle": 0,
+            "content": "2.1. Neural Radiance Field"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.549,
+                0.895,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Recently, Neural Radiance Field (NeRF) [24] has shown impressive performance and potential in the novel view synthesis task. NeRF represents a scene with an MLP, mapping coordinates and viewing directions to its colors and volume density, and then creates a novel view through volume rendering. Subsequent studies have developed NeRF in several directions, e.g. using conical frustums instead of rays [1], reparameterizing an input viewing direction as its reflection direction [36], and so on. These works have made significant progress by addressing the various issues in novel view synthesis, but there still exists a limitation in that NeRF requires a dense set of training images and a lengthy training time. Many studies have addressed these issues [10, 28, 5], including the utilization of various data structures for faster training and inference [9, 42] and attempts to train NeRF with only a few training images. Our work focuses on enhancing the performance of NeRF when a sparse set of views are provided as training images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.832,
+                0.779,
+                0.848
+            ],
+            "angle": 0,
+            "content": "2.2. Few-Shot Novel View Synthesis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.856,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "There are two main approaches for a few-shot novel view synthesis: the pre-training and the regularization method. The pre-training methods require a large dataset of multi-"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.472,
+                0.901
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>The term 'flipped' is used because the reflected ray has an opposite direction (from an object to a camera)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22884"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.128,
+                0.089,
+                0.845,
+                0.212
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.223,
+                0.895,
+                0.27
+            ],
+            "angle": 0,
+            "content": "Figure 2: Overall framework of FlipNeRF. Our FlipNeRF utilize the newly generated flipped reflection rays with our proposed UE Loss and BFC Loss as well as existing MSE, NLL and Orientation losses. See Sec. 3 and Fig. 3 for more details about generation process of flipped reflection rays and the loss terms."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.285,
+                0.473,
+                0.542
+            ],
+            "angle": 0,
+            "content": "view scenes to provide prior knowledges of 3D geometry to a NeRF model and then optionally finetune on the target scene [5, 6, 12, 19, 29, 35, 39, 43]. On the contrary, the regularization methods [31, 15, 11, 25, 8, 30, 17] are optimized per scene without pre-training process by exploiting additional training resources, e.g. depth maps [8, 30] and semantic consistency [11], as an extra supervision. Among them, [25, 15, 17] adopt an unseen viewpoint sampling strategy to make up for insufficient training views. However, these sampling processes require many hand-designed factors such as the ranges of rotation, translation, jittering, and so on, which can introduce artificial biases. Our work proposes a novel regularization approach to derive a set of flipped reflection rays from estimated surface normals and utilizes these for regularization, which does not require a heuristic factor to be finetuned, resulting in more effective training strategy with limited inputs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.559,
+                0.358,
+                0.573
+            ],
+            "angle": 0,
+            "content": "2.3. Surface Normal Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.584,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "There is a line of research to recover accurate textures and lighting conditions of objects with NeRF [26, 41, 38, 7, 34, 44, 3]. Although these earlier studies successfully reconstruct the high-quality isosurfaces derived from the scene representations, their rendering quality for novel views is still inferior to the NeRF-like models. Meanwhile, Ref-NeRF [36] achieved superior performance with remarkable quality of surface normals compared to the existing NeRF models. Since the normal vectors utilized in NeRF framework are derived from the negative normalized density gradients [34, 3, 36], which represent the underlying geometry of 3D scenes, learning an accurate density distribution along a ray is a key factor for surface normal reconstruction. However, for the few-shot novel view synthesis, the prior works mostly focus on the accurate depth estimation without attention to the surface normals, both of which are derived from the estimated volume densities. In this work, we approach the few-shot novel view synthesis problem with focusing on the surface normals, which is another critical factor for an effective learning of 3D scene geometry. To the best of our knowledge, our work is the first attempt to focus on the sur"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.285,
+                0.881,
+                0.3
+            ],
+            "angle": 0,
+            "content": "face normal estimation for few-shot novel view synthesis."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.313,
+                0.593,
+                0.329
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.338,
+                0.892,
+                0.581
+            ],
+            "angle": 0,
+            "content": "In this work, we propose an effective regularization method for few-shot novel view synthesis with flipped reflection rays. Our FlipNeRF is built upon MixNeRF [31] which leverages a mixture model framework (Sec. 3.1). We derive a batch of flipped reflection rays and cast them toward the identical target pixels as additional training rays (Sec. 3.2). Furthermore, we propose the Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss to alleviate the floating artifacts adaptively based on the uncertainty and enhance the consistency between the bottleneck feature distributions of the original and flipped reflection rays, respectively (Sec. 3.3 and Sec. 3.4). Finally, our FlipNeRF is trained to minimize the MSE and NLL losses as well as the proposed regularization loss terms with their corresponding balancing weights (Sec. 3.5). Fig. 2 shows an overview of our FlipNeRF."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.589,
+                0.642,
+                0.603
+            ],
+            "angle": 0,
+            "content": "3.1. Preliminaries"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.611,
+                0.892,
+                0.702
+            ],
+            "angle": 0,
+            "content": "NeRF. The NeRF [24], which is an MLP-based neural network, represents a 3D scene as a continuous radiance field of RGB color and volume density. For every point sampled along a ray, the 3D coordinates \\(\\mathbf{x} = (x,y,z)\\) and viewing directions \\((\\theta ,\\phi)\\) are mapped to the colors \\(\\mathbf{c} = (r,g,b)\\) and densities \\(\\sigma\\) .."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.611,
+                0.711,
+                0.892,
+                0.731
+            ],
+            "angle": 0,
+            "content": "\\[\nF (\\gamma (\\mathbf {x}), \\gamma (\\hat {\\mathbf {d}})) \\rightarrow (\\mathbf {c}, \\sigma), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.739,
+                0.892,
+                0.785
+            ],
+            "angle": 0,
+            "content": "where \\(F(\\cdot), \\gamma(\\cdot)\\), and \\(\\hat{\\mathbf{d}}\\) indicate an MLP, the positional encoding for the inputs, and the 3D Cartesian unit vector used as an input viewing direction in practice, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.786,
+                0.892,
+                0.861
+            ],
+            "angle": 0,
+            "content": "The volumetric radiance field is rendered by alpha composing the RGB values along an input ray \\(\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}\\) [22], where \\(\\mathbf{o}\\) and \\(\\mathbf{d}\\) denote the camera origin and unnormalized direction vector, i.e. \\(\\mathbf{d} = \\| \\mathbf{d}\\| _2\\cdot \\hat{\\mathbf{d}}\\) respectively. The volume rendering integrals are denoted as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.568,
+                0.869,
+                0.892,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathbf {c}} (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) \\mathbf {c} (\\mathbf {r} (t), \\hat {\\mathbf {d}}) d t, \\tag {2}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22885"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.117,
+                0.099,
+                0.411,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+                0.469
+            ],
+            "angle": 0,
+            "content": "Figure 3: Flipped reflection ray generation. Our FlipNeRF generates the flipped reflection ray \\(\\mathbf{r}'\\) from the estimated normal vector \\(\\hat{\\mathbf{n}}\\) and original input ray direction \\(\\mathbf{d}\\). With our masking strategy, \\(\\mathbf{r}_2'\\) is filtered out since it does not satisfy the photo-consistency condition, i.e. \\(\\theta_{2}\\) is bigger than \\(90^{\\circ}\\). The smaller \\(\\theta\\) is, the more photo-consistent the target pixel is, where the pair of \\(\\mathbf{r}\\) and \\(\\mathbf{r}'\\) are cast."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.481,
+                0.47,
+                0.528
+            ],
+            "angle": 0,
+            "content": "where \\( T(t) = \\exp(-\\int_{t_n}^t \\sigma(s) ds) \\) indicates the degree of transparency. In practice, it is approximated with numerical quadrature [24] by sampling points along a ray."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.528,
+                0.469,
+                0.559
+            ],
+            "angle": 0,
+            "content": "The radiance field is trained to minimize the mean squared error (MSE) between rendered and GT pixels:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.165,
+                0.566,
+                0.47,
+                0.597
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {M S E}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} | | \\hat {\\mathbf {c}} (\\mathbf {r}) - \\mathbf {c} ^ {\\mathrm {G T}} (\\mathbf {r}) | | _ {2} ^ {2}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.606,
+                0.315,
+                0.621
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{R}\\) is denoted as a set of rays."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.638,
+                0.47,
+                0.714
+            ],
+            "angle": 0,
+            "content": "MixNeRF. Built upon mip-NeRF [1], which leveraged a cone tracing method and proposed an integrated positional encoding to address an aliasing problem, MixNeRF [31] estimates the joint probability distribution of color values and models a ray with a mixture of densities:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.175,
+                0.722,
+                0.47,
+                0.763
+            ],
+            "angle": 0,
+            "content": "\\[\np (\\mathbf {c} | \\mathbf {r}) = \\sum_ {i = 1} ^ {M} \\pi_ {i} \\mathcal {F} (\\mathbf {c}; \\mu_ {i} ^ {\\mathbf {c}}, \\beta_ {i}), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.77,
+                0.47,
+                0.862
+            ],
+            "angle": 0,
+            "content": "where \\(M\\) is the number of sampled points, \\(\\mathcal{F}(\\mathbf{c};\\mu_i^{\\mathbf{c}},\\beta_i)\\) denotes the Laplacian distribution of RGB \\(\\mathbf{c}\\) with location parameter \\(\\mu_i^{\\mathbf{c}}\\in \\{\\mu_i^r,\\mu_i^g,\\mu_i^b\\}\\), i.e. estimated RGB values of sample, and scale parameter \\(\\beta_{i}\\in \\{\\beta_{i}^{r},\\beta_{i}^{g},\\beta_{i}^{b}\\}\\). The mixture coefficient \\(\\pi_{i}\\) is derived from the estimated volume density \\(\\sigma_{i}\\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.088,
+                0.869,
+                0.47,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\n\\pi_ {i} = \\frac {w _ {i}}{\\sum_ {m = 1} ^ {M} w _ {m}} = \\frac {T _ {i} (1 - \\exp (- \\sigma_ {i} \\delta_ {i}))}{\\sum_ {m = 1} ^ {M} T _ {m} (1 - \\exp (- \\sigma_ {m} \\delta_ {m}))}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "where \\(w_{i}\\) and \\(\\delta_{i}\\) indicate the alpha blending weight and sample interval, respectively. Thanks to the mixture model's capacity of representing complex distributions, MixNeRF learns the density distribution effectively with sparse inputs by minimizing the negative log-likelihood (NLL) in Eq. 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.168,
+                0.892,
+                0.227
+            ],
+            "angle": 0,
+            "content": "Our FlipNeRF is built upon MixNeRF leveraging the mixture modeling framework while achieving superior rendering quality with noticeably fewer artifacts and more accurate surface normals to MixNeRF."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.236,
+                0.788,
+                0.253
+            ],
+            "angle": 0,
+            "content": "3.2. Auxiliary Flipped Reflection Ray"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.259,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": "As shown in Fig. 3, we exploit a batch of flipped reflection rays \\(\\mathbf{r}' \\in \\mathcal{R}'\\) as extra training resources, which are derived from the original input ray directions \\(\\mathbf{d}\\) and estimated surface normals \\(\\hat{\\mathbf{n}}\\). First, we derive a flipped reflection direction \\(\\mathbf{d}'\\) from \\(\\mathbf{d}\\) and \\(\\hat{\\mathbf{n}}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.625,
+                0.344,
+                0.892,
+                0.361
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {d} ^ {\\prime} = 2 (\\mathbf {d} \\cdot \\hat {\\mathbf {n}}) \\hat {\\mathbf {n}} - \\mathbf {d}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.37,
+                0.892,
+                0.43
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{\\mathbf{n}}\\) denotes the weighted sum of blending weights and estimated normal vectors along a ray, i.e. \\(\\hat{\\mathbf{n}} = \\sum_{i=1}^{M} w_i \\mathbf{n}_i\\). Note that we use the gradient of volume density as estimated surface normals following [3, 34, 36]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.431,
+                0.892,
+                0.567
+            ],
+            "angle": 0,
+            "content": "To generate the additional training rays based on \\(\\mathbf{d}'\\), we need a set of imaginary ray origins \\(\\mathbf{o}'\\) located in a suitable space considering the hitting point and the original input ray origins \\(\\mathbf{o}\\). Since the vanilla NeRF models, which are trained with a dense set of images, tend to have the blending weight distribution whose peak is located on the point around the object surface \\(\\mathbf{p}_s = \\mathbf{o} + t_s\\mathbf{d}\\) [8, 31], i.e. the \\(s\\)-th sample whose blending weight is the highest along a ray. Therefore, we place \\(\\mathbf{o}'\\) so that the \\(s\\)-th sample of \\(\\mathbf{r}'\\) is \\(\\mathbf{p}_s\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.64,
+                0.576,
+                0.891,
+                0.592
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {o} ^ {\\prime} = \\mathbf {p} _ {s} - t _ {s} \\mathbf {d} ^ {\\prime}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.602,
+                0.892,
+                0.768
+            ],
+            "angle": 0,
+            "content": "resulting in our proposed flipped reflection ray, \\(\\mathbf{r}'(t) = \\mathbf{o}' + t\\mathbf{d}'\\). Compared to the previous unseen viewpoint sampling strategies [15, 25, 17], our proposed strategy does not rely on the randomness of unseen viewpoint sampling and reduces the heuristic factors for sampling schemes, e.g. the range of rotation, translation, and so on. Furthermore, since our newly generated \\(\\mathbf{r}'\\) are cast on the identical object surfaces where the original input rays \\(\\mathbf{r}\\) are cast, i.e. the target pixels are photo-consistent for the pair of \\(\\mathbf{r}\\) and \\(\\mathbf{r}'\\) without any sophisticated viewpoint sampling process, we are able to train \\(\\mathbf{r}'\\) effectively with the same GT pixels of \\(\\mathbf{r}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.768,
+                0.892,
+                0.844
+            ],
+            "angle": 0,
+            "content": "However, since \\(\\hat{\\mathbf{n}}\\), which are used to derive \\(\\mathbf{d}'\\), are not the ground truth but the estimation, there exists a concern that even miscreated \\(\\mathbf{r}'\\), which do not satisfy photo-consistency, can be used for training. As a result, it might lead to performance degradation while providing misleading training"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.851,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "\\( {}^{2} \\) Technically, \\( \\widehat{\\mathbf{n}} \\) is not guaranteed to be a unit vector without an explicit normalization process. However, we empirically found that the normalization rather destabilizes the training and leads to the performance degradation. Kindly refer to our supplementary material for related experiments."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.946,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22886"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.122
+            ],
+            "angle": 0,
+            "content": "cues. To address this problem, we mask the ineffective \\(\\mathbf{r}'\\) by considering the angle \\(\\theta\\) between \\(\\hat{\\mathbf{n}}\\) and \\(-\\hat{\\mathbf{d}}\\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.133,
+                0.133,
+                0.47,
+                0.175
+            ],
+            "angle": 0,
+            "content": "\\[\nM \\left(\\mathbf {r} ^ {\\prime}\\right) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\arccos  \\left(- (\\hat {\\mathbf {d}} \\cdot \\hat {\\mathbf {n}})\\right) <   \\tau \\\\ 0 & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.188,
+                0.469,
+                0.295
+            ],
+            "angle": 0,
+            "content": "where \\(-(\\hat{\\mathbf{d}}\\cdot \\hat{\\mathbf{n}})\\) amounts to \\(\\cos \\theta\\) of original input rays and normal vectors, and \\(\\tau\\) indicates the threshold for filtering the invalid rays, which we set as \\(90^{\\circ}\\) unless specified. Through this masking process, only \\(\\mathbf{r}'\\) which are cast toward the photo-consistent point can be remained as we intend. Finally, our proposed flipped reflection rays are modeled by mixture density like the original input rays:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.17,
+                0.306,
+                0.47,
+                0.348
+            ],
+            "angle": 0,
+            "content": "\\[\np \\left(\\mathbf {c} \\mid \\mathbf {r} ^ {\\prime}\\right) = \\sum_ {i = 1} ^ {M} \\pi_ {i} ^ {\\prime} \\mathcal {F} \\left(\\mathbf {c}; \\mu_ {i} ^ {\\mathbf {c} ^ {\\prime}}, \\beta_ {i} ^ {\\prime}\\right). \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.359,
+                0.469,
+                0.405
+            ],
+            "angle": 0,
+            "content": "Additionally, we leverage the Orientation Loss proposed in Ref-NeRF [36] to penalize the backward-facing normal vectors for learning accurate surface normals:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.16,
+                0.417,
+                0.469,
+                0.457
+            ],
+            "angle": 0,
+            "content": "\\[\nl _ {\\text {O r i .}} (\\mathbf {r}) = \\sum_ {i = 1} ^ {M} w _ {i} \\max  (0, \\mathbf {n} _ {i} \\cdot \\hat {\\mathbf {d}}) ^ {2}. \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.469,
+                0.469,
+                0.498
+            ],
+            "angle": 0,
+            "content": "Unlike Ref-NeRF, we penalize underlying density gradient normal \\(\\mathbf{n}_i\\) instead of predicted normals."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.5,
+                0.469,
+                0.591
+            ],
+            "angle": 0,
+            "content": "Note that our FlipNeRF is fundamentally different compared to Ref-NeRF since ours generates additional training rays through the derivation of reflection direction without modification to original representations while Ref-NeRF replaced the input viewing direction with its reflection direction, reparameterizing the outgoing radiance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.601,
+                0.377,
+                0.618
+            ],
+            "angle": 0,
+            "content": "3.3. Uncertainty-aware Regularization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.624,
+                0.469,
+                0.701
+            ],
+            "angle": 0,
+            "content": "Several regularization techniques have been proposed to reduce the floating artifacts present in synthesized images, which is one of the major problems of NeRF. Among them, we leverage the Emptiness Loss [37] which penalizes the small blending weights along a ray as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.156,
+                0.712,
+                0.469,
+                0.754
+            ],
+            "angle": 0,
+            "content": "\\[\nl _ {\\text {E m p .}} (\\mathbf {r}) = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\log (1 + \\eta \\cdot w _ {i}), \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.469,
+                0.794
+            ],
+            "angle": 0,
+            "content": "where the bigger \\(\\eta\\) is, the steeper the loss function becomes around 0."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "However, the naive application of existing regularization techniques with limited training views might not be consistently helpful across the different scenes due to the scene-by-scene different structure, resulting in overall performance degradation. To address this problem, we propose Uncertainty-aware Emptiness Loss (UE Loss) developed upon the Emptiness Loss, which reduces the floating"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.89,
+                0.122
+            ],
+            "angle": 0,
+            "content": "artifacts consistently over the different scenes by considering the output uncertainty:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.574,
+                0.137,
+                0.89,
+                0.187
+            ],
+            "angle": 0,
+            "content": "\\[\nl _ {\\mathrm {U E}} (\\mathbf {r}) = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\log (1 + \\rho \\cdot \\eta \\cdot w _ {i}), \\tag {12}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.623,
+                0.182,
+                0.816,
+                0.224
+            ],
+            "angle": 0,
+            "content": "\\[\n\\text {w h e r e} \\quad \\rho = \\frac {1}{3} \\sum_ {c} ^ {\\{r, g, b \\}} \\sum_ {i = 1} ^ {M} \\beta_ {i} ^ {c}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.239,
+                0.892,
+                0.375
+            ],
+            "angle": 0,
+            "content": "\\(\\rho\\) amounts to the average of the summation of estimated scale parameters of RGB color distributions from all samples along a ray, which we use as the uncertainty of a ray. By our proposed UE Loss, we are able to regularize the blending weights adaptively, i.e. the more uncertain a ray is, the more penalized the blending weights along the ray are. It is able to reduce floating artifacts consistently across the scenes with different structures and enables to synthesize more reliable outputs by considering uncertainty."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.39,
+                0.779,
+                0.406
+            ],
+            "angle": 0,
+            "content": "3.4. Bottleneck Feature Consistency"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.415,
+                0.892,
+                0.506
+            ],
+            "angle": 0,
+            "content": "Motivated by previous works addressing the feature-level consistency of multiple views for few-shot novel view synthesis [6, 11, 15], we encourage the consistency of bottleneck feature distributions between \\(\\mathbf{r}\\) and \\(\\mathbf{r}'\\), which are intermediate feature vectors, i.e. outputs of the spatial MLP of NeRF, by Jensen-Shannon Divergence (JSD):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.521,
+                0.89,
+                0.539
+            ],
+            "angle": 0,
+            "content": "\\[\nl _ {\\mathrm {B F C}} \\left(\\mathbf {r}, \\mathbf {r} ^ {\\prime}\\right) = J S D \\left(\\psi (\\mathbf {b}), \\psi \\left(\\mathbf {b} ^ {\\prime}\\right)\\right), \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.553,
+                0.892,
+                0.659
+            ],
+            "angle": 0,
+            "content": "where \\(\\psi (\\cdot)\\), \\(\\mathbf{b}\\) and \\(\\mathbf{b}^{\\prime}\\) denote the softmax function, the bottleneck features of \\(\\mathbf{r}\\) and \\(\\mathbf{r}^{\\prime}\\), respectively. While the existing methods [6, 11] rely on off-the-shelf feature extractors like 2D CNN or CLIP [27] to address high-level feature consistency, we regulate the pair of features effectively by enhancing consistency between bottleneck features without depending on additional feature extractors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.675,
+                0.616,
+                0.689
+            ],
+            "angle": 0,
+            "content": "3.5. Total Loss"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.7,
+                0.892,
+                0.791
+            ],
+            "angle": 0,
+            "content": "Our FlipNeRF is not only trained to maximize the log-likelihood of the target pixel \\(\\mathbf{c}_{\\mathrm{GT}}\\) for a set of original input rays \\(\\mathcal{R}\\), but also for flipped reflection rays \\(\\mathcal{R}_M^\\prime\\), where the ineffective rays are excluded from the total flipped reflection rays \\(\\mathcal{R}^\\prime\\) by our masking strategy in Eq. 8. Likewise, the UE Losses are applied for both \\(\\mathcal{R}\\) and \\(\\mathcal{R}_M^\\prime\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.793,
+                0.89,
+                0.808
+            ],
+            "angle": 0,
+            "content": "Aggregating all, our total loss over a batch is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.527,
+                0.836,
+                0.89,
+                0.871
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {T o t a l}} = \\mathcal {L} _ {\\text {M S E}} + \\lambda_ {1} \\mathcal {L} _ {\\text {N L L}} + \\lambda_ {2} \\mathcal {L} _ {\\text {N L L}} ^ {\\prime} \\tag {14} \\\\ + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {U E}} + \\lambda_ {4} \\mathcal {L} _ {\\mathrm {U E}} ^ {\\prime} + \\lambda_ {5} \\mathcal {L} _ {\\mathrm {B F C}} + \\lambda_ {6} \\mathcal {L} _ {\\mathrm {O r i}}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.886,
+                0.89,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where a set of \\(\\lambda\\)'s are balancing weight terms for the losses."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22887"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.09,
+                0.468,
+                0.162
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>τ</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>30°</td><td>18.62</td><td>0.747</td><td>0.206</td><td>0.121</td></tr><tr><td>60°</td><td>18.12</td><td>0.723</td><td>0.237</td><td>0.126</td></tr><tr><td>90°</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr><tr><td>180° (No masking)</td><td>18.76</td><td>0.755</td><td>0.190</td><td>0.111</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.168,
+                0.47,
+                0.214
+            ],
+            "angle": 0,
+            "content": "Table 1: Comparison of masking conditions. Our masking strategy with \\(\\tau\\) of \\(90^{\\circ}\\) achieves the best results, filtering out the ineffective flipped reflection rays successfully."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.224,
+                0.268,
+                0.324
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.1,
+                0.326,
+                0.251,
+                0.34
+            ],
+            "angle": 0,
+            "content": "(a) Effective \\(\\mathbf{r}'\\) ratio by \\(\\tau\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.284,
+                0.222,
+                0.45,
+                0.326
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.308,
+                0.327,
+                0.429,
+                0.339
+            ],
+            "angle": 0,
+            "content": "(b) Distribution of \\(\\theta\\)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.125,
+                0.345,
+                0.421,
+                0.361
+            ],
+            "angle": 0,
+            "content": "Figure 4: Analysis of the masking strategy."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.373,
+                0.209,
+                0.39
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.399,
+                0.284,
+                0.417
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.424,
+                0.47,
+                0.665
+            ],
+            "angle": 0,
+            "content": "Implementation details. Our FlipNeRF is built upon MixNeRF [31] based on the JAX codebase [4], which is developed upon mip-NeRF [1]. The overall training scheme follows [25, 31]. We adopt a scene space annealing strategy for the early training phase. Also, we apply the exponential decay and warm up for the learning rate. The Adam optimizer [16] and the gradient clippings by value at 0.1 and norm at 0.1 are used. We train our FlipNeRF for 500 pixel epochs with a batch size of 4,096 on 4 NVIDIA RTX 3090. Additionally, since the LLFF dataset [23] consists of scenes with much more static movement of viewpoints compared to other datasets, we set the threshold \\((\\tau)\\) of our masking strategy as \\(30^{\\circ}\\) for the experiments on LLFF. More detailed hyperparameters and our loss balancing terms by the datasets and the number of training views are provided in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets and metrics. We evaluate the performance of our FlipNeRF and baselines on the representative benchmarks: Realistic Synthetic \\(360^{\\circ}\\) [24], DTU [13], and LLFF [23]. Realistic Synthetic \\(360^{\\circ}\\) contains 8 synthetic scenes, each consisting of 400 multi-view rendered images with white background. To compare against other representative baselines [15, 11, 31, 25, 1], we evaluate our FlipNeRF under the scenarios of 4 and 8 views. For a fair comparison, we sample the first \\(n\\)-image of the training set for the \\(n\\)-view scenario so that the identical images are provided for training different methods following [31]. We use 200 images of the test set for evaluation. For DTU, which provide various scenes including objects put on a white table with a black background, we conduct experiments on the 15"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.272
+            ],
+            "angle": 0,
+            "content": "specific scenes under the scenarios of 3, 6, and 9-view, following the experimental protocol of [43]. We also conduct a series of experiments for the analysis of FlipNeRF under 3-view setting as well as comparison against other baselines. Additionally, we compare our FlipNeRF against other baselines on LLFF consisting of real forward-facing scenes, which is often tested as an out-of-distribution dataset for pre-training methods. Following [24], every 8th image of each scene is used for a held-out test set and the training views are evenly selected from the remaining images. Like DTU, we report our results of the 3, 6, and 9-view scenarios, following [43]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.273,
+                0.892,
+                0.469
+            ],
+            "angle": 0,
+            "content": "For the quantitative evaluation for rendered images, we adopt the mean of PSNR, SSIM [40], LPIPS [45], and the geometric average [1]. Furthermore, we also adopt the mean angular error \\((\\mathrm{MAE}^{\\circ})\\) [36] and NLL [33, 32, 21, 18] for evaluating the surface normals and uncertainty, respectively. Specifically, following [33], we compute the NLL by deriving the probability of the GT pixel values given a Gaussian distribution with the estimated RGB values as mean and the uncertainty as variance, which is derived from the weighted sum of the blending weights and estimated scale parameters along a ray in our FlipNeRF. For DTU, we report the results evaluated by masked metrics to prevent background bias, following [25, 31]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.489,
+                0.892,
+                0.732
+            ],
+            "angle": 0,
+            "content": "Baselines. We compare our FlipNeRF against the SOTA regularization methods [11, 15, 25, 31] on Realistic Synthetic \\(360^{\\circ}\\) as well as the vanilla mip-NeRF [1] and Ref-NeRF [36], which is known for achieving promising results with accurate surface normals. Furthermore, we compare ours against the representative pre-training methods [5, 6, 43] as well as regularization methods on DTU and LLFF. The pre-training baselines exploit the DTU and LLFF as pre-training dataset and out-of-distribution test set, respectively, while the regularization methods, mip-NeRF and Ref-NeRF are optimized per scene. Note that we report the quantitative results of other baselines on DTU and LLFF from [25], which achieved better results than its original papers by the modified training scheme, and those on Realistic Synthetic \\(360^{\\circ}\\) from [31], which trained the baselines with the identical training views for a fair comparison."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.741,
+                0.702,
+                0.758
+            ],
+            "angle": 0,
+            "content": "4.2. Analysis of FlipNeRF"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Analysis of flipped reflection rays. As shown in Tab. 1, our masking strategy of filtering out the ineffective flipped reflection rays with the threshold \\((\\tau)\\) of \\(90^{\\circ}\\) achieves the best performance among different options. With \\(\\tau\\) of \\(30^{\\circ}\\) and \\(60^{\\circ}\\), the rendering quality is rather degraded since the newly generated rays are overly-filtered and do not provide enough additional supervision as demonstrated in Fig. 4a. On the other hand, when we exploit all the flipped reflection rays without masking, there exists a little improvement"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22888"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.472,
+                0.173
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average ↓</td><td>NLL ↓</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>0.744</td><td>0.203</td><td>0.113</td><td>9.99</td></tr><tr><td>FlipNeRF (Ours)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>w/o LEmp. or LUE</td><td>19.30</td><td>0.758</td><td>0.196</td><td>0.108</td><td>4.88</td></tr><tr><td>w/ LEmptiness</td><td>18.62</td><td>0.749</td><td>0.204</td><td>0.118</td><td>4.92</td></tr><tr><td>w/ LUE</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td><td>2.56</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.178,
+                0.47,
+                0.224
+            ],
+            "angle": 0,
+            "content": "Table 2: Effectiveness of \\(\\mathcal{L}_{\\mathrm{UE}}\\). Our proposed \\(\\mathcal{L}_{\\mathrm{UE}}\\) improves the rendering quality consistently across the scenes with considering the uncertainty."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.233,
+                0.468,
+                0.363
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.369,
+                0.47,
+                0.476
+            ],
+            "angle": 0,
+            "content": "Figure 5: Comparison of FlipNeRF and MixNeRF. Our FlipNeRF renders the images from novel views with much fewer artifacts and more accurate depth maps than MixNeRF. Considering the standard deviation of RGB and depths, our FlipNeRF is able to estimate more reliable outputs than MixNeRF. For the std. map, the darker the pixel is, the more certain the output is."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.503,
+                0.47,
+                0.716
+            ],
+            "angle": 0,
+            "content": "of performance compared to \\(30^{\\circ}\\) and \\(60^{\\circ}\\) masking, but it is still much inferior to \\(90^{\\circ}\\) due to the negative impact from the ineffective rays. Additionally, Fig. 4b shows the distribution of \\(\\theta\\), i.e. angles between the input viewing directions and normal vectors. As the smaller \\(\\theta\\) is, the more photo-consistent the target pixel is, i.e. the more effective the newly generated flipped reflection rays are for training. Since our FlipNeRF is trained to estimate the accurate normal vectors, we are able to exploit a set of more effective flipped reflection rays through the training, which are cast on the more photo-consistent target pixels. Furthermore, at the initial training phase, the invalid additional rays are filtered effectively by our masking strategy, leading to high-quality supervision and stabilizing the training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Uncertainty-aware regularization. Tab. 2 shows the effectiveness of our proposed UE Loss. Compared to MixNeRF [31] which models a ray with mixture of distributions as our FlipNeRF, ours consistently achieves more reliable rendering results with much lower NLL. Without \\(\\mathcal{L}_{\\mathrm{Emp}}\\), [37] or our proposed \\(\\mathcal{L}_{\\mathrm{UE}}\\), ours already outperforms MixNeRF by a large margin. However, ours with naively leveraged \\(\\mathcal{L}_{\\mathrm{Emp}}\\) rather shows inferior results to MixNeRF. It shows that naive application of the existing regularization technique for reducing artifacts under the few-shot setting can lead to overall performance degradation due to the scene"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.89,
+                0.193
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>w/o LBCF</td><td>18.79</td><td>0.755</td><td>0.200</td><td>0.115</td></tr><tr><td>w/ LBCF</td><td></td><td></td><td></td><td></td></tr><tr><td>MSE on b</td><td>18.83</td><td>0.755</td><td>0.197</td><td>0.113</td></tr><tr><td>Cos. Sim. on b</td><td>18.77</td><td>0.755</td><td>0.193</td><td>0.115</td></tr><tr><td>JSD on bhat</td><td>18.43</td><td>0.749</td><td>0.204</td><td>0.120</td></tr><tr><td>JSD on b</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.198,
+                0.892,
+                0.245
+            ],
+            "angle": 0,
+            "content": "Table 3: Comparison of different strategies for \\(\\mathcal{L}_{\\mathrm{BFC}}\\). Our \\(\\mathcal{L}_{\\mathrm{BFC}}\\) achieves a significant performance gain compared to other regularization schemes for feature consistency."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.258,
+                0.89,
+                0.35
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>\\( \\mathcal{L}_{\\text{NLL}} \\)</td><td>\\( \\mathcal{L}_{\\text{NLL}}^{\\prime} \\)</td><td>\\( \\mathcal{L}_{\\text{UE}}^\\dagger \\)</td><td>\\( \\mathcal{L}_{\\text{BFC}} \\)</td><td>\\( \\mathcal{L}_{\\text{Ori.}} \\)</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average ↓</td></tr><tr><td>(1)</td><td>✓</td><td></td><td></td><td></td><td></td><td>17.44</td><td>0.729</td><td>0.187</td><td>0.130</td></tr><tr><td>(2)</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>16.94</td><td>0.727</td><td>0.217</td><td>0.143</td></tr><tr><td>(3)</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>17.89</td><td>0.736</td><td>0.206</td><td>0.130</td></tr><tr><td>(4)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>19.01</td><td>0.755</td><td>0.181</td><td>0.107</td></tr><tr><td>(5)</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>18.79</td><td>0.755</td><td>0.200</td><td>0.115</td></tr><tr><td>(6)</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>19.30</td><td>0.758</td><td>0.196</td><td>0.108</td></tr><tr><td>(7)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.355,
+                0.892,
+                0.386
+            ],
+            "angle": 0,
+            "content": "Table 4: Ablation study. \\(\\dagger\\) indicate that the losses are applied to both \\(\\mathbf{r}\\) and \\(\\mathbf{r}'\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.42,
+                0.892,
+                0.48
+            ],
+            "angle": 0,
+            "content": "by-scene various structures. As illustrated in Fig. 5, with our proposed \\(\\mathcal{L}_{\\mathrm{UE}}\\), ours improves both of the rendering quality and the reliability of the model outputs by a large margin compared to MixNeRF."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.519,
+                0.892,
+                0.673
+            ],
+            "angle": 0,
+            "content": "Bottleneck feature consistency. As shown in Tab. 3, there is no significant impact on the performance with regularizing the bottleneck feature \\(\\mathbf{b}\\) using MSE or cosine similarity. By our proposed \\(\\mathcal{L}_{\\mathrm{BFC}}\\) with JSD, we achieve a considerable performance improvement. Interestingly, the performance rather degrades when we apply \\(\\mathcal{L}_{\\mathrm{BFC}}\\) with JSD to \\(\\mathbf{b}_{\\hat{\\mathbf{d}}}\\), i.e. the bottleneck feature conditioned with input viewing direction \\(\\hat{\\mathbf{d}}\\). We conjecture that the reduced feature dimension of \\(\\mathbf{b}_{\\hat{\\mathbf{d}}}\\) reduces the capacity of feature representations and prevents the model from improving robustness."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.693,
+                0.655,
+                0.71
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The quantitative results of our ablation study are reported in Tab. 4. With only additionally exploiting our proposed flipped reflection rays, our FlipNeRF achieves more degenerate results compared to the baseline \\(((1) \\rightarrow (2))\\). However, we are able to achieve performance improvement by a large margin with our proposed \\(\\mathcal{L}_{\\mathrm{UE}}\\) and \\(\\mathcal{L}_{\\mathrm{BFC}}\\) \\(((2) \\rightarrow (3) \\rightarrow (4))\\). \\((5) \\rightarrow (7)\\) shows that enhancing the consistency of bottleneck features between the pair of original and flipped reflection rays is considerably effective. Additionally, by leveraging \\(\\mathcal{L}_{\\mathrm{Ori}}\\), from Ref-NeRF, we are able to estimate more accurate normal vectors, leading to more effective flipped reflection rays and performance gain \\(((4) \\rightarrow (7))\\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22889"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.12,
+                0.089,
+                0.849,
+                0.234
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">PSNR ↑</td><td colspan=\"2\">SSIM ↑</td><td colspan=\"2\">LPIPS ↓</td><td colspan=\"2\">Average Err. ↓</td><td colspan=\"2\">MAE° ↓</td></tr><tr><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td></tr><tr><td>mip-NeRF [1]</td><td>14.12</td><td>18.74</td><td>0.722</td><td>0.828</td><td>0.382</td><td>0.238</td><td>0.221</td><td>0.121</td><td>96.05</td><td>101.21</td></tr><tr><td>Ref-NeRF [36]</td><td>18.09</td><td>24.00</td><td>0.764</td><td>0.879</td><td>0.269</td><td>0.106</td><td>0.150</td><td>0.058</td><td>65.62</td><td>57.93</td></tr><tr><td>DietNeRF [11]</td><td>15.42</td><td>21.31</td><td>0.730</td><td>0.847</td><td>0.314</td><td>0.153</td><td>0.201</td><td>0.086</td><td>-</td><td>-</td></tr><tr><td>InfoNeRF [15]</td><td>18.44</td><td>22.01</td><td>0.792</td><td>0.852</td><td>0.223</td><td>0.133</td><td>0.119</td><td>0.073</td><td>-</td><td>-</td></tr><tr><td>RegNeRF [25]</td><td>13.71</td><td>19.11</td><td>0.786</td><td>0.841</td><td>0.346</td><td>0.200</td><td>0.210</td><td>0.122</td><td>62.78</td><td>60.37</td></tr><tr><td>MixNeRF [31]</td><td>18.99</td><td>23.84</td><td>0.807</td><td>0.878</td><td>0.199</td><td>0.103</td><td>0.113</td><td>0.060</td><td>70.90</td><td>62.04</td></tr><tr><td>FlipNeRF (Ours)</td><td>20.60</td><td>24.38</td><td>0.822</td><td>0.883</td><td>0.159</td><td>0.095</td><td>0.091</td><td>0.055</td><td>58.72</td><td>57.17</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.238,
+                0.892,
+                0.268
+            ],
+            "angle": 0,
+            "content": "Table 5: Quantitative results on Realistic Synthetic \\( {360}^{ \\circ  } \\) . Our FlipNeRF achieves the SOTA performance among other baselines across all the scenarios and metrics."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.099,
+                0.275,
+                0.872,
+                0.506
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">PSNR ↑ 6-view</td><td rowspan=\"2\">9-view</td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">SSIM ↑ 6-view</td><td rowspan=\"2\">9-view</td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">LPIPS ↓ 6-view</td><td rowspan=\"2\">9-view</td><td colspan=\"3\">Average Error ↓</td></tr><tr><td>3-view</td><td>6-view</td><td>9-view</td></tr><tr><td>mip-NeRF [1]</td><td>8.68</td><td>16.54</td><td>23.58</td><td>0.571</td><td>0.741</td><td>0.879</td><td>0.353</td><td>0.198</td><td>0.092</td><td>0.323</td><td>0.148</td><td>0.056</td></tr><tr><td colspan=\"13\">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>16.82</td><td>19.11</td><td>20.40</td><td>0.695</td><td>0.745</td><td>0.768</td><td>0.270</td><td>0.232</td><td>0.220</td><td>0.147</td><td>0.115</td><td>0.100</td></tr><tr><td>PixelNeRF†[43]</td><td>18.95</td><td>20.56</td><td>21.83</td><td>0.710</td><td>0.753</td><td>0.781</td><td>0.269</td><td>0.223</td><td>0.203</td><td>0.125</td><td>0.104</td><td>0.090</td></tr><tr><td>SRF [6]</td><td>15.32</td><td>17.54</td><td>18.35</td><td>0.671</td><td>0.730</td><td>0.752</td><td>0.304</td><td>0.250</td><td>0.232</td><td>0.171</td><td>0.132</td><td>0.120</td></tr><tr><td>SRF†[6]</td><td>15.68</td><td>18.87</td><td>20.75</td><td>0.698</td><td>0.757</td><td>0.785</td><td>0.281</td><td>0.225</td><td>0.205</td><td>0.162</td><td>0.114</td><td>0.093</td></tr><tr><td>MVSNeRF [5]</td><td>18.63</td><td>20.70</td><td>22.40</td><td>0.769</td><td>0.823</td><td>0.853</td><td>0.197</td><td>0.156</td><td>0.135</td><td>0.113</td><td>0.088</td><td>0.068</td></tr><tr><td>MVSNeRF†[5]</td><td>18.54</td><td>20.49</td><td>22.22</td><td>0.769</td><td>0.822</td><td>0.853</td><td>0.197</td><td>0.155</td><td>0.135</td><td>0.113</td><td>0.089</td><td>0.069</td></tr><tr><td colspan=\"13\">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>11.85</td><td>20.63</td><td>23.83</td><td>0.633</td><td>0.778</td><td>0.823</td><td>0.314</td><td>0.201</td><td>0.173</td><td>0.243</td><td>0.101</td><td>0.068</td></tr><tr><td>RegNeRF [25]</td><td>18.89</td><td>22.20</td><td>24.93</td><td>0.745</td><td>0.841</td><td>0.884</td><td>0.190</td><td>0.117</td><td>0.089</td><td>0.112</td><td>0.071</td><td>0.047</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>22.30</td><td>25.03</td><td>0.744</td><td>0.835</td><td>0.879</td><td>0.203</td><td>0.102</td><td>0.065</td><td>0.113</td><td>0.066</td><td>0.042</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.55</td><td>22.45</td><td>25.12</td><td>0.767</td><td>0.839</td><td>0.882</td><td>0.180</td><td>0.098</td><td>0.062</td><td>0.101</td><td>0.064</td><td>0.041</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.51,
+                0.893,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Table 6: Comparison with baselines on DTU. Our FlipNeRF outperforms all the pre-training and regularization methods in every scenario, especially by a large margin under the 3-view setting. \\(\\dagger\\) indicates fine-tuning."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
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+            "angle": 0,
+            "content": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>mip-NeRF [1]</td><td>14.62</td><td>0.351</td><td>0.495</td><td>0.246</td></tr><tr><td colspan=\"5\">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>7.93</td><td>0.272</td><td>0.682</td><td>0.461</td></tr><tr><td>PixelNeRF† [43]</td><td>16.17</td><td>0.438</td><td>0.512</td><td>0.217</td></tr><tr><td>SRF [6]</td><td>12.34</td><td>0.250</td><td>0.591</td><td>0.313</td></tr><tr><td>SRF† [6]</td><td>17.07</td><td>0.436</td><td>0.529</td><td>0.203</td></tr><tr><td>MVSNeRF [5]</td><td>17.25</td><td>0.557</td><td>0.356</td><td>0.171</td></tr><tr><td>MVSNeRF† [5]</td><td>17.88</td><td>0.584</td><td>0.327</td><td>0.157</td></tr><tr><td colspan=\"5\">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>14.94</td><td>0.370</td><td>0.496</td><td>0.240</td></tr><tr><td>RegNeRF [25]</td><td>19.08</td><td>0.587</td><td>0.336</td><td>0.146</td></tr><tr><td>MixNeRF [31]</td><td>19.27</td><td>0.629</td><td>0.236</td><td>0.124</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.34</td><td>0.631</td><td>0.235</td><td>0.123</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Table 7: Comparison with baselines on LLFF 3-view. † indicates fine-tuning."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4.4. Comparison with other SOTA Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Realistic Synthetic \\(360^{\\circ}\\). As demonstrated in Tab. 5, our FlipNeRF achieves the SOTA performance across all the evaluation metrics. Compared to MixNeRF which leverages a mixture model framework as ours, our FlipNeRF"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.56,
+                0.892,
+                0.758
+            ],
+            "angle": 0,
+            "content": "improves the performance by a large margin. Noticeably, our FlipNeRF estimates more accurate surface normals than other baselines, leading to the performance gain with better reconstructed fine details from limited input views as shown in Fig. 6a. Additionally, the vanilla Ref-NeRF, which shows great performance with accurate normal vectors, achieves comparable or even better performance than other regularization methods except ours. From this result, we are able to expect that estimating the accurate surface normals is one of the key factors for learning 3D geometry with sparse inputs. Note that the comparable \\(\\mathrm{MAE}^{\\circ}\\) of RegNeRF results from the overly-smoothed depth estimation, not indicating the high-quality of rendering results, as shown in Fig. 6a."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "DTU. Our FlipNeRF achieves the best results across all the scenarios and most of the evaluation metrics on DTU as shown in Tab. 6. Remarkably, ours trained with 6-view outperforms all the pre-training methods trained with 9-view in every metric except SSIM. Furthermore, ours trained with 3-view still outperforms PixelNeRF [43] and SRF [6] trained with 6-view. Similar to the results on Realistic Synthetic \\(360^{\\circ}\\), ours outperforms other baselines by a large"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "22890"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.09,
+                0.861,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.223,
+                0.861,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.098,
+                0.332,
+                0.87,
+                0.349
+            ],
+            "angle": 0,
+            "content": "Figure 6: Qualitative results on Realistic Synthetic \\(360^{\\circ}\\) and DTU. More results are provided in the supp. material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.361,
+                0.473,
+                0.455
+            ],
+            "angle": 0,
+            "content": "margin especially under the 3-view, which is the most challenging scenario, with reducing the floating artifacts successfully as shown in Fig. 6b. Since the flipped reflection rays are effective training resources for unseen views, the fewer the training views are provided, the more performance gain is expected."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.469,
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+            ],
+            "angle": 0,
+            "content": "LLFF. Table 7 compares our FlipNeRF against other baselines on LLFF, which is a real forward-facing dataset. Although ours achieves the SOTA performance among other baselines, it is much more marginal than those on Realistic Synthetic \\(360^{\\circ}\\) and DTU. We conjecture the reason for the marginal improvement of our proposed method can be the fact that a set of flipped reflection rays, which are able to widely cover the unseen views, are not very useful for the scenes in LLFF, where a set of camera poses are much less dynamic than other datasets. In other words, our FlipNeRF is able to not only achieve a competitive performance for the scenes consisting of a set of simple camera poses, but also render the novel views in much higher quality for more dynamically captured scenes with only a few shots. The rendered images are provided in the supp. material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.71,
+                0.196,
+                0.725
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this work, we have focused on accurate surface normals, which is another key factor for the few-shot novel view synthesis. Our proposed FlipNeRF utilizes a set of flipped reflection rays as additional training resources, which are simply derived from the estimated normal vectors and the input ray directions. Since it does not require a heuristic factor to be finetuned delicately for unseen view generation, we are able to exploit these additional training resources with much less burden. Furthermore, with our proposed UE Loss, FlipNeRF reduces the floating artifacts consistently across the different scene structures while"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.361,
+                0.895,
+                0.513
+            ],
+            "angle": 0,
+            "content": "considering the output uncertainty, leading to more reliable outputs. Also, our proposed BFC Loss enhances the bottleneck feature consistency between the rays cast on the photo-consistent pixels without leveraging the off-the-shelf feature extractor, leading to performance improvement under the few-shot setting. Our FlipNeRF achieves the SOTA performance with limited input views among the other few-shot baselines and vanilla NeRF-like models. We expect that our work is able to open another meaningful direction for the research of few-shot novel view synthesis."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.547,
+                0.895,
+                0.807
+            ],
+            "angle": 0,
+            "content": "Limitations and future work. Our FlipNeRF exploits the flipped reflection rays as a set of additional training rays, leading to more accurate surface normal estimation. Although Ref-NeRF achieved promising results with the high-quality surface reconstruction, we use mip-NeRF representation instead of Ref-NeRF for a fair comparison with other methods which are based on mip-NeRF. However, as shown in Tab. 6 and Fig. 6a, Ref-NeRF shows promising results without any additional consideration for few-shot setting compared to the vanilla mip-NeRF. Like our FlipNeRF, the accurate surface normal estimation leads to the competitive performance of Ref-NeRF even in the few-shot scenarios. Therefore, a combination of our FlipNeRF training framework with the Ref-NeRF representation or further exploration with regard to the view-dependent appearance for the few-shot novel view synthesis can be interesting directions for future research."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work was supported by NRF (2021R1A2C3006659) and IITP (2021-0-01343) both funded by Korean Government. It was also supported by Samsung Electronics (IO201223-08260-01)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
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+            "angle": 0,
+            "content": "22891"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
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+# FlipNeRF: Flipped Reflection Rays for Few-shot Novel View Synthesis
+
+Seunghyeon Seo Yeonjin Chang Nojun Kwak Seoul National Univeristy
+
+{zzzzlssh, yjean8315, nojunk}@snu.ac.kr
+
+# Abstract
+
+Neural Radiance Field (NeRF) has been a mainstream in novel view synthesis with its remarkable quality of rendered images and simple architecture. Although NeRF has been developed in various directions improving continuously its performance, the necessity of a dense set of multi-view images still exists as a stumbling block to progress for practical application. In this work, we propose FlipNeRF, a novel regularization method for few-shot novel view synthesis by utilizing our proposed flipped reflection rays. The flipped reflection rays are explicitly derived from the input ray directions and estimated normal vectors, and play a role of effective additional training rays while enabling to estimate more accurate surface normals and learn the 3D geometry effectively. Since the surface normal and the scene depth are both derived from the estimated densities along a ray, the accurate surface normal leads to more exact depth estimation, which is a key factor for few-shot novel view synthesis. Furthermore, with our proposed Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss, FlipNeRF is able to estimate more reliable outputs with reducing floating artifacts effectively across the different scene structures, and enhance the feature-level consistency between the pair of the rays cast toward the photo-consistent pixels without any additional feature extractor, respectively. Our FlipNeRF achieves the SOTA performance on the multiple benchmarks across all the scenarios.
+
+# 1. Introduction
+
+Neural Radiance Field (NeRF) [24] has achieved great success in rendering photo-realistic images from novel viewpoints. However, the necessity of a dense set of training images remains as a practical bottleneck since it suffers from significant performance degradation when trained with sparse views.
+
+There are two main streams for few-shot novel view synthesis: pre-training and regularization methods, both of which focus on learning the 3D geometry efficiently from sparse inputs. The pre-training methods [43, 5, 6, 39, 20,
+
+![](images/27bc8df263d7f84132970d2f10ae9723e8255e44b240716d2f0a1eea707cdb41.jpg)
+
+![](images/37fa4ba39e9bd6e9e4d350ca2dbf254da9266aeb58bb89a0e1509046e1cb22cc.jpg)  
+(a) Sparse training views  
+(b) Synthesized unseen views  
+Figure 1: Synthesis results from sparse inputs. Our Flip-NeRF significantly improves rendering quality compared to other baselines. Compared to the vanilla mip-NeRF [1] and MixNeRF [31], which is the state-of-the-art regularization method, ours reduces the noises and floating artifacts noticeably with superior surface normal estimation. Although Ref-NeRF [36] estimates smooth normal vectors, it shows much inferior rendering results to ours with a large chunk of noise under the few-shot setting.
+
+12, 19, 29, 35, 14] require large-scale datasets consisting of different scenes with multi-view images for injecting prior knowledge during the pre-training, while the regularization methods [25, 31, 15, 11, 30, 8, 17] are optimized per scene, exploiting additional training resources, e.g. unseen viewpoints [25, 15, 17], depth map generation [8, 30], off-the
+
+shelf models [11, 25], and so on, for an effective regularization to alleviate overfitting. Although the prior arts achieved promising results in novel view synthesis from sparse inputs, there still exist hurdles to overcome. The large-scale datasets, which are used for pre-training methods, are expensive to collect and the NeRF model is prone to performance degradation for the out-of-distribution dataset. On the other hand, the regularization methods heavily rely on additional training resources which might not always be available and require many heuristic factors, e.g. the choice of off-the-shelf models, the hyperparameters for sampling unseen viewpoints, and so on.
+
+In this paper, we propose FlipNeRF, which is an effective regularization method exploiting the flipped reflection rays<sup>1</sup> as additional training resources with filtering the ineffective newly generated rays. We derive a batch of flipped reflection rays from the original ray directions and estimated surface normals so that they are cast toward the same target pixels of the original input ray. Compared to the existing regularization methods which have mainly focused on the accurate depth estimation from limited input views [31, 25, 15, 30, 8], our FlipNeRF is trained to reconstruct surface normals accurately by learning to generate effective reflection rays to be used in training. Since both estimated surface normals and depths are derived from the volume densities representing underlying 3D geometry, accurately estimating the surface normals of an object naturally leads to more accurate depth maps.
+
+Furthermore, we propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), to reduce the floating artifacts effectively while considering the uncertainty of the model's outputs by using the estimated scale parameters for mixture models. Since our FlipNeRF is built upon MixNeRF [31], which is a regularization method achieving promising results by modeling input rays with mixture density models [2], we are able to apply our proposed loss without any modification of the architecture by using the estimated scale parameters of each sample along a ray, which stand for the uncertainty of the samples' estimated probability density distributions.
+
+Additionally, inspired by [6, 11, 15] which address the feature-level consistency of targets under the sparse input setting, we encourage the consistency for the pairs of bottleneck features between the original input rays and flipped reflection rays. We leverage a Jensen-Shannon Divergence, which is based on the similarity between the probability distributions, to make the pairs of bottleneck feature distributions of original and flipped reflection rays more similar to each other improving feature consistency.
+
+We demonstrate the effectiveness of our proposed FlipNeRF through the experiments on the multiple bench
+
+marks, e.g. Realistic Synthetic  $360^{\circ}$  [24], DTU [13], and LLFF [23]. Our method achieves state-of-the-art (SOTA) performances compared to other baselines. Especially, ours outperforms other baselines by a large margin with more accurate surface normals under the extremely sparse settings such as 3/4-view setting which are the most challenging ones. Our contributions are summarized as follows:
+
+- We propose an effective training framework for NeRF with sparse training views, called FlipNeRF. It leverages flipped reflection rays to provide additional training resources, resulting in more precise surface normals with our proposed masking strategy to filter the ineffective rays.  
+- We also propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), which reduces floating artifacts with considering the uncertainty of outputs, leading to more reliable estimation.  
+- We enhance the consistency of bottleneck features between the original input rays and flipped reflection rays by Jensen-Shannon Divergence, coined as Bottleneck Feature Consistency Loss (BFC Loss), improving the robustness for rendering from unseen viewpoints.  
+- Our FlipNeRF achieves SOTA performance over the multiple benchmarks. Especially, ours outperforms other baselines by a large margin in more challenging scenarios, e.g. 3/4-view.
+
+# 2. Related Works
+
+# 2.1. Neural Radiance Field
+
+Recently, Neural Radiance Field (NeRF) [24] has shown impressive performance and potential in the novel view synthesis task. NeRF represents a scene with an MLP, mapping coordinates and viewing directions to its colors and volume density, and then creates a novel view through volume rendering. Subsequent studies have developed NeRF in several directions, e.g. using conical frustums instead of rays [1], reparameterizing an input viewing direction as its reflection direction [36], and so on. These works have made significant progress by addressing the various issues in novel view synthesis, but there still exists a limitation in that NeRF requires a dense set of training images and a lengthy training time. Many studies have addressed these issues [10, 28, 5], including the utilization of various data structures for faster training and inference [9, 42] and attempts to train NeRF with only a few training images. Our work focuses on enhancing the performance of NeRF when a sparse set of views are provided as training images.
+
+# 2.2. Few-Shot Novel View Synthesis
+
+There are two main approaches for a few-shot novel view synthesis: the pre-training and the regularization method. The pre-training methods require a large dataset of multi-
+
+![](images/e2d805983ce1e59396e6692534e95c4baf4d19df835d969af2247cb5dfead645.jpg)  
+Figure 2: Overall framework of FlipNeRF. Our FlipNeRF utilize the newly generated flipped reflection rays with our proposed UE Loss and BFC Loss as well as existing MSE, NLL and Orientation losses. See Sec. 3 and Fig. 3 for more details about generation process of flipped reflection rays and the loss terms.
+
+view scenes to provide prior knowledges of 3D geometry to a NeRF model and then optionally finetune on the target scene [5, 6, 12, 19, 29, 35, 39, 43]. On the contrary, the regularization methods [31, 15, 11, 25, 8, 30, 17] are optimized per scene without pre-training process by exploiting additional training resources, e.g. depth maps [8, 30] and semantic consistency [11], as an extra supervision. Among them, [25, 15, 17] adopt an unseen viewpoint sampling strategy to make up for insufficient training views. However, these sampling processes require many hand-designed factors such as the ranges of rotation, translation, jittering, and so on, which can introduce artificial biases. Our work proposes a novel regularization approach to derive a set of flipped reflection rays from estimated surface normals and utilizes these for regularization, which does not require a heuristic factor to be finetuned, resulting in more effective training strategy with limited inputs.
+
+# 2.3. Surface Normal Reconstruction
+
+There is a line of research to recover accurate textures and lighting conditions of objects with NeRF [26, 41, 38, 7, 34, 44, 3]. Although these earlier studies successfully reconstruct the high-quality isosurfaces derived from the scene representations, their rendering quality for novel views is still inferior to the NeRF-like models. Meanwhile, Ref-NeRF [36] achieved superior performance with remarkable quality of surface normals compared to the existing NeRF models. Since the normal vectors utilized in NeRF framework are derived from the negative normalized density gradients [34, 3, 36], which represent the underlying geometry of 3D scenes, learning an accurate density distribution along a ray is a key factor for surface normal reconstruction. However, for the few-shot novel view synthesis, the prior works mostly focus on the accurate depth estimation without attention to the surface normals, both of which are derived from the estimated volume densities. In this work, we approach the few-shot novel view synthesis problem with focusing on the surface normals, which is another critical factor for an effective learning of 3D scene geometry. To the best of our knowledge, our work is the first attempt to focus on the sur
+
+face normal estimation for few-shot novel view synthesis.
+
+# 3. Method
+
+In this work, we propose an effective regularization method for few-shot novel view synthesis with flipped reflection rays. Our FlipNeRF is built upon MixNeRF [31] which leverages a mixture model framework (Sec. 3.1). We derive a batch of flipped reflection rays and cast them toward the identical target pixels as additional training rays (Sec. 3.2). Furthermore, we propose the Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss to alleviate the floating artifacts adaptively based on the uncertainty and enhance the consistency between the bottleneck feature distributions of the original and flipped reflection rays, respectively (Sec. 3.3 and Sec. 3.4). Finally, our FlipNeRF is trained to minimize the MSE and NLL losses as well as the proposed regularization loss terms with their corresponding balancing weights (Sec. 3.5). Fig. 2 shows an overview of our FlipNeRF.
+
+# 3.1. Preliminaries
+
+NeRF. The NeRF [24], which is an MLP-based neural network, represents a 3D scene as a continuous radiance field of RGB color and volume density. For every point sampled along a ray, the 3D coordinates  $\mathbf{x} = (x,y,z)$  and viewing directions  $(\theta ,\phi)$  are mapped to the colors  $\mathbf{c} = (r,g,b)$  and densities  $\sigma$  ..
+
+$$
+F (\gamma (\mathbf {x}), \gamma (\hat {\mathbf {d}})) \rightarrow (\mathbf {c}, \sigma), \tag {1}
+$$
+
+where  $F(\cdot), \gamma(\cdot)$ , and  $\hat{\mathbf{d}}$  indicate an MLP, the positional encoding for the inputs, and the 3D Cartesian unit vector used as an input viewing direction in practice, respectively.
+
+The volumetric radiance field is rendered by alpha composing the RGB values along an input ray  $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d}$  [22], where  $\mathbf{o}$  and  $\mathbf{d}$  denote the camera origin and unnormalized direction vector, i.e.  $\mathbf{d} = \| \mathbf{d}\| _2\cdot \hat{\mathbf{d}}$  respectively. The volume rendering integrals are denoted as follows:
+
+$$
+\hat {\mathbf {c}} (\mathbf {r}) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \sigma (\mathbf {r} (t)) \mathbf {c} (\mathbf {r} (t), \hat {\mathbf {d}}) d t, \tag {2}
+$$
+
+![](images/1c49d188db66f370e6b42b74b935cd959508d01329287f592b38d125f29bc8a4.jpg)  
+Figure 3: Flipped reflection ray generation. Our FlipNeRF generates the flipped reflection ray  $\mathbf{r}'$  from the estimated normal vector  $\hat{\mathbf{n}}$  and original input ray direction  $\mathbf{d}$ . With our masking strategy,  $\mathbf{r}_2'$  is filtered out since it does not satisfy the photo-consistency condition, i.e.  $\theta_{2}$  is bigger than  $90^{\circ}$ . The smaller  $\theta$  is, the more photo-consistent the target pixel is, where the pair of  $\mathbf{r}$  and  $\mathbf{r}'$  are cast.
+
+where  $T(t) = \exp(-\int_{t_n}^t \sigma(s) ds)$  indicates the degree of transparency. In practice, it is approximated with numerical quadrature [24] by sampling points along a ray.
+
+The radiance field is trained to minimize the mean squared error (MSE) between rendered and GT pixels:
+
+$$
+\mathcal {L} _ {\mathrm {M S E}} = \sum_ {\mathbf {r} \in \mathcal {R}} | | \hat {\mathbf {c}} (\mathbf {r}) - \mathbf {c} ^ {\mathrm {G T}} (\mathbf {r}) | | _ {2} ^ {2}, \tag {3}
+$$
+
+where  $\mathcal{R}$  is denoted as a set of rays.
+
+MixNeRF. Built upon mip-NeRF [1], which leveraged a cone tracing method and proposed an integrated positional encoding to address an aliasing problem, MixNeRF [31] estimates the joint probability distribution of color values and models a ray with a mixture of densities:
+
+$$
+p (\mathbf {c} | \mathbf {r}) = \sum_ {i = 1} ^ {M} \pi_ {i} \mathcal {F} (\mathbf {c}; \mu_ {i} ^ {\mathbf {c}}, \beta_ {i}), \tag {4}
+$$
+
+where  $M$  is the number of sampled points,  $\mathcal{F}(\mathbf{c};\mu_i^{\mathbf{c}},\beta_i)$  denotes the Laplacian distribution of RGB  $\mathbf{c}$  with location parameter  $\mu_i^{\mathbf{c}}\in \{\mu_i^r,\mu_i^g,\mu_i^b\}$ , i.e. estimated RGB values of sample, and scale parameter  $\beta_{i}\in \{\beta_{i}^{r},\beta_{i}^{g},\beta_{i}^{b}\}$ . The mixture coefficient  $\pi_{i}$  is derived from the estimated volume density  $\sigma_{i}$  as follows:
+
+$$
+\pi_ {i} = \frac {w _ {i}}{\sum_ {m = 1} ^ {M} w _ {m}} = \frac {T _ {i} (1 - \exp (- \sigma_ {i} \delta_ {i}))}{\sum_ {m = 1} ^ {M} T _ {m} (1 - \exp (- \sigma_ {m} \delta_ {m}))}, \tag {5}
+$$
+
+where  $w_{i}$  and  $\delta_{i}$  indicate the alpha blending weight and sample interval, respectively. Thanks to the mixture model's capacity of representing complex distributions, MixNeRF learns the density distribution effectively with sparse inputs by minimizing the negative log-likelihood (NLL) in Eq. 4.
+
+Our FlipNeRF is built upon MixNeRF leveraging the mixture modeling framework while achieving superior rendering quality with noticeably fewer artifacts and more accurate surface normals to MixNeRF.
+
+# 3.2. Auxiliary Flipped Reflection Ray
+
+As shown in Fig. 3, we exploit a batch of flipped reflection rays  $\mathbf{r}' \in \mathcal{R}'$  as extra training resources, which are derived from the original input ray directions  $\mathbf{d}$  and estimated surface normals  $\hat{\mathbf{n}}$ . First, we derive a flipped reflection direction  $\mathbf{d}'$  from  $\mathbf{d}$  and  $\hat{\mathbf{n}}$ :
+
+$$
+\mathbf {d} ^ {\prime} = 2 (\mathbf {d} \cdot \hat {\mathbf {n}}) \hat {\mathbf {n}} - \mathbf {d}, \tag {6}
+$$
+
+where  $\hat{\mathbf{n}}$  denotes the weighted sum of blending weights and estimated normal vectors along a ray, i.e.  $\hat{\mathbf{n}} = \sum_{i=1}^{M} w_i \mathbf{n}_i$ . Note that we use the gradient of volume density as estimated surface normals following [3, 34, 36].
+
+To generate the additional training rays based on  $\mathbf{d}'$ , we need a set of imaginary ray origins  $\mathbf{o}'$  located in a suitable space considering the hitting point and the original input ray origins  $\mathbf{o}$ . Since the vanilla NeRF models, which are trained with a dense set of images, tend to have the blending weight distribution whose peak is located on the point around the object surface  $\mathbf{p}_s = \mathbf{o} + t_s\mathbf{d}$  [8, 31], i.e. the  $s$ -th sample whose blending weight is the highest along a ray. Therefore, we place  $\mathbf{o}'$  so that the  $s$ -th sample of  $\mathbf{r}'$  is  $\mathbf{p}_s$ :
+
+$$
+\mathbf {o} ^ {\prime} = \mathbf {p} _ {s} - t _ {s} \mathbf {d} ^ {\prime}, \tag {7}
+$$
+
+resulting in our proposed flipped reflection ray,  $\mathbf{r}'(t) = \mathbf{o}' + t\mathbf{d}'$ . Compared to the previous unseen viewpoint sampling strategies [15, 25, 17], our proposed strategy does not rely on the randomness of unseen viewpoint sampling and reduces the heuristic factors for sampling schemes, e.g. the range of rotation, translation, and so on. Furthermore, since our newly generated  $\mathbf{r}'$  are cast on the identical object surfaces where the original input rays  $\mathbf{r}$  are cast, i.e. the target pixels are photo-consistent for the pair of  $\mathbf{r}$  and  $\mathbf{r}'$  without any sophisticated viewpoint sampling process, we are able to train  $\mathbf{r}'$  effectively with the same GT pixels of  $\mathbf{r}$ .
+
+However, since  $\hat{\mathbf{n}}$ , which are used to derive  $\mathbf{d}'$ , are not the ground truth but the estimation, there exists a concern that even miscreated  $\mathbf{r}'$ , which do not satisfy photo-consistency, can be used for training. As a result, it might lead to performance degradation while providing misleading training
+
+cues. To address this problem, we mask the ineffective  $\mathbf{r}'$  by considering the angle  $\theta$  between  $\hat{\mathbf{n}}$  and  $-\hat{\mathbf{d}}$  as follows:
+
+$$
+M \left(\mathbf {r} ^ {\prime}\right) = \left\{ \begin{array}{l l} 1 & \text {i f} \arccos  \left(- (\hat {\mathbf {d}} \cdot \hat {\mathbf {n}})\right) <   \tau \\ 0 & \text {o t h e r w i s e} \end{array} , \right. \tag {8}
+$$
+
+where  $-(\hat{\mathbf{d}}\cdot \hat{\mathbf{n}})$  amounts to  $\cos \theta$  of original input rays and normal vectors, and  $\tau$  indicates the threshold for filtering the invalid rays, which we set as  $90^{\circ}$  unless specified. Through this masking process, only  $\mathbf{r}'$  which are cast toward the photo-consistent point can be remained as we intend. Finally, our proposed flipped reflection rays are modeled by mixture density like the original input rays:
+
+$$
+p \left(\mathbf {c} \mid \mathbf {r} ^ {\prime}\right) = \sum_ {i = 1} ^ {M} \pi_ {i} ^ {\prime} \mathcal {F} \left(\mathbf {c}; \mu_ {i} ^ {\mathbf {c} ^ {\prime}}, \beta_ {i} ^ {\prime}\right). \tag {9}
+$$
+
+Additionally, we leverage the Orientation Loss proposed in Ref-NeRF [36] to penalize the backward-facing normal vectors for learning accurate surface normals:
+
+$$
+l _ {\text {O r i .}} (\mathbf {r}) = \sum_ {i = 1} ^ {M} w _ {i} \max  (0, \mathbf {n} _ {i} \cdot \hat {\mathbf {d}}) ^ {2}. \tag {10}
+$$
+
+Unlike Ref-NeRF, we penalize underlying density gradient normal  $\mathbf{n}_i$  instead of predicted normals.
+
+Note that our FlipNeRF is fundamentally different compared to Ref-NeRF since ours generates additional training rays through the derivation of reflection direction without modification to original representations while Ref-NeRF replaced the input viewing direction with its reflection direction, reparameterizing the outgoing radiance.
+
+# 3.3. Uncertainty-aware Regularization
+
+Several regularization techniques have been proposed to reduce the floating artifacts present in synthesized images, which is one of the major problems of NeRF. Among them, we leverage the Emptiness Loss [37] which penalizes the small blending weights along a ray as follows:
+
+$$
+l _ {\text {E m p .}} (\mathbf {r}) = \frac {1}{M} \sum_ {i = 1} ^ {M} \log (1 + \eta \cdot w _ {i}), \tag {11}
+$$
+
+where the bigger  $\eta$  is, the steeper the loss function becomes around 0.
+
+However, the naive application of existing regularization techniques with limited training views might not be consistently helpful across the different scenes due to the scene-by-scene different structure, resulting in overall performance degradation. To address this problem, we propose Uncertainty-aware Emptiness Loss (UE Loss) developed upon the Emptiness Loss, which reduces the floating
+
+artifacts consistently over the different scenes by considering the output uncertainty:
+
+$$
+l _ {\mathrm {U E}} (\mathbf {r}) = \frac {1}{M} \sum_ {i = 1} ^ {M} \log (1 + \rho \cdot \eta \cdot w _ {i}), \tag {12}
+$$
+
+$$
+\text {w h e r e} \quad \rho = \frac {1}{3} \sum_ {c} ^ {\{r, g, b \}} \sum_ {i = 1} ^ {M} \beta_ {i} ^ {c}.
+$$
+
+$\rho$  amounts to the average of the summation of estimated scale parameters of RGB color distributions from all samples along a ray, which we use as the uncertainty of a ray. By our proposed UE Loss, we are able to regularize the blending weights adaptively, i.e. the more uncertain a ray is, the more penalized the blending weights along the ray are. It is able to reduce floating artifacts consistently across the scenes with different structures and enables to synthesize more reliable outputs by considering uncertainty.
+
+# 3.4. Bottleneck Feature Consistency
+
+Motivated by previous works addressing the feature-level consistency of multiple views for few-shot novel view synthesis [6, 11, 15], we encourage the consistency of bottleneck feature distributions between  $\mathbf{r}$  and  $\mathbf{r}'$ , which are intermediate feature vectors, i.e. outputs of the spatial MLP of NeRF, by Jensen-Shannon Divergence (JSD):
+
+$$
+l _ {\mathrm {B F C}} \left(\mathbf {r}, \mathbf {r} ^ {\prime}\right) = J S D \left(\psi (\mathbf {b}), \psi \left(\mathbf {b} ^ {\prime}\right)\right), \tag {13}
+$$
+
+where  $\psi (\cdot)$ ,  $\mathbf{b}$  and  $\mathbf{b}^{\prime}$  denote the softmax function, the bottleneck features of  $\mathbf{r}$  and  $\mathbf{r}^{\prime}$ , respectively. While the existing methods [6, 11] rely on off-the-shelf feature extractors like 2D CNN or CLIP [27] to address high-level feature consistency, we regulate the pair of features effectively by enhancing consistency between bottleneck features without depending on additional feature extractors.
+
+# 3.5. Total Loss
+
+Our FlipNeRF is not only trained to maximize the log-likelihood of the target pixel  $\mathbf{c}_{\mathrm{GT}}$  for a set of original input rays  $\mathcal{R}$ , but also for flipped reflection rays  $\mathcal{R}_M^\prime$ , where the ineffective rays are excluded from the total flipped reflection rays  $\mathcal{R}^\prime$  by our masking strategy in Eq. 8. Likewise, the UE Losses are applied for both  $\mathcal{R}$  and  $\mathcal{R}_M^\prime$ .
+
+Aggregating all, our total loss over a batch is as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {T o t a l}} = \mathcal {L} _ {\text {M S E}} + \lambda_ {1} \mathcal {L} _ {\text {N L L}} + \lambda_ {2} \mathcal {L} _ {\text {N L L}} ^ {\prime} \tag {14} \\ + \lambda_ {3} \mathcal {L} _ {\mathrm {U E}} + \lambda_ {4} \mathcal {L} _ {\mathrm {U E}} ^ {\prime} + \lambda_ {5} \mathcal {L} _ {\mathrm {B F C}} + \lambda_ {6} \mathcal {L} _ {\mathrm {O r i}}, \\ \end{array}
+$$
+
+where a set of  $\lambda$ 's are balancing weight terms for the losses.
+
+<table><tr><td>τ</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>30°</td><td>18.62</td><td>0.747</td><td>0.206</td><td>0.121</td></tr><tr><td>60°</td><td>18.12</td><td>0.723</td><td>0.237</td><td>0.126</td></tr><tr><td>90°</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr><tr><td>180° (No masking)</td><td>18.76</td><td>0.755</td><td>0.190</td><td>0.111</td></tr></table>
+
+Table 1: Comparison of masking conditions. Our masking strategy with  $\tau$  of  $90^{\circ}$  achieves the best results, filtering out the ineffective flipped reflection rays successfully.
+
+![](images/7bcdc432db4a80bd7668513f39889200756de9675845cec296540b823c91c78b.jpg)  
+(a) Effective  $\mathbf{r}'$  ratio by  $\tau$
+
+![](images/2ed9f0b59d0c0e1bbf7375d42d236a2fef8f035db90d3709ff30b00fafd53cc9.jpg)  
+(b) Distribution of  $\theta$  
+Figure 4: Analysis of the masking strategy.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Implementation details. Our FlipNeRF is built upon MixNeRF [31] based on the JAX codebase [4], which is developed upon mip-NeRF [1]. The overall training scheme follows [25, 31]. We adopt a scene space annealing strategy for the early training phase. Also, we apply the exponential decay and warm up for the learning rate. The Adam optimizer [16] and the gradient clippings by value at 0.1 and norm at 0.1 are used. We train our FlipNeRF for 500 pixel epochs with a batch size of 4,096 on 4 NVIDIA RTX 3090. Additionally, since the LLFF dataset [23] consists of scenes with much more static movement of viewpoints compared to other datasets, we set the threshold  $(\tau)$  of our masking strategy as  $30^{\circ}$  for the experiments on LLFF. More detailed hyperparameters and our loss balancing terms by the datasets and the number of training views are provided in the supplementary material.
+
+Datasets and metrics. We evaluate the performance of our FlipNeRF and baselines on the representative benchmarks: Realistic Synthetic  $360^{\circ}$  [24], DTU [13], and LLFF [23]. Realistic Synthetic  $360^{\circ}$  contains 8 synthetic scenes, each consisting of 400 multi-view rendered images with white background. To compare against other representative baselines [15, 11, 31, 25, 1], we evaluate our FlipNeRF under the scenarios of 4 and 8 views. For a fair comparison, we sample the first  $n$ -image of the training set for the  $n$ -view scenario so that the identical images are provided for training different methods following [31]. We use 200 images of the test set for evaluation. For DTU, which provide various scenes including objects put on a white table with a black background, we conduct experiments on the 15
+
+specific scenes under the scenarios of 3, 6, and 9-view, following the experimental protocol of [43]. We also conduct a series of experiments for the analysis of FlipNeRF under 3-view setting as well as comparison against other baselines. Additionally, we compare our FlipNeRF against other baselines on LLFF consisting of real forward-facing scenes, which is often tested as an out-of-distribution dataset for pre-training methods. Following [24], every 8th image of each scene is used for a held-out test set and the training views are evenly selected from the remaining images. Like DTU, we report our results of the 3, 6, and 9-view scenarios, following [43].
+
+For the quantitative evaluation for rendered images, we adopt the mean of PSNR, SSIM [40], LPIPS [45], and the geometric average [1]. Furthermore, we also adopt the mean angular error  $(\mathrm{MAE}^{\circ})$  [36] and NLL [33, 32, 21, 18] for evaluating the surface normals and uncertainty, respectively. Specifically, following [33], we compute the NLL by deriving the probability of the GT pixel values given a Gaussian distribution with the estimated RGB values as mean and the uncertainty as variance, which is derived from the weighted sum of the blending weights and estimated scale parameters along a ray in our FlipNeRF. For DTU, we report the results evaluated by masked metrics to prevent background bias, following [25, 31].
+
+Baselines. We compare our FlipNeRF against the SOTA regularization methods [11, 15, 25, 31] on Realistic Synthetic  $360^{\circ}$  as well as the vanilla mip-NeRF [1] and Ref-NeRF [36], which is known for achieving promising results with accurate surface normals. Furthermore, we compare ours against the representative pre-training methods [5, 6, 43] as well as regularization methods on DTU and LLFF. The pre-training baselines exploit the DTU and LLFF as pre-training dataset and out-of-distribution test set, respectively, while the regularization methods, mip-NeRF and Ref-NeRF are optimized per scene. Note that we report the quantitative results of other baselines on DTU and LLFF from [25], which achieved better results than its original papers by the modified training scheme, and those on Realistic Synthetic  $360^{\circ}$  from [31], which trained the baselines with the identical training views for a fair comparison.
+
+# 4.2. Analysis of FlipNeRF
+
+Analysis of flipped reflection rays. As shown in Tab. 1, our masking strategy of filtering out the ineffective flipped reflection rays with the threshold  $(\tau)$  of  $90^{\circ}$  achieves the best performance among different options. With  $\tau$  of  $30^{\circ}$  and  $60^{\circ}$ , the rendering quality is rather degraded since the newly generated rays are overly-filtered and do not provide enough additional supervision as demonstrated in Fig. 4a. On the other hand, when we exploit all the flipped reflection rays without masking, there exists a little improvement
+
+<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average ↓</td><td>NLL ↓</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>0.744</td><td>0.203</td><td>0.113</td><td>9.99</td></tr><tr><td>FlipNeRF (Ours)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>w/o LEmp. or LUE</td><td>19.30</td><td>0.758</td><td>0.196</td><td>0.108</td><td>4.88</td></tr><tr><td>w/ LEmptiness</td><td>18.62</td><td>0.749</td><td>0.204</td><td>0.118</td><td>4.92</td></tr><tr><td>w/ LUE</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td><td>2.56</td></tr></table>
+
+![](images/76b16cabab8c3f7355fe9205a6f5a29c4ba1f29f97fec83e6add3d1d3c0fbb97.jpg)  
+Figure 5: Comparison of FlipNeRF and MixNeRF. Our FlipNeRF renders the images from novel views with much fewer artifacts and more accurate depth maps than MixNeRF. Considering the standard deviation of RGB and depths, our FlipNeRF is able to estimate more reliable outputs than MixNeRF. For the std. map, the darker the pixel is, the more certain the output is.
+
+of performance compared to  $30^{\circ}$  and  $60^{\circ}$  masking, but it is still much inferior to  $90^{\circ}$  due to the negative impact from the ineffective rays. Additionally, Fig. 4b shows the distribution of  $\theta$ , i.e. angles between the input viewing directions and normal vectors. As the smaller  $\theta$  is, the more photo-consistent the target pixel is, i.e. the more effective the newly generated flipped reflection rays are for training. Since our FlipNeRF is trained to estimate the accurate normal vectors, we are able to exploit a set of more effective flipped reflection rays through the training, which are cast on the more photo-consistent target pixels. Furthermore, at the initial training phase, the invalid additional rays are filtered effectively by our masking strategy, leading to high-quality supervision and stabilizing the training.
+
+Uncertainty-aware regularization. Tab. 2 shows the effectiveness of our proposed UE Loss. Compared to MixNeRF [31] which models a ray with mixture of distributions as our FlipNeRF, ours consistently achieves more reliable rendering results with much lower NLL. Without  $\mathcal{L}_{\mathrm{Emp}}$ , [37] or our proposed  $\mathcal{L}_{\mathrm{UE}}$ , ours already outperforms MixNeRF by a large margin. However, ours with naively leveraged  $\mathcal{L}_{\mathrm{Emp}}$  rather shows inferior results to MixNeRF. It shows that naive application of the existing regularization technique for reducing artifacts under the few-shot setting can lead to overall performance degradation due to the scene
+
+Table 2: Effectiveness of  $\mathcal{L}_{\mathrm{UE}}$ . Our proposed  $\mathcal{L}_{\mathrm{UE}}$  improves the rendering quality consistently across the scenes with considering the uncertainty.  
+
+<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>w/o LBCF</td><td>18.79</td><td>0.755</td><td>0.200</td><td>0.115</td></tr><tr><td>w/ LBCF</td><td></td><td></td><td></td><td></td></tr><tr><td>MSE on b</td><td>18.83</td><td>0.755</td><td>0.197</td><td>0.113</td></tr><tr><td>Cos. Sim. on b</td><td>18.77</td><td>0.755</td><td>0.193</td><td>0.115</td></tr><tr><td>JSD on bhat</td><td>18.43</td><td>0.749</td><td>0.204</td><td>0.120</td></tr><tr><td>JSD on b</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr></table>
+
+Table 3: Comparison of different strategies for  $\mathcal{L}_{\mathrm{BFC}}$ . Our  $\mathcal{L}_{\mathrm{BFC}}$  achieves a significant performance gain compared to other regularization schemes for feature consistency.  
+
+<table><tr><td></td><td>\( \mathcal{L}_{\text{NLL}} \)</td><td>\( \mathcal{L}_{\text{NLL}}^{\prime} \)</td><td>\( \mathcal{L}_{\text{UE}}^\dagger \)</td><td>\( \mathcal{L}_{\text{BFC}} \)</td><td>\( \mathcal{L}_{\text{Ori.}} \)</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average ↓</td></tr><tr><td>(1)</td><td>✓</td><td></td><td></td><td></td><td></td><td>17.44</td><td>0.729</td><td>0.187</td><td>0.130</td></tr><tr><td>(2)</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>16.94</td><td>0.727</td><td>0.217</td><td>0.143</td></tr><tr><td>(3)</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>17.89</td><td>0.736</td><td>0.206</td><td>0.130</td></tr><tr><td>(4)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>19.01</td><td>0.755</td><td>0.181</td><td>0.107</td></tr><tr><td>(5)</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>18.79</td><td>0.755</td><td>0.200</td><td>0.115</td></tr><tr><td>(6)</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>19.30</td><td>0.758</td><td>0.196</td><td>0.108</td></tr><tr><td>(7)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr></table>
+
+Table 4: Ablation study.  $\dagger$  indicate that the losses are applied to both  $\mathbf{r}$  and  $\mathbf{r}'$ .
+
+by-scene various structures. As illustrated in Fig. 5, with our proposed  $\mathcal{L}_{\mathrm{UE}}$ , ours improves both of the rendering quality and the reliability of the model outputs by a large margin compared to MixNeRF.
+
+Bottleneck feature consistency. As shown in Tab. 3, there is no significant impact on the performance with regularizing the bottleneck feature  $\mathbf{b}$  using MSE or cosine similarity. By our proposed  $\mathcal{L}_{\mathrm{BFC}}$  with JSD, we achieve a considerable performance improvement. Interestingly, the performance rather degrades when we apply  $\mathcal{L}_{\mathrm{BFC}}$  with JSD to  $\mathbf{b}_{\hat{\mathbf{d}}}$ , i.e. the bottleneck feature conditioned with input viewing direction  $\hat{\mathbf{d}}$ . We conjecture that the reduced feature dimension of  $\mathbf{b}_{\hat{\mathbf{d}}}$  reduces the capacity of feature representations and prevents the model from improving robustness.
+
+# 4.3. Ablation Study
+
+The quantitative results of our ablation study are reported in Tab. 4. With only additionally exploiting our proposed flipped reflection rays, our FlipNeRF achieves more degenerate results compared to the baseline  $((1) \rightarrow (2))$ . However, we are able to achieve performance improvement by a large margin with our proposed  $\mathcal{L}_{\mathrm{UE}}$  and  $\mathcal{L}_{\mathrm{BFC}}$ $((2) \rightarrow (3) \rightarrow (4))$ .  $(5) \rightarrow (7)$  shows that enhancing the consistency of bottleneck features between the pair of original and flipped reflection rays is considerably effective. Additionally, by leveraging  $\mathcal{L}_{\mathrm{Ori}}$ , from Ref-NeRF, we are able to estimate more accurate normal vectors, leading to more effective flipped reflection rays and performance gain  $((4) \rightarrow (7))$ .
+
+<table><tr><td rowspan="2"></td><td colspan="2">PSNR ↑</td><td colspan="2">SSIM ↑</td><td colspan="2">LPIPS ↓</td><td colspan="2">Average Err. ↓</td><td colspan="2">MAE° ↓</td></tr><tr><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td></tr><tr><td>mip-NeRF [1]</td><td>14.12</td><td>18.74</td><td>0.722</td><td>0.828</td><td>0.382</td><td>0.238</td><td>0.221</td><td>0.121</td><td>96.05</td><td>101.21</td></tr><tr><td>Ref-NeRF [36]</td><td>18.09</td><td>24.00</td><td>0.764</td><td>0.879</td><td>0.269</td><td>0.106</td><td>0.150</td><td>0.058</td><td>65.62</td><td>57.93</td></tr><tr><td>DietNeRF [11]</td><td>15.42</td><td>21.31</td><td>0.730</td><td>0.847</td><td>0.314</td><td>0.153</td><td>0.201</td><td>0.086</td><td>-</td><td>-</td></tr><tr><td>InfoNeRF [15]</td><td>18.44</td><td>22.01</td><td>0.792</td><td>0.852</td><td>0.223</td><td>0.133</td><td>0.119</td><td>0.073</td><td>-</td><td>-</td></tr><tr><td>RegNeRF [25]</td><td>13.71</td><td>19.11</td><td>0.786</td><td>0.841</td><td>0.346</td><td>0.200</td><td>0.210</td><td>0.122</td><td>62.78</td><td>60.37</td></tr><tr><td>MixNeRF [31]</td><td>18.99</td><td>23.84</td><td>0.807</td><td>0.878</td><td>0.199</td><td>0.103</td><td>0.113</td><td>0.060</td><td>70.90</td><td>62.04</td></tr><tr><td>FlipNeRF (Ours)</td><td>20.60</td><td>24.38</td><td>0.822</td><td>0.883</td><td>0.159</td><td>0.095</td><td>0.091</td><td>0.055</td><td>58.72</td><td>57.17</td></tr></table>
+
+Table 5: Quantitative results on Realistic Synthetic  ${360}^{ \circ  }$  . Our FlipNeRF achieves the SOTA performance among other baselines across all the scenarios and metrics.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">3-view</td><td rowspan="2">PSNR ↑ 6-view</td><td rowspan="2">9-view</td><td rowspan="2">3-view</td><td rowspan="2">SSIM ↑ 6-view</td><td rowspan="2">9-view</td><td rowspan="2">3-view</td><td rowspan="2">LPIPS ↓ 6-view</td><td rowspan="2">9-view</td><td colspan="3">Average Error ↓</td></tr><tr><td>3-view</td><td>6-view</td><td>9-view</td></tr><tr><td>mip-NeRF [1]</td><td>8.68</td><td>16.54</td><td>23.58</td><td>0.571</td><td>0.741</td><td>0.879</td><td>0.353</td><td>0.198</td><td>0.092</td><td>0.323</td><td>0.148</td><td>0.056</td></tr><tr><td colspan="13">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>16.82</td><td>19.11</td><td>20.40</td><td>0.695</td><td>0.745</td><td>0.768</td><td>0.270</td><td>0.232</td><td>0.220</td><td>0.147</td><td>0.115</td><td>0.100</td></tr><tr><td>PixelNeRF†[43]</td><td>18.95</td><td>20.56</td><td>21.83</td><td>0.710</td><td>0.753</td><td>0.781</td><td>0.269</td><td>0.223</td><td>0.203</td><td>0.125</td><td>0.104</td><td>0.090</td></tr><tr><td>SRF [6]</td><td>15.32</td><td>17.54</td><td>18.35</td><td>0.671</td><td>0.730</td><td>0.752</td><td>0.304</td><td>0.250</td><td>0.232</td><td>0.171</td><td>0.132</td><td>0.120</td></tr><tr><td>SRF†[6]</td><td>15.68</td><td>18.87</td><td>20.75</td><td>0.698</td><td>0.757</td><td>0.785</td><td>0.281</td><td>0.225</td><td>0.205</td><td>0.162</td><td>0.114</td><td>0.093</td></tr><tr><td>MVSNeRF [5]</td><td>18.63</td><td>20.70</td><td>22.40</td><td>0.769</td><td>0.823</td><td>0.853</td><td>0.197</td><td>0.156</td><td>0.135</td><td>0.113</td><td>0.088</td><td>0.068</td></tr><tr><td>MVSNeRF†[5]</td><td>18.54</td><td>20.49</td><td>22.22</td><td>0.769</td><td>0.822</td><td>0.853</td><td>0.197</td><td>0.155</td><td>0.135</td><td>0.113</td><td>0.089</td><td>0.069</td></tr><tr><td colspan="13">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>11.85</td><td>20.63</td><td>23.83</td><td>0.633</td><td>0.778</td><td>0.823</td><td>0.314</td><td>0.201</td><td>0.173</td><td>0.243</td><td>0.101</td><td>0.068</td></tr><tr><td>RegNeRF [25]</td><td>18.89</td><td>22.20</td><td>24.93</td><td>0.745</td><td>0.841</td><td>0.884</td><td>0.190</td><td>0.117</td><td>0.089</td><td>0.112</td><td>0.071</td><td>0.047</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>22.30</td><td>25.03</td><td>0.744</td><td>0.835</td><td>0.879</td><td>0.203</td><td>0.102</td><td>0.065</td><td>0.113</td><td>0.066</td><td>0.042</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.55</td><td>22.45</td><td>25.12</td><td>0.767</td><td>0.839</td><td>0.882</td><td>0.180</td><td>0.098</td><td>0.062</td><td>0.101</td><td>0.064</td><td>0.041</td></tr></table>
+
+Table 6: Comparison with baselines on DTU. Our FlipNeRF outperforms all the pre-training and regularization methods in every scenario, especially by a large margin under the 3-view setting.  $\dagger$  indicates fine-tuning.  
+
+<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>mip-NeRF [1]</td><td>14.62</td><td>0.351</td><td>0.495</td><td>0.246</td></tr><tr><td colspan="5">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>7.93</td><td>0.272</td><td>0.682</td><td>0.461</td></tr><tr><td>PixelNeRF† [43]</td><td>16.17</td><td>0.438</td><td>0.512</td><td>0.217</td></tr><tr><td>SRF [6]</td><td>12.34</td><td>0.250</td><td>0.591</td><td>0.313</td></tr><tr><td>SRF† [6]</td><td>17.07</td><td>0.436</td><td>0.529</td><td>0.203</td></tr><tr><td>MVSNeRF [5]</td><td>17.25</td><td>0.557</td><td>0.356</td><td>0.171</td></tr><tr><td>MVSNeRF† [5]</td><td>17.88</td><td>0.584</td><td>0.327</td><td>0.157</td></tr><tr><td colspan="5">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>14.94</td><td>0.370</td><td>0.496</td><td>0.240</td></tr><tr><td>RegNeRF [25]</td><td>19.08</td><td>0.587</td><td>0.336</td><td>0.146</td></tr><tr><td>MixNeRF [31]</td><td>19.27</td><td>0.629</td><td>0.236</td><td>0.124</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.34</td><td>0.631</td><td>0.235</td><td>0.123</td></tr></table>
+
+Table 7: Comparison with baselines on LLFF 3-view. † indicates fine-tuning.
+
+# 4.4. Comparison with other SOTA Methods
+
+Realistic Synthetic  $360^{\circ}$ . As demonstrated in Tab. 5, our FlipNeRF achieves the SOTA performance across all the evaluation metrics. Compared to MixNeRF which leverages a mixture model framework as ours, our FlipNeRF
+
+improves the performance by a large margin. Noticeably, our FlipNeRF estimates more accurate surface normals than other baselines, leading to the performance gain with better reconstructed fine details from limited input views as shown in Fig. 6a. Additionally, the vanilla Ref-NeRF, which shows great performance with accurate normal vectors, achieves comparable or even better performance than other regularization methods except ours. From this result, we are able to expect that estimating the accurate surface normals is one of the key factors for learning 3D geometry with sparse inputs. Note that the comparable  $\mathrm{MAE}^{\circ}$  of RegNeRF results from the overly-smoothed depth estimation, not indicating the high-quality of rendering results, as shown in Fig. 6a.
+
+DTU. Our FlipNeRF achieves the best results across all the scenarios and most of the evaluation metrics on DTU as shown in Tab. 6. Remarkably, ours trained with 6-view outperforms all the pre-training methods trained with 9-view in every metric except SSIM. Furthermore, ours trained with 3-view still outperforms PixelNeRF [43] and SRF [6] trained with 6-view. Similar to the results on Realistic Synthetic  $360^{\circ}$ , ours outperforms other baselines by a large
+
+![](images/d9a0cc943fffec29d76e0447f76d5d66d7964b6be6e9c319ea98bc020970f699.jpg)
+
+![](images/4b90633e79c8847ab9c7aea9648f23c200f093d7677463dd16ab8123b501d088.jpg)  
+Figure 6: Qualitative results on Realistic Synthetic  $360^{\circ}$  and DTU. More results are provided in the supp. material.
+
+margin especially under the 3-view, which is the most challenging scenario, with reducing the floating artifacts successfully as shown in Fig. 6b. Since the flipped reflection rays are effective training resources for unseen views, the fewer the training views are provided, the more performance gain is expected.
+
+LLFF. Table 7 compares our FlipNeRF against other baselines on LLFF, which is a real forward-facing dataset. Although ours achieves the SOTA performance among other baselines, it is much more marginal than those on Realistic Synthetic  $360^{\circ}$  and DTU. We conjecture the reason for the marginal improvement of our proposed method can be the fact that a set of flipped reflection rays, which are able to widely cover the unseen views, are not very useful for the scenes in LLFF, where a set of camera poses are much less dynamic than other datasets. In other words, our FlipNeRF is able to not only achieve a competitive performance for the scenes consisting of a set of simple camera poses, but also render the novel views in much higher quality for more dynamically captured scenes with only a few shots. The rendered images are provided in the supp. material.
+
+# 5. Conclusion
+
+In this work, we have focused on accurate surface normals, which is another key factor for the few-shot novel view synthesis. Our proposed FlipNeRF utilizes a set of flipped reflection rays as additional training resources, which are simply derived from the estimated normal vectors and the input ray directions. Since it does not require a heuristic factor to be finetuned delicately for unseen view generation, we are able to exploit these additional training resources with much less burden. Furthermore, with our proposed UE Loss, FlipNeRF reduces the floating artifacts consistently across the different scene structures while
+
+considering the output uncertainty, leading to more reliable outputs. Also, our proposed BFC Loss enhances the bottleneck feature consistency between the rays cast on the photo-consistent pixels without leveraging the off-the-shelf feature extractor, leading to performance improvement under the few-shot setting. Our FlipNeRF achieves the SOTA performance with limited input views among the other few-shot baselines and vanilla NeRF-like models. We expect that our work is able to open another meaningful direction for the research of few-shot novel view synthesis.
+
+Limitations and future work. Our FlipNeRF exploits the flipped reflection rays as a set of additional training rays, leading to more accurate surface normal estimation. Although Ref-NeRF achieved promising results with the high-quality surface reconstruction, we use mip-NeRF representation instead of Ref-NeRF for a fair comparison with other methods which are based on mip-NeRF. However, as shown in Tab. 6 and Fig. 6a, Ref-NeRF shows promising results without any additional consideration for few-shot setting compared to the vanilla mip-NeRF. Like our FlipNeRF, the accurate surface normal estimation leads to the competitive performance of Ref-NeRF even in the few-shot scenarios. Therefore, a combination of our FlipNeRF training framework with the Ref-NeRF representation or further exploration with regard to the view-dependent appearance for the few-shot novel view synthesis can be interesting directions for future research.
+
+Acknowledgements. This work was supported by NRF (2021R1A2C3006659) and IITP (2021-0-01343) both funded by Korean Government. It was also supported by Samsung Electronics (IO201223-08260-01).
+
+# References
+
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\ No newline at end of file
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+                                            "content": "Figure 1: Synthesis results from sparse inputs. Our Flip-NeRF significantly improves rendering quality compared to other baselines. Compared to the vanilla mip-NeRF [1] and MixNeRF [31], which is the state-of-the-art regularization method, ours reduces the noises and floating artifacts noticeably with superior surface normal estimation. Although Ref-NeRF [36] estimates smooth normal vectors, it shows much inferior rendering results to ours with a large chunk of noise under the few-shot setting."
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+                                    "content": "12, 19, 29, 35, 14] require large-scale datasets consisting of different scenes with multi-view images for injecting prior knowledge during the pre-training, while the regularization methods [25, 31, 15, 11, 30, 8, 17] are optimized per scene, exploiting additional training resources, e.g. unseen viewpoints [25, 15, 17], depth map generation [8, 30], off-the"
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+                                    "type": "text",
+                                    "content": "shelf models [11, 25], and so on, for an effective regularization to alleviate overfitting. Although the prior arts achieved promising results in novel view synthesis from sparse inputs, there still exist hurdles to overcome. The large-scale datasets, which are used for pre-training methods, are expensive to collect and the NeRF model is prone to performance degradation for the out-of-distribution dataset. On the other hand, the regularization methods heavily rely on additional training resources which might not always be available and require many heuristic factors, e.g. the choice of off-the-shelf models, the hyperparameters for sampling unseen viewpoints, and so on."
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+                                    "content": "In this paper, we propose FlipNeRF, which is an effective regularization method exploiting the flipped reflection rays<sup>1</sup> as additional training resources with filtering the ineffective newly generated rays. We derive a batch of flipped reflection rays from the original ray directions and estimated surface normals so that they are cast toward the same target pixels of the original input ray. Compared to the existing regularization methods which have mainly focused on the accurate depth estimation from limited input views [31, 25, 15, 30, 8], our FlipNeRF is trained to reconstruct surface normals accurately by learning to generate effective reflection rays to be used in training. Since both estimated surface normals and depths are derived from the volume densities representing underlying 3D geometry, accurately estimating the surface normals of an object naturally leads to more accurate depth maps."
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+                                    "content": "Furthermore, we propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), to reduce the floating artifacts effectively while considering the uncertainty of the model's outputs by using the estimated scale parameters for mixture models. Since our FlipNeRF is built upon MixNeRF [31], which is a regularization method achieving promising results by modeling input rays with mixture density models [2], we are able to apply our proposed loss without any modification of the architecture by using the estimated scale parameters of each sample along a ray, which stand for the uncertainty of the samples' estimated probability density distributions."
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+                                    "content": "Additionally, inspired by [6, 11, 15] which address the feature-level consistency of targets under the sparse input setting, we encourage the consistency for the pairs of bottleneck features between the original input rays and flipped reflection rays. We leverage a Jensen-Shannon Divergence, which is based on the similarity between the probability distributions, to make the pairs of bottleneck feature distributions of original and flipped reflection rays more similar to each other improving feature consistency."
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+                                    "content": "We demonstrate the effectiveness of our proposed FlipNeRF through the experiments on the multiple bench"
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+                                    "content": "marks, e.g. Realistic Synthetic "
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+                                    "type": "text",
+                                    "content": " [24], DTU [13], and LLFF [23]. Our method achieves state-of-the-art (SOTA) performances compared to other baselines. Especially, ours outperforms other baselines by a large margin with more accurate surface normals under the extremely sparse settings such as 3/4-view setting which are the most challenging ones. Our contributions are summarized as follows:"
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+                                            "content": "- We propose an effective training framework for NeRF with sparse training views, called FlipNeRF. It leverages flipped reflection rays to provide additional training resources, resulting in more precise surface normals with our proposed masking strategy to filter the ineffective rays."
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+                                            "content": "- We also propose an effective regularization loss, Uncertainty-aware Emptiness Loss (UE Loss), which reduces floating artifacts with considering the uncertainty of outputs, leading to more reliable estimation."
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+                                            "content": "- We enhance the consistency of bottleneck features between the original input rays and flipped reflection rays by Jensen-Shannon Divergence, coined as Bottleneck Feature Consistency Loss (BFC Loss), improving the robustness for rendering from unseen viewpoints."
+                                        }
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+                                            "content": "- Our FlipNeRF achieves SOTA performance over the multiple benchmarks. Especially, ours outperforms other baselines by a large margin in more challenging scenarios, e.g. 3/4-view."
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+                                    "content": "2. Related Works"
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+                                    "content": "2.1. Neural Radiance Field"
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+                                    "content": "Recently, Neural Radiance Field (NeRF) [24] has shown impressive performance and potential in the novel view synthesis task. NeRF represents a scene with an MLP, mapping coordinates and viewing directions to its colors and volume density, and then creates a novel view through volume rendering. Subsequent studies have developed NeRF in several directions, e.g. using conical frustums instead of rays [1], reparameterizing an input viewing direction as its reflection direction [36], and so on. These works have made significant progress by addressing the various issues in novel view synthesis, but there still exists a limitation in that NeRF requires a dense set of training images and a lengthy training time. Many studies have addressed these issues [10, 28, 5], including the utilization of various data structures for faster training and inference [9, 42] and attempts to train NeRF with only a few training images. Our work focuses on enhancing the performance of NeRF when a sparse set of views are provided as training images."
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+                                    "content": "<sup>1</sup>The term 'flipped' is used because the reflected ray has an opposite direction (from an object to a camera)."
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+                                            "type": "text",
+                                            "content": "Figure 2: Overall framework of FlipNeRF. Our FlipNeRF utilize the newly generated flipped reflection rays with our proposed UE Loss and BFC Loss as well as existing MSE, NLL and Orientation losses. See Sec. 3 and Fig. 3 for more details about generation process of flipped reflection rays and the loss terms."
+                                        }
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+                                    "type": "text",
+                                    "content": "view scenes to provide prior knowledges of 3D geometry to a NeRF model and then optionally finetune on the target scene [5, 6, 12, 19, 29, 35, 39, 43]. On the contrary, the regularization methods [31, 15, 11, 25, 8, 30, 17] are optimized per scene without pre-training process by exploiting additional training resources, e.g. depth maps [8, 30] and semantic consistency [11], as an extra supervision. Among them, [25, 15, 17] adopt an unseen viewpoint sampling strategy to make up for insufficient training views. However, these sampling processes require many hand-designed factors such as the ranges of rotation, translation, jittering, and so on, which can introduce artificial biases. Our work proposes a novel regularization approach to derive a set of flipped reflection rays from estimated surface normals and utilizes these for regularization, which does not require a heuristic factor to be finetuned, resulting in more effective training strategy with limited inputs."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "2.3. Surface Normal Reconstruction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
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+                                    "type": "text",
+                                    "content": "There is a line of research to recover accurate textures and lighting conditions of objects with NeRF [26, 41, 38, 7, 34, 44, 3]. Although these earlier studies successfully reconstruct the high-quality isosurfaces derived from the scene representations, their rendering quality for novel views is still inferior to the NeRF-like models. Meanwhile, Ref-NeRF [36] achieved superior performance with remarkable quality of surface normals compared to the existing NeRF models. Since the normal vectors utilized in NeRF framework are derived from the negative normalized density gradients [34, 3, 36], which represent the underlying geometry of 3D scenes, learning an accurate density distribution along a ray is a key factor for surface normal reconstruction. However, for the few-shot novel view synthesis, the prior works mostly focus on the accurate depth estimation without attention to the surface normals, both of which are derived from the estimated volume densities. In this work, we approach the few-shot novel view synthesis problem with focusing on the surface normals, which is another critical factor for an effective learning of 3D scene geometry. To the best of our knowledge, our work is the first attempt to focus on the sur"
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+                                    "content": "face normal estimation for few-shot novel view synthesis."
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+                                    "content": "3. Method"
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+                },
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+                                    "content": "In this work, we propose an effective regularization method for few-shot novel view synthesis with flipped reflection rays. Our FlipNeRF is built upon MixNeRF [31] which leverages a mixture model framework (Sec. 3.1). We derive a batch of flipped reflection rays and cast them toward the identical target pixels as additional training rays (Sec. 3.2). Furthermore, we propose the Uncertainty-aware Emptiness Loss and Bottleneck Feature Consistency Loss to alleviate the floating artifacts adaptively based on the uncertainty and enhance the consistency between the bottleneck feature distributions of the original and flipped reflection rays, respectively (Sec. 3.3 and Sec. 3.4). Finally, our FlipNeRF is trained to minimize the MSE and NLL losses as well as the proposed regularization loss terms with their corresponding balancing weights (Sec. 3.5). Fig. 2 shows an overview of our FlipNeRF."
+                                }
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+                                    "content": "NeRF. The NeRF [24], which is an MLP-based neural network, represents a 3D scene as a continuous radiance field of RGB color and volume density. For every point sampled along a ray, the 3D coordinates "
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+                                    "type": "text",
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+                                    "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}"
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+                                    "content": "\\mathbf{d} = \\| \\mathbf{d}\\| _2\\cdot \\hat{\\mathbf{d}}"
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+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        47,
+                        380,
+                        287,
+                        418
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                380,
+                                287,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        380,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        380,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T(t) = \\exp(-\\int_{t_n}^t \\sigma(s) ds)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        380,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": " indicates the degree of transparency. In practice, it is approximated with numerical quadrature [24] by sampling points along a ray."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        47,
+                        418,
+                        287,
+                        442
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                418,
+                                287,
+                                442
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        418,
+                                        287,
+                                        442
+                                    ],
+                                    "type": "text",
+                                    "content": "The radiance field is trained to minimize the mean squared error (MSE) between rendered and GT pixels:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        100,
+                        448,
+                        287,
+                        472
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        100,
+                                        448,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {M S E}} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} | | \\hat {\\mathbf {c}} (\\mathbf {r}) - \\mathbf {c} ^ {\\mathrm {G T}} (\\mathbf {r}) | | _ {2} ^ {2}, \\tag {3}",
+                                    "image_path": "ff1f18cca0f5435934c2c972d61fd00de41e4d815dff73b60c7e6fd148e5a557.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
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+                        192,
+                        491
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                479,
+                                192,
+                                491
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        479,
+                                        192,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        479,
+                                        192,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        479,
+                                        192,
+                                        491
+                                    ],
+                                    "type": "text",
+                                    "content": " is denoted as a set of rays."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        47,
+                        505,
+                        287,
+                        565
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                                287,
+                                565
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        505,
+                                        287,
+                                        565
+                                    ],
+                                    "type": "text",
+                                    "content": "MixNeRF. Built upon mip-NeRF [1], which leveraged a cone tracing method and proposed an integrated positional encoding to address an aliasing problem, MixNeRF [31] estimates the joint probability distribution of color values and models a ray with a mixture of densities:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        107,
+                        571,
+                        287,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        571,
+                                        287,
+                                        604
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "p (\\mathbf {c} | \\mathbf {r}) = \\sum_ {i = 1} ^ {M} \\pi_ {i} \\mathcal {F} (\\mathbf {c}; \\mu_ {i} ^ {\\mathbf {c}}, \\beta_ {i}), \\tag {4}",
+                                    "image_path": "c30a86cff555177af6705d16bf9b6dfb22e573f526ed42b9ae40e288486d2e92.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        47,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                                287,
+                                682
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of sampled points, "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\mathbf{c};\\mu_i^{\\mathbf{c}},\\beta_i)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the Laplacian distribution of RGB "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": " with location parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mu_i^{\\mathbf{c}}\\in \\{\\mu_i^r,\\mu_i^g,\\mu_i^b\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e. estimated RGB values of sample, and scale parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta_{i}\\in \\{\\beta_{i}^{r},\\beta_{i}^{g},\\beta_{i}^{b}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": ". The mixture coefficient "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pi_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": " is derived from the estimated volume density "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        609,
+                                        287,
+                                        682
+                                    ],
+                                    "type": "text",
+                                    "content": " as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        53,
+                        688,
+                        287,
+                        717
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                53,
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+                                287,
+                                717
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        53,
+                                        688,
+                                        287,
+                                        717
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\pi_ {i} = \\frac {w _ {i}}{\\sum_ {m = 1} ^ {M} w _ {m}} = \\frac {T _ {i} (1 - \\exp (- \\sigma_ {i} \\delta_ {i}))}{\\sum_ {m = 1} ^ {M} T _ {m} (1 - \\exp (- \\sigma_ {m} \\delta_ {m}))}, \\tag {5}",
+                                    "image_path": "6afea8d62deac787ca16eba34feecc5e2e13aa5eaa69e9d4661538190df29194.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        305,
+                        72,
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+                        133
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                72,
+                                545,
+                                133
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": " indicate the alpha blending weight and sample interval, respectively. Thanks to the mixture model's capacity of representing complex distributions, MixNeRF learns the density distribution effectively with sparse inputs by minimizing the negative log-likelihood (NLL) in Eq. 4."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        305,
+                        133,
+                        545,
+                        179
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                133,
+                                545,
+                                179
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        133,
+                                        545,
+                                        179
+                                    ],
+                                    "type": "text",
+                                    "content": "Our FlipNeRF is built upon MixNeRF leveraging the mixture modeling framework while achieving superior rendering quality with noticeably fewer artifacts and more accurate surface normals to MixNeRF."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        306,
+                        186,
+                        482,
+                        200
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                186,
+                                482,
+                                200
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        186,
+                                        482,
+                                        200
+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Auxiliary Flipped Reflection Ray"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        305,
+                        205,
+                        545,
+                        264
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                205,
+                                545,
+                                264
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": "As shown in Fig. 3, we exploit a batch of flipped reflection rays "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}' \\in \\mathcal{R}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": " as extra training resources, which are derived from the original input ray directions "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": " and estimated surface normals "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": ". First, we derive a flipped reflection direction "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": " from "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        205,
+                                        545,
+                                        264
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        382,
+                        272,
+                        545,
+                        285
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                382,
+                                272,
+                                545,
+                                285
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        382,
+                                        272,
+                                        545,
+                                        285
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {d} ^ {\\prime} = 2 (\\mathbf {d} \\cdot \\hat {\\mathbf {n}}) \\hat {\\mathbf {n}} - \\mathbf {d}, \\tag {6}",
+                                    "image_path": "a79c2fad3a0e702311cab95c4a3332e66cd44b6bf37672e1f40852acfe7ee6ec.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        305,
+                        293,
+                        545,
+                        340
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                293,
+                                545,
+                                340
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        293,
+                                        545,
+                                        340
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        293,
+                                        545,
+                                        340
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        293,
+                                        545,
+                                        340
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the weighted sum of blending weights and estimated normal vectors along a ray, i.e. "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        293,
+                                        545,
+                                        340
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{n}} = \\sum_{i=1}^{M} w_i \\mathbf{n}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        293,
+                                        545,
+                                        340
+                                    ],
+                                    "type": "text",
+                                    "content": ". Note that we use the gradient of volume density as estimated surface normals following [3, 34, 36]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        305,
+                        341,
+                        545,
+                        449
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                305,
+                                341,
+                                545,
+                                449
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": "To generate the additional training rays based on "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": ", we need a set of imaginary ray origins "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{o}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": " located in a suitable space considering the hitting point and the original input ray origins "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{o}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since the vanilla NeRF models, which are trained with a dense set of images, tend to have the blending weight distribution whose peak is located on the point around the object surface "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_s = \\mathbf{o} + t_s\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        341,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": " [8, 31], i.e. the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th sample whose blending weight is the highest along a ray. Therefore, we place "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{o}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " so that the "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th sample of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_s"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {o} ^ {\\prime} = \\mathbf {p} _ {s} - t _ {s} \\mathbf {d} ^ {\\prime}, \\tag {7}",
+                                    "image_path": "6fd2c3047513d9669e6311fea969213b5937f535bc3b4139c5e97884d4f3f7af.jpg"
+                                }
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "resulting in our proposed flipped reflection ray, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'(t) = \\mathbf{o}' + t\\mathbf{d}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        476,
+                                        545,
+                                        608
+                                    ],
+                                    "type": "text",
+                                    "content": ". Compared to the previous unseen viewpoint sampling strategies [15, 25, 17], our proposed strategy does not rely on the randomness of unseen viewpoint sampling and reduces the heuristic factors for sampling schemes, e.g. the range of rotation, translation, and so on. Furthermore, since our newly generated "
+                                },
+                                {
+                                    "bbox": [
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+                                        476,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        476,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are cast on the identical object surfaces where the original input rays "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        476,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are cast, i.e. the target pixels are photo-consistent for the pair of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        476,
+                                        545,
+                                        608
+                                    ],
+                                    "type": "text",
+                                    "content": " without any sophisticated viewpoint sampling process, we are able to train "
+                                },
+                                {
+                                    "bbox": [
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+                                        608
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " effectively with the same GT pixels of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "However, since "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which are used to derive "
+                                },
+                                {
+                                    "bbox": [
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+                                        668
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}'"
+                                },
+                                {
+                                    "bbox": [
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+                                        608,
+                                        545,
+                                        668
+                                    ],
+                                    "type": "text",
+                                    "content": ", are not the ground truth but the estimation, there exists a concern that even miscreated "
+                                },
+                                {
+                                    "bbox": [
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+                                        668
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
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+                                        608,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which do not satisfy photo-consistency, can be used for training. As a result, it might lead to performance degradation while providing misleading training"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                }
+            ],
+            "discarded_blocks": [
+                {
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+                    ],
+                    "type": "page_footnote",
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+                            ],
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+                                    "type": "inline_equation",
+                                    "content": "{}^{2}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " Technically, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is not guaranteed to be a unit vector without an explicit normalization process. However, we empirically found that the normalization rather destabilizes the training and leads to the performance degradation. Kindly refer to our supplementary material for related experiments."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "22886"
+                                }
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+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "cues. To address this problem, we mask the ineffective "
+                                },
+                                {
+                                    "bbox": [
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+                                        96
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " by considering the angle "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " between "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{n}}"
+                                },
+                                {
+                                    "bbox": [
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+                                        96
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        96
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-\\hat{\\mathbf{d}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        96
+                                    ],
+                                    "type": "text",
+                                    "content": " as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                    ],
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+                                    "bbox": [
+                                        81,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "M \\left(\\mathbf {r} ^ {\\prime}\\right) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\arccos  \\left(- (\\hat {\\mathbf {d}} \\cdot \\hat {\\mathbf {n}})\\right) <   \\tau \\\\ 0 & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {8}",
+                                    "image_path": "b08bbdd94f10724a31ee37bfc3f662fefd930c03659fc68d13dffd0493c32e09.jpg"
+                                }
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        287,
+                                        233
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-(\\hat{\\mathbf{d}}\\cdot \\hat{\\mathbf{n}})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        233
+                                    ],
+                                    "type": "text",
+                                    "content": " amounts to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        233
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\cos \\theta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        148,
+                                        287,
+                                        233
+                                    ],
+                                    "type": "text",
+                                    "content": " of original input rays and normal vectors, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        148,
+                                        287,
+                                        233
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        148,
+                                        287,
+                                        233
+                                    ],
+                                    "type": "text",
+                                    "content": " indicates the threshold for filtering the invalid rays, which we set as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        148,
+                                        287,
+                                        233
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "90^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        233
+                                    ],
+                                    "type": "text",
+                                    "content": " unless specified. Through this masking process, only "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        148,
+                                        287,
+                                        233
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        148,
+                                        287,
+                                        233
+                                    ],
+                                    "type": "text",
+                                    "content": " which are cast toward the photo-consistent point can be remained as we intend. Finally, our proposed flipped reflection rays are modeled by mixture density like the original input rays:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
+                                        104,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "p \\left(\\mathbf {c} \\mid \\mathbf {r} ^ {\\prime}\\right) = \\sum_ {i = 1} ^ {M} \\pi_ {i} ^ {\\prime} \\mathcal {F} \\left(\\mathbf {c}; \\mu_ {i} ^ {\\mathbf {c} ^ {\\prime}}, \\beta_ {i} ^ {\\prime}\\right). \\tag {9}",
+                                    "image_path": "f03daffeaa7a5da2684a586fe2ee26439104ce2b9aa9dc6a7aca4b85eaa8f6c9.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Additionally, we leverage the Orientation Loss proposed in Ref-NeRF [36] to penalize the backward-facing normal vectors for learning accurate surface normals:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "l _ {\\text {O r i .}} (\\mathbf {r}) = \\sum_ {i = 1} ^ {M} w _ {i} \\max  (0, \\mathbf {n} _ {i} \\cdot \\hat {\\mathbf {d}}) ^ {2}. \\tag {10}",
+                                    "image_path": "cde338abda3d9c791738e049929cb6222ffcd1a11b85b6e89984a4ccc6d6d820.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Unlike Ref-NeRF, we penalize underlying density gradient normal "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{n}_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " instead of predicted normals."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Note that our FlipNeRF is fundamentally different compared to Ref-NeRF since ours generates additional training rays through the derivation of reflection direction without modification to original representations while Ref-NeRF replaced the input viewing direction with its reflection direction, reparameterizing the outgoing radiance."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.3. Uncertainty-aware Regularization"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                                    "type": "text",
+                                    "content": "Several regularization techniques have been proposed to reduce the floating artifacts present in synthesized images, which is one of the major problems of NeRF. Among them, we leverage the Emptiness Loss [37] which penalizes the small blending weights along a ray as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
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+                                    "type": "interline_equation",
+                                    "content": "l _ {\\text {E m p .}} (\\mathbf {r}) = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\log (1 + \\eta \\cdot w _ {i}), \\tag {11}",
+                                    "image_path": "01f33ab115d56c0517b4a024214b8e0b6161fd284ea8be8ddabbfb2b768723df.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where the bigger "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\eta"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is, the steeper the loss function becomes around 0."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "However, the naive application of existing regularization techniques with limited training views might not be consistently helpful across the different scenes due to the scene-by-scene different structure, resulting in overall performance degradation. To address this problem, we propose Uncertainty-aware Emptiness Loss (UE Loss) developed upon the Emptiness Loss, which reduces the floating"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "artifacts consistently over the different scenes by considering the output uncertainty:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
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+                                    "type": "interline_equation",
+                                    "content": "l _ {\\mathrm {U E}} (\\mathbf {r}) = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\log (1 + \\rho \\cdot \\eta \\cdot w _ {i}), \\tag {12}",
+                                    "image_path": "fab3b2de06313ccb414d07fc71a953bcad5221d6fa4de5521dd5e8594359af1d.jpg"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\text {w h e r e} \\quad \\rho = \\frac {1}{3} \\sum_ {c} ^ {\\{r, g, b \\}} \\sum_ {i = 1} ^ {M} \\beta_ {i} ^ {c}.",
+                                    "image_path": "cf8fcb513a7076a1b0bdb779b117430d42c5293eda213d5ebcd16f688727eff8.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\rho"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " amounts to the average of the summation of estimated scale parameters of RGB color distributions from all samples along a ray, which we use as the uncertainty of a ray. By our proposed UE Loss, we are able to regularize the blending weights adaptively, i.e. the more uncertain a ray is, the more penalized the blending weights along the ray are. It is able to reduce floating artifacts consistently across the scenes with different structures and enables to synthesize more reliable outputs by considering uncertainty."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.4. Bottleneck Feature Consistency"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Motivated by previous works addressing the feature-level consistency of multiple views for few-shot novel view synthesis [6, 11, 15], we encourage the consistency of bottleneck feature distributions between "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which are intermediate feature vectors, i.e. outputs of the spatial MLP of NeRF, by Jensen-Shannon Divergence (JSD):"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "l _ {\\mathrm {B F C}} \\left(\\mathbf {r}, \\mathbf {r} ^ {\\prime}\\right) = J S D \\left(\\psi (\\mathbf {b}), \\psi \\left(\\mathbf {b} ^ {\\prime}\\right)\\right), \\tag {13}",
+                                    "image_path": "c0f4b0eb544758cc8b803fe372cce65e390b83443c3fec43fa1e250ee64de266.jpg"
+                                }
+                            ]
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\psi (\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denote the softmax function, the bottleneck features of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", respectively. While the existing methods [6, 11] rely on off-the-shelf feature extractors like 2D CNN or CLIP [27] to address high-level feature consistency, we regulate the pair of features effectively by enhancing consistency between bottleneck features without depending on additional feature extractors."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.5. Total Loss"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Our FlipNeRF is not only trained to maximize the log-likelihood of the target pixel "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}_{\\mathrm{GT}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for a set of original input rays "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", but also for flipped reflection rays "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}_M^\\prime"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where the ineffective rays are excluded from the total flipped reflection rays "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}^\\prime"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        554,
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+                                        626
+                                    ],
+                                    "type": "text",
+                                    "content": " by our masking strategy in Eq. 8. Likewise, the UE Losses are applied for both "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        626
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}_M^\\prime"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Aggregating all, our total loss over a batch is as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {T o t a l}} = \\mathcal {L} _ {\\text {M S E}} + \\lambda_ {1} \\mathcal {L} _ {\\text {N L L}} + \\lambda_ {2} \\mathcal {L} _ {\\text {N L L}} ^ {\\prime} \\tag {14} \\\\ + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {U E}} + \\lambda_ {4} \\mathcal {L} _ {\\mathrm {U E}} ^ {\\prime} + \\lambda_ {5} \\mathcal {L} _ {\\mathrm {B F C}} + \\lambda_ {6} \\mathcal {L} _ {\\mathrm {O r i}}, \\\\ \\end{array}",
+                                    "image_path": "60fb94e8bb86dbc2e5b431c5812b4cb55f52e735d0ae8d58d186a41c6b8f9724.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where a set of "
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
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+                                    "type": "text",
+                                    "content": "'s are balancing weight terms for the losses."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                }
+            ],
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+                                            "html": "<table><tr><td>τ</td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>30°</td><td>18.62</td><td>0.747</td><td>0.206</td><td>0.121</td></tr><tr><td>60°</td><td>18.12</td><td>0.723</td><td>0.237</td><td>0.126</td></tr><tr><td>90°</td><td>19.55</td><td>0.767</td><td>0.180</td><td>0.101</td></tr><tr><td>180° (No masking)</td><td>18.76</td><td>0.755</td><td>0.190</td><td>0.111</td></tr></table>",
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+                                    "content": "Implementation details. Our FlipNeRF is built upon MixNeRF [31] based on the JAX codebase [4], which is developed upon mip-NeRF [1]. The overall training scheme follows [25, 31]. We adopt a scene space annealing strategy for the early training phase. Also, we apply the exponential decay and warm up for the learning rate. The Adam optimizer [16] and the gradient clippings by value at 0.1 and norm at 0.1 are used. We train our FlipNeRF for 500 pixel epochs with a batch size of 4,096 on 4 NVIDIA RTX 3090. Additionally, since the LLFF dataset [23] consists of scenes with much more static movement of viewpoints compared to other datasets, we set the threshold "
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+                                    "type": "text",
+                                    "content": " of our masking strategy as "
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+                                    "type": "text",
+                                    "content": " for the experiments on LLFF. More detailed hyperparameters and our loss balancing terms by the datasets and the number of training views are provided in the supplementary material."
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+                                    "content": "Datasets and metrics. We evaluate the performance of our FlipNeRF and baselines on the representative benchmarks: Realistic Synthetic "
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+                                    "content": " [24], DTU [13], and LLFF [23]. Realistic Synthetic "
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+                                    "content": " contains 8 synthetic scenes, each consisting of 400 multi-view rendered images with white background. To compare against other representative baselines [15, 11, 31, 25, 1], we evaluate our FlipNeRF under the scenarios of 4 and 8 views. For a fair comparison, we sample the first "
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+                                    "type": "text",
+                                    "content": "-image of the training set for the "
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+                                    "type": "text",
+                                    "content": "-view scenario so that the identical images are provided for training different methods following [31]. We use 200 images of the test set for evaluation. For DTU, which provide various scenes including objects put on a white table with a black background, we conduct experiments on the 15"
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+                                    "type": "text",
+                                    "content": "specific scenes under the scenarios of 3, 6, and 9-view, following the experimental protocol of [43]. We also conduct a series of experiments for the analysis of FlipNeRF under 3-view setting as well as comparison against other baselines. Additionally, we compare our FlipNeRF against other baselines on LLFF consisting of real forward-facing scenes, which is often tested as an out-of-distribution dataset for pre-training methods. Following [24], every 8th image of each scene is used for a held-out test set and the training views are evenly selected from the remaining images. Like DTU, we report our results of the 3, 6, and 9-view scenarios, following [43]."
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+                                    "type": "text",
+                                    "content": "For the quantitative evaluation for rendered images, we adopt the mean of PSNR, SSIM [40], LPIPS [45], and the geometric average [1]. Furthermore, we also adopt the mean angular error "
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+                                    "content": " [36] and NLL [33, 32, 21, 18] for evaluating the surface normals and uncertainty, respectively. Specifically, following [33], we compute the NLL by deriving the probability of the GT pixel values given a Gaussian distribution with the estimated RGB values as mean and the uncertainty as variance, which is derived from the weighted sum of the blending weights and estimated scale parameters along a ray in our FlipNeRF. For DTU, we report the results evaluated by masked metrics to prevent background bias, following [25, 31]."
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+                                    "type": "text",
+                                    "content": "Baselines. We compare our FlipNeRF against the SOTA regularization methods [11, 15, 25, 31] on Realistic Synthetic "
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+                                    "type": "text",
+                                    "content": " as well as the vanilla mip-NeRF [1] and Ref-NeRF [36], which is known for achieving promising results with accurate surface normals. Furthermore, we compare ours against the representative pre-training methods [5, 6, 43] as well as regularization methods on DTU and LLFF. The pre-training baselines exploit the DTU and LLFF as pre-training dataset and out-of-distribution test set, respectively, while the regularization methods, mip-NeRF and Ref-NeRF are optimized per scene. Note that we report the quantitative results of other baselines on DTU and LLFF from [25], which achieved better results than its original papers by the modified training scheme, and those on Realistic Synthetic "
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+                                    "type": "text",
+                                    "content": " from [31], which trained the baselines with the identical training views for a fair comparison."
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+                                    "content": "Analysis of flipped reflection rays. As shown in Tab. 1, our masking strategy of filtering out the ineffective flipped reflection rays with the threshold "
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+                                    "content": " achieves the best performance among different options. With "
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+                                    "content": ", the rendering quality is rather degraded since the newly generated rays are overly-filtered and do not provide enough additional supervision as demonstrated in Fig. 4a. On the other hand, when we exploit all the flipped reflection rays without masking, there exists a little improvement"
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+                                    "content": " due to the negative impact from the ineffective rays. Additionally, Fig. 4b shows the distribution of "
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+                                    "content": ", i.e. angles between the input viewing directions and normal vectors. As the smaller "
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+                                    "content": " is, the more photo-consistent the target pixel is, i.e. the more effective the newly generated flipped reflection rays are for training. Since our FlipNeRF is trained to estimate the accurate normal vectors, we are able to exploit a set of more effective flipped reflection rays through the training, which are cast on the more photo-consistent target pixels. Furthermore, at the initial training phase, the invalid additional rays are filtered effectively by our masking strategy, leading to high-quality supervision and stabilizing the training."
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Bottleneck feature consistency. As shown in Tab. 3, there is no significant impact on the performance with regularizing the bottleneck feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " using MSE or cosine similarity. By our proposed "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{BFC}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with JSD, we achieve a considerable performance improvement. Interestingly, the performance rather degrades when we apply "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{BFC}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with JSD to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}_{\\hat{\\mathbf{d}}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", i.e. the bottleneck feature conditioned with input viewing direction "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{d}}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We conjecture that the reduced feature dimension of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}_{\\hat{\\mathbf{d}}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " reduces the capacity of feature representations and prevents the model from improving robustness."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "4.3. Ablation Study"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "The quantitative results of our ablation study are reported in Tab. 4. With only additionally exploiting our proposed flipped reflection rays, our FlipNeRF achieves more degenerate results compared to the baseline "
+                                },
+                                {
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+                                    "content": "((1) \\rightarrow (2))"
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+                                    "type": "text",
+                                    "content": ". However, we are able to achieve performance improvement by a large margin with our proposed "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "((2) \\rightarrow (3) \\rightarrow (4))"
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+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(5) \\rightarrow (7)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " shows that enhancing the consistency of bottleneck features between the pair of original and flipped reflection rays is considerably effective. Additionally, by leveraging "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{Ori}}"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", from Ref-NeRF, we are able to estimate more accurate normal vectors, leading to more effective flipped reflection rays and performance gain "
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+                                    "type": "text",
+                                    "content": "."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">PSNR ↑</td><td colspan=\"2\">SSIM ↑</td><td colspan=\"2\">LPIPS ↓</td><td colspan=\"2\">Average Err. ↓</td><td colspan=\"2\">MAE° ↓</td></tr><tr><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td><td>4-view</td><td>8-view</td></tr><tr><td>mip-NeRF [1]</td><td>14.12</td><td>18.74</td><td>0.722</td><td>0.828</td><td>0.382</td><td>0.238</td><td>0.221</td><td>0.121</td><td>96.05</td><td>101.21</td></tr><tr><td>Ref-NeRF [36]</td><td>18.09</td><td>24.00</td><td>0.764</td><td>0.879</td><td>0.269</td><td>0.106</td><td>0.150</td><td>0.058</td><td>65.62</td><td>57.93</td></tr><tr><td>DietNeRF [11]</td><td>15.42</td><td>21.31</td><td>0.730</td><td>0.847</td><td>0.314</td><td>0.153</td><td>0.201</td><td>0.086</td><td>-</td><td>-</td></tr><tr><td>InfoNeRF [15]</td><td>18.44</td><td>22.01</td><td>0.792</td><td>0.852</td><td>0.223</td><td>0.133</td><td>0.119</td><td>0.073</td><td>-</td><td>-</td></tr><tr><td>RegNeRF [25]</td><td>13.71</td><td>19.11</td><td>0.786</td><td>0.841</td><td>0.346</td><td>0.200</td><td>0.210</td><td>0.122</td><td>62.78</td><td>60.37</td></tr><tr><td>MixNeRF [31]</td><td>18.99</td><td>23.84</td><td>0.807</td><td>0.878</td><td>0.199</td><td>0.103</td><td>0.113</td><td>0.060</td><td>70.90</td><td>62.04</td></tr><tr><td>FlipNeRF (Ours)</td><td>20.60</td><td>24.38</td><td>0.822</td><td>0.883</td><td>0.159</td><td>0.095</td><td>0.091</td><td>0.055</td><td>58.72</td><td>57.17</td></tr></table>",
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+                                            "content": "Table 5: Quantitative results on Realistic Synthetic "
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+                                            "content": " . Our FlipNeRF achieves the SOTA performance among other baselines across all the scenarios and metrics."
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+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">PSNR ↑ 6-view</td><td rowspan=\"2\">9-view</td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">SSIM ↑ 6-view</td><td rowspan=\"2\">9-view</td><td rowspan=\"2\">3-view</td><td rowspan=\"2\">LPIPS ↓ 6-view</td><td rowspan=\"2\">9-view</td><td colspan=\"3\">Average Error ↓</td></tr><tr><td>3-view</td><td>6-view</td><td>9-view</td></tr><tr><td>mip-NeRF [1]</td><td>8.68</td><td>16.54</td><td>23.58</td><td>0.571</td><td>0.741</td><td>0.879</td><td>0.353</td><td>0.198</td><td>0.092</td><td>0.323</td><td>0.148</td><td>0.056</td></tr><tr><td colspan=\"13\">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>16.82</td><td>19.11</td><td>20.40</td><td>0.695</td><td>0.745</td><td>0.768</td><td>0.270</td><td>0.232</td><td>0.220</td><td>0.147</td><td>0.115</td><td>0.100</td></tr><tr><td>PixelNeRF†[43]</td><td>18.95</td><td>20.56</td><td>21.83</td><td>0.710</td><td>0.753</td><td>0.781</td><td>0.269</td><td>0.223</td><td>0.203</td><td>0.125</td><td>0.104</td><td>0.090</td></tr><tr><td>SRF [6]</td><td>15.32</td><td>17.54</td><td>18.35</td><td>0.671</td><td>0.730</td><td>0.752</td><td>0.304</td><td>0.250</td><td>0.232</td><td>0.171</td><td>0.132</td><td>0.120</td></tr><tr><td>SRF†[6]</td><td>15.68</td><td>18.87</td><td>20.75</td><td>0.698</td><td>0.757</td><td>0.785</td><td>0.281</td><td>0.225</td><td>0.205</td><td>0.162</td><td>0.114</td><td>0.093</td></tr><tr><td>MVSNeRF [5]</td><td>18.63</td><td>20.70</td><td>22.40</td><td>0.769</td><td>0.823</td><td>0.853</td><td>0.197</td><td>0.156</td><td>0.135</td><td>0.113</td><td>0.088</td><td>0.068</td></tr><tr><td>MVSNeRF†[5]</td><td>18.54</td><td>20.49</td><td>22.22</td><td>0.769</td><td>0.822</td><td>0.853</td><td>0.197</td><td>0.155</td><td>0.135</td><td>0.113</td><td>0.089</td><td>0.069</td></tr><tr><td colspan=\"13\">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>11.85</td><td>20.63</td><td>23.83</td><td>0.633</td><td>0.778</td><td>0.823</td><td>0.314</td><td>0.201</td><td>0.173</td><td>0.243</td><td>0.101</td><td>0.068</td></tr><tr><td>RegNeRF [25]</td><td>18.89</td><td>22.20</td><td>24.93</td><td>0.745</td><td>0.841</td><td>0.884</td><td>0.190</td><td>0.117</td><td>0.089</td><td>0.112</td><td>0.071</td><td>0.047</td></tr><tr><td>MixNeRF [31]</td><td>18.95</td><td>22.30</td><td>25.03</td><td>0.744</td><td>0.835</td><td>0.879</td><td>0.203</td><td>0.102</td><td>0.065</td><td>0.113</td><td>0.066</td><td>0.042</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.55</td><td>22.45</td><td>25.12</td><td>0.767</td><td>0.839</td><td>0.882</td><td>0.180</td><td>0.098</td><td>0.062</td><td>0.101</td><td>0.064</td><td>0.041</td></tr></table>",
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+                                            "content": "Table 6: Comparison with baselines on DTU. Our FlipNeRF outperforms all the pre-training and regularization methods in every scenario, especially by a large margin under the 3-view setting. "
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+                                            "content": " indicates fine-tuning."
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+                                            "html": "<table><tr><td></td><td>PSNR ↑</td><td>SSIM ↑</td><td>LPIPS ↓</td><td>Average Err. ↓</td></tr><tr><td>mip-NeRF [1]</td><td>14.62</td><td>0.351</td><td>0.495</td><td>0.246</td></tr><tr><td colspan=\"5\">Pre-training.</td></tr><tr><td>PixelNeRF [43]</td><td>7.93</td><td>0.272</td><td>0.682</td><td>0.461</td></tr><tr><td>PixelNeRF† [43]</td><td>16.17</td><td>0.438</td><td>0.512</td><td>0.217</td></tr><tr><td>SRF [6]</td><td>12.34</td><td>0.250</td><td>0.591</td><td>0.313</td></tr><tr><td>SRF† [6]</td><td>17.07</td><td>0.436</td><td>0.529</td><td>0.203</td></tr><tr><td>MVSNeRF [5]</td><td>17.25</td><td>0.557</td><td>0.356</td><td>0.171</td></tr><tr><td>MVSNeRF† [5]</td><td>17.88</td><td>0.584</td><td>0.327</td><td>0.157</td></tr><tr><td colspan=\"5\">Regularization.</td></tr><tr><td>DietNeRF [11]</td><td>14.94</td><td>0.370</td><td>0.496</td><td>0.240</td></tr><tr><td>RegNeRF [25]</td><td>19.08</td><td>0.587</td><td>0.336</td><td>0.146</td></tr><tr><td>MixNeRF [31]</td><td>19.27</td><td>0.629</td><td>0.236</td><td>0.124</td></tr><tr><td>FlipNeRF (Ours)</td><td>19.34</td><td>0.631</td><td>0.235</td><td>0.123</td></tr></table>",
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+                                    "content": ". As demonstrated in Tab. 5, our FlipNeRF achieves the SOTA performance across all the evaluation metrics. Compared to MixNeRF which leverages a mixture model framework as ours, our FlipNeRF"
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+                                    "content": "improves the performance by a large margin. Noticeably, our FlipNeRF estimates more accurate surface normals than other baselines, leading to the performance gain with better reconstructed fine details from limited input views as shown in Fig. 6a. Additionally, the vanilla Ref-NeRF, which shows great performance with accurate normal vectors, achieves comparable or even better performance than other regularization methods except ours. From this result, we are able to expect that estimating the accurate surface normals is one of the key factors for learning 3D geometry with sparse inputs. Note that the comparable "
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+                                    "content": " of RegNeRF results from the overly-smoothed depth estimation, not indicating the high-quality of rendering results, as shown in Fig. 6a."
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+                                    "content": "DTU. Our FlipNeRF achieves the best results across all the scenarios and most of the evaluation metrics on DTU as shown in Tab. 6. Remarkably, ours trained with 6-view outperforms all the pre-training methods trained with 9-view in every metric except SSIM. Furthermore, ours trained with 3-view still outperforms PixelNeRF [43] and SRF [6] trained with 6-view. Similar to the results on Realistic Synthetic "
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+                                            "content": " and DTU. More results are provided in the supp. material."
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+                                    "content": "margin especially under the 3-view, which is the most challenging scenario, with reducing the floating artifacts successfully as shown in Fig. 6b. Since the flipped reflection rays are effective training resources for unseen views, the fewer the training views are provided, the more performance gain is expected."
+                                }
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+                                    "type": "text",
+                                    "content": "LLFF. Table 7 compares our FlipNeRF against other baselines on LLFF, which is a real forward-facing dataset. Although ours achieves the SOTA performance among other baselines, it is much more marginal than those on Realistic Synthetic "
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+                                    "type": "text",
+                                    "content": " and DTU. We conjecture the reason for the marginal improvement of our proposed method can be the fact that a set of flipped reflection rays, which are able to widely cover the unseen views, are not very useful for the scenes in LLFF, where a set of camera poses are much less dynamic than other datasets. In other words, our FlipNeRF is able to not only achieve a competitive performance for the scenes consisting of a set of simple camera poses, but also render the novel views in much higher quality for more dynamically captured scenes with only a few shots. The rendered images are provided in the supp. material."
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+                                    "content": "5. Conclusion"
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+                                    "content": "In this work, we have focused on accurate surface normals, which is another key factor for the few-shot novel view synthesis. Our proposed FlipNeRF utilizes a set of flipped reflection rays as additional training resources, which are simply derived from the estimated normal vectors and the input ray directions. Since it does not require a heuristic factor to be finetuned delicately for unseen view generation, we are able to exploit these additional training resources with much less burden. Furthermore, with our proposed UE Loss, FlipNeRF reduces the floating artifacts consistently across the different scene structures while"
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+                                    "type": "text",
+                                    "content": "considering the output uncertainty, leading to more reliable outputs. Also, our proposed BFC Loss enhances the bottleneck feature consistency between the rays cast on the photo-consistent pixels without leveraging the off-the-shelf feature extractor, leading to performance improvement under the few-shot setting. Our FlipNeRF achieves the SOTA performance with limited input views among the other few-shot baselines and vanilla NeRF-like models. We expect that our work is able to open another meaningful direction for the research of few-shot novel view synthesis."
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+                                    "type": "text",
+                                    "content": "Limitations and future work. Our FlipNeRF exploits the flipped reflection rays as a set of additional training rays, leading to more accurate surface normal estimation. Although Ref-NeRF achieved promising results with the high-quality surface reconstruction, we use mip-NeRF representation instead of Ref-NeRF for a fair comparison with other methods which are based on mip-NeRF. However, as shown in Tab. 6 and Fig. 6a, Ref-NeRF shows promising results without any additional consideration for few-shot setting compared to the vanilla mip-NeRF. Like our FlipNeRF, the accurate surface normal estimation leads to the competitive performance of Ref-NeRF even in the few-shot scenarios. Therefore, a combination of our FlipNeRF training framework with the Ref-NeRF representation or further exploration with regard to the view-dependent appearance for the few-shot novel view synthesis can be interesting directions for future research."
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work was supported by NRF (2021R1A2C3006659) and IITP (2021-0-01343) both funded by Korean Government. It was also supported by Samsung Electronics (IO201223-08260-01)."
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+                                }
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
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+                                        }
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diff --git a/2023/Focal Network for Image Restoration/8fcb7aa2-a8ca-4dca-97f1-3bf63a15581e_content_list.json b/2023/Focal Network for Image Restoration/8fcb7aa2-a8ca-4dca-97f1-3bf63a15581e_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..20da0f392c18c73b346fea100777e291fa36084d
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+    {
+        "type": "text",
+        "text": "Focal Network for Image Restoration",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yuning Cui $^{1}$  Wenqi Ren $^{2*}$  Xiaochun Cao $^{2}$  Alois Knoll $^{1}$ $^{1}$ Technical University of Munich  $^{2}$ Shenzhen Campus of Sun Yat-sen University  \n{yuning.cui,knoll}@in.tum.de {renwq3, caoxiaochun}@mail.sysu.edu.cn",
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+        "bbox": [
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+            268,
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+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Image restoration aims to reconstruct a sharp image from its degraded counterpart, which plays an important role in many fields. Recently, Transformer models have achieved promising performance on various image restoration tasks. However, their quadratic complexity remains an intractable issue for practical applications. The aim of this study is to develop an efficient and effective framework for image restoration. Inspired by the fact that different regions in a corrupted image always undergo degradations in various degrees, we propose to focus more on the important areas for reconstruction. To this end, we introduce a dual-domain selection mechanism to emphasize crucial information for restoration, such as edge signals and hard regions. In addition, we split high-resolution features to insert multiscale receptive fields into the network, which improves both efficiency and performance. Finally, the proposed network, dubbed FocalNet, is built by incorporating these designs into a U-shaped backbone. Extensive experiments demonstrate that our model achieves state-of-the-art performance on ten datasets for three tasks, including single-image defocus deblurring, image dehazing, and image desnowing. Our code is available at https://github.com/c-yn/FocalNet.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1. Introduction",
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Bad weather or physical limitations of cameras will degrade visibility of captured images and further exert a negative impact on robustness of downstream tasks. In this regard, image restoration is immensely useful to remove those undesired degradations, e.g., haze, snowflake, and blur, thus playing an essential role in surveillance, autonomous vehicles, remote sensing, and medical imaging [48]. Due to its ill-posed property, many conventional methods have been proposed by resorting to assumptions and hand-crafted features to reduce the solution space. However, these methods are inapplicable to complicated real-world scenarios [66].",
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+        "text": "The rapid development of convolutional neural networks",
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+    },
+    {
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+        "image_caption": [
+            "Figure 1. PSNR vs. FLOPs on the SOTS-Indoor [27] dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "(CNNs) has alleviated the above issue to some extent by learning generalizable image priors from large-scale collected datasets [25, 44]. Recently, Transformer models have injected vitality into image restoration and have achieved promising performance by providing powerful ability of modeling long-range pixel interactions, which is useful for recovering large-scale degradations [7, 32, 61]. Despite a few remedies, the quadratic complexity of self-attention still remains a formidable issue for practical applications.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "How to effectively capture critical information parsimoniously has long been a key problem in the computer vision and pattern recognition community. Successful examples include attention mechanism [53], focal loss [34], and the recent advance of partial AUC optimization [58]. Inspired by this, in this study, instead of pursuing large receptive field or exploring modification for the Transformer architecture, we aim to develop an efficient and effective CNN-based framework by paying more attention to informative signals for reconstruction, such as edge information or regions that are difficult to recover. In this direction, existing approaches can be roughly divided into two categories: auxiliary training and attention based methods. The former mainly leverages auxiliary techniques or data, e.g., semantic segmentation [12], depth estimation [29], and optical flow estimation [60], to locate degradations or edge information. Nonetheless, these algorithms always need additional com",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "image_caption": [
+            "Blurry Image"
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+        "image_caption": [
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+        "image_caption": [
+            "Initial Feature",
+            "Figure 2. Effects of our dual-domain selection mechanism (DSM). From left to right: blurry images obtained from DPDD [1], ground-truth images, input features of our DSM, results of spatial selection, and results of spatial&frequency selection. SSM helps focus on degradation regions while FSM emphasizes edge information. Zoom in for the best view."
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+        "img_path": "images/37d02c86885a18dafc1f706e31eb9a395ffbfb3cfbf2e7ac97f54b9cace9afc4.jpg",
+        "image_caption": [
+            "w/SSM"
+        ],
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+        "type": "image",
+        "img_path": "images/a98516a110a5e5a19a7af50197c19dbada21a650c4b2641af4525821ad01e61e.jpg",
+        "image_caption": [
+            "w/SSM&FSM"
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+    {
+        "type": "text",
+        "text": "plicated branch and elaborately devised training strategies to generate supervisory information. The other line on this topic is to design attention mechanisms to attend to informative regions or control information transmission [8, 41, 62]. These approaches mostly lie in the spatial domain while ignoring the usage of spectral information, which can also provide useful information for reconstruction.",
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+        "type": "text",
+        "text": "To prompt models to focus more on critical regions, we propose a novel dual-domain selection mechanism (DSM) by sufficiently leveraging discrepancies between sharp/degraded image pairs in both spatial and spectral domains. Concretely, our mechanism comprises two components: spatial selection module (SSM) and frequency selection module (FSM). SSM takes features as input and determines general locations of degradations for each channel by deploying depthwise convolution layers. Then FSM is used to amplify high-frequency signals or hard regions by removing low frequency from features. The proposed network, FocalNet, is established by incorporating DSM into a U-shaped CNN backbone. To save computation overhead, we only insert DSM into the bottleneck module of our FocalNet, which includes the lowest-resolution features.",
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+    {
+        "type": "text",
+        "text": "Moreover, we split the high-resolution features into two parts over channel dimension. Half features are downsampled to lower resolution, which can not only reduce complexity but also boost performance by providing multiscale receptive fields for degradations of different sizes.",
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+        "type": "text",
+        "text": "Based on the above designs, our FocalNet exhibits state-of-the-art performance on three image restoration tasks. For dehazing, FocalNet outperforms PMNet [59] on both synthetic and real-world benchmark datasets with lower computational complexity, as illustrated in Figure 1. For the desnowing task, FocalNet is superior to Transformer-based framework TransWeather [50] on three commonly used desnowing datasets. Our network also shows potential on defocus deblurring problem by producing a performance gain of  $0.2\\mathrm{dB}$  PSNR over Restormer [61] on the combined",
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+    },
+    {
+        "type": "text",
+        "text": "category of DPDD [1] dataset. Overall, the main contributions of this study are summarized as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel dual-domain selection mechanism (DSM) that amplifies the response of important regions to assist in recovering clean features.",
+            "- We develop an efficient and effective focal network that provides multi-scale representation learning for image restoration.",
+            "- Extensive experiments on ten datasets demonstrate that the proposed network, FocalNet, performs favorably against state-of-the-art algorithms on three representative image restoration tasks."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image Restoration Architectures. As a long-standing task, image restoration aims to remove undesired degradations in corrupted images, which plays an important role in many fields, such as robot vision, medical applications, and surveillance [48, 66]. Recently, CNN-based architectures have significantly advanced the performance compared to conventional methods [1, 8, 14, 16]. Among these architectures, the encoder-decoder paradigm is a popular solution to learn hierarchical representations [39, 44]. In addition, a great number of functional units have been developed or borrowed from other realms, such as dilated convolution [68], skip connections [13], dynamic filter [25], and various attention mechanisms [41]. More recently, Transformer models have been imported into low-level vision tasks and provided promising performance [7, 32]. Thereafter, a few measures have been taken to reduce the computational complexity of self-attention by restricting the operation region [32] or switching the operation dimension [61].",
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+    },
+    {
+        "type": "text",
+        "text": "Spectral Networks. Apart from spatial representation learning, numerous deep frameworks have been proposed",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "13002",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/1c0c6be16be4097395a9ac2bc56cd62a469677f6bded47bc705158b5f753d33c.jpg",
+        "image_caption": [
+            "Figure 3. Architecture of the proposed FocalNet with dual-domain selection mechanism (DSM) that consists of two components, i.e., spatial selection module (SSM) and frequency selection module (FSM). ResBlock contains  $n$  residual blocks, comprising two  $3 \\times 3$  convolution layers and activation function in between."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "to bridge frequency gaps between sharp/degraded image pairs [15, 39, 68]. The common practice is to decompose features into different frequency components via transformation tools such as wavelet transform [10, 68], Fourier transform [22, 39], pooling technique [15], and conventional filters [35], and then treat each component individually via convolution layers. In addition, a few researches have investigated the different roles of phase and amplitude, and proposed architectures to recover them separately [28]. In our work, we simply remove the lowest-frequency signal from the resulting features of SSM to provide guidance for further reconstruction.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Auxiliary Training. In addition to the provided ground-truth images in training sets of image restoration tasks, a great number of networks have been proposed to resort to auxiliary supervision. Semantic priors have been introduced into low-level tasks to provide color, boundary or location information [12, 43, 45]. However, global semantic priors are less effective for degradations caused by large depth variations. Thus many methods have proposed to estimate depth map to generate edge and structure signals for restoration [24, 29]. Moreover, there are many works that integrate other auxiliary information such as optical flow [56, 60] and event data [57]. However, the above solutions always require additional data, expensive convolution branch, and complicated training strategies [45].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first delineate the overall architecture of FocalNet. Then we describe our modules: Multi-scale ResBlock (MResBlock) and Dual-domain Selection Mech-",
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+    },
+    {
+        "type": "text",
+        "text": "anism (DSM). Finally, we detail the loss functions.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overall Pipeline",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Figure 3, the proposed FocalNet adopts the popular encoder-decoder architecture to learn hierarchical representations efficiently. Both encoder and decoder networks consist of three scales. In our paper, we refer to the first scale as the sub-network that involves the highest-resolution features. MResBlock constitutes the main part of the first scale. The other two scales are mainly composed of ResBlock, which consists of  $n$  residual blocks. Given a degraded image of size  $H \\times W \\times 3$ , where  $H \\times W$  and  $C$  represent spatial locations and the number of channels respectively, a  $3 \\times 3$  convolution layer is used to extract shallow features of size  $H \\times W \\times C$ . Then, the shallow features pass through three-scale symmetric encoder-decoder and are transformed into restored features, i.e., output features of MResBlock in the first scale of decoder. Starting from the highest-resolution input, the encoder gradually reduces spatial size and expands the number of channels. The decoder does the opposite to restore clean features from the deepest features. During this process, the decoder features are concatenated with the encoder features to assist recovery, followed by a  $1 \\times 1$  convolution to adjust channel dimension. Finally, the predicted clean image is generated by the last  $3 \\times 3$  convolution layer and image-level residual connection. Upsampling (UP) and downsampling (DOWN) operations are implemented by transposed and strided convolutions except for the upsampling layer in MResBlock that adopts bilinear interpolation. The proposed DSM is injected into the bottleneck location to select the most im",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "13003",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "portant regions for reconstruction. In addition, we apply the multi-input and multi-output strategies to ease training difficulty following previous methods [13, 15, 39, 49].",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Multi-scale ResBlock (MResBlock)",
+        "text_level": 1,
+        "bbox": [
+            76,
+            145,
+            382,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Recently, pursuing multi-scale receptive fields is a hot topic in computer vision community [5, 20, 42, 55], especially for Transformer-based models [33, 42]. Inspired by [11, 40, 46], we adopt multi-scale mechanism in ResBlock to form our MResBlock via splitting and downsampling operations, as illustrated in Figure 3. Specifically, given input features, we first split them equally along channel dimension into two components. Next, half features are reduced to a quarter of the original resolution using strided convolution. The resulting features are fed into ResBlock, and then up-sampled to the original size. The other half are directly processed by ResBlock. The final output of MResBlock is obtained by concatenating resulting features of two branches. MResBlock enjoys two main advantages. Firstly, it improves performance by realizing multi-scale representation learning for degradations of different sizes and enhances spectral learning for different frequencies [40]. Secondly, it improves efficiency by reducing feature resolution.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Dual-domain Selection Mechanism (DSM)",
+        "text_level": 1,
+        "bbox": [
+            76,
+            450,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The main goal of this study is to develop an efficient network for image restoration by focusing on the more important regions. This aim is achieved by the proposed DSM, which amplifies the response of informative information in two domains (see Figure 2). As illustrated in the bottom part of Figure 3, it consists of two components: spatial selection module (SSM) and frequency selection module (FSM). Given input features  $F \\in \\mathbb{R}^{H \\times W \\times C}$ , SSM and FSM are employed successively, which can be expressed as:",
+        "bbox": [
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+            473,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {F} = \\operatorname {F S M} (\\operatorname {S S M} (F)). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Next, we introduce these two elements in details.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Spatial Selection Module (SSM). SSM helps the network focus on important regions in the spatial domain, providing initial locations of severe degradations for subsequent FSM. Our SSM has three branches. The main path is built upon the CBAM [53] to produce the general feature representation for locations of degradations to focus. Specifically, given an intermediate feature map  $F$ , we first squeeze  $F$  along channel dimension through two types of pooling techniques, i.e., max pooling and average pooling, and then generate the general feature map via a convolution layer, which is formally expressed as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF ^ {\\prime} = \\operatorname {C o n v} _ {3} ([ \\operatorname {A v g P o o l} (F), \\operatorname {M a x P o o l} (F) ]), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            124,
+            840,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $[\\cdot, \\cdot]$  indicates concatenation; AvgPool, MaxPool and Conv3 represent average pooling, max pooling, and con",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "volution layer of  $3 \\times 3$  kernel size. By doing this,  $F' \\in \\mathbb{R}^{H \\times W \\times 1}$  contains degradation locations to focus [53].",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since each channel differs in degradation patterns, we further generate channel-wise representation by performing the channel-separated transformation for the input feature  $F$  via depth-wise convolutions, and then modulate resulting features with  $F'$ . This process is expressed as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {s} = \\mathrm {D C o n v s} _ {5, 7} (F) \\otimes \\mathrm {T} \\left(F ^ {\\prime}, C\\right) + \\mathrm {D C o n v} _ {3} (F), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{DConv}_{5,7}$  denotes cascaded depth-wise convolution layers of kernel sizes  $5\\times 5$  and  $7\\times 7$ ;  $\\mathrm{DConv}_3$  represents depth-wise convolution with  $3\\times 3$  kernel;  $\\otimes$  indicates an element-wise multiplication; and  $\\mathrm{T}(F',C)$  is the tile function that copies  $F'$  for  $C$  times along the channel dimension to  $\\mathbb{R}^{H\\times W\\times C}$ . We then feed the spatially selected features  $F_{s}\\in \\mathbb{R}^{H\\times W\\times C}$  to FSM for frequency selection.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Frequency Selection Module (FSM). We can directly utilize  $F_{s}$  to assist the recovery process. Motivated by the fact that degraded/sharp image pairs have similar low-frequency components, while differing at high frequencies, we further emphasize regions that contain the real difference between input/sharp image pairs by removing lowest frequency via the proposed FSM. To this end, we first apply the mean filter to  $F_{s}$  to generate low-frequency features, and then obtain the complementary high-frequency features by subtracting the resulting low-frequency signals from the input, which is expressed by:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {s} ^ {h} = F _ {s} - \\operatorname {M e a n} \\left(F _ {s}\\right). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our case, the mean filter is implemented by the channelwise global average pooling. The final output of FSM/DSM is generated using the element-wise multiplication between  $F_{s}^{h}$  and  $F_{s}$ , and residual connection, which is expressed as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {F} = F _ {s} ^ {h} \\otimes F _ {s} + F _ {s}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            624,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After DSM, the important regions are emphasized, e.g., edge signals in Figure 2 for defocus deblurring.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Loss Function",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To facilitate the selection process in both spatial and frequency domains, we adopt dual-domain  $l_{1}$  loss functions following [13, 15]. For each output/target image pair with the same resolution, loss functions are given by:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s} = \\frac {1}{P} \\| \\hat {I} - G \\| _ {1} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {f} = \\frac {1}{P} \\| \\mathcal {F} (\\hat {I}) - \\mathcal {F} (G) \\| _ {1} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {s} + \\lambda \\mathcal {L} _ {f} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{I}$  and  $G$  denote the output and ground-truth images, respectively;  $P$  indicates total elements for normalization;  $\\mathcal{F}$  represents fast Fourier transform; and  $\\lambda$  is empirically set to 0.1 for balancing dual-domain training.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "13004",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/5b6b283d04df04a37fd25cdc944019706769659f9d1b9e4328b01c28570e0d85.jpg",
+        "image_caption": [
+            "Figure 4. Image dehazing comparisons on the SOTS [27] test sets."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments and Analysis",
+        "text_level": 1,
+        "bbox": [
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+            431,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate FocalNet on 10 datasets for three image restoration tasks, including image dehazing, image desnowing, and single-image defocus deblurring. We provide experimental results for image motion deblurring and image denoising in the supplementary material.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Evaluation Protocol",
+        "text_level": 1,
+        "bbox": [
+            76,
+            544,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We measure the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity index (SSIM) [52] between predicted results and ground-truth images for all datasets. Mean Absolute Error (MAE) and Learned Perceptual Image Patch Similarity (LPIPS) [67] are additionally adopted for defocus deblurring. FLOPs are measured on  $256 \\times 256$  patch. In tables, the best performance is marked in bold.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Image Dehazing. We train and evaluate our models on both synthetic and real-world datasets for image dehazing. Following [21, 59], we train separate models on the RESIDE-Indoor and RESIDE-Outdoor datasets [27], and evaluate the resulting models on the corresponding test sets of RESIDE, i.e., SOTS-Indoor and SOTS-Outdoor, respectively. In addition, we adopt three real-world datasets, i.e., Dense-Haze [2], NH-HAZE [3], and O-HAZE [4], to verify the robustness of our model in more challenging real-world scenarios. Apart from the above daytime dehazing datasets, we also demonstrate the effectiveness of FocalNet on the nighttime dataset NHR [65].",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Image Defocus Deblurring. Consistent with previous algorithms [25, 44, 61], we use the DPDD [1] dataset that consists of 350 scenes for training, 74 scenes for validation, and 100 scenes for validation with a 1:1 ratio.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "tion, and 76 scenes for testing. Each scene comprises four images, labeled as center view, left view, right view, and all-in-focus ground-truth images. FocalNet is trained by taking the center view image as input and calculating loss values between the predicted clean image and ground truth.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Image Desnowing. For the desnowing problem, we train and evaluate our models on three commonly used datasets, i.e., SRRS [9], CSD [10], and Snow100K [37]. Dataset selection and testing methods are consistent with the recent algorithm [9] for a fair and convincing comparison.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Unless stated otherwise, the following hyper-parameters are adopted. Depending on the task complexity, we scale the model by varying the number of residual blocks in all ResBlock, i.e., 16 for deblurring and 4 for dehazing/desnowing. In our FocalNet, we only deploy MResBlock in the first scale of encoder/decoder. Convolution parameters are not shared between two branches of MResBlock. The models are trained using Adam [23] with initial learning rate as  $8e^{-4}$ , which is gradually reduced to  $1e^{-6}$  with cosine annealing [38]. For data augmentation, we adopt random horizontal flips with a probability of 0.5. Models are trained on 32 samples of size  $256 \\times 256$  for each iteration. More details of training configuration for each specific dataset are provided in the supplementary material.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Image Dehazing Results",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Comparisons. We report the quantitative performance of image dehazing approaches on both syn",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "13005",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/566ccddc48f09acde47d27005039b99c74f1d85850ce8cb59e01b8d522e04bed.jpg",
+        "image_caption": [
+            "Figure 5. Image desnowing comparisons on the CSD [10] dataset. Our method is more effective in snow removal than other algorithms."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            90,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/93d3ae9a26c568afac0224bc82130ba118d1119617d43bd0a6a4977465c26672.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">SOTS-Indoor [27]</td><td colspan=\"2\">SOTS-Outdoor [27]</td><td colspan=\"2\">Dense-Haze [2]</td><td colspan=\"2\">NH-HAZE [3]</td><td colspan=\"2\">O-HAZE [4]</td><td rowspan=\"2\">Params (M)</td><td rowspan=\"2\">FLOPs (G)</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DehazeNet [6]</td><td>19.82</td><td>0.821</td><td>24.75</td><td>0.927</td><td>13.84</td><td>0.43</td><td>16.62</td><td>0.52</td><td>17.57</td><td>0.77</td><td>0.009</td><td>0.581</td></tr><tr><td>AOD-Net [26]</td><td>20.51</td><td>0.816</td><td>24.14</td><td>0.920</td><td>13.14</td><td>0.41</td><td>15.40</td><td>0.57</td><td>15.03</td><td>0.54</td><td>0.002</td><td>0.115</td></tr><tr><td>GridDehazeNet [36]</td><td>32.16</td><td>0.984</td><td>30.86</td><td>0.982</td><td>-</td><td>-</td><td>13.80</td><td>0.54</td><td>-</td><td>-</td><td>0.956</td><td>21.49</td></tr><tr><td>MSBDN [17]</td><td>33.67</td><td>0.985</td><td>33.48</td><td>0.982</td><td>15.37</td><td>0.49</td><td>19.23</td><td>0.71</td><td>24.36</td><td>0.75</td><td>31.35</td><td>41.54</td></tr><tr><td>FFA-Net [41]</td><td>36.39</td><td>0.989</td><td>33.57</td><td>0.984</td><td>14.39</td><td>0.45</td><td>19.87</td><td>0.69</td><td>22.12</td><td>0.77</td><td>4.456</td><td>287.8</td></tr><tr><td>AECR-Net [54]</td><td>37.17</td><td>0.990</td><td>-</td><td>-</td><td>15.80</td><td>0.47</td><td>19.88</td><td>0.72</td><td>-</td><td>-</td><td>2.611</td><td>52.20</td></tr><tr><td>DeHamer [21]</td><td>36.63</td><td>0.988</td><td>35.18</td><td>0.986</td><td>16.62</td><td>0.56</td><td>20.66</td><td>0.68</td><td>-</td><td>-</td><td>132.45</td><td>48.93</td></tr><tr><td>PMNet[59]</td><td>38.41</td><td>0.990</td><td>34.74</td><td>0.985</td><td>16.79</td><td>0.51</td><td>20.42</td><td>0.73</td><td>24.64</td><td>0.83</td><td>18.90</td><td>81.13</td></tr><tr><td>FocalNet (Ours)</td><td>40.82</td><td>0.996</td><td>37.71</td><td>0.995</td><td>17.07</td><td>0.63</td><td>20.43</td><td>0.79</td><td>25.50</td><td>0.94</td><td>3.74</td><td>30.63</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/b84599eabacc9e9c76102343276589b97881fdc4f3fc38aaa6195ea26858c180.jpg",
+        "table_caption": [
+            "Table 1. Image dehazing results on both synthetic dataset [27] and real-world datasets [2, 3, 4]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>NDIM [64]</td><td>GS [31]</td><td>MRPF [63]</td><td>MRP [63]</td><td>OSFD [65]</td><td>HCD [51]</td><td>FocalNet Ours</td></tr><tr><td>PSNR</td><td>14.31</td><td>17.32</td><td>16.95</td><td>19.93</td><td>21.32</td><td>23.43</td><td>25.35</td></tr><tr><td>SSIM</td><td>0.526</td><td>0.629</td><td>0.667</td><td>0.777</td><td>0.804</td><td>0.953</td><td>0.969</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Nighttime image dehazing results on NHR [65] dataset.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "thetic [27] and real-world [2, 3, 4] datasets in Table 1. Overall, our method receives better performance on all datasets than other state-of-the-art algorithms. Specifically, on the daytime synthetic dataset SOTS-Indoor [27], our method outperforms PMNet [59] by 2.41 dB PSNR with only  $20\\%$  parameters and  $38\\%$  FLOPs. Furthermore, our model yields a significant performance gain of 2.53 dB in terms of PSNR over Transformer model DeHamer [21] on SOTS-Outdoor [27] with  $97\\%$  fewer parameters.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In addition, our method is well generalized to the more challenging real-world scenarios and obtains the best performance on most metrics. Particularly on the O-HAZE [4] dataset, FocalNet yields considerable gain of 0.86 dB PSNR and 0.11 SSIM over PMNet [59].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Apart from daytime dehazing datasets, we also evaluate the effectiveness of our model on the nighttime dehazing dataset NHR [65]. As shown in Table 2, FocalNet signifi",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2d942c537d09c375ec6859aa5e9cd9caaaa10ae91196e7ae38edc5fc28a3a032.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            504,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/acde12e7ff242731789beba937804a0ac715d3c3a55d0eb2b541dbb923dc2fd1.jpg",
+        "table_caption": [
+            "Figure 6. Nighttime dehazing comparisons on NHR [65] dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CSD [10]</td><td colspan=\"2\">SRRS [9]</td><td colspan=\"2\">Snow100K [37]</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DesnowNet [37]</td><td>20.13</td><td>0.81</td><td>20.38</td><td>0.84</td><td>30.50</td><td>0.94</td></tr><tr><td>CycleGAN [19]</td><td>20.98</td><td>0.80</td><td>20.21</td><td>0.74</td><td>26.81</td><td>0.89</td></tr><tr><td>All in One [30]</td><td>26.31</td><td>0.87</td><td>24.98</td><td>0.88</td><td>26.07</td><td>0.88</td></tr><tr><td>JSTASR [9]</td><td>27.96</td><td>0.88</td><td>25.82</td><td>0.89</td><td>23.12</td><td>0.86</td></tr><tr><td>HDCW-Net [10]</td><td>29.06</td><td>0.91</td><td>27.78</td><td>0.92</td><td>31.54</td><td>0.95</td></tr><tr><td>TransWeather [50]</td><td>31.76</td><td>0.93</td><td>28.29</td><td>0.92</td><td>31.82</td><td>0.93</td></tr><tr><td>NAFNet [8]</td><td>33.13</td><td>0.96</td><td>29.72</td><td>0.94</td><td>32.41</td><td>0.95</td></tr><tr><td>FocalNet (Ours)</td><td>37.18</td><td>0.99</td><td>31.34</td><td>0.98</td><td>33.53</td><td>0.95</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Image desnowing results on three widely used datasets.",
+        "bbox": [
+            500,
+            810,
+            879,
+            824
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "cantly outperforms the recent HCD [51] by  $1.92\\mathrm{dB}$  PSNR. The results demonstrate the efficacy of our design.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Visual Comparisons. The daytime and nighttime visual results produced by several dehazing methods are illustrated",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "13006",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/b260cdfcad3d474c012b169052a16351f8a3cff02ac2d19e203986c6cde55aa5.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/80a1e6de83704e7dac61c797459eadfb2eb479edfe3cc77a4d5368cd96be5614.jpg",
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+    {
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+        "img_path": "images/146a0e1ee6851b6618a3e121398b493991420a1f873d55446291a58a567b39cb.jpg",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/981ba2674c6bd5d253e19a38eed62fbecae847a1ab1e9cad309625b3f998f53a.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/1fa58e1792b7ba96e1ed0a2cbafec3dc66996dd51791e5d818fd023d6a1748b3.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3935ea4274fed00d82acba0f73a65a51218928a27810972bd121f2c328d970fe.jpg",
+        "image_caption": [
+            "Figure 7. Single-image defocus deblurring results on the DPDD [1] dataset. We display the magnified parts of the produced images for clarity. From left-top to right-bottom: input blurry images, ground-truth images, and the predicted images obtained by KPAC [47], IFAN [25], DeepRFT [39], DRBNet [44], Restormer [61], and our FocalNet, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/088941e1ec48ebc84656ece32359be240e3e1c2912916dd3bb3a9b83ff631683.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f07d50461578edd1d2fd7e34cd8c4f887187ac11ec4eab4ac3a2814f4407280d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4f3627cfd594aa205f18a609c66e764dd81815f8e10f2156ec5555b8775ff092.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            212,
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+            332
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/fe7472167a86c2b66cb73fd40da8d487e545f7d88f42ede7db55c834972d4a74.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            738,
+            212,
+            887,
+            332
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5d506cb32bbb6731d940085f22b77dadae003542c4c593dde81a571c98f197af.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Indoor Scenes</td><td colspan=\"4\">Outdoor Scenes</td><td colspan=\"4\">Combined</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td></tr><tr><td>DPDNet [1]</td><td>26.54</td><td>0.816</td><td>0.031</td><td>0.239</td><td>22.25</td><td>0.682</td><td>0.056</td><td>0.313</td><td>24.34</td><td>0.747</td><td>0.044</td><td>0.277</td></tr><tr><td>KPAC [47]</td><td>27.97</td><td>0.852</td><td>0.026</td><td>0.182</td><td>22.62</td><td>0.701</td><td>0.053</td><td>0.269</td><td>25.22</td><td>0.774</td><td>0.040</td><td>0.227</td></tr><tr><td>DeepRFT [39]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.71</td><td>0.801</td><td>0.039</td><td>0.218</td></tr><tr><td>IFAN [25]</td><td>28.11</td><td>0.861</td><td>0.026</td><td>0.179</td><td>22.76</td><td>0.720</td><td>0.052</td><td>0.254</td><td>25.37</td><td>0.789</td><td>0.039</td><td>0.217</td></tr><tr><td>DRBNet [44]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.73</td><td>0.791</td><td>-</td><td>0.183</td></tr><tr><td>Restormer [61]</td><td>28.87</td><td>0.882</td><td>0.025</td><td>0.145</td><td>23.24</td><td>0.743</td><td>0.050</td><td>0.209</td><td>25.98</td><td>0.811</td><td>0.038</td><td>0.178</td></tr><tr><td>FocalNet (Ours)</td><td>29.10</td><td>0.876</td><td>0.024</td><td>0.173</td><td>23.41</td><td>0.743</td><td>0.049</td><td>0.246</td><td>26.18</td><td>0.808</td><td>0.037</td><td>0.210</td></tr></table>",
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Single-image defocus deblurring results on the DPDD [1] dataset.",
+        "bbox": [
+            261,
+            565,
+            705,
+            579
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "in Figure 4 and Figure 6, respectively. Our method is more effective in removing haze blurs in both daytime (indoor and outdoor) and nighttime scenes than other algorithms, such as blurs on the doors in top two images of Figure 4.",
+        "bbox": [
+            75,
+            604,
+            470,
+            666
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Image Desnowing Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            678,
+            310,
+            695
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Comparisons. The numerical results on three desnowing datasets, i.e., SRRS [9], CSD [10], and Snow100K [37], are reported in Table 3. As can be seen, our model shows strong ability on snow removal by consistently achieving better or comparable PSNR/SSIM scores on all metrics. Compared to NAFNet [8], FocalNet obtains significant performance gains of  $1.62\\mathrm{dB}$  and  $4.05\\mathrm{dB}$  PSNR on the SRRS [9] and lately proposed CSD [10] datasets, respectively. In addition, our model yields much higher scores than TransWeather [50] with  $17\\%$  parameters.",
+        "bbox": [
+            75,
+            703,
+            468,
+            853
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Visual Comparisons. The visual results are shown in Figure 5. Images produced by our model are of high quality without artifacts and visually closer to ground-truth images.",
+        "bbox": [
+            75,
+            854,
+            470,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Image Defocus Deblurring Results",
+        "text_level": 1,
+        "bbox": [
+            498,
+            603,
+            802,
+            619
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Comparisons. The quantitative comparisons on the DPDD [1] dataset are provided in Table 4. Our method performs favorably against state-of-the-art algorithms. Specifically, FocalNet obtains significant gains over the CNN-based approaches on the combined category, i.e.,  $0.45\\mathrm{dB}$  over DRBNet [44] and  $0.47\\mathrm{dB}$  over DeepRFT [39]. In addition, compared to Transformer model Restormer [61], our method still obtains a performance improvement of  $0.2\\mathrm{dB}$  PSNR with only half parameters.",
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+    {
+        "type": "text",
+        "text": "Visual Comparisons. Figure 7 illustrates visual results. Compared to other approaches, our model recovers more fine details, such as patterns on pages.",
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+        "text": "4.6. Ablation Studies",
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+        "text": "We conduct ablation studies to demonstrate the effectiveness of our modules by training the tiny model on RESIDE-Indoor [27] and testing on SOTS-Indoor [27]. The number of residual block is set to 1 in all ResBlock. The model is",
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+        "text": "13007",
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+        "type": "table",
+        "img_path": "images/b342a308d698650e243756e2bf74d4e058ed624d30612c40ab2cb5f4ed5e56c4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>MResBlock</td><td>SSM</td><td>FSM</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td></td><td></td><td></td><td>31.33</td><td>15.44</td><td>1.48</td></tr><tr><td>(b)</td><td></td><td>✓</td><td></td><td>33.51</td><td>15.48</td><td>1.49</td></tr><tr><td>(c)</td><td></td><td></td><td>✓</td><td>32.44</td><td>15.44</td><td>1.49</td></tr><tr><td>(d)</td><td></td><td>✓</td><td>✓</td><td>35.56</td><td>15.48</td><td>1.49</td></tr><tr><td>(e)</td><td>✓</td><td>✓</td><td></td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(f)</td><td>✓</td><td></td><td>✓</td><td>32.60</td><td>13.77</td><td>1.47</td></tr><tr><td>(g)</td><td>✓</td><td>✓</td><td>✓</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "Table 5. Ablation studies for different components of FocalNet on the SOTS-Indoor [27] dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td>Simple Gate [8]</td><td>32.23</td><td>13.81</td><td>1.47</td></tr><tr><td>(b)</td><td>Supervised Attention [62]</td><td>32.29</td><td>14.98</td><td>1.76</td></tr><tr><td>(c)</td><td>CBAM [53]</td><td>32.71</td><td>13.77</td><td>1.46</td></tr><tr><td>(d)</td><td>SSM</td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(e)</td><td>CBAM [53]+FSM</td><td>33.23</td><td>13.77</td><td>1.46</td></tr><tr><td>(f)</td><td>SSM+FSM</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "trained for only 300 epochs with the initial learning rate as  $1e^{-4}$  and batch size as 4. Other settings are identical with that of our final dehazing model. The baseline network is obtained by substituting ResBlock for MResBlock and removing DSM from the tiny model. More ablation studies are provided in the supplementary material.",
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+    {
+        "type": "text",
+        "text": "Effects of Individual Components. As shown in Table 5a, the baseline receives 31.33 dB PSNR. SSM (Table 5b) and FSM (Table 5c) yield accuracy gains of 2.18 dB and 1.11 dB over the baseline, respectively. Equipped with DSM, the model (Table 5d) receives further performance boost by 4.23 dB over the baseline. By replacing ResBlock with MResBlock in the first scale, models consistently receive higher scores than those without MResBlock. Specifically, our choice (Table 5g) outperforms the counterpart (Table 5d) by 0.04 dB with lower computation overhead.",
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+    {
+        "type": "text",
+        "text": "In addition, the visual results of our DSM are illustrated in Figure 2 (defocus deblurring) and Figure 8 (dehazing). As shown in Figure 2, SSM helps the model focus more on the severe degradation regions, e.g., metal fence. FSM further highlights the edge signals by removing low-frequency information. For dehazing, the hard regions that are difficult to recover are emphasized by our DSM (see Figure 8). More examples are available in the supplementary material.",
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+    {
+        "type": "text",
+        "text": "Comparisons with Alternatives to SSM. We further demonstrate superiority of our SSM by replacing it with three popular attention mechanisms. As represented in Table 6, the simple gate [8] and supervised attention [62] lead to performance degradation from 33.71 to  $32.23\\mathrm{dB}$  and  $32.29\\mathrm{dBPSNR}$ , respectively. Compared to CBAM [53], which includes both spatial and channel attention, our SSM",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/8a18441fa51ac1f746eebc4b215269f4257ab4ea004a8eeccf5ad595d04e9a54.jpg",
+        "image_caption": [
+            "Figure 8. Visual results of DSM for dehazing. From left to right: hazy images obtained from SOTS-Indoor [27], ground-truth images, input and output features of DSM. The complicated regions worthy of more attention are highlighted by our DSM."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/9f83dd9cee82e6a9128c2f895c4aa5a5c834e430310042c071596b452651a7e7.jpg",
+        "table_caption": [
+            "Table 6. Comparisons with other attention mechanisms."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a) FocalNet w/o MResBlock</td><td>40.69</td><td>33.96</td><td>3.76</td></tr><tr><td>(b) FocalNet</td><td>40.82</td><td>30.63</td><td>3.74</td></tr><tr><td>(c) FocalNet-S</td><td>40.32</td><td>17.33</td><td>2.27</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 7. Design choices for MResBlock.",
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+    {
+        "type": "text",
+        "text": "(Table 6d) receives 1 dB performance gain with comparable computation overhead. The similar conclusion can also be drawn by comparing models of Table 6e and Table 6f, where FSM is additionally used. It is worth mentioning that our FSM boosts the performance when cooperating with CBAM (see Table 6c and Table 6e), demonstrating the efficacy and generalization ability of our design.",
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+    {
+        "type": "text",
+        "text": "Order of FSM and SSM. When we swap the order in which FSM and SSM are used, the performance drops from 35.60 dB (Table 5g) to 35.17 dB PSNR. This phenomenon verifies the efficacy of our design, where we first apply SSM to attend to general degradation regions and then leverage FSM to emphasize the more important parts, such as edge signal in Figure 2 and hard regions in Figure 8.",
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+    {
+        "type": "text",
+        "text": "Design Choices for MResBlock. We study the effect of the multi-scale mechanism in our final dehazing model. The training settings are identical with FocalNet in Table 1. As represented in Table 7, MResBlock leads to performance gain of  $0.13\\mathrm{dB}$  PSNR with high efficiency. We further explore the potential of MResBlock by using it in all scales of encoder/decoder to form FocalNet-S (Figure 7c). This version degrades the performance by  $0.5\\mathrm{dB}$  compared to FocalNet, which is probably because the disadvantage of losing spatial information caused by reducing size of low-resolution features outweighs the advantage of multi-scale learning. It is worth mentioning that FocalNet-S still achieves  $40.32\\mathrm{dB}$  PSNR with much lower computation overhead compared to other algorithms (see Figure 1).",
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+    {
+        "type": "page_number",
+        "text": "13008",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this study, we present a focal network for image restoration, dubbed FocalNet, which is effective and computationally efficient. The core idea of our work is to focus on the important regions for reconstruction. To this end, we propose two modules: SSM and FSM. SSM is built on spatial attention to detect the degradation regions for subsequent frequency selection. FSM further emphasizes the edge signals or regions that are difficult to recover. By deploying two modules successively, the network is capable of paying more attention to regions that really matter to reconstruction. In addition, we insert the multi-scale mechanism into the network by reducing resolution of half the channels of input feature. This design not only improves performance but also reduces complexity. Experiments on 10 datasets demonstrate that our model achieves state-of-the-art performance for several image restoration tasks.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work was supported by the National Natural Science Foundation of China (No. 62025604, U1803264) and Shenzhen Science and Technology Program (No. 20220016).",
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+    {
+        "type": "text",
+        "text": "References",
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+        ],
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+    },
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+            "[49] Zhengzhong Tu, Hossein Talebi, Han Zhang, Feng Yang, Peyman Milanfar, Alan Bovik, and Yinxiao Li. Maxim: Multi-axis mlp for image processing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5769-5780, 2022. 1, 4, 5",
+            "[50] Jeya Maria Jose Valanarasu, Rajeev Yasarla, and Vishal M. Patel. Transweather: Transformer-based restoration of images degraded by adverse weather conditions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2353-2363, 2022. 2, 6, 7",
+            "[51] Tao Wang, Guangpin Tao, Wanglong Lu, Kaihao Zhang, Wenhan Luo, Xiaoqin Zhang, and Tong Lu. Restoring vision in hazy weather with hierarchical contrastive learning. arXiv preprint arXiv:2212.11473, 2022. 6",
+            "[52] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4):600-612, 2004. 5",
+            "[53] Sanghyun Woo, Jongchan Park, Joon-Young Lee, and In So Kweon. Cbam: Convolutional block attention module. In European Conference on Computer Vision, 2018. 1, 4, 8",
+            "[54] Haiyan Wu, Yanyun Qu, Shaohui Lin, Jian Zhou, Ruizhi Qiao, Zhizhong Zhang, Yuan Xie, and Lizhuang Ma. Contrastive learning for compact single image dehazing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 10551-10560, 2021. 1, 6",
+            "[55] Yu-Huan Wu, Yun Liu, Xin Zhan, and Ming-Ming Cheng. P2t: Pyramid pooling transformer for scene understanding. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. 4",
+            "[56] Yanyang Yan, Qingbo Wu, Bo Xu, Jingang Zhang, and Wenqi Ren. Vdflow: Joint learning for optical flow and video deblurring. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2020. 3",
+            "[57] Dan Yang and Mehmet Yamac. Motion aware double attention network for dynamic scene deblurring. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 1113-1123, 2022. 3",
+            "[58] Zhiyong Yang, Qianqian Xu, Shilong Bao, Yuan He, Xiaochun Cao, and Qingming Huang. Optimizing two-way partial auc with an end-to-end framework. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. 1",
+            "[59] Tian Ye, Yunchen Zhang, Mingchao Jiang, Liang Chen, Yun Liu, Sixiang Chen, and Erkang Chen. Perceiving and modeling density for image dehazing. In European Conference on Computer Vision, pages 130-145, 2022. 1, 2, 5, 6",
+            "[60] Yuan Yuan, Wei Su, and Dandan Ma. Efficient dynamic scene deblurring using spatially variant deconvolution network with optical flow guided training. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2020. 1, 3",
+            "[61] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Ming-Hsuan Yang. Restormer: Efficient transformer for high-resolution image"
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
+            900
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "restoration. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5728-5739, 2022. 1, 2, 5, 7",
+            "[62] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, Ming-Hsuan Yang, and Ling Shao. Multi-stage progressive image restoration. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 14821-14831, 2021. 2, 8",
+            "[63] Jing Zhang, Yang Cao, Shuai Fang, Yu Kang, and Chang Wen Chen. Fast haze removal for nighttime image using maximum reflectance prior. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017. 6",
+            "[64] Jing Zhang, Yang Cao, and Zengfu Wang. Nighttime haze removal based on a new imaging model. In IEEE International Conference on Image Processing, pages 4557-4561, 2014. 6",
+            "[65] Jing Zhang, Yang Cao, Zheng-Jun Zha, and Dacheng Tao. Nighttime dehazing with a synthetic benchmark. In Proceedings of the ACM International Conference on Multimedia, pages 2355-2363, 2020. 5, 6",
+            "[66] Kaihao Zhang, Wenqi Ren, Wenhan Luo, Wei-Sheng Lai, Björn Stenger, Ming-Hsuan Yang, and Hongdong Li. Deep image deblurring: A survey. International Journal of Computer Vision, 130(9):2103-2130, 2022. 1, 2",
+            "[67] Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018. 5",
+            "[68] Wenbin Zou, Mingchao Jiang, Yunchen Zhang, Liang Chen, Zhiyong Lu, and Yi Wu. Sdwnet: A straight dilated network with wavelet transformation for image deblurring. In Proceedings of the IEEE International Conference on Computer Vision, pages 1895-1904, 2021. 2, 3"
+        ],
+        "bbox": [
+            503,
+            92,
+            890,
+            585
+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "13011",
+        "bbox": [
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+            945,
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+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/Focal Network for Image Restoration/8fcb7aa2-a8ca-4dca-97f1-3bf63a15581e_model.json b/2023/Focal Network for Image Restoration/8fcb7aa2-a8ca-4dca-97f1-3bf63a15581e_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..06a1ce81a665ddda3472313559d20f6e11487ad0
--- /dev/null
+++ b/2023/Focal Network for Image Restoration/8fcb7aa2-a8ca-4dca-97f1-3bf63a15581e_model.json	
@@ -0,0 +1,2554 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.296,
+                0.131,
+                0.674,
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+            ],
+            "angle": 0,
+            "content": "Focal Network for Image Restoration"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.165,
+                0.18,
+                0.806,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Yuning Cui\\(^{1}\\) Wenqi Ren\\(^{2*}\\) Xiaochun Cao\\(^{2}\\) Alois Knoll\\(^{1}\\)  \n\\(^{1}\\)Technical University of Munich \\(^{2}\\)Shenzhen Campus of Sun Yat-sen University  \n{yuning.cui,knoll}@in.tum.de {renwq3, caoxiaochun}@mail.sysu.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.269,
+                0.314,
+                0.285
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.302,
+                0.474,
+                0.635
+            ],
+            "angle": 0,
+            "content": "Image restoration aims to reconstruct a sharp image from its degraded counterpart, which plays an important role in many fields. Recently, Transformer models have achieved promising performance on various image restoration tasks. However, their quadratic complexity remains an intractable issue for practical applications. The aim of this study is to develop an efficient and effective framework for image restoration. Inspired by the fact that different regions in a corrupted image always undergo degradations in various degrees, we propose to focus more on the important areas for reconstruction. To this end, we introduce a dual-domain selection mechanism to emphasize crucial information for restoration, such as edge signals and hard regions. In addition, we split high-resolution features to insert multiscale receptive fields into the network, which improves both efficiency and performance. Finally, the proposed network, dubbed FocalNet, is built by incorporating these designs into a U-shaped backbone. Extensive experiments demonstrate that our model achieves state-of-the-art performance on ten datasets for three tasks, including single-image defocus deblurring, image dehazing, and image desnowing. Our code is available at https://github.com/c-yn/FocalNet."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.666,
+                0.21,
+                0.682
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.692,
+                0.47,
+                0.858
+            ],
+            "angle": 0,
+            "content": "Bad weather or physical limitations of cameras will degrade visibility of captured images and further exert a negative impact on robustness of downstream tasks. In this regard, image restoration is immensely useful to remove those undesired degradations, e.g., haze, snowflake, and blur, thus playing an essential role in surveillance, autonomous vehicles, remote sensing, and medical imaging [48]. Due to its ill-posed property, many conventional methods have been proposed by resorting to assumptions and hand-crafted features to reduce the solution space. However, these methods are inapplicable to complicated real-world scenarios [66]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.86,
+                0.47,
+                0.875
+            ],
+            "angle": 0,
+            "content": "The rapid development of convolutional neural networks"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.512,
+                0.27,
+                0.88,
+                0.449
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.454,
+                0.864,
+                0.469
+            ],
+            "angle": 0,
+            "content": "Figure 1. PSNR vs. FLOPs on the SOTS-Indoor [27] dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.508,
+                0.892,
+                0.644
+            ],
+            "angle": 0,
+            "content": "(CNNs) has alleviated the above issue to some extent by learning generalizable image priors from large-scale collected datasets [25, 44]. Recently, Transformer models have injected vitality into image restoration and have achieved promising performance by providing powerful ability of modeling long-range pixel interactions, which is useful for recovering large-scale degradations [7, 32, 61]. Despite a few remedies, the quadratic complexity of self-attention still remains a formidable issue for practical applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.644,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "How to effectively capture critical information parsimoniously has long been a key problem in the computer vision and pattern recognition community. Successful examples include attention mechanism [53], focal loss [34], and the recent advance of partial AUC optimization [58]. Inspired by this, in this study, instead of pursuing large receptive field or exploring modification for the Transformer architecture, we aim to develop an efficient and effective CNN-based framework by paying more attention to informative signals for reconstruction, such as edge information or regions that are difficult to recover. In this direction, existing approaches can be roughly divided into two categories: auxiliary training and attention based methods. The former mainly leverages auxiliary techniques or data, e.g., semantic segmentation [12], depth estimation [29], and optical flow estimation [60], to locate degradations or edge information. Nonetheless, these algorithms always need additional com"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.225,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding Author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.518,
+                0.957
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+            "angle": 0,
+            "content": "13001"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.092,
+                0.245,
+                0.258
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.129,
+                0.259,
+                0.201,
+                0.271
+            ],
+            "angle": 0,
+            "content": "Blurry Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.245,
+                0.091,
+                0.408,
+                0.259
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.307,
+                0.26,
+                0.344,
+                0.27
+            ],
+            "angle": 0,
+            "content": "Target"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.41,
+                0.092,
+                0.566,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.45,
+                0.26,
+                0.525,
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+            "angle": 0,
+            "content": "Initial Feature"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.568,
+                0.092,
+                0.726,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.626,
+                0.26,
+                0.669,
+                0.27
+            ],
+            "angle": 0,
+            "content": "w/SSM"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.727,
+                0.092,
+                0.886,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.767,
+                0.259,
+                0.847,
+                0.269
+            ],
+            "angle": 0,
+            "content": "w/SSM&FSM"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.274,
+                0.893,
+                0.316
+            ],
+            "angle": 0,
+            "content": "Figure 2. Effects of our dual-domain selection mechanism (DSM). From left to right: blurry images obtained from DPDD [1], ground-truth images, input features of our DSM, results of spatial selection, and results of spatial&frequency selection. SSM helps focus on degradation regions while FSM emphasizes edge information. Zoom in for the best view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.341,
+                0.468,
+                0.446
+            ],
+            "angle": 0,
+            "content": "plicated branch and elaborately devised training strategies to generate supervisory information. The other line on this topic is to design attention mechanisms to attend to informative regions or control information transmission [8, 41, 62]. These approaches mostly lie in the spatial domain while ignoring the usage of spectral information, which can also provide useful information for reconstruction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.448,
+                0.468,
+                0.673
+            ],
+            "angle": 0,
+            "content": "To prompt models to focus more on critical regions, we propose a novel dual-domain selection mechanism (DSM) by sufficiently leveraging discrepancies between sharp/degraded image pairs in both spatial and spectral domains. Concretely, our mechanism comprises two components: spatial selection module (SSM) and frequency selection module (FSM). SSM takes features as input and determines general locations of degradations for each channel by deploying depthwise convolution layers. Then FSM is used to amplify high-frequency signals or hard regions by removing low frequency from features. The proposed network, FocalNet, is established by incorporating DSM into a U-shaped CNN backbone. To save computation overhead, we only insert DSM into the bottleneck module of our FocalNet, which includes the lowest-resolution features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.468,
+                0.749
+            ],
+            "angle": 0,
+            "content": "Moreover, we split the high-resolution features into two parts over channel dimension. Half features are downsampled to lower resolution, which can not only reduce complexity but also boost performance by providing multiscale receptive fields for degradations of different sizes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Based on the above designs, our FocalNet exhibits state-of-the-art performance on three image restoration tasks. For dehazing, FocalNet outperforms PMNet [59] on both synthetic and real-world benchmark datasets with lower computational complexity, as illustrated in Figure 1. For the desnowing task, FocalNet is superior to Transformer-based framework TransWeather [50] on three commonly used desnowing datasets. Our network also shows potential on defocus deblurring problem by producing a performance gain of \\(0.2\\mathrm{dB}\\) PSNR over Restormer [61] on the combined"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.341,
+                0.892,
+                0.371
+            ],
+            "angle": 0,
+            "content": "category of DPDD [1] dataset. Overall, the main contributions of this study are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.38,
+                0.892,
+                0.426
+            ],
+            "angle": 0,
+            "content": "- We propose a novel dual-domain selection mechanism (DSM) that amplifies the response of important regions to assist in recovering clean features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.435,
+                0.892,
+                0.481
+            ],
+            "angle": 0,
+            "content": "- We develop an efficient and effective focal network that provides multi-scale representation learning for image restoration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.49,
+                0.892,
+                0.551
+            ],
+            "angle": 0,
+            "content": "- Extensive experiments on ten datasets demonstrate that the proposed network, FocalNet, performs favorably against state-of-the-art algorithms on three representative image restoration tasks."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.38,
+                0.892,
+                0.551
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.573,
+                0.642,
+                0.589
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.871
+            ],
+            "angle": 0,
+            "content": "Image Restoration Architectures. As a long-standing task, image restoration aims to remove undesired degradations in corrupted images, which plays an important role in many fields, such as robot vision, medical applications, and surveillance [48, 66]. Recently, CNN-based architectures have significantly advanced the performance compared to conventional methods [1, 8, 14, 16]. Among these architectures, the encoder-decoder paradigm is a popular solution to learn hierarchical representations [39, 44]. In addition, a great number of functional units have been developed or borrowed from other realms, such as dilated convolution [68], skip connections [13], dynamic filter [25], and various attention mechanisms [41]. More recently, Transformer models have been imported into low-level vision tasks and provided promising performance [7, 32]. Thereafter, a few measures have been taken to reduce the computational complexity of self-attention by restricting the operation region [32] or switching the operation dimension [61]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Spectral Networks. Apart from spatial representation learning, numerous deep frameworks have been proposed"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13002"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.092,
+                0.891,
+                0.341
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.359,
+                0.895,
+                0.403
+            ],
+            "angle": 0,
+            "content": "Figure 3. Architecture of the proposed FocalNet with dual-domain selection mechanism (DSM) that consists of two components, i.e., spatial selection module (SSM) and frequency selection module (FSM). ResBlock contains \\( n \\) residual blocks, comprising two \\( 3 \\times 3 \\) convolution layers and activation function in between."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.426,
+                0.473,
+                0.606
+            ],
+            "angle": 0,
+            "content": "to bridge frequency gaps between sharp/degraded image pairs [15, 39, 68]. The common practice is to decompose features into different frequency components via transformation tools such as wavelet transform [10, 68], Fourier transform [22, 39], pooling technique [15], and conventional filters [35], and then treat each component individually via convolution layers. In addition, a few researches have investigated the different roles of phase and amplitude, and proposed architectures to recover them separately [28]. In our work, we simply remove the lowest-frequency signal from the resulting features of SSM to provide guidance for further reconstruction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.607,
+                0.473,
+                0.82
+            ],
+            "angle": 0,
+            "content": "Auxiliary Training. In addition to the provided ground-truth images in training sets of image restoration tasks, a great number of networks have been proposed to resort to auxiliary supervision. Semantic priors have been introduced into low-level tasks to provide color, boundary or location information [12, 43, 45]. However, global semantic priors are less effective for degradations caused by large depth variations. Thus many methods have proposed to estimate depth map to generate edge and structure signals for restoration [24, 29]. Moreover, there are many works that integrate other auxiliary information such as optical flow [56, 60] and event data [57]. However, the above solutions always require additional data, expensive convolution branch, and complicated training strategies [45]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.83,
+                0.17,
+                0.847
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we first delineate the overall architecture of FocalNet. Then we describe our modules: Multi-scale ResBlock (MResBlock) and Dual-domain Selection Mech-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.426,
+                0.837,
+                0.442
+            ],
+            "angle": 0,
+            "content": "anism (DSM). Finally, we detail the loss functions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.454,
+                0.662,
+                0.47
+            ],
+            "angle": 0,
+            "content": "3.1. Overall Pipeline"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.478,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "As illustrated in Figure 3, the proposed FocalNet adopts the popular encoder-decoder architecture to learn hierarchical representations efficiently. Both encoder and decoder networks consist of three scales. In our paper, we refer to the first scale as the sub-network that involves the highest-resolution features. MResBlock constitutes the main part of the first scale. The other two scales are mainly composed of ResBlock, which consists of \\( n \\) residual blocks. Given a degraded image of size \\( H \\times W \\times 3 \\), where \\( H \\times W \\) and \\( C \\) represent spatial locations and the number of channels respectively, a \\( 3 \\times 3 \\) convolution layer is used to extract shallow features of size \\( H \\times W \\times C \\). Then, the shallow features pass through three-scale symmetric encoder-decoder and are transformed into restored features, i.e., output features of MResBlock in the first scale of decoder. Starting from the highest-resolution input, the encoder gradually reduces spatial size and expands the number of channels. The decoder does the opposite to restore clean features from the deepest features. During this process, the decoder features are concatenated with the encoder features to assist recovery, followed by a \\( 1 \\times 1 \\) convolution to adjust channel dimension. Finally, the predicted clean image is generated by the last \\( 3 \\times 3 \\) convolution layer and image-level residual connection. Upsampling (UP) and downsampling (DOWN) operations are implemented by transposed and strided convolutions except for the upsampling layer in MResBlock that adopts bilinear interpolation. The proposed DSM is injected into the bottleneck location to select the most im"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13003"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.138
+            ],
+            "angle": 0,
+            "content": "portant regions for reconstruction. In addition, we apply the multi-input and multi-output strategies to ease training difficulty following previous methods [13, 15, 39, 49]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.146,
+                0.383,
+                0.163
+            ],
+            "angle": 0,
+            "content": "3.2. Multi-scale ResBlock (MResBlock)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.169,
+                0.473,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Recently, pursuing multi-scale receptive fields is a hot topic in computer vision community [5, 20, 42, 55], especially for Transformer-based models [33, 42]. Inspired by [11, 40, 46], we adopt multi-scale mechanism in ResBlock to form our MResBlock via splitting and downsampling operations, as illustrated in Figure 3. Specifically, given input features, we first split them equally along channel dimension into two components. Next, half features are reduced to a quarter of the original resolution using strided convolution. The resulting features are fed into ResBlock, and then up-sampled to the original size. The other half are directly processed by ResBlock. The final output of MResBlock is obtained by concatenating resulting features of two branches. MResBlock enjoys two main advantages. Firstly, it improves performance by realizing multi-scale representation learning for degradations of different sizes and enhances spectral learning for different frequencies [40]. Secondly, it improves efficiency by reducing feature resolution."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.451,
+                0.438,
+                0.467
+            ],
+            "angle": 0,
+            "content": "3.3. Dual-domain Selection Mechanism (DSM)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.474,
+                0.47,
+                0.61
+            ],
+            "angle": 0,
+            "content": "The main goal of this study is to develop an efficient network for image restoration by focusing on the more important regions. This aim is achieved by the proposed DSM, which amplifies the response of informative information in two domains (see Figure 2). As illustrated in the bottom part of Figure 3, it consists of two components: spatial selection module (SSM) and frequency selection module (FSM). Given input features \\( F \\in \\mathbb{R}^{H \\times W \\times C} \\), SSM and FSM are employed successively, which can be expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.199,
+                0.621,
+                0.47,
+                0.639
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {F} = \\operatorname {F S M} (\\operatorname {S S M} (F)). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.65,
+                0.402,
+                0.664
+            ],
+            "angle": 0,
+            "content": "Next, we introduce these two elements in details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.665,
+                0.473,
+                0.831
+            ],
+            "angle": 0,
+            "content": "Spatial Selection Module (SSM). SSM helps the network focus on important regions in the spatial domain, providing initial locations of severe degradations for subsequent FSM. Our SSM has three branches. The main path is built upon the CBAM [53] to produce the general feature representation for locations of degradations to focus. Specifically, given an intermediate feature map \\( F \\), we first squeeze \\( F \\) along channel dimension through two types of pooling techniques, i.e., max pooling and average pooling, and then generate the general feature map via a convolution layer, which is formally expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.125,
+                0.842,
+                0.47,
+                0.86
+            ],
+            "angle": 0,
+            "content": "\\[\nF ^ {\\prime} = \\operatorname {C o n v} _ {3} ([ \\operatorname {A v g P o o l} (F), \\operatorname {M a x P o o l} (F) ]), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.87,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\([\\cdot, \\cdot]\\) indicates concatenation; AvgPool, MaxPool and Conv3 represent average pooling, max pooling, and con"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "volution layer of \\(3 \\times 3\\) kernel size. By doing this, \\(F' \\in \\mathbb{R}^{H \\times W \\times 1}\\) contains degradation locations to focus [53]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.122,
+                0.894,
+                0.198
+            ],
+            "angle": 0,
+            "content": "Since each channel differs in degradation patterns, we further generate channel-wise representation by performing the channel-separated transformation for the input feature \\( F \\) via depth-wise convolutions, and then modulate resulting features with \\( F' \\). This process is expressed as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.204,
+                0.892,
+                0.222
+            ],
+            "angle": 0,
+            "content": "\\[\nF _ {s} = \\mathrm {D C o n v s} _ {5, 7} (F) \\otimes \\mathrm {T} \\left(F ^ {\\prime}, C\\right) + \\mathrm {D C o n v} _ {3} (F), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.228,
+                0.892,
+                0.333
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathrm{DConv}_{5,7}\\) denotes cascaded depth-wise convolution layers of kernel sizes \\(5\\times 5\\) and \\(7\\times 7\\); \\(\\mathrm{DConv}_3\\) represents depth-wise convolution with \\(3\\times 3\\) kernel; \\(\\otimes\\) indicates an element-wise multiplication; and \\(\\mathrm{T}(F',C)\\) is the tile function that copies \\(F'\\) for \\(C\\) times along the channel dimension to \\(\\mathbb{R}^{H\\times W\\times C}\\). We then feed the spatially selected features \\(F_{s}\\in \\mathbb{R}^{H\\times W\\times C}\\) to FSM for frequency selection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.334,
+                0.892,
+                0.501
+            ],
+            "angle": 0,
+            "content": "Frequency Selection Module (FSM). We can directly utilize \\( F_{s} \\) to assist the recovery process. Motivated by the fact that degraded/sharp image pairs have similar low-frequency components, while differing at high frequencies, we further emphasize regions that contain the real difference between input/sharp image pairs by removing lowest frequency via the proposed FSM. To this end, we first apply the mean filter to \\( F_{s} \\) to generate low-frequency features, and then obtain the complementary high-frequency features by subtracting the resulting low-frequency signals from the input, which is expressed by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.616,
+                0.506,
+                0.892,
+                0.525
+            ],
+            "angle": 0,
+            "content": "\\[\nF _ {s} ^ {h} = F _ {s} - \\operatorname {M e a n} \\left(F _ {s}\\right). \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.531,
+                0.892,
+                0.593
+            ],
+            "angle": 0,
+            "content": "In our case, the mean filter is implemented by the channelwise global average pooling. The final output of FSM/DSM is generated using the element-wise multiplication between \\( F_{s}^{h} \\) and \\( F_{s} \\), and residual connection, which is expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.625,
+                0.604,
+                0.892,
+                0.623
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {F} = F _ {s} ^ {h} \\otimes F _ {s} + F _ {s}. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.626,
+                0.891,
+                0.657
+            ],
+            "angle": 0,
+            "content": "After DSM, the important regions are emphasized, e.g., edge signals in Figure 2 for defocus deblurring."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.664,
+                0.646,
+                0.678
+            ],
+            "angle": 0,
+            "content": "3.4. Loss Function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.687,
+                0.892,
+                0.748
+            ],
+            "angle": 0,
+            "content": "To facilitate the selection process in both spatial and frequency domains, we adopt dual-domain \\( l_{1} \\) loss functions following [13, 15]. For each output/target image pair with the same resolution, loss functions are given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.607,
+                0.754,
+                0.892,
+                0.782
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {s} = \\frac {1}{P} \\| \\hat {I} - G \\| _ {1} \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.607,
+                0.784,
+                0.892,
+                0.813
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {f} = \\frac {1}{P} \\| \\mathcal {F} (\\hat {I}) - \\mathcal {F} (G) \\| _ {1} \\tag {7}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.615,
+                0.815,
+                0.892,
+                0.832
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {s} + \\lambda \\mathcal {L} _ {f} \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{I}\\) and \\(G\\) denote the output and ground-truth images, respectively; \\(P\\) indicates total elements for normalization; \\(\\mathcal{F}\\) represents fast Fourier transform; and \\(\\lambda\\) is empirically set to 0.1 for balancing dual-domain training."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "13004"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.09,
+                0.891,
+                0.393
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.288,
+                0.395,
+                0.68,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Figure 4. Image dehazing comparisons on the SOTS [27] test sets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.433,
+                0.321,
+                0.451
+            ],
+            "angle": 0,
+            "content": "4. Experiments and Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.459,
+                0.47,
+                0.536
+            ],
+            "angle": 0,
+            "content": "We evaluate FocalNet on 10 datasets for three image restoration tasks, including image dehazing, image desnowing, and single-image defocus deblurring. We provide experimental results for image motion deblurring and image denoising in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.545,
+                0.371,
+                0.56
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Evaluation Protocol"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.568,
+                0.47,
+                0.674
+            ],
+            "angle": 0,
+            "content": "We measure the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity index (SSIM) [52] between predicted results and ground-truth images for all datasets. Mean Absolute Error (MAE) and Learned Perceptual Image Patch Similarity (LPIPS) [67] are additionally adopted for defocus deblurring. FLOPs are measured on \\(256 \\times 256\\) patch. In tables, the best performance is marked in bold."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.471,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Image Dehazing. We train and evaluate our models on both synthetic and real-world datasets for image dehazing. Following [21, 59], we train separate models on the RESIDE-Indoor and RESIDE-Outdoor datasets [27], and evaluate the resulting models on the corresponding test sets of RESIDE, i.e., SOTS-Indoor and SOTS-Outdoor, respectively. In addition, we adopt three real-world datasets, i.e., Dense-Haze [2], NH-HAZE [3], and O-HAZE [4], to verify the robustness of our model in more challenging real-world scenarios. Apart from the above daytime dehazing datasets, we also demonstrate the effectiveness of FocalNet on the nighttime dataset NHR [65]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Image Defocus Deblurring. Consistent with previous algorithms [25, 44, 61], we use the DPDD [1] dataset that consists of 350 scenes for training, 74 scenes for validation, and 100 scenes for validation with a 1:1 ratio."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.435,
+                0.892,
+                0.51
+            ],
+            "angle": 0,
+            "content": "tion, and 76 scenes for testing. Each scene comprises four images, labeled as center view, left view, right view, and all-in-focus ground-truth images. FocalNet is trained by taking the center view image as input and calculating loss values between the predicted clean image and ground truth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.511,
+                0.892,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Image Desnowing. For the desnowing problem, we train and evaluate our models on three commonly used datasets, i.e., SRRS [9], CSD [10], and Snow100K [37]. Dataset selection and testing methods are consistent with the recent algorithm [9] for a fair and convincing comparison."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.599,
+                0.719,
+                0.615
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.623,
+                0.892,
+                0.835
+            ],
+            "angle": 0,
+            "content": "Unless stated otherwise, the following hyper-parameters are adopted. Depending on the task complexity, we scale the model by varying the number of residual blocks in all ResBlock, i.e., 16 for deblurring and 4 for dehazing/desnowing. In our FocalNet, we only deploy MResBlock in the first scale of encoder/decoder. Convolution parameters are not shared between two branches of MResBlock. The models are trained using Adam [23] with initial learning rate as \\(8e^{-4}\\), which is gradually reduced to \\(1e^{-6}\\) with cosine annealing [38]. For data augmentation, we adopt random horizontal flips with a probability of 0.5. Models are trained on 32 samples of size \\(256 \\times 256\\) for each iteration. More details of training configuration for each specific dataset are provided in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.847,
+                0.722,
+                0.864
+            ],
+            "angle": 0,
+            "content": "4.3. Image Dehazing Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Quantitative Comparisons. We report the quantitative performance of image dehazing approaches on both syn"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13005"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.092,
+                0.891,
+                0.29
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.078,
+                0.294,
+                0.878,
+                0.309
+            ],
+            "angle": 0,
+            "content": "Figure 5. Image desnowing comparisons on the CSD [10] dataset. Our method is more effective in snow removal than other algorithms."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.32,
+                0.891,
+                0.476
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">SOTS-Indoor [27]</td><td colspan=\"2\">SOTS-Outdoor [27]</td><td colspan=\"2\">Dense-Haze [2]</td><td colspan=\"2\">NH-HAZE [3]</td><td colspan=\"2\">O-HAZE [4]</td><td rowspan=\"2\">Params (M)</td><td rowspan=\"2\">FLOPs (G)</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DehazeNet [6]</td><td>19.82</td><td>0.821</td><td>24.75</td><td>0.927</td><td>13.84</td><td>0.43</td><td>16.62</td><td>0.52</td><td>17.57</td><td>0.77</td><td>0.009</td><td>0.581</td></tr><tr><td>AOD-Net [26]</td><td>20.51</td><td>0.816</td><td>24.14</td><td>0.920</td><td>13.14</td><td>0.41</td><td>15.40</td><td>0.57</td><td>15.03</td><td>0.54</td><td>0.002</td><td>0.115</td></tr><tr><td>GridDehazeNet [36]</td><td>32.16</td><td>0.984</td><td>30.86</td><td>0.982</td><td>-</td><td>-</td><td>13.80</td><td>0.54</td><td>-</td><td>-</td><td>0.956</td><td>21.49</td></tr><tr><td>MSBDN [17]</td><td>33.67</td><td>0.985</td><td>33.48</td><td>0.982</td><td>15.37</td><td>0.49</td><td>19.23</td><td>0.71</td><td>24.36</td><td>0.75</td><td>31.35</td><td>41.54</td></tr><tr><td>FFA-Net [41]</td><td>36.39</td><td>0.989</td><td>33.57</td><td>0.984</td><td>14.39</td><td>0.45</td><td>19.87</td><td>0.69</td><td>22.12</td><td>0.77</td><td>4.456</td><td>287.8</td></tr><tr><td>AECR-Net [54]</td><td>37.17</td><td>0.990</td><td>-</td><td>-</td><td>15.80</td><td>0.47</td><td>19.88</td><td>0.72</td><td>-</td><td>-</td><td>2.611</td><td>52.20</td></tr><tr><td>DeHamer [21]</td><td>36.63</td><td>0.988</td><td>35.18</td><td>0.986</td><td>16.62</td><td>0.56</td><td>20.66</td><td>0.68</td><td>-</td><td>-</td><td>132.45</td><td>48.93</td></tr><tr><td>PMNet[59]</td><td>38.41</td><td>0.990</td><td>34.74</td><td>0.985</td><td>16.79</td><td>0.51</td><td>20.42</td><td>0.73</td><td>24.64</td><td>0.83</td><td>18.90</td><td>81.13</td></tr><tr><td>FocalNet (Ours)</td><td>40.82</td><td>0.996</td><td>37.71</td><td>0.995</td><td>17.07</td><td>0.63</td><td>20.43</td><td>0.79</td><td>25.50</td><td>0.94</td><td>3.74</td><td>30.63</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.204,
+                0.485,
+                0.766,
+                0.5
+            ],
+            "angle": 0,
+            "content": "Table 1. Image dehazing results on both synthetic dataset [27] and real-world datasets [2, 3, 4]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.521,
+                0.466,
+                0.587
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>NDIM [64]</td><td>GS [31]</td><td>MRPF [63]</td><td>MRP [63]</td><td>OSFD [65]</td><td>HCD [51]</td><td>FocalNet Ours</td></tr><tr><td>PSNR</td><td>14.31</td><td>17.32</td><td>16.95</td><td>19.93</td><td>21.32</td><td>23.43</td><td>25.35</td></tr><tr><td>SSIM</td><td>0.526</td><td>0.629</td><td>0.667</td><td>0.777</td><td>0.804</td><td>0.953</td><td>0.969</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.596,
+                0.46,
+                0.61
+            ],
+            "angle": 0,
+            "content": "Table 2. Nighttime image dehazing results on NHR [65] dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.639,
+                0.469,
+                0.776
+            ],
+            "angle": 0,
+            "content": "thetic [27] and real-world [2, 3, 4] datasets in Table 1. Overall, our method receives better performance on all datasets than other state-of-the-art algorithms. Specifically, on the daytime synthetic dataset SOTS-Indoor [27], our method outperforms PMNet [59] by 2.41 dB PSNR with only \\(20\\%\\) parameters and \\(38\\%\\) FLOPs. Furthermore, our model yields a significant performance gain of 2.53 dB in terms of PSNR over Transformer model DeHamer [21] on SOTS-Outdoor [27] with \\(97\\%\\) fewer parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.778,
+                0.469,
+                0.854
+            ],
+            "angle": 0,
+            "content": "In addition, our method is well generalized to the more challenging real-world scenarios and obtains the best performance on most metrics. Particularly on the O-HAZE [4] dataset, FocalNet yields considerable gain of 0.86 dB PSNR and 0.11 SSIM over PMNet [59]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Apart from daytime dehazing datasets, we also evaluate the effectiveness of our model on the nighttime dehazing dataset NHR [65]. As shown in Table 2, FocalNet signifi"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.522,
+                0.89,
+                0.623
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.625,
+                0.885,
+                0.639
+            ],
+            "angle": 0,
+            "content": "Figure 6. Nighttime dehazing comparisons on NHR [65] dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.503,
+                0.652,
+                0.892,
+                0.801
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CSD [10]</td><td colspan=\"2\">SRRS [9]</td><td colspan=\"2\">Snow100K [37]</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DesnowNet [37]</td><td>20.13</td><td>0.81</td><td>20.38</td><td>0.84</td><td>30.50</td><td>0.94</td></tr><tr><td>CycleGAN [19]</td><td>20.98</td><td>0.80</td><td>20.21</td><td>0.74</td><td>26.81</td><td>0.89</td></tr><tr><td>All in One [30]</td><td>26.31</td><td>0.87</td><td>24.98</td><td>0.88</td><td>26.07</td><td>0.88</td></tr><tr><td>JSTASR [9]</td><td>27.96</td><td>0.88</td><td>25.82</td><td>0.89</td><td>23.12</td><td>0.86</td></tr><tr><td>HDCW-Net [10]</td><td>29.06</td><td>0.91</td><td>27.78</td><td>0.92</td><td>31.54</td><td>0.95</td></tr><tr><td>TransWeather [50]</td><td>31.76</td><td>0.93</td><td>28.29</td><td>0.92</td><td>31.82</td><td>0.93</td></tr><tr><td>NAFNet [8]</td><td>33.13</td><td>0.96</td><td>29.72</td><td>0.94</td><td>32.41</td><td>0.95</td></tr><tr><td>FocalNet (Ours)</td><td>37.18</td><td>0.99</td><td>31.34</td><td>0.98</td><td>33.53</td><td>0.95</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.811,
+                0.88,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Table 3. Image desnowing results on three widely used datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.84,
+                0.892,
+                0.87
+            ],
+            "angle": 0,
+            "content": "cantly outperforms the recent HCD [51] by \\(1.92\\mathrm{dB}\\) PSNR. The results demonstrate the efficacy of our design."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visual Comparisons. The daytime and nighttime visual results produced by several dehazing methods are illustrated"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "13006"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.091,
+                0.312,
+                0.211
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.312,
+                0.091,
+                0.455,
+                0.211
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.455,
+                0.091,
+                0.599,
+                0.211
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.598,
+                0.091,
+                0.74,
+                0.211
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.74,
+                0.091,
+                0.887,
+                0.211
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.213,
+                0.312,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.312,
+                0.213,
+                0.455,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.455,
+                0.213,
+                0.599,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.598,
+                0.213,
+                0.74,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.74,
+                0.213,
+                0.888,
+                0.333
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.335,
+                0.895,
+                0.38
+            ],
+            "angle": 0,
+            "content": "Figure 7. Single-image defocus deblurring results on the DPDD [1] dataset. We display the magnified parts of the produced images for clarity. From left-top to right-bottom: input blurry images, ground-truth images, and the predicted images obtained by KPAC [47], IFAN [25], DeepRFT [39], DRBNet [44], Restormer [61], and our FocalNet, respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.402,
+                0.892,
+                0.556
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Indoor Scenes</td><td colspan=\"4\">Outdoor Scenes</td><td colspan=\"4\">Combined</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td></tr><tr><td>DPDNet [1]</td><td>26.54</td><td>0.816</td><td>0.031</td><td>0.239</td><td>22.25</td><td>0.682</td><td>0.056</td><td>0.313</td><td>24.34</td><td>0.747</td><td>0.044</td><td>0.277</td></tr><tr><td>KPAC [47]</td><td>27.97</td><td>0.852</td><td>0.026</td><td>0.182</td><td>22.62</td><td>0.701</td><td>0.053</td><td>0.269</td><td>25.22</td><td>0.774</td><td>0.040</td><td>0.227</td></tr><tr><td>DeepRFT [39]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.71</td><td>0.801</td><td>0.039</td><td>0.218</td></tr><tr><td>IFAN [25]</td><td>28.11</td><td>0.861</td><td>0.026</td><td>0.179</td><td>22.76</td><td>0.720</td><td>0.052</td><td>0.254</td><td>25.37</td><td>0.789</td><td>0.039</td><td>0.217</td></tr><tr><td>DRBNet [44]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.73</td><td>0.791</td><td>-</td><td>0.183</td></tr><tr><td>Restormer [61]</td><td>28.87</td><td>0.882</td><td>0.025</td><td>0.145</td><td>23.24</td><td>0.743</td><td>0.050</td><td>0.209</td><td>25.98</td><td>0.811</td><td>0.038</td><td>0.178</td></tr><tr><td>FocalNet (Ours)</td><td>29.10</td><td>0.876</td><td>0.024</td><td>0.173</td><td>23.41</td><td>0.743</td><td>0.049</td><td>0.246</td><td>26.18</td><td>0.808</td><td>0.037</td><td>0.210</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.263,
+                0.566,
+                0.707,
+                0.58
+            ],
+            "angle": 0,
+            "content": "Table 4. Single-image defocus deblurring results on the DPDD [1] dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.605,
+                0.471,
+                0.667
+            ],
+            "angle": 0,
+            "content": "in Figure 4 and Figure 6, respectively. Our method is more effective in removing haze blurs in both daytime (indoor and outdoor) and nighttime scenes than other algorithms, such as blurs on the doors in top two images of Figure 4."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.679,
+                0.312,
+                0.696
+            ],
+            "angle": 0,
+            "content": "4.4. Image Desnowing Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.704,
+                0.47,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Quantitative Comparisons. The numerical results on three desnowing datasets, i.e., SRRS [9], CSD [10], and Snow100K [37], are reported in Table 3. As can be seen, our model shows strong ability on snow removal by consistently achieving better or comparable PSNR/SSIM scores on all metrics. Compared to NAFNet [8], FocalNet obtains significant performance gains of \\(1.62\\mathrm{dB}\\) and \\(4.05\\mathrm{dB}\\) PSNR on the SRRS [9] and lately proposed CSD [10] datasets, respectively. In addition, our model yields much higher scores than TransWeather [50] with \\(17\\%\\) parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Visual Comparisons. The visual results are shown in Figure 5. Images produced by our model are of high quality without artifacts and visually closer to ground-truth images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.604,
+                0.803,
+                0.621
+            ],
+            "angle": 0,
+            "content": "4.5. Image Defocus Deblurring Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.628,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Quantitative Comparisons. The quantitative comparisons on the DPDD [1] dataset are provided in Table 4. Our method performs favorably against state-of-the-art algorithms. Specifically, FocalNet obtains significant gains over the CNN-based approaches on the combined category, i.e., \\(0.45\\mathrm{dB}\\) over DRBNet [44] and \\(0.47\\mathrm{dB}\\) over DeepRFT [39]. In addition, compared to Transformer model Restormer [61], our method still obtains a performance improvement of \\(0.2\\mathrm{dB}\\) PSNR with only half parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.764,
+                0.892,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Visual Comparisons. Figure 7 illustrates visual results. Compared to other approaches, our model recovers more fine details, such as patterns on pages."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.818,
+                0.666,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.6. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We conduct ablation studies to demonstrate the effectiveness of our modules by training the tiny model on RESIDE-Indoor [27] and testing on SOTS-Indoor [27]. The number of residual block is set to 1 in all ResBlock. The model is"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "13007"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.468,
+                0.216
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>MResBlock</td><td>SSM</td><td>FSM</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td></td><td></td><td></td><td>31.33</td><td>15.44</td><td>1.48</td></tr><tr><td>(b)</td><td></td><td>✓</td><td></td><td>33.51</td><td>15.48</td><td>1.49</td></tr><tr><td>(c)</td><td></td><td></td><td>✓</td><td>32.44</td><td>15.44</td><td>1.49</td></tr><tr><td>(d)</td><td></td><td>✓</td><td>✓</td><td>35.56</td><td>15.48</td><td>1.49</td></tr><tr><td>(e)</td><td>✓</td><td>✓</td><td></td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(f)</td><td>✓</td><td></td><td>✓</td><td>32.60</td><td>13.77</td><td>1.47</td></tr><tr><td>(g)</td><td>✓</td><td>✓</td><td>✓</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.226,
+                0.47,
+                0.254
+            ],
+            "angle": 0,
+            "content": "Table 5. Ablation studies for different components of FocalNet on the SOTS-Indoor [27] dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.267,
+                0.468,
+                0.381
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td>Simple Gate [8]</td><td>32.23</td><td>13.81</td><td>1.47</td></tr><tr><td>(b)</td><td>Supervised Attention [62]</td><td>32.29</td><td>14.98</td><td>1.76</td></tr><tr><td>(c)</td><td>CBAM [53]</td><td>32.71</td><td>13.77</td><td>1.46</td></tr><tr><td>(d)</td><td>SSM</td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(e)</td><td>CBAM [53]+FSM</td><td>33.23</td><td>13.77</td><td>1.46</td></tr><tr><td>(f)</td><td>SSM+FSM</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.107,
+                0.391,
+                0.438,
+                0.404
+            ],
+            "angle": 0,
+            "content": "Table 6. Comparisons with other attention mechanisms."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.431,
+                0.469,
+                0.522
+            ],
+            "angle": 0,
+            "content": "trained for only 300 epochs with the initial learning rate as \\(1e^{-4}\\) and batch size as 4. Other settings are identical with that of our final dehazing model. The baseline network is obtained by substituting ResBlock for MResBlock and removing DSM from the tiny model. More ablation studies are provided in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.522,
+                0.469,
+                0.674
+            ],
+            "angle": 0,
+            "content": "Effects of Individual Components. As shown in Table 5a, the baseline receives 31.33 dB PSNR. SSM (Table 5b) and FSM (Table 5c) yield accuracy gains of 2.18 dB and 1.11 dB over the baseline, respectively. Equipped with DSM, the model (Table 5d) receives further performance boost by 4.23 dB over the baseline. By replacing ResBlock with MResBlock in the first scale, models consistently receive higher scores than those without MResBlock. Specifically, our choice (Table 5g) outperforms the counterpart (Table 5d) by 0.04 dB with lower computation overhead."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.469,
+                0.795
+            ],
+            "angle": 0,
+            "content": "In addition, the visual results of our DSM are illustrated in Figure 2 (defocus deblurring) and Figure 8 (dehazing). As shown in Figure 2, SSM helps the model focus more on the severe degradation regions, e.g., metal fence. FSM further highlights the edge signals by removing low-frequency information. For dehazing, the hard regions that are difficult to recover are emphasized by our DSM (see Figure 8). More examples are available in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Comparisons with Alternatives to SSM. We further demonstrate superiority of our SSM by replacing it with three popular attention mechanisms. As represented in Table 6, the simple gate [8] and supervised attention [62] lead to performance degradation from 33.71 to \\(32.23\\mathrm{dB}\\) and \\(32.29\\mathrm{dBPSNR}\\), respectively. Compared to CBAM [53], which includes both spatial and channel attention, our SSM"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.092,
+                0.889,
+                0.27
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.272,
+                0.892,
+                0.328
+            ],
+            "angle": 0,
+            "content": "Figure 8. Visual results of DSM for dehazing. From left to right: hazy images obtained from SOTS-Indoor [27], ground-truth images, input and output features of DSM. The complicated regions worthy of more attention are highlighted by our DSM."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.506,
+                0.343,
+                0.888,
+                0.416
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a) FocalNet w/o MResBlock</td><td>40.69</td><td>33.96</td><td>3.76</td></tr><tr><td>(b) FocalNet</td><td>40.82</td><td>30.63</td><td>3.74</td></tr><tr><td>(c) FocalNet-S</td><td>40.32</td><td>17.33</td><td>2.27</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.574,
+                0.426,
+                0.816,
+                0.439
+            ],
+            "angle": 0,
+            "content": "Table 7. Design choices for MResBlock."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.471,
+                0.892,
+                0.577
+            ],
+            "angle": 0,
+            "content": "(Table 6d) receives 1 dB performance gain with comparable computation overhead. The similar conclusion can also be drawn by comparing models of Table 6e and Table 6f, where FSM is additionally used. It is worth mentioning that our FSM boosts the performance when cooperating with CBAM (see Table 6c and Table 6e), demonstrating the efficacy and generalization ability of our design."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.58,
+                0.892,
+                0.687
+            ],
+            "angle": 0,
+            "content": "Order of FSM and SSM. When we swap the order in which FSM and SSM are used, the performance drops from 35.60 dB (Table 5g) to 35.17 dB PSNR. This phenomenon verifies the efficacy of our design, where we first apply SSM to attend to general degradation regions and then leverage FSM to emphasize the more important parts, such as edge signal in Figure 2 and hard regions in Figure 8."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Design Choices for MResBlock. We study the effect of the multi-scale mechanism in our final dehazing model. The training settings are identical with FocalNet in Table 1. As represented in Table 7, MResBlock leads to performance gain of \\(0.13\\mathrm{dB}\\) PSNR with high efficiency. We further explore the potential of MResBlock by using it in all scales of encoder/decoder to form FocalNet-S (Figure 7c). This version degrades the performance by \\(0.5\\mathrm{dB}\\) compared to FocalNet, which is probably because the disadvantage of losing spatial information caused by reducing size of low-resolution features outweighs the advantage of multi-scale learning. It is worth mentioning that FocalNet-S still achieves \\(40.32\\mathrm{dB}\\) PSNR with much lower computation overhead compared to other algorithms (see Figure 1)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "13008"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.116,
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+            ],
+            "angle": 0,
+            "content": "In this study, we present a focal network for image restoration, dubbed FocalNet, which is effective and computationally efficient. The core idea of our work is to focus on the important regions for reconstruction. To this end, we propose two modules: SSM and FSM. SSM is built on spatial attention to detect the degradation regions for subsequent frequency selection. FSM further emphasizes the edge signals or regions that are difficult to recover. By deploying two modules successively, the network is capable of paying more attention to regions that really matter to reconstruction. In addition, we insert the multi-scale mechanism into the network by reducing resolution of half the channels of input feature. This design not only improves performance but also reduces complexity. Experiments on 10 datasets demonstrate that our model achieves state-of-the-art performance for several image restoration tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.374,
+                0.238,
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+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.399,
+                0.47,
+                0.46
+            ],
+            "angle": 0,
+            "content": "This work was supported by the National Natural Science Foundation of China (No. 62025604, U1803264) and Shenzhen Science and Technology Program (No. 20220016)."
+        },
+        {
+            "type": "title",
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+            "angle": 0,
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+# Focal Network for Image Restoration
+
+Yuning Cui $^{1}$  Wenqi Ren $^{2*}$  Xiaochun Cao $^{2}$  Alois Knoll $^{1}$ $^{1}$ Technical University of Munich  $^{2}$ Shenzhen Campus of Sun Yat-sen University  
+{yuning.cui,knoll}@in.tum.de {renwq3, caoxiaochun}@mail.sysu.edu.cn
+
+# Abstract
+
+Image restoration aims to reconstruct a sharp image from its degraded counterpart, which plays an important role in many fields. Recently, Transformer models have achieved promising performance on various image restoration tasks. However, their quadratic complexity remains an intractable issue for practical applications. The aim of this study is to develop an efficient and effective framework for image restoration. Inspired by the fact that different regions in a corrupted image always undergo degradations in various degrees, we propose to focus more on the important areas for reconstruction. To this end, we introduce a dual-domain selection mechanism to emphasize crucial information for restoration, such as edge signals and hard regions. In addition, we split high-resolution features to insert multiscale receptive fields into the network, which improves both efficiency and performance. Finally, the proposed network, dubbed FocalNet, is built by incorporating these designs into a U-shaped backbone. Extensive experiments demonstrate that our model achieves state-of-the-art performance on ten datasets for three tasks, including single-image defocus deblurring, image dehazing, and image desnowing. Our code is available at https://github.com/c-yn/FocalNet.
+
+# 1. Introduction
+
+Bad weather or physical limitations of cameras will degrade visibility of captured images and further exert a negative impact on robustness of downstream tasks. In this regard, image restoration is immensely useful to remove those undesired degradations, e.g., haze, snowflake, and blur, thus playing an essential role in surveillance, autonomous vehicles, remote sensing, and medical imaging [48]. Due to its ill-posed property, many conventional methods have been proposed by resorting to assumptions and hand-crafted features to reduce the solution space. However, these methods are inapplicable to complicated real-world scenarios [66].
+
+The rapid development of convolutional neural networks
+
+![](images/733e89dc8f227dd2fde747204d4e481440082a2903f8d7e48b2e01c4e6e7594c.jpg)  
+Figure 1. PSNR vs. FLOPs on the SOTS-Indoor [27] dataset.
+
+(CNNs) has alleviated the above issue to some extent by learning generalizable image priors from large-scale collected datasets [25, 44]. Recently, Transformer models have injected vitality into image restoration and have achieved promising performance by providing powerful ability of modeling long-range pixel interactions, which is useful for recovering large-scale degradations [7, 32, 61]. Despite a few remedies, the quadratic complexity of self-attention still remains a formidable issue for practical applications.
+
+How to effectively capture critical information parsimoniously has long been a key problem in the computer vision and pattern recognition community. Successful examples include attention mechanism [53], focal loss [34], and the recent advance of partial AUC optimization [58]. Inspired by this, in this study, instead of pursuing large receptive field or exploring modification for the Transformer architecture, we aim to develop an efficient and effective CNN-based framework by paying more attention to informative signals for reconstruction, such as edge information or regions that are difficult to recover. In this direction, existing approaches can be roughly divided into two categories: auxiliary training and attention based methods. The former mainly leverages auxiliary techniques or data, e.g., semantic segmentation [12], depth estimation [29], and optical flow estimation [60], to locate degradations or edge information. Nonetheless, these algorithms always need additional com
+
+![](images/b425b6d2de87b3820f3b694fb9773acf2be8d3bc1d9cae262ac07fa340b668f4.jpg)  
+Blurry Image
+
+![](images/2aaca05f4efc938cdcb94f2f7e3fc25c118232bb61a22e9efffd799d04c1b0bf.jpg)  
+Target
+
+![](images/b2de1db2bac856b9e762e78c1b2c22a033d7c4ec39d9da00d038a865fb38ca72.jpg)  
+Initial Feature  
+Figure 2. Effects of our dual-domain selection mechanism (DSM). From left to right: blurry images obtained from DPDD [1], ground-truth images, input features of our DSM, results of spatial selection, and results of spatial&frequency selection. SSM helps focus on degradation regions while FSM emphasizes edge information. Zoom in for the best view.
+
+![](images/37d02c86885a18dafc1f706e31eb9a395ffbfb3cfbf2e7ac97f54b9cace9afc4.jpg)  
+w/SSM
+
+![](images/a98516a110a5e5a19a7af50197c19dbada21a650c4b2641af4525821ad01e61e.jpg)  
+w/SSM&FSM
+
+plicated branch and elaborately devised training strategies to generate supervisory information. The other line on this topic is to design attention mechanisms to attend to informative regions or control information transmission [8, 41, 62]. These approaches mostly lie in the spatial domain while ignoring the usage of spectral information, which can also provide useful information for reconstruction.
+
+To prompt models to focus more on critical regions, we propose a novel dual-domain selection mechanism (DSM) by sufficiently leveraging discrepancies between sharp/degraded image pairs in both spatial and spectral domains. Concretely, our mechanism comprises two components: spatial selection module (SSM) and frequency selection module (FSM). SSM takes features as input and determines general locations of degradations for each channel by deploying depthwise convolution layers. Then FSM is used to amplify high-frequency signals or hard regions by removing low frequency from features. The proposed network, FocalNet, is established by incorporating DSM into a U-shaped CNN backbone. To save computation overhead, we only insert DSM into the bottleneck module of our FocalNet, which includes the lowest-resolution features.
+
+Moreover, we split the high-resolution features into two parts over channel dimension. Half features are downsampled to lower resolution, which can not only reduce complexity but also boost performance by providing multiscale receptive fields for degradations of different sizes.
+
+Based on the above designs, our FocalNet exhibits state-of-the-art performance on three image restoration tasks. For dehazing, FocalNet outperforms PMNet [59] on both synthetic and real-world benchmark datasets with lower computational complexity, as illustrated in Figure 1. For the desnowing task, FocalNet is superior to Transformer-based framework TransWeather [50] on three commonly used desnowing datasets. Our network also shows potential on defocus deblurring problem by producing a performance gain of  $0.2\mathrm{dB}$  PSNR over Restormer [61] on the combined
+
+category of DPDD [1] dataset. Overall, the main contributions of this study are summarized as follows:
+
+- We propose a novel dual-domain selection mechanism (DSM) that amplifies the response of important regions to assist in recovering clean features.  
+- We develop an efficient and effective focal network that provides multi-scale representation learning for image restoration.  
+- Extensive experiments on ten datasets demonstrate that the proposed network, FocalNet, performs favorably against state-of-the-art algorithms on three representative image restoration tasks.
+
+# 2. Related Work
+
+Image Restoration Architectures. As a long-standing task, image restoration aims to remove undesired degradations in corrupted images, which plays an important role in many fields, such as robot vision, medical applications, and surveillance [48, 66]. Recently, CNN-based architectures have significantly advanced the performance compared to conventional methods [1, 8, 14, 16]. Among these architectures, the encoder-decoder paradigm is a popular solution to learn hierarchical representations [39, 44]. In addition, a great number of functional units have been developed or borrowed from other realms, such as dilated convolution [68], skip connections [13], dynamic filter [25], and various attention mechanisms [41]. More recently, Transformer models have been imported into low-level vision tasks and provided promising performance [7, 32]. Thereafter, a few measures have been taken to reduce the computational complexity of self-attention by restricting the operation region [32] or switching the operation dimension [61].
+
+Spectral Networks. Apart from spatial representation learning, numerous deep frameworks have been proposed
+
+![](images/1c0c6be16be4097395a9ac2bc56cd62a469677f6bded47bc705158b5f753d33c.jpg)  
+Figure 3. Architecture of the proposed FocalNet with dual-domain selection mechanism (DSM) that consists of two components, i.e., spatial selection module (SSM) and frequency selection module (FSM). ResBlock contains  $n$  residual blocks, comprising two  $3 \times 3$  convolution layers and activation function in between.
+
+to bridge frequency gaps between sharp/degraded image pairs [15, 39, 68]. The common practice is to decompose features into different frequency components via transformation tools such as wavelet transform [10, 68], Fourier transform [22, 39], pooling technique [15], and conventional filters [35], and then treat each component individually via convolution layers. In addition, a few researches have investigated the different roles of phase and amplitude, and proposed architectures to recover them separately [28]. In our work, we simply remove the lowest-frequency signal from the resulting features of SSM to provide guidance for further reconstruction.
+
+Auxiliary Training. In addition to the provided ground-truth images in training sets of image restoration tasks, a great number of networks have been proposed to resort to auxiliary supervision. Semantic priors have been introduced into low-level tasks to provide color, boundary or location information [12, 43, 45]. However, global semantic priors are less effective for degradations caused by large depth variations. Thus many methods have proposed to estimate depth map to generate edge and structure signals for restoration [24, 29]. Moreover, there are many works that integrate other auxiliary information such as optical flow [56, 60] and event data [57]. However, the above solutions always require additional data, expensive convolution branch, and complicated training strategies [45].
+
+# 3. Method
+
+In this section, we first delineate the overall architecture of FocalNet. Then we describe our modules: Multi-scale ResBlock (MResBlock) and Dual-domain Selection Mech-
+
+anism (DSM). Finally, we detail the loss functions.
+
+# 3.1. Overall Pipeline
+
+As illustrated in Figure 3, the proposed FocalNet adopts the popular encoder-decoder architecture to learn hierarchical representations efficiently. Both encoder and decoder networks consist of three scales. In our paper, we refer to the first scale as the sub-network that involves the highest-resolution features. MResBlock constitutes the main part of the first scale. The other two scales are mainly composed of ResBlock, which consists of  $n$  residual blocks. Given a degraded image of size  $H \times W \times 3$ , where  $H \times W$  and  $C$  represent spatial locations and the number of channels respectively, a  $3 \times 3$  convolution layer is used to extract shallow features of size  $H \times W \times C$ . Then, the shallow features pass through three-scale symmetric encoder-decoder and are transformed into restored features, i.e., output features of MResBlock in the first scale of decoder. Starting from the highest-resolution input, the encoder gradually reduces spatial size and expands the number of channels. The decoder does the opposite to restore clean features from the deepest features. During this process, the decoder features are concatenated with the encoder features to assist recovery, followed by a  $1 \times 1$  convolution to adjust channel dimension. Finally, the predicted clean image is generated by the last  $3 \times 3$  convolution layer and image-level residual connection. Upsampling (UP) and downsampling (DOWN) operations are implemented by transposed and strided convolutions except for the upsampling layer in MResBlock that adopts bilinear interpolation. The proposed DSM is injected into the bottleneck location to select the most im
+
+portant regions for reconstruction. In addition, we apply the multi-input and multi-output strategies to ease training difficulty following previous methods [13, 15, 39, 49].
+
+# 3.2. Multi-scale ResBlock (MResBlock)
+
+Recently, pursuing multi-scale receptive fields is a hot topic in computer vision community [5, 20, 42, 55], especially for Transformer-based models [33, 42]. Inspired by [11, 40, 46], we adopt multi-scale mechanism in ResBlock to form our MResBlock via splitting and downsampling operations, as illustrated in Figure 3. Specifically, given input features, we first split them equally along channel dimension into two components. Next, half features are reduced to a quarter of the original resolution using strided convolution. The resulting features are fed into ResBlock, and then up-sampled to the original size. The other half are directly processed by ResBlock. The final output of MResBlock is obtained by concatenating resulting features of two branches. MResBlock enjoys two main advantages. Firstly, it improves performance by realizing multi-scale representation learning for degradations of different sizes and enhances spectral learning for different frequencies [40]. Secondly, it improves efficiency by reducing feature resolution.
+
+# 3.3. Dual-domain Selection Mechanism (DSM)
+
+The main goal of this study is to develop an efficient network for image restoration by focusing on the more important regions. This aim is achieved by the proposed DSM, which amplifies the response of informative information in two domains (see Figure 2). As illustrated in the bottom part of Figure 3, it consists of two components: spatial selection module (SSM) and frequency selection module (FSM). Given input features  $F \in \mathbb{R}^{H \times W \times C}$ , SSM and FSM are employed successively, which can be expressed as:
+
+$$
+\hat {F} = \operatorname {F S M} (\operatorname {S S M} (F)). \tag {1}
+$$
+
+Next, we introduce these two elements in details.
+
+Spatial Selection Module (SSM). SSM helps the network focus on important regions in the spatial domain, providing initial locations of severe degradations for subsequent FSM. Our SSM has three branches. The main path is built upon the CBAM [53] to produce the general feature representation for locations of degradations to focus. Specifically, given an intermediate feature map  $F$ , we first squeeze  $F$  along channel dimension through two types of pooling techniques, i.e., max pooling and average pooling, and then generate the general feature map via a convolution layer, which is formally expressed as:
+
+$$
+F ^ {\prime} = \operatorname {C o n v} _ {3} ([ \operatorname {A v g P o o l} (F), \operatorname {M a x P o o l} (F) ]), \tag {2}
+$$
+
+where  $[\cdot, \cdot]$  indicates concatenation; AvgPool, MaxPool and Conv3 represent average pooling, max pooling, and con
+
+volution layer of  $3 \times 3$  kernel size. By doing this,  $F' \in \mathbb{R}^{H \times W \times 1}$  contains degradation locations to focus [53].
+
+Since each channel differs in degradation patterns, we further generate channel-wise representation by performing the channel-separated transformation for the input feature  $F$  via depth-wise convolutions, and then modulate resulting features with  $F'$ . This process is expressed as follows:
+
+$$
+F _ {s} = \mathrm {D C o n v s} _ {5, 7} (F) \otimes \mathrm {T} \left(F ^ {\prime}, C\right) + \mathrm {D C o n v} _ {3} (F), \tag {3}
+$$
+
+where  $\mathrm{DConv}_{5,7}$  denotes cascaded depth-wise convolution layers of kernel sizes  $5\times 5$  and  $7\times 7$ ;  $\mathrm{DConv}_3$  represents depth-wise convolution with  $3\times 3$  kernel;  $\otimes$  indicates an element-wise multiplication; and  $\mathrm{T}(F',C)$  is the tile function that copies  $F'$  for  $C$  times along the channel dimension to  $\mathbb{R}^{H\times W\times C}$ . We then feed the spatially selected features  $F_{s}\in \mathbb{R}^{H\times W\times C}$  to FSM for frequency selection.
+
+Frequency Selection Module (FSM). We can directly utilize  $F_{s}$  to assist the recovery process. Motivated by the fact that degraded/sharp image pairs have similar low-frequency components, while differing at high frequencies, we further emphasize regions that contain the real difference between input/sharp image pairs by removing lowest frequency via the proposed FSM. To this end, we first apply the mean filter to  $F_{s}$  to generate low-frequency features, and then obtain the complementary high-frequency features by subtracting the resulting low-frequency signals from the input, which is expressed by:
+
+$$
+F _ {s} ^ {h} = F _ {s} - \operatorname {M e a n} \left(F _ {s}\right). \tag {4}
+$$
+
+In our case, the mean filter is implemented by the channelwise global average pooling. The final output of FSM/DSM is generated using the element-wise multiplication between  $F_{s}^{h}$  and  $F_{s}$ , and residual connection, which is expressed as:
+
+$$
+\hat {F} = F _ {s} ^ {h} \otimes F _ {s} + F _ {s}. \tag {5}
+$$
+
+After DSM, the important regions are emphasized, e.g., edge signals in Figure 2 for defocus deblurring.
+
+# 3.4. Loss Function
+
+To facilitate the selection process in both spatial and frequency domains, we adopt dual-domain  $l_{1}$  loss functions following [13, 15]. For each output/target image pair with the same resolution, loss functions are given by:
+
+$$
+\mathcal {L} _ {s} = \frac {1}{P} \| \hat {I} - G \| _ {1} \tag {6}
+$$
+
+$$
+\mathcal {L} _ {f} = \frac {1}{P} \| \mathcal {F} (\hat {I}) - \mathcal {F} (G) \| _ {1} \tag {7}
+$$
+
+$$
+\mathcal {L} = \mathcal {L} _ {s} + \lambda \mathcal {L} _ {f} \tag {8}
+$$
+
+where  $\hat{I}$  and  $G$  denote the output and ground-truth images, respectively;  $P$  indicates total elements for normalization;  $\mathcal{F}$  represents fast Fourier transform; and  $\lambda$  is empirically set to 0.1 for balancing dual-domain training.
+
+![](images/5b6b283d04df04a37fd25cdc944019706769659f9d1b9e4328b01c28570e0d85.jpg)  
+Figure 4. Image dehazing comparisons on the SOTS [27] test sets.
+
+# 4. Experiments and Analysis
+
+We evaluate FocalNet on 10 datasets for three image restoration tasks, including image dehazing, image desnowing, and single-image defocus deblurring. We provide experimental results for image motion deblurring and image denoising in the supplementary material.
+
+# 4.1. Datasets and Evaluation Protocol
+
+We measure the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity index (SSIM) [52] between predicted results and ground-truth images for all datasets. Mean Absolute Error (MAE) and Learned Perceptual Image Patch Similarity (LPIPS) [67] are additionally adopted for defocus deblurring. FLOPs are measured on  $256 \times 256$  patch. In tables, the best performance is marked in bold.
+
+Image Dehazing. We train and evaluate our models on both synthetic and real-world datasets for image dehazing. Following [21, 59], we train separate models on the RESIDE-Indoor and RESIDE-Outdoor datasets [27], and evaluate the resulting models on the corresponding test sets of RESIDE, i.e., SOTS-Indoor and SOTS-Outdoor, respectively. In addition, we adopt three real-world datasets, i.e., Dense-Haze [2], NH-HAZE [3], and O-HAZE [4], to verify the robustness of our model in more challenging real-world scenarios. Apart from the above daytime dehazing datasets, we also demonstrate the effectiveness of FocalNet on the nighttime dataset NHR [65].
+
+Image Defocus Deblurring. Consistent with previous algorithms [25, 44, 61], we use the DPDD [1] dataset that consists of 350 scenes for training, 74 scenes for validation, and 100 scenes for validation with a 1:1 ratio.
+
+tion, and 76 scenes for testing. Each scene comprises four images, labeled as center view, left view, right view, and all-in-focus ground-truth images. FocalNet is trained by taking the center view image as input and calculating loss values between the predicted clean image and ground truth.
+
+Image Desnowing. For the desnowing problem, we train and evaluate our models on three commonly used datasets, i.e., SRRS [9], CSD [10], and Snow100K [37]. Dataset selection and testing methods are consistent with the recent algorithm [9] for a fair and convincing comparison.
+
+# 4.2. Implementation Details
+
+Unless stated otherwise, the following hyper-parameters are adopted. Depending on the task complexity, we scale the model by varying the number of residual blocks in all ResBlock, i.e., 16 for deblurring and 4 for dehazing/desnowing. In our FocalNet, we only deploy MResBlock in the first scale of encoder/decoder. Convolution parameters are not shared between two branches of MResBlock. The models are trained using Adam [23] with initial learning rate as  $8e^{-4}$ , which is gradually reduced to  $1e^{-6}$  with cosine annealing [38]. For data augmentation, we adopt random horizontal flips with a probability of 0.5. Models are trained on 32 samples of size  $256 \times 256$  for each iteration. More details of training configuration for each specific dataset are provided in the supplementary material.
+
+# 4.3. Image Dehazing Results
+
+Quantitative Comparisons. We report the quantitative performance of image dehazing approaches on both syn
+
+![](images/566ccddc48f09acde47d27005039b99c74f1d85850ce8cb59e01b8d522e04bed.jpg)  
+Figure 5. Image desnowing comparisons on the CSD [10] dataset. Our method is more effective in snow removal than other algorithms.
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">SOTS-Indoor [27]</td><td colspan="2">SOTS-Outdoor [27]</td><td colspan="2">Dense-Haze [2]</td><td colspan="2">NH-HAZE [3]</td><td colspan="2">O-HAZE [4]</td><td rowspan="2">Params (M)</td><td rowspan="2">FLOPs (G)</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DehazeNet [6]</td><td>19.82</td><td>0.821</td><td>24.75</td><td>0.927</td><td>13.84</td><td>0.43</td><td>16.62</td><td>0.52</td><td>17.57</td><td>0.77</td><td>0.009</td><td>0.581</td></tr><tr><td>AOD-Net [26]</td><td>20.51</td><td>0.816</td><td>24.14</td><td>0.920</td><td>13.14</td><td>0.41</td><td>15.40</td><td>0.57</td><td>15.03</td><td>0.54</td><td>0.002</td><td>0.115</td></tr><tr><td>GridDehazeNet [36]</td><td>32.16</td><td>0.984</td><td>30.86</td><td>0.982</td><td>-</td><td>-</td><td>13.80</td><td>0.54</td><td>-</td><td>-</td><td>0.956</td><td>21.49</td></tr><tr><td>MSBDN [17]</td><td>33.67</td><td>0.985</td><td>33.48</td><td>0.982</td><td>15.37</td><td>0.49</td><td>19.23</td><td>0.71</td><td>24.36</td><td>0.75</td><td>31.35</td><td>41.54</td></tr><tr><td>FFA-Net [41]</td><td>36.39</td><td>0.989</td><td>33.57</td><td>0.984</td><td>14.39</td><td>0.45</td><td>19.87</td><td>0.69</td><td>22.12</td><td>0.77</td><td>4.456</td><td>287.8</td></tr><tr><td>AECR-Net [54]</td><td>37.17</td><td>0.990</td><td>-</td><td>-</td><td>15.80</td><td>0.47</td><td>19.88</td><td>0.72</td><td>-</td><td>-</td><td>2.611</td><td>52.20</td></tr><tr><td>DeHamer [21]</td><td>36.63</td><td>0.988</td><td>35.18</td><td>0.986</td><td>16.62</td><td>0.56</td><td>20.66</td><td>0.68</td><td>-</td><td>-</td><td>132.45</td><td>48.93</td></tr><tr><td>PMNet[59]</td><td>38.41</td><td>0.990</td><td>34.74</td><td>0.985</td><td>16.79</td><td>0.51</td><td>20.42</td><td>0.73</td><td>24.64</td><td>0.83</td><td>18.90</td><td>81.13</td></tr><tr><td>FocalNet (Ours)</td><td>40.82</td><td>0.996</td><td>37.71</td><td>0.995</td><td>17.07</td><td>0.63</td><td>20.43</td><td>0.79</td><td>25.50</td><td>0.94</td><td>3.74</td><td>30.63</td></tr></table>
+
+Table 1. Image dehazing results on both synthetic dataset [27] and real-world datasets [2, 3, 4].  
+
+<table><tr><td>Method</td><td>NDIM [64]</td><td>GS [31]</td><td>MRPF [63]</td><td>MRP [63]</td><td>OSFD [65]</td><td>HCD [51]</td><td>FocalNet Ours</td></tr><tr><td>PSNR</td><td>14.31</td><td>17.32</td><td>16.95</td><td>19.93</td><td>21.32</td><td>23.43</td><td>25.35</td></tr><tr><td>SSIM</td><td>0.526</td><td>0.629</td><td>0.667</td><td>0.777</td><td>0.804</td><td>0.953</td><td>0.969</td></tr></table>
+
+Table 2. Nighttime image dehazing results on NHR [65] dataset.
+
+thetic [27] and real-world [2, 3, 4] datasets in Table 1. Overall, our method receives better performance on all datasets than other state-of-the-art algorithms. Specifically, on the daytime synthetic dataset SOTS-Indoor [27], our method outperforms PMNet [59] by 2.41 dB PSNR with only  $20\%$  parameters and  $38\%$  FLOPs. Furthermore, our model yields a significant performance gain of 2.53 dB in terms of PSNR over Transformer model DeHamer [21] on SOTS-Outdoor [27] with  $97\%$  fewer parameters.
+
+In addition, our method is well generalized to the more challenging real-world scenarios and obtains the best performance on most metrics. Particularly on the O-HAZE [4] dataset, FocalNet yields considerable gain of 0.86 dB PSNR and 0.11 SSIM over PMNet [59].
+
+Apart from daytime dehazing datasets, we also evaluate the effectiveness of our model on the nighttime dehazing dataset NHR [65]. As shown in Table 2, FocalNet signifi
+
+![](images/2d942c537d09c375ec6859aa5e9cd9caaaa10ae91196e7ae38edc5fc28a3a032.jpg)
+
+Figure 6. Nighttime dehazing comparisons on NHR [65] dataset.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">CSD [10]</td><td colspan="2">SRRS [9]</td><td colspan="2">Snow100K [37]</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DesnowNet [37]</td><td>20.13</td><td>0.81</td><td>20.38</td><td>0.84</td><td>30.50</td><td>0.94</td></tr><tr><td>CycleGAN [19]</td><td>20.98</td><td>0.80</td><td>20.21</td><td>0.74</td><td>26.81</td><td>0.89</td></tr><tr><td>All in One [30]</td><td>26.31</td><td>0.87</td><td>24.98</td><td>0.88</td><td>26.07</td><td>0.88</td></tr><tr><td>JSTASR [9]</td><td>27.96</td><td>0.88</td><td>25.82</td><td>0.89</td><td>23.12</td><td>0.86</td></tr><tr><td>HDCW-Net [10]</td><td>29.06</td><td>0.91</td><td>27.78</td><td>0.92</td><td>31.54</td><td>0.95</td></tr><tr><td>TransWeather [50]</td><td>31.76</td><td>0.93</td><td>28.29</td><td>0.92</td><td>31.82</td><td>0.93</td></tr><tr><td>NAFNet [8]</td><td>33.13</td><td>0.96</td><td>29.72</td><td>0.94</td><td>32.41</td><td>0.95</td></tr><tr><td>FocalNet (Ours)</td><td>37.18</td><td>0.99</td><td>31.34</td><td>0.98</td><td>33.53</td><td>0.95</td></tr></table>
+
+Table 3. Image desnowing results on three widely used datasets.
+
+cantly outperforms the recent HCD [51] by  $1.92\mathrm{dB}$  PSNR. The results demonstrate the efficacy of our design.
+
+Visual Comparisons. The daytime and nighttime visual results produced by several dehazing methods are illustrated
+
+![](images/b260cdfcad3d474c012b169052a16351f8a3cff02ac2d19e203986c6cde55aa5.jpg)
+
+![](images/80a1e6de83704e7dac61c797459eadfb2eb479edfe3cc77a4d5368cd96be5614.jpg)
+
+![](images/146a0e1ee6851b6618a3e121398b493991420a1f873d55446291a58a567b39cb.jpg)
+
+![](images/981ba2674c6bd5d253e19a38eed62fbecae847a1ab1e9cad309625b3f998f53a.jpg)
+
+![](images/1fa58e1792b7ba96e1ed0a2cbafec3dc66996dd51791e5d818fd023d6a1748b3.jpg)
+
+![](images/3935ea4274fed00d82acba0f73a65a51218928a27810972bd121f2c328d970fe.jpg)  
+Figure 7. Single-image defocus deblurring results on the DPDD [1] dataset. We display the magnified parts of the produced images for clarity. From left-top to right-bottom: input blurry images, ground-truth images, and the predicted images obtained by KPAC [47], IFAN [25], DeepRFT [39], DRBNet [44], Restormer [61], and our FocalNet, respectively.
+
+![](images/088941e1ec48ebc84656ece32359be240e3e1c2912916dd3bb3a9b83ff631683.jpg)
+
+![](images/f07d50461578edd1d2fd7e34cd8c4f887187ac11ec4eab4ac3a2814f4407280d.jpg)
+
+![](images/4f3627cfd594aa205f18a609c66e764dd81815f8e10f2156ec5555b8775ff092.jpg)
+
+![](images/fe7472167a86c2b66cb73fd40da8d487e545f7d88f42ede7db55c834972d4a74.jpg)
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Indoor Scenes</td><td colspan="4">Outdoor Scenes</td><td colspan="4">Combined</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td></tr><tr><td>DPDNet [1]</td><td>26.54</td><td>0.816</td><td>0.031</td><td>0.239</td><td>22.25</td><td>0.682</td><td>0.056</td><td>0.313</td><td>24.34</td><td>0.747</td><td>0.044</td><td>0.277</td></tr><tr><td>KPAC [47]</td><td>27.97</td><td>0.852</td><td>0.026</td><td>0.182</td><td>22.62</td><td>0.701</td><td>0.053</td><td>0.269</td><td>25.22</td><td>0.774</td><td>0.040</td><td>0.227</td></tr><tr><td>DeepRFT [39]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.71</td><td>0.801</td><td>0.039</td><td>0.218</td></tr><tr><td>IFAN [25]</td><td>28.11</td><td>0.861</td><td>0.026</td><td>0.179</td><td>22.76</td><td>0.720</td><td>0.052</td><td>0.254</td><td>25.37</td><td>0.789</td><td>0.039</td><td>0.217</td></tr><tr><td>DRBNet [44]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.73</td><td>0.791</td><td>-</td><td>0.183</td></tr><tr><td>Restormer [61]</td><td>28.87</td><td>0.882</td><td>0.025</td><td>0.145</td><td>23.24</td><td>0.743</td><td>0.050</td><td>0.209</td><td>25.98</td><td>0.811</td><td>0.038</td><td>0.178</td></tr><tr><td>FocalNet (Ours)</td><td>29.10</td><td>0.876</td><td>0.024</td><td>0.173</td><td>23.41</td><td>0.743</td><td>0.049</td><td>0.246</td><td>26.18</td><td>0.808</td><td>0.037</td><td>0.210</td></tr></table>
+
+Table 4. Single-image defocus deblurring results on the DPDD [1] dataset.
+
+in Figure 4 and Figure 6, respectively. Our method is more effective in removing haze blurs in both daytime (indoor and outdoor) and nighttime scenes than other algorithms, such as blurs on the doors in top two images of Figure 4.
+
+# 4.4. Image Desnowing Results
+
+Quantitative Comparisons. The numerical results on three desnowing datasets, i.e., SRRS [9], CSD [10], and Snow100K [37], are reported in Table 3. As can be seen, our model shows strong ability on snow removal by consistently achieving better or comparable PSNR/SSIM scores on all metrics. Compared to NAFNet [8], FocalNet obtains significant performance gains of  $1.62\mathrm{dB}$  and  $4.05\mathrm{dB}$  PSNR on the SRRS [9] and lately proposed CSD [10] datasets, respectively. In addition, our model yields much higher scores than TransWeather [50] with  $17\%$  parameters.
+
+Visual Comparisons. The visual results are shown in Figure 5. Images produced by our model are of high quality without artifacts and visually closer to ground-truth images.
+
+# 4.5. Image Defocus Deblurring Results
+
+Quantitative Comparisons. The quantitative comparisons on the DPDD [1] dataset are provided in Table 4. Our method performs favorably against state-of-the-art algorithms. Specifically, FocalNet obtains significant gains over the CNN-based approaches on the combined category, i.e.,  $0.45\mathrm{dB}$  over DRBNet [44] and  $0.47\mathrm{dB}$  over DeepRFT [39]. In addition, compared to Transformer model Restormer [61], our method still obtains a performance improvement of  $0.2\mathrm{dB}$  PSNR with only half parameters.
+
+Visual Comparisons. Figure 7 illustrates visual results. Compared to other approaches, our model recovers more fine details, such as patterns on pages.
+
+# 4.6. Ablation Studies
+
+We conduct ablation studies to demonstrate the effectiveness of our modules by training the tiny model on RESIDE-Indoor [27] and testing on SOTS-Indoor [27]. The number of residual block is set to 1 in all ResBlock. The model is
+
+<table><tr><td></td><td>MResBlock</td><td>SSM</td><td>FSM</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td></td><td></td><td></td><td>31.33</td><td>15.44</td><td>1.48</td></tr><tr><td>(b)</td><td></td><td>✓</td><td></td><td>33.51</td><td>15.48</td><td>1.49</td></tr><tr><td>(c)</td><td></td><td></td><td>✓</td><td>32.44</td><td>15.44</td><td>1.49</td></tr><tr><td>(d)</td><td></td><td>✓</td><td>✓</td><td>35.56</td><td>15.48</td><td>1.49</td></tr><tr><td>(e)</td><td>✓</td><td>✓</td><td></td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(f)</td><td>✓</td><td></td><td>✓</td><td>32.60</td><td>13.77</td><td>1.47</td></tr><tr><td>(g)</td><td>✓</td><td>✓</td><td>✓</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>
+
+Table 5. Ablation studies for different components of FocalNet on the SOTS-Indoor [27] dataset.  
+
+<table><tr><td></td><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td>Simple Gate [8]</td><td>32.23</td><td>13.81</td><td>1.47</td></tr><tr><td>(b)</td><td>Supervised Attention [62]</td><td>32.29</td><td>14.98</td><td>1.76</td></tr><tr><td>(c)</td><td>CBAM [53]</td><td>32.71</td><td>13.77</td><td>1.46</td></tr><tr><td>(d)</td><td>SSM</td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(e)</td><td>CBAM [53]+FSM</td><td>33.23</td><td>13.77</td><td>1.46</td></tr><tr><td>(f)</td><td>SSM+FSM</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>
+
+trained for only 300 epochs with the initial learning rate as  $1e^{-4}$  and batch size as 4. Other settings are identical with that of our final dehazing model. The baseline network is obtained by substituting ResBlock for MResBlock and removing DSM from the tiny model. More ablation studies are provided in the supplementary material.
+
+Effects of Individual Components. As shown in Table 5a, the baseline receives 31.33 dB PSNR. SSM (Table 5b) and FSM (Table 5c) yield accuracy gains of 2.18 dB and 1.11 dB over the baseline, respectively. Equipped with DSM, the model (Table 5d) receives further performance boost by 4.23 dB over the baseline. By replacing ResBlock with MResBlock in the first scale, models consistently receive higher scores than those without MResBlock. Specifically, our choice (Table 5g) outperforms the counterpart (Table 5d) by 0.04 dB with lower computation overhead.
+
+In addition, the visual results of our DSM are illustrated in Figure 2 (defocus deblurring) and Figure 8 (dehazing). As shown in Figure 2, SSM helps the model focus more on the severe degradation regions, e.g., metal fence. FSM further highlights the edge signals by removing low-frequency information. For dehazing, the hard regions that are difficult to recover are emphasized by our DSM (see Figure 8). More examples are available in the supplementary material.
+
+Comparisons with Alternatives to SSM. We further demonstrate superiority of our SSM by replacing it with three popular attention mechanisms. As represented in Table 6, the simple gate [8] and supervised attention [62] lead to performance degradation from 33.71 to  $32.23\mathrm{dB}$  and  $32.29\mathrm{dBPSNR}$ , respectively. Compared to CBAM [53], which includes both spatial and channel attention, our SSM
+
+![](images/8a18441fa51ac1f746eebc4b215269f4257ab4ea004a8eeccf5ad595d04e9a54.jpg)  
+Figure 8. Visual results of DSM for dehazing. From left to right: hazy images obtained from SOTS-Indoor [27], ground-truth images, input and output features of DSM. The complicated regions worthy of more attention are highlighted by our DSM.
+
+Table 6. Comparisons with other attention mechanisms.  
+
+<table><tr><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a) FocalNet w/o MResBlock</td><td>40.69</td><td>33.96</td><td>3.76</td></tr><tr><td>(b) FocalNet</td><td>40.82</td><td>30.63</td><td>3.74</td></tr><tr><td>(c) FocalNet-S</td><td>40.32</td><td>17.33</td><td>2.27</td></tr></table>
+
+Table 7. Design choices for MResBlock.
+
+(Table 6d) receives 1 dB performance gain with comparable computation overhead. The similar conclusion can also be drawn by comparing models of Table 6e and Table 6f, where FSM is additionally used. It is worth mentioning that our FSM boosts the performance when cooperating with CBAM (see Table 6c and Table 6e), demonstrating the efficacy and generalization ability of our design.
+
+Order of FSM and SSM. When we swap the order in which FSM and SSM are used, the performance drops from 35.60 dB (Table 5g) to 35.17 dB PSNR. This phenomenon verifies the efficacy of our design, where we first apply SSM to attend to general degradation regions and then leverage FSM to emphasize the more important parts, such as edge signal in Figure 2 and hard regions in Figure 8.
+
+Design Choices for MResBlock. We study the effect of the multi-scale mechanism in our final dehazing model. The training settings are identical with FocalNet in Table 1. As represented in Table 7, MResBlock leads to performance gain of  $0.13\mathrm{dB}$  PSNR with high efficiency. We further explore the potential of MResBlock by using it in all scales of encoder/decoder to form FocalNet-S (Figure 7c). This version degrades the performance by  $0.5\mathrm{dB}$  compared to FocalNet, which is probably because the disadvantage of losing spatial information caused by reducing size of low-resolution features outweighs the advantage of multi-scale learning. It is worth mentioning that FocalNet-S still achieves  $40.32\mathrm{dB}$  PSNR with much lower computation overhead compared to other algorithms (see Figure 1).
+
+# 5. Conclusion
+
+In this study, we present a focal network for image restoration, dubbed FocalNet, which is effective and computationally efficient. The core idea of our work is to focus on the important regions for reconstruction. To this end, we propose two modules: SSM and FSM. SSM is built on spatial attention to detect the degradation regions for subsequent frequency selection. FSM further emphasizes the edge signals or regions that are difficult to recover. By deploying two modules successively, the network is capable of paying more attention to regions that really matter to reconstruction. In addition, we insert the multi-scale mechanism into the network by reducing resolution of half the channels of input feature. This design not only improves performance but also reduces complexity. Experiments on 10 datasets demonstrate that our model achieves state-of-the-art performance for several image restoration tasks.
+
+# Acknowledgement
+
+This work was supported by the National Natural Science Foundation of China (No. 62025604, U1803264) and Shenzhen Science and Technology Program (No. 20220016).
+
+# References
+
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+                                    "content": "(CNNs) has alleviated the above issue to some extent by learning generalizable image priors from large-scale collected datasets [25, 44]. Recently, Transformer models have injected vitality into image restoration and have achieved promising performance by providing powerful ability of modeling long-range pixel interactions, which is useful for recovering large-scale degradations [7, 32, 61]. Despite a few remedies, the quadratic complexity of self-attention still remains a formidable issue for practical applications."
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+                                    "content": "Based on the above designs, our FocalNet exhibits state-of-the-art performance on three image restoration tasks. For dehazing, FocalNet outperforms PMNet [59] on both synthetic and real-world benchmark datasets with lower computational complexity, as illustrated in Figure 1. For the desnowing task, FocalNet is superior to Transformer-based framework TransWeather [50] on three commonly used desnowing datasets. Our network also shows potential on defocus deblurring problem by producing a performance gain of "
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+                                    "content": "0.2\\mathrm{dB}"
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+                                    "content": " PSNR over Restormer [61] on the combined"
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+                                    "content": "category of DPDD [1] dataset. Overall, the main contributions of this study are summarized as follows:"
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+                                            "content": "- We develop an efficient and effective focal network that provides multi-scale representation learning for image restoration."
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+                                            "content": "- Extensive experiments on ten datasets demonstrate that the proposed network, FocalNet, performs favorably against state-of-the-art algorithms on three representative image restoration tasks."
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+                                    "content": "2. Related Work"
+                                }
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+                                    "content": "Image Restoration Architectures. As a long-standing task, image restoration aims to remove undesired degradations in corrupted images, which plays an important role in many fields, such as robot vision, medical applications, and surveillance [48, 66]. Recently, CNN-based architectures have significantly advanced the performance compared to conventional methods [1, 8, 14, 16]. Among these architectures, the encoder-decoder paradigm is a popular solution to learn hierarchical representations [39, 44]. In addition, a great number of functional units have been developed or borrowed from other realms, such as dilated convolution [68], skip connections [13], dynamic filter [25], and various attention mechanisms [41]. More recently, Transformer models have been imported into low-level vision tasks and provided promising performance [7, 32]. Thereafter, a few measures have been taken to reduce the computational complexity of self-attention by restricting the operation region [32] or switching the operation dimension [61]."
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+                                    "content": "Spectral Networks. Apart from spatial representation learning, numerous deep frameworks have been proposed"
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+                                            "content": "Figure 3. Architecture of the proposed FocalNet with dual-domain selection mechanism (DSM) that consists of two components, i.e., spatial selection module (SSM) and frequency selection module (FSM). ResBlock contains "
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+                                    "content": "to bridge frequency gaps between sharp/degraded image pairs [15, 39, 68]. The common practice is to decompose features into different frequency components via transformation tools such as wavelet transform [10, 68], Fourier transform [22, 39], pooling technique [15], and conventional filters [35], and then treat each component individually via convolution layers. In addition, a few researches have investigated the different roles of phase and amplitude, and proposed architectures to recover them separately [28]. In our work, we simply remove the lowest-frequency signal from the resulting features of SSM to provide guidance for further reconstruction."
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+                                    "content": "Auxiliary Training. In addition to the provided ground-truth images in training sets of image restoration tasks, a great number of networks have been proposed to resort to auxiliary supervision. Semantic priors have been introduced into low-level tasks to provide color, boundary or location information [12, 43, 45]. However, global semantic priors are less effective for degradations caused by large depth variations. Thus many methods have proposed to estimate depth map to generate edge and structure signals for restoration [24, 29]. Moreover, there are many works that integrate other auxiliary information such as optical flow [56, 60] and event data [57]. However, the above solutions always require additional data, expensive convolution branch, and complicated training strategies [45]."
+                                }
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+                                    "content": "3. Method"
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+                                    "content": "In this section, we first delineate the overall architecture of FocalNet. Then we describe our modules: Multi-scale ResBlock (MResBlock) and Dual-domain Selection Mech-"
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+                                    "content": "anism (DSM). Finally, we detail the loss functions."
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+                                    "content": "As illustrated in Figure 3, the proposed FocalNet adopts the popular encoder-decoder architecture to learn hierarchical representations efficiently. Both encoder and decoder networks consist of three scales. In our paper, we refer to the first scale as the sub-network that involves the highest-resolution features. MResBlock constitutes the main part of the first scale. The other two scales are mainly composed of ResBlock, which consists of "
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+                                    "content": " residual blocks. Given a degraded image of size "
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+                                    "type": "inline_equation",
+                                    "content": "H \\times W \\times 3"
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "text",
+                                    "content": " represent spatial locations and the number of channels respectively, a "
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+                                    "content": ". Then, the shallow features pass through three-scale symmetric encoder-decoder and are transformed into restored features, i.e., output features of MResBlock in the first scale of decoder. Starting from the highest-resolution input, the encoder gradually reduces spatial size and expands the number of channels. The decoder does the opposite to restore clean features from the deepest features. During this process, the decoder features are concatenated with the encoder features to assist recovery, followed by a "
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+                                    "content": " convolution to adjust channel dimension. Finally, the predicted clean image is generated by the last "
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+                                    "content": " convolution layer and image-level residual connection. Upsampling (UP) and downsampling (DOWN) operations are implemented by transposed and strided convolutions except for the upsampling layer in MResBlock that adopts bilinear interpolation. The proposed DSM is injected into the bottleneck location to select the most im"
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+                                    "content": "portant regions for reconstruction. In addition, we apply the multi-input and multi-output strategies to ease training difficulty following previous methods [13, 15, 39, 49]."
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+                                    "content": "Recently, pursuing multi-scale receptive fields is a hot topic in computer vision community [5, 20, 42, 55], especially for Transformer-based models [33, 42]. Inspired by [11, 40, 46], we adopt multi-scale mechanism in ResBlock to form our MResBlock via splitting and downsampling operations, as illustrated in Figure 3. Specifically, given input features, we first split them equally along channel dimension into two components. Next, half features are reduced to a quarter of the original resolution using strided convolution. The resulting features are fed into ResBlock, and then up-sampled to the original size. The other half are directly processed by ResBlock. The final output of MResBlock is obtained by concatenating resulting features of two branches. MResBlock enjoys two main advantages. Firstly, it improves performance by realizing multi-scale representation learning for degradations of different sizes and enhances spectral learning for different frequencies [40]. Secondly, it improves efficiency by reducing feature resolution."
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+                                    "content": "The main goal of this study is to develop an efficient network for image restoration by focusing on the more important regions. This aim is achieved by the proposed DSM, which amplifies the response of informative information in two domains (see Figure 2). As illustrated in the bottom part of Figure 3, it consists of two components: spatial selection module (SSM) and frequency selection module (FSM). Given input features "
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+                                        287,
+                                        483
+                                    ],
+                                    "type": "text",
+                                    "content": ", SSM and FSM are employed successively, which can be expressed as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {F} = \\operatorname {F S M} (\\operatorname {S S M} (F)). \\tag {1}",
+                                    "image_path": "aaa342fa5436b9592edb18d4a7567da188547ffdba61ef219328b09a97e68921.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Next, we introduce these two elements in details."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Spatial Selection Module (SSM). SSM helps the network focus on important regions in the spatial domain, providing initial locations of severe degradations for subsequent FSM. Our SSM has three branches. The main path is built upon the CBAM [53] to produce the general feature representation for locations of degradations to focus. Specifically, given an intermediate feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        526,
+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        526,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we first squeeze "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        526,
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+                                        658
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        526,
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+                                    ],
+                                    "type": "text",
+                                    "content": " along channel dimension through two types of pooling techniques, i.e., max pooling and average pooling, and then generate the general feature map via a convolution layer, which is formally expressed as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "F ^ {\\prime} = \\operatorname {C o n v} _ {3} ([ \\operatorname {A v g P o o l} (F), \\operatorname {M a x P o o l} (F) ]), \\tag {2}",
+                                    "image_path": "2773e69dcfc289bf90bb07e6181963fab4c554fe8840887fc30a4adae3fb0805.jpg"
+                                }
+                            ]
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+                    ],
+                    "index": 8
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
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+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\cdot, \\cdot]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates concatenation; AvgPool, MaxPool and Conv3 represent average pooling, max pooling, and con"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "volution layer of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "3 \\times 3"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " kernel size. By doing this, "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F' \\in \\mathbb{R}^{H \\times W \\times 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "text",
+                                    "content": " contains degradation locations to focus [53]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
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+                                        156
+                                    ],
+                                    "type": "text",
+                                    "content": "Since each channel differs in degradation patterns, we further generate channel-wise representation by performing the channel-separated transformation for the input feature "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
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+                                    ],
+                                    "type": "text",
+                                    "content": " via depth-wise convolutions, and then modulate resulting features with "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F'"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        96,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This process is expressed as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "type": "interline_equation",
+                                    "content": "F _ {s} = \\mathrm {D C o n v s} _ {5, 7} (F) \\otimes \\mathrm {T} \\left(F ^ {\\prime}, C\\right) + \\mathrm {D C o n v} _ {3} (F), \\tag {3}",
+                                    "image_path": "44b254935ade72a1af8a111ce0a548a35cecf1b80656c9c27b3330537196f66e.jpg"
+                                }
+                            ]
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+                    ],
+                    "index": 12
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{DConv}_{5,7}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes cascaded depth-wise convolution layers of kernel sizes "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "5\\times 5"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "7\\times 7"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "; "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{DConv}_3"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " represents depth-wise convolution with "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "3\\times 3"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " kernel; "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\otimes"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates an element-wise multiplication; and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{T}(F',C)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " is the tile function that copies "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F'"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " for "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
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+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " times along the channel dimension to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{H\\times W\\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then feed the spatially selected features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{s}\\in \\mathbb{R}^{H\\times W\\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        180,
+                                        545,
+                                        263
+                                    ],
+                                    "type": "text",
+                                    "content": " to FSM for frequency selection."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Frequency Selection Module (FSM). We can directly utilize "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        264,
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+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        264,
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+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " to assist the recovery process. Motivated by the fact that degraded/sharp image pairs have similar low-frequency components, while differing at high frequencies, we further emphasize regions that contain the real difference between input/sharp image pairs by removing lowest frequency via the proposed FSM. To this end, we first apply the mean filter to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        264,
+                                        545,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        264,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to generate low-frequency features, and then obtain the complementary high-frequency features by subtracting the resulting low-frequency signals from the input, which is expressed by:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        376,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "F _ {s} ^ {h} = F _ {s} - \\operatorname {M e a n} \\left(F _ {s}\\right). \\tag {4}",
+                                    "image_path": "9bfc5524f3ac012e1f3dd05643f21cd1743ae45897519d8df871abd2b412186b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "In our case, the mean filter is implemented by the channelwise global average pooling. The final output of FSM/DSM is generated using the element-wise multiplication between "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        420,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{s}^{h}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        420,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{s}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        420,
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+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": ", and residual connection, which is expressed as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {F} = F _ {s} ^ {h} \\otimes F _ {s} + F _ {s}. \\tag {5}",
+                                    "image_path": "4b2effa2792916f2d88a2ccfcf409952bb33c7856dde315d72fa3f13a70aa6d7.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "After DSM, the important regions are emphasized, e.g., edge signals in Figure 2 for defocus deblurring."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.4. Loss Function"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
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+                                    "content": " loss functions following [13, 15]. For each output/target image pair with the same resolution, loss functions are given by:"
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+                                    "content": "\\mathcal {L} _ {s} = \\frac {1}{P} \\| \\hat {I} - G \\| _ {1} \\tag {6}",
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+                                    "content": " represents fast Fourier transform; and "
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+                                    "content": "We evaluate FocalNet on 10 datasets for three image restoration tasks, including image dehazing, image desnowing, and single-image defocus deblurring. We provide experimental results for image motion deblurring and image denoising in the supplementary material."
+                                }
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+                                    "type": "text",
+                                    "content": "We measure the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity index (SSIM) [52] between predicted results and ground-truth images for all datasets. Mean Absolute Error (MAE) and Learned Perceptual Image Patch Similarity (LPIPS) [67] are additionally adopted for defocus deblurring. FLOPs are measured on "
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+                                    "content": "256 \\times 256"
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+                                    "type": "text",
+                                    "content": " patch. In tables, the best performance is marked in bold."
+                                }
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+                                    "type": "text",
+                                    "content": "Image Dehazing. We train and evaluate our models on both synthetic and real-world datasets for image dehazing. Following [21, 59], we train separate models on the RESIDE-Indoor and RESIDE-Outdoor datasets [27], and evaluate the resulting models on the corresponding test sets of RESIDE, i.e., SOTS-Indoor and SOTS-Outdoor, respectively. In addition, we adopt three real-world datasets, i.e., Dense-Haze [2], NH-HAZE [3], and O-HAZE [4], to verify the robustness of our model in more challenging real-world scenarios. Apart from the above daytime dehazing datasets, we also demonstrate the effectiveness of FocalNet on the nighttime dataset NHR [65]."
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+                                    "type": "text",
+                                    "content": "Image Defocus Deblurring. Consistent with previous algorithms [25, 44, 61], we use the DPDD [1] dataset that consists of 350 scenes for training, 74 scenes for validation, and 100 scenes for validation with a 1:1 ratio."
+                                }
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+                                    "type": "text",
+                                    "content": "tion, and 76 scenes for testing. Each scene comprises four images, labeled as center view, left view, right view, and all-in-focus ground-truth images. FocalNet is trained by taking the center view image as input and calculating loss values between the predicted clean image and ground truth."
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+                                    "content": "Image Desnowing. For the desnowing problem, we train and evaluate our models on three commonly used datasets, i.e., SRRS [9], CSD [10], and Snow100K [37]. Dataset selection and testing methods are consistent with the recent algorithm [9] for a fair and convincing comparison."
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+                                    "content": "4.2. Implementation Details"
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+                                    "content": "Unless stated otherwise, the following hyper-parameters are adopted. Depending on the task complexity, we scale the model by varying the number of residual blocks in all ResBlock, i.e., 16 for deblurring and 4 for dehazing/desnowing. In our FocalNet, we only deploy MResBlock in the first scale of encoder/decoder. Convolution parameters are not shared between two branches of MResBlock. The models are trained using Adam [23] with initial learning rate as "
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+                                    "type": "text",
+                                    "content": ", which is gradually reduced to "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " with cosine annealing [38]. For data augmentation, we adopt random horizontal flips with a probability of 0.5. Models are trained on 32 samples of size "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "256 \\times 256"
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+                                    "type": "text",
+                                    "content": " for each iteration. More details of training configuration for each specific dataset are provided in the supplementary material."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">SOTS-Indoor [27]</td><td colspan=\"2\">SOTS-Outdoor [27]</td><td colspan=\"2\">Dense-Haze [2]</td><td colspan=\"2\">NH-HAZE [3]</td><td colspan=\"2\">O-HAZE [4]</td><td rowspan=\"2\">Params (M)</td><td rowspan=\"2\">FLOPs (G)</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DehazeNet [6]</td><td>19.82</td><td>0.821</td><td>24.75</td><td>0.927</td><td>13.84</td><td>0.43</td><td>16.62</td><td>0.52</td><td>17.57</td><td>0.77</td><td>0.009</td><td>0.581</td></tr><tr><td>AOD-Net [26]</td><td>20.51</td><td>0.816</td><td>24.14</td><td>0.920</td><td>13.14</td><td>0.41</td><td>15.40</td><td>0.57</td><td>15.03</td><td>0.54</td><td>0.002</td><td>0.115</td></tr><tr><td>GridDehazeNet [36]</td><td>32.16</td><td>0.984</td><td>30.86</td><td>0.982</td><td>-</td><td>-</td><td>13.80</td><td>0.54</td><td>-</td><td>-</td><td>0.956</td><td>21.49</td></tr><tr><td>MSBDN [17]</td><td>33.67</td><td>0.985</td><td>33.48</td><td>0.982</td><td>15.37</td><td>0.49</td><td>19.23</td><td>0.71</td><td>24.36</td><td>0.75</td><td>31.35</td><td>41.54</td></tr><tr><td>FFA-Net [41]</td><td>36.39</td><td>0.989</td><td>33.57</td><td>0.984</td><td>14.39</td><td>0.45</td><td>19.87</td><td>0.69</td><td>22.12</td><td>0.77</td><td>4.456</td><td>287.8</td></tr><tr><td>AECR-Net [54]</td><td>37.17</td><td>0.990</td><td>-</td><td>-</td><td>15.80</td><td>0.47</td><td>19.88</td><td>0.72</td><td>-</td><td>-</td><td>2.611</td><td>52.20</td></tr><tr><td>DeHamer [21]</td><td>36.63</td><td>0.988</td><td>35.18</td><td>0.986</td><td>16.62</td><td>0.56</td><td>20.66</td><td>0.68</td><td>-</td><td>-</td><td>132.45</td><td>48.93</td></tr><tr><td>PMNet[59]</td><td>38.41</td><td>0.990</td><td>34.74</td><td>0.985</td><td>16.79</td><td>0.51</td><td>20.42</td><td>0.73</td><td>24.64</td><td>0.83</td><td>18.90</td><td>81.13</td></tr><tr><td>FocalNet (Ours)</td><td>40.82</td><td>0.996</td><td>37.71</td><td>0.995</td><td>17.07</td><td>0.63</td><td>20.43</td><td>0.79</td><td>25.50</td><td>0.94</td><td>3.74</td><td>30.63</td></tr></table>",
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+                                            "content": "Table 1. Image dehazing results on both synthetic dataset [27] and real-world datasets [2, 3, 4]."
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+                                    "content": "Table 2. Nighttime image dehazing results on NHR [65] dataset."
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+                                    "content": "thetic [27] and real-world [2, 3, 4] datasets in Table 1. Overall, our method receives better performance on all datasets than other state-of-the-art algorithms. Specifically, on the daytime synthetic dataset SOTS-Indoor [27], our method outperforms PMNet [59] by 2.41 dB PSNR with only "
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+                                    "content": " FLOPs. Furthermore, our model yields a significant performance gain of 2.53 dB in terms of PSNR over Transformer model DeHamer [21] on SOTS-Outdoor [27] with "
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+                                    "content": "In addition, our method is well generalized to the more challenging real-world scenarios and obtains the best performance on most metrics. Particularly on the O-HAZE [4] dataset, FocalNet yields considerable gain of 0.86 dB PSNR and 0.11 SSIM over PMNet [59]."
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+                                    "content": "Apart from daytime dehazing datasets, we also evaluate the effectiveness of our model on the nighttime dehazing dataset NHR [65]. As shown in Table 2, FocalNet signifi"
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+                                            "content": "Figure 6. Nighttime dehazing comparisons on NHR [65] dataset."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">CSD [10]</td><td colspan=\"2\">SRRS [9]</td><td colspan=\"2\">Snow100K [37]</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>DesnowNet [37]</td><td>20.13</td><td>0.81</td><td>20.38</td><td>0.84</td><td>30.50</td><td>0.94</td></tr><tr><td>CycleGAN [19]</td><td>20.98</td><td>0.80</td><td>20.21</td><td>0.74</td><td>26.81</td><td>0.89</td></tr><tr><td>All in One [30]</td><td>26.31</td><td>0.87</td><td>24.98</td><td>0.88</td><td>26.07</td><td>0.88</td></tr><tr><td>JSTASR [9]</td><td>27.96</td><td>0.88</td><td>25.82</td><td>0.89</td><td>23.12</td><td>0.86</td></tr><tr><td>HDCW-Net [10]</td><td>29.06</td><td>0.91</td><td>27.78</td><td>0.92</td><td>31.54</td><td>0.95</td></tr><tr><td>TransWeather [50]</td><td>31.76</td><td>0.93</td><td>28.29</td><td>0.92</td><td>31.82</td><td>0.93</td></tr><tr><td>NAFNet [8]</td><td>33.13</td><td>0.96</td><td>29.72</td><td>0.94</td><td>32.41</td><td>0.95</td></tr><tr><td>FocalNet (Ours)</td><td>37.18</td><td>0.99</td><td>31.34</td><td>0.98</td><td>33.53</td><td>0.95</td></tr></table>",
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Indoor Scenes</td><td colspan=\"4\">Outdoor Scenes</td><td colspan=\"4\">Combined</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>MAE↓</td><td>LPIPS↓</td></tr><tr><td>DPDNet [1]</td><td>26.54</td><td>0.816</td><td>0.031</td><td>0.239</td><td>22.25</td><td>0.682</td><td>0.056</td><td>0.313</td><td>24.34</td><td>0.747</td><td>0.044</td><td>0.277</td></tr><tr><td>KPAC [47]</td><td>27.97</td><td>0.852</td><td>0.026</td><td>0.182</td><td>22.62</td><td>0.701</td><td>0.053</td><td>0.269</td><td>25.22</td><td>0.774</td><td>0.040</td><td>0.227</td></tr><tr><td>DeepRFT [39]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.71</td><td>0.801</td><td>0.039</td><td>0.218</td></tr><tr><td>IFAN [25]</td><td>28.11</td><td>0.861</td><td>0.026</td><td>0.179</td><td>22.76</td><td>0.720</td><td>0.052</td><td>0.254</td><td>25.37</td><td>0.789</td><td>0.039</td><td>0.217</td></tr><tr><td>DRBNet [44]</td><td></td><td>-</td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>25.73</td><td>0.791</td><td>-</td><td>0.183</td></tr><tr><td>Restormer [61]</td><td>28.87</td><td>0.882</td><td>0.025</td><td>0.145</td><td>23.24</td><td>0.743</td><td>0.050</td><td>0.209</td><td>25.98</td><td>0.811</td><td>0.038</td><td>0.178</td></tr><tr><td>FocalNet (Ours)</td><td>29.10</td><td>0.876</td><td>0.024</td><td>0.173</td><td>23.41</td><td>0.743</td><td>0.049</td><td>0.246</td><td>26.18</td><td>0.808</td><td>0.037</td><td>0.210</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "in Figure 4 and Figure 6, respectively. Our method is more effective in removing haze blurs in both daytime (indoor and outdoor) and nighttime scenes than other algorithms, such as blurs on the doors in top two images of Figure 4."
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+                                    "content": "Quantitative Comparisons. The numerical results on three desnowing datasets, i.e., SRRS [9], CSD [10], and Snow100K [37], are reported in Table 3. As can be seen, our model shows strong ability on snow removal by consistently achieving better or comparable PSNR/SSIM scores on all metrics. Compared to NAFNet [8], FocalNet obtains significant performance gains of "
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+                                    "content": " PSNR on the SRRS [9] and lately proposed CSD [10] datasets, respectively. In addition, our model yields much higher scores than TransWeather [50] with "
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+                                    "type": "text",
+                                    "content": " parameters."
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+                                    "content": "Visual Comparisons. The visual results are shown in Figure 5. Images produced by our model are of high quality without artifacts and visually closer to ground-truth images."
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+                                    "content": "Quantitative Comparisons. The quantitative comparisons on the DPDD [1] dataset are provided in Table 4. Our method performs favorably against state-of-the-art algorithms. Specifically, FocalNet obtains significant gains over the CNN-based approaches on the combined category, i.e., "
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+                                    "content": " over DRBNet [44] and "
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+                                    "content": " over DeepRFT [39]. In addition, compared to Transformer model Restormer [61], our method still obtains a performance improvement of "
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+                                    "content": " PSNR with only half parameters."
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+                                    "content": "Visual Comparisons. Figure 7 illustrates visual results. Compared to other approaches, our model recovers more fine details, such as patterns on pages."
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+                                    "content": "We conduct ablation studies to demonstrate the effectiveness of our modules by training the tiny model on RESIDE-Indoor [27] and testing on SOTS-Indoor [27]. The number of residual block is set to 1 in all ResBlock. The model is"
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+                                            "content": "Table 5. Ablation studies for different components of FocalNet on the SOTS-Indoor [27] dataset."
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+                                            "html": "<table><tr><td></td><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a)</td><td>Simple Gate [8]</td><td>32.23</td><td>13.81</td><td>1.47</td></tr><tr><td>(b)</td><td>Supervised Attention [62]</td><td>32.29</td><td>14.98</td><td>1.76</td></tr><tr><td>(c)</td><td>CBAM [53]</td><td>32.71</td><td>13.77</td><td>1.46</td></tr><tr><td>(d)</td><td>SSM</td><td>33.71</td><td>13.82</td><td>1.47</td></tr><tr><td>(e)</td><td>CBAM [53]+FSM</td><td>33.23</td><td>13.77</td><td>1.46</td></tr><tr><td>(f)</td><td>SSM+FSM</td><td>35.60</td><td>13.82</td><td>1.47</td></tr></table>",
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+                                    "content": "trained for only 300 epochs with the initial learning rate as "
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+                                    "type": "text",
+                                    "content": " and batch size as 4. Other settings are identical with that of our final dehazing model. The baseline network is obtained by substituting ResBlock for MResBlock and removing DSM from the tiny model. More ablation studies are provided in the supplementary material."
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+                                    "type": "text",
+                                    "content": "Effects of Individual Components. As shown in Table 5a, the baseline receives 31.33 dB PSNR. SSM (Table 5b) and FSM (Table 5c) yield accuracy gains of 2.18 dB and 1.11 dB over the baseline, respectively. Equipped with DSM, the model (Table 5d) receives further performance boost by 4.23 dB over the baseline. By replacing ResBlock with MResBlock in the first scale, models consistently receive higher scores than those without MResBlock. Specifically, our choice (Table 5g) outperforms the counterpart (Table 5d) by 0.04 dB with lower computation overhead."
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+                                    "content": "In addition, the visual results of our DSM are illustrated in Figure 2 (defocus deblurring) and Figure 8 (dehazing). As shown in Figure 2, SSM helps the model focus more on the severe degradation regions, e.g., metal fence. FSM further highlights the edge signals by removing low-frequency information. For dehazing, the hard regions that are difficult to recover are emphasized by our DSM (see Figure 8). More examples are available in the supplementary material."
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+                                    "content": "Comparisons with Alternatives to SSM. We further demonstrate superiority of our SSM by replacing it with three popular attention mechanisms. As represented in Table 6, the simple gate [8] and supervised attention [62] lead to performance degradation from 33.71 to "
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+                                    "content": ", respectively. Compared to CBAM [53], which includes both spatial and channel attention, our SSM"
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+                                            "content": "Figure 8. Visual results of DSM for dehazing. From left to right: hazy images obtained from SOTS-Indoor [27], ground-truth images, input and output features of DSM. The complicated regions worthy of more attention are highlighted by our DSM."
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+                                            "html": "<table><tr><td>Method</td><td>PSNR</td><td>FLOPs/G</td><td>Params/M</td></tr><tr><td>(a) FocalNet w/o MResBlock</td><td>40.69</td><td>33.96</td><td>3.76</td></tr><tr><td>(b) FocalNet</td><td>40.82</td><td>30.63</td><td>3.74</td></tr><tr><td>(c) FocalNet-S</td><td>40.32</td><td>17.33</td><td>2.27</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "(Table 6d) receives 1 dB performance gain with comparable computation overhead. The similar conclusion can also be drawn by comparing models of Table 6e and Table 6f, where FSM is additionally used. It is worth mentioning that our FSM boosts the performance when cooperating with CBAM (see Table 6c and Table 6e), demonstrating the efficacy and generalization ability of our design."
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+                                    "content": "Order of FSM and SSM. When we swap the order in which FSM and SSM are used, the performance drops from 35.60 dB (Table 5g) to 35.17 dB PSNR. This phenomenon verifies the efficacy of our design, where we first apply SSM to attend to general degradation regions and then leverage FSM to emphasize the more important parts, such as edge signal in Figure 2 and hard regions in Figure 8."
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+                                    "content": "Design Choices for MResBlock. We study the effect of the multi-scale mechanism in our final dehazing model. The training settings are identical with FocalNet in Table 1. As represented in Table 7, MResBlock leads to performance gain of "
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+                                    "content": " PSNR with high efficiency. We further explore the potential of MResBlock by using it in all scales of encoder/decoder to form FocalNet-S (Figure 7c). This version degrades the performance by "
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+                                    "content": " compared to FocalNet, which is probably because the disadvantage of losing spatial information caused by reducing size of low-resolution features outweighs the advantage of multi-scale learning. It is worth mentioning that FocalNet-S still achieves "
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+                                    "type": "text",
+                                    "content": " PSNR with much lower computation overhead compared to other algorithms (see Figure 1)."
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+                                    "content": "In this study, we present a focal network for image restoration, dubbed FocalNet, which is effective and computationally efficient. The core idea of our work is to focus on the important regions for reconstruction. To this end, we propose two modules: SSM and FSM. SSM is built on spatial attention to detect the degradation regions for subsequent frequency selection. FSM further emphasizes the edge signals or regions that are difficult to recover. By deploying two modules successively, the network is capable of paying more attention to regions that really matter to reconstruction. In addition, we insert the multi-scale mechanism into the network by reducing resolution of half the channels of input feature. This design not only improves performance but also reduces complexity. Experiments on 10 datasets demonstrate that our model achieves state-of-the-art performance for several image restoration tasks."
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+                                    "type": "text",
+                                    "content": "Acknowledgement"
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+                                    "content": "This work was supported by the National Natural Science Foundation of China (No. 62025604, U1803264) and Shenzhen Science and Technology Program (No. 20220016)."
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diff --git a/2023/FocalFormer3D_ Focusing on Hard Instance for 3D Object Detection/9285b2b7-cbfa-4b94-8361-0cc2abdf86b2_content_list.json b/2023/FocalFormer3D_ Focusing on Hard Instance for 3D Object Detection/9285b2b7-cbfa-4b94-8361-0cc2abdf86b2_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..a2fbcf73809e41fa2d66c9738ae567393c47e97b
--- /dev/null
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+        "text": "False negatives (FN) in 3D object detection, e.g., missing predictions of pedestrians, vehicles, or other obstacles, can lead to potentially dangerous situations in autonomous driving. While being fatal, this issue is understudied in many current 3D detection methods. In this work, we propose Hard Instance Probing (HIP), a general pipeline that identifies FN in a multi-stage manner and guides the models to focus on excavating difficult instances. For 3D object detection, we instantiate this method as FocalFormer3D, a simple yet effective detector that excels at excavating difficult objects and improving prediction recall. FocalFormer3D features a multi-stage query generation to discover hard objects and a box-level transformer decoder to efficiently distinguish objects from massive object candidates. Experimental results on the nuScenes and Waymo datasets validate the superior performance of FocalFormer3D. The advantage leads to strong performance on both detection and tracking, in both Li-DAR and multi-modal settings. Notably, FocalFormer3D achieves a 70.5 mAP and 73.9 NDS on nuScenes detection benchmark, while the nuScenes tracking benchmark shows 72.1 AMOTA, both ranking 1st place on the nuScenes LiDAR leaderboard. Our code is available at https://github.com/NVlabs/FocalFormer3D.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "3D object detection is an important yet challenging perception task. Recent state-of-the-art 3D object detectors mainly rely on bird's eye view (BEV) representation [1-3], where features from multiple sensors are aggregated to construct a unified representation in the ego-vehicle coordinate space. There is a rich yet growing literature on BEV-based 3D detection, including multi-modal fusion [4-10], second-stage refinements (surface point pooling [3], RoIPool [11-14], and cross attention modules [4, 15]).",
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+        "img_path": "images/d2d0aa8da817f0ab4dee248828d84936bae251bc55f687decfab6554315893f7.jpg",
+        "image_caption": [
+            "Figure 1. Visual example for Hard Instance Probing (HIP). By utilizing this multi-stage prediction approach, our model can progressively focus on hard instances and facilitate its ability to gradually detect them. At each stage, the model generates some Positive object candidates (represented by green circles). Object candidates assigned to the ground-truth objects can be classified as either True Positives (TP, represented by green boxes) and False Negatives (FN, represented by red boxes) during training. We explicitly model the unmatched ground-truth objects as the hard instances, which become the main targets for the subsequent stage. Conversely, Positives are considered easy samples (represented by gray boxes) and will be ignored in subsequent stages at both training and inference time. At last, all heatmap predictions across stages are collected as the initial object candidates. We ignored the False Positives for better visualizations."
+        ],
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+        "type": "text",
+        "text": "Despite the tremendous efforts, there has been limited exploration to explicitly address false negatives or missed",
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Work done during an internship at NVIDIA.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author.",
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+    },
+    {
+        "type": "page_number",
+        "text": "8394",
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+    {
+        "type": "text",
+        "text": "objects often caused by occlusions and clutter background. False negatives are particularly concerning in autonomous driving as they cause missing information in the prediction and planning stacks. When an object or a part of an object is not detected, this can result in the autonomous vehicle being unaware of potential obstacles such as pedestrians, cyclists, or other vehicles. This is especially hazardous when the vehicle is moving at high speeds and can lead to potentially dangerous situations. Therefore, reducing false negatives is crucial to ensure the safety of autonomous driving.",
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+    {
+        "type": "text",
+        "text": "To address the challenge of False Negatives in 3D detection, we propose and formulate a pipeline called Hard Instance Probing (HIP). Motivated by cascade-style decoder head for object detection [16-18], we propose a pipeline to probe false negative samples progressively, which significantly improves the recall rate Fig. 1 illustrates the pipeline in a cascade manner. In each stage, HIP suppresses the true positive candidates and focuses on the false negative candidates from the previous stages. By iterating the HIP stage, our approach can save those hard false negatives.",
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+    {
+        "type": "text",
+        "text": "Based on HIP, we introduce a 3D object detector, FocalFormer3D, as shown in Fig. 2. Especially, multi-stage heatmap predictions [3, 19] are employed to excavate difficult instances. We maintain a class-aware Accumulated Positive Mask, indicating positive regions from prior stages. Through this masking design, the model omits the training of easy positive candidates and thereby focuses on the hard instances (False Negatives). Finally, our decoder collects the positive predictions from all stages to produce the object candidates. FocalFormer3D consistently demonstrates considerable gains over baselines in terms of average recall.",
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+    {
+        "type": "text",
+        "text": "In addition, we also introduce a box-level refinement step to eliminate redundant object candidates. The approach employs a deformable transformer decoder [17] and represents the candidates as box-level queries using RoIAlign. This allows for box-level query interaction and iterative box refinements, binding the object queries with sufficient box context through RoIAlign [20, 21] on the bird's eye view to perform relative bounding box refinements. Finally, a rescoring strategy is adopted to select positive objects from object candidates. Our ablation study in Table 6 demonstrates the effectiveness of the local refinement approach in processing adequate object candidates.",
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+    {
+        "type": "text",
+        "text": "Our contributions can be summarized as follows:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- We propose Hard Instance Probing (HIP), a learnable scheme to automatically identify False Negatives in a multi-stage manner.",
+            "- We present FocalFormer3D for 3D object detection that effectively harvests hard instances on the BEV and demonstrates effectiveness in terms of average recall.",
+            "- Without bells and whistles, our model achieves state-of-the-art detection performance on both LiDAR-"
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "based and multi-modal settings. Notably, our model ranks 1st places on both nuScenes 3D LiDAR detection and tracking leaderboard at time of submission.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Modern 3D object detectors, either LiDAR-based [1-3, 12, 13, 22-29], or Camera-based [30-37], or MultiModal [4-8, 38-45] 3D object detectors generally rely on BEV view representation [46]. These methods adopt dense feature maps or dense anchors, for conducting object prediction in a bird's eye view (BEV) space. Among these methods, VoxelNet [22] as the pioneer works discretize point clouds into voxel representation and applies dense convolution to generate BEV heatmaps. SECOND [22] accelerates VoxelNet with 3D sparse convolution [47] to extract 3D features. Some Pillar-based detectors [2, 23, 48, 49] collapse the height dimension and utilize 2D CNNs for efficient 3D detection.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Different from dense detectors, point-based 3D detectors [11, 50-52] directly process point clouds via PointNet [53, 54] and perform grouping or predictions on the sparse representations. Concerning involvement of neighborhood query on point clouds, it becomes time-consuming and unaffordable for large-scale point clouds. Concerning computation and spatial cost, another line of 3D detectors directly predicts objects on sparse point clouds to avoid dense feature construction. SST [55] applies sparse regional attention and avoids downsampling for small-object detection. FSD [56] instead further recognize instances directly on sparse representations obtained by SST [55] and SparseConv for long-range detection.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recent multi-modal detectors [5-7, 39, 42, 57] follow the similar paradigm of BEV detectors and incorporate the multi-view image features by physical projection or learnable alignments between LiDAR and cameras. TransFusion [4] applies cross attention to obtain image features for each object query. Despite various kinds of modal-specific voxel feature encoders, these detectors finally produce dense BEV features for classification and regression at the heatmap level.",
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+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We introduce Hard Instance Probing (HIP) for automated identifying hard instances (False Negatives) in Section 3.1. We then present the implementations for the two main components of FocalFormer3D. Section 3.2 describes our multi-stage heatmap encoder that harvests the False Negatives for producing high-recall initial object candidates following HIP. Section 3.3 introduces a box-level deformable decoder network that further distinguishes objects from these candidates.",
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+    {
+        "type": "page_number",
+        "text": "8395",
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+    {
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+        "img_path": "images/129b55a2e0254c60a0526382d34d4b91f20b7d944a2e74902591f49a9f574163.jpg",
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+    {
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+        "img_path": "images/ed51815c9498c7b1fe93be0a0b0c646a79f09eb6a1d176c426a9ca2aef16f376.jpg",
+        "image_caption": [
+            "Figure 2. Overall architecture of FocalFormer3D. The overall framework comprises two novel components: a multi-stage heatmap encoder network that uses the Hard Instance Probing (HIP) strategy to produce high-recall object queries (candidates), and a deformable transformer decoder network with rescoring mechanism that is responsible for eliminating false positives from the large set of candidates. (a) Following feature extraction from modalities, the map-view features produce a set of multi-stage BEV features and then BEV heatmaps. The positive mask accumulates to exclude the easy positive candidates of prior stages from BEV heatmaps. The left object candidates are chosen and collected according to the response of BEV heatmap in a multi-stage process. (b) A deformable transformer decoder is adapted to effectively handle diverse object queries. The query embedding is enhanced with a box pooling module, which leverages the intermediate object supervision to identify local regions. It refines object queries in a local-scope manner, rather than at a point level. Residual connections and normalization layers have been excluded from the figure for clarity."
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/00748ca20f40ece5a022d2c2b3f43f1c8e521cf1984a11b1e661e1ee3fcc3c65.jpg",
+        "image_caption": [
+            "Figure 3. Hard Instance Probing. We use the symbol “G” to indicate the object candidates that are labeled as ground-truth objects during the target assignment process in training. To ensure clarity, we omit numerous negative predictions for detection, given that background takes up most of the images."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "3.1. Hard Instance Probing (HIP)",
+        "text_level": 1,
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Real-world applications, such as autonomous driving, require a high level of scene understanding to ensure safe and secure operation. In particular, false negatives in object detection can present severe risks, emphasizing the need for high recall rates. However, accurately identifying objects in complex scenes or when occlusion occurs is challenging in",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3D object detection, resulting in many false negative predictions. Unfortunately, few studies have explicitly focused on addressing false negatives in the design of detection heads. Motivated by the cascade-style detectors, we formulate a training pipeline to emulate the process of identifying false negative predictions at inference time.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "**Formulation of Hard Instance Probing.** Our strategy to identify hard instances operates stage by stage, as illustrated by a toy example in Fig. 3. Initially, we annotate the groundtruth objects as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {O} = \\left\\{o _ {i}, i = 1, 2, \\dots \\right\\},\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "which is the main targets for initial stages. The neural network makes Positive or Negative predictions given a set of initial object candidates  $\\mathcal{A} = \\{a_i, i = 1,2,\\ldots\\}$ , which is not limited to anchors [58], point-based anchors [3], and object queries [59]. Suppose the detected objects (Positive predictions) at  $k$ -th stage are",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {P} _ {k} = \\left\\{p _ {i}, i = 1, 2, \\dots \\right\\}.\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "We are then allowed to classify the ground-truth objects according to their assigned candidates:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {O} _ {k} ^ {T P} = \\left\\{o _ {j} \\mid \\exists p _ {i} \\in \\mathcal {P} _ {k}, \\sigma \\left(p _ {i}, o _ {j}\\right) > \\eta \\right\\}.\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where an object matching metric  $\\sigma (\\cdot ,\\cdot)$  (e.g. Intersection over Union [60, 61] and center distance [62]) and a predefined threshold  $\\eta$ . Thus, the left unmatched targets can be",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "8396",
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+    {
+        "type": "text",
+        "text": "regarded as hard instances:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {O} _ {k} ^ {F N} = O - \\bigcup_ {i = 1} ^ {k} O _ {k} ^ {T P}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The training of  $(k + 1)$ -th stages is to detect these targets  $\\mathcal{O}_k^{FN}$  from the object candidates while omitting all prior Positive object candidates.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Despite the cascade way mimicking the process of identifying false negative samples, we might collect a number of object candidates across all stages. Thus, a second-stage object-level refinement model is necessary to eliminate any potential false positives.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Relation with hard example mining. The most relevant topic close to our approach is hard example mining [63, 64], which samples hard examples during training. Recent research [65-67] has further explored soft-sampling, such as adjusting the loss distribution to mitigate foreground-background imbalance issues. In contrast, our method operates in stages. Specifically, we use False Negative predictions from prior stages to guide the subsequent stage of the model toward learning from these challenging objects.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.2. Multi-stage Heatmap Encoder",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The upcoming subsections outline the key implementations of FocalFormer3D as depicted in Fig. 2. We begin by detailing the implementation of hard instance probing for BEV detection. This involves using the BEV center heatmap to generate the initial object candidate in a cascade manner.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Preliminary of center heatmap in BEV perception. In common practice [3, 4, 19], the objective of the BEV heatmap head is to produce heatmap peaks at the center locations of detected objects. The BEV heatmaps are represented by a tensor  $S \\in \\mathbb{R}^{X \\times Y \\times C}$ , where  $X \\times Y$  indicates the size of BEV feature map and  $C$  is the number of object categories. The target is achieved by producing 2D Gaussians near the BEV object points, which are obtained by projecting 3D box centers onto the map view. In top views such as Fig. 4, objects are more sparsely distributed than in a 2D image. Moreover, it is assumed that objects do not have intra-class overlaps on the bird's eye view.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Based on the non-overlapping assumption, excluding prior easy positive candidates from BEV heatmap predictions can be achieved easily. In the following, we illustrate the implementation details of HIP, which utilizes an accumulated positive mask.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Positive mask accumulation. To keep track of all easy positive object candidates of prior stages, we generate a positive mask (PM) on the BEV space for each stage and accumulated them to an accumulated positive mask (APM):",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {M} _ {k} \\in \\{0, 1 \\} ^ {X \\times Y \\times C},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3a2e0f590240435df66d42982a0e5e3df1124ece67835a647559808e53d5bff7.jpg",
+        "image_caption": [
+            "Figure 4. Example visualization for the positive mask. (left) and predicted BEV heatmap (right). The positive mask is class-aware and we show different categories with different colors for visualization. The masking area for objects of different categories can differ in the pooling-based masking method."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4c759323f500f8343fa83557cdcfe03a00a7937fd01da3e3349a8edbe2cf87b9.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "which is initialized as all zeros.",
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+    },
+    {
+        "type": "text",
+        "text": "The generation of multi-stage BEV features is accomplished in a cascade manner using a lightweight inversed residual block [68] between stages. Multi-stage BEV heatmaps are generated by adding an extra convolution layer. At each stage, we generate the positive mask according to the positive predictions. To emulate the process of identifying False Negatives, we use a test-time selection strategy that ranks the scores according to BEV heatmap response [3, 4]. Specifically, at the  $k$ -th stage, Top-K selection is performed on the BEV heatmap across all BEV positions and categories, producing a set of object predictions  $\\mathcal{P}_k$ . Then the positive mask  $M_{k}\\in \\{0,1\\}^{X\\times Y\\times C}$  records the all the positions of positive predictions by setting  $M_{(x,y,c)} = 1$  for each predicted object  $p_i\\in \\mathcal{P}_k$ , where  $(x,y)$  represents  $p_i$ 's location and  $c$  is  $p_i$ 's class. The left points are set to 0 by default.",
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+    {
+        "type": "text",
+        "text": "According to the non-overlapping assumption, the ideal way to indicate the existence of a positive object candidate (represented as a point in the center heatmap) on the mask is by masking the box if there is a matched ground truth box. However, since the ground-truth boxes are not available at inference time, we propose the following masking methods during training:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Point Masking. This method involves no change, where only the center point of the positive candidates is filled.",
+            "- Pooling-based Masking. In this method, smaller objects fill in the center points while larger objects fill in with a kernel size of  $3 \\times 3$ .",
+            "- Box Masking. This method requires an additional box prediction branch and involves filling the internal region of the predicted BEV box."
+        ],
+        "bbox": [
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+            720,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The accumulated positive mask (APM) for the  $k$ -th stage",
+        "bbox": [
+            519,
+            885,
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+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "8397",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "is obtained by simply accumulating prior Positive Masks as follows:",
+        "bbox": [
+            75,
+            90,
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+            119
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat{M}_{k} = \\max_{1\\leq i\\leq k}M_{i}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            214,
+            119,
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+            143
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "By masking the BEV heatmap  $S_{k}$  with",
+        "bbox": [
+            76,
+            148,
+            334,
+            164
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {S} _ {k} = S _ {k} \\cdot (1 - \\hat {M} _ {k}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
+            172,
+            344,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "we omit prior easy positive regions in the current stage, thus enabling the model to focus on the false negative samples of the prior stage (hard instances). To train the multi-stage heatmap encoder, we adopt Gaussian Focal Loss [4] as the training loss function. We sum up the BEV heatmap losses across stages to obtain the final heatmap loss.",
+        "bbox": [
+            75,
+            203,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During both training and inference, we collect the positive candidates from all stages as the object candidates for the second-stage rescoring as the potential false positive predictions.",
+        "bbox": [
+            75,
+            292,
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+            354
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Discussion on implementation validity for HIP. Although the HIP strategy is simple, the masking way has two critical criteria that need to be met to ensure valid implementation of HIP:",
+        "bbox": [
+            75,
+            357,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Exclusion of prior positive object candidates at the current stage.",
+            "- Avoidance of removal of potential real objects (false negatives)."
+        ],
+        "bbox": [
+            94,
+            426,
+            468,
+            496
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Point masking satisfies both requirements based on the following facts. As the Top-K selection is based on ranking predicted BEV heatmap scores, the hottest response points are automatically excluded when a point is masked. Besides, the design of a class-aware positive mask ensures that non-overlapping assumptions at the intra-class level on the BEV are met.",
+        "bbox": [
+            75,
+            505,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However, the point masking strategy is less efficient as only one BEV object candidate is excluded for each positive prediction compared with the ideal masking with ground-truth box guidance. Therefore, there is a trade-off between the masking area and the validity of the exclusion operation. We compare all three strategies in Table 5 and pooling-based masking performs better than others.",
+        "bbox": [
+            75,
+            611,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Box-level Deformable Decoder",
+        "text_level": 1,
+        "bbox": [
+            76,
+            726,
+            346,
+            739
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The object candidates obtained from the multi-stage heatmap encoder can be treated as positional object queries [4, 69]. The recall of initial candidates improves with an increase in the number of collected candidates. However, redundant candidates introduce false positives, thereby necessitating a high level of performance for the following object-level refinement blocks.",
+        "bbox": [
+            75,
+            750,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To enhance the efficiency of object query processing, we employ deformable attention [17] instead of computationally intensive modules such as cross attention [59] or box",
+        "bbox": [
+            75,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "attention [70]. Unlike previous methods that used center point features as the query embedding [4, 69], we model the object candidates as box-level queries. Specifically, Specifically, we introduce object supervision between deformable decoder layers, facilitating relative box prediction.",
+        "bbox": [
+            496,
+            90,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Box-pooling module. To better model the relations between objects and local regions in the regular grid manner, we extract the box context information from the BEV features using simple RoIAlign [20] in the Box-pooling module as Fig. 2. In specific, given the intermediate predicted box, each object query extracts  $7 \\times 7$  feature grid points [20] from the BEV map followed by two MLP layers. The positional encoding is also applied both for queries and all BEV points for extracting positional information. This allows us to update both the content and positional information into the query embedding. This lightweight module enhances the query feature for the deformable decoder (See Table 6).",
+        "bbox": [
+            496,
+            170,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Decoder implementation. Following Deformable DETR [17], our model employs 8 heads in all attention modules, including multi-head attention and multi-head deformable attention. The deformable attention utilizes 4 sampling points across 3 scales. To generate three scales of BEV features, we apply  $2 \\times$  and  $4 \\times$  downsampling operations to the original BEV features. The box-pooling module extracts  $7 \\times 7$  feature grid points within each rotated BEV box followed by 2 FC layers and adds the object feature to query embedding. We expand the predicted box to  $1.2 \\times$  size of its original size.",
+        "bbox": [
+            496,
+            356,
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+            523
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Model Training",
+        "text_level": 1,
+        "bbox": [
+            500,
+            534,
+            656,
+            550
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The model is trained in two stages. In the first stage, we train the LiDAR backbone using a deformable transformer decoder head, which we refer to as DeformFormer3D (Table 4 (a)). After initializing the weights from DeformFormer3D, we train the FocalFormer3D detector, which consists of a multi-stage heatmap encoder and a box-level deformable decoder. However, during the training of the deformable decoder with bipartite graph matching, we encounter slow convergence issues in the early stages [18]. To address this, we generate noisy queries from ground-truth objects [18, 77, 78], enabling effective training of the model from scratch. Additionally, we improve the training process by excluding matching pairs with a center distance between the prediction and its GT object exceeding 7 meters.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            786,
+            632,
+            803
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
+            811,
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+            828
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset and metric. We evaluate our approach on nuScenes and Waymo 3D detection dataset.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "nuScenes Dataset [62] is a large-scale outdoor dataset. nuScenes contains 1,000 scenes of multi-modal data, in",
+        "bbox": [
+            500,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "8398",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/173da81ef3b2fd5760f002ebdb3c8285dea836afccbf28ddd2c92304ad023192.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Modality</td><td>mAP</td><td>NDS</td><td>Car</td><td>Truck</td><td>C.V.</td><td>Bus</td><td>Trailer</td><td>Barrier</td><td>Motor.</td><td>Bike</td><td>Ped.</td><td>T.C.</td></tr><tr><td colspan=\"14\">LiDAR-based 3D Detection</td></tr><tr><td>PointPillars [2]</td><td>L</td><td>30.5</td><td>45.3</td><td>68.4</td><td>23.0</td><td>4.1</td><td>28.2</td><td>23.4</td><td>38.9</td><td>27.4</td><td>1.1</td><td>59.7</td><td>30.8</td></tr><tr><td>CBGS [71]</td><td>L</td><td>52.8</td><td>63.3</td><td>81.1</td><td>48.5</td><td>10.5</td><td>54.9</td><td>42.9</td><td>65.7</td><td>51.5</td><td>22.3</td><td>80.1</td><td>70.9</td></tr><tr><td>LargeKernel3D [28]</td><td>L</td><td>65.3</td><td>70.5</td><td>85.9</td><td>55.3</td><td>26.8</td><td>66.2</td><td>60.2</td><td>74.3</td><td>72.5</td><td>46.6</td><td>85.6</td><td>80.0</td></tr><tr><td>TransFusion-L [4]</td><td>L</td><td>65.5</td><td>70.2</td><td>86.2</td><td>56.7</td><td>28.2</td><td>66.3</td><td>58.8</td><td>78.2</td><td>68.3</td><td>44.2</td><td>86.1</td><td>82.0</td></tr><tr><td>PillarNet-34 [48]</td><td>L</td><td>66.0</td><td>71.4</td><td>87.6</td><td>57.5</td><td>27.9</td><td>63.6</td><td>63.1</td><td>77.2</td><td>70.1</td><td>42.3</td><td>87.3</td><td>83.3</td></tr><tr><td>LiDARMultiNet [72]</td><td>L</td><td>67.0</td><td>71.6</td><td>86.9</td><td>57.4</td><td>31.5</td><td>64.7</td><td>61.0</td><td>73.5</td><td>75.3</td><td>47.6</td><td>87.2</td><td>85.1</td></tr><tr><td>FocalFormer3D</td><td>L</td><td>68.7</td><td>72.6</td><td>87.2</td><td>57.1</td><td>34.4</td><td>69.6</td><td>64.9</td><td>77.8</td><td>76.2</td><td>49.6</td><td>88.2</td><td>82.3</td></tr><tr><td>CenterPoint [3]†</td><td>L</td><td>60.3</td><td>67.3</td><td>85.2</td><td>53.5</td><td>20.0</td><td>63.6</td><td>56.0</td><td>71.1</td><td>59.5</td><td>30.7</td><td>84.6</td><td>78.4</td></tr><tr><td>MGTANet†[73]</td><td>L</td><td>67.5</td><td>72.7</td><td>88.5</td><td>59.8</td><td>30.6</td><td>67.2</td><td>61.5</td><td>66.3</td><td>75.8</td><td>52.5</td><td>87.3</td><td>85.5</td></tr><tr><td>LargeKernel3D‡[28]</td><td>L</td><td>68.8</td><td>72.8</td><td>87.3</td><td>59.1</td><td>30.2</td><td>68.5</td><td>65.6</td><td>75.0</td><td>77.8</td><td>53.5</td><td>88.3</td><td>82.4</td></tr><tr><td>FocalFormer3D†</td><td>L</td><td>70.5</td><td>73.9</td><td>87.8</td><td>59.4</td><td>37.8</td><td>73.0</td><td>65.7</td><td>77.8</td><td>77.4</td><td>52.4</td><td>90.0</td><td>83.4</td></tr><tr><td colspan=\"14\">Multi-Modal 3D Detection</td></tr><tr><td>PointPainting [74]</td><td>L+C</td><td>46.4</td><td>58.1</td><td>77.9</td><td>35.8</td><td>15.8</td><td>36.2</td><td>37.3</td><td>60.2</td><td>41.5</td><td>24.1</td><td>73.3</td><td>62.4</td></tr><tr><td>3D-CVF [75]</td><td>L+C</td><td>52.7</td><td>62.3</td><td>83.0</td><td>45.0</td><td>15.9</td><td>48.8</td><td>49.6</td><td>65.9</td><td>51.2</td><td>30.4</td><td>74.2</td><td>62.9</td></tr><tr><td>MVP [41]</td><td>L+C</td><td>66.4</td><td>70.5</td><td>86.8</td><td>58.5</td><td>26.1</td><td>67.4</td><td>57.3</td><td>74.8</td><td>70.0</td><td>49.3</td><td>89.1</td><td>85.0</td></tr><tr><td>FusionPainting [76]</td><td>L+C</td><td>68.1</td><td>71.6</td><td>87.1</td><td>60.8</td><td>30.0</td><td>68.5</td><td>61.7</td><td>71.8</td><td>74.7</td><td>53.5</td><td>88.3</td><td>85.0</td></tr><tr><td>TransFusion [4]</td><td>L+C</td><td>68.9</td><td>71.7</td><td>87.1</td><td>60.0</td><td>33.1</td><td>68.3</td><td>60.8</td><td>78.1</td><td>73.6</td><td>52.9</td><td>88.4</td><td>86.7</td></tr><tr><td>BEVFusion [5]</td><td>L+C</td><td>69.2</td><td>71.8</td><td>88.1</td><td>60.9</td><td>34.4</td><td>69.3</td><td>62.1</td><td>78.2</td><td>72.2</td><td>52.2</td><td>89.2</td><td>85.2</td></tr><tr><td>BEVFusion-MIT [6]</td><td>L+C</td><td>70.2</td><td>72.9</td><td>88.6</td><td>60.1</td><td>39.3</td><td>69.8</td><td>63.8</td><td>80.0</td><td>74.1</td><td>51.0</td><td>89.2</td><td>86.5</td></tr><tr><td>DeepInteraction [10]</td><td>L+C</td><td>70.8</td><td>73.4</td><td>87.9</td><td>60.2</td><td>37.5</td><td>70.8</td><td>63.8</td><td>80.4</td><td>75.4</td><td>54.5</td><td>91.7</td><td>87.2</td></tr><tr><td>FocalFormer3D</td><td>L+C</td><td>71.6</td><td>73.9</td><td>88.5</td><td>61.4</td><td>35.9</td><td>71.7</td><td>66.4</td><td>79.3</td><td>80.3</td><td>57.1</td><td>89.7</td><td>85.3</td></tr><tr><td>PointAugmenting [57]†</td><td>L+C</td><td>66.8</td><td>71.0</td><td>87.5</td><td>57.3</td><td>28.0</td><td>65.2</td><td>60.7</td><td>72.6</td><td>74.3</td><td>50.9</td><td>87.9</td><td>83.6</td></tr><tr><td>Focals Conv-F [27]‡</td><td>L+C</td><td>70.1</td><td>73.6</td><td>87.5</td><td>60.0</td><td>32.6</td><td>69.9</td><td>64.0</td><td>71.8</td><td>81.1</td><td>59.2</td><td>89.0</td><td>85.5</td></tr><tr><td>LargeKernel3D-F [28]‡</td><td>L+C</td><td>71.1</td><td>74.2</td><td>88.1</td><td>60.3</td><td>34.3</td><td>69.1</td><td>66.5</td><td>75.5</td><td>82.0</td><td>60.3</td><td>89.6</td><td>85.7</td></tr><tr><td>FocalFormer3D-F†</td><td>L+C</td><td>72.9</td><td>75.0</td><td>88.8</td><td>63.5</td><td>39.0</td><td>73.7</td><td>66.9</td><td>79.2</td><td>81.0</td><td>58.1</td><td>91.1</td><td>87.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Performance comparison on the nuScenes 3D detection test set. † represents using flipping test-time augmentation. ‡ means using both flipping and rotation test-time augmentation. C.V, Motor., Ped. and T.C. are short for construction vehicle, motorcycle, pedestrian, and traffic cones, respectively.",
+        "bbox": [
+            75,
+            513,
+            892,
+            555
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "cluding 32-beams LiDAR with 20FPS and 6-view camera images. We mainly evaluate our method on both LiDAR-only and LiDAR-Camera fusion settings. The evaluation metrics follow nuScenes official metrics including mean average precision (mAP) and nuScenes detection score (NDS) defined by averaging the matching thresholds of center distance  $\\mathbb{D} = \\{0.5,1.,2.,4.\\}$  (m). For evaluating the quality of object queries, we also introduce the Average Recall (AR) defined by center distance as well. The ablation studies in our research primarily utilize the nuScenes dataset, unless explicitly stated otherwise.",
+        "bbox": [
+            75,
+            580,
+            468,
+            747
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Waymo Open Dataset [61] has a wider detection range of  $150m \\times 150m$  compared to the nuScenes dataset. Waymo dataset comprises of 798 scenes for training and 202 scenes for validation. The official evaluation metrics used are mean Average Precision (mAP) and mean Average Precision with Heading (mAPH), where the mAP is weighted by the heading accuracy. The mAP and mAPH scores are computed with a 3D Intersection over Union (IoU) threshold of 0.7 for Vehicle and 0.5 for Pedestrian and Cyclist. The evaluation has two difficulty levels: Level 1, for boxes with more",
+        "bbox": [
+            75,
+            750,
+            470,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "than five LiDAR points, and Level 2, for boxes with at least one LiDAR point. Of the two difficulty levels, Level 2 is prioritized as the primary evaluation metric for all experiments.",
+        "bbox": [
+            496,
+            580,
+            890,
+            641
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. Our implementation is mainly based on the open-sourced codebase MMDetection3D [79]. For the LiDAR backbone, we use CenterPoint-Voxel as the point cloud feature extractor. For the multi-stage heatmap encoder, we apply 3 stages, generating a total of 600 queries by default. Data augmentation includes random double flipping along both  $X$  and  $Y$  axes, random global rotation between  $[- \\pi /4, \\pi /4]$ , the random scale of [0.9, 1.1], and random translation with a standard deviation of 0.5 in all axes. All models are trained with a batch size of 16 on eight V100 GPUs. More implementation details are referred to in supplementary files.",
+        "bbox": [
+            496,
+            647,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Main Results",
+        "text_level": 1,
+        "bbox": [
+            500,
+            844,
+            638,
+            859
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "nuScenes LiDAR-based 3D object detection. We evaluate the performance of FocalFormer3D on the nuScenes",
+        "bbox": [
+            500,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "8399",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "test set. As shown in Table 1, the results demonstrate its superiority over state-of-the-art methods on various evaluation metrics and settings. Our single-model FocalFormer3D achieved  $68.7\\mathrm{mAP}$  and 72.6 NDS, which surpasses the prior TransFusion-L method by  $+3.2$  points on mAP and  $+2.4$  points on NDS. Notably, even compared with the previous best method that was trained with segmentation-level labels, our method without extra supervision still outperformed LiDARMultiNet by  $+1.7\\mathrm{mAP}$  and  $+1.0$  NDS.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "nuScenes multi-modal 3D object detection. We extend our approach to a simple multi-modal variant and demonstrate its generality. Following TransFusion [4], we use a pre-trained ResNet-50 model on COCO [80] and nuImage [62] dataset as the image model and freeze its weights during training. To reduce computation costs, the input images are downscaled to  $1/2$  of their original size. Unlike heavy lift-splat-shot [32] camera encoders used in BEVFusion [5, 6], the multi-view camera images are projected onto a pre-defined voxel space and fused with LiDAR BEV feature. Additional details are available in the supplementary files. Without test-time augmentation, our simple multi-modal variant model outperforms all other state-of-the-art with less inference time (Table 2). With TTA, FocalFormer3D achieves  $72.9\\mathrm{mAP}$  and 75.0 NDS, ranking first among all single-model solutions on the nuScenes benchmark. Interestingly, our model achieves high results for some rare classes such as (Trailer, Motorcycle, Bicycle) compared to other methods.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "nuScenes 3D object tracking. To further demonstrate the versatility, we also extend FocalFormer3D to 3D multi-object tracking (MOT) by using the tracking-by-detection algorithm SimpleTrack. Interested readers can refer to the original paper [81] for more comprehensive details. As depicted in Table 2, FocalFormer3D gets 2.9 points better than prior state-of-the-art TransFusion-L [4] in LiDAR settings and FocalFormer3D-F achieves 2.1 points over TransFusion in terms of AMOTA. Moreover, our single model FocalFormer3D-F with double-flip testing results performs even better than the BEVFusion [6] with model ensembling.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Waymo LiDAR 3D object detection. The results of our single-frame LiDAR 3D detection method on the Waymo dataset are presented in Table 3, alongside the comparison with other approaches. Employing with the same VoxelNet backbone as nuScenes, our method achieves competitive performance without any fine-tuning of the model hyperparameters specifically for the Waymo dataset. Particularly, when compared to TransFusion-L with the same backbone, our method exhibits a  $+1.1$  mAPH improvement.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Recall Analysis",
+        "text_level": 1,
+        "bbox": [
+            76,
+            847,
+            232,
+            863
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To diagnose the performance improvements, we compare several recent methods in terms of AR for both stages",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/34b3e03bfd2ef0094f9e01108fbb3e2213798554d417117f1c49decd055252b3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>AMOTA</td><td>AMOTP</td><td>MOTA</td><td>IDS</td></tr><tr><td colspan=\"5\">LiDAR-based 3D Tracking</td></tr><tr><td>AB3DMOT [82]</td><td>15.1</td><td>150.1</td><td>15.4</td><td>9027</td></tr><tr><td>CenterPoint [3]</td><td>63.8</td><td>55.5</td><td>53.7</td><td>760</td></tr><tr><td>CBMOT [83]</td><td>64.9</td><td>59.2</td><td>54.5</td><td>557</td></tr><tr><td>OGR3MOT [84]</td><td>65.6</td><td>62.0</td><td>55.4</td><td>288</td></tr><tr><td>SimpleTrack [81]</td><td>66.8</td><td>55.0</td><td>56.6</td><td>575</td></tr><tr><td>UVTR-L [7]</td><td>67.0</td><td>55.0</td><td>56.6</td><td>774</td></tr><tr><td>TransFusion-L [4]</td><td>68.6</td><td>52.9</td><td>57.1</td><td>893</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>54.9</td><td>60.1</td><td>888</td></tr><tr><td>FocalFormer3D†</td><td>72.1</td><td>47.0</td><td>60.0</td><td>701</td></tr><tr><td colspan=\"5\">Multi-Modal 3D Tracking</td></tr><tr><td>UVTR-MultiModal [7]</td><td>70.1</td><td>68.6</td><td>61.8</td><td>941</td></tr><tr><td>TransFusion [4]</td><td>71.8</td><td>55.1</td><td>60.7</td><td>944</td></tr><tr><td>BEVFusion-MIT [6]‡</td><td>74.1</td><td>40.3</td><td>60.3</td><td>506</td></tr><tr><td>FocalFormer3D-F</td><td>73.9</td><td>51.4</td><td>61.8</td><td>824</td></tr><tr><td>FocalFormer3D-F†</td><td>74.6</td><td>47.3</td><td>63.0</td><td>849</td></tr></table>",
+        "bbox": [
+            504,
+            89,
+            893,
+            361
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/eeb09471e9271ed5a4d1be32c3a495812e140053e0461d42f19932ca1a18bf2f.jpg",
+        "table_caption": [
+            "Table 2. Performance comparison on nuScenes 3D tracking test set.  ${}^{ \\dagger  }$  is based on the double-flip testing results in Table 1.  ${}^{ \\ddagger  }$  is based on model ensembling."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>mAP</td><td>mAPH</td><td>Vel.</td><td>Ped.</td><td>Cyc.</td></tr><tr><td colspan=\"6\">LiDAR-based 3D Detection</td></tr><tr><td>RSN* [85]</td><td>-</td><td>-</td><td>65.5</td><td>63.7</td><td>-</td></tr><tr><td>AFDetV2* [86]</td><td>71.0</td><td>68.8</td><td>69.2</td><td>67.0</td><td>70.1</td></tr><tr><td>SST* [55]</td><td>67.8</td><td>64.6</td><td>65.1</td><td>61.7</td><td>66.9</td></tr><tr><td>PV-RCNN* [24]</td><td>66.8</td><td>63.3</td><td>68.4</td><td>65.8</td><td>68.5</td></tr><tr><td>PV-RCNN++* [25]</td><td>71.7</td><td>69.5</td><td>70.2</td><td>68.0</td><td>70.2</td></tr><tr><td>PillarNet-34* [48]</td><td>71.0</td><td>68.8</td><td>70.5</td><td>66.2</td><td>68.7</td></tr><tr><td>FSD-spconv* [56]</td><td>71.9</td><td>69.7</td><td>68.5</td><td>68.0</td><td>72.5</td></tr><tr><td>CenterPoint [3]</td><td>69.8</td><td>67.6</td><td>73.4</td><td>65.8</td><td>68.5</td></tr><tr><td>TransFusion-L^ [4]</td><td>70.5</td><td>67.9</td><td>66.8</td><td>66.1</td><td>70.9</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>69.0</td><td>67.6</td><td>66.8</td><td>72.6</td></tr></table>",
+        "bbox": [
+            503,
+            422,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Performance comparison on the Waymo val set. All models inputs single-frame point clouds. The methods marked with * indicate the utilization of different point cloud backbones in VoxelNet. The method marked with ^ indicates our reproduction. The evaluation metric used is the LEVEL 2 difficulty, and the results are reported on the full Waymo validation set.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "- initial BEV heatmap predictions and final box predictions in Fig. 5. The metric of AR is computed based on center distance following the nuScenes metrics and different distance thresholds (e.g.,  $0.5m$ ,  $1.0m$ ,  $2.0m$ ,  $4.0m$ ), and the mean AR (mAR) are compared.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Recall comparison on initial object candidates. Figure 5 compares the recall of state-of-the-art methods that share the same SparseUNet backbone. With total 200 queries, FocalFormer3D-200P reaches  $75.2\\mathrm{mAR}$ , achieving considerable and consistent improvements by +4.5",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "8400",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/40f1845444fbc2dd5d26d2ad15dbedf98b1112166cc2d417fba4d8c1ca1f574e.jpg",
+        "image_caption": [
+            "Figure 5. Average recall comparisons between initial object predictions and final object prediction centers on the nuScenes val set. The subfigures are shown over center distance thresholds (\\%) following nuScenes detection metrics."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            85,
+            326,
+            200
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/7dbd0851e135aade0bb92271ec19f5fc76798938175e20cc83cd5554f368c9d8.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            87,
+            606,
+            200
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b55dddbb3e32f95e44371b53d7b21da2baecb41ea3d64aeac189b61e98f6d575.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            606,
+            88,
+            888,
+            200
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/9b74916b88dfa57c6b03a15da828dc14889a1961042dd331c5e755d20186a938.jpg",
+        "image_caption": [
+            "Figure 6. Class-wise recall comparison on nuScenes val set between TransFusion-L and FocalFormer3D in terms of recall values across nuScenes center distance (CD) threshes  $(0.25 / 0.5 / 1.0\\mathrm{m})$  on the nuScenes val set. The red bars are normalized to  $100\\%$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            89,
+            266,
+            460,
+            441
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "mAR compared with the prior state-of-the-art LiDAR approach TransFusion-L. Surprisingly, our LiDAR-based FocalFormer even achieves better results than the prior multimodal approach DeepInteraction by 2.6 points in terms of mAR as well. As the query sizes get 600, FocalFormer3D achieves  $79.2\\mathrm{mAR}$ , surpassing the fusion approach DeepInteraction by 6.6 points. Further, by incorporating multi-view camera features, our multi-modal version FocalFormer-F gets improved to  $80.9\\mathrm{mAR}$ .",
+        "bbox": [
+            75,
+            537,
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+            674
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Recall comparison on final object prediction. Concerning the final predictions of 3D detectors, most LiDAR and fusion approaches obtain fewer performance improvements as the distance thresholds increase as shown in Fig. 5. This can be explained by higher distance thresholds indicating the performance for the extreme cases of missing detections. The introduction of camera features helps the model see the context in the perspective view, which leads to better performance such as DeepInteraction. However, their final prediction recall falls far behind FocalFormer-F with a large margin of 6.8 points.",
+        "bbox": [
+            75,
+            681,
+            468,
+            848
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Class-wise recall comparison. We compare the class-wise recall analysis for object candidates in Fig. 6 at the category level. The findings highlight the effectiveness of",
+        "bbox": [
+            75,
+            854,
+            470,
+            901
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/248316580a0c10eb144e8082128a13b325ab2f014b7912c2a2a187d4f3e50207.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>#</td><td># Stages</td><td>#Total Queries</td><td>mAP</td><td>NDS</td></tr><tr><td>(a)</td><td>1</td><td>200</td><td>65.3</td><td>70.5</td></tr><tr><td>(b)</td><td>2</td><td>200</td><td>66.0</td><td>70.7</td></tr><tr><td>(c)</td><td>1</td><td>600</td><td>65.4</td><td>70.5</td></tr><tr><td>(d)</td><td>2</td><td>600</td><td>66.4</td><td>70.9</td></tr><tr><td>(e)</td><td>3</td><td>600</td><td>66.5</td><td>71.1</td></tr></table>",
+        "bbox": [
+            527,
+            265,
+            867,
+            372
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/70dd994958418acfa797f725b92cecfc98a12106057a98c3ab0ae6e9aa21681c.jpg",
+        "table_caption": [
+            "Table 4. Effects of numbers of stages and total queries. Here one stage stands for the baseline method without using hard instance probing."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Mask Type</td><td>mAP</td><td>NDS</td></tr><tr><td>None</td><td>65.3</td><td>70.4</td></tr><tr><td>Point-based</td><td>65.9</td><td>70.5</td></tr><tr><td>Box-based</td><td>66.1</td><td>70.9</td></tr><tr><td>Pooling-based</td><td>66.5</td><td>71.1</td></tr></table>",
+        "bbox": [
+            584,
+            436,
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+            536
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5. Effects of various positive mask types. All models adopt the same network except for the masking way.",
+        "bbox": [
+            498,
+            545,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "FocalFormer3D in improving the relative recall of initial BEV queries by a relative  $+10.9\\%$  improvement against TransFusion-L. Large objects such as Construction Vehicles and Trailer get the most improvements so that the predictions of their initial centers are challenging.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
+            681,
+            653,
+            698
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "HIP query sizes and generation stages. Table 4 ablates the impacts of the number of queries and stages in the multi-stage heatmap encoder. When using the same query size of rough 200, approaches (b), which uses additional one stage of HIP, demonstrates better performance than baseline (a) by a margin of  $+0.7$  mAP. When provided with more queries (600), our approach (d) and (e) achieve over 1.1-point improvement in terms of mAP.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Positive mask type. Table 5 presents an ablation study on the effectiveness of Hard Instance Probing in terms of various mask types. Specifically, we compare the performance of our method with none masking, point-based masking,",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8401",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/3956d9d606488283fc39d6a2ce87d4b21f6329f81cd0bd0582c329227cd19e4a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">#</td><td rowspan=\"2\">M.S. Heat</td><td colspan=\"2\">Refinement Module</td><td rowspan=\"2\">mAP</td><td rowspan=\"2\">NDS</td></tr><tr><td>BoxPool</td><td>C.A.</td></tr><tr><td>(a)</td><td>X</td><td>X</td><td>X</td><td>63.1</td><td>69.1</td></tr><tr><td>(b)</td><td>✓</td><td>X</td><td>X</td><td>63.3</td><td>69.3</td></tr><tr><td>(c)</td><td>✓</td><td>✓</td><td>X</td><td>65.1</td><td>69.9</td></tr><tr><td>(d)</td><td>✓</td><td>X</td><td>✓</td><td>65.9</td><td>70.9</td></tr><tr><td>(e)</td><td>✓</td><td>✓</td><td>✓</td><td>66.5</td><td>71.1</td></tr><tr><td>(f)</td><td>✓</td><td colspan=\"2\">Rescoring Only</td><td>66.1</td><td>68.8</td></tr></table>",
+        "bbox": [
+            81,
+            89,
+            467,
+            239
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "and pooling-based masking. The results demonstrate that even with single-point masking, HIP improves the performance of the baseline by a gain of  $+0.6$  points in terms of mAP. Furthermore, the pooling-based masking shows the best gain with  $+1.2$  mAP and  $+0.7$  NDS, outperforming the box-based masking. This can be attributed to two facts. Point or pooling-based masking can already effectively exclude positive objects as the center heatmap [3] only highlights a Gaussian peak. Second, the wrong false positive predictions or predicted boxes might lead to false masking of the ground-truth boxes, resulting in missed detection.",
+        "bbox": [
+            75,
+            388,
+            470,
+            555
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Step-by-step module refinement. We conduct ablation studies on the step-by-step improvements by each module, presented in Table 6, to illustrate the component effectiveness within hard instance probing (HIP) pipeline. Initially, without second-stage refinement, we used simple center-based predictions [3] (a), which estimate boxes directly from BEV feature by another convolutional layer.",
+        "bbox": [
+            75,
+            564,
+            468,
+            671
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Despite an improvement in the average recall by over 9 points in Fig. 5, we found little improvement of (b) over (a) in performance after using the multi-stage heatmap encoder to generate the object candidates. By applying simple object-level rescoring (c), with RoI-based refinement (using two hidden MLP layers), the performance is boosted to 65.1 mAP and 69.9 NDS. Remarkably, our complete box-level deformable decoder (e) further improves the performance by a margin of  $+1.4$  mAP and  $+1.2$  NDS.",
+        "bbox": [
+            75,
+            671,
+            470,
+            808
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To assess the effects of rescoring alone, we perform experiment (f), which excludes the effects of box regression by not using any box or position regression in the object-level refinement module. Despite this, experiment (f) still achieves high center accuracy (66.1 mAP) compared to (a). This finding highlights the limitations of the initial rank-",
+        "bbox": [
+            75,
+            810,
+            470,
+            902
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/736f1e6f9d415d5253c932c3bb7371b2e053bc08728e1ab1c2834d8737fc2064.jpg",
+        "table_caption": [
+            "Table 6. Step-by-step improvements made by modules. \"M.S. Heat\" represents the application of the multi-stage heatmap encoder for hard instance probing. \"C.A.\" denotes using deformable cross attention for second-stage refinement. \"BoxPool\" represents the Box-pooling module. The term \"Rescoring Only\" refers to the model that directly generates box prediction from BEV feature and uses its decoder head to rescore the candidate predictions from heatmap without performing additional bounding box refinement."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Models/Components</td><td>Latency</td></tr><tr><td>TransFusion-L</td><td>93ms</td></tr><tr><td>FocalFormer3D</td><td>109ms</td></tr><tr><td>- VoxelNet backbone</td><td>78ms</td></tr><tr><td>- Multi-stage heatmap encoder</td><td>13ms</td></tr><tr><td>- Box-level deformable decoder</td><td>18ms</td></tr></table>",
+        "bbox": [
+            542,
+            88,
+            851,
+            202
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 7. Latency analysis for model components. Latency is measured on a V100 GPU for reference.",
+        "bbox": [
+            498,
+            210,
+            890,
+            239
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ing of object candidates across stages based solely on BEV heatmap scores. Therefore, it validates the necessity for a second-stage object-level rescoring in the hard instance probing pipeline (Fig. 3).",
+        "bbox": [
+            496,
+            267,
+            890,
+            329
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Latency analysis for model components. We conduct a latency analysis for FocalFormer3D on the nuScenes dataset. The runtimes are measured on the same V100 GPU machine for comparison. To ensure a fair speed comparison with CenterPoint [3], dynamic voxelization [87] is employed for speed testing of both TransFusion-L and FocalFormer3D. The computation time is mostly taken up by the sparse convolution-based backbone network (VoxelNet [1, 22]), which takes 78ms. Our multi-stage heatmap encoder takes 13ms to collect queries from the heatmaps across stages, while the box-level deformable decoder head takes 18ms. Note that, the generation of multi-stage heatmaps only takes 5ms, and additional operations such as Top-K selection takes 7ms, indicating potential optimization opportunities for future work.",
+        "bbox": [
+            496,
+            337,
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+            564
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            584,
+            617,
+            599
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this work, we explicitly focus on the fatal problem in autonomous driving, i.e., false negative detections. We present FocalFormer3D as solution. It progressively probes hard instances and improves prediction recall, via the hard instance probing (HIP). Nontrivial improvements are introduced with limited overhead upon transformer-based 3D detectors. The HIP algorithm enables FocalFormer3D to effectively reduce false negatives in 3D object detection.",
+        "bbox": [
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+        "text": "Limitation. A key limitation is that FocalFormer3D's hard instance probing (HIP) relies on the assumption that object centers produce Gaussian-like peaks in the BEV heatmap, which may not hold for camera-based detectors where heatmaps tend to be fan-shaped. Additionally, few studies have explored hard instances in long-range detection, so more research is needed to evaluate HIP in this area. We leave more investigation of hard instance probing as future work.",
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+        "text": "References",
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diff --git a/2023/FocalFormer3D_ Focusing on Hard Instance for 3D Object Detection/9285b2b7-cbfa-4b94-8361-0cc2abdf86b2_model.json b/2023/FocalFormer3D_ Focusing on Hard Instance for 3D Object Detection/9285b2b7-cbfa-4b94-8361-0cc2abdf86b2_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..ba778b41ac60b152c3a19e0e58a219ce5891d434
--- /dev/null
+++ b/2023/FocalFormer3D_ Focusing on Hard Instance for 3D Object Detection/9285b2b7-cbfa-4b94-8361-0cc2abdf86b2_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "FocalFormer3D : Focusing on Hard Instance for 3D Object Detection"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Yilun Chen\\(^{1*}\\) Zhiding Yu\\(^{3\\dagger}\\) Yukang Chen\\(^{1}\\)  \nShiyi Lan\\(^{3}\\) Anima Anandkumar\\(^{2,3}\\) Jiaya Jia\\(^{1}\\) Jose M. Alvarez\\(^{3}\\)  \n\\(^{1}\\)The Chinese University of Hong Kong \\({}^{2}\\)Caltech \\({}^{3}\\)NVIDIA"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
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+            "angle": 0,
+            "content": "Abstract"
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+            "content": "False negatives (FN) in 3D object detection, e.g., missing predictions of pedestrians, vehicles, or other obstacles, can lead to potentially dangerous situations in autonomous driving. While being fatal, this issue is understudied in many current 3D detection methods. In this work, we propose Hard Instance Probing (HIP), a general pipeline that identifies FN in a multi-stage manner and guides the models to focus on excavating difficult instances. For 3D object detection, we instantiate this method as FocalFormer3D, a simple yet effective detector that excels at excavating difficult objects and improving prediction recall. FocalFormer3D features a multi-stage query generation to discover hard objects and a box-level transformer decoder to efficiently distinguish objects from massive object candidates. Experimental results on the nuScenes and Waymo datasets validate the superior performance of FocalFormer3D. The advantage leads to strong performance on both detection and tracking, in both Li-DAR and multi-modal settings. Notably, FocalFormer3D achieves a 70.5 mAP and 73.9 NDS on nuScenes detection benchmark, while the nuScenes tracking benchmark shows 72.1 AMOTA, both ranking 1st place on the nuScenes LiDAR leaderboard. Our code is available at https://github.com/NVlabs/FocalFormer3D."
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+        {
+            "type": "title",
+            "bbox": [
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+            "content": "1. Introduction"
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+            ],
+            "angle": 0,
+            "content": "3D object detection is an important yet challenging perception task. Recent state-of-the-art 3D object detectors mainly rely on bird's eye view (BEV) representation [1-3], where features from multiple sensors are aggregated to construct a unified representation in the ego-vehicle coordinate space. There is a rich yet growing literature on BEV-based 3D detection, including multi-modal fusion [4-10], second-stage refinements (surface point pooling [3], RoIPool [11-14], and cross attention modules [4, 15])."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.267,
+                0.892,
+                0.627
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.639,
+                0.895,
+                0.849
+            ],
+            "angle": 0,
+            "content": "Figure 1. Visual example for Hard Instance Probing (HIP). By utilizing this multi-stage prediction approach, our model can progressively focus on hard instances and facilitate its ability to gradually detect them. At each stage, the model generates some Positive object candidates (represented by green circles). Object candidates assigned to the ground-truth objects can be classified as either True Positives (TP, represented by green boxes) and False Negatives (FN, represented by red boxes) during training. We explicitly model the unmatched ground-truth objects as the hard instances, which become the main targets for the subsequent stage. Conversely, Positives are considered easy samples (represented by gray boxes) and will be ignored in subsequent stages at both training and inference time. At last, all heatmap predictions across stages are collected as the initial object candidates. We ignored the False Positives for better visualizations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Despite the tremendous efforts, there has been limited exploration to explicitly address false negatives or missed"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.095,
+                0.875,
+                0.337,
+                0.888
+            ],
+            "angle": 0,
+            "content": "*Work done during an internship at NVIDIA."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.098,
+                0.888,
+                0.223,
+                0.9
+            ],
+            "angle": 0,
+            "content": "† Corresponding author."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.095,
+                0.871,
+                0.337,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8394"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.242
+            ],
+            "angle": 0,
+            "content": "objects often caused by occlusions and clutter background. False negatives are particularly concerning in autonomous driving as they cause missing information in the prediction and planning stacks. When an object or a part of an object is not detected, this can result in the autonomous vehicle being unaware of potential obstacles such as pedestrians, cyclists, or other vehicles. This is especially hazardous when the vehicle is moving at high speeds and can lead to potentially dangerous situations. Therefore, reducing false negatives is crucial to ensure the safety of autonomous driving."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.243,
+                0.473,
+                0.394
+            ],
+            "angle": 0,
+            "content": "To address the challenge of False Negatives in 3D detection, we propose and formulate a pipeline called Hard Instance Probing (HIP). Motivated by cascade-style decoder head for object detection [16-18], we propose a pipeline to probe false negative samples progressively, which significantly improves the recall rate Fig. 1 illustrates the pipeline in a cascade manner. In each stage, HIP suppresses the true positive candidates and focuses on the false negative candidates from the previous stages. By iterating the HIP stage, our approach can save those hard false negatives."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.394,
+                0.473,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Based on HIP, we introduce a 3D object detector, FocalFormer3D, as shown in Fig. 2. Especially, multi-stage heatmap predictions [3, 19] are employed to excavate difficult instances. We maintain a class-aware Accumulated Positive Mask, indicating positive regions from prior stages. Through this masking design, the model omits the training of easy positive candidates and thereby focuses on the hard instances (False Negatives). Finally, our decoder collects the positive predictions from all stages to produce the object candidates. FocalFormer3D consistently demonstrates considerable gains over baselines in terms of average recall."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.56,
+                0.473,
+                0.741
+            ],
+            "angle": 0,
+            "content": "In addition, we also introduce a box-level refinement step to eliminate redundant object candidates. The approach employs a deformable transformer decoder [17] and represents the candidates as box-level queries using RoIAlign. This allows for box-level query interaction and iterative box refinements, binding the object queries with sufficient box context through RoIAlign [20, 21] on the bird's eye view to perform relative bounding box refinements. Finally, a rescoring strategy is adopted to select positive objects from object candidates. Our ablation study in Table 6 demonstrates the effectiveness of the local refinement approach in processing adequate object candidates."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.741,
+                0.423,
+                0.756
+            ],
+            "angle": 0,
+            "content": "Our contributions can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.763,
+                0.47,
+                0.809
+            ],
+            "angle": 0,
+            "content": "- We propose Hard Instance Probing (HIP), a learnable scheme to automatically identify False Negatives in a multi-stage manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.817,
+                0.47,
+                0.863
+            ],
+            "angle": 0,
+            "content": "- We present FocalFormer3D for 3D object detection that effectively harvests hard instances on the BEV and demonstrates effectiveness in terms of average recall."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.871,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "- Without bells and whistles, our model achieves state-of-the-art detection performance on both LiDAR-"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.763,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.532,
+                0.092,
+                0.892,
+                0.138
+            ],
+            "angle": 0,
+            "content": "based and multi-modal settings. Notably, our model ranks 1st places on both nuScenes 3D LiDAR detection and tracking leaderboard at time of submission."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.157,
+                0.642,
+                0.173
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.184,
+                0.892,
+                0.38
+            ],
+            "angle": 0,
+            "content": "Modern 3D object detectors, either LiDAR-based [1-3, 12, 13, 22-29], or Camera-based [30-37], or MultiModal [4-8, 38-45] 3D object detectors generally rely on BEV view representation [46]. These methods adopt dense feature maps or dense anchors, for conducting object prediction in a bird's eye view (BEV) space. Among these methods, VoxelNet [22] as the pioneer works discretize point clouds into voxel representation and applies dense convolution to generate BEV heatmaps. SECOND [22] accelerates VoxelNet with 3D sparse convolution [47] to extract 3D features. Some Pillar-based detectors [2, 23, 48, 49] collapse the height dimension and utilize 2D CNNs for efficient 3D detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.383,
+                0.892,
+                0.58
+            ],
+            "angle": 0,
+            "content": "Different from dense detectors, point-based 3D detectors [11, 50-52] directly process point clouds via PointNet [53, 54] and perform grouping or predictions on the sparse representations. Concerning involvement of neighborhood query on point clouds, it becomes time-consuming and unaffordable for large-scale point clouds. Concerning computation and spatial cost, another line of 3D detectors directly predicts objects on sparse point clouds to avoid dense feature construction. SST [55] applies sparse regional attention and avoids downsampling for small-object detection. FSD [56] instead further recognize instances directly on sparse representations obtained by SST [55] and SparseConv for long-range detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.581,
+                0.892,
+                0.718
+            ],
+            "angle": 0,
+            "content": "Recent multi-modal detectors [5-7, 39, 42, 57] follow the similar paradigm of BEV detectors and incorporate the multi-view image features by physical projection or learnable alignments between LiDAR and cameras. TransFusion [4] applies cross attention to obtain image features for each object query. Despite various kinds of modal-specific voxel feature encoders, these detectors finally produce dense BEV features for classification and regression at the heatmap level."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.738,
+                0.636,
+                0.755
+            ],
+            "angle": 0,
+            "content": "3. Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We introduce Hard Instance Probing (HIP) for automated identifying hard instances (False Negatives) in Section 3.1. We then present the implementations for the two main components of FocalFormer3D. Section 3.2 describes our multi-stage heatmap encoder that harvests the False Negatives for producing high-recall initial object candidates following HIP. Section 3.3 introduces a box-level deformable decoder network that further distinguishes objects from these candidates."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.958
+            ],
+            "angle": 0,
+            "content": "8395"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.088,
+                0.891,
+                0.254
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.258,
+                0.862,
+                0.297
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.316,
+                0.892,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overall architecture of FocalFormer3D. The overall framework comprises two novel components: a multi-stage heatmap encoder network that uses the Hard Instance Probing (HIP) strategy to produce high-recall object queries (candidates), and a deformable transformer decoder network with rescoring mechanism that is responsible for eliminating false positives from the large set of candidates. (a) Following feature extraction from modalities, the map-view features produce a set of multi-stage BEV features and then BEV heatmaps. The positive mask accumulates to exclude the easy positive candidates of prior stages from BEV heatmaps. The left object candidates are chosen and collected according to the response of BEV heatmap in a multi-stage process. (b) A deformable transformer decoder is adapted to effectively handle diverse object queries. The query embedding is enhanced with a box pooling module, which leverages the intermediate object supervision to identify local regions. It refines object queries in a local-scope manner, rather than at a point level. Residual connections and normalization layers have been excluded from the figure for clarity."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.464,
+                0.445,
+                0.671
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.69,
+                0.47,
+                0.76
+            ],
+            "angle": 0,
+            "content": "Figure 3. Hard Instance Probing. We use the symbol “G” to indicate the object candidates that are labeled as ground-truth objects during the target assignment process in training. To ensure clarity, we omit numerous negative predictions for detection, given that background takes up most of the images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.786,
+                0.339,
+                0.803
+            ],
+            "angle": 0,
+            "content": "3.1. Hard Instance Probing (HIP)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Real-world applications, such as autonomous driving, require a high level of scene understanding to ensure safe and secure operation. In particular, false negatives in object detection can present severe risks, emphasizing the need for high recall rates. However, accurately identifying objects in complex scenes or when occlusion occurs is challenging in"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.466,
+                0.892,
+                0.557
+            ],
+            "angle": 0,
+            "content": "3D object detection, resulting in many false negative predictions. Unfortunately, few studies have explicitly focused on addressing false negatives in the design of detection heads. Motivated by the cascade-style detectors, we formulate a training pipeline to emulate the process of identifying false negative predictions at inference time."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.564,
+                0.892,
+                0.624
+            ],
+            "angle": 0,
+            "content": "**Formulation of Hard Instance Probing.** Our strategy to identify hard instances operates stage by stage, as illustrated by a toy example in Fig. 3. Initially, we annotate the groundtruth objects as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.618,
+                0.635,
+                0.774,
+                0.652
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {O} = \\left\\{o _ {i}, i = 1, 2, \\dots \\right\\},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.661,
+                0.892,
+                0.752
+            ],
+            "angle": 0,
+            "content": "which is the main targets for initial stages. The neural network makes Positive or Negative predictions given a set of initial object candidates \\(\\mathcal{A} = \\{a_i, i = 1,2,\\ldots\\}\\), which is not limited to anchors [58], point-based anchors [3], and object queries [59]. Suppose the detected objects (Positive predictions) at \\(k\\)-th stage are"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.614,
+                0.762,
+                0.776,
+                0.779
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {P} _ {k} = \\left\\{p _ {i}, i = 1, 2, \\dots \\right\\}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.789,
+                0.891,
+                0.819
+            ],
+            "angle": 0,
+            "content": "We are then allowed to classify the ground-truth objects according to their assigned candidates:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.563,
+                0.828,
+                0.828,
+                0.848
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {O} _ {k} ^ {T P} = \\left\\{o _ {j} \\mid \\exists p _ {i} \\in \\mathcal {P} _ {k}, \\sigma \\left(p _ {i}, o _ {j}\\right) > \\eta \\right\\}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where an object matching metric \\(\\sigma (\\cdot ,\\cdot)\\) (e.g. Intersection over Union [60, 61] and center distance [62]) and a predefined threshold \\(\\eta\\). Thus, the left unmatched targets can be"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8396"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.258,
+                0.106
+            ],
+            "angle": 0,
+            "content": "regarded as hard instances:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.194,
+                0.115,
+                0.353,
+                0.157
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {O} _ {k} ^ {F N} = O - \\bigcup_ {i = 1} ^ {k} O _ {k} ^ {T P}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.166,
+                0.47,
+                0.21
+            ],
+            "angle": 0,
+            "content": "The training of \\((k + 1)\\)-th stages is to detect these targets \\(\\mathcal{O}_k^{FN}\\) from the object candidates while omitting all prior Positive object candidates."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.211,
+                0.469,
+                0.287
+            ],
+            "angle": 0,
+            "content": "Despite the cascade way mimicking the process of identifying false negative samples, we might collect a number of object candidates across all stages. Thus, a second-stage object-level refinement model is necessary to eliminate any potential false positives."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.293,
+                0.469,
+                0.43
+            ],
+            "angle": 0,
+            "content": "Relation with hard example mining. The most relevant topic close to our approach is hard example mining [63, 64], which samples hard examples during training. Recent research [65-67] has further explored soft-sampling, such as adjusting the loss distribution to mitigate foreground-background imbalance issues. In contrast, our method operates in stages. Specifically, we use False Negative predictions from prior stages to guide the subsequent stage of the model toward learning from these challenging objects."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.438,
+                0.347,
+                0.455
+            ],
+            "angle": 0,
+            "content": "3.2. Multi-stage Heatmap Encoder"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.461,
+                0.469,
+                0.55
+            ],
+            "angle": 0,
+            "content": "The upcoming subsections outline the key implementations of FocalFormer3D as depicted in Fig. 2. We begin by detailing the implementation of hard instance probing for BEV detection. This involves using the BEV center heatmap to generate the initial object candidate in a cascade manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.555,
+                0.469,
+                0.736
+            ],
+            "angle": 0,
+            "content": "Preliminary of center heatmap in BEV perception. In common practice [3, 4, 19], the objective of the BEV heatmap head is to produce heatmap peaks at the center locations of detected objects. The BEV heatmaps are represented by a tensor \\( S \\in \\mathbb{R}^{X \\times Y \\times C} \\), where \\( X \\times Y \\) indicates the size of BEV feature map and \\( C \\) is the number of object categories. The target is achieved by producing 2D Gaussians near the BEV object points, which are obtained by projecting 3D box centers onto the map view. In top views such as Fig. 4, objects are more sparsely distributed than in a 2D image. Moreover, it is assumed that objects do not have intra-class overlaps on the bird's eye view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.737,
+                0.469,
+                0.812
+            ],
+            "angle": 0,
+            "content": "Based on the non-overlapping assumption, excluding prior easy positive candidates from BEV heatmap predictions can be achieved easily. In the following, we illustrate the implementation details of HIP, which utilizes an accumulated positive mask."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.815,
+                0.469,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Positive mask accumulation. To keep track of all easy positive object candidates of prior stages, we generate a positive mask (PM) on the BEV space for each stage and accumulated them to an accumulated positive mask (APM):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.199,
+                0.882,
+                0.348,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {M} _ {k} \\in \\{0, 1 \\} ^ {X \\times Y \\times C},\n\\]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.09,
+                0.693,
+                0.239
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.696,
+                0.09,
+                0.889,
+                0.239
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.255,
+                0.892,
+                0.326
+            ],
+            "angle": 0,
+            "content": "Figure 4. Example visualization for the positive mask. (left) and predicted BEV heatmap (right). The positive mask is class-aware and we show different categories with different colors for visualization. The masking area for objects of different categories can differ in the pooling-based masking method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.35,
+                0.71,
+                0.363
+            ],
+            "angle": 0,
+            "content": "which is initialized as all zeros."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.365,
+                0.892,
+                0.605
+            ],
+            "angle": 0,
+            "content": "The generation of multi-stage BEV features is accomplished in a cascade manner using a lightweight inversed residual block [68] between stages. Multi-stage BEV heatmaps are generated by adding an extra convolution layer. At each stage, we generate the positive mask according to the positive predictions. To emulate the process of identifying False Negatives, we use a test-time selection strategy that ranks the scores according to BEV heatmap response [3, 4]. Specifically, at the \\(k\\)-th stage, Top-K selection is performed on the BEV heatmap across all BEV positions and categories, producing a set of object predictions \\(\\mathcal{P}_k\\). Then the positive mask \\(M_{k}\\in \\{0,1\\}^{X\\times Y\\times C}\\) records the all the positions of positive predictions by setting \\(M_{(x,y,c)} = 1\\) for each predicted object \\(p_i\\in \\mathcal{P}_k\\), where \\((x,y)\\) represents \\(p_i\\)'s location and \\(c\\) is \\(p_i\\)'s class. The left points are set to 0 by default."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.606,
+                0.892,
+                0.713
+            ],
+            "angle": 0,
+            "content": "According to the non-overlapping assumption, the ideal way to indicate the existence of a positive object candidate (represented as a point in the center heatmap) on the mask is by masking the box if there is a matched ground truth box. However, since the ground-truth boxes are not available at inference time, we propose the following masking methods during training:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.721,
+                0.891,
+                0.765
+            ],
+            "angle": 0,
+            "content": "- Point Masking. This method involves no change, where only the center point of the positive candidates is filled."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.776,
+                0.891,
+                0.82
+            ],
+            "angle": 0,
+            "content": "- Pooling-based Masking. In this method, smaller objects fill in the center points while larger objects fill in with a kernel size of \\(3 \\times 3\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.831,
+                0.891,
+                0.876
+            ],
+            "angle": 0,
+            "content": "- Box Masking. This method requires an additional box prediction branch and involves filling the internal region of the predicted BEV box."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.721,
+                0.891,
+                0.876
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.886,
+                0.891,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The accumulated positive mask (APM) for the \\(k\\)-th stage"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8397"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.12
+            ],
+            "angle": 0,
+            "content": "is obtained by simply accumulating prior Positive Masks as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.215,
+                0.121,
+                0.332,
+                0.144
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat{M}_{k} = \\max_{1\\leq i\\leq k}M_{i}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.15,
+                0.336,
+                0.165
+            ],
+            "angle": 0,
+            "content": "By masking the BEV heatmap \\( S_{k} \\) with"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.201,
+                0.174,
+                0.345,
+                0.192
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {S} _ {k} = S _ {k} \\cdot (1 - \\hat {M} _ {k}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.204,
+                0.469,
+                0.293
+            ],
+            "angle": 0,
+            "content": "we omit prior easy positive regions in the current stage, thus enabling the model to focus on the false negative samples of the prior stage (hard instances). To train the multi-stage heatmap encoder, we adopt Gaussian Focal Loss [4] as the training loss function. We sum up the BEV heatmap losses across stages to obtain the final heatmap loss."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.294,
+                0.469,
+                0.355
+            ],
+            "angle": 0,
+            "content": "During both training and inference, we collect the positive candidates from all stages as the object candidates for the second-stage rescoring as the potential false positive predictions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.358,
+                0.469,
+                0.417
+            ],
+            "angle": 0,
+            "content": "Discussion on implementation validity for HIP. Although the HIP strategy is simple, the masking way has two critical criteria that need to be met to ensure valid implementation of HIP:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.427,
+                0.468,
+                0.457
+            ],
+            "angle": 0,
+            "content": "- Exclusion of prior positive object candidates at the current stage."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.467,
+                0.469,
+                0.497
+            ],
+            "angle": 0,
+            "content": "- Avoidance of removal of potential real objects (false negatives)."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.427,
+                0.469,
+                0.497
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.506,
+                0.469,
+                0.61
+            ],
+            "angle": 0,
+            "content": "Point masking satisfies both requirements based on the following facts. As the Top-K selection is based on ranking predicted BEV heatmap scores, the hottest response points are automatically excluded when a point is masked. Besides, the design of a class-aware positive mask ensures that non-overlapping assumptions at the intra-class level on the BEV are met."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.612,
+                0.469,
+                0.718
+            ],
+            "angle": 0,
+            "content": "However, the point masking strategy is less efficient as only one BEV object candidate is excluded for each positive prediction compared with the ideal masking with ground-truth box guidance. Therefore, there is a trade-off between the masking area and the validity of the exclusion operation. We compare all three strategies in Table 5 and pooling-based masking performs better than others."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.727,
+                0.347,
+                0.741
+            ],
+            "angle": 0,
+            "content": "3.3. Box-level Deformable Decoder"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.469,
+                0.855
+            ],
+            "angle": 0,
+            "content": "The object candidates obtained from the multi-stage heatmap encoder can be treated as positional object queries [4, 69]. The recall of initial candidates improves with an increase in the number of collected candidates. However, redundant candidates introduce false positives, thereby necessitating a high level of performance for the following object-level refinement blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To enhance the efficiency of object query processing, we employ deformable attention [17] instead of computationally intensive modules such as cross attention [59] or box"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "attention [70]. Unlike previous methods that used center point features as the query embedding [4, 69], we model the object candidates as box-level queries. Specifically, Specifically, we introduce object supervision between deformable decoder layers, facilitating relative box prediction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.171,
+                0.892,
+                0.353
+            ],
+            "angle": 0,
+            "content": "Box-pooling module. To better model the relations between objects and local regions in the regular grid manner, we extract the box context information from the BEV features using simple RoIAlign [20] in the Box-pooling module as Fig. 2. In specific, given the intermediate predicted box, each object query extracts \\(7 \\times 7\\) feature grid points [20] from the BEV map followed by two MLP layers. The positional encoding is also applied both for queries and all BEV points for extracting positional information. This allows us to update both the content and positional information into the query embedding. This lightweight module enhances the query feature for the deformable decoder (See Table 6)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.357,
+                0.892,
+                0.524
+            ],
+            "angle": 0,
+            "content": "Decoder implementation. Following Deformable DETR [17], our model employs 8 heads in all attention modules, including multi-head attention and multi-head deformable attention. The deformable attention utilizes 4 sampling points across 3 scales. To generate three scales of BEV features, we apply \\(2 \\times\\) and \\(4 \\times\\) downsampling operations to the original BEV features. The box-pooling module extracts \\(7 \\times 7\\) feature grid points within each rotated BEV box followed by 2 FC layers and adds the object feature to query embedding. We expand the predicted box to \\(1.2 \\times\\) size of its original size."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.535,
+                0.657,
+                0.551
+            ],
+            "angle": 0,
+            "content": "3.4. Model Training"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.559,
+                0.892,
+                0.772
+            ],
+            "angle": 0,
+            "content": "The model is trained in two stages. In the first stage, we train the LiDAR backbone using a deformable transformer decoder head, which we refer to as DeformFormer3D (Table 4 (a)). After initializing the weights from DeformFormer3D, we train the FocalFormer3D detector, which consists of a multi-stage heatmap encoder and a box-level deformable decoder. However, during the training of the deformable decoder with bipartite graph matching, we encounter slow convergence issues in the early stages [18]. To address this, we generate noisy queries from ground-truth objects [18, 77, 78], enabling effective training of the model from scratch. Additionally, we improve the training process by excluding matching pairs with a center distance between the prediction and its GT object exceeding 7 meters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.633,
+                0.804
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.812,
+                0.691,
+                0.829
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Dataset and metric. We evaluate our approach on nuScenes and Waymo 3D detection dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "nuScenes Dataset [62] is a large-scale outdoor dataset. nuScenes contains 1,000 scenes of multi-modal data, in"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8398"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.089,
+                0.892,
+                0.504
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Modality</td><td>mAP</td><td>NDS</td><td>Car</td><td>Truck</td><td>C.V.</td><td>Bus</td><td>Trailer</td><td>Barrier</td><td>Motor.</td><td>Bike</td><td>Ped.</td><td>T.C.</td></tr><tr><td colspan=\"14\">LiDAR-based 3D Detection</td></tr><tr><td>PointPillars [2]</td><td>L</td><td>30.5</td><td>45.3</td><td>68.4</td><td>23.0</td><td>4.1</td><td>28.2</td><td>23.4</td><td>38.9</td><td>27.4</td><td>1.1</td><td>59.7</td><td>30.8</td></tr><tr><td>CBGS [71]</td><td>L</td><td>52.8</td><td>63.3</td><td>81.1</td><td>48.5</td><td>10.5</td><td>54.9</td><td>42.9</td><td>65.7</td><td>51.5</td><td>22.3</td><td>80.1</td><td>70.9</td></tr><tr><td>LargeKernel3D [28]</td><td>L</td><td>65.3</td><td>70.5</td><td>85.9</td><td>55.3</td><td>26.8</td><td>66.2</td><td>60.2</td><td>74.3</td><td>72.5</td><td>46.6</td><td>85.6</td><td>80.0</td></tr><tr><td>TransFusion-L [4]</td><td>L</td><td>65.5</td><td>70.2</td><td>86.2</td><td>56.7</td><td>28.2</td><td>66.3</td><td>58.8</td><td>78.2</td><td>68.3</td><td>44.2</td><td>86.1</td><td>82.0</td></tr><tr><td>PillarNet-34 [48]</td><td>L</td><td>66.0</td><td>71.4</td><td>87.6</td><td>57.5</td><td>27.9</td><td>63.6</td><td>63.1</td><td>77.2</td><td>70.1</td><td>42.3</td><td>87.3</td><td>83.3</td></tr><tr><td>LiDARMultiNet [72]</td><td>L</td><td>67.0</td><td>71.6</td><td>86.9</td><td>57.4</td><td>31.5</td><td>64.7</td><td>61.0</td><td>73.5</td><td>75.3</td><td>47.6</td><td>87.2</td><td>85.1</td></tr><tr><td>FocalFormer3D</td><td>L</td><td>68.7</td><td>72.6</td><td>87.2</td><td>57.1</td><td>34.4</td><td>69.6</td><td>64.9</td><td>77.8</td><td>76.2</td><td>49.6</td><td>88.2</td><td>82.3</td></tr><tr><td>CenterPoint [3]†</td><td>L</td><td>60.3</td><td>67.3</td><td>85.2</td><td>53.5</td><td>20.0</td><td>63.6</td><td>56.0</td><td>71.1</td><td>59.5</td><td>30.7</td><td>84.6</td><td>78.4</td></tr><tr><td>MGTANet†[73]</td><td>L</td><td>67.5</td><td>72.7</td><td>88.5</td><td>59.8</td><td>30.6</td><td>67.2</td><td>61.5</td><td>66.3</td><td>75.8</td><td>52.5</td><td>87.3</td><td>85.5</td></tr><tr><td>LargeKernel3D‡[28]</td><td>L</td><td>68.8</td><td>72.8</td><td>87.3</td><td>59.1</td><td>30.2</td><td>68.5</td><td>65.6</td><td>75.0</td><td>77.8</td><td>53.5</td><td>88.3</td><td>82.4</td></tr><tr><td>FocalFormer3D†</td><td>L</td><td>70.5</td><td>73.9</td><td>87.8</td><td>59.4</td><td>37.8</td><td>73.0</td><td>65.7</td><td>77.8</td><td>77.4</td><td>52.4</td><td>90.0</td><td>83.4</td></tr><tr><td colspan=\"14\">Multi-Modal 3D Detection</td></tr><tr><td>PointPainting [74]</td><td>L+C</td><td>46.4</td><td>58.1</td><td>77.9</td><td>35.8</td><td>15.8</td><td>36.2</td><td>37.3</td><td>60.2</td><td>41.5</td><td>24.1</td><td>73.3</td><td>62.4</td></tr><tr><td>3D-CVF [75]</td><td>L+C</td><td>52.7</td><td>62.3</td><td>83.0</td><td>45.0</td><td>15.9</td><td>48.8</td><td>49.6</td><td>65.9</td><td>51.2</td><td>30.4</td><td>74.2</td><td>62.9</td></tr><tr><td>MVP [41]</td><td>L+C</td><td>66.4</td><td>70.5</td><td>86.8</td><td>58.5</td><td>26.1</td><td>67.4</td><td>57.3</td><td>74.8</td><td>70.0</td><td>49.3</td><td>89.1</td><td>85.0</td></tr><tr><td>FusionPainting [76]</td><td>L+C</td><td>68.1</td><td>71.6</td><td>87.1</td><td>60.8</td><td>30.0</td><td>68.5</td><td>61.7</td><td>71.8</td><td>74.7</td><td>53.5</td><td>88.3</td><td>85.0</td></tr><tr><td>TransFusion [4]</td><td>L+C</td><td>68.9</td><td>71.7</td><td>87.1</td><td>60.0</td><td>33.1</td><td>68.3</td><td>60.8</td><td>78.1</td><td>73.6</td><td>52.9</td><td>88.4</td><td>86.7</td></tr><tr><td>BEVFusion [5]</td><td>L+C</td><td>69.2</td><td>71.8</td><td>88.1</td><td>60.9</td><td>34.4</td><td>69.3</td><td>62.1</td><td>78.2</td><td>72.2</td><td>52.2</td><td>89.2</td><td>85.2</td></tr><tr><td>BEVFusion-MIT [6]</td><td>L+C</td><td>70.2</td><td>72.9</td><td>88.6</td><td>60.1</td><td>39.3</td><td>69.8</td><td>63.8</td><td>80.0</td><td>74.1</td><td>51.0</td><td>89.2</td><td>86.5</td></tr><tr><td>DeepInteraction [10]</td><td>L+C</td><td>70.8</td><td>73.4</td><td>87.9</td><td>60.2</td><td>37.5</td><td>70.8</td><td>63.8</td><td>80.4</td><td>75.4</td><td>54.5</td><td>91.7</td><td>87.2</td></tr><tr><td>FocalFormer3D</td><td>L+C</td><td>71.6</td><td>73.9</td><td>88.5</td><td>61.4</td><td>35.9</td><td>71.7</td><td>66.4</td><td>79.3</td><td>80.3</td><td>57.1</td><td>89.7</td><td>85.3</td></tr><tr><td>PointAugmenting [57]†</td><td>L+C</td><td>66.8</td><td>71.0</td><td>87.5</td><td>57.3</td><td>28.0</td><td>65.2</td><td>60.7</td><td>72.6</td><td>74.3</td><td>50.9</td><td>87.9</td><td>83.6</td></tr><tr><td>Focals Conv-F [27]‡</td><td>L+C</td><td>70.1</td><td>73.6</td><td>87.5</td><td>60.0</td><td>32.6</td><td>69.9</td><td>64.0</td><td>71.8</td><td>81.1</td><td>59.2</td><td>89.0</td><td>85.5</td></tr><tr><td>LargeKernel3D-F [28]‡</td><td>L+C</td><td>71.1</td><td>74.2</td><td>88.1</td><td>60.3</td><td>34.3</td><td>69.1</td><td>66.5</td><td>75.5</td><td>82.0</td><td>60.3</td><td>89.6</td><td>85.7</td></tr><tr><td>FocalFormer3D-F†</td><td>L+C</td><td>72.9</td><td>75.0</td><td>88.8</td><td>63.5</td><td>39.0</td><td>73.7</td><td>66.9</td><td>79.2</td><td>81.0</td><td>58.1</td><td>91.1</td><td>87.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.514,
+                0.893,
+                0.556
+            ],
+            "angle": 0,
+            "content": "Table 1. Performance comparison on the nuScenes 3D detection test set. † represents using flipping test-time augmentation. ‡ means using both flipping and rotation test-time augmentation. C.V, Motor., Ped. and T.C. are short for construction vehicle, motorcycle, pedestrian, and traffic cones, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.581,
+                0.47,
+                0.748
+            ],
+            "angle": 0,
+            "content": "cluding 32-beams LiDAR with 20FPS and 6-view camera images. We mainly evaluate our method on both LiDAR-only and LiDAR-Camera fusion settings. The evaluation metrics follow nuScenes official metrics including mean average precision (mAP) and nuScenes detection score (NDS) defined by averaging the matching thresholds of center distance \\(\\mathbb{D} = \\{0.5,1.,2.,4.\\}\\) (m). For evaluating the quality of object queries, we also introduce the Average Recall (AR) defined by center distance as well. The ablation studies in our research primarily utilize the nuScenes dataset, unless explicitly stated otherwise."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Waymo Open Dataset [61] has a wider detection range of \\(150m \\times 150m\\) compared to the nuScenes dataset. Waymo dataset comprises of 798 scenes for training and 202 scenes for validation. The official evaluation metrics used are mean Average Precision (mAP) and mean Average Precision with Heading (mAPH), where the mAP is weighted by the heading accuracy. The mAP and mAPH scores are computed with a 3D Intersection over Union (IoU) threshold of 0.7 for Vehicle and 0.5 for Pedestrian and Cyclist. The evaluation has two difficulty levels: Level 1, for boxes with more"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.581,
+                0.892,
+                0.642
+            ],
+            "angle": 0,
+            "content": "than five LiDAR points, and Level 2, for boxes with at least one LiDAR point. Of the two difficulty levels, Level 2 is prioritized as the primary evaluation metric for all experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.648,
+                0.893,
+                0.83
+            ],
+            "angle": 0,
+            "content": "Implementation details. Our implementation is mainly based on the open-sourced codebase MMDetection3D [79]. For the LiDAR backbone, we use CenterPoint-Voxel as the point cloud feature extractor. For the multi-stage heatmap encoder, we apply 3 stages, generating a total of 600 queries by default. Data augmentation includes random double flipping along both \\(X\\) and \\(Y\\) axes, random global rotation between \\([- \\pi /4, \\pi /4]\\), the random scale of [0.9, 1.1], and random translation with a standard deviation of 0.5 in all axes. All models are trained with a batch size of 16 on eight V100 GPUs. More implementation details are referred to in supplementary files."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.845,
+                0.64,
+                0.86
+            ],
+            "angle": 0,
+            "content": "4.2. Main Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "nuScenes LiDAR-based 3D object detection. We evaluate the performance of FocalFormer3D on the nuScenes"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8399"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.228
+            ],
+            "angle": 0,
+            "content": "test set. As shown in Table 1, the results demonstrate its superiority over state-of-the-art methods on various evaluation metrics and settings. Our single-model FocalFormer3D achieved \\(68.7\\mathrm{mAP}\\) and 72.6 NDS, which surpasses the prior TransFusion-L method by \\(+3.2\\) points on mAP and \\(+2.4\\) points on NDS. Notably, even compared with the previous best method that was trained with segmentation-level labels, our method without extra supervision still outperformed LiDARMultiNet by \\(+1.7\\mathrm{mAP}\\) and \\(+1.0\\) NDS."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.234,
+                0.473,
+                0.522
+            ],
+            "angle": 0,
+            "content": "nuScenes multi-modal 3D object detection. We extend our approach to a simple multi-modal variant and demonstrate its generality. Following TransFusion [4], we use a pre-trained ResNet-50 model on COCO [80] and nuImage [62] dataset as the image model and freeze its weights during training. To reduce computation costs, the input images are downscaled to \\(1/2\\) of their original size. Unlike heavy lift-splat-shot [32] camera encoders used in BEVFusion [5, 6], the multi-view camera images are projected onto a pre-defined voxel space and fused with LiDAR BEV feature. Additional details are available in the supplementary files. Without test-time augmentation, our simple multi-modal variant model outperforms all other state-of-the-art with less inference time (Table 2). With TTA, FocalFormer3D achieves \\(72.9\\mathrm{mAP}\\) and 75.0 NDS, ranking first among all single-model solutions on the nuScenes benchmark. Interestingly, our model achieves high results for some rare classes such as (Trailer, Motorcycle, Bicycle) compared to other methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.528,
+                0.472,
+                0.696
+            ],
+            "angle": 0,
+            "content": "nuScenes 3D object tracking. To further demonstrate the versatility, we also extend FocalFormer3D to 3D multi-object tracking (MOT) by using the tracking-by-detection algorithm SimpleTrack. Interested readers can refer to the original paper [81] for more comprehensive details. As depicted in Table 2, FocalFormer3D gets 2.9 points better than prior state-of-the-art TransFusion-L [4] in LiDAR settings and FocalFormer3D-F achieves 2.1 points over TransFusion in terms of AMOTA. Moreover, our single model FocalFormer3D-F with double-flip testing results performs even better than the BEVFusion [6] with model ensembling."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.701,
+                0.472,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Waymo LiDAR 3D object detection. The results of our single-frame LiDAR 3D detection method on the Waymo dataset are presented in Table 3, alongside the comparison with other approaches. Employing with the same VoxelNet backbone as nuScenes, our method achieves competitive performance without any fine-tuning of the model hyperparameters specifically for the Waymo dataset. Particularly, when compared to TransFusion-L with the same backbone, our method exhibits a \\(+1.1\\) mAPH improvement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.233,
+                0.864
+            ],
+            "angle": 0,
+            "content": "4.3. Recall Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To diagnose the performance improvements, we compare several recent methods in terms of AR for both stages"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.09,
+                0.895,
+                0.362
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>AMOTA</td><td>AMOTP</td><td>MOTA</td><td>IDS</td></tr><tr><td colspan=\"5\">LiDAR-based 3D Tracking</td></tr><tr><td>AB3DMOT [82]</td><td>15.1</td><td>150.1</td><td>15.4</td><td>9027</td></tr><tr><td>CenterPoint [3]</td><td>63.8</td><td>55.5</td><td>53.7</td><td>760</td></tr><tr><td>CBMOT [83]</td><td>64.9</td><td>59.2</td><td>54.5</td><td>557</td></tr><tr><td>OGR3MOT [84]</td><td>65.6</td><td>62.0</td><td>55.4</td><td>288</td></tr><tr><td>SimpleTrack [81]</td><td>66.8</td><td>55.0</td><td>56.6</td><td>575</td></tr><tr><td>UVTR-L [7]</td><td>67.0</td><td>55.0</td><td>56.6</td><td>774</td></tr><tr><td>TransFusion-L [4]</td><td>68.6</td><td>52.9</td><td>57.1</td><td>893</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>54.9</td><td>60.1</td><td>888</td></tr><tr><td>FocalFormer3D†</td><td>72.1</td><td>47.0</td><td>60.0</td><td>701</td></tr><tr><td colspan=\"5\">Multi-Modal 3D Tracking</td></tr><tr><td>UVTR-MultiModal [7]</td><td>70.1</td><td>68.6</td><td>61.8</td><td>941</td></tr><tr><td>TransFusion [4]</td><td>71.8</td><td>55.1</td><td>60.7</td><td>944</td></tr><tr><td>BEVFusion-MIT [6]‡</td><td>74.1</td><td>40.3</td><td>60.3</td><td>506</td></tr><tr><td>FocalFormer3D-F</td><td>73.9</td><td>51.4</td><td>61.8</td><td>824</td></tr><tr><td>FocalFormer3D-F†</td><td>74.6</td><td>47.3</td><td>63.0</td><td>849</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.37,
+                0.895,
+                0.414
+            ],
+            "angle": 0,
+            "content": "Table 2. Performance comparison on nuScenes 3D tracking test set. \\( {}^{ \\dagger  } \\) is based on the double-flip testing results in Table 1. \\( {}^{ \\ddagger  } \\) is based on model ensembling."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.424,
+                0.891,
+                0.622
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>mAP</td><td>mAPH</td><td>Vel.</td><td>Ped.</td><td>Cyc.</td></tr><tr><td colspan=\"6\">LiDAR-based 3D Detection</td></tr><tr><td>RSN* [85]</td><td>-</td><td>-</td><td>65.5</td><td>63.7</td><td>-</td></tr><tr><td>AFDetV2* [86]</td><td>71.0</td><td>68.8</td><td>69.2</td><td>67.0</td><td>70.1</td></tr><tr><td>SST* [55]</td><td>67.8</td><td>64.6</td><td>65.1</td><td>61.7</td><td>66.9</td></tr><tr><td>PV-RCNN* [24]</td><td>66.8</td><td>63.3</td><td>68.4</td><td>65.8</td><td>68.5</td></tr><tr><td>PV-RCNN++* [25]</td><td>71.7</td><td>69.5</td><td>70.2</td><td>68.0</td><td>70.2</td></tr><tr><td>PillarNet-34* [48]</td><td>71.0</td><td>68.8</td><td>70.5</td><td>66.2</td><td>68.7</td></tr><tr><td>FSD-spconv* [56]</td><td>71.9</td><td>69.7</td><td>68.5</td><td>68.0</td><td>72.5</td></tr><tr><td>CenterPoint [3]</td><td>69.8</td><td>67.6</td><td>73.4</td><td>65.8</td><td>68.5</td></tr><tr><td>TransFusion-L^ [4]</td><td>70.5</td><td>67.9</td><td>66.8</td><td>66.1</td><td>70.9</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>69.0</td><td>67.6</td><td>66.8</td><td>72.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.631,
+                0.895,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Table 3. Performance comparison on the Waymo val set. All models inputs single-frame point clouds. The methods marked with * indicate the utilization of different point cloud backbones in VoxelNet. The method marked with ^ indicates our reproduction. The evaluation metric used is the LEVEL 2 difficulty, and the results are reported on the full Waymo validation set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.742,
+                0.894,
+                0.819
+            ],
+            "angle": 0,
+            "content": "- initial BEV heatmap predictions and final box predictions in Fig. 5. The metric of AR is computed based on center distance following the nuScenes metrics and different distance thresholds (e.g., \\(0.5m\\), \\(1.0m\\), \\(2.0m\\), \\(4.0m\\)), and the mean AR (mAR) are compared."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Recall comparison on initial object candidates. Figure 5 compares the recall of state-of-the-art methods that share the same SparseUNet backbone. With total 200 queries, FocalFormer3D-200P reaches \\(75.2\\mathrm{mAR}\\), achieving considerable and consistent improvements by +4.5"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8400"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.087,
+                0.327,
+                0.202
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.329,
+                0.088,
+                0.607,
+                0.201
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.607,
+                0.089,
+                0.89,
+                0.201
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.216,
+                0.893,
+                0.245
+            ],
+            "angle": 0,
+            "content": "Figure 5. Average recall comparisons between initial object predictions and final object prediction centers on the nuScenes val set. The subfigures are shown over center distance thresholds (\\%) following nuScenes detection metrics."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.267,
+                0.462,
+                0.442
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.457,
+                0.47,
+                0.514
+            ],
+            "angle": 0,
+            "content": "Figure 6. Class-wise recall comparison on nuScenes val set between TransFusion-L and FocalFormer3D in terms of recall values across nuScenes center distance (CD) threshes \\((0.25 / 0.5 / 1.0\\mathrm{m})\\) on the nuScenes val set. The red bars are normalized to \\(100\\%\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.538,
+                0.47,
+                0.675
+            ],
+            "angle": 0,
+            "content": "mAR compared with the prior state-of-the-art LiDAR approach TransFusion-L. Surprisingly, our LiDAR-based FocalFormer even achieves better results than the prior multimodal approach DeepInteraction by 2.6 points in terms of mAR as well. As the query sizes get 600, FocalFormer3D achieves \\(79.2\\mathrm{mAR}\\), surpassing the fusion approach DeepInteraction by 6.6 points. Further, by incorporating multi-view camera features, our multi-modal version FocalFormer-F gets improved to \\(80.9\\mathrm{mAR}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.682,
+                0.47,
+                0.849
+            ],
+            "angle": 0,
+            "content": "Recall comparison on final object prediction. Concerning the final predictions of 3D detectors, most LiDAR and fusion approaches obtain fewer performance improvements as the distance thresholds increase as shown in Fig. 5. This can be explained by higher distance thresholds indicating the performance for the extreme cases of missing detections. The introduction of camera features helps the model see the context in the perspective view, which leads to better performance such as DeepInteraction. However, their final prediction recall falls far behind FocalFormer-F with a large margin of 6.8 points."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Class-wise recall comparison. We compare the class-wise recall analysis for object candidates in Fig. 6 at the category level. The findings highlight the effectiveness of"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.528,
+                0.266,
+                0.868,
+                0.373
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>#</td><td># Stages</td><td>#Total Queries</td><td>mAP</td><td>NDS</td></tr><tr><td>(a)</td><td>1</td><td>200</td><td>65.3</td><td>70.5</td></tr><tr><td>(b)</td><td>2</td><td>200</td><td>66.0</td><td>70.7</td></tr><tr><td>(c)</td><td>1</td><td>600</td><td>65.4</td><td>70.5</td></tr><tr><td>(d)</td><td>2</td><td>600</td><td>66.4</td><td>70.9</td></tr><tr><td>(e)</td><td>3</td><td>600</td><td>66.5</td><td>71.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.384,
+                0.893,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Table 4. Effects of numbers of stages and total queries. Here one stage stands for the baseline method without using hard instance probing."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.586,
+                0.437,
+                0.809,
+                0.537
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Mask Type</td><td>mAP</td><td>NDS</td></tr><tr><td>None</td><td>65.3</td><td>70.4</td></tr><tr><td>Point-based</td><td>65.9</td><td>70.5</td></tr><tr><td>Box-based</td><td>66.1</td><td>70.9</td></tr><tr><td>Pooling-based</td><td>66.5</td><td>71.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.546,
+                0.893,
+                0.575
+            ],
+            "angle": 0,
+            "content": "Table 5. Effects of various positive mask types. All models adopt the same network except for the masking way."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.598,
+                0.892,
+                0.675
+            ],
+            "angle": 0,
+            "content": "FocalFormer3D in improving the relative recall of initial BEV queries by a relative \\(+10.9\\%\\) improvement against TransFusion-L. Large objects such as Construction Vehicles and Trailer get the most improvements so that the predictions of their initial centers are challenging."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.682,
+                0.654,
+                0.699
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.713,
+                0.892,
+                0.834
+            ],
+            "angle": 0,
+            "content": "HIP query sizes and generation stages. Table 4 ablates the impacts of the number of queries and stages in the multi-stage heatmap encoder. When using the same query size of rough 200, approaches (b), which uses additional one stage of HIP, demonstrates better performance than baseline (a) by a margin of \\(+0.7\\) mAP. When provided with more queries (600), our approach (d) and (e) achieve over 1.1-point improvement in terms of mAP."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Positive mask type. Table 5 presents an ablation study on the effectiveness of Hard Instance Probing in terms of various mask types. Specifically, we compare the performance of our method with none masking, point-based masking,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8401"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.09,
+                0.468,
+                0.24
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">#</td><td rowspan=\"2\">M.S. Heat</td><td colspan=\"2\">Refinement Module</td><td rowspan=\"2\">mAP</td><td rowspan=\"2\">NDS</td></tr><tr><td>BoxPool</td><td>C.A.</td></tr><tr><td>(a)</td><td>X</td><td>X</td><td>X</td><td>63.1</td><td>69.1</td></tr><tr><td>(b)</td><td>✓</td><td>X</td><td>X</td><td>63.3</td><td>69.3</td></tr><tr><td>(c)</td><td>✓</td><td>✓</td><td>X</td><td>65.1</td><td>69.9</td></tr><tr><td>(d)</td><td>✓</td><td>X</td><td>✓</td><td>65.9</td><td>70.9</td></tr><tr><td>(e)</td><td>✓</td><td>✓</td><td>✓</td><td>66.5</td><td>71.1</td></tr><tr><td>(f)</td><td>✓</td><td colspan=\"2\">Rescoring Only</td><td>66.1</td><td>68.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.249,
+                0.47,
+                0.364
+            ],
+            "angle": 0,
+            "content": "Table 6. Step-by-step improvements made by modules. \"M.S. Heat\" represents the application of the multi-stage heatmap encoder for hard instance probing. \"C.A.\" denotes using deformable cross attention for second-stage refinement. \"BoxPool\" represents the Box-pooling module. The term \"Rescoring Only\" refers to the model that directly generates box prediction from BEV feature and uses its decoder head to rescore the candidate predictions from heatmap without performing additional bounding box refinement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.389,
+                0.471,
+                0.556
+            ],
+            "angle": 0,
+            "content": "and pooling-based masking. The results demonstrate that even with single-point masking, HIP improves the performance of the baseline by a gain of \\(+0.6\\) points in terms of mAP. Furthermore, the pooling-based masking shows the best gain with \\(+1.2\\) mAP and \\(+0.7\\) NDS, outperforming the box-based masking. This can be attributed to two facts. Point or pooling-based masking can already effectively exclude positive objects as the center heatmap [3] only highlights a Gaussian peak. Second, the wrong false positive predictions or predicted boxes might lead to false masking of the ground-truth boxes, resulting in missed detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.565,
+                0.47,
+                0.672
+            ],
+            "angle": 0,
+            "content": "Step-by-step module refinement. We conduct ablation studies on the step-by-step improvements by each module, presented in Table 6, to illustrate the component effectiveness within hard instance probing (HIP) pipeline. Initially, without second-stage refinement, we used simple center-based predictions [3] (a), which estimate boxes directly from BEV feature by another convolutional layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.672,
+                0.471,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Despite an improvement in the average recall by over 9 points in Fig. 5, we found little improvement of (b) over (a) in performance after using the multi-stage heatmap encoder to generate the object candidates. By applying simple object-level rescoring (c), with RoI-based refinement (using two hidden MLP layers), the performance is boosted to 65.1 mAP and 69.9 NDS. Remarkably, our complete box-level deformable decoder (e) further improves the performance by a margin of \\(+1.4\\) mAP and \\(+1.2\\) NDS."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To assess the effects of rescoring alone, we perform experiment (f), which excludes the effects of box regression by not using any box or position regression in the object-level refinement module. Despite this, experiment (f) still achieves high center accuracy (66.1 mAP) compared to (a). This finding highlights the limitations of the initial rank-"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.543,
+                0.089,
+                0.852,
+                0.203
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Models/Components</td><td>Latency</td></tr><tr><td>TransFusion-L</td><td>93ms</td></tr><tr><td>FocalFormer3D</td><td>109ms</td></tr><tr><td>- VoxelNet backbone</td><td>78ms</td></tr><tr><td>- Multi-stage heatmap encoder</td><td>13ms</td></tr><tr><td>- Box-level deformable decoder</td><td>18ms</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.212,
+                0.892,
+                0.24
+            ],
+            "angle": 0,
+            "content": "Table 7. Latency analysis for model components. Latency is measured on a V100 GPU for reference."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.268,
+                0.892,
+                0.33
+            ],
+            "angle": 0,
+            "content": "ing of object candidates across stages based solely on BEV heatmap scores. Therefore, it validates the necessity for a second-stage object-level rescoring in the hard instance probing pipeline (Fig. 3)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.338,
+                0.893,
+                0.565
+            ],
+            "angle": 0,
+            "content": "Latency analysis for model components. We conduct a latency analysis for FocalFormer3D on the nuScenes dataset. The runtimes are measured on the same V100 GPU machine for comparison. To ensure a fair speed comparison with CenterPoint [3], dynamic voxelization [87] is employed for speed testing of both TransFusion-L and FocalFormer3D. The computation time is mostly taken up by the sparse convolution-based backbone network (VoxelNet [1, 22]), which takes 78ms. Our multi-stage heatmap encoder takes 13ms to collect queries from the heatmaps across stages, while the box-level deformable decoder head takes 18ms. Note that, the generation of multi-stage heatmaps only takes 5ms, and additional operations such as Top-K selection takes 7ms, indicating potential optimization opportunities for future work."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.585,
+                0.619,
+                0.601
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.613,
+                0.892,
+                0.735
+            ],
+            "angle": 0,
+            "content": "In this work, we explicitly focus on the fatal problem in autonomous driving, i.e., false negative detections. We present FocalFormer3D as solution. It progressively probes hard instances and improves prediction recall, via the hard instance probing (HIP). Nontrivial improvements are introduced with limited overhead upon transformer-based 3D detectors. The HIP algorithm enables FocalFormer3D to effectively reduce false negatives in 3D object detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Limitation. A key limitation is that FocalFormer3D's hard instance probing (HIP) relies on the assumption that object centers produce Gaussian-like peaks in the BEV heatmap, which may not hold for camera-based detectors where heatmaps tend to be fan-shaped. Additionally, few studies have explored hard instances in long-range detection, so more research is needed to evaluate HIP in this area. We leave more investigation of hard instance probing as future work."
+        },
+        {
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+        }
+    ],
+    [
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+# FocalFormer3D : Focusing on Hard Instance for 3D Object Detection
+
+Yilun Chen $^{1*}$  Zhiding Yu $^{3\dagger}$  Yukang Chen $^{1}$   
+Shiyi Lan $^{3}$  Anima Anandkumar $^{2,3}$  Jiaya Jia $^{1}$  Jose M. Alvarez $^{3}$ $^{1}$ The Chinese University of Hong Kong  ${}^{2}$ Caltech  ${}^{3}$ NVIDIA
+
+# Abstract
+
+False negatives (FN) in 3D object detection, e.g., missing predictions of pedestrians, vehicles, or other obstacles, can lead to potentially dangerous situations in autonomous driving. While being fatal, this issue is understudied in many current 3D detection methods. In this work, we propose Hard Instance Probing (HIP), a general pipeline that identifies FN in a multi-stage manner and guides the models to focus on excavating difficult instances. For 3D object detection, we instantiate this method as FocalFormer3D, a simple yet effective detector that excels at excavating difficult objects and improving prediction recall. FocalFormer3D features a multi-stage query generation to discover hard objects and a box-level transformer decoder to efficiently distinguish objects from massive object candidates. Experimental results on the nuScenes and Waymo datasets validate the superior performance of FocalFormer3D. The advantage leads to strong performance on both detection and tracking, in both Li-DAR and multi-modal settings. Notably, FocalFormer3D achieves a 70.5 mAP and 73.9 NDS on nuScenes detection benchmark, while the nuScenes tracking benchmark shows 72.1 AMOTA, both ranking 1st place on the nuScenes LiDAR leaderboard. Our code is available at https://github.com/NVlabs/FocalFormer3D.
+
+# 1. Introduction
+
+3D object detection is an important yet challenging perception task. Recent state-of-the-art 3D object detectors mainly rely on bird's eye view (BEV) representation [1-3], where features from multiple sensors are aggregated to construct a unified representation in the ego-vehicle coordinate space. There is a rich yet growing literature on BEV-based 3D detection, including multi-modal fusion [4-10], second-stage refinements (surface point pooling [3], RoIPool [11-14], and cross attention modules [4, 15]).
+
+![](images/d2d0aa8da817f0ab4dee248828d84936bae251bc55f687decfab6554315893f7.jpg)  
+Figure 1. Visual example for Hard Instance Probing (HIP). By utilizing this multi-stage prediction approach, our model can progressively focus on hard instances and facilitate its ability to gradually detect them. At each stage, the model generates some Positive object candidates (represented by green circles). Object candidates assigned to the ground-truth objects can be classified as either True Positives (TP, represented by green boxes) and False Negatives (FN, represented by red boxes) during training. We explicitly model the unmatched ground-truth objects as the hard instances, which become the main targets for the subsequent stage. Conversely, Positives are considered easy samples (represented by gray boxes) and will be ignored in subsequent stages at both training and inference time. At last, all heatmap predictions across stages are collected as the initial object candidates. We ignored the False Positives for better visualizations.
+
+Despite the tremendous efforts, there has been limited exploration to explicitly address false negatives or missed
+
+objects often caused by occlusions and clutter background. False negatives are particularly concerning in autonomous driving as they cause missing information in the prediction and planning stacks. When an object or a part of an object is not detected, this can result in the autonomous vehicle being unaware of potential obstacles such as pedestrians, cyclists, or other vehicles. This is especially hazardous when the vehicle is moving at high speeds and can lead to potentially dangerous situations. Therefore, reducing false negatives is crucial to ensure the safety of autonomous driving.
+
+To address the challenge of False Negatives in 3D detection, we propose and formulate a pipeline called Hard Instance Probing (HIP). Motivated by cascade-style decoder head for object detection [16-18], we propose a pipeline to probe false negative samples progressively, which significantly improves the recall rate Fig. 1 illustrates the pipeline in a cascade manner. In each stage, HIP suppresses the true positive candidates and focuses on the false negative candidates from the previous stages. By iterating the HIP stage, our approach can save those hard false negatives.
+
+Based on HIP, we introduce a 3D object detector, FocalFormer3D, as shown in Fig. 2. Especially, multi-stage heatmap predictions [3, 19] are employed to excavate difficult instances. We maintain a class-aware Accumulated Positive Mask, indicating positive regions from prior stages. Through this masking design, the model omits the training of easy positive candidates and thereby focuses on the hard instances (False Negatives). Finally, our decoder collects the positive predictions from all stages to produce the object candidates. FocalFormer3D consistently demonstrates considerable gains over baselines in terms of average recall.
+
+In addition, we also introduce a box-level refinement step to eliminate redundant object candidates. The approach employs a deformable transformer decoder [17] and represents the candidates as box-level queries using RoIAlign. This allows for box-level query interaction and iterative box refinements, binding the object queries with sufficient box context through RoIAlign [20, 21] on the bird's eye view to perform relative bounding box refinements. Finally, a rescoring strategy is adopted to select positive objects from object candidates. Our ablation study in Table 6 demonstrates the effectiveness of the local refinement approach in processing adequate object candidates.
+
+Our contributions can be summarized as follows:
+
+- We propose Hard Instance Probing (HIP), a learnable scheme to automatically identify False Negatives in a multi-stage manner.  
+- We present FocalFormer3D for 3D object detection that effectively harvests hard instances on the BEV and demonstrates effectiveness in terms of average recall.  
+- Without bells and whistles, our model achieves state-of-the-art detection performance on both LiDAR-
+
+based and multi-modal settings. Notably, our model ranks 1st places on both nuScenes 3D LiDAR detection and tracking leaderboard at time of submission.
+
+# 2. Related Work
+
+Modern 3D object detectors, either LiDAR-based [1-3, 12, 13, 22-29], or Camera-based [30-37], or MultiModal [4-8, 38-45] 3D object detectors generally rely on BEV view representation [46]. These methods adopt dense feature maps or dense anchors, for conducting object prediction in a bird's eye view (BEV) space. Among these methods, VoxelNet [22] as the pioneer works discretize point clouds into voxel representation and applies dense convolution to generate BEV heatmaps. SECOND [22] accelerates VoxelNet with 3D sparse convolution [47] to extract 3D features. Some Pillar-based detectors [2, 23, 48, 49] collapse the height dimension and utilize 2D CNNs for efficient 3D detection.
+
+Different from dense detectors, point-based 3D detectors [11, 50-52] directly process point clouds via PointNet [53, 54] and perform grouping or predictions on the sparse representations. Concerning involvement of neighborhood query on point clouds, it becomes time-consuming and unaffordable for large-scale point clouds. Concerning computation and spatial cost, another line of 3D detectors directly predicts objects on sparse point clouds to avoid dense feature construction. SST [55] applies sparse regional attention and avoids downsampling for small-object detection. FSD [56] instead further recognize instances directly on sparse representations obtained by SST [55] and SparseConv for long-range detection.
+
+Recent multi-modal detectors [5-7, 39, 42, 57] follow the similar paradigm of BEV detectors and incorporate the multi-view image features by physical projection or learnable alignments between LiDAR and cameras. TransFusion [4] applies cross attention to obtain image features for each object query. Despite various kinds of modal-specific voxel feature encoders, these detectors finally produce dense BEV features for classification and regression at the heatmap level.
+
+# 3. Methodology
+
+We introduce Hard Instance Probing (HIP) for automated identifying hard instances (False Negatives) in Section 3.1. We then present the implementations for the two main components of FocalFormer3D. Section 3.2 describes our multi-stage heatmap encoder that harvests the False Negatives for producing high-recall initial object candidates following HIP. Section 3.3 introduces a box-level deformable decoder network that further distinguishes objects from these candidates.
+
+![](images/129b55a2e0254c60a0526382d34d4b91f20b7d944a2e74902591f49a9f574163.jpg)
+
+![](images/ed51815c9498c7b1fe93be0a0b0c646a79f09eb6a1d176c426a9ca2aef16f376.jpg)  
+Figure 2. Overall architecture of FocalFormer3D. The overall framework comprises two novel components: a multi-stage heatmap encoder network that uses the Hard Instance Probing (HIP) strategy to produce high-recall object queries (candidates), and a deformable transformer decoder network with rescoring mechanism that is responsible for eliminating false positives from the large set of candidates. (a) Following feature extraction from modalities, the map-view features produce a set of multi-stage BEV features and then BEV heatmaps. The positive mask accumulates to exclude the easy positive candidates of prior stages from BEV heatmaps. The left object candidates are chosen and collected according to the response of BEV heatmap in a multi-stage process. (b) A deformable transformer decoder is adapted to effectively handle diverse object queries. The query embedding is enhanced with a box pooling module, which leverages the intermediate object supervision to identify local regions. It refines object queries in a local-scope manner, rather than at a point level. Residual connections and normalization layers have been excluded from the figure for clarity.
+
+![](images/00748ca20f40ece5a022d2c2b3f43f1c8e521cf1984a11b1e661e1ee3fcc3c65.jpg)  
+Figure 3. Hard Instance Probing. We use the symbol “G” to indicate the object candidates that are labeled as ground-truth objects during the target assignment process in training. To ensure clarity, we omit numerous negative predictions for detection, given that background takes up most of the images.
+
+# 3.1. Hard Instance Probing (HIP)
+
+Real-world applications, such as autonomous driving, require a high level of scene understanding to ensure safe and secure operation. In particular, false negatives in object detection can present severe risks, emphasizing the need for high recall rates. However, accurately identifying objects in complex scenes or when occlusion occurs is challenging in
+
+3D object detection, resulting in many false negative predictions. Unfortunately, few studies have explicitly focused on addressing false negatives in the design of detection heads. Motivated by the cascade-style detectors, we formulate a training pipeline to emulate the process of identifying false negative predictions at inference time.
+
+**Formulation of Hard Instance Probing.** Our strategy to identify hard instances operates stage by stage, as illustrated by a toy example in Fig. 3. Initially, we annotate the groundtruth objects as
+
+$$
+\mathcal {O} = \left\{o _ {i}, i = 1, 2, \dots \right\},
+$$
+
+which is the main targets for initial stages. The neural network makes Positive or Negative predictions given a set of initial object candidates  $\mathcal{A} = \{a_i, i = 1,2,\ldots\}$ , which is not limited to anchors [58], point-based anchors [3], and object queries [59]. Suppose the detected objects (Positive predictions) at  $k$ -th stage are
+
+$$
+\mathcal {P} _ {k} = \left\{p _ {i}, i = 1, 2, \dots \right\}.
+$$
+
+We are then allowed to classify the ground-truth objects according to their assigned candidates:
+
+$$
+\mathcal {O} _ {k} ^ {T P} = \left\{o _ {j} \mid \exists p _ {i} \in \mathcal {P} _ {k}, \sigma \left(p _ {i}, o _ {j}\right) > \eta \right\}.
+$$
+
+where an object matching metric  $\sigma (\cdot ,\cdot)$  (e.g. Intersection over Union [60, 61] and center distance [62]) and a predefined threshold  $\eta$ . Thus, the left unmatched targets can be
+
+regarded as hard instances:
+
+$$
+\mathcal {O} _ {k} ^ {F N} = O - \bigcup_ {i = 1} ^ {k} O _ {k} ^ {T P}.
+$$
+
+The training of  $(k + 1)$ -th stages is to detect these targets  $\mathcal{O}_k^{FN}$  from the object candidates while omitting all prior Positive object candidates.
+
+Despite the cascade way mimicking the process of identifying false negative samples, we might collect a number of object candidates across all stages. Thus, a second-stage object-level refinement model is necessary to eliminate any potential false positives.
+
+Relation with hard example mining. The most relevant topic close to our approach is hard example mining [63, 64], which samples hard examples during training. Recent research [65-67] has further explored soft-sampling, such as adjusting the loss distribution to mitigate foreground-background imbalance issues. In contrast, our method operates in stages. Specifically, we use False Negative predictions from prior stages to guide the subsequent stage of the model toward learning from these challenging objects.
+
+# 3.2. Multi-stage Heatmap Encoder
+
+The upcoming subsections outline the key implementations of FocalFormer3D as depicted in Fig. 2. We begin by detailing the implementation of hard instance probing for BEV detection. This involves using the BEV center heatmap to generate the initial object candidate in a cascade manner.
+
+Preliminary of center heatmap in BEV perception. In common practice [3, 4, 19], the objective of the BEV heatmap head is to produce heatmap peaks at the center locations of detected objects. The BEV heatmaps are represented by a tensor  $S \in \mathbb{R}^{X \times Y \times C}$ , where  $X \times Y$  indicates the size of BEV feature map and  $C$  is the number of object categories. The target is achieved by producing 2D Gaussians near the BEV object points, which are obtained by projecting 3D box centers onto the map view. In top views such as Fig. 4, objects are more sparsely distributed than in a 2D image. Moreover, it is assumed that objects do not have intra-class overlaps on the bird's eye view.
+
+Based on the non-overlapping assumption, excluding prior easy positive candidates from BEV heatmap predictions can be achieved easily. In the following, we illustrate the implementation details of HIP, which utilizes an accumulated positive mask.
+
+Positive mask accumulation. To keep track of all easy positive object candidates of prior stages, we generate a positive mask (PM) on the BEV space for each stage and accumulated them to an accumulated positive mask (APM):
+
+$$
+\hat {M} _ {k} \in \{0, 1 \} ^ {X \times Y \times C},
+$$
+
+![](images/3a2e0f590240435df66d42982a0e5e3df1124ece67835a647559808e53d5bff7.jpg)  
+Figure 4. Example visualization for the positive mask. (left) and predicted BEV heatmap (right). The positive mask is class-aware and we show different categories with different colors for visualization. The masking area for objects of different categories can differ in the pooling-based masking method.
+
+![](images/4c759323f500f8343fa83557cdcfe03a00a7937fd01da3e3349a8edbe2cf87b9.jpg)
+
+which is initialized as all zeros.
+
+The generation of multi-stage BEV features is accomplished in a cascade manner using a lightweight inversed residual block [68] between stages. Multi-stage BEV heatmaps are generated by adding an extra convolution layer. At each stage, we generate the positive mask according to the positive predictions. To emulate the process of identifying False Negatives, we use a test-time selection strategy that ranks the scores according to BEV heatmap response [3, 4]. Specifically, at the  $k$ -th stage, Top-K selection is performed on the BEV heatmap across all BEV positions and categories, producing a set of object predictions  $\mathcal{P}_k$ . Then the positive mask  $M_{k}\in \{0,1\}^{X\times Y\times C}$  records the all the positions of positive predictions by setting  $M_{(x,y,c)} = 1$  for each predicted object  $p_i\in \mathcal{P}_k$ , where  $(x,y)$  represents  $p_i$ 's location and  $c$  is  $p_i$ 's class. The left points are set to 0 by default.
+
+According to the non-overlapping assumption, the ideal way to indicate the existence of a positive object candidate (represented as a point in the center heatmap) on the mask is by masking the box if there is a matched ground truth box. However, since the ground-truth boxes are not available at inference time, we propose the following masking methods during training:
+
+- Point Masking. This method involves no change, where only the center point of the positive candidates is filled.  
+- Pooling-based Masking. In this method, smaller objects fill in the center points while larger objects fill in with a kernel size of  $3 \times 3$ .  
+- Box Masking. This method requires an additional box prediction branch and involves filling the internal region of the predicted BEV box.
+
+The accumulated positive mask (APM) for the  $k$ -th stage
+
+is obtained by simply accumulating prior Positive Masks as follows:
+
+$$
+\hat{M}_{k} = \max_{1\leq i\leq k}M_{i}.
+$$
+
+By masking the BEV heatmap  $S_{k}$  with
+
+$$
+\hat {S} _ {k} = S _ {k} \cdot (1 - \hat {M} _ {k}),
+$$
+
+we omit prior easy positive regions in the current stage, thus enabling the model to focus on the false negative samples of the prior stage (hard instances). To train the multi-stage heatmap encoder, we adopt Gaussian Focal Loss [4] as the training loss function. We sum up the BEV heatmap losses across stages to obtain the final heatmap loss.
+
+During both training and inference, we collect the positive candidates from all stages as the object candidates for the second-stage rescoring as the potential false positive predictions.
+
+Discussion on implementation validity for HIP. Although the HIP strategy is simple, the masking way has two critical criteria that need to be met to ensure valid implementation of HIP:
+
+- Exclusion of prior positive object candidates at the current stage.  
+- Avoidance of removal of potential real objects (false negatives).
+
+Point masking satisfies both requirements based on the following facts. As the Top-K selection is based on ranking predicted BEV heatmap scores, the hottest response points are automatically excluded when a point is masked. Besides, the design of a class-aware positive mask ensures that non-overlapping assumptions at the intra-class level on the BEV are met.
+
+However, the point masking strategy is less efficient as only one BEV object candidate is excluded for each positive prediction compared with the ideal masking with ground-truth box guidance. Therefore, there is a trade-off between the masking area and the validity of the exclusion operation. We compare all three strategies in Table 5 and pooling-based masking performs better than others.
+
+# 3.3. Box-level Deformable Decoder
+
+The object candidates obtained from the multi-stage heatmap encoder can be treated as positional object queries [4, 69]. The recall of initial candidates improves with an increase in the number of collected candidates. However, redundant candidates introduce false positives, thereby necessitating a high level of performance for the following object-level refinement blocks.
+
+To enhance the efficiency of object query processing, we employ deformable attention [17] instead of computationally intensive modules such as cross attention [59] or box
+
+attention [70]. Unlike previous methods that used center point features as the query embedding [4, 69], we model the object candidates as box-level queries. Specifically, Specifically, we introduce object supervision between deformable decoder layers, facilitating relative box prediction.
+
+Box-pooling module. To better model the relations between objects and local regions in the regular grid manner, we extract the box context information from the BEV features using simple RoIAlign [20] in the Box-pooling module as Fig. 2. In specific, given the intermediate predicted box, each object query extracts  $7 \times 7$  feature grid points [20] from the BEV map followed by two MLP layers. The positional encoding is also applied both for queries and all BEV points for extracting positional information. This allows us to update both the content and positional information into the query embedding. This lightweight module enhances the query feature for the deformable decoder (See Table 6).
+
+Decoder implementation. Following Deformable DETR [17], our model employs 8 heads in all attention modules, including multi-head attention and multi-head deformable attention. The deformable attention utilizes 4 sampling points across 3 scales. To generate three scales of BEV features, we apply  $2 \times$  and  $4 \times$  downsampling operations to the original BEV features. The box-pooling module extracts  $7 \times 7$  feature grid points within each rotated BEV box followed by 2 FC layers and adds the object feature to query embedding. We expand the predicted box to  $1.2 \times$  size of its original size.
+
+# 3.4. Model Training
+
+The model is trained in two stages. In the first stage, we train the LiDAR backbone using a deformable transformer decoder head, which we refer to as DeformFormer3D (Table 4 (a)). After initializing the weights from DeformFormer3D, we train the FocalFormer3D detector, which consists of a multi-stage heatmap encoder and a box-level deformable decoder. However, during the training of the deformable decoder with bipartite graph matching, we encounter slow convergence issues in the early stages [18]. To address this, we generate noisy queries from ground-truth objects [18, 77, 78], enabling effective training of the model from scratch. Additionally, we improve the training process by excluding matching pairs with a center distance between the prediction and its GT object exceeding 7 meters.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Dataset and metric. We evaluate our approach on nuScenes and Waymo 3D detection dataset.
+
+nuScenes Dataset [62] is a large-scale outdoor dataset. nuScenes contains 1,000 scenes of multi-modal data, in
+
+<table><tr><td>Methods</td><td>Modality</td><td>mAP</td><td>NDS</td><td>Car</td><td>Truck</td><td>C.V.</td><td>Bus</td><td>Trailer</td><td>Barrier</td><td>Motor.</td><td>Bike</td><td>Ped.</td><td>T.C.</td></tr><tr><td colspan="14">LiDAR-based 3D Detection</td></tr><tr><td>PointPillars [2]</td><td>L</td><td>30.5</td><td>45.3</td><td>68.4</td><td>23.0</td><td>4.1</td><td>28.2</td><td>23.4</td><td>38.9</td><td>27.4</td><td>1.1</td><td>59.7</td><td>30.8</td></tr><tr><td>CBGS [71]</td><td>L</td><td>52.8</td><td>63.3</td><td>81.1</td><td>48.5</td><td>10.5</td><td>54.9</td><td>42.9</td><td>65.7</td><td>51.5</td><td>22.3</td><td>80.1</td><td>70.9</td></tr><tr><td>LargeKernel3D [28]</td><td>L</td><td>65.3</td><td>70.5</td><td>85.9</td><td>55.3</td><td>26.8</td><td>66.2</td><td>60.2</td><td>74.3</td><td>72.5</td><td>46.6</td><td>85.6</td><td>80.0</td></tr><tr><td>TransFusion-L [4]</td><td>L</td><td>65.5</td><td>70.2</td><td>86.2</td><td>56.7</td><td>28.2</td><td>66.3</td><td>58.8</td><td>78.2</td><td>68.3</td><td>44.2</td><td>86.1</td><td>82.0</td></tr><tr><td>PillarNet-34 [48]</td><td>L</td><td>66.0</td><td>71.4</td><td>87.6</td><td>57.5</td><td>27.9</td><td>63.6</td><td>63.1</td><td>77.2</td><td>70.1</td><td>42.3</td><td>87.3</td><td>83.3</td></tr><tr><td>LiDARMultiNet [72]</td><td>L</td><td>67.0</td><td>71.6</td><td>86.9</td><td>57.4</td><td>31.5</td><td>64.7</td><td>61.0</td><td>73.5</td><td>75.3</td><td>47.6</td><td>87.2</td><td>85.1</td></tr><tr><td>FocalFormer3D</td><td>L</td><td>68.7</td><td>72.6</td><td>87.2</td><td>57.1</td><td>34.4</td><td>69.6</td><td>64.9</td><td>77.8</td><td>76.2</td><td>49.6</td><td>88.2</td><td>82.3</td></tr><tr><td>CenterPoint [3]†</td><td>L</td><td>60.3</td><td>67.3</td><td>85.2</td><td>53.5</td><td>20.0</td><td>63.6</td><td>56.0</td><td>71.1</td><td>59.5</td><td>30.7</td><td>84.6</td><td>78.4</td></tr><tr><td>MGTANet†[73]</td><td>L</td><td>67.5</td><td>72.7</td><td>88.5</td><td>59.8</td><td>30.6</td><td>67.2</td><td>61.5</td><td>66.3</td><td>75.8</td><td>52.5</td><td>87.3</td><td>85.5</td></tr><tr><td>LargeKernel3D‡[28]</td><td>L</td><td>68.8</td><td>72.8</td><td>87.3</td><td>59.1</td><td>30.2</td><td>68.5</td><td>65.6</td><td>75.0</td><td>77.8</td><td>53.5</td><td>88.3</td><td>82.4</td></tr><tr><td>FocalFormer3D†</td><td>L</td><td>70.5</td><td>73.9</td><td>87.8</td><td>59.4</td><td>37.8</td><td>73.0</td><td>65.7</td><td>77.8</td><td>77.4</td><td>52.4</td><td>90.0</td><td>83.4</td></tr><tr><td colspan="14">Multi-Modal 3D Detection</td></tr><tr><td>PointPainting [74]</td><td>L+C</td><td>46.4</td><td>58.1</td><td>77.9</td><td>35.8</td><td>15.8</td><td>36.2</td><td>37.3</td><td>60.2</td><td>41.5</td><td>24.1</td><td>73.3</td><td>62.4</td></tr><tr><td>3D-CVF [75]</td><td>L+C</td><td>52.7</td><td>62.3</td><td>83.0</td><td>45.0</td><td>15.9</td><td>48.8</td><td>49.6</td><td>65.9</td><td>51.2</td><td>30.4</td><td>74.2</td><td>62.9</td></tr><tr><td>MVP [41]</td><td>L+C</td><td>66.4</td><td>70.5</td><td>86.8</td><td>58.5</td><td>26.1</td><td>67.4</td><td>57.3</td><td>74.8</td><td>70.0</td><td>49.3</td><td>89.1</td><td>85.0</td></tr><tr><td>FusionPainting [76]</td><td>L+C</td><td>68.1</td><td>71.6</td><td>87.1</td><td>60.8</td><td>30.0</td><td>68.5</td><td>61.7</td><td>71.8</td><td>74.7</td><td>53.5</td><td>88.3</td><td>85.0</td></tr><tr><td>TransFusion [4]</td><td>L+C</td><td>68.9</td><td>71.7</td><td>87.1</td><td>60.0</td><td>33.1</td><td>68.3</td><td>60.8</td><td>78.1</td><td>73.6</td><td>52.9</td><td>88.4</td><td>86.7</td></tr><tr><td>BEVFusion [5]</td><td>L+C</td><td>69.2</td><td>71.8</td><td>88.1</td><td>60.9</td><td>34.4</td><td>69.3</td><td>62.1</td><td>78.2</td><td>72.2</td><td>52.2</td><td>89.2</td><td>85.2</td></tr><tr><td>BEVFusion-MIT [6]</td><td>L+C</td><td>70.2</td><td>72.9</td><td>88.6</td><td>60.1</td><td>39.3</td><td>69.8</td><td>63.8</td><td>80.0</td><td>74.1</td><td>51.0</td><td>89.2</td><td>86.5</td></tr><tr><td>DeepInteraction [10]</td><td>L+C</td><td>70.8</td><td>73.4</td><td>87.9</td><td>60.2</td><td>37.5</td><td>70.8</td><td>63.8</td><td>80.4</td><td>75.4</td><td>54.5</td><td>91.7</td><td>87.2</td></tr><tr><td>FocalFormer3D</td><td>L+C</td><td>71.6</td><td>73.9</td><td>88.5</td><td>61.4</td><td>35.9</td><td>71.7</td><td>66.4</td><td>79.3</td><td>80.3</td><td>57.1</td><td>89.7</td><td>85.3</td></tr><tr><td>PointAugmenting [57]†</td><td>L+C</td><td>66.8</td><td>71.0</td><td>87.5</td><td>57.3</td><td>28.0</td><td>65.2</td><td>60.7</td><td>72.6</td><td>74.3</td><td>50.9</td><td>87.9</td><td>83.6</td></tr><tr><td>Focals Conv-F [27]‡</td><td>L+C</td><td>70.1</td><td>73.6</td><td>87.5</td><td>60.0</td><td>32.6</td><td>69.9</td><td>64.0</td><td>71.8</td><td>81.1</td><td>59.2</td><td>89.0</td><td>85.5</td></tr><tr><td>LargeKernel3D-F [28]‡</td><td>L+C</td><td>71.1</td><td>74.2</td><td>88.1</td><td>60.3</td><td>34.3</td><td>69.1</td><td>66.5</td><td>75.5</td><td>82.0</td><td>60.3</td><td>89.6</td><td>85.7</td></tr><tr><td>FocalFormer3D-F†</td><td>L+C</td><td>72.9</td><td>75.0</td><td>88.8</td><td>63.5</td><td>39.0</td><td>73.7</td><td>66.9</td><td>79.2</td><td>81.0</td><td>58.1</td><td>91.1</td><td>87.1</td></tr></table>
+
+Table 1. Performance comparison on the nuScenes 3D detection test set. † represents using flipping test-time augmentation. ‡ means using both flipping and rotation test-time augmentation. C.V, Motor., Ped. and T.C. are short for construction vehicle, motorcycle, pedestrian, and traffic cones, respectively.
+
+cluding 32-beams LiDAR with 20FPS and 6-view camera images. We mainly evaluate our method on both LiDAR-only and LiDAR-Camera fusion settings. The evaluation metrics follow nuScenes official metrics including mean average precision (mAP) and nuScenes detection score (NDS) defined by averaging the matching thresholds of center distance  $\mathbb{D} = \{0.5,1.,2.,4.\}$  (m). For evaluating the quality of object queries, we also introduce the Average Recall (AR) defined by center distance as well. The ablation studies in our research primarily utilize the nuScenes dataset, unless explicitly stated otherwise.
+
+Waymo Open Dataset [61] has a wider detection range of  $150m \times 150m$  compared to the nuScenes dataset. Waymo dataset comprises of 798 scenes for training and 202 scenes for validation. The official evaluation metrics used are mean Average Precision (mAP) and mean Average Precision with Heading (mAPH), where the mAP is weighted by the heading accuracy. The mAP and mAPH scores are computed with a 3D Intersection over Union (IoU) threshold of 0.7 for Vehicle and 0.5 for Pedestrian and Cyclist. The evaluation has two difficulty levels: Level 1, for boxes with more
+
+than five LiDAR points, and Level 2, for boxes with at least one LiDAR point. Of the two difficulty levels, Level 2 is prioritized as the primary evaluation metric for all experiments.
+
+Implementation details. Our implementation is mainly based on the open-sourced codebase MMDetection3D [79]. For the LiDAR backbone, we use CenterPoint-Voxel as the point cloud feature extractor. For the multi-stage heatmap encoder, we apply 3 stages, generating a total of 600 queries by default. Data augmentation includes random double flipping along both  $X$  and  $Y$  axes, random global rotation between  $[- \pi /4, \pi /4]$ , the random scale of [0.9, 1.1], and random translation with a standard deviation of 0.5 in all axes. All models are trained with a batch size of 16 on eight V100 GPUs. More implementation details are referred to in supplementary files.
+
+# 4.2. Main Results
+
+nuScenes LiDAR-based 3D object detection. We evaluate the performance of FocalFormer3D on the nuScenes
+
+test set. As shown in Table 1, the results demonstrate its superiority over state-of-the-art methods on various evaluation metrics and settings. Our single-model FocalFormer3D achieved  $68.7\mathrm{mAP}$  and 72.6 NDS, which surpasses the prior TransFusion-L method by  $+3.2$  points on mAP and  $+2.4$  points on NDS. Notably, even compared with the previous best method that was trained with segmentation-level labels, our method without extra supervision still outperformed LiDARMultiNet by  $+1.7\mathrm{mAP}$  and  $+1.0$  NDS.
+
+nuScenes multi-modal 3D object detection. We extend our approach to a simple multi-modal variant and demonstrate its generality. Following TransFusion [4], we use a pre-trained ResNet-50 model on COCO [80] and nuImage [62] dataset as the image model and freeze its weights during training. To reduce computation costs, the input images are downscaled to  $1/2$  of their original size. Unlike heavy lift-splat-shot [32] camera encoders used in BEVFusion [5, 6], the multi-view camera images are projected onto a pre-defined voxel space and fused with LiDAR BEV feature. Additional details are available in the supplementary files. Without test-time augmentation, our simple multi-modal variant model outperforms all other state-of-the-art with less inference time (Table 2). With TTA, FocalFormer3D achieves  $72.9\mathrm{mAP}$  and 75.0 NDS, ranking first among all single-model solutions on the nuScenes benchmark. Interestingly, our model achieves high results for some rare classes such as (Trailer, Motorcycle, Bicycle) compared to other methods.
+
+nuScenes 3D object tracking. To further demonstrate the versatility, we also extend FocalFormer3D to 3D multi-object tracking (MOT) by using the tracking-by-detection algorithm SimpleTrack. Interested readers can refer to the original paper [81] for more comprehensive details. As depicted in Table 2, FocalFormer3D gets 2.9 points better than prior state-of-the-art TransFusion-L [4] in LiDAR settings and FocalFormer3D-F achieves 2.1 points over TransFusion in terms of AMOTA. Moreover, our single model FocalFormer3D-F with double-flip testing results performs even better than the BEVFusion [6] with model ensembling.
+
+Waymo LiDAR 3D object detection. The results of our single-frame LiDAR 3D detection method on the Waymo dataset are presented in Table 3, alongside the comparison with other approaches. Employing with the same VoxelNet backbone as nuScenes, our method achieves competitive performance without any fine-tuning of the model hyperparameters specifically for the Waymo dataset. Particularly, when compared to TransFusion-L with the same backbone, our method exhibits a  $+1.1$  mAPH improvement.
+
+# 4.3. Recall Analysis
+
+To diagnose the performance improvements, we compare several recent methods in terms of AR for both stages
+
+<table><tr><td>Methods</td><td>AMOTA</td><td>AMOTP</td><td>MOTA</td><td>IDS</td></tr><tr><td colspan="5">LiDAR-based 3D Tracking</td></tr><tr><td>AB3DMOT [82]</td><td>15.1</td><td>150.1</td><td>15.4</td><td>9027</td></tr><tr><td>CenterPoint [3]</td><td>63.8</td><td>55.5</td><td>53.7</td><td>760</td></tr><tr><td>CBMOT [83]</td><td>64.9</td><td>59.2</td><td>54.5</td><td>557</td></tr><tr><td>OGR3MOT [84]</td><td>65.6</td><td>62.0</td><td>55.4</td><td>288</td></tr><tr><td>SimpleTrack [81]</td><td>66.8</td><td>55.0</td><td>56.6</td><td>575</td></tr><tr><td>UVTR-L [7]</td><td>67.0</td><td>55.0</td><td>56.6</td><td>774</td></tr><tr><td>TransFusion-L [4]</td><td>68.6</td><td>52.9</td><td>57.1</td><td>893</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>54.9</td><td>60.1</td><td>888</td></tr><tr><td>FocalFormer3D†</td><td>72.1</td><td>47.0</td><td>60.0</td><td>701</td></tr><tr><td colspan="5">Multi-Modal 3D Tracking</td></tr><tr><td>UVTR-MultiModal [7]</td><td>70.1</td><td>68.6</td><td>61.8</td><td>941</td></tr><tr><td>TransFusion [4]</td><td>71.8</td><td>55.1</td><td>60.7</td><td>944</td></tr><tr><td>BEVFusion-MIT [6]‡</td><td>74.1</td><td>40.3</td><td>60.3</td><td>506</td></tr><tr><td>FocalFormer3D-F</td><td>73.9</td><td>51.4</td><td>61.8</td><td>824</td></tr><tr><td>FocalFormer3D-F†</td><td>74.6</td><td>47.3</td><td>63.0</td><td>849</td></tr></table>
+
+Table 2. Performance comparison on nuScenes 3D tracking test set.  ${}^{ \dagger  }$  is based on the double-flip testing results in Table 1.  ${}^{ \ddagger  }$  is based on model ensembling.  
+
+<table><tr><td>Methods</td><td>mAP</td><td>mAPH</td><td>Vel.</td><td>Ped.</td><td>Cyc.</td></tr><tr><td colspan="6">LiDAR-based 3D Detection</td></tr><tr><td>RSN* [85]</td><td>-</td><td>-</td><td>65.5</td><td>63.7</td><td>-</td></tr><tr><td>AFDetV2* [86]</td><td>71.0</td><td>68.8</td><td>69.2</td><td>67.0</td><td>70.1</td></tr><tr><td>SST* [55]</td><td>67.8</td><td>64.6</td><td>65.1</td><td>61.7</td><td>66.9</td></tr><tr><td>PV-RCNN* [24]</td><td>66.8</td><td>63.3</td><td>68.4</td><td>65.8</td><td>68.5</td></tr><tr><td>PV-RCNN++* [25]</td><td>71.7</td><td>69.5</td><td>70.2</td><td>68.0</td><td>70.2</td></tr><tr><td>PillarNet-34* [48]</td><td>71.0</td><td>68.8</td><td>70.5</td><td>66.2</td><td>68.7</td></tr><tr><td>FSD-spconv* [56]</td><td>71.9</td><td>69.7</td><td>68.5</td><td>68.0</td><td>72.5</td></tr><tr><td>CenterPoint [3]</td><td>69.8</td><td>67.6</td><td>73.4</td><td>65.8</td><td>68.5</td></tr><tr><td>TransFusion-L^ [4]</td><td>70.5</td><td>67.9</td><td>66.8</td><td>66.1</td><td>70.9</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>69.0</td><td>67.6</td><td>66.8</td><td>72.6</td></tr></table>
+
+Table 3. Performance comparison on the Waymo val set. All models inputs single-frame point clouds. The methods marked with * indicate the utilization of different point cloud backbones in VoxelNet. The method marked with ^ indicates our reproduction. The evaluation metric used is the LEVEL 2 difficulty, and the results are reported on the full Waymo validation set.
+
+- initial BEV heatmap predictions and final box predictions in Fig. 5. The metric of AR is computed based on center distance following the nuScenes metrics and different distance thresholds (e.g.,  $0.5m$ ,  $1.0m$ ,  $2.0m$ ,  $4.0m$ ), and the mean AR (mAR) are compared.
+
+Recall comparison on initial object candidates. Figure 5 compares the recall of state-of-the-art methods that share the same SparseUNet backbone. With total 200 queries, FocalFormer3D-200P reaches  $75.2\mathrm{mAR}$ , achieving considerable and consistent improvements by +4.5
+
+![](images/40f1845444fbc2dd5d26d2ad15dbedf98b1112166cc2d417fba4d8c1ca1f574e.jpg)  
+Figure 5. Average recall comparisons between initial object predictions and final object prediction centers on the nuScenes val set. The subfigures are shown over center distance thresholds (\%) following nuScenes detection metrics.
+
+![](images/7dbd0851e135aade0bb92271ec19f5fc76798938175e20cc83cd5554f368c9d8.jpg)
+
+![](images/b55dddbb3e32f95e44371b53d7b21da2baecb41ea3d64aeac189b61e98f6d575.jpg)
+
+![](images/9b74916b88dfa57c6b03a15da828dc14889a1961042dd331c5e755d20186a938.jpg)  
+Figure 6. Class-wise recall comparison on nuScenes val set between TransFusion-L and FocalFormer3D in terms of recall values across nuScenes center distance (CD) threshes  $(0.25 / 0.5 / 1.0\mathrm{m})$  on the nuScenes val set. The red bars are normalized to  $100\%$ .
+
+mAR compared with the prior state-of-the-art LiDAR approach TransFusion-L. Surprisingly, our LiDAR-based FocalFormer even achieves better results than the prior multimodal approach DeepInteraction by 2.6 points in terms of mAR as well. As the query sizes get 600, FocalFormer3D achieves  $79.2\mathrm{mAR}$ , surpassing the fusion approach DeepInteraction by 6.6 points. Further, by incorporating multi-view camera features, our multi-modal version FocalFormer-F gets improved to  $80.9\mathrm{mAR}$ .
+
+Recall comparison on final object prediction. Concerning the final predictions of 3D detectors, most LiDAR and fusion approaches obtain fewer performance improvements as the distance thresholds increase as shown in Fig. 5. This can be explained by higher distance thresholds indicating the performance for the extreme cases of missing detections. The introduction of camera features helps the model see the context in the perspective view, which leads to better performance such as DeepInteraction. However, their final prediction recall falls far behind FocalFormer-F with a large margin of 6.8 points.
+
+Class-wise recall comparison. We compare the class-wise recall analysis for object candidates in Fig. 6 at the category level. The findings highlight the effectiveness of
+
+<table><tr><td>#</td><td># Stages</td><td>#Total Queries</td><td>mAP</td><td>NDS</td></tr><tr><td>(a)</td><td>1</td><td>200</td><td>65.3</td><td>70.5</td></tr><tr><td>(b)</td><td>2</td><td>200</td><td>66.0</td><td>70.7</td></tr><tr><td>(c)</td><td>1</td><td>600</td><td>65.4</td><td>70.5</td></tr><tr><td>(d)</td><td>2</td><td>600</td><td>66.4</td><td>70.9</td></tr><tr><td>(e)</td><td>3</td><td>600</td><td>66.5</td><td>71.1</td></tr></table>
+
+Table 4. Effects of numbers of stages and total queries. Here one stage stands for the baseline method without using hard instance probing.  
+
+<table><tr><td>Mask Type</td><td>mAP</td><td>NDS</td></tr><tr><td>None</td><td>65.3</td><td>70.4</td></tr><tr><td>Point-based</td><td>65.9</td><td>70.5</td></tr><tr><td>Box-based</td><td>66.1</td><td>70.9</td></tr><tr><td>Pooling-based</td><td>66.5</td><td>71.1</td></tr></table>
+
+Table 5. Effects of various positive mask types. All models adopt the same network except for the masking way.
+
+FocalFormer3D in improving the relative recall of initial BEV queries by a relative  $+10.9\%$  improvement against TransFusion-L. Large objects such as Construction Vehicles and Trailer get the most improvements so that the predictions of their initial centers are challenging.
+
+# 4.4. Ablation Study
+
+HIP query sizes and generation stages. Table 4 ablates the impacts of the number of queries and stages in the multi-stage heatmap encoder. When using the same query size of rough 200, approaches (b), which uses additional one stage of HIP, demonstrates better performance than baseline (a) by a margin of  $+0.7$  mAP. When provided with more queries (600), our approach (d) and (e) achieve over 1.1-point improvement in terms of mAP.
+
+Positive mask type. Table 5 presents an ablation study on the effectiveness of Hard Instance Probing in terms of various mask types. Specifically, we compare the performance of our method with none masking, point-based masking,
+
+<table><tr><td rowspan="2">#</td><td rowspan="2">M.S. Heat</td><td colspan="2">Refinement Module</td><td rowspan="2">mAP</td><td rowspan="2">NDS</td></tr><tr><td>BoxPool</td><td>C.A.</td></tr><tr><td>(a)</td><td>X</td><td>X</td><td>X</td><td>63.1</td><td>69.1</td></tr><tr><td>(b)</td><td>✓</td><td>X</td><td>X</td><td>63.3</td><td>69.3</td></tr><tr><td>(c)</td><td>✓</td><td>✓</td><td>X</td><td>65.1</td><td>69.9</td></tr><tr><td>(d)</td><td>✓</td><td>X</td><td>✓</td><td>65.9</td><td>70.9</td></tr><tr><td>(e)</td><td>✓</td><td>✓</td><td>✓</td><td>66.5</td><td>71.1</td></tr><tr><td>(f)</td><td>✓</td><td colspan="2">Rescoring Only</td><td>66.1</td><td>68.8</td></tr></table>
+
+and pooling-based masking. The results demonstrate that even with single-point masking, HIP improves the performance of the baseline by a gain of  $+0.6$  points in terms of mAP. Furthermore, the pooling-based masking shows the best gain with  $+1.2$  mAP and  $+0.7$  NDS, outperforming the box-based masking. This can be attributed to two facts. Point or pooling-based masking can already effectively exclude positive objects as the center heatmap [3] only highlights a Gaussian peak. Second, the wrong false positive predictions or predicted boxes might lead to false masking of the ground-truth boxes, resulting in missed detection.
+
+Step-by-step module refinement. We conduct ablation studies on the step-by-step improvements by each module, presented in Table 6, to illustrate the component effectiveness within hard instance probing (HIP) pipeline. Initially, without second-stage refinement, we used simple center-based predictions [3] (a), which estimate boxes directly from BEV feature by another convolutional layer.
+
+Despite an improvement in the average recall by over 9 points in Fig. 5, we found little improvement of (b) over (a) in performance after using the multi-stage heatmap encoder to generate the object candidates. By applying simple object-level rescoring (c), with RoI-based refinement (using two hidden MLP layers), the performance is boosted to 65.1 mAP and 69.9 NDS. Remarkably, our complete box-level deformable decoder (e) further improves the performance by a margin of  $+1.4$  mAP and  $+1.2$  NDS.
+
+To assess the effects of rescoring alone, we perform experiment (f), which excludes the effects of box regression by not using any box or position regression in the object-level refinement module. Despite this, experiment (f) still achieves high center accuracy (66.1 mAP) compared to (a). This finding highlights the limitations of the initial rank-
+
+Table 6. Step-by-step improvements made by modules. "M.S. Heat" represents the application of the multi-stage heatmap encoder for hard instance probing. "C.A." denotes using deformable cross attention for second-stage refinement. "BoxPool" represents the Box-pooling module. The term "Rescoring Only" refers to the model that directly generates box prediction from BEV feature and uses its decoder head to rescore the candidate predictions from heatmap without performing additional bounding box refinement.  
+
+<table><tr><td>Models/Components</td><td>Latency</td></tr><tr><td>TransFusion-L</td><td>93ms</td></tr><tr><td>FocalFormer3D</td><td>109ms</td></tr><tr><td>- VoxelNet backbone</td><td>78ms</td></tr><tr><td>- Multi-stage heatmap encoder</td><td>13ms</td></tr><tr><td>- Box-level deformable decoder</td><td>18ms</td></tr></table>
+
+Table 7. Latency analysis for model components. Latency is measured on a V100 GPU for reference.
+
+ing of object candidates across stages based solely on BEV heatmap scores. Therefore, it validates the necessity for a second-stage object-level rescoring in the hard instance probing pipeline (Fig. 3).
+
+Latency analysis for model components. We conduct a latency analysis for FocalFormer3D on the nuScenes dataset. The runtimes are measured on the same V100 GPU machine for comparison. To ensure a fair speed comparison with CenterPoint [3], dynamic voxelization [87] is employed for speed testing of both TransFusion-L and FocalFormer3D. The computation time is mostly taken up by the sparse convolution-based backbone network (VoxelNet [1, 22]), which takes 78ms. Our multi-stage heatmap encoder takes 13ms to collect queries from the heatmaps across stages, while the box-level deformable decoder head takes 18ms. Note that, the generation of multi-stage heatmaps only takes 5ms, and additional operations such as Top-K selection takes 7ms, indicating potential optimization opportunities for future work.
+
+# 5. Conclusion
+
+In this work, we explicitly focus on the fatal problem in autonomous driving, i.e., false negative detections. We present FocalFormer3D as solution. It progressively probes hard instances and improves prediction recall, via the hard instance probing (HIP). Nontrivial improvements are introduced with limited overhead upon transformer-based 3D detectors. The HIP algorithm enables FocalFormer3D to effectively reduce false negatives in 3D object detection.
+
+Limitation. A key limitation is that FocalFormer3D's hard instance probing (HIP) relies on the assumption that object centers produce Gaussian-like peaks in the BEV heatmap, which may not hold for camera-based detectors where heatmaps tend to be fan-shaped. Additionally, few studies have explored hard instances in long-range detection, so more research is needed to evaluate HIP in this area. We leave more investigation of hard instance probing as future work.
+
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+                                    "type": "text",
+                                    "content": "objects often caused by occlusions and clutter background. False negatives are particularly concerning in autonomous driving as they cause missing information in the prediction and planning stacks. When an object or a part of an object is not detected, this can result in the autonomous vehicle being unaware of potential obstacles such as pedestrians, cyclists, or other vehicles. This is especially hazardous when the vehicle is moving at high speeds and can lead to potentially dangerous situations. Therefore, reducing false negatives is crucial to ensure the safety of autonomous driving."
+                                }
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+                                    "content": "To address the challenge of False Negatives in 3D detection, we propose and formulate a pipeline called Hard Instance Probing (HIP). Motivated by cascade-style decoder head for object detection [16-18], we propose a pipeline to probe false negative samples progressively, which significantly improves the recall rate Fig. 1 illustrates the pipeline in a cascade manner. In each stage, HIP suppresses the true positive candidates and focuses on the false negative candidates from the previous stages. By iterating the HIP stage, our approach can save those hard false negatives."
+                                }
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+                                    "content": "Based on HIP, we introduce a 3D object detector, FocalFormer3D, as shown in Fig. 2. Especially, multi-stage heatmap predictions [3, 19] are employed to excavate difficult instances. We maintain a class-aware Accumulated Positive Mask, indicating positive regions from prior stages. Through this masking design, the model omits the training of easy positive candidates and thereby focuses on the hard instances (False Negatives). Finally, our decoder collects the positive predictions from all stages to produce the object candidates. FocalFormer3D consistently demonstrates considerable gains over baselines in terms of average recall."
+                                }
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+                                    "content": "In addition, we also introduce a box-level refinement step to eliminate redundant object candidates. The approach employs a deformable transformer decoder [17] and represents the candidates as box-level queries using RoIAlign. This allows for box-level query interaction and iterative box refinements, binding the object queries with sufficient box context through RoIAlign [20, 21] on the bird's eye view to perform relative bounding box refinements. Finally, a rescoring strategy is adopted to select positive objects from object candidates. Our ablation study in Table 6 demonstrates the effectiveness of the local refinement approach in processing adequate object candidates."
+                                }
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+                                    "type": "text",
+                                    "content": "Our contributions can be summarized as follows:"
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "- We propose Hard Instance Probing (HIP), a learnable scheme to automatically identify False Negatives in a multi-stage manner."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
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+                                            "content": "- We present FocalFormer3D for 3D object detection that effectively harvests hard instances on the BEV and demonstrates effectiveness in terms of average recall."
+                                        }
+                                    ]
+                                }
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+                            "index": 6
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+                                            "type": "text",
+                                            "content": "- Without bells and whistles, our model achieves state-of-the-art detection performance on both LiDAR-"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
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+                                    "content": "based and multi-modal settings. Notably, our model ranks 1st places on both nuScenes 3D LiDAR detection and tracking leaderboard at time of submission."
+                                }
+                            ]
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+                                    "content": "2. Related Work"
+                                }
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+                                    "content": "Modern 3D object detectors, either LiDAR-based [1-3, 12, 13, 22-29], or Camera-based [30-37], or MultiModal [4-8, 38-45] 3D object detectors generally rely on BEV view representation [46]. These methods adopt dense feature maps or dense anchors, for conducting object prediction in a bird's eye view (BEV) space. Among these methods, VoxelNet [22] as the pioneer works discretize point clouds into voxel representation and applies dense convolution to generate BEV heatmaps. SECOND [22] accelerates VoxelNet with 3D sparse convolution [47] to extract 3D features. Some Pillar-based detectors [2, 23, 48, 49] collapse the height dimension and utilize 2D CNNs for efficient 3D detection."
+                                }
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+                                    "content": "Different from dense detectors, point-based 3D detectors [11, 50-52] directly process point clouds via PointNet [53, 54] and perform grouping or predictions on the sparse representations. Concerning involvement of neighborhood query on point clouds, it becomes time-consuming and unaffordable for large-scale point clouds. Concerning computation and spatial cost, another line of 3D detectors directly predicts objects on sparse point clouds to avoid dense feature construction. SST [55] applies sparse regional attention and avoids downsampling for small-object detection. FSD [56] instead further recognize instances directly on sparse representations obtained by SST [55] and SparseConv for long-range detection."
+                                }
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+                                    "content": "Recent multi-modal detectors [5-7, 39, 42, 57] follow the similar paradigm of BEV detectors and incorporate the multi-view image features by physical projection or learnable alignments between LiDAR and cameras. TransFusion [4] applies cross attention to obtain image features for each object query. Despite various kinds of modal-specific voxel feature encoders, these detectors finally produce dense BEV features for classification and regression at the heatmap level."
+                                }
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+                                    "content": "3. Methodology"
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+                                    "content": "We introduce Hard Instance Probing (HIP) for automated identifying hard instances (False Negatives) in Section 3.1. We then present the implementations for the two main components of FocalFormer3D. Section 3.2 describes our multi-stage heatmap encoder that harvests the False Negatives for producing high-recall initial object candidates following HIP. Section 3.3 introduces a box-level deformable decoder network that further distinguishes objects from these candidates."
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+                                            "content": "Figure 2. Overall architecture of FocalFormer3D. The overall framework comprises two novel components: a multi-stage heatmap encoder network that uses the Hard Instance Probing (HIP) strategy to produce high-recall object queries (candidates), and a deformable transformer decoder network with rescoring mechanism that is responsible for eliminating false positives from the large set of candidates. (a) Following feature extraction from modalities, the map-view features produce a set of multi-stage BEV features and then BEV heatmaps. The positive mask accumulates to exclude the easy positive candidates of prior stages from BEV heatmaps. The left object candidates are chosen and collected according to the response of BEV heatmap in a multi-stage process. (b) A deformable transformer decoder is adapted to effectively handle diverse object queries. The query embedding is enhanced with a box pooling module, which leverages the intermediate object supervision to identify local regions. It refines object queries in a local-scope manner, rather than at a point level. Residual connections and normalization layers have been excluded from the figure for clarity."
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+                                        }
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+                                }
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+                                    "content": "3D object detection, resulting in many false negative predictions. Unfortunately, few studies have explicitly focused on addressing false negatives in the design of detection heads. Motivated by the cascade-style detectors, we formulate a training pipeline to emulate the process of identifying false negative predictions at inference time."
+                                }
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+                                    "content": "**Formulation of Hard Instance Probing.** Our strategy to identify hard instances operates stage by stage, as illustrated by a toy example in Fig. 3. Initially, we annotate the groundtruth objects as"
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+                                    "content": "\\mathcal {O} = \\left\\{o _ {i}, i = 1, 2, \\dots \\right\\},",
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+                                    "type": "text",
+                                    "content": "which is the main targets for initial stages. The neural network makes Positive or Negative predictions given a set of initial object candidates "
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+                                    "content": ", which is not limited to anchors [58], point-based anchors [3], and object queries [59]. Suppose the detected objects (Positive predictions) at "
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+                                    "content": "\\mathcal {P} _ {k} = \\left\\{p _ {i}, i = 1, 2, \\dots \\right\\}.",
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+                                    "type": "text",
+                                    "content": "We are then allowed to classify the ground-truth objects according to their assigned candidates:"
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+                                    "content": "\\mathcal {O} _ {k} ^ {T P} = \\left\\{o _ {j} \\mid \\exists p _ {i} \\in \\mathcal {P} _ {k}, \\sigma \\left(p _ {i}, o _ {j}\\right) > \\eta \\right\\}.",
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+                                    "content": "where an object matching metric "
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+                                    "content": " (e.g. Intersection over Union [60, 61] and center distance [62]) and a predefined threshold "
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+                                    "type": "text",
+                                    "content": ". Thus, the left unmatched targets can be"
+                                }
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+            ],
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+                                    "content": "regarded as hard instances:"
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+                                    "content": "\\mathcal {O} _ {k} ^ {F N} = O - \\bigcup_ {i = 1} ^ {k} O _ {k} ^ {T P}.",
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+                                    "content": "The training of "
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+                                    "type": "inline_equation",
+                                    "content": "(k + 1)"
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+                                    "type": "text",
+                                    "content": "-th stages is to detect these targets "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}_k^{FN}"
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+                                    "type": "text",
+                                    "content": " from the object candidates while omitting all prior Positive object candidates."
+                                }
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+                                    "type": "text",
+                                    "content": "Despite the cascade way mimicking the process of identifying false negative samples, we might collect a number of object candidates across all stages. Thus, a second-stage object-level refinement model is necessary to eliminate any potential false positives."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Relation with hard example mining. The most relevant topic close to our approach is hard example mining [63, 64], which samples hard examples during training. Recent research [65-67] has further explored soft-sampling, such as adjusting the loss distribution to mitigate foreground-background imbalance issues. In contrast, our method operates in stages. Specifically, we use False Negative predictions from prior stages to guide the subsequent stage of the model toward learning from these challenging objects."
+                                }
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+                                    "content": "3.2. Multi-stage Heatmap Encoder"
+                                }
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+                                    "content": "The upcoming subsections outline the key implementations of FocalFormer3D as depicted in Fig. 2. We begin by detailing the implementation of hard instance probing for BEV detection. This involves using the BEV center heatmap to generate the initial object candidate in a cascade manner."
+                                }
+                            ]
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+                                    "content": "Preliminary of center heatmap in BEV perception. In common practice [3, 4, 19], the objective of the BEV heatmap head is to produce heatmap peaks at the center locations of detected objects. The BEV heatmaps are represented by a tensor "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "S \\in \\mathbb{R}^{X \\times Y \\times C}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "text",
+                                    "content": " indicates the size of BEV feature map and "
+                                },
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+                                {
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+                                    "type": "text",
+                                    "content": " is the number of object categories. The target is achieved by producing 2D Gaussians near the BEV object points, which are obtained by projecting 3D box centers onto the map view. In top views such as Fig. 4, objects are more sparsely distributed than in a 2D image. Moreover, it is assumed that objects do not have intra-class overlaps on the bird's eye view."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Based on the non-overlapping assumption, excluding prior easy positive candidates from BEV heatmap predictions can be achieved easily. In the following, we illustrate the implementation details of HIP, which utilizes an accumulated positive mask."
+                                }
+                            ]
+                        }
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+                                    "content": "Positive mask accumulation. To keep track of all easy positive object candidates of prior stages, we generate a positive mask (PM) on the BEV space for each stage and accumulated them to an accumulated positive mask (APM):"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {M} _ {k} \\in \\{0, 1 \\} ^ {X \\times Y \\times C},",
+                                    "image_path": "0dc5d8bb3416396d7f101193483112e3efa4f761f7c424d12578e15dcd43ea6f.jpg"
+                                }
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+                                            "content": "Figure 4. Example visualization for the positive mask. (left) and predicted BEV heatmap (right). The positive mask is class-aware and we show different categories with different colors for visualization. The masking area for objects of different categories can differ in the pooling-based masking method."
+                                        }
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+                                    "type": "text",
+                                    "content": "which is initialized as all zeros."
+                                }
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+                                    "type": "text",
+                                    "content": "The generation of multi-stage BEV features is accomplished in a cascade manner using a lightweight inversed residual block [68] between stages. Multi-stage BEV heatmaps are generated by adding an extra convolution layer. At each stage, we generate the positive mask according to the positive predictions. To emulate the process of identifying False Negatives, we use a test-time selection strategy that ranks the scores according to BEV heatmap response [3, 4]. Specifically, at the "
+                                },
+                                {
+                                    "bbox": [
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+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th stage, Top-K selection is performed on the BEV heatmap across all BEV positions and categories, producing a set of object predictions "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
+                                        545,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
+                                        545,
+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then the positive mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
+                                        545,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{k}\\in \\{0,1\\}^{X\\times Y\\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
+                                        545,
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+                                    ],
+                                    "type": "text",
+                                    "content": " records the all the positions of positive predictions by setting "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{(x,y,c)} = 1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
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+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": " for each predicted object "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
+                                        545,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_i\\in \\mathcal{P}_k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        289,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(x,y)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "'s location and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "'s class. The left points are set to 0 by default."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                        564
+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "According to the non-overlapping assumption, the ideal way to indicate the existence of a positive object candidate (represented as a point in the center heatmap) on the mask is by masking the box if there is a matched ground truth box. However, since the ground-truth boxes are not available at inference time, we propose the following masking methods during training:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                        {
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+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "- Point Masking. This method involves no change, where only the center point of the positive candidates is filled."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Pooling-based Masking. In this method, smaller objects fill in the center points while larger objects fill in with a kernel size of "
+                                        },
+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "3 \\times 3"
+                                        },
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+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Box Masking. This method requires an additional box prediction branch and involves filling the internal region of the predicted BEV box."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 19
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "The accumulated positive mask (APM) for the "
+                                },
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+                                    "type": "text",
+                                    "content": "-th stage"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "is obtained by simply accumulating prior Positive Masks as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "type": "interline_equation",
+                                    "content": "\\hat{M}_{k} = \\max_{1\\leq i\\leq k}M_{i}.",
+                                    "image_path": "e15b6994c752f3dddb87097223a0cc3a753b6d7ef567208686de647bfad6ba3d.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "By masking the BEV heatmap "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{k}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " with"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {S} _ {k} = S _ {k} \\cdot (1 - \\hat {M} _ {k}),",
+                                    "image_path": "59ac99e2a58a2dd76be37cd6214720905399bb32133e08b9def3e21a592336e6.jpg"
+                                }
+                            ]
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+                },
+                {
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+                    ],
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "we omit prior easy positive regions in the current stage, thus enabling the model to focus on the false negative samples of the prior stage (hard instances). To train the multi-stage heatmap encoder, we adopt Gaussian Focal Loss [4] as the training loss function. We sum up the BEV heatmap losses across stages to obtain the final heatmap loss."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "During both training and inference, we collect the positive candidates from all stages as the object candidates for the second-stage rescoring as the potential false positive predictions."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Discussion on implementation validity for HIP. Although the HIP strategy is simple, the masking way has two critical criteria that need to be met to ensure valid implementation of HIP:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "blocks": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "- Exclusion of prior positive object candidates at the current stage."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "- Avoidance of removal of potential real objects (false negatives)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Point masking satisfies both requirements based on the following facts. As the Top-K selection is based on ranking predicted BEV heatmap scores, the hottest response points are automatically excluded when a point is masked. Besides, the design of a class-aware positive mask ensures that non-overlapping assumptions at the intra-class level on the BEV are met."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "However, the point masking strategy is less efficient as only one BEV object candidate is excluded for each positive prediction compared with the ideal masking with ground-truth box guidance. Therefore, there is a trade-off between the masking area and the validity of the exclusion operation. We compare all three strategies in Table 5 and pooling-based masking performs better than others."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.3. Box-level Deformable Decoder"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The object candidates obtained from the multi-stage heatmap encoder can be treated as positional object queries [4, 69]. The recall of initial candidates improves with an increase in the number of collected candidates. However, redundant candidates introduce false positives, thereby necessitating a high level of performance for the following object-level refinement blocks."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "To enhance the efficiency of object query processing, we employ deformable attention [17] instead of computationally intensive modules such as cross attention [59] or box"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "attention [70]. Unlike previous methods that used center point features as the query embedding [4, 69], we model the object candidates as box-level queries. Specifically, Specifically, we introduce object supervision between deformable decoder layers, facilitating relative box prediction."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                    ],
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+                                    "type": "text",
+                                    "content": "Box-pooling module. To better model the relations between objects and local regions in the regular grid manner, we extract the box context information from the BEV features using simple RoIAlign [20] in the Box-pooling module as Fig. 2. In specific, given the intermediate predicted box, each object query extracts "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "7 \\times 7"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " feature grid points [20] from the BEV map followed by two MLP layers. The positional encoding is also applied both for queries and all BEV points for extracting positional information. This allows us to update both the content and positional information into the query embedding. This lightweight module enhances the query feature for the deformable decoder (See Table 6)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
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+                                    "content": "Decoder implementation. Following Deformable DETR [17], our model employs 8 heads in all attention modules, including multi-head attention and multi-head deformable attention. The deformable attention utilizes 4 sampling points across 3 scales. To generate three scales of BEV features, we apply "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "4 \\times"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
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+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " downsampling operations to the original BEV features. The box-pooling module extracts "
+                                },
+                                {
+                                    "bbox": [
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+                                        282,
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+                                    "type": "inline_equation",
+                                    "content": "7 \\times 7"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " feature grid points within each rotated BEV box followed by 2 FC layers and adds the object feature to query embedding. We expand the predicted box to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1.2 \\times"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " size of its original size."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.4. Model Training"
+                                }
+                            ]
+                        }
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+                    "index": 18
+                },
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+                                    "content": "The model is trained in two stages. In the first stage, we train the LiDAR backbone using a deformable transformer decoder head, which we refer to as DeformFormer3D (Table 4 (a)). After initializing the weights from DeformFormer3D, we train the FocalFormer3D detector, which consists of a multi-stage heatmap encoder and a box-level deformable decoder. However, during the training of the deformable decoder with bipartite graph matching, we encounter slow convergence issues in the early stages [18]. To address this, we generate noisy queries from ground-truth objects [18, 77, 78], enabling effective training of the model from scratch. Additionally, we improve the training process by excluding matching pairs with a center distance between the prediction and its GT object exceeding 7 meters."
+                                }
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+                                    "type": "text",
+                                    "content": "4. Experiments"
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+                                    "content": "4.1. Experimental Setup"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "Dataset and metric. We evaluate our approach on nuScenes and Waymo 3D detection dataset."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "nuScenes Dataset [62] is a large-scale outdoor dataset. nuScenes contains 1,000 scenes of multi-modal data, in"
+                                }
+                            ]
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Methods</td><td>Modality</td><td>mAP</td><td>NDS</td><td>Car</td><td>Truck</td><td>C.V.</td><td>Bus</td><td>Trailer</td><td>Barrier</td><td>Motor.</td><td>Bike</td><td>Ped.</td><td>T.C.</td></tr><tr><td colspan=\"14\">LiDAR-based 3D Detection</td></tr><tr><td>PointPillars [2]</td><td>L</td><td>30.5</td><td>45.3</td><td>68.4</td><td>23.0</td><td>4.1</td><td>28.2</td><td>23.4</td><td>38.9</td><td>27.4</td><td>1.1</td><td>59.7</td><td>30.8</td></tr><tr><td>CBGS [71]</td><td>L</td><td>52.8</td><td>63.3</td><td>81.1</td><td>48.5</td><td>10.5</td><td>54.9</td><td>42.9</td><td>65.7</td><td>51.5</td><td>22.3</td><td>80.1</td><td>70.9</td></tr><tr><td>LargeKernel3D [28]</td><td>L</td><td>65.3</td><td>70.5</td><td>85.9</td><td>55.3</td><td>26.8</td><td>66.2</td><td>60.2</td><td>74.3</td><td>72.5</td><td>46.6</td><td>85.6</td><td>80.0</td></tr><tr><td>TransFusion-L [4]</td><td>L</td><td>65.5</td><td>70.2</td><td>86.2</td><td>56.7</td><td>28.2</td><td>66.3</td><td>58.8</td><td>78.2</td><td>68.3</td><td>44.2</td><td>86.1</td><td>82.0</td></tr><tr><td>PillarNet-34 [48]</td><td>L</td><td>66.0</td><td>71.4</td><td>87.6</td><td>57.5</td><td>27.9</td><td>63.6</td><td>63.1</td><td>77.2</td><td>70.1</td><td>42.3</td><td>87.3</td><td>83.3</td></tr><tr><td>LiDARMultiNet [72]</td><td>L</td><td>67.0</td><td>71.6</td><td>86.9</td><td>57.4</td><td>31.5</td><td>64.7</td><td>61.0</td><td>73.5</td><td>75.3</td><td>47.6</td><td>87.2</td><td>85.1</td></tr><tr><td>FocalFormer3D</td><td>L</td><td>68.7</td><td>72.6</td><td>87.2</td><td>57.1</td><td>34.4</td><td>69.6</td><td>64.9</td><td>77.8</td><td>76.2</td><td>49.6</td><td>88.2</td><td>82.3</td></tr><tr><td>CenterPoint [3]†</td><td>L</td><td>60.3</td><td>67.3</td><td>85.2</td><td>53.5</td><td>20.0</td><td>63.6</td><td>56.0</td><td>71.1</td><td>59.5</td><td>30.7</td><td>84.6</td><td>78.4</td></tr><tr><td>MGTANet†[73]</td><td>L</td><td>67.5</td><td>72.7</td><td>88.5</td><td>59.8</td><td>30.6</td><td>67.2</td><td>61.5</td><td>66.3</td><td>75.8</td><td>52.5</td><td>87.3</td><td>85.5</td></tr><tr><td>LargeKernel3D‡[28]</td><td>L</td><td>68.8</td><td>72.8</td><td>87.3</td><td>59.1</td><td>30.2</td><td>68.5</td><td>65.6</td><td>75.0</td><td>77.8</td><td>53.5</td><td>88.3</td><td>82.4</td></tr><tr><td>FocalFormer3D†</td><td>L</td><td>70.5</td><td>73.9</td><td>87.8</td><td>59.4</td><td>37.8</td><td>73.0</td><td>65.7</td><td>77.8</td><td>77.4</td><td>52.4</td><td>90.0</td><td>83.4</td></tr><tr><td colspan=\"14\">Multi-Modal 3D Detection</td></tr><tr><td>PointPainting [74]</td><td>L+C</td><td>46.4</td><td>58.1</td><td>77.9</td><td>35.8</td><td>15.8</td><td>36.2</td><td>37.3</td><td>60.2</td><td>41.5</td><td>24.1</td><td>73.3</td><td>62.4</td></tr><tr><td>3D-CVF [75]</td><td>L+C</td><td>52.7</td><td>62.3</td><td>83.0</td><td>45.0</td><td>15.9</td><td>48.8</td><td>49.6</td><td>65.9</td><td>51.2</td><td>30.4</td><td>74.2</td><td>62.9</td></tr><tr><td>MVP [41]</td><td>L+C</td><td>66.4</td><td>70.5</td><td>86.8</td><td>58.5</td><td>26.1</td><td>67.4</td><td>57.3</td><td>74.8</td><td>70.0</td><td>49.3</td><td>89.1</td><td>85.0</td></tr><tr><td>FusionPainting [76]</td><td>L+C</td><td>68.1</td><td>71.6</td><td>87.1</td><td>60.8</td><td>30.0</td><td>68.5</td><td>61.7</td><td>71.8</td><td>74.7</td><td>53.5</td><td>88.3</td><td>85.0</td></tr><tr><td>TransFusion [4]</td><td>L+C</td><td>68.9</td><td>71.7</td><td>87.1</td><td>60.0</td><td>33.1</td><td>68.3</td><td>60.8</td><td>78.1</td><td>73.6</td><td>52.9</td><td>88.4</td><td>86.7</td></tr><tr><td>BEVFusion [5]</td><td>L+C</td><td>69.2</td><td>71.8</td><td>88.1</td><td>60.9</td><td>34.4</td><td>69.3</td><td>62.1</td><td>78.2</td><td>72.2</td><td>52.2</td><td>89.2</td><td>85.2</td></tr><tr><td>BEVFusion-MIT [6]</td><td>L+C</td><td>70.2</td><td>72.9</td><td>88.6</td><td>60.1</td><td>39.3</td><td>69.8</td><td>63.8</td><td>80.0</td><td>74.1</td><td>51.0</td><td>89.2</td><td>86.5</td></tr><tr><td>DeepInteraction [10]</td><td>L+C</td><td>70.8</td><td>73.4</td><td>87.9</td><td>60.2</td><td>37.5</td><td>70.8</td><td>63.8</td><td>80.4</td><td>75.4</td><td>54.5</td><td>91.7</td><td>87.2</td></tr><tr><td>FocalFormer3D</td><td>L+C</td><td>71.6</td><td>73.9</td><td>88.5</td><td>61.4</td><td>35.9</td><td>71.7</td><td>66.4</td><td>79.3</td><td>80.3</td><td>57.1</td><td>89.7</td><td>85.3</td></tr><tr><td>PointAugmenting [57]†</td><td>L+C</td><td>66.8</td><td>71.0</td><td>87.5</td><td>57.3</td><td>28.0</td><td>65.2</td><td>60.7</td><td>72.6</td><td>74.3</td><td>50.9</td><td>87.9</td><td>83.6</td></tr><tr><td>Focals Conv-F [27]‡</td><td>L+C</td><td>70.1</td><td>73.6</td><td>87.5</td><td>60.0</td><td>32.6</td><td>69.9</td><td>64.0</td><td>71.8</td><td>81.1</td><td>59.2</td><td>89.0</td><td>85.5</td></tr><tr><td>LargeKernel3D-F [28]‡</td><td>L+C</td><td>71.1</td><td>74.2</td><td>88.1</td><td>60.3</td><td>34.3</td><td>69.1</td><td>66.5</td><td>75.5</td><td>82.0</td><td>60.3</td><td>89.6</td><td>85.7</td></tr><tr><td>FocalFormer3D-F†</td><td>L+C</td><td>72.9</td><td>75.0</td><td>88.8</td><td>63.5</td><td>39.0</td><td>73.7</td><td>66.9</td><td>79.2</td><td>81.0</td><td>58.1</td><td>91.1</td><td>87.1</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1. Performance comparison on the nuScenes 3D detection test set. † represents using flipping test-time augmentation. ‡ means using both flipping and rotation test-time augmentation. C.V, Motor., Ped. and T.C. are short for construction vehicle, motorcycle, pedestrian, and traffic cones, respectively."
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "cluding 32-beams LiDAR with 20FPS and 6-view camera images. We mainly evaluate our method on both LiDAR-only and LiDAR-Camera fusion settings. The evaluation metrics follow nuScenes official metrics including mean average precision (mAP) and nuScenes detection score (NDS) defined by averaging the matching thresholds of center distance "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{D} = \\{0.5,1.,2.,4.\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (m). For evaluating the quality of object queries, we also introduce the Average Recall (AR) defined by center distance as well. The ablation studies in our research primarily utilize the nuScenes dataset, unless explicitly stated otherwise."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
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+                                    "type": "text",
+                                    "content": "Waymo Open Dataset [61] has a wider detection range of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "150m \\times 150m"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " compared to the nuScenes dataset. Waymo dataset comprises of 798 scenes for training and 202 scenes for validation. The official evaluation metrics used are mean Average Precision (mAP) and mean Average Precision with Heading (mAPH), where the mAP is weighted by the heading accuracy. The mAP and mAPH scores are computed with a 3D Intersection over Union (IoU) threshold of 0.7 for Vehicle and 0.5 for Pedestrian and Cyclist. The evaluation has two difficulty levels: Level 1, for boxes with more"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "than five LiDAR points, and Level 2, for boxes with at least one LiDAR point. Of the two difficulty levels, Level 2 is prioritized as the primary evaluation metric for all experiments."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Implementation details. Our implementation is mainly based on the open-sourced codebase MMDetection3D [79]. For the LiDAR backbone, we use CenterPoint-Voxel as the point cloud feature extractor. For the multi-stage heatmap encoder, we apply 3 stages, generating a total of 600 queries by default. Data augmentation includes random double flipping along both "
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+                                    "type": "text",
+                                    "content": " axes, random global rotation between "
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+                                    "type": "inline_equation",
+                                    "content": "[- \\pi /4, \\pi /4]"
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+                                    "type": "text",
+                                    "content": ", the random scale of [0.9, 1.1], and random translation with a standard deviation of 0.5 in all axes. All models are trained with a batch size of 16 on eight V100 GPUs. More implementation details are referred to in supplementary files."
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+                                    "content": "4.2. Main Results"
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+                                    "content": "nuScenes LiDAR-based 3D object detection. We evaluate the performance of FocalFormer3D on the nuScenes"
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+                                    "content": "test set. As shown in Table 1, the results demonstrate its superiority over state-of-the-art methods on various evaluation metrics and settings. Our single-model FocalFormer3D achieved "
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+                                    "content": " points on NDS. Notably, even compared with the previous best method that was trained with segmentation-level labels, our method without extra supervision still outperformed LiDARMultiNet by "
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+                                    "type": "text",
+                                    "content": "nuScenes multi-modal 3D object detection. We extend our approach to a simple multi-modal variant and demonstrate its generality. Following TransFusion [4], we use a pre-trained ResNet-50 model on COCO [80] and nuImage [62] dataset as the image model and freeze its weights during training. To reduce computation costs, the input images are downscaled to "
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+                                    "type": "inline_equation",
+                                    "content": "1/2"
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+                                    "type": "text",
+                                    "content": " of their original size. Unlike heavy lift-splat-shot [32] camera encoders used in BEVFusion [5, 6], the multi-view camera images are projected onto a pre-defined voxel space and fused with LiDAR BEV feature. Additional details are available in the supplementary files. Without test-time augmentation, our simple multi-modal variant model outperforms all other state-of-the-art with less inference time (Table 2). With TTA, FocalFormer3D achieves "
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+                                    "type": "text",
+                                    "content": " and 75.0 NDS, ranking first among all single-model solutions on the nuScenes benchmark. Interestingly, our model achieves high results for some rare classes such as (Trailer, Motorcycle, Bicycle) compared to other methods."
+                                }
+                            ]
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+                    ],
+                    "index": 1
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+                {
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+                                    "type": "text",
+                                    "content": "nuScenes 3D object tracking. To further demonstrate the versatility, we also extend FocalFormer3D to 3D multi-object tracking (MOT) by using the tracking-by-detection algorithm SimpleTrack. Interested readers can refer to the original paper [81] for more comprehensive details. As depicted in Table 2, FocalFormer3D gets 2.9 points better than prior state-of-the-art TransFusion-L [4] in LiDAR settings and FocalFormer3D-F achieves 2.1 points over TransFusion in terms of AMOTA. Moreover, our single model FocalFormer3D-F with double-flip testing results performs even better than the BEVFusion [6] with model ensembling."
+                                }
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+                                    "type": "text",
+                                    "content": "Waymo LiDAR 3D object detection. The results of our single-frame LiDAR 3D detection method on the Waymo dataset are presented in Table 3, alongside the comparison with other approaches. Employing with the same VoxelNet backbone as nuScenes, our method achieves competitive performance without any fine-tuning of the model hyperparameters specifically for the Waymo dataset. Particularly, when compared to TransFusion-L with the same backbone, our method exhibits a "
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+                                    "type": "text",
+                                    "content": " mAPH improvement."
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+                                    "type": "text",
+                                    "content": "4.3. Recall Analysis"
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+                                    "type": "text",
+                                    "content": "To diagnose the performance improvements, we compare several recent methods in terms of AR for both stages"
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+                                            "html": "<table><tr><td>Methods</td><td>AMOTA</td><td>AMOTP</td><td>MOTA</td><td>IDS</td></tr><tr><td colspan=\"5\">LiDAR-based 3D Tracking</td></tr><tr><td>AB3DMOT [82]</td><td>15.1</td><td>150.1</td><td>15.4</td><td>9027</td></tr><tr><td>CenterPoint [3]</td><td>63.8</td><td>55.5</td><td>53.7</td><td>760</td></tr><tr><td>CBMOT [83]</td><td>64.9</td><td>59.2</td><td>54.5</td><td>557</td></tr><tr><td>OGR3MOT [84]</td><td>65.6</td><td>62.0</td><td>55.4</td><td>288</td></tr><tr><td>SimpleTrack [81]</td><td>66.8</td><td>55.0</td><td>56.6</td><td>575</td></tr><tr><td>UVTR-L [7]</td><td>67.0</td><td>55.0</td><td>56.6</td><td>774</td></tr><tr><td>TransFusion-L [4]</td><td>68.6</td><td>52.9</td><td>57.1</td><td>893</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>54.9</td><td>60.1</td><td>888</td></tr><tr><td>FocalFormer3D†</td><td>72.1</td><td>47.0</td><td>60.0</td><td>701</td></tr><tr><td colspan=\"5\">Multi-Modal 3D Tracking</td></tr><tr><td>UVTR-MultiModal [7]</td><td>70.1</td><td>68.6</td><td>61.8</td><td>941</td></tr><tr><td>TransFusion [4]</td><td>71.8</td><td>55.1</td><td>60.7</td><td>944</td></tr><tr><td>BEVFusion-MIT [6]‡</td><td>74.1</td><td>40.3</td><td>60.3</td><td>506</td></tr><tr><td>FocalFormer3D-F</td><td>73.9</td><td>51.4</td><td>61.8</td><td>824</td></tr><tr><td>FocalFormer3D-F†</td><td>74.6</td><td>47.3</td><td>63.0</td><td>849</td></tr></table>",
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+                                            "content": "Table 2. Performance comparison on nuScenes 3D tracking test set. "
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+                                            "content": " is based on the double-flip testing results in Table 1. "
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+                                            "type": "text",
+                                            "content": " is based on model ensembling."
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+                            "index": 7,
+                            "angle": 0,
+                            "type": "table_caption"
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+                                            "html": "<table><tr><td>Methods</td><td>mAP</td><td>mAPH</td><td>Vel.</td><td>Ped.</td><td>Cyc.</td></tr><tr><td colspan=\"6\">LiDAR-based 3D Detection</td></tr><tr><td>RSN* [85]</td><td>-</td><td>-</td><td>65.5</td><td>63.7</td><td>-</td></tr><tr><td>AFDetV2* [86]</td><td>71.0</td><td>68.8</td><td>69.2</td><td>67.0</td><td>70.1</td></tr><tr><td>SST* [55]</td><td>67.8</td><td>64.6</td><td>65.1</td><td>61.7</td><td>66.9</td></tr><tr><td>PV-RCNN* [24]</td><td>66.8</td><td>63.3</td><td>68.4</td><td>65.8</td><td>68.5</td></tr><tr><td>PV-RCNN++* [25]</td><td>71.7</td><td>69.5</td><td>70.2</td><td>68.0</td><td>70.2</td></tr><tr><td>PillarNet-34* [48]</td><td>71.0</td><td>68.8</td><td>70.5</td><td>66.2</td><td>68.7</td></tr><tr><td>FSD-spconv* [56]</td><td>71.9</td><td>69.7</td><td>68.5</td><td>68.0</td><td>72.5</td></tr><tr><td>CenterPoint [3]</td><td>69.8</td><td>67.6</td><td>73.4</td><td>65.8</td><td>68.5</td></tr><tr><td>TransFusion-L^ [4]</td><td>70.5</td><td>67.9</td><td>66.8</td><td>66.1</td><td>70.9</td></tr><tr><td>FocalFormer3D</td><td>71.5</td><td>69.0</td><td>67.6</td><td>66.8</td><td>72.6</td></tr></table>",
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+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "Table 3. Performance comparison on the Waymo val set. All models inputs single-frame point clouds. The methods marked with * indicate the utilization of different point cloud backbones in VoxelNet. The method marked with ^ indicates our reproduction. The evaluation metric used is the LEVEL 2 difficulty, and the results are reported on the full Waymo validation set."
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+                                    "content": " improvement against TransFusion-L. Large objects such as Construction Vehicles and Trailer get the most improvements so that the predictions of their initial centers are challenging."
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+                                    "content": "Positive mask type. Table 5 presents an ablation study on the effectiveness of Hard Instance Probing in terms of various mask types. Specifically, we compare the performance of our method with none masking, point-based masking,"
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+                                    "content": "and pooling-based masking. The results demonstrate that even with single-point masking, HIP improves the performance of the baseline by a gain of "
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+                                    "content": " points in terms of mAP. Furthermore, the pooling-based masking shows the best gain with "
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+                                    "content": " NDS, outperforming the box-based masking. This can be attributed to two facts. Point or pooling-based masking can already effectively exclude positive objects as the center heatmap [3] only highlights a Gaussian peak. Second, the wrong false positive predictions or predicted boxes might lead to false masking of the ground-truth boxes, resulting in missed detection."
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+                                    "type": "text",
+                                    "content": "Step-by-step module refinement. We conduct ablation studies on the step-by-step improvements by each module, presented in Table 6, to illustrate the component effectiveness within hard instance probing (HIP) pipeline. Initially, without second-stage refinement, we used simple center-based predictions [3] (a), which estimate boxes directly from BEV feature by another convolutional layer."
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+                                    "content": "Despite an improvement in the average recall by over 9 points in Fig. 5, we found little improvement of (b) over (a) in performance after using the multi-stage heatmap encoder to generate the object candidates. By applying simple object-level rescoring (c), with RoI-based refinement (using two hidden MLP layers), the performance is boosted to 65.1 mAP and 69.9 NDS. Remarkably, our complete box-level deformable decoder (e) further improves the performance by a margin of "
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+                                    "content": " mAP and "
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+                                    "type": "text",
+                                    "content": " NDS."
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+                    "index": 4
+                },
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+                                    "content": "To assess the effects of rescoring alone, we perform experiment (f), which excludes the effects of box regression by not using any box or position regression in the object-level refinement module. Despite this, experiment (f) still achieves high center accuracy (66.1 mAP) compared to (a). This finding highlights the limitations of the initial rank-"
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+                                            "type": "text",
+                                            "content": "Table 6. Step-by-step improvements made by modules. \"M.S. Heat\" represents the application of the multi-stage heatmap encoder for hard instance probing. \"C.A.\" denotes using deformable cross attention for second-stage refinement. \"BoxPool\" represents the Box-pooling module. The term \"Rescoring Only\" refers to the model that directly generates box prediction from BEV feature and uses its decoder head to rescore the candidate predictions from heatmap without performing additional bounding box refinement."
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+                                            "html": "<table><tr><td>Models/Components</td><td>Latency</td></tr><tr><td>TransFusion-L</td><td>93ms</td></tr><tr><td>FocalFormer3D</td><td>109ms</td></tr><tr><td>- VoxelNet backbone</td><td>78ms</td></tr><tr><td>- Multi-stage heatmap encoder</td><td>13ms</td></tr><tr><td>- Box-level deformable decoder</td><td>18ms</td></tr></table>",
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+                                    "content": "Table 7. Latency analysis for model components. Latency is measured on a V100 GPU for reference."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "ing of object candidates across stages based solely on BEV heatmap scores. Therefore, it validates the necessity for a second-stage object-level rescoring in the hard instance probing pipeline (Fig. 3)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Latency analysis for model components. We conduct a latency analysis for FocalFormer3D on the nuScenes dataset. The runtimes are measured on the same V100 GPU machine for comparison. To ensure a fair speed comparison with CenterPoint [3], dynamic voxelization [87] is employed for speed testing of both TransFusion-L and FocalFormer3D. The computation time is mostly taken up by the sparse convolution-based backbone network (VoxelNet [1, 22]), which takes 78ms. Our multi-stage heatmap encoder takes 13ms to collect queries from the heatmaps across stages, while the box-level deformable decoder head takes 18ms. Note that, the generation of multi-stage heatmaps only takes 5ms, and additional operations such as Top-K selection takes 7ms, indicating potential optimization opportunities for future work."
+                                }
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "type": "text",
+                                    "content": "In this work, we explicitly focus on the fatal problem in autonomous driving, i.e., false negative detections. We present FocalFormer3D as solution. It progressively probes hard instances and improves prediction recall, via the hard instance probing (HIP). Nontrivial improvements are introduced with limited overhead upon transformer-based 3D detectors. The HIP algorithm enables FocalFormer3D to effectively reduce false negatives in 3D object detection."
+                                }
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+                                    "content": "Limitation. A key limitation is that FocalFormer3D's hard instance probing (HIP) relies on the assumption that object centers produce Gaussian-like peaks in the BEV heatmap, which may not hold for camera-based detectors where heatmaps tend to be fan-shaped. Additionally, few studies have explored hard instances in long-range detection, so more research is needed to evaluate HIP in this area. We leave more investigation of hard instance probing as future work."
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+                                }
+                            ]
+                        }
+                    ],
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+                                            "bbox": [
+                                                53,
+                                                91,
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+                                            "type": "text",
+                                            "content": "[1] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. In CVPR, 2018. 1, 2, 9"
+                                        }
+                                    ]
+                                }
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+                        },
+                        {
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+                                162
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                129,
+                                                287,
+                                                162
+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                166,
+                                287,
+                                199
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                166,
+                                                287,
+                                                199
+                                            ],
+                                            "type": "text",
+                                            "content": "[3] Tianwei Yin, Xingyi Zhou, and Philipp Krahenbuhl. Center-based 3d object detection and tracking. In CVPR, pages 11784-11793, 2021. 1, 2, 3, 4, 6, 7, 9"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                203,
+                                286,
+                                247
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                203,
+                                                286,
+                                                247
+                                            ],
+                                            "type": "text",
+                                            "content": "[4] Xuyang Bai, Zeyu Hu, Xinge Zhu, Qingqiu Huang, Yilun Chen, Hongbo Fu, and Chiew-Lan Tai. Transfusion: Robust lidar-camera fusion for 3d object detection with transformers. In CVPR, pages 1080-1089, 2022. 1, 2, 4, 5, 6, 7"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                251,
+                                286,
+                                306
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                {
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+                                            "bbox": [
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diff --git a/2023/Focus on Your Target_ A Dual Teacher-Student Framework for Domain-Adaptive Semantic Segmentation/93139a7c-5176-4d19-a1d3-a4deb1b068c7_content_list.json b/2023/Focus on Your Target_ A Dual Teacher-Student Framework for Domain-Adaptive Semantic Segmentation/93139a7c-5176-4d19-a1d3-a4deb1b068c7_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..837231e2484e4f3c7f09992ba3a5710bb3ef2e8b
--- /dev/null
+++ b/2023/Focus on Your Target_ A Dual Teacher-Student Framework for Domain-Adaptive Semantic Segmentation/93139a7c-5176-4d19-a1d3-a4deb1b068c7_content_list.json	
@@ -0,0 +1,1994 @@
+[
+    {
+        "type": "text",
+        "text": "Focus on Your Target: A Dual Teacher-Student Framework for Domain-adaptive Semantic Segmentation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xinyue Huo $^{1,2}$  Lingxi Xie $^{2}$  Wengang Zhou $^{1}$  Houqiang Li $^{1}$  Qi Tian $^{2*}$ $^{1}$ University of Science and Technology of China  ${}^{2}$ Huawei Inc.",
+        "bbox": [
+            189,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "xinyueh@mail.ustc.edu.cn 198808xc@gmail.com",
+        "bbox": [
+            289,
+            241,
+            679,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{zhwg, lihq}  $@$  ustc.edu.cn tian.qil@huawei.com",
+        "bbox": [
+            292,
+            258,
+            678,
+            273
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            308,
+            313,
+            325
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We study unsupervised domain adaptation (UDA) for semantic segmentation. Currently, a popular UDA framework lies in self-training which endows the model with two-fold abilities: (i) learning reliable semantics from the labeled images in the source domain, and (ii) adapting to the target domain via generating pseudo labels on the unlabeled images. We find that, by decreasing/increasing the proportion of training samples from the target domain, the 'learning ability' is strengthened/weakened while the 'adapting ability' goes in the opposite direction, implying a conflict between these two abilities, especially for a single model. To alleviate the issue, we propose a novel dual teacher-student (DTS) framework and equip it with a bidirectional learning strategy. By increasing the proportion of target-domain data, the second teacher-student model learns to 'Focus on Your Target' while the first model is not affected. DTS is easily plugged into existing self-training approaches. In a standard UDA scenario (training on synthetic, labeled data and real, unlabeled data), DTS shows consistent gains over the baselines and sets new state-of-the-art results of  $76.5\\%$  and  $75.1\\%$  mIoUs on GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes, respectively. The implementation is available at https://github.com/xinyuehuo/DTS.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep neural networks [28] have been proven effective in learning from labeled, in-domain visual data, but their ability to adapt to unlabeled data or unknown domains is often not guaranteed. We delve into this topic by studying the unsupervised domain adaptation (UDA) problem for semantic segmentation, where densely (pixel-wise) labeled data are available for the source domain but only unlabeled images are provided for the target domain. The setting is useful",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/e16d7e5e759810ed46d4833d08b64a28ec176e858f1d1af229543701176ccc6e.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "image_caption": [
+            "Target A"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            434
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/f1b07bd18066f49636045e28f872e8d368922ae308c7c16f769927ea737c6ff0.jpg",
+        "image_caption": [
+            "Target B"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/43da1fbe3b0ca48f5ecc25002d3085f38d8ea1428e361d7b4ee301ad076bc915.jpg",
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+        "page_idx": 0
+    },
+    {
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+        "img_path": "images/35ef052feb46323f73aec837d5b8102dcc893a983dca980a391e8f1157760335.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
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+        "img_path": "images/20508a7da125b4b0f5b55dc70923f416abf581044f327cced0ab76da557e7381.jpg",
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+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/eb1313ed42189749b010d5721a4568f72b571549c7a41ddc38fb328c809116c7.jpg",
+        "image_caption": [
+            "DAFormer"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            446,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/0599455a8620961a47847cebe0565166e36020f4c2cc81650c9f2c20c525cd10.jpg",
+        "image_caption": [
+            "Ground Truth",
+            "Figure 1. Segmentation results on a test image from Cityscapes (the model is trained on GTAv). There are two traffic signs with different styles, where Target A is similar to the training data in the source domain while Target B is not. The baseline (DAFormer) gradually improves the accuracy on Target A but achieves the best accuracy on Target B in the midst (at 12K iterations). Our method, DTS, achieves good accuracy for both targets and the trend is more stable throughout the training process (see the curves)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
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+        "img_path": "images/0bb8dcd72a0473a3834ec9017e26f50763fd210fd3ab9254772e9a1717e563aa.jpg",
+        "image_caption": [
+            "DTS"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "in real-world applications where new domains emerge frequently but annotating them is a major burden.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The state-of-the-art UDA approaches for semantic segmentation are mostly built upon a self-training framework. It first learns semantics from labeled data in the source domain and then generates pseudo labels in the target domain, so that the model adapts to the target domain by fitting the pseudo labels. Conceptually, the two steps of self-training endow the model with two-fold abilities, namely, learning knowledge (semantics) from the source domain and adapt-",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding Author.",
+        "bbox": [
+            94,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "19027",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ing the knowledge to the target domain.",
+        "bbox": [
+            76,
+            90,
+            341,
+            104
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "However, these two abilities can conflict with each other. Figure 1 shows an example of two targets of the same class (traffic sign), where Target  $A$  is close to the typical training samples in the source domain, while Target  $B$  has a quite different appearance. Using the default setting of DAFormer [19] (a UDA baseline), the recognition accuracy of Target  $A$  gradually increases while that of Target  $B$  grows first but eventually drops to 0. Interestingly, if one increases the proportion of training samples from the target domain, the recognition quality of Target  $B$  will be better while the recognition accuracy of some unexpected classes (e.g., sidewalk) may drop significantly (more details and examples can be found in the Appendix). The conflict sets an obstacle to achieving higher UDA accuracy.",
+        "bbox": [
+            75,
+            106,
+            468,
+            316
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The above analysis prompts us to design a dual teacher-student (DTS) framework. The key is to train two individual models (with different network weights) so that the aforementioned conflict is alleviated. DTS can be built upon most existing self-training approaches in three steps: (1) making two copies of the original teacher-student model, (2) increasing the proportion of training data from the target domain in the second group, and (3) applying a bidirectional learning strategy so that two models supervise each other via pseudo labels. DTS allows the system to pursue a stronger adapting ability (with the second model) meanwhile the learning ability (guaranteed by the first model) is mostly unaffected.",
+        "bbox": [
+            75,
+            316,
+            470,
+            513
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We conduct semantic segmentation experiments with the standard UDA setting. Two synthetic datasets with dense labels, GTAv [38] and SYNTHIA [39], are used as the source domains, and a real dataset with only images, Cityscapes [6], is used as the target domain. We establish the DTS framework upon three recent self-training baselines, namely, DAFormer [19], HRDA [20], and MIC [21]. DTS improves the segmentation accuracy in every single trial, demonstrating its generalized ability across baselines and datasets. In particular, when integrated with MIC, the prior state-of-the-art, DTS reports  $76.5\\%$  and  $67.8\\%$  mIoUs on GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes, respectively, setting new records for both benchmarks.",
+        "bbox": [
+            75,
+            513,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            724,
+            218,
+            739
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Unsupervised domain adaptation (UDA), the task of transferring semantics from labeled source domains to unlabeled target domains, has been widely studied for many computer vision fields, e.g., classification [33, 58, 51], object detection [15, 24, 45], face recognition [25, 18, 43], semantic segmentation [17, 60], etc.",
+        "bbox": [
+            75,
+            750,
+            468,
+            839
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We briefly review two representative UDA approaches for semantic segmentation. Adversarial learning [47, 49] reduces the gap between the source and target domains by confusing a discriminator trained to judge which domain",
+        "bbox": [
+            75,
+            839,
+            468,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "the extracted visual features come from. It is closely related to style transfer methods [16, 55, 12, 56] that synthesize data to simulate the target domain. Self-training instead generates pseudo labels for the unlabeled target images and fits the model accordingly. There is a specific class of self-training methods [48, 10, 62] which further bridge the domain gap by creating mixed images that cover both domains [36, 1], inheriting benefits from style transferring. Many follow-up works [19, 20, 21], including this paper, were based on the self-training framework. Besides UDA, other data-efficient learning scenarios such as semi-supervised [22, 40] and few-shot [31, 35] learning also made use of self-training. Generating high-quality pseudo labels is crucial for self-training. Researchers developed various strategies, such as entropy minimization [4], class-balanced training [30], consistency regularization [21], auxiliary task learning [23, 53], etc., for this purpose.",
+        "bbox": [
+            496,
+            90,
+            890,
+            348
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "A fundamental concept in self-training is teacher-student optimization. To boost the effect of teacher-student optimization, efforts were made in generating high-quality pseudo labels with stronger teacher models [46, 27, 29, 11] and/or preventing error transmission from the teacher model to the student model [26, 63, 22, 5]. There are also other improvements including using multiple student models [61], designing a better loss function [11], etc. Another closely related concept is co-training [37, 44], which facilitates cross-view consistency with a teacher-student loss. The idea of DTS is to alleviate the discrepancy between teacher and student models from different groups with an indirect consistency constraint.",
+        "bbox": [
+            496,
+            348,
+            892,
+            544
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Our Approach",
+        "text_level": 1,
+        "bbox": [
+            500,
+            556,
+            648,
+            573
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We investigate the task of unsupervised domain adaptation (UDA) for semantic segmentation, where a labeled source domain  $\\mathbb{S}$  and an unlabeled target domain  $\\mathbb{T}$  are available. We denote the source dataset as  $\\mathcal{D}^{\\mathbb{S}} = \\{(\\mathbf{x}_n^{\\mathbb{S}},\\mathbf{y}_n^{\\mathbb{S}})\\}_{n = 1}^{N_{\\mathbb{S}}}$ , where  $\\mathbf{x}_n^{\\mathbb{S}}$  is an image and  $\\mathbf{y}_n^{\\mathbb{S}}$  is the corresponding dense label map. The target dataset  $\\mathcal{D}^{\\mathbb{T}}$  is another set of images without labels, denoted as  $\\{(x_{n}^{\\mathbb{T}})\\}_{n = 1}^{N_{\\mathbb{T}}}$ . The two domains share the same set of categories. The goal of UDA is to train a segmentation network  $f(\\mathbf{x};\\pmb {\\theta})$  that eventually works well in the target domain.",
+        "bbox": [
+            496,
+            582,
+            890,
+            733
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first introduce a self-training baseline where a single teacher-student framework is established (Section 3.1). Then, we reveal a conflict when the model is facilitated to focus on the target domain (Section 3.2), which drives us to propose a dual teacher-student framework towards better UDA performance (Section 3.3).",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3.1. Single Teacher-Student Baseline",
+        "text_level": 1,
+        "bbox": [
+            500,
+            832,
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+            847
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We start with a standard self-training (i.e., teacher-student) baseline which trains a teacher model and a student model denoted as  $f^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}^{\\mathrm{te}})$  and  $f^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}^{\\mathrm{st}})$ , respectively.",
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+    {
+        "type": "page_number",
+        "text": "19028",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The teacher model is updated using the exponential moving average (EMA) strategy [46]:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {\\theta} ^ {\\mathrm {t e}} \\leftarrow \\boldsymbol {\\theta} ^ {\\mathrm {t e}} \\times \\lambda + \\boldsymbol {\\theta} ^ {\\mathrm {s t}} \\times (1 - \\lambda), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  is a constant coefficient which is often close to 1. The student model is trained for segmentation in both the source and target domains. For the source images, semantic labels are available for supervised learning:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} ^ {\\mathbb {S}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(f ^ {\\mathrm {s t}} \\left(\\mathbf {x} ^ {\\mathbb {S}}\\right), \\mathbf {y} ^ {\\mathbb {S}}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            189,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{\\mathrm{CE}}$  denotes the pixel-wise cross-entropy loss. For the target images, the teacher model is used to generate a pseudo label  $\\tilde{\\mathbf{y}}^{\\mathbb{T}}$  for  $\\mathbf{x}^{\\mathbb{T}}$ , and the pixel-wise loss function is computed in a similar way:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} ^ {\\mathbb {T}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(f ^ {\\mathrm {s t}} \\left(\\mathbf {x} ^ {\\mathbb {T}}\\right), \\tilde {\\mathbf {y}} ^ {\\mathbb {T}}\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The overall loss is written as  $\\mathcal{L} = \\mathcal{L}^{\\mathbb{S}} + \\mathcal{L}^{\\mathbb{T}}$ . In practice, a balancing mechanism is applied [48, 19]: all pixel-wise loss terms computed on the target domain is multiplied by a factor of  $\\gamma$ , which is the proportion of the pseudo-label confidence surpassing a given threshold,  $\\tau$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recently, a series of methods [48, 19, 20, 21] validated that introducing a mixed domain between the source and target domains is helpful for domain adaptation. A typical operation is named ClassMix [36] which samples mixed images by computing",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {i, j} ^ {\\langle \\mathrm {S}, \\mathrm {T} \\rangle} = \\mathcal {M} \\left(\\mathbf {x} _ {i} ^ {\\mathrm {S}}, \\mathbf {x} _ {j} ^ {\\mathrm {T}}\\right) = \\mathbf {x} _ {i} ^ {\\mathrm {S}} \\odot \\mathbf {M} _ {i} ^ {\\mathrm {S}} + \\mathbf {x} _ {j} ^ {\\mathrm {T}} \\odot \\left(\\mathbf {1} - \\mathbf {M} _ {i} ^ {\\mathrm {S}}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            520,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$  denotes a mixed domain,  $\\odot$  is element-wise multiplication, and  $\\mathbf{M}^{\\mathbb{S}}$  is a mask generated by randomly a few class-level masks from the  $\\mathbf{y}^{\\mathbb{S}}$ . Accordingly, the target domain in Eqn (3) and the overall loss is replaced with the mixed domain. Note that pseudo labels are only computed for the target portion of the mixed images - we refer the reader to [36] for technical details.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Conflict between Learning and Adapting",
+        "text_level": 1,
+        "bbox": [
+            76,
+            665,
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+            681
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Although domain mixing improves the accuracy of UDA segmentation on several benchmarks, we observe that the trained model is easily biased towards the source domain and thus ignores the target domain to some extent. A typical example is shown in Figure 1.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We conjecture that it is the 'over-focus' on the source domain that prevents the model from achieving higher segmentation accuracy. To reveal this, we revisit the working mechanism of ClassMix. Compared to the original strategy that directly generates pseudo labels on the target images, ClassMix increases the proportion of data from the source domain (in a default setting of Eqn (4), an average of half target-domain pixels are replaced with source-domain pixels). This brings two differences. On the one hand, the",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "table",
+        "img_path": "images/a0d7741b5ce9959caaeb87ba6b968fb9dc3c86f865395265364dd27ca9ff3a56.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. UDA segmentation mIoU (%) using DAFourner [19] on the GTAv→Cityscapes benchmark with different options. An italic number indicates a result that uses target-domain labels. The pseudo accuracy is computed on the training set of Cityscapes."
+        ],
+        "table_body": "<table><tr><td>Label</td><td>{S, T}</td><td>{T, T}</td><td>Supervised</td></tr><tr><td>w/ pseudo labels</td><td>68.3</td><td>67.2</td><td>-</td></tr><tr><td>(pseudo acc.)</td><td>64.9</td><td>64.2</td><td>-</td></tr><tr><td>w/ ground-truth</td><td>74.4</td><td>76.9</td><td>77.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "quality of pseudo labels is improved because part of them are inherited from the labels in the source domain; on the other hand, the focus on the target domain is weakened, increasing the risk of domain adaptation.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The above analysis prompts us to perform the 'Focus on Your Target' trail towards higher UDA accuracy. We replace the mixed domain of ClassMix,  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$  , with another domain,  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  , in which the mixed samples are generated using two target images:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {j _ {1}, j _ {2}} ^ {\\langle \\mathbb {T}, \\mathbb {T} \\rangle} = \\mathcal {M} \\left(\\mathbf {x} _ {j _ {1}} ^ {\\mathbb {T}}, \\mathbf {x} _ {j _ {2}} ^ {\\mathbb {T}}\\right) = \\mathbf {x} _ {j _ {1}} ^ {\\mathbb {T}} \\odot \\mathbf {M} _ {j _ {1}} ^ {\\mathbb {T}} + \\mathbf {x} _ {j _ {2}} ^ {\\mathbb {T}} \\odot \\left(\\mathbf {1} - \\mathbf {M} _ {j _ {1}} ^ {\\mathbb {T}}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            388,
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+            411
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and the pseudo label is adjusted accordingly.",
+        "bbox": [
+            500,
+            416,
+            795,
+            431
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In Table 1, we run DAFormer [19] with either  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$  or  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  for UDA segmentation on GTAv  $\\rightarrow$  Cityscapes. Compared to  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$ ,  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  achieves an inferior mIoU of  $67.2\\%$  (a  $1.3\\%$  drop). But, interestingly, when ground-truth labels are used for the mixed images, the mIoU surpasses the original option by  $2.5\\%$ , with merely a  $0.9\\%$  mIoU lower than the supervised baseline. In other words, 'Focus on Your Target' improves the upper bound, but the models cannot achieve the upper bound because the pseudo labels deteriorate: it is a side effect of decreasing the proportion of training data from the source domain.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In summary, a strong algorithm for UDA shall be equipped with two critical abilities: (i) learning reliable semantics from the source domain, and (ii) adapting the learned semantics to the target domain. However, in the above self-training framework where a single teacher-student model is used, there seems a conflict between these two abilities, e.g., increasing the proportion of target-domain data strengthens the 'adapting ability' but weakens the 'learning ability', setting an obstacle to better performance. In what follows, we offer a solution by training two teacher-student models simultaneously.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Dual Teacher-Student Framework",
+        "text_level": 1,
+        "bbox": [
+            500,
+            771,
+            797,
+            786
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The proposed dual teacher-student (DTS) framework is illustrated in Figure 2. We denote the models used in the two teacher-student groups as  $f_1^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}_1^{\\mathrm{te}})$ ,  $f_1^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}_1^{\\mathrm{st}})$  and  $f_2^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}_2^{\\mathrm{te}})$ ,  $f_2^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}_2^{\\mathrm{st}})$ , respectively, where we use a subscript (1 or 2) to indicate the group ID. As described above, we expect the first teacher-student model to stick to learning reliable semantics from the source domain, while the",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "19029",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/5a90aed397753cfdb0bc0058bae7d6d413d1a52e33505fb5c137ed53118b81b0.jpg",
+        "image_caption": [
+            "Figure 2. An illustration of the proposed DTS framework, where we use Setting  $B$  as an example. The left and right parts describe the optimization of the first and second group models, respectively. The bottom-left part (in gray) corresponds to a single teacher-student framework where ClassMix is used for domain mixing, and the top part (in purple) shows the bidirectional learning strategy, i.e., models from the other group are used for pseudo label generation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            95,
+            483,
+            351
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3b4d1de1075aacaee15f96db0c92c1b48320d2c8e00a0d823b8000ad5352a52c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            483,
+            93,
+            885,
+            351
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/b7b6a05f8d4957771b931f1fe8dd97c0392d499ec26ef3879cf82ed6c747da80.jpg",
+        "image_caption": [
+            "Figure 3. An illustration of different combinations of training data. We use magenta to represent source-domain patches and two types of blue to represent target-domain patches from different images. In practice, the images are not partitioned into regular grids, but into semantic regions according to the (real or pseudo) labels."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            89,
+            439,
+            459,
+            570
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "second teacher-student model learns to 'Focus on Your Target' to enhance the adapting ability.",
+        "bbox": [
+            75,
+            672,
+            468,
+            703
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We achieve the goal by using different data proportions for the two groups. An illustration is provided in Figure 3. The first group remains the same as in the baseline, i.e., half of the training samples are simply source images and another half are ClassMix-ed images covering the source and target domains. Using the previously defined notations, we denote the combination as  $\\{\\mathbb{S},\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}$ . To increase the proportion of the target-domain data, we first change the mixture of data from  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$  to  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  (i.e., same as that used in the 'Focus on Your Target' trial), and then replace the pure source domain with  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$ . That said, we create two settings for data combination,  $\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}$  and  $\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle ,\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}$ . We name them Setting  $A$  and Setting  $B$  of the second group",
+        "bbox": [
+            75,
+            704,
+            470,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "throughout the remainder of this paper. Intuitively, the proportion of the target-domain data is increased from around  $25\\%$  in the first group (as well as the baselines) to around  $50\\% / 75\\%$  using Setting A/Setting B in the second group.",
+        "bbox": [
+            496,
+            439,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "There are two teacher models and two student models to be optimized. We perform iterative optimization and propose a bidirectional learning strategy so that each teacher-student model propagates information to the other by contributing to the generation of pseudo labels. The detailed training process is shown in Algorithm 1.",
+        "bbox": [
+            496,
+            500,
+            890,
+            590
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that, if  $f_{2,t}^{\\mathrm{te}}(\\cdot)$  is not used in Step 2 (i.e., all pseudo labels are generated using  $f_{1,t+1}^{\\mathrm{te}}(\\cdot)$ ), the information is only propagated from the first teacher-student model to the second one, hence the optimization strategy degenerates from bidirectional to unidirectional. The advantage of the bidirectional strategy and other design choices will be diagnosed in the experimental section.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Technical Details",
+        "text_level": 1,
+        "bbox": [
+            500,
+            703,
+            666,
+            718
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Choosing the proper option for data combination. We compute the averaged confidence of pseudo labels generated by the corresponding teacher models,  $f_{1}^{\\mathrm{st}}(\\cdot)$  and  $f_{2}^{\\mathrm{te}}(\\cdot)$ . Following [48, 19],  $\\gamma$  is defined as the proportion of pixels with the max class score surpassing a given threshold,  $\\tau$ . For each training image  $\\mathbf{x}$ , we use  $\\gamma_{1}^{\\mathrm{st}}(\\mathbf{x})$  and  $\\gamma_{2}^{\\mathrm{te}}(\\mathbf{x})$  to denote the average  $\\gamma$  values over all pixels when the teacher models are  $f_{1}^{\\mathrm{st}}(\\cdot)$  and  $f_{2}^{\\mathrm{te}}(\\cdot)$ , respectively. Then, we estimate the chance that  $f_{2}^{\\mathrm{te}}(\\cdot)$  generates better pseudo labels than  $f_{1}^{\\mathrm{st}}(\\cdot)$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {P r o b} = \\mathbb {E} _ {\\mathbf {x} \\sim \\mathcal {D} ^ {\\mathbb {T}}} \\left[ \\mathbb {I} \\left(\\gamma_ {2} ^ {\\mathrm {t e}} (\\mathbf {x}) > \\gamma_ {1} ^ {\\mathrm {s t}} (\\mathbf {x})\\right) \\right], \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            565,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19030",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1: DTS: Dual Teacher-Student"
+        ],
+        "code_body": "Input: Source data  $\\{\\mathbf{x}^{\\mathbb{S}},\\mathbf{y}^{\\mathbb{S}}\\}$ , target data  $\\{\\mathbf{x}^{\\mathbb{T}}\\}$ , the total iteration number T;  \n1 repeat  \n2 Update  $f_{1,t+1}^{\\mathrm{te}}(\\cdot)$  using the EMA of  $f_{1,t}^{\\mathrm{st}}(\\cdot)$ ;  \n3 Get pseudo labels  $\\tilde{\\mathbf{y}}^{\\mathbb{T}}$  by  $f_{1,t+1}^{\\mathrm{te}}(\\cdot)$  and  $f_{2,t}^{\\mathrm{te}}(\\cdot)$ ;  \n4 Generate mixed data  $\\{\\mathbf{x}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle}\\}$ , and train  $f_{1,t+1}^{\\mathrm{st}}(\\cdot)$  on  $\\{\\mathbb{S},\\langle \\mathbb{S},\\mathbb{T}\\rangle\\}$ ;  \n5 Update  $f_{2,t+1}^{\\mathrm{te}}(\\cdot)$  using the EMA of  $f_{2,t}^{\\mathrm{st}}(\\cdot)$ ;  \n6 Get pseudo labels  $\\tilde{\\mathbf{y}}^{\\mathbb{T}}$  by  $f_{1,t+1}^{\\mathrm{st}}(\\cdot)$  and  $f_{2,t+1}^{\\mathrm{te}}$ ;  \n7 if Setting A: Generate data  $\\{\\mathbf{x}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle}\\}$ , and Train  $f_{2,t+1}^{\\mathrm{st}}(\\cdot)$  on  $\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle\\}$ ;  \n8 if Setting B: Generate data  $\\{\\mathbf{x}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{x}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle}\\}$ , and train  $f_{2,t+1}^{\\mathrm{st}}(\\cdot)$  on them;  \n9  $t \\gets t + 1$ ;  \n10 until  $t = T$ ;  \nReturn:  $f_{2,\\mathrm{T}}^{\\mathrm{st}}(\\cdot)$ .",
+        "bbox": [
+            78,
+            111,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbb{I}(\\cdot)$  is the indicator function that outputs 1 if the statement is true and 0 otherwise. Note that the estimation is performed individually for two training procedures using Setting  $A$  and Setting  $B$ . Finally, we choose the setting with a higher chance that  $f_{2}^{\\mathrm{te}}(\\cdot)$  is more confident because  $f_{2}^{\\mathrm{st}}(\\cdot)$  is eventually used for inference. We shall see in Section 4.3 that this criterion always leads to the better choice.",
+        "bbox": [
+            75,
+            422,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Generating the mask. In the domain mixing operation, we compute the mask  $\\mathbf{M}$  by choosing the class label of one image. If the  $\\langle \\mathbb{S},\\mathbb{T}\\rangle$  is used, the source image with groundtruth is chosen; if  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  is used, the image with a larger average value of  $\\gamma$  is chosen.",
+        "bbox": [
+            75,
+            529,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Generating pseudo labels. The details are slightly different between Setting  $A$  and Setting  $B$ . When the batch size is  $k$ , the number of target images used for the second group in Setting  $A$  and Setting  $B$  are  $2k$  and  $3k$ , respectively. For Setting  $A$ ,  $k$  pseudo labels used are generated by  $f_{1,t+1}^{\\mathrm{st}}(\\cdot)$  and other  $k$  by  $f_{2,t+1}^{\\mathrm{te}}(\\cdot)$ . For Setting  $B$ , the  $2k$  pseudo labels used in  $\\langle \\mathbb{T}, \\mathbb{T} \\rangle$  are generated by  $f_{1,t+1}^{\\mathrm{st}}(\\cdot)$  and the  $k$  labels used in  $\\langle \\mathbb{S}, \\mathbb{T} \\rangle$  are generated by  $f_{2,t+1}^{\\mathrm{te}}(\\cdot)$ .",
+        "bbox": [
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+            729
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            744,
+            209,
+            762
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Settings",
+        "text_level": 1,
+        "bbox": [
+            76,
+            770,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We train the models on a labeled source domain and an unlabeled target domain and test them on the target domain. We follow the convention to set the source domain to be a synthesized dataset (either GTAv [38] which contains 24,966 densely labeled training images at a resolution of  $1914 \\times 1052$  or SYNTHIA [39] which contains 9,400 densely labeled training images at a resolution of",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$1280 \\times 760$ ), and the target dataset to be a real dataset (Cityscapes [6] where only the finely-annotated subset is used, containing 2,975 training images and 500 validation images at a resolution of  $2048 \\times 1024$ ). Following the convention to report the mean IoU (mIoU) over 19 classes when GTAv is used as the source domain, and 13 or 16 classes when SYNTHIA is the source domain.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Training details. Our framework is applied to different self-training frameworks. Specifically, we follow the DAFformer series [19, 20, 21] where the encoder is a MiT-B5 model pre-trained on ImageNet-1K [7] and the decoder involves a context-aware feature fusion module. We train the framework on a single NVIDIA Tesla-V100 GPU for 40K iterations with a batch size of 2 for both groups. We use an AdamW optimizer [34] with learning rates of  $6 \\times 10^{-5}$  for the encoder and  $6 \\times 10^{-4}$  for the decoder, a weight decay of 0.01, and linear warm-up of the learning rate for the first 1.5K iterations. The input image size is always  $512 \\times 512$ . During the training phase, we apply random rescaling and cropping to the source and target data, as well as color jittering and Gaussian blur as strong augmentations for the mixed data. The EMA coefficient,  $\\lambda$ , is set to be 0.999. The pseudo-label confidence threshold,  $\\tau$ , is 0.968 as in [48].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison to the State-of-the-art Methods",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We compare DTS to state-of-the-art UDA approaches on the GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes benchmarks. Results are summarized in Table 2 and Table 3, respectively. We establish DTS upon three recently published works, namely, DAFormer [19], HRDA [20], and MIC [21].",
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+    {
+        "type": "text",
+        "text": "DTS reports consistent gains in terms of segmentation accuracy beyond all three baselines. On GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes (13 classes), the mIoU gains over DAFormer, HRDA, MIC are  $2.9\\%$ ,  $1.4\\%$ ,  $0.6\\%$  and  $4.0\\%$ ,  $1.0\\%$ ,  $1.1\\%$  respectively. The gain generally becomes smaller when the baseline is stronger, which is as expected. Specifically, when added to MIC, the previous best approach, DTS achieves new records on these benchmarks: a  $76.5\\%$  mIoU on GTAv  $\\rightarrow$  Cityscapes and  $67.8\\%$  and  $75.1\\%$  mIoUs on SYNTHIA  $\\rightarrow$  Cityscapes with 16 and 13 classes, respectively.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Comparison to FST. We compare DTS to another plugin approach, FST [8]. On DAFormer, the gains brought by FST on the two benchmarks (SYNTHIA using 13 classes) are  $1.0\\%$  and  $1.3\\%$ , while the numbers for DTS are  $2.9\\%$  and  $4.0\\%$ , respectively. That said, besides the contribution of FST that allows us to 'learn from future', the higher accuracy also owes to the design of the DTS framework that alleviates the conflict of learning and adapting.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Class-level analysis. We investigate which classes are best improved by DTS. On  $\\mathrm{GTAv} \\rightarrow \\mathrm{Cityscapes}$ , we detect two classes, sign and truck, on which the IoU gain on the three baselines is always higher than the mIoU gain. In the",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "19031",
+        "bbox": [
+            480,
+            944,
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/ef0dcb922cbca557a46b6e3a899db5448d828c49f361ef972ee3701613824f06.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 2. UDA segmentation accuracy (mIoU, %) on the GTAv→Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone."
+        ],
+        "table_body": "<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall</td><td>Fence</td><td>Pole</td><td>Light</td><td>Sign</td><td>Veg</td><td>Terrain</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Train</td><td>Motor</td><td>Bike</td><td>mIoU</td></tr><tr><td>AdaptSegNet [49]</td><td>86.5</td><td>36.0</td><td>79.9</td><td>23.4</td><td>23.3</td><td>23.9</td><td>35.2</td><td>14.8</td><td>83.4</td><td>33.3</td><td>75.6</td><td>58.5</td><td>27.6</td><td>73.7</td><td>32.5</td><td>35.4</td><td>3.9</td><td>30.1</td><td>28.1</td><td>42.4</td></tr><tr><td>PatchAligne [50]</td><td>92.3</td><td>51.9</td><td>82.1</td><td>29.2</td><td>25.1</td><td>24.5</td><td>33.8</td><td>33.0</td><td>82.4</td><td>32.8</td><td>82.2</td><td>58.6</td><td>27.2</td><td>84.3</td><td>33.4</td><td>46.3</td><td>2.2</td><td>29.5</td><td>32.3</td><td>46.5</td></tr><tr><td>FDA [56]</td><td>92.5</td><td>53.3</td><td>82.4</td><td>26.5</td><td>27.6</td><td>36.4</td><td>40.6</td><td>38.9</td><td>82.3</td><td>39.8</td><td>78.0</td><td>62.6</td><td>34.4</td><td>84.9</td><td>34.1</td><td>53.1</td><td>16.9</td><td>27.7</td><td>46.4</td><td>50.5</td></tr><tr><td>DACS [48]</td><td>89.9</td><td>39.7</td><td>87.9</td><td>39.7</td><td>39.5</td><td>38.5</td><td>46.4</td><td>52.8</td><td>88.0</td><td>44.0</td><td>88.8</td><td>67.2</td><td>35.8</td><td>84.5</td><td>45.7</td><td>50.2</td><td>0.0</td><td>27.3</td><td>34.0</td><td>52.1</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>56.0</td><td>79.7</td><td>46.3</td><td>44.8</td><td>45.6</td><td>53.5</td><td>53.5</td><td>88.6</td><td>45.2</td><td>82.1</td><td>70.7</td><td>39.2</td><td>88.8</td><td>45.5</td><td>50.4</td><td>1.0</td><td>48.9</td><td>56.4</td><td>57.5</td></tr><tr><td>DAP [23]</td><td>94.5</td><td>63.1</td><td>89.1</td><td>29.8</td><td>47.5</td><td>50.4</td><td>56.7</td><td>58.7</td><td>89.5</td><td>50.2</td><td>87.0</td><td>73.6</td><td>38.6</td><td>91.3</td><td>50.2</td><td>52.9</td><td>0.0</td><td>50.2</td><td>63.5</td><td>59.8</td></tr><tr><td>CPSL [30]</td><td>92.3</td><td>59.9</td><td>84.9</td><td>45.7</td><td>29.7</td><td>52.8</td><td>61.5</td><td>59.5</td><td>87.9</td><td>41.6</td><td>85.0</td><td>73.0</td><td>35.5</td><td>90.4</td><td>48.7</td><td>73.9</td><td>26.3</td><td>53.8</td><td>53.9</td><td>60.8</td></tr><tr><td>DAFormer [19]</td><td>95.7</td><td>70.2</td><td>89.4</td><td>53.5</td><td>48.1</td><td>49.6</td><td>55.8</td><td>59.4</td><td>89.9</td><td>47.9</td><td>92.5</td><td>72.2</td><td>44.7</td><td>92.3</td><td>74.5</td><td>78.2</td><td>65.1</td><td>55.9</td><td>61.8</td><td>68.3</td></tr><tr><td>DAFormer+FST [8]</td><td>95.3</td><td>67.7</td><td>89.3</td><td>55.5</td><td>47.1</td><td>50.1</td><td>57.2</td><td>58.6</td><td>89.9</td><td>51.0</td><td>92.9</td><td>72.7</td><td>46.3</td><td>92.5</td><td>78.0</td><td>81.6</td><td>74.4</td><td>57.7</td><td>62.6</td><td>69.3</td></tr><tr><td>DAFormer+CAMix [62]</td><td>96.0</td><td>73.1</td><td>89.5</td><td>53.9</td><td>50.8</td><td>51.7</td><td>58.7</td><td>64.9</td><td>90.0</td><td>51.2</td><td>92.2</td><td>71.8</td><td>44.0</td><td>92.8</td><td>78.7</td><td>82.3</td><td>70.9</td><td>54.1</td><td>64.3</td><td>70.0</td></tr><tr><td>DAFormer+DTS (ours)</td><td>96.8</td><td>76.0</td><td>90.0</td><td>56.5</td><td>50.1</td><td>51.9</td><td>57.4</td><td>65.1</td><td>90.5</td><td>50.5</td><td>92.4</td><td>73.5</td><td>46.9</td><td>93.0</td><td>80.4</td><td>85.2</td><td>74.0</td><td>58.7</td><td>63.5</td><td>71.2</td></tr><tr><td>HRDA [20]</td><td>96.4</td><td>74.4</td><td>91.0</td><td>61.6</td><td>51.5</td><td>57.1</td><td>63.9</td><td>69.3</td><td>91.3</td><td>48.4</td><td>94.2</td><td>79.0</td><td>52.9</td><td>93.9</td><td>84.1</td><td>85.7</td><td>75.9</td><td>63.9</td><td>67.5</td><td>73.8</td></tr><tr><td>HRDA+DTS (ours)</td><td>96.7</td><td>76.3</td><td>91.3</td><td>60.7</td><td>55.9</td><td>59.9</td><td>67.3</td><td>72.5</td><td>91.8</td><td>50.1</td><td>94.4</td><td>80.7</td><td>56.8</td><td>94.4</td><td>86.0</td><td>86.0</td><td>73.9</td><td>65.7</td><td>68.4</td><td>75.2</td></tr><tr><td>MIC [21]</td><td>97.4</td><td>80.1</td><td>91.7</td><td>61.2</td><td>56.9</td><td>59.7</td><td>66.0</td><td>71.3</td><td>91.7</td><td>51.4</td><td>94.3</td><td>79.8</td><td>56.1</td><td>94.6</td><td>85.4</td><td>90.3</td><td>80.4</td><td>64.5</td><td>68.5</td><td>75.9</td></tr><tr><td>MIC+DTS (ours)</td><td>97.0</td><td>80.4</td><td>91.8</td><td>60.6</td><td>58.7</td><td>61.7</td><td>67.9</td><td>73.2</td><td>92.0</td><td>45.4</td><td>94.3</td><td>81.3</td><td>58.7</td><td>95.0</td><td>87.9</td><td>90.7</td><td>82.2</td><td>65.7</td><td>69.0</td><td>76.5</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/529f991b714207830c8cf0f7ec73ce115d88878fc3653a3d104f3355c4f5e898.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3. UDA segmentation accuracy (mIoU, %) on the SYNTHIA  $\\rightarrow$ Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone. The mIoU and mIoU* columns denote the averaged IoU over 16 and 13 classes, where the latter does not contain the classes marked with * ."
+        ],
+        "table_body": "<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall*</td><td>Fence*</td><td>Pole*</td><td>Light</td><td>Sign</td><td>Veg</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Bus</td><td>Motor</td><td>Bike</td><td>mIoU</td><td>mIoU*</td></tr><tr><td>PatchAlign [50]</td><td>82.4</td><td>38.0</td><td>78.6</td><td>8.7</td><td>0.6</td><td>26.0</td><td>3.9</td><td>11.1</td><td>75.5</td><td>84.6</td><td>53.5</td><td>21.6</td><td>71.4</td><td>32.6</td><td>19.3</td><td>31.7</td><td>40.0</td><td>46.5</td></tr><tr><td>AdaptSegNet [49]</td><td>84.3</td><td>42.7</td><td>77.5</td><td>-</td><td>-</td><td>-</td><td>4.7</td><td>7.0</td><td>77.9</td><td>82.5</td><td>54.3</td><td>21.0</td><td>72.3</td><td>32.2</td><td>18.9</td><td>32.3</td><td>-</td><td>46.7</td></tr><tr><td>FDA [56]</td><td>79.3</td><td>35.0</td><td>73.2</td><td>-</td><td>-</td><td>-</td><td>19.9</td><td>24.0</td><td>61.7</td><td>82.6</td><td>61.4</td><td>31.1</td><td>83.9</td><td>40.8</td><td>38.4</td><td>51.1</td><td>-</td><td>52.5</td></tr><tr><td>DACS [48]</td><td>80.6</td><td>25.1</td><td>81.9</td><td>21.5</td><td>2.9</td><td>37.2</td><td>22.7</td><td>24.0</td><td>83.7</td><td>90.8</td><td>67.6</td><td>38.3</td><td>82.9</td><td>38.9</td><td>28.5</td><td>47.6</td><td>48.3</td><td>54.8</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>45.7</td><td>84.6</td><td>37.1</td><td>0.6</td><td>44.0</td><td>54.6</td><td>37.0</td><td>88.1</td><td>84.4</td><td>74.2</td><td>24.3</td><td>88.2</td><td>51.1</td><td>40.5</td><td>45.6</td><td>55.5</td><td>62.0</td></tr><tr><td>DAP [23]</td><td>84.2</td><td>46.5</td><td>82.5</td><td>35.1</td><td>0.2</td><td>46.7</td><td>53.6</td><td>45.7</td><td>89.3</td><td>87.5</td><td>75.7</td><td>34.6</td><td>91.7</td><td>73.5</td><td>49.4</td><td>60.5</td><td>59.8</td><td>64.3</td></tr><tr><td>CPSL [30]</td><td>87.2</td><td>43.9</td><td>85.5</td><td>33.6</td><td>0.3</td><td>47.7</td><td>57.4</td><td>37.2</td><td>87.8</td><td>88.5</td><td>79.0</td><td>32.0</td><td>90.6</td><td>49.4</td><td>50.8</td><td>59.8</td><td>57.9</td><td>65.3</td></tr><tr><td>DAFormer [19]</td><td>84.5</td><td>40.7</td><td>88.4</td><td>41.5</td><td>6.5</td><td>50.0</td><td>55.0</td><td>54.6</td><td>86.0</td><td>89.8</td><td>73.2</td><td>48.2</td><td>87.2</td><td>53.2</td><td>53.9</td><td>61.7</td><td>60.9</td><td>67.4</td></tr><tr><td>DAFormer+FST [8]</td><td>88.3</td><td>46.1</td><td>88.0</td><td>41.7</td><td>7.3</td><td>50.1</td><td>53.6</td><td>52.5</td><td>87.4</td><td>91.5</td><td>73.9</td><td>48.1</td><td>85.3</td><td>58.6</td><td>55.9</td><td>63.4</td><td>61.9</td><td>68.7</td></tr><tr><td>DAFormer+CAMix [62]</td><td>87.4</td><td>47.5</td><td>88.8</td><td>-</td><td>-</td><td>-</td><td>55.2</td><td>55.4</td><td>87.0</td><td>91.7</td><td>72.0</td><td>49.3</td><td>86.9</td><td>57.0</td><td>57.5</td><td>63.6</td><td>-</td><td>69.2</td></tr><tr><td>DAFormer+DTS (ours)</td><td>88.5</td><td>51.4</td><td>88.0</td><td>37.2</td><td>4.8</td><td>51.4</td><td>59.4</td><td>59.0</td><td>88.1</td><td>92.7</td><td>71.3</td><td>51.3</td><td>89.2</td><td>67.7</td><td>58.4</td><td>62.8</td><td>63.8</td><td>71.4</td></tr><tr><td>HRDA [20]</td><td>85.2</td><td>47.7</td><td>88.8</td><td>49.5</td><td>4.8</td><td>57.2</td><td>65.7</td><td>60.9</td><td>85.3</td><td>92.9</td><td>79.4</td><td>52.8</td><td>89.0</td><td>64.7</td><td>63.9</td><td>64.9</td><td>65.8</td><td>72.4</td></tr><tr><td>HRDA+DTS (ours)</td><td>88.5</td><td>53.1</td><td>88.7</td><td>44.0</td><td>5.8</td><td>59.2</td><td>68.3</td><td>60.7</td><td>87.7</td><td>93.4</td><td>79.5</td><td>46.4</td><td>91.3</td><td>64.2</td><td>66.8</td><td>65.9</td><td>66.5</td><td>73.4</td></tr><tr><td>MIC [21]</td><td>86.6</td><td>50.5</td><td>89.3</td><td>47.9</td><td>7.8</td><td>59.4</td><td>66.7</td><td>63.4</td><td>87.1</td><td>94.6</td><td>81.0</td><td>58.9</td><td>90.1</td><td>61.9</td><td>67.1</td><td>64.3</td><td>67.3</td><td>74.0</td></tr><tr><td>MIC+DTS (ours)</td><td>89.1</td><td>54.9</td><td>89.0</td><td>39.1</td><td>8.7</td><td>61.6</td><td>67.4</td><td>64.3</td><td>88.8</td><td>94.0</td><td>82.2</td><td>60.7</td><td>89.6</td><td>62.6</td><td>68.5</td><td>64.9</td><td>67.8</td><td>75.1</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Appendix material, we show that these classes suffer larger variations between the source-domain and target-domain appearances, and hence the learned features are more difficult to transfer. They are largely benefited by the 'Focus on Your Target' ability of DTS.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Visualization. We visualize the segmentation results of DAFormer and DAFormer+DTS in Figure 4. For the real images, the advantage of DTS is significant on the classes that are easily confused with others (e.g., sidewalk which is visually similar to road) or suffer large domain shifts (e.g., sign or truck). For the mixed images, we find that the baseline model is easily confused by the unusual stitching and/or discontinuous textures because it has never seen such pat",
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+    {
+        "type": "text",
+        "text": "terns in the source domain – in such cases, the model of the second group is generally better and sometimes it can propagate the advantages to the model of the first group, revealing the advantage of bidirectional learning.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Diagnostic Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablative studies. We first diagnose the proposed approach by ablating the contribution of three components, namely, applying the dual teacher-student (DTS) framework, increasing the proportion of data from the target domain (i.e., 'Focus on Your Target'), and adopting the bidirectional learning strategy. Results are summarized in Table 4. Note that some combinations are not valid, e.g.,",
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+        "text": "19032",
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+    {
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+        "img_path": "images/247cd9150a8a3c10de4c58ed9953a63866f5b80ddc0acf2de68a4126b31e8e4f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/894bd4c2418c51fd55435c71de9c22abf7bfb665a4eb865e290f7f050b96754a.jpg",
+        "image_caption": [],
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+    {
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+            "DTS (1st group)"
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+        "image_caption": [
+            "DTS  $(2^{\\mathrm{nd}}$  group)"
+        ],
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+    {
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+        "img_path": "images/238a5059446e64d46a20119e146c049ba96b45effaf7997cfde77903e15d5b2e.jpg",
+        "image_caption": [
+            "ground truth",
+            "Figure 4. Visualization of the segmentation results of DAFormer [19] and DTS. The top two rows display two real images and the bottom two rows display two synthesized images from  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  . In each group, the first example is from GTAv  $\\rightarrow$  Cityscapes and the second one is from SYNTHIA  $\\rightarrow$  Cityscapes. The white, dashed circles highlight the regions that are significantly improved by DTS."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/b099781a290c34ed5bc61a3c9bae2bbbdb1b0c306e7444a4a641400112137d8d.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 4. Ablative studies of DTS with respect to the UDA segmentation accuracy (mIoU, %) on both benchmarks. All these experiments are based on DAFformer [19]. For SYNTHIA→Cityscapes, the mIoUs are computed over 16 classes. Note that DTS alone (without the latter two options) is equivalent to the baseline (the leftmost column) and is simply ignored in the table."
+        ],
+        "table_body": "<table><tr><td>Setting</td><td colspan=\"5\">Choice and Accuracy</td></tr><tr><td>Dual Teacher-Student ‘Focus on Your Target’</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td></tr><tr><td>Bidirectional Learning</td><td></td><td></td><td>✓</td><td>✓</td><td></td></tr><tr><td>GTAv→Cityscapes</td><td>68.3</td><td>67.2</td><td>69.7</td><td>68.6</td><td>71.2</td></tr><tr><td>SYNTHIA→Cityscapes</td><td>60.9</td><td>58.4</td><td>63.3</td><td>61.2</td><td>63.7</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "solely applying DTS (without adjusting the proportion of training data nor applying bidirectional learning) does not make any difference from the baseline; also, bidirectional learning must be built upon DTS.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "From Columns 1-3, one can learn the importance of the DTS framework. When DTS is not established, simply increasing the proportion of target data (Col 2) incurs an accuracy drop on both GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes. This validates our motivation, i.e., there is a conflict between the learning and adapting abilities. However, after the dual teacher-student framework is established (Col 3, where the first teacher-student group focuses on learning and the second group focuses on adapting), the conflict is weakened and the accuracy gain becomes clear (1.6% on GTAv  $\\rightarrow$  Cityscapes and 2.4% on SYNTHIA  $\\rightarrow$  Cityscapes).",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/eb1bbb3e5318eb6825f57515e72623695133ef6d4288be5fa358aa111646d473.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 5. The results of DTS with different data mixing options. For SYNTHIA  $\\rightarrow$  Cityscapes, the mIoUs are computed over 16 classes."
+        ],
+        "table_body": "<table><tr><td colspan=\"2\">Baseline</td><td>DAFormer</td><td>HRDA</td><td>MIC</td></tr><tr><td rowspan=\"2\">GTAv</td><td>Setting A</td><td>70.3</td><td>74.7</td><td>76.5</td></tr><tr><td>Setting B</td><td>71.2</td><td>75.2</td><td>76.2</td></tr><tr><td rowspan=\"2\">SYNTHIA</td><td>Setting A</td><td>63.8</td><td>66.5</td><td>67.8</td></tr><tr><td>Setting B</td><td>61.2</td><td>66.0</td><td>67.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "From Columns 3-5, one can observe the contribution of 'Focus on Your Target' (i.e., increasing the proportion of target data) and bidirectional learning on top of the DTS framework. The best practice is obtained when all the modules are used (Col 5), aligning with the results reported in Tables 2 and 3. Interestingly, when bidirectional learning is adopted alone (Col 4), the accuracy gain is much smaller than that of using 'Focus on Your Target' alone, because the two groups are using the same proportion of data mixing, and thus the bidirectional learning carries limited complementary information.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Choose the option for data combination. We validate that the data combination option can be chosen by comparing the pseudo-label confidence, as described in Section 3.4. We plot the Prob curves throughout training procedure of Setting  $A$  and Setting  $B$  in Figure 5. On GTAv→Cityscapes, the Prob value of Setting  $B$  is eventually higher than that of Setting  $A$ , and DTS with Setting  $B$  outperforms DTS with Setting  $A$  by a  $0.9\\%$  mIoU (see Table 5). However, on SYNTHIA→Cityscapes, the Prob value of Setting  $A$  is always higher than that of Setting",
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+    {
+        "type": "page_number",
+        "text": "19033",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/0ba16677835052872464769e60c20a30a41ff4bc9b17dcf571ea892c6aa53a80.jpg",
+        "image_caption": [
+            "Figure 5. The curves of Prob computed on the GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes benchmarks. DAFormer is used as the baseline. These curves suggest that, on DAFormer, Setting  $B$  is better for GTAv  $\\rightarrow$  Cityscapes while Setting  $A$  is better for SYNTHIA  $\\rightarrow$  Cityscapes."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+    },
+    {
+        "type": "table",
+        "img_path": "images/9bc5e4944c1804bdafa5260eb79431eba523f70dfc083273ed8200e9fc663c02.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Options</td><td>GTAv</td><td>SYNTHIA</td></tr><tr><td>{&lt;T,T&gt;}</td><td>69.1</td><td>61.1</td></tr><tr><td>{&lt;S,T&gt;}</td><td>69.3</td><td>59.4</td></tr><tr><td>{S, &lt;T,T&gt;}</td><td>70.3</td><td>63.8</td></tr><tr><td>{&lt;S,T&gt;, &lt;T,T&gt;}</td><td>71.2</td><td>61.2</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$B$ , and DTS with Setting  $A$  outperforms DTS with Setting  $B$  by a  $2.4\\%$  mIoU. Table 5 also shows the segmentation accuracy on the other two baselines. All choices of advantageous results align with the aforementioned criterion. From an intuitive view, Setting  $B$  has a smaller portion of source data, so it works better in the GTAv  $\\rightarrow$  Cityscapes scenario because GTAv has a smaller domain gap to Cityscapes than SYNTHIA, which can be validated by vanilla transfer experiments (GTAv  $\\rightarrow$  Cityscapes:  $46.2\\%$ , SYNTHIA  $\\rightarrow$  Cityscapes:  $41.3\\%$ ).",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Except for Setting  $A$  and Setting  $B$ , there are two other options to increase the focus on the target domain as well, namely  $\\{\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}$  and  $\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}$ . The two options do not include any mixing data and have a disadvantage compared to the previous two combinations.  $\\{\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}$  means that the second teacher-student group achieves the ability of learning only from the pseudo labels provided by  $f_1^{\\mathrm{st}}(\\mathbf{x};\\pmb {\\theta}_1^{\\mathrm{st}})$ . As a result, noise can easily persist without accurate supervision from the source data.  $\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}$  has a similar data proportion as  $\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}$  but cannot solve the problem of inconsistency between the training and testing data. Using  $\\langle \\mathbb{T},\\mathbb{T}\\rangle$  as the training domain is an effective way to bridge the gap between the training and testing phases. Therefore, the two combinations containing two different types of data used in DTS are more suitable for balancing the learning and adapting abilities.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Models for pseudo label generation. We study the impact of different models for generating pseudo labels. Re",
+        "bbox": [
+            75,
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+            468,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/a89a0478d64b184ff68c15bea0ec42ca8633468bdf40ccf010b06b2fc35e263a.jpg",
+        "table_caption": [
+            "Table 6. The results of DTS with more data mixing options. We show the mIoU of the 16 classes in SYNTHIA and make this comparison based on the DAFourner baseline."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Group #1</td><td colspan=\"2\">Group #2</td><td rowspan=\"2\">mIoU</td></tr><tr><td>f2,st(·)</td><td>f2,te(·)</td><td>f1,t+1(·)</td><td>f1,t+1(·)</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>68.5†</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>69.0</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>69.5</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>70.2</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>71.3</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2adccb4008805c5688581ee646ec9b4385ededd066d11673b467227de281b257.jpg",
+        "table_caption": [
+            "Table 7. UDA segmentation accuracy (mIoU, %) using different models to generate pseudo labels on GTAv→Citysacpes. †: In the first row, each group only uses the teacher model from the other group; in other cases, each group also uses its own teacher models (not presented in the table)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">GTAv→City.</td><td colspan=\"2\">SYNTHIA→City.</td></tr><tr><td>DACS</td><td>DAFormer</td><td>DACS</td><td>DAFormer</td></tr><tr><td>w/o DTS</td><td>53.9</td><td>56.0</td><td>54.2</td><td>53.5</td></tr><tr><td>w DTS</td><td>55.2</td><td>59.9</td><td>56.6</td><td>56.9</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 8. UDA segmentation accuracy (mIoU, %) on two CNN-based backbones and two benchmarks.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "sults are summarized in Table 7. When each teacher-student group only uses the teacher model from another group (the first row), there is almost no accuracy gain (the baseline is  $68.3\\%$ ), indicating the necessity of the supervision signals from its own teacher.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Then, we discuss the situations where each group uses its teacher and one model from the other group. For the second teacher-student group, using  $f_{1,t+1}^{\\mathrm{st}}(\\cdot)$  as the teacher is superior to using  $f_{1,t+1}^{\\mathrm{te}}(\\cdot)$ , because the former model is optimized one more iteration and thus produces better semantics (i.e., 'learning from future'). For the first teacher-student group, only models from the current iteration of the second group can be used, and  $f_{2,t}^{\\mathrm{te}}(\\cdot)$  always works better than  $f_{2,t}^{\\mathrm{st}}(\\cdot)$ , implying the advantage of EMA.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "DTS applied to other backbones. To show that DTS adapts to different network backbones (e.g., CNNs), we follow the previous approaches [56, 48, 23] to inherit a ResNet101 [14] pre-trained on ImageNet and MSCOCO and train it using DeepLabV2 [2]. The other settings remain unchanged. Results are listed in Table 8. Still, DTS brings consistent accuracy gains, improving DACs and DAfromer by  $1.3\\%$  and  $3.9\\%$  on  $\\mathrm{GTAv}\\rightarrow \\mathrm{Cityscapes}$ , and by  $2.4\\%$  and  $3.4\\%$  on SYNTHIA  $\\rightarrow$  Cityscapes. These experiments validate that DTS is a generalized UDA framework that does not rely on specific network architectures.",
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+    },
+    {
+        "type": "text",
+        "text": "Comparison of training time and compute. DTS trains two teacher-student groups, so the computational cost is about  $2 \\times$  of the baseline (e.g., on a single V100 GPU, DAFormer/DTS needs 13.5/30 hours). The inference cost remains unchanged. We further compare DTS and DAFormer under the same training cost. DTS with half (20K) iterations achieves favorable accuracy (68.6% and",
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "19034",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/b4f582a41f3f62bccf0ba7935966fec8f9b2a148ad9d320f736b0e078dcb755a.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 9. UDA segmentation accuracy (mIoU, %) on more driving datasets. 'BDD', 'IDD', 'FZ', 'DZ', and 'CS' for Berkeley Driving Dataset, India Driving Dataset, Foggy Zurich, Dark Zurich, and Cityscapes, respectively. Baselines are DAFormer except for the last two columns in CS2DZ, which are HRDA and MIC. *: are numbers inherited from [20, 21]."
+        ],
+        "table_body": "<table><tr><td></td><td>GTAv2BDD</td><td>GTAv2IDD</td><td>CS2BDD</td><td>CS2IDD</td></tr><tr><td>Baseline</td><td>46.3</td><td>54.7</td><td>53.7</td><td>51.6</td></tr><tr><td>DTS</td><td>53.6</td><td>59.6</td><td>57.5</td><td>56.1</td></tr><tr><td></td><td>CS2FZ</td><td colspan=\"3\">CS2DZ</td></tr><tr><td>Baseline</td><td>39.7</td><td>34.0</td><td>42.1*</td><td>43.6*</td></tr><tr><td>DTS</td><td>40.4</td><td>37.6</td><td>45.2</td><td>45.6</td></tr></table>",
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+        "type": "text",
+        "text": "61.8% on GTAv  $\\rightarrow$  Cityscapes and SYNTHIA  $\\rightarrow$  Cityscapes) over DAFormer with full (40K) iterations (68.3% and 60.9%), meanwhile, DTS with full (40K) iterations reports 71.2% and 63.8%, surpassing DAFormer with doubled (80K) iterations (69.3% and 61.2%).",
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+        "type": "text",
+        "text": "Performance on more driving datasets. We conduct experiments from synthesized and real datasets to more driving datasets, i.e., Berkeley Driving Dataset (BDD) [57], India Driving Dataset (IDD) [52], Foggy Zurich (FZ) [41], and Dark Zurich (DZ) [42]. The comparable results on validation sets of target domain datasets are summarized in Table 9. DTS reports consistent improvement in these transfer scenarios. On the test set of CS2DZ, DTS is also superior to DAformer  $(54.2\\%$  vs  $53.8\\%)$  and HRDA  $(58.9\\%$  vs  $55.9\\%)$ .",
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+    {
+        "type": "text",
+        "text": "4.4. Semi-supervised Semantic Segmentation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Dataset. As a generalized self-training framework, DTS can also be applied to semi-supervised segmentation. We perform semi-supervised segmentation on the widely used PASCAL VOC dataset [9], which comprises 20 object classes and a background class. The training, validation, and testing sets contain 1,464, 1,449, and 1,456 images, respectively. To align with prior works, we use the augmented set, which contains 10,582 images, as the complete training set. During the training, we apply random flipping and cropping to augment the image data and resize the image to  $513 \\times 513$  before feeding it to the models.",
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+        "type": "text",
+        "text": "Implementation. We perform all experiments using the DeepLabV3+ [3] network with a ResNet-101 backbone pretrained on ImageNet. An SGD optimizer, with a learning rate of 0.0001 for the encoder and 0.001 for the decoder, and a weight decay of 0.0001, is used. The batch size of both labeled and unlabeled data is 16 for each group teacher-student. We train the models for 40 epochs and report the average of three runs for all the results. Since there is no domain gap between the labeled and unlabeled parts, only a dual teacher-student framework and bidirectional learning are applied in the semi-supervised experiments.",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 10. Semi-supervised segmentation accuracy (mIoU, %) on PASCAL VOC."
+        ],
+        "table_body": "<table><tr><td>Methods</td><td>1/16 (662)</td><td>1/8 (1323)</td><td>1/4 (2646)</td></tr><tr><td>Mean Teacher [46]</td><td>71.3</td><td>75.4</td><td>76.5</td></tr><tr><td>FST [8]</td><td>73.9</td><td>76.1</td><td>78.1</td></tr><tr><td>USRN [13]</td><td>72.3</td><td>-</td><td>-</td></tr><tr><td>PS-MT [32]</td><td>75.5</td><td>78.2</td><td>78.7</td></tr><tr><td>U²PL [54]</td><td>77.2</td><td>79.0</td><td>79.3</td></tr><tr><td>DTS (ours)</td><td>74.8</td><td>77.1</td><td>77.3</td></tr><tr><td>U²PL + DTS (ours)</td><td>78.9</td><td>80.1</td><td>80.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Comparison. The segmentation results are summarized in Table 10. Using  $1/16$ ,  $1/8$ ,  $1/4$  labeled data, DTS produces consistent accuracy gains of  $3.5\\%$ ,  $1.7\\%$ ,  $0.8\\%$  over the Mean Teacher baseline [46], and  $1.7\\%$ ,  $1.1\\%$ ,  $1.1\\%$  over the  $\\mathrm{U}^2\\mathrm{PL}$  baseline [54]. This validates that semi-supervised learning also benefits from bidirectional learning which effectively improves the ability to learn from the pseudo labels generated from other groups.",
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+        "text": "5. Conclusions",
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+        "type": "text",
+        "text": "In this paper, we study the UDA segmentation problem from the perspective of endowing the model with twofold abilities, i.e., learning from the reliable semantics, and adapting to the target domain. We show that these two abilities can conflict with each other in a single teacher-student model, and hence we propose a dual teacher-student (DTS) framework, where the two models stick to the 'learning ability' and 'adapting ability', respectively. Specifically, the second model learns to 'focus on your target' to improve its accuracy in the target domain. We further design a bidirectional learning strategy to facilitate the two models to communicate via generating pseudo labels. We validate the effectiveness of DTS and set new records on two standard UDA segmentation benchmarks.",
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+    {
+        "type": "text",
+        "text": "As the accuracy on the two benchmarks fast approaches the supervised baseline (e.g., a  $77.8\\%$  mIoU on Cityscapes), we look forward to building larger and higher-quality synthesized datasets to break through the baseline. This is of value to real-world applications, as synthesized data can be generated at low costs. We expect that the proposed methodology can be applied to other scenarios such as domain generalization, with the second group focusing on a generic, unbiased feature space.",
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+        "type": "text",
+        "text": "Acknowledgment This work was supported by NSFC under Contract U20A20183 and 62021001. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC, and the Supercomputing Center of the USTC.",
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+        "type": "text",
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+            "content": "Xinyue Huo\\(^{1,2}\\) Lingxi Xie\\(^{2}\\) Wengang Zhou\\(^{1}\\) Houqiang Li\\(^{1}\\) Qi Tian\\(^{2*}\\)  \n\\(^{1}\\)University of Science and Technology of China \\({}^{2}\\)Huawei Inc."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.29,
+                0.242,
+                0.681,
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+            ],
+            "angle": 0,
+            "content": "xinyueh@mail.ustc.edu.cn 198808xc@gmail.com"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.293,
+                0.26,
+                0.679,
+                0.275
+            ],
+            "angle": 0,
+            "content": "{zhwg, lihq} \\(@\\) ustc.edu.cn tian.qil@huawei.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.309,
+                0.314,
+                0.326
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.343,
+                0.474,
+                0.691
+            ],
+            "angle": 0,
+            "content": "We study unsupervised domain adaptation (UDA) for semantic segmentation. Currently, a popular UDA framework lies in self-training which endows the model with two-fold abilities: (i) learning reliable semantics from the labeled images in the source domain, and (ii) adapting to the target domain via generating pseudo labels on the unlabeled images. We find that, by decreasing/increasing the proportion of training samples from the target domain, the 'learning ability' is strengthened/weakened while the 'adapting ability' goes in the opposite direction, implying a conflict between these two abilities, especially for a single model. To alleviate the issue, we propose a novel dual teacher-student (DTS) framework and equip it with a bidirectional learning strategy. By increasing the proportion of target-domain data, the second teacher-student model learns to 'Focus on Your Target' while the first model is not affected. DTS is easily plugged into existing self-training approaches. In a standard UDA scenario (training on synthetic, labeled data and real, unlabeled data), DTS shows consistent gains over the baselines and sets new state-of-the-art results of \\(76.5\\%\\) and \\(75.1\\%\\) mIoUs on GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes, respectively. The implementation is available at https://github.com/xinyuehuo/DTS."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.724,
+                0.21,
+                0.74
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.751,
+                0.47,
+                0.873
+            ],
+            "angle": 0,
+            "content": "Deep neural networks [28] have been proven effective in learning from labeled, in-domain visual data, but their ability to adapt to unlabeled data or unknown domains is often not guaranteed. We delve into this topic by studying the unsupervised domain adaptation (UDA) problem for semantic segmentation, where densely (pixel-wise) labeled data are available for the source domain but only unlabeled images are provided for the target domain. The setting is useful"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.311,
+                0.688,
+                0.378
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.515,
+                0.381,
+                0.593,
+                0.435
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.534,
+                0.435,
+                0.573,
+                0.445
+            ],
+            "angle": 0,
+            "content": "Target A"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.604,
+                0.381,
+                0.678,
+                0.435
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.616,
+                0.435,
+                0.657,
+                0.445
+            ],
+            "angle": 0,
+            "content": "Target B"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.312,
+                0.888,
+                0.376
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.71,
+                0.38,
+                0.888,
+                0.444
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.448,
+                0.686,
+                0.51
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.568,
+                0.511,
+                0.629,
+                0.52
+            ],
+            "angle": 0,
+            "content": "Ground Truth"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.447,
+                0.888,
+                0.51
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.774,
+                0.511,
+                0.822,
+                0.519
+            ],
+            "angle": 0,
+            "content": "DAFormer"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.52,
+                0.685,
+                0.595
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.522,
+                0.888,
+                0.584
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.791,
+                0.586,
+                0.814,
+                0.595
+            ],
+            "angle": 0,
+            "content": "DTS"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.6,
+                0.892,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Figure 1. Segmentation results on a test image from Cityscapes (the model is trained on GTAv). There are two traffic signs with different styles, where Target A is similar to the training data in the source domain while Target B is not. The baseline (DAFormer) gradually improves the accuracy on Target A but achieves the best accuracy on Target B in the midst (at 12K iterations). Our method, DTS, achieves good accuracy for both targets and the trend is more stable throughout the training process (see the curves)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.745,
+                0.892,
+                0.776
+            ],
+            "angle": 0,
+            "content": "in real-world applications where new domains emerge frequently but annotating them is a major burden."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The state-of-the-art UDA approaches for semantic segmentation are mostly built upon a self-training framework. It first learns semantics from labeled data in the source domain and then generates pseudo labels in the target domain, so that the model adapts to the target domain by fitting the pseudo labels. Conceptually, the two steps of self-training endow the model with two-fold abilities, namely, learning knowledge (semantics) from the source domain and adapt-"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.227,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding Author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19027"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.342,
+                0.106
+            ],
+            "angle": 0,
+            "content": "ing the knowledge to the target domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.107,
+                0.47,
+                0.318
+            ],
+            "angle": 0,
+            "content": "However, these two abilities can conflict with each other. Figure 1 shows an example of two targets of the same class (traffic sign), where Target \\( A \\) is close to the typical training samples in the source domain, while Target \\( B \\) has a quite different appearance. Using the default setting of DAFormer [19] (a UDA baseline), the recognition accuracy of Target \\( A \\) gradually increases while that of Target \\( B \\) grows first but eventually drops to 0. Interestingly, if one increases the proportion of training samples from the target domain, the recognition quality of Target \\( B \\) will be better while the recognition accuracy of some unexpected classes (e.g., sidewalk) may drop significantly (more details and examples can be found in the Appendix). The conflict sets an obstacle to achieving higher UDA accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.318,
+                0.471,
+                0.514
+            ],
+            "angle": 0,
+            "content": "The above analysis prompts us to design a dual teacher-student (DTS) framework. The key is to train two individual models (with different network weights) so that the aforementioned conflict is alleviated. DTS can be built upon most existing self-training approaches in three steps: (1) making two copies of the original teacher-student model, (2) increasing the proportion of training data from the target domain in the second group, and (3) applying a bidirectional learning strategy so that two models supervise each other via pseudo labels. DTS allows the system to pursue a stronger adapting ability (with the second model) meanwhile the learning ability (guaranteed by the first model) is mostly unaffected."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.515,
+                0.47,
+                0.711
+            ],
+            "angle": 0,
+            "content": "We conduct semantic segmentation experiments with the standard UDA setting. Two synthetic datasets with dense labels, GTAv [38] and SYNTHIA [39], are used as the source domains, and a real dataset with only images, Cityscapes [6], is used as the target domain. We establish the DTS framework upon three recent self-training baselines, namely, DAFormer [19], HRDA [20], and MIC [21]. DTS improves the segmentation accuracy in every single trial, demonstrating its generalized ability across baselines and datasets. In particular, when integrated with MIC, the prior state-of-the-art, DTS reports \\(76.5\\%\\) and \\(67.8\\%\\) mIoUs on GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes, respectively, setting new records for both benchmarks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.22,
+                0.74
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Unsupervised domain adaptation (UDA), the task of transferring semantics from labeled source domains to unlabeled target domains, has been widely studied for many computer vision fields, e.g., classification [33, 58, 51], object detection [15, 24, 45], face recognition [25, 18, 43], semantic segmentation [17, 60], etc."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We briefly review two representative UDA approaches for semantic segmentation. Adversarial learning [47, 49] reduces the gap between the source and target domains by confusing a discriminator trained to judge which domain"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.349
+            ],
+            "angle": 0,
+            "content": "the extracted visual features come from. It is closely related to style transfer methods [16, 55, 12, 56] that synthesize data to simulate the target domain. Self-training instead generates pseudo labels for the unlabeled target images and fits the model accordingly. There is a specific class of self-training methods [48, 10, 62] which further bridge the domain gap by creating mixed images that cover both domains [36, 1], inheriting benefits from style transferring. Many follow-up works [19, 20, 21], including this paper, were based on the self-training framework. Besides UDA, other data-efficient learning scenarios such as semi-supervised [22, 40] and few-shot [31, 35] learning also made use of self-training. Generating high-quality pseudo labels is crucial for self-training. Researchers developed various strategies, such as entropy minimization [4], class-balanced training [30], consistency regularization [21], auxiliary task learning [23, 53], etc., for this purpose."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.349,
+                0.893,
+                0.545
+            ],
+            "angle": 0,
+            "content": "A fundamental concept in self-training is teacher-student optimization. To boost the effect of teacher-student optimization, efforts were made in generating high-quality pseudo labels with stronger teacher models [46, 27, 29, 11] and/or preventing error transmission from the teacher model to the student model [26, 63, 22, 5]. There are also other improvements including using multiple student models [61], designing a better loss function [11], etc. Another closely related concept is co-training [37, 44], which facilitates cross-view consistency with a teacher-student loss. The idea of DTS is to alleviate the discrepancy between teacher and student models from different groups with an indirect consistency constraint."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.558,
+                0.649,
+                0.574
+            ],
+            "angle": 0,
+            "content": "3. Our Approach"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "We investigate the task of unsupervised domain adaptation (UDA) for semantic segmentation, where a labeled source domain \\(\\mathbb{S}\\) and an unlabeled target domain \\(\\mathbb{T}\\) are available. We denote the source dataset as \\(\\mathcal{D}^{\\mathbb{S}} = \\{(\\mathbf{x}_n^{\\mathbb{S}},\\mathbf{y}_n^{\\mathbb{S}})\\}_{n = 1}^{N_{\\mathbb{S}}}\\), where \\(\\mathbf{x}_n^{\\mathbb{S}}\\) is an image and \\(\\mathbf{y}_n^{\\mathbb{S}}\\) is the corresponding dense label map. The target dataset \\(\\mathcal{D}^{\\mathbb{T}}\\) is another set of images without labels, denoted as \\(\\{(x_{n}^{\\mathbb{T}})\\}_{n = 1}^{N_{\\mathbb{T}}}\\). The two domains share the same set of categories. The goal of UDA is to train a segmentation network \\(f(\\mathbf{x};\\pmb {\\theta})\\) that eventually works well in the target domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.734,
+                0.892,
+                0.825
+            ],
+            "angle": 0,
+            "content": "We first introduce a self-training baseline where a single teacher-student framework is established (Section 3.1). Then, we reveal a conflict when the model is facilitated to focus on the target domain (Section 3.2), which drives us to propose a dual teacher-student framework towards better UDA performance (Section 3.3)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.833,
+                0.783,
+                0.848
+            ],
+            "angle": 0,
+            "content": "3.1. Single Teacher-Student Baseline"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We start with a standard self-training (i.e., teacher-student) baseline which trains a teacher model and a student model denoted as \\( f^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}^{\\mathrm{te}}) \\) and \\( f^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}^{\\mathrm{st}}) \\), respectively."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19028"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.122
+            ],
+            "angle": 0,
+            "content": "The teacher model is updated using the exponential moving average (EMA) strategy [46]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.164,
+                0.132,
+                0.469,
+                0.15
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {\\theta} ^ {\\mathrm {t e}} \\leftarrow \\boldsymbol {\\theta} ^ {\\mathrm {t e}} \\times \\lambda + \\boldsymbol {\\theta} ^ {\\mathrm {s t}} \\times (1 - \\lambda), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.161,
+                0.469,
+                0.222
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) is a constant coefficient which is often close to 1. The student model is trained for segmentation in both the source and target domains. For the source images, semantic labels are available for supervised learning:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.19,
+                0.231,
+                0.469,
+                0.25
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} ^ {\\mathbb {S}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(f ^ {\\mathrm {s t}} \\left(\\mathbf {x} ^ {\\mathbb {S}}\\right), \\mathbf {y} ^ {\\mathbb {S}}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.26,
+                0.469,
+                0.32
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}_{\\mathrm{CE}}\\) denotes the pixel-wise cross-entropy loss. For the target images, the teacher model is used to generate a pseudo label \\(\\tilde{\\mathbf{y}}^{\\mathbb{T}}\\) for \\(\\mathbf{x}^{\\mathbb{T}}\\), and the pixel-wise loss function is computed in a similar way:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.33,
+                0.469,
+                0.35
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} ^ {\\mathbb {T}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(f ^ {\\mathrm {s t}} \\left(\\mathbf {x} ^ {\\mathbb {T}}\\right), \\tilde {\\mathbf {y}} ^ {\\mathbb {T}}\\right). \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.359,
+                0.469,
+                0.435
+            ],
+            "angle": 0,
+            "content": "The overall loss is written as \\(\\mathcal{L} = \\mathcal{L}^{\\mathbb{S}} + \\mathcal{L}^{\\mathbb{T}}\\). In practice, a balancing mechanism is applied [48, 19]: all pixel-wise loss terms computed on the target domain is multiplied by a factor of \\(\\gamma\\), which is the proportion of the pseudo-label confidence surpassing a given threshold, \\(\\tau\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.435,
+                0.469,
+                0.511
+            ],
+            "angle": 0,
+            "content": "Recently, a series of methods [48, 19, 20, 21] validated that introducing a mixed domain between the source and target domains is helpful for domain adaptation. A typical operation is named ClassMix [36] which samples mixed images by computing"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.521,
+                0.469,
+                0.543
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {x} _ {i, j} ^ {\\langle \\mathrm {S}, \\mathrm {T} \\rangle} = \\mathcal {M} \\left(\\mathbf {x} _ {i} ^ {\\mathrm {S}}, \\mathbf {x} _ {j} ^ {\\mathrm {T}}\\right) = \\mathbf {x} _ {i} ^ {\\mathrm {S}} \\odot \\mathbf {M} _ {i} ^ {\\mathrm {S}} + \\mathbf {x} _ {j} ^ {\\mathrm {T}} \\odot \\left(\\mathbf {1} - \\mathbf {M} _ {i} ^ {\\mathrm {S}}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.551,
+                0.469,
+                0.657
+            ],
+            "angle": 0,
+            "content": "where \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\) denotes a mixed domain, \\(\\odot\\) is element-wise multiplication, and \\(\\mathbf{M}^{\\mathbb{S}}\\) is a mask generated by randomly a few class-level masks from the \\(\\mathbf{y}^{\\mathbb{S}}\\). Accordingly, the target domain in Eqn (3) and the overall loss is replaced with the mixed domain. Note that pseudo labels are only computed for the target portion of the mixed images - we refer the reader to [36] for technical details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.666,
+                0.427,
+                0.683
+            ],
+            "angle": 0,
+            "content": "3.2. Conflict between Learning and Adapting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.689,
+                0.469,
+                0.764
+            ],
+            "angle": 0,
+            "content": "Although domain mixing improves the accuracy of UDA segmentation on several benchmarks, we observe that the trained model is easily biased towards the source domain and thus ignores the target domain to some extent. A typical example is shown in Figure 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We conjecture that it is the 'over-focus' on the source domain that prevents the model from achieving higher segmentation accuracy. To reveal this, we revisit the working mechanism of ClassMix. Compared to the original strategy that directly generates pseudo labels on the target images, ClassMix increases the proportion of data from the source domain (in a default setting of Eqn (4), an average of half target-domain pixels are replaced with source-domain pixels). This brings two differences. On the one hand, the"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.525,
+                0.09,
+                0.869,
+                0.17
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Label</td><td>{S, T}</td><td>{T, T}</td><td>Supervised</td></tr><tr><td>w/ pseudo labels</td><td>68.3</td><td>67.2</td><td>-</td></tr><tr><td>(pseudo acc.)</td><td>64.9</td><td>64.2</td><td>-</td></tr><tr><td>w/ ground-truth</td><td>74.4</td><td>76.9</td><td>77.8</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.499,
+                0.17,
+                0.892,
+                0.226
+            ],
+            "angle": 0,
+            "content": "Table 1. UDA segmentation mIoU (%) using DAFourner [19] on the GTAv→Cityscapes benchmark with different options. An italic number indicates a result that uses target-domain labels. The pseudo accuracy is computed on the training set of Cityscapes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.247,
+                0.892,
+                0.307
+            ],
+            "angle": 0,
+            "content": "quality of pseudo labels is improved because part of them are inherited from the labels in the source domain; on the other hand, the focus on the target domain is weakened, increasing the risk of domain adaptation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.308,
+                0.892,
+                0.383
+            ],
+            "angle": 0,
+            "content": "The above analysis prompts us to perform the 'Focus on Your Target' trail towards higher UDA accuracy. We replace the mixed domain of ClassMix, \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\) , with another domain, \\(\\langle \\mathbb{T},\\mathbb{T}\\rangle\\) , in which the mixed samples are generated using two target images:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.507,
+                0.39,
+                0.891,
+                0.412
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {x} _ {j _ {1}, j _ {2}} ^ {\\langle \\mathbb {T}, \\mathbb {T} \\rangle} = \\mathcal {M} \\left(\\mathbf {x} _ {j _ {1}} ^ {\\mathbb {T}}, \\mathbf {x} _ {j _ {2}} ^ {\\mathbb {T}}\\right) = \\mathbf {x} _ {j _ {1}} ^ {\\mathbb {T}} \\odot \\mathbf {M} _ {j _ {1}} ^ {\\mathbb {T}} + \\mathbf {x} _ {j _ {2}} ^ {\\mathbb {T}} \\odot \\left(\\mathbf {1} - \\mathbf {M} _ {j _ {1}} ^ {\\mathbb {T}}\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.417,
+                0.796,
+                0.432
+            ],
+            "angle": 0,
+            "content": "and the pseudo label is adjusted accordingly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.432,
+                0.892,
+                0.597
+            ],
+            "angle": 0,
+            "content": "In Table 1, we run DAFormer [19] with either \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\) or \\(\\langle \\mathbb{T},\\mathbb{T}\\rangle\\) for UDA segmentation on GTAv \\(\\rightarrow\\) Cityscapes. Compared to \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\), \\(\\langle \\mathbb{T},\\mathbb{T}\\rangle\\) achieves an inferior mIoU of \\(67.2\\%\\) (a \\(1.3\\%\\) drop). But, interestingly, when ground-truth labels are used for the mixed images, the mIoU surpasses the original option by \\(2.5\\%\\), with merely a \\(0.9\\%\\) mIoU lower than the supervised baseline. In other words, 'Focus on Your Target' improves the upper bound, but the models cannot achieve the upper bound because the pseudo labels deteriorate: it is a side effect of decreasing the proportion of training data from the source domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.598,
+                0.892,
+                0.765
+            ],
+            "angle": 0,
+            "content": "In summary, a strong algorithm for UDA shall be equipped with two critical abilities: (i) learning reliable semantics from the source domain, and (ii) adapting the learned semantics to the target domain. However, in the above self-training framework where a single teacher-student model is used, there seems a conflict between these two abilities, e.g., increasing the proportion of target-domain data strengthens the 'adapting ability' but weakens the 'learning ability', setting an obstacle to better performance. In what follows, we offer a solution by training two teacher-student models simultaneously."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.772,
+                0.799,
+                0.787
+            ],
+            "angle": 0,
+            "content": "3.3. Dual Teacher-Student Framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The proposed dual teacher-student (DTS) framework is illustrated in Figure 2. We denote the models used in the two teacher-student groups as \\( f_1^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}_1^{\\mathrm{te}}) \\), \\( f_1^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}_1^{\\mathrm{st}}) \\) and \\( f_2^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}_2^{\\mathrm{te}}) \\), \\( f_2^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}_2^{\\mathrm{st}}) \\), respectively, where we use a subscript (1 or 2) to indicate the group ID. As described above, we expect the first teacher-student model to stick to learning reliable semantics from the source domain, while the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19029"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.097,
+                0.484,
+                0.352
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.484,
+                0.094,
+                0.887,
+                0.352
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.359,
+                0.895,
+                0.416
+            ],
+            "angle": 0,
+            "content": "Figure 2. An illustration of the proposed DTS framework, where we use Setting \\( B \\) as an example. The left and right parts describe the optimization of the first and second group models, respectively. The bottom-left part (in gray) corresponds to a single teacher-student framework where ClassMix is used for domain mixing, and the top part (in purple) shows the bidirectional learning strategy, i.e., models from the other group are used for pseudo label generation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.44,
+                0.46,
+                0.571
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.577,
+                0.47,
+                0.649
+            ],
+            "angle": 0,
+            "content": "Figure 3. An illustration of different combinations of training data. We use magenta to represent source-domain patches and two types of blue to represent target-domain patches from different images. In practice, the images are not partitioned into regular grids, but into semantic regions according to the (real or pseudo) labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.47,
+                0.704
+            ],
+            "angle": 0,
+            "content": "second teacher-student model learns to 'Focus on Your Target' to enhance the adapting ability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We achieve the goal by using different data proportions for the two groups. An illustration is provided in Figure 3. The first group remains the same as in the baseline, i.e., half of the training samples are simply source images and another half are ClassMix-ed images covering the source and target domains. Using the previously defined notations, we denote the combination as \\(\\{\\mathbb{S},\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}\\). To increase the proportion of the target-domain data, we first change the mixture of data from \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\) to \\(\\langle \\mathbb{T},\\mathbb{T}\\rangle\\) (i.e., same as that used in the 'Focus on Your Target' trial), and then replace the pure source domain with \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\). That said, we create two settings for data combination, \\(\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}\\) and \\(\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle ,\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}\\). We name them Setting \\(A\\) and Setting \\(B\\) of the second group"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.44,
+                0.892,
+                0.501
+            ],
+            "angle": 0,
+            "content": "throughout the remainder of this paper. Intuitively, the proportion of the target-domain data is increased from around \\(25\\%\\) in the first group (as well as the baselines) to around \\(50\\% / 75\\%\\) using Setting A/Setting B in the second group."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.501,
+                0.892,
+                0.591
+            ],
+            "angle": 0,
+            "content": "There are two teacher models and two student models to be optimized. We perform iterative optimization and propose a bidirectional learning strategy so that each teacher-student model propagates information to the other by contributing to the generation of pseudo labels. The detailed training process is shown in Algorithm 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.591,
+                0.892,
+                0.697
+            ],
+            "angle": 0,
+            "content": "Note that, if \\( f_{2,t}^{\\mathrm{te}}(\\cdot) \\) is not used in Step 2 (i.e., all pseudo labels are generated using \\( f_{1,t+1}^{\\mathrm{te}}(\\cdot) \\)), the information is only propagated from the first teacher-student model to the second one, hence the optimization strategy degenerates from bidirectional to unidirectional. The advantage of the bidirectional strategy and other design choices will be diagnosed in the experimental section."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.704,
+                0.667,
+                0.719
+            ],
+            "angle": 0,
+            "content": "3.4. Technical Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.727,
+                0.892,
+                0.879
+            ],
+            "angle": 0,
+            "content": "Choosing the proper option for data combination. We compute the averaged confidence of pseudo labels generated by the corresponding teacher models, \\( f_{1}^{\\mathrm{st}}(\\cdot) \\) and \\( f_{2}^{\\mathrm{te}}(\\cdot) \\). Following [48, 19], \\( \\gamma \\) is defined as the proportion of pixels with the max class score surpassing a given threshold, \\( \\tau \\). For each training image \\( \\mathbf{x} \\), we use \\( \\gamma_{1}^{\\mathrm{st}}(\\mathbf{x}) \\) and \\( \\gamma_{2}^{\\mathrm{te}}(\\mathbf{x}) \\) to denote the average \\( \\gamma \\) values over all pixels when the teacher models are \\( f_{1}^{\\mathrm{st}}(\\cdot) \\) and \\( f_{2}^{\\mathrm{te}}(\\cdot) \\), respectively. Then, we estimate the chance that \\( f_{2}^{\\mathrm{te}}(\\cdot) \\) generates better pseudo labels than \\( f_{1}^{\\mathrm{st}}(\\cdot) \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.566,
+                0.884,
+                0.892,
+                0.904
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {P r o b} = \\mathbb {E} _ {\\mathbf {x} \\sim \\mathcal {D} ^ {\\mathbb {T}}} \\left[ \\mathbb {I} \\left(\\gamma_ {2} ^ {\\mathrm {t e}} (\\mathbf {x}) > \\gamma_ {1} ^ {\\mathrm {s t}} (\\mathbf {x})\\right) \\right], \\tag {6}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19030"
+        }
+    ],
+    [
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.088,
+                0.095,
+                0.368,
+                0.11
+            ],
+            "angle": 0,
+            "content": "Algorithm 1: DTS: Dual Teacher-Student"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.08,
+                0.112,
+                0.445,
+                0.39
+            ],
+            "angle": 0,
+            "content": "Input: Source data \\(\\{\\mathbf{x}^{\\mathbb{S}},\\mathbf{y}^{\\mathbb{S}}\\}\\), target data \\(\\{\\mathbf{x}^{\\mathbb{T}}\\}\\), the total iteration number T;  \n1 repeat  \n2 Update \\(f_{1,t+1}^{\\mathrm{te}}(\\cdot)\\) using the EMA of \\(f_{1,t}^{\\mathrm{st}}(\\cdot)\\);  \n3 Get pseudo labels \\(\\tilde{\\mathbf{y}}^{\\mathbb{T}}\\) by \\(f_{1,t+1}^{\\mathrm{te}}(\\cdot)\\) and \\(f_{2,t}^{\\mathrm{te}}(\\cdot)\\);  \n4 Generate mixed data \\(\\{\\mathbf{x}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle}\\}\\), and train \\(f_{1,t+1}^{\\mathrm{st}}(\\cdot)\\) on \\(\\{\\mathbb{S},\\langle \\mathbb{S},\\mathbb{T}\\rangle\\}\\);  \n5 Update \\(f_{2,t+1}^{\\mathrm{te}}(\\cdot)\\) using the EMA of \\(f_{2,t}^{\\mathrm{st}}(\\cdot)\\);  \n6 Get pseudo labels \\(\\tilde{\\mathbf{y}}^{\\mathbb{T}}\\) by \\(f_{1,t+1}^{\\mathrm{st}}(\\cdot)\\) and \\(f_{2,t+1}^{\\mathrm{te}}\\);  \n7 if Setting A: Generate data \\(\\{\\mathbf{x}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle}\\}\\), and Train \\(f_{2,t+1}^{\\mathrm{st}}(\\cdot)\\) on \\(\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle\\}\\);  \n8 if Setting B: Generate data \\(\\{\\mathbf{x}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{x}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle}\\}\\), and train \\(f_{2,t+1}^{\\mathrm{st}}(\\cdot)\\) on them;  \n9 \\(t \\gets t + 1\\);  \n10 until \\(t = T\\);  \nReturn: \\(f_{2,\\mathrm{T}}^{\\mathrm{st}}(\\cdot)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.424,
+                0.47,
+                0.528
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbb{I}(\\cdot)\\) is the indicator function that outputs 1 if the statement is true and 0 otherwise. Note that the estimation is performed individually for two training procedures using Setting \\(A\\) and Setting \\(B\\). Finally, we choose the setting with a higher chance that \\(f_{2}^{\\mathrm{te}}(\\cdot)\\) is more confident because \\(f_{2}^{\\mathrm{st}}(\\cdot)\\) is eventually used for inference. We shall see in Section 4.3 that this criterion always leads to the better choice."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.53,
+                0.47,
+                0.606
+            ],
+            "angle": 0,
+            "content": "Generating the mask. In the domain mixing operation, we compute the mask \\(\\mathbf{M}\\) by choosing the class label of one image. If the \\(\\langle \\mathbb{S},\\mathbb{T}\\rangle\\) is used, the source image with groundtruth is chosen; if \\(\\langle \\mathbb{T},\\mathbb{T}\\rangle\\) is used, the image with a larger average value of \\(\\gamma\\) is chosen."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.607,
+                0.47,
+                0.73
+            ],
+            "angle": 0,
+            "content": "Generating pseudo labels. The details are slightly different between Setting \\(A\\) and Setting \\(B\\). When the batch size is \\(k\\), the number of target images used for the second group in Setting \\(A\\) and Setting \\(B\\) are \\(2k\\) and \\(3k\\), respectively. For Setting \\(A\\), \\(k\\) pseudo labels used are generated by \\(f_{1,t+1}^{\\mathrm{st}}(\\cdot)\\) and other \\(k\\) by \\(f_{2,t+1}^{\\mathrm{te}}(\\cdot)\\). For Setting \\(B\\), the \\(2k\\) pseudo labels used in \\(\\langle \\mathbb{T}, \\mathbb{T} \\rangle\\) are generated by \\(f_{1,t+1}^{\\mathrm{st}}(\\cdot)\\) and the \\(k\\) labels used in \\(\\langle \\mathbb{S}, \\mathbb{T} \\rangle\\) are generated by \\(f_{2,t+1}^{\\mathrm{te}}(\\cdot)\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.745,
+                0.21,
+                0.763
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.771,
+                0.277,
+                0.787
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets. We train the models on a labeled source domain and an unlabeled target domain and test them on the target domain. We follow the convention to set the source domain to be a synthesized dataset (either GTAv [38] which contains 24,966 densely labeled training images at a resolution of \\(1914 \\times 1052\\) or SYNTHIA [39] which contains 9,400 densely labeled training images at a resolution of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.196
+            ],
+            "angle": 0,
+            "content": "\\(1280 \\times 760\\)), and the target dataset to be a real dataset (Cityscapes [6] where only the finely-annotated subset is used, containing 2,975 training images and 500 validation images at a resolution of \\(2048 \\times 1024\\)). Following the convention to report the mean IoU (mIoU) over 19 classes when GTAv is used as the source domain, and 13 or 16 classes when SYNTHIA is the source domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.198,
+                0.893,
+                0.44
+            ],
+            "angle": 0,
+            "content": "Training details. Our framework is applied to different self-training frameworks. Specifically, we follow the DAFformer series [19, 20, 21] where the encoder is a MiT-B5 model pre-trained on ImageNet-1K [7] and the decoder involves a context-aware feature fusion module. We train the framework on a single NVIDIA Tesla-V100 GPU for 40K iterations with a batch size of 2 for both groups. We use an AdamW optimizer [34] with learning rates of \\(6 \\times 10^{-5}\\) for the encoder and \\(6 \\times 10^{-4}\\) for the decoder, a weight decay of 0.01, and linear warm-up of the learning rate for the first 1.5K iterations. The input image size is always \\(512 \\times 512\\). During the training phase, we apply random rescaling and cropping to the source and target data, as well as color jittering and Gaussian blur as strong augmentations for the mixed data. The EMA coefficient, \\(\\lambda\\), is set to be 0.999. The pseudo-label confidence threshold, \\(\\tau\\), is 0.968 as in [48]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.452,
+                0.874,
+                0.468
+            ],
+            "angle": 0,
+            "content": "4.2. Comparison to the State-of-the-art Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.476,
+                0.892,
+                0.552
+            ],
+            "angle": 0,
+            "content": "We compare DTS to state-of-the-art UDA approaches on the GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes benchmarks. Results are summarized in Table 2 and Table 3, respectively. We establish DTS upon three recently published works, namely, DAFormer [19], HRDA [20], and MIC [21]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.553,
+                0.892,
+                0.718
+            ],
+            "angle": 0,
+            "content": "DTS reports consistent gains in terms of segmentation accuracy beyond all three baselines. On GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes (13 classes), the mIoU gains over DAFormer, HRDA, MIC are \\(2.9\\%\\), \\(1.4\\%\\), \\(0.6\\%\\) and \\(4.0\\%\\), \\(1.0\\%\\), \\(1.1\\%\\) respectively. The gain generally becomes smaller when the baseline is stronger, which is as expected. Specifically, when added to MIC, the previous best approach, DTS achieves new records on these benchmarks: a \\(76.5\\%\\) mIoU on GTAv \\(\\rightarrow\\) Cityscapes and \\(67.8\\%\\) and \\(75.1\\%\\) mIoUs on SYNTHIA \\(\\rightarrow\\) Cityscapes with 16 and 13 classes, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.719,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Comparison to FST. We compare DTS to another plugin approach, FST [8]. On DAFormer, the gains brought by FST on the two benchmarks (SYNTHIA using 13 classes) are \\(1.0\\%\\) and \\(1.3\\%\\), while the numbers for DTS are \\(2.9\\%\\) and \\(4.0\\%\\), respectively. That said, besides the contribution of FST that allows us to 'learn from future', the higher accuracy also owes to the design of the DTS framework that alleviates the conflict of learning and adapting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Class-level analysis. We investigate which classes are best improved by DTS. On \\(\\mathrm{GTAv} \\rightarrow \\mathrm{Cityscapes}\\), we detect two classes, sign and truck, on which the IoU gain on the three baselines is always higher than the mIoU gain. In the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19031"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.09,
+                0.892,
+                0.337
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall</td><td>Fence</td><td>Pole</td><td>Light</td><td>Sign</td><td>Veg</td><td>Terrain</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Train</td><td>Motor</td><td>Bike</td><td>mIoU</td></tr><tr><td>AdaptSegNet [49]</td><td>86.5</td><td>36.0</td><td>79.9</td><td>23.4</td><td>23.3</td><td>23.9</td><td>35.2</td><td>14.8</td><td>83.4</td><td>33.3</td><td>75.6</td><td>58.5</td><td>27.6</td><td>73.7</td><td>32.5</td><td>35.4</td><td>3.9</td><td>30.1</td><td>28.1</td><td>42.4</td></tr><tr><td>PatchAligne [50]</td><td>92.3</td><td>51.9</td><td>82.1</td><td>29.2</td><td>25.1</td><td>24.5</td><td>33.8</td><td>33.0</td><td>82.4</td><td>32.8</td><td>82.2</td><td>58.6</td><td>27.2</td><td>84.3</td><td>33.4</td><td>46.3</td><td>2.2</td><td>29.5</td><td>32.3</td><td>46.5</td></tr><tr><td>FDA [56]</td><td>92.5</td><td>53.3</td><td>82.4</td><td>26.5</td><td>27.6</td><td>36.4</td><td>40.6</td><td>38.9</td><td>82.3</td><td>39.8</td><td>78.0</td><td>62.6</td><td>34.4</td><td>84.9</td><td>34.1</td><td>53.1</td><td>16.9</td><td>27.7</td><td>46.4</td><td>50.5</td></tr><tr><td>DACS [48]</td><td>89.9</td><td>39.7</td><td>87.9</td><td>39.7</td><td>39.5</td><td>38.5</td><td>46.4</td><td>52.8</td><td>88.0</td><td>44.0</td><td>88.8</td><td>67.2</td><td>35.8</td><td>84.5</td><td>45.7</td><td>50.2</td><td>0.0</td><td>27.3</td><td>34.0</td><td>52.1</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>56.0</td><td>79.7</td><td>46.3</td><td>44.8</td><td>45.6</td><td>53.5</td><td>53.5</td><td>88.6</td><td>45.2</td><td>82.1</td><td>70.7</td><td>39.2</td><td>88.8</td><td>45.5</td><td>50.4</td><td>1.0</td><td>48.9</td><td>56.4</td><td>57.5</td></tr><tr><td>DAP [23]</td><td>94.5</td><td>63.1</td><td>89.1</td><td>29.8</td><td>47.5</td><td>50.4</td><td>56.7</td><td>58.7</td><td>89.5</td><td>50.2</td><td>87.0</td><td>73.6</td><td>38.6</td><td>91.3</td><td>50.2</td><td>52.9</td><td>0.0</td><td>50.2</td><td>63.5</td><td>59.8</td></tr><tr><td>CPSL [30]</td><td>92.3</td><td>59.9</td><td>84.9</td><td>45.7</td><td>29.7</td><td>52.8</td><td>61.5</td><td>59.5</td><td>87.9</td><td>41.6</td><td>85.0</td><td>73.0</td><td>35.5</td><td>90.4</td><td>48.7</td><td>73.9</td><td>26.3</td><td>53.8</td><td>53.9</td><td>60.8</td></tr><tr><td>DAFormer [19]</td><td>95.7</td><td>70.2</td><td>89.4</td><td>53.5</td><td>48.1</td><td>49.6</td><td>55.8</td><td>59.4</td><td>89.9</td><td>47.9</td><td>92.5</td><td>72.2</td><td>44.7</td><td>92.3</td><td>74.5</td><td>78.2</td><td>65.1</td><td>55.9</td><td>61.8</td><td>68.3</td></tr><tr><td>DAFormer+FST [8]</td><td>95.3</td><td>67.7</td><td>89.3</td><td>55.5</td><td>47.1</td><td>50.1</td><td>57.2</td><td>58.6</td><td>89.9</td><td>51.0</td><td>92.9</td><td>72.7</td><td>46.3</td><td>92.5</td><td>78.0</td><td>81.6</td><td>74.4</td><td>57.7</td><td>62.6</td><td>69.3</td></tr><tr><td>DAFormer+CAMix [62]</td><td>96.0</td><td>73.1</td><td>89.5</td><td>53.9</td><td>50.8</td><td>51.7</td><td>58.7</td><td>64.9</td><td>90.0</td><td>51.2</td><td>92.2</td><td>71.8</td><td>44.0</td><td>92.8</td><td>78.7</td><td>82.3</td><td>70.9</td><td>54.1</td><td>64.3</td><td>70.0</td></tr><tr><td>DAFormer+DTS (ours)</td><td>96.8</td><td>76.0</td><td>90.0</td><td>56.5</td><td>50.1</td><td>51.9</td><td>57.4</td><td>65.1</td><td>90.5</td><td>50.5</td><td>92.4</td><td>73.5</td><td>46.9</td><td>93.0</td><td>80.4</td><td>85.2</td><td>74.0</td><td>58.7</td><td>63.5</td><td>71.2</td></tr><tr><td>HRDA [20]</td><td>96.4</td><td>74.4</td><td>91.0</td><td>61.6</td><td>51.5</td><td>57.1</td><td>63.9</td><td>69.3</td><td>91.3</td><td>48.4</td><td>94.2</td><td>79.0</td><td>52.9</td><td>93.9</td><td>84.1</td><td>85.7</td><td>75.9</td><td>63.9</td><td>67.5</td><td>73.8</td></tr><tr><td>HRDA+DTS (ours)</td><td>96.7</td><td>76.3</td><td>91.3</td><td>60.7</td><td>55.9</td><td>59.9</td><td>67.3</td><td>72.5</td><td>91.8</td><td>50.1</td><td>94.4</td><td>80.7</td><td>56.8</td><td>94.4</td><td>86.0</td><td>86.0</td><td>73.9</td><td>65.7</td><td>68.4</td><td>75.2</td></tr><tr><td>MIC [21]</td><td>97.4</td><td>80.1</td><td>91.7</td><td>61.2</td><td>56.9</td><td>59.7</td><td>66.0</td><td>71.3</td><td>91.7</td><td>51.4</td><td>94.3</td><td>79.8</td><td>56.1</td><td>94.6</td><td>85.4</td><td>90.3</td><td>80.4</td><td>64.5</td><td>68.5</td><td>75.9</td></tr><tr><td>MIC+DTS (ours)</td><td>97.0</td><td>80.4</td><td>91.8</td><td>60.6</td><td>58.7</td><td>61.7</td><td>67.9</td><td>73.2</td><td>92.0</td><td>45.4</td><td>94.3</td><td>81.3</td><td>58.7</td><td>95.0</td><td>87.9</td><td>90.7</td><td>82.2</td><td>65.7</td><td>69.0</td><td>76.5</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.08,
+                0.339,
+                0.892,
+                0.365
+            ],
+            "angle": 0,
+            "content": "Table 2. UDA segmentation accuracy (mIoU, %) on the GTAv→Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.378,
+                0.892,
+                0.629
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall*</td><td>Fence*</td><td>Pole*</td><td>Light</td><td>Sign</td><td>Veg</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Bus</td><td>Motor</td><td>Bike</td><td>mIoU</td><td>mIoU*</td></tr><tr><td>PatchAlign [50]</td><td>82.4</td><td>38.0</td><td>78.6</td><td>8.7</td><td>0.6</td><td>26.0</td><td>3.9</td><td>11.1</td><td>75.5</td><td>84.6</td><td>53.5</td><td>21.6</td><td>71.4</td><td>32.6</td><td>19.3</td><td>31.7</td><td>40.0</td><td>46.5</td></tr><tr><td>AdaptSegNet [49]</td><td>84.3</td><td>42.7</td><td>77.5</td><td>-</td><td>-</td><td>-</td><td>4.7</td><td>7.0</td><td>77.9</td><td>82.5</td><td>54.3</td><td>21.0</td><td>72.3</td><td>32.2</td><td>18.9</td><td>32.3</td><td>-</td><td>46.7</td></tr><tr><td>FDA [56]</td><td>79.3</td><td>35.0</td><td>73.2</td><td>-</td><td>-</td><td>-</td><td>19.9</td><td>24.0</td><td>61.7</td><td>82.6</td><td>61.4</td><td>31.1</td><td>83.9</td><td>40.8</td><td>38.4</td><td>51.1</td><td>-</td><td>52.5</td></tr><tr><td>DACS [48]</td><td>80.6</td><td>25.1</td><td>81.9</td><td>21.5</td><td>2.9</td><td>37.2</td><td>22.7</td><td>24.0</td><td>83.7</td><td>90.8</td><td>67.6</td><td>38.3</td><td>82.9</td><td>38.9</td><td>28.5</td><td>47.6</td><td>48.3</td><td>54.8</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>45.7</td><td>84.6</td><td>37.1</td><td>0.6</td><td>44.0</td><td>54.6</td><td>37.0</td><td>88.1</td><td>84.4</td><td>74.2</td><td>24.3</td><td>88.2</td><td>51.1</td><td>40.5</td><td>45.6</td><td>55.5</td><td>62.0</td></tr><tr><td>DAP [23]</td><td>84.2</td><td>46.5</td><td>82.5</td><td>35.1</td><td>0.2</td><td>46.7</td><td>53.6</td><td>45.7</td><td>89.3</td><td>87.5</td><td>75.7</td><td>34.6</td><td>91.7</td><td>73.5</td><td>49.4</td><td>60.5</td><td>59.8</td><td>64.3</td></tr><tr><td>CPSL [30]</td><td>87.2</td><td>43.9</td><td>85.5</td><td>33.6</td><td>0.3</td><td>47.7</td><td>57.4</td><td>37.2</td><td>87.8</td><td>88.5</td><td>79.0</td><td>32.0</td><td>90.6</td><td>49.4</td><td>50.8</td><td>59.8</td><td>57.9</td><td>65.3</td></tr><tr><td>DAFormer [19]</td><td>84.5</td><td>40.7</td><td>88.4</td><td>41.5</td><td>6.5</td><td>50.0</td><td>55.0</td><td>54.6</td><td>86.0</td><td>89.8</td><td>73.2</td><td>48.2</td><td>87.2</td><td>53.2</td><td>53.9</td><td>61.7</td><td>60.9</td><td>67.4</td></tr><tr><td>DAFormer+FST [8]</td><td>88.3</td><td>46.1</td><td>88.0</td><td>41.7</td><td>7.3</td><td>50.1</td><td>53.6</td><td>52.5</td><td>87.4</td><td>91.5</td><td>73.9</td><td>48.1</td><td>85.3</td><td>58.6</td><td>55.9</td><td>63.4</td><td>61.9</td><td>68.7</td></tr><tr><td>DAFormer+CAMix [62]</td><td>87.4</td><td>47.5</td><td>88.8</td><td>-</td><td>-</td><td>-</td><td>55.2</td><td>55.4</td><td>87.0</td><td>91.7</td><td>72.0</td><td>49.3</td><td>86.9</td><td>57.0</td><td>57.5</td><td>63.6</td><td>-</td><td>69.2</td></tr><tr><td>DAFormer+DTS (ours)</td><td>88.5</td><td>51.4</td><td>88.0</td><td>37.2</td><td>4.8</td><td>51.4</td><td>59.4</td><td>59.0</td><td>88.1</td><td>92.7</td><td>71.3</td><td>51.3</td><td>89.2</td><td>67.7</td><td>58.4</td><td>62.8</td><td>63.8</td><td>71.4</td></tr><tr><td>HRDA [20]</td><td>85.2</td><td>47.7</td><td>88.8</td><td>49.5</td><td>4.8</td><td>57.2</td><td>65.7</td><td>60.9</td><td>85.3</td><td>92.9</td><td>79.4</td><td>52.8</td><td>89.0</td><td>64.7</td><td>63.9</td><td>64.9</td><td>65.8</td><td>72.4</td></tr><tr><td>HRDA+DTS (ours)</td><td>88.5</td><td>53.1</td><td>88.7</td><td>44.0</td><td>5.8</td><td>59.2</td><td>68.3</td><td>60.7</td><td>87.7</td><td>93.4</td><td>79.5</td><td>46.4</td><td>91.3</td><td>64.2</td><td>66.8</td><td>65.9</td><td>66.5</td><td>73.4</td></tr><tr><td>MIC [21]</td><td>86.6</td><td>50.5</td><td>89.3</td><td>47.9</td><td>7.8</td><td>59.4</td><td>66.7</td><td>63.4</td><td>87.1</td><td>94.6</td><td>81.0</td><td>58.9</td><td>90.1</td><td>61.9</td><td>67.1</td><td>64.3</td><td>67.3</td><td>74.0</td></tr><tr><td>MIC+DTS (ours)</td><td>89.1</td><td>54.9</td><td>89.0</td><td>39.1</td><td>8.7</td><td>61.6</td><td>67.4</td><td>64.3</td><td>88.8</td><td>94.0</td><td>82.2</td><td>60.7</td><td>89.6</td><td>62.6</td><td>68.5</td><td>64.9</td><td>67.8</td><td>75.1</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.08,
+                0.63,
+                0.892,
+                0.67
+            ],
+            "angle": 0,
+            "content": "Table 3. UDA segmentation accuracy (mIoU, %) on the SYNTHIA \\(\\rightarrow\\)Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone. The mIoU and mIoU* columns denote the averaged IoU over 16 and 13 classes, where the latter does not contain the classes marked with * ."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.695,
+                0.47,
+                0.771
+            ],
+            "angle": 0,
+            "content": "Appendix material, we show that these classes suffer larger variations between the source-domain and target-domain appearances, and hence the learned features are more difficult to transfer. They are largely benefited by the 'Focus on Your Target' ability of DTS."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.08,
+                0.78,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visualization. We visualize the segmentation results of DAFormer and DAFormer+DTS in Figure 4. For the real images, the advantage of DTS is significant on the classes that are easily confused with others (e.g., sidewalk which is visually similar to road) or suffer large domain shifts (e.g., sign or truck). For the mixed images, we find that the baseline model is easily confused by the unusual stitching and/or discontinuous textures because it has never seen such pat"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.695,
+                0.892,
+                0.756
+            ],
+            "angle": 0,
+            "content": "terns in the source domain – in such cases, the model of the second group is generally better and sometimes it can propagate the advantages to the model of the first group, revealing the advantage of bidirectional learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.77,
+                0.679,
+                0.787
+            ],
+            "angle": 0,
+            "content": "4.3. Diagnostic Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Ablative studies. We first diagnose the proposed approach by ablating the contribution of three components, namely, applying the dual teacher-student (DTS) framework, increasing the proportion of data from the target domain (i.e., 'Focus on Your Target'), and adopting the bidirectional learning strategy. Results are summarized in Table 4. Note that some combinations are not valid, e.g.,"
+        },
+        {
+            "type": "page_number",
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+        }
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+        {
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "images"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "content": "DAFormer"
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+        {
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+            "content": "DTS (1st group)"
+        },
+        {
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+            "bbox": [
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+                0.285,
+                0.722,
+                0.345
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.597,
+                0.347,
+                0.703,
+                0.362
+            ],
+            "angle": 0,
+            "content": "DTS \\((2^{\\mathrm{nd}}\\) group)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.726,
+                0.222,
+                0.88,
+                0.283
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.726,
+                0.285,
+                0.88,
+                0.346
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.757,
+                0.348,
+                0.839,
+                0.361
+            ],
+            "angle": 0,
+            "content": "ground truth"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.369,
+                0.894,
+                0.412
+            ],
+            "angle": 0,
+            "content": "Figure 4. Visualization of the segmentation results of DAFormer [19] and DTS. The top two rows display two real images and the bottom two rows display two synthesized images from \\(\\langle \\mathbb{T},\\mathbb{T}\\rangle\\) . In each group, the first example is from GTAv \\(\\rightarrow\\) Cityscapes and the second one is from SYNTHIA \\(\\rightarrow\\) Cityscapes. The white, dashed circles highlight the regions that are significantly improved by DTS."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.434,
+                0.462,
+                0.542
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Setting</td><td colspan=\"5\">Choice and Accuracy</td></tr><tr><td>Dual Teacher-Student ‘Focus on Your Target’</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td></tr><tr><td>Bidirectional Learning</td><td></td><td></td><td>✓</td><td>✓</td><td></td></tr><tr><td>GTAv→Cityscapes</td><td>68.3</td><td>67.2</td><td>69.7</td><td>68.6</td><td>71.2</td></tr><tr><td>SYNTHIA→Cityscapes</td><td>60.9</td><td>58.4</td><td>63.3</td><td>61.2</td><td>63.7</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.544,
+                0.47,
+                0.629
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablative studies of DTS with respect to the UDA segmentation accuracy (mIoU, %) on both benchmarks. All these experiments are based on DAFformer [19]. For SYNTHIA→Cityscapes, the mIoUs are computed over 16 classes. Note that DTS alone (without the latter two options) is equivalent to the baseline (the leftmost column) and is simply ignored in the table."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.657,
+                0.47,
+                0.718
+            ],
+            "angle": 0,
+            "content": "solely applying DTS (without adjusting the proportion of training data nor applying bidirectional learning) does not make any difference from the baseline; also, bidirectional learning must be built upon DTS."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "From Columns 1-3, one can learn the importance of the DTS framework. When DTS is not established, simply increasing the proportion of target data (Col 2) incurs an accuracy drop on both GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes. This validates our motivation, i.e., there is a conflict between the learning and adapting abilities. However, after the dual teacher-student framework is established (Col 3, where the first teacher-student group focuses on learning and the second group focuses on adapting), the conflict is weakened and the accuracy gain becomes clear (1.6% on GTAv \\(\\rightarrow\\) Cityscapes and 2.4% on SYNTHIA \\(\\rightarrow\\) Cityscapes)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.434,
+                0.89,
+                0.529
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\">Baseline</td><td>DAFormer</td><td>HRDA</td><td>MIC</td></tr><tr><td rowspan=\"2\">GTAv</td><td>Setting A</td><td>70.3</td><td>74.7</td><td>76.5</td></tr><tr><td>Setting B</td><td>71.2</td><td>75.2</td><td>76.2</td></tr><tr><td rowspan=\"2\">SYNTHIA</td><td>Setting A</td><td>63.8</td><td>66.5</td><td>67.8</td></tr><tr><td>Setting B</td><td>61.2</td><td>66.0</td><td>67.2</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.53,
+                0.892,
+                0.557
+            ],
+            "angle": 0,
+            "content": "Table 5. The results of DTS with different data mixing options. For SYNTHIA \\(\\rightarrow\\) Cityscapes, the mIoUs are computed over 16 classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.893,
+                0.749
+            ],
+            "angle": 0,
+            "content": "From Columns 3-5, one can observe the contribution of 'Focus on Your Target' (i.e., increasing the proportion of target data) and bidirectional learning on top of the DTS framework. The best practice is obtained when all the modules are used (Col 5), aligning with the results reported in Tables 2 and 3. Interestingly, when bidirectional learning is adopted alone (Col 4), the accuracy gain is much smaller than that of using 'Focus on Your Target' alone, because the two groups are using the same proportion of data mixing, and thus the bidirectional learning carries limited complementary information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Choose the option for data combination. We validate that the data combination option can be chosen by comparing the pseudo-label confidence, as described in Section 3.4. We plot the Prob curves throughout training procedure of Setting \\( A \\) and Setting \\( B \\) in Figure 5. On GTAv→Cityscapes, the Prob value of Setting \\( B \\) is eventually higher than that of Setting \\( A \\), and DTS with Setting \\( B \\) outperforms DTS with Setting \\( A \\) by a \\( 0.9\\% \\) mIoU (see Table 5). However, on SYNTHIA→Cityscapes, the Prob value of Setting \\( A \\) is always higher than that of Setting"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19033"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.092,
+                0.27,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.276,
+                0.092,
+                0.465,
+                0.224
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.229,
+                0.47,
+                0.299
+            ],
+            "angle": 0,
+            "content": "Figure 5. The curves of Prob computed on the GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes benchmarks. DAFormer is used as the baseline. These curves suggest that, on DAFormer, Setting \\(B\\) is better for GTAv \\(\\rightarrow\\) Cityscapes while Setting \\(A\\) is better for SYNTHIA \\(\\rightarrow\\) Cityscapes."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.134,
+                0.315,
+                0.413,
+                0.402
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Options</td><td>GTAv</td><td>SYNTHIA</td></tr><tr><td>{&lt;T,T&gt;}</td><td>69.1</td><td>61.1</td></tr><tr><td>{&lt;S,T&gt;}</td><td>69.3</td><td>59.4</td></tr><tr><td>{S, &lt;T,T&gt;}</td><td>70.3</td><td>63.8</td></tr><tr><td>{&lt;S,T&gt;, &lt;T,T&gt;}</td><td>71.2</td><td>61.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.402,
+                0.469,
+                0.444
+            ],
+            "angle": 0,
+            "content": "Table 6. The results of DTS with more data mixing options. We show the mIoU of the 16 classes in SYNTHIA and make this comparison based on the DAFourner baseline."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.473,
+                0.469,
+                0.625
+            ],
+            "angle": 0,
+            "content": "\\(B\\), and DTS with Setting \\(A\\) outperforms DTS with Setting \\(B\\) by a \\(2.4\\%\\) mIoU. Table 5 also shows the segmentation accuracy on the other two baselines. All choices of advantageous results align with the aforementioned criterion. From an intuitive view, Setting \\(B\\) has a smaller portion of source data, so it works better in the GTAv \\(\\rightarrow\\) Cityscapes scenario because GTAv has a smaller domain gap to Cityscapes than SYNTHIA, which can be validated by vanilla transfer experiments (GTAv \\(\\rightarrow\\) Cityscapes: \\(46.2\\%\\), SYNTHIA \\(\\rightarrow\\) Cityscapes: \\(41.3\\%\\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.628,
+                0.469,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Except for Setting \\( A \\) and Setting \\( B \\), there are two other options to increase the focus on the target domain as well, namely \\( \\{\\langle \\mathbb{T},\\mathbb{T}\\rangle \\} \\) and \\( \\{\\langle \\mathbb{S},\\mathbb{T}\\rangle \\} \\). The two options do not include any mixing data and have a disadvantage compared to the previous two combinations. \\( \\{\\langle \\mathbb{T},\\mathbb{T}\\rangle \\} \\) means that the second teacher-student group achieves the ability of learning only from the pseudo labels provided by \\( f_1^{\\mathrm{st}}(\\mathbf{x};\\pmb {\\theta}_1^{\\mathrm{st}}) \\). As a result, noise can easily persist without accurate supervision from the source data. \\( \\{\\langle \\mathbb{S},\\mathbb{T}\\rangle \\} \\) has a similar data proportion as \\( \\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle \\} \\) but cannot solve the problem of inconsistency between the training and testing data. Using \\( \\langle \\mathbb{T},\\mathbb{T}\\rangle \\) as the training domain is an effective way to bridge the gap between the training and testing phases. Therefore, the two combinations containing two different types of data used in DTS are more suitable for balancing the learning and adapting abilities."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Models for pseudo label generation. We study the impact of different models for generating pseudo labels. Re"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.527,
+                0.09,
+                0.867,
+                0.209
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\">Group #1</td><td colspan=\"2\">Group #2</td><td rowspan=\"2\">mIoU</td></tr><tr><td>f2,st(·)</td><td>f2,te(·)</td><td>f1,t+1(·)</td><td>f1,t+1(·)</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>68.5†</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>69.0</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>69.5</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>70.2</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>71.3</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.209,
+                0.892,
+                0.278
+            ],
+            "angle": 0,
+            "content": "Table 7. UDA segmentation accuracy (mIoU, %) using different models to generate pseudo labels on GTAv→Citysacpes. †: In the first row, each group only uses the teacher model from the other group; in other cases, each group also uses its own teacher models (not presented in the table)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.292,
+                0.891,
+                0.366
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">GTAv→City.</td><td colspan=\"2\">SYNTHIA→City.</td></tr><tr><td>DACS</td><td>DAFormer</td><td>DACS</td><td>DAFormer</td></tr><tr><td>w/o DTS</td><td>53.9</td><td>56.0</td><td>54.2</td><td>53.5</td></tr><tr><td>w DTS</td><td>55.2</td><td>59.9</td><td>56.6</td><td>56.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.367,
+                0.891,
+                0.392
+            ],
+            "angle": 0,
+            "content": "Table 8. UDA segmentation accuracy (mIoU, %) on two CNN-based backbones and two benchmarks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.417,
+                0.892,
+                0.492
+            ],
+            "angle": 0,
+            "content": "sults are summarized in Table 7. When each teacher-student group only uses the teacher model from another group (the first row), there is almost no accuracy gain (the baseline is \\(68.3\\%\\)), indicating the necessity of the supervision signals from its own teacher."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.493,
+                0.892,
+                0.629
+            ],
+            "angle": 0,
+            "content": "Then, we discuss the situations where each group uses its teacher and one model from the other group. For the second teacher-student group, using \\( f_{1,t+1}^{\\mathrm{st}}(\\cdot) \\) as the teacher is superior to using \\( f_{1,t+1}^{\\mathrm{te}}(\\cdot) \\), because the former model is optimized one more iteration and thus produces better semantics (i.e., 'learning from future'). For the first teacher-student group, only models from the current iteration of the second group can be used, and \\( f_{2,t}^{\\mathrm{te}}(\\cdot) \\) always works better than \\( f_{2,t}^{\\mathrm{st}}(\\cdot) \\), implying the advantage of EMA."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.63,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "DTS applied to other backbones. To show that DTS adapts to different network backbones (e.g., CNNs), we follow the previous approaches [56, 48, 23] to inherit a ResNet101 [14] pre-trained on ImageNet and MSCOCO and train it using DeepLabV2 [2]. The other settings remain unchanged. Results are listed in Table 8. Still, DTS brings consistent accuracy gains, improving DACs and DAfromer by \\(1.3\\%\\) and \\(3.9\\%\\) on \\(\\mathrm{GTAv}\\rightarrow \\mathrm{Cityscapes}\\), and by \\(2.4\\%\\) and \\(3.4\\%\\) on SYNTHIA \\(\\rightarrow\\) Cityscapes. These experiments validate that DTS is a generalized UDA framework that does not rely on specific network architectures."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Comparison of training time and compute. DTS trains two teacher-student groups, so the computational cost is about \\(2 \\times\\) of the baseline (e.g., on a single V100 GPU, DAFormer/DTS needs 13.5/30 hours). The inference cost remains unchanged. We further compare DTS and DAFormer under the same training cost. DTS with half (20K) iterations achieves favorable accuracy (68.6% and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19034"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.089,
+                0.48,
+                0.209
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>GTAv2BDD</td><td>GTAv2IDD</td><td>CS2BDD</td><td>CS2IDD</td></tr><tr><td>Baseline</td><td>46.3</td><td>54.7</td><td>53.7</td><td>51.6</td></tr><tr><td>DTS</td><td>53.6</td><td>59.6</td><td>57.5</td><td>56.1</td></tr><tr><td></td><td>CS2FZ</td><td colspan=\"3\">CS2DZ</td></tr><tr><td>Baseline</td><td>39.7</td><td>34.0</td><td>42.1*</td><td>43.6*</td></tr><tr><td>DTS</td><td>40.4</td><td>37.6</td><td>45.2</td><td>45.6</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.077,
+                0.209,
+                0.47,
+                0.292
+            ],
+            "angle": 0,
+            "content": "Table 9. UDA segmentation accuracy (mIoU, %) on more driving datasets. 'BDD', 'IDD', 'FZ', 'DZ', and 'CS' for Berkeley Driving Dataset, India Driving Dataset, Foggy Zurich, Dark Zurich, and Cityscapes, respectively. Baselines are DAFormer except for the last two columns in CS2DZ, which are HRDA and MIC. *: are numbers inherited from [20, 21]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.317,
+                0.47,
+                0.394
+            ],
+            "angle": 0,
+            "content": "61.8% on GTAv \\(\\rightarrow\\) Cityscapes and SYNTHIA \\(\\rightarrow\\) Cityscapes) over DAFormer with full (40K) iterations (68.3% and 60.9%), meanwhile, DTS with full (40K) iterations reports 71.2% and 63.8%, surpassing DAFormer with doubled (80K) iterations (69.3% and 61.2%)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.395,
+                0.47,
+                0.531
+            ],
+            "angle": 0,
+            "content": "Performance on more driving datasets. We conduct experiments from synthesized and real datasets to more driving datasets, i.e., Berkeley Driving Dataset (BDD) [57], India Driving Dataset (IDD) [52], Foggy Zurich (FZ) [41], and Dark Zurich (DZ) [42]. The comparable results on validation sets of target domain datasets are summarized in Table 9. DTS reports consistent improvement in these transfer scenarios. On the test set of CS2DZ, DTS is also superior to DAformer \\((54.2\\%\\) vs \\(53.8\\%)\\) and HRDA \\((58.9\\%\\) vs \\(55.9\\%)\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.544,
+                0.424,
+                0.56
+            ],
+            "angle": 0,
+            "content": "4.4. Semi-supervised Semantic Segmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.567,
+                0.47,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Dataset. As a generalized self-training framework, DTS can also be applied to semi-supervised segmentation. We perform semi-supervised segmentation on the widely used PASCAL VOC dataset [9], which comprises 20 object classes and a background class. The training, validation, and testing sets contain 1,464, 1,449, and 1,456 images, respectively. To align with prior works, we use the augmented set, which contains 10,582 images, as the complete training set. During the training, we apply random flipping and cropping to augment the image data and resize the image to \\(513 \\times 513\\) before feeding it to the models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Implementation. We perform all experiments using the DeepLabV3+ [3] network with a ResNet-101 backbone pretrained on ImageNet. An SGD optimizer, with a learning rate of 0.0001 for the encoder and 0.001 for the decoder, and a weight decay of 0.0001, is used. The batch size of both labeled and unlabeled data is 16 for each group teacher-student. We train the models for 40 epochs and report the average of three runs for all the results. Since there is no domain gap between the labeled and unlabeled parts, only a dual teacher-student framework and bidirectional learning are applied in the semi-supervised experiments."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.503,
+                0.089,
+                0.892,
+                0.231
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>1/16 (662)</td><td>1/8 (1323)</td><td>1/4 (2646)</td></tr><tr><td>Mean Teacher [46]</td><td>71.3</td><td>75.4</td><td>76.5</td></tr><tr><td>FST [8]</td><td>73.9</td><td>76.1</td><td>78.1</td></tr><tr><td>USRN [13]</td><td>72.3</td><td>-</td><td>-</td></tr><tr><td>PS-MT [32]</td><td>75.5</td><td>78.2</td><td>78.7</td></tr><tr><td>U²PL [54]</td><td>77.2</td><td>79.0</td><td>79.3</td></tr><tr><td>DTS (ours)</td><td>74.8</td><td>77.1</td><td>77.3</td></tr><tr><td>U²PL + DTS (ours)</td><td>78.9</td><td>80.1</td><td>80.4</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.231,
+                0.892,
+                0.257
+            ],
+            "angle": 0,
+            "content": "Table 10. Semi-supervised segmentation accuracy (mIoU, %) on PASCAL VOC."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.289,
+                0.895,
+                0.412
+            ],
+            "angle": 0,
+            "content": "Comparison. The segmentation results are summarized in Table 10. Using \\(1/16\\), \\(1/8\\), \\(1/4\\) labeled data, DTS produces consistent accuracy gains of \\(3.5\\%\\), \\(1.7\\%\\), \\(0.8\\%\\) over the Mean Teacher baseline [46], and \\(1.7\\%\\), \\(1.1\\%\\), \\(1.1\\%\\) over the \\(\\mathrm{U}^2\\mathrm{PL}\\) baseline [54]. This validates that semi-supervised learning also benefits from bidirectional learning which effectively improves the ability to learn from the pseudo labels generated from other groups."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.437,
+                0.628,
+                0.453
+            ],
+            "angle": 0,
+            "content": "5. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.467,
+                0.892,
+                0.678
+            ],
+            "angle": 0,
+            "content": "In this paper, we study the UDA segmentation problem from the perspective of endowing the model with twofold abilities, i.e., learning from the reliable semantics, and adapting to the target domain. We show that these two abilities can conflict with each other in a single teacher-student model, and hence we propose a dual teacher-student (DTS) framework, where the two models stick to the 'learning ability' and 'adapting ability', respectively. Specifically, the second model learns to 'focus on your target' to improve its accuracy in the target domain. We further design a bidirectional learning strategy to facilitate the two models to communicate via generating pseudo labels. We validate the effectiveness of DTS and set new records on two standard UDA segmentation benchmarks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.682,
+                0.892,
+                0.819
+            ],
+            "angle": 0,
+            "content": "As the accuracy on the two benchmarks fast approaches the supervised baseline (e.g., a \\(77.8\\%\\) mIoU on Cityscapes), we look forward to building larger and higher-quality synthesized datasets to break through the baseline. This is of value to real-world applications, as synthesized data can be generated at low costs. We expect that the proposed methodology can be applied to other scenarios such as domain generalization, with the second group focusing on a generic, unbiased feature space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
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+                0.903
+            ],
+            "angle": 0,
+            "content": "Acknowledgment This work was supported by NSFC under Contract U20A20183 and 62021001. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC, and the Supercomputing Center of the USTC."
+        },
+        {
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+    ],
+    [
+        {
+            "type": "title",
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+            "angle": 0,
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+# Focus on Your Target: A Dual Teacher-Student Framework for Domain-adaptive Semantic Segmentation
+
+Xinyue Huo $^{1,2}$  Lingxi Xie $^{2}$  Wengang Zhou $^{1}$  Houqiang Li $^{1}$  Qi Tian $^{2*}$ $^{1}$ University of Science and Technology of China  ${}^{2}$ Huawei Inc.
+
+xinyueh@mail.ustc.edu.cn 198808xc@gmail.com
+
+{zhwg, lihq}  $@$  ustc.edu.cn tian.qil@huawei.com
+
+# Abstract
+
+We study unsupervised domain adaptation (UDA) for semantic segmentation. Currently, a popular UDA framework lies in self-training which endows the model with two-fold abilities: (i) learning reliable semantics from the labeled images in the source domain, and (ii) adapting to the target domain via generating pseudo labels on the unlabeled images. We find that, by decreasing/increasing the proportion of training samples from the target domain, the 'learning ability' is strengthened/weakened while the 'adapting ability' goes in the opposite direction, implying a conflict between these two abilities, especially for a single model. To alleviate the issue, we propose a novel dual teacher-student (DTS) framework and equip it with a bidirectional learning strategy. By increasing the proportion of target-domain data, the second teacher-student model learns to 'Focus on Your Target' while the first model is not affected. DTS is easily plugged into existing self-training approaches. In a standard UDA scenario (training on synthetic, labeled data and real, unlabeled data), DTS shows consistent gains over the baselines and sets new state-of-the-art results of  $76.5\%$  and  $75.1\%$  mIoUs on GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes, respectively. The implementation is available at https://github.com/xinyuehuo/DTS.
+
+# 1. Introduction
+
+Deep neural networks [28] have been proven effective in learning from labeled, in-domain visual data, but their ability to adapt to unlabeled data or unknown domains is often not guaranteed. We delve into this topic by studying the unsupervised domain adaptation (UDA) problem for semantic segmentation, where densely (pixel-wise) labeled data are available for the source domain but only unlabeled images are provided for the target domain. The setting is useful
+
+![](images/e16d7e5e759810ed46d4833d08b64a28ec176e858f1d1af229543701176ccc6e.jpg)
+
+![](images/1a3ce5d2bfe6569b824a9a8c352c28bd7d196dd0330849daed8a9e2139d764fb.jpg)  
+Target A
+
+![](images/f1b07bd18066f49636045e28f872e8d368922ae308c7c16f769927ea737c6ff0.jpg)  
+Target B
+
+![](images/43da1fbe3b0ca48f5ecc25002d3085f38d8ea1428e361d7b4ee301ad076bc915.jpg)
+
+![](images/35ef052feb46323f73aec837d5b8102dcc893a983dca980a391e8f1157760335.jpg)
+
+![](images/20508a7da125b4b0f5b55dc70923f416abf581044f327cced0ab76da557e7381.jpg)
+
+![](images/eb1313ed42189749b010d5721a4568f72b571549c7a41ddc38fb328c809116c7.jpg)  
+DAFormer
+
+![](images/0599455a8620961a47847cebe0565166e36020f4c2cc81650c9f2c20c525cd10.jpg)  
+Ground Truth  
+Figure 1. Segmentation results on a test image from Cityscapes (the model is trained on GTAv). There are two traffic signs with different styles, where Target A is similar to the training data in the source domain while Target B is not. The baseline (DAFormer) gradually improves the accuracy on Target A but achieves the best accuracy on Target B in the midst (at 12K iterations). Our method, DTS, achieves good accuracy for both targets and the trend is more stable throughout the training process (see the curves).
+
+![](images/0bb8dcd72a0473a3834ec9017e26f50763fd210fd3ab9254772e9a1717e563aa.jpg)  
+DTS
+
+in real-world applications where new domains emerge frequently but annotating them is a major burden.
+
+The state-of-the-art UDA approaches for semantic segmentation are mostly built upon a self-training framework. It first learns semantics from labeled data in the source domain and then generates pseudo labels in the target domain, so that the model adapts to the target domain by fitting the pseudo labels. Conceptually, the two steps of self-training endow the model with two-fold abilities, namely, learning knowledge (semantics) from the source domain and adapt-
+
+ing the knowledge to the target domain.
+
+However, these two abilities can conflict with each other. Figure 1 shows an example of two targets of the same class (traffic sign), where Target  $A$  is close to the typical training samples in the source domain, while Target  $B$  has a quite different appearance. Using the default setting of DAFormer [19] (a UDA baseline), the recognition accuracy of Target  $A$  gradually increases while that of Target  $B$  grows first but eventually drops to 0. Interestingly, if one increases the proportion of training samples from the target domain, the recognition quality of Target  $B$  will be better while the recognition accuracy of some unexpected classes (e.g., sidewalk) may drop significantly (more details and examples can be found in the Appendix). The conflict sets an obstacle to achieving higher UDA accuracy.
+
+The above analysis prompts us to design a dual teacher-student (DTS) framework. The key is to train two individual models (with different network weights) so that the aforementioned conflict is alleviated. DTS can be built upon most existing self-training approaches in three steps: (1) making two copies of the original teacher-student model, (2) increasing the proportion of training data from the target domain in the second group, and (3) applying a bidirectional learning strategy so that two models supervise each other via pseudo labels. DTS allows the system to pursue a stronger adapting ability (with the second model) meanwhile the learning ability (guaranteed by the first model) is mostly unaffected.
+
+We conduct semantic segmentation experiments with the standard UDA setting. Two synthetic datasets with dense labels, GTAv [38] and SYNTHIA [39], are used as the source domains, and a real dataset with only images, Cityscapes [6], is used as the target domain. We establish the DTS framework upon three recent self-training baselines, namely, DAFormer [19], HRDA [20], and MIC [21]. DTS improves the segmentation accuracy in every single trial, demonstrating its generalized ability across baselines and datasets. In particular, when integrated with MIC, the prior state-of-the-art, DTS reports  $76.5\%$  and  $67.8\%$  mIoUs on GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes, respectively, setting new records for both benchmarks.
+
+# 2. Related Work
+
+Unsupervised domain adaptation (UDA), the task of transferring semantics from labeled source domains to unlabeled target domains, has been widely studied for many computer vision fields, e.g., classification [33, 58, 51], object detection [15, 24, 45], face recognition [25, 18, 43], semantic segmentation [17, 60], etc.
+
+We briefly review two representative UDA approaches for semantic segmentation. Adversarial learning [47, 49] reduces the gap between the source and target domains by confusing a discriminator trained to judge which domain
+
+the extracted visual features come from. It is closely related to style transfer methods [16, 55, 12, 56] that synthesize data to simulate the target domain. Self-training instead generates pseudo labels for the unlabeled target images and fits the model accordingly. There is a specific class of self-training methods [48, 10, 62] which further bridge the domain gap by creating mixed images that cover both domains [36, 1], inheriting benefits from style transferring. Many follow-up works [19, 20, 21], including this paper, were based on the self-training framework. Besides UDA, other data-efficient learning scenarios such as semi-supervised [22, 40] and few-shot [31, 35] learning also made use of self-training. Generating high-quality pseudo labels is crucial for self-training. Researchers developed various strategies, such as entropy minimization [4], class-balanced training [30], consistency regularization [21], auxiliary task learning [23, 53], etc., for this purpose.
+
+A fundamental concept in self-training is teacher-student optimization. To boost the effect of teacher-student optimization, efforts were made in generating high-quality pseudo labels with stronger teacher models [46, 27, 29, 11] and/or preventing error transmission from the teacher model to the student model [26, 63, 22, 5]. There are also other improvements including using multiple student models [61], designing a better loss function [11], etc. Another closely related concept is co-training [37, 44], which facilitates cross-view consistency with a teacher-student loss. The idea of DTS is to alleviate the discrepancy between teacher and student models from different groups with an indirect consistency constraint.
+
+# 3. Our Approach
+
+We investigate the task of unsupervised domain adaptation (UDA) for semantic segmentation, where a labeled source domain  $\mathbb{S}$  and an unlabeled target domain  $\mathbb{T}$  are available. We denote the source dataset as  $\mathcal{D}^{\mathbb{S}} = \{(\mathbf{x}_n^{\mathbb{S}},\mathbf{y}_n^{\mathbb{S}})\}_{n = 1}^{N_{\mathbb{S}}}$ , where  $\mathbf{x}_n^{\mathbb{S}}$  is an image and  $\mathbf{y}_n^{\mathbb{S}}$  is the corresponding dense label map. The target dataset  $\mathcal{D}^{\mathbb{T}}$  is another set of images without labels, denoted as  $\{(x_{n}^{\mathbb{T}})\}_{n = 1}^{N_{\mathbb{T}}}$ . The two domains share the same set of categories. The goal of UDA is to train a segmentation network  $f(\mathbf{x};\pmb {\theta})$  that eventually works well in the target domain.
+
+We first introduce a self-training baseline where a single teacher-student framework is established (Section 3.1). Then, we reveal a conflict when the model is facilitated to focus on the target domain (Section 3.2), which drives us to propose a dual teacher-student framework towards better UDA performance (Section 3.3).
+
+# 3.1. Single Teacher-Student Baseline
+
+We start with a standard self-training (i.e., teacher-student) baseline which trains a teacher model and a student model denoted as  $f^{\mathrm{te}}(\mathbf{x};\boldsymbol{\theta}^{\mathrm{te}})$  and  $f^{\mathrm{st}}(\mathbf{x};\boldsymbol{\theta}^{\mathrm{st}})$ , respectively.
+
+The teacher model is updated using the exponential moving average (EMA) strategy [46]:
+
+$$
+\boldsymbol {\theta} ^ {\mathrm {t e}} \leftarrow \boldsymbol {\theta} ^ {\mathrm {t e}} \times \lambda + \boldsymbol {\theta} ^ {\mathrm {s t}} \times (1 - \lambda), \tag {1}
+$$
+
+where  $\lambda$  is a constant coefficient which is often close to 1. The student model is trained for segmentation in both the source and target domains. For the source images, semantic labels are available for supervised learning:
+
+$$
+\mathcal {L} ^ {\mathbb {S}} = \mathcal {L} _ {\mathrm {C E}} \left(f ^ {\mathrm {s t}} \left(\mathbf {x} ^ {\mathbb {S}}\right), \mathbf {y} ^ {\mathbb {S}}\right), \tag {2}
+$$
+
+where  $\mathcal{L}_{\mathrm{CE}}$  denotes the pixel-wise cross-entropy loss. For the target images, the teacher model is used to generate a pseudo label  $\tilde{\mathbf{y}}^{\mathbb{T}}$  for  $\mathbf{x}^{\mathbb{T}}$ , and the pixel-wise loss function is computed in a similar way:
+
+$$
+\mathcal {L} ^ {\mathbb {T}} = \mathcal {L} _ {\mathrm {C E}} \left(f ^ {\mathrm {s t}} \left(\mathbf {x} ^ {\mathbb {T}}\right), \tilde {\mathbf {y}} ^ {\mathbb {T}}\right). \tag {3}
+$$
+
+The overall loss is written as  $\mathcal{L} = \mathcal{L}^{\mathbb{S}} + \mathcal{L}^{\mathbb{T}}$ . In practice, a balancing mechanism is applied [48, 19]: all pixel-wise loss terms computed on the target domain is multiplied by a factor of  $\gamma$ , which is the proportion of the pseudo-label confidence surpassing a given threshold,  $\tau$ .
+
+Recently, a series of methods [48, 19, 20, 21] validated that introducing a mixed domain between the source and target domains is helpful for domain adaptation. A typical operation is named ClassMix [36] which samples mixed images by computing
+
+$$
+\mathbf {x} _ {i, j} ^ {\langle \mathrm {S}, \mathrm {T} \rangle} = \mathcal {M} \left(\mathbf {x} _ {i} ^ {\mathrm {S}}, \mathbf {x} _ {j} ^ {\mathrm {T}}\right) = \mathbf {x} _ {i} ^ {\mathrm {S}} \odot \mathbf {M} _ {i} ^ {\mathrm {S}} + \mathbf {x} _ {j} ^ {\mathrm {T}} \odot \left(\mathbf {1} - \mathbf {M} _ {i} ^ {\mathrm {S}}\right), \tag {4}
+$$
+
+where  $\langle \mathbb{S},\mathbb{T}\rangle$  denotes a mixed domain,  $\odot$  is element-wise multiplication, and  $\mathbf{M}^{\mathbb{S}}$  is a mask generated by randomly a few class-level masks from the  $\mathbf{y}^{\mathbb{S}}$ . Accordingly, the target domain in Eqn (3) and the overall loss is replaced with the mixed domain. Note that pseudo labels are only computed for the target portion of the mixed images - we refer the reader to [36] for technical details.
+
+# 3.2. Conflict between Learning and Adapting
+
+Although domain mixing improves the accuracy of UDA segmentation on several benchmarks, we observe that the trained model is easily biased towards the source domain and thus ignores the target domain to some extent. A typical example is shown in Figure 1.
+
+We conjecture that it is the 'over-focus' on the source domain that prevents the model from achieving higher segmentation accuracy. To reveal this, we revisit the working mechanism of ClassMix. Compared to the original strategy that directly generates pseudo labels on the target images, ClassMix increases the proportion of data from the source domain (in a default setting of Eqn (4), an average of half target-domain pixels are replaced with source-domain pixels). This brings two differences. On the one hand, the
+
+<table><tr><td>Label</td><td>{S, T}</td><td>{T, T}</td><td>Supervised</td></tr><tr><td>w/ pseudo labels</td><td>68.3</td><td>67.2</td><td>-</td></tr><tr><td>(pseudo acc.)</td><td>64.9</td><td>64.2</td><td>-</td></tr><tr><td>w/ ground-truth</td><td>74.4</td><td>76.9</td><td>77.8</td></tr></table>
+
+Table 1. UDA segmentation mIoU (%) using DAFourner [19] on the GTAv→Cityscapes benchmark with different options. An italic number indicates a result that uses target-domain labels. The pseudo accuracy is computed on the training set of Cityscapes.
+
+quality of pseudo labels is improved because part of them are inherited from the labels in the source domain; on the other hand, the focus on the target domain is weakened, increasing the risk of domain adaptation.
+
+The above analysis prompts us to perform the 'Focus on Your Target' trail towards higher UDA accuracy. We replace the mixed domain of ClassMix,  $\langle \mathbb{S},\mathbb{T}\rangle$  , with another domain,  $\langle \mathbb{T},\mathbb{T}\rangle$  , in which the mixed samples are generated using two target images:
+
+$$
+\mathbf {x} _ {j _ {1}, j _ {2}} ^ {\langle \mathbb {T}, \mathbb {T} \rangle} = \mathcal {M} \left(\mathbf {x} _ {j _ {1}} ^ {\mathbb {T}}, \mathbf {x} _ {j _ {2}} ^ {\mathbb {T}}\right) = \mathbf {x} _ {j _ {1}} ^ {\mathbb {T}} \odot \mathbf {M} _ {j _ {1}} ^ {\mathbb {T}} + \mathbf {x} _ {j _ {2}} ^ {\mathbb {T}} \odot \left(\mathbf {1} - \mathbf {M} _ {j _ {1}} ^ {\mathbb {T}}\right), \tag {5}
+$$
+
+and the pseudo label is adjusted accordingly.
+
+In Table 1, we run DAFormer [19] with either  $\langle \mathbb{S},\mathbb{T}\rangle$  or  $\langle \mathbb{T},\mathbb{T}\rangle$  for UDA segmentation on GTAv  $\rightarrow$  Cityscapes. Compared to  $\langle \mathbb{S},\mathbb{T}\rangle$ ,  $\langle \mathbb{T},\mathbb{T}\rangle$  achieves an inferior mIoU of  $67.2\%$  (a  $1.3\%$  drop). But, interestingly, when ground-truth labels are used for the mixed images, the mIoU surpasses the original option by  $2.5\%$ , with merely a  $0.9\%$  mIoU lower than the supervised baseline. In other words, 'Focus on Your Target' improves the upper bound, but the models cannot achieve the upper bound because the pseudo labels deteriorate: it is a side effect of decreasing the proportion of training data from the source domain.
+
+In summary, a strong algorithm for UDA shall be equipped with two critical abilities: (i) learning reliable semantics from the source domain, and (ii) adapting the learned semantics to the target domain. However, in the above self-training framework where a single teacher-student model is used, there seems a conflict between these two abilities, e.g., increasing the proportion of target-domain data strengthens the 'adapting ability' but weakens the 'learning ability', setting an obstacle to better performance. In what follows, we offer a solution by training two teacher-student models simultaneously.
+
+# 3.3. Dual Teacher-Student Framework
+
+The proposed dual teacher-student (DTS) framework is illustrated in Figure 2. We denote the models used in the two teacher-student groups as  $f_1^{\mathrm{te}}(\mathbf{x};\boldsymbol{\theta}_1^{\mathrm{te}})$ ,  $f_1^{\mathrm{st}}(\mathbf{x};\boldsymbol{\theta}_1^{\mathrm{st}})$  and  $f_2^{\mathrm{te}}(\mathbf{x};\boldsymbol{\theta}_2^{\mathrm{te}})$ ,  $f_2^{\mathrm{st}}(\mathbf{x};\boldsymbol{\theta}_2^{\mathrm{st}})$ , respectively, where we use a subscript (1 or 2) to indicate the group ID. As described above, we expect the first teacher-student model to stick to learning reliable semantics from the source domain, while the
+
+![](images/5a90aed397753cfdb0bc0058bae7d6d413d1a52e33505fb5c137ed53118b81b0.jpg)  
+Figure 2. An illustration of the proposed DTS framework, where we use Setting  $B$  as an example. The left and right parts describe the optimization of the first and second group models, respectively. The bottom-left part (in gray) corresponds to a single teacher-student framework where ClassMix is used for domain mixing, and the top part (in purple) shows the bidirectional learning strategy, i.e., models from the other group are used for pseudo label generation.
+
+![](images/3b4d1de1075aacaee15f96db0c92c1b48320d2c8e00a0d823b8000ad5352a52c.jpg)
+
+![](images/b7b6a05f8d4957771b931f1fe8dd97c0392d499ec26ef3879cf82ed6c747da80.jpg)  
+Figure 3. An illustration of different combinations of training data. We use magenta to represent source-domain patches and two types of blue to represent target-domain patches from different images. In practice, the images are not partitioned into regular grids, but into semantic regions according to the (real or pseudo) labels.
+
+second teacher-student model learns to 'Focus on Your Target' to enhance the adapting ability.
+
+We achieve the goal by using different data proportions for the two groups. An illustration is provided in Figure 3. The first group remains the same as in the baseline, i.e., half of the training samples are simply source images and another half are ClassMix-ed images covering the source and target domains. Using the previously defined notations, we denote the combination as  $\{\mathbb{S},\langle \mathbb{S},\mathbb{T}\rangle \}$ . To increase the proportion of the target-domain data, we first change the mixture of data from  $\langle \mathbb{S},\mathbb{T}\rangle$  to  $\langle \mathbb{T},\mathbb{T}\rangle$  (i.e., same as that used in the 'Focus on Your Target' trial), and then replace the pure source domain with  $\langle \mathbb{S},\mathbb{T}\rangle$ . That said, we create two settings for data combination,  $\{\mathbb{S},\langle \mathbb{T},\mathbb{T}\rangle \}$  and  $\{\langle \mathbb{S},\mathbb{T}\rangle ,\langle \mathbb{T},\mathbb{T}\rangle \}$ . We name them Setting  $A$  and Setting  $B$  of the second group
+
+throughout the remainder of this paper. Intuitively, the proportion of the target-domain data is increased from around  $25\%$  in the first group (as well as the baselines) to around  $50\% / 75\%$  using Setting A/Setting B in the second group.
+
+There are two teacher models and two student models to be optimized. We perform iterative optimization and propose a bidirectional learning strategy so that each teacher-student model propagates information to the other by contributing to the generation of pseudo labels. The detailed training process is shown in Algorithm 1.
+
+Note that, if  $f_{2,t}^{\mathrm{te}}(\cdot)$  is not used in Step 2 (i.e., all pseudo labels are generated using  $f_{1,t+1}^{\mathrm{te}}(\cdot)$ ), the information is only propagated from the first teacher-student model to the second one, hence the optimization strategy degenerates from bidirectional to unidirectional. The advantage of the bidirectional strategy and other design choices will be diagnosed in the experimental section.
+
+# 3.4. Technical Details
+
+Choosing the proper option for data combination. We compute the averaged confidence of pseudo labels generated by the corresponding teacher models,  $f_{1}^{\mathrm{st}}(\cdot)$  and  $f_{2}^{\mathrm{te}}(\cdot)$ . Following [48, 19],  $\gamma$  is defined as the proportion of pixels with the max class score surpassing a given threshold,  $\tau$ . For each training image  $\mathbf{x}$ , we use  $\gamma_{1}^{\mathrm{st}}(\mathbf{x})$  and  $\gamma_{2}^{\mathrm{te}}(\mathbf{x})$  to denote the average  $\gamma$  values over all pixels when the teacher models are  $f_{1}^{\mathrm{st}}(\cdot)$  and  $f_{2}^{\mathrm{te}}(\cdot)$ , respectively. Then, we estimate the chance that  $f_{2}^{\mathrm{te}}(\cdot)$  generates better pseudo labels than  $f_{1}^{\mathrm{st}}(\cdot)$ :
+
+$$
+\operatorname {P r o b} = \mathbb {E} _ {\mathbf {x} \sim \mathcal {D} ^ {\mathbb {T}}} \left[ \mathbb {I} \left(\gamma_ {2} ^ {\mathrm {t e}} (\mathbf {x}) > \gamma_ {1} ^ {\mathrm {s t}} (\mathbf {x})\right) \right], \tag {6}
+$$
+
+Algorithm 1: DTS: Dual Teacher-Student  
+Input: Source data  $\{\mathbf{x}^{\mathbb{S}},\mathbf{y}^{\mathbb{S}}\}$ , target data  $\{\mathbf{x}^{\mathbb{T}}\}$ , the total iteration number T;  
+1 repeat  
+2 Update  $f_{1,t+1}^{\mathrm{te}}(\cdot)$  using the EMA of  $f_{1,t}^{\mathrm{st}}(\cdot)$ ;  
+3 Get pseudo labels  $\tilde{\mathbf{y}}^{\mathbb{T}}$  by  $f_{1,t+1}^{\mathrm{te}}(\cdot)$  and  $f_{2,t}^{\mathrm{te}}(\cdot)$ ;  
+4 Generate mixed data  $\{\mathbf{x}^{\langle \mathbb{S},\mathbb{T}\rangle},\mathbf{y}^{\langle \mathbb{S},\mathbb{T}\rangle}\}$ , and train  $f_{1,t+1}^{\mathrm{st}}(\cdot)$  on  $\{\mathbb{S},\langle \mathbb{S},\mathbb{T}\rangle\}$ ;  
+5 Update  $f_{2,t+1}^{\mathrm{te}}(\cdot)$  using the EMA of  $f_{2,t}^{\mathrm{st}}(\cdot)$ ;  
+6 Get pseudo labels  $\tilde{\mathbf{y}}^{\mathbb{T}}$  by  $f_{1,t+1}^{\mathrm{st}}(\cdot)$  and  $f_{2,t+1}^{\mathrm{te}}$ ;  
+7 if Setting A: Generate data  $\{\mathbf{x}^{\langle \mathbb{T},\mathbb{T}\rangle},\mathbf{y}^{\langle \mathbb{T},\mathbb{T}\rangle}\}$ , and Train  $f_{2,t+1}^{\mathrm{st}}(\cdot)$  on  $\{\mathbb{S},\langle \mathbb{T},\mathbb{T}\rangle\}$ ;  
+8 if Setting B: Generate data  $\{\mathbf{x}^{\langle \mathbb{S},\mathbb{T}\rangle},\mathbf{y}^{\langle \mathbb{S},\mathbb{T}\rangle},\mathbf{x}^{\langle \mathbb{T},\mathbb{T}\rangle},\mathbf{y}^{\langle \mathbb{T},\mathbb{T}\rangle}\}$ , and train  $f_{2,t+1}^{\mathrm{st}}(\cdot)$  on them;  
+9  $t \gets t + 1$ ;  
+10 until  $t = T$ ;  
+Return:  $f_{2,\mathrm{T}}^{\mathrm{st}}(\cdot)$ .
+
+where  $\mathbb{I}(\cdot)$  is the indicator function that outputs 1 if the statement is true and 0 otherwise. Note that the estimation is performed individually for two training procedures using Setting  $A$  and Setting  $B$ . Finally, we choose the setting with a higher chance that  $f_{2}^{\mathrm{te}}(\cdot)$  is more confident because  $f_{2}^{\mathrm{st}}(\cdot)$  is eventually used for inference. We shall see in Section 4.3 that this criterion always leads to the better choice.
+
+Generating the mask. In the domain mixing operation, we compute the mask  $\mathbf{M}$  by choosing the class label of one image. If the  $\langle \mathbb{S},\mathbb{T}\rangle$  is used, the source image with groundtruth is chosen; if  $\langle \mathbb{T},\mathbb{T}\rangle$  is used, the image with a larger average value of  $\gamma$  is chosen.
+
+Generating pseudo labels. The details are slightly different between Setting  $A$  and Setting  $B$ . When the batch size is  $k$ , the number of target images used for the second group in Setting  $A$  and Setting  $B$  are  $2k$  and  $3k$ , respectively. For Setting  $A$ ,  $k$  pseudo labels used are generated by  $f_{1,t+1}^{\mathrm{st}}(\cdot)$  and other  $k$  by  $f_{2,t+1}^{\mathrm{te}}(\cdot)$ . For Setting  $B$ , the  $2k$  pseudo labels used in  $\langle \mathbb{T}, \mathbb{T} \rangle$  are generated by  $f_{1,t+1}^{\mathrm{st}}(\cdot)$  and the  $k$  labels used in  $\langle \mathbb{S}, \mathbb{T} \rangle$  are generated by  $f_{2,t+1}^{\mathrm{te}}(\cdot)$ .
+
+# 4. Experiments
+
+# 4.1. Datasets and Settings
+
+Datasets. We train the models on a labeled source domain and an unlabeled target domain and test them on the target domain. We follow the convention to set the source domain to be a synthesized dataset (either GTAv [38] which contains 24,966 densely labeled training images at a resolution of  $1914 \times 1052$  or SYNTHIA [39] which contains 9,400 densely labeled training images at a resolution of
+
+$1280 \times 760$ ), and the target dataset to be a real dataset (Cityscapes [6] where only the finely-annotated subset is used, containing 2,975 training images and 500 validation images at a resolution of  $2048 \times 1024$ ). Following the convention to report the mean IoU (mIoU) over 19 classes when GTAv is used as the source domain, and 13 or 16 classes when SYNTHIA is the source domain.
+
+Training details. Our framework is applied to different self-training frameworks. Specifically, we follow the DAFformer series [19, 20, 21] where the encoder is a MiT-B5 model pre-trained on ImageNet-1K [7] and the decoder involves a context-aware feature fusion module. We train the framework on a single NVIDIA Tesla-V100 GPU for 40K iterations with a batch size of 2 for both groups. We use an AdamW optimizer [34] with learning rates of  $6 \times 10^{-5}$  for the encoder and  $6 \times 10^{-4}$  for the decoder, a weight decay of 0.01, and linear warm-up of the learning rate for the first 1.5K iterations. The input image size is always  $512 \times 512$ . During the training phase, we apply random rescaling and cropping to the source and target data, as well as color jittering and Gaussian blur as strong augmentations for the mixed data. The EMA coefficient,  $\lambda$ , is set to be 0.999. The pseudo-label confidence threshold,  $\tau$ , is 0.968 as in [48].
+
+# 4.2. Comparison to the State-of-the-art Methods
+
+We compare DTS to state-of-the-art UDA approaches on the GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes benchmarks. Results are summarized in Table 2 and Table 3, respectively. We establish DTS upon three recently published works, namely, DAFormer [19], HRDA [20], and MIC [21].
+
+DTS reports consistent gains in terms of segmentation accuracy beyond all three baselines. On GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes (13 classes), the mIoU gains over DAFormer, HRDA, MIC are  $2.9\%$ ,  $1.4\%$ ,  $0.6\%$  and  $4.0\%$ ,  $1.0\%$ ,  $1.1\%$  respectively. The gain generally becomes smaller when the baseline is stronger, which is as expected. Specifically, when added to MIC, the previous best approach, DTS achieves new records on these benchmarks: a  $76.5\%$  mIoU on GTAv  $\rightarrow$  Cityscapes and  $67.8\%$  and  $75.1\%$  mIoUs on SYNTHIA  $\rightarrow$  Cityscapes with 16 and 13 classes, respectively.
+
+Comparison to FST. We compare DTS to another plugin approach, FST [8]. On DAFormer, the gains brought by FST on the two benchmarks (SYNTHIA using 13 classes) are  $1.0\%$  and  $1.3\%$ , while the numbers for DTS are  $2.9\%$  and  $4.0\%$ , respectively. That said, besides the contribution of FST that allows us to 'learn from future', the higher accuracy also owes to the design of the DTS framework that alleviates the conflict of learning and adapting.
+
+Class-level analysis. We investigate which classes are best improved by DTS. On  $\mathrm{GTAv} \rightarrow \mathrm{Cityscapes}$ , we detect two classes, sign and truck, on which the IoU gain on the three baselines is always higher than the mIoU gain. In the
+
+<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall</td><td>Fence</td><td>Pole</td><td>Light</td><td>Sign</td><td>Veg</td><td>Terrain</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Train</td><td>Motor</td><td>Bike</td><td>mIoU</td></tr><tr><td>AdaptSegNet [49]</td><td>86.5</td><td>36.0</td><td>79.9</td><td>23.4</td><td>23.3</td><td>23.9</td><td>35.2</td><td>14.8</td><td>83.4</td><td>33.3</td><td>75.6</td><td>58.5</td><td>27.6</td><td>73.7</td><td>32.5</td><td>35.4</td><td>3.9</td><td>30.1</td><td>28.1</td><td>42.4</td></tr><tr><td>PatchAligne [50]</td><td>92.3</td><td>51.9</td><td>82.1</td><td>29.2</td><td>25.1</td><td>24.5</td><td>33.8</td><td>33.0</td><td>82.4</td><td>32.8</td><td>82.2</td><td>58.6</td><td>27.2</td><td>84.3</td><td>33.4</td><td>46.3</td><td>2.2</td><td>29.5</td><td>32.3</td><td>46.5</td></tr><tr><td>FDA [56]</td><td>92.5</td><td>53.3</td><td>82.4</td><td>26.5</td><td>27.6</td><td>36.4</td><td>40.6</td><td>38.9</td><td>82.3</td><td>39.8</td><td>78.0</td><td>62.6</td><td>34.4</td><td>84.9</td><td>34.1</td><td>53.1</td><td>16.9</td><td>27.7</td><td>46.4</td><td>50.5</td></tr><tr><td>DACS [48]</td><td>89.9</td><td>39.7</td><td>87.9</td><td>39.7</td><td>39.5</td><td>38.5</td><td>46.4</td><td>52.8</td><td>88.0</td><td>44.0</td><td>88.8</td><td>67.2</td><td>35.8</td><td>84.5</td><td>45.7</td><td>50.2</td><td>0.0</td><td>27.3</td><td>34.0</td><td>52.1</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>56.0</td><td>79.7</td><td>46.3</td><td>44.8</td><td>45.6</td><td>53.5</td><td>53.5</td><td>88.6</td><td>45.2</td><td>82.1</td><td>70.7</td><td>39.2</td><td>88.8</td><td>45.5</td><td>50.4</td><td>1.0</td><td>48.9</td><td>56.4</td><td>57.5</td></tr><tr><td>DAP [23]</td><td>94.5</td><td>63.1</td><td>89.1</td><td>29.8</td><td>47.5</td><td>50.4</td><td>56.7</td><td>58.7</td><td>89.5</td><td>50.2</td><td>87.0</td><td>73.6</td><td>38.6</td><td>91.3</td><td>50.2</td><td>52.9</td><td>0.0</td><td>50.2</td><td>63.5</td><td>59.8</td></tr><tr><td>CPSL [30]</td><td>92.3</td><td>59.9</td><td>84.9</td><td>45.7</td><td>29.7</td><td>52.8</td><td>61.5</td><td>59.5</td><td>87.9</td><td>41.6</td><td>85.0</td><td>73.0</td><td>35.5</td><td>90.4</td><td>48.7</td><td>73.9</td><td>26.3</td><td>53.8</td><td>53.9</td><td>60.8</td></tr><tr><td>DAFormer [19]</td><td>95.7</td><td>70.2</td><td>89.4</td><td>53.5</td><td>48.1</td><td>49.6</td><td>55.8</td><td>59.4</td><td>89.9</td><td>47.9</td><td>92.5</td><td>72.2</td><td>44.7</td><td>92.3</td><td>74.5</td><td>78.2</td><td>65.1</td><td>55.9</td><td>61.8</td><td>68.3</td></tr><tr><td>DAFormer+FST [8]</td><td>95.3</td><td>67.7</td><td>89.3</td><td>55.5</td><td>47.1</td><td>50.1</td><td>57.2</td><td>58.6</td><td>89.9</td><td>51.0</td><td>92.9</td><td>72.7</td><td>46.3</td><td>92.5</td><td>78.0</td><td>81.6</td><td>74.4</td><td>57.7</td><td>62.6</td><td>69.3</td></tr><tr><td>DAFormer+CAMix [62]</td><td>96.0</td><td>73.1</td><td>89.5</td><td>53.9</td><td>50.8</td><td>51.7</td><td>58.7</td><td>64.9</td><td>90.0</td><td>51.2</td><td>92.2</td><td>71.8</td><td>44.0</td><td>92.8</td><td>78.7</td><td>82.3</td><td>70.9</td><td>54.1</td><td>64.3</td><td>70.0</td></tr><tr><td>DAFormer+DTS (ours)</td><td>96.8</td><td>76.0</td><td>90.0</td><td>56.5</td><td>50.1</td><td>51.9</td><td>57.4</td><td>65.1</td><td>90.5</td><td>50.5</td><td>92.4</td><td>73.5</td><td>46.9</td><td>93.0</td><td>80.4</td><td>85.2</td><td>74.0</td><td>58.7</td><td>63.5</td><td>71.2</td></tr><tr><td>HRDA [20]</td><td>96.4</td><td>74.4</td><td>91.0</td><td>61.6</td><td>51.5</td><td>57.1</td><td>63.9</td><td>69.3</td><td>91.3</td><td>48.4</td><td>94.2</td><td>79.0</td><td>52.9</td><td>93.9</td><td>84.1</td><td>85.7</td><td>75.9</td><td>63.9</td><td>67.5</td><td>73.8</td></tr><tr><td>HRDA+DTS (ours)</td><td>96.7</td><td>76.3</td><td>91.3</td><td>60.7</td><td>55.9</td><td>59.9</td><td>67.3</td><td>72.5</td><td>91.8</td><td>50.1</td><td>94.4</td><td>80.7</td><td>56.8</td><td>94.4</td><td>86.0</td><td>86.0</td><td>73.9</td><td>65.7</td><td>68.4</td><td>75.2</td></tr><tr><td>MIC [21]</td><td>97.4</td><td>80.1</td><td>91.7</td><td>61.2</td><td>56.9</td><td>59.7</td><td>66.0</td><td>71.3</td><td>91.7</td><td>51.4</td><td>94.3</td><td>79.8</td><td>56.1</td><td>94.6</td><td>85.4</td><td>90.3</td><td>80.4</td><td>64.5</td><td>68.5</td><td>75.9</td></tr><tr><td>MIC+DTS (ours)</td><td>97.0</td><td>80.4</td><td>91.8</td><td>60.6</td><td>58.7</td><td>61.7</td><td>67.9</td><td>73.2</td><td>92.0</td><td>45.4</td><td>94.3</td><td>81.3</td><td>58.7</td><td>95.0</td><td>87.9</td><td>90.7</td><td>82.2</td><td>65.7</td><td>69.0</td><td>76.5</td></tr></table>
+
+Table 2. UDA segmentation accuracy (mIoU, %) on the GTAv→Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone.
+
+<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall*</td><td>Fence*</td><td>Pole*</td><td>Light</td><td>Sign</td><td>Veg</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Bus</td><td>Motor</td><td>Bike</td><td>mIoU</td><td>mIoU*</td></tr><tr><td>PatchAlign [50]</td><td>82.4</td><td>38.0</td><td>78.6</td><td>8.7</td><td>0.6</td><td>26.0</td><td>3.9</td><td>11.1</td><td>75.5</td><td>84.6</td><td>53.5</td><td>21.6</td><td>71.4</td><td>32.6</td><td>19.3</td><td>31.7</td><td>40.0</td><td>46.5</td></tr><tr><td>AdaptSegNet [49]</td><td>84.3</td><td>42.7</td><td>77.5</td><td>-</td><td>-</td><td>-</td><td>4.7</td><td>7.0</td><td>77.9</td><td>82.5</td><td>54.3</td><td>21.0</td><td>72.3</td><td>32.2</td><td>18.9</td><td>32.3</td><td>-</td><td>46.7</td></tr><tr><td>FDA [56]</td><td>79.3</td><td>35.0</td><td>73.2</td><td>-</td><td>-</td><td>-</td><td>19.9</td><td>24.0</td><td>61.7</td><td>82.6</td><td>61.4</td><td>31.1</td><td>83.9</td><td>40.8</td><td>38.4</td><td>51.1</td><td>-</td><td>52.5</td></tr><tr><td>DACS [48]</td><td>80.6</td><td>25.1</td><td>81.9</td><td>21.5</td><td>2.9</td><td>37.2</td><td>22.7</td><td>24.0</td><td>83.7</td><td>90.8</td><td>67.6</td><td>38.3</td><td>82.9</td><td>38.9</td><td>28.5</td><td>47.6</td><td>48.3</td><td>54.8</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>45.7</td><td>84.6</td><td>37.1</td><td>0.6</td><td>44.0</td><td>54.6</td><td>37.0</td><td>88.1</td><td>84.4</td><td>74.2</td><td>24.3</td><td>88.2</td><td>51.1</td><td>40.5</td><td>45.6</td><td>55.5</td><td>62.0</td></tr><tr><td>DAP [23]</td><td>84.2</td><td>46.5</td><td>82.5</td><td>35.1</td><td>0.2</td><td>46.7</td><td>53.6</td><td>45.7</td><td>89.3</td><td>87.5</td><td>75.7</td><td>34.6</td><td>91.7</td><td>73.5</td><td>49.4</td><td>60.5</td><td>59.8</td><td>64.3</td></tr><tr><td>CPSL [30]</td><td>87.2</td><td>43.9</td><td>85.5</td><td>33.6</td><td>0.3</td><td>47.7</td><td>57.4</td><td>37.2</td><td>87.8</td><td>88.5</td><td>79.0</td><td>32.0</td><td>90.6</td><td>49.4</td><td>50.8</td><td>59.8</td><td>57.9</td><td>65.3</td></tr><tr><td>DAFormer [19]</td><td>84.5</td><td>40.7</td><td>88.4</td><td>41.5</td><td>6.5</td><td>50.0</td><td>55.0</td><td>54.6</td><td>86.0</td><td>89.8</td><td>73.2</td><td>48.2</td><td>87.2</td><td>53.2</td><td>53.9</td><td>61.7</td><td>60.9</td><td>67.4</td></tr><tr><td>DAFormer+FST [8]</td><td>88.3</td><td>46.1</td><td>88.0</td><td>41.7</td><td>7.3</td><td>50.1</td><td>53.6</td><td>52.5</td><td>87.4</td><td>91.5</td><td>73.9</td><td>48.1</td><td>85.3</td><td>58.6</td><td>55.9</td><td>63.4</td><td>61.9</td><td>68.7</td></tr><tr><td>DAFormer+CAMix [62]</td><td>87.4</td><td>47.5</td><td>88.8</td><td>-</td><td>-</td><td>-</td><td>55.2</td><td>55.4</td><td>87.0</td><td>91.7</td><td>72.0</td><td>49.3</td><td>86.9</td><td>57.0</td><td>57.5</td><td>63.6</td><td>-</td><td>69.2</td></tr><tr><td>DAFormer+DTS (ours)</td><td>88.5</td><td>51.4</td><td>88.0</td><td>37.2</td><td>4.8</td><td>51.4</td><td>59.4</td><td>59.0</td><td>88.1</td><td>92.7</td><td>71.3</td><td>51.3</td><td>89.2</td><td>67.7</td><td>58.4</td><td>62.8</td><td>63.8</td><td>71.4</td></tr><tr><td>HRDA [20]</td><td>85.2</td><td>47.7</td><td>88.8</td><td>49.5</td><td>4.8</td><td>57.2</td><td>65.7</td><td>60.9</td><td>85.3</td><td>92.9</td><td>79.4</td><td>52.8</td><td>89.0</td><td>64.7</td><td>63.9</td><td>64.9</td><td>65.8</td><td>72.4</td></tr><tr><td>HRDA+DTS (ours)</td><td>88.5</td><td>53.1</td><td>88.7</td><td>44.0</td><td>5.8</td><td>59.2</td><td>68.3</td><td>60.7</td><td>87.7</td><td>93.4</td><td>79.5</td><td>46.4</td><td>91.3</td><td>64.2</td><td>66.8</td><td>65.9</td><td>66.5</td><td>73.4</td></tr><tr><td>MIC [21]</td><td>86.6</td><td>50.5</td><td>89.3</td><td>47.9</td><td>7.8</td><td>59.4</td><td>66.7</td><td>63.4</td><td>87.1</td><td>94.6</td><td>81.0</td><td>58.9</td><td>90.1</td><td>61.9</td><td>67.1</td><td>64.3</td><td>67.3</td><td>74.0</td></tr><tr><td>MIC+DTS (ours)</td><td>89.1</td><td>54.9</td><td>89.0</td><td>39.1</td><td>8.7</td><td>61.6</td><td>67.4</td><td>64.3</td><td>88.8</td><td>94.0</td><td>82.2</td><td>60.7</td><td>89.6</td><td>62.6</td><td>68.5</td><td>64.9</td><td>67.8</td><td>75.1</td></tr></table>
+
+Table 3. UDA segmentation accuracy (mIoU, %) on the SYNTHIA  $\rightarrow$ Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone. The mIoU and mIoU* columns denote the averaged IoU over 16 and 13 classes, where the latter does not contain the classes marked with * .
+
+Appendix material, we show that these classes suffer larger variations between the source-domain and target-domain appearances, and hence the learned features are more difficult to transfer. They are largely benefited by the 'Focus on Your Target' ability of DTS.
+
+Visualization. We visualize the segmentation results of DAFormer and DAFormer+DTS in Figure 4. For the real images, the advantage of DTS is significant on the classes that are easily confused with others (e.g., sidewalk which is visually similar to road) or suffer large domain shifts (e.g., sign or truck). For the mixed images, we find that the baseline model is easily confused by the unusual stitching and/or discontinuous textures because it has never seen such pat
+
+terns in the source domain – in such cases, the model of the second group is generally better and sometimes it can propagate the advantages to the model of the first group, revealing the advantage of bidirectional learning.
+
+# 4.3. Diagnostic Studies
+
+Ablative studies. We first diagnose the proposed approach by ablating the contribution of three components, namely, applying the dual teacher-student (DTS) framework, increasing the proportion of data from the target domain (i.e., 'Focus on Your Target'), and adopting the bidirectional learning strategy. Results are summarized in Table 4. Note that some combinations are not valid, e.g.,
+
+![](images/247cd9150a8a3c10de4c58ed9953a63866f5b80ddc0acf2de68a4126b31e8e4f.jpg)
+
+![](images/894bd4c2418c51fd55435c71de9c22abf7bfb665a4eb865e290f7f050b96754a.jpg)
+
+![](images/7f0935645e1f251455c6ae7b7f0b2c14a017bed8910730b6501c9eead52b6618.jpg)
+
+![](images/bbde4cabce46796de72790c54e17b8c1734a93a432dd23ba06773291153c5976.jpg)
+
+![](images/b03c553943c2d81e7d3ebfbf316d51614eda880154de765a77ff962bc348ac75.jpg)
+
+![](images/dd9dac01f1b066bc14d961c3d0642552c87e6ab48217eb0dc70cdab981674c96.jpg)
+
+![](images/0c600514ca616eaaf9fa8da95a610ad66d447128c3d0cdf2a7d66fed0044d99f.jpg)
+
+![](images/448144a1f3a6cb89bef74087e0827338a563f9b7e80ee22bf6ce692216e7de0c.jpg)
+
+![](images/a5bfd39528f90f226f37ad4dcbad0362e87d98bf6b43c9f1db7fc9a6b42efe78.jpg)
+
+![](images/94d7e9dc7f3ccc98ccb1b3ad3481558c24a54aeeb46943eb8e3a21fa4d34084d.jpg)
+
+![](images/ba25a996e0ad0679ad1d547073a413762e2061085149144a764712274944d26b.jpg)
+
+![](images/801a5a6fdfa1d4fe4d564c62c55f270735974bd864e9770ea2ff38f1c77be8ec.jpg)  
+images
+
+![](images/4843f456f29fa61ee7d380eabff5d524dcf61b7383792d2fa3bffba33c74ab88.jpg)
+
+![](images/04f064144e80317d658c43e8f4312b029776f906f5527b7a2a6c2237a41df614.jpg)  
+DAFormer
+
+![](images/337747308e8e9bf0d708b595ef86a9f1242a3554543a60e193d0cc6d3fdd18e0.jpg)
+
+![](images/68329d8b49b2c77160c6f11e27373ec34dc729d7c4ab28496bfcbee3422e6564.jpg)  
+DTS (1st group)
+
+![](images/ad0c26e5ceb4b3c56735829ade0a357c11f201188c96ffcf2d7e2f8a8e0dafdf.jpg)
+
+![](images/ea8614046d8a0e250f53b83a0002ee9b052d9b5433042c0b38f26ef9e1cbeb70.jpg)  
+DTS  $(2^{\mathrm{nd}}$  group)
+
+![](images/af6f4877cec83293438847e9cdf47e293fa58b9b10bcad0970efdecbb2709669.jpg)
+
+![](images/238a5059446e64d46a20119e146c049ba96b45effaf7997cfde77903e15d5b2e.jpg)  
+ground truth  
+Figure 4. Visualization of the segmentation results of DAFormer [19] and DTS. The top two rows display two real images and the bottom two rows display two synthesized images from  $\langle \mathbb{T},\mathbb{T}\rangle$  . In each group, the first example is from GTAv  $\rightarrow$  Cityscapes and the second one is from SYNTHIA  $\rightarrow$  Cityscapes. The white, dashed circles highlight the regions that are significantly improved by DTS.
+
+<table><tr><td>Setting</td><td colspan="5">Choice and Accuracy</td></tr><tr><td>Dual Teacher-Student ‘Focus on Your Target’</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td></tr><tr><td>Bidirectional Learning</td><td></td><td></td><td>✓</td><td>✓</td><td></td></tr><tr><td>GTAv→Cityscapes</td><td>68.3</td><td>67.2</td><td>69.7</td><td>68.6</td><td>71.2</td></tr><tr><td>SYNTHIA→Cityscapes</td><td>60.9</td><td>58.4</td><td>63.3</td><td>61.2</td><td>63.7</td></tr></table>
+
+Table 4. Ablative studies of DTS with respect to the UDA segmentation accuracy (mIoU, %) on both benchmarks. All these experiments are based on DAFformer [19]. For SYNTHIA→Cityscapes, the mIoUs are computed over 16 classes. Note that DTS alone (without the latter two options) is equivalent to the baseline (the leftmost column) and is simply ignored in the table.
+
+solely applying DTS (without adjusting the proportion of training data nor applying bidirectional learning) does not make any difference from the baseline; also, bidirectional learning must be built upon DTS.
+
+From Columns 1-3, one can learn the importance of the DTS framework. When DTS is not established, simply increasing the proportion of target data (Col 2) incurs an accuracy drop on both GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes. This validates our motivation, i.e., there is a conflict between the learning and adapting abilities. However, after the dual teacher-student framework is established (Col 3, where the first teacher-student group focuses on learning and the second group focuses on adapting), the conflict is weakened and the accuracy gain becomes clear (1.6% on GTAv  $\rightarrow$  Cityscapes and 2.4% on SYNTHIA  $\rightarrow$  Cityscapes).
+
+<table><tr><td colspan="2">Baseline</td><td>DAFormer</td><td>HRDA</td><td>MIC</td></tr><tr><td rowspan="2">GTAv</td><td>Setting A</td><td>70.3</td><td>74.7</td><td>76.5</td></tr><tr><td>Setting B</td><td>71.2</td><td>75.2</td><td>76.2</td></tr><tr><td rowspan="2">SYNTHIA</td><td>Setting A</td><td>63.8</td><td>66.5</td><td>67.8</td></tr><tr><td>Setting B</td><td>61.2</td><td>66.0</td><td>67.2</td></tr></table>
+
+Table 5. The results of DTS with different data mixing options. For SYNTHIA  $\rightarrow$  Cityscapes, the mIoUs are computed over 16 classes.
+
+From Columns 3-5, one can observe the contribution of 'Focus on Your Target' (i.e., increasing the proportion of target data) and bidirectional learning on top of the DTS framework. The best practice is obtained when all the modules are used (Col 5), aligning with the results reported in Tables 2 and 3. Interestingly, when bidirectional learning is adopted alone (Col 4), the accuracy gain is much smaller than that of using 'Focus on Your Target' alone, because the two groups are using the same proportion of data mixing, and thus the bidirectional learning carries limited complementary information.
+
+Choose the option for data combination. We validate that the data combination option can be chosen by comparing the pseudo-label confidence, as described in Section 3.4. We plot the Prob curves throughout training procedure of Setting  $A$  and Setting  $B$  in Figure 5. On GTAv→Cityscapes, the Prob value of Setting  $B$  is eventually higher than that of Setting  $A$ , and DTS with Setting  $B$  outperforms DTS with Setting  $A$  by a  $0.9\%$  mIoU (see Table 5). However, on SYNTHIA→Cityscapes, the Prob value of Setting  $A$  is always higher than that of Setting
+
+![](images/0ba16677835052872464769e60c20a30a41ff4bc9b17dcf571ea892c6aa53a80.jpg)  
+Figure 5. The curves of Prob computed on the GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes benchmarks. DAFormer is used as the baseline. These curves suggest that, on DAFormer, Setting  $B$  is better for GTAv  $\rightarrow$  Cityscapes while Setting  $A$  is better for SYNTHIA  $\rightarrow$  Cityscapes.
+
+![](images/332950032f26605fea7dba4a26cfb15726b7849f2ec84f22bbf8c7912e11dc5b.jpg)
+
+<table><tr><td>Options</td><td>GTAv</td><td>SYNTHIA</td></tr><tr><td>{&lt;T,T&gt;}</td><td>69.1</td><td>61.1</td></tr><tr><td>{&lt;S,T&gt;}</td><td>69.3</td><td>59.4</td></tr><tr><td>{S, &lt;T,T&gt;}</td><td>70.3</td><td>63.8</td></tr><tr><td>{&lt;S,T&gt;, &lt;T,T&gt;}</td><td>71.2</td><td>61.2</td></tr></table>
+
+$B$ , and DTS with Setting  $A$  outperforms DTS with Setting  $B$  by a  $2.4\%$  mIoU. Table 5 also shows the segmentation accuracy on the other two baselines. All choices of advantageous results align with the aforementioned criterion. From an intuitive view, Setting  $B$  has a smaller portion of source data, so it works better in the GTAv  $\rightarrow$  Cityscapes scenario because GTAv has a smaller domain gap to Cityscapes than SYNTHIA, which can be validated by vanilla transfer experiments (GTAv  $\rightarrow$  Cityscapes:  $46.2\%$ , SYNTHIA  $\rightarrow$  Cityscapes:  $41.3\%$ ).
+
+Except for Setting  $A$  and Setting  $B$ , there are two other options to increase the focus on the target domain as well, namely  $\{\langle \mathbb{T},\mathbb{T}\rangle \}$  and  $\{\langle \mathbb{S},\mathbb{T}\rangle \}$ . The two options do not include any mixing data and have a disadvantage compared to the previous two combinations.  $\{\langle \mathbb{T},\mathbb{T}\rangle \}$  means that the second teacher-student group achieves the ability of learning only from the pseudo labels provided by  $f_1^{\mathrm{st}}(\mathbf{x};\pmb {\theta}_1^{\mathrm{st}})$ . As a result, noise can easily persist without accurate supervision from the source data.  $\{\langle \mathbb{S},\mathbb{T}\rangle \}$  has a similar data proportion as  $\{\mathbb{S},\langle \mathbb{T},\mathbb{T}\rangle \}$  but cannot solve the problem of inconsistency between the training and testing data. Using  $\langle \mathbb{T},\mathbb{T}\rangle$  as the training domain is an effective way to bridge the gap between the training and testing phases. Therefore, the two combinations containing two different types of data used in DTS are more suitable for balancing the learning and adapting abilities.
+
+Models for pseudo label generation. We study the impact of different models for generating pseudo labels. Re
+
+Table 6. The results of DTS with more data mixing options. We show the mIoU of the 16 classes in SYNTHIA and make this comparison based on the DAFourner baseline.  
+
+<table><tr><td colspan="2">Group #1</td><td colspan="2">Group #2</td><td rowspan="2">mIoU</td></tr><tr><td>f2,st(·)</td><td>f2,te(·)</td><td>f1,t+1(·)</td><td>f1,t+1(·)</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>68.5†</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>69.0</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>69.5</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>70.2</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>71.3</td></tr></table>
+
+Table 7. UDA segmentation accuracy (mIoU, %) using different models to generate pseudo labels on GTAv→Citysacpes. †: In the first row, each group only uses the teacher model from the other group; in other cases, each group also uses its own teacher models (not presented in the table).  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">GTAv→City.</td><td colspan="2">SYNTHIA→City.</td></tr><tr><td>DACS</td><td>DAFormer</td><td>DACS</td><td>DAFormer</td></tr><tr><td>w/o DTS</td><td>53.9</td><td>56.0</td><td>54.2</td><td>53.5</td></tr><tr><td>w DTS</td><td>55.2</td><td>59.9</td><td>56.6</td><td>56.9</td></tr></table>
+
+Table 8. UDA segmentation accuracy (mIoU, %) on two CNN-based backbones and two benchmarks.
+
+sults are summarized in Table 7. When each teacher-student group only uses the teacher model from another group (the first row), there is almost no accuracy gain (the baseline is  $68.3\%$ ), indicating the necessity of the supervision signals from its own teacher.
+
+Then, we discuss the situations where each group uses its teacher and one model from the other group. For the second teacher-student group, using  $f_{1,t+1}^{\mathrm{st}}(\cdot)$  as the teacher is superior to using  $f_{1,t+1}^{\mathrm{te}}(\cdot)$ , because the former model is optimized one more iteration and thus produces better semantics (i.e., 'learning from future'). For the first teacher-student group, only models from the current iteration of the second group can be used, and  $f_{2,t}^{\mathrm{te}}(\cdot)$  always works better than  $f_{2,t}^{\mathrm{st}}(\cdot)$ , implying the advantage of EMA.
+
+DTS applied to other backbones. To show that DTS adapts to different network backbones (e.g., CNNs), we follow the previous approaches [56, 48, 23] to inherit a ResNet101 [14] pre-trained on ImageNet and MSCOCO and train it using DeepLabV2 [2]. The other settings remain unchanged. Results are listed in Table 8. Still, DTS brings consistent accuracy gains, improving DACs and DAfromer by  $1.3\%$  and  $3.9\%$  on  $\mathrm{GTAv}\rightarrow \mathrm{Cityscapes}$ , and by  $2.4\%$  and  $3.4\%$  on SYNTHIA  $\rightarrow$  Cityscapes. These experiments validate that DTS is a generalized UDA framework that does not rely on specific network architectures.
+
+Comparison of training time and compute. DTS trains two teacher-student groups, so the computational cost is about  $2 \times$  of the baseline (e.g., on a single V100 GPU, DAFormer/DTS needs 13.5/30 hours). The inference cost remains unchanged. We further compare DTS and DAFormer under the same training cost. DTS with half (20K) iterations achieves favorable accuracy (68.6% and
+
+<table><tr><td></td><td>GTAv2BDD</td><td>GTAv2IDD</td><td>CS2BDD</td><td>CS2IDD</td></tr><tr><td>Baseline</td><td>46.3</td><td>54.7</td><td>53.7</td><td>51.6</td></tr><tr><td>DTS</td><td>53.6</td><td>59.6</td><td>57.5</td><td>56.1</td></tr><tr><td></td><td>CS2FZ</td><td colspan="3">CS2DZ</td></tr><tr><td>Baseline</td><td>39.7</td><td>34.0</td><td>42.1*</td><td>43.6*</td></tr><tr><td>DTS</td><td>40.4</td><td>37.6</td><td>45.2</td><td>45.6</td></tr></table>
+
+Table 9. UDA segmentation accuracy (mIoU, %) on more driving datasets. 'BDD', 'IDD', 'FZ', 'DZ', and 'CS' for Berkeley Driving Dataset, India Driving Dataset, Foggy Zurich, Dark Zurich, and Cityscapes, respectively. Baselines are DAFormer except for the last two columns in CS2DZ, which are HRDA and MIC. *: are numbers inherited from [20, 21].
+
+61.8% on GTAv  $\rightarrow$  Cityscapes and SYNTHIA  $\rightarrow$  Cityscapes) over DAFormer with full (40K) iterations (68.3% and 60.9%), meanwhile, DTS with full (40K) iterations reports 71.2% and 63.8%, surpassing DAFormer with doubled (80K) iterations (69.3% and 61.2%).
+
+Performance on more driving datasets. We conduct experiments from synthesized and real datasets to more driving datasets, i.e., Berkeley Driving Dataset (BDD) [57], India Driving Dataset (IDD) [52], Foggy Zurich (FZ) [41], and Dark Zurich (DZ) [42]. The comparable results on validation sets of target domain datasets are summarized in Table 9. DTS reports consistent improvement in these transfer scenarios. On the test set of CS2DZ, DTS is also superior to DAformer  $(54.2\%$  vs  $53.8\%)$  and HRDA  $(58.9\%$  vs  $55.9\%)$ .
+
+# 4.4. Semi-supervised Semantic Segmentation
+
+Dataset. As a generalized self-training framework, DTS can also be applied to semi-supervised segmentation. We perform semi-supervised segmentation on the widely used PASCAL VOC dataset [9], which comprises 20 object classes and a background class. The training, validation, and testing sets contain 1,464, 1,449, and 1,456 images, respectively. To align with prior works, we use the augmented set, which contains 10,582 images, as the complete training set. During the training, we apply random flipping and cropping to augment the image data and resize the image to  $513 \times 513$  before feeding it to the models.
+
+Implementation. We perform all experiments using the DeepLabV3+ [3] network with a ResNet-101 backbone pretrained on ImageNet. An SGD optimizer, with a learning rate of 0.0001 for the encoder and 0.001 for the decoder, and a weight decay of 0.0001, is used. The batch size of both labeled and unlabeled data is 16 for each group teacher-student. We train the models for 40 epochs and report the average of three runs for all the results. Since there is no domain gap between the labeled and unlabeled parts, only a dual teacher-student framework and bidirectional learning are applied in the semi-supervised experiments.
+
+<table><tr><td>Methods</td><td>1/16 (662)</td><td>1/8 (1323)</td><td>1/4 (2646)</td></tr><tr><td>Mean Teacher [46]</td><td>71.3</td><td>75.4</td><td>76.5</td></tr><tr><td>FST [8]</td><td>73.9</td><td>76.1</td><td>78.1</td></tr><tr><td>USRN [13]</td><td>72.3</td><td>-</td><td>-</td></tr><tr><td>PS-MT [32]</td><td>75.5</td><td>78.2</td><td>78.7</td></tr><tr><td>U²PL [54]</td><td>77.2</td><td>79.0</td><td>79.3</td></tr><tr><td>DTS (ours)</td><td>74.8</td><td>77.1</td><td>77.3</td></tr><tr><td>U²PL + DTS (ours)</td><td>78.9</td><td>80.1</td><td>80.4</td></tr></table>
+
+Table 10. Semi-supervised segmentation accuracy (mIoU, %) on PASCAL VOC.
+
+Comparison. The segmentation results are summarized in Table 10. Using  $1/16$ ,  $1/8$ ,  $1/4$  labeled data, DTS produces consistent accuracy gains of  $3.5\%$ ,  $1.7\%$ ,  $0.8\%$  over the Mean Teacher baseline [46], and  $1.7\%$ ,  $1.1\%$ ,  $1.1\%$  over the  $\mathrm{U}^2\mathrm{PL}$  baseline [54]. This validates that semi-supervised learning also benefits from bidirectional learning which effectively improves the ability to learn from the pseudo labels generated from other groups.
+
+# 5. Conclusions
+
+In this paper, we study the UDA segmentation problem from the perspective of endowing the model with twofold abilities, i.e., learning from the reliable semantics, and adapting to the target domain. We show that these two abilities can conflict with each other in a single teacher-student model, and hence we propose a dual teacher-student (DTS) framework, where the two models stick to the 'learning ability' and 'adapting ability', respectively. Specifically, the second model learns to 'focus on your target' to improve its accuracy in the target domain. We further design a bidirectional learning strategy to facilitate the two models to communicate via generating pseudo labels. We validate the effectiveness of DTS and set new records on two standard UDA segmentation benchmarks.
+
+As the accuracy on the two benchmarks fast approaches the supervised baseline (e.g., a  $77.8\%$  mIoU on Cityscapes), we look forward to building larger and higher-quality synthesized datasets to break through the baseline. This is of value to real-world applications, as synthesized data can be generated at low costs. We expect that the proposed methodology can be applied to other scenarios such as domain generalization, with the second group focusing on a generic, unbiased feature space.
+
+Acknowledgment This work was supported by NSFC under Contract U20A20183 and 62021001. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC, and the Supercomputing Center of the USTC.
+
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+                                    "content": "in real-world applications where new domains emerge frequently but annotating them is a major burden."
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+                                    "type": "text",
+                                    "content": "ing the knowledge to the target domain."
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+                                    "type": "text",
+                                    "content": "However, these two abilities can conflict with each other. Figure 1 shows an example of two targets of the same class (traffic sign), where Target "
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+                                    "content": " is close to the typical training samples in the source domain, while Target "
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+                                    "type": "text",
+                                    "content": " has a quite different appearance. Using the default setting of DAFormer [19] (a UDA baseline), the recognition accuracy of Target "
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+                                    "content": " gradually increases while that of Target "
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+                                    "content": " grows first but eventually drops to 0. Interestingly, if one increases the proportion of training samples from the target domain, the recognition quality of Target "
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+                                    "type": "text",
+                                    "content": " will be better while the recognition accuracy of some unexpected classes (e.g., sidewalk) may drop significantly (more details and examples can be found in the Appendix). The conflict sets an obstacle to achieving higher UDA accuracy."
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+                                    "content": "The above analysis prompts us to design a dual teacher-student (DTS) framework. The key is to train two individual models (with different network weights) so that the aforementioned conflict is alleviated. DTS can be built upon most existing self-training approaches in three steps: (1) making two copies of the original teacher-student model, (2) increasing the proportion of training data from the target domain in the second group, and (3) applying a bidirectional learning strategy so that two models supervise each other via pseudo labels. DTS allows the system to pursue a stronger adapting ability (with the second model) meanwhile the learning ability (guaranteed by the first model) is mostly unaffected."
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+                                    "content": "We conduct semantic segmentation experiments with the standard UDA setting. Two synthetic datasets with dense labels, GTAv [38] and SYNTHIA [39], are used as the source domains, and a real dataset with only images, Cityscapes [6], is used as the target domain. We establish the DTS framework upon three recent self-training baselines, namely, DAFormer [19], HRDA [20], and MIC [21]. DTS improves the segmentation accuracy in every single trial, demonstrating its generalized ability across baselines and datasets. In particular, when integrated with MIC, the prior state-of-the-art, DTS reports "
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+                                    "type": "inline_equation",
+                                    "content": "76.5\\%"
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+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "67.8\\%"
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+                                    "type": "text",
+                                    "content": " mIoUs on GTAv "
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+                                    "type": "text",
+                                    "content": " Cityscapes and SYNTHIA "
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+                                    "type": "text",
+                                    "content": " Cityscapes, respectively, setting new records for both benchmarks."
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+                                    "content": "2. Related Work"
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Unsupervised domain adaptation (UDA), the task of transferring semantics from labeled source domains to unlabeled target domains, has been widely studied for many computer vision fields, e.g., classification [33, 58, 51], object detection [15, 24, 45], face recognition [25, 18, 43], semantic segmentation [17, 60], etc."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": "We briefly review two representative UDA approaches for semantic segmentation. Adversarial learning [47, 49] reduces the gap between the source and target domains by confusing a discriminator trained to judge which domain"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": "the extracted visual features come from. It is closely related to style transfer methods [16, 55, 12, 56] that synthesize data to simulate the target domain. Self-training instead generates pseudo labels for the unlabeled target images and fits the model accordingly. There is a specific class of self-training methods [48, 10, 62] which further bridge the domain gap by creating mixed images that cover both domains [36, 1], inheriting benefits from style transferring. Many follow-up works [19, 20, 21], including this paper, were based on the self-training framework. Besides UDA, other data-efficient learning scenarios such as semi-supervised [22, 40] and few-shot [31, 35] learning also made use of self-training. Generating high-quality pseudo labels is crucial for self-training. Researchers developed various strategies, such as entropy minimization [4], class-balanced training [30], consistency regularization [21], auxiliary task learning [23, 53], etc., for this purpose."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
+                                        276,
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+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": "A fundamental concept in self-training is teacher-student optimization. To boost the effect of teacher-student optimization, efforts were made in generating high-quality pseudo labels with stronger teacher models [46, 27, 29, 11] and/or preventing error transmission from the teacher model to the student model [26, 63, 22, 5]. There are also other improvements including using multiple student models [61], designing a better loss function [11], etc. Another closely related concept is co-training [37, 44], which facilitates cross-view consistency with a teacher-student loss. The idea of DTS is to alleviate the discrepancy between teacher and student models from different groups with an indirect consistency constraint."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "3. Our Approach"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We investigate the task of unsupervised domain adaptation (UDA) for semantic segmentation, where a labeled source domain "
+                                },
+                                {
+                                    "bbox": [
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+                                        461,
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and an unlabeled target domain "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{T}"
+                                },
+                                {
+                                    "bbox": [
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+                                        461,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are available. We denote the source dataset as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}^{\\mathbb{S}} = \\{(\\mathbf{x}_n^{\\mathbb{S}},\\mathbf{y}_n^{\\mathbb{S}})\\}_{n = 1}^{N_{\\mathbb{S}}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_n^{\\mathbb{S}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " is an image and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y}_n^{\\mathbb{S}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " is the corresponding dense label map. The target dataset "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}^{\\mathbb{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " is another set of images without labels, denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{(x_{n}^{\\mathbb{T}})\\}_{n = 1}^{N_{\\mathbb{T}}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": ". The two domains share the same set of categories. The goal of UDA is to train a segmentation network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\mathbf{x};\\pmb {\\theta})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " that eventually works well in the target domain."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We first introduce a self-training baseline where a single teacher-student framework is established (Section 3.1). Then, we reveal a conflict when the model is facilitated to focus on the target domain (Section 3.2), which drives us to propose a dual teacher-student framework towards better UDA performance (Section 3.3)."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.1. Single Teacher-Student Baseline"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
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+                                    "type": "text",
+                                    "content": "We start with a standard self-training (i.e., teacher-student) baseline which trains a teacher model and a student model denoted as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}^{\\mathrm{te}})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}^{\\mathrm{st}})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "The teacher model is updated using the exponential moving average (EMA) strategy [46]:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {\\theta} ^ {\\mathrm {t e}} \\leftarrow \\boldsymbol {\\theta} ^ {\\mathrm {t e}} \\times \\lambda + \\boldsymbol {\\theta} ^ {\\mathrm {s t}} \\times (1 - \\lambda), \\tag {1}",
+                                    "image_path": "097116edf8b73132d51b13986d8d3472990fa9cc88947fbca340dcf18fe1ecd3.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a constant coefficient which is often close to 1. The student model is trained for segmentation in both the source and target domains. For the source images, semantic labels are available for supervised learning:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} ^ {\\mathbb {S}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(f ^ {\\mathrm {s t}} \\left(\\mathbf {x} ^ {\\mathbb {S}}\\right), \\mathbf {y} ^ {\\mathbb {S}}\\right), \\tag {2}",
+                                    "image_path": "725729cca70148955ffa027ca8730ff4d2f11293e7d3a1f083cd547b6f0dc2e2.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{CE}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        205,
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+                                        253
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the pixel-wise cross-entropy loss. For the target images, the teacher model is used to generate a pseudo label "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        205,
+                                        287,
+                                        253
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathbf{y}}^{\\mathbb{T}}"
+                                },
+                                {
+                                    "bbox": [
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+                                        205,
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+                                    ],
+                                    "type": "text",
+                                    "content": " for "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}^{\\mathbb{T}}"
+                                },
+                                {
+                                    "bbox": [
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+                                        253
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the pixel-wise loss function is computed in a similar way:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} ^ {\\mathbb {T}} = \\mathcal {L} _ {\\mathrm {C E}} \\left(f ^ {\\mathrm {s t}} \\left(\\mathbf {x} ^ {\\mathbb {T}}\\right), \\tilde {\\mathbf {y}} ^ {\\mathbb {T}}\\right). \\tag {3}",
+                                    "image_path": "42a46cae462783d3731acd50cdea3e6e95aee43da36ed0ae682c69570364c0d1.jpg"
+                                }
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The overall loss is written as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L} = \\mathcal{L}^{\\mathbb{S}} + \\mathcal{L}^{\\mathbb{T}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        284,
+                                        287,
+                                        344
+                                    ],
+                                    "type": "text",
+                                    "content": ". In practice, a balancing mechanism is applied [48, 19]: all pixel-wise loss terms computed on the target domain is multiplied by a factor of "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which is the proportion of the pseudo-label confidence surpassing a given threshold, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    ],
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Recently, a series of methods [48, 19, 20, 21] validated that introducing a mixed domain between the source and target domains is helpful for domain adaptation. A typical operation is named ClassMix [36] which samples mixed images by computing"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {x} _ {i, j} ^ {\\langle \\mathrm {S}, \\mathrm {T} \\rangle} = \\mathcal {M} \\left(\\mathbf {x} _ {i} ^ {\\mathrm {S}}, \\mathbf {x} _ {j} ^ {\\mathrm {T}}\\right) = \\mathbf {x} _ {i} ^ {\\mathrm {S}} \\odot \\mathbf {M} _ {i} ^ {\\mathrm {S}} + \\mathbf {x} _ {j} ^ {\\mathrm {T}} \\odot \\left(\\mathbf {1} - \\mathbf {M} _ {i} ^ {\\mathrm {S}}\\right), \\tag {4}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "text",
+                                    "content": " denotes a mixed domain, "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is element-wise multiplication, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{M}^{\\mathbb{S}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a mask generated by randomly a few class-level masks from the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y}^{\\mathbb{S}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Accordingly, the target domain in Eqn (3) and the overall loss is replaced with the mixed domain. Note that pseudo labels are only computed for the target portion of the mixed images - we refer the reader to [36] for technical details."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.2. Conflict between Learning and Adapting"
+                                }
+                            ]
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+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Although domain mixing improves the accuracy of UDA segmentation on several benchmarks, we observe that the trained model is easily biased towards the source domain and thus ignores the target domain to some extent. A typical example is shown in Figure 1."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "We conjecture that it is the 'over-focus' on the source domain that prevents the model from achieving higher segmentation accuracy. To reveal this, we revisit the working mechanism of ClassMix. Compared to the original strategy that directly generates pseudo labels on the target images, ClassMix increases the proportion of data from the source domain (in a default setting of Eqn (4), an average of half target-domain pixels are replaced with source-domain pixels). This brings two differences. On the one hand, the"
+                                }
+                            ]
+                        }
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Label</td><td>{S, T}</td><td>{T, T}</td><td>Supervised</td></tr><tr><td>w/ pseudo labels</td><td>68.3</td><td>67.2</td><td>-</td></tr><tr><td>(pseudo acc.)</td><td>64.9</td><td>64.2</td><td>-</td></tr><tr><td>w/ ground-truth</td><td>74.4</td><td>76.9</td><td>77.8</td></tr></table>",
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+                                        }
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+                                            "type": "text",
+                                            "content": "Table 1. UDA segmentation mIoU (%) using DAFourner [19] on the GTAv→Cityscapes benchmark with different options. An italic number indicates a result that uses target-domain labels. The pseudo accuracy is computed on the training set of Cityscapes."
+                                        }
+                                    ]
+                                }
+                            ],
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+                            "type": "table_footnote"
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+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "quality of pseudo labels is improved because part of them are inherited from the labels in the source domain; on the other hand, the focus on the target domain is weakened, increasing the risk of domain adaptation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
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+                {
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+                                    "type": "text",
+                                    "content": "The above analysis prompts us to perform the 'Focus on Your Target' trail towards higher UDA accuracy. We replace the mixed domain of ClassMix, "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{S},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " , with another domain, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{T},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " , in which the mixed samples are generated using two target images:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {x} _ {j _ {1}, j _ {2}} ^ {\\langle \\mathbb {T}, \\mathbb {T} \\rangle} = \\mathcal {M} \\left(\\mathbf {x} _ {j _ {1}} ^ {\\mathbb {T}}, \\mathbf {x} _ {j _ {2}} ^ {\\mathbb {T}}\\right) = \\mathbf {x} _ {j _ {1}} ^ {\\mathbb {T}} \\odot \\mathbf {M} _ {j _ {1}} ^ {\\mathbb {T}} + \\mathbf {x} _ {j _ {2}} ^ {\\mathbb {T}} \\odot \\left(\\mathbf {1} - \\mathbf {M} _ {j _ {1}} ^ {\\mathbb {T}}\\right), \\tag {5}",
+                                    "image_path": "f79dc3dc1ffab25982bfd7387ccfd959539a5e0fe80a466d2d6041023b1901d8.jpg"
+                                }
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+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "and the pseudo label is adjusted accordingly."
+                                }
+                            ]
+                        }
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In Table 1, we run DAFormer [19] with either "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{S},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " or "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{T},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for UDA segmentation on GTAv "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rightarrow"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " Cityscapes. Compared to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{S},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{T},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " achieves an inferior mIoU of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "67.2\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (a "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "1.3\\%"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " drop). But, interestingly, when ground-truth labels are used for the mixed images, the mIoU surpasses the original option by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "2.5\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", with merely a "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "0.9\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " mIoU lower than the supervised baseline. In other words, 'Focus on Your Target' improves the upper bound, but the models cannot achieve the upper bound because the pseudo labels deteriorate: it is a side effect of decreasing the proportion of training data from the source domain."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In summary, a strong algorithm for UDA shall be equipped with two critical abilities: (i) learning reliable semantics from the source domain, and (ii) adapting the learned semantics to the target domain. However, in the above self-training framework where a single teacher-student model is used, there seems a conflict between these two abilities, e.g., increasing the proportion of target-domain data strengthens the 'adapting ability' but weakens the 'learning ability', setting an obstacle to better performance. In what follows, we offer a solution by training two teacher-student models simultaneously."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.3. Dual Teacher-Student Framework"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The proposed dual teacher-student (DTS) framework is illustrated in Figure 2. We denote the models used in the two teacher-student groups as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_1^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}_1^{\\mathrm{te}})"
+                                },
+                                {
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+                                    "type": "text",
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+                                    "content": "f_1^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}_1^{\\mathrm{st}})"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "f_2^{\\mathrm{te}}(\\mathbf{x};\\boldsymbol{\\theta}_2^{\\mathrm{te}})"
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+                                {
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "f_2^{\\mathrm{st}}(\\mathbf{x};\\boldsymbol{\\theta}_2^{\\mathrm{st}})"
+                                },
+                                {
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+                                    "content": ", respectively, where we use a subscript (1 or 2) to indicate the group ID. As described above, we expect the first teacher-student model to stick to learning reliable semantics from the source domain, while the"
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+                                            "type": "text",
+                                            "content": "Figure 2. An illustration of the proposed DTS framework, where we use Setting "
+                                        },
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+                                            "type": "text",
+                                            "content": " as an example. The left and right parts describe the optimization of the first and second group models, respectively. The bottom-left part (in gray) corresponds to a single teacher-student framework where ClassMix is used for domain mixing, and the top part (in purple) shows the bidirectional learning strategy, i.e., models from the other group are used for pseudo label generation."
+                                        }
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+                                            "type": "text",
+                                            "content": "Figure 3. An illustration of different combinations of training data. We use magenta to represent source-domain patches and two types of blue to represent target-domain patches from different images. In practice, the images are not partitioned into regular grids, but into semantic regions according to the (real or pseudo) labels."
+                                        }
+                                    ]
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+                            ],
+                            "index": 4,
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+                                    "type": "text",
+                                    "content": "second teacher-student model learns to 'Focus on Your Target' to enhance the adapting ability."
+                                }
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+                {
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+                                    "type": "text",
+                                    "content": "We achieve the goal by using different data proportions for the two groups. An illustration is provided in Figure 3. The first group remains the same as in the baseline, i.e., half of the training samples are simply source images and another half are ClassMix-ed images covering the source and target domains. Using the previously defined notations, we denote the combination as "
+                                },
+                                {
+                                    "bbox": [
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+                                        558,
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+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbb{S},\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ". To increase the proportion of the target-domain data, we first change the mixture of data from "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{S},\\mathbb{T}\\rangle"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to "
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+                                {
+                                    "bbox": [
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+                                        558,
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+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{T},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " (i.e., same as that used in the 'Focus on Your Target' trial), and then replace the pure source domain with "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{S},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ". That said, we create two settings for data combination, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        288,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle ,\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We name them Setting "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "A"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and Setting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of the second group"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "throughout the remainder of this paper. Intuitively, the proportion of the target-domain data is increased from around "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        348,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "25\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "text",
+                                    "content": " in the first group (as well as the baselines) to around "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        348,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "50\\% / 75\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " using Setting A/Setting B in the second group."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "There are two teacher models and two student models to be optimized. We perform iterative optimization and propose a bidirectional learning strategy so that each teacher-student model propagates information to the other by contributing to the generation of pseudo labels. The detailed training process is shown in Algorithm 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                        {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Note that, if "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        468,
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+                                        552
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2,t}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is not used in Step 2 (i.e., all pseudo labels are generated using "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        552
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1,t+1}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "), the information is only propagated from the first teacher-student model to the second one, hence the optimization strategy degenerates from bidirectional to unidirectional. The advantage of the bidirectional strategy and other design choices will be diagnosed in the experimental section."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.4. Technical Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Choosing the proper option for data combination. We compute the averaged confidence of pseudo labels generated by the corresponding teacher models, "
+                                },
+                                {
+                                    "bbox": [
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+                                        575,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1}^{\\mathrm{st}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        575,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Following [48, 19], "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is defined as the proportion of pixels with the max class score surpassing a given threshold, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        575,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". For each training image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we use "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{1}^{\\mathrm{st}}(\\mathbf{x})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma_{2}^{\\mathrm{te}}(\\mathbf{x})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to denote the average "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        575,
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+                                    ],
+                                    "type": "text",
+                                    "content": " values over all pixels when the teacher models are "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        575,
+                                        545,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1}^{\\mathrm{st}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        696
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. Then, we estimate the chance that "
+                                },
+                                {
+                                    "bbox": [
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+                                        575,
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+                                        696
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " generates better pseudo labels than "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{1}^{\\mathrm{st}}(\\cdot)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {P r o b} = \\mathbb {E} _ {\\mathbf {x} \\sim \\mathcal {D} ^ {\\mathbb {T}}} \\left[ \\mathbb {I} \\left(\\gamma_ {2} ^ {\\mathrm {t e}} (\\mathbf {x}) > \\gamma_ {1} ^ {\\mathrm {s t}} (\\mathbf {x})\\right) \\right], \\tag {6}",
+                                    "image_path": "7ed2c34901b7857435cc858751d3ebfcd46a5ceddaa96947015375b32f1c1b21.jpg"
+                                }
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+                }
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+                                            "type": "text",
+                                            "content": "Algorithm 1: DTS: Dual Teacher-Student"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 0,
+                            "angle": 0,
+                            "type": "code_caption"
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+                                            "type": "text",
+                                            "content": "Input: Source data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{x}^{\\mathbb{S}},\\mathbf{y}^{\\mathbb{S}}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ", target data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{x}^{\\mathbb{T}}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ", the total iteration number T;  \n1 repeat  \n2 Update "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{1,t+1}^{\\mathrm{te}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " using the EMA of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{1,t}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n3 Get pseudo labels "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tilde{\\mathbf{y}}^{\\mathbb{T}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " by "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{1,t+1}^{\\mathrm{te}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,t}^{\\mathrm{te}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n4 Generate mixed data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{x}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ", and train "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{1,t+1}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " on "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbb{S},\\langle \\mathbb{S},\\mathbb{T}\\rangle\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n5 Update "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,t+1}^{\\mathrm{te}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " using the EMA of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,t}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n6 Get pseudo labels "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tilde{\\mathbf{y}}^{\\mathbb{T}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " by "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{1,t+1}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,t+1}^{\\mathrm{te}}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n7 if Setting A: Generate data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{x}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ", and Train "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,t+1}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " on "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n8 if Setting B: Generate data "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{x}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{S},\\mathbb{T}\\rangle},\\mathbf{x}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle},\\mathbf{y}^{\\langle \\mathbb{T},\\mathbb{T}\\rangle}\\}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ", and train "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,t+1}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": " on them;  \n9 "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "t \\gets t + 1"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \n10 until "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "t = T"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": ";  \nReturn: "
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "f_{2,\\mathrm{T}}^{\\mathrm{st}}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
+                                                48,
+                                                88,
+                                                272,
+                                                308
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "code_body"
+                        }
+                    ],
+                    "index": 1,
+                    "sub_type": "algorithm"
+                },
+                {
+                    "bbox": [
+                        46,
+                        335,
+                        287,
+                        418
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                335,
+                                287,
+                                418
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{I}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": " is the indicator function that outputs 1 if the statement is true and 0 otherwise. Note that the estimation is performed individually for two training procedures using Setting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": " and Setting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": ". Finally, we choose the setting with a higher chance that "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": " is more confident because "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2}^{\\mathrm{st}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        335,
+                                        287,
+                                        418
+                                    ],
+                                    "type": "text",
+                                    "content": " is eventually used for inference. We shall see in Section 4.3 that this criterion always leads to the better choice."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        419,
+                        287,
+                        479
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                419,
+                                287,
+                                479
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": "Generating the mask. In the domain mixing operation, we compute the mask "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": " by choosing the class label of one image. If the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{S},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": " is used, the source image with groundtruth is chosen; if "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{T},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": " is used, the image with a larger average value of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        419,
+                                        287,
+                                        479
+                                    ],
+                                    "type": "text",
+                                    "content": " is chosen."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        480,
+                        287,
+                        578
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                480,
+                                287,
+                                578
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        578
+                                    ],
+                                    "type": "text",
+                                    "content": "Generating pseudo labels. The details are slightly different between Setting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        578
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        578
+                                    ],
+                                    "type": "text",
+                                    "content": " and Setting "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        578
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        578
+                                    ],
+                                    "type": "text",
+                                    "content": ". When the batch size is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        480,
+                                        287,
+                                        578
+                                    ],
+                                    "type": "inline_equation",
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+                                    "content": "Datasets. We train the models on a labeled source domain and an unlabeled target domain and test them on the target domain. We follow the convention to set the source domain to be a synthesized dataset (either GTAv [38] which contains 24,966 densely labeled training images at a resolution of "
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+                                    "content": " or SYNTHIA [39] which contains 9,400 densely labeled training images at a resolution of"
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+                                    "content": "1280 \\times 760"
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+                                    "type": "text",
+                                    "content": "), and the target dataset to be a real dataset (Cityscapes [6] where only the finely-annotated subset is used, containing 2,975 training images and 500 validation images at a resolution of "
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+                                    "content": "2048 \\times 1024"
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+                                    "type": "text",
+                                    "content": "). Following the convention to report the mean IoU (mIoU) over 19 classes when GTAv is used as the source domain, and 13 or 16 classes when SYNTHIA is the source domain."
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+                        }
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+                                    "content": "Training details. Our framework is applied to different self-training frameworks. Specifically, we follow the DAFformer series [19, 20, 21] where the encoder is a MiT-B5 model pre-trained on ImageNet-1K [7] and the decoder involves a context-aware feature fusion module. We train the framework on a single NVIDIA Tesla-V100 GPU for 40K iterations with a batch size of 2 for both groups. We use an AdamW optimizer [34] with learning rates of "
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+                                    "type": "text",
+                                    "content": " for the decoder, a weight decay of 0.01, and linear warm-up of the learning rate for the first 1.5K iterations. The input image size is always "
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+                                    "type": "inline_equation",
+                                    "content": "512 \\times 512"
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+                                    "type": "text",
+                                    "content": ". During the training phase, we apply random rescaling and cropping to the source and target data, as well as color jittering and Gaussian blur as strong augmentations for the mixed data. The EMA coefficient, "
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+                                    "type": "text",
+                                    "content": ", is set to be 0.999. The pseudo-label confidence threshold, "
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+                                    "type": "text",
+                                    "content": ", is 0.968 as in [48]."
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+                                    "content": "4.2. Comparison to the State-of-the-art Methods"
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+                                    "content": "We compare DTS to state-of-the-art UDA approaches on the GTAv "
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+                                    "content": " Cityscapes and SYNTHIA "
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+                                    "type": "text",
+                                    "content": " Cityscapes benchmarks. Results are summarized in Table 2 and Table 3, respectively. We establish DTS upon three recently published works, namely, DAFormer [19], HRDA [20], and MIC [21]."
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+                                    "type": "text",
+                                    "content": " Cityscapes and "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": " mIoUs on SYNTHIA "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\rightarrow"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " Cityscapes with 16 and 13 classes, respectively."
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+                        }
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+                                    "type": "text",
+                                    "content": "Comparison to FST. We compare DTS to another plugin approach, FST [8]. On DAFormer, the gains brought by FST on the two benchmarks (SYNTHIA using 13 classes) are "
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+                                    "type": "text",
+                                    "content": ", while the numbers for DTS are "
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+                                    "type": "text",
+                                    "content": ", respectively. That said, besides the contribution of FST that allows us to 'learn from future', the higher accuracy also owes to the design of the DTS framework that alleviates the conflict of learning and adapting."
+                                }
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+                                    "type": "text",
+                                    "content": "Class-level analysis. We investigate which classes are best improved by DTS. On "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GTAv} \\rightarrow \\mathrm{Cityscapes}"
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+                                    "type": "text",
+                                    "content": ", we detect two classes, sign and truck, on which the IoU gain on the three baselines is always higher than the mIoU gain. In the"
+                                }
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Method</td><td>Road</td><td>Sidewalk</td><td>Building</td><td>Wall</td><td>Fence</td><td>Pole</td><td>Light</td><td>Sign</td><td>Veg</td><td>Terrain</td><td>Sky</td><td>Person</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Train</td><td>Motor</td><td>Bike</td><td>mIoU</td></tr><tr><td>AdaptSegNet [49]</td><td>86.5</td><td>36.0</td><td>79.9</td><td>23.4</td><td>23.3</td><td>23.9</td><td>35.2</td><td>14.8</td><td>83.4</td><td>33.3</td><td>75.6</td><td>58.5</td><td>27.6</td><td>73.7</td><td>32.5</td><td>35.4</td><td>3.9</td><td>30.1</td><td>28.1</td><td>42.4</td></tr><tr><td>PatchAligne [50]</td><td>92.3</td><td>51.9</td><td>82.1</td><td>29.2</td><td>25.1</td><td>24.5</td><td>33.8</td><td>33.0</td><td>82.4</td><td>32.8</td><td>82.2</td><td>58.6</td><td>27.2</td><td>84.3</td><td>33.4</td><td>46.3</td><td>2.2</td><td>29.5</td><td>32.3</td><td>46.5</td></tr><tr><td>FDA [56]</td><td>92.5</td><td>53.3</td><td>82.4</td><td>26.5</td><td>27.6</td><td>36.4</td><td>40.6</td><td>38.9</td><td>82.3</td><td>39.8</td><td>78.0</td><td>62.6</td><td>34.4</td><td>84.9</td><td>34.1</td><td>53.1</td><td>16.9</td><td>27.7</td><td>46.4</td><td>50.5</td></tr><tr><td>DACS [48]</td><td>89.9</td><td>39.7</td><td>87.9</td><td>39.7</td><td>39.5</td><td>38.5</td><td>46.4</td><td>52.8</td><td>88.0</td><td>44.0</td><td>88.8</td><td>67.2</td><td>35.8</td><td>84.5</td><td>45.7</td><td>50.2</td><td>0.0</td><td>27.3</td><td>34.0</td><td>52.1</td></tr><tr><td>ProDA [59]</td><td>87.8</td><td>56.0</td><td>79.7</td><td>46.3</td><td>44.8</td><td>45.6</td><td>53.5</td><td>53.5</td><td>88.6</td><td>45.2</td><td>82.1</td><td>70.7</td><td>39.2</td><td>88.8</td><td>45.5</td><td>50.4</td><td>1.0</td><td>48.9</td><td>56.4</td><td>57.5</td></tr><tr><td>DAP [23]</td><td>94.5</td><td>63.1</td><td>89.1</td><td>29.8</td><td>47.5</td><td>50.4</td><td>56.7</td><td>58.7</td><td>89.5</td><td>50.2</td><td>87.0</td><td>73.6</td><td>38.6</td><td>91.3</td><td>50.2</td><td>52.9</td><td>0.0</td><td>50.2</td><td>63.5</td><td>59.8</td></tr><tr><td>CPSL [30]</td><td>92.3</td><td>59.9</td><td>84.9</td><td>45.7</td><td>29.7</td><td>52.8</td><td>61.5</td><td>59.5</td><td>87.9</td><td>41.6</td><td>85.0</td><td>73.0</td><td>35.5</td><td>90.4</td><td>48.7</td><td>73.9</td><td>26.3</td><td>53.8</td><td>53.9</td><td>60.8</td></tr><tr><td>DAFormer [19]</td><td>95.7</td><td>70.2</td><td>89.4</td><td>53.5</td><td>48.1</td><td>49.6</td><td>55.8</td><td>59.4</td><td>89.9</td><td>47.9</td><td>92.5</td><td>72.2</td><td>44.7</td><td>92.3</td><td>74.5</td><td>78.2</td><td>65.1</td><td>55.9</td><td>61.8</td><td>68.3</td></tr><tr><td>DAFormer+FST [8]</td><td>95.3</td><td>67.7</td><td>89.3</td><td>55.5</td><td>47.1</td><td>50.1</td><td>57.2</td><td>58.6</td><td>89.9</td><td>51.0</td><td>92.9</td><td>72.7</td><td>46.3</td><td>92.5</td><td>78.0</td><td>81.6</td><td>74.4</td><td>57.7</td><td>62.6</td><td>69.3</td></tr><tr><td>DAFormer+CAMix [62]</td><td>96.0</td><td>73.1</td><td>89.5</td><td>53.9</td><td>50.8</td><td>51.7</td><td>58.7</td><td>64.9</td><td>90.0</td><td>51.2</td><td>92.2</td><td>71.8</td><td>44.0</td><td>92.8</td><td>78.7</td><td>82.3</td><td>70.9</td><td>54.1</td><td>64.3</td><td>70.0</td></tr><tr><td>DAFormer+DTS (ours)</td><td>96.8</td><td>76.0</td><td>90.0</td><td>56.5</td><td>50.1</td><td>51.9</td><td>57.4</td><td>65.1</td><td>90.5</td><td>50.5</td><td>92.4</td><td>73.5</td><td>46.9</td><td>93.0</td><td>80.4</td><td>85.2</td><td>74.0</td><td>58.7</td><td>63.5</td><td>71.2</td></tr><tr><td>HRDA [20]</td><td>96.4</td><td>74.4</td><td>91.0</td><td>61.6</td><td>51.5</td><td>57.1</td><td>63.9</td><td>69.3</td><td>91.3</td><td>48.4</td><td>94.2</td><td>79.0</td><td>52.9</td><td>93.9</td><td>84.1</td><td>85.7</td><td>75.9</td><td>63.9</td><td>67.5</td><td>73.8</td></tr><tr><td>HRDA+DTS (ours)</td><td>96.7</td><td>76.3</td><td>91.3</td><td>60.7</td><td>55.9</td><td>59.9</td><td>67.3</td><td>72.5</td><td>91.8</td><td>50.1</td><td>94.4</td><td>80.7</td><td>56.8</td><td>94.4</td><td>86.0</td><td>86.0</td><td>73.9</td><td>65.7</td><td>68.4</td><td>75.2</td></tr><tr><td>MIC [21]</td><td>97.4</td><td>80.1</td><td>91.7</td><td>61.2</td><td>56.9</td><td>59.7</td><td>66.0</td><td>71.3</td><td>91.7</td><td>51.4</td><td>94.3</td><td>79.8</td><td>56.1</td><td>94.6</td><td>85.4</td><td>90.3</td><td>80.4</td><td>64.5</td><td>68.5</td><td>75.9</td></tr><tr><td>MIC+DTS (ours)</td><td>97.0</td><td>80.4</td><td>91.8</td><td>60.6</td><td>58.7</td><td>61.7</td><td>67.9</td><td>73.2</td><td>92.0</td><td>45.4</td><td>94.3</td><td>81.3</td><td>58.7</td><td>95.0</td><td>87.9</td><td>90.7</td><td>82.2</td><td>65.7</td><td>69.0</td><td>76.5</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 2. UDA segmentation accuracy (mIoU, %) on the GTAv→Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone."
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+                                            "content": "Table 3. UDA segmentation accuracy (mIoU, %) on the SYNTHIA "
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+                                            "type": "text",
+                                            "content": "Cityscapes benchmark. The highest number in each column is marked with bold. The results in the first group are obtained on a ResNet101 backbone and the others are obtained on a MiT-B5 backbone. The mIoU and mIoU* columns denote the averaged IoU over 16 and 13 classes, where the latter does not contain the classes marked with * ."
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+                                    "content": "Appendix material, we show that these classes suffer larger variations between the source-domain and target-domain appearances, and hence the learned features are more difficult to transfer. They are largely benefited by the 'Focus on Your Target' ability of DTS."
+                                }
+                            ]
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+                                    "content": "Visualization. We visualize the segmentation results of DAFormer and DAFormer+DTS in Figure 4. For the real images, the advantage of DTS is significant on the classes that are easily confused with others (e.g., sidewalk which is visually similar to road) or suffer large domain shifts (e.g., sign or truck). For the mixed images, we find that the baseline model is easily confused by the unusual stitching and/or discontinuous textures because it has never seen such pat"
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+                                    "content": "terns in the source domain – in such cases, the model of the second group is generally better and sometimes it can propagate the advantages to the model of the first group, revealing the advantage of bidirectional learning."
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+                                    "content": "4.3. Diagnostic Studies"
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+                                            "content": "Figure 4. Visualization of the segmentation results of DAFormer [19] and DTS. The top two rows display two real images and the bottom two rows display two synthesized images from "
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+                                            "content": " . In each group, the first example is from GTAv "
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+                                            "content": " Cityscapes and the second one is from SYNTHIA "
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+                                            "content": " Cityscapes. The white, dashed circles highlight the regions that are significantly improved by DTS."
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+                                            "html": "<table><tr><td>Setting</td><td colspan=\"5\">Choice and Accuracy</td></tr><tr><td>Dual Teacher-Student ‘Focus on Your Target’</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td></tr><tr><td>Bidirectional Learning</td><td></td><td></td><td>✓</td><td>✓</td><td></td></tr><tr><td>GTAv→Cityscapes</td><td>68.3</td><td>67.2</td><td>69.7</td><td>68.6</td><td>71.2</td></tr><tr><td>SYNTHIA→Cityscapes</td><td>60.9</td><td>58.4</td><td>63.3</td><td>61.2</td><td>63.7</td></tr></table>",
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+                                            "content": "Table 4. Ablative studies of DTS with respect to the UDA segmentation accuracy (mIoU, %) on both benchmarks. All these experiments are based on DAFformer [19]. For SYNTHIA→Cityscapes, the mIoUs are computed over 16 classes. Note that DTS alone (without the latter two options) is equivalent to the baseline (the leftmost column) and is simply ignored in the table."
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+                                    "content": "solely applying DTS (without adjusting the proportion of training data nor applying bidirectional learning) does not make any difference from the baseline; also, bidirectional learning must be built upon DTS."
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+                                    "content": "From Columns 1-3, one can learn the importance of the DTS framework. When DTS is not established, simply increasing the proportion of target data (Col 2) incurs an accuracy drop on both GTAv "
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+                                    "type": "text",
+                                    "content": " Cityscapes and SYNTHIA "
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+                                    "type": "text",
+                                    "content": " Cityscapes. This validates our motivation, i.e., there is a conflict between the learning and adapting abilities. However, after the dual teacher-student framework is established (Col 3, where the first teacher-student group focuses on learning and the second group focuses on adapting), the conflict is weakened and the accuracy gain becomes clear (1.6% on GTAv "
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+                                    "content": " Cityscapes)."
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+                                            "html": "<table><tr><td colspan=\"2\">Baseline</td><td>DAFormer</td><td>HRDA</td><td>MIC</td></tr><tr><td rowspan=\"2\">GTAv</td><td>Setting A</td><td>70.3</td><td>74.7</td><td>76.5</td></tr><tr><td>Setting B</td><td>71.2</td><td>75.2</td><td>76.2</td></tr><tr><td rowspan=\"2\">SYNTHIA</td><td>Setting A</td><td>63.8</td><td>66.5</td><td>67.8</td></tr><tr><td>Setting B</td><td>61.2</td><td>66.0</td><td>67.2</td></tr></table>",
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+                                            "content": "Table 5. The results of DTS with different data mixing options. For SYNTHIA "
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+                                    "content": "From Columns 3-5, one can observe the contribution of 'Focus on Your Target' (i.e., increasing the proportion of target data) and bidirectional learning on top of the DTS framework. The best practice is obtained when all the modules are used (Col 5), aligning with the results reported in Tables 2 and 3. Interestingly, when bidirectional learning is adopted alone (Col 4), the accuracy gain is much smaller than that of using 'Focus on Your Target' alone, because the two groups are using the same proportion of data mixing, and thus the bidirectional learning carries limited complementary information."
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+                                    "content": "Choose the option for data combination. We validate that the data combination option can be chosen by comparing the pseudo-label confidence, as described in Section 3.4. We plot the Prob curves throughout training procedure of Setting "
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+                                    "type": "text",
+                                    "content": "Except for Setting "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and Setting "
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", there are two other options to increase the focus on the target domain as well, namely "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The two options do not include any mixing data and have a disadvantage compared to the previous two combinations. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        497,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " means that the second teacher-student group achieves the ability of learning only from the pseudo labels provided by "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_1^{\\mathrm{st}}(\\mathbf{x};\\pmb {\\theta}_1^{\\mathrm{st}})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". As a result, noise can easily persist without accurate supervision from the source data. "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\langle \\mathbb{S},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " has a similar data proportion as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbb{S},\\langle \\mathbb{T},\\mathbb{T}\\rangle \\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " but cannot solve the problem of inconsistency between the training and testing data. Using "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\langle \\mathbb{T},\\mathbb{T}\\rangle"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as the training domain is an effective way to bridge the gap between the training and testing phases. Therefore, the two combinations containing two different types of data used in DTS are more suitable for balancing the learning and adapting abilities."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Models for pseudo label generation. We study the impact of different models for generating pseudo labels. Re"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "table",
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+                                            "type": "text",
+                                            "content": "Table 6. The results of DTS with more data mixing options. We show the mIoU of the 16 classes in SYNTHIA and make this comparison based on the DAFourner baseline."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "angle": 0,
+                            "type": "table_caption"
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+                                            "type": "table",
+                                            "html": "<table><tr><td colspan=\"2\">Group #1</td><td colspan=\"2\">Group #2</td><td rowspan=\"2\">mIoU</td></tr><tr><td>f2,st(·)</td><td>f2,te(·)</td><td>f1,t+1(·)</td><td>f1,t+1(·)</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>68.5†</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td>69.0</td></tr><tr><td></td><td>✓</td><td></td><td>✓</td><td>69.5</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>70.2</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>71.3</td></tr></table>",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "type": "table",
+                    "bbox": [
+                        307,
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+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
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+                            ],
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+                                            "type": "text",
+                                            "content": "Table 7. UDA segmentation accuracy (mIoU, %) using different models to generate pseudo labels on GTAv→Citysacpes. †: In the first row, each group only uses the teacher model from the other group; in other cases, each group also uses its own teacher models (not presented in the table)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
+                        {
+                            "bbox": [
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+                                            ],
+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">GTAv→City.</td><td colspan=\"2\">SYNTHIA→City.</td></tr><tr><td>DACS</td><td>DAFormer</td><td>DACS</td><td>DAFormer</td></tr><tr><td>w/o DTS</td><td>53.9</td><td>56.0</td><td>54.2</td><td>53.5</td></tr><tr><td>w DTS</td><td>55.2</td><td>59.9</td><td>56.6</td><td>56.9</td></tr></table>",
+                                            "image_path": "2adccb4008805c5688581ee646ec9b4385ededd066d11673b467227de281b257.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
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+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Table 8. UDA segmentation accuracy (mIoU, %) on two CNN-based backbones and two benchmarks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11,
+                    "angle": 0,
+                    "type": "text"
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                            ],
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+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "sults are summarized in Table 7. When each teacher-student group only uses the teacher model from another group (the first row), there is almost no accuracy gain (the baseline is "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        330,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "68.3\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "), indicating the necessity of the supervision signals from its own teacher."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Then, we discuss the situations where each group uses its teacher and one model from the other group. For the second teacher-student group, using "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1,t+1}^{\\mathrm{st}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        390,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as the teacher is superior to using "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        390,
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+                                        498
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{1,t+1}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        390,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", because the former model is optimized one more iteration and thus produces better semantics (i.e., 'learning from future'). For the first teacher-student group, only models from the current iteration of the second group can be used, and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        390,
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+                                        498
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2,t}^{\\mathrm{te}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " always works better than "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        390,
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+                                        498
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{2,t}^{\\mathrm{st}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", implying the advantage of EMA."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "DTS applied to other backbones. To show that DTS adapts to different network backbones (e.g., CNNs), we follow the previous approaches [56, 48, 23] to inherit a ResNet101 [14] pre-trained on ImageNet and MSCOCO and train it using DeepLabV2 [2]. The other settings remain unchanged. Results are listed in Table 8. Still, DTS brings consistent accuracy gains, improving DACs and DAfromer by "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1.3\\%"
+                                },
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "3.9\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " on "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GTAv}\\rightarrow \\mathrm{Cityscapes}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and by "
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+                                    "type": "inline_equation",
+                                    "content": "2.4\\%"
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "3.4\\%"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " on SYNTHIA "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rightarrow"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " Cityscapes. These experiments validate that DTS is a generalized UDA framework that does not rely on specific network architectures."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Comparison of training time and compute. DTS trains two teacher-student groups, so the computational cost is about "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        630,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2 \\times"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the baseline (e.g., on a single V100 GPU, DAFormer/DTS needs 13.5/30 hours). The inference cost remains unchanged. We further compare DTS and DAFormer under the same training cost. DTS with half (20K) iterations achieves favorable accuracy (68.6% and"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                }
+            ],
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+            ],
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+        {
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+                                            "html": "<table><tr><td></td><td>GTAv2BDD</td><td>GTAv2IDD</td><td>CS2BDD</td><td>CS2IDD</td></tr><tr><td>Baseline</td><td>46.3</td><td>54.7</td><td>53.7</td><td>51.6</td></tr><tr><td>DTS</td><td>53.6</td><td>59.6</td><td>57.5</td><td>56.1</td></tr><tr><td></td><td>CS2FZ</td><td colspan=\"3\">CS2DZ</td></tr><tr><td>Baseline</td><td>39.7</td><td>34.0</td><td>42.1*</td><td>43.6*</td></tr><tr><td>DTS</td><td>40.4</td><td>37.6</td><td>45.2</td><td>45.6</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 9. UDA segmentation accuracy (mIoU, %) on more driving datasets. 'BDD', 'IDD', 'FZ', 'DZ', and 'CS' for Berkeley Driving Dataset, India Driving Dataset, Foggy Zurich, Dark Zurich, and Cityscapes, respectively. Baselines are DAFormer except for the last two columns in CS2DZ, which are HRDA and MIC. *: are numbers inherited from [20, 21]."
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+                                    "content": "61.8% on GTAv "
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+                                    "content": " Cityscapes and SYNTHIA "
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+                                    "type": "text",
+                                    "content": " Cityscapes) over DAFormer with full (40K) iterations (68.3% and 60.9%), meanwhile, DTS with full (40K) iterations reports 71.2% and 63.8%, surpassing DAFormer with doubled (80K) iterations (69.3% and 61.2%)."
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+                                    "content": "Performance on more driving datasets. We conduct experiments from synthesized and real datasets to more driving datasets, i.e., Berkeley Driving Dataset (BDD) [57], India Driving Dataset (IDD) [52], Foggy Zurich (FZ) [41], and Dark Zurich (DZ) [42]. The comparable results on validation sets of target domain datasets are summarized in Table 9. DTS reports consistent improvement in these transfer scenarios. On the test set of CS2DZ, DTS is also superior to DAformer "
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "4.4. Semi-supervised Semantic Segmentation"
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+                                    "type": "text",
+                                    "content": "Dataset. As a generalized self-training framework, DTS can also be applied to semi-supervised segmentation. We perform semi-supervised segmentation on the widely used PASCAL VOC dataset [9], which comprises 20 object classes and a background class. The training, validation, and testing sets contain 1,464, 1,449, and 1,456 images, respectively. To align with prior works, we use the augmented set, which contains 10,582 images, as the complete training set. During the training, we apply random flipping and cropping to augment the image data and resize the image to "
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+                                    "type": "inline_equation",
+                                    "content": "513 \\times 513"
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+                                    "type": "text",
+                                    "content": " before feeding it to the models."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "Implementation. We perform all experiments using the DeepLabV3+ [3] network with a ResNet-101 backbone pretrained on ImageNet. An SGD optimizer, with a learning rate of 0.0001 for the encoder and 0.001 for the decoder, and a weight decay of 0.0001, is used. The batch size of both labeled and unlabeled data is 16 for each group teacher-student. We train the models for 40 epochs and report the average of three runs for all the results. Since there is no domain gap between the labeled and unlabeled parts, only a dual teacher-student framework and bidirectional learning are applied in the semi-supervised experiments."
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Methods</td><td>1/16 (662)</td><td>1/8 (1323)</td><td>1/4 (2646)</td></tr><tr><td>Mean Teacher [46]</td><td>71.3</td><td>75.4</td><td>76.5</td></tr><tr><td>FST [8]</td><td>73.9</td><td>76.1</td><td>78.1</td></tr><tr><td>USRN [13]</td><td>72.3</td><td>-</td><td>-</td></tr><tr><td>PS-MT [32]</td><td>75.5</td><td>78.2</td><td>78.7</td></tr><tr><td>U²PL [54]</td><td>77.2</td><td>79.0</td><td>79.3</td></tr><tr><td>DTS (ours)</td><td>74.8</td><td>77.1</td><td>77.3</td></tr><tr><td>U²PL + DTS (ours)</td><td>78.9</td><td>80.1</td><td>80.4</td></tr></table>",
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+                                            "content": "Table 10. Semi-supervised segmentation accuracy (mIoU, %) on PASCAL VOC."
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+                                    "type": "text",
+                                    "content": "Comparison. The segmentation results are summarized in Table 10. Using "
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+                                    "content": " labeled data, DTS produces consistent accuracy gains of "
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+                                    "content": " over the Mean Teacher baseline [46], and "
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+                                    "content": " over the "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{U}^2\\mathrm{PL}"
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+                                    "type": "text",
+                                    "content": " baseline [54]. This validates that semi-supervised learning also benefits from bidirectional learning which effectively improves the ability to learn from the pseudo labels generated from other groups."
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+                                    "type": "text",
+                                    "content": "5. Conclusions"
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+                                    "type": "text",
+                                    "content": "In this paper, we study the UDA segmentation problem from the perspective of endowing the model with twofold abilities, i.e., learning from the reliable semantics, and adapting to the target domain. We show that these two abilities can conflict with each other in a single teacher-student model, and hence we propose a dual teacher-student (DTS) framework, where the two models stick to the 'learning ability' and 'adapting ability', respectively. Specifically, the second model learns to 'focus on your target' to improve its accuracy in the target domain. We further design a bidirectional learning strategy to facilitate the two models to communicate via generating pseudo labels. We validate the effectiveness of DTS and set new records on two standard UDA segmentation benchmarks."
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+                                    "type": "text",
+                                    "content": "As the accuracy on the two benchmarks fast approaches the supervised baseline (e.g., a "
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+                                    "type": "text",
+                                    "content": " mIoU on Cityscapes), we look forward to building larger and higher-quality synthesized datasets to break through the baseline. This is of value to real-world applications, as synthesized data can be generated at low costs. We expect that the proposed methodology can be applied to other scenarios such as domain generalization, with the second group focusing on a generic, unbiased feature space."
+                                }
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+                                    "type": "text",
+                                    "content": "Acknowledgment This work was supported by NSFC under Contract U20A20183 and 62021001. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC, and the Supercomputing Center of the USTC."
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+                                        }
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diff --git a/2023/Focus the Discrepancy_ Intra- and Inter-Correlation Learning for Image Anomaly Detection/9a627ddc-8c15-4383-a8ac-8266b31abdaf_content_list.json b/2023/Focus the Discrepancy_ Intra- and Inter-Correlation Learning for Image Anomaly Detection/9a627ddc-8c15-4383-a8ac-8266b31abdaf_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..ed0abef257fe00099c88db05d642bb5298286ede
--- /dev/null
+++ b/2023/Focus the Discrepancy_ Intra- and Inter-Correlation Learning for Image Anomaly Detection/9a627ddc-8c15-4383-a8ac-8266b31abdaf_content_list.json	
@@ -0,0 +1,1616 @@
+[
+    {
+        "type": "text",
+        "text": "Focus the Discrepancy: Intra- and Inter-Correlation Learning for Image Anomaly Detection",
+        "text_level": 1,
+        "bbox": [
+            119,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xincheng Yao $^{1}$ , Ruoqi Li $^{1}$ , Zefeng Qian $^{1}$ , Yan Luo $^{1}$ , Chongyang Zhang $^{1,2*}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University",
+        "bbox": [
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+            245,
+            850,
+            260
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{2}$ MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University",
+        "bbox": [
+            152,
+            261,
+            816,
+            277
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{i-Dover, nilponi, zefeng.qian, luoyan.bb, sunny_zhang}@sjtu.edu.cn",
+        "bbox": [
+            189,
+            277,
+            774,
+            293
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            324,
+            312,
+            339
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Humans recognize anomalies through two aspects: larger patch-wise representation discrepancies and weaker patch-to-normal-patch correlations. However, the previous AD methods didn't sufficiently combine the two complementary aspects to design AD models. To this end, we find that Transformer can ideally satisfy the two aspects as its great power in the unified modeling of patchwise representations and patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can simultaneously spot the patch-wise, intra- and inter-discrepancies of anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to Intra-Inter-Correlation (I2Correlation). The I2Correlation contains a two-branch structure to first explicitly establish intra- and inter-image correlations, and then fuses the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning. Besides, we introduce an entropy constraint strategy to solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability. Extensive experiments on three unsupervised real-world AD benchmarks show the superior performance of our approach. Code will be available at https://github.com/xcyao00/FOD.",
+        "bbox": [
+            75,
+            353,
+            473,
+            714
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            77,
+            739,
+            208,
+            754
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The goal of anomaly detection (AD) is to distinguish an instance containing anomalous patterns from those normal samples and further localize those anomalous regions. Anomalies are defined as opposite to normal samples and are usually rare, which means that we need to tackle AD tasks under the unsupervised setting with only normal sam",
+        "bbox": [
+            75,
+            762,
+            468,
+            847
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/9b6bfebd8a09d0cb6ae61b0b307d004463e3e20f73e02aaa5107b883d83cfc47.jpg",
+        "image_caption": [
+            "Figure 1. Anomaly detection examples on MVTecAD [3]. Multiresolution Knowledge Distillation (MKD) [41] adopts the conventional patch-wise representation discrepancies. Row 1 shows the hard global anomalies (i.e., they are not significantly different from normal visuals). Rows 3 and 4 show the logical anomalies (i.e., they may be easily recognized as normal if only from the patch-wise discrepancy)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            502,
+            325,
+            889,
+            511
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "plies accessible. The core idea of most unsupervised AD methods is to compare with normal samples to distinguish anomalies [46, 35, 60, 11, 28, 58]. Even for humans, we also recognize anomalies in this way, specifically through three discrepancies, i.e., 1. patch patterns that differentiate from the normal visuals; 2. image regions that destroy textures or structures; 3. novel appearances that deviate from our accumulated knowledge of normality. Namely, anomalous patches usually have three characteristics: their patchwise representations are different from the normal visuals; they are different from most patches within one image; they deviate from our accumulated knowledge of normality. These views intrinsically reveal that humans' recognition of anomalies depends on two aspects: patch-wise representations (1) and intra- and inter-image correlations (2, 3).",
+        "bbox": [
+            497,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Previous methods mainly follow the former aspect to learn distinguishable representations or reconstructions,",
+        "bbox": [
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+            866
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            129,
+            49,
+            200,
+            84
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            253,
+            48,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding Author.",
+        "bbox": [
+            95,
+            853,
+            226,
+            866
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "6803",
+        "bbox": [
+            468,
+            885,
+            500,
+            897
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "such as reconstruct-based methods [6, 57, 1] and knowledge distillation AD models [4, 41]. The goal of these methods is to generate reconstructed samples or feature representations, and larger patch-wise representation discrepancies can appear in the abnormal patches. However, only the patch-wise representation discrepancies are insufficient for detecting more complex anomalies (e.g., rows 3 and 4 in Figure 1), since the patch-wise errors can't provide comprehensive descriptions of the spatial context. Other mainstream AD methods, such as embedding-based [11, 35] and one-class-classification-based (OCC) [39, 60] methods, are much similar to the latter aspect. These methods achieve anomaly detection by measuring the distances between the features of test samples and normal features. Compared with the non-learnable feature distances, the explicit intra- and inter-image correlations in our method are more effective to detect diverse anomalies (see Table 1, 2, 3). Moreover, patch-wise representation discrepancies and intra- and inter-correlation discrepancies are complementary, and can be combined to develop more powerful AD models.",
+        "bbox": [
+            75,
+            125,
+            472,
+            402
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, with the self-attention mechanism and long-range modeling ability, transformers [50] have significantly renovated many computer vision tasks [14, 24, 7, 67, 56] and recently popular language-vision multimodal tasks [30, 22]. Transformers have shown great power in the unified modeling of patch-wise representations and patch-to-patch correlations. Transformers are quite suitable for AD tasks as their modeling ability can satisfy the two aspects of anomaly recognition quite well. Some works [26, 18, 8, 62] also attempt to employ transformers to construct AD models. However, these methods only use transformers to extract vision features, which didn't sufficiently adapt transformers' long-range correlation modeling capability to AD tasks. Different from these works, we explicitly exploit transformers' self-attention maps to establish the intra- and inter-image correlations. The correlation distribution of each patch can provide more informative descriptions of the spatial context, which can reveal more intricate and semantic anomaly patterns.",
+        "bbox": [
+            75,
+            406,
+            472,
+            669
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, motivated by humans' anomaly recognition process, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can exploit transformers' unified modeling ability to simultaneously spot the patch-wise, intra- and inter-discrepancies. Our key designs are composed of three recognition branches: the patch-wise discrepancy branch is to reconstruct the input patch features for distinguishing simple anomalies; the intra-correlation branch is to explicitly model patch-to-patch correlations in one image for distinguishing hard global anomalies (e.g., row 1 in Figure 1); the inter-correlation branch is to explicitly learn inter-image correlations with known normal patterns from the whole normal training set. To implement the intra- and inter-correlation branches, we adapt",
+        "bbox": [
+            75,
+            672,
+            472,
+            866
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Transformer and renovate the self-attention mechanism to the I2Correlation, which contains a two-branch structure to first separately model the intra- and inter-correlation distribution of each image patch, and then fuse the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning, the RBF kernel is used to present the neighborhood continuity of each image patch. Besides, an entropy constraint strategy is applied in the two branches, which can solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability.",
+        "bbox": [
+            497,
+            125,
+            890,
+            290
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In summary, we make the following main contributions:",
+        "bbox": [
+            517,
+            292,
+            889,
+            305
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. We propose a novel AD framework: FOD, which can effectively detect anomalies by simultaneously spotting the patch-wise, intra- and inter-discrepancies.",
+            "2. We renovate the self-attention mechanism to the I2Correlation, which can explicitly establish intra- and inter-correlations in a self-supervised way with the target-correlations. An entropy constraint strategy is proposed to further amplify the normal-abnormal distinguishability.",
+            "3. Our method can achieve SOTA results on three real-world AD datasets, this shows our method can more effectively determine anomalies from complementary views."
+        ],
+        "bbox": [
+            497,
+            305,
+            890,
+            458
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            499,
+            469,
+            640,
+            484
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Anomaly Detection. In this paper, we divide the mainstream AD methods into five categories: reconstruction-based, embedding-based, OCC-based methods, knowledge distillation and normalizing flow AD models. The reconstruction-based methods are the most popular AD methods and also widely studied, where the assumption is that models trained by normal samples only can reconstruct normal regions but fail in abnormal regions. Many previous works attempt to train AutoEncoders [6, 28, 57, 8, 17, 64], Variational AutoEncoders [23] and GANs [42, 1, 29, 40] to reconstruct the input images. Overfitting to the input images is the most serious issue of these methods, which means that the anomalies are also well reconstructed [62].",
+        "bbox": [
+            497,
+            492,
+            890,
+            672
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, some embedding-based methods [2, 33, 9, 11, 35] show better AD performance by using ImageNet pretrained networks as feature extractors. In [33], the authors fit a multivariate Gaussian to model the image-level features for further Mahalanobis distance measurement. PaDiM [11] extends the above method to localize pixel-level anomalies. PatchCore [35] extends on this line by utilizing locally aggregated, mid-level features and introducing greedy coreset subsampling to form nominal feature banks. However, these methods directly utilize pre-trained networks without any adaptation to the target dataset. Some works [31, 10, 32] attempt to adapt pre-trained features to the target data distribution. There are also some other methods for using pre-trained networks by freezing them and only",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "6804",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "optimizing a sub-network, e.g., via knowledge distillation [4, 41, 12, 38], or normalizing flows [36, 15, 37, 63].",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "OCC is another classical AD paradigm, the earliest works are mainly to extend the OCC models such as OC-SVM [44] or SVDD [47, 39] for anomaly detection. Recently, in [60], a patch-based SVDD that contains multiple cores rather than a single core in [39] is proposed to enable anomaly localization. In [25], a Fully Convolutional Data Description combined with receptive field upsampling is proposed to generate anomaly maps. In [48], the authors further extend the PatchSVDD [60] model by the proposed multi-scale patch-based representation learning method.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Transformer-based Anomaly Detection Methods. Recently, transformers [50] have shown great power in modeling long-range dependencies. For image anomaly detection, some works [26, 18, 62, 8, 59] also attempt to exploit transformers to design AD models. However, most of these methods only use transformers as backbones to extract vision features, and don't effectively adapt the long-range modeling capacity of transformers to AD tasks. Unlike the previous usage of transformers, we explicitly exploit the self-attention maps of transformers to establish intra- and inter-correlations. Our work shares some similarities with a recent work [20]. But we point out that our work has some significant differences from [20]: 1) Different Insight: [20] aims to unify the pointwise representation and pairwise association for time series AD, whereas our work aims to more sufficiently detect image anomalies through three complementary recognition views. 2) Novel Method: we propose entropy constraint, inter-correlation branch, and I2Correlation by effectively combining intra- and inter-correlation branches. 3) Different Task: [20] focuses on time-series AD, whereas we focus on image AD.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Approach",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Model Overview",
+        "text_level": 1,
+        "bbox": [
+            77,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Figure 2 overviews our proposed approach. The model consists of three branches: patch-wise discrepancy branch, intra-correlation branch, and inter-correlation branch. The input 2D image is first sent into a pre-trained backbone to extract multi-scale feature maps. At each feature level, we construct a subsequent transformer network to explicitly model the intra- and inter-image correlations for spotting the intra- and inter-discrepancies. Each network is implemented by stacking the I2Correlation blocks and feedforward layers alternately. Suppose each network contains  $K$  layers with length-  $N$  input features  $X\\in \\mathbb{R}^{N\\times d}$ , the output of  $k$ th layer  $X_{k}\\in \\mathbb{R}^{N\\times d_{m}}$  is calculated as follows:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nZ _ {k} = \\mathrm {L N} (\\mathrm {I 2 C o r r e l a t i o n} (X _ {k - 1}, X _ {f}) + X _ {k - 1}) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {k} = \\mathrm {L N} (\\text {F e e d F o r w a r d} (Z _ {k}) + Z _ {k}) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $X_{f}$  is the reference features used by the intercorrelation branch,  $LN$  means LayerNorm, and  $Z_{k} \\in \\mathbb{R}^{N \\times d_{m}}$  is the  $k$ th layer's hidden features. The final output features are calculated by linear projection:  $\\hat{X} = Z_{K}W_{o}$ , where  $W_{o} \\in \\mathbb{R}^{d_{m} \\times d}$  is the output projection matrix.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Patch-Wise Reconstruction Discrepancy",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Adopted from previous reconstruction-based AD methods, we employ feature reconstruction as our patch-wise recognition view for simplicity. In our approach, we construct a transformer network to reconstruct the input features. With the long-range dependency modeling ability, the features reconstructed by Transformer can have larger effective receptive fields [13], which are more conducive to detect hard global anomalies and logical anomalies. Moreover, with the further introduced inter-correlation branch (sec.3.4), the features can even perceive normal regions of images from the whole normal training set. Therefore, the reconstructed features generated by our model have better global perception and more discriminative semantic representation capability, which are more suitable for anomaly detection by patch-wise representation discrepancies.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Learning Objective. We can utilize classical reconstruction losses as the learning objective. We combine the  $\\ell 2$  distance and cosine distance to measure the feature distances between the reconstructed features  $\\hat{X}$  and the input features  $X$ . The loss function is defined as follows:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {l} = \\left| \\left| \\hat {X} - X \\right| \\right| _ {2} + \\left(1 - \\frac {\\hat {X} \\cdot X}{\\left| \\left| \\hat {X} \\right| \\right| _ {2} \\left| \\left| X \\right| \\right| _ {2}}\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Intra-Correlation Learning",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The intra-correlation learning branch aims to learn informative patch-to-patch correlations from the input patch sequence adaptively. As shown in the right part of Figure 2, we explicitly take advantage of the self-attention maps of transformers as intra-correlation matrices. Formally, the intra-correlation matrix of the  $k$ th layer is calculated by:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Intra Correlation:  $S_{k}^{g} = \\mathrm{Softmax}\\Big(Q_{k}^{g}(K_{k}^{g})^{T} / \\sqrt{d_{m}}\\Big)$",
+        "bbox": [
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+            663,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ Q _ {k} ^ {g}, K _ {k} ^ {g}, V _ {k} ^ {g} \\right] = X _ {k - 1} \\left[ W _ {k} ^ {Q _ {g}}, W _ {k} ^ {K _ {g}}, W _ {k} ^ {V _ {g}} \\right] \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            687,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $Q_{k}^{g}, K_{k}^{g}, V_{k}^{g} \\in \\mathbb{R}^{N \\times d_{m}}$  represent the query, key, and value of the  $k$ th layer.  $W_{k}^{Q_{g}}, W_{k}^{K_{g}}, W_{k}^{V_{g}} \\in \\mathbb{R}^{d_{m} \\times d_{m}}$  represent the learnable projection matrices for  $Q_{k}^{g}, K_{k}^{g}, V_{k}^{g}$ , respectively.  $S_{k}^{g} \\in \\mathbb{R}^{N \\times N}$  denotes the learned intra-image patch-to-patch correlations. Since  $\\text{Softmax}(\\cdot)$  can convert the values in the similarity map into range [0, 1] along the horizontal axis, each row of  $S_{k}^{g}$  can represent a discrete correlation distribution for each corresponding image patch. But different from the vanilla transformers, we further introduce target correlation matrices as the learning objective to explicitly optimize the intra-image correlations.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "6805",
+        "bbox": [
+            468,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/03100b0e00e71a18e9d2565d4382cb4814e72684981e01340ce323f19b45f0fc.jpg",
+        "image_caption": [
+            "Figure 2. Model overview. The model is composed of three parts: patch-wise discrepancy branch, intra-correlation branch, and intercorrelation branch. The input image patch sequence will be transformed into the hidden features by a pre-trained backbone, and then sent into the intra-correlation branch for learning intra-image patch-to-patch correlations. The input of the inter-correlation branch is composed of hidden features (as Query) and reference features (as Key and Value). The final output features are used to reconstruct the input features."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            124,
+            349,
+            385
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/f0dbe9311c31da7595e1f11ae8cbfd7fd7203dca1184ebaefdb83d41a7a548fb.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            366,
+            124,
+            589,
+            381
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c4b43d45f5d2d1e87aa079e44d01dc72234eb6d81244536df05fa580e49a8638.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            600,
+            130,
+            889,
+            384
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Target Correlation. Inspired by the contrastive learning method BarlowTwins [66], we can construct a target correlation matrix  $T \\in \\mathbb{R}^{N \\times N}$  as the learning target. The objective function of BarlowTwins measures the correlation matrix between the embeddings of two identical networks fed with distorted versions of a batch of samples, and tries to make this matrix close to the identity. In our work, the role of the target correlation is to introduce a prior correlation of patches as a pretext learning target, where each patch can be highly correlated to itself and also correlated to its neighborhood patches and the correlation decreases with the increase of distance. This allows us to optimize the intra- and inter-correlations in a self-supervised way. To this end, we use the radial basis function (RBF) to construct the target correlation matrix. We further adopt two learnable kernel variances  $\\sigma_x$  and  $\\sigma_y$  for horizontal and vertical axes to make the target correlation of each patch can adapt to the specific pattern of itself. The target correlation matrix of the  $k$ th layer is defined as:",
+        "bbox": [
+            75,
+            461,
+            472,
+            725
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT _ {k} ^ {g} = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} \\exp \\left(- \\frac {\\left| \\left| x _ {i j} - x _ {i ^ {\\prime} j ^ {\\prime}} \\right| \\right| _ {2} ^ {2}}{2 \\left(\\sigma_ {x} ^ {2} + \\sigma_ {y} ^ {2}\\right)}\\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            137,
+            735,
+            403,
+            767
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ni, i ^ {\\prime} \\in \\{1, \\dots , H \\}; j, j ^ {\\prime} \\in \\{1, \\dots , W \\} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            139,
+            769,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $||x_{ij} - x_{i'j'}||_2^2$  means the Square Euclidean distance between point  $x_{ij}$  and  $x_{i'j'}$ ,  $i, i'$  and  $j, j'$  means vertical and horizontal coordinates, respectively.",
+        "bbox": [
+            75,
+            796,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we need to measure the distance between target- and intra-correlation distributions. This can usually be",
+        "bbox": [
+            75,
+            839,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "achieved by calculating the KL divergence. We can obtain a KL divergence value from each level of the network. Thus, we average all KL divergence values to combine the patch-to-patch correlations from multi-layer features into a more informative measure as follows:",
+        "bbox": [
+            497,
+            461,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {D i v} \\left(\\mathcal {T} ^ {g}, \\mathcal {S} ^ {g}\\right) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(K L \\left(T _ {k} ^ {g} \\mid \\mid S _ {k} ^ {g}\\right) + K L \\left(S _ {k} ^ {g} \\mid \\mid T _ {k} ^ {g}\\right)\\right) \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            507,
+            539,
+            890,
+            578
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $KL(\\cdot ||\\cdot)\\in \\mathbb{R}^N$  and its each element means the KL divergence between two discrete distributions corresponding to each row of  $T_{k}^{g}$  and  $S_{k}^{g}$ .",
+        "bbox": [
+            497,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Due to the rarity of anomalies and the dominance of normal patterns, the normal patches should build strong correlations with most patches in the whole image, while the weights of abnormal correlation distributions are harder to distribute to most patches and are more likely to concentrate on the adjacent image patches due to the neighborhood continuity. Since normal and abnormal patches have different correlation distributions, this is a distinguishable criterion for anomaly detection. Note that the intra-correlation branch explicitly exploits the spatial dependencies of each image patch, which are more informative than the patchwise representations for anomaly detection.",
+        "bbox": [
+            497,
+            631,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Entropy constraint. Since the normal image patterns are usually diverse, the learned correlation distributions of the normal patches may also easily concentrate on the adjacent patches, which can cause the distinguishability between normal and abnormal to be downscaled. To address",
+        "bbox": [
+            497,
+            796,
+            890,
+            866
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "6806",
+        "bbox": [
+            468,
+            885,
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "this, we further introduce an entropy constraint item for making normal patches establish strong associations with most normal patches in the whole image as much as possible. The entropy constraint item is defined as:",
+        "bbox": [
+            75,
+            125,
+            468,
+            181
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {E n t} \\left(\\mathcal {S} ^ {g}\\right) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} \\left(- S _ {k (i, j)} ^ {g} \\log \\left(S _ {k (i, j)} ^ {g}\\right)\\right)\\right) \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            191,
+            468,
+            231
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We will maximize the entropy constraint item. The loss function for the intra-correlation branch is defined as:",
+        "bbox": [
+            77,
+            239,
+            468,
+            266
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {g} = \\lambda_ {1} \\operatorname {D i v} \\left(\\mathcal {T} ^ {g}, \\mathcal {S} ^ {g}\\right) - \\lambda_ {2} \\operatorname {E n t} \\left(\\mathcal {S} ^ {g}\\right) \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            154,
+            277,
+            468,
+            294
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{1}$  and  $\\lambda_{2}$  are used to trade off the loss items. The optimization of intra-correlation  $S^g$  is actually an alternating process with the guidance of target correlation  $T^g$  (see App. A.1), ultimately resulting that each normal patch can establish strong correlations with most normal patches.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Inter-Correlation Learning",
+        "text_level": 1,
+        "bbox": [
+            77,
+            380,
+            321,
+            395
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Through the intra-correlation branch, we can establish patch-to-patch correlations within a single image. However, an image usually doesn't contain all possible normal patterns, which may cause it difficult to distinguish some ambiguous abnormal patches (see rows 2, 3, 4 in Figure 1) only through the intra-correlations. To address this, we should effectively take advantage of the known normal patterns from the normal training set, which are more likely to contain more informative normal patterns. Specifically, we further propose an inter-correlation learning branch to explicitly model pairwise correlations with the whole normal training set. In this branch, the features of each patch establish a discrete inter-correlation distribution with the reference features extracted from all normal samples (see Figure 2). The inter-correlation matrix of the  $k$ th layer is similar to the corresponding intra-correlation, and is defined as:",
+        "bbox": [
+            75,
+            401,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inter Correlation:  $S_{k}^{e} = \\mathrm{Softmax}\\Big(Q_{k}^{e}(K_{k}^{e})^{T} / \\sqrt{d_{m}}\\Big)$",
+        "bbox": [
+            87,
+            633,
+            453,
+            655
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ _ {k} ^ {e}, K _ {k} ^ {e}, V _ {k} ^ {e} = X _ {k - 1} W _ {k} ^ {Q _ {e}}, X _ {f} W _ {k} ^ {K _ {e}}, X _ {f} W _ {k} ^ {V _ {e}} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            90,
+            657,
+            468,
+            676
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $X_{f}\\in \\mathbb{R}^{N_{e}\\times d_{e}}$  represents the external reference features,  $N_{e}$  is the length of the reference features and  $d_{e}$  is the feature dimension.  $W_{k}^{Q_{e}}\\in \\mathbb{R}^{d_{m}\\times d_{m}}$  and  $W_{k}^{K_{e}},W_{k}^{V_{e}}\\in$ $\\mathbb{R}^{d_e\\times d_m}$  are learnable matrices for  $Q_{k}^{e},K_{k}^{e},V_{k}^{e}$ $S_k^e\\in$ $\\mathbb{R}^{N\\times N_e}$  denotes the learned inter-image correlations.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Loss. The loss function for the inter-correlation branch has the opposite optimization direction to  $\\mathcal{L}_g$ . Because the external reference features contain more comprehensive normal patterns, normal patches can establish stronger correlations with the closest reference normal patterns, instead of establishing strong correlations with most reference patterns. By contrast, it shall be harder for anomalous patches to establish strong correlations with any of the reference",
+        "bbox": [
+            75,
+            756,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "patterns. So the inter-correlation distributions of anomalies are more dispersed, while the normal inter-correction distributions are more likely to be concentrated. To this end, we maximize the KL divergence and minimize the entropy item in the training process. The practical optimization strategy is also opposite to the intra-correlation branch (see App. A.1 for details). The loss function is defined as:",
+        "bbox": [
+            499,
+            125,
+            890,
+            222
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {e} = - \\lambda_ {1} \\operatorname {D i v} \\left(\\mathcal {T} ^ {e}, \\mathcal {S} ^ {e}\\right) + \\lambda_ {2} \\operatorname {E n t} \\left(\\mathcal {S} ^ {e}\\right) \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "External Reference Features. External reference features are used for providing accumulated knowledge of normality for the inter-correlation learning branch. Thus, these features should represent all possible normal patterns of all normal samples from the whole normal training set. To this end, we can employ many methods to generate the reference features, such as sampling key features by coreset subsampling algorithm [35], generating prototype features by memory module [28], or learning codebook features through vector quantization [65] or sparse coding techniques [55]. However, because the RBF-kernel in  $\\mathcal{T}^e$  is position-sensitive, our reference features are better to preserve the positional information. The ablation results in App.B.2 show that the methods that can't preserve the position information perform worse. From comprehensive ablation studies, we find that using patch-wise averaged features as the external reference features is a simple but effective way. We think that features extracted by deep neural networks are highly redundant [16, 52], and different normal patterns generally correspond to larger activation values at different channels in the feature vector [61]. So feature averaging will not eliminate some rare normal patterns [11], these patterns may be preserved at specific channels. And averaging can greatly reduce the feature redundancy, making the obtained reference features more representative. Formally, for position  $(i,j)$ , we first extract the set of patch features at  $(i,j)$ ,  $X_{ij} = \\{x_{ij}^k\\}$ ,  $k \\in [1,N]$  from the  $N$  normal training images. Then, the reference features at position  $(i,j)$  is computed as  $x_{ij}^f = \\frac{1}{N}\\sum_{k=1}^{N}x_{ij}^k$ . The final external reference features are composed of averaged features at all locations and then flattened into 1D:  $X_f = \\text{Flatten}(\\{x_{ij}^f\\})$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. I2Correlation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            705,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We further combine the intra-correlation and intercorrelation branches to form the I2Correlation block. The output features of the intra- and inter-correlation branches are defined as:  $Z_{k}^{g} = S_{k}^{g}V_{k}^{g}$  and  $Z_{k}^{e} = S_{k}^{e}V_{k}^{e}$ , respectively. Then, we use the residual feature  $Z_{k}^{ge} = Z_{k}^{g} - Z_{k}^{e}$  as the output of the I2Correlation block. The feature  $Z_{k}^{e}$  is generated from the external reference features, which can contain rich normal patterns. Thus, by subtracting  $Z_{k}^{e}$  from the feature  $Z_{k}^{g}$ , it is conducive to spotlight the abnormal patterns in the  $Z_{k}^{g}$ . This is beneficial for anomaly detection.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "6807",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The total loss function consists of the there branch loss functions, and is combined as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {l} + \\mathcal {L} _ {g} + \\mathcal {L} _ {e} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.6. Anomaly Scoring",
+        "text_level": 1,
+        "bbox": [
+            77,
+            188,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We utilize reconstruction errors as the baseline anomaly criterion and incorporate the normalized correlation distribution distances into the reconstruction criterion. The final anomaly score of the  $i$ th patch in the input patch sequence is shown as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ns _ {i} = \\left[ | | X _ {i,:} - \\hat {X} _ {i,:} | | _ {2} + \\left(1 - \\frac {X _ {i , :} \\cdot \\hat {X} _ {i , :}}{| | X _ {i , :} | | _ {2} | | \\hat {X} _ {i , :} | | _ {2}}\\right) \\right] \\odot \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            287,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(1 - \\operatorname {S o f t m a x} \\left(- \\operatorname {D i v} \\left(\\mathcal {T} _ {i,:} ^ {e}, \\mathcal {S} _ {i,:} ^ {e}\\right)\\right)\\right)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            193,
+            321,
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+            346
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\odot$  is the element-wise multiplication.",
+        "bbox": [
+            77,
+            353,
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+            368
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We extensively evaluate our approach on two widely used industrial AD datasets: the MVTecAD [3] and BTAD [26], and one recent challenging dataset: the MVTecAD-3D [5]. MVTecAD is established as a standard benchmark for evaluating unsupervised image anomaly detection methods. This dataset contains 5354 high-resolution images from 15 real-world categories. 5 classes consist of textures and the other 10 classes contain objects. A total of 73 different anomaly types are presented. BTAD is another popular benchmark for unsupervised image anomaly detection, which contains 2540 RGB images of three industrial products. All classes in this dataset belong to textures. MVTecAD-3D is recently proposed, which contains 4147 2D RGB images paired with high-resolution 3D point cloud scans from 10 real-world categories. Even though this dataset is mainly designed for 3D anomaly detection, most anomalies can also be detected only through RGB images without 3D point clouds. Since we focus on image anomaly detection, we only use RGB images of the MVTecAD-3D dataset. We refer to this subset as MVTec3D-RGB.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. The standard metric in anomaly detection, AUROC, is used to evaluate the performance of AD methods. Image-level AUROC is used for anomaly detection and a pixel-based AUROC for evaluating anomaly localization [3, 4, 11, 64].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We use EfficientNet-b6 [45] to extract two levels of feature maps with  $\\{8\\times ,16\\times \\}$  downsampling ratios, the pre-trained networks are from the timm library [53]. Then, we construct a subsequent transformer network (see Figure 2) at each feature level to reconstruct patch features and learn patch-to-patch correlations. The parameters of the feature extractor are frozen in the training",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/92c4040bef81e953acb8cdfe6b670574813f8db448a7d968413692525972c4f9.jpg",
+        "table_caption": [
+            "Table 1. Comparison of our method with the SOTA methods on the MVTecAD dataset. Red and blue indicate the first and the second best result, respectively. According to the anomaly recognition process, we divide these methods into the patch-wise representation discrepancy, patch-to-patch feature distance, and others."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Discrepancy Type</td><td>Method</td><td>Venue</td><td>Image-level AUROC</td><td>Pixel-level AUROC</td></tr><tr><td rowspan=\"14\">Patch-wise Representation Discrepancy</td><td>STAD [4]</td><td>CVPR 2020</td><td>0.877</td><td>0.939</td></tr><tr><td>PaDiM [11]</td><td>ICPR 2020</td><td>0.955</td><td>0.975</td></tr><tr><td>DFR [57]</td><td>Neurocomputing 2021</td><td>/</td><td>0.950</td></tr><tr><td>FCDD [25]</td><td>ICLR 2021</td><td>/</td><td>0.920</td></tr><tr><td>MKD [41]</td><td>CVPR 2021</td><td>0.877</td><td>0.907</td></tr><tr><td>Hou et al. [17]</td><td>ICCV 2021</td><td>0.895</td><td>/</td></tr><tr><td>Metaformer [54]</td><td>ICCV 2021</td><td>0.958</td><td>/</td></tr><tr><td>DRAEM [64]</td><td>ICCV 2021</td><td>0.980</td><td>0.973</td></tr><tr><td>RDAD [12]</td><td>CVPR 2022</td><td>0.985</td><td>0.978</td></tr><tr><td>SSPCAB [34]</td><td>CVPR 2022</td><td>0.989</td><td>0.972</td></tr><tr><td>DSR [65]</td><td>ECCV 2022</td><td>0.982</td><td>/</td></tr><tr><td>NSA [43]</td><td>ECCV 2022</td><td>0.972</td><td>0.963</td></tr><tr><td>UniAD [62]</td><td>NIPS 2022</td><td>0.966</td><td>0.966</td></tr><tr><td>UTRAD [8]</td><td>Neural Networks 2022</td><td>0.960</td><td>0.967</td></tr><tr><td rowspan=\"6\">Patch-to-patch Feature Distance</td><td>PatchSVDD [60]</td><td>ACCV 2020</td><td>0.921</td><td>0.957</td></tr><tr><td>DifferNet [36]</td><td>WAVC 2020</td><td>0.949</td><td>/</td></tr><tr><td>CFLOW [15]</td><td>WAVC 2022</td><td>0.983</td><td>0.986</td></tr><tr><td>CS-FLOW [37]</td><td>WAVC 2022</td><td>0.987</td><td>/</td></tr><tr><td>Tsai et al. [15]</td><td>WAVC 2022</td><td>0.981</td><td>0.981</td></tr><tr><td>PatchCore [35]</td><td>CVPR 2022</td><td>0.991</td><td>0.980</td></tr><tr><td rowspan=\"3\">Others</td><td>CutPaste [21]</td><td>CVPR 2021</td><td>0.952</td><td>0.960</td></tr><tr><td>Wang et al. [51]</td><td>CVPR 2021</td><td>/</td><td>0.91</td></tr><tr><td>SPD [68]</td><td>ECCV 2022</td><td>0.946</td><td>0.946</td></tr><tr><td>Patch-wise&amp;Intra&amp;Inter</td><td>FOD (Ours)</td><td>-</td><td>0.992</td><td>0.983</td></tr></table>",
+        "bbox": [
+            502,
+            185,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/850f7be7fd0057c29e30298f7244d7cb9e6d14b708cd792b7ddd7d51b8ea7314.jpg",
+        "table_caption": [
+            "Table 2. Detailed image-level AUROCs on the MVTecAD dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Category</td><td colspan=\"6\">Image-level Anomaly Detection</td></tr><tr><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td>Carpet</td><td>0.978</td><td>0.963</td><td>1.000</td><td>1.000</td><td>0.987</td><td>1.000</td></tr><tr><td>Grid</td><td>1.000</td><td>0.892</td><td>0.975</td><td>0.992</td><td>0.996</td><td>1.000</td></tr><tr><td>Leather</td><td>1.000</td><td>0.953</td><td>0.956</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Tile</td><td>0.998</td><td>0.969</td><td>0.999</td><td>1.000</td><td>0.999</td><td>1.000</td></tr><tr><td>Wood</td><td>0.991</td><td>0.989</td><td>0.989</td><td>0.985</td><td>0.991</td><td>0.991</td></tr><tr><td>Bottle</td><td>0.993</td><td>0.976</td><td>0.989</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Cable</td><td>0.929</td><td>0.899</td><td>0.972</td><td>0.992</td><td>0.976</td><td>0.995</td></tr><tr><td>Capsule</td><td>0.984</td><td>0.763</td><td>0.979</td><td>0.984</td><td>0.977</td><td>1.000</td></tr><tr><td>Hazelnut</td><td>1.000</td><td>0.912</td><td>0.997</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Metal nut</td><td>0.989</td><td>0.941</td><td>0.972</td><td>1.000</td><td>0.993</td><td>1.000</td></tr><tr><td>Pill</td><td>0.981</td><td>0.791</td><td>0.971</td><td>0.954</td><td>0.968</td><td>0.984</td></tr><tr><td>Screw</td><td>0.939</td><td>0.825</td><td>0.870</td><td>0.953</td><td>0.919</td><td>0.967</td></tr><tr><td>Toothbrush</td><td>1.000</td><td>0.992</td><td>0.886</td><td>0.906</td><td>0.997</td><td>0.944</td></tr><tr><td>Transistor</td><td>0.914</td><td>0.874</td><td>0.956</td><td>0.995</td><td>0.952</td><td>1.000</td></tr><tr><td>Zipper</td><td>1.000</td><td>0.982</td><td>0.981</td><td>0.989</td><td>0.985</td><td>0.997</td></tr><tr><td>Mean</td><td>0.980</td><td>0.915</td><td>0.966</td><td>0.983</td><td>0.983</td><td>0.992</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "process, only the parameters of the subsequent transformer networks are learnable. All the subsequent transformer networks in our model contain 3 layers. We set the hidden dimension  $d_{m}$  as  $\\{256,512\\}$  and the number of heads as 8. The hyperparameters  $\\lambda_{1}$  and  $\\lambda_{2}$  are set as 0.5 and 0.5 to trade off two parts of the  $\\mathcal{L}_g$  and  $\\mathcal{L}_e$  loss functions (see App. B.2 for hyperparameter sensitivity analysis). We use the Adam [19] optimizer with an initial learning rate of  $1\\mathrm{e}^{-4}$ . The total training epochs are set as 100 and the batch size is 1 by default. All the training and test images are resized and cropped to  $256\\times 256$  resolution from the original resolution.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Main Results",
+        "text_level": 1,
+        "bbox": [
+            499,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "SOTA Methods. We extensively compare our method with those published SOTA methods in the past three years.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6808",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The comparison results on MVTecAD are shown in Table 1. Then, we select five reproducible methods to report the detailed results on MVTecAD, these methods are representative and SOTA AD methods in the mainstream categories of image anomaly detection as we discuss in Related Work, including: DRAEM [64], PatchSVDD[60], PatchCore [35], MKD[41], CFLOW[15]. For a fair comparison, we reproduce all these methods with the same backbone as in our model. Thus, despite using the unmodified code from the official repositories, we are not able to exactly reproduce the original results, but our numbers are very close. The detailed image-level AUROC results are shown in Table 2, and detailed pixel-level AUROC results are in the App. Table 6. Most of the methods in Table 1 don't report results on the BTAD and MVTec3D-RGB datasets, so we reproduce the five representative methods on the two datasets for comparison. The image-level and pixel-level AUROC results on BTAD and MVTec3D-RGB are shown in Table 3. Additional detailed results are in the App. Table 7, 8.",
+        "bbox": [
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+            125,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Anomaly Detection. On MVTecAD, we set the SOTA performance on the mean detection AUROC, which is slightly higher than the best competitor, PatchCore [35]. Note that the results in Table 2 show that our method can achieve much better results than PatchCore when using the same backbone. What's more, in addition to the pill, screw and toothbrush classes, our method achieves more than  $99\\%$  AUROC in all other classes, while other methods only achieve more than  $99\\%$  AUROC in most nine classes. This shows that our method is more stable and effective in real-world applications. In the classes (e.g. metal nut, screw, and transistor) with more global and logical anomalies, our method can achieve significantly better results than those methods depending on patch-wise discrepancy (e.g. DRAEM [64] and MKD [41]), and can also achieve better results compared with other methods. This verifies that the three discrepancies are complementary factors and our model can simultaneously spot these discrepancies to recognize harder global and logical anomalies. On BTAD, our FOD can achieve  $96.0\\%$  mean detection AUROC, which can outperform the best competitor CFLOW [15] by a margin of  $1.2\\%$ . On MVTec3D-RGB, we can outperform all previous SOTA methods by a margin of  $3.3\\%$ . Note that this dataset is much more challenging than the MVTecAD dataset when comparing the best results  $(99.2\\%)$  for MVTecAD vs.  $88.4\\%$  AUROC for MVTec3D-RGB). This demonstrates the robustness of our method.",
+        "bbox": [
+            75,
+            391,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Anomaly Localization. Our method can achieve comparable results with the best competitors on all three datasets. Our method is slightly lower than CFLOW [15] and PatchCore [35] on the three datasets, but we observe that our model that considers the intra- and intercorrelations outperforms the vanilla reconstruction AD models (e.g. DRAEM [64] and MKD [41]) on all three",
+        "bbox": [
+            75,
+            769,
+            470,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/79afbeb73514656fc4e62b4a0df2b12d9186180902bb5d3db70fa954f5712658.jpg",
+        "table_caption": [
+            "Table 3. Comparison of our method with the SOTA methods for image-level anomaly detection and pixel-level anomaly localization performance on the BTAD and MVTec3D-RGB datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td colspan=\"7\">BTAD Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.922</td><td>0.924</td><td>0.935</td><td>0.934</td><td>0.948</td><td>0.960</td></tr><tr><td>Pixel-level AUROC</td><td>0.942</td><td>0.964</td><td>0.965</td><td>0.976</td><td>0.978</td><td>0.975</td></tr><tr><td colspan=\"7\">MVTec3D-RGB Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.757</td><td>0.743</td><td>0.688</td><td>0.839</td><td>0.851</td><td>0.884</td></tr><tr><td>Pixel-level AUROC</td><td>0.974</td><td>0.852</td><td>0.970</td><td>0.977</td><td>0.974</td><td>0.976</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "datasets, which verifies the effectiveness of correlation modeling. Compared with patch-wise reconstruction methods, our method is more effective and robust to detect hard global and logical anomalies (see Figure 3).",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Qualitative Results. Samples in Figure 1 show qualitative impressions of accurate anomaly localization from our method. It can be found that our approach can achieve the best anomaly score maps by combining the three discrepancies. Additional visualizations are in the App. Figure 6.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study and Model Analysis",
+        "text_level": 1,
+        "bbox": [
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+            388,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation Study. To explain how our model works effectively, we further investigate the effect of the three key designs in our model: recognition views, entropy constraint and reference features. The quantitative results are shown in Table 4, more results can be found in App. Table 9. The entropy constraint is quite effective and necessary in the intra-correlation branch. Specifically, it brings a remarkable  $7.7\\%$  averaged absolute AUROC promotion, which demonstrates that the entropy constraint strategy is really conducive to increase the distinguishability between abnormal and normal. Only utilizing pure reconstruction criterion or pure KL divergence can't get the most superior detection results, the combined criterion can outperform each single criterion consistently by a margin of  $1.0\\%$  and  $9.8\\%$ . Thus the reconstruction errors and the intra- and inter-correlations can collaborate to improve detection performance. For the external reference features, we compare the simple mean features with more elaborate coreset features [35] (see App. Table 15 for more comparison methods). The results show that the simple mean features are more effective than the coreset features (0.923 vs. 0.836), which means that mean features are effective enough to represent all possible normal patterns and preserve the positional information. Finally, our proposed FOD surpasses the pure reconstruction Transformer by  $4.0\\%$  absolute improvement. These verify that our proposed explicit correlation learning approach is effective.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effect for Different Anomalies. To illustrate the effectiveness of our model intuitively, we explore the anomaly localization quality under different types of anomalies (see Figure 3). E.g., simple local anomalies (Column 1) are obviously different from normal visuals; hard global anomalies (Columns 2,3) have less obvious visual appearances,",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "6809",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/27028949e77541ca13217d8b256b918f8343aae7929f6bcfcbe0cddf2cbdd9a4.jpg",
+        "table_caption": [
+            "Table 4. Ablation results in recognition views, entropy constraint, external reference features and anomaly scoring. Patch-wise, Intra and Inter mean patch-wise discrepancy, intra- and intercorrelation, respectively. w/o and w/ mean without and with entropy constraint. Mean and Coreset refer to mean and coreset features [35] as the external reference features (see more details in App. B.3). Rec, Div and Rec&Div mean the pure reconstruction criterion, pure KL divergence (E.q.6) and the combined criterion (E.q.12)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Recognition Views</td><td>Entropy Constraint</td><td>Reference Features</td><td>Anomaly Scoring</td><td>MVTecAD</td><td>BTAD</td><td>MVTec3D-RGB</td><td>Avg</td></tr><tr><td rowspan=\"2\">Patch-wise</td><td>/</td><td>/</td><td>Rec</td><td>0.972</td><td>0.954</td><td>0.790</td><td>0.905</td></tr><tr><td>w/o</td><td>/</td><td>Div</td><td>0.700</td><td>0.811</td><td>0.708</td><td>0.740</td></tr><tr><td rowspan=\"2\">Intra</td><td>w/</td><td>/</td><td>Div</td><td>0.911</td><td>0.822</td><td>0.717</td><td>0.817</td></tr><tr><td>w/</td><td>/</td><td>Rec&amp;Div</td><td>0.974</td><td>0.952</td><td>0.818</td><td>0.915</td></tr><tr><td rowspan=\"2\">Inter</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.980</td><td>0.958</td><td>0.832</td><td>0.923</td></tr><tr><td>w/</td><td>Coreset</td><td>Rec&amp;Div</td><td>0.925</td><td>0.884</td><td>0.700</td><td>0.836</td></tr><tr><td>Intra+Inter</td><td>w/</td><td>Mean</td><td>Div</td><td>0.896</td><td>0.922</td><td>0.814</td><td>0.877</td></tr><tr><td>Patch-wise+Intra+Inter (Ours)</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.992</td><td>0.960</td><td>0.884</td><td>0.945</td></tr></table>",
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+    {
+        "type": "image",
+        "img_path": "images/1ec96a1b48d3d708d0e0d07fc8f802ff95ab7f821d92fe29939d02ed45eb21df.jpg",
+        "image_caption": [
+            "Figure 3. Visualization of different anomalies. The patch-wise reconstruction is only suitable for simple local anomalies, while for hard global and logical anomalies, it cannot detect or only detect partial anomalies. In contrast, our FOD can detect these anomalies more effectively."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "which usually need to be effectively compared with normal regions to detect; logical anomalies (Columns 4,5) may be locally normal and can be detected correctly through the overall semantic understanding. We can find that our FOD is more distinguishable in general. For simple local anomalies, patch-wise reconstruction methods can also achieve good results. While for hard global anomalies, these methods cannot detect or only detect partial anomalies. However, for logical anomalies, these methods cannot detect them at all. In contrast, our method is conducive to detect diverse anomalies because of its complementary recognition views. This verifies that our method can make more precise detection and reduce the false-negative rate compared with the pure patch-wise reconstruction methods.",
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+    {
+        "type": "text",
+        "text": "Correlations Visualization. To explain what our model has learned intuitively, we visualize some learned correlations in Figure 4 with the MVtecAD dataset. For the intra",
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+        "img_path": "images/60147049f647c70f6f8c9847dd64a6245a72e0577ace31001eb7536ad693d4ad.jpg",
+        "image_caption": [
+            "(a) Intra-Correlations"
+        ],
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+        "img_path": "images/f0c65d6500e59c6335307d358e06e2273570110d923d9bde6d32df0fbcc4446b.jpg",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/9b93c1fc3dade151c6d07dc4adcb3594ad34ce22acbea732248bdd58d83528de.jpg",
+        "image_caption": [],
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+    {
+        "type": "image",
+        "img_path": "images/b521b7fbdabbf6d817948b2f171c60c2a30c5dc0610b683ee1af20dee6d7d1d5.jpg",
+        "image_caption": [
+            "Figure 4. Visualization of intra- and inter-correlations. Each red point in the figure can represent an image patch, we plot its discrete correlation distribution with all the other image patches."
+        ],
+        "image_footnote": [],
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+        "img_path": "images/2486c4e5bdc4f01d027842e0e34c5f4e81b4e8f630e0d5266649149c4ec43a5f.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/79e9209ea383b56702bc78e419999bccdf3799bbb36521921adab7ee64ed903c.jpg",
+        "image_caption": [
+            "(b) Inter-Correlations"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/3c167c9e8e243475d97e7539a9c30467a5c8532b630069c2716e358f518fcd52.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "correlation branch, the normal patches learn to build strong correlations with most patches in the whole image, while the correlation distributions of anomalies usually concentrate in the adjacent image patches. It can be found that the normal correlations are much spread and the abnormal correlations are more concentrated in the adjacent regions. For the inter-correlation branch, most normal correlations only concentrate in one point and the abnormal correlations are more spread, which exactly means that each normal patch can build strong correlations with one special normal pattern and abnormal patches are harder to establish correlations with normal patterns.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Humans recognize anomalies through two aspects: patch-wise representation discrepancies and weak patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy, to simultaneously spot the patch-wise, intra- and inter-discrepancies. The patch-wise discrepancies and intra- and inter-correlations are complementary factors, and can be combined to detect more complex and diverse anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to I2Correlation to explicitly establish intra- and inter-image correlations for AD modeling. The combination of explicit correlation learning and transformer architecture can match the core idea of anomaly detection quite well.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This work was supported in part by the National Natural Science Fund of China (61971281), the Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Science and Technology Commission of Shanghai Municipality (22DZ2229005).",
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+        "text": "6810",
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+    },
+    {
+        "type": "text",
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diff --git a/2023/Focus the Discrepancy_ Intra- and Inter-Correlation Learning for Image Anomaly Detection/9a627ddc-8c15-4383-a8ac-8266b31abdaf_model.json b/2023/Focus the Discrepancy_ Intra- and Inter-Correlation Learning for Image Anomaly Detection/9a627ddc-8c15-4383-a8ac-8266b31abdaf_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..0adb74593c7f67ab081397234df92a83624216d3
--- /dev/null
+++ b/2023/Focus the Discrepancy_ Intra- and Inter-Correlation Learning for Image Anomaly Detection/9a627ddc-8c15-4383-a8ac-8266b31abdaf_model.json	
@@ -0,0 +1,2356 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.13,
+                0.051,
+                0.201,
+                0.085
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.254,
+                0.049,
+                0.79,
+                0.088
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.12,
+                0.162,
+                0.85,
+                0.205
+            ],
+            "angle": 0,
+            "content": "Focus the Discrepancy: Intra- and Inter-Correlation Learning for Image Anomaly Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.19,
+                0.228,
+                0.783,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Xincheng Yao\\(^{1}\\), Ruoqi Li\\(^{1}\\), Zefeng Qian\\(^{1}\\), Yan Luo\\(^{1}\\), Chongyang Zhang\\(^{1,2*}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.119,
+                0.246,
+                0.851,
+                0.261
+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.153,
+                0.262,
+                0.817,
+                0.278
+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.19,
+                0.279,
+                0.776,
+                0.294
+            ],
+            "angle": 0,
+            "content": "{i-Dover, nilponi, zefeng.qian, luoyan.bb, sunny_zhang}@sjtu.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.325,
+                0.314,
+                0.34
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.355,
+                0.474,
+                0.715
+            ],
+            "angle": 0,
+            "content": "Humans recognize anomalies through two aspects: larger patch-wise representation discrepancies and weaker patch-to-normal-patch correlations. However, the previous AD methods didn't sufficiently combine the two complementary aspects to design AD models. To this end, we find that Transformer can ideally satisfy the two aspects as its great power in the unified modeling of patchwise representations and patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can simultaneously spot the patch-wise, intra- and inter-discrepancies of anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to Intra-Inter-Correlation (I2Correlation). The I2Correlation contains a two-branch structure to first explicitly establish intra- and inter-image correlations, and then fuses the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning. Besides, we introduce an entropy constraint strategy to solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability. Extensive experiments on three unsupervised real-world AD benchmarks show the superior performance of our approach. Code will be available at https://github.com/xcyao00/FOD."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.74,
+                0.21,
+                0.755
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.763,
+                0.47,
+                0.848
+            ],
+            "angle": 0,
+            "content": "The goal of anomaly detection (AD) is to distinguish an instance containing anomalous patterns from those normal samples and further localize those anomalous regions. Anomalies are defined as opposite to normal samples and are usually rare, which means that we need to tackle AD tasks under the unsupervised setting with only normal sam"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.326,
+                0.89,
+                0.513
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.515,
+                0.893,
+                0.606
+            ],
+            "angle": 0,
+            "content": "Figure 1. Anomaly detection examples on MVTecAD [3]. Multiresolution Knowledge Distillation (MKD) [41] adopts the conventional patch-wise representation discrepancies. Row 1 shows the hard global anomalies (i.e., they are not significantly different from normal visuals). Rows 3 and 4 show the logical anomalies (i.e., they may be easily recognized as normal if only from the patch-wise discrepancy)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.63,
+                0.893,
+                0.838
+            ],
+            "angle": 0,
+            "content": "plies accessible. The core idea of most unsupervised AD methods is to compare with normal samples to distinguish anomalies [46, 35, 60, 11, 28, 58]. Even for humans, we also recognize anomalies in this way, specifically through three discrepancies, i.e., 1. patch patterns that differentiate from the normal visuals; 2. image regions that destroy textures or structures; 3. novel appearances that deviate from our accumulated knowledge of normality. Namely, anomalous patches usually have three characteristics: their patchwise representations are different from the normal visuals; they are different from most patches within one image; they deviate from our accumulated knowledge of normality. These views intrinsically reveal that humans' recognition of anomalies depends on two aspects: patch-wise representations (1) and intra- and inter-image correlations (2, 3)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.839,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Previous methods mainly follow the former aspect to learn distinguishable representations or reconstructions,"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.854,
+                0.227,
+                0.867
+            ],
+            "angle": 0,
+            "content": "*Corresponding Author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.887,
+                0.501,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6803"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.126,
+                0.473,
+                0.403
+            ],
+            "angle": 0,
+            "content": "such as reconstruct-based methods [6, 57, 1] and knowledge distillation AD models [4, 41]. The goal of these methods is to generate reconstructed samples or feature representations, and larger patch-wise representation discrepancies can appear in the abnormal patches. However, only the patch-wise representation discrepancies are insufficient for detecting more complex anomalies (e.g., rows 3 and 4 in Figure 1), since the patch-wise errors can't provide comprehensive descriptions of the spatial context. Other mainstream AD methods, such as embedding-based [11, 35] and one-class-classification-based (OCC) [39, 60] methods, are much similar to the latter aspect. These methods achieve anomaly detection by measuring the distances between the features of test samples and normal features. Compared with the non-learnable feature distances, the explicit intra- and inter-image correlations in our method are more effective to detect diverse anomalies (see Table 1, 2, 3). Moreover, patch-wise representation discrepancies and intra- and inter-correlation discrepancies are complementary, and can be combined to develop more powerful AD models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.407,
+                0.473,
+                0.67
+            ],
+            "angle": 0,
+            "content": "Recently, with the self-attention mechanism and long-range modeling ability, transformers [50] have significantly renovated many computer vision tasks [14, 24, 7, 67, 56] and recently popular language-vision multimodal tasks [30, 22]. Transformers have shown great power in the unified modeling of patch-wise representations and patch-to-patch correlations. Transformers are quite suitable for AD tasks as their modeling ability can satisfy the two aspects of anomaly recognition quite well. Some works [26, 18, 8, 62] also attempt to employ transformers to construct AD models. However, these methods only use transformers to extract vision features, which didn't sufficiently adapt transformers' long-range correlation modeling capability to AD tasks. Different from these works, we explicitly exploit transformers' self-attention maps to establish the intra- and inter-image correlations. The correlation distribution of each patch can provide more informative descriptions of the spatial context, which can reveal more intricate and semantic anomaly patterns."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.673,
+                0.473,
+                0.868
+            ],
+            "angle": 0,
+            "content": "In this paper, motivated by humans' anomaly recognition process, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can exploit transformers' unified modeling ability to simultaneously spot the patch-wise, intra- and inter-discrepancies. Our key designs are composed of three recognition branches: the patch-wise discrepancy branch is to reconstruct the input patch features for distinguishing simple anomalies; the intra-correlation branch is to explicitly model patch-to-patch correlations in one image for distinguishing hard global anomalies (e.g., row 1 in Figure 1); the inter-correlation branch is to explicitly learn inter-image correlations with known normal patterns from the whole normal training set. To implement the intra- and inter-correlation branches, we adapt"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.127,
+                0.892,
+                0.292
+            ],
+            "angle": 0,
+            "content": "Transformer and renovate the self-attention mechanism to the I2Correlation, which contains a two-branch structure to first separately model the intra- and inter-correlation distribution of each image patch, and then fuse the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning, the RBF kernel is used to present the neighborhood continuity of each image patch. Besides, an entropy constraint strategy is applied in the two branches, which can solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.293,
+                0.89,
+                0.306
+            ],
+            "angle": 0,
+            "content": "In summary, we make the following main contributions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.306,
+                0.891,
+                0.347
+            ],
+            "angle": 0,
+            "content": "1. We propose a novel AD framework: FOD, which can effectively detect anomalies by simultaneously spotting the patch-wise, intra- and inter-discrepancies."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.348,
+                0.892,
+                0.416
+            ],
+            "angle": 0,
+            "content": "2. We renovate the self-attention mechanism to the I2Correlation, which can explicitly establish intra- and inter-correlations in a self-supervised way with the target-correlations. An entropy constraint strategy is proposed to further amplify the normal-abnormal distinguishability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.417,
+                0.892,
+                0.459
+            ],
+            "angle": 0,
+            "content": "3. Our method can achieve SOTA results on three real-world AD datasets, this shows our method can more effectively determine anomalies from complementary views."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.498,
+                0.306,
+                0.892,
+                0.459
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.47,
+                0.642,
+                0.485
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.494,
+                0.892,
+                0.673
+            ],
+            "angle": 0,
+            "content": "Anomaly Detection. In this paper, we divide the mainstream AD methods into five categories: reconstruction-based, embedding-based, OCC-based methods, knowledge distillation and normalizing flow AD models. The reconstruction-based methods are the most popular AD methods and also widely studied, where the assumption is that models trained by normal samples only can reconstruct normal regions but fail in abnormal regions. Many previous works attempt to train AutoEncoders [6, 28, 57, 8, 17, 64], Variational AutoEncoders [23] and GANs [42, 1, 29, 40] to reconstruct the input images. Overfitting to the input images is the most serious issue of these methods, which means that the anomalies are also well reconstructed [62]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.673,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Recently, some embedding-based methods [2, 33, 9, 11, 35] show better AD performance by using ImageNet pretrained networks as feature extractors. In [33], the authors fit a multivariate Gaussian to model the image-level features for further Mahalanobis distance measurement. PaDiM [11] extends the above method to localize pixel-level anomalies. PatchCore [35] extends on this line by utilizing locally aggregated, mid-level features and introducing greedy coreset subsampling to form nominal feature banks. However, these methods directly utilize pre-trained networks without any adaptation to the target dataset. Some works [31, 10, 32] attempt to adapt pre-trained features to the target data distribution. There are also some other methods for using pre-trained networks by freezing them and only"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.887,
+                0.502,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6804"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.127,
+                0.47,
+                0.154
+            ],
+            "angle": 0,
+            "content": "optimizing a sub-network, e.g., via knowledge distillation [4, 41, 12, 38], or normalizing flows [36, 15, 37, 63]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.156,
+                0.47,
+                0.294
+            ],
+            "angle": 0,
+            "content": "OCC is another classical AD paradigm, the earliest works are mainly to extend the OCC models such as OC-SVM [44] or SVDD [47, 39] for anomaly detection. Recently, in [60], a patch-based SVDD that contains multiple cores rather than a single core in [39] is proposed to enable anomaly localization. In [25], a Fully Convolutional Data Description combined with receptive field upsampling is proposed to generate anomaly maps. In [48], the authors further extend the PatchSVDD [60] model by the proposed multi-scale patch-based representation learning method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.296,
+                0.471,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Transformer-based Anomaly Detection Methods. Recently, transformers [50] have shown great power in modeling long-range dependencies. For image anomaly detection, some works [26, 18, 62, 8, 59] also attempt to exploit transformers to design AD models. However, most of these methods only use transformers as backbones to extract vision features, and don't effectively adapt the long-range modeling capacity of transformers to AD tasks. Unlike the previous usage of transformers, we explicitly exploit the self-attention maps of transformers to establish intra- and inter-correlations. Our work shares some similarities with a recent work [20]. But we point out that our work has some significant differences from [20]: 1) Different Insight: [20] aims to unify the pointwise representation and pairwise association for time series AD, whereas our work aims to more sufficiently detect image anomalies through three complementary recognition views. 2) Novel Method: we propose entropy constraint, inter-correlation branch, and I2Correlation by effectively combining intra- and inter-correlation branches. 3) Different Task: [20] focuses on time-series AD, whereas we focus on image AD."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.604,
+                0.188,
+                0.619
+            ],
+            "angle": 0,
+            "content": "3. Approach"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.628,
+                0.24,
+                0.641
+            ],
+            "angle": 0,
+            "content": "3.1. Model Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.65,
+                0.47,
+                0.817
+            ],
+            "angle": 0,
+            "content": "Figure 2 overviews our proposed approach. The model consists of three branches: patch-wise discrepancy branch, intra-correlation branch, and inter-correlation branch. The input 2D image is first sent into a pre-trained backbone to extract multi-scale feature maps. At each feature level, we construct a subsequent transformer network to explicitly model the intra- and inter-image correlations for spotting the intra- and inter-discrepancies. Each network is implemented by stacking the I2Correlation blocks and feedforward layers alternately. Suppose each network contains \\(K\\) layers with length- \\(N\\) input features \\(X\\in \\mathbb{R}^{N\\times d}\\), the output of \\(k\\)th layer \\(X_{k}\\in \\mathbb{R}^{N\\times d_{m}}\\) is calculated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.116,
+                0.83,
+                0.469,
+                0.846
+            ],
+            "angle": 0,
+            "content": "\\[\nZ _ {k} = \\mathrm {L N} (\\mathrm {I 2 C o r r e l a t i o n} (X _ {k - 1}, X _ {f}) + X _ {k - 1}) \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.117,
+                0.849,
+                0.469,
+                0.863
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {k} = \\mathrm {L N} (\\text {F e e d F o r w a r d} (Z _ {k}) + Z _ {k}) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.127,
+                0.892,
+                0.196
+            ],
+            "angle": 0,
+            "content": "where \\(X_{f}\\) is the reference features used by the intercorrelation branch, \\(LN\\) means LayerNorm, and \\(Z_{k} \\in \\mathbb{R}^{N \\times d_{m}}\\) is the \\(k\\)th layer's hidden features. The final output features are calculated by linear projection: \\(\\hat{X} = Z_{K}W_{o}\\), where \\(W_{o} \\in \\mathbb{R}^{d_{m} \\times d}\\) is the output projection matrix."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.202,
+                0.844,
+                0.217
+            ],
+            "angle": 0,
+            "content": "3.2. Patch-Wise Reconstruction Discrepancy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.223,
+                0.892,
+                0.431
+            ],
+            "angle": 0,
+            "content": "Adopted from previous reconstruction-based AD methods, we employ feature reconstruction as our patch-wise recognition view for simplicity. In our approach, we construct a transformer network to reconstruct the input features. With the long-range dependency modeling ability, the features reconstructed by Transformer can have larger effective receptive fields [13], which are more conducive to detect hard global anomalies and logical anomalies. Moreover, with the further introduced inter-correlation branch (sec.3.4), the features can even perceive normal regions of images from the whole normal training set. Therefore, the reconstructed features generated by our model have better global perception and more discriminative semantic representation capability, which are more suitable for anomaly detection by patch-wise representation discrepancies."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.431,
+                0.892,
+                0.498
+            ],
+            "angle": 0,
+            "content": "Learning Objective. We can utilize classical reconstruction losses as the learning objective. We combine the \\(\\ell 2\\) distance and cosine distance to measure the feature distances between the reconstructed features \\(\\hat{X}\\) and the input features \\(X\\). The loss function is defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.502,
+                0.892,
+                0.54
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {l} = \\left| \\left| \\hat {X} - X \\right| \\right| _ {2} + \\left(1 - \\frac {\\hat {X} \\cdot X}{\\left| \\left| \\hat {X} \\right| \\right| _ {2} \\left| \\left| X \\right| \\right| _ {2}}\\right) \\tag {3}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.543,
+                0.749,
+                0.558
+            ],
+            "angle": 0,
+            "content": "3.3. Intra-Correlation Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.564,
+                0.892,
+                0.648
+            ],
+            "angle": 0,
+            "content": "The intra-correlation learning branch aims to learn informative patch-to-patch correlations from the input patch sequence adaptively. As shown in the right part of Figure 2, we explicitly take advantage of the self-attention maps of transformers as intra-correlation matrices. Formally, the intra-correlation matrix of the \\(k\\)th layer is calculated by:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.664,
+                0.88,
+                0.687
+            ],
+            "angle": 0,
+            "content": "Intra Correlation: \\( S_{k}^{g} = \\mathrm{Softmax}\\Big(Q_{k}^{g}(K_{k}^{g})^{T} / \\sqrt{d_{m}}\\Big) \\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.512,
+                0.688,
+                0.891,
+                0.707
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left[ Q _ {k} ^ {g}, K _ {k} ^ {g}, V _ {k} ^ {g} \\right] = X _ {k - 1} \\left[ W _ {k} ^ {Q _ {g}}, W _ {k} ^ {K _ {g}}, W _ {k} ^ {V _ {g}} \\right] \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.711,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "where \\( Q_{k}^{g}, K_{k}^{g}, V_{k}^{g} \\in \\mathbb{R}^{N \\times d_{m}} \\) represent the query, key, and value of the \\( k \\)th layer. \\( W_{k}^{Q_{g}}, W_{k}^{K_{g}}, W_{k}^{V_{g}} \\in \\mathbb{R}^{d_{m} \\times d_{m}} \\) represent the learnable projection matrices for \\( Q_{k}^{g}, K_{k}^{g}, V_{k}^{g} \\), respectively. \\( S_{k}^{g} \\in \\mathbb{R}^{N \\times N} \\) denotes the learned intra-image patch-to-patch correlations. Since \\( \\text{Softmax}(\\cdot) \\) can convert the values in the similarity map into range [0, 1] along the horizontal axis, each row of \\( S_{k}^{g} \\) can represent a discrete correlation distribution for each corresponding image patch. But different from the vanilla transformers, we further introduce target correlation matrices as the learning objective to explicitly optimize the intra-image correlations."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.887,
+                0.502,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6805"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.125,
+                0.351,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.368,
+                0.125,
+                0.59,
+                0.382
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.6,
+                0.131,
+                0.89,
+                0.385
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.389,
+                0.893,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Figure 2. Model overview. The model is composed of three parts: patch-wise discrepancy branch, intra-correlation branch, and intercorrelation branch. The input image patch sequence will be transformed into the hidden features by a pre-trained backbone, and then sent into the intra-correlation branch for learning intra-image patch-to-patch correlations. The input of the inter-correlation branch is composed of hidden features (as Query) and reference features (as Key and Value). The final output features are used to reconstruct the input features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.463,
+                0.473,
+                0.726
+            ],
+            "angle": 0,
+            "content": "Target Correlation. Inspired by the contrastive learning method BarlowTwins [66], we can construct a target correlation matrix \\( T \\in \\mathbb{R}^{N \\times N} \\) as the learning target. The objective function of BarlowTwins measures the correlation matrix between the embeddings of two identical networks fed with distorted versions of a batch of samples, and tries to make this matrix close to the identity. In our work, the role of the target correlation is to introduce a prior correlation of patches as a pretext learning target, where each patch can be highly correlated to itself and also correlated to its neighborhood patches and the correlation decreases with the increase of distance. This allows us to optimize the intra- and inter-correlations in a self-supervised way. To this end, we use the radial basis function (RBF) to construct the target correlation matrix. We further adopt two learnable kernel variances \\( \\sigma_x \\) and \\( \\sigma_y \\) for horizontal and vertical axes to make the target correlation of each patch can adapt to the specific pattern of itself. The target correlation matrix of the \\( k \\)th layer is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.138,
+                0.736,
+                0.404,
+                0.768
+            ],
+            "angle": 0,
+            "content": "\\[\nT _ {k} ^ {g} = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} \\exp \\left(- \\frac {\\left| \\left| x _ {i j} - x _ {i ^ {\\prime} j ^ {\\prime}} \\right| \\right| _ {2} ^ {2}}{2 \\left(\\sigma_ {x} ^ {2} + \\sigma_ {y} ^ {2}\\right)}\\right)\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.141,
+                0.77,
+                0.469,
+                0.787
+            ],
+            "angle": 0,
+            "content": "\\[\ni, i ^ {\\prime} \\in \\{1, \\dots , H \\}; j, j ^ {\\prime} \\in \\{1, \\dots , W \\} \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.797,
+                0.47,
+                0.839
+            ],
+            "angle": 0,
+            "content": "where \\(||x_{ij} - x_{i'j'}||_2^2\\) means the Square Euclidean distance between point \\(x_{ij}\\) and \\(x_{i'j'}\\), \\(i, i'\\) and \\(j, j'\\) means vertical and horizontal coordinates, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.84,
+                0.47,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Next, we need to measure the distance between target- and intra-correlation distributions. This can usually be"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.463,
+                0.892,
+                0.532
+            ],
+            "angle": 0,
+            "content": "achieved by calculating the KL divergence. We can obtain a KL divergence value from each level of the network. Thus, we average all KL divergence values to combine the patch-to-patch correlations from multi-layer features into a more informative measure as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.508,
+                0.54,
+                0.892,
+                0.579
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {D i v} \\left(\\mathcal {T} ^ {g}, \\mathcal {S} ^ {g}\\right) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(K L \\left(T _ {k} ^ {g} \\mid \\mid S _ {k} ^ {g}\\right) + K L \\left(S _ {k} ^ {g} \\mid \\mid T _ {k} ^ {g}\\right)\\right) \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.589,
+                0.891,
+                0.633
+            ],
+            "angle": 0,
+            "content": "where \\(KL(\\cdot ||\\cdot)\\in \\mathbb{R}^N\\) and its each element means the KL divergence between two discrete distributions corresponding to each row of \\(T_{k}^{g}\\) and \\(S_{k}^{g}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.632,
+                0.892,
+                0.797
+            ],
+            "angle": 0,
+            "content": "Due to the rarity of anomalies and the dominance of normal patterns, the normal patches should build strong correlations with most patches in the whole image, while the weights of abnormal correlation distributions are harder to distribute to most patches and are more likely to concentrate on the adjacent image patches due to the neighborhood continuity. Since normal and abnormal patches have different correlation distributions, this is a distinguishable criterion for anomaly detection. Note that the intra-correlation branch explicitly exploits the spatial dependencies of each image patch, which are more informative than the patchwise representations for anomaly detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.798,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Entropy constraint. Since the normal image patterns are usually diverse, the learned correlation distributions of the normal patches may also easily concentrate on the adjacent patches, which can cause the distinguishability between normal and abnormal to be downscaled. To address"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.887,
+                0.502,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6806"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.127,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "this, we further introduce an entropy constraint item for making normal patches establish strong associations with most normal patches in the whole image as much as possible. The entropy constraint item is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.192,
+                0.469,
+                0.232
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {E n t} \\left(\\mathcal {S} ^ {g}\\right) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} \\left(- S _ {k (i, j)} ^ {g} \\log \\left(S _ {k (i, j)} ^ {g}\\right)\\right)\\right) \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.24,
+                0.469,
+                0.267
+            ],
+            "angle": 0,
+            "content": "We will maximize the entropy constraint item. The loss function for the intra-correlation branch is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.155,
+                0.279,
+                0.469,
+                0.295
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {g} = \\lambda_ {1} \\operatorname {D i v} \\left(\\mathcal {T} ^ {g}, \\mathcal {S} ^ {g}\\right) - \\lambda_ {2} \\operatorname {E n t} \\left(\\mathcal {S} ^ {g}\\right) \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.304,
+                0.469,
+                0.373
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are used to trade off the loss items. The optimization of intra-correlation \\(S^g\\) is actually an alternating process with the guidance of target correlation \\(T^g\\) (see App. A.1), ultimately resulting that each normal patch can establish strong correlations with most normal patches."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.381,
+                0.322,
+                0.396
+            ],
+            "angle": 0,
+            "content": "3.4. Inter-Correlation Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.402,
+                0.469,
+                0.623
+            ],
+            "angle": 0,
+            "content": "Through the intra-correlation branch, we can establish patch-to-patch correlations within a single image. However, an image usually doesn't contain all possible normal patterns, which may cause it difficult to distinguish some ambiguous abnormal patches (see rows 2, 3, 4 in Figure 1) only through the intra-correlations. To address this, we should effectively take advantage of the known normal patterns from the normal training set, which are more likely to contain more informative normal patterns. Specifically, we further propose an inter-correlation learning branch to explicitly model pairwise correlations with the whole normal training set. In this branch, the features of each patch establish a discrete inter-correlation distribution with the reference features extracted from all normal samples (see Figure 2). The inter-correlation matrix of the \\(k\\)th layer is similar to the corresponding intra-correlation, and is defined as:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.634,
+                0.454,
+                0.656
+            ],
+            "angle": 0,
+            "content": "Inter Correlation: \\( S_{k}^{e} = \\mathrm{Softmax}\\Big(Q_{k}^{e}(K_{k}^{e})^{T} / \\sqrt{d_{m}}\\Big) \\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.091,
+                0.658,
+                0.469,
+                0.677
+            ],
+            "angle": 0,
+            "content": "\\[\nQ _ {k} ^ {e}, K _ {k} ^ {e}, V _ {k} ^ {e} = X _ {k - 1} W _ {k} ^ {Q _ {e}}, X _ {f} W _ {k} ^ {K _ {e}}, X _ {f} W _ {k} ^ {V _ {e}} \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.687,
+                0.469,
+                0.756
+            ],
+            "angle": 0,
+            "content": "where \\(X_{f}\\in \\mathbb{R}^{N_{e}\\times d_{e}}\\) represents the external reference features, \\(N_{e}\\) is the length of the reference features and \\(d_{e}\\) is the feature dimension. \\(W_{k}^{Q_{e}}\\in \\mathbb{R}^{d_{m}\\times d_{m}}\\) and \\(W_{k}^{K_{e}},W_{k}^{V_{e}}\\in\\) \\(\\mathbb{R}^{d_e\\times d_m}\\) are learnable matrices for \\(Q_{k}^{e},K_{k}^{e},V_{k}^{e}\\) \\(S_k^e\\in\\) \\(\\mathbb{R}^{N\\times N_e}\\) denotes the learned inter-image correlations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.757,
+                0.469,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Loss. The loss function for the inter-correlation branch has the opposite optimization direction to \\(\\mathcal{L}_g\\). Because the external reference features contain more comprehensive normal patterns, normal patches can establish stronger correlations with the closest reference normal patterns, instead of establishing strong correlations with most reference patterns. By contrast, it shall be harder for anomalous patches to establish strong correlations with any of the reference"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.127,
+                0.892,
+                0.223
+            ],
+            "angle": 0,
+            "content": "patterns. So the inter-correlation distributions of anomalies are more dispersed, while the normal inter-correction distributions are more likely to be concentrated. To this end, we maximize the KL divergence and minimize the entropy item in the training process. The practical optimization strategy is also opposite to the intra-correlation branch (see App. A.1 for details). The loss function is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.571,
+                0.237,
+                0.892,
+                0.252
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {e} = - \\lambda_ {1} \\operatorname {D i v} \\left(\\mathcal {T} ^ {e}, \\mathcal {S} ^ {e}\\right) + \\lambda_ {2} \\operatorname {E n t} \\left(\\mathcal {S} ^ {e}\\right) \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.266,
+                0.892,
+                0.697
+            ],
+            "angle": 0,
+            "content": "External Reference Features. External reference features are used for providing accumulated knowledge of normality for the inter-correlation learning branch. Thus, these features should represent all possible normal patterns of all normal samples from the whole normal training set. To this end, we can employ many methods to generate the reference features, such as sampling key features by coreset subsampling algorithm [35], generating prototype features by memory module [28], or learning codebook features through vector quantization [65] or sparse coding techniques [55]. However, because the RBF-kernel in \\(\\mathcal{T}^e\\) is position-sensitive, our reference features are better to preserve the positional information. The ablation results in App.B.2 show that the methods that can't preserve the position information perform worse. From comprehensive ablation studies, we find that using patch-wise averaged features as the external reference features is a simple but effective way. We think that features extracted by deep neural networks are highly redundant [16, 52], and different normal patterns generally correspond to larger activation values at different channels in the feature vector [61]. So feature averaging will not eliminate some rare normal patterns [11], these patterns may be preserved at specific channels. And averaging can greatly reduce the feature redundancy, making the obtained reference features more representative. Formally, for position \\((i,j)\\), we first extract the set of patch features at \\((i,j)\\), \\(X_{ij} = \\{x_{ij}^k\\}\\), \\(k \\in [1,N]\\) from the \\(N\\) normal training images. Then, the reference features at position \\((i,j)\\) is computed as \\(x_{ij}^f = \\frac{1}{N}\\sum_{k=1}^{N}x_{ij}^k\\). The final external reference features are composed of averaged features at all locations and then flattened into 1D: \\(X_f = \\text{Flatten}(\\{x_{ij}^f\\})\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.706,
+                0.642,
+                0.719
+            ],
+            "angle": 0,
+            "content": "3.5. I2Correlation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.729,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "We further combine the intra-correlation and intercorrelation branches to form the I2Correlation block. The output features of the intra- and inter-correlation branches are defined as: \\( Z_{k}^{g} = S_{k}^{g}V_{k}^{g} \\) and \\( Z_{k}^{e} = S_{k}^{e}V_{k}^{e} \\), respectively. Then, we use the residual feature \\( Z_{k}^{ge} = Z_{k}^{g} - Z_{k}^{e} \\) as the output of the I2Correlation block. The feature \\( Z_{k}^{e} \\) is generated from the external reference features, which can contain rich normal patterns. Thus, by subtracting \\( Z_{k}^{e} \\) from the feature \\( Z_{k}^{g} \\), it is conducive to spotlight the abnormal patterns in the \\( Z_{k}^{g} \\). This is beneficial for anomaly detection."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.888,
+                0.501,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6807"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.127,
+                0.47,
+                0.154
+            ],
+            "angle": 0,
+            "content": "The total loss function consists of the there branch loss functions, and is combined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.193,
+                0.165,
+                0.469,
+                0.18
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {l} + \\mathcal {L} _ {g} + \\mathcal {L} _ {e} \\tag {11}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.189,
+                0.248,
+                0.205
+            ],
+            "angle": 0,
+            "content": "3.6. Anomaly Scoring"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.211,
+                0.469,
+                0.28
+            ],
+            "angle": 0,
+            "content": "We utilize reconstruction errors as the baseline anomaly criterion and incorporate the normalized correlation distribution distances into the reconstruction criterion. The final anomaly score of the \\(i\\)th patch in the input patch sequence is shown as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.095,
+                0.288,
+                0.469,
+                0.321
+            ],
+            "angle": 0,
+            "content": "\\[\ns _ {i} = \\left[ | | X _ {i,:} - \\hat {X} _ {i,:} | | _ {2} + \\left(1 - \\frac {X _ {i , :} \\cdot \\hat {X} _ {i , :}}{| | X _ {i , :} | | _ {2} | | \\hat {X} _ {i , :} | | _ {2}}\\right) \\right] \\odot \\tag {12}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.194,
+                0.323,
+                0.423,
+                0.347
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(1 - \\operatorname {S o f t m a x} \\left(- \\operatorname {D i v} \\left(\\mathcal {T} _ {i,:} ^ {e}, \\mathcal {S} _ {i,:} ^ {e}\\right)\\right)\\right)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.355,
+                0.368,
+                0.369
+            ],
+            "angle": 0,
+            "content": "where \\(\\odot\\) is the element-wise multiplication."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.381,
+                0.21,
+                0.397
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.404,
+                0.267,
+                0.419
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.425,
+                0.469,
+                0.7
+            ],
+            "angle": 0,
+            "content": "Datasets. We extensively evaluate our approach on two widely used industrial AD datasets: the MVTecAD [3] and BTAD [26], and one recent challenging dataset: the MVTecAD-3D [5]. MVTecAD is established as a standard benchmark for evaluating unsupervised image anomaly detection methods. This dataset contains 5354 high-resolution images from 15 real-world categories. 5 classes consist of textures and the other 10 classes contain objects. A total of 73 different anomaly types are presented. BTAD is another popular benchmark for unsupervised image anomaly detection, which contains 2540 RGB images of three industrial products. All classes in this dataset belong to textures. MVTecAD-3D is recently proposed, which contains 4147 2D RGB images paired with high-resolution 3D point cloud scans from 10 real-world categories. Even though this dataset is mainly designed for 3D anomaly detection, most anomalies can also be detected only through RGB images without 3D point clouds. Since we focus on image anomaly detection, we only use RGB images of the MVTecAD-3D dataset. We refer to this subset as MVTec3D-RGB."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.701,
+                0.469,
+                0.77
+            ],
+            "angle": 0,
+            "content": "Evaluation Metrics. The standard metric in anomaly detection, AUROC, is used to evaluate the performance of AD methods. Image-level AUROC is used for anomaly detection and a pixel-based AUROC for evaluating anomaly localization [3, 4, 11, 64]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.77,
+                0.469,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Implementation Details. We use EfficientNet-b6 [45] to extract two levels of feature maps with \\(\\{8\\times ,16\\times \\}\\) downsampling ratios, the pre-trained networks are from the timm library [53]. Then, we construct a subsequent transformer network (see Figure 2) at each feature level to reconstruct patch features and learn patch-to-patch correlations. The parameters of the feature extractor are frozen in the training"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.123,
+                0.892,
+                0.186
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison of our method with the SOTA methods on the MVTecAD dataset. Red and blue indicate the first and the second best result, respectively. According to the anomaly recognition process, we divide these methods into the patch-wise representation discrepancy, patch-to-patch feature distance, and others."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.186,
+                0.892,
+                0.402
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Discrepancy Type</td><td>Method</td><td>Venue</td><td>Image-level AUROC</td><td>Pixel-level AUROC</td></tr><tr><td rowspan=\"14\">Patch-wise Representation Discrepancy</td><td>STAD [4]</td><td>CVPR 2020</td><td>0.877</td><td>0.939</td></tr><tr><td>PaDiM [11]</td><td>ICPR 2020</td><td>0.955</td><td>0.975</td></tr><tr><td>DFR [57]</td><td>Neurocomputing 2021</td><td>/</td><td>0.950</td></tr><tr><td>FCDD [25]</td><td>ICLR 2021</td><td>/</td><td>0.920</td></tr><tr><td>MKD [41]</td><td>CVPR 2021</td><td>0.877</td><td>0.907</td></tr><tr><td>Hou et al. [17]</td><td>ICCV 2021</td><td>0.895</td><td>/</td></tr><tr><td>Metaformer [54]</td><td>ICCV 2021</td><td>0.958</td><td>/</td></tr><tr><td>DRAEM [64]</td><td>ICCV 2021</td><td>0.980</td><td>0.973</td></tr><tr><td>RDAD [12]</td><td>CVPR 2022</td><td>0.985</td><td>0.978</td></tr><tr><td>SSPCAB [34]</td><td>CVPR 2022</td><td>0.989</td><td>0.972</td></tr><tr><td>DSR [65]</td><td>ECCV 2022</td><td>0.982</td><td>/</td></tr><tr><td>NSA [43]</td><td>ECCV 2022</td><td>0.972</td><td>0.963</td></tr><tr><td>UniAD [62]</td><td>NIPS 2022</td><td>0.966</td><td>0.966</td></tr><tr><td>UTRAD [8]</td><td>Neural Networks 2022</td><td>0.960</td><td>0.967</td></tr><tr><td rowspan=\"6\">Patch-to-patch Feature Distance</td><td>PatchSVDD [60]</td><td>ACCV 2020</td><td>0.921</td><td>0.957</td></tr><tr><td>DifferNet [36]</td><td>WAVC 2020</td><td>0.949</td><td>/</td></tr><tr><td>CFLOW [15]</td><td>WAVC 2022</td><td>0.983</td><td>0.986</td></tr><tr><td>CS-FLOW [37]</td><td>WAVC 2022</td><td>0.987</td><td>/</td></tr><tr><td>Tsai et al. [15]</td><td>WAVC 2022</td><td>0.981</td><td>0.981</td></tr><tr><td>PatchCore [35]</td><td>CVPR 2022</td><td>0.991</td><td>0.980</td></tr><tr><td rowspan=\"3\">Others</td><td>CutPaste [21]</td><td>CVPR 2021</td><td>0.952</td><td>0.960</td></tr><tr><td>Wang et al. [51]</td><td>CVPR 2021</td><td>/</td><td>0.91</td></tr><tr><td>SPD [68]</td><td>ECCV 2022</td><td>0.946</td><td>0.946</td></tr><tr><td>Patch-wise&amp;Intra&amp;Inter</td><td>FOD (Ours)</td><td>-</td><td>0.992</td><td>0.983</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.501,
+                0.415,
+                0.891,
+                0.427
+            ],
+            "angle": 0,
+            "content": "Table 2. Detailed image-level AUROCs on the MVTecAD dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.428,
+                0.892,
+                0.613
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Category</td><td colspan=\"6\">Image-level Anomaly Detection</td></tr><tr><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td>Carpet</td><td>0.978</td><td>0.963</td><td>1.000</td><td>1.000</td><td>0.987</td><td>1.000</td></tr><tr><td>Grid</td><td>1.000</td><td>0.892</td><td>0.975</td><td>0.992</td><td>0.996</td><td>1.000</td></tr><tr><td>Leather</td><td>1.000</td><td>0.953</td><td>0.956</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Tile</td><td>0.998</td><td>0.969</td><td>0.999</td><td>1.000</td><td>0.999</td><td>1.000</td></tr><tr><td>Wood</td><td>0.991</td><td>0.989</td><td>0.989</td><td>0.985</td><td>0.991</td><td>0.991</td></tr><tr><td>Bottle</td><td>0.993</td><td>0.976</td><td>0.989</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Cable</td><td>0.929</td><td>0.899</td><td>0.972</td><td>0.992</td><td>0.976</td><td>0.995</td></tr><tr><td>Capsule</td><td>0.984</td><td>0.763</td><td>0.979</td><td>0.984</td><td>0.977</td><td>1.000</td></tr><tr><td>Hazelnut</td><td>1.000</td><td>0.912</td><td>0.997</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Metal nut</td><td>0.989</td><td>0.941</td><td>0.972</td><td>1.000</td><td>0.993</td><td>1.000</td></tr><tr><td>Pill</td><td>0.981</td><td>0.791</td><td>0.971</td><td>0.954</td><td>0.968</td><td>0.984</td></tr><tr><td>Screw</td><td>0.939</td><td>0.825</td><td>0.870</td><td>0.953</td><td>0.919</td><td>0.967</td></tr><tr><td>Toothbrush</td><td>1.000</td><td>0.992</td><td>0.886</td><td>0.906</td><td>0.997</td><td>0.944</td></tr><tr><td>Transistor</td><td>0.914</td><td>0.874</td><td>0.956</td><td>0.995</td><td>0.952</td><td>1.000</td></tr><tr><td>Zipper</td><td>1.000</td><td>0.982</td><td>0.981</td><td>0.989</td><td>0.985</td><td>0.997</td></tr><tr><td>Mean</td><td>0.980</td><td>0.915</td><td>0.966</td><td>0.983</td><td>0.983</td><td>0.992</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.639,
+                0.892,
+                0.804
+            ],
+            "angle": 0,
+            "content": "process, only the parameters of the subsequent transformer networks are learnable. All the subsequent transformer networks in our model contain 3 layers. We set the hidden dimension \\(d_{m}\\) as \\(\\{256,512\\}\\) and the number of heads as 8. The hyperparameters \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are set as 0.5 and 0.5 to trade off two parts of the \\(\\mathcal{L}_g\\) and \\(\\mathcal{L}_e\\) loss functions (see App. B.2 for hyperparameter sensitivity analysis). We use the Adam [19] optimizer with an initial learning rate of \\(1\\mathrm{e}^{-4}\\). The total training epochs are set as 100 and the batch size is 1 by default. All the training and test images are resized and cropped to \\(256\\times 256\\) resolution from the original resolution."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.817,
+                0.638,
+                0.83
+            ],
+            "angle": 0,
+            "content": "4.2. Main Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.839,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "SOTA Methods. We extensively compare our method with those published SOTA methods in the past three years."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.888,
+                0.501,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6808"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.126,
+                0.473,
+                0.389
+            ],
+            "angle": 0,
+            "content": "The comparison results on MVTecAD are shown in Table 1. Then, we select five reproducible methods to report the detailed results on MVTecAD, these methods are representative and SOTA AD methods in the mainstream categories of image anomaly detection as we discuss in Related Work, including: DRAEM [64], PatchSVDD[60], PatchCore [35], MKD[41], CFLOW[15]. For a fair comparison, we reproduce all these methods with the same backbone as in our model. Thus, despite using the unmodified code from the official repositories, we are not able to exactly reproduce the original results, but our numbers are very close. The detailed image-level AUROC results are shown in Table 2, and detailed pixel-level AUROC results are in the App. Table 6. Most of the methods in Table 1 don't report results on the BTAD and MVTec3D-RGB datasets, so we reproduce the five representative methods on the two datasets for comparison. The image-level and pixel-level AUROC results on BTAD and MVTec3D-RGB are shown in Table 3. Additional detailed results are in the App. Table 7, 8."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.393,
+                0.473,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Anomaly Detection. On MVTecAD, we set the SOTA performance on the mean detection AUROC, which is slightly higher than the best competitor, PatchCore [35]. Note that the results in Table 2 show that our method can achieve much better results than PatchCore when using the same backbone. What's more, in addition to the pill, screw and toothbrush classes, our method achieves more than \\(99\\%\\) AUROC in all other classes, while other methods only achieve more than \\(99\\%\\) AUROC in most nine classes. This shows that our method is more stable and effective in real-world applications. In the classes (e.g. metal nut, screw, and transistor) with more global and logical anomalies, our method can achieve significantly better results than those methods depending on patch-wise discrepancy (e.g. DRAEM [64] and MKD [41]), and can also achieve better results compared with other methods. This verifies that the three discrepancies are complementary factors and our model can simultaneously spot these discrepancies to recognize harder global and logical anomalies. On BTAD, our FOD can achieve \\(96.0\\%\\) mean detection AUROC, which can outperform the best competitor CFLOW [15] by a margin of \\(1.2\\%\\). On MVTec3D-RGB, we can outperform all previous SOTA methods by a margin of \\(3.3\\%\\). Note that this dataset is much more challenging than the MVTecAD dataset when comparing the best results \\((99.2\\%)\\) for MVTecAD vs. \\(88.4\\%\\) AUROC for MVTec3D-RGB). This demonstrates the robustness of our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.77,
+                0.472,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Anomaly Localization. Our method can achieve comparable results with the best competitors on all three datasets. Our method is slightly lower than CFLOW [15] and PatchCore [35] on the three datasets, but we observe that our model that considers the intra- and intercorrelations outperforms the vanilla reconstruction AD models (e.g. DRAEM [64] and MKD [41]) on all three"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.123,
+                0.892,
+                0.159
+            ],
+            "angle": 0,
+            "content": "Table 3. Comparison of our method with the SOTA methods for image-level anomaly detection and pixel-level anomaly localization performance on the BTAD and MVTec3D-RGB datasets."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.16,
+                0.894,
+                0.232
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td colspan=\"7\">BTAD Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.922</td><td>0.924</td><td>0.935</td><td>0.934</td><td>0.948</td><td>0.960</td></tr><tr><td>Pixel-level AUROC</td><td>0.942</td><td>0.964</td><td>0.965</td><td>0.976</td><td>0.978</td><td>0.975</td></tr><tr><td colspan=\"7\">MVTec3D-RGB Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.757</td><td>0.743</td><td>0.688</td><td>0.839</td><td>0.851</td><td>0.884</td></tr><tr><td>Pixel-level AUROC</td><td>0.974</td><td>0.852</td><td>0.970</td><td>0.977</td><td>0.974</td><td>0.976</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.255,
+                0.892,
+                0.31
+            ],
+            "angle": 0,
+            "content": "datasets, which verifies the effectiveness of correlation modeling. Compared with patch-wise reconstruction methods, our method is more effective and robust to detect hard global and logical anomalies (see Figure 3)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.311,
+                0.892,
+                0.38
+            ],
+            "angle": 0,
+            "content": "Qualitative Results. Samples in Figure 1 show qualitative impressions of accurate anomaly localization from our method. It can be found that our approach can achieve the best anomaly score maps by combining the three discrepancies. Additional visualizations are in the App. Figure 6."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.389,
+                0.809,
+                0.404
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Study and Model Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.411,
+                0.893,
+                0.782
+            ],
+            "angle": 0,
+            "content": "Ablation Study. To explain how our model works effectively, we further investigate the effect of the three key designs in our model: recognition views, entropy constraint and reference features. The quantitative results are shown in Table 4, more results can be found in App. Table 9. The entropy constraint is quite effective and necessary in the intra-correlation branch. Specifically, it brings a remarkable \\(7.7\\%\\) averaged absolute AUROC promotion, which demonstrates that the entropy constraint strategy is really conducive to increase the distinguishability between abnormal and normal. Only utilizing pure reconstruction criterion or pure KL divergence can't get the most superior detection results, the combined criterion can outperform each single criterion consistently by a margin of \\(1.0\\%\\) and \\(9.8\\%\\). Thus the reconstruction errors and the intra- and inter-correlations can collaborate to improve detection performance. For the external reference features, we compare the simple mean features with more elaborate coreset features [35] (see App. Table 15 for more comparison methods). The results show that the simple mean features are more effective than the coreset features (0.923 vs. 0.836), which means that mean features are effective enough to represent all possible normal patterns and preserve the positional information. Finally, our proposed FOD surpasses the pure reconstruction Transformer by \\(4.0\\%\\) absolute improvement. These verify that our proposed explicit correlation learning approach is effective."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.784,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Effect for Different Anomalies. To illustrate the effectiveness of our model intuitively, we explore the anomaly localization quality under different types of anomalies (see Figure 3). E.g., simple local anomalies (Column 1) are obviously different from normal visuals; hard global anomalies (Columns 2,3) have less obvious visual appearances,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.888,
+                0.502,
+                0.898
+            ],
+            "angle": 0,
+            "content": "6809"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.123,
+                0.473,
+                0.236
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation results in recognition views, entropy constraint, external reference features and anomaly scoring. Patch-wise, Intra and Inter mean patch-wise discrepancy, intra- and intercorrelation, respectively. w/o and w/ mean without and with entropy constraint. Mean and Coreset refer to mean and coreset features [35] as the external reference features (see more details in App. B.3). Rec, Div and Rec&Div mean the pure reconstruction criterion, pure KL divergence (E.q.6) and the combined criterion (E.q.12)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.237,
+                0.469,
+                0.318
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Recognition Views</td><td>Entropy Constraint</td><td>Reference Features</td><td>Anomaly Scoring</td><td>MVTecAD</td><td>BTAD</td><td>MVTec3D-RGB</td><td>Avg</td></tr><tr><td rowspan=\"2\">Patch-wise</td><td>/</td><td>/</td><td>Rec</td><td>0.972</td><td>0.954</td><td>0.790</td><td>0.905</td></tr><tr><td>w/o</td><td>/</td><td>Div</td><td>0.700</td><td>0.811</td><td>0.708</td><td>0.740</td></tr><tr><td rowspan=\"2\">Intra</td><td>w/</td><td>/</td><td>Div</td><td>0.911</td><td>0.822</td><td>0.717</td><td>0.817</td></tr><tr><td>w/</td><td>/</td><td>Rec&amp;Div</td><td>0.974</td><td>0.952</td><td>0.818</td><td>0.915</td></tr><tr><td rowspan=\"2\">Inter</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.980</td><td>0.958</td><td>0.832</td><td>0.923</td></tr><tr><td>w/</td><td>Coreset</td><td>Rec&amp;Div</td><td>0.925</td><td>0.884</td><td>0.700</td><td>0.836</td></tr><tr><td>Intra+Inter</td><td>w/</td><td>Mean</td><td>Div</td><td>0.896</td><td>0.922</td><td>0.814</td><td>0.877</td></tr><tr><td>Patch-wise+Intra+Inter (Ours)</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.992</td><td>0.960</td><td>0.884</td><td>0.945</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.331,
+                0.465,
+                0.54
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.544,
+                0.471,
+                0.608
+            ],
+            "angle": 0,
+            "content": "Figure 3. Visualization of different anomalies. The patch-wise reconstruction is only suitable for simple local anomalies, while for hard global and logical anomalies, it cannot detect or only detect partial anomalies. In contrast, our FOD can detect these anomalies more effectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.632,
+                0.47,
+                0.824
+            ],
+            "angle": 0,
+            "content": "which usually need to be effectively compared with normal regions to detect; logical anomalies (Columns 4,5) may be locally normal and can be detected correctly through the overall semantic understanding. We can find that our FOD is more distinguishable in general. For simple local anomalies, patch-wise reconstruction methods can also achieve good results. While for hard global anomalies, these methods cannot detect or only detect partial anomalies. However, for logical anomalies, these methods cannot detect them at all. In contrast, our method is conducive to detect diverse anomalies because of its complementary recognition views. This verifies that our method can make more precise detection and reduce the false-negative rate compared with the pure patch-wise reconstruction methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Correlations Visualization. To explain what our model has learned intuitively, we visualize some learned correlations in Figure 4 with the MVtecAD dataset. For the intra"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.125,
+                0.667,
+                0.193
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.671,
+                0.126,
+                0.742,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.656,
+                0.194,
+                0.724,
+                0.2
+            ],
+            "angle": 0,
+            "content": "(a) Intra-Correlations"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.746,
+                0.126,
+                0.84,
+                0.193
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.844,
+                0.126,
+                0.89,
+                0.193
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.203,
+                0.639,
+                0.27
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.642,
+                0.203,
+                0.688,
+                0.233
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.696,
+                0.203,
+                0.841,
+                0.27
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.844,
+                0.203,
+                0.89,
+                0.233
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.656,
+                0.271,
+                0.724,
+                0.277
+            ],
+            "angle": 0,
+            "content": "(b) Inter-Correlations"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.28,
+                0.892,
+                0.32
+            ],
+            "angle": 0,
+            "content": "Figure 4. Visualization of intra- and inter-correlations. Each red point in the figure can represent an image patch, we plot its discrete correlation distribution with all the other image patches."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.346,
+                0.893,
+                0.513
+            ],
+            "angle": 0,
+            "content": "correlation branch, the normal patches learn to build strong correlations with most patches in the whole image, while the correlation distributions of anomalies usually concentrate in the adjacent image patches. It can be found that the normal correlations are much spread and the abnormal correlations are more concentrated in the adjacent regions. For the inter-correlation branch, most normal correlations only concentrate in one point and the abnormal correlations are more spread, which exactly means that each normal patch can build strong correlations with one special normal pattern and abnormal patches are harder to establish correlations with normal patterns."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.533,
+                0.619,
+                0.547
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.558,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "Humans recognize anomalies through two aspects: patch-wise representation discrepancies and weak patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy, to simultaneously spot the patch-wise, intra- and inter-discrepancies. The patch-wise discrepancies and intra- and inter-correlations are complementary factors, and can be combined to detect more complex and diverse anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to I2Correlation to explicitly establish intra- and inter-image correlations for AD modeling. The combination of explicit correlation learning and transformer architecture can match the core idea of anomaly detection quite well."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Acknowledgements"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.797,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "This work was supported in part by the National Natural Science Fund of China (61971281), the Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Science and Technology Commission of Shanghai Municipality (22DZ2229005)."
+        },
+        {
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+            "content": "6810"
+        }
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+# Focus the Discrepancy: Intra- and Inter-Correlation Learning for Image Anomaly Detection
+
+Xincheng Yao $^{1}$ , Ruoqi Li $^{1}$ , Zefeng Qian $^{1}$ , Yan Luo $^{1}$ , Chongyang Zhang $^{1,2*}$
+
+$^{1}$ School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University
+
+$^{2}$ MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University
+
+{i-Dover, nilponi, zefeng.qian, luoyan.bb, sunny_zhang}@sjtu.edu.cn
+
+# Abstract
+
+Humans recognize anomalies through two aspects: larger patch-wise representation discrepancies and weaker patch-to-normal-patch correlations. However, the previous AD methods didn't sufficiently combine the two complementary aspects to design AD models. To this end, we find that Transformer can ideally satisfy the two aspects as its great power in the unified modeling of patchwise representations and patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can simultaneously spot the patch-wise, intra- and inter-discrepancies of anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to Intra-Inter-Correlation (I2Correlation). The I2Correlation contains a two-branch structure to first explicitly establish intra- and inter-image correlations, and then fuses the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning. Besides, we introduce an entropy constraint strategy to solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability. Extensive experiments on three unsupervised real-world AD benchmarks show the superior performance of our approach. Code will be available at https://github.com/xcyao00/FOD.
+
+# 1. Introduction
+
+The goal of anomaly detection (AD) is to distinguish an instance containing anomalous patterns from those normal samples and further localize those anomalous regions. Anomalies are defined as opposite to normal samples and are usually rare, which means that we need to tackle AD tasks under the unsupervised setting with only normal sam
+
+![](images/9b6bfebd8a09d0cb6ae61b0b307d004463e3e20f73e02aaa5107b883d83cfc47.jpg)  
+Figure 1. Anomaly detection examples on MVTecAD [3]. Multiresolution Knowledge Distillation (MKD) [41] adopts the conventional patch-wise representation discrepancies. Row 1 shows the hard global anomalies (i.e., they are not significantly different from normal visuals). Rows 3 and 4 show the logical anomalies (i.e., they may be easily recognized as normal if only from the patch-wise discrepancy).
+
+plies accessible. The core idea of most unsupervised AD methods is to compare with normal samples to distinguish anomalies [46, 35, 60, 11, 28, 58]. Even for humans, we also recognize anomalies in this way, specifically through three discrepancies, i.e., 1. patch patterns that differentiate from the normal visuals; 2. image regions that destroy textures or structures; 3. novel appearances that deviate from our accumulated knowledge of normality. Namely, anomalous patches usually have three characteristics: their patchwise representations are different from the normal visuals; they are different from most patches within one image; they deviate from our accumulated knowledge of normality. These views intrinsically reveal that humans' recognition of anomalies depends on two aspects: patch-wise representations (1) and intra- and inter-image correlations (2, 3).
+
+Previous methods mainly follow the former aspect to learn distinguishable representations or reconstructions,
+
+such as reconstruct-based methods [6, 57, 1] and knowledge distillation AD models [4, 41]. The goal of these methods is to generate reconstructed samples or feature representations, and larger patch-wise representation discrepancies can appear in the abnormal patches. However, only the patch-wise representation discrepancies are insufficient for detecting more complex anomalies (e.g., rows 3 and 4 in Figure 1), since the patch-wise errors can't provide comprehensive descriptions of the spatial context. Other mainstream AD methods, such as embedding-based [11, 35] and one-class-classification-based (OCC) [39, 60] methods, are much similar to the latter aspect. These methods achieve anomaly detection by measuring the distances between the features of test samples and normal features. Compared with the non-learnable feature distances, the explicit intra- and inter-image correlations in our method are more effective to detect diverse anomalies (see Table 1, 2, 3). Moreover, patch-wise representation discrepancies and intra- and inter-correlation discrepancies are complementary, and can be combined to develop more powerful AD models.
+
+Recently, with the self-attention mechanism and long-range modeling ability, transformers [50] have significantly renovated many computer vision tasks [14, 24, 7, 67, 56] and recently popular language-vision multimodal tasks [30, 22]. Transformers have shown great power in the unified modeling of patch-wise representations and patch-to-patch correlations. Transformers are quite suitable for AD tasks as their modeling ability can satisfy the two aspects of anomaly recognition quite well. Some works [26, 18, 8, 62] also attempt to employ transformers to construct AD models. However, these methods only use transformers to extract vision features, which didn't sufficiently adapt transformers' long-range correlation modeling capability to AD tasks. Different from these works, we explicitly exploit transformers' self-attention maps to establish the intra- and inter-image correlations. The correlation distribution of each patch can provide more informative descriptions of the spatial context, which can reveal more intricate and semantic anomaly patterns.
+
+In this paper, motivated by humans' anomaly recognition process, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can exploit transformers' unified modeling ability to simultaneously spot the patch-wise, intra- and inter-discrepancies. Our key designs are composed of three recognition branches: the patch-wise discrepancy branch is to reconstruct the input patch features for distinguishing simple anomalies; the intra-correlation branch is to explicitly model patch-to-patch correlations in one image for distinguishing hard global anomalies (e.g., row 1 in Figure 1); the inter-correlation branch is to explicitly learn inter-image correlations with known normal patterns from the whole normal training set. To implement the intra- and inter-correlation branches, we adapt
+
+Transformer and renovate the self-attention mechanism to the I2Correlation, which contains a two-branch structure to first separately model the intra- and inter-correlation distribution of each image patch, and then fuse the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning, the RBF kernel is used to present the neighborhood continuity of each image patch. Besides, an entropy constraint strategy is applied in the two branches, which can solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability.
+
+In summary, we make the following main contributions:
+
+1. We propose a novel AD framework: FOD, which can effectively detect anomalies by simultaneously spotting the patch-wise, intra- and inter-discrepancies.  
+2. We renovate the self-attention mechanism to the I2Correlation, which can explicitly establish intra- and inter-correlations in a self-supervised way with the target-correlations. An entropy constraint strategy is proposed to further amplify the normal-abnormal distinguishability.  
+3. Our method can achieve SOTA results on three real-world AD datasets, this shows our method can more effectively determine anomalies from complementary views.
+
+# 2. Related Work
+
+Anomaly Detection. In this paper, we divide the mainstream AD methods into five categories: reconstruction-based, embedding-based, OCC-based methods, knowledge distillation and normalizing flow AD models. The reconstruction-based methods are the most popular AD methods and also widely studied, where the assumption is that models trained by normal samples only can reconstruct normal regions but fail in abnormal regions. Many previous works attempt to train AutoEncoders [6, 28, 57, 8, 17, 64], Variational AutoEncoders [23] and GANs [42, 1, 29, 40] to reconstruct the input images. Overfitting to the input images is the most serious issue of these methods, which means that the anomalies are also well reconstructed [62].
+
+Recently, some embedding-based methods [2, 33, 9, 11, 35] show better AD performance by using ImageNet pretrained networks as feature extractors. In [33], the authors fit a multivariate Gaussian to model the image-level features for further Mahalanobis distance measurement. PaDiM [11] extends the above method to localize pixel-level anomalies. PatchCore [35] extends on this line by utilizing locally aggregated, mid-level features and introducing greedy coreset subsampling to form nominal feature banks. However, these methods directly utilize pre-trained networks without any adaptation to the target dataset. Some works [31, 10, 32] attempt to adapt pre-trained features to the target data distribution. There are also some other methods for using pre-trained networks by freezing them and only
+
+optimizing a sub-network, e.g., via knowledge distillation [4, 41, 12, 38], or normalizing flows [36, 15, 37, 63].
+
+OCC is another classical AD paradigm, the earliest works are mainly to extend the OCC models such as OC-SVM [44] or SVDD [47, 39] for anomaly detection. Recently, in [60], a patch-based SVDD that contains multiple cores rather than a single core in [39] is proposed to enable anomaly localization. In [25], a Fully Convolutional Data Description combined with receptive field upsampling is proposed to generate anomaly maps. In [48], the authors further extend the PatchSVDD [60] model by the proposed multi-scale patch-based representation learning method.
+
+Transformer-based Anomaly Detection Methods. Recently, transformers [50] have shown great power in modeling long-range dependencies. For image anomaly detection, some works [26, 18, 62, 8, 59] also attempt to exploit transformers to design AD models. However, most of these methods only use transformers as backbones to extract vision features, and don't effectively adapt the long-range modeling capacity of transformers to AD tasks. Unlike the previous usage of transformers, we explicitly exploit the self-attention maps of transformers to establish intra- and inter-correlations. Our work shares some similarities with a recent work [20]. But we point out that our work has some significant differences from [20]: 1) Different Insight: [20] aims to unify the pointwise representation and pairwise association for time series AD, whereas our work aims to more sufficiently detect image anomalies through three complementary recognition views. 2) Novel Method: we propose entropy constraint, inter-correlation branch, and I2Correlation by effectively combining intra- and inter-correlation branches. 3) Different Task: [20] focuses on time-series AD, whereas we focus on image AD.
+
+# 3. Approach
+
+# 3.1. Model Overview
+
+Figure 2 overviews our proposed approach. The model consists of three branches: patch-wise discrepancy branch, intra-correlation branch, and inter-correlation branch. The input 2D image is first sent into a pre-trained backbone to extract multi-scale feature maps. At each feature level, we construct a subsequent transformer network to explicitly model the intra- and inter-image correlations for spotting the intra- and inter-discrepancies. Each network is implemented by stacking the I2Correlation blocks and feedforward layers alternately. Suppose each network contains  $K$  layers with length-  $N$  input features  $X\in \mathbb{R}^{N\times d}$ , the output of  $k$ th layer  $X_{k}\in \mathbb{R}^{N\times d_{m}}$  is calculated as follows:
+
+$$
+Z _ {k} = \mathrm {L N} (\mathrm {I 2 C o r r e l a t i o n} (X _ {k - 1}, X _ {f}) + X _ {k - 1}) \tag {1}
+$$
+
+$$
+X _ {k} = \mathrm {L N} (\text {F e e d F o r w a r d} (Z _ {k}) + Z _ {k}) \tag {2}
+$$
+
+where  $X_{f}$  is the reference features used by the intercorrelation branch,  $LN$  means LayerNorm, and  $Z_{k} \in \mathbb{R}^{N \times d_{m}}$  is the  $k$ th layer's hidden features. The final output features are calculated by linear projection:  $\hat{X} = Z_{K}W_{o}$ , where  $W_{o} \in \mathbb{R}^{d_{m} \times d}$  is the output projection matrix.
+
+# 3.2. Patch-Wise Reconstruction Discrepancy
+
+Adopted from previous reconstruction-based AD methods, we employ feature reconstruction as our patch-wise recognition view for simplicity. In our approach, we construct a transformer network to reconstruct the input features. With the long-range dependency modeling ability, the features reconstructed by Transformer can have larger effective receptive fields [13], which are more conducive to detect hard global anomalies and logical anomalies. Moreover, with the further introduced inter-correlation branch (sec.3.4), the features can even perceive normal regions of images from the whole normal training set. Therefore, the reconstructed features generated by our model have better global perception and more discriminative semantic representation capability, which are more suitable for anomaly detection by patch-wise representation discrepancies.
+
+Learning Objective. We can utilize classical reconstruction losses as the learning objective. We combine the  $\ell 2$  distance and cosine distance to measure the feature distances between the reconstructed features  $\hat{X}$  and the input features  $X$ . The loss function is defined as follows:
+
+$$
+\mathcal {L} _ {l} = \left| \left| \hat {X} - X \right| \right| _ {2} + \left(1 - \frac {\hat {X} \cdot X}{\left| \left| \hat {X} \right| \right| _ {2} \left| \left| X \right| \right| _ {2}}\right) \tag {3}
+$$
+
+# 3.3. Intra-Correlation Learning
+
+The intra-correlation learning branch aims to learn informative patch-to-patch correlations from the input patch sequence adaptively. As shown in the right part of Figure 2, we explicitly take advantage of the self-attention maps of transformers as intra-correlation matrices. Formally, the intra-correlation matrix of the  $k$ th layer is calculated by:
+
+Intra Correlation:  $S_{k}^{g} = \mathrm{Softmax}\Big(Q_{k}^{g}(K_{k}^{g})^{T} / \sqrt{d_{m}}\Big)$
+
+$$
+\left[ Q _ {k} ^ {g}, K _ {k} ^ {g}, V _ {k} ^ {g} \right] = X _ {k - 1} \left[ W _ {k} ^ {Q _ {g}}, W _ {k} ^ {K _ {g}}, W _ {k} ^ {V _ {g}} \right] \tag {4}
+$$
+
+where  $Q_{k}^{g}, K_{k}^{g}, V_{k}^{g} \in \mathbb{R}^{N \times d_{m}}$  represent the query, key, and value of the  $k$ th layer.  $W_{k}^{Q_{g}}, W_{k}^{K_{g}}, W_{k}^{V_{g}} \in \mathbb{R}^{d_{m} \times d_{m}}$  represent the learnable projection matrices for  $Q_{k}^{g}, K_{k}^{g}, V_{k}^{g}$ , respectively.  $S_{k}^{g} \in \mathbb{R}^{N \times N}$  denotes the learned intra-image patch-to-patch correlations. Since  $\text{Softmax}(\cdot)$  can convert the values in the similarity map into range [0, 1] along the horizontal axis, each row of  $S_{k}^{g}$  can represent a discrete correlation distribution for each corresponding image patch. But different from the vanilla transformers, we further introduce target correlation matrices as the learning objective to explicitly optimize the intra-image correlations.
+
+![](images/03100b0e00e71a18e9d2565d4382cb4814e72684981e01340ce323f19b45f0fc.jpg)  
+Figure 2. Model overview. The model is composed of three parts: patch-wise discrepancy branch, intra-correlation branch, and intercorrelation branch. The input image patch sequence will be transformed into the hidden features by a pre-trained backbone, and then sent into the intra-correlation branch for learning intra-image patch-to-patch correlations. The input of the inter-correlation branch is composed of hidden features (as Query) and reference features (as Key and Value). The final output features are used to reconstruct the input features.
+
+![](images/f0dbe9311c31da7595e1f11ae8cbfd7fd7203dca1184ebaefdb83d41a7a548fb.jpg)
+
+![](images/c4b43d45f5d2d1e87aa079e44d01dc72234eb6d81244536df05fa580e49a8638.jpg)
+
+Target Correlation. Inspired by the contrastive learning method BarlowTwins [66], we can construct a target correlation matrix  $T \in \mathbb{R}^{N \times N}$  as the learning target. The objective function of BarlowTwins measures the correlation matrix between the embeddings of two identical networks fed with distorted versions of a batch of samples, and tries to make this matrix close to the identity. In our work, the role of the target correlation is to introduce a prior correlation of patches as a pretext learning target, where each patch can be highly correlated to itself and also correlated to its neighborhood patches and the correlation decreases with the increase of distance. This allows us to optimize the intra- and inter-correlations in a self-supervised way. To this end, we use the radial basis function (RBF) to construct the target correlation matrix. We further adopt two learnable kernel variances  $\sigma_x$  and  $\sigma_y$  for horizontal and vertical axes to make the target correlation of each patch can adapt to the specific pattern of itself. The target correlation matrix of the  $k$ th layer is defined as:
+
+$$
+T _ {k} ^ {g} = \frac {1}{2 \pi \sigma_ {x} \sigma_ {y}} \exp \left(- \frac {\left| \left| x _ {i j} - x _ {i ^ {\prime} j ^ {\prime}} \right| \right| _ {2} ^ {2}}{2 \left(\sigma_ {x} ^ {2} + \sigma_ {y} ^ {2}\right)}\right)
+$$
+
+$$
+i, i ^ {\prime} \in \{1, \dots , H \}; j, j ^ {\prime} \in \{1, \dots , W \} \tag {5}
+$$
+
+where  $||x_{ij} - x_{i'j'}||_2^2$  means the Square Euclidean distance between point  $x_{ij}$  and  $x_{i'j'}$ ,  $i, i'$  and  $j, j'$  means vertical and horizontal coordinates, respectively.
+
+Next, we need to measure the distance between target- and intra-correlation distributions. This can usually be
+
+achieved by calculating the KL divergence. We can obtain a KL divergence value from each level of the network. Thus, we average all KL divergence values to combine the patch-to-patch correlations from multi-layer features into a more informative measure as follows:
+
+$$
+\operatorname {D i v} \left(\mathcal {T} ^ {g}, \mathcal {S} ^ {g}\right) = \frac {1}{K} \sum_ {k = 1} ^ {K} \left(K L \left(T _ {k} ^ {g} \mid \mid S _ {k} ^ {g}\right) + K L \left(S _ {k} ^ {g} \mid \mid T _ {k} ^ {g}\right)\right) \tag {6}
+$$
+
+where  $KL(\cdot ||\cdot)\in \mathbb{R}^N$  and its each element means the KL divergence between two discrete distributions corresponding to each row of  $T_{k}^{g}$  and  $S_{k}^{g}$ .
+
+Due to the rarity of anomalies and the dominance of normal patterns, the normal patches should build strong correlations with most patches in the whole image, while the weights of abnormal correlation distributions are harder to distribute to most patches and are more likely to concentrate on the adjacent image patches due to the neighborhood continuity. Since normal and abnormal patches have different correlation distributions, this is a distinguishable criterion for anomaly detection. Note that the intra-correlation branch explicitly exploits the spatial dependencies of each image patch, which are more informative than the patchwise representations for anomaly detection.
+
+Entropy constraint. Since the normal image patterns are usually diverse, the learned correlation distributions of the normal patches may also easily concentrate on the adjacent patches, which can cause the distinguishability between normal and abnormal to be downscaled. To address
+
+this, we further introduce an entropy constraint item for making normal patches establish strong associations with most normal patches in the whole image as much as possible. The entropy constraint item is defined as:
+
+$$
+\operatorname {E n t} \left(\mathcal {S} ^ {g}\right) = \frac {1}{K} \sum_ {k = 1} ^ {K} \left(\sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {N} \left(- S _ {k (i, j)} ^ {g} \log \left(S _ {k (i, j)} ^ {g}\right)\right)\right) \tag {7}
+$$
+
+We will maximize the entropy constraint item. The loss function for the intra-correlation branch is defined as:
+
+$$
+\mathcal {L} _ {g} = \lambda_ {1} \operatorname {D i v} \left(\mathcal {T} ^ {g}, \mathcal {S} ^ {g}\right) - \lambda_ {2} \operatorname {E n t} \left(\mathcal {S} ^ {g}\right) \tag {8}
+$$
+
+where  $\lambda_{1}$  and  $\lambda_{2}$  are used to trade off the loss items. The optimization of intra-correlation  $S^g$  is actually an alternating process with the guidance of target correlation  $T^g$  (see App. A.1), ultimately resulting that each normal patch can establish strong correlations with most normal patches.
+
+# 3.4. Inter-Correlation Learning
+
+Through the intra-correlation branch, we can establish patch-to-patch correlations within a single image. However, an image usually doesn't contain all possible normal patterns, which may cause it difficult to distinguish some ambiguous abnormal patches (see rows 2, 3, 4 in Figure 1) only through the intra-correlations. To address this, we should effectively take advantage of the known normal patterns from the normal training set, which are more likely to contain more informative normal patterns. Specifically, we further propose an inter-correlation learning branch to explicitly model pairwise correlations with the whole normal training set. In this branch, the features of each patch establish a discrete inter-correlation distribution with the reference features extracted from all normal samples (see Figure 2). The inter-correlation matrix of the  $k$ th layer is similar to the corresponding intra-correlation, and is defined as:
+
+Inter Correlation:  $S_{k}^{e} = \mathrm{Softmax}\Big(Q_{k}^{e}(K_{k}^{e})^{T} / \sqrt{d_{m}}\Big)$
+
+$$
+Q _ {k} ^ {e}, K _ {k} ^ {e}, V _ {k} ^ {e} = X _ {k - 1} W _ {k} ^ {Q _ {e}}, X _ {f} W _ {k} ^ {K _ {e}}, X _ {f} W _ {k} ^ {V _ {e}} \tag {9}
+$$
+
+where  $X_{f}\in \mathbb{R}^{N_{e}\times d_{e}}$  represents the external reference features,  $N_{e}$  is the length of the reference features and  $d_{e}$  is the feature dimension.  $W_{k}^{Q_{e}}\in \mathbb{R}^{d_{m}\times d_{m}}$  and  $W_{k}^{K_{e}},W_{k}^{V_{e}}\in$ $\mathbb{R}^{d_e\times d_m}$  are learnable matrices for  $Q_{k}^{e},K_{k}^{e},V_{k}^{e}$ $S_k^e\in$ $\mathbb{R}^{N\times N_e}$  denotes the learned inter-image correlations.
+
+Loss. The loss function for the inter-correlation branch has the opposite optimization direction to  $\mathcal{L}_g$ . Because the external reference features contain more comprehensive normal patterns, normal patches can establish stronger correlations with the closest reference normal patterns, instead of establishing strong correlations with most reference patterns. By contrast, it shall be harder for anomalous patches to establish strong correlations with any of the reference
+
+patterns. So the inter-correlation distributions of anomalies are more dispersed, while the normal inter-correction distributions are more likely to be concentrated. To this end, we maximize the KL divergence and minimize the entropy item in the training process. The practical optimization strategy is also opposite to the intra-correlation branch (see App. A.1 for details). The loss function is defined as:
+
+$$
+\mathcal {L} _ {e} = - \lambda_ {1} \operatorname {D i v} \left(\mathcal {T} ^ {e}, \mathcal {S} ^ {e}\right) + \lambda_ {2} \operatorname {E n t} \left(\mathcal {S} ^ {e}\right) \tag {10}
+$$
+
+External Reference Features. External reference features are used for providing accumulated knowledge of normality for the inter-correlation learning branch. Thus, these features should represent all possible normal patterns of all normal samples from the whole normal training set. To this end, we can employ many methods to generate the reference features, such as sampling key features by coreset subsampling algorithm [35], generating prototype features by memory module [28], or learning codebook features through vector quantization [65] or sparse coding techniques [55]. However, because the RBF-kernel in  $\mathcal{T}^e$  is position-sensitive, our reference features are better to preserve the positional information. The ablation results in App.B.2 show that the methods that can't preserve the position information perform worse. From comprehensive ablation studies, we find that using patch-wise averaged features as the external reference features is a simple but effective way. We think that features extracted by deep neural networks are highly redundant [16, 52], and different normal patterns generally correspond to larger activation values at different channels in the feature vector [61]. So feature averaging will not eliminate some rare normal patterns [11], these patterns may be preserved at specific channels. And averaging can greatly reduce the feature redundancy, making the obtained reference features more representative. Formally, for position  $(i,j)$ , we first extract the set of patch features at  $(i,j)$ ,  $X_{ij} = \{x_{ij}^k\}$ ,  $k \in [1,N]$  from the  $N$  normal training images. Then, the reference features at position  $(i,j)$  is computed as  $x_{ij}^f = \frac{1}{N}\sum_{k=1}^{N}x_{ij}^k$ . The final external reference features are composed of averaged features at all locations and then flattened into 1D:  $X_f = \text{Flatten}(\{x_{ij}^f\})$ .
+
+# 3.5. I2Correlation
+
+We further combine the intra-correlation and intercorrelation branches to form the I2Correlation block. The output features of the intra- and inter-correlation branches are defined as:  $Z_{k}^{g} = S_{k}^{g}V_{k}^{g}$  and  $Z_{k}^{e} = S_{k}^{e}V_{k}^{e}$ , respectively. Then, we use the residual feature  $Z_{k}^{ge} = Z_{k}^{g} - Z_{k}^{e}$  as the output of the I2Correlation block. The feature  $Z_{k}^{e}$  is generated from the external reference features, which can contain rich normal patterns. Thus, by subtracting  $Z_{k}^{e}$  from the feature  $Z_{k}^{g}$ , it is conducive to spotlight the abnormal patterns in the  $Z_{k}^{g}$ . This is beneficial for anomaly detection.
+
+The total loss function consists of the there branch loss functions, and is combined as follows:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {l} + \mathcal {L} _ {g} + \mathcal {L} _ {e} \tag {11}
+$$
+
+# 3.6. Anomaly Scoring
+
+We utilize reconstruction errors as the baseline anomaly criterion and incorporate the normalized correlation distribution distances into the reconstruction criterion. The final anomaly score of the  $i$ th patch in the input patch sequence is shown as follows:
+
+$$
+s _ {i} = \left[ | | X _ {i,:} - \hat {X} _ {i,:} | | _ {2} + \left(1 - \frac {X _ {i , :} \cdot \hat {X} _ {i , :}}{| | X _ {i , :} | | _ {2} | | \hat {X} _ {i , :} | | _ {2}}\right) \right] \odot \tag {12}
+$$
+
+$$
+\left(1 - \operatorname {S o f t m a x} \left(- \operatorname {D i v} \left(\mathcal {T} _ {i,:} ^ {e}, \mathcal {S} _ {i,:} ^ {e}\right)\right)\right)
+$$
+
+where  $\odot$  is the element-wise multiplication.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We extensively evaluate our approach on two widely used industrial AD datasets: the MVTecAD [3] and BTAD [26], and one recent challenging dataset: the MVTecAD-3D [5]. MVTecAD is established as a standard benchmark for evaluating unsupervised image anomaly detection methods. This dataset contains 5354 high-resolution images from 15 real-world categories. 5 classes consist of textures and the other 10 classes contain objects. A total of 73 different anomaly types are presented. BTAD is another popular benchmark for unsupervised image anomaly detection, which contains 2540 RGB images of three industrial products. All classes in this dataset belong to textures. MVTecAD-3D is recently proposed, which contains 4147 2D RGB images paired with high-resolution 3D point cloud scans from 10 real-world categories. Even though this dataset is mainly designed for 3D anomaly detection, most anomalies can also be detected only through RGB images without 3D point clouds. Since we focus on image anomaly detection, we only use RGB images of the MVTecAD-3D dataset. We refer to this subset as MVTec3D-RGB.
+
+Evaluation Metrics. The standard metric in anomaly detection, AUROC, is used to evaluate the performance of AD methods. Image-level AUROC is used for anomaly detection and a pixel-based AUROC for evaluating anomaly localization [3, 4, 11, 64].
+
+Implementation Details. We use EfficientNet-b6 [45] to extract two levels of feature maps with  $\{8\times ,16\times \}$  downsampling ratios, the pre-trained networks are from the timm library [53]. Then, we construct a subsequent transformer network (see Figure 2) at each feature level to reconstruct patch features and learn patch-to-patch correlations. The parameters of the feature extractor are frozen in the training
+
+Table 1. Comparison of our method with the SOTA methods on the MVTecAD dataset. Red and blue indicate the first and the second best result, respectively. According to the anomaly recognition process, we divide these methods into the patch-wise representation discrepancy, patch-to-patch feature distance, and others.  
+
+<table><tr><td>Discrepancy Type</td><td>Method</td><td>Venue</td><td>Image-level AUROC</td><td>Pixel-level AUROC</td></tr><tr><td rowspan="14">Patch-wise Representation Discrepancy</td><td>STAD [4]</td><td>CVPR 2020</td><td>0.877</td><td>0.939</td></tr><tr><td>PaDiM [11]</td><td>ICPR 2020</td><td>0.955</td><td>0.975</td></tr><tr><td>DFR [57]</td><td>Neurocomputing 2021</td><td>/</td><td>0.950</td></tr><tr><td>FCDD [25]</td><td>ICLR 2021</td><td>/</td><td>0.920</td></tr><tr><td>MKD [41]</td><td>CVPR 2021</td><td>0.877</td><td>0.907</td></tr><tr><td>Hou et al. [17]</td><td>ICCV 2021</td><td>0.895</td><td>/</td></tr><tr><td>Metaformer [54]</td><td>ICCV 2021</td><td>0.958</td><td>/</td></tr><tr><td>DRAEM [64]</td><td>ICCV 2021</td><td>0.980</td><td>0.973</td></tr><tr><td>RDAD [12]</td><td>CVPR 2022</td><td>0.985</td><td>0.978</td></tr><tr><td>SSPCAB [34]</td><td>CVPR 2022</td><td>0.989</td><td>0.972</td></tr><tr><td>DSR [65]</td><td>ECCV 2022</td><td>0.982</td><td>/</td></tr><tr><td>NSA [43]</td><td>ECCV 2022</td><td>0.972</td><td>0.963</td></tr><tr><td>UniAD [62]</td><td>NIPS 2022</td><td>0.966</td><td>0.966</td></tr><tr><td>UTRAD [8]</td><td>Neural Networks 2022</td><td>0.960</td><td>0.967</td></tr><tr><td rowspan="6">Patch-to-patch Feature Distance</td><td>PatchSVDD [60]</td><td>ACCV 2020</td><td>0.921</td><td>0.957</td></tr><tr><td>DifferNet [36]</td><td>WAVC 2020</td><td>0.949</td><td>/</td></tr><tr><td>CFLOW [15]</td><td>WAVC 2022</td><td>0.983</td><td>0.986</td></tr><tr><td>CS-FLOW [37]</td><td>WAVC 2022</td><td>0.987</td><td>/</td></tr><tr><td>Tsai et al. [15]</td><td>WAVC 2022</td><td>0.981</td><td>0.981</td></tr><tr><td>PatchCore [35]</td><td>CVPR 2022</td><td>0.991</td><td>0.980</td></tr><tr><td rowspan="3">Others</td><td>CutPaste [21]</td><td>CVPR 2021</td><td>0.952</td><td>0.960</td></tr><tr><td>Wang et al. [51]</td><td>CVPR 2021</td><td>/</td><td>0.91</td></tr><tr><td>SPD [68]</td><td>ECCV 2022</td><td>0.946</td><td>0.946</td></tr><tr><td>Patch-wise&amp;Intra&amp;Inter</td><td>FOD (Ours)</td><td>-</td><td>0.992</td><td>0.983</td></tr></table>
+
+Table 2. Detailed image-level AUROCs on the MVTecAD dataset.  
+
+<table><tr><td rowspan="2">Category</td><td colspan="6">Image-level Anomaly Detection</td></tr><tr><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td>Carpet</td><td>0.978</td><td>0.963</td><td>1.000</td><td>1.000</td><td>0.987</td><td>1.000</td></tr><tr><td>Grid</td><td>1.000</td><td>0.892</td><td>0.975</td><td>0.992</td><td>0.996</td><td>1.000</td></tr><tr><td>Leather</td><td>1.000</td><td>0.953</td><td>0.956</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Tile</td><td>0.998</td><td>0.969</td><td>0.999</td><td>1.000</td><td>0.999</td><td>1.000</td></tr><tr><td>Wood</td><td>0.991</td><td>0.989</td><td>0.989</td><td>0.985</td><td>0.991</td><td>0.991</td></tr><tr><td>Bottle</td><td>0.993</td><td>0.976</td><td>0.989</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Cable</td><td>0.929</td><td>0.899</td><td>0.972</td><td>0.992</td><td>0.976</td><td>0.995</td></tr><tr><td>Capsule</td><td>0.984</td><td>0.763</td><td>0.979</td><td>0.984</td><td>0.977</td><td>1.000</td></tr><tr><td>Hazelnut</td><td>1.000</td><td>0.912</td><td>0.997</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Metal nut</td><td>0.989</td><td>0.941</td><td>0.972</td><td>1.000</td><td>0.993</td><td>1.000</td></tr><tr><td>Pill</td><td>0.981</td><td>0.791</td><td>0.971</td><td>0.954</td><td>0.968</td><td>0.984</td></tr><tr><td>Screw</td><td>0.939</td><td>0.825</td><td>0.870</td><td>0.953</td><td>0.919</td><td>0.967</td></tr><tr><td>Toothbrush</td><td>1.000</td><td>0.992</td><td>0.886</td><td>0.906</td><td>0.997</td><td>0.944</td></tr><tr><td>Transistor</td><td>0.914</td><td>0.874</td><td>0.956</td><td>0.995</td><td>0.952</td><td>1.000</td></tr><tr><td>Zipper</td><td>1.000</td><td>0.982</td><td>0.981</td><td>0.989</td><td>0.985</td><td>0.997</td></tr><tr><td>Mean</td><td>0.980</td><td>0.915</td><td>0.966</td><td>0.983</td><td>0.983</td><td>0.992</td></tr></table>
+
+process, only the parameters of the subsequent transformer networks are learnable. All the subsequent transformer networks in our model contain 3 layers. We set the hidden dimension  $d_{m}$  as  $\{256,512\}$  and the number of heads as 8. The hyperparameters  $\lambda_{1}$  and  $\lambda_{2}$  are set as 0.5 and 0.5 to trade off two parts of the  $\mathcal{L}_g$  and  $\mathcal{L}_e$  loss functions (see App. B.2 for hyperparameter sensitivity analysis). We use the Adam [19] optimizer with an initial learning rate of  $1\mathrm{e}^{-4}$ . The total training epochs are set as 100 and the batch size is 1 by default. All the training and test images are resized and cropped to  $256\times 256$  resolution from the original resolution.
+
+# 4.2. Main Results
+
+SOTA Methods. We extensively compare our method with those published SOTA methods in the past three years.
+
+The comparison results on MVTecAD are shown in Table 1. Then, we select five reproducible methods to report the detailed results on MVTecAD, these methods are representative and SOTA AD methods in the mainstream categories of image anomaly detection as we discuss in Related Work, including: DRAEM [64], PatchSVDD[60], PatchCore [35], MKD[41], CFLOW[15]. For a fair comparison, we reproduce all these methods with the same backbone as in our model. Thus, despite using the unmodified code from the official repositories, we are not able to exactly reproduce the original results, but our numbers are very close. The detailed image-level AUROC results are shown in Table 2, and detailed pixel-level AUROC results are in the App. Table 6. Most of the methods in Table 1 don't report results on the BTAD and MVTec3D-RGB datasets, so we reproduce the five representative methods on the two datasets for comparison. The image-level and pixel-level AUROC results on BTAD and MVTec3D-RGB are shown in Table 3. Additional detailed results are in the App. Table 7, 8.
+
+Anomaly Detection. On MVTecAD, we set the SOTA performance on the mean detection AUROC, which is slightly higher than the best competitor, PatchCore [35]. Note that the results in Table 2 show that our method can achieve much better results than PatchCore when using the same backbone. What's more, in addition to the pill, screw and toothbrush classes, our method achieves more than  $99\%$  AUROC in all other classes, while other methods only achieve more than  $99\%$  AUROC in most nine classes. This shows that our method is more stable and effective in real-world applications. In the classes (e.g. metal nut, screw, and transistor) with more global and logical anomalies, our method can achieve significantly better results than those methods depending on patch-wise discrepancy (e.g. DRAEM [64] and MKD [41]), and can also achieve better results compared with other methods. This verifies that the three discrepancies are complementary factors and our model can simultaneously spot these discrepancies to recognize harder global and logical anomalies. On BTAD, our FOD can achieve  $96.0\%$  mean detection AUROC, which can outperform the best competitor CFLOW [15] by a margin of  $1.2\%$ . On MVTec3D-RGB, we can outperform all previous SOTA methods by a margin of  $3.3\%$ . Note that this dataset is much more challenging than the MVTecAD dataset when comparing the best results  $(99.2\%)$  for MVTecAD vs.  $88.4\%$  AUROC for MVTec3D-RGB). This demonstrates the robustness of our method.
+
+Anomaly Localization. Our method can achieve comparable results with the best competitors on all three datasets. Our method is slightly lower than CFLOW [15] and PatchCore [35] on the three datasets, but we observe that our model that considers the intra- and intercorrelations outperforms the vanilla reconstruction AD models (e.g. DRAEM [64] and MKD [41]) on all three
+
+Table 3. Comparison of our method with the SOTA methods for image-level anomaly detection and pixel-level anomaly localization performance on the BTAD and MVTec3D-RGB datasets.  
+
+<table><tr><td>Method</td><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td colspan="7">BTAD Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.922</td><td>0.924</td><td>0.935</td><td>0.934</td><td>0.948</td><td>0.960</td></tr><tr><td>Pixel-level AUROC</td><td>0.942</td><td>0.964</td><td>0.965</td><td>0.976</td><td>0.978</td><td>0.975</td></tr><tr><td colspan="7">MVTec3D-RGB Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.757</td><td>0.743</td><td>0.688</td><td>0.839</td><td>0.851</td><td>0.884</td></tr><tr><td>Pixel-level AUROC</td><td>0.974</td><td>0.852</td><td>0.970</td><td>0.977</td><td>0.974</td><td>0.976</td></tr></table>
+
+datasets, which verifies the effectiveness of correlation modeling. Compared with patch-wise reconstruction methods, our method is more effective and robust to detect hard global and logical anomalies (see Figure 3).
+
+Qualitative Results. Samples in Figure 1 show qualitative impressions of accurate anomaly localization from our method. It can be found that our approach can achieve the best anomaly score maps by combining the three discrepancies. Additional visualizations are in the App. Figure 6.
+
+# 4.3. Ablation Study and Model Analysis
+
+Ablation Study. To explain how our model works effectively, we further investigate the effect of the three key designs in our model: recognition views, entropy constraint and reference features. The quantitative results are shown in Table 4, more results can be found in App. Table 9. The entropy constraint is quite effective and necessary in the intra-correlation branch. Specifically, it brings a remarkable  $7.7\%$  averaged absolute AUROC promotion, which demonstrates that the entropy constraint strategy is really conducive to increase the distinguishability between abnormal and normal. Only utilizing pure reconstruction criterion or pure KL divergence can't get the most superior detection results, the combined criterion can outperform each single criterion consistently by a margin of  $1.0\%$  and  $9.8\%$ . Thus the reconstruction errors and the intra- and inter-correlations can collaborate to improve detection performance. For the external reference features, we compare the simple mean features with more elaborate coreset features [35] (see App. Table 15 for more comparison methods). The results show that the simple mean features are more effective than the coreset features (0.923 vs. 0.836), which means that mean features are effective enough to represent all possible normal patterns and preserve the positional information. Finally, our proposed FOD surpasses the pure reconstruction Transformer by  $4.0\%$  absolute improvement. These verify that our proposed explicit correlation learning approach is effective.
+
+Effect for Different Anomalies. To illustrate the effectiveness of our model intuitively, we explore the anomaly localization quality under different types of anomalies (see Figure 3). E.g., simple local anomalies (Column 1) are obviously different from normal visuals; hard global anomalies (Columns 2,3) have less obvious visual appearances,
+
+Table 4. Ablation results in recognition views, entropy constraint, external reference features and anomaly scoring. Patch-wise, Intra and Inter mean patch-wise discrepancy, intra- and intercorrelation, respectively. w/o and w/ mean without and with entropy constraint. Mean and Coreset refer to mean and coreset features [35] as the external reference features (see more details in App. B.3). Rec, Div and Rec&Div mean the pure reconstruction criterion, pure KL divergence (E.q.6) and the combined criterion (E.q.12).  
+
+<table><tr><td>Recognition Views</td><td>Entropy Constraint</td><td>Reference Features</td><td>Anomaly Scoring</td><td>MVTecAD</td><td>BTAD</td><td>MVTec3D-RGB</td><td>Avg</td></tr><tr><td rowspan="2">Patch-wise</td><td>/</td><td>/</td><td>Rec</td><td>0.972</td><td>0.954</td><td>0.790</td><td>0.905</td></tr><tr><td>w/o</td><td>/</td><td>Div</td><td>0.700</td><td>0.811</td><td>0.708</td><td>0.740</td></tr><tr><td rowspan="2">Intra</td><td>w/</td><td>/</td><td>Div</td><td>0.911</td><td>0.822</td><td>0.717</td><td>0.817</td></tr><tr><td>w/</td><td>/</td><td>Rec&amp;Div</td><td>0.974</td><td>0.952</td><td>0.818</td><td>0.915</td></tr><tr><td rowspan="2">Inter</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.980</td><td>0.958</td><td>0.832</td><td>0.923</td></tr><tr><td>w/</td><td>Coreset</td><td>Rec&amp;Div</td><td>0.925</td><td>0.884</td><td>0.700</td><td>0.836</td></tr><tr><td>Intra+Inter</td><td>w/</td><td>Mean</td><td>Div</td><td>0.896</td><td>0.922</td><td>0.814</td><td>0.877</td></tr><tr><td>Patch-wise+Intra+Inter (Ours)</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.992</td><td>0.960</td><td>0.884</td><td>0.945</td></tr></table>
+
+![](images/1ec96a1b48d3d708d0e0d07fc8f802ff95ab7f821d92fe29939d02ed45eb21df.jpg)  
+Figure 3. Visualization of different anomalies. The patch-wise reconstruction is only suitable for simple local anomalies, while for hard global and logical anomalies, it cannot detect or only detect partial anomalies. In contrast, our FOD can detect these anomalies more effectively.
+
+which usually need to be effectively compared with normal regions to detect; logical anomalies (Columns 4,5) may be locally normal and can be detected correctly through the overall semantic understanding. We can find that our FOD is more distinguishable in general. For simple local anomalies, patch-wise reconstruction methods can also achieve good results. While for hard global anomalies, these methods cannot detect or only detect partial anomalies. However, for logical anomalies, these methods cannot detect them at all. In contrast, our method is conducive to detect diverse anomalies because of its complementary recognition views. This verifies that our method can make more precise detection and reduce the false-negative rate compared with the pure patch-wise reconstruction methods.
+
+Correlations Visualization. To explain what our model has learned intuitively, we visualize some learned correlations in Figure 4 with the MVtecAD dataset. For the intra
+
+![](images/60147049f647c70f6f8c9847dd64a6245a72e0577ace31001eb7536ad693d4ad.jpg)  
+(a) Intra-Correlations
+
+![](images/b54f719f5c07974eb0239b922876b0a9161d8ff7b5ad468806ae1f7132118991.jpg)
+
+![](images/f0c65d6500e59c6335307d358e06e2273570110d923d9bde6d32df0fbcc4446b.jpg)
+
+![](images/9b93c1fc3dade151c6d07dc4adcb3594ad34ce22acbea732248bdd58d83528de.jpg)
+
+![](images/b521b7fbdabbf6d817948b2f171c60c2a30c5dc0610b683ee1af20dee6d7d1d5.jpg)  
+Figure 4. Visualization of intra- and inter-correlations. Each red point in the figure can represent an image patch, we plot its discrete correlation distribution with all the other image patches.
+
+![](images/2486c4e5bdc4f01d027842e0e34c5f4e81b4e8f630e0d5266649149c4ec43a5f.jpg)
+
+![](images/79e9209ea383b56702bc78e419999bccdf3799bbb36521921adab7ee64ed903c.jpg)  
+(b) Inter-Correlations
+
+![](images/3c167c9e8e243475d97e7539a9c30467a5c8532b630069c2716e358f518fcd52.jpg)
+
+correlation branch, the normal patches learn to build strong correlations with most patches in the whole image, while the correlation distributions of anomalies usually concentrate in the adjacent image patches. It can be found that the normal correlations are much spread and the abnormal correlations are more concentrated in the adjacent regions. For the inter-correlation branch, most normal correlations only concentrate in one point and the abnormal correlations are more spread, which exactly means that each normal patch can build strong correlations with one special normal pattern and abnormal patches are harder to establish correlations with normal patterns.
+
+# 5. Conclusion
+
+Humans recognize anomalies through two aspects: patch-wise representation discrepancies and weak patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy, to simultaneously spot the patch-wise, intra- and inter-discrepancies. The patch-wise discrepancies and intra- and inter-correlations are complementary factors, and can be combined to detect more complex and diverse anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to I2Correlation to explicitly establish intra- and inter-image correlations for AD modeling. The combination of explicit correlation learning and transformer architecture can match the core idea of anomaly detection quite well.
+
+# Acknowledgements
+
+This work was supported in part by the National Natural Science Fund of China (61971281), the Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Science and Technology Commission of Shanghai Municipality (22DZ2229005).
+
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+
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\ No newline at end of file
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+                                            "type": "text",
+                                            "content": "Figure 1. Anomaly detection examples on MVTecAD [3]. Multiresolution Knowledge Distillation (MKD) [41] adopts the conventional patch-wise representation discrepancies. Row 1 shows the hard global anomalies (i.e., they are not significantly different from normal visuals). Rows 3 and 4 show the logical anomalies (i.e., they may be easily recognized as normal if only from the patch-wise discrepancy)."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "plies accessible. The core idea of most unsupervised AD methods is to compare with normal samples to distinguish anomalies [46, 35, 60, 11, 28, 58]. Even for humans, we also recognize anomalies in this way, specifically through three discrepancies, i.e., 1. patch patterns that differentiate from the normal visuals; 2. image regions that destroy textures or structures; 3. novel appearances that deviate from our accumulated knowledge of normality. Namely, anomalous patches usually have three characteristics: their patchwise representations are different from the normal visuals; they are different from most patches within one image; they deviate from our accumulated knowledge of normality. These views intrinsically reveal that humans' recognition of anomalies depends on two aspects: patch-wise representations (1) and intra- and inter-image correlations (2, 3)."
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+                                    "content": "Previous methods mainly follow the former aspect to learn distinguishable representations or reconstructions,"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+                                }
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+                                    "content": "*Corresponding Author."
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+                                    "type": "text",
+                                    "content": "such as reconstruct-based methods [6, 57, 1] and knowledge distillation AD models [4, 41]. The goal of these methods is to generate reconstructed samples or feature representations, and larger patch-wise representation discrepancies can appear in the abnormal patches. However, only the patch-wise representation discrepancies are insufficient for detecting more complex anomalies (e.g., rows 3 and 4 in Figure 1), since the patch-wise errors can't provide comprehensive descriptions of the spatial context. Other mainstream AD methods, such as embedding-based [11, 35] and one-class-classification-based (OCC) [39, 60] methods, are much similar to the latter aspect. These methods achieve anomaly detection by measuring the distances between the features of test samples and normal features. Compared with the non-learnable feature distances, the explicit intra- and inter-image correlations in our method are more effective to detect diverse anomalies (see Table 1, 2, 3). Moreover, patch-wise representation discrepancies and intra- and inter-correlation discrepancies are complementary, and can be combined to develop more powerful AD models."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Recently, with the self-attention mechanism and long-range modeling ability, transformers [50] have significantly renovated many computer vision tasks [14, 24, 7, 67, 56] and recently popular language-vision multimodal tasks [30, 22]. Transformers have shown great power in the unified modeling of patch-wise representations and patch-to-patch correlations. Transformers are quite suitable for AD tasks as their modeling ability can satisfy the two aspects of anomaly recognition quite well. Some works [26, 18, 8, 62] also attempt to employ transformers to construct AD models. However, these methods only use transformers to extract vision features, which didn't sufficiently adapt transformers' long-range correlation modeling capability to AD tasks. Different from these works, we explicitly exploit transformers' self-attention maps to establish the intra- and inter-image correlations. The correlation distribution of each patch can provide more informative descriptions of the spatial context, which can reveal more intricate and semantic anomaly patterns."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "In this paper, motivated by humans' anomaly recognition process, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can exploit transformers' unified modeling ability to simultaneously spot the patch-wise, intra- and inter-discrepancies. Our key designs are composed of three recognition branches: the patch-wise discrepancy branch is to reconstruct the input patch features for distinguishing simple anomalies; the intra-correlation branch is to explicitly model patch-to-patch correlations in one image for distinguishing hard global anomalies (e.g., row 1 in Figure 1); the inter-correlation branch is to explicitly learn inter-image correlations with known normal patterns from the whole normal training set. To implement the intra- and inter-correlation branches, we adapt"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Transformer and renovate the self-attention mechanism to the I2Correlation, which contains a two-branch structure to first separately model the intra- and inter-correlation distribution of each image patch, and then fuse the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning, the RBF kernel is used to present the neighborhood continuity of each image patch. Besides, an entropy constraint strategy is applied in the two branches, which can solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "In summary, we make the following main contributions:"
+                                }
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+                                            "type": "text",
+                                            "content": "1. We propose a novel AD framework: FOD, which can effectively detect anomalies by simultaneously spotting the patch-wise, intra- and inter-discrepancies."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
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+                        {
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+                                            "type": "text",
+                                            "content": "2. We renovate the self-attention mechanism to the I2Correlation, which can explicitly establish intra- and inter-correlations in a self-supervised way with the target-correlations. An entropy constraint strategy is proposed to further amplify the normal-abnormal distinguishability."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "type": "text",
+                                            "content": "3. Our method can achieve SOTA results on three real-world AD datasets, this shows our method can more effectively determine anomalies from complementary views."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        }
+                    ],
+                    "sub_type": "text"
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+                                    "type": "text",
+                                    "content": "2. Related Work"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "Anomaly Detection. In this paper, we divide the mainstream AD methods into five categories: reconstruction-based, embedding-based, OCC-based methods, knowledge distillation and normalizing flow AD models. The reconstruction-based methods are the most popular AD methods and also widely studied, where the assumption is that models trained by normal samples only can reconstruct normal regions but fail in abnormal regions. Many previous works attempt to train AutoEncoders [6, 28, 57, 8, 17, 64], Variational AutoEncoders [23] and GANs [42, 1, 29, 40] to reconstruct the input images. Overfitting to the input images is the most serious issue of these methods, which means that the anomalies are also well reconstructed [62]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Recently, some embedding-based methods [2, 33, 9, 11, 35] show better AD performance by using ImageNet pretrained networks as feature extractors. In [33], the authors fit a multivariate Gaussian to model the image-level features for further Mahalanobis distance measurement. PaDiM [11] extends the above method to localize pixel-level anomalies. PatchCore [35] extends on this line by utilizing locally aggregated, mid-level features and introducing greedy coreset subsampling to form nominal feature banks. However, these methods directly utilize pre-trained networks without any adaptation to the target dataset. Some works [31, 10, 32] attempt to adapt pre-trained features to the target data distribution. There are also some other methods for using pre-trained networks by freezing them and only"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "optimizing a sub-network, e.g., via knowledge distillation [4, 41, 12, 38], or normalizing flows [36, 15, 37, 63]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "type": "text",
+                                    "content": "OCC is another classical AD paradigm, the earliest works are mainly to extend the OCC models such as OC-SVM [44] or SVDD [47, 39] for anomaly detection. Recently, in [60], a patch-based SVDD that contains multiple cores rather than a single core in [39] is proposed to enable anomaly localization. In [25], a Fully Convolutional Data Description combined with receptive field upsampling is proposed to generate anomaly maps. In [48], the authors further extend the PatchSVDD [60] model by the proposed multi-scale patch-based representation learning method."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Transformer-based Anomaly Detection Methods. Recently, transformers [50] have shown great power in modeling long-range dependencies. For image anomaly detection, some works [26, 18, 62, 8, 59] also attempt to exploit transformers to design AD models. However, most of these methods only use transformers as backbones to extract vision features, and don't effectively adapt the long-range modeling capacity of transformers to AD tasks. Unlike the previous usage of transformers, we explicitly exploit the self-attention maps of transformers to establish intra- and inter-correlations. Our work shares some similarities with a recent work [20]. But we point out that our work has some significant differences from [20]: 1) Different Insight: [20] aims to unify the pointwise representation and pairwise association for time series AD, whereas our work aims to more sufficiently detect image anomalies through three complementary recognition views. 2) Novel Method: we propose entropy constraint, inter-correlation branch, and I2Correlation by effectively combining intra- and inter-correlation branches. 3) Different Task: [20] focuses on time-series AD, whereas we focus on image AD."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "content": "3. Approach"
+                                }
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+                                    "content": "3.1. Model Overview"
+                                }
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+                                    "type": "text",
+                                    "content": "Figure 2 overviews our proposed approach. The model consists of three branches: patch-wise discrepancy branch, intra-correlation branch, and inter-correlation branch. The input 2D image is first sent into a pre-trained backbone to extract multi-scale feature maps. At each feature level, we construct a subsequent transformer network to explicitly model the intra- and inter-image correlations for spotting the intra- and inter-discrepancies. Each network is implemented by stacking the I2Correlation blocks and feedforward layers alternately. Suppose each network contains "
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+                                    "type": "text",
+                                    "content": " layers with length- "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " input features "
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+                                    "type": "inline_equation",
+                                    "content": "X\\in \\mathbb{R}^{N\\times d}"
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+                                    "type": "text",
+                                    "content": ", the output of "
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+                                    "type": "inline_equation",
+                                    "content": "k"
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+                                    "type": "text",
+                                    "content": "th layer "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "X_{k}\\in \\mathbb{R}^{N\\times d_{m}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is calculated as follows:"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "Z _ {k} = \\mathrm {L N} (\\mathrm {I 2 C o r r e l a t i o n} (X _ {k - 1}, X _ {f}) + X _ {k - 1}) \\tag {1}",
+                                    "image_path": "c694d29385a19be77b7e34fc410ae5ca8708e61bae3c1bc4e68954b94140614a.jpg"
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+                                    "content": "X _ {k} = \\mathrm {L N} (\\text {F e e d F o r w a r d} (Z _ {k}) + Z _ {k}) \\tag {2}",
+                                    "image_path": "0bf71e0b29872dc37479bd75fcee771f37fb704a8f370539579e5161d3847154.jpg"
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+                                    "content": "where "
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+                                    "type": "text",
+                                    "content": " is the reference features used by the intercorrelation branch, "
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+                                    "type": "text",
+                                    "content": " means LayerNorm, and "
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+                                    "type": "inline_equation",
+                                    "content": "Z_{k} \\in \\mathbb{R}^{N \\times d_{m}}"
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+                                    "type": "text",
+                                    "content": " is the "
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+                                    "type": "text",
+                                    "content": "th layer's hidden features. The final output features are calculated by linear projection: "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{X} = Z_{K}W_{o}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
+                                    "content": "W_{o} \\in \\mathbb{R}^{d_{m} \\times d}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the output projection matrix."
+                                }
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+                                    "type": "text",
+                                    "content": "3.2. Patch-Wise Reconstruction Discrepancy"
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+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Adopted from previous reconstruction-based AD methods, we employ feature reconstruction as our patch-wise recognition view for simplicity. In our approach, we construct a transformer network to reconstruct the input features. With the long-range dependency modeling ability, the features reconstructed by Transformer can have larger effective receptive fields [13], which are more conducive to detect hard global anomalies and logical anomalies. Moreover, with the further introduced inter-correlation branch (sec.3.4), the features can even perceive normal regions of images from the whole normal training set. Therefore, the reconstructed features generated by our model have better global perception and more discriminative semantic representation capability, which are more suitable for anomaly detection by patch-wise representation discrepancies."
+                                }
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+                                    "type": "text",
+                                    "content": "Learning Objective. We can utilize classical reconstruction losses as the learning objective. We combine the "
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+                                    "content": "\\ell 2"
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+                                    "type": "text",
+                                    "content": " distance and cosine distance to measure the feature distances between the reconstructed features "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{X}"
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+                                    "type": "text",
+                                    "content": " and the input features "
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+                                    "type": "text",
+                                    "content": ". The loss function is defined as follows:"
+                                }
+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {l} = \\left| \\left| \\hat {X} - X \\right| \\right| _ {2} + \\left(1 - \\frac {\\hat {X} \\cdot X}{\\left| \\left| \\hat {X} \\right| \\right| _ {2} \\left| \\left| X \\right| \\right| _ {2}}\\right) \\tag {3}",
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+                                    "content": "The intra-correlation learning branch aims to learn informative patch-to-patch correlations from the input patch sequence adaptively. As shown in the right part of Figure 2, we explicitly take advantage of the self-attention maps of transformers as intra-correlation matrices. Formally, the intra-correlation matrix of the "
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+                                    "type": "inline_equation",
+                                    "content": "S_{k}^{g} = \\mathrm{Softmax}\\Big(Q_{k}^{g}(K_{k}^{g})^{T} / \\sqrt{d_{m}}\\Big)"
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+                                    "type": "interline_equation",
+                                    "content": "\\left[ Q _ {k} ^ {g}, K _ {k} ^ {g}, V _ {k} ^ {g} \\right] = X _ {k - 1} \\left[ W _ {k} ^ {Q _ {g}}, W _ {k} ^ {K _ {g}}, W _ {k} ^ {V _ {g}} \\right] \\tag {4}",
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+                                    "content": " represent the query, key, and value of the "
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+                                    "content": " represent the learnable projection matrices for "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "S_{k}^{g} \\in \\mathbb{R}^{N \\times N}"
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+                                    "content": " denotes the learned intra-image patch-to-patch correlations. Since "
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+                                    "content": "\\text{Softmax}(\\cdot)"
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+                                    "type": "text",
+                                    "content": " can convert the values in the similarity map into range [0, 1] along the horizontal axis, each row of "
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+                                    "type": "text",
+                                    "content": " can represent a discrete correlation distribution for each corresponding image patch. But different from the vanilla transformers, we further introduce target correlation matrices as the learning objective to explicitly optimize the intra-image correlations."
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 2. Model overview. The model is composed of three parts: patch-wise discrepancy branch, intra-correlation branch, and intercorrelation branch. The input image patch sequence will be transformed into the hidden features by a pre-trained backbone, and then sent into the intra-correlation branch for learning intra-image patch-to-patch correlations. The input of the inter-correlation branch is composed of hidden features (as Query) and reference features (as Key and Value). The final output features are used to reconstruct the input features."
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+                                    "type": "text",
+                                    "content": "Target Correlation. Inspired by the contrastive learning method BarlowTwins [66], we can construct a target correlation matrix "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "T \\in \\mathbb{R}^{N \\times N}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " as the learning target. The objective function of BarlowTwins measures the correlation matrix between the embeddings of two identical networks fed with distorted versions of a batch of samples, and tries to make this matrix close to the identity. In our work, the role of the target correlation is to introduce a prior correlation of patches as a pretext learning target, where each patch can be highly correlated to itself and also correlated to its neighborhood patches and the correlation decreases with the increase of distance. This allows us to optimize the intra- and inter-correlations in a self-supervised way. To this end, we use the radial basis function (RBF) to construct the target correlation matrix. We further adopt two learnable kernel variances "
+                                },
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\sigma_y"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " for horizontal and vertical axes to make the target correlation of each patch can adapt to the specific pattern of itself. The target correlation matrix of the "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "th layer is defined as:"
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+                                    "content": "T _ {k} ^ {g} = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} \\exp \\left(- \\frac {\\left| \\left| x _ {i j} - x _ {i ^ {\\prime} j ^ {\\prime}} \\right| \\right| _ {2} ^ {2}}{2 \\left(\\sigma_ {x} ^ {2} + \\sigma_ {y} ^ {2}\\right)}\\right)",
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+                                    "type": "interline_equation",
+                                    "content": "i, i ^ {\\prime} \\in \\{1, \\dots , H \\}; j, j ^ {\\prime} \\in \\{1, \\dots , W \\} \\tag {5}",
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+                                    "type": "inline_equation",
+                                    "content": "||x_{ij} - x_{i'j'}||_2^2"
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+                                    "type": "text",
+                                    "content": " means the Square Euclidean distance between point "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "j, j'"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " means vertical and horizontal coordinates, respectively."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Next, we need to measure the distance between target- and intra-correlation distributions. This can usually be"
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "achieved by calculating the KL divergence. We can obtain a KL divergence value from each level of the network. Thus, we average all KL divergence values to combine the patch-to-patch correlations from multi-layer features into a more informative measure as follows:"
+                                }
+                            ]
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {D i v} \\left(\\mathcal {T} ^ {g}, \\mathcal {S} ^ {g}\\right) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(K L \\left(T _ {k} ^ {g} \\mid \\mid S _ {k} ^ {g}\\right) + K L \\left(S _ {k} ^ {g} \\mid \\mid T _ {k} ^ {g}\\right)\\right) \\tag {6}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "KL(\\cdot ||\\cdot)\\in \\mathbb{R}^N"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and its each element means the KL divergence between two discrete distributions corresponding to each row of "
+                                },
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+                                    "content": "T_{k}^{g}"
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                },
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+                                    "type": "text",
+                                    "content": "."
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+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Due to the rarity of anomalies and the dominance of normal patterns, the normal patches should build strong correlations with most patches in the whole image, while the weights of abnormal correlation distributions are harder to distribute to most patches and are more likely to concentrate on the adjacent image patches due to the neighborhood continuity. Since normal and abnormal patches have different correlation distributions, this is a distinguishable criterion for anomaly detection. Note that the intra-correlation branch explicitly exploits the spatial dependencies of each image patch, which are more informative than the patchwise representations for anomaly detection."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Entropy constraint. Since the normal image patterns are usually diverse, the learned correlation distributions of the normal patches may also easily concentrate on the adjacent patches, which can cause the distinguishability between normal and abnormal to be downscaled. To address"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "this, we further introduce an entropy constraint item for making normal patches establish strong associations with most normal patches in the whole image as much as possible. The entropy constraint item is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {E n t} \\left(\\mathcal {S} ^ {g}\\right) = \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(\\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} \\left(- S _ {k (i, j)} ^ {g} \\log \\left(S _ {k (i, j)} ^ {g}\\right)\\right)\\right) \\tag {7}",
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We will maximize the entropy constraint item. The loss function for the intra-correlation branch is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {g} = \\lambda_ {1} \\operatorname {D i v} \\left(\\mathcal {T} ^ {g}, \\mathcal {S} ^ {g}\\right) - \\lambda_ {2} \\operatorname {E n t} \\left(\\mathcal {S} ^ {g}\\right) \\tag {8}",
+                                    "image_path": "dfcf103a8b6c350a68e74ebd720a4e182139893e826c07082fd2b8ee93c93df0.jpg"
+                                }
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+                    ],
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{1}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        255,
+                                        279,
+                                        314
+                                    ],
+                                    "type": "text",
+                                    "content": " are used to trade off the loss items. The optimization of intra-correlation "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        255,
+                                        279,
+                                        314
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S^g"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        255,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is actually an alternating process with the guidance of target correlation "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        255,
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+                                        314
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T^g"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        255,
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+                                        314
+                                    ],
+                                    "type": "text",
+                                    "content": " (see App. A.1), ultimately resulting that each normal patch can establish strong correlations with most normal patches."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                        333
+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.4. Inter-Correlation Learning"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Through the intra-correlation branch, we can establish patch-to-patch correlations within a single image. However, an image usually doesn't contain all possible normal patterns, which may cause it difficult to distinguish some ambiguous abnormal patches (see rows 2, 3, 4 in Figure 1) only through the intra-correlations. To address this, we should effectively take advantage of the known normal patterns from the normal training set, which are more likely to contain more informative normal patterns. Specifically, we further propose an inter-correlation learning branch to explicitly model pairwise correlations with the whole normal training set. In this branch, the features of each patch establish a discrete inter-correlation distribution with the reference features extracted from all normal samples (see Figure 2). The inter-correlation matrix of the "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        338,
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+                                    ],
+                                    "type": "text",
+                                    "content": "th layer is similar to the corresponding intra-correlation, and is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Inter Correlation: "
+                                },
+                                {
+                                    "bbox": [
+                                        52,
+                                        533,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{k}^{e} = \\mathrm{Softmax}\\Big(Q_{k}^{e}(K_{k}^{e})^{T} / \\sqrt{d_{m}}\\Big)"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "Q _ {k} ^ {e}, K _ {k} ^ {e}, V _ {k} ^ {e} = X _ {k - 1} W _ {k} ^ {Q _ {e}}, X _ {f} W _ {k} ^ {K _ {e}}, X _ {f} W _ {k} ^ {V _ {e}} \\tag {9}",
+                                    "image_path": "f1acc90aa1bfcb1f4da34404067f115f1afb160af98064d5f1fa917eae26280a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{f}\\in \\mathbb{R}^{N_{e}\\times d_{e}}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents the external reference features, "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{e}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "text",
+                                    "content": " is the length of the reference features and "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d_{e}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the feature dimension. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{k}^{Q_{e}}\\in \\mathbb{R}^{d_{m}\\times d_{m}}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_{k}^{K_{e}},W_{k}^{V_{e}}\\in"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{d_e\\times d_m}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "text",
+                                    "content": " are learnable matrices for "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_{k}^{e},K_{k}^{e},V_{k}^{e}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_k^e\\in"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
+                                        279,
+                                        636
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{N\\times N_e}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        578,
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+                                        636
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the learned inter-image correlations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        45,
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+                        729
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        45,
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+                                        729
+                                    ],
+                                    "type": "text",
+                                    "content": "Loss. The loss function for the inter-correlation branch has the opposite optimization direction to "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        637,
+                                        279,
+                                        729
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_g"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        637,
+                                        279,
+                                        729
+                                    ],
+                                    "type": "text",
+                                    "content": ". Because the external reference features contain more comprehensive normal patterns, normal patches can establish stronger correlations with the closest reference normal patterns, instead of establishing strong correlations with most reference patterns. By contrast, it shall be harder for anomalous patches to establish strong correlations with any of the reference"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        297,
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+                        530,
+                        187
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        297,
+                                        106,
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+                                        187
+                                    ],
+                                    "type": "text",
+                                    "content": "patterns. So the inter-correlation distributions of anomalies are more dispersed, while the normal inter-correction distributions are more likely to be concentrated. To this end, we maximize the KL divergence and minimize the entropy item in the training process. The practical optimization strategy is also opposite to the intra-correlation branch (see App. A.1 for details). The loss function is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        339,
+                                        199,
+                                        530,
+                                        212
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {e} = - \\lambda_ {1} \\operatorname {D i v} \\left(\\mathcal {T} ^ {e}, \\mathcal {S} ^ {e}\\right) + \\lambda_ {2} \\operatorname {E n t} \\left(\\mathcal {S} ^ {e}\\right) \\tag {10}",
+                                    "image_path": "746c27463dbebcc1a2bbc22c6df15d1d5b5c7801d8c72faf660ca2f602c6c6fa.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        223,
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+                                    ],
+                                    "type": "text",
+                                    "content": "External Reference Features. External reference features are used for providing accumulated knowledge of normality for the inter-correlation learning branch. Thus, these features should represent all possible normal patterns of all normal samples from the whole normal training set. To this end, we can employ many methods to generate the reference features, such as sampling key features by coreset subsampling algorithm [35], generating prototype features by memory module [28], or learning codebook features through vector quantization [65] or sparse coding techniques [55]. However, because the RBF-kernel in "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}^e"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": " is position-sensitive, our reference features are better to preserve the positional information. The ablation results in App.B.2 show that the methods that can't preserve the position information perform worse. From comprehensive ablation studies, we find that using patch-wise averaged features as the external reference features is a simple but effective way. We think that features extracted by deep neural networks are highly redundant [16, 52], and different normal patterns generally correspond to larger activation values at different channels in the feature vector [61]. So feature averaging will not eliminate some rare normal patterns [11], these patterns may be preserved at specific channels. And averaging can greatly reduce the feature redundancy, making the obtained reference features more representative. Formally, for position "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(i,j)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": ", we first extract the set of patch features at "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(i,j)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{ij} = \\{x_{ij}^k\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k \\in [1,N]"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": " from the "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": " normal training images. Then, the reference features at position "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(i,j)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": " is computed as "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{ij}^f = \\frac{1}{N}\\sum_{k=1}^{N}x_{ij}^k"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": ". The final external reference features are composed of averaged features at all locations and then flattened into 1D: "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_f = \\text{Flatten}(\\{x_{ij}^f\\})"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        223,
+                                        530,
+                                        586
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        298,
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+                        605
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        298,
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.5. I2Correlation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
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+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": "We further combine the intra-correlation and intercorrelation branches to form the I2Correlation block. The output features of the intra- and inter-correlation branches are defined as: "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z_{k}^{g} = S_{k}^{g}V_{k}^{g}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z_{k}^{e} = S_{k}^{e}V_{k}^{e}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. Then, we use the residual feature "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z_{k}^{ge} = Z_{k}^{g} - Z_{k}^{e}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        613,
+                                        530,
+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": " as the output of the I2Correlation block. The feature "
+                                },
+                                {
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+                                    "content": ", it is conducive to spotlight the abnormal patterns in the "
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+                                    "content": "We utilize reconstruction errors as the baseline anomaly criterion and incorporate the normalized correlation distribution distances into the reconstruction criterion. The final anomaly score of the "
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+                                    "content": "Datasets. We extensively evaluate our approach on two widely used industrial AD datasets: the MVTecAD [3] and BTAD [26], and one recent challenging dataset: the MVTecAD-3D [5]. MVTecAD is established as a standard benchmark for evaluating unsupervised image anomaly detection methods. This dataset contains 5354 high-resolution images from 15 real-world categories. 5 classes consist of textures and the other 10 classes contain objects. A total of 73 different anomaly types are presented. BTAD is another popular benchmark for unsupervised image anomaly detection, which contains 2540 RGB images of three industrial products. All classes in this dataset belong to textures. MVTecAD-3D is recently proposed, which contains 4147 2D RGB images paired with high-resolution 3D point cloud scans from 10 real-world categories. Even though this dataset is mainly designed for 3D anomaly detection, most anomalies can also be detected only through RGB images without 3D point clouds. Since we focus on image anomaly detection, we only use RGB images of the MVTecAD-3D dataset. We refer to this subset as MVTec3D-RGB."
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+                                    "content": "Evaluation Metrics. The standard metric in anomaly detection, AUROC, is used to evaluate the performance of AD methods. Image-level AUROC is used for anomaly detection and a pixel-based AUROC for evaluating anomaly localization [3, 4, 11, 64]."
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+                                    "content": "Implementation Details. We use EfficientNet-b6 [45] to extract two levels of feature maps with "
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+                                    "content": " downsampling ratios, the pre-trained networks are from the timm library [53]. Then, we construct a subsequent transformer network (see Figure 2) at each feature level to reconstruct patch features and learn patch-to-patch correlations. The parameters of the feature extractor are frozen in the training"
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+                                            "content": "Table 1. Comparison of our method with the SOTA methods on the MVTecAD dataset. Red and blue indicate the first and the second best result, respectively. According to the anomaly recognition process, we divide these methods into the patch-wise representation discrepancy, patch-to-patch feature distance, and others."
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+                                            "html": "<table><tr><td>Discrepancy Type</td><td>Method</td><td>Venue</td><td>Image-level AUROC</td><td>Pixel-level AUROC</td></tr><tr><td rowspan=\"14\">Patch-wise Representation Discrepancy</td><td>STAD [4]</td><td>CVPR 2020</td><td>0.877</td><td>0.939</td></tr><tr><td>PaDiM [11]</td><td>ICPR 2020</td><td>0.955</td><td>0.975</td></tr><tr><td>DFR [57]</td><td>Neurocomputing 2021</td><td>/</td><td>0.950</td></tr><tr><td>FCDD [25]</td><td>ICLR 2021</td><td>/</td><td>0.920</td></tr><tr><td>MKD [41]</td><td>CVPR 2021</td><td>0.877</td><td>0.907</td></tr><tr><td>Hou et al. [17]</td><td>ICCV 2021</td><td>0.895</td><td>/</td></tr><tr><td>Metaformer [54]</td><td>ICCV 2021</td><td>0.958</td><td>/</td></tr><tr><td>DRAEM [64]</td><td>ICCV 2021</td><td>0.980</td><td>0.973</td></tr><tr><td>RDAD [12]</td><td>CVPR 2022</td><td>0.985</td><td>0.978</td></tr><tr><td>SSPCAB [34]</td><td>CVPR 2022</td><td>0.989</td><td>0.972</td></tr><tr><td>DSR [65]</td><td>ECCV 2022</td><td>0.982</td><td>/</td></tr><tr><td>NSA [43]</td><td>ECCV 2022</td><td>0.972</td><td>0.963</td></tr><tr><td>UniAD [62]</td><td>NIPS 2022</td><td>0.966</td><td>0.966</td></tr><tr><td>UTRAD [8]</td><td>Neural Networks 2022</td><td>0.960</td><td>0.967</td></tr><tr><td rowspan=\"6\">Patch-to-patch Feature Distance</td><td>PatchSVDD [60]</td><td>ACCV 2020</td><td>0.921</td><td>0.957</td></tr><tr><td>DifferNet [36]</td><td>WAVC 2020</td><td>0.949</td><td>/</td></tr><tr><td>CFLOW [15]</td><td>WAVC 2022</td><td>0.983</td><td>0.986</td></tr><tr><td>CS-FLOW [37]</td><td>WAVC 2022</td><td>0.987</td><td>/</td></tr><tr><td>Tsai et al. [15]</td><td>WAVC 2022</td><td>0.981</td><td>0.981</td></tr><tr><td>PatchCore [35]</td><td>CVPR 2022</td><td>0.991</td><td>0.980</td></tr><tr><td rowspan=\"3\">Others</td><td>CutPaste [21]</td><td>CVPR 2021</td><td>0.952</td><td>0.960</td></tr><tr><td>Wang et al. [51]</td><td>CVPR 2021</td><td>/</td><td>0.91</td></tr><tr><td>SPD [68]</td><td>ECCV 2022</td><td>0.946</td><td>0.946</td></tr><tr><td>Patch-wise&amp;Intra&amp;Inter</td><td>FOD (Ours)</td><td>-</td><td>0.992</td><td>0.983</td></tr></table>",
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+                                            "html": "<table><tr><td rowspan=\"2\">Category</td><td colspan=\"6\">Image-level Anomaly Detection</td></tr><tr><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td>Carpet</td><td>0.978</td><td>0.963</td><td>1.000</td><td>1.000</td><td>0.987</td><td>1.000</td></tr><tr><td>Grid</td><td>1.000</td><td>0.892</td><td>0.975</td><td>0.992</td><td>0.996</td><td>1.000</td></tr><tr><td>Leather</td><td>1.000</td><td>0.953</td><td>0.956</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Tile</td><td>0.998</td><td>0.969</td><td>0.999</td><td>1.000</td><td>0.999</td><td>1.000</td></tr><tr><td>Wood</td><td>0.991</td><td>0.989</td><td>0.989</td><td>0.985</td><td>0.991</td><td>0.991</td></tr><tr><td>Bottle</td><td>0.993</td><td>0.976</td><td>0.989</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Cable</td><td>0.929</td><td>0.899</td><td>0.972</td><td>0.992</td><td>0.976</td><td>0.995</td></tr><tr><td>Capsule</td><td>0.984</td><td>0.763</td><td>0.979</td><td>0.984</td><td>0.977</td><td>1.000</td></tr><tr><td>Hazelnut</td><td>1.000</td><td>0.912</td><td>0.997</td><td>1.000</td><td>1.000</td><td>1.000</td></tr><tr><td>Metal nut</td><td>0.989</td><td>0.941</td><td>0.972</td><td>1.000</td><td>0.993</td><td>1.000</td></tr><tr><td>Pill</td><td>0.981</td><td>0.791</td><td>0.971</td><td>0.954</td><td>0.968</td><td>0.984</td></tr><tr><td>Screw</td><td>0.939</td><td>0.825</td><td>0.870</td><td>0.953</td><td>0.919</td><td>0.967</td></tr><tr><td>Toothbrush</td><td>1.000</td><td>0.992</td><td>0.886</td><td>0.906</td><td>0.997</td><td>0.944</td></tr><tr><td>Transistor</td><td>0.914</td><td>0.874</td><td>0.956</td><td>0.995</td><td>0.952</td><td>1.000</td></tr><tr><td>Zipper</td><td>1.000</td><td>0.982</td><td>0.981</td><td>0.989</td><td>0.985</td><td>0.997</td></tr><tr><td>Mean</td><td>0.980</td><td>0.915</td><td>0.966</td><td>0.983</td><td>0.983</td><td>0.992</td></tr></table>",
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+                                    "content": "process, only the parameters of the subsequent transformer networks are learnable. All the subsequent transformer networks in our model contain 3 layers. We set the hidden dimension "
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+                                    "content": " and the number of heads as 8. The hyperparameters "
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+                                    "type": "text",
+                                    "content": " are set as 0.5 and 0.5 to trade off two parts of the "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": " loss functions (see App. B.2 for hyperparameter sensitivity analysis). We use the Adam [19] optimizer with an initial learning rate of "
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+                                    "content": ". The total training epochs are set as 100 and the batch size is 1 by default. All the training and test images are resized and cropped to "
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+                                    "type": "text",
+                                    "content": " resolution from the original resolution."
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+                                    "type": "text",
+                                    "content": "4.2. Main Results"
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+                                    "type": "text",
+                                    "content": "SOTA Methods. We extensively compare our method with those published SOTA methods in the past three years."
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+                                    "type": "text",
+                                    "content": "The comparison results on MVTecAD are shown in Table 1. Then, we select five reproducible methods to report the detailed results on MVTecAD, these methods are representative and SOTA AD methods in the mainstream categories of image anomaly detection as we discuss in Related Work, including: DRAEM [64], PatchSVDD[60], PatchCore [35], MKD[41], CFLOW[15]. For a fair comparison, we reproduce all these methods with the same backbone as in our model. Thus, despite using the unmodified code from the official repositories, we are not able to exactly reproduce the original results, but our numbers are very close. The detailed image-level AUROC results are shown in Table 2, and detailed pixel-level AUROC results are in the App. Table 6. Most of the methods in Table 1 don't report results on the BTAD and MVTec3D-RGB datasets, so we reproduce the five representative methods on the two datasets for comparison. The image-level and pixel-level AUROC results on BTAD and MVTec3D-RGB are shown in Table 3. Additional detailed results are in the App. Table 7, 8."
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+                                    "type": "text",
+                                    "content": "Anomaly Detection. On MVTecAD, we set the SOTA performance on the mean detection AUROC, which is slightly higher than the best competitor, PatchCore [35]. Note that the results in Table 2 show that our method can achieve much better results than PatchCore when using the same backbone. What's more, in addition to the pill, screw and toothbrush classes, our method achieves more than "
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+                                    "type": "text",
+                                    "content": " AUROC in all other classes, while other methods only achieve more than "
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+                                    "type": "text",
+                                    "content": " AUROC in most nine classes. This shows that our method is more stable and effective in real-world applications. In the classes (e.g. metal nut, screw, and transistor) with more global and logical anomalies, our method can achieve significantly better results than those methods depending on patch-wise discrepancy (e.g. DRAEM [64] and MKD [41]), and can also achieve better results compared with other methods. This verifies that the three discrepancies are complementary factors and our model can simultaneously spot these discrepancies to recognize harder global and logical anomalies. On BTAD, our FOD can achieve "
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+                                    "content": " mean detection AUROC, which can outperform the best competitor CFLOW [15] by a margin of "
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+                                    "content": ". On MVTec3D-RGB, we can outperform all previous SOTA methods by a margin of "
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+                                    "content": ". Note that this dataset is much more challenging than the MVTecAD dataset when comparing the best results "
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+                                    "type": "text",
+                                    "content": " for MVTecAD vs. "
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+                                    "type": "text",
+                                    "content": " AUROC for MVTec3D-RGB). This demonstrates the robustness of our method."
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+                                    "type": "text",
+                                    "content": "Anomaly Localization. Our method can achieve comparable results with the best competitors on all three datasets. Our method is slightly lower than CFLOW [15] and PatchCore [35] on the three datasets, but we observe that our model that considers the intra- and intercorrelations outperforms the vanilla reconstruction AD models (e.g. DRAEM [64] and MKD [41]) on all three"
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+                                            "type": "text",
+                                            "content": "Table 3. Comparison of our method with the SOTA methods for image-level anomaly detection and pixel-level anomaly localization performance on the BTAD and MVTec3D-RGB datasets."
+                                        }
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+                                            "html": "<table><tr><td>Method</td><td>DRAEM [64]</td><td>PatchSVDD [60]</td><td>MKD [41]</td><td>PatchCore [35]</td><td>CFLOW [15]</td><td>FOD (Ours)</td></tr><tr><td colspan=\"7\">BTAD Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.922</td><td>0.924</td><td>0.935</td><td>0.934</td><td>0.948</td><td>0.960</td></tr><tr><td>Pixel-level AUROC</td><td>0.942</td><td>0.964</td><td>0.965</td><td>0.976</td><td>0.978</td><td>0.975</td></tr><tr><td colspan=\"7\">MVTec3D-RGB Dataset</td></tr><tr><td>Image-level AUROC</td><td>0.757</td><td>0.743</td><td>0.688</td><td>0.839</td><td>0.851</td><td>0.884</td></tr><tr><td>Pixel-level AUROC</td><td>0.974</td><td>0.852</td><td>0.970</td><td>0.977</td><td>0.974</td><td>0.976</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "datasets, which verifies the effectiveness of correlation modeling. Compared with patch-wise reconstruction methods, our method is more effective and robust to detect hard global and logical anomalies (see Figure 3)."
+                                }
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+                    ],
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+                                    "type": "text",
+                                    "content": "Qualitative Results. Samples in Figure 1 show qualitative impressions of accurate anomaly localization from our method. It can be found that our approach can achieve the best anomaly score maps by combining the three discrepancies. Additional visualizations are in the App. Figure 6."
+                                }
+                            ]
+                        }
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+                                    "content": "4.3. Ablation Study and Model Analysis"
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+                                    "content": "Ablation Study. To explain how our model works effectively, we further investigate the effect of the three key designs in our model: recognition views, entropy constraint and reference features. The quantitative results are shown in Table 4, more results can be found in App. Table 9. The entropy constraint is quite effective and necessary in the intra-correlation branch. Specifically, it brings a remarkable "
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+                                    "content": " averaged absolute AUROC promotion, which demonstrates that the entropy constraint strategy is really conducive to increase the distinguishability between abnormal and normal. Only utilizing pure reconstruction criterion or pure KL divergence can't get the most superior detection results, the combined criterion can outperform each single criterion consistently by a margin of "
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+                                    "type": "text",
+                                    "content": ". Thus the reconstruction errors and the intra- and inter-correlations can collaborate to improve detection performance. For the external reference features, we compare the simple mean features with more elaborate coreset features [35] (see App. Table 15 for more comparison methods). The results show that the simple mean features are more effective than the coreset features (0.923 vs. 0.836), which means that mean features are effective enough to represent all possible normal patterns and preserve the positional information. Finally, our proposed FOD surpasses the pure reconstruction Transformer by "
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+                                    "type": "text",
+                                    "content": " absolute improvement. These verify that our proposed explicit correlation learning approach is effective."
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+                                    "content": "Effect for Different Anomalies. To illustrate the effectiveness of our model intuitively, we explore the anomaly localization quality under different types of anomalies (see Figure 3). E.g., simple local anomalies (Column 1) are obviously different from normal visuals; hard global anomalies (Columns 2,3) have less obvious visual appearances,"
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+                                            "content": "Table 4. Ablation results in recognition views, entropy constraint, external reference features and anomaly scoring. Patch-wise, Intra and Inter mean patch-wise discrepancy, intra- and intercorrelation, respectively. w/o and w/ mean without and with entropy constraint. Mean and Coreset refer to mean and coreset features [35] as the external reference features (see more details in App. B.3). Rec, Div and Rec&Div mean the pure reconstruction criterion, pure KL divergence (E.q.6) and the combined criterion (E.q.12)."
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+                                            "html": "<table><tr><td>Recognition Views</td><td>Entropy Constraint</td><td>Reference Features</td><td>Anomaly Scoring</td><td>MVTecAD</td><td>BTAD</td><td>MVTec3D-RGB</td><td>Avg</td></tr><tr><td rowspan=\"2\">Patch-wise</td><td>/</td><td>/</td><td>Rec</td><td>0.972</td><td>0.954</td><td>0.790</td><td>0.905</td></tr><tr><td>w/o</td><td>/</td><td>Div</td><td>0.700</td><td>0.811</td><td>0.708</td><td>0.740</td></tr><tr><td rowspan=\"2\">Intra</td><td>w/</td><td>/</td><td>Div</td><td>0.911</td><td>0.822</td><td>0.717</td><td>0.817</td></tr><tr><td>w/</td><td>/</td><td>Rec&amp;Div</td><td>0.974</td><td>0.952</td><td>0.818</td><td>0.915</td></tr><tr><td rowspan=\"2\">Inter</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.980</td><td>0.958</td><td>0.832</td><td>0.923</td></tr><tr><td>w/</td><td>Coreset</td><td>Rec&amp;Div</td><td>0.925</td><td>0.884</td><td>0.700</td><td>0.836</td></tr><tr><td>Intra+Inter</td><td>w/</td><td>Mean</td><td>Div</td><td>0.896</td><td>0.922</td><td>0.814</td><td>0.877</td></tr><tr><td>Patch-wise+Intra+Inter (Ours)</td><td>w/</td><td>Mean</td><td>Rec&amp;Div</td><td>0.992</td><td>0.960</td><td>0.884</td><td>0.945</td></tr></table>",
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+                                            "content": "Figure 3. Visualization of different anomalies. The patch-wise reconstruction is only suitable for simple local anomalies, while for hard global and logical anomalies, it cannot detect or only detect partial anomalies. In contrast, our FOD can detect these anomalies more effectively."
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+                                    "content": "which usually need to be effectively compared with normal regions to detect; logical anomalies (Columns 4,5) may be locally normal and can be detected correctly through the overall semantic understanding. We can find that our FOD is more distinguishable in general. For simple local anomalies, patch-wise reconstruction methods can also achieve good results. While for hard global anomalies, these methods cannot detect or only detect partial anomalies. However, for logical anomalies, these methods cannot detect them at all. In contrast, our method is conducive to detect diverse anomalies because of its complementary recognition views. This verifies that our method can make more precise detection and reduce the false-negative rate compared with the pure patch-wise reconstruction methods."
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+                                    "content": "Correlations Visualization. To explain what our model has learned intuitively, we visualize some learned correlations in Figure 4 with the MVtecAD dataset. For the intra"
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+                                    "content": "correlation branch, the normal patches learn to build strong correlations with most patches in the whole image, while the correlation distributions of anomalies usually concentrate in the adjacent image patches. It can be found that the normal correlations are much spread and the abnormal correlations are more concentrated in the adjacent regions. For the inter-correlation branch, most normal correlations only concentrate in one point and the abnormal correlations are more spread, which exactly means that each normal patch can build strong correlations with one special normal pattern and abnormal patches are harder to establish correlations with normal patterns."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Humans recognize anomalies through two aspects: patch-wise representation discrepancies and weak patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy, to simultaneously spot the patch-wise, intra- and inter-discrepancies. The patch-wise discrepancies and intra- and inter-correlations are complementary factors, and can be combined to detect more complex and diverse anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to I2Correlation to explicitly establish intra- and inter-image correlations for AD modeling. The combination of explicit correlation learning and transformer architecture can match the core idea of anomaly detection quite well."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Acknowledgements"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
+                        296,
+                        671,
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+                                    "content": "This work was supported in part by the National Natural Science Fund of China (61971281), the Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Science and Technology Commission of Shanghai Municipality (22DZ2229005)."
+                                }
+                            ]
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+                                    "content": "References"
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+                                        }
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+                                        }
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diff --git a/2023/Forecast-MAE_ Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders/f4fc3c51-7cb9-491a-9580-072217774d3e_content_list.json b/2023/Forecast-MAE_ Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders/f4fc3c51-7cb9-491a-9580-072217774d3e_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..914f00f20721b736028f8437bbca61a1e8b76700
--- /dev/null
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+        "text": "This study explores the application of self-supervised learning (SSL) to the task of motion forecasting, an area that has not yet been extensively investigated despite the widespread success of SSL in computer vision and natural language processing. To address this gap, we introduce Forecast-MAE, an extension of the mask autoencoders framework that is specifically designed for self-supervised learning of the motion forecasting task. Our approach includes a novel masking strategy that leverages the strong interconnections between agents' trajectories and road networks, involving complementary masking of agents' future or history trajectories and random masking of lane segments. Our experiments on the challenging Argoverse 2 motion forecasting benchmark show that Forecast-MAE, which utilizes standard Transformer blocks with minimal inductive bias, achieves competitive performance compared to state-of-the-art methods that rely on supervised learning and sophisticated designs. Moreover, it outperforms the previous self-supervised learning method by a significant margin. Code is available at https://github.com/jchengai/forecast-mae.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Motion forecasting is a rapidly developing research field that plays a critical role in advanced autonomous driving systems [22]. This task involves predicting the future trajectories of other vehicles and pedestrians, while taking into account the intricate interactions and road layouts. The inherent multi-modal driving behaviors of agents, combined with diverse road networks, make motion forecasting an especially challenging undertaking.",
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+        "text": "Self-supervised learning (SSL) is an innovative approach that enables the acquisition of valuable latent features from unlabelled data. By pre-training the model on pretext tasks and pseudo-labels derived from the data, and subsequently",
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+            "Figure 1. Reconstruction result on Argoverse 2 validation scenario. (a) The origin scenario. (b)  $50\\%$  of agents' trajectory is masked using a complementary masking strategy (either history or future is masked).  $50\\%$  of the lane segments are masked randomly. (c) Scenario reconstructed by the proposed Forecast-MAE."
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+        "text": "fine-tuning on downstream tasks, SSL has demonstrated an ability to learn more extensive and adaptable latent features, leading to remarkable advancements in computer vision [3] and natural language processing (NLP) [10]. Nevertheless, despite its widespread popularity and success, there remains a notable lack of exploration of SSL in the motion forecasting domain. We have identified two principal challenges associated with integrating SSL into motion forecasting:",
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+        "text": "(i) Motion forecasting pre-training requires annotated data, which sets it apart from fields such as computer vision and NLP where unlabeled raw inputs are easily accessible. In motion forecasting, we rely on annotated tracking sequences and hand-crafted high-definition maps that are typically collected by expensive onboard sensors and",
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author: Ming Liu",
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+    {
+        "type": "page_number",
+        "text": "8679",
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+    {
+        "type": "text",
+        "text": "require human annotation labor [5, 43, 12]. This poses a challenge to scaling up self-supervised pre-training, a key aspect of SSL's success. To address this challenge, very recent work PreTraM [44] proposed generating additional rasterized map patches (28.8M) cropped from local regions of the entire HD map to train a robust map encoder with contrastive learning. Although this approach yielded notable performance improvements compared to the baseline, it is limited to models based on rasterized map representations, which have a significant performance gap compared to more recent vector-based or graph-based models. However, another pioneering work, SSL-Lanes [1], demonstrated that carefully designed pretext tasks can significantly enhance performance without using extra data by learning richer features. In this paper, we follow this approach to learn better and more generalized features using the existing dataset.",
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+    {
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+        "text": "(ii) The task of motion forecasting involves incorporating multiple modal inputs, such as static map features, spatiotemporal agent motion features, and semantic scene contexts [39, 26, 13, 4, 36, 50, 29, 9, 52]. While various self-supervised learning methods have proven successful in dealing with single-modal inputs such as the image [3], text [10], or point cloud [47, 32], developing pretexts that establish cross-modal interconnections is not an easy task. SSL-Lanes concentrated on designing pretext tasks for each specific input modality, such as lane node masking or agent maneuver classification. Nevertheless, they did not explore the combination of these different tasks or develop pretext tasks that explicitly involve multiple modal inputs. Authors of PreTraM drew inspiration from CLIP's [35] cross-modal contrastive learning framework involving text and images. They devised a technique for pre-training map and trajectory encoders by pairing batches of (map, trajectory) training instances. Nevertheless, their approach merely encompasses the history trajectory-map connection, thereby restricting the scope of modality interconnections to a particular type. This study confronts this challenge by utilizing a masked autoencoder framework that can assimilate all cross-modal interdependencies within a unified scene reconstruction task.",
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+    {
+        "type": "text",
+        "text": "The masked autoencoder (MAE) [20] has garnered significant attention due to its recent achievements in image-based self-supervised learning. This approach involves masking a portion of the input data and reconstructing the missing part using an autoencoder structure. The effectiveness of MAE has also been demonstrated in other domains, such as audio [21] and point cloud [32]. An intriguing question arises: can we extend MAE to motion forecasting? Indeed, motion forecasting itself can be viewed as a masking and reconstructing task, wherein the future trajectory of agents is masked and predicted. Based on the strong correlation between agents' historical and future trajectories and road networks, we further extend this concept to the en",
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+    {
+        "type": "text",
+        "text": "tire scene reconstruction. Specifically, we mask agents' history trajectory or future trajectory in a complementary manner (i.e. either history or future is masked), and randomly mask non-overlapping lane segments, shown in Figure 1. This masking scheme offers several advantages. Firstly, the model must learn how to reconstruct the future from past motion and, in turn, infer history from the future, with limited access to lane structures. This pretext task allows the model to establish a robust bidirectional relationship between past and future motion. Secondly, the model learns to reconstruct lane segments by jointly utilizing neighboring visible lanes, agents' history and future trajectories, thereby establishing a more profound cross-modal understanding.",
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+        "type": "text",
+        "text": "To this end, we introduce Forecast-MAE, an extension of the masked autoencoder framework specifically designed for self-supervised learning of the motion forecasting task. Our methodology comprises a novel masking design that exploits the strong interdependencies among all agents' trajectories and road networks. Despite being simple and incorporating minimal inductive bias, our proposed Forecast-MAE performs strongly on the challenging Argoverse 2 (AV2) motion forecasting benchmark [43] and significantly outperforms the previous self-supervised learning method.",
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+    {
+        "type": "text",
+        "text": "Our contribution can be summarized as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- To our best knowledge, we propose the first masked autoencoding framework for self-supervised learning on the motion forecasting task. Without extra data or pseudo-labels, our method greatly improves the performance of motion forecasting through pre-training compared to training from scratch.",
+            "- We introduce a straightforward yet highly effective masking scheme that facilitates the learning of bidirectional motion connections and cross-modal relationships within a single reconstruction pretext task.",
+            "- We show that our approach, based entirely on standard Transformers with minimal inductive bias, achieves competitive performance compared to the state-of-the-art with supervised learning on the challenging Argov-verse 2 benchmark, and significantly outperforms the previous self-supervised learning method.",
+            "- Our findings suggest that SSL can be a promising approach for motion forecasting, and we anticipate that this may spark greater interest in the field."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Motion Forecasting. The performance of motion forecasting models has significantly advanced in recent years, primarily attributable to the amplified interest in self-driving vehicles and the widespread availability of standard benchmarks. Herein, we concisely outline three key aspects contributing to its improvements.",
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+    {
+        "type": "text",
+        "text": "(i) Improvement on scene representation. In the early stages, rasterized top-down semantic images are commonly",
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "8680",
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+    {
+        "type": "text",
+        "text": "utilized for scene representation, and off-the-shelf image encoders are used for learning [39, 33, 4, 15]. Although this image-based representation is simple and unified, it inevitably results in the loss of detailed structural information during rasterization. The popularity of vectorized representations has increased significantly with the introduction of VectorNet [13], owing to their higher representation capacity and significantly stronger performance. Furthermore, graphs [26, 48, 9, 16, 25] are widely used as another promising scene representation. TPCN [45], as a standalone approach, achieves impressive results by treating the agents' trajectories and lanes as the point cloud.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "(ii) Improvement on model architectures. Early rasterized methods naturally relied on well-established convolutional networks. Later, inspired by the impressive performance of Transformer [41], attention mechanisms have been extensively used for interaction modeling and information aggregation, given their superior flexibility and efficacy. Some works [31, 29, 52, 17] have directly incorporated transformers for forecasting and achieved satisfactory outcomes. A more recent work, MTR [36], builds on cutting-edge vision object detection architecture DETR [2], resulting in state-of-the-art performance. Advances in the graph neural network (GNN) domain are also widely explored [48, 16, 25, 9, 6, 28, 7]. LaneGCN [26] modified graph convolutional operation tailed for lane graph encoding. HDGT [24] uses the heterogeneous graph to encode different types of agents and map elements. HiVT [52], QCNet [51] and [23] explores different correlating systems.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "(iii) Introducing of prior knowledge. Incorporating prior knowledge to tackle the complex problem of multi-modal future prediction has become increasingly prevalent in recent literature. Several works utilize predefined candidate trajectories [33, 37] or anchor points [4, 40] by clustering the ground truth or generating with planners. Another line of research involves sampling goals within the drivable areas and utilizing a two-stage prediction pipeline [48, 9, 50, 18, 15, 16]. DCMS [46] introduces temporal consistent constraints based on the assumption that predictions should not change abruptly. However, these methods typically require additional computation or have a higher model complexity.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite significant advancements in motion forecasting, there is a recent trend towards greater architectural complexity and utilization of prior knowledge. In this study, we explore a different direction for enhancing performance, namely self-supervised learning. By leveraging the simplicity of the MAE framework, we demonstrate that our proposed Forecast-MAE, employing a standard transformer architecture with minimal prior knowledge, can achieve competitive performance compared to state-of-the-art supervised learning-based methods with sophisticated designs.",
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+    },
+    {
+        "type": "text",
+        "text": "Self-supervised Learning in Motion Forecasting. There are only a few studies that explore SSL in motion forecast-",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "ing. To the best of our knowledge, VectorNet is the earliest work that incorporates a BERT-like [10] graph completion task to better capture interactions between agents and maps. However, it is a very preliminary attempt, and the graph completion is treated as an auxiliary training objective that is jointly optimized with the motion forecasting task. PreTraM and SSL-Lanes are two recent works that systematically study SSL. The authors of PreTraM believe that the scarcity of trajectory data restricts the application of SSL in motion forecasting. They generate additional local map patches from the entire maps and leverage single-modal and cross-modal contrastive learning to pretrain the map and trajectory encoders separately. In contrast, our method adopts a completely different MAE-based framework, where representations of different modalities are learned jointly. SSL-Lanes demonstrated that SSL could learn better latent features without using extra data. It studied four pretext tasks, each focusing on one specific input modality, such as lane masking or agents' maneuver classification. However, they do not explore combining these different tasks or designing pretext tasks involving multimodal inputs. On the contrary, the proposed Forecast-MAE learns cross-modal interconnections by design and outperforms SSL-Lanes by a large margin.",
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+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose Forecast-MAE, a simple and neat MAE-based framework for self-supervised pre-training of the motion forecasting task. The pre-training process is illustrated in Figure 2. Visible agents' history/future trajectories and lane segments are embedded as tokens and then processed with a standard transformer encoder. Following the asymmetric design of the vision MAE [20], different mask tokens are added to the decoder's input sequence and later used to reconstruct the masked trajectories and lane segments with simple prediction heads.",
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+    {
+        "type": "text",
+        "text": "3.1. Masking",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In contrast to all current self-supervised learning frameworks for motion forecasting, we utilize the future trajectories of agents as an additional input for pre-training. Our experiments reveal that masking future trajectories is a crucial aspect for Forecast-MAE to be effective. To begin, the road maps are initially segmented into non-overlapping lane sections. We then randomly mask a subset of lane segments according to a uniform distribution. The masking technique for agents differs slightly. Although random masking is still employed for agent trajectories, we only mask the history or future trajectory of each agent (e.g.,  $40\\%$  of agents retain their history, while the remaining  $60\\%$  retain their future). We refer to this process as complementary random masking. This constraint is sensible, as reconstructing trajectories from a single pose is not a meaningful pretext task",
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+    {
+        "type": "page_number",
+        "text": "8681",
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+    {
+        "type": "image",
+        "img_path": "images/ab11c8f3f5012a801b69a629aad698b376b8711c67fe9a0e9fd2db2d47256af3.jpg",
+        "image_caption": [
+            "Figure 2. Overall pre-training scheme of our Forecast-MAE. The left part shows the masking process of an example scenario (two agents are static within the observation horizon). We randomly mask out the entire agents' history or future trajectory, as well as lane segments. The pre-training scheme is shown on the right. Only the visible history, future trajectory, and lane segments will be embedded into tokens and processed by the encoder. Three different types of mask tokens are added to the input sequence of the decoder to reconstruct history, future trajectory and lane segment, respectively."
+        ],
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+    {
+        "type": "text",
+        "text": "when both history and future trajectories are masked.",
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+    {
+        "type": "text",
+        "text": "3.2. Input Representation and Embedding",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Following the popular vectorized representation, we treat all agents' trajectories and lane segments as polylines. Specifically, we denote the history trajectories of  $N$  agents as  $A_{H} \\in \\mathbb{R}^{N \\times T_{H} \\times C_{H}}$ , where  $T_{H}$  is the number of history frames and  $C_{H}$  is the history feature channels including step-wise displacement/velocity difference, and a padding flag indicating the observation status of this frame. Similarly, the future trajectories are denoted as  $A_{F} \\in \\mathbb{R}^{N \\times T_{F} \\times C_{F}}$ , where  $T_{F}$  is the number of future frames,  $C_{F}$  is the future feature channels, including future coordinates normalized to the current position of agents and a padding flag indicating availability. The non-overlapping lane segments are denoted as  $L \\in \\mathbb{R}^{M \\times P \\times C_{L}}$ , where  $M$  is the number of lane segments within a certain radius of the target agent,  $P$  is the number of points of each polyline and  $C_{L}$  is the lane feature channels (e.g., coordinates, availability). Note that we normalize all the coordinates of each lane polyline to its geometric center.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The primary goal of the embedding layer is to encode sequential features into one-dimensional vectors or tokens that can be directly processed by the standard Transformer. We use a Feature Pyramid Network (FPN) [27] similar to LaneGCN to fuse multi-scale agent motion features. 1D neighborhood attention [19] is employed at each scale to extract local motion features. Agents' historical and future features are embedded separately. To capture a broader",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "range of the road map, we employ a lightweight mini-PointNet [34], mainly comprising MLPs and max pooling layers, to embed lane polylines. The embedding process can be formulated as",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\nT _ {H} = \\operatorname {F P N} \\left(A _ {H}\\right), T _ {F} = \\operatorname {F P N} \\left(A _ {F}\\right), T _ {H, F} \\in \\mathbb {R} ^ {N \\times C} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT _ {L} = \\operatorname {M i n i P o i n t N e t} (L), T _ {L} \\in \\mathbb {R} ^ {M \\times C}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $T_{H}, T_{F}, T_{L}$  are history, future, lane tokens respectively,  $C$  is the embedding dimension.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Semantic attributions such as agent category (e.g., vehicle, pedestrian, cyclist) or lane types are initialized as learnable embeddings and added to the embedded tokens. Given that the coordinates of agents and lane features are normalized, it is crucial to include global position information in the tokens. The position embedding (PE) is implemented with a simple two-layer MLP following [47], formulated as",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {P E} = \\operatorname {M L P} \\left(\\left[ x, y, \\cos (\\theta), \\sin (\\theta) \\right], \\mathrm {P E} \\in \\mathbb {R} ^ {C} \\quad (3) \\right.\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $(x,y,\\theta)$  is the latest observed pose of agents or the geometric center pose for lane polylines. The PE is added to the tokens before being processed by the autoencoder.",
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+    {
+        "type": "text",
+        "text": "3.3. AutoEncoder",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The autoencoder is entirely based on standard Transformers. The encoder consists of several Transformer blocks and only encodes concatenated visible agents and lane tokens, resulting in encoded latent tokens  $T_{E} \\in$",
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+        "type": "page_number",
+        "text": "8682",
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+    {
+        "type": "text",
+        "text": "$\\mathbb{R}^{(N + M)\\times C}$ . Following the asymmetric autoencoder design of MAE, history, future, and lane mask tokens  $M = (M_H,M_F,M_L)$  are added together with the encoded latent tokens as the input sequence of the decoder and then output the decoded mask tokens  $M^{\\prime} = (M_H^{\\prime},M_F^{\\prime},M_L^{\\prime})$  after the decoding. Positional embeddings are added to the full input sequence, including the mask tokens. Each type of mask token is a learned vector shared by the corresponding type of masked element. The autoencoding process is formulated as",
+        "bbox": [
+            76,
+            89,
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+            241
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT _ {E} = \\operatorname {E n c o d e r} \\left(\\operatorname {c o n c a t} \\left(T _ {H}, T _ {F}, T _ {L}\\right) + \\mathrm {P E}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM ^ {\\prime} = \\operatorname {D e c o d e r} \\left(\\operatorname {c o n c a t} \\left(T _ {E}, M\\right) + \\mathrm {P E}\\right). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The decoded mask tokens are subsequently used for reconstructing the masked element through a simple prediction head, which is implemented as a linear projection layer in practice.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Reconstruction Target",
+        "text_level": 1,
+        "bbox": [
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+            359,
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+            376
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The prediction heads predict the normalized 2-dimensional coordinates of history/future trajectories  $P_{H / F}$  and lane polylines  $P_L$ ,",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {H} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {H} ^ {\\prime}\\right), P _ {H} \\in \\mathbb {R} ^ {\\alpha N \\times T _ {H} \\times 2}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            86,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {F} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {F} ^ {\\prime}\\right), P _ {F} \\in \\mathbb {R} ^ {(1 - \\alpha) N \\times T _ {F} \\times 2}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {L} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {L} ^ {\\prime}\\right), P _ {L} \\in \\mathbb {R} ^ {\\beta M \\times P \\times 2}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
+            474,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha$  is the agents' history mask ratio,  $\\beta$  is the lane segments mask ratio. We use L1 loss  $\\mathcal{L}_H,\\mathcal{L}_F$  for trajectory reconstruction and mean squared error (MSE) loss  $\\mathcal{L}_L$  for lane polyline reconstruction, and  $w_{H},w_{F},w_{L}$  correspond to the loss weight respectively. The final loss is",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {M A E} = w _ {H} \\mathcal {L} _ {H} + w _ {F} \\mathcal {L} _ {F} + w _ {L} \\mathcal {L} _ {L}. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Motion Forecasting",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For the target motion forecasting task, we adopt an end-to-end fine-tuning approach. During fine-tuning, the following modifications are made to the pre-training model: (1) we discard the MAE decoder and mask tokens; (2) agents' future features are eliminated from the input, and masking is not employed; (3) the pretext prediction heads are substituted with a multi-modal future decoder.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Multi-modal decoder. Given the multi-modal nature of agents' behavior, motion forecasting entails producing multiple potential future predictions, distinct from the masked future reconstruction pretext task. To maintain a neat framework with minimal inductive bias, we implement the multimodal decoder using a simple three-layer MLP. A separate three-layer MLP is utilized to generate the confidence score for each prediction. The decoding process can be formulated as",
+        "bbox": [
+            75,
+            737,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {T r a j} = \\operatorname {M L P} \\left(T _ {H} ^ {\\prime}\\right), P _ {T r a j} \\in \\mathbb {R} ^ {N \\times K \\times T _ {F} \\times 2}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            109,
+            878,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $T_H'$  is the encoded history tokens and  $K$  is the number of output modes. The predicted future trajectories are normalized to each agent's latest observed position.",
+        "bbox": [
+            498,
+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training loss. We adopt the widely used Huber loss for trajectory regression and cross-entropy loss for confidence classification with equal weights. The winner-take-all strategy is employed, which only optimizes the best prediction with minimal average prediction error to the ground truth. We compute the loss using all agents present in the scene.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            244,
+            630,
+            260
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset. We evaluate the proposed framework on the recently released large-scale Argoverse 2 (AV2) dataset. This dataset includes 250K non-overlapping scenarios, divided into 199,908, 24,988, and 24,984 samples for training, validation, and testing, respectively. Each sample contains 5 seconds of history and requires a prediction of 6 seconds in the future, with a sampling rate of  $10\\mathrm{Hz}$ . Every scenario includes a focal track agent that needs to be predicted, with detailed high-definition map patches provided for each sample. We choose to evaluate on the Argoverse 2 dataset as it offers the best balance between diversity and dataset size. The popular Argoverse 1 [5] dataset has a similar size but lacks scenario diversity (e.g., the majority of vehicles driving straight-forward). Conversely, Argoverse 2 is intended to be more varied and complicated. Another widely-used dataset, the Waymo Open Motion Dataset (WOMD) [12], has similar scenario complexity but only contains less than half the number of scenarios (104K). We believe that a larger and more complex dataset is more appropriate for evaluating SSL frameworks.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Metrics. We use the official benchmark metrics, including minADE, minFDE, MR, and brier-minFDE, which refer to six prediction modes, if not specified.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Detailed model architecture and training settings are provided in the supplementary.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conduct ablation studies on the Argoverse 2 validation set. By default, the pre-training epoch is set to 40, the fine-tuning epoch to 30, the history and lane mask ratio to 0.5, and the encoder and decoder depth to 4. The pre-training is only conducted on the training set.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Masking ratio. Figure 3 depicts the impact of varying masking ratios. Employing a well-balanced masking ratio, ranging from  $40\\%$  to  $50\\%$ , between an agent's history and future leads to the most favorable outcomes, in agreement with common sense. We posit that a balanced masking ratio for agent trajectory helps prevent the learning of biased features by the model and enhances its comprehension of",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "8683",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/4fa762b5a6b043ba053b00ec3a145ffcdb0ae25ddfd5cec6028b03e37446952e.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/9e5cc871af27663c6b5044dcd7722c6146275205b264e55ffaf79fa602dabc7b.jpg",
+        "image_caption": [
+            "Figure 3. The impact of the history and lane masking ratio. The marked blue lines show the fine-tuning results on different metrics (lower is better). The dashed lines in grey correspond to the results of the baseline model (trained from scratch for 30 epochs)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            260,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the bidirectional relationship between historical and future motion. This is further demonstrated by the performance of extreme history masking ratios (20% and 80%), which significantly underperform.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Forecast-MAE is relatively insensitive to lane masking ratio, as a wide range of ratios (30% to 60%) perform well. Nonetheless, when the lane masking ratio exceeds 70%, performance suffers notably. The possible reason is with a masking ratio of more than 70%, most of the road structure information loses, which tremendously increases the difficulty of scene reconstruction and geometry feature extraction from the map. Conversely, when the lane masking ratio is below 20%, both ADE and FDE experience a significant increase. We deduce that the masked lanes can be easily extrapolated by nearby visible lanes when only a small subset of lanes are masked.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Masking strategy. One distinctive aspect of our approach, compared to existing SSL methods, is the introduction of agents' future trajectories as additional input during pretraining. The outcomes of various inputs and masking strategies are presented in Table 3. When only lane masking is employed, the utilization of future trajectories as input makes a significant difference (minADE is 0.865 without using future, and 0.828 using future). One possible explanation is that the model can establish better connections between lanes and future trajectories through lane reconstruction, which is beneficial for the forecasting task. In-",
+        "bbox": [
+            75,
+            734,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/5b4fafccafaf7db54a6c694bfaf8560687af2037468087f66ac71b77e76f40f7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hist. mask</td><td>Lane mask</td><td>Fut. input</td><td>Fut. mask</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>0.865</td><td>1.51</td><td>0.212</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>0.828</td><td>1.47</td><td>0.203</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>0.864</td><td>1.53</td><td>0.216</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>0.866</td><td>1.52</td><td>0.214</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>0.820</td><td>1.45</td><td>0.198</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td colspan=\"4\">training from scratch</td><td>0.8314</td><td>1.471</td><td>0.2038</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f62c8ca149e6e78b350026791fdd4e7ff30f167868cc28014240bbd02ebb42e5.jpg",
+        "table_caption": [
+            "Table 1. Results of different input and masking strategies. History and lane are used as input for experiments. When history and future trajectories are simultaneously masked, it is masked in a complementary manner. For other situations, we use random masking by default."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>encoder depth</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>2</td><td>0.854</td><td>1.55</td><td>0.221</td></tr><tr><td>3</td><td>0.823</td><td>1.46</td><td>0.198</td></tr><tr><td>4</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td>5</td><td>0.815</td><td>1.43</td><td>0.188</td></tr></table>",
+        "bbox": [
+            504,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Results of different encoder depth. A encoder depth of 4 offers the best performance-efficiency trade-off.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "terestingly, if we use the future as input and do not mask it, merely masking the history performs even worse than training from scratch (minADE 0.864/0.866 vs. 0.8314). A reasonable justification is that the dataset is intended to make the distribution of agents' future trajectories diverse and multi-modal (e.g., an agent is beginning to pass an intersection), while the historical trajectory is much simpler and more predictable. The model might take a shortcut to reconstruct the history by extrapolating the future trajectory, resulting in a failure to learn meaningful features from the agents' motion. As a result, the learned latent features are useless and even harmful for the later forecasting task. Adding future masking promptly addresses this problem, and minADE improves to 0.820 and 0.814. The proposed complementary masking strategy achieves the best performance in all metrics.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Encoder depth. A relative deep encoder is necessary, as studied in Table 2. The performance improved  $4.6\\%$  in terms of minADE by increasing encoder depth from 2 to 4. Adding more encoder layers does not make a significant difference. We use an encoder depth of 4 as our default setting for its better efficiency-performance trade-off.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Results",
+        "text_level": 1,
+        "bbox": [
+            500,
+            786,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For the final leaderboard submission, we use a depth of 4 for both the decoder and encoder. The history and lane masking ratios are 0.4 and 0.5, respectively. We set the pretraining and fine-tuning epochs both to 60. Our final motion forecasting model is simple and lightweight, with only 1.9M parameters in total.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "8684",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/8ac6c69dfb3523dd6b186a23ad94c1f46f458cd86891b8e038ddc97317f69342.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Method</td><td>minADE1</td><td>minFDE1</td><td>MR1</td><td>minADE6</td><td>minFDE6</td><td>MR6</td><td>b-FDE6</td></tr><tr><td rowspan=\"5\">Supervised Learning</td><td>THOMAS [14]</td><td>1.96</td><td>4.71</td><td>0.64</td><td>0.88</td><td>1.51</td><td>0.20</td><td>2.16</td></tr><tr><td>GoReLa [8]</td><td>1.82</td><td>4.62</td><td>0.61</td><td>0.76</td><td>1.48</td><td>0.22</td><td>2.01</td></tr><tr><td>GANet [42]</td><td>1.78</td><td>4.48</td><td>0.60</td><td>0.73</td><td>1.35</td><td>0.17</td><td>1.97</td></tr><tr><td>QML w/ ensemble [38]</td><td>1.84</td><td>4.98</td><td>0.59</td><td>0.69</td><td>1.39</td><td>0.19</td><td>1.95</td></tr><tr><td>BANet w/ ensemble [49]</td><td>1.79</td><td>4.61</td><td>0.60</td><td>0.71</td><td>1.36</td><td>0.19</td><td>1.92</td></tr><tr><td rowspan=\"3\">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.167</td><td>5.675</td><td>0.671</td><td>0.835</td><td>1.698</td><td>0.248</td><td>2.379</td></tr><tr><td>Dist. to Inter.</td><td>2.176</td><td>5.71</td><td>0.667</td><td>0.839</td><td>1.710</td><td>0.248</td><td>2.391</td></tr><tr><td>S/F Classification</td><td>2.218</td><td>5.905</td><td>0.687</td><td>0.828</td><td>1.671</td><td>0.249</td><td>2.352</td></tr><tr><td rowspan=\"3\">Forecast-MAE</td><td>Scratch</td><td>1.845</td><td>4.602</td><td>0.623</td><td>0.727</td><td>1.427</td><td>0.187</td><td>2.062</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.741</td><td>4.355</td><td>0.607</td><td>0.709</td><td>1.392</td><td>0.172</td><td>2.029</td></tr><tr><td>Fine-tune w/ ensemble</td><td>1.658</td><td>4.145</td><td>0.592</td><td>0.690</td><td>1.338</td><td>0.173</td><td>1.911</td></tr><tr><td rowspan=\"3\">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.014</td><td>5.194</td><td>0.649</td><td>0.850</td><td>1.520</td><td>0.220</td><td>2.197</td></tr><tr><td>Dist. to Inter.</td><td>2.006</td><td>5.187</td><td>0.651</td><td>0.840</td><td>1.490</td><td>0.212</td><td>2.182</td></tr><tr><td>S/F Classification</td><td>2.120</td><td>5.613</td><td>0.675</td><td>0.861</td><td>1.536</td><td>0.224</td><td>2.216</td></tr><tr><td rowspan=\"2\">Forecast-MAE</td><td>Scratch</td><td>1.813</td><td>4.570</td><td>0.622</td><td>0.811</td><td>1.436</td><td>0.189</td><td>2.074</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.755</td><td>4.388</td><td>0.609</td><td>0.801</td><td>1.409</td><td>0.178</td><td>2.042</td></tr></table>",
+        "bbox": [
+            99,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/572bebdd832ee39afcaf9e3cd750b90d4fe5c271f3ca9d143a8fe061b2621354.jpg",
+        "table_caption": [
+            "Table 3. Comparisons with previous results on the Argovesrse 2 test set (upper group) and validation set (lower group). For all the metrics, the lower is the better. We bold the best results and underline the second best results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>epochs</td><td>minADE6</td><td>minFDE6</td><td>MR6</td></tr><tr><td rowspan=\"3\">Scratch</td><td>60</td><td>0.811</td><td>1.436</td><td>0.189</td></tr><tr><td>70</td><td>0.815</td><td>1.436</td><td>0.187</td></tr><tr><td>80</td><td>0.814</td><td>1.450</td><td>0.190</td></tr><tr><td>Fine-tune</td><td>60</td><td>0.801</td><td>1.409</td><td>0.178</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Comparison with training from scratch of different training epochs. Continue increase training iterations does not further improves the performance of training from scratch.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Comparison with the other SSL method. We compare our method with SSL-Lanes, as it is the only published approach that employs vector representation and SSL. We make minimal modifications to its official code base<sup>1</sup> to adapt it to the AV2 dataset. Our experiments utilize three of its pretext tasks, specifically lane making, distance to the intersection (Dist. to Inter.), and success-failure classification (S/F classification). We do not implement the maneuver classification pretext task, as AV2 lacks lane-turning information. Table 3 (lower group) displays the comparison results on the AV2 validation set. Our Forecast-MAE outperforms all SSL-Lanes variants significantly across all metrics. Notably, SSL-Lanes suffers from performance degradation between the validation and test sets, whereas our approach achieves consistent performance on both sets and even performs slightly better on the test set. This suggests that our method learns superior and more generalized features through MAE-based self-supervised pre-training.",
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+    {
+        "type": "text",
+        "text": "Comparison with State-of-the-art. Our Forecast-MAE, developed using standard Transformer blocks and minimal",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "prior knowledge, demonstrates impressive performance on the leaderboard, depicted in Table 3 upper group. Particularly noteworthy is that our approach (w/o ensemble) outperforms all other methods, including ensemble models, in terms of  $\\mathrm{minADE}_1$  and  $\\mathrm{minFDE}_1$ , indicating its superior ability to predict the most likely future. We attribute this to our SSL pre-training scheme, which requires the model to reconstruct the most likely masked history and future trajectories. Additionally, Forecast-MAE (w/o ensemble) achieves the best  $\\mathrm{minADE}_6$  among all non-ensemble methods and performs on par with QML (w/ ensemble). Through the adoption of an ensemble strategy involving 6 variants of our framework (e.g., different masking ratios, encoder depth), our ensemble model achieves the best performance among all methods across six metrics. In particular, our ensemble model outperforms the second-best (GANet) by  $7.5\\%$  in terms of  $\\mathrm{minFDE}_1$ .",
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+    {
+        "type": "text",
+        "text": "Comparison with training from scratch. The comparison results between the fine-tuned model and the model trained from scratch are presented in Table 3. It is noteworthy that the vanilla model, despite its simplicity, serves as a strong baseline. However, our fine-tuned model outperforms the baseline in all metrics, exhibiting improvements of  $5.1\\%$  on  $\\min\\mathrm{ADE}_1$ ,  $5.7\\%$  on  $\\min\\mathrm{FDE}_1$ ,  $2.4\\%$  on  $\\min\\mathrm{ADE}_6$ , and  $\\min\\mathrm{FDE}_6$ , without the utilization of additional data or a more complex model.",
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+    {
+        "type": "text",
+        "text": "As we incorporate agents' future trajectories as inputs during the pre-training, a plausible concern is that the finetuned model may benefit from additional training iterations. To address this, we conduct further training of the vanilla model with more epochs using cosine learning rate decay.",
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+    {
+        "type": "page_footnote",
+        "text": "1https://github.com/AutoVision-cloud/SSL-Lanes",
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+        "text": "8685",
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+    {
+        "type": "image",
+        "img_path": "images/b9381698265ce8905c045858e6ed6d1b206a77ac5db9d9842104c9165ec181d8.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative results of Forecast-MAE The predicted trajectories  $(\\mathrm{K} = 6)$  are in blue and the ground truth is in gradient pink. The bounding box in orange indicates the focal agent."
+        ],
+        "image_footnote": [],
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>Scratch</td><td>0.9098</td><td>1.645</td><td>0.2346</td></tr><tr><td>Fine-tune</td><td>0.8968</td><td>1.613</td><td>0.2164</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 5. Evaluation results on different data distribution.. Models are trained or pre-trained on scenarios in Miami, Pittsburgh and Austin and validated in Dearborn, Palo-alto and Washington-DC.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The results presented in Table 4 indicate that continuing to increase the training iterations fails to enhance the performance of the model trained from scratch, underscoring the importance of pre-training.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Generalization ability. Our method demonstrates strong generalization ability in the AV2 benchmark, as evidenced by the results in Table 3. To further investigate this point, we design an experiment where training and testing employ different data distributions. Specifically, we partition all scenarios involving six cities in the AV2 dataset into two distinct and non-overlapping groups. We then train or pretrain the models solely on scenarios in Miami, Pittsburgh, and Austin, and evaluate them on Dearborn, Palo-Alto, and Washington-DC. Results presented in Table 5 indicate that the fine-tuned model surpasses the baseline in all metrics, signifying that self-supervised pre-training enables learning of more generalizable features.",
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+    },
+    {
+        "type": "text",
+        "text": "Qualitative Results. We visualize the qualitative results of our fine-tuned model on the AV2 validation set, as shown in Figure 4. We leave more results to the supplementary, due to the limited space.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We present Forecast-MAE, a simple and neat framework for self-supervised pre-training on the motion forecasting task. Based on the asymmetric architecture of MAE, we devise a scene reconstruction pretext task that utilizes a novel masking strategy. By leveraging the complementary masking of the agents' trajectories and the random masking of lane segments during the pre-training process, the model acquires the ability to capture the bidirectional agent motion features, road geometry features, and cross-modal intercon",
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+    },
+    {
+        "type": "text",
+        "text": "nections jointly. Our experiments on the challenging Argoverse 2 benchmark demonstrate that our Forecast-MAE surpasses supervised learning methods and previous self-supervised learning works, especially in terms of  $\\min\\mathrm{ADE}_1$  and  $\\min\\mathrm{FDE}_1$ , indicating its superior ability to predict the most likely future.",
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+    {
+        "type": "text",
+        "text": "Limitaion and Discussion. One constraint of our work is the lack of exploration of transfer learning or few-shot learning for the proposed method (e.g., pre-training on WMOD and fine-tuning on AV2). Such exploration is hindered by the different problem settings, namely observation/prediction horizons, of different datasets. Besides, due to the relatively limited size of publicly available motion forecasting datasets compared to those in computer vision or natural language processing, we are unable to determine whether the performance of Forecast-MAE will scale up with increased training data and model capacity. However, we are positive about this point by drawing intuition from MAE and our minimal inductive bias design. Our approach could be advantageous for autonomous driving companies with large-scale internal datasets. Although Forecast-MAE already achieves strong performance while designed to be simple, we anticipate it can be further improved. Drawing inspiration from the development of techniques such as ViT [11] to Swin-Trainsformer [30], properly incorporating inductive bias such as relative position design [52, 8, 51] or local attention [36] may further boost Forecast-MAE in terms of performance and efficiency. Another possible direction is to generate realistic traffic scenarios building upon this work. These possibilities are left for future works.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement This work was supported by Guangdong Basic and Applied Basic Research Foundation, under project 2021B1515120032, Jiangsu Province Science and Technology Project BZ2021056, and Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (HZQB-KCZYB-2020083), awarded to Prof. Ming Liu.",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "page_idx": 7
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diff --git a/2023/Forecast-MAE_ Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders/f4fc3c51-7cb9-491a-9580-072217774d3e_model.json b/2023/Forecast-MAE_ Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders/f4fc3c51-7cb9-491a-9580-072217774d3e_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..f28de9440fac6eb6b0e0aa767dda2298e45aea00
--- /dev/null
+++ b/2023/Forecast-MAE_ Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders/f4fc3c51-7cb9-491a-9580-072217774d3e_model.json	
@@ -0,0 +1,2136 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.044
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.119,
+                0.13,
+                0.853,
+                0.175
+            ],
+            "angle": 0,
+            "content": "Forecast-MAE: Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.307,
+                0.203,
+                0.669,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Jie Cheng\\(^{1}\\) Xiaodong Mei\\(^{1}\\) Ming Liu\\(^{1,2*}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.378,
+                0.222,
+                0.59,
+                0.239
+            ],
+            "angle": 0,
+            "content": "HKUST\\(^{1}\\) HKUST(GZ)\\(^{2}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.271,
+                0.242,
+                0.7,
+                0.256
+            ],
+            "angle": 0,
+            "content": "{jchengai, xmeiab}@connect.ust.hk, eelium@ust.hk"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.474,
+                0.643
+            ],
+            "angle": 0,
+            "content": "This study explores the application of self-supervised learning (SSL) to the task of motion forecasting, an area that has not yet been extensively investigated despite the widespread success of SSL in computer vision and natural language processing. To address this gap, we introduce Forecast-MAE, an extension of the mask autoencoders framework that is specifically designed for self-supervised learning of the motion forecasting task. Our approach includes a novel masking strategy that leverages the strong interconnections between agents' trajectories and road networks, involving complementary masking of agents' future or history trajectories and random masking of lane segments. Our experiments on the challenging Argoverse 2 motion forecasting benchmark show that Forecast-MAE, which utilizes standard Transformer blocks with minimal inductive bias, achieves competitive performance compared to state-of-the-art methods that rely on supervised learning and sophisticated designs. Moreover, it outperforms the previous self-supervised learning method by a significant margin. Code is available at https://github.com/jchengai/forecast-mae."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.67,
+                0.21,
+                0.687
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.696,
+                0.47,
+                0.817
+            ],
+            "angle": 0,
+            "content": "Motion forecasting is a rapidly developing research field that plays a critical role in advanced autonomous driving systems [22]. This task involves predicting the future trajectories of other vehicles and pedestrians, while taking into account the intricate interactions and road layouts. The inherent multi-modal driving behaviors of agents, combined with diverse road networks, make motion forecasting an especially challenging undertaking."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.817,
+                0.47,
+                0.879
+            ],
+            "angle": 0,
+            "content": "Self-supervised learning (SSL) is an innovative approach that enables the acquisition of valuable latent features from unlabelled data. By pre-training the model on pretext tasks and pseudo-labels derived from the data, and subsequently"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.291,
+                0.891,
+                0.383
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.384,
+                0.891,
+                0.47
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.506,
+                0.472,
+                0.891,
+                0.597
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.602,
+                0.894,
+                0.673
+            ],
+            "angle": 0,
+            "content": "Figure 1. Reconstruction result on Argoverse 2 validation scenario. (a) The origin scenario. (b) \\(50\\%\\) of agents' trajectory is masked using a complementary masking strategy (either history or future is masked). \\(50\\%\\) of the lane segments are masked randomly. (c) Scenario reconstructed by the proposed Forecast-MAE."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.687,
+                0.892,
+                0.809
+            ],
+            "angle": 0,
+            "content": "fine-tuning on downstream tasks, SSL has demonstrated an ability to learn more extensive and adaptable latent features, leading to remarkable advancements in computer vision [3] and natural language processing (NLP) [10]. Nevertheless, despite its widespread popularity and success, there remains a notable lack of exploration of SSL in the motion forecasting domain. We have identified two principal challenges associated with integrating SSL into motion forecasting:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "(i) Motion forecasting pre-training requires annotated data, which sets it apart from fields such as computer vision and NLP where unlabeled raw inputs are easily accessible. In motion forecasting, we rely on annotated tracking sequences and hand-crafted high-definition maps that are typically collected by expensive onboard sensors and"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.277,
+                0.901
+            ],
+            "angle": 0,
+            "content": "*Corresponding author: Ming Liu"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8679"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.334
+            ],
+            "angle": 0,
+            "content": "require human annotation labor [5, 43, 12]. This poses a challenge to scaling up self-supervised pre-training, a key aspect of SSL's success. To address this challenge, very recent work PreTraM [44] proposed generating additional rasterized map patches (28.8M) cropped from local regions of the entire HD map to train a robust map encoder with contrastive learning. Although this approach yielded notable performance improvements compared to the baseline, it is limited to models based on rasterized map representations, which have a significant performance gap compared to more recent vector-based or graph-based models. However, another pioneering work, SSL-Lanes [1], demonstrated that carefully designed pretext tasks can significantly enhance performance without using extra data by learning richer features. In this paper, we follow this approach to learn better and more generalized features using the existing dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.338,
+                0.473,
+                0.7
+            ],
+            "angle": 0,
+            "content": "(ii) The task of motion forecasting involves incorporating multiple modal inputs, such as static map features, spatiotemporal agent motion features, and semantic scene contexts [39, 26, 13, 4, 36, 50, 29, 9, 52]. While various self-supervised learning methods have proven successful in dealing with single-modal inputs such as the image [3], text [10], or point cloud [47, 32], developing pretexts that establish cross-modal interconnections is not an easy task. SSL-Lanes concentrated on designing pretext tasks for each specific input modality, such as lane node masking or agent maneuver classification. Nevertheless, they did not explore the combination of these different tasks or develop pretext tasks that explicitly involve multiple modal inputs. Authors of PreTraM drew inspiration from CLIP's [35] cross-modal contrastive learning framework involving text and images. They devised a technique for pre-training map and trajectory encoders by pairing batches of (map, trajectory) training instances. Nevertheless, their approach merely encompasses the history trajectory-map connection, thereby restricting the scope of modality interconnections to a particular type. This study confronts this challenge by utilizing a masked autoencoder framework that can assimilate all cross-modal interdependencies within a unified scene reconstruction task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The masked autoencoder (MAE) [20] has garnered significant attention due to its recent achievements in image-based self-supervised learning. This approach involves masking a portion of the input data and reconstructing the missing part using an autoencoder structure. The effectiveness of MAE has also been demonstrated in other domains, such as audio [21] and point cloud [32]. An intriguing question arises: can we extend MAE to motion forecasting? Indeed, motion forecasting itself can be viewed as a masking and reconstructing task, wherein the future trajectory of agents is masked and predicted. Based on the strong correlation between agents' historical and future trajectories and road networks, we further extend this concept to the en"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.288
+            ],
+            "angle": 0,
+            "content": "tire scene reconstruction. Specifically, we mask agents' history trajectory or future trajectory in a complementary manner (i.e. either history or future is masked), and randomly mask non-overlapping lane segments, shown in Figure 1. This masking scheme offers several advantages. Firstly, the model must learn how to reconstruct the future from past motion and, in turn, infer history from the future, with limited access to lane structures. This pretext task allows the model to establish a robust bidirectional relationship between past and future motion. Secondly, the model learns to reconstruct lane segments by jointly utilizing neighboring visible lanes, agents' history and future trajectories, thereby establishing a more profound cross-modal understanding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.289,
+                0.893,
+                0.438
+            ],
+            "angle": 0,
+            "content": "To this end, we introduce Forecast-MAE, an extension of the masked autoencoder framework specifically designed for self-supervised learning of the motion forecasting task. Our methodology comprises a novel masking design that exploits the strong interdependencies among all agents' trajectories and road networks. Despite being simple and incorporating minimal inductive bias, our proposed Forecast-MAE performs strongly on the challenging Argoverse 2 (AV2) motion forecasting benchmark [43] and significantly outperforms the previous self-supervised learning method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.44,
+                0.838,
+                0.453
+            ],
+            "angle": 0,
+            "content": "Our contribution can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.454,
+                0.892,
+                0.544
+            ],
+            "angle": 0,
+            "content": "- To our best knowledge, we propose the first masked autoencoding framework for self-supervised learning on the motion forecasting task. Without extra data or pseudo-labels, our method greatly improves the performance of motion forecasting through pre-training compared to training from scratch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.545,
+                0.892,
+                0.605
+            ],
+            "angle": 0,
+            "content": "- We introduce a straightforward yet highly effective masking scheme that facilitates the learning of bidirectional motion connections and cross-modal relationships within a single reconstruction pretext task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.606,
+                0.892,
+                0.695
+            ],
+            "angle": 0,
+            "content": "- We show that our approach, based entirely on standard Transformers with minimal inductive bias, achieves competitive performance compared to the state-of-the-art with supervised learning on the challenging Argov-verse 2 benchmark, and significantly outperforms the previous self-supervised learning method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.696,
+                0.892,
+                0.741
+            ],
+            "angle": 0,
+            "content": "- Our findings suggest that SSL can be a promising approach for motion forecasting, and we anticipate that this may spark greater interest in the field."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.454,
+                0.892,
+                0.741
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.755,
+                0.642,
+                0.77
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Motion Forecasting. The performance of motion forecasting models has significantly advanced in recent years, primarily attributable to the amplified interest in self-driving vehicles and the widespread availability of standard benchmarks. Herein, we concisely outline three key aspects contributing to its improvements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "(i) Improvement on scene representation. In the early stages, rasterized top-down semantic images are commonly"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8680"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "utilized for scene representation, and off-the-shelf image encoders are used for learning [39, 33, 4, 15]. Although this image-based representation is simple and unified, it inevitably results in the loss of detailed structural information during rasterization. The popularity of vectorized representations has increased significantly with the introduction of VectorNet [13], owing to their higher representation capacity and significantly stronger performance. Furthermore, graphs [26, 48, 9, 16, 25] are widely used as another promising scene representation. TPCN [45], as a standalone approach, achieves impressive results by treating the agents' trajectories and lanes as the point cloud."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.274,
+                0.473,
+                0.532
+            ],
+            "angle": 0,
+            "content": "(ii) Improvement on model architectures. Early rasterized methods naturally relied on well-established convolutional networks. Later, inspired by the impressive performance of Transformer [41], attention mechanisms have been extensively used for interaction modeling and information aggregation, given their superior flexibility and efficacy. Some works [31, 29, 52, 17] have directly incorporated transformers for forecasting and achieved satisfactory outcomes. A more recent work, MTR [36], builds on cutting-edge vision object detection architecture DETR [2], resulting in state-of-the-art performance. Advances in the graph neural network (GNN) domain are also widely explored [48, 16, 25, 9, 6, 28, 7]. LaneGCN [26] modified graph convolutional operation tailed for lane graph encoding. HDGT [24] uses the heterogeneous graph to encode different types of agents and map elements. HiVT [52], QCNet [51] and [23] explores different correlating systems."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.532,
+                0.473,
+                0.715
+            ],
+            "angle": 0,
+            "content": "(iii) Introducing of prior knowledge. Incorporating prior knowledge to tackle the complex problem of multi-modal future prediction has become increasingly prevalent in recent literature. Several works utilize predefined candidate trajectories [33, 37] or anchor points [4, 40] by clustering the ground truth or generating with planners. Another line of research involves sampling goals within the drivable areas and utilizing a two-stage prediction pipeline [48, 9, 50, 18, 15, 16]. DCMS [46] introduces temporal consistent constraints based on the assumption that predictions should not change abruptly. However, these methods typically require additional computation or have a higher model complexity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.714,
+                0.473,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Despite significant advancements in motion forecasting, there is a recent trend towards greater architectural complexity and utilization of prior knowledge. In this study, we explore a different direction for enhancing performance, namely self-supervised learning. By leveraging the simplicity of the MAE framework, we demonstrate that our proposed Forecast-MAE, employing a standard transformer architecture with minimal prior knowledge, can achieve competitive performance compared to state-of-the-art supervised learning-based methods with sophisticated designs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Self-supervised Learning in Motion Forecasting. There are only a few studies that explore SSL in motion forecast-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.456
+            ],
+            "angle": 0,
+            "content": "ing. To the best of our knowledge, VectorNet is the earliest work that incorporates a BERT-like [10] graph completion task to better capture interactions between agents and maps. However, it is a very preliminary attempt, and the graph completion is treated as an auxiliary training objective that is jointly optimized with the motion forecasting task. PreTraM and SSL-Lanes are two recent works that systematically study SSL. The authors of PreTraM believe that the scarcity of trajectory data restricts the application of SSL in motion forecasting. They generate additional local map patches from the entire maps and leverage single-modal and cross-modal contrastive learning to pretrain the map and trajectory encoders separately. In contrast, our method adopts a completely different MAE-based framework, where representations of different modalities are learned jointly. SSL-Lanes demonstrated that SSL could learn better latent features without using extra data. It studied four pretext tasks, each focusing on one specific input modality, such as lane masking or agents' maneuver classification. However, they do not explore combining these different tasks or designing pretext tasks involving multimodal inputs. On the contrary, the proposed Forecast-MAE learns cross-modal interconnections by design and outperforms SSL-Lanes by a large margin."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.467,
+                0.637,
+                0.485
+            ],
+            "angle": 0,
+            "content": "3. Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.895,
+                0.645
+            ],
+            "angle": 0,
+            "content": "We propose Forecast-MAE, a simple and neat MAE-based framework for self-supervised pre-training of the motion forecasting task. The pre-training process is illustrated in Figure 2. Visible agents' history/future trajectories and lane segments are embedded as tokens and then processed with a standard transformer encoder. Following the asymmetric design of the vision MAE [20], different mask tokens are added to the decoder's input sequence and later used to reconstruct the masked trajectories and lane segments with simple prediction heads."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.651,
+                0.608,
+                0.668
+            ],
+            "angle": 0,
+            "content": "3.1. Masking"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In contrast to all current self-supervised learning frameworks for motion forecasting, we utilize the future trajectories of agents as an additional input for pre-training. Our experiments reveal that masking future trajectories is a crucial aspect for Forecast-MAE to be effective. To begin, the road maps are initially segmented into non-overlapping lane sections. We then randomly mask a subset of lane segments according to a uniform distribution. The masking technique for agents differs slightly. Although random masking is still employed for agent trajectories, we only mask the history or future trajectory of each agent (e.g., \\(40\\%\\) of agents retain their history, while the remaining \\(60\\%\\) retain their future). We refer to this process as complementary random masking. This constraint is sensible, as reconstructing trajectories from a single pose is not a meaningful pretext task"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.515,
+                0.958
+            ],
+            "angle": 0,
+            "content": "8681"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.098,
+                0.089,
+                0.873,
+                0.368
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.375,
+                0.896,
+                0.447
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overall pre-training scheme of our Forecast-MAE. The left part shows the masking process of an example scenario (two agents are static within the observation horizon). We randomly mask out the entire agents' history or future trajectory, as well as lane segments. The pre-training scheme is shown on the right. Only the visible history, future trajectory, and lane segments will be embedded into tokens and processed by the encoder. Three different types of mask tokens are added to the input sequence of the decoder to reconstruct history, future trajectory and lane segment, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.458,
+                0.431,
+                0.473
+            ],
+            "angle": 0,
+            "content": "when both history and future trajectories are masked."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.484,
+                0.406,
+                0.501
+            ],
+            "angle": 0,
+            "content": "3.2. Input Representation and Embedding"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.508,
+                0.474,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Following the popular vectorized representation, we treat all agents' trajectories and lane segments as polylines. Specifically, we denote the history trajectories of \\(N\\) agents as \\(A_{H} \\in \\mathbb{R}^{N \\times T_{H} \\times C_{H}}\\), where \\(T_{H}\\) is the number of history frames and \\(C_{H}\\) is the history feature channels including step-wise displacement/velocity difference, and a padding flag indicating the observation status of this frame. Similarly, the future trajectories are denoted as \\(A_{F} \\in \\mathbb{R}^{N \\times T_{F} \\times C_{F}}\\), where \\(T_{F}\\) is the number of future frames, \\(C_{F}\\) is the future feature channels, including future coordinates normalized to the current position of agents and a padding flag indicating availability. The non-overlapping lane segments are denoted as \\(L \\in \\mathbb{R}^{M \\times P \\times C_{L}}\\), where \\(M\\) is the number of lane segments within a certain radius of the target agent, \\(P\\) is the number of points of each polyline and \\(C_{L}\\) is the lane feature channels (e.g., coordinates, availability). Note that we normalize all the coordinates of each lane polyline to its geometric center."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.781,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The primary goal of the embedding layer is to encode sequential features into one-dimensional vectors or tokens that can be directly processed by the standard Transformer. We use a Feature Pyramid Network (FPN) [27] similar to LaneGCN to fuse multi-scale agent motion features. 1D neighborhood attention [19] is employed at each scale to extract local motion features. Agents' historical and future features are embedded separately. To capture a broader"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.458,
+                0.893,
+                0.518
+            ],
+            "angle": 0,
+            "content": "range of the road map, we employ a lightweight mini-PointNet [34], mainly comprising MLPs and max pooling layers, to embed lane polylines. The embedding process can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.512,
+                0.526,
+                0.893,
+                0.545
+            ],
+            "angle": 0,
+            "content": "\\[\nT _ {H} = \\operatorname {F P N} \\left(A _ {H}\\right), T _ {F} = \\operatorname {F P N} \\left(A _ {F}\\right), T _ {H, F} \\in \\mathbb {R} ^ {N \\times C} \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.588,
+                0.548,
+                0.892,
+                0.566
+            ],
+            "angle": 0,
+            "content": "\\[\nT _ {L} = \\operatorname {M i n i P o i n t N e t} (L), T _ {L} \\in \\mathbb {R} ^ {M \\times C}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.575,
+                0.891,
+                0.606
+            ],
+            "angle": 0,
+            "content": "where \\(T_{H}, T_{F}, T_{L}\\) are history, future, lane tokens respectively, \\(C\\) is the embedding dimension."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.606,
+                0.892,
+                0.713
+            ],
+            "angle": 0,
+            "content": "Semantic attributions such as agent category (e.g., vehicle, pedestrian, cyclist) or lane types are initialized as learnable embeddings and added to the embedded tokens. Given that the coordinates of agents and lane features are normalized, it is crucial to include global position information in the tokens. The position embedding (PE) is implemented with a simple two-layer MLP following [47], formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.548,
+                0.736,
+                0.892,
+                0.755
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {P E} = \\operatorname {M L P} \\left(\\left[ x, y, \\cos (\\theta), \\sin (\\theta) \\right], \\mathrm {P E} \\in \\mathbb {R} ^ {C} \\quad (3) \\right.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.763,
+                0.893,
+                0.81
+            ],
+            "angle": 0,
+            "content": "where \\((x,y,\\theta)\\) is the latest observed pose of agents or the geometric center pose for lane polylines. The PE is added to the tokens before being processed by the autoencoder."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.818,
+                0.64,
+                0.832
+            ],
+            "angle": 0,
+            "content": "3.3. AutoEncoder"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The autoencoder is entirely based on standard Transformers. The encoder consists of several Transformer blocks and only encodes concatenated visible agents and lane tokens, resulting in encoded latent tokens \\( T_{E} \\in \\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8682"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.09,
+                0.473,
+                0.242
+            ],
+            "angle": 0,
+            "content": "\\(\\mathbb{R}^{(N + M)\\times C}\\). Following the asymmetric autoencoder design of MAE, history, future, and lane mask tokens \\(M = (M_H,M_F,M_L)\\) are added together with the encoded latent tokens as the input sequence of the decoder and then output the decoded mask tokens \\(M^{\\prime} = (M_H^{\\prime},M_F^{\\prime},M_L^{\\prime})\\) after the decoding. Positional embeddings are added to the full input sequence, including the mask tokens. Each type of mask token is a learned vector shared by the corresponding type of masked element. The autoencoding process is formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.127,
+                0.249,
+                0.47,
+                0.266
+            ],
+            "angle": 0,
+            "content": "\\[\nT _ {E} = \\operatorname {E n c o d e r} \\left(\\operatorname {c o n c a t} \\left(T _ {H}, T _ {F}, T _ {L}\\right) + \\mathrm {P E}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.127,
+                0.269,
+                0.469,
+                0.287
+            ],
+            "angle": 0,
+            "content": "\\[\nM ^ {\\prime} = \\operatorname {D e c o d e r} \\left(\\operatorname {c o n c a t} \\left(T _ {E}, M\\right) + \\mathrm {P E}\\right). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.292,
+                0.47,
+                0.354
+            ],
+            "angle": 0,
+            "content": "The decoded mask tokens are subsequently used for reconstructing the masked element through a simple prediction head, which is implemented as a linear projection layer in practice."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.36,
+                0.285,
+                0.377
+            ],
+            "angle": 0,
+            "content": "3.4. Reconstruction Target"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.383,
+                0.469,
+                0.429
+            ],
+            "angle": 0,
+            "content": "The prediction heads predict the normalized 2-dimensional coordinates of history/future trajectories \\( P_{H / F} \\) and lane polylines \\( P_L \\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.088,
+                0.434,
+                0.469,
+                0.452
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {H} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {H} ^ {\\prime}\\right), P _ {H} \\in \\mathbb {R} ^ {\\alpha N \\times T _ {H} \\times 2}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.455,
+                0.469,
+                0.473
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {F} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {F} ^ {\\prime}\\right), P _ {F} \\in \\mathbb {R} ^ {(1 - \\alpha) N \\times T _ {F} \\times 2}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.091,
+                0.476,
+                0.469,
+                0.495
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {L} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {L} ^ {\\prime}\\right), P _ {L} \\in \\mathbb {R} ^ {\\beta M \\times P \\times 2}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.5,
+                0.469,
+                0.576
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) is the agents' history mask ratio, \\(\\beta\\) is the lane segments mask ratio. We use L1 loss \\(\\mathcal{L}_H,\\mathcal{L}_F\\) for trajectory reconstruction and mean squared error (MSE) loss \\(\\mathcal{L}_L\\) for lane polyline reconstruction, and \\(w_{H},w_{F},w_{L}\\) correspond to the loss weight respectively. The final loss is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.148,
+                0.584,
+                0.469,
+                0.599
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {M A E} = w _ {H} \\mathcal {L} _ {H} + w _ {F} \\mathcal {L} _ {F} + w _ {L} \\mathcal {L} _ {L}. \\tag {9}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.605,
+                0.265,
+                0.621
+            ],
+            "angle": 0,
+            "content": "3.5. Motion Forecasting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.629,
+                0.469,
+                0.734
+            ],
+            "angle": 0,
+            "content": "For the target motion forecasting task, we adopt an end-to-end fine-tuning approach. During fine-tuning, the following modifications are made to the pre-training model: (1) we discard the MAE decoder and mask tokens; (2) agents' future features are eliminated from the input, and masking is not employed; (3) the pretext prediction heads are substituted with a multi-modal future decoder."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.738,
+                0.469,
+                0.873
+            ],
+            "angle": 0,
+            "content": "Multi-modal decoder. Given the multi-modal nature of agents' behavior, motion forecasting entails producing multiple potential future predictions, distinct from the masked future reconstruction pretext task. To maintain a neat framework with minimal inductive bias, we implement the multimodal decoder using a simple three-layer MLP. A separate three-layer MLP is utilized to generate the confidence score for each prediction. The decoding process can be formulated as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.11,
+                0.879,
+                0.469,
+                0.898
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {T r a j} = \\operatorname {M L P} \\left(T _ {H} ^ {\\prime}\\right), P _ {T r a j} \\in \\mathbb {R} ^ {N \\times K \\times T _ {F} \\times 2}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.137
+            ],
+            "angle": 0,
+            "content": "where \\( T_H' \\) is the encoded history tokens and \\( K \\) is the number of output modes. The predicted future trajectories are normalized to each agent's latest observed position."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.141,
+                0.892,
+                0.232
+            ],
+            "angle": 0,
+            "content": "Training loss. We adopt the widely used Huber loss for trajectory regression and cross-entropy loss for confidence classification with equal weights. The winner-take-all strategy is employed, which only optimizes the best prediction with minimal average prediction error to the ground truth. We compute the loss using all agents present in the scene."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.245,
+                0.632,
+                0.261
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.269,
+                0.691,
+                0.286
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.297,
+                0.892,
+                0.6
+            ],
+            "angle": 0,
+            "content": "Dataset. We evaluate the proposed framework on the recently released large-scale Argoverse 2 (AV2) dataset. This dataset includes 250K non-overlapping scenarios, divided into 199,908, 24,988, and 24,984 samples for training, validation, and testing, respectively. Each sample contains 5 seconds of history and requires a prediction of 6 seconds in the future, with a sampling rate of \\(10\\mathrm{Hz}\\). Every scenario includes a focal track agent that needs to be predicted, with detailed high-definition map patches provided for each sample. We choose to evaluate on the Argoverse 2 dataset as it offers the best balance between diversity and dataset size. The popular Argoverse 1 [5] dataset has a similar size but lacks scenario diversity (e.g., the majority of vehicles driving straight-forward). Conversely, Argoverse 2 is intended to be more varied and complicated. Another widely-used dataset, the Waymo Open Motion Dataset (WOMD) [12], has similar scenario complexity but only contains less than half the number of scenarios (104K). We believe that a larger and more complex dataset is more appropriate for evaluating SSL frameworks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.604,
+                0.892,
+                0.649
+            ],
+            "angle": 0,
+            "content": "Metrics. We use the official benchmark metrics, including minADE, minFDE, MR, and brier-minFDE, which refer to six prediction modes, if not specified."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.653,
+                0.892,
+                0.685
+            ],
+            "angle": 0,
+            "content": "Implementation Details. Detailed model architecture and training settings are provided in the supplementary."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.692,
+                0.654,
+                0.708
+            ],
+            "angle": 0,
+            "content": "4.2. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.715,
+                0.892,
+                0.791
+            ],
+            "angle": 0,
+            "content": "We conduct ablation studies on the Argoverse 2 validation set. By default, the pre-training epoch is set to 40, the fine-tuning epoch to 30, the history and lane mask ratio to 0.5, and the encoder and decoder depth to 4. The pre-training is only conducted on the training set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Masking ratio. Figure 3 depicts the impact of varying masking ratios. Employing a well-balanced masking ratio, ranging from \\(40\\%\\) to \\(50\\%\\), between an agent's history and future leads to the most favorable outcomes, in agreement with common sense. We posit that a balanced masking ratio for agent trajectory helps prevent the learning of biased features by the model and enhances its comprehension of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8683"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.089,
+                0.473,
+                0.252
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.261,
+                0.473,
+                0.41
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.417,
+                0.471,
+                0.475
+            ],
+            "angle": 0,
+            "content": "Figure 3. The impact of the history and lane masking ratio. The marked blue lines show the fine-tuning results on different metrics (lower is better). The dashed lines in grey correspond to the results of the baseline model (trained from scratch for 30 epochs)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.488,
+                0.47,
+                0.549
+            ],
+            "angle": 0,
+            "content": "the bidirectional relationship between historical and future motion. This is further demonstrated by the performance of extreme history masking ratios (20% and 80%), which significantly underperform."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.549,
+                0.471,
+                0.73
+            ],
+            "angle": 0,
+            "content": "Forecast-MAE is relatively insensitive to lane masking ratio, as a wide range of ratios (30% to 60%) perform well. Nonetheless, when the lane masking ratio exceeds 70%, performance suffers notably. The possible reason is with a masking ratio of more than 70%, most of the road structure information loses, which tremendously increases the difficulty of scene reconstruction and geometry feature extraction from the map. Conversely, when the lane masking ratio is below 20%, both ADE and FDE experience a significant increase. We deduce that the masked lanes can be easily extrapolated by nearby visible lanes when only a small subset of lanes are masked."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Masking strategy. One distinctive aspect of our approach, compared to existing SSL methods, is the introduction of agents' future trajectories as additional input during pretraining. The outcomes of various inputs and masking strategies are presented in Table 3. When only lane masking is employed, the utilization of future trajectories as input makes a significant difference (minADE is 0.865 without using future, and 0.828 using future). One possible explanation is that the model can establish better connections between lanes and future trajectories through lane reconstruction, which is beneficial for the forecasting task. In-"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.511,
+                0.089,
+                0.885,
+                0.23
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Hist. mask</td><td>Lane mask</td><td>Fut. input</td><td>Fut. mask</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>0.865</td><td>1.51</td><td>0.212</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>0.828</td><td>1.47</td><td>0.203</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>0.864</td><td>1.53</td><td>0.216</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>0.866</td><td>1.52</td><td>0.214</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>0.820</td><td>1.45</td><td>0.198</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td colspan=\"4\">training from scratch</td><td>0.8314</td><td>1.471</td><td>0.2038</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.235,
+                0.892,
+                0.306
+            ],
+            "angle": 0,
+            "content": "Table 1. Results of different input and masking strategies. History and lane are used as input for experiments. When history and future trajectories are simultaneously masked, it is masked in a complementary manner. For other situations, we use random masking by default."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.506,
+                0.312,
+                0.885,
+                0.395
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>encoder depth</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>2</td><td>0.854</td><td>1.55</td><td>0.221</td></tr><tr><td>3</td><td>0.823</td><td>1.46</td><td>0.198</td></tr><tr><td>4</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td>5</td><td>0.815</td><td>1.43</td><td>0.188</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.4,
+                0.892,
+                0.428
+            ],
+            "angle": 0,
+            "content": "Table 2. Results of different encoder depth. A encoder depth of 4 offers the best performance-efficiency trade-off."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.442,
+                0.892,
+                0.683
+            ],
+            "angle": 0,
+            "content": "terestingly, if we use the future as input and do not mask it, merely masking the history performs even worse than training from scratch (minADE 0.864/0.866 vs. 0.8314). A reasonable justification is that the dataset is intended to make the distribution of agents' future trajectories diverse and multi-modal (e.g., an agent is beginning to pass an intersection), while the historical trajectory is much simpler and more predictable. The model might take a shortcut to reconstruct the history by extrapolating the future trajectory, resulting in a failure to learn meaningful features from the agents' motion. As a result, the learned latent features are useless and even harmful for the later forecasting task. Adding future masking promptly addresses this problem, and minADE improves to 0.820 and 0.814. The proposed complementary masking strategy achieves the best performance in all metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.688,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Encoder depth. A relative deep encoder is necessary, as studied in Table 2. The performance improved \\(4.6\\%\\) in terms of minADE by increasing encoder depth from 2 to 4. Adding more encoder layers does not make a significant difference. We use an encoder depth of 4 as our default setting for its better efficiency-performance trade-off."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.593,
+                0.802
+            ],
+            "angle": 0,
+            "content": "4.3. Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "For the final leaderboard submission, we use a depth of 4 for both the decoder and encoder. The history and lane masking ratios are 0.4 and 0.5, respectively. We set the pretraining and fine-tuning epochs both to 60. Our final motion forecasting model is simple and lightweight, with only 1.9M parameters in total."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "8684"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.1,
+                0.089,
+                0.868,
+                0.366
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Method</td><td>minADE1</td><td>minFDE1</td><td>MR1</td><td>minADE6</td><td>minFDE6</td><td>MR6</td><td>b-FDE6</td></tr><tr><td rowspan=\"5\">Supervised Learning</td><td>THOMAS [14]</td><td>1.96</td><td>4.71</td><td>0.64</td><td>0.88</td><td>1.51</td><td>0.20</td><td>2.16</td></tr><tr><td>GoReLa [8]</td><td>1.82</td><td>4.62</td><td>0.61</td><td>0.76</td><td>1.48</td><td>0.22</td><td>2.01</td></tr><tr><td>GANet [42]</td><td>1.78</td><td>4.48</td><td>0.60</td><td>0.73</td><td>1.35</td><td>0.17</td><td>1.97</td></tr><tr><td>QML w/ ensemble [38]</td><td>1.84</td><td>4.98</td><td>0.59</td><td>0.69</td><td>1.39</td><td>0.19</td><td>1.95</td></tr><tr><td>BANet w/ ensemble [49]</td><td>1.79</td><td>4.61</td><td>0.60</td><td>0.71</td><td>1.36</td><td>0.19</td><td>1.92</td></tr><tr><td rowspan=\"3\">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.167</td><td>5.675</td><td>0.671</td><td>0.835</td><td>1.698</td><td>0.248</td><td>2.379</td></tr><tr><td>Dist. to Inter.</td><td>2.176</td><td>5.71</td><td>0.667</td><td>0.839</td><td>1.710</td><td>0.248</td><td>2.391</td></tr><tr><td>S/F Classification</td><td>2.218</td><td>5.905</td><td>0.687</td><td>0.828</td><td>1.671</td><td>0.249</td><td>2.352</td></tr><tr><td rowspan=\"3\">Forecast-MAE</td><td>Scratch</td><td>1.845</td><td>4.602</td><td>0.623</td><td>0.727</td><td>1.427</td><td>0.187</td><td>2.062</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.741</td><td>4.355</td><td>0.607</td><td>0.709</td><td>1.392</td><td>0.172</td><td>2.029</td></tr><tr><td>Fine-tune w/ ensemble</td><td>1.658</td><td>4.145</td><td>0.592</td><td>0.690</td><td>1.338</td><td>0.173</td><td>1.911</td></tr><tr><td rowspan=\"3\">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.014</td><td>5.194</td><td>0.649</td><td>0.850</td><td>1.520</td><td>0.220</td><td>2.197</td></tr><tr><td>Dist. to Inter.</td><td>2.006</td><td>5.187</td><td>0.651</td><td>0.840</td><td>1.490</td><td>0.212</td><td>2.182</td></tr><tr><td>S/F Classification</td><td>2.120</td><td>5.613</td><td>0.675</td><td>0.861</td><td>1.536</td><td>0.224</td><td>2.216</td></tr><tr><td rowspan=\"2\">Forecast-MAE</td><td>Scratch</td><td>1.813</td><td>4.570</td><td>0.622</td><td>0.811</td><td>1.436</td><td>0.189</td><td>2.074</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.755</td><td>4.388</td><td>0.609</td><td>0.801</td><td>1.409</td><td>0.178</td><td>2.042</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.376,
+                0.892,
+                0.404
+            ],
+            "angle": 0,
+            "content": "Table 3. Comparisons with previous results on the Argovesrse 2 test set (upper group) and validation set (lower group). For all the metrics, the lower is the better. We bold the best results and underline the second best results."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.42,
+                0.462,
+                0.502
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>epochs</td><td>minADE6</td><td>minFDE6</td><td>MR6</td></tr><tr><td rowspan=\"3\">Scratch</td><td>60</td><td>0.811</td><td>1.436</td><td>0.189</td></tr><tr><td>70</td><td>0.815</td><td>1.436</td><td>0.187</td></tr><tr><td>80</td><td>0.814</td><td>1.450</td><td>0.190</td></tr><tr><td>Fine-tune</td><td>60</td><td>0.801</td><td>1.409</td><td>0.178</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.511,
+                0.47,
+                0.553
+            ],
+            "angle": 0,
+            "content": "Table 4. Comparison with training from scratch of different training epochs. Continue increase training iterations does not further improves the performance of training from scratch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.47,
+                0.842
+            ],
+            "angle": 0,
+            "content": "Comparison with the other SSL method. We compare our method with SSL-Lanes, as it is the only published approach that employs vector representation and SSL. We make minimal modifications to its official code base<sup>1</sup> to adapt it to the AV2 dataset. Our experiments utilize three of its pretext tasks, specifically lane making, distance to the intersection (Dist. to Inter.), and success-failure classification (S/F classification). We do not implement the maneuver classification pretext task, as AV2 lacks lane-turning information. Table 3 (lower group) displays the comparison results on the AV2 validation set. Our Forecast-MAE outperforms all SSL-Lanes variants significantly across all metrics. Notably, SSL-Lanes suffers from performance degradation between the validation and test sets, whereas our approach achieves consistent performance on both sets and even performs slightly better on the test set. This suggests that our method learns superior and more generalized features through MAE-based self-supervised pre-training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.846,
+                0.469,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Comparison with State-of-the-art. Our Forecast-MAE, developed using standard Transformer blocks and minimal"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.423,
+                0.892,
+                0.68
+            ],
+            "angle": 0,
+            "content": "prior knowledge, demonstrates impressive performance on the leaderboard, depicted in Table 3 upper group. Particularly noteworthy is that our approach (w/o ensemble) outperforms all other methods, including ensemble models, in terms of \\(\\mathrm{minADE}_1\\) and \\(\\mathrm{minFDE}_1\\), indicating its superior ability to predict the most likely future. We attribute this to our SSL pre-training scheme, which requires the model to reconstruct the most likely masked history and future trajectories. Additionally, Forecast-MAE (w/o ensemble) achieves the best \\(\\mathrm{minADE}_6\\) among all non-ensemble methods and performs on par with QML (w/ ensemble). Through the adoption of an ensemble strategy involving 6 variants of our framework (e.g., different masking ratios, encoder depth), our ensemble model achieves the best performance among all methods across six metrics. In particular, our ensemble model outperforms the second-best (GANet) by \\(7.5\\%\\) in terms of \\(\\mathrm{minFDE}_1\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.687,
+                0.892,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Comparison with training from scratch. The comparison results between the fine-tuned model and the model trained from scratch are presented in Table 3. It is noteworthy that the vanilla model, despite its simplicity, serves as a strong baseline. However, our fine-tuned model outperforms the baseline in all metrics, exhibiting improvements of \\(5.1\\%\\) on \\(\\min\\mathrm{ADE}_1\\), \\(5.7\\%\\) on \\(\\min\\mathrm{FDE}_1\\), \\(2.4\\%\\) on \\(\\min\\mathrm{ADE}_6\\), and \\(\\min\\mathrm{FDE}_6\\), without the utilization of additional data or a more complex model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "As we incorporate agents' future trajectories as inputs during the pre-training, a plausible concern is that the finetuned model may benefit from additional training iterations. To address this, we conduct further training of the vanilla model with more epochs using cosine learning rate decay."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.46,
+                0.9
+            ],
+            "angle": 0,
+            "content": "1https://github.com/AutoVision-cloud/SSL-Lanes"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8685"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.079,
+                0.885,
+                0.205
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.219,
+                0.895,
+                0.248
+            ],
+            "angle": 0,
+            "content": "Figure 4. Qualitative results of Forecast-MAE The predicted trajectories \\((\\mathrm{K} = 6)\\) are in blue and the ground truth is in gradient pink. The bounding box in orange indicates the focal agent."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.26,
+                0.458,
+                0.315
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>Scratch</td><td>0.9098</td><td>1.645</td><td>0.2346</td></tr><tr><td>Fine-tune</td><td>0.8968</td><td>1.613</td><td>0.2164</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.319,
+                0.47,
+                0.375
+            ],
+            "angle": 0,
+            "content": "Table 5. Evaluation results on different data distribution.. Models are trained or pre-trained on scenarios in Miami, Pittsburgh and Austin and validated in Dearborn, Palo-alto and Washington-DC."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.393,
+                0.47,
+                0.455
+            ],
+            "angle": 0,
+            "content": "The results presented in Table 4 indicate that continuing to increase the training iterations fails to enhance the performance of the model trained from scratch, underscoring the importance of pre-training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.459,
+                0.471,
+                0.655
+            ],
+            "angle": 0,
+            "content": "Generalization ability. Our method demonstrates strong generalization ability in the AV2 benchmark, as evidenced by the results in Table 3. To further investigate this point, we design an experiment where training and testing employ different data distributions. Specifically, we partition all scenarios involving six cities in the AV2 dataset into two distinct and non-overlapping groups. We then train or pretrain the models solely on scenarios in Miami, Pittsburgh, and Austin, and evaluate them on Dearborn, Palo-Alto, and Washington-DC. Results presented in Table 5 indicate that the fine-tuned model surpasses the baseline in all metrics, signifying that self-supervised pre-training enables learning of more generalizable features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.661,
+                0.47,
+                0.722
+            ],
+            "angle": 0,
+            "content": "Qualitative Results. We visualize the qualitative results of our fine-tuned model on the AV2 validation set, as shown in Figure 4. We leave more results to the supplementary, due to the limited space."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.738,
+                0.196,
+                0.755
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We present Forecast-MAE, a simple and neat framework for self-supervised pre-training on the motion forecasting task. Based on the asymmetric architecture of MAE, we devise a scene reconstruction pretext task that utilizes a novel masking strategy. By leveraging the complementary masking of the agents' trajectories and the random masking of lane segments during the pre-training process, the model acquires the ability to capture the bidirectional agent motion features, road geometry features, and cross-modal intercon"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.262,
+                0.892,
+                0.354
+            ],
+            "angle": 0,
+            "content": "nections jointly. Our experiments on the challenging Argoverse 2 benchmark demonstrate that our Forecast-MAE surpasses supervised learning methods and previous self-supervised learning works, especially in terms of \\(\\min\\mathrm{ADE}_1\\) and \\(\\min\\mathrm{FDE}_1\\), indicating its superior ability to predict the most likely future."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.358,
+                0.893,
+                0.72
+            ],
+            "angle": 0,
+            "content": "Limitaion and Discussion. One constraint of our work is the lack of exploration of transfer learning or few-shot learning for the proposed method (e.g., pre-training on WMOD and fine-tuning on AV2). Such exploration is hindered by the different problem settings, namely observation/prediction horizons, of different datasets. Besides, due to the relatively limited size of publicly available motion forecasting datasets compared to those in computer vision or natural language processing, we are unable to determine whether the performance of Forecast-MAE will scale up with increased training data and model capacity. However, we are positive about this point by drawing intuition from MAE and our minimal inductive bias design. Our approach could be advantageous for autonomous driving companies with large-scale internal datasets. Although Forecast-MAE already achieves strong performance while designed to be simple, we anticipate it can be further improved. Drawing inspiration from the development of techniques such as ViT [11] to Swin-Trainsformer [30], properly incorporating inductive bias such as relative position design [52, 8, 51] or local attention [36] may further boost Forecast-MAE in terms of performance and efficiency. Another possible direction is to generate realistic traffic scenarios building upon this work. These possibilities are left for future works."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.725,
+                0.892,
+                0.832
+            ],
+            "angle": 0,
+            "content": "Acknowledgement This work was supported by Guangdong Basic and Applied Basic Research Foundation, under project 2021B1515120032, Jiangsu Province Science and Technology Project BZ2021056, and Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (HZQB-KCZYB-2020083), awarded to Prof. Ming Liu."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.847,
+                0.597,
+                0.862
+            ],
+            "angle": 0,
+            "content": "References"
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+# Forecast-MAE: Self-supervised Pre-training for Motion Forecasting with Masked Autoencoders
+
+Jie Cheng $^{1}$  Xiaodong Mei $^{1}$  Ming Liu $^{1,2*}$
+
+HKUST $^{1}$  HKUST(GZ) $^{2}$
+
+{jchengai, xmeiab}@connect.ust.hk, eelium@ust.hk
+
+# Abstract
+
+This study explores the application of self-supervised learning (SSL) to the task of motion forecasting, an area that has not yet been extensively investigated despite the widespread success of SSL in computer vision and natural language processing. To address this gap, we introduce Forecast-MAE, an extension of the mask autoencoders framework that is specifically designed for self-supervised learning of the motion forecasting task. Our approach includes a novel masking strategy that leverages the strong interconnections between agents' trajectories and road networks, involving complementary masking of agents' future or history trajectories and random masking of lane segments. Our experiments on the challenging Argoverse 2 motion forecasting benchmark show that Forecast-MAE, which utilizes standard Transformer blocks with minimal inductive bias, achieves competitive performance compared to state-of-the-art methods that rely on supervised learning and sophisticated designs. Moreover, it outperforms the previous self-supervised learning method by a significant margin. Code is available at https://github.com/jchengai/forecast-mae.
+
+# 1. Introduction
+
+Motion forecasting is a rapidly developing research field that plays a critical role in advanced autonomous driving systems [22]. This task involves predicting the future trajectories of other vehicles and pedestrians, while taking into account the intricate interactions and road layouts. The inherent multi-modal driving behaviors of agents, combined with diverse road networks, make motion forecasting an especially challenging undertaking.
+
+Self-supervised learning (SSL) is an innovative approach that enables the acquisition of valuable latent features from unlabelled data. By pre-training the model on pretext tasks and pseudo-labels derived from the data, and subsequently
+
+![](images/57b65f8dd844d3a4a354152698b399846cc000fed74ee9878b0e06734a2ce236.jpg)
+
+![](images/2014c6918afe17fe6894ce1b23fd9bcfe1ace8d8d9a42f34e102e8500c9d455c.jpg)
+
+![](images/9bd0ce89de7a8c9daa92a6060cc7374a9b87e87275cc87779acfec536712271b.jpg)  
+Figure 1. Reconstruction result on Argoverse 2 validation scenario. (a) The origin scenario. (b)  $50\%$  of agents' trajectory is masked using a complementary masking strategy (either history or future is masked).  $50\%$  of the lane segments are masked randomly. (c) Scenario reconstructed by the proposed Forecast-MAE.
+
+fine-tuning on downstream tasks, SSL has demonstrated an ability to learn more extensive and adaptable latent features, leading to remarkable advancements in computer vision [3] and natural language processing (NLP) [10]. Nevertheless, despite its widespread popularity and success, there remains a notable lack of exploration of SSL in the motion forecasting domain. We have identified two principal challenges associated with integrating SSL into motion forecasting:
+
+(i) Motion forecasting pre-training requires annotated data, which sets it apart from fields such as computer vision and NLP where unlabeled raw inputs are easily accessible. In motion forecasting, we rely on annotated tracking sequences and hand-crafted high-definition maps that are typically collected by expensive onboard sensors and
+
+require human annotation labor [5, 43, 12]. This poses a challenge to scaling up self-supervised pre-training, a key aspect of SSL's success. To address this challenge, very recent work PreTraM [44] proposed generating additional rasterized map patches (28.8M) cropped from local regions of the entire HD map to train a robust map encoder with contrastive learning. Although this approach yielded notable performance improvements compared to the baseline, it is limited to models based on rasterized map representations, which have a significant performance gap compared to more recent vector-based or graph-based models. However, another pioneering work, SSL-Lanes [1], demonstrated that carefully designed pretext tasks can significantly enhance performance without using extra data by learning richer features. In this paper, we follow this approach to learn better and more generalized features using the existing dataset.
+
+(ii) The task of motion forecasting involves incorporating multiple modal inputs, such as static map features, spatiotemporal agent motion features, and semantic scene contexts [39, 26, 13, 4, 36, 50, 29, 9, 52]. While various self-supervised learning methods have proven successful in dealing with single-modal inputs such as the image [3], text [10], or point cloud [47, 32], developing pretexts that establish cross-modal interconnections is not an easy task. SSL-Lanes concentrated on designing pretext tasks for each specific input modality, such as lane node masking or agent maneuver classification. Nevertheless, they did not explore the combination of these different tasks or develop pretext tasks that explicitly involve multiple modal inputs. Authors of PreTraM drew inspiration from CLIP's [35] cross-modal contrastive learning framework involving text and images. They devised a technique for pre-training map and trajectory encoders by pairing batches of (map, trajectory) training instances. Nevertheless, their approach merely encompasses the history trajectory-map connection, thereby restricting the scope of modality interconnections to a particular type. This study confronts this challenge by utilizing a masked autoencoder framework that can assimilate all cross-modal interdependencies within a unified scene reconstruction task.
+
+The masked autoencoder (MAE) [20] has garnered significant attention due to its recent achievements in image-based self-supervised learning. This approach involves masking a portion of the input data and reconstructing the missing part using an autoencoder structure. The effectiveness of MAE has also been demonstrated in other domains, such as audio [21] and point cloud [32]. An intriguing question arises: can we extend MAE to motion forecasting? Indeed, motion forecasting itself can be viewed as a masking and reconstructing task, wherein the future trajectory of agents is masked and predicted. Based on the strong correlation between agents' historical and future trajectories and road networks, we further extend this concept to the en
+
+tire scene reconstruction. Specifically, we mask agents' history trajectory or future trajectory in a complementary manner (i.e. either history or future is masked), and randomly mask non-overlapping lane segments, shown in Figure 1. This masking scheme offers several advantages. Firstly, the model must learn how to reconstruct the future from past motion and, in turn, infer history from the future, with limited access to lane structures. This pretext task allows the model to establish a robust bidirectional relationship between past and future motion. Secondly, the model learns to reconstruct lane segments by jointly utilizing neighboring visible lanes, agents' history and future trajectories, thereby establishing a more profound cross-modal understanding.
+
+To this end, we introduce Forecast-MAE, an extension of the masked autoencoder framework specifically designed for self-supervised learning of the motion forecasting task. Our methodology comprises a novel masking design that exploits the strong interdependencies among all agents' trajectories and road networks. Despite being simple and incorporating minimal inductive bias, our proposed Forecast-MAE performs strongly on the challenging Argoverse 2 (AV2) motion forecasting benchmark [43] and significantly outperforms the previous self-supervised learning method.
+
+Our contribution can be summarized as follows:
+
+- To our best knowledge, we propose the first masked autoencoding framework for self-supervised learning on the motion forecasting task. Without extra data or pseudo-labels, our method greatly improves the performance of motion forecasting through pre-training compared to training from scratch.  
+- We introduce a straightforward yet highly effective masking scheme that facilitates the learning of bidirectional motion connections and cross-modal relationships within a single reconstruction pretext task.  
+- We show that our approach, based entirely on standard Transformers with minimal inductive bias, achieves competitive performance compared to the state-of-the-art with supervised learning on the challenging Argov-verse 2 benchmark, and significantly outperforms the previous self-supervised learning method.  
+- Our findings suggest that SSL can be a promising approach for motion forecasting, and we anticipate that this may spark greater interest in the field.
+
+# 2. Related Work
+
+Motion Forecasting. The performance of motion forecasting models has significantly advanced in recent years, primarily attributable to the amplified interest in self-driving vehicles and the widespread availability of standard benchmarks. Herein, we concisely outline three key aspects contributing to its improvements.
+
+(i) Improvement on scene representation. In the early stages, rasterized top-down semantic images are commonly
+
+utilized for scene representation, and off-the-shelf image encoders are used for learning [39, 33, 4, 15]. Although this image-based representation is simple and unified, it inevitably results in the loss of detailed structural information during rasterization. The popularity of vectorized representations has increased significantly with the introduction of VectorNet [13], owing to their higher representation capacity and significantly stronger performance. Furthermore, graphs [26, 48, 9, 16, 25] are widely used as another promising scene representation. TPCN [45], as a standalone approach, achieves impressive results by treating the agents' trajectories and lanes as the point cloud.
+
+(ii) Improvement on model architectures. Early rasterized methods naturally relied on well-established convolutional networks. Later, inspired by the impressive performance of Transformer [41], attention mechanisms have been extensively used for interaction modeling and information aggregation, given their superior flexibility and efficacy. Some works [31, 29, 52, 17] have directly incorporated transformers for forecasting and achieved satisfactory outcomes. A more recent work, MTR [36], builds on cutting-edge vision object detection architecture DETR [2], resulting in state-of-the-art performance. Advances in the graph neural network (GNN) domain are also widely explored [48, 16, 25, 9, 6, 28, 7]. LaneGCN [26] modified graph convolutional operation tailed for lane graph encoding. HDGT [24] uses the heterogeneous graph to encode different types of agents and map elements. HiVT [52], QCNet [51] and [23] explores different correlating systems.
+
+(iii) Introducing of prior knowledge. Incorporating prior knowledge to tackle the complex problem of multi-modal future prediction has become increasingly prevalent in recent literature. Several works utilize predefined candidate trajectories [33, 37] or anchor points [4, 40] by clustering the ground truth or generating with planners. Another line of research involves sampling goals within the drivable areas and utilizing a two-stage prediction pipeline [48, 9, 50, 18, 15, 16]. DCMS [46] introduces temporal consistent constraints based on the assumption that predictions should not change abruptly. However, these methods typically require additional computation or have a higher model complexity.
+
+Despite significant advancements in motion forecasting, there is a recent trend towards greater architectural complexity and utilization of prior knowledge. In this study, we explore a different direction for enhancing performance, namely self-supervised learning. By leveraging the simplicity of the MAE framework, we demonstrate that our proposed Forecast-MAE, employing a standard transformer architecture with minimal prior knowledge, can achieve competitive performance compared to state-of-the-art supervised learning-based methods with sophisticated designs.
+
+Self-supervised Learning in Motion Forecasting. There are only a few studies that explore SSL in motion forecast-
+
+ing. To the best of our knowledge, VectorNet is the earliest work that incorporates a BERT-like [10] graph completion task to better capture interactions between agents and maps. However, it is a very preliminary attempt, and the graph completion is treated as an auxiliary training objective that is jointly optimized with the motion forecasting task. PreTraM and SSL-Lanes are two recent works that systematically study SSL. The authors of PreTraM believe that the scarcity of trajectory data restricts the application of SSL in motion forecasting. They generate additional local map patches from the entire maps and leverage single-modal and cross-modal contrastive learning to pretrain the map and trajectory encoders separately. In contrast, our method adopts a completely different MAE-based framework, where representations of different modalities are learned jointly. SSL-Lanes demonstrated that SSL could learn better latent features without using extra data. It studied four pretext tasks, each focusing on one specific input modality, such as lane masking or agents' maneuver classification. However, they do not explore combining these different tasks or designing pretext tasks involving multimodal inputs. On the contrary, the proposed Forecast-MAE learns cross-modal interconnections by design and outperforms SSL-Lanes by a large margin.
+
+# 3. Methodology
+
+We propose Forecast-MAE, a simple and neat MAE-based framework for self-supervised pre-training of the motion forecasting task. The pre-training process is illustrated in Figure 2. Visible agents' history/future trajectories and lane segments are embedded as tokens and then processed with a standard transformer encoder. Following the asymmetric design of the vision MAE [20], different mask tokens are added to the decoder's input sequence and later used to reconstruct the masked trajectories and lane segments with simple prediction heads.
+
+# 3.1. Masking
+
+In contrast to all current self-supervised learning frameworks for motion forecasting, we utilize the future trajectories of agents as an additional input for pre-training. Our experiments reveal that masking future trajectories is a crucial aspect for Forecast-MAE to be effective. To begin, the road maps are initially segmented into non-overlapping lane sections. We then randomly mask a subset of lane segments according to a uniform distribution. The masking technique for agents differs slightly. Although random masking is still employed for agent trajectories, we only mask the history or future trajectory of each agent (e.g.,  $40\%$  of agents retain their history, while the remaining  $60\%$  retain their future). We refer to this process as complementary random masking. This constraint is sensible, as reconstructing trajectories from a single pose is not a meaningful pretext task
+
+![](images/ab11c8f3f5012a801b69a629aad698b376b8711c67fe9a0e9fd2db2d47256af3.jpg)  
+Figure 2. Overall pre-training scheme of our Forecast-MAE. The left part shows the masking process of an example scenario (two agents are static within the observation horizon). We randomly mask out the entire agents' history or future trajectory, as well as lane segments. The pre-training scheme is shown on the right. Only the visible history, future trajectory, and lane segments will be embedded into tokens and processed by the encoder. Three different types of mask tokens are added to the input sequence of the decoder to reconstruct history, future trajectory and lane segment, respectively.
+
+when both history and future trajectories are masked.
+
+# 3.2. Input Representation and Embedding
+
+Following the popular vectorized representation, we treat all agents' trajectories and lane segments as polylines. Specifically, we denote the history trajectories of  $N$  agents as  $A_{H} \in \mathbb{R}^{N \times T_{H} \times C_{H}}$ , where  $T_{H}$  is the number of history frames and  $C_{H}$  is the history feature channels including step-wise displacement/velocity difference, and a padding flag indicating the observation status of this frame. Similarly, the future trajectories are denoted as  $A_{F} \in \mathbb{R}^{N \times T_{F} \times C_{F}}$ , where  $T_{F}$  is the number of future frames,  $C_{F}$  is the future feature channels, including future coordinates normalized to the current position of agents and a padding flag indicating availability. The non-overlapping lane segments are denoted as  $L \in \mathbb{R}^{M \times P \times C_{L}}$ , where  $M$  is the number of lane segments within a certain radius of the target agent,  $P$  is the number of points of each polyline and  $C_{L}$  is the lane feature channels (e.g., coordinates, availability). Note that we normalize all the coordinates of each lane polyline to its geometric center.
+
+The primary goal of the embedding layer is to encode sequential features into one-dimensional vectors or tokens that can be directly processed by the standard Transformer. We use a Feature Pyramid Network (FPN) [27] similar to LaneGCN to fuse multi-scale agent motion features. 1D neighborhood attention [19] is employed at each scale to extract local motion features. Agents' historical and future features are embedded separately. To capture a broader
+
+range of the road map, we employ a lightweight mini-PointNet [34], mainly comprising MLPs and max pooling layers, to embed lane polylines. The embedding process can be formulated as
+
+$$
+T _ {H} = \operatorname {F P N} \left(A _ {H}\right), T _ {F} = \operatorname {F P N} \left(A _ {F}\right), T _ {H, F} \in \mathbb {R} ^ {N \times C} \tag {1}
+$$
+
+$$
+T _ {L} = \operatorname {M i n i P o i n t N e t} (L), T _ {L} \in \mathbb {R} ^ {M \times C}, \tag {2}
+$$
+
+where  $T_{H}, T_{F}, T_{L}$  are history, future, lane tokens respectively,  $C$  is the embedding dimension.
+
+Semantic attributions such as agent category (e.g., vehicle, pedestrian, cyclist) or lane types are initialized as learnable embeddings and added to the embedded tokens. Given that the coordinates of agents and lane features are normalized, it is crucial to include global position information in the tokens. The position embedding (PE) is implemented with a simple two-layer MLP following [47], formulated as
+
+$$
+\mathrm {P E} = \operatorname {M L P} \left(\left[ x, y, \cos (\theta), \sin (\theta) \right], \mathrm {P E} \in \mathbb {R} ^ {C} \quad (3) \right.
+$$
+
+where  $(x,y,\theta)$  is the latest observed pose of agents or the geometric center pose for lane polylines. The PE is added to the tokens before being processed by the autoencoder.
+
+# 3.3. AutoEncoder
+
+The autoencoder is entirely based on standard Transformers. The encoder consists of several Transformer blocks and only encodes concatenated visible agents and lane tokens, resulting in encoded latent tokens  $T_{E} \in$
+
+$\mathbb{R}^{(N + M)\times C}$ . Following the asymmetric autoencoder design of MAE, history, future, and lane mask tokens  $M = (M_H,M_F,M_L)$  are added together with the encoded latent tokens as the input sequence of the decoder and then output the decoded mask tokens  $M^{\prime} = (M_H^{\prime},M_F^{\prime},M_L^{\prime})$  after the decoding. Positional embeddings are added to the full input sequence, including the mask tokens. Each type of mask token is a learned vector shared by the corresponding type of masked element. The autoencoding process is formulated as
+
+$$
+T _ {E} = \operatorname {E n c o d e r} \left(\operatorname {c o n c a t} \left(T _ {H}, T _ {F}, T _ {L}\right) + \mathrm {P E}\right), \tag {4}
+$$
+
+$$
+M ^ {\prime} = \operatorname {D e c o d e r} \left(\operatorname {c o n c a t} \left(T _ {E}, M\right) + \mathrm {P E}\right). \tag {5}
+$$
+
+The decoded mask tokens are subsequently used for reconstructing the masked element through a simple prediction head, which is implemented as a linear projection layer in practice.
+
+# 3.4. Reconstruction Target
+
+The prediction heads predict the normalized 2-dimensional coordinates of history/future trajectories  $P_{H / F}$  and lane polylines  $P_L$ ,
+
+$$
+P _ {H} = \operatorname {P r e d i c t i o n H e a d} \left(M _ {H} ^ {\prime}\right), P _ {H} \in \mathbb {R} ^ {\alpha N \times T _ {H} \times 2}, \tag {6}
+$$
+
+$$
+P _ {F} = \operatorname {P r e d i c t i o n H e a d} \left(M _ {F} ^ {\prime}\right), P _ {F} \in \mathbb {R} ^ {(1 - \alpha) N \times T _ {F} \times 2}, \tag {7}
+$$
+
+$$
+P _ {L} = \operatorname {P r e d i c t i o n H e a d} \left(M _ {L} ^ {\prime}\right), P _ {L} \in \mathbb {R} ^ {\beta M \times P \times 2}, \tag {8}
+$$
+
+where  $\alpha$  is the agents' history mask ratio,  $\beta$  is the lane segments mask ratio. We use L1 loss  $\mathcal{L}_H,\mathcal{L}_F$  for trajectory reconstruction and mean squared error (MSE) loss  $\mathcal{L}_L$  for lane polyline reconstruction, and  $w_{H},w_{F},w_{L}$  correspond to the loss weight respectively. The final loss is
+
+$$
+\mathcal {L} _ {M A E} = w _ {H} \mathcal {L} _ {H} + w _ {F} \mathcal {L} _ {F} + w _ {L} \mathcal {L} _ {L}. \tag {9}
+$$
+
+# 3.5. Motion Forecasting
+
+For the target motion forecasting task, we adopt an end-to-end fine-tuning approach. During fine-tuning, the following modifications are made to the pre-training model: (1) we discard the MAE decoder and mask tokens; (2) agents' future features are eliminated from the input, and masking is not employed; (3) the pretext prediction heads are substituted with a multi-modal future decoder.
+
+Multi-modal decoder. Given the multi-modal nature of agents' behavior, motion forecasting entails producing multiple potential future predictions, distinct from the masked future reconstruction pretext task. To maintain a neat framework with minimal inductive bias, we implement the multimodal decoder using a simple three-layer MLP. A separate three-layer MLP is utilized to generate the confidence score for each prediction. The decoding process can be formulated as
+
+$$
+P _ {T r a j} = \operatorname {M L P} \left(T _ {H} ^ {\prime}\right), P _ {T r a j} \in \mathbb {R} ^ {N \times K \times T _ {F} \times 2}, \tag {10}
+$$
+
+where  $T_H'$  is the encoded history tokens and  $K$  is the number of output modes. The predicted future trajectories are normalized to each agent's latest observed position.
+
+Training loss. We adopt the widely used Huber loss for trajectory regression and cross-entropy loss for confidence classification with equal weights. The winner-take-all strategy is employed, which only optimizes the best prediction with minimal average prediction error to the ground truth. We compute the loss using all agents present in the scene.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Dataset. We evaluate the proposed framework on the recently released large-scale Argoverse 2 (AV2) dataset. This dataset includes 250K non-overlapping scenarios, divided into 199,908, 24,988, and 24,984 samples for training, validation, and testing, respectively. Each sample contains 5 seconds of history and requires a prediction of 6 seconds in the future, with a sampling rate of  $10\mathrm{Hz}$ . Every scenario includes a focal track agent that needs to be predicted, with detailed high-definition map patches provided for each sample. We choose to evaluate on the Argoverse 2 dataset as it offers the best balance between diversity and dataset size. The popular Argoverse 1 [5] dataset has a similar size but lacks scenario diversity (e.g., the majority of vehicles driving straight-forward). Conversely, Argoverse 2 is intended to be more varied and complicated. Another widely-used dataset, the Waymo Open Motion Dataset (WOMD) [12], has similar scenario complexity but only contains less than half the number of scenarios (104K). We believe that a larger and more complex dataset is more appropriate for evaluating SSL frameworks.
+
+Metrics. We use the official benchmark metrics, including minADE, minFDE, MR, and brier-minFDE, which refer to six prediction modes, if not specified.
+
+Implementation Details. Detailed model architecture and training settings are provided in the supplementary.
+
+# 4.2. Ablation Study
+
+We conduct ablation studies on the Argoverse 2 validation set. By default, the pre-training epoch is set to 40, the fine-tuning epoch to 30, the history and lane mask ratio to 0.5, and the encoder and decoder depth to 4. The pre-training is only conducted on the training set.
+
+Masking ratio. Figure 3 depicts the impact of varying masking ratios. Employing a well-balanced masking ratio, ranging from  $40\%$  to  $50\%$ , between an agent's history and future leads to the most favorable outcomes, in agreement with common sense. We posit that a balanced masking ratio for agent trajectory helps prevent the learning of biased features by the model and enhances its comprehension of
+
+![](images/4fa762b5a6b043ba053b00ec3a145ffcdb0ae25ddfd5cec6028b03e37446952e.jpg)
+
+![](images/9e5cc871af27663c6b5044dcd7722c6146275205b264e55ffaf79fa602dabc7b.jpg)  
+Figure 3. The impact of the history and lane masking ratio. The marked blue lines show the fine-tuning results on different metrics (lower is better). The dashed lines in grey correspond to the results of the baseline model (trained from scratch for 30 epochs).
+
+the bidirectional relationship between historical and future motion. This is further demonstrated by the performance of extreme history masking ratios (20% and 80%), which significantly underperform.
+
+Forecast-MAE is relatively insensitive to lane masking ratio, as a wide range of ratios (30% to 60%) perform well. Nonetheless, when the lane masking ratio exceeds 70%, performance suffers notably. The possible reason is with a masking ratio of more than 70%, most of the road structure information loses, which tremendously increases the difficulty of scene reconstruction and geometry feature extraction from the map. Conversely, when the lane masking ratio is below 20%, both ADE and FDE experience a significant increase. We deduce that the masked lanes can be easily extrapolated by nearby visible lanes when only a small subset of lanes are masked.
+
+Masking strategy. One distinctive aspect of our approach, compared to existing SSL methods, is the introduction of agents' future trajectories as additional input during pretraining. The outcomes of various inputs and masking strategies are presented in Table 3. When only lane masking is employed, the utilization of future trajectories as input makes a significant difference (minADE is 0.865 without using future, and 0.828 using future). One possible explanation is that the model can establish better connections between lanes and future trajectories through lane reconstruction, which is beneficial for the forecasting task. In-
+
+<table><tr><td>Hist. mask</td><td>Lane mask</td><td>Fut. input</td><td>Fut. mask</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>0.865</td><td>1.51</td><td>0.212</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>0.828</td><td>1.47</td><td>0.203</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>0.864</td><td>1.53</td><td>0.216</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>0.866</td><td>1.52</td><td>0.214</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>0.820</td><td>1.45</td><td>0.198</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td colspan="4">training from scratch</td><td>0.8314</td><td>1.471</td><td>0.2038</td></tr></table>
+
+Table 1. Results of different input and masking strategies. History and lane are used as input for experiments. When history and future trajectories are simultaneously masked, it is masked in a complementary manner. For other situations, we use random masking by default.  
+
+<table><tr><td>encoder depth</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>2</td><td>0.854</td><td>1.55</td><td>0.221</td></tr><tr><td>3</td><td>0.823</td><td>1.46</td><td>0.198</td></tr><tr><td>4</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td>5</td><td>0.815</td><td>1.43</td><td>0.188</td></tr></table>
+
+Table 2. Results of different encoder depth. A encoder depth of 4 offers the best performance-efficiency trade-off.
+
+terestingly, if we use the future as input and do not mask it, merely masking the history performs even worse than training from scratch (minADE 0.864/0.866 vs. 0.8314). A reasonable justification is that the dataset is intended to make the distribution of agents' future trajectories diverse and multi-modal (e.g., an agent is beginning to pass an intersection), while the historical trajectory is much simpler and more predictable. The model might take a shortcut to reconstruct the history by extrapolating the future trajectory, resulting in a failure to learn meaningful features from the agents' motion. As a result, the learned latent features are useless and even harmful for the later forecasting task. Adding future masking promptly addresses this problem, and minADE improves to 0.820 and 0.814. The proposed complementary masking strategy achieves the best performance in all metrics.
+
+Encoder depth. A relative deep encoder is necessary, as studied in Table 2. The performance improved  $4.6\%$  in terms of minADE by increasing encoder depth from 2 to 4. Adding more encoder layers does not make a significant difference. We use an encoder depth of 4 as our default setting for its better efficiency-performance trade-off.
+
+# 4.3. Results
+
+For the final leaderboard submission, we use a depth of 4 for both the decoder and encoder. The history and lane masking ratios are 0.4 and 0.5, respectively. We set the pretraining and fine-tuning epochs both to 60. Our final motion forecasting model is simple and lightweight, with only 1.9M parameters in total.
+
+<table><tr><td></td><td>Method</td><td>minADE1</td><td>minFDE1</td><td>MR1</td><td>minADE6</td><td>minFDE6</td><td>MR6</td><td>b-FDE6</td></tr><tr><td rowspan="5">Supervised Learning</td><td>THOMAS [14]</td><td>1.96</td><td>4.71</td><td>0.64</td><td>0.88</td><td>1.51</td><td>0.20</td><td>2.16</td></tr><tr><td>GoReLa [8]</td><td>1.82</td><td>4.62</td><td>0.61</td><td>0.76</td><td>1.48</td><td>0.22</td><td>2.01</td></tr><tr><td>GANet [42]</td><td>1.78</td><td>4.48</td><td>0.60</td><td>0.73</td><td>1.35</td><td>0.17</td><td>1.97</td></tr><tr><td>QML w/ ensemble [38]</td><td>1.84</td><td>4.98</td><td>0.59</td><td>0.69</td><td>1.39</td><td>0.19</td><td>1.95</td></tr><tr><td>BANet w/ ensemble [49]</td><td>1.79</td><td>4.61</td><td>0.60</td><td>0.71</td><td>1.36</td><td>0.19</td><td>1.92</td></tr><tr><td rowspan="3">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.167</td><td>5.675</td><td>0.671</td><td>0.835</td><td>1.698</td><td>0.248</td><td>2.379</td></tr><tr><td>Dist. to Inter.</td><td>2.176</td><td>5.71</td><td>0.667</td><td>0.839</td><td>1.710</td><td>0.248</td><td>2.391</td></tr><tr><td>S/F Classification</td><td>2.218</td><td>5.905</td><td>0.687</td><td>0.828</td><td>1.671</td><td>0.249</td><td>2.352</td></tr><tr><td rowspan="3">Forecast-MAE</td><td>Scratch</td><td>1.845</td><td>4.602</td><td>0.623</td><td>0.727</td><td>1.427</td><td>0.187</td><td>2.062</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.741</td><td>4.355</td><td>0.607</td><td>0.709</td><td>1.392</td><td>0.172</td><td>2.029</td></tr><tr><td>Fine-tune w/ ensemble</td><td>1.658</td><td>4.145</td><td>0.592</td><td>0.690</td><td>1.338</td><td>0.173</td><td>1.911</td></tr><tr><td rowspan="3">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.014</td><td>5.194</td><td>0.649</td><td>0.850</td><td>1.520</td><td>0.220</td><td>2.197</td></tr><tr><td>Dist. to Inter.</td><td>2.006</td><td>5.187</td><td>0.651</td><td>0.840</td><td>1.490</td><td>0.212</td><td>2.182</td></tr><tr><td>S/F Classification</td><td>2.120</td><td>5.613</td><td>0.675</td><td>0.861</td><td>1.536</td><td>0.224</td><td>2.216</td></tr><tr><td rowspan="2">Forecast-MAE</td><td>Scratch</td><td>1.813</td><td>4.570</td><td>0.622</td><td>0.811</td><td>1.436</td><td>0.189</td><td>2.074</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.755</td><td>4.388</td><td>0.609</td><td>0.801</td><td>1.409</td><td>0.178</td><td>2.042</td></tr></table>
+
+Table 3. Comparisons with previous results on the Argovesrse 2 test set (upper group) and validation set (lower group). For all the metrics, the lower is the better. We bold the best results and underline the second best results.  
+
+<table><tr><td></td><td>epochs</td><td>minADE6</td><td>minFDE6</td><td>MR6</td></tr><tr><td rowspan="3">Scratch</td><td>60</td><td>0.811</td><td>1.436</td><td>0.189</td></tr><tr><td>70</td><td>0.815</td><td>1.436</td><td>0.187</td></tr><tr><td>80</td><td>0.814</td><td>1.450</td><td>0.190</td></tr><tr><td>Fine-tune</td><td>60</td><td>0.801</td><td>1.409</td><td>0.178</td></tr></table>
+
+Table 4. Comparison with training from scratch of different training epochs. Continue increase training iterations does not further improves the performance of training from scratch.
+
+Comparison with the other SSL method. We compare our method with SSL-Lanes, as it is the only published approach that employs vector representation and SSL. We make minimal modifications to its official code base<sup>1</sup> to adapt it to the AV2 dataset. Our experiments utilize three of its pretext tasks, specifically lane making, distance to the intersection (Dist. to Inter.), and success-failure classification (S/F classification). We do not implement the maneuver classification pretext task, as AV2 lacks lane-turning information. Table 3 (lower group) displays the comparison results on the AV2 validation set. Our Forecast-MAE outperforms all SSL-Lanes variants significantly across all metrics. Notably, SSL-Lanes suffers from performance degradation between the validation and test sets, whereas our approach achieves consistent performance on both sets and even performs slightly better on the test set. This suggests that our method learns superior and more generalized features through MAE-based self-supervised pre-training.
+
+Comparison with State-of-the-art. Our Forecast-MAE, developed using standard Transformer blocks and minimal
+
+prior knowledge, demonstrates impressive performance on the leaderboard, depicted in Table 3 upper group. Particularly noteworthy is that our approach (w/o ensemble) outperforms all other methods, including ensemble models, in terms of  $\mathrm{minADE}_1$  and  $\mathrm{minFDE}_1$ , indicating its superior ability to predict the most likely future. We attribute this to our SSL pre-training scheme, which requires the model to reconstruct the most likely masked history and future trajectories. Additionally, Forecast-MAE (w/o ensemble) achieves the best  $\mathrm{minADE}_6$  among all non-ensemble methods and performs on par with QML (w/ ensemble). Through the adoption of an ensemble strategy involving 6 variants of our framework (e.g., different masking ratios, encoder depth), our ensemble model achieves the best performance among all methods across six metrics. In particular, our ensemble model outperforms the second-best (GANet) by  $7.5\%$  in terms of  $\mathrm{minFDE}_1$ .
+
+Comparison with training from scratch. The comparison results between the fine-tuned model and the model trained from scratch are presented in Table 3. It is noteworthy that the vanilla model, despite its simplicity, serves as a strong baseline. However, our fine-tuned model outperforms the baseline in all metrics, exhibiting improvements of  $5.1\%$  on  $\min\mathrm{ADE}_1$ ,  $5.7\%$  on  $\min\mathrm{FDE}_1$ ,  $2.4\%$  on  $\min\mathrm{ADE}_6$ , and  $\min\mathrm{FDE}_6$ , without the utilization of additional data or a more complex model.
+
+As we incorporate agents' future trajectories as inputs during the pre-training, a plausible concern is that the finetuned model may benefit from additional training iterations. To address this, we conduct further training of the vanilla model with more epochs using cosine learning rate decay.
+
+![](images/b9381698265ce8905c045858e6ed6d1b206a77ac5db9d9842104c9165ec181d8.jpg)  
+Figure 4. Qualitative results of Forecast-MAE The predicted trajectories  $(\mathrm{K} = 6)$  are in blue and the ground truth is in gradient pink. The bounding box in orange indicates the focal agent.
+
+<table><tr><td></td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>Scratch</td><td>0.9098</td><td>1.645</td><td>0.2346</td></tr><tr><td>Fine-tune</td><td>0.8968</td><td>1.613</td><td>0.2164</td></tr></table>
+
+Table 5. Evaluation results on different data distribution.. Models are trained or pre-trained on scenarios in Miami, Pittsburgh and Austin and validated in Dearborn, Palo-alto and Washington-DC.
+
+The results presented in Table 4 indicate that continuing to increase the training iterations fails to enhance the performance of the model trained from scratch, underscoring the importance of pre-training.
+
+Generalization ability. Our method demonstrates strong generalization ability in the AV2 benchmark, as evidenced by the results in Table 3. To further investigate this point, we design an experiment where training and testing employ different data distributions. Specifically, we partition all scenarios involving six cities in the AV2 dataset into two distinct and non-overlapping groups. We then train or pretrain the models solely on scenarios in Miami, Pittsburgh, and Austin, and evaluate them on Dearborn, Palo-Alto, and Washington-DC. Results presented in Table 5 indicate that the fine-tuned model surpasses the baseline in all metrics, signifying that self-supervised pre-training enables learning of more generalizable features.
+
+Qualitative Results. We visualize the qualitative results of our fine-tuned model on the AV2 validation set, as shown in Figure 4. We leave more results to the supplementary, due to the limited space.
+
+# 5. Conclusion
+
+We present Forecast-MAE, a simple and neat framework for self-supervised pre-training on the motion forecasting task. Based on the asymmetric architecture of MAE, we devise a scene reconstruction pretext task that utilizes a novel masking strategy. By leveraging the complementary masking of the agents' trajectories and the random masking of lane segments during the pre-training process, the model acquires the ability to capture the bidirectional agent motion features, road geometry features, and cross-modal intercon
+
+nections jointly. Our experiments on the challenging Argoverse 2 benchmark demonstrate that our Forecast-MAE surpasses supervised learning methods and previous self-supervised learning works, especially in terms of  $\min\mathrm{ADE}_1$  and  $\min\mathrm{FDE}_1$ , indicating its superior ability to predict the most likely future.
+
+Limitaion and Discussion. One constraint of our work is the lack of exploration of transfer learning or few-shot learning for the proposed method (e.g., pre-training on WMOD and fine-tuning on AV2). Such exploration is hindered by the different problem settings, namely observation/prediction horizons, of different datasets. Besides, due to the relatively limited size of publicly available motion forecasting datasets compared to those in computer vision or natural language processing, we are unable to determine whether the performance of Forecast-MAE will scale up with increased training data and model capacity. However, we are positive about this point by drawing intuition from MAE and our minimal inductive bias design. Our approach could be advantageous for autonomous driving companies with large-scale internal datasets. Although Forecast-MAE already achieves strong performance while designed to be simple, we anticipate it can be further improved. Drawing inspiration from the development of techniques such as ViT [11] to Swin-Trainsformer [30], properly incorporating inductive bias such as relative position design [52, 8, 51] or local attention [36] may further boost Forecast-MAE in terms of performance and efficiency. Another possible direction is to generate realistic traffic scenarios building upon this work. These possibilities are left for future works.
+
+Acknowledgement This work was supported by Guangdong Basic and Applied Basic Research Foundation, under project 2021B1515120032, Jiangsu Province Science and Technology Project BZ2021056, and Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (HZQB-KCZYB-2020083), awarded to Prof. Ming Liu.
+
+# References
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+                                    "content": "This study explores the application of self-supervised learning (SSL) to the task of motion forecasting, an area that has not yet been extensively investigated despite the widespread success of SSL in computer vision and natural language processing. To address this gap, we introduce Forecast-MAE, an extension of the mask autoencoders framework that is specifically designed for self-supervised learning of the motion forecasting task. Our approach includes a novel masking strategy that leverages the strong interconnections between agents' trajectories and road networks, involving complementary masking of agents' future or history trajectories and random masking of lane segments. Our experiments on the challenging Argoverse 2 motion forecasting benchmark show that Forecast-MAE, which utilizes standard Transformer blocks with minimal inductive bias, achieves competitive performance compared to state-of-the-art methods that rely on supervised learning and sophisticated designs. Moreover, it outperforms the previous self-supervised learning method by a significant margin. Code is available at https://github.com/jchengai/forecast-mae."
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+                                    "content": "Motion forecasting is a rapidly developing research field that plays a critical role in advanced autonomous driving systems [22]. This task involves predicting the future trajectories of other vehicles and pedestrians, while taking into account the intricate interactions and road layouts. The inherent multi-modal driving behaviors of agents, combined with diverse road networks, make motion forecasting an especially challenging undertaking."
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+                                            "type": "text",
+                                            "content": "Figure 1. Reconstruction result on Argoverse 2 validation scenario. (a) The origin scenario. (b) "
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+                                            "content": " of agents' trajectory is masked using a complementary masking strategy (either history or future is masked). "
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+                                            "content": " of the lane segments are masked randomly. (c) Scenario reconstructed by the proposed Forecast-MAE."
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+                                    "content": "fine-tuning on downstream tasks, SSL has demonstrated an ability to learn more extensive and adaptable latent features, leading to remarkable advancements in computer vision [3] and natural language processing (NLP) [10]. Nevertheless, despite its widespread popularity and success, there remains a notable lack of exploration of SSL in the motion forecasting domain. We have identified two principal challenges associated with integrating SSL into motion forecasting:"
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+                                    "content": "(i) Motion forecasting pre-training requires annotated data, which sets it apart from fields such as computer vision and NLP where unlabeled raw inputs are easily accessible. In motion forecasting, we rely on annotated tracking sequences and hand-crafted high-definition maps that are typically collected by expensive onboard sensors and"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+                                }
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+                                    "type": "text",
+                                    "content": "*Corresponding author: Ming Liu"
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+                                    "type": "text",
+                                    "content": "require human annotation labor [5, 43, 12]. This poses a challenge to scaling up self-supervised pre-training, a key aspect of SSL's success. To address this challenge, very recent work PreTraM [44] proposed generating additional rasterized map patches (28.8M) cropped from local regions of the entire HD map to train a robust map encoder with contrastive learning. Although this approach yielded notable performance improvements compared to the baseline, it is limited to models based on rasterized map representations, which have a significant performance gap compared to more recent vector-based or graph-based models. However, another pioneering work, SSL-Lanes [1], demonstrated that carefully designed pretext tasks can significantly enhance performance without using extra data by learning richer features. In this paper, we follow this approach to learn better and more generalized features using the existing dataset."
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+                                    "content": "(ii) The task of motion forecasting involves incorporating multiple modal inputs, such as static map features, spatiotemporal agent motion features, and semantic scene contexts [39, 26, 13, 4, 36, 50, 29, 9, 52]. While various self-supervised learning methods have proven successful in dealing with single-modal inputs such as the image [3], text [10], or point cloud [47, 32], developing pretexts that establish cross-modal interconnections is not an easy task. SSL-Lanes concentrated on designing pretext tasks for each specific input modality, such as lane node masking or agent maneuver classification. Nevertheless, they did not explore the combination of these different tasks or develop pretext tasks that explicitly involve multiple modal inputs. Authors of PreTraM drew inspiration from CLIP's [35] cross-modal contrastive learning framework involving text and images. They devised a technique for pre-training map and trajectory encoders by pairing batches of (map, trajectory) training instances. Nevertheless, their approach merely encompasses the history trajectory-map connection, thereby restricting the scope of modality interconnections to a particular type. This study confronts this challenge by utilizing a masked autoencoder framework that can assimilate all cross-modal interdependencies within a unified scene reconstruction task."
+                                }
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+                                    "content": "The masked autoencoder (MAE) [20] has garnered significant attention due to its recent achievements in image-based self-supervised learning. This approach involves masking a portion of the input data and reconstructing the missing part using an autoencoder structure. The effectiveness of MAE has also been demonstrated in other domains, such as audio [21] and point cloud [32]. An intriguing question arises: can we extend MAE to motion forecasting? Indeed, motion forecasting itself can be viewed as a masking and reconstructing task, wherein the future trajectory of agents is masked and predicted. Based on the strong correlation between agents' historical and future trajectories and road networks, we further extend this concept to the en"
+                                }
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+                                    "type": "text",
+                                    "content": "tire scene reconstruction. Specifically, we mask agents' history trajectory or future trajectory in a complementary manner (i.e. either history or future is masked), and randomly mask non-overlapping lane segments, shown in Figure 1. This masking scheme offers several advantages. Firstly, the model must learn how to reconstruct the future from past motion and, in turn, infer history from the future, with limited access to lane structures. This pretext task allows the model to establish a robust bidirectional relationship between past and future motion. Secondly, the model learns to reconstruct lane segments by jointly utilizing neighboring visible lanes, agents' history and future trajectories, thereby establishing a more profound cross-modal understanding."
+                                }
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+                                    "content": "To this end, we introduce Forecast-MAE, an extension of the masked autoencoder framework specifically designed for self-supervised learning of the motion forecasting task. Our methodology comprises a novel masking design that exploits the strong interdependencies among all agents' trajectories and road networks. Despite being simple and incorporating minimal inductive bias, our proposed Forecast-MAE performs strongly on the challenging Argoverse 2 (AV2) motion forecasting benchmark [43] and significantly outperforms the previous self-supervised learning method."
+                                }
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+                                    "content": "Our contribution can be summarized as follows:"
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+                                            "type": "text",
+                                            "content": "- To our best knowledge, we propose the first masked autoencoding framework for self-supervised learning on the motion forecasting task. Without extra data or pseudo-labels, our method greatly improves the performance of motion forecasting through pre-training compared to training from scratch."
+                                        }
+                                    ]
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+                                            "type": "text",
+                                            "content": "- We introduce a straightforward yet highly effective masking scheme that facilitates the learning of bidirectional motion connections and cross-modal relationships within a single reconstruction pretext task."
+                                        }
+                                    ]
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+                                            "type": "text",
+                                            "content": "- We show that our approach, based entirely on standard Transformers with minimal inductive bias, achieves competitive performance compared to the state-of-the-art with supervised learning on the challenging Argov-verse 2 benchmark, and significantly outperforms the previous self-supervised learning method."
+                                        }
+                                    ]
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+                                            "type": "text",
+                                            "content": "- Our findings suggest that SSL can be a promising approach for motion forecasting, and we anticipate that this may spark greater interest in the field."
+                                        }
+                                    ]
+                                }
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+                            "index": 9
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+                                    "content": "2. Related Work"
+                                }
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+                                    "type": "text",
+                                    "content": "Motion Forecasting. The performance of motion forecasting models has significantly advanced in recent years, primarily attributable to the amplified interest in self-driving vehicles and the widespread availability of standard benchmarks. Herein, we concisely outline three key aspects contributing to its improvements."
+                                }
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+                                    "content": "(i) Improvement on scene representation. In the early stages, rasterized top-down semantic images are commonly"
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+                                    "type": "text",
+                                    "content": "utilized for scene representation, and off-the-shelf image encoders are used for learning [39, 33, 4, 15]. Although this image-based representation is simple and unified, it inevitably results in the loss of detailed structural information during rasterization. The popularity of vectorized representations has increased significantly with the introduction of VectorNet [13], owing to their higher representation capacity and significantly stronger performance. Furthermore, graphs [26, 48, 9, 16, 25] are widely used as another promising scene representation. TPCN [45], as a standalone approach, achieves impressive results by treating the agents' trajectories and lanes as the point cloud."
+                                }
+                            ]
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+                    ],
+                    "index": 0
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+                                    "content": "(ii) Improvement on model architectures. Early rasterized methods naturally relied on well-established convolutional networks. Later, inspired by the impressive performance of Transformer [41], attention mechanisms have been extensively used for interaction modeling and information aggregation, given their superior flexibility and efficacy. Some works [31, 29, 52, 17] have directly incorporated transformers for forecasting and achieved satisfactory outcomes. A more recent work, MTR [36], builds on cutting-edge vision object detection architecture DETR [2], resulting in state-of-the-art performance. Advances in the graph neural network (GNN) domain are also widely explored [48, 16, 25, 9, 6, 28, 7]. LaneGCN [26] modified graph convolutional operation tailed for lane graph encoding. HDGT [24] uses the heterogeneous graph to encode different types of agents and map elements. HiVT [52], QCNet [51] and [23] explores different correlating systems."
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+                                    "type": "text",
+                                    "content": "(iii) Introducing of prior knowledge. Incorporating prior knowledge to tackle the complex problem of multi-modal future prediction has become increasingly prevalent in recent literature. Several works utilize predefined candidate trajectories [33, 37] or anchor points [4, 40] by clustering the ground truth or generating with planners. Another line of research involves sampling goals within the drivable areas and utilizing a two-stage prediction pipeline [48, 9, 50, 18, 15, 16]. DCMS [46] introduces temporal consistent constraints based on the assumption that predictions should not change abruptly. However, these methods typically require additional computation or have a higher model complexity."
+                                }
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+                                    "content": "Despite significant advancements in motion forecasting, there is a recent trend towards greater architectural complexity and utilization of prior knowledge. In this study, we explore a different direction for enhancing performance, namely self-supervised learning. By leveraging the simplicity of the MAE framework, we demonstrate that our proposed Forecast-MAE, employing a standard transformer architecture with minimal prior knowledge, can achieve competitive performance compared to state-of-the-art supervised learning-based methods with sophisticated designs."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "Self-supervised Learning in Motion Forecasting. There are only a few studies that explore SSL in motion forecast-"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "ing. To the best of our knowledge, VectorNet is the earliest work that incorporates a BERT-like [10] graph completion task to better capture interactions between agents and maps. However, it is a very preliminary attempt, and the graph completion is treated as an auxiliary training objective that is jointly optimized with the motion forecasting task. PreTraM and SSL-Lanes are two recent works that systematically study SSL. The authors of PreTraM believe that the scarcity of trajectory data restricts the application of SSL in motion forecasting. They generate additional local map patches from the entire maps and leverage single-modal and cross-modal contrastive learning to pretrain the map and trajectory encoders separately. In contrast, our method adopts a completely different MAE-based framework, where representations of different modalities are learned jointly. SSL-Lanes demonstrated that SSL could learn better latent features without using extra data. It studied four pretext tasks, each focusing on one specific input modality, such as lane masking or agents' maneuver classification. However, they do not explore combining these different tasks or designing pretext tasks involving multimodal inputs. On the contrary, the proposed Forecast-MAE learns cross-modal interconnections by design and outperforms SSL-Lanes by a large margin."
+                                }
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+                                    "type": "text",
+                                    "content": "3. Methodology"
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+                                    "content": "We propose Forecast-MAE, a simple and neat MAE-based framework for self-supervised pre-training of the motion forecasting task. The pre-training process is illustrated in Figure 2. Visible agents' history/future trajectories and lane segments are embedded as tokens and then processed with a standard transformer encoder. Following the asymmetric design of the vision MAE [20], different mask tokens are added to the decoder's input sequence and later used to reconstruct the masked trajectories and lane segments with simple prediction heads."
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+                                    "content": "3.1. Masking"
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+                                    "content": "In contrast to all current self-supervised learning frameworks for motion forecasting, we utilize the future trajectories of agents as an additional input for pre-training. Our experiments reveal that masking future trajectories is a crucial aspect for Forecast-MAE to be effective. To begin, the road maps are initially segmented into non-overlapping lane sections. We then randomly mask a subset of lane segments according to a uniform distribution. The masking technique for agents differs slightly. Although random masking is still employed for agent trajectories, we only mask the history or future trajectory of each agent (e.g., "
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+                                    "type": "text",
+                                    "content": " retain their future). We refer to this process as complementary random masking. This constraint is sensible, as reconstructing trajectories from a single pose is not a meaningful pretext task"
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+                                            "content": "Figure 2. Overall pre-training scheme of our Forecast-MAE. The left part shows the masking process of an example scenario (two agents are static within the observation horizon). We randomly mask out the entire agents' history or future trajectory, as well as lane segments. The pre-training scheme is shown on the right. Only the visible history, future trajectory, and lane segments will be embedded into tokens and processed by the encoder. Three different types of mask tokens are added to the input sequence of the decoder to reconstruct history, future trajectory and lane segment, respectively."
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+                                    "content": "when both history and future trajectories are masked."
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+                                    "content": "Following the popular vectorized representation, we treat all agents' trajectories and lane segments as polylines. Specifically, we denote the history trajectories of "
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+                                    "content": " agents as "
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+                                    "type": "inline_equation",
+                                    "content": "A_{H} \\in \\mathbb{R}^{N \\times T_{H} \\times C_{H}}"
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+                                    "content": "C_{L}"
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+                                {
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+                                    "type": "text",
+                                    "content": " is the lane feature channels (e.g., coordinates, availability). Note that we normalize all the coordinates of each lane polyline to its geometric center."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The primary goal of the embedding layer is to encode sequential features into one-dimensional vectors or tokens that can be directly processed by the standard Transformer. We use a Feature Pyramid Network (FPN) [27] similar to LaneGCN to fuse multi-scale agent motion features. 1D neighborhood attention [19] is employed at each scale to extract local motion features. Agents' historical and future features are embedded separately. To capture a broader"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "range of the road map, we employ a lightweight mini-PointNet [34], mainly comprising MLPs and max pooling layers, to embed lane polylines. The embedding process can be formulated as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "T _ {H} = \\operatorname {F P N} \\left(A _ {H}\\right), T _ {F} = \\operatorname {F P N} \\left(A _ {F}\\right), T _ {H, F} \\in \\mathbb {R} ^ {N \\times C} \\tag {1}",
+                                    "image_path": "e158a2465228427568a498cf1ccbbdfe95d77204198b57e094671383e644280e.jpg"
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+                                    "content": "T _ {L} = \\operatorname {M i n i P o i n t N e t} (L), T _ {L} \\in \\mathbb {R} ^ {M \\times C}, \\tag {2}",
+                                    "image_path": "53c52d43386cb6e96706ba3e8b34f77cadc497eaf50447c06d010aa01531aa37.jpg"
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+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "T_{H}, T_{F}, T_{L}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " are history, future, lane tokens respectively, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the embedding dimension."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Semantic attributions such as agent category (e.g., vehicle, pedestrian, cyclist) or lane types are initialized as learnable embeddings and added to the embedded tokens. Given that the coordinates of agents and lane features are normalized, it is crucial to include global position information in the tokens. The position embedding (PE) is implemented with a simple two-layer MLP following [47], formulated as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {P E} = \\operatorname {M L P} \\left(\\left[ x, y, \\cos (\\theta), \\sin (\\theta) \\right], \\mathrm {P E} \\in \\mathbb {R} ^ {C} \\quad (3) \\right.",
+                                    "image_path": "0d9ee616f43896befd045735f9e72502e0004a1da3020719328ac6716cf95f1c.jpg"
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "(x,y,\\theta)"
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+                                    "type": "text",
+                                    "content": " is the latest observed pose of agents or the geometric center pose for lane polylines. The PE is added to the tokens before being processed by the autoencoder."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
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+                                    "content": "3.3. AutoEncoder"
+                                }
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+                                    "type": "text",
+                                    "content": "The autoencoder is entirely based on standard Transformers. The encoder consists of several Transformer blocks and only encodes concatenated visible agents and lane tokens, resulting in encoded latent tokens "
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+                                    "type": "inline_equation",
+                                    "content": "T_{E} \\in"
+                                }
+                            ]
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+                }
+            ],
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{(N + M)\\times C}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Following the asymmetric autoencoder design of MAE, history, future, and lane mask tokens "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "M = (M_H,M_F,M_L)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are added together with the encoded latent tokens as the input sequence of the decoder and then output the decoded mask tokens "
+                                },
+                                {
+                                    "bbox": [
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+                                        71,
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+                                    "type": "inline_equation",
+                                    "content": "M^{\\prime} = (M_H^{\\prime},M_F^{\\prime},M_L^{\\prime})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        71,
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+                                    "type": "text",
+                                    "content": " after the decoding. Positional embeddings are added to the full input sequence, including the mask tokens. Each type of mask token is a learned vector shared by the corresponding type of masked element. The autoencoding process is formulated as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "type": "interline_equation",
+                                    "content": "T _ {E} = \\operatorname {E n c o d e r} \\left(\\operatorname {c o n c a t} \\left(T _ {H}, T _ {F}, T _ {L}\\right) + \\mathrm {P E}\\right), \\tag {4}",
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+                                    "content": "M ^ {\\prime} = \\operatorname {D e c o d e r} \\left(\\operatorname {c o n c a t} \\left(T _ {E}, M\\right) + \\mathrm {P E}\\right). \\tag {5}",
+                                    "image_path": "a81c2f4e937564c802fc10c10ea65cb100a20e1514eb4e6e2bec788066b063de.jpg"
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+                                    "content": "The decoded mask tokens are subsequently used for reconstructing the masked element through a simple prediction head, which is implemented as a linear projection layer in practice."
+                                }
+                            ]
+                        }
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+                                    "content": "3.4. Reconstruction Target"
+                                }
+                            ]
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "The prediction heads predict the normalized 2-dimensional coordinates of history/future trajectories "
+                                },
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+                                    "content": "P_{H / F}"
+                                },
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+                                    "type": "text",
+                                    "content": " and lane polylines "
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+                                    "type": "interline_equation",
+                                    "content": "P _ {H} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {H} ^ {\\prime}\\right), P _ {H} \\in \\mathbb {R} ^ {\\alpha N \\times T _ {H} \\times 2}, \\tag {6}",
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+                                    "content": "P _ {F} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {F} ^ {\\prime}\\right), P _ {F} \\in \\mathbb {R} ^ {(1 - \\alpha) N \\times T _ {F} \\times 2}, \\tag {7}",
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+                                    "type": "interline_equation",
+                                    "content": "P _ {L} = \\operatorname {P r e d i c t i o n H e a d} \\left(M _ {L} ^ {\\prime}\\right), P _ {L} \\in \\mathbb {R} ^ {\\beta M \\times P \\times 2}, \\tag {8}",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the agents' history mask ratio, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the lane segments mask ratio. We use L1 loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_H,\\mathcal{L}_F"
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+                                    "type": "text",
+                                    "content": " for trajectory reconstruction and mean squared error (MSE) loss "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_L"
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+                                    "type": "text",
+                                    "content": " for lane polyline reconstruction, and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "w_{H},w_{F},w_{L}"
+                                },
+                                {
+                                    "bbox": [
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+                                        396,
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+                                    ],
+                                    "type": "text",
+                                    "content": " correspond to the loss weight respectively. The final loss is"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {M A E} = w _ {H} \\mathcal {L} _ {H} + w _ {F} \\mathcal {L} _ {F} + w _ {L} \\mathcal {L} _ {L}. \\tag {9}",
+                                    "image_path": "194d0fe88ab4a926b631a2486760d588a11282b9149a1cc246ee8a3b61178458.jpg"
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+                                    "type": "text",
+                                    "content": "3.5. Motion Forecasting"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "For the target motion forecasting task, we adopt an end-to-end fine-tuning approach. During fine-tuning, the following modifications are made to the pre-training model: (1) we discard the MAE decoder and mask tokens; (2) agents' future features are eliminated from the input, and masking is not employed; (3) the pretext prediction heads are substituted with a multi-modal future decoder."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Multi-modal decoder. Given the multi-modal nature of agents' behavior, motion forecasting entails producing multiple potential future predictions, distinct from the masked future reconstruction pretext task. To maintain a neat framework with minimal inductive bias, we implement the multimodal decoder using a simple three-layer MLP. A separate three-layer MLP is utilized to generate the confidence score for each prediction. The decoding process can be formulated as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "P _ {T r a j} = \\operatorname {M L P} \\left(T _ {H} ^ {\\prime}\\right), P _ {T r a j} \\in \\mathbb {R} ^ {N \\times K \\times T _ {F} \\times 2}, \\tag {10}",
+                                    "image_path": "249cdf7548911b265d818cf5b925fbcd12c6504ac2c25d417ce51f4d7ad13f01.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "T_H'"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the encoded history tokens and "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the number of output modes. The predicted future trajectories are normalized to each agent's latest observed position."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Training loss. We adopt the widely used Huber loss for trajectory regression and cross-entropy loss for confidence classification with equal weights. The winner-take-all strategy is employed, which only optimizes the best prediction with minimal average prediction error to the ground truth. We compute the loss using all agents present in the scene."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Experimental Setup"
+                                }
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+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Dataset. We evaluate the proposed framework on the recently released large-scale Argoverse 2 (AV2) dataset. This dataset includes 250K non-overlapping scenarios, divided into 199,908, 24,988, and 24,984 samples for training, validation, and testing, respectively. Each sample contains 5 seconds of history and requires a prediction of 6 seconds in the future, with a sampling rate of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "inline_equation",
+                                    "content": "10\\mathrm{Hz}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Every scenario includes a focal track agent that needs to be predicted, with detailed high-definition map patches provided for each sample. We choose to evaluate on the Argoverse 2 dataset as it offers the best balance between diversity and dataset size. The popular Argoverse 1 [5] dataset has a similar size but lacks scenario diversity (e.g., the majority of vehicles driving straight-forward). Conversely, Argoverse 2 is intended to be more varied and complicated. Another widely-used dataset, the Waymo Open Motion Dataset (WOMD) [12], has similar scenario complexity but only contains less than half the number of scenarios (104K). We believe that a larger and more complex dataset is more appropriate for evaluating SSL frameworks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
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+                {
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+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Metrics. We use the official benchmark metrics, including minADE, minFDE, MR, and brier-minFDE, which refer to six prediction modes, if not specified."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Implementation Details. Detailed model architecture and training settings are provided in the supplementary."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
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+                                    "type": "text",
+                                    "content": "4.2. Ablation Study"
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+                    "index": 22
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+                                    "type": "text",
+                                    "content": "We conduct ablation studies on the Argoverse 2 validation set. By default, the pre-training epoch is set to 40, the fine-tuning epoch to 30, the history and lane mask ratio to 0.5, and the encoder and decoder depth to 4. The pre-training is only conducted on the training set."
+                                }
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+                                    "content": "Masking ratio. Figure 3 depicts the impact of varying masking ratios. Employing a well-balanced masking ratio, ranging from "
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+                                    "type": "text",
+                                    "content": ", between an agent's history and future leads to the most favorable outcomes, in agreement with common sense. We posit that a balanced masking ratio for agent trajectory helps prevent the learning of biased features by the model and enhances its comprehension of"
+                                }
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+                                            "content": "Figure 3. The impact of the history and lane masking ratio. The marked blue lines show the fine-tuning results on different metrics (lower is better). The dashed lines in grey correspond to the results of the baseline model (trained from scratch for 30 epochs)."
+                                        }
+                                    ]
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+                                    "type": "text",
+                                    "content": "the bidirectional relationship between historical and future motion. This is further demonstrated by the performance of extreme history masking ratios (20% and 80%), which significantly underperform."
+                                }
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+                                    "content": "Forecast-MAE is relatively insensitive to lane masking ratio, as a wide range of ratios (30% to 60%) perform well. Nonetheless, when the lane masking ratio exceeds 70%, performance suffers notably. The possible reason is with a masking ratio of more than 70%, most of the road structure information loses, which tremendously increases the difficulty of scene reconstruction and geometry feature extraction from the map. Conversely, when the lane masking ratio is below 20%, both ADE and FDE experience a significant increase. We deduce that the masked lanes can be easily extrapolated by nearby visible lanes when only a small subset of lanes are masked."
+                                }
+                            ]
+                        }
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+                    "index": 4
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+                                    "type": "text",
+                                    "content": "Masking strategy. One distinctive aspect of our approach, compared to existing SSL methods, is the introduction of agents' future trajectories as additional input during pretraining. The outcomes of various inputs and masking strategies are presented in Table 3. When only lane masking is employed, the utilization of future trajectories as input makes a significant difference (minADE is 0.865 without using future, and 0.828 using future). One possible explanation is that the model can establish better connections between lanes and future trajectories through lane reconstruction, which is beneficial for the forecasting task. In-"
+                                }
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+                                            "html": "<table><tr><td>Hist. mask</td><td>Lane mask</td><td>Fut. input</td><td>Fut. mask</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td></td><td>✓</td><td></td><td></td><td>0.865</td><td>1.51</td><td>0.212</td></tr><tr><td></td><td>✓</td><td>✓</td><td></td><td>0.828</td><td>1.47</td><td>0.203</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>0.864</td><td>1.53</td><td>0.216</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>0.866</td><td>1.52</td><td>0.214</td></tr><tr><td></td><td>✓</td><td>✓</td><td>✓</td><td>0.820</td><td>1.45</td><td>0.198</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td colspan=\"4\">training from scratch</td><td>0.8314</td><td>1.471</td><td>0.2038</td></tr></table>",
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+                                            "content": "Table 1. Results of different input and masking strategies. History and lane are used as input for experiments. When history and future trajectories are simultaneously masked, it is masked in a complementary manner. For other situations, we use random masking by default."
+                                        }
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+                                            "html": "<table><tr><td>encoder depth</td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>2</td><td>0.854</td><td>1.55</td><td>0.221</td></tr><tr><td>3</td><td>0.823</td><td>1.46</td><td>0.198</td></tr><tr><td>4</td><td>0.814</td><td>1.44</td><td>0.189</td></tr><tr><td>5</td><td>0.815</td><td>1.43</td><td>0.188</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 2. Results of different encoder depth. A encoder depth of 4 offers the best performance-efficiency trade-off."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "terestingly, if we use the future as input and do not mask it, merely masking the history performs even worse than training from scratch (minADE 0.864/0.866 vs. 0.8314). A reasonable justification is that the dataset is intended to make the distribution of agents' future trajectories diverse and multi-modal (e.g., an agent is beginning to pass an intersection), while the historical trajectory is much simpler and more predictable. The model might take a shortcut to reconstruct the history by extrapolating the future trajectory, resulting in a failure to learn meaningful features from the agents' motion. As a result, the learned latent features are useless and even harmful for the later forecasting task. Adding future masking promptly addresses this problem, and minADE improves to 0.820 and 0.814. The proposed complementary masking strategy achieves the best performance in all metrics."
+                                }
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+                                    "type": "text",
+                                    "content": "Encoder depth. A relative deep encoder is necessary, as studied in Table 2. The performance improved "
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+                                {
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+                                    "type": "text",
+                                    "content": " in terms of minADE by increasing encoder depth from 2 to 4. Adding more encoder layers does not make a significant difference. We use an encoder depth of 4 as our default setting for its better efficiency-performance trade-off."
+                                }
+                            ]
+                        }
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+                    "index": 11
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+                                    "type": "text",
+                                    "content": "4.3. Results"
+                                }
+                            ]
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+                    "index": 12
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+                {
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+                                    "content": "For the final leaderboard submission, we use a depth of 4 for both the decoder and encoder. The history and lane masking ratios are 0.4 and 0.5, respectively. We set the pretraining and fine-tuning epochs both to 60. Our final motion forecasting model is simple and lightweight, with only 1.9M parameters in total."
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+                                            "html": "<table><tr><td></td><td>Method</td><td>minADE1</td><td>minFDE1</td><td>MR1</td><td>minADE6</td><td>minFDE6</td><td>MR6</td><td>b-FDE6</td></tr><tr><td rowspan=\"5\">Supervised Learning</td><td>THOMAS [14]</td><td>1.96</td><td>4.71</td><td>0.64</td><td>0.88</td><td>1.51</td><td>0.20</td><td>2.16</td></tr><tr><td>GoReLa [8]</td><td>1.82</td><td>4.62</td><td>0.61</td><td>0.76</td><td>1.48</td><td>0.22</td><td>2.01</td></tr><tr><td>GANet [42]</td><td>1.78</td><td>4.48</td><td>0.60</td><td>0.73</td><td>1.35</td><td>0.17</td><td>1.97</td></tr><tr><td>QML w/ ensemble [38]</td><td>1.84</td><td>4.98</td><td>0.59</td><td>0.69</td><td>1.39</td><td>0.19</td><td>1.95</td></tr><tr><td>BANet w/ ensemble [49]</td><td>1.79</td><td>4.61</td><td>0.60</td><td>0.71</td><td>1.36</td><td>0.19</td><td>1.92</td></tr><tr><td rowspan=\"3\">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.167</td><td>5.675</td><td>0.671</td><td>0.835</td><td>1.698</td><td>0.248</td><td>2.379</td></tr><tr><td>Dist. to Inter.</td><td>2.176</td><td>5.71</td><td>0.667</td><td>0.839</td><td>1.710</td><td>0.248</td><td>2.391</td></tr><tr><td>S/F Classification</td><td>2.218</td><td>5.905</td><td>0.687</td><td>0.828</td><td>1.671</td><td>0.249</td><td>2.352</td></tr><tr><td rowspan=\"3\">Forecast-MAE</td><td>Scratch</td><td>1.845</td><td>4.602</td><td>0.623</td><td>0.727</td><td>1.427</td><td>0.187</td><td>2.062</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.741</td><td>4.355</td><td>0.607</td><td>0.709</td><td>1.392</td><td>0.172</td><td>2.029</td></tr><tr><td>Fine-tune w/ ensemble</td><td>1.658</td><td>4.145</td><td>0.592</td><td>0.690</td><td>1.338</td><td>0.173</td><td>1.911</td></tr><tr><td rowspan=\"3\">SSL-Lanes [1]</td><td>Lane Masking</td><td>2.014</td><td>5.194</td><td>0.649</td><td>0.850</td><td>1.520</td><td>0.220</td><td>2.197</td></tr><tr><td>Dist. to Inter.</td><td>2.006</td><td>5.187</td><td>0.651</td><td>0.840</td><td>1.490</td><td>0.212</td><td>2.182</td></tr><tr><td>S/F Classification</td><td>2.120</td><td>5.613</td><td>0.675</td><td>0.861</td><td>1.536</td><td>0.224</td><td>2.216</td></tr><tr><td rowspan=\"2\">Forecast-MAE</td><td>Scratch</td><td>1.813</td><td>4.570</td><td>0.622</td><td>0.811</td><td>1.436</td><td>0.189</td><td>2.074</td></tr><tr><td>Fine-tune w/o ensemble</td><td>1.755</td><td>4.388</td><td>0.609</td><td>0.801</td><td>1.409</td><td>0.178</td><td>2.042</td></tr></table>",
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+                            "index": 0,
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Table 3. Comparisons with previous results on the Argovesrse 2 test set (upper group) and validation set (lower group). For all the metrics, the lower is the better. We bold the best results and underline the second best results."
+                                        }
+                                    ]
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+                                            "html": "<table><tr><td></td><td>epochs</td><td>minADE6</td><td>minFDE6</td><td>MR6</td></tr><tr><td rowspan=\"3\">Scratch</td><td>60</td><td>0.811</td><td>1.436</td><td>0.189</td></tr><tr><td>70</td><td>0.815</td><td>1.436</td><td>0.187</td></tr><tr><td>80</td><td>0.814</td><td>1.450</td><td>0.190</td></tr><tr><td>Fine-tune</td><td>60</td><td>0.801</td><td>1.409</td><td>0.178</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 4. Comparison with training from scratch of different training epochs. Continue increase training iterations does not further improves the performance of training from scratch."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Comparison with the other SSL method. We compare our method with SSL-Lanes, as it is the only published approach that employs vector representation and SSL. We make minimal modifications to its official code base<sup>1</sup> to adapt it to the AV2 dataset. Our experiments utilize three of its pretext tasks, specifically lane making, distance to the intersection (Dist. to Inter.), and success-failure classification (S/F classification). We do not implement the maneuver classification pretext task, as AV2 lacks lane-turning information. Table 3 (lower group) displays the comparison results on the AV2 validation set. Our Forecast-MAE outperforms all SSL-Lanes variants significantly across all metrics. Notably, SSL-Lanes suffers from performance degradation between the validation and test sets, whereas our approach achieves consistent performance on both sets and even performs slightly better on the test set. This suggests that our method learns superior and more generalized features through MAE-based self-supervised pre-training."
+                                }
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+                                    "type": "text",
+                                    "content": "Comparison with State-of-the-art. Our Forecast-MAE, developed using standard Transformer blocks and minimal"
+                                }
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+                                    "type": "text",
+                                    "content": "prior knowledge, demonstrates impressive performance on the leaderboard, depicted in Table 3 upper group. Particularly noteworthy is that our approach (w/o ensemble) outperforms all other methods, including ensemble models, in terms of "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", indicating its superior ability to predict the most likely future. We attribute this to our SSL pre-training scheme, which requires the model to reconstruct the most likely masked history and future trajectories. Additionally, Forecast-MAE (w/o ensemble) achieves the best "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " among all non-ensemble methods and performs on par with QML (w/ ensemble). Through the adoption of an ensemble strategy involving 6 variants of our framework (e.g., different masking ratios, encoder depth), our ensemble model achieves the best performance among all methods across six metrics. In particular, our ensemble model outperforms the second-best (GANet) by "
+                                },
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+                                    "type": "text",
+                                    "content": " in terms of "
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+                                    "content": "As we incorporate agents' future trajectories as inputs during the pre-training, a plausible concern is that the finetuned model may benefit from additional training iterations. To address this, we conduct further training of the vanilla model with more epochs using cosine learning rate decay."
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+                                            "html": "<table><tr><td></td><td>minADE</td><td>minFDE</td><td>MR</td></tr><tr><td>Scratch</td><td>0.9098</td><td>1.645</td><td>0.2346</td></tr><tr><td>Fine-tune</td><td>0.8968</td><td>1.613</td><td>0.2164</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 5. Evaluation results on different data distribution.. Models are trained or pre-trained on scenarios in Miami, Pittsburgh and Austin and validated in Dearborn, Palo-alto and Washington-DC."
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+                                    "type": "text",
+                                    "content": "The results presented in Table 4 indicate that continuing to increase the training iterations fails to enhance the performance of the model trained from scratch, underscoring the importance of pre-training."
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+                                    "type": "text",
+                                    "content": "Generalization ability. Our method demonstrates strong generalization ability in the AV2 benchmark, as evidenced by the results in Table 3. To further investigate this point, we design an experiment where training and testing employ different data distributions. Specifically, we partition all scenarios involving six cities in the AV2 dataset into two distinct and non-overlapping groups. We then train or pretrain the models solely on scenarios in Miami, Pittsburgh, and Austin, and evaluate them on Dearborn, Palo-Alto, and Washington-DC. Results presented in Table 5 indicate that the fine-tuned model surpasses the baseline in all metrics, signifying that self-supervised pre-training enables learning of more generalizable features."
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+                                    "type": "text",
+                                    "content": "Qualitative Results. We visualize the qualitative results of our fine-tuned model on the AV2 validation set, as shown in Figure 4. We leave more results to the supplementary, due to the limited space."
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+                                    "content": "5. Conclusion"
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+                                    "content": "We present Forecast-MAE, a simple and neat framework for self-supervised pre-training on the motion forecasting task. Based on the asymmetric architecture of MAE, we devise a scene reconstruction pretext task that utilizes a novel masking strategy. By leveraging the complementary masking of the agents' trajectories and the random masking of lane segments during the pre-training process, the model acquires the ability to capture the bidirectional agent motion features, road geometry features, and cross-modal intercon"
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+                                    "type": "text",
+                                    "content": "nections jointly. Our experiments on the challenging Argoverse 2 benchmark demonstrate that our Forecast-MAE surpasses supervised learning methods and previous self-supervised learning works, especially in terms of "
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+                                    "type": "text",
+                                    "content": ", indicating its superior ability to predict the most likely future."
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+                                    "type": "text",
+                                    "content": "Limitaion and Discussion. One constraint of our work is the lack of exploration of transfer learning or few-shot learning for the proposed method (e.g., pre-training on WMOD and fine-tuning on AV2). Such exploration is hindered by the different problem settings, namely observation/prediction horizons, of different datasets. Besides, due to the relatively limited size of publicly available motion forecasting datasets compared to those in computer vision or natural language processing, we are unable to determine whether the performance of Forecast-MAE will scale up with increased training data and model capacity. However, we are positive about this point by drawing intuition from MAE and our minimal inductive bias design. Our approach could be advantageous for autonomous driving companies with large-scale internal datasets. Although Forecast-MAE already achieves strong performance while designed to be simple, we anticipate it can be further improved. Drawing inspiration from the development of techniques such as ViT [11] to Swin-Trainsformer [30], properly incorporating inductive bias such as relative position design [52, 8, 51] or local attention [36] may further boost Forecast-MAE in terms of performance and efficiency. Another possible direction is to generate realistic traffic scenarios building upon this work. These possibilities are left for future works."
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+                                    "type": "text",
+                                    "content": "Acknowledgement This work was supported by Guangdong Basic and Applied Basic Research Foundation, under project 2021B1515120032, Jiangsu Province Science and Technology Project BZ2021056, and Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (HZQB-KCZYB-2020083), awarded to Prof. Ming Liu."
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+                                }
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+                                    "content": "[1] Prarthana Bhattacharyya, Chengjie Huang, and Krzysztof Czarnecki. Ssl-lanes: Self-supervised learning for motion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
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+                                            "content": "ence on Intelligent Robots and Systems (IROS), pages 532-539. IEEE, 2021. 3"
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+                                            "content": "[49] Chen Zhang, Honglin Sun, Chen Chen, and Yandong Guo. Banet: Motion forecasting with boundary aware network. 7"
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+                            "index": 1
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+                                            "content": "[50] Hang Zhao, Jiyang Gao, Tian Lan, Chen Sun, Ben Sapp, Balakrishnan Varadarajan, Yue Shen, Yi Shen, Yuning Chai, Cordelia Schmid, et al. Tnt: Target-driven trajectory prediction. In Conference on Robot Learning, pages 895-904. PMLR, 2021. 2, 3"
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+                                            "content": "[51] Zikang Zhou, Jianping Wang, Yung-Hui Li, and Yu-Kai Huang. Query-centric trajectory prediction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17863-17873, 2023. 3, 8"
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diff --git a/2023/Foreground Object Search by Distilling Composite Image Feature/2f22dc81-3b09-4682-9d0e-7e47efe03306_content_list.json b/2023/Foreground Object Search by Distilling Composite Image Feature/2f22dc81-3b09-4682-9d0e-7e47efe03306_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc6b6021fba1af666493cb530601afa415025390
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+++ b/2023/Foreground Object Search by Distilling Composite Image Feature/2f22dc81-3b09-4682-9d0e-7e47efe03306_content_list.json	
@@ -0,0 +1,1576 @@
+[
+    {
+        "type": "text",
+        "text": "Foreground Object Search by Distilling Composite Image Feature",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Bo Zhang $^{1}$ , Jiacheng Sui $^{2}$ , and Li Niu $^{*1}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup>Center for Machine Cognitive Computing of Artificial Intelligence Institute, Artificial Intelligence Institute, Shanghai Jiao Tong University",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{bo-zhang, ustcnewly}@sjtu.edu.cn",
+        "bbox": [
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+            262,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{2}$ Xian Jiao Tong University",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "rookiecharles99@gmail.com",
+        "bbox": [
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+            311
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            354,
+            313,
+            371
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Foreground object search (FOS) aims to find compatible foreground objects for a given background image, producing realistic composite image. We observe that competitive retrieval performance could be achieved by using a discriminator to predict the compatibility of composite image, but this approach has unaffordable time cost. To this end, we propose a novel FOS method via distilling composite feature (DiscoFOS). Specifically, the abovementioned discriminator serves as teacher network. The student network employs two encoders to extract foreground feature and background feature. Their interaction output is enforced to match the composite image feature from the teacher network. Additionally, previous works did not release their datasets, so we contribute two datasets for FOS task: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. Extensive experiments on our two datasets demonstrate the superiority of the proposed method over previous approaches. The dataset and code are available at https://github.com/bcmi/Foreground-Object-Search-Dataset-FOSD.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            732,
+            209,
+            748
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Foreground Object Search (FOS) aims to find compatible foregrounds from specified category for a given background image which has a query bounding box indicating the foreground location [42]. More precisely, an object is compatible with a background image if it can be realistically composited into the image [44], as illustrated in Figure 1. FOS is a core technique in many image composition applications [24]. For example, FOS technique can help",
+        "bbox": [
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+            468,
+            878
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/b1a89b645802ae5099c6a8e4b58824206c316e93c5945c9238147f8cbb2322ea.jpg",
+        "image_caption": [
+            "Figure 1. Illustration of foreground object search. Given a background image with query bounding box (yellow), foreground object search aims to find compatible foreground objects of a specified category from a database, which is composited with the background to produce a realistic composite image."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            358,
+            882,
+            540
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "users acquire suitable foregrounds from a foreground pool automatically and efficiently for object insertion in photo editing [19]. Moreover, FOS also can be used to fill a region comprising undesired objects using new foreground [44].",
+        "bbox": [
+            496,
+            657,
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+            718
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There exist many factors that affect the compatibility between background and foreground, including semantics, style (e.g., color and texture), lighting, and geometry (e.g., shape and viewpoint). Previous works on FOS may consider different factors. For example, early methods [42, 44] focused on the semantic compatibility. Recent works [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this paper, we focus on semantics and geometry compatibility following [19], because incompatible color and lighting between the background and foreground can be tackled to some extent by image harmonization [6, 21, 4].",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author",
+        "bbox": [
+            94,
+            887,
+            220,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "22986",
+        "bbox": [
+            478,
+            945,
+            519,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The general pipeline of most existing methods [42, 44, 47, 19, 37] is to learn an embedding space with two encoders respectively for background and foreground, so that compatible background and foreground are close to each other in this space. Alternatively, some approaches [46, 44] trained a discriminator to predict background-foreground compatibility by feeding the composite image. Based on preliminary experiments, we observe that the discriminator can achieve much better results than encoders when taking the cropped composite image as input (see teacher network in Figure 3). We conjecture that the forward pass in the discriminator allows thorough interaction between background and foreground, which could provide useful contextual cues for estimating background-foreground compatibility. However, given a background image, it is very time-consuming to compose with each foreground image and perform forward computation for each composite image. Motivated by this, we propose a novel FOS framework called DiscoFOS via knowledge distillation. Specifically, we distill the knowledge of composite image from the discriminator to two encoders, in which we enforce the interaction output of foreground feature and background feature to match with the composite image feature. How to design the interaction between two encoders is challenging, due to the trade-off between performance and computational cost. On the one hand, insufficient interaction between two encoders may be unable to mimic the rich knowledge in composite image feature. On the other hand, sufficient interaction would largely increase the computational burden. Considering the abovementioned trade-off, we perform interaction only on the last feature maps of two encoders, which achieves significant performance improvement with acceptable computational overhead.",
+        "bbox": [
+            76,
+            90,
+            472,
+            590
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since previous works (CAIS [42], UFO [44], and GALA [47]) did not release their datasets, we build our own datasets based on an existing large-scale real-world dataset, i.e., Open Images [15], as illustrated in Figure 2. We construct two FOS Datasets respectively containing Synthetic composite images and Real composite images, abbreviated as S-FOSD and R-FOSD respectively. We first introduce the S-FOSD dataset. Given a real image with instance segmentation mask, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out this object as foreground. After removing unsuitable categories and occluded foregrounds, the resultant dataset contains 57,859 backgrounds and 63,619 foregrounds. Following [42, 47], for each background image, we deem the foreground object from the same image as ground-truth. For R-FOSD dataset, we collect images from Internet as background images and draw a bounding box at the expected foreground location as query bounding box. R-FOSD dataset shares the same foregrounds with the test set of S-FOSD dataset. Then we employ multiple human",
+        "bbox": [
+            76,
+            598,
+            472,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "annotators to label the compatibility of each pair of background and foreground. In summary, S-FOSD dataset is lowcost and highly scalable, but has neither complete background nor ground-truth negative samples. Oppositely, R-FOSD dataset has complete background image with both positive and negative foregrounds annotated by human, yet is unscalable due to the high annotation cost. In our experiments, S-FOSD dataset is used for both training and validating model, while R-FOSD dataset is only used for model evaluation. More details about dataset construction could be found in Section 3.",
+        "bbox": [
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+            90,
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+            256
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our method on the proposed datasets, which validates the superiority of the proposed method over previous approaches. Our major contributions can be summarized as follows: 1) To facilitate the research on FOS task, we contribute two public datasets: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. 2) We propose a novel method named DiscoFOS that improves foreground object search by distilling the knowledge of composite image feature into two encoders. 3) Extensive experiments demonstrate the superiority of the proposed method over previous baselines on our datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            500,
+            465,
+            650,
+            479
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Foreground Object Search",
+        "text_level": 1,
+        "bbox": [
+            500,
+            493,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Early works [16, 3] employed hand-crafted features to match background with foreground, yet their performance may be limited by the representation ability of hand-crafted features. Recent work applied deep learning based feature for foreground retrieval. For example, [32] utilized deep features to capture local context particularly for person compositing. [46] trained a discriminator to estimate the realism of composites, which is available for selecting compatible foregrounds by compositing each foreground with the background, but is computationally expensive.",
+        "bbox": [
+            496,
+            520,
+            893,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "More recent methods [42, 44, 47, 37, 19] typically trained two encoders to extract background feature and foreground feature, and then measured background foreground compatibility by calculating feature similarity. These methods considered different factors that affect the compatibility between background and foreground. For example, the methods [42, 44] considered the semantic compatibility, while the approaches [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this work, we focus on semantic compatibility and geometry compatibility following [19], and propose a novel foreground object search method that improves the encoders with knowledge distillation. Additionally, previous works [42, 44, 37, 47] did not release their datasets, we contribute two datasets to facilitate the research in this field.",
+        "bbox": [
+            496,
+            674,
+            895,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "22987",
+        "bbox": [
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+            944,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Image Composition",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            264,
+            107
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As summarized in [24], existing image composition works attempted to solve one or some issues which affect the quality of composite image, such as illumination, shadow, and geometry. Image harmonization methods [34, 6, 7, 5] focused on eliminating the color and illumination discrepancy between background and foreground. Besides, some shadow generation works [14, 9, 40, 22, 12] aimed to generate plausible shadow for the inserted foreground. To blend the foreground into the background more naturally, image blending methods [26, 18, 35] paid attention to smoothing the boundary between background and foreground. The closest subtask to ours is object placement [45, 25, 23, 17, 33], which generates reasonable locations and sizes to place foreground over background. Given a background, object placement focuses on predicting bounding box for the inserted foreground, while our task targets at retrieving compatible foregrounds from a specified category for a given query bounding box.",
+        "bbox": [
+            75,
+            114,
+            472,
+            387
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Knowledge Distillation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            397,
+            289,
+            412
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Knowledge distillation methods usually improve the student network by forcing to mimic the behaviors of the teacher network, such as soft predictions [11], logits [1], intermediate feature maps [27], or attention maps [39]. Apart from the above works on image classification, some recent works extend knowledge distillation to more complex vision tasks, including semantic segmentation [41, 29], object detection [20, 2], face recognition [13], and so on.",
+        "bbox": [
+            75,
+            420,
+            468,
+            541
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Previous works [19, 37] have also considered introducing knowledge distillation to foreground object search, in which foreground (resp., background) encoder plays the role of the teacher (resp., student) network and the foreground information is distilled from foreground embedding to background embedding. However, these approaches rely on fine-grained annotations of foreground attributes [19] or multiple pretrained models [37], which may hinder the generalization to unseen foreground categories. Unlike the above methods, our method adopts a composite image discriminator as teacher network and two encoders as student network, in which we distill composite image feature from discriminator to the interaction output of foreground feature and background feature, which proves to be effective and computationally affordable.",
+        "bbox": [
+            75,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Dataset Construction",
+        "text_level": 1,
+        "bbox": [
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+            784,
+            279,
+            800
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our datasets are constructed on existing Open Images dataset [15] that contains 9.2 million images covering diverse scenes, making it very suitable for real-world evaluation. We build two datasets for foreground object search: S-FOSD with synthetic composite images and R-FOSD with real composite images, which have different ways to acquire",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/e11aad6b6ca0ad109bc03020621b642c4bdf58c2dd4f9779a7c486d10f13fbe2.jpg",
+        "image_caption": [
+            "(a) Source & Mask"
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+        "page_idx": 2
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+    {
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+        "img_path": "images/b3cbf48296c1c2b0e0bfe7132a9ee2c6849afc9b78d3332f3434361fa0c3b446.jpg",
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+        "image_caption": [
+            "(c) Foreground"
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+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "image",
+        "img_path": "images/6290fdd373d71d30233d480961fe3c420aea10ee9df3236768b1505b9b90fdf3.jpg",
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+            "(d) Synthetic Composite"
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+        "image_caption": [
+            "(e) Source Image"
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+    {
+        "type": "image",
+        "img_path": "images/891714b51562c9b66564b4f0a93de1e11c24e777c4f0af653f1ed742eb12cc1f.jpg",
+        "image_caption": [
+            "(g) Foreground",
+            "Figure 2. The illustration of building our foreground object search (FOS) datasets. Top: FOS Dataset with Synthetic composite images (S-FOSD). Bottom: FOS Dataset with Real composite images (R-FOSD). More details about dataset construction can be seen in Section 3."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/e9d27e09195ba7fb55788e2069f74ae858cf1d8bbd6f240672822e3f5e55191d.jpg",
+        "image_caption": [
+            "(h) Real Composite"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "backgrounds and foregrounds (see Figure 2).",
+        "bbox": [
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+            325,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. S-FOSD Dataset",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Foreground Object Selection. Open Images dataset [15] provides instance segmentation masks for 2.8 million object instances in 350 categories. To accommodate our task, we delete the categories and objects that are unsuitable for the task or beyond our focus (geometry and semantic compatibility), after which 32 categories remain. The detailed rules for object selection and the complete category list can be found in Supplementary.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Background and Foreground Generation. By using the segmentation masks, we generate background and foreground images in a similar way to previous works [42, 47, 44]. Specifically, as shown in Figure 2 (a)  $\\sim$  (c), given an image with instance segmentation masks, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out the object and paste it on white background, producing the foreground. With the background and foreground, we can obtain the synthetic composite image by resizing the foreground and placing it in the query bounding box on the background (see Figure 2 (d)). Additionally, we have also tried image inpainting [31, 43, 38] to fill the object bounding box, but got unsatisfactory results, probably due to large missing content and the residues of erased object (e.g., shadow). After that, we obtain over 63,000 pairs of background and foreground covering 32 categories, with a maximum of 5,000 images and a minimum of 500 images in each category. For a given background, the foreground cropped from the same image is naturally compatible and thus deemed as ground-truth following [42, 47, 44].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Dataset Split. S-FOSD dataset is employed for both training and testing, as its construction is low-cost and highly scalable. We first select test samples to build the test set and the rest forms the training set. For reliable performance evaluation, we build test set mainly concerning its diversity and quality. Finally, we get 20 backgrounds and 200",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "22988",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "foregrounds for each category, which contains 20 pairs of background and foreground. The remaining 57,219 pairs of background and foreground form the training set.",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. R-FOSD Dataset",
+        "text_level": 1,
+        "bbox": [
+            76,
+            143,
+            243,
+            159
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Background and Foreground Generation. When building R-FOSD dataset, we directly adopt the foregrounds of the test set in S-FOSD dataset and collect images from Internet as backgrounds. It is very likely that a random image is unsuitable for compositing with any test foreground. Thus, we collect candidate backgrounds by searching similar images to the test backgrounds of S-FOSD dataset. After that, we draw a bounding box at the desired foreground location as query bounding box (see Figure 2 (f)). The size and location of the bounding box are decided by first mimicking the foreground in the similar background of S-FOSD dataset and then manual inspection. For each pair of background and foreground, we resize the foreground and place it in the query bounding box on the source image, generating a real composite image (see Figure 2 (h)). Finally, R-FOSD dataset contains 32 categories, each of which has 20 background images and 200 foreground images.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Compatibility Labelling. To acquire the binary compatibility label (1 for compatible background foreground pair and 0 for incompatible pair), we employ three human annotators to label the compatibility for  $32 \\times 20 \\times 200$  pairs of background and foreground. During annotation, we show real composite images and request annotators to assign binary labels by considering the semantics and geometry compatibility between background and foreground. Finally, for one background, we only consider the foregrounds for which all three human annotators label 1 as compatible and the others are treated as incompatible. Note that manually annotating the dataset is expensive, as it requires labelling a quadratically growing number of background and foreground pairs. Therefore, we only use R-FOSD dataset as a test set. To keep consistent with training data, we also fill the query bounding box of the background in R-FOSD dataset with image mean values at test time and the complete background image of R-FOSD dataset is only used to obtain the final composite image (Figure 2 (h)).",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Methodology",
+        "text_level": 1,
+        "bbox": [
+            76,
+            724,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this section, we describe our proposed method for foreground object search. As illustrated in Figure 3, we train a discriminator  $D$  to predict the compatibility of composite image, which serves as the teacher network (see Section 4.1). We employ two encoders  $E^{b}$  and  $E^{f}$  (see Section 4.2) as well as a light-weight knowledge distillation module  $E^{d}$  (see Section 4.3) as the student network. The two encoders respectively extract background feature  $\\mathbf{F}^{b}$  and foreground feature  $\\mathbf{F}^{f}$ , which are fed into distillation module to interact with each other. During training",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "stage, we enforce the interaction output  $\\mathbf{F}^d$  to match with the composite image feature  $\\mathbf{F}^c$ , in which the background foreground compatibility information is distilled to  $\\mathbf{F}^d$ . Finally, we predict compatibility scores for pairwise background and foreground based on the distilled feature  $\\mathbf{F}^d$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Composite Image Discriminator",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Network Architecture. Given a background image  $\\mathbf{I}^b$  with a query bounding box and a foreground image  $\\mathbf{I}^f$ , we first generate a synthetic composite image  $\\mathbf{I}^c$  as in Figure 2 (d). Then, we employ a discriminator  $D$  that takes a composite image as input to predict whether background and foreground of the composite image are compatible. We implement the discriminator as a binary classifier that consists of backbone network and classification head. Moreover, based on preliminary experiments, we find that feeding a cropped composite image into the discriminator achieves significantly better performance than feeding the whole composite image. Specifically, we crop the composite image, ensuring that the foreground object is located at the center and the area of foreground bounding box is about 50 percent of the whole crop. Then, we resize the crop to the input size 224 × 224, which is denoted as  $\\widetilde{\\mathbf{I}}^c$ . The superiority of feeding cropped composite image can be attributed to that the contextual information near the foreground may be more helpful and the foreground is aligned with crop center. Here we refer to the crop box as  $B$ . With the cropped composite image, the discriminator first extracts the composite image feature map  $\\mathbf{F}^c$  by backbone network and then apply global average pooling (GAP) layer followed by a binary classifier. We train the discriminator using binary cross-entropy loss:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {D} = - \\log (p (\\widetilde {\\mathbf {I}} ^ {c}) _ {y}), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "in which  $p(\\cdot)_y$  means the predicted probability corresponding to the ground-truth compatibility label  $y$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Positive and Negative Samples Generation. During training phase, we consider compatible (resp., incompatible) foreground objects as positive (resp., negative) samples for a given background. The foreground cropped from the same image as the background is naturally viewed as positive sample. However, other foreground objects may also be compatible with the background. To guarantee the effectiveness of training samples, similar to [44], we train a binary classifier using VGG-19 [30] pretrained on ImageNet [8] as backbone network to help filter out training samples. Given a pair of background image and foreground image, the classifier takes their composite image as input and predicts the compatibility score. When training this classifier, we assume that only background foreground pairs from same images are positive and others are negative. With the trained classifier, we restrict negative samples to only include those foreground objects which are confidently",
+        "bbox": [
+            496,
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+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22989",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8e80d8ceaa9392f5530f3ea02671226c0901f472dcdda63374b88cb0b6171e9b.jpg",
+        "image_caption": [
+            "Figure 3. Illustration of the proposed DiscoFOS for foreground object search. The discriminator  $D$  is first trained to predict the background-foreground compatibility of input composite image  $\\mathbf{I}^c$ , whose intermediate feature map  $\\mathbf{F}^c$  then servers as distillation target to train the student model. The student network first extracts background feature  $\\mathbf{F}^b$  and foreground feature  $\\mathbf{F}^f$  by two encoders  $\\{E^f, E^b\\}$ , then applies the features to generate distilled feature  $\\mathbf{F}^d$  and compatibility prediction by knowledge distillation module  $E^d$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            89,
+            480,
+            281
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8c11d8a2fd640c26010a9caccb6665a6791a1f65def5b028aebd03f9861068cd.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            488,
+            89,
+            851,
+            280
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8b69c5e9bffe0cb82d4fb617ad8ccd48ec02960f85412ec31827d6fbc316dd91.jpg",
+        "image_caption": [
+            "Figure 4. Examples of positive and negative samples used to train our models. Given a background in S-FOSD dataset, we have one positive foreground and one or more negative foregrounds, which are filled with white background pixels."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            378,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "classified as incompatible, that is, compatibility score is lower than a threshold (0.3 in our experiments). Therefore, given a background image, we have a single positive foreground and one or more negative foregrounds in S-FOSD dataset (see Figure 4). The obtained positive and negative samples are used to train the composite image discriminator in this section and the student network in Section 4.2, 4.3.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Background and Foreground Encoders",
+        "text_level": 1,
+        "bbox": [
+            76,
+            756,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We employ two encoders  $E^b$  and  $E^f$  to extract feature respectively from background image  $\\mathbf{I}^b$  and foreground image  $\\mathbf{I}^f$ . Correspondingly, the background encoder  $E^b$  outputs background feature map  $\\mathbf{F}^b$  and the foreground encoder  $E^f$  outputs foreground feature map  $\\mathbf{F}^f$ , both of which have the same shape, i.e.,  $\\mathbf{F}^b$ ,  $\\mathbf{F}^f \\in \\mathcal{R}^{h \\times w \\times c}$ . Here  $h \\times w$  is the spatial size and  $c$  is the number of channels. Then we apply GAP layer to yield background and foreground fea",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "ture vectors, denoted as  $\\bar{\\mathbf{F}}^b$ ,  $\\bar{\\mathbf{F}}^f \\in \\mathcal{R}^c$ . After mapping the foreground and background into the common feature space, we enforce the compatible background and foreground to be close to each other in this space. Thus, the compatibility between foreground and background can be measured by computing the cosine similarity between their features. To this end, following previous works [37, 42, 44, 47], we train the encoders using triplet loss [28], which tends to pull the positive sample (i.e., compatible foreground) to the anchor (i.e., given background) and push the negative sample (i.e., incompatible foreground) away from the anchor in the feature space. During training stage, we tend to minimize the following loss function:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {t r p} = \\max \\left(0, m + S (\\bar {\\mathbf {F}} ^ {b}, \\bar {\\mathbf {F}} _ {n} ^ {f}) - S (\\bar {\\mathbf {F}} ^ {b}, \\bar {\\mathbf {F}} _ {p} ^ {f})\\right), \\quad (2)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            524,
+            582,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $S(\\cdot)$  represents cosine similarity and  $m$  is a positive margin in the range of (0, 1).  $\\bar{\\mathbf{F}}_p^f$  (resp.,  $\\bar{\\mathbf{F}}_n^f$ ) is the feature of positive (resp., negative) foreground for background  $\\bar{\\mathbf{F}}^b$ . By minimizing  $\\mathcal{L}_{trp}$ , for a given background, the feature similarity with compatible foreground is expected to be greater than that with incompatible foreground by the margin  $m$ . Additionally, the above encoders are usually employed in previous methods [42, 44, 47]. Given a query background and a foreground database, these approaches rank the compatibility of different foregrounds by measuring their feature similarity to the given background.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Knowledge Distillation Module",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After evaluating the discriminator in Section 4.1 and the encoders in Section 4.2, we observe that discriminator can achieve much better results than encoders, probably because the forward propagation in the discriminator allows thorough interaction between background and foreground, providing useful contextual cues for estimating background",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "22990",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "foreground compatibility. However, retrieving foreground images using discriminator requires to composite with each foreground image, which brings heavy computational burden. On the contrary, encoders achieve inferior performance, yet have significantly faster speed due to the exemption from background-foreground interaction. This motivates us to distill discriminator knowledge into encoders.",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To achieve this goal, we design a knowledge distillation module  $E^{d}$ , which interacts foreground feature with background feature and enforces the interaction output to match with the composite image feature  $\\mathbf{F}^{c}$  from the discriminator. Recall that the composite image feature is extracted from cropped composite image, with the crop bounding box denoted as  $B$  (see Section 4.1). So we apply RoIAlign [10] with the bounding box  $B$  to obtain local background feature map  $\\widetilde{\\mathbf{F}}^{b}$  from global background feature map  $\\mathbf{F}^{b}$  produced by background encoder  $E^{b}$ . Then, we resize RoIAlign output to be of the same shape as  $\\mathbf{F}^{b}$ , i.e.,  $\\widetilde{\\mathbf{F}}^{b} \\in \\mathcal{R}^{h \\times w \\times c}$ . The local background feature is supposed to encode contextual information surrounding the foreground. Meanwhile, we utilize foreground encoder  $E^{f}$  to extract foreground feature map  $\\mathbf{F}^{f}$ . Given the foreground feature map  $\\mathbf{F}^{f}$  and local background feature map  $\\widetilde{\\mathbf{F}}^{b}$ , we feed their concatenation into  $E^{d}$  to produce a distilled feature map  $\\mathbf{F}^{d} \\in \\mathcal{R}^{h \\times w \\times c}$ . Note the discriminator and two encoders adopt the same backbone network and input image size in our implementation, so their feature maps have the same shape, i.e.,  $\\mathbf{F}^{c}, \\mathbf{F}^{d} \\in \\mathcal{R}^{h \\times w \\times c}$ . During training phase, we enforce the distilled feature  $\\mathbf{F}^{d}$  to mimic the composite image feature  $\\mathbf{F}^{c}$  by  $L_{1}$  loss:",
+        "bbox": [
+            75,
+            198,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {k d} = \\left\\| \\mathbf {F} ^ {d} - \\mathbf {F} ^ {c} \\right\\| _ {1}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We pool the distilled feature map into a vector and send it to a binary classifier to predict the compatibility. The classifier is also trained using binary cross-entropy loss:",
+        "bbox": [
+            76,
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {c l s} = - \\log (p (\\mathbf {F} ^ {d}) _ {y}), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            189,
+            636,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "in which  $p(\\cdot)_y$  is similarly defined as in Eqn. 1.",
+        "bbox": [
+            76,
+            664,
+            390,
+            679
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, we train the encoders  $\\{E^f,E^b\\}$  and distillation module  $E^{d}$  simultaneously. The overall optimization function can be written as",
+        "bbox": [
+            76,
+            679,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {t r p} + \\lambda_ {k d} \\mathcal {L} _ {k d} + \\lambda_ {c l s} \\mathcal {L} _ {c l s}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            736,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{kd}$  and  $\\lambda_{cls}$  are trade-off parameters. During inference, our model finds compatible foregrounds for a given background by ranking the predicted compatibility scores.",
+        "bbox": [
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+            762,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Generalization to Real-world Application",
+        "text_level": 1,
+        "bbox": [
+            76,
+            816,
+            429,
+            833
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To boost the performance of our method on real-world data, we make some modifications to the training procedure of our teacher network and student network, which helps achieve more competitive results on the R-FOSD dataset.",
+        "bbox": [
+            76,
+            839,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For the teacher network, we utilize the binary classifier in Section 4.1 to extend training samples. Specifically, given a background image, we use the classifier to predict compatibility score for each foreground and treat those with scores larger than 0.8 as positive samples (including the ground-truth foreground), based on which the ratio of positive and negative foregrounds per background is increased from 1:10 to 5:10. Besides, we apply data augmentation to generate additional positive and negative samples from the ground-truth foreground for each background image. Precisely, based on the ground-truth foreground, we produce 2 positive foregrounds through color jitter and Gaussian blur, and 1 negative foreground through affine transformation. After augmentation, the ratio of positive and negative samples changes from 5:10 to 7:11.",
+        "bbox": [
+            496,
+            90,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For the student network, we select the top-5 foregrounds returned by pretrained teacher network as positive samples (including the ground-truth foreground) and adopt the same negative samples as the teacher network. After applying the same data augmentation scheme as the teacher network, we also have positive and negative samples with the ratio 7:11 to train the student network.",
+        "bbox": [
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+            318,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, considering that user-provided bounding boxes may not be very accurate, we also augment bounding boxes when training teacher network and student network. Specifically, we randomly pad the bounding box with the maximum padding space being  $30\\%$  of the bounding box's width and height.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            532,
+            633,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Dataset and Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            500,
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+    {
+        "type": "text",
+        "text": "Our S-FOSD dataset is employed for both training and testing, while R-FOSD dataset is only for testing. We employ different evaluation metrics for two datasets considering their difference in the acquisition of ground-truth foregrounds. For each metric, we report the mean evaluation results by averaging the results over all categories. Moreover, we leave the implementation details in Supplementary.",
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+    {
+        "type": "text",
+        "text": "S-FOSD Dataset. The training set has 57,219 pairs of foregrounds and backgrounds covering 32 categories, with a maximum of 4800 pairs and a minimum of 300 pairs in each category. The test set provides 20 backgrounds and 200 foregrounds (including 20 foregrounds from the same images as the backgrounds) for each category. The foreground/background images in the training set and test set have no overlap. Following previous works [42, 47], only the foreground object from the same image is viewed as ground-truth for each background and we adopt Recall@k (R@k) as evaluation metric, which represents the percentage of background queries whose ground-truth foreground appears in top  $k$  retrievals ( $k = 1, 5, 10, 20$  in our experiments).",
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+    {
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+        "text": "22991",
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+    {
+        "type": "text",
+        "text": "R-FOSD Dataset. The R-FOSD dataset adopts the same foreground set as the test set of S-FOSD dataset and collects 20 backgrounds for each category. Each pair of background and foreground is shown to three human annotators to label the compatibility. The resulting dataset contains  $4\\sim 190$  compatible foregrounds per background, and we adopt mean Average Precision (mAP), mAP@20, and Precision@k (P@k) for evaluation, which are widely used in image retrieval and previous works [44, 47]. Precision@k means the percentage of compatible foreground objects in the top k retrievals,  $k = 1,5,10,20$  in our experiments. To reduce unplausible results on the R-FOSD dataset, we exclude the objects with aspect ratios deviating more than 1.2 from that of query bounding box for all methods and compute metrics on the remaining objects.",
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+    {
+        "type": "text",
+        "text": "5.2. Comparison with Existing Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Baselines. We compare our approach with previous methods [42, 44, 37, 47] on our two datasets. Shape [42] ranks foreground objects by comparing their aspect ratios with that of the query bounding box on background. CFO [42], UFO [44], FFR [37], and GALA [47] adopt the pipeline described in Section 4.2, which use two encoders to extract background and foreground features, and then rank the compatibility of foreground by computing its feature similarity with background. To adapt to our focus on geometric and semantic incompatibility, we replace the style feature of FFR [37] with semantic feature, in which we obtain the semantic feature by using VGG-19 [30] pretrained on ImageNet [8] following [44]. For GALA [47] that considers lighting and geometry compatibility, we discard lighting transformation and only keep geometry transformation [47] to match our scenario. Besides, we do not compare with IFR [19], as it requires pattern labels of the foreground, which are unavailable in our datasets. For fair comparison, we employ the same backbone network and training set for all baseline methods except Shape [42]. We use the same positive and negative samples for different methods when training on S-FOSD dataset.",
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+    {
+        "type": "text",
+        "text": "Quantitative comparison. The results of baselines and our method on the proposed two datasets are summarized in Table 1. Moreover, when evaluating on S-FOSD dataset, the only ground-truth foreground has the same aspect ratio as the query bounding box, thus Shape [42] can find the ground-truth by shortcut, making the evaluation results meaningless. It can be seen that among all baselines, GALA [47] and FFR [37] are two competitive ones, which employ contrastive learning with self-transformation [47] and MarrNet [36] to enhance the perception of geometric information of foreground, respectively. Nevertheless, our method outperforms all previous approaches by an obvious margin on both S-FOSD and R-FOSD datasets.",
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+    {
+        "type": "text",
+        "text": "Qualitative comparison. We show the retrieval results of",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a22802f7f261d7c7715b2d557bd25240f7669c6e1cfaeb9515ad635eb244ec9c.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative comparison on our S-FOSD (left) and R-FOSD (right) datasets. Each of the four examples contains a background image and several rows of the retrieval results, from top to bottom: CFO [42], UFO [44], GALA [47], FFR [37], and ours. Additionally, in the right part, green (resp., red) box represents the foreground with compatible (resp., incompatible) label."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "different baselines on our two datasets in Figure 5. For each query background, we show the returned top-5 foregrounds by different methods, which shows that our method can generally find compatible foregrounds by taking both semantic and geometric factors into account. For example, for the top-left example, given a query bounding box at the bottom-right seat, the baseline methods may return a standing or frontal person, which is unsuitable to be placed in the query bounding box. In contrast, the top returned persons by our method all have sitting posture, which appear more reasonable in terms of semantic compatibility. In the bottom-right example, given the geometry of background scene, the annotated ground-truth positive foregrounds (green box) have consistent orientation with respect to the train track in background. Our method retrieves more positive foregrounds than other approaches, demonstrating the effectiveness of our method on geometry compatibility. More qualitative results are present in Supplementary.",
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+    {
+        "type": "text",
+        "text": "5.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we start from the general pipeline with two encoders of previous methods [42, 44, 47, 19, 37] and evaluate the effectiveness of each component in our method. Different models are evaluated on our S-FOSD dataset and the results are summarized in Table 2. In row 1, we apply two encoders  $\\{E^b,E^f\\}$  to extract background feature  $\\bar{\\mathbf{F}}^b$  and foreground feature  $\\bar{\\mathbf{F}}^f$ , which are used to predict the background foreground compatibility by measuring their feature similarity. It is worth mentioning that all models in Table 2 rank different foregrounds by predicted compatibility scores except the row 1 and row 2, which measure compatibility by calculating feature similarity.",
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+        "text": "22992",
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+    {
+        "type": "table",
+        "img_path": "images/360a757b01a1e93ff36285d790410d1efc98049f5304895bcdb893ba20433ab0.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">S-FOSD Dataset</td><td colspan=\"6\">R-FOSD Dataset</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td><td>mAP↑</td><td>mAP@20↑</td><td>P@1↑</td><td>P@5↑</td><td>P@10↑</td><td>P@20↑</td></tr><tr><td>Shape [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>50.49</td><td>56.22</td><td>47.66</td><td>49.72</td><td>50.03</td><td>49.92</td></tr><tr><td>CFO [42]</td><td>56.09</td><td>83.59</td><td>91.25</td><td>96.88</td><td>52.06</td><td>62.17</td><td>58.33</td><td>56.29</td><td>55.90</td><td>52.85</td></tr><tr><td>UFO [44]</td><td>54.69</td><td>81.72</td><td>90.94</td><td>95.31</td><td>52.73</td><td>63.63</td><td>64.12</td><td>59.11</td><td>56.30</td><td>53.82</td></tr><tr><td>FFR [37]</td><td>57.03</td><td>86.25</td><td>93.28</td><td>97.97</td><td>53.10</td><td>64.12</td><td>61.92</td><td>59.64</td><td>57.56</td><td>55.06</td></tr><tr><td>GALA [47]</td><td>57.50</td><td>85.17</td><td>93.00</td><td>97.33</td><td>52.02</td><td>62.83</td><td>62.56</td><td>57.33</td><td>55.76</td><td>52.93</td></tr><tr><td>DiscoFOS</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td><td>56.70</td><td>68.56</td><td>67.75</td><td>64.64</td><td>62.25</td><td>58.90</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a72a2dd07d3ec317c09fa90a6c402f6bc37e9bc0334502dec51866ebca069460.jpg",
+        "table_caption": [
+            "Table 1. Comparison with existing methods on our S-FOSD dataset and R-FOSD dataset. Best results are denoted in boldface."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Eb</td><td>Ed</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td></tr><tr><td>1</td><td>Fb</td><td></td><td>54.83</td><td>81.17</td><td>90.67</td><td>95.00</td></tr><tr><td>2</td><td>Fb</td><td></td><td>52.50</td><td>79.69</td><td>88.75</td><td>93.00</td></tr><tr><td>3</td><td>Fb</td><td>p(·)y</td><td>56.72</td><td>87.19</td><td>94.69</td><td>97.97</td></tr><tr><td>4</td><td>Fb</td><td>[Fb, Ff]</td><td>60.83</td><td>87.33</td><td>95.00</td><td>98.17</td></tr><tr><td>5</td><td>Fb</td><td>[Hatb, Ff]</td><td>65.16</td><td>90.31</td><td>95.31</td><td>98.59</td></tr><tr><td>6</td><td>Fb</td><td>[Fb, Ff]</td><td>68.28</td><td>90.94</td><td>95.63</td><td>98.75</td></tr><tr><td>7</td><td>Fb</td><td>Fb ⊕ Ff</td><td>64.53</td><td>87.66</td><td>92.97</td><td>96.72</td></tr><tr><td>8</td><td>Fb</td><td>[Fb, Ff]</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td></tr><tr><td>9</td><td></td><td>D(Ic)</td><td>49.22</td><td>76.72</td><td>84.53</td><td>91.88</td></tr><tr><td>10</td><td></td><td>D(Ic)</td><td>84.38</td><td>97.03</td><td>98.91</td><td>99.84</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2. The ablation studies of our method on S-FOSD dataset.  $\\bar{\\mathbf{F}}^b, \\hat{\\mathbf{F}}^b$ : global/local background feature vector.  $\\mathbf{F}^b, \\widetilde{\\mathbf{F}}^b$ : global/local background feature map.  $\\mathbf{F}^f, \\widetilde{\\mathbf{F}}^f$ : foreground feature map/vector.  $[\\cdot, \\cdot]$ : feature concatenation.  $\\oplus$ : feature map composition. The detailed explanations can be found in Section 5.3.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Background Encoder  $E^b$ . Based on row 1 of Table 2, we replace the global background feature vector  $\\bar{\\mathbf{F}}^b$  with local background feature vector  $\\hat{\\mathbf{F}}^b$ , which is obtained by applying RoIAlign [10] with the crop bounding box  $B$  to background feature map  $\\mathbf{F}^b$ , resulting in worse results in row 2. This is probably because that the global background feature contains more useful information than the local background feature. So we adopt the global background feature for background encoder in other experiments.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Composite Image Discriminator  $D$ . In our network, the discriminator plays the role of teacher. In row 9 and 10 of Table 2, we feed the discriminator with the whole composite image  $\\mathbf{I}^c$  and the cropped composite image  $\\widetilde{\\mathbf{I}}^c$ , respectively. We see that row 10 achieves significantly better performance than row 9, which can be attributed to the aligned foreground and useful surrounding foreground context in the cropped composite. Then, the discriminator with the whole composite image is inferior to the encoders of row 1, which is roughly consistent with previous findings [44, 42]. Additionally, the discriminator with cropped composite image outperforms the encoders (row 1) with a remarkable margin, which motivates us to build our method.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Knowledge Distillation Module  $E^d$ . Based on row 1 of",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Table 2, we introduce the distillation module without using feature distillation, which is essentially a compatibility classifier  $p(\\cdot)_y$ , in row 3. The classifier takes the concatenation of foreground feature vector  $\\bar{\\mathbf{F}}^f$  and background feature vector  $\\bar{\\mathbf{F}}^b$  as input, and outputs the compatibility score. The comparison between row 1 and 3 verifies that adding compatibility classification is helpful for our task.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Then we add feature distillation and explore the impact of using different forms of background-foreground interactions. In row 4 and 5, we perform interaction based on the pooled feature vectors of two encoders. Specifically, we concatenate the foreground feature vector  $\\overline{\\mathbf{F}}^f$  with global background feature vector  $\\overline{\\mathbf{F}}^b$  (resp., local background feature vector  $\\hat{\\mathbf{F}}^b$ ) to feed into distillation module in row 4 (resp., row 5). Both results are better than row 3, proving the utility of distilling composite image feature to predict compatibility.",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Next, we perform interaction based on the last feature maps of two encoders. To this end, we explore several different ways to fuse background and foreground features. First, we directly concatenate background feature map  $\\mathbf{F}^b$  and foreground feature map  $\\mathbf{F}^f$  in row 6. By comparing row 6 and 4, it verifies the advantage of more sufficient interaction. In row 7, we extend to a more intuitive way by applying composition operation to local background feature maps  $\\widetilde{\\mathbf{F}}^b$  and foreground feature map  $\\mathbf{F}^f$ . Specifically, we resize the foreground feature and place it in the query bounding box on the local background feature. Unexpectedly, this leads to slight performance drop compared with row 5, which may be caused by downsampling the foreground feature. Finally, we concatenate the local background feature  $\\widetilde{\\mathbf{F}}^b$  and foreground feature  $\\mathbf{F}^f$ , corresponding to our complete method. As shown in row 8, our full method produces remarkably better results than the abovementioned row 6, indicating that the representation ability of the distilled feature can benefit from adequate interaction between two encoders.",
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+    {
+        "type": "text",
+        "text": "5.4. Inference Efficiency Analyses",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To study the efficiency of our method, we compare our method (\"Ours\") with the composite image discriminator (\"Discriminator\"), and background and foreground",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "22993",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2728aaa4aeaedc3ab980af15683de68504002dfa8e71eb04ed42b6a990878831.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Time(200)↓</td><td>Time(2000)↓</td><td>#Params↓</td></tr><tr><td>Discriminator</td><td>700.0ms</td><td>7000.1ms</td><td>20.03M</td></tr><tr><td>Encoders</td><td>4.0ms</td><td>4.3ms</td><td>40.05M</td></tr><tr><td>Ours</td><td>5.2ms</td><td>6.0ms</td><td>47.13M</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Comparing inference efficiency of different models, including the discriminator  $D$ , encoders  $\\{E^b, E^f\\}$ , and our method in the Figure 3. \"Time(N)\" represents the average time of retrieving compatible foregrounds from  $N$  candidates per background.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "encoders (\"Encoders\") on retrieval time and number of parameters, the results of which are reported in the Table 3. We test different models on an NVIDIA RTX 3090 GPU and measure the time of retrieving compatible foreground from  $N$  candidates as retrieval time  $(\\mathrm{Time}(N))$ . We repeat the retrieval 50 times and calculate the average time as final result. To mimic the practical application scenarios of foreground object search, we assume that the features of all foregrounds have been extracted and saved before retrieval. In particular, for \"Encoders\" and \"Ours\", we save the feature vector and the last feature map of the foreground encoder, respectively. In this way, the retrieval time of \"Encoders\" and \"Ours\" only considers the background feature extraction and the matching between background and foreground, in which background feature extraction takes 3.1ms per image.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We can see that the discriminator  $D$  is the slowest method due to compositing with each foreground and sending each composite through forward pass. \"Ours\" runs slower than \"Encoders\" due to introducing additional interaction between background and foreground, yet only takes 6ms to retrieve from 2000 foregrounds, which enables our model for real-time applications. Regarding the number of parameters, the comparison between two encoders and ours indicates that the additional parameters (7.08M) introduced by distillation module are affordable.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.5. Additional Experiments in Supplementary",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Due to space limitation, we present some experiments in Supplementary, including quantitative comparison on different categories, generalization to new categories, the results of our method using different hyper-parameters in Eqn. (5) and Eqn. (2), and different ratios of positive and negative training samples, the discussion on the limitation of our method, and the results of significance test.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this work, we have contributed two public datasets for Foreground Object Search (FOS), S-FOSD with Synthetic composite images and R-FOSD with Real composite images. We have also proposed a novel FOS method, which improves the general pipeline of previous methods by feature distillation. Extensive experiments on our dataset have",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "demonstrated the utility of our proposed method on foreground object search.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300).",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            500,
+            246,
+            596,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+        ],
+        "page_idx": 8
+    },
+    {
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[15] Alina Kuznetsova, Hassan Rom, Neil Gordon Alldrin, Jasper R. R. Uijlings, Ivan Krasin, Jordi Pont-Tuset, Shahab Kamali, Stefan Popov, Matteo Malloci, Alexander Kolesnikov, Tom Duerig, and Vittorio Ferrari. The open images dataset v4. International Journal of Computer Vision, 128:1956-1981, 2020. 2, 3",
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+        ],
+        "bbox": [
+            78,
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+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[32] Fuwen Tan, Crispin Bernier, Benjamin Cohen, Vicente Ordonez, and Connelly Barnes. Where and who? automatic semantic-aware person composition. In WACV, 2018. 2",
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+            "[39] Sergey Zagoruyko and Nikos Komodakis. Paying more attention to attention: Improving the performance of convolutional neural networks via attention transfer. In ICLR, 2017. 3",
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+            "[41] Zheng Zhang, Chunluan Zhou, and Zhigang Tu. Distilling inter-class distance for semantic segmentation. In *IJCAI*, 2022. 3",
+            "[42] Hengshuang Zhao, Xiaohui Shen, Zhe L. Lin, Kalyan Sunkavalli, Brian L. Price, and Jiaya Jia. Compositing-aware image search. In ECCV, 2018. 1, 2, 3, 5, 6, 7, 8",
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+            "[47] Sijie Zhu, Zhe Lin, Scott D. Cohen, Jason Kuen, Zhifei Zhang, and Chen Chen. GALA: Toward geometry-andlighting-aware object search for compositing. In ECCV, 2022. 1, 2, 3, 5, 6, 7, 8"
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diff --git a/2023/Foreground Object Search by Distilling Composite Image Feature/2f22dc81-3b09-4682-9d0e-7e47efe03306_model.json b/2023/Foreground Object Search by Distilling Composite Image Feature/2f22dc81-3b09-4682-9d0e-7e47efe03306_model.json
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index 0000000000000000000000000000000000000000..911055486e61a6af047b44b0291a7c3f2a5c0513
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+++ b/2023/Foreground Object Search by Distilling Composite Image Feature/2f22dc81-3b09-4682-9d0e-7e47efe03306_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.154,
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+            "angle": 0,
+            "content": "Foreground Object Search by Distilling Composite Image Feature"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Bo Zhang\\(^{1}\\), Jiacheng Sui\\(^{2}\\), and Li Niu\\(^{*1}\\)"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "<sup>1</sup>Center for Machine Cognitive Computing of Artificial Intelligence Institute, Artificial Intelligence Institute, Shanghai Jiao Tong University"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "{bo-zhang, ustcnewly}@sjtu.edu.cn"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)Xian Jiao Tong University"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.312
+            ],
+            "angle": 0,
+            "content": "rookiecharles99@gmail.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.356,
+                0.314,
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+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.388,
+                0.474,
+                0.706
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+            "angle": 0,
+            "content": "Foreground object search (FOS) aims to find compatible foreground objects for a given background image, producing realistic composite image. We observe that competitive retrieval performance could be achieved by using a discriminator to predict the compatibility of composite image, but this approach has unaffordable time cost. To this end, we propose a novel FOS method via distilling composite feature (DiscoFOS). Specifically, the abovementioned discriminator serves as teacher network. The student network employs two encoders to extract foreground feature and background feature. Their interaction output is enforced to match the composite image feature from the teacher network. Additionally, previous works did not release their datasets, so we contribute two datasets for FOS task: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. Extensive experiments on our two datasets demonstrate the superiority of the proposed method over previous approaches. The dataset and code are available at https://github.com/bcmi/Foreground-Object-Search-Dataset-FOSD."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
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+                0.21,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.758,
+                0.47,
+                0.88
+            ],
+            "angle": 0,
+            "content": "Foreground Object Search (FOS) aims to find compatible foregrounds from specified category for a given background image which has a query bounding box indicating the foreground location [42]. More precisely, an object is compatible with a background image if it can be realistically composited into the image [44], as illustrated in Figure 1. FOS is a core technique in many image composition applications [24]. For example, FOS technique can help"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.359,
+                0.883,
+                0.541
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.559,
+                0.892,
+                0.63
+            ],
+            "angle": 0,
+            "content": "Figure 1. Illustration of foreground object search. Given a background image with query bounding box (yellow), foreground object search aims to find compatible foreground objects of a specified category from a database, which is composited with the background to produce a realistic composite image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.658,
+                0.892,
+                0.719
+            ],
+            "angle": 0,
+            "content": "users acquire suitable foregrounds from a foreground pool automatically and efficiently for object insertion in photo editing [19]. Moreover, FOS also can be used to fill a region comprising undesired objects using new foreground [44]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "There exist many factors that affect the compatibility between background and foreground, including semantics, style (e.g., color and texture), lighting, and geometry (e.g., shape and viewpoint). Previous works on FOS may consider different factors. For example, early methods [42, 44] focused on the semantic compatibility. Recent works [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this paper, we focus on semantics and geometry compatibility following [19], because incompatible color and lighting between the background and foreground can be tackled to some extent by image harmonization [6, 21, 4]."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+                0.221,
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+            ],
+            "angle": 0,
+            "content": "*Corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.946,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22986"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.591
+            ],
+            "angle": 0,
+            "content": "The general pipeline of most existing methods [42, 44, 47, 19, 37] is to learn an embedding space with two encoders respectively for background and foreground, so that compatible background and foreground are close to each other in this space. Alternatively, some approaches [46, 44] trained a discriminator to predict background-foreground compatibility by feeding the composite image. Based on preliminary experiments, we observe that the discriminator can achieve much better results than encoders when taking the cropped composite image as input (see teacher network in Figure 3). We conjecture that the forward pass in the discriminator allows thorough interaction between background and foreground, which could provide useful contextual cues for estimating background-foreground compatibility. However, given a background image, it is very time-consuming to compose with each foreground image and perform forward computation for each composite image. Motivated by this, we propose a novel FOS framework called DiscoFOS via knowledge distillation. Specifically, we distill the knowledge of composite image from the discriminator to two encoders, in which we enforce the interaction output of foreground feature and background feature to match with the composite image feature. How to design the interaction between two encoders is challenging, due to the trade-off between performance and computational cost. On the one hand, insufficient interaction between two encoders may be unable to mimic the rich knowledge in composite image feature. On the other hand, sufficient interaction would largely increase the computational burden. Considering the abovementioned trade-off, we perform interaction only on the last feature maps of two encoders, which achieves significant performance improvement with acceptable computational overhead."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.599,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Since previous works (CAIS [42], UFO [44], and GALA [47]) did not release their datasets, we build our own datasets based on an existing large-scale real-world dataset, i.e., Open Images [15], as illustrated in Figure 2. We construct two FOS Datasets respectively containing Synthetic composite images and Real composite images, abbreviated as S-FOSD and R-FOSD respectively. We first introduce the S-FOSD dataset. Given a real image with instance segmentation mask, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out this object as foreground. After removing unsuitable categories and occluded foregrounds, the resultant dataset contains 57,859 backgrounds and 63,619 foregrounds. Following [42, 47], for each background image, we deem the foreground object from the same image as ground-truth. For R-FOSD dataset, we collect images from Internet as background images and draw a bounding box at the expected foreground location as query bounding box. R-FOSD dataset shares the same foregrounds with the test set of S-FOSD dataset. Then we employ multiple human"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.257
+            ],
+            "angle": 0,
+            "content": "annotators to label the compatibility of each pair of background and foreground. In summary, S-FOSD dataset is lowcost and highly scalable, but has neither complete background nor ground-truth negative samples. Oppositely, R-FOSD dataset has complete background image with both positive and negative foregrounds annotated by human, yet is unscalable due to the high annotation cost. In our experiments, S-FOSD dataset is used for both training and validating model, while R-FOSD dataset is only used for model evaluation. More details about dataset construction could be found in Section 3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.261,
+                0.895,
+                0.442
+            ],
+            "angle": 0,
+            "content": "We evaluate our method on the proposed datasets, which validates the superiority of the proposed method over previous approaches. Our major contributions can be summarized as follows: 1) To facilitate the research on FOS task, we contribute two public datasets: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. 2) We propose a novel method named DiscoFOS that improves foreground object search by distilling the knowledge of composite image feature into two encoders. 3) Extensive experiments demonstrate the superiority of the proposed method over previous baselines on our datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.466,
+                0.651,
+                0.481
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.494,
+                0.742,
+                0.51
+            ],
+            "angle": 0,
+            "content": "2.1. Foreground Object Search"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.895,
+                0.672
+            ],
+            "angle": 0,
+            "content": "Early works [16, 3] employed hand-crafted features to match background with foreground, yet their performance may be limited by the representation ability of hand-crafted features. Recent work applied deep learning based feature for foreground retrieval. For example, [32] utilized deep features to capture local context particularly for person compositing. [46] trained a discriminator to estimate the realism of composites, which is available for selecting compatible foregrounds by compositing each foreground with the background, but is computationally expensive."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.896,
+                0.901
+            ],
+            "angle": 0,
+            "content": "More recent methods [42, 44, 47, 37, 19] typically trained two encoders to extract background feature and foreground feature, and then measured background foreground compatibility by calculating feature similarity. These methods considered different factors that affect the compatibility between background and foreground. For example, the methods [42, 44] considered the semantic compatibility, while the approaches [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this work, we focus on semantic compatibility and geometry compatibility following [19], and propose a novel foreground object search method that improves the encoders with knowledge distillation. Additionally, previous works [42, 44, 37, 47] did not release their datasets, we contribute two datasets to facilitate the research in this field."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22987"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.265,
+                0.108
+            ],
+            "angle": 0,
+            "content": "2.2. Image Composition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.115,
+                0.473,
+                0.388
+            ],
+            "angle": 0,
+            "content": "As summarized in [24], existing image composition works attempted to solve one or some issues which affect the quality of composite image, such as illumination, shadow, and geometry. Image harmonization methods [34, 6, 7, 5] focused on eliminating the color and illumination discrepancy between background and foreground. Besides, some shadow generation works [14, 9, 40, 22, 12] aimed to generate plausible shadow for the inserted foreground. To blend the foreground into the background more naturally, image blending methods [26, 18, 35] paid attention to smoothing the boundary between background and foreground. The closest subtask to ours is object placement [45, 25, 23, 17, 33], which generates reasonable locations and sizes to place foreground over background. Given a background, object placement focuses on predicting bounding box for the inserted foreground, while our task targets at retrieving compatible foregrounds from a specified category for a given query bounding box."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.398,
+                0.29,
+                0.414
+            ],
+            "angle": 0,
+            "content": "2.3. Knowledge Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.421,
+                0.47,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Knowledge distillation methods usually improve the student network by forcing to mimic the behaviors of the teacher network, such as soft predictions [11], logits [1], intermediate feature maps [27], or attention maps [39]. Apart from the above works on image classification, some recent works extend knowledge distillation to more complex vision tasks, including semantic segmentation [41, 29], object detection [20, 2], face recognition [13], and so on."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.543,
+                0.473,
+                0.771
+            ],
+            "angle": 0,
+            "content": "Previous works [19, 37] have also considered introducing knowledge distillation to foreground object search, in which foreground (resp., background) encoder plays the role of the teacher (resp., student) network and the foreground information is distilled from foreground embedding to background embedding. However, these approaches rely on fine-grained annotations of foreground attributes [19] or multiple pretrained models [37], which may hinder the generalization to unseen foreground categories. Unlike the above methods, our method adopts a composite image discriminator as teacher network and two encoders as student network, in which we distill composite image feature from discriminator to the interaction output of foreground feature and background feature, which proves to be effective and computationally affordable."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.785,
+                0.281,
+                0.801
+            ],
+            "angle": 0,
+            "content": "3. Dataset Construction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Our datasets are constructed on existing Open Images dataset [15] that contains 9.2 million images covering diverse scenes, making it very suitable for real-world evaluation. We build two datasets for foreground object search: S-FOSD with synthetic composite images and R-FOSD with real composite images, which have different ways to acquire"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.089,
+                0.599,
+                0.135
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.509,
+                0.136,
+                0.592,
+                0.145
+            ],
+            "angle": 0,
+            "content": "(a) Source & Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.611,
+                0.089,
+                0.703,
+                0.135
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.623,
+                0.137,
+                0.692,
+                0.147
+            ],
+            "angle": 0,
+            "content": "(b) Background"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.713,
+                0.089,
+                0.775,
+                0.136
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.712,
+                0.137,
+                0.777,
+                0.147
+            ],
+            "angle": 0,
+            "content": "(c) Foreground"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.787,
+                0.089,
+                0.88,
+                0.135
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.785,
+                0.137,
+                0.886,
+                0.147
+            ],
+            "angle": 0,
+            "content": "(d) Synthetic Composite"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.506,
+                0.154,
+                0.599,
+                0.203
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.514,
+                0.204,
+                0.589,
+                0.215
+            ],
+            "angle": 0,
+            "content": "(e) Source Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.611,
+                0.154,
+                0.704,
+                0.203
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.624,
+                0.204,
+                0.691,
+                0.215
+            ],
+            "angle": 0,
+            "content": "(f) Background"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.726,
+                0.153,
+                0.761,
+                0.203
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.711,
+                0.204,
+                0.778,
+                0.214
+            ],
+            "angle": 0,
+            "content": "(g) Foreground"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.787,
+                0.154,
+                0.88,
+                0.203
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.791,
+                0.204,
+                0.875,
+                0.215
+            ],
+            "angle": 0,
+            "content": "(h) Real Composite"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.235,
+                0.894,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Figure 2. The illustration of building our foreground object search (FOS) datasets. Top: FOS Dataset with Synthetic composite images (S-FOSD). Bottom: FOS Dataset with Real composite images (R-FOSD). More details about dataset construction can be seen in Section 3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.326,
+                0.797,
+                0.341
+            ],
+            "angle": 0,
+            "content": "backgrounds and foregrounds (see Figure 2)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.349,
+                0.664,
+                0.364
+            ],
+            "angle": 0,
+            "content": "3.1. S-FOSD Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.373,
+                0.892,
+                0.493
+            ],
+            "angle": 0,
+            "content": "Foreground Object Selection. Open Images dataset [15] provides instance segmentation masks for 2.8 million object instances in 350 categories. To accommodate our task, we delete the categories and objects that are unsuitable for the task or beyond our focus (geometry and semantic compatibility), after which 32 categories remain. The detailed rules for object selection and the complete category list can be found in Supplementary."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.494,
+                0.893,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Background and Foreground Generation. By using the segmentation masks, we generate background and foreground images in a similar way to previous works [42, 47, 44]. Specifically, as shown in Figure 2 (a) \\(\\sim\\) (c), given an image with instance segmentation masks, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out the object and paste it on white background, producing the foreground. With the background and foreground, we can obtain the synthetic composite image by resizing the foreground and placing it in the query bounding box on the background (see Figure 2 (d)). Additionally, we have also tried image inpainting [31, 43, 38] to fill the object bounding box, but got unsatisfactory results, probably due to large missing content and the residues of erased object (e.g., shadow). After that, we obtain over 63,000 pairs of background and foreground covering 32 categories, with a maximum of 5,000 images and a minimum of 500 images in each category. For a given background, the foreground cropped from the same image is naturally compatible and thus deemed as ground-truth following [42, 47, 44]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Dataset Split. S-FOSD dataset is employed for both training and testing, as its construction is low-cost and highly scalable. We first select test samples to build the test set and the rest forms the training set. For reliable performance evaluation, we build test set mainly concerning its diversity and quality. Finally, we get 20 backgrounds and 200"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22988"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.472,
+                0.138
+            ],
+            "angle": 0,
+            "content": "foregrounds for each category, which contains 20 pairs of background and foreground. The remaining 57,219 pairs of background and foreground form the training set."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.145,
+                0.245,
+                0.16
+            ],
+            "angle": 0,
+            "content": "3.2. R-FOSD Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.168,
+                0.47,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Background and Foreground Generation. When building R-FOSD dataset, we directly adopt the foregrounds of the test set in S-FOSD dataset and collect images from Internet as backgrounds. It is very likely that a random image is unsuitable for compositing with any test foreground. Thus, we collect candidate backgrounds by searching similar images to the test backgrounds of S-FOSD dataset. After that, we draw a bounding box at the desired foreground location as query bounding box (see Figure 2 (f)). The size and location of the bounding box are decided by first mimicking the foreground in the similar background of S-FOSD dataset and then manual inspection. For each pair of background and foreground, we resize the foreground and place it in the query bounding box on the source image, generating a real composite image (see Figure 2 (h)). Finally, R-FOSD dataset contains 32 categories, each of which has 20 background images and 200 foreground images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.426,
+                0.471,
+                0.713
+            ],
+            "angle": 0,
+            "content": "Compatibility Labelling. To acquire the binary compatibility label (1 for compatible background foreground pair and 0 for incompatible pair), we employ three human annotators to label the compatibility for \\(32 \\times 20 \\times 200\\) pairs of background and foreground. During annotation, we show real composite images and request annotators to assign binary labels by considering the semantics and geometry compatibility between background and foreground. Finally, for one background, we only consider the foregrounds for which all three human annotators label 1 as compatible and the others are treated as incompatible. Note that manually annotating the dataset is expensive, as it requires labelling a quadratically growing number of background and foreground pairs. Therefore, we only use R-FOSD dataset as a test set. To keep consistent with training data, we also fill the query bounding box of the background in R-FOSD dataset with image mean values at test time and the complete background image of R-FOSD dataset is only used to obtain the final composite image (Figure 2 (h))."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.212,
+                0.743
+            ],
+            "angle": 0,
+            "content": "4. Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, we describe our proposed method for foreground object search. As illustrated in Figure 3, we train a discriminator \\( D \\) to predict the compatibility of composite image, which serves as the teacher network (see Section 4.1). We employ two encoders \\( E^{b} \\) and \\( E^{f} \\) (see Section 4.2) as well as a light-weight knowledge distillation module \\( E^{d} \\) (see Section 4.3) as the student network. The two encoders respectively extract background feature \\( \\mathbf{F}^{b} \\) and foreground feature \\( \\mathbf{F}^{f} \\), which are fed into distillation module to interact with each other. During training"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "stage, we enforce the interaction output \\(\\mathbf{F}^d\\) to match with the composite image feature \\(\\mathbf{F}^c\\), in which the background foreground compatibility information is distilled to \\(\\mathbf{F}^d\\). Finally, we predict compatibility scores for pairwise background and foreground based on the distilled feature \\(\\mathbf{F}^d\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.178,
+                0.783,
+                0.194
+            ],
+            "angle": 0,
+            "content": "4.1. Composite Image Discriminator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.201,
+                0.893,
+                0.565
+            ],
+            "angle": 0,
+            "content": "Network Architecture. Given a background image \\(\\mathbf{I}^b\\) with a query bounding box and a foreground image \\(\\mathbf{I}^f\\), we first generate a synthetic composite image \\(\\mathbf{I}^c\\) as in Figure 2 (d). Then, we employ a discriminator \\(D\\) that takes a composite image as input to predict whether background and foreground of the composite image are compatible. We implement the discriminator as a binary classifier that consists of backbone network and classification head. Moreover, based on preliminary experiments, we find that feeding a cropped composite image into the discriminator achieves significantly better performance than feeding the whole composite image. Specifically, we crop the composite image, ensuring that the foreground object is located at the center and the area of foreground bounding box is about 50 percent of the whole crop. Then, we resize the crop to the input size 224 × 224, which is denoted as \\(\\widetilde{\\mathbf{I}}^c\\). The superiority of feeding cropped composite image can be attributed to that the contextual information near the foreground may be more helpful and the foreground is aligned with crop center. Here we refer to the crop box as \\(B\\). With the cropped composite image, the discriminator first extracts the composite image feature map \\(\\mathbf{F}^c\\) by backbone network and then apply global average pooling (GAP) layer followed by a binary classifier. We train the discriminator using binary cross-entropy loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.617,
+                0.577,
+                0.892,
+                0.602
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {D} = - \\log (p (\\widetilde {\\mathbf {I}} ^ {c}) _ {y}), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.891,
+                0.644
+            ],
+            "angle": 0,
+            "content": "in which \\(p(\\cdot)_y\\) means the predicted probability corresponding to the ground-truth compatibility label \\(y\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.645,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Positive and Negative Samples Generation. During training phase, we consider compatible (resp., incompatible) foreground objects as positive (resp., negative) samples for a given background. The foreground cropped from the same image as the background is naturally viewed as positive sample. However, other foreground objects may also be compatible with the background. To guarantee the effectiveness of training samples, similar to [44], we train a binary classifier using VGG-19 [30] pretrained on ImageNet [8] as backbone network to help filter out training samples. Given a pair of background image and foreground image, the classifier takes their composite image as input and predicts the compatibility score. When training this classifier, we assume that only background foreground pairs from same images are positive and others are negative. With the trained classifier, we restrict negative samples to only include those foreground objects which are confidently"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22989"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.119,
+                0.09,
+                0.482,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.49,
+                0.09,
+                0.852,
+                0.281
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.298,
+                0.895,
+                0.355
+            ],
+            "angle": 0,
+            "content": "Figure 3. Illustration of the proposed DiscoFOS for foreground object search. The discriminator \\(D\\) is first trained to predict the background-foreground compatibility of input composite image \\(\\mathbf{I}^c\\), whose intermediate feature map \\(\\mathbf{F}^c\\) then servers as distillation target to train the student model. The student network first extracts background feature \\(\\mathbf{F}^b\\) and foreground feature \\(\\mathbf{F}^f\\) by two encoders \\(\\{E^f, E^b\\}\\), then applies the features to generate distilled feature \\(\\mathbf{F}^d\\) and compatibility prediction by knowledge distillation module \\(E^d\\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.079,
+                0.379,
+                0.473,
+                0.546
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.56,
+                0.471,
+                0.618
+            ],
+            "angle": 0,
+            "content": "Figure 4. Examples of positive and negative samples used to train our models. Given a background in S-FOSD dataset, we have one positive foreground and one or more negative foregrounds, which are filled with white background pixels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.641,
+                0.47,
+                0.748
+            ],
+            "angle": 0,
+            "content": "classified as incompatible, that is, compatibility score is lower than a threshold (0.3 in our experiments). Therefore, given a background image, we have a single positive foreground and one or more negative foregrounds in S-FOSD dataset (see Figure 4). The obtained positive and negative samples are used to train the composite image discriminator in this section and the student network in Section 4.2, 4.3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.757,
+                0.416,
+                0.773
+            ],
+            "angle": 0,
+            "content": "4.2. Background and Foreground Encoders"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We employ two encoders \\( E^b \\) and \\( E^f \\) to extract feature respectively from background image \\( \\mathbf{I}^b \\) and foreground image \\( \\mathbf{I}^f \\). Correspondingly, the background encoder \\( E^b \\) outputs background feature map \\( \\mathbf{F}^b \\) and the foreground encoder \\( E^f \\) outputs foreground feature map \\( \\mathbf{F}^f \\), both of which have the same shape, i.e., \\( \\mathbf{F}^b \\), \\( \\mathbf{F}^f \\in \\mathcal{R}^{h \\times w \\times c} \\). Here \\( h \\times w \\) is the spatial size and \\( c \\) is the number of channels. Then we apply GAP layer to yield background and foreground fea"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.378,
+                0.892,
+                0.575
+            ],
+            "angle": 0,
+            "content": "ture vectors, denoted as \\(\\bar{\\mathbf{F}}^b\\), \\(\\bar{\\mathbf{F}}^f \\in \\mathcal{R}^c\\). After mapping the foreground and background into the common feature space, we enforce the compatible background and foreground to be close to each other in this space. Thus, the compatibility between foreground and background can be measured by computing the cosine similarity between their features. To this end, following previous works [37, 42, 44, 47], we train the encoders using triplet loss [28], which tends to pull the positive sample (i.e., compatible foreground) to the anchor (i.e., given background) and push the negative sample (i.e., incompatible foreground) away from the anchor in the feature space. During training stage, we tend to minimize the following loss function:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.525,
+                0.583,
+                0.892,
+                0.604
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {t r p} = \\max \\left(0, m + S (\\bar {\\mathbf {F}} ^ {b}, \\bar {\\mathbf {F}} _ {n} ^ {f}) - S (\\bar {\\mathbf {F}} ^ {b}, \\bar {\\mathbf {F}} _ {p} ^ {f})\\right), \\quad (2)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.611,
+                0.893,
+                0.78
+            ],
+            "angle": 0,
+            "content": "where \\( S(\\cdot) \\) represents cosine similarity and \\( m \\) is a positive margin in the range of (0, 1). \\( \\bar{\\mathbf{F}}_p^f \\) (resp., \\( \\bar{\\mathbf{F}}_n^f \\)) is the feature of positive (resp., negative) foreground for background \\( \\bar{\\mathbf{F}}^b \\). By minimizing \\( \\mathcal{L}_{trp} \\), for a given background, the feature similarity with compatible foreground is expected to be greater than that with incompatible foreground by the margin \\( m \\). Additionally, the above encoders are usually employed in previous methods [42, 44, 47]. Given a query background and a foreground database, these approaches rank the compatibility of different foregrounds by measuring their feature similarity to the given background."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.787,
+                0.776,
+                0.803
+            ],
+            "angle": 0,
+            "content": "4.3. Knowledge Distillation Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "After evaluating the discriminator in Section 4.1 and the encoders in Section 4.2, we observe that discriminator can achieve much better results than encoders, probably because the forward propagation in the discriminator allows thorough interaction between background and foreground, providing useful contextual cues for estimating background"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22990"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.198
+            ],
+            "angle": 0,
+            "content": "foreground compatibility. However, retrieving foreground images using discriminator requires to composite with each foreground image, which brings heavy computational burden. On the contrary, encoders achieve inferior performance, yet have significantly faster speed due to the exemption from background-foreground interaction. This motivates us to distill discriminator knowledge into encoders."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.199,
+                0.47,
+                0.545
+            ],
+            "angle": 0,
+            "content": "To achieve this goal, we design a knowledge distillation module \\( E^{d} \\), which interacts foreground feature with background feature and enforces the interaction output to match with the composite image feature \\( \\mathbf{F}^{c} \\) from the discriminator. Recall that the composite image feature is extracted from cropped composite image, with the crop bounding box denoted as \\( B \\) (see Section 4.1). So we apply RoIAlign [10] with the bounding box \\( B \\) to obtain local background feature map \\( \\widetilde{\\mathbf{F}}^{b} \\) from global background feature map \\( \\mathbf{F}^{b} \\) produced by background encoder \\( E^{b} \\). Then, we resize RoIAlign output to be of the same shape as \\( \\mathbf{F}^{b} \\), i.e., \\( \\widetilde{\\mathbf{F}}^{b} \\in \\mathcal{R}^{h \\times w \\times c} \\). The local background feature is supposed to encode contextual information surrounding the foreground. Meanwhile, we utilize foreground encoder \\( E^{f} \\) to extract foreground feature map \\( \\mathbf{F}^{f} \\). Given the foreground feature map \\( \\mathbf{F}^{f} \\) and local background feature map \\( \\widetilde{\\mathbf{F}}^{b} \\), we feed their concatenation into \\( E^{d} \\) to produce a distilled feature map \\( \\mathbf{F}^{d} \\in \\mathcal{R}^{h \\times w \\times c} \\). Note the discriminator and two encoders adopt the same backbone network and input image size in our implementation, so their feature maps have the same shape, i.e., \\( \\mathbf{F}^{c}, \\mathbf{F}^{d} \\in \\mathcal{R}^{h \\times w \\times c} \\). During training phase, we enforce the distilled feature \\( \\mathbf{F}^{d} \\) to mimic the composite image feature \\( \\mathbf{F}^{c} \\) by \\( L_{1} \\) loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.204,
+                0.554,
+                0.469,
+                0.573
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {k d} = \\left\\| \\mathbf {F} ^ {d} - \\mathbf {F} ^ {c} \\right\\| _ {1}. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.583,
+                0.469,
+                0.628
+            ],
+            "angle": 0,
+            "content": "We pool the distilled feature map into a vector and send it to a binary classifier to predict the compatibility. The classifier is also trained using binary cross-entropy loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.191,
+                0.637,
+                0.469,
+                0.656
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {c l s} = - \\log (p (\\mathbf {F} ^ {d}) _ {y}), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.665,
+                0.391,
+                0.68
+            ],
+            "angle": 0,
+            "content": "in which \\(p(\\cdot)_y\\) is similarly defined as in Eqn. 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.68,
+                0.469,
+                0.724
+            ],
+            "angle": 0,
+            "content": "Finally, we train the encoders \\(\\{E^f,E^b\\}\\) and distillation module \\(E^{d}\\) simultaneously. The overall optimization function can be written as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.165,
+                0.737,
+                0.469,
+                0.753
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {t r p} + \\lambda_ {k d} \\mathcal {L} _ {k d} + \\lambda_ {c l s} \\mathcal {L} _ {c l s}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.763,
+                0.469,
+                0.809
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{kd}\\) and \\(\\lambda_{cls}\\) are trade-off parameters. During inference, our model finds compatible foregrounds for a given background by ranking the predicted compatibility scores."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.818,
+                0.431,
+                0.834
+            ],
+            "angle": 0,
+            "content": "4.4. Generalization to Real-world Application"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.84,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "To boost the performance of our method on real-world data, we make some modifications to the training procedure of our teacher network and student network, which helps achieve more competitive results on the R-FOSD dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.317
+            ],
+            "angle": 0,
+            "content": "For the teacher network, we utilize the binary classifier in Section 4.1 to extend training samples. Specifically, given a background image, we use the classifier to predict compatibility score for each foreground and treat those with scores larger than 0.8 as positive samples (including the ground-truth foreground), based on which the ratio of positive and negative foregrounds per background is increased from 1:10 to 5:10. Besides, we apply data augmentation to generate additional positive and negative samples from the ground-truth foreground for each background image. Precisely, based on the ground-truth foreground, we produce 2 positive foregrounds through color jitter and Gaussian blur, and 1 negative foreground through affine transformation. After augmentation, the ratio of positive and negative samples changes from 5:10 to 7:11."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.319,
+                0.892,
+                0.424
+            ],
+            "angle": 0,
+            "content": "For the student network, we select the top-5 foregrounds returned by pretrained teacher network as positive samples (including the ground-truth foreground) and adopt the same negative samples as the teacher network. After applying the same data augmentation scheme as the teacher network, we also have positive and negative samples with the ratio 7:11 to train the student network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.426,
+                0.892,
+                0.516
+            ],
+            "angle": 0,
+            "content": "Finally, considering that user-provided bounding boxes may not be very accurate, we also augment bounding boxes when training teacher network and student network. Specifically, we randomly pad the bounding box with the maximum padding space being \\(30\\%\\) of the bounding box's width and height."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.533,
+                0.634,
+                0.55
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.559,
+                0.779,
+                0.573
+            ],
+            "angle": 0,
+            "content": "5.1. Dataset and Evaluation Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.688
+            ],
+            "angle": 0,
+            "content": "Our S-FOSD dataset is employed for both training and testing, while R-FOSD dataset is only for testing. We employ different evaluation metrics for two datasets considering their difference in the acquisition of ground-truth foregrounds. For each metric, we report the mean evaluation results by averaging the results over all categories. Moreover, we leave the implementation details in Supplementary."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "S-FOSD Dataset. The training set has 57,219 pairs of foregrounds and backgrounds covering 32 categories, with a maximum of 4800 pairs and a minimum of 300 pairs in each category. The test set provides 20 backgrounds and 200 foregrounds (including 20 foregrounds from the same images as the backgrounds) for each category. The foreground/background images in the training set and test set have no overlap. Following previous works [42, 47], only the foreground object from the same image is viewed as ground-truth for each background and we adopt Recall@k (R@k) as evaluation metric, which represents the percentage of background queries whose ground-truth foreground appears in top \\( k \\) retrievals (\\( k = 1, 5, 10, 20 \\) in our experiments)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.946,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22991"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.473,
+                0.319
+            ],
+            "angle": 0,
+            "content": "R-FOSD Dataset. The R-FOSD dataset adopts the same foreground set as the test set of S-FOSD dataset and collects 20 backgrounds for each category. Each pair of background and foreground is shown to three human annotators to label the compatibility. The resulting dataset contains \\(4\\sim 190\\) compatible foregrounds per background, and we adopt mean Average Precision (mAP), mAP@20, and Precision@k (P@k) for evaluation, which are widely used in image retrieval and previous works [44, 47]. Precision@k means the percentage of compatible foreground objects in the top k retrievals, \\(k = 1,5,10,20\\) in our experiments. To reduce unplausible results on the R-FOSD dataset, we exclude the objects with aspect ratios deviating more than 1.2 from that of query bounding box for all methods and compute metrics on the remaining objects."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.331,
+                0.388,
+                0.347
+            ],
+            "angle": 0,
+            "content": "5.2. Comparison with Existing Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.355,
+                0.473,
+                0.687
+            ],
+            "angle": 0,
+            "content": "Baselines. We compare our approach with previous methods [42, 44, 37, 47] on our two datasets. Shape [42] ranks foreground objects by comparing their aspect ratios with that of the query bounding box on background. CFO [42], UFO [44], FFR [37], and GALA [47] adopt the pipeline described in Section 4.2, which use two encoders to extract background and foreground features, and then rank the compatibility of foreground by computing its feature similarity with background. To adapt to our focus on geometric and semantic incompatibility, we replace the style feature of FFR [37] with semantic feature, in which we obtain the semantic feature by using VGG-19 [30] pretrained on ImageNet [8] following [44]. For GALA [47] that considers lighting and geometry compatibility, we discard lighting transformation and only keep geometry transformation [47] to match our scenario. Besides, we do not compare with IFR [19], as it requires pattern labels of the foreground, which are unavailable in our datasets. For fair comparison, we employ the same backbone network and training set for all baseline methods except Shape [42]. We use the same positive and negative samples for different methods when training on S-FOSD dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.472,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Quantitative comparison. The results of baselines and our method on the proposed two datasets are summarized in Table 1. Moreover, when evaluating on S-FOSD dataset, the only ground-truth foreground has the same aspect ratio as the query bounding box, thus Shape [42] can find the ground-truth by shortcut, making the evaluation results meaningless. It can be seen that among all baselines, GALA [47] and FFR [37] are two competitive ones, which employ contrastive learning with self-transformation [47] and MarrNet [36] to enhance the perception of geometric information of foreground, respectively. Nevertheless, our method outperforms all previous approaches by an obvious margin on both S-FOSD and R-FOSD datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.886,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Qualitative comparison. We show the retrieval results of"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.089,
+                0.895,
+                0.298
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.309,
+                0.895,
+                0.395
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative comparison on our S-FOSD (left) and R-FOSD (right) datasets. Each of the four examples contains a background image and several rows of the retrieval results, from top to bottom: CFO [42], UFO [44], GALA [47], FFR [37], and ours. Additionally, in the right part, green (resp., red) box represents the foreground with compatible (resp., incompatible) label."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.416,
+                0.896,
+                0.689
+            ],
+            "angle": 0,
+            "content": "different baselines on our two datasets in Figure 5. For each query background, we show the returned top-5 foregrounds by different methods, which shows that our method can generally find compatible foregrounds by taking both semantic and geometric factors into account. For example, for the top-left example, given a query bounding box at the bottom-right seat, the baseline methods may return a standing or frontal person, which is unsuitable to be placed in the query bounding box. In contrast, the top returned persons by our method all have sitting posture, which appear more reasonable in terms of semantic compatibility. In the bottom-right example, given the geometry of background scene, the annotated ground-truth positive foregrounds (green box) have consistent orientation with respect to the train track in background. Our method retrieves more positive foregrounds than other approaches, demonstrating the effectiveness of our method on geometry compatibility. More qualitative results are present in Supplementary."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.697,
+                0.655,
+                0.713
+            ],
+            "angle": 0,
+            "content": "5.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, we start from the general pipeline with two encoders of previous methods [42, 44, 47, 19, 37] and evaluate the effectiveness of each component in our method. Different models are evaluated on our S-FOSD dataset and the results are summarized in Table 2. In row 1, we apply two encoders \\(\\{E^b,E^f\\}\\) to extract background feature \\(\\bar{\\mathbf{F}}^b\\) and foreground feature \\(\\bar{\\mathbf{F}}^f\\), which are used to predict the background foreground compatibility by measuring their feature similarity. It is worth mentioning that all models in Table 2 rank different foregrounds by predicted compatibility scores except the row 1 and row 2, which measure compatibility by calculating feature similarity."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "22992"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.1,
+                0.089,
+                0.872,
+                0.216
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">S-FOSD Dataset</td><td colspan=\"6\">R-FOSD Dataset</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td><td>mAP↑</td><td>mAP@20↑</td><td>P@1↑</td><td>P@5↑</td><td>P@10↑</td><td>P@20↑</td></tr><tr><td>Shape [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>50.49</td><td>56.22</td><td>47.66</td><td>49.72</td><td>50.03</td><td>49.92</td></tr><tr><td>CFO [42]</td><td>56.09</td><td>83.59</td><td>91.25</td><td>96.88</td><td>52.06</td><td>62.17</td><td>58.33</td><td>56.29</td><td>55.90</td><td>52.85</td></tr><tr><td>UFO [44]</td><td>54.69</td><td>81.72</td><td>90.94</td><td>95.31</td><td>52.73</td><td>63.63</td><td>64.12</td><td>59.11</td><td>56.30</td><td>53.82</td></tr><tr><td>FFR [37]</td><td>57.03</td><td>86.25</td><td>93.28</td><td>97.97</td><td>53.10</td><td>64.12</td><td>61.92</td><td>59.64</td><td>57.56</td><td>55.06</td></tr><tr><td>GALA [47]</td><td>57.50</td><td>85.17</td><td>93.00</td><td>97.33</td><td>52.02</td><td>62.83</td><td>62.56</td><td>57.33</td><td>55.76</td><td>52.93</td></tr><tr><td>DiscoFOS</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td><td>56.70</td><td>68.56</td><td>67.75</td><td>64.64</td><td>62.25</td><td>58.90</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.111,
+                0.226,
+                0.856,
+                0.24
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison with existing methods on our S-FOSD dataset and R-FOSD dataset. Best results are denoted in boldface."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.262,
+                0.462,
+                0.443
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Eb</td><td>Ed</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td></tr><tr><td>1</td><td>Fb</td><td></td><td>54.83</td><td>81.17</td><td>90.67</td><td>95.00</td></tr><tr><td>2</td><td>Fb</td><td></td><td>52.50</td><td>79.69</td><td>88.75</td><td>93.00</td></tr><tr><td>3</td><td>Fb</td><td>p(·)y</td><td>56.72</td><td>87.19</td><td>94.69</td><td>97.97</td></tr><tr><td>4</td><td>Fb</td><td>[Fb, Ff]</td><td>60.83</td><td>87.33</td><td>95.00</td><td>98.17</td></tr><tr><td>5</td><td>Fb</td><td>[Hatb, Ff]</td><td>65.16</td><td>90.31</td><td>95.31</td><td>98.59</td></tr><tr><td>6</td><td>Fb</td><td>[Fb, Ff]</td><td>68.28</td><td>90.94</td><td>95.63</td><td>98.75</td></tr><tr><td>7</td><td>Fb</td><td>Fb ⊕ Ff</td><td>64.53</td><td>87.66</td><td>92.97</td><td>96.72</td></tr><tr><td>8</td><td>Fb</td><td>[Fb, Ff]</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td></tr><tr><td>9</td><td></td><td>D(Ic)</td><td>49.22</td><td>76.72</td><td>84.53</td><td>91.88</td></tr><tr><td>10</td><td></td><td>D(Ic)</td><td>84.38</td><td>97.03</td><td>98.91</td><td>99.84</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.454,
+                0.47,
+                0.525
+            ],
+            "angle": 0,
+            "content": "Table 2. The ablation studies of our method on S-FOSD dataset. \\(\\bar{\\mathbf{F}}^b, \\hat{\\mathbf{F}}^b\\): global/local background feature vector. \\(\\mathbf{F}^b, \\widetilde{\\mathbf{F}}^b\\): global/local background feature map. \\(\\mathbf{F}^f, \\widetilde{\\mathbf{F}}^f\\): foreground feature map/vector. \\([\\cdot, \\cdot]\\): feature concatenation. \\(\\oplus\\): feature map composition. The detailed explanations can be found in Section 5.3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.551,
+                0.468,
+                0.687
+            ],
+            "angle": 0,
+            "content": "Background Encoder \\( E^b \\). Based on row 1 of Table 2, we replace the global background feature vector \\( \\bar{\\mathbf{F}}^b \\) with local background feature vector \\( \\hat{\\mathbf{F}}^b \\), which is obtained by applying RoIAlign [10] with the crop bounding box \\( B \\) to background feature map \\( \\mathbf{F}^b \\), resulting in worse results in row 2. This is probably because that the global background feature contains more useful information than the local background feature. So we adopt the global background feature for background encoder in other experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.688,
+                0.468,
+                0.883
+            ],
+            "angle": 0,
+            "content": "Composite Image Discriminator \\(D\\). In our network, the discriminator plays the role of teacher. In row 9 and 10 of Table 2, we feed the discriminator with the whole composite image \\(\\mathbf{I}^c\\) and the cropped composite image \\(\\widetilde{\\mathbf{I}}^c\\), respectively. We see that row 10 achieves significantly better performance than row 9, which can be attributed to the aligned foreground and useful surrounding foreground context in the cropped composite. Then, the discriminator with the whole composite image is inferior to the encoders of row 1, which is roughly consistent with previous findings [44, 42]. Additionally, the discriminator with cropped composite image outperforms the encoders (row 1) with a remarkable margin, which motivates us to build our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.885,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Knowledge Distillation Module \\(E^d\\). Based on row 1 of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.265,
+                0.892,
+                0.37
+            ],
+            "angle": 0,
+            "content": "Table 2, we introduce the distillation module without using feature distillation, which is essentially a compatibility classifier \\( p(\\cdot)_y \\), in row 3. The classifier takes the concatenation of foreground feature vector \\( \\bar{\\mathbf{F}}^f \\) and background feature vector \\( \\bar{\\mathbf{F}}^b \\) as input, and outputs the compatibility score. The comparison between row 1 and 3 verifies that adding compatibility classification is helpful for our task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.371,
+                0.892,
+                0.522
+            ],
+            "angle": 0,
+            "content": "Then we add feature distillation and explore the impact of using different forms of background-foreground interactions. In row 4 and 5, we perform interaction based on the pooled feature vectors of two encoders. Specifically, we concatenate the foreground feature vector \\(\\overline{\\mathbf{F}}^f\\) with global background feature vector \\(\\overline{\\mathbf{F}}^b\\) (resp., local background feature vector \\(\\hat{\\mathbf{F}}^b\\)) to feed into distillation module in row 4 (resp., row 5). Both results are better than row 3, proving the utility of distilling composite image feature to predict compatibility."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.522,
+                0.892,
+                0.823
+            ],
+            "angle": 0,
+            "content": "Next, we perform interaction based on the last feature maps of two encoders. To this end, we explore several different ways to fuse background and foreground features. First, we directly concatenate background feature map \\(\\mathbf{F}^b\\) and foreground feature map \\(\\mathbf{F}^f\\) in row 6. By comparing row 6 and 4, it verifies the advantage of more sufficient interaction. In row 7, we extend to a more intuitive way by applying composition operation to local background feature maps \\(\\widetilde{\\mathbf{F}}^b\\) and foreground feature map \\(\\mathbf{F}^f\\). Specifically, we resize the foreground feature and place it in the query bounding box on the local background feature. Unexpectedly, this leads to slight performance drop compared with row 5, which may be caused by downsampling the foreground feature. Finally, we concatenate the local background feature \\(\\widetilde{\\mathbf{F}}^b\\) and foreground feature \\(\\mathbf{F}^f\\), corresponding to our complete method. As shown in row 8, our full method produces remarkably better results than the abovementioned row 6, indicating that the representation ability of the distilled feature can benefit from adequate interaction between two encoders."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.833,
+                0.761,
+                0.849
+            ],
+            "angle": 0,
+            "content": "5.4. Inference Efficiency Analyses"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To study the efficiency of our method, we compare our method (\"Ours\") with the composite image discriminator (\"Discriminator\"), and background and foreground"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "22993"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.089,
+                0.462,
+                0.153
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Time(200)↓</td><td>Time(2000)↓</td><td>#Params↓</td></tr><tr><td>Discriminator</td><td>700.0ms</td><td>7000.1ms</td><td>20.03M</td></tr><tr><td>Encoders</td><td>4.0ms</td><td>4.3ms</td><td>40.05M</td></tr><tr><td>Ours</td><td>5.2ms</td><td>6.0ms</td><td>47.13M</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.163,
+                0.47,
+                0.22
+            ],
+            "angle": 0,
+            "content": "Table 3. Comparing inference efficiency of different models, including the discriminator \\( D \\), encoders \\( \\{E^b, E^f\\} \\), and our method in the Figure 3. \"Time(N)\" represents the average time of retrieving compatible foregrounds from \\( N \\) candidates per background."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.242,
+                0.47,
+                0.483
+            ],
+            "angle": 0,
+            "content": "encoders (\"Encoders\") on retrieval time and number of parameters, the results of which are reported in the Table 3. We test different models on an NVIDIA RTX 3090 GPU and measure the time of retrieving compatible foreground from \\(N\\) candidates as retrieval time \\((\\mathrm{Time}(N))\\). We repeat the retrieval 50 times and calculate the average time as final result. To mimic the practical application scenarios of foreground object search, we assume that the features of all foregrounds have been extracted and saved before retrieval. In particular, for \"Encoders\" and \"Ours\", we save the feature vector and the last feature map of the foreground encoder, respectively. In this way, the retrieval time of \"Encoders\" and \"Ours\" only considers the background feature extraction and the matching between background and foreground, in which background feature extraction takes 3.1ms per image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.485,
+                0.47,
+                0.635
+            ],
+            "angle": 0,
+            "content": "We can see that the discriminator \\( D \\) is the slowest method due to compositing with each foreground and sending each composite through forward pass. \"Ours\" runs slower than \"Encoders\" due to introducing additional interaction between background and foreground, yet only takes 6ms to retrieve from 2000 foregrounds, which enables our model for real-time applications. Regarding the number of parameters, the comparison between two encoders and ours indicates that the additional parameters (7.08M) introduced by distillation module are affordable."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.644,
+                0.44,
+                0.661
+            ],
+            "angle": 0,
+            "content": "5.5. Additional Experiments in Supplementary"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.667,
+                0.468,
+                0.773
+            ],
+            "angle": 0,
+            "content": "Due to space limitation, we present some experiments in Supplementary, including quantitative comparison on different categories, generalization to new categories, the results of our method using different hyper-parameters in Eqn. (5) and Eqn. (2), and different ratios of positive and negative training samples, the discussion on the limitation of our method, and the results of significance test."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.785,
+                0.196,
+                0.8
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+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, we have contributed two public datasets for Foreground Object Search (FOS), S-FOSD with Synthetic composite images and R-FOSD with Real composite images. We have also proposed a novel FOS method, which improves the general pipeline of previous methods by feature distillation. Extensive experiments on our dataset have"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "demonstrated the utility of our proposed method on foreground object search."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.134,
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+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.159,
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+            "angle": 0,
+            "content": "The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300)."
+        },
+        {
+            "type": "title",
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+# Foreground Object Search by Distilling Composite Image Feature
+
+Bo Zhang $^{1}$ , Jiacheng Sui $^{2}$ , and Li Niu $^{*1}$
+
+<sup>1</sup>Center for Machine Cognitive Computing of Artificial Intelligence Institute, Artificial Intelligence Institute, Shanghai Jiao Tong University
+
+{bo-zhang, ustcnewly}@sjtu.edu.cn
+
+$^{2}$ Xian Jiao Tong University
+
+rookiecharles99@gmail.com
+
+# Abstract
+
+Foreground object search (FOS) aims to find compatible foreground objects for a given background image, producing realistic composite image. We observe that competitive retrieval performance could be achieved by using a discriminator to predict the compatibility of composite image, but this approach has unaffordable time cost. To this end, we propose a novel FOS method via distilling composite feature (DiscoFOS). Specifically, the abovementioned discriminator serves as teacher network. The student network employs two encoders to extract foreground feature and background feature. Their interaction output is enforced to match the composite image feature from the teacher network. Additionally, previous works did not release their datasets, so we contribute two datasets for FOS task: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. Extensive experiments on our two datasets demonstrate the superiority of the proposed method over previous approaches. The dataset and code are available at https://github.com/bcmi/Foreground-Object-Search-Dataset-FOSD.
+
+# 1. Introduction
+
+Foreground Object Search (FOS) aims to find compatible foregrounds from specified category for a given background image which has a query bounding box indicating the foreground location [42]. More precisely, an object is compatible with a background image if it can be realistically composited into the image [44], as illustrated in Figure 1. FOS is a core technique in many image composition applications [24]. For example, FOS technique can help
+
+![](images/b1a89b645802ae5099c6a8e4b58824206c316e93c5945c9238147f8cbb2322ea.jpg)  
+Figure 1. Illustration of foreground object search. Given a background image with query bounding box (yellow), foreground object search aims to find compatible foreground objects of a specified category from a database, which is composited with the background to produce a realistic composite image.
+
+users acquire suitable foregrounds from a foreground pool automatically and efficiently for object insertion in photo editing [19]. Moreover, FOS also can be used to fill a region comprising undesired objects using new foreground [44].
+
+There exist many factors that affect the compatibility between background and foreground, including semantics, style (e.g., color and texture), lighting, and geometry (e.g., shape and viewpoint). Previous works on FOS may consider different factors. For example, early methods [42, 44] focused on the semantic compatibility. Recent works [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this paper, we focus on semantics and geometry compatibility following [19], because incompatible color and lighting between the background and foreground can be tackled to some extent by image harmonization [6, 21, 4].
+
+The general pipeline of most existing methods [42, 44, 47, 19, 37] is to learn an embedding space with two encoders respectively for background and foreground, so that compatible background and foreground are close to each other in this space. Alternatively, some approaches [46, 44] trained a discriminator to predict background-foreground compatibility by feeding the composite image. Based on preliminary experiments, we observe that the discriminator can achieve much better results than encoders when taking the cropped composite image as input (see teacher network in Figure 3). We conjecture that the forward pass in the discriminator allows thorough interaction between background and foreground, which could provide useful contextual cues for estimating background-foreground compatibility. However, given a background image, it is very time-consuming to compose with each foreground image and perform forward computation for each composite image. Motivated by this, we propose a novel FOS framework called DiscoFOS via knowledge distillation. Specifically, we distill the knowledge of composite image from the discriminator to two encoders, in which we enforce the interaction output of foreground feature and background feature to match with the composite image feature. How to design the interaction between two encoders is challenging, due to the trade-off between performance and computational cost. On the one hand, insufficient interaction between two encoders may be unable to mimic the rich knowledge in composite image feature. On the other hand, sufficient interaction would largely increase the computational burden. Considering the abovementioned trade-off, we perform interaction only on the last feature maps of two encoders, which achieves significant performance improvement with acceptable computational overhead.
+
+Since previous works (CAIS [42], UFO [44], and GALA [47]) did not release their datasets, we build our own datasets based on an existing large-scale real-world dataset, i.e., Open Images [15], as illustrated in Figure 2. We construct two FOS Datasets respectively containing Synthetic composite images and Real composite images, abbreviated as S-FOSD and R-FOSD respectively. We first introduce the S-FOSD dataset. Given a real image with instance segmentation mask, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out this object as foreground. After removing unsuitable categories and occluded foregrounds, the resultant dataset contains 57,859 backgrounds and 63,619 foregrounds. Following [42, 47], for each background image, we deem the foreground object from the same image as ground-truth. For R-FOSD dataset, we collect images from Internet as background images and draw a bounding box at the expected foreground location as query bounding box. R-FOSD dataset shares the same foregrounds with the test set of S-FOSD dataset. Then we employ multiple human
+
+annotators to label the compatibility of each pair of background and foreground. In summary, S-FOSD dataset is lowcost and highly scalable, but has neither complete background nor ground-truth negative samples. Oppositely, R-FOSD dataset has complete background image with both positive and negative foregrounds annotated by human, yet is unscalable due to the high annotation cost. In our experiments, S-FOSD dataset is used for both training and validating model, while R-FOSD dataset is only used for model evaluation. More details about dataset construction could be found in Section 3.
+
+We evaluate our method on the proposed datasets, which validates the superiority of the proposed method over previous approaches. Our major contributions can be summarized as follows: 1) To facilitate the research on FOS task, we contribute two public datasets: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. 2) We propose a novel method named DiscoFOS that improves foreground object search by distilling the knowledge of composite image feature into two encoders. 3) Extensive experiments demonstrate the superiority of the proposed method over previous baselines on our datasets.
+
+# 2. Related Works
+
+# 2.1. Foreground Object Search
+
+Early works [16, 3] employed hand-crafted features to match background with foreground, yet their performance may be limited by the representation ability of hand-crafted features. Recent work applied deep learning based feature for foreground retrieval. For example, [32] utilized deep features to capture local context particularly for person compositing. [46] trained a discriminator to estimate the realism of composites, which is available for selecting compatible foregrounds by compositing each foreground with the background, but is computationally expensive.
+
+More recent methods [42, 44, 47, 37, 19] typically trained two encoders to extract background feature and foreground feature, and then measured background foreground compatibility by calculating feature similarity. These methods considered different factors that affect the compatibility between background and foreground. For example, the methods [42, 44] considered the semantic compatibility, while the approaches [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this work, we focus on semantic compatibility and geometry compatibility following [19], and propose a novel foreground object search method that improves the encoders with knowledge distillation. Additionally, previous works [42, 44, 37, 47] did not release their datasets, we contribute two datasets to facilitate the research in this field.
+
+# 2.2. Image Composition
+
+As summarized in [24], existing image composition works attempted to solve one or some issues which affect the quality of composite image, such as illumination, shadow, and geometry. Image harmonization methods [34, 6, 7, 5] focused on eliminating the color and illumination discrepancy between background and foreground. Besides, some shadow generation works [14, 9, 40, 22, 12] aimed to generate plausible shadow for the inserted foreground. To blend the foreground into the background more naturally, image blending methods [26, 18, 35] paid attention to smoothing the boundary between background and foreground. The closest subtask to ours is object placement [45, 25, 23, 17, 33], which generates reasonable locations and sizes to place foreground over background. Given a background, object placement focuses on predicting bounding box for the inserted foreground, while our task targets at retrieving compatible foregrounds from a specified category for a given query bounding box.
+
+# 2.3. Knowledge Distillation
+
+Knowledge distillation methods usually improve the student network by forcing to mimic the behaviors of the teacher network, such as soft predictions [11], logits [1], intermediate feature maps [27], or attention maps [39]. Apart from the above works on image classification, some recent works extend knowledge distillation to more complex vision tasks, including semantic segmentation [41, 29], object detection [20, 2], face recognition [13], and so on.
+
+Previous works [19, 37] have also considered introducing knowledge distillation to foreground object search, in which foreground (resp., background) encoder plays the role of the teacher (resp., student) network and the foreground information is distilled from foreground embedding to background embedding. However, these approaches rely on fine-grained annotations of foreground attributes [19] or multiple pretrained models [37], which may hinder the generalization to unseen foreground categories. Unlike the above methods, our method adopts a composite image discriminator as teacher network and two encoders as student network, in which we distill composite image feature from discriminator to the interaction output of foreground feature and background feature, which proves to be effective and computationally affordable.
+
+# 3. Dataset Construction
+
+Our datasets are constructed on existing Open Images dataset [15] that contains 9.2 million images covering diverse scenes, making it very suitable for real-world evaluation. We build two datasets for foreground object search: S-FOSD with synthetic composite images and R-FOSD with real composite images, which have different ways to acquire
+
+![](images/e11aad6b6ca0ad109bc03020621b642c4bdf58c2dd4f9779a7c486d10f13fbe2.jpg)  
+(a) Source & Mask
+
+![](images/b3cbf48296c1c2b0e0bfe7132a9ee2c6849afc9b78d3332f3434361fa0c3b446.jpg)  
+(b) Background
+
+![](images/d9f4b38deab97e02919c2bbe080ed68ddeebf36daf8014a1b09457a6d35f1885.jpg)  
+(c) Foreground
+
+![](images/6290fdd373d71d30233d480961fe3c420aea10ee9df3236768b1505b9b90fdf3.jpg)  
+(d) Synthetic Composite
+
+![](images/ea8febc0e70f8bdae612325d704e3f07ef8b385b98f10679a931959961ef1686.jpg)  
+(e) Source Image
+
+![](images/3eeceb6e9f89d1782c094bedd613fec1bb57886a941209d940428cd39581a472.jpg)  
+(f) Background
+
+![](images/891714b51562c9b66564b4f0a93de1e11c24e777c4f0af653f1ed742eb12cc1f.jpg)  
+(g) Foreground  
+Figure 2. The illustration of building our foreground object search (FOS) datasets. Top: FOS Dataset with Synthetic composite images (S-FOSD). Bottom: FOS Dataset with Real composite images (R-FOSD). More details about dataset construction can be seen in Section 3.
+
+![](images/e9d27e09195ba7fb55788e2069f74ae858cf1d8bbd6f240672822e3f5e55191d.jpg)  
+(h) Real Composite
+
+backgrounds and foregrounds (see Figure 2).
+
+# 3.1. S-FOSD Dataset
+
+Foreground Object Selection. Open Images dataset [15] provides instance segmentation masks for 2.8 million object instances in 350 categories. To accommodate our task, we delete the categories and objects that are unsuitable for the task or beyond our focus (geometry and semantic compatibility), after which 32 categories remain. The detailed rules for object selection and the complete category list can be found in Supplementary.
+
+Background and Foreground Generation. By using the segmentation masks, we generate background and foreground images in a similar way to previous works [42, 47, 44]. Specifically, as shown in Figure 2 (a)  $\sim$  (c), given an image with instance segmentation masks, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out the object and paste it on white background, producing the foreground. With the background and foreground, we can obtain the synthetic composite image by resizing the foreground and placing it in the query bounding box on the background (see Figure 2 (d)). Additionally, we have also tried image inpainting [31, 43, 38] to fill the object bounding box, but got unsatisfactory results, probably due to large missing content and the residues of erased object (e.g., shadow). After that, we obtain over 63,000 pairs of background and foreground covering 32 categories, with a maximum of 5,000 images and a minimum of 500 images in each category. For a given background, the foreground cropped from the same image is naturally compatible and thus deemed as ground-truth following [42, 47, 44].
+
+Dataset Split. S-FOSD dataset is employed for both training and testing, as its construction is low-cost and highly scalable. We first select test samples to build the test set and the rest forms the training set. For reliable performance evaluation, we build test set mainly concerning its diversity and quality. Finally, we get 20 backgrounds and 200
+
+foregrounds for each category, which contains 20 pairs of background and foreground. The remaining 57,219 pairs of background and foreground form the training set.
+
+# 3.2. R-FOSD Dataset
+
+Background and Foreground Generation. When building R-FOSD dataset, we directly adopt the foregrounds of the test set in S-FOSD dataset and collect images from Internet as backgrounds. It is very likely that a random image is unsuitable for compositing with any test foreground. Thus, we collect candidate backgrounds by searching similar images to the test backgrounds of S-FOSD dataset. After that, we draw a bounding box at the desired foreground location as query bounding box (see Figure 2 (f)). The size and location of the bounding box are decided by first mimicking the foreground in the similar background of S-FOSD dataset and then manual inspection. For each pair of background and foreground, we resize the foreground and place it in the query bounding box on the source image, generating a real composite image (see Figure 2 (h)). Finally, R-FOSD dataset contains 32 categories, each of which has 20 background images and 200 foreground images.
+
+Compatibility Labelling. To acquire the binary compatibility label (1 for compatible background foreground pair and 0 for incompatible pair), we employ three human annotators to label the compatibility for  $32 \times 20 \times 200$  pairs of background and foreground. During annotation, we show real composite images and request annotators to assign binary labels by considering the semantics and geometry compatibility between background and foreground. Finally, for one background, we only consider the foregrounds for which all three human annotators label 1 as compatible and the others are treated as incompatible. Note that manually annotating the dataset is expensive, as it requires labelling a quadratically growing number of background and foreground pairs. Therefore, we only use R-FOSD dataset as a test set. To keep consistent with training data, we also fill the query bounding box of the background in R-FOSD dataset with image mean values at test time and the complete background image of R-FOSD dataset is only used to obtain the final composite image (Figure 2 (h)).
+
+# 4. Methodology
+
+In this section, we describe our proposed method for foreground object search. As illustrated in Figure 3, we train a discriminator  $D$  to predict the compatibility of composite image, which serves as the teacher network (see Section 4.1). We employ two encoders  $E^{b}$  and  $E^{f}$  (see Section 4.2) as well as a light-weight knowledge distillation module  $E^{d}$  (see Section 4.3) as the student network. The two encoders respectively extract background feature  $\mathbf{F}^{b}$  and foreground feature  $\mathbf{F}^{f}$ , which are fed into distillation module to interact with each other. During training
+
+stage, we enforce the interaction output  $\mathbf{F}^d$  to match with the composite image feature  $\mathbf{F}^c$ , in which the background foreground compatibility information is distilled to  $\mathbf{F}^d$ . Finally, we predict compatibility scores for pairwise background and foreground based on the distilled feature  $\mathbf{F}^d$ .
+
+# 4.1. Composite Image Discriminator
+
+Network Architecture. Given a background image  $\mathbf{I}^b$  with a query bounding box and a foreground image  $\mathbf{I}^f$ , we first generate a synthetic composite image  $\mathbf{I}^c$  as in Figure 2 (d). Then, we employ a discriminator  $D$  that takes a composite image as input to predict whether background and foreground of the composite image are compatible. We implement the discriminator as a binary classifier that consists of backbone network and classification head. Moreover, based on preliminary experiments, we find that feeding a cropped composite image into the discriminator achieves significantly better performance than feeding the whole composite image. Specifically, we crop the composite image, ensuring that the foreground object is located at the center and the area of foreground bounding box is about 50 percent of the whole crop. Then, we resize the crop to the input size 224 × 224, which is denoted as  $\widetilde{\mathbf{I}}^c$ . The superiority of feeding cropped composite image can be attributed to that the contextual information near the foreground may be more helpful and the foreground is aligned with crop center. Here we refer to the crop box as  $B$ . With the cropped composite image, the discriminator first extracts the composite image feature map  $\mathbf{F}^c$  by backbone network and then apply global average pooling (GAP) layer followed by a binary classifier. We train the discriminator using binary cross-entropy loss:
+
+$$
+\mathcal {L} _ {D} = - \log (p (\widetilde {\mathbf {I}} ^ {c}) _ {y}), \tag {1}
+$$
+
+in which  $p(\cdot)_y$  means the predicted probability corresponding to the ground-truth compatibility label  $y$ .
+
+Positive and Negative Samples Generation. During training phase, we consider compatible (resp., incompatible) foreground objects as positive (resp., negative) samples for a given background. The foreground cropped from the same image as the background is naturally viewed as positive sample. However, other foreground objects may also be compatible with the background. To guarantee the effectiveness of training samples, similar to [44], we train a binary classifier using VGG-19 [30] pretrained on ImageNet [8] as backbone network to help filter out training samples. Given a pair of background image and foreground image, the classifier takes their composite image as input and predicts the compatibility score. When training this classifier, we assume that only background foreground pairs from same images are positive and others are negative. With the trained classifier, we restrict negative samples to only include those foreground objects which are confidently
+
+![](images/8e80d8ceaa9392f5530f3ea02671226c0901f472dcdda63374b88cb0b6171e9b.jpg)  
+Figure 3. Illustration of the proposed DiscoFOS for foreground object search. The discriminator  $D$  is first trained to predict the background-foreground compatibility of input composite image  $\mathbf{I}^c$ , whose intermediate feature map  $\mathbf{F}^c$  then servers as distillation target to train the student model. The student network first extracts background feature  $\mathbf{F}^b$  and foreground feature  $\mathbf{F}^f$  by two encoders  $\{E^f, E^b\}$ , then applies the features to generate distilled feature  $\mathbf{F}^d$  and compatibility prediction by knowledge distillation module  $E^d$ .
+
+![](images/8c11d8a2fd640c26010a9caccb6665a6791a1f65def5b028aebd03f9861068cd.jpg)
+
+![](images/8b69c5e9bffe0cb82d4fb617ad8ccd48ec02960f85412ec31827d6fbc316dd91.jpg)  
+Figure 4. Examples of positive and negative samples used to train our models. Given a background in S-FOSD dataset, we have one positive foreground and one or more negative foregrounds, which are filled with white background pixels.
+
+classified as incompatible, that is, compatibility score is lower than a threshold (0.3 in our experiments). Therefore, given a background image, we have a single positive foreground and one or more negative foregrounds in S-FOSD dataset (see Figure 4). The obtained positive and negative samples are used to train the composite image discriminator in this section and the student network in Section 4.2, 4.3.
+
+# 4.2. Background and Foreground Encoders
+
+We employ two encoders  $E^b$  and  $E^f$  to extract feature respectively from background image  $\mathbf{I}^b$  and foreground image  $\mathbf{I}^f$ . Correspondingly, the background encoder  $E^b$  outputs background feature map  $\mathbf{F}^b$  and the foreground encoder  $E^f$  outputs foreground feature map  $\mathbf{F}^f$ , both of which have the same shape, i.e.,  $\mathbf{F}^b$ ,  $\mathbf{F}^f \in \mathcal{R}^{h \times w \times c}$ . Here  $h \times w$  is the spatial size and  $c$  is the number of channels. Then we apply GAP layer to yield background and foreground fea
+
+ture vectors, denoted as  $\bar{\mathbf{F}}^b$ ,  $\bar{\mathbf{F}}^f \in \mathcal{R}^c$ . After mapping the foreground and background into the common feature space, we enforce the compatible background and foreground to be close to each other in this space. Thus, the compatibility between foreground and background can be measured by computing the cosine similarity between their features. To this end, following previous works [37, 42, 44, 47], we train the encoders using triplet loss [28], which tends to pull the positive sample (i.e., compatible foreground) to the anchor (i.e., given background) and push the negative sample (i.e., incompatible foreground) away from the anchor in the feature space. During training stage, we tend to minimize the following loss function:
+
+$$
+\mathcal {L} _ {t r p} = \max \left(0, m + S (\bar {\mathbf {F}} ^ {b}, \bar {\mathbf {F}} _ {n} ^ {f}) - S (\bar {\mathbf {F}} ^ {b}, \bar {\mathbf {F}} _ {p} ^ {f})\right), \quad (2)
+$$
+
+where  $S(\cdot)$  represents cosine similarity and  $m$  is a positive margin in the range of (0, 1).  $\bar{\mathbf{F}}_p^f$  (resp.,  $\bar{\mathbf{F}}_n^f$ ) is the feature of positive (resp., negative) foreground for background  $\bar{\mathbf{F}}^b$ . By minimizing  $\mathcal{L}_{trp}$ , for a given background, the feature similarity with compatible foreground is expected to be greater than that with incompatible foreground by the margin  $m$ . Additionally, the above encoders are usually employed in previous methods [42, 44, 47]. Given a query background and a foreground database, these approaches rank the compatibility of different foregrounds by measuring their feature similarity to the given background.
+
+# 4.3. Knowledge Distillation Module
+
+After evaluating the discriminator in Section 4.1 and the encoders in Section 4.2, we observe that discriminator can achieve much better results than encoders, probably because the forward propagation in the discriminator allows thorough interaction between background and foreground, providing useful contextual cues for estimating background
+
+foreground compatibility. However, retrieving foreground images using discriminator requires to composite with each foreground image, which brings heavy computational burden. On the contrary, encoders achieve inferior performance, yet have significantly faster speed due to the exemption from background-foreground interaction. This motivates us to distill discriminator knowledge into encoders.
+
+To achieve this goal, we design a knowledge distillation module  $E^{d}$ , which interacts foreground feature with background feature and enforces the interaction output to match with the composite image feature  $\mathbf{F}^{c}$  from the discriminator. Recall that the composite image feature is extracted from cropped composite image, with the crop bounding box denoted as  $B$  (see Section 4.1). So we apply RoIAlign [10] with the bounding box  $B$  to obtain local background feature map  $\widetilde{\mathbf{F}}^{b}$  from global background feature map  $\mathbf{F}^{b}$  produced by background encoder  $E^{b}$ . Then, we resize RoIAlign output to be of the same shape as  $\mathbf{F}^{b}$ , i.e.,  $\widetilde{\mathbf{F}}^{b} \in \mathcal{R}^{h \times w \times c}$ . The local background feature is supposed to encode contextual information surrounding the foreground. Meanwhile, we utilize foreground encoder  $E^{f}$  to extract foreground feature map  $\mathbf{F}^{f}$ . Given the foreground feature map  $\mathbf{F}^{f}$  and local background feature map  $\widetilde{\mathbf{F}}^{b}$ , we feed their concatenation into  $E^{d}$  to produce a distilled feature map  $\mathbf{F}^{d} \in \mathcal{R}^{h \times w \times c}$ . Note the discriminator and two encoders adopt the same backbone network and input image size in our implementation, so their feature maps have the same shape, i.e.,  $\mathbf{F}^{c}, \mathbf{F}^{d} \in \mathcal{R}^{h \times w \times c}$ . During training phase, we enforce the distilled feature  $\mathbf{F}^{d}$  to mimic the composite image feature  $\mathbf{F}^{c}$  by  $L_{1}$  loss:
+
+$$
+\mathcal {L} _ {k d} = \left\| \mathbf {F} ^ {d} - \mathbf {F} ^ {c} \right\| _ {1}. \tag {3}
+$$
+
+We pool the distilled feature map into a vector and send it to a binary classifier to predict the compatibility. The classifier is also trained using binary cross-entropy loss:
+
+$$
+\mathcal {L} _ {c l s} = - \log (p (\mathbf {F} ^ {d}) _ {y}), \tag {4}
+$$
+
+in which  $p(\cdot)_y$  is similarly defined as in Eqn. 1.
+
+Finally, we train the encoders  $\{E^f,E^b\}$  and distillation module  $E^{d}$  simultaneously. The overall optimization function can be written as
+
+$$
+\mathcal {L} = \mathcal {L} _ {t r p} + \lambda_ {k d} \mathcal {L} _ {k d} + \lambda_ {c l s} \mathcal {L} _ {c l s}, \tag {5}
+$$
+
+where  $\lambda_{kd}$  and  $\lambda_{cls}$  are trade-off parameters. During inference, our model finds compatible foregrounds for a given background by ranking the predicted compatibility scores.
+
+# 4.4. Generalization to Real-world Application
+
+To boost the performance of our method on real-world data, we make some modifications to the training procedure of our teacher network and student network, which helps achieve more competitive results on the R-FOSD dataset.
+
+For the teacher network, we utilize the binary classifier in Section 4.1 to extend training samples. Specifically, given a background image, we use the classifier to predict compatibility score for each foreground and treat those with scores larger than 0.8 as positive samples (including the ground-truth foreground), based on which the ratio of positive and negative foregrounds per background is increased from 1:10 to 5:10. Besides, we apply data augmentation to generate additional positive and negative samples from the ground-truth foreground for each background image. Precisely, based on the ground-truth foreground, we produce 2 positive foregrounds through color jitter and Gaussian blur, and 1 negative foreground through affine transformation. After augmentation, the ratio of positive and negative samples changes from 5:10 to 7:11.
+
+For the student network, we select the top-5 foregrounds returned by pretrained teacher network as positive samples (including the ground-truth foreground) and adopt the same negative samples as the teacher network. After applying the same data augmentation scheme as the teacher network, we also have positive and negative samples with the ratio 7:11 to train the student network.
+
+Finally, considering that user-provided bounding boxes may not be very accurate, we also augment bounding boxes when training teacher network and student network. Specifically, we randomly pad the bounding box with the maximum padding space being  $30\%$  of the bounding box's width and height.
+
+# 5. Experiments
+
+# 5.1. Dataset and Evaluation Metrics
+
+Our S-FOSD dataset is employed for both training and testing, while R-FOSD dataset is only for testing. We employ different evaluation metrics for two datasets considering their difference in the acquisition of ground-truth foregrounds. For each metric, we report the mean evaluation results by averaging the results over all categories. Moreover, we leave the implementation details in Supplementary.
+
+S-FOSD Dataset. The training set has 57,219 pairs of foregrounds and backgrounds covering 32 categories, with a maximum of 4800 pairs and a minimum of 300 pairs in each category. The test set provides 20 backgrounds and 200 foregrounds (including 20 foregrounds from the same images as the backgrounds) for each category. The foreground/background images in the training set and test set have no overlap. Following previous works [42, 47], only the foreground object from the same image is viewed as ground-truth for each background and we adopt Recall@k (R@k) as evaluation metric, which represents the percentage of background queries whose ground-truth foreground appears in top  $k$  retrievals ( $k = 1, 5, 10, 20$  in our experiments).
+
+R-FOSD Dataset. The R-FOSD dataset adopts the same foreground set as the test set of S-FOSD dataset and collects 20 backgrounds for each category. Each pair of background and foreground is shown to three human annotators to label the compatibility. The resulting dataset contains  $4\sim 190$  compatible foregrounds per background, and we adopt mean Average Precision (mAP), mAP@20, and Precision@k (P@k) for evaluation, which are widely used in image retrieval and previous works [44, 47]. Precision@k means the percentage of compatible foreground objects in the top k retrievals,  $k = 1,5,10,20$  in our experiments. To reduce unplausible results on the R-FOSD dataset, we exclude the objects with aspect ratios deviating more than 1.2 from that of query bounding box for all methods and compute metrics on the remaining objects.
+
+# 5.2. Comparison with Existing Methods
+
+Baselines. We compare our approach with previous methods [42, 44, 37, 47] on our two datasets. Shape [42] ranks foreground objects by comparing their aspect ratios with that of the query bounding box on background. CFO [42], UFO [44], FFR [37], and GALA [47] adopt the pipeline described in Section 4.2, which use two encoders to extract background and foreground features, and then rank the compatibility of foreground by computing its feature similarity with background. To adapt to our focus on geometric and semantic incompatibility, we replace the style feature of FFR [37] with semantic feature, in which we obtain the semantic feature by using VGG-19 [30] pretrained on ImageNet [8] following [44]. For GALA [47] that considers lighting and geometry compatibility, we discard lighting transformation and only keep geometry transformation [47] to match our scenario. Besides, we do not compare with IFR [19], as it requires pattern labels of the foreground, which are unavailable in our datasets. For fair comparison, we employ the same backbone network and training set for all baseline methods except Shape [42]. We use the same positive and negative samples for different methods when training on S-FOSD dataset.
+
+Quantitative comparison. The results of baselines and our method on the proposed two datasets are summarized in Table 1. Moreover, when evaluating on S-FOSD dataset, the only ground-truth foreground has the same aspect ratio as the query bounding box, thus Shape [42] can find the ground-truth by shortcut, making the evaluation results meaningless. It can be seen that among all baselines, GALA [47] and FFR [37] are two competitive ones, which employ contrastive learning with self-transformation [47] and MarrNet [36] to enhance the perception of geometric information of foreground, respectively. Nevertheless, our method outperforms all previous approaches by an obvious margin on both S-FOSD and R-FOSD datasets.
+
+Qualitative comparison. We show the retrieval results of
+
+![](images/a22802f7f261d7c7715b2d557bd25240f7669c6e1cfaeb9515ad635eb244ec9c.jpg)  
+Figure 5. Qualitative comparison on our S-FOSD (left) and R-FOSD (right) datasets. Each of the four examples contains a background image and several rows of the retrieval results, from top to bottom: CFO [42], UFO [44], GALA [47], FFR [37], and ours. Additionally, in the right part, green (resp., red) box represents the foreground with compatible (resp., incompatible) label.
+
+different baselines on our two datasets in Figure 5. For each query background, we show the returned top-5 foregrounds by different methods, which shows that our method can generally find compatible foregrounds by taking both semantic and geometric factors into account. For example, for the top-left example, given a query bounding box at the bottom-right seat, the baseline methods may return a standing or frontal person, which is unsuitable to be placed in the query bounding box. In contrast, the top returned persons by our method all have sitting posture, which appear more reasonable in terms of semantic compatibility. In the bottom-right example, given the geometry of background scene, the annotated ground-truth positive foregrounds (green box) have consistent orientation with respect to the train track in background. Our method retrieves more positive foregrounds than other approaches, demonstrating the effectiveness of our method on geometry compatibility. More qualitative results are present in Supplementary.
+
+# 5.3. Ablation Study
+
+In this section, we start from the general pipeline with two encoders of previous methods [42, 44, 47, 19, 37] and evaluate the effectiveness of each component in our method. Different models are evaluated on our S-FOSD dataset and the results are summarized in Table 2. In row 1, we apply two encoders  $\{E^b,E^f\}$  to extract background feature  $\bar{\mathbf{F}}^b$  and foreground feature  $\bar{\mathbf{F}}^f$ , which are used to predict the background foreground compatibility by measuring their feature similarity. It is worth mentioning that all models in Table 2 rank different foregrounds by predicted compatibility scores except the row 1 and row 2, which measure compatibility by calculating feature similarity.
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">S-FOSD Dataset</td><td colspan="6">R-FOSD Dataset</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td><td>mAP↑</td><td>mAP@20↑</td><td>P@1↑</td><td>P@5↑</td><td>P@10↑</td><td>P@20↑</td></tr><tr><td>Shape [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>50.49</td><td>56.22</td><td>47.66</td><td>49.72</td><td>50.03</td><td>49.92</td></tr><tr><td>CFO [42]</td><td>56.09</td><td>83.59</td><td>91.25</td><td>96.88</td><td>52.06</td><td>62.17</td><td>58.33</td><td>56.29</td><td>55.90</td><td>52.85</td></tr><tr><td>UFO [44]</td><td>54.69</td><td>81.72</td><td>90.94</td><td>95.31</td><td>52.73</td><td>63.63</td><td>64.12</td><td>59.11</td><td>56.30</td><td>53.82</td></tr><tr><td>FFR [37]</td><td>57.03</td><td>86.25</td><td>93.28</td><td>97.97</td><td>53.10</td><td>64.12</td><td>61.92</td><td>59.64</td><td>57.56</td><td>55.06</td></tr><tr><td>GALA [47]</td><td>57.50</td><td>85.17</td><td>93.00</td><td>97.33</td><td>52.02</td><td>62.83</td><td>62.56</td><td>57.33</td><td>55.76</td><td>52.93</td></tr><tr><td>DiscoFOS</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td><td>56.70</td><td>68.56</td><td>67.75</td><td>64.64</td><td>62.25</td><td>58.90</td></tr></table>
+
+Table 1. Comparison with existing methods on our S-FOSD dataset and R-FOSD dataset. Best results are denoted in boldface.  
+
+<table><tr><td></td><td>Eb</td><td>Ed</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td></tr><tr><td>1</td><td>Fb</td><td></td><td>54.83</td><td>81.17</td><td>90.67</td><td>95.00</td></tr><tr><td>2</td><td>Fb</td><td></td><td>52.50</td><td>79.69</td><td>88.75</td><td>93.00</td></tr><tr><td>3</td><td>Fb</td><td>p(·)y</td><td>56.72</td><td>87.19</td><td>94.69</td><td>97.97</td></tr><tr><td>4</td><td>Fb</td><td>[Fb, Ff]</td><td>60.83</td><td>87.33</td><td>95.00</td><td>98.17</td></tr><tr><td>5</td><td>Fb</td><td>[Hatb, Ff]</td><td>65.16</td><td>90.31</td><td>95.31</td><td>98.59</td></tr><tr><td>6</td><td>Fb</td><td>[Fb, Ff]</td><td>68.28</td><td>90.94</td><td>95.63</td><td>98.75</td></tr><tr><td>7</td><td>Fb</td><td>Fb ⊕ Ff</td><td>64.53</td><td>87.66</td><td>92.97</td><td>96.72</td></tr><tr><td>8</td><td>Fb</td><td>[Fb, Ff]</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td></tr><tr><td>9</td><td></td><td>D(Ic)</td><td>49.22</td><td>76.72</td><td>84.53</td><td>91.88</td></tr><tr><td>10</td><td></td><td>D(Ic)</td><td>84.38</td><td>97.03</td><td>98.91</td><td>99.84</td></tr></table>
+
+Table 2. The ablation studies of our method on S-FOSD dataset.  $\bar{\mathbf{F}}^b, \hat{\mathbf{F}}^b$ : global/local background feature vector.  $\mathbf{F}^b, \widetilde{\mathbf{F}}^b$ : global/local background feature map.  $\mathbf{F}^f, \widetilde{\mathbf{F}}^f$ : foreground feature map/vector.  $[\cdot, \cdot]$ : feature concatenation.  $\oplus$ : feature map composition. The detailed explanations can be found in Section 5.3.
+
+Background Encoder  $E^b$ . Based on row 1 of Table 2, we replace the global background feature vector  $\bar{\mathbf{F}}^b$  with local background feature vector  $\hat{\mathbf{F}}^b$ , which is obtained by applying RoIAlign [10] with the crop bounding box  $B$  to background feature map  $\mathbf{F}^b$ , resulting in worse results in row 2. This is probably because that the global background feature contains more useful information than the local background feature. So we adopt the global background feature for background encoder in other experiments.
+
+Composite Image Discriminator  $D$ . In our network, the discriminator plays the role of teacher. In row 9 and 10 of Table 2, we feed the discriminator with the whole composite image  $\mathbf{I}^c$  and the cropped composite image  $\widetilde{\mathbf{I}}^c$ , respectively. We see that row 10 achieves significantly better performance than row 9, which can be attributed to the aligned foreground and useful surrounding foreground context in the cropped composite. Then, the discriminator with the whole composite image is inferior to the encoders of row 1, which is roughly consistent with previous findings [44, 42]. Additionally, the discriminator with cropped composite image outperforms the encoders (row 1) with a remarkable margin, which motivates us to build our method.
+
+Knowledge Distillation Module  $E^d$ . Based on row 1 of
+
+Table 2, we introduce the distillation module without using feature distillation, which is essentially a compatibility classifier  $p(\cdot)_y$ , in row 3. The classifier takes the concatenation of foreground feature vector  $\bar{\mathbf{F}}^f$  and background feature vector  $\bar{\mathbf{F}}^b$  as input, and outputs the compatibility score. The comparison between row 1 and 3 verifies that adding compatibility classification is helpful for our task.
+
+Then we add feature distillation and explore the impact of using different forms of background-foreground interactions. In row 4 and 5, we perform interaction based on the pooled feature vectors of two encoders. Specifically, we concatenate the foreground feature vector  $\overline{\mathbf{F}}^f$  with global background feature vector  $\overline{\mathbf{F}}^b$  (resp., local background feature vector  $\hat{\mathbf{F}}^b$ ) to feed into distillation module in row 4 (resp., row 5). Both results are better than row 3, proving the utility of distilling composite image feature to predict compatibility.
+
+Next, we perform interaction based on the last feature maps of two encoders. To this end, we explore several different ways to fuse background and foreground features. First, we directly concatenate background feature map  $\mathbf{F}^b$  and foreground feature map  $\mathbf{F}^f$  in row 6. By comparing row 6 and 4, it verifies the advantage of more sufficient interaction. In row 7, we extend to a more intuitive way by applying composition operation to local background feature maps  $\widetilde{\mathbf{F}}^b$  and foreground feature map  $\mathbf{F}^f$ . Specifically, we resize the foreground feature and place it in the query bounding box on the local background feature. Unexpectedly, this leads to slight performance drop compared with row 5, which may be caused by downsampling the foreground feature. Finally, we concatenate the local background feature  $\widetilde{\mathbf{F}}^b$  and foreground feature  $\mathbf{F}^f$ , corresponding to our complete method. As shown in row 8, our full method produces remarkably better results than the abovementioned row 6, indicating that the representation ability of the distilled feature can benefit from adequate interaction between two encoders.
+
+# 5.4. Inference Efficiency Analyses
+
+To study the efficiency of our method, we compare our method ("Ours") with the composite image discriminator ("Discriminator"), and background and foreground
+
+<table><tr><td>Model</td><td>Time(200)↓</td><td>Time(2000)↓</td><td>#Params↓</td></tr><tr><td>Discriminator</td><td>700.0ms</td><td>7000.1ms</td><td>20.03M</td></tr><tr><td>Encoders</td><td>4.0ms</td><td>4.3ms</td><td>40.05M</td></tr><tr><td>Ours</td><td>5.2ms</td><td>6.0ms</td><td>47.13M</td></tr></table>
+
+Table 3. Comparing inference efficiency of different models, including the discriminator  $D$ , encoders  $\{E^b, E^f\}$ , and our method in the Figure 3. "Time(N)" represents the average time of retrieving compatible foregrounds from  $N$  candidates per background.
+
+encoders ("Encoders") on retrieval time and number of parameters, the results of which are reported in the Table 3. We test different models on an NVIDIA RTX 3090 GPU and measure the time of retrieving compatible foreground from  $N$  candidates as retrieval time  $(\mathrm{Time}(N))$ . We repeat the retrieval 50 times and calculate the average time as final result. To mimic the practical application scenarios of foreground object search, we assume that the features of all foregrounds have been extracted and saved before retrieval. In particular, for "Encoders" and "Ours", we save the feature vector and the last feature map of the foreground encoder, respectively. In this way, the retrieval time of "Encoders" and "Ours" only considers the background feature extraction and the matching between background and foreground, in which background feature extraction takes 3.1ms per image.
+
+We can see that the discriminator  $D$  is the slowest method due to compositing with each foreground and sending each composite through forward pass. "Ours" runs slower than "Encoders" due to introducing additional interaction between background and foreground, yet only takes 6ms to retrieve from 2000 foregrounds, which enables our model for real-time applications. Regarding the number of parameters, the comparison between two encoders and ours indicates that the additional parameters (7.08M) introduced by distillation module are affordable.
+
+# 5.5. Additional Experiments in Supplementary
+
+Due to space limitation, we present some experiments in Supplementary, including quantitative comparison on different categories, generalization to new categories, the results of our method using different hyper-parameters in Eqn. (5) and Eqn. (2), and different ratios of positive and negative training samples, the discussion on the limitation of our method, and the results of significance test.
+
+# 6. Conclusion
+
+In this work, we have contributed two public datasets for Foreground Object Search (FOS), S-FOSD with Synthetic composite images and R-FOSD with Real composite images. We have also proposed a novel FOS method, which improves the general pipeline of previous methods by feature distillation. Extensive experiments on our dataset have
+
+demonstrated the utility of our proposed method on foreground object search.
+
+# Acknowledgement
+
+The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300).
+
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+                                    "type": "text",
+                                    "content": "Foreground object search (FOS) aims to find compatible foreground objects for a given background image, producing realistic composite image. We observe that competitive retrieval performance could be achieved by using a discriminator to predict the compatibility of composite image, but this approach has unaffordable time cost. To this end, we propose a novel FOS method via distilling composite feature (DiscoFOS). Specifically, the abovementioned discriminator serves as teacher network. The student network employs two encoders to extract foreground feature and background feature. Their interaction output is enforced to match the composite image feature from the teacher network. Additionally, previous works did not release their datasets, so we contribute two datasets for FOS task: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. Extensive experiments on our two datasets demonstrate the superiority of the proposed method over previous approaches. The dataset and code are available at https://github.com/bcmi/Foreground-Object-Search-Dataset-FOSD."
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+                                    "content": "1. Introduction"
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+                                    "content": "Foreground Object Search (FOS) aims to find compatible foregrounds from specified category for a given background image which has a query bounding box indicating the foreground location [42]. More precisely, an object is compatible with a background image if it can be realistically composited into the image [44], as illustrated in Figure 1. FOS is a core technique in many image composition applications [24]. For example, FOS technique can help"
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+                                            "type": "text",
+                                            "content": "Figure 1. Illustration of foreground object search. Given a background image with query bounding box (yellow), foreground object search aims to find compatible foreground objects of a specified category from a database, which is composited with the background to produce a realistic composite image."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "users acquire suitable foregrounds from a foreground pool automatically and efficiently for object insertion in photo editing [19]. Moreover, FOS also can be used to fill a region comprising undesired objects using new foreground [44]."
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+                                    "content": "There exist many factors that affect the compatibility between background and foreground, including semantics, style (e.g., color and texture), lighting, and geometry (e.g., shape and viewpoint). Previous works on FOS may consider different factors. For example, early methods [42, 44] focused on the semantic compatibility. Recent works [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this paper, we focus on semantics and geometry compatibility following [19], because incompatible color and lighting between the background and foreground can be tackled to some extent by image harmonization [6, 21, 4]."
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "*Corresponding author"
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+                                    "type": "text",
+                                    "content": "The general pipeline of most existing methods [42, 44, 47, 19, 37] is to learn an embedding space with two encoders respectively for background and foreground, so that compatible background and foreground are close to each other in this space. Alternatively, some approaches [46, 44] trained a discriminator to predict background-foreground compatibility by feeding the composite image. Based on preliminary experiments, we observe that the discriminator can achieve much better results than encoders when taking the cropped composite image as input (see teacher network in Figure 3). We conjecture that the forward pass in the discriminator allows thorough interaction between background and foreground, which could provide useful contextual cues for estimating background-foreground compatibility. However, given a background image, it is very time-consuming to compose with each foreground image and perform forward computation for each composite image. Motivated by this, we propose a novel FOS framework called DiscoFOS via knowledge distillation. Specifically, we distill the knowledge of composite image from the discriminator to two encoders, in which we enforce the interaction output of foreground feature and background feature to match with the composite image feature. How to design the interaction between two encoders is challenging, due to the trade-off between performance and computational cost. On the one hand, insufficient interaction between two encoders may be unable to mimic the rich knowledge in composite image feature. On the other hand, sufficient interaction would largely increase the computational burden. Considering the abovementioned trade-off, we perform interaction only on the last feature maps of two encoders, which achieves significant performance improvement with acceptable computational overhead."
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+                                    "content": "Since previous works (CAIS [42], UFO [44], and GALA [47]) did not release their datasets, we build our own datasets based on an existing large-scale real-world dataset, i.e., Open Images [15], as illustrated in Figure 2. We construct two FOS Datasets respectively containing Synthetic composite images and Real composite images, abbreviated as S-FOSD and R-FOSD respectively. We first introduce the S-FOSD dataset. Given a real image with instance segmentation mask, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out this object as foreground. After removing unsuitable categories and occluded foregrounds, the resultant dataset contains 57,859 backgrounds and 63,619 foregrounds. Following [42, 47], for each background image, we deem the foreground object from the same image as ground-truth. For R-FOSD dataset, we collect images from Internet as background images and draw a bounding box at the expected foreground location as query bounding box. R-FOSD dataset shares the same foregrounds with the test set of S-FOSD dataset. Then we employ multiple human"
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+                                    "content": "annotators to label the compatibility of each pair of background and foreground. In summary, S-FOSD dataset is lowcost and highly scalable, but has neither complete background nor ground-truth negative samples. Oppositely, R-FOSD dataset has complete background image with both positive and negative foregrounds annotated by human, yet is unscalable due to the high annotation cost. In our experiments, S-FOSD dataset is used for both training and validating model, while R-FOSD dataset is only used for model evaluation. More details about dataset construction could be found in Section 3."
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+                                    "content": "We evaluate our method on the proposed datasets, which validates the superiority of the proposed method over previous approaches. Our major contributions can be summarized as follows: 1) To facilitate the research on FOS task, we contribute two public datasets: S-FOSD dataset with synthetic composite images and R-FOSD dataset with real composite images. 2) We propose a novel method named DiscoFOS that improves foreground object search by distilling the knowledge of composite image feature into two encoders. 3) Extensive experiments demonstrate the superiority of the proposed method over previous baselines on our datasets."
+                                }
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+                                    "content": "2. Related Works"
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+                                    "content": "2.1. Foreground Object Search"
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+                                    "content": "Early works [16, 3] employed hand-crafted features to match background with foreground, yet their performance may be limited by the representation ability of hand-crafted features. Recent work applied deep learning based feature for foreground retrieval. For example, [32] utilized deep features to capture local context particularly for person compositing. [46] trained a discriminator to estimate the realism of composites, which is available for selecting compatible foregrounds by compositing each foreground with the background, but is computationally expensive."
+                                }
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+                                    "content": "More recent methods [42, 44, 47, 37, 19] typically trained two encoders to extract background feature and foreground feature, and then measured background foreground compatibility by calculating feature similarity. These methods considered different factors that affect the compatibility between background and foreground. For example, the methods [42, 44] considered the semantic compatibility, while the approaches [19, 37, 47] considered geometry and other factors, including style [37] and lighting [47]. In this work, we focus on semantic compatibility and geometry compatibility following [19], and propose a novel foreground object search method that improves the encoders with knowledge distillation. Additionally, previous works [42, 44, 37, 47] did not release their datasets, we contribute two datasets to facilitate the research in this field."
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+                                    "content": "As summarized in [24], existing image composition works attempted to solve one or some issues which affect the quality of composite image, such as illumination, shadow, and geometry. Image harmonization methods [34, 6, 7, 5] focused on eliminating the color and illumination discrepancy between background and foreground. Besides, some shadow generation works [14, 9, 40, 22, 12] aimed to generate plausible shadow for the inserted foreground. To blend the foreground into the background more naturally, image blending methods [26, 18, 35] paid attention to smoothing the boundary between background and foreground. The closest subtask to ours is object placement [45, 25, 23, 17, 33], which generates reasonable locations and sizes to place foreground over background. Given a background, object placement focuses on predicting bounding box for the inserted foreground, while our task targets at retrieving compatible foregrounds from a specified category for a given query bounding box."
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+                                    "content": "2.3. Knowledge Distillation"
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+                                    "content": "Knowledge distillation methods usually improve the student network by forcing to mimic the behaviors of the teacher network, such as soft predictions [11], logits [1], intermediate feature maps [27], or attention maps [39]. Apart from the above works on image classification, some recent works extend knowledge distillation to more complex vision tasks, including semantic segmentation [41, 29], object detection [20, 2], face recognition [13], and so on."
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+                                    "content": "backgrounds and foregrounds (see Figure 2)."
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+                                    "content": "Foreground Object Selection. Open Images dataset [15] provides instance segmentation masks for 2.8 million object instances in 350 categories. To accommodate our task, we delete the categories and objects that are unsuitable for the task or beyond our focus (geometry and semantic compatibility), after which 32 categories remain. The detailed rules for object selection and the complete category list can be found in Supplementary."
+                                }
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+                                    "content": "Background and Foreground Generation. By using the segmentation masks, we generate background and foreground images in a similar way to previous works [42, 47, 44]. Specifically, as shown in Figure 2 (a) "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " (c), given an image with instance segmentation masks, we choose one object and fill its bounding box with image mean values to get the background. Meanwhile, we crop out the object and paste it on white background, producing the foreground. With the background and foreground, we can obtain the synthetic composite image by resizing the foreground and placing it in the query bounding box on the background (see Figure 2 (d)). Additionally, we have also tried image inpainting [31, 43, 38] to fill the object bounding box, but got unsatisfactory results, probably due to large missing content and the residues of erased object (e.g., shadow). After that, we obtain over 63,000 pairs of background and foreground covering 32 categories, with a maximum of 5,000 images and a minimum of 500 images in each category. For a given background, the foreground cropped from the same image is naturally compatible and thus deemed as ground-truth following [42, 47, 44]."
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+                                    "content": "Dataset Split. S-FOSD dataset is employed for both training and testing, as its construction is low-cost and highly scalable. We first select test samples to build the test set and the rest forms the training set. For reliable performance evaluation, we build test set mainly concerning its diversity and quality. Finally, we get 20 backgrounds and 200"
+                                }
+                            ]
+                        }
+                    ],
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+                }
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+                                    "type": "text",
+                                    "content": "foregrounds for each category, which contains 20 pairs of background and foreground. The remaining 57,219 pairs of background and foreground form the training set."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    "type": "text",
+                                    "content": "3.2. R-FOSD Dataset"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Background and Foreground Generation. When building R-FOSD dataset, we directly adopt the foregrounds of the test set in S-FOSD dataset and collect images from Internet as backgrounds. It is very likely that a random image is unsuitable for compositing with any test foreground. Thus, we collect candidate backgrounds by searching similar images to the test backgrounds of S-FOSD dataset. After that, we draw a bounding box at the desired foreground location as query bounding box (see Figure 2 (f)). The size and location of the bounding box are decided by first mimicking the foreground in the similar background of S-FOSD dataset and then manual inspection. For each pair of background and foreground, we resize the foreground and place it in the query bounding box on the source image, generating a real composite image (see Figure 2 (h)). Finally, R-FOSD dataset contains 32 categories, each of which has 20 background images and 200 foreground images."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Compatibility Labelling. To acquire the binary compatibility label (1 for compatible background foreground pair and 0 for incompatible pair), we employ three human annotators to label the compatibility for "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        337,
+                                        288,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "32 \\times 20 \\times 200"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        337,
+                                        288,
+                                        564
+                                    ],
+                                    "type": "text",
+                                    "content": " pairs of background and foreground. During annotation, we show real composite images and request annotators to assign binary labels by considering the semantics and geometry compatibility between background and foreground. Finally, for one background, we only consider the foregrounds for which all three human annotators label 1 as compatible and the others are treated as incompatible. Note that manually annotating the dataset is expensive, as it requires labelling a quadratically growing number of background and foreground pairs. Therefore, we only use R-FOSD dataset as a test set. To keep consistent with training data, we also fill the query bounding box of the background in R-FOSD dataset with image mean values at test time and the complete background image of R-FOSD dataset is only used to obtain the final composite image (Figure 2 (h))."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4. Methodology"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In this section, we describe our proposed method for foreground object search. As illustrated in Figure 3, we train a discriminator "
+                                },
+                                {
+                                    "bbox": [
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+                                        594,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to predict the compatibility of composite image, which serves as the teacher network (see Section 4.1). We employ two encoders "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "E^{b}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "E^{f}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " (see Section 4.2) as well as a light-weight knowledge distillation module "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (see Section 4.3) as the student network. The two encoders respectively extract background feature "
+                                },
+                                {
+                                    "bbox": [
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+                                        594,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{b}"
+                                },
+                                {
+                                    "bbox": [
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+                                        594,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " and foreground feature "
+                                },
+                                {
+                                    "bbox": [
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+                                        594,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{f}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        594,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which are fed into distillation module to interact with each other. During training"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "stage, we enforce the interaction output "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^d"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to match with the composite image feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", in which the background foreground compatibility information is distilled to "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
+                                        545,
+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^d"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        133
+                                    ],
+                                    "type": "text",
+                                    "content": ". Finally, we predict compatibility scores for pairwise background and foreground based on the distilled feature "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
+                                        545,
+                                        133
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^d"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Composite Image Discriminator"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Network Architecture. Given a background image "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}^b"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with a query bounding box and a foreground image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}^f"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
+                                        546,
+                                        447
+                                    ],
+                                    "type": "text",
+                                    "content": ", we first generate a synthetic composite image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
+                                        546,
+                                        447
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}^c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
+                                        546,
+                                        447
+                                    ],
+                                    "type": "text",
+                                    "content": " as in Figure 2 (d). Then, we employ a discriminator "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
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+                                        447
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
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+                                    ],
+                                    "type": "text",
+                                    "content": " that takes a composite image as input to predict whether background and foreground of the composite image are compatible. We implement the discriminator as a binary classifier that consists of backbone network and classification head. Moreover, based on preliminary experiments, we find that feeding a cropped composite image into the discriminator achieves significantly better performance than feeding the whole composite image. Specifically, we crop the composite image, ensuring that the foreground object is located at the center and the area of foreground bounding box is about 50 percent of the whole crop. Then, we resize the crop to the input size 224 × 224, which is denoted as "
+                                },
+                                {
+                                    "bbox": [
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+                                        159,
+                                        546,
+                                        447
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{I}}^c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
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+                                        447
+                                    ],
+                                    "type": "text",
+                                    "content": ". The superiority of feeding cropped composite image can be attributed to that the contextual information near the foreground may be more helpful and the foreground is aligned with crop center. Here we refer to the crop box as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
+                                        546,
+                                        447
+                                    ],
+                                    "type": "text",
+                                    "content": ". With the cropped composite image, the discriminator first extracts the composite image feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
+                                        546,
+                                        447
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        159,
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+                                    ],
+                                    "type": "text",
+                                    "content": " by backbone network and then apply global average pooling (GAP) layer followed by a binary classifier. We train the discriminator using binary cross-entropy loss:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {D} = - \\log (p (\\widetilde {\\mathbf {I}} ^ {c}) _ {y}), \\tag {1}",
+                                    "image_path": "4ebb18c10759d727f8c70529da6b6ebdc17dc6519a2026a1715182941091c70a.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "in which "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "p(\\cdot)_y"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " means the predicted probability corresponding to the ground-truth compatibility label "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
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+                                    "content": "y"
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Positive and Negative Samples Generation. During training phase, we consider compatible (resp., incompatible) foreground objects as positive (resp., negative) samples for a given background. The foreground cropped from the same image as the background is naturally viewed as positive sample. However, other foreground objects may also be compatible with the background. To guarantee the effectiveness of training samples, similar to [44], we train a binary classifier using VGG-19 [30] pretrained on ImageNet [8] as backbone network to help filter out training samples. Given a pair of background image and foreground image, the classifier takes their composite image as input and predicts the compatibility score. When training this classifier, we assume that only background foreground pairs from same images are positive and others are negative. With the trained classifier, we restrict negative samples to only include those foreground objects which are confidently"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
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+                }
+            ],
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+            "page_idx": 3
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+                                            "content": "Figure 3. Illustration of the proposed DiscoFOS for foreground object search. The discriminator "
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+                                            "content": " is first trained to predict the background-foreground compatibility of input composite image "
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+                                            "type": "text",
+                                            "content": " then servers as distillation target to train the student model. The student network first extracts background feature "
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+                                            "type": "text",
+                                            "content": "Figure 4. Examples of positive and negative samples used to train our models. Given a background in S-FOSD dataset, we have one positive foreground and one or more negative foregrounds, which are filled with white background pixels."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "classified as incompatible, that is, compatibility score is lower than a threshold (0.3 in our experiments). Therefore, given a background image, we have a single positive foreground and one or more negative foregrounds in S-FOSD dataset (see Figure 4). The obtained positive and negative samples are used to train the composite image discriminator in this section and the student network in Section 4.2, 4.3."
+                                }
+                            ]
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+                                    "content": "4.2. Background and Foreground Encoders"
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+                                    "content": "We employ two encoders "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to extract feature respectively from background image "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}^b"
+                                },
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+                                    "type": "text",
+                                    "content": " and foreground image "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}^f"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Correspondingly, the background encoder "
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+                                    "type": "inline_equation",
+                                    "content": "E^b"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " outputs background feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^b"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and the foreground encoder "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " outputs foreground feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", both of which have the same shape, i.e., "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^f \\in \\mathcal{R}^{h \\times w \\times c}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Here "
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+                                    "type": "inline_equation",
+                                    "content": "h \\times w"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the spatial size and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the number of channels. Then we apply GAP layer to yield background and foreground fea"
+                                }
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+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "ture vectors, denoted as "
+                                },
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+                                    "type": "inline_equation",
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+                                    "content": "\\bar{\\mathbf{F}}^f \\in \\mathcal{R}^c"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". After mapping the foreground and background into the common feature space, we enforce the compatible background and foreground to be close to each other in this space. Thus, the compatibility between foreground and background can be measured by computing the cosine similarity between their features. To this end, following previous works [37, 42, 44, 47], we train the encoders using triplet loss [28], which tends to pull the positive sample (i.e., compatible foreground) to the anchor (i.e., given background) and push the negative sample (i.e., incompatible foreground) away from the anchor in the feature space. During training stage, we tend to minimize the following loss function:"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {t r p} = \\max \\left(0, m + S (\\bar {\\mathbf {F}} ^ {b}, \\bar {\\mathbf {F}} _ {n} ^ {f}) - S (\\bar {\\mathbf {F}} ^ {b}, \\bar {\\mathbf {F}} _ {p} ^ {f})\\right), \\quad (2)",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "content": "S(\\cdot)"
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+                                    "type": "text",
+                                    "content": " represents cosine similarity and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is a positive margin in the range of (0, 1). "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbf{F}}_p^f"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (resp., "
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+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbf{F}}_n^f"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ") is the feature of positive (resp., negative) foreground for background "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbf{F}}^b"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". By minimizing "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{trp}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", for a given background, the feature similarity with compatible foreground is expected to be greater than that with incompatible foreground by the margin "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Additionally, the above encoders are usually employed in previous methods [42, 44, 47]. Given a query background and a foreground database, these approaches rank the compatibility of different foregrounds by measuring their feature similarity to the given background."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "4.3. Knowledge Distillation Module"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "After evaluating the discriminator in Section 4.1 and the encoders in Section 4.2, we observe that discriminator can achieve much better results than encoders, probably because the forward propagation in the discriminator allows thorough interaction between background and foreground, providing useful contextual cues for estimating background"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "22990"
+                                }
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+                    ],
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+                }
+            ],
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+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": "foreground compatibility. However, retrieving foreground images using discriminator requires to composite with each foreground image, which brings heavy computational burden. On the contrary, encoders achieve inferior performance, yet have significantly faster speed due to the exemption from background-foreground interaction. This motivates us to distill discriminator knowledge into encoders."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": "To achieve this goal, we design a knowledge distillation module "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which interacts foreground feature with background feature and enforces the interaction output to match with the composite image feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " from the discriminator. Recall that the composite image feature is extracted from cropped composite image, with the crop bounding box denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " (see Section 4.1). So we apply RoIAlign [10] with the bounding box "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to obtain local background feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{F}}^{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " from global background feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " produced by background encoder "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, we resize RoIAlign output to be of the same shape as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{F}}^{b} \\in \\mathcal{R}^{h \\times w \\times c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": ". The local background feature is supposed to encode contextual information surrounding the foreground. Meanwhile, we utilize foreground encoder "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{f}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " to extract foreground feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{f}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": ". Given the foreground feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{f}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " and local background feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{F}}^{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": ", we feed their concatenation into "
+                                },
+                                {
+                                    "bbox": [
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+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " to produce a distilled feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{d} \\in \\mathcal{R}^{h \\times w \\times c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": ". Note the discriminator and two encoders adopt the same backbone network and input image size in our implementation, so their feature maps have the same shape, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{c}, \\mathbf{F}^{d} \\in \\mathcal{R}^{h \\times w \\times c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": ". During training phase, we enforce the distilled feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " to mimic the composite image feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
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+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " by "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        157,
+                                        287,
+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " loss:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                        438,
+                        287,
+                        453
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        124,
+                                        438,
+                                        287,
+                                        453
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {k d} = \\left\\| \\mathbf {F} ^ {d} - \\mathbf {F} ^ {c} \\right\\| _ {1}. \\tag {3}",
+                                    "image_path": "f9044a13c3245e4bf7c3e308800dfbe14f02abb47744f0041ff358f773e35052.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        461,
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+                                        497
+                                    ],
+                                    "type": "text",
+                                    "content": "We pool the distilled feature map into a vector and send it to a binary classifier to predict the compatibility. The classifier is also trained using binary cross-entropy loss:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        116,
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+                        287,
+                        519
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        116,
+                                        504,
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+                                        519
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {c l s} = - \\log (p (\\mathbf {F} ^ {d}) _ {y}), \\tag {4}",
+                                    "image_path": "189d125beb610762ca9e89d68ab8910cf6fc84fff5eaedfd9540163d3771d32f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        47,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        526,
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+                                        538
+                                    ],
+                                    "type": "text",
+                                    "content": "in which "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        526,
+                                        239,
+                                        538
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\cdot)_y"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        526,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is similarly defined as in Eqn. 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        47,
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+                    "type": "text",
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+                                {
+                                    "bbox": [
+                                        47,
+                                        538,
+                                        287,
+                                        573
+                                    ],
+                                    "type": "text",
+                                    "content": "Finally, we train the encoders "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        538,
+                                        287,
+                                        573
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{E^f,E^b\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        538,
+                                        287,
+                                        573
+                                    ],
+                                    "type": "text",
+                                    "content": " and distillation module "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        538,
+                                        287,
+                                        573
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        538,
+                                        287,
+                                        573
+                                    ],
+                                    "type": "text",
+                                    "content": " simultaneously. The overall optimization function can be written as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        100,
+                        583,
+                        287,
+                        596
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
+                                        100,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {L} _ {t r p} + \\lambda_ {k d} \\mathcal {L} _ {k d} + \\lambda_ {c l s} \\mathcal {L} _ {c l s}, \\tag {5}",
+                                    "image_path": "2c71aea2d6bf19bf70dd04de9ef7fedf8069af02cf75a6eab0bd1072d29b4957.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        287,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{kd}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        604,
+                                        287,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        604,
+                                        287,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{cls}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        604,
+                                        287,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": " are trade-off parameters. During inference, our model finds compatible foregrounds for a given background by ranking the predicted compatibility scores."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.4. Generalization to Real-world Application"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        47,
+                        665,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "To boost the performance of our method on real-world data, we make some modifications to the training procedure of our teacher network and student network, which helps achieve more competitive results on the R-FOSD dataset."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
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+                        251
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": "For the teacher network, we utilize the binary classifier in Section 4.1 to extend training samples. Specifically, given a background image, we use the classifier to predict compatibility score for each foreground and treat those with scores larger than 0.8 as positive samples (including the ground-truth foreground), based on which the ratio of positive and negative foregrounds per background is increased from 1:10 to 5:10. Besides, we apply data augmentation to generate additional positive and negative samples from the ground-truth foreground for each background image. Precisely, based on the ground-truth foreground, we produce 2 positive foregrounds through color jitter and Gaussian blur, and 1 negative foreground through affine transformation. After augmentation, the ratio of positive and negative samples changes from 5:10 to 7:11."
+                                }
+                            ]
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+                    "index": 11
+                },
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+                                    "type": "text",
+                                    "content": "For the student network, we select the top-5 foregrounds returned by pretrained teacher network as positive samples (including the ground-truth foreground) and adopt the same negative samples as the teacher network. After applying the same data augmentation scheme as the teacher network, we also have positive and negative samples with the ratio 7:11 to train the student network."
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+                                    "type": "text",
+                                    "content": "Finally, considering that user-provided bounding boxes may not be very accurate, we also augment bounding boxes when training teacher network and student network. Specifically, we randomly pad the bounding box with the maximum padding space being "
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+                                    "type": "text",
+                                    "content": " of the bounding box's width and height."
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+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "5. Experiments"
+                                }
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+                                    "content": "5.1. Dataset and Evaluation Metrics"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "Our S-FOSD dataset is employed for both training and testing, while R-FOSD dataset is only for testing. We employ different evaluation metrics for two datasets considering their difference in the acquisition of ground-truth foregrounds. For each metric, we report the mean evaluation results by averaging the results over all categories. Moreover, we leave the implementation details in Supplementary."
+                                }
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+                                    "type": "text",
+                                    "content": "S-FOSD Dataset. The training set has 57,219 pairs of foregrounds and backgrounds covering 32 categories, with a maximum of 4800 pairs and a minimum of 300 pairs in each category. The test set provides 20 backgrounds and 200 foregrounds (including 20 foregrounds from the same images as the backgrounds) for each category. The foreground/background images in the training set and test set have no overlap. Following previous works [42, 47], only the foreground object from the same image is viewed as ground-truth for each background and we adopt Recall@k (R@k) as evaluation metric, which represents the percentage of background queries whose ground-truth foreground appears in top "
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+                                    "type": "text",
+                                    "content": " retrievals ("
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+                                    "type": "inline_equation",
+                                    "content": "k = 1, 5, 10, 20"
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+                                    "type": "text",
+                                    "content": " in our experiments)."
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+                                    "content": "R-FOSD Dataset. The R-FOSD dataset adopts the same foreground set as the test set of S-FOSD dataset and collects 20 backgrounds for each category. Each pair of background and foreground is shown to three human annotators to label the compatibility. The resulting dataset contains "
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+                                    "type": "text",
+                                    "content": " compatible foregrounds per background, and we adopt mean Average Precision (mAP), mAP@20, and Precision@k (P@k) for evaluation, which are widely used in image retrieval and previous works [44, 47]. Precision@k means the percentage of compatible foreground objects in the top k retrievals, "
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+                                    "content": " in our experiments. To reduce unplausible results on the R-FOSD dataset, we exclude the objects with aspect ratios deviating more than 1.2 from that of query bounding box for all methods and compute metrics on the remaining objects."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "5.2. Comparison with Existing Methods"
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+                                    "content": "Baselines. We compare our approach with previous methods [42, 44, 37, 47] on our two datasets. Shape [42] ranks foreground objects by comparing their aspect ratios with that of the query bounding box on background. CFO [42], UFO [44], FFR [37], and GALA [47] adopt the pipeline described in Section 4.2, which use two encoders to extract background and foreground features, and then rank the compatibility of foreground by computing its feature similarity with background. To adapt to our focus on geometric and semantic incompatibility, we replace the style feature of FFR [37] with semantic feature, in which we obtain the semantic feature by using VGG-19 [30] pretrained on ImageNet [8] following [44]. For GALA [47] that considers lighting and geometry compatibility, we discard lighting transformation and only keep geometry transformation [47] to match our scenario. Besides, we do not compare with IFR [19], as it requires pattern labels of the foreground, which are unavailable in our datasets. For fair comparison, we employ the same backbone network and training set for all baseline methods except Shape [42]. We use the same positive and negative samples for different methods when training on S-FOSD dataset."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Quantitative comparison. The results of baselines and our method on the proposed two datasets are summarized in Table 1. Moreover, when evaluating on S-FOSD dataset, the only ground-truth foreground has the same aspect ratio as the query bounding box, thus Shape [42] can find the ground-truth by shortcut, making the evaluation results meaningless. It can be seen that among all baselines, GALA [47] and FFR [37] are two competitive ones, which employ contrastive learning with self-transformation [47] and MarrNet [36] to enhance the perception of geometric information of foreground, respectively. Nevertheless, our method outperforms all previous approaches by an obvious margin on both S-FOSD and R-FOSD datasets."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "Qualitative comparison. We show the retrieval results of"
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+                                            "type": "text",
+                                            "content": "Figure 5. Qualitative comparison on our S-FOSD (left) and R-FOSD (right) datasets. Each of the four examples contains a background image and several rows of the retrieval results, from top to bottom: CFO [42], UFO [44], GALA [47], FFR [37], and ours. Additionally, in the right part, green (resp., red) box represents the foreground with compatible (resp., incompatible) label."
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+                                    "type": "text",
+                                    "content": "different baselines on our two datasets in Figure 5. For each query background, we show the returned top-5 foregrounds by different methods, which shows that our method can generally find compatible foregrounds by taking both semantic and geometric factors into account. For example, for the top-left example, given a query bounding box at the bottom-right seat, the baseline methods may return a standing or frontal person, which is unsuitable to be placed in the query bounding box. In contrast, the top returned persons by our method all have sitting posture, which appear more reasonable in terms of semantic compatibility. In the bottom-right example, given the geometry of background scene, the annotated ground-truth positive foregrounds (green box) have consistent orientation with respect to the train track in background. Our method retrieves more positive foregrounds than other approaches, demonstrating the effectiveness of our method on geometry compatibility. More qualitative results are present in Supplementary."
+                                }
+                            ]
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+                                    "content": "5.3. Ablation Study"
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+                                    "content": "In this section, we start from the general pipeline with two encoders of previous methods [42, 44, 47, 19, 37] and evaluate the effectiveness of each component in our method. Different models are evaluated on our S-FOSD dataset and the results are summarized in Table 2. In row 1, we apply two encoders "
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+                                    "content": " and foreground feature "
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+                                    "type": "text",
+                                    "content": ", which are used to predict the background foreground compatibility by measuring their feature similarity. It is worth mentioning that all models in Table 2 rank different foregrounds by predicted compatibility scores except the row 1 and row 2, which measure compatibility by calculating feature similarity."
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">S-FOSD Dataset</td><td colspan=\"6\">R-FOSD Dataset</td></tr><tr><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td><td>mAP↑</td><td>mAP@20↑</td><td>P@1↑</td><td>P@5↑</td><td>P@10↑</td><td>P@20↑</td></tr><tr><td>Shape [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>50.49</td><td>56.22</td><td>47.66</td><td>49.72</td><td>50.03</td><td>49.92</td></tr><tr><td>CFO [42]</td><td>56.09</td><td>83.59</td><td>91.25</td><td>96.88</td><td>52.06</td><td>62.17</td><td>58.33</td><td>56.29</td><td>55.90</td><td>52.85</td></tr><tr><td>UFO [44]</td><td>54.69</td><td>81.72</td><td>90.94</td><td>95.31</td><td>52.73</td><td>63.63</td><td>64.12</td><td>59.11</td><td>56.30</td><td>53.82</td></tr><tr><td>FFR [37]</td><td>57.03</td><td>86.25</td><td>93.28</td><td>97.97</td><td>53.10</td><td>64.12</td><td>61.92</td><td>59.64</td><td>57.56</td><td>55.06</td></tr><tr><td>GALA [47]</td><td>57.50</td><td>85.17</td><td>93.00</td><td>97.33</td><td>52.02</td><td>62.83</td><td>62.56</td><td>57.33</td><td>55.76</td><td>52.93</td></tr><tr><td>DiscoFOS</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td><td>56.70</td><td>68.56</td><td>67.75</td><td>64.64</td><td>62.25</td><td>58.90</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. Comparison with existing methods on our S-FOSD dataset and R-FOSD dataset. Best results are denoted in boldface."
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+                                            "html": "<table><tr><td></td><td>Eb</td><td>Ed</td><td>R@1↑</td><td>R@5↑</td><td>R@10↑</td><td>R@20↑</td></tr><tr><td>1</td><td>Fb</td><td></td><td>54.83</td><td>81.17</td><td>90.67</td><td>95.00</td></tr><tr><td>2</td><td>Fb</td><td></td><td>52.50</td><td>79.69</td><td>88.75</td><td>93.00</td></tr><tr><td>3</td><td>Fb</td><td>p(·)y</td><td>56.72</td><td>87.19</td><td>94.69</td><td>97.97</td></tr><tr><td>4</td><td>Fb</td><td>[Fb, Ff]</td><td>60.83</td><td>87.33</td><td>95.00</td><td>98.17</td></tr><tr><td>5</td><td>Fb</td><td>[Hatb, Ff]</td><td>65.16</td><td>90.31</td><td>95.31</td><td>98.59</td></tr><tr><td>6</td><td>Fb</td><td>[Fb, Ff]</td><td>68.28</td><td>90.94</td><td>95.63</td><td>98.75</td></tr><tr><td>7</td><td>Fb</td><td>Fb ⊕ Ff</td><td>64.53</td><td>87.66</td><td>92.97</td><td>96.72</td></tr><tr><td>8</td><td>Fb</td><td>[Fb, Ff]</td><td>79.06</td><td>94.84</td><td>97.34</td><td>99.38</td></tr><tr><td>9</td><td></td><td>D(Ic)</td><td>49.22</td><td>76.72</td><td>84.53</td><td>91.88</td></tr><tr><td>10</td><td></td><td>D(Ic)</td><td>84.38</td><td>97.03</td><td>98.91</td><td>99.84</td></tr></table>",
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+                                    "content": "Table 2. The ablation studies of our method on S-FOSD dataset. "
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+                                    "type": "text",
+                                    "content": ": global/local background feature vector. "
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+                                    "type": "text",
+                                    "content": ": global/local background feature map. "
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+                                    "type": "text",
+                                    "content": ": foreground feature map/vector. "
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+                                    "type": "text",
+                                    "content": ": feature concatenation. "
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+                                    "type": "text",
+                                    "content": ": feature map composition. The detailed explanations can be found in Section 5.3."
+                                }
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+                        }
+                    ],
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+                                    "content": "Background Encoder "
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+                                    "type": "inline_equation",
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Based on row 1 of Table 2, we replace the global background feature vector "
+                                },
+                                {
+                                    "bbox": [
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+                                        436,
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " with local background feature vector "
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+                                    "type": "text",
+                                    "content": ", which is obtained by applying RoIAlign [10] with the crop bounding box "
+                                },
+                                {
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+                                    "content": "B"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to background feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^b"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", resulting in worse results in row 2. This is probably because that the global background feature contains more useful information than the local background feature. So we adopt the global background feature for background encoder in other experiments."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Composite Image Discriminator "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". In our network, the discriminator plays the role of teacher. In row 9 and 10 of Table 2, we feed the discriminator with the whole composite image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}^c"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the cropped composite image "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{I}}^c"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", respectively. We see that row 10 achieves significantly better performance than row 9, which can be attributed to the aligned foreground and useful surrounding foreground context in the cropped composite. Then, the discriminator with the whole composite image is inferior to the encoders of row 1, which is roughly consistent with previous findings [44, 42]. Additionally, the discriminator with cropped composite image outperforms the encoders (row 1) with a remarkable margin, which motivates us to build our method."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Knowledge Distillation Module "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Based on row 1 of"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Table 2, we introduce the distillation module without using feature distillation, which is essentially a compatibility classifier "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "p(\\cdot)_y"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", in row 3. The classifier takes the concatenation of foreground feature vector "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbf{F}}^f"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and background feature vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathbf{F}}^b"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as input, and outputs the compatibility score. The comparison between row 1 and 3 verifies that adding compatibility classification is helpful for our task."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Then we add feature distillation and explore the impact of using different forms of background-foreground interactions. In row 4 and 5, we perform interaction based on the pooled feature vectors of two encoders. Specifically, we concatenate the foreground feature vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{F}}^f"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with global background feature vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{F}}^b"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (resp., local background feature vector "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{F}}^b"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ") to feed into distillation module in row 4 (resp., row 5). Both results are better than row 3, proving the utility of distilling composite image feature to predict compatibility."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Next, we perform interaction based on the last feature maps of two encoders. To this end, we explore several different ways to fuse background and foreground features. First, we directly concatenate background feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^b"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and foreground feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^f"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in row 6. By comparing row 6 and 4, it verifies the advantage of more sufficient interaction. In row 7, we extend to a more intuitive way by applying composition operation to local background feature maps "
+                                },
+                                {
+                                    "bbox": [
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+                                        545,
+                                        651
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{F}}^b"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        413,
+                                        545,
+                                        651
+                                    ],
+                                    "type": "text",
+                                    "content": " and foreground feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}^f"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Specifically, we resize the foreground feature and place it in the query bounding box on the local background feature. Unexpectedly, this leads to slight performance drop compared with row 5, which may be caused by downsampling the foreground feature. Finally, we concatenate the local background feature "
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+                                    "content": " and foreground feature "
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+                                    "content": ", corresponding to our complete method. As shown in row 8, our full method produces remarkably better results than the abovementioned row 6, indicating that the representation ability of the distilled feature can benefit from adequate interaction between two encoders."
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+                                    "content": "5.4. Inference Efficiency Analyses"
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+                                    "content": "To study the efficiency of our method, we compare our method (\"Ours\") with the composite image discriminator (\"Discriminator\"), and background and foreground"
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+                                            "html": "<table><tr><td>Model</td><td>Time(200)↓</td><td>Time(2000)↓</td><td>#Params↓</td></tr><tr><td>Discriminator</td><td>700.0ms</td><td>7000.1ms</td><td>20.03M</td></tr><tr><td>Encoders</td><td>4.0ms</td><td>4.3ms</td><td>40.05M</td></tr><tr><td>Ours</td><td>5.2ms</td><td>6.0ms</td><td>47.13M</td></tr></table>",
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+                                    "content": ", encoders "
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+                                    "type": "text",
+                                    "content": ", and our method in the Figure 3. \"Time(N)\" represents the average time of retrieving compatible foregrounds from "
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+                                    "type": "text",
+                                    "content": " candidates per background."
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+                {
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+                                    "type": "text",
+                                    "content": "encoders (\"Encoders\") on retrieval time and number of parameters, the results of which are reported in the Table 3. We test different models on an NVIDIA RTX 3090 GPU and measure the time of retrieving compatible foreground from "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N"
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+                                    "type": "text",
+                                    "content": " candidates as retrieval time "
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+                                    "type": "inline_equation",
+                                    "content": "(\\mathrm{Time}(N))"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". We repeat the retrieval 50 times and calculate the average time as final result. To mimic the practical application scenarios of foreground object search, we assume that the features of all foregrounds have been extracted and saved before retrieval. In particular, for \"Encoders\" and \"Ours\", we save the feature vector and the last feature map of the foreground encoder, respectively. In this way, the retrieval time of \"Encoders\" and \"Ours\" only considers the background feature extraction and the matching between background and foreground, in which background feature extraction takes 3.1ms per image."
+                                }
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+                                    "type": "text",
+                                    "content": "We can see that the discriminator "
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+                                    "type": "text",
+                                    "content": " is the slowest method due to compositing with each foreground and sending each composite through forward pass. \"Ours\" runs slower than \"Encoders\" due to introducing additional interaction between background and foreground, yet only takes 6ms to retrieve from 2000 foregrounds, which enables our model for real-time applications. Regarding the number of parameters, the comparison between two encoders and ours indicates that the additional parameters (7.08M) introduced by distillation module are affordable."
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+                                    "type": "text",
+                                    "content": "5.5. Additional Experiments in Supplementary"
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+                            ]
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+                    "index": 4
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+                                    "type": "text",
+                                    "content": "Due to space limitation, we present some experiments in Supplementary, including quantitative comparison on different categories, generalization to new categories, the results of our method using different hyper-parameters in Eqn. (5) and Eqn. (2), and different ratios of positive and negative training samples, the discussion on the limitation of our method, and the results of significance test."
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+                            ]
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+                                    "type": "text",
+                                    "content": "6. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this work, we have contributed two public datasets for Foreground Object Search (FOS), S-FOSD with Synthetic composite images and R-FOSD with Real composite images. We have also proposed a novel FOS method, which improves the general pipeline of previous methods by feature distillation. Extensive experiments on our dataset have"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "demonstrated the utility of our proposed method on foreground object search."
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+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                    "type": "text",
+                                    "content": "Acknowledgement"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The work was supported by the National Natural Science Foundation of China (Grant No. 62076162), the Shanghai Municipal Science and Technology Major/Key Project, China (Grant No. 2021SHZDZX0102, Grant No. 20511100300)."
+                                }
+                            ]
+                        }
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                        {
+                            "bbox": [
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+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
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+                                        {
+                                            "bbox": [
+                                                311,
+                                                215,
+                                                545,
+                                                236
+                                            ],
+                                            "type": "text",
+                                            "content": "[1] Jimmy Ba and Rich Caruana. Do deep nets really need to be deep? In NIPS, 2014. 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
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+                        {
+                            "bbox": [
+                                311,
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+                                270
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
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+                                    ],
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
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+                                        }
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
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+                                    ],
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+                                        {
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
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+                            "bbox": [
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                {
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
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+                            "bbox": [
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+                                415,
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "[7] Xiaodong Cun and Chi-Man Pun. Improving the harmony of the composite image by spatial-separated attention module. IEEE Transactions on Image Processing, 29:4759-4771, 2020. 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
+                        },
+                        {
+                            "bbox": [
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diff --git a/2023/Foreground and Text-lines Aware Document Image Rectification/3650c92e-47cd-4562-b763-9e2e457518cc_content_list.json b/2023/Foreground and Text-lines Aware Document Image Rectification/3650c92e-47cd-4562-b763-9e2e457518cc_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..d34eca7eb10c5387a8cf0662e53cf2d74a36811d
--- /dev/null
+++ b/2023/Foreground and Text-lines Aware Document Image Rectification/3650c92e-47cd-4562-b763-9e2e457518cc_content_list.json	
@@ -0,0 +1,1692 @@
+[
+    {
+        "type": "text",
+        "text": "Foreground and Text-lines Aware Document Image Rectification",
+        "text_level": 1,
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+        "text": "Heng Li",
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+    {
+        "type": "text",
+        "text": "Xiangping  $\\mathbf{W}\\mathbf{u}^{1,3*}$",
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+        "text": "Qingcai Chen $^{1,2*}$",
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+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ Harbin Institute of Technology Shenzhen, China,  $^{2}$ PengCheng Laboratory, Shenzhen China  $^{3}$ The Hong Kong Polytechnic University, Hung Hom Kowloon, Hong Kong",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "hengli.lh@outlook.com, wxpleduole@gmail.com, qingcai.chen@hit.edu.cn, randy19991009@outlook.com",
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+    {
+        "type": "text",
+        "text": "Abstract",
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+    },
+    {
+        "type": "text",
+        "text": "This paper aims at the distorted document image rectification problem, the objective to eliminate the geometric distortion in the document images and realize document intelligence. Improving the readability of distorted documents is crucial to effectively extract information from deformed images. According to our observations, the foreground and text-line of the original warped image can represent the deformation tendency. However, previous distorted image rectification methods pay little attention to the readability of the warped paper. In this paper, we focus on the foreground and text-line regions of distorted paper and proposes a global and local fusion method to improve the rectification effect of distorted images and enhance the readability of document images. We introduce cross attention to capture the features of the foreground and text-lines in the warped document and effectively fuse them. The proposed method is evaluated quantitatively and qualitatively on the public DocUNet benchmark and DIR300 Dataset, which achieve state-of-the-art performances. Experimental analysis shows the proposed method can well perform overall geometric rectification of distorted images and effectively improve document readability (using the metrics of Character Error Rate and Edit Distance). The code is available at https://github.com/xiaomore/Document-Image-Dewarping.",
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+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In our daily life, there are various documents, such as papers, posters, receipts and so on. These documents contain a wealth of information. At present, document intelligence can automatically extract the information in the document, and then obtain structured data (text content, key field extraction, table structure, document layout analysis), which greatly facilitates people's lives. However, with the popu",
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+        "img_path": "images/5715362dc53b0a7feb9c819a0b1f4870b8e74a3244768dddceadff5f9171e080.jpg",
+        "image_caption": [
+            "Figure 1. Compared with the text results using Tesseract [32] as OCR engine. Row 1: distorted images. Row 2: rectified by our method. We use color to highlight the detected text boxes."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
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+    {
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+        "img_path": "images/4446cc6c7612362cce0ed75bb1feb2e4d4ed014ad92b3661e9f32f1332b0c556.jpg",
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/76b587699a996207031ae426f48a1d23deb9f85540edc5162da3042023b1d4e2.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            420,
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+            537
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "larization of mobile electronic devices, it is more and more convenient for people to take pictures with smart phones or portable cameras to capture electronic documents. When taking pictures, due to the different positions, illumination conditions of these devices, the angle of paper placement, deformation and other problems, the images taken are distorted or deformed to varying degrees, and it is difficult to extract useful information from these distorted pictures, as shown in Figure 1. Even wrong information is extracted, which brings great challenges to obtaining key information of documents and realizing document intelligence.",
+        "bbox": [
+            496,
+            608,
+            892,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "As early as many years ago, the problem of document image distortion rectification has been paid attention to. In the traditional rectification method before deep learning was widely used, several previous methods [3, 36, 17] according to the deformation characteristics of the image, relying on multi-view, get the best boundary through the regression method, and use the boundary segmentation method to dewarped the segmentation graphics. Tian and Narasimhan",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding authors.",
+        "bbox": [
+            94,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "19574",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "[35] reconstructs warped document images from 2D to 3D by detecting text-lines in the image. In the time since, some works [16, 15] have also captured prior knowledge in deformed images by detecting text lines in order to bring gains to image rectification. However, these methods of restoring the 3D shape of images through auxiliary hardware or multi-view methods will bring time consuming and expensive problems.",
+        "bbox": [
+            75,
+            90,
+            468,
+            210
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "With the arrival of the era of deep learning, Convolutional Neural Network (CNN) and Transformer have been introduced to solve the geometric rectification of distorted document images. Most current methods dewarping the input image by learning the mapping relationship between the input distorted image and the dense 2D coordinate map area [26, 8, 1, 11, 14, 10]. The method of [26, 8] used the UNet structure networks to regress the dense 2D coordinates mapping according to the input distorted image. However, it is difficult for CNN to capture the long-distance dependence of distorted paper. For methods [11, 10] that focus on image foreground, they proposed to remove the document background in the preprocessing stage before geometric rectification the network. And then introduces the multi-layer transformer of Encoder-Decoder structure after the convolution network to dewarp the distorted paper. But these methods based on setting the binarization threshold to remove the background will lose the information of the original image. There are also some works such as [14, 10] proposed to use document boundaries, 3D world coordinates and text-lines to construct deformation fields, which reduces the error rate of text recognition. These two methods have no obvious interaction between the text-line and the original distorted image, which makes the text-line area unable to be effectively focused.",
+        "bbox": [
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+            593
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In geometrically deformed images, the distortion degree of image foreground and text-lines varies with different scenes. It is necessary to establish an explicit invariant feature in the distorted image foreground to represent the core document and text-line region features robustly, to suppress the interference of background and deformation. Since the foreground information of the document image can clearly represent the deformation amplitude, we use the foreground features representation of the input image. The text-line regions can represent the distorted state of the local position in dewarped images. In order to enhance the reading quality of the image, we considering it is necessary to pay more attention to the area of the text-lines. Therefore, we propose to represent local information using text-line information, extract the characteristics of the corresponding position in the image. Besides, based on our observations, when using the deformation field for distortion rectification, for the dewarped image, the areas in the same horizontal direction should have the same vertical coordinates in the deformation field. For example, for text-lines, the text area of the",
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+    {
+        "type": "text",
+        "text": "same line should have the same ordinate. This is a very critical starting point for our design model.",
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+    {
+        "type": "text",
+        "text": "From the perspective of readability, we propose a novel distortion image rectification model based on cross attention mechanism, which fuses the features of the image foreground and text line. The features of the foreground and text-line regions respectively focus on the features of the corresponding positions in the original warped image. The foreground and text-line features are each represent the global and local information of the distorted image, which have complementary effects. In addition, in order to enhance the interaction between global and local features, we share the two cross attention branches of foreground and text-lines, which also reduces the amount of model parameters to a certain extent.",
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+        "type": "text",
+        "text": "The main contributions of our work are summarized as follows:",
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+        "list_items": [
+            "- We propose to use foreground and text line information to guide the model to focus on the global and local features of distorted paper, so as to reduce background interference and improve the readability of document images.",
+            "- We introduce cross-attention to explore more effective interaction between paper deformation trend and original distorted image.",
+            "- We conduct extensive experiments and show the state-of-the-art results on the existing prevalent benchmarks."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Document Image Geometric Unwarping",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The goal of rectifying distorted images is to enhance the visual quality of images, thereby reducing the difficulty of text extraction and improving the readability of paper. Early document image rectification methods performed parametric rectification by using cues easily observed from the image, such as text-lines proposed by Huang et al. [12], cylindrical surfaces [38, 6, 21, 18, 48, 27], document boundaries [3, 36] or laser beams from external devices used by Narain et al. [29].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In recent years, many works such as [26, 8, 1, 11, 14, 10] proposed to use deep learning to rectify distorted document images. These models solve the rectification problem by directly predicting the deformation field of the image.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ma et al. [26] is the first work using deep neural networks on this task. They used a stacked UNet structure to predict the deformation field for each pixel in the warped document. This is an end-to-end structure that inverts the input image to obtain the result after the prediction result is obtained. In view of the lack of a large number of warped datasets to train the model, Das et al. [8] subsequently contributed a warped document image dataset (Doc3D) containing about 100,000 Distorted images. In addition, they",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "19575",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/9c84efeb446f2c1f93e148050b475fa17a3ba4245e30e5f8a8e5e1137a3cacdd.jpg",
+        "image_caption": [
+            "Figure 2. The overview architecture of our proposed method. FAM is Foreground Attention Module and TAM is Text-lines Attention Module."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            160,
+            89,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "proposed a UNet structure network that uses 3D shape (World Coordinates) to replace the original warped document to predict the deformation field.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In order to reduce the interference of the background on the dewarping effect, Feng et al. [11] proposed to remove the background of the document before rectification, and introduced a transformer on this task for the first time. For reasons of improving the reading quality of the rectified document, other works of Jiang et al. [14] and Feng et al. [10] proposed to introduce the text-line feature in the document to enhance the rectification effect of text-line areas.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Attention in Vision",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The attention mechanism focuses the attention of the network on the most important parts of the data by enhancing the weight of some parts of the input data of the neural network while weakening the weight of other parts. It was originally developed in 2017 for natural language processing tasks by Vaswani et al. [37], and greatly improved new state-of-the-art performance on many downstream tasks. However, in recent years, great success has been achieved in computer vision-related tasks such as image or video classification [39, 31, 2, 33, 7], image segmentation [49, 41, 4, 23], visual question answering [51, 34, 5, 46], and scene text recognition [44].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Different from the self-attention mechanism, cross attention is able to exploit the intra-modal relations of each modality to complement each other and enhance the feature relations between different modalities. On multimodal tasks, cross attention is widely used to match the visual semantic similarity between images and texts [51, 34, 5, 46], and the key step is how to design fusion modules to effectively connect multimodal inputs. In this distorted im",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "age geometry rectification task, in order to minimize background interference, we propose to use the foreground information to aware corresponding regions in image features in a cross-attention manner. Furthermore, in order to increase the attention on the text-line regions, similar to the foreground cross-attention, we use the text-lines information to obtain the features of the text regions in the image, which can ensure that the same line of text is horizontal on the rectified image.",
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+    {
+        "type": "text",
+        "text": "3. The Proposed Approach",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we propose a noval framework for document image dewarping. The overview architecture of our model is shown in Figure 2.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Network Architecture. Our model consists of CNNs Encoder, the Foreground and Text-line Attention Module, and the Transformer Decoder. We use these three modules to obtain the features of foreground regions except background and text-line regions in distorted document images, respectively. After obtaining text-line and foreground information, cross-attention used to enhance the foreground and text-line attention. And then concatenate the feature map of these two cross feature map in the channel dimension, input it to the multi-layer decoder to predict the 2D grid coordinates, and finally use the coordinates to dewarp the input document image.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given a warped document image  $\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}$ , we first resize it to  $\\mathbf{I}_r \\in \\mathbb{R}^{H_r \\times W_r \\times C_r}$ , where  $H_r = W_r = 224$  and  $C_r = 3$  is the number of RGB channels of the original image. Then,  $\\mathbf{I}_r$  is fed into an encoder consisting of multiple layers of convolutional neural networks (CNNs) to obtain the feature map  $\\mathbf{F}_i \\in \\mathbb{R}^{H_i \\times W_i \\times C_i}$  of the original warped image. Then, through the cross-attention of fore",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "19576",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7307c8f8498cdc26cbd53fff352697d68aeb0c96954e271ace2d6d55187f0387.jpg",
+        "image_caption": [
+            "Figure 3. Text-line detection results of the Doc3D dataset. Row 1: Input warped images. Row 2: Detection results for text lines."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            91,
+            93,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ground and text-line, the region of interest is extracted from the image features  $\\mathbf{F}_i$ . Finally, a 2D dense grid coordinate  $\\hat{G} \\in \\mathbb{R}^{H_r \\times W_r \\times 2}$  (backward mapping or deformation field) is predicted through a transformer network composed of a multi-layer self-attention and feed-forward network architecture. According to the obtained grid coordinates, the input image can be dwarped to obtain an dwarped picture  $\\mathbf{D} \\in \\mathbb{R}^{H \\times W \\times 3}$ . Each coordinate  $(x, y)$  in grid coordinates represents the position of the pixel value on the input image in the rectified image.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "CNNs Encoder. For the resized image  $\\mathbf{I}_r$ , we first use the convolutional neural network module as an encoder to extract image features. The encoder contains 3 layers of residual blocks, and each layer downsamples the feature map to half the size. The resolution of the final output feature map  $\\mathbf{F}_i \\in \\mathbb{R}^{H_i \\times W_i \\times C_i}$  is one-eighth of that of  $\\mathbf{I}_r$ . Where  $H_i = H_r / 8$ ,  $W_i = W_r / 8$ ,  $C_i$  is the number of channels of the feature map  $\\mathbf{F}_i$ . We set  $\\mathbf{C}_i$  to 256.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Foreground and Text-line Queries. In the previous work on distorted image rectification, there have been related works on foreground [11, 10] and text-line mask [14] extraction. We initialize the foreground and text-line queries on the basis of these two works. For foreground mask extraction, Feng et al. [11] used a lightweight semantic segmentation architecture network to predict the confidence map of foreground. The network is an Encoder-Decoder structure. We do not directly use the resulting binarized mask. Instead, use the six-layer feature maps in the decoder, and first resize them to the same size as  $\\mathbf{F}_i$ , which is one-eighth the size of  $\\mathbf{I}_r$ . And after concatenating in the channel dimension, use a layer of  $3 \\times 3$  convolution module and BatchNorm [13] to reduce the number of channels to 256. Compared with directly using the binary mask output by the last layer of the network, this method can obtain richer image feature information.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the text-lines information, since the Doc3D training dataset proposed by DewarpNet [8] used by our model lacks corresponding text-line annotations, we use the detection",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "text-line method proposed in RDGR [14] to obtain text-line features. This detection method used the U-Net network to train on PubLayNet [50] and the Scanned Script Dataset<sup>1</sup>. Its detection effect on the Doc3D dataset is shown in Figure 3. Although the text-line detected by this method has certain errors due to the deformation of the image, illumination effects and other reasons, it is within the network fault tolerance range. For text-line queries initialization, we use the last feature map of the U-Net network decoder (not the final confidence map). Its resolution is consistent with U-net network input. Then, we apply a layer of  $3 \\times 3$  convolution and BatchNorm [13] to change the number of channels to 256, and finally bilinear interpolation is utilized to downsample the feature map size to one-eighth the size of  $\\mathbf{I}_r$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Foreground and Text-line Attention Module. For the initialized foreground queries, we use the cross-attention mechanism to extract features in distorted images. This module consists of three parts: self-attention, cross-attention, and feed forward networks. First, the image feature map  $\\mathbf{F}_i$  is flattened, and then the long-distance dependencies between patches are calculated using self-attention.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "However, in the process of flattening the feature map, 2D coordinate information will be lost, which is crucial to obtain the local and global relationship, so we add a learnable 2D coordinate information. The same operation is performed on foreground queries. And then, in order to pay more attention to the foreground area and ignore the background, we use a foreground-guided cross-attention module. Specifically, a multi-head cross-attention layer is applied after self-attention. We utilize image features  $\\mathbf{F}_i$  as key and value, and the foreground feature  $\\mathbf{F}_f$  as query. Similar to the foreground-query cross-attention mechanism, in order to extract the features of the text-line positions of interest. The text-line features  $\\mathbf{F}_t$  is treated as query. Finally, we utilize a layer of convolutions to enhance local feature extraction after obtaining the attention feature map. The formula for the foreground query and text-line query cross-attention mechanism is as follows:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} C A _ {f} = C A (Q, K, V) = C A \\left(F _ {f}, F _ {i}, F _ {i}\\right) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {F _ {f} F _ {i} ^ {\\mathrm {T}}}{\\sigma}\\right) F _ {i} \\tag {1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} C A _ {t} = C A (Q, K, V) = C A \\left(F _ {t}, F _ {i}, F _ {i}\\right) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {F _ {t} F _ {i} ^ {\\mathrm {T}}}{\\sigma}\\right) F _ {i} \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $CA$  is Cross-Attention and  $\\sigma$  is a scaling factor.  $CA_{f}$  and  $CA_{t}$  are the foreground and text-line cross-attention map respectively.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Transformer Decoder. After extracting the interesting feature  $\\mathbf{C}A_{f}$  and  $\\mathbf{C}A_{t}$  of the foreground and text-line, we concatenate the two features and feed them into the transformer",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "<https://github.com/zzzDavid/ICDAR-2019-SROIE",
+        "bbox": [
+            516,
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+            898
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "19577",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/84e1d93029ca65e4b1d194c667fe7135ace651dfaf25603410d77c0ca66b6dd0.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.2459</td><td>20.51</td><td>1.0134</td><td>2111.56</td><td>0.5352</td></tr><tr><td>DocUNet [26]</td><td>CVPR&#x27;18</td><td>0.4103</td><td>14.19</td><td>-</td><td>1933.66</td><td>0.4632</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.2946</td><td>18.01</td><td>-</td><td>1712.48</td><td>0.4267</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4735</td><td>8.39</td><td>0.4260</td><td>885.90</td><td>0.2373</td></tr><tr><td>FCN-based [42]</td><td>DAS&#x27;20</td><td>0.4288</td><td>7.75</td><td>0.4017</td><td>1792.60</td><td>0.4213</td></tr><tr><td>PWUNet [9]</td><td>ICCV&#x27;21</td><td>0.4915</td><td>8.64</td><td>-</td><td>1069.28</td><td>0.2677</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.5105</td><td>7.76</td><td>0.3682</td><td>724.84</td><td>0.1832</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.4726</td><td>8.97</td><td>0.4287</td><td>1411.38</td><td>0.3573</td></tr><tr><td>FDRNet [45]</td><td>CVPR&#x27;22</td><td>0.5420</td><td>8.21</td><td>-</td><td>829.78</td><td>0.2068</td></tr><tr><td>RDGR [14]</td><td>CVPR&#x27;22</td><td>0.4950</td><td>8.51</td><td>0.4382</td><td>729.52</td><td>0.1717</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.5040</td><td>7.71</td><td>0.3800</td><td>713.94</td><td>0.1821</td></tr><tr><td>Ours</td><td>-</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1. On the DocUNet Benchmark [26], compare our proposed with existing methods in terms of Multi-Scale Structural Similarity (MS-SSIM), Local Distortion (LD) and OCR accuracy (ED and CER). “↑” indicates the higher the better and “↓” means the opposite.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "decoder composed of multi-head self-attention mechanism to predict the grid map. Consistent with the cross-attention module, we also add 2D learnable position coordinates. The structure of each decoder layer consists of self-attention and feed-forward network. Finally, we adopt the upsampling method in DocTr [11] and GeoDewarpNet [10] to obtain high-resolution 2D deformation field  $\\mathbf{G}$ . This upsampling method trains a learnable weight on the basis of initializing the grid coordinates to perform weighted optimization on it. Training Loss Function. The loss function of our distorted document image rectification model is to compute the  $L_{1}$  distance between the predicted grid coordinate  $\\hat{\\pmb{G}}$  and the label  $\\mathbf{G}$ . The formula as follows:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {g r i d}} = \\left\\| \\mathbf {G} - \\hat {\\boldsymbol {G}} \\right\\| _ {\\mathbf {1}} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+            564,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first review the existing training dataset (Doc3D) and evaluation benchmark (DocUNet and DIR300 dataset) for distorted image dewarping. Second, we introduce the evaluation metrics and training details of this method. And then, we evaluate our document image rectification method on two datasets, DocUNet Benchmark [26] and DIR300 [10]. Finally, we demonstrate our rectification performance on several evaluation metrics.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Dataset",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Doc3D. We train the geometric rectification model on the Doc3D dataset contributed by DewarpNet [8]. Doc3D is the largest distortion dewarping dataset so far, containing a total of 100K distorted images. It is created by about 4000 real document images and rendering software. Among them, different camera positions and various illumination are applied when rendering. For each distorted document image, the corresponding labels include 3D coordinate maps, albedo maps, normals, depth maps, UV maps and backward mapping map.",
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+    {
+        "type": "text",
+        "text": "DocUNet Benchmark. In current deep learning-based document dewarping methods, the DocUNet Benchmark [26] dataset is widely used. This evaluation dataset contains 130 distorted images in natural scenes captured by mobile devices. In addition, for better comparison with previous methods, we follow the proposal in DocGeoNet [10] and rotate the  $127^{th}$  and  $128^{th}$  images in DocUNet [26] that do not match the labels by 180 degrees.",
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+    {
+        "type": "text",
+        "text": "DIR300 Dataset. DIR300 dataset is a new test dataset proposed by DocGeoNet [10] captured by moving camera. It contains 300 images of real distorted documents involving more complex backgrounds, distorted degrees, and various lighting conditions.",
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+    {
+        "type": "text",
+        "text": "4.2. Evaluation metrics",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "MS-SSIM, LD and AD. We follow previous methods [26, 8, 1, 11, 14, 10] to perceive image quality using an image-based Multi-Scale Structural Similarity method (MS-SSIM) [40]. Computationally dense SIFT-flow [22], Local Distortion (LD) [47] computes the average of the  $L_{2}$  distances between all pixels in the ground-truth scanned image and the rectified image pixels, which measures the average local deformation of the rectified image. Following DocUNet [26], all rectified images and their labels are resized to 598400 pixel area. We use the code provided by DocUNet [26] for evaluation. Aligned Distortion (AD) is a more robust evaluation metric proposed by [25], which aligns unwarped images and ground truth scans by unifying translation and scale before computing distortions.",
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+    {
+        "type": "text",
+        "text": "CER and ED. We use Character Error Rate (CER) [28] and Edit Distance (ED) [19] to measure the performance of our method. ED is a string metric that measures the difference between two character sequences. The edit distance between two strings is the minimum number of single-character edits (insertions  $(i)$ , deletions  $(d)$ , or substitutions  $(s)$ ) required to transform one string into the reference string. Then, the calculation of CER is:  $(i + d + s) / N$ , where  $N$  is the number of reference strings. Following the latest methods DocTr [11] and DocGeoNet [10], we use Tesseract",
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "19578",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/2b68a773f97fca6dec8468f658e267826ba244c42eabe5cf9e29794824762d02.jpg",
+        "image_caption": [
+            "Figure 4. Comparisons on DocUNet Benchmark [26]. Column 1: Distorted images. Columns 2-6: Results of DewarpNet [8], DocTr [11], RDGR [14], DocGeoNet [10] and ours method. Last column: Flatbed scanned images. We highlight the differences by using red and yellow arrows."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e8cde38f52542cfe169d3f7dcd8c58d468b548037ab06f24b502646c8b77e9e7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.3169</td><td>39.58</td><td>0.7707</td><td>1500.56</td><td>0.5234</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.3246</td><td>30.63</td><td>-</td><td>958.89</td><td>0.3540</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4921</td><td>13.94</td><td>0.3320</td><td>1059.57</td><td>0.3557</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.6160</td><td>7.21</td><td>0.2552</td><td>699.63</td><td>0.2237</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.5524</td><td>10.97</td><td>0.3554</td><td>2130.01</td><td>0.5524</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.6380</td><td>6.40</td><td>0.2418</td><td>664.96</td><td>0.2189</td></tr><tr><td>Ours</td><td>-</td><td>0.6070</td><td>7.68</td><td>0.2440</td><td>652.80</td><td>0.2115</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 2. On the DIR300 Dataset [10], compare our proposed with existing methods.",
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+    },
+    {
+        "type": "text",
+        "text": "act (v5.0.1) [32] as an OCR engine to recognize text in the images. And, following the settings in DocUNet [26], DewarpNet [8] and RDGR [14], 50 images are selected from DocUNet Benchmark [26] to evaluate OCR performance. On DIR300 dataset [10], we compute CER and ED for 90 text-rich images following the setting in DocGeoNet [10].",
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+    {
+        "type": "text",
+        "text": "4.3. Implementation Details",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We implement the entire model architecture on the PyTorch [30] framework. We train our document rectification model on the Doc3D dataset of 100,000 images. The image size for training is  $224 \\times 224$ . We set the layers of cross-attention and transformer decoder to 12 and 6, respectively. We use the AdamW optimizer [24] with a batch size of 24. The initial learning rate is  $1 \\times 10^{-4}$ . The whole model is trained on two NVIDIA A100 GPUs for 30 epochs until the model converges.",
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+    {
+        "type": "text",
+        "text": "4.4. Experimental Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We use OCR performance (CER and ED) and image distortion metrics (MS-SSIM and LD) to compare our method with existing deep learning-based state-of-the-art rectification models on DocUNet Benchmark [26] and DIR300 Dataset [10].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Evaluation on DocUNet Benchmark. As shown in Table 1, in the setting of 50 images, compared with the existing works, our method for distorted document image dewarping improves both ED and CER. Among them, the ED metric dropped below 700 for the first time to reach 697.52, an increase of  $2.3\\%$ . At the same time, it reached 0.1705 on the CER. Our method outperforms almost all non-textline methods [26, 20, 8, 42, 9, 11, 43, 45] on distortion metrics. It can be seen that making the model focus on the features of the text-line regions significantly improves the rectification effect. Overall, in addition, compared with RDGR [14] and DocGeoNet [10], which also use text-line for distor",
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+    {
+        "type": "page_number",
+        "text": "19579",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f220d5bd377b166cf94e5f5502fe11f432f33ef573dd098917f82bfe6d5a8068.jpg",
+        "image_caption": [
+            "Figure 5. Comparisons on DIR300 [10]. Column 1: Distorted images. Column 2-4: Results of DewarpNet [8], DDCP [43], DocGeoNet [10]. Column 5: Rectification results of our model."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "tion images dewarping, our method performs better in OCR evaluation metrics.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on DIR300 Dataset. In the evaluation of the DIR300 dataset, the results are shown in Table 2. We follow the settings in DocGeoNet [10], and select 90 of the pictures for evaluation in terms of OCR accuracy. For previous state-of-the-art methods, our method has improved both CER and ED, and ED has increased by  $1.8\\%$  and dropped to 652.8. Compared with the existing state-of-the-art methods, from the experimental results, our method can more effectively improve the OCR performance of the rectified image. In order to show the rectification effect more intuitively, we visualize and compare the results between existing and our methods on DocUNet Benchmark [26] and DIR300 Dataset [10], as shown in Figure 4 and Figure 5. It can be seen from the first two rows of these two figures that our method pays more attention to the foreground of distorted document images. The last two lines of images show that the dewarping effect of the text-line is more horizontal after the introduction of the text-line information. This is crucial for improving OCR accuracy and paper readability.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.5. Experimental Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Visualizations of OCR Results. We visualized the recognition results of OCR after image rectification, as shown in the Figure 6. We compared the effect of the distorted images, dewarping results of DocGeoNet [10] and our method on OCR recognition. We highlight the text area detected by Tesseract (v5.0.1) [32] OCR engine with three different colors. It can be seen from the figure that the OCR performance can be greatly improved after dewarping the dis",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/29ba75176afc12a7b324d33aadb3e370ca80d895826823851af4a4de2200741e.jpg",
+        "image_caption": [
+            "Figure 6. Visualizations of OCR results. Left to right: Original deformed images, rectified by DocGeoNet [10], rectified by ours method. The color is the highlighted text detection results. Yellow arrows indicate differences."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "torted image. By fusing the information of text-lines, the model can be made to pay more attention to the text area, improving the reading quality of the document image.",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Visualizations of Cross-attention Maps. In order to further show the feature extraction effect of foreground and text-lines, we provide the attention map visualization for the foreground and text-line attention map from our cross-attention module (FAM and TAM) in Figure 7. We can see that our model can acquire the ability to localize the foreground and text-line regions.",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Bad Case Analysis. Although our method improves the OCR accuracy to some extent, it has not reached SOTA on MS-SSIM, LD and AD. According to our analysis, as shown in the Figure 8, after observing the rectified samples, we found that the characteristics of the input distorted image itself, such as the influence of illumination condition, shadows, and background that is very close to the foreground boundary, although these do not affect the attention feature extraction of text-line regions. It is also because of these attributes that the effect of our method to segment the margins between foreground and background on similar images with these characteristics still needs to be improved.",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Besides, We analyzed the influence of the text content ratio on the DocUNet Benchmark. Sorting in ascending order of the proportion of text content, the first  $30\\%$  of images as Low, the next  $40\\%$  of images as Middle, and the last  $30\\%$  of images as High. As shown in table 3, Due to MS-SSIM is sensitive to pixel location, highly subtle image differences can result in large MS-SSIM differences. Since the connectivity of text area is lower than general images, the more text content may cause lower MS-SSIM. This phenomenon is also manifested in AD. As the ratio of text increases, LD tends to be better, which indicates that the text line feature",
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+        "page_idx": 6
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+    {
+        "type": "page_number",
+        "text": "19580",
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+    {
+        "type": "table",
+        "img_path": "images/4566b6c147da5de0b1c3aea990a9286791d1eea548acf2863c6d03ba4c304be4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Text Content Ratio</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td></tr><tr><td>Low</td><td>0.54</td><td>10.74</td><td>0.35</td></tr><tr><td>Middle</td><td>0.51</td><td>8.27</td><td>0.35</td></tr><tr><td>High</td><td>0.44</td><td>6.34</td><td>0.44</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/6022b00bfe80875b306799f7184e61415500117100217a03f1c3c090ea4ccf2f.jpg",
+        "table_caption": [
+            "Table 3. The relationship between the proportion of text content and each evaluation metric."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>FAM</td><td>TAM</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>✓</td><td></td><td>0.4785</td><td>8.53</td><td>0.3619</td><td>761.22</td><td>0.1952</td></tr><tr><td></td><td>✓</td><td>0.4778</td><td>8.86</td><td>0.3529</td><td>748.46</td><td>0.1889</td></tr><tr><td>✓</td><td>✓</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 4. Ablation experiments. FAM is Foreground Attention Module and TAM is Text-lines Attention Module.",
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+        "image_caption": [
+            "Figure 7. Visualizations of attention maps. Left to right: distorted images, foreground attention maps, text-line attention maps, rectification results of our model."
+        ],
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+        "img_path": "images/ba9912d27891e1400caca758e2e406cb84dfb1660b34453bb3e9d3e09750be9a.jpg",
+        "image_caption": [],
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+        "page_idx": 7
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+    {
+        "type": "image",
+        "img_path": "images/8e06eebd1f8e1af0eb351690aada4ee718a725aeaae736436a068dee7c560793.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "is beneficial for local distortion correction, which is also reflected from the CER and ED metrics.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ablation Studies. Table 4 shows the performance of our method when foreground and text-line information are used respectively. We compared the performance when only one of the two features mentioned above is used. This experimental results demonstrate that using foreground and text-line feature extraction modules together, the MS-SSIM and Local Distortion (LD) are increased by at least  $4\\%$  and  $1.2\\%$  respectively. It can be seen that the overall rectification effect of the distorted document image is the best when the two features are combined to extract the region of interest in the original image. It is precisely due to the foreground contains the overall distorted outline of the deformed image, and the text-line contains the local deformation trend of the text area, so that the global and local information can be complementary with each other, and the overall rectification effect can be greatly improved.",
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+            "Figure 8. Visualizations of attention maps for bad case analysis. Left to right: distorted images, foreground attention maps, text-line attention maps, rectification results of our model. Row 1: influence of illumination condition. Row 2: the boundary of the foreground close to background. Row 3: the shadow interference of the document image."
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+        "text": "5. Conclusion",
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+        "text": "In this work, we explored how to optimize the rectification of distorted document images from the perspective of readability. We propose an efficient method for warped document rectification by focusing on the foreground and text-line regions of the original deformed image separately via cross-attention. We use this method to improve the readability of the rectified document images from the perspective of global and local features. The effectiveness of this feature fusion mechanism is proved by experiments on two public benchmark datasets. In the future, since the current training dataset lacks text-line annotations, we will further explore how to obtain more accurate text-line annotations. This is also a limitation of our method. Besides, for extracting distorted image features, we will also explore more fine-grained and multi-attribute feature fusion methods to improve image quality and OCR performance.",
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+        "text": "Acknowledgement: We thank the reviewers for their thoughtful and constructive comments. This work was supported by the National Key R&D Program of China (2022ZD0116002), Natural Science Foundation of China (62276075, 61872113), Science and Technology Planning Project of Shenzhen (JCYJ20190806112210067), Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, China (2022B1212010005) and China Mobile Information Technology Co., Ltd. It was also supported by Music Style Transfer for Anxiety Therapy (P0042962), Artificial Intelligence and Robotics (AIR) Group: Artificial Intelligence Art (P0033738).",
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+        "text": "References",
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diff --git a/2023/Foreground and Text-lines Aware Document Image Rectification/3650c92e-47cd-4562-b763-9e2e457518cc_model.json b/2023/Foreground and Text-lines Aware Document Image Rectification/3650c92e-47cd-4562-b763-9e2e457518cc_model.json
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+            "content": "Xiangping \\(\\mathbf{W}\\mathbf{u}^{1,3*}\\)"
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+            "content": "\\(^{1}\\)Harbin Institute of Technology Shenzhen, China, \\(^{2}\\)PengCheng Laboratory, Shenzhen China \\(^{3}\\)The Hong Kong Polytechnic University, Hung Hom Kowloon, Hong Kong"
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+        {
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+            "content": "hengli.lh@outlook.com, wxpleduole@gmail.com, qingcai.chen@hit.edu.cn, randy19991009@outlook.com"
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+            "content": "This paper aims at the distorted document image rectification problem, the objective to eliminate the geometric distortion in the document images and realize document intelligence. Improving the readability of distorted documents is crucial to effectively extract information from deformed images. According to our observations, the foreground and text-line of the original warped image can represent the deformation tendency. However, previous distorted image rectification methods pay little attention to the readability of the warped paper. In this paper, we focus on the foreground and text-line regions of distorted paper and proposes a global and local fusion method to improve the rectification effect of distorted images and enhance the readability of document images. We introduce cross attention to capture the features of the foreground and text-lines in the warped document and effectively fuse them. The proposed method is evaluated quantitatively and qualitatively on the public DocUNet benchmark and DIR300 Dataset, which achieve state-of-the-art performances. Experimental analysis shows the proposed method can well perform overall geometric rectification of distorted images and effectively improve document readability (using the metrics of Character Error Rate and Edit Distance). The code is available at https://github.com/xiaomore/Document-Image-Dewarping."
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+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.64,
+                0.421,
+                0.753,
+                0.538
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.754,
+                0.421,
+                0.869,
+                0.538
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.541,
+                0.894,
+                0.583
+            ],
+            "angle": 0,
+            "content": "Figure 1. Compared with the text results using Tesseract [32] as OCR engine. Row 1: distorted images. Row 2: rectified by our method. We use color to highlight the detected text boxes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.609,
+                0.893,
+                0.776
+            ],
+            "angle": 0,
+            "content": "larization of mobile electronic devices, it is more and more convenient for people to take pictures with smart phones or portable cameras to capture electronic documents. When taking pictures, due to the different positions, illumination conditions of these devices, the angle of paper placement, deformation and other problems, the images taken are distorted or deformed to varying degrees, and it is difficult to extract useful information from these distorted pictures, as shown in Figure 1. Even wrong information is extracted, which brings great challenges to obtaining key information of documents and realizing document intelligence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "As early as many years ago, the problem of document image distortion rectification has been paid attention to. In the traditional rectification method before deep learning was widely used, several previous methods [3, 36, 17] according to the deformation characteristics of the image, relying on multi-view, get the best boundary through the regression method, and use the boundary segmentation method to dewarped the segmentation graphics. Tian and Narasimhan"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.228,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding authors."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19574"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.212
+            ],
+            "angle": 0,
+            "content": "[35] reconstructs warped document images from 2D to 3D by detecting text-lines in the image. In the time since, some works [16, 15] have also captured prior knowledge in deformed images by detecting text lines in order to bring gains to image rectification. However, these methods of restoring the 3D shape of images through auxiliary hardware or multi-view methods will bring time consuming and expensive problems."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.217,
+                0.471,
+                0.594
+            ],
+            "angle": 0,
+            "content": "With the arrival of the era of deep learning, Convolutional Neural Network (CNN) and Transformer have been introduced to solve the geometric rectification of distorted document images. Most current methods dewarping the input image by learning the mapping relationship between the input distorted image and the dense 2D coordinate map area [26, 8, 1, 11, 14, 10]. The method of [26, 8] used the UNet structure networks to regress the dense 2D coordinates mapping according to the input distorted image. However, it is difficult for CNN to capture the long-distance dependence of distorted paper. For methods [11, 10] that focus on image foreground, they proposed to remove the document background in the preprocessing stage before geometric rectification the network. And then introduces the multi-layer transformer of Encoder-Decoder structure after the convolution network to dewarp the distorted paper. But these methods based on setting the binarization threshold to remove the background will lose the information of the original image. There are also some works such as [14, 10] proposed to use document boundaries, 3D world coordinates and text-lines to construct deformation fields, which reduces the error rate of text recognition. These two methods have no obvious interaction between the text-line and the original distorted image, which makes the text-line area unable to be effectively focused."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In geometrically deformed images, the distortion degree of image foreground and text-lines varies with different scenes. It is necessary to establish an explicit invariant feature in the distorted image foreground to represent the core document and text-line region features robustly, to suppress the interference of background and deformation. Since the foreground information of the document image can clearly represent the deformation amplitude, we use the foreground features representation of the input image. The text-line regions can represent the distorted state of the local position in dewarped images. In order to enhance the reading quality of the image, we considering it is necessary to pay more attention to the area of the text-lines. Therefore, we propose to represent local information using text-line information, extract the characteristics of the corresponding position in the image. Besides, based on our observations, when using the deformation field for distortion rectification, for the dewarped image, the areas in the same horizontal direction should have the same vertical coordinates in the deformation field. For example, for text-lines, the text area of the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "same line should have the same ordinate. This is a very critical starting point for our design model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.122,
+                0.892,
+                0.317
+            ],
+            "angle": 0,
+            "content": "From the perspective of readability, we propose a novel distortion image rectification model based on cross attention mechanism, which fuses the features of the image foreground and text line. The features of the foreground and text-line regions respectively focus on the features of the corresponding positions in the original warped image. The foreground and text-line features are each represent the global and local information of the distorted image, which have complementary effects. In addition, in order to enhance the interaction between global and local features, we share the two cross attention branches of foreground and text-lines, which also reduces the amount of model parameters to a certain extent."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.318,
+                0.892,
+                0.348
+            ],
+            "angle": 0,
+            "content": "The main contributions of our work are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.354,
+                0.892,
+                0.43
+            ],
+            "angle": 0,
+            "content": "- We propose to use foreground and text line information to guide the model to focus on the global and local features of distorted paper, so as to reduce background interference and improve the readability of document images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.434,
+                0.892,
+                0.479
+            ],
+            "angle": 0,
+            "content": "- We introduce cross-attention to explore more effective interaction between paper deformation trend and original distorted image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.483,
+                0.892,
+                0.514
+            ],
+            "angle": 0,
+            "content": "- We conduct extensive experiments and show the state-of-the-art results on the existing prevalent benchmarks."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.354,
+                0.892,
+                0.514
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.521,
+                0.642,
+                0.537
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.545,
+                0.845,
+                0.563
+            ],
+            "angle": 0,
+            "content": "2.1. Document Image Geometric Unwarping"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
+                0.704
+            ],
+            "angle": 0,
+            "content": "The goal of rectifying distorted images is to enhance the visual quality of images, thereby reducing the difficulty of text extraction and improving the readability of paper. Early document image rectification methods performed parametric rectification by using cues easily observed from the image, such as text-lines proposed by Huang et al. [12], cylindrical surfaces [38, 6, 21, 18, 48, 27], document boundaries [3, 36] or laser beams from external devices used by Narain et al. [29]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.892,
+                0.765
+            ],
+            "angle": 0,
+            "content": "In recent years, many works such as [26, 8, 1, 11, 14, 10] proposed to use deep learning to rectify distorted document images. These models solve the rectification problem by directly predicting the deformation field of the image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.766,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Ma et al. [26] is the first work using deep neural networks on this task. They used a stacked UNet structure to predict the deformation field for each pixel in the warped document. This is an end-to-end structure that inverts the input image to obtain the result after the prediction result is obtained. In view of the lack of a large number of warped datasets to train the model, Das et al. [8] subsequently contributed a warped document image dataset (Doc3D) containing about 100,000 Distorted images. In addition, they"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19575"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.161,
+                0.09,
+                0.812,
+                0.345
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.352,
+                0.895,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Figure 2. The overview architecture of our proposed method. FAM is Foreground Attention Module and TAM is Text-lines Attention Module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.396,
+                0.471,
+                0.442
+            ],
+            "angle": 0,
+            "content": "proposed a UNet structure network that uses 3D shape (World Coordinates) to replace the original warped document to predict the deformation field."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.442,
+                0.47,
+                0.562
+            ],
+            "angle": 0,
+            "content": "In order to reduce the interference of the background on the dewarping effect, Feng et al. [11] proposed to remove the background of the document before rectification, and introduced a transformer on this task for the first time. For reasons of improving the reading quality of the rectified document, other works of Jiang et al. [14] and Feng et al. [10] proposed to introduce the text-line feature in the document to enhance the rectification effect of text-line areas."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.574,
+                0.26,
+                0.59
+            ],
+            "angle": 0,
+            "content": "2.2. Attention in Vision"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.47,
+                0.78
+            ],
+            "angle": 0,
+            "content": "The attention mechanism focuses the attention of the network on the most important parts of the data by enhancing the weight of some parts of the input data of the neural network while weakening the weight of other parts. It was originally developed in 2017 for natural language processing tasks by Vaswani et al. [37], and greatly improved new state-of-the-art performance on many downstream tasks. However, in recent years, great success has been achieved in computer vision-related tasks such as image or video classification [39, 31, 2, 33, 7], image segmentation [49, 41, 4, 23], visual question answering [51, 34, 5, 46], and scene text recognition [44]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.781,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Different from the self-attention mechanism, cross attention is able to exploit the intra-modal relations of each modality to complement each other and enhance the feature relations between different modalities. On multimodal tasks, cross attention is widely used to match the visual semantic similarity between images and texts [51, 34, 5, 46], and the key step is how to design fusion modules to effectively connect multimodal inputs. In this distorted im"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.396,
+                0.895,
+                0.533
+            ],
+            "angle": 0,
+            "content": "age geometry rectification task, in order to minimize background interference, we propose to use the foreground information to aware corresponding regions in image features in a cross-attention manner. Furthermore, in order to increase the attention on the text-line regions, similar to the foreground cross-attention, we use the text-lines information to obtain the features of the text regions in the image, which can ensure that the same line of text is horizontal on the rectified image."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.543,
+                0.73,
+                0.561
+            ],
+            "angle": 0,
+            "content": "3. The Proposed Approach"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
+                0.614
+            ],
+            "angle": 0,
+            "content": "In this section, we propose a noval framework for document image dewarping. The overview architecture of our model is shown in Figure 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.893,
+                0.795
+            ],
+            "angle": 0,
+            "content": "Network Architecture. Our model consists of CNNs Encoder, the Foreground and Text-line Attention Module, and the Transformer Decoder. We use these three modules to obtain the features of foreground regions except background and text-line regions in distorted document images, respectively. After obtaining text-line and foreground information, cross-attention used to enhance the foreground and text-line attention. And then concatenate the feature map of these two cross feature map in the channel dimension, input it to the multi-layer decoder to predict the 2D grid coordinates, and finally use the coordinates to dewarp the input document image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Given a warped document image \\(\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}\\), we first resize it to \\(\\mathbf{I}_r \\in \\mathbb{R}^{H_r \\times W_r \\times C_r}\\), where \\(H_r = W_r = 224\\) and \\(C_r = 3\\) is the number of RGB channels of the original image. Then, \\(\\mathbf{I}_r\\) is fed into an encoder consisting of multiple layers of convolutional neural networks (CNNs) to obtain the feature map \\(\\mathbf{F}_i \\in \\mathbb{R}^{H_i \\times W_i \\times C_i}\\) of the original warped image. Then, through the cross-attention of fore"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19576"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.092,
+                0.094,
+                0.461,
+                0.279
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.281,
+                0.468,
+                0.31
+            ],
+            "angle": 0,
+            "content": "Figure 3. Text-line detection results of the Doc3D dataset. Row 1: Input warped images. Row 2: Detection results for text lines."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.47,
+                0.475
+            ],
+            "angle": 0,
+            "content": "ground and text-line, the region of interest is extracted from the image features \\(\\mathbf{F}_i\\). Finally, a 2D dense grid coordinate \\(\\hat{G} \\in \\mathbb{R}^{H_r \\times W_r \\times 2}\\) (backward mapping or deformation field) is predicted through a transformer network composed of a multi-layer self-attention and feed-forward network architecture. According to the obtained grid coordinates, the input image can be dwarped to obtain an dwarped picture \\(\\mathbf{D} \\in \\mathbb{R}^{H \\times W \\times 3}\\). Each coordinate \\((x, y)\\) in grid coordinates represents the position of the pixel value on the input image in the rectified image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.476,
+                0.47,
+                0.597
+            ],
+            "angle": 0,
+            "content": "CNNs Encoder. For the resized image \\(\\mathbf{I}_r\\), we first use the convolutional neural network module as an encoder to extract image features. The encoder contains 3 layers of residual blocks, and each layer downsamples the feature map to half the size. The resolution of the final output feature map \\(\\mathbf{F}_i \\in \\mathbb{R}^{H_i \\times W_i \\times C_i}\\) is one-eighth of that of \\(\\mathbf{I}_r\\). Where \\(H_i = H_r / 8\\), \\(W_i = W_r / 8\\), \\(C_i\\) is the number of channels of the feature map \\(\\mathbf{F}_i\\). We set \\(\\mathbf{C}_i\\) to 256."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.471,
+                0.853
+            ],
+            "angle": 0,
+            "content": "Foreground and Text-line Queries. In the previous work on distorted image rectification, there have been related works on foreground [11, 10] and text-line mask [14] extraction. We initialize the foreground and text-line queries on the basis of these two works. For foreground mask extraction, Feng et al. [11] used a lightweight semantic segmentation architecture network to predict the confidence map of foreground. The network is an Encoder-Decoder structure. We do not directly use the resulting binarized mask. Instead, use the six-layer feature maps in the decoder, and first resize them to the same size as \\(\\mathbf{F}_i\\), which is one-eighth the size of \\(\\mathbf{I}_r\\). And after concatenating in the channel dimension, use a layer of \\(3 \\times 3\\) convolution module and BatchNorm [13] to reduce the number of channels to 256. Compared with directly using the binary mask output by the last layer of the network, this method can obtain richer image feature information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For the text-lines information, since the Doc3D training dataset proposed by DewarpNet [8] used by our model lacks corresponding text-line annotations, we use the detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.303
+            ],
+            "angle": 0,
+            "content": "text-line method proposed in RDGR [14] to obtain text-line features. This detection method used the U-Net network to train on PubLayNet [50] and the Scanned Script Dataset<sup>1</sup>. Its detection effect on the Doc3D dataset is shown in Figure 3. Although the text-line detected by this method has certain errors due to the deformation of the image, illumination effects and other reasons, it is within the network fault tolerance range. For text-line queries initialization, we use the last feature map of the U-Net network decoder (not the final confidence map). Its resolution is consistent with U-net network input. Then, we apply a layer of \\(3 \\times 3\\) convolution and BatchNorm [13] to change the number of channels to 256, and finally bilinear interpolation is utilized to downsample the feature map size to one-eighth the size of \\(\\mathbf{I}_r\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.304,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Foreground and Text-line Attention Module. For the initialized foreground queries, we use the cross-attention mechanism to extract features in distorted images. This module consists of three parts: self-attention, cross-attention, and feed forward networks. First, the image feature map \\(\\mathbf{F}_i\\) is flattened, and then the long-distance dependencies between patches are calculated using self-attention."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.41,
+                0.893,
+                0.668
+            ],
+            "angle": 0,
+            "content": "However, in the process of flattening the feature map, 2D coordinate information will be lost, which is crucial to obtain the local and global relationship, so we add a learnable 2D coordinate information. The same operation is performed on foreground queries. And then, in order to pay more attention to the foreground area and ignore the background, we use a foreground-guided cross-attention module. Specifically, a multi-head cross-attention layer is applied after self-attention. We utilize image features \\(\\mathbf{F}_i\\) as key and value, and the foreground feature \\(\\mathbf{F}_f\\) as query. Similar to the foreground-query cross-attention mechanism, in order to extract the features of the text-line positions of interest. The text-line features \\(\\mathbf{F}_t\\) is treated as query. Finally, we utilize a layer of convolutions to enhance local feature extraction after obtaining the attention feature map. The formula for the foreground query and text-line query cross-attention mechanism is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.545,
+                0.681,
+                0.891,
+                0.732
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} C A _ {f} = C A (Q, K, V) = C A \\left(F _ {f}, F _ {i}, F _ {i}\\right) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {F _ {f} F _ {i} ^ {\\mathrm {T}}}{\\sigma}\\right) F _ {i} \\tag {1} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.55,
+                0.735,
+                0.891,
+                0.786
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} C A _ {t} = C A (Q, K, V) = C A \\left(F _ {t}, F _ {i}, F _ {i}\\right) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {F _ {t} F _ {i} ^ {\\mathrm {T}}}{\\sigma}\\right) F _ {i} \\tag {2} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.786,
+                0.892,
+                0.831
+            ],
+            "angle": 0,
+            "content": "where \\(CA\\) is Cross-Attention and \\(\\sigma\\) is a scaling factor. \\(CA_{f}\\) and \\(CA_{t}\\) are the foreground and text-line cross-attention map respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.832,
+                0.892,
+                0.877
+            ],
+            "angle": 0,
+            "content": "Transformer Decoder. After extracting the interesting feature \\(\\mathbf{C}A_{f}\\) and \\(\\mathbf{C}A_{t}\\) of the foreground and text-line, we concatenate the two features and feed them into the transformer"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.517,
+                0.887,
+                0.875,
+                0.9
+            ],
+            "angle": 0,
+            "content": "<https://github.com/zzzDavid/ICDAR-2019-SROIE"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
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+            "angle": 0,
+            "content": "19577"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.229,
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+                0.744,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.2459</td><td>20.51</td><td>1.0134</td><td>2111.56</td><td>0.5352</td></tr><tr><td>DocUNet [26]</td><td>CVPR&#x27;18</td><td>0.4103</td><td>14.19</td><td>-</td><td>1933.66</td><td>0.4632</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.2946</td><td>18.01</td><td>-</td><td>1712.48</td><td>0.4267</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4735</td><td>8.39</td><td>0.4260</td><td>885.90</td><td>0.2373</td></tr><tr><td>FCN-based [42]</td><td>DAS&#x27;20</td><td>0.4288</td><td>7.75</td><td>0.4017</td><td>1792.60</td><td>0.4213</td></tr><tr><td>PWUNet [9]</td><td>ICCV&#x27;21</td><td>0.4915</td><td>8.64</td><td>-</td><td>1069.28</td><td>0.2677</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.5105</td><td>7.76</td><td>0.3682</td><td>724.84</td><td>0.1832</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.4726</td><td>8.97</td><td>0.4287</td><td>1411.38</td><td>0.3573</td></tr><tr><td>FDRNet [45]</td><td>CVPR&#x27;22</td><td>0.5420</td><td>8.21</td><td>-</td><td>829.78</td><td>0.2068</td></tr><tr><td>RDGR [14]</td><td>CVPR&#x27;22</td><td>0.4950</td><td>8.51</td><td>0.4382</td><td>729.52</td><td>0.1717</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.5040</td><td>7.71</td><td>0.3800</td><td>713.94</td><td>0.1821</td></tr><tr><td>Ours</td><td>-</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.254,
+                0.892,
+                0.283
+            ],
+            "angle": 0,
+            "content": "Table 1. On the DocUNet Benchmark [26], compare our proposed with existing methods in terms of Multi-Scale Structural Similarity (MS-SSIM), Local Distortion (LD) and OCR accuracy (ED and CER). “↑” indicates the higher the better and “↓” means the opposite."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.075,
+                0.3,
+                0.47,
+                0.496
+            ],
+            "angle": 0,
+            "content": "decoder composed of multi-head self-attention mechanism to predict the grid map. Consistent with the cross-attention module, we also add 2D learnable position coordinates. The structure of each decoder layer consists of self-attention and feed-forward network. Finally, we adopt the upsampling method in DocTr [11] and GeoDewarpNet [10] to obtain high-resolution 2D deformation field \\(\\mathbf{G}\\). This upsampling method trains a learnable weight on the basis of initializing the grid coordinates to perform weighted optimization on it. Training Loss Function. The loss function of our distorted document image rectification model is to compute the \\(L_{1}\\) distance between the predicted grid coordinate \\(\\hat{\\pmb{G}}\\) and the label \\(\\mathbf{G}\\). The formula as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.206,
+                0.512,
+                0.47,
+                0.54
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {g r i d}} = \\left\\| \\mathbf {G} - \\hat {\\boldsymbol {G}} \\right\\| _ {\\mathbf {1}} \\tag {3}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.565,
+                0.21,
+                0.582
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.592,
+                0.47,
+                0.712
+            ],
+            "angle": 0,
+            "content": "In this section, we first review the existing training dataset (Doc3D) and evaluation benchmark (DocUNet and DIR300 dataset) for distorted image dewarping. Second, we introduce the evaluation metrics and training details of this method. And then, we evaluate our document image rectification method on two datasets, DocUNet Benchmark [26] and DIR300 [10]. Finally, we demonstrate our rectification performance on several evaluation metrics."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.173,
+                0.74
+            ],
+            "angle": 0,
+            "content": "4.1. Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Doc3D. We train the geometric rectification model on the Doc3D dataset contributed by DewarpNet [8]. Doc3D is the largest distortion dewarping dataset so far, containing a total of 100K distorted images. It is created by about 4000 real document images and rendering software. Among them, different camera positions and various illumination are applied when rendering. For each distorted document image, the corresponding labels include 3D coordinate maps, albedo maps, normals, depth maps, UV maps and backward mapping map."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.3,
+                0.892,
+                0.421
+            ],
+            "angle": 0,
+            "content": "DocUNet Benchmark. In current deep learning-based document dewarping methods, the DocUNet Benchmark [26] dataset is widely used. This evaluation dataset contains 130 distorted images in natural scenes captured by mobile devices. In addition, for better comparison with previous methods, we follow the proposal in DocGeoNet [10] and rotate the \\(127^{th}\\) and \\(128^{th}\\) images in DocUNet [26] that do not match the labels by 180 degrees."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.423,
+                0.894,
+                0.499
+            ],
+            "angle": 0,
+            "content": "DIR300 Dataset. DIR300 dataset is a new test dataset proposed by DocGeoNet [10] captured by moving camera. It contains 300 images of real distorted documents involving more complex backgrounds, distorted degrees, and various lighting conditions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.512,
+                0.682,
+                0.527
+            ],
+            "angle": 0,
+            "content": "4.2. Evaluation metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.537,
+                0.892,
+                0.748
+            ],
+            "angle": 0,
+            "content": "MS-SSIM, LD and AD. We follow previous methods [26, 8, 1, 11, 14, 10] to perceive image quality using an image-based Multi-Scale Structural Similarity method (MS-SSIM) [40]. Computationally dense SIFT-flow [22], Local Distortion (LD) [47] computes the average of the \\( L_{2} \\) distances between all pixels in the ground-truth scanned image and the rectified image pixels, which measures the average local deformation of the rectified image. Following DocUNet [26], all rectified images and their labels are resized to 598400 pixel area. We use the code provided by DocUNet [26] for evaluation. Aligned Distortion (AD) is a more robust evaluation metric proposed by [25], which aligns unwarped images and ground truth scans by unifying translation and scale before computing distortions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "CER and ED. We use Character Error Rate (CER) [28] and Edit Distance (ED) [19] to measure the performance of our method. ED is a string metric that measures the difference between two character sequences. The edit distance between two strings is the minimum number of single-character edits (insertions \\((i)\\), deletions \\((d)\\), or substitutions \\((s)\\)) required to transform one string into the reference string. Then, the calculation of CER is: \\((i + d + s) / N\\), where \\(N\\) is the number of reference strings. Following the latest methods DocTr [11] and DocGeoNet [10], we use Tesseract"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19578"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.162,
+                0.089,
+                0.812,
+                0.434
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.435,
+                0.895,
+                0.478
+            ],
+            "angle": 0,
+            "content": "Figure 4. Comparisons on DocUNet Benchmark [26]. Column 1: Distorted images. Columns 2-6: Results of DewarpNet [8], DocTr [11], RDGR [14], DocGeoNet [10] and ours method. Last column: Flatbed scanned images. We highlight the differences by using red and yellow arrows."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.229,
+                0.482,
+                0.744,
+                0.585
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.3169</td><td>39.58</td><td>0.7707</td><td>1500.56</td><td>0.5234</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.3246</td><td>30.63</td><td>-</td><td>958.89</td><td>0.3540</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4921</td><td>13.94</td><td>0.3320</td><td>1059.57</td><td>0.3557</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.6160</td><td>7.21</td><td>0.2552</td><td>699.63</td><td>0.2237</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.5524</td><td>10.97</td><td>0.3554</td><td>2130.01</td><td>0.5524</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.6380</td><td>6.40</td><td>0.2418</td><td>664.96</td><td>0.2189</td></tr><tr><td>Ours</td><td>-</td><td>0.6070</td><td>7.68</td><td>0.2440</td><td>652.80</td><td>0.2115</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.236,
+                0.588,
+                0.733,
+                0.602
+            ],
+            "angle": 0,
+            "content": "Table 2. On the DIR300 Dataset [10], compare our proposed with existing methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.616,
+                0.471,
+                0.709
+            ],
+            "angle": 0,
+            "content": "act (v5.0.1) [32] as an OCR engine to recognize text in the images. And, following the settings in DocUNet [26], DewarpNet [8] and RDGR [14], 50 images are selected from DocUNet Benchmark [26] to evaluate OCR performance. On DIR300 dataset [10], we compute CER and ED for 90 text-rich images following the setting in DocGeoNet [10]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.735,
+                0.295,
+                0.751
+            ],
+            "angle": 0,
+            "content": "4.3. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We implement the entire model architecture on the PyTorch [30] framework. We train our document rectification model on the Doc3D dataset of 100,000 images. The image size for training is \\(224 \\times 224\\). We set the layers of cross-attention and transformer decoder to 12 and 6, respectively. We use the AdamW optimizer [24] with a batch size of 24. The initial learning rate is \\(1 \\times 10^{-4}\\). The whole model is trained on two NVIDIA A100 GPUs for 30 epochs until the model converges."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.616,
+                0.704,
+                0.632
+            ],
+            "angle": 0,
+            "content": "4.4. Experimental Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.642,
+                0.894,
+                0.718
+            ],
+            "angle": 0,
+            "content": "We use OCR performance (CER and ED) and image distortion metrics (MS-SSIM and LD) to compare our method with existing deep learning-based state-of-the-art rectification models on DocUNet Benchmark [26] and DIR300 Dataset [10]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Evaluation on DocUNet Benchmark. As shown in Table 1, in the setting of 50 images, compared with the existing works, our method for distorted document image dewarping improves both ED and CER. Among them, the ED metric dropped below 700 for the first time to reach 697.52, an increase of \\(2.3\\%\\). At the same time, it reached 0.1705 on the CER. Our method outperforms almost all non-textline methods [26, 20, 8, 42, 9, 11, 43, 45] on distortion metrics. It can be seen that making the model focus on the features of the text-line regions significantly improves the rectification effect. Overall, in addition, compared with RDGR [14] and DocGeoNet [10], which also use text-line for distor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "19579"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.098,
+                0.089,
+                0.447,
+                0.371
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.379,
+                0.47,
+                0.421
+            ],
+            "angle": 0,
+            "content": "Figure 5. Comparisons on DIR300 [10]. Column 1: Distorted images. Column 2-4: Results of DewarpNet [8], DDCP [43], DocGeoNet [10]. Column 5: Rectification results of our model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.431,
+                0.468,
+                0.459
+            ],
+            "angle": 0,
+            "content": "tion images dewarping, our method performs better in OCR evaluation metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.461,
+                0.47,
+                0.749
+            ],
+            "angle": 0,
+            "content": "Evaluation on DIR300 Dataset. In the evaluation of the DIR300 dataset, the results are shown in Table 2. We follow the settings in DocGeoNet [10], and select 90 of the pictures for evaluation in terms of OCR accuracy. For previous state-of-the-art methods, our method has improved both CER and ED, and ED has increased by \\(1.8\\%\\) and dropped to 652.8. Compared with the existing state-of-the-art methods, from the experimental results, our method can more effectively improve the OCR performance of the rectified image. In order to show the rectification effect more intuitively, we visualize and compare the results between existing and our methods on DocUNet Benchmark [26] and DIR300 Dataset [10], as shown in Figure 4 and Figure 5. It can be seen from the first two rows of these two figures that our method pays more attention to the foreground of distorted document images. The last two lines of images show that the dewarping effect of the text-line is more horizontal after the introduction of the text-line information. This is crucial for improving OCR accuracy and paper readability."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.757,
+                0.288,
+                0.773
+            ],
+            "angle": 0,
+            "content": "4.5. Experimental Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visualizations of OCR Results. We visualized the recognition results of OCR after image rectification, as shown in the Figure 6. We compared the effect of the distorted images, dewarping results of DocGeoNet [10] and our method on OCR recognition. We highlight the text area detected by Tesseract (v5.0.1) [32] OCR engine with three different colors. It can be seen from the figure that the OCR performance can be greatly improved after dewarping the dis"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.523,
+                0.09,
+                0.869,
+                0.325
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.335,
+                0.892,
+                0.39
+            ],
+            "angle": 0,
+            "content": "Figure 6. Visualizations of OCR results. Left to right: Original deformed images, rectified by DocGeoNet [10], rectified by ours method. The color is the highlighted text detection results. Yellow arrows indicate differences."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.401,
+                0.891,
+                0.446
+            ],
+            "angle": 0,
+            "content": "torted image. By fusing the information of text-lines, the model can be made to pay more attention to the text area, improving the reading quality of the document image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.447,
+                0.892,
+                0.552
+            ],
+            "angle": 0,
+            "content": "Visualizations of Cross-attention Maps. In order to further show the feature extraction effect of foreground and text-lines, we provide the attention map visualization for the foreground and text-line attention map from our cross-attention module (FAM and TAM) in Figure 7. We can see that our model can acquire the ability to localize the foreground and text-line regions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.553,
+                0.892,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Bad Case Analysis. Although our method improves the OCR accuracy to some extent, it has not reached SOTA on MS-SSIM, LD and AD. According to our analysis, as shown in the Figure 8, after observing the rectified samples, we found that the characteristics of the input distorted image itself, such as the influence of illumination condition, shadows, and background that is very close to the foreground boundary, although these do not affect the attention feature extraction of text-line regions. It is also because of these attributes that the effect of our method to segment the margins between foreground and background on similar images with these characteristics still needs to be improved."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Besides, We analyzed the influence of the text content ratio on the DocUNet Benchmark. Sorting in ascending order of the proportion of text content, the first \\(30\\%\\) of images as Low, the next \\(40\\%\\) of images as Middle, and the last \\(30\\%\\) of images as High. As shown in table 3, Due to MS-SSIM is sensitive to pixel location, highly subtle image differences can result in large MS-SSIM differences. Since the connectivity of text area is lower than general images, the more text content may cause lower MS-SSIM. This phenomenon is also manifested in AD. As the ratio of text increases, LD tends to be better, which indicates that the text line feature"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "19580"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.122,
+                0.096,
+                0.427,
+                0.151
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Text Content Ratio</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td></tr><tr><td>Low</td><td>0.54</td><td>10.74</td><td>0.35</td></tr><tr><td>Middle</td><td>0.51</td><td>8.27</td><td>0.35</td></tr><tr><td>High</td><td>0.44</td><td>6.34</td><td>0.44</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.155,
+                0.47,
+                0.181
+            ],
+            "angle": 0,
+            "content": "Table 3. The relationship between the proportion of text content and each evaluation metric."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.193,
+                0.479,
+                0.248
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>FAM</td><td>TAM</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>✓</td><td></td><td>0.4785</td><td>8.53</td><td>0.3619</td><td>761.22</td><td>0.1952</td></tr><tr><td></td><td>✓</td><td>0.4778</td><td>8.86</td><td>0.3529</td><td>748.46</td><td>0.1889</td></tr><tr><td>✓</td><td>✓</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.251,
+                0.47,
+                0.278
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation experiments. FAM is Foreground Attention Module and TAM is Text-lines Attention Module."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.293,
+                0.184,
+                0.38
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.184,
+                0.293,
+                0.272,
+                0.38
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.274,
+                0.293,
+                0.36,
+                0.38
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.361,
+                0.293,
+                0.446,
+                0.38
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.38,
+                0.183,
+                0.465
+            ],
+            "angle": 0,
+            "content": null
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+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 7. Visualizations of attention maps. Left to right: distorted images, foreground attention maps, text-line attention maps, rectification results of our model."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "is beneficial for local distortion correction, which is also reflected from the CER and ED metrics."
+        },
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+            "angle": 0,
+            "content": "Ablation Studies. Table 4 shows the performance of our method when foreground and text-line information are used respectively. We compared the performance when only one of the two features mentioned above is used. This experimental results demonstrate that using foreground and text-line feature extraction modules together, the MS-SSIM and Local Distortion (LD) are increased by at least \\(4\\%\\) and \\(1.2\\%\\) respectively. It can be seen that the overall rectification effect of the distorted document image is the best when the two features are combined to extract the region of interest in the original image. It is precisely due to the foreground contains the overall distorted outline of the deformed image, and the text-line contains the local deformation trend of the text area, so that the global and local information can be complementary with each other, and the overall rectification effect can be greatly improved."
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+            "angle": 0,
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+        },
+        {
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+            "bbox": [
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+            "angle": 0,
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.355,
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+            ],
+            "angle": 0,
+            "content": "Figure 8. Visualizations of attention maps for bad case analysis. Left to right: distorted images, foreground attention maps, text-line attention maps, rectification results of our model. Row 1: influence of illumination condition. Row 2: the boundary of the foreground close to background. Row 3: the shadow interference of the document image."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.477,
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+            "angle": 0,
+            "content": "In this work, we explored how to optimize the rectification of distorted document images from the perspective of readability. We propose an efficient method for warped document rectification by focusing on the foreground and text-line regions of the original deformed image separately via cross-attention. We use this method to improve the readability of the rectified document images from the perspective of global and local features. The effectiveness of this feature fusion mechanism is proved by experiments on two public benchmark datasets. In the future, since the current training dataset lacks text-line annotations, we will further explore how to obtain more accurate text-line annotations. This is also a limitation of our method. Besides, for extracting distorted image features, we will also explore more fine-grained and multi-attribute feature fusion methods to improve image quality and OCR performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Acknowledgement: We thank the reviewers for their thoughtful and constructive comments. This work was supported by the National Key R&D Program of China (2022ZD0116002), Natural Science Foundation of China (62276075, 61872113), Science and Technology Planning Project of Shenzhen (JCYJ20190806112210067), Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, China (2022B1212010005) and China Mobile Information Technology Co., Ltd. It was also supported by Music Style Transfer for Anxiety Therapy (P0042962), Artificial Intelligence and Robotics (AIR) Group: Artificial Intelligence Art (P0033738)."
+        },
+        {
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+# Foreground and Text-lines Aware Document Image Rectification
+
+Heng Li
+
+Xiangping  $\mathbf{W}\mathbf{u}^{1,3*}$
+
+Qingcai Chen $^{1,2*}$
+
+Qianjin Xiang
+
+$^{1}$ Harbin Institute of Technology Shenzhen, China,  $^{2}$ PengCheng Laboratory, Shenzhen China  $^{3}$ The Hong Kong Polytechnic University, Hung Hom Kowloon, Hong Kong
+
+hengli.lh@outlook.com, wxpleduole@gmail.com, qingcai.chen@hit.edu.cn, randy19991009@outlook.com
+
+# Abstract
+
+This paper aims at the distorted document image rectification problem, the objective to eliminate the geometric distortion in the document images and realize document intelligence. Improving the readability of distorted documents is crucial to effectively extract information from deformed images. According to our observations, the foreground and text-line of the original warped image can represent the deformation tendency. However, previous distorted image rectification methods pay little attention to the readability of the warped paper. In this paper, we focus on the foreground and text-line regions of distorted paper and proposes a global and local fusion method to improve the rectification effect of distorted images and enhance the readability of document images. We introduce cross attention to capture the features of the foreground and text-lines in the warped document and effectively fuse them. The proposed method is evaluated quantitatively and qualitatively on the public DocUNet benchmark and DIR300 Dataset, which achieve state-of-the-art performances. Experimental analysis shows the proposed method can well perform overall geometric rectification of distorted images and effectively improve document readability (using the metrics of Character Error Rate and Edit Distance). The code is available at https://github.com/xiaomore/Document-Image-Dewarping.
+
+# 1. Introduction
+
+In our daily life, there are various documents, such as papers, posters, receipts and so on. These documents contain a wealth of information. At present, document intelligence can automatically extract the information in the document, and then obtain structured data (text content, key field extraction, table structure, document layout analysis), which greatly facilitates people's lives. However, with the popu
+
+![](images/a7262022df9bef7d4f3b5b8038372db586fef31eba5514b536b55398f703f3ae.jpg)
+
+![](images/78b12818f918fd8478e1aefaa00c75fcc32ca505e5815055922365ae214bd1bd.jpg)
+
+![](images/03b10d68aa473c42141a2efd52ddc0227d70f1de09d9ad8587f469f74b542b33.jpg)
+
+![](images/5715362dc53b0a7feb9c819a0b1f4870b8e74a3244768dddceadff5f9171e080.jpg)  
+Figure 1. Compared with the text results using Tesseract [32] as OCR engine. Row 1: distorted images. Row 2: rectified by our method. We use color to highlight the detected text boxes.
+
+![](images/4446cc6c7612362cce0ed75bb1feb2e4d4ed014ad92b3661e9f32f1332b0c556.jpg)
+
+![](images/76b587699a996207031ae426f48a1d23deb9f85540edc5162da3042023b1d4e2.jpg)
+
+larization of mobile electronic devices, it is more and more convenient for people to take pictures with smart phones or portable cameras to capture electronic documents. When taking pictures, due to the different positions, illumination conditions of these devices, the angle of paper placement, deformation and other problems, the images taken are distorted or deformed to varying degrees, and it is difficult to extract useful information from these distorted pictures, as shown in Figure 1. Even wrong information is extracted, which brings great challenges to obtaining key information of documents and realizing document intelligence.
+
+As early as many years ago, the problem of document image distortion rectification has been paid attention to. In the traditional rectification method before deep learning was widely used, several previous methods [3, 36, 17] according to the deformation characteristics of the image, relying on multi-view, get the best boundary through the regression method, and use the boundary segmentation method to dewarped the segmentation graphics. Tian and Narasimhan
+
+[35] reconstructs warped document images from 2D to 3D by detecting text-lines in the image. In the time since, some works [16, 15] have also captured prior knowledge in deformed images by detecting text lines in order to bring gains to image rectification. However, these methods of restoring the 3D shape of images through auxiliary hardware or multi-view methods will bring time consuming and expensive problems.
+
+With the arrival of the era of deep learning, Convolutional Neural Network (CNN) and Transformer have been introduced to solve the geometric rectification of distorted document images. Most current methods dewarping the input image by learning the mapping relationship between the input distorted image and the dense 2D coordinate map area [26, 8, 1, 11, 14, 10]. The method of [26, 8] used the UNet structure networks to regress the dense 2D coordinates mapping according to the input distorted image. However, it is difficult for CNN to capture the long-distance dependence of distorted paper. For methods [11, 10] that focus on image foreground, they proposed to remove the document background in the preprocessing stage before geometric rectification the network. And then introduces the multi-layer transformer of Encoder-Decoder structure after the convolution network to dewarp the distorted paper. But these methods based on setting the binarization threshold to remove the background will lose the information of the original image. There are also some works such as [14, 10] proposed to use document boundaries, 3D world coordinates and text-lines to construct deformation fields, which reduces the error rate of text recognition. These two methods have no obvious interaction between the text-line and the original distorted image, which makes the text-line area unable to be effectively focused.
+
+In geometrically deformed images, the distortion degree of image foreground and text-lines varies with different scenes. It is necessary to establish an explicit invariant feature in the distorted image foreground to represent the core document and text-line region features robustly, to suppress the interference of background and deformation. Since the foreground information of the document image can clearly represent the deformation amplitude, we use the foreground features representation of the input image. The text-line regions can represent the distorted state of the local position in dewarped images. In order to enhance the reading quality of the image, we considering it is necessary to pay more attention to the area of the text-lines. Therefore, we propose to represent local information using text-line information, extract the characteristics of the corresponding position in the image. Besides, based on our observations, when using the deformation field for distortion rectification, for the dewarped image, the areas in the same horizontal direction should have the same vertical coordinates in the deformation field. For example, for text-lines, the text area of the
+
+same line should have the same ordinate. This is a very critical starting point for our design model.
+
+From the perspective of readability, we propose a novel distortion image rectification model based on cross attention mechanism, which fuses the features of the image foreground and text line. The features of the foreground and text-line regions respectively focus on the features of the corresponding positions in the original warped image. The foreground and text-line features are each represent the global and local information of the distorted image, which have complementary effects. In addition, in order to enhance the interaction between global and local features, we share the two cross attention branches of foreground and text-lines, which also reduces the amount of model parameters to a certain extent.
+
+The main contributions of our work are summarized as follows:
+
+- We propose to use foreground and text line information to guide the model to focus on the global and local features of distorted paper, so as to reduce background interference and improve the readability of document images.  
+- We introduce cross-attention to explore more effective interaction between paper deformation trend and original distorted image.  
+- We conduct extensive experiments and show the state-of-the-art results on the existing prevalent benchmarks.
+
+# 2. Related Work
+
+# 2.1. Document Image Geometric Unwarping
+
+The goal of rectifying distorted images is to enhance the visual quality of images, thereby reducing the difficulty of text extraction and improving the readability of paper. Early document image rectification methods performed parametric rectification by using cues easily observed from the image, such as text-lines proposed by Huang et al. [12], cylindrical surfaces [38, 6, 21, 18, 48, 27], document boundaries [3, 36] or laser beams from external devices used by Narain et al. [29].
+
+In recent years, many works such as [26, 8, 1, 11, 14, 10] proposed to use deep learning to rectify distorted document images. These models solve the rectification problem by directly predicting the deformation field of the image.
+
+Ma et al. [26] is the first work using deep neural networks on this task. They used a stacked UNet structure to predict the deformation field for each pixel in the warped document. This is an end-to-end structure that inverts the input image to obtain the result after the prediction result is obtained. In view of the lack of a large number of warped datasets to train the model, Das et al. [8] subsequently contributed a warped document image dataset (Doc3D) containing about 100,000 Distorted images. In addition, they
+
+![](images/9c84efeb446f2c1f93e148050b475fa17a3ba4245e30e5f8a8e5e1137a3cacdd.jpg)  
+Figure 2. The overview architecture of our proposed method. FAM is Foreground Attention Module and TAM is Text-lines Attention Module.
+
+proposed a UNet structure network that uses 3D shape (World Coordinates) to replace the original warped document to predict the deformation field.
+
+In order to reduce the interference of the background on the dewarping effect, Feng et al. [11] proposed to remove the background of the document before rectification, and introduced a transformer on this task for the first time. For reasons of improving the reading quality of the rectified document, other works of Jiang et al. [14] and Feng et al. [10] proposed to introduce the text-line feature in the document to enhance the rectification effect of text-line areas.
+
+# 2.2. Attention in Vision
+
+The attention mechanism focuses the attention of the network on the most important parts of the data by enhancing the weight of some parts of the input data of the neural network while weakening the weight of other parts. It was originally developed in 2017 for natural language processing tasks by Vaswani et al. [37], and greatly improved new state-of-the-art performance on many downstream tasks. However, in recent years, great success has been achieved in computer vision-related tasks such as image or video classification [39, 31, 2, 33, 7], image segmentation [49, 41, 4, 23], visual question answering [51, 34, 5, 46], and scene text recognition [44].
+
+Different from the self-attention mechanism, cross attention is able to exploit the intra-modal relations of each modality to complement each other and enhance the feature relations between different modalities. On multimodal tasks, cross attention is widely used to match the visual semantic similarity between images and texts [51, 34, 5, 46], and the key step is how to design fusion modules to effectively connect multimodal inputs. In this distorted im
+
+age geometry rectification task, in order to minimize background interference, we propose to use the foreground information to aware corresponding regions in image features in a cross-attention manner. Furthermore, in order to increase the attention on the text-line regions, similar to the foreground cross-attention, we use the text-lines information to obtain the features of the text regions in the image, which can ensure that the same line of text is horizontal on the rectified image.
+
+# 3. The Proposed Approach
+
+In this section, we propose a noval framework for document image dewarping. The overview architecture of our model is shown in Figure 2.
+
+Network Architecture. Our model consists of CNNs Encoder, the Foreground and Text-line Attention Module, and the Transformer Decoder. We use these three modules to obtain the features of foreground regions except background and text-line regions in distorted document images, respectively. After obtaining text-line and foreground information, cross-attention used to enhance the foreground and text-line attention. And then concatenate the feature map of these two cross feature map in the channel dimension, input it to the multi-layer decoder to predict the 2D grid coordinates, and finally use the coordinates to dewarp the input document image.
+
+Given a warped document image  $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ , we first resize it to  $\mathbf{I}_r \in \mathbb{R}^{H_r \times W_r \times C_r}$ , where  $H_r = W_r = 224$  and  $C_r = 3$  is the number of RGB channels of the original image. Then,  $\mathbf{I}_r$  is fed into an encoder consisting of multiple layers of convolutional neural networks (CNNs) to obtain the feature map  $\mathbf{F}_i \in \mathbb{R}^{H_i \times W_i \times C_i}$  of the original warped image. Then, through the cross-attention of fore
+
+![](images/7307c8f8498cdc26cbd53fff352697d68aeb0c96954e271ace2d6d55187f0387.jpg)  
+Figure 3. Text-line detection results of the Doc3D dataset. Row 1: Input warped images. Row 2: Detection results for text lines.
+
+ground and text-line, the region of interest is extracted from the image features  $\mathbf{F}_i$ . Finally, a 2D dense grid coordinate  $\hat{G} \in \mathbb{R}^{H_r \times W_r \times 2}$  (backward mapping or deformation field) is predicted through a transformer network composed of a multi-layer self-attention and feed-forward network architecture. According to the obtained grid coordinates, the input image can be dwarped to obtain an dwarped picture  $\mathbf{D} \in \mathbb{R}^{H \times W \times 3}$ . Each coordinate  $(x, y)$  in grid coordinates represents the position of the pixel value on the input image in the rectified image.
+
+CNNs Encoder. For the resized image  $\mathbf{I}_r$ , we first use the convolutional neural network module as an encoder to extract image features. The encoder contains 3 layers of residual blocks, and each layer downsamples the feature map to half the size. The resolution of the final output feature map  $\mathbf{F}_i \in \mathbb{R}^{H_i \times W_i \times C_i}$  is one-eighth of that of  $\mathbf{I}_r$ . Where  $H_i = H_r / 8$ ,  $W_i = W_r / 8$ ,  $C_i$  is the number of channels of the feature map  $\mathbf{F}_i$ . We set  $\mathbf{C}_i$  to 256.
+
+Foreground and Text-line Queries. In the previous work on distorted image rectification, there have been related works on foreground [11, 10] and text-line mask [14] extraction. We initialize the foreground and text-line queries on the basis of these two works. For foreground mask extraction, Feng et al. [11] used a lightweight semantic segmentation architecture network to predict the confidence map of foreground. The network is an Encoder-Decoder structure. We do not directly use the resulting binarized mask. Instead, use the six-layer feature maps in the decoder, and first resize them to the same size as  $\mathbf{F}_i$ , which is one-eighth the size of  $\mathbf{I}_r$ . And after concatenating in the channel dimension, use a layer of  $3 \times 3$  convolution module and BatchNorm [13] to reduce the number of channels to 256. Compared with directly using the binary mask output by the last layer of the network, this method can obtain richer image feature information.
+
+For the text-lines information, since the Doc3D training dataset proposed by DewarpNet [8] used by our model lacks corresponding text-line annotations, we use the detection
+
+text-line method proposed in RDGR [14] to obtain text-line features. This detection method used the U-Net network to train on PubLayNet [50] and the Scanned Script Dataset<sup>1</sup>. Its detection effect on the Doc3D dataset is shown in Figure 3. Although the text-line detected by this method has certain errors due to the deformation of the image, illumination effects and other reasons, it is within the network fault tolerance range. For text-line queries initialization, we use the last feature map of the U-Net network decoder (not the final confidence map). Its resolution is consistent with U-net network input. Then, we apply a layer of  $3 \times 3$  convolution and BatchNorm [13] to change the number of channels to 256, and finally bilinear interpolation is utilized to downsample the feature map size to one-eighth the size of  $\mathbf{I}_r$ .
+
+Foreground and Text-line Attention Module. For the initialized foreground queries, we use the cross-attention mechanism to extract features in distorted images. This module consists of three parts: self-attention, cross-attention, and feed forward networks. First, the image feature map  $\mathbf{F}_i$  is flattened, and then the long-distance dependencies between patches are calculated using self-attention.
+
+However, in the process of flattening the feature map, 2D coordinate information will be lost, which is crucial to obtain the local and global relationship, so we add a learnable 2D coordinate information. The same operation is performed on foreground queries. And then, in order to pay more attention to the foreground area and ignore the background, we use a foreground-guided cross-attention module. Specifically, a multi-head cross-attention layer is applied after self-attention. We utilize image features  $\mathbf{F}_i$  as key and value, and the foreground feature  $\mathbf{F}_f$  as query. Similar to the foreground-query cross-attention mechanism, in order to extract the features of the text-line positions of interest. The text-line features  $\mathbf{F}_t$  is treated as query. Finally, we utilize a layer of convolutions to enhance local feature extraction after obtaining the attention feature map. The formula for the foreground query and text-line query cross-attention mechanism is as follows:
+
+$$
+\begin{array}{l} C A _ {f} = C A (Q, K, V) = C A \left(F _ {f}, F _ {i}, F _ {i}\right) \\ = \operatorname {s o f t m a x} \left(\frac {F _ {f} F _ {i} ^ {\mathrm {T}}}{\sigma}\right) F _ {i} \tag {1} \\ \end{array}
+$$
+
+$$
+\begin{array}{l} C A _ {t} = C A (Q, K, V) = C A \left(F _ {t}, F _ {i}, F _ {i}\right) \\ = \operatorname {s o f t m a x} \left(\frac {F _ {t} F _ {i} ^ {\mathrm {T}}}{\sigma}\right) F _ {i} \tag {2} \\ \end{array}
+$$
+
+where  $CA$  is Cross-Attention and  $\sigma$  is a scaling factor.  $CA_{f}$  and  $CA_{t}$  are the foreground and text-line cross-attention map respectively.
+
+Transformer Decoder. After extracting the interesting feature  $\mathbf{C}A_{f}$  and  $\mathbf{C}A_{t}$  of the foreground and text-line, we concatenate the two features and feed them into the transformer
+
+<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.2459</td><td>20.51</td><td>1.0134</td><td>2111.56</td><td>0.5352</td></tr><tr><td>DocUNet [26]</td><td>CVPR&#x27;18</td><td>0.4103</td><td>14.19</td><td>-</td><td>1933.66</td><td>0.4632</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.2946</td><td>18.01</td><td>-</td><td>1712.48</td><td>0.4267</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4735</td><td>8.39</td><td>0.4260</td><td>885.90</td><td>0.2373</td></tr><tr><td>FCN-based [42]</td><td>DAS&#x27;20</td><td>0.4288</td><td>7.75</td><td>0.4017</td><td>1792.60</td><td>0.4213</td></tr><tr><td>PWUNet [9]</td><td>ICCV&#x27;21</td><td>0.4915</td><td>8.64</td><td>-</td><td>1069.28</td><td>0.2677</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.5105</td><td>7.76</td><td>0.3682</td><td>724.84</td><td>0.1832</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.4726</td><td>8.97</td><td>0.4287</td><td>1411.38</td><td>0.3573</td></tr><tr><td>FDRNet [45]</td><td>CVPR&#x27;22</td><td>0.5420</td><td>8.21</td><td>-</td><td>829.78</td><td>0.2068</td></tr><tr><td>RDGR [14]</td><td>CVPR&#x27;22</td><td>0.4950</td><td>8.51</td><td>0.4382</td><td>729.52</td><td>0.1717</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.5040</td><td>7.71</td><td>0.3800</td><td>713.94</td><td>0.1821</td></tr><tr><td>Ours</td><td>-</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>
+
+Table 1. On the DocUNet Benchmark [26], compare our proposed with existing methods in terms of Multi-Scale Structural Similarity (MS-SSIM), Local Distortion (LD) and OCR accuracy (ED and CER). “↑” indicates the higher the better and “↓” means the opposite.
+
+decoder composed of multi-head self-attention mechanism to predict the grid map. Consistent with the cross-attention module, we also add 2D learnable position coordinates. The structure of each decoder layer consists of self-attention and feed-forward network. Finally, we adopt the upsampling method in DocTr [11] and GeoDewarpNet [10] to obtain high-resolution 2D deformation field  $\mathbf{G}$ . This upsampling method trains a learnable weight on the basis of initializing the grid coordinates to perform weighted optimization on it. Training Loss Function. The loss function of our distorted document image rectification model is to compute the  $L_{1}$  distance between the predicted grid coordinate  $\hat{\pmb{G}}$  and the label  $\mathbf{G}$ . The formula as follows:
+
+$$
+\mathcal {L} _ {\text {g r i d}} = \left\| \mathbf {G} - \hat {\boldsymbol {G}} \right\| _ {\mathbf {1}} \tag {3}
+$$
+
+# 4. Experiments
+
+In this section, we first review the existing training dataset (Doc3D) and evaluation benchmark (DocUNet and DIR300 dataset) for distorted image dewarping. Second, we introduce the evaluation metrics and training details of this method. And then, we evaluate our document image rectification method on two datasets, DocUNet Benchmark [26] and DIR300 [10]. Finally, we demonstrate our rectification performance on several evaluation metrics.
+
+# 4.1. Dataset
+
+Doc3D. We train the geometric rectification model on the Doc3D dataset contributed by DewarpNet [8]. Doc3D is the largest distortion dewarping dataset so far, containing a total of 100K distorted images. It is created by about 4000 real document images and rendering software. Among them, different camera positions and various illumination are applied when rendering. For each distorted document image, the corresponding labels include 3D coordinate maps, albedo maps, normals, depth maps, UV maps and backward mapping map.
+
+DocUNet Benchmark. In current deep learning-based document dewarping methods, the DocUNet Benchmark [26] dataset is widely used. This evaluation dataset contains 130 distorted images in natural scenes captured by mobile devices. In addition, for better comparison with previous methods, we follow the proposal in DocGeoNet [10] and rotate the  $127^{th}$  and  $128^{th}$  images in DocUNet [26] that do not match the labels by 180 degrees.
+
+DIR300 Dataset. DIR300 dataset is a new test dataset proposed by DocGeoNet [10] captured by moving camera. It contains 300 images of real distorted documents involving more complex backgrounds, distorted degrees, and various lighting conditions.
+
+# 4.2. Evaluation metrics
+
+MS-SSIM, LD and AD. We follow previous methods [26, 8, 1, 11, 14, 10] to perceive image quality using an image-based Multi-Scale Structural Similarity method (MS-SSIM) [40]. Computationally dense SIFT-flow [22], Local Distortion (LD) [47] computes the average of the  $L_{2}$  distances between all pixels in the ground-truth scanned image and the rectified image pixels, which measures the average local deformation of the rectified image. Following DocUNet [26], all rectified images and their labels are resized to 598400 pixel area. We use the code provided by DocUNet [26] for evaluation. Aligned Distortion (AD) is a more robust evaluation metric proposed by [25], which aligns unwarped images and ground truth scans by unifying translation and scale before computing distortions.
+
+CER and ED. We use Character Error Rate (CER) [28] and Edit Distance (ED) [19] to measure the performance of our method. ED is a string metric that measures the difference between two character sequences. The edit distance between two strings is the minimum number of single-character edits (insertions  $(i)$ , deletions  $(d)$ , or substitutions  $(s)$ ) required to transform one string into the reference string. Then, the calculation of CER is:  $(i + d + s) / N$ , where  $N$  is the number of reference strings. Following the latest methods DocTr [11] and DocGeoNet [10], we use Tesseract
+
+![](images/2b68a773f97fca6dec8468f658e267826ba244c42eabe5cf9e29794824762d02.jpg)  
+Figure 4. Comparisons on DocUNet Benchmark [26]. Column 1: Distorted images. Columns 2-6: Results of DewarpNet [8], DocTr [11], RDGR [14], DocGeoNet [10] and ours method. Last column: Flatbed scanned images. We highlight the differences by using red and yellow arrows.
+
+<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.3169</td><td>39.58</td><td>0.7707</td><td>1500.56</td><td>0.5234</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.3246</td><td>30.63</td><td>-</td><td>958.89</td><td>0.3540</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4921</td><td>13.94</td><td>0.3320</td><td>1059.57</td><td>0.3557</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.6160</td><td>7.21</td><td>0.2552</td><td>699.63</td><td>0.2237</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.5524</td><td>10.97</td><td>0.3554</td><td>2130.01</td><td>0.5524</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.6380</td><td>6.40</td><td>0.2418</td><td>664.96</td><td>0.2189</td></tr><tr><td>Ours</td><td>-</td><td>0.6070</td><td>7.68</td><td>0.2440</td><td>652.80</td><td>0.2115</td></tr></table>
+
+Table 2. On the DIR300 Dataset [10], compare our proposed with existing methods.
+
+act (v5.0.1) [32] as an OCR engine to recognize text in the images. And, following the settings in DocUNet [26], DewarpNet [8] and RDGR [14], 50 images are selected from DocUNet Benchmark [26] to evaluate OCR performance. On DIR300 dataset [10], we compute CER and ED for 90 text-rich images following the setting in DocGeoNet [10].
+
+# 4.3. Implementation Details
+
+We implement the entire model architecture on the PyTorch [30] framework. We train our document rectification model on the Doc3D dataset of 100,000 images. The image size for training is  $224 \times 224$ . We set the layers of cross-attention and transformer decoder to 12 and 6, respectively. We use the AdamW optimizer [24] with a batch size of 24. The initial learning rate is  $1 \times 10^{-4}$ . The whole model is trained on two NVIDIA A100 GPUs for 30 epochs until the model converges.
+
+# 4.4. Experimental Results
+
+We use OCR performance (CER and ED) and image distortion metrics (MS-SSIM and LD) to compare our method with existing deep learning-based state-of-the-art rectification models on DocUNet Benchmark [26] and DIR300 Dataset [10].
+
+Evaluation on DocUNet Benchmark. As shown in Table 1, in the setting of 50 images, compared with the existing works, our method for distorted document image dewarping improves both ED and CER. Among them, the ED metric dropped below 700 for the first time to reach 697.52, an increase of  $2.3\%$ . At the same time, it reached 0.1705 on the CER. Our method outperforms almost all non-textline methods [26, 20, 8, 42, 9, 11, 43, 45] on distortion metrics. It can be seen that making the model focus on the features of the text-line regions significantly improves the rectification effect. Overall, in addition, compared with RDGR [14] and DocGeoNet [10], which also use text-line for distor
+
+![](images/f220d5bd377b166cf94e5f5502fe11f432f33ef573dd098917f82bfe6d5a8068.jpg)  
+Figure 5. Comparisons on DIR300 [10]. Column 1: Distorted images. Column 2-4: Results of DewarpNet [8], DDCP [43], DocGeoNet [10]. Column 5: Rectification results of our model.
+
+tion images dewarping, our method performs better in OCR evaluation metrics.
+
+Evaluation on DIR300 Dataset. In the evaluation of the DIR300 dataset, the results are shown in Table 2. We follow the settings in DocGeoNet [10], and select 90 of the pictures for evaluation in terms of OCR accuracy. For previous state-of-the-art methods, our method has improved both CER and ED, and ED has increased by  $1.8\%$  and dropped to 652.8. Compared with the existing state-of-the-art methods, from the experimental results, our method can more effectively improve the OCR performance of the rectified image. In order to show the rectification effect more intuitively, we visualize and compare the results between existing and our methods on DocUNet Benchmark [26] and DIR300 Dataset [10], as shown in Figure 4 and Figure 5. It can be seen from the first two rows of these two figures that our method pays more attention to the foreground of distorted document images. The last two lines of images show that the dewarping effect of the text-line is more horizontal after the introduction of the text-line information. This is crucial for improving OCR accuracy and paper readability.
+
+# 4.5. Experimental Analysis
+
+Visualizations of OCR Results. We visualized the recognition results of OCR after image rectification, as shown in the Figure 6. We compared the effect of the distorted images, dewarping results of DocGeoNet [10] and our method on OCR recognition. We highlight the text area detected by Tesseract (v5.0.1) [32] OCR engine with three different colors. It can be seen from the figure that the OCR performance can be greatly improved after dewarping the dis
+
+![](images/29ba75176afc12a7b324d33aadb3e370ca80d895826823851af4a4de2200741e.jpg)  
+Figure 6. Visualizations of OCR results. Left to right: Original deformed images, rectified by DocGeoNet [10], rectified by ours method. The color is the highlighted text detection results. Yellow arrows indicate differences.
+
+torted image. By fusing the information of text-lines, the model can be made to pay more attention to the text area, improving the reading quality of the document image.
+
+Visualizations of Cross-attention Maps. In order to further show the feature extraction effect of foreground and text-lines, we provide the attention map visualization for the foreground and text-line attention map from our cross-attention module (FAM and TAM) in Figure 7. We can see that our model can acquire the ability to localize the foreground and text-line regions.
+
+Bad Case Analysis. Although our method improves the OCR accuracy to some extent, it has not reached SOTA on MS-SSIM, LD and AD. According to our analysis, as shown in the Figure 8, after observing the rectified samples, we found that the characteristics of the input distorted image itself, such as the influence of illumination condition, shadows, and background that is very close to the foreground boundary, although these do not affect the attention feature extraction of text-line regions. It is also because of these attributes that the effect of our method to segment the margins between foreground and background on similar images with these characteristics still needs to be improved.
+
+Besides, We analyzed the influence of the text content ratio on the DocUNet Benchmark. Sorting in ascending order of the proportion of text content, the first  $30\%$  of images as Low, the next  $40\%$  of images as Middle, and the last  $30\%$  of images as High. As shown in table 3, Due to MS-SSIM is sensitive to pixel location, highly subtle image differences can result in large MS-SSIM differences. Since the connectivity of text area is lower than general images, the more text content may cause lower MS-SSIM. This phenomenon is also manifested in AD. As the ratio of text increases, LD tends to be better, which indicates that the text line feature
+
+<table><tr><td>Text Content Ratio</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td></tr><tr><td>Low</td><td>0.54</td><td>10.74</td><td>0.35</td></tr><tr><td>Middle</td><td>0.51</td><td>8.27</td><td>0.35</td></tr><tr><td>High</td><td>0.44</td><td>6.34</td><td>0.44</td></tr></table>
+
+Table 3. The relationship between the proportion of text content and each evaluation metric.  
+
+<table><tr><td>FAM</td><td>TAM</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>✓</td><td></td><td>0.4785</td><td>8.53</td><td>0.3619</td><td>761.22</td><td>0.1952</td></tr><tr><td></td><td>✓</td><td>0.4778</td><td>8.86</td><td>0.3529</td><td>748.46</td><td>0.1889</td></tr><tr><td>✓</td><td>✓</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>
+
+Table 4. Ablation experiments. FAM is Foreground Attention Module and TAM is Text-lines Attention Module.
+
+![](images/77a6d46133608fe30df222f050fcd88cddb0057f62ce26fb4a6691877f9a9ec2.jpg)
+
+![](images/854e4c54dead889e4986ca90383cf61bbb22f44dc1b66618546843dc20ecd104.jpg)
+
+![](images/7325cd9649ce2fef061f895423dc302f4d658afe3e9bb977de66f954a638836d.jpg)
+
+![](images/76fbbc6f52d656c04d77f4de40ad5f5f8fcc351f5a0568720cda3b13c8d950bc.jpg)
+
+![](images/bb1d1349190105d7d6952eaf3923cf998760343b78fc4a04027c72c852846862.jpg)
+
+![](images/564367f7b94242f382e54fa25a082174e3804118af9c47a81391226480bc4b5b.jpg)
+
+![](images/42130f312af1ea7e5b83e137063d905e8c4706f35012b504c81c52bb2695dee6.jpg)
+
+![](images/053d82d392a022b8f14e481b094432836418c02250172b9e2d3f2aed71acb5a6.jpg)
+
+![](images/5e262eaaba71f7a2bb216c189b2dc5ed9d83f876e0672d398334941967b5e6c4.jpg)  
+Figure 7. Visualizations of attention maps. Left to right: distorted images, foreground attention maps, text-line attention maps, rectification results of our model.
+
+![](images/dd183342977b63d995770fa976da799a67519ce73a253f52be6f741c26c08d67.jpg)
+
+![](images/ba9912d27891e1400caca758e2e406cb84dfb1660b34453bb3e9d3e09750be9a.jpg)
+
+![](images/8e06eebd1f8e1af0eb351690aada4ee718a725aeaae736436a068dee7c560793.jpg)
+
+is beneficial for local distortion correction, which is also reflected from the CER and ED metrics.
+
+Ablation Studies. Table 4 shows the performance of our method when foreground and text-line information are used respectively. We compared the performance when only one of the two features mentioned above is used. This experimental results demonstrate that using foreground and text-line feature extraction modules together, the MS-SSIM and Local Distortion (LD) are increased by at least  $4\%$  and  $1.2\%$  respectively. It can be seen that the overall rectification effect of the distorted document image is the best when the two features are combined to extract the region of interest in the original image. It is precisely due to the foreground contains the overall distorted outline of the deformed image, and the text-line contains the local deformation trend of the text area, so that the global and local information can be complementary with each other, and the overall rectification effect can be greatly improved.
+
+![](images/820f950b03b5e1177288c482e462f0892f873a1b7cfaf3f00653eac7c4595627.jpg)
+
+![](images/93e0acece540c0b2d1673638361f33daa9414e12d4d5522c49ef532244123637.jpg)
+
+![](images/1acf08902c565d913902e7f4c32ced10202484c055bc723230fa8abe46d0bff4.jpg)
+
+![](images/ef64da361bc50fa12648115bfa5f837f09939295f27fd3cd67344faa2f138d5d.jpg)
+
+![](images/437bef5b0bde420097443267781c93fc5dfedcc19ce0b3f1e188d19c324de20a.jpg)
+
+![](images/ed88e76b5ab2e47b1333fd9faba2926a2c0d01edfdfc9b50e9cb2cec1333aebe.jpg)
+
+![](images/fd1a9a717632469f5d4c6bce878dec1b5a595a0b516a04775f03df047992b2ad.jpg)
+
+![](images/bb19a31973b5f901af9401616b99adeb943528712c5da8da7bb8f2b8bdf6b606.jpg)
+
+![](images/c3a1b31c8ff315e15d7560bd0590d3f7c52b726f310c6f0a4630f1e144ae6c00.jpg)  
+Figure 8. Visualizations of attention maps for bad case analysis. Left to right: distorted images, foreground attention maps, text-line attention maps, rectification results of our model. Row 1: influence of illumination condition. Row 2: the boundary of the foreground close to background. Row 3: the shadow interference of the document image.
+
+![](images/f2cb95c58db376ebfccea547ce97d2b979983c667b117c1270e3a4f97b3a7511.jpg)
+
+![](images/07f4c62110ca0564f9d267817ff54e2e7179dfc17cb5366b34308d643e4a3e0d.jpg)
+
+![](images/11db4024cc24c5a5a8c7346ebb53e9b9560dc16881c00469d863b839a39dbb11.jpg)
+
+# 5. Conclusion
+
+In this work, we explored how to optimize the rectification of distorted document images from the perspective of readability. We propose an efficient method for warped document rectification by focusing on the foreground and text-line regions of the original deformed image separately via cross-attention. We use this method to improve the readability of the rectified document images from the perspective of global and local features. The effectiveness of this feature fusion mechanism is proved by experiments on two public benchmark datasets. In the future, since the current training dataset lacks text-line annotations, we will further explore how to obtain more accurate text-line annotations. This is also a limitation of our method. Besides, for extracting distorted image features, we will also explore more fine-grained and multi-attribute feature fusion methods to improve image quality and OCR performance.
+
+Acknowledgement: We thank the reviewers for their thoughtful and constructive comments. This work was supported by the National Key R&D Program of China (2022ZD0116002), Natural Science Foundation of China (62276075, 61872113), Science and Technology Planning Project of Shenzhen (JCYJ20190806112210067), Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, China (2022B1212010005) and China Mobile Information Technology Co., Ltd. It was also supported by Music Style Transfer for Anxiety Therapy (P0042962), Artificial Intelligence and Robotics (AIR) Group: Artificial Intelligence Art (P0033738).
+
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+                                    "content": "larization of mobile electronic devices, it is more and more convenient for people to take pictures with smart phones or portable cameras to capture electronic documents. When taking pictures, due to the different positions, illumination conditions of these devices, the angle of paper placement, deformation and other problems, the images taken are distorted or deformed to varying degrees, and it is difficult to extract useful information from these distorted pictures, as shown in Figure 1. Even wrong information is extracted, which brings great challenges to obtaining key information of documents and realizing document intelligence."
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+                                    "content": "As early as many years ago, the problem of document image distortion rectification has been paid attention to. In the traditional rectification method before deep learning was widely used, several previous methods [3, 36, 17] according to the deformation characteristics of the image, relying on multi-view, get the best boundary through the regression method, and use the boundary segmentation method to dewarped the segmentation graphics. Tian and Narasimhan"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "[35] reconstructs warped document images from 2D to 3D by detecting text-lines in the image. In the time since, some works [16, 15] have also captured prior knowledge in deformed images by detecting text lines in order to bring gains to image rectification. However, these methods of restoring the 3D shape of images through auxiliary hardware or multi-view methods will bring time consuming and expensive problems."
+                                }
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+                                    "content": "With the arrival of the era of deep learning, Convolutional Neural Network (CNN) and Transformer have been introduced to solve the geometric rectification of distorted document images. Most current methods dewarping the input image by learning the mapping relationship between the input distorted image and the dense 2D coordinate map area [26, 8, 1, 11, 14, 10]. The method of [26, 8] used the UNet structure networks to regress the dense 2D coordinates mapping according to the input distorted image. However, it is difficult for CNN to capture the long-distance dependence of distorted paper. For methods [11, 10] that focus on image foreground, they proposed to remove the document background in the preprocessing stage before geometric rectification the network. And then introduces the multi-layer transformer of Encoder-Decoder structure after the convolution network to dewarp the distorted paper. But these methods based on setting the binarization threshold to remove the background will lose the information of the original image. There are also some works such as [14, 10] proposed to use document boundaries, 3D world coordinates and text-lines to construct deformation fields, which reduces the error rate of text recognition. These two methods have no obvious interaction between the text-line and the original distorted image, which makes the text-line area unable to be effectively focused."
+                                }
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+                                    "content": "In geometrically deformed images, the distortion degree of image foreground and text-lines varies with different scenes. It is necessary to establish an explicit invariant feature in the distorted image foreground to represent the core document and text-line region features robustly, to suppress the interference of background and deformation. Since the foreground information of the document image can clearly represent the deformation amplitude, we use the foreground features representation of the input image. The text-line regions can represent the distorted state of the local position in dewarped images. In order to enhance the reading quality of the image, we considering it is necessary to pay more attention to the area of the text-lines. Therefore, we propose to represent local information using text-line information, extract the characteristics of the corresponding position in the image. Besides, based on our observations, when using the deformation field for distortion rectification, for the dewarped image, the areas in the same horizontal direction should have the same vertical coordinates in the deformation field. For example, for text-lines, the text area of the"
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+                                    "content": "same line should have the same ordinate. This is a very critical starting point for our design model."
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+                                    "content": "The main contributions of our work are summarized as follows:"
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+                                            "content": "- We propose to use foreground and text line information to guide the model to focus on the global and local features of distorted paper, so as to reduce background interference and improve the readability of document images."
+                                        }
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+                                            "content": "- We introduce cross-attention to explore more effective interaction between paper deformation trend and original distorted image."
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+                                            "content": "- We conduct extensive experiments and show the state-of-the-art results on the existing prevalent benchmarks."
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+                                    "content": "2. Related Work"
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+                                    "content": "The goal of rectifying distorted images is to enhance the visual quality of images, thereby reducing the difficulty of text extraction and improving the readability of paper. Early document image rectification methods performed parametric rectification by using cues easily observed from the image, such as text-lines proposed by Huang et al. [12], cylindrical surfaces [38, 6, 21, 18, 48, 27], document boundaries [3, 36] or laser beams from external devices used by Narain et al. [29]."
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+                                    "content": "In recent years, many works such as [26, 8, 1, 11, 14, 10] proposed to use deep learning to rectify distorted document images. These models solve the rectification problem by directly predicting the deformation field of the image."
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+                                    "content": "Ma et al. [26] is the first work using deep neural networks on this task. They used a stacked UNet structure to predict the deformation field for each pixel in the warped document. This is an end-to-end structure that inverts the input image to obtain the result after the prediction result is obtained. In view of the lack of a large number of warped datasets to train the model, Das et al. [8] subsequently contributed a warped document image dataset (Doc3D) containing about 100,000 Distorted images. In addition, they"
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+                                            "content": "Figure 2. The overview architecture of our proposed method. FAM is Foreground Attention Module and TAM is Text-lines Attention Module."
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+                                    "content": "proposed a UNet structure network that uses 3D shape (World Coordinates) to replace the original warped document to predict the deformation field."
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+                                    "content": "In order to reduce the interference of the background on the dewarping effect, Feng et al. [11] proposed to remove the background of the document before rectification, and introduced a transformer on this task for the first time. For reasons of improving the reading quality of the rectified document, other works of Jiang et al. [14] and Feng et al. [10] proposed to introduce the text-line feature in the document to enhance the rectification effect of text-line areas."
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+                                    "content": "The attention mechanism focuses the attention of the network on the most important parts of the data by enhancing the weight of some parts of the input data of the neural network while weakening the weight of other parts. It was originally developed in 2017 for natural language processing tasks by Vaswani et al. [37], and greatly improved new state-of-the-art performance on many downstream tasks. However, in recent years, great success has been achieved in computer vision-related tasks such as image or video classification [39, 31, 2, 33, 7], image segmentation [49, 41, 4, 23], visual question answering [51, 34, 5, 46], and scene text recognition [44]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                        288,
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Different from the self-attention mechanism, cross attention is able to exploit the intra-modal relations of each modality to complement each other and enhance the feature relations between different modalities. On multimodal tasks, cross attention is widely used to match the visual semantic similarity between images and texts [51, 34, 5, 46], and the key step is how to design fusion modules to effectively connect multimodal inputs. In this distorted im"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "type": "text",
+                                    "content": "age geometry rectification task, in order to minimize background interference, we propose to use the foreground information to aware corresponding regions in image features in a cross-attention manner. Furthermore, in order to increase the attention on the text-line regions, similar to the foreground cross-attention, we use the text-lines information to obtain the features of the text regions in the image, which can ensure that the same line of text is horizontal on the rectified image."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "3. The Proposed Approach"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this section, we propose a noval framework for document image dewarping. The overview architecture of our model is shown in Figure 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Network Architecture. Our model consists of CNNs Encoder, the Foreground and Text-line Attention Module, and the Transformer Decoder. We use these three modules to obtain the features of foreground regions except background and text-line regions in distorted document images, respectively. After obtaining text-line and foreground information, cross-attention used to enhance the foreground and text-line attention. And then concatenate the feature map of these two cross feature map in the channel dimension, input it to the multi-layer decoder to predict the 2D grid coordinates, and finally use the coordinates to dewarp the input document image."
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Given a warped document image "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we first resize it to "
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_r \\in \\mathbb{R}^{H_r \\times W_r \\times C_r}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_r = W_r = 224"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_r = 3"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of RGB channels of the original image. Then, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_r"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is fed into an encoder consisting of multiple layers of convolutional neural networks (CNNs) to obtain the feature map "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i \\in \\mathbb{R}^{H_i \\times W_i \\times C_i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of the original warped image. Then, through the cross-attention of fore"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "19576"
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+                    "blocks": [
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+                                            "type": "image",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 0,
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+                            "type": "image_body"
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+                                            "type": "text",
+                                            "content": "Figure 3. Text-line detection results of the Doc3D dataset. Row 1: Input warped images. Row 2: Detection results for text lines."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "ground and text-line, the region of interest is extracted from the image features "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "text",
+                                    "content": ". Finally, a 2D dense grid coordinate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{G} \\in \\mathbb{R}^{H_r \\times W_r \\times 2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "text",
+                                    "content": " (backward mapping or deformation field) is predicted through a transformer network composed of a multi-layer self-attention and feed-forward network architecture. According to the obtained grid coordinates, the input image can be dwarped to obtain an dwarped picture "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D} \\in \\mathbb{R}^{H \\times W \\times 3}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "text",
+                                    "content": ". Each coordinate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(x, y)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        255,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in grid coordinates represents the position of the pixel value on the input image in the rectified image."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "CNNs Encoder. For the resized image "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_r"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ", we first use the convolutional neural network module as an encoder to extract image features. The encoder contains 3 layers of residual blocks, and each layer downsamples the feature map to half the size. The resolution of the final output feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i \\in \\mathbb{R}^{H_i \\times W_i \\times C_i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is one-eighth of that of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_r"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ". Where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_i = H_r / 8"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "W_i = W_r / 8"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of channels of the feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "text",
+                                    "content": ". We set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
+                                        287,
+                                        472
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{C}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        376,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to 256."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Foreground and Text-line Queries. In the previous work on distorted image rectification, there have been related works on foreground [11, 10] and text-line mask [14] extraction. We initialize the foreground and text-line queries on the basis of these two works. For foreground mask extraction, Feng et al. [11] used a lightweight semantic segmentation architecture network to predict the confidence map of foreground. The network is an Encoder-Decoder structure. We do not directly use the resulting binarized mask. Instead, use the six-layer feature maps in the decoder, and first resize them to the same size as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
+                                        675
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
+                                        675
+                                    ],
+                                    "type": "text",
+                                    "content": ", which is one-eighth the size of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
+                                        675
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_r"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
+                                        675
+                                    ],
+                                    "type": "text",
+                                    "content": ". And after concatenating in the channel dimension, use a layer of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
+                                        675
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "3 \\times 3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        288,
+                                        675
+                                    ],
+                                    "type": "text",
+                                    "content": " convolution module and BatchNorm [13] to reduce the number of channels to 256. Compared with directly using the binary mask output by the last layer of the network, this method can obtain richer image feature information."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        46,
+                        677,
+                        287,
+                        713
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For the text-lines information, since the Doc3D training dataset proposed by DewarpNet [8] used by our model lacks corresponding text-line annotations, we use the detection"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
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+                        239
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "text-line method proposed in RDGR [14] to obtain text-line features. This detection method used the U-Net network to train on PubLayNet [50] and the Scanned Script Dataset<sup>1</sup>. Its detection effect on the Doc3D dataset is shown in Figure 3. Although the text-line detected by this method has certain errors due to the deformation of the image, illumination effects and other reasons, it is within the network fault tolerance range. For text-line queries initialization, we use the last feature map of the U-Net network decoder (not the final confidence map). Its resolution is consistent with U-net network input. Then, we apply a layer of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        239
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "3 \\times 3"
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+                                    "type": "text",
+                                    "content": " convolution and BatchNorm [13] to change the number of channels to 256, and finally bilinear interpolation is utilized to downsample the feature map size to one-eighth the size of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_r"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Foreground and Text-line Attention Module. For the initialized foreground queries, we use the cross-attention mechanism to extract features in distorted images. This module consists of three parts: self-attention, cross-attention, and feed forward networks. First, the image feature map "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_i"
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+                                    "type": "text",
+                                    "content": " is flattened, and then the long-distance dependencies between patches are calculated using self-attention."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "However, in the process of flattening the feature map, 2D coordinate information will be lost, which is crucial to obtain the local and global relationship, so we add a learnable 2D coordinate information. The same operation is performed on foreground queries. And then, in order to pay more attention to the foreground area and ignore the background, we use a foreground-guided cross-attention module. Specifically, a multi-head cross-attention layer is applied after self-attention. We utilize image features "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " as key and value, and the foreground feature "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_f"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as query. Similar to the foreground-query cross-attention mechanism, in order to extract the features of the text-line positions of interest. The text-line features "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is treated as query. Finally, we utilize a layer of convolutions to enhance local feature extraction after obtaining the attention feature map. The formula for the foreground query and text-line query cross-attention mechanism is as follows:"
+                                }
+                            ]
+                        }
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+                                    "content": "\\begin{array}{l} C A _ {f} = C A (Q, K, V) = C A \\left(F _ {f}, F _ {i}, F _ {i}\\right) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {F _ {f} F _ {i} ^ {\\mathrm {T}}}{\\sigma}\\right) F _ {i} \\tag {1} \\\\ \\end{array}",
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+                                    "content": "\\begin{array}{l} C A _ {t} = C A (Q, K, V) = C A \\left(F _ {t}, F _ {i}, F _ {i}\\right) \\\\ = \\operatorname {s o f t m a x} \\left(\\frac {F _ {t} F _ {i} ^ {\\mathrm {T}}}{\\sigma}\\right) F _ {i} \\tag {2} \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "CA"
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+                                    "type": "text",
+                                    "content": " is Cross-Attention and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\sigma"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a scaling factor. "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "CA_{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are the foreground and text-line cross-attention map respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
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+                                    "type": "text",
+                                    "content": "Transformer Decoder. After extracting the interesting feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{C}A_{f}"
+                                },
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+                                    "type": "text",
+                                    "content": " and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{C}A_{t}"
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+                                    "type": "text",
+                                    "content": " of the foreground and text-line, we concatenate the two features and feed them into the transformer"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+            ],
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+                                    "type": "text",
+                                    "content": "<https://github.com/zzzDavid/ICDAR-2019-SROIE"
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+                                            "html": "<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.2459</td><td>20.51</td><td>1.0134</td><td>2111.56</td><td>0.5352</td></tr><tr><td>DocUNet [26]</td><td>CVPR&#x27;18</td><td>0.4103</td><td>14.19</td><td>-</td><td>1933.66</td><td>0.4632</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.2946</td><td>18.01</td><td>-</td><td>1712.48</td><td>0.4267</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4735</td><td>8.39</td><td>0.4260</td><td>885.90</td><td>0.2373</td></tr><tr><td>FCN-based [42]</td><td>DAS&#x27;20</td><td>0.4288</td><td>7.75</td><td>0.4017</td><td>1792.60</td><td>0.4213</td></tr><tr><td>PWUNet [9]</td><td>ICCV&#x27;21</td><td>0.4915</td><td>8.64</td><td>-</td><td>1069.28</td><td>0.2677</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.5105</td><td>7.76</td><td>0.3682</td><td>724.84</td><td>0.1832</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.4726</td><td>8.97</td><td>0.4287</td><td>1411.38</td><td>0.3573</td></tr><tr><td>FDRNet [45]</td><td>CVPR&#x27;22</td><td>0.5420</td><td>8.21</td><td>-</td><td>829.78</td><td>0.2068</td></tr><tr><td>RDGR [14]</td><td>CVPR&#x27;22</td><td>0.4950</td><td>8.51</td><td>0.4382</td><td>729.52</td><td>0.1717</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.5040</td><td>7.71</td><td>0.3800</td><td>713.94</td><td>0.1821</td></tr><tr><td>Ours</td><td>-</td><td>0.4978</td><td>8.43</td><td>0.3761</td><td>697.52</td><td>0.1705</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1. On the DocUNet Benchmark [26], compare our proposed with existing methods in terms of Multi-Scale Structural Similarity (MS-SSIM), Local Distortion (LD) and OCR accuracy (ED and CER). “↑” indicates the higher the better and “↓” means the opposite."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "decoder composed of multi-head self-attention mechanism to predict the grid map. Consistent with the cross-attention module, we also add 2D learnable position coordinates. The structure of each decoder layer consists of self-attention and feed-forward network. Finally, we adopt the upsampling method in DocTr [11] and GeoDewarpNet [10] to obtain high-resolution 2D deformation field "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{G}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This upsampling method trains a learnable weight on the basis of initializing the grid coordinates to perform weighted optimization on it. Training Loss Function. The loss function of our distorted document image rectification model is to compute the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{1}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " distance between the predicted grid coordinate "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\pmb{G}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the label "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{G}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The formula as follows:"
+                                }
+                            ]
+                        }
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+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\text {g r i d}} = \\left\\| \\mathbf {G} - \\hat {\\boldsymbol {G}} \\right\\| _ {\\mathbf {1}} \\tag {3}",
+                                    "image_path": "831457315623dcf9c3785c46db8d9b12d6dfd34288a424f8223ba99c3f434cd3.jpg"
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In this section, we first review the existing training dataset (Doc3D) and evaluation benchmark (DocUNet and DIR300 dataset) for distorted image dewarping. Second, we introduce the evaluation metrics and training details of this method. And then, we evaluate our document image rectification method on two datasets, DocUNet Benchmark [26] and DIR300 [10]. Finally, we demonstrate our rectification performance on several evaluation metrics."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
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+                                    "content": "4.1. Dataset"
+                                }
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+                                    "content": "Doc3D. We train the geometric rectification model on the Doc3D dataset contributed by DewarpNet [8]. Doc3D is the largest distortion dewarping dataset so far, containing a total of 100K distorted images. It is created by about 4000 real document images and rendering software. Among them, different camera positions and various illumination are applied when rendering. For each distorted document image, the corresponding labels include 3D coordinate maps, albedo maps, normals, depth maps, UV maps and backward mapping map."
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+                                    "content": "DocUNet Benchmark. In current deep learning-based document dewarping methods, the DocUNet Benchmark [26] dataset is widely used. This evaluation dataset contains 130 distorted images in natural scenes captured by mobile devices. In addition, for better comparison with previous methods, we follow the proposal in DocGeoNet [10] and rotate the "
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+                                    "content": "127^{th}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "128^{th}"
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+                                    "type": "text",
+                                    "content": " images in DocUNet [26] that do not match the labels by 180 degrees."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
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+                                    "content": "DIR300 Dataset. DIR300 dataset is a new test dataset proposed by DocGeoNet [10] captured by moving camera. It contains 300 images of real distorted documents involving more complex backgrounds, distorted degrees, and various lighting conditions."
+                                }
+                            ]
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+                                    "content": "4.2. Evaluation metrics"
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+                                    "content": "MS-SSIM, LD and AD. We follow previous methods [26, 8, 1, 11, 14, 10] to perceive image quality using an image-based Multi-Scale Structural Similarity method (MS-SSIM) [40]. Computationally dense SIFT-flow [22], Local Distortion (LD) [47] computes the average of the "
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+                                    "type": "inline_equation",
+                                    "content": "L_{2}"
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+                                    "type": "text",
+                                    "content": " distances between all pixels in the ground-truth scanned image and the rectified image pixels, which measures the average local deformation of the rectified image. Following DocUNet [26], all rectified images and their labels are resized to 598400 pixel area. We use the code provided by DocUNet [26] for evaluation. Aligned Distortion (AD) is a more robust evaluation metric proposed by [25], which aligns unwarped images and ground truth scans by unifying translation and scale before computing distortions."
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+                                    "content": "CER and ED. We use Character Error Rate (CER) [28] and Edit Distance (ED) [19] to measure the performance of our method. ED is a string metric that measures the difference between two character sequences. The edit distance between two strings is the minimum number of single-character edits (insertions "
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+                                    "type": "text",
+                                    "content": ", deletions "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": ") required to transform one string into the reference string. Then, the calculation of CER is: "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(i + d + s) / N"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "text",
+                                    "content": " is the number of reference strings. Following the latest methods DocTr [11] and DocGeoNet [10], we use Tesseract"
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+                                            "content": "Figure 4. Comparisons on DocUNet Benchmark [26]. Column 1: Distorted images. Columns 2-6: Results of DewarpNet [8], DocTr [11], RDGR [14], DocGeoNet [10] and ours method. Last column: Flatbed scanned images. We highlight the differences by using red and yellow arrows."
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+                                            "html": "<table><tr><td>Method</td><td>Pub.</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td><td>ED ↓</td><td>CER ↓</td></tr><tr><td>Distorted</td><td>-</td><td>0.3169</td><td>39.58</td><td>0.7707</td><td>1500.56</td><td>0.5234</td></tr><tr><td>DocProj [20]</td><td>TOG&#x27;19</td><td>0.3246</td><td>30.63</td><td>-</td><td>958.89</td><td>0.3540</td></tr><tr><td>DewarpNet [8]</td><td>ICCV&#x27;19</td><td>0.4921</td><td>13.94</td><td>0.3320</td><td>1059.57</td><td>0.3557</td></tr><tr><td>DocTr [11]</td><td>ACM MM&#x27;21</td><td>0.6160</td><td>7.21</td><td>0.2552</td><td>699.63</td><td>0.2237</td></tr><tr><td>DDCP [43]</td><td>ICDAR&#x27;21</td><td>0.5524</td><td>10.97</td><td>0.3554</td><td>2130.01</td><td>0.5524</td></tr><tr><td>DocGeoNet [10]</td><td>ECCV&#x27;22</td><td>0.6380</td><td>6.40</td><td>0.2418</td><td>664.96</td><td>0.2189</td></tr><tr><td>Ours</td><td>-</td><td>0.6070</td><td>7.68</td><td>0.2440</td><td>652.80</td><td>0.2115</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 2. On the DIR300 Dataset [10], compare our proposed with existing methods."
+                                }
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+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "act (v5.0.1) [32] as an OCR engine to recognize text in the images. And, following the settings in DocUNet [26], DewarpNet [8] and RDGR [14], 50 images are selected from DocUNet Benchmark [26] to evaluate OCR performance. On DIR300 dataset [10], we compute CER and ED for 90 text-rich images following the setting in DocGeoNet [10]."
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+                                    "type": "text",
+                                    "content": "4.3. Implementation Details"
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+                                    "content": "We implement the entire model architecture on the PyTorch [30] framework. We train our document rectification model on the Doc3D dataset of 100,000 images. The image size for training is "
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+                                    "content": "224 \\times 224"
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+                                    "content": ". We set the layers of cross-attention and transformer decoder to 12 and 6, respectively. We use the AdamW optimizer [24] with a batch size of 24. The initial learning rate is "
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+                                    "type": "inline_equation",
+                                    "content": "1 \\times 10^{-4}"
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+                                    "content": ". The whole model is trained on two NVIDIA A100 GPUs for 30 epochs until the model converges."
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+                                    "content": "We use OCR performance (CER and ED) and image distortion metrics (MS-SSIM and LD) to compare our method with existing deep learning-based state-of-the-art rectification models on DocUNet Benchmark [26] and DIR300 Dataset [10]."
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+                                    "content": "Evaluation on DocUNet Benchmark. As shown in Table 1, in the setting of 50 images, compared with the existing works, our method for distorted document image dewarping improves both ED and CER. Among them, the ED metric dropped below 700 for the first time to reach 697.52, an increase of "
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+                                    "content": ". At the same time, it reached 0.1705 on the CER. Our method outperforms almost all non-textline methods [26, 20, 8, 42, 9, 11, 43, 45] on distortion metrics. It can be seen that making the model focus on the features of the text-line regions significantly improves the rectification effect. Overall, in addition, compared with RDGR [14] and DocGeoNet [10], which also use text-line for distor"
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+                                            "type": "text",
+                                            "content": "Figure 5. Comparisons on DIR300 [10]. Column 1: Distorted images. Column 2-4: Results of DewarpNet [8], DDCP [43], DocGeoNet [10]. Column 5: Rectification results of our model."
+                                        }
+                                    ]
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+                                    "type": "text",
+                                    "content": "tion images dewarping, our method performs better in OCR evaluation metrics."
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+                                    "type": "text",
+                                    "content": "Evaluation on DIR300 Dataset. In the evaluation of the DIR300 dataset, the results are shown in Table 2. We follow the settings in DocGeoNet [10], and select 90 of the pictures for evaluation in terms of OCR accuracy. For previous state-of-the-art methods, our method has improved both CER and ED, and ED has increased by "
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+                                    "content": "1.8\\%"
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+                                    "type": "text",
+                                    "content": " and dropped to 652.8. Compared with the existing state-of-the-art methods, from the experimental results, our method can more effectively improve the OCR performance of the rectified image. In order to show the rectification effect more intuitively, we visualize and compare the results between existing and our methods on DocUNet Benchmark [26] and DIR300 Dataset [10], as shown in Figure 4 and Figure 5. It can be seen from the first two rows of these two figures that our method pays more attention to the foreground of distorted document images. The last two lines of images show that the dewarping effect of the text-line is more horizontal after the introduction of the text-line information. This is crucial for improving OCR accuracy and paper readability."
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+                                    "content": "4.5. Experimental Analysis"
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+                                    "content": "Visualizations of OCR Results. We visualized the recognition results of OCR after image rectification, as shown in the Figure 6. We compared the effect of the distorted images, dewarping results of DocGeoNet [10] and our method on OCR recognition. We highlight the text area detected by Tesseract (v5.0.1) [32] OCR engine with three different colors. It can be seen from the figure that the OCR performance can be greatly improved after dewarping the dis"
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+                                            "content": "Figure 6. Visualizations of OCR results. Left to right: Original deformed images, rectified by DocGeoNet [10], rectified by ours method. The color is the highlighted text detection results. Yellow arrows indicate differences."
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+                                    "type": "text",
+                                    "content": "torted image. By fusing the information of text-lines, the model can be made to pay more attention to the text area, improving the reading quality of the document image."
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+                                    "content": "Visualizations of Cross-attention Maps. In order to further show the feature extraction effect of foreground and text-lines, we provide the attention map visualization for the foreground and text-line attention map from our cross-attention module (FAM and TAM) in Figure 7. We can see that our model can acquire the ability to localize the foreground and text-line regions."
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+                                    "type": "text",
+                                    "content": "Bad Case Analysis. Although our method improves the OCR accuracy to some extent, it has not reached SOTA on MS-SSIM, LD and AD. According to our analysis, as shown in the Figure 8, after observing the rectified samples, we found that the characteristics of the input distorted image itself, such as the influence of illumination condition, shadows, and background that is very close to the foreground boundary, although these do not affect the attention feature extraction of text-line regions. It is also because of these attributes that the effect of our method to segment the margins between foreground and background on similar images with these characteristics still needs to be improved."
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+                                    "content": "Besides, We analyzed the influence of the text content ratio on the DocUNet Benchmark. Sorting in ascending order of the proportion of text content, the first "
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+                                    "content": " of images as Middle, and the last "
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+                                    "content": " of images as High. As shown in table 3, Due to MS-SSIM is sensitive to pixel location, highly subtle image differences can result in large MS-SSIM differences. Since the connectivity of text area is lower than general images, the more text content may cause lower MS-SSIM. This phenomenon is also manifested in AD. As the ratio of text increases, LD tends to be better, which indicates that the text line feature"
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+                                            "html": "<table><tr><td>Text Content Ratio</td><td>MS-SSIM ↑</td><td>LD ↓</td><td>AD ↓</td></tr><tr><td>Low</td><td>0.54</td><td>10.74</td><td>0.35</td></tr><tr><td>Middle</td><td>0.51</td><td>8.27</td><td>0.35</td></tr><tr><td>High</td><td>0.44</td><td>6.34</td><td>0.44</td></tr></table>",
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+                                    "content": "5. Conclusion"
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+                                    "content": "In this work, we explored how to optimize the rectification of distorted document images from the perspective of readability. We propose an efficient method for warped document rectification by focusing on the foreground and text-line regions of the original deformed image separately via cross-attention. We use this method to improve the readability of the rectified document images from the perspective of global and local features. The effectiveness of this feature fusion mechanism is proved by experiments on two public benchmark datasets. In the future, since the current training dataset lacks text-line annotations, we will further explore how to obtain more accurate text-line annotations. This is also a limitation of our method. Besides, for extracting distorted image features, we will also explore more fine-grained and multi-attribute feature fusion methods to improve image quality and OCR performance."
+                                }
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+                                    "content": "Acknowledgement: We thank the reviewers for their thoughtful and constructive comments. This work was supported by the National Key R&D Program of China (2022ZD0116002), Natural Science Foundation of China (62276075, 61872113), Science and Technology Planning Project of Shenzhen (JCYJ20190806112210067), Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, China (2022B1212010005) and China Mobile Information Technology Co., Ltd. It was also supported by Music Style Transfer for Anxiety Therapy (P0042962), Artificial Intelligence and Robotics (AIR) Group: Artificial Intelligence Art (P0033738)."
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+                                            "type": "text",
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+                                        }
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+                                            "content": "[46] Ziyi Yang, Yuwei Fang, Chenguang Zhu, Reid Pryzant, Dongdong Chen, Yu Shi, Yichong Xu, Yao Qian, Mei Gao, Yi-Ling Chen, Liyang Lu, Yujia Xie, Robert Gmyr, Noel C. F. Codella, Naoyuki Kanda, Bin Xiao, Yuanxun Lu, Takuya Yoshioka, Michael Zeng, and Xuedong Huang. i-code: An integrative and composable multimodal learning framework. ArXiv, abs/2205.01818, 2022."
+                                        }
+                                    ]
+                                }
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+                                        }
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+                                        }
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+                            ],
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+                        },
+                        {
+                            "bbox": [
+                                307,
+                                365,
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22
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+                                            "type": "text",
+                                            "content": "[51] Linchao Zhu and Yi Yang. Actbert: Learning global-local video-text representations. 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8743-8752, 2020."
+                                        }
+                                    ]
+                                }
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diff --git a/2023/Foreground-Background Distribution Modeling Transformer for Visual Object Tracking/82259de0-16cb-4749-9fd9-5e68b3f9f014_content_list.json b/2023/Foreground-Background Distribution Modeling Transformer for Visual Object Tracking/82259de0-16cb-4749-9fd9-5e68b3f9f014_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2c9ccb8719f2e053485e292be9090c386d6e1e9c
--- /dev/null
+++ b/2023/Foreground-Background Distribution Modeling Transformer for Visual Object Tracking/82259de0-16cb-4749-9fd9-5e68b3f9f014_content_list.json	
@@ -0,0 +1,1522 @@
+[
+    {
+        "type": "text",
+        "text": "Foreground-Background Distribution Modeling Transformer for Visual Object Tracking",
+        "text_level": 1,
+        "bbox": [
+            86,
+            128,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Dawei Yang $^{1,\\ast}$ , Jianfeng He $^{1,\\ast}$ , Yinchao Ma $^{1}$ , Qianjin Yu $^{1}$ , Tianzhu Zhang $^{1,\\dagger}$",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup> University of Science and Technology of China",
+        "bbox": [
+            292,
+            237,
+            679,
+            255
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{yangdawei, hejf, imyc, sa21010105}@mail.ustc.edu.cn, {tzzhang}@ustc.edu.cn",
+        "bbox": [
+            166,
+            258,
+            803,
+            272
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            316,
+            313,
+            333
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Visual object tracking is a fundamental research topic with a broad range of applications. Benefiting from the rapid development of Transformer, pure Transformer trackers have achieved great progress. However, the feature learning of these Transformer-based trackers is easily disturbed by complex backgrounds. To address the above limitations, we propose a novel foreground-background distribution modeling transformer for visual object tracking (FBDMTrack), including a fore-background agent learning (FBAL) module and a distribution-aware attention  $(DA^{2})$  module in a unified transformer architecture. The proposed F-BDMTrack enjoys several merits. First, the proposed FBAL module can effectively mine fore-background information with designed fore-background agents. Second, the  $DA^{2}$  module can suppress the incorrect interaction between foreground and background by modeling fore-background distribution similarities. Finally, F-BDMTrack can extract discriminative features under ever-changing tracking scenarios for more accurate target state estimation. Extensive experiments show that our F-BDMTrack outperforms previous state-of-the-art trackers on eight tracking benchmarks.",
+        "bbox": [
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+            340,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            679,
+            209,
+            695
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Visual object tracking(VOT) aims to locate the position of a class-agnostic target in a video sequence given the target in the first frame, which is a fundamental and essential research topic in computer vision. Due to its great application potential (such as video surveillance [9, 49, 9], antiUAV tracking [64, 25, 29], and automatic driving [47, 41, 15]), VOT has attracted substantial attention and has been developed tremendously [56, 31, 17]. However, as a video processing task, visual object tracking still faces various challenges including deformation, motion blur, and susceptibility to background interference [51, 27, 24].",
+        "bbox": [
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+            700,
+            470,
+            867
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/8b0c4878c763fe80d25faa7b43fa15e8fd3898c97e6673997a5835cf329edc5b.jpg",
+        "image_caption": [
+            "Figure 1. Response map comparisons among different attention mechanisms. Both (a) and (b) have incorrect similarities between the target (green square patch) and background distractor (yellow triangle patch) due to similar appearance, causing messy response map. Differently, in our proposed  $\\mathrm{DA}^2$  module (c), the similarity between target and distractor is suppressed, since the similarity is obtained according to their fore-background distributions."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            521,
+            316,
+            870,
+            435
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To deal with the above challenges, numerous approaches have been proposed [23, 2, 3, 59, 10, 5, 62]. These methods can be generally divided into three main paradigms, including CNN-based [8, 52, 58, 35, 3, 13], hybrid CNN-Transformer [7, 59, 36, 50, 42], and pure Transformer trackers [5, 62, 32, 57]. CNN-based trackers first extract features from the template and search region separately through a shared convolutional neural network (CNN), and then the target state is estimated by calculating cross-correlation [2, 58, 52] between features in template and search regions, or learning a discriminative correlation filter [12, 3, 13]. With the successful development of transformer in the computer vision field, an increasing number of hybrid CNN-Transformer trackers [7, 59, 42] have been proposed. These trackers also leverage CNN to extract features separately, but adopt transformer to realize the feature interaction between the template and search region, which can alleviate the loss of discriminative foreground information. However, for the above two paradigm trackers, there is no interaction between the template and the search region when extracting features. These target-unaware feature extraction ways have limited target-background discriminative power, especially when the target category is not seen",
+        "bbox": [
+            496,
+            553,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Equal Contribution",
+        "bbox": [
+            94,
+            875,
+            207,
+            887
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding Author",
+        "bbox": [
+            96,
+            887,
+            223,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "10117",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "in the training dataset. To this end, pure Transformer trackers [5, 62, 32, 57] are proposed to build interaction between template and search region along with the feature extraction. Thanks to the strong representation and interaction capability of ViT/SwinT variants [14, 38, 55], pure Transformer trackers have achieved remarkable improvements.",
+        "bbox": [
+            75,
+            90,
+            470,
+            181
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Despite the success of the above pure Transformer trackers, the feature learning of these methods are easily disturbed by complex backgrounds due to insufficient consideration of fore-background relationship. To make pure Transformer architectures more suitable for discriminative feature learning in visual object tracking, there are two core points that need to be considered. (1) Fore-background information mining. Previous methods [5, 22, 21] usually mine fore-background information from the template according to the given bounding box (bbox). However, the tracking target can be continuously changing, making it difficult to learn target discriminative features for current search region, if only guided by fore-background information of the template. Therefore, it is necessary to propose a effective way to mine fore-background information for both template and search region. (2) Target-aware feature interaction. Most of popular Transformer trackers [62, 10, 57] adopt the plain attention mechanism to build interaction between template and search region. Since attention scores are obtained by appearance similarity, the template features will mistakenly aggregate background information and further affect features of search region during feature interaction, resulting messy response map (Figure 1 (a)). Although some methods [22, 42] introduce additional target embeddings to enhance the target information, they could still be disturbed by distractors, making features of the search region have limited target discriminative power. And the response map is also unsatisfactory (Figure 1 (b)). Therefore, it is urgent to design a new attention mechanism to achieve better target-aware feature interaction.",
+        "bbox": [
+            75,
+            185,
+            472,
+            638
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Motivated by the above discussion, we propose a novel Foreground-Background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which consists of a fore-background agent learning (FBAL) module and a distribution-aware attention  $(\\mathrm{DA}^2)$  module in a unified transformer architecture. In the fore-background agent learning module, we aim to mine foreground and background information from both the template and the search region. Specifically, we initialize a set of fore-background agents. And fore-background agents for the template (search region) are obtained by aggregating foreground and background information in the template (search region), which can be used to guide the subsequent feature interaction. In the distribution-aware attention module, it is proposed to realize target-aware feature interaction. Specifically, we calculate the similarity scores between each patch feature and the fore-background agents, which can",
+        "bbox": [
+            75,
+            643,
+            472,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "be regarded as fore-background distributions for each patch feature. Then we can obtain the attention score by compute the similarity between their distributions, which are later used for feature aggregation. As shown in Figure 1 (c), foreground patches and background patches could have different fore-background distributions even though they have similar appearance. Thus, we can aggregate more useful information and learn more discriminative features.",
+        "bbox": [
+            496,
+            90,
+            890,
+            210
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main contributions of this work are summarized as follows. (1) We develop a novel Foreground-background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which can extract features with high target discriminative power under ever-changing tracking scenarios. (2) The proposed FBAL module can effectively mine foreground information for both template and search region with designed foreground agents. And the proposed  $\\mathrm{DA}^2$  module can effectively suppress the interaction between foreground and background, which helps learn more discriminative features for visual tracking. (3) Extensive experimental results on eight benchmarks show that our method attains state-of-the-art performance, verifying the superiority of our F-BDMTrack.",
+        "bbox": [
+            496,
+            213,
+            892,
+            426
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            438,
+            640,
+            454
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Visual object tracking (VOT). Current popular trackers can be divided into CNN-based trackers [8, 2, 58, 35, 40, 12, 3, 13], hybrid CNN-Transformer trackers [59, 7, 50, 53, 42], and pure Transformer trackers [62, 5, 36, 32, 57] according to the network architecture. CNN-based trackers commonly learn features of template and search region via share-weighted convolutional neural networks (CNN), and the interaction between template and search region is realized by cross correlation [2, 58, 35] or correlation filter [12, 3, 13]. However, due to the lack of global perception and the simple interaction strategy, some target-background discriminative information may be lost, restricting the development of CNN-based trackers. Recently, Vision Transformer brings a new solution to visual tracking. Hybrid CNN-Transformer trackers reserve the extraction of features with CNNs and utilize attention mechanisms to establish global dependencies between features. Typically, STARK [59] utilizes the Transformer to aggregate spatial-temporal cues for target location. Moreover, ToMP [42] uses a Transformer-based architecture to encode a long-term target representation to localize the target. Nevertheless, these Hybrid CNN-Transformer trackers still extract features of template and search region separately, which causes extracted features to be unaware of the tracking target. To alleviate this limitation, pure Transformer-based trackers [62, 5, 57] are proposed. For example, OSTrack [62] and SimTrack [5] unify the feature extraction and the feature relation modeling in Vision Transformer [14]. They achieve superior performance, proving the potential of pure Transformer",
+        "bbox": [
+            496,
+            462,
+            892,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "10118",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "architectures in visual tracking. However, these trackers [62, 5] aggregate features according to appearance similarities through plain attention mechanisms. Without considering fore-background relationship for the template and search region, target features may mistakenly aggregate background noise in the search region. Differently, in our work, we propose the distribution aware attention module to aggregate features according to their fore-background distribution similarities, which can effectively suppress incorrect interaction between foreground and background.",
+        "bbox": [
+            75,
+            90,
+            472,
+            242
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Fore-background exploitation in visual object tracking. There are several tracking methods [21, 42, 5, 46, 19] actively exploring ways to mine fore-background information for robust tracking. STMTrack [21] leverages foreground-background masks derived by bounding boxes of template sequences to highlight target representations. And ToMP [42] is proposed to learn foreground embeddings from a set of template sequences, which can be used to enhance target features of the template and assist in target state estimation. However, the above methods for exploiting fore-background generally use fixed foreground embedding for template images, ignoring the fact that tracking target can be continuously changing. Besides, they do not analyze the fore-background information of the search region. Furthermo, RTS [46] utilizes an additional segmentation network to provide more precise object masks, leading to better performance improvements. And SNLT [19] adopts additional natural language labels to help extract better target embeddings for distinguishing foreground and background. These methods utilize additional network components and labels to mine fore-background information, which affects the independence of the network architecture. In contrast, our method is proposed to fully mine fore-background information from templates and search regions, and utilizes them to improve the discriminative ability without attaching additional models.",
+        "bbox": [
+            75,
+            246,
+            472,
+            638
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Visual transformer and attention variants. Nowadays, Transformer has been rapidly applied in the computer vision due to its global interaction ability. Typically, ViT [14] realizes image classification by learning global representations of patches through attention mechanisms. To optimize efficiency, Swin Transformer [38] restricts attention computation in non-overlapping local windows and exchange information between windows through a sliding operation. Thanks to these effective designs, Vision Transformers have been applied to visual tracking, such as MixFormer [10] (using CvT [55]) and OSTrack [62] (using ViT [14]). Further, some trackers improve attention mechanisms to better adapt to visual tracking task. AiATrack [22] proposes an attention in attention module to model the relationship of attention scores, which can improve the quality of attention maps. And SparseTT [20] proposes sparse attention to focus the most relevant information in the",
+        "bbox": [
+            75,
+            643,
+            472,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "search region. However, these methods still calculate attention scores with appearance similarities, which will inevitably disturbed by similar distractors. Differently, we propose a novel foreground-background distribution modeling tracker, which can accurately discriminate target features by perceiving the distribution of fore-background.",
+        "bbox": [
+            496,
+            90,
+            890,
+            183
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            189,
+            591,
+            204
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce our proposed foreground-background distribution modeling transformer for visual tracking (F-BDMTrack). The architecture is in Figure 2.",
+        "bbox": [
+            496,
+            208,
+            890,
+            253
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            500,
+            263,
+            609,
+            277
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Figure 2, our proposed tracker consists of  $L$  stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA $^2$ ) module. Given a pair of images including template image  $\\mathbf{z} \\in \\mathbb{R}^{3 \\times H_z \\times W_z}$  and search region image  $\\mathbf{x} \\in \\mathbb{R}^{H_x \\times W_x \\times 3}$ , we first split and flatten them to obtain the patch sequence of template  $\\mathbf{z}_p \\in \\mathbb{R}^{N_z \\times (3 \\cdot p^2)}$  and search region  $\\mathbf{x}_p \\in \\mathbb{R}^{N_x \\times (3 \\cdot p^2)}$ , where  $(p, p)$  is the patch resolution, and  $N_z = (H_z W_z) / p^2$ ,  $N_x = (H_x W_x) / p^2$  are the number of patches for template and search region respectively. Similar to plain vision transformers [14], these patch sequences are mapped into  $C$  dimensions by a linear projection, and learnable position embeddings are added to obtain template token embeddings  $\\mathbf{H}_z^0 \\in \\mathbb{R}^{N_z \\times C}$  and search region token embeddings  $\\mathbf{H}_x^0 \\in \\mathbb{R}^{N_x \\times C}$ . Then,  $\\mathbf{H}_z^0$  and  $\\mathbf{H}_x^0$  are concatenated as the input  $(\\mathbf{H}_{zx}^0 = [\\mathbf{H}_z^0; \\mathbf{H}_x^0])$  to the fore-background distribution modeling transformer block. In this transformer block, we intergraded two modules (the FBAL module and the DA $^2$  module) to help learn discriminative features for both search region and template (We will give a detailed introduction about how these two modules work in our proposed transformer block below). Here, we denote  $\\mathbf{H}_{zx}^l = [\\mathbf{H}_z^l; \\mathbf{H}_x^l]$  as token embeddings output from the  $l^{th}$  transformer block. Eventually, we reshape search region token features  $\\mathbf{H}_x^L$  from the last block, and send them into a box prediction head to estimate the target state.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Fore-background Agent Learning Module",
+        "text_level": 1,
+        "bbox": [
+            500,
+            724,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given token features  $[\\mathbf{H}_z^{l - 1};\\mathbf{H}_x^{l - 1}]$  from  $(l - 1)^{th}$  transformer block, we normalize them with Layer Normalization [1] to obtain  $\\hat{\\mathbf{H}}_z^l = \\mathrm{LN}(\\mathbf{H}_z^{l - 1})$  , and  $\\hat{\\mathbf{H}}_x^l = \\mathrm{LN}(\\mathbf{H}_x^{l - 1})$  These normalized features  $\\widehat{\\mathbf{H}}_z^l$  and  $\\widehat{\\mathbf{H}}_x^l$  are sent into the forebackground agent learning (FBAL) module to produce forebackground agent (FB-agent) for the template and search region. Specifically,  $\\widehat{\\mathbf{H}}_z^l$  and  $\\widehat{\\mathbf{H}}_x^l$  are first projected into  $C_e$  dimensions ( $C_e\\ll C$ ) to obtain  $\\mathbf{E}_z^l$  and  $\\mathbf{E}_x^l$  , which can reduce computational overhead. Then, we design a pseudo bounding box (bbox) generation strategy to obtain",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "10119",
+        "bbox": [
+            480,
+            944,
+            519,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/b5e34be09d99338cddf2d35d8f7ab74f930727f3534ea609c1c95fa99a9b8361.jpg",
+        "image_caption": [
+            "Figure 2. The architecture of our F-BDMTrack consists of  $L$  stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA $^2$ ) module. The FBAL module is used to produce fore-background agents for the template (template FB-agents) and the search region (search FB-agents). And the DA $^2$  module is used for feature aggregation by modeling the fore-background distribution. The output from the  $l^{th}$  transformer block is denoted as  $[\\mathbf{H}_z^l; \\mathbf{H}_x^l]$ . Finally, we reshape search region token features  $\\mathbf{H}_x^L$  from the last block, and send them into a box prediction head to estimate the target state. For more details, please refer to the text."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            138,
+            88,
+            401,
+            393
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/11d9f8f96451a51802e9ae045c1bec32f004141a23e7a9816f2dba65a34d6653.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            401,
+            97,
+            828,
+            391
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the bounding box for the template and search region. Finally, we can obtain fore-background agents (FB-agents) for the template and search region by leveraging a FB-agent decoder to aggregate information within or outside the bounding box. The pseudo bbox generation strategy and the FB-agent decoder are introduced as follows.",
+        "bbox": [
+            75,
+            500,
+            468,
+            589
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Pseudo bbox generation. Since the ground-truth bbox for the template is given in advance, the difficulty is how to generate pseudo bbox for the search region. To this end, we establish coarse matches between template and search region, which can help generate pseudo bbox. Specifically, given  $\\mathbf{E}_z^l$  and  $\\mathbf{E}_x^l$ , we first reshape them into  $\\widehat{\\mathbf{E}}_z^l \\in \\mathbb{R}^{\\frac{H_z}{p} \\times \\frac{W_z}{p} \\times C_e}$  and  $\\widehat{\\mathbf{E}}_x^l \\in \\mathbb{R}^{\\frac{H_x}{p} \\times \\frac{W_x}{p} \\times C_e}$ . Then the target feature  $\\widehat{\\mathbf{E}}_t^l \\in \\mathbb{R}^{h_t \\times w_t \\times C_e}$  is cropped according to the ground-truth bbox  $b_z$ , i.e.  $\\widehat{\\mathbf{E}}_t^l = \\mathrm{PrPool}(\\widehat{\\mathbf{E}}_z^l, b_z)$ . Here,  $\\mathrm{PrPool}(\\cdot, \\cdot)$  denotes the Precise RoI Pooling [28]. Next, we conduct similarity matching to compute the matching point in  $\\widehat{\\mathbf{E}}_x^l$  for each point in  $\\widehat{\\mathbf{E}}_t^l$  according to the probability  $D^l$ . Formally,",
+        "bbox": [
+            75,
+            590,
+            468,
+            780
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {D} ^ {l} (k, i) = \\frac {\\exp \\left(<   \\widehat {\\mathbf {E}} _ {t} ^ {l} (k) , \\widehat {\\mathbf {E}} _ {x} ^ {l} (i) >\\right)}{\\sum_ {i = 1} ^ {N _ {x}} \\exp \\left(<   \\widehat {\\mathbf {E}} _ {t} ^ {l} (k) , \\widehat {\\mathbf {E}} _ {x} ^ {l} (i) >\\right)},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            789,
+            416,
+            829
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}\\right) = \\sum_ {i = 1} ^ {N _ {x}} s \\cdot \\left(x _ {i}, y _ {i}\\right) \\cdot \\boldsymbol {D} ^ {l} (k, i), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            140,
+            830,
+            468,
+            858
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $k = (x_{k},y_{k})$  and  $i = (x_{i},y_{i})$  enumerate all 2D positions in  $\\widehat{\\mathbf{E}}_t^l$  and  $\\widehat{\\mathbf{E}}_x^l$ , respectively.  $s$  is the stride of the back",
+        "bbox": [
+            76,
+            868,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "bone network. In this way, we can obtain a set of matching points  $\\{(\\hat{x}_k^l,\\hat{y}_k^l)\\}_{k = 1}^K$ , where  $K = h_{t}w_{t}$ . Finally, we derive the pseudo bbox  $\\hat{b}_x^l = (\\hat{x}^l,\\hat{y}^l,\\hat{w}^l,\\hat{h}^l)$  with the mean and the standard deviation of all keypoints inspired by Rep-Point [60]. Please refer to the Supplementary Material for details to obtain  $\\hat{b}_x^l$ . During training, we use ground-truth bbox  $b_{x}$  of the search region as supervision for more accurate pseudo bbox generation. In specific, a set of keypoints  $\\{(x_j,y_j)\\}_{j = 1}^K$  are uniformly sampled within the bbox  $b_{x}$ . And the point loss  $\\mathcal{L}_{point}$  measured by Chamfer distance [18, 61] is introduced to constrain the predicted points  $\\{(\\hat{x}_k^l,\\hat{y}_k^l)\\}_{k = 1}^K$  scattered in the bbox  $b_{x}$ .",
+        "bbox": [
+            496,
+            500,
+            890,
+            684
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {p o i n t}} ^ {l} = \\frac {1}{K} \\sum_ {\\substack {j = 1 \\\\ K}} ^ {K} \\min _ {k} \\left\\| \\left(x _ {j}, y _ {j}\\right) - \\left(\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}\\right) \\right\\| _ {2} \\tag{2} \\\\ + \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\min _ {j} \\left\\| (x _ {j}, y _ {j}) - (\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}) \\right\\| _ {2}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            521,
+            690,
+            890,
+            752
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Besides, we introduce  $\\ell_1$  loss and generalized IoU loss [48] to directly constrain predicted pseudo bbox. And the final pseudo bbox generation loss is as follows.",
+        "bbox": [
+            496,
+            760,
+            890,
+            805
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {b o x} ^ {l} = \\mathcal {L} _ {p o i n t} ^ {l} + \\mathcal {L} _ {1} ^ {l} \\left(b _ {x}, \\hat {b} _ {x} ^ {l}\\right) + \\mathcal {L} _ {g i o u} ^ {l} \\left(b _ {x}, \\hat {b} _ {x} ^ {l}\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            544,
+            811,
+            890,
+            833
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "FB-agent decoder. After obtaining the bbox for the template  $b_{z}$  and search region  $\\hat{b}_x^l$ , we aim to aggregate information within or outside the bbox. To this end, we first initialize a set of prototypical foreground agents  $\\mathbf{F}_a^l \\in \\mathbb{R}^{N_a \\times C_e}$",
+        "bbox": [
+            496,
+            839,
+            890,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "10120",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "and prototypical background agents  $\\mathbf{B}_a^l\\in \\mathbb{R}^{N_a\\times C_e}$ . Inspired by CrossViT [6], we use masked cross-attention (M-CA) mechanism to aggregate information of  $\\mathbf{E}_z^l$  in the bbox  $b_{z}$ , and produce template foreground agents. Formally,",
+        "bbox": [
+            75,
+            89,
+            468,
+            151
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {A} _ {t t} = \\operatorname {S o f t m a x} \\left(\\left(\\mathbf {F} _ {a} ^ {l} \\mathbf {W} _ {Q}\\right) \\left(\\mathbf {E} _ {z} ^ {l} \\mathbf {W} _ {K}\\right) ^ {\\top} + \\mathbf {M} _ {z} ^ {l}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            116,
+            162,
+            468,
+            189
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} _ {z} ^ {l} = \\mathrm {M - C A} (\\mathbf {F} _ {a} ^ {l}, \\mathbf {E} _ {z} ^ {l}, \\mathbf {M} _ {z} ^ {l}) = \\mathbf {A} _ {t t} (\\mathbf {E} _ {z} ^ {l} \\mathbf {W} _ {V}),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            124,
+            185,
+            419,
+            203
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_Q, \\mathbf{W}_K,$  and  $\\mathbf{W}_V$  are linear projections. And the element in template foreground mask  $\\mathbf{M}_z^l$  is set to 0, if the corresponding position of this element is in the bbox  $b_{z}$ . Otherwise, it will be set to  $-\\infty$ . Similarly, for the template background mask  $\\overline{\\mathbf{M}}_z^l$ , the element is set to 0, if the corresponding position of this element is outside the bbox  $b_{z}$ . Otherwise, it will be set to  $-\\infty$ . And we can obtain template background agents  $\\mathbf{B}_z^l = \\mathrm{M - CA}(\\mathbf{B}_a^l, \\mathbf{E}_z^l, \\overline{\\mathbf{M}}_z^l)$ .",
+        "bbox": [
+            75,
+            214,
+            468,
+            340
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For search region features  $\\mathbf{E}_x^l$ , we can generate  $\\mathbf{M}_x^l$  and  $\\overline{\\mathbf{M}}_x^l$  according to the pseudo bbox  $\\hat{b}_x^l$ . Since  $\\hat{b}_x^l$  is not precise enough, we leverage updated template FB-agents  $[\\mathbf{F}_z^l; \\mathbf{B}_z^l]$  to serve as queries, which provides clearer fore-background priors than prototypical agents  $[\\mathbf{F}_a^l; \\mathbf{B}_a^l]$ . Formally,",
+        "bbox": [
+            75,
+            340,
+            468,
+            421
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} _ {x} ^ {l} = \\operatorname {M - C A} \\left(\\mathbf {F} _ {z} ^ {l}, \\mathbf {E} _ {x} ^ {l}, \\mathbf {M} _ {x} ^ {l}\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            176,
+            433,
+            367,
+            450
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {B} _ {x} ^ {l} = \\operatorname {M - C A} \\left(\\mathbf {B} _ {z} ^ {l}, \\mathbf {E} _ {x} ^ {l}, \\overline {{\\mathbf {M}}} _ {x} ^ {l}\\right). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            178,
+            449,
+            468,
+            474
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, we obtain template FB-agents  $[\\mathbf{F}_z^l;\\mathbf{B}_z^l]$ , and search region FB-agents  $[\\mathbf{F}_x^l;\\mathbf{B}_x^l]$  at the  $l^{th}$  block.",
+        "bbox": [
+            75,
+            488,
+            468,
+            520
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Distribution-aware Attention Module",
+        "text_level": 1,
+        "bbox": [
+            76,
+            531,
+            400,
+            545
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After obtaining template FB-agents  $[\\mathbf{F}_z^l;\\mathbf{B}_z^l]$  and search region FB-agents  $[\\mathbf{F}_x^l;\\mathbf{B}_x^l]$ , we begin to model the foreground distribution for each image token. Specifically, given token features  $[\\mathbf{H}_z^{l - 1};\\mathbf{H}_x^{l - 1}]$ , the initial query, key and value arise from these token features. Formally,",
+        "bbox": [
+            75,
+            554,
+            468,
+            630
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathbf {Q}} _ {z x} ^ {l} = \\left[ \\widetilde {\\mathbf {Q}} _ {z} ^ {l}; \\widetilde {\\mathbf {Q}} _ {x} ^ {l} \\right] = \\mathrm {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {Q} ^ {l},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            120,
+            642,
+            419,
+            662
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathbf {K}} _ {z x} ^ {l} = \\left[ \\widetilde {\\mathbf {K}} _ {z} ^ {l}; \\widetilde {\\mathbf {K}} _ {x} ^ {l} \\right] = \\operatorname {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {K} ^ {l}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            124,
+            664,
+            468,
+            684
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} _ {z x} ^ {l} = \\left[ \\mathbf {V} _ {z} ^ {l}; \\mathbf {V} _ {x} ^ {l} \\right] = \\mathrm {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {V} ^ {l},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            125,
+            686,
+            419,
+            705
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where LN denotes the layer normalization,  $\\mathbf{W}_K^l\\in$ $\\mathbb{R}^{C\\times C},\\mathbf{W}_Q^l\\in \\mathbb{R}^{C\\times C},\\mathbf{W}_V^l\\in \\mathbb{R}^{C\\times C}$  are linear projections. As can be seen, existing plain attention mechanism [14] generate queries and keys simply based on appearance features, which will easily have incorrect high attention score for regions with similar distractors. Differently, we use the fore-background distribution to serve as queries and keys instead of appearance features. To this end, we first project  $[\\mathbf{F}_z^l;\\mathbf{B}_z^l]$  and  $[\\mathbf{F}_x^l;\\mathbf{B}_x^l]$  into  $C$  dimensions. By calculating the similarity between each token and these fore-background agents, we can model the fore-background distribution of this token. Here, we take the",
+        "bbox": [
+            75,
+            719,
+            468,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "fore-background distribution of initial query token as updated queries  $\\mathbf{Q}_{zx}^{l} = [\\mathbf{Q}_{z}^{l};\\mathbf{Q}_{x}^{l}]$ . Formally,",
+        "bbox": [
+            498,
+            90,
+            890,
+            122
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbf {Q} _ {z} ^ {l} = \\widetilde {\\mathbf {Q}} _ {z} ^ {l} \\left[ \\mathbf {F} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l}; \\mathbf {B} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l} \\right] ^ {\\top}, \\tag {7} \\\\ \\mathbf {Q} _ {x} ^ {l} = \\tilde {\\mathbf {Q}} _ {x} ^ {l} \\left[ \\mathbf {F} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l}, \\mathbf {B} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l} \\right] ^ {\\top}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
+            133,
+            890,
+            175
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{W}_z^l, \\mathbf{W}_x^l \\in \\mathbb{R}^{C_e \\times C}$  are linear projections. Similarly, we can obtain updated keys  $\\mathbf{K}_{zx}^l = [\\mathbf{K}_z^l, \\mathbf{K}_x^l]$ .",
+        "bbox": [
+            498,
+            186,
+            890,
+            220
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbf {K} _ {z} ^ {l} = \\widetilde {\\mathbf {K}} _ {z} ^ {l} \\left[ \\mathbf {F} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l}; \\mathbf {B} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l} \\right] ^ {\\top}, \\tag {8} \\\\ \\mathbf {K} _ {x} ^ {l} = \\tilde {\\mathbf {K}} _ {x} ^ {l} \\left[ \\mathbf {F} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l}; \\mathbf {B} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l} \\right] ^ {\\top}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            232,
+            890,
+            273
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With updated queries and keys, the proposed distribution-aware attention module can achieve fore-background aware feature interaction. The output of the  $l^{th}$  transformer blocks  $\\mathbf{H}_{zx}^l$  can be formulated as follows,",
+        "bbox": [
+            498,
+            285,
+            890,
+            347
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathbf {H}} _ {z x} ^ {l} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {z x} ^ {l} \\left(\\mathbf {K} _ {z x} ^ {l}\\right) ^ {\\top}}{\\sqrt {C}}\\right) \\mathbf {V} _ {z x} ^ {l} + \\mathbf {H} _ {z x} ^ {l - 1} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            540,
+            358,
+            890,
+            393
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {H} _ {z x} ^ {l} = \\left[ \\mathbf {H} _ {z} ^ {l}; \\mathbf {H} _ {x} ^ {l} \\right] = \\operatorname {M L P} \\left(\\operatorname {L N} \\left(\\widetilde {\\mathbf {H}} _ {z x} ^ {l}\\right)\\right) + \\widetilde {\\mathbf {H}} _ {z x} ^ {l},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            542,
+            393,
+            848,
+            414
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where MLP denotes the multi-layer perception. The output token features  $\\mathbf{H}_{zx}^{l}$  will be sent into next transformer blocks. Eventually, token features are processed  $L$  times via our proposed fore-background distribution modeling transformer block, and we can obtain final token features  $\\mathbf{H}_{zx}^{L}$ .",
+        "bbox": [
+            500,
+            426,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Box Prediction Head and Objective Function",
+        "text_level": 1,
+        "bbox": [
+            500,
+            513,
+            879,
+            529
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 2, search region token features  $\\mathbf{H}_x^L$  are reshaped and fed into a box prediction head for target state estimation. Here, the box prediction head is inspired from OSTrack [62]. We use the weighted focal loss [33] as classification loss  $\\mathcal{L}_{cls}$ . Besides, we adopt  $\\ell_1$  loss  $\\mathcal{L}_1$  and generalized IoU loss [48]  $\\mathcal{L}_{giou}$  to supervise bounding box regression. More details about the box prediction head and losses can be referred to OSTrack [62]. As we introduced before, there are point loss and box loss for pseudo bbox generation at each block. In summary, the overall objective function is formulated as follows.",
+        "bbox": [
+            498,
+            537,
+            890,
+            702
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c l s} + \\lambda_ {1} \\mathcal {L} _ {1} + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u} + \\lambda_ {b o x} \\sum_ {l = 1} ^ {L} \\mathcal {L} _ {b o x} ^ {l}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            516,
+            714,
+            890,
+            753
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_1, \\lambda_{giou}$  and  $\\lambda_{box}$  are scalars to balance these losses.",
+        "bbox": [
+            500,
+            768,
+            888,
+            782
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            799,
+            630,
+            815
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first introduce implementation details. Then, we show experimental results on eight benchmarks. Finally, we conduct a series of ablation studies to verify the effectiveness of each component. Please refer to the Supplementary Material for more details and results.",
+        "bbox": [
+            498,
+            825,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "10121",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/1122a931e5752d35be156e420678db3e584d86e92b65fc4abb23af6fb55d07ce.jpg",
+        "table_caption": [
+            "Table 1. Comparisons with state-of-the-art trackers on GOT-10k, TNL2K, LaSOT,  $\\mathrm{LaSOT}_{ext}$ , and TrackingNet. The best three results are shown in red, blue and green fonts."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">GOT-10k [26]</td><td colspan=\"2\">TNL2K [54]</td><td colspan=\"3\">LaSOT [17]</td><td colspan=\"3\">\\( LaSOT_{ext} \\) [16]</td><td colspan=\"3\">TrackingNet [45]</td></tr><tr><td>AO</td><td>\\( SR_{0.5} \\)</td><td>\\( SR_{0.75} \\)</td><td>AUC</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td></tr><tr><td>SiamFC[2]</td><td>34.8</td><td>35.3</td><td>9.8</td><td>29.5</td><td>28.6</td><td>33.6</td><td>42.0</td><td>33.9</td><td>23.0</td><td>31.1</td><td>26.9</td><td>57.1</td><td>66.3</td><td>53.3</td></tr><tr><td>ECO [11]</td><td>31.6</td><td>30.9</td><td>11.1</td><td>32.6</td><td>31.7</td><td>32.4</td><td>33.8</td><td>30.1</td><td>22.0</td><td>25.2</td><td>24.0</td><td>55.4</td><td>61.8</td><td>49.2</td></tr><tr><td>SiamRPN++ [34]</td><td>51.7</td><td>61.6</td><td>32.5</td><td>41.3</td><td>41.2</td><td>49.6</td><td>56.9</td><td>49.1</td><td>34.0</td><td>41.6</td><td>39.6</td><td>73.3</td><td>80.0</td><td>69.4</td></tr><tr><td>SiamCAR [23]</td><td>56.9</td><td>67.0</td><td>41.5</td><td>35.5</td><td>38.4</td><td>50.7</td><td>60.0</td><td>51.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SiamFC++ [58]</td><td>59.5</td><td>69.5</td><td>47.9</td><td>38.6</td><td>36.9</td><td>54.4</td><td>62.3</td><td>54.7</td><td>-</td><td>-</td><td>-</td><td>75.4</td><td>80.0</td><td>70.5</td></tr><tr><td>D3S [39]</td><td>59.7</td><td>67.6</td><td>46.2</td><td>38.8</td><td>39.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>72.8</td><td>76.8</td><td>66.4</td></tr><tr><td>Ocean [63]</td><td>61.1</td><td>72.1</td><td>47.3</td><td>38.4</td><td>37.7</td><td>56.0</td><td>65.1</td><td>56.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiMP-50 [3]</td><td>61.1</td><td>71.7</td><td>49.2</td><td>44.7</td><td>43.4</td><td>56.9</td><td>65.0</td><td>56.7</td><td>39.2</td><td>47.6</td><td>45.1</td><td>74.0</td><td>80.1</td><td>68.7</td></tr><tr><td>PrDiMP-50 [13]</td><td>63.4</td><td>73.8</td><td>54.3</td><td>47.0</td><td>45.9</td><td>59.8</td><td>68.8</td><td>60.8</td><td>-</td><td>-</td><td>-</td><td>75.8</td><td>81.6</td><td>70.4</td></tr><tr><td>KeepTrack[43]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>67.1</td><td>77.2</td><td>70.2</td><td>48.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ToMP-101 [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>68.5</td><td>79.2</td><td>73.5</td><td>45.9</td><td>-</td><td>-</td><td>81.5</td><td>86.4</td><td>78.9</td></tr><tr><td>KYS [4]</td><td>63.6</td><td>75.1</td><td>51.5</td><td>44.9</td><td>43.5</td><td>55.4</td><td>63.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>74.0</td><td>80.0</td><td>68.8</td></tr><tr><td>STMTrack [21]</td><td>64.2</td><td>73.7</td><td>57.5</td><td>-</td><td>-</td><td>60.6</td><td>63.3</td><td>69.3</td><td>-</td><td>-</td><td>-</td><td>80.3</td><td>85.1</td><td>76.7</td></tr><tr><td>TransT [7]</td><td>67.1</td><td>76.8</td><td>60.9</td><td>50.7</td><td>51.7</td><td>64.9</td><td>69.0</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>81.4</td><td>86.7</td><td>80.3</td></tr><tr><td>STARK-ST101 [59]</td><td>68.8</td><td>78.1</td><td>64.1</td><td>-</td><td>-</td><td>67.1</td><td>77.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.0</td><td>86.9</td><td>-</td></tr><tr><td>CSWinTT [50]</td><td>69.4</td><td>78.9</td><td>65.4</td><td>-</td><td>-</td><td>66.2</td><td>75.2</td><td>70.9</td><td>-</td><td>-</td><td>-</td><td>81.9</td><td>86.7</td><td>79.5</td></tr><tr><td>SimTrack-B/16 [5]</td><td>68.6</td><td>78.9</td><td>62.4</td><td>54.8</td><td>53.8</td><td>69.3</td><td>78.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.3</td><td>86.5</td><td>-</td></tr><tr><td>SwinTrack-B [36]</td><td>69.4</td><td>78.0</td><td>64.3</td><td>-</td><td>-</td><td>69.6</td><td>78.6</td><td>74.1</td><td>47.6</td><td>58.2</td><td>54.1</td><td>82.5</td><td>87.0</td><td>80.4</td></tr><tr><td>AiATrack [22]</td><td>69.6</td><td>80.0</td><td>63.2</td><td>-</td><td>-</td><td>69.0</td><td>79.4</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>82.7</td><td>87.8</td><td>80.4</td></tr><tr><td>SBT-L [57]</td><td>70.4</td><td>80.8</td><td>64.7</td><td>-</td><td>-</td><td>66.7</td><td>77.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MixFormer [10]</td><td>70.7</td><td>80.0</td><td>67.8</td><td>-</td><td>-</td><td>69.2</td><td>78.7</td><td>74.7</td><td>-</td><td>-</td><td>-</td><td>83.1</td><td>88.1</td><td>81.6</td></tr><tr><td>RTS [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>69.7</td><td>76.2</td><td>73.7</td><td>-</td><td>-</td><td>-</td><td>81.6</td><td>86.0</td><td>79.4</td></tr><tr><td>OSTrack-256 [62]</td><td>71.0</td><td>80.4</td><td>68.2</td><td>54.3</td><td>-</td><td>69.1</td><td>78.7</td><td>75.2</td><td>47.4</td><td>57.3</td><td>53.3</td><td>83.1</td><td>87.8</td><td>82.0</td></tr><tr><td>OSTrack-384 [62]</td><td>73.7</td><td>83.2</td><td>70.8</td><td>55.9</td><td>-</td><td>71.1</td><td>81.1</td><td>77.6</td><td>50.5</td><td>61.3</td><td>57.6</td><td>83.9</td><td>88.5</td><td>83.2</td></tr><tr><td>F-BDMTrack-256</td><td>72.7</td><td>82.0</td><td>69.9</td><td>56.4</td><td>56.5</td><td>69.9</td><td>79.4</td><td>75.8</td><td>47.9</td><td>57.9</td><td>54.0</td><td>83.7</td><td>88.3</td><td>82.6</td></tr><tr><td>F-BDMTrack-384</td><td>75.4</td><td>84.3</td><td>72.9</td><td>57.8</td><td>59.4</td><td>72.0</td><td>81.5</td><td>77.7</td><td>50.8</td><td>61.3</td><td>57.8</td><td>84.5</td><td>89.0</td><td>84.0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
+            500,
+            294,
+            517
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Network details. We present two variants of our tracker, F-BDMTrack-256 and F-BDMTrack-384. Similar to OSTrack [62], we crop the template image and search region image which are  $2^{2}$  and  $4^{2}$  times of the target box area respectively. The F-BDMTrack-256 resizes search region to a resolution of  $256 \\times 256$  and template to a resolution of  $128 \\times 128$  as input. The F-BDMTrack-384 resizes search region to a resolution of  $384 \\times 384$  and template to  $192 \\times 192$ . These images are split into a set of patches, where the resolution of each patch is  $16 \\times 16$ . These patches are flattened and projected into  $C = 768$  channels to serve as the input of F-BDMTrack. The channel of  $\\mathbf{E}_z^l$  in the FBAL module is set to  $C_e = 256$ . We leverage the Precise RoI Pooling [28] operation to crop features according to the target bounding box, and obtain the target feature with shape  $(h_t, w_t) = (4, 4)$ . The number of foreground agents and background agents are both set to  $N_a = 4$ . And our F-BDMTrack consists of  $L = 12$  fore-background distribution modeling transformer blocks.",
+        "bbox": [
+            75,
+            531,
+            470,
+            818
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training details. We train our model on the training splits of LaSOT [17], GOT-10K [26], COCO2017 [37], and TrackingNet [45], which is a similar training setting to OSTrack [62]. Common data augmentations including horizontal flip and brightness jittering are applied in the training",
+        "bbox": [
+            75,
+            824,
+            468,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "process. We train our F-BDMTrack by the AdamW optimizer with the weight decay  $10^{-4}$ . The learning rates start from  $4 \\times 10^{-5}$  for the backbone including the FBAL module and the  $\\mathrm{DA}^2$  module, and  $4 \\times 10^{-4}$  for the box prediction head. Our model is trained on four NVIDIA RTX 3090 GPUs, each GPU holds 32 image pairs, resulting in a total batch size of 128. The total epochs are set to 300 with 60k samples per epoch and we decrease the learning rate by a factor of 10 after 240 epochs. The weights of training losses are set to  $\\lambda_1 = 5.0$ ,  $\\lambda_{giou} = 2.0$ , and  $\\lambda_{box} = 1.0$ .",
+        "bbox": [
+            496,
+            501,
+            890,
+            654
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Results and State-of-the-art Comparisons",
+        "text_level": 1,
+        "bbox": [
+            498,
+            664,
+            854,
+            681
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "GOT-10k. GOT-10k [26] is a large-scale dataset containing over 10k videos for training and 180 for testing. It forbids trackers to use external datasets for training. We follow its policy and retrain our model. The results are reported in Table 1. Our tracker has a satisfactory improvement in all metrics. Specifically, F-BDMTrack-256 improves by  $1.7\\%$  in success rate  $(\\mathrm{SR}_{0.75})$  compared with OSTrack-256. And F-BDMTrack-384 gives an improved new record  $75.4\\%$  in AO, indicating the effectiveness of foreground and background distribution modeling to extract discriminative features, resulting in more accurate state estimation.",
+        "bbox": [
+            496,
+            688,
+            890,
+            853
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "TNL2K. TNL2K [54] is a recently published dataset containing 700 video sequences for testing. In Table 1, F-BDMTrack-256 gains by  $2.1\\%$  AUC over OTrack-256 and",
+        "bbox": [
+            498,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "10122",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4050300e869287b708a1dfb0b6dd2ad85e7acdb10747cce7dd341f6c945d7f0f.jpg",
+        "table_caption": [
+            "Table 2. Comparisons with state-of-the-art trackers on NFS, OTB100 and UAV123 datasets in terms of overall AUC score. The best three results are shown in red, blue and green fonts."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>SiamFC [2]</td><td>Ocean [63]</td><td>ATOM [12]</td><td>DiMP-50 [3]</td><td>PrDiMP-50 [13]</td><td>TransT [7]</td><td>OSTrack-256 [62]</td><td>OSTrack-384 [62]</td><td>F-BDMTrack-256</td><td>F-BDMTrack-384</td></tr><tr><td>NFS [30]</td><td>37.7</td><td>49.4</td><td>58.3</td><td>61.8</td><td>63.5</td><td>65.3</td><td>64.7</td><td>66.5</td><td>66.0</td><td>67.3</td></tr><tr><td>OTB100 [56]</td><td>61.2</td><td>68.4</td><td>66.3</td><td>68.4</td><td>69.6</td><td>69.4</td><td>68.1</td><td>69.2</td><td>69.5</td><td>69.9</td></tr><tr><td>UAV123 [44]</td><td>46.8</td><td>57.4</td><td>63.2</td><td>64.3</td><td>68.0</td><td>68.1</td><td>68.3</td><td>70.7</td><td>69.0</td><td>70.9</td></tr></table>",
+        "bbox": [
+            78,
+            114,
+            890,
+            155
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/eda4bebd02dc50da6fa2dc31d754e3e43828ff0e01d9cfd2f672ad936460fddc.jpg",
+        "image_caption": [
+            "Figure 3. Visualizations of fore-background agent activation maps for the template and search region."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            93,
+            170,
+            460,
+            345
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6d121b099648546f05122ee6f0c5afa03bcc0a2d917a8fe9a13d6ad1afaafcf3.jpg",
+        "table_caption": [
+            "Table 3. Effectiveness of each component on the LaSOT"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>FBAL</td><td>DA2</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>[A]</td><td>X</td><td>X</td><td>68.5</td><td>77.8</td><td>74.2</td></tr><tr><td>[B]</td><td>✓</td><td>X</td><td>68.8</td><td>78.1</td><td>74.6</td></tr><tr><td>[C]</td><td>X</td><td>✓</td><td>69.4</td><td>78.7</td><td>75.4</td></tr><tr><td>[D]</td><td>✓</td><td>✓</td><td>69.9</td><td>79.4</td><td>75.8</td></tr></table>",
+        "bbox": [
+            127,
+            401,
+            419,
+            472
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "even performances better than larger models (OTrack-384). When also leveraging a large model (F-BDMTrack-384), we can further improve the AUC score to  $57.8\\%$ .",
+        "bbox": [
+            75,
+            491,
+            468,
+            535
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "LaSOT. LaSOT [17] is a densely annotated large-scale dataset containing a total of 1400 long-term video sequences, of which the test set contains 280 video sequences. This is a challenging tracking dataset. As shown in Table 1, F-BDMTrack-256 outperforms OSTrack-256 by  $0.8\\%$  AUC. Further, F-BDMTrack-384 achieves the best performance of  $72.0\\%$  AUC. Our tracker does not add additional timing strategies [22, 10, 59] in this long-term tracking task, but can still obtain performance improvement with the aid of fore-background distribution modeling design, which demonstrates that our approach can fundamentally mitigate complex scenarios and distractors.",
+        "bbox": [
+            75,
+            536,
+            468,
+            717
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf{LaSOT}_{ext}$ . The recent  $\\mathrm{LaSOT}_{ext}$  [16] is an extended subset of LaSOT, containing 150 additional new sequences. This dataset has many similar distractors, making it difficult for tracking. And our F-BDMTrack can achieve competitive or even better performance. In specific, F-BDMTrack-256 achieves superior results, outperforming OSTrack-256 by  $0.5\\%$  AUC. And F-BDMTrack-356 obtains a much higher performance with  $50.8\\%$  AUC.",
+        "bbox": [
+            75,
+            718,
+            468,
+            839
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Trackingnet. Trackingnet [45] provides over 30k video sequences, which are sampled from Youtube to cover target categories and scenes of real-world. It provides 511 testing video sequences without publicly available annotation,",
+        "bbox": [
+            75,
+            839,
+            468,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/33543c545be77996d0f4266823100860dce4438828c407b85617cc66d39775f7.jpg",
+        "image_caption": [
+            "Figure 4. Visualization of pseudo bboxes using the pseudo-bbox generation strategy at all blocks."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "so results reported in Table 1 are obtained from the online evaluation server. As can be seen, our F-BDMTrack-384 achieves  $84.5\\%$  AUC and sets a new state of the art.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "NFS. Videos in Need for Speed(NFS) [30] are captured from a high frame rate camera, which contains fast motions and distractors. We report results on its commonly used version NFS30. As shown in Table 2, F-BDMTrack-256 achieves  $66.0\\%$  AUC, outperforming OSTrack-256 by  $1.3\\%$ . And F-BDMTrack-384 achieves best results (67.3% AUC score) as expected, demonstrating the superior competitiveness of our tracker in the presence of interferer-challenged benchmark.",
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+    {
+        "type": "text",
+        "text": "OTB100. OTB [56] is a pioneering visual tracking benchmark. It has been noticed that this benchmark is approaching saturation [53, 59, 43]. In Table 2, two versions of our tracker both achieve promising AUC scores (69.5 and 69.9). UAV123. UAV123 [44] provides 123 unmanned aerial vehicle(UAV) sequences, including different scale sizes of UAV in real-world dynamic scenarios. As shown in Table 2, our tracker achieves the best AUC score  $(70.9\\%)$  and is suitable for UAV tracking scenarios.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To validate the effectiveness of each component, we perform a detailed ablation study on LaSOT [17]. The following experiments use F-BDMTrack-256 as the base model.",
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+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of key components in our F-BDMTrack. Our tracker consists of two key components, including a fore-background agent learning (FBAL) module and a distribution-aware attention  $(\\mathrm{DA}^2)$  module. Here, we explore the exact impact of these modules. The model [A] is the baseline, which means that we directly use plain attention mechanism without using the FBAL and the  $\\mathrm{DA}^2$  module. For the model [B], we add the FBAL module, and",
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "10123",
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+    {
+        "type": "table",
+        "img_path": "images/31f9a7838edf367635a2bb05d8689b3514fd7a9b698763a98f03c56f9804d748.jpg",
+        "table_caption": [
+            "Table 4. Effects with different numbers of prototypical FB-agents."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Na</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>1</td><td>69.3</td><td>78.8</td><td>75.5</td></tr><tr><td>2</td><td>69.6</td><td>79.1</td><td>75.6</td></tr><tr><td>4</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>8</td><td>69.3</td><td>78.9</td><td>75.2</td></tr><tr><td>16</td><td>69.0</td><td>78.6</td><td>75.1</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/52a0e314772f4a65416ac8b5784ed7cc399321cbd21d27990adde06dcd69f45f.jpg",
+        "table_caption": [
+            "Table 5. Effects of the pseudo bbox generation at different blocks."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>blocks</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>None</td><td>69.0</td><td>78.5</td><td>75.0</td></tr><tr><td>10-12</td><td>69.5</td><td>79.1</td><td>75.5</td></tr><tr><td>6-12</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>4-12</td><td>69.8</td><td>79.2</td><td>75.8</td></tr><tr><td>1-12</td><td>69.2</td><td>78.7</td><td>75.2</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "adopt plain attention mechanism to replace our designed  $\\mathrm{DA}^2$  module. The plain attention mechanism does not require fore-background agents (FB-agents) produced by our FBAL module. Thus, the model [B] is used to validate the impacts of pseudo bbox generation loss  $\\mathcal{L}_{box}^{l}$  introduced in the FBAL module. As shown in Table 3, the performance of model [B] gains by  $0.3\\%$  compared to the model [A], demonstrating that the pseudo bbox loss has some positive effects to constrain foreground features interact with features in foreground regions. For the model [C], we adopt the  $\\mathrm{DA}^2$  module for feature interaction, and FB-agents are obtained by pooling features within or outside the bounding box for the template and search region. As can be seen, the performance of model [C] gains by  $0.9\\%$  compared to the model [A], which demonstrates that the proposed  $\\mathrm{DA}^2$  module can significantly help learn discriminative features even if FB-agents are not good enough. When adding the FBAL module for better FB-agents generation, the performance of model [D] gains by  $0.5\\%$  compared to the model [C], showing the superiority of proposed FBAL module.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Study on the number of prototypical FB-agents in the FBAL module. Here, we explore the effects about different numbers of prototypical FB-agents. As shown in Table 4, our tracker achieves the optimal result (69.9% AUC score) when  $N_{a} = 4$ . A small number of prototypical FB-agents cannot fully model the fore-background distribution, leading to decreased performance. Meanwhile, more prototypical FB-agents will introduce useless noise, which is harmful for feature interaction. Besides, without explicit constraints to guide foreground and background agent learning, an excessive number of agents are unable to focus on their respective discriminative information better. A more effective FB-agent learning way can be explored in future work. Finally, we show the fore-background agent activation maps for the template and search region in Figure 3. It can be seen that these FB-agents generated by our FBAL module can focus on the foreground and background well.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Study on the pseudo bbox generation strategy at differ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/2ce3904d0c46982c4e1ffbba90609ede7306bd04aabc06ed2c92eefdfed08873.jpg",
+        "image_caption": [
+            "Figure 5. Response maps of the template central feature to all search region features. It can be seen that although the template target has similar appearance with the background distractor in the search region, their fore-background distributions are different."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ent blocks. High-quality pseudo bbox is more conducive to the FB-agent learning for the search region. However, as shown in Figure 4, the pseudo-bboxes in shallow blocks tend to have a large bias, which is harmful to learn effective FB-agents. We conduct a detailed experiment to find which blocks are optimal for using pseudo bbox generation strategy. As shown in Table 5, our tracker achieves the best results when we leverage the pseudo bbox generation strategy at the  $6^{th}$  to  $12^{th}$  ('6-12') transformer blocks. This is because the last few blocks provide more reliable pseudo bbox to guide fore-background agent learning.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Comparisons between the plain attention mechanism and our  $\\mathbf{DA}^2$  mechanism. Here, we visualize response maps of the plain attention mechanism and our  $\\mathrm{DA}^2$  mechanism in Figure 5. As we can see, the plain attention mechanism easily focus on complex backgrounds or distractors. This is because attention scores are obtained based on appearance similarities, while targets usually have similar appearance with distractors, resulting in incorrect response map. Differently, our proposed  $\\mathrm{DA}^2$  mechanism discriminates features from the perspective of fore-background distributions instead of appearance similarities, which can effectively suppress the response of the template to background distractors in the search region, and strengthen the response of the template to the foreground target in the search region. Finally, based on the proposed distribution",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "10124",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "aware attention mechanism, our tracker can achieve superior performance on all eight tracking benchmarks.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a novel foreground-background distribution modeling transformer for visual tracking, including a FBAL module and a  $\\mathrm{DA}^2$  module. With these two elegant designs, our proposed tracker can extract features with high target discriminative power under ever-changing tracking scenarios, which is essential for accurate target state estimation. Extensive experiments on eight tracking benchmarks verify the superiority of our proposed tracker.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Acknowledgement",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), and National Defense Basic Scientific Research Program of China (Grant JCKY2020903B002).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            419
+        ],
+        "page_idx": 8
+    },
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+            "[51] Janani Thangavel, Thanikasalam Kokul, Amirthalingam Ramanan, and Subha Fernando. Transformers in single object tracking: An experimental survey. arXiv preprint arXiv:2302.11867, 2023. 1",
+            "[52] Paul Voigtlaender, Jonathon Luiten, Philip H. S. Torr, and Bastian Leibe. Siam R-CNN: Visual tracking by redetection. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2020. 1",
+            "[53] Ning Wang, Wengang Zhou, Jie Wang, and Houqiang Li. Transformer meets tracker: Exploiting temporal context for robust visual tracking. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pages 1571-1580, 2021. 2, 7",
+            "[54] Xiao Wang, Xiujun Shu, Zhipeng Zhang, Bo Jiang, Yaowei Wang, Yonghong Tian, and Feng Wu. Towards more flexible and accurate object tracking with natural language: Algorithms and benchmark. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pages 13763-13773, 2021. 6",
+            "[55] Haiping Wu, Bin Xiao, Noel Codella, Mengchen Liu, Xiyang Dai, Lu Yuan, and Lei Zhang. Cvt: Introducing convolutions to vision transformers. In Proceedings of the IEEE International Conference on Computer Vision, pages 22-31, 2021. 2, 3",
+            "[56] Yi Wu, Jongwoo Lim, and Ming Hsuan Yang. Object tracking benchmark. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015. 1, 7",
+            "[57] Fei Xie, Chunyu Wang, Guangting Wang, Yue Cao, Wankou Yang, and Wenjun Zeng. Correlation-aware deep tracking. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8751-8760, 2022. 1, 2, 6"
+        ],
+        "bbox": [
+            78,
+            90,
+            470,
+            898
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[58] Yinda Xu, Zeyu Wang, Zuoxin Li, Ye Yuan, and Gang Yu. SiamFC++: Towards robust and accurate visual tracking with target estimation guidelines. In Proceedings of the AAAI Conference on Artificial Intelligence, 2020. 1, 2, 6",
+            "[59] Bin Yan, Houwen Peng, Jianlong Fu, Dong Wang, and Huchuan Lu. Learning spatio-temporal transformer for visual tracking. In Proceedings of the IEEE International Conference on Computer Vision, pages 10448-10457, 2021. 1, 2, 6, 7",
+            "[60] Ze Yang, Shaohui Liu, Han Hu, Liwei Wang, and Stephen Lin. Repoints: Point set representation for object detection. In Proceedings of the IEEE International Conference on Computer Vision, pages 9657-9666, 2019. 4",
+            "[61] Ze Yang, Yinghao Xu, Han Xue, Zheng Zhang, Raquel Urtasun, Liwei Wang, Stephen Lin, and Han Hu. Dense repoints: Representing visual objects with dense point sets. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXI 16, pages 227-244. Springer, 2020. 4",
+            "[62] Botao Ye, Hong Chang, Bingpeng Ma, and Shiguang Shan. Joint feature learning and relation modeling for tracking: A one-stream framework. Proceedings of the European Conference on Computer Vision, 2022. 1, 2, 3, 5, 6, 7",
+            "[63] Zhipeng Zhang, Houwen Peng, Jianlong Fu, Bing Li, and Weiming Hu. Ocean: Object-aware anchor-free tracking. In Proceedings of the European Conference on Computer Vision, 2020. 6, 7",
+            "[64] Jie Zhao, Jingshu Zhang, Dongdong Li, and Dong Wang. Vision-based anti-uav detection and tracking. IEEE Transactions on Intelligent Transportation Systems, 23(12):25323-25334, 2022. 1"
+        ],
+        "bbox": [
+            501,
+            90,
+            890,
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+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "10127",
+        "bbox": [
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+            955
+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/Foreground-Background Distribution Modeling Transformer for Visual Object Tracking/82259de0-16cb-4749-9fd9-5e68b3f9f014_model.json b/2023/Foreground-Background Distribution Modeling Transformer for Visual Object Tracking/82259de0-16cb-4749-9fd9-5e68b3f9f014_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..e540067a3ade013f8bd5e596ab2c48d18b0d186a
--- /dev/null
+++ b/2023/Foreground-Background Distribution Modeling Transformer for Visual Object Tracking/82259de0-16cb-4749-9fd9-5e68b3f9f014_model.json	
@@ -0,0 +1,2224 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.088,
+                0.13,
+                0.885,
+                0.178
+            ],
+            "angle": 0,
+            "content": "Foreground-Background Distribution Modeling Transformer for Visual Object Tracking"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.189,
+                0.215,
+                0.788,
+                0.235
+            ],
+            "angle": 0,
+            "content": "Dawei Yang\\(^{1,\\ast}\\), Jianfeng He\\(^{1,\\ast}\\), Yinchao Ma\\(^{1}\\), Qianjin Yu\\(^{1}\\), Tianzhu Zhang\\(^{1,\\dagger}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.293,
+                0.238,
+                0.68,
+                0.256
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup> University of Science and Technology of China"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.168,
+                0.259,
+                0.804,
+                0.273
+            ],
+            "angle": 0,
+            "content": "{yangdawei, hejf, imyc, sa21010105}@mail.ustc.edu.cn, {tzzhang}@ustc.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.317,
+                0.314,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.342,
+                0.474,
+                0.661
+            ],
+            "angle": 0,
+            "content": "Visual object tracking is a fundamental research topic with a broad range of applications. Benefiting from the rapid development of Transformer, pure Transformer trackers have achieved great progress. However, the feature learning of these Transformer-based trackers is easily disturbed by complex backgrounds. To address the above limitations, we propose a novel foreground-background distribution modeling transformer for visual object tracking (FBDMTrack), including a fore-background agent learning (FBAL) module and a distribution-aware attention \\((DA^{2})\\) module in a unified transformer architecture. The proposed F-BDMTrack enjoys several merits. First, the proposed FBAL module can effectively mine fore-background information with designed fore-background agents. Second, the \\(DA^{2}\\) module can suppress the incorrect interaction between foreground and background by modeling fore-background distribution similarities. Finally, F-BDMTrack can extract discriminative features under ever-changing tracking scenarios for more accurate target state estimation. Extensive experiments show that our F-BDMTrack outperforms previous state-of-the-art trackers on eight tracking benchmarks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.68,
+                0.21,
+                0.696
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.701,
+                0.471,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Visual object tracking(VOT) aims to locate the position of a class-agnostic target in a video sequence given the target in the first frame, which is a fundamental and essential research topic in computer vision. Due to its great application potential (such as video surveillance [9, 49, 9], antiUAV tracking [64, 25, 29], and automatic driving [47, 41, 15]), VOT has attracted substantial attention and has been developed tremendously [56, 31, 17]. However, as a video processing task, visual object tracking still faces various challenges including deformation, motion blur, and susceptibility to background interference [51, 27, 24]."
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.317,
+                0.872,
+                0.436
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.439,
+                0.895,
+                0.537
+            ],
+            "angle": 0,
+            "content": "Figure 1. Response map comparisons among different attention mechanisms. Both (a) and (b) have incorrect similarities between the target (green square patch) and background distractor (yellow triangle patch) due to similar appearance, causing messy response map. Differently, in our proposed \\(\\mathrm{DA}^2\\) module (c), the similarity between target and distractor is suppressed, since the similarity is obtained according to their fore-background distributions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.554,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To deal with the above challenges, numerous approaches have been proposed [23, 2, 3, 59, 10, 5, 62]. These methods can be generally divided into three main paradigms, including CNN-based [8, 52, 58, 35, 3, 13], hybrid CNN-Transformer [7, 59, 36, 50, 42], and pure Transformer trackers [5, 62, 32, 57]. CNN-based trackers first extract features from the template and search region separately through a shared convolutional neural network (CNN), and then the target state is estimated by calculating cross-correlation [2, 58, 52] between features in template and search regions, or learning a discriminative correlation filter [12, 3, 13]. With the successful development of transformer in the computer vision field, an increasing number of hybrid CNN-Transformer trackers [7, 59, 42] have been proposed. These trackers also leverage CNN to extract features separately, but adopt transformer to realize the feature interaction between the template and search region, which can alleviate the loss of discriminative foreground information. However, for the above two paradigm trackers, there is no interaction between the template and the search region when extracting features. These target-unaware feature extraction ways have limited target-background discriminative power, especially when the target category is not seen"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.875,
+                0.208,
+                0.888
+            ],
+            "angle": 0,
+            "content": "*Equal Contribution"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.098,
+                0.888,
+                0.225,
+                0.9
+            ],
+            "angle": 0,
+            "content": "† Corresponding Author"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.875,
+                0.225,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "10117"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.182
+            ],
+            "angle": 0,
+            "content": "in the training dataset. To this end, pure Transformer trackers [5, 62, 32, 57] are proposed to build interaction between template and search region along with the feature extraction. Thanks to the strong representation and interaction capability of ViT/SwinT variants [14, 38, 55], pure Transformer trackers have achieved remarkable improvements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.186,
+                0.473,
+                0.64
+            ],
+            "angle": 0,
+            "content": "Despite the success of the above pure Transformer trackers, the feature learning of these methods are easily disturbed by complex backgrounds due to insufficient consideration of fore-background relationship. To make pure Transformer architectures more suitable for discriminative feature learning in visual object tracking, there are two core points that need to be considered. (1) Fore-background information mining. Previous methods [5, 22, 21] usually mine fore-background information from the template according to the given bounding box (bbox). However, the tracking target can be continuously changing, making it difficult to learn target discriminative features for current search region, if only guided by fore-background information of the template. Therefore, it is necessary to propose a effective way to mine fore-background information for both template and search region. (2) Target-aware feature interaction. Most of popular Transformer trackers [62, 10, 57] adopt the plain attention mechanism to build interaction between template and search region. Since attention scores are obtained by appearance similarity, the template features will mistakenly aggregate background information and further affect features of search region during feature interaction, resulting messy response map (Figure 1 (a)). Although some methods [22, 42] introduce additional target embeddings to enhance the target information, they could still be disturbed by distractors, making features of the search region have limited target discriminative power. And the response map is also unsatisfactory (Figure 1 (b)). Therefore, it is urgent to design a new attention mechanism to achieve better target-aware feature interaction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Motivated by the above discussion, we propose a novel Foreground-Background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which consists of a fore-background agent learning (FBAL) module and a distribution-aware attention \\((\\mathrm{DA}^2)\\) module in a unified transformer architecture. In the fore-background agent learning module, we aim to mine foreground and background information from both the template and the search region. Specifically, we initialize a set of fore-background agents. And fore-background agents for the template (search region) are obtained by aggregating foreground and background information in the template (search region), which can be used to guide the subsequent feature interaction. In the distribution-aware attention module, it is proposed to realize target-aware feature interaction. Specifically, we calculate the similarity scores between each patch feature and the fore-background agents, which can"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "be regarded as fore-background distributions for each patch feature. Then we can obtain the attention score by compute the similarity between their distributions, which are later used for feature aggregation. As shown in Figure 1 (c), foreground patches and background patches could have different fore-background distributions even though they have similar appearance. Thus, we can aggregate more useful information and learn more discriminative features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.214,
+                0.893,
+                0.427
+            ],
+            "angle": 0,
+            "content": "The main contributions of this work are summarized as follows. (1) We develop a novel Foreground-background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which can extract features with high target discriminative power under ever-changing tracking scenarios. (2) The proposed FBAL module can effectively mine foreground information for both template and search region with designed foreground agents. And the proposed \\(\\mathrm{DA}^2\\) module can effectively suppress the interaction between foreground and background, which helps learn more discriminative features for visual tracking. (3) Extensive experimental results on eight benchmarks show that our method attains state-of-the-art performance, verifying the superiority of our F-BDMTrack."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.439,
+                0.642,
+                0.455
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.463,
+                0.893,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Visual object tracking (VOT). Current popular trackers can be divided into CNN-based trackers [8, 2, 58, 35, 40, 12, 3, 13], hybrid CNN-Transformer trackers [59, 7, 50, 53, 42], and pure Transformer trackers [62, 5, 36, 32, 57] according to the network architecture. CNN-based trackers commonly learn features of template and search region via share-weighted convolutional neural networks (CNN), and the interaction between template and search region is realized by cross correlation [2, 58, 35] or correlation filter [12, 3, 13]. However, due to the lack of global perception and the simple interaction strategy, some target-background discriminative information may be lost, restricting the development of CNN-based trackers. Recently, Vision Transformer brings a new solution to visual tracking. Hybrid CNN-Transformer trackers reserve the extraction of features with CNNs and utilize attention mechanisms to establish global dependencies between features. Typically, STARK [59] utilizes the Transformer to aggregate spatial-temporal cues for target location. Moreover, ToMP [42] uses a Transformer-based architecture to encode a long-term target representation to localize the target. Nevertheless, these Hybrid CNN-Transformer trackers still extract features of template and search region separately, which causes extracted features to be unaware of the tracking target. To alleviate this limitation, pure Transformer-based trackers [62, 5, 57] are proposed. For example, OSTrack [62] and SimTrack [5] unify the feature extraction and the feature relation modeling in Vision Transformer [14]. They achieve superior performance, proving the potential of pure Transformer"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10118"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.243
+            ],
+            "angle": 0,
+            "content": "architectures in visual tracking. However, these trackers [62, 5] aggregate features according to appearance similarities through plain attention mechanisms. Without considering fore-background relationship for the template and search region, target features may mistakenly aggregate background noise in the search region. Differently, in our work, we propose the distribution aware attention module to aggregate features according to their fore-background distribution similarities, which can effectively suppress incorrect interaction between foreground and background."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.247,
+                0.473,
+                0.64
+            ],
+            "angle": 0,
+            "content": "Fore-background exploitation in visual object tracking. There are several tracking methods [21, 42, 5, 46, 19] actively exploring ways to mine fore-background information for robust tracking. STMTrack [21] leverages foreground-background masks derived by bounding boxes of template sequences to highlight target representations. And ToMP [42] is proposed to learn foreground embeddings from a set of template sequences, which can be used to enhance target features of the template and assist in target state estimation. However, the above methods for exploiting fore-background generally use fixed foreground embedding for template images, ignoring the fact that tracking target can be continuously changing. Besides, they do not analyze the fore-background information of the search region. Furthermo, RTS [46] utilizes an additional segmentation network to provide more precise object masks, leading to better performance improvements. And SNLT [19] adopts additional natural language labels to help extract better target embeddings for distinguishing foreground and background. These methods utilize additional network components and labels to mine fore-background information, which affects the independence of the network architecture. In contrast, our method is proposed to fully mine fore-background information from templates and search regions, and utilizes them to improve the discriminative ability without attaching additional models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.473,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Visual transformer and attention variants. Nowadays, Transformer has been rapidly applied in the computer vision due to its global interaction ability. Typically, ViT [14] realizes image classification by learning global representations of patches through attention mechanisms. To optimize efficiency, Swin Transformer [38] restricts attention computation in non-overlapping local windows and exchange information between windows through a sliding operation. Thanks to these effective designs, Vision Transformers have been applied to visual tracking, such as MixFormer [10] (using CvT [55]) and OSTrack [62] (using ViT [14]). Further, some trackers improve attention mechanisms to better adapt to visual tracking task. AiATrack [22] proposes an attention in attention module to model the relationship of attention scores, which can improve the quality of attention maps. And SparseTT [20] proposes sparse attention to focus the most relevant information in the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.184
+            ],
+            "angle": 0,
+            "content": "search region. However, these methods still calculate attention scores with appearance similarities, which will inevitably disturbed by similar distractors. Differently, we propose a novel foreground-background distribution modeling tracker, which can accurately discriminate target features by perceiving the distribution of fore-background."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.19,
+                0.593,
+                0.205
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.209,
+                0.892,
+                0.254
+            ],
+            "angle": 0,
+            "content": "In this section, we introduce our proposed foreground-background distribution modeling transformer for visual tracking (F-BDMTrack). The architecture is in Figure 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.265,
+                0.611,
+                0.279
+            ],
+            "angle": 0,
+            "content": "3.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.288,
+                0.892,
+                0.715
+            ],
+            "angle": 0,
+            "content": "As illustrated in Figure 2, our proposed tracker consists of \\( L \\) stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA\\(^2\\)) module. Given a pair of images including template image \\( \\mathbf{z} \\in \\mathbb{R}^{3 \\times H_z \\times W_z} \\) and search region image \\( \\mathbf{x} \\in \\mathbb{R}^{H_x \\times W_x \\times 3} \\), we first split and flatten them to obtain the patch sequence of template \\( \\mathbf{z}_p \\in \\mathbb{R}^{N_z \\times (3 \\cdot p^2)} \\) and search region \\( \\mathbf{x}_p \\in \\mathbb{R}^{N_x \\times (3 \\cdot p^2)} \\), where \\( (p, p) \\) is the patch resolution, and \\( N_z = (H_z W_z) / p^2 \\), \\( N_x = (H_x W_x) / p^2 \\) are the number of patches for template and search region respectively. Similar to plain vision transformers [14], these patch sequences are mapped into \\( C \\) dimensions by a linear projection, and learnable position embeddings are added to obtain template token embeddings \\( \\mathbf{H}_z^0 \\in \\mathbb{R}^{N_z \\times C} \\) and search region token embeddings \\( \\mathbf{H}_x^0 \\in \\mathbb{R}^{N_x \\times C} \\). Then, \\( \\mathbf{H}_z^0 \\) and \\( \\mathbf{H}_x^0 \\) are concatenated as the input \\( (\\mathbf{H}_{zx}^0 = [\\mathbf{H}_z^0; \\mathbf{H}_x^0]) \\) to the fore-background distribution modeling transformer block. In this transformer block, we intergraded two modules (the FBAL module and the DA\\(^2\\) module) to help learn discriminative features for both search region and template (We will give a detailed introduction about how these two modules work in our proposed transformer block below). Here, we denote \\( \\mathbf{H}_{zx}^l = [\\mathbf{H}_z^l; \\mathbf{H}_x^l] \\) as token embeddings output from the \\( l^{th} \\) transformer block. Eventually, we reshape search region token features \\( \\mathbf{H}_x^L \\) from the last block, and send them into a box prediction head to estimate the target state."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.725,
+                0.859,
+                0.741
+            ],
+            "angle": 0,
+            "content": "3.2. Fore-background Agent Learning Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.747,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Given token features \\([\\mathbf{H}_z^{l - 1};\\mathbf{H}_x^{l - 1}]\\) from \\((l - 1)^{th}\\) transformer block, we normalize them with Layer Normalization [1] to obtain \\(\\hat{\\mathbf{H}}_z^l = \\mathrm{LN}(\\mathbf{H}_z^{l - 1})\\) , and \\(\\hat{\\mathbf{H}}_x^l = \\mathrm{LN}(\\mathbf{H}_x^{l - 1})\\) These normalized features \\(\\widehat{\\mathbf{H}}_z^l\\) and \\(\\widehat{\\mathbf{H}}_x^l\\) are sent into the forebackground agent learning (FBAL) module to produce forebackground agent (FB-agent) for the template and search region. Specifically, \\(\\widehat{\\mathbf{H}}_z^l\\) and \\(\\widehat{\\mathbf{H}}_x^l\\) are first projected into \\(C_e\\) dimensions (\\(C_e\\ll C\\)) to obtain \\(\\mathbf{E}_z^l\\) and \\(\\mathbf{E}_x^l\\) , which can reduce computational overhead. Then, we design a pseudo bounding box (bbox) generation strategy to obtain"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10119"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.139,
+                0.089,
+                0.403,
+                0.395
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.403,
+                0.098,
+                0.83,
+                0.392
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.399,
+                0.892,
+                0.482
+            ],
+            "angle": 0,
+            "content": "Figure 2. The architecture of our F-BDMTrack consists of \\( L \\) stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA\\(^2\\)) module. The FBAL module is used to produce fore-background agents for the template (template FB-agents) and the search region (search FB-agents). And the DA\\(^2\\) module is used for feature aggregation by modeling the fore-background distribution. The output from the \\( l^{th} \\) transformer block is denoted as \\( [\\mathbf{H}_z^l; \\mathbf{H}_x^l] \\). Finally, we reshape search region token features \\( \\mathbf{H}_x^L \\) from the last block, and send them into a box prediction head to estimate the target state. For more details, please refer to the text."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.5,
+                0.47,
+                0.59
+            ],
+            "angle": 0,
+            "content": "the bounding box for the template and search region. Finally, we can obtain fore-background agents (FB-agents) for the template and search region by leveraging a FB-agent decoder to aggregate information within or outside the bounding box. The pseudo bbox generation strategy and the FB-agent decoder are introduced as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.591,
+                0.47,
+                0.781
+            ],
+            "angle": 0,
+            "content": "Pseudo bbox generation. Since the ground-truth bbox for the template is given in advance, the difficulty is how to generate pseudo bbox for the search region. To this end, we establish coarse matches between template and search region, which can help generate pseudo bbox. Specifically, given \\(\\mathbf{E}_z^l\\) and \\(\\mathbf{E}_x^l\\), we first reshape them into \\(\\widehat{\\mathbf{E}}_z^l \\in \\mathbb{R}^{\\frac{H_z}{p} \\times \\frac{W_z}{p} \\times C_e}\\) and \\(\\widehat{\\mathbf{E}}_x^l \\in \\mathbb{R}^{\\frac{H_x}{p} \\times \\frac{W_x}{p} \\times C_e}\\). Then the target feature \\(\\widehat{\\mathbf{E}}_t^l \\in \\mathbb{R}^{h_t \\times w_t \\times C_e}\\) is cropped according to the ground-truth bbox \\(b_z\\), i.e. \\(\\widehat{\\mathbf{E}}_t^l = \\mathrm{PrPool}(\\widehat{\\mathbf{E}}_z^l, b_z)\\). Here, \\(\\mathrm{PrPool}(\\cdot, \\cdot)\\) denotes the Precise RoI Pooling [28]. Next, we conduct similarity matching to compute the matching point in \\(\\widehat{\\mathbf{E}}_x^l\\) for each point in \\(\\widehat{\\mathbf{E}}_t^l\\) according to the probability \\(D^l\\). Formally,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.128,
+                0.79,
+                0.418,
+                0.83
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {D} ^ {l} (k, i) = \\frac {\\exp \\left(<   \\widehat {\\mathbf {E}} _ {t} ^ {l} (k) , \\widehat {\\mathbf {E}} _ {x} ^ {l} (i) >\\right)}{\\sum_ {i = 1} ^ {N _ {x}} \\exp \\left(<   \\widehat {\\mathbf {E}} _ {t} ^ {l} (k) , \\widehat {\\mathbf {E}} _ {x} ^ {l} (i) >\\right)},\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.141,
+                0.832,
+                0.469,
+                0.859
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}\\right) = \\sum_ {i = 1} ^ {N _ {x}} s \\cdot \\left(x _ {i}, y _ {i}\\right) \\cdot \\boldsymbol {D} ^ {l} (k, i), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.869,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\( k = (x_{k},y_{k}) \\) and \\( i = (x_{i},y_{i}) \\) enumerate all 2D positions in \\( \\widehat{\\mathbf{E}}_t^l \\) and \\( \\widehat{\\mathbf{E}}_x^l \\), respectively. \\( s \\) is the stride of the back"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.5,
+                0.892,
+                0.685
+            ],
+            "angle": 0,
+            "content": "bone network. In this way, we can obtain a set of matching points \\(\\{(\\hat{x}_k^l,\\hat{y}_k^l)\\}_{k = 1}^K\\), where \\(K = h_{t}w_{t}\\). Finally, we derive the pseudo bbox \\(\\hat{b}_x^l = (\\hat{x}^l,\\hat{y}^l,\\hat{w}^l,\\hat{h}^l)\\) with the mean and the standard deviation of all keypoints inspired by Rep-Point [60]. Please refer to the Supplementary Material for details to obtain \\(\\hat{b}_x^l\\). During training, we use ground-truth bbox \\(b_{x}\\) of the search region as supervision for more accurate pseudo bbox generation. In specific, a set of keypoints \\(\\{(x_j,y_j)\\}_{j = 1}^K\\) are uniformly sampled within the bbox \\(b_{x}\\). And the point loss \\(\\mathcal{L}_{point}\\) measured by Chamfer distance [18, 61] is introduced to constrain the predicted points \\(\\{(\\hat{x}_k^l,\\hat{y}_k^l)\\}_{k = 1}^K\\) scattered in the bbox \\(b_{x}\\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.522,
+                0.691,
+                0.892,
+                0.753
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {p o i n t}} ^ {l} = \\frac {1}{K} \\sum_ {\\substack {j = 1 \\\\ K}} ^ {K} \\min _ {k} \\left\\| \\left(x _ {j}, y _ {j}\\right) - \\left(\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}\\right) \\right\\| _ {2} \\tag{2} \\\\ + \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\min _ {j} \\left\\| (x _ {j}, y _ {j}) - (\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}) \\right\\| _ {2}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.761,
+                0.892,
+                0.806
+            ],
+            "angle": 0,
+            "content": "Besides, we introduce \\(\\ell_1\\) loss and generalized IoU loss [48] to directly constrain predicted pseudo bbox. And the final pseudo bbox generation loss is as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.545,
+                0.813,
+                0.891,
+                0.834
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {b o x} ^ {l} = \\mathcal {L} _ {p o i n t} ^ {l} + \\mathcal {L} _ {1} ^ {l} \\left(b _ {x}, \\hat {b} _ {x} ^ {l}\\right) + \\mathcal {L} _ {g i o u} ^ {l} \\left(b _ {x}, \\hat {b} _ {x} ^ {l}\\right). \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "FB-agent decoder. After obtaining the bbox for the template \\(b_{z}\\) and search region \\(\\hat{b}_x^l\\), we aim to aggregate information within or outside the bbox. To this end, we first initialize a set of prototypical foreground agents \\(\\mathbf{F}_a^l \\in \\mathbb{R}^{N_a \\times C_e}\\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10120"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.09,
+                0.47,
+                0.152
+            ],
+            "angle": 0,
+            "content": "and prototypical background agents \\(\\mathbf{B}_a^l\\in \\mathbb{R}^{N_a\\times C_e}\\). Inspired by CrossViT [6], we use masked cross-attention (M-CA) mechanism to aggregate information of \\(\\mathbf{E}_z^l\\) in the bbox \\(b_{z}\\), and produce template foreground agents. Formally,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.117,
+                0.164,
+                0.47,
+                0.19
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {A} _ {t t} = \\operatorname {S o f t m a x} \\left(\\left(\\mathbf {F} _ {a} ^ {l} \\mathbf {W} _ {Q}\\right) \\left(\\mathbf {E} _ {z} ^ {l} \\mathbf {W} _ {K}\\right) ^ {\\top} + \\mathbf {M} _ {z} ^ {l}\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.125,
+                0.186,
+                0.42,
+                0.204
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {F} _ {z} ^ {l} = \\mathrm {M - C A} (\\mathbf {F} _ {a} ^ {l}, \\mathbf {E} _ {z} ^ {l}, \\mathbf {M} _ {z} ^ {l}) = \\mathbf {A} _ {t t} (\\mathbf {E} _ {z} ^ {l} \\mathbf {W} _ {V}),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.215,
+                0.469,
+                0.342
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{W}_Q, \\mathbf{W}_K,\\) and \\(\\mathbf{W}_V\\) are linear projections. And the element in template foreground mask \\(\\mathbf{M}_z^l\\) is set to 0, if the corresponding position of this element is in the bbox \\(b_{z}\\). Otherwise, it will be set to \\(-\\infty\\). Similarly, for the template background mask \\(\\overline{\\mathbf{M}}_z^l\\), the element is set to 0, if the corresponding position of this element is outside the bbox \\(b_{z}\\). Otherwise, it will be set to \\(-\\infty\\). And we can obtain template background agents \\(\\mathbf{B}_z^l = \\mathrm{M - CA}(\\mathbf{B}_a^l, \\mathbf{E}_z^l, \\overline{\\mathbf{M}}_z^l)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.342,
+                0.469,
+                0.422
+            ],
+            "angle": 0,
+            "content": "For search region features \\(\\mathbf{E}_x^l\\), we can generate \\(\\mathbf{M}_x^l\\) and \\(\\overline{\\mathbf{M}}_x^l\\) according to the pseudo bbox \\(\\hat{b}_x^l\\). Since \\(\\hat{b}_x^l\\) is not precise enough, we leverage updated template FB-agents \\([\\mathbf{F}_z^l; \\mathbf{B}_z^l]\\) to serve as queries, which provides clearer fore-background priors than prototypical agents \\([\\mathbf{F}_a^l; \\mathbf{B}_a^l]\\). Formally,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.177,
+                0.434,
+                0.369,
+                0.452
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {F} _ {x} ^ {l} = \\operatorname {M - C A} \\left(\\mathbf {F} _ {z} ^ {l}, \\mathbf {E} _ {x} ^ {l}, \\mathbf {M} _ {x} ^ {l}\\right),\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.179,
+                0.45,
+                0.469,
+                0.476
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {B} _ {x} ^ {l} = \\operatorname {M - C A} \\left(\\mathbf {B} _ {z} ^ {l}, \\mathbf {E} _ {x} ^ {l}, \\overline {{\\mathbf {M}}} _ {x} ^ {l}\\right). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.489,
+                0.469,
+                0.521
+            ],
+            "angle": 0,
+            "content": "Finally, we obtain template FB-agents \\([\\mathbf{F}_z^l;\\mathbf{B}_z^l]\\), and search region FB-agents \\([\\mathbf{F}_x^l;\\mathbf{B}_x^l]\\) at the \\(l^{th}\\) block."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.532,
+                0.401,
+                0.546
+            ],
+            "angle": 0,
+            "content": "3.3. Distribution-aware Attention Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.555,
+                0.469,
+                0.631
+            ],
+            "angle": 0,
+            "content": "After obtaining template FB-agents \\([\\mathbf{F}_z^l;\\mathbf{B}_z^l]\\) and search region FB-agents \\([\\mathbf{F}_x^l;\\mathbf{B}_x^l]\\), we begin to model the foreground distribution for each image token. Specifically, given token features \\([\\mathbf{H}_z^{l - 1};\\mathbf{H}_x^{l - 1}]\\), the initial query, key and value arise from these token features. Formally,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.122,
+                0.643,
+                0.42,
+                0.663
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\mathbf {Q}} _ {z x} ^ {l} = \\left[ \\widetilde {\\mathbf {Q}} _ {z} ^ {l}; \\widetilde {\\mathbf {Q}} _ {x} ^ {l} \\right] = \\mathrm {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {Q} ^ {l},\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.125,
+                0.665,
+                0.469,
+                0.685
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\mathbf {K}} _ {z x} ^ {l} = \\left[ \\widetilde {\\mathbf {K}} _ {z} ^ {l}; \\widetilde {\\mathbf {K}} _ {x} ^ {l} \\right] = \\operatorname {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {K} ^ {l}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.126,
+                0.687,
+                0.42,
+                0.706
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {V} _ {z x} ^ {l} = \\left[ \\mathbf {V} _ {z} ^ {l}; \\mathbf {V} _ {x} ^ {l} \\right] = \\mathrm {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {V} ^ {l},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "where LN denotes the layer normalization, \\(\\mathbf{W}_K^l\\in\\) \\(\\mathbb{R}^{C\\times C},\\mathbf{W}_Q^l\\in \\mathbb{R}^{C\\times C},\\mathbf{W}_V^l\\in \\mathbb{R}^{C\\times C}\\) are linear projections. As can be seen, existing plain attention mechanism [14] generate queries and keys simply based on appearance features, which will easily have incorrect high attention score for regions with similar distractors. Differently, we use the fore-background distribution to serve as queries and keys instead of appearance features. To this end, we first project \\([\\mathbf{F}_z^l;\\mathbf{B}_z^l]\\) and \\([\\mathbf{F}_x^l;\\mathbf{B}_x^l]\\) into \\(C\\) dimensions. By calculating the similarity between each token and these fore-background agents, we can model the fore-background distribution of this token. Here, we take the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.123
+            ],
+            "angle": 0,
+            "content": "fore-background distribution of initial query token as updated queries \\(\\mathbf{Q}_{zx}^{l} = [\\mathbf{Q}_{z}^{l};\\mathbf{Q}_{x}^{l}]\\). Formally,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.597,
+                0.134,
+                0.892,
+                0.176
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathbf {Q} _ {z} ^ {l} = \\widetilde {\\mathbf {Q}} _ {z} ^ {l} \\left[ \\mathbf {F} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l}; \\mathbf {B} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l} \\right] ^ {\\top}, \\tag {7} \\\\ \\mathbf {Q} _ {x} ^ {l} = \\tilde {\\mathbf {Q}} _ {x} ^ {l} \\left[ \\mathbf {F} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l}, \\mathbf {B} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l} \\right] ^ {\\top}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.188,
+                0.891,
+                0.221
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{W}_z^l, \\mathbf{W}_x^l \\in \\mathbb{R}^{C_e \\times C}\\) are linear projections. Similarly, we can obtain updated keys \\(\\mathbf{K}_{zx}^l = [\\mathbf{K}_z^l, \\mathbf{K}_x^l]\\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.596,
+                0.233,
+                0.891,
+                0.274
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathbf {K} _ {z} ^ {l} = \\widetilde {\\mathbf {K}} _ {z} ^ {l} \\left[ \\mathbf {F} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l}; \\mathbf {B} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l} \\right] ^ {\\top}, \\tag {8} \\\\ \\mathbf {K} _ {x} ^ {l} = \\tilde {\\mathbf {K}} _ {x} ^ {l} \\left[ \\mathbf {F} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l}; \\mathbf {B} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l} \\right] ^ {\\top}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.286,
+                0.892,
+                0.348
+            ],
+            "angle": 0,
+            "content": "With updated queries and keys, the proposed distribution-aware attention module can achieve fore-background aware feature interaction. The output of the \\( l^{th} \\) transformer blocks \\( \\mathbf{H}_{zx}^l \\) can be formulated as follows,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.541,
+                0.359,
+                0.891,
+                0.394
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widetilde {\\mathbf {H}} _ {z x} ^ {l} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {z x} ^ {l} \\left(\\mathbf {K} _ {z x} ^ {l}\\right) ^ {\\top}}{\\sqrt {C}}\\right) \\mathbf {V} _ {z x} ^ {l} + \\mathbf {H} _ {z x} ^ {l - 1} \\tag {9}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.543,
+                0.395,
+                0.849,
+                0.415
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {H} _ {z x} ^ {l} = \\left[ \\mathbf {H} _ {z} ^ {l}; \\mathbf {H} _ {x} ^ {l} \\right] = \\operatorname {M L P} \\left(\\operatorname {L N} \\left(\\widetilde {\\mathbf {H}} _ {z x} ^ {l}\\right)\\right) + \\widetilde {\\mathbf {H}} _ {z x} ^ {l},\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.427,
+                0.892,
+                0.503
+            ],
+            "angle": 0,
+            "content": "where MLP denotes the multi-layer perception. The output token features \\(\\mathbf{H}_{zx}^{l}\\) will be sent into next transformer blocks. Eventually, token features are processed \\(L\\) times via our proposed fore-background distribution modeling transformer block, and we can obtain final token features \\(\\mathbf{H}_{zx}^{L}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.515,
+                0.88,
+                0.53
+            ],
+            "angle": 0,
+            "content": "3.4. Box Prediction Head and Objective Function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.538,
+                0.892,
+                0.703
+            ],
+            "angle": 0,
+            "content": "As shown in Figure 2, search region token features \\(\\mathbf{H}_x^L\\) are reshaped and fed into a box prediction head for target state estimation. Here, the box prediction head is inspired from OSTrack [62]. We use the weighted focal loss [33] as classification loss \\(\\mathcal{L}_{cls}\\). Besides, we adopt \\(\\ell_1\\) loss \\(\\mathcal{L}_1\\) and generalized IoU loss [48] \\(\\mathcal{L}_{giou}\\) to supervise bounding box regression. More details about the box prediction head and losses can be referred to OSTrack [62]. As we introduced before, there are point loss and box loss for pseudo bbox generation at each block. In summary, the overall objective function is formulated as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.517,
+                0.715,
+                0.891,
+                0.755
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c l s} + \\lambda_ {1} \\mathcal {L} _ {1} + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u} + \\lambda_ {b o x} \\sum_ {l = 1} ^ {L} \\mathcal {L} _ {b o x} ^ {l}, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.769,
+                0.89,
+                0.784
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_1, \\lambda_{giou}\\) and \\(\\lambda_{box}\\) are scalars to balance these losses."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.8,
+                0.632,
+                0.816
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we first introduce implementation details. Then, we show experimental results on eight benchmarks. Finally, we conduct a series of ablation studies to verify the effectiveness of each component. Please refer to the Supplementary Material for more details and results."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10121"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.113
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparisons with state-of-the-art trackers on GOT-10k, TNL2K, LaSOT, \\(\\mathrm{LaSOT}_{ext}\\), and TrackingNet. The best three results are shown in red, blue and green fonts."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.088,
+                0.115,
+                0.884,
+                0.478
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">GOT-10k [26]</td><td colspan=\"2\">TNL2K [54]</td><td colspan=\"3\">LaSOT [17]</td><td colspan=\"3\">\\( LaSOT_{ext} \\) [16]</td><td colspan=\"3\">TrackingNet [45]</td></tr><tr><td>AO</td><td>\\( SR_{0.5} \\)</td><td>\\( SR_{0.75} \\)</td><td>AUC</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td></tr><tr><td>SiamFC[2]</td><td>34.8</td><td>35.3</td><td>9.8</td><td>29.5</td><td>28.6</td><td>33.6</td><td>42.0</td><td>33.9</td><td>23.0</td><td>31.1</td><td>26.9</td><td>57.1</td><td>66.3</td><td>53.3</td></tr><tr><td>ECO [11]</td><td>31.6</td><td>30.9</td><td>11.1</td><td>32.6</td><td>31.7</td><td>32.4</td><td>33.8</td><td>30.1</td><td>22.0</td><td>25.2</td><td>24.0</td><td>55.4</td><td>61.8</td><td>49.2</td></tr><tr><td>SiamRPN++ [34]</td><td>51.7</td><td>61.6</td><td>32.5</td><td>41.3</td><td>41.2</td><td>49.6</td><td>56.9</td><td>49.1</td><td>34.0</td><td>41.6</td><td>39.6</td><td>73.3</td><td>80.0</td><td>69.4</td></tr><tr><td>SiamCAR [23]</td><td>56.9</td><td>67.0</td><td>41.5</td><td>35.5</td><td>38.4</td><td>50.7</td><td>60.0</td><td>51.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SiamFC++ [58]</td><td>59.5</td><td>69.5</td><td>47.9</td><td>38.6</td><td>36.9</td><td>54.4</td><td>62.3</td><td>54.7</td><td>-</td><td>-</td><td>-</td><td>75.4</td><td>80.0</td><td>70.5</td></tr><tr><td>D3S [39]</td><td>59.7</td><td>67.6</td><td>46.2</td><td>38.8</td><td>39.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>72.8</td><td>76.8</td><td>66.4</td></tr><tr><td>Ocean [63]</td><td>61.1</td><td>72.1</td><td>47.3</td><td>38.4</td><td>37.7</td><td>56.0</td><td>65.1</td><td>56.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiMP-50 [3]</td><td>61.1</td><td>71.7</td><td>49.2</td><td>44.7</td><td>43.4</td><td>56.9</td><td>65.0</td><td>56.7</td><td>39.2</td><td>47.6</td><td>45.1</td><td>74.0</td><td>80.1</td><td>68.7</td></tr><tr><td>PrDiMP-50 [13]</td><td>63.4</td><td>73.8</td><td>54.3</td><td>47.0</td><td>45.9</td><td>59.8</td><td>68.8</td><td>60.8</td><td>-</td><td>-</td><td>-</td><td>75.8</td><td>81.6</td><td>70.4</td></tr><tr><td>KeepTrack[43]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>67.1</td><td>77.2</td><td>70.2</td><td>48.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ToMP-101 [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>68.5</td><td>79.2</td><td>73.5</td><td>45.9</td><td>-</td><td>-</td><td>81.5</td><td>86.4</td><td>78.9</td></tr><tr><td>KYS [4]</td><td>63.6</td><td>75.1</td><td>51.5</td><td>44.9</td><td>43.5</td><td>55.4</td><td>63.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>74.0</td><td>80.0</td><td>68.8</td></tr><tr><td>STMTrack [21]</td><td>64.2</td><td>73.7</td><td>57.5</td><td>-</td><td>-</td><td>60.6</td><td>63.3</td><td>69.3</td><td>-</td><td>-</td><td>-</td><td>80.3</td><td>85.1</td><td>76.7</td></tr><tr><td>TransT [7]</td><td>67.1</td><td>76.8</td><td>60.9</td><td>50.7</td><td>51.7</td><td>64.9</td><td>69.0</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>81.4</td><td>86.7</td><td>80.3</td></tr><tr><td>STARK-ST101 [59]</td><td>68.8</td><td>78.1</td><td>64.1</td><td>-</td><td>-</td><td>67.1</td><td>77.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.0</td><td>86.9</td><td>-</td></tr><tr><td>CSWinTT [50]</td><td>69.4</td><td>78.9</td><td>65.4</td><td>-</td><td>-</td><td>66.2</td><td>75.2</td><td>70.9</td><td>-</td><td>-</td><td>-</td><td>81.9</td><td>86.7</td><td>79.5</td></tr><tr><td>SimTrack-B/16 [5]</td><td>68.6</td><td>78.9</td><td>62.4</td><td>54.8</td><td>53.8</td><td>69.3</td><td>78.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.3</td><td>86.5</td><td>-</td></tr><tr><td>SwinTrack-B [36]</td><td>69.4</td><td>78.0</td><td>64.3</td><td>-</td><td>-</td><td>69.6</td><td>78.6</td><td>74.1</td><td>47.6</td><td>58.2</td><td>54.1</td><td>82.5</td><td>87.0</td><td>80.4</td></tr><tr><td>AiATrack [22]</td><td>69.6</td><td>80.0</td><td>63.2</td><td>-</td><td>-</td><td>69.0</td><td>79.4</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>82.7</td><td>87.8</td><td>80.4</td></tr><tr><td>SBT-L [57]</td><td>70.4</td><td>80.8</td><td>64.7</td><td>-</td><td>-</td><td>66.7</td><td>77.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MixFormer [10]</td><td>70.7</td><td>80.0</td><td>67.8</td><td>-</td><td>-</td><td>69.2</td><td>78.7</td><td>74.7</td><td>-</td><td>-</td><td>-</td><td>83.1</td><td>88.1</td><td>81.6</td></tr><tr><td>RTS [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>69.7</td><td>76.2</td><td>73.7</td><td>-</td><td>-</td><td>-</td><td>81.6</td><td>86.0</td><td>79.4</td></tr><tr><td>OSTrack-256 [62]</td><td>71.0</td><td>80.4</td><td>68.2</td><td>54.3</td><td>-</td><td>69.1</td><td>78.7</td><td>75.2</td><td>47.4</td><td>57.3</td><td>53.3</td><td>83.1</td><td>87.8</td><td>82.0</td></tr><tr><td>OSTrack-384 [62]</td><td>73.7</td><td>83.2</td><td>70.8</td><td>55.9</td><td>-</td><td>71.1</td><td>81.1</td><td>77.6</td><td>50.5</td><td>61.3</td><td>57.6</td><td>83.9</td><td>88.5</td><td>83.2</td></tr><tr><td>F-BDMTrack-256</td><td>72.7</td><td>82.0</td><td>69.9</td><td>56.4</td><td>56.5</td><td>69.9</td><td>79.4</td><td>75.8</td><td>47.9</td><td>57.9</td><td>54.0</td><td>83.7</td><td>88.3</td><td>82.6</td></tr><tr><td>F-BDMTrack-384</td><td>75.4</td><td>84.3</td><td>72.9</td><td>57.8</td><td>59.4</td><td>72.0</td><td>81.5</td><td>77.7</td><td>50.8</td><td>61.3</td><td>57.8</td><td>84.5</td><td>89.0</td><td>84.0</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.501,
+                0.295,
+                0.518
+            ],
+            "angle": 0,
+            "content": "4.1. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.532,
+                0.471,
+                0.819
+            ],
+            "angle": 0,
+            "content": "Network details. We present two variants of our tracker, F-BDMTrack-256 and F-BDMTrack-384. Similar to OSTrack [62], we crop the template image and search region image which are \\( 2^{2} \\) and \\( 4^{2} \\) times of the target box area respectively. The F-BDMTrack-256 resizes search region to a resolution of \\( 256 \\times 256 \\) and template to a resolution of \\( 128 \\times 128 \\) as input. The F-BDMTrack-384 resizes search region to a resolution of \\( 384 \\times 384 \\) and template to \\( 192 \\times 192 \\). These images are split into a set of patches, where the resolution of each patch is \\( 16 \\times 16 \\). These patches are flattened and projected into \\( C = 768 \\) channels to serve as the input of F-BDMTrack. The channel of \\( \\mathbf{E}_z^l \\) in the FBAL module is set to \\( C_e = 256 \\). We leverage the Precise RoI Pooling [28] operation to crop features according to the target bounding box, and obtain the target feature with shape \\( (h_t, w_t) = (4, 4) \\). The number of foreground agents and background agents are both set to \\( N_a = 4 \\). And our F-BDMTrack consists of \\( L = 12 \\) fore-background distribution modeling transformer blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Training details. We train our model on the training splits of LaSOT [17], GOT-10K [26], COCO2017 [37], and TrackingNet [45], which is a similar training setting to OSTrack [62]. Common data augmentations including horizontal flip and brightness jittering are applied in the training"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.502,
+                0.892,
+                0.655
+            ],
+            "angle": 0,
+            "content": "process. We train our F-BDMTrack by the AdamW optimizer with the weight decay \\(10^{-4}\\). The learning rates start from \\(4 \\times 10^{-5}\\) for the backbone including the FBAL module and the \\(\\mathrm{DA}^2\\) module, and \\(4 \\times 10^{-4}\\) for the box prediction head. Our model is trained on four NVIDIA RTX 3090 GPUs, each GPU holds 32 image pairs, resulting in a total batch size of 128. The total epochs are set to 300 with 60k samples per epoch and we decrease the learning rate by a factor of 10 after 240 epochs. The weights of training losses are set to \\(\\lambda_1 = 5.0\\), \\(\\lambda_{giou} = 2.0\\), and \\(\\lambda_{box} = 1.0\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.665,
+                0.856,
+                0.682
+            ],
+            "angle": 0,
+            "content": "4.2. Results and State-of-the-art Comparisons"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.854
+            ],
+            "angle": 0,
+            "content": "GOT-10k. GOT-10k [26] is a large-scale dataset containing over 10k videos for training and 180 for testing. It forbids trackers to use external datasets for training. We follow its policy and retrain our model. The results are reported in Table 1. Our tracker has a satisfactory improvement in all metrics. Specifically, F-BDMTrack-256 improves by \\(1.7\\%\\) in success rate \\((\\mathrm{SR}_{0.75})\\) compared with OSTrack-256. And F-BDMTrack-384 gives an improved new record \\(75.4\\%\\) in AO, indicating the effectiveness of foreground and background distribution modeling to extract discriminative features, resulting in more accurate state estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "TNL2K. TNL2K [54] is a recently published dataset containing 700 video sequences for testing. In Table 1, F-BDMTrack-256 gains by \\(2.1\\%\\) AUC over OTrack-256 and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10122"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.088,
+                0.892,
+                0.113
+            ],
+            "angle": 0,
+            "content": "Table 2. Comparisons with state-of-the-art trackers on NFS, OTB100 and UAV123 datasets in terms of overall AUC score. The best three results are shown in red, blue and green fonts."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.115,
+                0.891,
+                0.156
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>SiamFC [2]</td><td>Ocean [63]</td><td>ATOM [12]</td><td>DiMP-50 [3]</td><td>PrDiMP-50 [13]</td><td>TransT [7]</td><td>OSTrack-256 [62]</td><td>OSTrack-384 [62]</td><td>F-BDMTrack-256</td><td>F-BDMTrack-384</td></tr><tr><td>NFS [30]</td><td>37.7</td><td>49.4</td><td>58.3</td><td>61.8</td><td>63.5</td><td>65.3</td><td>64.7</td><td>66.5</td><td>66.0</td><td>67.3</td></tr><tr><td>OTB100 [56]</td><td>61.2</td><td>68.4</td><td>66.3</td><td>68.4</td><td>69.6</td><td>69.4</td><td>68.1</td><td>69.2</td><td>69.5</td><td>69.9</td></tr><tr><td>UAV123 [44]</td><td>46.8</td><td>57.4</td><td>63.2</td><td>64.3</td><td>68.0</td><td>68.1</td><td>68.3</td><td>70.7</td><td>69.0</td><td>70.9</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.094,
+                0.171,
+                0.462,
+                0.346
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.349,
+                0.47,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Figure 3. Visualizations of fore-background agent activation maps for the template and search region."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.106,
+                0.39,
+                0.441,
+                0.402
+            ],
+            "angle": 0,
+            "content": "Table 3. Effectiveness of each component on the LaSOT"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.129,
+                0.402,
+                0.42,
+                0.473
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>FBAL</td><td>DA2</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>[A]</td><td>X</td><td>X</td><td>68.5</td><td>77.8</td><td>74.2</td></tr><tr><td>[B]</td><td>✓</td><td>X</td><td>68.8</td><td>78.1</td><td>74.6</td></tr><tr><td>[C]</td><td>X</td><td>✓</td><td>69.4</td><td>78.7</td><td>75.4</td></tr><tr><td>[D]</td><td>✓</td><td>✓</td><td>69.9</td><td>79.4</td><td>75.8</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.469,
+                0.536
+            ],
+            "angle": 0,
+            "content": "even performances better than larger models (OTrack-384). When also leveraging a large model (F-BDMTrack-384), we can further improve the AUC score to \\(57.8\\%\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.537,
+                0.469,
+                0.718
+            ],
+            "angle": 0,
+            "content": "LaSOT. LaSOT [17] is a densely annotated large-scale dataset containing a total of 1400 long-term video sequences, of which the test set contains 280 video sequences. This is a challenging tracking dataset. As shown in Table 1, F-BDMTrack-256 outperforms OSTrack-256 by \\(0.8\\%\\) AUC. Further, F-BDMTrack-384 achieves the best performance of \\(72.0\\%\\) AUC. Our tracker does not add additional timing strategies [22, 10, 59] in this long-term tracking task, but can still obtain performance improvement with the aid of fore-background distribution modeling design, which demonstrates that our approach can fundamentally mitigate complex scenarios and distractors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.719,
+                0.469,
+                0.84
+            ],
+            "angle": 0,
+            "content": "\\(\\mathbf{LaSOT}_{ext}\\). The recent \\(\\mathrm{LaSOT}_{ext}\\) [16] is an extended subset of LaSOT, containing 150 additional new sequences. This dataset has many similar distractors, making it difficult for tracking. And our F-BDMTrack can achieve competitive or even better performance. In specific, F-BDMTrack-256 achieves superior results, outperforming OSTrack-256 by \\(0.5\\%\\) AUC. And F-BDMTrack-356 obtains a much higher performance with \\(50.8\\%\\) AUC."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Trackingnet. Trackingnet [45] provides over 30k video sequences, which are sampled from Youtube to cover target categories and scenes of real-world. It provides 511 testing video sequences without publicly available annotation,"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.171,
+                0.882,
+                0.339
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.34,
+                0.892,
+                0.369
+            ],
+            "angle": 0,
+            "content": "Figure 4. Visualization of pseudo bboxes using the pseudo-bbox generation strategy at all blocks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.386,
+                0.892,
+                0.43
+            ],
+            "angle": 0,
+            "content": "so results reported in Table 1 are obtained from the online evaluation server. As can be seen, our F-BDMTrack-384 achieves \\(84.5\\%\\) AUC and sets a new state of the art."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.431,
+                0.893,
+                0.567
+            ],
+            "angle": 0,
+            "content": "NFS. Videos in Need for Speed(NFS) [30] are captured from a high frame rate camera, which contains fast motions and distractors. We report results on its commonly used version NFS30. As shown in Table 2, F-BDMTrack-256 achieves \\(66.0\\%\\) AUC, outperforming OSTrack-256 by \\(1.3\\%\\). And F-BDMTrack-384 achieves best results (67.3% AUC score) as expected, demonstrating the superior competitiveness of our tracker in the presence of interferer-challenged benchmark."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.567,
+                0.892,
+                0.703
+            ],
+            "angle": 0,
+            "content": "OTB100. OTB [56] is a pioneering visual tracking benchmark. It has been noticed that this benchmark is approaching saturation [53, 59, 43]. In Table 2, two versions of our tracker both achieve promising AUC scores (69.5 and 69.9). UAV123. UAV123 [44] provides 123 unmanned aerial vehicle(UAV) sequences, including different scale sizes of UAV in real-world dynamic scenarios. As shown in Table 2, our tracker achieves the best AUC score \\((70.9\\%)\\) and is suitable for UAV tracking scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.712,
+                0.654,
+                0.728
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.735,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "To validate the effectiveness of each component, we perform a detailed ablation study on LaSOT [17]. The following experiments use F-BDMTrack-256 as the base model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Effectiveness of key components in our F-BDMTrack. Our tracker consists of two key components, including a fore-background agent learning (FBAL) module and a distribution-aware attention \\((\\mathrm{DA}^2)\\) module. Here, we explore the exact impact of these modules. The model [A] is the baseline, which means that we directly use plain attention mechanism without using the FBAL and the \\(\\mathrm{DA}^2\\) module. For the model [B], we add the FBAL module, and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10123"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.088,
+                0.468,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 4. Effects with different numbers of prototypical FB-agents."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.185,
+                0.102,
+                0.367,
+                0.186
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Na</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>1</td><td>69.3</td><td>78.8</td><td>75.5</td></tr><tr><td>2</td><td>69.6</td><td>79.1</td><td>75.6</td></tr><tr><td>4</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>8</td><td>69.3</td><td>78.9</td><td>75.2</td></tr><tr><td>16</td><td>69.0</td><td>78.6</td><td>75.1</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.201,
+                0.468,
+                0.214
+            ],
+            "angle": 0,
+            "content": "Table 5. Effects of the pseudo bbox generation at different blocks."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.169,
+                0.214,
+                0.38,
+                0.3
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>blocks</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>None</td><td>69.0</td><td>78.5</td><td>75.0</td></tr><tr><td>10-12</td><td>69.5</td><td>79.1</td><td>75.5</td></tr><tr><td>6-12</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>4-12</td><td>69.8</td><td>79.2</td><td>75.8</td></tr><tr><td>1-12</td><td>69.2</td><td>78.7</td><td>75.2</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.323,
+                0.47,
+                0.625
+            ],
+            "angle": 0,
+            "content": "adopt plain attention mechanism to replace our designed \\(\\mathrm{DA}^2\\) module. The plain attention mechanism does not require fore-background agents (FB-agents) produced by our FBAL module. Thus, the model [B] is used to validate the impacts of pseudo bbox generation loss \\(\\mathcal{L}_{box}^{l}\\) introduced in the FBAL module. As shown in Table 3, the performance of model [B] gains by \\(0.3\\%\\) compared to the model [A], demonstrating that the pseudo bbox loss has some positive effects to constrain foreground features interact with features in foreground regions. For the model [C], we adopt the \\(\\mathrm{DA}^2\\) module for feature interaction, and FB-agents are obtained by pooling features within or outside the bounding box for the template and search region. As can be seen, the performance of model [C] gains by \\(0.9\\%\\) compared to the model [A], which demonstrates that the proposed \\(\\mathrm{DA}^2\\) module can significantly help learn discriminative features even if FB-agents are not good enough. When adding the FBAL module for better FB-agents generation, the performance of model [D] gains by \\(0.5\\%\\) compared to the model [C], showing the superiority of proposed FBAL module."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.627,
+                0.47,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Study on the number of prototypical FB-agents in the FBAL module. Here, we explore the effects about different numbers of prototypical FB-agents. As shown in Table 4, our tracker achieves the optimal result (69.9% AUC score) when \\( N_{a} = 4 \\). A small number of prototypical FB-agents cannot fully model the fore-background distribution, leading to decreased performance. Meanwhile, more prototypical FB-agents will introduce useless noise, which is harmful for feature interaction. Besides, without explicit constraints to guide foreground and background agent learning, an excessive number of agents are unable to focus on their respective discriminative information better. A more effective FB-agent learning way can be explored in future work. Finally, we show the fore-background agent activation maps for the template and search region in Figure 3. It can be seen that these FB-agents generated by our FBAL module can focus on the foreground and background well."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.886,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Study on the pseudo bbox generation strategy at differ"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.09,
+                0.886,
+                0.426
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.43,
+                0.892,
+                0.486
+            ],
+            "angle": 0,
+            "content": "Figure 5. Response maps of the template central feature to all search region features. It can be seen that although the template target has similar appearance with the background distractor in the search region, their fore-background distributions are different."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.507,
+                0.892,
+                0.674
+            ],
+            "angle": 0,
+            "content": "ent blocks. High-quality pseudo bbox is more conducive to the FB-agent learning for the search region. However, as shown in Figure 4, the pseudo-bboxes in shallow blocks tend to have a large bias, which is harmful to learn effective FB-agents. We conduct a detailed experiment to find which blocks are optimal for using pseudo bbox generation strategy. As shown in Table 5, our tracker achieves the best results when we leverage the pseudo bbox generation strategy at the \\(6^{th}\\) to \\(12^{th}\\) ('6-12') transformer blocks. This is because the last few blocks provide more reliable pseudo bbox to guide fore-background agent learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Comparisons between the plain attention mechanism and our \\(\\mathbf{DA}^2\\) mechanism. Here, we visualize response maps of the plain attention mechanism and our \\(\\mathrm{DA}^2\\) mechanism in Figure 5. As we can see, the plain attention mechanism easily focus on complex backgrounds or distractors. This is because attention scores are obtained based on appearance similarities, while targets usually have similar appearance with distractors, resulting in incorrect response map. Differently, our proposed \\(\\mathrm{DA}^2\\) mechanism discriminates features from the perspective of fore-background distributions instead of appearance similarities, which can effectively suppress the response of the template to background distractors in the search region, and strengthen the response of the template to the foreground target in the search region. Finally, based on the proposed distribution"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "10124"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.123
+            ],
+            "angle": 0,
+            "content": "aware attention mechanism, our tracker can achieve superior performance on all eight tracking benchmarks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.138,
+                0.196,
+                0.154
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.164,
+                0.47,
+                0.286
+            ],
+            "angle": 0,
+            "content": "In this work, we propose a novel foreground-background distribution modeling transformer for visual tracking, including a FBAL module and a \\(\\mathrm{DA}^2\\) module. With these two elegant designs, our proposed tracker can extract features with high target discriminative power under ever-changing tracking scenarios, which is essential for accurate target state estimation. Extensive experiments on eight tracking benchmarks verify the superiority of our proposed tracker."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.301,
+                0.258,
+                0.318
+            ],
+            "angle": 0,
+            "content": "6. Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.327,
+                0.47,
+                0.388
+            ],
+            "angle": 0,
+            "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), and National Defense Basic Scientific Research Program of China (Grant JCKY2020903B002)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
+                0.403,
+                0.175,
+                0.42
+            ],
+            "angle": 0,
+            "content": "References"
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+# Foreground-Background Distribution Modeling Transformer for Visual Object Tracking
+
+Dawei Yang $^{1,\ast}$ , Jianfeng He $^{1,\ast}$ , Yinchao Ma $^{1}$ , Qianjin Yu $^{1}$ , Tianzhu Zhang $^{1,\dagger}$
+
+<sup>1</sup> University of Science and Technology of China
+
+{yangdawei, hejf, imyc, sa21010105}@mail.ustc.edu.cn, {tzzhang}@ustc.edu.cn
+
+# Abstract
+
+Visual object tracking is a fundamental research topic with a broad range of applications. Benefiting from the rapid development of Transformer, pure Transformer trackers have achieved great progress. However, the feature learning of these Transformer-based trackers is easily disturbed by complex backgrounds. To address the above limitations, we propose a novel foreground-background distribution modeling transformer for visual object tracking (FBDMTrack), including a fore-background agent learning (FBAL) module and a distribution-aware attention  $(DA^{2})$  module in a unified transformer architecture. The proposed F-BDMTrack enjoys several merits. First, the proposed FBAL module can effectively mine fore-background information with designed fore-background agents. Second, the  $DA^{2}$  module can suppress the incorrect interaction between foreground and background by modeling fore-background distribution similarities. Finally, F-BDMTrack can extract discriminative features under ever-changing tracking scenarios for more accurate target state estimation. Extensive experiments show that our F-BDMTrack outperforms previous state-of-the-art trackers on eight tracking benchmarks.
+
+# 1. Introduction
+
+Visual object tracking(VOT) aims to locate the position of a class-agnostic target in a video sequence given the target in the first frame, which is a fundamental and essential research topic in computer vision. Due to its great application potential (such as video surveillance [9, 49, 9], antiUAV tracking [64, 25, 29], and automatic driving [47, 41, 15]), VOT has attracted substantial attention and has been developed tremendously [56, 31, 17]. However, as a video processing task, visual object tracking still faces various challenges including deformation, motion blur, and susceptibility to background interference [51, 27, 24].
+
+![](images/8b0c4878c763fe80d25faa7b43fa15e8fd3898c97e6673997a5835cf329edc5b.jpg)  
+Figure 1. Response map comparisons among different attention mechanisms. Both (a) and (b) have incorrect similarities between the target (green square patch) and background distractor (yellow triangle patch) due to similar appearance, causing messy response map. Differently, in our proposed  $\mathrm{DA}^2$  module (c), the similarity between target and distractor is suppressed, since the similarity is obtained according to their fore-background distributions.
+
+To deal with the above challenges, numerous approaches have been proposed [23, 2, 3, 59, 10, 5, 62]. These methods can be generally divided into three main paradigms, including CNN-based [8, 52, 58, 35, 3, 13], hybrid CNN-Transformer [7, 59, 36, 50, 42], and pure Transformer trackers [5, 62, 32, 57]. CNN-based trackers first extract features from the template and search region separately through a shared convolutional neural network (CNN), and then the target state is estimated by calculating cross-correlation [2, 58, 52] between features in template and search regions, or learning a discriminative correlation filter [12, 3, 13]. With the successful development of transformer in the computer vision field, an increasing number of hybrid CNN-Transformer trackers [7, 59, 42] have been proposed. These trackers also leverage CNN to extract features separately, but adopt transformer to realize the feature interaction between the template and search region, which can alleviate the loss of discriminative foreground information. However, for the above two paradigm trackers, there is no interaction between the template and the search region when extracting features. These target-unaware feature extraction ways have limited target-background discriminative power, especially when the target category is not seen
+
+in the training dataset. To this end, pure Transformer trackers [5, 62, 32, 57] are proposed to build interaction between template and search region along with the feature extraction. Thanks to the strong representation and interaction capability of ViT/SwinT variants [14, 38, 55], pure Transformer trackers have achieved remarkable improvements.
+
+Despite the success of the above pure Transformer trackers, the feature learning of these methods are easily disturbed by complex backgrounds due to insufficient consideration of fore-background relationship. To make pure Transformer architectures more suitable for discriminative feature learning in visual object tracking, there are two core points that need to be considered. (1) Fore-background information mining. Previous methods [5, 22, 21] usually mine fore-background information from the template according to the given bounding box (bbox). However, the tracking target can be continuously changing, making it difficult to learn target discriminative features for current search region, if only guided by fore-background information of the template. Therefore, it is necessary to propose a effective way to mine fore-background information for both template and search region. (2) Target-aware feature interaction. Most of popular Transformer trackers [62, 10, 57] adopt the plain attention mechanism to build interaction between template and search region. Since attention scores are obtained by appearance similarity, the template features will mistakenly aggregate background information and further affect features of search region during feature interaction, resulting messy response map (Figure 1 (a)). Although some methods [22, 42] introduce additional target embeddings to enhance the target information, they could still be disturbed by distractors, making features of the search region have limited target discriminative power. And the response map is also unsatisfactory (Figure 1 (b)). Therefore, it is urgent to design a new attention mechanism to achieve better target-aware feature interaction.
+
+Motivated by the above discussion, we propose a novel Foreground-Background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which consists of a fore-background agent learning (FBAL) module and a distribution-aware attention  $(\mathrm{DA}^2)$  module in a unified transformer architecture. In the fore-background agent learning module, we aim to mine foreground and background information from both the template and the search region. Specifically, we initialize a set of fore-background agents. And fore-background agents for the template (search region) are obtained by aggregating foreground and background information in the template (search region), which can be used to guide the subsequent feature interaction. In the distribution-aware attention module, it is proposed to realize target-aware feature interaction. Specifically, we calculate the similarity scores between each patch feature and the fore-background agents, which can
+
+be regarded as fore-background distributions for each patch feature. Then we can obtain the attention score by compute the similarity between their distributions, which are later used for feature aggregation. As shown in Figure 1 (c), foreground patches and background patches could have different fore-background distributions even though they have similar appearance. Thus, we can aggregate more useful information and learn more discriminative features.
+
+The main contributions of this work are summarized as follows. (1) We develop a novel Foreground-background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which can extract features with high target discriminative power under ever-changing tracking scenarios. (2) The proposed FBAL module can effectively mine foreground information for both template and search region with designed foreground agents. And the proposed  $\mathrm{DA}^2$  module can effectively suppress the interaction between foreground and background, which helps learn more discriminative features for visual tracking. (3) Extensive experimental results on eight benchmarks show that our method attains state-of-the-art performance, verifying the superiority of our F-BDMTrack.
+
+# 2. Related Work
+
+Visual object tracking (VOT). Current popular trackers can be divided into CNN-based trackers [8, 2, 58, 35, 40, 12, 3, 13], hybrid CNN-Transformer trackers [59, 7, 50, 53, 42], and pure Transformer trackers [62, 5, 36, 32, 57] according to the network architecture. CNN-based trackers commonly learn features of template and search region via share-weighted convolutional neural networks (CNN), and the interaction between template and search region is realized by cross correlation [2, 58, 35] or correlation filter [12, 3, 13]. However, due to the lack of global perception and the simple interaction strategy, some target-background discriminative information may be lost, restricting the development of CNN-based trackers. Recently, Vision Transformer brings a new solution to visual tracking. Hybrid CNN-Transformer trackers reserve the extraction of features with CNNs and utilize attention mechanisms to establish global dependencies between features. Typically, STARK [59] utilizes the Transformer to aggregate spatial-temporal cues for target location. Moreover, ToMP [42] uses a Transformer-based architecture to encode a long-term target representation to localize the target. Nevertheless, these Hybrid CNN-Transformer trackers still extract features of template and search region separately, which causes extracted features to be unaware of the tracking target. To alleviate this limitation, pure Transformer-based trackers [62, 5, 57] are proposed. For example, OSTrack [62] and SimTrack [5] unify the feature extraction and the feature relation modeling in Vision Transformer [14]. They achieve superior performance, proving the potential of pure Transformer
+
+architectures in visual tracking. However, these trackers [62, 5] aggregate features according to appearance similarities through plain attention mechanisms. Without considering fore-background relationship for the template and search region, target features may mistakenly aggregate background noise in the search region. Differently, in our work, we propose the distribution aware attention module to aggregate features according to their fore-background distribution similarities, which can effectively suppress incorrect interaction between foreground and background.
+
+Fore-background exploitation in visual object tracking. There are several tracking methods [21, 42, 5, 46, 19] actively exploring ways to mine fore-background information for robust tracking. STMTrack [21] leverages foreground-background masks derived by bounding boxes of template sequences to highlight target representations. And ToMP [42] is proposed to learn foreground embeddings from a set of template sequences, which can be used to enhance target features of the template and assist in target state estimation. However, the above methods for exploiting fore-background generally use fixed foreground embedding for template images, ignoring the fact that tracking target can be continuously changing. Besides, they do not analyze the fore-background information of the search region. Furthermo, RTS [46] utilizes an additional segmentation network to provide more precise object masks, leading to better performance improvements. And SNLT [19] adopts additional natural language labels to help extract better target embeddings for distinguishing foreground and background. These methods utilize additional network components and labels to mine fore-background information, which affects the independence of the network architecture. In contrast, our method is proposed to fully mine fore-background information from templates and search regions, and utilizes them to improve the discriminative ability without attaching additional models.
+
+Visual transformer and attention variants. Nowadays, Transformer has been rapidly applied in the computer vision due to its global interaction ability. Typically, ViT [14] realizes image classification by learning global representations of patches through attention mechanisms. To optimize efficiency, Swin Transformer [38] restricts attention computation in non-overlapping local windows and exchange information between windows through a sliding operation. Thanks to these effective designs, Vision Transformers have been applied to visual tracking, such as MixFormer [10] (using CvT [55]) and OSTrack [62] (using ViT [14]). Further, some trackers improve attention mechanisms to better adapt to visual tracking task. AiATrack [22] proposes an attention in attention module to model the relationship of attention scores, which can improve the quality of attention maps. And SparseTT [20] proposes sparse attention to focus the most relevant information in the
+
+search region. However, these methods still calculate attention scores with appearance similarities, which will inevitably disturbed by similar distractors. Differently, we propose a novel foreground-background distribution modeling tracker, which can accurately discriminate target features by perceiving the distribution of fore-background.
+
+# 3. Method
+
+In this section, we introduce our proposed foreground-background distribution modeling transformer for visual tracking (F-BDMTrack). The architecture is in Figure 2.
+
+# 3.1. Overview
+
+As illustrated in Figure 2, our proposed tracker consists of  $L$  stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA $^2$ ) module. Given a pair of images including template image  $\mathbf{z} \in \mathbb{R}^{3 \times H_z \times W_z}$  and search region image  $\mathbf{x} \in \mathbb{R}^{H_x \times W_x \times 3}$ , we first split and flatten them to obtain the patch sequence of template  $\mathbf{z}_p \in \mathbb{R}^{N_z \times (3 \cdot p^2)}$  and search region  $\mathbf{x}_p \in \mathbb{R}^{N_x \times (3 \cdot p^2)}$ , where  $(p, p)$  is the patch resolution, and  $N_z = (H_z W_z) / p^2$ ,  $N_x = (H_x W_x) / p^2$  are the number of patches for template and search region respectively. Similar to plain vision transformers [14], these patch sequences are mapped into  $C$  dimensions by a linear projection, and learnable position embeddings are added to obtain template token embeddings  $\mathbf{H}_z^0 \in \mathbb{R}^{N_z \times C}$  and search region token embeddings  $\mathbf{H}_x^0 \in \mathbb{R}^{N_x \times C}$ . Then,  $\mathbf{H}_z^0$  and  $\mathbf{H}_x^0$  are concatenated as the input  $(\mathbf{H}_{zx}^0 = [\mathbf{H}_z^0; \mathbf{H}_x^0])$  to the fore-background distribution modeling transformer block. In this transformer block, we intergraded two modules (the FBAL module and the DA $^2$  module) to help learn discriminative features for both search region and template (We will give a detailed introduction about how these two modules work in our proposed transformer block below). Here, we denote  $\mathbf{H}_{zx}^l = [\mathbf{H}_z^l; \mathbf{H}_x^l]$  as token embeddings output from the  $l^{th}$  transformer block. Eventually, we reshape search region token features  $\mathbf{H}_x^L$  from the last block, and send them into a box prediction head to estimate the target state.
+
+# 3.2. Fore-background Agent Learning Module
+
+Given token features  $[\mathbf{H}_z^{l - 1};\mathbf{H}_x^{l - 1}]$  from  $(l - 1)^{th}$  transformer block, we normalize them with Layer Normalization [1] to obtain  $\hat{\mathbf{H}}_z^l = \mathrm{LN}(\mathbf{H}_z^{l - 1})$  , and  $\hat{\mathbf{H}}_x^l = \mathrm{LN}(\mathbf{H}_x^{l - 1})$  These normalized features  $\widehat{\mathbf{H}}_z^l$  and  $\widehat{\mathbf{H}}_x^l$  are sent into the forebackground agent learning (FBAL) module to produce forebackground agent (FB-agent) for the template and search region. Specifically,  $\widehat{\mathbf{H}}_z^l$  and  $\widehat{\mathbf{H}}_x^l$  are first projected into  $C_e$  dimensions ( $C_e\ll C$ ) to obtain  $\mathbf{E}_z^l$  and  $\mathbf{E}_x^l$  , which can reduce computational overhead. Then, we design a pseudo bounding box (bbox) generation strategy to obtain
+
+![](images/b5e34be09d99338cddf2d35d8f7ab74f930727f3534ea609c1c95fa99a9b8361.jpg)  
+Figure 2. The architecture of our F-BDMTrack consists of  $L$  stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA $^2$ ) module. The FBAL module is used to produce fore-background agents for the template (template FB-agents) and the search region (search FB-agents). And the DA $^2$  module is used for feature aggregation by modeling the fore-background distribution. The output from the  $l^{th}$  transformer block is denoted as  $[\mathbf{H}_z^l; \mathbf{H}_x^l]$ . Finally, we reshape search region token features  $\mathbf{H}_x^L$  from the last block, and send them into a box prediction head to estimate the target state. For more details, please refer to the text.
+
+![](images/11d9f8f96451a51802e9ae045c1bec32f004141a23e7a9816f2dba65a34d6653.jpg)
+
+the bounding box for the template and search region. Finally, we can obtain fore-background agents (FB-agents) for the template and search region by leveraging a FB-agent decoder to aggregate information within or outside the bounding box. The pseudo bbox generation strategy and the FB-agent decoder are introduced as follows.
+
+Pseudo bbox generation. Since the ground-truth bbox for the template is given in advance, the difficulty is how to generate pseudo bbox for the search region. To this end, we establish coarse matches between template and search region, which can help generate pseudo bbox. Specifically, given  $\mathbf{E}_z^l$  and  $\mathbf{E}_x^l$ , we first reshape them into  $\widehat{\mathbf{E}}_z^l \in \mathbb{R}^{\frac{H_z}{p} \times \frac{W_z}{p} \times C_e}$  and  $\widehat{\mathbf{E}}_x^l \in \mathbb{R}^{\frac{H_x}{p} \times \frac{W_x}{p} \times C_e}$ . Then the target feature  $\widehat{\mathbf{E}}_t^l \in \mathbb{R}^{h_t \times w_t \times C_e}$  is cropped according to the ground-truth bbox  $b_z$ , i.e.  $\widehat{\mathbf{E}}_t^l = \mathrm{PrPool}(\widehat{\mathbf{E}}_z^l, b_z)$ . Here,  $\mathrm{PrPool}(\cdot, \cdot)$  denotes the Precise RoI Pooling [28]. Next, we conduct similarity matching to compute the matching point in  $\widehat{\mathbf{E}}_x^l$  for each point in  $\widehat{\mathbf{E}}_t^l$  according to the probability  $D^l$ . Formally,
+
+$$
+\boldsymbol {D} ^ {l} (k, i) = \frac {\exp \left(<   \widehat {\mathbf {E}} _ {t} ^ {l} (k) , \widehat {\mathbf {E}} _ {x} ^ {l} (i) >\right)}{\sum_ {i = 1} ^ {N _ {x}} \exp \left(<   \widehat {\mathbf {E}} _ {t} ^ {l} (k) , \widehat {\mathbf {E}} _ {x} ^ {l} (i) >\right)},
+$$
+
+$$
+\left(\hat {x} _ {k} ^ {l}, \hat {y} _ {k} ^ {l}\right) = \sum_ {i = 1} ^ {N _ {x}} s \cdot \left(x _ {i}, y _ {i}\right) \cdot \boldsymbol {D} ^ {l} (k, i), \tag {1}
+$$
+
+where  $k = (x_{k},y_{k})$  and  $i = (x_{i},y_{i})$  enumerate all 2D positions in  $\widehat{\mathbf{E}}_t^l$  and  $\widehat{\mathbf{E}}_x^l$ , respectively.  $s$  is the stride of the back
+
+bone network. In this way, we can obtain a set of matching points  $\{(\hat{x}_k^l,\hat{y}_k^l)\}_{k = 1}^K$ , where  $K = h_{t}w_{t}$ . Finally, we derive the pseudo bbox  $\hat{b}_x^l = (\hat{x}^l,\hat{y}^l,\hat{w}^l,\hat{h}^l)$  with the mean and the standard deviation of all keypoints inspired by Rep-Point [60]. Please refer to the Supplementary Material for details to obtain  $\hat{b}_x^l$ . During training, we use ground-truth bbox  $b_{x}$  of the search region as supervision for more accurate pseudo bbox generation. In specific, a set of keypoints  $\{(x_j,y_j)\}_{j = 1}^K$  are uniformly sampled within the bbox  $b_{x}$ . And the point loss  $\mathcal{L}_{point}$  measured by Chamfer distance [18, 61] is introduced to constrain the predicted points  $\{(\hat{x}_k^l,\hat{y}_k^l)\}_{k = 1}^K$  scattered in the bbox  $b_{x}$ .
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {p o i n t}} ^ {l} = \frac {1}{K} \sum_ {\substack {j = 1 \\ K}} ^ {K} \min _ {k} \left\| \left(x _ {j}, y _ {j}\right) - \left(\hat {x} _ {k} ^ {l}, \hat {y} _ {k} ^ {l}\right) \right\| _ {2} \tag{2} \\ + \frac {1}{K} \sum_ {k = 1} ^ {K} \min _ {j} \left\| (x _ {j}, y _ {j}) - (\hat {x} _ {k} ^ {l}, \hat {y} _ {k} ^ {l}) \right\| _ {2}. \\ \end{array}
+$$
+
+Besides, we introduce  $\ell_1$  loss and generalized IoU loss [48] to directly constrain predicted pseudo bbox. And the final pseudo bbox generation loss is as follows.
+
+$$
+\mathcal {L} _ {b o x} ^ {l} = \mathcal {L} _ {p o i n t} ^ {l} + \mathcal {L} _ {1} ^ {l} \left(b _ {x}, \hat {b} _ {x} ^ {l}\right) + \mathcal {L} _ {g i o u} ^ {l} \left(b _ {x}, \hat {b} _ {x} ^ {l}\right). \tag {3}
+$$
+
+FB-agent decoder. After obtaining the bbox for the template  $b_{z}$  and search region  $\hat{b}_x^l$ , we aim to aggregate information within or outside the bbox. To this end, we first initialize a set of prototypical foreground agents  $\mathbf{F}_a^l \in \mathbb{R}^{N_a \times C_e}$
+
+and prototypical background agents  $\mathbf{B}_a^l\in \mathbb{R}^{N_a\times C_e}$ . Inspired by CrossViT [6], we use masked cross-attention (M-CA) mechanism to aggregate information of  $\mathbf{E}_z^l$  in the bbox  $b_{z}$ , and produce template foreground agents. Formally,
+
+$$
+\mathbf {A} _ {t t} = \operatorname {S o f t m a x} \left(\left(\mathbf {F} _ {a} ^ {l} \mathbf {W} _ {Q}\right) \left(\mathbf {E} _ {z} ^ {l} \mathbf {W} _ {K}\right) ^ {\top} + \mathbf {M} _ {z} ^ {l}\right), \tag {4}
+$$
+
+$$
+\mathbf {F} _ {z} ^ {l} = \mathrm {M - C A} (\mathbf {F} _ {a} ^ {l}, \mathbf {E} _ {z} ^ {l}, \mathbf {M} _ {z} ^ {l}) = \mathbf {A} _ {t t} (\mathbf {E} _ {z} ^ {l} \mathbf {W} _ {V}),
+$$
+
+where  $\mathbf{W}_Q, \mathbf{W}_K,$  and  $\mathbf{W}_V$  are linear projections. And the element in template foreground mask  $\mathbf{M}_z^l$  is set to 0, if the corresponding position of this element is in the bbox  $b_{z}$ . Otherwise, it will be set to  $-\infty$ . Similarly, for the template background mask  $\overline{\mathbf{M}}_z^l$ , the element is set to 0, if the corresponding position of this element is outside the bbox  $b_{z}$ . Otherwise, it will be set to  $-\infty$ . And we can obtain template background agents  $\mathbf{B}_z^l = \mathrm{M - CA}(\mathbf{B}_a^l, \mathbf{E}_z^l, \overline{\mathbf{M}}_z^l)$ .
+
+For search region features  $\mathbf{E}_x^l$ , we can generate  $\mathbf{M}_x^l$  and  $\overline{\mathbf{M}}_x^l$  according to the pseudo bbox  $\hat{b}_x^l$ . Since  $\hat{b}_x^l$  is not precise enough, we leverage updated template FB-agents  $[\mathbf{F}_z^l; \mathbf{B}_z^l]$  to serve as queries, which provides clearer fore-background priors than prototypical agents  $[\mathbf{F}_a^l; \mathbf{B}_a^l]$ . Formally,
+
+$$
+\mathbf {F} _ {x} ^ {l} = \operatorname {M - C A} \left(\mathbf {F} _ {z} ^ {l}, \mathbf {E} _ {x} ^ {l}, \mathbf {M} _ {x} ^ {l}\right),
+$$
+
+$$
+\mathbf {B} _ {x} ^ {l} = \operatorname {M - C A} \left(\mathbf {B} _ {z} ^ {l}, \mathbf {E} _ {x} ^ {l}, \overline {{\mathbf {M}}} _ {x} ^ {l}\right). \tag {5}
+$$
+
+Finally, we obtain template FB-agents  $[\mathbf{F}_z^l;\mathbf{B}_z^l]$ , and search region FB-agents  $[\mathbf{F}_x^l;\mathbf{B}_x^l]$  at the  $l^{th}$  block.
+
+# 3.3. Distribution-aware Attention Module
+
+After obtaining template FB-agents  $[\mathbf{F}_z^l;\mathbf{B}_z^l]$  and search region FB-agents  $[\mathbf{F}_x^l;\mathbf{B}_x^l]$ , we begin to model the foreground distribution for each image token. Specifically, given token features  $[\mathbf{H}_z^{l - 1};\mathbf{H}_x^{l - 1}]$ , the initial query, key and value arise from these token features. Formally,
+
+$$
+\widetilde {\mathbf {Q}} _ {z x} ^ {l} = \left[ \widetilde {\mathbf {Q}} _ {z} ^ {l}; \widetilde {\mathbf {Q}} _ {x} ^ {l} \right] = \mathrm {L N} \left(\left[ \mathbf {H} _ {z} ^ {l - 1}; \mathbf {H} _ {x} ^ {l - 1} \right]\right) \mathbf {W} _ {Q} ^ {l},
+$$
+
+$$
+\widetilde {\mathbf {K}} _ {z x} ^ {l} = \left[ \widetilde {\mathbf {K}} _ {z} ^ {l}; \widetilde {\mathbf {K}} _ {x} ^ {l} \right] = \operatorname {L N} \left(\left[ \mathbf {H} _ {z} ^ {l - 1}; \mathbf {H} _ {x} ^ {l - 1} \right]\right) \mathbf {W} _ {K} ^ {l}, \tag {6}
+$$
+
+$$
+\mathbf {V} _ {z x} ^ {l} = \left[ \mathbf {V} _ {z} ^ {l}; \mathbf {V} _ {x} ^ {l} \right] = \mathrm {L N} \left(\left[ \mathbf {H} _ {z} ^ {l - 1}; \mathbf {H} _ {x} ^ {l - 1} \right]\right) \mathbf {W} _ {V} ^ {l},
+$$
+
+where LN denotes the layer normalization,  $\mathbf{W}_K^l\in$ $\mathbb{R}^{C\times C},\mathbf{W}_Q^l\in \mathbb{R}^{C\times C},\mathbf{W}_V^l\in \mathbb{R}^{C\times C}$  are linear projections. As can be seen, existing plain attention mechanism [14] generate queries and keys simply based on appearance features, which will easily have incorrect high attention score for regions with similar distractors. Differently, we use the fore-background distribution to serve as queries and keys instead of appearance features. To this end, we first project  $[\mathbf{F}_z^l;\mathbf{B}_z^l]$  and  $[\mathbf{F}_x^l;\mathbf{B}_x^l]$  into  $C$  dimensions. By calculating the similarity between each token and these fore-background agents, we can model the fore-background distribution of this token. Here, we take the
+
+fore-background distribution of initial query token as updated queries  $\mathbf{Q}_{zx}^{l} = [\mathbf{Q}_{z}^{l};\mathbf{Q}_{x}^{l}]$ . Formally,
+
+$$
+\begin{array}{l} \mathbf {Q} _ {z} ^ {l} = \widetilde {\mathbf {Q}} _ {z} ^ {l} \left[ \mathbf {F} _ {z} ^ {l} \mathbf {W} _ {z} ^ {l}; \mathbf {B} _ {z} ^ {l} \mathbf {W} _ {z} ^ {l} \right] ^ {\top}, \tag {7} \\ \mathbf {Q} _ {x} ^ {l} = \tilde {\mathbf {Q}} _ {x} ^ {l} \left[ \mathbf {F} _ {x} ^ {l} \mathbf {W} _ {x} ^ {l}, \mathbf {B} _ {x} ^ {l} \mathbf {W} _ {x} ^ {l} \right] ^ {\top}, \\ \end{array}
+$$
+
+where  $\mathbf{W}_z^l, \mathbf{W}_x^l \in \mathbb{R}^{C_e \times C}$  are linear projections. Similarly, we can obtain updated keys  $\mathbf{K}_{zx}^l = [\mathbf{K}_z^l, \mathbf{K}_x^l]$ .
+
+$$
+\begin{array}{l} \mathbf {K} _ {z} ^ {l} = \widetilde {\mathbf {K}} _ {z} ^ {l} \left[ \mathbf {F} _ {z} ^ {l} \mathbf {W} _ {z} ^ {l}; \mathbf {B} _ {z} ^ {l} \mathbf {W} _ {z} ^ {l} \right] ^ {\top}, \tag {8} \\ \mathbf {K} _ {x} ^ {l} = \tilde {\mathbf {K}} _ {x} ^ {l} \left[ \mathbf {F} _ {x} ^ {l} \mathbf {W} _ {x} ^ {l}; \mathbf {B} _ {x} ^ {l} \mathbf {W} _ {x} ^ {l} \right] ^ {\top}. \\ \end{array}
+$$
+
+With updated queries and keys, the proposed distribution-aware attention module can achieve fore-background aware feature interaction. The output of the  $l^{th}$  transformer blocks  $\mathbf{H}_{zx}^l$  can be formulated as follows,
+
+$$
+\widetilde {\mathbf {H}} _ {z x} ^ {l} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} _ {z x} ^ {l} \left(\mathbf {K} _ {z x} ^ {l}\right) ^ {\top}}{\sqrt {C}}\right) \mathbf {V} _ {z x} ^ {l} + \mathbf {H} _ {z x} ^ {l - 1} \tag {9}
+$$
+
+$$
+\mathbf {H} _ {z x} ^ {l} = \left[ \mathbf {H} _ {z} ^ {l}; \mathbf {H} _ {x} ^ {l} \right] = \operatorname {M L P} \left(\operatorname {L N} \left(\widetilde {\mathbf {H}} _ {z x} ^ {l}\right)\right) + \widetilde {\mathbf {H}} _ {z x} ^ {l},
+$$
+
+where MLP denotes the multi-layer perception. The output token features  $\mathbf{H}_{zx}^{l}$  will be sent into next transformer blocks. Eventually, token features are processed  $L$  times via our proposed fore-background distribution modeling transformer block, and we can obtain final token features  $\mathbf{H}_{zx}^{L}$ .
+
+# 3.4. Box Prediction Head and Objective Function
+
+As shown in Figure 2, search region token features  $\mathbf{H}_x^L$  are reshaped and fed into a box prediction head for target state estimation. Here, the box prediction head is inspired from OSTrack [62]. We use the weighted focal loss [33] as classification loss  $\mathcal{L}_{cls}$ . Besides, we adopt  $\ell_1$  loss  $\mathcal{L}_1$  and generalized IoU loss [48]  $\mathcal{L}_{giou}$  to supervise bounding box regression. More details about the box prediction head and losses can be referred to OSTrack [62]. As we introduced before, there are point loss and box loss for pseudo bbox generation at each block. In summary, the overall objective function is formulated as follows.
+
+$$
+\mathcal {L} = \mathcal {L} _ {c l s} + \lambda_ {1} \mathcal {L} _ {1} + \lambda_ {g i o u} \mathcal {L} _ {g i o u} + \lambda_ {b o x} \sum_ {l = 1} ^ {L} \mathcal {L} _ {b o x} ^ {l}, \tag {10}
+$$
+
+where  $\lambda_1, \lambda_{giou}$  and  $\lambda_{box}$  are scalars to balance these losses.
+
+# 4. Experiments
+
+In this section, we first introduce implementation details. Then, we show experimental results on eight benchmarks. Finally, we conduct a series of ablation studies to verify the effectiveness of each component. Please refer to the Supplementary Material for more details and results.
+
+Table 1. Comparisons with state-of-the-art trackers on GOT-10k, TNL2K, LaSOT,  $\mathrm{LaSOT}_{ext}$ , and TrackingNet. The best three results are shown in red, blue and green fonts.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">GOT-10k [26]</td><td colspan="2">TNL2K [54]</td><td colspan="3">LaSOT [17]</td><td colspan="3">\( LaSOT_{ext} \) [16]</td><td colspan="3">TrackingNet [45]</td></tr><tr><td>AO</td><td>\( SR_{0.5} \)</td><td>\( SR_{0.75} \)</td><td>AUC</td><td>P</td><td>AUC</td><td>\( P_{Norm} \)</td><td>P</td><td>AUC</td><td>\( P_{Norm} \)</td><td>P</td><td>AUC</td><td>\( P_{Norm} \)</td><td>P</td></tr><tr><td>SiamFC[2]</td><td>34.8</td><td>35.3</td><td>9.8</td><td>29.5</td><td>28.6</td><td>33.6</td><td>42.0</td><td>33.9</td><td>23.0</td><td>31.1</td><td>26.9</td><td>57.1</td><td>66.3</td><td>53.3</td></tr><tr><td>ECO [11]</td><td>31.6</td><td>30.9</td><td>11.1</td><td>32.6</td><td>31.7</td><td>32.4</td><td>33.8</td><td>30.1</td><td>22.0</td><td>25.2</td><td>24.0</td><td>55.4</td><td>61.8</td><td>49.2</td></tr><tr><td>SiamRPN++ [34]</td><td>51.7</td><td>61.6</td><td>32.5</td><td>41.3</td><td>41.2</td><td>49.6</td><td>56.9</td><td>49.1</td><td>34.0</td><td>41.6</td><td>39.6</td><td>73.3</td><td>80.0</td><td>69.4</td></tr><tr><td>SiamCAR [23]</td><td>56.9</td><td>67.0</td><td>41.5</td><td>35.5</td><td>38.4</td><td>50.7</td><td>60.0</td><td>51.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SiamFC++ [58]</td><td>59.5</td><td>69.5</td><td>47.9</td><td>38.6</td><td>36.9</td><td>54.4</td><td>62.3</td><td>54.7</td><td>-</td><td>-</td><td>-</td><td>75.4</td><td>80.0</td><td>70.5</td></tr><tr><td>D3S [39]</td><td>59.7</td><td>67.6</td><td>46.2</td><td>38.8</td><td>39.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>72.8</td><td>76.8</td><td>66.4</td></tr><tr><td>Ocean [63]</td><td>61.1</td><td>72.1</td><td>47.3</td><td>38.4</td><td>37.7</td><td>56.0</td><td>65.1</td><td>56.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiMP-50 [3]</td><td>61.1</td><td>71.7</td><td>49.2</td><td>44.7</td><td>43.4</td><td>56.9</td><td>65.0</td><td>56.7</td><td>39.2</td><td>47.6</td><td>45.1</td><td>74.0</td><td>80.1</td><td>68.7</td></tr><tr><td>PrDiMP-50 [13]</td><td>63.4</td><td>73.8</td><td>54.3</td><td>47.0</td><td>45.9</td><td>59.8</td><td>68.8</td><td>60.8</td><td>-</td><td>-</td><td>-</td><td>75.8</td><td>81.6</td><td>70.4</td></tr><tr><td>KeepTrack[43]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>67.1</td><td>77.2</td><td>70.2</td><td>48.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ToMP-101 [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>68.5</td><td>79.2</td><td>73.5</td><td>45.9</td><td>-</td><td>-</td><td>81.5</td><td>86.4</td><td>78.9</td></tr><tr><td>KYS [4]</td><td>63.6</td><td>75.1</td><td>51.5</td><td>44.9</td><td>43.5</td><td>55.4</td><td>63.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>74.0</td><td>80.0</td><td>68.8</td></tr><tr><td>STMTrack [21]</td><td>64.2</td><td>73.7</td><td>57.5</td><td>-</td><td>-</td><td>60.6</td><td>63.3</td><td>69.3</td><td>-</td><td>-</td><td>-</td><td>80.3</td><td>85.1</td><td>76.7</td></tr><tr><td>TransT [7]</td><td>67.1</td><td>76.8</td><td>60.9</td><td>50.7</td><td>51.7</td><td>64.9</td><td>69.0</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>81.4</td><td>86.7</td><td>80.3</td></tr><tr><td>STARK-ST101 [59]</td><td>68.8</td><td>78.1</td><td>64.1</td><td>-</td><td>-</td><td>67.1</td><td>77.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.0</td><td>86.9</td><td>-</td></tr><tr><td>CSWinTT [50]</td><td>69.4</td><td>78.9</td><td>65.4</td><td>-</td><td>-</td><td>66.2</td><td>75.2</td><td>70.9</td><td>-</td><td>-</td><td>-</td><td>81.9</td><td>86.7</td><td>79.5</td></tr><tr><td>SimTrack-B/16 [5]</td><td>68.6</td><td>78.9</td><td>62.4</td><td>54.8</td><td>53.8</td><td>69.3</td><td>78.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.3</td><td>86.5</td><td>-</td></tr><tr><td>SwinTrack-B [36]</td><td>69.4</td><td>78.0</td><td>64.3</td><td>-</td><td>-</td><td>69.6</td><td>78.6</td><td>74.1</td><td>47.6</td><td>58.2</td><td>54.1</td><td>82.5</td><td>87.0</td><td>80.4</td></tr><tr><td>AiATrack [22]</td><td>69.6</td><td>80.0</td><td>63.2</td><td>-</td><td>-</td><td>69.0</td><td>79.4</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>82.7</td><td>87.8</td><td>80.4</td></tr><tr><td>SBT-L [57]</td><td>70.4</td><td>80.8</td><td>64.7</td><td>-</td><td>-</td><td>66.7</td><td>77.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MixFormer [10]</td><td>70.7</td><td>80.0</td><td>67.8</td><td>-</td><td>-</td><td>69.2</td><td>78.7</td><td>74.7</td><td>-</td><td>-</td><td>-</td><td>83.1</td><td>88.1</td><td>81.6</td></tr><tr><td>RTS [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>69.7</td><td>76.2</td><td>73.7</td><td>-</td><td>-</td><td>-</td><td>81.6</td><td>86.0</td><td>79.4</td></tr><tr><td>OSTrack-256 [62]</td><td>71.0</td><td>80.4</td><td>68.2</td><td>54.3</td><td>-</td><td>69.1</td><td>78.7</td><td>75.2</td><td>47.4</td><td>57.3</td><td>53.3</td><td>83.1</td><td>87.8</td><td>82.0</td></tr><tr><td>OSTrack-384 [62]</td><td>73.7</td><td>83.2</td><td>70.8</td><td>55.9</td><td>-</td><td>71.1</td><td>81.1</td><td>77.6</td><td>50.5</td><td>61.3</td><td>57.6</td><td>83.9</td><td>88.5</td><td>83.2</td></tr><tr><td>F-BDMTrack-256</td><td>72.7</td><td>82.0</td><td>69.9</td><td>56.4</td><td>56.5</td><td>69.9</td><td>79.4</td><td>75.8</td><td>47.9</td><td>57.9</td><td>54.0</td><td>83.7</td><td>88.3</td><td>82.6</td></tr><tr><td>F-BDMTrack-384</td><td>75.4</td><td>84.3</td><td>72.9</td><td>57.8</td><td>59.4</td><td>72.0</td><td>81.5</td><td>77.7</td><td>50.8</td><td>61.3</td><td>57.8</td><td>84.5</td><td>89.0</td><td>84.0</td></tr></table>
+
+# 4.1. Implementation Details
+
+Network details. We present two variants of our tracker, F-BDMTrack-256 and F-BDMTrack-384. Similar to OSTrack [62], we crop the template image and search region image which are  $2^{2}$  and  $4^{2}$  times of the target box area respectively. The F-BDMTrack-256 resizes search region to a resolution of  $256 \times 256$  and template to a resolution of  $128 \times 128$  as input. The F-BDMTrack-384 resizes search region to a resolution of  $384 \times 384$  and template to  $192 \times 192$ . These images are split into a set of patches, where the resolution of each patch is  $16 \times 16$ . These patches are flattened and projected into  $C = 768$  channels to serve as the input of F-BDMTrack. The channel of  $\mathbf{E}_z^l$  in the FBAL module is set to  $C_e = 256$ . We leverage the Precise RoI Pooling [28] operation to crop features according to the target bounding box, and obtain the target feature with shape  $(h_t, w_t) = (4, 4)$ . The number of foreground agents and background agents are both set to  $N_a = 4$ . And our F-BDMTrack consists of  $L = 12$  fore-background distribution modeling transformer blocks.
+
+Training details. We train our model on the training splits of LaSOT [17], GOT-10K [26], COCO2017 [37], and TrackingNet [45], which is a similar training setting to OSTrack [62]. Common data augmentations including horizontal flip and brightness jittering are applied in the training
+
+process. We train our F-BDMTrack by the AdamW optimizer with the weight decay  $10^{-4}$ . The learning rates start from  $4 \times 10^{-5}$  for the backbone including the FBAL module and the  $\mathrm{DA}^2$  module, and  $4 \times 10^{-4}$  for the box prediction head. Our model is trained on four NVIDIA RTX 3090 GPUs, each GPU holds 32 image pairs, resulting in a total batch size of 128. The total epochs are set to 300 with 60k samples per epoch and we decrease the learning rate by a factor of 10 after 240 epochs. The weights of training losses are set to  $\lambda_1 = 5.0$ ,  $\lambda_{giou} = 2.0$ , and  $\lambda_{box} = 1.0$ .
+
+# 4.2. Results and State-of-the-art Comparisons
+
+GOT-10k. GOT-10k [26] is a large-scale dataset containing over 10k videos for training and 180 for testing. It forbids trackers to use external datasets for training. We follow its policy and retrain our model. The results are reported in Table 1. Our tracker has a satisfactory improvement in all metrics. Specifically, F-BDMTrack-256 improves by  $1.7\%$  in success rate  $(\mathrm{SR}_{0.75})$  compared with OSTrack-256. And F-BDMTrack-384 gives an improved new record  $75.4\%$  in AO, indicating the effectiveness of foreground and background distribution modeling to extract discriminative features, resulting in more accurate state estimation.
+
+TNL2K. TNL2K [54] is a recently published dataset containing 700 video sequences for testing. In Table 1, F-BDMTrack-256 gains by  $2.1\%$  AUC over OTrack-256 and
+
+Table 2. Comparisons with state-of-the-art trackers on NFS, OTB100 and UAV123 datasets in terms of overall AUC score. The best three results are shown in red, blue and green fonts.  
+
+<table><tr><td></td><td>SiamFC [2]</td><td>Ocean [63]</td><td>ATOM [12]</td><td>DiMP-50 [3]</td><td>PrDiMP-50 [13]</td><td>TransT [7]</td><td>OSTrack-256 [62]</td><td>OSTrack-384 [62]</td><td>F-BDMTrack-256</td><td>F-BDMTrack-384</td></tr><tr><td>NFS [30]</td><td>37.7</td><td>49.4</td><td>58.3</td><td>61.8</td><td>63.5</td><td>65.3</td><td>64.7</td><td>66.5</td><td>66.0</td><td>67.3</td></tr><tr><td>OTB100 [56]</td><td>61.2</td><td>68.4</td><td>66.3</td><td>68.4</td><td>69.6</td><td>69.4</td><td>68.1</td><td>69.2</td><td>69.5</td><td>69.9</td></tr><tr><td>UAV123 [44]</td><td>46.8</td><td>57.4</td><td>63.2</td><td>64.3</td><td>68.0</td><td>68.1</td><td>68.3</td><td>70.7</td><td>69.0</td><td>70.9</td></tr></table>
+
+![](images/eda4bebd02dc50da6fa2dc31d754e3e43828ff0e01d9cfd2f672ad936460fddc.jpg)  
+Figure 3. Visualizations of fore-background agent activation maps for the template and search region.
+
+Table 3. Effectiveness of each component on the LaSOT  
+
+<table><tr><td>Model</td><td>FBAL</td><td>DA2</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>[A]</td><td>X</td><td>X</td><td>68.5</td><td>77.8</td><td>74.2</td></tr><tr><td>[B]</td><td>✓</td><td>X</td><td>68.8</td><td>78.1</td><td>74.6</td></tr><tr><td>[C]</td><td>X</td><td>✓</td><td>69.4</td><td>78.7</td><td>75.4</td></tr><tr><td>[D]</td><td>✓</td><td>✓</td><td>69.9</td><td>79.4</td><td>75.8</td></tr></table>
+
+even performances better than larger models (OTrack-384). When also leveraging a large model (F-BDMTrack-384), we can further improve the AUC score to  $57.8\%$ .
+
+LaSOT. LaSOT [17] is a densely annotated large-scale dataset containing a total of 1400 long-term video sequences, of which the test set contains 280 video sequences. This is a challenging tracking dataset. As shown in Table 1, F-BDMTrack-256 outperforms OSTrack-256 by  $0.8\%$  AUC. Further, F-BDMTrack-384 achieves the best performance of  $72.0\%$  AUC. Our tracker does not add additional timing strategies [22, 10, 59] in this long-term tracking task, but can still obtain performance improvement with the aid of fore-background distribution modeling design, which demonstrates that our approach can fundamentally mitigate complex scenarios and distractors.
+
+$\mathbf{LaSOT}_{ext}$ . The recent  $\mathrm{LaSOT}_{ext}$  [16] is an extended subset of LaSOT, containing 150 additional new sequences. This dataset has many similar distractors, making it difficult for tracking. And our F-BDMTrack can achieve competitive or even better performance. In specific, F-BDMTrack-256 achieves superior results, outperforming OSTrack-256 by  $0.5\%$  AUC. And F-BDMTrack-356 obtains a much higher performance with  $50.8\%$  AUC.
+
+Trackingnet. Trackingnet [45] provides over 30k video sequences, which are sampled from Youtube to cover target categories and scenes of real-world. It provides 511 testing video sequences without publicly available annotation,
+
+![](images/33543c545be77996d0f4266823100860dce4438828c407b85617cc66d39775f7.jpg)  
+Figure 4. Visualization of pseudo bboxes using the pseudo-bbox generation strategy at all blocks.
+
+so results reported in Table 1 are obtained from the online evaluation server. As can be seen, our F-BDMTrack-384 achieves  $84.5\%$  AUC and sets a new state of the art.
+
+NFS. Videos in Need for Speed(NFS) [30] are captured from a high frame rate camera, which contains fast motions and distractors. We report results on its commonly used version NFS30. As shown in Table 2, F-BDMTrack-256 achieves  $66.0\%$  AUC, outperforming OSTrack-256 by  $1.3\%$ . And F-BDMTrack-384 achieves best results (67.3% AUC score) as expected, demonstrating the superior competitiveness of our tracker in the presence of interferer-challenged benchmark.
+
+OTB100. OTB [56] is a pioneering visual tracking benchmark. It has been noticed that this benchmark is approaching saturation [53, 59, 43]. In Table 2, two versions of our tracker both achieve promising AUC scores (69.5 and 69.9). UAV123. UAV123 [44] provides 123 unmanned aerial vehicle(UAV) sequences, including different scale sizes of UAV in real-world dynamic scenarios. As shown in Table 2, our tracker achieves the best AUC score  $(70.9\%)$  and is suitable for UAV tracking scenarios.
+
+# 4.3. Ablation Study
+
+To validate the effectiveness of each component, we perform a detailed ablation study on LaSOT [17]. The following experiments use F-BDMTrack-256 as the base model.
+
+Effectiveness of key components in our F-BDMTrack. Our tracker consists of two key components, including a fore-background agent learning (FBAL) module and a distribution-aware attention  $(\mathrm{DA}^2)$  module. Here, we explore the exact impact of these modules. The model [A] is the baseline, which means that we directly use plain attention mechanism without using the FBAL and the  $\mathrm{DA}^2$  module. For the model [B], we add the FBAL module, and
+
+Table 4. Effects with different numbers of prototypical FB-agents.  
+
+<table><tr><td>Na</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>1</td><td>69.3</td><td>78.8</td><td>75.5</td></tr><tr><td>2</td><td>69.6</td><td>79.1</td><td>75.6</td></tr><tr><td>4</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>8</td><td>69.3</td><td>78.9</td><td>75.2</td></tr><tr><td>16</td><td>69.0</td><td>78.6</td><td>75.1</td></tr></table>
+
+Table 5. Effects of the pseudo bbox generation at different blocks.  
+
+<table><tr><td>blocks</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>None</td><td>69.0</td><td>78.5</td><td>75.0</td></tr><tr><td>10-12</td><td>69.5</td><td>79.1</td><td>75.5</td></tr><tr><td>6-12</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>4-12</td><td>69.8</td><td>79.2</td><td>75.8</td></tr><tr><td>1-12</td><td>69.2</td><td>78.7</td><td>75.2</td></tr></table>
+
+adopt plain attention mechanism to replace our designed  $\mathrm{DA}^2$  module. The plain attention mechanism does not require fore-background agents (FB-agents) produced by our FBAL module. Thus, the model [B] is used to validate the impacts of pseudo bbox generation loss  $\mathcal{L}_{box}^{l}$  introduced in the FBAL module. As shown in Table 3, the performance of model [B] gains by  $0.3\%$  compared to the model [A], demonstrating that the pseudo bbox loss has some positive effects to constrain foreground features interact with features in foreground regions. For the model [C], we adopt the  $\mathrm{DA}^2$  module for feature interaction, and FB-agents are obtained by pooling features within or outside the bounding box for the template and search region. As can be seen, the performance of model [C] gains by  $0.9\%$  compared to the model [A], which demonstrates that the proposed  $\mathrm{DA}^2$  module can significantly help learn discriminative features even if FB-agents are not good enough. When adding the FBAL module for better FB-agents generation, the performance of model [D] gains by  $0.5\%$  compared to the model [C], showing the superiority of proposed FBAL module.
+
+Study on the number of prototypical FB-agents in the FBAL module. Here, we explore the effects about different numbers of prototypical FB-agents. As shown in Table 4, our tracker achieves the optimal result (69.9% AUC score) when  $N_{a} = 4$ . A small number of prototypical FB-agents cannot fully model the fore-background distribution, leading to decreased performance. Meanwhile, more prototypical FB-agents will introduce useless noise, which is harmful for feature interaction. Besides, without explicit constraints to guide foreground and background agent learning, an excessive number of agents are unable to focus on their respective discriminative information better. A more effective FB-agent learning way can be explored in future work. Finally, we show the fore-background agent activation maps for the template and search region in Figure 3. It can be seen that these FB-agents generated by our FBAL module can focus on the foreground and background well.
+
+Study on the pseudo bbox generation strategy at differ
+
+![](images/2ce3904d0c46982c4e1ffbba90609ede7306bd04aabc06ed2c92eefdfed08873.jpg)  
+Figure 5. Response maps of the template central feature to all search region features. It can be seen that although the template target has similar appearance with the background distractor in the search region, their fore-background distributions are different.
+
+ent blocks. High-quality pseudo bbox is more conducive to the FB-agent learning for the search region. However, as shown in Figure 4, the pseudo-bboxes in shallow blocks tend to have a large bias, which is harmful to learn effective FB-agents. We conduct a detailed experiment to find which blocks are optimal for using pseudo bbox generation strategy. As shown in Table 5, our tracker achieves the best results when we leverage the pseudo bbox generation strategy at the  $6^{th}$  to  $12^{th}$  ('6-12') transformer blocks. This is because the last few blocks provide more reliable pseudo bbox to guide fore-background agent learning.
+
+Comparisons between the plain attention mechanism and our  $\mathbf{DA}^2$  mechanism. Here, we visualize response maps of the plain attention mechanism and our  $\mathrm{DA}^2$  mechanism in Figure 5. As we can see, the plain attention mechanism easily focus on complex backgrounds or distractors. This is because attention scores are obtained based on appearance similarities, while targets usually have similar appearance with distractors, resulting in incorrect response map. Differently, our proposed  $\mathrm{DA}^2$  mechanism discriminates features from the perspective of fore-background distributions instead of appearance similarities, which can effectively suppress the response of the template to background distractors in the search region, and strengthen the response of the template to the foreground target in the search region. Finally, based on the proposed distribution
+
+aware attention mechanism, our tracker can achieve superior performance on all eight tracking benchmarks.
+
+# 5. Conclusion
+
+In this work, we propose a novel foreground-background distribution modeling transformer for visual tracking, including a FBAL module and a  $\mathrm{DA}^2$  module. With these two elegant designs, our proposed tracker can extract features with high target discriminative power under ever-changing tracking scenarios, which is essential for accurate target state estimation. Extensive experiments on eight tracking benchmarks verify the superiority of our proposed tracker.
+
+# 6. Acknowledgement
+
+This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), and National Defense Basic Scientific Research Program of China (Grant JCKY2020903B002).
+
+# References
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+                                    "content": "To deal with the above challenges, numerous approaches have been proposed [23, 2, 3, 59, 10, 5, 62]. These methods can be generally divided into three main paradigms, including CNN-based [8, 52, 58, 35, 3, 13], hybrid CNN-Transformer [7, 59, 36, 50, 42], and pure Transformer trackers [5, 62, 32, 57]. CNN-based trackers first extract features from the template and search region separately through a shared convolutional neural network (CNN), and then the target state is estimated by calculating cross-correlation [2, 58, 52] between features in template and search regions, or learning a discriminative correlation filter [12, 3, 13]. With the successful development of transformer in the computer vision field, an increasing number of hybrid CNN-Transformer trackers [7, 59, 42] have been proposed. These trackers also leverage CNN to extract features separately, but adopt transformer to realize the feature interaction between the template and search region, which can alleviate the loss of discriminative foreground information. However, for the above two paradigm trackers, there is no interaction between the template and the search region when extracting features. These target-unaware feature extraction ways have limited target-background discriminative power, especially when the target category is not seen"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "*Equal Contribution"
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+                },
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+                                    "type": "text",
+                                    "content": "† Corresponding Author"
+                                }
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+            ],
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+                                    "content": "in the training dataset. To this end, pure Transformer trackers [5, 62, 32, 57] are proposed to build interaction between template and search region along with the feature extraction. Thanks to the strong representation and interaction capability of ViT/SwinT variants [14, 38, 55], pure Transformer trackers have achieved remarkable improvements."
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+                                    "content": "Despite the success of the above pure Transformer trackers, the feature learning of these methods are easily disturbed by complex backgrounds due to insufficient consideration of fore-background relationship. To make pure Transformer architectures more suitable for discriminative feature learning in visual object tracking, there are two core points that need to be considered. (1) Fore-background information mining. Previous methods [5, 22, 21] usually mine fore-background information from the template according to the given bounding box (bbox). However, the tracking target can be continuously changing, making it difficult to learn target discriminative features for current search region, if only guided by fore-background information of the template. Therefore, it is necessary to propose a effective way to mine fore-background information for both template and search region. (2) Target-aware feature interaction. Most of popular Transformer trackers [62, 10, 57] adopt the plain attention mechanism to build interaction between template and search region. Since attention scores are obtained by appearance similarity, the template features will mistakenly aggregate background information and further affect features of search region during feature interaction, resulting messy response map (Figure 1 (a)). Although some methods [22, 42] introduce additional target embeddings to enhance the target information, they could still be disturbed by distractors, making features of the search region have limited target discriminative power. And the response map is also unsatisfactory (Figure 1 (b)). Therefore, it is urgent to design a new attention mechanism to achieve better target-aware feature interaction."
+                                }
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+                                    "content": "Motivated by the above discussion, we propose a novel Foreground-Background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which consists of a fore-background agent learning (FBAL) module and a distribution-aware attention "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "(\\mathrm{DA}^2)"
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+                                    "content": " module in a unified transformer architecture. In the fore-background agent learning module, we aim to mine foreground and background information from both the template and the search region. Specifically, we initialize a set of fore-background agents. And fore-background agents for the template (search region) are obtained by aggregating foreground and background information in the template (search region), which can be used to guide the subsequent feature interaction. In the distribution-aware attention module, it is proposed to realize target-aware feature interaction. Specifically, we calculate the similarity scores between each patch feature and the fore-background agents, which can"
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+                    ],
+                    "index": 2
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+                                    "type": "text",
+                                    "content": "be regarded as fore-background distributions for each patch feature. Then we can obtain the attention score by compute the similarity between their distributions, which are later used for feature aggregation. As shown in Figure 1 (c), foreground patches and background patches could have different fore-background distributions even though they have similar appearance. Thus, we can aggregate more useful information and learn more discriminative features."
+                                }
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+                    ],
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+                                    "content": "The main contributions of this work are summarized as follows. (1) We develop a novel Foreground-background Distribution Modeling Transformer for visual object tracking (F-BDMTrack), which can extract features with high target discriminative power under ever-changing tracking scenarios. (2) The proposed FBAL module can effectively mine foreground information for both template and search region with designed foreground agents. And the proposed "
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+                                    "content": "\\mathrm{DA}^2"
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+                                    "type": "text",
+                                    "content": " module can effectively suppress the interaction between foreground and background, which helps learn more discriminative features for visual tracking. (3) Extensive experimental results on eight benchmarks show that our method attains state-of-the-art performance, verifying the superiority of our F-BDMTrack."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "content": "2. Related Work"
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+                },
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+                                    "content": "Visual object tracking (VOT). Current popular trackers can be divided into CNN-based trackers [8, 2, 58, 35, 40, 12, 3, 13], hybrid CNN-Transformer trackers [59, 7, 50, 53, 42], and pure Transformer trackers [62, 5, 36, 32, 57] according to the network architecture. CNN-based trackers commonly learn features of template and search region via share-weighted convolutional neural networks (CNN), and the interaction between template and search region is realized by cross correlation [2, 58, 35] or correlation filter [12, 3, 13]. However, due to the lack of global perception and the simple interaction strategy, some target-background discriminative information may be lost, restricting the development of CNN-based trackers. Recently, Vision Transformer brings a new solution to visual tracking. Hybrid CNN-Transformer trackers reserve the extraction of features with CNNs and utilize attention mechanisms to establish global dependencies between features. Typically, STARK [59] utilizes the Transformer to aggregate spatial-temporal cues for target location. Moreover, ToMP [42] uses a Transformer-based architecture to encode a long-term target representation to localize the target. Nevertheless, these Hybrid CNN-Transformer trackers still extract features of template and search region separately, which causes extracted features to be unaware of the tracking target. To alleviate this limitation, pure Transformer-based trackers [62, 5, 57] are proposed. For example, OSTrack [62] and SimTrack [5] unify the feature extraction and the feature relation modeling in Vision Transformer [14]. They achieve superior performance, proving the potential of pure Transformer"
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+                                    "content": "architectures in visual tracking. However, these trackers [62, 5] aggregate features according to appearance similarities through plain attention mechanisms. Without considering fore-background relationship for the template and search region, target features may mistakenly aggregate background noise in the search region. Differently, in our work, we propose the distribution aware attention module to aggregate features according to their fore-background distribution similarities, which can effectively suppress incorrect interaction between foreground and background."
+                                }
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+                    ],
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+                                    "type": "text",
+                                    "content": "Fore-background exploitation in visual object tracking. There are several tracking methods [21, 42, 5, 46, 19] actively exploring ways to mine fore-background information for robust tracking. STMTrack [21] leverages foreground-background masks derived by bounding boxes of template sequences to highlight target representations. And ToMP [42] is proposed to learn foreground embeddings from a set of template sequences, which can be used to enhance target features of the template and assist in target state estimation. However, the above methods for exploiting fore-background generally use fixed foreground embedding for template images, ignoring the fact that tracking target can be continuously changing. Besides, they do not analyze the fore-background information of the search region. Furthermo, RTS [46] utilizes an additional segmentation network to provide more precise object masks, leading to better performance improvements. And SNLT [19] adopts additional natural language labels to help extract better target embeddings for distinguishing foreground and background. These methods utilize additional network components and labels to mine fore-background information, which affects the independence of the network architecture. In contrast, our method is proposed to fully mine fore-background information from templates and search regions, and utilizes them to improve the discriminative ability without attaching additional models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
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+                                    "content": "Visual transformer and attention variants. Nowadays, Transformer has been rapidly applied in the computer vision due to its global interaction ability. Typically, ViT [14] realizes image classification by learning global representations of patches through attention mechanisms. To optimize efficiency, Swin Transformer [38] restricts attention computation in non-overlapping local windows and exchange information between windows through a sliding operation. Thanks to these effective designs, Vision Transformers have been applied to visual tracking, such as MixFormer [10] (using CvT [55]) and OSTrack [62] (using ViT [14]). Further, some trackers improve attention mechanisms to better adapt to visual tracking task. AiATrack [22] proposes an attention in attention module to model the relationship of attention scores, which can improve the quality of attention maps. And SparseTT [20] proposes sparse attention to focus the most relevant information in the"
+                                }
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+                    ],
+                    "index": 2
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+                {
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+                                    "type": "text",
+                                    "content": "search region. However, these methods still calculate attention scores with appearance similarities, which will inevitably disturbed by similar distractors. Differently, we propose a novel foreground-background distribution modeling tracker, which can accurately discriminate target features by perceiving the distribution of fore-background."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
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+                {
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+                                    "content": "3. Method"
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+                                    "content": "In this section, we introduce our proposed foreground-background distribution modeling transformer for visual tracking (F-BDMTrack). The architecture is in Figure 2."
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+                            ]
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+                                    "content": "3.1. Overview"
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+                                    "content": "As illustrated in Figure 2, our proposed tracker consists of "
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+                                    "content": " stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA"
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+                                    "content": ") module. Given a pair of images including template image "
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+                                    "content": "\\mathbf{z} \\in \\mathbb{R}^{3 \\times H_z \\times W_z}"
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x} \\in \\mathbb{R}^{H_x \\times W_x \\times 3}"
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we first split and flatten them to obtain the patch sequence of template "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}_p \\in \\mathbb{R}^{N_z \\times (3 \\cdot p^2)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " and search region "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_p \\in \\mathbb{R}^{N_x \\times (3 \\cdot p^2)}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(p, p)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " is the patch resolution, and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_z = (H_z W_z) / p^2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_x = (H_x W_x) / p^2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " are the number of patches for template and search region respectively. Similar to plain vision transformers [14], these patch sequences are mapped into "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " dimensions by a linear projection, and learnable position embeddings are added to obtain template token embeddings "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_z^0 \\in \\mathbb{R}^{N_z \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " and search region token embeddings "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_x^0 \\in \\mathbb{R}^{N_x \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_z^0"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_x^0"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " are concatenated as the input "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathbf{H}_{zx}^0 = [\\mathbf{H}_z^0; \\mathbf{H}_x^0])"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " to the fore-background distribution modeling transformer block. In this transformer block, we intergraded two modules (the FBAL module and the DA"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "^2"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " module) to help learn discriminative features for both search region and template (We will give a detailed introduction about how these two modules work in our proposed transformer block below). Here, we denote "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_{zx}^l = [\\mathbf{H}_z^l; \\mathbf{H}_x^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " as token embeddings output from the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l^{th}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " transformer block. Eventually, we reshape search region token features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_x^L"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        228,
+                                        545,
+                                        566
+                                    ],
+                                    "type": "text",
+                                    "content": " from the last block, and send them into a box prediction head to estimate the target state."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        306,
+                        574,
+                        525,
+                        586
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                574,
+                                525,
+                                586
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Fore-background Agent Learning Module"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
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+                                545,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "Given token features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{H}_z^{l - 1};\\mathbf{H}_x^{l - 1}]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(l - 1)^{th}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " transformer block, we normalize them with Layer Normalization [1] to obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{H}}_z^l = \\mathrm{LN}(\\mathbf{H}_z^{l - 1})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " , and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathbf{H}}_x^l = \\mathrm{LN}(\\mathbf{H}_x^{l - 1})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " These normalized features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{H}}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{H}}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " are sent into the forebackground agent learning (FBAL) module to produce forebackground agent (FB-agent) for the template and search region. Specifically, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{H}}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{H}}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " are first projected into "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_e"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " dimensions ("
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_e\\ll C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ") to obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        591,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " , which can reduce computational overhead. Then, we design a pseudo bounding box (bbox) generation strategy to obtain"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "10119"
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+                                            "image_path": "b5e34be09d99338cddf2d35d8f7ab74f930727f3534ea609c1c95fa99a9b8361.jpg"
+                                        }
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Figure 2. The architecture of our F-BDMTrack consists of "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "L"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " stacked fore-background distribution modeling transformer blocks, where each block has two key components including the fore-background agent learning (FBAL) module and the distribution-aware attention (DA"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            "type": "inline_equation",
+                                            "content": "^2"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ") module. The FBAL module is used to produce fore-background agents for the template (template FB-agents) and the search region (search FB-agents). And the DA"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                316,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "^2"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " module is used for feature aggregation by modeling the fore-background distribution. The output from the "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "l^{th}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " transformer block is denoted as "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "[\\mathbf{H}_z^l; \\mathbf{H}_x^l]"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                316,
+                                                545,
+                                                381
+                                            ],
+                                            "type": "text",
+                                            "content": ". Finally, we reshape search region token features "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                316,
+                                                545,
+                                                381
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{H}_x^L"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                316,
+                                                545,
+                                                381
+                                            ],
+                                            "type": "text",
+                                            "content": " from the last block, and send them into a box prediction head to estimate the target state. For more details, please refer to the text."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
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+                                        }
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+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_body"
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+                    ],
+                    "index": 1
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
+                                        46,
+                                        396,
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+                                    "type": "text",
+                                    "content": "the bounding box for the template and search region. Finally, we can obtain fore-background agents (FB-agents) for the template and search region by leveraging a FB-agent decoder to aggregate information within or outside the bounding box. The pseudo bbox generation strategy and the FB-agent decoder are introduced as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": "Pseudo bbox generation. Since the ground-truth bbox for the template is given in advance, the difficulty is how to generate pseudo bbox for the search region. To this end, we establish coarse matches between template and search region, which can help generate pseudo bbox. Specifically, given "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": ", we first reshape them into "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_z^l \\in \\mathbb{R}^{\\frac{H_z}{p} \\times \\frac{W_z}{p} \\times C_e}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_x^l \\in \\mathbb{R}^{\\frac{H_x}{p} \\times \\frac{W_x}{p} \\times C_e}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then the target feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_t^l \\in \\mathbb{R}^{h_t \\times w_t \\times C_e}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " is cropped according to the ground-truth bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_z"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_t^l = \\mathrm{PrPool}(\\widehat{\\mathbf{E}}_z^l, b_z)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": ". Here, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{PrPool}(\\cdot, \\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the Precise RoI Pooling [28]. Next, we conduct similarity matching to compute the matching point in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " for each point in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_t^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " according to the probability "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        468,
+                                        287,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": ". Formally,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        78,
+                        625,
+                        255,
+                        657
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                78,
+                                625,
+                                255,
+                                657
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        78,
+                                        625,
+                                        255,
+                                        657
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\boldsymbol {D} ^ {l} (k, i) = \\frac {\\exp \\left(<   \\widehat {\\mathbf {E}} _ {t} ^ {l} (k) , \\widehat {\\mathbf {E}} _ {x} ^ {l} (i) >\\right)}{\\sum_ {i = 1} ^ {N _ {x}} \\exp \\left(<   \\widehat {\\mathbf {E}} _ {t} ^ {l} (k) , \\widehat {\\mathbf {E}} _ {x} ^ {l} (i) >\\right)},",
+                                    "image_path": "9bc1e08e351dc280b3407a1decc83f830c3c1a554172a1d2614c338f028f2dd6.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        86,
+                        658,
+                        287,
+                        680
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                86,
+                                658,
+                                287,
+                                680
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        86,
+                                        658,
+                                        287,
+                                        680
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\left(\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}\\right) = \\sum_ {i = 1} ^ {N _ {x}} s \\cdot \\left(x _ {i}, y _ {i}\\right) \\cdot \\boldsymbol {D} ^ {l} (k, i), \\tag {1}",
+                                    "image_path": "9f9fcbda7eb041afcd5704e7f4f92b418e1384edaee9715ac4202b94d1d6b267.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        47,
+                        688,
+                        287,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                688,
+                                287,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k = (x_{k},y_{k})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i = (x_{i},y_{i})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " enumerate all 2D positions in "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_t^l"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{\\mathbf{E}}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        688,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " is the stride of the back"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        304,
+                        396,
+                        545,
+                        542
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                396,
+                                545,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": "bone network. In this way, we can obtain a set of matching points "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{(\\hat{x}_k^l,\\hat{y}_k^l)\\}_{k = 1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = h_{t}w_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": ". Finally, we derive the pseudo bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{b}_x^l = (\\hat{x}^l,\\hat{y}^l,\\hat{w}^l,\\hat{h}^l)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": " with the mean and the standard deviation of all keypoints inspired by Rep-Point [60]. Please refer to the Supplementary Material for details to obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{b}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": ". During training, we use ground-truth bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": " of the search region as supervision for more accurate pseudo bbox generation. In specific, a set of keypoints "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{(x_j,y_j)\\}_{j = 1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": " are uniformly sampled within the bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": ". And the point loss "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{point}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": " measured by Chamfer distance [18, 61] is introduced to constrain the predicted points "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{(\\hat{x}_k^l,\\hat{y}_k^l)\\}_{k = 1}^K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": " scattered in the bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        396,
+                                        545,
+                                        542
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        319,
+                        547,
+                        545,
+                        596
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                319,
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+                                545,
+                                596
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        319,
+                                        547,
+                                        545,
+                                        596
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {p o i n t}} ^ {l} = \\frac {1}{K} \\sum_ {\\substack {j = 1 \\\\ K}} ^ {K} \\min _ {k} \\left\\| \\left(x _ {j}, y _ {j}\\right) - \\left(\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}\\right) \\right\\| _ {2} \\tag{2} \\\\ + \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\min _ {j} \\left\\| (x _ {j}, y _ {j}) - (\\hat {x} _ {k} ^ {l}, \\hat {y} _ {k} ^ {l}) \\right\\| _ {2}. \\\\ \\end{array}",
+                                    "image_path": "3dee007e29968fa13646cfe90334e8893f07de2987394adbc4c4f5d29fffd234.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
+                        602,
+                        545,
+                        638
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                602,
+                                545,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        602,
+                                        545,
+                                        638
+                                    ],
+                                    "type": "text",
+                                    "content": "Besides, we introduce "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        602,
+                                        545,
+                                        638
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell_1"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        602,
+                                        545,
+                                        638
+                                    ],
+                                    "type": "text",
+                                    "content": " loss and generalized IoU loss [48] to directly constrain predicted pseudo bbox. And the final pseudo bbox generation loss is as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        333,
+                        643,
+                        545,
+                        660
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                333,
+                                643,
+                                545,
+                                660
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        333,
+                                        643,
+                                        545,
+                                        660
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {b o x} ^ {l} = \\mathcal {L} _ {p o i n t} ^ {l} + \\mathcal {L} _ {1} ^ {l} \\left(b _ {x}, \\hat {b} _ {x} ^ {l}\\right) + \\mathcal {L} _ {g i o u} ^ {l} \\left(b _ {x}, \\hat {b} _ {x} ^ {l}\\right). \\tag {3}",
+                                    "image_path": "ba252fc8db0d30902f5708174f96006504c33fadf67a31b18ff05ba8c8e051ef.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
+                        665,
+                        545,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                665,
+                                545,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        665,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "FB-agent decoder. After obtaining the bbox for the template "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        665,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        665,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and search region "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        665,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{b}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        665,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ", we aim to aggregate information within or outside the bbox. To this end, we first initialize a set of prototypical foreground agents "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        665,
+                                        545,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{F}_a^l \\in \\mathbb{R}^{N_a \\times C_e}"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
+            "discarded_blocks": [
+                {
+                    "bbox": [
+                        294,
+                        748,
+                        317,
+                        757
+                    ],
+                    "type": "page_number",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        294,
+                                        748,
+                                        317,
+                                        757
+                                    ],
+                                    "type": "text",
+                                    "content": "10120"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
+            "page_size": [
+                612,
+                792
+            ],
+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
+                        46,
+                        71,
+                        287,
+                        120
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                71,
+                                287,
+                                120
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": "and prototypical background agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{B}_a^l\\in \\mathbb{R}^{N_a\\times C_e}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": ". Inspired by CrossViT [6], we use masked cross-attention (M-CA) mechanism to aggregate information of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": " in the bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        71,
+                                        287,
+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": ", and produce template foreground agents. Formally,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        71,
+                        129,
+                        287,
+                        150
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                71,
+                                129,
+                                287,
+                                150
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        71,
+                                        129,
+                                        287,
+                                        150
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {A} _ {t t} = \\operatorname {S o f t m a x} \\left(\\left(\\mathbf {F} _ {a} ^ {l} \\mathbf {W} _ {Q}\\right) \\left(\\mathbf {E} _ {z} ^ {l} \\mathbf {W} _ {K}\\right) ^ {\\top} + \\mathbf {M} _ {z} ^ {l}\\right), \\tag {4}",
+                                    "image_path": "6648057c78434f127165c821e059d9af844c49c240e8f874fd0cfb7833f8a58d.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        76,
+                        147,
+                        257,
+                        161
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                76,
+                                147,
+                                257,
+                                161
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        76,
+                                        147,
+                                        257,
+                                        161
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {F} _ {z} ^ {l} = \\mathrm {M - C A} (\\mathbf {F} _ {a} ^ {l}, \\mathbf {E} _ {z} ^ {l}, \\mathbf {M} _ {z} ^ {l}) = \\mathbf {A} _ {t t} (\\mathbf {E} _ {z} ^ {l} \\mathbf {W} _ {V}),",
+                                    "image_path": "78762f6234a5dea6757c893a85a4fe7a8d78c7bcdae7609bd3b4bd8621323ce1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        170,
+                        287,
+                        270
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                170,
+                                287,
+                                270
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_Q, \\mathbf{W}_K,"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_V"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": " are linear projections. And the element in template foreground mask "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{M}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": " is set to 0, if the corresponding position of this element is in the bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ". Otherwise, it will be set to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-\\infty"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ". Similarly, for the template background mask "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{M}}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ", the element is set to 0, if the corresponding position of this element is outside the bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "b_{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ". Otherwise, it will be set to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-\\infty"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": ". And we can obtain template background agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{B}_z^l = \\mathrm{M - CA}(\\mathbf{B}_a^l, \\mathbf{E}_z^l, \\overline{\\mathbf{M}}_z^l)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        170,
+                                        287,
+                                        270
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        270,
+                        287,
+                        334
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                270,
+                                287,
+                                334
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": "For search region features "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can generate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{M}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\overline{\\mathbf{M}}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " according to the pseudo bbox "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{b}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{b}_x^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " is not precise enough, we leverage updated template FB-agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_z^l; \\mathbf{B}_z^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": " to serve as queries, which provides clearer fore-background priors than prototypical agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_a^l; \\mathbf{B}_a^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        270,
+                                        287,
+                                        334
+                                    ],
+                                    "type": "text",
+                                    "content": ". Formally,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        108,
+                        343,
+                        225,
+                        357
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                108,
+                                343,
+                                225,
+                                357
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
+                                        343,
+                                        225,
+                                        357
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {F} _ {x} ^ {l} = \\operatorname {M - C A} \\left(\\mathbf {F} _ {z} ^ {l}, \\mathbf {E} _ {x} ^ {l}, \\mathbf {M} _ {x} ^ {l}\\right),",
+                                    "image_path": "d718c674ca8bd797da06bf6e91e46a1d12c47d3739ca06a3f37009e4a483dc6a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        109,
+                        356,
+                        287,
+                        376
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                109,
+                                356,
+                                287,
+                                376
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        109,
+                                        356,
+                                        287,
+                                        376
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {B} _ {x} ^ {l} = \\operatorname {M - C A} \\left(\\mathbf {B} _ {z} ^ {l}, \\mathbf {E} _ {x} ^ {l}, \\overline {{\\mathbf {M}}} _ {x} ^ {l}\\right). \\tag {5}",
+                                    "image_path": "c6c022c15a150f5f574de2083c3426ca1bfc06435f556f147e6be7b982c9d636.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        46,
+                        387,
+                        287,
+                        412
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                387,
+                                287,
+                                412
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "text",
+                                    "content": "Finally, we obtain template FB-agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_z^l;\\mathbf{B}_z^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "text",
+                                    "content": ", and search region FB-agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_x^l;\\mathbf{B}_x^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "text",
+                                    "content": " at the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l^{th}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        387,
+                                        287,
+                                        412
+                                    ],
+                                    "type": "text",
+                                    "content": " block."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        47,
+                        421,
+                        245,
+                        432
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                421,
+                                245,
+                                432
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        421,
+                                        245,
+                                        432
+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Distribution-aware Attention Module"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        46,
+                        439,
+                        287,
+                        499
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                439,
+                                287,
+                                499
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "text",
+                                    "content": "After obtaining template FB-agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_z^l;\\mathbf{B}_z^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "text",
+                                    "content": " and search region FB-agents "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_x^l;\\mathbf{B}_x^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "text",
+                                    "content": ", we begin to model the foreground distribution for each image token. Specifically, given token features "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{H}_z^{l - 1};\\mathbf{H}_x^{l - 1}]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
+                                        287,
+                                        499
+                                    ],
+                                    "type": "text",
+                                    "content": ", the initial query, key and value arise from these token features. Formally,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        74,
+                        509,
+                        257,
+                        525
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                74,
+                                509,
+                                257,
+                                525
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        74,
+                                        509,
+                                        257,
+                                        525
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\mathbf {Q}} _ {z x} ^ {l} = \\left[ \\widetilde {\\mathbf {Q}} _ {z} ^ {l}; \\widetilde {\\mathbf {Q}} _ {x} ^ {l} \\right] = \\mathrm {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {Q} ^ {l},",
+                                    "image_path": "3f0cf579fe019ce3f922c945a3d7a49559e29815c2da108265ba6aaebf2e2359.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        76,
+                        526,
+                        287,
+                        542
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                76,
+                                526,
+                                287,
+                                542
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        76,
+                                        526,
+                                        287,
+                                        542
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\mathbf {K}} _ {z x} ^ {l} = \\left[ \\widetilde {\\mathbf {K}} _ {z} ^ {l}; \\widetilde {\\mathbf {K}} _ {x} ^ {l} \\right] = \\operatorname {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {K} ^ {l}, \\tag {6}",
+                                    "image_path": "552e28558ae8e10bb58f5a0989356d9dc89cd973ff00172301a4adad470e7faf.jpg"
+                                }
+                            ]
+                        }
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {V} _ {z x} ^ {l} = \\left[ \\mathbf {V} _ {z} ^ {l}; \\mathbf {V} _ {x} ^ {l} \\right] = \\mathrm {L N} \\left(\\left[ \\mathbf {H} _ {z} ^ {l - 1}; \\mathbf {H} _ {x} ^ {l - 1} \\right]\\right) \\mathbf {W} _ {V} ^ {l},",
+                                    "image_path": "4c86ad5fbc5390f579f84bec795ed5b39e4b08da4935a54c7d6494fe20971b2d.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where LN denotes the layer normalization, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_K^l\\in"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{C\\times C},\\mathbf{W}_Q^l\\in \\mathbb{R}^{C\\times C},\\mathbf{W}_V^l\\in \\mathbb{R}^{C\\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are linear projections. As can be seen, existing plain attention mechanism [14] generate queries and keys simply based on appearance features, which will easily have incorrect high attention score for regions with similar distractors. Differently, we use the fore-background distribution to serve as queries and keys instead of appearance features. To this end, we first project "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_z^l;\\mathbf{B}_z^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{F}_x^l;\\mathbf{B}_x^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
+                                        287,
+                                        712
+                                    ],
+                                    "type": "text",
+                                    "content": " into "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        570,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " dimensions. By calculating the similarity between each token and these fore-background agents, we can model the fore-background distribution of this token. Here, we take the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "fore-background distribution of initial query token as updated queries "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Q}_{zx}^{l} = [\\mathbf{Q}_{z}^{l};\\mathbf{Q}_{x}^{l}]"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Formally,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "bbox": [
+                                        365,
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+                                        139
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathbf {Q} _ {z} ^ {l} = \\widetilde {\\mathbf {Q}} _ {z} ^ {l} \\left[ \\mathbf {F} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l}; \\mathbf {B} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l} \\right] ^ {\\top}, \\tag {7} \\\\ \\mathbf {Q} _ {x} ^ {l} = \\tilde {\\mathbf {Q}} _ {x} ^ {l} \\left[ \\mathbf {F} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l}, \\mathbf {B} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l} \\right] ^ {\\top}, \\\\ \\end{array}",
+                                    "image_path": "05e29763097042d365a440b7cc33fdfbd4d1b20ec238c198491db0e6afa70052.jpg"
+                                }
+                            ]
+                        }
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+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        175
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{W}_z^l, \\mathbf{W}_x^l \\in \\mathbb{R}^{C_e \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        148,
+                                        545,
+                                        175
+                                    ],
+                                    "type": "text",
+                                    "content": " are linear projections. Similarly, we can obtain updated keys "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        148,
+                                        545,
+                                        175
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{K}_{zx}^l = [\\mathbf{K}_z^l, \\mathbf{K}_x^l]"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        148,
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+                                        175
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "lines": [
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+                                    "bbox": [
+                                        364,
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+                                        217
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathbf {K} _ {z} ^ {l} = \\widetilde {\\mathbf {K}} _ {z} ^ {l} \\left[ \\mathbf {F} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l}; \\mathbf {B} _ {z} ^ {l} \\mathbf {W} _ {z} ^ {l} \\right] ^ {\\top}, \\tag {8} \\\\ \\mathbf {K} _ {x} ^ {l} = \\tilde {\\mathbf {K}} _ {x} ^ {l} \\left[ \\mathbf {F} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l}; \\mathbf {B} _ {x} ^ {l} \\mathbf {W} _ {x} ^ {l} \\right] ^ {\\top}. \\\\ \\end{array}",
+                                    "image_path": "b668141606f66ba9ce347d759f4d66e50b7245a0e9a3edce64c43c008d49283f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "With updated queries and keys, the proposed distribution-aware attention module can achieve fore-background aware feature interaction. The output of the "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        226,
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+                                        275
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l^{th}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        226,
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+                                        275
+                                    ],
+                                    "type": "text",
+                                    "content": " transformer blocks "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        226,
+                                        545,
+                                        275
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_{zx}^l"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        226,
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+                                        275
+                                    ],
+                                    "type": "text",
+                                    "content": " can be formulated as follows,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widetilde {\\mathbf {H}} _ {z x} ^ {l} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} _ {z x} ^ {l} \\left(\\mathbf {K} _ {z x} ^ {l}\\right) ^ {\\top}}{\\sqrt {C}}\\right) \\mathbf {V} _ {z x} ^ {l} + \\mathbf {H} _ {z x} ^ {l - 1} \\tag {9}",
+                                    "image_path": "db604dbd4b27a92d8ebee6760783d53a5f5bbff67ad66cf93abe663dad45da7a.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "bbox": [
+                                        332,
+                                        312,
+                                        519,
+                                        328
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {H} _ {z x} ^ {l} = \\left[ \\mathbf {H} _ {z} ^ {l}; \\mathbf {H} _ {x} ^ {l} \\right] = \\operatorname {M L P} \\left(\\operatorname {L N} \\left(\\widetilde {\\mathbf {H}} _ {z x} ^ {l}\\right)\\right) + \\widetilde {\\mathbf {H}} _ {z x} ^ {l},",
+                                    "image_path": "bd055540ad06dbe3e42b61fbb5e35731dd23ec55b15c147fa1e19d0993ed4041.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
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+                                        398
+                                    ],
+                                    "type": "text",
+                                    "content": "where MLP denotes the multi-layer perception. The output token features "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
+                                        545,
+                                        398
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_{zx}^{l}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
+                                        545,
+                                        398
+                                    ],
+                                    "type": "text",
+                                    "content": " will be sent into next transformer blocks. Eventually, token features are processed "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
+                                        545,
+                                        398
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
+                                        545,
+                                        398
+                                    ],
+                                    "type": "text",
+                                    "content": " times via our proposed fore-background distribution modeling transformer block, and we can obtain final token features "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
+                                        545,
+                                        398
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_{zx}^{L}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        338,
+                                        545,
+                                        398
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.4. Box Prediction Head and Objective Function"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "As shown in Figure 2, search region token features "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{H}_x^L"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " are reshaped and fed into a box prediction head for target state estimation. Here, the box prediction head is inspired from OSTrack [62]. We use the weighted focal loss [33] as classification loss "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{cls}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": ". Besides, we adopt "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell_1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " loss "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_1"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " and generalized IoU loss [48] "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{giou}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        426,
+                                        545,
+                                        556
+                                    ],
+                                    "type": "text",
+                                    "content": " to supervise bounding box regression. More details about the box prediction head and losses can be referred to OSTrack [62]. As we introduced before, there are point loss and box loss for pseudo bbox generation at each block. In summary, the overall objective function is formulated as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
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+                                    "bbox": [
+                                        316,
+                                        566,
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+                                        597
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {L} _ {c l s} + \\lambda_ {1} \\mathcal {L} _ {1} + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u} + \\lambda_ {b o x} \\sum_ {l = 1} ^ {L} \\mathcal {L} _ {b o x} ^ {l}, \\tag {10}",
+                                    "image_path": "698495c6e89b5007590b857b118013886d48b6294f49e503d3e8c69332c922b8.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 24
+                },
+                {
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_1, \\lambda_{giou}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{box}"
+                                },
+                                {
+                                    "bbox": [
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+                                        609,
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+                                    "type": "text",
+                                    "content": " are scalars to balance these losses."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 26
+                },
+                {
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+                                    "content": "In this section, we first introduce implementation details. Then, we show experimental results on eight benchmarks. Finally, we conduct a series of ablation studies to verify the effectiveness of each component. Please refer to the Supplementary Material for more details and results."
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "Table 1. Comparisons with state-of-the-art trackers on GOT-10k, TNL2K, LaSOT, "
+                                        },
+                                        {
+                                            "bbox": [
+                                                47,
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+                                            "type": "inline_equation",
+                                            "content": "\\mathrm{LaSOT}_{ext}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ", and TrackingNet. The best three results are shown in red, blue and green fonts."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 0,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
+                        {
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">GOT-10k [26]</td><td colspan=\"2\">TNL2K [54]</td><td colspan=\"3\">LaSOT [17]</td><td colspan=\"3\">\\( LaSOT_{ext} \\) [16]</td><td colspan=\"3\">TrackingNet [45]</td></tr><tr><td>AO</td><td>\\( SR_{0.5} \\)</td><td>\\( SR_{0.75} \\)</td><td>AUC</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td><td>AUC</td><td>\\( P_{Norm} \\)</td><td>P</td></tr><tr><td>SiamFC[2]</td><td>34.8</td><td>35.3</td><td>9.8</td><td>29.5</td><td>28.6</td><td>33.6</td><td>42.0</td><td>33.9</td><td>23.0</td><td>31.1</td><td>26.9</td><td>57.1</td><td>66.3</td><td>53.3</td></tr><tr><td>ECO [11]</td><td>31.6</td><td>30.9</td><td>11.1</td><td>32.6</td><td>31.7</td><td>32.4</td><td>33.8</td><td>30.1</td><td>22.0</td><td>25.2</td><td>24.0</td><td>55.4</td><td>61.8</td><td>49.2</td></tr><tr><td>SiamRPN++ [34]</td><td>51.7</td><td>61.6</td><td>32.5</td><td>41.3</td><td>41.2</td><td>49.6</td><td>56.9</td><td>49.1</td><td>34.0</td><td>41.6</td><td>39.6</td><td>73.3</td><td>80.0</td><td>69.4</td></tr><tr><td>SiamCAR [23]</td><td>56.9</td><td>67.0</td><td>41.5</td><td>35.5</td><td>38.4</td><td>50.7</td><td>60.0</td><td>51.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SiamFC++ [58]</td><td>59.5</td><td>69.5</td><td>47.9</td><td>38.6</td><td>36.9</td><td>54.4</td><td>62.3</td><td>54.7</td><td>-</td><td>-</td><td>-</td><td>75.4</td><td>80.0</td><td>70.5</td></tr><tr><td>D3S [39]</td><td>59.7</td><td>67.6</td><td>46.2</td><td>38.8</td><td>39.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>72.8</td><td>76.8</td><td>66.4</td></tr><tr><td>Ocean [63]</td><td>61.1</td><td>72.1</td><td>47.3</td><td>38.4</td><td>37.7</td><td>56.0</td><td>65.1</td><td>56.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DiMP-50 [3]</td><td>61.1</td><td>71.7</td><td>49.2</td><td>44.7</td><td>43.4</td><td>56.9</td><td>65.0</td><td>56.7</td><td>39.2</td><td>47.6</td><td>45.1</td><td>74.0</td><td>80.1</td><td>68.7</td></tr><tr><td>PrDiMP-50 [13]</td><td>63.4</td><td>73.8</td><td>54.3</td><td>47.0</td><td>45.9</td><td>59.8</td><td>68.8</td><td>60.8</td><td>-</td><td>-</td><td>-</td><td>75.8</td><td>81.6</td><td>70.4</td></tr><tr><td>KeepTrack[43]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>67.1</td><td>77.2</td><td>70.2</td><td>48.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ToMP-101 [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>68.5</td><td>79.2</td><td>73.5</td><td>45.9</td><td>-</td><td>-</td><td>81.5</td><td>86.4</td><td>78.9</td></tr><tr><td>KYS [4]</td><td>63.6</td><td>75.1</td><td>51.5</td><td>44.9</td><td>43.5</td><td>55.4</td><td>63.3</td><td>-</td><td>-</td><td>-</td><td>-</td><td>74.0</td><td>80.0</td><td>68.8</td></tr><tr><td>STMTrack [21]</td><td>64.2</td><td>73.7</td><td>57.5</td><td>-</td><td>-</td><td>60.6</td><td>63.3</td><td>69.3</td><td>-</td><td>-</td><td>-</td><td>80.3</td><td>85.1</td><td>76.7</td></tr><tr><td>TransT [7]</td><td>67.1</td><td>76.8</td><td>60.9</td><td>50.7</td><td>51.7</td><td>64.9</td><td>69.0</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>81.4</td><td>86.7</td><td>80.3</td></tr><tr><td>STARK-ST101 [59]</td><td>68.8</td><td>78.1</td><td>64.1</td><td>-</td><td>-</td><td>67.1</td><td>77.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.0</td><td>86.9</td><td>-</td></tr><tr><td>CSWinTT [50]</td><td>69.4</td><td>78.9</td><td>65.4</td><td>-</td><td>-</td><td>66.2</td><td>75.2</td><td>70.9</td><td>-</td><td>-</td><td>-</td><td>81.9</td><td>86.7</td><td>79.5</td></tr><tr><td>SimTrack-B/16 [5]</td><td>68.6</td><td>78.9</td><td>62.4</td><td>54.8</td><td>53.8</td><td>69.3</td><td>78.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>82.3</td><td>86.5</td><td>-</td></tr><tr><td>SwinTrack-B [36]</td><td>69.4</td><td>78.0</td><td>64.3</td><td>-</td><td>-</td><td>69.6</td><td>78.6</td><td>74.1</td><td>47.6</td><td>58.2</td><td>54.1</td><td>82.5</td><td>87.0</td><td>80.4</td></tr><tr><td>AiATrack [22]</td><td>69.6</td><td>80.0</td><td>63.2</td><td>-</td><td>-</td><td>69.0</td><td>79.4</td><td>73.8</td><td>-</td><td>-</td><td>-</td><td>82.7</td><td>87.8</td><td>80.4</td></tr><tr><td>SBT-L [57]</td><td>70.4</td><td>80.8</td><td>64.7</td><td>-</td><td>-</td><td>66.7</td><td>77.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MixFormer [10]</td><td>70.7</td><td>80.0</td><td>67.8</td><td>-</td><td>-</td><td>69.2</td><td>78.7</td><td>74.7</td><td>-</td><td>-</td><td>-</td><td>83.1</td><td>88.1</td><td>81.6</td></tr><tr><td>RTS [42]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>69.7</td><td>76.2</td><td>73.7</td><td>-</td><td>-</td><td>-</td><td>81.6</td><td>86.0</td><td>79.4</td></tr><tr><td>OSTrack-256 [62]</td><td>71.0</td><td>80.4</td><td>68.2</td><td>54.3</td><td>-</td><td>69.1</td><td>78.7</td><td>75.2</td><td>47.4</td><td>57.3</td><td>53.3</td><td>83.1</td><td>87.8</td><td>82.0</td></tr><tr><td>OSTrack-384 [62]</td><td>73.7</td><td>83.2</td><td>70.8</td><td>55.9</td><td>-</td><td>71.1</td><td>81.1</td><td>77.6</td><td>50.5</td><td>61.3</td><td>57.6</td><td>83.9</td><td>88.5</td><td>83.2</td></tr><tr><td>F-BDMTrack-256</td><td>72.7</td><td>82.0</td><td>69.9</td><td>56.4</td><td>56.5</td><td>69.9</td><td>79.4</td><td>75.8</td><td>47.9</td><td>57.9</td><td>54.0</td><td>83.7</td><td>88.3</td><td>82.6</td></tr><tr><td>F-BDMTrack-384</td><td>75.4</td><td>84.3</td><td>72.9</td><td>57.8</td><td>59.4</td><td>72.0</td><td>81.5</td><td>77.7</td><td>50.8</td><td>61.3</td><td>57.8</td><td>84.5</td><td>89.0</td><td>84.0</td></tr></table>",
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+                                        }
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+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Implementation Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Network details. We present two variants of our tracker, F-BDMTrack-256 and F-BDMTrack-384. Similar to OSTrack [62], we crop the template image and search region image which are "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2^{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
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+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "4^{2}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " times of the target box area respectively. The F-BDMTrack-256 resizes search region to a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "256 \\times 256"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " and template to a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "128 \\times 128"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " as input. The F-BDMTrack-384 resizes search region to a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "384 \\times 384"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " and template to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "192 \\times 192"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ". These images are split into a set of patches, where the resolution of each patch is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "16 \\times 16"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ". These patches are flattened and projected into "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C = 768"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " channels to serve as the input of F-BDMTrack. The channel of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_z^l"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " in the FBAL module is set to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_e = 256"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ". We leverage the Precise RoI Pooling [28] operation to crop features according to the target bounding box, and obtain the target feature with shape "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(h_t, w_t) = (4, 4)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ". The number of foreground agents and background agents are both set to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_a = 4"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": ". And our F-BDMTrack consists of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L = 12"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        421,
+                                        288,
+                                        648
+                                    ],
+                                    "type": "text",
+                                    "content": " fore-background distribution modeling transformer blocks."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        653,
+                        287,
+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        653,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "Training details. We train our model on the training splits of LaSOT [17], GOT-10K [26], COCO2017 [37], and TrackingNet [45], which is a similar training setting to OSTrack [62]. Common data augmentations including horizontal flip and brightness jittering are applied in the training"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "content": "process. We train our F-BDMTrack by the AdamW optimizer with the weight decay "
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+                                    "content": ". The learning rates start from "
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+                                    "content": " for the backbone including the FBAL module and the "
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+                                    "type": "text",
+                                    "content": " module, and "
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+                                    "type": "inline_equation",
+                                    "content": "4 \\times 10^{-4}"
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+                                    "type": "text",
+                                    "content": " for the box prediction head. Our model is trained on four NVIDIA RTX 3090 GPUs, each GPU holds 32 image pairs, resulting in a total batch size of 128. The total epochs are set to 300 with 60k samples per epoch and we decrease the learning rate by a factor of 10 after 240 epochs. The weights of training losses are set to "
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+                                    "content": "\\lambda_1 = 5.0"
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+                                    "content": "\\lambda_{giou} = 2.0"
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{box} = 1.0"
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+                                    "type": "text",
+                                    "content": "."
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+                                    "content": "4.2. Results and State-of-the-art Comparisons"
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+                                    "content": "GOT-10k. GOT-10k [26] is a large-scale dataset containing over 10k videos for training and 180 for testing. It forbids trackers to use external datasets for training. We follow its policy and retrain our model. The results are reported in Table 1. Our tracker has a satisfactory improvement in all metrics. Specifically, F-BDMTrack-256 improves by "
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+                                    "type": "text",
+                                    "content": " compared with OSTrack-256. And F-BDMTrack-384 gives an improved new record "
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+                                    "content": " in AO, indicating the effectiveness of foreground and background distribution modeling to extract discriminative features, resulting in more accurate state estimation."
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+                                    "content": "TNL2K. TNL2K [54] is a recently published dataset containing 700 video sequences for testing. In Table 1, F-BDMTrack-256 gains by "
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+                                            "content": "Table 2. Comparisons with state-of-the-art trackers on NFS, OTB100 and UAV123 datasets in terms of overall AUC score. The best three results are shown in red, blue and green fonts."
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+                                            "html": "<table><tr><td></td><td>SiamFC [2]</td><td>Ocean [63]</td><td>ATOM [12]</td><td>DiMP-50 [3]</td><td>PrDiMP-50 [13]</td><td>TransT [7]</td><td>OSTrack-256 [62]</td><td>OSTrack-384 [62]</td><td>F-BDMTrack-256</td><td>F-BDMTrack-384</td></tr><tr><td>NFS [30]</td><td>37.7</td><td>49.4</td><td>58.3</td><td>61.8</td><td>63.5</td><td>65.3</td><td>64.7</td><td>66.5</td><td>66.0</td><td>67.3</td></tr><tr><td>OTB100 [56]</td><td>61.2</td><td>68.4</td><td>66.3</td><td>68.4</td><td>69.6</td><td>69.4</td><td>68.1</td><td>69.2</td><td>69.5</td><td>69.9</td></tr><tr><td>UAV123 [44]</td><td>46.8</td><td>57.4</td><td>63.2</td><td>64.3</td><td>68.0</td><td>68.1</td><td>68.3</td><td>70.7</td><td>69.0</td><td>70.9</td></tr></table>",
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+                                            "content": "Figure 3. Visualizations of fore-background agent activation maps for the template and search region."
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+                                            "content": "Table 3. Effectiveness of each component on the LaSOT"
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+                                            "html": "<table><tr><td>Model</td><td>FBAL</td><td>DA2</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>[A]</td><td>X</td><td>X</td><td>68.5</td><td>77.8</td><td>74.2</td></tr><tr><td>[B]</td><td>✓</td><td>X</td><td>68.8</td><td>78.1</td><td>74.6</td></tr><tr><td>[C]</td><td>X</td><td>✓</td><td>69.4</td><td>78.7</td><td>75.4</td></tr><tr><td>[D]</td><td>✓</td><td>✓</td><td>69.9</td><td>79.4</td><td>75.8</td></tr></table>",
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+                                    "content": "even performances better than larger models (OTrack-384). When also leveraging a large model (F-BDMTrack-384), we can further improve the AUC score to "
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+                                    "content": "LaSOT. LaSOT [17] is a densely annotated large-scale dataset containing a total of 1400 long-term video sequences, of which the test set contains 280 video sequences. This is a challenging tracking dataset. As shown in Table 1, F-BDMTrack-256 outperforms OSTrack-256 by "
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+                                    "content": " [16] is an extended subset of LaSOT, containing 150 additional new sequences. This dataset has many similar distractors, making it difficult for tracking. And our F-BDMTrack can achieve competitive or even better performance. In specific, F-BDMTrack-256 achieves superior results, outperforming OSTrack-256 by "
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+                                            "content": "Figure 4. Visualization of pseudo bboxes using the pseudo-bbox generation strategy at all blocks."
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+                                    "type": "text",
+                                    "content": "so results reported in Table 1 are obtained from the online evaluation server. As can be seen, our F-BDMTrack-384 achieves "
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+                                    "content": " AUC and sets a new state of the art."
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+                                    "type": "text",
+                                    "content": "NFS. Videos in Need for Speed(NFS) [30] are captured from a high frame rate camera, which contains fast motions and distractors. We report results on its commonly used version NFS30. As shown in Table 2, F-BDMTrack-256 achieves "
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+                                    "content": " AUC, outperforming OSTrack-256 by "
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+                                    "type": "text",
+                                    "content": ". And F-BDMTrack-384 achieves best results (67.3% AUC score) as expected, demonstrating the superior competitiveness of our tracker in the presence of interferer-challenged benchmark."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "OTB100. OTB [56] is a pioneering visual tracking benchmark. It has been noticed that this benchmark is approaching saturation [53, 59, 43]. In Table 2, two versions of our tracker both achieve promising AUC scores (69.5 and 69.9). UAV123. UAV123 [44] provides 123 unmanned aerial vehicle(UAV) sequences, including different scale sizes of UAV in real-world dynamic scenarios. As shown in Table 2, our tracker achieves the best AUC score "
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+                                    "content": "(70.9\\%)"
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+                                    "type": "text",
+                                    "content": " and is suitable for UAV tracking scenarios."
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+                                    "type": "text",
+                                    "content": "4.3. Ablation Study"
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+                                    "content": "To validate the effectiveness of each component, we perform a detailed ablation study on LaSOT [17]. The following experiments use F-BDMTrack-256 as the base model."
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+                                    "content": "Effectiveness of key components in our F-BDMTrack. Our tracker consists of two key components, including a fore-background agent learning (FBAL) module and a distribution-aware attention "
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+                                    "type": "text",
+                                    "content": " module. Here, we explore the exact impact of these modules. The model [A] is the baseline, which means that we directly use plain attention mechanism without using the FBAL and the "
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+                                    "type": "text",
+                                    "content": " module. For the model [B], we add the FBAL module, and"
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+                                            "content": "Table 4. Effects with different numbers of prototypical FB-agents."
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+                                            "html": "<table><tr><td>Na</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>1</td><td>69.3</td><td>78.8</td><td>75.5</td></tr><tr><td>2</td><td>69.6</td><td>79.1</td><td>75.6</td></tr><tr><td>4</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>8</td><td>69.3</td><td>78.9</td><td>75.2</td></tr><tr><td>16</td><td>69.0</td><td>78.6</td><td>75.1</td></tr></table>",
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+                                            "content": "Table 5. Effects of the pseudo bbox generation at different blocks."
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+                                            "html": "<table><tr><td>blocks</td><td>AUC</td><td>PNorm</td><td>P</td></tr><tr><td>None</td><td>69.0</td><td>78.5</td><td>75.0</td></tr><tr><td>10-12</td><td>69.5</td><td>79.1</td><td>75.5</td></tr><tr><td>6-12</td><td>69.9</td><td>79.4</td><td>75.8</td></tr><tr><td>4-12</td><td>69.8</td><td>79.2</td><td>75.8</td></tr><tr><td>1-12</td><td>69.2</td><td>78.7</td><td>75.2</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "adopt plain attention mechanism to replace our designed "
+                                },
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+                                    "type": "text",
+                                    "content": " module. The plain attention mechanism does not require fore-background agents (FB-agents) produced by our FBAL module. Thus, the model [B] is used to validate the impacts of pseudo bbox generation loss "
+                                },
+                                {
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+                                    "content": " introduced in the FBAL module. As shown in Table 3, the performance of model [B] gains by "
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+                                    "type": "text",
+                                    "content": " compared to the model [A], demonstrating that the pseudo bbox loss has some positive effects to constrain foreground features interact with features in foreground regions. For the model [C], we adopt the "
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+                                    "type": "text",
+                                    "content": " module for feature interaction, and FB-agents are obtained by pooling features within or outside the bounding box for the template and search region. As can be seen, the performance of model [C] gains by "
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+                                    "content": " compared to the model [A], which demonstrates that the proposed "
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+                                    "type": "text",
+                                    "content": " module can significantly help learn discriminative features even if FB-agents are not good enough. When adding the FBAL module for better FB-agents generation, the performance of model [D] gains by "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " compared to the model [C], showing the superiority of proposed FBAL module."
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+                                    "type": "text",
+                                    "content": "Study on the number of prototypical FB-agents in the FBAL module. Here, we explore the effects about different numbers of prototypical FB-agents. As shown in Table 4, our tracker achieves the optimal result (69.9% AUC score) when "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N_{a} = 4"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". A small number of prototypical FB-agents cannot fully model the fore-background distribution, leading to decreased performance. Meanwhile, more prototypical FB-agents will introduce useless noise, which is harmful for feature interaction. Besides, without explicit constraints to guide foreground and background agent learning, an excessive number of agents are unable to focus on their respective discriminative information better. A more effective FB-agent learning way can be explored in future work. Finally, we show the fore-background agent activation maps for the template and search region in Figure 3. It can be seen that these FB-agents generated by our FBAL module can focus on the foreground and background well."
+                                }
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+                                            "content": "Figure 5. Response maps of the template central feature to all search region features. It can be seen that although the template target has similar appearance with the background distractor in the search region, their fore-background distributions are different."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8,
+                            "angle": 0,
+                            "type": "image_caption"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "ent blocks. High-quality pseudo bbox is more conducive to the FB-agent learning for the search region. However, as shown in Figure 4, the pseudo-bboxes in shallow blocks tend to have a large bias, which is harmful to learn effective FB-agents. We conduct a detailed experiment to find which blocks are optimal for using pseudo bbox generation strategy. As shown in Table 5, our tracker achieves the best results when we leverage the pseudo bbox generation strategy at the "
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+                                    "content": "6^{th}"
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " ('6-12') transformer blocks. This is because the last few blocks provide more reliable pseudo bbox to guide fore-background agent learning."
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+                                    "content": "Comparisons between the plain attention mechanism and our "
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+                                    "type": "text",
+                                    "content": " mechanism. Here, we visualize response maps of the plain attention mechanism and our "
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+                                    "type": "text",
+                                    "content": " mechanism in Figure 5. As we can see, the plain attention mechanism easily focus on complex backgrounds or distractors. This is because attention scores are obtained based on appearance similarities, while targets usually have similar appearance with distractors, resulting in incorrect response map. Differently, our proposed "
+                                },
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+                                    "type": "text",
+                                    "content": " mechanism discriminates features from the perspective of fore-background distributions instead of appearance similarities, which can effectively suppress the response of the template to background distractors in the search region, and strengthen the response of the template to the foreground target in the search region. Finally, based on the proposed distribution"
+                                }
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+                                    "content": "In this work, we propose a novel foreground-background distribution modeling transformer for visual tracking, including a FBAL module and a "
+                                },
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+                                    "type": "text",
+                                    "content": " module. With these two elegant designs, our proposed tracker can extract features with high target discriminative power under ever-changing tracking scenarios, which is essential for accurate target state estimation. Extensive experiments on eight tracking benchmarks verify the superiority of our proposed tracker."
+                                }
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+                                    "content": "6. Acknowledgement"
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+                                    "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, 62021001), and National Defense Basic Scientific Research Program of China (Grant JCKY2020903B002)."
+                                }
+                            ]
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                                {
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+                                        {
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+                                        }
+                                    ]
+                                }
+                            ],
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+                        },
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+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
+                                                53,
+                                                465,
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                511,
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+                                566
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                    "bbox": [
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+                                        }
+                                    ]
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+                        },
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+                            "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[6] Chun-Fu Richard Chen, Quanfu Fan, and Rameswar Panda. Crossvit: Cross-attention multi-scale vision transformer for image classification. In Proceedings of the IEEE/CVF international conference on computer vision, pages 357–366, 2021. 5"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
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+                        {
+                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[8] Zedu Chen, Bineng Zhong, Guorong Li, Shengping Zhang, and Rongrong Ji. Siamese box adaptive network for visual tracking. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2020. 1, 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
+                        }
+                    ],
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+                                            "type": "text",
+                                            "content": "[9] Linsong Cheng, Jiliang Wang, and Yinghui Li. Vitrack: Efficient tracking on the edge for commodity video surveillance systems. IEEE Transactions on Parallel and Distributed Systems, 33(3):723-735, 2021. 1"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15
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+                        {
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+                                            "type": "text",
+                                            "content": "[10] Yutao Cui, Jiang Cheng, Limin Wang, and Gangshan Wu. Mixformer: End-to-end tracking with iterative mixed attention. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2022. 1, 2, 3, 6, 7"
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "type": "text",
+                                            "content": "[11] Martin Danelljan, Goutam Bhat, Fahad Shahbaz Khan, and Michael Felsberg. ECO: Efficient convolution operators for tracking. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2017. 6"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 17
+                        },
+                        {
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+                                            "content": "[12] Martin Danelljan, Goutam Bhat, Fahad Shahbaz Khan, and Michael Felsberg. ATOM: Accurate tracking by overlap maximization. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2019. 1, 2, 7"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 18
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+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[13] Martin Danelljan, Luc Van Gool, and Radu Timofte. Probabilistic regression for visual tracking. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2020. 1, 2, 6, 7"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 19
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+                                            "content": "[14] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. International Conference on Learning Representations, 2021. 2, 3, 5"
+                                        }
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+                                            "content": "[63] Zhipeng Zhang, Houwen Peng, Jianlong Fu, Bing Li, and Weiming Hu. Ocean: Object-aware anchor-free tracking. In Proceedings of the European Conference on Computer Vision, 2020. 6, 7"
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+                                            "content": "[64] Jie Zhao, Jingshu Zhang, Dongdong Li, and Dong Wang. Vision-based anti-uav detection and tracking. IEEE Transactions on Intelligent Transportation Systems, 23(12):25323-25334, 2022. 1"
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diff --git a/2023/Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models/5ee0597f-a7d5-4c09-a624-657832eb9d0e_content_list.json b/2023/Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models/5ee0597f-a7d5-4c09-a624-657832eb9d0e_content_list.json
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+++ b/2023/Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models/5ee0597f-a7d5-4c09-a624-657832eb9d0e_content_list.json	
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+[
+    {
+        "type": "text",
+        "text": "Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models",
+        "text_level": 1,
+        "bbox": [
+            125,
+            128,
+            843,
+            174
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Mischa Dombrowski $^{1}$  Hadrien Reynaud $^{2}$  Matthew Baugh $^{2}$  Bernhard Kainz $^{1,2}$ $^{1}$ Friedrich-Alexander-Universität Erlangen-Nürnberg  $^{2}$ Imperial College London mischa.dombrowski@fau.de",
+        "bbox": [
+            119,
+            202,
+            849,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Curating datasets for object segmentation is a difficult task. With the advent of large-scale pre-trained generative models, conditional image generation has been given a significant boost in result quality and ease of use. In this paper, we present a novel method that enables the generation of general foreground-background segmentation models from simple textual descriptions, without requiring segmentation labels. We leverage and explore pre-trained latent diffusion models, to automatically generate weak segmentation masks for concepts and objects. The masks are then used to fine-tune the diffusion model on an inpainting task, which enables fine-grained removal of the object, while at the same time providing a synthetic foreground and background dataset. We demonstrate that using this method beats previous methods in both discriminative and generative performance and closes the gap with fully supervised training while requiring no pixel-wise object labels. We show results on the task of segmenting four different objects (humans, dogs, cars, birds) and a use case scenario in medical image analysis. The code is available at https://github.com/MischaD/fobadiffusion.",
+        "bbox": [
+            75,
+            324,
+            473,
+            643
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            675,
+            209,
+            690
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Supervised pretraining, e.g., with ImageNet[16], has demonstrated reduced training times and boosted performance. This gave rise to models that could be trained once over large amounts of data before being adapted to specialised tasks, such as image recognition, object detection, image segmentation[52], and medical image analysis[50]. The recent development of self-supervision techniques and their ability to learn without manual labels led to much larger scale training datasets [9] and to the creation of foundation models [6]. At present, the use of pre-trained models for a wide range of diverse downstream tasks defines a very active and intriguing area of research.",
+        "bbox": [
+            75,
+            702,
+            468,
+            883
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Large scale foundation models are already established in",
+        "bbox": [
+            96,
+            885,
+            468,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/21d2d01d24891b25156c9155295b930e3c179c2a355c5b5cfd76b5847da8fca2.jpg",
+        "image_caption": [
+            "Figure 1. High level overview of our proposed method: Without needing a single labelled image, our method is able to generate foreground, background, and segmentation masks for any concept that is known to a text-to-image generative network."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
+            289,
+            844,
+            494
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "natural language processing, with most of them being based on the Transformer architecture [57, 17, 7]. A crucial part of this architecture are cross- and self-attention layers, which compute interpretable importance weightings [39, 12].",
+        "bbox": [
+            496,
+            580,
+            890,
+            642
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Diffusion models are based on the U-Net architecture [45] with additional attention layers [37] to condition on textual prompts. Therefore, we can extract inherently interpretable pixel importance scores from conditioning on textual prompts. Furthermore, the reverse diffusion process teaches the U-Net to successively remove noise from images, starting from pure Gaussian noise. In the early steps of this process, where the images resemble pure noise, the texture is non-existent, and the model only learns structures.",
+        "bbox": [
+            496,
+            642,
+            892,
+            777
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, latent diffusion models have emerged as state-of-the-art generative models for the task of text-to-image generation [18, 44, 41]. However, training such models requires a significant amount of  $\\mathrm{CO}_{2}$ -intensive resources and until recently, pre-trained model weights have not been publicly available. Rombach et al. were the first to published their weights and model architecture [44], which facilitated the development of numerous derived applica",
+        "bbox": [
+            496,
+            779,
+            893,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "988",
+        "bbox": [
+            485,
+            945,
+            511,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "tions [60, 15, 53] and established this model as the foundation model for tasks that require generalised representations of concepts in images. State-of-the-art latent diffusion models are able to generate high resolution images of a vast amount of different objects, suggesting that a highly expressive latent representation of the data has been learned.",
+        "bbox": [
+            75,
+            90,
+            467,
+            181
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We hypothesize that we can leverage these learned latent representations for our own downstream tasks of zero-shot foreground-background generation. Using a generative latent diffusion foundation model, we are able to extract a weak segmentation mask around an arbitrary object by computing the importance maps based on the textual input prompts. Weak segmentation masks have been shown to be an effective prior for segmentation models, given that enough training samples are available [34, 40]. We then use these preliminary masks to fine-tune a latent diffusion model on (1) generating new images from this dataset, as well as (2) inpainting regions where the object is not present according to our preliminary masks. The resulting model is able to perform full-image synthesis, as well as foreground, background and mask generation, as summarized in Fig. 1. A segmentation model trained using these masks can then achieve a level of performance that is close to direct supervision, despite not requiring manual segmentation masks at any point in the pipeline. This suggests that labour-intensive ground-truth image annotation workflows could become obsolete in the future, and be replaced by concept distillation from generative foundation models.",
+        "bbox": [
+            75,
+            181,
+            468,
+            513
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our main contributions are:",
+        "bbox": [
+            76,
+            515,
+            261,
+            527
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a self-supervised, hyperparameter-free, approach for dataset-independent foreground-background segmentation, based on latent diffusion models, capable of synthesizing foreground, background, and segmentation masks.",
+            "- We describe a general framework to extract importance scores obtained from pretrained diffusion models and detail how to use them to improve segmentation performance.",
+            "- We verify the feasibility of our method on a set of four different foreground background segmentation tasks, spanning humans, birds, dogs, and cars and show that our method achieves results close to supervised methods while being trained without direct supervision.",
+            "- We experiment with the extension of our method to domain-adapted diffusion models by showing promising results on a medical segmentation task."
+        ],
+        "bbox": [
+            94,
+            542,
+            467,
+            796
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            814,
+            217,
+            829
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Semantic Segmentation refers to the identification of high level concepts in an image, which enable their extraction from the image. [33, 36] introduced the use of fully convolutional networks for this task, which superseded previous",
+        "bbox": [
+            75,
+            839,
+            467,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "shallow feature classification approaches [20]. Currently, the most common segmentation network architectures are designed as encoder-decoder pairs, as it enforces an information bottleneck that facilitates generalisation. The encoder provides meaningful low dimensional representations and the decoder reconstructs high-resolution segmentation maps [10, 45, 33, 36]. Recent approaches maximise the use of multi-scale information with multi-scale attention [56], squeeze-and-attention [63], and Transformers [62]. The final pixel classification operation, which creates the segmentation mask, is performed through multinomial logistic regression. These methods require large amounts of manually labelled training samples, which can be labour-intensive and expensive.",
+        "bbox": [
+            496,
+            90,
+            890,
+            301
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Weakly Supervised Semantic Segmentation partially mitigates that by learning from weak global labels, such as image-wise class labels, and perform rough semantic-segmentation tasks. These approaches often leverage the learned representations in intermediate layers through attention maps [26] or saliency maps [31] extraction. These representations are learned in a supervised manner through a classification task, as opposed to our approach that leverages an even weaker signal: free-form text-embeddings. Furthermore, these methods cannot generate images and are, therefore, not suitable for foreground-background synthesis.",
+        "bbox": [
+            496,
+            305,
+            890,
+            484
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Foreground background separation is a segmentation task where the goal is to apply binary classification over all the pixels of an image to separate the object of interest, the foreground, from the contextual background. For example, in video analysis tasks, the background is often defined as parts of scenes that are at rest [51]. More recently, decomposing individual images into potential foreground and background layers became an intriguing research topic [25]. Since the foreground-background separation factors are not known a priori, many related works formulate the problem as a category-agnostic unsupervised segmentation approach. While deep neural networks can learn pixel clustering in an unsupervised way [25, 29, 38], it often leads to inferior performance when compared to fully supervised methods. Other works also tried to learn image segmentation from generative models, for example via direct sampling from the training distribution with cut-and-paste [43], image combinations via styleGAN [1], erasing and redrawing [11], and through inpainting [49].",
+        "bbox": [
+            496,
+            489,
+            890,
+            776
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The work closest related to ours is [61] who employ layered generative adversarial networks (GANs) to generate distinct images for the foreground and background. As opposed to [61], we are not relying on the unknown structure of the latent manifold to separate the embedding codes that represent foreground and background, but instead follow the directly interpretable paradigm 'textual concept description'  $\\rightarrow$  'segmentation model'. Both approaches in",
+        "bbox": [
+            496,
+            779,
+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "989",
+        "bbox": [
+            485,
+            945,
+            509,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "troduce a similar bias, ours through the textual concept description and them through object-specific models, making our method similarly conditioned but more flexible.",
+        "bbox": [
+            75,
+            90,
+            468,
+            135
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Diffusion models are generative methods. Generative modeling has always been an important task in deep learning. Recently, Diffusion models gained a lot of attention thanks to the impressive results achieved by [42, 48]. Based on [22, 55], these models currently define the state-of-the-art in conditional image generation, and have been extended towards text-to-image models such as unCLIP [41] and Stable Diffusion [44]. Part of that success is due to the efficacy of straightforward extensions to diffusion models, such as classifier-free guidance [23]. Current research about diffusion models focuses mostly on inpainting [14, 13, 44]. Depending on the task, it might be easier to learn the object itself and then train a diffusion model on the task of inpainting regions where the object is not present. However, we focus on the scenario where we have the object itself present and try to remove it.",
+        "bbox": [
+            75,
+            136,
+            468,
+            377
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Shortly after latent diffusion models showed superiority in terms of image sample quality compared to GANs [18], they were conditioned on the description of concepts [42]. These models became widely available online, including on commodity hardware after the computationally expensive denoising process was accelerated on a fundamental level [32]. Direct translation of text into object-centric representations has been attempted but rather in the context of attention editing [21], subject specific image generation [47], and textual concept-refined image-to-image translation [59]. Textual inversion, where examples of concepts are provided to a diffusion model as text and image tuples to teach the model a new concept [19], operates on the same fundamental input level as our approach. However, it is not able to provide object segmentation masks or concept-specific pixel importance scores. Recent advances on diffusion models have led to a spike in research around how latent features can be extracted [21, 2] however, their potential to be used for zero-shot segmentation has yet to be explored.",
+        "bbox": [
+            75,
+            378,
+            470,
+            680
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            693,
+            168,
+            709
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our approach is summarized in Fig. 2. At a high level, we first use the attention maps from a pretrained latent diffusion model to compute coarse foreground segmentations (preliminary masks). We use these masks to fine-tune the diffusion model to be able to remove the object from the image, replacing it with background information, whilst also being able to generate new samples from the true distribution  $p(\\mathbf{x})$  of the dataset. By comparing the original images to those with the background inpainted over the foreground, we are then able to produce much more refined masks. We can also then use the fine-tuned model to sample an arbitrary number of new images, including only the foreground,",
+        "bbox": [
+            75,
+            719,
+            468,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "only the background, and the masks separating them. The only assumptions this method uses is that we have access to a dataset of images where the chosen object is always present, and that the foundation model we use has learned a meaningful representation of the object we want to identify. In this context, objects can describe concepts like birds, cars, dogs, humans, but also parts of objects such as arms or legs.",
+        "bbox": [
+            496,
+            90,
+            890,
+            210
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We start from the latent diffusion model (LDM) [44], a foundation model pretrained on the task of text-to-image generation, denoted as  $m$ . It generates images by sampling gaussian noise and iteratively denoising them in  $T$  diffusion steps. Throughout this work, we keep the default value from [44] of  $T = 50$  steps.",
+        "bbox": [
+            496,
+            212,
+            890,
+            303
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\mathbf{D}$  denote a dataset where all the images contain our desired object. Formally, we aim to generate unsupervised segmentation masks of the original dataset  $\\mathbf{D}_{\\mathbf{m}}$  as well as a synthetic dataset that contains synthetic images  $\\mathbf{D}'$ , masks  $\\mathbf{D}_{\\mathbf{m}}'$ , foreground  $\\mathbf{D}_{\\mathbf{f}}'$ , and background  $\\mathbf{D}_{\\mathbf{b}}'$  denoted as set  $\\mathbf{D}_{\\mathbf{s}}' = \\{\\mathbf{D}', \\mathbf{D}_{\\mathbf{m}}', \\mathbf{D}_{\\mathbf{f}}', \\mathbf{D}_{\\mathbf{b}}'\\}$ .",
+        "bbox": [
+            496,
+            304,
+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Preliminary Masks: The LDM was trained on paired text-image data. Thus, the output is conditioned on a text input, which we have to carefully choose to generate our initial attention maps. In practice, self- and cross-attention work well for conditioning on different inputs, especially across different modalities [57]. As input, we propose the prompt \"a photo of a {object}\" where \"object\" is a high level description of our foreground object (e.g. \"bird\").",
+        "bbox": [
+            496,
+            395,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The first step in computing the preliminary masks is to leverage the raw attention maps computed in every cross-attention layer of the U-Net architecture. We decide against cherry-picking different attention layers for different tasks to remain task-agnostic, but would like to point out that this could lead to task-specific improvements as an hyperparameter option.",
+        "bbox": [
+            496,
+            517,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let  $z_0$  denote the latent space representation of some input image  $x$ . In each layer, attention is computed as:",
+        "bbox": [
+            496,
+            623,
+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\psi \\left(Q _ {l}, K _ {l} ^ {T}\\right) \\cdot V _ {l} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with the attention probabilities  $\\psi(Q_l, K_l^T)$  defined as:",
+        "bbox": [
+            500,
+            696,
+            856,
+            714
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\psi_ {\\mathbf {z} _ {\\mathbf {t}, 1}} \\left(Q _ {l}, K _ {l} ^ {T}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}}\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            580,
+            726,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with  $Q = W_{Q}^{(i,l)} \\cdot \\phi(\\mathbf{z}_{\\mathbf{t},1})$ ,  $K = W_{K}^{(i,l)} \\cdot \\tau_{\\theta}(y)$ , and  $V = W_{V}^{(i,l)} \\cdot \\tau_{\\theta}(y)$  denoting the learnable projection matrices according to [57],  $\\phi(\\mathbf{z}_{\\mathbf{t},1})$  the latent code of the l-th U-Net layer in the t-th reverse diffusion step, and  $\\tau_{\\theta}(y)$  the learned latent representation for the textual input prompt [44].  $z_{t,l}$  denotes the latent representation of the stable diffusion model in layer 1, conditioned at diffusion  $t$ .",
+        "bbox": [
+            496,
+            770,
+            890,
+            883
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The next step is to compute the mean attention maps  $\\hat{M}$",
+        "bbox": [
+            517,
+            883,
+            890,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "990",
+        "bbox": [
+            485,
+            945,
+            511,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/812bc4ee37993a1b3ad7a37f61695768970bba86626541f6377a493c2d702a0a.jpg",
+        "image_caption": [
+            "Figure 2. Overview of our model pipeline for self-supervised foreground-background segmentation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            88,
+            893,
+            218
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/e940a896ead2b702dabc74df3a1a712f5651bf37e093cf624f450032bfdf0379.jpg",
+        "image_caption": [
+            "Figure 3.  $T_{0}$  vs AUC-ROC on CUB. Incorporating more reverse diffusion steps into the attention computation improves the AUC-ROC against the groundtruth only up to roughly  $T_{0} = 40$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "as expectations over multiple repeated diffusion steps according to",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {M} = \\sum_ {t = 1} ^ {T _ {0}} \\mathbb {E} _ {\\mathbf {z} \\sim p (\\mathbf {z} _ {t} | \\mathbf {z} _ {t + 1}, \\mathbf {z} _ {0})} [ \\sum_ {l} \\psi_ {\\mathbf {z} _ {t, 1}} (Q _ {l}, K _ {l} ^ {T}) ]. \\quad (3)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We empirically show in our supplementary material that this can be simplified to performing single reverse diffusion steps which leads to a simplified importance score",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {M} = \\sum_ {t = 1} ^ {T _ {0}} \\sum_ {l} \\psi_ {\\mathbf {z} _ {\\mathbf {t}, 1}} \\left(Q _ {l}, K _ {l} ^ {T}\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 shows AUCROC of using  $\\hat{M}$  to identify the foreground as a function of the number of reverse steps. There is a clear improvement visible computing the mean over up to roughly  $T_0 = 40$  reverse diffusion steps. Including higher diffusion steps seems to deteriorate the accuracy of  $\\phi$ . This is because for higher values of  $t$  the input images approach pure Gaussian noise. However, for medium values of  $t$  the input and output images already approximate the basic structure of the final objects. Other details, like texture, appear at later stages but do not bear any valuable information for this use case. This observation could mean that for time critical applications, starting from lower  $t$  should suffice.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The third and final step in retrieving the preliminary masks is to binarize the mean attention maps. To do so, we",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "take advantage of the observation that all attention maps resemble a bimodal distribution, with one mode at a low value for the non-object pixels and one mode at a high value for the object pixels. Hence, we model absolute values of the instance-wise attention scores as a bimodal Gaussian mixture model (GMM) to produce GMM masks. Additionally, we remove orphan pixels by computing the mean filter over the resulting binary classification map to produce our preliminary masks  $M_{pre}$ . These preliminary masks could potentially already be used to detect objects as evaluated in Sec. 4.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Fine-tuning and Mask Refinement: The main problem with the preliminary masks is that, because they are derived from the latent space of the LDM, their resolution is only  $64 \\times 64$ . This limits them to being a coarse segmentation, which often overestimates the size of the object rather than following the object's sharp edges. A rough segmentation is sufficient for tasks like inpainting, especially if the area around the object is homogeneous, but for the task of extracting the foreground object it produces unwanted artefacts. To work around this, we leverage the same diffusion model that we used to extract the masks. We use the binary classification prediction of the GMM mask  $M_{pre}$  to select random rectangles within the image that only contain background. Then we fine-tune the model to inpaint only the background of these images by conditioning on the prompt  $y_{b} =$  \"a photo of a background\" using the image as ground truth (See supplements for examples). Simultaneously, the model is fine-tuned on the task of full image synthesis to generate new samples for  $\\mathbf{D}'$  by conditioning on  $y_{f} =$  \"a photo of a  $\\{\\mathrm{object}\\}$ \".",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To generate the final foreground masks  $\\mathbf{D}_{\\mathbf{m}}$  we use the fine-tuned LDM  $m^{\\prime}$  to inpaint the background over the area covered by the preliminary mask conditioning on the background prompt. To identify the foreground region, we take the pixel-wise intensity difference between the background-inpainted and original images. As the inpainted images are conditioned to generate background, the difference is higher in the true foreground region. We apply a Gaussian mixture model to the pixel-wise difference map to create a binary classification map. Formally the refined masks  $M$  are computed as",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "991",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM = M _ {p r e, u p} \\odot g \\left(\\left| \\mathbf {x} - m ^ {\\prime} \\left(\\tilde {\\mathbf {z}} _ {0}, y _ {b}\\right) \\right|\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            147,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {\\mathbf {z}} _ {\\mathbf {0}} = \\mathbf {z} _ {\\mathbf {0}} \\odot (1 - M _ {p r e}) + \\mathbf {z} \\odot M _ {p r e} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
+            138,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $M_{pre,up}$  denotes the preliminary mask upsampled to the input image's resolution,  $g$  applies the bimodal Gaussian mixture model to the pixel values and  $\\tilde{\\mathbf{z}}_0$  is the latent code of an image with the foreground region replaced with random noise  $\\mathbf{z}$ . This produces refined masks, as the use of pixel-wise error improves the segmentation around the sharp edges of the object. Additionally, the computation of the refined masks is performed in pixel-space of the images instead of the latent space of  $m$  and therefore produces even more detailed masks.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, to further improve our mask prediction we use the refined masks as labels to train a U-Net [45] to directly segment the foreground of the images, similar to the approach in [61], which follows a standardized approach of training a U-Net on a fixed number of steps and hence does not require any hyperparameter tuning. We experiment with training the segmentation network on refined masks of the original unlabelled training data  $(\\mathbf{D_s})$ , as well as training it with the fully synthetic dataset  $\\mathbf{D_s}'$  as an augmentation method, which we generate by prompting the fine-tuned model with the foreground conditioning  $y_{f}$  and repeating our pipeline of mask refinement on this synthetic dataset to get segmentation labels.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Evaluation and Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Implementation: We use PyTorch 1.11 and run our experiments on a workstation with two A6000 Nvidia GPUs. Concept distillation training takes on average one day. The forward pass is fast, equivalent to that of a standard U-Net. Datasets: We choose our datasets such that they cover a variety of different objects, including in-the-wild animals and cars, as well as humans in static setups.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Human3.6m [24] is a dataset of 3.6 million images of humans in different scenarios and situations. To show that our method does not rely on large datasets we take a subset of 6000 randomly chosen images centred around the human and cropped to  $256 \\times 256$  pixels from the training dataset of Human3.6m.",
+        "bbox": [
+            75,
+            657,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To test the method on representations of animals, we use two datasets: the Stanford Dog Dataset [28], which contains 20,580 images of dogs divided into different categories, and the Caltech-UCSD Birds 200 (CUB) dataset [58], which contains 11,788 images of birds from 200 different species.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, we also experiment with the detection of cars using [30], which consists of 16,185 images of cars in different natural and non-natural settings. All these datasets come with subcategories grouping the images based on selected features. For our use case, we consolidate these groups",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "when prompting the model and use the classes cars, dogs, human, and birds to simulate the absence of manual labels.",
+        "bbox": [
+            498,
+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/8716b1eae931e6ac7b9510c4e1efb6d4afb688af4be297f1e8a81cdcac72ef0f.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. Comparison to other segmentation methods. Baselines taken from [61]. Details on the training of the U-Nets can be found in the appendix."
+        ],
+        "table_body": "<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Fully supervised U-Net</td><td>97.9</td><td>88.3</td><td>93.0</td></tr><tr><td>GrabCut [46] by [49]</td><td>72.3</td><td>36.0</td><td>52.3</td></tr><tr><td>ReDO [11]</td><td>84.5</td><td>42.6</td><td>-</td></tr><tr><td>PerturbGAN [4]</td><td>-</td><td>-</td><td>38.0</td></tr><tr><td>IEM + SegNet [49]</td><td>89.3</td><td>55.1</td><td>71.4</td></tr><tr><td>Melas-Kyriazi et al. [35]</td><td>92.1</td><td>66.4</td><td>-</td></tr><tr><td>Layered GAN [61]</td><td>94.3</td><td>69.7</td><td>81.7</td></tr><tr><td>Ours (U-Net trained on Ds)</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>Ours (U-Net trained on Ds ∪ D&#x27;s&#x27;)</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>",
+        "bbox": [
+            501,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Self-supervised Segmentation Performance: Table 1 compares our methods performance against other unsupervised methods on the CUB dataset, showing the pixel-wise accuracy, the Intersection over Union (IoU) of the foreground segmentation and the mean IoU. From this we see that training a U-Net on our self-supervised labels produces a model that outperforms all other methods, achieving an overall foreground IoU improvement of 5.4 compared to [61]. Furthermore, by adding the fully synthetic dataset  $\\mathbf{D}_{\\mathbf{s}}^{\\prime}$  to the training data we are able to improve the performance even further, reaching a foreground IoU of 77.2. Table 3 also shows high foreground IoU values across the other datasets, with Fig. 4 showing qualitative examples.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Mean Attention Map Performance: Computing the mean attention maps  $\\hat{M}$  and comparing them to the ground-truth yields a remarkable AUC-ROC for the bird dataset of 97.1. Scores are normalized instance-wise to a range of 0 to 1. We also experiment with no normalization, which gives a slightly worse AUC-ROC of 97.08. Qualitative examples from all datasets are shown in Fig. 5, displaying the mean attention maps' ability to localize the foreground in different scenarios. To compare this to our classification results we compute the threshold such that we reach over  $95\\%$  true positive rate on a reserved training set of 100 images. True positive rate is more important in our case because we observe that falsely classifying pixels as background leads the inpainting model taking these foreground pixels as sources to inpaint larger parts of the image. We reach a pixel-wise accuracy of  $86\\%$  on a set of 1000 test images suggesting that our method of extracting the classification masks already can provide meaningful results.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "While these results are encouraging, they also require a ground-truth dataset and thresholding that we do not want to rely on. The results indicate that our computed masks",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "992",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/d0b15c23058f4db52098020eff32e7543f9edd1cc99899be44e0dbfec202b41d.jpg",
+        "image_caption": [
+            "CUB"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/82aada856470a715b72a73b61e78e438294bb55a6663ac617ab38a1aeb709dee.jpg",
+        "image_caption": [
+            "Human3.6"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/1ca0f619801f68ee2830fb39ae37c2244fd11fe88ac90aef3241a0c60af0ffaf.jpg",
+        "image_caption": [
+            "Stanford Cars"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2ae37a5406b634f4471bdd904a08f419c344714b5844c5e917ef0cb06d3e3ae6.jpg",
+        "image_caption": [
+            "Stanford Dogs",
+            "Figure 4. Unsupervised Segmentation Masks generated by our proposed approach."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "are very good at locating the objects, albeit they do not reach state-of-the-art performance despite adding supervision. Training on refined masks and integrating synthetic data surpasses supervised results without using any labels as shown in the next section.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/859aa860f818381aeae830b9b865a4564ca93ac66949850436167384670d2170.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Preliminary Masks Mpre</td><td>83.5</td><td>29.0</td><td>55.7</td></tr><tr><td>Simple Inpainting Mcrop</td><td>90.0</td><td>30.7</td><td>60.0</td></tr><tr><td>U-Net trained on (D, Mpre)</td><td>91.7</td><td>66.5</td><td>78.2</td></tr><tr><td>Refined Masks M</td><td>92.4</td><td>63.6</td><td>77.4</td></tr><tr><td>U-Net trained on Ds</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>U-Net trained on Ds ∪ D&#x27;s&#x27;</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Segmentation results for different steps of our pipeline.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablation study: Table 2 shows an ablation study for the individual components of our method. Initially, the zero-shot preliminary masks generated from the foundation model achieve good accuracy (83.5), but poor foreground IoU (29.0). This reflects our earlier intuition that masks overestimate the size of the object due to the maps being computed at a lower resolution. Thanks to this, the GMM overestimates the boundaries and spares the need for any hyperparameter. Optimizing the threshold to maximise the accuracy over a set of 100 training images would increase the accuracy to  $93.9\\%$ , but requires a ground-truth dataset.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training a U-Net on these labels  $(M_{pre})$  increases the",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "IoU to 66.5, showing the value in training the segmentation network. Using the refined masks as foreground segmentation gives comparable performance, with higher accuracy but lower foreground IoU. Additionally, we experiment with replacing the inpainting step used to improve  $M_{pre}$  with a simpler approach that crops background areas and uses them as inpainting in Eq. (5) instead of  $m'$ . The resulting masks  $M_{crop}$  are worse than the masks from our proposed refinement step (For more details see supplements). However, training a U-Net on these refined masks produces the best results, being further boosted by incorporating additional synthetic data. The progressive refinement of the segmentation masks is shown in Fig. 6.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Data synthesis: Table 3 compares the generative ability of our fine-tuned diffusion model using the Fréchet inception distance (FID). Our method achieves higher generation quality than all other methods across the CUB, Stanford Dogs, and Stanford Cars datasets. We improve upon LayeredGAN's remarkably low FID scores for CUB and Stanford Cars by 3.1 and 5.6 respectively.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our method allows for the generation of samples covered entirely by the background, as shown in Fig. 7, without ever seeing such an image during training. The success of this component is what enables the refined masks to be generated, as accurately inpainting the foreground allows us to use the pixel-wise difference between the original and inpainted images to precisely identify the foreground.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Concept Distillation: Finally we can evaluate if our model",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "993",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8946094ccf2431774c5f5829ae461346def06db6b066a37ffbea50c838bd9c0c.jpg",
+        "image_caption": [
+            "Figure 5. Mean attention maps for all datasets in latent space  $\\mathbf{z}$  of the diffusion model. Prompts are \"a photo of a {object}\", where {object} is replaced by \"bird\" for the first pair of rows, then \"car\", \"dog\", and \"human\"."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            88,
+            883,
+            295
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c488f98a2f12f68396cbb0ba8919a8dd2b81db46882c0153dd6a364716a0edaf.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Sup.</td><td colspan=\"2\">CUB</td><td colspan=\"2\">Stanford Dogs</td><td colspan=\"2\">Stanford Cars</td><td colspan=\"2\">Human3.6m</td></tr><tr><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td></tr><tr><td>FineGAN [54]</td><td>Weak</td><td>23.0</td><td>44.5</td><td>54.9</td><td>-</td><td>24.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>OneGAN [3]</td><td>Weak</td><td>20.5</td><td>55.5</td><td>48.7</td><td>-</td><td>24.2</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LayeredGAN [61]</td><td>Unsup.</td><td>12.9</td><td>69.7</td><td>59.3</td><td>-</td><td>19.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>Self</td><td>9.8</td><td>75.1</td><td>43.1</td><td>63.8</td><td>13.4</td><td>55.2</td><td>63.7</td><td>69.2</td></tr></table>",
+        "bbox": [
+            148,
+            337,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Quantitative Results on  $\\mathbf{D_s}$ . Training details are shown in the supplements. Values are taken from [61]. Source code for [54, 3, 61] was not available for re-evaluation on the Dogs, Cars and Human3.6m datasets. IoU on CUB are reported using the prediction of our model and the ground truth provided with the dataset. For the other datasets we use the IoU of the bounding boxes.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0096596307b82017ff4fe8c7751d445517da6a6b1ee949c06dd3e625cbe01ec4.jpg",
+        "image_caption": [
+            "Figure 6. Progressive refinement of the segmentation masks."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "has indeed learned to distinguish between foreground and background by looking at the output of different classifier-free guidance scales starting from the same seed  $\\mathbf{z}_{\\mathbf{t}}$ . Since we have fine-tuned our model only on two distinct textual prompts the conditional image generation should have collapsed to two clusters, one for the object and the other one for the background. Hence, instead of performing classifier-free guidance using the predictions of  $m^{\\prime}$  conditioned on empty prompts we can directly use the predictions of  $m^{\\prime}(\\mathbf{z}_{\\mathbf{t}},y_{b})$  and  $m^{\\prime}(\\mathbf{z}_{\\mathbf{t}},y_{f})$  to perform image interpolation. We define classifier-free guidance in the direction of the foreground, hence, a higher score means that latent representations are pushed further in the direction of the object. The results are shown in Fig. 8. For negative guidance scales, the background is more detailed and there is no bird",
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+        "text": "present. Increasing this scale leads to less detail in the background while birds often seem to naturally grow from the details in the background. The quality of the birds visually improves while the quality of the rest of the image keeps degrading resulting in less detailed backgrounds. We confirm this quantitatively by computing the FID for different classifier-free guidance scales. Without classifier-free guidance, i.e., scale  $= 1$ , the method reaches a FID of 9.8, at scale  $= 3$  a FID of 11.3, and at scale  $= 7.5$  a FID of 22.3.",
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+        "text": "Medical Image Analysis: We want to evaluate if this approach can be applied to other domains, such as medical imaging. Since the LDM does not have any medical understanding, we first need to fine-tune it using MIMIC [27], which provides chest x-ray images paired with radiology reports. We can fine-tune the model using a similar approach as the one suggested by [8] (Details on the fine-tuning can be found in the supplements). Then we report the pixelwise AUC-ROC on MS-CXR [5], a subset of MIMIC with bounding box labels for diseases. Qualitative results can be seen in Fig. 9. The pixel-wise accuracy of the attention mask is already at  $79.6\\%$  AUC-ROC across eight different diseases, however, the bimodal GMM assumption no longer holds in many cases because the model distinguishes three regions, namely: background, foreground, and the rest of the chest region.",
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+        "text": "994",
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+    {
+        "type": "image",
+        "img_path": "images/74747f9bb420661d26b970d4cef36e16eef61c9238fb72f195e4a76504d8b14d.jpg",
+        "image_caption": [
+            "Figure 7. Full background image synthesis from the fine-tuned model, conditioned on  $y_{b}$ . Using our proposed fine-tuning method, the diffusion model is successfully able to generate images without birds from a dataset only consisting of images with birds."
+        ],
+        "image_footnote": [],
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+    {
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+        "image_caption": [
+            "Figure 8. Synthetic results of  $m'$  with changing scales of classifier-free-guidance, ranging from -2 on the left to +7.5 on the right."
+        ],
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+        "img_path": "images/9c44e2fad178d71e909189b1aac2184a264fb77b16698e19cc64469d8f697a68.jpg",
+        "image_caption": [
+            "Figure 9.  $\\hat{M}$  and  $M_{pre}$  extraction on a medical task."
+        ],
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+        "type": "text",
+        "text": "5. Discussion",
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+    {
+        "type": "text",
+        "text": "'startofstring' 'a' 'photo' 'of' 'a' 'human' with ' arms' 'and' 'legs'",
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+        "img_path": "images/4d81549adcd5633c66590fa22c9ef6d27eb199aa17367eb314335a6a4bb7c03d.jpg",
+        "image_caption": [
+            "Figure 10. Input image and mean attention maps for every word of the textual input prompt \"startofstring a photo of a human with arms and legs\". The attention of \"human\" focuses on the torso, the one for the \"arms\" on the arms, and the one for the \"legs\" on the legs."
+        ],
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+    {
+        "type": "text",
+        "text": "We show in Sec. 4 that our method to extract the segmen",
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+    {
+        "type": "text",
+        "text": "tation masks  $M$  from the preliminary attention masks yields better results than computing an optimised threshold over a reserved miniset. This is possible because comparing to the inpainted background provides sharp edges around the object. However, our model is currently limited to detecting single object concepts. An extension to multiple objects could be achieved by prompt engineering in combination with data augmentation techniques. Taking the foreground masks and using them to extract objects would enable multi-instance and multi-object segmentation by layering multiple objects over each other and extending the final U-Net to a multi-label segmentation model.",
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+    {
+        "type": "text",
+        "text": "Furthermore, learning from weak labels has the disadvantage that the segmentation model may learn and reproduce weaknesses of the initial method. In our case, the bimodal GMM fails if the image has more than two distinct contrast clusters. This is especially the case on the Human3.6m dataset where the floor, walls, and person have vastly different contrast-levels. Consequently, the final segmentation sometimes fails to detect the lower part of the body as shown in Fig. 4. However, our method could easily be adapted to only a part of the human body, such as the legs. We show this in Fig. 10, as by conditioning images from [24] on the prompt \"A photo of a human with arms and legs\" and computing  $\\hat{M}$  for the three concepts (human, arms, and legs) we are able to produce attention maps focused on specific body parts.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this work, we have presented a generalizable framework to train segmentation networks without any hyperparameter tuning using an unsupervised zero-shot approach following the paradigm of 'textual concept description'  $\\rightarrow$  'segmentation model'. We leverage the power of large generative latent diffusion models and fine-tune the model on the task of generating foreground and background images, which can be used as data augmentation methods. We show, that this method can achieve results close to supervised methods, without requiring any manually generated ground",
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+        "type": "page_number",
+        "text": "995",
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+    {
+        "type": "text",
+        "text": "truth labels. Our approach is amenable to supervised deep learning and can be combined with existing models to boost segmentation performance even further.",
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+    {
+        "type": "text",
+        "text": "In future work we will explore how multi-object, multi-instance segmentation can be facilitated with concept distillation from generative image foundation models.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements: The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR projects b143dc and b180dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) - 440719683. Additional support was also received by the ERC - project MIA-NORMAL 101083647, DFG KA 5801/2-1, INST 90/1351-1 and by the state of Bavarian. H. Reynaud was supported by Ultromics Ltd. and the UKRI Centre or Doctoral Training in Artificial Intelligence for Healthcare (EP/S023283/1).",
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+    {
+        "type": "text",
+        "text": "References",
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+        ],
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+        ],
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+    },
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+        "text": "998",
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+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models/5ee0597f-a7d5-4c09-a624-657832eb9d0e_model.json b/2023/Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models/5ee0597f-a7d5-4c09-a624-657832eb9d0e_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..a354582e891843c59e4cfe6eb5ea343af1c4b76b
--- /dev/null
+++ b/2023/Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models/5ee0597f-a7d5-4c09-a624-657832eb9d0e_model.json	
@@ -0,0 +1,2224 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.127,
+                0.13,
+                0.844,
+                0.175
+            ],
+            "angle": 0,
+            "content": "Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.12,
+                0.203,
+                0.851,
+                0.257
+            ],
+            "angle": 0,
+            "content": "Mischa Dombrowski\\(^{1}\\) Hadrien Reynaud\\(^{2}\\) Matthew Baugh\\(^{2}\\) Bernhard Kainz\\(^{1,2}\\)  \n\\(^{1}\\)Friedrich-Alexander-Universität Erlangen-Nürnberg \\(^{2}\\)Imperial College London mischa.dombrowski@fau.de"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.325,
+                0.474,
+                0.645
+            ],
+            "angle": 0,
+            "content": "Curating datasets for object segmentation is a difficult task. With the advent of large-scale pre-trained generative models, conditional image generation has been given a significant boost in result quality and ease of use. In this paper, we present a novel method that enables the generation of general foreground-background segmentation models from simple textual descriptions, without requiring segmentation labels. We leverage and explore pre-trained latent diffusion models, to automatically generate weak segmentation masks for concepts and objects. The masks are then used to fine-tune the diffusion model on an inpainting task, which enables fine-grained removal of the object, while at the same time providing a synthetic foreground and background dataset. We demonstrate that using this method beats previous methods in both discriminative and generative performance and closes the gap with fully supervised training while requiring no pixel-wise object labels. We show results on the task of segmenting four different objects (humans, dogs, cars, birds) and a use case scenario in medical image analysis. The code is available at https://github.com/MischaD/fobadiffusion."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.676,
+                0.21,
+                0.691
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.703,
+                0.47,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Supervised pretraining, e.g., with ImageNet[16], has demonstrated reduced training times and boosted performance. This gave rise to models that could be trained once over large amounts of data before being adapted to specialised tasks, such as image recognition, object detection, image segmentation[52], and medical image analysis[50]. The recent development of self-supervision techniques and their ability to learn without manual labels led to much larger scale training datasets [9] and to the creation of foundation models [6]. At present, the use of pre-trained models for a wide range of diverse downstream tasks defines a very active and intriguing area of research."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Large scale foundation models are already established in"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.29,
+                0.845,
+                0.496
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.499,
+                0.895,
+                0.555
+            ],
+            "angle": 0,
+            "content": "Figure 1. High level overview of our proposed method: Without needing a single labelled image, our method is able to generate foreground, background, and segmentation masks for any concept that is known to a text-to-image generative network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.582,
+                0.892,
+                0.643
+            ],
+            "angle": 0,
+            "content": "natural language processing, with most of them being based on the Transformer architecture [57, 17, 7]. A crucial part of this architecture are cross- and self-attention layers, which compute interpretable importance weightings [39, 12]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.893,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Diffusion models are based on the U-Net architecture [45] with additional attention layers [37] to condition on textual prompts. Therefore, we can extract inherently interpretable pixel importance scores from conditioning on textual prompts. Furthermore, the reverse diffusion process teaches the U-Net to successively remove noise from images, starting from pure Gaussian noise. In the early steps of this process, where the images resemble pure noise, the texture is non-existent, and the model only learns structures."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Recently, latent diffusion models have emerged as state-of-the-art generative models for the task of text-to-image generation [18, 44, 41]. However, training such models requires a significant amount of \\(\\mathrm{CO}_{2}\\)-intensive resources and until recently, pre-trained model weights have not been publicly available. Rombach et al. were the first to published their weights and model architecture [44], which facilitated the development of numerous derived applica"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "988"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.182
+            ],
+            "angle": 0,
+            "content": "tions [60, 15, 53] and established this model as the foundation model for tasks that require generalised representations of concepts in images. State-of-the-art latent diffusion models are able to generate high resolution images of a vast amount of different objects, suggesting that a highly expressive latent representation of the data has been learned."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.183,
+                0.47,
+                0.514
+            ],
+            "angle": 0,
+            "content": "We hypothesize that we can leverage these learned latent representations for our own downstream tasks of zero-shot foreground-background generation. Using a generative latent diffusion foundation model, we are able to extract a weak segmentation mask around an arbitrary object by computing the importance maps based on the textual input prompts. Weak segmentation masks have been shown to be an effective prior for segmentation models, given that enough training samples are available [34, 40]. We then use these preliminary masks to fine-tune a latent diffusion model on (1) generating new images from this dataset, as well as (2) inpainting regions where the object is not present according to our preliminary masks. The resulting model is able to perform full-image synthesis, as well as foreground, background and mask generation, as summarized in Fig. 1. A segmentation model trained using these masks can then achieve a level of performance that is close to direct supervision, despite not requiring manual segmentation masks at any point in the pipeline. This suggests that labour-intensive ground-truth image annotation workflows could become obsolete in the future, and be replaced by concept distillation from generative foundation models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.516,
+                0.263,
+                0.529
+            ],
+            "angle": 0,
+            "content": "Our main contributions are:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.543,
+                0.468,
+                0.616
+            ],
+            "angle": 0,
+            "content": "- We propose a self-supervised, hyperparameter-free, approach for dataset-independent foreground-background segmentation, based on latent diffusion models, capable of synthesizing foreground, background, and segmentation masks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.619,
+                0.468,
+                0.675
+            ],
+            "angle": 0,
+            "content": "- We describe a general framework to extract importance scores obtained from pretrained diffusion models and detail how to use them to improve segmentation performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.679,
+                0.468,
+                0.751
+            ],
+            "angle": 0,
+            "content": "- We verify the feasibility of our method on a set of four different foreground background segmentation tasks, spanning humans, birds, dogs, and cars and show that our method achieves results close to supervised methods while being trained without direct supervision."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.755,
+                0.468,
+                0.797
+            ],
+            "angle": 0,
+            "content": "- We experiment with the extension of our method to domain-adapted diffusion models by showing promising results on a medical segmentation task."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.543,
+                0.468,
+                0.797
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.815,
+                0.218,
+                0.83
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Semantic Segmentation refers to the identification of high level concepts in an image, which enable their extraction from the image. [33, 36] introduced the use of fully convolutional networks for this task, which superseded previous"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.302
+            ],
+            "angle": 0,
+            "content": "shallow feature classification approaches [20]. Currently, the most common segmentation network architectures are designed as encoder-decoder pairs, as it enforces an information bottleneck that facilitates generalisation. The encoder provides meaningful low dimensional representations and the decoder reconstructs high-resolution segmentation maps [10, 45, 33, 36]. Recent approaches maximise the use of multi-scale information with multi-scale attention [56], squeeze-and-attention [63], and Transformers [62]. The final pixel classification operation, which creates the segmentation mask, is performed through multinomial logistic regression. These methods require large amounts of manually labelled training samples, which can be labour-intensive and expensive."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.306,
+                0.892,
+                0.486
+            ],
+            "angle": 0,
+            "content": "Weakly Supervised Semantic Segmentation partially mitigates that by learning from weak global labels, such as image-wise class labels, and perform rough semantic-segmentation tasks. These approaches often leverage the learned representations in intermediate layers through attention maps [26] or saliency maps [31] extraction. These representations are learned in a supervised manner through a classification task, as opposed to our approach that leverages an even weaker signal: free-form text-embeddings. Furthermore, these methods cannot generate images and are, therefore, not suitable for foreground-background synthesis."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.491,
+                0.892,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Foreground background separation is a segmentation task where the goal is to apply binary classification over all the pixels of an image to separate the object of interest, the foreground, from the contextual background. For example, in video analysis tasks, the background is often defined as parts of scenes that are at rest [51]. More recently, decomposing individual images into potential foreground and background layers became an intriguing research topic [25]. Since the foreground-background separation factors are not known a priori, many related works formulate the problem as a category-agnostic unsupervised segmentation approach. While deep neural networks can learn pixel clustering in an unsupervised way [25, 29, 38], it often leads to inferior performance when compared to fully supervised methods. Other works also tried to learn image segmentation from generative models, for example via direct sampling from the training distribution with cut-and-paste [43], image combinations via styleGAN [1], erasing and redrawing [11], and through inpainting [49]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The work closest related to ours is [61] who employ layered generative adversarial networks (GANs) to generate distinct images for the foreground and background. As opposed to [61], we are not relying on the unknown structure of the latent manifold to separate the embedding codes that represent foreground and background, but instead follow the directly interpretable paradigm 'textual concept description' \\(\\rightarrow\\) 'segmentation model'. Both approaches in"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.956
+            ],
+            "angle": 0,
+            "content": "989"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.136
+            ],
+            "angle": 0,
+            "content": "troduce a similar bias, ours through the textual concept description and them through object-specific models, making our method similarly conditioned but more flexible."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.137,
+                0.47,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Diffusion models are generative methods. Generative modeling has always been an important task in deep learning. Recently, Diffusion models gained a lot of attention thanks to the impressive results achieved by [42, 48]. Based on [22, 55], these models currently define the state-of-the-art in conditional image generation, and have been extended towards text-to-image models such as unCLIP [41] and Stable Diffusion [44]. Part of that success is due to the efficacy of straightforward extensions to diffusion models, such as classifier-free guidance [23]. Current research about diffusion models focuses mostly on inpainting [14, 13, 44]. Depending on the task, it might be easier to learn the object itself and then train a diffusion model on the task of inpainting regions where the object is not present. However, we focus on the scenario where we have the object itself present and try to remove it."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.379,
+                0.471,
+                0.681
+            ],
+            "angle": 0,
+            "content": "Shortly after latent diffusion models showed superiority in terms of image sample quality compared to GANs [18], they were conditioned on the description of concepts [42]. These models became widely available online, including on commodity hardware after the computationally expensive denoising process was accelerated on a fundamental level [32]. Direct translation of text into object-centric representations has been attempted but rather in the context of attention editing [21], subject specific image generation [47], and textual concept-refined image-to-image translation [59]. Textual inversion, where examples of concepts are provided to a diffusion model as text and image tuples to teach the model a new concept [19], operates on the same fundamental input level as our approach. However, it is not able to provide object segmentation masks or concept-specific pixel importance scores. Recent advances on diffusion models have led to a spike in research around how latent features can be extracted [21, 2] however, their potential to be used for zero-shot segmentation has yet to be explored."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.694,
+                0.169,
+                0.71
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Our approach is summarized in Fig. 2. At a high level, we first use the attention maps from a pretrained latent diffusion model to compute coarse foreground segmentations (preliminary masks). We use these masks to fine-tune the diffusion model to be able to remove the object from the image, replacing it with background information, whilst also being able to generate new samples from the true distribution \\( p(\\mathbf{x}) \\) of the dataset. By comparing the original images to those with the background inpainted over the foreground, we are then able to produce much more refined masks. We can also then use the fine-tuned model to sample an arbitrary number of new images, including only the foreground,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.212
+            ],
+            "angle": 0,
+            "content": "only the background, and the masks separating them. The only assumptions this method uses is that we have access to a dataset of images where the chosen object is always present, and that the foundation model we use has learned a meaningful representation of the object we want to identify. In this context, objects can describe concepts like birds, cars, dogs, humans, but also parts of objects such as arms or legs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.213,
+                0.892,
+                0.304
+            ],
+            "angle": 0,
+            "content": "We start from the latent diffusion model (LDM) [44], a foundation model pretrained on the task of text-to-image generation, denoted as \\( m \\). It generates images by sampling gaussian noise and iteratively denoising them in \\( T \\) diffusion steps. Throughout this work, we keep the default value from [44] of \\( T = 50 \\) steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.305,
+                0.892,
+                0.396
+            ],
+            "angle": 0,
+            "content": "Let \\(\\mathbf{D}\\) denote a dataset where all the images contain our desired object. Formally, we aim to generate unsupervised segmentation masks of the original dataset \\(\\mathbf{D}_{\\mathbf{m}}\\) as well as a synthetic dataset that contains synthetic images \\(\\mathbf{D}'\\), masks \\(\\mathbf{D}_{\\mathbf{m}}'\\), foreground \\(\\mathbf{D}_{\\mathbf{f}}'\\), and background \\(\\mathbf{D}_{\\mathbf{b}}'\\) denoted as set \\(\\mathbf{D}_{\\mathbf{s}}' = \\{\\mathbf{D}', \\mathbf{D}_{\\mathbf{m}}', \\mathbf{D}_{\\mathbf{f}}', \\mathbf{D}_{\\mathbf{b}}'\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.396,
+                0.892,
+                0.517
+            ],
+            "angle": 0,
+            "content": "Preliminary Masks: The LDM was trained on paired text-image data. Thus, the output is conditioned on a text input, which we have to carefully choose to generate our initial attention maps. In practice, self- and cross-attention work well for conditioning on different inputs, especially across different modalities [57]. As input, we propose the prompt \"a photo of a {object}\" where \"object\" is a high level description of our foreground object (e.g. \"bird\")."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.518,
+                0.892,
+                0.623
+            ],
+            "angle": 0,
+            "content": "The first step in computing the preliminary masks is to leverage the raw attention maps computed in every cross-attention layer of the U-Net architecture. We decide against cherry-picking different attention layers for different tasks to remain task-agnostic, but would like to point out that this could lead to task-specific improvements as an hyperparameter option."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.624,
+                0.892,
+                0.655
+            ],
+            "angle": 0,
+            "content": "Let \\( z_0 \\) denote the latent space representation of some input image \\( x \\). In each layer, attention is computed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.568,
+                0.671,
+                0.892,
+                0.689
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\psi \\left(Q _ {l}, K _ {l} ^ {T}\\right) \\cdot V _ {l} \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.698,
+                0.857,
+                0.715
+            ],
+            "angle": 0,
+            "content": "with the attention probabilities \\(\\psi(Q_l, K_l^T)\\) defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.727,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "\\[\n\\psi_ {\\mathbf {z} _ {\\mathbf {t}, 1}} \\left(Q _ {l}, K _ {l} ^ {T}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}}\\right) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.771,
+                0.892,
+                0.884
+            ],
+            "angle": 0,
+            "content": "with \\( Q = W_{Q}^{(i,l)} \\cdot \\phi(\\mathbf{z}_{\\mathbf{t},1}) \\), \\( K = W_{K}^{(i,l)} \\cdot \\tau_{\\theta}(y) \\), and \\( V = W_{V}^{(i,l)} \\cdot \\tau_{\\theta}(y) \\) denoting the learnable projection matrices according to [57], \\( \\phi(\\mathbf{z}_{\\mathbf{t},1}) \\) the latent code of the l-th U-Net layer in the t-th reverse diffusion step, and \\( \\tau_{\\theta}(y) \\) the learned latent representation for the textual input prompt [44]. \\( z_{t,l} \\) denotes the latent representation of the stable diffusion model in layer 1, conditioned at diffusion \\( t \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.885,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The next step is to compute the mean attention maps \\(\\hat{M}\\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "990"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.089,
+                0.895,
+                0.219
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.188,
+                0.223,
+                0.781,
+                0.239
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overview of our model pipeline for self-supervised foreground-background segmentation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.267,
+                0.462,
+                0.395
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.407,
+                0.471,
+                0.451
+            ],
+            "angle": 0,
+            "content": "Figure 3. \\( T_{0} \\) vs AUC-ROC on CUB. Incorporating more reverse diffusion steps into the attention computation improves the AUC-ROC against the groundtruth only up to roughly \\( T_{0} = 40 \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.472,
+                0.47,
+                0.503
+            ],
+            "angle": 0,
+            "content": "as expectations over multiple repeated diffusion steps according to"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.118,
+                0.522,
+                0.47,
+                0.565
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {M} = \\sum_ {t = 1} ^ {T _ {0}} \\mathbb {E} _ {\\mathbf {z} \\sim p (\\mathbf {z} _ {t} | \\mathbf {z} _ {t + 1}, \\mathbf {z} _ {0})} [ \\sum_ {l} \\psi_ {\\mathbf {z} _ {t, 1}} (Q _ {l}, K _ {l} ^ {T}) ]. \\quad (3)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.57,
+                0.471,
+                0.618
+            ],
+            "angle": 0,
+            "content": "We empirically show in our supplementary material that this can be simplified to performing single reverse diffusion steps which leads to a simplified importance score"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.178,
+                0.627,
+                0.47,
+                0.669
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {M} = \\sum_ {t = 1} ^ {T _ {0}} \\sum_ {l} \\psi_ {\\mathbf {z} _ {\\mathbf {t}, 1}} \\left(Q _ {l}, K _ {l} ^ {T}\\right) \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.47,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Figure 3 shows AUCROC of using \\(\\hat{M}\\) to identify the foreground as a function of the number of reverse steps. There is a clear improvement visible computing the mean over up to roughly \\(T_0 = 40\\) reverse diffusion steps. Including higher diffusion steps seems to deteriorate the accuracy of \\(\\phi\\). This is because for higher values of \\(t\\) the input images approach pure Gaussian noise. However, for medium values of \\(t\\) the input and output images already approximate the basic structure of the final objects. Other details, like texture, appear at later stages but do not bear any valuable information for this use case. This observation could mean that for time critical applications, starting from lower \\(t\\) should suffice."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The third and final step in retrieving the preliminary masks is to binarize the mean attention maps. To do so, we"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.263,
+                0.892,
+                0.428
+            ],
+            "angle": 0,
+            "content": "take advantage of the observation that all attention maps resemble a bimodal distribution, with one mode at a low value for the non-object pixels and one mode at a high value for the object pixels. Hence, we model absolute values of the instance-wise attention scores as a bimodal Gaussian mixture model (GMM) to produce GMM masks. Additionally, we remove orphan pixels by computing the mean filter over the resulting binary classification map to produce our preliminary masks \\( M_{pre} \\). These preliminary masks could potentially already be used to detect objects as evaluated in Sec. 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.431,
+                0.893,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Fine-tuning and Mask Refinement: The main problem with the preliminary masks is that, because they are derived from the latent space of the LDM, their resolution is only \\(64 \\times 64\\). This limits them to being a coarse segmentation, which often overestimates the size of the object rather than following the object's sharp edges. A rough segmentation is sufficient for tasks like inpainting, especially if the area around the object is homogeneous, but for the task of extracting the foreground object it produces unwanted artefacts. To work around this, we leverage the same diffusion model that we used to extract the masks. We use the binary classification prediction of the GMM mask \\(M_{pre}\\) to select random rectangles within the image that only contain background. Then we fine-tune the model to inpaint only the background of these images by conditioning on the prompt \\(y_{b} =\\) \"a photo of a background\" using the image as ground truth (See supplements for examples). Simultaneously, the model is fine-tuned on the task of full image synthesis to generate new samples for \\(\\mathbf{D}'\\) by conditioning on \\(y_{f} =\\) \"a photo of a \\(\\{\\mathrm{object}\\}\\)\"."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To generate the final foreground masks \\(\\mathbf{D}_{\\mathbf{m}}\\) we use the fine-tuned LDM \\(m^{\\prime}\\) to inpaint the background over the area covered by the preliminary mask conditioning on the background prompt. To identify the foreground region, we take the pixel-wise intensity difference between the background-inpainted and original images. As the inpainted images are conditioned to generate background, the difference is higher in the true foreground region. We apply a Gaussian mixture model to the pixel-wise difference map to create a binary classification map. Formally the refined masks \\(M\\) are computed as"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "991"
+        }
+    ],
+    [
+        {
+            "type": "equation",
+            "bbox": [
+                0.148,
+                0.119,
+                0.468,
+                0.136
+            ],
+            "angle": 0,
+            "content": "\\[\nM = M _ {p r e, u p} \\odot g \\left(\\left| \\mathbf {x} - m ^ {\\prime} \\left(\\tilde {\\mathbf {z}} _ {0}, y _ {b}\\right) \\right|\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.16,
+                0.139,
+                0.468,
+                0.155
+            ],
+            "angle": 0,
+            "content": "\\[\n\\tilde {\\mathbf {z}} _ {\\mathbf {0}} = \\mathbf {z} _ {\\mathbf {0}} \\odot (1 - M _ {p r e}) + \\mathbf {z} \\odot M _ {p r e} \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.167,
+                0.47,
+                0.317
+            ],
+            "angle": 0,
+            "content": "where \\( M_{pre,up} \\) denotes the preliminary mask upsampled to the input image's resolution, \\( g \\) applies the bimodal Gaussian mixture model to the pixel values and \\( \\tilde{\\mathbf{z}}_0 \\) is the latent code of an image with the foreground region replaced with random noise \\( \\mathbf{z} \\). This produces refined masks, as the use of pixel-wise error improves the segmentation around the sharp edges of the object. Additionally, the computation of the refined masks is performed in pixel-space of the images instead of the latent space of \\( m \\) and therefore produces even more detailed masks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.318,
+                0.471,
+                0.514
+            ],
+            "angle": 0,
+            "content": "Finally, to further improve our mask prediction we use the refined masks as labels to train a U-Net [45] to directly segment the foreground of the images, similar to the approach in [61], which follows a standardized approach of training a U-Net on a fixed number of steps and hence does not require any hyperparameter tuning. We experiment with training the segmentation network on refined masks of the original unlabelled training data \\((\\mathbf{D_s})\\), as well as training it with the fully synthetic dataset \\(\\mathbf{D_s}'\\) as an augmentation method, which we generate by prompting the fine-tuned model with the foreground conditioning \\(y_{f}\\) and repeating our pipeline of mask refinement on this synthetic dataset to get segmentation labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.528,
+                0.295,
+                0.543
+            ],
+            "angle": 0,
+            "content": "4. Evaluation and Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.553,
+                0.468,
+                0.659
+            ],
+            "angle": 0,
+            "content": "Implementation: We use PyTorch 1.11 and run our experiments on a workstation with two A6000 Nvidia GPUs. Concept distillation training takes on average one day. The forward pass is fast, equivalent to that of a standard U-Net. Datasets: We choose our datasets such that they cover a variety of different objects, including in-the-wild animals and cars, as well as humans in static setups."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.659,
+                0.468,
+                0.748
+            ],
+            "angle": 0,
+            "content": "Human3.6m [24] is a dataset of 3.6 million images of humans in different scenarios and situations. To show that our method does not rely on large datasets we take a subset of 6000 randomly chosen images centred around the human and cropped to \\(256 \\times 256\\) pixels from the training dataset of Human3.6m."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.468,
+                0.825
+            ],
+            "angle": 0,
+            "content": "To test the method on representations of animals, we use two datasets: the Stanford Dog Dataset [28], which contains 20,580 images of dogs divided into different categories, and the Caltech-UCSD Birds 200 (CUB) dataset [58], which contains 11,788 images of birds from 200 different species."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.826,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Finally, we also experiment with the detection of cars using [30], which consists of 16,185 images of cars in different natural and non-natural settings. All these datasets come with subcategories grouping the images based on selected features. For our use case, we consolidate these groups"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "when prompting the model and use the classes cars, dogs, human, and birds to simulate the absence of manual labels."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.135,
+                0.908,
+                0.327
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Fully supervised U-Net</td><td>97.9</td><td>88.3</td><td>93.0</td></tr><tr><td>GrabCut [46] by [49]</td><td>72.3</td><td>36.0</td><td>52.3</td></tr><tr><td>ReDO [11]</td><td>84.5</td><td>42.6</td><td>-</td></tr><tr><td>PerturbGAN [4]</td><td>-</td><td>-</td><td>38.0</td></tr><tr><td>IEM + SegNet [49]</td><td>89.3</td><td>55.1</td><td>71.4</td></tr><tr><td>Melas-Kyriazi et al. [35]</td><td>92.1</td><td>66.4</td><td>-</td></tr><tr><td>Layered GAN [61]</td><td>94.3</td><td>69.7</td><td>81.7</td></tr><tr><td>Ours (U-Net trained on Ds)</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>Ours (U-Net trained on Ds ∪ D&#x27;s&#x27;)</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.328,
+                0.892,
+                0.369
+            ],
+            "angle": 0,
+            "content": "Table 1. Comparison to other segmentation methods. Baselines taken from [61]. Details on the training of the U-Nets can be found in the appendix."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.386,
+                0.892,
+                0.583
+            ],
+            "angle": 0,
+            "content": "Self-supervised Segmentation Performance: Table 1 compares our methods performance against other unsupervised methods on the CUB dataset, showing the pixel-wise accuracy, the Intersection over Union (IoU) of the foreground segmentation and the mean IoU. From this we see that training a U-Net on our self-supervised labels produces a model that outperforms all other methods, achieving an overall foreground IoU improvement of 5.4 compared to [61]. Furthermore, by adding the fully synthetic dataset \\(\\mathbf{D}_{\\mathbf{s}}^{\\prime}\\) to the training data we are able to improve the performance even further, reaching a foreground IoU of 77.2. Table 3 also shows high foreground IoU values across the other datasets, with Fig. 4 showing qualitative examples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.854
+            ],
+            "angle": 0,
+            "content": "Mean Attention Map Performance: Computing the mean attention maps \\(\\hat{M}\\) and comparing them to the ground-truth yields a remarkable AUC-ROC for the bird dataset of 97.1. Scores are normalized instance-wise to a range of 0 to 1. We also experiment with no normalization, which gives a slightly worse AUC-ROC of 97.08. Qualitative examples from all datasets are shown in Fig. 5, displaying the mean attention maps' ability to localize the foreground in different scenarios. To compare this to our classification results we compute the threshold such that we reach over \\(95\\%\\) true positive rate on a reserved training set of 100 images. True positive rate is more important in our case because we observe that falsely classifying pixels as background leads the inpainting model taking these foreground pixels as sources to inpaint larger parts of the image. We reach a pixel-wise accuracy of \\(86\\%\\) on a set of 1000 test images suggesting that our method of extracting the classification masks already can provide meaningful results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "While these results are encouraging, they also require a ground-truth dataset and thresholding that we do not want to rely on. The results indicate that our computed masks"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "992"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.268,
+                0.089,
+                0.3,
+                0.1
+            ],
+            "angle": 0,
+            "content": "CUB"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.103,
+                0.48,
+                0.255
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.251,
+                0.26,
+                0.317,
+                0.271
+            ],
+            "angle": 0,
+            "content": "Human3.6"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.273,
+                0.48,
+                0.425
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.645,
+                0.089,
+                0.731,
+                0.1
+            ],
+            "angle": 0,
+            "content": "Stanford Cars"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.493,
+                0.103,
+                0.885,
+                0.255
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.643,
+                0.259,
+                0.732,
+                0.272
+            ],
+            "angle": 0,
+            "content": "Stanford Dogs"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.493,
+                0.273,
+                0.884,
+                0.425
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.237,
+                0.429,
+                0.726,
+                0.444
+            ],
+            "angle": 0,
+            "content": "Figure 4. Unsupervised Segmentation Masks generated by our proposed approach."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.469,
+                0.47,
+                0.543
+            ],
+            "angle": 0,
+            "content": "are very good at locating the objects, albeit they do not reach state-of-the-art performance despite adding supervision. Training on refined masks and integrating synthetic data surpasses supervised results without using any labels as shown in the next section."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.089,
+                0.553,
+                0.458,
+                0.689
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Preliminary Masks Mpre</td><td>83.5</td><td>29.0</td><td>55.7</td></tr><tr><td>Simple Inpainting Mcrop</td><td>90.0</td><td>30.7</td><td>60.0</td></tr><tr><td>U-Net trained on (D, Mpre)</td><td>91.7</td><td>66.5</td><td>78.2</td></tr><tr><td>Refined Masks M</td><td>92.4</td><td>63.6</td><td>77.4</td></tr><tr><td>U-Net trained on Ds</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>U-Net trained on Ds ∪ D&#x27;s&#x27;</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.69,
+                0.456,
+                0.703
+            ],
+            "angle": 0,
+            "content": "Table 2. Segmentation results for different steps of our pipeline."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.468,
+                0.885
+            ],
+            "angle": 0,
+            "content": "Ablation study: Table 2 shows an ablation study for the individual components of our method. Initially, the zero-shot preliminary masks generated from the foundation model achieve good accuracy (83.5), but poor foreground IoU (29.0). This reflects our earlier intuition that masks overestimate the size of the object due to the maps being computed at a lower resolution. Thanks to this, the GMM overestimates the boundaries and spares the need for any hyperparameter. Optimizing the threshold to maximise the accuracy over a set of 100 training images would increase the accuracy to \\(93.9\\%\\), but requires a ground-truth dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Training a U-Net on these labels \\((M_{pre})\\) increases the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.469,
+                0.892,
+                0.665
+            ],
+            "angle": 0,
+            "content": "IoU to 66.5, showing the value in training the segmentation network. Using the refined masks as foreground segmentation gives comparable performance, with higher accuracy but lower foreground IoU. Additionally, we experiment with replacing the inpainting step used to improve \\( M_{pre} \\) with a simpler approach that crops background areas and uses them as inpainting in Eq. (5) instead of \\( m' \\). The resulting masks \\( M_{crop} \\) are worse than the masks from our proposed refinement step (For more details see supplements). However, training a U-Net on these refined masks produces the best results, being further boosted by incorporating additional synthetic data. The progressive refinement of the segmentation masks is shown in Fig. 6."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.668,
+                0.892,
+                0.774
+            ],
+            "angle": 0,
+            "content": "Data synthesis: Table 3 compares the generative ability of our fine-tuned diffusion model using the Fréchet inception distance (FID). Our method achieves higher generation quality than all other methods across the CUB, Stanford Dogs, and Stanford Cars datasets. We improve upon LayeredGAN's remarkably low FID scores for CUB and Stanford Cars by 3.1 and 5.6 respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.777,
+                0.892,
+                0.883
+            ],
+            "angle": 0,
+            "content": "Our method allows for the generation of samples covered entirely by the background, as shown in Fig. 7, without ever seeing such an image during training. The success of this component is what enables the refined masks to be generated, as accurately inpainting the foreground allows us to use the pixel-wise difference between the original and inpainted images to precisely identify the foreground."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.886,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Concept Distillation: Finally we can evaluate if our model"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "993"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.087,
+                0.089,
+                0.885,
+                0.296
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.299,
+                0.89,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Figure 5. Mean attention maps for all datasets in latent space \\(\\mathbf{z}\\) of the diffusion model. Prompts are \"a photo of a {object}\", where {object} is replaced by \"bird\" for the first pair of rows, then \"car\", \"dog\", and \"human\"."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.15,
+                0.338,
+                0.825,
+                0.449
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Sup.</td><td colspan=\"2\">CUB</td><td colspan=\"2\">Stanford Dogs</td><td colspan=\"2\">Stanford Cars</td><td colspan=\"2\">Human3.6m</td></tr><tr><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td></tr><tr><td>FineGAN [54]</td><td>Weak</td><td>23.0</td><td>44.5</td><td>54.9</td><td>-</td><td>24.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>OneGAN [3]</td><td>Weak</td><td>20.5</td><td>55.5</td><td>48.7</td><td>-</td><td>24.2</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LayeredGAN [61]</td><td>Unsup.</td><td>12.9</td><td>69.7</td><td>59.3</td><td>-</td><td>19.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>Self</td><td>9.8</td><td>75.1</td><td>43.1</td><td>63.8</td><td>13.4</td><td>55.2</td><td>63.7</td><td>69.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.45,
+                0.893,
+                0.491
+            ],
+            "angle": 0,
+            "content": "Table 3. Quantitative Results on \\( \\mathbf{D_s} \\). Training details are shown in the supplements. Values are taken from [61]. Source code for [54, 3, 61] was not available for re-evaluation on the Dogs, Cars and Human3.6m datasets. IoU on CUB are reported using the prediction of our model and the ground truth provided with the dataset. For the other datasets we use the IoU of the bounding boxes."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.083,
+                0.517,
+                0.465,
+                0.616
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.624,
+                0.436,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Figure 6. Progressive refinement of the segmentation masks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.674,
+                0.473,
+                0.901
+            ],
+            "angle": 0,
+            "content": "has indeed learned to distinguish between foreground and background by looking at the output of different classifier-free guidance scales starting from the same seed \\(\\mathbf{z}_{\\mathbf{t}}\\). Since we have fine-tuned our model only on two distinct textual prompts the conditional image generation should have collapsed to two clusters, one for the object and the other one for the background. Hence, instead of performing classifier-free guidance using the predictions of \\(m^{\\prime}\\) conditioned on empty prompts we can directly use the predictions of \\(m^{\\prime}(\\mathbf{z}_{\\mathbf{t}},y_{b})\\) and \\(m^{\\prime}(\\mathbf{z}_{\\mathbf{t}},y_{f})\\) to perform image interpolation. We define classifier-free guidance in the direction of the foreground, hence, a higher score means that latent representations are pushed further in the direction of the object. The results are shown in Fig. 8. For negative guidance scales, the background is more detailed and there is no bird"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.517,
+                0.892,
+                0.653
+            ],
+            "angle": 0,
+            "content": "present. Increasing this scale leads to less detail in the background while birds often seem to naturally grow from the details in the background. The quality of the birds visually improves while the quality of the rest of the image keeps degrading resulting in less detailed backgrounds. We confirm this quantitatively by computing the FID for different classifier-free guidance scales. Without classifier-free guidance, i.e., scale \\(= 1\\), the method reaches a FID of 9.8, at scale \\(= 3\\) a FID of 11.3, and at scale \\(= 7.5\\) a FID of 22.3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Medical Image Analysis: We want to evaluate if this approach can be applied to other domains, such as medical imaging. Since the LDM does not have any medical understanding, we first need to fine-tune it using MIMIC [27], which provides chest x-ray images paired with radiology reports. We can fine-tune the model using a similar approach as the one suggested by [8] (Details on the fine-tuning can be found in the supplements). Then we report the pixelwise AUC-ROC on MS-CXR [5], a subset of MIMIC with bounding box labels for diseases. Qualitative results can be seen in Fig. 9. The pixel-wise accuracy of the attention mask is already at \\(79.6\\%\\) AUC-ROC across eight different diseases, however, the bimodal GMM assumption no longer holds in many cases because the model distinguishes three regions, namely: background, foreground, and the rest of the chest region."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.511,
+                0.956
+            ],
+            "angle": 0,
+            "content": "994"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.09,
+                0.891,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.251,
+                0.893,
+                0.278
+            ],
+            "angle": 0,
+            "content": "Figure 7. Full background image synthesis from the fine-tuned model, conditioned on \\( y_{b} \\). Using our proposed fine-tuning method, the diffusion model is successfully able to generate images without birds from a dataset only consisting of images with birds."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.303,
+                0.468,
+                0.444
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.447,
+                0.468,
+                0.476
+            ],
+            "angle": 0,
+            "content": "Figure 8. Synthetic results of \\( m' \\) with changing scales of classifier-free-guidance, ranging from -2 on the left to +7.5 on the right."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.501,
+                0.468,
+                0.59
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.117,
+                0.595,
+                0.428,
+                0.609
+            ],
+            "angle": 0,
+            "content": "Figure 9. \\(\\hat{M}\\) and \\(M_{pre}\\) extraction on a medical task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.633,
+                0.192,
+                0.648
+            ],
+            "angle": 0,
+            "content": "5. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.677,
+                0.466,
+                0.685
+            ],
+            "angle": 0,
+            "content": "'startofstring' 'a' 'photo' 'of' 'a' 'human' with ' arms' 'and' 'legs'"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.687,
+                0.468,
+                0.796
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.8,
+                0.468,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Figure 10. Input image and mean attention maps for every word of the textual input prompt \"startofstring a photo of a human with arms and legs\". The attention of \"human\" focuses on the torso, the one for the \"arms\" on the arms, and the one for the \"legs\" on the legs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We show in Sec. 4 that our method to extract the segmen"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.304,
+                0.892,
+                0.484
+            ],
+            "angle": 0,
+            "content": "tation masks \\(M\\) from the preliminary attention masks yields better results than computing an optimised threshold over a reserved miniset. This is possible because comparing to the inpainted background provides sharp edges around the object. However, our model is currently limited to detecting single object concepts. An extension to multiple objects could be achieved by prompt engineering in combination with data augmentation techniques. Taking the foreground masks and using them to extract objects would enable multi-instance and multi-object segmentation by layering multiple objects over each other and extending the final U-Net to a multi-label segmentation model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.485,
+                0.892,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Furthermore, learning from weak labels has the disadvantage that the segmentation model may learn and reproduce weaknesses of the initial method. In our case, the bimodal GMM fails if the image has more than two distinct contrast clusters. This is especially the case on the Human3.6m dataset where the floor, walls, and person have vastly different contrast-levels. Consequently, the final segmentation sometimes fails to detect the lower part of the body as shown in Fig. 4. However, our method could easily be adapted to only a part of the human body, such as the legs. We show this in Fig. 10, as by conditioning images from [24] on the prompt \"A photo of a human with arms and legs\" and computing \\(\\hat{M}\\) for the three concepts (human, arms, and legs) we are able to produce attention maps focused on specific body parts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.725,
+                0.618,
+                0.74
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, we have presented a generalizable framework to train segmentation networks without any hyperparameter tuning using an unsupervised zero-shot approach following the paradigm of 'textual concept description' \\(\\rightarrow\\) 'segmentation model'. We leverage the power of large generative latent diffusion models and fine-tune the model on the task of generating foreground and background images, which can be used as data augmentation methods. We show, that this method can achieve results close to supervised methods, without requiring any manually generated ground"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "995"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "truth labels. Our approach is amenable to supervised deep learning and can be combined with existing models to boost segmentation performance even further."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.137,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "In future work we will explore how multi-object, multi-instance segmentation can be facilitated with concept distillation from generative image foundation models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.183,
+                0.471,
+                0.394
+            ],
+            "angle": 0,
+            "content": "Acknowledgements: The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR projects b143dc and b180dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) - 440719683. Additional support was also received by the ERC - project MIA-NORMAL 101083647, DFG KA 5801/2-1, INST 90/1351-1 and by the state of Bavarian. H. Reynaud was supported by Ultromics Ltd. and the UKRI Centre or Doctoral Training in Artificial Intelligence for Healthcare (EP/S023283/1)."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.424
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+            "angle": 0,
+            "content": "References"
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+# Foreground-Background Separation through Concept Distillation from Generative Image Foundation Models
+
+Mischa Dombrowski $^{1}$  Hadrien Reynaud $^{2}$  Matthew Baugh $^{2}$  Bernhard Kainz $^{1,2}$ $^{1}$ Friedrich-Alexander-Universität Erlangen-Nürnberg  $^{2}$ Imperial College London mischa.dombrowski@fau.de
+
+# Abstract
+
+Curating datasets for object segmentation is a difficult task. With the advent of large-scale pre-trained generative models, conditional image generation has been given a significant boost in result quality and ease of use. In this paper, we present a novel method that enables the generation of general foreground-background segmentation models from simple textual descriptions, without requiring segmentation labels. We leverage and explore pre-trained latent diffusion models, to automatically generate weak segmentation masks for concepts and objects. The masks are then used to fine-tune the diffusion model on an inpainting task, which enables fine-grained removal of the object, while at the same time providing a synthetic foreground and background dataset. We demonstrate that using this method beats previous methods in both discriminative and generative performance and closes the gap with fully supervised training while requiring no pixel-wise object labels. We show results on the task of segmenting four different objects (humans, dogs, cars, birds) and a use case scenario in medical image analysis. The code is available at https://github.com/MischaD/fobadiffusion.
+
+# 1. Introduction
+
+Supervised pretraining, e.g., with ImageNet[16], has demonstrated reduced training times and boosted performance. This gave rise to models that could be trained once over large amounts of data before being adapted to specialised tasks, such as image recognition, object detection, image segmentation[52], and medical image analysis[50]. The recent development of self-supervision techniques and their ability to learn without manual labels led to much larger scale training datasets [9] and to the creation of foundation models [6]. At present, the use of pre-trained models for a wide range of diverse downstream tasks defines a very active and intriguing area of research.
+
+Large scale foundation models are already established in
+
+![](images/21d2d01d24891b25156c9155295b930e3c179c2a355c5b5cfd76b5847da8fca2.jpg)  
+Figure 1. High level overview of our proposed method: Without needing a single labelled image, our method is able to generate foreground, background, and segmentation masks for any concept that is known to a text-to-image generative network.
+
+natural language processing, with most of them being based on the Transformer architecture [57, 17, 7]. A crucial part of this architecture are cross- and self-attention layers, which compute interpretable importance weightings [39, 12].
+
+Diffusion models are based on the U-Net architecture [45] with additional attention layers [37] to condition on textual prompts. Therefore, we can extract inherently interpretable pixel importance scores from conditioning on textual prompts. Furthermore, the reverse diffusion process teaches the U-Net to successively remove noise from images, starting from pure Gaussian noise. In the early steps of this process, where the images resemble pure noise, the texture is non-existent, and the model only learns structures.
+
+Recently, latent diffusion models have emerged as state-of-the-art generative models for the task of text-to-image generation [18, 44, 41]. However, training such models requires a significant amount of  $\mathrm{CO}_{2}$ -intensive resources and until recently, pre-trained model weights have not been publicly available. Rombach et al. were the first to published their weights and model architecture [44], which facilitated the development of numerous derived applica
+
+tions [60, 15, 53] and established this model as the foundation model for tasks that require generalised representations of concepts in images. State-of-the-art latent diffusion models are able to generate high resolution images of a vast amount of different objects, suggesting that a highly expressive latent representation of the data has been learned.
+
+We hypothesize that we can leverage these learned latent representations for our own downstream tasks of zero-shot foreground-background generation. Using a generative latent diffusion foundation model, we are able to extract a weak segmentation mask around an arbitrary object by computing the importance maps based on the textual input prompts. Weak segmentation masks have been shown to be an effective prior for segmentation models, given that enough training samples are available [34, 40]. We then use these preliminary masks to fine-tune a latent diffusion model on (1) generating new images from this dataset, as well as (2) inpainting regions where the object is not present according to our preliminary masks. The resulting model is able to perform full-image synthesis, as well as foreground, background and mask generation, as summarized in Fig. 1. A segmentation model trained using these masks can then achieve a level of performance that is close to direct supervision, despite not requiring manual segmentation masks at any point in the pipeline. This suggests that labour-intensive ground-truth image annotation workflows could become obsolete in the future, and be replaced by concept distillation from generative foundation models.
+
+Our main contributions are:
+
+- We propose a self-supervised, hyperparameter-free, approach for dataset-independent foreground-background segmentation, based on latent diffusion models, capable of synthesizing foreground, background, and segmentation masks.  
+- We describe a general framework to extract importance scores obtained from pretrained diffusion models and detail how to use them to improve segmentation performance.  
+- We verify the feasibility of our method on a set of four different foreground background segmentation tasks, spanning humans, birds, dogs, and cars and show that our method achieves results close to supervised methods while being trained without direct supervision.  
+- We experiment with the extension of our method to domain-adapted diffusion models by showing promising results on a medical segmentation task.
+
+# 2. Related Work
+
+Semantic Segmentation refers to the identification of high level concepts in an image, which enable their extraction from the image. [33, 36] introduced the use of fully convolutional networks for this task, which superseded previous
+
+shallow feature classification approaches [20]. Currently, the most common segmentation network architectures are designed as encoder-decoder pairs, as it enforces an information bottleneck that facilitates generalisation. The encoder provides meaningful low dimensional representations and the decoder reconstructs high-resolution segmentation maps [10, 45, 33, 36]. Recent approaches maximise the use of multi-scale information with multi-scale attention [56], squeeze-and-attention [63], and Transformers [62]. The final pixel classification operation, which creates the segmentation mask, is performed through multinomial logistic regression. These methods require large amounts of manually labelled training samples, which can be labour-intensive and expensive.
+
+Weakly Supervised Semantic Segmentation partially mitigates that by learning from weak global labels, such as image-wise class labels, and perform rough semantic-segmentation tasks. These approaches often leverage the learned representations in intermediate layers through attention maps [26] or saliency maps [31] extraction. These representations are learned in a supervised manner through a classification task, as opposed to our approach that leverages an even weaker signal: free-form text-embeddings. Furthermore, these methods cannot generate images and are, therefore, not suitable for foreground-background synthesis.
+
+Foreground background separation is a segmentation task where the goal is to apply binary classification over all the pixels of an image to separate the object of interest, the foreground, from the contextual background. For example, in video analysis tasks, the background is often defined as parts of scenes that are at rest [51]. More recently, decomposing individual images into potential foreground and background layers became an intriguing research topic [25]. Since the foreground-background separation factors are not known a priori, many related works formulate the problem as a category-agnostic unsupervised segmentation approach. While deep neural networks can learn pixel clustering in an unsupervised way [25, 29, 38], it often leads to inferior performance when compared to fully supervised methods. Other works also tried to learn image segmentation from generative models, for example via direct sampling from the training distribution with cut-and-paste [43], image combinations via styleGAN [1], erasing and redrawing [11], and through inpainting [49].
+
+The work closest related to ours is [61] who employ layered generative adversarial networks (GANs) to generate distinct images for the foreground and background. As opposed to [61], we are not relying on the unknown structure of the latent manifold to separate the embedding codes that represent foreground and background, but instead follow the directly interpretable paradigm 'textual concept description'  $\rightarrow$  'segmentation model'. Both approaches in
+
+troduce a similar bias, ours through the textual concept description and them through object-specific models, making our method similarly conditioned but more flexible.
+
+Diffusion models are generative methods. Generative modeling has always been an important task in deep learning. Recently, Diffusion models gained a lot of attention thanks to the impressive results achieved by [42, 48]. Based on [22, 55], these models currently define the state-of-the-art in conditional image generation, and have been extended towards text-to-image models such as unCLIP [41] and Stable Diffusion [44]. Part of that success is due to the efficacy of straightforward extensions to diffusion models, such as classifier-free guidance [23]. Current research about diffusion models focuses mostly on inpainting [14, 13, 44]. Depending on the task, it might be easier to learn the object itself and then train a diffusion model on the task of inpainting regions where the object is not present. However, we focus on the scenario where we have the object itself present and try to remove it.
+
+Shortly after latent diffusion models showed superiority in terms of image sample quality compared to GANs [18], they were conditioned on the description of concepts [42]. These models became widely available online, including on commodity hardware after the computationally expensive denoising process was accelerated on a fundamental level [32]. Direct translation of text into object-centric representations has been attempted but rather in the context of attention editing [21], subject specific image generation [47], and textual concept-refined image-to-image translation [59]. Textual inversion, where examples of concepts are provided to a diffusion model as text and image tuples to teach the model a new concept [19], operates on the same fundamental input level as our approach. However, it is not able to provide object segmentation masks or concept-specific pixel importance scores. Recent advances on diffusion models have led to a spike in research around how latent features can be extracted [21, 2] however, their potential to be used for zero-shot segmentation has yet to be explored.
+
+# 3. Method
+
+Our approach is summarized in Fig. 2. At a high level, we first use the attention maps from a pretrained latent diffusion model to compute coarse foreground segmentations (preliminary masks). We use these masks to fine-tune the diffusion model to be able to remove the object from the image, replacing it with background information, whilst also being able to generate new samples from the true distribution  $p(\mathbf{x})$  of the dataset. By comparing the original images to those with the background inpainted over the foreground, we are then able to produce much more refined masks. We can also then use the fine-tuned model to sample an arbitrary number of new images, including only the foreground,
+
+only the background, and the masks separating them. The only assumptions this method uses is that we have access to a dataset of images where the chosen object is always present, and that the foundation model we use has learned a meaningful representation of the object we want to identify. In this context, objects can describe concepts like birds, cars, dogs, humans, but also parts of objects such as arms or legs.
+
+We start from the latent diffusion model (LDM) [44], a foundation model pretrained on the task of text-to-image generation, denoted as  $m$ . It generates images by sampling gaussian noise and iteratively denoising them in  $T$  diffusion steps. Throughout this work, we keep the default value from [44] of  $T = 50$  steps.
+
+Let  $\mathbf{D}$  denote a dataset where all the images contain our desired object. Formally, we aim to generate unsupervised segmentation masks of the original dataset  $\mathbf{D}_{\mathbf{m}}$  as well as a synthetic dataset that contains synthetic images  $\mathbf{D}'$ , masks  $\mathbf{D}_{\mathbf{m}}'$ , foreground  $\mathbf{D}_{\mathbf{f}}'$ , and background  $\mathbf{D}_{\mathbf{b}}'$  denoted as set  $\mathbf{D}_{\mathbf{s}}' = \{\mathbf{D}', \mathbf{D}_{\mathbf{m}}', \mathbf{D}_{\mathbf{f}}', \mathbf{D}_{\mathbf{b}}'\}$ .
+
+Preliminary Masks: The LDM was trained on paired text-image data. Thus, the output is conditioned on a text input, which we have to carefully choose to generate our initial attention maps. In practice, self- and cross-attention work well for conditioning on different inputs, especially across different modalities [57]. As input, we propose the prompt "a photo of a {object}" where "object" is a high level description of our foreground object (e.g. "bird").
+
+The first step in computing the preliminary masks is to leverage the raw attention maps computed in every cross-attention layer of the U-Net architecture. We decide against cherry-picking different attention layers for different tasks to remain task-agnostic, but would like to point out that this could lead to task-specific improvements as an hyperparameter option.
+
+Let  $z_0$  denote the latent space representation of some input image  $x$ . In each layer, attention is computed as:
+
+$$
+\operatorname {A t t e n t i o n} (Q, K, V) = \psi \left(Q _ {l}, K _ {l} ^ {T}\right) \cdot V _ {l} \tag {1}
+$$
+
+with the attention probabilities  $\psi(Q_l, K_l^T)$  defined as:
+
+$$
+\psi_ {\mathbf {z} _ {\mathbf {t}, 1}} \left(Q _ {l}, K _ {l} ^ {T}\right) = \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d}}\right) \tag {2}
+$$
+
+with  $Q = W_{Q}^{(i,l)} \cdot \phi(\mathbf{z}_{\mathbf{t},1})$ ,  $K = W_{K}^{(i,l)} \cdot \tau_{\theta}(y)$ , and  $V = W_{V}^{(i,l)} \cdot \tau_{\theta}(y)$  denoting the learnable projection matrices according to [57],  $\phi(\mathbf{z}_{\mathbf{t},1})$  the latent code of the l-th U-Net layer in the t-th reverse diffusion step, and  $\tau_{\theta}(y)$  the learned latent representation for the textual input prompt [44].  $z_{t,l}$  denotes the latent representation of the stable diffusion model in layer 1, conditioned at diffusion  $t$ .
+
+The next step is to compute the mean attention maps  $\hat{M}$
+
+![](images/812bc4ee37993a1b3ad7a37f61695768970bba86626541f6377a493c2d702a0a.jpg)  
+Figure 2. Overview of our model pipeline for self-supervised foreground-background segmentation.
+
+![](images/e940a896ead2b702dabc74df3a1a712f5651bf37e093cf624f450032bfdf0379.jpg)  
+Figure 3.  $T_{0}$  vs AUC-ROC on CUB. Incorporating more reverse diffusion steps into the attention computation improves the AUC-ROC against the groundtruth only up to roughly  $T_{0} = 40$ .
+
+as expectations over multiple repeated diffusion steps according to
+
+$$
+\hat {M} = \sum_ {t = 1} ^ {T _ {0}} \mathbb {E} _ {\mathbf {z} \sim p (\mathbf {z} _ {t} | \mathbf {z} _ {t + 1}, \mathbf {z} _ {0})} [ \sum_ {l} \psi_ {\mathbf {z} _ {t, 1}} (Q _ {l}, K _ {l} ^ {T}) ]. \quad (3)
+$$
+
+We empirically show in our supplementary material that this can be simplified to performing single reverse diffusion steps which leads to a simplified importance score
+
+$$
+\hat {M} = \sum_ {t = 1} ^ {T _ {0}} \sum_ {l} \psi_ {\mathbf {z} _ {\mathbf {t}, 1}} \left(Q _ {l}, K _ {l} ^ {T}\right) \tag {4}
+$$
+
+Figure 3 shows AUCROC of using  $\hat{M}$  to identify the foreground as a function of the number of reverse steps. There is a clear improvement visible computing the mean over up to roughly  $T_0 = 40$  reverse diffusion steps. Including higher diffusion steps seems to deteriorate the accuracy of  $\phi$ . This is because for higher values of  $t$  the input images approach pure Gaussian noise. However, for medium values of  $t$  the input and output images already approximate the basic structure of the final objects. Other details, like texture, appear at later stages but do not bear any valuable information for this use case. This observation could mean that for time critical applications, starting from lower  $t$  should suffice.
+
+The third and final step in retrieving the preliminary masks is to binarize the mean attention maps. To do so, we
+
+take advantage of the observation that all attention maps resemble a bimodal distribution, with one mode at a low value for the non-object pixels and one mode at a high value for the object pixels. Hence, we model absolute values of the instance-wise attention scores as a bimodal Gaussian mixture model (GMM) to produce GMM masks. Additionally, we remove orphan pixels by computing the mean filter over the resulting binary classification map to produce our preliminary masks  $M_{pre}$ . These preliminary masks could potentially already be used to detect objects as evaluated in Sec. 4.
+
+Fine-tuning and Mask Refinement: The main problem with the preliminary masks is that, because they are derived from the latent space of the LDM, their resolution is only  $64 \times 64$ . This limits them to being a coarse segmentation, which often overestimates the size of the object rather than following the object's sharp edges. A rough segmentation is sufficient for tasks like inpainting, especially if the area around the object is homogeneous, but for the task of extracting the foreground object it produces unwanted artefacts. To work around this, we leverage the same diffusion model that we used to extract the masks. We use the binary classification prediction of the GMM mask  $M_{pre}$  to select random rectangles within the image that only contain background. Then we fine-tune the model to inpaint only the background of these images by conditioning on the prompt  $y_{b} =$  "a photo of a background" using the image as ground truth (See supplements for examples). Simultaneously, the model is fine-tuned on the task of full image synthesis to generate new samples for  $\mathbf{D}'$  by conditioning on  $y_{f} =$  "a photo of a  $\{\mathrm{object}\}$ ".
+
+To generate the final foreground masks  $\mathbf{D}_{\mathbf{m}}$  we use the fine-tuned LDM  $m^{\prime}$  to inpaint the background over the area covered by the preliminary mask conditioning on the background prompt. To identify the foreground region, we take the pixel-wise intensity difference between the background-inpainted and original images. As the inpainted images are conditioned to generate background, the difference is higher in the true foreground region. We apply a Gaussian mixture model to the pixel-wise difference map to create a binary classification map. Formally the refined masks  $M$  are computed as
+
+$$
+M = M _ {p r e, u p} \odot g \left(\left| \mathbf {x} - m ^ {\prime} \left(\tilde {\mathbf {z}} _ {0}, y _ {b}\right) \right|\right), \tag {5}
+$$
+
+$$
+\tilde {\mathbf {z}} _ {\mathbf {0}} = \mathbf {z} _ {\mathbf {0}} \odot (1 - M _ {p r e}) + \mathbf {z} \odot M _ {p r e} \tag {6}
+$$
+
+where  $M_{pre,up}$  denotes the preliminary mask upsampled to the input image's resolution,  $g$  applies the bimodal Gaussian mixture model to the pixel values and  $\tilde{\mathbf{z}}_0$  is the latent code of an image with the foreground region replaced with random noise  $\mathbf{z}$ . This produces refined masks, as the use of pixel-wise error improves the segmentation around the sharp edges of the object. Additionally, the computation of the refined masks is performed in pixel-space of the images instead of the latent space of  $m$  and therefore produces even more detailed masks.
+
+Finally, to further improve our mask prediction we use the refined masks as labels to train a U-Net [45] to directly segment the foreground of the images, similar to the approach in [61], which follows a standardized approach of training a U-Net on a fixed number of steps and hence does not require any hyperparameter tuning. We experiment with training the segmentation network on refined masks of the original unlabelled training data  $(\mathbf{D_s})$ , as well as training it with the fully synthetic dataset  $\mathbf{D_s}'$  as an augmentation method, which we generate by prompting the fine-tuned model with the foreground conditioning  $y_{f}$  and repeating our pipeline of mask refinement on this synthetic dataset to get segmentation labels.
+
+# 4. Evaluation and Results
+
+Implementation: We use PyTorch 1.11 and run our experiments on a workstation with two A6000 Nvidia GPUs. Concept distillation training takes on average one day. The forward pass is fast, equivalent to that of a standard U-Net. Datasets: We choose our datasets such that they cover a variety of different objects, including in-the-wild animals and cars, as well as humans in static setups.
+
+Human3.6m [24] is a dataset of 3.6 million images of humans in different scenarios and situations. To show that our method does not rely on large datasets we take a subset of 6000 randomly chosen images centred around the human and cropped to  $256 \times 256$  pixels from the training dataset of Human3.6m.
+
+To test the method on representations of animals, we use two datasets: the Stanford Dog Dataset [28], which contains 20,580 images of dogs divided into different categories, and the Caltech-UCSD Birds 200 (CUB) dataset [58], which contains 11,788 images of birds from 200 different species.
+
+Finally, we also experiment with the detection of cars using [30], which consists of 16,185 images of cars in different natural and non-natural settings. All these datasets come with subcategories grouping the images based on selected features. For our use case, we consolidate these groups
+
+when prompting the model and use the classes cars, dogs, human, and birds to simulate the absence of manual labels.
+
+<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Fully supervised U-Net</td><td>97.9</td><td>88.3</td><td>93.0</td></tr><tr><td>GrabCut [46] by [49]</td><td>72.3</td><td>36.0</td><td>52.3</td></tr><tr><td>ReDO [11]</td><td>84.5</td><td>42.6</td><td>-</td></tr><tr><td>PerturbGAN [4]</td><td>-</td><td>-</td><td>38.0</td></tr><tr><td>IEM + SegNet [49]</td><td>89.3</td><td>55.1</td><td>71.4</td></tr><tr><td>Melas-Kyriazi et al. [35]</td><td>92.1</td><td>66.4</td><td>-</td></tr><tr><td>Layered GAN [61]</td><td>94.3</td><td>69.7</td><td>81.7</td></tr><tr><td>Ours (U-Net trained on Ds)</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>Ours (U-Net trained on Ds ∪ D&#x27;s&#x27;)</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>
+
+Table 1. Comparison to other segmentation methods. Baselines taken from [61]. Details on the training of the U-Nets can be found in the appendix.
+
+Self-supervised Segmentation Performance: Table 1 compares our methods performance against other unsupervised methods on the CUB dataset, showing the pixel-wise accuracy, the Intersection over Union (IoU) of the foreground segmentation and the mean IoU. From this we see that training a U-Net on our self-supervised labels produces a model that outperforms all other methods, achieving an overall foreground IoU improvement of 5.4 compared to [61]. Furthermore, by adding the fully synthetic dataset  $\mathbf{D}_{\mathbf{s}}^{\prime}$  to the training data we are able to improve the performance even further, reaching a foreground IoU of 77.2. Table 3 also shows high foreground IoU values across the other datasets, with Fig. 4 showing qualitative examples.
+
+Mean Attention Map Performance: Computing the mean attention maps  $\hat{M}$  and comparing them to the ground-truth yields a remarkable AUC-ROC for the bird dataset of 97.1. Scores are normalized instance-wise to a range of 0 to 1. We also experiment with no normalization, which gives a slightly worse AUC-ROC of 97.08. Qualitative examples from all datasets are shown in Fig. 5, displaying the mean attention maps' ability to localize the foreground in different scenarios. To compare this to our classification results we compute the threshold such that we reach over  $95\%$  true positive rate on a reserved training set of 100 images. True positive rate is more important in our case because we observe that falsely classifying pixels as background leads the inpainting model taking these foreground pixels as sources to inpaint larger parts of the image. We reach a pixel-wise accuracy of  $86\%$  on a set of 1000 test images suggesting that our method of extracting the classification masks already can provide meaningful results.
+
+While these results are encouraging, they also require a ground-truth dataset and thresholding that we do not want to rely on. The results indicate that our computed masks
+
+![](images/d0b15c23058f4db52098020eff32e7543f9edd1cc99899be44e0dbfec202b41d.jpg)  
+CUB
+
+![](images/82aada856470a715b72a73b61e78e438294bb55a6663ac617ab38a1aeb709dee.jpg)  
+Human3.6
+
+![](images/1ca0f619801f68ee2830fb39ae37c2244fd11fe88ac90aef3241a0c60af0ffaf.jpg)  
+Stanford Cars
+
+![](images/2ae37a5406b634f4471bdd904a08f419c344714b5844c5e917ef0cb06d3e3ae6.jpg)  
+Stanford Dogs  
+Figure 4. Unsupervised Segmentation Masks generated by our proposed approach.
+
+are very good at locating the objects, albeit they do not reach state-of-the-art performance despite adding supervision. Training on refined masks and integrating synthetic data surpasses supervised results without using any labels as shown in the next section.
+
+<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Preliminary Masks Mpre</td><td>83.5</td><td>29.0</td><td>55.7</td></tr><tr><td>Simple Inpainting Mcrop</td><td>90.0</td><td>30.7</td><td>60.0</td></tr><tr><td>U-Net trained on (D, Mpre)</td><td>91.7</td><td>66.5</td><td>78.2</td></tr><tr><td>Refined Masks M</td><td>92.4</td><td>63.6</td><td>77.4</td></tr><tr><td>U-Net trained on Ds</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>U-Net trained on Ds ∪ D&#x27;s&#x27;</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>
+
+Table 2. Segmentation results for different steps of our pipeline.
+
+Ablation study: Table 2 shows an ablation study for the individual components of our method. Initially, the zero-shot preliminary masks generated from the foundation model achieve good accuracy (83.5), but poor foreground IoU (29.0). This reflects our earlier intuition that masks overestimate the size of the object due to the maps being computed at a lower resolution. Thanks to this, the GMM overestimates the boundaries and spares the need for any hyperparameter. Optimizing the threshold to maximise the accuracy over a set of 100 training images would increase the accuracy to  $93.9\%$ , but requires a ground-truth dataset.
+
+Training a U-Net on these labels  $(M_{pre})$  increases the
+
+IoU to 66.5, showing the value in training the segmentation network. Using the refined masks as foreground segmentation gives comparable performance, with higher accuracy but lower foreground IoU. Additionally, we experiment with replacing the inpainting step used to improve  $M_{pre}$  with a simpler approach that crops background areas and uses them as inpainting in Eq. (5) instead of  $m'$ . The resulting masks  $M_{crop}$  are worse than the masks from our proposed refinement step (For more details see supplements). However, training a U-Net on these refined masks produces the best results, being further boosted by incorporating additional synthetic data. The progressive refinement of the segmentation masks is shown in Fig. 6.
+
+Data synthesis: Table 3 compares the generative ability of our fine-tuned diffusion model using the Fréchet inception distance (FID). Our method achieves higher generation quality than all other methods across the CUB, Stanford Dogs, and Stanford Cars datasets. We improve upon LayeredGAN's remarkably low FID scores for CUB and Stanford Cars by 3.1 and 5.6 respectively.
+
+Our method allows for the generation of samples covered entirely by the background, as shown in Fig. 7, without ever seeing such an image during training. The success of this component is what enables the refined masks to be generated, as accurately inpainting the foreground allows us to use the pixel-wise difference between the original and inpainted images to precisely identify the foreground.
+
+Concept Distillation: Finally we can evaluate if our model
+
+![](images/8946094ccf2431774c5f5829ae461346def06db6b066a37ffbea50c838bd9c0c.jpg)  
+Figure 5. Mean attention maps for all datasets in latent space  $\mathbf{z}$  of the diffusion model. Prompts are "a photo of a {object}", where {object} is replaced by "bird" for the first pair of rows, then "car", "dog", and "human".
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Sup.</td><td colspan="2">CUB</td><td colspan="2">Stanford Dogs</td><td colspan="2">Stanford Cars</td><td colspan="2">Human3.6m</td></tr><tr><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td></tr><tr><td>FineGAN [54]</td><td>Weak</td><td>23.0</td><td>44.5</td><td>54.9</td><td>-</td><td>24.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>OneGAN [3]</td><td>Weak</td><td>20.5</td><td>55.5</td><td>48.7</td><td>-</td><td>24.2</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LayeredGAN [61]</td><td>Unsup.</td><td>12.9</td><td>69.7</td><td>59.3</td><td>-</td><td>19.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>Self</td><td>9.8</td><td>75.1</td><td>43.1</td><td>63.8</td><td>13.4</td><td>55.2</td><td>63.7</td><td>69.2</td></tr></table>
+
+Table 3. Quantitative Results on  $\mathbf{D_s}$ . Training details are shown in the supplements. Values are taken from [61]. Source code for [54, 3, 61] was not available for re-evaluation on the Dogs, Cars and Human3.6m datasets. IoU on CUB are reported using the prediction of our model and the ground truth provided with the dataset. For the other datasets we use the IoU of the bounding boxes.
+
+![](images/0096596307b82017ff4fe8c7751d445517da6a6b1ee949c06dd3e625cbe01ec4.jpg)  
+Figure 6. Progressive refinement of the segmentation masks.
+
+has indeed learned to distinguish between foreground and background by looking at the output of different classifier-free guidance scales starting from the same seed  $\mathbf{z}_{\mathbf{t}}$ . Since we have fine-tuned our model only on two distinct textual prompts the conditional image generation should have collapsed to two clusters, one for the object and the other one for the background. Hence, instead of performing classifier-free guidance using the predictions of  $m^{\prime}$  conditioned on empty prompts we can directly use the predictions of  $m^{\prime}(\mathbf{z}_{\mathbf{t}},y_{b})$  and  $m^{\prime}(\mathbf{z}_{\mathbf{t}},y_{f})$  to perform image interpolation. We define classifier-free guidance in the direction of the foreground, hence, a higher score means that latent representations are pushed further in the direction of the object. The results are shown in Fig. 8. For negative guidance scales, the background is more detailed and there is no bird
+
+present. Increasing this scale leads to less detail in the background while birds often seem to naturally grow from the details in the background. The quality of the birds visually improves while the quality of the rest of the image keeps degrading resulting in less detailed backgrounds. We confirm this quantitatively by computing the FID for different classifier-free guidance scales. Without classifier-free guidance, i.e., scale  $= 1$ , the method reaches a FID of 9.8, at scale  $= 3$  a FID of 11.3, and at scale  $= 7.5$  a FID of 22.3.
+
+Medical Image Analysis: We want to evaluate if this approach can be applied to other domains, such as medical imaging. Since the LDM does not have any medical understanding, we first need to fine-tune it using MIMIC [27], which provides chest x-ray images paired with radiology reports. We can fine-tune the model using a similar approach as the one suggested by [8] (Details on the fine-tuning can be found in the supplements). Then we report the pixelwise AUC-ROC on MS-CXR [5], a subset of MIMIC with bounding box labels for diseases. Qualitative results can be seen in Fig. 9. The pixel-wise accuracy of the attention mask is already at  $79.6\%$  AUC-ROC across eight different diseases, however, the bimodal GMM assumption no longer holds in many cases because the model distinguishes three regions, namely: background, foreground, and the rest of the chest region.
+
+![](images/74747f9bb420661d26b970d4cef36e16eef61c9238fb72f195e4a76504d8b14d.jpg)  
+Figure 7. Full background image synthesis from the fine-tuned model, conditioned on  $y_{b}$ . Using our proposed fine-tuning method, the diffusion model is successfully able to generate images without birds from a dataset only consisting of images with birds.
+
+![](images/6b9027d32dd7f960d2479013d5fae8a59ff5669adb08c577f623cb727b339d7b.jpg)  
+Figure 8. Synthetic results of  $m'$  with changing scales of classifier-free-guidance, ranging from -2 on the left to +7.5 on the right.
+
+![](images/9c44e2fad178d71e909189b1aac2184a264fb77b16698e19cc64469d8f697a68.jpg)  
+Figure 9.  $\hat{M}$  and  $M_{pre}$  extraction on a medical task.
+
+# 5. Discussion
+
+'startofstring' 'a' 'photo' 'of' 'a' 'human' with ' arms' 'and' 'legs'
+
+![](images/4d81549adcd5633c66590fa22c9ef6d27eb199aa17367eb314335a6a4bb7c03d.jpg)  
+Figure 10. Input image and mean attention maps for every word of the textual input prompt "startofstring a photo of a human with arms and legs". The attention of "human" focuses on the torso, the one for the "arms" on the arms, and the one for the "legs" on the legs.
+
+We show in Sec. 4 that our method to extract the segmen
+
+tation masks  $M$  from the preliminary attention masks yields better results than computing an optimised threshold over a reserved miniset. This is possible because comparing to the inpainted background provides sharp edges around the object. However, our model is currently limited to detecting single object concepts. An extension to multiple objects could be achieved by prompt engineering in combination with data augmentation techniques. Taking the foreground masks and using them to extract objects would enable multi-instance and multi-object segmentation by layering multiple objects over each other and extending the final U-Net to a multi-label segmentation model.
+
+Furthermore, learning from weak labels has the disadvantage that the segmentation model may learn and reproduce weaknesses of the initial method. In our case, the bimodal GMM fails if the image has more than two distinct contrast clusters. This is especially the case on the Human3.6m dataset where the floor, walls, and person have vastly different contrast-levels. Consequently, the final segmentation sometimes fails to detect the lower part of the body as shown in Fig. 4. However, our method could easily be adapted to only a part of the human body, such as the legs. We show this in Fig. 10, as by conditioning images from [24] on the prompt "A photo of a human with arms and legs" and computing  $\hat{M}$  for the three concepts (human, arms, and legs) we are able to produce attention maps focused on specific body parts.
+
+# 6. Conclusion
+
+In this work, we have presented a generalizable framework to train segmentation networks without any hyperparameter tuning using an unsupervised zero-shot approach following the paradigm of 'textual concept description'  $\rightarrow$  'segmentation model'. We leverage the power of large generative latent diffusion models and fine-tune the model on the task of generating foreground and background images, which can be used as data augmentation methods. We show, that this method can achieve results close to supervised methods, without requiring any manually generated ground
+
+truth labels. Our approach is amenable to supervised deep learning and can be combined with existing models to boost segmentation performance even further.
+
+In future work we will explore how multi-object, multi-instance segmentation can be facilitated with concept distillation from generative image foundation models.
+
+Acknowledgements: The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR projects b143dc and b180dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) - 440719683. Additional support was also received by the ERC - project MIA-NORMAL 101083647, DFG KA 5801/2-1, INST 90/1351-1 and by the state of Bavarian. H. Reynaud was supported by Ultromics Ltd. and the UKRI Centre or Doctoral Training in Artificial Intelligence for Healthcare (EP/S023283/1).
+
+# References
+
+[1] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Labels4free: Unsupervised segmentation using stylegan. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13970-13979, 2021.  
+[2] Dmitry Baranchuk, Andrey Voynov, Ivan Rubachev, Valentin Khrulkov, and Artem Babenko. Label-efficient semantic segmentation with diffusion models. In International Conference on Learning Representations, 2021.  
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+                                    "content": "Recently, latent diffusion models have emerged as state-of-the-art generative models for the task of text-to-image generation [18, 44, 41]. However, training such models requires a significant amount of "
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+                                    "content": "-intensive resources and until recently, pre-trained model weights have not been publicly available. Rombach et al. were the first to published their weights and model architecture [44], which facilitated the development of numerous derived applica"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "tions [60, 15, 53] and established this model as the foundation model for tasks that require generalised representations of concepts in images. State-of-the-art latent diffusion models are able to generate high resolution images of a vast amount of different objects, suggesting that a highly expressive latent representation of the data has been learned."
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+                                    "content": "We hypothesize that we can leverage these learned latent representations for our own downstream tasks of zero-shot foreground-background generation. Using a generative latent diffusion foundation model, we are able to extract a weak segmentation mask around an arbitrary object by computing the importance maps based on the textual input prompts. Weak segmentation masks have been shown to be an effective prior for segmentation models, given that enough training samples are available [34, 40]. We then use these preliminary masks to fine-tune a latent diffusion model on (1) generating new images from this dataset, as well as (2) inpainting regions where the object is not present according to our preliminary masks. The resulting model is able to perform full-image synthesis, as well as foreground, background and mask generation, as summarized in Fig. 1. A segmentation model trained using these masks can then achieve a level of performance that is close to direct supervision, despite not requiring manual segmentation masks at any point in the pipeline. This suggests that labour-intensive ground-truth image annotation workflows could become obsolete in the future, and be replaced by concept distillation from generative foundation models."
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+                                    "content": "Our main contributions are:"
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+                                            "content": "- We propose a self-supervised, hyperparameter-free, approach for dataset-independent foreground-background segmentation, based on latent diffusion models, capable of synthesizing foreground, background, and segmentation masks."
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+                                            "content": "- We describe a general framework to extract importance scores obtained from pretrained diffusion models and detail how to use them to improve segmentation performance."
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+                                            "content": "- We verify the feasibility of our method on a set of four different foreground background segmentation tasks, spanning humans, birds, dogs, and cars and show that our method achieves results close to supervised methods while being trained without direct supervision."
+                                        }
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+                                }
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+                                            "content": "- We experiment with the extension of our method to domain-adapted diffusion models by showing promising results on a medical segmentation task."
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+                                    "content": "2. Related Work"
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+                                    "content": "Semantic Segmentation refers to the identification of high level concepts in an image, which enable their extraction from the image. [33, 36] introduced the use of fully convolutional networks for this task, which superseded previous"
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+                                    "type": "text",
+                                    "content": "shallow feature classification approaches [20]. Currently, the most common segmentation network architectures are designed as encoder-decoder pairs, as it enforces an information bottleneck that facilitates generalisation. The encoder provides meaningful low dimensional representations and the decoder reconstructs high-resolution segmentation maps [10, 45, 33, 36]. Recent approaches maximise the use of multi-scale information with multi-scale attention [56], squeeze-and-attention [63], and Transformers [62]. The final pixel classification operation, which creates the segmentation mask, is performed through multinomial logistic regression. These methods require large amounts of manually labelled training samples, which can be labour-intensive and expensive."
+                                }
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+                                    "type": "text",
+                                    "content": "Weakly Supervised Semantic Segmentation partially mitigates that by learning from weak global labels, such as image-wise class labels, and perform rough semantic-segmentation tasks. These approaches often leverage the learned representations in intermediate layers through attention maps [26] or saliency maps [31] extraction. These representations are learned in a supervised manner through a classification task, as opposed to our approach that leverages an even weaker signal: free-form text-embeddings. Furthermore, these methods cannot generate images and are, therefore, not suitable for foreground-background synthesis."
+                                }
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+                                    "content": "Foreground background separation is a segmentation task where the goal is to apply binary classification over all the pixels of an image to separate the object of interest, the foreground, from the contextual background. For example, in video analysis tasks, the background is often defined as parts of scenes that are at rest [51]. More recently, decomposing individual images into potential foreground and background layers became an intriguing research topic [25]. Since the foreground-background separation factors are not known a priori, many related works formulate the problem as a category-agnostic unsupervised segmentation approach. While deep neural networks can learn pixel clustering in an unsupervised way [25, 29, 38], it often leads to inferior performance when compared to fully supervised methods. Other works also tried to learn image segmentation from generative models, for example via direct sampling from the training distribution with cut-and-paste [43], image combinations via styleGAN [1], erasing and redrawing [11], and through inpainting [49]."
+                                }
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+                                    "content": "The work closest related to ours is [61] who employ layered generative adversarial networks (GANs) to generate distinct images for the foreground and background. As opposed to [61], we are not relying on the unknown structure of the latent manifold to separate the embedding codes that represent foreground and background, but instead follow the directly interpretable paradigm 'textual concept description' "
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+                                    "type": "text",
+                                    "content": " 'segmentation model'. Both approaches in"
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+                                    "content": "Diffusion models are generative methods. Generative modeling has always been an important task in deep learning. Recently, Diffusion models gained a lot of attention thanks to the impressive results achieved by [42, 48]. Based on [22, 55], these models currently define the state-of-the-art in conditional image generation, and have been extended towards text-to-image models such as unCLIP [41] and Stable Diffusion [44]. Part of that success is due to the efficacy of straightforward extensions to diffusion models, such as classifier-free guidance [23]. Current research about diffusion models focuses mostly on inpainting [14, 13, 44]. Depending on the task, it might be easier to learn the object itself and then train a diffusion model on the task of inpainting regions where the object is not present. However, we focus on the scenario where we have the object itself present and try to remove it."
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+                                    "content": "Shortly after latent diffusion models showed superiority in terms of image sample quality compared to GANs [18], they were conditioned on the description of concepts [42]. These models became widely available online, including on commodity hardware after the computationally expensive denoising process was accelerated on a fundamental level [32]. Direct translation of text into object-centric representations has been attempted but rather in the context of attention editing [21], subject specific image generation [47], and textual concept-refined image-to-image translation [59]. Textual inversion, where examples of concepts are provided to a diffusion model as text and image tuples to teach the model a new concept [19], operates on the same fundamental input level as our approach. However, it is not able to provide object segmentation masks or concept-specific pixel importance scores. Recent advances on diffusion models have led to a spike in research around how latent features can be extracted [21, 2] however, their potential to be used for zero-shot segmentation has yet to be explored."
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+                                    "content": "Our approach is summarized in Fig. 2. At a high level, we first use the attention maps from a pretrained latent diffusion model to compute coarse foreground segmentations (preliminary masks). We use these masks to fine-tune the diffusion model to be able to remove the object from the image, replacing it with background information, whilst also being able to generate new samples from the true distribution "
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+                                    "type": "inline_equation",
+                                    "content": "p(\\mathbf{x})"
+                                },
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+                                    "type": "text",
+                                    "content": " of the dataset. By comparing the original images to those with the background inpainted over the foreground, we are then able to produce much more refined masks. We can also then use the fine-tuned model to sample an arbitrary number of new images, including only the foreground,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "only the background, and the masks separating them. The only assumptions this method uses is that we have access to a dataset of images where the chosen object is always present, and that the foundation model we use has learned a meaningful representation of the object we want to identify. In this context, objects can describe concepts like birds, cars, dogs, humans, but also parts of objects such as arms or legs."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "We start from the latent diffusion model (LDM) [44], a foundation model pretrained on the task of text-to-image generation, denoted as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". It generates images by sampling gaussian noise and iteratively denoising them in "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " diffusion steps. Throughout this work, we keep the default value from [44] of "
+                                },
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+                                    "content": "T = 50"
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+                                    "type": "text",
+                                    "content": " steps."
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denote a dataset where all the images contain our desired object. Formally, we aim to generate unsupervised segmentation masks of the original dataset "
+                                },
+                                {
+                                    "bbox": [
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+                                        241,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{\\mathbf{m}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as well as a synthetic dataset that contains synthetic images "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", masks "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{\\mathbf{m}}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", foreground "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{\\mathbf{f}}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and background "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{\\mathbf{b}}'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denoted as set "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{\\mathbf{s}}' = \\{\\mathbf{D}', \\mathbf{D}_{\\mathbf{m}}', \\mathbf{D}_{\\mathbf{f}}', \\mathbf{D}_{\\mathbf{b}}'\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                {
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+                                    "type": "text",
+                                    "content": "Preliminary Masks: The LDM was trained on paired text-image data. Thus, the output is conditioned on a text input, which we have to carefully choose to generate our initial attention maps. In practice, self- and cross-attention work well for conditioning on different inputs, especially across different modalities [57]. As input, we propose the prompt \"a photo of a {object}\" where \"object\" is a high level description of our foreground object (e.g. \"bird\")."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The first step in computing the preliminary masks is to leverage the raw attention maps computed in every cross-attention layer of the U-Net architecture. We decide against cherry-picking different attention layers for different tasks to remain task-agnostic, but would like to point out that this could lead to task-specific improvements as an hyperparameter option."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Let "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "z_0"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denote the latent space representation of some input image "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". In each layer, attention is computed as:"
+                                }
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+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {A t t e n t i o n} (Q, K, V) = \\psi \\left(Q _ {l}, K _ {l} ^ {T}\\right) \\cdot V _ {l} \\tag {1}",
+                                    "image_path": "18d285fc3ab54581d3ed920f542df9bc7a45b5b008f355fa0f7b6af589df9087.jpg"
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+                                    "type": "text",
+                                    "content": "with the attention probabilities "
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+                                    "type": "inline_equation",
+                                    "content": "\\psi(Q_l, K_l^T)"
+                                },
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+                                    "type": "text",
+                                    "content": " defined as:"
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+                                    "type": "interline_equation",
+                                    "content": "\\psi_ {\\mathbf {z} _ {\\mathbf {t}, 1}} \\left(Q _ {l}, K _ {l} ^ {T}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d}}\\right) \\tag {2}",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "Q = W_{Q}^{(i,l)} \\cdot \\phi(\\mathbf{z}_{\\mathbf{t},1})"
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+                                    "content": "K = W_{K}^{(i,l)} \\cdot \\tau_{\\theta}(y)"
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+                                    "content": "V = W_{V}^{(i,l)} \\cdot \\tau_{\\theta}(y)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denoting the learnable projection matrices according to [57], "
+                                },
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+                                    "type": "text",
+                                    "content": " the latent code of the l-th U-Net layer in the t-th reverse diffusion step, and "
+                                },
+                                {
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": " denotes the latent representation of the stable diffusion model in layer 1, conditioned at diffusion "
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+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                                322,
+                                                288,
+                                                357
+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 3. "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                322,
+                                                288,
+                                                357
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "T_{0}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                322,
+                                                288,
+                                                357
+                                            ],
+                                            "type": "text",
+                                            "content": " vs AUC-ROC on CUB. Incorporating more reverse diffusion steps into the attention computation improves the AUC-ROC against the groundtruth only up to roughly "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                322,
+                                                288,
+                                                357
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "T_{0} = 40"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                322,
+                                                288,
+                                                357
+                                            ],
+                                            "type": "text",
+                                            "content": "."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                        398
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                373,
+                                287,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        373,
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+                                    ],
+                                    "type": "text",
+                                    "content": "as expectations over multiple repeated diffusion steps according to"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        72,
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+                    "angle": 0,
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+                                    "bbox": [
+                                        72,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {M} = \\sum_ {t = 1} ^ {T _ {0}} \\mathbb {E} _ {\\mathbf {z} \\sim p (\\mathbf {z} _ {t} | \\mathbf {z} _ {t + 1}, \\mathbf {z} _ {0})} [ \\sum_ {l} \\psi_ {\\mathbf {z} _ {t, 1}} (Q _ {l}, K _ {l} ^ {T}) ]. \\quad (3)",
+                                    "image_path": "44ab0cb9a08b3e6b606ff7731a6216d8e03e2710531d8a7fdb7252960c666bc8.jpg"
+                                }
+                            ]
+                        }
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+                {
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We empirically show in our supplementary material that this can be simplified to performing single reverse diffusion steps which leads to a simplified importance score"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        108,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {M} = \\sum_ {t = 1} ^ {T _ {0}} \\sum_ {l} \\psi_ {\\mathbf {z} _ {\\mathbf {t}, 1}} \\left(Q _ {l}, K _ {l} ^ {T}\\right) \\tag {4}",
+                                    "image_path": "babd98f58b9990e11bd913f4b1781c7bc8e53e72aaceeda46b5ee87f68b8eec5.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Figure 3 shows AUCROC of using "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "text",
+                                    "content": " to identify the foreground as a function of the number of reverse steps. There is a clear improvement visible computing the mean over up to roughly "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_0 = 40"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "text",
+                                    "content": " reverse diffusion steps. Including higher diffusion steps seems to deteriorate the accuracy of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\phi"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This is because for higher values of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "text",
+                                    "content": " the input images approach pure Gaussian noise. However, for medium values of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
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+                                    ],
+                                    "type": "text",
+                                    "content": " the input and output images already approximate the basic structure of the final objects. Other details, like texture, appear at later stages but do not bear any valuable information for this use case. This observation could mean that for time critical applications, starting from lower "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
+                                        287,
+                                        688
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        533,
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+                                    ],
+                                    "type": "text",
+                                    "content": " should suffice."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        47,
+                        689,
+                        288,
+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
+                                689,
+                                288,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
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+                                    "type": "text",
+                                    "content": "The third and final step in retrieving the preliminary masks is to binarize the mean attention maps. To do so, we"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
+                        208,
+                        545,
+                        338
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                545,
+                                338
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        208,
+                                        545,
+                                        338
+                                    ],
+                                    "type": "text",
+                                    "content": "take advantage of the observation that all attention maps resemble a bimodal distribution, with one mode at a low value for the non-object pixels and one mode at a high value for the object pixels. Hence, we model absolute values of the instance-wise attention scores as a bimodal Gaussian mixture model (GMM) to produce GMM masks. Additionally, we remove orphan pixels by computing the mean filter over the resulting binary classification map to produce our preliminary masks "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        208,
+                                        545,
+                                        338
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{pre}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        208,
+                                        545,
+                                        338
+                                    ],
+                                    "type": "text",
+                                    "content": ". These preliminary masks could potentially already be used to detect objects as evaluated in Sec. 4."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
+                        341,
+                        546,
+                        581
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": "Fine-tuning and Mask Refinement: The main problem with the preliminary masks is that, because they are derived from the latent space of the LDM, their resolution is only "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "64 \\times 64"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": ". This limits them to being a coarse segmentation, which often overestimates the size of the object rather than following the object's sharp edges. A rough segmentation is sufficient for tasks like inpainting, especially if the area around the object is homogeneous, but for the task of extracting the foreground object it produces unwanted artefacts. To work around this, we leverage the same diffusion model that we used to extract the masks. We use the binary classification prediction of the GMM mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{pre}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " to select random rectangles within the image that only contain background. Then we fine-tune the model to inpaint only the background of these images by conditioning on the prompt "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{b} ="
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " \"a photo of a background\" using the image as ground truth (See supplements for examples). Simultaneously, the model is fine-tuned on the task of full image synthesis to generate new samples for "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}'"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " by conditioning on "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{f} ="
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " \"a photo of a "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathrm{object}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        341,
+                                        546,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": "\"."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "To generate the final foreground masks "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{\\mathbf{m}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " we use the fine-tuned LDM "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " to inpaint the background over the area covered by the preliminary mask conditioning on the background prompt. To identify the foreground region, we take the pixel-wise intensity difference between the background-inpainted and original images. As the inpainted images are conditioned to generate background, the difference is higher in the true foreground region. We apply a Gaussian mixture model to the pixel-wise difference map to create a binary classification map. Formally the refined masks "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        582,
+                                        547,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are computed as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "991"
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+                                    "type": "interline_equation",
+                                    "content": "M = M _ {p r e, u p} \\odot g \\left(\\left| \\mathbf {x} - m ^ {\\prime} \\left(\\tilde {\\mathbf {z}} _ {0}, y _ {b}\\right) \\right|\\right), \\tag {5}",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\tilde {\\mathbf {z}} _ {\\mathbf {0}} = \\mathbf {z} _ {\\mathbf {0}} \\odot (1 - M _ {p r e}) + \\mathbf {z} \\odot M _ {p r e} \\tag {6}",
+                                    "image_path": "f160630c1c5b3c8f2e009310c023e1e40ceb8f46947ddfae6e932a1862942423.jpg"
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+                    "index": 1
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M_{pre,up}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the preliminary mask upsampled to the input image's resolution, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
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+                                        251
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": " applies the bimodal Gaussian mixture model to the pixel values and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathbf{z}}_0"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": " is the latent code of an image with the foreground region replaced with random noise "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{z}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": ". This produces refined masks, as the use of pixel-wise error improves the segmentation around the sharp edges of the object. Additionally, the computation of the refined masks is performed in pixel-space of the images instead of the latent space of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        132,
+                                        287,
+                                        251
+                                    ],
+                                    "type": "text",
+                                    "content": " and therefore produces even more detailed masks."
+                                }
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+                                    "content": "Finally, to further improve our mask prediction we use the refined masks as labels to train a U-Net [45] to directly segment the foreground of the images, similar to the approach in [61], which follows a standardized approach of training a U-Net on a fixed number of steps and hence does not require any hyperparameter tuning. We experiment with training the segmentation network on refined masks of the original unlabelled training data "
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+                                    "content": ", as well as training it with the fully synthetic dataset "
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+                                    "type": "text",
+                                    "content": " as an augmentation method, which we generate by prompting the fine-tuned model with the foreground conditioning "
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+                                    "type": "text",
+                                    "content": " and repeating our pipeline of mask refinement on this synthetic dataset to get segmentation labels."
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+                                    "type": "text",
+                                    "content": "4. Evaluation and Results"
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+                                    "content": "Implementation: We use PyTorch 1.11 and run our experiments on a workstation with two A6000 Nvidia GPUs. Concept distillation training takes on average one day. The forward pass is fast, equivalent to that of a standard U-Net. Datasets: We choose our datasets such that they cover a variety of different objects, including in-the-wild animals and cars, as well as humans in static setups."
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+                                    "content": "Human3.6m [24] is a dataset of 3.6 million images of humans in different scenarios and situations. To show that our method does not rely on large datasets we take a subset of 6000 randomly chosen images centred around the human and cropped to "
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+                                    "content": " pixels from the training dataset of Human3.6m."
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+                                    "content": "To test the method on representations of animals, we use two datasets: the Stanford Dog Dataset [28], which contains 20,580 images of dogs divided into different categories, and the Caltech-UCSD Birds 200 (CUB) dataset [58], which contains 11,788 images of birds from 200 different species."
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+                                    "content": "Finally, we also experiment with the detection of cars using [30], which consists of 16,185 images of cars in different natural and non-natural settings. All these datasets come with subcategories grouping the images based on selected features. For our use case, we consolidate these groups"
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+                                    "content": "when prompting the model and use the classes cars, dogs, human, and birds to simulate the absence of manual labels."
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+                                            "html": "<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Fully supervised U-Net</td><td>97.9</td><td>88.3</td><td>93.0</td></tr><tr><td>GrabCut [46] by [49]</td><td>72.3</td><td>36.0</td><td>52.3</td></tr><tr><td>ReDO [11]</td><td>84.5</td><td>42.6</td><td>-</td></tr><tr><td>PerturbGAN [4]</td><td>-</td><td>-</td><td>38.0</td></tr><tr><td>IEM + SegNet [49]</td><td>89.3</td><td>55.1</td><td>71.4</td></tr><tr><td>Melas-Kyriazi et al. [35]</td><td>92.1</td><td>66.4</td><td>-</td></tr><tr><td>Layered GAN [61]</td><td>94.3</td><td>69.7</td><td>81.7</td></tr><tr><td>Ours (U-Net trained on Ds)</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>Ours (U-Net trained on Ds ∪ D&#x27;s&#x27;)</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>",
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+                                            "content": "Table 1. Comparison to other segmentation methods. Baselines taken from [61]. Details on the training of the U-Nets can be found in the appendix."
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+                                    "content": "Self-supervised Segmentation Performance: Table 1 compares our methods performance against other unsupervised methods on the CUB dataset, showing the pixel-wise accuracy, the Intersection over Union (IoU) of the foreground segmentation and the mean IoU. From this we see that training a U-Net on our self-supervised labels produces a model that outperforms all other methods, achieving an overall foreground IoU improvement of 5.4 compared to [61]. Furthermore, by adding the fully synthetic dataset "
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+                                    "content": " to the training data we are able to improve the performance even further, reaching a foreground IoU of 77.2. Table 3 also shows high foreground IoU values across the other datasets, with Fig. 4 showing qualitative examples."
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+                                    "content": " and comparing them to the ground-truth yields a remarkable AUC-ROC for the bird dataset of 97.1. Scores are normalized instance-wise to a range of 0 to 1. We also experiment with no normalization, which gives a slightly worse AUC-ROC of 97.08. Qualitative examples from all datasets are shown in Fig. 5, displaying the mean attention maps' ability to localize the foreground in different scenarios. To compare this to our classification results we compute the threshold such that we reach over "
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+                                    "content": " true positive rate on a reserved training set of 100 images. True positive rate is more important in our case because we observe that falsely classifying pixels as background leads the inpainting model taking these foreground pixels as sources to inpaint larger parts of the image. We reach a pixel-wise accuracy of "
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+                                    "content": " on a set of 1000 test images suggesting that our method of extracting the classification masks already can provide meaningful results."
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+                                            "content": "Figure 4. Unsupervised Segmentation Masks generated by our proposed approach."
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+                                    "content": "are very good at locating the objects, albeit they do not reach state-of-the-art performance despite adding supervision. Training on refined masks and integrating synthetic data surpasses supervised results without using any labels as shown in the next section."
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+                                            "html": "<table><tr><td>Methods</td><td>ACC</td><td>CUB IoU</td><td>mIoU</td></tr><tr><td>Preliminary Masks Mpre</td><td>83.5</td><td>29.0</td><td>55.7</td></tr><tr><td>Simple Inpainting Mcrop</td><td>90.0</td><td>30.7</td><td>60.0</td></tr><tr><td>U-Net trained on (D, Mpre)</td><td>91.7</td><td>66.5</td><td>78.2</td></tr><tr><td>Refined Masks M</td><td>92.4</td><td>63.6</td><td>77.4</td></tr><tr><td>U-Net trained on Ds</td><td>95.2</td><td>75.1</td><td>84.8</td></tr><tr><td>U-Net trained on Ds ∪ D&#x27;s&#x27;</td><td>95.6</td><td>77.2</td><td>86.0</td></tr></table>",
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+                                    "content": "Table 2. Segmentation results for different steps of our pipeline."
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+                                    "content": "Ablation study: Table 2 shows an ablation study for the individual components of our method. Initially, the zero-shot preliminary masks generated from the foundation model achieve good accuracy (83.5), but poor foreground IoU (29.0). This reflects our earlier intuition that masks overestimate the size of the object due to the maps being computed at a lower resolution. Thanks to this, the GMM overestimates the boundaries and spares the need for any hyperparameter. Optimizing the threshold to maximise the accuracy over a set of 100 training images would increase the accuracy to "
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+                                    "type": "text",
+                                    "content": " increases the"
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+                                    "content": "IoU to 66.5, showing the value in training the segmentation network. Using the refined masks as foreground segmentation gives comparable performance, with higher accuracy but lower foreground IoU. Additionally, we experiment with replacing the inpainting step used to improve "
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+                                    "type": "text",
+                                    "content": " with a simpler approach that crops background areas and uses them as inpainting in Eq. (5) instead of "
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+                                    "content": ". The resulting masks "
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+                                    "content": " are worse than the masks from our proposed refinement step (For more details see supplements). However, training a U-Net on these refined masks produces the best results, being further boosted by incorporating additional synthetic data. The progressive refinement of the segmentation masks is shown in Fig. 6."
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+                                    "content": "Data synthesis: Table 3 compares the generative ability of our fine-tuned diffusion model using the Fréchet inception distance (FID). Our method achieves higher generation quality than all other methods across the CUB, Stanford Dogs, and Stanford Cars datasets. We improve upon LayeredGAN's remarkably low FID scores for CUB and Stanford Cars by 3.1 and 5.6 respectively."
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+                                    "content": "Our method allows for the generation of samples covered entirely by the background, as shown in Fig. 7, without ever seeing such an image during training. The success of this component is what enables the refined masks to be generated, as accurately inpainting the foreground allows us to use the pixel-wise difference between the original and inpainted images to precisely identify the foreground."
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+                                    "content": "Concept Distillation: Finally we can evaluate if our model"
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+                                            "content": " of the diffusion model. Prompts are \"a photo of a {object}\", where {object} is replaced by \"bird\" for the first pair of rows, then \"car\", \"dog\", and \"human\"."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Sup.</td><td colspan=\"2\">CUB</td><td colspan=\"2\">Stanford Dogs</td><td colspan=\"2\">Stanford Cars</td><td colspan=\"2\">Human3.6m</td></tr><tr><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td><td>FID ↓</td><td>IoU ↑</td></tr><tr><td>FineGAN [54]</td><td>Weak</td><td>23.0</td><td>44.5</td><td>54.9</td><td>-</td><td>24.8</td><td>-</td><td>-</td><td>-</td></tr><tr><td>OneGAN [3]</td><td>Weak</td><td>20.5</td><td>55.5</td><td>48.7</td><td>-</td><td>24.2</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LayeredGAN [61]</td><td>Unsup.</td><td>12.9</td><td>69.7</td><td>59.3</td><td>-</td><td>19.0</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>Self</td><td>9.8</td><td>75.1</td><td>43.1</td><td>63.8</td><td>13.4</td><td>55.2</td><td>63.7</td><td>69.2</td></tr></table>",
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+                                    "content": ". Training details are shown in the supplements. Values are taken from [61]. Source code for [54, 3, 61] was not available for re-evaluation on the Dogs, Cars and Human3.6m datasets. IoU on CUB are reported using the prediction of our model and the ground truth provided with the dataset. For the other datasets we use the IoU of the bounding boxes."
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+                                    "type": "text",
+                                    "content": " to perform image interpolation. We define classifier-free guidance in the direction of the foreground, hence, a higher score means that latent representations are pushed further in the direction of the object. The results are shown in Fig. 8. For negative guidance scales, the background is more detailed and there is no bird"
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+                                    "content": "present. Increasing this scale leads to less detail in the background while birds often seem to naturally grow from the details in the background. The quality of the birds visually improves while the quality of the rest of the image keeps degrading resulting in less detailed backgrounds. We confirm this quantitatively by computing the FID for different classifier-free guidance scales. Without classifier-free guidance, i.e., scale "
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+                                    "content": ", the method reaches a FID of 9.8, at scale "
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+                                    "content": " a FID of 11.3, and at scale "
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+                                    "type": "text",
+                                    "content": " a FID of 22.3."
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+                                    "type": "text",
+                                    "content": "Medical Image Analysis: We want to evaluate if this approach can be applied to other domains, such as medical imaging. Since the LDM does not have any medical understanding, we first need to fine-tune it using MIMIC [27], which provides chest x-ray images paired with radiology reports. We can fine-tune the model using a similar approach as the one suggested by [8] (Details on the fine-tuning can be found in the supplements). Then we report the pixelwise AUC-ROC on MS-CXR [5], a subset of MIMIC with bounding box labels for diseases. Qualitative results can be seen in Fig. 9. The pixel-wise accuracy of the attention mask is already at "
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+                                    "type": "text",
+                                    "content": " AUC-ROC across eight different diseases, however, the bimodal GMM assumption no longer holds in many cases because the model distinguishes three regions, namely: background, foreground, and the rest of the chest region."
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+                                            "content": ". Using our proposed fine-tuning method, the diffusion model is successfully able to generate images without birds from a dataset only consisting of images with birds."
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+                                            "content": "Figure 9. "
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+                                            "type": "inline_equation",
+                                            "content": "\\hat{M}"
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+                                            "type": "text",
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+                                            "type": "text",
+                                            "content": " extraction on a medical task."
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+                                    "type": "text",
+                                    "content": "'startofstring' 'a' 'photo' 'of' 'a' 'human' with ' arms' 'and' 'legs'"
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+                                            "content": "Figure 10. Input image and mean attention maps for every word of the textual input prompt \"startofstring a photo of a human with arms and legs\". The attention of \"human\" focuses on the torso, the one for the \"arms\" on the arms, and the one for the \"legs\" on the legs."
+                                        }
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+                                    "type": "text",
+                                    "content": "We show in Sec. 4 that our method to extract the segmen"
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+                                    "content": "tation masks "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " from the preliminary attention masks yields better results than computing an optimised threshold over a reserved miniset. This is possible because comparing to the inpainted background provides sharp edges around the object. However, our model is currently limited to detecting single object concepts. An extension to multiple objects could be achieved by prompt engineering in combination with data augmentation techniques. Taking the foreground masks and using them to extract objects would enable multi-instance and multi-object segmentation by layering multiple objects over each other and extending the final U-Net to a multi-label segmentation model."
+                                }
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+                                    "type": "text",
+                                    "content": "Furthermore, learning from weak labels has the disadvantage that the segmentation model may learn and reproduce weaknesses of the initial method. In our case, the bimodal GMM fails if the image has more than two distinct contrast clusters. This is especially the case on the Human3.6m dataset where the floor, walls, and person have vastly different contrast-levels. Consequently, the final segmentation sometimes fails to detect the lower part of the body as shown in Fig. 4. However, our method could easily be adapted to only a part of the human body, such as the legs. We show this in Fig. 10, as by conditioning images from [24] on the prompt \"A photo of a human with arms and legs\" and computing "
+                                },
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+                                    "type": "text",
+                                    "content": " for the three concepts (human, arms, and legs) we are able to produce attention maps focused on specific body parts."
+                                }
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+                                    "content": "6. Conclusion"
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+                                    "content": "In this work, we have presented a generalizable framework to train segmentation networks without any hyperparameter tuning using an unsupervised zero-shot approach following the paradigm of 'textual concept description' "
+                                },
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+                                    "type": "text",
+                                    "content": " 'segmentation model'. We leverage the power of large generative latent diffusion models and fine-tune the model on the task of generating foreground and background images, which can be used as data augmentation methods. We show, that this method can achieve results close to supervised methods, without requiring any manually generated ground"
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+                                    "content": "In future work we will explore how multi-object, multi-instance segmentation can be facilitated with concept distillation from generative image foundation models."
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+                                    "content": "Acknowledgements: The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR projects b143dc and b180dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) - 440719683. Additional support was also received by the ERC - project MIA-NORMAL 101083647, DFG KA 5801/2-1, INST 90/1351-1 and by the state of Bavarian. H. Reynaud was supported by Ultromics Ltd. and the UKRI Centre or Doctoral Training in Artificial Intelligence for Healthcare (EP/S023283/1)."
+                                }
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+                                        }
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diff --git a/2023/Forward Flow for Novel View Synthesis of Dynamic Scenes/0cdaae9f-cb85-4e33-8452-a1e60f8c4484_content_list.json b/2023/Forward Flow for Novel View Synthesis of Dynamic Scenes/0cdaae9f-cb85-4e33-8452-a1e60f8c4484_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..231eaa1cfde17ac74ed3ae1c8cd9c324bc2d2e7e
--- /dev/null
+++ b/2023/Forward Flow for Novel View Synthesis of Dynamic Scenes/0cdaae9f-cb85-4e33-8452-a1e60f8c4484_content_list.json	
@@ -0,0 +1,1919 @@
+[
+    {
+        "type": "text",
+        "text": "Forward Flow for Novel View Synthesis of Dynamic Scenes",
+        "text_level": 1,
+        "bbox": [
+            187,
+            130,
+            782,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xiang Guo $^{1}$ , Jiadai Sun $^{1,3}$ , Yuchao Dai $^{1}$ , Guanying Chen $^{2}$ , Xiaqing Ye $^{3}$ , Xiao Tan $^{3}$ , Errui Ding $^{3}$ , Yumeng Zhang $^{3}$ , Jingdong Wang $^{3}$",
+        "bbox": [
+            96,
+            191,
+            870,
+            229
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup>Northwestern Polytechnical University, <sup>2</sup>FNii and SSE, CUHK-Shenzhen, <sup>3</sup>Baidu Inc.",
+        "bbox": [
+            140,
+            239,
+            826,
+            258
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+            233,
+            319,
+            313,
+            335
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "This paper proposes a neural radiance field (NeRF) approach for novel view synthesis of dynamic scenes using forward warping. Existing methods often adopt a static NeRF to represent the canonical space, and render dynamic images at other time steps by mapping the sampled 3D points back to the canonical space with the learned backward flow field. However, this backward flow field is non-smooth and discontinuous, which is difficult to be fitted by commonly used smooth motion models. To address this problem, we propose to estimate the forward flow field and directly warp the canonical radiance field to other time steps. Such forward flow field is smooth and continuous within the object region, which benefits the motion model learning. To achieve this goal, we represent the canonical radiance field with voxel grids to enable efficient forward warping, and propose a differentiable warping process, including an average splatting operation and an inpaint network, to resolve the many-to-one and one-to-many mapping issues. Thorough experiments show that our method outperforms existing methods in both novel view rendering and motion modeling, demonstrating the effectiveness of our forward flow motion modeling. Project page: https://npucvr.github.io/ForwardFlowDNeRF.",
+        "bbox": [
+            75,
+            352,
+            473,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            732,
+            209,
+            748
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Novel view synthesis (NVS) is a challenging and longstanding problem in computer vision and graphics, which has many applications in virtual reality, augmented reality, data augmentation, image editing, etc. Recently, differentiable neural rendering [26, 30, 59] has been introduced into this area. In particular, the neural radiance field (NeRF) [26]",
+        "bbox": [
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+            468,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/e3bf25df32093517aea0c8394238217909709d3534ba60da6f44fcb467087448.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            304,
+            647,
+            435
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/3475db0ab9134a9ab7f46e6cf7a0bc93421dbb2f0e9ceb51d4c8fd0bec01e673.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "image",
+        "img_path": "images/1f265ea20acfad9ea9a931ad882beb52b91a1142e1be4f1eeeaa23f4e157769d.jpg",
+        "image_caption": [
+            "Figure 1. Comparison of backward flow and forward flow. This figure shows an example of backward and forward flow changes. (a) An example of dynamic scene. (b) With the bucket lifting up, different types of points cover the green point  $\\mathbf{p}$ , which needs very different backward flows to map this point back to canonical space. (d) shows the norm changes of the backward flow, which is not smooth. (c) On the other hand, the forward flow of position  $\\mathbf{q}$ , which maps the constant object point from canonical space to other times, is smooth and continuous. (e) shows the norm changes of the forward flow."
+        ],
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "promotes this area significantly and attracts lots of interest within a short time. NeRF [26] produces realistic images by representing the 3D world with a multi-layer perceptron (MLP), which maps the input 3D coordinates and 2D view direction to target density and color.",
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+        "type": "text",
+        "text": "While the original NeRF [26] can only model static scenes, a series of works extend the NeRF-based framework from static to dynamic scenes [9, 13, 19, 32, 36, 49, 51, 55]. One of the promising directions is using a canonical space representation [15, 36, 49]. This representation sets one of the time steps as canonical time and models the static scene with a canonical radiance field. To render images at other time steps, a deformation field is used to estimate the",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author (daiyuchao@nwpu.edu.cn). The first three authors also with the Shaanxi Key Laboratory of Information Acquisition and Processing.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "16022",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "backward flow for moving the 3D points from the current time step back to the canonical time step. Although the canonical-based representation with the backward flow is easy to implement, the backward flow field is non-smooth and discontinuous. As shown in Fig. 1(b), for a fixed 3D position along the timeline, there will be different types of points covering the position  $\\mathbf{p}$ , which needs discontinuous flows to map them back to canonical space (Fig. 1(d)). So the backward flow cannot be fitted well with commonly used smooth motion models (MLP, for example). Also, distortions are introduced to the static canonical space geometry due to the failure of the motion model, as shown in Fig. 8.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "To solve the problem of backward flow, we propose using forward flow as the deformation model. Instead of warping the sampled points on image rays at other time steps back to the canonical time and rendering at the canonical space, we propose to warp the whole canonical radiance field from the canonical time to other time steps using forward deformation flow and render at corresponding time steps. In this way, the forward flow estimated by the deformation model will be smooth and continuous for the same 3D position along the timeline (Fig. 1(c) and (e)). Note that SNARF [7] has also used forward warping based on an inverse skinning model, but it is designed for dynamic human modeling and cannot be used in general scenes. In this paper, we aim to achieve forward warping for general scenes, which means we must warp the whole space.",
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+    {
+        "type": "text",
+        "text": "However, introducing forward warping into the canonical space based NeRF methods is not straightforward as there are three main problems to be solved. First, the traditional canonical radiance field in existing methods cannot be warped explicitly, since the radiance field is represented as a continuous function parameterized by an MLP. To solve this problem, we propose to use the voxel grid to represent the canonical radiance field as it is finite and discrete. Recent voxel-based methods [27,44,62] have proven the effectiveness of this representation. The other two problems are the many-to-one and one-to-many mapping issues brought by the inherent property of the forward warping operation. To address them, we propose a differentiable forward warping method consisting of an average splatting operation and an inpaint network to solve the many-to-one and one-to-many issue, respectively. Extensive experiments have been conducted to verify the effectiveness of our method.",
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+    {
+        "type": "text",
+        "text": "Our key contributions can be summarized as follows:",
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+    {
+        "type": "text",
+        "text": "- To the best of our knowledge, we are the first to investigate forward warping in dynamic view synthesis for general scenes. We propose a novel canonical based NeRF with forward flow motion modeling for dynamic view synthesis. Thanks to the forward flow field, our method can better represent the object motions, and explicitly recover the trajectory of a surface point.",
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+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We introduce voxel grid based canonical radiance field to enable reasonable computation of forward warping, and propose a differentiable forward warping method, including an average splatting operation and an inpaint network, to solve the many-to-one and one-to-many issues of forward warping.",
+            "- Experiments on multiple datasets show that our method outperforms existing methods on the D-NeRF [36] dataset, Hypernerf [33] dataset, NHR [54] dataset and our proposed dataset."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Novel View Synthesis (NVS) is a long-standing task in both computer vision and graphics [4, 6, 14, 18], and surveys of recent methods can be found in [42, 46, 47]. Some methods require to reconstruct an explicit 3D model to represent the scene, such as point clouds [1], voxels or meshes [16, 40, 41, 48]. Then novel images from arbitrary views can be rendered from this geometry. Another methods try to estimate depth map through multi-view geometry, and then aggregate features from multiple frames through the co-visibility, such as [8, 11, 17, 34, 40, 41, 57]. Recently, neural implicit representations have shown great promise for novel view synthesis and 3D modeling. In this section, we focus more on the neural implicit rendering methods and mainly summarize these schemes according to whether they can handle dynamic scenes.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "NVS for Static Scenes NeRF [26], as a seminal work, uses MLPs to model a 5D radiance field, which can render impressive view synthesis for static scenes captured. Numerous subsequent works have extended NeRF to kinds of scenarios, such as larger and unbounded scenes [25, 39, 45, 56, 64], relighting [3, 43, 58, 66], incorporating anti-aliasing for multi-scale rendering [2], and generalization ability [5, 50, 52, 63]. In addition, some methods are devoted to more efficient neural rendering and optimization in NeRF-like framework, such as [20, 22, 24, 28, 35, 62] focus more on efficient sampling along each ray for color accumulation, [37, 38] subdivide the scene into multiple cells for efficient processing, and [27, 44, 61] exploit voxel-grid representation to speed up the optimization of radiance field. However, these methods are mainly applicable to static scenes, leaving out the scenes with dynamic objects, which are actually more extensive and practical.",
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+    {
+        "type": "text",
+        "text": "NVS for Dynamic Scenes There are several works that extend NeRF from static scenes to dynamic scenes with nonrigid deformable objects. One feasible way is to build a 4D spatial-temporal representation. For example, Yoon et al. [60] combine single-view depth and depth from multiview stereo to render virtual views with 3D warping. Gao et al. [13] use a time-invariant model (static) and a time-varying model (dynamic) to represent the scenes, and reg-",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "16023",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/3489969a15c5866b2a68f81794c695d2f858a460349e24d236874eefaaad40f0.jpg",
+        "image_caption": [
+            "1. Voxel Grid Based Canonical Field"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/75fb6f7c8bd9d8ddf7e9e5b2ddc4cf92b298e5f0a5629047208836b3a2cbd170.jpg",
+        "image_caption": [
+            "2. Differentiable Forward Warping",
+            "Figure 2. Overview of our proposed method. a) We represent a static scene at canonical time with a voxel grid based radiance field for density&color and a voxel grid based trajectory field for deformations; b) We propose to first forward warp canonical radiance field using the forward flow by average splating; c) We then inpaint the warped radiance field using a inpaint network; Specifically, 1. Voxel Grid Based Canonical Field contains two models. The canonical radiance field  $\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}}$  is estimated by a Light MLP which takes canonical radiance feature  $\\mathbf{V}_{\\mathrm{Rf}}^{\\mathrm{Can}}$  and corresponding 3D coordinates  $\\mathbf{V}_{\\mathrm{p}}^{\\mathrm{Can}}$  as input. The canonical trajectory field  $\\mathbf{V}_{\\mathrm{T}}^{\\mathrm{Can}}$  is estimated by another Light MLP which takes deformation feature and coordinates as input. The deformation flow  $\\mathbf{V}_{\\mathrm{flow}}^{t}$  from canonical to time  $t$  can then be obtained; 2. Differential Forward Warping first warp  $\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}}$  to get radiance field  $\\mathbf{V}_{\\mathrm{R}}^{t}$  at time  $t$ . Then, the  $\\mathbf{V}_{\\mathrm{R}}^{t}$  is inpainted by a inpaint network, which is  $\\mathbf{V}_{\\mathrm{R_{inp}}}^{t}$ ; 3. Volume Rendering render colors of rays at time  $t$  based on  $\\mathbf{V}_{\\mathrm{R_{inp}}}^{t}$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ularize the dynamic model by scene flow estimation. NeRF-Flow [9] learns a 4D spatial-temporal representation of a dynamic scene from a set of RGB images. Xian et al. [55] build a 4D space-time irradiance field to map a spatial-temporal location to the emitted color and volume density. Similarly, NSFF [19] models the dynamic scene as a time-variant continuous function of appearance, geometry, and 3D scene motion. DCT-NeRF [51] uses the Discrete Cosine Transform (DCT) to capture dynamic motion, i.e. learning smooth and stable trajectories over time for each point in space.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "On the other hand, D-NeRF [36], Nerfies [32], HyperNeRF [33] and NR-NeRF [49] use a static canonical radiance field to capture geometry and appearance, and then learn a deformation/displacement field at each time step w.r.t. the canonical space. Specifically, to render an image at an arbitrary time step, a deformation field is used to estimate backward scene flow, moving 3D points from the current time step back to the canonical step. However, for the same 3D location along the timeline, the backward flow field is not guaranteed to be smooth and continuous. As a result, the canonical geometry usually has distortions and resembles the mean shape of a moving object. We focus on solving the problem of backward flow in this paper.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Along with the two main directions, there is a trend to speed up the training of dynamic NeRF, which is based on voxel grid representation. TiNeuVox [10] models the de",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "formation using a tiny MLP and uses multi-distance interpolation to get the feature for the radiance network which estimates the density and color. V4D [12] uses the 3D feature voxel to model the 4D radiance field with additional time dimension concatenated and proposes look-up tables for pixel-level refinement. Although V4D mainly focuses on improving image quality, the training speed is not significant compared to TiNeuVox. DeVRF [21] also builds on voxel-grid representation, which proposes to use multi-view data to overcome the nontrivial problem of the monocular setup. Multi-view data simplifies the learning of motion and geometry compared with others using monocular images.",
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Motivation Backward-warping based methods [15, 36] propose a network  $f_{t\\to \\mathrm{Can}} = F(p,t)$  to estimate the deformation flow  $f_{t\\rightarrow \\mathrm{Can}}$  which moves the point at the position  $p$  from other time steps  $t$  back to canonical time Can. However, for the same position  $p$ , at different time steps  $ts$ , there could be different object points or even the empty point at this position, as shown in Fig. 1. This means the deformation flow  $f_{t\\to \\mathrm{Can}}$  is non-smooth and discontinuous along the timeline for a fixed position  $p$ . This could introduce difficulties for motion learning and produce distortion in the canonical radiance field, because the backward flow network has limited capacities in learning a correct non-smooth and dis",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "16024",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/b34fd3ffba8feb7ae2fe118cca197e35bda97ffa83ff381a6bdc48e89a5e55a2.jpg",
+        "image_caption": [
+            "Figure 3. Two issues of the forward warping. Many-to-one: multiple positions in the source correspond to the same position in the target. One-to-many: one position in the source corresponds to multiple positions in the target, causing holes if warping naively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "continuous deformation field. On the other hand, our proposed forward warping strategy estimates the deformation  $f_{\\mathrm{Can} \\to t}$  from the canonical time to another time step of a 3D point in canonical space. The set of the deformation flows of one position along the timeline is actually the trajectory of this point. This guarantees the flows to be smooth and continuous along the timeline as we assume the motions in reality have these properties.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Method Overview We model a static scene at the canonical time using the voxel grid representation with a canonical radiance field and a canonical trajectory field. To synthesize dynamic images, we propose to forward warp the canonical radiance field to corresponding time steps and render the images using volume rendering based on the warped radiance field. Fig. 2 shows the overview of our method. In the following, we will introduce three main components of our method: voxel grid based canonical field, differentiable forward warping, and volume rendering. Finally, the model optimization is represented, including the proposed loss functions and training strategy.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1. Voxel Grid Based Canonical Field",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Canonical Radiance Field To warp a static scene in canonical time to other time steps using forward warping, the radiance field should be represented by finite 3D points. The original heavy MLP in NeRF [26] is not practical, as we cannot query infinite 3D points in the canonical space. Inspired by recent works [27,44,61] on voxel grid presentations, we propose to use a learnable voxel radiance feature grid  $\\mathbf{V}_{\\mathrm{Rf}}^{\\mathrm{Can}}$  and a lightweight MLP network  $F_{\\theta_1}$  to model the radiance of the static scene as shown in Fig. 2. The canonical radiance field is defined as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} _ {\\mathrm {R}} ^ {\\text {C a n}} = F _ {\\theta_ {1}} \\left(\\mathbf {V} _ {\\mathrm {p}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\mathrm {R f}} ^ {\\text {C a n}}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}} = \\{\\mathbf{V}_{\\sigma}^{\\mathrm{Can}}, \\mathbf{V}_{\\mathrm{cf}}^{\\mathrm{Can}}\\}$  consists of density voxel grid  $\\mathbf{V}_{\\sigma}^{\\mathrm{Can}}$  and color feature voxel grid  $\\mathbf{V}_{\\mathrm{cf}}^{\\mathrm{Can}}$ .  $\\mathbf{V}_{\\mathrm{p}}^{\\mathrm{Can}}$  are the 3D coordinates of the voxel grid in canonical space, embedded according to NeRF [26].",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Canonical Trajectory Field We propose to use Discrete Cosine Transform (DCT) [51] to represent the trajectory of",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "a 3D point, which ensures the smoothness of the motion. Similar to canonical radiance field, we also use a deformation feature grid  $\\mathbf{V}_{\\mathrm{Df}}^{\\mathrm{Can}}$  and a lightweight MLP network  $F_{\\theta_2}$  to model the canonical trajectory field, which is defined as",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} _ {T} ^ {\\text {C a n}} = F _ {\\theta_ {2}} \\left(\\mathbf {V} _ {\\mathrm {p}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\mathrm {D f}} ^ {\\text {C a n}}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{V}_T^{\\mathrm{Can}}$  contains the DCT coefficients of the voxels. Given time step  $t$ , we could get the deformation flow of these voxels from canonical to time step  $t$  by",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} _ {\\text {f l o w}} ^ {t} = f _ {\\mathrm {D C T} ^ {- 1}} \\left(\\mathbf {V} _ {T} ^ {\\text {C a n}}, t\\right) - f _ {\\mathrm {D C T} ^ {- 1}} \\left(\\mathbf {V} _ {T} ^ {\\text {C a n}}, \\text {C a n}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $f_{\\mathrm{DCT}^{-1}}$  is the inverse DCT transform of the DCT coefficients as described in TrajectoryNeRF [51].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.2. Differentiable Forward Warping",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Forward warping has two major issues: many-to-one and one-to-many. Fig. 3 shows a simple example, where we aim to warp the source to the target using forward warping: a) Many-to-one: if a circle shrinks, there will be multiple positions corresponding to one position from the source to the target. b) One-to-many: if a circle expands, multiple positions in the target will correspond to the same position in the source, which leaves holes of the target if we warp the source to target naively. For the many-to-one issue, we propose to use the average splating to fuse multiple values into one. For the one-to-many issue, we use an inpaint network to inpaint the missing positions of the warped grids. More details are in the following sections.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Average Splatting We propose to fuse possible multiple values from the source grid that are mapped into the same voxel position of the target grid, motivated by Softmax-splatting [31]. Specifically, we propose a simple yet effective method that calculates the \"average\" of these values with a trilinear kernel. Formally, suppose that we need to warp the source grid  $\\mathbf{V}^{\\mathrm{S}}$  to target grid  $\\mathbf{V}^{\\mathrm{T}}$  by the flow  $f_{\\mathrm{S}\\rightarrow \\mathrm{T}}$ , and  $\\mathbf{p}$ ,  $\\mathbf{q}$  are indexes of a voxel grid. We define  $\\mathbf{V}^{\\mathrm{T}} = F_{\\mathrm{warp}}(\\mathbf{V}^{\\mathrm{S}}, f_{\\mathrm{S}\\rightarrow \\mathrm{T}})$  as follows,",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} ^ {\\mathrm {T}} [ \\mathbf {p} ] = \\frac {\\sum_ {\\forall \\mathbf {q} \\in \\mathbf {V} ^ {\\mathrm {s}}} b [ \\mathbf {u} ] \\cdot \\mathbf {V} ^ {\\mathrm {S}} [ \\mathbf {q} ]}{\\sum_ {\\forall \\mathbf {q} \\in \\mathbf {V} ^ {\\mathrm {s}}} b [ \\mathbf {u} ]}, \\tag {4}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nb [ \\mathbf {u} ] = \\prod \\max  (0, 1 - | \\mathbf {u} _ {i} |), i \\in \\{x, y, z \\}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {u} = \\left(\\mathbf {q} + f _ {\\mathrm {S} \\rightarrow \\mathrm {T}} [ \\mathbf {q} ]\\right) - \\mathbf {p}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where  $x, y, z$  are three axes of the voxel grid, and  $\\mathbf{u}_i \\in \\mathbb{R}$  is one element of the vector  $\\mathbf{u} \\in \\mathbb{R}^3$ .",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "So, we warp the canonical radiance field to time step  $t$  by",
+        "bbox": [
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+            813,
+            879,
+            828
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} _ {\\mathrm {R}} ^ {t} = F _ {\\text {w a r p}} \\left(\\mathbf {V} _ {\\mathrm {R}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\text {f l o w}} ^ {t}\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Inpaint Network Another issue of forward warping is one-to-many, which leaves holes in the voxel grid after",
+        "bbox": [
+            496,
+            869,
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+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "16025",
+        "bbox": [
+            480,
+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/a16d6a4ff97928569408dbd64c84065323443b6393410b3b15a648139d14e916.jpg",
+        "image_caption": [
+            "Figure 4. Inpaint network. It consists of a 3D U-Net structure and an up-sampling layer, which could inpaint and upsample the input voxel grid."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            89,
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+            215
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "warping. To resolve this issue, we propose building an inpaint network to fill these holes. As shown in Fig. 4, we modify a 3D U-Net structure network [53] followed by an up-sampling layer, which is  $\\mathbf{V}_{\\mathrm{R_{Inp}}}^{t} = F_{\\theta_{3}}(\\mathbf{V}_{\\mathrm{R}}^{t})$ , where  $\\mathbf{V}_{\\mathrm{R_{Inp}}}^{t}$  is the inpainted and up-sampled voxel grid.",
+        "bbox": [
+            75,
+            281,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This structure helps encoding layers to learn information from local neighboring voxels and decoding layers to recover the original resolution with filled content. We only feed the warped voxel grid to the inpaint network, which has no access to temporal information. Thus, the inpaint network can not learn to warp, limiting its ability only to inpainting. Since warping operations and the inpaint network are relatively expensive to compute, we propose to attach an up-sample layer after the U-Net structure. In this way, we could warp the grids with a low resolution to save time and memory, while rendering with a higher resolution for better image quality. The up-sample layer consists of a interpolation layer, convolution layers, and activation layers.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Volume Rendering",
+        "text_level": 1,
+        "bbox": [
+            76,
+            571,
+            256,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After we get the radiance voxel grid at time  $t$ , the pixel colors of the image rays can be rendered using volume rendering techniques [26]. Given a ray  $\\mathbf{r}(w) = \\mathbf{o} + w\\mathbf{d}$  emitted from the camera center  $\\mathbf{o}$  with view direction  $\\mathbf{d}$  through a given pixel on the image plane, we render the corresponding pixel color  $\\mathbf{C}_{\\mathrm{Inp}}(\\mathbf{r}) = F_{\\mathrm{render}}(\\mathbf{V}_{\\mathrm{R_{inp}}}^{t},\\mathbf{r})$ . To do this, we get all 3D points  $\\mathbf{p}$  that the ray intersects with voxel grids. Next, trilinear interpolation is applied to obtain the density and color feature of each 3D point.",
+        "bbox": [
+            75,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n(\\sigma , \\mathbf {c} _ {\\mathbf {f}}) = F _ {\\text {i n t e r}} \\left(\\mathbf {V} _ {\\mathrm {R} _ {\\mathrm {l n p}}} ^ {t}, \\mathbf {p}\\right). \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            187,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then, we get the color of this 3D point  $\\mathbf{p}$  by",
+        "bbox": [
+            76,
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+            369,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {c} = \\left\\{ \\begin{array}{l l} \\mathbf {c} _ {\\mathbf {f}} & \\text {i f} \\mathbf {c} _ {\\mathbf {f}} \\in \\mathbb {R} ^ {3}, \\\\ F _ {\\theta_ {4}} \\left(\\mathbf {c} _ {\\mathbf {f}}, \\mathbf {d}\\right) & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            161,
+            814,
+            467,
+            854
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $F_{\\theta_4}$  is a small MLP network that is used to produce colors that depend on the direction of the ray.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, the pixel color could be rendered by",
+        "bbox": [
+            519,
+            90,
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+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {C} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T \\left(w _ {k}\\right) \\alpha \\left(\\sigma \\left(w _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} \\left(w _ {k}\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            532,
+            114,
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+            142
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nT \\left(w _ {k}\\right) = \\exp \\left(- \\sum_ {j = 1} ^ {k - 1} \\sigma \\left(w _ {j}\\right) \\delta_ {j}\\right), \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            145,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $K$  is the number of sampled points along the ray,  $\\delta_{k}$  is the distance between adjacent samples along the ray, and  $\\alpha (\\sigma (w_k)\\delta_k) = 1 - \\exp (-\\sigma (w_k)\\delta_k)$ .",
+        "bbox": [
+            500,
+            186,
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+            232
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Note that the warped radiance grid  $\\mathbf{V}_{\\mathrm{R}}^{t}$  should also render reasonable images. So we directly up-sample  $\\mathbf{V}_{\\mathrm{R}}^{t}$  to get  $\\mathbf{V}_{\\mathrm{RUp}}^{t}$  without inpainting, and render the corresponding pixel color  $\\mathbf{C}_{\\mathrm{Up}}(\\mathbf{r}) = F_{\\mathrm{render}}(\\mathbf{V}_{\\mathrm{RUp}}^{t},\\mathbf{r})$",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Model Optimization",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To optimize the model, we design a series of loss functions. Photometric Loss First, the most important loss is the photometric loss, which is the mean square error (MSE) of the rendered color and ground truth color  $\\mathbf{C}_{\\mathrm{gt}}(\\mathbf{r})$",
+        "bbox": [
+            500,
+            329,
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+            392
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} ^ {\\mathrm {p h o t o}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\| \\mathbf {C} _ {\\operatorname {I n p}} (\\mathbf {r}) - \\mathbf {C} _ {\\mathrm {g t}} (\\mathbf {r}) \\| _ {2} ^ {2} \\\\ + \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\| \\mathbf {C} _ {\\mathrm {U p}} (\\mathbf {r}) - \\mathbf {C} _ {\\mathrm {g t}} (\\mathbf {r}) \\| _ {2} ^ {2}, \\tag {12} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            553,
+            402,
+            890,
+            477
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{R}$  is the set of rays sampled in one batch.",
+        "bbox": [
+            500,
+            487,
+            816,
+            502
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following DVGO [44], we use  $\\mathcal{L}^{\\mathrm{ptc}}$  to directly supervise the color of sampled points. The intuition is that sampled points with larger weights contribute more to the rendered color. Also, we use the background entropy loss  $\\mathcal{L}^{\\mathrm{bg}}$  to encourage the densities concentrating on either the foreground or the background.",
+        "bbox": [
+            498,
+            502,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inpaint Network Loss As the inpaint network is used to complete the warped voxel grids, the output of the inpaint network should be close to the input. Therefore, we propose to use the L1 norm of the difference between the input and output of the inpaint network.",
+        "bbox": [
+            498,
+            595,
+            890,
+            671
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} ^ {\\mathrm {v d i f f}} = \\left\\| \\mathbf {V} _ {\\mathrm {R} _ {\\text {I n p}}} ^ {t} - \\mathbf {V} _ {\\mathrm {R} _ {\\mathrm {U p}}} ^ {t} \\right\\| _ {1}. \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            680,
+            890,
+            708
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Regularization Terms Since modeling the appearance and motion of a dynamic scene from monocular images is a nontrivial problem, we propose a series of regularization terms.",
+        "bbox": [
+            498,
+            719,
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+            763
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "First, we encourage most 3D points in canonical space to be static by introducing  $\\mathcal{L}^{\\mathrm{flow}}$  to be the L1 norm of  $\\mathbf{V}_{\\mathrm{flow}}^{t}$ . Second, denoting  $\\mathcal{L}^{\\mathrm{tv}}$  as the total variation function. We compute  $\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{V}_{\\sigma}^{\\mathrm{Can}})$  to ensure the spatial smoothness of the density in canonical space, and introduce  $\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{V}_{\\mathrm{flow}}^{t})$  to encourage the spatial smoothness of the motions. Finally, inspired by RegNeRF [29], we render depths  $\\mathbf{D}$  of image patches sampled from random views and minimize their total variations  $\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{D})$ .",
+        "bbox": [
+            496,
+            765,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "16026",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/a6abc630c82cd702d92a968f236a84a7e963c92ce44a5bc64f1735f6eb33298e.jpg",
+        "table_caption": [
+            "Table 1. Quantitative comparison on D-NeRF Dataset. Comparison of our method with others on LPIPS and PSNR/SSIM. The Red text indicates the best and blue text is the second best result."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Type</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>T-NeRF [36]</td><td>N</td><td>29.51</td><td>0.95</td><td>0.08</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>30.75</td><td>0.96</td><td>0.07</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>32.67</td><td>0.97</td><td>0.04</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>30.50</td><td>0.95</td><td>0.07</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>30.54</td><td>0.96</td><td>0.05</td></tr><tr><td>Ours (803)</td><td>PC</td><td>32.68</td><td>0.97</td><td>0.04</td></tr></table>",
+        "bbox": [
+            99,
+            148,
+            442,
+            263
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Overall Loss The overall loss function used for optimization defined as follow, where  $w_{1\\sim 7}$  are weights to balance each component in the final coarse loss.",
+        "bbox": [
+            75,
+            276,
+            468,
+            321
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} ^ {\\text {p h o t o}} + w _ {1} \\mathcal {L} ^ {\\text {p t c}} + w _ {2} \\mathcal {L} ^ {\\text {b g}} + w _ {3} \\mathcal {L} ^ {\\text {f l o w}} + w _ {4} \\mathcal {L} ^ {\\text {v d i f f}} \\tag {14} \\\\ + w _ {5} \\mathcal {L} ^ {\\mathrm {t v}} \\left(\\mathbf {V} _ {\\sigma} ^ {\\text {C a n}}\\right) + w _ {6} \\mathcal {L} ^ {\\mathrm {t v}} \\left(\\mathbf {V} _ {\\text {f l o w}} ^ {t}\\right) + w _ {7} \\mathcal {L} ^ {\\mathrm {t v}} (\\mathbf {D}), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            86,
+            329,
+            468,
+            369
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training Strategy First, we propose progressive training, which starts training with images close to the canonical time and progressively adds images with farther time steps until all images are added. Second, we set up a coarse-to-fine training strategy. In the coarse stage, we set the color feature to be the color itself, without considering the ray directions. We compute a smaller bounding box with the proxy geometry learned from the coarse stage, which could filter a large portion of empty space for the fine stage training. The model trained in the fine stage is our final model, and we set the color features to be high dimensional features and model the ray direction dependency with  $F_{\\theta_4}$ .",
+        "bbox": [
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+            381,
+            470,
+            564
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            575,
+            209,
+            590
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Baselines and Evaluation Datasets",
+        "text_level": 1,
+        "bbox": [
+            76,
+            599,
+            375,
+            616
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baselines The methods compared in this paper are classified into three types. First, we compare methods which are non-canonical based (N), including NeRF[26], and T-NeRF[36]. Second, physical canonical based methods (PC) contain D-NeRF [36], NDVG[15] and Ours. These methods set their canonical space as one frame of the whole timeline by explicitly giving zeros to estimated flows at the canonical time. The canonical space of these methods should have reasonable physical 3D reconstructions of the scene at the canonical time. Third, non-physical canonical based methods (NPC) consists of NV[23], Nerfies[32], HyperNeRF[33] and TiNeuVox[10]. Their canonical space geometries do not necessarily have physical meanings.",
+        "bbox": [
+            75,
+            626,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "D-NeRF Dataset We evaluate our method on 8 dynamic scenes of D-NeRF [36] dataset. We report several common metrics for the evaluation: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and Learned Perceptual Image Patch Similarity (LPIPS) [65].",
+        "bbox": [
+            75,
+            824,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f6758833fec2e5cfc70883349c037dba9f7e548025613445e124bde7fd22d724.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative comparison on D-NeRF Dataset. We show some novel view synthesized images on the selected test set of the dataset. Comparing ours with ground truth, D-NeRF [36] and TiNeuVox [10]. Our model yields cleaner images with more details."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            503,
+            89,
+            890,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "HyerNeRF Dataset Besides synthetic datasets, we also conduct experiments on real scenes, proposed by HyperN-eRF [33]. This dataset uses a multi-view camera rig consisting of 2 phones to capture real unbounded scenes with challenging rigid and non-rigid deformations.",
+        "bbox": [
+            496,
+            371,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "NHR Dataset NHR [54] dataset capture dynamic human data using a multi-camera dome system with up to 80 cameras arranged on a cylinder. We conduct experiments on four scenes where the performers are in different clothing and perform different actions. We test with 100 frames of each scene, selecting  $90\\%$  views for training and  $10\\%$  views for testing.",
+        "bbox": [
+            496,
+            455,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Lego Complete Dataset The D-NeRF [36] dataset only contains 20 test images for each scene, and the evaluations of D-NeRF do not contain images in the canonical space. However, for physical canonical based methods (PC), canonical space geometry is important, as it affects images quality rendered at the canonical time and reflects the quality of flow estimation. Hence, we build a new dataset, named Lego Complete Dataset, which animates the object LEGO in D-NeRF dataset with 3 different motion patterns. For each scene, the test set is split into 3 categories to evaluate three abilities: space interpolation (rand views for each train time step), time interpolation (times between trained time steps), and canonical interpolation (rand views for canonical time step) abilities. For more details, please refer to our supp.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Besides the image quality, we also consider geometry precision by evaluating the depth of each test image to analyze the reconstructed geometry. For depth metrics, we use the relative error  $\\delta = \\max \\left(\\frac{d}{d_{\\mathrm{gt}}}, \\frac{d_{\\mathrm{gt}}}{d}\\right)$ , where  $d$  is the estimated depth and  $d_{\\mathrm{gt}}$  is the ground truth depth. We report the percentage of the pixels with  $\\delta <$  Threshold.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "16027",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/082dc662abd569ce8d5757695111ba4fcb14ae409f3b77cc7ef3818c8d745675.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Type</td><td colspan=\"2\">3D Printer</td><td colspan=\"2\">Broom</td><td colspan=\"2\">Chicken</td><td colspan=\"2\">Peel Banana</td><td colspan=\"2\">Mean</td></tr><tr><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>NeRF [26]</td><td>N</td><td>20.7</td><td>0.780</td><td>19.9</td><td>0.653</td><td>19.9</td><td>0.777</td><td>20.0</td><td>0.769</td><td>20.1</td><td>0.745</td></tr><tr><td>NV [23]</td><td>NPC</td><td>16.2</td><td>0.665</td><td>17.7</td><td>0.623</td><td>17.6</td><td>0.615</td><td>15.9</td><td>0.380</td><td>16.9</td><td>0.571</td></tr><tr><td>Nerfies [32]</td><td>NPC</td><td>20.6</td><td>0.830</td><td>19.2</td><td>0.567</td><td>26.7</td><td>0.943</td><td>22.4</td><td>0.872</td><td>22.2</td><td>0.803</td></tr><tr><td>HyperNeRF [33]</td><td>NPC</td><td>20.0</td><td>0.821</td><td>19.3</td><td>0.591</td><td>26.9</td><td>0.948</td><td>23.3</td><td>0.896</td><td>22.4</td><td>0.814</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>22.7</td><td>0.836</td><td>21.9</td><td>0.707</td><td>27.0</td><td>0.929</td><td>22.1</td><td>0.780</td><td>23.4</td><td>0.813</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>22.8</td><td>0.841</td><td>21.5</td><td>0.686</td><td>28.3</td><td>0.947</td><td>24.4</td><td>0.873</td><td>24.3</td><td>0.837</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>22.4</td><td>0.839</td><td>21.5</td><td>0.703</td><td>27.1</td><td>0.939</td><td>22.8</td><td>0.828</td><td>23.3</td><td>0.823</td></tr><tr><td>Ours (703)</td><td>PC</td><td>22.8</td><td>0.845</td><td>21.9</td><td>0.715</td><td>28.0</td><td>0.944</td><td>24.3</td><td>0.865</td><td>24.2</td><td>0.842</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d1ba8de626b061530fd13e2a8bca14b3dc5bb8ce2f8ba70fbc5a04be0dedb817.jpg",
+        "image_caption": [
+            "Figure 6. Qualitative comparison on HyperNeRF Dataset. Our results are closer to ground truth than other methods."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.2. Experimental Results",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation on D-NeRF Dataset We compared our method with the canonical-based backward flow methods D-NeRF [36], NDVG [15] and TiNeuVox [10] on D-NeRF Dataset. As shown in Table 1, our method achieves significant improvements in terms of all three metrics for physical canonical based methods. On average, our method improves PSNR by 2.18 compared with D-NeRF and 2.14 compared with NDVG. For non-physical canonical based methods, our method also achieves the best result. Ours show obviously better qualitative rendering quality compared with TiNeuVox-S  $(100^{3})$  [10] with even smaller voxel resolution. More detailed statistics are provided in supp.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also provide some visual comparisons in Fig. 5. Ours could recover accurate and detailed images, e.g., the helmet and arm in the top scene, and could also produce cleaner boundaries, e.g. the hand and feet in the bottom scene.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation on HyperNeRF Dataset We further compare our method with some highly related works on real scene dataset proposed by [33]. As shown in Table 2, our method achieves consistently better performance among physical canonical based methods. Our method has a voxel grid resolution limitation, due to we need to warp the whole voxel grid for rendering. Compared with other voxel grid based methods, our voxel grid resolution is limited to  $70^{3}$ , along with a  $160^{3}$  static voxel grid for background modeling. However, the performance of our method is still com",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/53c532b06c22bc7fbd0c4f62b69a9f919b26974d3caa9f2b6d9d4d34254067ba.jpg",
+        "image_caption": [
+            "Figure 7. Visual comparisons on NHR dataset."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "parable with SOTA of non-physical canonical based methods, proving the effectiveness of our forward flow design.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 6, we show visual comparisons with NDVG [15], and TiNueVox [10]. The forward flow helps to recover the correct structure of dynamic objects, like the eye and edges of the chicken (top left) and the broom (top right). The relatively low resolution may harm the ability to recover very fine details, like the patterns on the 3D printer compared with TiNueVox-B [10] (bottom right).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on NHR Dataset We also test our method on NHR dataset. Quantitative results are shown in Table 3, which shows ours achieving best results consistently. We show qualitative comparison in Fig. 7, and our method could render clean and detailed images.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "16028",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8f15e98d57c6a85785167d90e2826dac89caf84046d2dacee9da7878cc5670a4.jpg",
+        "table_caption": [
+            "Table 3. Quantitative comparison on NHR dataset. The red text indicates the best and blue text is the second best result."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">type</td><td colspan=\"3\">Sport 1</td><td colspan=\"3\">Sport 2</td><td colspan=\"3\">Sport 3</td><td colspan=\"3\">BacSKetball</td><td colspan=\"3\">Mean</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>TiNeuVox-S [10]</td><td>NPC</td><td>26.06</td><td>0.93</td><td>0.10</td><td>25.98</td><td>0.93</td><td>0.11</td><td>25.90</td><td>0.93</td><td>0.11</td><td>23.75</td><td>0.91</td><td>0.14</td><td>25.42</td><td>0.92</td><td>0.12</td></tr><tr><td>TiNeuVox-B [10]</td><td>NPC</td><td>26.44</td><td>0.93</td><td>0.10</td><td>26.68</td><td>0.94</td><td>0.10</td><td>26.09</td><td>0.93</td><td>0.11</td><td>25.06</td><td>0.92</td><td>0.12</td><td>26.07</td><td>0.93</td><td>0.11</td></tr><tr><td>NDVG [15]</td><td>PC</td><td>23.66</td><td>0.89</td><td>0.15</td><td>24.43</td><td>0.91</td><td>0.13</td><td>22.54</td><td>0.88</td><td>0.16</td><td>22.55</td><td>0.89</td><td>0.17</td><td>23.29</td><td>0.89</td><td>0.15</td></tr><tr><td>Ours</td><td>PC</td><td>27.71</td><td>0.95</td><td>0.08</td><td>27.89</td><td>0.95</td><td>0.08</td><td>27.57</td><td>0.94</td><td>0.08</td><td>24.85</td><td>0.93</td><td>0.11</td><td>27.00</td><td>0.94</td><td>0.09</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/4941ab757a210566f48ac43afb76cc2288d77bc9589b780f8ed0972e2080921d.jpg",
+        "table_caption": [
+            "Table 4. Quantitative comparison on Lego Complete Dataset. We report the average PSNR, LPIPS and the average relative depth error."
+        ],
+        "table_footnote": [
+            "${}^{1}$  not use the all total variation losses  ${}^{2}$  not up-sample the voxel grid  ${}^{3}$  not use the inpaint network"
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Type</td><td colspan=\"4\">Space Interpolation</td><td colspan=\"4\">Time Interpolation</td><td colspan=\"4\">Canonical Interpolation</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>23.98</td><td>0.15</td><td>98.720</td><td>99.328</td><td>24.18</td><td>0.15</td><td>98.854</td><td>99.378</td><td>17.36</td><td>0.23</td><td>97.341</td><td>98.868</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>28.12</td><td>0.06</td><td>99.655</td><td>99.853</td><td>28.19</td><td>0.06</td><td>99.749</td><td>99.953</td><td>19.90</td><td>0.11</td><td>94.828</td><td>97.560</td></tr><tr><td>Ours.notv (803)1</td><td>PC</td><td>27.58</td><td>0.07</td><td>99.758</td><td>99.958</td><td>27.63</td><td>0.07</td><td>99.788</td><td>99.966</td><td>23.56</td><td>0.13</td><td>99.238</td><td>99.820</td></tr><tr><td>Ours.noup (803)2</td><td>PC</td><td>26.11</td><td>0.09</td><td>99.596</td><td>99.981</td><td>26.19</td><td>0.09</td><td>99.636</td><td>99.983</td><td>24.64</td><td>0.10</td><td>99.230</td><td>99.925</td></tr><tr><td>Ours.noinp (803)3</td><td>PC</td><td>27.21</td><td>0.08</td><td>99.783</td><td>99.979</td><td>27.27</td><td>0.08</td><td>99.797</td><td>99.980</td><td>23.91</td><td>0.09</td><td>99.586</td><td>99.963</td></tr><tr><td>Ours (803)</td><td>PC</td><td>28.18</td><td>0.06</td><td>99.818</td><td>99.985</td><td>28.22</td><td>0.06</td><td>99.839</td><td>99.987</td><td>25.63</td><td>0.07</td><td>99.654</td><td>99.968</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.3. Method Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Flow Estimation and Canonical Space Geometry Since evaluating the estimated flow with ground truth is not practical, we choose to compare the reconstructed canonical geometry of physical canonical based methods. The idea is that if the canonical space is one frame of the whole timeline (like D-NeRF [36] and NDVG [15]), better flow estimation will result in better canonical scene geometry. We test these methods on Lego Complete Dataset, and all set the canonical space as the first frame of the image sequence.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Table 4, D-NeRF can not reconstruct the canonical radiance field well, since both the image and depth quality in canonical interpolation are significantly worse than those in space interpolation and time interpolation. NDVG [15] could recover much better images and geometry for other time steps, but the differences between canonical interpolation with the other two are even more significant. This means NDVG [15] has difficulty estimating correct backward flows. To render good quality images at other time steps, the correct geometries (depth) at these time steps are warped back into distorted canonical geometry due to incorrect backward flows.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This is the proof of our claim that the non-smooth and discontinuous nature of the backward flow deformation field makes it difficult to fit with smooth functions, especially for NDVG [15], which has limited MLP capacity for fast training. However, our method performs significantly better for both image quality and depth, and there are fewer variations between canonical, space, and temporal interpolations. This demonstrates the benefit of forward warping, which makes it easier for the deformation model to learn deformation flows from canonical time to other times.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We compare the canonical image of our method with DNeRF [36] in Fig. 8. Our method could recover the correct",
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+    {
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+        "img_path": "images/1f985130934b30e057231d66b56b973abf952c6a12fe0c2ea8c26764892415a2.jpg",
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+    {
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/4b962c34bbd99ff8819624efec03dbc50b14cfe9aa9c5db746362fe4a8551a77.jpg",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/009132b84cd615ba6fd7974062517b16b9c9c82cf6b76869b6ec2f1e30cea065.jpg",
+        "image_caption": [
+            "Figure 8. Canonical qualitative comparison. We show canonical radiance field comparison with D-NeRF [36]. Given the error map between the ground truth and rendered images, we can see that the canonical frame yielded by ours is closer to the ground truth. The results of D-NeRF are blurry and have large displacements."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
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+        "img_path": "images/15cfcfc1282ce768ae528372aa0695f28d579af1a43f568d9206ad49a019fe82.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/af472cd5bfb363221d60f0c406a20763f3e75fbe49d337df5e40737836a97d17.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "geometry and image details of the canonical frame. For example, the arms of the bucket produced by D-NeRF are at the \"mean\" positions of the whole trajectory, and ours recover the correct status.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Trajectory Visualization We show the learned DCT trajectories generated by our canonical trajectory field in Fig. 7 and Fig. 9. The canonical trajectory field is capable of recovering reasonable object point trajectories. Backward warping designs cannot track the motions of the same object point, so this is not a viable solution. With this feature, geometry constraints, motion models, and prior knowledge could be introduced in future work.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "16029",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/3a4054b1ca5aeb8a2d459c4598529c87b2414269dd74bbe6c8ba3f299c2d7736.jpg",
+        "image_caption": [
+            "Figure 9. Trajectory learned by the canonical trajectory field. Light blue is the canonical frame, the curve represents the historical motion trajectory. More videos can be found in supp."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            89,
+            84,
+            455,
+            359
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Regularization terms We study the effect of all regularization terms we proposed, including  $\\mathcal{L}^{\\mathrm{flow}}$ ,  $\\mathcal{L}^{\\mathrm{vdiff}}$  and  $\\mathcal{L}^{\\mathrm{tv}}$  in Table 5. We could observe that all these three regularization terms have positive effect on the performance, but the improvement is minor. This proves the improvement of our method compared with others come from the forward warping desgin we proposed in the paper. Also, backward flow based method NDVG [15] use similar regularization terms with ours, and our method has clear advantage compared with NDVG [15].",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Canonical setup In our method, we set canonical time to be the first frame for D-NeRF dataset to compare with physical canonical based method and the middle frame for HyperNeRF dataset for better performance. Setting canonical time to be the middle frame helps improving the performance as the state of the middle frame geometry is closer to other time steps compared with the first frame. To prove this, we set canonical time to be middel frame in Table 5 (can-time t at mid), and the PSNR improves slightly.",
+        "bbox": [
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+        "type": "text",
+        "text": "Photometric loss for  $\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}$  We use photometric terms on  $\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}$  to make sure the warped grid before inpainting could already render reasonable images. This makes sure the UNet is actually doing 'inpainting'. Also, we do observe inpainting and upsampling could refine grids. In Fig. 7 and Fig. 9, the trajectories are reasonable which means we do learn trajectories without inpainting overfitting. We also test w/o photometric terms of  $\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}$  in Table 5 (w/o  $\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}$  photo) and the performance drops as there is no direct supervise signal for trajectory learning.",
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+    {
+        "type": "text",
+        "text": "More Ablations We study the effects of the total variation losses, the up-sample strategy, and the inpaint network we proposed in Table 6. The total variation losses help to",
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+        "type": "table",
+        "img_path": "images/7edc7e6882555f8d710da4ccb2ec57b0e42eadf30aa87445562da0e2b1a37dc1.jpg",
+        "table_caption": [
+            "Table 5. Ablations. Mean of Hell Warrior, Mutant, Hook and Bouncing Balls in D-NeRF dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Ours</td><td>w/o Ltv</td><td>w/o Lflow</td><td>w/o Lvdiff</td><td>can-time t at mid</td><td>w/o VRup photo</td></tr><tr><td>PSNR</td><td>33.75</td><td>33.30</td><td>33.74</td><td>33.57</td><td>34.09</td><td>31.56</td></tr><tr><td>SSIM</td><td>0.979</td><td>0.974</td><td>0.978</td><td>0.977</td><td>0.980</td><td>0.966</td></tr><tr><td>LPIPS</td><td>0.040</td><td>0.048</td><td>0.039</td><td>0.041</td><td>0.037</td><td>0.057</td></tr></table>",
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+        "img_path": "images/d65d104b857f32175ff3c4fbfbd9ccd31ce766f68570c686c2111759216d8f5d.jpg",
+        "table_caption": [
+            "Table 6. Ablation of losses on two dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">D-NeRF</td><td colspan=\"2\">HyperNeRF</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>Ours.notv1</td><td>33.09</td><td>0.046</td><td>23.84</td><td>0.831</td></tr><tr><td>Ours.noup2</td><td>32.03</td><td>0.043</td><td>23.72</td><td>0.822</td></tr><tr><td>Ours.noinp3</td><td>31.78</td><td>0.044</td><td>23.25</td><td>0.814</td></tr><tr><td>Ours</td><td>32.68</td><td>0.037</td><td>24.23</td><td>0.842</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "improve visual quality (LPIPS) in D-NeRF dataset as it applies smoothness over the deformation and radiance space, but may harm the high-frequency details (PSNR) for some of the scenes in D-NeRF dataset. For HyperNeRF dataset, the total variation losses improve the results, as the camera settings are more challenging than D-NeRF dataset. However, this improvement is minor compared with the other two factors. Since the resolution is critical for voxel grid based method, up-sampling operation of inpaint network is vital to improve the performance. Finally, the inpaint network plays the most essential role among these three factors in our method. More ablations are provided in our supp.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper presents a canonical-based representation with forward warping for novel view synthesis of dynamic scenes. Our method models a static scene at the canonical field and forward warp this whole field to other time steps for dynamic scene rendering. To address the many-to-one and one-to-many mapping difficulties, we present a differentiable forward warping with an average splatting process and an inpaint network. Our proposed forward warping pipeline achieves SOTA performance on the public datasets and our newly built dataset, especially for canonical frames.",
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+    {
+        "type": "text",
+        "text": "Limitations and Future Directions Our current implementation is relatively memory-consuming, especially for real scenes. Also, the training speed is relatively slow (one day for each scene). Since we have a smooth trajectory field thanks to the forward warping, additional constraints and motion models could be introduced to learn better trajectories in future works.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements This research was supported in part by the National Natural Science Foundation of China (Grant Nos. 62271410, 62293482, 62202409), the Fundamental Research Funds for the Central Universities, and Shenzhen Science and Technology Program (Grant No. RCBS20221008093241052).",
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+        "text": "References",
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+            "content": "Xiang Guo\\(^{1}\\), Jiadai Sun\\(^{1,3}\\), Yuchao Dai\\(^{1}\\), Guanying Chen\\(^{2}\\), Xiaqing Ye\\(^{3}\\), Xiao Tan\\(^{3}\\), Errui Ding\\(^{3}\\), Yumeng Zhang\\(^{3}\\), Jingdong Wang\\(^{3}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.142,
+                0.241,
+                0.828,
+                0.26
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>Northwestern Polytechnical University, <sup>2</sup>FNii and SSE, CUHK-Shenzhen, <sup>3</sup>Baidu Inc."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.32,
+                0.314,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.353,
+                0.474,
+                0.701
+            ],
+            "angle": 0,
+            "content": "This paper proposes a neural radiance field (NeRF) approach for novel view synthesis of dynamic scenes using forward warping. Existing methods often adopt a static NeRF to represent the canonical space, and render dynamic images at other time steps by mapping the sampled 3D points back to the canonical space with the learned backward flow field. However, this backward flow field is non-smooth and discontinuous, which is difficult to be fitted by commonly used smooth motion models. To address this problem, we propose to estimate the forward flow field and directly warp the canonical radiance field to other time steps. Such forward flow field is smooth and continuous within the object region, which benefits the motion model learning. To achieve this goal, we represent the canonical radiance field with voxel grids to enable efficient forward warping, and propose a differentiable warping process, including an average splatting operation and an inpaint network, to resolve the many-to-one and one-to-many mapping issues. Thorough experiments show that our method outperforms existing methods in both novel view rendering and motion modeling, demonstrating the effectiveness of our forward flow motion modeling. Project page: https://npucvr.github.io/ForwardFlowDNeRF."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.733,
+                0.21,
+                0.749
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.759,
+                0.47,
+                0.851
+            ],
+            "angle": 0,
+            "content": "Novel view synthesis (NVS) is a challenging and longstanding problem in computer vision and graphics, which has many applications in virtual reality, augmented reality, data augmentation, image editing, etc. Recently, differentiable neural rendering [26, 30, 59] has been introduced into this area. In particular, the neural radiance field (NeRF) [26]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.305,
+                0.648,
+                0.436
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.648,
+                0.306,
+                0.892,
+                0.44
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.444,
+                0.685,
+                0.537
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.704,
+                0.444,
+                0.88,
+                0.537
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.545,
+                0.895,
+                0.684
+            ],
+            "angle": 0,
+            "content": "Figure 1. Comparison of backward flow and forward flow. This figure shows an example of backward and forward flow changes. (a) An example of dynamic scene. (b) With the bucket lifting up, different types of points cover the green point \\(\\mathbf{p}\\), which needs very different backward flows to map this point back to canonical space. (d) shows the norm changes of the backward flow, which is not smooth. (c) On the other hand, the forward flow of position \\(\\mathbf{q}\\), which maps the constant object point from canonical space to other times, is smooth and continuous. (e) shows the norm changes of the forward flow."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.7,
+                0.892,
+                0.776
+            ],
+            "angle": 0,
+            "content": "promotes this area significantly and attracts lots of interest within a short time. NeRF [26] produces realistic images by representing the 3D world with a multi-layer perceptron (MLP), which maps the input 3D coordinates and 2D view direction to target density and color."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "While the original NeRF [26] can only model static scenes, a series of works extend the NeRF-based framework from static to dynamic scenes [9, 13, 19, 32, 36, 49, 51, 55]. One of the promising directions is using a canonical space representation [15, 36, 49]. This representation sets one of the time steps as canonical time and models the static scene with a canonical radiance field. To render images at other time steps, a deformation field is used to estimate the"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.076,
+                0.863,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "† Corresponding author (daiyuchao@nwpu.edu.cn). The first three authors also with the Shaanxi Key Laboratory of Information Acquisition and Processing."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "16022"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.288
+            ],
+            "angle": 0,
+            "content": "backward flow for moving the 3D points from the current time step back to the canonical time step. Although the canonical-based representation with the backward flow is easy to implement, the backward flow field is non-smooth and discontinuous. As shown in Fig. 1(b), for a fixed 3D position along the timeline, there will be different types of points covering the position \\(\\mathbf{p}\\), which needs discontinuous flows to map them back to canonical space (Fig. 1(d)). So the backward flow cannot be fitted well with commonly used smooth motion models (MLP, for example). Also, distortions are introduced to the static canonical space geometry due to the failure of the motion model, as shown in Fig. 8."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.289,
+                0.473,
+                0.518
+            ],
+            "angle": 0,
+            "content": "To solve the problem of backward flow, we propose using forward flow as the deformation model. Instead of warping the sampled points on image rays at other time steps back to the canonical time and rendering at the canonical space, we propose to warp the whole canonical radiance field from the canonical time to other time steps using forward deformation flow and render at corresponding time steps. In this way, the forward flow estimated by the deformation model will be smooth and continuous for the same 3D position along the timeline (Fig. 1(c) and (e)). Note that SNARF [7] has also used forward warping based on an inverse skinning model, but it is designed for dynamic human modeling and cannot be used in general scenes. In this paper, we aim to achieve forward warping for general scenes, which means we must warp the whole space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.518,
+                0.473,
+                0.775
+            ],
+            "angle": 0,
+            "content": "However, introducing forward warping into the canonical space based NeRF methods is not straightforward as there are three main problems to be solved. First, the traditional canonical radiance field in existing methods cannot be warped explicitly, since the radiance field is represented as a continuous function parameterized by an MLP. To solve this problem, we propose to use the voxel grid to represent the canonical radiance field as it is finite and discrete. Recent voxel-based methods [27,44,62] have proven the effectiveness of this representation. The other two problems are the many-to-one and one-to-many mapping issues brought by the inherent property of the forward warping operation. To address them, we propose a differentiable forward warping method consisting of an average splatting operation and an inpaint network to solve the many-to-one and one-to-many issue, respectively. Extensive experiments have been conducted to verify the effectiveness of our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.776,
+                0.451,
+                0.792
+            ],
+            "angle": 0,
+            "content": "Our key contributions can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.795,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "- To the best of our knowledge, we are the first to investigate forward warping in dynamic view synthesis for general scenes. We propose a novel canonical based NeRF with forward flow motion modeling for dynamic view synthesis. Thanks to the forward flow field, our method can better represent the object motions, and explicitly recover the trajectory of a surface point."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.092,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "- We introduce voxel grid based canonical radiance field to enable reasonable computation of forward warping, and propose a differentiable forward warping method, including an average splatting operation and an inpaint network, to solve the many-to-one and one-to-many issues of forward warping."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.183,
+                0.894,
+                0.243
+            ],
+            "angle": 0,
+            "content": "- Experiments on multiple datasets show that our method outperforms existing methods on the D-NeRF [36] dataset, Hypernerf [33] dataset, NHR [54] dataset and our proposed dataset."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.092,
+                0.894,
+                0.243
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.261,
+                0.651,
+                0.278
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.288,
+                0.895,
+                0.516
+            ],
+            "angle": 0,
+            "content": "Novel View Synthesis (NVS) is a long-standing task in both computer vision and graphics [4, 6, 14, 18], and surveys of recent methods can be found in [42, 46, 47]. Some methods require to reconstruct an explicit 3D model to represent the scene, such as point clouds [1], voxels or meshes [16, 40, 41, 48]. Then novel images from arbitrary views can be rendered from this geometry. Another methods try to estimate depth map through multi-view geometry, and then aggregate features from multiple frames through the co-visibility, such as [8, 11, 17, 34, 40, 41, 57]. Recently, neural implicit representations have shown great promise for novel view synthesis and 3D modeling. In this section, we focus more on the neural implicit rendering methods and mainly summarize these schemes according to whether they can handle dynamic scenes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.519,
+                0.895,
+                0.777
+            ],
+            "angle": 0,
+            "content": "NVS for Static Scenes NeRF [26], as a seminal work, uses MLPs to model a 5D radiance field, which can render impressive view synthesis for static scenes captured. Numerous subsequent works have extended NeRF to kinds of scenarios, such as larger and unbounded scenes [25, 39, 45, 56, 64], relighting [3, 43, 58, 66], incorporating anti-aliasing for multi-scale rendering [2], and generalization ability [5, 50, 52, 63]. In addition, some methods are devoted to more efficient neural rendering and optimization in NeRF-like framework, such as [20, 22, 24, 28, 35, 62] focus more on efficient sampling along each ray for color accumulation, [37, 38] subdivide the scene into multiple cells for efficient processing, and [27, 44, 61] exploit voxel-grid representation to speed up the optimization of radiance field. However, these methods are mainly applicable to static scenes, leaving out the scenes with dynamic objects, which are actually more extensive and practical."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.897,
+                0.903
+            ],
+            "angle": 0,
+            "content": "NVS for Dynamic Scenes There are several works that extend NeRF from static scenes to dynamic scenes with nonrigid deformable objects. One feasible way is to build a 4D spatial-temporal representation. For example, Yoon et al. [60] combine single-view depth and depth from multiview stereo to render virtual views with 3D warping. Gao et al. [13] use a time-invariant model (static) and a time-varying model (dynamic) to represent the scenes, and reg-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "16023"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.179,
+                0.09,
+                0.394,
+                0.103
+            ],
+            "angle": 0,
+            "content": "1. Voxel Grid Based Canonical Field"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.557,
+                0.092,
+                0.766,
+                0.105
+            ],
+            "angle": 0,
+            "content": "2. Differentiable Forward Warping"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.102,
+                0.107,
+                0.46,
+                0.362
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.46,
+                0.107,
+                0.867,
+                0.362
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.372,
+                0.892,
+                0.486
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overview of our proposed method. a) We represent a static scene at canonical time with a voxel grid based radiance field for density&color and a voxel grid based trajectory field for deformations; b) We propose to first forward warp canonical radiance field using the forward flow by average splating; c) We then inpaint the warped radiance field using a inpaint network; Specifically, 1. Voxel Grid Based Canonical Field contains two models. The canonical radiance field \\(\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}}\\) is estimated by a Light MLP which takes canonical radiance feature \\(\\mathbf{V}_{\\mathrm{Rf}}^{\\mathrm{Can}}\\) and corresponding 3D coordinates \\(\\mathbf{V}_{\\mathrm{p}}^{\\mathrm{Can}}\\) as input. The canonical trajectory field \\(\\mathbf{V}_{\\mathrm{T}}^{\\mathrm{Can}}\\) is estimated by another Light MLP which takes deformation feature and coordinates as input. The deformation flow \\(\\mathbf{V}_{\\mathrm{flow}}^{t}\\) from canonical to time \\(t\\) can then be obtained; 2. Differential Forward Warping first warp \\(\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}}\\) to get radiance field \\(\\mathbf{V}_{\\mathrm{R}}^{t}\\) at time \\(t\\). Then, the \\(\\mathbf{V}_{\\mathrm{R}}^{t}\\) is inpainted by a inpaint network, which is \\(\\mathbf{V}_{\\mathrm{R_{inp}}}^{t}\\); 3. Volume Rendering render colors of rays at time \\(t\\) based on \\(\\mathbf{V}_{\\mathrm{R_{inp}}}^{t}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.47,
+                0.657
+            ],
+            "angle": 0,
+            "content": "ularize the dynamic model by scene flow estimation. NeRF-Flow [9] learns a 4D spatial-temporal representation of a dynamic scene from a set of RGB images. Xian et al. [55] build a 4D space-time irradiance field to map a spatial-temporal location to the emitted color and volume density. Similarly, NSFF [19] models the dynamic scene as a time-variant continuous function of appearance, geometry, and 3D scene motion. DCT-NeRF [51] uses the Discrete Cosine Transform (DCT) to capture dynamic motion, i.e. learning smooth and stable trajectories over time for each point in space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.659,
+                0.47,
+                0.854
+            ],
+            "angle": 0,
+            "content": "On the other hand, D-NeRF [36], Nerfies [32], HyperNeRF [33] and NR-NeRF [49] use a static canonical radiance field to capture geometry and appearance, and then learn a deformation/displacement field at each time step w.r.t. the canonical space. Specifically, to render an image at an arbitrary time step, a deformation field is used to estimate backward scene flow, moving 3D points from the current time step back to the canonical step. However, for the same 3D location along the timeline, the backward flow field is not guaranteed to be smooth and continuous. As a result, the canonical geometry usually has distortions and resembles the mean shape of a moving object. We focus on solving the problem of backward flow in this paper."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Along with the two main directions, there is a trend to speed up the training of dynamic NeRF, which is based on voxel grid representation. TiNeuVox [10] models the de"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.892,
+                0.674
+            ],
+            "angle": 0,
+            "content": "formation using a tiny MLP and uses multi-distance interpolation to get the feature for the radiance network which estimates the density and color. V4D [12] uses the 3D feature voxel to model the 4D radiance field with additional time dimension concatenated and proposes look-up tables for pixel-level refinement. Although V4D mainly focuses on improving image quality, the training speed is not significant compared to TiNeuVox. DeVRF [21] also builds on voxel-grid representation, which proposes to use multi-view data to overcome the nontrivial problem of the monocular setup. Multi-view data simplifies the learning of motion and geometry compared with others using monocular images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.691,
+                0.59,
+                0.706
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Motivation Backward-warping based methods [15, 36] propose a network \\( f_{t\\to \\mathrm{Can}} = F(p,t) \\) to estimate the deformation flow \\( f_{t\\rightarrow \\mathrm{Can}} \\) which moves the point at the position \\( p \\) from other time steps \\( t \\) back to canonical time Can. However, for the same position \\( p \\), at different time steps \\( ts \\), there could be different object points or even the empty point at this position, as shown in Fig. 1. This means the deformation flow \\( f_{t\\to \\mathrm{Can}} \\) is non-smooth and discontinuous along the timeline for a fixed position \\( p \\). This could introduce difficulties for motion learning and produce distortion in the canonical radiance field, because the backward flow network has limited capacities in learning a correct non-smooth and dis"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16024"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.093,
+                0.468,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.208,
+                0.471,
+                0.265
+            ],
+            "angle": 0,
+            "content": "Figure 3. Two issues of the forward warping. Many-to-one: multiple positions in the source correspond to the same position in the target. One-to-many: one position in the source corresponds to multiple positions in the target, causing holes if warping naively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.271,
+                0.47,
+                0.392
+            ],
+            "angle": 0,
+            "content": "continuous deformation field. On the other hand, our proposed forward warping strategy estimates the deformation \\( f_{\\mathrm{Can} \\to t} \\) from the canonical time to another time step of a 3D point in canonical space. The set of the deformation flows of one position along the timeline is actually the trajectory of this point. This guarantees the flows to be smooth and continuous along the timeline as we assume the motions in reality have these properties."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.395,
+                0.471,
+                0.576
+            ],
+            "angle": 0,
+            "content": "Method Overview We model a static scene at the canonical time using the voxel grid representation with a canonical radiance field and a canonical trajectory field. To synthesize dynamic images, we propose to forward warp the canonical radiance field to corresponding time steps and render the images using volume rendering based on the warped radiance field. Fig. 2 shows the overview of our method. In the following, we will introduce three main components of our method: voxel grid based canonical field, differentiable forward warping, and volume rendering. Finally, the model optimization is represented, including the proposed loss functions and training strategy."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.587,
+                0.375,
+                0.601
+            ],
+            "angle": 0,
+            "content": "3.1. Voxel Grid Based Canonical Field"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.613,
+                0.47,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Canonical Radiance Field To warp a static scene in canonical time to other time steps using forward warping, the radiance field should be represented by finite 3D points. The original heavy MLP in NeRF [26] is not practical, as we cannot query infinite 3D points in the canonical space. Inspired by recent works [27,44,61] on voxel grid presentations, we propose to use a learnable voxel radiance feature grid \\(\\mathbf{V}_{\\mathrm{Rf}}^{\\mathrm{Can}}\\) and a lightweight MLP network \\(F_{\\theta_1}\\) to model the radiance of the static scene as shown in Fig. 2. The canonical radiance field is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.185,
+                0.775,
+                0.469,
+                0.795
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {V} _ {\\mathrm {R}} ^ {\\text {C a n}} = F _ {\\theta_ {1}} \\left(\\mathbf {V} _ {\\mathrm {p}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\mathrm {R f}} ^ {\\text {C a n}}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.807,
+                0.469,
+                0.868
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}} = \\{\\mathbf{V}_{\\sigma}^{\\mathrm{Can}}, \\mathbf{V}_{\\mathrm{cf}}^{\\mathrm{Can}}\\}\\) consists of density voxel grid \\(\\mathbf{V}_{\\sigma}^{\\mathrm{Can}}\\) and color feature voxel grid \\(\\mathbf{V}_{\\mathrm{cf}}^{\\mathrm{Can}}\\). \\(\\mathbf{V}_{\\mathrm{p}}^{\\mathrm{Can}}\\) are the 3D coordinates of the voxel grid in canonical space, embedded according to NeRF [26]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Canonical Trajectory Field We propose to use Discrete Cosine Transform (DCT) [51] to represent the trajectory of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "a 3D point, which ensures the smoothness of the motion. Similar to canonical radiance field, we also use a deformation feature grid \\(\\mathbf{V}_{\\mathrm{Df}}^{\\mathrm{Can}}\\) and a lightweight MLP network \\(F_{\\theta_2}\\) to model the canonical trajectory field, which is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.608,
+                0.162,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {V} _ {T} ^ {\\text {C a n}} = F _ {\\theta_ {2}} \\left(\\mathbf {V} _ {\\mathrm {p}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\mathrm {D f}} ^ {\\text {C a n}}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.193,
+                0.894,
+                0.239
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{V}_T^{\\mathrm{Can}}\\) contains the DCT coefficients of the voxels. Given time step \\(t\\), we could get the deformation flow of these voxels from canonical to time step \\(t\\) by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.527,
+                0.25,
+                0.892,
+                0.268
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {V} _ {\\text {f l o w}} ^ {t} = f _ {\\mathrm {D C T} ^ {- 1}} \\left(\\mathbf {V} _ {T} ^ {\\text {C a n}}, t\\right) - f _ {\\mathrm {D C T} ^ {- 1}} \\left(\\mathbf {V} _ {T} ^ {\\text {C a n}}, \\text {C a n}\\right), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.279,
+                0.892,
+                0.31
+            ],
+            "angle": 0,
+            "content": "where \\( f_{\\mathrm{DCT}^{-1}} \\) is the inverse DCT transform of the DCT coefficients as described in TrajectoryNeRF [51]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.318,
+                0.787,
+                0.334
+            ],
+            "angle": 0,
+            "content": "3.2. Differentiable Forward Warping"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.341,
+                0.892,
+                0.538
+            ],
+            "angle": 0,
+            "content": "Forward warping has two major issues: many-to-one and one-to-many. Fig. 3 shows a simple example, where we aim to warp the source to the target using forward warping: a) Many-to-one: if a circle shrinks, there will be multiple positions corresponding to one position from the source to the target. b) One-to-many: if a circle expands, multiple positions in the target will correspond to the same position in the source, which leaves holes of the target if we warp the source to target naively. For the many-to-one issue, we propose to use the average splating to fuse multiple values into one. For the one-to-many issue, we use an inpaint network to inpaint the missing positions of the warped grids. More details are in the following sections."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.54,
+                0.892,
+                0.678
+            ],
+            "angle": 0,
+            "content": "Average Splatting We propose to fuse possible multiple values from the source grid that are mapped into the same voxel position of the target grid, motivated by Softmax-splatting [31]. Specifically, we propose a simple yet effective method that calculates the \"average\" of these values with a trilinear kernel. Formally, suppose that we need to warp the source grid \\(\\mathbf{V}^{\\mathrm{S}}\\) to target grid \\(\\mathbf{V}^{\\mathrm{T}}\\) by the flow \\(f_{\\mathrm{S}\\rightarrow \\mathrm{T}}\\), and \\(\\mathbf{p}\\), \\(\\mathbf{q}\\) are indexes of a voxel grid. We define \\(\\mathbf{V}^{\\mathrm{T}} = F_{\\mathrm{warp}}(\\mathbf{V}^{\\mathrm{S}}, f_{\\mathrm{S}\\rightarrow \\mathrm{T}})\\) as follows,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.587,
+                0.688,
+                0.892,
+                0.728
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {V} ^ {\\mathrm {T}} [ \\mathbf {p} ] = \\frac {\\sum_ {\\forall \\mathbf {q} \\in \\mathbf {V} ^ {\\mathrm {s}}} b [ \\mathbf {u} ] \\cdot \\mathbf {V} ^ {\\mathrm {S}} [ \\mathbf {q} ]}{\\sum_ {\\forall \\mathbf {q} \\in \\mathbf {V} ^ {\\mathrm {s}}} b [ \\mathbf {u} ]}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.561,
+                0.731,
+                0.891,
+                0.753
+            ],
+            "angle": 0,
+            "content": "\\[\nb [ \\mathbf {u} ] = \\prod \\max  (0, 1 - | \\mathbf {u} _ {i} |), i \\in \\{x, y, z \\}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.612,
+                0.756,
+                0.891,
+                0.772
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {u} = \\left(\\mathbf {q} + f _ {\\mathrm {S} \\rightarrow \\mathrm {T}} [ \\mathbf {q} ]\\right) - \\mathbf {p}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.784,
+                0.89,
+                0.812
+            ],
+            "angle": 0,
+            "content": "where \\(x, y, z\\) are three axes of the voxel grid, and \\(\\mathbf{u}_i \\in \\mathbb{R}\\) is one element of the vector \\(\\mathbf{u} \\in \\mathbb{R}^3\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.814,
+                0.88,
+                0.829
+            ],
+            "angle": 0,
+            "content": "So, we warp the canonical radiance field to time step \\(t\\) by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.608,
+                0.839,
+                0.891,
+                0.858
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {V} _ {\\mathrm {R}} ^ {t} = F _ {\\text {w a r p}} \\left(\\mathbf {V} _ {\\mathrm {R}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\text {f l o w}} ^ {t}\\right). \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Inpaint Network Another issue of forward warping is one-to-many, which leaves holes in the voxel grid after"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16025"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.09,
+                0.468,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.228,
+                0.47,
+                0.271
+            ],
+            "angle": 0,
+            "content": "Figure 4. Inpaint network. It consists of a 3D U-Net structure and an up-sampling layer, which could inpaint and upsample the input voxel grid."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.282,
+                0.468,
+                0.357
+            ],
+            "angle": 0,
+            "content": "warping. To resolve this issue, we propose building an inpaint network to fill these holes. As shown in Fig. 4, we modify a 3D U-Net structure network [53] followed by an up-sampling layer, which is \\(\\mathbf{V}_{\\mathrm{R_{Inp}}}^{t} = F_{\\theta_{3}}(\\mathbf{V}_{\\mathrm{R}}^{t})\\), where \\(\\mathbf{V}_{\\mathrm{R_{Inp}}}^{t}\\) is the inpainted and up-sampled voxel grid."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.36,
+                0.468,
+                0.555
+            ],
+            "angle": 0,
+            "content": "This structure helps encoding layers to learn information from local neighboring voxels and decoding layers to recover the original resolution with filled content. We only feed the warped voxel grid to the inpaint network, which has no access to temporal information. Thus, the inpaint network can not learn to warp, limiting its ability only to inpainting. Since warping operations and the inpaint network are relatively expensive to compute, we propose to attach an up-sample layer after the U-Net structure. In this way, we could warp the grids with a low resolution to save time and memory, while rendering with a higher resolution for better image quality. The up-sample layer consists of a interpolation layer, convolution layers, and activation layers."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.572,
+                0.258,
+                0.589
+            ],
+            "angle": 0,
+            "content": "3.3. Volume Rendering"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.598,
+                0.468,
+                0.734
+            ],
+            "angle": 0,
+            "content": "After we get the radiance voxel grid at time \\(t\\), the pixel colors of the image rays can be rendered using volume rendering techniques [26]. Given a ray \\(\\mathbf{r}(w) = \\mathbf{o} + w\\mathbf{d}\\) emitted from the camera center \\(\\mathbf{o}\\) with view direction \\(\\mathbf{d}\\) through a given pixel on the image plane, we render the corresponding pixel color \\(\\mathbf{C}_{\\mathrm{Inp}}(\\mathbf{r}) = F_{\\mathrm{render}}(\\mathbf{V}_{\\mathrm{R_{inp}}}^{t},\\mathbf{r})\\). To do this, we get all 3D points \\(\\mathbf{p}\\) that the ray intersects with voxel grids. Next, trilinear interpolation is applied to obtain the density and color feature of each 3D point."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.751,
+                0.468,
+                0.769
+            ],
+            "angle": 0,
+            "content": "\\[\n(\\sigma , \\mathbf {c} _ {\\mathbf {f}}) = F _ {\\text {i n t e r}} \\left(\\mathbf {V} _ {\\mathrm {R} _ {\\mathrm {l n p}}} ^ {t}, \\mathbf {p}\\right). \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.785,
+                0.37,
+                0.8
+            ],
+            "angle": 0,
+            "content": "Then, we get the color of this 3D point \\(\\mathbf{p}\\) by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.163,
+                0.815,
+                0.468,
+                0.856
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {c} = \\left\\{ \\begin{array}{l l} \\mathbf {c} _ {\\mathbf {f}} & \\text {i f} \\mathbf {c} _ {\\mathbf {f}} \\in \\mathbb {R} ^ {3}, \\\\ F _ {\\theta_ {4}} \\left(\\mathbf {c} _ {\\mathbf {f}}, \\mathbf {d}\\right) & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.871,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(F_{\\theta_4}\\) is a small MLP network that is used to produce colors that depend on the direction of the ray."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.092,
+                0.814,
+                0.107
+            ],
+            "angle": 0,
+            "content": "Finally, the pixel color could be rendered by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.534,
+                0.116,
+                0.892,
+                0.143
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {C} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T \\left(w _ {k}\\right) \\alpha \\left(\\sigma \\left(w _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} \\left(w _ {k}\\right), \\tag {10}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.569,
+                0.146,
+                0.892,
+                0.179
+            ],
+            "angle": 0,
+            "content": "\\[\nT \\left(w _ {k}\\right) = \\exp \\left(- \\sum_ {j = 1} ^ {k - 1} \\sigma \\left(w _ {j}\\right) \\delta_ {j}\\right), \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.188,
+                0.892,
+                0.233
+            ],
+            "angle": 0,
+            "content": "where \\(K\\) is the number of sampled points along the ray, \\(\\delta_{k}\\) is the distance between adjacent samples along the ray, and \\(\\alpha (\\sigma (w_k)\\delta_k) = 1 - \\exp (-\\sigma (w_k)\\delta_k)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.234,
+                0.892,
+                0.299
+            ],
+            "angle": 0,
+            "content": "Note that the warped radiance grid \\(\\mathbf{V}_{\\mathrm{R}}^{t}\\) should also render reasonable images. So we directly up-sample \\(\\mathbf{V}_{\\mathrm{R}}^{t}\\) to get \\(\\mathbf{V}_{\\mathrm{RUp}}^{t}\\) without inpainting, and render the corresponding pixel color \\(\\mathbf{C}_{\\mathrm{Up}}(\\mathbf{r}) = F_{\\mathrm{render}}(\\mathbf{V}_{\\mathrm{RUp}}^{t},\\mathbf{r})\\)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.307,
+                0.692,
+                0.323
+            ],
+            "angle": 0,
+            "content": "3.4. Model Optimization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.33,
+                0.892,
+                0.393
+            ],
+            "angle": 0,
+            "content": "To optimize the model, we design a series of loss functions. Photometric Loss First, the most important loss is the photometric loss, which is the mean square error (MSE) of the rendered color and ground truth color \\(\\mathbf{C}_{\\mathrm{gt}}(\\mathbf{r})\\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.555,
+                0.403,
+                0.891,
+                0.478
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} ^ {\\mathrm {p h o t o}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\| \\mathbf {C} _ {\\operatorname {I n p}} (\\mathbf {r}) - \\mathbf {C} _ {\\mathrm {g t}} (\\mathbf {r}) \\| _ {2} ^ {2} \\\\ + \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\| \\mathbf {C} _ {\\mathrm {U p}} (\\mathbf {r}) - \\mathbf {C} _ {\\mathrm {g t}} (\\mathbf {r}) \\| _ {2} ^ {2}, \\tag {12} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.488,
+                0.818,
+                0.503
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{R}\\) is the set of rays sampled in one batch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.503,
+                0.892,
+                0.594
+            ],
+            "angle": 0,
+            "content": "Following DVGO [44], we use \\(\\mathcal{L}^{\\mathrm{ptc}}\\) to directly supervise the color of sampled points. The intuition is that sampled points with larger weights contribute more to the rendered color. Also, we use the background entropy loss \\(\\mathcal{L}^{\\mathrm{bg}}\\) to encourage the densities concentrating on either the foreground or the background."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.597,
+                0.892,
+                0.672
+            ],
+            "angle": 0,
+            "content": "Inpaint Network Loss As the inpaint network is used to complete the warped voxel grids, the output of the inpaint network should be close to the input. Therefore, we propose to use the L1 norm of the difference between the input and output of the inpaint network."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.605,
+                0.681,
+                0.891,
+                0.709
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} ^ {\\mathrm {v d i f f}} = \\left\\| \\mathbf {V} _ {\\mathrm {R} _ {\\text {I n p}}} ^ {t} - \\mathbf {V} _ {\\mathrm {R} _ {\\mathrm {U p}}} ^ {t} \\right\\| _ {1}. \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.72,
+                0.891,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Regularization Terms Since modeling the appearance and motion of a dynamic scene from monocular images is a nontrivial problem, we propose a series of regularization terms."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.766,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "First, we encourage most 3D points in canonical space to be static by introducing \\(\\mathcal{L}^{\\mathrm{flow}}\\) to be the L1 norm of \\(\\mathbf{V}_{\\mathrm{flow}}^{t}\\). Second, denoting \\(\\mathcal{L}^{\\mathrm{tv}}\\) as the total variation function. We compute \\(\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{V}_{\\sigma}^{\\mathrm{Can}})\\) to ensure the spatial smoothness of the density in canonical space, and introduce \\(\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{V}_{\\mathrm{flow}}^{t})\\) to encourage the spatial smoothness of the motions. Finally, inspired by RegNeRF [29], we render depths \\(\\mathbf{D}\\) of image patches sampled from random views and minimize their total variations \\(\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{D})\\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16026"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.099,
+                0.47,
+                0.141
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative comparison on D-NeRF Dataset. Comparison of our method with others on LPIPS and PSNR/SSIM. The Red text indicates the best and blue text is the second best result."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.1,
+                0.15,
+                0.444,
+                0.264
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Type</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>T-NeRF [36]</td><td>N</td><td>29.51</td><td>0.95</td><td>0.08</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>30.75</td><td>0.96</td><td>0.07</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>32.67</td><td>0.97</td><td>0.04</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>30.50</td><td>0.95</td><td>0.07</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>30.54</td><td>0.96</td><td>0.05</td></tr><tr><td>Ours (803)</td><td>PC</td><td>32.68</td><td>0.97</td><td>0.04</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.277,
+                0.47,
+                0.322
+            ],
+            "angle": 0,
+            "content": "Overall Loss The overall loss function used for optimization defined as follow, where \\( w_{1\\sim 7} \\) are weights to balance each component in the final coarse loss."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.087,
+                0.33,
+                0.47,
+                0.37
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} ^ {\\text {p h o t o}} + w _ {1} \\mathcal {L} ^ {\\text {p t c}} + w _ {2} \\mathcal {L} ^ {\\text {b g}} + w _ {3} \\mathcal {L} ^ {\\text {f l o w}} + w _ {4} \\mathcal {L} ^ {\\text {v d i f f}} \\tag {14} \\\\ + w _ {5} \\mathcal {L} ^ {\\mathrm {t v}} \\left(\\mathbf {V} _ {\\sigma} ^ {\\text {C a n}}\\right) + w _ {6} \\mathcal {L} ^ {\\mathrm {t v}} \\left(\\mathbf {V} _ {\\text {f l o w}} ^ {t}\\right) + w _ {7} \\mathcal {L} ^ {\\mathrm {t v}} (\\mathbf {D}), \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.382,
+                0.471,
+                0.565
+            ],
+            "angle": 0,
+            "content": "Training Strategy First, we propose progressive training, which starts training with images close to the canonical time and progressively adds images with farther time steps until all images are added. Second, we set up a coarse-to-fine training strategy. In the coarse stage, we set the color feature to be the color itself, without considering the ray directions. We compute a smaller bounding box with the proxy geometry learned from the coarse stage, which could filter a large portion of empty space for the fine stage training. The model trained in the fine stage is our final model, and we set the color features to be high dimensional features and model the ray direction dependency with \\( F_{\\theta_4} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.576,
+                0.21,
+                0.592
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.601,
+                0.376,
+                0.617
+            ],
+            "angle": 0,
+            "content": "4.1. Baselines and Evaluation Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.627,
+                0.47,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Baselines The methods compared in this paper are classified into three types. First, we compare methods which are non-canonical based (N), including NeRF[26], and T-NeRF[36]. Second, physical canonical based methods (PC) contain D-NeRF [36], NDVG[15] and Ours. These methods set their canonical space as one frame of the whole timeline by explicitly giving zeros to estimated flows at the canonical time. The canonical space of these methods should have reasonable physical 3D reconstructions of the scene at the canonical time. Third, non-physical canonical based methods (NPC) consists of NV[23], Nerfies[32], HyperNeRF[33] and TiNeuVox[10]. Their canonical space geometries do not necessarily have physical meanings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.903
+            ],
+            "angle": 0,
+            "content": "D-NeRF Dataset We evaluate our method on 8 dynamic scenes of D-NeRF [36] dataset. We report several common metrics for the evaluation: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and Learned Perceptual Image Patch Similarity (LPIPS) [65]."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.09,
+                0.892,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.284,
+                0.894,
+                0.354
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative comparison on D-NeRF Dataset. We show some novel view synthesized images on the selected test set of the dataset. Comparing ours with ground truth, D-NeRF [36] and TiNeuVox [10]. Our model yields cleaner images with more details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.372,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "HyerNeRF Dataset Besides synthetic datasets, we also conduct experiments on real scenes, proposed by HyperN-eRF [33]. This dataset uses a multi-view camera rig consisting of 2 phones to capture real unbounded scenes with challenging rigid and non-rigid deformations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.457,
+                0.893,
+                0.563
+            ],
+            "angle": 0,
+            "content": "NHR Dataset NHR [54] dataset capture dynamic human data using a multi-camera dome system with up to 80 cameras arranged on a cylinder. We conduct experiments on four scenes where the performers are in different clothing and perform different actions. We test with 100 frames of each scene, selecting \\(90\\%\\) views for training and \\(10\\%\\) views for testing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.571,
+                0.892,
+                0.799
+            ],
+            "angle": 0,
+            "content": "Lego Complete Dataset The D-NeRF [36] dataset only contains 20 test images for each scene, and the evaluations of D-NeRF do not contain images in the canonical space. However, for physical canonical based methods (PC), canonical space geometry is important, as it affects images quality rendered at the canonical time and reflects the quality of flow estimation. Hence, we build a new dataset, named Lego Complete Dataset, which animates the object LEGO in D-NeRF dataset with 3 different motion patterns. For each scene, the test set is split into 3 categories to evaluate three abilities: space interpolation (rand views for each train time step), time interpolation (times between trained time steps), and canonical interpolation (rand views for canonical time step) abilities. For more details, please refer to our supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.804,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Besides the image quality, we also consider geometry precision by evaluating the depth of each test image to analyze the reconstructed geometry. For depth metrics, we use the relative error \\( \\delta = \\max \\left(\\frac{d}{d_{\\mathrm{gt}}}, \\frac{d_{\\mathrm{gt}}}{d}\\right) \\), where \\( d \\) is the estimated depth and \\( d_{\\mathrm{gt}} \\) is the ground truth depth. We report the percentage of the pixels with \\( \\delta < \\) Threshold."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16027"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.115,
+                0.877,
+                0.265
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Type</td><td colspan=\"2\">3D Printer</td><td colspan=\"2\">Broom</td><td colspan=\"2\">Chicken</td><td colspan=\"2\">Peel Banana</td><td colspan=\"2\">Mean</td></tr><tr><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>NeRF [26]</td><td>N</td><td>20.7</td><td>0.780</td><td>19.9</td><td>0.653</td><td>19.9</td><td>0.777</td><td>20.0</td><td>0.769</td><td>20.1</td><td>0.745</td></tr><tr><td>NV [23]</td><td>NPC</td><td>16.2</td><td>0.665</td><td>17.7</td><td>0.623</td><td>17.6</td><td>0.615</td><td>15.9</td><td>0.380</td><td>16.9</td><td>0.571</td></tr><tr><td>Nerfies [32]</td><td>NPC</td><td>20.6</td><td>0.830</td><td>19.2</td><td>0.567</td><td>26.7</td><td>0.943</td><td>22.4</td><td>0.872</td><td>22.2</td><td>0.803</td></tr><tr><td>HyperNeRF [33]</td><td>NPC</td><td>20.0</td><td>0.821</td><td>19.3</td><td>0.591</td><td>26.9</td><td>0.948</td><td>23.3</td><td>0.896</td><td>22.4</td><td>0.814</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>22.7</td><td>0.836</td><td>21.9</td><td>0.707</td><td>27.0</td><td>0.929</td><td>22.1</td><td>0.780</td><td>23.4</td><td>0.813</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>22.8</td><td>0.841</td><td>21.5</td><td>0.686</td><td>28.3</td><td>0.947</td><td>24.4</td><td>0.873</td><td>24.3</td><td>0.837</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>22.4</td><td>0.839</td><td>21.5</td><td>0.703</td><td>27.1</td><td>0.939</td><td>22.8</td><td>0.828</td><td>23.3</td><td>0.823</td></tr><tr><td>Ours (703)</td><td>PC</td><td>22.8</td><td>0.845</td><td>21.9</td><td>0.715</td><td>28.0</td><td>0.944</td><td>24.3</td><td>0.865</td><td>24.2</td><td>0.842</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.079,
+                0.267,
+                0.891,
+                0.445
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.132,
+                0.447,
+                0.837,
+                0.461
+            ],
+            "angle": 0,
+            "content": "Figure 6. Qualitative comparison on HyperNeRF Dataset. Our results are closer to ground truth than other methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.473,
+                0.281,
+                0.49
+            ],
+            "angle": 0,
+            "content": "4.2. Experimental Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.502,
+                0.47,
+                0.684
+            ],
+            "angle": 0,
+            "content": "Evaluation on D-NeRF Dataset We compared our method with the canonical-based backward flow methods D-NeRF [36], NDVG [15] and TiNeuVox [10] on D-NeRF Dataset. As shown in Table 1, our method achieves significant improvements in terms of all three metrics for physical canonical based methods. On average, our method improves PSNR by 2.18 compared with D-NeRF and 2.14 compared with NDVG. For non-physical canonical based methods, our method also achieves the best result. Ours show obviously better qualitative rendering quality compared with TiNeuVox-S \\((100^{3})\\) [10] with even smaller voxel resolution. More detailed statistics are provided in supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.685,
+                0.47,
+                0.746
+            ],
+            "angle": 0,
+            "content": "We also provide some visual comparisons in Fig. 5. Ours could recover accurate and detailed images, e.g., the helmet and arm in the top scene, and could also produce cleaner boundaries, e.g. the hand and feet in the bottom scene."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Evaluation on HyperNeRF Dataset We further compare our method with some highly related works on real scene dataset proposed by [33]. As shown in Table 2, our method achieves consistently better performance among physical canonical based methods. Our method has a voxel grid resolution limitation, due to we need to warp the whole voxel grid for rendering. Compared with other voxel grid based methods, our voxel grid resolution is limited to \\(70^{3}\\), along with a \\(160^{3}\\) static voxel grid for background modeling. However, the performance of our method is still com"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.473,
+                0.892,
+                0.626
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.56,
+                0.634,
+                0.828,
+                0.648
+            ],
+            "angle": 0,
+            "content": "Figure 7. Visual comparisons on NHR dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.672,
+                0.89,
+                0.703
+            ],
+            "angle": 0,
+            "content": "parable with SOTA of non-physical canonical based methods, proving the effectiveness of our forward flow design."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.71,
+                0.892,
+                0.816
+            ],
+            "angle": 0,
+            "content": "In Fig. 6, we show visual comparisons with NDVG [15], and TiNueVox [10]. The forward flow helps to recover the correct structure of dynamic objects, like the eye and edges of the chicken (top left) and the broom (top right). The relatively low resolution may harm the ability to recover very fine details, like the patterns on the 3D printer compared with TiNueVox-B [10] (bottom right)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Evaluation on NHR Dataset We also test our method on NHR dataset. Quantitative results are shown in Table 3, which shows ours achieving best results consistently. We show qualitative comparison in Fig. 7, and our method could render clean and detailed images."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16028"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.118,
+                0.1,
+                0.851,
+                0.113
+            ],
+            "angle": 0,
+            "content": "Table 3. Quantitative comparison on NHR dataset. The red text indicates the best and blue text is the second best result."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.123,
+                0.89,
+                0.209
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">type</td><td colspan=\"3\">Sport 1</td><td colspan=\"3\">Sport 2</td><td colspan=\"3\">Sport 3</td><td colspan=\"3\">BacSKetball</td><td colspan=\"3\">Mean</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>TiNeuVox-S [10]</td><td>NPC</td><td>26.06</td><td>0.93</td><td>0.10</td><td>25.98</td><td>0.93</td><td>0.11</td><td>25.90</td><td>0.93</td><td>0.11</td><td>23.75</td><td>0.91</td><td>0.14</td><td>25.42</td><td>0.92</td><td>0.12</td></tr><tr><td>TiNeuVox-B [10]</td><td>NPC</td><td>26.44</td><td>0.93</td><td>0.10</td><td>26.68</td><td>0.94</td><td>0.10</td><td>26.09</td><td>0.93</td><td>0.11</td><td>25.06</td><td>0.92</td><td>0.12</td><td>26.07</td><td>0.93</td><td>0.11</td></tr><tr><td>NDVG [15]</td><td>PC</td><td>23.66</td><td>0.89</td><td>0.15</td><td>24.43</td><td>0.91</td><td>0.13</td><td>22.54</td><td>0.88</td><td>0.16</td><td>22.55</td><td>0.89</td><td>0.17</td><td>23.29</td><td>0.89</td><td>0.15</td></tr><tr><td>Ours</td><td>PC</td><td>27.71</td><td>0.95</td><td>0.08</td><td>27.89</td><td>0.95</td><td>0.08</td><td>27.57</td><td>0.94</td><td>0.08</td><td>24.85</td><td>0.93</td><td>0.11</td><td>27.00</td><td>0.94</td><td>0.09</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.224,
+                0.89,
+                0.239
+            ],
+            "angle": 0,
+            "content": "Table 4. Quantitative comparison on Lego Complete Dataset. We report the average PSNR, LPIPS and the average relative depth error."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.24,
+                0.888,
+                0.357
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Type</td><td colspan=\"4\">Space Interpolation</td><td colspan=\"4\">Time Interpolation</td><td colspan=\"4\">Canonical Interpolation</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>23.98</td><td>0.15</td><td>98.720</td><td>99.328</td><td>24.18</td><td>0.15</td><td>98.854</td><td>99.378</td><td>17.36</td><td>0.23</td><td>97.341</td><td>98.868</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>28.12</td><td>0.06</td><td>99.655</td><td>99.853</td><td>28.19</td><td>0.06</td><td>99.749</td><td>99.953</td><td>19.90</td><td>0.11</td><td>94.828</td><td>97.560</td></tr><tr><td>Ours.notv (803)1</td><td>PC</td><td>27.58</td><td>0.07</td><td>99.758</td><td>99.958</td><td>27.63</td><td>0.07</td><td>99.788</td><td>99.966</td><td>23.56</td><td>0.13</td><td>99.238</td><td>99.820</td></tr><tr><td>Ours.noup (803)2</td><td>PC</td><td>26.11</td><td>0.09</td><td>99.596</td><td>99.981</td><td>26.19</td><td>0.09</td><td>99.636</td><td>99.983</td><td>24.64</td><td>0.10</td><td>99.230</td><td>99.925</td></tr><tr><td>Ours.noinp (803)3</td><td>PC</td><td>27.21</td><td>0.08</td><td>99.783</td><td>99.979</td><td>27.27</td><td>0.08</td><td>99.797</td><td>99.980</td><td>23.91</td><td>0.09</td><td>99.586</td><td>99.963</td></tr><tr><td>Ours (803)</td><td>PC</td><td>28.18</td><td>0.06</td><td>99.818</td><td>99.985</td><td>28.22</td><td>0.06</td><td>99.839</td><td>99.987</td><td>25.63</td><td>0.07</td><td>99.654</td><td>99.968</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.093,
+                0.357,
+                0.631,
+                0.369
+            ],
+            "angle": 0,
+            "content": "\\( {}^{1} \\) not use the all total variation losses \\( {}^{2} \\) not up-sample the voxel grid \\( {}^{3} \\) not use the inpaint network"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.377,
+                0.243,
+                0.392
+            ],
+            "angle": 0,
+            "content": "4.3. Method Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.403,
+                0.469,
+                0.538
+            ],
+            "angle": 0,
+            "content": "Flow Estimation and Canonical Space Geometry Since evaluating the estimated flow with ground truth is not practical, we choose to compare the reconstructed canonical geometry of physical canonical based methods. The idea is that if the canonical space is one frame of the whole timeline (like D-NeRF [36] and NDVG [15]), better flow estimation will result in better canonical scene geometry. We test these methods on Lego Complete Dataset, and all set the canonical space as the first frame of the image sequence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.539,
+                0.469,
+                0.718
+            ],
+            "angle": 0,
+            "content": "In Table 4, D-NeRF can not reconstruct the canonical radiance field well, since both the image and depth quality in canonical interpolation are significantly worse than those in space interpolation and time interpolation. NDVG [15] could recover much better images and geometry for other time steps, but the differences between canonical interpolation with the other two are even more significant. This means NDVG [15] has difficulty estimating correct backward flows. To render good quality images at other time steps, the correct geometries (depth) at these time steps are warped back into distorted canonical geometry due to incorrect backward flows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.469,
+                0.87
+            ],
+            "angle": 0,
+            "content": "This is the proof of our claim that the non-smooth and discontinuous nature of the backward flow deformation field makes it difficult to fit with smooth functions, especially for NDVG [15], which has limited MLP capacity for fast training. However, our method performs significantly better for both image quality and depth, and there are fewer variations between canonical, space, and temporal interpolations. This demonstrates the benefit of forward warping, which makes it easier for the deformation model to learn deformation flows from canonical time to other times."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We compare the canonical image of our method with DNeRF [36] in Fig. 8. Our method could recover the correct"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.52,
+                0.377,
+                0.609,
+                0.439
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.644,
+                0.378,
+                0.742,
+                0.439
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.748,
+                0.376,
+                0.868,
+                0.442
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.521,
+                0.443,
+                0.64,
+                0.496
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.644,
+                0.444,
+                0.744,
+                0.498
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.75,
+                0.445,
+                0.868,
+                0.5
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.531,
+                0.502,
+                0.634,
+                0.57
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.647,
+                0.505,
+                0.745,
+                0.57
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.75,
+                0.502,
+                0.868,
+                0.572
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.524,
+                0.577,
+                0.643,
+                0.641
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.646,
+                0.577,
+                0.744,
+                0.642
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.75,
+                0.574,
+                0.868,
+                0.644
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.647,
+                0.892,
+                0.716
+            ],
+            "angle": 0,
+            "content": "Figure 8. Canonical qualitative comparison. We show canonical radiance field comparison with D-NeRF [36]. Given the error map between the ground truth and rendered images, we can see that the canonical frame yielded by ours is closer to the ground truth. The results of D-NeRF are blurry and have large displacements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.717,
+                0.892,
+                0.775
+            ],
+            "angle": 0,
+            "content": "geometry and image details of the canonical frame. For example, the arms of the bucket produced by D-NeRF are at the \"mean\" positions of the whole trajectory, and ours recover the correct status."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Trajectory Visualization We show the learned DCT trajectories generated by our canonical trajectory field in Fig. 7 and Fig. 9. The canonical trajectory field is capable of recovering reasonable object point trajectories. Backward warping designs cannot track the motions of the same object point, so this is not a viable solution. With this feature, geometry constraints, motion models, and prior knowledge could be introduced in future work."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "16029"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.091,
+                0.085,
+                0.457,
+                0.361
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.359,
+                0.47,
+                0.401
+            ],
+            "angle": 0,
+            "content": "Figure 9. Trajectory learned by the canonical trajectory field. Light blue is the canonical frame, the curve represents the historical motion trajectory. More videos can be found in supp."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.403,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "Regularization terms We study the effect of all regularization terms we proposed, including \\(\\mathcal{L}^{\\mathrm{flow}}\\), \\(\\mathcal{L}^{\\mathrm{vdiff}}\\) and \\(\\mathcal{L}^{\\mathrm{tv}}\\) in Table 5. We could observe that all these three regularization terms have positive effect on the performance, but the improvement is minor. This proves the improvement of our method compared with others come from the forward warping desgin we proposed in the paper. Also, backward flow based method NDVG [15] use similar regularization terms with ours, and our method has clear advantage compared with NDVG [15]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.56,
+                0.47,
+                0.696
+            ],
+            "angle": 0,
+            "content": "Canonical setup In our method, we set canonical time to be the first frame for D-NeRF dataset to compare with physical canonical based method and the middle frame for HyperNeRF dataset for better performance. Setting canonical time to be the middle frame helps improving the performance as the state of the middle frame geometry is closer to other time steps compared with the first frame. To prove this, we set canonical time to be middel frame in Table 5 (can-time t at mid), and the PSNR improves slightly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.7,
+                0.47,
+                0.852
+            ],
+            "angle": 0,
+            "content": "Photometric loss for \\(\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}\\) We use photometric terms on \\(\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}\\) to make sure the warped grid before inpainting could already render reasonable images. This makes sure the UNet is actually doing 'inpainting'. Also, we do observe inpainting and upsampling could refine grids. In Fig. 7 and Fig. 9, the trajectories are reasonable which means we do learn trajectories without inpainting overfitting. We also test w/o photometric terms of \\(\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}\\) in Table 5 (w/o \\(\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}\\) photo) and the performance drops as there is no direct supervise signal for trajectory learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "More Ablations We study the effects of the total variation losses, the up-sample strategy, and the inpaint network we proposed in Table 6. The total variation losses help to"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.1,
+                0.894,
+                0.128
+            ],
+            "angle": 0,
+            "content": "Table 5. Ablations. Mean of Hell Warrior, Mutant, Hook and Bouncing Balls in D-NeRF dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.522,
+                0.137,
+                0.868,
+                0.217
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Ours</td><td>w/o Ltv</td><td>w/o Lflow</td><td>w/o Lvdiff</td><td>can-time t at mid</td><td>w/o VRup photo</td></tr><tr><td>PSNR</td><td>33.75</td><td>33.30</td><td>33.74</td><td>33.57</td><td>34.09</td><td>31.56</td></tr><tr><td>SSIM</td><td>0.979</td><td>0.974</td><td>0.978</td><td>0.977</td><td>0.980</td><td>0.966</td></tr><tr><td>LPIPS</td><td>0.040</td><td>0.048</td><td>0.039</td><td>0.041</td><td>0.037</td><td>0.057</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.565,
+                0.218,
+                0.828,
+                0.23
+            ],
+            "angle": 0,
+            "content": "Table 6. Ablation of losses on two dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.533,
+                0.232,
+                0.853,
+                0.326
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">D-NeRF</td><td colspan=\"2\">HyperNeRF</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>Ours.notv1</td><td>33.09</td><td>0.046</td><td>23.84</td><td>0.831</td></tr><tr><td>Ours.noup2</td><td>32.03</td><td>0.043</td><td>23.72</td><td>0.822</td></tr><tr><td>Ours.noinp3</td><td>31.78</td><td>0.044</td><td>23.25</td><td>0.814</td></tr><tr><td>Ours</td><td>32.68</td><td>0.037</td><td>24.23</td><td>0.842</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.328,
+                0.892,
+                0.51
+            ],
+            "angle": 0,
+            "content": "improve visual quality (LPIPS) in D-NeRF dataset as it applies smoothness over the deformation and radiance space, but may harm the high-frequency details (PSNR) for some of the scenes in D-NeRF dataset. For HyperNeRF dataset, the total variation losses improve the results, as the camera settings are more challenging than D-NeRF dataset. However, this improvement is minor compared with the other two factors. Since the resolution is critical for voxel grid based method, up-sampling operation of inpaint network is vital to improve the performance. Finally, the inpaint network plays the most essential role among these three factors in our method. More ablations are provided in our supp."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.523,
+                0.619,
+                0.538
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.549,
+                0.892,
+                0.7
+            ],
+            "angle": 0,
+            "content": "This paper presents a canonical-based representation with forward warping for novel view synthesis of dynamic scenes. Our method models a static scene at the canonical field and forward warp this whole field to other time steps for dynamic scene rendering. To address the many-to-one and one-to-many mapping difficulties, we present a differentiable forward warping with an average splatting process and an inpaint network. Our proposed forward warping pipeline achieves SOTA performance on the public datasets and our newly built dataset, especially for canonical frames."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.702,
+                0.892,
+                0.807
+            ],
+            "angle": 0,
+            "content": "Limitations and Future Directions Our current implementation is relatively memory-consuming, especially for real scenes. Also, the training speed is relatively slow (one day for each scene). Since we have a smooth trajectory field thanks to the forward warping, additional constraints and motion models could be introduced to learn better trajectories in future works."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Acknowledgements This research was supported in part by the National Natural Science Foundation of China (Grant Nos. 62271410, 62293482, 62202409), the Fundamental Research Funds for the Central Universities, and Shenzhen Science and Technology Program (Grant No. RCBS20221008093241052)."
+        },
+        {
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+            "angle": 0,
+            "content": "16030"
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+            "angle": 0,
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+# Forward Flow for Novel View Synthesis of Dynamic Scenes
+
+Xiang Guo $^{1}$ , Jiadai Sun $^{1,3}$ , Yuchao Dai $^{1}$ , Guanying Chen $^{2}$ , Xiaqing Ye $^{3}$ , Xiao Tan $^{3}$ , Errui Ding $^{3}$ , Yumeng Zhang $^{3}$ , Jingdong Wang $^{3}$
+
+<sup>1</sup>Northwestern Polytechnical University, <sup>2</sup>FNii and SSE, CUHK-Shenzhen, <sup>3</sup>Baidu Inc.
+
+# Abstract
+
+This paper proposes a neural radiance field (NeRF) approach for novel view synthesis of dynamic scenes using forward warping. Existing methods often adopt a static NeRF to represent the canonical space, and render dynamic images at other time steps by mapping the sampled 3D points back to the canonical space with the learned backward flow field. However, this backward flow field is non-smooth and discontinuous, which is difficult to be fitted by commonly used smooth motion models. To address this problem, we propose to estimate the forward flow field and directly warp the canonical radiance field to other time steps. Such forward flow field is smooth and continuous within the object region, which benefits the motion model learning. To achieve this goal, we represent the canonical radiance field with voxel grids to enable efficient forward warping, and propose a differentiable warping process, including an average splatting operation and an inpaint network, to resolve the many-to-one and one-to-many mapping issues. Thorough experiments show that our method outperforms existing methods in both novel view rendering and motion modeling, demonstrating the effectiveness of our forward flow motion modeling. Project page: https://npucvr.github.io/ForwardFlowDNeRF.
+
+# 1. Introduction
+
+Novel view synthesis (NVS) is a challenging and longstanding problem in computer vision and graphics, which has many applications in virtual reality, augmented reality, data augmentation, image editing, etc. Recently, differentiable neural rendering [26, 30, 59] has been introduced into this area. In particular, the neural radiance field (NeRF) [26]
+
+![](images/e3bf25df32093517aea0c8394238217909709d3534ba60da6f44fcb467087448.jpg)
+
+![](images/3475db0ab9134a9ab7f46e6cf7a0bc93421dbb2f0e9ceb51d4c8fd0bec01e673.jpg)
+
+![](images/1f265ea20acfad9ea9a931ad882beb52b91a1142e1be4f1eeeaa23f4e157769d.jpg)  
+Figure 1. Comparison of backward flow and forward flow. This figure shows an example of backward and forward flow changes. (a) An example of dynamic scene. (b) With the bucket lifting up, different types of points cover the green point  $\mathbf{p}$ , which needs very different backward flows to map this point back to canonical space. (d) shows the norm changes of the backward flow, which is not smooth. (c) On the other hand, the forward flow of position  $\mathbf{q}$ , which maps the constant object point from canonical space to other times, is smooth and continuous. (e) shows the norm changes of the forward flow.
+
+![](images/8da1e7401842d48ae85e5829346b2046fe48e4d4567f0e808e132d2771a0b3d9.jpg)
+
+promotes this area significantly and attracts lots of interest within a short time. NeRF [26] produces realistic images by representing the 3D world with a multi-layer perceptron (MLP), which maps the input 3D coordinates and 2D view direction to target density and color.
+
+While the original NeRF [26] can only model static scenes, a series of works extend the NeRF-based framework from static to dynamic scenes [9, 13, 19, 32, 36, 49, 51, 55]. One of the promising directions is using a canonical space representation [15, 36, 49]. This representation sets one of the time steps as canonical time and models the static scene with a canonical radiance field. To render images at other time steps, a deformation field is used to estimate the
+
+backward flow for moving the 3D points from the current time step back to the canonical time step. Although the canonical-based representation with the backward flow is easy to implement, the backward flow field is non-smooth and discontinuous. As shown in Fig. 1(b), for a fixed 3D position along the timeline, there will be different types of points covering the position  $\mathbf{p}$ , which needs discontinuous flows to map them back to canonical space (Fig. 1(d)). So the backward flow cannot be fitted well with commonly used smooth motion models (MLP, for example). Also, distortions are introduced to the static canonical space geometry due to the failure of the motion model, as shown in Fig. 8.
+
+To solve the problem of backward flow, we propose using forward flow as the deformation model. Instead of warping the sampled points on image rays at other time steps back to the canonical time and rendering at the canonical space, we propose to warp the whole canonical radiance field from the canonical time to other time steps using forward deformation flow and render at corresponding time steps. In this way, the forward flow estimated by the deformation model will be smooth and continuous for the same 3D position along the timeline (Fig. 1(c) and (e)). Note that SNARF [7] has also used forward warping based on an inverse skinning model, but it is designed for dynamic human modeling and cannot be used in general scenes. In this paper, we aim to achieve forward warping for general scenes, which means we must warp the whole space.
+
+However, introducing forward warping into the canonical space based NeRF methods is not straightforward as there are three main problems to be solved. First, the traditional canonical radiance field in existing methods cannot be warped explicitly, since the radiance field is represented as a continuous function parameterized by an MLP. To solve this problem, we propose to use the voxel grid to represent the canonical radiance field as it is finite and discrete. Recent voxel-based methods [27,44,62] have proven the effectiveness of this representation. The other two problems are the many-to-one and one-to-many mapping issues brought by the inherent property of the forward warping operation. To address them, we propose a differentiable forward warping method consisting of an average splatting operation and an inpaint network to solve the many-to-one and one-to-many issue, respectively. Extensive experiments have been conducted to verify the effectiveness of our method.
+
+Our key contributions can be summarized as follows:
+
+- To the best of our knowledge, we are the first to investigate forward warping in dynamic view synthesis for general scenes. We propose a novel canonical based NeRF with forward flow motion modeling for dynamic view synthesis. Thanks to the forward flow field, our method can better represent the object motions, and explicitly recover the trajectory of a surface point.
+
+- We introduce voxel grid based canonical radiance field to enable reasonable computation of forward warping, and propose a differentiable forward warping method, including an average splatting operation and an inpaint network, to solve the many-to-one and one-to-many issues of forward warping.  
+- Experiments on multiple datasets show that our method outperforms existing methods on the D-NeRF [36] dataset, Hypernerf [33] dataset, NHR [54] dataset and our proposed dataset.
+
+# 2. Related Works
+
+Novel View Synthesis (NVS) is a long-standing task in both computer vision and graphics [4, 6, 14, 18], and surveys of recent methods can be found in [42, 46, 47]. Some methods require to reconstruct an explicit 3D model to represent the scene, such as point clouds [1], voxels or meshes [16, 40, 41, 48]. Then novel images from arbitrary views can be rendered from this geometry. Another methods try to estimate depth map through multi-view geometry, and then aggregate features from multiple frames through the co-visibility, such as [8, 11, 17, 34, 40, 41, 57]. Recently, neural implicit representations have shown great promise for novel view synthesis and 3D modeling. In this section, we focus more on the neural implicit rendering methods and mainly summarize these schemes according to whether they can handle dynamic scenes.
+
+NVS for Static Scenes NeRF [26], as a seminal work, uses MLPs to model a 5D radiance field, which can render impressive view synthesis for static scenes captured. Numerous subsequent works have extended NeRF to kinds of scenarios, such as larger and unbounded scenes [25, 39, 45, 56, 64], relighting [3, 43, 58, 66], incorporating anti-aliasing for multi-scale rendering [2], and generalization ability [5, 50, 52, 63]. In addition, some methods are devoted to more efficient neural rendering and optimization in NeRF-like framework, such as [20, 22, 24, 28, 35, 62] focus more on efficient sampling along each ray for color accumulation, [37, 38] subdivide the scene into multiple cells for efficient processing, and [27, 44, 61] exploit voxel-grid representation to speed up the optimization of radiance field. However, these methods are mainly applicable to static scenes, leaving out the scenes with dynamic objects, which are actually more extensive and practical.
+
+NVS for Dynamic Scenes There are several works that extend NeRF from static scenes to dynamic scenes with nonrigid deformable objects. One feasible way is to build a 4D spatial-temporal representation. For example, Yoon et al. [60] combine single-view depth and depth from multiview stereo to render virtual views with 3D warping. Gao et al. [13] use a time-invariant model (static) and a time-varying model (dynamic) to represent the scenes, and reg-
+
+![](images/3489969a15c5866b2a68f81794c695d2f858a460349e24d236874eefaaad40f0.jpg)  
+1. Voxel Grid Based Canonical Field
+
+![](images/75fb6f7c8bd9d8ddf7e9e5b2ddc4cf92b298e5f0a5629047208836b3a2cbd170.jpg)  
+2. Differentiable Forward Warping  
+Figure 2. Overview of our proposed method. a) We represent a static scene at canonical time with a voxel grid based radiance field for density&color and a voxel grid based trajectory field for deformations; b) We propose to first forward warp canonical radiance field using the forward flow by average splating; c) We then inpaint the warped radiance field using a inpaint network; Specifically, 1. Voxel Grid Based Canonical Field contains two models. The canonical radiance field  $\mathbf{V}_{\mathrm{R}}^{\mathrm{Can}}$  is estimated by a Light MLP which takes canonical radiance feature  $\mathbf{V}_{\mathrm{Rf}}^{\mathrm{Can}}$  and corresponding 3D coordinates  $\mathbf{V}_{\mathrm{p}}^{\mathrm{Can}}$  as input. The canonical trajectory field  $\mathbf{V}_{\mathrm{T}}^{\mathrm{Can}}$  is estimated by another Light MLP which takes deformation feature and coordinates as input. The deformation flow  $\mathbf{V}_{\mathrm{flow}}^{t}$  from canonical to time  $t$  can then be obtained; 2. Differential Forward Warping first warp  $\mathbf{V}_{\mathrm{R}}^{\mathrm{Can}}$  to get radiance field  $\mathbf{V}_{\mathrm{R}}^{t}$  at time  $t$ . Then, the  $\mathbf{V}_{\mathrm{R}}^{t}$  is inpainted by a inpaint network, which is  $\mathbf{V}_{\mathrm{R_{inp}}}^{t}$ ; 3. Volume Rendering render colors of rays at time  $t$  based on  $\mathbf{V}_{\mathrm{R_{inp}}}^{t}$
+
+ularize the dynamic model by scene flow estimation. NeRF-Flow [9] learns a 4D spatial-temporal representation of a dynamic scene from a set of RGB images. Xian et al. [55] build a 4D space-time irradiance field to map a spatial-temporal location to the emitted color and volume density. Similarly, NSFF [19] models the dynamic scene as a time-variant continuous function of appearance, geometry, and 3D scene motion. DCT-NeRF [51] uses the Discrete Cosine Transform (DCT) to capture dynamic motion, i.e. learning smooth and stable trajectories over time for each point in space.
+
+On the other hand, D-NeRF [36], Nerfies [32], HyperNeRF [33] and NR-NeRF [49] use a static canonical radiance field to capture geometry and appearance, and then learn a deformation/displacement field at each time step w.r.t. the canonical space. Specifically, to render an image at an arbitrary time step, a deformation field is used to estimate backward scene flow, moving 3D points from the current time step back to the canonical step. However, for the same 3D location along the timeline, the backward flow field is not guaranteed to be smooth and continuous. As a result, the canonical geometry usually has distortions and resembles the mean shape of a moving object. We focus on solving the problem of backward flow in this paper.
+
+Along with the two main directions, there is a trend to speed up the training of dynamic NeRF, which is based on voxel grid representation. TiNeuVox [10] models the de
+
+formation using a tiny MLP and uses multi-distance interpolation to get the feature for the radiance network which estimates the density and color. V4D [12] uses the 3D feature voxel to model the 4D radiance field with additional time dimension concatenated and proposes look-up tables for pixel-level refinement. Although V4D mainly focuses on improving image quality, the training speed is not significant compared to TiNeuVox. DeVRF [21] also builds on voxel-grid representation, which proposes to use multi-view data to overcome the nontrivial problem of the monocular setup. Multi-view data simplifies the learning of motion and geometry compared with others using monocular images.
+
+# 3. Method
+
+Motivation Backward-warping based methods [15, 36] propose a network  $f_{t\to \mathrm{Can}} = F(p,t)$  to estimate the deformation flow  $f_{t\rightarrow \mathrm{Can}}$  which moves the point at the position  $p$  from other time steps  $t$  back to canonical time Can. However, for the same position  $p$ , at different time steps  $ts$ , there could be different object points or even the empty point at this position, as shown in Fig. 1. This means the deformation flow  $f_{t\to \mathrm{Can}}$  is non-smooth and discontinuous along the timeline for a fixed position  $p$ . This could introduce difficulties for motion learning and produce distortion in the canonical radiance field, because the backward flow network has limited capacities in learning a correct non-smooth and dis
+
+![](images/b34fd3ffba8feb7ae2fe118cca197e35bda97ffa83ff381a6bdc48e89a5e55a2.jpg)  
+Figure 3. Two issues of the forward warping. Many-to-one: multiple positions in the source correspond to the same position in the target. One-to-many: one position in the source corresponds to multiple positions in the target, causing holes if warping naively.
+
+continuous deformation field. On the other hand, our proposed forward warping strategy estimates the deformation  $f_{\mathrm{Can} \to t}$  from the canonical time to another time step of a 3D point in canonical space. The set of the deformation flows of one position along the timeline is actually the trajectory of this point. This guarantees the flows to be smooth and continuous along the timeline as we assume the motions in reality have these properties.
+
+Method Overview We model a static scene at the canonical time using the voxel grid representation with a canonical radiance field and a canonical trajectory field. To synthesize dynamic images, we propose to forward warp the canonical radiance field to corresponding time steps and render the images using volume rendering based on the warped radiance field. Fig. 2 shows the overview of our method. In the following, we will introduce three main components of our method: voxel grid based canonical field, differentiable forward warping, and volume rendering. Finally, the model optimization is represented, including the proposed loss functions and training strategy.
+
+# 3.1. Voxel Grid Based Canonical Field
+
+Canonical Radiance Field To warp a static scene in canonical time to other time steps using forward warping, the radiance field should be represented by finite 3D points. The original heavy MLP in NeRF [26] is not practical, as we cannot query infinite 3D points in the canonical space. Inspired by recent works [27,44,61] on voxel grid presentations, we propose to use a learnable voxel radiance feature grid  $\mathbf{V}_{\mathrm{Rf}}^{\mathrm{Can}}$  and a lightweight MLP network  $F_{\theta_1}$  to model the radiance of the static scene as shown in Fig. 2. The canonical radiance field is defined as
+
+$$
+\mathbf {V} _ {\mathrm {R}} ^ {\text {C a n}} = F _ {\theta_ {1}} \left(\mathbf {V} _ {\mathrm {p}} ^ {\text {C a n}}, \mathbf {V} _ {\mathrm {R f}} ^ {\text {C a n}}\right), \tag {1}
+$$
+
+where  $\mathbf{V}_{\mathrm{R}}^{\mathrm{Can}} = \{\mathbf{V}_{\sigma}^{\mathrm{Can}}, \mathbf{V}_{\mathrm{cf}}^{\mathrm{Can}}\}$  consists of density voxel grid  $\mathbf{V}_{\sigma}^{\mathrm{Can}}$  and color feature voxel grid  $\mathbf{V}_{\mathrm{cf}}^{\mathrm{Can}}$ .  $\mathbf{V}_{\mathrm{p}}^{\mathrm{Can}}$  are the 3D coordinates of the voxel grid in canonical space, embedded according to NeRF [26].
+
+Canonical Trajectory Field We propose to use Discrete Cosine Transform (DCT) [51] to represent the trajectory of
+
+a 3D point, which ensures the smoothness of the motion. Similar to canonical radiance field, we also use a deformation feature grid  $\mathbf{V}_{\mathrm{Df}}^{\mathrm{Can}}$  and a lightweight MLP network  $F_{\theta_2}$  to model the canonical trajectory field, which is defined as
+
+$$
+\mathbf {V} _ {T} ^ {\text {C a n}} = F _ {\theta_ {2}} \left(\mathbf {V} _ {\mathrm {p}} ^ {\text {C a n}}, \mathbf {V} _ {\mathrm {D f}} ^ {\text {C a n}}\right), \tag {2}
+$$
+
+where  $\mathbf{V}_T^{\mathrm{Can}}$  contains the DCT coefficients of the voxels. Given time step  $t$ , we could get the deformation flow of these voxels from canonical to time step  $t$  by
+
+$$
+\mathbf {V} _ {\text {f l o w}} ^ {t} = f _ {\mathrm {D C T} ^ {- 1}} \left(\mathbf {V} _ {T} ^ {\text {C a n}}, t\right) - f _ {\mathrm {D C T} ^ {- 1}} \left(\mathbf {V} _ {T} ^ {\text {C a n}}, \text {C a n}\right), \tag {3}
+$$
+
+where  $f_{\mathrm{DCT}^{-1}}$  is the inverse DCT transform of the DCT coefficients as described in TrajectoryNeRF [51].
+
+# 3.2. Differentiable Forward Warping
+
+Forward warping has two major issues: many-to-one and one-to-many. Fig. 3 shows a simple example, where we aim to warp the source to the target using forward warping: a) Many-to-one: if a circle shrinks, there will be multiple positions corresponding to one position from the source to the target. b) One-to-many: if a circle expands, multiple positions in the target will correspond to the same position in the source, which leaves holes of the target if we warp the source to target naively. For the many-to-one issue, we propose to use the average splating to fuse multiple values into one. For the one-to-many issue, we use an inpaint network to inpaint the missing positions of the warped grids. More details are in the following sections.
+
+Average Splatting We propose to fuse possible multiple values from the source grid that are mapped into the same voxel position of the target grid, motivated by Softmax-splatting [31]. Specifically, we propose a simple yet effective method that calculates the "average" of these values with a trilinear kernel. Formally, suppose that we need to warp the source grid  $\mathbf{V}^{\mathrm{S}}$  to target grid  $\mathbf{V}^{\mathrm{T}}$  by the flow  $f_{\mathrm{S}\rightarrow \mathrm{T}}$ , and  $\mathbf{p}$ ,  $\mathbf{q}$  are indexes of a voxel grid. We define  $\mathbf{V}^{\mathrm{T}} = F_{\mathrm{warp}}(\mathbf{V}^{\mathrm{S}}, f_{\mathrm{S}\rightarrow \mathrm{T}})$  as follows,
+
+$$
+\mathbf {V} ^ {\mathrm {T}} [ \mathbf {p} ] = \frac {\sum_ {\forall \mathbf {q} \in \mathbf {V} ^ {\mathrm {s}}} b [ \mathbf {u} ] \cdot \mathbf {V} ^ {\mathrm {S}} [ \mathbf {q} ]}{\sum_ {\forall \mathbf {q} \in \mathbf {V} ^ {\mathrm {s}}} b [ \mathbf {u} ]}, \tag {4}
+$$
+
+$$
+b [ \mathbf {u} ] = \prod \max  (0, 1 - | \mathbf {u} _ {i} |), i \in \{x, y, z \}, \tag {5}
+$$
+
+$$
+\mathbf {u} = \left(\mathbf {q} + f _ {\mathrm {S} \rightarrow \mathrm {T}} [ \mathbf {q} ]\right) - \mathbf {p}, \tag {6}
+$$
+
+where  $x, y, z$  are three axes of the voxel grid, and  $\mathbf{u}_i \in \mathbb{R}$  is one element of the vector  $\mathbf{u} \in \mathbb{R}^3$ .
+
+So, we warp the canonical radiance field to time step  $t$  by
+
+$$
+\mathbf {V} _ {\mathrm {R}} ^ {t} = F _ {\text {w a r p}} \left(\mathbf {V} _ {\mathrm {R}} ^ {\text {C a n}}, \mathbf {V} _ {\text {f l o w}} ^ {t}\right). \tag {7}
+$$
+
+Inpaint Network Another issue of forward warping is one-to-many, which leaves holes in the voxel grid after
+
+![](images/a16d6a4ff97928569408dbd64c84065323443b6393410b3b15a648139d14e916.jpg)  
+Figure 4. Inpaint network. It consists of a 3D U-Net structure and an up-sampling layer, which could inpaint and upsample the input voxel grid.
+
+warping. To resolve this issue, we propose building an inpaint network to fill these holes. As shown in Fig. 4, we modify a 3D U-Net structure network [53] followed by an up-sampling layer, which is  $\mathbf{V}_{\mathrm{R_{Inp}}}^{t} = F_{\theta_{3}}(\mathbf{V}_{\mathrm{R}}^{t})$ , where  $\mathbf{V}_{\mathrm{R_{Inp}}}^{t}$  is the inpainted and up-sampled voxel grid.
+
+This structure helps encoding layers to learn information from local neighboring voxels and decoding layers to recover the original resolution with filled content. We only feed the warped voxel grid to the inpaint network, which has no access to temporal information. Thus, the inpaint network can not learn to warp, limiting its ability only to inpainting. Since warping operations and the inpaint network are relatively expensive to compute, we propose to attach an up-sample layer after the U-Net structure. In this way, we could warp the grids with a low resolution to save time and memory, while rendering with a higher resolution for better image quality. The up-sample layer consists of a interpolation layer, convolution layers, and activation layers.
+
+# 3.3. Volume Rendering
+
+After we get the radiance voxel grid at time  $t$ , the pixel colors of the image rays can be rendered using volume rendering techniques [26]. Given a ray  $\mathbf{r}(w) = \mathbf{o} + w\mathbf{d}$  emitted from the camera center  $\mathbf{o}$  with view direction  $\mathbf{d}$  through a given pixel on the image plane, we render the corresponding pixel color  $\mathbf{C}_{\mathrm{Inp}}(\mathbf{r}) = F_{\mathrm{render}}(\mathbf{V}_{\mathrm{R_{inp}}}^{t},\mathbf{r})$ . To do this, we get all 3D points  $\mathbf{p}$  that the ray intersects with voxel grids. Next, trilinear interpolation is applied to obtain the density and color feature of each 3D point.
+
+$$
+(\sigma , \mathbf {c} _ {\mathbf {f}}) = F _ {\text {i n t e r}} \left(\mathbf {V} _ {\mathrm {R} _ {\mathrm {l n p}}} ^ {t}, \mathbf {p}\right). \tag {8}
+$$
+
+Then, we get the color of this 3D point  $\mathbf{p}$  by
+
+$$
+\mathbf {c} = \left\{ \begin{array}{l l} \mathbf {c} _ {\mathbf {f}} & \text {i f} \mathbf {c} _ {\mathbf {f}} \in \mathbb {R} ^ {3}, \\ F _ {\theta_ {4}} \left(\mathbf {c} _ {\mathbf {f}}, \mathbf {d}\right) & \text {o t h e r w i s e}, \end{array} \right. \tag {9}
+$$
+
+where  $F_{\theta_4}$  is a small MLP network that is used to produce colors that depend on the direction of the ray.
+
+Finally, the pixel color could be rendered by
+
+$$
+\mathbf {C} (\mathbf {r}) = \sum_ {k = 1} ^ {K} T \left(w _ {k}\right) \alpha \left(\sigma \left(w _ {k}\right) \delta_ {k}\right) \mathbf {c} \left(w _ {k}\right), \tag {10}
+$$
+
+$$
+T \left(w _ {k}\right) = \exp \left(- \sum_ {j = 1} ^ {k - 1} \sigma \left(w _ {j}\right) \delta_ {j}\right), \tag {11}
+$$
+
+where  $K$  is the number of sampled points along the ray,  $\delta_{k}$  is the distance between adjacent samples along the ray, and  $\alpha (\sigma (w_k)\delta_k) = 1 - \exp (-\sigma (w_k)\delta_k)$ .
+
+Note that the warped radiance grid  $\mathbf{V}_{\mathrm{R}}^{t}$  should also render reasonable images. So we directly up-sample  $\mathbf{V}_{\mathrm{R}}^{t}$  to get  $\mathbf{V}_{\mathrm{RUp}}^{t}$  without inpainting, and render the corresponding pixel color  $\mathbf{C}_{\mathrm{Up}}(\mathbf{r}) = F_{\mathrm{render}}(\mathbf{V}_{\mathrm{RUp}}^{t},\mathbf{r})$
+
+# 3.4. Model Optimization
+
+To optimize the model, we design a series of loss functions. Photometric Loss First, the most important loss is the photometric loss, which is the mean square error (MSE) of the rendered color and ground truth color  $\mathbf{C}_{\mathrm{gt}}(\mathbf{r})$
+
+$$
+\begin{array}{l} \mathcal {L} ^ {\mathrm {p h o t o}} = \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} \| \mathbf {C} _ {\operatorname {I n p}} (\mathbf {r}) - \mathbf {C} _ {\mathrm {g t}} (\mathbf {r}) \| _ {2} ^ {2} \\ + \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} \| \mathbf {C} _ {\mathrm {U p}} (\mathbf {r}) - \mathbf {C} _ {\mathrm {g t}} (\mathbf {r}) \| _ {2} ^ {2}, \tag {12} \\ \end{array}
+$$
+
+where  $\mathcal{R}$  is the set of rays sampled in one batch.
+
+Following DVGO [44], we use  $\mathcal{L}^{\mathrm{ptc}}$  to directly supervise the color of sampled points. The intuition is that sampled points with larger weights contribute more to the rendered color. Also, we use the background entropy loss  $\mathcal{L}^{\mathrm{bg}}$  to encourage the densities concentrating on either the foreground or the background.
+
+Inpaint Network Loss As the inpaint network is used to complete the warped voxel grids, the output of the inpaint network should be close to the input. Therefore, we propose to use the L1 norm of the difference between the input and output of the inpaint network.
+
+$$
+\mathcal {L} ^ {\mathrm {v d i f f}} = \left\| \mathbf {V} _ {\mathrm {R} _ {\text {I n p}}} ^ {t} - \mathbf {V} _ {\mathrm {R} _ {\mathrm {U p}}} ^ {t} \right\| _ {1}. \tag {13}
+$$
+
+Regularization Terms Since modeling the appearance and motion of a dynamic scene from monocular images is a nontrivial problem, we propose a series of regularization terms.
+
+First, we encourage most 3D points in canonical space to be static by introducing  $\mathcal{L}^{\mathrm{flow}}$  to be the L1 norm of  $\mathbf{V}_{\mathrm{flow}}^{t}$ . Second, denoting  $\mathcal{L}^{\mathrm{tv}}$  as the total variation function. We compute  $\mathcal{L}^{\mathrm{tv}}(\mathbf{V}_{\sigma}^{\mathrm{Can}})$  to ensure the spatial smoothness of the density in canonical space, and introduce  $\mathcal{L}^{\mathrm{tv}}(\mathbf{V}_{\mathrm{flow}}^{t})$  to encourage the spatial smoothness of the motions. Finally, inspired by RegNeRF [29], we render depths  $\mathbf{D}$  of image patches sampled from random views and minimize their total variations  $\mathcal{L}^{\mathrm{tv}}(\mathbf{D})$ .
+
+Table 1. Quantitative comparison on D-NeRF Dataset. Comparison of our method with others on LPIPS and PSNR/SSIM. The Red text indicates the best and blue text is the second best result.  
+
+<table><tr><td>Methods</td><td>Type</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>T-NeRF [36]</td><td>N</td><td>29.51</td><td>0.95</td><td>0.08</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>30.75</td><td>0.96</td><td>0.07</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>32.67</td><td>0.97</td><td>0.04</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>30.50</td><td>0.95</td><td>0.07</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>30.54</td><td>0.96</td><td>0.05</td></tr><tr><td>Ours (803)</td><td>PC</td><td>32.68</td><td>0.97</td><td>0.04</td></tr></table>
+
+Overall Loss The overall loss function used for optimization defined as follow, where  $w_{1\sim 7}$  are weights to balance each component in the final coarse loss.
+
+$$
+\begin{array}{l} \mathcal {L} = \mathcal {L} ^ {\text {p h o t o}} + w _ {1} \mathcal {L} ^ {\text {p t c}} + w _ {2} \mathcal {L} ^ {\text {b g}} + w _ {3} \mathcal {L} ^ {\text {f l o w}} + w _ {4} \mathcal {L} ^ {\text {v d i f f}} \tag {14} \\ + w _ {5} \mathcal {L} ^ {\mathrm {t v}} \left(\mathbf {V} _ {\sigma} ^ {\text {C a n}}\right) + w _ {6} \mathcal {L} ^ {\mathrm {t v}} \left(\mathbf {V} _ {\text {f l o w}} ^ {t}\right) + w _ {7} \mathcal {L} ^ {\mathrm {t v}} (\mathbf {D}), \\ \end{array}
+$$
+
+Training Strategy First, we propose progressive training, which starts training with images close to the canonical time and progressively adds images with farther time steps until all images are added. Second, we set up a coarse-to-fine training strategy. In the coarse stage, we set the color feature to be the color itself, without considering the ray directions. We compute a smaller bounding box with the proxy geometry learned from the coarse stage, which could filter a large portion of empty space for the fine stage training. The model trained in the fine stage is our final model, and we set the color features to be high dimensional features and model the ray direction dependency with  $F_{\theta_4}$ .
+
+# 4. Experiments
+
+# 4.1. Baselines and Evaluation Datasets
+
+Baselines The methods compared in this paper are classified into three types. First, we compare methods which are non-canonical based (N), including NeRF[26], and T-NeRF[36]. Second, physical canonical based methods (PC) contain D-NeRF [36], NDVG[15] and Ours. These methods set their canonical space as one frame of the whole timeline by explicitly giving zeros to estimated flows at the canonical time. The canonical space of these methods should have reasonable physical 3D reconstructions of the scene at the canonical time. Third, non-physical canonical based methods (NPC) consists of NV[23], Nerfies[32], HyperNeRF[33] and TiNeuVox[10]. Their canonical space geometries do not necessarily have physical meanings.
+
+D-NeRF Dataset We evaluate our method on 8 dynamic scenes of D-NeRF [36] dataset. We report several common metrics for the evaluation: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and Learned Perceptual Image Patch Similarity (LPIPS) [65].
+
+![](images/f6758833fec2e5cfc70883349c037dba9f7e548025613445e124bde7fd22d724.jpg)  
+Figure 5. Qualitative comparison on D-NeRF Dataset. We show some novel view synthesized images on the selected test set of the dataset. Comparing ours with ground truth, D-NeRF [36] and TiNeuVox [10]. Our model yields cleaner images with more details.
+
+HyerNeRF Dataset Besides synthetic datasets, we also conduct experiments on real scenes, proposed by HyperN-eRF [33]. This dataset uses a multi-view camera rig consisting of 2 phones to capture real unbounded scenes with challenging rigid and non-rigid deformations.
+
+NHR Dataset NHR [54] dataset capture dynamic human data using a multi-camera dome system with up to 80 cameras arranged on a cylinder. We conduct experiments on four scenes where the performers are in different clothing and perform different actions. We test with 100 frames of each scene, selecting  $90\%$  views for training and  $10\%$  views for testing.
+
+Lego Complete Dataset The D-NeRF [36] dataset only contains 20 test images for each scene, and the evaluations of D-NeRF do not contain images in the canonical space. However, for physical canonical based methods (PC), canonical space geometry is important, as it affects images quality rendered at the canonical time and reflects the quality of flow estimation. Hence, we build a new dataset, named Lego Complete Dataset, which animates the object LEGO in D-NeRF dataset with 3 different motion patterns. For each scene, the test set is split into 3 categories to evaluate three abilities: space interpolation (rand views for each train time step), time interpolation (times between trained time steps), and canonical interpolation (rand views for canonical time step) abilities. For more details, please refer to our supp.
+
+Besides the image quality, we also consider geometry precision by evaluating the depth of each test image to analyze the reconstructed geometry. For depth metrics, we use the relative error  $\delta = \max \left(\frac{d}{d_{\mathrm{gt}}}, \frac{d_{\mathrm{gt}}}{d}\right)$ , where  $d$  is the estimated depth and  $d_{\mathrm{gt}}$  is the ground truth depth. We report the percentage of the pixels with  $\delta <$  Threshold.
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Type</td><td colspan="2">3D Printer</td><td colspan="2">Broom</td><td colspan="2">Chicken</td><td colspan="2">Peel Banana</td><td colspan="2">Mean</td></tr><tr><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>NeRF [26]</td><td>N</td><td>20.7</td><td>0.780</td><td>19.9</td><td>0.653</td><td>19.9</td><td>0.777</td><td>20.0</td><td>0.769</td><td>20.1</td><td>0.745</td></tr><tr><td>NV [23]</td><td>NPC</td><td>16.2</td><td>0.665</td><td>17.7</td><td>0.623</td><td>17.6</td><td>0.615</td><td>15.9</td><td>0.380</td><td>16.9</td><td>0.571</td></tr><tr><td>Nerfies [32]</td><td>NPC</td><td>20.6</td><td>0.830</td><td>19.2</td><td>0.567</td><td>26.7</td><td>0.943</td><td>22.4</td><td>0.872</td><td>22.2</td><td>0.803</td></tr><tr><td>HyperNeRF [33]</td><td>NPC</td><td>20.0</td><td>0.821</td><td>19.3</td><td>0.591</td><td>26.9</td><td>0.948</td><td>23.3</td><td>0.896</td><td>22.4</td><td>0.814</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>22.7</td><td>0.836</td><td>21.9</td><td>0.707</td><td>27.0</td><td>0.929</td><td>22.1</td><td>0.780</td><td>23.4</td><td>0.813</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>22.8</td><td>0.841</td><td>21.5</td><td>0.686</td><td>28.3</td><td>0.947</td><td>24.4</td><td>0.873</td><td>24.3</td><td>0.837</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>22.4</td><td>0.839</td><td>21.5</td><td>0.703</td><td>27.1</td><td>0.939</td><td>22.8</td><td>0.828</td><td>23.3</td><td>0.823</td></tr><tr><td>Ours (703)</td><td>PC</td><td>22.8</td><td>0.845</td><td>21.9</td><td>0.715</td><td>28.0</td><td>0.944</td><td>24.3</td><td>0.865</td><td>24.2</td><td>0.842</td></tr></table>
+
+![](images/d1ba8de626b061530fd13e2a8bca14b3dc5bb8ce2f8ba70fbc5a04be0dedb817.jpg)  
+Figure 6. Qualitative comparison on HyperNeRF Dataset. Our results are closer to ground truth than other methods.
+
+# 4.2. Experimental Results
+
+Evaluation on D-NeRF Dataset We compared our method with the canonical-based backward flow methods D-NeRF [36], NDVG [15] and TiNeuVox [10] on D-NeRF Dataset. As shown in Table 1, our method achieves significant improvements in terms of all three metrics for physical canonical based methods. On average, our method improves PSNR by 2.18 compared with D-NeRF and 2.14 compared with NDVG. For non-physical canonical based methods, our method also achieves the best result. Ours show obviously better qualitative rendering quality compared with TiNeuVox-S  $(100^{3})$  [10] with even smaller voxel resolution. More detailed statistics are provided in supp.
+
+We also provide some visual comparisons in Fig. 5. Ours could recover accurate and detailed images, e.g., the helmet and arm in the top scene, and could also produce cleaner boundaries, e.g. the hand and feet in the bottom scene.
+
+Evaluation on HyperNeRF Dataset We further compare our method with some highly related works on real scene dataset proposed by [33]. As shown in Table 2, our method achieves consistently better performance among physical canonical based methods. Our method has a voxel grid resolution limitation, due to we need to warp the whole voxel grid for rendering. Compared with other voxel grid based methods, our voxel grid resolution is limited to  $70^{3}$ , along with a  $160^{3}$  static voxel grid for background modeling. However, the performance of our method is still com
+
+![](images/53c532b06c22bc7fbd0c4f62b69a9f919b26974d3caa9f2b6d9d4d34254067ba.jpg)  
+Figure 7. Visual comparisons on NHR dataset.
+
+parable with SOTA of non-physical canonical based methods, proving the effectiveness of our forward flow design.
+
+In Fig. 6, we show visual comparisons with NDVG [15], and TiNueVox [10]. The forward flow helps to recover the correct structure of dynamic objects, like the eye and edges of the chicken (top left) and the broom (top right). The relatively low resolution may harm the ability to recover very fine details, like the patterns on the 3D printer compared with TiNueVox-B [10] (bottom right).
+
+Evaluation on NHR Dataset We also test our method on NHR dataset. Quantitative results are shown in Table 3, which shows ours achieving best results consistently. We show qualitative comparison in Fig. 7, and our method could render clean and detailed images.
+
+Table 3. Quantitative comparison on NHR dataset. The red text indicates the best and blue text is the second best result.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">type</td><td colspan="3">Sport 1</td><td colspan="3">Sport 2</td><td colspan="3">Sport 3</td><td colspan="3">BacSKetball</td><td colspan="3">Mean</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>TiNeuVox-S [10]</td><td>NPC</td><td>26.06</td><td>0.93</td><td>0.10</td><td>25.98</td><td>0.93</td><td>0.11</td><td>25.90</td><td>0.93</td><td>0.11</td><td>23.75</td><td>0.91</td><td>0.14</td><td>25.42</td><td>0.92</td><td>0.12</td></tr><tr><td>TiNeuVox-B [10]</td><td>NPC</td><td>26.44</td><td>0.93</td><td>0.10</td><td>26.68</td><td>0.94</td><td>0.10</td><td>26.09</td><td>0.93</td><td>0.11</td><td>25.06</td><td>0.92</td><td>0.12</td><td>26.07</td><td>0.93</td><td>0.11</td></tr><tr><td>NDVG [15]</td><td>PC</td><td>23.66</td><td>0.89</td><td>0.15</td><td>24.43</td><td>0.91</td><td>0.13</td><td>22.54</td><td>0.88</td><td>0.16</td><td>22.55</td><td>0.89</td><td>0.17</td><td>23.29</td><td>0.89</td><td>0.15</td></tr><tr><td>Ours</td><td>PC</td><td>27.71</td><td>0.95</td><td>0.08</td><td>27.89</td><td>0.95</td><td>0.08</td><td>27.57</td><td>0.94</td><td>0.08</td><td>24.85</td><td>0.93</td><td>0.11</td><td>27.00</td><td>0.94</td><td>0.09</td></tr></table>
+
+Table 4. Quantitative comparison on Lego Complete Dataset. We report the average PSNR, LPIPS and the average relative depth error.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Type</td><td colspan="4">Space Interpolation</td><td colspan="4">Time Interpolation</td><td colspan="4">Canonical Interpolation</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>23.98</td><td>0.15</td><td>98.720</td><td>99.328</td><td>24.18</td><td>0.15</td><td>98.854</td><td>99.378</td><td>17.36</td><td>0.23</td><td>97.341</td><td>98.868</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>28.12</td><td>0.06</td><td>99.655</td><td>99.853</td><td>28.19</td><td>0.06</td><td>99.749</td><td>99.953</td><td>19.90</td><td>0.11</td><td>94.828</td><td>97.560</td></tr><tr><td>Ours.notv (803)1</td><td>PC</td><td>27.58</td><td>0.07</td><td>99.758</td><td>99.958</td><td>27.63</td><td>0.07</td><td>99.788</td><td>99.966</td><td>23.56</td><td>0.13</td><td>99.238</td><td>99.820</td></tr><tr><td>Ours.noup (803)2</td><td>PC</td><td>26.11</td><td>0.09</td><td>99.596</td><td>99.981</td><td>26.19</td><td>0.09</td><td>99.636</td><td>99.983</td><td>24.64</td><td>0.10</td><td>99.230</td><td>99.925</td></tr><tr><td>Ours.noinp (803)3</td><td>PC</td><td>27.21</td><td>0.08</td><td>99.783</td><td>99.979</td><td>27.27</td><td>0.08</td><td>99.797</td><td>99.980</td><td>23.91</td><td>0.09</td><td>99.586</td><td>99.963</td></tr><tr><td>Ours (803)</td><td>PC</td><td>28.18</td><td>0.06</td><td>99.818</td><td>99.985</td><td>28.22</td><td>0.06</td><td>99.839</td><td>99.987</td><td>25.63</td><td>0.07</td><td>99.654</td><td>99.968</td></tr></table>
+
+${}^{1}$  not use the all total variation losses  ${}^{2}$  not up-sample the voxel grid  ${}^{3}$  not use the inpaint network
+
+# 4.3. Method Analysis
+
+Flow Estimation and Canonical Space Geometry Since evaluating the estimated flow with ground truth is not practical, we choose to compare the reconstructed canonical geometry of physical canonical based methods. The idea is that if the canonical space is one frame of the whole timeline (like D-NeRF [36] and NDVG [15]), better flow estimation will result in better canonical scene geometry. We test these methods on Lego Complete Dataset, and all set the canonical space as the first frame of the image sequence.
+
+In Table 4, D-NeRF can not reconstruct the canonical radiance field well, since both the image and depth quality in canonical interpolation are significantly worse than those in space interpolation and time interpolation. NDVG [15] could recover much better images and geometry for other time steps, but the differences between canonical interpolation with the other two are even more significant. This means NDVG [15] has difficulty estimating correct backward flows. To render good quality images at other time steps, the correct geometries (depth) at these time steps are warped back into distorted canonical geometry due to incorrect backward flows.
+
+This is the proof of our claim that the non-smooth and discontinuous nature of the backward flow deformation field makes it difficult to fit with smooth functions, especially for NDVG [15], which has limited MLP capacity for fast training. However, our method performs significantly better for both image quality and depth, and there are fewer variations between canonical, space, and temporal interpolations. This demonstrates the benefit of forward warping, which makes it easier for the deformation model to learn deformation flows from canonical time to other times.
+
+We compare the canonical image of our method with DNeRF [36] in Fig. 8. Our method could recover the correct
+
+![](images/a48d7770ab4bf15306534c06be5e078d4008e4d1f0417afd2a013df46ebb6d8e.jpg)
+
+![](images/fc63bb9f32ea64ef1de9151c4db5056ce5f2ffe90fa88d76a91c1092b840f74c.jpg)
+
+![](images/b66a8f0f0fc9de5340f2246dc4000ba1bad9523434cb13146d15230fdca67d30.jpg)
+
+![](images/1482f60c99e055aacc2f220669d04ffa840f03187a4acbfdf58cc074ed06ca41.jpg)
+
+![](images/e6fb36dce6881c8cc8f6353c35f11f9239409efd21418ed97bf55592bc8ad194.jpg)
+
+![](images/26f84116c92fd9e82b1140fb2a881c8d3cbb390dcfa9779bb6b24e1f68e0a941.jpg)
+
+![](images/1f985130934b30e057231d66b56b973abf952c6a12fe0c2ea8c26764892415a2.jpg)
+
+![](images/a8c18abc22483f908ea658f487becead2ca40e219ed1dcf290ce8db87b02a06e.jpg)
+
+![](images/4b962c34bbd99ff8819624efec03dbc50b14cfe9aa9c5db746362fe4a8551a77.jpg)
+
+![](images/009132b84cd615ba6fd7974062517b16b9c9c82cf6b76869b6ec2f1e30cea065.jpg)  
+Figure 8. Canonical qualitative comparison. We show canonical radiance field comparison with D-NeRF [36]. Given the error map between the ground truth and rendered images, we can see that the canonical frame yielded by ours is closer to the ground truth. The results of D-NeRF are blurry and have large displacements.
+
+![](images/15cfcfc1282ce768ae528372aa0695f28d579af1a43f568d9206ad49a019fe82.jpg)
+
+![](images/af472cd5bfb363221d60f0c406a20763f3e75fbe49d337df5e40737836a97d17.jpg)
+
+geometry and image details of the canonical frame. For example, the arms of the bucket produced by D-NeRF are at the "mean" positions of the whole trajectory, and ours recover the correct status.
+
+Trajectory Visualization We show the learned DCT trajectories generated by our canonical trajectory field in Fig. 7 and Fig. 9. The canonical trajectory field is capable of recovering reasonable object point trajectories. Backward warping designs cannot track the motions of the same object point, so this is not a viable solution. With this feature, geometry constraints, motion models, and prior knowledge could be introduced in future work.
+
+![](images/3a4054b1ca5aeb8a2d459c4598529c87b2414269dd74bbe6c8ba3f299c2d7736.jpg)  
+Figure 9. Trajectory learned by the canonical trajectory field. Light blue is the canonical frame, the curve represents the historical motion trajectory. More videos can be found in supp.
+
+Regularization terms We study the effect of all regularization terms we proposed, including  $\mathcal{L}^{\mathrm{flow}}$ ,  $\mathcal{L}^{\mathrm{vdiff}}$  and  $\mathcal{L}^{\mathrm{tv}}$  in Table 5. We could observe that all these three regularization terms have positive effect on the performance, but the improvement is minor. This proves the improvement of our method compared with others come from the forward warping desgin we proposed in the paper. Also, backward flow based method NDVG [15] use similar regularization terms with ours, and our method has clear advantage compared with NDVG [15].
+
+Canonical setup In our method, we set canonical time to be the first frame for D-NeRF dataset to compare with physical canonical based method and the middle frame for HyperNeRF dataset for better performance. Setting canonical time to be the middle frame helps improving the performance as the state of the middle frame geometry is closer to other time steps compared with the first frame. To prove this, we set canonical time to be middel frame in Table 5 (can-time t at mid), and the PSNR improves slightly.
+
+Photometric loss for  $\mathbf{V}_{\mathbf{R}_{\mathrm{Up}}}$  We use photometric terms on  $\mathbf{V}_{\mathbf{R}_{\mathrm{Up}}}$  to make sure the warped grid before inpainting could already render reasonable images. This makes sure the UNet is actually doing 'inpainting'. Also, we do observe inpainting and upsampling could refine grids. In Fig. 7 and Fig. 9, the trajectories are reasonable which means we do learn trajectories without inpainting overfitting. We also test w/o photometric terms of  $\mathbf{V}_{\mathbf{R}_{\mathrm{Up}}}$  in Table 5 (w/o  $\mathbf{V}_{\mathbf{R}_{\mathrm{Up}}}$  photo) and the performance drops as there is no direct supervise signal for trajectory learning.
+
+More Ablations We study the effects of the total variation losses, the up-sample strategy, and the inpaint network we proposed in Table 6. The total variation losses help to
+
+Table 5. Ablations. Mean of Hell Warrior, Mutant, Hook and Bouncing Balls in D-NeRF dataset.  
+
+<table><tr><td>Method</td><td>Ours</td><td>w/o Ltv</td><td>w/o Lflow</td><td>w/o Lvdiff</td><td>can-time t at mid</td><td>w/o VRup photo</td></tr><tr><td>PSNR</td><td>33.75</td><td>33.30</td><td>33.74</td><td>33.57</td><td>34.09</td><td>31.56</td></tr><tr><td>SSIM</td><td>0.979</td><td>0.974</td><td>0.978</td><td>0.977</td><td>0.980</td><td>0.966</td></tr><tr><td>LPIPS</td><td>0.040</td><td>0.048</td><td>0.039</td><td>0.041</td><td>0.037</td><td>0.057</td></tr></table>
+
+Table 6. Ablation of losses on two dataset.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">D-NeRF</td><td colspan="2">HyperNeRF</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>Ours.notv1</td><td>33.09</td><td>0.046</td><td>23.84</td><td>0.831</td></tr><tr><td>Ours.noup2</td><td>32.03</td><td>0.043</td><td>23.72</td><td>0.822</td></tr><tr><td>Ours.noinp3</td><td>31.78</td><td>0.044</td><td>23.25</td><td>0.814</td></tr><tr><td>Ours</td><td>32.68</td><td>0.037</td><td>24.23</td><td>0.842</td></tr></table>
+
+improve visual quality (LPIPS) in D-NeRF dataset as it applies smoothness over the deformation and radiance space, but may harm the high-frequency details (PSNR) for some of the scenes in D-NeRF dataset. For HyperNeRF dataset, the total variation losses improve the results, as the camera settings are more challenging than D-NeRF dataset. However, this improvement is minor compared with the other two factors. Since the resolution is critical for voxel grid based method, up-sampling operation of inpaint network is vital to improve the performance. Finally, the inpaint network plays the most essential role among these three factors in our method. More ablations are provided in our supp.
+
+# 5. Conclusion
+
+This paper presents a canonical-based representation with forward warping for novel view synthesis of dynamic scenes. Our method models a static scene at the canonical field and forward warp this whole field to other time steps for dynamic scene rendering. To address the many-to-one and one-to-many mapping difficulties, we present a differentiable forward warping with an average splatting process and an inpaint network. Our proposed forward warping pipeline achieves SOTA performance on the public datasets and our newly built dataset, especially for canonical frames.
+
+Limitations and Future Directions Our current implementation is relatively memory-consuming, especially for real scenes. Also, the training speed is relatively slow (one day for each scene). Since we have a smooth trajectory field thanks to the forward warping, additional constraints and motion models could be introduced to learn better trajectories in future works.
+
+Acknowledgements This research was supported in part by the National Natural Science Foundation of China (Grant Nos. 62271410, 62293482, 62202409), the Fundamental Research Funds for the Central Universities, and Shenzhen Science and Technology Program (Grant No. RCBS20221008093241052).
+
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+[50] Alex Trevithick and Bo Yang. Grf: Learning a general radiance field for 3d representation and rendering. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2021. 2  
+[51] Chaoyang Wang, Ben Eckart, Simon Lucey, and Orazio Gallo. Neural trajectory fields for dynamic novel view synthesis. arXiv preprint arXiv:2105.05994, 2021. 1, 3, 4  
+[52] Qianqian Wang, Zhicheng Wang, Kyle Genova, Pratul P Srinivasan, Howard Zhou, Jonathan T Barron, Ricardo Martin-Brualla, Noah Snavely, and Thomas Funkhouser. Ibrnet: Learning multi-view image-based rendering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 2
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+[54] Minye Wu, Yuehao Wang, Qiang Hu, and Jingyi Yu. Multiview neural human rendering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 2, 6  
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+[61] Alex Yu, Sara Fridovich-Keil, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 2, 4  
+[62] Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural radiance fields. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2021. 2  
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+[66] Xiuming Zhang, Pratul P Srinivasan, Boyang Deng, Paul Debevec, William T Freeman, and Jonathan T Barron. Nerfactor: Neural factorization of shape and reflectance under an unknown illumination. ACM Transactions on Graphics (TOG), 2021. 2
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+                                            "content": "Figure 1. Comparison of backward flow and forward flow. This figure shows an example of backward and forward flow changes. (a) An example of dynamic scene. (b) With the bucket lifting up, different types of points cover the green point "
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+                                            "content": ", which needs very different backward flows to map this point back to canonical space. (d) shows the norm changes of the backward flow, which is not smooth. (c) On the other hand, the forward flow of position "
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+                                            "content": ", which maps the constant object point from canonical space to other times, is smooth and continuous. (e) shows the norm changes of the forward flow."
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+                                    "content": "promotes this area significantly and attracts lots of interest within a short time. NeRF [26] produces realistic images by representing the 3D world with a multi-layer perceptron (MLP), which maps the input 3D coordinates and 2D view direction to target density and color."
+                                }
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+                                    "type": "text",
+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "† Corresponding author (daiyuchao@nwpu.edu.cn). The first three authors also with the Shaanxi Key Laboratory of Information Acquisition and Processing."
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+                                    "content": "backward flow for moving the 3D points from the current time step back to the canonical time step. Although the canonical-based representation with the backward flow is easy to implement, the backward flow field is non-smooth and discontinuous. As shown in Fig. 1(b), for a fixed 3D position along the timeline, there will be different types of points covering the position "
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+                                    "content": ", which needs discontinuous flows to map them back to canonical space (Fig. 1(d)). So the backward flow cannot be fitted well with commonly used smooth motion models (MLP, for example). Also, distortions are introduced to the static canonical space geometry due to the failure of the motion model, as shown in Fig. 8."
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+                                    "content": "To solve the problem of backward flow, we propose using forward flow as the deformation model. Instead of warping the sampled points on image rays at other time steps back to the canonical time and rendering at the canonical space, we propose to warp the whole canonical radiance field from the canonical time to other time steps using forward deformation flow and render at corresponding time steps. In this way, the forward flow estimated by the deformation model will be smooth and continuous for the same 3D position along the timeline (Fig. 1(c) and (e)). Note that SNARF [7] has also used forward warping based on an inverse skinning model, but it is designed for dynamic human modeling and cannot be used in general scenes. In this paper, we aim to achieve forward warping for general scenes, which means we must warp the whole space."
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+                                    "content": "However, introducing forward warping into the canonical space based NeRF methods is not straightforward as there are three main problems to be solved. First, the traditional canonical radiance field in existing methods cannot be warped explicitly, since the radiance field is represented as a continuous function parameterized by an MLP. To solve this problem, we propose to use the voxel grid to represent the canonical radiance field as it is finite and discrete. Recent voxel-based methods [27,44,62] have proven the effectiveness of this representation. The other two problems are the many-to-one and one-to-many mapping issues brought by the inherent property of the forward warping operation. To address them, we propose a differentiable forward warping method consisting of an average splatting operation and an inpaint network to solve the many-to-one and one-to-many issue, respectively. Extensive experiments have been conducted to verify the effectiveness of our method."
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+                                    "content": "Our key contributions can be summarized as follows:"
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+                                    "content": "- To the best of our knowledge, we are the first to investigate forward warping in dynamic view synthesis for general scenes. We propose a novel canonical based NeRF with forward flow motion modeling for dynamic view synthesis. Thanks to the forward flow field, our method can better represent the object motions, and explicitly recover the trajectory of a surface point."
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+                                            "content": "- We introduce voxel grid based canonical radiance field to enable reasonable computation of forward warping, and propose a differentiable forward warping method, including an average splatting operation and an inpaint network, to solve the many-to-one and one-to-many issues of forward warping."
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+                                            "content": "- Experiments on multiple datasets show that our method outperforms existing methods on the D-NeRF [36] dataset, Hypernerf [33] dataset, NHR [54] dataset and our proposed dataset."
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+                                    "content": "2. Related Works"
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+                                    "content": "Novel View Synthesis (NVS) is a long-standing task in both computer vision and graphics [4, 6, 14, 18], and surveys of recent methods can be found in [42, 46, 47]. Some methods require to reconstruct an explicit 3D model to represent the scene, such as point clouds [1], voxels or meshes [16, 40, 41, 48]. Then novel images from arbitrary views can be rendered from this geometry. Another methods try to estimate depth map through multi-view geometry, and then aggregate features from multiple frames through the co-visibility, such as [8, 11, 17, 34, 40, 41, 57]. Recently, neural implicit representations have shown great promise for novel view synthesis and 3D modeling. In this section, we focus more on the neural implicit rendering methods and mainly summarize these schemes according to whether they can handle dynamic scenes."
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+                                    "content": "NVS for Static Scenes NeRF [26], as a seminal work, uses MLPs to model a 5D radiance field, which can render impressive view synthesis for static scenes captured. Numerous subsequent works have extended NeRF to kinds of scenarios, such as larger and unbounded scenes [25, 39, 45, 56, 64], relighting [3, 43, 58, 66], incorporating anti-aliasing for multi-scale rendering [2], and generalization ability [5, 50, 52, 63]. In addition, some methods are devoted to more efficient neural rendering and optimization in NeRF-like framework, such as [20, 22, 24, 28, 35, 62] focus more on efficient sampling along each ray for color accumulation, [37, 38] subdivide the scene into multiple cells for efficient processing, and [27, 44, 61] exploit voxel-grid representation to speed up the optimization of radiance field. However, these methods are mainly applicable to static scenes, leaving out the scenes with dynamic objects, which are actually more extensive and practical."
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+                                    "content": "NVS for Dynamic Scenes There are several works that extend NeRF from static scenes to dynamic scenes with nonrigid deformable objects. One feasible way is to build a 4D spatial-temporal representation. For example, Yoon et al. [60] combine single-view depth and depth from multiview stereo to render virtual views with 3D warping. Gao et al. [13] use a time-invariant model (static) and a time-varying model (dynamic) to represent the scenes, and reg-"
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+                                            "content": " is estimated by another Light MLP which takes deformation feature and coordinates as input. The deformation flow "
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+                                            "content": " from canonical to time "
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+                                            "type": "text",
+                                            "content": " can then be obtained; 2. Differential Forward Warping first warp "
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+                                            "type": "text",
+                                            "content": ". Then, the "
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+                                            "type": "text",
+                                            "content": " is inpainted by a inpaint network, which is "
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+                                            "type": "text",
+                                            "content": "; 3. Volume Rendering render colors of rays at time "
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+                                            "type": "text",
+                                            "content": " based on "
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+                                    ]
+                                }
+                            ],
+                            "index": 4,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
+                    "index": 3
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "ularize the dynamic model by scene flow estimation. NeRF-Flow [9] learns a 4D spatial-temporal representation of a dynamic scene from a set of RGB images. Xian et al. [55] build a 4D space-time irradiance field to map a spatial-temporal location to the emitted color and volume density. Similarly, NSFF [19] models the dynamic scene as a time-variant continuous function of appearance, geometry, and 3D scene motion. DCT-NeRF [51] uses the Discrete Cosine Transform (DCT) to capture dynamic motion, i.e. learning smooth and stable trajectories over time for each point in space."
+                                }
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+                                    "type": "text",
+                                    "content": "On the other hand, D-NeRF [36], Nerfies [32], HyperNeRF [33] and NR-NeRF [49] use a static canonical radiance field to capture geometry and appearance, and then learn a deformation/displacement field at each time step w.r.t. the canonical space. Specifically, to render an image at an arbitrary time step, a deformation field is used to estimate backward scene flow, moving 3D points from the current time step back to the canonical step. However, for the same 3D location along the timeline, the backward flow field is not guaranteed to be smooth and continuous. As a result, the canonical geometry usually has distortions and resembles the mean shape of a moving object. We focus on solving the problem of backward flow in this paper."
+                                }
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+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Along with the two main directions, there is a trend to speed up the training of dynamic NeRF, which is based on voxel grid representation. TiNeuVox [10] models the de"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "formation using a tiny MLP and uses multi-distance interpolation to get the feature for the radiance network which estimates the density and color. V4D [12] uses the 3D feature voxel to model the 4D radiance field with additional time dimension concatenated and proposes look-up tables for pixel-level refinement. Although V4D mainly focuses on improving image quality, the training speed is not significant compared to TiNeuVox. DeVRF [21] also builds on voxel-grid representation, which proposes to use multi-view data to overcome the nontrivial problem of the monocular setup. Multi-view data simplifies the learning of motion and geometry compared with others using monocular images."
+                                }
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+                                    "type": "text",
+                                    "content": "3. Method"
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+                                    "type": "text",
+                                    "content": "Motivation Backward-warping based methods [15, 36] propose a network "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "f_{t\\to \\mathrm{Can}} = F(p,t)"
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+                                    "type": "text",
+                                    "content": " to estimate the deformation flow "
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+                                    "type": "inline_equation",
+                                    "content": "f_{t\\rightarrow \\mathrm{Can}}"
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+                                    "type": "text",
+                                    "content": " which moves the point at the position "
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+                                    "type": "inline_equation",
+                                    "content": "p"
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+                                    "type": "text",
+                                    "content": " from other time steps "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " back to canonical time Can. However, for the same position "
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+                                    "type": "text",
+                                    "content": ", at different time steps "
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+                                    "type": "inline_equation",
+                                    "content": "ts"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", there could be different object points or even the empty point at this position, as shown in Fig. 1. This means the deformation flow "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f_{t\\to \\mathrm{Can}}"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is non-smooth and discontinuous along the timeline for a fixed position "
+                                },
+                                {
+                                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". This could introduce difficulties for motion learning and produce distortion in the canonical radiance field, because the backward flow network has limited capacities in learning a correct non-smooth and dis"
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 3. Two issues of the forward warping. Many-to-one: multiple positions in the source correspond to the same position in the target. One-to-many: one position in the source corresponds to multiple positions in the target, causing holes if warping naively."
+                                        }
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+                                    "type": "text",
+                                    "content": "continuous deformation field. On the other hand, our proposed forward warping strategy estimates the deformation "
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{Can} \\to t}"
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+                                    "type": "text",
+                                    "content": " from the canonical time to another time step of a 3D point in canonical space. The set of the deformation flows of one position along the timeline is actually the trajectory of this point. This guarantees the flows to be smooth and continuous along the timeline as we assume the motions in reality have these properties."
+                                }
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+                                    "content": "Method Overview We model a static scene at the canonical time using the voxel grid representation with a canonical radiance field and a canonical trajectory field. To synthesize dynamic images, we propose to forward warp the canonical radiance field to corresponding time steps and render the images using volume rendering based on the warped radiance field. Fig. 2 shows the overview of our method. In the following, we will introduce three main components of our method: voxel grid based canonical field, differentiable forward warping, and volume rendering. Finally, the model optimization is represented, including the proposed loss functions and training strategy."
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+                                    "content": "3.1. Voxel Grid Based Canonical Field"
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+                                    "content": "Canonical Radiance Field To warp a static scene in canonical time to other time steps using forward warping, the radiance field should be represented by finite 3D points. The original heavy MLP in NeRF [26] is not practical, as we cannot query infinite 3D points in the canonical space. Inspired by recent works [27,44,61] on voxel grid presentations, we propose to use a learnable voxel radiance feature grid "
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+                                    "type": "text",
+                                    "content": " to model the radiance of the static scene as shown in Fig. 2. The canonical radiance field is defined as"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {V} _ {\\mathrm {R}} ^ {\\text {C a n}} = F _ {\\theta_ {1}} \\left(\\mathbf {V} _ {\\mathrm {p}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\mathrm {R f}} ^ {\\text {C a n}}\\right), \\tag {1}",
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+                                    "content": "\\mathbf{V}_{\\mathrm{R}}^{\\mathrm{Can}} = \\{\\mathbf{V}_{\\sigma}^{\\mathrm{Can}}, \\mathbf{V}_{\\mathrm{cf}}^{\\mathrm{Can}}\\}"
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+                                    "content": " are the 3D coordinates of the voxel grid in canonical space, embedded according to NeRF [26]."
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+                                    "type": "text",
+                                    "content": "Canonical Trajectory Field We propose to use Discrete Cosine Transform (DCT) [51] to represent the trajectory of"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                    "type": "text",
+                                    "content": "a 3D point, which ensures the smoothness of the motion. Similar to canonical radiance field, we also use a deformation feature grid "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathrm{Df}}^{\\mathrm{Can}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and a lightweight MLP network "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "F_{\\theta_2}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to model the canonical trajectory field, which is defined as"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {V} _ {T} ^ {\\text {C a n}} = F _ {\\theta_ {2}} \\left(\\mathbf {V} _ {\\mathrm {p}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\mathrm {D f}} ^ {\\text {C a n}}\\right), \\tag {2}",
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_T^{\\mathrm{Can}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " contains the DCT coefficients of the voxels. Given time step "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we could get the deformation flow of these voxels from canonical to time step "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " by"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {V} _ {\\text {f l o w}} ^ {t} = f _ {\\mathrm {D C T} ^ {- 1}} \\left(\\mathbf {V} _ {T} ^ {\\text {C a n}}, t\\right) - f _ {\\mathrm {D C T} ^ {- 1}} \\left(\\mathbf {V} _ {T} ^ {\\text {C a n}}, \\text {C a n}\\right), \\tag {3}",
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{DCT}^{-1}}"
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+                                    "type": "text",
+                                    "content": " is the inverse DCT transform of the DCT coefficients as described in TrajectoryNeRF [51]."
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+                                    "type": "text",
+                                    "content": "3.2. Differentiable Forward Warping"
+                                }
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+                        }
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+                {
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+                                    "type": "text",
+                                    "content": "Forward warping has two major issues: many-to-one and one-to-many. Fig. 3 shows a simple example, where we aim to warp the source to the target using forward warping: a) Many-to-one: if a circle shrinks, there will be multiple positions corresponding to one position from the source to the target. b) One-to-many: if a circle expands, multiple positions in the target will correspond to the same position in the source, which leaves holes of the target if we warp the source to target naively. For the many-to-one issue, we propose to use the average splating to fuse multiple values into one. For the one-to-many issue, we use an inpaint network to inpaint the missing positions of the warped grids. More details are in the following sections."
+                                }
+                            ]
+                        }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Average Splatting We propose to fuse possible multiple values from the source grid that are mapped into the same voxel position of the target grid, motivated by Softmax-splatting [31]. Specifically, we propose a simple yet effective method that calculates the \"average\" of these values with a trilinear kernel. Formally, suppose that we need to warp the source grid "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}^{\\mathrm{S}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to target grid "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}^{\\mathrm{T}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " by the flow "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{S}\\rightarrow \\mathrm{T}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}"
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+                                {
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+                                    "type": "text",
+                                    "content": ", "
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+                                    "content": "\\mathbf{q}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are indexes of a voxel grid. We define "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}^{\\mathrm{T}} = F_{\\mathrm{warp}}(\\mathbf{V}^{\\mathrm{S}}, f_{\\mathrm{S}\\rightarrow \\mathrm{T}})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as follows,"
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+                                    "content": "\\mathbf {V} ^ {\\mathrm {T}} [ \\mathbf {p} ] = \\frac {\\sum_ {\\forall \\mathbf {q} \\in \\mathbf {V} ^ {\\mathrm {s}}} b [ \\mathbf {u} ] \\cdot \\mathbf {V} ^ {\\mathrm {S}} [ \\mathbf {q} ]}{\\sum_ {\\forall \\mathbf {q} \\in \\mathbf {V} ^ {\\mathrm {s}}} b [ \\mathbf {u} ]}, \\tag {4}",
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+                                    "content": "b [ \\mathbf {u} ] = \\prod \\max  (0, 1 - | \\mathbf {u} _ {i} |), i \\in \\{x, y, z \\}, \\tag {5}",
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+                                    "type": "text",
+                                    "content": " are three axes of the voxel grid, and "
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+                                    "content": "\\mathbf{u}_i \\in \\mathbb{R}"
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+                                    "type": "text",
+                                    "content": " is one element of the vector "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "text",
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+                                    "content": "\\mathbf {V} _ {\\mathrm {R}} ^ {t} = F _ {\\text {w a r p}} \\left(\\mathbf {V} _ {\\mathrm {R}} ^ {\\text {C a n}}, \\mathbf {V} _ {\\text {f l o w}} ^ {t}\\right). \\tag {7}",
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+                                    "type": "text",
+                                    "content": "Inpaint Network Another issue of forward warping is one-to-many, which leaves holes in the voxel grid after"
+                                }
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+                                }
+                            ],
+                            "index": 0,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
+                                46,
+                                180,
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+                                214
+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                46,
+                                                180,
+                                                287,
+                                                214
+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 4. Inpaint network. It consists of a 3D U-Net structure and an up-sampling layer, which could inpaint and upsample the input voxel grid."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "warping. To resolve this issue, we propose building an inpaint network to fill these holes. As shown in Fig. 4, we modify a 3D U-Net structure network [53] followed by an up-sampling layer, which is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        223,
+                                        286,
+                                        282
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathrm{R_{Inp}}}^{t} = F_{\\theta_{3}}(\\mathbf{V}_{\\mathrm{R}}^{t})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        223,
+                                        286,
+                                        282
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        223,
+                                        286,
+                                        282
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathrm{R_{Inp}}}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        223,
+                                        286,
+                                        282
+                                    ],
+                                    "type": "text",
+                                    "content": " is the inpainted and up-sampled voxel grid."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        285,
+                        286,
+                        439
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "This structure helps encoding layers to learn information from local neighboring voxels and decoding layers to recover the original resolution with filled content. We only feed the warped voxel grid to the inpaint network, which has no access to temporal information. Thus, the inpaint network can not learn to warp, limiting its ability only to inpainting. Since warping operations and the inpaint network are relatively expensive to compute, we propose to attach an up-sample layer after the U-Net structure. In this way, we could warp the grids with a low resolution to save time and memory, while rendering with a higher resolution for better image quality. The up-sample layer consists of a interpolation layer, convolution layers, and activation layers."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                            ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Volume Rendering"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "After we get the radiance voxel grid at time "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the pixel colors of the image rays can be rendered using volume rendering techniques [26]. Given a ray "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{r}(w) = \\mathbf{o} + w\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " emitted from the camera center "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{o}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " with view direction "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{d}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " through a given pixel on the image plane, we render the corresponding pixel color "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{C}_{\\mathrm{Inp}}(\\mathbf{r}) = F_{\\mathrm{render}}(\\mathbf{V}_{\\mathrm{R_{inp}}}^{t},\\mathbf{r})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": ". To do this, we get all 3D points "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        473,
+                                        286,
+                                        581
+                                    ],
+                                    "type": "text",
+                                    "content": " that the ray intersects with voxel grids. Next, trilinear interpolation is applied to obtain the density and color feature of each 3D point."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        115,
+                                        594,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "(\\sigma , \\mathbf {c} _ {\\mathbf {f}}) = F _ {\\text {i n t e r}} \\left(\\mathbf {V} _ {\\mathrm {R} _ {\\mathrm {l n p}}} ^ {t}, \\mathbf {p}\\right). \\tag {8}",
+                                    "image_path": "4e7740c107e6ac3ff81bfda69385daed0f5a2b2d81b6a9cf9abbc1af3af5e20f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    ],
+                    "type": "text",
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+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Then, we get the color of this 3D point "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        633
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        99,
+                                        645,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {c} = \\left\\{ \\begin{array}{l l} \\mathbf {c} _ {\\mathbf {f}} & \\text {i f} \\mathbf {c} _ {\\mathbf {f}} \\in \\mathbb {R} ^ {3}, \\\\ F _ {\\theta_ {4}} \\left(\\mathbf {c} _ {\\mathbf {f}}, \\mathbf {d}\\right) & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {9}",
+                                    "image_path": "7b2fe140da3ba2648ec9ace4558b79a5e0a11206225a85cce48f2b706d67e52e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{\\theta_4}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        689,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " is a small MLP network that is used to produce colors that depend on the direction of the ray."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        318,
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+                                        84
+                                    ],
+                                    "type": "text",
+                                    "content": "Finally, the pixel color could be rendered by"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        326,
+                                        91,
+                                        545,
+                                        113
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {C} (\\mathbf {r}) = \\sum_ {k = 1} ^ {K} T \\left(w _ {k}\\right) \\alpha \\left(\\sigma \\left(w _ {k}\\right) \\delta_ {k}\\right) \\mathbf {c} \\left(w _ {k}\\right), \\tag {10}",
+                                    "image_path": "9df7911ef6c95d7da386867443066c75bb2f3c06b49b9de568db7f433f84c1e0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                        141
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                348,
+                                115,
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+                                141
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        348,
+                                        115,
+                                        545,
+                                        141
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "T \\left(w _ {k}\\right) = \\exp \\left(- \\sum_ {j = 1} ^ {k - 1} \\sigma \\left(w _ {j}\\right) \\delta_ {j}\\right), \\tag {11}",
+                                    "image_path": "bb77931e788f7f6129747f112fe47502972acdd06f90d574761ef3245ed02114.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        306,
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+                        545,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                148,
+                                545,
+                                184
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of sampled points along the ray, "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{k}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "text",
+                                    "content": " is the distance between adjacent samples along the ray, and "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha (\\sigma (w_k)\\delta_k) = 1 - \\exp (-\\sigma (w_k)\\delta_k)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        148,
+                                        545,
+                                        184
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        306,
+                        185,
+                        545,
+                        236
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                185,
+                                545,
+                                236
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": "Note that the warped radiance grid "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathrm{R}}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " should also render reasonable images. So we directly up-sample "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathrm{R}}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " to get "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathrm{RUp}}^{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "text",
+                                    "content": " without inpainting, and render the corresponding pixel color "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        185,
+                                        545,
+                                        236
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{C}_{\\mathrm{Up}}(\\mathbf{r}) = F_{\\mathrm{render}}(\\mathbf{V}_{\\mathrm{RUp}}^{t},\\mathbf{r})"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        306,
+                        243,
+                        423,
+                        255
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                243,
+                                423,
+                                255
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        243,
+                                        423,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": "3.4. Model Optimization"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        306,
+                        261,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        261,
+                                        545,
+                                        311
+                                    ],
+                                    "type": "text",
+                                    "content": "To optimize the model, we design a series of loss functions. Photometric Loss First, the most important loss is the photometric loss, which is the mean square error (MSE) of the rendered color and ground truth color "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        261,
+                                        545,
+                                        311
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{C}_{\\mathrm{gt}}(\\mathbf{r})"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        339,
+                                        319,
+                                        545,
+                                        378
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} ^ {\\mathrm {p h o t o}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\| \\mathbf {C} _ {\\operatorname {I n p}} (\\mathbf {r}) - \\mathbf {C} _ {\\mathrm {g t}} (\\mathbf {r}) \\| _ {2} ^ {2} \\\\ + \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\| \\mathbf {C} _ {\\mathrm {U p}} (\\mathbf {r}) - \\mathbf {C} _ {\\mathrm {g t}} (\\mathbf {r}) \\| _ {2} ^ {2}, \\tag {12} \\\\ \\end{array}",
+                                    "image_path": "5cd1bf59bd225aed655691cbe150768fc23d651162180ab67ad9d0e088f73c36.jpg"
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+                                    "content": "Following DVGO [44], we use "
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+                                    "type": "text",
+                                    "content": " to directly supervise the color of sampled points. The intuition is that sampled points with larger weights contribute more to the rendered color. Also, we use the background entropy loss "
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+                                    "type": "text",
+                                    "content": " to encourage the densities concentrating on either the foreground or the background."
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+                                    "content": "Inpaint Network Loss As the inpaint network is used to complete the warped voxel grids, the output of the inpaint network should be close to the input. Therefore, we propose to use the L1 norm of the difference between the input and output of the inpaint network."
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+                                    "content": "\\mathcal {L} ^ {\\mathrm {v d i f f}} = \\left\\| \\mathbf {V} _ {\\mathrm {R} _ {\\text {I n p}}} ^ {t} - \\mathbf {V} _ {\\mathrm {R} _ {\\mathrm {U p}}} ^ {t} \\right\\| _ {1}. \\tag {13}",
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+                                    "content": "Regularization Terms Since modeling the appearance and motion of a dynamic scene from monocular images is a nontrivial problem, we propose a series of regularization terms."
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+                                    "content": "First, we encourage most 3D points in canonical space to be static by introducing "
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+                                    "type": "text",
+                                    "content": " to be the L1 norm of "
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+                                    "type": "text",
+                                    "content": ". Second, denoting "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " as the total variation function. We compute "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}^{\\mathrm{tv}}(\\mathbf{V}_{\\sigma}^{\\mathrm{Can}})"
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+                                    "type": "text",
+                                    "content": " to ensure the spatial smoothness of the density in canonical space, and introduce "
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+                                    "type": "text",
+                                    "content": " to encourage the spatial smoothness of the motions. Finally, inspired by RegNeRF [29], we render depths "
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+                                    "type": "text",
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+                                    "type": "text",
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+                                            "type": "text",
+                                            "content": "Table 1. Quantitative comparison on D-NeRF Dataset. Comparison of our method with others on LPIPS and PSNR/SSIM. The Red text indicates the best and blue text is the second best result."
+                                        }
+                                    ]
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Methods</td><td>Type</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>T-NeRF [36]</td><td>N</td><td>29.51</td><td>0.95</td><td>0.08</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>30.75</td><td>0.96</td><td>0.07</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>32.67</td><td>0.97</td><td>0.04</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>30.50</td><td>0.95</td><td>0.07</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>30.54</td><td>0.96</td><td>0.05</td></tr><tr><td>Ours (803)</td><td>PC</td><td>32.68</td><td>0.97</td><td>0.04</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Overall Loss The overall loss function used for optimization defined as follow, where "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "w_{1\\sim 7}"
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+                                    "type": "text",
+                                    "content": " are weights to balance each component in the final coarse loss."
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} ^ {\\text {p h o t o}} + w _ {1} \\mathcal {L} ^ {\\text {p t c}} + w _ {2} \\mathcal {L} ^ {\\text {b g}} + w _ {3} \\mathcal {L} ^ {\\text {f l o w}} + w _ {4} \\mathcal {L} ^ {\\text {v d i f f}} \\tag {14} \\\\ + w _ {5} \\mathcal {L} ^ {\\mathrm {t v}} \\left(\\mathbf {V} _ {\\sigma} ^ {\\text {C a n}}\\right) + w _ {6} \\mathcal {L} ^ {\\mathrm {t v}} \\left(\\mathbf {V} _ {\\text {f l o w}} ^ {t}\\right) + w _ {7} \\mathcal {L} ^ {\\mathrm {t v}} (\\mathbf {D}), \\\\ \\end{array}",
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+                                    "content": "Training Strategy First, we propose progressive training, which starts training with images close to the canonical time and progressively adds images with farther time steps until all images are added. Second, we set up a coarse-to-fine training strategy. In the coarse stage, we set the color feature to be the color itself, without considering the ray directions. We compute a smaller bounding box with the proxy geometry learned from the coarse stage, which could filter a large portion of empty space for the fine stage training. The model trained in the fine stage is our final model, and we set the color features to be high dimensional features and model the ray direction dependency with "
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+                                    "content": "F_{\\theta_4}"
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+                                    "type": "text",
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+                                    "content": "4. Experiments"
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+                                    "content": "4.1. Baselines and Evaluation Datasets"
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+                                    "type": "text",
+                                    "content": "Baselines The methods compared in this paper are classified into three types. First, we compare methods which are non-canonical based (N), including NeRF[26], and T-NeRF[36]. Second, physical canonical based methods (PC) contain D-NeRF [36], NDVG[15] and Ours. These methods set their canonical space as one frame of the whole timeline by explicitly giving zeros to estimated flows at the canonical time. The canonical space of these methods should have reasonable physical 3D reconstructions of the scene at the canonical time. Third, non-physical canonical based methods (NPC) consists of NV[23], Nerfies[32], HyperNeRF[33] and TiNeuVox[10]. Their canonical space geometries do not necessarily have physical meanings."
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+                                    "content": "D-NeRF Dataset We evaluate our method on 8 dynamic scenes of D-NeRF [36] dataset. We report several common metrics for the evaluation: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and Learned Perceptual Image Patch Similarity (LPIPS) [65]."
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+                                            "content": "Figure 5. Qualitative comparison on D-NeRF Dataset. We show some novel view synthesized images on the selected test set of the dataset. Comparing ours with ground truth, D-NeRF [36] and TiNeuVox [10]. Our model yields cleaner images with more details."
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+                                    "content": "HyerNeRF Dataset Besides synthetic datasets, we also conduct experiments on real scenes, proposed by HyperN-eRF [33]. This dataset uses a multi-view camera rig consisting of 2 phones to capture real unbounded scenes with challenging rigid and non-rigid deformations."
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+                                    "content": "Lego Complete Dataset The D-NeRF [36] dataset only contains 20 test images for each scene, and the evaluations of D-NeRF do not contain images in the canonical space. However, for physical canonical based methods (PC), canonical space geometry is important, as it affects images quality rendered at the canonical time and reflects the quality of flow estimation. Hence, we build a new dataset, named Lego Complete Dataset, which animates the object LEGO in D-NeRF dataset with 3 different motion patterns. For each scene, the test set is split into 3 categories to evaluate three abilities: space interpolation (rand views for each train time step), time interpolation (times between trained time steps), and canonical interpolation (rand views for canonical time step) abilities. For more details, please refer to our supp."
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+                                    "content": "Besides the image quality, we also consider geometry precision by evaluating the depth of each test image to analyze the reconstructed geometry. For depth metrics, we use the relative error "
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Type</td><td colspan=\"2\">3D Printer</td><td colspan=\"2\">Broom</td><td colspan=\"2\">Chicken</td><td colspan=\"2\">Peel Banana</td><td colspan=\"2\">Mean</td></tr><tr><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>NeRF [26]</td><td>N</td><td>20.7</td><td>0.780</td><td>19.9</td><td>0.653</td><td>19.9</td><td>0.777</td><td>20.0</td><td>0.769</td><td>20.1</td><td>0.745</td></tr><tr><td>NV [23]</td><td>NPC</td><td>16.2</td><td>0.665</td><td>17.7</td><td>0.623</td><td>17.6</td><td>0.615</td><td>15.9</td><td>0.380</td><td>16.9</td><td>0.571</td></tr><tr><td>Nerfies [32]</td><td>NPC</td><td>20.6</td><td>0.830</td><td>19.2</td><td>0.567</td><td>26.7</td><td>0.943</td><td>22.4</td><td>0.872</td><td>22.2</td><td>0.803</td></tr><tr><td>HyperNeRF [33]</td><td>NPC</td><td>20.0</td><td>0.821</td><td>19.3</td><td>0.591</td><td>26.9</td><td>0.948</td><td>23.3</td><td>0.896</td><td>22.4</td><td>0.814</td></tr><tr><td>TiNeuVox-S (1003) [10]</td><td>NPC</td><td>22.7</td><td>0.836</td><td>21.9</td><td>0.707</td><td>27.0</td><td>0.929</td><td>22.1</td><td>0.780</td><td>23.4</td><td>0.813</td></tr><tr><td>TiNeuVox-B (1603) [10]</td><td>NPC</td><td>22.8</td><td>0.841</td><td>21.5</td><td>0.686</td><td>28.3</td><td>0.947</td><td>24.4</td><td>0.873</td><td>24.3</td><td>0.837</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>22.4</td><td>0.839</td><td>21.5</td><td>0.703</td><td>27.1</td><td>0.939</td><td>22.8</td><td>0.828</td><td>23.3</td><td>0.823</td></tr><tr><td>Ours (703)</td><td>PC</td><td>22.8</td><td>0.845</td><td>21.9</td><td>0.715</td><td>28.0</td><td>0.944</td><td>24.3</td><td>0.865</td><td>24.2</td><td>0.842</td></tr></table>",
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+                                    "content": "Evaluation on D-NeRF Dataset We compared our method with the canonical-based backward flow methods D-NeRF [36], NDVG [15] and TiNeuVox [10] on D-NeRF Dataset. As shown in Table 1, our method achieves significant improvements in terms of all three metrics for physical canonical based methods. On average, our method improves PSNR by 2.18 compared with D-NeRF and 2.14 compared with NDVG. For non-physical canonical based methods, our method also achieves the best result. Ours show obviously better qualitative rendering quality compared with TiNeuVox-S "
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+                                    "content": " [10] with even smaller voxel resolution. More detailed statistics are provided in supp."
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+                                    "content": "We also provide some visual comparisons in Fig. 5. Ours could recover accurate and detailed images, e.g., the helmet and arm in the top scene, and could also produce cleaner boundaries, e.g. the hand and feet in the bottom scene."
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+                                    "content": "Evaluation on HyperNeRF Dataset We further compare our method with some highly related works on real scene dataset proposed by [33]. As shown in Table 2, our method achieves consistently better performance among physical canonical based methods. Our method has a voxel grid resolution limitation, due to we need to warp the whole voxel grid for rendering. Compared with other voxel grid based methods, our voxel grid resolution is limited to "
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+                                    "type": "text",
+                                    "content": " static voxel grid for background modeling. However, the performance of our method is still com"
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+                                    "content": "parable with SOTA of non-physical canonical based methods, proving the effectiveness of our forward flow design."
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+                                    "content": "In Fig. 6, we show visual comparisons with NDVG [15], and TiNueVox [10]. The forward flow helps to recover the correct structure of dynamic objects, like the eye and edges of the chicken (top left) and the broom (top right). The relatively low resolution may harm the ability to recover very fine details, like the patterns on the 3D printer compared with TiNueVox-B [10] (bottom right)."
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+                                    "content": "Evaluation on NHR Dataset We also test our method on NHR dataset. Quantitative results are shown in Table 3, which shows ours achieving best results consistently. We show qualitative comparison in Fig. 7, and our method could render clean and detailed images."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">type</td><td colspan=\"3\">Sport 1</td><td colspan=\"3\">Sport 2</td><td colspan=\"3\">Sport 3</td><td colspan=\"3\">BacSKetball</td><td colspan=\"3\">Mean</td></tr><tr><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>TiNeuVox-S [10]</td><td>NPC</td><td>26.06</td><td>0.93</td><td>0.10</td><td>25.98</td><td>0.93</td><td>0.11</td><td>25.90</td><td>0.93</td><td>0.11</td><td>23.75</td><td>0.91</td><td>0.14</td><td>25.42</td><td>0.92</td><td>0.12</td></tr><tr><td>TiNeuVox-B [10]</td><td>NPC</td><td>26.44</td><td>0.93</td><td>0.10</td><td>26.68</td><td>0.94</td><td>0.10</td><td>26.09</td><td>0.93</td><td>0.11</td><td>25.06</td><td>0.92</td><td>0.12</td><td>26.07</td><td>0.93</td><td>0.11</td></tr><tr><td>NDVG [15]</td><td>PC</td><td>23.66</td><td>0.89</td><td>0.15</td><td>24.43</td><td>0.91</td><td>0.13</td><td>22.54</td><td>0.88</td><td>0.16</td><td>22.55</td><td>0.89</td><td>0.17</td><td>23.29</td><td>0.89</td><td>0.15</td></tr><tr><td>Ours</td><td>PC</td><td>27.71</td><td>0.95</td><td>0.08</td><td>27.89</td><td>0.95</td><td>0.08</td><td>27.57</td><td>0.94</td><td>0.08</td><td>24.85</td><td>0.93</td><td>0.11</td><td>27.00</td><td>0.94</td><td>0.09</td></tr></table>",
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+                                            "content": "Table 4. Quantitative comparison on Lego Complete Dataset. We report the average PSNR, LPIPS and the average relative depth error."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Type</td><td colspan=\"4\">Space Interpolation</td><td colspan=\"4\">Time Interpolation</td><td colspan=\"4\">Canonical Interpolation</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td><td>PSNR↑</td><td>LPIPS↓</td><td>δ&lt;1.25</td><td>δ&lt;1.252</td></tr><tr><td>D-NeRF [36]</td><td>PC</td><td>23.98</td><td>0.15</td><td>98.720</td><td>99.328</td><td>24.18</td><td>0.15</td><td>98.854</td><td>99.378</td><td>17.36</td><td>0.23</td><td>97.341</td><td>98.868</td></tr><tr><td>NDVG (1603) [15]</td><td>PC</td><td>28.12</td><td>0.06</td><td>99.655</td><td>99.853</td><td>28.19</td><td>0.06</td><td>99.749</td><td>99.953</td><td>19.90</td><td>0.11</td><td>94.828</td><td>97.560</td></tr><tr><td>Ours.notv (803)1</td><td>PC</td><td>27.58</td><td>0.07</td><td>99.758</td><td>99.958</td><td>27.63</td><td>0.07</td><td>99.788</td><td>99.966</td><td>23.56</td><td>0.13</td><td>99.238</td><td>99.820</td></tr><tr><td>Ours.noup (803)2</td><td>PC</td><td>26.11</td><td>0.09</td><td>99.596</td><td>99.981</td><td>26.19</td><td>0.09</td><td>99.636</td><td>99.983</td><td>24.64</td><td>0.10</td><td>99.230</td><td>99.925</td></tr><tr><td>Ours.noinp (803)3</td><td>PC</td><td>27.21</td><td>0.08</td><td>99.783</td><td>99.979</td><td>27.27</td><td>0.08</td><td>99.797</td><td>99.980</td><td>23.91</td><td>0.09</td><td>99.586</td><td>99.963</td></tr><tr><td>Ours (803)</td><td>PC</td><td>28.18</td><td>0.06</td><td>99.818</td><td>99.985</td><td>28.22</td><td>0.06</td><td>99.839</td><td>99.987</td><td>25.63</td><td>0.07</td><td>99.654</td><td>99.968</td></tr></table>",
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+                                            "type": "text",
+                                            "content": " not use the all total variation losses "
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+                                            "type": "text",
+                                            "content": " not up-sample the voxel grid "
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+                                            "type": "text",
+                                            "content": " not use the inpaint network"
+                                        }
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+                            "angle": 0,
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+                                    "content": "4.3. Method Analysis"
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+                                    "content": "Flow Estimation and Canonical Space Geometry Since evaluating the estimated flow with ground truth is not practical, we choose to compare the reconstructed canonical geometry of physical canonical based methods. The idea is that if the canonical space is one frame of the whole timeline (like D-NeRF [36] and NDVG [15]), better flow estimation will result in better canonical scene geometry. We test these methods on Lego Complete Dataset, and all set the canonical space as the first frame of the image sequence."
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+                                    "content": "In Table 4, D-NeRF can not reconstruct the canonical radiance field well, since both the image and depth quality in canonical interpolation are significantly worse than those in space interpolation and time interpolation. NDVG [15] could recover much better images and geometry for other time steps, but the differences between canonical interpolation with the other two are even more significant. This means NDVG [15] has difficulty estimating correct backward flows. To render good quality images at other time steps, the correct geometries (depth) at these time steps are warped back into distorted canonical geometry due to incorrect backward flows."
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+                                    "content": "This is the proof of our claim that the non-smooth and discontinuous nature of the backward flow deformation field makes it difficult to fit with smooth functions, especially for NDVG [15], which has limited MLP capacity for fast training. However, our method performs significantly better for both image quality and depth, and there are fewer variations between canonical, space, and temporal interpolations. This demonstrates the benefit of forward warping, which makes it easier for the deformation model to learn deformation flows from canonical time to other times."
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+                                    "content": "We compare the canonical image of our method with DNeRF [36] in Fig. 8. Our method could recover the correct"
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+                                            "content": "Figure 8. Canonical qualitative comparison. We show canonical radiance field comparison with D-NeRF [36]. Given the error map between the ground truth and rendered images, we can see that the canonical frame yielded by ours is closer to the ground truth. The results of D-NeRF are blurry and have large displacements."
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+                                    "type": "text",
+                                    "content": "geometry and image details of the canonical frame. For example, the arms of the bucket produced by D-NeRF are at the \"mean\" positions of the whole trajectory, and ours recover the correct status."
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+                                    "content": "Trajectory Visualization We show the learned DCT trajectories generated by our canonical trajectory field in Fig. 7 and Fig. 9. The canonical trajectory field is capable of recovering reasonable object point trajectories. Backward warping designs cannot track the motions of the same object point, so this is not a viable solution. With this feature, geometry constraints, motion models, and prior knowledge could be introduced in future work."
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+                                            "content": "Figure 9. Trajectory learned by the canonical trajectory field. Light blue is the canonical frame, the curve represents the historical motion trajectory. More videos can be found in supp."
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+                                    "content": "Regularization terms We study the effect of all regularization terms we proposed, including "
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+                                    "type": "text",
+                                    "content": " in Table 5. We could observe that all these three regularization terms have positive effect on the performance, but the improvement is minor. This proves the improvement of our method compared with others come from the forward warping desgin we proposed in the paper. Also, backward flow based method NDVG [15] use similar regularization terms with ours, and our method has clear advantage compared with NDVG [15]."
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+                                    "content": "Canonical setup In our method, we set canonical time to be the first frame for D-NeRF dataset to compare with physical canonical based method and the middle frame for HyperNeRF dataset for better performance. Setting canonical time to be the middle frame helps improving the performance as the state of the middle frame geometry is closer to other time steps compared with the first frame. To prove this, we set canonical time to be middel frame in Table 5 (can-time t at mid), and the PSNR improves slightly."
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+                                    "content": "Photometric loss for "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}"
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+                                    "type": "text",
+                                    "content": " We use photometric terms on "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to make sure the warped grid before inpainting could already render reasonable images. This makes sure the UNet is actually doing 'inpainting'. Also, we do observe inpainting and upsampling could refine grids. In Fig. 7 and Fig. 9, the trajectories are reasonable which means we do learn trajectories without inpainting overfitting. We also test w/o photometric terms of "
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+                                    "type": "text",
+                                    "content": " in Table 5 (w/o "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{V}_{\\mathbf{R}_{\\mathrm{Up}}}"
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+                                    "type": "text",
+                                    "content": " photo) and the performance drops as there is no direct supervise signal for trajectory learning."
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+                                    "type": "text",
+                                    "content": "More Ablations We study the effects of the total variation losses, the up-sample strategy, and the inpaint network we proposed in Table 6. The total variation losses help to"
+                                }
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+                                            "content": "Table 5. Ablations. Mean of Hell Warrior, Mutant, Hook and Bouncing Balls in D-NeRF dataset."
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+                                            "html": "<table><tr><td>Method</td><td>Ours</td><td>w/o Ltv</td><td>w/o Lflow</td><td>w/o Lvdiff</td><td>can-time t at mid</td><td>w/o VRup photo</td></tr><tr><td>PSNR</td><td>33.75</td><td>33.30</td><td>33.74</td><td>33.57</td><td>34.09</td><td>31.56</td></tr><tr><td>SSIM</td><td>0.979</td><td>0.974</td><td>0.978</td><td>0.977</td><td>0.980</td><td>0.966</td></tr><tr><td>LPIPS</td><td>0.040</td><td>0.048</td><td>0.039</td><td>0.041</td><td>0.037</td><td>0.057</td></tr></table>",
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+                                            "content": "Table 6. Ablation of losses on two dataset."
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+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">D-NeRF</td><td colspan=\"2\">HyperNeRF</td></tr><tr><td>PSNR↑</td><td>LPIPS↓</td><td>PSNR↑</td><td>MS-SSIM↑</td></tr><tr><td>Ours.notv1</td><td>33.09</td><td>0.046</td><td>23.84</td><td>0.831</td></tr><tr><td>Ours.noup2</td><td>32.03</td><td>0.043</td><td>23.72</td><td>0.822</td></tr><tr><td>Ours.noinp3</td><td>31.78</td><td>0.044</td><td>23.25</td><td>0.814</td></tr><tr><td>Ours</td><td>32.68</td><td>0.037</td><td>24.23</td><td>0.842</td></tr></table>",
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+                                    "content": "improve visual quality (LPIPS) in D-NeRF dataset as it applies smoothness over the deformation and radiance space, but may harm the high-frequency details (PSNR) for some of the scenes in D-NeRF dataset. For HyperNeRF dataset, the total variation losses improve the results, as the camera settings are more challenging than D-NeRF dataset. However, this improvement is minor compared with the other two factors. Since the resolution is critical for voxel grid based method, up-sampling operation of inpaint network is vital to improve the performance. Finally, the inpaint network plays the most essential role among these three factors in our method. More ablations are provided in our supp."
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+                                    "content": "5. Conclusion"
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+                                    "content": "This paper presents a canonical-based representation with forward warping for novel view synthesis of dynamic scenes. Our method models a static scene at the canonical field and forward warp this whole field to other time steps for dynamic scene rendering. To address the many-to-one and one-to-many mapping difficulties, we present a differentiable forward warping with an average splatting process and an inpaint network. Our proposed forward warping pipeline achieves SOTA performance on the public datasets and our newly built dataset, especially for canonical frames."
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+                                    "content": "Limitations and Future Directions Our current implementation is relatively memory-consuming, especially for real scenes. Also, the training speed is relatively slow (one day for each scene). Since we have a smooth trajectory field thanks to the forward warping, additional constraints and motion models could be introduced to learn better trajectories in future works."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Acknowledgements This research was supported in part by the National Natural Science Foundation of China (Grant Nos. 62271410, 62293482, 62202409), the Fundamental Research Funds for the Central Universities, and Shenzhen Science and Technology Program (Grant No. RCBS20221008093241052)."
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@@ -0,0 +1,1765 @@
+[
+    {
+        "type": "text",
+        "text": "FreeCOS: Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Tianyi Shi, Xiaohuan Ding, Liang Zhang, Xin Yang†  \nSchool of EIC, Huazhong University of Science & Technology  \n{shitianyihust, dingxiaohuan, liangz, xinyang2014}@hust.edu.cn",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Curvilinear object segmentation is critical for many applications. However, manually annotating curvilinear objects is very time-consuming and error-prone, yielding insufficiently available annotated datasets for existing supervised methods and domain adaptation methods. This paper proposes a self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. The key contributions include a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. FFS generates curvilinear structures based on the parametric Fractal L-system and integrates the generated structures into unlabeled images to obtain synthetic training images via Fourier Domain Adaptation. GIA reduces the intensity differences between the synthetic and unlabeled images by comparing the intensity order of a given pixel to the values of its nearby neighbors. Such image alignment can explicitly remove the dependency on absolute intensity values and enhance the inherent geometric characteristics which are common in both synthetic and real images. In addition, GIA aligns features of synthetic and real images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). Extensive experimental results on four public datasets, i.e., XCAD, DRIVE, STARE and CrackTree demonstrate that our method outperforms the state-of-the-art unsupervised methods, self-supervised methods and traditional methods by a large margin. The source code of this work is available at https://github.com/TY-Shi/FreeCOS.",
+        "bbox": [
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+            323,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            790,
+            209,
+            806
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Automatically segmenting curvilinear structures (such as vascular trees in medical images and road systems in aerial photography) is critical for many applications, including retinal fundus disease screening [2, 14], diagnosing",
+        "bbox": [
+            76,
+            816,
+            468,
+            878
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "coronary artery disease [38], road condition evaluation and maintenance [51]. Despite a plethora of research works in the literature, accurately segmenting curvilinear objects remains challenging due to their complex structures with numerous tiny branches, tortuosity shapes, ambiguous boundaries due to imaging issues and noisy backgrounds.",
+        "bbox": [
+            500,
+            292,
+            890,
+            383
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Most recent methods [39, 10, 36, 42, 18, 29, 7, 28, 6, 35] leverage supervised deep learning for curvilinear object segmentation and have achieved encouraging results. However, those methods require a large number of pixel-wise manual annotations for training which are very expensive to obtain and error-prone due to poor image quality, annotator's fatigue and lack of experience. Although, there are several publically available annotated datasets for curvilinear object segmentation [37, 17, 51, 25], the large appearance variations between different curvilinear object images, e.g., X-ray coronary angiography images vs. retinal fundus images, yields significant performance degradation for supervised models across different types of images (even across the same type of images acquired using different equipments). As a result, expensive manual annotations are inevitably demanded to tune the segmentation model for a particular application. Potential solutions to alleviate the annotation burden include domain adaption [8, 32] and unsupervised segmentation [9, 19, 24, 11, 9, 1]. However, the effectiveness of domain adaptation is largely dependent on the quality of annotated data in the source domain and constrained by the gap between the source and target domain. Existing unsupervised segmentation methods [9, 19] can hardly achieve satisfactory performance for curvilinear objects due to their thin, long, and tortuosity shapes, complex branching structures, and confusing background artifacts.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite the high complexity and great variety of curvilinear structures in different applications, they share some common characteristics (i.e., the tube-like shape and the branching structure). Thus, existing studies [47, 46, 48] have demonstrated that several curvilinear structures (e.g., arterial trees of the circulation system) can be generated via the fractal systems with proper branching parameters to mimic the fractal and physiological characteristics, and",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "876",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "some observed variability. These results motivate us to use the generated curvilinear objects via the fractal systems to explicitly encode geometric properties and varieties (i.e., different diameters and lengths of branches, and different branching angles) into training samples and to assist feature learning of a curvilinear structure segmentation model. However, such formulas generated training samples can hardly mimic the appearance patterns within curvilinear objects, the transition regions between curvilinear objects and backgrounds, which are also key information for learning a segmentation model and contained in easily-obtained unlabeled target images. This paper asks the question, how to combine fractals and unlabeled target images to encode sufficient and comprehensive visual cues for learning robust and distinctive features of curvilinear structures?",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main contribution of this paper is a self-supervised segmentation method based on a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. Specifically, curvilinear structures are synthesized by the parametric fractal L-Systems [47] and serve as segmentation labels of synthetic training samples. To simulate appearance patterns in the object-background transition regions and background regions, we apply Fourier Domain Adaptation [45] (FDA) to fuse synthetic curvilinear structures and unlabeled target images. The synthetic images via our FFS module can effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds. To further improve the robustness to differences between intensity distributions of synthetic and real target images, we design a novel geometric information alignment (GIA) approach which aligns information of synthetic and target images at both image and feature levels. Specifically, GIA first converts each training image (synthetic and target images) into four geometry-enhanced images by comparing the intensity order of a given pixel to the values of its nearby neighbors (i.e., along with the up, down, left and right directions). In this way, the four converted images do not depend on the absolute intensity values but the relative intensity in order to capture the inherent geometric characteristic of the curvilinear structure, reducing the intensity differences between synthetic and target images. Then, we extract features from the 4-channel converted images and propose two loss functions, i.e., a prediction space adaptation loss (PSAL) and a curvilinear mask contrastive loss (CMCL), to align the geometric features of synthetic and target images. The PSAL minimizes the distance between the segmentation masks of the target images and synthetic curvilinear objects and the CMCL minimizes the distance between features of segmented masks and synthetic objects.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The FreeCOS based on FFS and GIA approaches applies to several public curvilinear object datasets, including XCAD [25], DRIVE [37], STARE [17] and CrackTree [51]. Extensive experimental results demonstrate that FreeCOS",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "outperforms the state-of-the-art self-supervised [25, 21], unsupervised [9, 19], and traditional methods [13, 22]. To summarize, the main contributions of this work are as follows:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We propose a novel self-supervised curvilinear feature learning method which intelligently combines tree-like fractals and unlabeled images to assist in learning robust and distinctive feature representations.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We propose Fractal-FDA synthesis (FFS) and geometric information alignment (GIA), which are the two key enabling modules of our method. FFS integrates the synthetic curvilinear structures into unlabeled images to guide learning distinctive features to distinguish foregrounds and backgrounds. GIA enhances geometric features and meanwhile improves the feature robustness to intensity differences between synthetic and target unlabeled images.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We develop a novel self-supervised segmentation network that can be trained using only target images and fractal synthetic curvilinear objects. Our network performs significantly better than state-of-the-art self-supervised/unsupervised methods on multiple public datasets with various curvilinear objects.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Traditional Methods",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Traditional curvilinear object segmentation methods [20, 26, 13, 40, 22] design heuristic rules and/or filters to capture features of the target curvilinear objects. For instance, Frangi et al. introduce the vesselness filter [13] based on the Hessian matrix to represent and enhance tube-like curvilinear objects. Khan et al. [20] further design B-COSFIRE filters to denoise retinal images and segment retinal vessels. Memari et al. [26] enhance image contrast via contrast-limited adaptive histogram equalization and then segment retinal vessels based on hand-crafted filters. In [40, 22], the authors propose optimally oriented flux (OOF) to enhance curvilinear tube-like objects. OOF exhibits better performance for segmenting adjacent curvilinear objects yet is sensitive to different sizes of curvilinear objects.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Traditional methods based on hand-crafted filters do not require any training yet they require careful parameter tuning for optimized performance. And the optimized parameter settings are usually data-dependent or even region-dependent, limiting their convenience in segmenting a wide variety of curvilinear objects.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Unsupervised Segmentation Methods",
+        "text_level": 1,
+        "bbox": [
+            500,
+            847,
+            821,
+            863
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Unsupervised segmentation methods can be generally divided into two classes: clustering based [19, 24, 11] and ad",
+        "bbox": [
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+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "877",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/530a9781843d8275a9097eae1d127e3ef32e17ca632af8fbe3e8d5d575312342.jpg",
+        "image_caption": [
+            "Figure 1. The pipeline of Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation (FreeCOS)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "versarial learning based [9, 1]. Xu et al. [19] propose Invariant Information Clustering (IIC) which automatically partitions input images into regions of different semantic classes by optimizing mutual information between related region pairs. Such a clustering-based method is more suitable for segmenting objects with aspect ratios close to one while becoming ineffective for curvilinear objects due to their thin, long, tortuous shapes. Redo [9] is based on an adversarial architecture where the generator is guided by an image and extracts the object mask, then redraws a new object at the same location with different textures/colors. However, this adversarial learning-based unsupervised method only performs well for objects which are visually distinguishable from backgrounds. For the segmentation of curvilinear objects with complex and numerous tiny branching structures, embedded in confusing and cluttered backgrounds, the efficacy of such a method degrades significantly.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In contrast to unsupervised methods, our method explicitly encodes geometric and photometric characteristics, as well as some observed varieties of curvilinear objects in target application into synthetic images. Those synthetic images provide labels to effectively guide the model to learn robust and distinctive features and thus yield superior performance to state-of-the-art unsupervised methods [9, 19].",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Self-supervised Learning Methods",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-supervised learning methods construct pretexts from large-scale unsupervised data and utilize contrastive learning losses to measure the similarities of sample pairs in the representation space. To this end, various pretext tasks have been designed, including jigsaw [12], hole-fill [31] and transformation invariance [16]. Although existing self-supervised methods have achieved outstanding performance in classification [27, 4], detection [44, 5], and image translation [30, 43], few of them provide a suitable pretext task for curvilinear object segmentation. A potential solu",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "tion is the pixel-level contrastive-based method [41, 3, 49], while it requires heavy manual annotations to prepare pixel-level positive and negative samples. Similar work to ours is [25, 21] which designs a self-supervised vessel segmentation method via adversarial learning and fractals. But this method requires clean background images as input (i.e., the first frame of the angiography sequence) for synthesis which greatly limits its applications. In addition, adversarial learning cannot explicitly and precisely enforce visual cues, which are important for learning segmentation-oriented features, being encoded in the synthetic images. As a result, although their synthetic images visually look similar to the target images, the segmentation accuracy is also quite low.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Figure. 1 shows the framework of FreeCOS which consists of two main modules, i.e., Fractal-FDA Synthesis (FFS) and Geometric Information Alignment (GIA). In FFS, we generate synthetic curvilinear structures via the parametric Fractal L-Systems and use the generated structures as segmentation maps to guide self-supervised training of a segmentation network. The synthetic curvilinear structures are then integrated into unlabeled images via FDA to form synthetic images of curvilinear structures. The intensity distributions of synthetic images could deviate from those of real target images and hence yield poor feature robustness. To address this problem, our GIA module first reduces image-level differences between the synthetic and target images by converting intensity images into four-channel intensity order images. The converted images of both synthetic images and target images are then input into U-Net to extract feature representations. Our GIA further aligns features of synthetic images and target images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). In the following, we present the details of FFS and GIA.",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "878",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/8387819f7bfc976b14eba261aeeaea5afd19e6d64104b5de4e60c6f586ee40aa.jpg",
+        "image_caption": [
+            "Figure 2. Exemplar results of the generated curvilinear structures from the basic and parametric Fractal L-system."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Fractal-FDA Synthesis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We first generate curvilinear structures via the parametric Fractal L-Systems and then integrate the synthetic objects into unlabeled target images to obtain synthetic training samples via FDA.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Fractal-based curvilinear structure generation. Fractals are simple graphic patterns rendered by mathematical formulas. In this work, we adopt the parametric Fractal L-systems proposed by Zamir et al. [47] to generate fractal tree structures and meanwhile select proper branching parameters according to physiological laws of curvilinear objects in target applications. Specifically, \"grammar\" for generating curvilinear structures with repeated bifurcations based on Fractal L-systems method is defined as follows:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l l} \\omega : & F \\\\ 1: & F, \\end{array} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr u l e: \\quad F \\rightarrow F [ - F ] [ + F ]\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The generated object by iteration iter:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {D r a w} (\\text {i t e r}, F, \\text {r u l e}) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            202,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $F$  represents a line of unit length in the horizontal direction,  $\\omega$  denotes an axiom, iter denotes the iteration and rule denotes the production rule. The square brackets represent the departure from  $[]$  and return to  $[]$  a branch point. The plus and minus signs represent turns through a given angle  $\\delta$  in the clockwise and anticlockwise directions, respectively. For example, the first three stages of a tree produced by the basic Fractal L-system, denoted by  $iter = 1 \\sim 3$ , are given by the:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} i t e r = 1 F \\\\ i t e r = 2 \\quad F [ - F ] [ + F ] \\\\ i t e r = 3 \\quad F [ - F ] [ + F ] [ - F [ - F ] [ + F ] ] [ + F [ - F ] [ + F ] ] \\tag {3} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The left part of Figure. 2 illustrates exemplar results of the generated curvilinear structures based on the basic Fractal system.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To synthesize curvilinear structures with various widths and lengths, we replace  $F$  using  $F_{random}(w_i, l_i, c_i)$  which represents a line of width  $w_i$ , length  $l_i$  and intensity  $c_i$ . We set the initial width  $w_{init}$ , length  $l_{init}$  and decreased parameter  $\\gamma$  by the repeated  $F_{random}$  in the Draw grammar. For the index number  $i$  of  $F_{random}$ ,  $w_i$  and  $l_i$  are given by:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} w _ {i} = w _ {i n i t} \\cdot \\gamma^ {i - 1} \\tag {4} \\\\ l _ {i} = l _ {i n i t} \\cdot \\gamma^ {i - 1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "We randomly choose a value within the range of (0, 255) and set this value as the intensity  $c_{i}$  for the index  $i$  of  $F_{random}$ . For the branching angle  $\\delta$ , we replace  $\\delta$  using  $\\delta_{random}$  (defined by  $\\delta_{init} \\pm \\delta_{delta}$ ,  $\\delta_{init}$  within the range of  $(20^{\\circ}, 120^{\\circ})$ ), in which  $\\delta_{delta}$  is a random angle ranging from  $10^{\\circ}$  to  $40^{\\circ}$ .",
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+    {
+        "type": "text",
+        "text": "To mimic the geometric characteristics of a target application, we incorporate the above-mentioned parameters into the L-Systems. Specifically, we design a set of rules  $\\text{ruleset} : (rule_1, \\dots, rule_n)$  for different fractal structures, like  $F_{random} \\rightarrow F_{random} - F_{random} [+F_{random} - F_{random}] [-F_{random} + F_{random}]$ . For each iteration iter, we randomly select a rule from the  $\\text{ruleset}$  as the production rule. In this way, we can increase the diversity of structures. The generated fractal curvilinear object  $X_{\\text{frac}} \\in \\mathbb{R}^{H \\times W}$  by iteration is given by:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {f r a c} = \\operatorname {D r a w} (i t e r, F _ {r a n d o m}, r u l e s e t, w _ {i}, l _ {i}, c _ {i}) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "FDA-based curvilinear object image synthesis. We further incorporate synthetic curvilinear objects into the target unlabeled images via FDA [45]. We define the target images as  $X_{t} \\in \\mathbb{R}^{H \\times W}$  and the synthetic images of fractal curvilinear object as  $X_{\\text{frac}}$ . Let  $\\mathcal{F}^A : \\in \\mathbb{R}^{H \\times W} \\to \\in \\mathbb{R}^{H \\times W}$  be the amplitude component of the Fourier transform  $\\mathcal{F}$  of a grayscale image. We define a  $\\beta \\in (0,1)$  to select the center region of the amplitude map.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Given two randomly sampled synthetic image  $X_{frac}$  and target image  $X_{t}$ , we follow FDA [45] to replace the low-frequency part in the amplitude map of  $X_{frac}$  by the FFT [15], denotes as  $\\mathcal{F}^A (X_{frac})$ , with that of the target image  $X_{t}$ , denoted as  $\\mathcal{F}^A (X_t)$ . Then, the modified spectral representation of  $X_{frac}$ , with its phase component unaltered, is mapped back to image  $X_{frac\\rightarrow t}$  by the inverse FFT [15], whose content is the same as  $X_{frac}$ , but will resemble the appearance of a sample  $X_{t}$ . After that, we apply a Gaussian blur to the output synthetic image of FDA to obtain synthetic images from FFS, denoted as  $X_{F}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Geometric Information Alignment",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Synthetic images generated by FFS could still have nontrivial intensity differences from that of real images. To address this problem, we further align synthetic images and real target images at both image and feature levels.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "879",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Image-level Alignment. We aim to explicitly remove the dependency on raw intensity values for both synthetic and real images and meanwhile enhance the geometric characteristics of curvilinear structures. To this end, for each image pixel  $j$  we compare its intensity value  $X(j)$  with its 8 neighboring pixels  $\\{n_d^m | m = 1, \\dots, 8\\}$  (yellow box in Figure. 1) lying perpendicular to  $j$  (red box in Figure. 1), where directional  $d$  denotes left, right, top, and bottom side of  $j$ . If  $X(j) > X(n_d^m)$ , we set the corresponding value for  $n_d^m$  to 0. Otherwise, we set the value for  $n_d^m$  to 1. Such operation produces four 8-bit images for each input image, where the  $m$ -th bit on the  $d$ -th image denotes the relative intensity order between  $j$  and its neighbor  $m$  along the  $d$ -th direction. For each input image  $X$  (denote as  $X_F$  and  $X_t$ ), we concatenate four 8-bit images  $(X_{IA}^1, \\dots, X_{IA}^d)$ , where  $X_{IA}^d(j)$  is represented as",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {I A} ^ {d} (j) = \\sum_ {m = 1} ^ {8} [ X (j) > X \\left(n _ {d} ^ {m}\\right) ] \\times 2 ^ {m - 1} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Such local intensity order transformation [34] can capture the intrinsic of the curvilinear object and meanwhile reduces the intensity gap between synthetic and real images.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Feature-level Alignment. Given the 4-channel transformed images, we utilize U-Net [33] to extract features. We align curvilinear objects' features of synthetic images and unlabeled target images based on two loss functions, i.e., the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1) Prediction space adaptation loss. We utilize adversarial learning to explicitly align the prediction space distribution of target images and synthetic images. We denote the prediction segmentation masks of the target images and the synthetic images as  $Y_{target} \\in \\mathbb{R}^{H \\times W}$  and  $Y_{syn} \\in \\mathbb{R}^{H \\times W}$ , respectively. We input  $Y_{target}$  and  $Y_{syn}$  into a fully-convolutional discriminator  $D$  as [50] trained via a binary cross-entropy loss  $\\mathcal{L}_d$ :",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {d} = \\mathbb {E} \\left[ \\log \\left(D \\left(Y _ {s y n}\\right)\\right) \\right] + \\mathbb {E} \\left[ \\log \\left(1 - D \\left(Y _ {t a r g e t}\\right)\\right) \\right] (7)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Accordingly, the PSAL is computed as:",
+        "bbox": [
+            76,
+            693,
+            339,
+            709
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {P S A L} = \\mathbb {E} \\left[ \\log \\left(D \\left(Y _ {\\text {t a r g e t}}\\right)\\right) \\right] \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2) Curvilinear mask contrastive loss. The CMCL aims to reduce the distance between features of synthetic images and true target images, and meanwhile to improve the feature distinctiveness between curvilinear objects and backgrounds. To this end, we take the feature maps (denoted as  $f \\in \\mathbb{R}^{H \\times W \\times C}$ ) from the final decoder layer of U-Net, the mask of synthetic image (denoted as  $G_{syn} \\in \\{0,1\\}^{H \\times W}$ ) and prediction mask of target image (denoted  $Y_{target} \\in [0,1]^{H \\times W}$ ) as input. We process  $f$  using a lightweight contrastive encoder and a contrastive projector as [41] to map",
+        "bbox": [
+            76,
+            750,
+            470,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$f$  to the feature space where the pixel-level contrastive loss is applied for  $Z \\in \\mathbb{R}^{H \\times W \\times C}$ .",
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We denote  $I$  as  $H\\times W$  spatial location of the projected feature maps  $Z$ , then for a location  $i\\in I$ , we can obtain a feature vector  $z_{i}$  at location  $i$  from feature map  $Z$ , label values  $g_{i}$  and  $y_{i}$  at  $i$  from the mask of synthetic image  $G_{syn}$  and the prediction mask  $Y_{target}$  respectively. We partition pixels of  $I$  into two groups: curvilinear object locations  $I^{+}$  and background locations  $I^{-}$ . For synthetic images, we perform the partition directly based on the mask  $G_{syn}$ , i.e.,  $I_{syn}^{+} = \\{i\\in I_{syn}\\mid g_{i} = 1\\}$  and  $I_{syn}^{-} = \\{i\\in I_{syn}\\mid g_{i} = 0\\}$ . For target images, as the ground-truth mask is not available, we alternatively perform the partition based on the prediction probability mask  $Y_{target}$ , i.e.,  $I_{target}^{+} = \\{i\\in I_{target}\\mid y_{i}\\geq 1 - \\alpha \\}$  and  $I_{target}^{-} = \\{i\\in I_{target}\\mid y_{i}\\leq \\alpha \\}$ , where  $\\alpha = 0.1$  is a small threshold and is fixed in our method.",
+        "bbox": [
+            496,
+            121,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We let  $q_{syn}^{+} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{syn}^{+}, \\sigma\\right) \\right\\}$  and  $k_{target}^{+} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{target}^{+}, \\sigma\\right) \\right\\}$  denote the curvilinear keys of synthetic and target images respectively. Similarly, we define  $k_{syn}^{-} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{syn}^{-}, \\sigma\\right) \\right\\}$  and  $k_{target}^{-} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{target}^{-}, \\sigma\\right) \\right\\}$  as the background keys of synthetic and target images, where  $\\S (\\bullet, \\sigma)$  is a random sampling operator which samples a subset from a set randomly with a proportion ratio  $\\sigma$ . We combine  $N$  negative queries of the features of synthetic and target images to form a negative set  $k^{-} = (k_{syn}^{-}, k_{target}^{-})$ . The CMCL is defined as:",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C M C L} = - \\log \\left(\\exp \\left(q _ {\\text {s y n}} ^ {+} \\cdot k _ {\\text {t a r g e t}} ^ {+} / \\tau\\right)\\right) + \\\\ \\log \\left(\\exp \\left(q _ {s y n} ^ {+} \\cdot k _ {t a r g e t} ^ {+} / \\tau\\right) + \\sum_ {i = 0} ^ {N} \\exp \\left(q _ {s y n} ^ {+} \\cdot k _ {i} ^ {-} / \\tau\\right)\\right) \\tag {9} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            518,
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+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau$  is a temperature hyper-parameter.",
+        "bbox": [
+            503,
+            587,
+            785,
+            601
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3) Final Loss. The final loss is a combination of the segmentation loss, the PSAL and CMCL as:",
+        "bbox": [
+            500,
+            601,
+            890,
+            632
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s e g} = \\mathbb {E} \\left[ G _ {s y n} \\cdot \\log \\left(Y _ {s y n}\\right) \\right] \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {s e g}} + \\mathcal {L} _ {\\text {P S A L}} + \\lambda \\mathcal {L} _ {\\text {C M C L}} \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            723,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "XCAD dataset. The X-ray angiography coronary artery disease (XCAD) dataset [25] is obtained during stent placement using a General Electric Innova IGS 520 system. Each image has a resolution of  $512 \\times 512$  pixels with one channel. The training set contains 1621 coronary angiograms without annotations as target images. The testing set contains 126 independent coronary angiograms with vessel segmentation maps annotated by experienced radiologists.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Retinal dataset. We also employ two public retin al datasets to validate the effectiveness of the proposed",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "880",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "method. The DRIVE dataset [37] consists of 40 color retinal images of size  $565 \\times 584$  pixels. We use 20 images as target images and 20 remaining as test images. The STARE dataset [17] contains 20 color retinal images of size  $700 \\times 605$  pixels with annotations as test images. There are 377 images without annotation which are used as target images.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "CrackTree dataset. The CrackTree dataset [51] contains 206  $800 \\times 600$  pavement images with different kinds of cracks with curvilinear structures. The whole dataset is split into 160 target images and 46 test images by [34] setting. Following [34], we dilate the annotated centerlines by 4 pixels to form the ground-truth segmentation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            76,
+            282,
+            261,
+            297
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For XCAD and CrackTree, we follow [25, 34] to use the following widely-used metrics in our evaluation, i.e., Jaccard Index (Jaccard), Dice Coefficient (Dice), accuracy (Acc.), sensitivity (Sn.) and specificity (Sp.). For the DRIVE and STARE datasets, we follow the state-of-the-art works for retina vessel segmentation [25] to report accuracy (Acc.), sensitivity (Sn.) specificity (Sp.) and area under curve (AUC) in our evaluation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For FFS, we set the ruleset as  $(\\text{rule}_1, \\dots, \\text{rule}_4)$ , such as:",
+        "bbox": [
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+            460,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} r u l e _ {1}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} [ + F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} ]. \\\\ \\operatorname {r u l e} _ {2}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} [ - F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} ]. \\\\ r u l e _ {3}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}}. \\\\ \\text {r u l e} _ {4}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} + F _ {\\text {r a n d o m}} + F _ {\\text {r a n d o m}}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            491,
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+            553
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We set the initial parameters of the Fractal system as follows. For all four datasets, the angle is randomly selected from  $(20^{\\circ},120^{\\circ})$ , the initial length is randomly selected from  $(120\\mathrm{px}$ $200\\mathrm{px})$  , the decreased parameter  $\\gamma$  is randomly selected from (0.7, 1). The initial width  $w_{init}$  is ranging from (8px, 14px) for XCAD, DRIVE and STARE. For CrackTree, the  $w_{init}$  is selected from (2px, 6px). The kernel size of Gaussian blur for FFS is 13. We generate 150, 150, 600 synthetic fractal images  $X_{frac}$  for XCAD, CrackTree, and retinal datasets, respectively.",
+        "bbox": [
+            75,
+            554,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We apply data augmentation including horizontal flipping, random brightness and contrast changes ranging from (1.0, 2.1), random saturation ranging from (0.5, 1.5), and random rotation with  $90^{\\circ}$ ,  $180^{\\circ}$ , and  $270^{\\circ}$ . The standard deviation for Gaussian noise is set to a random value within  $(-5, +5)$ . All images are cropped to  $256 \\times 256$  pixels for training. All the data-augmented operations are applied before the GIA module. The segmentation network is trained using the SGD with a momentum of 0.9 for optimization and the initial learning rate is 0.01. The discriminator network is trained using an Adam optimizer with an initial learning rate of  $10^{-3}$ . We employ a batch size of 8 to train the network for 600 epochs. The number of negative queries  $q_{syn}^{+}$",
+        "bbox": [
+            75,
+            704,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/c4909f84445490eab88944f0e5c43f93ca240d94624a4dae37f2cde4c9a9562d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Methods</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Upper bound</td><td>U-Net [33]</td><td>0.571</td><td>0.724</td><td>0.981</td><td>0.868</td><td>0.996</td></tr><tr><td rowspan=\"3\">Domain Adaptation</td><td>U-Net [33]</td><td>0.228</td><td>0.365</td><td>0.831</td><td>0.444</td><td>0.906</td></tr><tr><td>MMD [8]</td><td>0.262</td><td>0.416</td><td>0.873</td><td>0.553</td><td>0.920</td></tr><tr><td>YNet [32]</td><td>0.287</td><td>0.434</td><td>0.891</td><td>0.523</td><td>0.935</td></tr><tr><td rowspan=\"2\">Traditional</td><td>Hessian [13]</td><td>0.307</td><td>0.465</td><td>0.948</td><td>0.406</td><td>0.981</td></tr><tr><td>OOF [22]</td><td>0.241</td><td>0.386</td><td>0.899</td><td>0.566</td><td>0.920</td></tr><tr><td rowspan=\"2\">Unsupervised</td><td>IIC [19]</td><td>0.124</td><td>0.178</td><td>0.738</td><td>0.487</td><td>0.754</td></tr><tr><td>ReDO [9]</td><td>0.151</td><td>0.261</td><td>0.753</td><td>0.392</td><td>0.923</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.389</td><td>0.557</td><td>0.945</td><td>0.583</td><td>0.972</td></tr><tr><td>DARL [21]</td><td>0.471</td><td>0.636</td><td>0.962</td><td>0.597</td><td>0.985</td></tr><tr><td>Ours</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>",
+        "bbox": [
+            504,
+            88,
+            888,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/bfc6fff5de8e9a921c95b5c51ea9828cc3e061b77c2dfffa28f0aefa8010980f.jpg",
+        "table_caption": [
+            "Table 1. Quantitative evaluation of FreeCOS compared with different methods on the XCAD dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Methods</td><td colspan=\"4\">DRIVE</td><td colspan=\"4\">STARE</td></tr><tr><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td></tr><tr><td rowspan=\"4\">Traditional</td><td>Hessian [13]</td><td>0.941</td><td>0.644</td><td>0.97</td><td>0.847</td><td>0.938</td><td>0.690</td><td>0.957</td><td>0.858</td></tr><tr><td>OOF [22]</td><td>0.936</td><td>0.688</td><td>0.959</td><td>0.920</td><td>0.920</td><td>0.770</td><td>0.932</td><td>0.955</td></tr><tr><td>Memari [26]</td><td>0.961</td><td>0.761</td><td>0.981</td><td>0.871</td><td>0.951</td><td>0.782</td><td>0.965</td><td>0.783</td></tr><tr><td>Khan [20]</td><td>0.958</td><td>0.797</td><td>0.973</td><td>0.885</td><td>0.996</td><td>0.792</td><td>0.998</td><td>0.895</td></tr><tr><td rowspan=\"2\">Unsupervised</td><td>IIC [19]</td><td>0.738</td><td>0.632</td><td>0.840</td><td>0.736</td><td>0.710</td><td>0.586</td><td>0.832</td><td>0.709</td></tr><tr><td>ReDO [9]</td><td>0.761</td><td>0.593</td><td>0.927</td><td>0.760</td><td>0.756</td><td>0.567</td><td>0.899</td><td>0.733</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.913</td><td>0.794</td><td>0.982</td><td>0.888</td><td>0.910</td><td>0.774</td><td>0.980</td><td>0.877</td></tr><tr><td>DARL [21]</td><td>-</td><td>0.456</td><td>-</td><td>-</td><td>-</td><td>0.480</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>0.921</td><td>0.810</td><td>0.932</td><td>0.941</td><td>0.952</td><td>0.797</td><td>0.964</td><td>0.971</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/e1a6fd696bbda7ff647f19cede07039b2b5123b06b9e0d3a26d0746d5c690f5b.jpg",
+        "table_caption": [
+            "Table 2. Quantitative evaluation of FreeCOS compared with different methods on the retinal dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Methods</td><td>AUC</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td rowspan=\"2\">Traditional</td><td>Hessian [13]</td><td>0.780</td><td>0.122</td><td>0.935</td><td>0.310</td><td>0.945</td></tr><tr><td>OOF [22]</td><td>0.482</td><td>0.031</td><td>0.770</td><td>0.244</td><td>0.778</td></tr><tr><td>Unsupervised</td><td>ReDO [9]</td><td>0.422</td><td>0.035</td><td>0.632</td><td>0.450</td><td>0.635</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.477</td><td>0.078</td><td>0.299</td><td>0.042</td><td>0.912</td></tr><tr><td>DARL [21]</td><td>0.888</td><td>0.395</td><td>0.974</td><td>0.542</td><td>0.981</td></tr><tr><td>Ours</td><td>0.920</td><td>0.525</td><td>0.974</td><td>0.576</td><td>0.979</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Quantitative evaluation of FreeCOS compared with different methods on the CrackTree dataset.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "$k_{target}^{+}$  and  $k^{-}$  per batch is taken up to 500, 500 and 1000. The amplitude map center region selection parameter of  $\\beta$  is set to 0.3. the sampling ratio is 0.3, the hyper-parameter  $\\lambda$  is 0.4 and the temperature hyper-parameter  $\\tau$  is 0.1.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Experimental Results",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.3.1 Comparison with State-of-the-art",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Table. 1 compares the performance of vessel segmentation on XCAD between FreeCOS and the state-of-the-art methods, including the unsupervised methods [9, 19], the self-supervised methods [25, 21], domain adaptation methods [8, 32] and the traditional methods [13, 22]. The results in the 1st row are based on supervised U-Net as [25] (i.e., identical segmentation network trained using real images with manual labels) which are the upper bound.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For domain adaption methods, we pretrain a vessel segmentation model based on U-Net using training images of DRIVE. Then we adapt the pre-trained model to XCAD using MMD [8] and Ynet [32]. Even with supervised information in the annotated source domain, the performance of",
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+    },
+    {
+        "type": "page_number",
+        "text": "881",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/05509e8acafa82855ee9aa382cf25980ad71352b6e4a84a4765aa43280a8cc4b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr><tr><td>FFS+PSAL</td><td>0.468</td><td>0.633</td><td>0.957</td><td>0.680</td><td>0.974</td></tr><tr><td>FFS+PSAL+IA</td><td>0.485</td><td>0.647</td><td>0.958</td><td>0.667</td><td>0.976</td></tr><tr><td>FFS+GIA</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "MMD and YNet is still inferior to ours. Specifically, our method achieves  $21.2\\%$  improvement in Jaccard,  $22.7\\%$  improvement in Dice,  $6.9\\%$  improvement in Acc.,  $16.4\\%$  improvement in Sn., and  $4.2\\%$  improvement in Sp. compared with YNet.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Compared with the unsupervised methods IIC [19] and ReDO [9], our method achieves significantly better performance for all metrics on XCAD. The results show that unsupervised methods cannot achieve satisfactory performance on the gray-scale X-ray images where the segmentation objects can be hardly distinguished from the background.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Self-supervised method SSVS [25] is specifically designed for XCAD, yet our method still achieves much better performance for all metrics, i.e.,  $11\\%$  improvement in Jaccard,  $10.4\\%$  improvement in Dice and  $10.4\\%$  improvement in Sn.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table. 2 and 3 further compare our method with the existing methods on the retinal and crack datasets and a similar trend can be observed in these three datasets. Figure. 3 shows the visualization results of images from various kinds of curvilinear datasets.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "FreeCOS not only achieves state-of-the-art (SOTA) performance but also demonstrates unique advantages compared to various types of methods. a) Compared with traditional methods, FreeCOS does not require complex parameter tuning as traditional methods and achieves much better performance. b) FreeCOS can better tolerate large domain shifts than domain adaptation methods. But the effectiveness of current domain adaptation methods may struggle to achieve satisfactory performance facing a large domain gap. c) Unsupervised methods are more suitable for segmenting objects with aspect ratios close to one and perform well when objects are visually distinct from backgrounds. But their performance greatly degrades when segmenting curvilinear objects with branching structures in cluttered backgrounds. d) Self-supervised methods based on GAN/Diffusion require training with clean background images which limits applications to practical scenarios.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3.2 Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We first conduct ablation studies to evaluate the impact of different modules. To this end, we build the following variants based on our method. For all the variant models and our",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/1b707ebbab3ff7f8afdd272a16958a0bf5550e2773156189164ec8d026e85dad.jpg",
+        "table_caption": [
+            "Table 4. Ablation study for modules."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS w/o Gaussian blur</td><td>0.383</td><td>0.547</td><td>0.940</td><td>0.654</td><td>0.959</td></tr><tr><td>FFS w/o FDA</td><td>0.302</td><td>0.459</td><td>0.920</td><td>0.609</td><td>0.940</td></tr><tr><td>FFS w/o various intensities</td><td>0.405</td><td>0.569</td><td>0.957</td><td>0.525</td><td>0.984</td></tr><tr><td>FFS w/o various angles</td><td>0.267</td><td>0.415</td><td>0.939</td><td>0.409</td><td>0.972</td></tr><tr><td>FFS w/o various lengths</td><td>0.224</td><td>0.358</td><td>0.943</td><td>0.300</td><td>0.983</td></tr><tr><td>FFS w/o various widths</td><td>0.224</td><td>0.354</td><td>0.935</td><td>0.348</td><td>0.972</td></tr><tr><td>FFS</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/254a64cb1cc3c94fc96ebbc468d1e1180742752605e19dcb03b42fe703a016e4.jpg",
+        "table_caption": [
+            "Table 5. Ablation study for FFS."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Architecture</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS</td><td>U-Net [33]</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr><tr><td>FFS</td><td>Iternet [23]</td><td>0.481</td><td>0.645</td><td>0.959</td><td>0.670</td><td>0.976</td></tr><tr><td>FFS+GIA</td><td>Iternet [23]</td><td>0.505</td><td>0.664</td><td>0.964</td><td>0.641</td><td>0.984</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c5e336723daf4322ad6275620518b5eb33045c933ac1e223e62b19b793d7965a.jpg",
+        "table_caption": [
+            "Table 6. Ablation study for architecture."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Numbers of images</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Synthetic-15</td><td>0.464</td><td>0.629</td><td>0.958</td><td>0.630</td><td>0.979</td></tr><tr><td>Synthetic-45</td><td>0.478</td><td>0.642</td><td>0.958</td><td>0.674</td><td>0.976</td></tr><tr><td>Synthetic-75</td><td>0.488</td><td>0.652</td><td>0.960</td><td>0.668</td><td>0.978</td></tr><tr><td>Synthetic-150</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/cfb6557ebc1ff06d418bed725e6b8131515f41372e0b50ef98c9b0d89220db20.jpg",
+        "table_caption": [
+            "Table 7. Ablation study for different numbers of synthetic images."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Numbers of images</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Target-162</td><td>0.455</td><td>0.620</td><td>0.952</td><td>0.678</td><td>0.969</td></tr><tr><td>Target-486</td><td>0.476</td><td>0.637</td><td>0.955</td><td>0.683</td><td>0.972</td></tr><tr><td>Target-810</td><td>0.466</td><td>0.630</td><td>0.958</td><td>0.635</td><td>0.978</td></tr><tr><td>Target-1620</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 8. Ablation study for different numbers of target images.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "final model, we use the same U-Net model as our backbone. 1) FFS. We utilize the FFS to generate synthetic training images and the corresponding labels to train the U-Net segmentation model. 2) FFS+PSAL. We further apply PSAL to align features of synthetic and real target images on top of FFS. 3) FFS+PSAL+IA. We apply image-level alignment via relative intensity order transformation (i.e., IA) on top of FFS+PSAL. 4) FFS+GIA. We apply our GIA module (including IA, PSAL and CMCL) on top of FFS. This model is also our final curvilinear segmentation model. The ablation studies are conducted on XCAD. The trend on other datasets are similar and thus the results on the other datasets are omitted due to the space limit.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The results in Table 4 show that 1) by training a U-Net model using synthetic images from FFS, we can already achieve better performance than the SOTA self-supervised method SSVS which is based on adversarial learning [25]. Such results reveal a very interesting phenomenon although adversarial learning can synthesize visually similar images as real target images, it cannot explicitly control the generated visual patterns and thus fail to enforce",
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+        "text": "882",
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+        "image_caption": [],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/b3960a667a20f2026635849a359b45a229652498b1aff06f194dc683e63a2ed1.jpg",
+        "image_caption": [
+            "Image",
+            "Figure 3. The visualization results of images from the various kinds of curvilinear datasets."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
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+    {
+        "type": "image",
+        "img_path": "images/2ed174d431162fa11d653395591f64f70f58e51666ef6e204006178c815a98cd.jpg",
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+    },
+    {
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+        "img_path": "images/198f12f50e355dcc19c727ee2ca3740fb2b4df4cb1801a844c54fd9b8ddc9ef6.jpg",
+        "image_caption": [
+            "Hessian"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c164e0083859feba3f8e40cb5f2d971eb5648436fa2496a3ef17b2675f5169bd.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/6b82133fa8b714da483009b495b35a148af91312c0059ab8dfc2956ebf52c0eb.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/2e24529f65789588d3917df086afdfb92af7e29b0a07ed5f21e6c7222e29eea4.jpg",
+        "image_caption": [
+            "OOF"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/7df60fdc2de28746f7fc80914942c039d2e9b41abe2e6fa5fb9bbfd0180feb5b.jpg",
+        "image_caption": [
+            "Ours",
+            "GT"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            566,
+            90,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "the segmentation-oriented patterns and properties to be encoded in synthetic images. In comparison, FFS can explicitly control the synthesis of both curvilinear structures and background patterns and hence can achieve better performance. 2) Aligning features via prediction space adaptation loss (PSAL) can help reduce domain shifts between synthetic images and real target images and thus FFS+PSAL achieves performance improvements compared with FFS. 3) Aligning synthetic images and real target images via IA method can also reduce the domain shifts and thus FFS+PSAL+IA can provide complementary improvements to FFS+PSAL. 4) Finally, the best performance is obtained when combining both FFS and GIA.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We further explore the importance of different parameters in FFS on the final performance and discuss how to generate images of curvilinear structures to encode sufficient and comprehensive visual cues for learning robust and distinctive features. To this end, we build 6 variant models based on FFS. 1) FFS w/o Gaussian blur. We do not perform Gaussian blur to synthetic images from FFS. 2) FFS w/o FDA. We remove FDA-based synthesis from FFS and only generate curvilinear structures without backgrounds. 3) FFS w/o various intensities. We remove intensity variations  $c_{i}$  in the Fractal system and set the intensity to a fixed value 60. 4) FFS w/o various angles. We utilize a small branching angle range from  $(1^{\\circ}, 5^{\\circ})$  to reduce the branching angle variations. 5) FFS w/o various lengths. We reduce",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "the length variation range to (10px, 20px). 6) FFS w/o various widths. We reduce the width variation to (1px, 5px).",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The results in Table 5 show that 1) Gaussian blur can smooth the transition region between curvilinear objects and backgrounds, better mimicking the target images and providing more challenging samples for training than those with sharp boundaries. As a result, excluding Gaussian blur decreases the performance of FFS by  $6.8\\%$  in Dice. 2) FDA could provide background patterns of target images which are essential for learning features of negative samples. Thus, FFS w/o FDA is  $15.6\\%$  worse than FFS in Dice. 3) Among the four parameters of the Fractal system, i.e., intensity, angle, length and width, width plays the most important role in the final performance, i.e., FFS w/o various widths decreases the performance by  $26.1\\%$  compared with FFS in Dice. To summarize, we identify that the appearance patterns in the curvilinear object, object-background transition regions and background regions are important for self-supervised segmentation. Meanwhile, proper parameter settings which can provide similar geometric characteristics with the real target images are key to the success of our self-supervised method.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3.3 Ablation Study on Architecture",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "By replacing the U-Net with Iternet in FFS, We conduct ablation studies on two backbone networks U-Net [33]",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "883",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "and Iternet [23]. FFS using Iternet segmentation model gets better performance than FFS using U-Net in Table 6. FFS+GIA also demonstrates performance improvement, showing FreeCOS's effectiveness on different architectures. This indicates that the use of a more advanced segmentation network architecture for FreeCOS has the potential to improve performance.",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3.4 Self-supervised training with more data",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We also examine the segmentation performance when varying the number of synthetic images on the XCAD dataset. Results in Tables. 7 and 8 provide the results when using different numbers of synthetic structures and real target images for generating synthetic images for self-supervised training respectively. Synthetic-  $15\\sim$  Synthetic-150 denote using the number of synthetic fractal object images  $X_{frac}$  from 15 to 150, and Target-  $162\\sim$  Target-1620 denote using the number of target images  $X_{t}$  from 162 to 1620. Increasing both synthetic structures and real target images can accordingly improve the final segmentation performance.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. Different from existing methods, FreeCOS applies the proposed FFS and GIA approach to effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds and aligns information of synthetic and target images at both image and feature levels. One limitation of FreeCOS is that may generate false positives in other curvilinear objects (e.g., catheters in XCAD) and requires proper selection for width range. However, we have successfully utilized this self-supervised learning method for coronary vessel segmentation, retinal vessel segmentation and crack segmentation by reasonable parameter selection. To the best of our knowledge, FreeOCS is the first self-supervised learning method for various curvilinear object segmentation applications.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by the National Natural Science Foundation of China under Grants 62061160490, 62122029, and U20B2064.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            76,
+            773,
+            174,
+            789
+        ],
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+        ],
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diff --git a/2023/FreeCOS_ Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation/be0041d5-bbab-4e78-87f4-f20982dd3329_model.json b/2023/FreeCOS_ Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation/be0041d5-bbab-4e78-87f4-f20982dd3329_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..28bea531497187acc56b529a5ec3e8d8a761e88b
--- /dev/null
+++ b/2023/FreeCOS_ Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation/be0041d5-bbab-4e78-87f4-f20982dd3329_model.json	
@@ -0,0 +1,2334 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.807,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.1,
+                0.13,
+                0.872,
+                0.177
+            ],
+            "angle": 0,
+            "content": "FreeCOS: Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.211,
+                0.203,
+                0.758,
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+            ],
+            "angle": 0,
+            "content": "Tianyi Shi, Xiaohuan Ding, Liang Zhang, Xin Yang†  \nSchool of EIC, Huazhong University of Science & Technology  \n{shitianyihust, dingxiaohuan, liangz, xinyang2014}@hust.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.324,
+                0.473,
+                0.761
+            ],
+            "angle": 0,
+            "content": "Curvilinear object segmentation is critical for many applications. However, manually annotating curvilinear objects is very time-consuming and error-prone, yielding insufficiently available annotated datasets for existing supervised methods and domain adaptation methods. This paper proposes a self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. The key contributions include a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. FFS generates curvilinear structures based on the parametric Fractal L-system and integrates the generated structures into unlabeled images to obtain synthetic training images via Fourier Domain Adaptation. GIA reduces the intensity differences between the synthetic and unlabeled images by comparing the intensity order of a given pixel to the values of its nearby neighbors. Such image alignment can explicitly remove the dependency on absolute intensity values and enhance the inherent geometric characteristics which are common in both synthetic and real images. In addition, GIA aligns features of synthetic and real images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). Extensive experimental results on four public datasets, i.e., XCAD, DRIVE, STARE and CrackTree demonstrate that our method outperforms the state-of-the-art unsupervised methods, self-supervised methods and traditional methods by a large margin. The source code of this work is available at https://github.com/TY-Shi/FreeCOS."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.791,
+                0.21,
+                0.807
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.817,
+                0.47,
+                0.879
+            ],
+            "angle": 0,
+            "content": "Automatically segmenting curvilinear structures (such as vascular trees in medical images and road systems in aerial photography) is critical for many applications, including retinal fundus disease screening [2, 14], diagnosing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.293,
+                0.892,
+                0.384
+            ],
+            "angle": 0,
+            "content": "coronary artery disease [38], road condition evaluation and maintenance [51]. Despite a plethora of research works in the literature, accurately segmenting curvilinear objects remains challenging due to their complex structures with numerous tiny branches, tortuosity shapes, ambiguous boundaries due to imaging issues and noisy backgrounds."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.386,
+                0.893,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Most recent methods [39, 10, 36, 42, 18, 29, 7, 28, 6, 35] leverage supervised deep learning for curvilinear object segmentation and have achieved encouraging results. However, those methods require a large number of pixel-wise manual annotations for training which are very expensive to obtain and error-prone due to poor image quality, annotator's fatigue and lack of experience. Although, there are several publically available annotated datasets for curvilinear object segmentation [37, 17, 51, 25], the large appearance variations between different curvilinear object images, e.g., X-ray coronary angiography images vs. retinal fundus images, yields significant performance degradation for supervised models across different types of images (even across the same type of images acquired using different equipments). As a result, expensive manual annotations are inevitably demanded to tune the segmentation model for a particular application. Potential solutions to alleviate the annotation burden include domain adaption [8, 32] and unsupervised segmentation [9, 19, 24, 11, 9, 1]. However, the effectiveness of domain adaptation is largely dependent on the quality of annotated data in the source domain and constrained by the gap between the source and target domain. Existing unsupervised segmentation methods [9, 19] can hardly achieve satisfactory performance for curvilinear objects due to their thin, long, and tortuosity shapes, complex branching structures, and confusing background artifacts."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Despite the high complexity and great variety of curvilinear structures in different applications, they share some common characteristics (i.e., the tube-like shape and the branching structure). Thus, existing studies [47, 46, 48] have demonstrated that several curvilinear structures (e.g., arterial trees of the circulation system) can be generated via the fractal systems with proper branching parameters to mimic the fractal and physiological characteristics, and"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.222,
+                0.9
+            ],
+            "angle": 0,
+            "content": "† Corresponding author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "876"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.318
+            ],
+            "angle": 0,
+            "content": "some observed variability. These results motivate us to use the generated curvilinear objects via the fractal systems to explicitly encode geometric properties and varieties (i.e., different diameters and lengths of branches, and different branching angles) into training samples and to assist feature learning of a curvilinear structure segmentation model. However, such formulas generated training samples can hardly mimic the appearance patterns within curvilinear objects, the transition regions between curvilinear objects and backgrounds, which are also key information for learning a segmentation model and contained in easily-obtained unlabeled target images. This paper asks the question, how to combine fractals and unlabeled target images to encode sufficient and comprehensive visual cues for learning robust and distinctive features of curvilinear structures?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.322,
+                0.473,
+                0.838
+            ],
+            "angle": 0,
+            "content": "The main contribution of this paper is a self-supervised segmentation method based on a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. Specifically, curvilinear structures are synthesized by the parametric fractal L-Systems [47] and serve as segmentation labels of synthetic training samples. To simulate appearance patterns in the object-background transition regions and background regions, we apply Fourier Domain Adaptation [45] (FDA) to fuse synthetic curvilinear structures and unlabeled target images. The synthetic images via our FFS module can effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds. To further improve the robustness to differences between intensity distributions of synthetic and real target images, we design a novel geometric information alignment (GIA) approach which aligns information of synthetic and target images at both image and feature levels. Specifically, GIA first converts each training image (synthetic and target images) into four geometry-enhanced images by comparing the intensity order of a given pixel to the values of its nearby neighbors (i.e., along with the up, down, left and right directions). In this way, the four converted images do not depend on the absolute intensity values but the relative intensity in order to capture the inherent geometric characteristic of the curvilinear structure, reducing the intensity differences between synthetic and target images. Then, we extract features from the 4-channel converted images and propose two loss functions, i.e., a prediction space adaptation loss (PSAL) and a curvilinear mask contrastive loss (CMCL), to align the geometric features of synthetic and target images. The PSAL minimizes the distance between the segmentation masks of the target images and synthetic curvilinear objects and the CMCL minimizes the distance between features of segmented masks and synthetic objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.84,
+                0.472,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The FreeCOS based on FFS and GIA approaches applies to several public curvilinear object datasets, including XCAD [25], DRIVE [37], STARE [17] and CrackTree [51]. Extensive experimental results demonstrate that FreeCOS"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.151
+            ],
+            "angle": 0,
+            "content": "outperforms the state-of-the-art self-supervised [25, 21], unsupervised [9, 19], and traditional methods [13, 22]. To summarize, the main contributions of this work are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.162,
+                0.892,
+                0.222
+            ],
+            "angle": 0,
+            "content": "- We propose a novel self-supervised curvilinear feature learning method which intelligently combines tree-like fractals and unlabeled images to assist in learning robust and distinctive feature representations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.231,
+                0.892,
+                0.368
+            ],
+            "angle": 0,
+            "content": "- We propose Fractal-FDA synthesis (FFS) and geometric information alignment (GIA), which are the two key enabling modules of our method. FFS integrates the synthetic curvilinear structures into unlabeled images to guide learning distinctive features to distinguish foregrounds and backgrounds. GIA enhances geometric features and meanwhile improves the feature robustness to intensity differences between synthetic and target unlabeled images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.377,
+                0.892,
+                0.467
+            ],
+            "angle": 0,
+            "content": "- We develop a novel self-supervised segmentation network that can be trained using only target images and fractal synthetic curvilinear objects. Our network performs significantly better than state-of-the-art self-supervised/unsupervised methods on multiple public datasets with various curvilinear objects."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.489,
+                0.642,
+                0.505
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.514,
+                0.695,
+                0.529
+            ],
+            "angle": 0,
+            "content": "2.1. Traditional Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.537,
+                0.892,
+                0.748
+            ],
+            "angle": 0,
+            "content": "Traditional curvilinear object segmentation methods [20, 26, 13, 40, 22] design heuristic rules and/or filters to capture features of the target curvilinear objects. For instance, Frangi et al. introduce the vesselness filter [13] based on the Hessian matrix to represent and enhance tube-like curvilinear objects. Khan et al. [20] further design B-COSFIRE filters to denoise retinal images and segment retinal vessels. Memari et al. [26] enhance image contrast via contrast-limited adaptive histogram equalization and then segment retinal vessels based on hand-crafted filters. In [40, 22], the authors propose optimally oriented flux (OOF) to enhance curvilinear tube-like objects. OOF exhibits better performance for segmenting adjacent curvilinear objects yet is sensitive to different sizes of curvilinear objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.749,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Traditional methods based on hand-crafted filters do not require any training yet they require careful parameter tuning for optimized performance. And the optimized parameter settings are usually data-dependent or even region-dependent, limiting their convenience in segmenting a wide variety of curvilinear objects."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.822,
+                0.864
+            ],
+            "angle": 0,
+            "content": "2.2. Unsupervised Segmentation Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Unsupervised segmentation methods can be generally divided into two classes: clustering based [19, 24, 11] and ad"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "877"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.088,
+                0.891,
+                0.304
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.309,
+                0.89,
+                0.324
+            ],
+            "angle": 0,
+            "content": "Figure 1. The pipeline of Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation (FreeCOS)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.347,
+                0.473,
+                0.604
+            ],
+            "angle": 0,
+            "content": "versarial learning based [9, 1]. Xu et al. [19] propose Invariant Information Clustering (IIC) which automatically partitions input images into regions of different semantic classes by optimizing mutual information between related region pairs. Such a clustering-based method is more suitable for segmenting objects with aspect ratios close to one while becoming ineffective for curvilinear objects due to their thin, long, tortuous shapes. Redo [9] is based on an adversarial architecture where the generator is guided by an image and extracts the object mask, then redraws a new object at the same location with different textures/colors. However, this adversarial learning-based unsupervised method only performs well for objects which are visually distinguishable from backgrounds. For the segmentation of curvilinear objects with complex and numerous tiny branching structures, embedded in confusing and cluttered backgrounds, the efficacy of such a method degrades significantly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.606,
+                0.47,
+                0.712
+            ],
+            "angle": 0,
+            "content": "In contrast to unsupervised methods, our method explicitly encodes geometric and photometric characteristics, as well as some observed varieties of curvilinear objects in target application into synthetic images. Those synthetic images provide labels to effectively guide the model to learn robust and distinctive features and thus yield superior performance to state-of-the-art unsupervised methods [9, 19]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.379,
+                0.741
+            ],
+            "angle": 0,
+            "content": "2.3. Self-supervised Learning Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Self-supervised learning methods construct pretexts from large-scale unsupervised data and utilize contrastive learning losses to measure the similarities of sample pairs in the representation space. To this end, various pretext tasks have been designed, including jigsaw [12], hole-fill [31] and transformation invariance [16]. Although existing self-supervised methods have achieved outstanding performance in classification [27, 4], detection [44, 5], and image translation [30, 43], few of them provide a suitable pretext task for curvilinear object segmentation. A potential solu"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.347,
+                0.892,
+                0.545
+            ],
+            "angle": 0,
+            "content": "tion is the pixel-level contrastive-based method [41, 3, 49], while it requires heavy manual annotations to prepare pixel-level positive and negative samples. Similar work to ours is [25, 21] which designs a self-supervised vessel segmentation method via adversarial learning and fractals. But this method requires clean background images as input (i.e., the first frame of the angiography sequence) for synthesis which greatly limits its applications. In addition, adversarial learning cannot explicitly and precisely enforce visual cues, which are important for learning segmentation-oriented features, being encoded in the synthetic images. As a result, although their synthetic images visually look similar to the target images, the segmentation accuracy is also quite low."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.559,
+                0.591,
+                0.573
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Figure. 1 shows the framework of FreeCOS which consists of two main modules, i.e., Fractal-FDA Synthesis (FFS) and Geometric Information Alignment (GIA). In FFS, we generate synthetic curvilinear structures via the parametric Fractal L-Systems and use the generated structures as segmentation maps to guide self-supervised training of a segmentation network. The synthetic curvilinear structures are then integrated into unlabeled images via FDA to form synthetic images of curvilinear structures. The intensity distributions of synthetic images could deviate from those of real target images and hence yield poor feature robustness. To address this problem, our GIA module first reduces image-level differences between the synthetic and target images by converting intensity images into four-channel intensity order images. The converted images of both synthetic images and target images are then input into U-Net to extract feature representations. Our GIA further aligns features of synthetic images and target images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). In the following, we present the details of FFS and GIA."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "878"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.087,
+                0.473,
+                0.274
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.282,
+                0.47,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Figure 2. Exemplar results of the generated curvilinear structures from the basic and parametric Fractal L-system."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.332,
+                0.291,
+                0.349
+            ],
+            "angle": 0,
+            "content": "3.1. Fractal-FDA Synthesis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.355,
+                0.47,
+                0.415
+            ],
+            "angle": 0,
+            "content": "We first generate curvilinear structures via the parametric Fractal L-Systems and then integrate the synthetic objects into unlabeled target images to obtain synthetic training samples via FDA."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.416,
+                0.473,
+                0.552
+            ],
+            "angle": 0,
+            "content": "Fractal-based curvilinear structure generation. Fractals are simple graphic patterns rendered by mathematical formulas. In this work, we adopt the parametric Fractal L-systems proposed by Zamir et al. [47] to generate fractal tree structures and meanwhile select proper branching parameters according to physiological laws of curvilinear objects in target applications. Specifically, \"grammar\" for generating curvilinear structures with repeated bifurcations based on Fractal L-systems method is defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.561,
+                0.469,
+                0.584
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l l} \\omega : & F \\\\ 1: & F, \\end{array} \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.58,
+                0.365,
+                0.595
+            ],
+            "angle": 0,
+            "content": "\\[\nr u l e: \\quad F \\rightarrow F [ - F ] [ + F ]\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.603,
+                0.336,
+                0.619
+            ],
+            "angle": 0,
+            "content": "The generated object by iteration iter:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.204,
+                0.627,
+                0.47,
+                0.643
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {D r a w} (\\text {i t e r}, F, \\text {r u l e}) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.651,
+                0.47,
+                0.788
+            ],
+            "angle": 0,
+            "content": "where \\(F\\) represents a line of unit length in the horizontal direction, \\(\\omega\\) denotes an axiom, iter denotes the iteration and rule denotes the production rule. The square brackets represent the departure from \\([]\\) and return to \\([]\\) a branch point. The plus and minus signs represent turns through a given angle \\(\\delta\\) in the clockwise and anticlockwise directions, respectively. For example, the first three stages of a tree produced by the basic Fractal L-system, denoted by \\(iter = 1 \\sim 3\\), are given by the:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.089,
+                0.796,
+                0.47,
+                0.855
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} i t e r = 1 F \\\\ i t e r = 2 \\quad F [ - F ] [ + F ] \\\\ i t e r = 3 \\quad F [ - F ] [ + F ] [ - F [ - F ] [ + F ] ] [ + F [ - F ] [ + F ] ] \\tag {3} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The left part of Figure. 2 illustrates exemplar results of the generated curvilinear structures based on the basic Fractal system."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.893,
+                0.184
+            ],
+            "angle": 0,
+            "content": "To synthesize curvilinear structures with various widths and lengths, we replace \\( F \\) using \\( F_{random}(w_i, l_i, c_i) \\) which represents a line of width \\( w_i \\), length \\( l_i \\) and intensity \\( c_i \\). We set the initial width \\( w_{init} \\), length \\( l_{init} \\) and decreased parameter \\( \\gamma \\) by the repeated \\( F_{random} \\) in the Draw grammar. For the index number \\( i \\) of \\( F_{random} \\), \\( w_i \\) and \\( l_i \\) are given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.634,
+                0.192,
+                0.892,
+                0.231
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} w _ {i} = w _ {i n i t} \\cdot \\gamma^ {i - 1} \\tag {4} \\\\ l _ {i} = l _ {i n i t} \\cdot \\gamma^ {i - 1} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.241,
+                0.893,
+                0.33
+            ],
+            "angle": 0,
+            "content": "We randomly choose a value within the range of (0, 255) and set this value as the intensity \\( c_{i} \\) for the index \\( i \\) of \\( F_{random} \\). For the branching angle \\( \\delta \\), we replace \\( \\delta \\) using \\( \\delta_{random} \\) (defined by \\( \\delta_{init} \\pm \\delta_{delta} \\), \\( \\delta_{init} \\) within the range of \\( (20^{\\circ}, 120^{\\circ}) \\)), in which \\( \\delta_{delta} \\) is a random angle ranging from \\( 10^{\\circ} \\) to \\( 40^{\\circ} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.332,
+                0.894,
+                0.483
+            ],
+            "angle": 0,
+            "content": "To mimic the geometric characteristics of a target application, we incorporate the above-mentioned parameters into the L-Systems. Specifically, we design a set of rules \\( \\text{ruleset} : (rule_1, \\dots, rule_n) \\) for different fractal structures, like \\( F_{random} \\rightarrow F_{random} - F_{random} [+F_{random} - F_{random}] [-F_{random} + F_{random}] \\). For each iteration iter, we randomly select a rule from the \\( \\text{ruleset} \\) as the production rule. In this way, we can increase the diversity of structures. The generated fractal curvilinear object \\( X_{\\text{frac}} \\in \\mathbb{R}^{H \\times W} \\) by iteration is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.521,
+                0.494,
+                0.892,
+                0.512
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {f r a c} = \\operatorname {D r a w} (i t e r, F _ {r a n d o m}, r u l e s e t, w _ {i}, l _ {i}, c _ {i}) \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.892,
+                0.642
+            ],
+            "angle": 0,
+            "content": "FDA-based curvilinear object image synthesis. We further incorporate synthetic curvilinear objects into the target unlabeled images via FDA [45]. We define the target images as \\( X_{t} \\in \\mathbb{R}^{H \\times W} \\) and the synthetic images of fractal curvilinear object as \\( X_{\\text{frac}} \\). Let \\( \\mathcal{F}^A : \\in \\mathbb{R}^{H \\times W} \\to \\in \\mathbb{R}^{H \\times W} \\) be the amplitude component of the Fourier transform \\( \\mathcal{F} \\) of a grayscale image. We define a \\( \\beta \\in (0,1) \\) to select the center region of the amplitude map."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.643,
+                0.893,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Given two randomly sampled synthetic image \\(X_{frac}\\) and target image \\(X_{t}\\), we follow FDA [45] to replace the low-frequency part in the amplitude map of \\(X_{frac}\\) by the FFT [15], denotes as \\(\\mathcal{F}^A (X_{frac})\\), with that of the target image \\(X_{t}\\), denoted as \\(\\mathcal{F}^A (X_t)\\). Then, the modified spectral representation of \\(X_{frac}\\), with its phase component unaltered, is mapped back to image \\(X_{frac\\rightarrow t}\\) by the inverse FFT [15], whose content is the same as \\(X_{frac}\\), but will resemble the appearance of a sample \\(X_{t}\\). After that, we apply a Gaussian blur to the output synthetic image of FDA to obtain synthetic images from FFS, denoted as \\(X_{F}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.818,
+                0.803,
+                0.835
+            ],
+            "angle": 0,
+            "content": "3.2. Geometric Information Alignment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Synthetic images generated by FFS could still have nontrivial intensity differences from that of real images. To address this problem, we further align synthetic images and real target images at both image and feature levels."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.945,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "879"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Image-level Alignment. We aim to explicitly remove the dependency on raw intensity values for both synthetic and real images and meanwhile enhance the geometric characteristics of curvilinear structures. To this end, for each image pixel \\( j \\) we compare its intensity value \\( X(j) \\) with its 8 neighboring pixels \\( \\{n_d^m | m = 1, \\dots, 8\\} \\) (yellow box in Figure. 1) lying perpendicular to \\( j \\) (red box in Figure. 1), where directional \\( d \\) denotes left, right, top, and bottom side of \\( j \\). If \\( X(j) > X(n_d^m) \\), we set the corresponding value for \\( n_d^m \\) to 0. Otherwise, we set the value for \\( n_d^m \\) to 1. Such operation produces four 8-bit images for each input image, where the \\( m \\)-th bit on the \\( d \\)-th image denotes the relative intensity order between \\( j \\) and its neighbor \\( m \\) along the \\( d \\)-th direction. For each input image \\( X \\) (denote as \\( X_F \\) and \\( X_t \\)), we concatenate four 8-bit images \\( (X_{IA}^1, \\dots, X_{IA}^d) \\), where \\( X_{IA}^d(j) \\) is represented as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.131,
+                0.346,
+                0.47,
+                0.387
+            ],
+            "angle": 0,
+            "content": "\\[\nX _ {I A} ^ {d} (j) = \\sum_ {m = 1} ^ {8} [ X (j) > X \\left(n _ {d} ^ {m}\\right) ] \\times 2 ^ {m - 1} \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.397,
+                0.47,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Such local intensity order transformation [34] can capture the intrinsic of the curvilinear object and meanwhile reduces the intensity gap between synthetic and real images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.443,
+                0.469,
+                0.532
+            ],
+            "angle": 0,
+            "content": "Feature-level Alignment. Given the 4-channel transformed images, we utilize U-Net [33] to extract features. We align curvilinear objects' features of synthetic images and unlabeled target images based on two loss functions, i.e., the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.533,
+                0.47,
+                0.655
+            ],
+            "angle": 0,
+            "content": "1) Prediction space adaptation loss. We utilize adversarial learning to explicitly align the prediction space distribution of target images and synthetic images. We denote the prediction segmentation masks of the target images and the synthetic images as \\( Y_{target} \\in \\mathbb{R}^{H \\times W} \\) and \\( Y_{syn} \\in \\mathbb{R}^{H \\times W} \\), respectively. We input \\( Y_{target} \\) and \\( Y_{syn} \\) into a fully-convolutional discriminator \\( D \\) as [50] trained via a binary cross-entropy loss \\( \\mathcal{L}_d \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.665,
+                0.47,
+                0.684
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {d} = \\mathbb {E} \\left[ \\log \\left(D \\left(Y _ {s y n}\\right)\\right) \\right] + \\mathbb {E} \\left[ \\log \\left(1 - D \\left(Y _ {t a r g e t}\\right)\\right) \\right] (7)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.694,
+                0.341,
+                0.71
+            ],
+            "angle": 0,
+            "content": "Accordingly, the PSAL is computed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.168,
+                0.722,
+                0.47,
+                0.74
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {P S A L} = \\mathbb {E} \\left[ \\log \\left(D \\left(Y _ {\\text {t a r g e t}}\\right)\\right) \\right] \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.75,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "2) Curvilinear mask contrastive loss. The CMCL aims to reduce the distance between features of synthetic images and true target images, and meanwhile to improve the feature distinctiveness between curvilinear objects and backgrounds. To this end, we take the feature maps (denoted as \\( f \\in \\mathbb{R}^{H \\times W \\times C} \\)) from the final decoder layer of U-Net, the mask of synthetic image (denoted as \\( G_{syn} \\in \\{0,1\\}^{H \\times W} \\)) and prediction mask of target image (denoted \\( Y_{target} \\in [0,1]^{H \\times W} \\)) as input. We process \\( f \\) using a lightweight contrastive encoder and a contrastive projector as [41] to map"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "\\(f\\) to the feature space where the pixel-level contrastive loss is applied for \\(Z \\in \\mathbb{R}^{H \\times W \\times C}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.122,
+                0.893,
+                0.349
+            ],
+            "angle": 0,
+            "content": "We denote \\(I\\) as \\(H\\times W\\) spatial location of the projected feature maps \\(Z\\), then for a location \\(i\\in I\\), we can obtain a feature vector \\(z_{i}\\) at location \\(i\\) from feature map \\(Z\\), label values \\(g_{i}\\) and \\(y_{i}\\) at \\(i\\) from the mask of synthetic image \\(G_{syn}\\) and the prediction mask \\(Y_{target}\\) respectively. We partition pixels of \\(I\\) into two groups: curvilinear object locations \\(I^{+}\\) and background locations \\(I^{-}\\). For synthetic images, we perform the partition directly based on the mask \\(G_{syn}\\), i.e., \\(I_{syn}^{+} = \\{i\\in I_{syn}\\mid g_{i} = 1\\}\\) and \\(I_{syn}^{-} = \\{i\\in I_{syn}\\mid g_{i} = 0\\}\\). For target images, as the ground-truth mask is not available, we alternatively perform the partition based on the prediction probability mask \\(Y_{target}\\), i.e., \\(I_{target}^{+} = \\{i\\in I_{target}\\mid y_{i}\\geq 1 - \\alpha \\}\\) and \\(I_{target}^{-} = \\{i\\in I_{target}\\mid y_{i}\\leq \\alpha \\}\\), where \\(\\alpha = 0.1\\) is a small threshold and is fixed in our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.349,
+                0.894,
+                0.501
+            ],
+            "angle": 0,
+            "content": "We let \\( q_{syn}^{+} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{syn}^{+}, \\sigma\\right) \\right\\} \\) and \\( k_{target}^{+} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{target}^{+}, \\sigma\\right) \\right\\} \\) denote the curvilinear keys of synthetic and target images respectively. Similarly, we define \\( k_{syn}^{-} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{syn}^{-}, \\sigma\\right) \\right\\} \\) and \\( k_{target}^{-} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{target}^{-}, \\sigma\\right) \\right\\} \\) as the background keys of synthetic and target images, where \\( \\S (\\bullet, \\sigma) \\) is a random sampling operator which samples a subset from a set randomly with a proportion ratio \\( \\sigma \\). We combine \\( N \\) negative queries of the features of synthetic and target images to form a negative set \\( k^{-} = (k_{syn}^{-}, k_{target}^{-}) \\). The CMCL is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.515,
+                0.52,
+                0.892,
+                0.577
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {C M C L} = - \\log \\left(\\exp \\left(q _ {\\text {s y n}} ^ {+} \\cdot k _ {\\text {t a r g e t}} ^ {+} / \\tau\\right)\\right) + \\\\ \\log \\left(\\exp \\left(q _ {s y n} ^ {+} \\cdot k _ {t a r g e t} ^ {+} / \\tau\\right) + \\sum_ {i = 0} ^ {N} \\exp \\left(q _ {s y n} ^ {+} \\cdot k _ {i} ^ {-} / \\tau\\right)\\right) \\tag {9} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.588,
+                0.786,
+                0.602
+            ],
+            "angle": 0,
+            "content": "where \\(\\tau\\) is a temperature hyper-parameter."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.602,
+                0.891,
+                0.633
+            ],
+            "angle": 0,
+            "content": "3) Final Loss. The final loss is a combination of the segmentation loss, the PSAL and CMCL as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.599,
+                0.646,
+                0.892,
+                0.665
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {s e g} = \\mathbb {E} \\left[ G _ {s y n} \\cdot \\log \\left(Y _ {s y n}\\right) \\right] \\tag {10}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.585,
+                0.693,
+                0.892,
+                0.71
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {s e g}} + \\mathcal {L} _ {\\text {P S A L}} + \\lambda \\mathcal {L} _ {\\text {C M C L}} \\tag {11}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.724,
+                0.634,
+                0.74
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.87
+            ],
+            "angle": 0,
+            "content": "XCAD dataset. The X-ray angiography coronary artery disease (XCAD) dataset [25] is obtained during stent placement using a General Electric Innova IGS 520 system. Each image has a resolution of \\(512 \\times 512\\) pixels with one channel. The training set contains 1621 coronary angiograms without annotations as target images. The testing set contains 126 independent coronary angiograms with vessel segmentation maps annotated by experienced radiologists."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Retinal dataset. We also employ two public retin al datasets to validate the effectiveness of the proposed"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.512,
+                0.957
+            ],
+            "angle": 0,
+            "content": "880"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.47,
+                0.182
+            ],
+            "angle": 0,
+            "content": "method. The DRIVE dataset [37] consists of 40 color retinal images of size \\(565 \\times 584\\) pixels. We use 20 images as target images and 20 remaining as test images. The STARE dataset [17] contains 20 color retinal images of size \\(700 \\times 605\\) pixels with annotations as test images. There are 377 images without annotation which are used as target images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.183,
+                0.471,
+                0.274
+            ],
+            "angle": 0,
+            "content": "CrackTree dataset. The CrackTree dataset [51] contains 206 \\(800 \\times 600\\) pavement images with different kinds of cracks with curvilinear structures. The whole dataset is split into 160 target images and 46 test images by [34] setting. Following [34], we dilate the annotated centerlines by 4 pixels to form the ground-truth segmentation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.283,
+                0.262,
+                0.299
+            ],
+            "angle": 0,
+            "content": "4.1. Evaluation Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.306,
+                0.471,
+                0.428
+            ],
+            "angle": 0,
+            "content": "For XCAD and CrackTree, we follow [25, 34] to use the following widely-used metrics in our evaluation, i.e., Jaccard Index (Jaccard), Dice Coefficient (Dice), accuracy (Acc.), sensitivity (Sn.) and specificity (Sp.). For the DRIVE and STARE datasets, we follow the state-of-the-art works for retina vessel segmentation [25] to report accuracy (Acc.), sensitivity (Sn.) specificity (Sp.) and area under curve (AUC) in our evaluation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.438,
+                0.295,
+                0.455
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.461,
+                0.469,
+                0.49
+            ],
+            "angle": 0,
+            "content": "For FFS, we set the ruleset as \\((\\text{rule}_1, \\dots, \\text{rule}_4)\\), such as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.096,
+                0.492,
+                0.446,
+                0.554
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} r u l e _ {1}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} [ + F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} ]. \\\\ \\operatorname {r u l e} _ {2}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} [ - F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} ]. \\\\ r u l e _ {3}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}}. \\\\ \\text {r u l e} _ {4}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} + F _ {\\text {r a n d o m}} + F _ {\\text {r a n d o m}}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.555,
+                0.469,
+                0.705
+            ],
+            "angle": 0,
+            "content": "We set the initial parameters of the Fractal system as follows. For all four datasets, the angle is randomly selected from \\((20^{\\circ},120^{\\circ})\\), the initial length is randomly selected from \\((120\\mathrm{px}\\) \\(200\\mathrm{px})\\) , the decreased parameter \\(\\gamma\\) is randomly selected from (0.7, 1). The initial width \\(w_{init}\\) is ranging from (8px, 14px) for XCAD, DRIVE and STARE. For CrackTree, the \\(w_{init}\\) is selected from (2px, 6px). The kernel size of Gaussian blur for FFS is 13. We generate 150, 150, 600 synthetic fractal images \\(X_{frac}\\) for XCAD, CrackTree, and retinal datasets, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.47,
+                0.904
+            ],
+            "angle": 0,
+            "content": "We apply data augmentation including horizontal flipping, random brightness and contrast changes ranging from (1.0, 2.1), random saturation ranging from (0.5, 1.5), and random rotation with \\(90^{\\circ}\\), \\(180^{\\circ}\\), and \\(270^{\\circ}\\). The standard deviation for Gaussian noise is set to a random value within \\((-5, +5)\\). All images are cropped to \\(256 \\times 256\\) pixels for training. All the data-augmented operations are applied before the GIA module. The segmentation network is trained using the SGD with a momentum of 0.9 for optimization and the initial learning rate is 0.01. The discriminator network is trained using an Adam optimizer with an initial learning rate of \\(10^{-3}\\). We employ a batch size of 8 to train the network for 600 epochs. The number of negative queries \\(q_{syn}^{+}\\)"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.89,
+                0.252
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Methods</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Upper bound</td><td>U-Net [33]</td><td>0.571</td><td>0.724</td><td>0.981</td><td>0.868</td><td>0.996</td></tr><tr><td rowspan=\"3\">Domain Adaptation</td><td>U-Net [33]</td><td>0.228</td><td>0.365</td><td>0.831</td><td>0.444</td><td>0.906</td></tr><tr><td>MMD [8]</td><td>0.262</td><td>0.416</td><td>0.873</td><td>0.553</td><td>0.920</td></tr><tr><td>YNet [32]</td><td>0.287</td><td>0.434</td><td>0.891</td><td>0.523</td><td>0.935</td></tr><tr><td rowspan=\"2\">Traditional</td><td>Hessian [13]</td><td>0.307</td><td>0.465</td><td>0.948</td><td>0.406</td><td>0.981</td></tr><tr><td>OOF [22]</td><td>0.241</td><td>0.386</td><td>0.899</td><td>0.566</td><td>0.920</td></tr><tr><td rowspan=\"2\">Unsupervised</td><td>IIC [19]</td><td>0.124</td><td>0.178</td><td>0.738</td><td>0.487</td><td>0.754</td></tr><tr><td>ReDO [9]</td><td>0.151</td><td>0.261</td><td>0.753</td><td>0.392</td><td>0.923</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.389</td><td>0.557</td><td>0.945</td><td>0.583</td><td>0.972</td></tr><tr><td>DARL [21]</td><td>0.471</td><td>0.636</td><td>0.962</td><td>0.597</td><td>0.985</td></tr><tr><td>Ours</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.252,
+                0.892,
+                0.278
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative evaluation of FreeCOS compared with different methods on the XCAD dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.29,
+                0.89,
+                0.401
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Methods</td><td colspan=\"4\">DRIVE</td><td colspan=\"4\">STARE</td></tr><tr><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td></tr><tr><td rowspan=\"4\">Traditional</td><td>Hessian [13]</td><td>0.941</td><td>0.644</td><td>0.97</td><td>0.847</td><td>0.938</td><td>0.690</td><td>0.957</td><td>0.858</td></tr><tr><td>OOF [22]</td><td>0.936</td><td>0.688</td><td>0.959</td><td>0.920</td><td>0.920</td><td>0.770</td><td>0.932</td><td>0.955</td></tr><tr><td>Memari [26]</td><td>0.961</td><td>0.761</td><td>0.981</td><td>0.871</td><td>0.951</td><td>0.782</td><td>0.965</td><td>0.783</td></tr><tr><td>Khan [20]</td><td>0.958</td><td>0.797</td><td>0.973</td><td>0.885</td><td>0.996</td><td>0.792</td><td>0.998</td><td>0.895</td></tr><tr><td rowspan=\"2\">Unsupervised</td><td>IIC [19]</td><td>0.738</td><td>0.632</td><td>0.840</td><td>0.736</td><td>0.710</td><td>0.586</td><td>0.832</td><td>0.709</td></tr><tr><td>ReDO [9]</td><td>0.761</td><td>0.593</td><td>0.927</td><td>0.760</td><td>0.756</td><td>0.567</td><td>0.899</td><td>0.733</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.913</td><td>0.794</td><td>0.982</td><td>0.888</td><td>0.910</td><td>0.774</td><td>0.980</td><td>0.877</td></tr><tr><td>DARL [21]</td><td>-</td><td>0.456</td><td>-</td><td>-</td><td>-</td><td>0.480</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>0.921</td><td>0.810</td><td>0.932</td><td>0.941</td><td>0.952</td><td>0.797</td><td>0.964</td><td>0.971</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.401,
+                0.891,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Table 2. Quantitative evaluation of FreeCOS compared with different methods on the retinal dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.438,
+                0.89,
+                0.535
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Methods</td><td>AUC</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td rowspan=\"2\">Traditional</td><td>Hessian [13]</td><td>0.780</td><td>0.122</td><td>0.935</td><td>0.310</td><td>0.945</td></tr><tr><td>OOF [22]</td><td>0.482</td><td>0.031</td><td>0.770</td><td>0.244</td><td>0.778</td></tr><tr><td>Unsupervised</td><td>ReDO [9]</td><td>0.422</td><td>0.035</td><td>0.632</td><td>0.450</td><td>0.635</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.477</td><td>0.078</td><td>0.299</td><td>0.042</td><td>0.912</td></tr><tr><td>DARL [21]</td><td>0.888</td><td>0.395</td><td>0.974</td><td>0.542</td><td>0.981</td></tr><tr><td>Ours</td><td>0.920</td><td>0.525</td><td>0.974</td><td>0.576</td><td>0.979</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.535,
+                0.891,
+                0.561
+            ],
+            "angle": 0,
+            "content": "Table 3. Quantitative evaluation of FreeCOS compared with different methods on the CrackTree dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.584,
+                0.892,
+                0.647
+            ],
+            "angle": 0,
+            "content": "\\(k_{target}^{+}\\) and \\(k^{-}\\) per batch is taken up to 500, 500 and 1000. The amplitude map center region selection parameter of \\(\\beta\\) is set to 0.3. the sampling ratio is 0.3, the hyper-parameter \\(\\lambda\\) is 0.4 and the temperature hyper-parameter \\(\\tau\\) is 0.1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.656,
+                0.704,
+                0.672
+            ],
+            "angle": 0,
+            "content": "4.3. Experimental Results"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.68,
+                0.787,
+                0.695
+            ],
+            "angle": 0,
+            "content": "4.3.1 Comparison with State-of-the-art"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.892,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Table. 1 compares the performance of vessel segmentation on XCAD between FreeCOS and the state-of-the-art methods, including the unsupervised methods [9, 19], the self-supervised methods [25, 21], domain adaptation methods [8, 32] and the traditional methods [13, 22]. The results in the 1st row are based on supervised U-Net as [25] (i.e., identical segmentation network trained using real images with manual labels) which are the upper bound."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "For domain adaption methods, we pretrain a vessel segmentation model based on U-Net using training images of DRIVE. Then we adapt the pre-trained model to XCAD using MMD [8] and Ynet [32]. Even with supervised information in the annotated source domain, the performance of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.51,
+                0.957
+            ],
+            "angle": 0,
+            "content": "881"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.465,
+                0.189
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr><tr><td>FFS+PSAL</td><td>0.468</td><td>0.633</td><td>0.957</td><td>0.680</td><td>0.974</td></tr><tr><td>FFS+PSAL+IA</td><td>0.485</td><td>0.647</td><td>0.958</td><td>0.667</td><td>0.976</td></tr><tr><td>FFS+GIA</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.165,
+                0.19,
+                0.382,
+                0.201
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation study for modules."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.228,
+                0.468,
+                0.303
+            ],
+            "angle": 0,
+            "content": "MMD and YNet is still inferior to ours. Specifically, our method achieves \\(21.2\\%\\) improvement in Jaccard, \\(22.7\\%\\) improvement in Dice, \\(6.9\\%\\) improvement in Acc., \\(16.4\\%\\) improvement in Sn., and \\(4.2\\%\\) improvement in Sp. compared with YNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.305,
+                0.468,
+                0.395
+            ],
+            "angle": 0,
+            "content": "Compared with the unsupervised methods IIC [19] and ReDO [9], our method achieves significantly better performance for all metrics on XCAD. The results show that unsupervised methods cannot achieve satisfactory performance on the gray-scale X-ray images where the segmentation objects can be hardly distinguished from the background."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.397,
+                0.468,
+                0.47
+            ],
+            "angle": 0,
+            "content": "Self-supervised method SSVS [25] is specifically designed for XCAD, yet our method still achieves much better performance for all metrics, i.e., \\(11\\%\\) improvement in Jaccard, \\(10.4\\%\\) improvement in Dice and \\(10.4\\%\\) improvement in Sn."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.473,
+                0.468,
+                0.548
+            ],
+            "angle": 0,
+            "content": "Table. 2 and 3 further compare our method with the existing methods on the retinal and crack datasets and a similar trend can be observed in these three datasets. Figure. 3 shows the visualization results of images from various kinds of curvilinear datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.55,
+                0.468,
+                0.806
+            ],
+            "angle": 0,
+            "content": "FreeCOS not only achieves state-of-the-art (SOTA) performance but also demonstrates unique advantages compared to various types of methods. a) Compared with traditional methods, FreeCOS does not require complex parameter tuning as traditional methods and achieves much better performance. b) FreeCOS can better tolerate large domain shifts than domain adaptation methods. But the effectiveness of current domain adaptation methods may struggle to achieve satisfactory performance facing a large domain gap. c) Unsupervised methods are more suitable for segmenting objects with aspect ratios close to one and perform well when objects are visually distinct from backgrounds. But their performance greatly degrades when segmenting curvilinear objects with branching structures in cluttered backgrounds. d) Self-supervised methods based on GAN/Diffusion require training with clean background images which limits applications to practical scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.831,
+                0.236,
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+            ],
+            "angle": 0,
+            "content": "4.3.2 Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.468,
+                0.899
+            ],
+            "angle": 0,
+            "content": "We first conduct ablation studies to evaluate the impact of different modules. To this end, we build the following variants based on our method. For all the variant models and our"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.888,
+                0.224
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS w/o Gaussian blur</td><td>0.383</td><td>0.547</td><td>0.940</td><td>0.654</td><td>0.959</td></tr><tr><td>FFS w/o FDA</td><td>0.302</td><td>0.459</td><td>0.920</td><td>0.609</td><td>0.940</td></tr><tr><td>FFS w/o various intensities</td><td>0.405</td><td>0.569</td><td>0.957</td><td>0.525</td><td>0.984</td></tr><tr><td>FFS w/o various angles</td><td>0.267</td><td>0.415</td><td>0.939</td><td>0.409</td><td>0.972</td></tr><tr><td>FFS w/o various lengths</td><td>0.224</td><td>0.358</td><td>0.943</td><td>0.300</td><td>0.983</td></tr><tr><td>FFS w/o various widths</td><td>0.224</td><td>0.354</td><td>0.935</td><td>0.348</td><td>0.972</td></tr><tr><td>FFS</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.601,
+                0.224,
+                0.792,
+                0.236
+            ],
+            "angle": 0,
+            "content": "Table 5. Ablation study for FFS."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.242,
+                0.888,
+                0.312
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Architecture</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS</td><td>U-Net [33]</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr><tr><td>FFS</td><td>Iternet [23]</td><td>0.481</td><td>0.645</td><td>0.959</td><td>0.670</td><td>0.976</td></tr><tr><td>FFS+GIA</td><td>Iternet [23]</td><td>0.505</td><td>0.664</td><td>0.964</td><td>0.641</td><td>0.984</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.577,
+                0.312,
+                0.815,
+                0.324
+            ],
+            "angle": 0,
+            "content": "Table 6. Ablation study for architecture."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.338,
+                0.888,
+                0.432
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Numbers of images</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Synthetic-15</td><td>0.464</td><td>0.629</td><td>0.958</td><td>0.630</td><td>0.979</td></tr><tr><td>Synthetic-45</td><td>0.478</td><td>0.642</td><td>0.958</td><td>0.674</td><td>0.976</td></tr><tr><td>Synthetic-75</td><td>0.488</td><td>0.652</td><td>0.960</td><td>0.668</td><td>0.978</td></tr><tr><td>Synthetic-150</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.503,
+                0.433,
+                0.89,
+                0.445
+            ],
+            "angle": 0,
+            "content": "Table 7. Ablation study for different numbers of synthetic images."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.459,
+                0.888,
+                0.554
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Numbers of images</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Target-162</td><td>0.455</td><td>0.620</td><td>0.952</td><td>0.678</td><td>0.969</td></tr><tr><td>Target-486</td><td>0.476</td><td>0.637</td><td>0.955</td><td>0.683</td><td>0.972</td></tr><tr><td>Target-810</td><td>0.466</td><td>0.630</td><td>0.958</td><td>0.635</td><td>0.978</td></tr><tr><td>Target-1620</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.502,
+                0.554,
+                0.871,
+                0.566
+            ],
+            "angle": 0,
+            "content": "Table 8. Ablation study for different numbers of target images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": "final model, we use the same U-Net model as our backbone. 1) FFS. We utilize the FFS to generate synthetic training images and the corresponding labels to train the U-Net segmentation model. 2) FFS+PSAL. We further apply PSAL to align features of synthetic and real target images on top of FFS. 3) FFS+PSAL+IA. We apply image-level alignment via relative intensity order transformation (i.e., IA) on top of FFS+PSAL. 4) FFS+GIA. We apply our GIA module (including IA, PSAL and CMCL) on top of FFS. This model is also our final curvilinear segmentation model. The ablation studies are conducted on XCAD. The trend on other datasets are similar and thus the results on the other datasets are omitted due to the space limit."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The results in Table 4 show that 1) by training a U-Net model using synthetic images from FFS, we can already achieve better performance than the SOTA self-supervised method SSVS which is based on adversarial learning [25]. Such results reveal a very interesting phenomenon although adversarial learning can synthesize visually similar images as real target images, it cannot explicitly control the generated visual patterns and thus fail to enforce"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "882"
+        }
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+            "angle": 0,
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+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
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+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Hessian"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.406,
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+                0.567,
+                0.216
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.465,
+                0.421,
+                0.507,
+                0.435
+            ],
+            "angle": 0,
+            "content": "OOF"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.568,
+                0.091,
+                0.892,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.627,
+                0.421,
+                0.669,
+                0.435
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.796,
+                0.421,
+                0.823,
+                0.434
+            ],
+            "angle": 0,
+            "content": "GT"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.214,
+                0.457,
+                0.753,
+                0.471
+            ],
+            "angle": 0,
+            "content": "Figure 3. The visualization results of images from the various kinds of curvilinear datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.488,
+                0.47,
+                0.684
+            ],
+            "angle": 0,
+            "content": "the segmentation-oriented patterns and properties to be encoded in synthetic images. In comparison, FFS can explicitly control the synthesis of both curvilinear structures and background patterns and hence can achieve better performance. 2) Aligning features via prediction space adaptation loss (PSAL) can help reduce domain shifts between synthetic images and real target images and thus FFS+PSAL achieves performance improvements compared with FFS. 3) Aligning synthetic images and real target images via IA method can also reduce the domain shifts and thus FFS+PSAL+IA can provide complementary improvements to FFS+PSAL. 4) Finally, the best performance is obtained when combining both FFS and GIA."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We further explore the importance of different parameters in FFS on the final performance and discuss how to generate images of curvilinear structures to encode sufficient and comprehensive visual cues for learning robust and distinctive features. To this end, we build 6 variant models based on FFS. 1) FFS w/o Gaussian blur. We do not perform Gaussian blur to synthetic images from FFS. 2) FFS w/o FDA. We remove FDA-based synthesis from FFS and only generate curvilinear structures without backgrounds. 3) FFS w/o various intensities. We remove intensity variations \\( c_{i} \\) in the Fractal system and set the intensity to a fixed value 60. 4) FFS w/o various angles. We utilize a small branching angle range from \\( (1^{\\circ}, 5^{\\circ}) \\) to reduce the branching angle variations. 5) FFS w/o various lengths. We reduce"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.488,
+                0.891,
+                0.518
+            ],
+            "angle": 0,
+            "content": "the length variation range to (10px, 20px). 6) FFS w/o various widths. We reduce the width variation to (1px, 5px)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.519,
+                0.893,
+                0.82
+            ],
+            "angle": 0,
+            "content": "The results in Table 5 show that 1) Gaussian blur can smooth the transition region between curvilinear objects and backgrounds, better mimicking the target images and providing more challenging samples for training than those with sharp boundaries. As a result, excluding Gaussian blur decreases the performance of FFS by \\(6.8\\%\\) in Dice. 2) FDA could provide background patterns of target images which are essential for learning features of negative samples. Thus, FFS w/o FDA is \\(15.6\\%\\) worse than FFS in Dice. 3) Among the four parameters of the Fractal system, i.e., intensity, angle, length and width, width plays the most important role in the final performance, i.e., FFS w/o various widths decreases the performance by \\(26.1\\%\\) compared with FFS in Dice. To summarize, we identify that the appearance patterns in the curvilinear object, object-background transition regions and background regions are important for self-supervised segmentation. Meanwhile, proper parameter settings which can provide similar geometric characteristics with the real target images are key to the success of our self-supervised method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.845,
+                0.774,
+                0.86
+            ],
+            "angle": 0,
+            "content": "4.3.3 Ablation Study on Architecture"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "By replacing the U-Net with Iternet in FFS, We conduct ablation studies on two backbone networks U-Net [33]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "883"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.198
+            ],
+            "angle": 0,
+            "content": "and Iternet [23]. FFS using Iternet segmentation model gets better performance than FFS using U-Net in Table 6. FFS+GIA also demonstrates performance improvement, showing FreeCOS's effectiveness on different architectures. This indicates that the use of a more advanced segmentation network architecture for FreeCOS has the potential to improve performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.222,
+                0.408,
+                0.236
+            ],
+            "angle": 0,
+            "content": "4.3.4 Self-supervised training with more data"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.247,
+                0.473,
+                0.414
+            ],
+            "angle": 0,
+            "content": "We also examine the segmentation performance when varying the number of synthetic images on the XCAD dataset. Results in Tables. 7 and 8 provide the results when using different numbers of synthetic structures and real target images for generating synthetic images for self-supervised training respectively. Synthetic- \\(15\\sim\\) Synthetic-150 denote using the number of synthetic fractal object images \\(X_{frac}\\) from 15 to 150, and Target- \\(162\\sim\\) Target-1620 denote using the number of target images \\(X_{t}\\) from 162 to 1620. Increasing both synthetic structures and real target images can accordingly improve the final segmentation performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.429,
+                0.196,
+                0.445
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.456,
+                0.473,
+                0.713
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a novel self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. Different from existing methods, FreeCOS applies the proposed FFS and GIA approach to effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds and aligns information of synthetic and target images at both image and feature levels. One limitation of FreeCOS is that may generate false positives in other curvilinear objects (e.g., catheters in XCAD) and requires proper selection for width range. However, we have successfully utilized this self-supervised learning method for coronary vessel segmentation, retinal vessel segmentation and crack segmentation by reasonable parameter selection. To the best of our knowledge, FreeOCS is the first self-supervised learning method for various curvilinear object segmentation applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.714,
+                0.471,
+                0.759
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work was supported by the National Natural Science Foundation of China under Grants 62061160490, 62122029, and U20B2064."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.775,
+                0.175,
+                0.79
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.085,
+                0.801,
+                0.47,
+                0.856
+            ],
+            "angle": 0,
+            "content": "[1] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Labels4free: Unsupervised segmentation using stylegan. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13970-13979, 2021. 1, 3"
+        },
+        {
+            "type": "ref_text",
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+                0.087,
+                0.859,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "[2] Michael D Abramoff, Mona K Garvin, and Milan Sonka. Retinal imaging and image analysis. IEEE Reviews in Biomedical Engineering, 3:169-208, 2010. 1"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.085,
+                0.801,
+                0.47,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.509,
+                0.093,
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+# FreeCOS: Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation
+
+Tianyi Shi, Xiaohuan Ding, Liang Zhang, Xin Yang†  
+School of EIC, Huazhong University of Science & Technology  
+{shitianyihust, dingxiaohuan, liangz, xinyang2014}@hust.edu.cn
+
+# Abstract
+
+Curvilinear object segmentation is critical for many applications. However, manually annotating curvilinear objects is very time-consuming and error-prone, yielding insufficiently available annotated datasets for existing supervised methods and domain adaptation methods. This paper proposes a self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. The key contributions include a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. FFS generates curvilinear structures based on the parametric Fractal L-system and integrates the generated structures into unlabeled images to obtain synthetic training images via Fourier Domain Adaptation. GIA reduces the intensity differences between the synthetic and unlabeled images by comparing the intensity order of a given pixel to the values of its nearby neighbors. Such image alignment can explicitly remove the dependency on absolute intensity values and enhance the inherent geometric characteristics which are common in both synthetic and real images. In addition, GIA aligns features of synthetic and real images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). Extensive experimental results on four public datasets, i.e., XCAD, DRIVE, STARE and CrackTree demonstrate that our method outperforms the state-of-the-art unsupervised methods, self-supervised methods and traditional methods by a large margin. The source code of this work is available at https://github.com/TY-Shi/FreeCOS.
+
+# 1. Introduction
+
+Automatically segmenting curvilinear structures (such as vascular trees in medical images and road systems in aerial photography) is critical for many applications, including retinal fundus disease screening [2, 14], diagnosing
+
+coronary artery disease [38], road condition evaluation and maintenance [51]. Despite a plethora of research works in the literature, accurately segmenting curvilinear objects remains challenging due to their complex structures with numerous tiny branches, tortuosity shapes, ambiguous boundaries due to imaging issues and noisy backgrounds.
+
+Most recent methods [39, 10, 36, 42, 18, 29, 7, 28, 6, 35] leverage supervised deep learning for curvilinear object segmentation and have achieved encouraging results. However, those methods require a large number of pixel-wise manual annotations for training which are very expensive to obtain and error-prone due to poor image quality, annotator's fatigue and lack of experience. Although, there are several publically available annotated datasets for curvilinear object segmentation [37, 17, 51, 25], the large appearance variations between different curvilinear object images, e.g., X-ray coronary angiography images vs. retinal fundus images, yields significant performance degradation for supervised models across different types of images (even across the same type of images acquired using different equipments). As a result, expensive manual annotations are inevitably demanded to tune the segmentation model for a particular application. Potential solutions to alleviate the annotation burden include domain adaption [8, 32] and unsupervised segmentation [9, 19, 24, 11, 9, 1]. However, the effectiveness of domain adaptation is largely dependent on the quality of annotated data in the source domain and constrained by the gap between the source and target domain. Existing unsupervised segmentation methods [9, 19] can hardly achieve satisfactory performance for curvilinear objects due to their thin, long, and tortuosity shapes, complex branching structures, and confusing background artifacts.
+
+Despite the high complexity and great variety of curvilinear structures in different applications, they share some common characteristics (i.e., the tube-like shape and the branching structure). Thus, existing studies [47, 46, 48] have demonstrated that several curvilinear structures (e.g., arterial trees of the circulation system) can be generated via the fractal systems with proper branching parameters to mimic the fractal and physiological characteristics, and
+
+some observed variability. These results motivate us to use the generated curvilinear objects via the fractal systems to explicitly encode geometric properties and varieties (i.e., different diameters and lengths of branches, and different branching angles) into training samples and to assist feature learning of a curvilinear structure segmentation model. However, such formulas generated training samples can hardly mimic the appearance patterns within curvilinear objects, the transition regions between curvilinear objects and backgrounds, which are also key information for learning a segmentation model and contained in easily-obtained unlabeled target images. This paper asks the question, how to combine fractals and unlabeled target images to encode sufficient and comprehensive visual cues for learning robust and distinctive features of curvilinear structures?
+
+The main contribution of this paper is a self-supervised segmentation method based on a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. Specifically, curvilinear structures are synthesized by the parametric fractal L-Systems [47] and serve as segmentation labels of synthetic training samples. To simulate appearance patterns in the object-background transition regions and background regions, we apply Fourier Domain Adaptation [45] (FDA) to fuse synthetic curvilinear structures and unlabeled target images. The synthetic images via our FFS module can effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds. To further improve the robustness to differences between intensity distributions of synthetic and real target images, we design a novel geometric information alignment (GIA) approach which aligns information of synthetic and target images at both image and feature levels. Specifically, GIA first converts each training image (synthetic and target images) into four geometry-enhanced images by comparing the intensity order of a given pixel to the values of its nearby neighbors (i.e., along with the up, down, left and right directions). In this way, the four converted images do not depend on the absolute intensity values but the relative intensity in order to capture the inherent geometric characteristic of the curvilinear structure, reducing the intensity differences between synthetic and target images. Then, we extract features from the 4-channel converted images and propose two loss functions, i.e., a prediction space adaptation loss (PSAL) and a curvilinear mask contrastive loss (CMCL), to align the geometric features of synthetic and target images. The PSAL minimizes the distance between the segmentation masks of the target images and synthetic curvilinear objects and the CMCL minimizes the distance between features of segmented masks and synthetic objects.
+
+The FreeCOS based on FFS and GIA approaches applies to several public curvilinear object datasets, including XCAD [25], DRIVE [37], STARE [17] and CrackTree [51]. Extensive experimental results demonstrate that FreeCOS
+
+outperforms the state-of-the-art self-supervised [25, 21], unsupervised [9, 19], and traditional methods [13, 22]. To summarize, the main contributions of this work are as follows:
+
+- We propose a novel self-supervised curvilinear feature learning method which intelligently combines tree-like fractals and unlabeled images to assist in learning robust and distinctive feature representations.
+
+- We propose Fractal-FDA synthesis (FFS) and geometric information alignment (GIA), which are the two key enabling modules of our method. FFS integrates the synthetic curvilinear structures into unlabeled images to guide learning distinctive features to distinguish foregrounds and backgrounds. GIA enhances geometric features and meanwhile improves the feature robustness to intensity differences between synthetic and target unlabeled images.
+
+- We develop a novel self-supervised segmentation network that can be trained using only target images and fractal synthetic curvilinear objects. Our network performs significantly better than state-of-the-art self-supervised/unsupervised methods on multiple public datasets with various curvilinear objects.
+
+# 2. Related Work
+
+# 2.1. Traditional Methods
+
+Traditional curvilinear object segmentation methods [20, 26, 13, 40, 22] design heuristic rules and/or filters to capture features of the target curvilinear objects. For instance, Frangi et al. introduce the vesselness filter [13] based on the Hessian matrix to represent and enhance tube-like curvilinear objects. Khan et al. [20] further design B-COSFIRE filters to denoise retinal images and segment retinal vessels. Memari et al. [26] enhance image contrast via contrast-limited adaptive histogram equalization and then segment retinal vessels based on hand-crafted filters. In [40, 22], the authors propose optimally oriented flux (OOF) to enhance curvilinear tube-like objects. OOF exhibits better performance for segmenting adjacent curvilinear objects yet is sensitive to different sizes of curvilinear objects.
+
+Traditional methods based on hand-crafted filters do not require any training yet they require careful parameter tuning for optimized performance. And the optimized parameter settings are usually data-dependent or even region-dependent, limiting their convenience in segmenting a wide variety of curvilinear objects.
+
+# 2.2. Unsupervised Segmentation Methods
+
+Unsupervised segmentation methods can be generally divided into two classes: clustering based [19, 24, 11] and ad
+
+![](images/530a9781843d8275a9097eae1d127e3ef32e17ca632af8fbe3e8d5d575312342.jpg)  
+Figure 1. The pipeline of Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation (FreeCOS).
+
+versarial learning based [9, 1]. Xu et al. [19] propose Invariant Information Clustering (IIC) which automatically partitions input images into regions of different semantic classes by optimizing mutual information between related region pairs. Such a clustering-based method is more suitable for segmenting objects with aspect ratios close to one while becoming ineffective for curvilinear objects due to their thin, long, tortuous shapes. Redo [9] is based on an adversarial architecture where the generator is guided by an image and extracts the object mask, then redraws a new object at the same location with different textures/colors. However, this adversarial learning-based unsupervised method only performs well for objects which are visually distinguishable from backgrounds. For the segmentation of curvilinear objects with complex and numerous tiny branching structures, embedded in confusing and cluttered backgrounds, the efficacy of such a method degrades significantly.
+
+In contrast to unsupervised methods, our method explicitly encodes geometric and photometric characteristics, as well as some observed varieties of curvilinear objects in target application into synthetic images. Those synthetic images provide labels to effectively guide the model to learn robust and distinctive features and thus yield superior performance to state-of-the-art unsupervised methods [9, 19].
+
+# 2.3. Self-supervised Learning Methods
+
+Self-supervised learning methods construct pretexts from large-scale unsupervised data and utilize contrastive learning losses to measure the similarities of sample pairs in the representation space. To this end, various pretext tasks have been designed, including jigsaw [12], hole-fill [31] and transformation invariance [16]. Although existing self-supervised methods have achieved outstanding performance in classification [27, 4], detection [44, 5], and image translation [30, 43], few of them provide a suitable pretext task for curvilinear object segmentation. A potential solu
+
+tion is the pixel-level contrastive-based method [41, 3, 49], while it requires heavy manual annotations to prepare pixel-level positive and negative samples. Similar work to ours is [25, 21] which designs a self-supervised vessel segmentation method via adversarial learning and fractals. But this method requires clean background images as input (i.e., the first frame of the angiography sequence) for synthesis which greatly limits its applications. In addition, adversarial learning cannot explicitly and precisely enforce visual cues, which are important for learning segmentation-oriented features, being encoded in the synthetic images. As a result, although their synthetic images visually look similar to the target images, the segmentation accuracy is also quite low.
+
+# 3. Method
+
+Figure. 1 shows the framework of FreeCOS which consists of two main modules, i.e., Fractal-FDA Synthesis (FFS) and Geometric Information Alignment (GIA). In FFS, we generate synthetic curvilinear structures via the parametric Fractal L-Systems and use the generated structures as segmentation maps to guide self-supervised training of a segmentation network. The synthetic curvilinear structures are then integrated into unlabeled images via FDA to form synthetic images of curvilinear structures. The intensity distributions of synthetic images could deviate from those of real target images and hence yield poor feature robustness. To address this problem, our GIA module first reduces image-level differences between the synthetic and target images by converting intensity images into four-channel intensity order images. The converted images of both synthetic images and target images are then input into U-Net to extract feature representations. Our GIA further aligns features of synthetic images and target images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). In the following, we present the details of FFS and GIA.
+
+![](images/8387819f7bfc976b14eba261aeeaea5afd19e6d64104b5de4e60c6f586ee40aa.jpg)  
+Figure 2. Exemplar results of the generated curvilinear structures from the basic and parametric Fractal L-system.
+
+# 3.1. Fractal-FDA Synthesis
+
+We first generate curvilinear structures via the parametric Fractal L-Systems and then integrate the synthetic objects into unlabeled target images to obtain synthetic training samples via FDA.
+
+Fractal-based curvilinear structure generation. Fractals are simple graphic patterns rendered by mathematical formulas. In this work, we adopt the parametric Fractal L-systems proposed by Zamir et al. [47] to generate fractal tree structures and meanwhile select proper branching parameters according to physiological laws of curvilinear objects in target applications. Specifically, "grammar" for generating curvilinear structures with repeated bifurcations based on Fractal L-systems method is defined as follows:
+
+$$
+\begin{array}{l l} \omega : & F \\ 1: & F, \end{array} \tag {1}
+$$
+
+$$
+r u l e: \quad F \rightarrow F [ - F ] [ + F ]
+$$
+
+The generated object by iteration iter:
+
+$$
+\operatorname {D r a w} (\text {i t e r}, F, \text {r u l e}) \tag {2}
+$$
+
+where  $F$  represents a line of unit length in the horizontal direction,  $\omega$  denotes an axiom, iter denotes the iteration and rule denotes the production rule. The square brackets represent the departure from  $[]$  and return to  $[]$  a branch point. The plus and minus signs represent turns through a given angle  $\delta$  in the clockwise and anticlockwise directions, respectively. For example, the first three stages of a tree produced by the basic Fractal L-system, denoted by  $iter = 1 \sim 3$ , are given by the:
+
+$$
+\begin{array}{l} i t e r = 1 F \\ i t e r = 2 \quad F [ - F ] [ + F ] \\ i t e r = 3 \quad F [ - F ] [ + F ] [ - F [ - F ] [ + F ] ] [ + F [ - F ] [ + F ] ] \tag {3} \\ \end{array}
+$$
+
+The left part of Figure. 2 illustrates exemplar results of the generated curvilinear structures based on the basic Fractal system.
+
+To synthesize curvilinear structures with various widths and lengths, we replace  $F$  using  $F_{random}(w_i, l_i, c_i)$  which represents a line of width  $w_i$ , length  $l_i$  and intensity  $c_i$ . We set the initial width  $w_{init}$ , length  $l_{init}$  and decreased parameter  $\gamma$  by the repeated  $F_{random}$  in the Draw grammar. For the index number  $i$  of  $F_{random}$ ,  $w_i$  and  $l_i$  are given by:
+
+$$
+\begin{array}{l} w _ {i} = w _ {i n i t} \cdot \gamma^ {i - 1} \tag {4} \\ l _ {i} = l _ {i n i t} \cdot \gamma^ {i - 1} \\ \end{array}
+$$
+
+We randomly choose a value within the range of (0, 255) and set this value as the intensity  $c_{i}$  for the index  $i$  of  $F_{random}$ . For the branching angle  $\delta$ , we replace  $\delta$  using  $\delta_{random}$  (defined by  $\delta_{init} \pm \delta_{delta}$ ,  $\delta_{init}$  within the range of  $(20^{\circ}, 120^{\circ})$ ), in which  $\delta_{delta}$  is a random angle ranging from  $10^{\circ}$  to  $40^{\circ}$ .
+
+To mimic the geometric characteristics of a target application, we incorporate the above-mentioned parameters into the L-Systems. Specifically, we design a set of rules  $\text{ruleset} : (rule_1, \dots, rule_n)$  for different fractal structures, like  $F_{random} \rightarrow F_{random} - F_{random} [+F_{random} - F_{random}] [-F_{random} + F_{random}]$ . For each iteration iter, we randomly select a rule from the  $\text{ruleset}$  as the production rule. In this way, we can increase the diversity of structures. The generated fractal curvilinear object  $X_{\text{frac}} \in \mathbb{R}^{H \times W}$  by iteration is given by:
+
+$$
+X _ {f r a c} = \operatorname {D r a w} (i t e r, F _ {r a n d o m}, r u l e s e t, w _ {i}, l _ {i}, c _ {i}) \tag {5}
+$$
+
+FDA-based curvilinear object image synthesis. We further incorporate synthetic curvilinear objects into the target unlabeled images via FDA [45]. We define the target images as  $X_{t} \in \mathbb{R}^{H \times W}$  and the synthetic images of fractal curvilinear object as  $X_{\text{frac}}$ . Let  $\mathcal{F}^A : \in \mathbb{R}^{H \times W} \to \in \mathbb{R}^{H \times W}$  be the amplitude component of the Fourier transform  $\mathcal{F}$  of a grayscale image. We define a  $\beta \in (0,1)$  to select the center region of the amplitude map.
+
+Given two randomly sampled synthetic image  $X_{frac}$  and target image  $X_{t}$ , we follow FDA [45] to replace the low-frequency part in the amplitude map of  $X_{frac}$  by the FFT [15], denotes as  $\mathcal{F}^A (X_{frac})$ , with that of the target image  $X_{t}$ , denoted as  $\mathcal{F}^A (X_t)$ . Then, the modified spectral representation of  $X_{frac}$ , with its phase component unaltered, is mapped back to image  $X_{frac\rightarrow t}$  by the inverse FFT [15], whose content is the same as  $X_{frac}$ , but will resemble the appearance of a sample  $X_{t}$ . After that, we apply a Gaussian blur to the output synthetic image of FDA to obtain synthetic images from FFS, denoted as  $X_{F}$ .
+
+# 3.2. Geometric Information Alignment
+
+Synthetic images generated by FFS could still have nontrivial intensity differences from that of real images. To address this problem, we further align synthetic images and real target images at both image and feature levels.
+
+Image-level Alignment. We aim to explicitly remove the dependency on raw intensity values for both synthetic and real images and meanwhile enhance the geometric characteristics of curvilinear structures. To this end, for each image pixel  $j$  we compare its intensity value  $X(j)$  with its 8 neighboring pixels  $\{n_d^m | m = 1, \dots, 8\}$  (yellow box in Figure. 1) lying perpendicular to  $j$  (red box in Figure. 1), where directional  $d$  denotes left, right, top, and bottom side of  $j$ . If  $X(j) > X(n_d^m)$ , we set the corresponding value for  $n_d^m$  to 0. Otherwise, we set the value for  $n_d^m$  to 1. Such operation produces four 8-bit images for each input image, where the  $m$ -th bit on the  $d$ -th image denotes the relative intensity order between  $j$  and its neighbor  $m$  along the  $d$ -th direction. For each input image  $X$  (denote as  $X_F$  and  $X_t$ ), we concatenate four 8-bit images  $(X_{IA}^1, \dots, X_{IA}^d)$ , where  $X_{IA}^d(j)$  is represented as
+
+$$
+X _ {I A} ^ {d} (j) = \sum_ {m = 1} ^ {8} [ X (j) > X \left(n _ {d} ^ {m}\right) ] \times 2 ^ {m - 1} \tag {6}
+$$
+
+Such local intensity order transformation [34] can capture the intrinsic of the curvilinear object and meanwhile reduces the intensity gap between synthetic and real images.
+
+Feature-level Alignment. Given the 4-channel transformed images, we utilize U-Net [33] to extract features. We align curvilinear objects' features of synthetic images and unlabeled target images based on two loss functions, i.e., the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL).
+
+1) Prediction space adaptation loss. We utilize adversarial learning to explicitly align the prediction space distribution of target images and synthetic images. We denote the prediction segmentation masks of the target images and the synthetic images as  $Y_{target} \in \mathbb{R}^{H \times W}$  and  $Y_{syn} \in \mathbb{R}^{H \times W}$ , respectively. We input  $Y_{target}$  and  $Y_{syn}$  into a fully-convolutional discriminator  $D$  as [50] trained via a binary cross-entropy loss  $\mathcal{L}_d$ :
+
+$$
+\mathcal {L} _ {d} = \mathbb {E} \left[ \log \left(D \left(Y _ {s y n}\right)\right) \right] + \mathbb {E} \left[ \log \left(1 - D \left(Y _ {t a r g e t}\right)\right) \right] (7)
+$$
+
+Accordingly, the PSAL is computed as:
+
+$$
+\mathcal {L} _ {P S A L} = \mathbb {E} \left[ \log \left(D \left(Y _ {\text {t a r g e t}}\right)\right) \right] \tag {8}
+$$
+
+2) Curvilinear mask contrastive loss. The CMCL aims to reduce the distance between features of synthetic images and true target images, and meanwhile to improve the feature distinctiveness between curvilinear objects and backgrounds. To this end, we take the feature maps (denoted as  $f \in \mathbb{R}^{H \times W \times C}$ ) from the final decoder layer of U-Net, the mask of synthetic image (denoted as  $G_{syn} \in \{0,1\}^{H \times W}$ ) and prediction mask of target image (denoted  $Y_{target} \in [0,1]^{H \times W}$ ) as input. We process  $f$  using a lightweight contrastive encoder and a contrastive projector as [41] to map
+
+$f$  to the feature space where the pixel-level contrastive loss is applied for  $Z \in \mathbb{R}^{H \times W \times C}$ .
+
+We denote  $I$  as  $H\times W$  spatial location of the projected feature maps  $Z$ , then for a location  $i\in I$ , we can obtain a feature vector  $z_{i}$  at location  $i$  from feature map  $Z$ , label values  $g_{i}$  and  $y_{i}$  at  $i$  from the mask of synthetic image  $G_{syn}$  and the prediction mask  $Y_{target}$  respectively. We partition pixels of  $I$  into two groups: curvilinear object locations  $I^{+}$  and background locations  $I^{-}$ . For synthetic images, we perform the partition directly based on the mask  $G_{syn}$ , i.e.,  $I_{syn}^{+} = \{i\in I_{syn}\mid g_{i} = 1\}$  and  $I_{syn}^{-} = \{i\in I_{syn}\mid g_{i} = 0\}$ . For target images, as the ground-truth mask is not available, we alternatively perform the partition based on the prediction probability mask  $Y_{target}$ , i.e.,  $I_{target}^{+} = \{i\in I_{target}\mid y_{i}\geq 1 - \alpha \}$  and  $I_{target}^{-} = \{i\in I_{target}\mid y_{i}\leq \alpha \}$ , where  $\alpha = 0.1$  is a small threshold and is fixed in our method.
+
+We let  $q_{syn}^{+} = \left\{\mathbf{z}_{i} \mid i \in \S \left(I_{syn}^{+}, \sigma\right) \right\}$  and  $k_{target}^{+} = \left\{\mathbf{z}_{i} \mid i \in \S \left(I_{target}^{+}, \sigma\right) \right\}$  denote the curvilinear keys of synthetic and target images respectively. Similarly, we define  $k_{syn}^{-} = \left\{\mathbf{z}_{i} \mid i \in \S \left(I_{syn}^{-}, \sigma\right) \right\}$  and  $k_{target}^{-} = \left\{\mathbf{z}_{i} \mid i \in \S \left(I_{target}^{-}, \sigma\right) \right\}$  as the background keys of synthetic and target images, where  $\S (\bullet, \sigma)$  is a random sampling operator which samples a subset from a set randomly with a proportion ratio  $\sigma$ . We combine  $N$  negative queries of the features of synthetic and target images to form a negative set  $k^{-} = (k_{syn}^{-}, k_{target}^{-})$ . The CMCL is defined as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {C M C L} = - \log \left(\exp \left(q _ {\text {s y n}} ^ {+} \cdot k _ {\text {t a r g e t}} ^ {+} / \tau\right)\right) + \\ \log \left(\exp \left(q _ {s y n} ^ {+} \cdot k _ {t a r g e t} ^ {+} / \tau\right) + \sum_ {i = 0} ^ {N} \exp \left(q _ {s y n} ^ {+} \cdot k _ {i} ^ {-} / \tau\right)\right) \tag {9} \\ \end{array}
+$$
+
+where  $\tau$  is a temperature hyper-parameter.
+
+3) Final Loss. The final loss is a combination of the segmentation loss, the PSAL and CMCL as:
+
+$$
+\mathcal {L} _ {s e g} = \mathbb {E} \left[ G _ {s y n} \cdot \log \left(Y _ {s y n}\right) \right] \tag {10}
+$$
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {s e g}} + \mathcal {L} _ {\text {P S A L}} + \lambda \mathcal {L} _ {\text {C M C L}} \tag {11}
+$$
+
+# 4. Experiments
+
+XCAD dataset. The X-ray angiography coronary artery disease (XCAD) dataset [25] is obtained during stent placement using a General Electric Innova IGS 520 system. Each image has a resolution of  $512 \times 512$  pixels with one channel. The training set contains 1621 coronary angiograms without annotations as target images. The testing set contains 126 independent coronary angiograms with vessel segmentation maps annotated by experienced radiologists.
+
+Retinal dataset. We also employ two public retin al datasets to validate the effectiveness of the proposed
+
+method. The DRIVE dataset [37] consists of 40 color retinal images of size  $565 \times 584$  pixels. We use 20 images as target images and 20 remaining as test images. The STARE dataset [17] contains 20 color retinal images of size  $700 \times 605$  pixels with annotations as test images. There are 377 images without annotation which are used as target images.
+
+CrackTree dataset. The CrackTree dataset [51] contains 206  $800 \times 600$  pavement images with different kinds of cracks with curvilinear structures. The whole dataset is split into 160 target images and 46 test images by [34] setting. Following [34], we dilate the annotated centerlines by 4 pixels to form the ground-truth segmentation.
+
+# 4.1. Evaluation Metrics
+
+For XCAD and CrackTree, we follow [25, 34] to use the following widely-used metrics in our evaluation, i.e., Jaccard Index (Jaccard), Dice Coefficient (Dice), accuracy (Acc.), sensitivity (Sn.) and specificity (Sp.). For the DRIVE and STARE datasets, we follow the state-of-the-art works for retina vessel segmentation [25] to report accuracy (Acc.), sensitivity (Sn.) specificity (Sp.) and area under curve (AUC) in our evaluation.
+
+# 4.2. Implementation Details
+
+For FFS, we set the ruleset as  $(\text{rule}_1, \dots, \text{rule}_4)$ , such as:
+
+$$
+\begin{array}{l} r u l e _ {1}: F _ {\text {r a n d o m}} \rightarrow F _ {\text {r a n d o m}} [ + F _ {\text {r a n d o m}} - F _ {\text {r a n d o m}} ]. \\ \operatorname {r u l e} _ {2}: F _ {\text {r a n d o m}} \rightarrow F _ {\text {r a n d o m}} [ - F _ {\text {r a n d o m}} - F _ {\text {r a n d o m}} ]. \\ r u l e _ {3}: F _ {\text {r a n d o m}} \rightarrow F _ {\text {r a n d o m}} - F _ {\text {r a n d o m}} - F _ {\text {r a n d o m}}. \\ \text {r u l e} _ {4}: F _ {\text {r a n d o m}} \rightarrow F _ {\text {r a n d o m}} + F _ {\text {r a n d o m}} + F _ {\text {r a n d o m}}. \\ \end{array}
+$$
+
+We set the initial parameters of the Fractal system as follows. For all four datasets, the angle is randomly selected from  $(20^{\circ},120^{\circ})$ , the initial length is randomly selected from  $(120\mathrm{px}$ $200\mathrm{px})$  , the decreased parameter  $\gamma$  is randomly selected from (0.7, 1). The initial width  $w_{init}$  is ranging from (8px, 14px) for XCAD, DRIVE and STARE. For CrackTree, the  $w_{init}$  is selected from (2px, 6px). The kernel size of Gaussian blur for FFS is 13. We generate 150, 150, 600 synthetic fractal images  $X_{frac}$  for XCAD, CrackTree, and retinal datasets, respectively.
+
+We apply data augmentation including horizontal flipping, random brightness and contrast changes ranging from (1.0, 2.1), random saturation ranging from (0.5, 1.5), and random rotation with  $90^{\circ}$ ,  $180^{\circ}$ , and  $270^{\circ}$ . The standard deviation for Gaussian noise is set to a random value within  $(-5, +5)$ . All images are cropped to  $256 \times 256$  pixels for training. All the data-augmented operations are applied before the GIA module. The segmentation network is trained using the SGD with a momentum of 0.9 for optimization and the initial learning rate is 0.01. The discriminator network is trained using an Adam optimizer with an initial learning rate of  $10^{-3}$ . We employ a batch size of 8 to train the network for 600 epochs. The number of negative queries  $q_{syn}^{+}$
+
+<table><tr><td></td><td>Methods</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Upper bound</td><td>U-Net [33]</td><td>0.571</td><td>0.724</td><td>0.981</td><td>0.868</td><td>0.996</td></tr><tr><td rowspan="3">Domain Adaptation</td><td>U-Net [33]</td><td>0.228</td><td>0.365</td><td>0.831</td><td>0.444</td><td>0.906</td></tr><tr><td>MMD [8]</td><td>0.262</td><td>0.416</td><td>0.873</td><td>0.553</td><td>0.920</td></tr><tr><td>YNet [32]</td><td>0.287</td><td>0.434</td><td>0.891</td><td>0.523</td><td>0.935</td></tr><tr><td rowspan="2">Traditional</td><td>Hessian [13]</td><td>0.307</td><td>0.465</td><td>0.948</td><td>0.406</td><td>0.981</td></tr><tr><td>OOF [22]</td><td>0.241</td><td>0.386</td><td>0.899</td><td>0.566</td><td>0.920</td></tr><tr><td rowspan="2">Unsupervised</td><td>IIC [19]</td><td>0.124</td><td>0.178</td><td>0.738</td><td>0.487</td><td>0.754</td></tr><tr><td>ReDO [9]</td><td>0.151</td><td>0.261</td><td>0.753</td><td>0.392</td><td>0.923</td></tr><tr><td rowspan="3">Self-supervised</td><td>SSVS [25]</td><td>0.389</td><td>0.557</td><td>0.945</td><td>0.583</td><td>0.972</td></tr><tr><td>DARL [21]</td><td>0.471</td><td>0.636</td><td>0.962</td><td>0.597</td><td>0.985</td></tr><tr><td>Ours</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>
+
+Table 1. Quantitative evaluation of FreeCOS compared with different methods on the XCAD dataset.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Methods</td><td colspan="4">DRIVE</td><td colspan="4">STARE</td></tr><tr><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td></tr><tr><td rowspan="4">Traditional</td><td>Hessian [13]</td><td>0.941</td><td>0.644</td><td>0.97</td><td>0.847</td><td>0.938</td><td>0.690</td><td>0.957</td><td>0.858</td></tr><tr><td>OOF [22]</td><td>0.936</td><td>0.688</td><td>0.959</td><td>0.920</td><td>0.920</td><td>0.770</td><td>0.932</td><td>0.955</td></tr><tr><td>Memari [26]</td><td>0.961</td><td>0.761</td><td>0.981</td><td>0.871</td><td>0.951</td><td>0.782</td><td>0.965</td><td>0.783</td></tr><tr><td>Khan [20]</td><td>0.958</td><td>0.797</td><td>0.973</td><td>0.885</td><td>0.996</td><td>0.792</td><td>0.998</td><td>0.895</td></tr><tr><td rowspan="2">Unsupervised</td><td>IIC [19]</td><td>0.738</td><td>0.632</td><td>0.840</td><td>0.736</td><td>0.710</td><td>0.586</td><td>0.832</td><td>0.709</td></tr><tr><td>ReDO [9]</td><td>0.761</td><td>0.593</td><td>0.927</td><td>0.760</td><td>0.756</td><td>0.567</td><td>0.899</td><td>0.733</td></tr><tr><td rowspan="3">Self-supervised</td><td>SSVS [25]</td><td>0.913</td><td>0.794</td><td>0.982</td><td>0.888</td><td>0.910</td><td>0.774</td><td>0.980</td><td>0.877</td></tr><tr><td>DARL [21]</td><td>-</td><td>0.456</td><td>-</td><td>-</td><td>-</td><td>0.480</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>0.921</td><td>0.810</td><td>0.932</td><td>0.941</td><td>0.952</td><td>0.797</td><td>0.964</td><td>0.971</td></tr></table>
+
+Table 2. Quantitative evaluation of FreeCOS compared with different methods on the retinal dataset.  
+
+<table><tr><td></td><td>Methods</td><td>AUC</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td rowspan="2">Traditional</td><td>Hessian [13]</td><td>0.780</td><td>0.122</td><td>0.935</td><td>0.310</td><td>0.945</td></tr><tr><td>OOF [22]</td><td>0.482</td><td>0.031</td><td>0.770</td><td>0.244</td><td>0.778</td></tr><tr><td>Unsupervised</td><td>ReDO [9]</td><td>0.422</td><td>0.035</td><td>0.632</td><td>0.450</td><td>0.635</td></tr><tr><td rowspan="3">Self-supervised</td><td>SSVS [25]</td><td>0.477</td><td>0.078</td><td>0.299</td><td>0.042</td><td>0.912</td></tr><tr><td>DARL [21]</td><td>0.888</td><td>0.395</td><td>0.974</td><td>0.542</td><td>0.981</td></tr><tr><td>Ours</td><td>0.920</td><td>0.525</td><td>0.974</td><td>0.576</td><td>0.979</td></tr></table>
+
+Table 3. Quantitative evaluation of FreeCOS compared with different methods on the CrackTree dataset.
+
+$k_{target}^{+}$  and  $k^{-}$  per batch is taken up to 500, 500 and 1000. The amplitude map center region selection parameter of  $\beta$  is set to 0.3. the sampling ratio is 0.3, the hyper-parameter  $\lambda$  is 0.4 and the temperature hyper-parameter  $\tau$  is 0.1.
+
+# 4.3. Experimental Results
+
+# 4.3.1 Comparison with State-of-the-art
+
+Table. 1 compares the performance of vessel segmentation on XCAD between FreeCOS and the state-of-the-art methods, including the unsupervised methods [9, 19], the self-supervised methods [25, 21], domain adaptation methods [8, 32] and the traditional methods [13, 22]. The results in the 1st row are based on supervised U-Net as [25] (i.e., identical segmentation network trained using real images with manual labels) which are the upper bound.
+
+For domain adaption methods, we pretrain a vessel segmentation model based on U-Net using training images of DRIVE. Then we adapt the pre-trained model to XCAD using MMD [8] and Ynet [32]. Even with supervised information in the annotated source domain, the performance of
+
+<table><tr><td></td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr><tr><td>FFS+PSAL</td><td>0.468</td><td>0.633</td><td>0.957</td><td>0.680</td><td>0.974</td></tr><tr><td>FFS+PSAL+IA</td><td>0.485</td><td>0.647</td><td>0.958</td><td>0.667</td><td>0.976</td></tr><tr><td>FFS+GIA</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>
+
+MMD and YNet is still inferior to ours. Specifically, our method achieves  $21.2\%$  improvement in Jaccard,  $22.7\%$  improvement in Dice,  $6.9\%$  improvement in Acc.,  $16.4\%$  improvement in Sn., and  $4.2\%$  improvement in Sp. compared with YNet.
+
+Compared with the unsupervised methods IIC [19] and ReDO [9], our method achieves significantly better performance for all metrics on XCAD. The results show that unsupervised methods cannot achieve satisfactory performance on the gray-scale X-ray images where the segmentation objects can be hardly distinguished from the background.
+
+Self-supervised method SSVS [25] is specifically designed for XCAD, yet our method still achieves much better performance for all metrics, i.e.,  $11\%$  improvement in Jaccard,  $10.4\%$  improvement in Dice and  $10.4\%$  improvement in Sn.
+
+Table. 2 and 3 further compare our method with the existing methods on the retinal and crack datasets and a similar trend can be observed in these three datasets. Figure. 3 shows the visualization results of images from various kinds of curvilinear datasets.
+
+FreeCOS not only achieves state-of-the-art (SOTA) performance but also demonstrates unique advantages compared to various types of methods. a) Compared with traditional methods, FreeCOS does not require complex parameter tuning as traditional methods and achieves much better performance. b) FreeCOS can better tolerate large domain shifts than domain adaptation methods. But the effectiveness of current domain adaptation methods may struggle to achieve satisfactory performance facing a large domain gap. c) Unsupervised methods are more suitable for segmenting objects with aspect ratios close to one and perform well when objects are visually distinct from backgrounds. But their performance greatly degrades when segmenting curvilinear objects with branching structures in cluttered backgrounds. d) Self-supervised methods based on GAN/Diffusion require training with clean background images which limits applications to practical scenarios.
+
+# 4.3.2 Ablation Study
+
+We first conduct ablation studies to evaluate the impact of different modules. To this end, we build the following variants based on our method. For all the variant models and our
+
+Table 4. Ablation study for modules.  
+
+<table><tr><td></td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS w/o Gaussian blur</td><td>0.383</td><td>0.547</td><td>0.940</td><td>0.654</td><td>0.959</td></tr><tr><td>FFS w/o FDA</td><td>0.302</td><td>0.459</td><td>0.920</td><td>0.609</td><td>0.940</td></tr><tr><td>FFS w/o various intensities</td><td>0.405</td><td>0.569</td><td>0.957</td><td>0.525</td><td>0.984</td></tr><tr><td>FFS w/o various angles</td><td>0.267</td><td>0.415</td><td>0.939</td><td>0.409</td><td>0.972</td></tr><tr><td>FFS w/o various lengths</td><td>0.224</td><td>0.358</td><td>0.943</td><td>0.300</td><td>0.983</td></tr><tr><td>FFS w/o various widths</td><td>0.224</td><td>0.354</td><td>0.935</td><td>0.348</td><td>0.972</td></tr><tr><td>FFS</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr></table>
+
+Table 5. Ablation study for FFS.  
+
+<table><tr><td></td><td>Architecture</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>FFS</td><td>U-Net [33]</td><td>0.450</td><td>0.615</td><td>0.955</td><td>0.664</td><td>0.974</td></tr><tr><td>FFS</td><td>Iternet [23]</td><td>0.481</td><td>0.645</td><td>0.959</td><td>0.670</td><td>0.976</td></tr><tr><td>FFS+GIA</td><td>Iternet [23]</td><td>0.505</td><td>0.664</td><td>0.964</td><td>0.641</td><td>0.984</td></tr></table>
+
+Table 6. Ablation study for architecture.  
+
+<table><tr><td>Numbers of images</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Synthetic-15</td><td>0.464</td><td>0.629</td><td>0.958</td><td>0.630</td><td>0.979</td></tr><tr><td>Synthetic-45</td><td>0.478</td><td>0.642</td><td>0.958</td><td>0.674</td><td>0.976</td></tr><tr><td>Synthetic-75</td><td>0.488</td><td>0.652</td><td>0.960</td><td>0.668</td><td>0.978</td></tr><tr><td>Synthetic-150</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>
+
+Table 7. Ablation study for different numbers of synthetic images.  
+
+<table><tr><td>Numbers of images</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Target-162</td><td>0.455</td><td>0.620</td><td>0.952</td><td>0.678</td><td>0.969</td></tr><tr><td>Target-486</td><td>0.476</td><td>0.637</td><td>0.955</td><td>0.683</td><td>0.972</td></tr><tr><td>Target-810</td><td>0.466</td><td>0.630</td><td>0.958</td><td>0.635</td><td>0.978</td></tr><tr><td>Target-1620</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>
+
+Table 8. Ablation study for different numbers of target images.
+
+final model, we use the same U-Net model as our backbone. 1) FFS. We utilize the FFS to generate synthetic training images and the corresponding labels to train the U-Net segmentation model. 2) FFS+PSAL. We further apply PSAL to align features of synthetic and real target images on top of FFS. 3) FFS+PSAL+IA. We apply image-level alignment via relative intensity order transformation (i.e., IA) on top of FFS+PSAL. 4) FFS+GIA. We apply our GIA module (including IA, PSAL and CMCL) on top of FFS. This model is also our final curvilinear segmentation model. The ablation studies are conducted on XCAD. The trend on other datasets are similar and thus the results on the other datasets are omitted due to the space limit.
+
+The results in Table 4 show that 1) by training a U-Net model using synthetic images from FFS, we can already achieve better performance than the SOTA self-supervised method SSVS which is based on adversarial learning [25]. Such results reveal a very interesting phenomenon although adversarial learning can synthesize visually similar images as real target images, it cannot explicitly control the generated visual patterns and thus fail to enforce
+
+![](images/4991ebe3c7a095b5b783b2cd67999ae76c706a85f42ba41f166fc7e75ebaa641.jpg)
+
+![](images/4d32eddacec5007e8c011085c0893c9ba576556c7f1f62bb34a8c256fd2c28d4.jpg)
+
+![](images/b3960a667a20f2026635849a359b45a229652498b1aff06f194dc683e63a2ed1.jpg)  
+Image  
+Figure 3. The visualization results of images from the various kinds of curvilinear datasets.
+
+![](images/f664cea514fed35ae9161b4b2800b3c974397d09bb35790b9c9e4861fa9859c7.jpg)
+
+![](images/2ed174d431162fa11d653395591f64f70f58e51666ef6e204006178c815a98cd.jpg)
+
+![](images/198f12f50e355dcc19c727ee2ca3740fb2b4df4cb1801a844c54fd9b8ddc9ef6.jpg)  
+Hessian
+
+![](images/c164e0083859feba3f8e40cb5f2d971eb5648436fa2496a3ef17b2675f5169bd.jpg)
+
+![](images/6b82133fa8b714da483009b495b35a148af91312c0059ab8dfc2956ebf52c0eb.jpg)
+
+![](images/2e24529f65789588d3917df086afdfb92af7e29b0a07ed5f21e6c7222e29eea4.jpg)  
+OOF
+
+![](images/7df60fdc2de28746f7fc80914942c039d2e9b41abe2e6fa5fb9bbfd0180feb5b.jpg)  
+Ours  
+GT
+
+the segmentation-oriented patterns and properties to be encoded in synthetic images. In comparison, FFS can explicitly control the synthesis of both curvilinear structures and background patterns and hence can achieve better performance. 2) Aligning features via prediction space adaptation loss (PSAL) can help reduce domain shifts between synthetic images and real target images and thus FFS+PSAL achieves performance improvements compared with FFS. 3) Aligning synthetic images and real target images via IA method can also reduce the domain shifts and thus FFS+PSAL+IA can provide complementary improvements to FFS+PSAL. 4) Finally, the best performance is obtained when combining both FFS and GIA.
+
+We further explore the importance of different parameters in FFS on the final performance and discuss how to generate images of curvilinear structures to encode sufficient and comprehensive visual cues for learning robust and distinctive features. To this end, we build 6 variant models based on FFS. 1) FFS w/o Gaussian blur. We do not perform Gaussian blur to synthetic images from FFS. 2) FFS w/o FDA. We remove FDA-based synthesis from FFS and only generate curvilinear structures without backgrounds. 3) FFS w/o various intensities. We remove intensity variations  $c_{i}$  in the Fractal system and set the intensity to a fixed value 60. 4) FFS w/o various angles. We utilize a small branching angle range from  $(1^{\circ}, 5^{\circ})$  to reduce the branching angle variations. 5) FFS w/o various lengths. We reduce
+
+the length variation range to (10px, 20px). 6) FFS w/o various widths. We reduce the width variation to (1px, 5px).
+
+The results in Table 5 show that 1) Gaussian blur can smooth the transition region between curvilinear objects and backgrounds, better mimicking the target images and providing more challenging samples for training than those with sharp boundaries. As a result, excluding Gaussian blur decreases the performance of FFS by  $6.8\%$  in Dice. 2) FDA could provide background patterns of target images which are essential for learning features of negative samples. Thus, FFS w/o FDA is  $15.6\%$  worse than FFS in Dice. 3) Among the four parameters of the Fractal system, i.e., intensity, angle, length and width, width plays the most important role in the final performance, i.e., FFS w/o various widths decreases the performance by  $26.1\%$  compared with FFS in Dice. To summarize, we identify that the appearance patterns in the curvilinear object, object-background transition regions and background regions are important for self-supervised segmentation. Meanwhile, proper parameter settings which can provide similar geometric characteristics with the real target images are key to the success of our self-supervised method.
+
+# 4.3.3 Ablation Study on Architecture
+
+By replacing the U-Net with Iternet in FFS, We conduct ablation studies on two backbone networks U-Net [33]
+
+and Iternet [23]. FFS using Iternet segmentation model gets better performance than FFS using U-Net in Table 6. FFS+GIA also demonstrates performance improvement, showing FreeCOS's effectiveness on different architectures. This indicates that the use of a more advanced segmentation network architecture for FreeCOS has the potential to improve performance.
+
+# 4.3.4 Self-supervised training with more data
+
+We also examine the segmentation performance when varying the number of synthetic images on the XCAD dataset. Results in Tables. 7 and 8 provide the results when using different numbers of synthetic structures and real target images for generating synthetic images for self-supervised training respectively. Synthetic-  $15\sim$  Synthetic-150 denote using the number of synthetic fractal object images  $X_{frac}$  from 15 to 150, and Target-  $162\sim$  Target-1620 denote using the number of target images  $X_{t}$  from 162 to 1620. Increasing both synthetic structures and real target images can accordingly improve the final segmentation performance.
+
+# 5. Conclusion
+
+In this paper, we propose a novel self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. Different from existing methods, FreeCOS applies the proposed FFS and GIA approach to effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds and aligns information of synthetic and target images at both image and feature levels. One limitation of FreeCOS is that may generate false positives in other curvilinear objects (e.g., catheters in XCAD) and requires proper selection for width range. However, we have successfully utilized this self-supervised learning method for coronary vessel segmentation, retinal vessel segmentation and crack segmentation by reasonable parameter selection. To the best of our knowledge, FreeOCS is the first self-supervised learning method for various curvilinear object segmentation applications.
+
+Acknowledgements. This work was supported by the National Natural Science Foundation of China under Grants 62061160490, 62122029, and U20B2064.
+
+# References
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+[24] Yunfan Li, Peng Hu, Zitao Liu, Dezhong Peng, Joel Tianyi Zhou, and Xi Peng. Contrastive clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 8547-8555, 2021. 1, 2  
+[25] Yuxin Ma, Yang Hua, Hanming Deng, Tao Song, Hao Wang, Zhengui Xue, Heng Cao, Ruhui Ma, and Haibing Guan. Self-supervised vessel segmentation via adversarial learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7536-7545, 2021. 1, 2, 3, 5, 6, 7  
+[26] Nogol Memari, Abd Rahman Ramli, M Saripan, Syamsiah Mashohor, and Mehrdad Moghbel. Retinal blood vessel segmentation by using matched filtering and fuzzy c-means clustering with integrated level set method for diabetic retinopathy assessment. Journal of Medical and Biological Engineering, 39(5):713-731, 2019. 2, 6
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+[32] Joris Roels, Julian Hennies, Yvan Saeys, Wilfried Philips, and Anna Kreshuk. Domain adaptive segmentation in volume electron microscopy imaging. In IEEE International Symposium on Biomedical Imaging, pages 1519-1522. IEEE, 2019. 1, 6  
+[33] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 234-241. Springer, 2015. 5, 6, 7, 8  
+[34] Tianyi Shi, Nicolas Boutry, Yongchao Xu, and Thierry Géraud. Local intensity order transformation for robust curvilinear object segmentation. IEEE Transactions on Image Processing, 31:2557-2569, 2022. 5, 6  
+[35] Tianyi Shi, Xiaohuan Ding, Wei Zhou, Feng Pan, Zengqiang Yan, Xiang Bai, and Xin Yang. Affinity feature strengthening for accurate, complete and robust vessel segmentation. IEEE Journal of Biomedical and Health Informatics, 27(8):4006-4017, 2023. 1  
+[36] Suprosanna Shit, Johannes C Paetzold, Anjany Sekuboyina, Ivan Ezhov, Alexander Unger, Andrey Zhylka, Josien PW Pluim, Ulrich Bauer, and Bjoern H Menze. cldice-a novel topology-preserving loss function for tubular structure segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16560-16569, 2021. 1  
+[37] Joes Staal, Michael D Abramoff, Meindert Niemeijer, Max A Viergever, and Bram Van Ginneken. Ridge-based vessel segmentation in color images of the retina. IEEE Transactions on Medical Imaging, 23(4):501-509, 2004. 1, 2, 6  
+[38] Joseph L Thomas, Simon Winther, Robert F Wilson, and Morten Böttcher. A novel approach to diagnosing coronary artery disease: acoustic detection of coronary turbulence. The International Journal of Cardiovascular Imaging, 33(1):129-136, 2017. 1
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+[39] Feigege Wang, Yue Gu, Wenxi Liu, Yuanlong Yu, Shengfeng He, and Jia Pan. Context-aware spatio-recurrent curvilinear structure segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12648-12657, 2019. 1  
+[40] Jierong Wang and Albert Chung. Higher-order flux with spherical harmonics transform for vascular analysis. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 55-65. Springer, 2020. 2  
+[41] Xuehui Wang, Kai Zhao, Ruixin Zhang, Shouhong Ding, Yan Wang, and Wei Shen. Contrastmask: Contrastive learning to segment every thing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11604-11613, 2022. 3, 5  
+[42] Yan Wang, Xu Wei, Fengze Liu, Jieneng Chen, Yuyin Zhou, Wei Shen, Elliot K Fishman, and Alan L Yuille. Deep distance transform for tubular structure segmentation in ct scans. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3833-3842, 2020. 1  
+[43] Haiyan Wu, Yanyun Qu, Shaohui Lin, Jian Zhou, Ruizhi Qiao, Zhizhong Zhang, Yuan Xie, and Lizhuang Ma. Contrastive learning for compact single image dehazing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10551-10560, 2021. 3  
+[44] Enze Xie, Jian Ding, Wenhai Wang, Xiaohang Zhan, Hang Xu, Peize Sun, Zhenguo Li, and Ping Luo. Detco: Unsupervised contrastive learning for object detection. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 8392-8401, 2021. 3  
+[45] Yanchao Yang and Stefano Soatto. Fda: Fourier domain adaptation for semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4085-4095, 2020. 2, 4  
+[46] Mair Zamir. On fractal properties of arterial trees. Journal of Theoretical Biology, 197(4):517-526, 1999. 1  
+[47] Mair Zamir. Arterial branching within the confines of fractal l-system formalism. The Journal of General Physiology, 118(3):267-276, 2001. 1, 2, 4  
+[48] Mair Zamir. Fractal dimensions and multifractility in vascular branching. Journal of Theoretical Biology, 212(2):183-190, 2001. 1  
+[49] Yuanyi Zhong, Bodi Yuan, Hong Wu, Zhiqiang Yuan, Jian Peng, and Yu-Xiong Wang. Pixel contrastive-consistent semi-supervised semantic segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7273-7282, 2021. 3  
+[50] Wei Zhou, Yukang Wang, Jiajia Chu, Jiehua Yang, Xiang Bai, and Yongchao Xu. Affinity space adaptation for semantic segmentation across domains. IEEE Transactions on Image Processing, 30:2549-2561, 2020. 5  
+[51] Qin Zou, Yu Cao, Qingquan Li, Qingzhou Mao, and Song Wang. Cracktree: Automatic crack detection from pavement images. Pattern Recognition Letters, 33(3):227-238, 2012. 1, 2, 6
\ No newline at end of file
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+                                    "content": "Tianyi Shi, Xiaohuan Ding, Liang Zhang, Xin Yang†  \nSchool of EIC, Huazhong University of Science & Technology  \n{shitianyihust, dingxiaohuan, liangz, xinyang2014}@hust.edu.cn"
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+                                    "content": "Curvilinear object segmentation is critical for many applications. However, manually annotating curvilinear objects is very time-consuming and error-prone, yielding insufficiently available annotated datasets for existing supervised methods and domain adaptation methods. This paper proposes a self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. The key contributions include a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. FFS generates curvilinear structures based on the parametric Fractal L-system and integrates the generated structures into unlabeled images to obtain synthetic training images via Fourier Domain Adaptation. GIA reduces the intensity differences between the synthetic and unlabeled images by comparing the intensity order of a given pixel to the values of its nearby neighbors. Such image alignment can explicitly remove the dependency on absolute intensity values and enhance the inherent geometric characteristics which are common in both synthetic and real images. In addition, GIA aligns features of synthetic and real images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). Extensive experimental results on four public datasets, i.e., XCAD, DRIVE, STARE and CrackTree demonstrate that our method outperforms the state-of-the-art unsupervised methods, self-supervised methods and traditional methods by a large margin. The source code of this work is available at https://github.com/TY-Shi/FreeCOS."
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+                                    "content": "some observed variability. These results motivate us to use the generated curvilinear objects via the fractal systems to explicitly encode geometric properties and varieties (i.e., different diameters and lengths of branches, and different branching angles) into training samples and to assist feature learning of a curvilinear structure segmentation model. However, such formulas generated training samples can hardly mimic the appearance patterns within curvilinear objects, the transition regions between curvilinear objects and backgrounds, which are also key information for learning a segmentation model and contained in easily-obtained unlabeled target images. This paper asks the question, how to combine fractals and unlabeled target images to encode sufficient and comprehensive visual cues for learning robust and distinctive features of curvilinear structures?"
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+                                    "content": "The main contribution of this paper is a self-supervised segmentation method based on a novel Fractal-FDA synthesis (FFS) module and a geometric information alignment (GIA) approach. Specifically, curvilinear structures are synthesized by the parametric fractal L-Systems [47] and serve as segmentation labels of synthetic training samples. To simulate appearance patterns in the object-background transition regions and background regions, we apply Fourier Domain Adaptation [45] (FDA) to fuse synthetic curvilinear structures and unlabeled target images. The synthetic images via our FFS module can effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds. To further improve the robustness to differences between intensity distributions of synthetic and real target images, we design a novel geometric information alignment (GIA) approach which aligns information of synthetic and target images at both image and feature levels. Specifically, GIA first converts each training image (synthetic and target images) into four geometry-enhanced images by comparing the intensity order of a given pixel to the values of its nearby neighbors (i.e., along with the up, down, left and right directions). In this way, the four converted images do not depend on the absolute intensity values but the relative intensity in order to capture the inherent geometric characteristic of the curvilinear structure, reducing the intensity differences between synthetic and target images. Then, we extract features from the 4-channel converted images and propose two loss functions, i.e., a prediction space adaptation loss (PSAL) and a curvilinear mask contrastive loss (CMCL), to align the geometric features of synthetic and target images. The PSAL minimizes the distance between the segmentation masks of the target images and synthetic curvilinear objects and the CMCL minimizes the distance between features of segmented masks and synthetic objects."
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+                                    "type": "text",
+                                    "content": "- We propose a novel self-supervised curvilinear feature learning method which intelligently combines tree-like fractals and unlabeled images to assist in learning robust and distinctive feature representations."
+                                }
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+                                    "content": "- We propose Fractal-FDA synthesis (FFS) and geometric information alignment (GIA), which are the two key enabling modules of our method. FFS integrates the synthetic curvilinear structures into unlabeled images to guide learning distinctive features to distinguish foregrounds and backgrounds. GIA enhances geometric features and meanwhile improves the feature robustness to intensity differences between synthetic and target unlabeled images."
+                                }
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+                                    "content": "- We develop a novel self-supervised segmentation network that can be trained using only target images and fractal synthetic curvilinear objects. Our network performs significantly better than state-of-the-art self-supervised/unsupervised methods on multiple public datasets with various curvilinear objects."
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+                                    "content": "2. Related Work"
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+                                    "content": "2.1. Traditional Methods"
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+                                    "type": "text",
+                                    "content": "Traditional curvilinear object segmentation methods [20, 26, 13, 40, 22] design heuristic rules and/or filters to capture features of the target curvilinear objects. For instance, Frangi et al. introduce the vesselness filter [13] based on the Hessian matrix to represent and enhance tube-like curvilinear objects. Khan et al. [20] further design B-COSFIRE filters to denoise retinal images and segment retinal vessels. Memari et al. [26] enhance image contrast via contrast-limited adaptive histogram equalization and then segment retinal vessels based on hand-crafted filters. In [40, 22], the authors propose optimally oriented flux (OOF) to enhance curvilinear tube-like objects. OOF exhibits better performance for segmenting adjacent curvilinear objects yet is sensitive to different sizes of curvilinear objects."
+                                }
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+                                    "content": "Traditional methods based on hand-crafted filters do not require any training yet they require careful parameter tuning for optimized performance. And the optimized parameter settings are usually data-dependent or even region-dependent, limiting their convenience in segmenting a wide variety of curvilinear objects."
+                                }
+                            ]
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+                                    "content": "2.2. Unsupervised Segmentation Methods"
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+                                    "content": "Unsupervised segmentation methods can be generally divided into two classes: clustering based [19, 24, 11] and ad"
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+                                            "content": "Figure 1. The pipeline of Self-Supervised Learning from Fractals and Unlabeled Images for Curvilinear Object Segmentation (FreeCOS)."
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+                                    "content": "versarial learning based [9, 1]. Xu et al. [19] propose Invariant Information Clustering (IIC) which automatically partitions input images into regions of different semantic classes by optimizing mutual information between related region pairs. Such a clustering-based method is more suitable for segmenting objects with aspect ratios close to one while becoming ineffective for curvilinear objects due to their thin, long, tortuous shapes. Redo [9] is based on an adversarial architecture where the generator is guided by an image and extracts the object mask, then redraws a new object at the same location with different textures/colors. However, this adversarial learning-based unsupervised method only performs well for objects which are visually distinguishable from backgrounds. For the segmentation of curvilinear objects with complex and numerous tiny branching structures, embedded in confusing and cluttered backgrounds, the efficacy of such a method degrades significantly."
+                                }
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+                                    "content": "In contrast to unsupervised methods, our method explicitly encodes geometric and photometric characteristics, as well as some observed varieties of curvilinear objects in target application into synthetic images. Those synthetic images provide labels to effectively guide the model to learn robust and distinctive features and thus yield superior performance to state-of-the-art unsupervised methods [9, 19]."
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+                                    "content": "2.3. Self-supervised Learning Methods"
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+                                    "content": "Self-supervised learning methods construct pretexts from large-scale unsupervised data and utilize contrastive learning losses to measure the similarities of sample pairs in the representation space. To this end, various pretext tasks have been designed, including jigsaw [12], hole-fill [31] and transformation invariance [16]. Although existing self-supervised methods have achieved outstanding performance in classification [27, 4], detection [44, 5], and image translation [30, 43], few of them provide a suitable pretext task for curvilinear object segmentation. A potential solu"
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+                                    "type": "text",
+                                    "content": "tion is the pixel-level contrastive-based method [41, 3, 49], while it requires heavy manual annotations to prepare pixel-level positive and negative samples. Similar work to ours is [25, 21] which designs a self-supervised vessel segmentation method via adversarial learning and fractals. But this method requires clean background images as input (i.e., the first frame of the angiography sequence) for synthesis which greatly limits its applications. In addition, adversarial learning cannot explicitly and precisely enforce visual cues, which are important for learning segmentation-oriented features, being encoded in the synthetic images. As a result, although their synthetic images visually look similar to the target images, the segmentation accuracy is also quite low."
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+                                    "content": "Figure. 1 shows the framework of FreeCOS which consists of two main modules, i.e., Fractal-FDA Synthesis (FFS) and Geometric Information Alignment (GIA). In FFS, we generate synthetic curvilinear structures via the parametric Fractal L-Systems and use the generated structures as segmentation maps to guide self-supervised training of a segmentation network. The synthetic curvilinear structures are then integrated into unlabeled images via FDA to form synthetic images of curvilinear structures. The intensity distributions of synthetic images could deviate from those of real target images and hence yield poor feature robustness. To address this problem, our GIA module first reduces image-level differences between the synthetic and target images by converting intensity images into four-channel intensity order images. The converted images of both synthetic images and target images are then input into U-Net to extract feature representations. Our GIA further aligns features of synthetic images and target images via the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL). In the following, we present the details of FFS and GIA."
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+                                    "content": "Fractal-based curvilinear structure generation. Fractals are simple graphic patterns rendered by mathematical formulas. In this work, we adopt the parametric Fractal L-systems proposed by Zamir et al. [47] to generate fractal tree structures and meanwhile select proper branching parameters according to physiological laws of curvilinear objects in target applications. Specifically, \"grammar\" for generating curvilinear structures with repeated bifurcations based on Fractal L-systems method is defined as follows:"
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+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        477,
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+                                        490
+                                    ],
+                                    "type": "text",
+                                    "content": "The generated object by iteration iter:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        124,
+                        496,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        124,
+                                        496,
+                                        287,
+                                        509
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {D r a w} (\\text {i t e r}, F, \\text {r u l e}) \\tag {2}",
+                                    "image_path": "0591f5768160ea4ca7b3d14b29bfe666a31c33c4768ec4c1ea10bd3f9ae5d388.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                        624
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                515,
+                                287,
+                                624
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " represents a line of unit length in the horizontal direction, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\omega"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes an axiom, iter denotes the iteration and rule denotes the production rule. The square brackets represent the departure from "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " and return to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[]"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " a branch point. The plus and minus signs represent turns through a given angle "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " in the clockwise and anticlockwise directions, respectively. For example, the first three stages of a tree produced by the basic Fractal L-system, denoted by "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "iter = 1 \\sim 3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        515,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": ", are given by the:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        54,
+                        630,
+                        287,
+                        677
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                54,
+                                630,
+                                287,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        54,
+                                        630,
+                                        287,
+                                        677
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} i t e r = 1 F \\\\ i t e r = 2 \\quad F [ - F ] [ + F ] \\\\ i t e r = 3 \\quad F [ - F ] [ + F ] [ - F [ - F ] [ + F ] ] [ + F [ - F ] [ + F ] ] \\tag {3} \\\\ \\end{array}",
+                                    "image_path": "b956611e8d95556457f9e9e8c30d47fed4637cea947bf5aef27361d3d9b1859e.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        46,
+                        677,
+                        287,
+                        714
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                677,
+                                287,
+                                714
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "The left part of Figure. 2 illustrates exemplar results of the generated curvilinear structures based on the basic Fractal system."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        546,
+                        145
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                72,
+                                546,
+                                145
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": "To synthesize curvilinear structures with various widths and lengths, we replace "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " using "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{random}(w_i, l_i, c_i)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " which represents a line of width "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ", length "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " and intensity "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ". We set the initial width "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{init}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ", length "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l_{init}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " and decreased parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " by the repeated "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{random}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " in the Draw grammar. For the index number "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{random}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "l_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        546,
+                                        145
+                                    ],
+                                    "type": "text",
+                                    "content": " are given by:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        388,
+                        152,
+                        545,
+                        182
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                388,
+                                152,
+                                545,
+                                182
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        388,
+                                        152,
+                                        545,
+                                        182
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} w _ {i} = w _ {i n i t} \\cdot \\gamma^ {i - 1} \\tag {4} \\\\ l _ {i} = l _ {i n i t} \\cdot \\gamma^ {i - 1} \\\\ \\end{array}",
+                                    "image_path": "35994bf647c702b3a8f7e2a6b09a31fb18082aef0f81d584b6f02c08c4397648.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        304,
+                        190,
+                        546,
+                        261
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                190,
+                                546,
+                                261
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": "We randomly choose a value within the range of (0, 255) and set this value as the intensity "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " for the index "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{random}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": ". For the branching angle "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": ", we replace "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " using "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{random}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " (defined by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{init} \\pm \\delta_{delta}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{init}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " within the range of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(20^{\\circ}, 120^{\\circ})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": "), in which "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta_{delta}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " is a random angle ranging from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "10^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "40^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        190,
+                                        546,
+                                        261
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        304,
+                        262,
+                        547,
+                        382
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                262,
+                                547,
+                                382
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "text",
+                                    "content": "To mimic the geometric characteristics of a target application, we incorporate the above-mentioned parameters into the L-Systems. Specifically, we design a set of rules "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\text{ruleset} : (rule_1, \\dots, rule_n)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "text",
+                                    "content": " for different fractal structures, like "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{random} \\rightarrow F_{random} - F_{random} [+F_{random} - F_{random}] [-F_{random} + F_{random}]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "text",
+                                    "content": ". For each iteration iter, we randomly select a rule from the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\text{ruleset}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "text",
+                                    "content": " as the production rule. In this way, we can increase the diversity of structures. The generated fractal curvilinear object "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
+                                        547,
+                                        382
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\text{frac}} \\in \\mathbb{R}^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
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+                                        382
+                                    ],
+                                    "type": "text",
+                                    "content": " by iteration is given by:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "X _ {f r a c} = \\operatorname {D r a w} (i t e r, F _ {r a n d o m}, r u l e s e t, w _ {i}, l _ {i}, c _ {i}) \\tag {5}",
+                                    "image_path": "1b45f11c8ca970ff7fd0f36505b38e4fd619251a6895f9a02b1861f828abd502.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "FDA-based curvilinear object image synthesis. We further incorporate synthetic curvilinear objects into the target unlabeled images via FDA [45]. We define the target images as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{t} \\in \\mathbb{R}^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "text",
+                                    "content": " and the synthetic images of fractal curvilinear object as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{\\text{frac}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "text",
+                                    "content": ". Let "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}^A : \\in \\mathbb{R}^{H \\times W} \\to \\in \\mathbb{R}^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "text",
+                                    "content": " be the amplitude component of the Fourier transform "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "text",
+                                    "content": " of a grayscale image. We define a "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
+                                        545,
+                                        508
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta \\in (0,1)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        412,
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+                                        508
+                                    ],
+                                    "type": "text",
+                                    "content": " to select the center region of the amplitude map."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                        546,
+                        640
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                546,
+                                640
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": "Given two randomly sampled synthetic image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{frac}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": " and target image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ", we follow FDA [45] to replace the low-frequency part in the amplitude map of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{frac}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": " by the FFT [15], denotes as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}^A (X_{frac})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ", with that of the target image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ", denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}^A (X_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, the modified spectral representation of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{frac}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ", with its phase component unaltered, is mapped back to image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{frac\\rightarrow t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": " by the inverse FFT [15], whose content is the same as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{frac}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ", but will resemble the appearance of a sample "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": ". After that, we apply a Gaussian blur to the output synthetic image of FDA to obtain synthetic images from FFS, denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        509,
+                                        546,
+                                        640
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        305,
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Geometric Information Alignment"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Synthetic images generated by FFS could still have nontrivial intensity differences from that of real images. To address this problem, we further align synthetic images and real target images at both image and feature levels."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "879"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                }
+            ],
+            "page_size": [
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+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Image-level Alignment. We aim to explicitly remove the dependency on raw intensity values for both synthetic and real images and meanwhile enhance the geometric characteristics of curvilinear structures. To this end, for each image pixel "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " we compare its intensity value "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X(j)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " with its 8 neighboring pixels "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{n_d^m | m = 1, \\dots, 8\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " (yellow box in Figure. 1) lying perpendicular to "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " (red box in Figure. 1), where directional "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes left, right, top, and bottom side of "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". If "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X(j) > X(n_d^m)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we set the corresponding value for "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_d^m"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to 0. Otherwise, we set the value for "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n_d^m"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to 1. Such operation produces four 8-bit images for each input image, where the "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th bit on the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th image denotes the relative intensity order between "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " and its neighbor "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " along the "
+                                },
+                                {
+                                    "bbox": [
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+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th direction. For each input image "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " (denote as "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_F"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_t"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": "), we concatenate four 8-bit images "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(X_{IA}^1, \\dots, X_{IA}^d)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{IA}^d(j)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        72,
+                                        289,
+                                        266
+                                    ],
+                                    "type": "text",
+                                    "content": " is represented as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "X _ {I A} ^ {d} (j) = \\sum_ {m = 1} ^ {8} [ X (j) > X \\left(n _ {d} ^ {m}\\right) ] \\times 2 ^ {m - 1} \\tag {6}",
+                                    "image_path": "51885a213f43d5f7cc1a87c0400092aa9cc4712234ff2e9d2b2bf577c1096ee9.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Such local intensity order transformation [34] can capture the intrinsic of the curvilinear object and meanwhile reduces the intensity gap between synthetic and real images."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Feature-level Alignment. Given the 4-channel transformed images, we utilize U-Net [33] to extract features. We align curvilinear objects' features of synthetic images and unlabeled target images based on two loss functions, i.e., the prediction space adaptation loss (PSAL) and the curvilinear mask contrastive loss (CMCL)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "1) Prediction space adaptation loss. We utilize adversarial learning to explicitly align the prediction space distribution of target images and synthetic images. We denote the prediction segmentation masks of the target images and the synthetic images as "
+                                },
+                                {
+                                    "bbox": [
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+                                        287,
+                                        518
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{target} \\in \\mathbb{R}^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        518
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        287,
+                                        518
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{syn} \\in \\mathbb{R}^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
+                                        518
+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively. We input "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
+                                        518
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{target}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        518
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{syn}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " into a fully-convolutional discriminator "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
+                                        518
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
+                                        518
+                                    ],
+                                    "type": "text",
+                                    "content": " as [50] trained via a binary cross-entropy loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
+                                        518
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_d"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        422,
+                                        287,
+                                        518
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        55,
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+                                        541
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {d} = \\mathbb {E} \\left[ \\log \\left(D \\left(Y _ {s y n}\\right)\\right) \\right] + \\mathbb {E} \\left[ \\log \\left(1 - D \\left(Y _ {t a r g e t}\\right)\\right) \\right] (7)",
+                                    "image_path": "a698ba730c6ae156bf00dfedcfb3214648da1d337b38ad5a426bd29136bbbe94.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Accordingly, the PSAL is computed as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                        586
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {P S A L} = \\mathbb {E} \\left[ \\log \\left(D \\left(Y _ {\\text {t a r g e t}}\\right)\\right) \\right] \\tag {8}",
+                                    "image_path": "0bfca5c1ff81e908a6a050387af5b3d3c0d5149dd83080a8aefa82be24ddab43.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "2) Curvilinear mask contrastive loss. The CMCL aims to reduce the distance between features of synthetic images and true target images, and meanwhile to improve the feature distinctiveness between curvilinear objects and backgrounds. To this end, we take the feature maps (denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f \\in \\mathbb{R}^{H \\times W \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ") from the final decoder layer of U-Net, the mask of synthetic image (denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_{syn} \\in \\{0,1\\}^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ") and prediction mask of target image (denoted "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{target} \\in [0,1]^{H \\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": ") as input. We process "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        594,
+                                        288,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " using a lightweight contrastive encoder and a contrastive projector as [41] to map"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                        95
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "text",
+                                    "content": " to the feature space where the pixel-level contrastive loss is applied for "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                        95
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z \\in \\mathbb{R}^{H \\times W \\times C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        545,
+                                        95
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                96,
+                                546,
+                                276
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": "We denote "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H\\times W"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " spatial location of the projected feature maps "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", then for a location "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i\\in I"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can obtain a feature vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "z_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " at location "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " from feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", label values "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "g_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " at "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " from the mask of synthetic image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_{syn}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " and the prediction mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{target}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " respectively. We partition pixels of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " into two groups: curvilinear object locations "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{+}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " and background locations "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I^{-}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ". For synthetic images, we perform the partition directly based on the mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G_{syn}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{syn}^{+} = \\{i\\in I_{syn}\\mid g_{i} = 1\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{syn}^{-} = \\{i\\in I_{syn}\\mid g_{i} = 0\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ". For target images, as the ground-truth mask is not available, we alternatively perform the partition based on the prediction probability mask "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Y_{target}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{target}^{+} = \\{i\\in I_{target}\\mid y_{i}\\geq 1 - \\alpha \\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I_{target}^{-} = \\{i\\in I_{target}\\mid y_{i}\\leq \\alpha \\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        96,
+                                        546,
+                                        276
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha = 0.1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a small threshold and is fixed in our method."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We let "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q_{syn}^{+} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{syn}^{+}, \\sigma\\right) \\right\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                        276,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{target}^{+} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{target}^{+}, \\sigma\\right) \\right\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the curvilinear keys of synthetic and target images respectively. Similarly, we define "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{syn}^{-} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{syn}^{-}, \\sigma\\right) \\right\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k_{target}^{-} = \\left\\{\\mathbf{z}_{i} \\mid i \\in \\S \\left(I_{target}^{-}, \\sigma\\right) \\right\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
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+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " as the background keys of synthetic and target images, where "
+                                },
+                                {
+                                    "bbox": [
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+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\S (\\bullet, \\sigma)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": " is a random sampling operator which samples a subset from a set randomly with a proportion ratio "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
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+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": ". We combine "
+                                },
+                                {
+                                    "bbox": [
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+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " negative queries of the features of synthetic and target images to form a negative set "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k^{-} = (k_{syn}^{-}, k_{target}^{-})"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        276,
+                                        547,
+                                        396
+                                    ],
+                                    "type": "text",
+                                    "content": ". The CMCL is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {L} _ {C M C L} = - \\log \\left(\\exp \\left(q _ {\\text {s y n}} ^ {+} \\cdot k _ {\\text {t a r g e t}} ^ {+} / \\tau\\right)\\right) + \\\\ \\log \\left(\\exp \\left(q _ {s y n} ^ {+} \\cdot k _ {t a r g e t} ^ {+} / \\tau\\right) + \\sum_ {i = 0} ^ {N} \\exp \\left(q _ {s y n} ^ {+} \\cdot k _ {i} ^ {-} / \\tau\\right)\\right) \\tag {9} \\\\ \\end{array}",
+                                    "image_path": "6acce45569a5c0f698c3cb68f8472d92d7a5518c472fed44d1a1a4a2e0174f48.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a temperature hyper-parameter."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3) Final Loss. The final loss is a combination of the segmentation loss, the PSAL and CMCL as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {s e g} = \\mathbb {E} \\left[ G _ {s y n} \\cdot \\log \\left(Y _ {s y n}\\right) \\right] \\tag {10}",
+                                    "image_path": "fbcedaf5def7eb9c08c5086ca82677c6d1faae1d8dfa4ef6e7da13163616c42e.jpg"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {s e g}} + \\mathcal {L} _ {\\text {P S A L}} + \\lambda \\mathcal {L} _ {\\text {C M C L}} \\tag {11}",
+                                    "image_path": "625a24e164c2a27caf7f60ad754099b4cb88877266f47445951c32fdbfef38f3.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "XCAD dataset. The X-ray angiography coronary artery disease (XCAD) dataset [25] is obtained during stent placement using a General Electric Innova IGS 520 system. Each image has a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "512 \\times 512"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        594,
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+                                    ],
+                                    "type": "text",
+                                    "content": " pixels with one channel. The training set contains 1621 coronary angiograms without annotations as target images. The testing set contains 126 independent coronary angiograms with vessel segmentation maps annotated by experienced radiologists."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Retinal dataset. We also employ two public retin al datasets to validate the effectiveness of the proposed"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                }
+            ],
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+                                    "content": "880"
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+                                    "type": "text",
+                                    "content": "method. The DRIVE dataset [37] consists of 40 color retinal images of size "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "565 \\times 584"
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+                                    "type": "text",
+                                    "content": " pixels. We use 20 images as target images and 20 remaining as test images. The STARE dataset [17] contains 20 color retinal images of size "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "700 \\times 605"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " pixels with annotations as test images. There are 377 images without annotation which are used as target images."
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "CrackTree dataset. The CrackTree dataset [51] contains 206 "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        144,
+                                        288,
+                                        217
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "800 \\times 600"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " pavement images with different kinds of cracks with curvilinear structures. The whole dataset is split into 160 target images and 46 test images by [34] setting. Following [34], we dilate the annotated centerlines by 4 pixels to form the ground-truth segmentation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                        236
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+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.1. Evaluation Metrics"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For XCAD and CrackTree, we follow [25, 34] to use the following widely-used metrics in our evaluation, i.e., Jaccard Index (Jaccard), Dice Coefficient (Dice), accuracy (Acc.), sensitivity (Sn.) and specificity (Sp.). For the DRIVE and STARE datasets, we follow the state-of-the-art works for retina vessel segmentation [25] to report accuracy (Acc.), sensitivity (Sn.) specificity (Sp.) and area under curve (AUC) in our evaluation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. Implementation Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "For FFS, we set the ruleset as "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        365,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\text{rule}_1, \\dots, \\text{rule}_4)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", such as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} r u l e _ {1}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} [ + F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} ]. \\\\ \\operatorname {r u l e} _ {2}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} [ - F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} ]. \\\\ r u l e _ {3}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}} - F _ {\\text {r a n d o m}}. \\\\ \\text {r u l e} _ {4}: F _ {\\text {r a n d o m}} \\rightarrow F _ {\\text {r a n d o m}} + F _ {\\text {r a n d o m}} + F _ {\\text {r a n d o m}}. \\\\ \\end{array}",
+                                    "image_path": "015755eaee155d5cbd8d8354c662b49a28f83c23c65b488d6d7217962d60aef9.jpg"
+                                }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We set the initial parameters of the Fractal system as follows. For all four datasets, the angle is randomly selected from "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(20^{\\circ},120^{\\circ})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", the initial length is randomly selected from "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "(120\\mathrm{px}"
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+                                    "type": "inline_equation",
+                                    "content": "200\\mathrm{px})"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " , the decreased parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is randomly selected from (0.7, 1). The initial width "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        439,
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+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{init}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is ranging from (8px, 14px) for XCAD, DRIVE and STARE. For CrackTree, the "
+                                },
+                                {
+                                    "bbox": [
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+                                        439,
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+                                    "type": "inline_equation",
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+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": " is selected from (2px, 6px). The kernel size of Gaussian blur for FFS is 13. We generate 150, 150, 600 synthetic fractal images "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{frac}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for XCAD, CrackTree, and retinal datasets, respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We apply data augmentation including horizontal flipping, random brightness and contrast changes ranging from (1.0, 2.1), random saturation ranging from (0.5, 1.5), and random rotation with "
+                                },
+                                {
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": ", and "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The standard deviation for Gaussian noise is set to a random value within "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(-5, +5)"
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+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
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+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ". All images are cropped to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        558,
+                                        287,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "256 \\times 256"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " pixels for training. All the data-augmented operations are applied before the GIA module. The segmentation network is trained using the SGD with a momentum of 0.9 for optimization and the initial learning rate is 0.01. The discriminator network is trained using an Adam optimizer with an initial learning rate of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "10^{-3}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We employ a batch size of 8 to train the network for 600 epochs. The number of negative queries "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "q_{syn}^{+}"
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+                                            "html": "<table><tr><td></td><td>Methods</td><td>Jaccard</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td>Upper bound</td><td>U-Net [33]</td><td>0.571</td><td>0.724</td><td>0.981</td><td>0.868</td><td>0.996</td></tr><tr><td rowspan=\"3\">Domain Adaptation</td><td>U-Net [33]</td><td>0.228</td><td>0.365</td><td>0.831</td><td>0.444</td><td>0.906</td></tr><tr><td>MMD [8]</td><td>0.262</td><td>0.416</td><td>0.873</td><td>0.553</td><td>0.920</td></tr><tr><td>YNet [32]</td><td>0.287</td><td>0.434</td><td>0.891</td><td>0.523</td><td>0.935</td></tr><tr><td rowspan=\"2\">Traditional</td><td>Hessian [13]</td><td>0.307</td><td>0.465</td><td>0.948</td><td>0.406</td><td>0.981</td></tr><tr><td>OOF [22]</td><td>0.241</td><td>0.386</td><td>0.899</td><td>0.566</td><td>0.920</td></tr><tr><td rowspan=\"2\">Unsupervised</td><td>IIC [19]</td><td>0.124</td><td>0.178</td><td>0.738</td><td>0.487</td><td>0.754</td></tr><tr><td>ReDO [9]</td><td>0.151</td><td>0.261</td><td>0.753</td><td>0.392</td><td>0.923</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.389</td><td>0.557</td><td>0.945</td><td>0.583</td><td>0.972</td></tr><tr><td>DARL [21]</td><td>0.471</td><td>0.636</td><td>0.962</td><td>0.597</td><td>0.985</td></tr><tr><td>Ours</td><td>0.499</td><td>0.661</td><td>0.960</td><td>0.687</td><td>0.977</td></tr></table>",
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+                            "angle": 0,
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+                    ],
+                    "index": 9
+                },
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+                                            "type": "text",
+                                            "content": "Table 1. Quantitative evaluation of FreeCOS compared with different methods on the XCAD dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Methods</td><td colspan=\"4\">DRIVE</td><td colspan=\"4\">STARE</td></tr><tr><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td><td>Acc.</td><td>Sn.</td><td>Sp.</td><td>AUC</td></tr><tr><td rowspan=\"4\">Traditional</td><td>Hessian [13]</td><td>0.941</td><td>0.644</td><td>0.97</td><td>0.847</td><td>0.938</td><td>0.690</td><td>0.957</td><td>0.858</td></tr><tr><td>OOF [22]</td><td>0.936</td><td>0.688</td><td>0.959</td><td>0.920</td><td>0.920</td><td>0.770</td><td>0.932</td><td>0.955</td></tr><tr><td>Memari [26]</td><td>0.961</td><td>0.761</td><td>0.981</td><td>0.871</td><td>0.951</td><td>0.782</td><td>0.965</td><td>0.783</td></tr><tr><td>Khan [20]</td><td>0.958</td><td>0.797</td><td>0.973</td><td>0.885</td><td>0.996</td><td>0.792</td><td>0.998</td><td>0.895</td></tr><tr><td rowspan=\"2\">Unsupervised</td><td>IIC [19]</td><td>0.738</td><td>0.632</td><td>0.840</td><td>0.736</td><td>0.710</td><td>0.586</td><td>0.832</td><td>0.709</td></tr><tr><td>ReDO [9]</td><td>0.761</td><td>0.593</td><td>0.927</td><td>0.760</td><td>0.756</td><td>0.567</td><td>0.899</td><td>0.733</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.913</td><td>0.794</td><td>0.982</td><td>0.888</td><td>0.910</td><td>0.774</td><td>0.980</td><td>0.877</td></tr><tr><td>DARL [21]</td><td>-</td><td>0.456</td><td>-</td><td>-</td><td>-</td><td>0.480</td><td>-</td><td>-</td></tr><tr><td>Ours</td><td>0.921</td><td>0.810</td><td>0.932</td><td>0.941</td><td>0.952</td><td>0.797</td><td>0.964</td><td>0.971</td></tr></table>",
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+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "type": "table",
+                    "bbox": [
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+                                            "type": "text",
+                                            "content": "Table 2. Quantitative evaluation of FreeCOS compared with different methods on the retinal dataset."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
+                        {
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+                                            "html": "<table><tr><td></td><td>Methods</td><td>AUC</td><td>Dice</td><td>Acc.</td><td>Sn.</td><td>Sp.</td></tr><tr><td rowspan=\"2\">Traditional</td><td>Hessian [13]</td><td>0.780</td><td>0.122</td><td>0.935</td><td>0.310</td><td>0.945</td></tr><tr><td>OOF [22]</td><td>0.482</td><td>0.031</td><td>0.770</td><td>0.244</td><td>0.778</td></tr><tr><td>Unsupervised</td><td>ReDO [9]</td><td>0.422</td><td>0.035</td><td>0.632</td><td>0.450</td><td>0.635</td></tr><tr><td rowspan=\"3\">Self-supervised</td><td>SSVS [25]</td><td>0.477</td><td>0.078</td><td>0.299</td><td>0.042</td><td>0.912</td></tr><tr><td>DARL [21]</td><td>0.888</td><td>0.395</td><td>0.974</td><td>0.542</td><td>0.981</td></tr><tr><td>Ours</td><td>0.920</td><td>0.525</td><td>0.974</td><td>0.576</td><td>0.979</td></tr></table>",
+                                            "image_path": "e1a6fd696bbda7ff647f19cede07039b2b5123b06b9e0d3a26d0746d5c690f5b.jpg"
+                                        }
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+                            "index": 13,
+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "type": "text",
+                                    "content": "Table 3. Quantitative evaluation of FreeCOS compared with different methods on the CrackTree dataset."
+                                }
+                            ]
+                        }
+                    ],
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+                    "angle": 0,
+                    "type": "text"
+                },
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+                                    "type": "inline_equation",
+                                    "content": "k_{target}^{+}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k^{-}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " per batch is taken up to 500, 500 and 1000. The amplitude map center region selection parameter of "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is set to 0.3. the sampling ratio is 0.3, the hyper-parameter "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is 0.4 and the temperature hyper-parameter "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is 0.1."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.3. Experimental Results"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    ],
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+                                    "type": "text",
+                                    "content": "4.3.1 Comparison with State-of-the-art"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Table. 1 compares the performance of vessel segmentation on XCAD between FreeCOS and the state-of-the-art methods, including the unsupervised methods [9, 19], the self-supervised methods [25, 21], domain adaptation methods [8, 32] and the traditional methods [13, 22]. The results in the 1st row are based on supervised U-Net as [25] (i.e., identical segmentation network trained using real images with manual labels) which are the upper bound."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
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+                                    "content": "Table. 2 and 3 further compare our method with the existing methods on the retinal and crack datasets and a similar trend can be observed in these three datasets. Figure. 3 shows the visualization results of images from various kinds of curvilinear datasets."
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+                                    "content": "final model, we use the same U-Net model as our backbone. 1) FFS. We utilize the FFS to generate synthetic training images and the corresponding labels to train the U-Net segmentation model. 2) FFS+PSAL. We further apply PSAL to align features of synthetic and real target images on top of FFS. 3) FFS+PSAL+IA. We apply image-level alignment via relative intensity order transformation (i.e., IA) on top of FFS+PSAL. 4) FFS+GIA. We apply our GIA module (including IA, PSAL and CMCL) on top of FFS. This model is also our final curvilinear segmentation model. The ablation studies are conducted on XCAD. The trend on other datasets are similar and thus the results on the other datasets are omitted due to the space limit."
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+                                    "content": " in the Fractal system and set the intensity to a fixed value 60. 4) FFS w/o various angles. We utilize a small branching angle range from "
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+                                    "content": "the length variation range to (10px, 20px). 6) FFS w/o various widths. We reduce the width variation to (1px, 5px)."
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+                                    "content": " worse than FFS in Dice. 3) Among the four parameters of the Fractal system, i.e., intensity, angle, length and width, width plays the most important role in the final performance, i.e., FFS w/o various widths decreases the performance by "
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+                                    "content": " compared with FFS in Dice. To summarize, we identify that the appearance patterns in the curvilinear object, object-background transition regions and background regions are important for self-supervised segmentation. Meanwhile, proper parameter settings which can provide similar geometric characteristics with the real target images are key to the success of our self-supervised method."
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+                                    "content": "By replacing the U-Net with Iternet in FFS, We conduct ablation studies on two backbone networks U-Net [33]"
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+                                    "content": "and Iternet [23]. FFS using Iternet segmentation model gets better performance than FFS using U-Net in Table 6. FFS+GIA also demonstrates performance improvement, showing FreeCOS's effectiveness on different architectures. This indicates that the use of a more advanced segmentation network architecture for FreeCOS has the potential to improve performance."
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+                                    "content": "We also examine the segmentation performance when varying the number of synthetic images on the XCAD dataset. Results in Tables. 7 and 8 provide the results when using different numbers of synthetic structures and real target images for generating synthetic images for self-supervised training respectively. Synthetic- "
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+                                    "content": " Synthetic-150 denote using the number of synthetic fractal object images "
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+                                    "content": "X_{frac}"
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+                                    "type": "text",
+                                    "content": " from 15 to 150, and Target- "
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+                                    "type": "text",
+                                    "content": " Target-1620 denote using the number of target images "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " from 162 to 1620. Increasing both synthetic structures and real target images can accordingly improve the final segmentation performance."
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+                            ]
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "type": "text",
+                                    "content": "In this paper, we propose a novel self-supervised curvilinear object segmentation method (FreeCOS) that learns robust and distinctive features from fractals and unlabeled images. Different from existing methods, FreeCOS applies the proposed FFS and GIA approach to effectively guide learning distinctive features to distinguish curvilinear objects and backgrounds and aligns information of synthetic and target images at both image and feature levels. One limitation of FreeCOS is that may generate false positives in other curvilinear objects (e.g., catheters in XCAD) and requires proper selection for width range. However, we have successfully utilized this self-supervised learning method for coronary vessel segmentation, retinal vessel segmentation and crack segmentation by reasonable parameter selection. To the best of our knowledge, FreeOCS is the first self-supervised learning method for various curvilinear object segmentation applications."
+                                }
+                            ]
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+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work was supported by the National Natural Science Foundation of China under Grants 62061160490, 62122029, and U20B2064."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "References"
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+                                        }
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+                                        }
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diff --git a/2023/FreeDoM_ Training-Free Energy-Guided Conditional Diffusion Model/6856ff82-c802-4528-9795-9924d03d4b41_content_list.json b/2023/FreeDoM_ Training-Free Energy-Guided Conditional Diffusion Model/6856ff82-c802-4528-9795-9924d03d4b41_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..7f869223007bd787febb5b36009f9ec0d8da75de
--- /dev/null
+++ b/2023/FreeDoM_ Training-Free Energy-Guided Conditional Diffusion Model/6856ff82-c802-4528-9795-9924d03d4b41_content_list.json	
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+        "image_caption": [
+            "Figure 1: FreeDoM controls the generation process of diffusion models in a training-free way. Here, we demonstrate some results of the applications FreeDoM supports. Part (a)-(c) show various face editing applications with training-free guidance. (a) We use the segmentation map, sketch, landmarks, and face ID as conditions to guide the generation process of an unconditional diffusion model; (b) We combine different conditions to control the generation process. (c) We use CLIP [34] based text guidance to control image synthesis and editing. For editing, we use the segmentation masks to limit the editing areas (see Fig. 4 for details); Part (d)-(f) show that training-free guidance can work with other training-required conditional diffusion models, like Stable Diffusion [36] and ControlNet [52], to achieve a more sophisticated control mechanism. The conditions of scribbles in (d), human poses in (e), and prompt texts in (f) are controlled by the training-required interfaces provided by ControlNet and Stable Diffusion. Training-free energy functions control the conditions of face IDs from the reference images in (e) and style images in (d) and (f). Zoom in for best view."
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
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+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Recently, conditional diffusion models have gained popularity in numerous applications due to their exceptional generation ability. However, many existing methods are training-required. They need to train a time-dependent classifier or a condition-dependent score estimator, which increases the cost of constructing conditional diffusion models and is inconvenient to transfer across different conditions. Some current works aim to overcome this limitation by proposing training-free solutions, but most can only be applied to a specific category of tasks and not to more general conditions. In this work, we propose a training-Free conditional Diffusion Model (FreeDoM) used for various conditions. Specifically, we leverage off-the-shelf pretrained networks, such as a face detection model, to construct time-independent energy functions, which guide the generation process without requiring training. Furthermore, because the construction of the energy function is very flexible and adaptable to various conditions, our proposed FreeDoM has a broader range of applications than existing training-free methods. FreeDoM is advantageous in its simplicity, effectiveness, and low cost. Experiments demonstrate that FreeDoM is effective for various conditions and suitable for diffusion models of diverse data domains, including image and latent code domains. Code is available at https://github.com/vvictoryuki/FreeDoM.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Recently, diffusion models have been demonstrated to outperform previous state-of-the-art generative models [10], such as GANs [12, 29, 3, 22, 24, 23]. The impressive generative power of diffusion models [15, 43, 45] has motivated researchers to apply diffusion models to various downstream tasks. Conditional generation is one of the most popular focus areas. Conditional diffusion models (CDMs) with diverse conditions have been proposed, such as text [20, 1, 13, 26, 36, 40, 35, 38, 25, 32], class labels [10], degraded images [5, 6, 7, 8, 19, 27, 42, 44, 47, 37, 39, 48], segmentation maps [31, 52], landmarks [31, 52], hand-drawn sketches [31, 52], style images [31, 52], etc. These CDMs can be roughly divided into two categories: training-required or training-free.",
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+    {
+        "type": "text",
+        "text": "A typical type of training-required CDMs trains a time-dependent classifier to guide the noisy image  $\\mathbf{x}_t$  toward the given condition  $\\mathbf{c}$  [10, 32, 53, 26]. Another branch of",
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+    {
+        "type": "text",
+        "text": "training-required CDMs directly trains a new score estimator  $s(\\mathbf{x}_t, t, \\mathbf{c})$  conditioned on  $\\mathbf{c}$  [31, 16, 36, 37, 39, 48, 52, 20, 1, 13, 35, 32]. These methods yield impressive performance but are not flexible. Once a new target condition is needed for generation, they have to retrain or finetune the models, which is inconvenient and expensive.",
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+    {
+        "type": "text",
+        "text": "In contrast, training-free CDMs try to solve the same problems without extra training. [30, 11, 14] attempt to use the cross-attention control to realize the conditional generation; [5, 6, 7, 8, 19, 27, 42, 44, 47, 46] directly modify the intermediate results to achieve zero-shot image restoration; [28] realizes image translation by adjusting the initial noisy images. While these methods are effective in a single application, they are difficult to generalize to a wider range of conditions, e.g., style, face ID, and segmentation masks.",
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+    {
+        "type": "text",
+        "text": "In order to make CDMs support a wide range of conditions in a training-free manner, this paper proposes a training-Free conditional Diffusion Model (FreeDoM) with the following two key points. Firstly, to emphasize generalization, we propose a sampling process guided by the energy function [53, 21], which is very flexible to construct and can be applied to various conditions. Secondly, to make the proposed method training-free, we use off-the-shelf pre-trained time-independent models, which are easily accessible online, to construct the energy function.",
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+        "text": "Our FreeDoM has the following advantages: (1) Simple and effective. We only insert a derivative step of the energy function gradient into the unconditional sampling process of the original diffusion models. Extensive experiments show its effective controlling capability. (2) Low cost and efficient. The energy functions we construct are time-independent and do not need to be retrained. The diffusion models we choose do not need to be trained on the desired conditions. Thanks to the efficient time-travel strategy we use for large data domains, the number of sampling steps we use is quite small, which speeds up the sampling process while ensuring good generated results. (3) Amenable to a wide range of applications. The conditions our method supports include, but are not limited to, text, segmentation maps, sketches, landmarks, face IDs, style images, etc. In addition, various complex but interesting applications can be realized by combining multiple conditions. (4) Supports different types of diffusion models. Regardless of the considered data domain, such as human face images, images in ImageNet, or latent codes extracted from an image encoder, extensive experiments demonstrate that our method does well on all of them.",
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+    {
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+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "2.1. Training-Required Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The training-required methods can obtain strong control generation ability thanks to supervised learning with",
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+        "text": "†Corresponding authors. This work was supported by Shenzhen General Research Project under Grant JCYJ20220531093215035, KAUST Office of Sponsored Research through the Visual Computing Center funding, and SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence.",
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+    {
+        "type": "page_number",
+        "text": "23175",
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+    {
+        "type": "text",
+        "text": "data pairs. One of the most prominent applications of these methods is the text-to-image task. The most widely used text-to-image model, Stable Diffusion [36], generates high-quality images that conform to the text description by inputting a prompt text. Recent works, such as ControlNet [52] and T2I-Adapter [31], have introduced more training-required conditional interfaces to Stable Diffusion, such as edge maps, segmentation maps, depth maps, etc.",
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+        "text": "Although these training-required methods can achieve satisfactory control results under trained conditions, the cost of training is still a factor to be considered, especially for the scenario that requires more complex control with multiple conditions. The training-required method is not the cheapest or most convenient solution in practical applications.",
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+    {
+        "type": "text",
+        "text": "2.2. Training-Free Methods",
+        "text_level": 1,
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+    {
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+        "text": "The training-free methods develop various interesting technologies to realize the training-free condition generation on some tasks exploiting the unique nature of the diffusion model, namely, the iterative denoising process. [14] proposes to inject the target cross attention maps to the source cross attention maps to solve the prompt-to-prompt task without training. The limitation of this method is that a text prompt is needed to anchor the content of the image to be edited in advance. DDNM [47] proposes to use the Range-Null Space Decomposition to modify the intermediate results to solve the image restoration in a training-free way. It is based on the degradation operators of image restoration tasks and is hard to be adopted in other applications. SDEdit [28] proposes to adjust the initial noisy images to control the generation process, which is useful in stroke-based image synthesis and editing. Its limitation is that the guidance of stroke is not precise and versatile.",
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+        "text": "According to the limitations mentioned above, the training-free CDMs for a broad range of applications need to be studied urgently. We have noticed some recent efforts [33, 2] in this area. Our FreeDoM has a faster generation speed and applies to a broader range of applications.",
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+        "text": "3. Preliminaries",
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+        "text": "3.1. Score-based Diffusion Models",
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+        "type": "text",
+        "text": "Score-based Diffusion Models (SBDMs) [43, 45] are a kind of diffusion model based on score theory, which reveals that the essence of diffusion models is to estimate the score function  $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)$ , where  $\\mathbf{x}_t$  is noisy data. During the sampling process, SBDMs predict  $\\mathbf{x}_{t - 1}$  from  $\\mathbf{x}_t$  using the estimated score step by step. In our work, we resort to discrete SBDMs with the setting of DDPM [15] and its sampling formula is:",
+        "bbox": [
+            75,
+            741,
+            468,
+            862
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\left(1 + \\frac {1}{2} \\beta_ {t}\\right) \\mathbf {x} _ {t} + \\beta_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
+            875,
+            468,
+            905
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$  is randomly sampled Gaussian noise and  $\\beta_{t}\\in \\mathbb{R}$  is a pre-defined parameter. In actual implementation, the score function will be estimated using a score estimator  $s(\\mathbf{x}_t,t)$ , that is,  $s(\\mathbf{x}_t,t)\\approx \\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)$ . However, the original diffusion models can only serve as an unconditional generator with randomly synthesized results.",
+        "bbox": [
+            496,
+            90,
+            890,
+            181
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Conditional Score Function",
+        "text_level": 1,
+        "bbox": [
+            498,
+            190,
+            746,
+            205
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In order to adapt the generative power of the diffusion models to different downstream tasks, conditional diffusion models (CDMs) are needed. SDE [45] proposed to control the generated results with a given condition  $\\mathbf{c}$  by modifying the score function as  $\\nabla_{\\mathbf{x}_t} \\log p(\\mathbf{x}_t | \\mathbf{c})$ . Using the Bayesian formula  $p(\\mathbf{x}_t | \\mathbf{c}) = \\frac{p(\\mathbf{c} | \\mathbf{x}_t) p(\\mathbf{x}_t)}{p(\\mathbf{c})}$ , we can rewrite the conditional score function as two terms:",
+        "bbox": [
+            496,
+            213,
+            890,
+            321
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t} | \\mathbf {c}) = \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) + \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {c} | \\mathbf {x} _ {t}), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            330,
+            890,
+            349
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where the first term  $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)$  can be estimated using the pre-trained unconditional score estimator  $s(\\cdot ,t)$  and the second term  $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)$  is the critical part of constructing conditional diffusion models. We can interpret the second term  $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)$  as a correction gradient, pointing  $\\mathbf{x}_t$  to a hyperplane in the data space, where all data are compatible with the given condition c. Classifier-based methods [10, 32, 53, 26] train a time-dependent classifier to compute this correction gradient for conditional guidance.",
+        "bbox": [
+            496,
+            356,
+            890,
+            492
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Energy Diffusion Guidance",
+        "text_level": 1,
+        "bbox": [
+            498,
+            501,
+            746,
+            517
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Modeling the correction gradient  $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)$  remains an open question. A flexible and straightforward way is resorting to the energy function [53, 21] as follows:",
+        "bbox": [
+            496,
+            523,
+            890,
+            570
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (\\mathbf {c} | \\mathbf {x} _ {t}) = \\frac {\\exp \\left\\{- \\lambda \\mathcal {E} (\\mathbf {c} , \\mathbf {x} _ {t}) \\right\\}}{Z}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            593,
+            577,
+            890,
+            608
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  denotes the positive temperature coefficient and  $Z > 0$  denotes a normalizing constant, computed as  $Z = \\int_{\\mathbf{c} \\in \\mathcal{C}} \\exp\\{-\\lambda \\mathcal{E}(\\mathbf{c}, \\mathbf{x}_t)\\}$  where  $\\mathcal{C}$  denotes the domain of the given conditions.  $\\mathcal{E}(\\mathbf{c}, \\mathbf{x}_t)$  is an energy function that measures the compatibility between the condition  $\\mathbf{c}$  and the noisy image  $\\mathbf{x}_t$  — its value will be smaller when  $\\mathbf{x}_t$  is more compatible with  $\\mathbf{c}$ . If  $\\mathbf{x}_t$  satisfies the constraint of  $\\mathbf{c}$  perfectly, the energy value should be zero. Any function satisfying the above property can serve as a feasible energy function, with which we just need to adjust the coefficient  $\\lambda$  to obtain  $p(\\mathbf{c} | \\mathbf{x}_t)$ .",
+        "bbox": [
+            498,
+            614,
+            890,
+            780
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Therefore, the correction gradient  $\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)$  can be implemented with the following:",
+        "bbox": [
+            496,
+            781,
+            890,
+            811
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {c} | \\mathbf {x} _ {t}) \\propto - \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            580,
+            819,
+            890,
+            837
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "which is referred to as energy guidance. With Eq. (1), Eq. (2), and Eq. (4), we get the conditional sampling:",
+        "bbox": [
+            496,
+            845,
+            890,
+            876
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mathbf {m} _ {t} - \\rho_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            885,
+            890,
+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "23176",
+        "bbox": [
+            478,
+            924,
+            519,
+            936
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{m}_t = (1 + \\frac{1}{2}\\beta_t)\\mathbf{x}_t + \\beta_t\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t) + \\sqrt{\\beta_t}\\epsilon,$  and  $\\rho_{t}$  is a scale factor, which can be seen as the learning rate of the correction term. Eq. (5) is a generic formulation of conditional diffusion models, which enables the use of different energy functions.",
+        "bbox": [
+            76,
+            89,
+            472,
+            167
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. The Proposed FreeDoM Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            181,
+            372,
+            199
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In Sec. 4.1, we approximate the time-dependent energy function using time-independent distance measuring functions, making our method training-free and flexible for various conditions. In Sec. 4.2, we first analyze the reason why the energy guidance fails in a large data domain and then propose an efficient version of the time-travel strategy [27, 47]. In Sec. 4.3, we describe the details of how to construct the energy functions. In Sec. 4.4, we provide specific examples of supported conditions.",
+        "bbox": [
+            75,
+            207,
+            468,
+            344
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Approximate Time-Dependent Energy",
+        "text_level": 1,
+        "bbox": [
+            76,
+            354,
+            406,
+            372
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use the energy function to guide the generation due to its flexibility to construct and suitability to various conditions. Existing classifier-based methods [10, 32, 53, 26] choose time-dependent distance measuring functions  $\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)$  to approximate the energy functions as follows:",
+        "bbox": [
+            75,
+            378,
+            468,
+            467
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\phi} (\\mathbf {c}, \\mathbf {x} _ {t}, t), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            189,
+            470,
+            468,
+            486
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\phi$  defines the pre-trained parameters.  $\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)$  computes the distance between the given condition  $\\mathbf{c}$  and noisy intermediate results  $\\mathbf{x}_t$ . The distance measuring functions for noisy data  $\\mathbf{x}_t$  cannot be directly constructed because it is difficult to find an existing pre-trained network for noisy images. In this case, we have to train (or finetune) a time-dependent network for each type of condition.",
+        "bbox": [
+            75,
+            494,
+            468,
+            599
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Compared with time-dependent networks, time-independent distance measuring functions for clean data  $\\mathbf{x}_0$  are widely available. Many off-the-shelf pre-trained networks such as classification networks, segmentation networks, and face ID encoding networks are open-source and work well on clean images. We denote these distance measuring networks for clean data as  $\\mathcal{D}_{\\theta}(\\mathbf{c},\\mathbf{x}_0)$ , where  $\\pmb{\\theta}$  denotes their pre-trained parameters. To use these networks for the energy functions, a straightforward way is to approximate  $\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)$  using  $\\mathcal{D}_{\\theta}(\\mathbf{c},\\mathbf{x}_0)$ , formulated as:",
+        "bbox": [
+            75,
+            601,
+            468,
+            753
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\phi} (\\mathbf {c}, \\mathbf {x} _ {t}, t) \\approx \\mathbb {E} _ {p \\left(\\mathbf {x} _ {0} \\mid \\mathbf {x} _ {t}\\right)} \\left[ \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0}) \\right]. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
+            765,
+            468,
+            782
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Eq. (7) is reasonable because if the distance between the noise image  $\\mathbf{x}_t$  and the condition  $\\mathbf{c}$  is small, the clean image  $\\mathbf{x}_0$  corresponding to the noise image  $\\mathbf{x}_t$  should also have a small distance with the condition  $\\mathbf{c}$ , especially during the late stage of the sampling process when the noise level of  $\\mathbf{x}_t$  is relatively small. However, during the sampling process, it is infeasible to get the clean image  $\\mathbf{x}_0$  corresponding to",
+        "bbox": [
+            75,
+            794,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Sampling Process of our proposed FreeDoM",
+        "text_level": 1,
+        "bbox": [
+            500,
+            90,
+            883,
+            104
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require: condition  $\\mathbf{c}$ , unconditional score estimator  $s(\\cdot, t)$ , time-independent distance measuring function  $\\mathcal{D}_{\\theta}(\\mathbf{c}, \\cdot)$ , pre-defined parameters  $\\beta_{t}$ ,  $\\bar{\\alpha}_{t}$  and learning rate  $\\rho_{t}$ .",
+        "bbox": [
+            500,
+            106,
+            890,
+            137
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1:  $\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$",
+            "2: for  $t = T, \\ldots$",
+            "3:  $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$  if  $t > 1$ , else  $\\epsilon = 0$ .",
+            "4:  $\\mathbf{x}_{t - 1} = (1 + \\frac{1}{\\beta}\\beta_{t})\\mathbf{x}_{t} + \\beta_{t}s(\\mathbf{x}_{t},t) + \\sqrt{\\beta_{t}}\\pmb{\\epsilon}$",
+            "5:  $\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{x}_t + (1 - \\bar{\\alpha}_t)s(\\mathbf{x}_t,t))$",
+            "6:  $\\pmb{g}_t = \\nabla_{\\mathbf{x}_t} \\mathcal{D}_{\\pmb{\\theta}}(\\mathbf{c}, \\mathbf{x}_{0|t}(\\mathbf{x}_t)))$",
+            "7:  $\\mathbf{x}_{t - 1} = \\mathbf{x}_{t - 1} - \\rho_t\\pmb {g}_t$",
+            "8: return  $\\mathbf{x}_0$"
+        ],
+        "bbox": [
+            506,
+            137,
+            767,
+            224
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/fed56280b321b926ec3aa3e3f79197212ddebe75de9f14fb7109aa63eb49ebfa.jpg",
+        "image_caption": [
+            "(a) Badly Generated Results",
+            "(b) Generated Results with the Time-Travel Strategy",
+            "Figure 2: Comparison of results generated before and after using the time-travel strategy. The prompt is \"orange\". We can see that the results in (a) do not match the given conditions. After using the time-travel strategy, we get better results in (b)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            238,
+            890,
+            333
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "an intermediate noisy result  $\\mathbf{x}_t$ , so we need to approximate  $\\mathbf{x}_0$ . Considering the expectation of  $p(\\mathbf{x}_0|\\mathbf{x}_t)$  [6]:",
+        "bbox": [
+            496,
+            455,
+            890,
+            487
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {0 \\mid t} := \\mathbb {E} [ \\mathbf {x} _ {0} | \\mathbf {x} _ {t} ] = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} (\\mathbf {x} _ {t} + (1 - \\bar {\\alpha} _ {t}) s (\\mathbf {x} _ {t}, t)), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            498,
+            890,
+            530
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{\\alpha}_t = \\prod_{i=1}^t (1 - \\beta_i)$  and  $s(\\cdot, t)$  is the pre-trained score estimator. According to Eq. (8), from  $\\mathbf{x}_t$ , we can estimate the clean image denoted as  $\\mathbf{x}_{0|t}$ . Then with Eq. (6) and Eq. (7), we can approximate the time-dependent energy function of noisy data  $\\mathbf{x}_t$ :",
+        "bbox": [
+            496,
+            541,
+            890,
+            619
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t}). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            614,
+            631,
+            890,
+            648
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "According to Eq. (5) and Eq. (9), the approximated sampling process can be written as:",
+        "bbox": [
+            496,
+            659,
+            890,
+            690
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {t - 1} = \\mathbf {m} _ {t} - \\rho_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t} (\\mathbf {x} _ {t})), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            703,
+            890,
+            719
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "and the detailed algorithm is shown in Algo. 1.",
+        "bbox": [
+            500,
+            731,
+            808,
+            746
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Efficient Time-Travel Strategy",
+        "text_level": 1,
+        "bbox": [
+            500,
+            756,
+            767,
+            772
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the process of applying Algo. 1, we find that the performance varies significantly on different data domains. For small data domains such as human faces, Algo. 1 can effectively produce results that satisfy the given conditions within 100 DDIM [41] sampling steps. However, for large data domains such as ImageNet, we often get results that are not closely related to the given conditions or even randomly generated results (shown in Fig. 2(a)). We attribute",
+        "bbox": [
+            496,
+            779,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "23177",
+        "bbox": [
+            478,
+            924,
+            517,
+            936
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/b700a5523d50f81b3f1f7f609e6a92f6f26bd349eb7c9ebc9afb701b6ccabc8d.jpg",
+        "image_caption": [
+            "Figure 3: Demonstration of the importance of different sampling stages. Most of the semantic content is generated during the semantic stage, so we only employ the time-travel strategy in this stage to achieve an efficient version of FreeDoM. The shown images are  $\\mathbf{x}_{0|t}$  generated by diffusion models pre-trained on the ImageNet data domain."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            88,
+            893,
+            198
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the failure of Algo. 1 on large data domains to poor guidance. The reason for poor guidance is that the direction of unconditional score generated by diffusion models in large data domains has more freedom, making it easier to deviate from the direction of conditional control. To solve this problem, we adopt the time-travel strategy [27, 47], which has been empirically shown to inhibit the generation of disharmonious results when solving hard generation tasks.",
+        "bbox": [
+            75,
+            268,
+            472,
+            390
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The time-travel strategy is a technique that takes the current intermediate result  $\\mathbf{x}_t$  back by  $j$  steps to  $\\mathbf{x}_{t + j}$  and resamples it to the  $t$ -th timestep again. This strategy inserts more sampling steps into the sampling process and refines the generated results. In our experiments specifically, we go back by  $j = 1$  step each time and resample. We repeat this resampling process  $r_t$  times at the  $t$ -th timestep. Our experiments demonstrate that the time travel strategy is effective in solving the poor guidance problem (shown in Fig. 2(b)). However, the time cost is also expensive because the number of sampling steps is larger, especially considering that each timestep will include the cost of calculating the gradient of the energy function.",
+        "bbox": [
+            75,
+            396,
+            472,
+            592
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Fortunately, we find that the time-travel strategy does not have the same effect in each time step. In fact, using this technique in most time steps will not significantly modify the final result, which means we can use this strategy only in a small portion of the timesteps, thus significantly reducing the number of additional iteration steps. In Fig. 3, we try to analyze this phenomenon by dividing the sampling process into three stages. In the early stage, i.e., the chaotic stage, the generated result  $\\mathbf{x}_{0|t}$  is extremely blurred, and the energy guidance is hard to make anything reasonable, so we do not need to employ the time-travel strategy. During the late stage, i.e., the refinement stage, the change in the generated results is minor, so the time-travel strategy is useless. During the intermediate stage, i.e., the semantic stage, the change in the generated result is significant, so this stage is critical for conditional generation. Based on this observation, we only apply the time-travel strategy in the semantic stage to implement efficient sampling while solving the problem of poor guidance. The range of the semantic stage is an experimental choice depending on the specific dif",
+        "bbox": [
+            75,
+            598,
+            472,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 2 FreeDoM + Efficient Time-Travel Strategy",
+        "text_level": 1,
+        "bbox": [
+            500,
+            268,
+            872,
+            282
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Require: condition  $\\mathbf{c}$ , unconditional score estimator  $s(\\cdot, t)$ , time-independent distance measuring function  $\\mathcal{D}_{\\theta}(\\mathbf{c}, \\cdot)$ , pre-defined parameters  $\\beta_t, \\bar{\\alpha}_t$ , learning rate  $\\rho_t$ , and the repeat times of time travel of each step  $\\{r_1, \\dots, r_T\\}$ .",
+        "bbox": [
+            500,
+            284,
+            890,
+            315
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1:  $\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$",
+            "2: for  $t = T, \\dots, 1$  do",
+            "3: for  $i = r_t,\\dots,1$  do",
+            "4:  $\\epsilon_{1} \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$  if  $t > 1$ , else  $\\epsilon_{1} = \\mathbf{0}$ .",
+            "5:  $\\mathbf{x}_{t - 1} = (1 + \\frac{1}{2}\\beta_t)\\mathbf{x}_t + \\beta_t s(\\mathbf{x}_t,t) + \\sqrt{\\beta_t}\\epsilon_1$",
+            "6:  $\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}} (\\bar{\\mathbf{x}}_t + (1 - \\bar{\\alpha}_t)s(\\mathbf{x}_t,t))$",
+            "7:  $\\pmb{g}_{t} = \\nabla_{\\mathbf{x}_{t}}\\mathcal{D}_{\\pmb{\\theta}}(\\mathbf{c},\\mathbf{x}_{0|t}(\\mathbf{x}_{t})))$",
+            "8:  $\\mathbf{x}_{t - 1} = \\mathbf{x}_{t - 1} - \\rho_t\\pmb {g}_t$",
+            "9: if  $i > 1$  then",
+            "10:  $\\epsilon_{2}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$",
+            "11:  $\\mathbf{x}_t = \\sqrt{1 - \\beta_t}\\mathbf{x}_{t-1} + \\sqrt{\\beta_t}\\pmb{\\epsilon}_2$",
+            "12: return  $\\mathbf{x}_0$"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "fusion models we choose. The detailed algorithm of our proposed FreeDoM with the efficient time-travel strategy is shown in Algo.2, where  $r_t = 1$  means we do not apply the time-travel strategy in the  $t$ -th timestep.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Construction of the Energy Function",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "- Single Condition Guidance. To incorporate in specific applications, we use the distance measuring function conforming to the following structure to construct the energy function:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t}) = \\operatorname {D i s t} \\left(\\mathcal {P} _ {\\boldsymbol {\\theta} _ {1}} (\\mathbf {c}), \\mathcal {P} _ {\\boldsymbol {\\theta} _ {2}} (\\mathbf {x} _ {0 | t})\\right), \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            642,
+            890,
+            660
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $Dist(\\cdot)$  denotes the distance measuring methods like Euclidean distance, and  $\\pmb{\\theta} = \\{\\pmb{\\theta}_1,\\pmb{\\theta}_2\\}$ .  $\\mathcal{P}_{\\theta_1}(\\cdot)$  and  $\\mathcal{P}_{\\theta_2}(\\cdot)$  project the condition and image to the same space for distance measurement. These projection networks can be off-the-shelf pre-trained classification networks, segmentation networks, etc. In most cases, we only need one network to project the clean image  $\\mathbf{x}_{0|t}$  to the condition space. In the cases with reference images  $\\mathbf{x}_{ref}$ , we also only need one feature encoder to project the reference image  $\\mathbf{x}_{ref}$  and  $\\mathbf{x}_{0|t}$  to the same feature space.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "- Multi Condition Guidance. In some more involved applications, multiple conditions can be available to provide control over the generated results. Take the image style transfer task as an example. Here, we have two conditions: the structure information from the source image and",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "23178",
+        "bbox": [
+            478,
+            924,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/c75b8984dc8f96e4b2954498df0c519d1fea6148aa8c7d86271d957c049c7353.jpg",
+        "image_caption": [
+            "Original Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            85,
+            145,
+            136
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/266cc80ac7fb2a00cadc1c8d232929d2459bf5183d747be6901bf4117067fd7e.jpg",
+        "image_caption": [
+            "Mask"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            145,
+            85,
+            200,
+            137
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/29a1a4f4abf5c530ddaab2d935cdbad9d1a0a93abbb4089987f2141cadd2bb90.jpg",
+        "image_caption": [
+            "\"Lipstick\""
+        ],
+        "image_footnote": [],
+        "bbox": [
+            207,
+            85,
+            272,
+            137
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/51742c8b82d252c5ae76e66fb6de30a71f4c9e846df04f547fb0ee81c55e7c4e.jpg",
+        "image_caption": [
+            "Original Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            274,
+            85,
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+            137
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/11cbc55c6cbc18000614d965693538c499de647a913499e9345bbea62550bef5.jpg",
+        "image_caption": [
+            "Mask"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            339,
+            85,
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+            137
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/883f29a19a9fee0d5ca3a45b0ff3a429d16b3c098f7e584285971d6f604dd9eb.jpg",
+        "image_caption": [
+            "\"Pale lips\""
+        ],
+        "image_footnote": [],
+        "bbox": [
+            403,
+            85,
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+            137
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/a89f1bb523a9e3e4b4bed88c95978ff50055984e5af1dcbdbd3ae1b8e14d9e9d.jpg",
+        "image_caption": [
+            "Original Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/ef64e94a6b68df0b12e27fcb465c9b2713e0ce1e69394cb66c78bf06759e1ba0.jpg",
+        "image_caption": [
+            "Mask"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/24466b41a925c2fb6956bb9c4ec6f30884ba7de8e9dd614859ac0a4725ad6c8f.jpg",
+        "image_caption": [
+            "\"Straight hair\""
+        ],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            146,
+            272,
+            199
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8c2476291a1e4e9faa79ec110babba4492e6e6360af5f913102aca2cb4cb610a.jpg",
+        "image_caption": [
+            "Original Image",
+            "Figure 4: Practical usage of face parsing maps. We can limit the gradient of the energy function to update the image only in the target semantic region indicated by the mask so that other regions remain unchanged while editing."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            274,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/7eb1adcab9a7d1be29a12dac3f80a5de251aa54f5e649d2cf4d43e5f078d5832.jpg",
+        "image_caption": [
+            "Mask"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            352,
+            146,
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+            199
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/e19ce3c30184588f7dd51014ecd0df32e1e4055eb7f0f9ae40ce6b040b2200e5.jpg",
+        "image_caption": [
+            "\"Red hair\""
+        ],
+        "image_footnote": [],
+        "bbox": [
+            406,
+            146,
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+            199
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the style information from the style image. In these multi-condition cases, assume that the given conditions are denoted as  $\\{\\mathbf{c}_1,\\dots ,\\mathbf{c}_n\\}$ , we can approximately construct the energy function as:",
+        "bbox": [
+            75,
+            284,
+            467,
+            345
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {E} \\left(\\left\\{\\mathbf {c} _ {1}, \\dots , \\mathbf {c} _ {n} \\right\\}, \\mathbf {x} _ {t}\\right) \\\\ \\approx \\eta_ {1} \\mathcal {D} _ {\\boldsymbol {\\theta} _ {1}} \\left(\\mathbf {c} _ {1}, \\mathbf {x} _ {0 | t}\\right) + \\dots + \\eta_ {n} \\mathcal {D} _ {\\boldsymbol {\\theta} _ {n}} \\left(\\mathbf {c} _ {n}, \\mathbf {x} _ {0 | t}\\right), \\tag {12} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            101,
+            358,
+            468,
+            395
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\eta_{i}$  is the weighting factor. We use different distance measuring functions  $\\{\\mathcal{D}_{\\theta_1}(\\cdot ,\\cdot),\\dots ,\\mathcal{D}_{\\theta_n}(\\cdot ,\\cdot)\\}$  for specific conditions and sum the whole for gradient computation.",
+        "bbox": [
+            75,
+            407,
+            467,
+            453
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Guidance for Latent Diffusion. Our method applies not only to image diffusions but also to latent diffusions, such as Stable Diffusion [36]. In this case, the intermediate results  $\\mathbf{x}_t$  are latent codes rather than images. We can use the latent decoder to project the generated latent codes to images and then use the same algorithm in the image domain.",
+        "bbox": [
+            76,
+            458,
+            468,
+            547
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Specific Examples of Supported Conditions",
+        "text_level": 1,
+        "bbox": [
+            76,
+            561,
+            444,
+            577
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "$\\square$  Text. For given text prompts, we construct the distance measuring function based on CLIP [34]. Specifically, we take the CLIP image encoder (as  $\\mathcal{P}_{\\theta_2}(\\cdot)$ ) and the CLIP text encoder (as  $\\mathcal{P}_{\\theta_1}(\\cdot)$ ) to project the image  $\\mathbf{x}_{0|t}$  and given text in the same CLIP feature space. Compared with the commonly used cosine distance measurement and for simplicity, we choose the  $\\ell_2$  Euclidean distance measurement, since the sampling quality in our experiments is not significantly different.",
+            "□ Segmentation Maps. For segmentation maps, we choose a face parsing network based on the real-time semantic segmentation network BiSeNet [51] to generate the parsing map of an input human face and directly compute the  $\\ell_2$  Euclidean distance between the given parsing map and the parsing results of  $\\mathbf{x}_{0|t}$ . An interesting usage of the face parsing network is to constrain the gradient update region so that we can edit the target semantic region without changing other regions (shown in Fig. 4).",
+            "Sketches. We choose an open-source pre-trained network [50] that transfers a given anime image to the style"
+        ],
+        "bbox": [
+            75,
+            589,
+            467,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "of hand-drawn sketches. Experiments prove that the network is still effective for real-world images. We use the  $\\ell_2$  Euclidean distance to compare the given sketches with transferred sketch-style results of  $\\mathbf{x}_{0|t}$ .",
+        "bbox": [
+            498,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "$\\square$  Landmarks. We use an open-source pre-trained human face landmark detection network [4] for this application. The detection network has two stages: the first stage finds the position of the center of a face and the second stage marks the landmarks of this detected face. We compute the  $\\ell_2$  Euclidean distance between predicted face landmarks of  $\\mathbf{x}_{0|t}$  and the given landmarks condition, and only use the gradient in the face area detected in the first stage to update the intermediate results.",
+            "$\\square$  Face IDs. We use ArcFace [9], an open-source pretrained human face recognition network, to extract the target features of reference faces to represent face IDs and compute the  $\\ell_2$  Euclidean distance between the extracted ID features of  $\\mathbf{x}_{0|t}$  and those of the reference image.",
+            "- Style Images. The style image is denoted as  $\\mathbf{x}_{style}$ . We use the following equation to compute the distance of the style information between  $\\mathbf{x}_{style}$  and  $\\mathbf{x}_{0|t}$ :"
+        ],
+        "bbox": [
+            498,
+            155,
+            890,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {D i s t} \\left(\\mathbf {x} _ {\\text {s t y l e}}, \\mathbf {x} _ {0 | t}\\right) = \\left| \\left| G \\left(\\mathbf {x} _ {\\text {s t y l e}}\\right) _ {j} - G \\left(\\mathbf {x} _ {0 | t}\\right) _ {j} \\right| \\right| _ {F} ^ {2}, \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            517,
+            436,
+            890,
+            454
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $G(\\cdot)_{j}$  denotes the Gram matrix [17] of the  $j$ -th layer feature map of an image encoder. In our experiments, we choose the features from the third layer of the CLIP image encoder to generate satisfactory results.",
+        "bbox": [
+            498,
+            465,
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+            527
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "- Low-pass Filters. For the image transferring task, we need an energy function to constrain the generated results conforming to the structure information of the source image  $\\mathbf{x}_{source}$ . Similar to EGSDE [53] and ILVR [5], we choose a low-pass filter  $\\mathcal{K}(\\cdot)$  in this setup. The distance between the source image  $\\mathbf{x}_{source}$  and  $\\mathbf{x}_{0|t}$  is computed as:",
+        "bbox": [
+            498,
+            531,
+            890,
+            622
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {D i s t} \\left(\\mathbf {x} _ {\\text {s o u r c e}}, \\mathbf {x} _ {0 | t}\\right) = \\left| \\left| \\mathcal {K} \\left(\\mathbf {x} _ {\\text {s o u r c e}}\\right) - \\mathcal {K} \\left(\\mathbf {x} _ {0 | t}\\right) \\right| \\right| _ {2} ^ {2}. \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            667,
+            630,
+            684
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            715,
+            709
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our proposed method applies to many open-source pretrained diffusion models (DMs). In our experiment, we have tried the following models and conditions:",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "> Unconditional Human Face Diffusion Model [28]. The supported image resolution of this model is  $256 \\times 256$ , and the pre-trained dataset is aligned human faces from CelebA-HQ [18]. We experiment with conditions that include text, parsing maps, sketches, landmarks, and face IDs.",
+            "> Unconditional ImageNet Diffusion Model [10]. The supported image resolution of this model is  $256 \\times 256$  and the pre-trained dataset is ImageNet. We experiment with conditions that include text and style images."
+        ],
+        "bbox": [
+            498,
+            763,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "23179",
+        "bbox": [
+            478,
+            924,
+            517,
+            935
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f4eeae5681fa7d830050c81513b5f7cde6a5b2a71b65b45d8545d4c58d8b6c09.jpg",
+        "image_caption": [
+            "Figure 5: Qualitative results of using a single condition for human face images. The included conditions are: (a) text; (b) face parsing maps; (c) sketches; (d) face landmarks; (e) IDs of reference images. Zoom in for best view."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/27e03d982775f233e58b50c3c9aa19cd7859f383067e0fcfe00fca5bef37d640.jpg",
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+    {
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+        "img_path": "images/77f122cff9a2026e5c4d8a0f315651f464e4f14a50d79aa1f182688fa74af8e7.jpg",
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+    {
+        "type": "image",
+        "img_path": "images/2769dcee6f1d11106fbbbf36b5cd740228d73627eb5296bf3460d315e060f1ce.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/27c7229d2f5a1d4bf4c78cd807f4b3fcf9d143a629835ea42849f7898c5a720d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/320a3ee53d0cce76630ff44c1ab810c502970059d9158ecce3f5869fa3bc2627.jpg",
+        "image_caption": [
+            "Figure 6: Qualitative results of using a single condition for ImageNet images. Pre-trained diffusion models are: (a) unconditional ImageNet diffusion model; (b) classifier-based ImageNet diffusion model. Zoom in for best view."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            319,
+            272,
+            385
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3cf75bd5dbba04c3a2316dd2bcb32861b4b8cf715af3a41c4b978be8a7ddae91.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            274,
+            319,
+            468,
+            390
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "$\\succ$  Classifier-based ImageNet Diffusion Model [10]. The supported image resolution of this model is  $256 \\times 256$ , and the pre-trained dataset is ImageNet. This model also has a time-dependent classifier to guide its generation process. We experiment with the condition of style images.",
+            "> Stable Diffusion [36]. Stable Diffusion is a widely used Latent Diffusion Model. The standard resolution of its output images is  $512 \\times 512$ , but it supports higher resolutions. In our work, we use its pre-trained text-to-image model. We experiment with the condition of style images.",
+            "> ControlNet [52]. ControlNet is a Stable Diffusion based model supporting extra conditions input with the original text input. In our work, we use the pre-trained pose-to-image and scribble-to-image models. We experiment with conditions that include face IDs and style images."
+        ],
+        "bbox": [
+            75,
+            472,
+            468,
+            699
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We choose DDIM [41] with 100 steps as the sampling strategy of all experiments, and other more detailed configurations will be provided in the supplementary material.",
+        "bbox": [
+            75,
+            700,
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+            744
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Qualitative Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            756,
+            259,
+            771
+        ],
+        "page_idx": 6
+    },
+    {
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+        "text": "Single Condition. We present the single-condition-guided results of human face images in Fig. 5. We can see that the generated results meet the requirements of the given conditions and have rich diversity and good quality. In Fig. 6, we show the single-condition-guided results of the ImageNet domain. The diversity of the generated results is still high. In order to ensure that the generated results can better meet the control of the given conditions, we use the",
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+            "Figure 7: Qualitative results of using multiple conditions. Pre-trained models are: (a) and (b): unconditional human face diffusion model; (c) and (d): unconditional ImageNet diffusion model. Zoom in for best view."
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+        "text": "proposed efficient time-travel strategy.",
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+            "- Multiple Conditions. Fig. 7 shows the synthesized results guided by multiple conditions in the domain of human faces and ImageNet. In the human face domain (a small data domain), we produce good results with rich diversity and high consistency with the conditions. We use the efficient time-travel strategy in the ImageNet domain (a large data domain) to produce acceptable results.",
+            "- Training-free Guidance for Latent Domain. It should be pointed out that FreeDoM supports diffusion models in both image and latent domains. In our work, we experiment with two latent diffusion models: Stable Diffusion [36] and ControlNet [52]. We try to add the training-free conditional interfaces based on their energy functions to work with the existing training-required conditional interfaces, leading to"
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+        "image_caption": [
+            "Figure 8: Comparison between FreeDoM and TediGAN [49] in three conditional image synthesis tasks: (a) segmentation maps to human faces; (b) sketches to human faces; (c) text prompts to human faces. Zoom in for best view."
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+    {
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+        "img_path": "images/81267587ef3ebe62fa6a3107037c746408978e6e323b5670d8324906411ffb58.jpg",
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+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">Segmentation maps</td><td colspan=\"2\">Sketches</td><td colspan=\"2\">Texts</td></tr><tr><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td></tr><tr><td>TediGAN [49]</td><td>2037.2</td><td>52.77</td><td>48.61</td><td>91.11</td><td>12.31</td><td>71.71</td></tr><tr><td>FreeDoM (ours)</td><td>1696.1</td><td>53.08</td><td>33.29</td><td>70.97</td><td>10.83</td><td>55.91</td></tr></table>",
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+        "text": "Table 1: We compare FreeDoM with the training-required method TediGAN [49] in three image conditional synthesis tasks. We compute the distance with given conditions and FID to judge the performance. The comparison shows that FreeDoM generates images matching given conditions better and having a comparable or better image quality.",
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+        "type": "text",
+        "text": "satisfactory results shown in Fig. 1(d)-(f). As such, we can see great application potential for mixing training-free and training-required conditional interfaces in various practical applications.",
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+        "text": "5.3. Further Studies",
+        "text_level": 1,
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+            "Comparison between FreeDoM and TediGAN [49]. We compare FreeDoM with the training-required conditional human face generation method TediGAN under three conditions: segmentation maps, sketches, and text. A qualitative comparison is shown in Fig. 8, and quantitative comparison results are reported in Tab. 1. For the comparison, we choose 1000 segmentation maps, 1000 sketches, and 1000 text prompts to generate 1000 results, respectively. Then we compute FID and the average distance with given conditions using the methods introduced in Sec. 4.4 to judge the performance. The comparison shows that the images generated by FreeDoM match the given conditions better and have a comparable or better image quality.",
+            "Comparison between FreeDoM and UGD [2]. We compare FreeDoM with Universal Guidance Diffusion (UGD) [2] in style-guided generations. From Fig. 9, we find that FreeDoM has significant advantages over UGD in the degree of alignment with the conditioned style image."
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+        "text": "\"A fantasy photo of volcanoes\" \"A fantasy photo of a lonely road\"A colorful photo of an Eiffel Towel",
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+        "image_caption": [
+            "Figure 9: Comparison between FreeDoM and UGD [2] in style-guided generation. The UGD results are taken from the original paper. The number in the lower right corner of each image represents its distance with the provided style image (smaller is better), which is calculated using the method described in Sec. 4.4. FreeDoM offers obvious advantages in image quality and in the degree of satisfaction of the conditions. Zoom in for best view."
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+        "image_caption": [
+            "Figure 10: Demonstration of the effect of different learning rates from small scale to large scale. (a): unconditional ImageNet diffusion models with prompt \"orange\"; (b): unconditional human face diffusion models with a face ID from the reference image. Zoom in for best view."
+        ],
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+            "Regarding the inference speed, UGD runs in about 40 minutes (using the open-source code) on a GeForce RTX 3090 GPU to synthesize one image with a resolution of  $512 \\times 512$ , while we only need about 84 seconds (nearly  $30 \\times$  faster).",
+            "□ Effect of different learning rates. We studied the effect of different learning rates on the results. Fig. 10 shows the results while increasing the energy function's learning rate  $(\\rho_{t}$  in Eq. (10)) from 0. We can see that FreeDoM is scalable"
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+        "text": "23181",
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+    {
+        "type": "text",
+        "text": "in terms of its control ability, which means that users can adjust the intensity of control as needed.",
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+    {
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+        "text": "6. Conclusions & Limitations",
+        "text_level": 1,
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+        "text": "We propose a training-free energy-guided conditional diffusion model, FreeDoM, to address a wide range of conditional generation tasks without training. Our method uses off-the-shelf pre-trained time-independent networks to approximate the time-dependent energy functions. Then, we use the gradient of the approximated energy to guide the generation process. Our method supports different diffusion models, including image and latent diffusion models. It is worth emphasizing that the applications presented in this paper are only a subset of the applications FreeDoM supports and should not be limited to these. In future work, we aim to explore even more energy functions for a broader range of tasks.",
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+        "text": "Despite its merits, our FreeDoM method has some limitations: (1) The time cost of the sampling is still higher than the training-required methods because each iteration adds a derivative operation for the energy function, and the timetravel strategy introduces more sampling steps. (2) It is difficult to use the energy function to control the fine-grained structure features in the large data domain. For example, using the Canny edge maps as the conditions may result in poor guidance, even if we use the time-travel strategy. In this case, the training-required methods will provide a better alternative. (3) Eq. 12 deals with multi-condition control and assumes that the provided conditions are independent, which is not necessarily true in practice. When conditions conflict with each other, FreeDoM may produce subpar generation results.",
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+    {
+        "type": "text",
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+        "sub_type": "ref_text",
+        "list_items": [
+            "[47] Yinhuai Wang, Jiwen Yu, and Jian Zhang. Zero-shot image restoration using denoising diffusion null-space model. In International Conference on Learning Representations, 2023.",
+            "[48] Jay Whang, Mauricio Delbracio, Hossein Talebi, Chitwan Sahara, Alexandros G Dimakis, and Peyman Milanfar. Deblurring via stochastic refinement. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022.",
+            "[49] Weihao Xia, Yujiu Yang, Jing-Hao Xue, and Baoyuan Wu. Tedigan: Text-guided diverse face image generation and manipulation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2021.",
+            "[50] Xiaoyu Xiang, Ding Liu, Xiao Yang, Yiheng Zhu, Xiaohui Shen, and Jan P Allebach. Adversarial open domain adaptation for sketch-to-photo synthesis. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, 2022.",
+            "[51] Changqian Yu, Jingbo Wang, Chao Peng, Changxin Gao, Gang Yu, and Nong Sang. Bisenet: Bilateral segmentation network for real-time semantic segmentation. In Proceedings of the European conference on computer vision (ECCV), 2018.",
+            "[52] Lvmin Zhang and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. arXiv preprint arXiv:2302.05543, 2023.",
+            "[53] Min Zhao, Fan Bao, Chongxuan Li, and Jun Zhu. Egsde: Unpaired image-to-image translation via energy-guided stochastic differential equations. Advances in Neural Information Processing Systems (NeurIPS), 2022."
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
+            513
+        ],
+        "page_idx": 10
+    },
+    {
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+        "text": "23184",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/FreeDoM_ Training-Free Energy-Guided Conditional Diffusion Model/6856ff82-c802-4528-9795-9924d03d4b41_model.json b/2023/FreeDoM_ Training-Free Energy-Guided Conditional Diffusion Model/6856ff82-c802-4528-9795-9924d03d4b41_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..0e0b778102eaea1b5296fe10cc12495df02d9b71
--- /dev/null
+++ b/2023/FreeDoM_ Training-Free Energy-Guided Conditional Diffusion Model/6856ff82-c802-4528-9795-9924d03d4b41_model.json	
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+            ],
+            "angle": 0,
+            "content": "\"cat rides bicycle\""
+        },
+        {
+            "type": "image",
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+            "angle": 0,
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+        },
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+            "bbox": [
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+            "content": "Figure 1: FreeDoM controls the generation process of diffusion models in a training-free way. Here, we demonstrate some results of the applications FreeDoM supports. Part (a)-(c) show various face editing applications with training-free guidance. (a) We use the segmentation map, sketch, landmarks, and face ID as conditions to guide the generation process of an unconditional diffusion model; (b) We combine different conditions to control the generation process. (c) We use CLIP [34] based text guidance to control image synthesis and editing. For editing, we use the segmentation masks to limit the editing areas (see Fig. 4 for details); Part (d)-(f) show that training-free guidance can work with other training-required conditional diffusion models, like Stable Diffusion [36] and ControlNet [52], to achieve a more sophisticated control mechanism. The conditions of scribbles in (d), human poses in (e), and prompt texts in (f) are controlled by the training-required interfaces provided by ControlNet and Stable Diffusion. Training-free energy functions control the conditions of face IDs from the reference images in (e) and style images in (d) and (f). Zoom in for best view."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "23174"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.123,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "Recently, conditional diffusion models have gained popularity in numerous applications due to their exceptional generation ability. However, many existing methods are training-required. They need to train a time-dependent classifier or a condition-dependent score estimator, which increases the cost of constructing conditional diffusion models and is inconvenient to transfer across different conditions. Some current works aim to overcome this limitation by proposing training-free solutions, but most can only be applied to a specific category of tasks and not to more general conditions. In this work, we propose a training-Free conditional Diffusion Model (FreeDoM) used for various conditions. Specifically, we leverage off-the-shelf pretrained networks, such as a face detection model, to construct time-independent energy functions, which guide the generation process without requiring training. Furthermore, because the construction of the energy function is very flexible and adaptable to various conditions, our proposed FreeDoM has a broader range of applications than existing training-free methods. FreeDoM is advantageous in its simplicity, effectiveness, and low cost. Experiments demonstrate that FreeDoM is effective for various conditions and suitable for diffusion models of diverse data domains, including image and latent code domains. Code is available at https://github.com/vvictoryuki/FreeDoM."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.571,
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+            "angle": 0,
+            "content": "Recently, diffusion models have been demonstrated to outperform previous state-of-the-art generative models [10], such as GANs [12, 29, 3, 22, 24, 23]. The impressive generative power of diffusion models [15, 43, 45] has motivated researchers to apply diffusion models to various downstream tasks. Conditional generation is one of the most popular focus areas. Conditional diffusion models (CDMs) with diverse conditions have been proposed, such as text [20, 1, 13, 26, 36, 40, 35, 38, 25, 32], class labels [10], degraded images [5, 6, 7, 8, 19, 27, 42, 44, 47, 37, 39, 48], segmentation maps [31, 52], landmarks [31, 52], hand-drawn sketches [31, 52], style images [31, 52], etc. These CDMs can be roughly divided into two categories: training-required or training-free."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.783,
+                0.472,
+                0.83
+            ],
+            "angle": 0,
+            "content": "A typical type of training-required CDMs trains a time-dependent classifier to guide the noisy image \\(\\mathbf{x}_t\\) toward the given condition \\(\\mathbf{c}\\) [10, 32, 53, 26]. Another branch of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "training-required CDMs directly trains a new score estimator \\( s(\\mathbf{x}_t, t, \\mathbf{c}) \\) conditioned on \\( \\mathbf{c} \\) [31, 16, 36, 37, 39, 48, 52, 20, 1, 13, 35, 32]. These methods yield impressive performance but are not flexible. Once a new target condition is needed for generation, they have to retrain or finetune the models, which is inconvenient and expensive."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.183,
+                0.895,
+                0.32
+            ],
+            "angle": 0,
+            "content": "In contrast, training-free CDMs try to solve the same problems without extra training. [30, 11, 14] attempt to use the cross-attention control to realize the conditional generation; [5, 6, 7, 8, 19, 27, 42, 44, 47, 46] directly modify the intermediate results to achieve zero-shot image restoration; [28] realizes image translation by adjusting the initial noisy images. While these methods are effective in a single application, they are difficult to generalize to a wider range of conditions, e.g., style, face ID, and segmentation masks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.32,
+                0.895,
+                0.472
+            ],
+            "angle": 0,
+            "content": "In order to make CDMs support a wide range of conditions in a training-free manner, this paper proposes a training-Free conditional Diffusion Model (FreeDoM) with the following two key points. Firstly, to emphasize generalization, we propose a sampling process guided by the energy function [53, 21], which is very flexible to construct and can be applied to various conditions. Secondly, to make the proposed method training-free, we use off-the-shelf pre-trained time-independent models, which are easily accessible online, to construct the energy function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.473,
+                0.895,
+                0.805
+            ],
+            "angle": 0,
+            "content": "Our FreeDoM has the following advantages: (1) Simple and effective. We only insert a derivative step of the energy function gradient into the unconditional sampling process of the original diffusion models. Extensive experiments show its effective controlling capability. (2) Low cost and efficient. The energy functions we construct are time-independent and do not need to be retrained. The diffusion models we choose do not need to be trained on the desired conditions. Thanks to the efficient time-travel strategy we use for large data domains, the number of sampling steps we use is quite small, which speeds up the sampling process while ensuring good generated results. (3) Amenable to a wide range of applications. The conditions our method supports include, but are not limited to, text, segmentation maps, sketches, landmarks, face IDs, style images, etc. In addition, various complex but interesting applications can be realized by combining multiple conditions. (4) Supports different types of diffusion models. Regardless of the considered data domain, such as human face images, images in ImageNet, or latent codes extracted from an image encoder, extensive experiments demonstrate that our method does well on all of them."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.821,
+                0.642,
+                0.837
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.846,
+                0.753,
+                0.864
+            ],
+            "angle": 0,
+            "content": "2.1. Training-Required Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The training-required methods can obtain strong control generation ability thanks to supervised learning with"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.076,
+                0.839,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "†Corresponding authors. This work was supported by Shenzhen General Research Project under Grant JCYJ20220531093215035, KAUST Office of Sponsored Research through the Visual Computing Center funding, and SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.925,
+                0.521,
+                0.938
+            ],
+            "angle": 0,
+            "content": "23175"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.47,
+                0.212
+            ],
+            "angle": 0,
+            "content": "data pairs. One of the most prominent applications of these methods is the text-to-image task. The most widely used text-to-image model, Stable Diffusion [36], generates high-quality images that conform to the text description by inputting a prompt text. Recent works, such as ControlNet [52] and T2I-Adapter [31], have introduced more training-required conditional interfaces to Stable Diffusion, such as edge maps, segmentation maps, depth maps, etc."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.214,
+                0.47,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Although these training-required methods can achieve satisfactory control results under trained conditions, the cost of training is still a factor to be considered, especially for the scenario that requires more complex control with multiple conditions. The training-required method is not the cheapest or most convenient solution in practical applications."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.317,
+                0.293,
+                0.332
+            ],
+            "angle": 0,
+            "content": "2.2. Training-Free Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.341,
+                0.47,
+                0.599
+            ],
+            "angle": 0,
+            "content": "The training-free methods develop various interesting technologies to realize the training-free condition generation on some tasks exploiting the unique nature of the diffusion model, namely, the iterative denoising process. [14] proposes to inject the target cross attention maps to the source cross attention maps to solve the prompt-to-prompt task without training. The limitation of this method is that a text prompt is needed to anchor the content of the image to be edited in advance. DDNM [47] proposes to use the Range-Null Space Decomposition to modify the intermediate results to solve the image restoration in a training-free way. It is based on the degradation operators of image restoration tasks and is hard to be adopted in other applications. SDEdit [28] proposes to adjust the initial noisy images to control the generation process, which is useful in stroke-based image synthesis and editing. Its limitation is that the guidance of stroke is not precise and versatile."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.6,
+                0.469,
+                0.676
+            ],
+            "angle": 0,
+            "content": "According to the limitations mentioned above, the training-free CDMs for a broad range of applications need to be studied urgently. We have noticed some recent efforts [33, 2] in this area. Our FreeDoM has a faster generation speed and applies to a broader range of applications."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.692,
+                0.216,
+                0.708
+            ],
+            "angle": 0,
+            "content": "3. Preliminaries"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.718,
+                0.342,
+                0.733
+            ],
+            "angle": 0,
+            "content": "3.1. Score-based Diffusion Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.742,
+                0.469,
+                0.863
+            ],
+            "angle": 0,
+            "content": "Score-based Diffusion Models (SBDMs) [43, 45] are a kind of diffusion model based on score theory, which reveals that the essence of diffusion models is to estimate the score function \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)\\), where \\(\\mathbf{x}_t\\) is noisy data. During the sampling process, SBDMs predict \\(\\mathbf{x}_{t - 1}\\) from \\(\\mathbf{x}_t\\) using the estimated score step by step. In our work, we resort to discrete SBDMs with the setting of DDPM [15] and its sampling formula is:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.097,
+                0.876,
+                0.47,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {x} _ {t - 1} = \\left(1 + \\frac {1}{2} \\beta_ {t}\\right) \\mathbf {x} _ {t} + \\beta_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "where \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) is randomly sampled Gaussian noise and \\(\\beta_{t}\\in \\mathbb{R}\\) is a pre-defined parameter. In actual implementation, the score function will be estimated using a score estimator \\(s(\\mathbf{x}_t,t)\\), that is, \\(s(\\mathbf{x}_t,t)\\approx \\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)\\). However, the original diffusion models can only serve as an unconditional generator with randomly synthesized results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.191,
+                0.748,
+                0.206
+            ],
+            "angle": 0,
+            "content": "3.2. Conditional Score Function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.214,
+                0.892,
+                0.322
+            ],
+            "angle": 0,
+            "content": "In order to adapt the generative power of the diffusion models to different downstream tasks, conditional diffusion models (CDMs) are needed. SDE [45] proposed to control the generated results with a given condition \\(\\mathbf{c}\\) by modifying the score function as \\(\\nabla_{\\mathbf{x}_t} \\log p(\\mathbf{x}_t | \\mathbf{c})\\). Using the Bayesian formula \\(p(\\mathbf{x}_t | \\mathbf{c}) = \\frac{p(\\mathbf{c} | \\mathbf{x}_t) p(\\mathbf{x}_t)}{p(\\mathbf{c})}\\), we can rewrite the conditional score function as two terms:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.512,
+                0.332,
+                0.892,
+                0.35
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t} | \\mathbf {c}) = \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) + \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {c} | \\mathbf {x} _ {t}), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.357,
+                0.892,
+                0.493
+            ],
+            "angle": 0,
+            "content": "where the first term \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)\\) can be estimated using the pre-trained unconditional score estimator \\(s(\\cdot ,t)\\) and the second term \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)\\) is the critical part of constructing conditional diffusion models. We can interpret the second term \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)\\) as a correction gradient, pointing \\(\\mathbf{x}_t\\) to a hyperplane in the data space, where all data are compatible with the given condition c. Classifier-based methods [10, 32, 53, 26] train a time-dependent classifier to compute this correction gradient for conditional guidance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.502,
+                0.747,
+                0.518
+            ],
+            "angle": 0,
+            "content": "3.3. Energy Diffusion Guidance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.525,
+                0.892,
+                0.571
+            ],
+            "angle": 0,
+            "content": "Modeling the correction gradient \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)\\) remains an open question. A flexible and straightforward way is resorting to the energy function [53, 21] as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.594,
+                0.578,
+                0.891,
+                0.609
+            ],
+            "angle": 0,
+            "content": "\\[\np (\\mathbf {c} | \\mathbf {x} _ {t}) = \\frac {\\exp \\left\\{- \\lambda \\mathcal {E} (\\mathbf {c} , \\mathbf {x} _ {t}) \\right\\}}{Z}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.615,
+                0.892,
+                0.781
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) denotes the positive temperature coefficient and \\(Z > 0\\) denotes a normalizing constant, computed as \\(Z = \\int_{\\mathbf{c} \\in \\mathcal{C}} \\exp\\{-\\lambda \\mathcal{E}(\\mathbf{c}, \\mathbf{x}_t)\\}\\) where \\(\\mathcal{C}\\) denotes the domain of the given conditions. \\(\\mathcal{E}(\\mathbf{c}, \\mathbf{x}_t)\\) is an energy function that measures the compatibility between the condition \\(\\mathbf{c}\\) and the noisy image \\(\\mathbf{x}_t\\) — its value will be smaller when \\(\\mathbf{x}_t\\) is more compatible with \\(\\mathbf{c}\\). If \\(\\mathbf{x}_t\\) satisfies the constraint of \\(\\mathbf{c}\\) perfectly, the energy value should be zero. Any function satisfying the above property can serve as a feasible energy function, with which we just need to adjust the coefficient \\(\\lambda\\) to obtain \\(p(\\mathbf{c} | \\mathbf{x}_t)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.782,
+                0.891,
+                0.812
+            ],
+            "angle": 0,
+            "content": "Therefore, the correction gradient \\(\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)\\) can be implemented with the following:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.82,
+                0.891,
+                0.838
+            ],
+            "angle": 0,
+            "content": "\\[\n\\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {c} | \\mathbf {x} _ {t}) \\propto - \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.846,
+                0.891,
+                0.877
+            ],
+            "angle": 0,
+            "content": "which is referred to as energy guidance. With Eq. (1), Eq. (2), and Eq. (4), we get the conditional sampling:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.595,
+                0.886,
+                0.891,
+                0.903
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mathbf {m} _ {t} - \\rho_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}), \\tag {5}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.925,
+                0.521,
+                0.937
+            ],
+            "angle": 0,
+            "content": "23176"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.09,
+                0.473,
+                0.168
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{m}_t = (1 + \\frac{1}{2}\\beta_t)\\mathbf{x}_t + \\beta_t\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t) + \\sqrt{\\beta_t}\\epsilon,\\) and \\(\\rho_{t}\\) is a scale factor, which can be seen as the learning rate of the correction term. Eq. (5) is a generic formulation of conditional diffusion models, which enables the use of different energy functions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.182,
+                0.373,
+                0.2
+            ],
+            "angle": 0,
+            "content": "4. The Proposed FreeDoM Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.208,
+                0.47,
+                0.345
+            ],
+            "angle": 0,
+            "content": "In Sec. 4.1, we approximate the time-dependent energy function using time-independent distance measuring functions, making our method training-free and flexible for various conditions. In Sec. 4.2, we first analyze the reason why the energy guidance fails in a large data domain and then propose an efficient version of the time-travel strategy [27, 47]. In Sec. 4.3, we describe the details of how to construct the energy functions. In Sec. 4.4, we provide specific examples of supported conditions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.355,
+                0.408,
+                0.373
+            ],
+            "angle": 0,
+            "content": "4.1. Approximate Time-Dependent Energy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.379,
+                0.47,
+                0.468
+            ],
+            "angle": 0,
+            "content": "We use the energy function to guide the generation due to its flexibility to construct and suitability to various conditions. Existing classifier-based methods [10, 32, 53, 26] choose time-dependent distance measuring functions \\(\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)\\) to approximate the energy functions as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.19,
+                0.471,
+                0.469,
+                0.487
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\phi} (\\mathbf {c}, \\mathbf {x} _ {t}, t), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.495,
+                0.469,
+                0.601
+            ],
+            "angle": 0,
+            "content": "where \\(\\phi\\) defines the pre-trained parameters. \\(\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)\\) computes the distance between the given condition \\(\\mathbf{c}\\) and noisy intermediate results \\(\\mathbf{x}_t\\). The distance measuring functions for noisy data \\(\\mathbf{x}_t\\) cannot be directly constructed because it is difficult to find an existing pre-trained network for noisy images. In this case, we have to train (or finetune) a time-dependent network for each type of condition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.602,
+                0.47,
+                0.754
+            ],
+            "angle": 0,
+            "content": "Compared with time-dependent networks, time-independent distance measuring functions for clean data \\(\\mathbf{x}_0\\) are widely available. Many off-the-shelf pre-trained networks such as classification networks, segmentation networks, and face ID encoding networks are open-source and work well on clean images. We denote these distance measuring networks for clean data as \\(\\mathcal{D}_{\\theta}(\\mathbf{c},\\mathbf{x}_0)\\), where \\(\\pmb{\\theta}\\) denotes their pre-trained parameters. To use these networks for the energy functions, a straightforward way is to approximate \\(\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)\\) using \\(\\mathcal{D}_{\\theta}(\\mathbf{c},\\mathbf{x}_0)\\), formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.766,
+                0.469,
+                0.784
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {\\phi} (\\mathbf {c}, \\mathbf {x} _ {t}, t) \\approx \\mathbb {E} _ {p \\left(\\mathbf {x} _ {0} \\mid \\mathbf {x} _ {t}\\right)} \\left[ \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0}) \\right]. \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Eq. (7) is reasonable because if the distance between the noise image \\(\\mathbf{x}_t\\) and the condition \\(\\mathbf{c}\\) is small, the clean image \\(\\mathbf{x}_0\\) corresponding to the noise image \\(\\mathbf{x}_t\\) should also have a small distance with the condition \\(\\mathbf{c}\\), especially during the late stage of the sampling process when the noise level of \\(\\mathbf{x}_t\\) is relatively small. However, during the sampling process, it is infeasible to get the clean image \\(\\mathbf{x}_0\\) corresponding to"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.091,
+                0.885,
+                0.106
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Sampling Process of our proposed FreeDoM"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.107,
+                0.892,
+                0.138
+            ],
+            "angle": 0,
+            "content": "Require: condition \\(\\mathbf{c}\\), unconditional score estimator \\(s(\\cdot, t)\\), time-independent distance measuring function \\(\\mathcal{D}_{\\theta}(\\mathbf{c}, \\cdot)\\), pre-defined parameters \\(\\beta_{t}\\), \\(\\bar{\\alpha}_{t}\\) and learning rate \\(\\rho_{t}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.138,
+                0.599,
+                0.148
+            ],
+            "angle": 0,
+            "content": "1: \\(\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.148,
+                0.592,
+                0.157
+            ],
+            "angle": 0,
+            "content": "2: for \\( t = T, \\ldots \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.157,
+                0.707,
+                0.167
+            ],
+            "angle": 0,
+            "content": "3: \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) if \\(t > 1\\), else \\(\\epsilon = 0\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.167,
+                0.769,
+                0.177
+            ],
+            "angle": 0,
+            "content": "4: \\(\\mathbf{x}_{t - 1} = (1 + \\frac{1}{\\beta}\\beta_{t})\\mathbf{x}_{t} + \\beta_{t}s(\\mathbf{x}_{t},t) + \\sqrt{\\beta_{t}}\\pmb{\\epsilon}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.177,
+                0.733,
+                0.193
+            ],
+            "angle": 0,
+            "content": "5: \\(\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{x}_t + (1 - \\bar{\\alpha}_t)s(\\mathbf{x}_t,t))\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.193,
+                0.686,
+                0.204
+            ],
+            "angle": 0,
+            "content": "6: \\( \\pmb{g}_t = \\nabla_{\\mathbf{x}_t} \\mathcal{D}_{\\pmb{\\theta}}(\\mathbf{c}, \\mathbf{x}_{0|t}(\\mathbf{x}_t))) \\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.204,
+                0.654,
+                0.214
+            ],
+            "angle": 0,
+            "content": "7: \\(\\mathbf{x}_{t - 1} = \\mathbf{x}_{t - 1} - \\rho_t\\pmb {g}_t\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.215,
+                0.572,
+                0.225
+            ],
+            "angle": 0,
+            "content": "8: return \\(\\mathbf{x}_0\\)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.507,
+                0.138,
+                0.769,
+                0.225
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.239,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.525,
+                0.34,
+                0.661,
+                0.35
+            ],
+            "angle": 0,
+            "content": "(a) Badly Generated Results"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.726,
+                0.335,
+                0.874,
+                0.356
+            ],
+            "angle": 0,
+            "content": "(b) Generated Results with the Time-Travel Strategy"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.358,
+                0.892,
+                0.433
+            ],
+            "angle": 0,
+            "content": "Figure 2: Comparison of results generated before and after using the time-travel strategy. The prompt is \"orange\". We can see that the results in (a) do not match the given conditions. After using the time-travel strategy, we get better results in (b)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.457,
+                0.892,
+                0.488
+            ],
+            "angle": 0,
+            "content": "an intermediate noisy result \\(\\mathbf{x}_t\\), so we need to approximate \\(\\mathbf{x}_0\\). Considering the expectation of \\(p(\\mathbf{x}_0|\\mathbf{x}_t)\\) [6]:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.521,
+                0.499,
+                0.891,
+                0.531
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {x} _ {0 \\mid t} := \\mathbb {E} [ \\mathbf {x} _ {0} | \\mathbf {x} _ {t} ] = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} (\\mathbf {x} _ {t} + (1 - \\bar {\\alpha} _ {t}) s (\\mathbf {x} _ {t}, t)), \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.542,
+                0.892,
+                0.62
+            ],
+            "angle": 0,
+            "content": "where \\(\\bar{\\alpha}_t = \\prod_{i=1}^t (1 - \\beta_i)\\) and \\(s(\\cdot, t)\\) is the pre-trained score estimator. According to Eq. (8), from \\(\\mathbf{x}_t\\), we can estimate the clean image denoted as \\(\\mathbf{x}_{0|t}\\). Then with Eq. (6) and Eq. (7), we can approximate the time-dependent energy function of noisy data \\(\\mathbf{x}_t\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.615,
+                0.632,
+                0.891,
+                0.649
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t}). \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.891,
+                0.691
+            ],
+            "angle": 0,
+            "content": "According to Eq. (5) and Eq. (9), the approximated sampling process can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.57,
+                0.704,
+                0.891,
+                0.72
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {x} _ {t - 1} = \\mathbf {m} _ {t} - \\rho_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t} (\\mathbf {x} _ {t})), \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.732,
+                0.81,
+                0.747
+            ],
+            "angle": 0,
+            "content": "and the detailed algorithm is shown in Algo. 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.757,
+                0.769,
+                0.773
+            ],
+            "angle": 0,
+            "content": "4.2. Efficient Time-Travel Strategy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In the process of applying Algo. 1, we find that the performance varies significantly on different data domains. For small data domains such as human faces, Algo. 1 can effectively produce results that satisfy the given conditions within 100 DDIM [41] sampling steps. However, for large data domains such as ImageNet, we often get results that are not closely related to the given conditions or even randomly generated results (shown in Fig. 2(a)). We attribute"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "23177"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.089,
+                0.895,
+                0.199
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.2,
+                0.895,
+                0.248
+            ],
+            "angle": 0,
+            "content": "Figure 3: Demonstration of the importance of different sampling stages. Most of the semantic content is generated during the semantic stage, so we only employ the time-travel strategy in this stage to achieve an efficient version of FreeDoM. The shown images are \\(\\mathbf{x}_{0|t}\\) generated by diffusion models pre-trained on the ImageNet data domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.269,
+                0.473,
+                0.391
+            ],
+            "angle": 0,
+            "content": "the failure of Algo. 1 on large data domains to poor guidance. The reason for poor guidance is that the direction of unconditional score generated by diffusion models in large data domains has more freedom, making it easier to deviate from the direction of conditional control. To solve this problem, we adopt the time-travel strategy [27, 47], which has been empirically shown to inhibit the generation of disharmonious results when solving hard generation tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.397,
+                0.473,
+                0.593
+            ],
+            "angle": 0,
+            "content": "The time-travel strategy is a technique that takes the current intermediate result \\(\\mathbf{x}_t\\) back by \\(j\\) steps to \\(\\mathbf{x}_{t + j}\\) and resamples it to the \\(t\\)-th timestep again. This strategy inserts more sampling steps into the sampling process and refines the generated results. In our experiments specifically, we go back by \\(j = 1\\) step each time and resample. We repeat this resampling process \\(r_t\\) times at the \\(t\\)-th timestep. Our experiments demonstrate that the time travel strategy is effective in solving the poor guidance problem (shown in Fig. 2(b)). However, the time cost is also expensive because the number of sampling steps is larger, especially considering that each timestep will include the cost of calculating the gradient of the energy function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.599,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Fortunately, we find that the time-travel strategy does not have the same effect in each time step. In fact, using this technique in most time steps will not significantly modify the final result, which means we can use this strategy only in a small portion of the timesteps, thus significantly reducing the number of additional iteration steps. In Fig. 3, we try to analyze this phenomenon by dividing the sampling process into three stages. In the early stage, i.e., the chaotic stage, the generated result \\(\\mathbf{x}_{0|t}\\) is extremely blurred, and the energy guidance is hard to make anything reasonable, so we do not need to employ the time-travel strategy. During the late stage, i.e., the refinement stage, the change in the generated results is minor, so the time-travel strategy is useless. During the intermediate stage, i.e., the semantic stage, the change in the generated result is significant, so this stage is critical for conditional generation. Based on this observation, we only apply the time-travel strategy in the semantic stage to implement efficient sampling while solving the problem of poor guidance. The range of the semantic stage is an experimental choice depending on the specific dif"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.269,
+                0.874,
+                0.284
+            ],
+            "angle": 0,
+            "content": "Algorithm 2 FreeDoM + Efficient Time-Travel Strategy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.285,
+                0.892,
+                0.316
+            ],
+            "angle": 0,
+            "content": "Require: condition \\(\\mathbf{c}\\), unconditional score estimator \\(s(\\cdot, t)\\), time-independent distance measuring function \\(\\mathcal{D}_{\\theta}(\\mathbf{c}, \\cdot)\\), pre-defined parameters \\(\\beta_t, \\bar{\\alpha}_t\\), learning rate \\(\\rho_t\\), and the repeat times of time travel of each step \\(\\{r_1, \\dots, r_T\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.316,
+                0.6,
+                0.325
+            ],
+            "angle": 0,
+            "content": "1: \\(\\mathbf{x}_T\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.325,
+                0.618,
+                0.335
+            ],
+            "angle": 0,
+            "content": "2: for \\( t = T, \\dots, 1 \\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.335,
+                0.639,
+                0.345
+            ],
+            "angle": 0,
+            "content": "3: for \\(i = r_t,\\dots,1\\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.345,
+                0.739,
+                0.355
+            ],
+            "angle": 0,
+            "content": "4: \\(\\epsilon_{1} \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) if \\(t > 1\\), else \\(\\epsilon_{1} = \\mathbf{0}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.355,
+                0.791,
+                0.366
+            ],
+            "angle": 0,
+            "content": "5: \\(\\mathbf{x}_{t - 1} = (1 + \\frac{1}{2}\\beta_t)\\mathbf{x}_t + \\beta_t s(\\mathbf{x}_t,t) + \\sqrt{\\beta_t}\\epsilon_1\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.366,
+                0.75,
+                0.38
+            ],
+            "angle": 0,
+            "content": "6: \\(\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}} (\\bar{\\mathbf{x}}_t + (1 - \\bar{\\alpha}_t)s(\\mathbf{x}_t,t))\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.38,
+                0.703,
+                0.392
+            ],
+            "angle": 0,
+            "content": "7: \\(\\pmb{g}_{t} = \\nabla_{\\mathbf{x}_{t}}\\mathcal{D}_{\\pmb{\\theta}}(\\mathbf{c},\\mathbf{x}_{0|t}(\\mathbf{x}_{t})))\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.392,
+                0.671,
+                0.402
+            ],
+            "angle": 0,
+            "content": "8: \\(\\mathbf{x}_{t - 1} = \\mathbf{x}_{t - 1} - \\rho_t\\pmb {g}_t\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.402,
+                0.624,
+                0.411
+            ],
+            "angle": 0,
+            "content": "9: if \\(i > 1\\) then"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.412,
+                0.65,
+                0.422
+            ],
+            "angle": 0,
+            "content": "10: \\(\\epsilon_{2}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.422,
+                0.734,
+                0.433
+            ],
+            "angle": 0,
+            "content": "11: \\(\\mathbf{x}_t = \\sqrt{1 - \\beta_t}\\mathbf{x}_{t-1} + \\sqrt{\\beta_t}\\pmb{\\epsilon}_2\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.434,
+                0.575,
+                0.445
+            ],
+            "angle": 0,
+            "content": "12: return \\(\\mathbf{x}_0\\)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.504,
+                0.316,
+                0.791,
+                0.445
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.474,
+                0.894,
+                0.536
+            ],
+            "angle": 0,
+            "content": "fusion models we choose. The detailed algorithm of our proposed FreeDoM with the efficient time-travel strategy is shown in Algo.2, where \\( r_t = 1 \\) means we do not apply the time-travel strategy in the \\( t \\)-th timestep."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.544,
+                0.82,
+                0.56
+            ],
+            "angle": 0,
+            "content": "4.3. Construction of the Energy Function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.571,
+                0.892,
+                0.631
+            ],
+            "angle": 0,
+            "content": "- Single Condition Guidance. To incorporate in specific applications, we use the distance measuring function conforming to the following structure to construct the energy function:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.508,
+                0.643,
+                0.892,
+                0.661
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t}) = \\operatorname {D i s t} \\left(\\mathcal {P} _ {\\boldsymbol {\\theta} _ {1}} (\\mathbf {c}), \\mathcal {P} _ {\\boldsymbol {\\theta} _ {2}} (\\mathbf {x} _ {0 | t})\\right), \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.671,
+                0.895,
+                0.822
+            ],
+            "angle": 0,
+            "content": "where \\(Dist(\\cdot)\\) denotes the distance measuring methods like Euclidean distance, and \\(\\pmb{\\theta} = \\{\\pmb{\\theta}_1,\\pmb{\\theta}_2\\}\\). \\(\\mathcal{P}_{\\theta_1}(\\cdot)\\) and \\(\\mathcal{P}_{\\theta_2}(\\cdot)\\) project the condition and image to the same space for distance measurement. These projection networks can be off-the-shelf pre-trained classification networks, segmentation networks, etc. In most cases, we only need one network to project the clean image \\(\\mathbf{x}_{0|t}\\) to the condition space. In the cases with reference images \\(\\mathbf{x}_{ref}\\), we also only need one feature encoder to project the reference image \\(\\mathbf{x}_{ref}\\) and \\(\\mathbf{x}_{0|t}\\) to the same feature space."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- Multi Condition Guidance. In some more involved applications, multiple conditions can be available to provide control over the generated results. Take the image style transfer task as an example. Here, we have two conditions: the structure information from the source image and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.925,
+                0.521,
+                0.937
+            ],
+            "angle": 0,
+            "content": "23178"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.087,
+                0.147,
+                0.137
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.087,
+                0.138,
+                0.139,
+                0.146
+            ],
+            "angle": 0,
+            "content": "Original Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.147,
+                0.087,
+                0.202,
+                0.138
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.167,
+                0.139,
+                0.187,
+                0.145
+            ],
+            "angle": 0,
+            "content": "Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.208,
+                0.087,
+                0.273,
+                0.138
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.225,
+                0.139,
+                0.258,
+                0.145
+            ],
+            "angle": 0,
+            "content": "\"Lipstick\""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.275,
+                0.087,
+                0.339,
+                0.138
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.281,
+                0.139,
+                0.333,
+                0.146
+            ],
+            "angle": 0,
+            "content": "Original Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.34,
+                0.087,
+                0.404,
+                0.138
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.361,
+                0.139,
+                0.381,
+                0.146
+            ],
+            "angle": 0,
+            "content": "Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.404,
+                0.087,
+                0.468,
+                0.138
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.417,
+                0.138,
+                0.452,
+                0.146
+            ],
+            "angle": 0,
+            "content": "\"Pale lips\""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.147,
+                0.147,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.088,
+                0.201,
+                0.138,
+                0.208
+            ],
+            "angle": 0,
+            "content": "Original Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.15,
+                0.147,
+                0.208,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.167,
+                0.201,
+                0.187,
+                0.208
+            ],
+            "angle": 0,
+            "content": "Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.21,
+                0.147,
+                0.274,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.217,
+                0.201,
+                0.265,
+                0.208
+            ],
+            "angle": 0,
+            "content": "\"Straight hair\""
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.275,
+                0.147,
+                0.352,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.282,
+                0.201,
+                0.333,
+                0.208
+            ],
+            "angle": 0,
+            "content": "Original Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.353,
+                0.147,
+                0.408,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.361,
+                0.201,
+                0.38,
+                0.208
+            ],
+            "angle": 0,
+            "content": "Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.408,
+                0.147,
+                0.468,
+                0.2
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.418,
+                0.201,
+                0.452,
+                0.208
+            ],
+            "angle": 0,
+            "content": "\"Red hair\""
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.211,
+                0.468,
+                0.271
+            ],
+            "angle": 0,
+            "content": "Figure 4: Practical usage of face parsing maps. We can limit the gradient of the energy function to update the image only in the target semantic region indicated by the mask so that other regions remain unchanged while editing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.285,
+                0.468,
+                0.346
+            ],
+            "angle": 0,
+            "content": "the style information from the style image. In these multi-condition cases, assume that the given conditions are denoted as \\(\\{\\mathbf{c}_1,\\dots ,\\mathbf{c}_n\\}\\), we can approximately construct the energy function as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.102,
+                0.359,
+                0.469,
+                0.396
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathcal {E} \\left(\\left\\{\\mathbf {c} _ {1}, \\dots , \\mathbf {c} _ {n} \\right\\}, \\mathbf {x} _ {t}\\right) \\\\ \\approx \\eta_ {1} \\mathcal {D} _ {\\boldsymbol {\\theta} _ {1}} \\left(\\mathbf {c} _ {1}, \\mathbf {x} _ {0 | t}\\right) + \\dots + \\eta_ {n} \\mathcal {D} _ {\\boldsymbol {\\theta} _ {n}} \\left(\\mathbf {c} _ {n}, \\mathbf {x} _ {0 | t}\\right), \\tag {12} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.409,
+                0.468,
+                0.454
+            ],
+            "angle": 0,
+            "content": "where \\(\\eta_{i}\\) is the weighting factor. We use different distance measuring functions \\(\\{\\mathcal{D}_{\\theta_1}(\\cdot ,\\cdot),\\dots ,\\mathcal{D}_{\\theta_n}(\\cdot ,\\cdot)\\}\\) for specific conditions and sum the whole for gradient computation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.459,
+                0.469,
+                0.549
+            ],
+            "angle": 0,
+            "content": "Guidance for Latent Diffusion. Our method applies not only to image diffusions but also to latent diffusions, such as Stable Diffusion [36]. In this case, the intermediate results \\(\\mathbf{x}_t\\) are latent codes rather than images. We can use the latent decoder to project the generated latent codes to images and then use the same algorithm in the image domain."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.562,
+                0.445,
+                0.578
+            ],
+            "angle": 0,
+            "content": "4.4. Specific Examples of Supported Conditions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.59,
+                0.468,
+                0.724
+            ],
+            "angle": 0,
+            "content": "\\(\\square\\) Text. For given text prompts, we construct the distance measuring function based on CLIP [34]. Specifically, we take the CLIP image encoder (as \\(\\mathcal{P}_{\\theta_2}(\\cdot)\\)) and the CLIP text encoder (as \\(\\mathcal{P}_{\\theta_1}(\\cdot)\\)) to project the image \\(\\mathbf{x}_{0|t}\\) and given text in the same CLIP feature space. Compared with the commonly used cosine distance measurement and for simplicity, we choose the \\(\\ell_2\\) Euclidean distance measurement, since the sampling quality in our experiments is not significantly different."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.73,
+                0.468,
+                0.866
+            ],
+            "angle": 0,
+            "content": "□ Segmentation Maps. For segmentation maps, we choose a face parsing network based on the real-time semantic segmentation network BiSeNet [51] to generate the parsing map of an input human face and directly compute the \\(\\ell_2\\) Euclidean distance between the given parsing map and the parsing results of \\(\\mathbf{x}_{0|t}\\). An interesting usage of the face parsing network is to constrain the gradient update region so that we can edit the target semantic region without changing other regions (shown in Fig. 4)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Sketches. We choose an open-source pre-trained network [50] that transfers a given anime image to the style"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.59,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.891,
+                0.152
+            ],
+            "angle": 0,
+            "content": "of hand-drawn sketches. Experiments prove that the network is still effective for real-world images. We use the \\(\\ell_2\\) Euclidean distance to compare the given sketches with transferred sketch-style results of \\(\\mathbf{x}_{0|t}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.156,
+                0.892,
+                0.291
+            ],
+            "angle": 0,
+            "content": "\\(\\square\\) Landmarks. We use an open-source pre-trained human face landmark detection network [4] for this application. The detection network has two stages: the first stage finds the position of the center of a face and the second stage marks the landmarks of this detected face. We compute the \\(\\ell_2\\) Euclidean distance between predicted face landmarks of \\(\\mathbf{x}_{0|t}\\) and the given landmarks condition, and only use the gradient in the face area detected in the first stage to update the intermediate results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.297,
+                0.891,
+                0.373
+            ],
+            "angle": 0,
+            "content": "\\(\\square\\) Face IDs. We use ArcFace [9], an open-source pretrained human face recognition network, to extract the target features of reference faces to represent face IDs and compute the \\(\\ell_2\\) Euclidean distance between the extracted ID features of \\(\\mathbf{x}_{0|t}\\) and those of the reference image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.377,
+                0.891,
+                0.424
+            ],
+            "angle": 0,
+            "content": "- Style Images. The style image is denoted as \\(\\mathbf{x}_{style}\\). We use the following equation to compute the distance of the style information between \\(\\mathbf{x}_{style}\\) and \\(\\mathbf{x}_{0|t}\\):"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.499,
+                0.156,
+                0.892,
+                0.424
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.437,
+                0.891,
+                0.455
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {D i s t} \\left(\\mathbf {x} _ {\\text {s t y l e}}, \\mathbf {x} _ {0 | t}\\right) = \\left| \\left| G \\left(\\mathbf {x} _ {\\text {s t y l e}}\\right) _ {j} - G \\left(\\mathbf {x} _ {0 | t}\\right) _ {j} \\right| \\right| _ {F} ^ {2}, \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.467,
+                0.891,
+                0.528
+            ],
+            "angle": 0,
+            "content": "where \\( G(\\cdot)_{j} \\) denotes the Gram matrix [17] of the \\( j \\)-th layer feature map of an image encoder. In our experiments, we choose the features from the third layer of the CLIP image encoder to generate satisfactory results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.532,
+                0.891,
+                0.623
+            ],
+            "angle": 0,
+            "content": "- Low-pass Filters. For the image transferring task, we need an energy function to constrain the generated results conforming to the structure information of the source image \\(\\mathbf{x}_{source}\\). Similar to EGSDE [53] and ILVR [5], we choose a low-pass filter \\(\\mathcal{K}(\\cdot)\\) in this setup. The distance between the source image \\(\\mathbf{x}_{source}\\) and \\(\\mathbf{x}_{0|t}\\) is computed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.517,
+                0.637,
+                0.891,
+                0.655
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {D i s t} \\left(\\mathbf {x} _ {\\text {s o u r c e}}, \\mathbf {x} _ {0 | t}\\right) = \\left| \\left| \\mathcal {K} \\left(\\mathbf {x} _ {\\text {s o u r c e}}\\right) - \\mathcal {K} \\left(\\mathbf {x} _ {0 | t}\\right) \\right| \\right| _ {2} ^ {2}. \\tag {14}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.669,
+                0.631,
+                0.685
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.695,
+                0.716,
+                0.71
+            ],
+            "angle": 0,
+            "content": "5.1. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.719,
+                0.891,
+                0.763
+            ],
+            "angle": 0,
+            "content": "Our proposed method applies to many open-source pretrained diffusion models (DMs). In our experiment, we have tried the following models and conditions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.765,
+                0.891,
+                0.84
+            ],
+            "angle": 0,
+            "content": "> Unconditional Human Face Diffusion Model [28]. The supported image resolution of this model is \\( 256 \\times 256 \\), and the pre-trained dataset is aligned human faces from CelebA-HQ [18]. We experiment with conditions that include text, parsing maps, sketches, landmarks, and face IDs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.84,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": "> Unconditional ImageNet Diffusion Model [10]. The supported image resolution of this model is \\(256 \\times 256\\) and the pre-trained dataset is ImageNet. We experiment with conditions that include text and style images."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.499,
+                0.765,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.925,
+                0.519,
+                0.936
+            ],
+            "angle": 0,
+            "content": "23179"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.089,
+                0.252,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.255,
+                0.099,
+                0.411,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.418,
+                0.099,
+                0.573,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.578,
+                0.089,
+                0.734,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.738,
+                0.099,
+                0.892,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.287,
+                0.892,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Figure 5: Qualitative results of using a single condition for human face images. The included conditions are: (a) text; (b) face parsing maps; (c) sketches; (d) face landmarks; (e) IDs of reference images. Zoom in for best view."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.32,
+                0.273,
+                0.386
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.275,
+                0.32,
+                0.47,
+                0.391
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.396,
+                0.471,
+                0.456
+            ],
+            "angle": 0,
+            "content": "Figure 6: Qualitative results of using a single condition for ImageNet images. Pre-trained diffusion models are: (a) unconditional ImageNet diffusion model; (b) classifier-based ImageNet diffusion model. Zoom in for best view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.473,
+                0.469,
+                0.548
+            ],
+            "angle": 0,
+            "content": "\\(\\succ\\) Classifier-based ImageNet Diffusion Model [10]. The supported image resolution of this model is \\(256 \\times 256\\), and the pre-trained dataset is ImageNet. This model also has a time-dependent classifier to guide its generation process. We experiment with the condition of style images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.549,
+                0.469,
+                0.625
+            ],
+            "angle": 0,
+            "content": "> Stable Diffusion [36]. Stable Diffusion is a widely used Latent Diffusion Model. The standard resolution of its output images is \\(512 \\times 512\\), but it supports higher resolutions. In our work, we use its pre-trained text-to-image model. We experiment with the condition of style images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.625,
+                0.469,
+                0.7
+            ],
+            "angle": 0,
+            "content": "> ControlNet [52]. ControlNet is a Stable Diffusion based model supporting extra conditions input with the original text input. In our work, we use the pre-trained pose-to-image and scribble-to-image models. We experiment with conditions that include face IDs and style images."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.473,
+                0.469,
+                0.7
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.701,
+                0.469,
+                0.746
+            ],
+            "angle": 0,
+            "content": "We choose DDIM [41] with 100 steps as the sampling strategy of all experiments, and other more detailed configurations will be provided in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.757,
+                0.26,
+                0.772
+            ],
+            "angle": 0,
+            "content": "5.2. Qualitative Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Single Condition. We present the single-condition-guided results of human face images in Fig. 5. We can see that the generated results meet the requirements of the given conditions and have rich diversity and good quality. In Fig. 6, we show the single-condition-guided results of the ImageNet domain. The diversity of the generated results is still high. In order to ensure that the generated results can better meet the control of the given conditions, we use the"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.32,
+                0.668,
+                0.405
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.677,
+                0.323,
+                0.887,
+                0.404
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.404,
+                0.668,
+                0.46
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.678,
+                0.404,
+                0.892,
+                0.46
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.46,
+                0.668,
+                0.53
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.677,
+                0.46,
+                0.892,
+                0.53
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.53,
+                0.892,
+                0.598
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.602,
+                0.892,
+                0.662
+            ],
+            "angle": 0,
+            "content": "Figure 7: Qualitative results of using multiple conditions. Pre-trained models are: (a) and (b): unconditional human face diffusion model; (c) and (d): unconditional ImageNet diffusion model. Zoom in for best view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.674,
+                0.755,
+                0.688
+            ],
+            "angle": 0,
+            "content": "proposed efficient time-travel strategy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "- Multiple Conditions. Fig. 7 shows the synthesized results guided by multiple conditions in the domain of human faces and ImageNet. In the human face domain (a small data domain), we produce good results with rich diversity and high consistency with the conditions. We use the efficient time-travel strategy in the ImageNet domain (a large data domain) to produce acceptable results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- Training-free Guidance for Latent Domain. It should be pointed out that FreeDoM supports diffusion models in both image and latent domains. In our work, we experiment with two latent diffusion models: Stable Diffusion [36] and ControlNet [52]. We try to add the training-free conditional interfaces based on their energy functions to work with the existing training-required conditional interfaces, leading to"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "23180"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.089,
+                0.362,
+                0.307
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.366,
+                0.089,
+                0.628,
+                0.307
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.63,
+                0.089,
+                0.891,
+                0.307
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.312,
+                0.893,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Figure 8: Comparison between FreeDoM and TediGAN [49] in three conditional image synthesis tasks: (a) segmentation maps to human faces; (b) sketches to human faces; (c) text prompts to human faces. Zoom in for best view."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.09,
+                0.349,
+                0.459,
+                0.414
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">Segmentation maps</td><td colspan=\"2\">Sketches</td><td colspan=\"2\">Texts</td></tr><tr><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td></tr><tr><td>TediGAN [49]</td><td>2037.2</td><td>52.77</td><td>48.61</td><td>91.11</td><td>12.31</td><td>71.71</td></tr><tr><td>FreeDoM (ours)</td><td>1696.1</td><td>53.08</td><td>33.29</td><td>70.97</td><td>10.83</td><td>55.91</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.424,
+                0.471,
+                0.515
+            ],
+            "angle": 0,
+            "content": "Table 1: We compare FreeDoM with the training-required method TediGAN [49] in three image conditional synthesis tasks. We compute the distance with given conditions and FID to judge the performance. The comparison shows that FreeDoM generates images matching given conditions better and having a comparable or better image quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.528,
+                0.47,
+                0.588
+            ],
+            "angle": 0,
+            "content": "satisfactory results shown in Fig. 1(d)-(f). As such, we can see great application potential for mixing training-free and training-required conditional interfaces in various practical applications."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.602,
+                0.236,
+                0.617
+            ],
+            "angle": 0,
+            "content": "5.3. Further Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.628,
+                0.47,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Comparison between FreeDoM and TediGAN [49]. We compare FreeDoM with the training-required conditional human face generation method TediGAN under three conditions: segmentation maps, sketches, and text. A qualitative comparison is shown in Fig. 8, and quantitative comparison results are reported in Tab. 1. For the comparison, we choose 1000 segmentation maps, 1000 sketches, and 1000 text prompts to generate 1000 results, respectively. Then we compute FID and the average distance with given conditions using the methods introduced in Sec. 4.4 to judge the performance. The comparison shows that the images generated by FreeDoM match the given conditions better and have a comparable or better image quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Comparison between FreeDoM and UGD [2]. We compare FreeDoM with Universal Guidance Diffusion (UGD) [2] in style-guided generations. From Fig. 9, we find that FreeDoM has significant advantages over UGD in the degree of alignment with the conditioned style image."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.628,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.581,
+                0.349,
+                0.891,
+                0.355
+            ],
+            "angle": 0,
+            "content": "\"A fantasy photo of volcanoes\" \"A fantasy photo of a lonely road\"A colorful photo of an Eiffel Towel"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.355,
+                0.887,
+                0.429
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.433,
+                0.893,
+                0.553
+            ],
+            "angle": 0,
+            "content": "Figure 9: Comparison between FreeDoM and UGD [2] in style-guided generation. The UGD results are taken from the original paper. The number in the lower right corner of each image represents its distance with the provided style image (smaller is better), which is calculated using the method described in Sec. 4.4. FreeDoM offers obvious advantages in image quality and in the degree of satisfaction of the conditions. Zoom in for best view."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.695,
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+            "angle": 0,
+            "content": "Figure 10: Demonstration of the effect of different learning rates from small scale to large scale. (a): unconditional ImageNet diffusion models with prompt \"orange\"; (b): unconditional human face diffusion models with a face ID from the reference image. Zoom in for best view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Regarding the inference speed, UGD runs in about 40 minutes (using the open-source code) on a GeForce RTX 3090 GPU to synthesize one image with a resolution of \\(512 \\times 512\\), while we only need about 84 seconds (nearly \\(30 \\times\\) faster)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "□ Effect of different learning rates. We studied the effect of different learning rates on the results. Fig. 10 shows the results while increasing the energy function's learning rate \\((\\rho_{t}\\) in Eq. (10)) from 0. We can see that FreeDoM is scalable"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.498,
+                0.78,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.518,
+                0.937
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+            "angle": 0,
+            "content": "23181"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.123
+            ],
+            "angle": 0,
+            "content": "in terms of its control ability, which means that users can adjust the intensity of control as needed."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.138,
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+            "angle": 0,
+            "content": "6. Conclusions & Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.164,
+                0.47,
+                0.36
+            ],
+            "angle": 0,
+            "content": "We propose a training-free energy-guided conditional diffusion model, FreeDoM, to address a wide range of conditional generation tasks without training. Our method uses off-the-shelf pre-trained time-independent networks to approximate the time-dependent energy functions. Then, we use the gradient of the approximated energy to guide the generation process. Our method supports different diffusion models, including image and latent diffusion models. It is worth emphasizing that the applications presented in this paper are only a subset of the applications FreeDoM supports and should not be limited to these. In future work, we aim to explore even more energy functions for a broader range of tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.362,
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+            ],
+            "angle": 0,
+            "content": "Despite its merits, our FreeDoM method has some limitations: (1) The time cost of the sampling is still higher than the training-required methods because each iteration adds a derivative operation for the energy function, and the timetravel strategy introduces more sampling steps. (2) It is difficult to use the energy function to control the fine-grained structure features in the large data domain. For example, using the Canny edge maps as the conditions may result in poor guidance, even if we use the time-travel strategy. In this case, the training-required methods will provide a better alternative. (3) Eq. 12 deals with multi-condition control and assumes that the provided conditions are independent, which is not necessarily true in practice. When conditions conflict with each other, FreeDoM may produce subpar generation results."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "References"
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\ No newline at end of file
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+# FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model
+
+Jiwen  $\mathbf{Y}\mathbf{u}^{1}$
+
+Yinhuai Wang
+
+<sup>1</sup> Peking University Shenzhen Graduate School {yujiwen, yinhuai}@stu.pku.edu.cn
+
+Chen Zhao $^{2\dagger}$
+
+Bernard Ghanem<sup>2</sup>
+
+Jian Zhang $^{1\dagger}$
+
+$^{2}$  King Abdullah University of Science and Technology (KAUST) {chen.zhao, bernard.ghanem}@kaust.edu.sa
+
+zhangjian.sz@pku.edu.cn
+
+![](images/4be15ce70376e4a9fd65f490456ff4ae02d0b00beec1950199266996ab7c9772.jpg)  
+(a) Training-free visual guidance
+
+![](images/3e7bcc9d3ae5f4cae7fde35f7a615052d76f488aacad75de255ee1d52ed98708.jpg)
+
+![](images/f94b79726c2bcd7f3b99fcdbf802a92697de1d602d82556485bd764a691ed4c8.jpg)
+
+![](images/17e059fc779cee9b0541002180f1de9ec987735ca8358537e75a8a04d01b97fc.jpg)
+
+![](images/a7abd912a23777adafaca3e9dcd18978fa8a7c454abca8fb0d89c7188e1cfae0.jpg)
+
+![](images/e68a55ff4cb05afd11add157bd978e6cb121f19628c1a298bfbd649fea9c7e31.jpg)
+
+![](images/bf0d03e3ffbb9a1d96948e5411201983047a1618f1e6a99c5aa5d2f6843d9a46.jpg)  
+(b) Training-free multi-source guidance  
+Face IDs
+
+![](images/e05f191f5b7cf41130e507c60311dc746b1341eb4a793490ffb2285f95c5b33e.jpg)
+
+![](images/f2d6cdc30c85917ea935c9ebe2c1cfc05988bca1dc5e5af7f12d03fa0af30995.jpg)
+
+![](images/7aded158d9b9bdd873b3845bc749763339953930120d4f5e16f678b82ef897b1.jpg)  
+Face IDs
+
+![](images/fecea1bb10c628bf37d3da18b45a0de01e0aee11e082b0f38f231fa1ca4569a9.jpg)
+
+![](images/673ec7d0a4615085597368ea70d4c58a8334a015781e86cdb30a96e9e59edc52.jpg)
+
+![](images/55976db496a7d263d64cbe214f0b2da100da1db53e284688ba111463bcab3087.jpg)  
+"old man"
+
+![](images/11b0c3cc4e55eac543e25fa4d1bc4c1d4788e5be89a8a9e70357eb776e81431f.jpg)
+
+![](images/99e873d60497155a8af1d50c96e5c384c3b891f183672b761fd0239ac0902372.jpg)  
+"old woman with makeup"
+
+![](images/0d05cbf6cd0b462495286ab35c00934ede3d5b0bf2d806ba42e4fda23a837c39.jpg)
+
+![](images/9c2904d540dba4e579cb35d3f4412c2cc1036f4341afb92d8efdcf04dd02b8e1.jpg)  
+(c) Training-free text guidance
+
+![](images/4c538d7097baa457eda04d7efe70bbc3157d3833fd046caaaa3a3cb96d1275fb.jpg)
+
+![](images/ed0063dadc19f8d0884d408d6404cf03cd99d68570e17a4b932ff3edff1369cf.jpg)
+
+![](images/4110e2d08f193abef7c74d2dafb914061b4f6ce06a677e8ac9a020f8e0454fa8.jpg)
+
+![](images/57c111e004e0872cf15184c16919fae3cce2a0b548403e1acd4a4de1047ad855.jpg)
+
+![](images/74aaff40553971dc9bac2be62ee1e00216ae64bdba81a72b67459ab7ffd5d4aa.jpg)  
+(d) Training-free style guidance + ControlNet
+
+![](images/b0a750c0d79beb9bbcab0bdc3bde0f1b93c9abdec50732b9fe28b2df9a45e433.jpg)
+
+![](images/f78cca242af361c4b6c046ca4e3c4235e0c6bbe6ee5f05f19348e227a98f2d17.jpg)  
+(e) Training-free face ID guidance + Human Pose ControlNet
+
+![](images/ab434e84906bc9e2314e20abe6ca5b20e94d7f41cc4b8cac1b1f4eff07a8da44.jpg)
+
+![](images/b360048e1a6b1f98de96ab751e57abeeccb60094f09498ec6cb3ab83e45b00cd.jpg)
+
+![](images/464cf246756e669cf90dae79f8d3d9a125dbf0054e59e31ecf20b95b9cf53ba4.jpg)
+
+![](images/32dc5a6951c5c947f4e3aa700a76c129f24816f7db4370ed8078f389a7f79e2a.jpg)
+
+![](images/e4a3930518d3c7b0cbfc2940aae016bb2b93b97933337980421eb7140f93fbf3.jpg)
+
+![](images/66969e1f4717b6a75b1cc38cf1b66fdb1a645b599c79a5fec16ccde662538f13.jpg)
+
+![](images/187b6870792a6ea50af790a17be2b1bd1a5354820374b705fde13cba51b95da4.jpg)
+
+![](images/276b8b221dae01cb5157704584285f637d446b19fcc3fa21b58d577e49ef593d.jpg)
+
+![](images/df891ec23313f163303120512375c4fdc486ddf76851c644129afc23b69c8867.jpg)  
+(f) Training-free style guidance + Stable Diffusion  
+"cat sitting on the grass"
+
+![](images/316606184db06182396fdb54b5c4a0e08b086b56db8ec9d6e1db232a05b64223.jpg)
+
+![](images/c35a1dd4d269f4b2444f87f0b99456bfa34f24213e2079bcc025fbced69210d2.jpg)  
+"astronaut rides horse"
+
+![](images/669ac504d98e0f340c5deb9bf1354a9adc71e1a89a046276bb9f8fefece03cbd.jpg)
+
+![](images/c90b7cb6eacb9941deb7d973a4197cfb63dcc7b9da6b16bf16e35c6369f06f35.jpg)  
+"dog wearing glasses"
+
+![](images/5c6c5db9e73812729db32bb86eba79f3f92a54e5aa837bd946c507ccc9e53679.jpg)  
+Figure 1: FreeDoM controls the generation process of diffusion models in a training-free way. Here, we demonstrate some results of the applications FreeDoM supports. Part (a)-(c) show various face editing applications with training-free guidance. (a) We use the segmentation map, sketch, landmarks, and face ID as conditions to guide the generation process of an unconditional diffusion model; (b) We combine different conditions to control the generation process. (c) We use CLIP [34] based text guidance to control image synthesis and editing. For editing, we use the segmentation masks to limit the editing areas (see Fig. 4 for details); Part (d)-(f) show that training-free guidance can work with other training-required conditional diffusion models, like Stable Diffusion [36] and ControlNet [52], to achieve a more sophisticated control mechanism. The conditions of scribbles in (d), human poses in (e), and prompt texts in (f) are controlled by the training-required interfaces provided by ControlNet and Stable Diffusion. Training-free energy functions control the conditions of face IDs from the reference images in (e) and style images in (d) and (f). Zoom in for best view.
+
+![](images/1056471452db2301e04f26245cf699e3a7269481975a61e8246d24d0c1821ec2.jpg)  
+"cat rides bicycle"
+
+![](images/1cde348e6a6fd951b56bfbd8199b01b001d290d63415c72c780d3e8412d79e41.jpg)
+
+# Abstract
+
+Recently, conditional diffusion models have gained popularity in numerous applications due to their exceptional generation ability. However, many existing methods are training-required. They need to train a time-dependent classifier or a condition-dependent score estimator, which increases the cost of constructing conditional diffusion models and is inconvenient to transfer across different conditions. Some current works aim to overcome this limitation by proposing training-free solutions, but most can only be applied to a specific category of tasks and not to more general conditions. In this work, we propose a training-Free conditional Diffusion Model (FreeDoM) used for various conditions. Specifically, we leverage off-the-shelf pretrained networks, such as a face detection model, to construct time-independent energy functions, which guide the generation process without requiring training. Furthermore, because the construction of the energy function is very flexible and adaptable to various conditions, our proposed FreeDoM has a broader range of applications than existing training-free methods. FreeDoM is advantageous in its simplicity, effectiveness, and low cost. Experiments demonstrate that FreeDoM is effective for various conditions and suitable for diffusion models of diverse data domains, including image and latent code domains. Code is available at https://github.com/vvictoryuki/FreeDoM.
+
+# 1. Introduction
+
+Recently, diffusion models have been demonstrated to outperform previous state-of-the-art generative models [10], such as GANs [12, 29, 3, 22, 24, 23]. The impressive generative power of diffusion models [15, 43, 45] has motivated researchers to apply diffusion models to various downstream tasks. Conditional generation is one of the most popular focus areas. Conditional diffusion models (CDMs) with diverse conditions have been proposed, such as text [20, 1, 13, 26, 36, 40, 35, 38, 25, 32], class labels [10], degraded images [5, 6, 7, 8, 19, 27, 42, 44, 47, 37, 39, 48], segmentation maps [31, 52], landmarks [31, 52], hand-drawn sketches [31, 52], style images [31, 52], etc. These CDMs can be roughly divided into two categories: training-required or training-free.
+
+A typical type of training-required CDMs trains a time-dependent classifier to guide the noisy image  $\mathbf{x}_t$  toward the given condition  $\mathbf{c}$  [10, 32, 53, 26]. Another branch of
+
+training-required CDMs directly trains a new score estimator  $s(\mathbf{x}_t, t, \mathbf{c})$  conditioned on  $\mathbf{c}$  [31, 16, 36, 37, 39, 48, 52, 20, 1, 13, 35, 32]. These methods yield impressive performance but are not flexible. Once a new target condition is needed for generation, they have to retrain or finetune the models, which is inconvenient and expensive.
+
+In contrast, training-free CDMs try to solve the same problems without extra training. [30, 11, 14] attempt to use the cross-attention control to realize the conditional generation; [5, 6, 7, 8, 19, 27, 42, 44, 47, 46] directly modify the intermediate results to achieve zero-shot image restoration; [28] realizes image translation by adjusting the initial noisy images. While these methods are effective in a single application, they are difficult to generalize to a wider range of conditions, e.g., style, face ID, and segmentation masks.
+
+In order to make CDMs support a wide range of conditions in a training-free manner, this paper proposes a training-Free conditional Diffusion Model (FreeDoM) with the following two key points. Firstly, to emphasize generalization, we propose a sampling process guided by the energy function [53, 21], which is very flexible to construct and can be applied to various conditions. Secondly, to make the proposed method training-free, we use off-the-shelf pre-trained time-independent models, which are easily accessible online, to construct the energy function.
+
+Our FreeDoM has the following advantages: (1) Simple and effective. We only insert a derivative step of the energy function gradient into the unconditional sampling process of the original diffusion models. Extensive experiments show its effective controlling capability. (2) Low cost and efficient. The energy functions we construct are time-independent and do not need to be retrained. The diffusion models we choose do not need to be trained on the desired conditions. Thanks to the efficient time-travel strategy we use for large data domains, the number of sampling steps we use is quite small, which speeds up the sampling process while ensuring good generated results. (3) Amenable to a wide range of applications. The conditions our method supports include, but are not limited to, text, segmentation maps, sketches, landmarks, face IDs, style images, etc. In addition, various complex but interesting applications can be realized by combining multiple conditions. (4) Supports different types of diffusion models. Regardless of the considered data domain, such as human face images, images in ImageNet, or latent codes extracted from an image encoder, extensive experiments demonstrate that our method does well on all of them.
+
+# 2. Related Work
+
+# 2.1. Training-Required Methods
+
+The training-required methods can obtain strong control generation ability thanks to supervised learning with
+
+data pairs. One of the most prominent applications of these methods is the text-to-image task. The most widely used text-to-image model, Stable Diffusion [36], generates high-quality images that conform to the text description by inputting a prompt text. Recent works, such as ControlNet [52] and T2I-Adapter [31], have introduced more training-required conditional interfaces to Stable Diffusion, such as edge maps, segmentation maps, depth maps, etc.
+
+Although these training-required methods can achieve satisfactory control results under trained conditions, the cost of training is still a factor to be considered, especially for the scenario that requires more complex control with multiple conditions. The training-required method is not the cheapest or most convenient solution in practical applications.
+
+# 2.2. Training-Free Methods
+
+The training-free methods develop various interesting technologies to realize the training-free condition generation on some tasks exploiting the unique nature of the diffusion model, namely, the iterative denoising process. [14] proposes to inject the target cross attention maps to the source cross attention maps to solve the prompt-to-prompt task without training. The limitation of this method is that a text prompt is needed to anchor the content of the image to be edited in advance. DDNM [47] proposes to use the Range-Null Space Decomposition to modify the intermediate results to solve the image restoration in a training-free way. It is based on the degradation operators of image restoration tasks and is hard to be adopted in other applications. SDEdit [28] proposes to adjust the initial noisy images to control the generation process, which is useful in stroke-based image synthesis and editing. Its limitation is that the guidance of stroke is not precise and versatile.
+
+According to the limitations mentioned above, the training-free CDMs for a broad range of applications need to be studied urgently. We have noticed some recent efforts [33, 2] in this area. Our FreeDoM has a faster generation speed and applies to a broader range of applications.
+
+# 3. Preliminaries
+
+# 3.1. Score-based Diffusion Models
+
+Score-based Diffusion Models (SBDMs) [43, 45] are a kind of diffusion model based on score theory, which reveals that the essence of diffusion models is to estimate the score function  $\nabla_{\mathbf{x}_t}\log p(\mathbf{x}_t)$ , where  $\mathbf{x}_t$  is noisy data. During the sampling process, SBDMs predict  $\mathbf{x}_{t - 1}$  from  $\mathbf{x}_t$  using the estimated score step by step. In our work, we resort to discrete SBDMs with the setting of DDPM [15] and its sampling formula is:
+
+$$
+\mathbf {x} _ {t - 1} = \left(1 + \frac {1}{2} \beta_ {t}\right) \mathbf {x} _ {t} + \beta_ {t} \nabla_ {\mathbf {x} _ {t}} \log p (\mathbf {x} _ {t}) + \sqrt {\beta_ {t}} \boldsymbol {\epsilon}, \tag {1}
+$$
+
+where  $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$  is randomly sampled Gaussian noise and  $\beta_{t}\in \mathbb{R}$  is a pre-defined parameter. In actual implementation, the score function will be estimated using a score estimator  $s(\mathbf{x}_t,t)$ , that is,  $s(\mathbf{x}_t,t)\approx \nabla_{\mathbf{x}_t}\log p(\mathbf{x}_t)$ . However, the original diffusion models can only serve as an unconditional generator with randomly synthesized results.
+
+# 3.2. Conditional Score Function
+
+In order to adapt the generative power of the diffusion models to different downstream tasks, conditional diffusion models (CDMs) are needed. SDE [45] proposed to control the generated results with a given condition  $\mathbf{c}$  by modifying the score function as  $\nabla_{\mathbf{x}_t} \log p(\mathbf{x}_t | \mathbf{c})$ . Using the Bayesian formula  $p(\mathbf{x}_t | \mathbf{c}) = \frac{p(\mathbf{c} | \mathbf{x}_t) p(\mathbf{x}_t)}{p(\mathbf{c})}$ , we can rewrite the conditional score function as two terms:
+
+$$
+\nabla_ {\mathbf {x} _ {t}} \log p (\mathbf {x} _ {t} | \mathbf {c}) = \nabla_ {\mathbf {x} _ {t}} \log p (\mathbf {x} _ {t}) + \nabla_ {\mathbf {x} _ {t}} \log p (\mathbf {c} | \mathbf {x} _ {t}), \tag {2}
+$$
+
+where the first term  $\nabla_{\mathbf{x}_t}\log p(\mathbf{x}_t)$  can be estimated using the pre-trained unconditional score estimator  $s(\cdot ,t)$  and the second term  $\nabla_{\mathbf{x}_t}\log p(\mathbf{c}|\mathbf{x}_t)$  is the critical part of constructing conditional diffusion models. We can interpret the second term  $\nabla_{\mathbf{x}_t}\log p(\mathbf{c}|\mathbf{x}_t)$  as a correction gradient, pointing  $\mathbf{x}_t$  to a hyperplane in the data space, where all data are compatible with the given condition c. Classifier-based methods [10, 32, 53, 26] train a time-dependent classifier to compute this correction gradient for conditional guidance.
+
+# 3.3. Energy Diffusion Guidance
+
+Modeling the correction gradient  $\nabla_{\mathbf{x}_t}\log p(\mathbf{c}|\mathbf{x}_t)$  remains an open question. A flexible and straightforward way is resorting to the energy function [53, 21] as follows:
+
+$$
+p (\mathbf {c} | \mathbf {x} _ {t}) = \frac {\exp \left\{- \lambda \mathcal {E} (\mathbf {c} , \mathbf {x} _ {t}) \right\}}{Z}, \tag {3}
+$$
+
+where  $\lambda$  denotes the positive temperature coefficient and  $Z > 0$  denotes a normalizing constant, computed as  $Z = \int_{\mathbf{c} \in \mathcal{C}} \exp\{-\lambda \mathcal{E}(\mathbf{c}, \mathbf{x}_t)\}$  where  $\mathcal{C}$  denotes the domain of the given conditions.  $\mathcal{E}(\mathbf{c}, \mathbf{x}_t)$  is an energy function that measures the compatibility between the condition  $\mathbf{c}$  and the noisy image  $\mathbf{x}_t$  — its value will be smaller when  $\mathbf{x}_t$  is more compatible with  $\mathbf{c}$ . If  $\mathbf{x}_t$  satisfies the constraint of  $\mathbf{c}$  perfectly, the energy value should be zero. Any function satisfying the above property can serve as a feasible energy function, with which we just need to adjust the coefficient  $\lambda$  to obtain  $p(\mathbf{c} | \mathbf{x}_t)$ .
+
+Therefore, the correction gradient  $\nabla_{\mathbf{x}_t}\log p(\mathbf{c}|\mathbf{x}_t)$  can be implemented with the following:
+
+$$
+\nabla_ {\mathbf {x} _ {t}} \log p (\mathbf {c} | \mathbf {x} _ {t}) \propto - \nabla_ {\mathbf {x} _ {t}} \mathcal {E} (\mathbf {c}, \mathbf {x} _ {t}), \tag {4}
+$$
+
+which is referred to as energy guidance. With Eq. (1), Eq. (2), and Eq. (4), we get the conditional sampling:
+
+$$
+\mathbf {x} _ {t - 1} = \mathbf {m} _ {t} - \rho_ {t} \nabla_ {\mathbf {x} _ {t}} \mathcal {E} (\mathbf {c}, \mathbf {x} _ {t}), \tag {5}
+$$
+
+where  $\mathbf{m}_t = (1 + \frac{1}{2}\beta_t)\mathbf{x}_t + \beta_t\nabla_{\mathbf{x}_t}\log p(\mathbf{x}_t) + \sqrt{\beta_t}\epsilon,$  and  $\rho_{t}$  is a scale factor, which can be seen as the learning rate of the correction term. Eq. (5) is a generic formulation of conditional diffusion models, which enables the use of different energy functions.
+
+# 4. The Proposed FreeDoM Method
+
+In Sec. 4.1, we approximate the time-dependent energy function using time-independent distance measuring functions, making our method training-free and flexible for various conditions. In Sec. 4.2, we first analyze the reason why the energy guidance fails in a large data domain and then propose an efficient version of the time-travel strategy [27, 47]. In Sec. 4.3, we describe the details of how to construct the energy functions. In Sec. 4.4, we provide specific examples of supported conditions.
+
+# 4.1. Approximate Time-Dependent Energy
+
+We use the energy function to guide the generation due to its flexibility to construct and suitability to various conditions. Existing classifier-based methods [10, 32, 53, 26] choose time-dependent distance measuring functions  $\mathcal{D}_{\phi}(\mathbf{c},\mathbf{x}_t,t)$  to approximate the energy functions as follows:
+
+$$
+\mathcal {E} (\mathbf {c}, \mathbf {x} _ {t}) \approx \mathcal {D} _ {\phi} (\mathbf {c}, \mathbf {x} _ {t}, t), \tag {6}
+$$
+
+where  $\phi$  defines the pre-trained parameters.  $\mathcal{D}_{\phi}(\mathbf{c},\mathbf{x}_t,t)$  computes the distance between the given condition  $\mathbf{c}$  and noisy intermediate results  $\mathbf{x}_t$ . The distance measuring functions for noisy data  $\mathbf{x}_t$  cannot be directly constructed because it is difficult to find an existing pre-trained network for noisy images. In this case, we have to train (or finetune) a time-dependent network for each type of condition.
+
+Compared with time-dependent networks, time-independent distance measuring functions for clean data  $\mathbf{x}_0$  are widely available. Many off-the-shelf pre-trained networks such as classification networks, segmentation networks, and face ID encoding networks are open-source and work well on clean images. We denote these distance measuring networks for clean data as  $\mathcal{D}_{\theta}(\mathbf{c},\mathbf{x}_0)$ , where  $\pmb{\theta}$  denotes their pre-trained parameters. To use these networks for the energy functions, a straightforward way is to approximate  $\mathcal{D}_{\phi}(\mathbf{c},\mathbf{x}_t,t)$  using  $\mathcal{D}_{\theta}(\mathbf{c},\mathbf{x}_0)$ , formulated as:
+
+$$
+\mathcal {D} _ {\phi} (\mathbf {c}, \mathbf {x} _ {t}, t) \approx \mathbb {E} _ {p \left(\mathbf {x} _ {0} \mid \mathbf {x} _ {t}\right)} \left[ \mathcal {D} _ {\boldsymbol {\theta}} (\mathbf {c}, \mathbf {x} _ {0}) \right]. \tag {7}
+$$
+
+Eq. (7) is reasonable because if the distance between the noise image  $\mathbf{x}_t$  and the condition  $\mathbf{c}$  is small, the clean image  $\mathbf{x}_0$  corresponding to the noise image  $\mathbf{x}_t$  should also have a small distance with the condition  $\mathbf{c}$ , especially during the late stage of the sampling process when the noise level of  $\mathbf{x}_t$  is relatively small. However, during the sampling process, it is infeasible to get the clean image  $\mathbf{x}_0$  corresponding to
+
+# Algorithm 1 Sampling Process of our proposed FreeDoM
+
+Require: condition  $\mathbf{c}$ , unconditional score estimator  $s(\cdot, t)$ , time-independent distance measuring function  $\mathcal{D}_{\theta}(\mathbf{c}, \cdot)$ , pre-defined parameters  $\beta_{t}$ ,  $\bar{\alpha}_{t}$  and learning rate  $\rho_{t}$ .
+
+1:  $\mathbf{x}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$  
+2: for  $t = T, \ldots$  
+3:  $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$  if  $t > 1$ , else  $\epsilon = 0$ .  
+4:  $\mathbf{x}_{t - 1} = (1 + \frac{1}{\beta}\beta_{t})\mathbf{x}_{t} + \beta_{t}s(\mathbf{x}_{t},t) + \sqrt{\beta_{t}}\pmb{\epsilon}$  
+5:  $\mathbf{x}_{0|t} = \frac{1}{\sqrt{\alpha_t}} (\mathbf{x}_t + (1 - \bar{\alpha}_t)s(\mathbf{x}_t,t))$  
+6:  $\pmb{g}_t = \nabla_{\mathbf{x}_t} \mathcal{D}_{\pmb{\theta}}(\mathbf{c}, \mathbf{x}_{0|t}(\mathbf{x}_t)))$  
+7:  $\mathbf{x}_{t - 1} = \mathbf{x}_{t - 1} - \rho_t\pmb {g}_t$  
+8: return  $\mathbf{x}_0$
+
+![](images/fed56280b321b926ec3aa3e3f79197212ddebe75de9f14fb7109aa63eb49ebfa.jpg)  
+(a) Badly Generated Results  
+(b) Generated Results with the Time-Travel Strategy  
+Figure 2: Comparison of results generated before and after using the time-travel strategy. The prompt is "orange". We can see that the results in (a) do not match the given conditions. After using the time-travel strategy, we get better results in (b).
+
+an intermediate noisy result  $\mathbf{x}_t$ , so we need to approximate  $\mathbf{x}_0$ . Considering the expectation of  $p(\mathbf{x}_0|\mathbf{x}_t)$  [6]:
+
+$$
+\mathbf {x} _ {0 \mid t} := \mathbb {E} [ \mathbf {x} _ {0} | \mathbf {x} _ {t} ] = \frac {1}{\sqrt {\bar {\alpha} _ {t}}} (\mathbf {x} _ {t} + (1 - \bar {\alpha} _ {t}) s (\mathbf {x} _ {t}, t)), \tag {8}
+$$
+
+where  $\bar{\alpha}_t = \prod_{i=1}^t (1 - \beta_i)$  and  $s(\cdot, t)$  is the pre-trained score estimator. According to Eq. (8), from  $\mathbf{x}_t$ , we can estimate the clean image denoted as  $\mathbf{x}_{0|t}$ . Then with Eq. (6) and Eq. (7), we can approximate the time-dependent energy function of noisy data  $\mathbf{x}_t$ :
+
+$$
+\mathcal {E} (\mathbf {c}, \mathbf {x} _ {t}) \approx \mathcal {D} _ {\boldsymbol {\theta}} (\mathbf {c}, \mathbf {x} _ {0 | t}). \tag {9}
+$$
+
+According to Eq. (5) and Eq. (9), the approximated sampling process can be written as:
+
+$$
+\mathbf {x} _ {t - 1} = \mathbf {m} _ {t} - \rho_ {t} \nabla_ {\mathbf {x} _ {t}} \mathcal {D} _ {\boldsymbol {\theta}} (\mathbf {c}, \mathbf {x} _ {0 | t} (\mathbf {x} _ {t})), \tag {10}
+$$
+
+and the detailed algorithm is shown in Algo. 1.
+
+# 4.2. Efficient Time-Travel Strategy
+
+In the process of applying Algo. 1, we find that the performance varies significantly on different data domains. For small data domains such as human faces, Algo. 1 can effectively produce results that satisfy the given conditions within 100 DDIM [41] sampling steps. However, for large data domains such as ImageNet, we often get results that are not closely related to the given conditions or even randomly generated results (shown in Fig. 2(a)). We attribute
+
+![](images/b700a5523d50f81b3f1f7f609e6a92f6f26bd349eb7c9ebc9afb701b6ccabc8d.jpg)  
+Figure 3: Demonstration of the importance of different sampling stages. Most of the semantic content is generated during the semantic stage, so we only employ the time-travel strategy in this stage to achieve an efficient version of FreeDoM. The shown images are  $\mathbf{x}_{0|t}$  generated by diffusion models pre-trained on the ImageNet data domain.
+
+the failure of Algo. 1 on large data domains to poor guidance. The reason for poor guidance is that the direction of unconditional score generated by diffusion models in large data domains has more freedom, making it easier to deviate from the direction of conditional control. To solve this problem, we adopt the time-travel strategy [27, 47], which has been empirically shown to inhibit the generation of disharmonious results when solving hard generation tasks.
+
+The time-travel strategy is a technique that takes the current intermediate result  $\mathbf{x}_t$  back by  $j$  steps to  $\mathbf{x}_{t + j}$  and resamples it to the  $t$ -th timestep again. This strategy inserts more sampling steps into the sampling process and refines the generated results. In our experiments specifically, we go back by  $j = 1$  step each time and resample. We repeat this resampling process  $r_t$  times at the  $t$ -th timestep. Our experiments demonstrate that the time travel strategy is effective in solving the poor guidance problem (shown in Fig. 2(b)). However, the time cost is also expensive because the number of sampling steps is larger, especially considering that each timestep will include the cost of calculating the gradient of the energy function.
+
+Fortunately, we find that the time-travel strategy does not have the same effect in each time step. In fact, using this technique in most time steps will not significantly modify the final result, which means we can use this strategy only in a small portion of the timesteps, thus significantly reducing the number of additional iteration steps. In Fig. 3, we try to analyze this phenomenon by dividing the sampling process into three stages. In the early stage, i.e., the chaotic stage, the generated result  $\mathbf{x}_{0|t}$  is extremely blurred, and the energy guidance is hard to make anything reasonable, so we do not need to employ the time-travel strategy. During the late stage, i.e., the refinement stage, the change in the generated results is minor, so the time-travel strategy is useless. During the intermediate stage, i.e., the semantic stage, the change in the generated result is significant, so this stage is critical for conditional generation. Based on this observation, we only apply the time-travel strategy in the semantic stage to implement efficient sampling while solving the problem of poor guidance. The range of the semantic stage is an experimental choice depending on the specific dif
+
+# Algorithm 2 FreeDoM + Efficient Time-Travel Strategy
+
+Require: condition  $\mathbf{c}$ , unconditional score estimator  $s(\cdot, t)$ , time-independent distance measuring function  $\mathcal{D}_{\theta}(\mathbf{c}, \cdot)$ , pre-defined parameters  $\beta_t, \bar{\alpha}_t$ , learning rate  $\rho_t$ , and the repeat times of time travel of each step  $\{r_1, \dots, r_T\}$ .
+
+1:  $\mathbf{x}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$  
+2: for  $t = T, \dots, 1$  do  
+3: for  $i = r_t,\dots,1$  do  
+4:  $\epsilon_{1} \sim \mathcal{N}(\mathbf{0},\mathbf{I})$  if  $t > 1$ , else  $\epsilon_{1} = \mathbf{0}$ .  
+5:  $\mathbf{x}_{t - 1} = (1 + \frac{1}{2}\beta_t)\mathbf{x}_t + \beta_t s(\mathbf{x}_t,t) + \sqrt{\beta_t}\epsilon_1$  
+6:  $\mathbf{x}_{0|t} = \frac{1}{\sqrt{\bar{\alpha}_t}} (\bar{\mathbf{x}}_t + (1 - \bar{\alpha}_t)s(\mathbf{x}_t,t))$  
+7:  $\pmb{g}_{t} = \nabla_{\mathbf{x}_{t}}\mathcal{D}_{\pmb{\theta}}(\mathbf{c},\mathbf{x}_{0|t}(\mathbf{x}_{t})))$  
+8:  $\mathbf{x}_{t - 1} = \mathbf{x}_{t - 1} - \rho_t\pmb {g}_t$  
+9: if  $i > 1$  then  
+10:  $\epsilon_{2}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$  
+11:  $\mathbf{x}_t = \sqrt{1 - \beta_t}\mathbf{x}_{t-1} + \sqrt{\beta_t}\pmb{\epsilon}_2$  
+12: return  $\mathbf{x}_0$
+
+fusion models we choose. The detailed algorithm of our proposed FreeDoM with the efficient time-travel strategy is shown in Algo.2, where  $r_t = 1$  means we do not apply the time-travel strategy in the  $t$ -th timestep.
+
+# 4.3. Construction of the Energy Function
+
+- Single Condition Guidance. To incorporate in specific applications, we use the distance measuring function conforming to the following structure to construct the energy function:
+
+$$
+\mathcal {E} (\mathbf {c}, \mathbf {x} _ {t}) \approx \mathcal {D} _ {\boldsymbol {\theta}} (\mathbf {c}, \mathbf {x} _ {0 | t}) = \operatorname {D i s t} \left(\mathcal {P} _ {\boldsymbol {\theta} _ {1}} (\mathbf {c}), \mathcal {P} _ {\boldsymbol {\theta} _ {2}} (\mathbf {x} _ {0 | t})\right), \tag {11}
+$$
+
+where  $Dist(\cdot)$  denotes the distance measuring methods like Euclidean distance, and  $\pmb{\theta} = \{\pmb{\theta}_1,\pmb{\theta}_2\}$ .  $\mathcal{P}_{\theta_1}(\cdot)$  and  $\mathcal{P}_{\theta_2}(\cdot)$  project the condition and image to the same space for distance measurement. These projection networks can be off-the-shelf pre-trained classification networks, segmentation networks, etc. In most cases, we only need one network to project the clean image  $\mathbf{x}_{0|t}$  to the condition space. In the cases with reference images  $\mathbf{x}_{ref}$ , we also only need one feature encoder to project the reference image  $\mathbf{x}_{ref}$  and  $\mathbf{x}_{0|t}$  to the same feature space.
+
+- Multi Condition Guidance. In some more involved applications, multiple conditions can be available to provide control over the generated results. Take the image style transfer task as an example. Here, we have two conditions: the structure information from the source image and
+
+![](images/c75b8984dc8f96e4b2954498df0c519d1fea6148aa8c7d86271d957c049c7353.jpg)  
+Original Image
+
+![](images/266cc80ac7fb2a00cadc1c8d232929d2459bf5183d747be6901bf4117067fd7e.jpg)  
+Mask
+
+![](images/29a1a4f4abf5c530ddaab2d935cdbad9d1a0a93abbb4089987f2141cadd2bb90.jpg)  
+"Lipstick"
+
+![](images/51742c8b82d252c5ae76e66fb6de30a71f4c9e846df04f547fb0ee81c55e7c4e.jpg)  
+Original Image
+
+![](images/11cbc55c6cbc18000614d965693538c499de647a913499e9345bbea62550bef5.jpg)  
+Mask
+
+![](images/883f29a19a9fee0d5ca3a45b0ff3a429d16b3c098f7e584285971d6f604dd9eb.jpg)  
+"Pale lips"
+
+![](images/a89f1bb523a9e3e4b4bed88c95978ff50055984e5af1dcbdbd3ae1b8e14d9e9d.jpg)  
+Original Image
+
+![](images/ef64e94a6b68df0b12e27fcb465c9b2713e0ce1e69394cb66c78bf06759e1ba0.jpg)  
+Mask
+
+![](images/24466b41a925c2fb6956bb9c4ec6f30884ba7de8e9dd614859ac0a4725ad6c8f.jpg)  
+"Straight hair"
+
+![](images/8c2476291a1e4e9faa79ec110babba4492e6e6360af5f913102aca2cb4cb610a.jpg)  
+Original Image  
+Figure 4: Practical usage of face parsing maps. We can limit the gradient of the energy function to update the image only in the target semantic region indicated by the mask so that other regions remain unchanged while editing.
+
+![](images/7eb1adcab9a7d1be29a12dac3f80a5de251aa54f5e649d2cf4d43e5f078d5832.jpg)  
+Mask
+
+![](images/e19ce3c30184588f7dd51014ecd0df32e1e4055eb7f0f9ae40ce6b040b2200e5.jpg)  
+"Red hair"
+
+the style information from the style image. In these multi-condition cases, assume that the given conditions are denoted as  $\{\mathbf{c}_1,\dots ,\mathbf{c}_n\}$ , we can approximately construct the energy function as:
+
+$$
+\begin{array}{l} \mathcal {E} \left(\left\{\mathbf {c} _ {1}, \dots , \mathbf {c} _ {n} \right\}, \mathbf {x} _ {t}\right) \\ \approx \eta_ {1} \mathcal {D} _ {\boldsymbol {\theta} _ {1}} \left(\mathbf {c} _ {1}, \mathbf {x} _ {0 | t}\right) + \dots + \eta_ {n} \mathcal {D} _ {\boldsymbol {\theta} _ {n}} \left(\mathbf {c} _ {n}, \mathbf {x} _ {0 | t}\right), \tag {12} \\ \end{array}
+$$
+
+where  $\eta_{i}$  is the weighting factor. We use different distance measuring functions  $\{\mathcal{D}_{\theta_1}(\cdot ,\cdot),\dots ,\mathcal{D}_{\theta_n}(\cdot ,\cdot)\}$  for specific conditions and sum the whole for gradient computation.
+
+Guidance for Latent Diffusion. Our method applies not only to image diffusions but also to latent diffusions, such as Stable Diffusion [36]. In this case, the intermediate results  $\mathbf{x}_t$  are latent codes rather than images. We can use the latent decoder to project the generated latent codes to images and then use the same algorithm in the image domain.
+
+# 4.4. Specific Examples of Supported Conditions
+
+$\square$  Text. For given text prompts, we construct the distance measuring function based on CLIP [34]. Specifically, we take the CLIP image encoder (as  $\mathcal{P}_{\theta_2}(\cdot)$ ) and the CLIP text encoder (as  $\mathcal{P}_{\theta_1}(\cdot)$ ) to project the image  $\mathbf{x}_{0|t}$  and given text in the same CLIP feature space. Compared with the commonly used cosine distance measurement and for simplicity, we choose the  $\ell_2$  Euclidean distance measurement, since the sampling quality in our experiments is not significantly different.  
+□ Segmentation Maps. For segmentation maps, we choose a face parsing network based on the real-time semantic segmentation network BiSeNet [51] to generate the parsing map of an input human face and directly compute the  $\ell_2$  Euclidean distance between the given parsing map and the parsing results of  $\mathbf{x}_{0|t}$ . An interesting usage of the face parsing network is to constrain the gradient update region so that we can edit the target semantic region without changing other regions (shown in Fig. 4).  
+Sketches. We choose an open-source pre-trained network [50] that transfers a given anime image to the style
+
+of hand-drawn sketches. Experiments prove that the network is still effective for real-world images. We use the  $\ell_2$  Euclidean distance to compare the given sketches with transferred sketch-style results of  $\mathbf{x}_{0|t}$ .
+
+$\square$  Landmarks. We use an open-source pre-trained human face landmark detection network [4] for this application. The detection network has two stages: the first stage finds the position of the center of a face and the second stage marks the landmarks of this detected face. We compute the  $\ell_2$  Euclidean distance between predicted face landmarks of  $\mathbf{x}_{0|t}$  and the given landmarks condition, and only use the gradient in the face area detected in the first stage to update the intermediate results.  
+$\square$  Face IDs. We use ArcFace [9], an open-source pretrained human face recognition network, to extract the target features of reference faces to represent face IDs and compute the  $\ell_2$  Euclidean distance between the extracted ID features of  $\mathbf{x}_{0|t}$  and those of the reference image.  
+- Style Images. The style image is denoted as  $\mathbf{x}_{style}$ . We use the following equation to compute the distance of the style information between  $\mathbf{x}_{style}$  and  $\mathbf{x}_{0|t}$ :
+
+$$
+\operatorname {D i s t} \left(\mathbf {x} _ {\text {s t y l e}}, \mathbf {x} _ {0 | t}\right) = \left| \left| G \left(\mathbf {x} _ {\text {s t y l e}}\right) _ {j} - G \left(\mathbf {x} _ {0 | t}\right) _ {j} \right| \right| _ {F} ^ {2}, \tag {13}
+$$
+
+where  $G(\cdot)_{j}$  denotes the Gram matrix [17] of the  $j$ -th layer feature map of an image encoder. In our experiments, we choose the features from the third layer of the CLIP image encoder to generate satisfactory results.
+
+- Low-pass Filters. For the image transferring task, we need an energy function to constrain the generated results conforming to the structure information of the source image  $\mathbf{x}_{source}$ . Similar to EGSDE [53] and ILVR [5], we choose a low-pass filter  $\mathcal{K}(\cdot)$  in this setup. The distance between the source image  $\mathbf{x}_{source}$  and  $\mathbf{x}_{0|t}$  is computed as:
+
+$$
+\operatorname {D i s t} \left(\mathbf {x} _ {\text {s o u r c e}}, \mathbf {x} _ {0 | t}\right) = \left| \left| \mathcal {K} \left(\mathbf {x} _ {\text {s o u r c e}}\right) - \mathcal {K} \left(\mathbf {x} _ {0 | t}\right) \right| \right| _ {2} ^ {2}. \tag {14}
+$$
+
+# 5. Experiments
+
+# 5.1. Implementation Details
+
+Our proposed method applies to many open-source pretrained diffusion models (DMs). In our experiment, we have tried the following models and conditions:
+
+> Unconditional Human Face Diffusion Model [28]. The supported image resolution of this model is  $256 \times 256$ , and the pre-trained dataset is aligned human faces from CelebA-HQ [18]. We experiment with conditions that include text, parsing maps, sketches, landmarks, and face IDs.  
+> Unconditional ImageNet Diffusion Model [10]. The supported image resolution of this model is  $256 \times 256$  and the pre-trained dataset is ImageNet. We experiment with conditions that include text and style images.
+
+![](images/f4eeae5681fa7d830050c81513b5f7cde6a5b2a71b65b45d8545d4c58d8b6c09.jpg)  
+Figure 5: Qualitative results of using a single condition for human face images. The included conditions are: (a) text; (b) face parsing maps; (c) sketches; (d) face landmarks; (e) IDs of reference images. Zoom in for best view.
+
+![](images/27e03d982775f233e58b50c3c9aa19cd7859f383067e0fcfe00fca5bef37d640.jpg)
+
+![](images/77f122cff9a2026e5c4d8a0f315651f464e4f14a50d79aa1f182688fa74af8e7.jpg)
+
+![](images/2769dcee6f1d11106fbbbf36b5cd740228d73627eb5296bf3460d315e060f1ce.jpg)
+
+![](images/27c7229d2f5a1d4bf4c78cd807f4b3fcf9d143a629835ea42849f7898c5a720d.jpg)
+
+![](images/320a3ee53d0cce76630ff44c1ab810c502970059d9158ecce3f5869fa3bc2627.jpg)  
+Figure 6: Qualitative results of using a single condition for ImageNet images. Pre-trained diffusion models are: (a) unconditional ImageNet diffusion model; (b) classifier-based ImageNet diffusion model. Zoom in for best view.
+
+![](images/3cf75bd5dbba04c3a2316dd2bcb32861b4b8cf715af3a41c4b978be8a7ddae91.jpg)
+
+$\succ$  Classifier-based ImageNet Diffusion Model [10]. The supported image resolution of this model is  $256 \times 256$ , and the pre-trained dataset is ImageNet. This model also has a time-dependent classifier to guide its generation process. We experiment with the condition of style images.  
+> Stable Diffusion [36]. Stable Diffusion is a widely used Latent Diffusion Model. The standard resolution of its output images is  $512 \times 512$ , but it supports higher resolutions. In our work, we use its pre-trained text-to-image model. We experiment with the condition of style images.  
+> ControlNet [52]. ControlNet is a Stable Diffusion based model supporting extra conditions input with the original text input. In our work, we use the pre-trained pose-to-image and scribble-to-image models. We experiment with conditions that include face IDs and style images.
+
+We choose DDIM [41] with 100 steps as the sampling strategy of all experiments, and other more detailed configurations will be provided in the supplementary material.
+
+# 5.2. Qualitative Results
+
+Single Condition. We present the single-condition-guided results of human face images in Fig. 5. We can see that the generated results meet the requirements of the given conditions and have rich diversity and good quality. In Fig. 6, we show the single-condition-guided results of the ImageNet domain. The diversity of the generated results is still high. In order to ensure that the generated results can better meet the control of the given conditions, we use the
+
+![](images/53e0b26fe301a3a9191095580c3337f1db39b04124ac5a53e7053f8d2f9696e1.jpg)
+
+![](images/2c80e6ef15919e19520a8b692c425e51bfaf1f3c677379482a8bae84ab333fd1.jpg)
+
+![](images/225106daa601d453686526411be255010292f7696cfce22c59bfc1a76a2aa274.jpg)
+
+![](images/87670d347646cc239dff17141d9d7f955efe6287630aa1892ad961054a5d2886.jpg)
+
+![](images/97755f786ebeaa7ff06c2fe2604d196692a1b074062c0926fc4464ebdbf7eda4.jpg)
+
+![](images/f3e929f6ec1a5178b25210bcfdfb72eaa06968c44fbf84f0be75f4e187d46a42.jpg)
+
+![](images/eeaeb61eefa1e6ad55b54d27a0d1d2d29dc36c20d15785b09ad1da26db6f87f2.jpg)  
+Figure 7: Qualitative results of using multiple conditions. Pre-trained models are: (a) and (b): unconditional human face diffusion model; (c) and (d): unconditional ImageNet diffusion model. Zoom in for best view.
+
+proposed efficient time-travel strategy.
+
+- Multiple Conditions. Fig. 7 shows the synthesized results guided by multiple conditions in the domain of human faces and ImageNet. In the human face domain (a small data domain), we produce good results with rich diversity and high consistency with the conditions. We use the efficient time-travel strategy in the ImageNet domain (a large data domain) to produce acceptable results.  
+- Training-free Guidance for Latent Domain. It should be pointed out that FreeDoM supports diffusion models in both image and latent domains. In our work, we experiment with two latent diffusion models: Stable Diffusion [36] and ControlNet [52]. We try to add the training-free conditional interfaces based on their energy functions to work with the existing training-required conditional interfaces, leading to
+
+![](images/bf2ec84834b15f1b21287d054995a0c797e93fc943570eb3ac6cefb90b4199b7.jpg)  
+Figure 8: Comparison between FreeDoM and TediGAN [49] in three conditional image synthesis tasks: (a) segmentation maps to human faces; (b) sketches to human faces; (c) text prompts to human faces. Zoom in for best view.
+
+![](images/56814bdd2bf86604d73f9e947a3ede1d93f080498ca3f7d15022f55dcac8496d.jpg)
+
+![](images/dd105d1daed7b37e53dab4af668aefc9ae7ea94c2cfa4796702e97664905542f.jpg)
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">Segmentation maps</td><td colspan="2">Sketches</td><td colspan="2">Texts</td></tr><tr><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td></tr><tr><td>TediGAN [49]</td><td>2037.2</td><td>52.77</td><td>48.61</td><td>91.11</td><td>12.31</td><td>71.71</td></tr><tr><td>FreeDoM (ours)</td><td>1696.1</td><td>53.08</td><td>33.29</td><td>70.97</td><td>10.83</td><td>55.91</td></tr></table>
+
+Table 1: We compare FreeDoM with the training-required method TediGAN [49] in three image conditional synthesis tasks. We compute the distance with given conditions and FID to judge the performance. The comparison shows that FreeDoM generates images matching given conditions better and having a comparable or better image quality.
+
+satisfactory results shown in Fig. 1(d)-(f). As such, we can see great application potential for mixing training-free and training-required conditional interfaces in various practical applications.
+
+# 5.3. Further Studies
+
+Comparison between FreeDoM and TediGAN [49]. We compare FreeDoM with the training-required conditional human face generation method TediGAN under three conditions: segmentation maps, sketches, and text. A qualitative comparison is shown in Fig. 8, and quantitative comparison results are reported in Tab. 1. For the comparison, we choose 1000 segmentation maps, 1000 sketches, and 1000 text prompts to generate 1000 results, respectively. Then we compute FID and the average distance with given conditions using the methods introduced in Sec. 4.4 to judge the performance. The comparison shows that the images generated by FreeDoM match the given conditions better and have a comparable or better image quality.  
+Comparison between FreeDoM and UGD [2]. We compare FreeDoM with Universal Guidance Diffusion (UGD) [2] in style-guided generations. From Fig. 9, we find that FreeDoM has significant advantages over UGD in the degree of alignment with the conditioned style image.
+
+"A fantasy photo of volcanoes" "A fantasy photo of a lonely road"A colorful photo of an Eiffel Towel
+
+![](images/05146104a8ae99f7fa71209b8a6deb7ed185fb51309101684a927d3db70473d2.jpg)  
+Figure 9: Comparison between FreeDoM and UGD [2] in style-guided generation. The UGD results are taken from the original paper. The number in the lower right corner of each image represents its distance with the provided style image (smaller is better), which is calculated using the method described in Sec. 4.4. FreeDoM offers obvious advantages in image quality and in the degree of satisfaction of the conditions. Zoom in for best view.
+
+![](images/1f9a1dcf2432e7e4935f89940f52b53d38298518573e125e4c2c05953f65c2c3.jpg)  
+Figure 10: Demonstration of the effect of different learning rates from small scale to large scale. (a): unconditional ImageNet diffusion models with prompt "orange"; (b): unconditional human face diffusion models with a face ID from the reference image. Zoom in for best view.
+
+Regarding the inference speed, UGD runs in about 40 minutes (using the open-source code) on a GeForce RTX 3090 GPU to synthesize one image with a resolution of  $512 \times 512$ , while we only need about 84 seconds (nearly  $30 \times$  faster).  
+□ Effect of different learning rates. We studied the effect of different learning rates on the results. Fig. 10 shows the results while increasing the energy function's learning rate  $(\rho_{t}$  in Eq. (10)) from 0. We can see that FreeDoM is scalable
+
+in terms of its control ability, which means that users can adjust the intensity of control as needed.
+
+# 6. Conclusions & Limitations
+
+We propose a training-free energy-guided conditional diffusion model, FreeDoM, to address a wide range of conditional generation tasks without training. Our method uses off-the-shelf pre-trained time-independent networks to approximate the time-dependent energy functions. Then, we use the gradient of the approximated energy to guide the generation process. Our method supports different diffusion models, including image and latent diffusion models. It is worth emphasizing that the applications presented in this paper are only a subset of the applications FreeDoM supports and should not be limited to these. In future work, we aim to explore even more energy functions for a broader range of tasks.
+
+Despite its merits, our FreeDoM method has some limitations: (1) The time cost of the sampling is still higher than the training-required methods because each iteration adds a derivative operation for the energy function, and the timetravel strategy introduces more sampling steps. (2) It is difficult to use the energy function to control the fine-grained structure features in the large data domain. For example, using the Canny edge maps as the conditions may result in poor guidance, even if we use the time-travel strategy. In this case, the training-required methods will provide a better alternative. (3) Eq. 12 deals with multi-condition control and assumes that the provided conditions are independent, which is not necessarily true in practice. When conditions conflict with each other, FreeDoM may produce subpar generation results.
+
+# References
+
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\ No newline at end of file
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+                                            "content": "Figure 1: FreeDoM controls the generation process of diffusion models in a training-free way. Here, we demonstrate some results of the applications FreeDoM supports. Part (a)-(c) show various face editing applications with training-free guidance. (a) We use the segmentation map, sketch, landmarks, and face ID as conditions to guide the generation process of an unconditional diffusion model; (b) We combine different conditions to control the generation process. (c) We use CLIP [34] based text guidance to control image synthesis and editing. For editing, we use the segmentation masks to limit the editing areas (see Fig. 4 for details); Part (d)-(f) show that training-free guidance can work with other training-required conditional diffusion models, like Stable Diffusion [36] and ControlNet [52], to achieve a more sophisticated control mechanism. The conditions of scribbles in (d), human poses in (e), and prompt texts in (f) are controlled by the training-required interfaces provided by ControlNet and Stable Diffusion. Training-free energy functions control the conditions of face IDs from the reference images in (e) and style images in (d) and (f). Zoom in for best view."
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+                                    "content": "Recently, conditional diffusion models have gained popularity in numerous applications due to their exceptional generation ability. However, many existing methods are training-required. They need to train a time-dependent classifier or a condition-dependent score estimator, which increases the cost of constructing conditional diffusion models and is inconvenient to transfer across different conditions. Some current works aim to overcome this limitation by proposing training-free solutions, but most can only be applied to a specific category of tasks and not to more general conditions. In this work, we propose a training-Free conditional Diffusion Model (FreeDoM) used for various conditions. Specifically, we leverage off-the-shelf pretrained networks, such as a face detection model, to construct time-independent energy functions, which guide the generation process without requiring training. Furthermore, because the construction of the energy function is very flexible and adaptable to various conditions, our proposed FreeDoM has a broader range of applications than existing training-free methods. FreeDoM is advantageous in its simplicity, effectiveness, and low cost. Experiments demonstrate that FreeDoM is effective for various conditions and suitable for diffusion models of diverse data domains, including image and latent code domains. Code is available at https://github.com/vvictoryuki/FreeDoM."
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+                                    "content": "1. Introduction"
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+                                    "content": "Recently, diffusion models have been demonstrated to outperform previous state-of-the-art generative models [10], such as GANs [12, 29, 3, 22, 24, 23]. The impressive generative power of diffusion models [15, 43, 45] has motivated researchers to apply diffusion models to various downstream tasks. Conditional generation is one of the most popular focus areas. Conditional diffusion models (CDMs) with diverse conditions have been proposed, such as text [20, 1, 13, 26, 36, 40, 35, 38, 25, 32], class labels [10], degraded images [5, 6, 7, 8, 19, 27, 42, 44, 47, 37, 39, 48], segmentation maps [31, 52], landmarks [31, 52], hand-drawn sketches [31, 52], style images [31, 52], etc. These CDMs can be roughly divided into two categories: training-required or training-free."
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+                                    "content": "A typical type of training-required CDMs trains a time-dependent classifier to guide the noisy image "
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+                                    "content": " toward the given condition "
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+                                    "type": "text",
+                                    "content": " [10, 32, 53, 26]. Another branch of"
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+                                    "content": "training-required CDMs directly trains a new score estimator "
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+                                    "content": " [31, 16, 36, 37, 39, 48, 52, 20, 1, 13, 35, 32]. These methods yield impressive performance but are not flexible. Once a new target condition is needed for generation, they have to retrain or finetune the models, which is inconvenient and expensive."
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+                                    "content": "In contrast, training-free CDMs try to solve the same problems without extra training. [30, 11, 14] attempt to use the cross-attention control to realize the conditional generation; [5, 6, 7, 8, 19, 27, 42, 44, 47, 46] directly modify the intermediate results to achieve zero-shot image restoration; [28] realizes image translation by adjusting the initial noisy images. While these methods are effective in a single application, they are difficult to generalize to a wider range of conditions, e.g., style, face ID, and segmentation masks."
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+                                    "content": "In order to make CDMs support a wide range of conditions in a training-free manner, this paper proposes a training-Free conditional Diffusion Model (FreeDoM) with the following two key points. Firstly, to emphasize generalization, we propose a sampling process guided by the energy function [53, 21], which is very flexible to construct and can be applied to various conditions. Secondly, to make the proposed method training-free, we use off-the-shelf pre-trained time-independent models, which are easily accessible online, to construct the energy function."
+                                }
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+                                    "content": "Our FreeDoM has the following advantages: (1) Simple and effective. We only insert a derivative step of the energy function gradient into the unconditional sampling process of the original diffusion models. Extensive experiments show its effective controlling capability. (2) Low cost and efficient. The energy functions we construct are time-independent and do not need to be retrained. The diffusion models we choose do not need to be trained on the desired conditions. Thanks to the efficient time-travel strategy we use for large data domains, the number of sampling steps we use is quite small, which speeds up the sampling process while ensuring good generated results. (3) Amenable to a wide range of applications. The conditions our method supports include, but are not limited to, text, segmentation maps, sketches, landmarks, face IDs, style images, etc. In addition, various complex but interesting applications can be realized by combining multiple conditions. (4) Supports different types of diffusion models. Regardless of the considered data domain, such as human face images, images in ImageNet, or latent codes extracted from an image encoder, extensive experiments demonstrate that our method does well on all of them."
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+                                    "content": "2. Related Work"
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+                                    "content": "2.1. Training-Required Methods"
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+                                    "content": "The training-required methods can obtain strong control generation ability thanks to supervised learning with"
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+                                    "content": "†Corresponding authors. This work was supported by Shenzhen General Research Project under Grant JCYJ20220531093215035, KAUST Office of Sponsored Research through the Visual Computing Center funding, and SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence."
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+                                    "content": "data pairs. One of the most prominent applications of these methods is the text-to-image task. The most widely used text-to-image model, Stable Diffusion [36], generates high-quality images that conform to the text description by inputting a prompt text. Recent works, such as ControlNet [52] and T2I-Adapter [31], have introduced more training-required conditional interfaces to Stable Diffusion, such as edge maps, segmentation maps, depth maps, etc."
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+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        47,
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+                        262
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "2.2. Training-Free Methods"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The training-free methods develop various interesting technologies to realize the training-free condition generation on some tasks exploiting the unique nature of the diffusion model, namely, the iterative denoising process. [14] proposes to inject the target cross attention maps to the source cross attention maps to solve the prompt-to-prompt task without training. The limitation of this method is that a text prompt is needed to anchor the content of the image to be edited in advance. DDNM [47] proposes to use the Range-Null Space Decomposition to modify the intermediate results to solve the image restoration in a training-free way. It is based on the degradation operators of image restoration tasks and is hard to be adopted in other applications. SDEdit [28] proposes to adjust the initial noisy images to control the generation process, which is useful in stroke-based image synthesis and editing. Its limitation is that the guidance of stroke is not precise and versatile."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        475,
+                        287,
+                        535
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "According to the limitations mentioned above, the training-free CDMs for a broad range of applications need to be studied urgently. We have noticed some recent efforts [33, 2] in this area. Our FreeDoM has a faster generation speed and applies to a broader range of applications."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
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+                                    ],
+                                    "type": "text",
+                                    "content": "3. Preliminaries"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.1. Score-based Diffusion Models"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Score-based Diffusion Models (SBDMs) [43, 45] are a kind of diffusion model based on score theory, which reveals that the essence of diffusion models is to estimate the score function "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "text",
+                                    "content": " is noisy data. During the sampling process, SBDMs predict "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{t - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "text",
+                                    "content": " from "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        587,
+                                        287,
+                                        683
+                                    ],
+                                    "type": "text",
+                                    "content": " using the estimated score step by step. In our work, we resort to discrete SBDMs with the setting of DDPM [15] and its sampling formula is:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {x} _ {t - 1} = \\left(1 + \\frac {1}{2} \\beta_ {t}\\right) \\mathbf {x} _ {t} + \\beta_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon}, \\tag {1}",
+                                    "image_path": "94e446fd1973ee99bc20874a3c66b8a3d24df3db775ad653541c2554583e0890.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": " is randomly sampled Gaussian noise and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta_{t}\\in \\mathbb{R}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": " is a pre-defined parameter. In actual implementation, the score function will be estimated using a score estimator "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s(\\mathbf{x}_t,t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ", that is, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s(\\mathbf{x}_t,t)\\approx \\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": ". However, the original diffusion models can only serve as an unconditional generator with randomly synthesized results."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                        163
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Conditional Score Function"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "In order to adapt the generative power of the diffusion models to different downstream tasks, conditional diffusion models (CDMs) are needed. SDE [45] proposed to control the generated results with a given condition "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        169,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        169,
+                                        545,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": " by modifying the score function as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        169,
+                                        545,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t} \\log p(\\mathbf{x}_t | \\mathbf{c})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        169,
+                                        545,
+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": ". Using the Bayesian formula "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        169,
+                                        545,
+                                        255
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\mathbf{x}_t | \\mathbf{c}) = \\frac{p(\\mathbf{c} | \\mathbf{x}_t) p(\\mathbf{x}_t)}{p(\\mathbf{c})}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        169,
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+                                        255
+                                    ],
+                                    "type": "text",
+                                    "content": ", we can rewrite the conditional score function as two terms:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t} | \\mathbf {c}) = \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {x} _ {t}) + \\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {c} | \\mathbf {x} _ {t}), \\tag {2}",
+                                    "image_path": "b25e2eb3a48517248e145f91da714b54e66e1b4b58d4875e7cec13ba55ec6823.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where the first term "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be estimated using the pre-trained unconditional score estimator "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s(\\cdot ,t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
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+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " and the second term "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
+                                        545,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
+                                        545,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " is the critical part of constructing conditional diffusion models. We can interpret the second term "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
+                                        545,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
+                                        545,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " as a correction gradient, pointing "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
+                                        545,
+                                        390
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        282,
+                                        545,
+                                        390
+                                    ],
+                                    "type": "text",
+                                    "content": " to a hyperplane in the data space, where all data are compatible with the given condition c. Classifier-based methods [10, 32, 53, 26] train a time-dependent classifier to compute this correction gradient for conditional guidance."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "3.3. Energy Diffusion Guidance"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Modeling the correction gradient "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        452
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " remains an open question. A flexible and straightforward way is resorting to the energy function [53, 21] as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "p (\\mathbf {c} | \\mathbf {x} _ {t}) = \\frac {\\exp \\left\\{- \\lambda \\mathcal {E} (\\mathbf {c} , \\mathbf {x} _ {t}) \\right\\}}{Z}, \\tag {3}",
+                                    "image_path": "ba112ed61dbe4b63cfc09700b4274c6f534a133e1dd9c256cac8dad3e67a7f6f.jpg"
+                                }
+                            ]
+                        }
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+                    "index": 16
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the positive temperature coefficient and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z > 0"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes a normalizing constant, computed as "
+                                },
+                                {
+                                    "bbox": [
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+                                        487,
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+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z = \\int_{\\mathbf{c} \\in \\mathcal{C}} \\exp\\{-\\lambda \\mathcal{E}(\\mathbf{c}, \\mathbf{x}_t)\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the domain of the given conditions. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{E}(\\mathbf{c}, \\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": " is an energy function that measures the compatibility between the condition "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the noisy image "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                    ],
+                                    "type": "text",
+                                    "content": " — its value will be smaller when "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " is more compatible with "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". If "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
+                                        545,
+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
+                                        545,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " satisfies the constraint of "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
+                                        545,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " perfectly, the energy value should be zero. Any function satisfying the above property can serve as a feasible energy function, with which we just need to adjust the coefficient "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
+                                        545,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": " to obtain "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
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+                                        618
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\mathbf{c} | \\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        487,
+                                        545,
+                                        618
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Therefore, the correction gradient "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{c}|\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " can be implemented with the following:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\nabla_ {\\mathbf {x} _ {t}} \\log p (\\mathbf {c} | \\mathbf {x} _ {t}) \\propto - \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}), \\tag {4}",
+                                    "image_path": "5b51ac6eec8c0cf14b19e04f12330917cd5a58ee6bc182425e23891948ef7f14.jpg"
+                                }
+                            ]
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+                    ],
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "which is referred to as energy guidance. With Eq. (1), Eq. (2), and Eq. (4), we get the conditional sampling:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {x} _ {t - 1} = \\mathbf {m} _ {t} - \\rho_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}), \\tag {5}",
+                                    "image_path": "d14ad6ca22b3f7113408c8bcf6cf1eeed0987d612ae0b68fee890d276b13e364.jpg"
+                                }
+                            ]
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+                {
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+                    "lines": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{m}_t = (1 + \\frac{1}{2}\\beta_t)\\mathbf{x}_t + \\beta_t\\nabla_{\\mathbf{x}_t}\\log p(\\mathbf{x}_t) + \\sqrt{\\beta_t}\\epsilon,"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\rho_{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a scale factor, which can be seen as the learning rate of the correction term. Eq. (5) is a generic formulation of conditional diffusion models, which enables the use of different energy functions."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4. The Proposed FreeDoM Method"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "In Sec. 4.1, we approximate the time-dependent energy function using time-independent distance measuring functions, making our method training-free and flexible for various conditions. In Sec. 4.2, we first analyze the reason why the energy guidance fails in a large data domain and then propose an efficient version of the time-travel strategy [27, 47]. In Sec. 4.3, we describe the details of how to construct the energy functions. In Sec. 4.4, we provide specific examples of supported conditions."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Approximate Time-Dependent Energy"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We use the energy function to guide the generation due to its flexibility to construct and suitability to various conditions. Existing classifier-based methods [10, 32, 53, 26] choose time-dependent distance measuring functions "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        300,
+                                        287,
+                                        370
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        300,
+                                        287,
+                                        370
+                                    ],
+                                    "type": "text",
+                                    "content": " to approximate the energy functions as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\phi} (\\mathbf {c}, \\mathbf {x} _ {t}, t), \\tag {6}",
+                                    "image_path": "458fae93d69e5d0b240171b882c89f59775fed1e9868ccd0f3fac30d6e07013d.jpg"
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\phi"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " defines the pre-trained parameters. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": " computes the distance between the given condition "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " and noisy intermediate results "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": ". The distance measuring functions for noisy data "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        392,
+                                        287,
+                                        475
+                                    ],
+                                    "type": "text",
+                                    "content": " cannot be directly constructed because it is difficult to find an existing pre-trained network for noisy images. In this case, we have to train (or finetune) a time-dependent network for each type of condition."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Compared with time-dependent networks, time-independent distance measuring functions for clean data "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_0"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are widely available. Many off-the-shelf pre-trained networks such as classification networks, segmentation networks, and face ID encoding networks are open-source and work well on clean images. We denote these distance measuring networks for clean data as "
+                                },
+                                {
+                                    "bbox": [
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+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\theta}(\\mathbf{c},\\mathbf{x}_0)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        476,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        476,
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+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        476,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes their pre-trained parameters. To use these networks for the energy functions, a straightforward way is to approximate "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        476,
+                                        287,
+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\phi}(\\mathbf{c},\\mathbf{x}_t,t)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        476,
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+                                    ],
+                                    "type": "text",
+                                    "content": " using "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        597
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\theta}(\\mathbf{c},\\mathbf{x}_0)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        476,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
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+                                    "content": "\\mathcal {D} _ {\\phi} (\\mathbf {c}, \\mathbf {x} _ {t}, t) \\approx \\mathbb {E} _ {p \\left(\\mathbf {x} _ {0} \\mid \\mathbf {x} _ {t}\\right)} \\left[ \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0}) \\right]. \\tag {7}",
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+                                    "content": " should also have a small distance with the condition "
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+                                    "content": ", especially during the late stage of the sampling process when the noise level of "
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+                                    "type": "text",
+                                    "content": " is relatively small. However, during the sampling process, it is infeasible to get the clean image "
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+                                    "type": "text",
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+                                    "content": "Algorithm 1 Sampling Process of our proposed FreeDoM"
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+                                    "content": ", time-independent distance measuring function "
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+                                    "content": ", pre-defined parameters "
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+                                    "type": "inline_equation",
+                                    "content": "\\beta_{t}"
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+                                    "type": "text",
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+                                    "content": "\\bar{\\alpha}_{t}"
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+                                    "type": "text",
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+                                            "content": "\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\alpha_t}} (\\mathbf{x}_t + (1 - \\bar{\\alpha}_t)s(\\mathbf{x}_t,t))"
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+                                            "content": "(a) Badly Generated Results"
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+                                            "content": "(b) Generated Results with the Time-Travel Strategy"
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+                                            "content": "Figure 2: Comparison of results generated before and after using the time-travel strategy. The prompt is \"orange\". We can see that the results in (a) do not match the given conditions. After using the time-travel strategy, we get better results in (b)."
+                                        }
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+                                    "type": "text",
+                                    "content": ", so we need to approximate "
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+                                    "type": "text",
+                                    "content": ". Considering the expectation of "
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+                                    "type": "inline_equation",
+                                    "content": "p(\\mathbf{x}_0|\\mathbf{x}_t)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " [6]:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {x} _ {0 \\mid t} := \\mathbb {E} [ \\mathbf {x} _ {0} | \\mathbf {x} _ {t} ] = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} (\\mathbf {x} _ {t} + (1 - \\bar {\\alpha} _ {t}) s (\\mathbf {x} _ {t}, t)), \\tag {8}",
+                                    "image_path": "5371e09250b4bfdd9b7efe6f72a0eed9351e48ef93bce9570a1dd080820c6250.jpg"
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\alpha}_t = \\prod_{i=1}^t (1 - \\beta_i)"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "s(\\cdot, t)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the pre-trained score estimator. According to Eq. (8), from "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        545,
+                                        491
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        429,
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+                                    "type": "text",
+                                    "content": ", we can estimate the clean image denoted as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{0|t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Then with Eq. (6) and Eq. (7), we can approximate the time-dependent energy function of noisy data "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
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+                                    "type": "text",
+                                    "content": ":"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t}). \\tag {9}",
+                                    "image_path": "1fca857272aa8dd37fbcbb9fdd10de624aed510bf1877633b37aa57739642459.jpg"
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+                                    "type": "text",
+                                    "content": "According to Eq. (5) and Eq. (9), the approximated sampling process can be written as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {x} _ {t - 1} = \\mathbf {m} _ {t} - \\rho_ {t} \\nabla_ {\\mathbf {x} _ {t}} \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t} (\\mathbf {x} _ {t})), \\tag {10}",
+                                    "image_path": "af4b51f46af94887d4b203eb8fe94315f6b59def4e814ab5315b5de7451bbdaa.jpg"
+                                }
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "and the detailed algorithm is shown in Algo. 1."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.2. Efficient Time-Travel Strategy"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 32
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In the process of applying Algo. 1, we find that the performance varies significantly on different data domains. For small data domains such as human faces, Algo. 1 can effectively produce results that satisfy the given conditions within 100 DDIM [41] sampling steps. However, for large data domains such as ImageNet, we often get results that are not closely related to the given conditions or even randomly generated results (shown in Fig. 2(a)). We attribute"
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "Figure 3: Demonstration of the importance of different sampling stages. Most of the semantic content is generated during the semantic stage, so we only employ the time-travel strategy in this stage to achieve an efficient version of FreeDoM. The shown images are "
+                                        },
+                                        {
+                                            "bbox": [
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+                                        {
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+                                            "type": "text",
+                                            "content": " generated by diffusion models pre-trained on the ImageNet data domain."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "the failure of Algo. 1 on large data domains to poor guidance. The reason for poor guidance is that the direction of unconditional score generated by diffusion models in large data domains has more freedom, making it easier to deviate from the direction of conditional control. To solve this problem, we adopt the time-travel strategy [27, 47], which has been empirically shown to inhibit the generation of disharmonious results when solving hard generation tasks."
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "The time-travel strategy is a technique that takes the current intermediate result "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " back by "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " steps to "
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{t + j}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        314,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and resamples it to the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        314,
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+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": "-th timestep again. This strategy inserts more sampling steps into the sampling process and refines the generated results. In our experiments specifically, we go back by "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        314,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j = 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " step each time and resample. We repeat this resampling process "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "r_t"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " times at the "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        314,
+                                        289,
+                                        469
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        314,
+                                        289,
+                                        469
+                                    ],
+                                    "type": "text",
+                                    "content": "-th timestep. Our experiments demonstrate that the time travel strategy is effective in solving the poor guidance problem (shown in Fig. 2(b)). However, the time cost is also expensive because the number of sampling steps is larger, especially considering that each timestep will include the cost of calculating the gradient of the energy function."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Fortunately, we find that the time-travel strategy does not have the same effect in each time step. In fact, using this technique in most time steps will not significantly modify the final result, which means we can use this strategy only in a small portion of the timesteps, thus significantly reducing the number of additional iteration steps. In Fig. 3, we try to analyze this phenomenon by dividing the sampling process into three stages. In the early stage, i.e., the chaotic stage, the generated result "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        289,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{0|t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        474,
+                                        289,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " is extremely blurred, and the energy guidance is hard to make anything reasonable, so we do not need to employ the time-travel strategy. During the late stage, i.e., the refinement stage, the change in the generated results is minor, so the time-travel strategy is useless. During the intermediate stage, i.e., the semantic stage, the change in the generated result is significant, so this stage is critical for conditional generation. Based on this observation, we only apply the time-travel strategy in the semantic stage to implement efficient sampling while solving the problem of poor guidance. The range of the semantic stage is an experimental choice depending on the specific dif"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Algorithm 2 FreeDoM + Efficient Time-Travel Strategy"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Require: condition "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
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+                                        250
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "text",
+                                    "content": ", unconditional score estimator "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s(\\cdot, t)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "text",
+                                    "content": ", time-independent distance measuring function "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{\\theta}(\\mathbf{c}, \\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "text",
+                                    "content": ", pre-defined parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta_t, \\bar{\\alpha}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        225,
+                                        545,
+                                        250
+                                    ],
+                                    "type": "text",
+                                    "content": ", learning rate "
+                                },
+                                {
+                                    "bbox": [
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+                                        225,
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+                                            "content": "\\mathbf{x}_{t - 1} = (1 + \\frac{1}{2}\\beta_t)\\mathbf{x}_t + \\beta_t s(\\mathbf{x}_t,t) + \\sqrt{\\beta_t}\\epsilon_1"
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+                                            "content": "\\mathbf{x}_{0|t} = \\frac{1}{\\sqrt{\\bar{\\alpha}_t}} (\\bar{\\mathbf{x}}_t + (1 - \\bar{\\alpha}_t)s(\\mathbf{x}_t,t))"
+                                        }
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+                                            "content": "\\pmb{g}_{t} = \\nabla_{\\mathbf{x}_{t}}\\mathcal{D}_{\\pmb{\\theta}}(\\mathbf{c},\\mathbf{x}_{0|t}(\\mathbf{x}_{t})))"
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+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_t = \\sqrt{1 - \\beta_t}\\mathbf{x}_{t-1} + \\sqrt{\\beta_t}\\pmb{\\epsilon}_2"
+                                        }
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+                                            "content": "12: return "
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+                                    "type": "text",
+                                    "content": "fusion models we choose. The detailed algorithm of our proposed FreeDoM with the efficient time-travel strategy is shown in Algo.2, where "
+                                },
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+                                    "content": "r_t = 1"
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+                                    "type": "text",
+                                    "content": " means we do not apply the time-travel strategy in the "
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+                                    "content": "t"
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+                                    "type": "text",
+                                    "content": "-th timestep."
+                                }
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+                                    "content": "4.3. Construction of the Energy Function"
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+                                    "type": "text",
+                                    "content": "- Single Condition Guidance. To incorporate in specific applications, we use the distance measuring function conforming to the following structure to construct the energy function:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {E} (\\mathbf {c}, \\mathbf {x} _ {t}) \\approx \\mathcal {D} _ {\\boldsymbol {\\theta}} (\\mathbf {c}, \\mathbf {x} _ {0 | t}) = \\operatorname {D i s t} \\left(\\mathcal {P} _ {\\boldsymbol {\\theta} _ {1}} (\\mathbf {c}), \\mathcal {P} _ {\\boldsymbol {\\theta} _ {2}} (\\mathbf {x} _ {0 | t})\\right), \\tag {11}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "Dist(\\cdot)"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " denotes the distance measuring methods like Euclidean distance, and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\pmb{\\theta} = \\{\\pmb{\\theta}_1,\\pmb{\\theta}_2\\}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{\\theta_1}(\\cdot)"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{\\theta_2}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " project the condition and image to the same space for distance measurement. These projection networks can be off-the-shelf pre-trained classification networks, segmentation networks, etc. In most cases, we only need one network to project the clean image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{0|t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to the condition space. In the cases with reference images "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{ref}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", we also only need one feature encoder to project the reference image "
+                                },
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+                                    "type": "inline_equation",
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+                                },
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "\"Red hair\""
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 23,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 22
+                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "the style information from the style image. In these multi-condition cases, assume that the given conditions are denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        225,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{c}_1,\\dots ,\\mathbf{c}_n\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we can approximately construct the energy function as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathcal {E} \\left(\\left\\{\\mathbf {c} _ {1}, \\dots , \\mathbf {c} _ {n} \\right\\}, \\mathbf {x} _ {t}\\right) \\\\ \\approx \\eta_ {1} \\mathcal {D} _ {\\boldsymbol {\\theta} _ {1}} \\left(\\mathbf {c} _ {1}, \\mathbf {x} _ {0 | t}\\right) + \\dots + \\eta_ {n} \\mathcal {D} _ {\\boldsymbol {\\theta} _ {n}} \\left(\\mathbf {c} _ {n}, \\mathbf {x} _ {0 | t}\\right), \\tag {12} \\\\ \\end{array}",
+                                    "image_path": "d98a3ed60d24783ad7a32db8a2b771561739fe40fbdc89d5b6dc98ae5bbbd7cd.jpg"
+                                }
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+                {
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+                    "angle": 0,
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        359
+                                    ],
+                                    "type": "text",
+                                    "content": " is the weighting factor. We use different distance measuring functions "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
+                                        286,
+                                        359
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathcal{D}_{\\theta_1}(\\cdot ,\\cdot),\\dots ,\\mathcal{D}_{\\theta_n}(\\cdot ,\\cdot)\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        323,
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+                                    ],
+                                    "type": "text",
+                                    "content": " for specific conditions and sum the whole for gradient computation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 27
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        47,
+                                        363,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Guidance for Latent Diffusion. Our method applies not only to image diffusions but also to latent diffusions, such as Stable Diffusion [36]. In this case, the intermediate results "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        363,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_t"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are latent codes rather than images. We can use the latent decoder to project the generated latent codes to images and then use the same algorithm in the image domain."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 28
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.4. Specific Examples of Supported Conditions"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 29
+                },
+                {
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+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " Text. For given text prompts, we construct the distance measuring function based on CLIP [34]. Specifically, we take the CLIP image encoder (as "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{P}_{\\theta_2}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ") and the CLIP text encoder (as "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{P}_{\\theta_1}(\\cdot)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ") to project the image "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{0|t}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " and given text in the same CLIP feature space. Compared with the commonly used cosine distance measurement and for simplicity, we choose the "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                467,
+                                                286,
+                                                573
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\ell_2"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                467,
+                                                286,
+                                                573
+                                            ],
+                                            "type": "text",
+                                            "content": " Euclidean distance measurement, since the sampling quality in our experiments is not significantly different."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 30
+                        },
+                        {
+                            "bbox": [
+                                46,
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "□ Segmentation Maps. For segmentation maps, we choose a face parsing network based on the real-time semantic segmentation network BiSeNet [51] to generate the parsing map of an input human face and directly compute the "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\ell_2"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                578,
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+                                            ],
+                                            "type": "text",
+                                            "content": " Euclidean distance between the given parsing map and the parsing results of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                578,
+                                                286,
+                                                685
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{0|t}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "text",
+                                            "content": ". An interesting usage of the face parsing network is to constrain the gradient update region so that we can edit the target semantic region without changing other regions (shown in Fig. 4)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 31
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                    "spans": [
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "Sketches. We choose an open-source pre-trained network [50] that transfers a given anime image to the style"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 32
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        305,
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+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": "of hand-drawn sketches. Experiments prove that the network is still effective for real-world images. We use the "
+                                },
+                                {
+                                    "bbox": [
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+                                        72,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\ell_2"
+                                },
+                                {
+                                    "bbox": [
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+                                        120
+                                    ],
+                                    "type": "text",
+                                    "content": " Euclidean distance to compare the given sketches with transferred sketch-style results of "
+                                },
+                                {
+                                    "bbox": [
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+                                        120
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{0|t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 34
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                            "type": "inline_equation",
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+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " Landmarks. We use an open-source pre-trained human face landmark detection network [4] for this application. The detection network has two stages: the first stage finds the position of the center of a face and the second stage marks the landmarks of this detected face. We compute the "
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                123,
+                                                545,
+                                                230
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\ell_2"
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                123,
+                                                545,
+                                                230
+                                            ],
+                                            "type": "text",
+                                            "content": " Euclidean distance between predicted face landmarks of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                123,
+                                                545,
+                                                230
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{0|t}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                123,
+                                                545,
+                                                230
+                                            ],
+                                            "type": "text",
+                                            "content": " and the given landmarks condition, and only use the gradient in the face area detected in the first stage to update the intermediate results."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\square"
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                235,
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+                                            ],
+                                            "type": "text",
+                                            "content": " Face IDs. We use ArcFace [9], an open-source pretrained human face recognition network, to extract the target features of reference faces to represent face IDs and compute the "
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                235,
+                                                545,
+                                                295
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\ell_2"
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                235,
+                                                545,
+                                                295
+                                            ],
+                                            "type": "text",
+                                            "content": " Euclidean distance between the extracted ID features of "
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                235,
+                                                545,
+                                                295
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{0|t}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                235,
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+                                                295
+                                            ],
+                                            "type": "text",
+                                            "content": " and those of the reference image."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
+                                305,
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
+                                                305,
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+                                            ],
+                                            "type": "text",
+                                            "content": "- Style Images. The style image is denoted as "
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                298,
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+                                                335
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{style}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                298,
+                                                545,
+                                                335
+                                            ],
+                                            "type": "text",
+                                            "content": ". We use the following equation to compute the distance of the style information between "
+                                        },
+                                        {
+                                            "bbox": [
+                                                305,
+                                                298,
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+                                                335
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{style}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{x}_{0|t}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ":"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 37
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        317,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {D i s t} \\left(\\mathbf {x} _ {\\text {s t y l e}}, \\mathbf {x} _ {0 | t}\\right) = \\left| \\left| G \\left(\\mathbf {x} _ {\\text {s t y l e}}\\right) _ {j} - G \\left(\\mathbf {x} _ {0 | t}\\right) _ {j} \\right| \\right| _ {F} ^ {2}, \\tag {13}",
+                                    "image_path": "352e2a2796ac54f189e998262da76fddb3f67211c810f2db78241ddca52d3a34.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 39
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "content": "G(\\cdot)_{j}"
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+                                    "type": "text",
+                                    "content": " denotes the Gram matrix [17] of the "
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+                                    "type": "text",
+                                    "content": "-th layer feature map of an image encoder. In our experiments, we choose the features from the third layer of the CLIP image encoder to generate satisfactory results."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "- Low-pass Filters. For the image transferring task, we need an energy function to constrain the generated results conforming to the structure information of the source image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{source}"
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+                                    "type": "text",
+                                    "content": ". Similar to EGSDE [53] and ILVR [5], we choose a low-pass filter "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{K}(\\cdot)"
+                                },
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+                                    "type": "text",
+                                    "content": " in this setup. The distance between the source image "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{source}"
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+                                {
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}_{0|t}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is computed as:"
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+                            ]
+                        }
+                    ],
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+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {D i s t} \\left(\\mathbf {x} _ {\\text {s o u r c e}}, \\mathbf {x} _ {0 | t}\\right) = \\left| \\left| \\mathcal {K} \\left(\\mathbf {x} _ {\\text {s o u r c e}}\\right) - \\mathcal {K} \\left(\\mathbf {x} _ {0 | t}\\right) \\right| \\right| _ {2} ^ {2}. \\tag {14}",
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+                                    "type": "text",
+                                    "content": "5. Experiments"
+                                }
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+                                    "type": "text",
+                                    "content": "5.1. Implementation Details"
+                                }
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+                                    "type": "text",
+                                    "content": "Our proposed method applies to many open-source pretrained diffusion models (DMs). In our experiment, we have tried the following models and conditions:"
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+                                            "type": "text",
+                                            "content": "> Unconditional Human Face Diffusion Model [28]. The supported image resolution of this model is "
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+                                            "type": "text",
+                                            "content": ", and the pre-trained dataset is aligned human faces from CelebA-HQ [18]. We experiment with conditions that include text, parsing maps, sketches, landmarks, and face IDs."
+                                        }
+                                    ]
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+                            ],
+                            "index": 46
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+                                            "type": "text",
+                                            "content": "> Unconditional ImageNet Diffusion Model [10]. The supported image resolution of this model is "
+                                        },
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+                                            "type": "text",
+                                            "content": " and the pre-trained dataset is ImageNet. We experiment with conditions that include text and style images."
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+                                            "type": "text",
+                                            "content": " Classifier-based ImageNet Diffusion Model [10]. The supported image resolution of this model is "
+                                        },
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+                                            "content": "256 \\times 256"
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+                                            "type": "text",
+                                            "content": ", and the pre-trained dataset is ImageNet. This model also has a time-dependent classifier to guide its generation process. We experiment with the condition of style images."
+                                        }
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+                            "index": 9
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+                                            "type": "text",
+                                            "content": "> Stable Diffusion [36]. Stable Diffusion is a widely used Latent Diffusion Model. The standard resolution of its output images is "
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+                                            "type": "text",
+                                            "content": ", but it supports higher resolutions. In our work, we use its pre-trained text-to-image model. We experiment with the condition of style images."
+                                        }
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+                            "index": 10
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+                                            "type": "text",
+                                            "content": "> ControlNet [52]. ControlNet is a Stable Diffusion based model supporting extra conditions input with the original text input. In our work, we use the pre-trained pose-to-image and scribble-to-image models. We experiment with conditions that include face IDs and style images."
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+                                    "content": "We choose DDIM [41] with 100 steps as the sampling strategy of all experiments, and other more detailed configurations will be provided in the supplementary material."
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+                                    "content": "5.2. Qualitative Results"
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+                                    "content": "Single Condition. We present the single-condition-guided results of human face images in Fig. 5. We can see that the generated results meet the requirements of the given conditions and have rich diversity and good quality. In Fig. 6, we show the single-condition-guided results of the ImageNet domain. The diversity of the generated results is still high. In order to ensure that the generated results can better meet the control of the given conditions, we use the"
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+                                            "content": "Figure 7: Qualitative results of using multiple conditions. Pre-trained models are: (a) and (b): unconditional human face diffusion model; (c) and (d): unconditional ImageNet diffusion model. Zoom in for best view."
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+                                    "content": "proposed efficient time-travel strategy."
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+                                            "content": "- Multiple Conditions. Fig. 7 shows the synthesized results guided by multiple conditions in the domain of human faces and ImageNet. In the human face domain (a small data domain), we produce good results with rich diversity and high consistency with the conditions. We use the efficient time-travel strategy in the ImageNet domain (a large data domain) to produce acceptable results."
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+                                            "content": "- Training-free Guidance for Latent Domain. It should be pointed out that FreeDoM supports diffusion models in both image and latent domains. In our work, we experiment with two latent diffusion models: Stable Diffusion [36] and ControlNet [52]. We try to add the training-free conditional interfaces based on their energy functions to work with the existing training-required conditional interfaces, leading to"
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">Segmentation maps</td><td colspan=\"2\">Sketches</td><td colspan=\"2\">Texts</td></tr><tr><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td><td>Distance↓</td><td>FID↓</td></tr><tr><td>TediGAN [49]</td><td>2037.2</td><td>52.77</td><td>48.61</td><td>91.11</td><td>12.31</td><td>71.71</td></tr><tr><td>FreeDoM (ours)</td><td>1696.1</td><td>53.08</td><td>33.29</td><td>70.97</td><td>10.83</td><td>55.91</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1: We compare FreeDoM with the training-required method TediGAN [49] in three image conditional synthesis tasks. We compute the distance with given conditions and FID to judge the performance. The comparison shows that FreeDoM generates images matching given conditions better and having a comparable or better image quality."
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+                                    "content": "satisfactory results shown in Fig. 1(d)-(f). As such, we can see great application potential for mixing training-free and training-required conditional interfaces in various practical applications."
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+                                    "content": "5.3. Further Studies"
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+                                            "content": "Comparison between FreeDoM and TediGAN [49]. We compare FreeDoM with the training-required conditional human face generation method TediGAN under three conditions: segmentation maps, sketches, and text. A qualitative comparison is shown in Fig. 8, and quantitative comparison results are reported in Tab. 1. For the comparison, we choose 1000 segmentation maps, 1000 sketches, and 1000 text prompts to generate 1000 results, respectively. Then we compute FID and the average distance with given conditions using the methods introduced in Sec. 4.4 to judge the performance. The comparison shows that the images generated by FreeDoM match the given conditions better and have a comparable or better image quality."
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+                                            "content": "Comparison between FreeDoM and UGD [2]. We compare FreeDoM with Universal Guidance Diffusion (UGD) [2] in style-guided generations. From Fig. 9, we find that FreeDoM has significant advantages over UGD in the degree of alignment with the conditioned style image."
+                                        }
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+                                    "content": "\"A fantasy photo of volcanoes\" \"A fantasy photo of a lonely road\"A colorful photo of an Eiffel Towel"
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+                                            "content": "Figure 9: Comparison between FreeDoM and UGD [2] in style-guided generation. The UGD results are taken from the original paper. The number in the lower right corner of each image represents its distance with the provided style image (smaller is better), which is calculated using the method described in Sec. 4.4. FreeDoM offers obvious advantages in image quality and in the degree of satisfaction of the conditions. Zoom in for best view."
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+                                            "content": "Figure 10: Demonstration of the effect of different learning rates from small scale to large scale. (a): unconditional ImageNet diffusion models with prompt \"orange\"; (b): unconditional human face diffusion models with a face ID from the reference image. Zoom in for best view."
+                                        }
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+                                            "content": "Regarding the inference speed, UGD runs in about 40 minutes (using the open-source code) on a GeForce RTX 3090 GPU to synthesize one image with a resolution of "
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+                                            "type": "text",
+                                            "content": ", while we only need about 84 seconds (nearly "
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+                                            "content": "30 \\times"
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+                                            "type": "text",
+                                            "content": " faster)."
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+                                            "type": "text",
+                                            "content": "□ Effect of different learning rates. We studied the effect of different learning rates on the results. Fig. 10 shows the results while increasing the energy function's learning rate "
+                                        },
+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "(\\rho_{t}"
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+                                            "type": "text",
+                                            "content": " in Eq. (10)) from 0. We can see that FreeDoM is scalable"
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+                                    "type": "text",
+                                    "content": "in terms of its control ability, which means that users can adjust the intensity of control as needed."
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+                                    "type": "text",
+                                    "content": "6. Conclusions & Limitations"
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+                                    "type": "text",
+                                    "content": "We propose a training-free energy-guided conditional diffusion model, FreeDoM, to address a wide range of conditional generation tasks without training. Our method uses off-the-shelf pre-trained time-independent networks to approximate the time-dependent energy functions. Then, we use the gradient of the approximated energy to guide the generation process. Our method supports different diffusion models, including image and latent diffusion models. It is worth emphasizing that the applications presented in this paper are only a subset of the applications FreeDoM supports and should not be limited to these. In future work, we aim to explore even more energy functions for a broader range of tasks."
+                                }
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+                                    "content": "Despite its merits, our FreeDoM method has some limitations: (1) The time cost of the sampling is still higher than the training-required methods because each iteration adds a derivative operation for the energy function, and the timetravel strategy introduces more sampling steps. (2) It is difficult to use the energy function to control the fine-grained structure features in the large data domain. For example, using the Canny edge maps as the conditions may result in poor guidance, even if we use the time-travel strategy. In this case, the training-required methods will provide a better alternative. (3) Eq. 12 deals with multi-condition control and assumes that the provided conditions are independent, which is not necessarily true in practice. When conditions conflict with each other, FreeDoM may produce subpar generation results."
+                                }
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+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                            "bbox": [
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+                            "angle": 0,
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+                                            "bbox": [
+                                                52,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[1] Omri Avrahami, Dani Lischinski, and Ohad Fried. Blended diffusion for text-driven editing of natural images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                53,
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+                                287,
+                                586
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "[2] Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Universal guidance for diffusion models. arXiv preprint arXiv:2302.07121, 2023."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                589,
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[3] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. In International Conference on Learning Representations (ICLR), 2019."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
+                                53,
+                                635,
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+                                656
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "[4] Cunjian Chen. PyTorch Face Landmark: A fast and accurate facial landmark detector, 2021."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
+                                53,
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+                                288,
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
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+                                        {
+                                            "bbox": [
+                                                53,
+                                                658,
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+                                            "type": "text",
+                                            "content": "[5] Jooyoung Choi, Sungwon Kim, Yonghyun Jeong, Youngjune Gwon, and Sungroh Yoon. Ilvr: Conditioning method for denoising diffusion probabilistic models. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "sub_type": "ref_text"
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "index": 26,
+                    "blocks": [
+                        {
+                            "bbox": [
+                                311,
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+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
+                                                311,
+                                                73,
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+                                            ],
+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                312,
+                                118,
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+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
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+                                            ],
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
+                            "bbox": [
+                                312,
+                                173,
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+                            ],
+                            "type": "ref_text",
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 13
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+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14
+                        },
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diff --git a/2023/Frequency Guidance Matters in Few-Shot Learning/de0a02db-ed96-44b6-8f21-932746535501_content_list.json b/2023/Frequency Guidance Matters in Few-Shot Learning/de0a02db-ed96-44b6-8f21-932746535501_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..eaf2e6798518f8a37970a03c6b947b06b1c641cc
--- /dev/null
+++ b/2023/Frequency Guidance Matters in Few-Shot Learning/de0a02db-ed96-44b6-8f21-932746535501_content_list.json	
@@ -0,0 +1,1778 @@
+[
+    {
+        "type": "text",
+        "text": "Frequency Guidance Matters in Few-Shot Learning",
+        "text_level": 1,
+        "bbox": [
+            222,
+            130,
+            746,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Hao Cheng $^{1}$  Siyuan Yang $^{1}$ $^{1}$ Nanyang Technological University",
+        "bbox": [
+            88,
+            178,
+            370,
+            215
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Joey Tianyi Zhou $^{2,3}$   \nLanqing Guo $^{1}$   \nBihan Wen $^{1*}$ $^{2}$ Centre for Frontier AI Research (CFAR), A*STAR, Singapore  \nFernance Computing (IHPC), A*STAR, Singapore",
+        "bbox": [
+            395,
+            179,
+            897,
+            234
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{hao006,siyuan005,lanqing001,bihan.wen}@ntu.edu.sg zhouty@cfar.a-star.edu.sg",
+        "bbox": [
+            140,
+            236,
+            844,
+            252
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            286,
+            313,
+            301
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Few-shot classification aims to learn a discriminative feature representation to recognize unseen classes with few labeled support samples. While most few-shot learning methods focus on exploiting the spatial information of image samples, frequency representation has also been proven essential in classification tasks. In this paper, we investigate the effect of different frequency components on the few-shot learning tasks. To enhance the performance and generalizability of few-shot methods, we propose a novel Frequency-Guided Few-shot Learning framework (dubbed FGFL), which leverages the task-specific frequency components to adaptively mask the corresponding image information, with a novel multi-level metric learning strategy including a triplet loss among original, masked and un-masked image as well as a contrastive loss between masked and original support and query sets to exploit more discriminative information. Extensive experiments on four benchmarks under several few-shot scenarios, i.e., standard, cross-dataset, cross-domain, and coarse-to-fine annotated classification, are conducted. Both qualitative and quantitative results show that our proposed FGFL scheme can attend to the class-discriminative frequency components, thus integrating those information towards more effective and generalizable few-shot learning.",
+        "bbox": [
+            73,
+            318,
+            473,
+            681
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            712,
+            209,
+            728
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep learning typically relies on large-scale annotated datasets to achieve superior results on image classification tasks. However, the learned deep models may fail to generalize under some severe conditions, e.g., few data or annotations. Correspondingly, the task to classify a query sample using only a few labeled data is known as few-shot classification [10, 40]. The key challenge is to learn the discriminative feature representation that can be generalized from the given training set to novel testing classes. Recently, sev",
+        "bbox": [
+            75,
+            738,
+            468,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/68f7b852e3bfc1524dfec6ad9086864bf861f142efe99186fb737cdc0776dd92.jpg",
+        "image_caption": [
+            "Figure 1: Visualizations of samples with different frequency masks on the CUB dataset [41]. Samples with the same color box belong to the same class. It is easier to distinguish two classes with masked specific frequency components. Each square on the left represents the masked status of corresponding frequency components, i.e., the dark and light color for masked and reserved, respectively. For each row (column), top-to-bottom and left-to-right represent low frequency to high frequency, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "eral few-shot methods [36, 48, 58] have applied the meta-learning framework [40] to build a discriminative feature space by simulating numerous meta-tasks to obtain the generalized feature representation, achieving superior performance for recognizing novel classes.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However, very recent studies [3, 17, 26, 39] report that existing methods may fail to generalize well to novel classes due to large domain gaps between training and testing sets, e.g., from general to fine-grained tasks or a specific domain. In these cases, the learned feature embeddings based on spatial images may capture excessive domain-invariant information from the training patterns, leading to degraded performance in the test scenario with a large domain gap. Several domain adaptation-based few-shot algorithms [26, 37, 39, 57] have been proposed to alleviate the domain shift issues on few-shot classification. These",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            2,
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+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
+        "bbox": [
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+            887,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "11814",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "methods focus on learning a flexible feature embedding or fine-tuning on less novel support samples to transfer knowledge across domains. However, they cannot achieve stable performance improvements for different few-shot scenarios. Moreover, most domain adaption-based methods only focused on exploiting the image spatial features.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Beyond spatial features, the frequency-domain representation plays a vital role for various computer vision tasks, e.g., deep fake recognition [12, 24, 27], domain generalization [19] and image classification [4, 32, 42, 50]. Different frequency components naturally convey discriminative and interpretive features for visual understanding [19, 32], e.g., the selected frequency components (FCs) of input images can be used to interpret the learned CNN features in classification [42, 50]. In few-shot learning, Chen et al. [4] is the first attempt to apply image frequency spectrum for classification, in which frequency information is naively concatenated as an extra feature, without exploiting different effects of its FCs. Figure 1 provides an example, clearly showing that certain FCs are more discriminative, thus should be selected and highlighted for more effective classification. However, no work to date has systematically investigated the roles of different FCs and how to adaptively select important FCs for effective few-shot learning.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel Frequency-Guided Few-shot Learning (FGFL) framework towards highly effective few-shot classification and generalization. For each input image, FGFL adaptively generates a task-specific class-discriminative mask in the frequency domain using Grad-CAM [35], where the activated FCs represent the important frequency information associated with the current task. Then we convert the masked and unmasked frequency components output back to the spatial domain for generating the masked and unmasked images, which contain limited and rich task-specific class-discriminative information, respectively. After that, for each image in the meta-task, we construct its triplet with its corresponding unmasked and masked images as positive and negative samples. We also construct two additional few-shot tasks by regrouping the masked and original support and query images, i.e.,  $\\mathcal{T}_{ms}$  with masked support set and original query set, and  $\\mathcal{T}_{mq}$  with original support set and masked query set. In addition, we propose two types of ranking losses, including the triplet and contrastive loss functions at single images and tasks (i.e.,  $\\mathcal{T}_{ms}$  and  $\\mathcal{T}_{mq}$ ) levels, respectively, to force the model to capture task-specific class-discriminative information that can well generalize to the novel classes. Moreover, the unmasked images are also added to the support set to enhance the discriminability of feature embeddings.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The contributions of this work are fourfold. First, we propose a Frequency-Guided Few-shot Learning (FGFL) framework to utilize the frequency information to enhance the performance and generalizability of few-shot methods",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "in the spatial domain. Second, we propose two types of ranking loss, including the triplet and contrastive loss functions at both sample and task levels based on original and generated images, to force the network to focus on class-discriminative frequency components for each few-shot meta-task. In addition, the generated unmasked images are also utilized to augment the support set to enhance the discriminability of feature embeddings. Third, we investigate the impact of frequency components on current methods under several generalized few-shot settings, namely cross-dataset, cross-domain, and coarse-to-fine annotated generalization. To the best of our knowledge, this is the first work that exploits the effect of different frequency components on few-shot classification and generalization tasks explicitly. Last, experimental results and visualizations demonstrate that the proposed FGFL can improve the performance and generalizability of few-shot methods and achieve superior results under several few-shot settings.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Few-shot Classification",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot learning aims to recognize novel query samples with only a few available support samples. Recently, existing deep few-shot methods can be divided into three main categories. First, optimization-based meta-learning methods [2, 11, 20, 28, 33] design a good model initialization or optimization strategy that can quickly adapt to novel tasks. Second, metric-based methods [7, 29, 30, 36, 48, 55, 58] focus on constructing an appropriate latent space to extract discriminative feature embeddings and then predict based on the similarity between support and query samples. Third, data generative and augmentation-based methods focus on generating more variant samples to learn a more accurate classifier, e.g., applying data rotation or transformation [21] by self-supervised learning, synthesizing new data with a generative model [14, 23], or using external data with pseudo labels [18, 44, 52].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Most above-mentioned algorithms only employ spatial images as the network input without exploiting the frequency information. In our work, we investigate the effect of the frequency information in the Discrete Cosine Transformation (DCT) domain and leverage it to guide few-shot classification in the spatial domain.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Learning in the Frequency Domain",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Frequency components contain rich patterns for image understanding and have been widely studied in several computer vision tasks such as compressed sensing [43, 51, 56], visual pre-training [47], domain transfer [19, 53], and image classification [4, 8, 32, 42, 50]. Yang et al. [53] use the Fast Fourier Transformation (FFT) to achieve domain alignment by simply swapping the low-frequency spectrum between",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "11815",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/bc120ff6a0dd7d07e7f630ef34906388960484f415e026f5cbcc2204822080ad.jpg",
+        "image_caption": [
+            "Figure 2: T-SNE visualization of all image features of 20 test classes in the CUB (top) and 15 test classes in the Quickdraw (bottom) dataset. The few-shot model is trained on the miniImageNet dataset. A cluster that is clearer and more compact within each class is better."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "table",
+        "img_path": "images/8e55f7c2249505e9bbb0972ead8e2fee4837116b0932b330a3d002609974b577.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>miniImageNet</td><td>CUB</td><td>Quickdraw</td></tr><tr><td>ProtoNet [36]</td><td>79.86</td><td>66.29</td><td>64.32</td></tr><tr><td>ProtoNet w/ High FCs</td><td>56.47</td><td>37.96</td><td>66.26</td></tr><tr><td>ProtoNet w/o High FCs</td><td>77.75</td><td>67.09</td><td>65.99</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Few-shot classification results under the 5-way 5-shot setting trained with the miniImageNet dataset. ProtoNet is trained on miniImageNet dataset and evaluated on several datasets with specific frequency components.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "source and target domain samples. GFNet [32] considers the attention in the FFT frequency domain to replace the self-attention module in the vision transformer. However, FFT requires double the memory for complex coefficients. Therefore, some recent works [4, 31, 50] consider applying the Discrete Cosine Transformation (DCT) to learn in the frequency domain. For example, Wang et al. [43] first applies the DCT to speed up the network. Instead of inputting RGB pixels, Gueguen et al. [16] convert the JPEG-compressed image to its  $8 \\times 8$  block DCT coefficients as the input of the neural network. FcaNET [31] adopts DCT to generalize the compression of the channel attention mechanism in the frequency domain. Specifically, Chen et al. [4] select pre-defined channels in the DCT frequency domain to improve the performance for few-shot classification.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this work, we also employ the DCT to transform the images to the frequency domain. Unlike previous work [4], we consider the interaction between spatial and frequency domains and learn to generate the discriminative frequency mask to enhance learning in the spatial domain.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Proposed Method",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first investigate the impact of frequency components in different few-shot classification scenarios. Then the proposed FGFL framework is described",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and explained in detail, followed by the loss function of our method and empirical validations.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Frequency Analysis on Few-shot Classification",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We first investigate the impact of frequency components on the generalized performance of current few-shot methods under different few-shot settings by removing and preserving partial frequency components of each image in the meta-task for class prediction.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To generate the frequency representation of an input RGB image  $X \\in \\mathbb{R}^{H \\times W \\times 3}$ , we apply the 2D-Discrete Cosine Transform [1] (2D-DCT) function as  $D = DCT(X) \\in \\mathbb{R}^{H \\times W \\times 3}$ . We can then remove or preserve partial frequency components of each input image, followed by an Inverse 2D-DCT function as  $\\hat{X} = IDCT(\\hat{D})$  to transform it back into the spatial domain with the original input size.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "With the help of the DCT functions, we can decompose the raw data into two parts,  $X = \\{X^{O}, X^{H}\\}$ , where  $X^{H}$  and  $X^{O}$  represent high-frequency components (dubbed w/ high FCs), and other components (dubbed w/o high FCs). For a given few-shot task  $\\mathcal{T}_{\\mathrm{test}} = (\\mathcal{S}, \\mathcal{Q})$  on the novel testing set, we can reconstruct images with partial frequency information to update the testing task as  $\\tilde{\\mathcal{T}}_{\\mathrm{test}} = \\{\\tilde{S}, \\tilde{\\mathcal{Q}}\\}$ . Then we adopt the existing few-shot methods to make predictions for each query sample  $\\tilde{X}_j$  with  $\\tilde{S}$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows classification accuracy on different test domains and Figure 2 plots the t-SNE visualizations of image features extracted by the trained feature encoder. We can observe that removing specific frequency components can improve the generalized performance of few-shot models but degrade standard few-shot performance in the same testing scenario.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To this end, frequency information plays different roles in different classification scenarios. Through evaluation and observation, it can be conjectured that the generalization behaviors of few-shot methods are relevant to frequency components which may vary across datasets and domains.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Frequency-Guided Few-shot Learning",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Different FCs encode specific image information, we propose the Frequency-Guided Few-shot Learning (FGFL) framework, which utilizes the frequency mask to guide the training in the spatial domain. As shown in Figure 3, FGFL has two branches with two encoders  $E^{fq}$  and  $E^{sp}$  for feature extraction in the frequency and spatial domains, respectively. FGFL generates the frequency mask based on the task-specific attention map for the given few-shot task, which is then adopted to generate additional images, guiding the network updates in the spatial domain. Moreover, we propose a multi-level metric to force the network to capture specific frequency components for classification.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "1More implementation details and evaluation results for all frequency components of more few-shot methods are provided in Supplementary.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "11816",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6bac4de8b4aafa42530a129a6866dd8c420a4d713faddc6ba12e5cf4d2ec2f22.jpg",
+        "image_caption": [
+            "Figure 3: Overview of our proposed Frequency-Guided Few-shot Learning framework (FGFL). We first generate the task-specific class-discriminative frequency mask based on the classification in the frequency domain. Then we convert the masked and unmasked frequency samples back to the spatial domain and generate two image sets (masked set  $X_{m}$  and unmasked set  $X_{um}$ ) according to the mask and unmask regions, respectively. Furthermore, we adopt novel multi-level metrics (shown in Figure 4) on the original and generated image sets to make class predictions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Task-Specific Frequency Mask Generation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To obtain a task-specific attention mask of frequency components for each few-shot task, we first transform the input spatial input image  $X$  to  $D$  in the frequency domain. Then we generate the attention map by Grad-CAM [35] based on the output feature map  $M \\in \\mathbb{R}^{C \\times h \\times w}$  of the last convolution layer in the frequency encoder (e.g., ResNet-12), where  $C$  is the channel number of the feature map,  $h$  and  $w$  indicate the height and width of the feature map, respectively.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For its ground-truth class  $c$ , we compute the gradient of the score  $s^c$  with respect to the feature map activation  $M_{k}\\in \\mathbb{R}^{h\\times w}$  as  $\\frac{\\partial s^c}{\\partial M_k}$ , where  $k$  indicates the channel index of the feature map. These gradients flowing back will pass through a global average pooling layer (denoted as  $GAP(\\cdot))$  to obtain the neuron importance weights  $w_{k}^{c}$ :",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {k} ^ {c} = G A P \\left(\\frac {\\partial s ^ {c}}{\\partial M _ {k}}\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The weight  $w_{k}^{c}$  reflects the importance of activation map  $M_{k}$  to make the prediction of class  $c$  for the input  $D$ . We then perform a weighted combination with a ReLU function to integrate the positive influence of feature maps across different channels of  $M$  for class  $c$  as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA ^ {c} = \\operatorname {R e L U} \\left(\\sum_ {k} w _ {k} ^ {c} M _ {k}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $A^c \\in \\mathbb{R}^{h \\times w}$  is the heatmap reflecting frequency components that have a positive impact on the ground-truth class  $c$  of a given frequency input.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that previous works [35, 22] utilize a fully connected (fc) layer to obtain the classification score  $s^c$  for the",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ground-truth class  $c$  with the same training and testing class set. However, since the training and testing classes in few-shot scenarios are non-overlap, directly applying fc layers for gradient computation may be prone to overfitting.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To this end, we compute the cosine similarity between each sample and class prototype as the classification score for each given  $N$ -way  $K$ -shot task in few-shot learning, where  $N$  and  $K$  indicates the number of selected classes and labeled support samples from each class, respectively. Specifically, given a few-shot task with support set  $\\mathcal{S}_f = \\{D_m, y_m\\}_{m=1}^{NK}$ , and a query set  $\\mathcal{Q}_f = \\{D_n, y_n\\}_{n=1}^Q$  in the frequency domain, we compute the cosine similarity score  $s^c$  between each query sample  $\\mathbf{q} \\in \\mathbb{R}^C$  and each class prototype  $\\mathbf{v}_c \\in \\mathbb{R}^C$  as:",
+        "bbox": [
+            498,
+            486,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ns ^ {c} = p (y = c \\mid \\mathbf {q}) = \\frac {\\mathbf {q} ^ {T} \\mathbf {v} _ {c}}{\\| \\mathbf {q} \\| \\| \\mathbf {v} _ {c} \\|}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            652,
+            890,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{v}_c = \\frac{1}{K}\\sum_{k=1}^{K}\\mathbf{z}_k$  is the mean feature vector of the support features  $\\mathbf{z}_k$  of the  $c$ -th class. Note that, it is easy to prove Eq. (3) is equivalent to an fc layer when neglecting the bias of the fc layer. Moreover, the classification weights  $\\mathbf{v}_c$  are flexible and task-dependent, i.e., only based on the current few-shot task. Hence, the network can learn to generate a task-specific heatmap  $A^c$  of each sample to find specific frequency components that contribute most to the current task, which avoids over-fitting to the training set.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We then up-sample  $A^c$  to the original size and generate the frequency mask following previous works [45, 22] as:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {M a s k} ^ {c} = \\mathbf {1} - \\operatorname {S i g m o i d} \\left(U p \\left(A ^ {c}\\right)\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            584,
+            883,
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+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "11817",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/f26241cbf946420420032915bd50ee12c23ec1152dd1e869f0cbc83b9f116a98.jpg",
+        "image_caption": [
+            "Figure 4: Illustration of the proposed multi-level metrics. Specifically, for each image in the image set  $X$  in the metask, we construct its triplet from the corresponding un-masked and masked set  $X^m$  and  $X^{um}$  as the positive and negative pair, respectively, and adopt the sample-wise triplet loss  $L_{sw\\_tri}$  to exploit the correlations them. At the task level, we construct two additional few-shot tasks by regrouping the images in  $X$  and  $X^m$ . (Here we take the query set as an example.) Then we propose a class-wise contrastive loss  $L_{cw\\_ctr}$  between positive pairs (original support and query samples) and negative pairs (support and query from different sets). Moreover, we use unmasked images to augment the support set for classification with a loss  $L_{aug}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            89,
+            93,
+            452,
+            281
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{1}$  is an all-ones matrix,  $Up(\\cdot)$  is the upsampling operation, and  $Sigmoid(\\cdot)$  is applied to make it derivable and constrains the value to the range [0, 1].",
+        "bbox": [
+            75,
+            513,
+            468,
+            559
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$Mask^c$  is then applied to  $D$  and converted back to the spatial domain to generate the masked spatial image  $X^m$  and corresponding unmasked spatial image  $X^{um}$  as:",
+        "bbox": [
+            75,
+            559,
+            468,
+            604
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX ^ {m} = I D C T \\left(M a s k ^ {c} \\odot D\\right), X ^ {u m} = I D C T \\left(\\left(1 - M a s k ^ {c}\\right) \\odot D\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            616,
+            468,
+            646
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\odot$  is the dot product function. Note that  $X^{m}$  and  $X^{um}$  are considered to contain limited and rich information belonging to the target class since the regions on the attention map beyond the class-aware range should be hard to identify the true class. We can then utilize  $X^{m}$  and  $X^{um}$  to guide few-shot learning in the spatial domain.",
+        "bbox": [
+            75,
+            647,
+            470,
+            738
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Mask-Guided Multi-Level Metrics",
+        "text_level": 1,
+        "bbox": [
+            76,
+            756,
+            372,
+            771
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the help of task-specific frequency mask generation, we already generate additional samples (i.e., masked images  $X^{m}$  and unmasked images  $X^{um}$ ). To incorporate frequency information to encourage the spatial network to capture class discriminative information, we propose two ranking losses at the sample and task levels, (i.e., sample-wise triplet loss  $L_{sw\\_tri}$  and class-wise contrastive loss  $L_{cw\\_ctr}$ , respectively.) to fully exploit the mask information in the",
+        "bbox": [
+            75,
+            780,
+            470,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "frequency signal, shown in Figure 4. Meanwhile, we also adopt the unmasked images to enhance the few-shot classification performance with an additional classification loss  $L_{\\text{aug}}$ .",
+        "bbox": [
+            496,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Sample-wise triplet loss. For each original image  $X_{i}$  in the meta-task, this loss aims to enhance the feature similarity between  $X_{i}$  and its corresponding unmasked image  $X_{i}^{um}$ , while reducing that between  $X_{i}$  and its corresponding masked image  $X_{i}^{m}$ . Formally, we construct the triplet for each image in the meta-task as  $(X_{i}, X_{i}^{m}, X_{i}^{um})$ , where  $X_{i}, X_{i}^{um}$ , and  $X_{i}^{m}$  are the anchor, positive, and negative samples, respectively. We define  $E^{sp} = f_{\\phi}(\\cdot)$  as the feature extractor with parameters  $\\phi$  to obtain the feature vector. Then the sample-level triplet loss can be formulated as:",
+        "bbox": [
+            496,
+            151,
+            892,
+            303
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {s w. t r i} \\left(X _ {i}, X _ {i} ^ {u m}, X _ {i} ^ {m}\\right) = \\max  \\left\\{d \\left(f _ {\\phi} \\left(X _ {i}\\right), f _ {\\phi} \\left(X _ {i} ^ {u m}\\right)\\right) \\right. \\\\ - d \\left(f _ {\\phi} \\left(X _ {i}\\right), f _ {\\phi} \\left(X _ {i} ^ {m}\\right)\\right) + \\eta , 0 \\}, \\tag {6} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            513,
+            308,
+            890,
+            359
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $d(\\cdot ,\\cdot)$  denotes the distance between two features and  $\\eta$  is the margin between positive and negative pairs.",
+        "bbox": [
+            496,
+            368,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Class-wise contrastive loss. To encourage the network to capture class discriminative information, we construct contrastive pairs for each query instance in the original and masked sets. Specifically, given masked support and query sets  $S_{m} = \\{X_{i}^{m},y_{i}\\}_{i = 1}^{NK}$  and  $\\mathcal{Q}_m = \\{X_j^m,y_j\\}_{j = 1}^Q$  , we first construct two additional masked few-shot tasks by regrouping the masked and original sets as:",
+        "bbox": [
+            496,
+            398,
+            892,
+            503
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {T} _ {m s} = \\left(\\mathcal {S} _ {m}, \\mathcal {Q}\\right), \\quad \\mathcal {T} _ {m q} = \\left(\\mathcal {S}, \\mathcal {Q} _ {m}\\right), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            573,
+            511,
+            890,
+            529
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{S} = \\{X_i, y_i\\}_{i=1}^{NK}$  and  $\\mathcal{Q} = \\{X_j, y_j\\}_{j=1}^Q$  are original support and query set, respectively.",
+        "bbox": [
+            496,
+            535,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Each masked sample consists of less class-discriminative information. To avoid being misled by class-irrelevant information (i.e., preserved in  $S_{m}$  and  $\\mathcal{Q}_{m}$ ), we regard the support and query samples from tasks  $T_{ms}$  and  $T_{mq}$  as negative pairs, and those from the original task with the same class as positive pairs. Then the contrastive loss corresponding to query sample  $X_{q} \\in \\mathcal{Q}$  can be written as:",
+        "bbox": [
+            496,
+            566,
+            890,
+            674
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {q} = - \\log \\frac {\\sum_ {y _ {j} = y _ {q} , X _ {j} \\in S} e ^ {d \\left(z _ {j} , z _ {q}\\right) / \\tau}}{\\sum_ {y _ {j} = y _ {q} , X _ {j} \\in S} e ^ {d \\left(z _ {j} , z _ {q}\\right) / \\tau} + \\sum_ {X _ {k} \\in S _ {m}} e ^ {d \\left(z _ {k} , z _ {q}\\right) / \\tau}}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            680,
+            898,
+            733
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $z_{i} = f_{\\phi}(X_{i})$  represents the feature vector extracted by the spatial backbone. Similarly, the contrastive loss for support sample  $X_{s}\\in S$  can be written as:",
+        "bbox": [
+            496,
+            733,
+            890,
+            779
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {s} = - \\log \\frac {\\sum_ {y _ {j} = y _ {s} , X _ {j} \\in Q} e ^ {d \\left(z _ {j} , z _ {s}\\right) / \\tau}}{\\sum_ {y _ {j} = y _ {s} , X _ {j} \\in Q} e ^ {d \\left(z _ {j} , z _ {s}\\right) / \\tau} + \\sum_ {X _ {k} \\in Q _ {m}} e ^ {d \\left(z _ {k} , z _ {s}\\right) / \\tau}}. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            784,
+            901,
+            837
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Overall, for one episode,  $L_{cw - ctr}$  can be written as:",
+        "bbox": [
+            500,
+            839,
+            836,
+            854
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {c w - c t r} = \\frac {1}{Q} \\sum_ {q = 1} ^ {Q} L _ {q} + \\frac {1}{N K} \\sum_ {s = 1} ^ {N K} L _ {s}. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            571,
+            859,
+            890,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "11818",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/5b5513f0a01810adeeb0a1356c2377b25fda5828abdd6c99f71fd1003c71087c.jpg",
+        "image_caption": [
+            "(a) Visualization results on Mean Magnitude features of Channels (MMC).",
+            "Figure 5: (a) MMC before and after applying the proposed FGFL method. (b) MMD results of few-shot methods trained over miniImageNet. The lower MMD value indicates a smaller gap and better performance. 'Pretrained' denotes the feature extractor (i.e., ResNet-12) pre-trained on the training set of miniImageNet."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            89,
+            269,
+            186
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/6a0f19781be14c96a98d3113d686feb65740943dcf4e2c01443ba4d8ed23cd72.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>mini</td><td>CUB</td></tr><tr><td>Pretrained</td><td>0.5567</td><td>1.5584</td></tr><tr><td>FEAT [55]</td><td>0.5386</td><td>1.5367</td></tr><tr><td>Ours</td><td>0.1256</td><td>1.2550</td></tr></table>",
+        "bbox": [
+            285,
+            108,
+            467,
+            170
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "(b) Maximum Mean Discrepancy (MMD) results on different test datasets.",
+        "bbox": [
+            281,
+            181,
+            467,
+            222
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Augmented classification loss. To better classify samples in the query set  $\\mathcal{Q}$ , we use generated support images  $S_{um}$  in  $X^{um}$  to enhance the support set for classification. Specifically, we build a new support set by combining the original support and unmasked support set as  $S_{aug} = S \\cup S_{um}$ . Hence, we conduct few-shot classification on query set  $\\mathcal{Q}$  based on  $S_{aug}$  and minimize the cross-entropy loss:",
+        "bbox": [
+            75,
+            372,
+            468,
+            479
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {a u g} = \\sum_ {j = 1} ^ {Q} L _ {C E} \\left(f _ {\\theta} \\left(X _ {j}; \\mathcal {S} _ {a u g}\\right), y _ {j}\\right). \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            143,
+            492,
+            468,
+            534
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.2.3 Objective, Model Training, and Inference",
+        "text_level": 1,
+        "bbox": [
+            76,
+            554,
+            419,
+            570
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Combining with the standard few-shot classification, the overall objective function is defined as:",
+        "bbox": [
+            75,
+            579,
+            468,
+            609
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {t o t a l} = L _ {c l s} ^ {s p} + L _ {c l s} ^ {f q} + \\lambda_ {1} \\cdot L _ {s w \\_ t r i} + \\lambda_ {2} \\cdot L _ {c w \\_ c t r} + \\lambda_ {3} \\cdot L _ {a u g}, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            621,
+            468,
+            652
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{cls}^{sp}$  and  $L_{cls}^{fq}$  represent the cross-entropy loss for few-shot classification in the spatial and frequency branch, respectively.  $\\lambda_1, \\lambda_2,$  and  $\\lambda_3$  denote the weighting parameters of the corresponding losses, respectively.",
+        "bbox": [
+            75,
+            652,
+            468,
+            714
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "During the training phase, we first generate frequency masks based on the frequency branch and then adopt the proposed multi-level metrics for model training. During the inference time, our proposed method strictly follows the inductive setting. We only feed the support set into the frequency branch to generate unmasked support images to refine the support set for classification.",
+        "bbox": [
+            75,
+            714,
+            468,
+            820
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3. Empirical Validation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            830,
+            272,
+            847
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The proposed FGFL framework aims to utilize frequency information to guide the spatial feature extractor towards class-discriminative features and avoid over-fitting to the",
+        "bbox": [
+            75,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "training patterns, thus generalizing well to testing scenarios. To validate the effectiveness of the proposed method, we conduct experiments about learned features on two aspects: channel distribution shift and domain distance.",
+        "bbox": [
+            496,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Mean Magnitude of Channels (MMC) Luo et al. [26] shows the channel bias problem affects the generalizability of few-shot methods and utilizes MMC to visualize and measure the channel response to features, where effective few-shot methods might have a more uniform MMC curve in the testing set. Inspired by this work, we visualize the MMC before and after applying FGFL over miniImageNet. We can observe a channel magnitude change in Figure 5 (a), which validates that our proposed method can alleviate the channel bias problem, thus improving the performance.",
+        "bbox": [
+            496,
+            152,
+            890,
+            303
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Maximum Mean Discrepancy (MMD) The MMD [15] is a distance measure between two domains based on the embedding of distribution measures in a reproducing kernel Hilbert space, which has been widely applied in transfer learning problems. We adopt class-wise MMD to measure the distribution gap between the training and testing sets with different methods trained over miniImageNet. Figure 5 (b) shows different gaps between one training set and different testing sets. We can also observe that our proposed method helps to reduce the domain shift.",
+        "bbox": [
+            496,
+            304,
+            890,
+            455
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            472,
+            632,
+            489
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
+            498,
+            689,
+            515
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We conduct extensive experiments on four few-shot datasets, i.e., miniImageNet [40], tieredImageNet [34], CUB [41], and FS-DomainNet [6].",
+        "bbox": [
+            496,
+            523,
+            890,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. For fair comparisons with previous methods, we adopt the ResNet-12 network with [64, 160, 320, 640] channels as our backbone in each branch, and set the input image size as  $84 \\times 84$  for all datasets. We combine our proposed FGFL with FEAT [55], which adopts a linear projection layer for feature adaptation. We randomly select 15 samples of each class to construct the query set for 5-way 1-shot and 5-way 5-shot settings. The backbone networks are pre-trained on the training set following the typical classification task. The weighting parameters  $\\lambda_{1}$ ,  $\\lambda_{2}$ , and  $\\lambda_{3}$  are all set to 0.1 to balance the scale between the classification loss and the corresponding losses for all datasets.",
+        "bbox": [
+            496,
+            570,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Few-shot Classification",
+        "text_level": 1,
+        "bbox": [
+            500,
+            779,
+            712,
+            792
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on two standard few-shot settings, i.e., general and fine-grained classification, shown in Table 2. Table 2 (a) shows that our proposed FGFL can",
+        "bbox": [
+            496,
+            804,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "2More details are included in Supplementary.",
+        "bbox": [
+            514,
+            862,
+            759,
+            875
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "3More details about datasets and experimental settings are included in Supplementary.",
+        "bbox": [
+            501,
+            875,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "11819",
+        "bbox": [
+            480,
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+            517,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/0bfc4904569f3ce49540c0aa4529f449fd514d3cb11964b7835b8fc0ea48a66d.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "(a) Average classification accuracy  $(\\%)$  on miniImageNet and tieredImageNet datasets with the ResNet-12 as backbone."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">miniImageNet</td><td colspan=\"2\">tieredImageNet</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>ProtoNet [36]†</td><td>61.83 ± 0.20</td><td>79.86 ± 0.14</td><td>66.84 ± 0.23</td><td>84.54 ± 0.16</td></tr><tr><td>Meta-Baseline [5]</td><td>63.17 ± 0.23</td><td>79.26 ± 0.17</td><td>68.62 ± 0.27</td><td>83.29 ± 0.18</td></tr><tr><td>Good-Embed [38]</td><td>64.82 ± 0.60</td><td>82.14 ± 0.43</td><td>71.52 ± 0.69</td><td>86.03 ± 0.58</td></tr><tr><td>DeepEMD [58]</td><td>65.91 ± 0.82</td><td>82.41 ± 0.56</td><td>71.16 ± 0.87</td><td>86.03 ± 0.58</td></tr><tr><td>FRN [46]</td><td>66.45 ± 0.19</td><td>82.83 ± 0.13</td><td>71.16 ± 0.22</td><td>86.01 ± 0.15</td></tr><tr><td>FEAT [55]†</td><td>66.52 ± 0.20</td><td>81.46 ± 0.14</td><td>70.30 ± 0.23</td><td>84.55 ± 0.16</td></tr><tr><td>BML [60]</td><td>67.04 ± 0.63</td><td>83.63 ± 0.29</td><td>68.99 ± 0.50</td><td>85.49 ± 0.34</td></tr><tr><td>IEPT [59]</td><td>67.05 ± 0.44</td><td>82.90 ± 0.30</td><td>72.24 ± 0.50</td><td>86.73 ± 0.34</td></tr><tr><td>MELR [9]</td><td>67.40 ± 0.43</td><td>83.40 ± 0.28</td><td>72.14 ± 0.51</td><td>87.01 ± 0.35</td></tr><tr><td>MCL-Katz [25]</td><td>67.51</td><td>83.99</td><td>72.01</td><td>86.02</td></tr><tr><td>CSEI [21]</td><td>67.59 ± 0.83</td><td>81.93 ± 0.36</td><td>72.57 ± 0.95</td><td>85.72 ± 0.63</td></tr><tr><td>Meta DeepBDC [48]</td><td>67.83 ± 0.43</td><td>84.46 ± 0.28</td><td>72.34 ± 0.49</td><td>87.31 ± 0.32</td></tr><tr><td>DFR [6]</td><td>68.12 ± 0.81</td><td>82.79 ± 0.56</td><td>72.38 ± 0.95</td><td>86.00 ± 0.61</td></tr><tr><td>Yang et al. [54]</td><td>70.19 ± 0.46</td><td>84.66 ± 0.29</td><td>72.62 ± 0.51</td><td>86.62 ± 0.33</td></tr><tr><td>Ours</td><td>69.14 ± 0.80</td><td>86.01 ± 0.62</td><td>73.21 ± 0.88</td><td>87.21 ± 0.61</td></tr></table>",
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+        "table_caption": [],
+        "table_footnote": [
+            "(b) Average classification accuracy  $(\\%)$  on CUB dataset."
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Backbone</td><td colspan=\"2\">CUB</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>MELR [9]</td><td>ConvNet-4</td><td>70.26 ± 0.50</td><td>85.01 ± 0.32</td></tr><tr><td>ProtoNet [36]†</td><td>ResNet-12</td><td>72.25 ± 0.21</td><td>87.47 ± 0.13</td></tr><tr><td>DeepEMD [58]</td><td>ResNet-12</td><td>75.65 ± 0.83</td><td>88.69 ± 0.50</td></tr><tr><td>FEAT [55]†</td><td>ResNet-12</td><td>75.68 ± 0.20</td><td>87.91 ± 0.13</td></tr><tr><td>BML [60]</td><td>ResNet-12</td><td>76.21 ± 0.63</td><td>90.45 ± 0.36</td></tr><tr><td>Good-Embed [38]‡</td><td>ResNet-18</td><td>77.92 ± 0.46</td><td>89.94 ± 0.26</td></tr><tr><td>DFR [6]</td><td>ResNet-12</td><td>78.07 ± 0.79</td><td>89.74 ± 0.51</td></tr><tr><td>VFD [49]</td><td>ResNet-12</td><td>79.12 ± 0.83</td><td>91.48 ± 0.39</td></tr><tr><td>FRN [46]†</td><td>ResNet-12</td><td>82.90 ± 0.19</td><td>92.61 ± 0.10</td></tr><tr><td>Ours</td><td>ResNet-12</td><td>80.77 ± 0.90</td><td>92.01 ± 0.71</td></tr></table>",
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 2: Comparison with state-of-the-art methods for general (a) and fine-grained (b) few-shot image classification. The best and second best results under each setting and dataset are highlighted as Red and Blue, respectively.  $\\dagger$ : implemented based on public code with our setting.  $\\ddagger$ : reported in [48]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"4\">Train Scenario</td><td colspan=\"4\">Test Scenario</td></tr><tr><td rowspan=\"2\">(a)</td><td rowspan=\"2\">Cross-Dataset Setting</td><td colspan=\"2\">minImageNet</td><td colspan=\"4\">CUB</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(b)</td><td rowspan=\"2\">Cross-Domain Setting 1</td><td colspan=\"2\">minImageNet</td><td colspan=\"4\">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(c)</td><td rowspan=\"2\">Cross-Domain Setting 2</td><td colspan=\"2\">FS-DomainNet</td><td colspan=\"4\">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(d)</td><td rowspan=\"2\">Cross-Annotated Setting</td><td colspan=\"2\">tieredImageNet (Coarse)</td><td colspan=\"4\">tieredImageNet (Fine)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Figure 6: Illustration of three challenging few-shot generalization scenarios under the 3-way 1-shot setting.",
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+    {
+        "type": "text",
+        "text": "significantly improve the performance of few-shot methods and outperform state-of-the-art methods for 5-shot setting on miniImageNet and 1-shot setting on tieredImageNet datasets. Moreover, FGFL is still on par with state-of-the-art methods under other settings. For CUB, as shown in Table 2 (b), we can observe that FGFL can improve the performance of FEAT by a large margin, i.e.,  $5.09\\%$  and  $4.1\\%$  for 1-shot and 5-shot settings, and is competitive with the state-of-the-art methods.",
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+    {
+        "type": "text",
+        "text": "4.3. Few-Shot Generalization",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To evaluate the generalized performance of few-shot methods, we propose three few-shot generalization settings for cross-domain classification based on challenging test scenarios, shown in Figure 6.",
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+    {
+        "type": "text",
+        "text": "4.3.1 Cross-Dataset Generalization",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this setting, we only consider the distribution gaps of classes between training and testing datasets with the same style, e.g., natural images. As shown in Figure 6 (a), we train on the miniImageNet dataset with natural images and evaluate the fine-grained CUB dataset with various bird species, i.e., mini  $\\rightarrow$  CUB.",
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+    {
+        "type": "text",
+        "text": "Table 3 shows that the proposed FGFL significantly improves the performance of the baseline FEAT method and outperforms the other methods. Figure 7 (a) shows that the proposed FGFL can force the network to capture discriminative task-specific frequency components for classification, e.g., high-frequency edge features for the first class and low-frequency color features for the third class.",
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+    {
+        "type": "text",
+        "text": "4.3.2 Cross-Domain Generalization",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unlike the cross-dataset setting, the visual similarity between the training (source) and testing (target) domains may have a significant gap, as the target domain may contain unnatural images, e.g., quickdraw. As shown in Figure 6 (b) and Figure 6 (c), we split the cross-domain scenario into two specific settings according to the number of the source domains, i.e., single (e.g., miniImageNet) or multiple domains (e.g., FS-DomainNet). For the second setting, each source domain only contains images with the same style such as paintings.",
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+    {
+        "type": "text",
+        "text": "Results in Table 3 show that our proposed FGFL outperforms other few-shot methods by a large margin under two cross-domain generalization settings, i.e., mini  $\\rightarrow$  Quickdraw and FS-DomainNet  $\\rightarrow$  Quickdraw. Figure 7 (b) also verifies that our proposed method can indeed learn to ex",
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+    {
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+        "text": "11820",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/2db14c0c5f58148fb23f990b90f6549eb6d99866e9ed5e74dc092c7c6174a6ca.jpg",
+        "image_caption": [
+            "Figure 7: Visualizations for few-shot generalization on three test datasets. (a), (b), and (c) represent different settings, i.e., cross-dataset, cross-domain, and cross-to-fine (C-to-F) annotated settings, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ploit high-frequency patterns rare in natural images to distinguish different classes on the quickdraw dataset. Another interesting observation is that few-shot methods generally perform better when generalizing from FS-DomainNet to quickdraw than from miniImageNet to quickdraw. A reasonable explanation is that compared to the miniImageNet dataset with small domain variations, the FS-DomainNet dataset includes multiple domains with obvious differences, which enables the network to capture domain-specific information from each meta-task for classification, resulting in better generalization ability to the unseen domain. Furthermore, our FGFL can still boost performance in this setting, illustrating the necessity of frequency domain information.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3.3 Coarse-to-Fine Annotated Generalization",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Different from existing settings, we consider the annotation difference between training and testing sets for few-shot generalization. In practice, an image may have different levels of class annotations due to the requirements of labeling tasks. For example, we only need a training set with two labels \"Furniture\" and \"Person\" to train a powerful classifier for a binary classification task. However, when we want to use the above classifier to identify the species of furniture, we need additional fine-grained labels such as \"Desk\" or \"Chair\". This is a practical scenario since fine-grained labeling requires a high cost of human collaboration. We conduct experiments on tieredImageNet with hierarchical annotations to evaluate the generalization performance under this setting, shown in Figure 6 (d). All competing methods are trained on the coarse-annotated training set with 20 super-classes and evaluated on the fine-annotated testing set with 160 sub-classes same as the standard few-shot setting, denoted as tiered(C)  $\\rightarrow$  (F).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As shown in Table 3, all methods perform worse than general classification results in Table 2. The reason is that the model tends to overfit the general features of high-level class prediction tasks while ignoring within-class differences. We observe that our proposed FGFL can still out",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8e0e26fbdc3c8ec781b0e66f99e0ebf8307eddbde75e0213d1b89ac7afa63cad.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td>Cross-Dataset</td><td colspan=\"2\">Cross-Domain</td><td>Cross-Annotated</td></tr><tr><td>mini → CUB</td><td>mini → Q</td><td>F → Q</td><td>tiered(C) → (F)</td></tr><tr><td>MatchingNet [39]</td><td>51.37</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GNN [13]</td><td>62.25</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GNN + FT [39]</td><td>66.98</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Meta DeepBDC [48]</td><td>77.87</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FEAT [55]†</td><td>62.28</td><td>55.96</td><td>77.23</td><td>64.67</td></tr><tr><td>ProtoNet [36]†</td><td>66.29</td><td>64.32</td><td>74.43</td><td>64.08</td></tr><tr><td>BML [60]†</td><td>71.22</td><td>75.47</td><td>65.38</td><td>52.63</td></tr><tr><td>DeepEMD [58]†</td><td>77.34</td><td>58.04</td><td>78.52</td><td>65.87</td></tr><tr><td>Ours</td><td>81.35</td><td>76.34</td><td>89.34</td><td>67.84</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8329409e79acb04234258b951f6605b60f1f75f8eff8adc6dbe4e4314efa5004.jpg",
+        "table_caption": [
+            "Table 3: Few-shot generalization results under the 5-way 5-shot setting. mini, Q, F, and tiered(C), (F) denote miniImageNet, QuickDraw, FS-DomainNet, tieredImageNet with coarse-grained or fine-grained annotations.  $\\dagger$ : reimplement based on public code with our setting. tieredImageNet with coarse-grained (super-classes) or fine-grained annotations (sub-classes).  $\\dagger$ : reimplemented based on public code with our setting."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">miniImageNet</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>Baseline</td><td>66.52 ± 0.20</td><td>81.46 ± 0.14</td></tr><tr><td>+Lsw.tri</td><td>67.38 ± 0.80</td><td>83.61 ± 0.61</td></tr><tr><td>+Lcw.ctr</td><td>68.44 ± 0.81</td><td>85.60 ± 0.60</td></tr><tr><td>+Laug</td><td>69.14 ± 0.80</td><td>86.01 ± 0.62</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 4: Ablation studies for our proposed FGFL framework over miniImageNet.",
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+    {
+        "type": "text",
+        "text": "perform all methods. Figure 7 (c) shows that our method can focus on specific frequency components (e.g., low and middle FCs corresponding to color and shape spatial features), which is discriminative for class prediction.",
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We perform ablation studies to investigate the effectiveness of the key components of FGFL on miniImageNet un-",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "11821",
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+    {
+        "type": "text",
+        "text": "der the 5-way settings with ResNet-12 as the backbone. As shown in Table 4, each proposed loss contributes to performance improvement. Moreover, we find that  $L_{sw\\_tri}$  and  $L_{cw\\_ctr}$  significantly improve the performance (1.92% and 4.14% for 1-shot and 5-shot, resp.), indicating that the proposed multi-level metrics can better utilize the frequency information to improve the generalizability of the model and avoid over-fitting to spatial features, leading to further improvements over spatial masks. Results also show that the two losses play different roles and complement each other, which further proves that our proposed method can utilize frequency information from different levels to help with classification. Noted that the performance gain under the 5-shot setting is much higher than the 1-shot setting. One plausible reason is that more supervised information introduced by support samples helps to generate a more precise frequency mask, which helps reduce the intra-class variation to learn a strong classifier, aligning with our idea.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we proposed a novel Frequency-Guided Few-shot Learning (FGFL) framework for few-shot classification and generalization. Specifically, the frequency masks generated by the classification gradients in the DCT domain can emphasize the class-discriminative frequency components in the current meta-task. Our proposed multi-level metrics, including sample-wise triplet loss and class-wise contrastive loss, can better utilize the frequency information at sample and task levels and encourage the model to capture more task-relevant frequency information to help the classification in the spatial domain. Besides, we systematically investigated the effects of frequency information on few-shot generalization behaviors. Extensive experiments demonstrated that FGFL achieves competitive results with state-of-the-art methods on the standard few-shot settings, and significantly improves the generalized performance on unseen testing domains.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            76,
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+    },
+    {
+        "type": "text",
+        "text": "This research is supported in part by the SUG and MOE AcRF Tier1 (RG61/22) Grant. This research work is also partially supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research), and the Singapore Government's Research, Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering domain) under Grant A18A1b0045.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            832,
+            174,
+            848
+        ],
+        "page_idx": 8
+    },
+    {
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+        ],
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diff --git a/2023/Frequency Guidance Matters in Few-Shot Learning/de0a02db-ed96-44b6-8f21-932746535501_model.json b/2023/Frequency Guidance Matters in Few-Shot Learning/de0a02db-ed96-44b6-8f21-932746535501_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..ccd4fc1ceb51c8b457e912b8308025bd8388928c
--- /dev/null
+++ b/2023/Frequency Guidance Matters in Few-Shot Learning/de0a02db-ed96-44b6-8f21-932746535501_model.json	
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+[
+    [
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Frequency Guidance Matters in Few-Shot Learning"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Hao Cheng\\(^{1}\\) Siyuan Yang\\(^{1}\\)  \n\\(^{1}\\)Nanyang Technological University"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Joey Tianyi Zhou\\(^{2,3}\\)  \nLanqing Guo\\(^{1}\\)  \nBihan Wen\\(^{1*}\\)  \n\\(^{2}\\)Centre for Frontier AI Research (CFAR), A*STAR, Singapore  \nFernance Computing (IHPC), A*STAR, Singapore"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "{hao006,siyuan005,lanqing001,bihan.wen}@ntu.edu.sg zhouty@cfar.a-star.edu.sg"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.319,
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+            "angle": 0,
+            "content": "Few-shot classification aims to learn a discriminative feature representation to recognize unseen classes with few labeled support samples. While most few-shot learning methods focus on exploiting the spatial information of image samples, frequency representation has also been proven essential in classification tasks. In this paper, we investigate the effect of different frequency components on the few-shot learning tasks. To enhance the performance and generalizability of few-shot methods, we propose a novel Frequency-Guided Few-shot Learning framework (dubbed FGFL), which leverages the task-specific frequency components to adaptively mask the corresponding image information, with a novel multi-level metric learning strategy including a triplet loss among original, masked and un-masked image as well as a contrastive loss between masked and original support and query sets to exploit more discriminative information. Extensive experiments on four benchmarks under several few-shot scenarios, i.e., standard, cross-dataset, cross-domain, and coarse-to-fine annotated classification, are conducted. Both qualitative and quantitative results show that our proposed FGFL scheme can attend to the class-discriminative frequency components, thus integrating those information towards more effective and generalizable few-shot learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
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+                0.21,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.739,
+                0.47,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Deep learning typically relies on large-scale annotated datasets to achieve superior results on image classification tasks. However, the learned deep models may fail to generalize under some severe conditions, e.g., few data or annotations. Correspondingly, the task to classify a query sample using only a few labeled data is known as few-shot classification [10, 40]. The key challenge is to learn the discriminative feature representation that can be generalized from the given training set to novel testing classes. Recently, sev"
+        },
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+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1: Visualizations of samples with different frequency masks on the CUB dataset [41]. Samples with the same color box belong to the same class. It is easier to distinguish two classes with masked specific frequency components. Each square on the left represents the masked status of corresponding frequency components, i.e., the dark and light color for masked and reserved, respectively. For each row (column), top-to-bottom and left-to-right represent low frequency to high frequency, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "eral few-shot methods [36, 48, 58] have applied the meta-learning framework [40] to build a discriminative feature space by simulating numerous meta-tasks to obtain the generalized feature representation, achieving superior performance for recognizing novel classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "However, very recent studies [3, 17, 26, 39] report that existing methods may fail to generalize well to novel classes due to large domain gaps between training and testing sets, e.g., from general to fine-grained tasks or a specific domain. In these cases, the learned feature embeddings based on spatial images may capture excessive domain-invariant information from the training patterns, leading to degraded performance in the test scenario with a large domain gap. Several domain adaptation-based few-shot algorithms [26, 37, 39, 57] have been proposed to alleviate the domain shift issues on few-shot classification. These"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "*Corresponding author."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "11814"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.183
+            ],
+            "angle": 0,
+            "content": "methods focus on learning a flexible feature embedding or fine-tuning on less novel support samples to transfer knowledge across domains. However, they cannot achieve stable performance improvements for different few-shot scenarios. Moreover, most domain adaption-based methods only focused on exploiting the image spatial features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.186,
+                0.471,
+                0.458
+            ],
+            "angle": 0,
+            "content": "Beyond spatial features, the frequency-domain representation plays a vital role for various computer vision tasks, e.g., deep fake recognition [12, 24, 27], domain generalization [19] and image classification [4, 32, 42, 50]. Different frequency components naturally convey discriminative and interpretive features for visual understanding [19, 32], e.g., the selected frequency components (FCs) of input images can be used to interpret the learned CNN features in classification [42, 50]. In few-shot learning, Chen et al. [4] is the first attempt to apply image frequency spectrum for classification, in which frequency information is naively concatenated as an extra feature, without exploiting different effects of its FCs. Figure 1 provides an example, clearly showing that certain FCs are more discriminative, thus should be selected and highlighted for more effective classification. However, no work to date has systematically investigated the roles of different FCs and how to adaptively select important FCs for effective few-shot learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.46,
+                0.471,
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+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a novel Frequency-Guided Few-shot Learning (FGFL) framework towards highly effective few-shot classification and generalization. For each input image, FGFL adaptively generates a task-specific class-discriminative mask in the frequency domain using Grad-CAM [35], where the activated FCs represent the important frequency information associated with the current task. Then we convert the masked and unmasked frequency components output back to the spatial domain for generating the masked and unmasked images, which contain limited and rich task-specific class-discriminative information, respectively. After that, for each image in the meta-task, we construct its triplet with its corresponding unmasked and masked images as positive and negative samples. We also construct two additional few-shot tasks by regrouping the masked and original support and query images, i.e., \\( \\mathcal{T}_{ms} \\) with masked support set and original query set, and \\( \\mathcal{T}_{mq} \\) with original support set and masked query set. In addition, we propose two types of ranking losses, including the triplet and contrastive loss functions at single images and tasks (i.e., \\( \\mathcal{T}_{ms} \\) and \\( \\mathcal{T}_{mq} \\)) levels, respectively, to force the model to capture task-specific class-discriminative information that can well generalize to the novel classes. Moreover, the unmasked images are also added to the support set to enhance the discriminability of feature embeddings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.472,
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+            ],
+            "angle": 0,
+            "content": "The contributions of this work are fourfold. First, we propose a Frequency-Guided Few-shot Learning (FGFL) framework to utilize the frequency information to enhance the performance and generalizability of few-shot methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.365
+            ],
+            "angle": 0,
+            "content": "in the spatial domain. Second, we propose two types of ranking loss, including the triplet and contrastive loss functions at both sample and task levels based on original and generated images, to force the network to focus on class-discriminative frequency components for each few-shot meta-task. In addition, the generated unmasked images are also utilized to augment the support set to enhance the discriminability of feature embeddings. Third, we investigate the impact of frequency components on current methods under several generalized few-shot settings, namely cross-dataset, cross-domain, and coarse-to-fine annotated generalization. To the best of our knowledge, this is the first work that exploits the effect of different frequency components on few-shot classification and generalization tasks explicitly. Last, experimental results and visualizations demonstrate that the proposed FGFL can improve the performance and generalizability of few-shot methods and achieve superior results under several few-shot settings."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.404,
+                0.715,
+                0.42
+            ],
+            "angle": 0,
+            "content": "2.1. Few-shot Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.428,
+                0.895,
+                0.669
+            ],
+            "angle": 0,
+            "content": "Few-shot learning aims to recognize novel query samples with only a few available support samples. Recently, existing deep few-shot methods can be divided into three main categories. First, optimization-based meta-learning methods [2, 11, 20, 28, 33] design a good model initialization or optimization strategy that can quickly adapt to novel tasks. Second, metric-based methods [7, 29, 30, 36, 48, 55, 58] focus on constructing an appropriate latent space to extract discriminative feature embeddings and then predict based on the similarity between support and query samples. Third, data generative and augmentation-based methods focus on generating more variant samples to learn a more accurate classifier, e.g., applying data rotation or transformation [21] by self-supervised learning, synthesizing new data with a generative model [14, 23], or using external data with pseudo labels [18, 44, 52]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.67,
+                0.895,
+                0.761
+            ],
+            "angle": 0,
+            "content": "Most above-mentioned algorithms only employ spatial images as the network input without exploiting the frequency information. In our work, we investigate the effect of the frequency information in the Discrete Cosine Transformation (DCT) domain and leverage it to guide few-shot classification in the spatial domain."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.772,
+                0.807,
+                0.789
+            ],
+            "angle": 0,
+            "content": "2.2. Learning in the Frequency Domain"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Frequency components contain rich patterns for image understanding and have been widely studied in several computer vision tasks such as compressed sensing [43, 51, 56], visual pre-training [47], domain transfer [19, 53], and image classification [4, 8, 32, 42, 50]. Yang et al. [53] use the Fast Fourier Transformation (FFT) to achieve domain alignment by simply swapping the low-frequency spectrum between"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "11815"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.109,
+                0.092,
+                0.429,
+                0.257
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.267,
+                0.473,
+                0.343
+            ],
+            "angle": 0,
+            "content": "Figure 2: T-SNE visualization of all image features of 20 test classes in the CUB (top) and 15 test classes in the Quickdraw (bottom) dataset. The few-shot model is trained on the miniImageNet dataset. A cluster that is clearer and more compact within each class is better."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.101,
+                0.356,
+                0.451,
+                0.417
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>miniImageNet</td><td>CUB</td><td>Quickdraw</td></tr><tr><td>ProtoNet [36]</td><td>79.86</td><td>66.29</td><td>64.32</td></tr><tr><td>ProtoNet w/ High FCs</td><td>56.47</td><td>37.96</td><td>66.26</td></tr><tr><td>ProtoNet w/o High FCs</td><td>77.75</td><td>67.09</td><td>65.99</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.427,
+                0.471,
+                0.489
+            ],
+            "angle": 0,
+            "content": "Table 1: Few-shot classification results under the 5-way 5-shot setting trained with the miniImageNet dataset. ProtoNet is trained on miniImageNet dataset and evaluated on several datasets with specific frequency components."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.515,
+                0.47,
+                0.741
+            ],
+            "angle": 0,
+            "content": "source and target domain samples. GFNet [32] considers the attention in the FFT frequency domain to replace the self-attention module in the vision transformer. However, FFT requires double the memory for complex coefficients. Therefore, some recent works [4, 31, 50] consider applying the Discrete Cosine Transformation (DCT) to learn in the frequency domain. For example, Wang et al. [43] first applies the DCT to speed up the network. Instead of inputting RGB pixels, Gueguen et al. [16] convert the JPEG-compressed image to its \\(8 \\times 8\\) block DCT coefficients as the input of the neural network. FcaNET [31] adopts DCT to generalize the compression of the channel attention mechanism in the frequency domain. Specifically, Chen et al. [4] select pre-defined channels in the DCT frequency domain to improve the performance for few-shot classification."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.742,
+                0.469,
+                0.817
+            ],
+            "angle": 0,
+            "content": "In this work, we also employ the DCT to transform the images to the frequency domain. Unlike previous work [4], we consider the interaction between spatial and frequency domains and learn to generate the discriminative frequency mask to enhance learning in the spatial domain."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.83,
+                0.251,
+                0.848
+            ],
+            "angle": 0,
+            "content": "3. Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section, we first investigate the impact of frequency components in different few-shot classification scenarios. Then the proposed FGFL framework is described"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.122
+            ],
+            "angle": 0,
+            "content": "and explained in detail, followed by the loss function of our method and empirical validations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.131,
+                0.892,
+                0.148
+            ],
+            "angle": 0,
+            "content": "3.1. Frequency Analysis on Few-shot Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.155,
+                0.892,
+                0.229
+            ],
+            "angle": 0,
+            "content": "We first investigate the impact of frequency components on the generalized performance of current few-shot methods under different few-shot settings by removing and preserving partial frequency components of each image in the meta-task for class prediction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.23,
+                0.892,
+                0.335
+            ],
+            "angle": 0,
+            "content": "To generate the frequency representation of an input RGB image \\(X \\in \\mathbb{R}^{H \\times W \\times 3}\\), we apply the 2D-Discrete Cosine Transform [1] (2D-DCT) function as \\(D = DCT(X) \\in \\mathbb{R}^{H \\times W \\times 3}\\). We can then remove or preserve partial frequency components of each input image, followed by an Inverse 2D-DCT function as \\(\\hat{X} = IDCT(\\hat{D})\\) to transform it back into the spatial domain with the original input size."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.336,
+                0.892,
+                0.472
+            ],
+            "angle": 0,
+            "content": "With the help of the DCT functions, we can decompose the raw data into two parts, \\( X = \\{X^{O}, X^{H}\\} \\), where \\( X^{H} \\) and \\( X^{O} \\) represent high-frequency components (dubbed w/ high FCs), and other components (dubbed w/o high FCs). For a given few-shot task \\( \\mathcal{T}_{\\mathrm{test}} = (\\mathcal{S}, \\mathcal{Q}) \\) on the novel testing set, we can reconstruct images with partial frequency information to update the testing task as \\( \\tilde{\\mathcal{T}}_{\\mathrm{test}} = \\{\\tilde{S}, \\tilde{\\mathcal{Q}}\\} \\). Then we adopt the existing few-shot methods to make predictions for each query sample \\( \\tilde{X}_j \\) with \\( \\tilde{S} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.472,
+                0.892,
+                0.577
+            ],
+            "angle": 0,
+            "content": "Table 1 shows classification accuracy on different test domains and Figure 2 plots the t-SNE visualizations of image features extracted by the trained feature encoder. We can observe that removing specific frequency components can improve the generalized performance of few-shot models but degrade standard few-shot performance in the same testing scenario."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.578,
+                0.892,
+                0.653
+            ],
+            "angle": 0,
+            "content": "To this end, frequency information plays different roles in different classification scenarios. Through evaluation and observation, it can be conjectured that the generalization behaviors of few-shot methods are relevant to frequency components which may vary across datasets and domains."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.662,
+                0.831,
+                0.679
+            ],
+            "angle": 0,
+            "content": "3.2. Frequency-Guided Few-shot Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.685,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Different FCs encode specific image information, we propose the Frequency-Guided Few-shot Learning (FGFL) framework, which utilizes the frequency mask to guide the training in the spatial domain. As shown in Figure 3, FGFL has two branches with two encoders \\( E^{fq} \\) and \\( E^{sp} \\) for feature extraction in the frequency and spatial domains, respectively. FGFL generates the frequency mask based on the task-specific attention map for the given few-shot task, which is then adopted to generate additional images, guiding the network updates in the spatial domain. Moreover, we propose a multi-level metric to force the network to capture specific frequency components for classification."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.5,
+                0.875,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "1More implementation details and evaluation results for all frequency components of more few-shot methods are provided in Supplementary."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11816"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.12,
+                0.094,
+                0.838,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.323,
+                0.892,
+                0.4
+            ],
+            "angle": 0,
+            "content": "Figure 3: Overview of our proposed Frequency-Guided Few-shot Learning framework (FGFL). We first generate the task-specific class-discriminative frequency mask based on the classification in the frequency domain. Then we convert the masked and unmasked frequency samples back to the spatial domain and generate two image sets (masked set \\( X_{m} \\) and unmasked set \\( X_{um} \\)) according to the mask and unmask regions, respectively. Furthermore, we adopt novel multi-level metrics (shown in Figure 4) on the original and generated image sets to make class predictions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.425,
+                0.427,
+                0.44
+            ],
+            "angle": 0,
+            "content": "3.2.1 Task-Specific Frequency Mask Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.449,
+                0.469,
+                0.569
+            ],
+            "angle": 0,
+            "content": "To obtain a task-specific attention mask of frequency components for each few-shot task, we first transform the input spatial input image \\(X\\) to \\(D\\) in the frequency domain. Then we generate the attention map by Grad-CAM [35] based on the output feature map \\(M \\in \\mathbb{R}^{C \\times h \\times w}\\) of the last convolution layer in the frequency encoder (e.g., ResNet-12), where \\(C\\) is the channel number of the feature map, \\(h\\) and \\(w\\) indicate the height and width of the feature map, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.57,
+                0.469,
+                0.661
+            ],
+            "angle": 0,
+            "content": "For its ground-truth class \\(c\\), we compute the gradient of the score \\(s^c\\) with respect to the feature map activation \\(M_{k}\\in \\mathbb{R}^{h\\times w}\\) as \\(\\frac{\\partial s^c}{\\partial M_k}\\), where \\(k\\) indicates the channel index of the feature map. These gradients flowing back will pass through a global average pooling layer (denoted as \\(GAP(\\cdot))\\) to obtain the neuron importance weights \\(w_{k}^{c}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.207,
+                0.667,
+                0.469,
+                0.7
+            ],
+            "angle": 0,
+            "content": "\\[\nw _ {k} ^ {c} = G A P \\left(\\frac {\\partial s ^ {c}}{\\partial M _ {k}}\\right). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.705,
+                0.469,
+                0.779
+            ],
+            "angle": 0,
+            "content": "The weight \\( w_{k}^{c} \\) reflects the importance of activation map \\( M_{k} \\) to make the prediction of class \\( c \\) for the input \\( D \\). We then perform a weighted combination with a ReLU function to integrate the positive influence of feature maps across different channels of \\( M \\) for class \\( c \\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.786,
+                0.469,
+                0.817
+            ],
+            "angle": 0,
+            "content": "\\[\nA ^ {c} = \\operatorname {R e L U} \\left(\\sum_ {k} w _ {k} ^ {c} M _ {k}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.87
+            ],
+            "angle": 0,
+            "content": "where \\(A^c \\in \\mathbb{R}^{h \\times w}\\) is the heatmap reflecting frequency components that have a positive impact on the ground-truth class \\(c\\) of a given frequency input."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Note that previous works [35, 22] utilize a fully connected (fc) layer to obtain the classification score \\( s^c \\) for the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.425,
+                0.891,
+                0.486
+            ],
+            "angle": 0,
+            "content": "ground-truth class \\( c \\) with the same training and testing class set. However, since the training and testing classes in few-shot scenarios are non-overlap, directly applying fc layers for gradient computation may be prone to overfitting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.487,
+                0.892,
+                0.64
+            ],
+            "angle": 0,
+            "content": "To this end, we compute the cosine similarity between each sample and class prototype as the classification score for each given \\(N\\)-way \\(K\\)-shot task in few-shot learning, where \\(N\\) and \\(K\\) indicates the number of selected classes and labeled support samples from each class, respectively. Specifically, given a few-shot task with support set \\(\\mathcal{S}_f = \\{D_m, y_m\\}_{m=1}^{NK}\\), and a query set \\(\\mathcal{Q}_f = \\{D_n, y_n\\}_{n=1}^Q\\) in the frequency domain, we compute the cosine similarity score \\(s^c\\) between each query sample \\(\\mathbf{q} \\in \\mathbb{R}^C\\) and each class prototype \\(\\mathbf{v}_c \\in \\mathbb{R}^C\\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.588,
+                0.653,
+                0.891,
+                0.687
+            ],
+            "angle": 0,
+            "content": "\\[\ns ^ {c} = p (y = c \\mid \\mathbf {q}) = \\frac {\\mathbf {q} ^ {T} \\mathbf {v} _ {c}}{\\| \\mathbf {q} \\| \\| \\mathbf {v} _ {c} \\|}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.702,
+                0.892,
+                0.839
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{v}_c = \\frac{1}{K}\\sum_{k=1}^{K}\\mathbf{z}_k\\) is the mean feature vector of the support features \\(\\mathbf{z}_k\\) of the \\(c\\)-th class. Note that, it is easy to prove Eq. (3) is equivalent to an fc layer when neglecting the bias of the fc layer. Moreover, the classification weights \\(\\mathbf{v}_c\\) are flexible and task-dependent, i.e., only based on the current few-shot task. Hence, the network can learn to generate a task-specific heatmap \\(A^c\\) of each sample to find specific frequency components that contribute most to the current task, which avoids over-fitting to the training set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.84,
+                0.891,
+                0.871
+            ],
+            "angle": 0,
+            "content": "We then up-sample \\(A^c\\) to the original size and generate the frequency mask following previous works [45, 22] as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.585,
+                0.885,
+                0.891,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {M a s k} ^ {c} = \\mathbf {1} - \\operatorname {S i g m o i d} \\left(U p \\left(A ^ {c}\\right)\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.518,
+                0.956
+            ],
+            "angle": 0,
+            "content": "11817"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.094,
+                0.454,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.291,
+                0.473,
+                0.49
+            ],
+            "angle": 0,
+            "content": "Figure 4: Illustration of the proposed multi-level metrics. Specifically, for each image in the image set \\( X \\) in the metask, we construct its triplet from the corresponding un-masked and masked set \\( X^m \\) and \\( X^{um} \\) as the positive and negative pair, respectively, and adopt the sample-wise triplet loss \\( L_{sw\\_tri} \\) to exploit the correlations them. At the task level, we construct two additional few-shot tasks by regrouping the images in \\( X \\) and \\( X^m \\). (Here we take the query set as an example.) Then we propose a class-wise contrastive loss \\( L_{cw\\_ctr} \\) between positive pairs (original support and query samples) and negative pairs (support and query from different sets). Moreover, we use unmasked images to augment the support set for classification with a loss \\( L_{aug} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.515,
+                0.47,
+                0.56
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{1}\\) is an all-ones matrix, \\(Up(\\cdot)\\) is the upsampling operation, and \\(Sigmoid(\\cdot)\\) is applied to make it derivable and constrains the value to the range [0, 1]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.56,
+                0.47,
+                0.606
+            ],
+            "angle": 0,
+            "content": "\\(Mask^c\\) is then applied to \\(D\\) and converted back to the spatial domain to generate the masked spatial image \\(X^m\\) and corresponding unmasked spatial image \\(X^{um}\\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.078,
+                0.617,
+                0.47,
+                0.647
+            ],
+            "angle": 0,
+            "content": "\\[\nX ^ {m} = I D C T \\left(M a s k ^ {c} \\odot D\\right), X ^ {u m} = I D C T \\left(\\left(1 - M a s k ^ {c}\\right) \\odot D\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.648,
+                0.471,
+                0.739
+            ],
+            "angle": 0,
+            "content": "where \\(\\odot\\) is the dot product function. Note that \\(X^{m}\\) and \\(X^{um}\\) are considered to contain limited and rich information belonging to the target class since the regions on the attention map beyond the class-aware range should be hard to identify the true class. We can then utilize \\(X^{m}\\) and \\(X^{um}\\) to guide few-shot learning in the spatial domain."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.757,
+                0.373,
+                0.772
+            ],
+            "angle": 0,
+            "content": "3.2.2 Mask-Guided Multi-Level Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.781,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "With the help of task-specific frequency mask generation, we already generate additional samples (i.e., masked images \\( X^{m} \\) and unmasked images \\( X^{um} \\)). To incorporate frequency information to encourage the spatial network to capture class discriminative information, we propose two ranking losses at the sample and task levels, (i.e., sample-wise triplet loss \\( L_{sw\\_tri} \\) and class-wise contrastive loss \\( L_{cw\\_ctr} \\), respectively.) to fully exploit the mask information in the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "frequency signal, shown in Figure 4. Meanwhile, we also adopt the unmasked images to enhance the few-shot classification performance with an additional classification loss \\( L_{\\text{aug}} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.152,
+                0.893,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Sample-wise triplet loss. For each original image \\(X_{i}\\) in the meta-task, this loss aims to enhance the feature similarity between \\(X_{i}\\) and its corresponding unmasked image \\(X_{i}^{um}\\), while reducing that between \\(X_{i}\\) and its corresponding masked image \\(X_{i}^{m}\\). Formally, we construct the triplet for each image in the meta-task as \\((X_{i}, X_{i}^{m}, X_{i}^{um})\\), where \\(X_{i}, X_{i}^{um}\\), and \\(X_{i}^{m}\\) are the anchor, positive, and negative samples, respectively. We define \\(E^{sp} = f_{\\phi}(\\cdot)\\) as the feature extractor with parameters \\(\\phi\\) to obtain the feature vector. Then the sample-level triplet loss can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.514,
+                0.309,
+                0.892,
+                0.361
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {s w. t r i} \\left(X _ {i}, X _ {i} ^ {u m}, X _ {i} ^ {m}\\right) = \\max  \\left\\{d \\left(f _ {\\phi} \\left(X _ {i}\\right), f _ {\\phi} \\left(X _ {i} ^ {u m}\\right)\\right) \\right. \\\\ - d \\left(f _ {\\phi} \\left(X _ {i}\\right), f _ {\\phi} \\left(X _ {i} ^ {m}\\right)\\right) + \\eta , 0 \\}, \\tag {6} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.369,
+                0.892,
+                0.399
+            ],
+            "angle": 0,
+            "content": "where \\(d(\\cdot ,\\cdot)\\) denotes the distance between two features and \\(\\eta\\) is the margin between positive and negative pairs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.4,
+                0.893,
+                0.505
+            ],
+            "angle": 0,
+            "content": "Class-wise contrastive loss. To encourage the network to capture class discriminative information, we construct contrastive pairs for each query instance in the original and masked sets. Specifically, given masked support and query sets \\(S_{m} = \\{X_{i}^{m},y_{i}\\}_{i = 1}^{NK}\\) and \\(\\mathcal{Q}_m = \\{X_j^m,y_j\\}_{j = 1}^Q\\) , we first construct two additional masked few-shot tasks by regrouping the masked and original sets as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.574,
+                0.512,
+                0.892,
+                0.53
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {T} _ {m s} = \\left(\\mathcal {S} _ {m}, \\mathcal {Q}\\right), \\quad \\mathcal {T} _ {m q} = \\left(\\mathcal {S}, \\mathcal {Q} _ {m}\\right), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.536,
+                0.892,
+                0.568
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{S} = \\{X_i, y_i\\}_{i=1}^{NK}\\) and \\(\\mathcal{Q} = \\{X_j, y_j\\}_{j=1}^Q\\) are original support and query set, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.568,
+                0.892,
+                0.675
+            ],
+            "angle": 0,
+            "content": "Each masked sample consists of less class-discriminative information. To avoid being misled by class-irrelevant information (i.e., preserved in \\( S_{m} \\) and \\( \\mathcal{Q}_{m} \\)), we regard the support and query samples from tasks \\( T_{ms} \\) and \\( T_{mq} \\) as negative pairs, and those from the original task with the same class as positive pairs. Then the contrastive loss corresponding to query sample \\( X_{q} \\in \\mathcal{Q} \\) can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.681,
+                0.9,
+                0.734
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {q} = - \\log \\frac {\\sum_ {y _ {j} = y _ {q} , X _ {j} \\in S} e ^ {d \\left(z _ {j} , z _ {q}\\right) / \\tau}}{\\sum_ {y _ {j} = y _ {q} , X _ {j} \\in S} e ^ {d \\left(z _ {j} , z _ {q}\\right) / \\tau} + \\sum_ {X _ {k} \\in S _ {m}} e ^ {d \\left(z _ {k} , z _ {q}\\right) / \\tau}}, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.734,
+                0.892,
+                0.78
+            ],
+            "angle": 0,
+            "content": "where \\( z_{i} = f_{\\phi}(X_{i}) \\) represents the feature vector extracted by the spatial backbone. Similarly, the contrastive loss for support sample \\( X_{s}\\in S \\) can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.785,
+                0.902,
+                0.838
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {s} = - \\log \\frac {\\sum_ {y _ {j} = y _ {s} , X _ {j} \\in Q} e ^ {d \\left(z _ {j} , z _ {s}\\right) / \\tau}}{\\sum_ {y _ {j} = y _ {s} , X _ {j} \\in Q} e ^ {d \\left(z _ {j} , z _ {s}\\right) / \\tau} + \\sum_ {X _ {k} \\in Q _ {m}} e ^ {d \\left(z _ {k} , z _ {s}\\right) / \\tau}}. \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.84,
+                0.838,
+                0.855
+            ],
+            "angle": 0,
+            "content": "Overall, for one episode, \\( L_{cw - ctr} \\) can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.573,
+                0.861,
+                0.892,
+                0.904
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {c w - c t r} = \\frac {1}{Q} \\sum_ {q = 1} ^ {Q} L _ {q} + \\frac {1}{N K} \\sum_ {s = 1} ^ {N K} L _ {s}. \\tag {10}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11818"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.09,
+                0.27,
+                0.187
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.078,
+                0.201,
+                0.273,
+                0.242
+            ],
+            "angle": 0,
+            "content": "(a) Visualization results on Mean Magnitude features of Channels (MMC)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.286,
+                0.109,
+                0.468,
+                0.171
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>mini</td><td>CUB</td></tr><tr><td>Pretrained</td><td>0.5567</td><td>1.5584</td></tr><tr><td>FEAT [55]</td><td>0.5386</td><td>1.5367</td></tr><tr><td>Ours</td><td>0.1256</td><td>1.2550</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.282,
+                0.182,
+                0.468,
+                0.223
+            ],
+            "angle": 0,
+            "content": "(b) Maximum Mean Discrepancy (MMD) results on different test datasets."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.255,
+                0.469,
+                0.346
+            ],
+            "angle": 0,
+            "content": "Figure 5: (a) MMC before and after applying the proposed FGFL method. (b) MMD results of few-shot methods trained over miniImageNet. The lower MMD value indicates a smaller gap and better performance. 'Pretrained' denotes the feature extractor (i.e., ResNet-12) pre-trained on the training set of miniImageNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.373,
+                0.469,
+                0.48
+            ],
+            "angle": 0,
+            "content": "Augmented classification loss. To better classify samples in the query set \\(\\mathcal{Q}\\), we use generated support images \\(S_{um}\\) in \\(X^{um}\\) to enhance the support set for classification. Specifically, we build a new support set by combining the original support and unmasked support set as \\(S_{aug} = S \\cup S_{um}\\). Hence, we conduct few-shot classification on query set \\(\\mathcal{Q}\\) based on \\(S_{aug}\\) and minimize the cross-entropy loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.144,
+                0.493,
+                0.469,
+                0.535
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {a u g} = \\sum_ {j = 1} ^ {Q} L _ {C E} \\left(f _ {\\theta} \\left(X _ {j}; \\mathcal {S} _ {a u g}\\right), y _ {j}\\right). \\tag {11}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.555,
+                0.42,
+                0.571
+            ],
+            "angle": 0,
+            "content": "3.2.3 Objective, Model Training, and Inference"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.58,
+                0.469,
+                0.61
+            ],
+            "angle": 0,
+            "content": "Combining with the standard few-shot classification, the overall objective function is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.078,
+                0.622,
+                0.469,
+                0.653
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {t o t a l} = L _ {c l s} ^ {s p} + L _ {c l s} ^ {f q} + \\lambda_ {1} \\cdot L _ {s w \\_ t r i} + \\lambda_ {2} \\cdot L _ {c w \\_ c t r} + \\lambda_ {3} \\cdot L _ {a u g}, \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.653,
+                0.469,
+                0.715
+            ],
+            "angle": 0,
+            "content": "where \\( L_{cls}^{sp} \\) and \\( L_{cls}^{fq} \\) represent the cross-entropy loss for few-shot classification in the spatial and frequency branch, respectively. \\( \\lambda_1, \\lambda_2, \\) and \\( \\lambda_3 \\) denote the weighting parameters of the corresponding losses, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.715,
+                0.469,
+                0.821
+            ],
+            "angle": 0,
+            "content": "During the training phase, we first generate frequency masks based on the frequency branch and then adopt the proposed multi-level metrics for model training. During the inference time, our proposed method strictly follows the inductive setting. We only feed the support set into the frequency branch to generate unmasked support images to refine the support set for classification."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.832,
+                0.274,
+                0.848
+            ],
+            "angle": 0,
+            "content": "3.3. Empirical Validation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The proposed FGFL framework aims to utilize frequency information to guide the spatial feature extractor towards class-discriminative features and avoid over-fitting to the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "training patterns, thus generalizing well to testing scenarios. To validate the effectiveness of the proposed method, we conduct experiments about learned features on two aspects: channel distribution shift and domain distance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.153,
+                0.892,
+                0.304
+            ],
+            "angle": 0,
+            "content": "Mean Magnitude of Channels (MMC) Luo et al. [26] shows the channel bias problem affects the generalizability of few-shot methods and utilizes MMC to visualize and measure the channel response to features, where effective few-shot methods might have a more uniform MMC curve in the testing set. Inspired by this work, we visualize the MMC before and after applying FGFL over miniImageNet. We can observe a channel magnitude change in Figure 5 (a), which validates that our proposed method can alleviate the channel bias problem, thus improving the performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.305,
+                0.892,
+                0.457
+            ],
+            "angle": 0,
+            "content": "Maximum Mean Discrepancy (MMD) The MMD [15] is a distance measure between two domains based on the embedding of distribution measures in a reproducing kernel Hilbert space, which has been widely applied in transfer learning problems. We adopt class-wise MMD to measure the distribution gap between the training and testing sets with different methods trained over miniImageNet. Figure 5 (b) shows different gaps between one training set and different testing sets. We can also observe that our proposed method helps to reduce the domain shift."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.473,
+                0.633,
+                0.49
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.499,
+                0.691,
+                0.516
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.524,
+                0.892,
+                0.569
+            ],
+            "angle": 0,
+            "content": "Datasets. We conduct extensive experiments on four few-shot datasets, i.e., miniImageNet [40], tieredImageNet [34], CUB [41], and FS-DomainNet [6]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.571,
+                0.892,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Implementation Details. For fair comparisons with previous methods, we adopt the ResNet-12 network with [64, 160, 320, 640] channels as our backbone in each branch, and set the input image size as \\(84 \\times 84\\) for all datasets. We combine our proposed FGFL with FEAT [55], which adopts a linear projection layer for feature adaptation. We randomly select 15 samples of each class to construct the query set for 5-way 1-shot and 5-way 5-shot settings. The backbone networks are pre-trained on the training set following the typical classification task. The weighting parameters \\(\\lambda_{1}\\), \\(\\lambda_{2}\\), and \\(\\lambda_{3}\\) are all set to 0.1 to balance the scale between the classification loss and the corresponding losses for all datasets."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.78,
+                0.714,
+                0.794
+            ],
+            "angle": 0,
+            "content": "4.2. Few-shot Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.805,
+                0.892,
+                0.85
+            ],
+            "angle": 0,
+            "content": "We conduct experiments on two standard few-shot settings, i.e., general and fine-grained classification, shown in Table 2. Table 2 (a) shows that our proposed FGFL can"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.516,
+                0.863,
+                0.76,
+                0.876
+            ],
+            "angle": 0,
+            "content": "2More details are included in Supplementary."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.502,
+                0.876,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "3More details about datasets and experimental settings are included in Supplementary."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.502,
+                0.863,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11819"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.089,
+                0.501,
+                0.294
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">miniImageNet</td><td colspan=\"2\">tieredImageNet</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>ProtoNet [36]†</td><td>61.83 ± 0.20</td><td>79.86 ± 0.14</td><td>66.84 ± 0.23</td><td>84.54 ± 0.16</td></tr><tr><td>Meta-Baseline [5]</td><td>63.17 ± 0.23</td><td>79.26 ± 0.17</td><td>68.62 ± 0.27</td><td>83.29 ± 0.18</td></tr><tr><td>Good-Embed [38]</td><td>64.82 ± 0.60</td><td>82.14 ± 0.43</td><td>71.52 ± 0.69</td><td>86.03 ± 0.58</td></tr><tr><td>DeepEMD [58]</td><td>65.91 ± 0.82</td><td>82.41 ± 0.56</td><td>71.16 ± 0.87</td><td>86.03 ± 0.58</td></tr><tr><td>FRN [46]</td><td>66.45 ± 0.19</td><td>82.83 ± 0.13</td><td>71.16 ± 0.22</td><td>86.01 ± 0.15</td></tr><tr><td>FEAT [55]†</td><td>66.52 ± 0.20</td><td>81.46 ± 0.14</td><td>70.30 ± 0.23</td><td>84.55 ± 0.16</td></tr><tr><td>BML [60]</td><td>67.04 ± 0.63</td><td>83.63 ± 0.29</td><td>68.99 ± 0.50</td><td>85.49 ± 0.34</td></tr><tr><td>IEPT [59]</td><td>67.05 ± 0.44</td><td>82.90 ± 0.30</td><td>72.24 ± 0.50</td><td>86.73 ± 0.34</td></tr><tr><td>MELR [9]</td><td>67.40 ± 0.43</td><td>83.40 ± 0.28</td><td>72.14 ± 0.51</td><td>87.01 ± 0.35</td></tr><tr><td>MCL-Katz [25]</td><td>67.51</td><td>83.99</td><td>72.01</td><td>86.02</td></tr><tr><td>CSEI [21]</td><td>67.59 ± 0.83</td><td>81.93 ± 0.36</td><td>72.57 ± 0.95</td><td>85.72 ± 0.63</td></tr><tr><td>Meta DeepBDC [48]</td><td>67.83 ± 0.43</td><td>84.46 ± 0.28</td><td>72.34 ± 0.49</td><td>87.31 ± 0.32</td></tr><tr><td>DFR [6]</td><td>68.12 ± 0.81</td><td>82.79 ± 0.56</td><td>72.38 ± 0.95</td><td>86.00 ± 0.61</td></tr><tr><td>Yang et al. [54]</td><td>70.19 ± 0.46</td><td>84.66 ± 0.29</td><td>72.62 ± 0.51</td><td>86.62 ± 0.33</td></tr><tr><td>Ours</td><td>69.14 ± 0.80</td><td>86.01 ± 0.62</td><td>73.21 ± 0.88</td><td>87.21 ± 0.61</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.076,
+                0.301,
+                0.505,
+                0.328
+            ],
+            "angle": 0,
+            "content": "(a) Average classification accuracy \\((\\%)\\) on miniImageNet and tieredImageNet datasets with the ResNet-12 as backbone."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.536,
+                0.109,
+                0.895,
+                0.274
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Backbone</td><td colspan=\"2\">CUB</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>MELR [9]</td><td>ConvNet-4</td><td>70.26 ± 0.50</td><td>85.01 ± 0.32</td></tr><tr><td>ProtoNet [36]†</td><td>ResNet-12</td><td>72.25 ± 0.21</td><td>87.47 ± 0.13</td></tr><tr><td>DeepEMD [58]</td><td>ResNet-12</td><td>75.65 ± 0.83</td><td>88.69 ± 0.50</td></tr><tr><td>FEAT [55]†</td><td>ResNet-12</td><td>75.68 ± 0.20</td><td>87.91 ± 0.13</td></tr><tr><td>BML [60]</td><td>ResNet-12</td><td>76.21 ± 0.63</td><td>90.45 ± 0.36</td></tr><tr><td>Good-Embed [38]‡</td><td>ResNet-18</td><td>77.92 ± 0.46</td><td>89.94 ± 0.26</td></tr><tr><td>DFR [6]</td><td>ResNet-12</td><td>78.07 ± 0.79</td><td>89.74 ± 0.51</td></tr><tr><td>VFD [49]</td><td>ResNet-12</td><td>79.12 ± 0.83</td><td>91.48 ± 0.39</td></tr><tr><td>FRN [46]†</td><td>ResNet-12</td><td>82.90 ± 0.19</td><td>92.61 ± 0.10</td></tr><tr><td>Ours</td><td>ResNet-12</td><td>80.77 ± 0.90</td><td>92.01 ± 0.71</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.542,
+                0.28,
+                0.88,
+                0.294
+            ],
+            "angle": 0,
+            "content": "(b) Average classification accuracy \\((\\%)\\) on CUB dataset."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.341,
+                0.895,
+                0.388
+            ],
+            "angle": 0,
+            "content": "Table 2: Comparison with state-of-the-art methods for general (a) and fine-grained (b) few-shot image classification. The best and second best results under each setting and dataset are highlighted as Red and Blue, respectively. \\(\\dagger\\): implemented based on public code with our setting. \\(\\ddagger\\): reported in [48]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.085,
+                0.409,
+                0.468,
+                0.589
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"4\">Train Scenario</td><td colspan=\"4\">Test Scenario</td></tr><tr><td rowspan=\"2\">(a)</td><td rowspan=\"2\">Cross-Dataset Setting</td><td colspan=\"2\">minImageNet</td><td colspan=\"4\">CUB</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(b)</td><td rowspan=\"2\">Cross-Domain Setting 1</td><td colspan=\"2\">minImageNet</td><td colspan=\"4\">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(c)</td><td rowspan=\"2\">Cross-Domain Setting 2</td><td colspan=\"2\">FS-DomainNet</td><td colspan=\"4\">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(d)</td><td rowspan=\"2\">Cross-Annotated Setting</td><td colspan=\"2\">tieredImageNet (Coarse)</td><td colspan=\"4\">tieredImageNet (Fine)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.602,
+                0.47,
+                0.633
+            ],
+            "angle": 0,
+            "content": "Figure 6: Illustration of three challenging few-shot generalization scenarios under the 3-way 1-shot setting."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.663,
+                0.47,
+                0.799
+            ],
+            "angle": 0,
+            "content": "significantly improve the performance of few-shot methods and outperform state-of-the-art methods for 5-shot setting on miniImageNet and 1-shot setting on tieredImageNet datasets. Moreover, FGFL is still on par with state-of-the-art methods under other settings. For CUB, as shown in Table 2 (b), we can observe that FGFL can improve the performance of FEAT by a large margin, i.e., \\(5.09\\%\\) and \\(4.1\\%\\) for 1-shot and 5-shot settings, and is competitive with the state-of-the-art methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.815,
+                0.305,
+                0.831
+            ],
+            "angle": 0,
+            "content": "4.3. Few-Shot Generalization"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "To evaluate the generalized performance of few-shot methods, we propose three few-shot generalization settings for cross-domain classification based on challenging test scenarios, shown in Figure 6."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4.3.1 Cross-Dataset Generalization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.437,
+                0.892,
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+            "angle": 0,
+            "content": "In this setting, we only consider the distribution gaps of classes between training and testing datasets with the same style, e.g., natural images. As shown in Figure 6 (a), we train on the miniImageNet dataset with natural images and evaluate the fine-grained CUB dataset with various bird species, i.e., mini \\(\\rightarrow\\) CUB."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.528,
+                0.892,
+                0.633
+            ],
+            "angle": 0,
+            "content": "Table 3 shows that the proposed FGFL significantly improves the performance of the baseline FEAT method and outperforms the other methods. Figure 7 (a) shows that the proposed FGFL can force the network to capture discriminative task-specific frequency components for classification, e.g., high-frequency edge features for the first class and low-frequency color features for the third class."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4.3.2 Cross-Domain Generalization"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Unlike the cross-dataset setting, the visual similarity between the training (source) and testing (target) domains may have a significant gap, as the target domain may contain unnatural images, e.g., quickdraw. As shown in Figure 6 (b) and Figure 6 (c), we split the cross-domain scenario into two specific settings according to the number of the source domains, i.e., single (e.g., miniImageNet) or multiple domains (e.g., FS-DomainNet). For the second setting, each source domain only contains images with the same style such as paintings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "Results in Table 3 show that our proposed FGFL outperforms other few-shot methods by a large margin under two cross-domain generalization settings, i.e., mini \\(\\rightarrow\\) Quickdraw and FS-DomainNet \\(\\rightarrow\\) Quickdraw. Figure 7 (b) also verifies that our proposed method can indeed learn to ex"
+        },
+        {
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+            "bbox": [
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+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.852,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.252,
+                0.895,
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+            "angle": 0,
+            "content": "Figure 7: Visualizations for few-shot generalization on three test datasets. (a), (b), and (c) represent different settings, i.e., cross-dataset, cross-domain, and cross-to-fine (C-to-F) annotated settings, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+                0.473,
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+            "angle": 0,
+            "content": "ploit high-frequency patterns rare in natural images to distinguish different classes on the quickdraw dataset. Another interesting observation is that few-shot methods generally perform better when generalizing from FS-DomainNet to quickdraw than from miniImageNet to quickdraw. A reasonable explanation is that compared to the miniImageNet dataset with small domain variations, the FS-DomainNet dataset includes multiple domains with obvious differences, which enables the network to capture domain-specific information from each meta-task for classification, resulting in better generalization ability to the unseen domain. Furthermore, our FGFL can still boost performance in this setting, illustrating the necessity of frequency domain information."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.528,
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+            ],
+            "angle": 0,
+            "content": "4.3.3 Coarse-to-Fine Annotated Generalization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.553,
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+            ],
+            "angle": 0,
+            "content": "Different from existing settings, we consider the annotation difference between training and testing sets for few-shot generalization. In practice, an image may have different levels of class annotations due to the requirements of labeling tasks. For example, we only need a training set with two labels \"Furniture\" and \"Person\" to train a powerful classifier for a binary classification task. However, when we want to use the above classifier to identify the species of furniture, we need additional fine-grained labels such as \"Desk\" or \"Chair\". This is a practical scenario since fine-grained labeling requires a high cost of human collaboration. We conduct experiments on tieredImageNet with hierarchical annotations to evaluate the generalization performance under this setting, shown in Figure 6 (d). All competing methods are trained on the coarse-annotated training set with 20 super-classes and evaluated on the fine-annotated testing set with 160 sub-classes same as the standard few-shot setting, denoted as tiered(C) \\(\\rightarrow\\) (F)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.826,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "As shown in Table 3, all methods perform worse than general classification results in Table 2. The reason is that the model tends to overfit the general features of high-level class prediction tasks while ignoring within-class differences. We observe that our proposed FGFL can still out"
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td>Cross-Dataset</td><td colspan=\"2\">Cross-Domain</td><td>Cross-Annotated</td></tr><tr><td>mini → CUB</td><td>mini → Q</td><td>F → Q</td><td>tiered(C) → (F)</td></tr><tr><td>MatchingNet [39]</td><td>51.37</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GNN [13]</td><td>62.25</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GNN + FT [39]</td><td>66.98</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Meta DeepBDC [48]</td><td>77.87</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FEAT [55]†</td><td>62.28</td><td>55.96</td><td>77.23</td><td>64.67</td></tr><tr><td>ProtoNet [36]†</td><td>66.29</td><td>64.32</td><td>74.43</td><td>64.08</td></tr><tr><td>BML [60]†</td><td>71.22</td><td>75.47</td><td>65.38</td><td>52.63</td></tr><tr><td>DeepEMD [58]†</td><td>77.34</td><td>58.04</td><td>78.52</td><td>65.87</td></tr><tr><td>Ours</td><td>81.35</td><td>76.34</td><td>89.34</td><td>67.84</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.474,
+                0.895,
+                0.597
+            ],
+            "angle": 0,
+            "content": "Table 3: Few-shot generalization results under the 5-way 5-shot setting. mini, Q, F, and tiered(C), (F) denote miniImageNet, QuickDraw, FS-DomainNet, tieredImageNet with coarse-grained or fine-grained annotations. \\(\\dagger\\): reimplement based on public code with our setting. tieredImageNet with coarse-grained (super-classes) or fine-grained annotations (sub-classes). \\(\\dagger\\): reimplemented based on public code with our setting."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.572,
+                0.611,
+                0.825,
+                0.707
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">miniImageNet</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>Baseline</td><td>66.52 ± 0.20</td><td>81.46 ± 0.14</td></tr><tr><td>+Lsw.tri</td><td>67.38 ± 0.80</td><td>83.61 ± 0.61</td></tr><tr><td>+Lcw.ctr</td><td>68.44 ± 0.81</td><td>85.60 ± 0.60</td></tr><tr><td>+Laug</td><td>69.14 ± 0.80</td><td>86.01 ± 0.62</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
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+                0.895,
+                0.75
+            ],
+            "angle": 0,
+            "content": "Table 4: Ablation studies for our proposed FGFL framework over miniImageNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.776,
+                0.895,
+                0.837
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+            "angle": 0,
+            "content": "perform all methods. Figure 7 (c) shows that our method can focus on specific frequency components (e.g., low and middle FCs corresponding to color and shape spatial features), which is discriminative for class prediction."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.847,
+                0.655,
+                0.864
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We perform ablation studies to investigate the effectiveness of the key components of FGFL on miniImageNet un-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11821"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.364
+            ],
+            "angle": 0,
+            "content": "der the 5-way settings with ResNet-12 as the backbone. As shown in Table 4, each proposed loss contributes to performance improvement. Moreover, we find that \\( L_{sw\\_tri} \\) and \\( L_{cw\\_ctr} \\) significantly improve the performance (1.92% and 4.14% for 1-shot and 5-shot, resp.), indicating that the proposed multi-level metrics can better utilize the frequency information to improve the generalizability of the model and avoid over-fitting to spatial features, leading to further improvements over spatial masks. Results also show that the two losses play different roles and complement each other, which further proves that our proposed method can utilize frequency information from different levels to help with classification. Noted that the performance gain under the 5-shot setting is much higher than the 1-shot setting. One plausible reason is that more supervised information introduced by support samples helps to generate a more precise frequency mask, which helps reduce the intra-class variation to learn a strong classifier, aligning with our idea."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.381,
+                0.196,
+                0.397
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+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.408,
+                0.473,
+                0.665
+            ],
+            "angle": 0,
+            "content": "In this paper, we proposed a novel Frequency-Guided Few-shot Learning (FGFL) framework for few-shot classification and generalization. Specifically, the frequency masks generated by the classification gradients in the DCT domain can emphasize the class-discriminative frequency components in the current meta-task. Our proposed multi-level metrics, including sample-wise triplet loss and class-wise contrastive loss, can better utilize the frequency information at sample and task levels and encourage the model to capture more task-relevant frequency information to help the classification in the spatial domain. Besides, we systematically investigated the effects of frequency information on few-shot generalization behaviors. Extensive experiments demonstrated that FGFL achieves competitive results with state-of-the-art methods on the standard few-shot settings, and significantly improves the generalized performance on unseen testing domains."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.683,
+                0.238,
+                0.7
+            ],
+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.709,
+                0.47,
+                0.815
+            ],
+            "angle": 0,
+            "content": "This research is supported in part by the SUG and MOE AcRF Tier1 (RG61/22) Grant. This research work is also partially supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research), and the Singapore Government's Research, Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering domain) under Grant A18A1b0045."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
+                0.833,
+                0.175,
+                0.849
+            ],
+            "angle": 0,
+            "content": "References"
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+# Frequency Guidance Matters in Few-Shot Learning
+
+Hao Cheng $^{1}$  Siyuan Yang $^{1}$ $^{1}$ Nanyang Technological University
+
+Joey Tianyi Zhou $^{2,3}$   
+Lanqing Guo $^{1}$   
+Bihan Wen $^{1*}$ $^{2}$ Centre for Frontier AI Research (CFAR), A*STAR, Singapore  
+Fernance Computing (IHPC), A*STAR, Singapore
+
+{hao006,siyuan005,lanqing001,bihan.wen}@ntu.edu.sg zhouty@cfar.a-star.edu.sg
+
+# Abstract
+
+Few-shot classification aims to learn a discriminative feature representation to recognize unseen classes with few labeled support samples. While most few-shot learning methods focus on exploiting the spatial information of image samples, frequency representation has also been proven essential in classification tasks. In this paper, we investigate the effect of different frequency components on the few-shot learning tasks. To enhance the performance and generalizability of few-shot methods, we propose a novel Frequency-Guided Few-shot Learning framework (dubbed FGFL), which leverages the task-specific frequency components to adaptively mask the corresponding image information, with a novel multi-level metric learning strategy including a triplet loss among original, masked and un-masked image as well as a contrastive loss between masked and original support and query sets to exploit more discriminative information. Extensive experiments on four benchmarks under several few-shot scenarios, i.e., standard, cross-dataset, cross-domain, and coarse-to-fine annotated classification, are conducted. Both qualitative and quantitative results show that our proposed FGFL scheme can attend to the class-discriminative frequency components, thus integrating those information towards more effective and generalizable few-shot learning.
+
+# 1. Introduction
+
+Deep learning typically relies on large-scale annotated datasets to achieve superior results on image classification tasks. However, the learned deep models may fail to generalize under some severe conditions, e.g., few data or annotations. Correspondingly, the task to classify a query sample using only a few labeled data is known as few-shot classification [10, 40]. The key challenge is to learn the discriminative feature representation that can be generalized from the given training set to novel testing classes. Recently, sev
+
+![](images/68f7b852e3bfc1524dfec6ad9086864bf861f142efe99186fb737cdc0776dd92.jpg)  
+Figure 1: Visualizations of samples with different frequency masks on the CUB dataset [41]. Samples with the same color box belong to the same class. It is easier to distinguish two classes with masked specific frequency components. Each square on the left represents the masked status of corresponding frequency components, i.e., the dark and light color for masked and reserved, respectively. For each row (column), top-to-bottom and left-to-right represent low frequency to high frequency, respectively.
+
+eral few-shot methods [36, 48, 58] have applied the meta-learning framework [40] to build a discriminative feature space by simulating numerous meta-tasks to obtain the generalized feature representation, achieving superior performance for recognizing novel classes.
+
+However, very recent studies [3, 17, 26, 39] report that existing methods may fail to generalize well to novel classes due to large domain gaps between training and testing sets, e.g., from general to fine-grained tasks or a specific domain. In these cases, the learned feature embeddings based on spatial images may capture excessive domain-invariant information from the training patterns, leading to degraded performance in the test scenario with a large domain gap. Several domain adaptation-based few-shot algorithms [26, 37, 39, 57] have been proposed to alleviate the domain shift issues on few-shot classification. These
+
+methods focus on learning a flexible feature embedding or fine-tuning on less novel support samples to transfer knowledge across domains. However, they cannot achieve stable performance improvements for different few-shot scenarios. Moreover, most domain adaption-based methods only focused on exploiting the image spatial features.
+
+Beyond spatial features, the frequency-domain representation plays a vital role for various computer vision tasks, e.g., deep fake recognition [12, 24, 27], domain generalization [19] and image classification [4, 32, 42, 50]. Different frequency components naturally convey discriminative and interpretive features for visual understanding [19, 32], e.g., the selected frequency components (FCs) of input images can be used to interpret the learned CNN features in classification [42, 50]. In few-shot learning, Chen et al. [4] is the first attempt to apply image frequency spectrum for classification, in which frequency information is naively concatenated as an extra feature, without exploiting different effects of its FCs. Figure 1 provides an example, clearly showing that certain FCs are more discriminative, thus should be selected and highlighted for more effective classification. However, no work to date has systematically investigated the roles of different FCs and how to adaptively select important FCs for effective few-shot learning.
+
+In this paper, we propose a novel Frequency-Guided Few-shot Learning (FGFL) framework towards highly effective few-shot classification and generalization. For each input image, FGFL adaptively generates a task-specific class-discriminative mask in the frequency domain using Grad-CAM [35], where the activated FCs represent the important frequency information associated with the current task. Then we convert the masked and unmasked frequency components output back to the spatial domain for generating the masked and unmasked images, which contain limited and rich task-specific class-discriminative information, respectively. After that, for each image in the meta-task, we construct its triplet with its corresponding unmasked and masked images as positive and negative samples. We also construct two additional few-shot tasks by regrouping the masked and original support and query images, i.e.,  $\mathcal{T}_{ms}$  with masked support set and original query set, and  $\mathcal{T}_{mq}$  with original support set and masked query set. In addition, we propose two types of ranking losses, including the triplet and contrastive loss functions at single images and tasks (i.e.,  $\mathcal{T}_{ms}$  and  $\mathcal{T}_{mq}$ ) levels, respectively, to force the model to capture task-specific class-discriminative information that can well generalize to the novel classes. Moreover, the unmasked images are also added to the support set to enhance the discriminability of feature embeddings.
+
+The contributions of this work are fourfold. First, we propose a Frequency-Guided Few-shot Learning (FGFL) framework to utilize the frequency information to enhance the performance and generalizability of few-shot methods
+
+in the spatial domain. Second, we propose two types of ranking loss, including the triplet and contrastive loss functions at both sample and task levels based on original and generated images, to force the network to focus on class-discriminative frequency components for each few-shot meta-task. In addition, the generated unmasked images are also utilized to augment the support set to enhance the discriminability of feature embeddings. Third, we investigate the impact of frequency components on current methods under several generalized few-shot settings, namely cross-dataset, cross-domain, and coarse-to-fine annotated generalization. To the best of our knowledge, this is the first work that exploits the effect of different frequency components on few-shot classification and generalization tasks explicitly. Last, experimental results and visualizations demonstrate that the proposed FGFL can improve the performance and generalizability of few-shot methods and achieve superior results under several few-shot settings.
+
+# 2. Related Work
+
+# 2.1. Few-shot Classification
+
+Few-shot learning aims to recognize novel query samples with only a few available support samples. Recently, existing deep few-shot methods can be divided into three main categories. First, optimization-based meta-learning methods [2, 11, 20, 28, 33] design a good model initialization or optimization strategy that can quickly adapt to novel tasks. Second, metric-based methods [7, 29, 30, 36, 48, 55, 58] focus on constructing an appropriate latent space to extract discriminative feature embeddings and then predict based on the similarity between support and query samples. Third, data generative and augmentation-based methods focus on generating more variant samples to learn a more accurate classifier, e.g., applying data rotation or transformation [21] by self-supervised learning, synthesizing new data with a generative model [14, 23], or using external data with pseudo labels [18, 44, 52].
+
+Most above-mentioned algorithms only employ spatial images as the network input without exploiting the frequency information. In our work, we investigate the effect of the frequency information in the Discrete Cosine Transformation (DCT) domain and leverage it to guide few-shot classification in the spatial domain.
+
+# 2.2. Learning in the Frequency Domain
+
+Frequency components contain rich patterns for image understanding and have been widely studied in several computer vision tasks such as compressed sensing [43, 51, 56], visual pre-training [47], domain transfer [19, 53], and image classification [4, 8, 32, 42, 50]. Yang et al. [53] use the Fast Fourier Transformation (FFT) to achieve domain alignment by simply swapping the low-frequency spectrum between
+
+![](images/bc120ff6a0dd7d07e7f630ef34906388960484f415e026f5cbcc2204822080ad.jpg)  
+Figure 2: T-SNE visualization of all image features of 20 test classes in the CUB (top) and 15 test classes in the Quickdraw (bottom) dataset. The few-shot model is trained on the miniImageNet dataset. A cluster that is clearer and more compact within each class is better.
+
+<table><tr><td>Method</td><td>miniImageNet</td><td>CUB</td><td>Quickdraw</td></tr><tr><td>ProtoNet [36]</td><td>79.86</td><td>66.29</td><td>64.32</td></tr><tr><td>ProtoNet w/ High FCs</td><td>56.47</td><td>37.96</td><td>66.26</td></tr><tr><td>ProtoNet w/o High FCs</td><td>77.75</td><td>67.09</td><td>65.99</td></tr></table>
+
+Table 1: Few-shot classification results under the 5-way 5-shot setting trained with the miniImageNet dataset. ProtoNet is trained on miniImageNet dataset and evaluated on several datasets with specific frequency components.
+
+source and target domain samples. GFNet [32] considers the attention in the FFT frequency domain to replace the self-attention module in the vision transformer. However, FFT requires double the memory for complex coefficients. Therefore, some recent works [4, 31, 50] consider applying the Discrete Cosine Transformation (DCT) to learn in the frequency domain. For example, Wang et al. [43] first applies the DCT to speed up the network. Instead of inputting RGB pixels, Gueguen et al. [16] convert the JPEG-compressed image to its  $8 \times 8$  block DCT coefficients as the input of the neural network. FcaNET [31] adopts DCT to generalize the compression of the channel attention mechanism in the frequency domain. Specifically, Chen et al. [4] select pre-defined channels in the DCT frequency domain to improve the performance for few-shot classification.
+
+In this work, we also employ the DCT to transform the images to the frequency domain. Unlike previous work [4], we consider the interaction between spatial and frequency domains and learn to generate the discriminative frequency mask to enhance learning in the spatial domain.
+
+# 3. Proposed Method
+
+In this section, we first investigate the impact of frequency components in different few-shot classification scenarios. Then the proposed FGFL framework is described
+
+and explained in detail, followed by the loss function of our method and empirical validations.
+
+# 3.1. Frequency Analysis on Few-shot Classification
+
+We first investigate the impact of frequency components on the generalized performance of current few-shot methods under different few-shot settings by removing and preserving partial frequency components of each image in the meta-task for class prediction.
+
+To generate the frequency representation of an input RGB image  $X \in \mathbb{R}^{H \times W \times 3}$ , we apply the 2D-Discrete Cosine Transform [1] (2D-DCT) function as  $D = DCT(X) \in \mathbb{R}^{H \times W \times 3}$ . We can then remove or preserve partial frequency components of each input image, followed by an Inverse 2D-DCT function as  $\hat{X} = IDCT(\hat{D})$  to transform it back into the spatial domain with the original input size.
+
+With the help of the DCT functions, we can decompose the raw data into two parts,  $X = \{X^{O}, X^{H}\}$ , where  $X^{H}$  and  $X^{O}$  represent high-frequency components (dubbed w/ high FCs), and other components (dubbed w/o high FCs). For a given few-shot task  $\mathcal{T}_{\mathrm{test}} = (\mathcal{S}, \mathcal{Q})$  on the novel testing set, we can reconstruct images with partial frequency information to update the testing task as  $\tilde{\mathcal{T}}_{\mathrm{test}} = \{\tilde{S}, \tilde{\mathcal{Q}}\}$ . Then we adopt the existing few-shot methods to make predictions for each query sample  $\tilde{X}_j$  with  $\tilde{S}$ .
+
+Table 1 shows classification accuracy on different test domains and Figure 2 plots the t-SNE visualizations of image features extracted by the trained feature encoder. We can observe that removing specific frequency components can improve the generalized performance of few-shot models but degrade standard few-shot performance in the same testing scenario.
+
+To this end, frequency information plays different roles in different classification scenarios. Through evaluation and observation, it can be conjectured that the generalization behaviors of few-shot methods are relevant to frequency components which may vary across datasets and domains.
+
+# 3.2. Frequency-Guided Few-shot Learning
+
+Different FCs encode specific image information, we propose the Frequency-Guided Few-shot Learning (FGFL) framework, which utilizes the frequency mask to guide the training in the spatial domain. As shown in Figure 3, FGFL has two branches with two encoders  $E^{fq}$  and  $E^{sp}$  for feature extraction in the frequency and spatial domains, respectively. FGFL generates the frequency mask based on the task-specific attention map for the given few-shot task, which is then adopted to generate additional images, guiding the network updates in the spatial domain. Moreover, we propose a multi-level metric to force the network to capture specific frequency components for classification.
+
+![](images/6bac4de8b4aafa42530a129a6866dd8c420a4d713faddc6ba12e5cf4d2ec2f22.jpg)  
+Figure 3: Overview of our proposed Frequency-Guided Few-shot Learning framework (FGFL). We first generate the task-specific class-discriminative frequency mask based on the classification in the frequency domain. Then we convert the masked and unmasked frequency samples back to the spatial domain and generate two image sets (masked set  $X_{m}$  and unmasked set  $X_{um}$ ) according to the mask and unmask regions, respectively. Furthermore, we adopt novel multi-level metrics (shown in Figure 4) on the original and generated image sets to make class predictions.
+
+# 3.2.1 Task-Specific Frequency Mask Generation
+
+To obtain a task-specific attention mask of frequency components for each few-shot task, we first transform the input spatial input image  $X$  to  $D$  in the frequency domain. Then we generate the attention map by Grad-CAM [35] based on the output feature map  $M \in \mathbb{R}^{C \times h \times w}$  of the last convolution layer in the frequency encoder (e.g., ResNet-12), where  $C$  is the channel number of the feature map,  $h$  and  $w$  indicate the height and width of the feature map, respectively.
+
+For its ground-truth class  $c$ , we compute the gradient of the score  $s^c$  with respect to the feature map activation  $M_{k}\in \mathbb{R}^{h\times w}$  as  $\frac{\partial s^c}{\partial M_k}$ , where  $k$  indicates the channel index of the feature map. These gradients flowing back will pass through a global average pooling layer (denoted as  $GAP(\cdot))$  to obtain the neuron importance weights  $w_{k}^{c}$ :
+
+$$
+w _ {k} ^ {c} = G A P \left(\frac {\partial s ^ {c}}{\partial M _ {k}}\right). \tag {1}
+$$
+
+The weight  $w_{k}^{c}$  reflects the importance of activation map  $M_{k}$  to make the prediction of class  $c$  for the input  $D$ . We then perform a weighted combination with a ReLU function to integrate the positive influence of feature maps across different channels of  $M$  for class  $c$  as:
+
+$$
+A ^ {c} = \operatorname {R e L U} \left(\sum_ {k} w _ {k} ^ {c} M _ {k}\right), \tag {2}
+$$
+
+where  $A^c \in \mathbb{R}^{h \times w}$  is the heatmap reflecting frequency components that have a positive impact on the ground-truth class  $c$  of a given frequency input.
+
+Note that previous works [35, 22] utilize a fully connected (fc) layer to obtain the classification score  $s^c$  for the
+
+ground-truth class  $c$  with the same training and testing class set. However, since the training and testing classes in few-shot scenarios are non-overlap, directly applying fc layers for gradient computation may be prone to overfitting.
+
+To this end, we compute the cosine similarity between each sample and class prototype as the classification score for each given  $N$ -way  $K$ -shot task in few-shot learning, where  $N$  and  $K$  indicates the number of selected classes and labeled support samples from each class, respectively. Specifically, given a few-shot task with support set  $\mathcal{S}_f = \{D_m, y_m\}_{m=1}^{NK}$ , and a query set  $\mathcal{Q}_f = \{D_n, y_n\}_{n=1}^Q$  in the frequency domain, we compute the cosine similarity score  $s^c$  between each query sample  $\mathbf{q} \in \mathbb{R}^C$  and each class prototype  $\mathbf{v}_c \in \mathbb{R}^C$  as:
+
+$$
+s ^ {c} = p (y = c \mid \mathbf {q}) = \frac {\mathbf {q} ^ {T} \mathbf {v} _ {c}}{\| \mathbf {q} \| \| \mathbf {v} _ {c} \|}, \tag {3}
+$$
+
+where  $\mathbf{v}_c = \frac{1}{K}\sum_{k=1}^{K}\mathbf{z}_k$  is the mean feature vector of the support features  $\mathbf{z}_k$  of the  $c$ -th class. Note that, it is easy to prove Eq. (3) is equivalent to an fc layer when neglecting the bias of the fc layer. Moreover, the classification weights  $\mathbf{v}_c$  are flexible and task-dependent, i.e., only based on the current few-shot task. Hence, the network can learn to generate a task-specific heatmap  $A^c$  of each sample to find specific frequency components that contribute most to the current task, which avoids over-fitting to the training set.
+
+We then up-sample  $A^c$  to the original size and generate the frequency mask following previous works [45, 22] as:
+
+$$
+\operatorname {M a s k} ^ {c} = \mathbf {1} - \operatorname {S i g m o i d} \left(U p \left(A ^ {c}\right)\right), \tag {4}
+$$
+
+![](images/f26241cbf946420420032915bd50ee12c23ec1152dd1e869f0cbc83b9f116a98.jpg)  
+Figure 4: Illustration of the proposed multi-level metrics. Specifically, for each image in the image set  $X$  in the metask, we construct its triplet from the corresponding un-masked and masked set  $X^m$  and  $X^{um}$  as the positive and negative pair, respectively, and adopt the sample-wise triplet loss  $L_{sw\_tri}$  to exploit the correlations them. At the task level, we construct two additional few-shot tasks by regrouping the images in  $X$  and  $X^m$ . (Here we take the query set as an example.) Then we propose a class-wise contrastive loss  $L_{cw\_ctr}$  between positive pairs (original support and query samples) and negative pairs (support and query from different sets). Moreover, we use unmasked images to augment the support set for classification with a loss  $L_{aug}$ .
+
+where  $\mathbf{1}$  is an all-ones matrix,  $Up(\cdot)$  is the upsampling operation, and  $Sigmoid(\cdot)$  is applied to make it derivable and constrains the value to the range [0, 1].
+
+$Mask^c$  is then applied to  $D$  and converted back to the spatial domain to generate the masked spatial image  $X^m$  and corresponding unmasked spatial image  $X^{um}$  as:
+
+$$
+X ^ {m} = I D C T \left(M a s k ^ {c} \odot D\right), X ^ {u m} = I D C T \left(\left(1 - M a s k ^ {c}\right) \odot D\right), \tag {5}
+$$
+
+where  $\odot$  is the dot product function. Note that  $X^{m}$  and  $X^{um}$  are considered to contain limited and rich information belonging to the target class since the regions on the attention map beyond the class-aware range should be hard to identify the true class. We can then utilize  $X^{m}$  and  $X^{um}$  to guide few-shot learning in the spatial domain.
+
+# 3.2.2 Mask-Guided Multi-Level Metrics
+
+With the help of task-specific frequency mask generation, we already generate additional samples (i.e., masked images  $X^{m}$  and unmasked images  $X^{um}$ ). To incorporate frequency information to encourage the spatial network to capture class discriminative information, we propose two ranking losses at the sample and task levels, (i.e., sample-wise triplet loss  $L_{sw\_tri}$  and class-wise contrastive loss  $L_{cw\_ctr}$ , respectively.) to fully exploit the mask information in the
+
+frequency signal, shown in Figure 4. Meanwhile, we also adopt the unmasked images to enhance the few-shot classification performance with an additional classification loss  $L_{\text{aug}}$ .
+
+Sample-wise triplet loss. For each original image  $X_{i}$  in the meta-task, this loss aims to enhance the feature similarity between  $X_{i}$  and its corresponding unmasked image  $X_{i}^{um}$ , while reducing that between  $X_{i}$  and its corresponding masked image  $X_{i}^{m}$ . Formally, we construct the triplet for each image in the meta-task as  $(X_{i}, X_{i}^{m}, X_{i}^{um})$ , where  $X_{i}, X_{i}^{um}$ , and  $X_{i}^{m}$  are the anchor, positive, and negative samples, respectively. We define  $E^{sp} = f_{\phi}(\cdot)$  as the feature extractor with parameters  $\phi$  to obtain the feature vector. Then the sample-level triplet loss can be formulated as:
+
+$$
+\begin{array}{l} L _ {s w. t r i} \left(X _ {i}, X _ {i} ^ {u m}, X _ {i} ^ {m}\right) = \max  \left\{d \left(f _ {\phi} \left(X _ {i}\right), f _ {\phi} \left(X _ {i} ^ {u m}\right)\right) \right. \\ - d \left(f _ {\phi} \left(X _ {i}\right), f _ {\phi} \left(X _ {i} ^ {m}\right)\right) + \eta , 0 \}, \tag {6} \\ \end{array}
+$$
+
+where  $d(\cdot ,\cdot)$  denotes the distance between two features and  $\eta$  is the margin between positive and negative pairs.
+
+Class-wise contrastive loss. To encourage the network to capture class discriminative information, we construct contrastive pairs for each query instance in the original and masked sets. Specifically, given masked support and query sets  $S_{m} = \{X_{i}^{m},y_{i}\}_{i = 1}^{NK}$  and  $\mathcal{Q}_m = \{X_j^m,y_j\}_{j = 1}^Q$  , we first construct two additional masked few-shot tasks by regrouping the masked and original sets as:
+
+$$
+\mathcal {T} _ {m s} = \left(\mathcal {S} _ {m}, \mathcal {Q}\right), \quad \mathcal {T} _ {m q} = \left(\mathcal {S}, \mathcal {Q} _ {m}\right), \tag {7}
+$$
+
+where  $\mathcal{S} = \{X_i, y_i\}_{i=1}^{NK}$  and  $\mathcal{Q} = \{X_j, y_j\}_{j=1}^Q$  are original support and query set, respectively.
+
+Each masked sample consists of less class-discriminative information. To avoid being misled by class-irrelevant information (i.e., preserved in  $S_{m}$  and  $\mathcal{Q}_{m}$ ), we regard the support and query samples from tasks  $T_{ms}$  and  $T_{mq}$  as negative pairs, and those from the original task with the same class as positive pairs. Then the contrastive loss corresponding to query sample  $X_{q} \in \mathcal{Q}$  can be written as:
+
+$$
+L _ {q} = - \log \frac {\sum_ {y _ {j} = y _ {q} , X _ {j} \in S} e ^ {d \left(z _ {j} , z _ {q}\right) / \tau}}{\sum_ {y _ {j} = y _ {q} , X _ {j} \in S} e ^ {d \left(z _ {j} , z _ {q}\right) / \tau} + \sum_ {X _ {k} \in S _ {m}} e ^ {d \left(z _ {k} , z _ {q}\right) / \tau}}, \tag {8}
+$$
+
+where  $z_{i} = f_{\phi}(X_{i})$  represents the feature vector extracted by the spatial backbone. Similarly, the contrastive loss for support sample  $X_{s}\in S$  can be written as:
+
+$$
+L _ {s} = - \log \frac {\sum_ {y _ {j} = y _ {s} , X _ {j} \in Q} e ^ {d \left(z _ {j} , z _ {s}\right) / \tau}}{\sum_ {y _ {j} = y _ {s} , X _ {j} \in Q} e ^ {d \left(z _ {j} , z _ {s}\right) / \tau} + \sum_ {X _ {k} \in Q _ {m}} e ^ {d \left(z _ {k} , z _ {s}\right) / \tau}}. \tag {9}
+$$
+
+Overall, for one episode,  $L_{cw - ctr}$  can be written as:
+
+$$
+L _ {c w - c t r} = \frac {1}{Q} \sum_ {q = 1} ^ {Q} L _ {q} + \frac {1}{N K} \sum_ {s = 1} ^ {N K} L _ {s}. \tag {10}
+$$
+
+![](images/5b5513f0a01810adeeb0a1356c2377b25fda5828abdd6c99f71fd1003c71087c.jpg)  
+(a) Visualization results on Mean Magnitude features of Channels (MMC).  
+Figure 5: (a) MMC before and after applying the proposed FGFL method. (b) MMD results of few-shot methods trained over miniImageNet. The lower MMD value indicates a smaller gap and better performance. 'Pretrained' denotes the feature extractor (i.e., ResNet-12) pre-trained on the training set of miniImageNet.
+
+<table><tr><td>Method</td><td>mini</td><td>CUB</td></tr><tr><td>Pretrained</td><td>0.5567</td><td>1.5584</td></tr><tr><td>FEAT [55]</td><td>0.5386</td><td>1.5367</td></tr><tr><td>Ours</td><td>0.1256</td><td>1.2550</td></tr></table>
+
+(b) Maximum Mean Discrepancy (MMD) results on different test datasets.
+
+Augmented classification loss. To better classify samples in the query set  $\mathcal{Q}$ , we use generated support images  $S_{um}$  in  $X^{um}$  to enhance the support set for classification. Specifically, we build a new support set by combining the original support and unmasked support set as  $S_{aug} = S \cup S_{um}$ . Hence, we conduct few-shot classification on query set  $\mathcal{Q}$  based on  $S_{aug}$  and minimize the cross-entropy loss:
+
+$$
+L _ {a u g} = \sum_ {j = 1} ^ {Q} L _ {C E} \left(f _ {\theta} \left(X _ {j}; \mathcal {S} _ {a u g}\right), y _ {j}\right). \tag {11}
+$$
+
+# 3.2.3 Objective, Model Training, and Inference
+
+Combining with the standard few-shot classification, the overall objective function is defined as:
+
+$$
+L _ {t o t a l} = L _ {c l s} ^ {s p} + L _ {c l s} ^ {f q} + \lambda_ {1} \cdot L _ {s w \_ t r i} + \lambda_ {2} \cdot L _ {c w \_ c t r} + \lambda_ {3} \cdot L _ {a u g}, \tag {12}
+$$
+
+where  $L_{cls}^{sp}$  and  $L_{cls}^{fq}$  represent the cross-entropy loss for few-shot classification in the spatial and frequency branch, respectively.  $\lambda_1, \lambda_2,$  and  $\lambda_3$  denote the weighting parameters of the corresponding losses, respectively.
+
+During the training phase, we first generate frequency masks based on the frequency branch and then adopt the proposed multi-level metrics for model training. During the inference time, our proposed method strictly follows the inductive setting. We only feed the support set into the frequency branch to generate unmasked support images to refine the support set for classification.
+
+# 3.3. Empirical Validation
+
+The proposed FGFL framework aims to utilize frequency information to guide the spatial feature extractor towards class-discriminative features and avoid over-fitting to the
+
+training patterns, thus generalizing well to testing scenarios. To validate the effectiveness of the proposed method, we conduct experiments about learned features on two aspects: channel distribution shift and domain distance.
+
+Mean Magnitude of Channels (MMC) Luo et al. [26] shows the channel bias problem affects the generalizability of few-shot methods and utilizes MMC to visualize and measure the channel response to features, where effective few-shot methods might have a more uniform MMC curve in the testing set. Inspired by this work, we visualize the MMC before and after applying FGFL over miniImageNet. We can observe a channel magnitude change in Figure 5 (a), which validates that our proposed method can alleviate the channel bias problem, thus improving the performance.
+
+Maximum Mean Discrepancy (MMD) The MMD [15] is a distance measure between two domains based on the embedding of distribution measures in a reproducing kernel Hilbert space, which has been widely applied in transfer learning problems. We adopt class-wise MMD to measure the distribution gap between the training and testing sets with different methods trained over miniImageNet. Figure 5 (b) shows different gaps between one training set and different testing sets. We can also observe that our proposed method helps to reduce the domain shift.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We conduct extensive experiments on four few-shot datasets, i.e., miniImageNet [40], tieredImageNet [34], CUB [41], and FS-DomainNet [6].
+
+Implementation Details. For fair comparisons with previous methods, we adopt the ResNet-12 network with [64, 160, 320, 640] channels as our backbone in each branch, and set the input image size as  $84 \times 84$  for all datasets. We combine our proposed FGFL with FEAT [55], which adopts a linear projection layer for feature adaptation. We randomly select 15 samples of each class to construct the query set for 5-way 1-shot and 5-way 5-shot settings. The backbone networks are pre-trained on the training set following the typical classification task. The weighting parameters  $\lambda_{1}$ ,  $\lambda_{2}$ , and  $\lambda_{3}$  are all set to 0.1 to balance the scale between the classification loss and the corresponding losses for all datasets.
+
+# 4.2. Few-shot Classification
+
+We conduct experiments on two standard few-shot settings, i.e., general and fine-grained classification, shown in Table 2. Table 2 (a) shows that our proposed FGFL can
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">miniImageNet</td><td colspan="2">tieredImageNet</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>ProtoNet [36]†</td><td>61.83 ± 0.20</td><td>79.86 ± 0.14</td><td>66.84 ± 0.23</td><td>84.54 ± 0.16</td></tr><tr><td>Meta-Baseline [5]</td><td>63.17 ± 0.23</td><td>79.26 ± 0.17</td><td>68.62 ± 0.27</td><td>83.29 ± 0.18</td></tr><tr><td>Good-Embed [38]</td><td>64.82 ± 0.60</td><td>82.14 ± 0.43</td><td>71.52 ± 0.69</td><td>86.03 ± 0.58</td></tr><tr><td>DeepEMD [58]</td><td>65.91 ± 0.82</td><td>82.41 ± 0.56</td><td>71.16 ± 0.87</td><td>86.03 ± 0.58</td></tr><tr><td>FRN [46]</td><td>66.45 ± 0.19</td><td>82.83 ± 0.13</td><td>71.16 ± 0.22</td><td>86.01 ± 0.15</td></tr><tr><td>FEAT [55]†</td><td>66.52 ± 0.20</td><td>81.46 ± 0.14</td><td>70.30 ± 0.23</td><td>84.55 ± 0.16</td></tr><tr><td>BML [60]</td><td>67.04 ± 0.63</td><td>83.63 ± 0.29</td><td>68.99 ± 0.50</td><td>85.49 ± 0.34</td></tr><tr><td>IEPT [59]</td><td>67.05 ± 0.44</td><td>82.90 ± 0.30</td><td>72.24 ± 0.50</td><td>86.73 ± 0.34</td></tr><tr><td>MELR [9]</td><td>67.40 ± 0.43</td><td>83.40 ± 0.28</td><td>72.14 ± 0.51</td><td>87.01 ± 0.35</td></tr><tr><td>MCL-Katz [25]</td><td>67.51</td><td>83.99</td><td>72.01</td><td>86.02</td></tr><tr><td>CSEI [21]</td><td>67.59 ± 0.83</td><td>81.93 ± 0.36</td><td>72.57 ± 0.95</td><td>85.72 ± 0.63</td></tr><tr><td>Meta DeepBDC [48]</td><td>67.83 ± 0.43</td><td>84.46 ± 0.28</td><td>72.34 ± 0.49</td><td>87.31 ± 0.32</td></tr><tr><td>DFR [6]</td><td>68.12 ± 0.81</td><td>82.79 ± 0.56</td><td>72.38 ± 0.95</td><td>86.00 ± 0.61</td></tr><tr><td>Yang et al. [54]</td><td>70.19 ± 0.46</td><td>84.66 ± 0.29</td><td>72.62 ± 0.51</td><td>86.62 ± 0.33</td></tr><tr><td>Ours</td><td>69.14 ± 0.80</td><td>86.01 ± 0.62</td><td>73.21 ± 0.88</td><td>87.21 ± 0.61</td></tr></table>
+
+(a) Average classification accuracy  $(\%)$  on miniImageNet and tieredImageNet datasets with the ResNet-12 as backbone.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Backbone</td><td colspan="2">CUB</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>MELR [9]</td><td>ConvNet-4</td><td>70.26 ± 0.50</td><td>85.01 ± 0.32</td></tr><tr><td>ProtoNet [36]†</td><td>ResNet-12</td><td>72.25 ± 0.21</td><td>87.47 ± 0.13</td></tr><tr><td>DeepEMD [58]</td><td>ResNet-12</td><td>75.65 ± 0.83</td><td>88.69 ± 0.50</td></tr><tr><td>FEAT [55]†</td><td>ResNet-12</td><td>75.68 ± 0.20</td><td>87.91 ± 0.13</td></tr><tr><td>BML [60]</td><td>ResNet-12</td><td>76.21 ± 0.63</td><td>90.45 ± 0.36</td></tr><tr><td>Good-Embed [38]‡</td><td>ResNet-18</td><td>77.92 ± 0.46</td><td>89.94 ± 0.26</td></tr><tr><td>DFR [6]</td><td>ResNet-12</td><td>78.07 ± 0.79</td><td>89.74 ± 0.51</td></tr><tr><td>VFD [49]</td><td>ResNet-12</td><td>79.12 ± 0.83</td><td>91.48 ± 0.39</td></tr><tr><td>FRN [46]†</td><td>ResNet-12</td><td>82.90 ± 0.19</td><td>92.61 ± 0.10</td></tr><tr><td>Ours</td><td>ResNet-12</td><td>80.77 ± 0.90</td><td>92.01 ± 0.71</td></tr></table>
+
+(b) Average classification accuracy  $(\%)$  on CUB dataset.
+
+Table 2: Comparison with state-of-the-art methods for general (a) and fine-grained (b) few-shot image classification. The best and second best results under each setting and dataset are highlighted as Red and Blue, respectively.  $\dagger$ : implemented based on public code with our setting.  $\ddagger$ : reported in [48].  
+
+<table><tr><td colspan="4">Train Scenario</td><td colspan="4">Test Scenario</td></tr><tr><td rowspan="2">(a)</td><td rowspan="2">Cross-Dataset Setting</td><td colspan="2">minImageNet</td><td colspan="4">CUB</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">(b)</td><td rowspan="2">Cross-Domain Setting 1</td><td colspan="2">minImageNet</td><td colspan="4">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">(c)</td><td rowspan="2">Cross-Domain Setting 2</td><td colspan="2">FS-DomainNet</td><td colspan="4">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">(d)</td><td rowspan="2">Cross-Annotated Setting</td><td colspan="2">tieredImageNet (Coarse)</td><td colspan="4">tieredImageNet (Fine)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Figure 6: Illustration of three challenging few-shot generalization scenarios under the 3-way 1-shot setting.
+
+significantly improve the performance of few-shot methods and outperform state-of-the-art methods for 5-shot setting on miniImageNet and 1-shot setting on tieredImageNet datasets. Moreover, FGFL is still on par with state-of-the-art methods under other settings. For CUB, as shown in Table 2 (b), we can observe that FGFL can improve the performance of FEAT by a large margin, i.e.,  $5.09\%$  and  $4.1\%$  for 1-shot and 5-shot settings, and is competitive with the state-of-the-art methods.
+
+# 4.3. Few-Shot Generalization
+
+To evaluate the generalized performance of few-shot methods, we propose three few-shot generalization settings for cross-domain classification based on challenging test scenarios, shown in Figure 6.
+
+# 4.3.1 Cross-Dataset Generalization
+
+In this setting, we only consider the distribution gaps of classes between training and testing datasets with the same style, e.g., natural images. As shown in Figure 6 (a), we train on the miniImageNet dataset with natural images and evaluate the fine-grained CUB dataset with various bird species, i.e., mini  $\rightarrow$  CUB.
+
+Table 3 shows that the proposed FGFL significantly improves the performance of the baseline FEAT method and outperforms the other methods. Figure 7 (a) shows that the proposed FGFL can force the network to capture discriminative task-specific frequency components for classification, e.g., high-frequency edge features for the first class and low-frequency color features for the third class.
+
+# 4.3.2 Cross-Domain Generalization
+
+Unlike the cross-dataset setting, the visual similarity between the training (source) and testing (target) domains may have a significant gap, as the target domain may contain unnatural images, e.g., quickdraw. As shown in Figure 6 (b) and Figure 6 (c), we split the cross-domain scenario into two specific settings according to the number of the source domains, i.e., single (e.g., miniImageNet) or multiple domains (e.g., FS-DomainNet). For the second setting, each source domain only contains images with the same style such as paintings.
+
+Results in Table 3 show that our proposed FGFL outperforms other few-shot methods by a large margin under two cross-domain generalization settings, i.e., mini  $\rightarrow$  Quickdraw and FS-DomainNet  $\rightarrow$  Quickdraw. Figure 7 (b) also verifies that our proposed method can indeed learn to ex
+
+![](images/2db14c0c5f58148fb23f990b90f6549eb6d99866e9ed5e74dc092c7c6174a6ca.jpg)  
+Figure 7: Visualizations for few-shot generalization on three test datasets. (a), (b), and (c) represent different settings, i.e., cross-dataset, cross-domain, and cross-to-fine (C-to-F) annotated settings, respectively.
+
+ploit high-frequency patterns rare in natural images to distinguish different classes on the quickdraw dataset. Another interesting observation is that few-shot methods generally perform better when generalizing from FS-DomainNet to quickdraw than from miniImageNet to quickdraw. A reasonable explanation is that compared to the miniImageNet dataset with small domain variations, the FS-DomainNet dataset includes multiple domains with obvious differences, which enables the network to capture domain-specific information from each meta-task for classification, resulting in better generalization ability to the unseen domain. Furthermore, our FGFL can still boost performance in this setting, illustrating the necessity of frequency domain information.
+
+# 4.3.3 Coarse-to-Fine Annotated Generalization
+
+Different from existing settings, we consider the annotation difference between training and testing sets for few-shot generalization. In practice, an image may have different levels of class annotations due to the requirements of labeling tasks. For example, we only need a training set with two labels "Furniture" and "Person" to train a powerful classifier for a binary classification task. However, when we want to use the above classifier to identify the species of furniture, we need additional fine-grained labels such as "Desk" or "Chair". This is a practical scenario since fine-grained labeling requires a high cost of human collaboration. We conduct experiments on tieredImageNet with hierarchical annotations to evaluate the generalization performance under this setting, shown in Figure 6 (d). All competing methods are trained on the coarse-annotated training set with 20 super-classes and evaluated on the fine-annotated testing set with 160 sub-classes same as the standard few-shot setting, denoted as tiered(C)  $\rightarrow$  (F).
+
+As shown in Table 3, all methods perform worse than general classification results in Table 2. The reason is that the model tends to overfit the general features of high-level class prediction tasks while ignoring within-class differences. We observe that our proposed FGFL can still out
+
+<table><tr><td rowspan="2">Method</td><td>Cross-Dataset</td><td colspan="2">Cross-Domain</td><td>Cross-Annotated</td></tr><tr><td>mini → CUB</td><td>mini → Q</td><td>F → Q</td><td>tiered(C) → (F)</td></tr><tr><td>MatchingNet [39]</td><td>51.37</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GNN [13]</td><td>62.25</td><td>-</td><td>-</td><td>-</td></tr><tr><td>GNN + FT [39]</td><td>66.98</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Meta DeepBDC [48]</td><td>77.87</td><td>-</td><td>-</td><td>-</td></tr><tr><td>FEAT [55]†</td><td>62.28</td><td>55.96</td><td>77.23</td><td>64.67</td></tr><tr><td>ProtoNet [36]†</td><td>66.29</td><td>64.32</td><td>74.43</td><td>64.08</td></tr><tr><td>BML [60]†</td><td>71.22</td><td>75.47</td><td>65.38</td><td>52.63</td></tr><tr><td>DeepEMD [58]†</td><td>77.34</td><td>58.04</td><td>78.52</td><td>65.87</td></tr><tr><td>Ours</td><td>81.35</td><td>76.34</td><td>89.34</td><td>67.84</td></tr></table>
+
+Table 3: Few-shot generalization results under the 5-way 5-shot setting. mini, Q, F, and tiered(C), (F) denote miniImageNet, QuickDraw, FS-DomainNet, tieredImageNet with coarse-grained or fine-grained annotations.  $\dagger$ : reimplement based on public code with our setting. tieredImageNet with coarse-grained (super-classes) or fine-grained annotations (sub-classes).  $\dagger$ : reimplemented based on public code with our setting.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">miniImageNet</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>Baseline</td><td>66.52 ± 0.20</td><td>81.46 ± 0.14</td></tr><tr><td>+Lsw.tri</td><td>67.38 ± 0.80</td><td>83.61 ± 0.61</td></tr><tr><td>+Lcw.ctr</td><td>68.44 ± 0.81</td><td>85.60 ± 0.60</td></tr><tr><td>+Laug</td><td>69.14 ± 0.80</td><td>86.01 ± 0.62</td></tr></table>
+
+Table 4: Ablation studies for our proposed FGFL framework over miniImageNet.
+
+perform all methods. Figure 7 (c) shows that our method can focus on specific frequency components (e.g., low and middle FCs corresponding to color and shape spatial features), which is discriminative for class prediction.
+
+# 4.4. Ablation Study
+
+We perform ablation studies to investigate the effectiveness of the key components of FGFL on miniImageNet un-
+
+der the 5-way settings with ResNet-12 as the backbone. As shown in Table 4, each proposed loss contributes to performance improvement. Moreover, we find that  $L_{sw\_tri}$  and  $L_{cw\_ctr}$  significantly improve the performance (1.92% and 4.14% for 1-shot and 5-shot, resp.), indicating that the proposed multi-level metrics can better utilize the frequency information to improve the generalizability of the model and avoid over-fitting to spatial features, leading to further improvements over spatial masks. Results also show that the two losses play different roles and complement each other, which further proves that our proposed method can utilize frequency information from different levels to help with classification. Noted that the performance gain under the 5-shot setting is much higher than the 1-shot setting. One plausible reason is that more supervised information introduced by support samples helps to generate a more precise frequency mask, which helps reduce the intra-class variation to learn a strong classifier, aligning with our idea.
+
+# 5. Conclusion
+
+In this paper, we proposed a novel Frequency-Guided Few-shot Learning (FGFL) framework for few-shot classification and generalization. Specifically, the frequency masks generated by the classification gradients in the DCT domain can emphasize the class-discriminative frequency components in the current meta-task. Our proposed multi-level metrics, including sample-wise triplet loss and class-wise contrastive loss, can better utilize the frequency information at sample and task levels and encourage the model to capture more task-relevant frequency information to help the classification in the spatial domain. Besides, we systematically investigated the effects of frequency information on few-shot generalization behaviors. Extensive experiments demonstrated that FGFL achieves competitive results with state-of-the-art methods on the standard few-shot settings, and significantly improves the generalized performance on unseen testing domains.
+
+# Acknowledgement
+
+This research is supported in part by the SUG and MOE AcRF Tier1 (RG61/22) Grant. This research work is also partially supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research), and the Singapore Government's Research, Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering domain) under Grant A18A1b0045.
+
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+                                    "content": "Few-shot classification aims to learn a discriminative feature representation to recognize unseen classes with few labeled support samples. While most few-shot learning methods focus on exploiting the spatial information of image samples, frequency representation has also been proven essential in classification tasks. In this paper, we investigate the effect of different frequency components on the few-shot learning tasks. To enhance the performance and generalizability of few-shot methods, we propose a novel Frequency-Guided Few-shot Learning framework (dubbed FGFL), which leverages the task-specific frequency components to adaptively mask the corresponding image information, with a novel multi-level metric learning strategy including a triplet loss among original, masked and un-masked image as well as a contrastive loss between masked and original support and query sets to exploit more discriminative information. Extensive experiments on four benchmarks under several few-shot scenarios, i.e., standard, cross-dataset, cross-domain, and coarse-to-fine annotated classification, are conducted. Both qualitative and quantitative results show that our proposed FGFL scheme can attend to the class-discriminative frequency components, thus integrating those information towards more effective and generalizable few-shot learning."
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+                                    "content": "1. Introduction"
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+                                    "content": "Deep learning typically relies on large-scale annotated datasets to achieve superior results on image classification tasks. However, the learned deep models may fail to generalize under some severe conditions, e.g., few data or annotations. Correspondingly, the task to classify a query sample using only a few labeled data is known as few-shot classification [10, 40]. The key challenge is to learn the discriminative feature representation that can be generalized from the given training set to novel testing classes. Recently, sev"
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+                                            "type": "text",
+                                            "content": "Figure 1: Visualizations of samples with different frequency masks on the CUB dataset [41]. Samples with the same color box belong to the same class. It is easier to distinguish two classes with masked specific frequency components. Each square on the left represents the masked status of corresponding frequency components, i.e., the dark and light color for masked and reserved, respectively. For each row (column), top-to-bottom and left-to-right represent low frequency to high frequency, respectively."
+                                        }
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+                                    "type": "text",
+                                    "content": "eral few-shot methods [36, 48, 58] have applied the meta-learning framework [40] to build a discriminative feature space by simulating numerous meta-tasks to obtain the generalized feature representation, achieving superior performance for recognizing novel classes."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "However, very recent studies [3, 17, 26, 39] report that existing methods may fail to generalize well to novel classes due to large domain gaps between training and testing sets, e.g., from general to fine-grained tasks or a specific domain. In these cases, the learned feature embeddings based on spatial images may capture excessive domain-invariant information from the training patterns, leading to degraded performance in the test scenario with a large domain gap. Several domain adaptation-based few-shot algorithms [26, 37, 39, 57] have been proposed to alleviate the domain shift issues on few-shot classification. These"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "type": "text",
+                                    "content": "methods focus on learning a flexible feature embedding or fine-tuning on less novel support samples to transfer knowledge across domains. However, they cannot achieve stable performance improvements for different few-shot scenarios. Moreover, most domain adaption-based methods only focused on exploiting the image spatial features."
+                                }
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+                                    "content": "Beyond spatial features, the frequency-domain representation plays a vital role for various computer vision tasks, e.g., deep fake recognition [12, 24, 27], domain generalization [19] and image classification [4, 32, 42, 50]. Different frequency components naturally convey discriminative and interpretive features for visual understanding [19, 32], e.g., the selected frequency components (FCs) of input images can be used to interpret the learned CNN features in classification [42, 50]. In few-shot learning, Chen et al. [4] is the first attempt to apply image frequency spectrum for classification, in which frequency information is naively concatenated as an extra feature, without exploiting different effects of its FCs. Figure 1 provides an example, clearly showing that certain FCs are more discriminative, thus should be selected and highlighted for more effective classification. However, no work to date has systematically investigated the roles of different FCs and how to adaptively select important FCs for effective few-shot learning."
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+                                    "content": "In this paper, we propose a novel Frequency-Guided Few-shot Learning (FGFL) framework towards highly effective few-shot classification and generalization. For each input image, FGFL adaptively generates a task-specific class-discriminative mask in the frequency domain using Grad-CAM [35], where the activated FCs represent the important frequency information associated with the current task. Then we convert the masked and unmasked frequency components output back to the spatial domain for generating the masked and unmasked images, which contain limited and rich task-specific class-discriminative information, respectively. After that, for each image in the meta-task, we construct its triplet with its corresponding unmasked and masked images as positive and negative samples. We also construct two additional few-shot tasks by regrouping the masked and original support and query images, i.e., "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{ms}"
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+                                    "type": "text",
+                                    "content": " with masked support set and original query set, and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{mq}"
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+                                    "type": "text",
+                                    "content": " with original support set and masked query set. In addition, we propose two types of ranking losses, including the triplet and contrastive loss functions at single images and tasks (i.e., "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{mq}"
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+                                    "type": "text",
+                                    "content": ") levels, respectively, to force the model to capture task-specific class-discriminative information that can well generalize to the novel classes. Moreover, the unmasked images are also added to the support set to enhance the discriminability of feature embeddings."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The contributions of this work are fourfold. First, we propose a Frequency-Guided Few-shot Learning (FGFL) framework to utilize the frequency information to enhance the performance and generalizability of few-shot methods"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "in the spatial domain. Second, we propose two types of ranking loss, including the triplet and contrastive loss functions at both sample and task levels based on original and generated images, to force the network to focus on class-discriminative frequency components for each few-shot meta-task. In addition, the generated unmasked images are also utilized to augment the support set to enhance the discriminability of feature embeddings. Third, we investigate the impact of frequency components on current methods under several generalized few-shot settings, namely cross-dataset, cross-domain, and coarse-to-fine annotated generalization. To the best of our knowledge, this is the first work that exploits the effect of different frequency components on few-shot classification and generalization tasks explicitly. Last, experimental results and visualizations demonstrate that the proposed FGFL can improve the performance and generalizability of few-shot methods and achieve superior results under several few-shot settings."
+                                }
+                            ]
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+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "2. Related Work"
+                                }
+                            ]
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+                                            "content": "Figure 2: T-SNE visualization of all image features of 20 test classes in the CUB (top) and 15 test classes in the Quickdraw (bottom) dataset. The few-shot model is trained on the miniImageNet dataset. A cluster that is clearer and more compact within each class is better."
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+                                            "html": "<table><tr><td>Method</td><td>miniImageNet</td><td>CUB</td><td>Quickdraw</td></tr><tr><td>ProtoNet [36]</td><td>79.86</td><td>66.29</td><td>64.32</td></tr><tr><td>ProtoNet w/ High FCs</td><td>56.47</td><td>37.96</td><td>66.26</td></tr><tr><td>ProtoNet w/o High FCs</td><td>77.75</td><td>67.09</td><td>65.99</td></tr></table>",
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+                                    "content": "Table 1: Few-shot classification results under the 5-way 5-shot setting trained with the miniImageNet dataset. ProtoNet is trained on miniImageNet dataset and evaluated on several datasets with specific frequency components."
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+                                    "content": "source and target domain samples. GFNet [32] considers the attention in the FFT frequency domain to replace the self-attention module in the vision transformer. However, FFT requires double the memory for complex coefficients. Therefore, some recent works [4, 31, 50] consider applying the Discrete Cosine Transformation (DCT) to learn in the frequency domain. For example, Wang et al. [43] first applies the DCT to speed up the network. Instead of inputting RGB pixels, Gueguen et al. [16] convert the JPEG-compressed image to its "
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+                                    "type": "inline_equation",
+                                    "content": "8 \\times 8"
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+                                    "type": "text",
+                                    "content": " block DCT coefficients as the input of the neural network. FcaNET [31] adopts DCT to generalize the compression of the channel attention mechanism in the frequency domain. Specifically, Chen et al. [4] select pre-defined channels in the DCT frequency domain to improve the performance for few-shot classification."
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+                                    "content": "In this work, we also employ the DCT to transform the images to the frequency domain. Unlike previous work [4], we consider the interaction between spatial and frequency domains and learn to generate the discriminative frequency mask to enhance learning in the spatial domain."
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+                                    "content": "3. Proposed Method"
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+                                    "content": "In this section, we first investigate the impact of frequency components in different few-shot classification scenarios. Then the proposed FGFL framework is described"
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+                                    "type": "text",
+                                    "content": "and explained in detail, followed by the loss function of our method and empirical validations."
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+                                    "content": "We first investigate the impact of frequency components on the generalized performance of current few-shot methods under different few-shot settings by removing and preserving partial frequency components of each image in the meta-task for class prediction."
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+                                    "content": "To generate the frequency representation of an input RGB image "
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+                                    "type": "inline_equation",
+                                    "content": "X \\in \\mathbb{R}^{H \\times W \\times 3}"
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+                                    "type": "text",
+                                    "content": ", we apply the 2D-Discrete Cosine Transform [1] (2D-DCT) function as "
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+                                    "type": "inline_equation",
+                                    "content": "D = DCT(X) \\in \\mathbb{R}^{H \\times W \\times 3}"
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+                                    "type": "text",
+                                    "content": ". We can then remove or preserve partial frequency components of each input image, followed by an Inverse 2D-DCT function as "
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{X} = IDCT(\\hat{D})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to transform it back into the spatial domain with the original input size."
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+                                    "type": "text",
+                                    "content": "With the help of the DCT functions, we can decompose the raw data into two parts, "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "X = \\{X^{O}, X^{H}\\}"
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "X^{O}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " represent high-frequency components (dubbed w/ high FCs), and other components (dubbed w/o high FCs). For a given few-shot task "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{T}_{\\mathrm{test}} = (\\mathcal{S}, \\mathcal{Q})"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " on the novel testing set, we can reconstruct images with partial frequency information to update the testing task as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{T}}_{\\mathrm{test}} = \\{\\tilde{S}, \\tilde{\\mathcal{Q}}\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we adopt the existing few-shot methods to make predictions for each query sample "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{X}_j"
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+                                    "type": "text",
+                                    "content": " with "
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+                                    "type": "inline_equation",
+                                    "content": "\\tilde{S}"
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "Table 1 shows classification accuracy on different test domains and Figure 2 plots the t-SNE visualizations of image features extracted by the trained feature encoder. We can observe that removing specific frequency components can improve the generalized performance of few-shot models but degrade standard few-shot performance in the same testing scenario."
+                                }
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+                                    "content": "Different FCs encode specific image information, we propose the Frequency-Guided Few-shot Learning (FGFL) framework, which utilizes the frequency mask to guide the training in the spatial domain. As shown in Figure 3, FGFL has two branches with two encoders "
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+                                    "content": " for feature extraction in the frequency and spatial domains, respectively. FGFL generates the frequency mask based on the task-specific attention map for the given few-shot task, which is then adopted to generate additional images, guiding the network updates in the spatial domain. Moreover, we propose a multi-level metric to force the network to capture specific frequency components for classification."
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+                                    "content": "1More implementation details and evaluation results for all frequency components of more few-shot methods are provided in Supplementary."
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+                                            "content": "Figure 3: Overview of our proposed Frequency-Guided Few-shot Learning framework (FGFL). We first generate the task-specific class-discriminative frequency mask based on the classification in the frequency domain. Then we convert the masked and unmasked frequency samples back to the spatial domain and generate two image sets (masked set "
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+                                            "content": ") according to the mask and unmask regions, respectively. Furthermore, we adopt novel multi-level metrics (shown in Figure 4) on the original and generated image sets to make class predictions."
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Note that previous works [35, 22] utilize a fully connected (fc) layer to obtain the classification score "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "ground-truth class "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " with the same training and testing class set. However, since the training and testing classes in few-shot scenarios are non-overlap, directly applying fc layers for gradient computation may be prone to overfitting."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "To this end, we compute the cosine similarity between each sample and class prototype as the classification score for each given "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": "-way "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "-shot task in few-shot learning, where "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates the number of selected classes and labeled support samples from each class, respectively. Specifically, given a few-shot task with support set "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{S}_f = \\{D_m, y_m\\}_{m=1}^{NK}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and a query set "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Q}_f = \\{D_n, y_n\\}_{n=1}^Q"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in the frequency domain, we compute the cosine similarity score "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " between each query sample "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{q} \\in \\mathbb{R}^C"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and each class prototype "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_c \\in \\mathbb{R}^C"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as:"
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+                                    "type": "interline_equation",
+                                    "content": "s ^ {c} = p (y = c \\mid \\mathbf {q}) = \\frac {\\mathbf {q} ^ {T} \\mathbf {v} _ {c}}{\\| \\mathbf {q} \\| \\| \\mathbf {v} _ {c} \\|}, \\tag {3}",
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_c = \\frac{1}{K}\\sum_{k=1}^{K}\\mathbf{z}_k"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the mean feature vector of the support features "
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " of the "
+                                },
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-th class. Note that, it is easy to prove Eq. (3) is equivalent to an fc layer when neglecting the bias of the fc layer. Moreover, the classification weights "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{v}_c"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are flexible and task-dependent, i.e., only based on the current few-shot task. Hence, the network can learn to generate a task-specific heatmap "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " of each sample to find specific frequency components that contribute most to the current task, which avoids over-fitting to the training set."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "We then up-sample "
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+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " to the original size and generate the frequency mask following previous works [45, 22] as:"
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+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {M a s k} ^ {c} = \\mathbf {1} - \\operatorname {S i g m o i d} \\left(U p \\left(A ^ {c}\\right)\\right), \\tag {4}",
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+                                            "type": "text",
+                                            "content": "Figure 4: Illustration of the proposed multi-level metrics. Specifically, for each image in the image set "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
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+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " in the metask, we construct its triplet from the corresponding un-masked and masked set "
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+                                            "type": "text",
+                                            "content": " and "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "X^{um}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                230,
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+                                            ],
+                                            "type": "text",
+                                            "content": " as the positive and negative pair, respectively, and adopt the sample-wise triplet loss "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " to exploit the correlations them. At the task level, we construct two additional few-shot tasks by regrouping the images in "
+                                        },
+                                        {
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+                                            "type": "inline_equation",
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+                                            "type": "text",
+                                            "content": " and "
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+                                            "type": "inline_equation",
+                                            "content": "X^m"
+                                        },
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ". (Here we take the query set as an example.) Then we propose a class-wise contrastive loss "
+                                        },
+                                        {
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+                                            "content": "L_{cw\\_ctr}"
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+                                            "type": "text",
+                                            "content": " between positive pairs (original support and query samples) and negative pairs (support and query from different sets). Moreover, we use unmasked images to augment the support set for classification with a loss "
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+                                            "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is an all-ones matrix, "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "Up(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the upsampling operation, and "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "Sigmoid(\\cdot)"
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+                                {
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+                                    "type": "text",
+                                    "content": " is applied to make it derivable and constrains the value to the range [0, 1]."
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+                                    "type": "inline_equation",
+                                    "content": "Mask^c"
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+                                    "type": "text",
+                                    "content": " is then applied to "
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+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and converted back to the spatial domain to generate the masked spatial image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X^m"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and corresponding unmasked spatial image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X^{um}"
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+                                    "type": "text",
+                                    "content": " as:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "X ^ {m} = I D C T \\left(M a s k ^ {c} \\odot D\\right), X ^ {u m} = I D C T \\left(\\left(1 - M a s k ^ {c}\\right) \\odot D\\right), \\tag {5}",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the dot product function. Note that "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "X^{um}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are considered to contain limited and rich information belonging to the target class since the regions on the attention map beyond the class-aware range should be hard to identify the true class. We can then utilize "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
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+                                    "content": "X^{um}"
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+                                    "type": "text",
+                                    "content": " to guide few-shot learning in the spatial domain."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.2.2 Mask-Guided Multi-Level Metrics"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
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+                                    "type": "text",
+                                    "content": "With the help of task-specific frequency mask generation, we already generate additional samples (i.e., masked images "
+                                },
+                                {
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+                                },
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+                                    "type": "text",
+                                    "content": " and unmasked images "
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+                                    "type": "inline_equation",
+                                    "content": "X^{um}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        618,
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+                                    ],
+                                    "type": "text",
+                                    "content": "). To incorporate frequency information to encourage the spatial network to capture class discriminative information, we propose two ranking losses at the sample and task levels, (i.e., sample-wise triplet loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "L_{sw\\_tri}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and class-wise contrastive loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{cw\\_ctr}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively.) to fully exploit the mask information in the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "frequency signal, shown in Figure 4. Meanwhile, we also adopt the unmasked images to enhance the few-shot classification performance with an additional classification loss "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": "."
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Sample-wise triplet loss. For each original image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " in the meta-task, this loss aims to enhance the feature similarity between "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
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+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
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+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " and its corresponding unmasked image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}^{um}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", while reducing that between "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " and its corresponding masked image "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}^{m}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": ". Formally, we construct the triplet for each image in the meta-task as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(X_{i}, X_{i}^{m}, X_{i}^{um})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}, X_{i}^{um}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_{i}^{m}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " are the anchor, positive, and negative samples, respectively. We define "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "E^{sp} = f_{\\phi}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " as the feature extractor with parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
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+                                        240
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\phi"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        120,
+                                        546,
+                                        240
+                                    ],
+                                    "type": "text",
+                                    "content": " to obtain the feature vector. Then the sample-level triplet loss can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                            "spans": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} L _ {s w. t r i} \\left(X _ {i}, X _ {i} ^ {u m}, X _ {i} ^ {m}\\right) = \\max  \\left\\{d \\left(f _ {\\phi} \\left(X _ {i}\\right), f _ {\\phi} \\left(X _ {i} ^ {u m}\\right)\\right) \\right. \\\\ - d \\left(f _ {\\phi} \\left(X _ {i}\\right), f _ {\\phi} \\left(X _ {i} ^ {m}\\right)\\right) + \\eta , 0 \\}, \\tag {6} \\\\ \\end{array}",
+                                    "image_path": "4eb705e32eba0611881477b12554adce385e3fa38d6dc5acca493956f1539380.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d(\\cdot ,\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the distance between two features and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\eta"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        292,
+                                        545,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " is the margin between positive and negative pairs."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Class-wise contrastive loss. To encourage the network to capture class discriminative information, we construct contrastive pairs for each query instance in the original and masked sets. Specifically, given masked support and query sets "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        316,
+                                        546,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{m} = \\{X_{i}^{m},y_{i}\\}_{i = 1}^{NK}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        316,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        399
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Q}_m = \\{X_j^m,y_j\\}_{j = 1}^Q"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        316,
+                                        546,
+                                        399
+                                    ],
+                                    "type": "text",
+                                    "content": " , we first construct two additional masked few-shot tasks by regrouping the masked and original sets as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {T} _ {m s} = \\left(\\mathcal {S} _ {m}, \\mathcal {Q}\\right), \\quad \\mathcal {T} _ {m q} = \\left(\\mathcal {S}, \\mathcal {Q} _ {m}\\right), \\tag {7}",
+                                    "image_path": "224d58156e817379ee1904c37088c7d43f5fc6a54560c7621fa90c2100346b61.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{S} = \\{X_i, y_i\\}_{i=1}^{NK}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Q} = \\{X_j, y_j\\}_{j=1}^Q"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        424,
+                                        545,
+                                        449
+                                    ],
+                                    "type": "text",
+                                    "content": " are original support and query set, respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Each masked sample consists of less class-discriminative information. To avoid being misled by class-irrelevant information (i.e., preserved in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_{m}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Q}_{m}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "), we regard the support and query samples from tasks "
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+                                    "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "T_{mq}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as negative pairs, and those from the original task with the same class as positive pairs. Then the contrastive loss corresponding to query sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X_{q} \\in \\mathcal{Q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " can be written as:"
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+                                    "content": "L _ {q} = - \\log \\frac {\\sum_ {y _ {j} = y _ {q} , X _ {j} \\in S} e ^ {d \\left(z _ {j} , z _ {q}\\right) / \\tau}}{\\sum_ {y _ {j} = y _ {q} , X _ {j} \\in S} e ^ {d \\left(z _ {j} , z _ {q}\\right) / \\tau} + \\sum_ {X _ {k} \\in S _ {m}} e ^ {d \\left(z _ {k} , z _ {q}\\right) / \\tau}}, \\tag {8}",
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+                                    "type": "inline_equation",
+                                    "content": "z_{i} = f_{\\phi}(X_{i})"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " represents the feature vector extracted by the spatial backbone. Similarly, the contrastive loss for support sample "
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+                                    "type": "text",
+                                    "content": " can be written as:"
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+                                    "type": "interline_equation",
+                                    "content": "L _ {s} = - \\log \\frac {\\sum_ {y _ {j} = y _ {s} , X _ {j} \\in Q} e ^ {d \\left(z _ {j} , z _ {s}\\right) / \\tau}}{\\sum_ {y _ {j} = y _ {s} , X _ {j} \\in Q} e ^ {d \\left(z _ {j} , z _ {s}\\right) / \\tau} + \\sum_ {X _ {k} \\in Q _ {m}} e ^ {d \\left(z _ {k} , z _ {s}\\right) / \\tau}}. \\tag {9}",
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+                                    "type": "text",
+                                    "content": "Overall, for one episode, "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "content": "L _ {c w - c t r} = \\frac {1}{Q} \\sum_ {q = 1} ^ {Q} L _ {q} + \\frac {1}{N K} \\sum_ {s = 1} ^ {N K} L _ {s}. \\tag {10}",
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+                                            "content": "Figure 5: (a) MMC before and after applying the proposed FGFL method. (b) MMD results of few-shot methods trained over miniImageNet. The lower MMD value indicates a smaller gap and better performance. 'Pretrained' denotes the feature extractor (i.e., ResNet-12) pre-trained on the training set of miniImageNet."
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+                                            "html": "<table><tr><td>Method</td><td>mini</td><td>CUB</td></tr><tr><td>Pretrained</td><td>0.5567</td><td>1.5584</td></tr><tr><td>FEAT [55]</td><td>0.5386</td><td>1.5367</td></tr><tr><td>Ours</td><td>0.1256</td><td>1.2550</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "(b) Maximum Mean Discrepancy (MMD) results on different test datasets."
+                                }
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+                    ],
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+                                    "type": "text",
+                                    "content": "Augmented classification loss. To better classify samples in the query set "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Q}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we use generated support images "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_{um}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "X^{um}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " to enhance the support set for classification. Specifically, we build a new support set by combining the original support and unmasked support set as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_{aug} = S \\cup S_{um}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Hence, we conduct few-shot classification on query set "
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{Q}"
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+                                    "type": "text",
+                                    "content": " based on "
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+                                    "type": "inline_equation",
+                                    "content": "S_{aug}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and minimize the cross-entropy loss:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "L _ {a u g} = \\sum_ {j = 1} ^ {Q} L _ {C E} \\left(f _ {\\theta} \\left(X _ {j}; \\mathcal {S} _ {a u g}\\right), y _ {j}\\right). \\tag {11}",
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+                                    "content": "3.2.3 Objective, Model Training, and Inference"
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+                                    "content": "Combining with the standard few-shot classification, the overall objective function is defined as:"
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+                                    "content": "L _ {t o t a l} = L _ {c l s} ^ {s p} + L _ {c l s} ^ {f q} + \\lambda_ {1} \\cdot L _ {s w \\_ t r i} + \\lambda_ {2} \\cdot L _ {c w \\_ c t r} + \\lambda_ {3} \\cdot L _ {a u g}, \\tag {12}",
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+                                    "content": "L_{cls}^{fq}"
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+                                    "type": "text",
+                                    "content": " represent the cross-entropy loss for few-shot classification in the spatial and frequency branch, respectively. "
+                                },
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+                                    "content": "\\lambda_1, \\lambda_2,"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda_3"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denote the weighting parameters of the corresponding losses, respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "During the training phase, we first generate frequency masks based on the frequency branch and then adopt the proposed multi-level metrics for model training. During the inference time, our proposed method strictly follows the inductive setting. We only feed the support set into the frequency branch to generate unmasked support images to refine the support set for classification."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.3. Empirical Validation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The proposed FGFL framework aims to utilize frequency information to guide the spatial feature extractor towards class-discriminative features and avoid over-fitting to the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
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+                                    "type": "text",
+                                    "content": "training patterns, thus generalizing well to testing scenarios. To validate the effectiveness of the proposed method, we conduct experiments about learned features on two aspects: channel distribution shift and domain distance."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Mean Magnitude of Channels (MMC) Luo et al. [26] shows the channel bias problem affects the generalizability of few-shot methods and utilizes MMC to visualize and measure the channel response to features, where effective few-shot methods might have a more uniform MMC curve in the testing set. Inspired by this work, we visualize the MMC before and after applying FGFL over miniImageNet. We can observe a channel magnitude change in Figure 5 (a), which validates that our proposed method can alleviate the channel bias problem, thus improving the performance."
+                                }
+                            ]
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+                                    "content": "Maximum Mean Discrepancy (MMD) The MMD [15] is a distance measure between two domains based on the embedding of distribution measures in a reproducing kernel Hilbert space, which has been widely applied in transfer learning problems. We adopt class-wise MMD to measure the distribution gap between the training and testing sets with different methods trained over miniImageNet. Figure 5 (b) shows different gaps between one training set and different testing sets. We can also observe that our proposed method helps to reduce the domain shift."
+                                }
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+                                    "content": "4. Experiments"
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+                                    "content": "4.1. Experimental Setup"
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+                                    "type": "text",
+                                    "content": "Datasets. We conduct extensive experiments on four few-shot datasets, i.e., miniImageNet [40], tieredImageNet [34], CUB [41], and FS-DomainNet [6]."
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+                                    "type": "text",
+                                    "content": "Implementation Details. For fair comparisons with previous methods, we adopt the ResNet-12 network with [64, 160, 320, 640] channels as our backbone in each branch, and set the input image size as "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "84 \\times 84"
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+                                    "type": "text",
+                                    "content": " for all datasets. We combine our proposed FGFL with FEAT [55], which adopts a linear projection layer for feature adaptation. We randomly select 15 samples of each class to construct the query set for 5-way 1-shot and 5-way 5-shot settings. The backbone networks are pre-trained on the training set following the typical classification task. The weighting parameters "
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+                                    "content": ", "
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " are all set to 0.1 to balance the scale between the classification loss and the corresponding losses for all datasets."
+                                }
+                            ]
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+                                    "content": "4.2. Few-shot Classification"
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+                                    "type": "text",
+                                    "content": "We conduct experiments on two standard few-shot settings, i.e., general and fine-grained classification, shown in Table 2. Table 2 (a) shows that our proposed FGFL can"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "2More details are included in Supplementary."
+                                }
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+                                    "content": "3More details about datasets and experimental settings are included in Supplementary."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Backbone</td><td colspan=\"2\">CUB</td></tr><tr><td>5-way 1-shot</td><td>5-way 5-shot</td></tr><tr><td>MELR [9]</td><td>ConvNet-4</td><td>70.26 ± 0.50</td><td>85.01 ± 0.32</td></tr><tr><td>ProtoNet [36]†</td><td>ResNet-12</td><td>72.25 ± 0.21</td><td>87.47 ± 0.13</td></tr><tr><td>DeepEMD [58]</td><td>ResNet-12</td><td>75.65 ± 0.83</td><td>88.69 ± 0.50</td></tr><tr><td>FEAT [55]†</td><td>ResNet-12</td><td>75.68 ± 0.20</td><td>87.91 ± 0.13</td></tr><tr><td>BML [60]</td><td>ResNet-12</td><td>76.21 ± 0.63</td><td>90.45 ± 0.36</td></tr><tr><td>Good-Embed [38]‡</td><td>ResNet-18</td><td>77.92 ± 0.46</td><td>89.94 ± 0.26</td></tr><tr><td>DFR [6]</td><td>ResNet-12</td><td>78.07 ± 0.79</td><td>89.74 ± 0.51</td></tr><tr><td>VFD [49]</td><td>ResNet-12</td><td>79.12 ± 0.83</td><td>91.48 ± 0.39</td></tr><tr><td>FRN [46]†</td><td>ResNet-12</td><td>82.90 ± 0.19</td><td>92.61 ± 0.10</td></tr><tr><td>Ours</td><td>ResNet-12</td><td>80.77 ± 0.90</td><td>92.01 ± 0.71</td></tr></table>",
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+                                            "content": "Table 2: Comparison with state-of-the-art methods for general (a) and fine-grained (b) few-shot image classification. The best and second best results under each setting and dataset are highlighted as Red and Blue, respectively. "
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+                                            "content": ": implemented based on public code with our setting. "
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+                                            "content": ": reported in [48]."
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+                                            "html": "<table><tr><td colspan=\"4\">Train Scenario</td><td colspan=\"4\">Test Scenario</td></tr><tr><td rowspan=\"2\">(a)</td><td rowspan=\"2\">Cross-Dataset Setting</td><td colspan=\"2\">minImageNet</td><td colspan=\"4\">CUB</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(b)</td><td rowspan=\"2\">Cross-Domain Setting 1</td><td colspan=\"2\">minImageNet</td><td colspan=\"4\">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(c)</td><td rowspan=\"2\">Cross-Domain Setting 2</td><td colspan=\"2\">FS-DomainNet</td><td colspan=\"4\">Quickdraw</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan=\"2\">(d)</td><td rowspan=\"2\">Cross-Annotated Setting</td><td colspan=\"2\">tieredImageNet (Coarse)</td><td colspan=\"4\">tieredImageNet (Fine)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
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+                                    "content": "Figure 6: Illustration of three challenging few-shot generalization scenarios under the 3-way 1-shot setting."
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+                                    "type": "text",
+                                    "content": "significantly improve the performance of few-shot methods and outperform state-of-the-art methods for 5-shot setting on miniImageNet and 1-shot setting on tieredImageNet datasets. Moreover, FGFL is still on par with state-of-the-art methods under other settings. For CUB, as shown in Table 2 (b), we can observe that FGFL can improve the performance of FEAT by a large margin, i.e., "
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+                                    "content": " for 1-shot and 5-shot settings, and is competitive with the state-of-the-art methods."
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+                                    "content": "4.3. Few-Shot Generalization"
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+                                    "content": "To evaluate the generalized performance of few-shot methods, we propose three few-shot generalization settings for cross-domain classification based on challenging test scenarios, shown in Figure 6."
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+                                    "content": "In this setting, we only consider the distribution gaps of classes between training and testing datasets with the same style, e.g., natural images. As shown in Figure 6 (a), we train on the miniImageNet dataset with natural images and evaluate the fine-grained CUB dataset with various bird species, i.e., mini "
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+                                    "type": "text",
+                                    "content": " CUB."
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+                                    "content": "Table 3 shows that the proposed FGFL significantly improves the performance of the baseline FEAT method and outperforms the other methods. Figure 7 (a) shows that the proposed FGFL can force the network to capture discriminative task-specific frequency components for classification, e.g., high-frequency edge features for the first class and low-frequency color features for the third class."
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+                                    "content": "Unlike the cross-dataset setting, the visual similarity between the training (source) and testing (target) domains may have a significant gap, as the target domain may contain unnatural images, e.g., quickdraw. As shown in Figure 6 (b) and Figure 6 (c), we split the cross-domain scenario into two specific settings according to the number of the source domains, i.e., single (e.g., miniImageNet) or multiple domains (e.g., FS-DomainNet). For the second setting, each source domain only contains images with the same style such as paintings."
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+                                    "content": "Results in Table 3 show that our proposed FGFL outperforms other few-shot methods by a large margin under two cross-domain generalization settings, i.e., mini "
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+                                    "content": " Quickdraw. Figure 7 (b) also verifies that our proposed method can indeed learn to ex"
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+                                    "content": "ploit high-frequency patterns rare in natural images to distinguish different classes on the quickdraw dataset. Another interesting observation is that few-shot methods generally perform better when generalizing from FS-DomainNet to quickdraw than from miniImageNet to quickdraw. A reasonable explanation is that compared to the miniImageNet dataset with small domain variations, the FS-DomainNet dataset includes multiple domains with obvious differences, which enables the network to capture domain-specific information from each meta-task for classification, resulting in better generalization ability to the unseen domain. Furthermore, our FGFL can still boost performance in this setting, illustrating the necessity of frequency domain information."
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+                                    "content": "Different from existing settings, we consider the annotation difference between training and testing sets for few-shot generalization. In practice, an image may have different levels of class annotations due to the requirements of labeling tasks. For example, we only need a training set with two labels \"Furniture\" and \"Person\" to train a powerful classifier for a binary classification task. However, when we want to use the above classifier to identify the species of furniture, we need additional fine-grained labels such as \"Desk\" or \"Chair\". This is a practical scenario since fine-grained labeling requires a high cost of human collaboration. We conduct experiments on tieredImageNet with hierarchical annotations to evaluate the generalization performance under this setting, shown in Figure 6 (d). All competing methods are trained on the coarse-annotated training set with 20 super-classes and evaluated on the fine-annotated testing set with 160 sub-classes same as the standard few-shot setting, denoted as tiered(C) "
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+                                    "type": "text",
+                                    "content": " (F)."
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+                                    "content": "As shown in Table 3, all methods perform worse than general classification results in Table 2. The reason is that the model tends to overfit the general features of high-level class prediction tasks while ignoring within-class differences. We observe that our proposed FGFL can still out"
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+                                            "content": "Table 3: Few-shot generalization results under the 5-way 5-shot setting. mini, Q, F, and tiered(C), (F) denote miniImageNet, QuickDraw, FS-DomainNet, tieredImageNet with coarse-grained or fine-grained annotations. "
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+                                            "content": ": reimplement based on public code with our setting. tieredImageNet with coarse-grained (super-classes) or fine-grained annotations (sub-classes). "
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+                                    "content": "perform all methods. Figure 7 (c) shows that our method can focus on specific frequency components (e.g., low and middle FCs corresponding to color and shape spatial features), which is discriminative for class prediction."
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+                                    "content": "der the 5-way settings with ResNet-12 as the backbone. As shown in Table 4, each proposed loss contributes to performance improvement. Moreover, we find that "
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+                                    "content": " significantly improve the performance (1.92% and 4.14% for 1-shot and 5-shot, resp.), indicating that the proposed multi-level metrics can better utilize the frequency information to improve the generalizability of the model and avoid over-fitting to spatial features, leading to further improvements over spatial masks. Results also show that the two losses play different roles and complement each other, which further proves that our proposed method can utilize frequency information from different levels to help with classification. Noted that the performance gain under the 5-shot setting is much higher than the 1-shot setting. One plausible reason is that more supervised information introduced by support samples helps to generate a more precise frequency mask, which helps reduce the intra-class variation to learn a strong classifier, aligning with our idea."
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+                                    "content": "5. Conclusion"
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+                                    "content": "In this paper, we proposed a novel Frequency-Guided Few-shot Learning (FGFL) framework for few-shot classification and generalization. Specifically, the frequency masks generated by the classification gradients in the DCT domain can emphasize the class-discriminative frequency components in the current meta-task. Our proposed multi-level metrics, including sample-wise triplet loss and class-wise contrastive loss, can better utilize the frequency information at sample and task levels and encourage the model to capture more task-relevant frequency information to help the classification in the spatial domain. Besides, we systematically investigated the effects of frequency information on few-shot generalization behaviors. Extensive experiments demonstrated that FGFL achieves competitive results with state-of-the-art methods on the standard few-shot settings, and significantly improves the generalized performance on unseen testing domains."
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+                                    "type": "text",
+                                    "content": "Acknowledgement"
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+                                    "type": "text",
+                                    "content": "This research is supported in part by the SUG and MOE AcRF Tier1 (RG61/22) Grant. This research work is also partially supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research), and the Singapore Government's Research, Innovation and Enterprise 2020 Plan (Advanced Manufacturing and Engineering domain) under Grant A18A1b0045."
+                                }
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+                                    "content": "References"
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+                            ]
+                        }
+                    ],
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+                                            "content": "[60] Ziqi Zhou, Xi Qiu, Jiangtao Xie, Jianan Wu, and Chi Zhang. Binocular mutual learning for improving few-shot classification. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 8402-8411, 2021. 7, 8"
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diff --git a/2023/Frequency-aware GAN for Adversarial Manipulation Generation/8bcc3433-dc75-4f7a-97ef-3808dc50d15f_content_list.json b/2023/Frequency-aware GAN for Adversarial Manipulation Generation/8bcc3433-dc75-4f7a-97ef-3808dc50d15f_content_list.json
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+++ b/2023/Frequency-aware GAN for Adversarial Manipulation Generation/8bcc3433-dc75-4f7a-97ef-3808dc50d15f_content_list.json	
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+[
+    {
+        "type": "text",
+        "text": "Frequency-aware GAN for Adversarial Manipulation Generation",
+        "text_level": 1,
+        "bbox": [
+            155,
+            130,
+            816,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Peifei Zhu, Genki Osada, Hirokatsu Kataoka, Tsubasa Takahashi LINE Corporation",
+        "bbox": [
+            227,
+            180,
+            743,
+            217
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{peifei.zhu, genki.osada, jpz4219, tsubasa.takahashi}@linecorp.com",
+        "bbox": [
+            192,
+            219,
+            777,
+            234
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            268,
+            313,
+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Image manipulation techniques have drawn growing concerns as manipulated images might cause morality and security problems. Various methods have been proposed to detect manipulations and achieved promising performance. However, these methods might be vulnerable to adversarial attacks. In this work, we design an Adversarial Manipulation Generation (AMG) task to explore the vulnerability of image manipulation detectors. We first propose an optimal loss function and extend existing attacks to generate adversarial examples. We observe that existing spatial attacks cause large degradation in image quality and find the loss of high-frequency detailed components might be its major reason. Inspired by this observation, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. We further design an encoder-decoder architecture with skip connections of high-frequency components to preserve fine details. We evaluated our method on three image manipulation detectors (FCN, ManTra-Net and MVSS-Net) with three benchmark datasets (DEFACTO, CASIAv2 and COVER). Experiments show that our method generates adversarial examples significantly fast (0.01s per image), preserves better image quality (PSNR 30% higher than spatial attacks), and achieves a high attack success rate. We also observe that the examples generated by AMG can fool both classification and segmentation models, which indicates better transferability among different tasks.",
+        "bbox": [
+            76,
+            301,
+            473,
+            709
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            738,
+            209,
+            753
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the rapid development of advanced editing software, manipulated images are becoming more common on social media. Despite the positive aspects, there are possibilities that manipulated images are used to spread fake news and misleading information. Therefore, it is important to develop methods that can automatically detect manipulated images.",
+        "bbox": [
+            76,
+            763,
+            468,
+            869
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Various image manipulation detectors [5, 20, 32, 4] have been proposed and achieved high performance on manip-",
+        "bbox": [
+            76,
+            869,
+            468,
+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/4dcb0d18ea3cec845812f43f5223069967a715c6b6b6b686fceb1a3869874ded.jpg",
+        "image_caption": [
+            "Figure 1. Adversarial examples generated under the proposed AMG task. For the manipulated image, the manipulations of the original image can be detected by a detector named MVSS-Net [5]. After applying attacks, the detector fails to correctly detect manipulations. For the authentic image, attacking the original image results in false-positive detection. Compared to previous attack methods, the examples generated by our method have much less noise and can successfully fool the detector at pixel-level."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            509,
+            272,
+            890,
+            494
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ulated image datasets [26, 7, 36, 16]. However, existing methods can be vulnerable to adversarial examples. For a manipulated image, adding imperceptible adversarial perturbations might cause the detector to detect a completely wrong result. Several works have already studied adversarial face forgery that fools the classification result of face forgery detector by the adversarial examples [15, 19, 14]. Since the detectors developed recently not only focus on classifying manipulated or authentic but also try to pinpoint the manipulated regions, we also go one step further to generate adversarial examples for the detectors that apply semantic segmentation. We name this task Adversarial Manipulation Generation (AMG). This topic has not been studied before and it is more difficult because instead of only fooling a class label, our target is to fool every pixel in both manipulated and authentic regions. We further show",
+        "bbox": [
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+            657,
+            893,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "4315",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "the examples generated by AMG have better transferability among different tasks (details in Section 5.5).",
+        "bbox": [
+            76,
+            90,
+            467,
+            119
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 1, images added with imperceptible perturbations generated by our task can successfully fool the detector. This task is also different from dense adversary generation [39, 3, 30] which is designed for segmentation and detection models under an untargeted attack setting. Our work considers applying targeted adversarial attacks on the manipulated and authentic images to explore the vulnerability of the image manipulation detectors. This is a specific scenario that the adversarial examples actually bring serious social problems. We first design a loss function that optimizes perturbation at pixel-level to generate such adversarial examples.",
+        "bbox": [
+            75,
+            121,
+            467,
+            301
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Algorithms such as FGSM [11] and PGD [25, 18] can be extended using our loss function to generate adversarial examples. However, these examples can be easily recognized by human eyes since the images are perturbated with visible noise. In addition, generating examples using iterative methods such as PGD can be time-consuming. To address these problems, we proposed a novel adversarial attack that generates perturbations using both frequency and spatial features to avoid image quality degradation. In addition, instead of optimizing each example against the target model, our method only needs to train the generator once, and then it can generate perturbation for any images extremely fast. The contributions of this work are three-fold:",
+        "bbox": [
+            75,
+            303,
+            467,
+            500
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We explore the vulnerability of the image manipulation detectors by proposing an AMG task. We design a loss function and extend existing attacks to generate adversarial examples. Although these attacks can fool the detectors, the perturbations added to the image are visible to human eyes. We perform an analysis and find the loss of high-frequency components can be the major reason to cause the degradation of image quality.",
+            "- Inspired by the above observation, we propose an adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. To preserve fine details, an encoder-decoder with skip connections of high-frequency components is also combined. Compared with previous attacks, our method generates more imperceptible perturbations for human observers.",
+            "- We evaluate our method on three manipulation detectors with three benchmark datasets, under both white-box and black-box settings. Experiments show that our method generates adversarial examples significantly fast, preserves better image quality, and achieves a high attack success rate. We further observe the examples generated by AMG have better transferability and can fool both classification and detection models."
+        ],
+        "bbox": [
+            94,
+            513,
+            467,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            89,
+            640,
+            106
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we briefly introduce the development of image manipulation generation and detection. Besides, we summarize recent adversarial attack methods that could be applied to image manipulation detectors.",
+        "bbox": [
+            498,
+            114,
+            890,
+            176
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Image Manipulation Generation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            186,
+            784,
+            204
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image manipulation generation (also known as image forensic) has gained growing attention as it is getting easier to create fake images and might cause problems, such as spreading fake news and misleading information [34, 33]. Common image manipulation generation includes copy-move (copy a region and paste it in the same image), splicing (copy a region and paste it to another image) and inpainting (remove a region) [26, 22]. Several datasets [26, 7, 36] have been created and released, i.e. DEFACTO [26] is a recently released large-scale dataset, containing 149k images sampled from MS-COCO [21]. Recently, generative adversarial networks (GANs) [10, 45] have also become popular to generate forged images, especially in the field of face forgery generation [15, 19, 14]. Instead of only focusing on face manipulation, this work explores how adversarial attack affects manipulation generation that includes various types of images.",
+        "bbox": [
+            498,
+            210,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Image Manipulation Detection",
+        "text_level": 1,
+        "bbox": [
+            500,
+            479,
+            769,
+            494
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Image manipulation detection can be considered as a classification task or a semantic segmentation task. In classification task, the goal is to distinguish the manipulated image from the real one. Methods such as [6, 1, 31] are proposed to learn the decision boundary between real and fake faces for face forgery detection. On the other hand, in semantic segmentation, the goal is to pinpoint manipulated regions at the pixel level. [20, 43] propose to implement a fully convolutional network (FCN) [23] to localize manipulations. ManTra-Net [37] designs a self-supervised learning task to learn robust image manipulation traces. MVSS-Net [5] exploits noise distribution and boundary artifacts surrounding manipulated regions to learn more generalizable features. Since this work mainly focuses on the semantic segmentation task, we selected one baseline method (FCN) and two state-of-the-art methods (ManTra-Net and MVSS-Net) for localizing manipulations and we demonstrate that our method can fool all of these detectors.",
+        "bbox": [
+            498,
+            503,
+            890,
+            773
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3. Adversarial Attack",
+        "text_level": 1,
+        "bbox": [
+            500,
+            786,
+            684,
+            801
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Adversarial examples are inputs added with small perturbations to confuse a neural network. FGSM [11] is a well-known one-step attack method that uses gradients of the loss with respect to the input image. PGD [25, 18] is an iterative attack that performs FGSM with a smaller step size and clips the updated adversarial sample into a valid",
+        "bbox": [
+            498,
+            809,
+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "4316",
+        "bbox": [
+            482,
+            945,
+            514,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "range. Other methods such as CW [29], JSMA [28], MIFGSM [8], are also widely used. However, such attacks using iterative optimization can be time-consuming, and each image should be optimized separately. Instead of optimizing each image, GAN-based methods [38, 17, 13] train a generator to learn the adversarial distribution by optimizing target loss and GAN loss. Once the generator is trained, it can generate perturbations for any input and is much faster than iterative-based methods. However, although the generated image can bypass the target model, it degrades the image quality and is visible to human eyes.",
+        "bbox": [
+            75,
+            90,
+            472,
+            257
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For adversarial examples in image manipulation detection, several works [9, 14, 19, 27, 44] were proposed to escape face forgery detection using adversarial attack. These methods mainly generate examples in the spatial domain. Recently, a few works [15, 24, 42] have been proposed to combine the frequency features to generate more imperceptible examples. However, these works are usually designed for the classification task, and the generation is optimization-based which can be time-consuming. We proposed a method that can generate high-quality adversarial images and is faster than most of the previous methods.",
+        "bbox": [
+            75,
+            257,
+            472,
+            422
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Adversarial Manipulation Generation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            434,
+            419,
+            450
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Definition",
+        "text_level": 1,
+        "bbox": [
+            76,
+            459,
+            261,
+            474
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given an original image  $x$  and an image manipulation detector  $f$  which segments the manipulated and authentic region at pixel-level, we aim for generating adversarial examples that can completely fool the detector by adding imperceptible perturbations. We name this task Adversarial Manipulation Generation (AMG). The original image  $x$  can be either manipulated or authentic. In this work, we mainly focus on the targeted attack which contains two cases: 1) for the manipulated images, we add perturbations so that the detector fails to segment any pixels in the manipulated region, and 2) for the authentic images, we generate examples that the detector detects false-positive regions. Therefore, we design two types of target map: authentic map  $S_0$  with all pixels labeled as authentic and manipulated map  $S_1$  with the manipulation regions generated by watershed segmentation [2]. We select one random region from the watershed segmentation results and let it be the target manipulation region for each image. In order to determine which target map to use, we first input  $x$  into  $f$  to obtain a predicted map  $\\{f(x)\\}$ , then we apply Global Max Pooling (GMP) to obtain the image-level prediction result  $GMP\\{f(x)\\}$  (authentic: 0, manipulated: 1).",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our loss function to generate the adversarial examples is as follows:",
+        "bbox": [
+            76,
+            814,
+            470,
+            844
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {a d v} = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {D L} [ f (x ^ {\\prime}), S _ {0} ] & G M P \\{f (x) \\} = 1 \\\\ \\mathcal {L} _ {D L} [ f (x ^ {\\prime}), S _ {1} ] & G M P \\{f (x) \\} = 0 \\end{array} \\right. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $x^{\\prime}$  is the adversarial example generated by adding",
+        "bbox": [
+            96,
+            885,
+            470,
+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "pixel-wise perturbation to the original image  $x$ . Since this is a semantic segmentation task, we use dice loss  $\\mathcal{L}_{DL}$  to calculate the difference between the predicted map and the target map.  $x'$  can be calculated by minimizing  $\\mathcal{L}_{adv}$ , where  $x'$  should be as close as possible to  $x$ .",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Extending Existing Attacks",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Existing adversarial attacks can be extended to AMG using Equation 1. We selected three widely used attacks, FGSM, PGD, and AdvGAN, and extend them to generate the adversarial examples for AMG.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Fast Gradient Sign Method (FGSM) [11] is a one-step attack method that uses gradients of the loss with respect to the input image to calculate perturbations. The adversarial example generation can be written as:",
+        "bbox": [
+            496,
+            258,
+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx ^ {\\prime} = x - \\varepsilon \\cdot \\operatorname {s i g n} \\left[ \\nabla_ {x} \\mathcal {L} _ {a d v} (x, S) \\right] \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Projected Gradient Descent (PGD) [25] is an iterative attack that performs FGSM with a smaller step size and projects the updated adversarial sample into a valid range, written as:",
+        "bbox": [
+            496,
+            352,
+            890,
+            411
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t + 1} ^ {\\prime} = \\operatorname {P r o j} \\left\\{x _ {t} ^ {\\prime} - \\omega \\cdot \\operatorname {s i g n} \\left[ \\nabla_ {x} \\mathcal {L} _ {a d v} (x, S) \\right] \\right\\} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            539,
+            420,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "AdvGAN [38] is a GAN-based attack that trains a generator to learn the adversarial distribution by maximizing the target loss and the GAN loss. A soft hinge loss is also incorporated to bound the magnitude of the perturbation. Therefore, the full objective can be expressed as  $\\mathcal{L}_{adv} + \\alpha \\mathcal{L}_{GAN} + \\beta \\mathcal{L}_{hinge}$ . By solving the minimax game over the objective, the generator and discriminator can be optimized, and the adversarial example can be obtained by putting the original image into the generator.",
+        "bbox": [
+            496,
+            446,
+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Although these methods generate examples that can fool the manipulation detectors, the generated images can be easily recognized by human eyes since the images are perturbed with visible noise. Our work focuses on generating examples that can fool both target detectors and human eyes. Such attacks are more dangerous and might cause serious security problems.",
+        "bbox": [
+            496,
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+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Exploring Frequency Components",
+        "text_level": 1,
+        "bbox": [
+            500,
+            696,
+            802,
+            713
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Previous works [40, 41, 35] have shown neural networks prefer to generate low-frequency signals that are more superficial in complexity. Therefore, part of the high-frequency signal might be lost during the feature extraction, and this results in generating images with noise and aliasing artifacts. In order to explore whether a similar phenomenon has occurred in generating the adversarial examples and thus design an optimized architecture, we first analyze the changes in frequency components when applying existing adversarial attacks.",
+        "bbox": [
+            496,
+            719,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The frequency components of the original image and the adversarial examples using existing attacks are visualized",
+        "bbox": [
+            500,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4317",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a9c72e6af0afb37ccf9fee8ec51c68566860361aa524e16a48b3085de113680.jpg",
+        "image_caption": [
+            "Figure 2. Visualization of the frequency components. Rows from top to bottom: original image, adversarial examples using FGSM, PGD and AdvGAN attack. Columns from left to right: image in the spatial domain, low-frequency component (LL), high-frequency horizontal component (LH), high-frequency vertical component (HL), high-frequency diagonal component (HH). For each component of the attack images, closer to that component of the original image indicates better preservation of the information."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "in Figure 2 (row 1-4). We use wavelet transform to obtain the frequency components. The low-frequency component (LL) contains the general structure and most of the color data, while the high-frequency component (LH, HL, HH) contains rich details like the edges of the contents and image texture. By comparing the components between the original image and adversarial examples, we find that many details of the high-frequency components such as the branches of the tree, and the edge of the building windows, are lost, meanwhile, artifacts appear in the background. We believe the loss of details and the increasing artifacts in the high-frequency components are major reasons that make adversarial perturbations visible to human eyes.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Frequency-aware GAN Attack",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Architecture Overview",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Inspired by the above observation, we propose an attack method to generate high-quality adversarial examples for AMG. As shown in Figure 3, the architecture of our method has three components: a generator  $G$ , a discriminator  $D$ , and a target model  $f$ . We focus on designing a  $G$  that can generate imperceptible perturbation.  $G$  consists of an encoder and a decoder to generate pixel-level perturbations. The encoder extracts high-level feature representation from the input image, and the decoder uses the representation to generate perturbations. In this work, instead of directly perturbing the image in the spatial domain, we transform the input image into the frequency domain, combine the fre",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "quency feature and the spatial feature and add noise on the mixed domain to avoid degradation of image quality. The perturbations are then added to the input image to obtain an adversarial image.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The discriminator  $D$  is a classifier that distinguishes the original input image from the adversarial image. A minimax GAN loss  $\\mathcal{L}_{GAN}$  can be obtained, where  $D$  tries to distinguish the adversarial image and the input image, and  $G$  tries to generate perturbations that are indistinguishable by the  $D$ . To obtain the adversarial example, we first apply the white-box attack, where the target model  $f$  is known and used to train the model. The input of  $f$  is the adversarial image, and the output is the predicted segmentation. An adversarial attack loss  $\\mathcal{L}_{adv}$  can be calculated between the predicted and target result.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Frequency-aware Generator",
+        "text_level": 1,
+        "bbox": [
+            500,
+            694,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We propose a generator that combines both spatial and frequency features as well as incorporates skip connections of the high-frequency components to generate imperceptible adversarial examples. The architecture of the generator is shown in Figure 3.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Encoder. The encoder consists of convolutional layers (conv), pooling layers, and discrete wavelet transform layers (dwt). The first conv layer extracts spatial features from the input image and passes the feature to the dwt layer. We used 2D discrete wavelet transform to decompose the features into the low-frequency component  $(L_{i})$  and the high-frequency component  $(H_{i})$ . These components are concate",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4318",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/1906061edb32c1318375dade32fbd81f57338e5e18ca88b5d3ad14ad63463764.jpg",
+        "image_caption": [
+            "Figure 3. Overview of our frequency-aware GAN attack."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            99,
+            88,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "nated channel-wise, denoted as  $\\text{concat}(L_i, H_i)$ . On the other hand, the spatial feature extracted by conv layer is downsampled and then combined with the frequency feature  $\\text{concat}(L_i, H_i)$ . Finally, the features containing both spatial and frequency information are sent to the next conv layer. We construct 4-level layers to extract the high-level feature representation.",
+        "bbox": [
+            75,
+            393,
+            470,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Decoder. The decoder consists of conv layers, upsampling layers, and inverse discrete wavelet transform layers (idwt). To avoid losing fine details, we conduct skip connections of the high-frequency components from the encoder to the decoder. This helps the decoder generate perturbations with more details and less noise, and thus makes the generated image less distinguishable by human eyes. The processing of the decoder is as follows. The feature generated by the encoder is upsampled to obtain feature  $A$ . On the other hand, 2D inverse discrete wavelet transform is performed on the high-frequency feature directly from the encoder, then we obtain feature  $B$ . These two features are combined as  $A + B$  and sent to the conv layer. We also construct 4-level layers to decode the feature and generate the perturbation for the input image.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Optimization",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As in the white-box attack setting, the target model  $f$  is known and fixed, we need to optimize the generator  $G$  and the discriminator  $D$  during training. The total loss consists of two terms: adversarial attack loss  $\\mathcal{L}_{adv}$  and GAN loss  $\\mathcal{L}_{GAN}$ .  $\\mathcal{L}_{adv}$  can be obtained by summarizing the loss in Equation 1 for a set of input image and  $\\mathcal{L}_{GAN}$  can be written as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {G A N} = \\mathbb {E} _ {x} \\log D (x) + \\mathbb {E} _ {x} \\log \\left\\{1 - D [ x + c l i p (G (x)) ] \\right\\}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            869,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbb{E}_x = \\mathbb{E}_{x\\sim \\mathcal{P}_{data}}$  and  $\\mathcal{P}_{data}$  is original data distribution, and clip stands for clipping  $G(x)$  into a valid range. The adversarial example can be obtained by  $x + \\text{clip}(G(x))$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, the objective function for training our model can be written as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {G} \\max  _ {D} V (D, G) = \\mathcal {L} _ {a d v} + \\gamma \\mathcal {L} _ {G A N}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            563,
+            474,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\gamma$  is a weight to control the importance of two losses. By minimax game between the  $G$  and  $D$ , optimal parameters of the model can be obtained.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            498,
+            558,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we evaluate our proposed methods under both white-box and black-box attack settings. In the white-box setting, we first train the generator and discriminator using a target model, then during the attack, we put images into the trained generator to generate adversarial examples for that target model. In the black-box setting, we use a transferability-based attack, where one target model is selected to train the generator and obtain adversarial examples, then these adversarial examples are directly used to attack another unknown model. We perform evaluations on several image manipulation datasets and compare our method with existing adversarial attack methods, FGSM, PGD and advGAN. We run all experiments on an NVIDIA A100 80GB GPU.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate the proposed method on three image manipulation datasets, DEFACTO [26], CASIAv2 [7] and COVERAGE [36]. DEFACTO contains 149k images with copy-move, splicing, and inpainting manipulations. This dataset is constructed over MS-COCO [21] and",
+        "bbox": [
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+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "4319",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "contains natural images with various contents, such as natural scenes, objects, etc. As we need both manipulated and authentic images, similar to [5], we randomly sample 64k manipulated images from DEFACTO and 20k authentic images from MSCOCO to construct a dataset. CASIAv2 is a natural image forgery dataset that contains 4795 images, 1701 authentic and 3274 forged with copy-move and splicing manipulations. COVERAGE (COVER) contains 100 copy-move forged images and their originals with similar but genuine objects. The ground-truth masks are provided in all datasets. Since AdvGAN and our method need training data, we further split each dataset into half and half. We use the half dataset to train AdvGAN and our method and use the other half to evaluate all attack methods.",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Target models. For the image manipulation detectors, we selected three models, FCN [23], ManTra-Net [37] and MVSS-Net [5]. These models are all trained on part of the DEFACTO dataset, and their performance has been compared in previous works [5]. As all these detectors with pretrained models and optimized parameters are already available, we directly use them as our target models.",
+        "bbox": [
+            75,
+            303,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. We compute pixel-level F1 (pF1) for semantic segmentation of the manipulated region. Since we also have authentic images, we report image-level F1 (imF1) as well. Please note authentic images are only used to calculate im-F1, while manipulated images are used to calculate both metrics. As the purpose of this work is to explore the robustness of the manipulation detectors by the adversarial attack, we also use attack success rate (ASR) as one of the evaluation metrics. We define \"success\" as the opposite of the ground-truth which means 1) for manipulated images, every pixel is detected as authentic, and 2) for authentic images, part of the image is detected as manipulated. The proportion of the image that is successfully attacked over the total test dataset is denoted as the ASR.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. The architecture of the generator is shown in Figure 3. For the discriminator, we use a similar architecture to the discriminator in AdvGAN [38]. We set the weight of GAN loss  $\\gamma = 0.1$  and clipping range  $clip = 0.1$ . During the model training, we set the batch size to 128 and the learning rate to 0.001. The input image size of three target models is  $512 \\times 512 \\times 3$ . For the FGSM and PGD attack, we set maximum perturbation  $\\epsilon = 0.05$ .",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. White-box Attack",
+        "text_level": 1,
+        "bbox": [
+            76,
+            755,
+            251,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this setting, we generate adversarial examples against each target model. We evaluate our method using different manipulation detectors with different datasets. We first measure the performance of original images using three manipulation detectors and then apply four types of adversarial attacks to see the changes in performance. The results of pF1, imF1, and ASR are shown in Table 1. We observe that for three different image manipulation detectors, p-F1 and",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "im-F1 largely drop when applying adversarial attacks. A similar trend can be observed for all datasets. These results show that even though the selected detectors perform well on specific manipulation datasets, they can still be vulnerable to adversarial examples that only have small changes from the original ones.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "On the other hand, compared with the existing attacks, the ASR of our method is higher than FGSM and slightly higher than PGD and AdvGAN for most of the cases. We also decompose the adversarial examples generated by our method into frequency components, and an example is shown in Figure 2 (row 5). Compared with existing attack methods, our method can preserve most of the details, especially the high-frequency components such as the branches of the tree, and the edge of the building windows, as well as keep noises and artifacts as fewer as possible. The running time of generating adversarial images for each dataset is shown in Table 1. For generating one image, the average running time is: FGSM 0.09s, PGD 20s, AdvGAN 0.02s, ours 0.01s. Our method is significantly fast than iterative-based attack methods.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3. Black-box Attack",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We also conduct experiments to evaluate the transferability of our attack method. We use one target model to train the generator and obtain adversarial examples, then directly use these examples to attack other target models.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We use the DEFACTO dataset, where half of the data is used to train AdvGAN and our method, and the other half is used to generate adversarial examples. Then these generated examples are sent to the target models to obtain the ASR. The results are shown in Table 2. The model used to generate the adversarial example is denoted as the trained model (Train), and the model used to calculate ASR is denoted as the target model (Target). For better comparison, we also add the result of the white-box setting (the trained model and the target model are the same). We denote FCN, ManTra-Net, and MVSS-Net as model A, B, and C.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "From Table 2, we observe that for FGSM and PGD attacks, the ASR of the black-box attack drops more than  $10\\%$  compared to the white-box attack in several cases, while AdvGAN and our method seem to have better transferability. This is probably because FGSM and PGD are optimized-based attacks where each image should be optimized separately against the target model, while AdvGAN and our method try to learn and approximate the distribution of the datasets. Another interesting finding is that for different target models, the adversarial examples generated by models with more complex architecture (i.e. MVSS-Net = model C) seem to have better transferability than the examples generated by the baseline model (FCN = model A). We consider the reason as complex models usually use the baseline model as their backbone, therefore the examples",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "4320",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4b850e6729eb20eb70310c8d915125cf8d303f6094ab85927f5e93d4b5677996.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Data</td><td rowspan=\"2\">Method</td><td colspan=\"3\">FCN</td><td colspan=\"3\">ManTra-Net</td><td colspan=\"3\">MVSS-Net</td><td rowspan=\"2\">Run Time</td></tr><tr><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td></tr><tr><td rowspan=\"5\">DEFACTO</td><td>Origin</td><td>0.68</td><td>0.65</td><td>-</td><td>0.70</td><td>0.66</td><td>-</td><td>0.72</td><td>0.68</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.28</td><td>0.25</td><td>50.5%</td><td>0.27</td><td>0.29</td><td>48.2%</td><td>0.28</td><td>0.27</td><td>50.2%</td><td>2.5h</td></tr><tr><td>PGD</td><td>0.21</td><td>0.19</td><td>58.5%</td><td>0.19</td><td>0.18</td><td>58.9%</td><td>0.23</td><td>0.19</td><td>57.2%</td><td>470h</td></tr><tr><td>AdvGAN</td><td>0.17</td><td>0.16</td><td>60.2%</td><td>0.18</td><td>0.17</td><td>59.9%</td><td>0.20</td><td>0.18</td><td>60.8%</td><td>30min</td></tr><tr><td>Ours</td><td>0.17</td><td>0.15</td><td>60.5%</td><td>0.16</td><td>0.16</td><td>60.6%</td><td>0.21</td><td>0.18</td><td>60.5%</td><td>15min</td></tr><tr><td rowspan=\"5\">CASIAv2</td><td>Origin</td><td>0.59</td><td>0.50</td><td>-</td><td>0.60</td><td>0.58</td><td>-</td><td>0.69</td><td>0.62</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.29</td><td>0.26</td><td>48.2%</td><td>0.26</td><td>0.25</td><td>48.5%</td><td>0.30</td><td>0.30</td><td>44.2%</td><td>10min</td></tr><tr><td>PGD</td><td>0.21</td><td>0.18</td><td>56.5%</td><td>0.20</td><td>0.21</td><td>50.7%</td><td>0.23</td><td>0.20</td><td>51.4%</td><td>36h</td></tr><tr><td>AdvGAN</td><td>0.18</td><td>0.16</td><td>59.7%</td><td>0.19</td><td>0.19</td><td>55.8%</td><td>0.20</td><td>0.15</td><td>58.8%</td><td>2.1min</td></tr><tr><td>Ours</td><td>0.20</td><td>0.17</td><td>58.8%</td><td>0.18</td><td>0.16</td><td>58.2%</td><td>0.18</td><td>0.14</td><td>60.2%</td><td>1.1min</td></tr><tr><td rowspan=\"5\">COVER</td><td>Origin</td><td>0.48</td><td>0.39</td><td>-</td><td>0.44</td><td>0.41</td><td>-</td><td>0.63</td><td>0.55</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.20</td><td>0.18</td><td>50.0%</td><td>0.19</td><td>0.17</td><td>52.3%</td><td>0.22</td><td>0.24</td><td>50.1%</td><td>18min</td></tr><tr><td>PGD</td><td>0.14</td><td>0.14</td><td>61.1%</td><td>0.14</td><td>0.14</td><td>55.3%</td><td>0.16</td><td>0.15</td><td>60.3%</td><td>68min</td></tr><tr><td>AdvGAN</td><td>0.14</td><td>0.13</td><td>61.5%</td><td>0.14</td><td>0.12</td><td>57.1%</td><td>0.15</td><td>0.15</td><td>60.6%</td><td>4.1s</td></tr><tr><td>Ours</td><td>0.14</td><td>0.12</td><td>61.9%</td><td>0.13</td><td>0.11</td><td>59.1%</td><td>0.13</td><td>0.12</td><td>62.2%</td><td>2.5s</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1. The performance of different attacks under AMG task. The evaluation is performed on three datasets (DEFACTO, CASIAv2 and COVER) with three manipulation detectors (FCN, ManTra-Net and MVSS-Net) as the target models. For the attack method, higher ASR (lower  $pF1$  and  $imF1$ ) means better performance. Run time shows the generation time for all examples in that dataset.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/34adcf1b97ce68c640ca6234315594d9850b7a723e9bdc6ca35624bfee01e3a2.jpg",
+        "image_caption": [
+            "Figure 4. Comparison of generated adversarial examples under different attack methods."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            125,
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+            680
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "generated by the complex model might naturally have the ability to attack baseline models. These findings give us a new perspective to generate adversarial examples with better transferability.",
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+        "text": "5.4. Image Quality Assessment",
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+        "text": "In this section, we show that our method could keep high image quality while fooling the target model. We evaluate the generated examples qualitatively and quantitatively on MVSS-Net with the CASIAv2 and COVER datasets. For qualitative evaluation, the visualization examples of four at",
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+        "type": "text",
+        "text": "tack methods are shown in Figure 4. We can observe that compared with the existing attacks, the adversarial examples generated by our method have much less noise, look more natural and are more imperceptible to human eyes. For quantitative evaluation, we use metrics MSE, PSNR, and SSIM to calculate the difference between the original image and the adversarial example. As shown in Table 3, the image quality of the adversarial examples generated by our method outperforms others by a large margin. This result suggests that our method is able to keep high image quality while successfully attacking target models.",
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+        "table_caption": [],
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+        "table_body": "<table><tr><td>Train</td><td>Target</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td rowspan=\"3\">A</td><td>A</td><td>50.5%</td><td>58.5%</td><td>60.2%</td><td>60.5%</td></tr><tr><td>B</td><td>39.3%</td><td>43.3%</td><td>50.2%</td><td>55.1%</td></tr><tr><td>C</td><td>42.6%</td><td>40.2%</td><td>52.1%</td><td>58.3%</td></tr><tr><td rowspan=\"3\">B</td><td>B</td><td>48.2%</td><td>58.9%</td><td>59.9%</td><td>60.6%</td></tr><tr><td>A</td><td>43.6%</td><td>50.7%</td><td>55.1%</td><td>53.1%</td></tr><tr><td>C</td><td>37.3%</td><td>46.2%</td><td>50.6%</td><td>52.4%</td></tr><tr><td rowspan=\"3\">C</td><td>C</td><td>50.2%</td><td>57.2%</td><td>60.8%</td><td>60.5%</td></tr><tr><td>A</td><td>45.3%</td><td>52.3%</td><td>54.2%</td><td>58.4%</td></tr><tr><td>B</td><td>42.3%</td><td>52.1%</td><td>56.3%</td><td>62.2%</td></tr></table>",
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+        "table_caption": [
+            "Table 2. Attack success rate under the black-box attack settings. First column (train) is the model we use to generate adversarial example, and second column (target) is the target model to attack. A, B and C represent FCN, ManTra-Net and MVSS-Net model."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td>MSE (↓)</td><td>0.71</td><td>0.69</td><td>0.59</td><td>0.50</td></tr><tr><td>PSNR (↑)</td><td>26.4</td><td>30.4</td><td>28.9</td><td>40.1</td></tr><tr><td>SSIM (↑)</td><td>0.61</td><td>0.79</td><td>0.71</td><td>0.98</td></tr></table>",
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+        "text": "5.5. Analysis",
+        "text_level": 1,
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+        "text": "In this section, we first analyze the advantage of the proposed AMG task and then design four ablations to study the mechanism of the proposed attack.",
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+        "type": "text",
+        "text": "To analyze the advantage of the proposed AMG task, we compared the adversarial examples generated under AMG and traditional classification task (CAE), shown in Figure 5. PGD attack is used to generate examples for both CAE and AMG task. We randomly selected 1000 manipulated images and 1000 authentic images from DEFACTO, CASIAv2 and COVERAGE datasets for evaluation. Two target models, a classification model named ResNet-50 [12] and a segmentation model named FCN [20] are selected as the target models. The adversarial examples generated under CAE are used to attack both ResNet-50 (white-box attack) and FCN (transferability-based attack), and vice versa. We observe that although the examples generated under CAE have a high ASR for attacking the classification model, the ASR drops largely when they are used to attack the detection model. On the other hand, the examples generated under our AMG task is able to attack both models, which indicates better transferability among different tasks.",
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+        "type": "text",
+        "text": "To analyze the behavior of each component in the proposed method, We evaluated four ablations: 1) we use discrete wavelet transform (DWT) but remove the skip connection (SC) when generating the perturbations, 2) we only apply the SC of the low-frequency components, 3) we remove both DWT and SC, 4) our method. The results are shown",
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+    {
+        "type": "image",
+        "img_path": "images/19065c5c29ee0bbf1b8314b957a5da2e996a63eb764c286ecf1de4ec25c3c61b.jpg",
+        "image_caption": [
+            "Figure 5. Comparing the transferability of the adversarial example generated by AMG and classification (CAE) task. Prediction (Pred.) and mask are obtained from ResNet-50 and FCN, respectively. ASR-class and ASR-pixel stand for the attack success rate of classification accuracy and pixel-level detection accuracy."
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+        "table_caption": [
+            "Table 3. Image quality assessment of the adversarial examples generated by different attacks. Our method has significantly better image quality than other attacks."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>DWT</td><td>SC</td><td>ASR (↑)</td><td>PSNR (↑)</td><td>SSIM (↑)</td></tr><tr><td>✓</td><td>×</td><td>59.8%</td><td>33.5</td><td>0.84</td></tr><tr><td>✓</td><td>Low</td><td>60.0%</td><td>35.5</td><td>0.89</td></tr><tr><td>×</td><td>×</td><td>58.6%</td><td>30.8</td><td>0.74</td></tr><tr><td>✓</td><td>High</td><td>60.5%</td><td>40.0</td><td>0.97</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4. Ablation study of the proposed method on DEFACTO dataset with MVSS-Net detector. DWT is discrete wavelet transform, and SC is skip-connection (low or high means low-/high-frequency component).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "in Table 4. By comparing 1st and 3rd rows, we observe that using the frequency features improves PSNR and SSIM by a large margin. By comparing the types of SC (1st, 3rd and 4th rows), we also observe that preserving high-frequency components have the most effect for improving the image quality. These quantitative results show the effect of two main components of the proposed method.",
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+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
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+        "text": "In this work, we propose an AMG task to explore the vulnerability of image manipulation detectors. We extend the existing attacks and explore the changes in frequency components during adversarial attacks. Moreover, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate imperceptible examples. Experiments show that our method generates adversarial examples significantly fast and preserves better image quality while achieving a high attack success rate. This work shows the vulnerability of current image manipulation detectors and suggests more robust detectors are needed to correctly detect the manipulations. Adversarial defense that can protect the detectors from various attacks is an interesting topic in future work.",
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+    {
+        "type": "text",
+        "text": "References",
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+        ],
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+            "content": "Image manipulation techniques have drawn growing concerns as manipulated images might cause morality and security problems. Various methods have been proposed to detect manipulations and achieved promising performance. However, these methods might be vulnerable to adversarial attacks. In this work, we design an Adversarial Manipulation Generation (AMG) task to explore the vulnerability of image manipulation detectors. We first propose an optimal loss function and extend existing attacks to generate adversarial examples. We observe that existing spatial attacks cause large degradation in image quality and find the loss of high-frequency detailed components might be its major reason. Inspired by this observation, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. We further design an encoder-decoder architecture with skip connections of high-frequency components to preserve fine details. We evaluated our method on three image manipulation detectors (FCN, ManTra-Net and MVSS-Net) with three benchmark datasets (DEFACTO, CASIAv2 and COVER). Experiments show that our method generates adversarial examples significantly fast (0.01s per image), preserves better image quality (PSNR 30% higher than spatial attacks), and achieves a high attack success rate. We also observe that the examples generated by AMG can fool both classification and segmentation models, which indicates better transferability among different tasks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.739,
+                0.21,
+                0.755
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.764,
+                0.47,
+                0.87
+            ],
+            "angle": 0,
+            "content": "With the rapid development of advanced editing software, manipulated images are becoming more common on social media. Despite the positive aspects, there are possibilities that manipulated images are used to spread fake news and misleading information. Therefore, it is important to develop methods that can automatically detect manipulated images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Various image manipulation detectors [5, 20, 32, 4] have been proposed and achieved high performance on manip-"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.511,
+                0.273,
+                0.891,
+                0.496
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.51,
+                0.895,
+                0.622
+            ],
+            "angle": 0,
+            "content": "Figure 1. Adversarial examples generated under the proposed AMG task. For the manipulated image, the manipulations of the original image can be detected by a detector named MVSS-Net [5]. After applying attacks, the detector fails to correctly detect manipulations. For the authentic image, attacking the original image results in false-positive detection. Compared to previous attack methods, the examples generated by our method have much less noise and can successfully fool the detector at pixel-level."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "ulated image datasets [26, 7, 36, 16]. However, existing methods can be vulnerable to adversarial examples. For a manipulated image, adding imperceptible adversarial perturbations might cause the detector to detect a completely wrong result. Several works have already studied adversarial face forgery that fools the classification result of face forgery detector by the adversarial examples [15, 19, 14]. Since the detectors developed recently not only focus on classifying manipulated or authentic but also try to pinpoint the manipulated regions, we also go one step further to generate adversarial examples for the detectors that apply semantic segmentation. We name this task Adversarial Manipulation Generation (AMG). This topic has not been studied before and it is more difficult because instead of only fooling a class label, our target is to fool every pixel in both manipulated and authentic regions. We further show"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4315"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.468,
+                0.121
+            ],
+            "angle": 0,
+            "content": "the examples generated by AMG have better transferability among different tasks (details in Section 5.5)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.122,
+                0.468,
+                0.303
+            ],
+            "angle": 0,
+            "content": "As shown in Figure 1, images added with imperceptible perturbations generated by our task can successfully fool the detector. This task is also different from dense adversary generation [39, 3, 30] which is designed for segmentation and detection models under an untargeted attack setting. Our work considers applying targeted adversarial attacks on the manipulated and authentic images to explore the vulnerability of the image manipulation detectors. This is a specific scenario that the adversarial examples actually bring serious social problems. We first design a loss function that optimizes perturbation at pixel-level to generate such adversarial examples."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.304,
+                0.468,
+                0.501
+            ],
+            "angle": 0,
+            "content": "Algorithms such as FGSM [11] and PGD [25, 18] can be extended using our loss function to generate adversarial examples. However, these examples can be easily recognized by human eyes since the images are perturbated with visible noise. In addition, generating examples using iterative methods such as PGD can be time-consuming. To address these problems, we proposed a novel adversarial attack that generates perturbations using both frequency and spatial features to avoid image quality degradation. In addition, instead of optimizing each example against the target model, our method only needs to train the generator once, and then it can generate perturbation for any images extremely fast. The contributions of this work are three-fold:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.515,
+                0.468,
+                0.636
+            ],
+            "angle": 0,
+            "content": "- We explore the vulnerability of the image manipulation detectors by proposing an AMG task. We design a loss function and extend existing attacks to generate adversarial examples. Although these attacks can fool the detectors, the perturbations added to the image are visible to human eyes. We perform an analysis and find the loss of high-frequency components can be the major reason to cause the degradation of image quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.648,
+                0.468,
+                0.768
+            ],
+            "angle": 0,
+            "content": "- Inspired by the above observation, we propose an adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. To preserve fine details, an encoder-decoder with skip connections of high-frequency components is also combined. Compared with previous attacks, our method generates more imperceptible perturbations for human observers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.781,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "- We evaluate our method on three manipulation detectors with three benchmark datasets, under both white-box and black-box settings. Experiments show that our method generates adversarial examples significantly fast, preserves better image quality, and achieves a high attack success rate. We further observe the examples generated by AMG have better transferability and can fool both classification and detection models."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.515,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.09,
+                0.642,
+                0.107
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.116,
+                0.892,
+                0.177
+            ],
+            "angle": 0,
+            "content": "In this section, we briefly introduce the development of image manipulation generation and detection. Besides, we summarize recent adversarial attack methods that could be applied to image manipulation detectors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.188,
+                0.785,
+                0.205
+            ],
+            "angle": 0,
+            "content": "2.1. Image Manipulation Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.212,
+                0.892,
+                0.469
+            ],
+            "angle": 0,
+            "content": "Image manipulation generation (also known as image forensic) has gained growing attention as it is getting easier to create fake images and might cause problems, such as spreading fake news and misleading information [34, 33]. Common image manipulation generation includes copy-move (copy a region and paste it in the same image), splicing (copy a region and paste it to another image) and inpainting (remove a region) [26, 22]. Several datasets [26, 7, 36] have been created and released, i.e. DEFACTO [26] is a recently released large-scale dataset, containing 149k images sampled from MS-COCO [21]. Recently, generative adversarial networks (GANs) [10, 45] have also become popular to generate forged images, especially in the field of face forgery generation [15, 19, 14]. Instead of only focusing on face manipulation, this work explores how adversarial attack affects manipulation generation that includes various types of images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.48,
+                0.771,
+                0.496
+            ],
+            "angle": 0,
+            "content": "2.2. Image Manipulation Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.504,
+                0.892,
+                0.775
+            ],
+            "angle": 0,
+            "content": "Image manipulation detection can be considered as a classification task or a semantic segmentation task. In classification task, the goal is to distinguish the manipulated image from the real one. Methods such as [6, 1, 31] are proposed to learn the decision boundary between real and fake faces for face forgery detection. On the other hand, in semantic segmentation, the goal is to pinpoint manipulated regions at the pixel level. [20, 43] propose to implement a fully convolutional network (FCN) [23] to localize manipulations. ManTra-Net [37] designs a self-supervised learning task to learn robust image manipulation traces. MVSS-Net [5] exploits noise distribution and boundary artifacts surrounding manipulated regions to learn more generalizable features. Since this work mainly focuses on the semantic segmentation task, we selected one baseline method (FCN) and two state-of-the-art methods (ManTra-Net and MVSS-Net) for localizing manipulations and we demonstrate that our method can fool all of these detectors."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.685,
+                0.802
+            ],
+            "angle": 0,
+            "content": "2.3. Adversarial Attack"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Adversarial examples are inputs added with small perturbations to confuse a neural network. FGSM [11] is a well-known one-step attack method that uses gradients of the loss with respect to the input image. PGD [25, 18] is an iterative attack that performs FGSM with a smaller step size and clips the updated adversarial sample into a valid"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4316"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.473,
+                0.258
+            ],
+            "angle": 0,
+            "content": "range. Other methods such as CW [29], JSMA [28], MIFGSM [8], are also widely used. However, such attacks using iterative optimization can be time-consuming, and each image should be optimized separately. Instead of optimizing each image, GAN-based methods [38, 17, 13] train a generator to learn the adversarial distribution by optimizing target loss and GAN loss. Once the generator is trained, it can generate perturbations for any input and is much faster than iterative-based methods. However, although the generated image can bypass the target model, it degrades the image quality and is visible to human eyes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.258,
+                0.473,
+                0.424
+            ],
+            "angle": 0,
+            "content": "For adversarial examples in image manipulation detection, several works [9, 14, 19, 27, 44] were proposed to escape face forgery detection using adversarial attack. These methods mainly generate examples in the spatial domain. Recently, a few works [15, 24, 42] have been proposed to combine the frequency features to generate more imperceptible examples. However, these works are usually designed for the classification task, and the generation is optimization-based which can be time-consuming. We proposed a method that can generate high-quality adversarial images and is faster than most of the previous methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.435,
+                0.421,
+                0.452
+            ],
+            "angle": 0,
+            "content": "3. Adversarial Manipulation Generation"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.46,
+                0.262,
+                0.475
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Definition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.483,
+                0.473,
+                0.814
+            ],
+            "angle": 0,
+            "content": "Given an original image \\( x \\) and an image manipulation detector \\( f \\) which segments the manipulated and authentic region at pixel-level, we aim for generating adversarial examples that can completely fool the detector by adding imperceptible perturbations. We name this task Adversarial Manipulation Generation (AMG). The original image \\( x \\) can be either manipulated or authentic. In this work, we mainly focus on the targeted attack which contains two cases: 1) for the manipulated images, we add perturbations so that the detector fails to segment any pixels in the manipulated region, and 2) for the authentic images, we generate examples that the detector detects false-positive regions. Therefore, we design two types of target map: authentic map \\( S_0 \\) with all pixels labeled as authentic and manipulated map \\( S_1 \\) with the manipulation regions generated by watershed segmentation [2]. We select one random region from the watershed segmentation results and let it be the target manipulation region for each image. In order to determine which target map to use, we first input \\( x \\) into \\( f \\) to obtain a predicted map \\( \\{f(x)\\} \\), then we apply Global Max Pooling (GMP) to obtain the image-level prediction result \\( GMP\\{f(x)\\} \\) (authentic: 0, manipulated: 1)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.815,
+                0.471,
+                0.845
+            ],
+            "angle": 0,
+            "content": "Our loss function to generate the adversarial examples is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.092,
+                0.848,
+                0.47,
+                0.882
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {a d v} = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {D L} [ f (x ^ {\\prime}), S _ {0} ] & G M P \\{f (x) \\} = 1 \\\\ \\mathcal {L} _ {D L} [ f (x ^ {\\prime}), S _ {1} ] & G M P \\{f (x) \\} = 0 \\end{array} \\right. \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(x^{\\prime}\\) is the adversarial example generated by adding"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.168
+            ],
+            "angle": 0,
+            "content": "pixel-wise perturbation to the original image \\( x \\). Since this is a semantic segmentation task, we use dice loss \\( \\mathcal{L}_{DL} \\) to calculate the difference between the predicted map and the target map. \\( x' \\) can be calculated by minimizing \\( \\mathcal{L}_{adv} \\), where \\( x' \\) should be as close as possible to \\( x \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.175,
+                0.748,
+                0.192
+            ],
+            "angle": 0,
+            "content": "3.2. Extending Existing Attacks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.198,
+                0.892,
+                0.258
+            ],
+            "angle": 0,
+            "content": "Existing adversarial attacks can be extended to AMG using Equation 1. We selected three widely used attacks, FGSM, PGD, and AdvGAN, and extend them to generate the adversarial examples for AMG."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.259,
+                0.892,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Fast Gradient Sign Method (FGSM) [11] is a one-step attack method that uses gradients of the loss with respect to the input image to calculate perturbations. The adversarial example generation can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.58,
+                0.328,
+                0.892,
+                0.345
+            ],
+            "angle": 0,
+            "content": "\\[\nx ^ {\\prime} = x - \\varepsilon \\cdot \\operatorname {s i g n} \\left[ \\nabla_ {x} \\mathcal {L} _ {a d v} (x, S) \\right] \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.353,
+                0.892,
+                0.412
+            ],
+            "angle": 0,
+            "content": "Projected Gradient Descent (PGD) [25] is an iterative attack that performs FGSM with a smaller step size and projects the updated adversarial sample into a valid range, written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.54,
+                0.421,
+                0.892,
+                0.44
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t + 1} ^ {\\prime} = \\operatorname {P r o j} \\left\\{x _ {t} ^ {\\prime} - \\omega \\cdot \\operatorname {s i g n} \\left[ \\nabla_ {x} \\mathcal {L} _ {a d v} (x, S) \\right] \\right\\} \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.447,
+                0.892,
+                0.583
+            ],
+            "angle": 0,
+            "content": "AdvGAN [38] is a GAN-based attack that trains a generator to learn the adversarial distribution by maximizing the target loss and the GAN loss. A soft hinge loss is also incorporated to bound the magnitude of the perturbation. Therefore, the full objective can be expressed as \\(\\mathcal{L}_{adv} + \\alpha \\mathcal{L}_{GAN} + \\beta \\mathcal{L}_{hinge}\\). By solving the minimax game over the objective, the generator and discriminator can be optimized, and the adversarial example can be obtained by putting the original image into the generator."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.688
+            ],
+            "angle": 0,
+            "content": "Although these methods generate examples that can fool the manipulation detectors, the generated images can be easily recognized by human eyes since the images are perturbed with visible noise. Our work focuses on generating examples that can fool both target detectors and human eyes. Such attacks are more dangerous and might cause serious security problems."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.697,
+                0.803,
+                0.714
+            ],
+            "angle": 0,
+            "content": "3.3. Exploring Frequency Components"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.892,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Previous works [40, 41, 35] have shown neural networks prefer to generate low-frequency signals that are more superficial in complexity. Therefore, part of the high-frequency signal might be lost during the feature extraction, and this results in generating images with noise and aliasing artifacts. In order to explore whether a similar phenomenon has occurred in generating the adversarial examples and thus design an optimized architecture, we first analyze the changes in frequency components when applying existing adversarial attacks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The frequency components of the original image and the adversarial examples using existing attacks are visualized"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4317"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.152,
+                0.092,
+                0.832,
+                0.364
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.375,
+                0.895,
+                0.434
+            ],
+            "angle": 0,
+            "content": "Figure 2. Visualization of the frequency components. Rows from top to bottom: original image, adversarial examples using FGSM, PGD and AdvGAN attack. Columns from left to right: image in the spatial domain, low-frequency component (LL), high-frequency horizontal component (LH), high-frequency vertical component (HL), high-frequency diagonal component (HH). For each component of the attack images, closer to that component of the original image indicates better preservation of the information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.456,
+                0.473,
+                0.653
+            ],
+            "angle": 0,
+            "content": "in Figure 2 (row 1-4). We use wavelet transform to obtain the frequency components. The low-frequency component (LL) contains the general structure and most of the color data, while the high-frequency component (LH, HL, HH) contains rich details like the edges of the contents and image texture. By comparing the components between the original image and adversarial examples, we find that many details of the high-frequency components such as the branches of the tree, and the edge of the building windows, are lost, meanwhile, artifacts appear in the background. We believe the loss of details and the increasing artifacts in the high-frequency components are major reasons that make adversarial perturbations visible to human eyes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.669,
+                0.36,
+                0.687
+            ],
+            "angle": 0,
+            "content": "4. Frequency-aware GAN Attack"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.695,
+                0.291,
+                0.71
+            ],
+            "angle": 0,
+            "content": "4.1. Architecture Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Inspired by the above observation, we propose an attack method to generate high-quality adversarial examples for AMG. As shown in Figure 3, the architecture of our method has three components: a generator \\( G \\), a discriminator \\( D \\), and a target model \\( f \\). We focus on designing a \\( G \\) that can generate imperceptible perturbation. \\( G \\) consists of an encoder and a decoder to generate pixel-level perturbations. The encoder extracts high-level feature representation from the input image, and the decoder uses the representation to generate perturbations. In this work, instead of directly perturbing the image in the spatial domain, we transform the input image into the frequency domain, combine the fre"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.892,
+                0.516
+            ],
+            "angle": 0,
+            "content": "quency feature and the spatial feature and add noise on the mixed domain to avoid degradation of image quality. The perturbations are then added to the input image to obtain an adversarial image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.517,
+                0.893,
+                0.684
+            ],
+            "angle": 0,
+            "content": "The discriminator \\( D \\) is a classifier that distinguishes the original input image from the adversarial image. A minimax GAN loss \\( \\mathcal{L}_{GAN} \\) can be obtained, where \\( D \\) tries to distinguish the adversarial image and the input image, and \\( G \\) tries to generate perturbations that are indistinguishable by the \\( D \\). To obtain the adversarial example, we first apply the white-box attack, where the target model \\( f \\) is known and used to train the model. The input of \\( f \\) is the adversarial image, and the output is the predicted segmentation. An adversarial attack loss \\( \\mathcal{L}_{adv} \\) can be calculated between the predicted and target result."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.695,
+                0.757,
+                0.712
+            ],
+            "angle": 0,
+            "content": "4.2. Frequency-aware Generator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.719,
+                0.892,
+                0.795
+            ],
+            "angle": 0,
+            "content": "We propose a generator that combines both spatial and frequency features as well as incorporates skip connections of the high-frequency components to generate imperceptible adversarial examples. The architecture of the generator is shown in Figure 3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Encoder. The encoder consists of convolutional layers (conv), pooling layers, and discrete wavelet transform layers (dwt). The first conv layer extracts spatial features from the input image and passes the feature to the dwt layer. We used 2D discrete wavelet transform to decompose the features into the low-frequency component \\((L_{i})\\) and the high-frequency component \\((H_{i})\\). These components are concate"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4318"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.1,
+                0.089,
+                0.878,
+                0.341
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.315,
+                0.355,
+                0.655,
+                0.371
+            ],
+            "angle": 0,
+            "content": "Figure 3. Overview of our frequency-aware GAN attack."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.394,
+                0.471,
+                0.501
+            ],
+            "angle": 0,
+            "content": "nated channel-wise, denoted as \\( \\text{concat}(L_i, H_i) \\). On the other hand, the spatial feature extracted by conv layer is downsampled and then combined with the frequency feature \\( \\text{concat}(L_i, H_i) \\). Finally, the features containing both spatial and frequency information are sent to the next conv layer. We construct 4-level layers to extract the high-level feature representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.501,
+                0.47,
+                0.728
+            ],
+            "angle": 0,
+            "content": "Decoder. The decoder consists of conv layers, upsampling layers, and inverse discrete wavelet transform layers (idwt). To avoid losing fine details, we conduct skip connections of the high-frequency components from the encoder to the decoder. This helps the decoder generate perturbations with more details and less noise, and thus makes the generated image less distinguishable by human eyes. The processing of the decoder is as follows. The feature generated by the encoder is upsampled to obtain feature \\( A \\). On the other hand, 2D inverse discrete wavelet transform is performed on the high-frequency feature directly from the encoder, then we obtain feature \\( B \\). These two features are combined as \\( A + B \\) and sent to the conv layer. We also construct 4-level layers to decode the feature and generate the perturbation for the input image."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.735,
+                0.217,
+                0.75
+            ],
+            "angle": 0,
+            "content": "4.3. Optimization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.757,
+                0.471,
+                0.864
+            ],
+            "angle": 0,
+            "content": "As in the white-box attack setting, the target model \\( f \\) is known and fixed, we need to optimize the generator \\( G \\) and the discriminator \\( D \\) during training. The total loss consists of two terms: adversarial attack loss \\( \\mathcal{L}_{adv} \\) and GAN loss \\( \\mathcal{L}_{GAN} \\). \\( \\mathcal{L}_{adv} \\) can be obtained by summarizing the loss in Equation 1 for a set of input image and \\( \\mathcal{L}_{GAN} \\) can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.077,
+                0.87,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {G A N} = \\mathbb {E} _ {x} \\log D (x) + \\mathbb {E} _ {x} \\log \\left\\{1 - D [ x + c l i p (G (x)) ] \\right\\}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.394,
+                0.892,
+                0.44
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbb{E}_x = \\mathbb{E}_{x\\sim \\mathcal{P}_{data}}\\) and \\(\\mathcal{P}_{data}\\) is original data distribution, and clip stands for clipping \\(G(x)\\) into a valid range. The adversarial example can be obtained by \\(x + \\text{clip}(G(x))\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.44,
+                0.892,
+                0.469
+            ],
+            "angle": 0,
+            "content": "Finally, the objective function for training our model can be written as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.565,
+                0.476,
+                0.892,
+                0.498
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {G} \\max  _ {D} V (D, G) = \\mathcal {L} _ {a d v} + \\gamma \\mathcal {L} _ {G A N}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.502,
+                0.892,
+                0.547
+            ],
+            "angle": 0,
+            "content": "where \\(\\gamma\\) is a weight to control the importance of two losses. By minimax game between the \\(G\\) and \\(D\\), optimal parameters of the model can be obtained."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.559,
+                0.634,
+                0.575
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "In this section, we evaluate our proposed methods under both white-box and black-box attack settings. In the white-box setting, we first train the generator and discriminator using a target model, then during the attack, we put images into the trained generator to generate adversarial examples for that target model. In the black-box setting, we use a transferability-based attack, where one target model is selected to train the generator and obtain adversarial examples, then these adversarial examples are directly used to attack another unknown model. We perform evaluations on several image manipulation datasets and compare our method with existing adversarial attack methods, FGSM, PGD and advGAN. We run all experiments on an NVIDIA A100 80GB GPU."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.802,
+                0.708,
+                0.818
+            ],
+            "angle": 0,
+            "content": "5.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets. We evaluate the proposed method on three image manipulation datasets, DEFACTO [26], CASIAv2 [7] and COVERAGE [36]. DEFACTO contains 149k images with copy-move, splicing, and inpainting manipulations. This dataset is constructed over MS-COCO [21] and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4319"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.302
+            ],
+            "angle": 0,
+            "content": "contains natural images with various contents, such as natural scenes, objects, etc. As we need both manipulated and authentic images, similar to [5], we randomly sample 64k manipulated images from DEFACTO and 20k authentic images from MSCOCO to construct a dataset. CASIAv2 is a natural image forgery dataset that contains 4795 images, 1701 authentic and 3274 forged with copy-move and splicing manipulations. COVERAGE (COVER) contains 100 copy-move forged images and their originals with similar but genuine objects. The ground-truth masks are provided in all datasets. Since AdvGAN and our method need training data, we further split each dataset into half and half. We use the half dataset to train AdvGAN and our method and use the other half to evaluate all attack methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.304,
+                0.473,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Target models. For the image manipulation detectors, we selected three models, FCN [23], ManTra-Net [37] and MVSS-Net [5]. These models are all trained on part of the DEFACTO dataset, and their performance has been compared in previous works [5]. As all these detectors with pretrained models and optimized parameters are already available, we directly use them as our target models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.411,
+                0.473,
+                0.622
+            ],
+            "angle": 0,
+            "content": "Evaluation metrics. We compute pixel-level F1 (pF1) for semantic segmentation of the manipulated region. Since we also have authentic images, we report image-level F1 (imF1) as well. Please note authentic images are only used to calculate im-F1, while manipulated images are used to calculate both metrics. As the purpose of this work is to explore the robustness of the manipulation detectors by the adversarial attack, we also use attack success rate (ASR) as one of the evaluation metrics. We define \"success\" as the opposite of the ground-truth which means 1) for manipulated images, every pixel is detected as authentic, and 2) for authentic images, part of the image is detected as manipulated. The proportion of the image that is successfully attacked over the total test dataset is denoted as the ASR."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.623,
+                0.473,
+                0.745
+            ],
+            "angle": 0,
+            "content": "Implementation details. The architecture of the generator is shown in Figure 3. For the discriminator, we use a similar architecture to the discriminator in AdvGAN [38]. We set the weight of GAN loss \\(\\gamma = 0.1\\) and clipping range \\(clip = 0.1\\). During the model training, we set the batch size to 128 and the learning rate to 0.001. The input image size of three target models is \\(512 \\times 512 \\times 3\\). For the FGSM and PGD attack, we set maximum perturbation \\(\\epsilon = 0.05\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.756,
+                0.253,
+                0.772
+            ],
+            "angle": 0,
+            "content": "5.2. White-box Attack"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.781,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this setting, we generate adversarial examples against each target model. We evaluate our method using different manipulation detectors with different datasets. We first measure the performance of original images using three manipulation detectors and then apply four types of adversarial attacks to see the changes in performance. The results of pF1, imF1, and ASR are shown in Table 1. We observe that for three different image manipulation detectors, p-F1 and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "im-F1 largely drop when applying adversarial attacks. A similar trend can be observed for all datasets. These results show that even though the selected detectors perform well on specific manipulation datasets, they can still be vulnerable to adversarial examples that only have small changes from the original ones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.184,
+                0.893,
+                0.41
+            ],
+            "angle": 0,
+            "content": "On the other hand, compared with the existing attacks, the ASR of our method is higher than FGSM and slightly higher than PGD and AdvGAN for most of the cases. We also decompose the adversarial examples generated by our method into frequency components, and an example is shown in Figure 2 (row 5). Compared with existing attack methods, our method can preserve most of the details, especially the high-frequency components such as the branches of the tree, and the edge of the building windows, as well as keep noises and artifacts as fewer as possible. The running time of generating adversarial images for each dataset is shown in Table 1. For generating one image, the average running time is: FGSM 0.09s, PGD 20s, AdvGAN 0.02s, ours 0.01s. Our method is significantly fast than iterative-based attack methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.422,
+                0.673,
+                0.437
+            ],
+            "angle": 0,
+            "content": "5.3. Black-box Attack"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.447,
+                0.892,
+                0.507
+            ],
+            "angle": 0,
+            "content": "We also conduct experiments to evaluate the transferability of our attack method. We use one target model to train the generator and obtain adversarial examples, then directly use these examples to attack other target models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.508,
+                0.893,
+                0.674
+            ],
+            "angle": 0,
+            "content": "We use the DEFACTO dataset, where half of the data is used to train AdvGAN and our method, and the other half is used to generate adversarial examples. Then these generated examples are sent to the target models to obtain the ASR. The results are shown in Table 2. The model used to generate the adversarial example is denoted as the trained model (Train), and the model used to calculate ASR is denoted as the target model (Target). For better comparison, we also add the result of the white-box setting (the trained model and the target model are the same). We denote FCN, ManTra-Net, and MVSS-Net as model A, B, and C."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "From Table 2, we observe that for FGSM and PGD attacks, the ASR of the black-box attack drops more than \\(10\\%\\) compared to the white-box attack in several cases, while AdvGAN and our method seem to have better transferability. This is probably because FGSM and PGD are optimized-based attacks where each image should be optimized separately against the target model, while AdvGAN and our method try to learn and approximate the distribution of the datasets. Another interesting finding is that for different target models, the adversarial examples generated by models with more complex architecture (i.e. MVSS-Net = model C) seem to have better transferability than the examples generated by the baseline model (FCN = model A). We consider the reason as complex models usually use the baseline model as their backbone, therefore the examples"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4320"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.11,
+                0.088,
+                0.862,
+                0.354
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Data</td><td rowspan=\"2\">Method</td><td colspan=\"3\">FCN</td><td colspan=\"3\">ManTra-Net</td><td colspan=\"3\">MVSS-Net</td><td rowspan=\"2\">Run Time</td></tr><tr><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td></tr><tr><td rowspan=\"5\">DEFACTO</td><td>Origin</td><td>0.68</td><td>0.65</td><td>-</td><td>0.70</td><td>0.66</td><td>-</td><td>0.72</td><td>0.68</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.28</td><td>0.25</td><td>50.5%</td><td>0.27</td><td>0.29</td><td>48.2%</td><td>0.28</td><td>0.27</td><td>50.2%</td><td>2.5h</td></tr><tr><td>PGD</td><td>0.21</td><td>0.19</td><td>58.5%</td><td>0.19</td><td>0.18</td><td>58.9%</td><td>0.23</td><td>0.19</td><td>57.2%</td><td>470h</td></tr><tr><td>AdvGAN</td><td>0.17</td><td>0.16</td><td>60.2%</td><td>0.18</td><td>0.17</td><td>59.9%</td><td>0.20</td><td>0.18</td><td>60.8%</td><td>30min</td></tr><tr><td>Ours</td><td>0.17</td><td>0.15</td><td>60.5%</td><td>0.16</td><td>0.16</td><td>60.6%</td><td>0.21</td><td>0.18</td><td>60.5%</td><td>15min</td></tr><tr><td rowspan=\"5\">CASIAv2</td><td>Origin</td><td>0.59</td><td>0.50</td><td>-</td><td>0.60</td><td>0.58</td><td>-</td><td>0.69</td><td>0.62</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.29</td><td>0.26</td><td>48.2%</td><td>0.26</td><td>0.25</td><td>48.5%</td><td>0.30</td><td>0.30</td><td>44.2%</td><td>10min</td></tr><tr><td>PGD</td><td>0.21</td><td>0.18</td><td>56.5%</td><td>0.20</td><td>0.21</td><td>50.7%</td><td>0.23</td><td>0.20</td><td>51.4%</td><td>36h</td></tr><tr><td>AdvGAN</td><td>0.18</td><td>0.16</td><td>59.7%</td><td>0.19</td><td>0.19</td><td>55.8%</td><td>0.20</td><td>0.15</td><td>58.8%</td><td>2.1min</td></tr><tr><td>Ours</td><td>0.20</td><td>0.17</td><td>58.8%</td><td>0.18</td><td>0.16</td><td>58.2%</td><td>0.18</td><td>0.14</td><td>60.2%</td><td>1.1min</td></tr><tr><td rowspan=\"5\">COVER</td><td>Origin</td><td>0.48</td><td>0.39</td><td>-</td><td>0.44</td><td>0.41</td><td>-</td><td>0.63</td><td>0.55</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.20</td><td>0.18</td><td>50.0%</td><td>0.19</td><td>0.17</td><td>52.3%</td><td>0.22</td><td>0.24</td><td>50.1%</td><td>18min</td></tr><tr><td>PGD</td><td>0.14</td><td>0.14</td><td>61.1%</td><td>0.14</td><td>0.14</td><td>55.3%</td><td>0.16</td><td>0.15</td><td>60.3%</td><td>68min</td></tr><tr><td>AdvGAN</td><td>0.14</td><td>0.13</td><td>61.5%</td><td>0.14</td><td>0.12</td><td>57.1%</td><td>0.15</td><td>0.15</td><td>60.6%</td><td>4.1s</td></tr><tr><td>Ours</td><td>0.14</td><td>0.12</td><td>61.9%</td><td>0.13</td><td>0.11</td><td>59.1%</td><td>0.13</td><td>0.12</td><td>62.2%</td><td>2.5s</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.363,
+                0.895,
+                0.406
+            ],
+            "angle": 0,
+            "content": "Table 1. The performance of different attacks under AMG task. The evaluation is performed on three datasets (DEFACTO, CASIAv2 and COVER) with three manipulation detectors (FCN, ManTra-Net and MVSS-Net) as the target models. For the attack method, higher ASR (lower \\( pF1 \\) and \\( imF1 \\)) means better performance. Run time shows the generation time for all examples in that dataset."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.127,
+                0.422,
+                0.847,
+                0.681
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.222,
+                0.695,
+                0.746,
+                0.71
+            ],
+            "angle": 0,
+            "content": "Figure 4. Comparison of generated adversarial examples under different attack methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.734,
+                0.471,
+                0.794
+            ],
+            "angle": 0,
+            "content": "generated by the complex model might naturally have the ability to attack baseline models. These findings give us a new perspective to generate adversarial examples with better transferability."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.802,
+                0.317,
+                0.818
+            ],
+            "angle": 0,
+            "content": "5.4. Image Quality Assessment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.826,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, we show that our method could keep high image quality while fooling the target model. We evaluate the generated examples qualitatively and quantitatively on MVSS-Net with the CASIAv2 and COVER datasets. For qualitative evaluation, the visualization examples of four at"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.734,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "tack methods are shown in Figure 4. We can observe that compared with the existing attacks, the adversarial examples generated by our method have much less noise, look more natural and are more imperceptible to human eyes. For quantitative evaluation, we use metrics MSE, PSNR, and SSIM to calculate the difference between the original image and the adversarial example. As shown in Table 3, the image quality of the adversarial examples generated by our method outperforms others by a large margin. This result suggests that our method is able to keep high image quality while successfully attacking target models."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "4321"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.09,
+                0.473,
+                0.248
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Train</td><td>Target</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td rowspan=\"3\">A</td><td>A</td><td>50.5%</td><td>58.5%</td><td>60.2%</td><td>60.5%</td></tr><tr><td>B</td><td>39.3%</td><td>43.3%</td><td>50.2%</td><td>55.1%</td></tr><tr><td>C</td><td>42.6%</td><td>40.2%</td><td>52.1%</td><td>58.3%</td></tr><tr><td rowspan=\"3\">B</td><td>B</td><td>48.2%</td><td>58.9%</td><td>59.9%</td><td>60.6%</td></tr><tr><td>A</td><td>43.6%</td><td>50.7%</td><td>55.1%</td><td>53.1%</td></tr><tr><td>C</td><td>37.3%</td><td>46.2%</td><td>50.6%</td><td>52.4%</td></tr><tr><td rowspan=\"3\">C</td><td>C</td><td>50.2%</td><td>57.2%</td><td>60.8%</td><td>60.5%</td></tr><tr><td>A</td><td>45.3%</td><td>52.3%</td><td>54.2%</td><td>58.4%</td></tr><tr><td>B</td><td>42.3%</td><td>52.1%</td><td>56.3%</td><td>62.2%</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.256,
+                0.47,
+                0.312
+            ],
+            "angle": 0,
+            "content": "Table 2. Attack success rate under the black-box attack settings. First column (train) is the model we use to generate adversarial example, and second column (target) is the target model to attack. A, B and C represent FCN, ManTra-Net and MVSS-Net model."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.107,
+                0.324,
+                0.442,
+                0.391
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Metric</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td>MSE (↓)</td><td>0.71</td><td>0.69</td><td>0.59</td><td>0.50</td></tr><tr><td>PSNR (↑)</td><td>26.4</td><td>30.4</td><td>28.9</td><td>40.1</td></tr><tr><td>SSIM (↑)</td><td>0.61</td><td>0.79</td><td>0.71</td><td>0.98</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.4,
+                0.471,
+                0.442
+            ],
+            "angle": 0,
+            "content": "Table 3. Image quality assessment of the adversarial examples generated by different attacks. Our method has significantly better image quality than other attacks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.468,
+                0.18,
+                0.484
+            ],
+            "angle": 0,
+            "content": "5.5. Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.47,
+                0.537
+            ],
+            "angle": 0,
+            "content": "In this section, we first analyze the advantage of the proposed AMG task and then design four ablations to study the mechanism of the proposed attack."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.538,
+                0.471,
+                0.81
+            ],
+            "angle": 0,
+            "content": "To analyze the advantage of the proposed AMG task, we compared the adversarial examples generated under AMG and traditional classification task (CAE), shown in Figure 5. PGD attack is used to generate examples for both CAE and AMG task. We randomly selected 1000 manipulated images and 1000 authentic images from DEFACTO, CASIAv2 and COVERAGE datasets for evaluation. Two target models, a classification model named ResNet-50 [12] and a segmentation model named FCN [20] are selected as the target models. The adversarial examples generated under CAE are used to attack both ResNet-50 (white-box attack) and FCN (transferability-based attack), and vice versa. We observe that although the examples generated under CAE have a high ASR for attacking the classification model, the ASR drops largely when they are used to attack the detection model. On the other hand, the examples generated under our AMG task is able to attack both models, which indicates better transferability among different tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To analyze the behavior of each component in the proposed method, We evaluated four ablations: 1) we use discrete wavelet transform (DWT) but remove the skip connection (SC) when generating the perturbations, 2) we only apply the SC of the low-frequency components, 3) we remove both DWT and SC, 4) our method. The results are shown"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.535,
+                0.095,
+                0.87,
+                0.243
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.262,
+                0.895,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Figure 5. Comparing the transferability of the adversarial example generated by AMG and classification (CAE) task. Prediction (Pred.) and mask are obtained from ResNet-50 and FCN, respectively. ASR-class and ASR-pixel stand for the attack success rate of classification accuracy and pixel-level detection accuracy."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.522,
+                0.351,
+                0.872,
+                0.432
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>DWT</td><td>SC</td><td>ASR (↑)</td><td>PSNR (↑)</td><td>SSIM (↑)</td></tr><tr><td>✓</td><td>×</td><td>59.8%</td><td>33.5</td><td>0.84</td></tr><tr><td>✓</td><td>Low</td><td>60.0%</td><td>35.5</td><td>0.89</td></tr><tr><td>×</td><td>×</td><td>58.6%</td><td>30.8</td><td>0.74</td></tr><tr><td>✓</td><td>High</td><td>60.5%</td><td>40.0</td><td>0.97</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.441,
+                0.893,
+                0.498
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation study of the proposed method on DEFACTO dataset with MVSS-Net detector. DWT is discrete wavelet transform, and SC is skip-connection (low or high means low-/high-frequency component)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.53,
+                0.894,
+                0.637
+            ],
+            "angle": 0,
+            "content": "in Table 4. By comparing 1st and 3rd rows, we observe that using the frequency features improves PSNR and SSIM by a large margin. By comparing the types of SC (1st, 3rd and 4th rows), we also observe that preserving high-frequency components have the most effect for improving the image quality. These quantitative results show the effect of two main components of the proposed method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.661,
+                0.62,
+                0.677
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, we propose an AMG task to explore the vulnerability of image manipulation detectors. We extend the existing attacks and explore the changes in frequency components during adversarial attacks. Moreover, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate imperceptible examples. Experiments show that our method generates adversarial examples significantly fast and preserves better image quality while achieving a high attack success rate. This work shows the vulnerability of current image manipulation detectors and suggests more robust detectors are needed to correctly detect the manipulations. Adversarial defense that can protect the detectors from various attacks is an interesting topic in future work."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
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+                0.516,
+                0.957
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+            "angle": 0,
+            "content": "4322"
+        }
+    ],
+    [
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+            "type": "title",
+            "bbox": [
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+                0.09,
+                0.174,
+                0.106
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+            "angle": 0,
+            "content": "References"
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+# Frequency-aware GAN for Adversarial Manipulation Generation
+
+Peifei Zhu, Genki Osada, Hirokatsu Kataoka, Tsubasa Takahashi LINE Corporation
+
+{peifei.zhu, genki.osada, jpz4219, tsubasa.takahashi}@linecorp.com
+
+# Abstract
+
+Image manipulation techniques have drawn growing concerns as manipulated images might cause morality and security problems. Various methods have been proposed to detect manipulations and achieved promising performance. However, these methods might be vulnerable to adversarial attacks. In this work, we design an Adversarial Manipulation Generation (AMG) task to explore the vulnerability of image manipulation detectors. We first propose an optimal loss function and extend existing attacks to generate adversarial examples. We observe that existing spatial attacks cause large degradation in image quality and find the loss of high-frequency detailed components might be its major reason. Inspired by this observation, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. We further design an encoder-decoder architecture with skip connections of high-frequency components to preserve fine details. We evaluated our method on three image manipulation detectors (FCN, ManTra-Net and MVSS-Net) with three benchmark datasets (DEFACTO, CASIAv2 and COVER). Experiments show that our method generates adversarial examples significantly fast (0.01s per image), preserves better image quality (PSNR 30% higher than spatial attacks), and achieves a high attack success rate. We also observe that the examples generated by AMG can fool both classification and segmentation models, which indicates better transferability among different tasks.
+
+# 1. Introduction
+
+With the rapid development of advanced editing software, manipulated images are becoming more common on social media. Despite the positive aspects, there are possibilities that manipulated images are used to spread fake news and misleading information. Therefore, it is important to develop methods that can automatically detect manipulated images.
+
+Various image manipulation detectors [5, 20, 32, 4] have been proposed and achieved high performance on manip-
+
+![](images/4dcb0d18ea3cec845812f43f5223069967a715c6b6b6b686fceb1a3869874ded.jpg)  
+Figure 1. Adversarial examples generated under the proposed AMG task. For the manipulated image, the manipulations of the original image can be detected by a detector named MVSS-Net [5]. After applying attacks, the detector fails to correctly detect manipulations. For the authentic image, attacking the original image results in false-positive detection. Compared to previous attack methods, the examples generated by our method have much less noise and can successfully fool the detector at pixel-level.
+
+ulated image datasets [26, 7, 36, 16]. However, existing methods can be vulnerable to adversarial examples. For a manipulated image, adding imperceptible adversarial perturbations might cause the detector to detect a completely wrong result. Several works have already studied adversarial face forgery that fools the classification result of face forgery detector by the adversarial examples [15, 19, 14]. Since the detectors developed recently not only focus on classifying manipulated or authentic but also try to pinpoint the manipulated regions, we also go one step further to generate adversarial examples for the detectors that apply semantic segmentation. We name this task Adversarial Manipulation Generation (AMG). This topic has not been studied before and it is more difficult because instead of only fooling a class label, our target is to fool every pixel in both manipulated and authentic regions. We further show
+
+the examples generated by AMG have better transferability among different tasks (details in Section 5.5).
+
+As shown in Figure 1, images added with imperceptible perturbations generated by our task can successfully fool the detector. This task is also different from dense adversary generation [39, 3, 30] which is designed for segmentation and detection models under an untargeted attack setting. Our work considers applying targeted adversarial attacks on the manipulated and authentic images to explore the vulnerability of the image manipulation detectors. This is a specific scenario that the adversarial examples actually bring serious social problems. We first design a loss function that optimizes perturbation at pixel-level to generate such adversarial examples.
+
+Algorithms such as FGSM [11] and PGD [25, 18] can be extended using our loss function to generate adversarial examples. However, these examples can be easily recognized by human eyes since the images are perturbated with visible noise. In addition, generating examples using iterative methods such as PGD can be time-consuming. To address these problems, we proposed a novel adversarial attack that generates perturbations using both frequency and spatial features to avoid image quality degradation. In addition, instead of optimizing each example against the target model, our method only needs to train the generator once, and then it can generate perturbation for any images extremely fast. The contributions of this work are three-fold:
+
+- We explore the vulnerability of the image manipulation detectors by proposing an AMG task. We design a loss function and extend existing attacks to generate adversarial examples. Although these attacks can fool the detectors, the perturbations added to the image are visible to human eyes. We perform an analysis and find the loss of high-frequency components can be the major reason to cause the degradation of image quality.  
+- Inspired by the above observation, we propose an adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. To preserve fine details, an encoder-decoder with skip connections of high-frequency components is also combined. Compared with previous attacks, our method generates more imperceptible perturbations for human observers.  
+- We evaluate our method on three manipulation detectors with three benchmark datasets, under both white-box and black-box settings. Experiments show that our method generates adversarial examples significantly fast, preserves better image quality, and achieves a high attack success rate. We further observe the examples generated by AMG have better transferability and can fool both classification and detection models.
+
+# 2. Related Work
+
+In this section, we briefly introduce the development of image manipulation generation and detection. Besides, we summarize recent adversarial attack methods that could be applied to image manipulation detectors.
+
+# 2.1. Image Manipulation Generation
+
+Image manipulation generation (also known as image forensic) has gained growing attention as it is getting easier to create fake images and might cause problems, such as spreading fake news and misleading information [34, 33]. Common image manipulation generation includes copy-move (copy a region and paste it in the same image), splicing (copy a region and paste it to another image) and inpainting (remove a region) [26, 22]. Several datasets [26, 7, 36] have been created and released, i.e. DEFACTO [26] is a recently released large-scale dataset, containing 149k images sampled from MS-COCO [21]. Recently, generative adversarial networks (GANs) [10, 45] have also become popular to generate forged images, especially in the field of face forgery generation [15, 19, 14]. Instead of only focusing on face manipulation, this work explores how adversarial attack affects manipulation generation that includes various types of images.
+
+# 2.2. Image Manipulation Detection
+
+Image manipulation detection can be considered as a classification task or a semantic segmentation task. In classification task, the goal is to distinguish the manipulated image from the real one. Methods such as [6, 1, 31] are proposed to learn the decision boundary between real and fake faces for face forgery detection. On the other hand, in semantic segmentation, the goal is to pinpoint manipulated regions at the pixel level. [20, 43] propose to implement a fully convolutional network (FCN) [23] to localize manipulations. ManTra-Net [37] designs a self-supervised learning task to learn robust image manipulation traces. MVSS-Net [5] exploits noise distribution and boundary artifacts surrounding manipulated regions to learn more generalizable features. Since this work mainly focuses on the semantic segmentation task, we selected one baseline method (FCN) and two state-of-the-art methods (ManTra-Net and MVSS-Net) for localizing manipulations and we demonstrate that our method can fool all of these detectors.
+
+# 2.3. Adversarial Attack
+
+Adversarial examples are inputs added with small perturbations to confuse a neural network. FGSM [11] is a well-known one-step attack method that uses gradients of the loss with respect to the input image. PGD [25, 18] is an iterative attack that performs FGSM with a smaller step size and clips the updated adversarial sample into a valid
+
+range. Other methods such as CW [29], JSMA [28], MIFGSM [8], are also widely used. However, such attacks using iterative optimization can be time-consuming, and each image should be optimized separately. Instead of optimizing each image, GAN-based methods [38, 17, 13] train a generator to learn the adversarial distribution by optimizing target loss and GAN loss. Once the generator is trained, it can generate perturbations for any input and is much faster than iterative-based methods. However, although the generated image can bypass the target model, it degrades the image quality and is visible to human eyes.
+
+For adversarial examples in image manipulation detection, several works [9, 14, 19, 27, 44] were proposed to escape face forgery detection using adversarial attack. These methods mainly generate examples in the spatial domain. Recently, a few works [15, 24, 42] have been proposed to combine the frequency features to generate more imperceptible examples. However, these works are usually designed for the classification task, and the generation is optimization-based which can be time-consuming. We proposed a method that can generate high-quality adversarial images and is faster than most of the previous methods.
+
+# 3. Adversarial Manipulation Generation
+
+# 3.1. Problem Definition
+
+Given an original image  $x$  and an image manipulation detector  $f$  which segments the manipulated and authentic region at pixel-level, we aim for generating adversarial examples that can completely fool the detector by adding imperceptible perturbations. We name this task Adversarial Manipulation Generation (AMG). The original image  $x$  can be either manipulated or authentic. In this work, we mainly focus on the targeted attack which contains two cases: 1) for the manipulated images, we add perturbations so that the detector fails to segment any pixels in the manipulated region, and 2) for the authentic images, we generate examples that the detector detects false-positive regions. Therefore, we design two types of target map: authentic map  $S_0$  with all pixels labeled as authentic and manipulated map  $S_1$  with the manipulation regions generated by watershed segmentation [2]. We select one random region from the watershed segmentation results and let it be the target manipulation region for each image. In order to determine which target map to use, we first input  $x$  into  $f$  to obtain a predicted map  $\{f(x)\}$ , then we apply Global Max Pooling (GMP) to obtain the image-level prediction result  $GMP\{f(x)\}$  (authentic: 0, manipulated: 1).
+
+Our loss function to generate the adversarial examples is as follows:
+
+$$
+\mathcal {L} _ {a d v} = \left\{ \begin{array}{l l} \mathcal {L} _ {D L} [ f (x ^ {\prime}), S _ {0} ] & G M P \{f (x) \} = 1 \\ \mathcal {L} _ {D L} [ f (x ^ {\prime}), S _ {1} ] & G M P \{f (x) \} = 0 \end{array} \right. \tag {1}
+$$
+
+where  $x^{\prime}$  is the adversarial example generated by adding
+
+pixel-wise perturbation to the original image  $x$ . Since this is a semantic segmentation task, we use dice loss  $\mathcal{L}_{DL}$  to calculate the difference between the predicted map and the target map.  $x'$  can be calculated by minimizing  $\mathcal{L}_{adv}$ , where  $x'$  should be as close as possible to  $x$ .
+
+# 3.2. Extending Existing Attacks
+
+Existing adversarial attacks can be extended to AMG using Equation 1. We selected three widely used attacks, FGSM, PGD, and AdvGAN, and extend them to generate the adversarial examples for AMG.
+
+Fast Gradient Sign Method (FGSM) [11] is a one-step attack method that uses gradients of the loss with respect to the input image to calculate perturbations. The adversarial example generation can be written as:
+
+$$
+x ^ {\prime} = x - \varepsilon \cdot \operatorname {s i g n} \left[ \nabla_ {x} \mathcal {L} _ {a d v} (x, S) \right] \tag {2}
+$$
+
+Projected Gradient Descent (PGD) [25] is an iterative attack that performs FGSM with a smaller step size and projects the updated adversarial sample into a valid range, written as:
+
+$$
+x _ {t + 1} ^ {\prime} = \operatorname {P r o j} \left\{x _ {t} ^ {\prime} - \omega \cdot \operatorname {s i g n} \left[ \nabla_ {x} \mathcal {L} _ {a d v} (x, S) \right] \right\} \tag {3}
+$$
+
+AdvGAN [38] is a GAN-based attack that trains a generator to learn the adversarial distribution by maximizing the target loss and the GAN loss. A soft hinge loss is also incorporated to bound the magnitude of the perturbation. Therefore, the full objective can be expressed as  $\mathcal{L}_{adv} + \alpha \mathcal{L}_{GAN} + \beta \mathcal{L}_{hinge}$ . By solving the minimax game over the objective, the generator and discriminator can be optimized, and the adversarial example can be obtained by putting the original image into the generator.
+
+Although these methods generate examples that can fool the manipulation detectors, the generated images can be easily recognized by human eyes since the images are perturbed with visible noise. Our work focuses on generating examples that can fool both target detectors and human eyes. Such attacks are more dangerous and might cause serious security problems.
+
+# 3.3. Exploring Frequency Components
+
+Previous works [40, 41, 35] have shown neural networks prefer to generate low-frequency signals that are more superficial in complexity. Therefore, part of the high-frequency signal might be lost during the feature extraction, and this results in generating images with noise and aliasing artifacts. In order to explore whether a similar phenomenon has occurred in generating the adversarial examples and thus design an optimized architecture, we first analyze the changes in frequency components when applying existing adversarial attacks.
+
+The frequency components of the original image and the adversarial examples using existing attacks are visualized
+
+![](images/9a9c72e6af0afb37ccf9fee8ec51c68566860361aa524e16a48b3085de113680.jpg)  
+Figure 2. Visualization of the frequency components. Rows from top to bottom: original image, adversarial examples using FGSM, PGD and AdvGAN attack. Columns from left to right: image in the spatial domain, low-frequency component (LL), high-frequency horizontal component (LH), high-frequency vertical component (HL), high-frequency diagonal component (HH). For each component of the attack images, closer to that component of the original image indicates better preservation of the information.
+
+in Figure 2 (row 1-4). We use wavelet transform to obtain the frequency components. The low-frequency component (LL) contains the general structure and most of the color data, while the high-frequency component (LH, HL, HH) contains rich details like the edges of the contents and image texture. By comparing the components between the original image and adversarial examples, we find that many details of the high-frequency components such as the branches of the tree, and the edge of the building windows, are lost, meanwhile, artifacts appear in the background. We believe the loss of details and the increasing artifacts in the high-frequency components are major reasons that make adversarial perturbations visible to human eyes.
+
+# 4. Frequency-aware GAN Attack
+
+# 4.1. Architecture Overview
+
+Inspired by the above observation, we propose an attack method to generate high-quality adversarial examples for AMG. As shown in Figure 3, the architecture of our method has three components: a generator  $G$ , a discriminator  $D$ , and a target model  $f$ . We focus on designing a  $G$  that can generate imperceptible perturbation.  $G$  consists of an encoder and a decoder to generate pixel-level perturbations. The encoder extracts high-level feature representation from the input image, and the decoder uses the representation to generate perturbations. In this work, instead of directly perturbing the image in the spatial domain, we transform the input image into the frequency domain, combine the fre
+
+quency feature and the spatial feature and add noise on the mixed domain to avoid degradation of image quality. The perturbations are then added to the input image to obtain an adversarial image.
+
+The discriminator  $D$  is a classifier that distinguishes the original input image from the adversarial image. A minimax GAN loss  $\mathcal{L}_{GAN}$  can be obtained, where  $D$  tries to distinguish the adversarial image and the input image, and  $G$  tries to generate perturbations that are indistinguishable by the  $D$ . To obtain the adversarial example, we first apply the white-box attack, where the target model  $f$  is known and used to train the model. The input of  $f$  is the adversarial image, and the output is the predicted segmentation. An adversarial attack loss  $\mathcal{L}_{adv}$  can be calculated between the predicted and target result.
+
+# 4.2. Frequency-aware Generator
+
+We propose a generator that combines both spatial and frequency features as well as incorporates skip connections of the high-frequency components to generate imperceptible adversarial examples. The architecture of the generator is shown in Figure 3.
+
+Encoder. The encoder consists of convolutional layers (conv), pooling layers, and discrete wavelet transform layers (dwt). The first conv layer extracts spatial features from the input image and passes the feature to the dwt layer. We used 2D discrete wavelet transform to decompose the features into the low-frequency component  $(L_{i})$  and the high-frequency component  $(H_{i})$ . These components are concate
+
+![](images/1906061edb32c1318375dade32fbd81f57338e5e18ca88b5d3ad14ad63463764.jpg)  
+Figure 3. Overview of our frequency-aware GAN attack.
+
+nated channel-wise, denoted as  $\text{concat}(L_i, H_i)$ . On the other hand, the spatial feature extracted by conv layer is downsampled and then combined with the frequency feature  $\text{concat}(L_i, H_i)$ . Finally, the features containing both spatial and frequency information are sent to the next conv layer. We construct 4-level layers to extract the high-level feature representation.
+
+Decoder. The decoder consists of conv layers, upsampling layers, and inverse discrete wavelet transform layers (idwt). To avoid losing fine details, we conduct skip connections of the high-frequency components from the encoder to the decoder. This helps the decoder generate perturbations with more details and less noise, and thus makes the generated image less distinguishable by human eyes. The processing of the decoder is as follows. The feature generated by the encoder is upsampled to obtain feature  $A$ . On the other hand, 2D inverse discrete wavelet transform is performed on the high-frequency feature directly from the encoder, then we obtain feature  $B$ . These two features are combined as  $A + B$  and sent to the conv layer. We also construct 4-level layers to decode the feature and generate the perturbation for the input image.
+
+# 4.3. Optimization
+
+As in the white-box attack setting, the target model  $f$  is known and fixed, we need to optimize the generator  $G$  and the discriminator  $D$  during training. The total loss consists of two terms: adversarial attack loss  $\mathcal{L}_{adv}$  and GAN loss  $\mathcal{L}_{GAN}$ .  $\mathcal{L}_{adv}$  can be obtained by summarizing the loss in Equation 1 for a set of input image and  $\mathcal{L}_{GAN}$  can be written as:
+
+$$
+\mathcal {L} _ {G A N} = \mathbb {E} _ {x} \log D (x) + \mathbb {E} _ {x} \log \left\{1 - D [ x + c l i p (G (x)) ] \right\}, \tag {4}
+$$
+
+where  $\mathbb{E}_x = \mathbb{E}_{x\sim \mathcal{P}_{data}}$  and  $\mathcal{P}_{data}$  is original data distribution, and clip stands for clipping  $G(x)$  into a valid range. The adversarial example can be obtained by  $x + \text{clip}(G(x))$ .
+
+Finally, the objective function for training our model can be written as:
+
+$$
+\min  _ {G} \max  _ {D} V (D, G) = \mathcal {L} _ {a d v} + \gamma \mathcal {L} _ {G A N}, \tag {5}
+$$
+
+where  $\gamma$  is a weight to control the importance of two losses. By minimax game between the  $G$  and  $D$ , optimal parameters of the model can be obtained.
+
+# 5. Experiments
+
+In this section, we evaluate our proposed methods under both white-box and black-box attack settings. In the white-box setting, we first train the generator and discriminator using a target model, then during the attack, we put images into the trained generator to generate adversarial examples for that target model. In the black-box setting, we use a transferability-based attack, where one target model is selected to train the generator and obtain adversarial examples, then these adversarial examples are directly used to attack another unknown model. We perform evaluations on several image manipulation datasets and compare our method with existing adversarial attack methods, FGSM, PGD and advGAN. We run all experiments on an NVIDIA A100 80GB GPU.
+
+# 5.1. Experimental Settings
+
+Datasets. We evaluate the proposed method on three image manipulation datasets, DEFACTO [26], CASIAv2 [7] and COVERAGE [36]. DEFACTO contains 149k images with copy-move, splicing, and inpainting manipulations. This dataset is constructed over MS-COCO [21] and
+
+contains natural images with various contents, such as natural scenes, objects, etc. As we need both manipulated and authentic images, similar to [5], we randomly sample 64k manipulated images from DEFACTO and 20k authentic images from MSCOCO to construct a dataset. CASIAv2 is a natural image forgery dataset that contains 4795 images, 1701 authentic and 3274 forged with copy-move and splicing manipulations. COVERAGE (COVER) contains 100 copy-move forged images and their originals with similar but genuine objects. The ground-truth masks are provided in all datasets. Since AdvGAN and our method need training data, we further split each dataset into half and half. We use the half dataset to train AdvGAN and our method and use the other half to evaluate all attack methods.
+
+Target models. For the image manipulation detectors, we selected three models, FCN [23], ManTra-Net [37] and MVSS-Net [5]. These models are all trained on part of the DEFACTO dataset, and their performance has been compared in previous works [5]. As all these detectors with pretrained models and optimized parameters are already available, we directly use them as our target models.
+
+Evaluation metrics. We compute pixel-level F1 (pF1) for semantic segmentation of the manipulated region. Since we also have authentic images, we report image-level F1 (imF1) as well. Please note authentic images are only used to calculate im-F1, while manipulated images are used to calculate both metrics. As the purpose of this work is to explore the robustness of the manipulation detectors by the adversarial attack, we also use attack success rate (ASR) as one of the evaluation metrics. We define "success" as the opposite of the ground-truth which means 1) for manipulated images, every pixel is detected as authentic, and 2) for authentic images, part of the image is detected as manipulated. The proportion of the image that is successfully attacked over the total test dataset is denoted as the ASR.
+
+Implementation details. The architecture of the generator is shown in Figure 3. For the discriminator, we use a similar architecture to the discriminator in AdvGAN [38]. We set the weight of GAN loss  $\gamma = 0.1$  and clipping range  $clip = 0.1$ . During the model training, we set the batch size to 128 and the learning rate to 0.001. The input image size of three target models is  $512 \times 512 \times 3$ . For the FGSM and PGD attack, we set maximum perturbation  $\epsilon = 0.05$ .
+
+# 5.2. White-box Attack
+
+In this setting, we generate adversarial examples against each target model. We evaluate our method using different manipulation detectors with different datasets. We first measure the performance of original images using three manipulation detectors and then apply four types of adversarial attacks to see the changes in performance. The results of pF1, imF1, and ASR are shown in Table 1. We observe that for three different image manipulation detectors, p-F1 and
+
+im-F1 largely drop when applying adversarial attacks. A similar trend can be observed for all datasets. These results show that even though the selected detectors perform well on specific manipulation datasets, they can still be vulnerable to adversarial examples that only have small changes from the original ones.
+
+On the other hand, compared with the existing attacks, the ASR of our method is higher than FGSM and slightly higher than PGD and AdvGAN for most of the cases. We also decompose the adversarial examples generated by our method into frequency components, and an example is shown in Figure 2 (row 5). Compared with existing attack methods, our method can preserve most of the details, especially the high-frequency components such as the branches of the tree, and the edge of the building windows, as well as keep noises and artifacts as fewer as possible. The running time of generating adversarial images for each dataset is shown in Table 1. For generating one image, the average running time is: FGSM 0.09s, PGD 20s, AdvGAN 0.02s, ours 0.01s. Our method is significantly fast than iterative-based attack methods.
+
+# 5.3. Black-box Attack
+
+We also conduct experiments to evaluate the transferability of our attack method. We use one target model to train the generator and obtain adversarial examples, then directly use these examples to attack other target models.
+
+We use the DEFACTO dataset, where half of the data is used to train AdvGAN and our method, and the other half is used to generate adversarial examples. Then these generated examples are sent to the target models to obtain the ASR. The results are shown in Table 2. The model used to generate the adversarial example is denoted as the trained model (Train), and the model used to calculate ASR is denoted as the target model (Target). For better comparison, we also add the result of the white-box setting (the trained model and the target model are the same). We denote FCN, ManTra-Net, and MVSS-Net as model A, B, and C.
+
+From Table 2, we observe that for FGSM and PGD attacks, the ASR of the black-box attack drops more than  $10\%$  compared to the white-box attack in several cases, while AdvGAN and our method seem to have better transferability. This is probably because FGSM and PGD are optimized-based attacks where each image should be optimized separately against the target model, while AdvGAN and our method try to learn and approximate the distribution of the datasets. Another interesting finding is that for different target models, the adversarial examples generated by models with more complex architecture (i.e. MVSS-Net = model C) seem to have better transferability than the examples generated by the baseline model (FCN = model A). We consider the reason as complex models usually use the baseline model as their backbone, therefore the examples
+
+<table><tr><td rowspan="2">Data</td><td rowspan="2">Method</td><td colspan="3">FCN</td><td colspan="3">ManTra-Net</td><td colspan="3">MVSS-Net</td><td rowspan="2">Run Time</td></tr><tr><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td></tr><tr><td rowspan="5">DEFACTO</td><td>Origin</td><td>0.68</td><td>0.65</td><td>-</td><td>0.70</td><td>0.66</td><td>-</td><td>0.72</td><td>0.68</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.28</td><td>0.25</td><td>50.5%</td><td>0.27</td><td>0.29</td><td>48.2%</td><td>0.28</td><td>0.27</td><td>50.2%</td><td>2.5h</td></tr><tr><td>PGD</td><td>0.21</td><td>0.19</td><td>58.5%</td><td>0.19</td><td>0.18</td><td>58.9%</td><td>0.23</td><td>0.19</td><td>57.2%</td><td>470h</td></tr><tr><td>AdvGAN</td><td>0.17</td><td>0.16</td><td>60.2%</td><td>0.18</td><td>0.17</td><td>59.9%</td><td>0.20</td><td>0.18</td><td>60.8%</td><td>30min</td></tr><tr><td>Ours</td><td>0.17</td><td>0.15</td><td>60.5%</td><td>0.16</td><td>0.16</td><td>60.6%</td><td>0.21</td><td>0.18</td><td>60.5%</td><td>15min</td></tr><tr><td rowspan="5">CASIAv2</td><td>Origin</td><td>0.59</td><td>0.50</td><td>-</td><td>0.60</td><td>0.58</td><td>-</td><td>0.69</td><td>0.62</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.29</td><td>0.26</td><td>48.2%</td><td>0.26</td><td>0.25</td><td>48.5%</td><td>0.30</td><td>0.30</td><td>44.2%</td><td>10min</td></tr><tr><td>PGD</td><td>0.21</td><td>0.18</td><td>56.5%</td><td>0.20</td><td>0.21</td><td>50.7%</td><td>0.23</td><td>0.20</td><td>51.4%</td><td>36h</td></tr><tr><td>AdvGAN</td><td>0.18</td><td>0.16</td><td>59.7%</td><td>0.19</td><td>0.19</td><td>55.8%</td><td>0.20</td><td>0.15</td><td>58.8%</td><td>2.1min</td></tr><tr><td>Ours</td><td>0.20</td><td>0.17</td><td>58.8%</td><td>0.18</td><td>0.16</td><td>58.2%</td><td>0.18</td><td>0.14</td><td>60.2%</td><td>1.1min</td></tr><tr><td rowspan="5">COVER</td><td>Origin</td><td>0.48</td><td>0.39</td><td>-</td><td>0.44</td><td>0.41</td><td>-</td><td>0.63</td><td>0.55</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.20</td><td>0.18</td><td>50.0%</td><td>0.19</td><td>0.17</td><td>52.3%</td><td>0.22</td><td>0.24</td><td>50.1%</td><td>18min</td></tr><tr><td>PGD</td><td>0.14</td><td>0.14</td><td>61.1%</td><td>0.14</td><td>0.14</td><td>55.3%</td><td>0.16</td><td>0.15</td><td>60.3%</td><td>68min</td></tr><tr><td>AdvGAN</td><td>0.14</td><td>0.13</td><td>61.5%</td><td>0.14</td><td>0.12</td><td>57.1%</td><td>0.15</td><td>0.15</td><td>60.6%</td><td>4.1s</td></tr><tr><td>Ours</td><td>0.14</td><td>0.12</td><td>61.9%</td><td>0.13</td><td>0.11</td><td>59.1%</td><td>0.13</td><td>0.12</td><td>62.2%</td><td>2.5s</td></tr></table>
+
+Table 1. The performance of different attacks under AMG task. The evaluation is performed on three datasets (DEFACTO, CASIAv2 and COVER) with three manipulation detectors (FCN, ManTra-Net and MVSS-Net) as the target models. For the attack method, higher ASR (lower  $pF1$  and  $imF1$ ) means better performance. Run time shows the generation time for all examples in that dataset.
+
+![](images/34adcf1b97ce68c640ca6234315594d9850b7a723e9bdc6ca35624bfee01e3a2.jpg)  
+Figure 4. Comparison of generated adversarial examples under different attack methods.
+
+generated by the complex model might naturally have the ability to attack baseline models. These findings give us a new perspective to generate adversarial examples with better transferability.
+
+# 5.4. Image Quality Assessment
+
+In this section, we show that our method could keep high image quality while fooling the target model. We evaluate the generated examples qualitatively and quantitatively on MVSS-Net with the CASIAv2 and COVER datasets. For qualitative evaluation, the visualization examples of four at
+
+tack methods are shown in Figure 4. We can observe that compared with the existing attacks, the adversarial examples generated by our method have much less noise, look more natural and are more imperceptible to human eyes. For quantitative evaluation, we use metrics MSE, PSNR, and SSIM to calculate the difference between the original image and the adversarial example. As shown in Table 3, the image quality of the adversarial examples generated by our method outperforms others by a large margin. This result suggests that our method is able to keep high image quality while successfully attacking target models.
+
+<table><tr><td>Train</td><td>Target</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td rowspan="3">A</td><td>A</td><td>50.5%</td><td>58.5%</td><td>60.2%</td><td>60.5%</td></tr><tr><td>B</td><td>39.3%</td><td>43.3%</td><td>50.2%</td><td>55.1%</td></tr><tr><td>C</td><td>42.6%</td><td>40.2%</td><td>52.1%</td><td>58.3%</td></tr><tr><td rowspan="3">B</td><td>B</td><td>48.2%</td><td>58.9%</td><td>59.9%</td><td>60.6%</td></tr><tr><td>A</td><td>43.6%</td><td>50.7%</td><td>55.1%</td><td>53.1%</td></tr><tr><td>C</td><td>37.3%</td><td>46.2%</td><td>50.6%</td><td>52.4%</td></tr><tr><td rowspan="3">C</td><td>C</td><td>50.2%</td><td>57.2%</td><td>60.8%</td><td>60.5%</td></tr><tr><td>A</td><td>45.3%</td><td>52.3%</td><td>54.2%</td><td>58.4%</td></tr><tr><td>B</td><td>42.3%</td><td>52.1%</td><td>56.3%</td><td>62.2%</td></tr></table>
+
+Table 2. Attack success rate under the black-box attack settings. First column (train) is the model we use to generate adversarial example, and second column (target) is the target model to attack. A, B and C represent FCN, ManTra-Net and MVSS-Net model.  
+
+<table><tr><td>Metric</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td>MSE (↓)</td><td>0.71</td><td>0.69</td><td>0.59</td><td>0.50</td></tr><tr><td>PSNR (↑)</td><td>26.4</td><td>30.4</td><td>28.9</td><td>40.1</td></tr><tr><td>SSIM (↑)</td><td>0.61</td><td>0.79</td><td>0.71</td><td>0.98</td></tr></table>
+
+# 5.5. Analysis
+
+In this section, we first analyze the advantage of the proposed AMG task and then design four ablations to study the mechanism of the proposed attack.
+
+To analyze the advantage of the proposed AMG task, we compared the adversarial examples generated under AMG and traditional classification task (CAE), shown in Figure 5. PGD attack is used to generate examples for both CAE and AMG task. We randomly selected 1000 manipulated images and 1000 authentic images from DEFACTO, CASIAv2 and COVERAGE datasets for evaluation. Two target models, a classification model named ResNet-50 [12] and a segmentation model named FCN [20] are selected as the target models. The adversarial examples generated under CAE are used to attack both ResNet-50 (white-box attack) and FCN (transferability-based attack), and vice versa. We observe that although the examples generated under CAE have a high ASR for attacking the classification model, the ASR drops largely when they are used to attack the detection model. On the other hand, the examples generated under our AMG task is able to attack both models, which indicates better transferability among different tasks.
+
+To analyze the behavior of each component in the proposed method, We evaluated four ablations: 1) we use discrete wavelet transform (DWT) but remove the skip connection (SC) when generating the perturbations, 2) we only apply the SC of the low-frequency components, 3) we remove both DWT and SC, 4) our method. The results are shown
+
+![](images/19065c5c29ee0bbf1b8314b957a5da2e996a63eb764c286ecf1de4ec25c3c61b.jpg)  
+Figure 5. Comparing the transferability of the adversarial example generated by AMG and classification (CAE) task. Prediction (Pred.) and mask are obtained from ResNet-50 and FCN, respectively. ASR-class and ASR-pixel stand for the attack success rate of classification accuracy and pixel-level detection accuracy.
+
+Table 3. Image quality assessment of the adversarial examples generated by different attacks. Our method has significantly better image quality than other attacks.  
+
+<table><tr><td>DWT</td><td>SC</td><td>ASR (↑)</td><td>PSNR (↑)</td><td>SSIM (↑)</td></tr><tr><td>✓</td><td>×</td><td>59.8%</td><td>33.5</td><td>0.84</td></tr><tr><td>✓</td><td>Low</td><td>60.0%</td><td>35.5</td><td>0.89</td></tr><tr><td>×</td><td>×</td><td>58.6%</td><td>30.8</td><td>0.74</td></tr><tr><td>✓</td><td>High</td><td>60.5%</td><td>40.0</td><td>0.97</td></tr></table>
+
+Table 4. Ablation study of the proposed method on DEFACTO dataset with MVSS-Net detector. DWT is discrete wavelet transform, and SC is skip-connection (low or high means low-/high-frequency component).
+
+in Table 4. By comparing 1st and 3rd rows, we observe that using the frequency features improves PSNR and SSIM by a large margin. By comparing the types of SC (1st, 3rd and 4th rows), we also observe that preserving high-frequency components have the most effect for improving the image quality. These quantitative results show the effect of two main components of the proposed method.
+
+# 6. Conclusion
+
+In this work, we propose an AMG task to explore the vulnerability of image manipulation detectors. We extend the existing attacks and explore the changes in frequency components during adversarial attacks. Moreover, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate imperceptible examples. Experiments show that our method generates adversarial examples significantly fast and preserves better image quality while achieving a high attack success rate. This work shows the vulnerability of current image manipulation detectors and suggests more robust detectors are needed to correctly detect the manipulations. Adversarial defense that can protect the detectors from various attacks is an interesting topic in future work.
+
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+                                    "content": "Image manipulation techniques have drawn growing concerns as manipulated images might cause morality and security problems. Various methods have been proposed to detect manipulations and achieved promising performance. However, these methods might be vulnerable to adversarial attacks. In this work, we design an Adversarial Manipulation Generation (AMG) task to explore the vulnerability of image manipulation detectors. We first propose an optimal loss function and extend existing attacks to generate adversarial examples. We observe that existing spatial attacks cause large degradation in image quality and find the loss of high-frequency detailed components might be its major reason. Inspired by this observation, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. We further design an encoder-decoder architecture with skip connections of high-frequency components to preserve fine details. We evaluated our method on three image manipulation detectors (FCN, ManTra-Net and MVSS-Net) with three benchmark datasets (DEFACTO, CASIAv2 and COVER). Experiments show that our method generates adversarial examples significantly fast (0.01s per image), preserves better image quality (PSNR 30% higher than spatial attacks), and achieves a high attack success rate. We also observe that the examples generated by AMG can fool both classification and segmentation models, which indicates better transferability among different tasks."
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+                                    "content": "With the rapid development of advanced editing software, manipulated images are becoming more common on social media. Despite the positive aspects, there are possibilities that manipulated images are used to spread fake news and misleading information. Therefore, it is important to develop methods that can automatically detect manipulated images."
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+                                    "content": "Various image manipulation detectors [5, 20, 32, 4] have been proposed and achieved high performance on manip-"
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+                                            "content": "Figure 1. Adversarial examples generated under the proposed AMG task. For the manipulated image, the manipulations of the original image can be detected by a detector named MVSS-Net [5]. After applying attacks, the detector fails to correctly detect manipulations. For the authentic image, attacking the original image results in false-positive detection. Compared to previous attack methods, the examples generated by our method have much less noise and can successfully fool the detector at pixel-level."
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+                                    "content": "ulated image datasets [26, 7, 36, 16]. However, existing methods can be vulnerable to adversarial examples. For a manipulated image, adding imperceptible adversarial perturbations might cause the detector to detect a completely wrong result. Several works have already studied adversarial face forgery that fools the classification result of face forgery detector by the adversarial examples [15, 19, 14]. Since the detectors developed recently not only focus on classifying manipulated or authentic but also try to pinpoint the manipulated regions, we also go one step further to generate adversarial examples for the detectors that apply semantic segmentation. We name this task Adversarial Manipulation Generation (AMG). This topic has not been studied before and it is more difficult because instead of only fooling a class label, our target is to fool every pixel in both manipulated and authentic regions. We further show"
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+                                    "content": "the examples generated by AMG have better transferability among different tasks (details in Section 5.5)."
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+                                    "content": "As shown in Figure 1, images added with imperceptible perturbations generated by our task can successfully fool the detector. This task is also different from dense adversary generation [39, 3, 30] which is designed for segmentation and detection models under an untargeted attack setting. Our work considers applying targeted adversarial attacks on the manipulated and authentic images to explore the vulnerability of the image manipulation detectors. This is a specific scenario that the adversarial examples actually bring serious social problems. We first design a loss function that optimizes perturbation at pixel-level to generate such adversarial examples."
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+                                            "content": "- We explore the vulnerability of the image manipulation detectors by proposing an AMG task. We design a loss function and extend existing attacks to generate adversarial examples. Although these attacks can fool the detectors, the perturbations added to the image are visible to human eyes. We perform an analysis and find the loss of high-frequency components can be the major reason to cause the degradation of image quality."
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+                                            "content": "- Inspired by the above observation, we propose an adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate adversarial examples. To preserve fine details, an encoder-decoder with skip connections of high-frequency components is also combined. Compared with previous attacks, our method generates more imperceptible perturbations for human observers."
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+                                    "content": "Image manipulation generation (also known as image forensic) has gained growing attention as it is getting easier to create fake images and might cause problems, such as spreading fake news and misleading information [34, 33]. Common image manipulation generation includes copy-move (copy a region and paste it in the same image), splicing (copy a region and paste it to another image) and inpainting (remove a region) [26, 22]. Several datasets [26, 7, 36] have been created and released, i.e. DEFACTO [26] is a recently released large-scale dataset, containing 149k images sampled from MS-COCO [21]. Recently, generative adversarial networks (GANs) [10, 45] have also become popular to generate forged images, especially in the field of face forgery generation [15, 19, 14]. Instead of only focusing on face manipulation, this work explores how adversarial attack affects manipulation generation that includes various types of images."
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+                                    "content": "Image manipulation detection can be considered as a classification task or a semantic segmentation task. In classification task, the goal is to distinguish the manipulated image from the real one. Methods such as [6, 1, 31] are proposed to learn the decision boundary between real and fake faces for face forgery detection. On the other hand, in semantic segmentation, the goal is to pinpoint manipulated regions at the pixel level. [20, 43] propose to implement a fully convolutional network (FCN) [23] to localize manipulations. ManTra-Net [37] designs a self-supervised learning task to learn robust image manipulation traces. MVSS-Net [5] exploits noise distribution and boundary artifacts surrounding manipulated regions to learn more generalizable features. Since this work mainly focuses on the semantic segmentation task, we selected one baseline method (FCN) and two state-of-the-art methods (ManTra-Net and MVSS-Net) for localizing manipulations and we demonstrate that our method can fool all of these detectors."
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "range. Other methods such as CW [29], JSMA [28], MIFGSM [8], are also widely used. However, such attacks using iterative optimization can be time-consuming, and each image should be optimized separately. Instead of optimizing each image, GAN-based methods [38, 17, 13] train a generator to learn the adversarial distribution by optimizing target loss and GAN loss. Once the generator is trained, it can generate perturbations for any input and is much faster than iterative-based methods. However, although the generated image can bypass the target model, it degrades the image quality and is visible to human eyes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "type": "text",
+                                    "content": "For adversarial examples in image manipulation detection, several works [9, 14, 19, 27, 44] were proposed to escape face forgery detection using adversarial attack. These methods mainly generate examples in the spatial domain. Recently, a few works [15, 24, 42] have been proposed to combine the frequency features to generate more imperceptible examples. However, these works are usually designed for the classification task, and the generation is optimization-based which can be time-consuming. We proposed a method that can generate high-quality adversarial images and is faster than most of the previous methods."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. Adversarial Manipulation Generation"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "3.1. Problem Definition"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Given an original image "
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+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " and an image manipulation detector "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f"
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+                                {
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+                                    "type": "text",
+                                    "content": " which segments the manipulated and authentic region at pixel-level, we aim for generating adversarial examples that can completely fool the detector by adding imperceptible perturbations. We name this task Adversarial Manipulation Generation (AMG). The original image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " can be either manipulated or authentic. In this work, we mainly focus on the targeted attack which contains two cases: 1) for the manipulated images, we add perturbations so that the detector fails to segment any pixels in the manipulated region, and 2) for the authentic images, we generate examples that the detector detects false-positive regions. Therefore, we design two types of target map: authentic map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_0"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " with all pixels labeled as authentic and manipulated map "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with the manipulation regions generated by watershed segmentation [2]. We select one random region from the watershed segmentation results and let it be the target manipulation region for each image. In order to determine which target map to use, we first input "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " into "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
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+                                        382,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to obtain a predicted map "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        382,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{f(x)\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", then we apply Global Max Pooling (GMP) to obtain the image-level prediction result "
+                                },
+                                {
+                                    "bbox": [
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+                                        382,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "GMP\\{f(x)\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                        382,
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+                                    ],
+                                    "type": "text",
+                                    "content": " (authentic: 0, manipulated: 1)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Our loss function to generate the adversarial examples is as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {a d v} = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {D L} [ f (x ^ {\\prime}), S _ {0} ] & G M P \\{f (x) \\} = 1 \\\\ \\mathcal {L} _ {D L} [ f (x ^ {\\prime}), S _ {1} ] & G M P \\{f (x) \\} = 0 \\end{array} \\right. \\tag {1}",
+                                    "image_path": "e78cdb73bc572a03e16d486abe517eff41c176f8de7418016024bf06452d57e2.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "x^{\\prime}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the adversarial example generated by adding"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "pixel-wise perturbation to the original image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Since this is a semantic segmentation task, we use dice loss "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{DL}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to calculate the difference between the predicted map and the target map. "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be calculated by minimizing "
+                                },
+                                {
+                                    "bbox": [
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+                                        133
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{adv}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x'"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " should be as close as possible to "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "x"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.2. Extending Existing Attacks"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Existing adversarial attacks can be extended to AMG using Equation 1. We selected three widely used attacks, FGSM, PGD, and AdvGAN, and extend them to generate the adversarial examples for AMG."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
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+                                    "type": "text",
+                                    "content": "Fast Gradient Sign Method (FGSM) [11] is a one-step attack method that uses gradients of the loss with respect to the input image to calculate perturbations. The adversarial example generation can be written as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
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+                                    "type": "interline_equation",
+                                    "content": "x ^ {\\prime} = x - \\varepsilon \\cdot \\operatorname {s i g n} \\left[ \\nabla_ {x} \\mathcal {L} _ {a d v} (x, S) \\right] \\tag {2}",
+                                    "image_path": "a8704d036c13e805afe0b9bf84fa0cc79957192cc3e9a40de1c2d70756fcda84.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Projected Gradient Descent (PGD) [25] is an iterative attack that performs FGSM with a smaller step size and projects the updated adversarial sample into a valid range, written as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
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+                                    "type": "interline_equation",
+                                    "content": "x _ {t + 1} ^ {\\prime} = \\operatorname {P r o j} \\left\\{x _ {t} ^ {\\prime} - \\omega \\cdot \\operatorname {s i g n} \\left[ \\nabla_ {x} \\mathcal {L} _ {a d v} (x, S) \\right] \\right\\} \\tag {3}",
+                                    "image_path": "51f6ee53a2e99502096fcf4777817c5e194b0e4c3d14911fda97f6de541340d7.jpg"
+                                }
+                            ]
+                        }
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+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "AdvGAN [38] is a GAN-based attack that trains a generator to learn the adversarial distribution by maximizing the target loss and the GAN loss. A soft hinge loss is also incorporated to bound the magnitude of the perturbation. Therefore, the full objective can be expressed as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{adv} + \\alpha \\mathcal{L}_{GAN} + \\beta \\mathcal{L}_{hinge}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". By solving the minimax game over the objective, the generator and discriminator can be optimized, and the adversarial example can be obtained by putting the original image into the generator."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Although these methods generate examples that can fool the manipulation detectors, the generated images can be easily recognized by human eyes since the images are perturbed with visible noise. Our work focuses on generating examples that can fool both target detectors and human eyes. Such attacks are more dangerous and might cause serious security problems."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
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+                                    "type": "text",
+                                    "content": "3.3. Exploring Frequency Components"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Previous works [40, 41, 35] have shown neural networks prefer to generate low-frequency signals that are more superficial in complexity. Therefore, part of the high-frequency signal might be lost during the feature extraction, and this results in generating images with noise and aliasing artifacts. In order to explore whether a similar phenomenon has occurred in generating the adversarial examples and thus design an optimized architecture, we first analyze the changes in frequency components when applying existing adversarial attacks."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "The frequency components of the original image and the adversarial examples using existing attacks are visualized"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                }
+            ],
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+                                            "type": "text",
+                                            "content": "Figure 2. Visualization of the frequency components. Rows from top to bottom: original image, adversarial examples using FGSM, PGD and AdvGAN attack. Columns from left to right: image in the spatial domain, low-frequency component (LL), high-frequency horizontal component (LH), high-frequency vertical component (HL), high-frequency diagonal component (HH). For each component of the attack images, closer to that component of the original image indicates better preservation of the information."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
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+                    ],
+                    "index": 0
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "in Figure 2 (row 1-4). We use wavelet transform to obtain the frequency components. The low-frequency component (LL) contains the general structure and most of the color data, while the high-frequency component (LH, HL, HH) contains rich details like the edges of the contents and image texture. By comparing the components between the original image and adversarial examples, we find that many details of the high-frequency components such as the branches of the tree, and the edge of the building windows, are lost, meanwhile, artifacts appear in the background. We believe the loss of details and the increasing artifacts in the high-frequency components are major reasons that make adversarial perturbations visible to human eyes."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4. Frequency-aware GAN Attack"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
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+                                    "type": "text",
+                                    "content": "4.1. Architecture Overview"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Inspired by the above observation, we propose an attack method to generate high-quality adversarial examples for AMG. As shown in Figure 3, the architecture of our method has three components: a generator "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", a discriminator "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", and a target model "
+                                },
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". We focus on designing a "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " that can generate imperceptible perturbation. "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " consists of an encoder and a decoder to generate pixel-level perturbations. The encoder extracts high-level feature representation from the input image, and the decoder uses the representation to generate perturbations. In this work, instead of directly perturbing the image in the spatial domain, we transform the input image into the frequency domain, combine the fre"
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "quency feature and the spatial feature and add noise on the mixed domain to avoid degradation of image quality. The perturbations are then added to the input image to obtain an adversarial image."
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "content": "The discriminator "
+                                },
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is a classifier that distinguishes the original input image from the adversarial image. A minimax GAN loss "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        409,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{GAN}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be obtained, where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " tries to distinguish the adversarial image and the input image, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " tries to generate perturbations that are indistinguishable by the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". To obtain the adversarial example, we first apply the white-box attack, where the target model "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is known and used to train the model. The input of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the adversarial image, and the output is the predicted segmentation. An adversarial attack loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{adv}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be calculated between the predicted and target result."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "4.2. Frequency-aware Generator"
+                                }
+                            ]
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "We propose a generator that combines both spatial and frequency features as well as incorporates skip connections of the high-frequency components to generate imperceptible adversarial examples. The architecture of the generator is shown in Figure 3."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Encoder. The encoder consists of convolutional layers (conv), pooling layers, and discrete wavelet transform layers (dwt). The first conv layer extracts spatial features from the input image and passes the feature to the dwt layer. We used 2D discrete wavelet transform to decompose the features into the low-frequency component "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(L_{i})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the high-frequency component "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(H_{i})"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". These components are concate"
+                                }
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+            ],
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+                                            "type": "text",
+                                            "content": "Figure 3. Overview of our frequency-aware GAN attack."
+                                        }
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+                                }
+                            ],
+                            "index": 1,
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+                                    "type": "text",
+                                    "content": "nated channel-wise, denoted as "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\text{concat}(L_i, H_i)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". On the other hand, the spatial feature extracted by conv layer is downsampled and then combined with the frequency feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\text{concat}(L_i, H_i)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Finally, the features containing both spatial and frequency information are sent to the next conv layer. We construct 4-level layers to extract the high-level feature representation."
+                                }
+                            ]
+                        }
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+                            "spans": [
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+                                    "type": "text",
+                                    "content": "Decoder. The decoder consists of conv layers, upsampling layers, and inverse discrete wavelet transform layers (idwt). To avoid losing fine details, we conduct skip connections of the high-frequency components from the encoder to the decoder. This helps the decoder generate perturbations with more details and less noise, and thus makes the generated image less distinguishable by human eyes. The processing of the decoder is as follows. The feature generated by the encoder is upsampled to obtain feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        396,
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+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
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+                                        396,
+                                        287,
+                                        576
+                                    ],
+                                    "type": "text",
+                                    "content": ". On the other hand, 2D inverse discrete wavelet transform is performed on the high-frequency feature directly from the encoder, then we obtain feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        396,
+                                        287,
+                                        576
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        396,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". These two features are combined as "
+                                },
+                                {
+                                    "bbox": [
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+                                        396,
+                                        287,
+                                        576
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A + B"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and sent to the conv layer. We also construct 4-level layers to decode the feature and generate the perturbation for the input image."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.3. Optimization"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "As in the white-box attack setting, the target model "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "f"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is known and fixed, we need to optimize the generator "
+                                },
+                                {
+                                    "bbox": [
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+                                        599,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the discriminator "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " during training. The total loss consists of two terms: adversarial attack loss "
+                                },
+                                {
+                                    "bbox": [
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+                                        599,
+                                        288,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{adv}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        599,
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+                                        684
+                                    ],
+                                    "type": "text",
+                                    "content": " and GAN loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{GAN}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        599,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        599,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{adv}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be obtained by summarizing the loss in Equation 1 for a set of input image and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        599,
+                                        288,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{GAN}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be written as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {G A N} = \\mathbb {E} _ {x} \\log D (x) + \\mathbb {E} _ {x} \\log \\left\\{1 - D [ x + c l i p (G (x)) ] \\right\\}, \\tag {4}",
+                                    "image_path": "28cf1bb42e1c1d357f407690d9d442d0456dd05d3f624372fe714d72426dfd9a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                        348
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{E}_x = \\mathbb{E}_{x\\sim \\mathcal{P}_{data}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        312,
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        312,
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+                                        348
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{data}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        312,
+                                        545,
+                                        348
+                                    ],
+                                    "type": "text",
+                                    "content": " is original data distribution, and clip stands for clipping "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        312,
+                                        545,
+                                        348
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G(x)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        312,
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+                                        348
+                                    ],
+                                    "type": "text",
+                                    "content": " into a valid range. The adversarial example can be obtained by "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        312,
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+                                        348
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x + \\text{clip}(G(x))"
+                                },
+                                {
+                                    "bbox": [
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+                                        348
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "Finally, the objective function for training our model can be written as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\min  _ {G} \\max  _ {D} V (D, G) = \\mathcal {L} _ {a d v} + \\gamma \\mathcal {L} _ {G A N}, \\tag {5}",
+                                    "image_path": "1779f57608e756c07300aabf0d2db49ddcf527441a5f5a7d071843a033957cc3.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        433
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
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+                                        433
+                                    ],
+                                    "type": "text",
+                                    "content": " is a weight to control the importance of two losses. By minimax game between the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
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+                                        433
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "G"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        397,
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+                                        433
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "D"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", optimal parameters of the model can be obtained."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this section, we evaluate our proposed methods under both white-box and black-box attack settings. In the white-box setting, we first train the generator and discriminator using a target model, then during the attack, we put images into the trained generator to generate adversarial examples for that target model. In the black-box setting, we use a transferability-based attack, where one target model is selected to train the generator and obtain adversarial examples, then these adversarial examples are directly used to attack another unknown model. We perform evaluations on several image manipulation datasets and compare our method with existing adversarial attack methods, FGSM, PGD and advGAN. We run all experiments on an NVIDIA A100 80GB GPU."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
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+                                    "type": "text",
+                                    "content": "5.1. Experimental Settings"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Datasets. We evaluate the proposed method on three image manipulation datasets, DEFACTO [26], CASIAv2 [7] and COVERAGE [36]. DEFACTO contains 149k images with copy-move, splicing, and inpainting manipulations. This dataset is constructed over MS-COCO [21] and"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                }
+            ],
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+                                    "content": "4319"
+                                }
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+                }
+            ],
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+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "contains natural images with various contents, such as natural scenes, objects, etc. As we need both manipulated and authentic images, similar to [5], we randomly sample 64k manipulated images from DEFACTO and 20k authentic images from MSCOCO to construct a dataset. CASIAv2 is a natural image forgery dataset that contains 4795 images, 1701 authentic and 3274 forged with copy-move and splicing manipulations. COVERAGE (COVER) contains 100 copy-move forged images and their originals with similar but genuine objects. The ground-truth masks are provided in all datasets. Since AdvGAN and our method need training data, we further split each dataset into half and half. We use the half dataset to train AdvGAN and our method and use the other half to evaluate all attack methods."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Target models. For the image manipulation detectors, we selected three models, FCN [23], ManTra-Net [37] and MVSS-Net [5]. These models are all trained on part of the DEFACTO dataset, and their performance has been compared in previous works [5]. As all these detectors with pretrained models and optimized parameters are already available, we directly use them as our target models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Evaluation metrics. We compute pixel-level F1 (pF1) for semantic segmentation of the manipulated region. Since we also have authentic images, we report image-level F1 (imF1) as well. Please note authentic images are only used to calculate im-F1, while manipulated images are used to calculate both metrics. As the purpose of this work is to explore the robustness of the manipulation detectors by the adversarial attack, we also use attack success rate (ASR) as one of the evaluation metrics. We define \"success\" as the opposite of the ground-truth which means 1) for manipulated images, every pixel is detected as authentic, and 2) for authentic images, part of the image is detected as manipulated. The proportion of the image that is successfully attacked over the total test dataset is denoted as the ASR."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": "Implementation details. The architecture of the generator is shown in Figure 3. For the discriminator, we use a similar architecture to the discriminator in AdvGAN [38]. We set the weight of GAN loss "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "inline_equation",
+                                    "content": "\\gamma = 0.1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        493,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and clipping range "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        493,
+                                        289,
+                                        590
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "clip = 0.1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        493,
+                                        289,
+                                        590
+                                    ],
+                                    "type": "text",
+                                    "content": ". During the model training, we set the batch size to 128 and the learning rate to 0.001. The input image size of three target models is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "content": "512 \\times 512 \\times 3"
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+                                    "type": "text",
+                                    "content": ". For the FGSM and PGD attack, we set maximum perturbation "
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+                                    "type": "text",
+                                    "content": "."
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+                                    "content": "5.2. White-box Attack"
+                                }
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+                                    "content": "In this setting, we generate adversarial examples against each target model. We evaluate our method using different manipulation detectors with different datasets. We first measure the performance of original images using three manipulation detectors and then apply four types of adversarial attacks to see the changes in performance. The results of pF1, imF1, and ASR are shown in Table 1. We observe that for three different image manipulation detectors, p-F1 and"
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+                                    "type": "text",
+                                    "content": "im-F1 largely drop when applying adversarial attacks. A similar trend can be observed for all datasets. These results show that even though the selected detectors perform well on specific manipulation datasets, they can still be vulnerable to adversarial examples that only have small changes from the original ones."
+                                }
+                            ]
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+                    ],
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+                                    "content": "On the other hand, compared with the existing attacks, the ASR of our method is higher than FGSM and slightly higher than PGD and AdvGAN for most of the cases. We also decompose the adversarial examples generated by our method into frequency components, and an example is shown in Figure 2 (row 5). Compared with existing attack methods, our method can preserve most of the details, especially the high-frequency components such as the branches of the tree, and the edge of the building windows, as well as keep noises and artifacts as fewer as possible. The running time of generating adversarial images for each dataset is shown in Table 1. For generating one image, the average running time is: FGSM 0.09s, PGD 20s, AdvGAN 0.02s, ours 0.01s. Our method is significantly fast than iterative-based attack methods."
+                                }
+                            ]
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+                                    "content": "5.3. Black-box Attack"
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+                                    "content": "We also conduct experiments to evaluate the transferability of our attack method. We use one target model to train the generator and obtain adversarial examples, then directly use these examples to attack other target models."
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+                                    "content": "We use the DEFACTO dataset, where half of the data is used to train AdvGAN and our method, and the other half is used to generate adversarial examples. Then these generated examples are sent to the target models to obtain the ASR. The results are shown in Table 2. The model used to generate the adversarial example is denoted as the trained model (Train), and the model used to calculate ASR is denoted as the target model (Target). For better comparison, we also add the result of the white-box setting (the trained model and the target model are the same). We denote FCN, ManTra-Net, and MVSS-Net as model A, B, and C."
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+                                    "type": "text",
+                                    "content": "From Table 2, we observe that for FGSM and PGD attacks, the ASR of the black-box attack drops more than "
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+                                    "type": "text",
+                                    "content": " compared to the white-box attack in several cases, while AdvGAN and our method seem to have better transferability. This is probably because FGSM and PGD are optimized-based attacks where each image should be optimized separately against the target model, while AdvGAN and our method try to learn and approximate the distribution of the datasets. Another interesting finding is that for different target models, the adversarial examples generated by models with more complex architecture (i.e. MVSS-Net = model C) seem to have better transferability than the examples generated by the baseline model (FCN = model A). We consider the reason as complex models usually use the baseline model as their backbone, therefore the examples"
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+                                            "html": "<table><tr><td rowspan=\"2\">Data</td><td rowspan=\"2\">Method</td><td colspan=\"3\">FCN</td><td colspan=\"3\">ManTra-Net</td><td colspan=\"3\">MVSS-Net</td><td rowspan=\"2\">Run Time</td></tr><tr><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td><td>pF1</td><td>imF1</td><td>ASR</td></tr><tr><td rowspan=\"5\">DEFACTO</td><td>Origin</td><td>0.68</td><td>0.65</td><td>-</td><td>0.70</td><td>0.66</td><td>-</td><td>0.72</td><td>0.68</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.28</td><td>0.25</td><td>50.5%</td><td>0.27</td><td>0.29</td><td>48.2%</td><td>0.28</td><td>0.27</td><td>50.2%</td><td>2.5h</td></tr><tr><td>PGD</td><td>0.21</td><td>0.19</td><td>58.5%</td><td>0.19</td><td>0.18</td><td>58.9%</td><td>0.23</td><td>0.19</td><td>57.2%</td><td>470h</td></tr><tr><td>AdvGAN</td><td>0.17</td><td>0.16</td><td>60.2%</td><td>0.18</td><td>0.17</td><td>59.9%</td><td>0.20</td><td>0.18</td><td>60.8%</td><td>30min</td></tr><tr><td>Ours</td><td>0.17</td><td>0.15</td><td>60.5%</td><td>0.16</td><td>0.16</td><td>60.6%</td><td>0.21</td><td>0.18</td><td>60.5%</td><td>15min</td></tr><tr><td rowspan=\"5\">CASIAv2</td><td>Origin</td><td>0.59</td><td>0.50</td><td>-</td><td>0.60</td><td>0.58</td><td>-</td><td>0.69</td><td>0.62</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.29</td><td>0.26</td><td>48.2%</td><td>0.26</td><td>0.25</td><td>48.5%</td><td>0.30</td><td>0.30</td><td>44.2%</td><td>10min</td></tr><tr><td>PGD</td><td>0.21</td><td>0.18</td><td>56.5%</td><td>0.20</td><td>0.21</td><td>50.7%</td><td>0.23</td><td>0.20</td><td>51.4%</td><td>36h</td></tr><tr><td>AdvGAN</td><td>0.18</td><td>0.16</td><td>59.7%</td><td>0.19</td><td>0.19</td><td>55.8%</td><td>0.20</td><td>0.15</td><td>58.8%</td><td>2.1min</td></tr><tr><td>Ours</td><td>0.20</td><td>0.17</td><td>58.8%</td><td>0.18</td><td>0.16</td><td>58.2%</td><td>0.18</td><td>0.14</td><td>60.2%</td><td>1.1min</td></tr><tr><td rowspan=\"5\">COVER</td><td>Origin</td><td>0.48</td><td>0.39</td><td>-</td><td>0.44</td><td>0.41</td><td>-</td><td>0.63</td><td>0.55</td><td>-</td><td>-</td></tr><tr><td>FGSM</td><td>0.20</td><td>0.18</td><td>50.0%</td><td>0.19</td><td>0.17</td><td>52.3%</td><td>0.22</td><td>0.24</td><td>50.1%</td><td>18min</td></tr><tr><td>PGD</td><td>0.14</td><td>0.14</td><td>61.1%</td><td>0.14</td><td>0.14</td><td>55.3%</td><td>0.16</td><td>0.15</td><td>60.3%</td><td>68min</td></tr><tr><td>AdvGAN</td><td>0.14</td><td>0.13</td><td>61.5%</td><td>0.14</td><td>0.12</td><td>57.1%</td><td>0.15</td><td>0.15</td><td>60.6%</td><td>4.1s</td></tr><tr><td>Ours</td><td>0.14</td><td>0.12</td><td>61.9%</td><td>0.13</td><td>0.11</td><td>59.1%</td><td>0.13</td><td>0.12</td><td>62.2%</td><td>2.5s</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1. The performance of different attacks under AMG task. The evaluation is performed on three datasets (DEFACTO, CASIAv2 and COVER) with three manipulation detectors (FCN, ManTra-Net and MVSS-Net) as the target models. For the attack method, higher ASR (lower "
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+                                    "content": " and "
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+                                    "type": "text",
+                                    "content": ") means better performance. Run time shows the generation time for all examples in that dataset."
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+                                            "content": "Figure 4. Comparison of generated adversarial examples under different attack methods."
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+                                    "type": "text",
+                                    "content": "generated by the complex model might naturally have the ability to attack baseline models. These findings give us a new perspective to generate adversarial examples with better transferability."
+                                }
+                            ]
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+                                    "content": "5.4. Image Quality Assessment"
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+                                    "content": "In this section, we show that our method could keep high image quality while fooling the target model. We evaluate the generated examples qualitatively and quantitatively on MVSS-Net with the CASIAv2 and COVER datasets. For qualitative evaluation, the visualization examples of four at"
+                                }
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+                                    "type": "text",
+                                    "content": "tack methods are shown in Figure 4. We can observe that compared with the existing attacks, the adversarial examples generated by our method have much less noise, look more natural and are more imperceptible to human eyes. For quantitative evaluation, we use metrics MSE, PSNR, and SSIM to calculate the difference between the original image and the adversarial example. As shown in Table 3, the image quality of the adversarial examples generated by our method outperforms others by a large margin. This result suggests that our method is able to keep high image quality while successfully attacking target models."
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+                                            "html": "<table><tr><td>Train</td><td>Target</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td rowspan=\"3\">A</td><td>A</td><td>50.5%</td><td>58.5%</td><td>60.2%</td><td>60.5%</td></tr><tr><td>B</td><td>39.3%</td><td>43.3%</td><td>50.2%</td><td>55.1%</td></tr><tr><td>C</td><td>42.6%</td><td>40.2%</td><td>52.1%</td><td>58.3%</td></tr><tr><td rowspan=\"3\">B</td><td>B</td><td>48.2%</td><td>58.9%</td><td>59.9%</td><td>60.6%</td></tr><tr><td>A</td><td>43.6%</td><td>50.7%</td><td>55.1%</td><td>53.1%</td></tr><tr><td>C</td><td>37.3%</td><td>46.2%</td><td>50.6%</td><td>52.4%</td></tr><tr><td rowspan=\"3\">C</td><td>C</td><td>50.2%</td><td>57.2%</td><td>60.8%</td><td>60.5%</td></tr><tr><td>A</td><td>45.3%</td><td>52.3%</td><td>54.2%</td><td>58.4%</td></tr><tr><td>B</td><td>42.3%</td><td>52.1%</td><td>56.3%</td><td>62.2%</td></tr></table>",
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+                                            "content": "Table 2. Attack success rate under the black-box attack settings. First column (train) is the model we use to generate adversarial example, and second column (target) is the target model to attack. A, B and C represent FCN, ManTra-Net and MVSS-Net model."
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+                                            "html": "<table><tr><td>Metric</td><td>FGSM</td><td>PGD</td><td>AdvGAN</td><td>ours</td></tr><tr><td>MSE (↓)</td><td>0.71</td><td>0.69</td><td>0.59</td><td>0.50</td></tr><tr><td>PSNR (↑)</td><td>26.4</td><td>30.4</td><td>28.9</td><td>40.1</td></tr><tr><td>SSIM (↑)</td><td>0.61</td><td>0.79</td><td>0.71</td><td>0.98</td></tr></table>",
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+                                    "content": "5.5. Analysis"
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+                                    "content": "In this section, we first analyze the advantage of the proposed AMG task and then design four ablations to study the mechanism of the proposed attack."
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+                                    "content": "To analyze the advantage of the proposed AMG task, we compared the adversarial examples generated under AMG and traditional classification task (CAE), shown in Figure 5. PGD attack is used to generate examples for both CAE and AMG task. We randomly selected 1000 manipulated images and 1000 authentic images from DEFACTO, CASIAv2 and COVERAGE datasets for evaluation. Two target models, a classification model named ResNet-50 [12] and a segmentation model named FCN [20] are selected as the target models. The adversarial examples generated under CAE are used to attack both ResNet-50 (white-box attack) and FCN (transferability-based attack), and vice versa. We observe that although the examples generated under CAE have a high ASR for attacking the classification model, the ASR drops largely when they are used to attack the detection model. On the other hand, the examples generated under our AMG task is able to attack both models, which indicates better transferability among different tasks."
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+                                    "content": "To analyze the behavior of each component in the proposed method, We evaluated four ablations: 1) we use discrete wavelet transform (DWT) but remove the skip connection (SC) when generating the perturbations, 2) we only apply the SC of the low-frequency components, 3) we remove both DWT and SC, 4) our method. The results are shown"
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+                                            "content": "Figure 5. Comparing the transferability of the adversarial example generated by AMG and classification (CAE) task. Prediction (Pred.) and mask are obtained from ResNet-50 and FCN, respectively. ASR-class and ASR-pixel stand for the attack success rate of classification accuracy and pixel-level detection accuracy."
+                                        }
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+                                            "content": "Table 3. Image quality assessment of the adversarial examples generated by different attacks. Our method has significantly better image quality than other attacks."
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+                                            "html": "<table><tr><td>DWT</td><td>SC</td><td>ASR (↑)</td><td>PSNR (↑)</td><td>SSIM (↑)</td></tr><tr><td>✓</td><td>×</td><td>59.8%</td><td>33.5</td><td>0.84</td></tr><tr><td>✓</td><td>Low</td><td>60.0%</td><td>35.5</td><td>0.89</td></tr><tr><td>×</td><td>×</td><td>58.6%</td><td>30.8</td><td>0.74</td></tr><tr><td>✓</td><td>High</td><td>60.5%</td><td>40.0</td><td>0.97</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 4. Ablation study of the proposed method on DEFACTO dataset with MVSS-Net detector. DWT is discrete wavelet transform, and SC is skip-connection (low or high means low-/high-frequency component)."
+                                }
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+                                    "type": "text",
+                                    "content": "in Table 4. By comparing 1st and 3rd rows, we observe that using the frequency features improves PSNR and SSIM by a large margin. By comparing the types of SC (1st, 3rd and 4th rows), we also observe that preserving high-frequency components have the most effect for improving the image quality. These quantitative results show the effect of two main components of the proposed method."
+                                }
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+                                    "content": "6. Conclusion"
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+                                    "type": "text",
+                                    "content": "In this work, we propose an AMG task to explore the vulnerability of image manipulation detectors. We extend the existing attacks and explore the changes in frequency components during adversarial attacks. Moreover, we propose a novel adversarial attack that incorporates both spatial and frequency features into the GAN architecture to generate imperceptible examples. Experiments show that our method generates adversarial examples significantly fast and preserves better image quality while achieving a high attack success rate. This work shows the vulnerability of current image manipulation detectors and suggests more robust detectors are needed to correctly detect the manipulations. Adversarial defense that can protect the detectors from various attacks is an interesting topic in future work."
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+                                }
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[1] Darius Afchar, Vincent Nozick, Junichi Yamagishi, and Isao Echizen. Mesonet: a compact facial video forgery detection network. In 2018 IEEE international workshop on information forensics and security (WIFS), pages 1-7. IEEE, 2018."
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+                                    ]
+                                }
+                            ],
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+                        {
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+                                            "bbox": [
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+                                        {
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+                                            "type": "text",
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+                                        }
+                                    ]
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+                        {
+                            "bbox": [
+                                53,
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+                                        {
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+                                        }
+                                    ]
+                                }
+                            ],
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+                        {
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+                                53,
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+                                        {
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+                                        }
+                                    ]
+                                }
+                            ],
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+                            ],
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+                            "lines": [
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+                                            "bbox": [
+                                                53,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[6] Hao Dang, Feng Liu, Joel Stehouwer, Xiaoming Liu, and Anil K Jain. On the detection of digital face manipulation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern recognition, pages 5781-5790, 2020."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
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diff --git a/2023/From Chaos Comes Order_ Ordering Event Representations for Object Recognition and Detection/d3f1e4dc-e3b8-48be-905a-0246e42863b1_content_list.json b/2023/From Chaos Comes Order_ Ordering Event Representations for Object Recognition and Detection/d3f1e4dc-e3b8-48be-905a-0246e42863b1_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..c8120d95637c863d0f8081c41d3e4e464045bd1a
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+++ b/2023/From Chaos Comes Order_ Ordering Event Representations for Object Recognition and Detection/d3f1e4dc-e3b8-48be-905a-0246e42863b1_content_list.json	
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+    {
+        "type": "text",
+        "text": "From Chaos Comes Order: Ordering Event Representations for Object Recognition and Detection",
+        "text_level": 1,
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+        "text": "Nikola Zubić*",
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+        "page_idx": 0
+    },
+    {
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Mathias Gehrig",
+        "bbox": [
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+            203,
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+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Davide Scaramuzza",
+        "bbox": [
+            643,
+            203,
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+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Robotics and Perception Group, University of Zurich, Switzerland",
+        "bbox": [
+            222,
+            226,
+            746,
+            244
+        ],
+        "page_idx": 0
+    },
+    {
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+        "img_path": "images/df91507725b9357860518a664565b519ec1ab6e2e46572b4f12eb091cc35f58b.jpg",
+        "image_caption": [
+            "(a) Method overview"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            425
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/303d5a5504dd7d7291a75f0087084d620940bb7bab5da711fdc72b2bab19a3df.jpg",
+        "image_caption": [
+            "(b) GW Discrepancy vs. Performance",
+            "Figure 1: Selecting dense event representations for deep neural networks is exceedingly slow since it involves training a neural network for each representation and selecting the best one based on the validation score. In this work, we eliminate this bottleneck by selecting the representation based on the Gromov-Wasserstein Discrepancy (GWD) on the validation set (a). This metric is 200 times faster to compute and preserves the task performance ranking of event representations across multiple representations, network backbones, datasets and tasks (b, showing object detection performance on the Gen1 [9] dataset). We use it to, for the first time, perform a hyperparameter search on a large family of event representations, revealing new and powerful event representations that exceed the state-of-the-art."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            422
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            570,
+            313,
+            585
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Today, state-of-the-art deep neural networks that process events first convert them into dense, grid-like input representations before using an off-the-shelf network. However, selecting the appropriate representation for the task traditionally requires training a neural network for each representation and selecting the best one based on the validation score, which is very time-consuming. This work eliminates this bottleneck by selecting representations based on the Gromov-Wasserstein Discrepancy (GWD) between raw events and their representation. It is about 200 times faster to compute than training a neural network and preserves the task performance ranking of event representations across multiple representations, network backbones, datasets, and tasks. Thus finding representations with high task scores is equivalent to finding representations with a low GWD. We use this insight to, for the first time, perform a hyperparameter search on a large family of event representations, revealing new and powerful representations that exceed the",
+        "bbox": [
+            75,
+            602,
+            473,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "state-of-the-art. Our optimized representations outperform existing representations by 1.7 mAP on the 1 Mpx dataset and 0.3 mAP on the Gen1 dataset, two established object detection benchmarks, and reach a  $3.8\\%$  higher classification score on the mini N-ImageNet benchmark. Moreover, we outperform state-of-the-art by 2.1 mAP on Gen1 and state-of-the-art feed-forward methods by 6.0 mAP on the 1 Mpx datasets. This work opens a new unexplored field of explicit representation optimization for event-based learning.",
+        "bbox": [
+            500,
+            571,
+            893,
+            709
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Multimedia Material",
+        "text_level": 1,
+        "bbox": [
+            500,
+            753,
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+            770
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "For open-source code please visit https://github. com/uzh-rpg/eventRepresentation_study.",
+        "bbox": [
+            500,
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+            888,
+            811
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            844
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Event cameras are biologically inspired vision sensors that function in a fundamentally distinct way [12]. Unlike traditional cameras that capture images at a fixed rate,",
+        "bbox": [
+            500,
+            854,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Equal contribution",
+        "bbox": [
+            94,
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+            204,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "12846",
+        "bbox": [
+            480,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "these cameras measure brightness changes independently for each pixel, and these changes are referred to as events. The events encode the time, location, and polarity (sign) of the brightness changes. Event cameras offer several advantages over frame-based cameras, including exceptionally high temporal resolution (in the order of  $\\mu$ s), a high dynamic range, and low power consumption. Their numerous benefits make them attractive for a wide range of applications like robotics, autonomous vehicles, and virtual reality. However, due to their sparse and asynchronous nature, applying classical computer vision algorithms remains challenging.",
+        "bbox": [
+            75,
+            90,
+            472,
+            272
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Many state-of-the-art deep learning models address this challenge by converting sparse and asynchronous events into dense grid-like representations before processing them with off-the-shelf deep neural networks. By using these networks, methods like this enjoy the advantages of mature learning algorithms and network architectures, and optimized hardware, but we need to make a non-trivial choice of event representation. In fact, the computer vision and robotics fields are witnessing a surge in the number of research papers utilizing event-based vision, resulting in a plethora of new event representations being proposed. Despite this, extensive comparisons of these representations remain rare, making it unclear whether these newer representations should be adopted.",
+        "bbox": [
+            75,
+            275,
+            472,
+            487
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "No efficient methodology exists for comparing these representations. Conventionally, comparing event representations involves training a fixed deep-learning model for each event representation separately and subsequently selecting the optimal one based on a validation score. This process is very time-intensive since it requires network training in the loop which often takes hours or days (Fig. 1 a top).",
+        "bbox": [
+            75,
+            489,
+            472,
+            597
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a fast method to compare event representations which circumvents the need to train a neural network and instead computes the Gromov-Wasserstein Discrepancy (GWD) between the raw events and event representation (Fig. 1 a bottom). This metric effectively measures the distortion that is introduced through converting raw events to representations and thus puts an upper bound on the amount of information that can be accessed by downstream neural networks. We show extensive experimental evidence, that this metric preserves the task-performance ranking across a wide range of input representations for several datasets, neural network backbones and tasks (Fig. 1 b). Due to its low computational cost, we apply the GWD to, for the first time, explicitly optimize over a large family of event representations, which reveals a new and powerful representation, which we term 12-channel Event Representation through Gromov-Wasserstein Optimization (ERGO-12). For the task of object detection, networks trained with these representations outperform other representations by  $1.9\\mathrm{mAP}$  on the 1 Mpx dataset and  $0.3\\mathrm{mAP}$",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "on Gen1, even outperforming state-of-the-art methods by  $2.1\\mathrm{mAP}$  on Gen1 and state-of-the-art feed-forward methods by  $6.0\\mathrm{mAP}$  on the 1 Mpx dataset. On object recognition, we instead find that our representation outperforms state-of-the-art representations by  $3.8\\%$ . We believe that the GWD is a powerful tool that opens up a new research field that searches for optimized event representations. Our contributions are summarized as follows:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- We introduce a novel, efficient approach for comparing dense event representations using the Gromov-Wasserstein Discrepancy (GWD).",
+            "- We show extensive experimental evidence that it preserves the task performance ranking of neural networks trained with these representations across datasets, neural network backbones and tasks.",
+            "- We use it to, for the first time, conduct a hyperparameter search on a vast family of event representations, unveiling novel and powerful event representations that outperform the current state-of-the-art representations on the object detection and object classification task."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In the field of event-based vision, two primary groups of representations exist: sparse and dense. Methods that use sparse representations [35, 51, 23, 37] preserve the sparsity in the events but do not yet scale to more complex tasks due to a lack of specialized hardware and mature neural networks architectures. This frequently results in lower performance on downstream tasks. In contrast, dense representations [31, 48, 53, 50] offer improved performance since they can leverage mature machine learning algorithms and neural network architectures. Sparse representations, pioneered by asynchronous SNNs [35, 23, 37], are limited by the lack of specialized hardware and computationally efficient backpropagation algorithms. Point cloud encoders [47, 40, 11] have been used due to the spatio-temporal nature of event data, but can be computationally expensive and noisy. Graph neural networks [26, 46, 4, 3, 33, 10] are scalable and have achieved high performance on various vision tasks but are still less accurate than dense methods for event-based vision. In this study, we focus on dense event representations and aim to achieve better task performance by utilizing existing efficient learning algorithms that are appropriate for current hardware.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Early dense representations converted events to histograms [31], generated time surfaces [48] or combined both [52] while relying on standard neural network backbones to process them. However, these representations only capture a low-dimensional representation of events since they typically only use a few channels. Later approaches have tried to capture more event information by either computing higher-order moments [1] or stacking multiple time",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "12847",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/1da40450cb10dd24289b70a4a37d2cf45a82e0fdbeae74098164ad510631ed8a.jpg",
+        "image_caption": [
+            "Figure 2: Overview of the Gromov-Wasserstein Discrepancy (GWD) between raw events and representations. Events  $\\mathcal{E}$  are converted to event representations, i.e. a set of features  $\\mathcal{F}$  at pixel locations  $\\mathbf{x}$ . It is defined as the solution to an optimal transport problem which transports events pairs  $(e_i,e_k)$  to feature pairs  $(f_{\\mathbf{x}_j},f_{\\mathbf{x}_l})$  via transport plan  $T_{ij},T_{kl}$ . If the transport plan preserves the similarities  $C_{ik}^{e}$  and  $C_{jm}^{f}$  between event and feature pairs, this results in a low GWD."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "windows of events [53]. These methods still stack events based on fixed time windows which is problematic when the event rate becomes too large or too small and lead to the introduction of stacking based on the number of events [50]. In parallel, a bio-inspired approach led to the introduction of Time Ordered Recent Event Volumes (TORE) [2], which aggregate events into queues. However, they are slow to compute and perform similarly to existing Voxel Grids [53]. Most recently, a powerful representation was proposed by Nam et al. [34], which divides events into multiple overlapping windows that halve the number of events at each stage, which are more robust during varying scene dynamics.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Few papers study the effect of event representations on task performance. While [38] and [21] show small-scale ablation studies to select event representations, only Gehrig et al. [13] performed a large-scale investigation of event representations by training models on various inputs for multiple tasks. Their study demonstrated the advantages of splitting polarities and incorporating timestamps into representations, and it introduced a learnable representation. However, training for a single task was still computationally expensive, which limited the number of representations that could be compared. For this reason, their study did not cover a large number of representations, and in particular, did not consider different window sizes as is done in later work [50, 34], or more advanced aggregations and measurements like in [1]. Our method instead introduces an efficient metric to compare event representations that solves these limitations, allowing us to perform a search over a large family of event representations and go beyond the representations in [50, 1, 34, 14], including even non-differentiable hyperparameters.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will first introduce the preliminaries on computing event representations (Sec. 3.1) and then pro",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "pose the metric we use to measure the discrepancy between events and their representation based on the GWD (Sec. 3.2) before concluding with Sec. 3.3 where we use Bayesian optimization to find an optimal event representation.",
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Event cameras measure brightness changes as an asynchronous stream of events. Each event is triggered when the intensity  $L(\\mathbf{u})$  at the pixel  $\\mathbf{u} = (x, y)$  changes by the contrast threshold  $C$  at time  $t$ , and thus satisfies",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np \\left[ L (\\mathbf {u}, t) - L (\\mathbf {u}, t - \\Delta t) \\right] = C \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $p\\in \\{-1,1\\}$  is the polarity of the event, and  $t - \\Delta t$  is the time of the last event. Within a time window  $\\Delta T$  an event camera thus generates an ordered set of events  $\\mathcal{E} = \\{e_k\\}_{k = 0}^{N_e - 1}$ , with each event  $e_k = (\\mathbf{u}_k,t_k,p_k)\\in \\mathbb{R}^4$ . To bridge the gap between asynchronous events and dense neural networks, they are usually converted to a dense event representation",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {R} = F (\\mathcal {E}), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "which has features  $f_{\\mathbf{x}} \\doteq \\mathcal{R}(\\mathbf{x}) \\in \\mathbb{R}^{N_f}$  indexed by the integer-valued pixel location  $\\mathbf{x}$ . The above representation thus generates a set of features  $\\mathcal{F} = \\{f_{\\mathbf{x}}\\}_{\\mathbf{x} \\in \\Omega}$ , where  $\\Omega$  denotes the image domain and has size  $|\\Omega| = N_f$  with  $N_f$  being the number of pixels in the image. In what follows, we will derive a measure to quantify the distortion between events  $\\mathcal{E}$  and features  $\\mathcal{F}$  based on the GWD.",
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Gromov-Wasserstein Discrepancy",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Converting raw events to a representation invariably distorts the events by removing important distinguishing features from the stream. We would like to measure this distortion since we expect it correlates strongly with a neural network's ability to extract features from these events. In what follows, we will derive a measure of this distortion rate based on the GWD.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "12848",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We show an overview of the GWD in Fig. 2. We start by measuring the similarity between a set of events and their representation by building a soft correspondence between events  $e_i$  and features  $f_{\\mathbf{x}_j}$ , which we denote as  $T_{ij}^1$ . This transport plan effectively moves each event to a corresponding feature, thereby distorting the original set and destroying information. Importantly, such a plan can be interpreted as follows: We transport the events with a total weight of 1, i.e. per-event weight  $\\frac{1}{N_e}$  to the output features, which also need to receive a total weight of 1 or per-feature weight of  $\\frac{1}{N_f}$ . By this construction,  $T_{ij}$  needs to satisfy  $\\sum_i T_{ij} = 1 / N_f$  and  $\\sum_j T_{ij} = 1 / N_e$ . This means that a total weight of  $1 / N_e$  moves from each event, and each feature receives a total weight of  $1 / N_f$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the next step, we measure the distortion introduced by this transportation plan by considering pairwise similarities of input events and features. Let  $e_i, e_k \\in \\mathcal{E}$  be a pair of events and  $f_{\\mathbf{x}_j}, f_{\\mathbf{x}_l} \\in \\mathcal{F}$  pair of features, with similarity scores  $C_{ik}^e \\doteq C^e(e_i, e_k)$  and  $C_{jl}^f \\doteq C^f(f_{\\mathbf{x}_j}, f_{\\mathbf{x}_l})$  between events and features respectively. Next, consider how the transport plan  $T$  acts on these pairs: Generally, a weight  $T_{ij}$  is moved from event  $e_i$  to feature  $f_{\\mathbf{x}_j}$ . Similarly, the weight  $T_{kl}$  is moved from event  $e_k$  to feature  $f_{\\mathbf{x}_l}$ . Ideally, such a transport plan should preserve the similarity between pairs of source events and target features, and thus the difference in similarity scores between pairs  $(i, k)$  and  $(j, l)$  can be used as a measure of distortion. For each event pair and feature pair, we define the distortion as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {i j k l} = T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}$  denotes some disparity measurement between  $C_{ik}^{e}$  and  $C_{jl}^{f}$ . Summing over all possible pairs of events and features we thus arrive at the transportation cost:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL (T; \\mathcal {E}, \\mathcal {F}) = \\sum_ {i, j, k, l} L _ {i j k l} = \\sum_ {i, j, k, l} T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Minimizing over transport plans, we arrive at the GWD:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL (\\mathcal {E}, \\mathcal {F}) = \\min  _ {T} \\sum_ {i, j, k, l} T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which can be optimized efficiently using [39]. Since the above metric is defined for a single time window of events, we may average it over multiple samples to find:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {G W D} _ {N} = \\frac {1}{N} \\sum_ {i} L \\left(\\mathcal {E} _ {i}, \\mathcal {F} _ {i}\\right). \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$\\mathrm{GWD}_N$  can be interpreted as an average distortion rate from raw events to event representations. In Sec. 4.2, we",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "show that  $\\mathrm{GWD}_N$  correlates with a  $NN$ 's performance with that representation across network backbones, datasets, and event representations. It's also efficient to compute, taking 9 seconds for 50,000 events. In what follows,  $\\mathrm{GWD}_N$  will denote the average over  $N$  samples, while GWD denotes the average over the whole validation set.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Similarity scores and distortion function As similarity scores, we choose Gaussian radial basis functions [45] for both events and image features. In detail,",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nC _ {i k} ^ {e} = e ^ {\\frac {- \\| e _ {i} - e _ {k} \\| ^ {2}}{2 h ^ {2} \\sigma_ {e} ^ {2}}}, \\quad C _ {j l} ^ {f} = e ^ {\\frac {- \\| f _ {\\mathbf {x} _ {j}} - f _ {\\mathbf {x} _ {l}} \\| ^ {2}}{2 h ^ {2} \\sigma_ {f} ^ {2}}} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma_ {e} ^ {2} = \\underset {i <   j} {\\operatorname {m e a n}} \\| e _ {i} - e _ {j} \\| ^ {2}, \\quad \\sigma_ {f} ^ {2} = \\underset {i <   j} {\\operatorname {m e a n}} \\| f _ {\\mathbf {x} _ {i}} - f _ {\\mathbf {x} _ {j}} \\| ^ {2}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with a bandwidth parameter  $h = 0.7$ . The selection of data-dependent variances normalizes the distances between pairs of events and features such that the similarity score is robust to the dimensionality of the data and the number of samples in the source and target domain. These details are discussed in [7, 45, 36]. While more complex similarity scores could be used, this simple function already achieved good results. As the distortion function, we chose the KL-Divergence i.e.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right) = C _ {i k} ^ {e} \\log \\left(C _ {i k} ^ {e} / C _ {j l} ^ {f}\\right). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As a result, the optimization already rejects terms for which  $C_{ik}^{e} \\approx 0$ , i.e. pairs of events that are far apart. We found that this property was also beneficial in improving the convergence of the optimization problem in Eq. (5)",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Improving Convergence of Eq. (5). We found that three features improved convergence and speed up the optimization: (i) Normalization of the event coordinates and timestamps by the sensor size and time window respectively, (ii) Concatenation of the normalized pixel position to the image features, and (iii) Sparsification of image features. Both (i) and (ii) make the optimization more numerically stable. In fact, without concatenating position information to image features, randomly pixel-wise shuffled event representations would retain the same GWD, although intuitively, neural networks would have a harder time learning from such representations since they typically process nearby features together. Thus reintroducing the position removes this ambiguity and improves the convergence. Finally, (iii) removes image features with  $\\| f_{\\mathbf{x}} \\| = 0$  since these correspond to pixels where no events were triggered. This step significantly sped up computation by reducing the size of the pair-wise similarity score matrix  $C^f$ , with a small impact on convergence.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Optimizing over Event Representations",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With a fast method to measure the effectiveness of an event representation, we can now search for the optimal rep",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>In the optimal transport literature, this correspondence is also called a transport plan.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12849",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c5763c85abebbc04f357dc22d145690e5a888ec5506621edf714a668ced5ebd8.jpg",
+        "image_caption": [
+            "Figure 3: Overview of the hyperparameters we use to construct an event representation (right). For each channel  $c$ , we select one of several event time windows  $w_{c} \\in \\mathcal{W}$  (in color, left), measurement functions  $m_{c} \\in \\mathcal{M}$  (timestamp, polarity, positive timestamps, etc.), and aggregation functions  $a_{c} \\in \\mathcal{A}$  (max, mean, sum, variance), resulting in  $3N_{c}$  parameters."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "resentation by minimizing Eq. (6) over a space of possible representations with a set of hyperparameters  $p$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np ^ {*} = \\arg \\min  _ {p} \\frac {1}{N} \\sum_ {i} L \\left(\\mathcal {E} _ {i}, \\mathcal {F} _ {i} (p)\\right). \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To simplify this optimization, we first describe a very general parametrization, which defines a large family of event representations, extending the family described in [13] in a few ways. These hyperparameters are a small set of categorical variables which can subsequently be optimized using Bayesian optimization.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Parametrization of Event Representations We illustrate the hyperparameters in Fig. 3. In general, we assume an event representation comprises a stack of features, indexed by  $c$  (right side), each of which is derived from  $(i)$  a specific time window  $w_{c}$  of events,  $(ii)$  a specific measurement  $m_{c}$  of events such as polarity or timestamps, and  $(iii)$  a specific aggregation  $a_{c}$ , such as summation or averaging. We write such a representation as  $N_{c}$  concatenated feature maps:",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {R} = \\left[ \\mathcal {R} _ {0} \\mid \\mathcal {R} _ {1} \\dots \\mid \\mathcal {R} _ {N _ {c} - 1} \\right] \\tag {11}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {w i t h} \\mathcal {R} _ {c} = a _ {c} \\left(m _ {c} \\left(w _ {c} (\\mathcal {E})\\right)\\right) \\tag {12}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "Here  $w_{c}$  is a windowing function which selects events within an interval,  $m_{c}$  is the measurement function which selects an event feature, and  $a_{c}$  is the aggregation function, which aggregates measurements into a single feature map.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Note, in our formulation each channel can have an independent set of parameters, different to [13], which assumes a shared aggregation and measurement function for all channels. This makes our parametrization substantially more expressive than the one in [13]. The number of (non-learnable) representations is  $\\left(|\\mathcal{A}||\\mathcal{M}||\\mathcal{W}|\\right)^{N_c}\\approx 3.21\\times 10^{27}$ , since each channel can be configured independently. Moreover, while  $a_{c}$  and  $m_{c}$  were already discussed in [13], the windowing function is a more general concept, illustrated in Fig. 3 (left). While these windows can be non-overlapping  $(w_{3},w_{4},w_{2})$ , as for Voxel Grids [53], they can also be overlapping,  $(w_{0},w_{1},w_{2})$  as in Mixed",
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+    },
+    {
+        "type": "text",
+        "text": "Density Event Stacks [34], or describe windows of a constant event count or constant time [50] In this work we allow each feature channel to select from a basis of windows  $\\mathcal{W} = \\{[t_{0,k}, t_{1,k}]\\}_{k=0}^{N_k-1}$ , which can combine all types of windows unifying these concepts. In summary, a representation is parametrized by:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np = \\left\\{\\left(w _ {c}, a _ {c}, m _ {c}\\right) \\right\\} _ {c = 0} ^ {N _ {c} - 1} \\tag {13}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {w i t h} \\quad m _ {c} \\in \\mathcal {M}, a _ {c} \\in \\mathcal {A}, w _ {c} \\in \\mathcal {W}.\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "For the sets of aggregation functions we select  $\\mathcal{A} = \\{\\max, \\text{sum}, \\text{mean}, \\text{variance}\\}$  and for the measurement functions  $\\mathcal{M} = \\{t_{+}, t_{-}, t, p, c_{+}, c_{-}, c\\}$  which are most commonly used. Here  $c, p,$  and  $t$  denote event count (discarding polarity), polarity, and timestamp. The subscripts  $+ / -$  select only positive or negative events. For the basis of time windows, we select three equally spaced, non-overlapping windows from [53] and four overlapping windows from [34], including the global window. These are illustrated in Fig. 7 (right).",
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+    },
+    {
+        "type": "text",
+        "text": "Optimization Procedure The aforementioned parametrization generates redundant combinations that can be obtained by permuting channels or selecting the same feature for different channels. To address this issue and expedite convergence, we propose a stage-wise optimization procedure. Initially, we start with a volume consisting of zeros with  $N_{c}$  channels and optimize over  $a_0, w_0$ , and  $m_0$  to fill in the first channel. Next, we optimize the feature for the second channel while keeping the first fixed. With this iterative process, we incrementally fill up the representation, avoiding the selection of redundant representations and resulting in faster optimization. At each stage, we use Gryffin [18], a specialized Bayesian optimizer for categorical variables.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "In Sec. 4.1, we first connect the GWD and event distortion, demonstrating its behavior on several toy examples. Next, in Sec. 4.2, we showcase the correlation between the",
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+    },
+    {
+        "type": "page_number",
+        "text": "12850",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/65ce4065ac4bcbd40835c6897c6bfaf07da55eead7399971718c31ccbe961092.jpg",
+        "image_caption": [
+            "Figure 4: Validation of our metric on the Gen1 validation set. (top) Our metric for Voxel Grids [53] and Mixed-Density Event Stacks [34] with an increasing number of channels. (bottom) Effect of applying Gaussian blur with different blur kernels to the event representation."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "metric and task performance across multiple tasks, datasets, backbones, and representations. Lastly, in Sec. 4.3, we show the outcome of Bayesian Optimization on the GWD and offer insights on the acquired event representation before comparing it against the state-of-the-art.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Toy Example",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As explained in Sec. 3.2, the GWD measures the distortion rate from raw events to event representation. Two experiments were designed to test this claim: (1) analyzing the behavior of the metric when varying the number of bins in Voxel Grid [53] and Mixed-Density Event Stack (MDES) [34] representations, and (2) blurring the event representation with increasing standard deviations before measuring the GWD. We perform experiments on the validation set of Gen1[9] and report the results in Fig. 4.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Fig. 4 (top) confirms that the GWD decreases as the number of channels increases in both Voxel Grids and Mixed-Density Event Stacks, which aligns with our intuition that using more channels preserves more information from raw events, resulting in a lower distortion rate. Similarly, the bottom part illustrates that with a growing blur radius, more edges in the event representation are removed, leading to an increase in the GWD. This verifies that the GWD measures the distortion from raw events to event representations.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Object Detection",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Next, we investigate the relationship between GWD and the task performance of a  $NN$  trained for object detection. We choose two widely used object detection datasets, the Gen1 [9] and 1 Mpx [38] Automotive Detection Dataset, which both deal with event streams featuring labeled bounding boxes for pedestrians, cars, and other vehicles. While",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/c75b215699f042097d2a7ba2d96f6d191fc3277e8a947080ac17c03eafd3ae07.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/73c5ae4bd1852ea41ee44657f8db6b00f24a74d4dccc4591ad54fe0016ea7153.jpg",
+        "image_caption": [
+            "Figure 5: Correlation of the Gromov-Wasserstein Discrepancy with the mAP (higher is better) for object detection on the Gen1 [9] (top) and 1 Mpx [38] (bottom) datasets. Note the spliced y-axis on 1 Mpx, due to the high GWD of the 2D Histogram."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "the former has a resolution of  $304 \\times 240$ , the latter has a resolution of  $1280 \\times 720$ . We report the GWD computed over the validation set of each dataset and then train an off-the-shelf object detection framework based on YOLOv6 [24], pre-trained on the Microsoft Common Objects in Context (MS-COCO) [28], on different input representations as in [13]. To accommodate the varying number of channels, we replace the 3-channel input convolution with a  $N_{c} = 12$  channel input convolution, where  $N_{c}$  represents the number of channels in the representation. To show the generality of the result, we also vary the detection backbone between ResNet-50 [17], EfficientRep [24] and Swin Transformer V2 [30], and report results for each.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Representations: We test a range of common representations listed below. We compute 12 channels for each representation, except for the 2D Histogram, which has 2.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Voxel Grid: Here, the event time window is split into  $N_{c}$  equal, non-overlapping time windows, and then events in the same time window are aggregated by summing their polarity on a per-pixel basis using bilinear voting [53].",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Mixed-Density Event Stack (MDES): For each channel  $c$ , this representation selects the most recent  $\\frac{N_e}{2^c}$  events, where  $N_e$  are the events in the time window. For each window, it aggregates the polarity at that pixel [34].",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Event Histograms: Events in the time window are split by polarity and then summed into two channels [31].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Time Surface: We convert events into time surfaces from [22] with a decay constant of  $\\tau = 5\\mathrm{ms}$ . We then sample it at  $\\frac{N_c}{2} = 6$  equally spaced timestamps, once for",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "12851",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "positive and negative events resulting in  $N_{c} = 12$  channels.  \nTORE: The Time-Ordered Recent Event Volumes store event timestamps in per-pixel queues. We use queues with capacity  $\\frac{N_c}{2} = 6$ , one for positive and one for negative events, and concatenate them to  $N_{c} = 12$  channels.",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Learned representation: Event Spike Tensor (EST) [13] is a learnable event representation that employs a Quantization Layer featuring a trainable kernel. This approach enables the model to effectively transform raw events, optimizing their performance for a given task.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Training Details We adopt the training procedure from YOLOv6 [24]. For each backbone, representation, and dataset, we train for 100 epochs, using Stochastic Gradient Descent with Nesterov momentum increasing from 0.5 to 0.83 over the first 2 epochs. We use a batch size of 32, and a Cosine learning rate schedule, starting at 0.00323 and ending at 0.000387 after 100 epochs. We adopt the classification and box regression losses in [24].",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results: Figs. 5 summarizes the results of the above experiments. For both datasets, Gen1 and 1 Mpx, and all backbones, there is a clear correlation between the GWD and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all three network backbones. In particular, MDES with a Swin-V2 detection backbone consistently achieves the highest mAP with 0.43 on Gen1 and 0.39 on 1 Mpx. It also consistently achieves the lowest GWD with 0.38 on Gen1 and 0.40 on 1 Mpx. Utilizing the learnable EST in YOLOv6 with SwinV2 backbone, we achieved a 45.31 mAP score on the Gen1 validation set and a GWD score of 0.3552, positioning EST between MDES and ERGO-12 in Fig. 1b, confirming the expected ranking. We also see that the Swin V2 backbone outperforms other backbones on both datasets for all tested representations. We conclude that while the representation affects task performance, the neural network also has an influence. However, we see that the overall ranking of the representations is preserved.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Using Fewer Samples While in the previous section, we reported the GWD over the validation set of the Gen1 and the 1 Mpx datasets, averaging this metric over such a large dataset still incurs a high computational cost and would make such a metric infeasible for optimization. Therefore, here we investigate if we can use smaller sample sizes to speed up the computation of GWD. In Fig. 6, we show the GWD for the representations in Sec. 4.2 while varying the number of samples. We see that as the sample number decreases, the mean values of the metric change, but the ranking between representations is still preserved reliably after around 100 samples, and thus we use  $\\mathrm{GWD}_{100}$  to optimize over representations. Below this number, the ranking of representations can fluctuate. However, we found that this happens due to a bad convergence of Eq. (5).",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Timing Results: We time the computation of the GWD",
+        "bbox": [
+            86,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/031abe41d5b5eafcda630b4c1592cc1a0d3524dffa39ace93806b47723b0243f.jpg",
+        "image_caption": [
+            "Figure 6: Gromov-Wasserstein Discrepancy for a varying number of samples from the validation set."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "over 100 samples of the Gen1 validation set, where each sample comprises 50,000 events. We run our experiment on an AMD EPYC 7702 32-core server-grade CPU with 32 GB RAM and achieve a runtime of 15 minutes. Note that computing the GWD does not require a GPU. By contrast, training the models in Fig. 5 requires 2 days on a single Tesla V100 GPU with 32 GB of memory, making GWD computation 192 times faster.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Optimization of Event Representations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Here we report the results of optimizing the event representation according to the procedure in Sec. 3.3. We optimize  $N_{c} = 12$  channels, and at each optimization cycle for channel  $c$ , the Bayesian Optimizer selects 100 configurations and then keeps the best-performing configuration.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We show the result of this optimization procedure in Fig. 7. The left shows how the GWD decreases as new channels are added to the representation. We see that after 2 channels, our method outperforms 2D Histograms, after 6 channels we outperform Time Surfaces, after 7 channels we outperform Voxel Grids / TORE, after 9 channels we outperform Mixed-Density Event Stacks and finally, after 12 channels, we achieve a  $\\mathrm{GWD}_{100}$  of 0.47. On the right, we show the different windows (columns) and measurement functions (rows) that are selected. We do not show the order since our representation is unique up to a random channel permutation. However, in the appendix, we show which features are selected at each stage. We see that all windows and all measurement functions are selected at least once, showing how our representation tries to diversify as much as possible. Moreover, timestamp-based measurements often show multiple aggregations, which we argue are necessary to replicate their complex continuous signal.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Comparison with State-of-the-Art Here we compare our method against state-of-the-art recurrent and feedforward methods on the Gen1 and 1 Mpx test sets. We summarize the results in Tab. 1. Recurrent methods in",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "12852",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/95482ddb6d0259ceb4b95c992f740cde923fc787f9745c5f3f2c2789f2e1433b.jpg",
+        "image_caption": [
+            "Figure 7: Gromov-Wasserstein Discrepancy for 100 samples (left). At each channel, a Bayesian optimizer selects the next best hyperparameter triple. The chosen hyperparameters are broken down by window and measurement function (right)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            114,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/53f167ee2dd1ab8b2bc4cf97b7c6033999dae12a1850aab5c386993710d8fd11.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td>\\( w_0 \\)</td><td>\\( w_1 \\)</td><td>\\( w_2 \\)</td><td>\\( w_3 \\)</td><td>\\( w_4 \\)</td><td>\\( w_5 \\)</td><td>\\( w_6 \\)</td></tr><tr><td rowspan=\"3\">t</td><td>+</td><td>sum</td><td>sum mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>-</td><td>sum</td><td>mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td>var max</td><td></td><td></td><td></td></tr><tr><td rowspan=\"3\">c</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>mean</td><td></td></tr><tr><td>-</td><td></td><td></td><td>sum</td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td></td><td>sum</td><td></td><td>sum</td></tr><tr><td colspan=\"2\">p</td><td></td><td></td><td></td><td>var</td><td></td><td></td><td></td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/9a52a378bedfb9558e2cb09c2480c343772e40cb1212ba4397485860d50c4b9f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>tNe-1</td></tr><tr><td>w6</td></tr><tr><td>w5</td></tr><tr><td>w4</td></tr><tr><td>w3</td></tr><tr><td>w2</td></tr><tr><td>w1</td></tr><tr><td>w0</td></tr><tr><td>t0</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7de24d1af607fe497187d416d6b6e03a5444b37ed3508ca666fbe7f79f439167.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Event Repr.</td><td rowspan=\"2\">Recurrent</td><td colspan=\"2\">mAP↑</td></tr><tr><td>Gen1 [9]</td><td>1 Mpx [38]</td></tr><tr><td>MatrixLSTM+YOLOv3 [5]</td><td>MatrixLSTM</td><td>✓</td><td>0.310</td><td>-</td></tr><tr><td>E2VID+RetinaNet [41]</td><td>Reconstructions</td><td>✓</td><td>0.270</td><td>0.250</td></tr><tr><td>RED [38]</td><td>Voxel Grid</td><td>✓</td><td>0.400</td><td>0.430</td></tr><tr><td>RVT-B [16]</td><td>2D Histogram</td><td>✓</td><td>0.472</td><td>0.474</td></tr><tr><td>ASTMNet [25]</td><td>Asynchronous attention embedding</td><td>✓</td><td>0.467</td><td>0.483</td></tr><tr><td>Events+RetinaNet [38]</td><td>Voxel Grid</td><td>✗</td><td>0.340</td><td>0.180</td></tr><tr><td>Events+SSD [19]</td><td>2D Histogram</td><td>✗</td><td>0.301</td><td>0.340</td></tr><tr><td>Events+RRC [6]</td><td>2D Histogram</td><td>✗</td><td>0.307</td><td>0.343</td></tr><tr><td>Events+YOLOv3 [20]</td><td>2D Histogram</td><td>✗</td><td>0.312</td><td>0.346</td></tr><tr><td>AEGNN [46]</td><td>Graph</td><td>✗</td><td>0.163</td><td>-</td></tr><tr><td>EAGR [15]</td><td>Graph</td><td>✗</td><td>0.321</td><td>-</td></tr><tr><td>Spiking DenseNet [8]</td><td>Spike Train</td><td>✗</td><td>0.189</td><td>-</td></tr><tr><td>AsyNet [32]</td><td>2D Histogram</td><td>✗</td><td>0.145</td><td>-</td></tr><tr><td></td><td>2D Histogram</td><td>✗</td><td>0.339</td><td>0.327</td></tr><tr><td></td><td>Time Surface</td><td>✗</td><td>0.490</td><td>0.383</td></tr><tr><td></td><td>TORE</td><td>✗</td><td>0.436</td><td>0.381</td></tr><tr><td></td><td>Voxel Grid</td><td>✗</td><td>0.395</td><td>0.375</td></tr><tr><td></td><td>MDES</td><td>✗</td><td>0.427</td><td>0.378</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.493</td><td>0.400</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.504*</td><td>0.406*</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: Comparison of state-of-the-art event-based object detectors on the test sets of Gen1 [9] and 1 Mpx [38].",
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+        "type": "text",
+        "text": "clude MatrixLSTM+YOLOv3 [5], which uses a recurrent, learned input representation with a YOLOv3 [42] detector, E2VID+RetinaNet [41] which uses recurrent E2VID reconstructions with a RetinaNet [27] detector, RVT-B which uses a recurrent transformer [16], and RED [38], a recurrent CNN. ASTMNet [25] utilizes asynchronous attention embedding and incorporates recurrent layers in deeper layers, claiming comparable results on both datasets. However, it is not open source. Feedforward methods are grouped into graph-based methods NVS-S [26], AEGNN [46] and EAGR [15], sparse method AsyNet [32], spiking method Spiking DenseNet [8], and finally feedforward dense methods Events+RetinaNet [38], Events+SSD [19] Events+RRC [6], and Events+YOLOv3 [20] which use events as input, and use the RetinaNet [27], SSD [29], RRC [43] or YOLOv3 [42] detector respectively.",
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+    {
+        "type": "text",
+        "text": "We compare these methods to our best-performing YOLOv6 detector from Sec. 4.2 with a SwinV2 transformer backbone trained on various input representations. These include the ones analyzed in Sec. 4.2, i.e. the 2D Histogram, Time Surface, TORE, Voxel Grid, and MDES, as well as the optimized representation ERGO-12. Note that these methods do not include data augmentation. We also trained our model with Mixup and Mosaic augmentation from [24], and is indicated by an asterisk * in Tab. 1.",
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+        "type": "text",
+        "text": "Results On the Gen1 dataset, we see that YOLOv6 with the SWINv2 backbone and ERGO-12 input and data augmentation outperforms all state-of-the-art methods by up to  $2.9\\%$  mAP by achieving an mAP of 0.504. The runner-up is RVT-B, which uses a recurrent vision transformer. Even without data augmentation, our network with ERGO-12 achieves 0.493, which improves the mAP by  $2.1\\%$  compared to RVT-B. Compared to the other feed-forward methods based on YOLOv6, ERGO-12 achieves an 0.3 mAP higher mAP, the next best being YOLOv6 with Time Surface [22] with 0.490. Interestingly, as indicated in Fig. 1 (b), the difference in mAP performance between ERGO-12 and Time Surface is 1.8 mAP on the validation set of the Gen1 dataset, which is substantially larger than on the test set.",
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+    {
+        "type": "text",
+        "text": "On 1 Mpx, the best-performing method is ASTMNet with an mAP of 0.483, followed by RVT-B with 0.474. From the feed-forward methods YOLOv6 with ERGO-12 and data augmentation achieves the highest score with 0.406, outperforming runner-up method YOLOv6 with Time Surfaces by  $2.3\\%$  mAP. Even without augmentation, ERGO-12 achieves a  $1.7\\%$  higher score than YOLOv6 with Time Surfaces. Compared to state-of-the-art feed-forward methods, ERGO-12 with data augmentation achieves a  $6.0\\%$  higher score, the runner-up being Events+YOLOv3 with 0.346. On this dataset, recurrent methods are known to perform better since many sequences include stops or slow-motion scenarios. This is challenging for feed-forward methods since they are not able to maintain long-term memory. In general, the improvement of ERGO-12 on 1 Mpx is higher compared to Gen1.",
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+    {
+        "type": "text",
+        "text": "4.4. Object Classification",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As an additional task, we investigate the relationship between GWD and the object classification task performance using the ResNet-34 [17] backbone classifier, pre-trained on ImageNet [44], while changing the input convolution to be compatible with  $N_{c} = 12$  channel",
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+    {
+        "type": "page_number",
+        "text": "12853",
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+    {
+        "type": "table",
+        "img_path": "images/1df5a8d317bf6fc876ff24f00c68122c92ecefffb0c50559dac1eb211d6ef826.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Representation</td><td>Description</td><td># of Channels</td><td>Accuracy(%)</td></tr><tr><td>2D Histogram</td><td>Positive and negative event counts</td><td>2</td><td>46.10</td></tr><tr><td>Time Surface</td><td>A hierarchy of event-based time-surfaces</td><td>12</td><td>57.58</td></tr><tr><td>TORE</td><td>Time-ordered recent event volumes</td><td>12</td><td>54.64</td></tr><tr><td>Voxel Grid</td><td>Voxelized grid with bilinear voting aggregation</td><td>12</td><td>52.40</td></tr><tr><td>MDES</td><td>Mixed density event stack</td><td>12</td><td>53.30</td></tr><tr><td>ERGO-12</td><td>Event representation from GWD optimization</td><td>12</td><td>61.40</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Mini N-ImageNet validation accuracy evaluated on various event representations.",
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+    {
+        "type": "text",
+        "text": "representations. We use the large-scale neuromorphic variant of the ImageNet dataset [44], captured from an event camera that observes monitor-displayed images from ImageNet. Event sequences were recorded using the  $480 \\times 640$  resolution Samsung DVS Gen3 event camera [49]. We report the GWD computed over the validation set of the Gen1 dataset. Subsequently, we train the model on Mini N-ImageNet. We opt for GWD on the Gen1 dataset to show the generalization capability of GWD across diverse datasets.",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Representations: Excluding the learned representation, we evaluate using identical representations as in object detection. Each representation is computed over 12 channels, except for the 2D Histogram, which uses two channels.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Training Details: Adopting the methodology from the N-ImageNet study [21], all inputs are resized to a  $224 \\times 224$  dimension, optimizing GPU memory and inference duration. Training is initialized from scratch with a learning rate set at  $3 \\cdot 10^{-4}$  and spans 100 epochs. The Adam optimizer with a Nesterov momentum of 0.9 and a weight decay of 0.0001 is used alongside a batch size of 64.",
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+    },
+    {
+        "type": "text",
+        "text": "Results: Table 2 summarizes the results of the experiments. There is a clear correlation between the GWD (even on different datasets, in this case, Gen1) and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all tested representations on the Mini N-ImageNet dataset. We obtained the following validation set accuracies: 2D Histogram  $(46.10\\%)$ , Time Surface  $(57.58\\%)$ , TORE  $(54.64\\%)$ , Voxel Grid  $(52.40\\%)$ , MDES  $(53.30\\%)$ , ERGO-12  $(61.4\\%)$ . Their ranking is consistent with the GWD ranking in Fig. 5. Therefore, the GWD can be used also for classification.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "State-of-the-art event-based deep learning methods typically need to convert raw events into dense input representations before they can be processed by standard net",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "works. However, selecting this representation is very expensive since it requires training a separate neural network for each representation and comparing the validation scores. In this work, we circumvent this bottleneck by measuring the quality of event representations with the Gromov Wasserstein Discrepancy (GWD), which is 200 times faster to compute. We validated extensively on multiple tasks, datasets and neural network backbones that the performance of neural networks trained with a representation correlates with its GWD. We then used this metric to, for the first time, optimize over a large family of representations, revealing a new, powerful representation, ERGO-12. With it, we outperform state-of-the-art representations by  $1.9\\mathrm{mAP}$  on the 1 Mpx dataset and  $0.3\\mathrm{mAP}$  on the Gen1 dataset, two object detection benchmarks. We also exceed existing representation by  $3.8\\%$  on the tasks of classification. Moreover, we even outperform the state-of-the-art by  $2.1\\mathrm{mAP}$  on Gen1 and state-of-the-art feed-forward methods by  $6.0\\mathrm{mAP}$  on the 1 Mpx dataset. This work thus opens a new unexplored field of explicit representation optimization that will push the limits of event-based learning methods.",
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+    {
+        "type": "text",
+        "text": "6. Acknowledgment",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work was supported by the Swiss National Science Foundation through the National Centre of Competence in Research (NCCR) Robotics (grant number 51NF40_185543), and the European Research Council (ERC) under grant agreement No. 864042 (AGILE-FLIGHT).",
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+        "text": "12854",
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+    {
+        "type": "text",
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+        ],
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+        "sub_type": "ref_text",
+        "list_items": [
+            "[44] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Fei-Fei Li. ImageNet large scale visual recognition challenge. Int. J. Com. Vis., 115(3):211-252, Apr. 2015. 8, 9",
+            "[45] Salem Said, Lionel Bombrun, Yannick Berthoumieu, and Jonathan H. Manton. Riemannian gaussian distributions on the space of symmetric positive definite matrices. IEEE Trans. Inf. Theory, 63(4):2153-2170, 2017. 4",
+            "[46] Simon Schaefer, Daniel Gehrig, and Davide Scaramuzza. AEGNN: Asynchronous event-based graph neural networks. 2022. 2, 8",
+            "[47] Yusuke Sekikawa, Kosuke Hara, and Hideo Saito. EventNet: Asynchronous recursive event processing. In Conference of Computer Vision and Pattern Recognition (CVPR), 2019. 2",
+            "[48] Amos Sironi, Manuele Brambilla, Nicolas Bourdis, Xavier Lagorce, and Ryad Benosman. HATS: Histograms of averaged time surfaces for robust event-based object classification. In Conference of Computer Vision and Pattern Recognition (CVPR), pages 1731-1740, 2018. 2",
+            "[49] Bongki Son, Yunjae Suh, Sungho Kim, Heejae Jung, Jun-Seok Kim, Changwoo Shin, Keunj Park, Kyoobin Lee, Jinman Park, Jooyeon Woo, Yohan Roh, Hyunku Lee, Yibing Wang, Ilia Ovsiannikov, and Hyunsurk Ryu. A 640x480 dynamic vision sensor with a  $9\\mu \\mathrm{m}$  pixel and 300Meps addres-event representation. In IEEE Intl. Solid-State Circuits Conf. (ISSCC), 2017. 9",
+            "[50] Lin Wang, S. Mohammad Mostafavi I., Yo-Sung Ho, and Kuk-Jin Yoon. Event-based high dynamic range image and very high frame rate video generation using conditional generative adversarial networks. Conference of Computer Vision and Pattern Recognition (CVPR), June 2019. 2, 3, 5",
+            "[51] Bo Zhao, Ruoxi Ding, Shoushun Chen, Bernabe Linares-Barranco, and Huajin Tang. Feedforward categorization on AER motion events using cortex-like features in a spiking neural network. IEEE Trans. Neural Netw. Learn. Syst., 26(9):1963-1978, Sept. 2015. 2",
+            "[52] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. EV-FlowNet: Self-supervised optical flow estimation for event-based cameras. In Robotics: Science and Systems (RSS), 2018. 2",
+            "[53] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based learning of optical flow, depth, and egomotion. In Conference of Computer Vision and Pattern Recognition (CVPR), 2019. 2, 3, 5, 6"
+        ],
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+        "text": "12856",
+        "bbox": [
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+            945,
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+            955
+        ],
+        "page_idx": 10
+    }
+]
\ No newline at end of file
diff --git a/2023/From Chaos Comes Order_ Ordering Event Representations for Object Recognition and Detection/d3f1e4dc-e3b8-48be-905a-0246e42863b1_model.json b/2023/From Chaos Comes Order_ Ordering Event Representations for Object Recognition and Detection/d3f1e4dc-e3b8-48be-905a-0246e42863b1_model.json
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index 0000000000000000000000000000000000000000..a1c574e80c4bb79bd7107ca59ad4a8e2839e7792
--- /dev/null
+++ b/2023/From Chaos Comes Order_ Ordering Event Representations for Object Recognition and Detection/d3f1e4dc-e3b8-48be-905a-0246e42863b1_model.json	
@@ -0,0 +1,2323 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.044
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.13,
+                0.131,
+                0.842,
+                0.177
+            ],
+            "angle": 0,
+            "content": "From Chaos Comes Order: Ordering Event Representations for Object Recognition and Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.165,
+                0.204,
+                0.283,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Nikola Zubić*"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.323,
+                0.204,
+                0.445,
+                0.222
+            ],
+            "angle": 0,
+            "content": "Daniel Gehrig*"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.478,
+                0.204,
+                0.605,
+                0.222
+            ],
+            "angle": 0,
+            "content": "Mathias Gehrig"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.644,
+                0.204,
+                0.804,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Davide Scaramuzza"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.223,
+                0.227,
+                0.748,
+                0.246
+            ],
+            "angle": 0,
+            "content": "Robotics and Perception Group, University of Zurich, Switzerland"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.277,
+                0.506,
+                0.426
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.235,
+                0.429,
+                0.375,
+                0.442
+            ],
+            "angle": 0,
+            "content": "(a) Method overview"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.281,
+                0.861,
+                0.423
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.564,
+                0.428,
+                0.815,
+                0.443
+            ],
+            "angle": 0,
+            "content": "(b) GW Discrepancy vs. Performance"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.449,
+                0.895,
+                0.556
+            ],
+            "angle": 0,
+            "content": "Figure 1: Selecting dense event representations for deep neural networks is exceedingly slow since it involves training a neural network for each representation and selecting the best one based on the validation score. In this work, we eliminate this bottleneck by selecting the representation based on the Gromov-Wasserstein Discrepancy (GWD) on the validation set (a). This metric is 200 times faster to compute and preserves the task performance ranking of event representations across multiple representations, network backbones, datasets and tasks (b, showing object detection performance on the Gen1 [9] dataset). We use it to, for the first time, perform a hyperparameter search on a large family of event representations, revealing new and powerful event representations that exceed the state-of-the-art."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.571,
+                0.314,
+                0.587
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.603,
+                0.474,
+                0.876
+            ],
+            "angle": 0,
+            "content": "Today, state-of-the-art deep neural networks that process events first convert them into dense, grid-like input representations before using an off-the-shelf network. However, selecting the appropriate representation for the task traditionally requires training a neural network for each representation and selecting the best one based on the validation score, which is very time-consuming. This work eliminates this bottleneck by selecting representations based on the Gromov-Wasserstein Discrepancy (GWD) between raw events and their representation. It is about 200 times faster to compute than training a neural network and preserves the task performance ranking of event representations across multiple representations, network backbones, datasets, and tasks. Thus finding representations with high task scores is equivalent to finding representations with a low GWD. We use this insight to, for the first time, perform a hyperparameter search on a large family of event representations, revealing new and powerful representations that exceed the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.572,
+                0.895,
+                0.71
+            ],
+            "angle": 0,
+            "content": "state-of-the-art. Our optimized representations outperform existing representations by 1.7 mAP on the 1 Mpx dataset and 0.3 mAP on the Gen1 dataset, two established object detection benchmarks, and reach a \\(3.8\\%\\) higher classification score on the mini N-ImageNet benchmark. Moreover, we outperform state-of-the-art by 2.1 mAP on Gen1 and state-of-the-art feed-forward methods by 6.0 mAP on the 1 Mpx datasets. This work opens a new unexplored field of explicit representation optimization for event-based learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.755,
+                0.682,
+                0.771
+            ],
+            "angle": 0,
+            "content": "Multimedia Material"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.782,
+                0.889,
+                0.813
+            ],
+            "angle": 0,
+            "content": "For open-source code please visit https://github. com/uzh-rpg/eventRepresentation_study."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.83,
+                0.633,
+                0.845
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.856,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Event cameras are biologically inspired vision sensors that function in a fundamentally distinct way [12]. Unlike traditional cameras that capture images at a fixed rate,"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.205,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Equal contribution"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "12846"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "these cameras measure brightness changes independently for each pixel, and these changes are referred to as events. The events encode the time, location, and polarity (sign) of the brightness changes. Event cameras offer several advantages over frame-based cameras, including exceptionally high temporal resolution (in the order of \\(\\mu\\)s), a high dynamic range, and low power consumption. Their numerous benefits make them attractive for a wide range of applications like robotics, autonomous vehicles, and virtual reality. However, due to their sparse and asynchronous nature, applying classical computer vision algorithms remains challenging."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.276,
+                0.473,
+                0.488
+            ],
+            "angle": 0,
+            "content": "Many state-of-the-art deep learning models address this challenge by converting sparse and asynchronous events into dense grid-like representations before processing them with off-the-shelf deep neural networks. By using these networks, methods like this enjoy the advantages of mature learning algorithms and network architectures, and optimized hardware, but we need to make a non-trivial choice of event representation. In fact, the computer vision and robotics fields are witnessing a surge in the number of research papers utilizing event-based vision, resulting in a plethora of new event representations being proposed. Despite this, extensive comparisons of these representations remain rare, making it unclear whether these newer representations should be adopted."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.491,
+                0.473,
+                0.598
+            ],
+            "angle": 0,
+            "content": "No efficient methodology exists for comparing these representations. Conventionally, comparing event representations involves training a fixed deep-learning model for each event representation separately and subsequently selecting the optimal one based on a validation score. This process is very time-intensive since it requires network training in the loop which often takes hours or days (Fig. 1 a top)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.6,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this work, we propose a fast method to compare event representations which circumvents the need to train a neural network and instead computes the Gromov-Wasserstein Discrepancy (GWD) between the raw events and event representation (Fig. 1 a bottom). This metric effectively measures the distortion that is introduced through converting raw events to representations and thus puts an upper bound on the amount of information that can be accessed by downstream neural networks. We show extensive experimental evidence, that this metric preserves the task-performance ranking across a wide range of input representations for several datasets, neural network backbones and tasks (Fig. 1 b). Due to its low computational cost, we apply the GWD to, for the first time, explicitly optimize over a large family of event representations, which reveals a new and powerful representation, which we term 12-channel Event Representation through Gromov-Wasserstein Optimization (ERGO-12). For the task of object detection, networks trained with these representations outperform other representations by \\(1.9\\mathrm{mAP}\\) on the 1 Mpx dataset and \\(0.3\\mathrm{mAP}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.213
+            ],
+            "angle": 0,
+            "content": "on Gen1, even outperforming state-of-the-art methods by \\(2.1\\mathrm{mAP}\\) on Gen1 and state-of-the-art feed-forward methods by \\(6.0\\mathrm{mAP}\\) on the 1 Mpx dataset. On object recognition, we instead find that our representation outperforms state-of-the-art representations by \\(3.8\\%\\). We believe that the GWD is a powerful tool that opens up a new research field that searches for optimized event representations. Our contributions are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.22,
+                0.891,
+                0.265
+            ],
+            "angle": 0,
+            "content": "- We introduce a novel, efficient approach for comparing dense event representations using the Gromov-Wasserstein Discrepancy (GWD)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.27,
+                0.892,
+                0.33
+            ],
+            "angle": 0,
+            "content": "- We show extensive experimental evidence that it preserves the task performance ranking of neural networks trained with these representations across datasets, neural network backbones and tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.335,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "- We use it to, for the first time, conduct a hyperparameter search on a vast family of event representations, unveiling novel and powerful event representations that outperform the current state-of-the-art representations on the object detection and object classification task."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.22,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.423,
+                0.642,
+                0.438
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.448,
+                0.895,
+                0.78
+            ],
+            "angle": 0,
+            "content": "In the field of event-based vision, two primary groups of representations exist: sparse and dense. Methods that use sparse representations [35, 51, 23, 37] preserve the sparsity in the events but do not yet scale to more complex tasks due to a lack of specialized hardware and mature neural networks architectures. This frequently results in lower performance on downstream tasks. In contrast, dense representations [31, 48, 53, 50] offer improved performance since they can leverage mature machine learning algorithms and neural network architectures. Sparse representations, pioneered by asynchronous SNNs [35, 23, 37], are limited by the lack of specialized hardware and computationally efficient backpropagation algorithms. Point cloud encoders [47, 40, 11] have been used due to the spatio-temporal nature of event data, but can be computationally expensive and noisy. Graph neural networks [26, 46, 4, 3, 33, 10] are scalable and have achieved high performance on various vision tasks but are still less accurate than dense methods for event-based vision. In this study, we focus on dense event representations and aim to achieve better task performance by utilizing existing efficient learning algorithms that are appropriate for current hardware."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Early dense representations converted events to histograms [31], generated time surfaces [48] or combined both [52] while relying on standard neural network backbones to process them. However, these representations only capture a low-dimensional representation of events since they typically only use a few channels. Later approaches have tried to capture more event information by either computing higher-order moments [1] or stacking multiple time"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12847"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.159,
+                0.086,
+                0.817,
+                0.253
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.261,
+                0.895,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Figure 2: Overview of the Gromov-Wasserstein Discrepancy (GWD) between raw events and representations. Events \\(\\mathcal{E}\\) are converted to event representations, i.e. a set of features \\(\\mathcal{F}\\) at pixel locations \\(\\mathbf{x}\\). It is defined as the solution to an optimal transport problem which transports events pairs \\((e_i,e_k)\\) to feature pairs \\((f_{\\mathbf{x}_j},f_{\\mathbf{x}_l})\\) via transport plan \\(T_{ij},T_{kl}\\). If the transport plan preserves the similarities \\(C_{ik}^{e}\\) and \\(C_{jm}^{f}\\) between event and feature pairs, this results in a low GWD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.34,
+                0.473,
+                0.522
+            ],
+            "angle": 0,
+            "content": "windows of events [53]. These methods still stack events based on fixed time windows which is problematic when the event rate becomes too large or too small and lead to the introduction of stacking based on the number of events [50]. In parallel, a bio-inspired approach led to the introduction of Time Ordered Recent Event Volumes (TORE) [2], which aggregate events into queues. However, they are slow to compute and perform similarly to existing Voxel Grids [53]. Most recently, a powerful representation was proposed by Nam et al. [34], which divides events into multiple overlapping windows that halve the number of events at each stage, which are more robust during varying scene dynamics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.524,
+                0.473,
+                0.829
+            ],
+            "angle": 0,
+            "content": "Few papers study the effect of event representations on task performance. While [38] and [21] show small-scale ablation studies to select event representations, only Gehrig et al. [13] performed a large-scale investigation of event representations by training models on various inputs for multiple tasks. Their study demonstrated the advantages of splitting polarities and incorporating timestamps into representations, and it introduced a learnable representation. However, training for a single task was still computationally expensive, which limited the number of representations that could be compared. For this reason, their study did not cover a large number of representations, and in particular, did not consider different window sizes as is done in later work [50, 34], or more advanced aggregations and measurements like in [1]. Our method instead introduces an efficient metric to compare event representations that solves these limitations, allowing us to perform a search over a large family of event representations and go beyond the representations in [50, 1, 34, 14], including even non-differentiable hyperparameters."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.844,
+                0.169,
+                0.859
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this section, we will first introduce the preliminaries on computing event representations (Sec. 3.1) and then pro"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.341,
+                0.895,
+                0.402
+            ],
+            "angle": 0,
+            "content": "pose the metric we use to measure the discrepancy between events and their representation based on the GWD (Sec. 3.2) before concluding with Sec. 3.3 where we use Bayesian optimization to find an optimal event representation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.41,
+                0.642,
+                0.424
+            ],
+            "angle": 0,
+            "content": "3.1. Preliminaries"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.433,
+                0.894,
+                0.493
+            ],
+            "angle": 0,
+            "content": "Event cameras measure brightness changes as an asynchronous stream of events. Each event is triggered when the intensity \\( L(\\mathbf{u}) \\) at the pixel \\( \\mathbf{u} = (x, y) \\) changes by the contrast threshold \\( C \\) at time \\( t \\), and thus satisfies"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.504,
+                0.892,
+                0.521
+            ],
+            "angle": 0,
+            "content": "\\[\np \\left[ L (\\mathbf {u}, t) - L (\\mathbf {u}, t - \\Delta t) \\right] = C \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.53,
+                0.895,
+                0.635
+            ],
+            "angle": 0,
+            "content": "where \\(p\\in \\{-1,1\\}\\) is the polarity of the event, and \\(t - \\Delta t\\) is the time of the last event. Within a time window \\(\\Delta T\\) an event camera thus generates an ordered set of events \\(\\mathcal{E} = \\{e_k\\}_{k = 0}^{N_e - 1}\\), with each event \\(e_k = (\\mathbf{u}_k,t_k,p_k)\\in \\mathbb{R}^4\\). To bridge the gap between asynchronous events and dense neural networks, they are usually converted to a dense event representation"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.655,
+                0.636,
+                0.892,
+                0.652
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {R} = F (\\mathcal {E}), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.657,
+                0.895,
+                0.764
+            ],
+            "angle": 0,
+            "content": "which has features \\( f_{\\mathbf{x}} \\doteq \\mathcal{R}(\\mathbf{x}) \\in \\mathbb{R}^{N_f} \\) indexed by the integer-valued pixel location \\( \\mathbf{x} \\). The above representation thus generates a set of features \\( \\mathcal{F} = \\{f_{\\mathbf{x}}\\}_{\\mathbf{x} \\in \\Omega} \\), where \\( \\Omega \\) denotes the image domain and has size \\( |\\Omega| = N_f \\) with \\( N_f \\) being the number of pixels in the image. In what follows, we will derive a measure to quantify the distortion between events \\( \\mathcal{E} \\) and features \\( \\mathcal{F} \\) based on the GWD."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.772,
+                0.798,
+                0.789
+            ],
+            "angle": 0,
+            "content": "3.2. Gromov-Wasserstein Discrepancy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.894,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Converting raw events to a representation invariably distorts the events by removing important distinguishing features from the stream. We would like to measure this distortion since we expect it correlates strongly with a neural network's ability to extract features from these events. In what follows, we will derive a measure of this distortion rate based on the GWD."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12848"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.305
+            ],
+            "angle": 0,
+            "content": "We show an overview of the GWD in Fig. 2. We start by measuring the similarity between a set of events and their representation by building a soft correspondence between events \\( e_i \\) and features \\( f_{\\mathbf{x}_j} \\), which we denote as \\( T_{ij}^1 \\). This transport plan effectively moves each event to a corresponding feature, thereby distorting the original set and destroying information. Importantly, such a plan can be interpreted as follows: We transport the events with a total weight of 1, i.e. per-event weight \\( \\frac{1}{N_e} \\) to the output features, which also need to receive a total weight of 1 or per-feature weight of \\( \\frac{1}{N_f} \\). By this construction, \\( T_{ij} \\) needs to satisfy \\( \\sum_i T_{ij} = 1 / N_f \\) and \\( \\sum_j T_{ij} = 1 / N_e \\). This means that a total weight of \\( 1 / N_e \\) moves from each event, and each feature receives a total weight of \\( 1 / N_f \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.306,
+                0.474,
+                0.52
+            ],
+            "angle": 0,
+            "content": "In the next step, we measure the distortion introduced by this transportation plan by considering pairwise similarities of input events and features. Let \\( e_i, e_k \\in \\mathcal{E} \\) be a pair of events and \\( f_{\\mathbf{x}_j}, f_{\\mathbf{x}_l} \\in \\mathcal{F} \\) pair of features, with similarity scores \\( C_{ik}^e \\doteq C^e(e_i, e_k) \\) and \\( C_{jl}^f \\doteq C^f(f_{\\mathbf{x}_j}, f_{\\mathbf{x}_l}) \\) between events and features respectively. Next, consider how the transport plan \\( T \\) acts on these pairs: Generally, a weight \\( T_{ij} \\) is moved from event \\( e_i \\) to feature \\( f_{\\mathbf{x}_j} \\). Similarly, the weight \\( T_{kl} \\) is moved from event \\( e_k \\) to feature \\( f_{\\mathbf{x}_l} \\). Ideally, such a transport plan should preserve the similarity between pairs of source events and target features, and thus the difference in similarity scores between pairs \\( (i, k) \\) and \\( (j, l) \\) can be used as a measure of distortion. For each event pair and feature pair, we define the distortion as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.18,
+                0.53,
+                0.47,
+                0.551
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {i j k l} = T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.56,
+                0.47,
+                0.608
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}\\) denotes some disparity measurement between \\(C_{ik}^{e}\\) and \\(C_{jl}^{f}\\). Summing over all possible pairs of events and features we thus arrive at the transportation cost:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.619,
+                0.47,
+                0.652
+            ],
+            "angle": 0,
+            "content": "\\[\nL (T; \\mathcal {E}, \\mathcal {F}) = \\sum_ {i, j, k, l} L _ {i j k l} = \\sum_ {i, j, k, l} T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right) \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.663,
+                0.449,
+                0.679
+            ],
+            "angle": 0,
+            "content": "Minimizing over transport plans, we arrive at the GWD:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.137,
+                0.689,
+                0.47,
+                0.723
+            ],
+            "angle": 0,
+            "content": "\\[\nL (\\mathcal {E}, \\mathcal {F}) = \\min  _ {T} \\sum_ {i, j, k, l} T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.733,
+                0.47,
+                0.78
+            ],
+            "angle": 0,
+            "content": "which can be optimized efficiently using [39]. Since the above metric is defined for a single time window of events, we may average it over multiple samples to find:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.176,
+                0.79,
+                0.47,
+                0.825
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {G W D} _ {N} = \\frac {1}{N} \\sum_ {i} L \\left(\\mathcal {E} _ {i}, \\mathcal {F} _ {i}\\right). \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.836,
+                0.47,
+                0.866
+            ],
+            "angle": 0,
+            "content": "\\(\\mathrm{GWD}_N\\) can be interpreted as an average distortion rate from raw events to event representations. In Sec. 4.2, we"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>In the optimal transport literature, this correspondence is also called a transport plan."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.181
+            ],
+            "angle": 0,
+            "content": "show that \\(\\mathrm{GWD}_N\\) correlates with a \\(NN\\)'s performance with that representation across network backbones, datasets, and event representations. It's also efficient to compute, taking 9 seconds for 50,000 events. In what follows, \\(\\mathrm{GWD}_N\\) will denote the average over \\(N\\) samples, while GWD denotes the average over the whole validation set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.182,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "Similarity scores and distortion function As similarity scores, we choose Gaussian radial basis functions [45] for both events and image features. In detail,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.56,
+                0.236,
+                0.892,
+                0.27
+            ],
+            "angle": 0,
+            "content": "\\[\nC _ {i k} ^ {e} = e ^ {\\frac {- \\| e _ {i} - e _ {k} \\| ^ {2}}{2 h ^ {2} \\sigma_ {e} ^ {2}}}, \\quad C _ {j l} ^ {f} = e ^ {\\frac {- \\| f _ {\\mathbf {x} _ {j}} - f _ {\\mathbf {x} _ {l}} \\| ^ {2}}{2 h ^ {2} \\sigma_ {f} ^ {2}}} \\tag {7}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.511,
+                0.299,
+                0.892,
+                0.324
+            ],
+            "angle": 0,
+            "content": "\\[\n\\sigma_ {e} ^ {2} = \\underset {i <   j} {\\operatorname {m e a n}} \\| e _ {i} - e _ {j} \\| ^ {2}, \\quad \\sigma_ {f} ^ {2} = \\underset {i <   j} {\\operatorname {m e a n}} \\| f _ {\\mathbf {x} _ {i}} - f _ {\\mathbf {x} _ {j}} \\| ^ {2}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.332,
+                0.892,
+                0.453
+            ],
+            "angle": 0,
+            "content": "with a bandwidth parameter \\( h = 0.7 \\). The selection of data-dependent variances normalizes the distances between pairs of events and features such that the similarity score is robust to the dimensionality of the data and the number of samples in the source and target domain. These details are discussed in [7, 45, 36]. While more complex similarity scores could be used, this simple function already achieved good results. As the distortion function, we chose the KL-Divergence i.e."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.577,
+                0.463,
+                0.892,
+                0.489
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right) = C _ {i k} ^ {e} \\log \\left(C _ {i k} ^ {e} / C _ {j l} ^ {f}\\right). \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.892,
+                0.553
+            ],
+            "angle": 0,
+            "content": "As a result, the optimization already rejects terms for which \\( C_{ik}^{e} \\approx 0 \\), i.e. pairs of events that are far apart. We found that this property was also beneficial in improving the convergence of the optimization problem in Eq. (5)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.553,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Improving Convergence of Eq. (5). We found that three features improved convergence and speed up the optimization: (i) Normalization of the event coordinates and timestamps by the sensor size and time window respectively, (ii) Concatenation of the normalized pixel position to the image features, and (iii) Sparsification of image features. Both (i) and (ii) make the optimization more numerically stable. In fact, without concatenating position information to image features, randomly pixel-wise shuffled event representations would retain the same GWD, although intuitively, neural networks would have a harder time learning from such representations since they typically process nearby features together. Thus reintroducing the position removes this ambiguity and improves the convergence. Finally, (iii) removes image features with \\( \\| f_{\\mathbf{x}} \\| = 0 \\) since these correspond to pixels where no events were triggered. This step significantly sped up computation by reducing the size of the pair-wise similarity score matrix \\( C^f \\), with a small impact on convergence."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.838,
+                0.864
+            ],
+            "angle": 0,
+            "content": "3.3. Optimizing over Event Representations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "With a fast method to measure the effectiveness of an event representation, we can now search for the optimal rep"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12849"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.156,
+                0.087,
+                0.813,
+                0.238
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.24,
+                0.895,
+                0.288
+            ],
+            "angle": 0,
+            "content": "Figure 3: Overview of the hyperparameters we use to construct an event representation (right). For each channel \\( c \\), we select one of several event time windows \\( w_{c} \\in \\mathcal{W} \\) (in color, left), measurement functions \\( m_{c} \\in \\mathcal{M} \\) (timestamp, polarity, positive timestamps, etc.), and aggregation functions \\( a_{c} \\in \\mathcal{A} \\) (max, mean, sum, variance), resulting in \\( 3N_{c} \\) parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.3,
+                0.471,
+                0.332
+            ],
+            "angle": 0,
+            "content": "resentation by minimizing Eq. (6) over a space of possible representations with a set of hyperparameters \\( p \\)."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.155,
+                0.342,
+                0.47,
+                0.378
+            ],
+            "angle": 0,
+            "content": "\\[\np ^ {*} = \\arg \\min  _ {p} \\frac {1}{N} \\sum_ {i} L \\left(\\mathcal {E} _ {i}, \\mathcal {F} _ {i} (p)\\right). \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.388,
+                0.47,
+                0.478
+            ],
+            "angle": 0,
+            "content": "To simplify this optimization, we first describe a very general parametrization, which defines a large family of event representations, extending the family described in [13] in a few ways. These hyperparameters are a small set of categorical variables which can subsequently be optimized using Bayesian optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.479,
+                0.471,
+                0.601
+            ],
+            "angle": 0,
+            "content": "Parametrization of Event Representations We illustrate the hyperparameters in Fig. 3. In general, we assume an event representation comprises a stack of features, indexed by \\( c \\) (right side), each of which is derived from \\( (i) \\) a specific time window \\( w_{c} \\) of events, \\( (ii) \\) a specific measurement \\( m_{c} \\) of events such as polarity or timestamps, and \\( (iii) \\) a specific aggregation \\( a_{c} \\), such as summation or averaging. We write such a representation as \\( N_{c} \\) concatenated feature maps:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.211,
+                0.612,
+                0.469,
+                0.629
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {R} = \\left[ \\mathcal {R} _ {0} \\mid \\mathcal {R} _ {1} \\dots \\mid \\mathcal {R} _ {N _ {c} - 1} \\right] \\tag {11}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.173,
+                0.631,
+                0.469,
+                0.647
+            ],
+            "angle": 0,
+            "content": "\\[\n\\text {w i t h} \\mathcal {R} _ {c} = a _ {c} \\left(m _ {c} \\left(w _ {c} (\\mathcal {E})\\right)\\right) \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.659,
+                0.469,
+                0.72
+            ],
+            "angle": 0,
+            "content": "Here \\( w_{c} \\) is a windowing function which selects events within an interval, \\( m_{c} \\) is the measurement function which selects an event feature, and \\( a_{c} \\) is the aggregation function, which aggregates measurements into a single feature map."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Note, in our formulation each channel can have an independent set of parameters, different to [13], which assumes a shared aggregation and measurement function for all channels. This makes our parametrization substantially more expressive than the one in [13]. The number of (non-learnable) representations is \\(\\left(|\\mathcal{A}||\\mathcal{M}||\\mathcal{W}|\\right)^{N_c}\\approx 3.21\\times 10^{27}\\), since each channel can be configured independently. Moreover, while \\(a_{c}\\) and \\(m_{c}\\) were already discussed in [13], the windowing function is a more general concept, illustrated in Fig. 3 (left). While these windows can be non-overlapping \\((w_{3},w_{4},w_{2})\\), as for Voxel Grids [53], they can also be overlapping, \\((w_{0},w_{1},w_{2})\\) as in Mixed"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.3,
+                0.895,
+                0.391
+            ],
+            "angle": 0,
+            "content": "Density Event Stacks [34], or describe windows of a constant event count or constant time [50] In this work we allow each feature channel to select from a basis of windows \\(\\mathcal{W} = \\{[t_{0,k}, t_{1,k}]\\}_{k=0}^{N_k-1}\\), which can combine all types of windows unifying these concepts. In summary, a representation is parametrized by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.645,
+                0.402,
+                0.891,
+                0.421
+            ],
+            "angle": 0,
+            "content": "\\[\np = \\left\\{\\left(w _ {c}, a _ {c}, m _ {c}\\right) \\right\\} _ {c = 0} ^ {N _ {c} - 1} \\tag {13}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.423,
+                0.813,
+                0.438
+            ],
+            "angle": 0,
+            "content": "\\[\n\\text {w i t h} \\quad m _ {c} \\in \\mathcal {M}, a _ {c} \\in \\mathcal {A}, w _ {c} \\in \\mathcal {W}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.453,
+                0.892,
+                0.603
+            ],
+            "angle": 0,
+            "content": "For the sets of aggregation functions we select \\(\\mathcal{A} = \\{\\max, \\text{sum}, \\text{mean}, \\text{variance}\\}\\) and for the measurement functions \\(\\mathcal{M} = \\{t_{+}, t_{-}, t, p, c_{+}, c_{-}, c\\}\\) which are most commonly used. Here \\(c, p,\\) and \\(t\\) denote event count (discarding polarity), polarity, and timestamp. The subscripts \\(+ / -\\) select only positive or negative events. For the basis of time windows, we select three equally spaced, non-overlapping windows from [53] and four overlapping windows from [34], including the global window. These are illustrated in Fig. 7 (right)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.604,
+                0.893,
+                0.815
+            ],
+            "angle": 0,
+            "content": "Optimization Procedure The aforementioned parametrization generates redundant combinations that can be obtained by permuting channels or selecting the same feature for different channels. To address this issue and expedite convergence, we propose a stage-wise optimization procedure. Initially, we start with a volume consisting of zeros with \\( N_{c} \\) channels and optimize over \\( a_0, w_0 \\), and \\( m_0 \\) to fill in the first channel. Next, we optimize the feature for the second channel while keeping the first fixed. With this iterative process, we incrementally fill up the representation, avoiding the selection of redundant representations and resulting in faster optimization. At each stage, we use Gryffin [18], a specialized Bayesian optimizer for categorical variables."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.83,
+                0.634,
+                0.848
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In Sec. 4.1, we first connect the GWD and event distortion, demonstrating its behavior on several toy examples. Next, in Sec. 4.2, we showcase the correlation between the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "12850"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.097,
+                0.088,
+                0.452,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.295,
+                0.471,
+                0.372
+            ],
+            "angle": 0,
+            "content": "Figure 4: Validation of our metric on the Gen1 validation set. (top) Our metric for Voxel Grids [53] and Mixed-Density Event Stacks [34] with an increasing number of channels. (bottom) Effect of applying Gaussian blur with different blur kernels to the event representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.385,
+                0.47,
+                0.462
+            ],
+            "angle": 0,
+            "content": "metric and task performance across multiple tasks, datasets, backbones, and representations. Lastly, in Sec. 4.3, we show the outcome of Bayesian Optimization on the GWD and offer insights on the acquired event representation before comparing it against the state-of-the-art."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.469,
+                0.216,
+                0.485
+            ],
+            "angle": 0,
+            "content": "4.1. Toy Example"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.492,
+                0.47,
+                0.627
+            ],
+            "angle": 0,
+            "content": "As explained in Sec. 3.2, the GWD measures the distortion rate from raw events to event representation. Two experiments were designed to test this claim: (1) analyzing the behavior of the metric when varying the number of bins in Voxel Grid [53] and Mixed-Density Event Stack (MDES) [34] representations, and (2) blurring the event representation with increasing standard deviations before measuring the GWD. We perform experiments on the validation set of Gen1[9] and report the results in Fig. 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.628,
+                0.471,
+                0.779
+            ],
+            "angle": 0,
+            "content": "Fig. 4 (top) confirms that the GWD decreases as the number of channels increases in both Voxel Grids and Mixed-Density Event Stacks, which aligns with our intuition that using more channels preserves more information from raw events, resulting in a lower distortion rate. Similarly, the bottom part illustrates that with a growing blur radius, more edges in the event representation are removed, leading to an increase in the GWD. This verifies that the GWD measures the distortion from raw events to event representations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.787,
+                0.245,
+                0.803
+            ],
+            "angle": 0,
+            "content": "4.2. Object Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Next, we investigate the relationship between GWD and the task performance of a \\(NN\\) trained for object detection. We choose two widely used object detection datasets, the Gen1 [9] and 1 Mpx [38] Automotive Detection Dataset, which both deal with event streams featuring labeled bounding boxes for pedestrians, cars, and other vehicles. While"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.52,
+                0.091,
+                0.885,
+                0.237
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.52,
+                0.239,
+                0.885,
+                0.378
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.381,
+                0.892,
+                0.457
+            ],
+            "angle": 0,
+            "content": "Figure 5: Correlation of the Gromov-Wasserstein Discrepancy with the mAP (higher is better) for object detection on the Gen1 [9] (top) and 1 Mpx [38] (bottom) datasets. Note the spliced y-axis on 1 Mpx, due to the high GWD of the 2D Histogram."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.463,
+                0.893,
+                0.659
+            ],
+            "angle": 0,
+            "content": "the former has a resolution of \\(304 \\times 240\\), the latter has a resolution of \\(1280 \\times 720\\). We report the GWD computed over the validation set of each dataset and then train an off-the-shelf object detection framework based on YOLOv6 [24], pre-trained on the Microsoft Common Objects in Context (MS-COCO) [28], on different input representations as in [13]. To accommodate the varying number of channels, we replace the 3-channel input convolution with a \\(N_{c} = 12\\) channel input convolution, where \\(N_{c}\\) represents the number of channels in the representation. To show the generality of the result, we also vary the detection backbone between ResNet-50 [17], EfficientRep [24] and Swin Transformer V2 [30], and report results for each."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Representations: We test a range of common representations listed below. We compute 12 channels for each representation, except for the 2D Histogram, which has 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.892,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Voxel Grid: Here, the event time window is split into \\( N_{c} \\) equal, non-overlapping time windows, and then events in the same time window are aggregated by summing their polarity on a per-pixel basis using bilinear voting [53]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.826
+            ],
+            "angle": 0,
+            "content": "Mixed-Density Event Stack (MDES): For each channel \\( c \\), this representation selects the most recent \\( \\frac{N_e}{2^c} \\) events, where \\( N_e \\) are the events in the time window. For each window, it aggregates the polarity at that pixel [34]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Event Histograms: Events in the time window are split by polarity and then summed into two channels [31]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Time Surface: We convert events into time surfaces from [22] with a decay constant of \\(\\tau = 5\\mathrm{ms}\\). We then sample it at \\(\\frac{N_c}{2} = 6\\) equally spaced timestamps, once for"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12851"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.167
+            ],
+            "angle": 0,
+            "content": "positive and negative events resulting in \\( N_{c} = 12 \\) channels.  \nTORE: The Time-Ordered Recent Event Volumes store event timestamps in per-pixel queues. We use queues with capacity \\( \\frac{N_c}{2} = 6 \\), one for positive and one for negative events, and concatenate them to \\( N_{c} = 12 \\) channels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.168,
+                0.468,
+                0.242
+            ],
+            "angle": 0,
+            "content": "Learned representation: Event Spike Tensor (EST) [13] is a learnable event representation that employs a Quantization Layer featuring a trainable kernel. This approach enables the model to effectively transform raw events, optimizing their performance for a given task."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.243,
+                0.468,
+                0.363
+            ],
+            "angle": 0,
+            "content": "Training Details We adopt the training procedure from YOLOv6 [24]. For each backbone, representation, and dataset, we train for 100 epochs, using Stochastic Gradient Descent with Nesterov momentum increasing from 0.5 to 0.83 over the first 2 epochs. We use a batch size of 32, and a Cosine learning rate schedule, starting at 0.00323 and ending at 0.000387 after 100 epochs. We adopt the classification and box regression losses in [24]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.373,
+                0.468,
+                0.659
+            ],
+            "angle": 0,
+            "content": "Results: Figs. 5 summarizes the results of the above experiments. For both datasets, Gen1 and 1 Mpx, and all backbones, there is a clear correlation between the GWD and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all three network backbones. In particular, MDES with a Swin-V2 detection backbone consistently achieves the highest mAP with 0.43 on Gen1 and 0.39 on 1 Mpx. It also consistently achieves the lowest GWD with 0.38 on Gen1 and 0.40 on 1 Mpx. Utilizing the learnable EST in YOLOv6 with SwinV2 backbone, we achieved a 45.31 mAP score on the Gen1 validation set and a GWD score of 0.3552, positioning EST between MDES and ERGO-12 in Fig. 1b, confirming the expected ranking. We also see that the Swin V2 backbone outperforms other backbones on both datasets for all tested representations. We conclude that while the representation affects task performance, the neural network also has an influence. However, we see that the overall ranking of the representations is preserved."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.468,
+                0.886
+            ],
+            "angle": 0,
+            "content": "Using Fewer Samples While in the previous section, we reported the GWD over the validation set of the Gen1 and the 1 Mpx datasets, averaging this metric over such a large dataset still incurs a high computational cost and would make such a metric infeasible for optimization. Therefore, here we investigate if we can use smaller sample sizes to speed up the computation of GWD. In Fig. 6, we show the GWD for the representations in Sec. 4.2 while varying the number of samples. We see that as the sample number decreases, the mean values of the metric change, but the ranking between representations is still preserved reliably after around 100 samples, and thus we use \\(\\mathrm{GWD}_{100}\\) to optimize over representations. Below this number, the ranking of representations can fluctuate. However, we found that this happens due to a bad convergence of Eq. (5)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.087,
+                0.886,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Timing Results: We time the computation of the GWD"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.527,
+                0.109,
+                0.837,
+                0.293
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.298,
+                0.892,
+                0.328
+            ],
+            "angle": 0,
+            "content": "Figure 6: Gromov-Wasserstein Discrepancy for a varying number of samples from the validation set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.338,
+                0.892,
+                0.459
+            ],
+            "angle": 0,
+            "content": "over 100 samples of the Gen1 validation set, where each sample comprises 50,000 events. We run our experiment on an AMD EPYC 7702 32-core server-grade CPU with 32 GB RAM and achieve a runtime of 15 minutes. Note that computing the GWD does not require a GPU. By contrast, training the models in Fig. 5 requires 2 days on a single Tesla V100 GPU with 32 GB of memory, making GWD computation 192 times faster."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.469,
+                0.835,
+                0.485
+            ],
+            "angle": 0,
+            "content": "4.3. Optimization of Event Representations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.493,
+                0.891,
+                0.568
+            ],
+            "angle": 0,
+            "content": "Here we report the results of optimizing the event representation according to the procedure in Sec. 3.3. We optimize \\( N_{c} = 12 \\) channels, and at each optimization cycle for channel \\( c \\), the Bayesian Optimizer selects 100 configurations and then keeps the best-performing configuration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "We show the result of this optimization procedure in Fig. 7. The left shows how the GWD decreases as new channels are added to the representation. We see that after 2 channels, our method outperforms 2D Histograms, after 6 channels we outperform Time Surfaces, after 7 channels we outperform Voxel Grids / TORE, after 9 channels we outperform Mixed-Density Event Stacks and finally, after 12 channels, we achieve a \\(\\mathrm{GWD}_{100}\\) of 0.47. On the right, we show the different windows (columns) and measurement functions (rows) that are selected. We do not show the order since our representation is unique up to a random channel permutation. However, in the appendix, we show which features are selected at each stage. We see that all windows and all measurement functions are selected at least once, showing how our representation tries to diversify as much as possible. Moreover, timestamp-based measurements often show multiple aggregations, which we argue are necessary to replicate their complex continuous signal."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Comparison with State-of-the-Art Here we compare our method against state-of-the-art recurrent and feedforward methods on the Gen1 and 1 Mpx test sets. We summarize the results in Tab. 1. Recurrent methods in"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12852"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.115,
+                0.089,
+                0.55,
+                0.266
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.554,
+                0.089,
+                0.758,
+                0.245
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\"></td><td>\\( w_0 \\)</td><td>\\( w_1 \\)</td><td>\\( w_2 \\)</td><td>\\( w_3 \\)</td><td>\\( w_4 \\)</td><td>\\( w_5 \\)</td><td>\\( w_6 \\)</td></tr><tr><td rowspan=\"3\">t</td><td>+</td><td>sum</td><td>sum mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>-</td><td>sum</td><td>mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td>var max</td><td></td><td></td><td></td></tr><tr><td rowspan=\"3\">c</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>mean</td><td></td></tr><tr><td>-</td><td></td><td></td><td>sum</td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td></td><td>sum</td><td></td><td>sum</td></tr><tr><td colspan=\"2\">p</td><td></td><td></td><td></td><td>var</td><td></td><td></td><td></td></tr></table>"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.762,
+                0.089,
+                0.851,
+                0.246
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>tNe-1</td></tr><tr><td>w6</td></tr><tr><td>w5</td></tr><tr><td>w4</td></tr><tr><td>w3</td></tr><tr><td>w2</td></tr><tr><td>w1</td></tr><tr><td>w0</td></tr><tr><td>t0</td></tr></table>"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.276,
+                0.895,
+                0.309
+            ],
+            "angle": 0,
+            "content": "Figure 7: Gromov-Wasserstein Discrepancy for 100 samples (left). At each channel, a Bayesian optimizer selects the next best hyperparameter triple. The chosen hyperparameters are broken down by window and measurement function (right)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.317,
+                0.47,
+                0.48
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Event Repr.</td><td rowspan=\"2\">Recurrent</td><td colspan=\"2\">mAP↑</td></tr><tr><td>Gen1 [9]</td><td>1 Mpx [38]</td></tr><tr><td>MatrixLSTM+YOLOv3 [5]</td><td>MatrixLSTM</td><td>✓</td><td>0.310</td><td>-</td></tr><tr><td>E2VID+RetinaNet [41]</td><td>Reconstructions</td><td>✓</td><td>0.270</td><td>0.250</td></tr><tr><td>RED [38]</td><td>Voxel Grid</td><td>✓</td><td>0.400</td><td>0.430</td></tr><tr><td>RVT-B [16]</td><td>2D Histogram</td><td>✓</td><td>0.472</td><td>0.474</td></tr><tr><td>ASTMNet [25]</td><td>Asynchronous attention embedding</td><td>✓</td><td>0.467</td><td>0.483</td></tr><tr><td>Events+RetinaNet [38]</td><td>Voxel Grid</td><td>✗</td><td>0.340</td><td>0.180</td></tr><tr><td>Events+SSD [19]</td><td>2D Histogram</td><td>✗</td><td>0.301</td><td>0.340</td></tr><tr><td>Events+RRC [6]</td><td>2D Histogram</td><td>✗</td><td>0.307</td><td>0.343</td></tr><tr><td>Events+YOLOv3 [20]</td><td>2D Histogram</td><td>✗</td><td>0.312</td><td>0.346</td></tr><tr><td>AEGNN [46]</td><td>Graph</td><td>✗</td><td>0.163</td><td>-</td></tr><tr><td>EAGR [15]</td><td>Graph</td><td>✗</td><td>0.321</td><td>-</td></tr><tr><td>Spiking DenseNet [8]</td><td>Spike Train</td><td>✗</td><td>0.189</td><td>-</td></tr><tr><td>AsyNet [32]</td><td>2D Histogram</td><td>✗</td><td>0.145</td><td>-</td></tr><tr><td></td><td>2D Histogram</td><td>✗</td><td>0.339</td><td>0.327</td></tr><tr><td></td><td>Time Surface</td><td>✗</td><td>0.490</td><td>0.383</td></tr><tr><td></td><td>TORE</td><td>✗</td><td>0.436</td><td>0.381</td></tr><tr><td></td><td>Voxel Grid</td><td>✗</td><td>0.395</td><td>0.375</td></tr><tr><td></td><td>MDES</td><td>✗</td><td>0.427</td><td>0.378</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.493</td><td>0.400</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.504*</td><td>0.406*</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.488,
+                0.47,
+                0.518
+            ],
+            "angle": 0,
+            "content": "Table 1: Comparison of state-of-the-art event-based object detectors on the test sets of Gen1 [9] and 1 Mpx [38]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.523,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "clude MatrixLSTM+YOLOv3 [5], which uses a recurrent, learned input representation with a YOLOv3 [42] detector, E2VID+RetinaNet [41] which uses recurrent E2VID reconstructions with a RetinaNet [27] detector, RVT-B which uses a recurrent transformer [16], and RED [38], a recurrent CNN. ASTMNet [25] utilizes asynchronous attention embedding and incorporates recurrent layers in deeper layers, claiming comparable results on both datasets. However, it is not open source. Feedforward methods are grouped into graph-based methods NVS-S [26], AEGNN [46] and EAGR [15], sparse method AsyNet [32], spiking method Spiking DenseNet [8], and finally feedforward dense methods Events+RetinaNet [38], Events+SSD [19] Events+RRC [6], and Events+YOLOv3 [20] which use events as input, and use the RetinaNet [27], SSD [29], RRC [43] or YOLOv3 [42] detector respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We compare these methods to our best-performing YOLOv6 detector from Sec. 4.2 with a SwinV2 transformer backbone trained on various input representations. These include the ones analyzed in Sec. 4.2, i.e. the 2D Histogram, Time Surface, TORE, Voxel Grid, and MDES, as well as the optimized representation ERGO-12. Note that these methods do not include data augmentation. We also trained our model with Mixup and Mosaic augmentation from [24], and is indicated by an asterisk * in Tab. 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.322,
+                0.895,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Results On the Gen1 dataset, we see that YOLOv6 with the SWINv2 backbone and ERGO-12 input and data augmentation outperforms all state-of-the-art methods by up to \\(2.9\\%\\) mAP by achieving an mAP of 0.504. The runner-up is RVT-B, which uses a recurrent vision transformer. Even without data augmentation, our network with ERGO-12 achieves 0.493, which improves the mAP by \\(2.1\\%\\) compared to RVT-B. Compared to the other feed-forward methods based on YOLOv6, ERGO-12 achieves an 0.3 mAP higher mAP, the next best being YOLOv6 with Time Surface [22] with 0.490. Interestingly, as indicated in Fig. 1 (b), the difference in mAP performance between ERGO-12 and Time Surface is 1.8 mAP on the validation set of the Gen1 dataset, which is substantially larger than on the test set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.549,
+                0.895,
+                0.791
+            ],
+            "angle": 0,
+            "content": "On 1 Mpx, the best-performing method is ASTMNet with an mAP of 0.483, followed by RVT-B with 0.474. From the feed-forward methods YOLOv6 with ERGO-12 and data augmentation achieves the highest score with 0.406, outperforming runner-up method YOLOv6 with Time Surfaces by \\(2.3\\%\\) mAP. Even without augmentation, ERGO-12 achieves a \\(1.7\\%\\) higher score than YOLOv6 with Time Surfaces. Compared to state-of-the-art feed-forward methods, ERGO-12 with data augmentation achieves a \\(6.0\\%\\) higher score, the runner-up being Events+YOLOv3 with 0.346. On this dataset, recurrent methods are known to perform better since many sequences include stops or slow-motion scenarios. This is challenging for feed-forward methods since they are not able to maintain long-term memory. In general, the improvement of ERGO-12 on 1 Mpx is higher compared to Gen1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.802,
+                0.696,
+                0.817
+            ],
+            "angle": 0,
+            "content": "4.4. Object Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "As an additional task, we investigate the relationship between GWD and the object classification task performance using the ResNet-34 [17] backbone classifier, pre-trained on ImageNet [44], while changing the input convolution to be compatible with \\( N_{c} = 12 \\) channel"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "12853"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.09,
+                0.468,
+                0.235
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Representation</td><td>Description</td><td># of Channels</td><td>Accuracy(%)</td></tr><tr><td>2D Histogram</td><td>Positive and negative event counts</td><td>2</td><td>46.10</td></tr><tr><td>Time Surface</td><td>A hierarchy of event-based time-surfaces</td><td>12</td><td>57.58</td></tr><tr><td>TORE</td><td>Time-ordered recent event volumes</td><td>12</td><td>54.64</td></tr><tr><td>Voxel Grid</td><td>Voxelized grid with bilinear voting aggregation</td><td>12</td><td>52.40</td></tr><tr><td>MDES</td><td>Mixed density event stack</td><td>12</td><td>53.30</td></tr><tr><td>ERGO-12</td><td>Event representation from GWD optimization</td><td>12</td><td>61.40</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.081,
+                0.247,
+                0.468,
+                0.276
+            ],
+            "angle": 0,
+            "content": "Table 2: Mini N-ImageNet validation accuracy evaluated on various event representations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.304,
+                0.468,
+                0.453
+            ],
+            "angle": 0,
+            "content": "representations. We use the large-scale neuromorphic variant of the ImageNet dataset [44], captured from an event camera that observes monitor-displayed images from ImageNet. Event sequences were recorded using the \\(480 \\times 640\\) resolution Samsung DVS Gen3 event camera [49]. We report the GWD computed over the validation set of the Gen1 dataset. Subsequently, we train the model on Mini N-ImageNet. We opt for GWD on the Gen1 dataset to show the generalization capability of GWD across diverse datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.455,
+                0.468,
+                0.514
+            ],
+            "angle": 0,
+            "content": "Representations: Excluding the learned representation, we evaluate using identical representations as in object detection. Each representation is computed over 12 channels, except for the 2D Histogram, which uses two channels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.515,
+                0.468,
+                0.62
+            ],
+            "angle": 0,
+            "content": "Training Details: Adopting the methodology from the N-ImageNet study [21], all inputs are resized to a \\(224 \\times 224\\) dimension, optimizing GPU memory and inference duration. Training is initialized from scratch with a learning rate set at \\(3 \\cdot 10^{-4}\\) and spans 100 epochs. The Adam optimizer with a Nesterov momentum of 0.9 and a weight decay of 0.0001 is used alongside a batch size of 64."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.636,
+                0.468,
+                0.8
+            ],
+            "angle": 0,
+            "content": "Results: Table 2 summarizes the results of the experiments. There is a clear correlation between the GWD (even on different datasets, in this case, Gen1) and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all tested representations on the Mini N-ImageNet dataset. We obtained the following validation set accuracies: 2D Histogram \\((46.10\\%)\\), Time Surface \\((57.58\\%)\\), TORE \\((54.64\\%)\\), Voxel Grid \\((52.40\\%)\\), MDES \\((53.30\\%)\\), ERGO-12 \\((61.4\\%)\\). Their ranking is consistent with the GWD ranking in Fig. 5. Therefore, the GWD can be used also for classification."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.081,
+                0.831,
+                0.194,
+                0.846
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.857,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "State-of-the-art event-based deep learning methods typically need to convert raw events into dense input representations before they can be processed by standard net"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.092,
+                0.892,
+                0.408
+            ],
+            "angle": 0,
+            "content": "works. However, selecting this representation is very expensive since it requires training a separate neural network for each representation and comparing the validation scores. In this work, we circumvent this bottleneck by measuring the quality of event representations with the Gromov Wasserstein Discrepancy (GWD), which is 200 times faster to compute. We validated extensively on multiple tasks, datasets and neural network backbones that the performance of neural networks trained with a representation correlates with its GWD. We then used this metric to, for the first time, optimize over a large family of representations, revealing a new, powerful representation, ERGO-12. With it, we outperform state-of-the-art representations by \\(1.9\\mathrm{mAP}\\) on the 1 Mpx dataset and \\(0.3\\mathrm{mAP}\\) on the Gen1 dataset, two object detection benchmarks. We also exceed existing representation by \\(3.8\\%\\) on the tasks of classification. Moreover, we even outperform the state-of-the-art by \\(2.1\\mathrm{mAP}\\) on Gen1 and state-of-the-art feed-forward methods by \\(6.0\\mathrm{mAP}\\) on the 1 Mpx dataset. This work thus opens a new unexplored field of explicit representation optimization that will push the limits of event-based learning methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.423,
+                0.669,
+                0.439
+            ],
+            "angle": 0,
+            "content": "6. Acknowledgment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.448,
+                0.892,
+                0.537
+            ],
+            "angle": 0,
+            "content": "This work was supported by the Swiss National Science Foundation through the National Centre of Competence in Research (NCCR) Robotics (grant number 51NF40_185543), and the European Research Council (ERC) under grant agreement No. 864042 (AGILE-FLIGHT)."
+        },
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+        {
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\ No newline at end of file
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+# From Chaos Comes Order: Ordering Event Representations for Object Recognition and Detection
+
+Nikola Zubić*
+
+Daniel Gehrig*
+
+Mathias Gehrig
+
+Davide Scaramuzza
+
+Robotics and Perception Group, University of Zurich, Switzerland
+
+![](images/df91507725b9357860518a664565b519ec1ab6e2e46572b4f12eb091cc35f58b.jpg)  
+(a) Method overview
+
+![](images/303d5a5504dd7d7291a75f0087084d620940bb7bab5da711fdc72b2bab19a3df.jpg)  
+(b) GW Discrepancy vs. Performance  
+Figure 1: Selecting dense event representations for deep neural networks is exceedingly slow since it involves training a neural network for each representation and selecting the best one based on the validation score. In this work, we eliminate this bottleneck by selecting the representation based on the Gromov-Wasserstein Discrepancy (GWD) on the validation set (a). This metric is 200 times faster to compute and preserves the task performance ranking of event representations across multiple representations, network backbones, datasets and tasks (b, showing object detection performance on the Gen1 [9] dataset). We use it to, for the first time, perform a hyperparameter search on a large family of event representations, revealing new and powerful event representations that exceed the state-of-the-art.
+
+# Abstract
+
+Today, state-of-the-art deep neural networks that process events first convert them into dense, grid-like input representations before using an off-the-shelf network. However, selecting the appropriate representation for the task traditionally requires training a neural network for each representation and selecting the best one based on the validation score, which is very time-consuming. This work eliminates this bottleneck by selecting representations based on the Gromov-Wasserstein Discrepancy (GWD) between raw events and their representation. It is about 200 times faster to compute than training a neural network and preserves the task performance ranking of event representations across multiple representations, network backbones, datasets, and tasks. Thus finding representations with high task scores is equivalent to finding representations with a low GWD. We use this insight to, for the first time, perform a hyperparameter search on a large family of event representations, revealing new and powerful representations that exceed the
+
+state-of-the-art. Our optimized representations outperform existing representations by 1.7 mAP on the 1 Mpx dataset and 0.3 mAP on the Gen1 dataset, two established object detection benchmarks, and reach a  $3.8\%$  higher classification score on the mini N-ImageNet benchmark. Moreover, we outperform state-of-the-art by 2.1 mAP on Gen1 and state-of-the-art feed-forward methods by 6.0 mAP on the 1 Mpx datasets. This work opens a new unexplored field of explicit representation optimization for event-based learning.
+
+# Multimedia Material
+
+For open-source code please visit https://github. com/uzh-rpg/eventRepresentation_study.
+
+# 1. Introduction
+
+Event cameras are biologically inspired vision sensors that function in a fundamentally distinct way [12]. Unlike traditional cameras that capture images at a fixed rate,
+
+these cameras measure brightness changes independently for each pixel, and these changes are referred to as events. The events encode the time, location, and polarity (sign) of the brightness changes. Event cameras offer several advantages over frame-based cameras, including exceptionally high temporal resolution (in the order of  $\mu$ s), a high dynamic range, and low power consumption. Their numerous benefits make them attractive for a wide range of applications like robotics, autonomous vehicles, and virtual reality. However, due to their sparse and asynchronous nature, applying classical computer vision algorithms remains challenging.
+
+Many state-of-the-art deep learning models address this challenge by converting sparse and asynchronous events into dense grid-like representations before processing them with off-the-shelf deep neural networks. By using these networks, methods like this enjoy the advantages of mature learning algorithms and network architectures, and optimized hardware, but we need to make a non-trivial choice of event representation. In fact, the computer vision and robotics fields are witnessing a surge in the number of research papers utilizing event-based vision, resulting in a plethora of new event representations being proposed. Despite this, extensive comparisons of these representations remain rare, making it unclear whether these newer representations should be adopted.
+
+No efficient methodology exists for comparing these representations. Conventionally, comparing event representations involves training a fixed deep-learning model for each event representation separately and subsequently selecting the optimal one based on a validation score. This process is very time-intensive since it requires network training in the loop which often takes hours or days (Fig. 1 a top).
+
+In this work, we propose a fast method to compare event representations which circumvents the need to train a neural network and instead computes the Gromov-Wasserstein Discrepancy (GWD) between the raw events and event representation (Fig. 1 a bottom). This metric effectively measures the distortion that is introduced through converting raw events to representations and thus puts an upper bound on the amount of information that can be accessed by downstream neural networks. We show extensive experimental evidence, that this metric preserves the task-performance ranking across a wide range of input representations for several datasets, neural network backbones and tasks (Fig. 1 b). Due to its low computational cost, we apply the GWD to, for the first time, explicitly optimize over a large family of event representations, which reveals a new and powerful representation, which we term 12-channel Event Representation through Gromov-Wasserstein Optimization (ERGO-12). For the task of object detection, networks trained with these representations outperform other representations by  $1.9\mathrm{mAP}$  on the 1 Mpx dataset and  $0.3\mathrm{mAP}$
+
+on Gen1, even outperforming state-of-the-art methods by  $2.1\mathrm{mAP}$  on Gen1 and state-of-the-art feed-forward methods by  $6.0\mathrm{mAP}$  on the 1 Mpx dataset. On object recognition, we instead find that our representation outperforms state-of-the-art representations by  $3.8\%$ . We believe that the GWD is a powerful tool that opens up a new research field that searches for optimized event representations. Our contributions are summarized as follows:
+
+- We introduce a novel, efficient approach for comparing dense event representations using the Gromov-Wasserstein Discrepancy (GWD).  
+- We show extensive experimental evidence that it preserves the task performance ranking of neural networks trained with these representations across datasets, neural network backbones and tasks.  
+- We use it to, for the first time, conduct a hyperparameter search on a vast family of event representations, unveiling novel and powerful event representations that outperform the current state-of-the-art representations on the object detection and object classification task.
+
+# 2. Related Work
+
+In the field of event-based vision, two primary groups of representations exist: sparse and dense. Methods that use sparse representations [35, 51, 23, 37] preserve the sparsity in the events but do not yet scale to more complex tasks due to a lack of specialized hardware and mature neural networks architectures. This frequently results in lower performance on downstream tasks. In contrast, dense representations [31, 48, 53, 50] offer improved performance since they can leverage mature machine learning algorithms and neural network architectures. Sparse representations, pioneered by asynchronous SNNs [35, 23, 37], are limited by the lack of specialized hardware and computationally efficient backpropagation algorithms. Point cloud encoders [47, 40, 11] have been used due to the spatio-temporal nature of event data, but can be computationally expensive and noisy. Graph neural networks [26, 46, 4, 3, 33, 10] are scalable and have achieved high performance on various vision tasks but are still less accurate than dense methods for event-based vision. In this study, we focus on dense event representations and aim to achieve better task performance by utilizing existing efficient learning algorithms that are appropriate for current hardware.
+
+Early dense representations converted events to histograms [31], generated time surfaces [48] or combined both [52] while relying on standard neural network backbones to process them. However, these representations only capture a low-dimensional representation of events since they typically only use a few channels. Later approaches have tried to capture more event information by either computing higher-order moments [1] or stacking multiple time
+
+![](images/1da40450cb10dd24289b70a4a37d2cf45a82e0fdbeae74098164ad510631ed8a.jpg)  
+Figure 2: Overview of the Gromov-Wasserstein Discrepancy (GWD) between raw events and representations. Events  $\mathcal{E}$  are converted to event representations, i.e. a set of features  $\mathcal{F}$  at pixel locations  $\mathbf{x}$ . It is defined as the solution to an optimal transport problem which transports events pairs  $(e_i,e_k)$  to feature pairs  $(f_{\mathbf{x}_j},f_{\mathbf{x}_l})$  via transport plan  $T_{ij},T_{kl}$ . If the transport plan preserves the similarities  $C_{ik}^{e}$  and  $C_{jm}^{f}$  between event and feature pairs, this results in a low GWD.
+
+windows of events [53]. These methods still stack events based on fixed time windows which is problematic when the event rate becomes too large or too small and lead to the introduction of stacking based on the number of events [50]. In parallel, a bio-inspired approach led to the introduction of Time Ordered Recent Event Volumes (TORE) [2], which aggregate events into queues. However, they are slow to compute and perform similarly to existing Voxel Grids [53]. Most recently, a powerful representation was proposed by Nam et al. [34], which divides events into multiple overlapping windows that halve the number of events at each stage, which are more robust during varying scene dynamics.
+
+Few papers study the effect of event representations on task performance. While [38] and [21] show small-scale ablation studies to select event representations, only Gehrig et al. [13] performed a large-scale investigation of event representations by training models on various inputs for multiple tasks. Their study demonstrated the advantages of splitting polarities and incorporating timestamps into representations, and it introduced a learnable representation. However, training for a single task was still computationally expensive, which limited the number of representations that could be compared. For this reason, their study did not cover a large number of representations, and in particular, did not consider different window sizes as is done in later work [50, 34], or more advanced aggregations and measurements like in [1]. Our method instead introduces an efficient metric to compare event representations that solves these limitations, allowing us to perform a search over a large family of event representations and go beyond the representations in [50, 1, 34, 14], including even non-differentiable hyperparameters.
+
+# 3. Method
+
+In this section, we will first introduce the preliminaries on computing event representations (Sec. 3.1) and then pro
+
+pose the metric we use to measure the discrepancy between events and their representation based on the GWD (Sec. 3.2) before concluding with Sec. 3.3 where we use Bayesian optimization to find an optimal event representation.
+
+# 3.1. Preliminaries
+
+Event cameras measure brightness changes as an asynchronous stream of events. Each event is triggered when the intensity  $L(\mathbf{u})$  at the pixel  $\mathbf{u} = (x, y)$  changes by the contrast threshold  $C$  at time  $t$ , and thus satisfies
+
+$$
+p \left[ L (\mathbf {u}, t) - L (\mathbf {u}, t - \Delta t) \right] = C \tag {1}
+$$
+
+where  $p\in \{-1,1\}$  is the polarity of the event, and  $t - \Delta t$  is the time of the last event. Within a time window  $\Delta T$  an event camera thus generates an ordered set of events  $\mathcal{E} = \{e_k\}_{k = 0}^{N_e - 1}$ , with each event  $e_k = (\mathbf{u}_k,t_k,p_k)\in \mathbb{R}^4$ . To bridge the gap between asynchronous events and dense neural networks, they are usually converted to a dense event representation
+
+$$
+\mathcal {R} = F (\mathcal {E}), \tag {2}
+$$
+
+which has features  $f_{\mathbf{x}} \doteq \mathcal{R}(\mathbf{x}) \in \mathbb{R}^{N_f}$  indexed by the integer-valued pixel location  $\mathbf{x}$ . The above representation thus generates a set of features  $\mathcal{F} = \{f_{\mathbf{x}}\}_{\mathbf{x} \in \Omega}$ , where  $\Omega$  denotes the image domain and has size  $|\Omega| = N_f$  with  $N_f$  being the number of pixels in the image. In what follows, we will derive a measure to quantify the distortion between events  $\mathcal{E}$  and features  $\mathcal{F}$  based on the GWD.
+
+# 3.2. Gromov-Wasserstein Discrepancy
+
+Converting raw events to a representation invariably distorts the events by removing important distinguishing features from the stream. We would like to measure this distortion since we expect it correlates strongly with a neural network's ability to extract features from these events. In what follows, we will derive a measure of this distortion rate based on the GWD.
+
+We show an overview of the GWD in Fig. 2. We start by measuring the similarity between a set of events and their representation by building a soft correspondence between events  $e_i$  and features  $f_{\mathbf{x}_j}$ , which we denote as  $T_{ij}^1$ . This transport plan effectively moves each event to a corresponding feature, thereby distorting the original set and destroying information. Importantly, such a plan can be interpreted as follows: We transport the events with a total weight of 1, i.e. per-event weight  $\frac{1}{N_e}$  to the output features, which also need to receive a total weight of 1 or per-feature weight of  $\frac{1}{N_f}$ . By this construction,  $T_{ij}$  needs to satisfy  $\sum_i T_{ij} = 1 / N_f$  and  $\sum_j T_{ij} = 1 / N_e$ . This means that a total weight of  $1 / N_e$  moves from each event, and each feature receives a total weight of  $1 / N_f$ .
+
+In the next step, we measure the distortion introduced by this transportation plan by considering pairwise similarities of input events and features. Let  $e_i, e_k \in \mathcal{E}$  be a pair of events and  $f_{\mathbf{x}_j}, f_{\mathbf{x}_l} \in \mathcal{F}$  pair of features, with similarity scores  $C_{ik}^e \doteq C^e(e_i, e_k)$  and  $C_{jl}^f \doteq C^f(f_{\mathbf{x}_j}, f_{\mathbf{x}_l})$  between events and features respectively. Next, consider how the transport plan  $T$  acts on these pairs: Generally, a weight  $T_{ij}$  is moved from event  $e_i$  to feature  $f_{\mathbf{x}_j}$ . Similarly, the weight  $T_{kl}$  is moved from event  $e_k$  to feature  $f_{\mathbf{x}_l}$ . Ideally, such a transport plan should preserve the similarity between pairs of source events and target features, and thus the difference in similarity scores between pairs  $(i, k)$  and  $(j, l)$  can be used as a measure of distortion. For each event pair and feature pair, we define the distortion as
+
+$$
+L _ {i j k l} = T _ {i j} T _ {k l} \mathcal {L} \left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\right), \tag {3}
+$$
+
+where  $\mathcal{L}$  denotes some disparity measurement between  $C_{ik}^{e}$  and  $C_{jl}^{f}$ . Summing over all possible pairs of events and features we thus arrive at the transportation cost:
+
+$$
+L (T; \mathcal {E}, \mathcal {F}) = \sum_ {i, j, k, l} L _ {i j k l} = \sum_ {i, j, k, l} T _ {i j} T _ {k l} \mathcal {L} \left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\right) \tag {4}
+$$
+
+Minimizing over transport plans, we arrive at the GWD:
+
+$$
+L (\mathcal {E}, \mathcal {F}) = \min  _ {T} \sum_ {i, j, k, l} T _ {i j} T _ {k l} \mathcal {L} \left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\right), \tag {5}
+$$
+
+which can be optimized efficiently using [39]. Since the above metric is defined for a single time window of events, we may average it over multiple samples to find:
+
+$$
+\mathrm {G W D} _ {N} = \frac {1}{N} \sum_ {i} L \left(\mathcal {E} _ {i}, \mathcal {F} _ {i}\right). \tag {6}
+$$
+
+$\mathrm{GWD}_N$  can be interpreted as an average distortion rate from raw events to event representations. In Sec. 4.2, we
+
+show that  $\mathrm{GWD}_N$  correlates with a  $NN$ 's performance with that representation across network backbones, datasets, and event representations. It's also efficient to compute, taking 9 seconds for 50,000 events. In what follows,  $\mathrm{GWD}_N$  will denote the average over  $N$  samples, while GWD denotes the average over the whole validation set.
+
+Similarity scores and distortion function As similarity scores, we choose Gaussian radial basis functions [45] for both events and image features. In detail,
+
+$$
+C _ {i k} ^ {e} = e ^ {\frac {- \| e _ {i} - e _ {k} \| ^ {2}}{2 h ^ {2} \sigma_ {e} ^ {2}}}, \quad C _ {j l} ^ {f} = e ^ {\frac {- \| f _ {\mathbf {x} _ {j}} - f _ {\mathbf {x} _ {l}} \| ^ {2}}{2 h ^ {2} \sigma_ {f} ^ {2}}} \tag {7}
+$$
+
+$$
+\sigma_ {e} ^ {2} = \underset {i <   j} {\operatorname {m e a n}} \| e _ {i} - e _ {j} \| ^ {2}, \quad \sigma_ {f} ^ {2} = \underset {i <   j} {\operatorname {m e a n}} \| f _ {\mathbf {x} _ {i}} - f _ {\mathbf {x} _ {j}} \| ^ {2}. \tag {8}
+$$
+
+with a bandwidth parameter  $h = 0.7$ . The selection of data-dependent variances normalizes the distances between pairs of events and features such that the similarity score is robust to the dimensionality of the data and the number of samples in the source and target domain. These details are discussed in [7, 45, 36]. While more complex similarity scores could be used, this simple function already achieved good results. As the distortion function, we chose the KL-Divergence i.e.
+
+$$
+\mathcal {L} \left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\right) = C _ {i k} ^ {e} \log \left(C _ {i k} ^ {e} / C _ {j l} ^ {f}\right). \tag {9}
+$$
+
+As a result, the optimization already rejects terms for which  $C_{ik}^{e} \approx 0$ , i.e. pairs of events that are far apart. We found that this property was also beneficial in improving the convergence of the optimization problem in Eq. (5)
+
+Improving Convergence of Eq. (5). We found that three features improved convergence and speed up the optimization: (i) Normalization of the event coordinates and timestamps by the sensor size and time window respectively, (ii) Concatenation of the normalized pixel position to the image features, and (iii) Sparsification of image features. Both (i) and (ii) make the optimization more numerically stable. In fact, without concatenating position information to image features, randomly pixel-wise shuffled event representations would retain the same GWD, although intuitively, neural networks would have a harder time learning from such representations since they typically process nearby features together. Thus reintroducing the position removes this ambiguity and improves the convergence. Finally, (iii) removes image features with  $\| f_{\mathbf{x}} \| = 0$  since these correspond to pixels where no events were triggered. This step significantly sped up computation by reducing the size of the pair-wise similarity score matrix  $C^f$ , with a small impact on convergence.
+
+# 3.3. Optimizing over Event Representations
+
+With a fast method to measure the effectiveness of an event representation, we can now search for the optimal rep
+
+![](images/c5763c85abebbc04f357dc22d145690e5a888ec5506621edf714a668ced5ebd8.jpg)  
+Figure 3: Overview of the hyperparameters we use to construct an event representation (right). For each channel  $c$ , we select one of several event time windows  $w_{c} \in \mathcal{W}$  (in color, left), measurement functions  $m_{c} \in \mathcal{M}$  (timestamp, polarity, positive timestamps, etc.), and aggregation functions  $a_{c} \in \mathcal{A}$  (max, mean, sum, variance), resulting in  $3N_{c}$  parameters.
+
+resentation by minimizing Eq. (6) over a space of possible representations with a set of hyperparameters  $p$ .
+
+$$
+p ^ {*} = \arg \min  _ {p} \frac {1}{N} \sum_ {i} L \left(\mathcal {E} _ {i}, \mathcal {F} _ {i} (p)\right). \tag {10}
+$$
+
+To simplify this optimization, we first describe a very general parametrization, which defines a large family of event representations, extending the family described in [13] in a few ways. These hyperparameters are a small set of categorical variables which can subsequently be optimized using Bayesian optimization.
+
+Parametrization of Event Representations We illustrate the hyperparameters in Fig. 3. In general, we assume an event representation comprises a stack of features, indexed by  $c$  (right side), each of which is derived from  $(i)$  a specific time window  $w_{c}$  of events,  $(ii)$  a specific measurement  $m_{c}$  of events such as polarity or timestamps, and  $(iii)$  a specific aggregation  $a_{c}$ , such as summation or averaging. We write such a representation as  $N_{c}$  concatenated feature maps:
+
+$$
+\mathcal {R} = \left[ \mathcal {R} _ {0} \mid \mathcal {R} _ {1} \dots \mid \mathcal {R} _ {N _ {c} - 1} \right] \tag {11}
+$$
+
+$$
+\text {w i t h} \mathcal {R} _ {c} = a _ {c} \left(m _ {c} \left(w _ {c} (\mathcal {E})\right)\right) \tag {12}
+$$
+
+Here  $w_{c}$  is a windowing function which selects events within an interval,  $m_{c}$  is the measurement function which selects an event feature, and  $a_{c}$  is the aggregation function, which aggregates measurements into a single feature map.
+
+Note, in our formulation each channel can have an independent set of parameters, different to [13], which assumes a shared aggregation and measurement function for all channels. This makes our parametrization substantially more expressive than the one in [13]. The number of (non-learnable) representations is  $\left(|\mathcal{A}||\mathcal{M}||\mathcal{W}|\right)^{N_c}\approx 3.21\times 10^{27}$ , since each channel can be configured independently. Moreover, while  $a_{c}$  and  $m_{c}$  were already discussed in [13], the windowing function is a more general concept, illustrated in Fig. 3 (left). While these windows can be non-overlapping  $(w_{3},w_{4},w_{2})$ , as for Voxel Grids [53], they can also be overlapping,  $(w_{0},w_{1},w_{2})$  as in Mixed
+
+Density Event Stacks [34], or describe windows of a constant event count or constant time [50] In this work we allow each feature channel to select from a basis of windows  $\mathcal{W} = \{[t_{0,k}, t_{1,k}]\}_{k=0}^{N_k-1}$ , which can combine all types of windows unifying these concepts. In summary, a representation is parametrized by:
+
+$$
+p = \left\{\left(w _ {c}, a _ {c}, m _ {c}\right) \right\} _ {c = 0} ^ {N _ {c} - 1} \tag {13}
+$$
+
+$$
+\text {w i t h} \quad m _ {c} \in \mathcal {M}, a _ {c} \in \mathcal {A}, w _ {c} \in \mathcal {W}.
+$$
+
+For the sets of aggregation functions we select  $\mathcal{A} = \{\max, \text{sum}, \text{mean}, \text{variance}\}$  and for the measurement functions  $\mathcal{M} = \{t_{+}, t_{-}, t, p, c_{+}, c_{-}, c\}$  which are most commonly used. Here  $c, p,$  and  $t$  denote event count (discarding polarity), polarity, and timestamp. The subscripts  $+ / -$  select only positive or negative events. For the basis of time windows, we select three equally spaced, non-overlapping windows from [53] and four overlapping windows from [34], including the global window. These are illustrated in Fig. 7 (right).
+
+Optimization Procedure The aforementioned parametrization generates redundant combinations that can be obtained by permuting channels or selecting the same feature for different channels. To address this issue and expedite convergence, we propose a stage-wise optimization procedure. Initially, we start with a volume consisting of zeros with  $N_{c}$  channels and optimize over  $a_0, w_0$ , and  $m_0$  to fill in the first channel. Next, we optimize the feature for the second channel while keeping the first fixed. With this iterative process, we incrementally fill up the representation, avoiding the selection of redundant representations and resulting in faster optimization. At each stage, we use Gryffin [18], a specialized Bayesian optimizer for categorical variables.
+
+# 4. Experiments
+
+In Sec. 4.1, we first connect the GWD and event distortion, demonstrating its behavior on several toy examples. Next, in Sec. 4.2, we showcase the correlation between the
+
+![](images/65ce4065ac4bcbd40835c6897c6bfaf07da55eead7399971718c31ccbe961092.jpg)  
+Figure 4: Validation of our metric on the Gen1 validation set. (top) Our metric for Voxel Grids [53] and Mixed-Density Event Stacks [34] with an increasing number of channels. (bottom) Effect of applying Gaussian blur with different blur kernels to the event representation.
+
+metric and task performance across multiple tasks, datasets, backbones, and representations. Lastly, in Sec. 4.3, we show the outcome of Bayesian Optimization on the GWD and offer insights on the acquired event representation before comparing it against the state-of-the-art.
+
+# 4.1. Toy Example
+
+As explained in Sec. 3.2, the GWD measures the distortion rate from raw events to event representation. Two experiments were designed to test this claim: (1) analyzing the behavior of the metric when varying the number of bins in Voxel Grid [53] and Mixed-Density Event Stack (MDES) [34] representations, and (2) blurring the event representation with increasing standard deviations before measuring the GWD. We perform experiments on the validation set of Gen1[9] and report the results in Fig. 4.
+
+Fig. 4 (top) confirms that the GWD decreases as the number of channels increases in both Voxel Grids and Mixed-Density Event Stacks, which aligns with our intuition that using more channels preserves more information from raw events, resulting in a lower distortion rate. Similarly, the bottom part illustrates that with a growing blur radius, more edges in the event representation are removed, leading to an increase in the GWD. This verifies that the GWD measures the distortion from raw events to event representations.
+
+# 4.2. Object Detection
+
+Next, we investigate the relationship between GWD and the task performance of a  $NN$  trained for object detection. We choose two widely used object detection datasets, the Gen1 [9] and 1 Mpx [38] Automotive Detection Dataset, which both deal with event streams featuring labeled bounding boxes for pedestrians, cars, and other vehicles. While
+
+![](images/c75b215699f042097d2a7ba2d96f6d191fc3277e8a947080ac17c03eafd3ae07.jpg)
+
+![](images/73c5ae4bd1852ea41ee44657f8db6b00f24a74d4dccc4591ad54fe0016ea7153.jpg)  
+Figure 5: Correlation of the Gromov-Wasserstein Discrepancy with the mAP (higher is better) for object detection on the Gen1 [9] (top) and 1 Mpx [38] (bottom) datasets. Note the spliced y-axis on 1 Mpx, due to the high GWD of the 2D Histogram.
+
+the former has a resolution of  $304 \times 240$ , the latter has a resolution of  $1280 \times 720$ . We report the GWD computed over the validation set of each dataset and then train an off-the-shelf object detection framework based on YOLOv6 [24], pre-trained on the Microsoft Common Objects in Context (MS-COCO) [28], on different input representations as in [13]. To accommodate the varying number of channels, we replace the 3-channel input convolution with a  $N_{c} = 12$  channel input convolution, where  $N_{c}$  represents the number of channels in the representation. To show the generality of the result, we also vary the detection backbone between ResNet-50 [17], EfficientRep [24] and Swin Transformer V2 [30], and report results for each.
+
+Representations: We test a range of common representations listed below. We compute 12 channels for each representation, except for the 2D Histogram, which has 2.
+
+Voxel Grid: Here, the event time window is split into  $N_{c}$  equal, non-overlapping time windows, and then events in the same time window are aggregated by summing their polarity on a per-pixel basis using bilinear voting [53].
+
+Mixed-Density Event Stack (MDES): For each channel  $c$ , this representation selects the most recent  $\frac{N_e}{2^c}$  events, where  $N_e$  are the events in the time window. For each window, it aggregates the polarity at that pixel [34].
+
+Event Histograms: Events in the time window are split by polarity and then summed into two channels [31].
+
+Time Surface: We convert events into time surfaces from [22] with a decay constant of  $\tau = 5\mathrm{ms}$ . We then sample it at  $\frac{N_c}{2} = 6$  equally spaced timestamps, once for
+
+positive and negative events resulting in  $N_{c} = 12$  channels.  
+TORE: The Time-Ordered Recent Event Volumes store event timestamps in per-pixel queues. We use queues with capacity  $\frac{N_c}{2} = 6$ , one for positive and one for negative events, and concatenate them to  $N_{c} = 12$  channels.
+
+Learned representation: Event Spike Tensor (EST) [13] is a learnable event representation that employs a Quantization Layer featuring a trainable kernel. This approach enables the model to effectively transform raw events, optimizing their performance for a given task.
+
+Training Details We adopt the training procedure from YOLOv6 [24]. For each backbone, representation, and dataset, we train for 100 epochs, using Stochastic Gradient Descent with Nesterov momentum increasing from 0.5 to 0.83 over the first 2 epochs. We use a batch size of 32, and a Cosine learning rate schedule, starting at 0.00323 and ending at 0.000387 after 100 epochs. We adopt the classification and box regression losses in [24].
+
+Results: Figs. 5 summarizes the results of the above experiments. For both datasets, Gen1 and 1 Mpx, and all backbones, there is a clear correlation between the GWD and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all three network backbones. In particular, MDES with a Swin-V2 detection backbone consistently achieves the highest mAP with 0.43 on Gen1 and 0.39 on 1 Mpx. It also consistently achieves the lowest GWD with 0.38 on Gen1 and 0.40 on 1 Mpx. Utilizing the learnable EST in YOLOv6 with SwinV2 backbone, we achieved a 45.31 mAP score on the Gen1 validation set and a GWD score of 0.3552, positioning EST between MDES and ERGO-12 in Fig. 1b, confirming the expected ranking. We also see that the Swin V2 backbone outperforms other backbones on both datasets for all tested representations. We conclude that while the representation affects task performance, the neural network also has an influence. However, we see that the overall ranking of the representations is preserved.
+
+Using Fewer Samples While in the previous section, we reported the GWD over the validation set of the Gen1 and the 1 Mpx datasets, averaging this metric over such a large dataset still incurs a high computational cost and would make such a metric infeasible for optimization. Therefore, here we investigate if we can use smaller sample sizes to speed up the computation of GWD. In Fig. 6, we show the GWD for the representations in Sec. 4.2 while varying the number of samples. We see that as the sample number decreases, the mean values of the metric change, but the ranking between representations is still preserved reliably after around 100 samples, and thus we use  $\mathrm{GWD}_{100}$  to optimize over representations. Below this number, the ranking of representations can fluctuate. However, we found that this happens due to a bad convergence of Eq. (5).
+
+Timing Results: We time the computation of the GWD
+
+![](images/031abe41d5b5eafcda630b4c1592cc1a0d3524dffa39ace93806b47723b0243f.jpg)  
+Figure 6: Gromov-Wasserstein Discrepancy for a varying number of samples from the validation set.
+
+over 100 samples of the Gen1 validation set, where each sample comprises 50,000 events. We run our experiment on an AMD EPYC 7702 32-core server-grade CPU with 32 GB RAM and achieve a runtime of 15 minutes. Note that computing the GWD does not require a GPU. By contrast, training the models in Fig. 5 requires 2 days on a single Tesla V100 GPU with 32 GB of memory, making GWD computation 192 times faster.
+
+# 4.3. Optimization of Event Representations
+
+Here we report the results of optimizing the event representation according to the procedure in Sec. 3.3. We optimize  $N_{c} = 12$  channels, and at each optimization cycle for channel  $c$ , the Bayesian Optimizer selects 100 configurations and then keeps the best-performing configuration.
+
+We show the result of this optimization procedure in Fig. 7. The left shows how the GWD decreases as new channels are added to the representation. We see that after 2 channels, our method outperforms 2D Histograms, after 6 channels we outperform Time Surfaces, after 7 channels we outperform Voxel Grids / TORE, after 9 channels we outperform Mixed-Density Event Stacks and finally, after 12 channels, we achieve a  $\mathrm{GWD}_{100}$  of 0.47. On the right, we show the different windows (columns) and measurement functions (rows) that are selected. We do not show the order since our representation is unique up to a random channel permutation. However, in the appendix, we show which features are selected at each stage. We see that all windows and all measurement functions are selected at least once, showing how our representation tries to diversify as much as possible. Moreover, timestamp-based measurements often show multiple aggregations, which we argue are necessary to replicate their complex continuous signal.
+
+Comparison with State-of-the-Art Here we compare our method against state-of-the-art recurrent and feedforward methods on the Gen1 and 1 Mpx test sets. We summarize the results in Tab. 1. Recurrent methods in
+
+![](images/95482ddb6d0259ceb4b95c992f740cde923fc787f9745c5f3f2c2789f2e1433b.jpg)  
+Figure 7: Gromov-Wasserstein Discrepancy for 100 samples (left). At each channel, a Bayesian optimizer selects the next best hyperparameter triple. The chosen hyperparameters are broken down by window and measurement function (right).
+
+<table><tr><td colspan="2"></td><td>\( w_0 \)</td><td>\( w_1 \)</td><td>\( w_2 \)</td><td>\( w_3 \)</td><td>\( w_4 \)</td><td>\( w_5 \)</td><td>\( w_6 \)</td></tr><tr><td rowspan="3">t</td><td>+</td><td>sum</td><td>sum mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>-</td><td>sum</td><td>mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td>var max</td><td></td><td></td><td></td></tr><tr><td rowspan="3">c</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>mean</td><td></td></tr><tr><td>-</td><td></td><td></td><td>sum</td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td></td><td>sum</td><td></td><td>sum</td></tr><tr><td colspan="2">p</td><td></td><td></td><td></td><td>var</td><td></td><td></td><td></td></tr></table>
+
+<table><tr><td>tNe-1</td></tr><tr><td>w6</td></tr><tr><td>w5</td></tr><tr><td>w4</td></tr><tr><td>w3</td></tr><tr><td>w2</td></tr><tr><td>w1</td></tr><tr><td>w0</td></tr><tr><td>t0</td></tr></table>
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Event Repr.</td><td rowspan="2">Recurrent</td><td colspan="2">mAP↑</td></tr><tr><td>Gen1 [9]</td><td>1 Mpx [38]</td></tr><tr><td>MatrixLSTM+YOLOv3 [5]</td><td>MatrixLSTM</td><td>✓</td><td>0.310</td><td>-</td></tr><tr><td>E2VID+RetinaNet [41]</td><td>Reconstructions</td><td>✓</td><td>0.270</td><td>0.250</td></tr><tr><td>RED [38]</td><td>Voxel Grid</td><td>✓</td><td>0.400</td><td>0.430</td></tr><tr><td>RVT-B [16]</td><td>2D Histogram</td><td>✓</td><td>0.472</td><td>0.474</td></tr><tr><td>ASTMNet [25]</td><td>Asynchronous attention embedding</td><td>✓</td><td>0.467</td><td>0.483</td></tr><tr><td>Events+RetinaNet [38]</td><td>Voxel Grid</td><td>✗</td><td>0.340</td><td>0.180</td></tr><tr><td>Events+SSD [19]</td><td>2D Histogram</td><td>✗</td><td>0.301</td><td>0.340</td></tr><tr><td>Events+RRC [6]</td><td>2D Histogram</td><td>✗</td><td>0.307</td><td>0.343</td></tr><tr><td>Events+YOLOv3 [20]</td><td>2D Histogram</td><td>✗</td><td>0.312</td><td>0.346</td></tr><tr><td>AEGNN [46]</td><td>Graph</td><td>✗</td><td>0.163</td><td>-</td></tr><tr><td>EAGR [15]</td><td>Graph</td><td>✗</td><td>0.321</td><td>-</td></tr><tr><td>Spiking DenseNet [8]</td><td>Spike Train</td><td>✗</td><td>0.189</td><td>-</td></tr><tr><td>AsyNet [32]</td><td>2D Histogram</td><td>✗</td><td>0.145</td><td>-</td></tr><tr><td></td><td>2D Histogram</td><td>✗</td><td>0.339</td><td>0.327</td></tr><tr><td></td><td>Time Surface</td><td>✗</td><td>0.490</td><td>0.383</td></tr><tr><td></td><td>TORE</td><td>✗</td><td>0.436</td><td>0.381</td></tr><tr><td></td><td>Voxel Grid</td><td>✗</td><td>0.395</td><td>0.375</td></tr><tr><td></td><td>MDES</td><td>✗</td><td>0.427</td><td>0.378</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.493</td><td>0.400</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.504*</td><td>0.406*</td></tr></table>
+
+Table 1: Comparison of state-of-the-art event-based object detectors on the test sets of Gen1 [9] and 1 Mpx [38].
+
+clude MatrixLSTM+YOLOv3 [5], which uses a recurrent, learned input representation with a YOLOv3 [42] detector, E2VID+RetinaNet [41] which uses recurrent E2VID reconstructions with a RetinaNet [27] detector, RVT-B which uses a recurrent transformer [16], and RED [38], a recurrent CNN. ASTMNet [25] utilizes asynchronous attention embedding and incorporates recurrent layers in deeper layers, claiming comparable results on both datasets. However, it is not open source. Feedforward methods are grouped into graph-based methods NVS-S [26], AEGNN [46] and EAGR [15], sparse method AsyNet [32], spiking method Spiking DenseNet [8], and finally feedforward dense methods Events+RetinaNet [38], Events+SSD [19] Events+RRC [6], and Events+YOLOv3 [20] which use events as input, and use the RetinaNet [27], SSD [29], RRC [43] or YOLOv3 [42] detector respectively.
+
+We compare these methods to our best-performing YOLOv6 detector from Sec. 4.2 with a SwinV2 transformer backbone trained on various input representations. These include the ones analyzed in Sec. 4.2, i.e. the 2D Histogram, Time Surface, TORE, Voxel Grid, and MDES, as well as the optimized representation ERGO-12. Note that these methods do not include data augmentation. We also trained our model with Mixup and Mosaic augmentation from [24], and is indicated by an asterisk * in Tab. 1.
+
+Results On the Gen1 dataset, we see that YOLOv6 with the SWINv2 backbone and ERGO-12 input and data augmentation outperforms all state-of-the-art methods by up to  $2.9\%$  mAP by achieving an mAP of 0.504. The runner-up is RVT-B, which uses a recurrent vision transformer. Even without data augmentation, our network with ERGO-12 achieves 0.493, which improves the mAP by  $2.1\%$  compared to RVT-B. Compared to the other feed-forward methods based on YOLOv6, ERGO-12 achieves an 0.3 mAP higher mAP, the next best being YOLOv6 with Time Surface [22] with 0.490. Interestingly, as indicated in Fig. 1 (b), the difference in mAP performance between ERGO-12 and Time Surface is 1.8 mAP on the validation set of the Gen1 dataset, which is substantially larger than on the test set.
+
+On 1 Mpx, the best-performing method is ASTMNet with an mAP of 0.483, followed by RVT-B with 0.474. From the feed-forward methods YOLOv6 with ERGO-12 and data augmentation achieves the highest score with 0.406, outperforming runner-up method YOLOv6 with Time Surfaces by  $2.3\%$  mAP. Even without augmentation, ERGO-12 achieves a  $1.7\%$  higher score than YOLOv6 with Time Surfaces. Compared to state-of-the-art feed-forward methods, ERGO-12 with data augmentation achieves a  $6.0\%$  higher score, the runner-up being Events+YOLOv3 with 0.346. On this dataset, recurrent methods are known to perform better since many sequences include stops or slow-motion scenarios. This is challenging for feed-forward methods since they are not able to maintain long-term memory. In general, the improvement of ERGO-12 on 1 Mpx is higher compared to Gen1.
+
+# 4.4. Object Classification
+
+As an additional task, we investigate the relationship between GWD and the object classification task performance using the ResNet-34 [17] backbone classifier, pre-trained on ImageNet [44], while changing the input convolution to be compatible with  $N_{c} = 12$  channel
+
+<table><tr><td>Representation</td><td>Description</td><td># of Channels</td><td>Accuracy(%)</td></tr><tr><td>2D Histogram</td><td>Positive and negative event counts</td><td>2</td><td>46.10</td></tr><tr><td>Time Surface</td><td>A hierarchy of event-based time-surfaces</td><td>12</td><td>57.58</td></tr><tr><td>TORE</td><td>Time-ordered recent event volumes</td><td>12</td><td>54.64</td></tr><tr><td>Voxel Grid</td><td>Voxelized grid with bilinear voting aggregation</td><td>12</td><td>52.40</td></tr><tr><td>MDES</td><td>Mixed density event stack</td><td>12</td><td>53.30</td></tr><tr><td>ERGO-12</td><td>Event representation from GWD optimization</td><td>12</td><td>61.40</td></tr></table>
+
+Table 2: Mini N-ImageNet validation accuracy evaluated on various event representations.
+
+representations. We use the large-scale neuromorphic variant of the ImageNet dataset [44], captured from an event camera that observes monitor-displayed images from ImageNet. Event sequences were recorded using the  $480 \times 640$  resolution Samsung DVS Gen3 event camera [49]. We report the GWD computed over the validation set of the Gen1 dataset. Subsequently, we train the model on Mini N-ImageNet. We opt for GWD on the Gen1 dataset to show the generalization capability of GWD across diverse datasets.
+
+Representations: Excluding the learned representation, we evaluate using identical representations as in object detection. Each representation is computed over 12 channels, except for the 2D Histogram, which uses two channels.
+
+Training Details: Adopting the methodology from the N-ImageNet study [21], all inputs are resized to a  $224 \times 224$  dimension, optimizing GPU memory and inference duration. Training is initialized from scratch with a learning rate set at  $3 \cdot 10^{-4}$  and spans 100 epochs. The Adam optimizer with a Nesterov momentum of 0.9 and a weight decay of 0.0001 is used alongside a batch size of 64.
+
+Results: Table 2 summarizes the results of the experiments. There is a clear correlation between the GWD (even on different datasets, in this case, Gen1) and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all tested representations on the Mini N-ImageNet dataset. We obtained the following validation set accuracies: 2D Histogram  $(46.10\%)$ , Time Surface  $(57.58\%)$ , TORE  $(54.64\%)$ , Voxel Grid  $(52.40\%)$ , MDES  $(53.30\%)$ , ERGO-12  $(61.4\%)$ . Their ranking is consistent with the GWD ranking in Fig. 5. Therefore, the GWD can be used also for classification.
+
+# 5. Conclusion
+
+State-of-the-art event-based deep learning methods typically need to convert raw events into dense input representations before they can be processed by standard net
+
+works. However, selecting this representation is very expensive since it requires training a separate neural network for each representation and comparing the validation scores. In this work, we circumvent this bottleneck by measuring the quality of event representations with the Gromov Wasserstein Discrepancy (GWD), which is 200 times faster to compute. We validated extensively on multiple tasks, datasets and neural network backbones that the performance of neural networks trained with a representation correlates with its GWD. We then used this metric to, for the first time, optimize over a large family of representations, revealing a new, powerful representation, ERGO-12. With it, we outperform state-of-the-art representations by  $1.9\mathrm{mAP}$  on the 1 Mpx dataset and  $0.3\mathrm{mAP}$  on the Gen1 dataset, two object detection benchmarks. We also exceed existing representation by  $3.8\%$  on the tasks of classification. Moreover, we even outperform the state-of-the-art by  $2.1\mathrm{mAP}$  on Gen1 and state-of-the-art feed-forward methods by  $6.0\mathrm{mAP}$  on the 1 Mpx dataset. This work thus opens a new unexplored field of explicit representation optimization that will push the limits of event-based learning methods.
+
+# 6. Acknowledgment
+
+This work was supported by the Swiss National Science Foundation through the National Centre of Competence in Research (NCCR) Robotics (grant number 51NF40_185543), and the European Research Council (ERC) under grant agreement No. 864042 (AGILE-FLIGHT).
+
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+
+[44] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Fei-Fei Li. ImageNet large scale visual recognition challenge. Int. J. Com. Vis., 115(3):211-252, Apr. 2015. 8, 9  
+[45] Salem Said, Lionel Bombrun, Yannick Berthoumieu, and Jonathan H. Manton. Riemannian gaussian distributions on the space of symmetric positive definite matrices. IEEE Trans. Inf. Theory, 63(4):2153-2170, 2017. 4  
+[46] Simon Schaefer, Daniel Gehrig, and Davide Scaramuzza. AEGNN: Asynchronous event-based graph neural networks. 2022. 2, 8  
+[47] Yusuke Sekikawa, Kosuke Hara, and Hideo Saito. EventNet: Asynchronous recursive event processing. In Conference of Computer Vision and Pattern Recognition (CVPR), 2019. 2  
+[48] Amos Sironi, Manuele Brambilla, Nicolas Bourdis, Xavier Lagorce, and Ryad Benosman. HATS: Histograms of averaged time surfaces for robust event-based object classification. In Conference of Computer Vision and Pattern Recognition (CVPR), pages 1731-1740, 2018. 2  
+[49] Bongki Son, Yunjae Suh, Sungho Kim, Heejae Jung, Jun-Seok Kim, Changwoo Shin, Keunj Park, Kyoobin Lee, Jinman Park, Jooyeon Woo, Yohan Roh, Hyunku Lee, Yibing Wang, Ilia Ovsiannikov, and Hyunsurk Ryu. A 640x480 dynamic vision sensor with a  $9\mu \mathrm{m}$  pixel and 300Meps addres-event representation. In IEEE Intl. Solid-State Circuits Conf. (ISSCC), 2017. 9  
+[50] Lin Wang, S. Mohammad Mostafavi I., Yo-Sung Ho, and Kuk-Jin Yoon. Event-based high dynamic range image and very high frame rate video generation using conditional generative adversarial networks. Conference of Computer Vision and Pattern Recognition (CVPR), June 2019. 2, 3, 5  
+[51] Bo Zhao, Ruoxi Ding, Shoushun Chen, Bernabe Linares-Barranco, and Huajin Tang. Feedforward categorization on AER motion events using cortex-like features in a spiking neural network. IEEE Trans. Neural Netw. Learn. Syst., 26(9):1963-1978, Sept. 2015. 2  
+[52] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. EV-FlowNet: Self-supervised optical flow estimation for event-based cameras. In Robotics: Science and Systems (RSS), 2018. 2  
+[53] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based learning of optical flow, depth, and egomotion. In Conference of Computer Vision and Pattern Recognition (CVPR), 2019. 2, 3, 5, 6
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "*Equal contribution"
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+                                    "content": "these cameras measure brightness changes independently for each pixel, and these changes are referred to as events. The events encode the time, location, and polarity (sign) of the brightness changes. Event cameras offer several advantages over frame-based cameras, including exceptionally high temporal resolution (in the order of "
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+                                    "type": "text",
+                                    "content": "s), a high dynamic range, and low power consumption. Their numerous benefits make them attractive for a wide range of applications like robotics, autonomous vehicles, and virtual reality. However, due to their sparse and asynchronous nature, applying classical computer vision algorithms remains challenging."
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+                                    "content": "Many state-of-the-art deep learning models address this challenge by converting sparse and asynchronous events into dense grid-like representations before processing them with off-the-shelf deep neural networks. By using these networks, methods like this enjoy the advantages of mature learning algorithms and network architectures, and optimized hardware, but we need to make a non-trivial choice of event representation. In fact, the computer vision and robotics fields are witnessing a surge in the number of research papers utilizing event-based vision, resulting in a plethora of new event representations being proposed. Despite this, extensive comparisons of these representations remain rare, making it unclear whether these newer representations should be adopted."
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+                                    "content": "No efficient methodology exists for comparing these representations. Conventionally, comparing event representations involves training a fixed deep-learning model for each event representation separately and subsequently selecting the optimal one based on a validation score. This process is very time-intensive since it requires network training in the loop which often takes hours or days (Fig. 1 a top)."
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+                                    "content": "In this work, we propose a fast method to compare event representations which circumvents the need to train a neural network and instead computes the Gromov-Wasserstein Discrepancy (GWD) between the raw events and event representation (Fig. 1 a bottom). This metric effectively measures the distortion that is introduced through converting raw events to representations and thus puts an upper bound on the amount of information that can be accessed by downstream neural networks. We show extensive experimental evidence, that this metric preserves the task-performance ranking across a wide range of input representations for several datasets, neural network backbones and tasks (Fig. 1 b). Due to its low computational cost, we apply the GWD to, for the first time, explicitly optimize over a large family of event representations, which reveals a new and powerful representation, which we term 12-channel Event Representation through Gromov-Wasserstein Optimization (ERGO-12). For the task of object detection, networks trained with these representations outperform other representations by "
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+                                    "type": "text",
+                                    "content": " on the 1 Mpx dataset and "
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+                                    "content": "on Gen1, even outperforming state-of-the-art methods by "
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+                                    "content": " on the 1 Mpx dataset. On object recognition, we instead find that our representation outperforms state-of-the-art representations by "
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+                                    "content": ". We believe that the GWD is a powerful tool that opens up a new research field that searches for optimized event representations. Our contributions are summarized as follows:"
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+                                            "content": "- We introduce a novel, efficient approach for comparing dense event representations using the Gromov-Wasserstein Discrepancy (GWD)."
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+                                            "content": "- We show extensive experimental evidence that it preserves the task performance ranking of neural networks trained with these representations across datasets, neural network backbones and tasks."
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+                                            "content": "- We use it to, for the first time, conduct a hyperparameter search on a vast family of event representations, unveiling novel and powerful event representations that outperform the current state-of-the-art representations on the object detection and object classification task."
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+                                    "content": "2. Related Work"
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+                                    "content": "In the field of event-based vision, two primary groups of representations exist: sparse and dense. Methods that use sparse representations [35, 51, 23, 37] preserve the sparsity in the events but do not yet scale to more complex tasks due to a lack of specialized hardware and mature neural networks architectures. This frequently results in lower performance on downstream tasks. In contrast, dense representations [31, 48, 53, 50] offer improved performance since they can leverage mature machine learning algorithms and neural network architectures. Sparse representations, pioneered by asynchronous SNNs [35, 23, 37], are limited by the lack of specialized hardware and computationally efficient backpropagation algorithms. Point cloud encoders [47, 40, 11] have been used due to the spatio-temporal nature of event data, but can be computationally expensive and noisy. Graph neural networks [26, 46, 4, 3, 33, 10] are scalable and have achieved high performance on various vision tasks but are still less accurate than dense methods for event-based vision. In this study, we focus on dense event representations and aim to achieve better task performance by utilizing existing efficient learning algorithms that are appropriate for current hardware."
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+                                    "content": "Early dense representations converted events to histograms [31], generated time surfaces [48] or combined both [52] while relying on standard neural network backbones to process them. However, these representations only capture a low-dimensional representation of events since they typically only use a few channels. Later approaches have tried to capture more event information by either computing higher-order moments [1] or stacking multiple time"
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+                                            "content": ". It is defined as the solution to an optimal transport problem which transports events pairs "
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+                                            "content": "T_{ij},T_{kl}"
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+                                            "type": "text",
+                                            "content": ". If the transport plan preserves the similarities "
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+                                            "content": " between event and feature pairs, this results in a low GWD."
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+                                    "content": "windows of events [53]. These methods still stack events based on fixed time windows which is problematic when the event rate becomes too large or too small and lead to the introduction of stacking based on the number of events [50]. In parallel, a bio-inspired approach led to the introduction of Time Ordered Recent Event Volumes (TORE) [2], which aggregate events into queues. However, they are slow to compute and perform similarly to existing Voxel Grids [53]. Most recently, a powerful representation was proposed by Nam et al. [34], which divides events into multiple overlapping windows that halve the number of events at each stage, which are more robust during varying scene dynamics."
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+                                    "type": "text",
+                                    "content": "Few papers study the effect of event representations on task performance. While [38] and [21] show small-scale ablation studies to select event representations, only Gehrig et al. [13] performed a large-scale investigation of event representations by training models on various inputs for multiple tasks. Their study demonstrated the advantages of splitting polarities and incorporating timestamps into representations, and it introduced a learnable representation. However, training for a single task was still computationally expensive, which limited the number of representations that could be compared. For this reason, their study did not cover a large number of representations, and in particular, did not consider different window sizes as is done in later work [50, 34], or more advanced aggregations and measurements like in [1]. Our method instead introduces an efficient metric to compare event representations that solves these limitations, allowing us to perform a search over a large family of event representations and go beyond the representations in [50, 1, 34, 14], including even non-differentiable hyperparameters."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "In this section, we will first introduce the preliminaries on computing event representations (Sec. 3.1) and then pro"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "pose the metric we use to measure the discrepancy between events and their representation based on the GWD (Sec. 3.2) before concluding with Sec. 3.3 where we use Bayesian optimization to find an optimal event representation."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "content": "3.1. Preliminaries"
+                                }
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+                                    "type": "text",
+                                    "content": "Event cameras measure brightness changes as an asynchronous stream of events. Each event is triggered when the intensity "
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+                                    "content": "L(\\mathbf{u})"
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+                                    "type": "text",
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{u} = (x, y)"
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+                                    "type": "text",
+                                    "content": " changes by the contrast threshold "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": ", and thus satisfies"
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+                {
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+                                    "type": "interline_equation",
+                                    "content": "p \\left[ L (\\mathbf {u}, t) - L (\\mathbf {u}, t - \\Delta t) \\right] = C \\tag {1}",
+                                    "image_path": "d0e5c305a63f2da54ac29c76cf10936544b6bdda741db94592191d83eb6f4215.jpg"
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "p\\in \\{-1,1\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the polarity of the event, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t - \\Delta t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the time of the last event. Within a time window "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        419,
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+                                        502
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Delta T"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        419,
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+                                        502
+                                    ],
+                                    "type": "text",
+                                    "content": " an event camera thus generates an ordered set of events "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        419,
+                                        547,
+                                        502
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{E} = \\{e_k\\}_{k = 0}^{N_e - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        419,
+                                        547,
+                                        502
+                                    ],
+                                    "type": "text",
+                                    "content": ", with each event "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_k = (\\mathbf{u}_k,t_k,p_k)\\in \\mathbb{R}^4"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". To bridge the gap between asynchronous events and dense neural networks, they are usually converted to a dense event representation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {R} = F (\\mathcal {E}), \\tag {2}",
+                                    "image_path": "a3edf268cdbc5f06332aeac62a78d37cc0fc290702534d09d72d0fd2d9c2a983.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "which has features "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathbf{x}} \\doteq \\mathcal{R}(\\mathbf{x}) \\in \\mathbb{R}^{N_f}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " indexed by the integer-valued pixel location "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The above representation thus generates a set of features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        520,
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+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F} = \\{f_{\\mathbf{x}}\\}_{\\mathbf{x} \\in \\Omega}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        520,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Omega"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the image domain and has size "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|\\Omega| = N_f"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N_f"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        520,
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+                                    ],
+                                    "type": "text",
+                                    "content": " being the number of pixels in the image. In what follows, we will derive a measure to quantify the distortion between events "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{E}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and features "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " based on the GWD."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "3.2. Gromov-Wasserstein Discrepancy"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Converting raw events to a representation invariably distorts the events by removing important distinguishing features from the stream. We would like to measure this distortion since we expect it correlates strongly with a neural network's ability to extract features from these events. In what follows, we will derive a measure of this distortion rate based on the GWD."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "We show an overview of the GWD in Fig. 2. We start by measuring the similarity between a set of events and their representation by building a soft correspondence between events "
+                                },
+                                {
+                                    "bbox": [
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+                                {
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+                                    "type": "text",
+                                    "content": " and features "
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+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathbf{x}_j}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which we denote as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{ij}^1"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". This transport plan effectively moves each event to a corresponding feature, thereby distorting the original set and destroying information. Importantly, such a plan can be interpreted as follows: We transport the events with a total weight of 1, i.e. per-event weight "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                        241
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{1}{N_e}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " to the output features, which also need to receive a total weight of 1 or per-feature weight of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{1}{N_f}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". By this construction, "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{ij}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " needs to satisfy "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sum_i T_{ij} = 1 / N_f"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sum_j T_{ij} = 1 / N_e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        241
+                                    ],
+                                    "type": "text",
+                                    "content": ". This means that a total weight of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        241
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1 / N_e"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        241
+                                    ],
+                                    "type": "text",
+                                    "content": " moves from each event, and each feature receives a total weight of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        241
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1 / N_f"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        289,
+                                        241
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
+                        242,
+                        290,
+                        411
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                242,
+                                290,
+                                411
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": "In the next step, we measure the distortion introduced by this transportation plan by considering pairwise similarities of input events and features. Let "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_i, e_k \\in \\mathcal{E}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " be a pair of events and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathbf{x}_j}, f_{\\mathbf{x}_l} \\in \\mathcal{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " pair of features, with similarity scores "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_{ik}^e \\doteq C^e(e_i, e_k)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_{jl}^f \\doteq C^f(f_{\\mathbf{x}_j}, f_{\\mathbf{x}_l})"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " between events and features respectively. Next, consider how the transport plan "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " acts on these pairs: Generally, a weight "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{ij}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " is moved from event "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " to feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathbf{x}_j}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": ". Similarly, the weight "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{kl}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " is moved from event "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " to feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathbf{x}_l}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": ". Ideally, such a transport plan should preserve the similarity between pairs of source events and target features, and thus the difference in similarity scores between pairs "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(i, k)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(j, l)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        242,
+                                        290,
+                                        411
+                                    ],
+                                    "type": "text",
+                                    "content": " can be used as a measure of distortion. For each event pair and feature pair, we define the distortion as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        110,
+                        419,
+                        287,
+                        436
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                436
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        110,
+                                        419,
+                                        287,
+                                        436
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {i j k l} = T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right), \\tag {3}",
+                                    "image_path": "352b8bf369fc33614fc61c6725dccdeaa3da4279d75c3ad53f946a12356ac5f9.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                                481
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        443,
+                                        287,
+                                        481
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        443,
+                                        287,
+                                        481
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes some disparity measurement between "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        443,
+                                        287,
+                                        481
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_{ik}^{e}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        443,
+                                        287,
+                                        481
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        443,
+                                        287,
+                                        481
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "C_{jl}^{f}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        443,
+                                        287,
+                                        481
+                                    ],
+                                    "type": "text",
+                                    "content": ". Summing over all possible pairs of events and features we thus arrive at the transportation cost:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        55,
+                        490,
+                        287,
+                        516
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                516
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        55,
+                                        490,
+                                        287,
+                                        516
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L (T; \\mathcal {E}, \\mathcal {F}) = \\sum_ {i, j, k, l} L _ {i j k l} = \\sum_ {i, j, k, l} T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right) \\tag {4}",
+                                    "image_path": "90d7a2c34f413b72fef2b9913882132a451d0cedc7924882da47a130baa62b10.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
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+                                        537
+                                    ],
+                                    "type": "text",
+                                    "content": "Minimizing over transport plans, we arrive at the GWD:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        83,
+                                        545,
+                                        287,
+                                        572
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L (\\mathcal {E}, \\mathcal {F}) = \\min  _ {T} \\sum_ {i, j, k, l} T _ {i j} T _ {k l} \\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right), \\tag {5}",
+                                    "image_path": "84883938997690efd31ed2f38f37b1b8defac6858cf6ae58432b04719af115b1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        47,
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+                        617
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                47,
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+                                617
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        580,
+                                        287,
+                                        617
+                                    ],
+                                    "type": "text",
+                                    "content": "which can be optimized efficiently using [39]. Since the above metric is defined for a single time window of events, we may average it over multiple samples to find:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        107,
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+                        287,
+                        653
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        107,
+                                        625,
+                                        287,
+                                        653
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {G W D} _ {N} = \\frac {1}{N} \\sum_ {i} L \\left(\\mathcal {E} _ {i}, \\mathcal {F} _ {i}\\right). \\tag {6}",
+                                    "image_path": "413dfac393129244bb2f90094c6e46a40d2d52e495cd29053d26745227b9c9f2.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        47,
+                                        662,
+                                        287,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GWD}_N"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        662,
+                                        287,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " can be interpreted as an average distortion rate from raw events to event representations. In Sec. 4.2, we"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
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+                                        143
+                                    ],
+                                    "type": "text",
+                                    "content": "show that "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GWD}_N"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "text",
+                                    "content": " correlates with a "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "NN"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "text",
+                                    "content": "'s performance with that representation across network backbones, datasets, and event representations. It's also efficient to compute, taking 9 seconds for 50,000 events. In what follows, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GWD}_N"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "text",
+                                    "content": " will denote the average over "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        72,
+                                        545,
+                                        143
+                                    ],
+                                    "type": "text",
+                                    "content": " samples, while GWD denotes the average over the whole validation set."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
+                        144,
+                        545,
+                        180
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                144,
+                                545,
+                                180
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        144,
+                                        545,
+                                        180
+                                    ],
+                                    "type": "text",
+                                    "content": "Similarity scores and distortion function As similarity scores, we choose Gaussian radial basis functions [45] for both events and image features. In detail,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        342,
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+                        545,
+                        213
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        342,
+                                        186,
+                                        545,
+                                        213
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "C _ {i k} ^ {e} = e ^ {\\frac {- \\| e _ {i} - e _ {k} \\| ^ {2}}{2 h ^ {2} \\sigma_ {e} ^ {2}}}, \\quad C _ {j l} ^ {f} = e ^ {\\frac {- \\| f _ {\\mathbf {x} _ {j}} - f _ {\\mathbf {x} _ {l}} \\| ^ {2}}{2 h ^ {2} \\sigma_ {f} ^ {2}}} \\tag {7}",
+                                    "image_path": "15fcbdfc2cea8e6a209d7610c2d895b976201bb95cc463fbe4729f298fe39ba4.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                        256
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        312,
+                                        236,
+                                        545,
+                                        256
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\sigma_ {e} ^ {2} = \\underset {i <   j} {\\operatorname {m e a n}} \\| e _ {i} - e _ {j} \\| ^ {2}, \\quad \\sigma_ {f} ^ {2} = \\underset {i <   j} {\\operatorname {m e a n}} \\| f _ {\\mathbf {x} _ {i}} - f _ {\\mathbf {x} _ {j}} \\| ^ {2}. \\tag {8}",
+                                    "image_path": "9496f4f084997ec86f8f16377059b3bc69a43f5f6e6acd6b82fc2e4abaca46b0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        304,
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+                        358
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "with a bandwidth parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h = 0.7"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        262,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The selection of data-dependent variances normalizes the distances between pairs of events and features such that the similarity score is robust to the dimensionality of the data and the number of samples in the source and target domain. These details are discussed in [7, 45, 36]. While more complex similarity scores could be used, this simple function already achieved good results. As the distortion function, we chose the KL-Divergence i.e."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} \\left(C _ {i k} ^ {e}, C _ {j l} ^ {f}\\right) = C _ {i k} ^ {e} \\log \\left(C _ {i k} ^ {e} / C _ {j l} ^ {f}\\right). \\tag {9}",
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+                                    "type": "text",
+                                    "content": "As a result, the optimization already rejects terms for which "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "C_{ik}^{e} \\approx 0"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", i.e. pairs of events that are far apart. We found that this property was also beneficial in improving the convergence of the optimization problem in Eq. (5)"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Improving Convergence of Eq. (5). We found that three features improved convergence and speed up the optimization: (i) Normalization of the event coordinates and timestamps by the sensor size and time window respectively, (ii) Concatenation of the normalized pixel position to the image features, and (iii) Sparsification of image features. Both (i) and (ii) make the optimization more numerically stable. In fact, without concatenating position information to image features, randomly pixel-wise shuffled event representations would retain the same GWD, although intuitively, neural networks would have a harder time learning from such representations since they typically process nearby features together. Thus reintroducing the position removes this ambiguity and improves the convergence. Finally, (iii) removes image features with "
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| f_{\\mathbf{x}} \\| = 0"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " since these correspond to pixels where no events were triggered. This step significantly sped up computation by reducing the size of the pair-wise similarity score matrix "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "C^f"
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+                                    "type": "text",
+                                    "content": ", with a small impact on convergence."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.3. Optimizing over Event Representations"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
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+                                    "type": "text",
+                                    "content": "With a fast method to measure the effectiveness of an event representation, we can now search for the optimal rep"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "<sup>1</sup>In the optimal transport literature, this correspondence is also called a transport plan."
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "Figure 3: Overview of the hyperparameters we use to construct an event representation (right). For each channel "
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+                                            "content": ", we select one of several event time windows "
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+                                            "content": "w_{c} \\in \\mathcal{W}"
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+                                            "type": "text",
+                                            "content": " (timestamp, polarity, positive timestamps, etc.), and aggregation functions "
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+                                            "type": "text",
+                                            "content": " parameters."
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "resentation by minimizing Eq. (6) over a space of possible representations with a set of hyperparameters "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "p"
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "interline_equation",
+                                    "content": "p ^ {*} = \\arg \\min  _ {p} \\frac {1}{N} \\sum_ {i} L \\left(\\mathcal {E} _ {i}, \\mathcal {F} _ {i} (p)\\right). \\tag {10}",
+                                    "image_path": "4f16b8c17b817472f64b7c821c0ae5cab00ed7210aa8de650abccd350bde174f.jpg"
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+                                    "type": "text",
+                                    "content": "To simplify this optimization, we first describe a very general parametrization, which defines a large family of event representations, extending the family described in [13] in a few ways. These hyperparameters are a small set of categorical variables which can subsequently be optimized using Bayesian optimization."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Parametrization of Event Representations We illustrate the hyperparameters in Fig. 3. In general, we assume an event representation comprises a stack of features, indexed by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " (right side), each of which is derived from "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(i)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " a specific time window "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "text",
+                                    "content": " of events, "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(ii)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " a specific measurement "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        379,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of events such as polarity or timestamps, and "
+                                },
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(iii)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " a specific aggregation "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", such as summation or averaging. We write such a representation as "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " concatenated feature maps:"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {R} = \\left[ \\mathcal {R} _ {0} \\mid \\mathcal {R} _ {1} \\dots \\mid \\mathcal {R} _ {N _ {c} - 1} \\right] \\tag {11}",
+                                    "image_path": "7ad52e63ee4144544bf7a54c2e00b9f254e7b62f961e04ee3ac9a15a8bd93c14.jpg"
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+                                    "type": "interline_equation",
+                                    "content": "\\text {w i t h} \\mathcal {R} _ {c} = a _ {c} \\left(m _ {c} \\left(w _ {c} (\\mathcal {E})\\right)\\right) \\tag {12}",
+                                    "image_path": "1091a3d45c0bdd3fa15724f1d88e24e646bbe69aafbe7d4f30fd094be3ec7cbb.jpg"
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+                                    "type": "text",
+                                    "content": "Here "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is a windowing function which selects events within an interval, "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " is the measurement function which selects an event feature, and "
+                                },
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is the aggregation function, which aggregates measurements into a single feature map."
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+                                    "content": "Note, in our formulation each channel can have an independent set of parameters, different to [13], which assumes a shared aggregation and measurement function for all channels. This makes our parametrization substantially more expressive than the one in [13]. The number of (non-learnable) representations is "
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+                                    "content": "\\left(|\\mathcal{A}||\\mathcal{M}||\\mathcal{W}|\\right)^{N_c}\\approx 3.21\\times 10^{27}"
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+                                    "content": ", since each channel can be configured independently. Moreover, while "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " were already discussed in [13], the windowing function is a more general concept, illustrated in Fig. 3 (left). While these windows can be non-overlapping "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "(w_{3},w_{4},w_{2})"
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+                                    "type": "text",
+                                    "content": ", as for Voxel Grids [53], they can also be overlapping, "
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+                                    "type": "text",
+                                    "content": " as in Mixed"
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+                                    "type": "text",
+                                    "content": "Density Event Stacks [34], or describe windows of a constant event count or constant time [50] In this work we allow each feature channel to select from a basis of windows "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{W} = \\{[t_{0,k}, t_{1,k}]\\}_{k=0}^{N_k-1}"
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+                                {
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+                                    "type": "text",
+                                    "content": ", which can combine all types of windows unifying these concepts. In summary, a representation is parametrized by:"
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+                            ]
+                        }
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+                                    "type": "interline_equation",
+                                    "content": "p = \\left\\{\\left(w _ {c}, a _ {c}, m _ {c}\\right) \\right\\} _ {c = 0} ^ {N _ {c} - 1} \\tag {13}",
+                                    "image_path": "60c0630c3e53fcc3e51779175bac09fee923dd7be40cd62cd41d82b0bfe9dd6e.jpg"
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+                                    "type": "interline_equation",
+                                    "content": "\\text {w i t h} \\quad m _ {c} \\in \\mathcal {M}, a _ {c} \\in \\mathcal {A}, w _ {c} \\in \\mathcal {W}.",
+                                    "image_path": "40fea0048f08b78f7851ed632715bc762c3d2399781045132713b27339100db9.jpg"
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+                                    "type": "text",
+                                    "content": "For the sets of aggregation functions we select "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A} = \\{\\max, \\text{sum}, \\text{mean}, \\text{variance}\\}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and for the measurement functions "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{M} = \\{t_{+}, t_{-}, t, p, c_{+}, c_{-}, c\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " which are most commonly used. Here "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "c, p,"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "t"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denote event count (discarding polarity), polarity, and timestamp. The subscripts "
+                                },
+                                {
+                                    "bbox": [
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+                                        358,
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+                                    "type": "inline_equation",
+                                    "content": "+ / -"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " select only positive or negative events. For the basis of time windows, we select three equally spaced, non-overlapping windows from [53] and four overlapping windows from [34], including the global window. These are illustrated in Fig. 7 (right)."
+                                }
+                            ]
+                        }
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+                {
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+                                    "type": "text",
+                                    "content": "Optimization Procedure The aforementioned parametrization generates redundant combinations that can be obtained by permuting channels or selecting the same feature for different channels. To address this issue and expedite convergence, we propose a stage-wise optimization procedure. Initially, we start with a volume consisting of zeros with "
+                                },
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+                                    "type": "text",
+                                    "content": " channels and optimize over "
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+                                    "type": "inline_equation",
+                                    "content": "a_0, w_0"
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "m_0"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to fill in the first channel. Next, we optimize the feature for the second channel while keeping the first fixed. With this iterative process, we incrementally fill up the representation, avoiding the selection of redundant representations and resulting in faster optimization. At each stage, we use Gryffin [18], a specialized Bayesian optimizer for categorical variables."
+                                }
+                            ]
+                        }
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+                                    "content": "4. Experiments"
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+                                    "content": "In Sec. 4.1, we first connect the GWD and event distortion, demonstrating its behavior on several toy examples. Next, in Sec. 4.2, we showcase the correlation between the"
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+                                            "content": "Figure 4: Validation of our metric on the Gen1 validation set. (top) Our metric for Voxel Grids [53] and Mixed-Density Event Stacks [34] with an increasing number of channels. (bottom) Effect of applying Gaussian blur with different blur kernels to the event representation."
+                                        }
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+                                    "content": "metric and task performance across multiple tasks, datasets, backbones, and representations. Lastly, in Sec. 4.3, we show the outcome of Bayesian Optimization on the GWD and offer insights on the acquired event representation before comparing it against the state-of-the-art."
+                                }
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+                                    "content": "As explained in Sec. 3.2, the GWD measures the distortion rate from raw events to event representation. Two experiments were designed to test this claim: (1) analyzing the behavior of the metric when varying the number of bins in Voxel Grid [53] and Mixed-Density Event Stack (MDES) [34] representations, and (2) blurring the event representation with increasing standard deviations before measuring the GWD. We perform experiments on the validation set of Gen1[9] and report the results in Fig. 4."
+                                }
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+                    ],
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+                                    "type": "text",
+                                    "content": "Fig. 4 (top) confirms that the GWD decreases as the number of channels increases in both Voxel Grids and Mixed-Density Event Stacks, which aligns with our intuition that using more channels preserves more information from raw events, resulting in a lower distortion rate. Similarly, the bottom part illustrates that with a growing blur radius, more edges in the event representation are removed, leading to an increase in the GWD. This verifies that the GWD measures the distortion from raw events to event representations."
+                                }
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+                                    "content": "4.2. Object Detection"
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+                                    "content": "Next, we investigate the relationship between GWD and the task performance of a "
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+                                    "content": " trained for object detection. We choose two widely used object detection datasets, the Gen1 [9] and 1 Mpx [38] Automotive Detection Dataset, which both deal with event streams featuring labeled bounding boxes for pedestrians, cars, and other vehicles. While"
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+                    "index": 8
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Figure 5: Correlation of the Gromov-Wasserstein Discrepancy with the mAP (higher is better) for object detection on the Gen1 [9] (top) and 1 Mpx [38] (bottom) datasets. Note the spliced y-axis on 1 Mpx, due to the high GWD of the 2D Histogram."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": "the former has a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "304 \\times 240"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": ", the latter has a resolution of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1280 \\times 720"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": ". We report the GWD computed over the validation set of each dataset and then train an off-the-shelf object detection framework based on YOLOv6 [24], pre-trained on the Microsoft Common Objects in Context (MS-COCO) [28], on different input representations as in [13]. To accommodate the varying number of channels, we replace the 3-channel input convolution with a "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{c} = 12"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " channel input convolution, where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        366,
+                                        546,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the number of channels in the representation. To show the generality of the result, we also vary the detection backbone between ResNet-50 [17], EfficientRep [24] and Swin Transformer V2 [30], and report results for each."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        304,
+                        522,
+                        545,
+                        557
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Representations: We test a range of common representations listed below. We compute 12 channels for each representation, except for the 2D Histogram, which has 2."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
+                                        558,
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+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": "Voxel Grid: Here, the event time window is split into "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        558,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        558,
+                                        545,
+                                        605
+                                    ],
+                                    "type": "text",
+                                    "content": " equal, non-overlapping time windows, and then events in the same time window are aggregated by summing their polarity on a per-pixel basis using bilinear voting [53]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        304,
+                        605,
+                        545,
+                        654
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Mixed-Density Event Stack (MDES): For each channel "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
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+                                        654
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        654
+                                    ],
+                                    "type": "text",
+                                    "content": ", this representation selects the most recent "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        654
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{N_e}{2^c}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        654
+                                    ],
+                                    "type": "text",
+                                    "content": " events, where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
+                                        545,
+                                        654
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_e"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        605,
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+                                        654
+                                    ],
+                                    "type": "text",
+                                    "content": " are the events in the time window. For each window, it aggregates the polarity at that pixel [34]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        304,
+                        654,
+                        545,
+                        677
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        677
+                                    ],
+                                    "type": "text",
+                                    "content": "Event Histograms: Events in the time window are split by polarity and then summed into two channels [31]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        304,
+                        677,
+                        545,
+                        715
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": "Time Surface: We convert events into time surfaces from [22] with a decay constant of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau = 5\\mathrm{ms}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then sample it at "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{N_c}{2} = 6"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        677,
+                                        545,
+                                        715
+                                    ],
+                                    "type": "text",
+                                    "content": " equally spaced timestamps, once for"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                }
+            ],
+            "discarded_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "page_number",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "12851"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                }
+            ],
+            "page_size": [
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+            ],
+            "page_idx": 5
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "positive and negative events resulting in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        132
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{c} = 12"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": " channels.  \nTORE: The Time-Ordered Recent Event Volumes store event timestamps in per-pixel queues. We use queues with capacity "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        132
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\frac{N_c}{2} = 6"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": ", one for positive and one for negative events, and concatenate them to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        132
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_{c} = 12"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        72,
+                                        286,
+                                        132
+                                    ],
+                                    "type": "text",
+                                    "content": " channels."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        46,
+                        133,
+                        286,
+                        191
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
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+                                286,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        133,
+                                        286,
+                                        191
+                                    ],
+                                    "type": "text",
+                                    "content": "Learned representation: Event Spike Tensor (EST) [13] is a learnable event representation that employs a Quantization Layer featuring a trainable kernel. This approach enables the model to effectively transform raw events, optimizing their performance for a given task."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        46,
+                        192,
+                        286,
+                        287
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
+                                        192,
+                                        286,
+                                        287
+                                    ],
+                                    "type": "text",
+                                    "content": "Training Details We adopt the training procedure from YOLOv6 [24]. For each backbone, representation, and dataset, we train for 100 epochs, using Stochastic Gradient Descent with Nesterov momentum increasing from 0.5 to 0.83 over the first 2 epochs. We use a batch size of 32, and a Cosine learning rate schedule, starting at 0.00323 and ending at 0.000387 after 100 epochs. We adopt the classification and box regression losses in [24]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        46,
+                        295,
+                        286,
+                        521
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                295,
+                                286,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        295,
+                                        286,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": "Results: Figs. 5 summarizes the results of the above experiments. For both datasets, Gen1 and 1 Mpx, and all backbones, there is a clear correlation between the GWD and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all three network backbones. In particular, MDES with a Swin-V2 detection backbone consistently achieves the highest mAP with 0.43 on Gen1 and 0.39 on 1 Mpx. It also consistently achieves the lowest GWD with 0.38 on Gen1 and 0.40 on 1 Mpx. Utilizing the learnable EST in YOLOv6 with SwinV2 backbone, we achieved a 45.31 mAP score on the Gen1 validation set and a GWD score of 0.3552, positioning EST between MDES and ERGO-12 in Fig. 1b, confirming the expected ranking. We also see that the Swin V2 backbone outperforms other backbones on both datasets for all tested representations. We conclude that while the representation affects task performance, the neural network also has an influence. However, we see that the overall ranking of the representations is preserved."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        46,
+                        522,
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+                        701
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        522,
+                                        286,
+                                        701
+                                    ],
+                                    "type": "text",
+                                    "content": "Using Fewer Samples While in the previous section, we reported the GWD over the validation set of the Gen1 and the 1 Mpx datasets, averaging this metric over such a large dataset still incurs a high computational cost and would make such a metric infeasible for optimization. Therefore, here we investigate if we can use smaller sample sizes to speed up the computation of GWD. In Fig. 6, we show the GWD for the representations in Sec. 4.2 while varying the number of samples. We see that as the sample number decreases, the mean values of the metric change, but the ranking between representations is still preserved reliably after around 100 samples, and thus we use "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        522,
+                                        286,
+                                        701
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GWD}_{100}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        522,
+                                        286,
+                                        701
+                                    ],
+                                    "type": "text",
+                                    "content": " to optimize over representations. Below this number, the ranking of representations can fluctuate. However, we found that this happens due to a bad convergence of Eq. (5)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        53,
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+                        713
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            ],
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+                                    "bbox": [
+                                        53,
+                                        701,
+                                        286,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": "Timing Results: We time the computation of the GWD"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "type": "image",
+                    "bbox": [
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+                        232
+                    ],
+                    "blocks": [
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+                            ],
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+                                            "bbox": [
+                                                322,
+                                                86,
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+                                            ],
+                                            "type": "image",
+                                            "image_path": "031abe41d5b5eafcda630b4c1592cc1a0d3524dffa39ace93806b47723b0243f.jpg"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6,
+                            "angle": 0,
+                            "type": "image_body"
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "lines": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                                236,
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+                                                259
+                                            ],
+                                            "type": "text",
+                                            "content": "Figure 6: Gromov-Wasserstein Discrepancy for a varying number of samples from the validation set."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        304,
+                        267,
+                        545,
+                        363
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
+                                267,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        267,
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+                                        363
+                                    ],
+                                    "type": "text",
+                                    "content": "over 100 samples of the Gen1 validation set, where each sample comprises 50,000 events. We run our experiment on an AMD EPYC 7702 32-core server-grade CPU with 32 GB RAM and achieve a runtime of 15 minutes. Note that computing the GWD does not require a GPU. By contrast, training the models in Fig. 5 requires 2 days on a single Tesla V100 GPU with 32 GB of memory, making GWD computation 192 times faster."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "4.3. Optimization of Event Representations"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                {
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+                                    "type": "text",
+                                    "content": "Here we report the results of optimizing the event representation according to the procedure in Sec. 3.3. We optimize "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N_{c} = 12"
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+                                    "type": "text",
+                                    "content": " channels, and at each optimization cycle for channel "
+                                },
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+                                    "type": "text",
+                                    "content": ", the Bayesian Optimizer selects 100 configurations and then keeps the best-performing configuration."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
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+                                    "type": "text",
+                                    "content": "We show the result of this optimization procedure in Fig. 7. The left shows how the GWD decreases as new channels are added to the representation. We see that after 2 channels, our method outperforms 2D Histograms, after 6 channels we outperform Time Surfaces, after 7 channels we outperform Voxel Grids / TORE, after 9 channels we outperform Mixed-Density Event Stacks and finally, after 12 channels, we achieve a "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{GWD}_{100}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " of 0.47. On the right, we show the different windows (columns) and measurement functions (rows) that are selected. We do not show the order since our representation is unique up to a random channel permutation. However, in the appendix, we show which features are selected at each stage. We see that all windows and all measurement functions are selected at least once, showing how our representation tries to diversify as much as possible. Moreover, timestamp-based measurements often show multiple aggregations, which we argue are necessary to replicate their complex continuous signal."
+                                }
+                            ]
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+                    "index": 11
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+                                    "type": "text",
+                                    "content": "Comparison with State-of-the-Art Here we compare our method against state-of-the-art recurrent and feedforward methods on the Gen1 and 1 Mpx test sets. We summarize the results in Tab. 1. Recurrent methods in"
+                                }
+                            ]
+                        }
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+                                            "content": "Figure 7: Gromov-Wasserstein Discrepancy for 100 samples (left). At each channel, a Bayesian optimizer selects the next best hyperparameter triple. The chosen hyperparameters are broken down by window and measurement function (right)."
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+                                            "html": "<table><tr><td colspan=\"2\"></td><td>\\( w_0 \\)</td><td>\\( w_1 \\)</td><td>\\( w_2 \\)</td><td>\\( w_3 \\)</td><td>\\( w_4 \\)</td><td>\\( w_5 \\)</td><td>\\( w_6 \\)</td></tr><tr><td rowspan=\"3\">t</td><td>+</td><td>sum</td><td>sum mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>-</td><td>sum</td><td>mean</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td>var max</td><td></td><td></td><td></td></tr><tr><td rowspan=\"3\">c</td><td>+</td><td></td><td></td><td></td><td></td><td></td><td>mean</td><td></td></tr><tr><td>-</td><td></td><td></td><td>sum</td><td></td><td></td><td></td><td></td></tr><tr><td>all</td><td></td><td></td><td></td><td></td><td>sum</td><td></td><td>sum</td></tr><tr><td colspan=\"2\">p</td><td></td><td></td><td></td><td>var</td><td></td><td></td><td></td></tr></table>",
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+                                            "html": "<table><tr><td>tNe-1</td></tr><tr><td>w6</td></tr><tr><td>w5</td></tr><tr><td>w4</td></tr><tr><td>w3</td></tr><tr><td>w2</td></tr><tr><td>w1</td></tr><tr><td>w0</td></tr><tr><td>t0</td></tr></table>",
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+                {
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+                    ],
+                    "blocks": [
+                        {
+                            "bbox": [
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+                            "lines": [
+                                {
+                                    "bbox": [
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Event Repr.</td><td rowspan=\"2\">Recurrent</td><td colspan=\"2\">mAP↑</td></tr><tr><td>Gen1 [9]</td><td>1 Mpx [38]</td></tr><tr><td>MatrixLSTM+YOLOv3 [5]</td><td>MatrixLSTM</td><td>✓</td><td>0.310</td><td>-</td></tr><tr><td>E2VID+RetinaNet [41]</td><td>Reconstructions</td><td>✓</td><td>0.270</td><td>0.250</td></tr><tr><td>RED [38]</td><td>Voxel Grid</td><td>✓</td><td>0.400</td><td>0.430</td></tr><tr><td>RVT-B [16]</td><td>2D Histogram</td><td>✓</td><td>0.472</td><td>0.474</td></tr><tr><td>ASTMNet [25]</td><td>Asynchronous attention embedding</td><td>✓</td><td>0.467</td><td>0.483</td></tr><tr><td>Events+RetinaNet [38]</td><td>Voxel Grid</td><td>✗</td><td>0.340</td><td>0.180</td></tr><tr><td>Events+SSD [19]</td><td>2D Histogram</td><td>✗</td><td>0.301</td><td>0.340</td></tr><tr><td>Events+RRC [6]</td><td>2D Histogram</td><td>✗</td><td>0.307</td><td>0.343</td></tr><tr><td>Events+YOLOv3 [20]</td><td>2D Histogram</td><td>✗</td><td>0.312</td><td>0.346</td></tr><tr><td>AEGNN [46]</td><td>Graph</td><td>✗</td><td>0.163</td><td>-</td></tr><tr><td>EAGR [15]</td><td>Graph</td><td>✗</td><td>0.321</td><td>-</td></tr><tr><td>Spiking DenseNet [8]</td><td>Spike Train</td><td>✗</td><td>0.189</td><td>-</td></tr><tr><td>AsyNet [32]</td><td>2D Histogram</td><td>✗</td><td>0.145</td><td>-</td></tr><tr><td></td><td>2D Histogram</td><td>✗</td><td>0.339</td><td>0.327</td></tr><tr><td></td><td>Time Surface</td><td>✗</td><td>0.490</td><td>0.383</td></tr><tr><td></td><td>TORE</td><td>✗</td><td>0.436</td><td>0.381</td></tr><tr><td></td><td>Voxel Grid</td><td>✗</td><td>0.395</td><td>0.375</td></tr><tr><td></td><td>MDES</td><td>✗</td><td>0.427</td><td>0.378</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.493</td><td>0.400</td></tr><tr><td></td><td>ERGO-12</td><td>✗</td><td>0.504*</td><td>0.406*</td></tr></table>",
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+                                        }
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+                            ],
+                            "index": 4,
+                            "angle": 0,
+                            "type": "table_body"
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Table 1: Comparison of state-of-the-art event-based object detectors on the test sets of Gen1 [9] and 1 Mpx [38]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5,
+                    "angle": 0,
+                    "type": "text"
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                414,
+                                287,
+                                605
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "clude MatrixLSTM+YOLOv3 [5], which uses a recurrent, learned input representation with a YOLOv3 [42] detector, E2VID+RetinaNet [41] which uses recurrent E2VID reconstructions with a RetinaNet [27] detector, RVT-B which uses a recurrent transformer [16], and RED [38], a recurrent CNN. ASTMNet [25] utilizes asynchronous attention embedding and incorporates recurrent layers in deeper layers, claiming comparable results on both datasets. However, it is not open source. Feedforward methods are grouped into graph-based methods NVS-S [26], AEGNN [46] and EAGR [15], sparse method AsyNet [32], spiking method Spiking DenseNet [8], and finally feedforward dense methods Events+RetinaNet [38], Events+SSD [19] Events+RRC [6], and Events+YOLOv3 [20] which use events as input, and use the RetinaNet [27], SSD [29], RRC [43] or YOLOv3 [42] detector respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        46,
+                        605,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We compare these methods to our best-performing YOLOv6 detector from Sec. 4.2 with a SwinV2 transformer backbone trained on various input representations. These include the ones analyzed in Sec. 4.2, i.e. the 2D Histogram, Time Surface, TORE, Voxel Grid, and MDES, as well as the optimized representation ERGO-12. Note that these methods do not include data augmentation. We also trained our model with Mixup and Mosaic augmentation from [24], and is indicated by an asterisk * in Tab. 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Results On the Gen1 dataset, we see that YOLOv6 with the SWINv2 backbone and ERGO-12 input and data augmentation outperforms all state-of-the-art methods by up to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "2.9\\%"
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+                                    "type": "text",
+                                    "content": " mAP by achieving an mAP of 0.504. The runner-up is RVT-B, which uses a recurrent vision transformer. Even without data augmentation, our network with ERGO-12 achieves 0.493, which improves the mAP by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "2.1\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " compared to RVT-B. Compared to the other feed-forward methods based on YOLOv6, ERGO-12 achieves an 0.3 mAP higher mAP, the next best being YOLOv6 with Time Surface [22] with 0.490. Interestingly, as indicated in Fig. 1 (b), the difference in mAP performance between ERGO-12 and Time Surface is 1.8 mAP on the validation set of the Gen1 dataset, which is substantially larger than on the test set."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
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+                    "type": "text",
+                    "angle": 0,
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+                        {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "On 1 Mpx, the best-performing method is ASTMNet with an mAP of 0.483, followed by RVT-B with 0.474. From the feed-forward methods YOLOv6 with ERGO-12 and data augmentation achieves the highest score with 0.406, outperforming runner-up method YOLOv6 with Time Surfaces by "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "2.3\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " mAP. Even without augmentation, ERGO-12 achieves a "
+                                },
+                                {
+                                    "bbox": [
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+                                        434,
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+                                        626
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1.7\\%"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " higher score than YOLOv6 with Time Surfaces. Compared to state-of-the-art feed-forward methods, ERGO-12 with data augmentation achieves a "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "6.0\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "text",
+                                    "content": " higher score, the runner-up being Events+YOLOv3 with 0.346. On this dataset, recurrent methods are known to perform better since many sequences include stops or slow-motion scenarios. This is challenging for feed-forward methods since they are not able to maintain long-term memory. In general, the improvement of ERGO-12 on 1 Mpx is higher compared to Gen1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.4. Object Classification"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                                            "html": "<table><tr><td>Representation</td><td>Description</td><td># of Channels</td><td>Accuracy(%)</td></tr><tr><td>2D Histogram</td><td>Positive and negative event counts</td><td>2</td><td>46.10</td></tr><tr><td>Time Surface</td><td>A hierarchy of event-based time-surfaces</td><td>12</td><td>57.58</td></tr><tr><td>TORE</td><td>Time-ordered recent event volumes</td><td>12</td><td>54.64</td></tr><tr><td>Voxel Grid</td><td>Voxelized grid with bilinear voting aggregation</td><td>12</td><td>52.40</td></tr><tr><td>MDES</td><td>Mixed density event stack</td><td>12</td><td>53.30</td></tr><tr><td>ERGO-12</td><td>Event representation from GWD optimization</td><td>12</td><td>61.40</td></tr></table>",
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+                                    "content": "Table 2: Mini N-ImageNet validation accuracy evaluated on various event representations."
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+                                    "type": "text",
+                                    "content": "representations. We use the large-scale neuromorphic variant of the ImageNet dataset [44], captured from an event camera that observes monitor-displayed images from ImageNet. Event sequences were recorded using the "
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+                                    "content": "480 \\times 640"
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+                                    "content": " resolution Samsung DVS Gen3 event camera [49]. We report the GWD computed over the validation set of the Gen1 dataset. Subsequently, we train the model on Mini N-ImageNet. We opt for GWD on the Gen1 dataset to show the generalization capability of GWD across diverse datasets."
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+                                    "content": "Representations: Excluding the learned representation, we evaluate using identical representations as in object detection. Each representation is computed over 12 channels, except for the 2D Histogram, which uses two channels."
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+                                    "content": "Training Details: Adopting the methodology from the N-ImageNet study [21], all inputs are resized to a "
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+                                    "content": " dimension, optimizing GPU memory and inference duration. Training is initialized from scratch with a learning rate set at "
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+                                    "content": "3 \\cdot 10^{-4}"
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+                                    "content": " and spans 100 epochs. The Adam optimizer with a Nesterov momentum of 0.9 and a weight decay of 0.0001 is used alongside a batch size of 64."
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+                                    "type": "text",
+                                    "content": "Results: Table 2 summarizes the results of the experiments. There is a clear correlation between the GWD (even on different datasets, in this case, Gen1) and the task performance, i.e. task performance increases as GWD decreases. This conclusion holds for all tested representations on the Mini N-ImageNet dataset. We obtained the following validation set accuracies: 2D Histogram "
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+                                    "content": "(46.10\\%)"
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+                                    "content": ", Time Surface "
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+                                    "type": "inline_equation",
+                                    "content": "(57.58\\%)"
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+                                    "content": ", TORE "
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+                                    "content": "(54.64\\%)"
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+                                    "type": "text",
+                                    "content": ", Voxel Grid "
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+                                    "type": "inline_equation",
+                                    "content": "(52.40\\%)"
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+                                    "type": "text",
+                                    "content": ", MDES "
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+                                    "type": "inline_equation",
+                                    "content": "(53.30\\%)"
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+                                {
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+                                    "type": "text",
+                                    "content": ", ERGO-12 "
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+                                    "type": "inline_equation",
+                                    "content": "(61.4\\%)"
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+                                    "type": "text",
+                                    "content": ". Their ranking is consistent with the GWD ranking in Fig. 5. Therefore, the GWD can be used also for classification."
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+                            ]
+                        }
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+                    "index": 5
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "type": "text",
+                                    "content": "State-of-the-art event-based deep learning methods typically need to convert raw events into dense input representations before they can be processed by standard net"
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+                            ]
+                        }
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+                {
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+                                    "type": "text",
+                                    "content": "works. However, selecting this representation is very expensive since it requires training a separate neural network for each representation and comparing the validation scores. In this work, we circumvent this bottleneck by measuring the quality of event representations with the Gromov Wasserstein Discrepancy (GWD), which is 200 times faster to compute. We validated extensively on multiple tasks, datasets and neural network backbones that the performance of neural networks trained with a representation correlates with its GWD. We then used this metric to, for the first time, optimize over a large family of representations, revealing a new, powerful representation, ERGO-12. With it, we outperform state-of-the-art representations by "
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+                                    "content": "1.9\\mathrm{mAP}"
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+                                    "type": "text",
+                                    "content": " on the 1 Mpx dataset and "
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+                                    "type": "inline_equation",
+                                    "content": "0.3\\mathrm{mAP}"
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+                                    "type": "text",
+                                    "content": " on the Gen1 dataset, two object detection benchmarks. We also exceed existing representation by "
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+                                    "type": "inline_equation",
+                                    "content": "3.8\\%"
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+                                    "type": "text",
+                                    "content": " on the tasks of classification. Moreover, we even outperform the state-of-the-art by "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "2.1\\mathrm{mAP}"
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+                                    "type": "text",
+                                    "content": " on Gen1 and state-of-the-art feed-forward methods by "
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+                                    "type": "inline_equation",
+                                    "content": "6.0\\mathrm{mAP}"
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+                                    "type": "text",
+                                    "content": " on the 1 Mpx dataset. This work thus opens a new unexplored field of explicit representation optimization that will push the limits of event-based learning methods."
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+                                    "content": "6. Acknowledgment"
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+                                    "content": "This work was supported by the Swiss National Science Foundation through the National Centre of Competence in Research (NCCR) Robotics (grant number 51NF40_185543), and the European Research Council (ERC) under grant agreement No. 864042 (AGILE-FLIGHT)."
+                                }
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+                                            "type": "text",
+                                            "content": "[1] Inigo Alonso and Ana C Murillo. EV-SegNet: Semantic segmentation for event-based cameras. In CVPRW, 2019. 2, 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[2] Robert W. Baldwin, Ruixu Liu, Mohammed Bakheet Almatrafi, Vijayan K. Asari, and Keigo Hirakawa. Time-ordered recent event (tore) volumes for event cameras. IEEE T-PAMI., 45:2519-2532, 2021. 3"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[3] Yin Bi, Aaron Chadha, Alhabib Abbas, Eirina Bourtsovatze, and Yiannis Andreopoulos. Graph-based object classification for neuromorphic vision sensing. IEEE Int. Conf. Comput. Vis. (ICCV), 2019. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
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diff --git a/2023/From Knowledge Distillation to Self-Knowledge Distillation_ A Unified Approach with Normalized Loss and Customized Soft Labels/7e406dac-df76-4483-b6be-35c6233f9e4a_content_list.json b/2023/From Knowledge Distillation to Self-Knowledge Distillation_ A Unified Approach with Normalized Loss and Customized Soft Labels/7e406dac-df76-4483-b6be-35c6233f9e4a_content_list.json
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+++ b/2023/From Knowledge Distillation to Self-Knowledge Distillation_ A Unified Approach with Normalized Loss and Customized Soft Labels/7e406dac-df76-4483-b6be-35c6233f9e4a_content_list.json	
@@ -0,0 +1,1842 @@
+[
+    {
+        "type": "text",
+        "text": "From Knowledge Distillation to Self-Knowledge Distillation: A Unified Approach with Normalized Loss and Customized Soft Labels",
+        "text_level": 1,
+        "bbox": [
+            129,
+            128,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zhendong Yang $^{1,2*}$  Ailing Zeng $^{2}$  Zhe Li $^{3}$  Tianke Zhang $^{1}$  Chun Yuan $^{1\\dagger}$  Yu Li $^{2\\dagger}$ $^{1}$ Tsinghua Shenzhen International Graduate School  $^{2}$ International Digital Economy Academy (IDEA) Institute of Automation, Chinese Academy of Sciences",
+        "bbox": [
+            86,
+            202,
+            908,
+            256
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{yangzd21,ztk21}@mails.tsinghua.edu.cn axel.li@outlook.com",
+        "bbox": [
+            233,
+            258,
+            761,
+            273
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "yuanc@sz.tsinghua.edu.cn {zengailing, liyu}@idea.edu.cn",
+        "bbox": [
+            246,
+            277,
+            746,
+            292
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            325,
+            313,
+            342
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Knowledge Distillation (KD) uses the teacher's logits as soft labels to guide the student, while self-KD does not need a real teacher to require the soft labels. This work unifies the formulations of the two tasks by decomposing and reorganizing the generic KD loss into a Normalized KD (NKD) loss and customized soft labels for both target class (image's category) and non-target classes named Universal Self-KD (USKD). We decompose the KD loss and find the non-target loss from it forces the student's non-target logits to match the teacher's, but the sum of the two nontarget logits is different, preventing them from being identical. NKD normalizes the non-target logits to equalize their sum. It can be generally used for KD and self-KD to better use the soft labels for distillation. USKD generates customized soft labels for both target and non-target classes without a teacher. It smoothes the target logit of the student as the soft target label and uses the rank of the intermediate feature to generate the soft non-target labels with Zipf's law. For KD with teachers, NKD achieves state-of-the-art performance on CIFAR-100 and ImageNet, boosting the ImageNet Top-1 accuracy of Res-18 from  $69.90\\%$  to  $71.96\\%$  with a Res-34 teacher. For self-KD without teachers, USKD is the first method that can be effectively applied to both CNN and ViT models with negligible additional time and memory cost, resulting in new state-of-the-art results, such as  $1.17\\%$  and  $0.55\\%$  accuracy gains on ImageNet for MobileNet and DeiT-Tiny, respectively. Code is available at https://github.com/yzd-v/cls_KD.",
+        "bbox": [
+            75,
+            358,
+            473,
+            781
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            809,
+            209,
+            825
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep convolutional neural networks (CNNs) have significantly advanced the performance in many tasks [8, 9,",
+        "bbox": [
+            76,
+            835,
+            468,
+            866
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/66561ba44ea736efefde5f465f06ed42f39bd614488f6db6eaec17d6dd1a9a26.jpg",
+        "image_caption": [
+            "Figure 1. Illustration of the proposed NKD and USKD for distillation loss calculations. NKD normalizes the non-target logits, using the soft labels more effectively, and achieves better performance. Meanwhile, USKD sets customized soft labels for both target and non-target classes, and can be applied to both CNNs and ViTs."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            503,
+            325,
+            893,
+            494
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "27, 29]. In general, a larger model performing better needs more computing resources. On the other hand, smaller models have lower computation complexity but are less competitive than larger models. To bridge this gap and improve the performance of smaller models, knowledge distillation (KD) has been proposed [11]. The core idea of KD is to employ the teacher's prediction logits as soft labels to guide the student. Self-knowledge distillation (self-KD) [33, 47] is inspired by the knowledge distillation method, but it does not require an actual teacher. Instead, it designs soft labels through auxiliary branches or special distribution. The similarity between KD and self-KD is that they utilize soft labels for distillation loss, while the key difference is in how they obtain the soft labels. This paper aims to 1) improve the utilization of soft labels for distillation loss and 2) propose a general and effective method to obtain customized soft labels for self-KD. The targets make us obtain the soft labels with a teacher and use our modified distillation loss for better performance. Alternatively, when we lack a teacher, we can use the proposed self-KD method",
+        "bbox": [
+            496,
+            598,
+            893,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*This work was done when Zhendong was an intern at IDEA.",
+        "bbox": [
+            94,
+            875,
+            419,
+            887
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding authors.",
+        "bbox": [
+            96,
+            887,
+            225,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "17185",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "to obtain the soft labels and then calculate the loss.",
+        "bbox": [
+            76,
+            90,
+            413,
+            104
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The original cross-entropy (CE) loss for classification calculates the loss on the target class (the image's category). While the soft labels from the teacher include target and non-target class, thus the KD loss also includes both target and non-target loss. The decoupled method has been proven effective for KD in DKD [49]. Unlike DKD's method of adjusting hyper-parameters on target and non-target loss, we present a simple yet effective way to decompose the KD loss. We decompose the KD loss into a combination of the target loss (like the original CE loss) and the non-target loss in CE form. The non-target loss transforms the internal distribution of the student's non-target logits to match the teacher's distribution. However, we find that the sum of the student's and teacher's non-target logits is changing and different, which hinders the alignment of their distributions. To address this issue, we normalize the non-target logits to equalize their sum, transferring teacher's non-target knowledge. With this slight modification, we introduce our Normalized Knowledge Distillation (NKD) loss, as depicted in Fig.1, significantly enhancing KD's performance.",
+        "bbox": [
+            75,
+            108,
+            472,
+            411
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our proposed NKD utilizes the teacher's target logit and normalized non-target logits to guide the student, resulting in state-of-the-art performance. This demonstrates the effectiveness of NKD loss formulation. Also, it can be generally used for self-KD to calculate the distillation loss, but how to generate the soft labels without a real teacher generally and efficiently is also important.",
+        "bbox": [
+            75,
+            412,
+            468,
+            518
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Various self-KD methods have explored using manually designed soft labels to enhance students with less time than KD. These methods [14, 38, 44, 47] typically obtain the labels from auxiliary branches or contrastive learning, as depicted in Fig. 2 (a), (b), and (c). However, despite requiring less time than KD, they still involve significant overhead compared to training the model directly. Recently, state-of-the-art Zipf's LS [17], as shown in Fig. 2 (d), introduced soft non-target labels based on a special distribution that can significantly reduce resource and time requirements. It classifies the student's feature in the spatial dimension and determines the rank of the non-target class using Zipf's law [25]. However, it requires the pixel-level features before average pooling, making it unsuitable for ViT-like models [6] with patch-wise tokenization.",
+        "bbox": [
+            75,
+            520,
+            468,
+            747
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address the limitations of existing methods, we propose a general and effective way to obtain soft labels. We design customized soft labels available for both CNN and ViT models. Following the NKD loss formulation, our customized soft labels comprise soft target label and soft nontarget labels for corresponding loss. For the soft target label, we replace the teacher's target logit with the smoother label value obtained from the student's prediction. Since the student's predictions vary drastically during training, especially in the beginning, we smooth the student's tar",
+        "bbox": [
+            75,
+            750,
+            470,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "get output within each training batch to stabilize the label values. For the soft non-target labels, we need their rank and distribution. First, for the rank, we get it from the intermediate feature, making our method available for both CNN and ViT models. We take weak supervision on the intermediate feature to get weak logit. Then, we normalize and combine it with the final logit and sort for the rank, as shown in Fig. 2 (f). The soft non-target labels' distribution follows Zipf's Law [25]. With the soft target and nontarget labels, we set our customized soft labels and propose Universal Self-Knowledge Distillation (USKD) as shown in Fig. 1. Besides, USKD only needs an extra linear layer for weak supervision. So it just takes a few more computing resources and time than training the model directly. USKD is a simple and effective method that achieves state-of-the-art performance on both CNN and ViT models.",
+        "bbox": [
+            496,
+            90,
+            890,
+            330
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As described above, we normalize KD's non-target logits and propose NKD, using the soft labels better and improving KD's performance significantly. For the generation of soft labels without a real teacher, we set soft target and nontarget labels, proposing USKD for self-KD. In a nutshell, the contributions of this paper are:",
+        "bbox": [
+            496,
+            332,
+            890,
+            422
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We normalize the non-target logits in the classical KD, making it better to optimize the cross-entropy loss. With this minor change, we propose Normalized KD (NKD) loss, using teacher's soft labels better and improving KD's performance significantly.",
+            "- We propose a novel way to set customized soft labels without a real teacher, including target and non-target classes for self-KD. We utilize the weak logit to obtain soft non-target labels. Besides, we enlarge the difference between student's target logit for different images and soften them for soft target labels.",
+            "- We propose a simple and effective self-KD method USKD with our customized soft labels, which applies to both CNN and ViT models. Importantly, USKD requires only almost negligible additional time and resources compared to training the model directly.",
+            "- We conduct extensive experiments on CIFAR-100 and ImageNet to verify the effectiveness of NKD and USKD, achieving state-of-the-art performance. Additionally, we demonstrate the efficacy of models trained with our self-KD method on COCO for detection."
+        ],
+        "bbox": [
+            517,
+            431,
+            890,
+            777
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            792,
+            637,
+            806
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Knowledge Distillation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            816,
+            710,
+            832
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Knowledge distillation is a method to improve the model while keeping the network unchanged. It was first proposed by Hinton et al. [11], where the student is supervised by the hard and soft labels from the teacher's output. Many",
+        "bbox": [
+            496,
+            839,
+            890,
+            901
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "17186",
+        "bbox": [
+            480,
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+            519,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/3b1464350c68c1c2d20ab4f5fb95e697067242768018bfbff37b23568a6aa9c5.jpg",
+        "image_caption": [
+            "Extra Parameters"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            104,
+            367,
+            194
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a5a3d86976637f8bdab04b0e724ed2fe463ede81473c26236086c29bbc6aa433.jpg",
+        "image_caption": [
+            "Extra Computation",
+            "(b) Self-KD with Contrastive Method"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            393,
+            104,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/489a0da303475cc80218101d5164d554aab3499aed3d2f39c1d90d36d1d6be52.jpg",
+        "image_caption": [
+            "(c) Self-KD with Image Mixture"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a0ca4a8051cc031941f03e4f1d3c8466801943c4eae9e571c52ab0d819a4ebc2.jpg",
+        "image_caption": [
+            "Modeling Distribution of Non-target Only",
+            "(d) Self-KD with Zipf's Label Smoothing"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            214,
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+            268
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a8d4e64c5c8ad96523f1a6ae53fa04279b22a6bdcc87f0fadeefec7071c8ed7e.jpg",
+        "image_caption": [
+            "(e) Self-KD with Label Smoothing"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            372,
+            220,
+            573,
+            268
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/14ff9d8ae1845723c5652cd9efb784e4fb1f0908c308694ee1b962c768cc8a29.jpg",
+        "image_caption": [
+            "(f) Self-KD with Customized Soft Labels",
+            "Figure 2. Comparison of different self-KD methods with (a) extra blocks and parameters [14], (b) contrastive method [37], (c) image mixture [38], (d) Zipf's label smoothing [17], and (e) label smoothing [22, 34]. (f) Self-KD with our customized soft labels including both target and non-target class for distillation. Note some methods can only be applied to CNN, while ours works for both CNN and ViT."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            581,
+            213,
+            885,
+            277
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "following works focus on better using soft labels to transfer more knowledge. WSLD [50] analyzes soft labels and distributes different weights for them from a perspective of bias-variance trade-off. SRRL [39] forces the output logits of the teacher's and student's features after the teacher's linear layer to be the same. DKD [49] decouples the logit and distributes different weights for the target and non-target classes. DIST [13] uses the Pearson correlation coefficient to replace the KL divergence and transfers the inter-relation and intra-relation together.",
+        "bbox": [
+            75,
+            362,
+            468,
+            513
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Besides distillation on logits, some works [1, 31, 40, 42] aim at transferring knowledge from intermediate features. FitNet [28] distill the semantic information from the intermediate feature directly. AT [45] transfers the attention of feature maps to the students. OFD [10] designs the margin ReLU and modifies the measurement for the distance between students and teachers. RKD [23] extracts the relation from the feature map. CRD [35] applies contrastive learning to distillation successfully. KR [3] transfers knowledge from multi-level features for distillation. TaT [18] helps the student to learn the teacher's every spatial component. MGD [41] masks the student's feature and forces it to generate the teacher's feature.",
+        "bbox": [
+            75,
+            513,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Self-Knowledge Distillation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            724,
+            321,
+            739
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-Knowledge Distillation has been proposed as an alternative approach to Knowledge Distillation that does not rely on an external teacher model. Self-KD aims to utilize the information within the student model to guide its learning process. Several self-KD methods have been proposed in recent years. DKS [33] introduces auxiliary supervision branches and pairwise knowledge alignments, while BYOT [47] adds blocks and layers to every stage and uses shallow and deep features as student and teacher, respectively. KDCL [7] trains two models for online knowledge",
+        "bbox": [
+            75,
+            750,
+            467,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "distillation, while FRSKD [14] adds a new branch supervised by the original feature and uses the logit of the new branch for self-KD. DDGSD [37] transfers knowledge between different distorted versions of the same training data. OLS [46] sets a matrix that is made up of the soft label for every class, while MixSKD [38] proposes incorporating self-knowledge distillation with image mixture and aggregates multi-stage feature to produce soft labels. Tf-FD [16] includes intra-layer and inter-layer distillation, reusing the channel-wise and layer-wise features to provide knowledge without an additional model. However, these methods require auxiliary architecture, adapt layers for alignment, or data augmentation, consuming much more time and computing resources than training the model directly.",
+        "bbox": [
+            496,
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+            574
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In contrast, some self-KD methods require little extra or even no more time than training the model directly. For example, Label Smoothing [34] sets the labels manually by distributing the same values to all non-target classes. TfKD [43] revisits KD via label smoothing, using a high temperature to generate the manual logit for distillation. Zipf's LS [17] utilizes the student's linear layer to obtain several logits for each pixel of the student's last feature map. The method uses these logits to vote for the non-target class's rank with Zipf distribution [25]. These methods set soft labels to achieve self-knowledge distillation without contrastive learning, data augmentation, or auxiliary branches, saving much training time and computing resources.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            799,
+            589,
+            814
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Normalized KD for Better Using Soft Labels",
+        "text_level": 1,
+        "bbox": [
+            500,
+            827,
+            875,
+            843
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Using  $t$  denote the target class,  $C$  denote the number of classes,  $V_{i}$  denote the label value for each class  $i$ , and  $S_{i}$  denote the student's output probability. The original loss",
+        "bbox": [
+            496,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "17187",
+        "bbox": [
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+            517,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "for image classification can be formulated as follows:",
+        "bbox": [
+            76,
+            90,
+            433,
+            107
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {o r i} = - \\sum_ {i} ^ {C} V _ {i} \\log \\left(S _ {i}\\right) = - V _ {t} \\log \\left(S _ {t}\\right) = - \\log \\left(S _ {t}\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Using  $T_{i}$  denote the teacher's soft labels. The classical KD utilizes them for distillation loss as:",
+        "bbox": [
+            76,
+            167,
+            468,
+            198
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {k d} = - \\sum_ {i} ^ {C} T _ {i} \\log \\left(S _ {i}\\right) (2) \\\\ = - T _ {t} \\log \\left(S _ {t}\\right) - \\sum_ {i \\neq t} ^ {C} T _ {i} \\log \\left(S _ {i}\\right). (3) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            147,
+            205,
+            468,
+            292
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As  $L_{kd}$  shows, the first loss  $-T_t\\log(S_t)$  is about the target class like the original  $L_{ori}$ . While for the second non-target loss  $-\\sum_{i \\neq t}^{C} T_i\\log(S_i)$ , it has the same form as CE loss  $-\\sum p(x)\\log(q(x))$ . The CE loss aims at making  $q(x)$  be the same as  $p(x)$ . However,  $\\sum_{i \\neq t}^{C} T_i = 1 - T_t$  and  $\\sum_{i \\neq t}^{C} S_i = 1 - S_t$ . Since the trainable  $S_i$  is unlikely to exactly match the fixed  $T_i$  during training, the sum of the two non-target logits is always different, preventing the two distributions from being the same. Thus we normalize  $T_i$  and  $S_i$  to force the sum of the two distributions to be the same. With  $\\mathcal{N}(\\cdot)$  denoting the normalized operation, we modify the KD loss and propose our Normalized Knowledge Distillation (NKD) loss as follows:",
+        "bbox": [
+            76,
+            303,
+            472,
+            507
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {n k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\gamma \\cdot \\lambda^ {2} \\cdot \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(T _ {i} ^ {\\lambda}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i} ^ {\\lambda}\\right)\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            516,
+            468,
+            574
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\gamma$  is a hyper-parameter to balance the loss and  $\\lambda$  is the temperature for KD [11]. Finally, combining the original loss  $L_{ori}$ , and NKD loss  $L_{nkd}$ , we train the students with:",
+        "bbox": [
+            76,
+            585,
+            468,
+            632
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {a l l} = L _ {o r i} + L _ {n k d}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.Customized Soft Labels for Self-KD",
+        "text_level": 1,
+        "bbox": [
+            76,
+            667,
+            390,
+            684
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We utilize NKD for better use of the soft labels. Following our NKD loss in Eq. 4, we propose a general and effective self-KD method, which sets soft labels on target and non-target classes without teachers.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Soft Target Label",
+        "text_level": 1,
+        "bbox": [
+            76,
+            771,
+            253,
+            786
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "First, for the soft target label, the weight  $T_{t}$  in Eq. 4 is obtained from the teacher's target output probability for the input image. We wonder if the soft target can be provided by adjusting the student's target output  $S_{t}$ . The differences between  $T_{t}$  and  $S_{t}$  mainly focus on two parts. The first is that  $T_{t}$  is fixed, and  $S_{t}$  varies gradually during training. The second part is that the difference between different samples'",
+        "bbox": [
+            76,
+            794,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$S_{t}$  is much smaller than  $T_{t}$  at the beginning of training. To overcome the problem, we first square  $S_{t}$  to enlarge the difference between different samples'  $S_{t}$ . Then we propose a way to adjust  $S_{t}$ , making it smoother to fit the training set without teachers. This strategy can be applied directly to different models, including CNN-liked and ViT-liked models. In this way, we get the soft target label  $P_{t}$ , which is detached and zero-grad in training for self-KD:",
+        "bbox": [
+            498,
+            90,
+            893,
+            212
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {t} = S _ {t} ^ {2} + V _ {t} - \\operatorname {m e a n} \\left(S _ {t} ^ {2}\\right). \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            599,
+            220,
+            890,
+            238
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With the  $P_{t}$ , we follow our NKD for the target loss:",
+        "bbox": [
+            500,
+            247,
+            841,
+            263
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {t a r g e t}} = - P _ {t} \\log \\left(S _ {t}\\right), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            616,
+            272,
+            890,
+            289
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $V_{t}$  denote the original target label value, e.g. [0.8, 0.2] for a mixed image. And  $mean(\\cdot)$  is calculated across different samples in a training batch. We discuss the effects of the smoothing ways for  $S_{t}$  in Sec. 5.6.",
+        "bbox": [
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+            297,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Soft Non-target Labels",
+        "text_level": 1,
+        "bbox": [
+            500,
+            376,
+            712,
+            391
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The knowledge from the teacher's soft non-target labels includes its rank and distribution. We also need them to set the soft non-target labels for self-KD. To get the rank, we first obtain a new weak logit by setting weak supervision on the intermediate feature. Using  $\\mathcal{F}$  denote the feature of stage 2 of the CNN-liked model or the mid layer's classification token of the ViT-liked model,  $GAP$  denote the global average pooling,  $FC$  denote a new linear layer, the weak logit of the CNN-liked model can be formulated as:",
+        "bbox": [
+            498,
+            398,
+            892,
+            535
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {i} = \\operatorname {s o f t m a x} (F C (G A P (\\mathcal {F}))), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            545,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As for the ViT-liked model, the weak logit is as follows:",
+        "bbox": [
+            500,
+            571,
+            890,
+            585
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {i} = \\operatorname {s o f t m a x} (F C (\\mathcal {F})).\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            611,
+            785,
+            628
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We aim to obtain another smoother non-target logit different from the original final logit. So we utilize a smooth label and take weak supervision to get the weak logit. Using  $V_{i}$  denote the label, which is the original label processed with label smoothing, the loss for obtaining the weak logit is as follows:",
+        "bbox": [
+            498,
+            636,
+            893,
+            727
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {w e a k}} = - \\mu \\cdot \\sum_ {i} ^ {C} V _ {i} \\log \\left(W _ {i}\\right), \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            591,
+            734,
+            890,
+            773
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu < 1$  is a hyper-parameter to achieve weak supervision. With the weak logit, we obtain the soft non-target labels' rank by normalizing and combining it with the final logit. This operation balances the two logits' effects for the rank, and the analysis is shown in Sec. 5.7.",
+        "bbox": [
+            498,
+            782,
+            890,
+            858
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {i} = \\frac {W _ {i}}{1 - W _ {t}} + \\frac {S _ {i}}{1 - S _ {t}}. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            609,
+            866,
+            890,
+            898
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "17188",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The soft non-target labels' distribution follows Zipf's law [25], which has been applied in Zipf's LS [17]. The formulation can be formulated as follows:",
+        "bbox": [
+            76,
+            90,
+            468,
+            135
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nZ _ {i} = \\frac {i ^ {- 1}}{\\sum_ {i = 1} ^ {C} i ^ {- 1}}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            214,
+            142,
+            468,
+            179
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the distribution, we sort it with the rank of  $R_{i}$  and obtain the soft non-target labels  $Z_{i}$  for self-KD. Following our NKD loss in Eq. 4, the non-target loss is as follows:",
+        "bbox": [
+            76,
+            186,
+            468,
+            231
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {n o n} = - \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(Z _ {i}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i}\\right)\\right). \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
+            252,
+            468,
+            294
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.3 Overall for Self-KD",
+        "text_level": 1,
+        "bbox": [
+            76,
+            311,
+            267,
+            325
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the proposed soft target label and soft non-target labels, we calculate the corresponding loss and propose USKD as shown in Fig. 1. We train all the models with the total loss for self-KD as follows:",
+        "bbox": [
+            76,
+            335,
+            468,
+            393
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {a l l}} = L _ {\\text {o r i}} + \\alpha \\cdot L _ {\\text {t a r g e t}} + \\beta \\cdot L _ {\\text {n o n}} + L _ {\\text {w e a k}}, \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            405,
+            468,
+            422
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{ori}$  is the original loss for the models among all the tasks,  $\\alpha$  and  $\\beta$  are two hyper-parameters to balance the loss scale.  $L_{weak}$  is used to generate the weak logit in Eq. 8.",
+        "bbox": [
+            76,
+            431,
+            468,
+            476
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            489,
+            209,
+            505
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Details",
+        "text_level": 1,
+        "bbox": [
+            76,
+            513,
+            267,
+            527
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conduct the experiments on CIFAR-100 [15] and ImageNet [5], which contain 100 and 1000 categories, respectively. For CIFAR-100, we use 50k images for training and 10k for validation. For ImageNet, we use 1.2 million images for training and 50k images for validation. In this paper, we use accuracy to evaluate all the models.",
+        "bbox": [
+            76,
+            536,
+            468,
+            626
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For KD with teachers, NKD has two hyper-parameters  $\\gamma$  and  $\\lambda$  in Eq. 4. For all the experiments, we adopt  $\\{\\gamma = 1.5, \\lambda = 1\\}$  on ImageNet. While for CIFAR-100, we follow the training setting from DKD [49] for a fair comparison. And USKD has two hyper-parameters  $\\alpha$  and  $\\beta$  to balance the loss scale in Eq. 13. Another hyper-parameter  $\\mu$  is used to achieve the weak supervision in Eq. 9. For all the experiments, we adopt  $\\{\\alpha = 1, \\beta = 0.1, \\mu = 0.005\\}$  on ImageNet and  $\\{\\alpha = 0.1, \\beta = 0.1, \\mu = 0.1\\}$  on CIFAR-100. The other training setting for KD and self-KD is the same as training the students without distillation. We use 8 GPUs to conduct the experiments with MMClassition [4] based on Pytorch [24]. More details and experimental results about the hyper-parameters are shown in the supplement.",
+        "bbox": [
+            76,
+            628,
+            468,
+            838
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Normalized KD with Teachers",
+        "text_level": 1,
+        "bbox": [
+            76,
+            847,
+            346,
+            861
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "When we get the soft labels from a real teacher, we can use NKD loss for better performance. To prove this, we",
+        "bbox": [
+            76,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "first conduct experiments with various teacher-student distillation pairs on CIFAR-100, shown in Tab. 1. In this setting, we evaluate our method on several models with different architectures, including VGGNet [32], ResNet [9], ShuffleNet [48] and MobileNetV2 [30]. We compare our method with KD [11] and several other state-of-the-art distillation methods. As the results show, our method brings the students remarkable accuracy gains over other methods. Our method achieves the best performance among logit-based distillation methods and even surpasses the feature-based distillation methods in some settings.",
+        "bbox": [
+            496,
+            90,
+            890,
+            256
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To further demonstrate the effectiveness and robustness of our NKD, we test it on a more challenging dataset, ImageNet. We set two popular teacher-student pairs, which include homogeneous and heterogeneous teacher-student structures for distillation. The homogeneous distillation is ResNet34-ResNet18, and the heterogeneous distillation is ResNet50-MobileNet. The results of different KD methods on ImageNet are shown in Tab. 1. As the results show, our method outperforms all the previous methods. It brings consistent and significant improvements to the students for both distillation settings. The student ResNet18 and MobileNet achieve  $71.96\\%$  and  $72.58\\%$  Top-1 accuracy, getting  $2.06\\%$  and  $3.37\\%$  accuracy gains with the knowledge transferred from the teacher's logits, respectively.",
+        "bbox": [
+            496,
+            258,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As described above, our NKD enhances KD's performance significantly with a slight modification. And in various settings, it also surpasses DKD, a method that improves KD according to a different decoupled way.",
+        "bbox": [
+            496,
+            470,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Universal Self-KD without Teachers",
+        "text_level": 1,
+        "bbox": [
+            498,
+            542,
+            812,
+            558
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "When we lack a teacher, we use the proposed self-KD method USKD to obtain the soft labels and then calculate the loss. To evaluate its effectiveness, we first conduct experiments with ResNets [9] and MobileNet [12] on CIFAR100 and ImageNet datasets. We compare with the other state-of-the-art methods, which also set manual labels and only bring little extra time consumption, including label smoothing [34], Tf-KD [43] and Zipf's LS [17]. As shown in Tab. 2, our method surpasses the previous related self-knowledge distillation methods on various settings and brings the model remarkable gains. For example, it brings MobileNet and ResNet-18  $1.17\\%$  and  $0.89\\%$  Top-1 accuracy gains on ImageNet.",
+        "bbox": [
+            496,
+            566,
+            890,
+            763
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we also test our USKD on more models, which include lighter models MobileNetV2 [30], ShuffleNetV2 [21] and a deeper ResNet. The results are shown in Tab. 3. For both the lightweight models, including MobileNetV2 and ShuffleNetV2, and the stronger model ResNet-101, our method also achieves considerable improvements. Besides, we also compare the time consumption to train the model for an epoch in Tab. 3. Compared with the baseline, the extra time we need for self-knowledge",
+        "bbox": [
+            496,
+            765,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "17189",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/a2dee5c6b16c795a506049747bcc255fb860df103185f9e784f1a61ab875f007.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Teacher Student</td><td>VGGNet13 VGGNet8</td><td>ResNet32x4 ResNet8x4</td><td>VGGNet13 MobileNetV2</td><td>ResNet50 MobileNetV2</td><td>ResNet34 ResNet18</td><td>ResNet50 MobileNet</td></tr><tr><td rowspan=\"2\">Accuracy</td><td>Teacher</td><td>74.64</td><td>79.42</td><td>74.64</td><td>79.34</td><td>73.62</td><td>76.55</td></tr><tr><td>Student</td><td>70.36</td><td>72.50</td><td>64.60</td><td>64.60</td><td>69.90</td><td>69.21</td></tr><tr><td rowspan=\"4\">Feature</td><td>RKD [23]</td><td>71.48</td><td>71.90</td><td>64.52</td><td>64.43</td><td>71.34</td><td>71.32</td></tr><tr><td>CRD [35]</td><td>73.94</td><td>75.51</td><td>69.73</td><td>69.11</td><td>71.17</td><td>71.40</td></tr><tr><td>OFD [10]</td><td>73.95</td><td>74.95</td><td>69.48</td><td>69.04</td><td>71.08</td><td>71.25</td></tr><tr><td>KR [3]</td><td>74.84</td><td>75.63</td><td>70.37</td><td>69.89</td><td>71.61</td><td>72.56</td></tr><tr><td rowspan=\"4\">Logit</td><td>KD [11]</td><td>72.98</td><td>73.33</td><td>67.37</td><td>67.35</td><td>71.03</td><td>70.68</td></tr><tr><td>WSLD [50]</td><td>74.36</td><td>76.05</td><td>69.02</td><td>70.15</td><td>71.73</td><td>72.02</td></tr><tr><td>DKD [49]</td><td>74.68</td><td>76.32</td><td>69.71</td><td>70.35</td><td>71.70</td><td>72.05</td></tr><tr><td>NKD (ours)</td><td>74.86</td><td>76.35</td><td>70.22</td><td>70.67</td><td>71.96</td><td>72.58</td></tr></table>",
+        "bbox": [
+            96,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/252bcbe71e20ab8f5b784b74c55846783df40758fb4cc74cb7942dbf1599d3cc.jpg",
+        "table_caption": [
+            "Table 1. Results of different knowledge distillation methods on CIFAR-100 (the left four columns) and ImageNet (the right two columns) dataset. The data that is underlined denotes the second-best result among all the results. The metric is the Top-1 accuracy (\\%)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>CIFAR100</td><td colspan=\"3\">ImageNet</td></tr><tr><td>Model</td><td>ResNet18</td><td>ResNet18</td><td>ResNet50</td><td>MobileNet</td></tr><tr><td>Baseline</td><td>78.58</td><td>69.90</td><td>76.55</td><td>69.21</td></tr><tr><td>LS [34]</td><td>79.42</td><td>69.92</td><td>76.64</td><td>68.98</td></tr><tr><td>Tf-KD [43]</td><td>79.53</td><td>70.14</td><td>76.59</td><td>69.20</td></tr><tr><td>Zipf&#x27;s LS [17]</td><td>79.63</td><td>70.30</td><td>76.96</td><td>69.59</td></tr><tr><td>USKD (ours)</td><td>79.90</td><td>70.79</td><td>77.07</td><td>70.38</td></tr></table>",
+        "bbox": [
+            80,
+            325,
+            509,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/ae51084d9af7cfeb6d8662f76c63417ec6fb906e39127034ab6777e896a1312c.jpg",
+        "table_caption": [
+            "Table 2. The comparative results of different self-knowledge distillation methods on CIFAR100 and ImageNet dataset. We report the models' performance with Top-1 accuracy  $(\\%)$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>77.30 (+0.46)</td></tr><tr><td>DeiT-Tiny</td><td>74.42</td><td>74.97 (+0.55)</td></tr><tr><td>DeiT-Small</td><td>80.55</td><td>80.77 (+0.22)</td></tr><tr><td>Swin-Tiny</td><td>81.18</td><td>81.49 (+0.31)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "distillation is very limited. Specifically, the time of training MobileNet-V2 with our proposed USKD for an epoch is 10.18 minutes, which is just 0.01 minutes higher than training the model directly. Our method brings considerable improvements to various models with negligible extra time consumption.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Universal Self-KD for More Models",
+        "text_level": 1,
+        "bbox": [
+            76,
+            771,
+            387,
+            787
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The previous self-KD methods are specially designed for CNN-liked models. However, some models like ViT [6] translate the image into different tokens and have a completely different architecture. Those self-KD methods fail to benefit ViT-liked models. For ViT-liked models, USKD can also set customized soft labels and bring remarkable improvements. As described in Eq. 8, we use an extra",
+        "bbox": [
+            75,
+            794,
+            470,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/6b953045b39c61ae0a72427bf18a907e7f82fc2e27f46215c756b8e05f146353.jpg",
+        "table_caption": [
+            "Table 4. Results of training more models, including ViT-liked models with our proposed method on ImageNet dataset. All the results are reported with Top-1 accuracy  $(\\%)$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td rowspan=\"3\">Accuracy (%)</td><td>ResNet-101</td><td>77.97</td><td>78.54 (+0.57)</td></tr><tr><td>MobileNet-V2</td><td>71.86</td><td>72.41 (+0.55)</td></tr><tr><td>ShuffleNet-V2</td><td>69.55</td><td>70.30 (+0.75)</td></tr><tr><td rowspan=\"3\">Time (min)</td><td>ResNet-101</td><td>13.78</td><td>13.95</td></tr><tr><td>MobileNet-V2</td><td>10.17</td><td>10.18</td></tr><tr><td>ShuffleNet-V2</td><td>8.63</td><td>8.68</td></tr></table>",
+        "bbox": [
+            519,
+            325,
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+            441
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. The results of the models' performance are Top-1 accuracy  $(\\%)$  on ImageNet dataset. The time data are reported with minutes (min) for a training epoch.",
+        "bbox": [
+            514,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "linear layer connected to ViT's middle layer for classification and obtain the weak logit. The rest operations are the same as CNN-liked models. To show the generalization of USKD, we apply it to more models, including RegNet [26], DeiT [36], and Swin-Transformer [20], which can be seen in Tab. 4. All the models can achieve remarkable Top-1 accuracy gains. Besides, our method even can bring  $0.55\\%$  gains for DeiT-Tiny. And it also brings  $0.31\\%$  Top-1 accuracy gains for the latest state-of-the-art model SwinTransformer. The results of more models show our method is both effective and general.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Analysis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Effects of Normalizing the Non-target Logits",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we proposed normalizing the non-target logits in the original KD to help the student perform better. In this subsection, we conduct experiments to demonstrate the effectiveness of our modification. As shown in Tab. 5, using the target loss alone leads to a  $1.16\\%$  increase in accuracy. Combining the knowledge from both target and nontarget classes allows us to better use the teacher's knowledge, resulting in a significant improvement of  $2.06\\%$  Top-1 accuracy for the student. Furthermore, we normalize the non-target logits in the KD loss for distillation and compare",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "17190",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/914e41f84add14345bcc29a1d52fc84edb36011d26f5a3fa3f8583c0903d4c40.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Loss</td><td colspan=\"4\">ResNet34 - ResNet18</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>KD&#x27;s Non-target</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>NKD&#x27;s Non-target</td><td>X</td><td>X</td><td>X</td><td>✓</td></tr><tr><td>Top-1 Acc. (%)</td><td>69.90</td><td>71.06</td><td>71.33</td><td>71.96</td></tr><tr><td>Top-5 Acc. (%)</td><td>89.43</td><td>89.51</td><td>90.25</td><td>90.48</td></tr></table>",
+        "bbox": [
+            88,
+            88,
+            459,
+            186
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "the non-target loss from both KD and NKD. Our non-target loss brings much greater gains than KD's non-target loss, as shown in the comparison. These results demonstrate the effectiveness of our proposed modification in improving KD's performance.",
+        "bbox": [
+            76,
+            244,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Difference between Our NKD and DKD",
+        "text_level": 1,
+        "bbox": [
+            76,
+            328,
+            419,
+            343
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To better use the soft labels, we decompose KD loss and normalize the non-target logits for a better performance. The decoupled method is inspired by DKD [49]. However, this paper presented a more straightforward and efficient decomposition method. DKD decouples KD loss as:",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\left(1 - T _ {t}\\right) \\log \\left(1 - S _ {t}\\right) (14) \\\\ - \\left(1 - T _ {t}\\right) \\sum_ {i \\neq t} ^ {C} \\hat {T} _ {i} \\log \\left(\\hat {S} _ {i}\\right) (15) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            436,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {T} _ {i} = \\frac {T _ {i}}{1 - T _ {t}}, \\quad \\hat {S} _ {i} = \\frac {S _ {i}}{1 - S _ {t}}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            521,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "DKD analyzed the effects of KD's components and set hyper-parameters for a new formulation:",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {d k d} = \\alpha \\cdot \\left(- T _ {t} \\log \\left(S _ {t}\\right) - \\left(1 - T _ {t}\\right) \\log \\left(1 - S _ {t}\\right)\\right) (16) \\\\ - \\beta \\cdot \\left(\\sum_ {i \\neq t} ^ {C} \\hat {T} _ {i} \\log \\left(\\hat {S} _ {i}\\right)\\right) (17) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "While we decompose KD loss into the target loss (like the original CE loss) and non-target loss in CE form:",
+        "bbox": [
+            76,
+            672,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\sum_ {i \\neq t} ^ {C} T _ {i} \\log \\left(S _ {i}\\right) \\tag {18}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
+            712,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Then we find the sum of student's and teacher's non-target logits is different, making them hard to be the same. So we normalize them to equalize the sum as follows:",
+        "bbox": [
+            76,
+            763,
+            468,
+            809
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {n k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\gamma \\cdot \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(T _ {i}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i}\\right)\\right) \\tag {19}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            93,
+            818,
+            468,
+            861
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "With this slight modification, we present our NKD loss and achieve better performance than DKD, as shown in Tab. 1.",
+        "bbox": [
+            76,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/92c95d239b6e160fc46b801f0d21bcb9235d804db127c5bdc109b2f8886f5c8e.jpg",
+        "table_caption": [
+            "Table 5. Effects of our normalized non-target loss on ImageNet dataset. The teacher is ResNet34 and the student is ResNet18."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Loss</td><td colspan=\"4\">Top-1 Accuracy (%)</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Non-target</td><td>X</td><td>X</td><td>✓</td><td>✓</td></tr><tr><td>MobileNet</td><td>69.21</td><td>70.18</td><td>69.43</td><td>70.38</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>76.87</td><td>77.25</td><td>77.30</td></tr></table>",
+        "bbox": [
+            509,
+            88,
+            883,
+            170
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/d710df6c5497acce65faf5ab792d40c30c00f55d11bb89c5d542a8d1df0fc391.jpg",
+        "table_caption": [
+            "Table 6. Ablation study of USKD's target and non-target loss. The experiments are conducted on the ImageNet dataset. All the results are the Top-1 accuracy  $(\\%)$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ImageNet Top-1 Acc. (%)</td><td colspan=\"2\">COCO</td></tr><tr><td>APbox</td><td>ARbox</td></tr><tr><td>Baseline (Res50)</td><td>76.55</td><td>38.0</td><td>52.4</td></tr><tr><td>USKD (ours)</td><td>77.07</td><td>38.3</td><td>52.9</td></tr></table>",
+        "bbox": [
+            504,
+            233,
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+            299
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 7. The detection results on the COCO dataset. We pre-train the backbone with USKD and use Mask-RCNN as the detector.",
+        "bbox": [
+            498,
+            309,
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+            337
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Effects of USKD's Target and Non-target Loss",
+        "text_level": 1,
+        "bbox": [
+            498,
+            359,
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+            376
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We propose a novel self-KD method called USKD, which utilizes customized soft labels that incorporate information from both target and non-target classes. To evaluate the impact of each type of information, we conduct experiments on MobileNet and RegNetX-1.6GF in Tab. 6. The experimental findings demonstrate that both types of information are beneficial and important for the two models, and their combination leads to further improvements in performance. For instance, by combining the target and non-target class distillation together, MobileNet achieves  $70.38\\%$ , which surpasses the accuracy achieved by using distillation on either the target or non-target class alone.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4. Models with USKD for Downstream Task",
+        "text_level": 1,
+        "bbox": [
+            498,
+            571,
+            854,
+            588
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our self-KD method yields remarkable accuracy gains for the classification task on CIFAR-100 and ImageNet datasets. To further evaluate its effectiveness and generalization, we also apply the pre-trained model to object detection using Mask R-CNN [8] as the detector and evaluate the model's performance with  $AP^{box}$  and  $AR^{box}$  on the COCO val2017 dataset [19]. We conduct the detection experiments for 12 epochs using MMDetection [2]. As shown in Tab. 7, the ResNet-50 backbone trained with our method improves the detector's performance by  $0.3\\mathrm{mAP}$  and  $0.5\\mathrm{mAR}$ . The results demonstrate that our self-KD method not only improves the model's classification performance but also generalizes well to downstream tasks like object detection.",
+        "bbox": [
+            496,
+            595,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.5.Customized Soft Labels for USKD",
+        "text_level": 1,
+        "bbox": [
+            498,
+            801,
+            799,
+            816
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our self-KD method, USKD, leverages customized soft labels for every image during training. Fig.3 shows several samples' soft labels, including the value for the target class and the top-3 non-target classes. For the target class, the value may be larger than 1 due to the smoothing method",
+        "bbox": [
+            496,
+            824,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "17191",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a87445d5ff7b8fa1bcbe920e503dcc54abf02d69fd1f2e460c200904dec77a45.jpg",
+        "image_caption": [
+            "Figure 3. The visualization of the target and top-3 non-target class values of our customized soft labels. The target class value is obtained by squaring and smoothing. The non-target class value is obtained by Zipf's law."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            89,
+            194,
+            215
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/f48f51c07727e1964f15a46d9f6fe997278466ff3b728f01f353aa3c8c4b06fa.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            217,
+            89,
+            330,
+            215
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b245c77efa68a5a162dff7f021bd61fba048168663c0fff34078c77f988f0954.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            352,
+            90,
+            467,
+            215
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "described in Eq. 6. For the non-target classes, USKD distributes larger values to the categories that are similar to the target class. For instance, the labels for the second image not only include the target 'linnet,' but also assign higher values to similar non-target classes like 'brambling', 'goldfinch', and 'bulbul'. This approach ensures that each image receives an appropriate customized soft label, which enables successful self-KD. The visualization also demonstrates how our USKD helps the model to perform better.",
+        "bbox": [
+            75,
+            299,
+            468,
+            435
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.6. Different Smooth Ways for Soft Target Label",
+        "text_level": 1,
+        "bbox": [
+            76,
+            446,
+            457,
+            464
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our USKD utilizes customized soft labels that include target and non-target classes for all the images during training. To create the soft labels, we replace the weights of NKD's target loss with a smoothed version of the student's target output  $S_{t}$ , as shown in Eq. 6. In this subsection, we investigate the impact of different methods for smoothing the student's target output  $S_{t}$  on the performance of the model. We conduct experiments on ResNet18 trained on ImageNet to compare these methods, as shown in Tab. 8. The experiments show that all the methods significantly improve the student model. Notably, using  $S_{t} + V_{t} - mean(S_{t})$  as the weights for smoothing the student's target output achieves  $0.86\\%$  improvement, even outperforming using the teacher ResNet18's output as the soft target label. Based on this observation, we choose this method for smoothing the student's target output and use it as our soft target label.",
+        "bbox": [
+            75,
+            470,
+            468,
+            714
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.7. Different Ranks for Soft Non-target Labels",
+        "text_level": 1,
+        "bbox": [
+            76,
+            724,
+            442,
+            742
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Eq. 10, we combine the normalized weak and final logit to obtain the soft non-target labels' rank. In this subsection, we explore the effects of different ways for the rank, as shown in Tab. 9. Specifically, we compare the performance when using the weak logit's rank alone, the final logit's rank alone, or a combination of both but without normalization. Interestingly, our results show that all these methods help improve the model's accuracy, with the combination of the two normalized logits achieving the best performance. It is also noteworthy that even directly using",
+        "bbox": [
+            75,
+            750,
+            468,
+            902
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/86974ea482f0a645268bd4f4724542a2481e7d6e7e4e8d929f006a62eb24fb87.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Smooth Ways</td><td>Teacher</td><td>Top-1 Acc. (%)</td></tr><tr><td>Baseline</td><td>-</td><td>69.90</td></tr><tr><td>St+Vt-mean(St)</td><td>X</td><td>70.76</td></tr><tr><td>softmax(St)*sum(Vt)</td><td>X</td><td>70.57</td></tr><tr><td>√St-min(St)</td><td>X</td><td>70.57</td></tr><tr><td>St/max(St)</td><td>X</td><td>70.53</td></tr><tr><td>St/mean(St)</td><td>X</td><td>70.50</td></tr><tr><td>Trained ResNet-18</td><td>✓</td><td>70.75</td></tr></table>",
+        "bbox": [
+            504,
+            88,
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+            215
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/20e88d933a2242cfda9f1706542db918595e3cd99f83cb5422ee61e7bbf70459.jpg",
+        "table_caption": [
+            "Table 8. Results of training ResNet18 with target loss on ImageNet dataset. All the operations are calculated with different samples in a training batch. Because the trained Res-18's output is  $S_{t}$ , we drop the square operation for different smoothing ways."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>ResNet-18</td><td>RegNetX-1.6GF</td></tr><tr><td>Baseline</td><td>69.90</td><td>76.84</td></tr><tr><td>Weak Logit</td><td>70.65</td><td>77.28</td></tr><tr><td>Final Logit</td><td>70.72</td><td>77.15</td></tr><tr><td>Combination</td><td>70.71</td><td>77.25</td></tr><tr><td>Normalization</td><td>70.79</td><td>77.30</td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 9. Results of different ranks for soft non-target labels. Normalization and Combination mean combining weak and final logit with normalization and without normalization, respectively.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "the final logit to obtain the rank can satisfy accuracy gains. These findings provide insights into the effectiveness of various approaches for the rank of the non-target labels.",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In this paper, we decompose KD loss into the target loss like original CE loss and non-target loss in a CE form. We then normalize the non-target logits to enhance the student's learning from the teacher. With this normalization, we introduce Normalized KD (NKD), which helps students to achieve state-of-the-art performance. Building on our NKD loss formulation, we further propose a new self-KD method, USKD, that works for both CNN-like and ViT-like models. USKD uses customized soft labels that include target and non-target classes for self-KD. We first square and smooth the student's target output logit as the soft target label. For the soft non-target labels, we use weak supervision to obtain the rank and utilize Zipf's law to generate the labels. In this way, USKD needs negligible extra time and resources than training the model directly. Extensive experiments on various models with different datasets demonstrate that both our NKD and USKD are simple and efficient.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), the SZSTC project Grant (JCYJ20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004).",
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+        "type": "text",
+        "text": "References",
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+    },
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+        "type": "list",
+        "sub_type": "ref_text",
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diff --git a/2023/From Knowledge Distillation to Self-Knowledge Distillation_ A Unified Approach with Normalized Loss and Customized Soft Labels/7e406dac-df76-4483-b6be-35c6233f9e4a_model.json b/2023/From Knowledge Distillation to Self-Knowledge Distillation_ A Unified Approach with Normalized Loss and Customized Soft Labels/7e406dac-df76-4483-b6be-35c6233f9e4a_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..cc1f8e4323321b2307c7d1d52c2d7277b69957fb
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+++ b/2023/From Knowledge Distillation to Self-Knowledge Distillation_ A Unified Approach with Normalized Loss and Customized Soft Labels/7e406dac-df76-4483-b6be-35c6233f9e4a_model.json	
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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
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+                0.001,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "From Knowledge Distillation to Self-Knowledge Distillation: A Unified Approach with Normalized Loss and Customized Soft Labels"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Zhendong Yang\\(^{1,2*}\\) Ailing Zeng\\(^{2}\\) Zhe Li\\(^{3}\\) Tianke Zhang\\(^{1}\\) Chun Yuan\\(^{1\\dagger}\\) Yu Li\\(^{2\\dagger}\\)  \n\\(^{1}\\)Tsinghua Shenzhen International Graduate School \\(^{2}\\)International Digital Economy Academy (IDEA) Institute of Automation, Chinese Academy of Sciences"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "{yangzd21,ztk21}@mails.tsinghua.edu.cn axel.li@outlook.com"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "yuanc@sz.tsinghua.edu.cn {zengailing, liyu}@idea.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.327,
+                0.314,
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+            ],
+            "angle": 0,
+            "content": "Knowledge Distillation (KD) uses the teacher's logits as soft labels to guide the student, while self-KD does not need a real teacher to require the soft labels. This work unifies the formulations of the two tasks by decomposing and reorganizing the generic KD loss into a Normalized KD (NKD) loss and customized soft labels for both target class (image's category) and non-target classes named Universal Self-KD (USKD). We decompose the KD loss and find the non-target loss from it forces the student's non-target logits to match the teacher's, but the sum of the two nontarget logits is different, preventing them from being identical. NKD normalizes the non-target logits to equalize their sum. It can be generally used for KD and self-KD to better use the soft labels for distillation. USKD generates customized soft labels for both target and non-target classes without a teacher. It smoothes the target logit of the student as the soft target label and uses the rank of the intermediate feature to generate the soft non-target labels with Zipf's law. For KD with teachers, NKD achieves state-of-the-art performance on CIFAR-100 and ImageNet, boosting the ImageNet Top-1 accuracy of Res-18 from \\(69.90\\%\\) to \\(71.96\\%\\) with a Res-34 teacher. For self-KD without teachers, USKD is the first method that can be effectively applied to both CNN and ViT models with negligible additional time and memory cost, resulting in new state-of-the-art results, such as \\(1.17\\%\\) and \\(0.55\\%\\) accuracy gains on ImageNet for MobileNet and DeiT-Tiny, respectively. Code is available at https://github.com/yzd-v/cls_KD."
+        },
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+            "content": "1. Introduction"
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+            "content": "Deep convolutional neural networks (CNNs) have significantly advanced the performance in many tasks [8, 9,"
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+            "content": "Figure 1. Illustration of the proposed NKD and USKD for distillation loss calculations. NKD normalizes the non-target logits, using the soft labels more effectively, and achieves better performance. Meanwhile, USKD sets customized soft labels for both target and non-target classes, and can be applied to both CNNs and ViTs."
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+            "content": "27, 29]. In general, a larger model performing better needs more computing resources. On the other hand, smaller models have lower computation complexity but are less competitive than larger models. To bridge this gap and improve the performance of smaller models, knowledge distillation (KD) has been proposed [11]. The core idea of KD is to employ the teacher's prediction logits as soft labels to guide the student. Self-knowledge distillation (self-KD) [33, 47] is inspired by the knowledge distillation method, but it does not require an actual teacher. Instead, it designs soft labels through auxiliary branches or special distribution. The similarity between KD and self-KD is that they utilize soft labels for distillation loss, while the key difference is in how they obtain the soft labels. This paper aims to 1) improve the utilization of soft labels for distillation loss and 2) propose a general and effective method to obtain customized soft labels for self-KD. The targets make us obtain the soft labels with a teacher and use our modified distillation loss for better performance. Alternatively, when we lack a teacher, we can use the proposed self-KD method"
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+            "content": "*This work was done when Zhendong was an intern at IDEA."
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+            ],
+            "angle": 0,
+            "content": "The original cross-entropy (CE) loss for classification calculates the loss on the target class (the image's category). While the soft labels from the teacher include target and non-target class, thus the KD loss also includes both target and non-target loss. The decoupled method has been proven effective for KD in DKD [49]. Unlike DKD's method of adjusting hyper-parameters on target and non-target loss, we present a simple yet effective way to decompose the KD loss. We decompose the KD loss into a combination of the target loss (like the original CE loss) and the non-target loss in CE form. The non-target loss transforms the internal distribution of the student's non-target logits to match the teacher's distribution. However, we find that the sum of the student's and teacher's non-target logits is changing and different, which hinders the alignment of their distributions. To address this issue, we normalize the non-target logits to equalize their sum, transferring teacher's non-target knowledge. With this slight modification, we introduce our Normalized Knowledge Distillation (NKD) loss, as depicted in Fig.1, significantly enhancing KD's performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.413,
+                0.47,
+                0.52
+            ],
+            "angle": 0,
+            "content": "Our proposed NKD utilizes the teacher's target logit and normalized non-target logits to guide the student, resulting in state-of-the-art performance. This demonstrates the effectiveness of NKD loss formulation. Also, it can be generally used for self-KD to calculate the distillation loss, but how to generate the soft labels without a real teacher generally and efficiently is also important."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.521,
+                0.47,
+                0.748
+            ],
+            "angle": 0,
+            "content": "Various self-KD methods have explored using manually designed soft labels to enhance students with less time than KD. These methods [14, 38, 44, 47] typically obtain the labels from auxiliary branches or contrastive learning, as depicted in Fig. 2 (a), (b), and (c). However, despite requiring less time than KD, they still involve significant overhead compared to training the model directly. Recently, state-of-the-art Zipf's LS [17], as shown in Fig. 2 (d), introduced soft non-target labels based on a special distribution that can significantly reduce resource and time requirements. It classifies the student's feature in the spatial dimension and determines the rank of the non-target class using Zipf's law [25]. However, it requires the pixel-level features before average pooling, making it unsuitable for ViT-like models [6] with patch-wise tokenization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "To address the limitations of existing methods, we propose a general and effective way to obtain soft labels. We design customized soft labels available for both CNN and ViT models. Following the NKD loss formulation, our customized soft labels comprise soft target label and soft nontarget labels for corresponding loss. For the soft target label, we replace the teacher's target logit with the smoother label value obtained from the student's prediction. Since the student's predictions vary drastically during training, especially in the beginning, we smooth the student's tar"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.332
+            ],
+            "angle": 0,
+            "content": "get output within each training batch to stabilize the label values. For the soft non-target labels, we need their rank and distribution. First, for the rank, we get it from the intermediate feature, making our method available for both CNN and ViT models. We take weak supervision on the intermediate feature to get weak logit. Then, we normalize and combine it with the final logit and sort for the rank, as shown in Fig. 2 (f). The soft non-target labels' distribution follows Zipf's Law [25]. With the soft target and nontarget labels, we set our customized soft labels and propose Universal Self-Knowledge Distillation (USKD) as shown in Fig. 1. Besides, USKD only needs an extra linear layer for weak supervision. So it just takes a few more computing resources and time than training the model directly. USKD is a simple and effective method that achieves state-of-the-art performance on both CNN and ViT models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.333,
+                0.892,
+                0.424
+            ],
+            "angle": 0,
+            "content": "As described above, we normalize KD's non-target logits and propose NKD, using the soft labels better and improving KD's performance significantly. For the generation of soft labels without a real teacher, we set soft target and nontarget labels, proposing USKD for self-KD. In a nutshell, the contributions of this paper are:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.433,
+                0.892,
+                0.51
+            ],
+            "angle": 0,
+            "content": "- We normalize the non-target logits in the classical KD, making it better to optimize the cross-entropy loss. With this minor change, we propose Normalized KD (NKD) loss, using teacher's soft labels better and improving KD's performance significantly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.518,
+                0.892,
+                0.609
+            ],
+            "angle": 0,
+            "content": "- We propose a novel way to set customized soft labels without a real teacher, including target and non-target classes for self-KD. We utilize the weak logit to obtain soft non-target labels. Besides, we enlarge the difference between student's target logit for different images and soften them for soft target labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.619,
+                0.892,
+                0.695
+            ],
+            "angle": 0,
+            "content": "- We propose a simple and effective self-KD method USKD with our customized soft labels, which applies to both CNN and ViT models. Importantly, USKD requires only almost negligible additional time and resources compared to training the model directly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.703,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": "- We conduct extensive experiments on CIFAR-100 and ImageNet to verify the effectiveness of NKD and USKD, achieving state-of-the-art performance. Additionally, we demonstrate the efficacy of models trained with our self-KD method on COCO for detection."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.433,
+                0.892,
+                0.779
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.793,
+                0.638,
+                0.808
+            ],
+            "angle": 0,
+            "content": "2. Related work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.818,
+                0.712,
+                0.833
+            ],
+            "angle": 0,
+            "content": "2.1. Knowledge Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Knowledge distillation is a method to improve the model while keeping the network unchanged. It was first proposed by Hinton et al. [11], where the student is supervised by the hard and soft labels from the teacher's output. Many"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17186"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.189,
+                0.092,
+                0.28,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Extra Parameters"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.105,
+                0.368,
+                0.195
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.549,
+                0.093,
+                0.647,
+                0.104
+            ],
+            "angle": 0,
+            "content": "Extra Computation"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.394,
+                0.106,
+                0.55,
+                0.18
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.383,
+                0.182,
+                0.574,
+                0.194
+            ],
+            "angle": 0,
+            "content": "(b) Self-KD with Contrastive Method"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.599,
+                0.105,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.625,
+                0.183,
+                0.786,
+                0.194
+            ],
+            "angle": 0,
+            "content": "(c) Self-KD with Image Mixture"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.226,
+                0.201,
+                0.435,
+                0.213
+            ],
+            "angle": 0,
+            "content": "Modeling Distribution of Non-target Only"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.083,
+                0.215,
+                0.349,
+                0.269
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.121,
+                0.278,
+                0.328,
+                0.291
+            ],
+            "angle": 0,
+            "content": "(d) Self-KD with Zipf's Label Smoothing"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.374,
+                0.222,
+                0.575,
+                0.27
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.387,
+                0.278,
+                0.563,
+                0.29
+            ],
+            "angle": 0,
+            "content": "(e) Self-KD with Label Smoothing"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.582,
+                0.214,
+                0.887,
+                0.279
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.596,
+                0.279,
+                0.802,
+                0.29
+            ],
+            "angle": 0,
+            "content": "(f) Self-KD with Customized Soft Labels"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.297,
+                0.894,
+                0.339
+            ],
+            "angle": 0,
+            "content": "Figure 2. Comparison of different self-KD methods with (a) extra blocks and parameters [14], (b) contrastive method [37], (c) image mixture [38], (d) Zipf's label smoothing [17], and (e) label smoothing [22, 34]. (f) Self-KD with our customized soft labels including both target and non-target class for distillation. Note some methods can only be applied to CNN, while ours works for both CNN and ViT."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.363,
+                0.47,
+                0.514
+            ],
+            "angle": 0,
+            "content": "following works focus on better using soft labels to transfer more knowledge. WSLD [50] analyzes soft labels and distributes different weights for them from a perspective of bias-variance trade-off. SRRL [39] forces the output logits of the teacher's and student's features after the teacher's linear layer to be the same. DKD [49] decouples the logit and distributes different weights for the target and non-target classes. DIST [13] uses the Pearson correlation coefficient to replace the KL divergence and transfers the inter-relation and intra-relation together."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.515,
+                0.47,
+                0.711
+            ],
+            "angle": 0,
+            "content": "Besides distillation on logits, some works [1, 31, 40, 42] aim at transferring knowledge from intermediate features. FitNet [28] distill the semantic information from the intermediate feature directly. AT [45] transfers the attention of feature maps to the students. OFD [10] designs the margin ReLU and modifies the measurement for the distance between students and teachers. RKD [23] extracts the relation from the feature map. CRD [35] applies contrastive learning to distillation successfully. KR [3] transfers knowledge from multi-level features for distillation. TaT [18] helps the student to learn the teacher's every spatial component. MGD [41] masks the student's feature and forces it to generate the teacher's feature."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.725,
+                0.323,
+                0.741
+            ],
+            "angle": 0,
+            "content": "2.2. Self-Knowledge Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Self-Knowledge Distillation has been proposed as an alternative approach to Knowledge Distillation that does not rely on an external teacher model. Self-KD aims to utilize the information within the student model to guide its learning process. Several self-KD methods have been proposed in recent years. DKS [33] introduces auxiliary supervision branches and pairwise knowledge alignments, while BYOT [47] adds blocks and layers to every stage and uses shallow and deep features as student and teacher, respectively. KDCL [7] trains two models for online knowledge"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.363,
+                0.892,
+                0.575
+            ],
+            "angle": 0,
+            "content": "distillation, while FRSKD [14] adds a new branch supervised by the original feature and uses the logit of the new branch for self-KD. DDGSD [37] transfers knowledge between different distorted versions of the same training data. OLS [46] sets a matrix that is made up of the soft label for every class, while MixSKD [38] proposes incorporating self-knowledge distillation with image mixture and aggregates multi-stage feature to produce soft labels. Tf-FD [16] includes intra-layer and inter-layer distillation, reusing the channel-wise and layer-wise features to provide knowledge without an additional model. However, these methods require auxiliary architecture, adapt layers for alignment, or data augmentation, consuming much more time and computing resources than training the model directly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.578,
+                0.892,
+                0.775
+            ],
+            "angle": 0,
+            "content": "In contrast, some self-KD methods require little extra or even no more time than training the model directly. For example, Label Smoothing [34] sets the labels manually by distributing the same values to all non-target classes. TfKD [43] revisits KD via label smoothing, using a high temperature to generate the manual logit for distillation. Zipf's LS [17] utilizes the student's linear layer to obtain several logits for each pixel of the student's last feature map. The method uses these logits to vote for the non-target class's rank with Zipf distribution [25]. These methods set soft labels to achieve self-knowledge distillation without contrastive learning, data augmentation, or auxiliary branches, saving much training time and computing resources."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.8,
+                0.591,
+                0.815
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.828,
+                0.876,
+                0.844
+            ],
+            "angle": 0,
+            "content": "3.1. Normalized KD for Better Using Soft Labels"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Using \\( t \\) denote the target class, \\( C \\) denote the number of classes, \\( V_{i} \\) denote the label value for each class \\( i \\), and \\( S_{i} \\) denote the student's output probability. The original loss"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17187"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.092,
+                0.434,
+                0.108
+            ],
+            "angle": 0,
+            "content": "for image classification can be formulated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.088,
+                0.117,
+                0.47,
+                0.158
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {o r i} = - \\sum_ {i} ^ {C} V _ {i} \\log \\left(S _ {i}\\right) = - V _ {t} \\log \\left(S _ {t}\\right) = - \\log \\left(S _ {t}\\right). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.168,
+                0.47,
+                0.199
+            ],
+            "angle": 0,
+            "content": "Using \\( T_{i} \\) denote the teacher's soft labels. The classical KD utilizes them for distillation loss as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.148,
+                0.206,
+                0.47,
+                0.294
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {k d} = - \\sum_ {i} ^ {C} T _ {i} \\log \\left(S _ {i}\\right) (2) \\\\ = - T _ {t} \\log \\left(S _ {t}\\right) - \\sum_ {i \\neq t} ^ {C} T _ {i} \\log \\left(S _ {i}\\right). (3) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.304,
+                0.473,
+                0.508
+            ],
+            "angle": 0,
+            "content": "As \\( L_{kd} \\) shows, the first loss \\( -T_t\\log(S_t) \\) is about the target class like the original \\( L_{ori} \\). While for the second non-target loss \\( -\\sum_{i \\neq t}^{C} T_i\\log(S_i) \\), it has the same form as CE loss \\( -\\sum p(x)\\log(q(x)) \\). The CE loss aims at making \\( q(x) \\) be the same as \\( p(x) \\). However, \\( \\sum_{i \\neq t}^{C} T_i = 1 - T_t \\) and \\( \\sum_{i \\neq t}^{C} S_i = 1 - S_t \\). Since the trainable \\( S_i \\) is unlikely to exactly match the fixed \\( T_i \\) during training, the sum of the two non-target logits is always different, preventing the two distributions from being the same. Thus we normalize \\( T_i \\) and \\( S_i \\) to force the sum of the two distributions to be the same. With \\( \\mathcal{N}(\\cdot) \\) denoting the normalized operation, we modify the KD loss and propose our Normalized Knowledge Distillation (NKD) loss as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.517,
+                0.469,
+                0.575
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {n k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\gamma \\cdot \\lambda^ {2} \\cdot \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(T _ {i} ^ {\\lambda}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i} ^ {\\lambda}\\right)\\right), \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.587,
+                0.47,
+                0.633
+            ],
+            "angle": 0,
+            "content": "where \\(\\gamma\\) is a hyper-parameter to balance the loss and \\(\\lambda\\) is the temperature for KD [11]. Finally, combining the original loss \\(L_{ori}\\), and NKD loss \\(L_{nkd}\\), we train the students with:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.202,
+                0.644,
+                0.469,
+                0.66
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {a l l} = L _ {o r i} + L _ {n k d}. \\tag {5}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.669,
+                0.391,
+                0.685
+            ],
+            "angle": 0,
+            "content": "3.2.Customized Soft Labels for Self-KD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.693,
+                0.47,
+                0.754
+            ],
+            "angle": 0,
+            "content": "We utilize NKD for better use of the soft labels. Following our NKD loss in Eq. 4, we propose a general and effective self-KD method, which sets soft labels on target and non-target classes without teachers."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.772,
+                0.254,
+                0.787
+            ],
+            "angle": 0,
+            "content": "3.2.1 Soft Target Label"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.795,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "First, for the soft target label, the weight \\( T_{t} \\) in Eq. 4 is obtained from the teacher's target output probability for the input image. We wonder if the soft target can be provided by adjusting the student's target output \\( S_{t} \\). The differences between \\( T_{t} \\) and \\( S_{t} \\) mainly focus on two parts. The first is that \\( T_{t} \\) is fixed, and \\( S_{t} \\) varies gradually during training. The second part is that the difference between different samples'"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.894,
+                0.213
+            ],
+            "angle": 0,
+            "content": "\\(S_{t}\\) is much smaller than \\(T_{t}\\) at the beginning of training. To overcome the problem, we first square \\(S_{t}\\) to enlarge the difference between different samples' \\(S_{t}\\). Then we propose a way to adjust \\(S_{t}\\), making it smoother to fit the training set without teachers. This strategy can be applied directly to different models, including CNN-liked and ViT-liked models. In this way, we get the soft target label \\(P_{t}\\), which is detached and zero-grad in training for self-KD:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.6,
+                0.221,
+                0.892,
+                0.239
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {t} = S _ {t} ^ {2} + V _ {t} - \\operatorname {m e a n} \\left(S _ {t} ^ {2}\\right). \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.248,
+                0.843,
+                0.264
+            ],
+            "angle": 0,
+            "content": "With the \\(P_{t}\\), we follow our NKD for the target loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.617,
+                0.273,
+                0.892,
+                0.29
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {t a r g e t}} = - P _ {t} \\log \\left(S _ {t}\\right), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.299,
+                0.894,
+                0.359
+            ],
+            "angle": 0,
+            "content": "where \\( V_{t} \\) denote the original target label value, e.g. [0.8, 0.2] for a mixed image. And \\( mean(\\cdot) \\) is calculated across different samples in a training batch. We discuss the effects of the smoothing ways for \\( S_{t} \\) in Sec. 5.6."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.377,
+                0.714,
+                0.392
+            ],
+            "angle": 0,
+            "content": "3.2.2 Soft Non-target Labels"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.4,
+                0.893,
+                0.536
+            ],
+            "angle": 0,
+            "content": "The knowledge from the teacher's soft non-target labels includes its rank and distribution. We also need them to set the soft non-target labels for self-KD. To get the rank, we first obtain a new weak logit by setting weak supervision on the intermediate feature. Using \\(\\mathcal{F}\\) denote the feature of stage 2 of the CNN-liked model or the mid layer's classification token of the ViT-liked model, \\(GAP\\) denote the global average pooling, \\(FC\\) denote a new linear layer, the weak logit of the CNN-liked model can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.546,
+                0.892,
+                0.563
+            ],
+            "angle": 0,
+            "content": "\\[\nW _ {i} = \\operatorname {s o f t m a x} (F C (G A P (\\mathcal {F}))), \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.572,
+                0.892,
+                0.587
+            ],
+            "angle": 0,
+            "content": "As for the ViT-liked model, the weak logit is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.606,
+                0.612,
+                0.786,
+                0.629
+            ],
+            "angle": 0,
+            "content": "\\[\nW _ {i} = \\operatorname {s o f t m a x} (F C (\\mathcal {F})).\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.637,
+                0.894,
+                0.728
+            ],
+            "angle": 0,
+            "content": "We aim to obtain another smoother non-target logit different from the original final logit. So we utilize a smooth label and take weak supervision to get the weak logit. Using \\( V_{i} \\) denote the label, which is the original label processed with label smoothing, the loss for obtaining the weak logit is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.592,
+                0.735,
+                0.892,
+                0.775
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {w e a k}} = - \\mu \\cdot \\sum_ {i} ^ {C} V _ {i} \\log \\left(W _ {i}\\right), \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.784,
+                0.892,
+                0.859
+            ],
+            "angle": 0,
+            "content": "where \\(\\mu < 1\\) is a hyper-parameter to achieve weak supervision. With the weak logit, we obtain the soft non-target labels' rank by normalizing and combining it with the final logit. This operation balances the two logits' effects for the rank, and the analysis is shown in Sec. 5.7."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.611,
+                0.867,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "\\[\nR _ {i} = \\frac {W _ {i}}{1 - W _ {t}} + \\frac {S _ {i}}{1 - S _ {t}}. \\tag {10}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17188"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.47,
+                0.136
+            ],
+            "angle": 0,
+            "content": "The soft non-target labels' distribution follows Zipf's law [25], which has been applied in Zipf's LS [17]. The formulation can be formulated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.215,
+                0.143,
+                0.47,
+                0.18
+            ],
+            "angle": 0,
+            "content": "\\[\nZ _ {i} = \\frac {i ^ {- 1}}{\\sum_ {i = 1} ^ {C} i ^ {- 1}}. \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.187,
+                0.469,
+                0.232
+            ],
+            "angle": 0,
+            "content": "With the distribution, we sort it with the rank of \\( R_{i} \\) and obtain the soft non-target labels \\( Z_{i} \\) for self-KD. Following our NKD loss in Eq. 4, the non-target loss is as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.158,
+                0.253,
+                0.469,
+                0.295
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {n o n} = - \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(Z _ {i}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i}\\right)\\right). \\tag {12}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.312,
+                0.269,
+                0.326
+            ],
+            "angle": 0,
+            "content": "3.2.3 Overall for Self-KD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.336,
+                0.469,
+                0.395
+            ],
+            "angle": 0,
+            "content": "With the proposed soft target label and soft non-target labels, we calculate the corresponding loss and propose USKD as shown in Fig. 1. We train all the models with the total loss for self-KD as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.101,
+                0.406,
+                0.469,
+                0.423
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {a l l}} = L _ {\\text {o r i}} + \\alpha \\cdot L _ {\\text {t a r g e t}} + \\beta \\cdot L _ {\\text {n o n}} + L _ {\\text {w e a k}}, \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.432,
+                0.469,
+                0.477
+            ],
+            "angle": 0,
+            "content": "where \\( L_{ori} \\) is the original loss for the models among all the tasks, \\( \\alpha \\) and \\( \\beta \\) are two hyper-parameters to balance the loss scale. \\( L_{weak} \\) is used to generate the weak logit in Eq. 8."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.49,
+                0.21,
+                0.506
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.514,
+                0.269,
+                0.529
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.537,
+                0.469,
+                0.627
+            ],
+            "angle": 0,
+            "content": "We conduct the experiments on CIFAR-100 [15] and ImageNet [5], which contain 100 and 1000 categories, respectively. For CIFAR-100, we use 50k images for training and 10k for validation. For ImageNet, we use 1.2 million images for training and 50k images for validation. In this paper, we use accuracy to evaluate all the models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.629,
+                0.469,
+                0.839
+            ],
+            "angle": 0,
+            "content": "For KD with teachers, NKD has two hyper-parameters \\(\\gamma\\) and \\(\\lambda\\) in Eq. 4. For all the experiments, we adopt \\(\\{\\gamma = 1.5, \\lambda = 1\\}\\) on ImageNet. While for CIFAR-100, we follow the training setting from DKD [49] for a fair comparison. And USKD has two hyper-parameters \\(\\alpha\\) and \\(\\beta\\) to balance the loss scale in Eq. 13. Another hyper-parameter \\(\\mu\\) is used to achieve the weak supervision in Eq. 9. For all the experiments, we adopt \\(\\{\\alpha = 1, \\beta = 0.1, \\mu = 0.005\\}\\) on ImageNet and \\(\\{\\alpha = 0.1, \\beta = 0.1, \\mu = 0.1\\}\\) on CIFAR-100. The other training setting for KD and self-KD is the same as training the students without distillation. We use 8 GPUs to conduct the experiments with MMClassition [4] based on Pytorch [24]. More details and experimental results about the hyper-parameters are shown in the supplement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.848,
+                0.347,
+                0.862
+            ],
+            "angle": 0,
+            "content": "4.2. Normalized KD with Teachers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "When we get the soft labels from a real teacher, we can use NKD loss for better performance. To prove this, we"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.257
+            ],
+            "angle": 0,
+            "content": "first conduct experiments with various teacher-student distillation pairs on CIFAR-100, shown in Tab. 1. In this setting, we evaluate our method on several models with different architectures, including VGGNet [32], ResNet [9], ShuffleNet [48] and MobileNetV2 [30]. We compare our method with KD [11] and several other state-of-the-art distillation methods. As the results show, our method brings the students remarkable accuracy gains over other methods. Our method achieves the best performance among logit-based distillation methods and even surpasses the feature-based distillation methods in some settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.259,
+                0.892,
+                0.47
+            ],
+            "angle": 0,
+            "content": "To further demonstrate the effectiveness and robustness of our NKD, we test it on a more challenging dataset, ImageNet. We set two popular teacher-student pairs, which include homogeneous and heterogeneous teacher-student structures for distillation. The homogeneous distillation is ResNet34-ResNet18, and the heterogeneous distillation is ResNet50-MobileNet. The results of different KD methods on ImageNet are shown in Tab. 1. As the results show, our method outperforms all the previous methods. It brings consistent and significant improvements to the students for both distillation settings. The student ResNet18 and MobileNet achieve \\(71.96\\%\\) and \\(72.58\\%\\) Top-1 accuracy, getting \\(2.06\\%\\) and \\(3.37\\%\\) accuracy gains with the knowledge transferred from the teacher's logits, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.471,
+                0.892,
+                0.532
+            ],
+            "angle": 0,
+            "content": "As described above, our NKD enhances KD's performance significantly with a slight modification. And in various settings, it also surpasses DKD, a method that improves KD according to a different decoupled way."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.544,
+                0.813,
+                0.559
+            ],
+            "angle": 0,
+            "content": "4.3. Universal Self-KD without Teachers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.568,
+                0.892,
+                0.764
+            ],
+            "angle": 0,
+            "content": "When we lack a teacher, we use the proposed self-KD method USKD to obtain the soft labels and then calculate the loss. To evaluate its effectiveness, we first conduct experiments with ResNets [9] and MobileNet [12] on CIFAR100 and ImageNet datasets. We compare with the other state-of-the-art methods, which also set manual labels and only bring little extra time consumption, including label smoothing [34], Tf-KD [43] and Zipf's LS [17]. As shown in Tab. 2, our method surpasses the previous related self-knowledge distillation methods on various settings and brings the model remarkable gains. For example, it brings MobileNet and ResNet-18 \\(1.17\\%\\) and \\(0.89\\%\\) Top-1 accuracy gains on ImageNet."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.766,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Furthermore, we also test our USKD on more models, which include lighter models MobileNetV2 [30], ShuffleNetV2 [21] and a deeper ResNet. The results are shown in Tab. 3. For both the lightweight models, including MobileNetV2 and ShuffleNetV2, and the stronger model ResNet-101, our method also achieves considerable improvements. Besides, we also compare the time consumption to train the model for an epoch in Tab. 3. Compared with the baseline, the extra time we need for self-knowledge"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17189"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.097,
+                0.089,
+                0.877,
+                0.278
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Teacher Student</td><td>VGGNet13 VGGNet8</td><td>ResNet32x4 ResNet8x4</td><td>VGGNet13 MobileNetV2</td><td>ResNet50 MobileNetV2</td><td>ResNet34 ResNet18</td><td>ResNet50 MobileNet</td></tr><tr><td rowspan=\"2\">Accuracy</td><td>Teacher</td><td>74.64</td><td>79.42</td><td>74.64</td><td>79.34</td><td>73.62</td><td>76.55</td></tr><tr><td>Student</td><td>70.36</td><td>72.50</td><td>64.60</td><td>64.60</td><td>69.90</td><td>69.21</td></tr><tr><td rowspan=\"4\">Feature</td><td>RKD [23]</td><td>71.48</td><td>71.90</td><td>64.52</td><td>64.43</td><td>71.34</td><td>71.32</td></tr><tr><td>CRD [35]</td><td>73.94</td><td>75.51</td><td>69.73</td><td>69.11</td><td>71.17</td><td>71.40</td></tr><tr><td>OFD [10]</td><td>73.95</td><td>74.95</td><td>69.48</td><td>69.04</td><td>71.08</td><td>71.25</td></tr><tr><td>KR [3]</td><td>74.84</td><td>75.63</td><td>70.37</td><td>69.89</td><td>71.61</td><td>72.56</td></tr><tr><td rowspan=\"4\">Logit</td><td>KD [11]</td><td>72.98</td><td>73.33</td><td>67.37</td><td>67.35</td><td>71.03</td><td>70.68</td></tr><tr><td>WSLD [50]</td><td>74.36</td><td>76.05</td><td>69.02</td><td>70.15</td><td>71.73</td><td>72.02</td></tr><tr><td>DKD [49]</td><td>74.68</td><td>76.32</td><td>69.71</td><td>70.35</td><td>71.70</td><td>72.05</td></tr><tr><td>NKD (ours)</td><td>74.86</td><td>76.35</td><td>70.22</td><td>70.67</td><td>71.96</td><td>72.58</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.287,
+                0.893,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Table 1. Results of different knowledge distillation methods on CIFAR-100 (the left four columns) and ImageNet (the right two columns) dataset. The data that is underlined denotes the second-best result among all the results. The metric is the Top-1 accuracy (\\%)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.081,
+                0.327,
+                0.511,
+                0.442
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>CIFAR100</td><td colspan=\"3\">ImageNet</td></tr><tr><td>Model</td><td>ResNet18</td><td>ResNet18</td><td>ResNet50</td><td>MobileNet</td></tr><tr><td>Baseline</td><td>78.58</td><td>69.90</td><td>76.55</td><td>69.21</td></tr><tr><td>LS [34]</td><td>79.42</td><td>69.92</td><td>76.64</td><td>68.98</td></tr><tr><td>Tf-KD [43]</td><td>79.53</td><td>70.14</td><td>76.59</td><td>69.20</td></tr><tr><td>Zipf&#x27;s LS [17]</td><td>79.63</td><td>70.30</td><td>76.96</td><td>69.59</td></tr><tr><td>USKD (ours)</td><td>79.90</td><td>70.79</td><td>77.07</td><td>70.38</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.451,
+                0.512,
+                0.495
+            ],
+            "angle": 0,
+            "content": "Table 2. The comparative results of different self-knowledge distillation methods on CIFAR100 and ImageNet dataset. We report the models' performance with Top-1 accuracy \\((\\%)\\)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.096,
+                0.514,
+                0.455,
+                0.597
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>77.30 (+0.46)</td></tr><tr><td>DeiT-Tiny</td><td>74.42</td><td>74.97 (+0.55)</td></tr><tr><td>DeiT-Small</td><td>80.55</td><td>80.77 (+0.22)</td></tr><tr><td>Swin-Tiny</td><td>81.18</td><td>81.49 (+0.31)</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.606,
+                0.472,
+                0.651
+            ],
+            "angle": 0,
+            "content": "Table 4. Results of training more models, including ViT-liked models with our proposed method on ImageNet dataset. All the results are reported with Top-1 accuracy \\((\\%)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.672,
+                0.47,
+                0.765
+            ],
+            "angle": 0,
+            "content": "distillation is very limited. Specifically, the time of training MobileNet-V2 with our proposed USKD for an epoch is 10.18 minutes, which is just 0.01 minutes higher than training the model directly. Our method brings considerable improvements to various models with negligible extra time consumption."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.772,
+                0.388,
+                0.788
+            ],
+            "angle": 0,
+            "content": "4.4. Universal Self-KD for More Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The previous self-KD methods are specially designed for CNN-liked models. However, some models like ViT [6] translate the image into different tokens and have a completely different architecture. Those self-KD methods fail to benefit ViT-liked models. For ViT-liked models, USKD can also set customized soft labels and bring remarkable improvements. As described in Eq. 8, we use an extra"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.521,
+                0.327,
+                0.88,
+                0.442
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td rowspan=\"3\">Accuracy (%)</td><td>ResNet-101</td><td>77.97</td><td>78.54 (+0.57)</td></tr><tr><td>MobileNet-V2</td><td>71.86</td><td>72.41 (+0.55)</td></tr><tr><td>ShuffleNet-V2</td><td>69.55</td><td>70.30 (+0.75)</td></tr><tr><td rowspan=\"3\">Time (min)</td><td>ResNet-101</td><td>13.78</td><td>13.95</td></tr><tr><td>MobileNet-V2</td><td>10.17</td><td>10.18</td></tr><tr><td>ShuffleNet-V2</td><td>8.63</td><td>8.68</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.516,
+                0.451,
+                0.88,
+                0.494
+            ],
+            "angle": 0,
+            "content": "Table 3. The results of the models' performance are Top-1 accuracy \\((\\%)\\) on ImageNet dataset. The time data are reported with minutes (min) for a training epoch."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.517,
+                0.892,
+                0.685
+            ],
+            "angle": 0,
+            "content": "linear layer connected to ViT's middle layer for classification and obtain the weak logit. The rest operations are the same as CNN-liked models. To show the generalization of USKD, we apply it to more models, including RegNet [26], DeiT [36], and Swin-Transformer [20], which can be seen in Tab. 4. All the models can achieve remarkable Top-1 accuracy gains. Besides, our method even can bring \\(0.55\\%\\) gains for DeiT-Tiny. And it also brings \\(0.31\\%\\) Top-1 accuracy gains for the latest state-of-the-art model SwinTransformer. The results of more models show our method is both effective and general."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.7,
+                0.597,
+                0.718
+            ],
+            "angle": 0,
+            "content": "5. Analysis"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.726,
+                0.879,
+                0.743
+            ],
+            "angle": 0,
+            "content": "5.1. Effects of Normalizing the Non-target Logits"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In this paper, we proposed normalizing the non-target logits in the original KD to help the student perform better. In this subsection, we conduct experiments to demonstrate the effectiveness of our modification. As shown in Tab. 5, using the target loss alone leads to a \\(1.16\\%\\) increase in accuracy. Combining the knowledge from both target and nontarget classes allows us to better use the teacher's knowledge, resulting in a significant improvement of \\(2.06\\%\\) Top-1 accuracy for the student. Furthermore, we normalize the non-target logits in the KD loss for distillation and compare"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.958
+            ],
+            "angle": 0,
+            "content": "17190"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.089,
+                0.089,
+                0.46,
+                0.187
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Loss</td><td colspan=\"4\">ResNet34 - ResNet18</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>KD&#x27;s Non-target</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>NKD&#x27;s Non-target</td><td>X</td><td>X</td><td>X</td><td>✓</td></tr><tr><td>Top-1 Acc. (%)</td><td>69.90</td><td>71.06</td><td>71.33</td><td>71.96</td></tr><tr><td>Top-5 Acc. (%)</td><td>89.43</td><td>89.51</td><td>90.25</td><td>90.48</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.195,
+                0.47,
+                0.224
+            ],
+            "angle": 0,
+            "content": "Table 5. Effects of our normalized non-target loss on ImageNet dataset. The teacher is ResNet34 and the student is ResNet18."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.245,
+                0.47,
+                0.32
+            ],
+            "angle": 0,
+            "content": "the non-target loss from both KD and NKD. Our non-target loss brings much greater gains than KD's non-target loss, as shown in the comparison. These results demonstrate the effectiveness of our proposed modification in improving KD's performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.329,
+                0.42,
+                0.344
+            ],
+            "angle": 0,
+            "content": "5.2. Difference between Our NKD and DKD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.352,
+                0.47,
+                0.429
+            ],
+            "angle": 0,
+            "content": "To better use the soft labels, we decompose KD loss and normalize the non-target logits for a better performance. The decoupled method is inspired by DKD [49]. However, this paper presented a more straightforward and efficient decomposition method. DKD decouples KD loss as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.116,
+                0.438,
+                0.469,
+                0.5
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\left(1 - T _ {t}\\right) \\log \\left(1 - S _ {t}\\right) (14) \\\\ - \\left(1 - T _ {t}\\right) \\sum_ {i \\neq t} ^ {C} \\hat {T} _ {i} \\log \\left(\\hat {S} _ {i}\\right) (15) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.174,
+                0.522,
+                0.372,
+                0.554
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {T} _ {i} = \\frac {T _ {i}}{1 - T _ {t}}, \\quad \\hat {S} _ {i} = \\frac {S _ {i}}{1 - S _ {t}}.\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.561,
+                0.47,
+                0.592
+            ],
+            "angle": 0,
+            "content": "DKD analyzed the effects of KD's components and set hyper-parameters for a new formulation:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.093,
+                0.6,
+                0.469,
+                0.664
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} L _ {d k d} = \\alpha \\cdot \\left(- T _ {t} \\log \\left(S _ {t}\\right) - \\left(1 - T _ {t}\\right) \\log \\left(1 - S _ {t}\\right)\\right) (16) \\\\ - \\beta \\cdot \\left(\\sum_ {i \\neq t} ^ {C} \\hat {T} _ {i} \\log \\left(\\hat {S} _ {i}\\right)\\right) (17) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.673,
+                0.469,
+                0.703
+            ],
+            "angle": 0,
+            "content": "While we decompose KD loss into the target loss (like the original CE loss) and non-target loss in CE form:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.713,
+                0.469,
+                0.755
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\sum_ {i \\neq t} ^ {C} T _ {i} \\log \\left(S _ {i}\\right) \\tag {18}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.765,
+                0.47,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Then we find the sum of student's and teacher's non-target logits is different, making them hard to be the same. So we normalize them to equalize the sum as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.094,
+                0.819,
+                0.469,
+                0.862
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {n k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\gamma \\cdot \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(T _ {i}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i}\\right)\\right) \\tag {19}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "With this slight modification, we present our NKD loss and achieve better performance than DKD, as shown in Tab. 1."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.511,
+                0.089,
+                0.885,
+                0.171
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Loss</td><td colspan=\"4\">Top-1 Accuracy (%)</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Non-target</td><td>X</td><td>X</td><td>✓</td><td>✓</td></tr><tr><td>MobileNet</td><td>69.21</td><td>70.18</td><td>69.43</td><td>70.38</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>76.87</td><td>77.25</td><td>77.30</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.18,
+                0.892,
+                0.223
+            ],
+            "angle": 0,
+            "content": "Table 6. Ablation study of USKD's target and non-target loss. The experiments are conducted on the ImageNet dataset. All the results are the Top-1 accuracy \\((\\%)\\)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.506,
+                0.234,
+                0.888,
+                0.3
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ImageNet Top-1 Acc. (%)</td><td colspan=\"2\">COCO</td></tr><tr><td>APbox</td><td>ARbox</td></tr><tr><td>Baseline (Res50)</td><td>76.55</td><td>38.0</td><td>52.4</td></tr><tr><td>USKD (ours)</td><td>77.07</td><td>38.3</td><td>52.9</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.31,
+                0.892,
+                0.338
+            ],
+            "angle": 0,
+            "content": "Table 7. The detection results on the COCO dataset. We pre-train the backbone with USKD and use Mask-RCNN as the detector."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.36,
+                0.891,
+                0.377
+            ],
+            "angle": 0,
+            "content": "5.3. Effects of USKD's Target and Non-target Loss"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.383,
+                0.892,
+                0.565
+            ],
+            "angle": 0,
+            "content": "We propose a novel self-KD method called USKD, which utilizes customized soft labels that incorporate information from both target and non-target classes. To evaluate the impact of each type of information, we conduct experiments on MobileNet and RegNetX-1.6GF in Tab. 6. The experimental findings demonstrate that both types of information are beneficial and important for the two models, and their combination leads to further improvements in performance. For instance, by combining the target and non-target class distillation together, MobileNet achieves \\(70.38\\%\\), which surpasses the accuracy achieved by using distillation on either the target or non-target class alone."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.573,
+                0.855,
+                0.589
+            ],
+            "angle": 0,
+            "content": "5.4. Models with USKD for Downstream Task"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.597,
+                0.892,
+                0.793
+            ],
+            "angle": 0,
+            "content": "Our self-KD method yields remarkable accuracy gains for the classification task on CIFAR-100 and ImageNet datasets. To further evaluate its effectiveness and generalization, we also apply the pre-trained model to object detection using Mask R-CNN [8] as the detector and evaluate the model's performance with \\( AP^{box} \\) and \\( AR^{box} \\) on the COCO val2017 dataset [19]. We conduct the detection experiments for 12 epochs using MMDetection [2]. As shown in Tab. 7, the ResNet-50 backbone trained with our method improves the detector's performance by \\( 0.3\\mathrm{mAP} \\) and \\( 0.5\\mathrm{mAR} \\). The results demonstrate that our self-KD method not only improves the model's classification performance but also generalizes well to downstream tasks like object detection."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.802,
+                0.8,
+                0.817
+            ],
+            "angle": 0,
+            "content": "5.5.Customized Soft Labels for USKD"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our self-KD method, USKD, leverages customized soft labels for every image during training. Fig.3 shows several samples' soft labels, including the value for the target class and the top-3 non-target classes. For the target class, the value may be larger than 1 due to the smoothing method"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17191"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.09,
+                0.195,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.218,
+                0.09,
+                0.331,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.354,
+                0.091,
+                0.468,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.218,
+                0.47,
+                0.273
+            ],
+            "angle": 0,
+            "content": "Figure 3. The visualization of the target and top-3 non-target class values of our customized soft labels. The target class value is obtained by squaring and smoothing. The non-target class value is obtained by Zipf's law."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.3,
+                0.47,
+                0.436
+            ],
+            "angle": 0,
+            "content": "described in Eq. 6. For the non-target classes, USKD distributes larger values to the categories that are similar to the target class. For instance, the labels for the second image not only include the target 'linnet,' but also assign higher values to similar non-target classes like 'brambling', 'goldfinch', and 'bulbul'. This approach ensures that each image receives an appropriate customized soft label, which enables successful self-KD. The visualization also demonstrates how our USKD helps the model to perform better."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.448,
+                0.458,
+                0.465
+            ],
+            "angle": 0,
+            "content": "5.6. Different Smooth Ways for Soft Target Label"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.472,
+                0.47,
+                0.715
+            ],
+            "angle": 0,
+            "content": "Our USKD utilizes customized soft labels that include target and non-target classes for all the images during training. To create the soft labels, we replace the weights of NKD's target loss with a smoothed version of the student's target output \\( S_{t} \\), as shown in Eq. 6. In this subsection, we investigate the impact of different methods for smoothing the student's target output \\( S_{t} \\) on the performance of the model. We conduct experiments on ResNet18 trained on ImageNet to compare these methods, as shown in Tab. 8. The experiments show that all the methods significantly improve the student model. Notably, using \\( S_{t} + V_{t} - mean(S_{t}) \\) as the weights for smoothing the student's target output achieves \\( 0.86\\% \\) improvement, even outperforming using the teacher ResNet18's output as the soft target label. Based on this observation, we choose this method for smoothing the student's target output and use it as our soft target label."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.726,
+                0.443,
+                0.743
+            ],
+            "angle": 0,
+            "content": "5.7. Different Ranks for Soft Non-target Labels"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In Eq. 10, we combine the normalized weak and final logit to obtain the soft non-target labels' rank. In this subsection, we explore the effects of different ways for the rank, as shown in Tab. 9. Specifically, we compare the performance when using the weak logit's rank alone, the final logit's rank alone, or a combination of both but without normalization. Interestingly, our results show that all these methods help improve the model's accuracy, with the combination of the two normalized logits achieving the best performance. It is also noteworthy that even directly using"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.888,
+                0.217
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Smooth Ways</td><td>Teacher</td><td>Top-1 Acc. (%)</td></tr><tr><td>Baseline</td><td>-</td><td>69.90</td></tr><tr><td>St+Vt-mean(St)</td><td>X</td><td>70.76</td></tr><tr><td>softmax(St)*sum(Vt)</td><td>X</td><td>70.57</td></tr><tr><td>√St-min(St)</td><td>X</td><td>70.57</td></tr><tr><td>St/max(St)</td><td>X</td><td>70.53</td></tr><tr><td>St/mean(St)</td><td>X</td><td>70.50</td></tr><tr><td>Trained ResNet-18</td><td>✓</td><td>70.75</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.227,
+                0.892,
+                0.284
+            ],
+            "angle": 0,
+            "content": "Table 8. Results of training ResNet18 with target loss on ImageNet dataset. All the operations are calculated with different samples in a training batch. Because the trained Res-18's output is \\( S_{t} \\), we drop the square operation for different smoothing ways."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.51,
+                0.298,
+                0.884,
+                0.396
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>ResNet-18</td><td>RegNetX-1.6GF</td></tr><tr><td>Baseline</td><td>69.90</td><td>76.84</td></tr><tr><td>Weak Logit</td><td>70.65</td><td>77.28</td></tr><tr><td>Final Logit</td><td>70.72</td><td>77.15</td></tr><tr><td>Combination</td><td>70.71</td><td>77.25</td></tr><tr><td>Normalization</td><td>70.79</td><td>77.30</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.405,
+                0.892,
+                0.448
+            ],
+            "angle": 0,
+            "content": "Table 9. Results of different ranks for soft non-target labels. Normalization and Combination mean combining weak and final logit with normalization and without normalization, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.476,
+                0.891,
+                0.522
+            ],
+            "angle": 0,
+            "content": "the final logit to obtain the rank can satisfy accuracy gains. These findings provide insights into the effectiveness of various approaches for the rank of the non-target labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.54,
+                0.619,
+                0.556
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.567,
+                0.892,
+                0.824
+            ],
+            "angle": 0,
+            "content": "In this paper, we decompose KD loss into the target loss like original CE loss and non-target loss in a CE form. We then normalize the non-target logits to enhance the student's learning from the teacher. With this normalization, we introduce Normalized KD (NKD), which helps students to achieve state-of-the-art performance. Building on our NKD loss formulation, we further propose a new self-KD method, USKD, that works for both CNN-like and ViT-like models. USKD uses customized soft labels that include target and non-target classes for self-KD. We first square and smooth the student's target output logit as the soft target label. For the soft non-target labels, we use weak supervision to obtain the rank and utilize Zipf's law to generate the labels. In this way, USKD needs negligible extra time and resources than training the model directly. Extensive experiments on various models with different datasets demonstrate that both our NKD and USKD are simple and efficient."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgement. This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), the SZSTC project Grant (JCYJ20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "17192"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+# From Knowledge Distillation to Self-Knowledge Distillation: A Unified Approach with Normalized Loss and Customized Soft Labels
+
+Zhendong Yang $^{1,2*}$  Ailing Zeng $^{2}$  Zhe Li $^{3}$  Tianke Zhang $^{1}$  Chun Yuan $^{1\dagger}$  Yu Li $^{2\dagger}$ $^{1}$ Tsinghua Shenzhen International Graduate School  $^{2}$ International Digital Economy Academy (IDEA) Institute of Automation, Chinese Academy of Sciences
+
+{yangzd21,ztk21}@mails.tsinghua.edu.cn axel.li@outlook.com
+
+yuanc@sz.tsinghua.edu.cn {zengailing, liyu}@idea.edu.cn
+
+# Abstract
+
+Knowledge Distillation (KD) uses the teacher's logits as soft labels to guide the student, while self-KD does not need a real teacher to require the soft labels. This work unifies the formulations of the two tasks by decomposing and reorganizing the generic KD loss into a Normalized KD (NKD) loss and customized soft labels for both target class (image's category) and non-target classes named Universal Self-KD (USKD). We decompose the KD loss and find the non-target loss from it forces the student's non-target logits to match the teacher's, but the sum of the two nontarget logits is different, preventing them from being identical. NKD normalizes the non-target logits to equalize their sum. It can be generally used for KD and self-KD to better use the soft labels for distillation. USKD generates customized soft labels for both target and non-target classes without a teacher. It smoothes the target logit of the student as the soft target label and uses the rank of the intermediate feature to generate the soft non-target labels with Zipf's law. For KD with teachers, NKD achieves state-of-the-art performance on CIFAR-100 and ImageNet, boosting the ImageNet Top-1 accuracy of Res-18 from  $69.90\%$  to  $71.96\%$  with a Res-34 teacher. For self-KD without teachers, USKD is the first method that can be effectively applied to both CNN and ViT models with negligible additional time and memory cost, resulting in new state-of-the-art results, such as  $1.17\%$  and  $0.55\%$  accuracy gains on ImageNet for MobileNet and DeiT-Tiny, respectively. Code is available at https://github.com/yzd-v/cls_KD.
+
+# 1. Introduction
+
+Deep convolutional neural networks (CNNs) have significantly advanced the performance in many tasks [8, 9,
+
+![](images/66561ba44ea736efefde5f465f06ed42f39bd614488f6db6eaec17d6dd1a9a26.jpg)  
+Figure 1. Illustration of the proposed NKD and USKD for distillation loss calculations. NKD normalizes the non-target logits, using the soft labels more effectively, and achieves better performance. Meanwhile, USKD sets customized soft labels for both target and non-target classes, and can be applied to both CNNs and ViTs.
+
+27, 29]. In general, a larger model performing better needs more computing resources. On the other hand, smaller models have lower computation complexity but are less competitive than larger models. To bridge this gap and improve the performance of smaller models, knowledge distillation (KD) has been proposed [11]. The core idea of KD is to employ the teacher's prediction logits as soft labels to guide the student. Self-knowledge distillation (self-KD) [33, 47] is inspired by the knowledge distillation method, but it does not require an actual teacher. Instead, it designs soft labels through auxiliary branches or special distribution. The similarity between KD and self-KD is that they utilize soft labels for distillation loss, while the key difference is in how they obtain the soft labels. This paper aims to 1) improve the utilization of soft labels for distillation loss and 2) propose a general and effective method to obtain customized soft labels for self-KD. The targets make us obtain the soft labels with a teacher and use our modified distillation loss for better performance. Alternatively, when we lack a teacher, we can use the proposed self-KD method
+
+to obtain the soft labels and then calculate the loss.
+
+The original cross-entropy (CE) loss for classification calculates the loss on the target class (the image's category). While the soft labels from the teacher include target and non-target class, thus the KD loss also includes both target and non-target loss. The decoupled method has been proven effective for KD in DKD [49]. Unlike DKD's method of adjusting hyper-parameters on target and non-target loss, we present a simple yet effective way to decompose the KD loss. We decompose the KD loss into a combination of the target loss (like the original CE loss) and the non-target loss in CE form. The non-target loss transforms the internal distribution of the student's non-target logits to match the teacher's distribution. However, we find that the sum of the student's and teacher's non-target logits is changing and different, which hinders the alignment of their distributions. To address this issue, we normalize the non-target logits to equalize their sum, transferring teacher's non-target knowledge. With this slight modification, we introduce our Normalized Knowledge Distillation (NKD) loss, as depicted in Fig.1, significantly enhancing KD's performance.
+
+Our proposed NKD utilizes the teacher's target logit and normalized non-target logits to guide the student, resulting in state-of-the-art performance. This demonstrates the effectiveness of NKD loss formulation. Also, it can be generally used for self-KD to calculate the distillation loss, but how to generate the soft labels without a real teacher generally and efficiently is also important.
+
+Various self-KD methods have explored using manually designed soft labels to enhance students with less time than KD. These methods [14, 38, 44, 47] typically obtain the labels from auxiliary branches or contrastive learning, as depicted in Fig. 2 (a), (b), and (c). However, despite requiring less time than KD, they still involve significant overhead compared to training the model directly. Recently, state-of-the-art Zipf's LS [17], as shown in Fig. 2 (d), introduced soft non-target labels based on a special distribution that can significantly reduce resource and time requirements. It classifies the student's feature in the spatial dimension and determines the rank of the non-target class using Zipf's law [25]. However, it requires the pixel-level features before average pooling, making it unsuitable for ViT-like models [6] with patch-wise tokenization.
+
+To address the limitations of existing methods, we propose a general and effective way to obtain soft labels. We design customized soft labels available for both CNN and ViT models. Following the NKD loss formulation, our customized soft labels comprise soft target label and soft nontarget labels for corresponding loss. For the soft target label, we replace the teacher's target logit with the smoother label value obtained from the student's prediction. Since the student's predictions vary drastically during training, especially in the beginning, we smooth the student's tar
+
+get output within each training batch to stabilize the label values. For the soft non-target labels, we need their rank and distribution. First, for the rank, we get it from the intermediate feature, making our method available for both CNN and ViT models. We take weak supervision on the intermediate feature to get weak logit. Then, we normalize and combine it with the final logit and sort for the rank, as shown in Fig. 2 (f). The soft non-target labels' distribution follows Zipf's Law [25]. With the soft target and nontarget labels, we set our customized soft labels and propose Universal Self-Knowledge Distillation (USKD) as shown in Fig. 1. Besides, USKD only needs an extra linear layer for weak supervision. So it just takes a few more computing resources and time than training the model directly. USKD is a simple and effective method that achieves state-of-the-art performance on both CNN and ViT models.
+
+As described above, we normalize KD's non-target logits and propose NKD, using the soft labels better and improving KD's performance significantly. For the generation of soft labels without a real teacher, we set soft target and nontarget labels, proposing USKD for self-KD. In a nutshell, the contributions of this paper are:
+
+- We normalize the non-target logits in the classical KD, making it better to optimize the cross-entropy loss. With this minor change, we propose Normalized KD (NKD) loss, using teacher's soft labels better and improving KD's performance significantly.  
+- We propose a novel way to set customized soft labels without a real teacher, including target and non-target classes for self-KD. We utilize the weak logit to obtain soft non-target labels. Besides, we enlarge the difference between student's target logit for different images and soften them for soft target labels.  
+- We propose a simple and effective self-KD method USKD with our customized soft labels, which applies to both CNN and ViT models. Importantly, USKD requires only almost negligible additional time and resources compared to training the model directly.  
+- We conduct extensive experiments on CIFAR-100 and ImageNet to verify the effectiveness of NKD and USKD, achieving state-of-the-art performance. Additionally, we demonstrate the efficacy of models trained with our self-KD method on COCO for detection.
+
+# 2. Related work
+
+# 2.1. Knowledge Distillation
+
+Knowledge distillation is a method to improve the model while keeping the network unchanged. It was first proposed by Hinton et al. [11], where the student is supervised by the hard and soft labels from the teacher's output. Many
+
+![](images/3b1464350c68c1c2d20ab4f5fb95e697067242768018bfbff37b23568a6aa9c5.jpg)  
+Extra Parameters
+
+![](images/a5a3d86976637f8bdab04b0e724ed2fe463ede81473c26236086c29bbc6aa433.jpg)  
+Extra Computation  
+(b) Self-KD with Contrastive Method
+
+![](images/489a0da303475cc80218101d5164d554aab3499aed3d2f39c1d90d36d1d6be52.jpg)  
+(c) Self-KD with Image Mixture
+
+![](images/a0ca4a8051cc031941f03e4f1d3c8466801943c4eae9e571c52ab0d819a4ebc2.jpg)  
+Modeling Distribution of Non-target Only  
+(d) Self-KD with Zipf's Label Smoothing
+
+![](images/a8d4e64c5c8ad96523f1a6ae53fa04279b22a6bdcc87f0fadeefec7071c8ed7e.jpg)  
+(e) Self-KD with Label Smoothing
+
+![](images/14ff9d8ae1845723c5652cd9efb784e4fb1f0908c308694ee1b962c768cc8a29.jpg)  
+(f) Self-KD with Customized Soft Labels  
+Figure 2. Comparison of different self-KD methods with (a) extra blocks and parameters [14], (b) contrastive method [37], (c) image mixture [38], (d) Zipf's label smoothing [17], and (e) label smoothing [22, 34]. (f) Self-KD with our customized soft labels including both target and non-target class for distillation. Note some methods can only be applied to CNN, while ours works for both CNN and ViT.
+
+following works focus on better using soft labels to transfer more knowledge. WSLD [50] analyzes soft labels and distributes different weights for them from a perspective of bias-variance trade-off. SRRL [39] forces the output logits of the teacher's and student's features after the teacher's linear layer to be the same. DKD [49] decouples the logit and distributes different weights for the target and non-target classes. DIST [13] uses the Pearson correlation coefficient to replace the KL divergence and transfers the inter-relation and intra-relation together.
+
+Besides distillation on logits, some works [1, 31, 40, 42] aim at transferring knowledge from intermediate features. FitNet [28] distill the semantic information from the intermediate feature directly. AT [45] transfers the attention of feature maps to the students. OFD [10] designs the margin ReLU and modifies the measurement for the distance between students and teachers. RKD [23] extracts the relation from the feature map. CRD [35] applies contrastive learning to distillation successfully. KR [3] transfers knowledge from multi-level features for distillation. TaT [18] helps the student to learn the teacher's every spatial component. MGD [41] masks the student's feature and forces it to generate the teacher's feature.
+
+# 2.2. Self-Knowledge Distillation
+
+Self-Knowledge Distillation has been proposed as an alternative approach to Knowledge Distillation that does not rely on an external teacher model. Self-KD aims to utilize the information within the student model to guide its learning process. Several self-KD methods have been proposed in recent years. DKS [33] introduces auxiliary supervision branches and pairwise knowledge alignments, while BYOT [47] adds blocks and layers to every stage and uses shallow and deep features as student and teacher, respectively. KDCL [7] trains two models for online knowledge
+
+distillation, while FRSKD [14] adds a new branch supervised by the original feature and uses the logit of the new branch for self-KD. DDGSD [37] transfers knowledge between different distorted versions of the same training data. OLS [46] sets a matrix that is made up of the soft label for every class, while MixSKD [38] proposes incorporating self-knowledge distillation with image mixture and aggregates multi-stage feature to produce soft labels. Tf-FD [16] includes intra-layer and inter-layer distillation, reusing the channel-wise and layer-wise features to provide knowledge without an additional model. However, these methods require auxiliary architecture, adapt layers for alignment, or data augmentation, consuming much more time and computing resources than training the model directly.
+
+In contrast, some self-KD methods require little extra or even no more time than training the model directly. For example, Label Smoothing [34] sets the labels manually by distributing the same values to all non-target classes. TfKD [43] revisits KD via label smoothing, using a high temperature to generate the manual logit for distillation. Zipf's LS [17] utilizes the student's linear layer to obtain several logits for each pixel of the student's last feature map. The method uses these logits to vote for the non-target class's rank with Zipf distribution [25]. These methods set soft labels to achieve self-knowledge distillation without contrastive learning, data augmentation, or auxiliary branches, saving much training time and computing resources.
+
+# 3. Method
+
+# 3.1. Normalized KD for Better Using Soft Labels
+
+Using  $t$  denote the target class,  $C$  denote the number of classes,  $V_{i}$  denote the label value for each class  $i$ , and  $S_{i}$  denote the student's output probability. The original loss
+
+for image classification can be formulated as follows:
+
+$$
+L _ {o r i} = - \sum_ {i} ^ {C} V _ {i} \log \left(S _ {i}\right) = - V _ {t} \log \left(S _ {t}\right) = - \log \left(S _ {t}\right). \tag {1}
+$$
+
+Using  $T_{i}$  denote the teacher's soft labels. The classical KD utilizes them for distillation loss as:
+
+$$
+\begin{array}{l} L _ {k d} = - \sum_ {i} ^ {C} T _ {i} \log \left(S _ {i}\right) (2) \\ = - T _ {t} \log \left(S _ {t}\right) - \sum_ {i \neq t} ^ {C} T _ {i} \log \left(S _ {i}\right). (3) \\ \end{array}
+$$
+
+As  $L_{kd}$  shows, the first loss  $-T_t\log(S_t)$  is about the target class like the original  $L_{ori}$ . While for the second non-target loss  $-\sum_{i \neq t}^{C} T_i\log(S_i)$ , it has the same form as CE loss  $-\sum p(x)\log(q(x))$ . The CE loss aims at making  $q(x)$  be the same as  $p(x)$ . However,  $\sum_{i \neq t}^{C} T_i = 1 - T_t$  and  $\sum_{i \neq t}^{C} S_i = 1 - S_t$ . Since the trainable  $S_i$  is unlikely to exactly match the fixed  $T_i$  during training, the sum of the two non-target logits is always different, preventing the two distributions from being the same. Thus we normalize  $T_i$  and  $S_i$  to force the sum of the two distributions to be the same. With  $\mathcal{N}(\cdot)$  denoting the normalized operation, we modify the KD loss and propose our Normalized Knowledge Distillation (NKD) loss as follows:
+
+$$
+L _ {n k d} = - T _ {t} \log \left(S _ {t}\right) - \gamma \cdot \lambda^ {2} \cdot \sum_ {i \neq t} ^ {C} \mathcal {N} \left(T _ {i} ^ {\lambda}\right) \log \left(\mathcal {N} \left(S _ {i} ^ {\lambda}\right)\right), \tag {4}
+$$
+
+where  $\gamma$  is a hyper-parameter to balance the loss and  $\lambda$  is the temperature for KD [11]. Finally, combining the original loss  $L_{ori}$ , and NKD loss  $L_{nkd}$ , we train the students with:
+
+$$
+L _ {a l l} = L _ {o r i} + L _ {n k d}. \tag {5}
+$$
+
+# 3.2.Customized Soft Labels for Self-KD
+
+We utilize NKD for better use of the soft labels. Following our NKD loss in Eq. 4, we propose a general and effective self-KD method, which sets soft labels on target and non-target classes without teachers.
+
+# 3.2.1 Soft Target Label
+
+First, for the soft target label, the weight  $T_{t}$  in Eq. 4 is obtained from the teacher's target output probability for the input image. We wonder if the soft target can be provided by adjusting the student's target output  $S_{t}$ . The differences between  $T_{t}$  and  $S_{t}$  mainly focus on two parts. The first is that  $T_{t}$  is fixed, and  $S_{t}$  varies gradually during training. The second part is that the difference between different samples'
+
+$S_{t}$  is much smaller than  $T_{t}$  at the beginning of training. To overcome the problem, we first square  $S_{t}$  to enlarge the difference between different samples'  $S_{t}$ . Then we propose a way to adjust  $S_{t}$ , making it smoother to fit the training set without teachers. This strategy can be applied directly to different models, including CNN-liked and ViT-liked models. In this way, we get the soft target label  $P_{t}$ , which is detached and zero-grad in training for self-KD:
+
+$$
+P _ {t} = S _ {t} ^ {2} + V _ {t} - \operatorname {m e a n} \left(S _ {t} ^ {2}\right). \tag {6}
+$$
+
+With the  $P_{t}$ , we follow our NKD for the target loss:
+
+$$
+L _ {\text {t a r g e t}} = - P _ {t} \log \left(S _ {t}\right), \tag {7}
+$$
+
+where  $V_{t}$  denote the original target label value, e.g. [0.8, 0.2] for a mixed image. And  $mean(\cdot)$  is calculated across different samples in a training batch. We discuss the effects of the smoothing ways for  $S_{t}$  in Sec. 5.6.
+
+# 3.2.2 Soft Non-target Labels
+
+The knowledge from the teacher's soft non-target labels includes its rank and distribution. We also need them to set the soft non-target labels for self-KD. To get the rank, we first obtain a new weak logit by setting weak supervision on the intermediate feature. Using  $\mathcal{F}$  denote the feature of stage 2 of the CNN-liked model or the mid layer's classification token of the ViT-liked model,  $GAP$  denote the global average pooling,  $FC$  denote a new linear layer, the weak logit of the CNN-liked model can be formulated as:
+
+$$
+W _ {i} = \operatorname {s o f t m a x} (F C (G A P (\mathcal {F}))), \tag {8}
+$$
+
+As for the ViT-liked model, the weak logit is as follows:
+
+$$
+W _ {i} = \operatorname {s o f t m a x} (F C (\mathcal {F})).
+$$
+
+We aim to obtain another smoother non-target logit different from the original final logit. So we utilize a smooth label and take weak supervision to get the weak logit. Using  $V_{i}$  denote the label, which is the original label processed with label smoothing, the loss for obtaining the weak logit is as follows:
+
+$$
+L _ {\text {w e a k}} = - \mu \cdot \sum_ {i} ^ {C} V _ {i} \log \left(W _ {i}\right), \tag {9}
+$$
+
+where  $\mu < 1$  is a hyper-parameter to achieve weak supervision. With the weak logit, we obtain the soft non-target labels' rank by normalizing and combining it with the final logit. This operation balances the two logits' effects for the rank, and the analysis is shown in Sec. 5.7.
+
+$$
+R _ {i} = \frac {W _ {i}}{1 - W _ {t}} + \frac {S _ {i}}{1 - S _ {t}}. \tag {10}
+$$
+
+The soft non-target labels' distribution follows Zipf's law [25], which has been applied in Zipf's LS [17]. The formulation can be formulated as follows:
+
+$$
+Z _ {i} = \frac {i ^ {- 1}}{\sum_ {i = 1} ^ {C} i ^ {- 1}}. \tag {11}
+$$
+
+With the distribution, we sort it with the rank of  $R_{i}$  and obtain the soft non-target labels  $Z_{i}$  for self-KD. Following our NKD loss in Eq. 4, the non-target loss is as follows:
+
+$$
+L _ {n o n} = - \sum_ {i \neq t} ^ {C} \mathcal {N} \left(Z _ {i}\right) \log \left(\mathcal {N} \left(S _ {i}\right)\right). \tag {12}
+$$
+
+# 3.2.3 Overall for Self-KD
+
+With the proposed soft target label and soft non-target labels, we calculate the corresponding loss and propose USKD as shown in Fig. 1. We train all the models with the total loss for self-KD as follows:
+
+$$
+L _ {\text {a l l}} = L _ {\text {o r i}} + \alpha \cdot L _ {\text {t a r g e t}} + \beta \cdot L _ {\text {n o n}} + L _ {\text {w e a k}}, \tag {13}
+$$
+
+where  $L_{ori}$  is the original loss for the models among all the tasks,  $\alpha$  and  $\beta$  are two hyper-parameters to balance the loss scale.  $L_{weak}$  is used to generate the weak logit in Eq. 8.
+
+# 4. Experiments
+
+# 4.1. Datasets and Details
+
+We conduct the experiments on CIFAR-100 [15] and ImageNet [5], which contain 100 and 1000 categories, respectively. For CIFAR-100, we use 50k images for training and 10k for validation. For ImageNet, we use 1.2 million images for training and 50k images for validation. In this paper, we use accuracy to evaluate all the models.
+
+For KD with teachers, NKD has two hyper-parameters  $\gamma$  and  $\lambda$  in Eq. 4. For all the experiments, we adopt  $\{\gamma = 1.5, \lambda = 1\}$  on ImageNet. While for CIFAR-100, we follow the training setting from DKD [49] for a fair comparison. And USKD has two hyper-parameters  $\alpha$  and  $\beta$  to balance the loss scale in Eq. 13. Another hyper-parameter  $\mu$  is used to achieve the weak supervision in Eq. 9. For all the experiments, we adopt  $\{\alpha = 1, \beta = 0.1, \mu = 0.005\}$  on ImageNet and  $\{\alpha = 0.1, \beta = 0.1, \mu = 0.1\}$  on CIFAR-100. The other training setting for KD and self-KD is the same as training the students without distillation. We use 8 GPUs to conduct the experiments with MMClassition [4] based on Pytorch [24]. More details and experimental results about the hyper-parameters are shown in the supplement.
+
+# 4.2. Normalized KD with Teachers
+
+When we get the soft labels from a real teacher, we can use NKD loss for better performance. To prove this, we
+
+first conduct experiments with various teacher-student distillation pairs on CIFAR-100, shown in Tab. 1. In this setting, we evaluate our method on several models with different architectures, including VGGNet [32], ResNet [9], ShuffleNet [48] and MobileNetV2 [30]. We compare our method with KD [11] and several other state-of-the-art distillation methods. As the results show, our method brings the students remarkable accuracy gains over other methods. Our method achieves the best performance among logit-based distillation methods and even surpasses the feature-based distillation methods in some settings.
+
+To further demonstrate the effectiveness and robustness of our NKD, we test it on a more challenging dataset, ImageNet. We set two popular teacher-student pairs, which include homogeneous and heterogeneous teacher-student structures for distillation. The homogeneous distillation is ResNet34-ResNet18, and the heterogeneous distillation is ResNet50-MobileNet. The results of different KD methods on ImageNet are shown in Tab. 1. As the results show, our method outperforms all the previous methods. It brings consistent and significant improvements to the students for both distillation settings. The student ResNet18 and MobileNet achieve  $71.96\%$  and  $72.58\%$  Top-1 accuracy, getting  $2.06\%$  and  $3.37\%$  accuracy gains with the knowledge transferred from the teacher's logits, respectively.
+
+As described above, our NKD enhances KD's performance significantly with a slight modification. And in various settings, it also surpasses DKD, a method that improves KD according to a different decoupled way.
+
+# 4.3. Universal Self-KD without Teachers
+
+When we lack a teacher, we use the proposed self-KD method USKD to obtain the soft labels and then calculate the loss. To evaluate its effectiveness, we first conduct experiments with ResNets [9] and MobileNet [12] on CIFAR100 and ImageNet datasets. We compare with the other state-of-the-art methods, which also set manual labels and only bring little extra time consumption, including label smoothing [34], Tf-KD [43] and Zipf's LS [17]. As shown in Tab. 2, our method surpasses the previous related self-knowledge distillation methods on various settings and brings the model remarkable gains. For example, it brings MobileNet and ResNet-18  $1.17\%$  and  $0.89\%$  Top-1 accuracy gains on ImageNet.
+
+Furthermore, we also test our USKD on more models, which include lighter models MobileNetV2 [30], ShuffleNetV2 [21] and a deeper ResNet. The results are shown in Tab. 3. For both the lightweight models, including MobileNetV2 and ShuffleNetV2, and the stronger model ResNet-101, our method also achieves considerable improvements. Besides, we also compare the time consumption to train the model for an epoch in Tab. 3. Compared with the baseline, the extra time we need for self-knowledge
+
+<table><tr><td>Model</td><td>Teacher Student</td><td>VGGNet13 VGGNet8</td><td>ResNet32x4 ResNet8x4</td><td>VGGNet13 MobileNetV2</td><td>ResNet50 MobileNetV2</td><td>ResNet34 ResNet18</td><td>ResNet50 MobileNet</td></tr><tr><td rowspan="2">Accuracy</td><td>Teacher</td><td>74.64</td><td>79.42</td><td>74.64</td><td>79.34</td><td>73.62</td><td>76.55</td></tr><tr><td>Student</td><td>70.36</td><td>72.50</td><td>64.60</td><td>64.60</td><td>69.90</td><td>69.21</td></tr><tr><td rowspan="4">Feature</td><td>RKD [23]</td><td>71.48</td><td>71.90</td><td>64.52</td><td>64.43</td><td>71.34</td><td>71.32</td></tr><tr><td>CRD [35]</td><td>73.94</td><td>75.51</td><td>69.73</td><td>69.11</td><td>71.17</td><td>71.40</td></tr><tr><td>OFD [10]</td><td>73.95</td><td>74.95</td><td>69.48</td><td>69.04</td><td>71.08</td><td>71.25</td></tr><tr><td>KR [3]</td><td>74.84</td><td>75.63</td><td>70.37</td><td>69.89</td><td>71.61</td><td>72.56</td></tr><tr><td rowspan="4">Logit</td><td>KD [11]</td><td>72.98</td><td>73.33</td><td>67.37</td><td>67.35</td><td>71.03</td><td>70.68</td></tr><tr><td>WSLD [50]</td><td>74.36</td><td>76.05</td><td>69.02</td><td>70.15</td><td>71.73</td><td>72.02</td></tr><tr><td>DKD [49]</td><td>74.68</td><td>76.32</td><td>69.71</td><td>70.35</td><td>71.70</td><td>72.05</td></tr><tr><td>NKD (ours)</td><td>74.86</td><td>76.35</td><td>70.22</td><td>70.67</td><td>71.96</td><td>72.58</td></tr></table>
+
+Table 1. Results of different knowledge distillation methods on CIFAR-100 (the left four columns) and ImageNet (the right two columns) dataset. The data that is underlined denotes the second-best result among all the results. The metric is the Top-1 accuracy (\%).  
+
+<table><tr><td>Dataset</td><td>CIFAR100</td><td colspan="3">ImageNet</td></tr><tr><td>Model</td><td>ResNet18</td><td>ResNet18</td><td>ResNet50</td><td>MobileNet</td></tr><tr><td>Baseline</td><td>78.58</td><td>69.90</td><td>76.55</td><td>69.21</td></tr><tr><td>LS [34]</td><td>79.42</td><td>69.92</td><td>76.64</td><td>68.98</td></tr><tr><td>Tf-KD [43]</td><td>79.53</td><td>70.14</td><td>76.59</td><td>69.20</td></tr><tr><td>Zipf&#x27;s LS [17]</td><td>79.63</td><td>70.30</td><td>76.96</td><td>69.59</td></tr><tr><td>USKD (ours)</td><td>79.90</td><td>70.79</td><td>77.07</td><td>70.38</td></tr></table>
+
+Table 2. The comparative results of different self-knowledge distillation methods on CIFAR100 and ImageNet dataset. We report the models' performance with Top-1 accuracy  $(\%)$ .  
+
+<table><tr><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>77.30 (+0.46)</td></tr><tr><td>DeiT-Tiny</td><td>74.42</td><td>74.97 (+0.55)</td></tr><tr><td>DeiT-Small</td><td>80.55</td><td>80.77 (+0.22)</td></tr><tr><td>Swin-Tiny</td><td>81.18</td><td>81.49 (+0.31)</td></tr></table>
+
+distillation is very limited. Specifically, the time of training MobileNet-V2 with our proposed USKD for an epoch is 10.18 minutes, which is just 0.01 minutes higher than training the model directly. Our method brings considerable improvements to various models with negligible extra time consumption.
+
+# 4.4. Universal Self-KD for More Models
+
+The previous self-KD methods are specially designed for CNN-liked models. However, some models like ViT [6] translate the image into different tokens and have a completely different architecture. Those self-KD methods fail to benefit ViT-liked models. For ViT-liked models, USKD can also set customized soft labels and bring remarkable improvements. As described in Eq. 8, we use an extra
+
+Table 4. Results of training more models, including ViT-liked models with our proposed method on ImageNet dataset. All the results are reported with Top-1 accuracy  $(\%)$ .  
+
+<table><tr><td></td><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td rowspan="3">Accuracy (%)</td><td>ResNet-101</td><td>77.97</td><td>78.54 (+0.57)</td></tr><tr><td>MobileNet-V2</td><td>71.86</td><td>72.41 (+0.55)</td></tr><tr><td>ShuffleNet-V2</td><td>69.55</td><td>70.30 (+0.75)</td></tr><tr><td rowspan="3">Time (min)</td><td>ResNet-101</td><td>13.78</td><td>13.95</td></tr><tr><td>MobileNet-V2</td><td>10.17</td><td>10.18</td></tr><tr><td>ShuffleNet-V2</td><td>8.63</td><td>8.68</td></tr></table>
+
+Table 3. The results of the models' performance are Top-1 accuracy  $(\%)$  on ImageNet dataset. The time data are reported with minutes (min) for a training epoch.
+
+linear layer connected to ViT's middle layer for classification and obtain the weak logit. The rest operations are the same as CNN-liked models. To show the generalization of USKD, we apply it to more models, including RegNet [26], DeiT [36], and Swin-Transformer [20], which can be seen in Tab. 4. All the models can achieve remarkable Top-1 accuracy gains. Besides, our method even can bring  $0.55\%$  gains for DeiT-Tiny. And it also brings  $0.31\%$  Top-1 accuracy gains for the latest state-of-the-art model SwinTransformer. The results of more models show our method is both effective and general.
+
+# 5. Analysis
+
+# 5.1. Effects of Normalizing the Non-target Logits
+
+In this paper, we proposed normalizing the non-target logits in the original KD to help the student perform better. In this subsection, we conduct experiments to demonstrate the effectiveness of our modification. As shown in Tab. 5, using the target loss alone leads to a  $1.16\%$  increase in accuracy. Combining the knowledge from both target and nontarget classes allows us to better use the teacher's knowledge, resulting in a significant improvement of  $2.06\%$  Top-1 accuracy for the student. Furthermore, we normalize the non-target logits in the KD loss for distillation and compare
+
+<table><tr><td>Loss</td><td colspan="4">ResNet34 - ResNet18</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>KD&#x27;s Non-target</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>NKD&#x27;s Non-target</td><td>X</td><td>X</td><td>X</td><td>✓</td></tr><tr><td>Top-1 Acc. (%)</td><td>69.90</td><td>71.06</td><td>71.33</td><td>71.96</td></tr><tr><td>Top-5 Acc. (%)</td><td>89.43</td><td>89.51</td><td>90.25</td><td>90.48</td></tr></table>
+
+the non-target loss from both KD and NKD. Our non-target loss brings much greater gains than KD's non-target loss, as shown in the comparison. These results demonstrate the effectiveness of our proposed modification in improving KD's performance.
+
+# 5.2. Difference between Our NKD and DKD
+
+To better use the soft labels, we decompose KD loss and normalize the non-target logits for a better performance. The decoupled method is inspired by DKD [49]. However, this paper presented a more straightforward and efficient decomposition method. DKD decouples KD loss as:
+
+$$
+\begin{array}{l} L _ {k d} = - T _ {t} \log \left(S _ {t}\right) - \left(1 - T _ {t}\right) \log \left(1 - S _ {t}\right) (14) \\ - \left(1 - T _ {t}\right) \sum_ {i \neq t} ^ {C} \hat {T} _ {i} \log \left(\hat {S} _ {i}\right) (15) \\ \end{array}
+$$
+
+$$
+\hat {T} _ {i} = \frac {T _ {i}}{1 - T _ {t}}, \quad \hat {S} _ {i} = \frac {S _ {i}}{1 - S _ {t}}.
+$$
+
+DKD analyzed the effects of KD's components and set hyper-parameters for a new formulation:
+
+$$
+\begin{array}{l} L _ {d k d} = \alpha \cdot \left(- T _ {t} \log \left(S _ {t}\right) - \left(1 - T _ {t}\right) \log \left(1 - S _ {t}\right)\right) (16) \\ - \beta \cdot \left(\sum_ {i \neq t} ^ {C} \hat {T} _ {i} \log \left(\hat {S} _ {i}\right)\right) (17) \\ \end{array}
+$$
+
+While we decompose KD loss into the target loss (like the original CE loss) and non-target loss in CE form:
+
+$$
+L _ {k d} = - T _ {t} \log \left(S _ {t}\right) - \sum_ {i \neq t} ^ {C} T _ {i} \log \left(S _ {i}\right) \tag {18}
+$$
+
+Then we find the sum of student's and teacher's non-target logits is different, making them hard to be the same. So we normalize them to equalize the sum as follows:
+
+$$
+L _ {n k d} = - T _ {t} \log \left(S _ {t}\right) - \gamma \cdot \sum_ {i \neq t} ^ {C} \mathcal {N} \left(T _ {i}\right) \log \left(\mathcal {N} \left(S _ {i}\right)\right) \tag {19}
+$$
+
+With this slight modification, we present our NKD loss and achieve better performance than DKD, as shown in Tab. 1.
+
+Table 5. Effects of our normalized non-target loss on ImageNet dataset. The teacher is ResNet34 and the student is ResNet18.  
+
+<table><tr><td>Loss</td><td colspan="4">Top-1 Accuracy (%)</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Non-target</td><td>X</td><td>X</td><td>✓</td><td>✓</td></tr><tr><td>MobileNet</td><td>69.21</td><td>70.18</td><td>69.43</td><td>70.38</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>76.87</td><td>77.25</td><td>77.30</td></tr></table>
+
+Table 6. Ablation study of USKD's target and non-target loss. The experiments are conducted on the ImageNet dataset. All the results are the Top-1 accuracy  $(\%)$ .  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">ImageNet Top-1 Acc. (%)</td><td colspan="2">COCO</td></tr><tr><td>APbox</td><td>ARbox</td></tr><tr><td>Baseline (Res50)</td><td>76.55</td><td>38.0</td><td>52.4</td></tr><tr><td>USKD (ours)</td><td>77.07</td><td>38.3</td><td>52.9</td></tr></table>
+
+Table 7. The detection results on the COCO dataset. We pre-train the backbone with USKD and use Mask-RCNN as the detector.
+
+# 5.3. Effects of USKD's Target and Non-target Loss
+
+We propose a novel self-KD method called USKD, which utilizes customized soft labels that incorporate information from both target and non-target classes. To evaluate the impact of each type of information, we conduct experiments on MobileNet and RegNetX-1.6GF in Tab. 6. The experimental findings demonstrate that both types of information are beneficial and important for the two models, and their combination leads to further improvements in performance. For instance, by combining the target and non-target class distillation together, MobileNet achieves  $70.38\%$ , which surpasses the accuracy achieved by using distillation on either the target or non-target class alone.
+
+# 5.4. Models with USKD for Downstream Task
+
+Our self-KD method yields remarkable accuracy gains for the classification task on CIFAR-100 and ImageNet datasets. To further evaluate its effectiveness and generalization, we also apply the pre-trained model to object detection using Mask R-CNN [8] as the detector and evaluate the model's performance with  $AP^{box}$  and  $AR^{box}$  on the COCO val2017 dataset [19]. We conduct the detection experiments for 12 epochs using MMDetection [2]. As shown in Tab. 7, the ResNet-50 backbone trained with our method improves the detector's performance by  $0.3\mathrm{mAP}$  and  $0.5\mathrm{mAR}$ . The results demonstrate that our self-KD method not only improves the model's classification performance but also generalizes well to downstream tasks like object detection.
+
+# 5.5.Customized Soft Labels for USKD
+
+Our self-KD method, USKD, leverages customized soft labels for every image during training. Fig.3 shows several samples' soft labels, including the value for the target class and the top-3 non-target classes. For the target class, the value may be larger than 1 due to the smoothing method
+
+![](images/a87445d5ff7b8fa1bcbe920e503dcc54abf02d69fd1f2e460c200904dec77a45.jpg)  
+Figure 3. The visualization of the target and top-3 non-target class values of our customized soft labels. The target class value is obtained by squaring and smoothing. The non-target class value is obtained by Zipf's law.
+
+![](images/f48f51c07727e1964f15a46d9f6fe997278466ff3b728f01f353aa3c8c4b06fa.jpg)
+
+![](images/b245c77efa68a5a162dff7f021bd61fba048168663c0fff34078c77f988f0954.jpg)
+
+described in Eq. 6. For the non-target classes, USKD distributes larger values to the categories that are similar to the target class. For instance, the labels for the second image not only include the target 'linnet,' but also assign higher values to similar non-target classes like 'brambling', 'goldfinch', and 'bulbul'. This approach ensures that each image receives an appropriate customized soft label, which enables successful self-KD. The visualization also demonstrates how our USKD helps the model to perform better.
+
+# 5.6. Different Smooth Ways for Soft Target Label
+
+Our USKD utilizes customized soft labels that include target and non-target classes for all the images during training. To create the soft labels, we replace the weights of NKD's target loss with a smoothed version of the student's target output  $S_{t}$ , as shown in Eq. 6. In this subsection, we investigate the impact of different methods for smoothing the student's target output  $S_{t}$  on the performance of the model. We conduct experiments on ResNet18 trained on ImageNet to compare these methods, as shown in Tab. 8. The experiments show that all the methods significantly improve the student model. Notably, using  $S_{t} + V_{t} - mean(S_{t})$  as the weights for smoothing the student's target output achieves  $0.86\%$  improvement, even outperforming using the teacher ResNet18's output as the soft target label. Based on this observation, we choose this method for smoothing the student's target output and use it as our soft target label.
+
+# 5.7. Different Ranks for Soft Non-target Labels
+
+In Eq. 10, we combine the normalized weak and final logit to obtain the soft non-target labels' rank. In this subsection, we explore the effects of different ways for the rank, as shown in Tab. 9. Specifically, we compare the performance when using the weak logit's rank alone, the final logit's rank alone, or a combination of both but without normalization. Interestingly, our results show that all these methods help improve the model's accuracy, with the combination of the two normalized logits achieving the best performance. It is also noteworthy that even directly using
+
+<table><tr><td>Smooth Ways</td><td>Teacher</td><td>Top-1 Acc. (%)</td></tr><tr><td>Baseline</td><td>-</td><td>69.90</td></tr><tr><td>St+Vt-mean(St)</td><td>X</td><td>70.76</td></tr><tr><td>softmax(St)*sum(Vt)</td><td>X</td><td>70.57</td></tr><tr><td>√St-min(St)</td><td>X</td><td>70.57</td></tr><tr><td>St/max(St)</td><td>X</td><td>70.53</td></tr><tr><td>St/mean(St)</td><td>X</td><td>70.50</td></tr><tr><td>Trained ResNet-18</td><td>✓</td><td>70.75</td></tr></table>
+
+Table 8. Results of training ResNet18 with target loss on ImageNet dataset. All the operations are calculated with different samples in a training batch. Because the trained Res-18's output is  $S_{t}$ , we drop the square operation for different smoothing ways.  
+
+<table><tr><td>Model</td><td>ResNet-18</td><td>RegNetX-1.6GF</td></tr><tr><td>Baseline</td><td>69.90</td><td>76.84</td></tr><tr><td>Weak Logit</td><td>70.65</td><td>77.28</td></tr><tr><td>Final Logit</td><td>70.72</td><td>77.15</td></tr><tr><td>Combination</td><td>70.71</td><td>77.25</td></tr><tr><td>Normalization</td><td>70.79</td><td>77.30</td></tr></table>
+
+Table 9. Results of different ranks for soft non-target labels. Normalization and Combination mean combining weak and final logit with normalization and without normalization, respectively.
+
+the final logit to obtain the rank can satisfy accuracy gains. These findings provide insights into the effectiveness of various approaches for the rank of the non-target labels.
+
+# 6. Conclusion
+
+In this paper, we decompose KD loss into the target loss like original CE loss and non-target loss in a CE form. We then normalize the non-target logits to enhance the student's learning from the teacher. With this normalization, we introduce Normalized KD (NKD), which helps students to achieve state-of-the-art performance. Building on our NKD loss formulation, we further propose a new self-KD method, USKD, that works for both CNN-like and ViT-like models. USKD uses customized soft labels that include target and non-target classes for self-KD. We first square and smooth the student's target output logit as the soft target label. For the soft non-target labels, we use weak supervision to obtain the rank and utilize Zipf's law to generate the labels. In this way, USKD needs negligible extra time and resources than training the model directly. Extensive experiments on various models with different datasets demonstrate that both our NKD and USKD are simple and efficient.
+
+Acknowledgement. This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), the SZSTC project Grant (JCYJ20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004).
+
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+                                    "content": "From Knowledge Distillation to Self-Knowledge Distillation: A Unified Approach with Normalized Loss and Customized Soft Labels"
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+                                    "content": "Tsinghua Shenzhen International Graduate School "
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+                                    "content": "International Digital Economy Academy (IDEA) Institute of Automation, Chinese Academy of Sciences"
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+                                    "content": "{yangzd21,ztk21}@mails.tsinghua.edu.cn axel.li@outlook.com"
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+                                    "content": "Knowledge Distillation (KD) uses the teacher's logits as soft labels to guide the student, while self-KD does not need a real teacher to require the soft labels. This work unifies the formulations of the two tasks by decomposing and reorganizing the generic KD loss into a Normalized KD (NKD) loss and customized soft labels for both target class (image's category) and non-target classes named Universal Self-KD (USKD). We decompose the KD loss and find the non-target loss from it forces the student's non-target logits to match the teacher's, but the sum of the two nontarget logits is different, preventing them from being identical. NKD normalizes the non-target logits to equalize their sum. It can be generally used for KD and self-KD to better use the soft labels for distillation. USKD generates customized soft labels for both target and non-target classes without a teacher. It smoothes the target logit of the student as the soft target label and uses the rank of the intermediate feature to generate the soft non-target labels with Zipf's law. For KD with teachers, NKD achieves state-of-the-art performance on CIFAR-100 and ImageNet, boosting the ImageNet Top-1 accuracy of Res-18 from "
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+                                    "content": "69.90\\%"
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+                                    "type": "text",
+                                    "content": " to "
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+                                    "content": " with a Res-34 teacher. For self-KD without teachers, USKD is the first method that can be effectively applied to both CNN and ViT models with negligible additional time and memory cost, resulting in new state-of-the-art results, such as "
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+                                    "type": "text",
+                                    "content": " accuracy gains on ImageNet for MobileNet and DeiT-Tiny, respectively. Code is available at https://github.com/yzd-v/cls_KD."
+                                }
+                            ]
+                        }
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+                                    "content": "1. Introduction"
+                                }
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+                                    "type": "text",
+                                    "content": "Deep convolutional neural networks (CNNs) have significantly advanced the performance in many tasks [8, 9,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                    "type": "image",
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+                                            "type": "text",
+                                            "content": "Figure 1. Illustration of the proposed NKD and USKD for distillation loss calculations. NKD normalizes the non-target logits, using the soft labels more effectively, and achieves better performance. Meanwhile, USKD sets customized soft labels for both target and non-target classes, and can be applied to both CNNs and ViTs."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "27, 29]. In general, a larger model performing better needs more computing resources. On the other hand, smaller models have lower computation complexity but are less competitive than larger models. To bridge this gap and improve the performance of smaller models, knowledge distillation (KD) has been proposed [11]. The core idea of KD is to employ the teacher's prediction logits as soft labels to guide the student. Self-knowledge distillation (self-KD) [33, 47] is inspired by the knowledge distillation method, but it does not require an actual teacher. Instead, it designs soft labels through auxiliary branches or special distribution. The similarity between KD and self-KD is that they utilize soft labels for distillation loss, while the key difference is in how they obtain the soft labels. This paper aims to 1) improve the utilization of soft labels for distillation loss and 2) propose a general and effective method to obtain customized soft labels for self-KD. The targets make us obtain the soft labels with a teacher and use our modified distillation loss for better performance. Alternatively, when we lack a teacher, we can use the proposed self-KD method"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "type": "text",
+                                    "content": "*This work was done when Zhendong was an intern at IDEA."
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+                                    "content": "to obtain the soft labels and then calculate the loss."
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+                                    "content": "The original cross-entropy (CE) loss for classification calculates the loss on the target class (the image's category). While the soft labels from the teacher include target and non-target class, thus the KD loss also includes both target and non-target loss. The decoupled method has been proven effective for KD in DKD [49]. Unlike DKD's method of adjusting hyper-parameters on target and non-target loss, we present a simple yet effective way to decompose the KD loss. We decompose the KD loss into a combination of the target loss (like the original CE loss) and the non-target loss in CE form. The non-target loss transforms the internal distribution of the student's non-target logits to match the teacher's distribution. However, we find that the sum of the student's and teacher's non-target logits is changing and different, which hinders the alignment of their distributions. To address this issue, we normalize the non-target logits to equalize their sum, transferring teacher's non-target knowledge. With this slight modification, we introduce our Normalized Knowledge Distillation (NKD) loss, as depicted in Fig.1, significantly enhancing KD's performance."
+                                }
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+                                    "content": "Our proposed NKD utilizes the teacher's target logit and normalized non-target logits to guide the student, resulting in state-of-the-art performance. This demonstrates the effectiveness of NKD loss formulation. Also, it can be generally used for self-KD to calculate the distillation loss, but how to generate the soft labels without a real teacher generally and efficiently is also important."
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+                                    "content": "Various self-KD methods have explored using manually designed soft labels to enhance students with less time than KD. These methods [14, 38, 44, 47] typically obtain the labels from auxiliary branches or contrastive learning, as depicted in Fig. 2 (a), (b), and (c). However, despite requiring less time than KD, they still involve significant overhead compared to training the model directly. Recently, state-of-the-art Zipf's LS [17], as shown in Fig. 2 (d), introduced soft non-target labels based on a special distribution that can significantly reduce resource and time requirements. It classifies the student's feature in the spatial dimension and determines the rank of the non-target class using Zipf's law [25]. However, it requires the pixel-level features before average pooling, making it unsuitable for ViT-like models [6] with patch-wise tokenization."
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+                                    "content": "To address the limitations of existing methods, we propose a general and effective way to obtain soft labels. We design customized soft labels available for both CNN and ViT models. Following the NKD loss formulation, our customized soft labels comprise soft target label and soft nontarget labels for corresponding loss. For the soft target label, we replace the teacher's target logit with the smoother label value obtained from the student's prediction. Since the student's predictions vary drastically during training, especially in the beginning, we smooth the student's tar"
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+                                    "content": "get output within each training batch to stabilize the label values. For the soft non-target labels, we need their rank and distribution. First, for the rank, we get it from the intermediate feature, making our method available for both CNN and ViT models. We take weak supervision on the intermediate feature to get weak logit. Then, we normalize and combine it with the final logit and sort for the rank, as shown in Fig. 2 (f). The soft non-target labels' distribution follows Zipf's Law [25]. With the soft target and nontarget labels, we set our customized soft labels and propose Universal Self-Knowledge Distillation (USKD) as shown in Fig. 1. Besides, USKD only needs an extra linear layer for weak supervision. So it just takes a few more computing resources and time than training the model directly. USKD is a simple and effective method that achieves state-of-the-art performance on both CNN and ViT models."
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+                                    "content": "As described above, we normalize KD's non-target logits and propose NKD, using the soft labels better and improving KD's performance significantly. For the generation of soft labels without a real teacher, we set soft target and nontarget labels, proposing USKD for self-KD. In a nutshell, the contributions of this paper are:"
+                                }
+                            ]
+                        }
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+                                            "content": "- We normalize the non-target logits in the classical KD, making it better to optimize the cross-entropy loss. With this minor change, we propose Normalized KD (NKD) loss, using teacher's soft labels better and improving KD's performance significantly."
+                                        }
+                                    ]
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+                        {
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+                                            "content": "- We propose a novel way to set customized soft labels without a real teacher, including target and non-target classes for self-KD. We utilize the weak logit to obtain soft non-target labels. Besides, we enlarge the difference between student's target logit for different images and soften them for soft target labels."
+                                        }
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+                                            "content": "- We propose a simple and effective self-KD method USKD with our customized soft labels, which applies to both CNN and ViT models. Importantly, USKD requires only almost negligible additional time and resources compared to training the model directly."
+                                        }
+                                    ]
+                                }
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+                                            "content": "- We conduct extensive experiments on CIFAR-100 and ImageNet to verify the effectiveness of NKD and USKD, achieving state-of-the-art performance. Additionally, we demonstrate the efficacy of models trained with our self-KD method on COCO for detection."
+                                        }
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+                                    "content": "2. Related work"
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+                                    "content": "Knowledge distillation is a method to improve the model while keeping the network unchanged. It was first proposed by Hinton et al. [11], where the student is supervised by the hard and soft labels from the teacher's output. Many"
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+                                            "content": "Modeling Distribution of Non-target Only"
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+                                    "content": "following works focus on better using soft labels to transfer more knowledge. WSLD [50] analyzes soft labels and distributes different weights for them from a perspective of bias-variance trade-off. SRRL [39] forces the output logits of the teacher's and student's features after the teacher's linear layer to be the same. DKD [49] decouples the logit and distributes different weights for the target and non-target classes. DIST [13] uses the Pearson correlation coefficient to replace the KL divergence and transfers the inter-relation and intra-relation together."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Besides distillation on logits, some works [1, 31, 40, 42] aim at transferring knowledge from intermediate features. FitNet [28] distill the semantic information from the intermediate feature directly. AT [45] transfers the attention of feature maps to the students. OFD [10] designs the margin ReLU and modifies the measurement for the distance between students and teachers. RKD [23] extracts the relation from the feature map. CRD [35] applies contrastive learning to distillation successfully. KR [3] transfers knowledge from multi-level features for distillation. TaT [18] helps the student to learn the teacher's every spatial component. MGD [41] masks the student's feature and forces it to generate the teacher's feature."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                                    "type": "text",
+                                    "content": "2.2. Self-Knowledge Distillation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Self-Knowledge Distillation has been proposed as an alternative approach to Knowledge Distillation that does not rely on an external teacher model. Self-KD aims to utilize the information within the student model to guide its learning process. Several self-KD methods have been proposed in recent years. DKS [33] introduces auxiliary supervision branches and pairwise knowledge alignments, while BYOT [47] adds blocks and layers to every stage and uses shallow and deep features as student and teacher, respectively. KDCL [7] trains two models for online knowledge"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "distillation, while FRSKD [14] adds a new branch supervised by the original feature and uses the logit of the new branch for self-KD. DDGSD [37] transfers knowledge between different distorted versions of the same training data. OLS [46] sets a matrix that is made up of the soft label for every class, while MixSKD [38] proposes incorporating self-knowledge distillation with image mixture and aggregates multi-stage feature to produce soft labels. Tf-FD [16] includes intra-layer and inter-layer distillation, reusing the channel-wise and layer-wise features to provide knowledge without an additional model. However, these methods require auxiliary architecture, adapt layers for alignment, or data augmentation, consuming much more time and computing resources than training the model directly."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "In contrast, some self-KD methods require little extra or even no more time than training the model directly. For example, Label Smoothing [34] sets the labels manually by distributing the same values to all non-target classes. TfKD [43] revisits KD via label smoothing, using a high temperature to generate the manual logit for distillation. Zipf's LS [17] utilizes the student's linear layer to obtain several logits for each pixel of the student's last feature map. The method uses these logits to vote for the non-target class's rank with Zipf distribution [25]. These methods set soft labels to achieve self-knowledge distillation without contrastive learning, data augmentation, or auxiliary branches, saving much training time and computing resources."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
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+                                    "type": "text",
+                                    "content": "3.1. Normalized KD for Better Using Soft Labels"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
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+                                    "type": "text",
+                                    "content": "Using "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "t"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denote the target class, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "C"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denote the number of classes, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "V_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denote the label value for each class "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "i"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "S_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denote the student's output probability. The original loss"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "for image classification can be formulated as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "L _ {o r i} = - \\sum_ {i} ^ {C} V _ {i} \\log \\left(S _ {i}\\right) = - V _ {t} \\log \\left(S _ {t}\\right) = - \\log \\left(S _ {t}\\right). \\tag {1}",
+                                    "image_path": "19e65d9fe4ec427fd819aa22aa15293ab872e8501e40a3f1040b84fb7bda6740.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "Using "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        133,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denote the teacher's soft labels. The classical KD utilizes them for distillation loss as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} L _ {k d} = - \\sum_ {i} ^ {C} T _ {i} \\log \\left(S _ {i}\\right) (2) \\\\ = - T _ {t} \\log \\left(S _ {t}\\right) - \\sum_ {i \\neq t} ^ {C} T _ {i} \\log \\left(S _ {i}\\right). (3) \\\\ \\end{array}",
+                                    "image_path": "7f23e7cf6d62d97b4326a9d118b725dc49e6a694047e137ec93f8d4d718926d5.jpg"
+                                }
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+                    ],
+                    "index": 3
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "As "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "L_{kd}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " shows, the first loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-T_t\\log(S_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is about the target class like the original "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "L_{ori}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". While for the second non-target loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-\\sum_{i \\neq t}^{C} T_i\\log(S_i)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", it has the same form as CE loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "-\\sum p(x)\\log(q(x))"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "text",
+                                    "content": ". The CE loss aims at making "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "q(x)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                    ],
+                                    "type": "text",
+                                    "content": " be the same as "
+                                },
+                                {
+                                    "bbox": [
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+                                        240,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(x)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". However, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sum_{i \\neq t}^{C} T_i = 1 - T_t"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sum_{i \\neq t}^{C} S_i = 1 - S_t"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "text",
+                                    "content": ". Since the trainable "
+                                },
+                                {
+                                    "bbox": [
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+                                        240,
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+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is unlikely to exactly match the fixed "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                        402
+                                    ],
+                                    "type": "text",
+                                    "content": " during training, the sum of the two non-target logits is always different, preventing the two distributions from being the same. Thus we normalize "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_i"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "text",
+                                    "content": " to force the sum of the two distributions to be the same. With "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
+                                        289,
+                                        402
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        240,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denoting the normalized operation, we modify the KD loss and propose our Normalized Knowledge Distillation (NKD) loss as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                    ],
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {n k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\gamma \\cdot \\lambda^ {2} \\cdot \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(T _ {i} ^ {\\lambda}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i} ^ {\\lambda}\\right)\\right), \\tag {4}",
+                                    "image_path": "a79ad6669d75c0c1c0028df13e564665d2cd584839754f3da25e61caba3380ee.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        464,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a hyper-parameter to balance the loss and "
+                                },
+                                {
+                                    "bbox": [
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+                                        464,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        464,
+                                        287,
+                                        501
+                                    ],
+                                    "type": "text",
+                                    "content": " is the temperature for KD [11]. Finally, combining the original loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        464,
+                                        287,
+                                        501
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{ori}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        464,
+                                        287,
+                                        501
+                                    ],
+                                    "type": "text",
+                                    "content": ", and NKD loss "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        464,
+                                        287,
+                                        501
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{nkd}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        464,
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+                                        501
+                                    ],
+                                    "type": "text",
+                                    "content": ", we train the students with:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {a l l} = L _ {o r i} + L _ {n k d}. \\tag {5}",
+                                    "image_path": "4377e6f21cd621e09b0ff199a35939f068b61f0211e8a4d5a0057e780755cae0.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.2.Customized Soft Labels for Self-KD"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We utilize NKD for better use of the soft labels. Following our NKD loss in Eq. 4, we propose a general and effective self-KD method, which sets soft labels on target and non-target classes without teachers."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.2.1 Soft Target Label"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    ],
+                                    "type": "text",
+                                    "content": "First, for the soft target label, the weight "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " in Eq. 4 is obtained from the teacher's target output probability for the input image. We wonder if the soft target can be provided by adjusting the student's target output "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The differences between "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " mainly focus on two parts. The first is that "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        629,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{t}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is fixed, and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " varies gradually during training. The second part is that the difference between different samples'"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is much smaller than "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
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+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": " at the beginning of training. To overcome the problem, we first square "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": " to enlarge the difference between different samples' "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we propose a way to adjust "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": ", making it smoother to fit the training set without teachers. This strategy can be applied directly to different models, including CNN-liked and ViT-liked models. In this way, we get the soft target label "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        72,
+                                        547,
+                                        168
+                                    ],
+                                    "type": "text",
+                                    "content": ", which is detached and zero-grad in training for self-KD:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        367,
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        367,
+                                        175,
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+                                        189
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "P _ {t} = S _ {t} ^ {2} + V _ {t} - \\operatorname {m e a n} \\left(S _ {t} ^ {2}\\right). \\tag {6}",
+                                    "image_path": "455bd3403b69662b71d1a24e80c1cc2faee9fc54da7cc283e8d1034b37a33e8f.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                        209
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
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+                                        209
+                                    ],
+                                    "type": "text",
+                                    "content": "With the "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        196,
+                                        515,
+                                        209
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
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+                                        515,
+                                        209
+                                    ],
+                                    "type": "text",
+                                    "content": ", we follow our NKD for the target loss:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {\\text {t a r g e t}} = - P _ {t} \\log \\left(S _ {t}\\right), \\tag {7}",
+                                    "image_path": "ae3032f73434b0a468a4c995474fc2d9581c8fa835fdaed25b642a2b1e28c669.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        236,
+                                        547,
+                                        284
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        236,
+                                        547,
+                                        284
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the original target label value, e.g. [0.8, 0.2] for a mixed image. And "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        236,
+                                        547,
+                                        284
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "mean(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        236,
+                                        547,
+                                        284
+                                    ],
+                                    "type": "text",
+                                    "content": " is calculated across different samples in a training batch. We discuss the effects of the smoothing ways for "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        236,
+                                        547,
+                                        284
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        236,
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+                                        284
+                                    ],
+                                    "type": "text",
+                                    "content": " in Sec. 5.6."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "type": "text",
+                                    "content": "3.2.2 Soft Non-target Labels"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The knowledge from the teacher's soft non-target labels includes its rank and distribution. We also need them to set the soft non-target labels for self-KD. To get the rank, we first obtain a new weak logit by setting weak supervision on the intermediate feature. Using "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        316,
+                                        546,
+                                        424
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        316,
+                                        546,
+                                        424
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the feature of stage 2 of the CNN-liked model or the mid layer's classification token of the ViT-liked model, "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        316,
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+                                        424
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "GAP"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        316,
+                                        546,
+                                        424
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the global average pooling, "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        316,
+                                        546,
+                                        424
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "FC"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        316,
+                                        546,
+                                        424
+                                    ],
+                                    "type": "text",
+                                    "content": " denote a new linear layer, the weak logit of the CNN-liked model can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "W _ {i} = \\operatorname {s o f t m a x} (F C (G A P (\\mathcal {F}))), \\tag {8}",
+                                    "image_path": "d9d5cb3b98035f1baf5a002c4a2dc2f78e4c7ad4826beb2f387ccf894e111a10.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "As for the ViT-liked model, the weak logit is as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "W _ {i} = \\operatorname {s o f t m a x} (F C (\\mathcal {F})).",
+                                    "image_path": "fc5781f60366b884dfad7f74a9ef3dbea6321569e129db981feb4f87ecd6e4f1.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We aim to obtain another smoother non-target logit different from the original final logit. So we utilize a smooth label and take weak supervision to get the weak logit. Using "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " denote the label, which is the original label processed with label smoothing, the loss for obtaining the weak logit is as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
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+                                    "type": "interline_equation",
+                                    "content": "L _ {\\text {w e a k}} = - \\mu \\cdot \\sum_ {i} ^ {C} V _ {i} \\log \\left(W _ {i}\\right), \\tag {9}",
+                                    "image_path": "d8b89c289588283c9ef472e5dbdc3845f71adf34282768e0f8165c28587dc93f.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mu < 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a hyper-parameter to achieve weak supervision. With the weak logit, we obtain the soft non-target labels' rank by normalizing and combining it with the final logit. This operation balances the two logits' effects for the rank, and the analysis is shown in Sec. 5.7."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "R _ {i} = \\frac {W _ {i}}{1 - W _ {t}} + \\frac {S _ {i}}{1 - S _ {t}}. \\tag {10}",
+                                    "image_path": "7a0187eaacf6372ce40741d89c5e61da3a825d00ed7ac85ec57b4115152b563c.jpg"
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+                                    "type": "text",
+                                    "content": "The soft non-target labels' distribution follows Zipf's law [25], which has been applied in Zipf's LS [17]. The formulation can be formulated as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
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+                                    "type": "interline_equation",
+                                    "content": "Z _ {i} = \\frac {i ^ {- 1}}{\\sum_ {i = 1} ^ {C} i ^ {- 1}}. \\tag {11}",
+                                    "image_path": "c342ada37e295698261607e62d2c8923c0196105e12c455345f3e7b99425b101.jpg"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "With the distribution, we sort it with the rank of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "R_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and obtain the soft non-target labels "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        148,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Z_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        148,
+                                        287,
+                                        183
+                                    ],
+                                    "type": "text",
+                                    "content": " for self-KD. Following our NKD loss in Eq. 4, the non-target loss is as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "L _ {n o n} = - \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(Z _ {i}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i}\\right)\\right). \\tag {12}",
+                                    "image_path": "f25d3ae417282f67c580b7dac4c1660a35d1a7e203286286f48ff9ca630965fb.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "3.2.3 Overall for Self-KD"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "With the proposed soft target label and soft non-target labels, we calculate the corresponding loss and propose USKD as shown in Fig. 1. We train all the models with the total loss for self-KD as follows:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "L _ {\\text {a l l}} = L _ {\\text {o r i}} + \\alpha \\cdot L _ {\\text {t a r g e t}} + \\beta \\cdot L _ {\\text {n o n}} + L _ {\\text {w e a k}}, \\tag {13}",
+                                    "image_path": "9c06b550e2bf4f4f681ca3b18c366da24319955dc7bffb5987b6c41911b1295f.jpg"
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        342,
+                                        287,
+                                        377
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{ori}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        342,
+                                        287,
+                                        377
+                                    ],
+                                    "type": "text",
+                                    "content": " is the original loss for the models among all the tasks, "
+                                },
+                                {
+                                    "bbox": [
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+                                        342,
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+                                        377
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        342,
+                                        287,
+                                        377
+                                    ],
+                                    "type": "text",
+                                    "content": " are two hyper-parameters to balance the loss scale. "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        342,
+                                        287,
+                                        377
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{weak}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        342,
+                                        287,
+                                        377
+                                    ],
+                                    "type": "text",
+                                    "content": " is used to generate the weak logit in Eq. 8."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Datasets and Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We conduct the experiments on CIFAR-100 [15] and ImageNet [5], which contain 100 and 1000 categories, respectively. For CIFAR-100, we use 50k images for training and 10k for validation. For ImageNet, we use 1.2 million images for training and 50k images for validation. In this paper, we use accuracy to evaluate all the models."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "For KD with teachers, NKD has two hyper-parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " in Eq. 4. For all the experiments, we adopt "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\gamma = 1.5, \\lambda = 1\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " on ImageNet. While for CIFAR-100, we follow the training setting from DKD [49] for a fair comparison. And USKD has two hyper-parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " to balance the loss scale in Eq. 13. Another hyper-parameter "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mu"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " is used to achieve the weak supervision in Eq. 9. For all the experiments, we adopt "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\alpha = 1, \\beta = 0.1, \\mu = 0.005\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " on ImageNet and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\alpha = 0.1, \\beta = 0.1, \\mu = 0.1\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        498,
+                                        287,
+                                        664
+                                    ],
+                                    "type": "text",
+                                    "content": " on CIFAR-100. The other training setting for KD and self-KD is the same as training the students without distillation. We use 8 GPUs to conduct the experiments with MMClassition [4] based on Pytorch [24]. More details and experimental results about the hyper-parameters are shown in the supplement."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. Normalized KD with Teachers"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "When we get the soft labels from a real teacher, we can use NKD loss for better performance. To prove this, we"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "first conduct experiments with various teacher-student distillation pairs on CIFAR-100, shown in Tab. 1. In this setting, we evaluate our method on several models with different architectures, including VGGNet [32], ResNet [9], ShuffleNet [48] and MobileNetV2 [30]. We compare our method with KD [11] and several other state-of-the-art distillation methods. As the results show, our method brings the students remarkable accuracy gains over other methods. Our method achieves the best performance among logit-based distillation methods and even surpasses the feature-based distillation methods in some settings."
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+                                    "content": "To further demonstrate the effectiveness and robustness of our NKD, we test it on a more challenging dataset, ImageNet. We set two popular teacher-student pairs, which include homogeneous and heterogeneous teacher-student structures for distillation. The homogeneous distillation is ResNet34-ResNet18, and the heterogeneous distillation is ResNet50-MobileNet. The results of different KD methods on ImageNet are shown in Tab. 1. As the results show, our method outperforms all the previous methods. It brings consistent and significant improvements to the students for both distillation settings. The student ResNet18 and MobileNet achieve "
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+                                    "type": "text",
+                                    "content": " Top-1 accuracy, getting "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "3.37\\%"
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+                                    "type": "text",
+                                    "content": " accuracy gains with the knowledge transferred from the teacher's logits, respectively."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "content": "As described above, our NKD enhances KD's performance significantly with a slight modification. And in various settings, it also surpasses DKD, a method that improves KD according to a different decoupled way."
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+                                    "content": "4.3. Universal Self-KD without Teachers"
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+                                    "content": "When we lack a teacher, we use the proposed self-KD method USKD to obtain the soft labels and then calculate the loss. To evaluate its effectiveness, we first conduct experiments with ResNets [9] and MobileNet [12] on CIFAR100 and ImageNet datasets. We compare with the other state-of-the-art methods, which also set manual labels and only bring little extra time consumption, including label smoothing [34], Tf-KD [43] and Zipf's LS [17]. As shown in Tab. 2, our method surpasses the previous related self-knowledge distillation methods on various settings and brings the model remarkable gains. For example, it brings MobileNet and ResNet-18 "
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+                                    "content": " Top-1 accuracy gains on ImageNet."
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+                                    "content": "Furthermore, we also test our USKD on more models, which include lighter models MobileNetV2 [30], ShuffleNetV2 [21] and a deeper ResNet. The results are shown in Tab. 3. For both the lightweight models, including MobileNetV2 and ShuffleNetV2, and the stronger model ResNet-101, our method also achieves considerable improvements. Besides, we also compare the time consumption to train the model for an epoch in Tab. 3. Compared with the baseline, the extra time we need for self-knowledge"
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+                                            "html": "<table><tr><td>Model</td><td>Teacher Student</td><td>VGGNet13 VGGNet8</td><td>ResNet32x4 ResNet8x4</td><td>VGGNet13 MobileNetV2</td><td>ResNet50 MobileNetV2</td><td>ResNet34 ResNet18</td><td>ResNet50 MobileNet</td></tr><tr><td rowspan=\"2\">Accuracy</td><td>Teacher</td><td>74.64</td><td>79.42</td><td>74.64</td><td>79.34</td><td>73.62</td><td>76.55</td></tr><tr><td>Student</td><td>70.36</td><td>72.50</td><td>64.60</td><td>64.60</td><td>69.90</td><td>69.21</td></tr><tr><td rowspan=\"4\">Feature</td><td>RKD [23]</td><td>71.48</td><td>71.90</td><td>64.52</td><td>64.43</td><td>71.34</td><td>71.32</td></tr><tr><td>CRD [35]</td><td>73.94</td><td>75.51</td><td>69.73</td><td>69.11</td><td>71.17</td><td>71.40</td></tr><tr><td>OFD [10]</td><td>73.95</td><td>74.95</td><td>69.48</td><td>69.04</td><td>71.08</td><td>71.25</td></tr><tr><td>KR [3]</td><td>74.84</td><td>75.63</td><td>70.37</td><td>69.89</td><td>71.61</td><td>72.56</td></tr><tr><td rowspan=\"4\">Logit</td><td>KD [11]</td><td>72.98</td><td>73.33</td><td>67.37</td><td>67.35</td><td>71.03</td><td>70.68</td></tr><tr><td>WSLD [50]</td><td>74.36</td><td>76.05</td><td>69.02</td><td>70.15</td><td>71.73</td><td>72.02</td></tr><tr><td>DKD [49]</td><td>74.68</td><td>76.32</td><td>69.71</td><td>70.35</td><td>71.70</td><td>72.05</td></tr><tr><td>NKD (ours)</td><td>74.86</td><td>76.35</td><td>70.22</td><td>70.67</td><td>71.96</td><td>72.58</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. Results of different knowledge distillation methods on CIFAR-100 (the left four columns) and ImageNet (the right two columns) dataset. The data that is underlined denotes the second-best result among all the results. The metric is the Top-1 accuracy (\\%)."
+                                        }
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+                                            "html": "<table><tr><td>Dataset</td><td>CIFAR100</td><td colspan=\"3\">ImageNet</td></tr><tr><td>Model</td><td>ResNet18</td><td>ResNet18</td><td>ResNet50</td><td>MobileNet</td></tr><tr><td>Baseline</td><td>78.58</td><td>69.90</td><td>76.55</td><td>69.21</td></tr><tr><td>LS [34]</td><td>79.42</td><td>69.92</td><td>76.64</td><td>68.98</td></tr><tr><td>Tf-KD [43]</td><td>79.53</td><td>70.14</td><td>76.59</td><td>69.20</td></tr><tr><td>Zipf&#x27;s LS [17]</td><td>79.63</td><td>70.30</td><td>76.96</td><td>69.59</td></tr><tr><td>USKD (ours)</td><td>79.90</td><td>70.79</td><td>77.07</td><td>70.38</td></tr></table>",
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+                                            "content": "Table 2. The comparative results of different self-knowledge distillation methods on CIFAR100 and ImageNet dataset. We report the models' performance with Top-1 accuracy "
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+                                            "html": "<table><tr><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>77.30 (+0.46)</td></tr><tr><td>DeiT-Tiny</td><td>74.42</td><td>74.97 (+0.55)</td></tr><tr><td>DeiT-Small</td><td>80.55</td><td>80.77 (+0.22)</td></tr><tr><td>Swin-Tiny</td><td>81.18</td><td>81.49 (+0.31)</td></tr></table>",
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+                                    "content": "distillation is very limited. Specifically, the time of training MobileNet-V2 with our proposed USKD for an epoch is 10.18 minutes, which is just 0.01 minutes higher than training the model directly. Our method brings considerable improvements to various models with negligible extra time consumption."
+                                }
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+                                    "content": "4.4. Universal Self-KD for More Models"
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+                                    "type": "text",
+                                    "content": "The previous self-KD methods are specially designed for CNN-liked models. However, some models like ViT [6] translate the image into different tokens and have a completely different architecture. Those self-KD methods fail to benefit ViT-liked models. For ViT-liked models, USKD can also set customized soft labels and bring remarkable improvements. As described in Eq. 8, we use an extra"
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+                                            "type": "text",
+                                            "content": "Table 4. Results of training more models, including ViT-liked models with our proposed method on ImageNet dataset. All the results are reported with Top-1 accuracy "
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+                                            "html": "<table><tr><td></td><td>Model</td><td>Baseline</td><td>USKD (ours)</td></tr><tr><td rowspan=\"3\">Accuracy (%)</td><td>ResNet-101</td><td>77.97</td><td>78.54 (+0.57)</td></tr><tr><td>MobileNet-V2</td><td>71.86</td><td>72.41 (+0.55)</td></tr><tr><td>ShuffleNet-V2</td><td>69.55</td><td>70.30 (+0.75)</td></tr><tr><td rowspan=\"3\">Time (min)</td><td>ResNet-101</td><td>13.78</td><td>13.95</td></tr><tr><td>MobileNet-V2</td><td>10.17</td><td>10.18</td></tr><tr><td>ShuffleNet-V2</td><td>8.63</td><td>8.68</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 3. The results of the models' performance are Top-1 accuracy "
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+                                    "content": " on ImageNet dataset. The time data are reported with minutes (min) for a training epoch."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "linear layer connected to ViT's middle layer for classification and obtain the weak logit. The rest operations are the same as CNN-liked models. To show the generalization of USKD, we apply it to more models, including RegNet [26], DeiT [36], and Swin-Transformer [20], which can be seen in Tab. 4. All the models can achieve remarkable Top-1 accuracy gains. Besides, our method even can bring "
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+                                    "type": "text",
+                                    "content": " gains for DeiT-Tiny. And it also brings "
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+                                    "type": "text",
+                                    "content": " Top-1 accuracy gains for the latest state-of-the-art model SwinTransformer. The results of more models show our method is both effective and general."
+                                }
+                            ]
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+                                    "content": "5. Analysis"
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+                                    "content": "5.1. Effects of Normalizing the Non-target Logits"
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+                                    "content": "In this paper, we proposed normalizing the non-target logits in the original KD to help the student perform better. In this subsection, we conduct experiments to demonstrate the effectiveness of our modification. As shown in Tab. 5, using the target loss alone leads to a "
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+                                    "type": "text",
+                                    "content": " increase in accuracy. Combining the knowledge from both target and nontarget classes allows us to better use the teacher's knowledge, resulting in a significant improvement of "
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+                                    "type": "text",
+                                    "content": " Top-1 accuracy for the student. Furthermore, we normalize the non-target logits in the KD loss for distillation and compare"
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+                                            "html": "<table><tr><td>Loss</td><td colspan=\"4\">ResNet34 - ResNet18</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>KD&#x27;s Non-target</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>NKD&#x27;s Non-target</td><td>X</td><td>X</td><td>X</td><td>✓</td></tr><tr><td>Top-1 Acc. (%)</td><td>69.90</td><td>71.06</td><td>71.33</td><td>71.96</td></tr><tr><td>Top-5 Acc. (%)</td><td>89.43</td><td>89.51</td><td>90.25</td><td>90.48</td></tr></table>",
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+                                    "content": "the non-target loss from both KD and NKD. Our non-target loss brings much greater gains than KD's non-target loss, as shown in the comparison. These results demonstrate the effectiveness of our proposed modification in improving KD's performance."
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+                                    "content": "\\begin{array}{l} L _ {k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\left(1 - T _ {t}\\right) \\log \\left(1 - S _ {t}\\right) (14) \\\\ - \\left(1 - T _ {t}\\right) \\sum_ {i \\neq t} ^ {C} \\hat {T} _ {i} \\log \\left(\\hat {S} _ {i}\\right) (15) \\\\ \\end{array}",
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+                                    "content": "\\begin{array}{l} L _ {d k d} = \\alpha \\cdot \\left(- T _ {t} \\log \\left(S _ {t}\\right) - \\left(1 - T _ {t}\\right) \\log \\left(1 - S _ {t}\\right)\\right) (16) \\\\ - \\beta \\cdot \\left(\\sum_ {i \\neq t} ^ {C} \\hat {T} _ {i} \\log \\left(\\hat {S} _ {i}\\right)\\right) (17) \\\\ \\end{array}",
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+                                    "content": "L _ {k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\sum_ {i \\neq t} ^ {C} T _ {i} \\log \\left(S _ {i}\\right) \\tag {18}",
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+                                    "content": "Then we find the sum of student's and teacher's non-target logits is different, making them hard to be the same. So we normalize them to equalize the sum as follows:"
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+                                    "content": "L _ {n k d} = - T _ {t} \\log \\left(S _ {t}\\right) - \\gamma \\cdot \\sum_ {i \\neq t} ^ {C} \\mathcal {N} \\left(T _ {i}\\right) \\log \\left(\\mathcal {N} \\left(S _ {i}\\right)\\right) \\tag {19}",
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+                                    "content": "With this slight modification, we present our NKD loss and achieve better performance than DKD, as shown in Tab. 1."
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+                                            "html": "<table><tr><td>Loss</td><td colspan=\"4\">Top-1 Accuracy (%)</td></tr><tr><td>Target</td><td>X</td><td>✓</td><td>X</td><td>✓</td></tr><tr><td>Non-target</td><td>X</td><td>X</td><td>✓</td><td>✓</td></tr><tr><td>MobileNet</td><td>69.21</td><td>70.18</td><td>69.43</td><td>70.38</td></tr><tr><td>RegNetX-1.6GF</td><td>76.84</td><td>76.87</td><td>77.25</td><td>77.30</td></tr></table>",
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+                                            "content": "Table 6. Ablation study of USKD's target and non-target loss. The experiments are conducted on the ImageNet dataset. All the results are the Top-1 accuracy "
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">ImageNet Top-1 Acc. (%)</td><td colspan=\"2\">COCO</td></tr><tr><td>APbox</td><td>ARbox</td></tr><tr><td>Baseline (Res50)</td><td>76.55</td><td>38.0</td><td>52.4</td></tr><tr><td>USKD (ours)</td><td>77.07</td><td>38.3</td><td>52.9</td></tr></table>",
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+                                    "content": "Table 7. The detection results on the COCO dataset. We pre-train the backbone with USKD and use Mask-RCNN as the detector."
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+                                    "content": "5.3. Effects of USKD's Target and Non-target Loss"
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+                                    "content": "We propose a novel self-KD method called USKD, which utilizes customized soft labels that incorporate information from both target and non-target classes. To evaluate the impact of each type of information, we conduct experiments on MobileNet and RegNetX-1.6GF in Tab. 6. The experimental findings demonstrate that both types of information are beneficial and important for the two models, and their combination leads to further improvements in performance. For instance, by combining the target and non-target class distillation together, MobileNet achieves "
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+                                    "content": ", which surpasses the accuracy achieved by using distillation on either the target or non-target class alone."
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+                                    "content": "5.4. Models with USKD for Downstream Task"
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+                                    "content": "Our self-KD method yields remarkable accuracy gains for the classification task on CIFAR-100 and ImageNet datasets. To further evaluate its effectiveness and generalization, we also apply the pre-trained model to object detection using Mask R-CNN [8] as the detector and evaluate the model's performance with "
+                                },
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+                                    "content": " on the COCO val2017 dataset [19]. We conduct the detection experiments for 12 epochs using MMDetection [2]. As shown in Tab. 7, the ResNet-50 backbone trained with our method improves the detector's performance by "
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+                                    "content": " and "
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+                                    "content": "0.5\\mathrm{mAR}"
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+                                    "type": "text",
+                                    "content": ". The results demonstrate that our self-KD method not only improves the model's classification performance but also generalizes well to downstream tasks like object detection."
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+                                    "content": "5.5.Customized Soft Labels for USKD"
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+                                    "content": "Our self-KD method, USKD, leverages customized soft labels for every image during training. Fig.3 shows several samples' soft labels, including the value for the target class and the top-3 non-target classes. For the target class, the value may be larger than 1 due to the smoothing method"
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+                                    "type": "text",
+                                    "content": "described in Eq. 6. For the non-target classes, USKD distributes larger values to the categories that are similar to the target class. For instance, the labels for the second image not only include the target 'linnet,' but also assign higher values to similar non-target classes like 'brambling', 'goldfinch', and 'bulbul'. This approach ensures that each image receives an appropriate customized soft label, which enables successful self-KD. The visualization also demonstrates how our USKD helps the model to perform better."
+                                }
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+                                    "content": "Our USKD utilizes customized soft labels that include target and non-target classes for all the images during training. To create the soft labels, we replace the weights of NKD's target loss with a smoothed version of the student's target output "
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+                                    "content": ", as shown in Eq. 6. In this subsection, we investigate the impact of different methods for smoothing the student's target output "
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+                                    "type": "text",
+                                    "content": " on the performance of the model. We conduct experiments on ResNet18 trained on ImageNet to compare these methods, as shown in Tab. 8. The experiments show that all the methods significantly improve the student model. Notably, using "
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+                                    "content": " as the weights for smoothing the student's target output achieves "
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+                                    "type": "text",
+                                    "content": " improvement, even outperforming using the teacher ResNet18's output as the soft target label. Based on this observation, we choose this method for smoothing the student's target output and use it as our soft target label."
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+                                    "content": "5.7. Different Ranks for Soft Non-target Labels"
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+                                    "content": "In Eq. 10, we combine the normalized weak and final logit to obtain the soft non-target labels' rank. In this subsection, we explore the effects of different ways for the rank, as shown in Tab. 9. Specifically, we compare the performance when using the weak logit's rank alone, the final logit's rank alone, or a combination of both but without normalization. Interestingly, our results show that all these methods help improve the model's accuracy, with the combination of the two normalized logits achieving the best performance. It is also noteworthy that even directly using"
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+                                            "html": "<table><tr><td>Smooth Ways</td><td>Teacher</td><td>Top-1 Acc. (%)</td></tr><tr><td>Baseline</td><td>-</td><td>69.90</td></tr><tr><td>St+Vt-mean(St)</td><td>X</td><td>70.76</td></tr><tr><td>softmax(St)*sum(Vt)</td><td>X</td><td>70.57</td></tr><tr><td>√St-min(St)</td><td>X</td><td>70.57</td></tr><tr><td>St/max(St)</td><td>X</td><td>70.53</td></tr><tr><td>St/mean(St)</td><td>X</td><td>70.50</td></tr><tr><td>Trained ResNet-18</td><td>✓</td><td>70.75</td></tr></table>",
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+                                            "content": "Table 8. Results of training ResNet18 with target loss on ImageNet dataset. All the operations are calculated with different samples in a training batch. Because the trained Res-18's output is "
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+                                            "type": "text",
+                                            "content": ", we drop the square operation for different smoothing ways."
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+                                            "html": "<table><tr><td>Model</td><td>ResNet-18</td><td>RegNetX-1.6GF</td></tr><tr><td>Baseline</td><td>69.90</td><td>76.84</td></tr><tr><td>Weak Logit</td><td>70.65</td><td>77.28</td></tr><tr><td>Final Logit</td><td>70.72</td><td>77.15</td></tr><tr><td>Combination</td><td>70.71</td><td>77.25</td></tr><tr><td>Normalization</td><td>70.79</td><td>77.30</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 9. Results of different ranks for soft non-target labels. Normalization and Combination mean combining weak and final logit with normalization and without normalization, respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12,
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+                                    "type": "text",
+                                    "content": "the final logit to obtain the rank can satisfy accuracy gains. These findings provide insights into the effectiveness of various approaches for the rank of the non-target labels."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "6. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this paper, we decompose KD loss into the target loss like original CE loss and non-target loss in a CE form. We then normalize the non-target logits to enhance the student's learning from the teacher. With this normalization, we introduce Normalized KD (NKD), which helps students to achieve state-of-the-art performance. Building on our NKD loss formulation, we further propose a new self-KD method, USKD, that works for both CNN-like and ViT-like models. USKD uses customized soft labels that include target and non-target classes for self-KD. We first square and smooth the student's target output logit as the soft target label. For the soft non-target labels, we use weak supervision to obtain the rank and utilize Zipf's law to generate the labels. In this way, USKD needs negligible extra time and resources than training the model directly. Extensive experiments on various models with different datasets demonstrate that both our NKD and USKD are simple and efficient."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Acknowledgement. This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), the SZSTC project Grant (JCYJ20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004)."
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+                                    "content": "References"
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diff --git a/2023/From Sky to the Ground_ A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal/8d7e8632-869f-4c0d-a983-de51fca56097_content_list.json b/2023/From Sky to the Ground_ A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal/8d7e8632-869f-4c0d-a983-de51fca56097_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..3d06c67c78ca7a7176732102a8dda9aa25962584
--- /dev/null
+++ b/2023/From Sky to the Ground_ A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal/8d7e8632-869f-4c0d-a983-de51fca56097_content_list.json	
@@ -0,0 +1,1875 @@
+[
+    {
+        "type": "text",
+        "text": "From Sky to the Ground: A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal",
+        "text_level": 1,
+        "bbox": [
+            117,
+            130,
+            852,
+            174
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yun Guo $^{1,\\dagger}$ , Xueyao Xiao $^{1,\\dagger}$ , Yi Chang $^{1,*}$ , Shumin Deng $^{1}$ , Luxin Yan $^{1}$",
+        "bbox": [
+            238,
+            202,
+            764,
+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, China {guoyun, xiaoxueyao, yichang, shumindeng, yanluxin}@hust.edu.cn https://github.com/yunguo224/LHP-Rain",
+        "bbox": [
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+            220,
+            921,
+            292
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/30aa67fbe8f6346863f56091c9d9defcfa83ae0ca98863e9cef5608cbb45d0f4.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of the proposed paired rainy/clean images dataset. The proposed real rain dataset is to cope with various rain categories, such as rain streaks, veiling effect, occlusion, and ground splashing. We recommend zooming in the figure on PC for better visualization."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            328,
+            890,
+            502
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            573,
+            313,
+            588
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Learning-based image deraining methods have made great progress. However, the lack of large-scale high-quality paired training samples is the main bottleneck to hamper the real image deraining (RID). To address this dilemma and advance RID, we construct a Large-scale High-quality Paired real rain benchmark (LHP-Rain), including 3000 video sequences with 1 million high-resolution (1920*1080) frame pairs. The advantages of the proposed dataset over the existing ones are three-fold: rain with higher-diversity and larger-scale, image with higher-resolution and higher-quality ground-truth. Specifically, the real rains in LHP-Rain not only contain the classical rain streak/veiling/occlusion in the sky, but also the splashing on the ground overlooked by deraining community. Moreover, we propose a novel robust low-rank tensor recovery model to generate the GT with better separating the static background from the dynamic rain. In addition, we design a simple transformer-based single image deraining baseline, which simultaneously utilize",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "the self-attention and cross-layer attention within the image and rain layer with discriminative feature representation. Extensive experiments verify the superiority of the proposed dataset and deraining method over state-of-the-art.",
+        "bbox": [
+            500,
+            574,
+            892,
+            633
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            500,
+            648,
+            632,
+            664
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Single image deraining is to improve the imaging quality by separating rain from image background. In recent years, significant progress has been made in learning-based single image deraining by various sophisticated CNN architectures [14, 36, 53, 10] and powerful Transformer models [35, 44]. Although these state-of-the-art supervised methods have achieved impressive results on simulated datasets, a fact cannot be ignored that those competitive methods perform unsatisfactory on diverse real rainy scenes. The core reason is the domain shift issue between the simplified synthetic rain and complex real rain [50, 32, 41, 51].",
+        "bbox": [
+            496,
+            672,
+            893,
+            839
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To solve this problem, an intuitive idea is to try the best to make rain degradation model as real as possible [11]. The researchers formulate the rain imaging procedure into a comprehensive rain simulation model [9, 48, 12, 24, 18],",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "These authors contributed equally to this work.",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
+        "bbox": [
+            96,
+            887,
+            222,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "12097",
+        "bbox": [
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+            924,
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+            936
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "table",
+        "img_path": "images/3e928c0e1ca81b3a889d9f6fc09612b668841da70f24a88ee2ddc4669e077d38.jpg",
+        "table_caption": [
+            "Table 1: Summary of existing real rain datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets</td><td>Year</td><td>Source</td><td>Sequence</td><td>Frame</td><td>Resolution</td><td>Rain Categories</td><td>Annotation</td><td>Paired</td></tr><tr><td>RID/RIS[19]</td><td>2019</td><td>Cam/Internet</td><td>None</td><td>4.5K</td><td>640*368</td><td>streak, raindrop</td><td>Object detection</td><td>-</td></tr><tr><td>NR-IQA[43]</td><td>2020</td><td>Internet</td><td>None</td><td>0.2K</td><td>1000*680</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>Real3000[25]</td><td>2021</td><td>Internet</td><td>None</td><td>3.0K</td><td>942*654</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>FCRealRain[51]</td><td>2022</td><td>Camera</td><td>None</td><td>4.0K</td><td>4240*2400</td><td>streak, veiling</td><td>Object detection</td><td>-</td></tr><tr><td>SPA-Data[37]</td><td>2019</td><td>Cam/Internet</td><td>170</td><td>29.5K</td><td>256*256</td><td>streak</td><td>None</td><td>✓</td></tr><tr><td>RainDS[32]</td><td>2021</td><td>Cam</td><td>None</td><td>1.0K</td><td>1296*728</td><td>streak, raindrop</td><td>None</td><td>✓</td></tr><tr><td>GT-Rain[1]</td><td>2022</td><td>Internet</td><td>202</td><td>31.5K</td><td>666*339</td><td>streak, veiling</td><td>None</td><td>✓</td></tr><tr><td>RealRain-1K[20]</td><td>2022</td><td>Cam/Internet</td><td>1120</td><td>1.1K</td><td>1512*973</td><td>streak, veiling, occlusion</td><td>None</td><td>✓</td></tr><tr><td>LHP-Rain</td><td>2023</td><td>Camera</td><td>3000</td><td>1.0M</td><td>1920*1080</td><td>streak, veiling, occlusion, splashing</td><td>Object detection/Lane</td><td>✓</td></tr></table>",
+        "bbox": [
+            78,
+            104,
+            898,
+            246
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "in which different visual appearance of rain streaks[9], accumulation veiling [48], haze [12, 18], and occlusion [24] factors are taken into consideration. Unfortunately, these linear simulation models still cannot well accommodate the distribution of realistic rains. For example, in Fig. 1, realistic rain streak is usually not exactly a regular line-pattern streak but possesses irregular non-uniform in terms of the intensity and width. Apart from the rain streaks, the existing rain simulation models could not handle the complicated rain splashing on the ground, which presents as dense point-shape texture, droplets or water waves, ruining visibility of traffic signs, such as lane lines, and also causes enormous negative effects for the high-level vision.",
+        "bbox": [
+            75,
+            258,
+            472,
+            455
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Another research line obtains the 'clean' counterpart from the realistic rainy videos [37, 20], which leverages the motion discrepancy between static image background and dynamic rain. Unfortunately, they simply employ naive filtering strategies such as percentile filter [37] and median filter [20], resulting in unsatisfactory GT with residual rain or over-smoothing phenomenon. Moreover, the number and diversity of the existing real paired rain datasets are still limited. Few datasets have considered the rain splash on the ground, which is commonly observed in the real world but still rarely mentioned in deraining community. And the number of existing video sequences and image frames are not sufficient to cover diverse rains in terms of the varied rain angle, intensity, density, length, width and so on. Last but not least, the existing realistic rainy images are mostly downloaded from the Internet with low-quality: compression, watermark, low-resolution, without annotation and so on. As such, constructing a large-scale high-quality paired realistic rain dataset is highly necessary.",
+        "bbox": [
+            75,
+            458,
+            472,
+            744
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we construct a new large-scale high-quality paired real rain benchmark. The strength of our benchmark is threefold. First, the LHP-Rain contains diverse rain categories with very large-scale, including 3000 video sequences with over 1 million frame pairs. Second, apart from the conventional streak and veiling, our benchmark is capable of removing the representative challenging ground splashing rain in the real world. Third, the LHP-Rain is collected by the smartphone with high-resolution (1920*1080 pixels) and abundant objects under self-driving and surveillance",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "scenes are captured for comprehensive evaluation. Moreover, we propose a novel robust low-rank tensor recovery method (RLRTR) for video deraining, which can generate higher-quality GT with better rain removal from sky to the ground and image structure preserving. We summary the main contributions as follows:",
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+        "list_items": [
+            "- We construct a large-scale high-quality paired real rain benchmark for real single image deraining. To our best knowledge, LHP-Rain is the largest paired real rain dataset (3000 video sequences, 1 million frames) with high image resolution (1920*1080), and the first benchmark to claim and tackle the problem of ground splashing rain removal.",
+            "- We design a novel robust low-rank tensor recovery model for video deraining to better acquire paired GT. We provide detailed analysis to show RLRTR can better differ the rain from static background than previous datasets.",
+            "- We propose a new transformer-based single image de- raining baseline, which exploits both self-attention and cross-layer attention between the rain and image layer for better representation. Extensive experiments on different real datasets verify the superiority of proposed method."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Real rain datasets. At present, the researchers have mostly focused on the network architecture design, while relative fewer attention has been paid on the real rain dataset. The insufficiency of realistic rain dataset is the main bottleneck to hamper single image deraining. In Table 1, we provide a comprehensive summary of existing real rain datasets, which can be classified into two categories: rainy image only and paired rain-image. The former can be utilized via semi-supervised [40, 13] or unsupervised methods [7, 51]. The latter can be conveniently utilized by the supervised training.",
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+    {
+        "type": "text",
+        "text": "The key to paired real dataset is how to acquire the pseudo-'clean' image from its rainy counterpart. There are two main ways to construct the pairs: video-based generation (SPAData [37], RealRain-1K [20]), and time-interval acquisition (RainDS [32], GT-Rain [1]). All these datasets should ensure that the camera is strictly immobile during the acquisition process. SPA-data [37] was the first presented paired real dataset which utilized the human-supervised percentile video",
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+        "type": "page_number",
+        "text": "12098",
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+        "image_caption": [
+            "(a)"
+        ],
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+        "image_caption": [
+            "(b)",
+            "Figure 2: Features of the proposed benchmark LHP-Rain. (a) Distribution of rain and scene of the proposed benchmark. (b) Our proposed LHP-Rain outperforms others in terms of rain diversity and sequence amount. (c) LHP-Rain collects high-resolution and annotated rainy images without copyright, compression and blur."
+        ],
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+        "img_path": "images/a144a0cb1bb4c02d3f526c9bed6e8f28ed2614902821bc2019800ca191ddd0df.jpg",
+        "image_caption": [
+            "(c)"
+        ],
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+    {
+        "type": "text",
+        "text": "filtering to obtain the GT. Instead of generation, GT-Rain [1] collected the pairs of same scene under rainy and good weather, respectively. Similar idea has been adopt in RainDS [32] by manually mimicking rainfall with a sprinkler.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite the rapid development promoted by those pioneer datasets, there remain some important issues to be solved: insufficient number and rain diversity (not consider ground splashing). In this work, we contribute a large-scale high-quality paired real rain dataset (Section 3.1) with diverse rain and abundant objects. Moreover, a novel GT generation method is proposed with higher-quality pairs (Section 3.3).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Single image deraining. The single image deraining methods have made great progress in last decade including the optimization models [26, 22, 4], deep convolutional network [12, 36, 10] and transformer [35, 44]. Fu et al. [9] first introduced the residual deep CNN for single image deraining. Latter, the researchers have further improved the network depth by stacking similar modules, such as the well-known recurrent [21, 49] and multi-stage progressive [33, 53] strategies. Meanwhile, the multi-scale has been widely explored to improve the representation such as the multi-scale fusion [14] and wavelet decomposition [46]. Further, the side information about the rain attribute: density [54], depth [12], directionality [38], location [47], non-local [17] have been extensively utilized to enhance the deraining performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Benefiting from self-attention mechanism for long-range relationships modelling, transformer-based methods have achieved significant performance for single image deraining [39, 35, 44, 6]. Very recently, Xiao et al.[44] proposed an image deraining transformer (IDT) with relative position enhanced and spatial-based multihead self-attention. Chen et al. [6] proposed a sparse Transformer architecture to solve the redundant feature issue. In this work, we propose a simple yet effective dual-branch transformer baseline which simultaneously utilizes the self-attention within rain/image layer and cross-layer attention between the rain and image layer, so as to jointly improve the discriminative disentanglement between the rain and image layer (Section 4).",
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+    {
+        "type": "text",
+        "text": "3. Large-scale high-quality paired Benchmark",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Benchmark Collection and Statistics",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Due to the difficulty and inconvenience of collecting real rain videos, the video sequences and frames of existing paired real rain datasets are still limited as shown in Table 1. In this work, we collect the real rain sequences by smartphones with  $24\\mathrm{mm}$  lens focal length, sampled in 30 fps. The data collection process is illustrated in Fig. 3(a). Firstly, to keep the camera immobile, we employ tripod to capture real rain videos with static background (no moving object except rain). For each sequence, we record approximate 15 seconds and extract the intermediate steady 10s into our dataset. Then, we manually pick out moving object to remove unexpected disturbance. Finally, we employ the proposed RLRTR (Section 3.3) to obtain high-quality GT.",
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+    {
+        "type": "text",
+        "text": "Overall, we collect 3000 video sequences with approximate 1 million frames across 8 cities from 4 countries around the world, China (2091 sequences), England (51 sequences), Philippines and Indonesia (858 sequences). We visualize the per-country image counts and location distribution of LHP-Rain in Fig. 3(b). The rainfall levels are varied from light rain (10mm/day) to rainstorm (300mm/day) due to diversity of local climates. Over 17 typical scenes are captured, including the parking lot, street, alley, playground, courtyard, and forest, etc. Besides, 2490 sequences are captured at daytime and 510 sequences are at night. More Rainy/GT pairs from LHP-Rain are displayed in Fig. 3(c). With the changing of location, backgrounds are varied from nature to city with diverse rain patterns, such as rain streak, veiling effect, occlusion and splashing. Note that, although the background is the same for each video sequence, the rain in each frame is vastly different from the appearance, including streak, veiling, occlusion and splashing. Here we separate 2100 sequences as training set, 600 sequences as validation set and the other 300 sequences as test set. To further visualize the quantity distribution of rain and scene for each sequence, a sunburst chart is illustrated in Fig. 2(a).",
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+            "Same position"
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+            "Rainy frames"
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+        "image_caption": [
+            "Rnny",
+            "Guangxi, China"
+        ],
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+        "image_caption": [
+            "Hunan, China"
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+        "image_caption": [
+            "Hubei, China",
+            "(c)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
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+    {
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+        "img_path": "images/1c2bc4a1aa33650d48fbe6de370874965d3a654ae8b364fedaef7a33d9bd97d0.jpg",
+        "image_caption": [
+            "Manila, Philippines"
+        ],
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+        "bbox": [
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+        "page_idx": 3
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+    {
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+        "img_path": "images/5ddd71ec065595c89f8db549d8765b9ef6a7d8c84141404395c8a6f186d5e2d3.jpg",
+        "image_caption": [
+            "London, England"
+        ],
+        "image_footnote": [],
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+        "page_idx": 3
+    },
+    {
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+        "img_path": "images/823802220f5839f4d30727b5217dd5649848e6cf957fbb4247bf741ac8b9b6fb.jpg",
+        "image_caption": [
+            "Jakarta, Indonesia"
+        ],
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "3.2. Benchmark Features",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Rain with higher-diversity and larger-scale. We concern not only the sequence number and total frames but also the rain diversity of realistic rain, which both have great impact on the generalization for real-world rain. In Fig. 2(b), we show the statistic distribution of rain diversity and sequences/frames in typical real paired rain dataset. All datasets concern about the noticeable rain streak, especially SPA-data [37]. RainDS [32] additionally takes the raindrop into consideration with 1000 frames, while GT-Rain [1] and RealRain-1K [20] further capture the accumulation veiling artifact in heavy rain. LHP-Rain contains not only rain streak and veiling in the sky, but also challenging highlight occlusion and splashing water on the ground. To our best knowledge, the proposed LHP-Rain is the first benchmark to collect and tackle ground splashing rain in the real world, which is commonly ignored by previous existing datasets.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Image with higher-resolution and abundant objects. The existing datasets pay much attention to the rain, ignoring that the high-quality image is also what we really need. Unfortunately, existing realistic rainy images are generally downloaded from the Internet with various problems about the image: compression artifact, watermark, low-resolution, out-of-focus blur, without objects to name a few, which may cause challenges for high-level vision applications. In Fig. 2(c), we show the typical examples in each dataset. The image background of RealRain-1K [20] suffers from serious out-of-focus blur, since they have manually focused on the rain on purpose. GT-Rain [1] contains obvious compression artifact, since it origins from the compressed Youtube stream. There are numerous scenes with narrow views and watermark in the SPA-data [37], because they only release patches (256*256) cropped from original frames.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/00d6ad79436f3668464f9169c4f367c9e35d4fe6f55e5e6905a39c5b36ddf2b3.jpg",
+        "image_caption": [
+            "Figure 3: Illustration of the proposed benchmark LHP-Rain. (a) Overall procedure of obtaining rainy/clean image pair. (b) Quantity and location distribution of LHP-Rain. (c) Rainy/GT samples of LHP-Rain from different locations. Scenes are varied from nature to city, over day and night with diverse rain patterns from sky to the ground.",
+            "Figure 4: The GT quality of LHP-Rain is superior to others on DIIVINE (lowest), NIQE (lowest) and B-FEN (highest)."
+        ],
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+        "img_path": "images/a3d9c88dbb82a5f434dae73a77cdb2c3d619ad41af1f2544270959647254cc29.jpg",
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+    {
+        "type": "text",
+        "text": "To improve the image quality, we personally capture high-resolution (1920*1080) realistic rain videos by smartphones. Moreover, LHP-Rain is not only designed for rain restoration, but also important for object detection and segmentation tasks under adverse weather, with abundant objects which are oriented for self-driving and video surveillance scenes. Thus, we provide annotations for object detection and lane segmentation. Five typical objects including person, car, bicycle, motorcycle and bus are annotated by bounding box with 326,961 instances totally. For lane segmentation, we annotate 24,464 lane masks to evaluate the effect of rain splashing removal. Note that the same object in different frames will be regarded as different instances because rain is inconstant and changing frame by frame.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Higher-quality ground-truth. The quality of GT is critical for paired real rain dataset. It is difficult to determine what is good or bad GT in an absolutely fair way. In this paper, we assume that the better the rain removal, the better the image quality is. Therefore, we employ several no reference image quality assessments: DIIVINE [29], NIQE [28] and B-FEN [43], to evaluate the image quality of the rain-free image. The former two are hand-crafted based general image quality indexes, and the last one B-FEN is the learning based index especially designed for de-raining quality assessment. We select all the video backgrounds in SPA-data [37], GT-Rain [1], RealRain-1K [20] and LHP-Rain for evaluation. In",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12100",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8ff7e958ad209ae7c1aca429094e433d098645e27439210919e1720bbb7cfc8f.jpg",
+        "image_caption": [
+            "Figure 5: Analysis of different video deraining results on our dataset. From left to right, the first column is the original rainy frame, and the remaining five columns represent different methods, namely Median Filter, SPA, FastDeRain, J4R-Net and the proposed RLRTR. From top to bottom, the first row shows the deraining results, the second row is the rain layer of the deraining results, the third row denotes the section line of the deraining results and the last row represents the horizontal and vertical gradient distributions of the deraining results.",
+            "Fig. 4, we can observe that the proposed LHP-Rain consistently obtains the best results in terms of different evaluation indexes which strongly support the higher-quality of the GT."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Robust Low-rank Tensor Recovery Model",
+        "text_level": 1,
+        "bbox": [
+            76,
+            517,
+            434,
+            534
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given the rainy video  $\\mathcal{O} \\in \\mathbb{R}^{h \\times w \\times t}$ , the key is how to properly obtain the paired GT. The existing methods simply employ the naive filtering technique benefiting from the temporal consistency of the static background. Due to the slight camera vibration caused by the wild wind, we further leverage an affine transformation operator  $\\tau$  [52] to achieve the pixel-level alignment of each frame. Thus, a multi-frame rainy video can be described as the following formula:",
+        "bbox": [
+            75,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {O} \\circ \\tau = \\mathcal {B} + \\mathcal {R} + \\mathcal {N}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            197,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{B} \\in \\mathbb{R}^{h \\times w \\times t}$  is the rain-free video,  $\\mathcal{R} \\in \\mathbb{R}^{h \\times w \\times t}$  represents the rains,  $\\mathcal{N} \\in \\mathbb{R}^{h \\times w \\times t}$  denotes the random noise, and  $\\tau$  denotes the affine transformation to ensure the rainy video of each frame is pixel-level aligned. In this work, we formulate the video deraining into inverse problem via the maximum-a-posterior as follow:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathcal {B}, \\mathcal {R}, \\tau} \\frac {1}{2} | | \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau | | _ {F} ^ {2} + \\omega P _ {b} (\\mathcal {B}) + \\mu P _ {r} (\\mathcal {R}), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            779,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $P_{b}$  and  $P_{r}$  are the prior knowledge for the image and rain, respectively,  $\\omega$  and  $\\mu$  are the corresponding hyperparameters. As for the aligned rainy video, when there are no moving objects except the rain, the rain-free background image is the same for all rainy frames. That is to say, clean video  $\\mathcal{B}$  has extreme global low-rank property along the",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "temporal dimension, ideally its rank is equal to one for each scene. On the other hand, the clean video  $\\mathcal{B}$  also has very non-local low-rank property along the spatial dimension, due to the self-similarity widely employed in image restoration [8]. Moreover, we further take the local smoothness of the video  $\\mathcal{B}$  into consideration via the total variation (TV) regularization [4]. Thus, the joint global-nonlocal-local prior along both the spatial and temporal dimension has been fully exploited for better representation of the static video  $\\mathcal{B}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {b} (\\mathcal {B}) = \\omega \\sum_ {i} \\left(\\frac {1}{\\lambda_ {i} ^ {2}} | | \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} | | _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}\\right) + \\gamma | | \\nabla_ {t} \\mathcal {B} | | _ {1}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            602,
+            890,
+            626
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{S}_i\\mathcal{B}\\in \\mathbb{R}^{p^2\\times k\\times t}$  is the constructed 3-D tensor via the non-local clustering of a sub-cubic  $u_{i}\\in \\mathbb{R}^{p\\times p\\times t}$  [3],  $p$  and  $k$  are the spatial size and number of the sub-cubic respectively,  $Q_{i}\\in \\mathbb{R}^{d\\times t}(d\\ll t)$  is an orthogonal subspace projection matrix used to capture the temporal low-rank property,  $\\times_3$  is the tensor product along the temporal dimension [16],  $\\mathcal{I}_i$  represents the low-rank approximation variable,  $||\\bullet ||_{ttn}$  means the tensor nuclear norm for simplicity [3],  $\\nabla_t$  is the difference operator,  $\\gamma$  and  $\\lambda_{i}$  is the regularization parameters. As for the rain  $\\mathcal{R}$ , we formulate it as the sparse error [42] via the  $L_{1}$  sparsity. Thus, the Eq. (2) can be expressed as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\left\\{\\hat {\\mathcal {B}}, \\hat {\\mathcal {R}}, \\hat {\\mathcal {J}} _ {i}, \\hat {\\tau}, \\hat {Q} _ {i} \\right\\} = \\arg \\min  _ {\\mathcal {B}, \\mathcal {R}, \\mathcal {J} _ {i}, \\tau , Q _ {i}} \\frac {1}{2} \\| \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau \\| _ {F} ^ {2} \\tag {4} \\\\ + \\mu | | \\mathcal {R} | | _ {1} + \\omega \\sum_ {i} \\left(\\frac {1}{\\lambda_ {i} ^ {2}} | | \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} | | _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}\\right) + \\gamma | | \\nabla_ {t} \\mathcal {B} | | _ {1}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Optimization. Due to the difficulty of estimating multiple variables directly, we adopt the alternating minimization",
+        "bbox": [
+            498,
+            861,
+            893,
+            892
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12101",
+        "bbox": [
+            478,
+            924,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/c4e48147f82df0984149b9d871629b2ae7acc5da887fbb6c71404bf4e4091cb7.jpg",
+        "table_caption": [
+            "Table 2: Quantitative comparisons with SOTA supervised methods on paired real datasets SPA-data (A), GT-Rain (B) and proposed LHP-Rain (C) under 9 different task settings. X→Y means training on the dataset X and testing on the dataset Y. The degraded results of the three datasets are also provided. Top  $1_{st}$  and  $2_{nd}$  results are marked in red and blue respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">A→A</td><td colspan=\"2\">B→A</td><td colspan=\"2\">C→A</td><td colspan=\"2\">A→B</td><td colspan=\"2\">B→B</td><td colspan=\"2\">C→B</td><td colspan=\"2\">A→C</td><td colspan=\"2\">B→C</td><td colspan=\"2\">C→C</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>Rainy Image</td><td colspan=\"6\">32.60 / 0.9173</td><td colspan=\"6\">19.48 / 0.5849</td><td colspan=\"6\">29.97 / 0.8497</td></tr><tr><td>SPANet</td><td>38.53</td><td>0.9875</td><td>22.93</td><td>0.8207</td><td>31.46</td><td>0.9612</td><td>20.01</td><td>0.6148</td><td>21.51</td><td>0.7145</td><td>19.20</td><td>0.5706</td><td>28.00</td><td>0.8905</td><td>20.10</td><td>0.8061</td><td>31.19</td><td>0.9346</td></tr><tr><td>PReNet</td><td>37.05</td><td>0.9696</td><td>22.44</td><td>0.7713</td><td>32.46</td><td>0.9387</td><td>20.29</td><td>0.5860</td><td>20.65</td><td>0.6005</td><td>19.34</td><td>0.5530</td><td>27.57</td><td>0.8595</td><td>20.91</td><td>0.7222</td><td>32.13</td><td>0.9177</td></tr><tr><td>RCDNet</td><td>39.74</td><td>0.9661</td><td>22.51</td><td>0.8392</td><td>32.30</td><td>0.9378</td><td>20.09</td><td>0.5785</td><td>21.04</td><td>0.6106</td><td>19.09</td><td>0.5264</td><td>25.46</td><td>0.7959</td><td>21.38</td><td>0.8047</td><td>32.34</td><td>0.9152</td></tr><tr><td>JORDER-E</td><td>40.63</td><td>0.9794</td><td>23.47</td><td>0.7426</td><td>31.23</td><td>0.9234</td><td>19.98</td><td>0.5799</td><td>21.24</td><td>0.6854</td><td>18.76</td><td>0.4861</td><td>27.13</td><td>0.8531</td><td>22.14</td><td>0.8433</td><td>31.24</td><td>0.8847</td></tr><tr><td>MPRNet</td><td>46.06</td><td>0.9894</td><td>24.27</td><td>0.8428</td><td>32.37</td><td>0.9379</td><td>19.87</td><td>0.6286</td><td>22.00</td><td>0.6515</td><td>19.47</td><td>0.5889</td><td>28.41</td><td>0.8807</td><td>23.82</td><td>0.8052</td><td>33.34</td><td>0.9309</td></tr><tr><td>GT-Rain</td><td>37.21</td><td>0.9827</td><td>25.30</td><td>0.9243</td><td>26.46</td><td>0.9145</td><td>20.07</td><td>0.6941</td><td>22.51</td><td>0.7300</td><td>21.14</td><td>0.5698</td><td>28.62</td><td>0.8675</td><td>23.19</td><td>0.8098</td><td>32.18</td><td>0.9132</td></tr><tr><td>Uformer-B</td><td>46.42</td><td>0.9917</td><td>24.08</td><td>0.8979</td><td>32.21</td><td>0.9667</td><td>19.70</td><td>0.6875</td><td>21.60</td><td>0.7124</td><td>19.10</td><td>0.6622</td><td>28.74</td><td>0.9262</td><td>22.91</td><td>0.8734</td><td>33.56</td><td>0.9317</td></tr><tr><td>IDT</td><td>45.74</td><td>0.9889</td><td>23.80</td><td>0.8334</td><td>32.38</td><td>0.9422</td><td>20.34</td><td>0.6306</td><td>21.98</td><td>0.6536</td><td>19.44</td><td>0.5977</td><td>26.90</td><td>0.8742</td><td>23.34</td><td>0.7897</td><td>33.02</td><td>0.9310</td></tr><tr><td>SCD-Former</td><td>46.89</td><td>0.9941</td><td>26.13</td><td>0.9122</td><td>34.38</td><td>0.9798</td><td>20.98</td><td>0.6985</td><td>22.79</td><td>0.7684</td><td>21.71</td><td>0.6893</td><td>29.41</td><td>0.9127</td><td>23.56</td><td>0.8626</td><td>34.33</td><td>0.9468</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "scheme to solve the Eq. (4) with respect to each variable.",
+        "bbox": [
+            76,
+            332,
+            454,
+            345
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1) Affine Transformation  $\\tau$ : Since  $\\mathcal{O} \\circ \\tau$  is a nonlinear geometric transform, it's difficult to directly optimize  $\\tau$ . A common technique is to linearize around the current estimate and iterate as follows:  $\\mathcal{O} \\circ \\tau + \\nabla \\mathcal{O} \\triangle \\tau = \\mathcal{B} + \\mathcal{R} + \\mathcal{N}$  [31], where  $\\nabla \\mathcal{O}$  is the Jacobian of the image  $\\mathcal{O}$  with respect to  $\\tau$ . This method iteratively approximates the original nonlinear transformation with a locally linear approximation [31].",
+            "2) Rain Estimation  $\\mathcal{R}$ : By ignoring variables independent of  $\\mathcal{R}$ , we can obtain following subproblem:"
+        ],
+        "bbox": [
+            75,
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+            468,
+            483
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathcal {R}} = \\arg \\min _ {\\mathcal {R}} \\frac {1}{2} | | \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau | | _ {F} ^ {2} + \\mu | | \\mathcal {R} | | _ {1}. (5)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
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+            513
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "Eq. (5) is a  $L_{1}$  minimization problem which can be easily solved by soft thresholding with closed-form solution [23].",
+            "3) Subspace Projection  $Q_{i}$ : We enforce the orthogonal constraint on  $Q_{i}^{T}Q_{i} = I$  with the following subproblem:"
+        ],
+        "bbox": [
+            75,
+            518,
+            468,
+            580
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {Q} _ {i} = \\arg \\min  _ {Q _ {i} ^ {T} Q _ {i} = I} \\frac {1}{\\lambda_ {i} ^ {2}} \\left\\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\right\\| _ {F} ^ {2}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            130,
+            585,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "According to [45], Eq. (6) has the closed-form solution, which can be obtained by the rank-  $d$  singular value decomposition of the folding matrix of  $\\mathcal{S}_i\\mathcal{B}$ , where  $d$  is the measurement of the intrinsic subspace of the temporal dimension. In this work, we empirically set  $d \\leq 3$ .",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4) Low-rank Approximation  $\\mathcal{J}_i$ : Dropping the irrelevant variables, we can get following subproblem:",
+        "bbox": [
+            75,
+            700,
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+            729
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathcal {J}} _ {i} = \\arg \\min  _ {\\mathcal {J} _ {i}} \\frac {1}{\\lambda_ {i} ^ {2}} \\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\| _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            93,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "This is a typical tensor nuclear norm minimization problem, can be solved by singular value thresholding algorithm [2, 3].",
+            "5) Clean Video Estimation  $\\mathcal{B}$ : We fix the other variables and optimize  $\\mathcal{B}$  with the following subproblem:"
+        ],
+        "bbox": [
+            75,
+            766,
+            468,
+            825
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathcal {B}} \\frac {1}{2} \\| \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau \\| _ {F} ^ {2} + \\omega \\sum_ {i} \\frac {1}{\\lambda_ {i} ^ {2}} \\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\| _ {F} ^ {2} + \\gamma \\| \\nabla_ {t} \\mathcal {B} \\| _ {1}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            93,
+            834,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Due to the non-differentiability of the  $L_{1}$  norm in Eq. (8), we apply the ADMM [23] to decouple this problem into several",
+        "bbox": [
+            75,
+            859,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/fb62f199f88f541bf5e7275bead92543acd21423b66e8cd05734f78b7a51a87d.jpg",
+        "image_caption": [
+            "Figure 6: Overall framework of the SCD-Former. It utilizes self and cross-layer attention from rain layer to image layer which serves as side information to recover image layer."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            329,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "sub-problems with closed-form solutions. Please refer to the supplementary material for the whole algorithm details.",
+        "bbox": [
+            498,
+            534,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Discussion. Figure 5 illustrates the comparison results of representative video deraining methods: filter-based methods (median filter[20], SPA[37]), optimization-based (FastDeRain[15]) and learning-based methods (J4R-Net[24]). The first and second rows show the video deraining of the image and rain layer, respectively. RLRTR removes almost all the rain from sky to the ground, including rain streaks and splashing, and preserve the image details well, while other methods more or less have rain streaks residual but also cause noticeable damage to the image. In third row, we randomly choose two 1D section lines of the deraining results. The section line of RLRTR is smoother with less burr than other methods. Moreover, the SPA, FastDeRain and the J4R-Net unexpectedly attenuate the spike signal of the share edge, while the proposed RLRTR has well preserve the spike signal. It is well-known the natural image is isotropic and its gradient distribution along different directions should be close to each other [34]. Compared with other results, in forth row the gradient distributions along the vertical and horizontal directions of RLRTR are most similar to each other, which further indirectly verify the naturalness of the deraining result and produce better paired clean-rainy GT.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "12102",
+        "bbox": [
+            478,
+            924,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/6246f277cd153287bf3b10dfec01637b5c9f07f0e0523dfb1a6f270e32bb80e7.jpg",
+        "image_caption": [
+            "Rainy Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            114,
+            243,
+            353
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c4987cce980065135f0c7d200798bad9bd6498e7251e94bec3b45ee208d48a23.jpg",
+        "image_caption": [
+            "JORDER-E"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            243,
+            114,
+            406,
+            354
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8382472e39e69e3148612357c9c62506daab057ab9af32545dd44a5405ca9f54.jpg",
+        "image_caption": [
+            "MPRNet",
+            "Figure 7: Visual comparisons on LHP-Rain. Comparing with state-of-the-arts, SCD-Former achieves more visual pleasing deraining results and it is capable of removing the highlight occlusion on the car and the splashing water on the ground."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            408,
+            114,
+            568,
+            354
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/619f6f60c4c1510bcc321b39547a203075ac1fe623e10340f23944d093838fd5.jpg",
+        "image_caption": [
+            "IDT"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            568,
+            114,
+            723,
+            354
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/490f67801807bd6200aae50674f7a9457a7455bf4f2c6f5b023c6cca2c6f13e6.jpg",
+        "image_caption": [
+            "SCD-Former"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            723,
+            114,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4. SCD-Former: Image Deraining Baseline",
+        "text_level": 1,
+        "bbox": [
+            76,
+            409,
+            437,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The degradation procedure can be formulated as:",
+        "bbox": [
+            96,
+            435,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nO = B + R. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            230,
+            452,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It has been proved that the rain such as location [47] serving as an attention would be informative in CNN-based image restoration. In this work, we show the rain attention would also be beneficial in transformer. In Fig. 6, we design a simple two-stream Self- and Cross-attention Deraining Transformer (SCD-Former), in which the two-stream network is designed to restore rain and image layer respectively. On one hand, we utilize the self-attention in each rain/image stream independently; on the other hand, we further exploit the cross-layer attention between the rain and image streams. Thus, the rain collaboratively interactive with the image layer to further improve the discriminative representation.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Self-attention and cross-layer attention. In this work, we exploit self-attention on rain and image layer as Rain layer Self-Attention (RSA) and Image layer Self-Attention (ISA). Given the input feature  $X$ , it will be projected into query  $(Q)$ , key  $(K)$  and value  $(V)$  by three learnable weight matrices  $W_{q}$ ,  $W_{k}$  and  $W_{v}$ . Then dot-product, scaling and softmax among  $Q$ ,  $K$  and  $V$  will be conducted. The self-attention function is defined as:",
+        "bbox": [
+            75,
+            652,
+            468,
+            768
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            140,
+            768,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We further design a Cross-Layer Attention (CLA) module which bridges the attention relationship between rain and image layer. The CLA conducts attention operation among  $Q_{r}$  from rain layer and  $K_{b}, V_{b}$  from image layer as follow:",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nC L A \\left(Q _ {r}, K _ {b}, V _ {b}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {r} K _ {b} {} ^ {T}}{\\sqrt {d _ {k}}}\\right) V _ {b}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The token of rain layer serves as a query token  $Q_{r}$  to interact with the patch tokens  $K_{b}$  and  $V_{b}$  from the image layer through attention mechanism. By calculating the correlation degree between both layers, the highly attentive location of rain residual can be acquired, which provides an extra prior for enhanced feature representation. Note that, the CLA module has been stacked over the whole network. Compared with previous work, SCD-Former exploits not only the self-attention but also cross-layer attention of the rain and image layer for better restoration.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. We train the network using the Charbonnier loss[5] supervised by the ground truth of rain and image layer:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\left| \\left| O - B - R \\right| \\right| _ {F} ^ {2} + \\lambda_ {r} \\left| \\left| R - \\hat {R} \\right| \\right| _ {1} + \\lambda_ {b} \\left| \\left| B - \\hat {B} \\right| \\right| _ {1}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The framework is implemented with two RTX 3090 GPUs. We set the hyperparameter  $\\lambda_{b}$  and  $\\lambda_{r}$  as 1. The images are randomly cropped into  $256*256$  for training. The learning rate of network is set as 0.0002. The Adam optimizer is adopted for optimization with a batch size of 32.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Datasets. We conduct the experiments on paired datasets SPA-data[37], GT-Rain[1] and LHP-Rain. For the SPA-data, training set is cropped from 29,500 images and 1000 rainy images are used for testing. For the GT-Rain, 89 sequences are used for training and 7 sequences are used for testing. For the LHP-Rain, 2100 sequences are used for training and 300 sequences are used for testing. To evaluate the deraining performance on real scenes, we choose typical real rainy images from Internet-data. For single image deraining methods, we select the representative supervised deraining methods, including the CNN-based SPANet[37],",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "12103",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/cefa5d50aa3c1d6b10a6c41a72095a58553572a4f6f0b826f7460994b48318a3.jpg",
+        "image_caption": [
+            "Figure 8: Evaluation of the diversity of the LHP-Rain. We train SCD-Former on different datasets: Rain100L, SPA-data, GT-Rain and LHP-Rain, and test on other datasets. The model trained on LHP-Rain has achieved better deraining results."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "PReNet[33], RCDNet[36], JORDER-E[47], MPRNet[27], GT-Rain[1], transformer-based Uformer[39] and IDT[44]. Evaluation metrics. We employ the full-reference PSNR and SSIM to evaluate the single image deraining results. Moreover, mean Average Precision (mAP) and Accuracy (Acc) are employed to evaluate object detection and lane segmentation after restoration by deraining methods.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.1. Quantitative Evaluation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Deraining results on benchmarks. We make comparisons with state-of-the-art deraining methods on three datasets SPA-data (A), GT-Rain (B) and LHP-Rain (C). The quantitative results are reported in Table 2 under the following columns:  $\\mathrm{A}\\rightarrow \\mathrm{A}$ ,  $\\mathrm{B}\\rightarrow \\mathrm{B}$  and  $\\mathrm{C}\\rightarrow \\mathrm{C}$ . It is observed that transformer-based methods perform better than most CNN-based methods except for MPRNet in terms of PSNR and SSIM because of the superior representation of self-attention. Note that SCD-Former outperforms the existing state-of-the-art methods on all benchmarks, which confirms the effectiveness of our method with both self and cross-layer attention.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2. Qualitative Evaluation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on LHP-Rain. To further validate the deraining performance, we compare with the qualitative results of typical methods on LHP-Rain. As shown in Fig. 7, SCD-Former achieves more visual pleasing results without rain residual and artifacts comparing with other methods, which cleans the rain streaks and veiling effect on the trees, highlight occlusion on the red car and the ground splashing water.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on real rainy images. To evaluate the performance on real rainy images, we train SCD-Former on synthetic rain Rain100L[48], real rain SPA-data, GT-Rain and LHP-Rain respectively and test on real rainy images. As shown in Fig. 8, the model trained on Rain100L performs poorly due to the huge domain gap. SPA-data and GT-Rain could remove real rain in the sky partially but they cannot handle the splashing water on the ground. The model trained on LHP-Rain has the best deraining performance which simultaneously removes rain streaks, veiling and ground splashing water without destroying image details.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c2c1c0e9c96e3bd1820ebe7e0d214bcddc201bb0d057bcb8b047977ebcc1029c.jpg",
+        "image_caption": [
+            "Figure 9: Ablation study of the robust low-rank tensor recovery model. The first row represents the deraining results, and the second row is corresponding rain. The first column is the original rainy frame and the remaining three columns represent the model without subspace projection, without affine transformation and full RLRTR."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/9aaf4fc121f71907dbc553a30193f2f101341eca74168030d531bb511c6289a7.jpg",
+        "table_caption": [
+            "Table 3: Ablation study of cross-layer attention."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Cross-layer attention</td><td>PSNR / SSIM</td></tr><tr><td>-</td><td>33.92 0.9384</td></tr><tr><td>✓</td><td>34.33 0.9403</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            575
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of subspace projection. The subspace projection is used to characterize the extreme global low-rank property along the temporal dimension. In Fig. 9, there are obvious rain residual without subspace projection, implying that it is insufficient to characterize the property of the temporal dimension relying on the local prior of the temporal smoothness. Since the temporal low-rank property is neglected, leading to the rain residual in the results.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of affine transformation. The affine transformation is exerted to guarantee the pixel-level alignment of rainy video. As shown in Fig. 9, it can be observed that background residual and distortion obviously exist in the rain layer without affine transformation, because the extreme low-rank property along the temporal dimension is affected by data alignment among each frame in the video.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of cross-layer attention. The design aims to find the correlations between rain layer and image layer. After iterations, the image layer sub-network obtains more attention on the rain features brought by cross-layer attention. In Table 3, We show that the complementary guidance from rain layer promotes the restoration of image layer.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "12104",
+        "bbox": [
+            478,
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+            519,
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/63b810fec0992f9bc5aa761615ee57ed88ab87e6b6210097a5bbe83541d8ed17.jpg",
+        "image_caption": [
+            "Rainy Image",
+            "Figure 10: Evaluation of high-level tasks on lane segmentation and object detection. The performance improves significantly after removing rain streak and ground splashing from lanes and bicycles by our proposed SCD-Former."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            98,
+            207,
+            224
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/1b99f8d2d58a8be4409546a11039a7872aa8ba70d4861b3475c369ed19ba666e.jpg",
+        "image_caption": [
+            "JORDER-E"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            210,
+            98,
+            338,
+            224
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/2276c582c5af92cfe5d58481f7f8d4390f86f4a7b82c4c89554dd28721bbb612.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/472afeb6f4a751d8c3ddb63c842a4eaf8b08c404eaaa60939ee7ab3791283176.jpg",
+        "table_caption": [
+            "Table 4: Evaluation of high-level tasks on deraining results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Det. (mAP)</td><td>Gain (Det.)</td><td>Seg. (Acc)</td><td>Gain (Seg.)</td></tr><tr><td>Rainy</td><td>0.543</td><td>-</td><td>0.237</td><td>-</td></tr><tr><td>SPANet</td><td>0.563</td><td>+0.020</td><td>0.268</td><td>+0.031</td></tr><tr><td>PReNet</td><td>0.560</td><td>+0.022</td><td>0.255</td><td>+0.018</td></tr><tr><td>RCDNet</td><td>0.556</td><td>+0.018</td><td>0.361</td><td>+0.124</td></tr><tr><td>JORDER-E</td><td>0.568</td><td>+0.025</td><td>0.385</td><td>+0.148</td></tr><tr><td>MPRNet</td><td>0.560</td><td>+0.017</td><td>0.350</td><td>+0.113</td></tr><tr><td>Uformer-B</td><td>0.568</td><td>+0.025</td><td>0.306</td><td>+0.069</td></tr><tr><td>IDT</td><td>0.570</td><td>+0.027</td><td>0.365</td><td>+0.128</td></tr><tr><td>SCD-Former</td><td>0.575</td><td>+0.031</td><td>0.449</td><td>+0.212</td></tr></table>",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.4. Discussion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Rain diversity of different datasets. The rain diversity of dataset can be validated by the experiment of training models on one dataset and testing on the other unseen datasets among SPA-data (A), GT-Rain (B) and LHP-Rain (C). As shown in Table 2, on one hand, the best results of  $\\mathrm{C} \\rightarrow \\mathrm{A}$  methods positively improve the performance of A, while all  $\\mathrm{A} \\rightarrow \\mathrm{C}$  results performing worse than degraded result of C. On the other hand, the best results of  $\\mathrm{C} \\rightarrow \\mathrm{B}$  have promotion while  $\\mathrm{B} \\rightarrow \\mathrm{C}$  drop severely. Therefore, the outcome proves that our LHP-Rain contains more diverse rain categories than others, because they could not handle extreme challenging cases such as occlusion and ground splashing.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on downstream tasks. We further evaluate the image deraining results on high-level tasks. For object detection, we apply the officialYOLOv5 model on deraning results and report the mean average precision (mAP) of different classes in Table 4, where SCD-Former reaches the best average mAP among typical objects. For lane segmentation, we choose the LaneNet[30] to predict the lane on LHP-Rain and SCD-Former has larger promotion on the segmentation accuracy. It is reasonable because SCD-Former performs well on removing ground splashing water and recovering the lane lines. The visualization results in Fig. 10 shows that the lane on the surface of ground and the bicycles could be properly predicted after deraining by SCD-Former.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "User study on benchmarks quality. We look for 126 volunteers to anonymously vote for the benchmark with best quality. Among existing benchmarks, we randomly select",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/9f87f7aa50574c34b86fd514f173533e17b3a6491d605ba12422f4d2d817d3fd.jpg",
+        "image_caption": [
+            "(a) Rainy Image",
+            "Figure 11: The limitation of RLRTR. The challenging occlusion effect could be removed by RLRTR from the background while the static haze is preserved."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            80,
+            696,
+            170
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/9dde83037729117b207c57552e4a888a68e791e9ee4313bab3ed7b31e579621c.jpg",
+        "image_caption": [
+            "(b) RLRTR Result"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            700,
+            80,
+            890,
+            170
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/d4621353e62e01e5dacb49496a30d1ffd8a1725ab4de58beed158d0737e5598b.jpg",
+        "table_caption": [
+            "Table 5: User study on benchmarks quality."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>LHP-Rain</td><td>SPA</td><td>RealRain1K</td><td>GT-Rain</td></tr><tr><td>Rain diversity</td><td>63%</td><td>8%</td><td>13%</td><td>16%</td></tr><tr><td>Image quality</td><td>51%</td><td>14%</td><td>20%</td><td>15%</td></tr><tr><td>GT quality</td><td>55%</td><td>15%</td><td>16%</td><td>14%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "100 samples and conduct user study including: rain diversity, image quality (resolution, JEPG, blur) and GT quality. The result is listed in Table 5, where LHP-Rain consistently outperforms other benchmarks more than  $50\\%$ .",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Limitation",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our proposed video deraining method is limited to remove the haze in the heavy rain scenes. RLRTR is adept at separating the static background from the dynamic rain. However, due to the steadiness of mist in the short interval, which is almost motionless in the background, RLRTR cannot decompose the haze from image layer well. Fig. 11 shows examples of rain and mist in our benchmark. Although the challenging rain patterns such as rain streaks are clearly removed, the result still contains haze. We look forward to handling the static haze in the future.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a large-scale and high-quality paired real rain benchmark. Our proposed LHP-Rain provides diverse rain categories, especially the ground splashing rain issue which is first claimed in deraining community. The model trained on LHP-Rain could generalize well on various real rainy scenes with great rain removal performance. Moreover, the proposed low-rank tensor recovery model could generate high-quality GT and detailed analysis confirms better results than others. In addition, we propose a single deraining baseline which performs well on removing rain from sky to the ground. Extensive experiments verify the superiority of the proposed benchmark and significantly improves segmentation task after removing splashing.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported in part by the National Natural Science Foundation of China under Grant 61971460 and Grant 62101294, in part by JCJQ Program under Grant 2021-JCJQ-JJ-0060 and in part by the Fundamental Research Funds for the Central Universities, HUST: 2022JYCXJJ001.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "12105",
+        "bbox": [
+            480,
+            924,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 9
+    },
+    {
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+        "sub_type": "ref_text",
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+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "12106",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
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+        "sub_type": "ref_text",
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+            "[44] Jie Xiao, Xueyang Fu, Aiping Liu, Feng Wu, and Zheng-Jun Zha. Image de-raining transformer. IEEE TPAMI, 2022. 1, 3, 9",
+            "[45] Qi Xie, Qian Zhao, Deyu Meng, and Zongben Xu. Kronecker-basis-representation based tensor sparsity and its applications to tensor recovery. IEEE TPAMI, 40(8):1888-1902, 2017. 6",
+            "[46] Wenhan Yang, Jiaying Liu, Shuai Yang, and Zongming Guo. Scale-free single image deraining via visibility-enhanced recurrent wavelet learning. IEEE TIP, 28(6):2948-2961, 2019. 3",
+            "[47] Wenhan Yang, Robby T Tan, Jiashi Feng, Zongming Guo, Shuicheng Yan, and Jiaying Liu. Joint rain detection and removal from a single image with contextualized deep networks. IEEE TPAMI, 42(6):1377-1393, 2019. 3, 9"
+        ],
+        "bbox": [
+            78,
+            90,
+            470,
+            898
+        ],
+        "page_idx": 10
+    },
+    {
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+        "sub_type": "ref_text",
+        "list_items": [
+            "[48] Wenhan Yang, Robby T Tan, Jiashi Feng, Jiaying Liu, Zongming Guo, and Shuicheng Yan. Deep joint rain detection and removal from a single image. In CVPR, pages 1357-1366, 2017. 1, 2, 9",
+            "[49] Youzhao Yang and Hong Lu. Single image deraining via recurrent hierarchy enhancement network. In ACM MM, pages 1814-1822, 2019. 3",
+            "[50] Yuntong Ye, Yi Chang, Hanyu Zhou, and Luxin Yan. Closing the loop: Joint rain generation and removal via disentangled image translation. In CVPR, pages 2053-2062, 2021. 1",
+            "[51] Yuntong Ye, Changfeng Yu, Yi Chang, Lin Zhu, Xi-Le Zhao, Luxin Yan, and Yonghong Tian. Unsupervised deraining: Where contrastive learning meets self-similarity. In CVPR, pages 5821-5830, 2022. 1, 2",
+            "[52] Hongwei Yong, Deyu Meng, Wangmeng Zuo, and Lei Zhang. Robust online matrix factorization for dynamic background subtraction. IEEE TPAMI, 40(7):1726-1740, 2017. 5",
+            "[53] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, Ming-Hsuan Yang, and Ling Shao. Multi-stage progressive image restoration. In CVPR, pages 14821-14831, 2021. 1, 3",
+            "[54] He Zhang and Vishal M Patel. Density-aware single image de-raining using a multi-stream dense network. In CVPR, pages 695-704, 2018. 3"
+        ],
+        "bbox": [
+            501,
+            92,
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+    }
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diff --git a/2023/From Sky to the Ground_ A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal/8d7e8632-869f-4c0d-a983-de51fca56097_model.json b/2023/From Sky to the Ground_ A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal/8d7e8632-869f-4c0d-a983-de51fca56097_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..56e014cc60464622d30a7d92dcd86434a35a1f45
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+++ b/2023/From Sky to the Ground_ A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal/8d7e8632-869f-4c0d-a983-de51fca56097_model.json	
@@ -0,0 +1,2807 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.118,
+                0.131,
+                0.853,
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+            ],
+            "angle": 0,
+            "content": "From Sky to the Ground: A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.239,
+                0.203,
+                0.766,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Yun Guo\\(^{1,\\dagger}\\), Xueyao Xiao\\(^{1,\\dagger}\\), Yi Chang\\(^{1,*}\\), Shumin Deng\\(^{1}\\), Luxin Yan\\(^{1}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.087,
+                0.222,
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+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, China {guoyun, xiaoxueyao, yichang, shumindeng, yanluxin}@hust.edu.cn https://github.com/yunguo224/LHP-Rain"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.329,
+                0.891,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.515,
+                0.893,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Figure 1: Illustration of the proposed paired rainy/clean images dataset. The proposed real rain dataset is to cope with various rain categories, such as rain streaks, veiling effect, occlusion, and ground splashing. We recommend zooming in the figure on PC for better visualization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.574,
+                0.314,
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+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.591,
+                0.472,
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+            ],
+            "angle": 0,
+            "content": "Learning-based image deraining methods have made great progress. However, the lack of large-scale high-quality paired training samples is the main bottleneck to hamper the real image deraining (RID). To address this dilemma and advance RID, we construct a Large-scale High-quality Paired real rain benchmark (LHP-Rain), including 3000 video sequences with 1 million high-resolution (1920*1080) frame pairs. The advantages of the proposed dataset over the existing ones are three-fold: rain with higher-diversity and larger-scale, image with higher-resolution and higher-quality ground-truth. Specifically, the real rains in LHP-Rain not only contain the classical rain streak/veiling/occlusion in the sky, but also the splashing on the ground overlooked by deraining community. Moreover, we propose a novel robust low-rank tensor recovery model to generate the GT with better separating the static background from the dynamic rain. In addition, we design a simple transformer-based single image deraining baseline, which simultaneously utilize"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.575,
+                0.893,
+                0.635
+            ],
+            "angle": 0,
+            "content": "the self-attention and cross-layer attention within the image and rain layer with discriminative feature representation. Extensive experiments verify the superiority of the proposed dataset and deraining method over state-of-the-art."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.649,
+                0.633,
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.674,
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+                0.84
+            ],
+            "angle": 0,
+            "content": "Single image deraining is to improve the imaging quality by separating rain from image background. In recent years, significant progress has been made in learning-based single image deraining by various sophisticated CNN architectures [14, 36, 53, 10] and powerful Transformer models [35, 44]. Although these state-of-the-art supervised methods have achieved impressive results on simulated datasets, a fact cannot be ignored that those competitive methods perform unsatisfactory on diverse real rainy scenes. The core reason is the domain shift issue between the simplified synthetic rain and complex real rain [50, 32, 41, 51]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
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+            ],
+            "angle": 0,
+            "content": "To solve this problem, an intuitive idea is to try the best to make rain degradation model as real as possible [11]. The researchers formulate the rain imaging procedure into a comprehensive rain simulation model [9, 48, 12, 24, 18],"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.094,
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+            ],
+            "angle": 0,
+            "content": "These authors contributed equally to this work."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.097,
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+            ],
+            "angle": 0,
+            "content": "*Corresponding author."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+            "content": null
+        },
+        {
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+            "angle": 0,
+            "content": "12097"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.327,
+                0.09,
+                0.642,
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+            ],
+            "angle": 0,
+            "content": "Table 1: Summary of existing real rain datasets."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.105,
+                0.9,
+                0.247
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Datasets</td><td>Year</td><td>Source</td><td>Sequence</td><td>Frame</td><td>Resolution</td><td>Rain Categories</td><td>Annotation</td><td>Paired</td></tr><tr><td>RID/RIS[19]</td><td>2019</td><td>Cam/Internet</td><td>None</td><td>4.5K</td><td>640*368</td><td>streak, raindrop</td><td>Object detection</td><td>-</td></tr><tr><td>NR-IQA[43]</td><td>2020</td><td>Internet</td><td>None</td><td>0.2K</td><td>1000*680</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>Real3000[25]</td><td>2021</td><td>Internet</td><td>None</td><td>3.0K</td><td>942*654</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>FCRealRain[51]</td><td>2022</td><td>Camera</td><td>None</td><td>4.0K</td><td>4240*2400</td><td>streak, veiling</td><td>Object detection</td><td>-</td></tr><tr><td>SPA-Data[37]</td><td>2019</td><td>Cam/Internet</td><td>170</td><td>29.5K</td><td>256*256</td><td>streak</td><td>None</td><td>✓</td></tr><tr><td>RainDS[32]</td><td>2021</td><td>Cam</td><td>None</td><td>1.0K</td><td>1296*728</td><td>streak, raindrop</td><td>None</td><td>✓</td></tr><tr><td>GT-Rain[1]</td><td>2022</td><td>Internet</td><td>202</td><td>31.5K</td><td>666*339</td><td>streak, veiling</td><td>None</td><td>✓</td></tr><tr><td>RealRain-1K[20]</td><td>2022</td><td>Cam/Internet</td><td>1120</td><td>1.1K</td><td>1512*973</td><td>streak, veiling, occlusion</td><td>None</td><td>✓</td></tr><tr><td>LHP-Rain</td><td>2023</td><td>Camera</td><td>3000</td><td>1.0M</td><td>1920*1080</td><td>streak, veiling, occlusion, splashing</td><td>Object detection/Lane</td><td>✓</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.259,
+                0.473,
+                0.456
+            ],
+            "angle": 0,
+            "content": "in which different visual appearance of rain streaks[9], accumulation veiling [48], haze [12, 18], and occlusion [24] factors are taken into consideration. Unfortunately, these linear simulation models still cannot well accommodate the distribution of realistic rains. For example, in Fig. 1, realistic rain streak is usually not exactly a regular line-pattern streak but possesses irregular non-uniform in terms of the intensity and width. Apart from the rain streaks, the existing rain simulation models could not handle the complicated rain splashing on the ground, which presents as dense point-shape texture, droplets or water waves, ruining visibility of traffic signs, such as lane lines, and also causes enormous negative effects for the high-level vision."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.459,
+                0.473,
+                0.746
+            ],
+            "angle": 0,
+            "content": "Another research line obtains the 'clean' counterpart from the realistic rainy videos [37, 20], which leverages the motion discrepancy between static image background and dynamic rain. Unfortunately, they simply employ naive filtering strategies such as percentile filter [37] and median filter [20], resulting in unsatisfactory GT with residual rain or over-smoothing phenomenon. Moreover, the number and diversity of the existing real paired rain datasets are still limited. Few datasets have considered the rain splash on the ground, which is commonly observed in the real world but still rarely mentioned in deraining community. And the number of existing video sequences and image frames are not sufficient to cover diverse rains in terms of the varied rain angle, intensity, density, length, width and so on. Last but not least, the existing realistic rainy images are mostly downloaded from the Internet with low-quality: compression, watermark, low-resolution, without annotation and so on. As such, constructing a large-scale high-quality paired realistic rain dataset is highly necessary."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this work, we construct a new large-scale high-quality paired real rain benchmark. The strength of our benchmark is threefold. First, the LHP-Rain contains diverse rain categories with very large-scale, including 3000 video sequences with over 1 million frame pairs. Second, apart from the conventional streak and veiling, our benchmark is capable of removing the representative challenging ground splashing rain in the real world. Third, the LHP-Rain is collected by the smartphone with high-resolution (1920*1080 pixels) and abundant objects under self-driving and surveillance"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.259,
+                0.895,
+                0.351
+            ],
+            "angle": 0,
+            "content": "scenes are captured for comprehensive evaluation. Moreover, we propose a novel robust low-rank tensor recovery method (RLRTR) for video deraining, which can generate higher-quality GT with better rain removal from sky to the ground and image structure preserving. We summary the main contributions as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.361,
+                0.895,
+                0.452
+            ],
+            "angle": 0,
+            "content": "- We construct a large-scale high-quality paired real rain benchmark for real single image deraining. To our best knowledge, LHP-Rain is the largest paired real rain dataset (3000 video sequences, 1 million frames) with high image resolution (1920*1080), and the first benchmark to claim and tackle the problem of ground splashing rain removal."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.453,
+                0.895,
+                0.514
+            ],
+            "angle": 0,
+            "content": "- We design a novel robust low-rank tensor recovery model for video deraining to better acquire paired GT. We provide detailed analysis to show RLRTR can better differ the rain from static background than previous datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.516,
+                0.895,
+                0.593
+            ],
+            "angle": 0,
+            "content": "- We propose a new transformer-based single image de- raining baseline, which exploits both self-attention and cross-layer attention between the rain and image layer for better representation. Extensive experiments on different real datasets verify the superiority of proposed method."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.501,
+                0.361,
+                0.895,
+                0.593
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.604,
+                0.642,
+                0.62
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.895,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Real rain datasets. At present, the researchers have mostly focused on the network architecture design, while relative fewer attention has been paid on the real rain dataset. The insufficiency of realistic rain dataset is the main bottleneck to hamper single image deraining. In Table 1, we provide a comprehensive summary of existing real rain datasets, which can be classified into two categories: rainy image only and paired rain-image. The former can be utilized via semi-supervised [40, 13] or unsupervised methods [7, 51]. The latter can be conveniently utilized by the supervised training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.781,
+                0.897,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The key to paired real dataset is how to acquire the pseudo-'clean' image from its rainy counterpart. There are two main ways to construct the pairs: video-based generation (SPAData [37], RealRain-1K [20]), and time-interval acquisition (RainDS [32], GT-Rain [1]). All these datasets should ensure that the camera is strictly immobile during the acquisition process. SPA-data [37] was the first presented paired real dataset which utilized the human-supervised percentile video"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.52,
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+            "angle": 0,
+            "content": "12098"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.089,
+                0.332,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.207,
+                0.251,
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+                0.261
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.335,
+                0.089,
+                0.675,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.522,
+                0.251,
+                0.538,
+                0.261
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.696,
+                0.092,
+                0.882,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.781,
+                0.251,
+                0.797,
+                0.262
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.264,
+                0.894,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Figure 2: Features of the proposed benchmark LHP-Rain. (a) Distribution of rain and scene of the proposed benchmark. (b) Our proposed LHP-Rain outperforms others in terms of rain diversity and sequence amount. (c) LHP-Rain collects high-resolution and annotated rainy images without copyright, compression and blur."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.322,
+                0.47,
+                0.384
+            ],
+            "angle": 0,
+            "content": "filtering to obtain the GT. Instead of generation, GT-Rain [1] collected the pairs of same scene under rainy and good weather, respectively. Similar idea has been adopt in RainDS [32] by manually mimicking rainfall with a sprinkler."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.388,
+                0.47,
+                0.493
+            ],
+            "angle": 0,
+            "content": "Despite the rapid development promoted by those pioneer datasets, there remain some important issues to be solved: insufficient number and rain diversity (not consider ground splashing). In this work, we contribute a large-scale high-quality paired real rain dataset (Section 3.1) with diverse rain and abundant objects. Moreover, a novel GT generation method is proposed with higher-quality pairs (Section 3.3)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.494,
+                0.471,
+                0.705
+            ],
+            "angle": 0,
+            "content": "Single image deraining. The single image deraining methods have made great progress in last decade including the optimization models [26, 22, 4], deep convolutional network [12, 36, 10] and transformer [35, 44]. Fu et al. [9] first introduced the residual deep CNN for single image deraining. Latter, the researchers have further improved the network depth by stacking similar modules, such as the well-known recurrent [21, 49] and multi-stage progressive [33, 53] strategies. Meanwhile, the multi-scale has been widely explored to improve the representation such as the multi-scale fusion [14] and wavelet decomposition [46]. Further, the side information about the rain attribute: density [54], depth [12], directionality [38], location [47], non-local [17] have been extensively utilized to enhance the deraining performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Benefiting from self-attention mechanism for long-range relationships modelling, transformer-based methods have achieved significant performance for single image deraining [39, 35, 44, 6]. Very recently, Xiao et al.[44] proposed an image deraining transformer (IDT) with relative position enhanced and spatial-based multihead self-attention. Chen et al. [6] proposed a sparse Transformer architecture to solve the redundant feature issue. In this work, we propose a simple yet effective dual-branch transformer baseline which simultaneously utilizes the self-attention within rain/image layer and cross-layer attention between the rain and image layer, so as to jointly improve the discriminative disentanglement between the rain and image layer (Section 4)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.321,
+                0.89,
+                0.339
+            ],
+            "angle": 0,
+            "content": "3. Large-scale high-quality paired Benchmark"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.345,
+                0.816,
+                0.361
+            ],
+            "angle": 0,
+            "content": "3.1. Benchmark Collection and Statistics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.369,
+                0.894,
+                0.566
+            ],
+            "angle": 0,
+            "content": "Due to the difficulty and inconvenience of collecting real rain videos, the video sequences and frames of existing paired real rain datasets are still limited as shown in Table 1. In this work, we collect the real rain sequences by smartphones with \\(24\\mathrm{mm}\\) lens focal length, sampled in 30 fps. The data collection process is illustrated in Fig. 3(a). Firstly, to keep the camera immobile, we employ tripod to capture real rain videos with static background (no moving object except rain). For each sequence, we record approximate 15 seconds and extract the intermediate steady 10s into our dataset. Then, we manually pick out moving object to remove unexpected disturbance. Finally, we employ the proposed RLRTR (Section 3.3) to obtain high-quality GT."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.566,
+                0.895,
+                0.898
+            ],
+            "angle": 0,
+            "content": "Overall, we collect 3000 video sequences with approximate 1 million frames across 8 cities from 4 countries around the world, China (2091 sequences), England (51 sequences), Philippines and Indonesia (858 sequences). We visualize the per-country image counts and location distribution of LHP-Rain in Fig. 3(b). The rainfall levels are varied from light rain (10mm/day) to rainstorm (300mm/day) due to diversity of local climates. Over 17 typical scenes are captured, including the parking lot, street, alley, playground, courtyard, and forest, etc. Besides, 2490 sequences are captured at daytime and 510 sequences are at night. More Rainy/GT pairs from LHP-Rain are displayed in Fig. 3(c). With the changing of location, backgrounds are varied from nature to city with diverse rain patterns, such as rain streak, veiling effect, occlusion and splashing. Note that, although the background is the same for each video sequence, the rain in each frame is vastly different from the appearance, including streak, veiling, occlusion and splashing. Here we separate 2100 sequences as training set, 600 sequences as validation set and the other 300 sequences as test set. To further visualize the quantity distribution of rain and scene for each sequence, a sunburst chart is illustrated in Fig. 2(a)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12099"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.099,
+                0.092,
+                0.266,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.159,
+                0.169,
+                0.232,
+                0.18
+            ],
+            "angle": 0,
+            "content": "Same position"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.263,
+                0.094,
+                0.368,
+                0.163
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.27,
+                0.165,
+                0.361,
+                0.189
+            ],
+            "angle": 0,
+            "content": "Static background Dynamic rain"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.369,
+                0.094,
+                0.491,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.392,
+                0.169,
+                0.459,
+                0.18
+            ],
+            "angle": 0,
+            "content": "Rainy frames"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.491,
+                0.094,
+                0.576,
+                0.164
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.502,
+                0.169,
+                0.568,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Clean frames"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.587,
+                0.088,
+                0.885,
+                0.203
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.716,
+                0.194,
+                0.735,
+                0.206
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.081,
+                0.228,
+                0.092,
+                0.248
+            ],
+            "angle": 0,
+            "content": "Rnny"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.092,
+                0.209,
+                0.208,
+                0.31
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.12,
+                0.31,
+                0.188,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Guangxi, China"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.21,
+                0.209,
+                0.322,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.226,
+                0.31,
+                0.306,
+                0.32
+            ],
+            "angle": 0,
+            "content": "Guangdong, China"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.323,
+                0.209,
+                0.435,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.35,
+                0.31,
+                0.409,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Hunan, China"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.437,
+                0.209,
+                0.55,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.463,
+                0.31,
+                0.521,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Hubei, China"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.552,
+                0.209,
+                0.663,
+                0.31
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.564,
+                0.31,
+                0.646,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Manila, Philippines"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.665,
+                0.209,
+                0.777,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.682,
+                0.31,
+                0.755,
+                0.319
+            ],
+            "angle": 0,
+            "content": "London, England"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.779,
+                0.209,
+                0.892,
+                0.309
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.796,
+                0.31,
+                0.872,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Jakarta, Indonesia"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.482,
+                0.323,
+                0.501,
+                0.335
+            ],
+            "angle": 0,
+            "content": "(c)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.335,
+                0.894,
+                0.381
+            ],
+            "angle": 0,
+            "content": "Figure 3: Illustration of the proposed benchmark LHP-Rain. (a) Overall procedure of obtaining rainy/clean image pair. (b) Quantity and location distribution of LHP-Rain. (c) Rainy/GT samples of LHP-Rain from different locations. Scenes are varied from nature to city, over day and night with diverse rain patterns from sky to the ground."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.393,
+                0.275,
+                0.407
+            ],
+            "angle": 0,
+            "content": "3.2. Benchmark Features"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.415,
+                0.47,
+                0.656
+            ],
+            "angle": 0,
+            "content": "Rain with higher-diversity and larger-scale. We concern not only the sequence number and total frames but also the rain diversity of realistic rain, which both have great impact on the generalization for real-world rain. In Fig. 2(b), we show the statistic distribution of rain diversity and sequences/frames in typical real paired rain dataset. All datasets concern about the noticeable rain streak, especially SPA-data [37]. RainDS [32] additionally takes the raindrop into consideration with 1000 frames, while GT-Rain [1] and RealRain-1K [20] further capture the accumulation veiling artifact in heavy rain. LHP-Rain contains not only rain streak and veiling in the sky, but also challenging highlight occlusion and splashing water on the ground. To our best knowledge, the proposed LHP-Rain is the first benchmark to collect and tackle ground splashing rain in the real world, which is commonly ignored by previous existing datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.658,
+                0.473,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Image with higher-resolution and abundant objects. The existing datasets pay much attention to the rain, ignoring that the high-quality image is also what we really need. Unfortunately, existing realistic rainy images are generally downloaded from the Internet with various problems about the image: compression artifact, watermark, low-resolution, out-of-focus blur, without objects to name a few, which may cause challenges for high-level vision applications. In Fig. 2(c), we show the typical examples in each dataset. The image background of RealRain-1K [20] suffers from serious out-of-focus blur, since they have manually focused on the rain on purpose. GT-Rain [1] contains obvious compression artifact, since it origins from the compressed Youtube stream. There are numerous scenes with narrow views and watermark in the SPA-data [37], because they only release patches (256*256) cropped from original frames."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.499,
+                0.39,
+                0.63,
+                0.456
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.632,
+                0.39,
+                0.753,
+                0.457
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.753,
+                0.39,
+                0.887,
+                0.457
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.461,
+                0.892,
+                0.491
+            ],
+            "angle": 0,
+            "content": "Figure 4: The GT quality of LHP-Rain is superior to others on DIIVINE (lowest), NIQE (lowest) and B-FEN (highest)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.509,
+                0.895,
+                0.719
+            ],
+            "angle": 0,
+            "content": "To improve the image quality, we personally capture high-resolution (1920*1080) realistic rain videos by smartphones. Moreover, LHP-Rain is not only designed for rain restoration, but also important for object detection and segmentation tasks under adverse weather, with abundant objects which are oriented for self-driving and video surveillance scenes. Thus, we provide annotations for object detection and lane segmentation. Five typical objects including person, car, bicycle, motorcycle and bus are annotated by bounding box with 326,961 instances totally. For lane segmentation, we annotate 24,464 lane masks to evaluate the effect of rain splashing removal. Note that the same object in different frames will be regarded as different instances because rain is inconstant and changing frame by frame."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.896,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Higher-quality ground-truth. The quality of GT is critical for paired real rain dataset. It is difficult to determine what is good or bad GT in an absolutely fair way. In this paper, we assume that the better the rain removal, the better the image quality is. Therefore, we employ several no reference image quality assessments: DIIVINE [29], NIQE [28] and B-FEN [43], to evaluate the image quality of the rain-free image. The former two are hand-crafted based general image quality indexes, and the last one B-FEN is the learning based index especially designed for de-raining quality assessment. We select all the video backgrounds in SPA-data [37], GT-Rain [1], RealRain-1K [20] and LHP-Rain for evaluation. In"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12100"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.086,
+                0.895,
+                0.365
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.373,
+                0.895,
+                0.45
+            ],
+            "angle": 0,
+            "content": "Figure 5: Analysis of different video deraining results on our dataset. From left to right, the first column is the original rainy frame, and the remaining five columns represent different methods, namely Median Filter, SPA, FastDeRain, J4R-Net and the proposed RLRTR. From top to bottom, the first row shows the deraining results, the second row is the rain layer of the deraining results, the third row denotes the section line of the deraining results and the last row represents the horizontal and vertical gradient distributions of the deraining results."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.461,
+                0.475,
+                0.508
+            ],
+            "angle": 0,
+            "content": "Fig. 4, we can observe that the proposed LHP-Rain consistently obtains the best results in terms of different evaluation indexes which strongly support the higher-quality of the GT."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.518,
+                0.436,
+                0.535
+            ],
+            "angle": 0,
+            "content": "3.3. Robust Low-rank Tensor Recovery Model"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.54,
+                0.471,
+                0.663
+            ],
+            "angle": 0,
+            "content": "Given the rainy video \\(\\mathcal{O} \\in \\mathbb{R}^{h \\times w \\times t}\\), the key is how to properly obtain the paired GT. The existing methods simply employ the naive filtering technique benefiting from the temporal consistency of the static background. Due to the slight camera vibration caused by the wild wind, we further leverage an affine transformation operator \\(\\tau\\) [52] to achieve the pixel-level alignment of each frame. Thus, a multi-frame rainy video can be described as the following formula:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.198,
+                0.669,
+                0.47,
+                0.686
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {O} \\circ \\tau = \\mathcal {B} + \\mathcal {R} + \\mathcal {N}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.688,
+                0.472,
+                0.779
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{B} \\in \\mathbb{R}^{h \\times w \\times t}\\) is the rain-free video, \\(\\mathcal{R} \\in \\mathbb{R}^{h \\times w \\times t}\\) represents the rains, \\(\\mathcal{N} \\in \\mathbb{R}^{h \\times w \\times t}\\) denotes the random noise, and \\(\\tau\\) denotes the affine transformation to ensure the rainy video of each frame is pixel-level aligned. In this work, we formulate the video deraining into inverse problem via the maximum-a-posterior as follow:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.096,
+                0.78,
+                0.47,
+                0.809
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\mathcal {B}, \\mathcal {R}, \\tau} \\frac {1}{2} | | \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau | | _ {F} ^ {2} + \\omega P _ {b} (\\mathcal {B}) + \\mu P _ {r} (\\mathcal {R}), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(P_{b}\\) and \\(P_{r}\\) are the prior knowledge for the image and rain, respectively, \\(\\omega\\) and \\(\\mu\\) are the corresponding hyperparameters. As for the aligned rainy video, when there are no moving objects except the rain, the rain-free background image is the same for all rainy frames. That is to say, clean video \\(\\mathcal{B}\\) has extreme global low-rank property along the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.461,
+                0.895,
+                0.598
+            ],
+            "angle": 0,
+            "content": "temporal dimension, ideally its rank is equal to one for each scene. On the other hand, the clean video \\(\\mathcal{B}\\) also has very non-local low-rank property along the spatial dimension, due to the self-similarity widely employed in image restoration [8]. Moreover, we further take the local smoothness of the video \\(\\mathcal{B}\\) into consideration via the total variation (TV) regularization [4]. Thus, the joint global-nonlocal-local prior along both the spatial and temporal dimension has been fully exploited for better representation of the static video \\(\\mathcal{B}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.508,
+                0.603,
+                0.892,
+                0.627
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {b} (\\mathcal {B}) = \\omega \\sum_ {i} \\left(\\frac {1}{\\lambda_ {i} ^ {2}} | | \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} | | _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}\\right) + \\gamma | | \\nabla_ {t} \\mathcal {B} | | _ {1}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.634,
+                0.895,
+                0.803
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{S}_i\\mathcal{B}\\in \\mathbb{R}^{p^2\\times k\\times t}\\) is the constructed 3-D tensor via the non-local clustering of a sub-cubic \\(u_{i}\\in \\mathbb{R}^{p\\times p\\times t}\\) [3], \\(p\\) and \\(k\\) are the spatial size and number of the sub-cubic respectively, \\(Q_{i}\\in \\mathbb{R}^{d\\times t}(d\\ll t)\\) is an orthogonal subspace projection matrix used to capture the temporal low-rank property, \\(\\times_3\\) is the tensor product along the temporal dimension [16], \\(\\mathcal{I}_i\\) represents the low-rank approximation variable, \\(||\\bullet ||_{ttn}\\) means the tensor nuclear norm for simplicity [3], \\(\\nabla_t\\) is the difference operator, \\(\\gamma\\) and \\(\\lambda_{i}\\) is the regularization parameters. As for the rain \\(\\mathcal{R}\\), we formulate it as the sparse error [42] via the \\(L_{1}\\) sparsity. Thus, the Eq. (2) can be expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.516,
+                0.806,
+                0.892,
+                0.856
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\left\\{\\hat {\\mathcal {B}}, \\hat {\\mathcal {R}}, \\hat {\\mathcal {J}} _ {i}, \\hat {\\tau}, \\hat {Q} _ {i} \\right\\} = \\arg \\min  _ {\\mathcal {B}, \\mathcal {R}, \\mathcal {J} _ {i}, \\tau , Q _ {i}} \\frac {1}{2} \\| \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau \\| _ {F} ^ {2} \\tag {4} \\\\ + \\mu | | \\mathcal {R} | | _ {1} + \\omega \\sum_ {i} \\left(\\frac {1}{\\lambda_ {i} ^ {2}} | | \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} | | _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}\\right) + \\gamma | | \\nabla_ {t} \\mathcal {B} | | _ {1}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.862,
+                0.895,
+                0.893
+            ],
+            "angle": 0,
+            "content": "Optimization. Due to the difficulty of estimating multiple variables directly, we adopt the alternating minimization"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.518,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12101"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.089,
+                0.895,
+                0.135
+            ],
+            "angle": 0,
+            "content": "Table 2: Quantitative comparisons with SOTA supervised methods on paired real datasets SPA-data (A), GT-Rain (B) and proposed LHP-Rain (C) under 9 different task settings. X→Y means training on the dataset X and testing on the dataset Y. The degraded results of the three datasets are also provided. Top \\(1_{st}\\) and \\(2_{nd}\\) results are marked in red and blue respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.085,
+                0.136,
+                0.88,
+                0.319
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">A→A</td><td colspan=\"2\">B→A</td><td colspan=\"2\">C→A</td><td colspan=\"2\">A→B</td><td colspan=\"2\">B→B</td><td colspan=\"2\">C→B</td><td colspan=\"2\">A→C</td><td colspan=\"2\">B→C</td><td colspan=\"2\">C→C</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>Rainy Image</td><td colspan=\"6\">32.60 / 0.9173</td><td colspan=\"6\">19.48 / 0.5849</td><td colspan=\"6\">29.97 / 0.8497</td></tr><tr><td>SPANet</td><td>38.53</td><td>0.9875</td><td>22.93</td><td>0.8207</td><td>31.46</td><td>0.9612</td><td>20.01</td><td>0.6148</td><td>21.51</td><td>0.7145</td><td>19.20</td><td>0.5706</td><td>28.00</td><td>0.8905</td><td>20.10</td><td>0.8061</td><td>31.19</td><td>0.9346</td></tr><tr><td>PReNet</td><td>37.05</td><td>0.9696</td><td>22.44</td><td>0.7713</td><td>32.46</td><td>0.9387</td><td>20.29</td><td>0.5860</td><td>20.65</td><td>0.6005</td><td>19.34</td><td>0.5530</td><td>27.57</td><td>0.8595</td><td>20.91</td><td>0.7222</td><td>32.13</td><td>0.9177</td></tr><tr><td>RCDNet</td><td>39.74</td><td>0.9661</td><td>22.51</td><td>0.8392</td><td>32.30</td><td>0.9378</td><td>20.09</td><td>0.5785</td><td>21.04</td><td>0.6106</td><td>19.09</td><td>0.5264</td><td>25.46</td><td>0.7959</td><td>21.38</td><td>0.8047</td><td>32.34</td><td>0.9152</td></tr><tr><td>JORDER-E</td><td>40.63</td><td>0.9794</td><td>23.47</td><td>0.7426</td><td>31.23</td><td>0.9234</td><td>19.98</td><td>0.5799</td><td>21.24</td><td>0.6854</td><td>18.76</td><td>0.4861</td><td>27.13</td><td>0.8531</td><td>22.14</td><td>0.8433</td><td>31.24</td><td>0.8847</td></tr><tr><td>MPRNet</td><td>46.06</td><td>0.9894</td><td>24.27</td><td>0.8428</td><td>32.37</td><td>0.9379</td><td>19.87</td><td>0.6286</td><td>22.00</td><td>0.6515</td><td>19.47</td><td>0.5889</td><td>28.41</td><td>0.8807</td><td>23.82</td><td>0.8052</td><td>33.34</td><td>0.9309</td></tr><tr><td>GT-Rain</td><td>37.21</td><td>0.9827</td><td>25.30</td><td>0.9243</td><td>26.46</td><td>0.9145</td><td>20.07</td><td>0.6941</td><td>22.51</td><td>0.7300</td><td>21.14</td><td>0.5698</td><td>28.62</td><td>0.8675</td><td>23.19</td><td>0.8098</td><td>32.18</td><td>0.9132</td></tr><tr><td>Uformer-B</td><td>46.42</td><td>0.9917</td><td>24.08</td><td>0.8979</td><td>32.21</td><td>0.9667</td><td>19.70</td><td>0.6875</td><td>21.60</td><td>0.7124</td><td>19.10</td><td>0.6622</td><td>28.74</td><td>0.9262</td><td>22.91</td><td>0.8734</td><td>33.56</td><td>0.9317</td></tr><tr><td>IDT</td><td>45.74</td><td>0.9889</td><td>23.80</td><td>0.8334</td><td>32.38</td><td>0.9422</td><td>20.34</td><td>0.6306</td><td>21.98</td><td>0.6536</td><td>19.44</td><td>0.5977</td><td>26.90</td><td>0.8742</td><td>23.34</td><td>0.7897</td><td>33.02</td><td>0.9310</td></tr><tr><td>SCD-Former</td><td>46.89</td><td>0.9941</td><td>26.13</td><td>0.9122</td><td>34.38</td><td>0.9798</td><td>20.98</td><td>0.6985</td><td>22.79</td><td>0.7684</td><td>21.71</td><td>0.6893</td><td>29.41</td><td>0.9127</td><td>23.56</td><td>0.8626</td><td>34.33</td><td>0.9468</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.333,
+                0.455,
+                0.347
+            ],
+            "angle": 0,
+            "content": "scheme to solve the Eq. (4) with respect to each variable."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.348,
+                0.47,
+                0.453
+            ],
+            "angle": 0,
+            "content": "1) Affine Transformation \\(\\tau\\): Since \\(\\mathcal{O} \\circ \\tau\\) is a nonlinear geometric transform, it's difficult to directly optimize \\(\\tau\\). A common technique is to linearize around the current estimate and iterate as follows: \\(\\mathcal{O} \\circ \\tau + \\nabla \\mathcal{O} \\triangle \\tau = \\mathcal{B} + \\mathcal{R} + \\mathcal{N}\\) [31], where \\(\\nabla \\mathcal{O}\\) is the Jacobian of the image \\(\\mathcal{O}\\) with respect to \\(\\tau\\). This method iteratively approximates the original nonlinear transformation with a locally linear approximation [31]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.454,
+                0.47,
+                0.484
+            ],
+            "angle": 0,
+            "content": "2) Rain Estimation \\(\\mathcal{R}\\): By ignoring variables independent of \\(\\mathcal{R}\\), we can obtain following subproblem:"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.348,
+                0.47,
+                0.484
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.097,
+                0.49,
+                0.47,
+                0.515
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathcal {R}} = \\arg \\min _ {\\mathcal {R}} \\frac {1}{2} | | \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau | | _ {F} ^ {2} + \\mu | | \\mathcal {R} | | _ {1}. (5)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.52,
+                0.469,
+                0.551
+            ],
+            "angle": 0,
+            "content": "Eq. (5) is a \\(L_{1}\\) minimization problem which can be easily solved by soft thresholding with closed-form solution [23]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.551,
+                0.469,
+                0.581
+            ],
+            "angle": 0,
+            "content": "3) Subspace Projection \\( Q_{i} \\): We enforce the orthogonal constraint on \\( Q_{i}^{T}Q_{i} = I \\) with the following subproblem:"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.52,
+                0.469,
+                0.581
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.132,
+                0.587,
+                0.469,
+                0.619
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {Q} _ {i} = \\arg \\min  _ {Q _ {i} ^ {T} Q _ {i} = I} \\frac {1}{\\lambda_ {i} ^ {2}} \\left\\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\right\\| _ {F} ^ {2}. \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.625,
+                0.47,
+                0.7
+            ],
+            "angle": 0,
+            "content": "According to [45], Eq. (6) has the closed-form solution, which can be obtained by the rank- \\(d\\) singular value decomposition of the folding matrix of \\(\\mathcal{S}_i\\mathcal{B}\\), where \\(d\\) is the measurement of the intrinsic subspace of the temporal dimension. In this work, we empirically set \\(d \\leq 3\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.701,
+                0.469,
+                0.731
+            ],
+            "angle": 0,
+            "content": "4) Low-rank Approximation \\(\\mathcal{J}_i\\): Dropping the irrelevant variables, we can get following subproblem:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.094,
+                0.736,
+                0.469,
+                0.761
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\mathcal {J}} _ {i} = \\arg \\min  _ {\\mathcal {J} _ {i}} \\frac {1}{\\lambda_ {i} ^ {2}} \\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\| _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}. \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.767,
+                0.47,
+                0.797
+            ],
+            "angle": 0,
+            "content": "This is a typical tensor nuclear norm minimization problem, can be solved by singular value thresholding algorithm [2, 3]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.797,
+                0.47,
+                0.827
+            ],
+            "angle": 0,
+            "content": "5) Clean Video Estimation \\(\\mathcal{B}\\): We fix the other variables and optimize \\(\\mathcal{B}\\) with the following subproblem:"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.767,
+                0.47,
+                0.827
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.094,
+                0.835,
+                0.469,
+                0.855
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\mathcal {B}} \\frac {1}{2} \\| \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau \\| _ {F} ^ {2} + \\omega \\sum_ {i} \\frac {1}{\\lambda_ {i} ^ {2}} \\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\| _ {F} ^ {2} + \\gamma \\| \\nabla_ {t} \\mathcal {B} \\| _ {1}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.861,
+                0.469,
+                0.891
+            ],
+            "angle": 0,
+            "content": "Due to the non-differentiability of the \\(L_{1}\\) norm in Eq. (8), we apply the ADMM [23] to decouple this problem into several"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.33,
+                0.892,
+                0.474
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.474,
+                0.892,
+                0.519
+            ],
+            "angle": 0,
+            "content": "Figure 6: Overall framework of the SCD-Former. It utilizes self and cross-layer attention from rain layer to image layer which serves as side information to recover image layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.535,
+                0.892,
+                0.565
+            ],
+            "angle": 0,
+            "content": "sub-problems with closed-form solutions. Please refer to the supplementary material for the whole algorithm details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.566,
+                0.893,
+                0.897
+            ],
+            "angle": 0,
+            "content": "Discussion. Figure 5 illustrates the comparison results of representative video deraining methods: filter-based methods (median filter[20], SPA[37]), optimization-based (FastDeRain[15]) and learning-based methods (J4R-Net[24]). The first and second rows show the video deraining of the image and rain layer, respectively. RLRTR removes almost all the rain from sky to the ground, including rain streaks and splashing, and preserve the image details well, while other methods more or less have rain streaks residual but also cause noticeable damage to the image. In third row, we randomly choose two 1D section lines of the deraining results. The section line of RLRTR is smoother with less burr than other methods. Moreover, the SPA, FastDeRain and the J4R-Net unexpectedly attenuate the spike signal of the share edge, while the proposed RLRTR has well preserve the spike signal. It is well-known the natural image is isotropic and its gradient distribution along different directions should be close to each other [34]. Compared with other results, in forth row the gradient distributions along the vertical and horizontal directions of RLRTR are most similar to each other, which further indirectly verify the naturalness of the deraining result and produce better paired clean-rainy GT."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12102"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.116,
+                0.244,
+                0.354
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.125,
+                0.356,
+                0.193,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Rainy Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.245,
+                0.116,
+                0.408,
+                0.355
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.295,
+                0.356,
+                0.358,
+                0.366
+            ],
+            "angle": 0,
+            "content": "JORDER-E"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.409,
+                0.116,
+                0.569,
+                0.355
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.463,
+                0.356,
+                0.512,
+                0.366
+            ],
+            "angle": 0,
+            "content": "MPRNet"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.569,
+                0.116,
+                0.725,
+                0.355
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.633,
+                0.356,
+                0.656,
+                0.366
+            ],
+            "angle": 0,
+            "content": "IDT"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.725,
+                0.116,
+                0.888,
+                0.355
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.773,
+                0.356,
+                0.843,
+                0.366
+            ],
+            "angle": 0,
+            "content": "SCD-Former"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.369,
+                0.89,
+                0.4
+            ],
+            "angle": 0,
+            "content": "Figure 7: Visual comparisons on LHP-Rain. Comparing with state-of-the-arts, SCD-Former achieves more visual pleasing deraining results and it is capable of removing the highlight occlusion on the car and the splashing water on the ground."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.41,
+                0.439,
+                0.428
+            ],
+            "angle": 0,
+            "content": "4. SCD-Former: Image Deraining Baseline"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.436,
+                0.421,
+                0.451
+            ],
+            "angle": 0,
+            "content": "The degradation procedure can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.232,
+                0.453,
+                0.469,
+                0.468
+            ],
+            "angle": 0,
+            "content": "\\[\nO = B + R. \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.471,
+                0.47,
+                0.651
+            ],
+            "angle": 0,
+            "content": "It has been proved that the rain such as location [47] serving as an attention would be informative in CNN-based image restoration. In this work, we show the rain attention would also be beneficial in transformer. In Fig. 6, we design a simple two-stream Self- and Cross-attention Deraining Transformer (SCD-Former), in which the two-stream network is designed to restore rain and image layer respectively. On one hand, we utilize the self-attention in each rain/image stream independently; on the other hand, we further exploit the cross-layer attention between the rain and image streams. Thus, the rain collaboratively interactive with the image layer to further improve the discriminative representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.653,
+                0.47,
+                0.77
+            ],
+            "angle": 0,
+            "content": "Self-attention and cross-layer attention. In this work, we exploit self-attention on rain and image layer as Rain layer Self-Attention (RSA) and Image layer Self-Attention (ISA). Given the input feature \\( X \\), it will be projected into query \\( (Q) \\), key \\( (K) \\) and value \\( (V) \\) by three learnable weight matrices \\( W_{q} \\), \\( W_{k} \\) and \\( W_{v} \\). Then dot-product, scaling and softmax among \\( Q \\), \\( K \\) and \\( V \\) will be conducted. The self-attention function is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.142,
+                0.769,
+                0.469,
+                0.802
+            ],
+            "angle": 0,
+            "content": "\\[\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V. \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.803,
+                0.469,
+                0.863
+            ],
+            "angle": 0,
+            "content": "We further design a Cross-Layer Attention (CLA) module which bridges the attention relationship between rain and image layer. The CLA conducts attention operation among \\( Q_{r} \\) from rain layer and \\( K_{b}, V_{b} \\) from image layer as follow:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.864,
+                0.469,
+                0.899
+            ],
+            "angle": 0,
+            "content": "\\[\nC L A \\left(Q _ {r}, K _ {b}, V _ {b}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {r} K _ {b} {} ^ {T}}{\\sqrt {d _ {k}}}\\right) V _ {b}. \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.412,
+                0.895,
+                0.562
+            ],
+            "angle": 0,
+            "content": "The token of rain layer serves as a query token \\( Q_{r} \\) to interact with the patch tokens \\( K_{b} \\) and \\( V_{b} \\) from the image layer through attention mechanism. By calculating the correlation degree between both layers, the highly attentive location of rain residual can be acquired, which provides an extra prior for enhanced feature representation. Note that, the CLA module has been stacked over the whole network. Compared with previous work, SCD-Former exploits not only the self-attention but also cross-layer attention of the rain and image layer for better restoration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.563,
+                0.892,
+                0.608
+            ],
+            "angle": 0,
+            "content": "Implementation details. We train the network using the Charbonnier loss[5] supervised by the ground truth of rain and image layer:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.508,
+                0.609,
+                0.892,
+                0.627
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\left| \\left| O - B - R \\right| \\right| _ {F} ^ {2} + \\lambda_ {r} \\left| \\left| R - \\hat {R} \\right| \\right| _ {1} + \\lambda_ {b} \\left| \\left| B - \\hat {B} \\right| \\right| _ {1}. \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.628,
+                0.894,
+                0.704
+            ],
+            "angle": 0,
+            "content": "The framework is implemented with two RTX 3090 GPUs. We set the hyperparameter \\(\\lambda_{b}\\) and \\(\\lambda_{r}\\) as 1. The images are randomly cropped into \\(256*256\\) for training. The learning rate of network is set as 0.0002. The Adam optimizer is adopted for optimization with a batch size of 32."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.713,
+                0.633,
+                0.73
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets. We conduct the experiments on paired datasets SPA-data[37], GT-Rain[1] and LHP-Rain. For the SPA-data, training set is cropped from 29,500 images and 1000 rainy images are used for testing. For the GT-Rain, 89 sequences are used for training and 7 sequences are used for testing. For the LHP-Rain, 2100 sequences are used for training and 300 sequences are used for testing. To evaluate the deraining performance on real scenes, we choose typical real rainy images from Internet-data. For single image deraining methods, we select the representative supervised deraining methods, including the CNN-based SPANet[37],"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12103"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.895,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.262,
+                0.895,
+                0.293
+            ],
+            "angle": 0,
+            "content": "Figure 8: Evaluation of the diversity of the LHP-Rain. We train SCD-Former on different datasets: Rain100L, SPA-data, GT-Rain and LHP-Rain, and test on other datasets. The model trained on LHP-Rain has achieved better deraining results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.301,
+                0.47,
+                0.407
+            ],
+            "angle": 0,
+            "content": "PReNet[33], RCDNet[36], JORDER-E[47], MPRNet[27], GT-Rain[1], transformer-based Uformer[39] and IDT[44]. Evaluation metrics. We employ the full-reference PSNR and SSIM to evaluate the single image deraining results. Moreover, mean Average Precision (mAP) and Accuracy (Acc) are employed to evaluate object detection and lane segmentation after restoration by deraining methods."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.411,
+                0.3,
+                0.427
+            ],
+            "angle": 0,
+            "content": "5.1. Quantitative Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.434,
+                0.474,
+                0.601
+            ],
+            "angle": 0,
+            "content": "Deraining results on benchmarks. We make comparisons with state-of-the-art deraining methods on three datasets SPA-data (A), GT-Rain (B) and LHP-Rain (C). The quantitative results are reported in Table 2 under the following columns: \\(\\mathrm{A}\\rightarrow \\mathrm{A}\\), \\(\\mathrm{B}\\rightarrow \\mathrm{B}\\) and \\(\\mathrm{C}\\rightarrow \\mathrm{C}\\). It is observed that transformer-based methods perform better than most CNN-based methods except for MPRNet in terms of PSNR and SSIM because of the superior representation of self-attention. Note that SCD-Former outperforms the existing state-of-the-art methods on all benchmarks, which confirms the effectiveness of our method with both self and cross-layer attention."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.606,
+                0.289,
+                0.621
+            ],
+            "angle": 0,
+            "content": "5.2. Qualitative Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.629,
+                0.47,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Evaluation on LHP-Rain. To further validate the deraining performance, we compare with the qualitative results of typical methods on LHP-Rain. As shown in Fig. 7, SCD-Former achieves more visual pleasing results without rain residual and artifacts comparing with other methods, which cleans the rain streaks and veiling effect on the trees, highlight occlusion on the red car and the ground splashing water."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Evaluation on real rainy images. To evaluate the performance on real rainy images, we train SCD-Former on synthetic rain Rain100L[48], real rain SPA-data, GT-Rain and LHP-Rain respectively and test on real rainy images. As shown in Fig. 8, the model trained on Rain100L performs poorly due to the huge domain gap. SPA-data and GT-Rain could remove real rain in the sky partially but they cannot handle the splashing water on the ground. The model trained on LHP-Rain has the best deraining performance which simultaneously removes rain streaks, veiling and ground splashing water without destroying image details."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.299,
+                0.895,
+                0.389
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.392,
+                0.895,
+                0.481
+            ],
+            "angle": 0,
+            "content": "Figure 9: Ablation study of the robust low-rank tensor recovery model. The first row represents the deraining results, and the second row is corresponding rain. The first column is the original rainy frame and the remaining three columns represent the model without subspace projection, without affine transformation and full RLRTR."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.537,
+                0.485,
+                0.855,
+                0.5
+            ],
+            "angle": 0,
+            "content": "Table 3: Ablation study of cross-layer attention."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.574,
+                0.505,
+                0.813,
+                0.556
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Cross-layer attention</td><td>PSNR / SSIM</td></tr><tr><td>-</td><td>33.92 0.9384</td></tr><tr><td>✓</td><td>34.33 0.9403</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.561,
+                0.655,
+                0.577
+            ],
+            "angle": 0,
+            "content": "5.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.584,
+                0.895,
+                0.704
+            ],
+            "angle": 0,
+            "content": "Effectiveness of subspace projection. The subspace projection is used to characterize the extreme global low-rank property along the temporal dimension. In Fig. 9, there are obvious rain residual without subspace projection, implying that it is insufficient to characterize the property of the temporal dimension relying on the local prior of the temporal smoothness. Since the temporal low-rank property is neglected, leading to the rain residual in the results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.895,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Effectiveness of affine transformation. The affine transformation is exerted to guarantee the pixel-level alignment of rainy video. As shown in Fig. 9, it can be observed that background residual and distortion obviously exist in the rain layer without affine transformation, because the extreme low-rank property along the temporal dimension is affected by data alignment among each frame in the video."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.895,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Effectiveness of cross-layer attention. The design aims to find the correlations between rain layer and image layer. After iterations, the image layer sub-network obtains more attention on the rain features brought by cross-layer attention. In Table 3, We show that the complementary guidance from rain layer promotes the restoration of image layer."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.925,
+                0.52,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12104"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.115,
+                0.09,
+                0.175,
+                0.099
+            ],
+            "angle": 0,
+            "content": "Rainy Image"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.249,
+                0.09,
+                0.303,
+                0.098
+            ],
+            "angle": 0,
+            "content": "JORDER-E"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.099,
+                0.209,
+                0.226
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.211,
+                0.099,
+                0.339,
+                0.226
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.342,
+                0.09,
+                0.468,
+                0.226
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.229,
+                0.471,
+                0.29
+            ],
+            "angle": 0,
+            "content": "Figure 10: Evaluation of high-level tasks on lane segmentation and object detection. The performance improves significantly after removing rain streak and ground splashing from lanes and bicycles by our proposed SCD-Former."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.078,
+                0.3,
+                0.468,
+                0.314
+            ],
+            "angle": 0,
+            "content": "Table 4: Evaluation of high-level tasks on deraining results."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.09,
+                0.315,
+                0.451,
+                0.442
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Det. (mAP)</td><td>Gain (Det.)</td><td>Seg. (Acc)</td><td>Gain (Seg.)</td></tr><tr><td>Rainy</td><td>0.543</td><td>-</td><td>0.237</td><td>-</td></tr><tr><td>SPANet</td><td>0.563</td><td>+0.020</td><td>0.268</td><td>+0.031</td></tr><tr><td>PReNet</td><td>0.560</td><td>+0.022</td><td>0.255</td><td>+0.018</td></tr><tr><td>RCDNet</td><td>0.556</td><td>+0.018</td><td>0.361</td><td>+0.124</td></tr><tr><td>JORDER-E</td><td>0.568</td><td>+0.025</td><td>0.385</td><td>+0.148</td></tr><tr><td>MPRNet</td><td>0.560</td><td>+0.017</td><td>0.350</td><td>+0.113</td></tr><tr><td>Uformer-B</td><td>0.568</td><td>+0.025</td><td>0.306</td><td>+0.069</td></tr><tr><td>IDT</td><td>0.570</td><td>+0.027</td><td>0.365</td><td>+0.128</td></tr><tr><td>SCD-Former</td><td>0.575</td><td>+0.031</td><td>0.449</td><td>+0.212</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.455,
+                0.195,
+                0.469
+            ],
+            "angle": 0,
+            "content": "5.4. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.478,
+                0.47,
+                0.659
+            ],
+            "angle": 0,
+            "content": "Rain diversity of different datasets. The rain diversity of dataset can be validated by the experiment of training models on one dataset and testing on the other unseen datasets among SPA-data (A), GT-Rain (B) and LHP-Rain (C). As shown in Table 2, on one hand, the best results of \\(\\mathrm{C} \\rightarrow \\mathrm{A}\\) methods positively improve the performance of A, while all \\(\\mathrm{A} \\rightarrow \\mathrm{C}\\) results performing worse than degraded result of C. On the other hand, the best results of \\(\\mathrm{C} \\rightarrow \\mathrm{B}\\) have promotion while \\(\\mathrm{B} \\rightarrow \\mathrm{C}\\) drop severely. Therefore, the outcome proves that our LHP-Rain contains more diverse rain categories than others, because they could not handle extreme challenging cases such as occlusion and ground splashing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.66,
+                0.47,
+                0.856
+            ],
+            "angle": 0,
+            "content": "Evaluation on downstream tasks. We further evaluate the image deraining results on high-level tasks. For object detection, we apply the officialYOLOv5 model on deraning results and report the mean average precision (mAP) of different classes in Table 4, where SCD-Former reaches the best average mAP among typical objects. For lane segmentation, we choose the LaneNet[30] to predict the lane on LHP-Rain and SCD-Former has larger promotion on the segmentation accuracy. It is reasonable because SCD-Former performs well on removing ground splashing water and recovering the lane lines. The visualization results in Fig. 10 shows that the lane on the surface of ground and the bicycles could be properly predicted after deraining by SCD-Former."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "User study on benchmarks quality. We look for 126 volunteers to anonymously vote for the benchmark with best quality. Among existing benchmarks, we randomly select"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.082,
+                0.697,
+                0.171
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.563,
+                0.172,
+                0.633,
+                0.182
+            ],
+            "angle": 0,
+            "content": "(a) Rainy Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.701,
+                0.082,
+                0.892,
+                0.171
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.759,
+                0.172,
+                0.836,
+                0.182
+            ],
+            "angle": 0,
+            "content": "(b) RLRTR Result"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.188,
+                0.895,
+                0.234
+            ],
+            "angle": 0,
+            "content": "Figure 11: The limitation of RLRTR. The challenging occlusion effect could be removed by RLRTR from the background while the static haze is preserved."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.551,
+                0.245,
+                0.84,
+                0.259
+            ],
+            "angle": 0,
+            "content": "Table 5: User study on benchmarks quality."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.524,
+                0.26,
+                0.862,
+                0.322
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>LHP-Rain</td><td>SPA</td><td>RealRain1K</td><td>GT-Rain</td></tr><tr><td>Rain diversity</td><td>63%</td><td>8%</td><td>13%</td><td>16%</td></tr><tr><td>Image quality</td><td>51%</td><td>14%</td><td>20%</td><td>15%</td></tr><tr><td>GT quality</td><td>55%</td><td>15%</td><td>16%</td><td>14%</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.333,
+                0.894,
+                0.393
+            ],
+            "angle": 0,
+            "content": "100 samples and conduct user study including: rain diversity, image quality (resolution, JEPG, blur) and GT quality. The result is listed in Table 5, where LHP-Rain consistently outperforms other benchmarks more than \\(50\\%\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.406,
+                0.614,
+                0.421
+            ],
+            "angle": 0,
+            "content": "6. Limitation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.428,
+                0.895,
+                0.58
+            ],
+            "angle": 0,
+            "content": "Our proposed video deraining method is limited to remove the haze in the heavy rain scenes. RLRTR is adept at separating the static background from the dynamic rain. However, due to the steadiness of mist in the short interval, which is almost motionless in the background, RLRTR cannot decompose the haze from image layer well. Fig. 11 shows examples of rain and mist in our benchmark. Although the challenging rain patterns such as rain streaks are clearly removed, the result still contains haze. We look forward to handling the static haze in the future."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.589,
+                0.619,
+                0.604
+            ],
+            "angle": 0,
+            "content": "7. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.614,
+                0.894,
+                0.811
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a large-scale and high-quality paired real rain benchmark. Our proposed LHP-Rain provides diverse rain categories, especially the ground splashing rain issue which is first claimed in deraining community. The model trained on LHP-Rain could generalize well on various real rainy scenes with great rain removal performance. Moreover, the proposed low-rank tensor recovery model could generate high-quality GT and detailed analysis confirms better results than others. In addition, we propose a single deraining baseline which performs well on removing rain from sky to the ground. Extensive experiments verify the superiority of the proposed benchmark and significantly improves segmentation task after removing splashing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.894,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work was supported in part by the National Natural Science Foundation of China under Grant 61971460 and Grant 62101294, in part by JCJQ Program under Grant 2021-JCJQ-JJ-0060 and in part by the Fundamental Research Funds for the Central Universities, HUST: 2022JYCXJJ001."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.925,
+                0.519,
+                0.937
+            ],
+            "angle": 0,
+            "content": "12105"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.106
+            ],
+            "angle": 0,
+            "content": "References"
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+        {
+            "type": "ref_text",
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+            ],
+            "angle": 0,
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+# From Sky to the Ground: A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal
+
+Yun Guo $^{1,\dagger}$ , Xueyao Xiao $^{1,\dagger}$ , Yi Chang $^{1,*}$ , Shumin Deng $^{1}$ , Luxin Yan $^{1}$
+
+$^{1}$ National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, China {guoyun, xiaoxueyao, yichang, shumindeng, yanluxin}@hust.edu.cn https://github.com/yunguo224/LHP-Rain
+
+![](images/30aa67fbe8f6346863f56091c9d9defcfa83ae0ca98863e9cef5608cbb45d0f4.jpg)  
+Figure 1: Illustration of the proposed paired rainy/clean images dataset. The proposed real rain dataset is to cope with various rain categories, such as rain streaks, veiling effect, occlusion, and ground splashing. We recommend zooming in the figure on PC for better visualization.
+
+# Abstract
+
+Learning-based image deraining methods have made great progress. However, the lack of large-scale high-quality paired training samples is the main bottleneck to hamper the real image deraining (RID). To address this dilemma and advance RID, we construct a Large-scale High-quality Paired real rain benchmark (LHP-Rain), including 3000 video sequences with 1 million high-resolution (1920*1080) frame pairs. The advantages of the proposed dataset over the existing ones are three-fold: rain with higher-diversity and larger-scale, image with higher-resolution and higher-quality ground-truth. Specifically, the real rains in LHP-Rain not only contain the classical rain streak/veiling/occlusion in the sky, but also the splashing on the ground overlooked by deraining community. Moreover, we propose a novel robust low-rank tensor recovery model to generate the GT with better separating the static background from the dynamic rain. In addition, we design a simple transformer-based single image deraining baseline, which simultaneously utilize
+
+the self-attention and cross-layer attention within the image and rain layer with discriminative feature representation. Extensive experiments verify the superiority of the proposed dataset and deraining method over state-of-the-art.
+
+# 1. Introduction
+
+Single image deraining is to improve the imaging quality by separating rain from image background. In recent years, significant progress has been made in learning-based single image deraining by various sophisticated CNN architectures [14, 36, 53, 10] and powerful Transformer models [35, 44]. Although these state-of-the-art supervised methods have achieved impressive results on simulated datasets, a fact cannot be ignored that those competitive methods perform unsatisfactory on diverse real rainy scenes. The core reason is the domain shift issue between the simplified synthetic rain and complex real rain [50, 32, 41, 51].
+
+To solve this problem, an intuitive idea is to try the best to make rain degradation model as real as possible [11]. The researchers formulate the rain imaging procedure into a comprehensive rain simulation model [9, 48, 12, 24, 18],
+
+Table 1: Summary of existing real rain datasets.  
+
+<table><tr><td>Datasets</td><td>Year</td><td>Source</td><td>Sequence</td><td>Frame</td><td>Resolution</td><td>Rain Categories</td><td>Annotation</td><td>Paired</td></tr><tr><td>RID/RIS[19]</td><td>2019</td><td>Cam/Internet</td><td>None</td><td>4.5K</td><td>640*368</td><td>streak, raindrop</td><td>Object detection</td><td>-</td></tr><tr><td>NR-IQA[43]</td><td>2020</td><td>Internet</td><td>None</td><td>0.2K</td><td>1000*680</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>Real3000[25]</td><td>2021</td><td>Internet</td><td>None</td><td>3.0K</td><td>942*654</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>FCRealRain[51]</td><td>2022</td><td>Camera</td><td>None</td><td>4.0K</td><td>4240*2400</td><td>streak, veiling</td><td>Object detection</td><td>-</td></tr><tr><td>SPA-Data[37]</td><td>2019</td><td>Cam/Internet</td><td>170</td><td>29.5K</td><td>256*256</td><td>streak</td><td>None</td><td>✓</td></tr><tr><td>RainDS[32]</td><td>2021</td><td>Cam</td><td>None</td><td>1.0K</td><td>1296*728</td><td>streak, raindrop</td><td>None</td><td>✓</td></tr><tr><td>GT-Rain[1]</td><td>2022</td><td>Internet</td><td>202</td><td>31.5K</td><td>666*339</td><td>streak, veiling</td><td>None</td><td>✓</td></tr><tr><td>RealRain-1K[20]</td><td>2022</td><td>Cam/Internet</td><td>1120</td><td>1.1K</td><td>1512*973</td><td>streak, veiling, occlusion</td><td>None</td><td>✓</td></tr><tr><td>LHP-Rain</td><td>2023</td><td>Camera</td><td>3000</td><td>1.0M</td><td>1920*1080</td><td>streak, veiling, occlusion, splashing</td><td>Object detection/Lane</td><td>✓</td></tr></table>
+
+in which different visual appearance of rain streaks[9], accumulation veiling [48], haze [12, 18], and occlusion [24] factors are taken into consideration. Unfortunately, these linear simulation models still cannot well accommodate the distribution of realistic rains. For example, in Fig. 1, realistic rain streak is usually not exactly a regular line-pattern streak but possesses irregular non-uniform in terms of the intensity and width. Apart from the rain streaks, the existing rain simulation models could not handle the complicated rain splashing on the ground, which presents as dense point-shape texture, droplets or water waves, ruining visibility of traffic signs, such as lane lines, and also causes enormous negative effects for the high-level vision.
+
+Another research line obtains the 'clean' counterpart from the realistic rainy videos [37, 20], which leverages the motion discrepancy between static image background and dynamic rain. Unfortunately, they simply employ naive filtering strategies such as percentile filter [37] and median filter [20], resulting in unsatisfactory GT with residual rain or over-smoothing phenomenon. Moreover, the number and diversity of the existing real paired rain datasets are still limited. Few datasets have considered the rain splash on the ground, which is commonly observed in the real world but still rarely mentioned in deraining community. And the number of existing video sequences and image frames are not sufficient to cover diverse rains in terms of the varied rain angle, intensity, density, length, width and so on. Last but not least, the existing realistic rainy images are mostly downloaded from the Internet with low-quality: compression, watermark, low-resolution, without annotation and so on. As such, constructing a large-scale high-quality paired realistic rain dataset is highly necessary.
+
+In this work, we construct a new large-scale high-quality paired real rain benchmark. The strength of our benchmark is threefold. First, the LHP-Rain contains diverse rain categories with very large-scale, including 3000 video sequences with over 1 million frame pairs. Second, apart from the conventional streak and veiling, our benchmark is capable of removing the representative challenging ground splashing rain in the real world. Third, the LHP-Rain is collected by the smartphone with high-resolution (1920*1080 pixels) and abundant objects under self-driving and surveillance
+
+scenes are captured for comprehensive evaluation. Moreover, we propose a novel robust low-rank tensor recovery method (RLRTR) for video deraining, which can generate higher-quality GT with better rain removal from sky to the ground and image structure preserving. We summary the main contributions as follows:
+
+- We construct a large-scale high-quality paired real rain benchmark for real single image deraining. To our best knowledge, LHP-Rain is the largest paired real rain dataset (3000 video sequences, 1 million frames) with high image resolution (1920*1080), and the first benchmark to claim and tackle the problem of ground splashing rain removal.  
+- We design a novel robust low-rank tensor recovery model for video deraining to better acquire paired GT. We provide detailed analysis to show RLRTR can better differ the rain from static background than previous datasets.  
+- We propose a new transformer-based single image de- raining baseline, which exploits both self-attention and cross-layer attention between the rain and image layer for better representation. Extensive experiments on different real datasets verify the superiority of proposed method.
+
+# 2. Related Work
+
+Real rain datasets. At present, the researchers have mostly focused on the network architecture design, while relative fewer attention has been paid on the real rain dataset. The insufficiency of realistic rain dataset is the main bottleneck to hamper single image deraining. In Table 1, we provide a comprehensive summary of existing real rain datasets, which can be classified into two categories: rainy image only and paired rain-image. The former can be utilized via semi-supervised [40, 13] or unsupervised methods [7, 51]. The latter can be conveniently utilized by the supervised training.
+
+The key to paired real dataset is how to acquire the pseudo-'clean' image from its rainy counterpart. There are two main ways to construct the pairs: video-based generation (SPAData [37], RealRain-1K [20]), and time-interval acquisition (RainDS [32], GT-Rain [1]). All these datasets should ensure that the camera is strictly immobile during the acquisition process. SPA-data [37] was the first presented paired real dataset which utilized the human-supervised percentile video
+
+![](images/af7698afe8bde61b8fe11f8a312b14648d7504e905749ff57f44d09ad16f0b3e.jpg)  
+(a)
+
+![](images/a67384e1bf05df1f7d859a1d77f2810181e14cc07a69ebd3967d7853eb4df448.jpg)  
+(b)  
+Figure 2: Features of the proposed benchmark LHP-Rain. (a) Distribution of rain and scene of the proposed benchmark. (b) Our proposed LHP-Rain outperforms others in terms of rain diversity and sequence amount. (c) LHP-Rain collects high-resolution and annotated rainy images without copyright, compression and blur.
+
+![](images/a144a0cb1bb4c02d3f526c9bed6e8f28ed2614902821bc2019800ca191ddd0df.jpg)  
+(c)
+
+filtering to obtain the GT. Instead of generation, GT-Rain [1] collected the pairs of same scene under rainy and good weather, respectively. Similar idea has been adopt in RainDS [32] by manually mimicking rainfall with a sprinkler.
+
+Despite the rapid development promoted by those pioneer datasets, there remain some important issues to be solved: insufficient number and rain diversity (not consider ground splashing). In this work, we contribute a large-scale high-quality paired real rain dataset (Section 3.1) with diverse rain and abundant objects. Moreover, a novel GT generation method is proposed with higher-quality pairs (Section 3.3).
+
+Single image deraining. The single image deraining methods have made great progress in last decade including the optimization models [26, 22, 4], deep convolutional network [12, 36, 10] and transformer [35, 44]. Fu et al. [9] first introduced the residual deep CNN for single image deraining. Latter, the researchers have further improved the network depth by stacking similar modules, such as the well-known recurrent [21, 49] and multi-stage progressive [33, 53] strategies. Meanwhile, the multi-scale has been widely explored to improve the representation such as the multi-scale fusion [14] and wavelet decomposition [46]. Further, the side information about the rain attribute: density [54], depth [12], directionality [38], location [47], non-local [17] have been extensively utilized to enhance the deraining performance.
+
+Benefiting from self-attention mechanism for long-range relationships modelling, transformer-based methods have achieved significant performance for single image deraining [39, 35, 44, 6]. Very recently, Xiao et al.[44] proposed an image deraining transformer (IDT) with relative position enhanced and spatial-based multihead self-attention. Chen et al. [6] proposed a sparse Transformer architecture to solve the redundant feature issue. In this work, we propose a simple yet effective dual-branch transformer baseline which simultaneously utilizes the self-attention within rain/image layer and cross-layer attention between the rain and image layer, so as to jointly improve the discriminative disentanglement between the rain and image layer (Section 4).
+
+# 3. Large-scale high-quality paired Benchmark
+
+# 3.1. Benchmark Collection and Statistics
+
+Due to the difficulty and inconvenience of collecting real rain videos, the video sequences and frames of existing paired real rain datasets are still limited as shown in Table 1. In this work, we collect the real rain sequences by smartphones with  $24\mathrm{mm}$  lens focal length, sampled in 30 fps. The data collection process is illustrated in Fig. 3(a). Firstly, to keep the camera immobile, we employ tripod to capture real rain videos with static background (no moving object except rain). For each sequence, we record approximate 15 seconds and extract the intermediate steady 10s into our dataset. Then, we manually pick out moving object to remove unexpected disturbance. Finally, we employ the proposed RLRTR (Section 3.3) to obtain high-quality GT.
+
+Overall, we collect 3000 video sequences with approximate 1 million frames across 8 cities from 4 countries around the world, China (2091 sequences), England (51 sequences), Philippines and Indonesia (858 sequences). We visualize the per-country image counts and location distribution of LHP-Rain in Fig. 3(b). The rainfall levels are varied from light rain (10mm/day) to rainstorm (300mm/day) due to diversity of local climates. Over 17 typical scenes are captured, including the parking lot, street, alley, playground, courtyard, and forest, etc. Besides, 2490 sequences are captured at daytime and 510 sequences are at night. More Rainy/GT pairs from LHP-Rain are displayed in Fig. 3(c). With the changing of location, backgrounds are varied from nature to city with diverse rain patterns, such as rain streak, veiling effect, occlusion and splashing. Note that, although the background is the same for each video sequence, the rain in each frame is vastly different from the appearance, including streak, veiling, occlusion and splashing. Here we separate 2100 sequences as training set, 600 sequences as validation set and the other 300 sequences as test set. To further visualize the quantity distribution of rain and scene for each sequence, a sunburst chart is illustrated in Fig. 2(a).
+
+![](images/f19538b9417c24a8059ce213e1f231b1ffde9ab5e759342b0c780e9aec43ca15.jpg)  
+Same position
+
+![](images/b02296d76cc6b2dee651c4d85be77eeaf1a50fbf1ee43aa3bc8272e6de06971b.jpg)  
+Static background Dynamic rain
+
+![](images/65a17486a46a811250b1f125970f792ff767cdf4c52874cff2e44a65a3cadc7e.jpg)  
+Rainy frames
+
+![](images/38f7ee6352dc895ae9ab84d6814e46cbb2a8409763fbed40835d91a4c80b0500.jpg)  
+Clean frames
+
+![](images/ff37672d598094a2b3741036d2fb00e26aa22ab91cb7ba616a24027fdf539af6.jpg)  
+(b)
+
+![](images/dd7378e332e53553a951b69564a8c04e8fcdeb51f7f8030058f30561add36ba2.jpg)  
+Rnny  
+Guangxi, China
+
+![](images/c719f31bb741f8b55e138bb8d20dfc09dbf0efaf0cc5929353928202ed5a7596.jpg)  
+Guangdong, China
+
+![](images/2222687694c72aa0f6226f0458438a2d8a16eff78f98b3dabd1475f90c062c0d.jpg)  
+Hunan, China
+
+![](images/6a13957751d56db20c41c428085275c8417b63a1bbe6b84e5879309404f27c4c.jpg)  
+Hubei, China  
+(c)
+
+![](images/1c2bc4a1aa33650d48fbe6de370874965d3a654ae8b364fedaef7a33d9bd97d0.jpg)  
+Manila, Philippines
+
+![](images/5ddd71ec065595c89f8db549d8765b9ef6a7d8c84141404395c8a6f186d5e2d3.jpg)  
+London, England
+
+![](images/823802220f5839f4d30727b5217dd5649848e6cf957fbb4247bf741ac8b9b6fb.jpg)  
+Jakarta, Indonesia
+
+# 3.2. Benchmark Features
+
+Rain with higher-diversity and larger-scale. We concern not only the sequence number and total frames but also the rain diversity of realistic rain, which both have great impact on the generalization for real-world rain. In Fig. 2(b), we show the statistic distribution of rain diversity and sequences/frames in typical real paired rain dataset. All datasets concern about the noticeable rain streak, especially SPA-data [37]. RainDS [32] additionally takes the raindrop into consideration with 1000 frames, while GT-Rain [1] and RealRain-1K [20] further capture the accumulation veiling artifact in heavy rain. LHP-Rain contains not only rain streak and veiling in the sky, but also challenging highlight occlusion and splashing water on the ground. To our best knowledge, the proposed LHP-Rain is the first benchmark to collect and tackle ground splashing rain in the real world, which is commonly ignored by previous existing datasets.
+
+Image with higher-resolution and abundant objects. The existing datasets pay much attention to the rain, ignoring that the high-quality image is also what we really need. Unfortunately, existing realistic rainy images are generally downloaded from the Internet with various problems about the image: compression artifact, watermark, low-resolution, out-of-focus blur, without objects to name a few, which may cause challenges for high-level vision applications. In Fig. 2(c), we show the typical examples in each dataset. The image background of RealRain-1K [20] suffers from serious out-of-focus blur, since they have manually focused on the rain on purpose. GT-Rain [1] contains obvious compression artifact, since it origins from the compressed Youtube stream. There are numerous scenes with narrow views and watermark in the SPA-data [37], because they only release patches (256*256) cropped from original frames.
+
+![](images/00d6ad79436f3668464f9169c4f367c9e35d4fe6f55e5e6905a39c5b36ddf2b3.jpg)  
+Figure 3: Illustration of the proposed benchmark LHP-Rain. (a) Overall procedure of obtaining rainy/clean image pair. (b) Quantity and location distribution of LHP-Rain. (c) Rainy/GT samples of LHP-Rain from different locations. Scenes are varied from nature to city, over day and night with diverse rain patterns from sky to the ground.  
+Figure 4: The GT quality of LHP-Rain is superior to others on DIIVINE (lowest), NIQE (lowest) and B-FEN (highest).
+
+![](images/c26d9414d69fc3f27c6561146973efdb0469323393125bfd6422dc6006201fb5.jpg)
+
+![](images/a3d9c88dbb82a5f434dae73a77cdb2c3d619ad41af1f2544270959647254cc29.jpg)
+
+To improve the image quality, we personally capture high-resolution (1920*1080) realistic rain videos by smartphones. Moreover, LHP-Rain is not only designed for rain restoration, but also important for object detection and segmentation tasks under adverse weather, with abundant objects which are oriented for self-driving and video surveillance scenes. Thus, we provide annotations for object detection and lane segmentation. Five typical objects including person, car, bicycle, motorcycle and bus are annotated by bounding box with 326,961 instances totally. For lane segmentation, we annotate 24,464 lane masks to evaluate the effect of rain splashing removal. Note that the same object in different frames will be regarded as different instances because rain is inconstant and changing frame by frame.
+
+Higher-quality ground-truth. The quality of GT is critical for paired real rain dataset. It is difficult to determine what is good or bad GT in an absolutely fair way. In this paper, we assume that the better the rain removal, the better the image quality is. Therefore, we employ several no reference image quality assessments: DIIVINE [29], NIQE [28] and B-FEN [43], to evaluate the image quality of the rain-free image. The former two are hand-crafted based general image quality indexes, and the last one B-FEN is the learning based index especially designed for de-raining quality assessment. We select all the video backgrounds in SPA-data [37], GT-Rain [1], RealRain-1K [20] and LHP-Rain for evaluation. In
+
+![](images/8ff7e958ad209ae7c1aca429094e433d098645e27439210919e1720bbb7cfc8f.jpg)  
+Figure 5: Analysis of different video deraining results on our dataset. From left to right, the first column is the original rainy frame, and the remaining five columns represent different methods, namely Median Filter, SPA, FastDeRain, J4R-Net and the proposed RLRTR. From top to bottom, the first row shows the deraining results, the second row is the rain layer of the deraining results, the third row denotes the section line of the deraining results and the last row represents the horizontal and vertical gradient distributions of the deraining results.  
+Fig. 4, we can observe that the proposed LHP-Rain consistently obtains the best results in terms of different evaluation indexes which strongly support the higher-quality of the GT.
+
+# 3.3. Robust Low-rank Tensor Recovery Model
+
+Given the rainy video  $\mathcal{O} \in \mathbb{R}^{h \times w \times t}$ , the key is how to properly obtain the paired GT. The existing methods simply employ the naive filtering technique benefiting from the temporal consistency of the static background. Due to the slight camera vibration caused by the wild wind, we further leverage an affine transformation operator  $\tau$  [52] to achieve the pixel-level alignment of each frame. Thus, a multi-frame rainy video can be described as the following formula:
+
+$$
+\mathcal {O} \circ \tau = \mathcal {B} + \mathcal {R} + \mathcal {N}, \tag {1}
+$$
+
+where  $\mathcal{B} \in \mathbb{R}^{h \times w \times t}$  is the rain-free video,  $\mathcal{R} \in \mathbb{R}^{h \times w \times t}$  represents the rains,  $\mathcal{N} \in \mathbb{R}^{h \times w \times t}$  denotes the random noise, and  $\tau$  denotes the affine transformation to ensure the rainy video of each frame is pixel-level aligned. In this work, we formulate the video deraining into inverse problem via the maximum-a-posterior as follow:
+
+$$
+\min  _ {\mathcal {B}, \mathcal {R}, \tau} \frac {1}{2} | | \mathcal {B} + \mathcal {R} - \mathcal {O} \circ \tau | | _ {F} ^ {2} + \omega P _ {b} (\mathcal {B}) + \mu P _ {r} (\mathcal {R}), \tag {2}
+$$
+
+where  $P_{b}$  and  $P_{r}$  are the prior knowledge for the image and rain, respectively,  $\omega$  and  $\mu$  are the corresponding hyperparameters. As for the aligned rainy video, when there are no moving objects except the rain, the rain-free background image is the same for all rainy frames. That is to say, clean video  $\mathcal{B}$  has extreme global low-rank property along the
+
+temporal dimension, ideally its rank is equal to one for each scene. On the other hand, the clean video  $\mathcal{B}$  also has very non-local low-rank property along the spatial dimension, due to the self-similarity widely employed in image restoration [8]. Moreover, we further take the local smoothness of the video  $\mathcal{B}$  into consideration via the total variation (TV) regularization [4]. Thus, the joint global-nonlocal-local prior along both the spatial and temporal dimension has been fully exploited for better representation of the static video  $\mathcal{B}$ :
+
+$$
+P _ {b} (\mathcal {B}) = \omega \sum_ {i} \left(\frac {1}{\lambda_ {i} ^ {2}} | | \mathcal {S} _ {i} \mathcal {B} \times_ {3} Q _ {i} - \mathcal {J} _ {i} | | _ {F} ^ {2} + | | \mathcal {J} _ {i} | | _ {t n n}\right) + \gamma | | \nabla_ {t} \mathcal {B} | | _ {1}, \tag {3}
+$$
+
+where  $\mathcal{S}_i\mathcal{B}\in \mathbb{R}^{p^2\times k\times t}$  is the constructed 3-D tensor via the non-local clustering of a sub-cubic  $u_{i}\in \mathbb{R}^{p\times p\times t}$  [3],  $p$  and  $k$  are the spatial size and number of the sub-cubic respectively,  $Q_{i}\in \mathbb{R}^{d\times t}(d\ll t)$  is an orthogonal subspace projection matrix used to capture the temporal low-rank property,  $\times_3$  is the tensor product along the temporal dimension [16],  $\mathcal{I}_i$  represents the low-rank approximation variable,  $||\bullet ||_{ttn}$  means the tensor nuclear norm for simplicity [3],  $\nabla_t$  is the difference operator,  $\gamma$  and  $\lambda_{i}$  is the regularization parameters. As for the rain  $\mathcal{R}$ , we formulate it as the sparse error [42] via the  $L_{1}$  sparsity. Thus, the Eq. (2) can be expressed as:
+
+$$
+\begin{array}{l} \left\{\hat {\mathcal {B}}, \hat {\mathcal {R}}, \hat {\mathcal {J}} _ {i}, \hat {\tau}, \hat {Q} _ {i} \right\} = \arg \min  _ {\mathcal {B}, \mathcal {R}, \mathcal {J} _ {i}, \tau , Q _ {i}} \frac {1}{2} \| \mathcal {B} + \mathcal {R} - \mathcal {O} \circ \tau \| _ {F} ^ {2} \tag {4} \\ + \mu | | \mathcal {R} | | _ {1} + \omega \sum_ {i} \left(\frac {1}{\lambda_ {i} ^ {2}} | | \mathcal {S} _ {i} \mathcal {B} \times_ {3} Q _ {i} - \mathcal {J} _ {i} | | _ {F} ^ {2} + | | \mathcal {J} _ {i} | | _ {t n n}\right) + \gamma | | \nabla_ {t} \mathcal {B} | | _ {1}. \\ \end{array}
+$$
+
+Optimization. Due to the difficulty of estimating multiple variables directly, we adopt the alternating minimization
+
+Table 2: Quantitative comparisons with SOTA supervised methods on paired real datasets SPA-data (A), GT-Rain (B) and proposed LHP-Rain (C) under 9 different task settings. X→Y means training on the dataset X and testing on the dataset Y. The degraded results of the three datasets are also provided. Top  $1_{st}$  and  $2_{nd}$  results are marked in red and blue respectively.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">A→A</td><td colspan="2">B→A</td><td colspan="2">C→A</td><td colspan="2">A→B</td><td colspan="2">B→B</td><td colspan="2">C→B</td><td colspan="2">A→C</td><td colspan="2">B→C</td><td colspan="2">C→C</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>Rainy Image</td><td colspan="6">32.60 / 0.9173</td><td colspan="6">19.48 / 0.5849</td><td colspan="6">29.97 / 0.8497</td></tr><tr><td>SPANet</td><td>38.53</td><td>0.9875</td><td>22.93</td><td>0.8207</td><td>31.46</td><td>0.9612</td><td>20.01</td><td>0.6148</td><td>21.51</td><td>0.7145</td><td>19.20</td><td>0.5706</td><td>28.00</td><td>0.8905</td><td>20.10</td><td>0.8061</td><td>31.19</td><td>0.9346</td></tr><tr><td>PReNet</td><td>37.05</td><td>0.9696</td><td>22.44</td><td>0.7713</td><td>32.46</td><td>0.9387</td><td>20.29</td><td>0.5860</td><td>20.65</td><td>0.6005</td><td>19.34</td><td>0.5530</td><td>27.57</td><td>0.8595</td><td>20.91</td><td>0.7222</td><td>32.13</td><td>0.9177</td></tr><tr><td>RCDNet</td><td>39.74</td><td>0.9661</td><td>22.51</td><td>0.8392</td><td>32.30</td><td>0.9378</td><td>20.09</td><td>0.5785</td><td>21.04</td><td>0.6106</td><td>19.09</td><td>0.5264</td><td>25.46</td><td>0.7959</td><td>21.38</td><td>0.8047</td><td>32.34</td><td>0.9152</td></tr><tr><td>JORDER-E</td><td>40.63</td><td>0.9794</td><td>23.47</td><td>0.7426</td><td>31.23</td><td>0.9234</td><td>19.98</td><td>0.5799</td><td>21.24</td><td>0.6854</td><td>18.76</td><td>0.4861</td><td>27.13</td><td>0.8531</td><td>22.14</td><td>0.8433</td><td>31.24</td><td>0.8847</td></tr><tr><td>MPRNet</td><td>46.06</td><td>0.9894</td><td>24.27</td><td>0.8428</td><td>32.37</td><td>0.9379</td><td>19.87</td><td>0.6286</td><td>22.00</td><td>0.6515</td><td>19.47</td><td>0.5889</td><td>28.41</td><td>0.8807</td><td>23.82</td><td>0.8052</td><td>33.34</td><td>0.9309</td></tr><tr><td>GT-Rain</td><td>37.21</td><td>0.9827</td><td>25.30</td><td>0.9243</td><td>26.46</td><td>0.9145</td><td>20.07</td><td>0.6941</td><td>22.51</td><td>0.7300</td><td>21.14</td><td>0.5698</td><td>28.62</td><td>0.8675</td><td>23.19</td><td>0.8098</td><td>32.18</td><td>0.9132</td></tr><tr><td>Uformer-B</td><td>46.42</td><td>0.9917</td><td>24.08</td><td>0.8979</td><td>32.21</td><td>0.9667</td><td>19.70</td><td>0.6875</td><td>21.60</td><td>0.7124</td><td>19.10</td><td>0.6622</td><td>28.74</td><td>0.9262</td><td>22.91</td><td>0.8734</td><td>33.56</td><td>0.9317</td></tr><tr><td>IDT</td><td>45.74</td><td>0.9889</td><td>23.80</td><td>0.8334</td><td>32.38</td><td>0.9422</td><td>20.34</td><td>0.6306</td><td>21.98</td><td>0.6536</td><td>19.44</td><td>0.5977</td><td>26.90</td><td>0.8742</td><td>23.34</td><td>0.7897</td><td>33.02</td><td>0.9310</td></tr><tr><td>SCD-Former</td><td>46.89</td><td>0.9941</td><td>26.13</td><td>0.9122</td><td>34.38</td><td>0.9798</td><td>20.98</td><td>0.6985</td><td>22.79</td><td>0.7684</td><td>21.71</td><td>0.6893</td><td>29.41</td><td>0.9127</td><td>23.56</td><td>0.8626</td><td>34.33</td><td>0.9468</td></tr></table>
+
+scheme to solve the Eq. (4) with respect to each variable.
+
+1) Affine Transformation  $\tau$ : Since  $\mathcal{O} \circ \tau$  is a nonlinear geometric transform, it's difficult to directly optimize  $\tau$ . A common technique is to linearize around the current estimate and iterate as follows:  $\mathcal{O} \circ \tau + \nabla \mathcal{O} \triangle \tau = \mathcal{B} + \mathcal{R} + \mathcal{N}$  [31], where  $\nabla \mathcal{O}$  is the Jacobian of the image  $\mathcal{O}$  with respect to  $\tau$ . This method iteratively approximates the original nonlinear transformation with a locally linear approximation [31].  
+2) Rain Estimation  $\mathcal{R}$ : By ignoring variables independent of  $\mathcal{R}$ , we can obtain following subproblem:
+
+$$
+\hat {\mathcal {R}} = \arg \min _ {\mathcal {R}} \frac {1}{2} | | \mathcal {B} + \mathcal {R} - \mathcal {O} \circ \tau | | _ {F} ^ {2} + \mu | | \mathcal {R} | | _ {1}. (5)
+$$
+
+Eq. (5) is a  $L_{1}$  minimization problem which can be easily solved by soft thresholding with closed-form solution [23].  
+3) Subspace Projection  $Q_{i}$ : We enforce the orthogonal constraint on  $Q_{i}^{T}Q_{i} = I$  with the following subproblem:
+
+$$
+\hat {Q} _ {i} = \arg \min  _ {Q _ {i} ^ {T} Q _ {i} = I} \frac {1}{\lambda_ {i} ^ {2}} \left\| \mathcal {S} _ {i} \mathcal {B} \times_ {3} Q _ {i} - \mathcal {J} _ {i} \right\| _ {F} ^ {2}. \tag {6}
+$$
+
+According to [45], Eq. (6) has the closed-form solution, which can be obtained by the rank-  $d$  singular value decomposition of the folding matrix of  $\mathcal{S}_i\mathcal{B}$ , where  $d$  is the measurement of the intrinsic subspace of the temporal dimension. In this work, we empirically set  $d \leq 3$ .
+
+4) Low-rank Approximation  $\mathcal{J}_i$ : Dropping the irrelevant variables, we can get following subproblem:
+
+$$
+\hat {\mathcal {J}} _ {i} = \arg \min  _ {\mathcal {J} _ {i}} \frac {1}{\lambda_ {i} ^ {2}} \| \mathcal {S} _ {i} \mathcal {B} \times_ {3} Q _ {i} - \mathcal {J} _ {i} \| _ {F} ^ {2} + | | \mathcal {J} _ {i} | | _ {t n n}. \tag {7}
+$$
+
+This is a typical tensor nuclear norm minimization problem, can be solved by singular value thresholding algorithm [2, 3].  
+5) Clean Video Estimation  $\mathcal{B}$ : We fix the other variables and optimize  $\mathcal{B}$  with the following subproblem:
+
+$$
+\min  _ {\mathcal {B}} \frac {1}{2} \| \mathcal {B} + \mathcal {R} - \mathcal {O} \circ \tau \| _ {F} ^ {2} + \omega \sum_ {i} \frac {1}{\lambda_ {i} ^ {2}} \| \mathcal {S} _ {i} \mathcal {B} \times_ {3} Q _ {i} - \mathcal {J} _ {i} \| _ {F} ^ {2} + \gamma \| \nabla_ {t} \mathcal {B} \| _ {1}. \tag {8}
+$$
+
+Due to the non-differentiability of the  $L_{1}$  norm in Eq. (8), we apply the ADMM [23] to decouple this problem into several
+
+![](images/fb62f199f88f541bf5e7275bead92543acd21423b66e8cd05734f78b7a51a87d.jpg)  
+Figure 6: Overall framework of the SCD-Former. It utilizes self and cross-layer attention from rain layer to image layer which serves as side information to recover image layer.
+
+sub-problems with closed-form solutions. Please refer to the supplementary material for the whole algorithm details.
+
+Discussion. Figure 5 illustrates the comparison results of representative video deraining methods: filter-based methods (median filter[20], SPA[37]), optimization-based (FastDeRain[15]) and learning-based methods (J4R-Net[24]). The first and second rows show the video deraining of the image and rain layer, respectively. RLRTR removes almost all the rain from sky to the ground, including rain streaks and splashing, and preserve the image details well, while other methods more or less have rain streaks residual but also cause noticeable damage to the image. In third row, we randomly choose two 1D section lines of the deraining results. The section line of RLRTR is smoother with less burr than other methods. Moreover, the SPA, FastDeRain and the J4R-Net unexpectedly attenuate the spike signal of the share edge, while the proposed RLRTR has well preserve the spike signal. It is well-known the natural image is isotropic and its gradient distribution along different directions should be close to each other [34]. Compared with other results, in forth row the gradient distributions along the vertical and horizontal directions of RLRTR are most similar to each other, which further indirectly verify the naturalness of the deraining result and produce better paired clean-rainy GT.
+
+![](images/6246f277cd153287bf3b10dfec01637b5c9f07f0e0523dfb1a6f270e32bb80e7.jpg)  
+Rainy Image
+
+![](images/c4987cce980065135f0c7d200798bad9bd6498e7251e94bec3b45ee208d48a23.jpg)  
+JORDER-E
+
+![](images/8382472e39e69e3148612357c9c62506daab057ab9af32545dd44a5405ca9f54.jpg)  
+MPRNet  
+Figure 7: Visual comparisons on LHP-Rain. Comparing with state-of-the-arts, SCD-Former achieves more visual pleasing deraining results and it is capable of removing the highlight occlusion on the car and the splashing water on the ground.
+
+![](images/619f6f60c4c1510bcc321b39547a203075ac1fe623e10340f23944d093838fd5.jpg)  
+IDT
+
+![](images/490f67801807bd6200aae50674f7a9457a7455bf4f2c6f5b023c6cca2c6f13e6.jpg)  
+SCD-Former
+
+# 4. SCD-Former: Image Deraining Baseline
+
+The degradation procedure can be formulated as:
+
+$$
+O = B + R. \tag {9}
+$$
+
+It has been proved that the rain such as location [47] serving as an attention would be informative in CNN-based image restoration. In this work, we show the rain attention would also be beneficial in transformer. In Fig. 6, we design a simple two-stream Self- and Cross-attention Deraining Transformer (SCD-Former), in which the two-stream network is designed to restore rain and image layer respectively. On one hand, we utilize the self-attention in each rain/image stream independently; on the other hand, we further exploit the cross-layer attention between the rain and image streams. Thus, the rain collaboratively interactive with the image layer to further improve the discriminative representation.
+
+Self-attention and cross-layer attention. In this work, we exploit self-attention on rain and image layer as Rain layer Self-Attention (RSA) and Image layer Self-Attention (ISA). Given the input feature  $X$ , it will be projected into query  $(Q)$ , key  $(K)$  and value  $(V)$  by three learnable weight matrices  $W_{q}$ ,  $W_{k}$  and  $W_{v}$ . Then dot-product, scaling and softmax among  $Q$ ,  $K$  and  $V$  will be conducted. The self-attention function is defined as:
+
+$$
+\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d _ {k}}}\right) V. \tag {10}
+$$
+
+We further design a Cross-Layer Attention (CLA) module which bridges the attention relationship between rain and image layer. The CLA conducts attention operation among  $Q_{r}$  from rain layer and  $K_{b}, V_{b}$  from image layer as follow:
+
+$$
+C L A \left(Q _ {r}, K _ {b}, V _ {b}\right) = \operatorname {s o f t m a x} \left(\frac {Q _ {r} K _ {b} {} ^ {T}}{\sqrt {d _ {k}}}\right) V _ {b}. \tag {11}
+$$
+
+The token of rain layer serves as a query token  $Q_{r}$  to interact with the patch tokens  $K_{b}$  and  $V_{b}$  from the image layer through attention mechanism. By calculating the correlation degree between both layers, the highly attentive location of rain residual can be acquired, which provides an extra prior for enhanced feature representation. Note that, the CLA module has been stacked over the whole network. Compared with previous work, SCD-Former exploits not only the self-attention but also cross-layer attention of the rain and image layer for better restoration.
+
+Implementation details. We train the network using the Charbonnier loss[5] supervised by the ground truth of rain and image layer:
+
+$$
+\mathcal {L} = \left| \left| O - B - R \right| \right| _ {F} ^ {2} + \lambda_ {r} \left| \left| R - \hat {R} \right| \right| _ {1} + \lambda_ {b} \left| \left| B - \hat {B} \right| \right| _ {1}. \tag {12}
+$$
+
+The framework is implemented with two RTX 3090 GPUs. We set the hyperparameter  $\lambda_{b}$  and  $\lambda_{r}$  as 1. The images are randomly cropped into  $256*256$  for training. The learning rate of network is set as 0.0002. The Adam optimizer is adopted for optimization with a batch size of 32.
+
+# 5. Experiments
+
+Datasets. We conduct the experiments on paired datasets SPA-data[37], GT-Rain[1] and LHP-Rain. For the SPA-data, training set is cropped from 29,500 images and 1000 rainy images are used for testing. For the GT-Rain, 89 sequences are used for training and 7 sequences are used for testing. For the LHP-Rain, 2100 sequences are used for training and 300 sequences are used for testing. To evaluate the deraining performance on real scenes, we choose typical real rainy images from Internet-data. For single image deraining methods, we select the representative supervised deraining methods, including the CNN-based SPANet[37],
+
+![](images/cefa5d50aa3c1d6b10a6c41a72095a58553572a4f6f0b826f7460994b48318a3.jpg)  
+Figure 8: Evaluation of the diversity of the LHP-Rain. We train SCD-Former on different datasets: Rain100L, SPA-data, GT-Rain and LHP-Rain, and test on other datasets. The model trained on LHP-Rain has achieved better deraining results.
+
+PReNet[33], RCDNet[36], JORDER-E[47], MPRNet[27], GT-Rain[1], transformer-based Uformer[39] and IDT[44]. Evaluation metrics. We employ the full-reference PSNR and SSIM to evaluate the single image deraining results. Moreover, mean Average Precision (mAP) and Accuracy (Acc) are employed to evaluate object detection and lane segmentation after restoration by deraining methods.
+
+# 5.1. Quantitative Evaluation
+
+Deraining results on benchmarks. We make comparisons with state-of-the-art deraining methods on three datasets SPA-data (A), GT-Rain (B) and LHP-Rain (C). The quantitative results are reported in Table 2 under the following columns:  $\mathrm{A}\rightarrow \mathrm{A}$ ,  $\mathrm{B}\rightarrow \mathrm{B}$  and  $\mathrm{C}\rightarrow \mathrm{C}$ . It is observed that transformer-based methods perform better than most CNN-based methods except for MPRNet in terms of PSNR and SSIM because of the superior representation of self-attention. Note that SCD-Former outperforms the existing state-of-the-art methods on all benchmarks, which confirms the effectiveness of our method with both self and cross-layer attention.
+
+# 5.2. Qualitative Evaluation
+
+Evaluation on LHP-Rain. To further validate the deraining performance, we compare with the qualitative results of typical methods on LHP-Rain. As shown in Fig. 7, SCD-Former achieves more visual pleasing results without rain residual and artifacts comparing with other methods, which cleans the rain streaks and veiling effect on the trees, highlight occlusion on the red car and the ground splashing water.
+
+Evaluation on real rainy images. To evaluate the performance on real rainy images, we train SCD-Former on synthetic rain Rain100L[48], real rain SPA-data, GT-Rain and LHP-Rain respectively and test on real rainy images. As shown in Fig. 8, the model trained on Rain100L performs poorly due to the huge domain gap. SPA-data and GT-Rain could remove real rain in the sky partially but they cannot handle the splashing water on the ground. The model trained on LHP-Rain has the best deraining performance which simultaneously removes rain streaks, veiling and ground splashing water without destroying image details.
+
+![](images/c2c1c0e9c96e3bd1820ebe7e0d214bcddc201bb0d057bcb8b047977ebcc1029c.jpg)  
+Figure 9: Ablation study of the robust low-rank tensor recovery model. The first row represents the deraining results, and the second row is corresponding rain. The first column is the original rainy frame and the remaining three columns represent the model without subspace projection, without affine transformation and full RLRTR.
+
+Table 3: Ablation study of cross-layer attention.  
+
+<table><tr><td>Cross-layer attention</td><td>PSNR / SSIM</td></tr><tr><td>-</td><td>33.92 0.9384</td></tr><tr><td>✓</td><td>34.33 0.9403</td></tr></table>
+
+# 5.3. Ablation Study
+
+Effectiveness of subspace projection. The subspace projection is used to characterize the extreme global low-rank property along the temporal dimension. In Fig. 9, there are obvious rain residual without subspace projection, implying that it is insufficient to characterize the property of the temporal dimension relying on the local prior of the temporal smoothness. Since the temporal low-rank property is neglected, leading to the rain residual in the results.
+
+Effectiveness of affine transformation. The affine transformation is exerted to guarantee the pixel-level alignment of rainy video. As shown in Fig. 9, it can be observed that background residual and distortion obviously exist in the rain layer without affine transformation, because the extreme low-rank property along the temporal dimension is affected by data alignment among each frame in the video.
+
+Effectiveness of cross-layer attention. The design aims to find the correlations between rain layer and image layer. After iterations, the image layer sub-network obtains more attention on the rain features brought by cross-layer attention. In Table 3, We show that the complementary guidance from rain layer promotes the restoration of image layer.
+
+![](images/63b810fec0992f9bc5aa761615ee57ed88ab87e6b6210097a5bbe83541d8ed17.jpg)  
+Rainy Image  
+Figure 10: Evaluation of high-level tasks on lane segmentation and object detection. The performance improves significantly after removing rain streak and ground splashing from lanes and bicycles by our proposed SCD-Former.
+
+![](images/1b99f8d2d58a8be4409546a11039a7872aa8ba70d4861b3475c369ed19ba666e.jpg)  
+JORDER-E
+
+![](images/2276c582c5af92cfe5d58481f7f8d4390f86f4a7b82c4c89554dd28721bbb612.jpg)
+
+Table 4: Evaluation of high-level tasks on deraining results.  
+
+<table><tr><td>Method</td><td>Det. (mAP)</td><td>Gain (Det.)</td><td>Seg. (Acc)</td><td>Gain (Seg.)</td></tr><tr><td>Rainy</td><td>0.543</td><td>-</td><td>0.237</td><td>-</td></tr><tr><td>SPANet</td><td>0.563</td><td>+0.020</td><td>0.268</td><td>+0.031</td></tr><tr><td>PReNet</td><td>0.560</td><td>+0.022</td><td>0.255</td><td>+0.018</td></tr><tr><td>RCDNet</td><td>0.556</td><td>+0.018</td><td>0.361</td><td>+0.124</td></tr><tr><td>JORDER-E</td><td>0.568</td><td>+0.025</td><td>0.385</td><td>+0.148</td></tr><tr><td>MPRNet</td><td>0.560</td><td>+0.017</td><td>0.350</td><td>+0.113</td></tr><tr><td>Uformer-B</td><td>0.568</td><td>+0.025</td><td>0.306</td><td>+0.069</td></tr><tr><td>IDT</td><td>0.570</td><td>+0.027</td><td>0.365</td><td>+0.128</td></tr><tr><td>SCD-Former</td><td>0.575</td><td>+0.031</td><td>0.449</td><td>+0.212</td></tr></table>
+
+# 5.4. Discussion
+
+Rain diversity of different datasets. The rain diversity of dataset can be validated by the experiment of training models on one dataset and testing on the other unseen datasets among SPA-data (A), GT-Rain (B) and LHP-Rain (C). As shown in Table 2, on one hand, the best results of  $\mathrm{C} \rightarrow \mathrm{A}$  methods positively improve the performance of A, while all  $\mathrm{A} \rightarrow \mathrm{C}$  results performing worse than degraded result of C. On the other hand, the best results of  $\mathrm{C} \rightarrow \mathrm{B}$  have promotion while  $\mathrm{B} \rightarrow \mathrm{C}$  drop severely. Therefore, the outcome proves that our LHP-Rain contains more diverse rain categories than others, because they could not handle extreme challenging cases such as occlusion and ground splashing.
+
+Evaluation on downstream tasks. We further evaluate the image deraining results on high-level tasks. For object detection, we apply the officialYOLOv5 model on deraning results and report the mean average precision (mAP) of different classes in Table 4, where SCD-Former reaches the best average mAP among typical objects. For lane segmentation, we choose the LaneNet[30] to predict the lane on LHP-Rain and SCD-Former has larger promotion on the segmentation accuracy. It is reasonable because SCD-Former performs well on removing ground splashing water and recovering the lane lines. The visualization results in Fig. 10 shows that the lane on the surface of ground and the bicycles could be properly predicted after deraining by SCD-Former.
+
+User study on benchmarks quality. We look for 126 volunteers to anonymously vote for the benchmark with best quality. Among existing benchmarks, we randomly select
+
+![](images/9f87f7aa50574c34b86fd514f173533e17b3a6491d605ba12422f4d2d817d3fd.jpg)  
+(a) Rainy Image  
+Figure 11: The limitation of RLRTR. The challenging occlusion effect could be removed by RLRTR from the background while the static haze is preserved.
+
+![](images/9dde83037729117b207c57552e4a888a68e791e9ee4313bab3ed7b31e579621c.jpg)  
+(b) RLRTR Result
+
+Table 5: User study on benchmarks quality.  
+
+<table><tr><td></td><td>LHP-Rain</td><td>SPA</td><td>RealRain1K</td><td>GT-Rain</td></tr><tr><td>Rain diversity</td><td>63%</td><td>8%</td><td>13%</td><td>16%</td></tr><tr><td>Image quality</td><td>51%</td><td>14%</td><td>20%</td><td>15%</td></tr><tr><td>GT quality</td><td>55%</td><td>15%</td><td>16%</td><td>14%</td></tr></table>
+
+100 samples and conduct user study including: rain diversity, image quality (resolution, JEPG, blur) and GT quality. The result is listed in Table 5, where LHP-Rain consistently outperforms other benchmarks more than  $50\%$ .
+
+# 6. Limitation
+
+Our proposed video deraining method is limited to remove the haze in the heavy rain scenes. RLRTR is adept at separating the static background from the dynamic rain. However, due to the steadiness of mist in the short interval, which is almost motionless in the background, RLRTR cannot decompose the haze from image layer well. Fig. 11 shows examples of rain and mist in our benchmark. Although the challenging rain patterns such as rain streaks are clearly removed, the result still contains haze. We look forward to handling the static haze in the future.
+
+# 7. Conclusion
+
+In this paper, we propose a large-scale and high-quality paired real rain benchmark. Our proposed LHP-Rain provides diverse rain categories, especially the ground splashing rain issue which is first claimed in deraining community. The model trained on LHP-Rain could generalize well on various real rainy scenes with great rain removal performance. Moreover, the proposed low-rank tensor recovery model could generate high-quality GT and detailed analysis confirms better results than others. In addition, we propose a single deraining baseline which performs well on removing rain from sky to the ground. Extensive experiments verify the superiority of the proposed benchmark and significantly improves segmentation task after removing splashing.
+
+Acknowledgements. This work was supported in part by the National Natural Science Foundation of China under Grant 61971460 and Grant 62101294, in part by JCJQ Program under Grant 2021-JCJQ-JJ-0060 and in part by the Fundamental Research Funds for the Central Universities, HUST: 2022JYCXJJ001.
+
+# References
+
+[1] Yunhao Ba, Howard Zhang, Ethan Yang, Akira Suzuki, Arnold Pfahnl, Chethan Chinder Chandrappa, Celso de Melo, Suya You, Stefano Soatto, Alex Wong, and Achuta Kadambi. Not just streaks: Towards ground truth for single image deraining. In ECCV, 2022. 2, 3, 4, 9  
+[2] Jian-Feng Cai, Emmanuel J Candès, and Zuowei Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal on optimization, 20(4):1956-1982, 2010. 6  
+[3] Yi Chang, Luxin Yan, and Sheng Zhong. Hyper-laplacian regularized unidirectional low-rank tensor recovery for multispectral image denoising. In CVPR, pages 4260-4268, 2017. 5, 6  
+[4] Yi Chang, Luxin Yan, and Sheng Zhong. Transformed low-rank model for line pattern noise removal. In ICCV, pages 1726-1734, 2017. 3, 5  
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+                                    "content": "These authors contributed equally to this work."
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+                                            "content": "Table 1: Summary of existing real rain datasets."
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+                                            "html": "<table><tr><td>Datasets</td><td>Year</td><td>Source</td><td>Sequence</td><td>Frame</td><td>Resolution</td><td>Rain Categories</td><td>Annotation</td><td>Paired</td></tr><tr><td>RID/RIS[19]</td><td>2019</td><td>Cam/Internet</td><td>None</td><td>4.5K</td><td>640*368</td><td>streak, raindrop</td><td>Object detection</td><td>-</td></tr><tr><td>NR-IQA[43]</td><td>2020</td><td>Internet</td><td>None</td><td>0.2K</td><td>1000*680</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>Real3000[25]</td><td>2021</td><td>Internet</td><td>None</td><td>3.0K</td><td>942*654</td><td>streak, veiling</td><td>None</td><td>-</td></tr><tr><td>FCRealRain[51]</td><td>2022</td><td>Camera</td><td>None</td><td>4.0K</td><td>4240*2400</td><td>streak, veiling</td><td>Object detection</td><td>-</td></tr><tr><td>SPA-Data[37]</td><td>2019</td><td>Cam/Internet</td><td>170</td><td>29.5K</td><td>256*256</td><td>streak</td><td>None</td><td>✓</td></tr><tr><td>RainDS[32]</td><td>2021</td><td>Cam</td><td>None</td><td>1.0K</td><td>1296*728</td><td>streak, raindrop</td><td>None</td><td>✓</td></tr><tr><td>GT-Rain[1]</td><td>2022</td><td>Internet</td><td>202</td><td>31.5K</td><td>666*339</td><td>streak, veiling</td><td>None</td><td>✓</td></tr><tr><td>RealRain-1K[20]</td><td>2022</td><td>Cam/Internet</td><td>1120</td><td>1.1K</td><td>1512*973</td><td>streak, veiling, occlusion</td><td>None</td><td>✓</td></tr><tr><td>LHP-Rain</td><td>2023</td><td>Camera</td><td>3000</td><td>1.0M</td><td>1920*1080</td><td>streak, veiling, occlusion, splashing</td><td>Object detection/Lane</td><td>✓</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "in which different visual appearance of rain streaks[9], accumulation veiling [48], haze [12, 18], and occlusion [24] factors are taken into consideration. Unfortunately, these linear simulation models still cannot well accommodate the distribution of realistic rains. For example, in Fig. 1, realistic rain streak is usually not exactly a regular line-pattern streak but possesses irregular non-uniform in terms of the intensity and width. Apart from the rain streaks, the existing rain simulation models could not handle the complicated rain splashing on the ground, which presents as dense point-shape texture, droplets or water waves, ruining visibility of traffic signs, such as lane lines, and also causes enormous negative effects for the high-level vision."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Another research line obtains the 'clean' counterpart from the realistic rainy videos [37, 20], which leverages the motion discrepancy between static image background and dynamic rain. Unfortunately, they simply employ naive filtering strategies such as percentile filter [37] and median filter [20], resulting in unsatisfactory GT with residual rain or over-smoothing phenomenon. Moreover, the number and diversity of the existing real paired rain datasets are still limited. Few datasets have considered the rain splash on the ground, which is commonly observed in the real world but still rarely mentioned in deraining community. And the number of existing video sequences and image frames are not sufficient to cover diverse rains in terms of the varied rain angle, intensity, density, length, width and so on. Last but not least, the existing realistic rainy images are mostly downloaded from the Internet with low-quality: compression, watermark, low-resolution, without annotation and so on. As such, constructing a large-scale high-quality paired realistic rain dataset is highly necessary."
+                                }
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+                                    "type": "text",
+                                    "content": "In this work, we construct a new large-scale high-quality paired real rain benchmark. The strength of our benchmark is threefold. First, the LHP-Rain contains diverse rain categories with very large-scale, including 3000 video sequences with over 1 million frame pairs. Second, apart from the conventional streak and veiling, our benchmark is capable of removing the representative challenging ground splashing rain in the real world. Third, the LHP-Rain is collected by the smartphone with high-resolution (1920*1080 pixels) and abundant objects under self-driving and surveillance"
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+                                    "content": "scenes are captured for comprehensive evaluation. Moreover, we propose a novel robust low-rank tensor recovery method (RLRTR) for video deraining, which can generate higher-quality GT with better rain removal from sky to the ground and image structure preserving. We summary the main contributions as follows:"
+                                }
+                            ]
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+                                            "type": "text",
+                                            "content": "- We construct a large-scale high-quality paired real rain benchmark for real single image deraining. To our best knowledge, LHP-Rain is the largest paired real rain dataset (3000 video sequences, 1 million frames) with high image resolution (1920*1080), and the first benchmark to claim and tackle the problem of ground splashing rain removal."
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+                                            "type": "text",
+                                            "content": "- We design a novel robust low-rank tensor recovery model for video deraining to better acquire paired GT. We provide detailed analysis to show RLRTR can better differ the rain from static background than previous datasets."
+                                        }
+                                    ]
+                                }
+                            ],
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+                        {
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+                                            "type": "text",
+                                            "content": "- We propose a new transformer-based single image de- raining baseline, which exploits both self-attention and cross-layer attention between the rain and image layer for better representation. Extensive experiments on different real datasets verify the superiority of proposed method."
+                                        }
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+                                    "type": "text",
+                                    "content": "2. Related Work"
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+                                    "content": "Real rain datasets. At present, the researchers have mostly focused on the network architecture design, while relative fewer attention has been paid on the real rain dataset. The insufficiency of realistic rain dataset is the main bottleneck to hamper single image deraining. In Table 1, we provide a comprehensive summary of existing real rain datasets, which can be classified into two categories: rainy image only and paired rain-image. The former can be utilized via semi-supervised [40, 13] or unsupervised methods [7, 51]. The latter can be conveniently utilized by the supervised training."
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+                                    "content": "The key to paired real dataset is how to acquire the pseudo-'clean' image from its rainy counterpart. There are two main ways to construct the pairs: video-based generation (SPAData [37], RealRain-1K [20]), and time-interval acquisition (RainDS [32], GT-Rain [1]). All these datasets should ensure that the camera is strictly immobile during the acquisition process. SPA-data [37] was the first presented paired real dataset which utilized the human-supervised percentile video"
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+                                            "type": "text",
+                                            "content": "Figure 2: Features of the proposed benchmark LHP-Rain. (a) Distribution of rain and scene of the proposed benchmark. (b) Our proposed LHP-Rain outperforms others in terms of rain diversity and sequence amount. (c) LHP-Rain collects high-resolution and annotated rainy images without copyright, compression and blur."
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+                                    "content": "filtering to obtain the GT. Instead of generation, GT-Rain [1] collected the pairs of same scene under rainy and good weather, respectively. Similar idea has been adopt in RainDS [32] by manually mimicking rainfall with a sprinkler."
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+                                    "content": "Single image deraining. The single image deraining methods have made great progress in last decade including the optimization models [26, 22, 4], deep convolutional network [12, 36, 10] and transformer [35, 44]. Fu et al. [9] first introduced the residual deep CNN for single image deraining. Latter, the researchers have further improved the network depth by stacking similar modules, such as the well-known recurrent [21, 49] and multi-stage progressive [33, 53] strategies. Meanwhile, the multi-scale has been widely explored to improve the representation such as the multi-scale fusion [14] and wavelet decomposition [46]. Further, the side information about the rain attribute: density [54], depth [12], directionality [38], location [47], non-local [17] have been extensively utilized to enhance the deraining performance."
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+                                    "content": "Due to the difficulty and inconvenience of collecting real rain videos, the video sequences and frames of existing paired real rain datasets are still limited as shown in Table 1. In this work, we collect the real rain sequences by smartphones with "
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+                                    "content": " lens focal length, sampled in 30 fps. The data collection process is illustrated in Fig. 3(a). Firstly, to keep the camera immobile, we employ tripod to capture real rain videos with static background (no moving object except rain). For each sequence, we record approximate 15 seconds and extract the intermediate steady 10s into our dataset. Then, we manually pick out moving object to remove unexpected disturbance. Finally, we employ the proposed RLRTR (Section 3.3) to obtain high-quality GT."
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+                                    "content": "Rain with higher-diversity and larger-scale. We concern not only the sequence number and total frames but also the rain diversity of realistic rain, which both have great impact on the generalization for real-world rain. In Fig. 2(b), we show the statistic distribution of rain diversity and sequences/frames in typical real paired rain dataset. All datasets concern about the noticeable rain streak, especially SPA-data [37]. RainDS [32] additionally takes the raindrop into consideration with 1000 frames, while GT-Rain [1] and RealRain-1K [20] further capture the accumulation veiling artifact in heavy rain. LHP-Rain contains not only rain streak and veiling in the sky, but also challenging highlight occlusion and splashing water on the ground. To our best knowledge, the proposed LHP-Rain is the first benchmark to collect and tackle ground splashing rain in the real world, which is commonly ignored by previous existing datasets."
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+                                    "content": "Image with higher-resolution and abundant objects. The existing datasets pay much attention to the rain, ignoring that the high-quality image is also what we really need. Unfortunately, existing realistic rainy images are generally downloaded from the Internet with various problems about the image: compression artifact, watermark, low-resolution, out-of-focus blur, without objects to name a few, which may cause challenges for high-level vision applications. In Fig. 2(c), we show the typical examples in each dataset. The image background of RealRain-1K [20] suffers from serious out-of-focus blur, since they have manually focused on the rain on purpose. GT-Rain [1] contains obvious compression artifact, since it origins from the compressed Youtube stream. There are numerous scenes with narrow views and watermark in the SPA-data [37], because they only release patches (256*256) cropped from original frames."
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+                                    "content": "To improve the image quality, we personally capture high-resolution (1920*1080) realistic rain videos by smartphones. Moreover, LHP-Rain is not only designed for rain restoration, but also important for object detection and segmentation tasks under adverse weather, with abundant objects which are oriented for self-driving and video surveillance scenes. Thus, we provide annotations for object detection and lane segmentation. Five typical objects including person, car, bicycle, motorcycle and bus are annotated by bounding box with 326,961 instances totally. For lane segmentation, we annotate 24,464 lane masks to evaluate the effect of rain splashing removal. Note that the same object in different frames will be regarded as different instances because rain is inconstant and changing frame by frame."
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+                                    "content": "Higher-quality ground-truth. The quality of GT is critical for paired real rain dataset. It is difficult to determine what is good or bad GT in an absolutely fair way. In this paper, we assume that the better the rain removal, the better the image quality is. Therefore, we employ several no reference image quality assessments: DIIVINE [29], NIQE [28] and B-FEN [43], to evaluate the image quality of the rain-free image. The former two are hand-crafted based general image quality indexes, and the last one B-FEN is the learning based index especially designed for de-raining quality assessment. We select all the video backgrounds in SPA-data [37], GT-Rain [1], RealRain-1K [20] and LHP-Rain for evaluation. In"
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+                                            "content": "Figure 5: Analysis of different video deraining results on our dataset. From left to right, the first column is the original rainy frame, and the remaining five columns represent different methods, namely Median Filter, SPA, FastDeRain, J4R-Net and the proposed RLRTR. From top to bottom, the first row shows the deraining results, the second row is the rain layer of the deraining results, the third row denotes the section line of the deraining results and the last row represents the horizontal and vertical gradient distributions of the deraining results."
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+                                            "content": "Fig. 4, we can observe that the proposed LHP-Rain consistently obtains the best results in terms of different evaluation indexes which strongly support the higher-quality of the GT."
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O} \\in \\mathbb{R}^{h \\times w \\times t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        427,
+                                        288,
+                                        525
+                                    ],
+                                    "type": "text",
+                                    "content": ", the key is how to properly obtain the paired GT. The existing methods simply employ the naive filtering technique benefiting from the temporal consistency of the static background. Due to the slight camera vibration caused by the wild wind, we further leverage an affine transformation operator "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        427,
+                                        288,
+                                        525
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        427,
+                                        288,
+                                        525
+                                    ],
+                                    "type": "text",
+                                    "content": " [52] to achieve the pixel-level alignment of each frame. Thus, a multi-frame rainy video can be described as the following formula:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        121,
+                        529,
+                        287,
+                        543
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        121,
+                                        529,
+                                        287,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {O} \\circ \\tau = \\mathcal {B} + \\mathcal {R} + \\mathcal {N}, \\tag {1}",
+                                    "image_path": "df1a6f3093f6d47e86a262f4c1a7d442460670c8147eb6398b53766b35af8087.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B} \\in \\mathbb{R}^{h \\times w \\times t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " is the rain-free video, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R} \\in \\mathbb{R}^{h \\times w \\times t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the rains, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N} \\in \\mathbb{R}^{h \\times w \\times t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the random noise, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        544,
+                                        288,
+                                        616
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the affine transformation to ensure the rainy video of each frame is pixel-level aligned. In this work, we formulate the video deraining into inverse problem via the maximum-a-posterior as follow:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\min  _ {\\mathcal {B}, \\mathcal {R}, \\tau} \\frac {1}{2} | | \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau | | _ {F} ^ {2} + \\omega P _ {b} (\\mathcal {B}) + \\mu P _ {r} (\\mathcal {R}), \\tag {2}",
+                                    "image_path": "1277f294a78ac5005a792915a0684b6a095d7ad71a6fdee92002135d35e3d5fe.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
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+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{r}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " are the prior knowledge for the image and rain, respectively, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\omega"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mu"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " are the corresponding hyperparameters. As for the aligned rainy video, when there are no moving objects except the rain, the rain-free background image is the same for all rainy frames. That is to say, clean video "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        642,
+                                        289,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " has extreme global low-rank property along the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        365,
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+                                    ],
+                                    "type": "text",
+                                    "content": "temporal dimension, ideally its rank is equal to one for each scene. On the other hand, the clean video "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        365,
+                                        547,
+                                        473
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        473
+                                    ],
+                                    "type": "text",
+                                    "content": " also has very non-local low-rank property along the spatial dimension, due to the self-similarity widely employed in image restoration [8]. Moreover, we further take the local smoothness of the video "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        365,
+                                        547,
+                                        473
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        365,
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+                                        473
+                                    ],
+                                    "type": "text",
+                                    "content": " into consideration via the total variation (TV) regularization [4]. Thus, the joint global-nonlocal-local prior along both the spatial and temporal dimension has been fully exploited for better representation of the static video "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        365,
+                                        547,
+                                        473
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        365,
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+                                        473
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "P _ {b} (\\mathcal {B}) = \\omega \\sum_ {i} \\left(\\frac {1}{\\lambda_ {i} ^ {2}} | | \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} | | _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}\\right) + \\gamma | | \\nabla_ {t} \\mathcal {B} | | _ {1}, \\tag {3}",
+                                    "image_path": "0c8a079db2f9a91d29908577cfabacec28b50c48d286c94e95b500bf5b565673.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{S}_i\\mathcal{B}\\in \\mathbb{R}^{p^2\\times k\\times t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " is the constructed 3-D tensor via the non-local clustering of a sub-cubic "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u_{i}\\in \\mathbb{R}^{p\\times p\\times t}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " [3], "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " are the spatial size and number of the sub-cubic respectively, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_{i}\\in \\mathbb{R}^{d\\times t}(d\\ll t)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " is an orthogonal subspace projection matrix used to capture the temporal low-rank property, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
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+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\times_3"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " is the tensor product along the temporal dimension [16], "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the low-rank approximation variable, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "||\\bullet ||_{ttn}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
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+                                    ],
+                                    "type": "text",
+                                    "content": " means the tensor nuclear norm for simplicity [3], "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nabla_t"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " is the difference operator, "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\gamma"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
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+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
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+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": " is the regularization parameters. As for the rain "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{R}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "text",
+                                    "content": ", we formulate it as the sparse error [42] via the "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
+                                        547,
+                                        635
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{1}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        502,
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+                                    ],
+                                    "type": "text",
+                                    "content": " sparsity. Thus, the Eq. (2) can be expressed as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\left\\{\\hat {\\mathcal {B}}, \\hat {\\mathcal {R}}, \\hat {\\mathcal {J}} _ {i}, \\hat {\\tau}, \\hat {Q} _ {i} \\right\\} = \\arg \\min  _ {\\mathcal {B}, \\mathcal {R}, \\mathcal {J} _ {i}, \\tau , Q _ {i}} \\frac {1}{2} \\| \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau \\| _ {F} ^ {2} \\tag {4} \\\\ + \\mu | | \\mathcal {R} | | _ {1} + \\omega \\sum_ {i} \\left(\\frac {1}{\\lambda_ {i} ^ {2}} | | \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} | | _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}\\right) + \\gamma | | \\nabla_ {t} \\mathcal {B} | | _ {1}. \\\\ \\end{array}",
+                                    "image_path": "43f7eba321b559551c011dc5186187d0a2095d2ea47080d79033524e32a26376.jpg"
+                                }
+                            ]
+                        }
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Optimization. Due to the difficulty of estimating multiple variables directly, we adopt the alternating minimization"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
+            "discarded_blocks": [
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+                                    "content": "12101"
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+                                            "content": "Table 2: Quantitative comparisons with SOTA supervised methods on paired real datasets SPA-data (A), GT-Rain (B) and proposed LHP-Rain (C) under 9 different task settings. X→Y means training on the dataset X and testing on the dataset Y. The degraded results of the three datasets are also provided. Top "
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+                                            "content": "1_{st}"
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+                                            ],
+                                            "type": "text",
+                                            "content": " and "
+                                        },
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+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "2_{nd}"
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " results are marked in red and blue respectively."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 0,
+                            "angle": 0,
+                            "type": "table_caption"
+                        },
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+                            ],
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">A→A</td><td colspan=\"2\">B→A</td><td colspan=\"2\">C→A</td><td colspan=\"2\">A→B</td><td colspan=\"2\">B→B</td><td colspan=\"2\">C→B</td><td colspan=\"2\">A→C</td><td colspan=\"2\">B→C</td><td colspan=\"2\">C→C</td></tr><tr><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td><td>PSNR</td><td>SSIM</td></tr><tr><td>Rainy Image</td><td colspan=\"6\">32.60 / 0.9173</td><td colspan=\"6\">19.48 / 0.5849</td><td colspan=\"6\">29.97 / 0.8497</td></tr><tr><td>SPANet</td><td>38.53</td><td>0.9875</td><td>22.93</td><td>0.8207</td><td>31.46</td><td>0.9612</td><td>20.01</td><td>0.6148</td><td>21.51</td><td>0.7145</td><td>19.20</td><td>0.5706</td><td>28.00</td><td>0.8905</td><td>20.10</td><td>0.8061</td><td>31.19</td><td>0.9346</td></tr><tr><td>PReNet</td><td>37.05</td><td>0.9696</td><td>22.44</td><td>0.7713</td><td>32.46</td><td>0.9387</td><td>20.29</td><td>0.5860</td><td>20.65</td><td>0.6005</td><td>19.34</td><td>0.5530</td><td>27.57</td><td>0.8595</td><td>20.91</td><td>0.7222</td><td>32.13</td><td>0.9177</td></tr><tr><td>RCDNet</td><td>39.74</td><td>0.9661</td><td>22.51</td><td>0.8392</td><td>32.30</td><td>0.9378</td><td>20.09</td><td>0.5785</td><td>21.04</td><td>0.6106</td><td>19.09</td><td>0.5264</td><td>25.46</td><td>0.7959</td><td>21.38</td><td>0.8047</td><td>32.34</td><td>0.9152</td></tr><tr><td>JORDER-E</td><td>40.63</td><td>0.9794</td><td>23.47</td><td>0.7426</td><td>31.23</td><td>0.9234</td><td>19.98</td><td>0.5799</td><td>21.24</td><td>0.6854</td><td>18.76</td><td>0.4861</td><td>27.13</td><td>0.8531</td><td>22.14</td><td>0.8433</td><td>31.24</td><td>0.8847</td></tr><tr><td>MPRNet</td><td>46.06</td><td>0.9894</td><td>24.27</td><td>0.8428</td><td>32.37</td><td>0.9379</td><td>19.87</td><td>0.6286</td><td>22.00</td><td>0.6515</td><td>19.47</td><td>0.5889</td><td>28.41</td><td>0.8807</td><td>23.82</td><td>0.8052</td><td>33.34</td><td>0.9309</td></tr><tr><td>GT-Rain</td><td>37.21</td><td>0.9827</td><td>25.30</td><td>0.9243</td><td>26.46</td><td>0.9145</td><td>20.07</td><td>0.6941</td><td>22.51</td><td>0.7300</td><td>21.14</td><td>0.5698</td><td>28.62</td><td>0.8675</td><td>23.19</td><td>0.8098</td><td>32.18</td><td>0.9132</td></tr><tr><td>Uformer-B</td><td>46.42</td><td>0.9917</td><td>24.08</td><td>0.8979</td><td>32.21</td><td>0.9667</td><td>19.70</td><td>0.6875</td><td>21.60</td><td>0.7124</td><td>19.10</td><td>0.6622</td><td>28.74</td><td>0.9262</td><td>22.91</td><td>0.8734</td><td>33.56</td><td>0.9317</td></tr><tr><td>IDT</td><td>45.74</td><td>0.9889</td><td>23.80</td><td>0.8334</td><td>32.38</td><td>0.9422</td><td>20.34</td><td>0.6306</td><td>21.98</td><td>0.6536</td><td>19.44</td><td>0.5977</td><td>26.90</td><td>0.8742</td><td>23.34</td><td>0.7897</td><td>33.02</td><td>0.9310</td></tr><tr><td>SCD-Former</td><td>46.89</td><td>0.9941</td><td>26.13</td><td>0.9122</td><td>34.38</td><td>0.9798</td><td>20.98</td><td>0.6985</td><td>22.79</td><td>0.7684</td><td>21.71</td><td>0.6893</td><td>29.41</td><td>0.9127</td><td>23.56</td><td>0.8626</td><td>34.33</td><td>0.9468</td></tr></table>",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "scheme to solve the Eq. (4) with respect to each variable."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                            "type": "text",
+                                            "content": "1) Affine Transformation "
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+                                            "type": "inline_equation",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": ": Since "
+                                        },
+                                        {
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{O} \\circ \\tau"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " is a nonlinear geometric transform, it's difficult to directly optimize "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\tau"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ". A common technique is to linearize around the current estimate and iterate as follows: "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{O} \\circ \\tau + \\nabla \\mathcal{O} \\triangle \\tau = \\mathcal{B} + \\mathcal{R} + \\mathcal{N}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " [31], where "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\nabla \\mathcal{O}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " is the Jacobian of the image "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{O}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " with respect to "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\tau"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                275,
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+                                            ],
+                                            "type": "text",
+                                            "content": ". This method iteratively approximates the original nonlinear transformation with a locally linear approximation [31]."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                                            "type": "text",
+                                            "content": "2) Rain Estimation "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{R}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": ": By ignoring variables independent of "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{R}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                359,
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+                                            ],
+                                            "type": "text",
+                                            "content": ", we can obtain following subproblem:"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "\\hat {\\mathcal {R}} = \\arg \\min _ {\\mathcal {R}} \\frac {1}{2} | | \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau | | _ {F} ^ {2} + \\mu | | \\mathcal {R} | | _ {1}. (5)",
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+                                }
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "Eq. (5) is a "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "L_{1}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " minimization problem which can be easily solved by soft thresholding with closed-form solution [23]."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "3) Subspace Projection "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "Q_{i}"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                436,
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+                                            ],
+                                            "type": "text",
+                                            "content": ": We enforce the orthogonal constraint on "
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "Q_{i}^{T}Q_{i} = I"
+                                        },
+                                        {
+                                            "bbox": [
+                                                46,
+                                                436,
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+                                            ],
+                                            "type": "text",
+                                            "content": " with the following subproblem:"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                    ],
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\hat {Q} _ {i} = \\arg \\min  _ {Q _ {i} ^ {T} Q _ {i} = I} \\frac {1}{\\lambda_ {i} ^ {2}} \\left\\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\right\\| _ {F} ^ {2}. \\tag {6}",
+                                    "image_path": "8db4c54ade68e9f9c6f4a3ea2fd2fcc2351e373c8988eb98d3499e6d3743e8ac.jpg"
+                                }
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+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "According to [45], Eq. (6) has the closed-form solution, which can be obtained by the rank- "
+                                },
+                                {
+                                    "bbox": [
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+                                        495,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        495,
+                                        287,
+                                        554
+                                    ],
+                                    "type": "text",
+                                    "content": " singular value decomposition of the folding matrix of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        495,
+                                        287,
+                                        554
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{S}_i\\mathcal{B}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        495,
+                                        287,
+                                        554
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        495,
+                                        287,
+                                        554
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        495,
+                                        287,
+                                        554
+                                    ],
+                                    "type": "text",
+                                    "content": " is the measurement of the intrinsic subspace of the temporal dimension. In this work, we empirically set "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        495,
+                                        287,
+                                        554
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d \\leq 3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4) Low-rank Approximation "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{J}_i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ": Dropping the irrelevant variables, we can get following subproblem:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
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+                                    "content": "\\hat {\\mathcal {J}} _ {i} = \\arg \\min  _ {\\mathcal {J} _ {i}} \\frac {1}{\\lambda_ {i} ^ {2}} \\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\| _ {F} ^ {2} + | | \\mathcal {J} _ {i} | | _ {t n n}. \\tag {7}",
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+                                            "content": "This is a typical tensor nuclear norm minimization problem, can be solved by singular value thresholding algorithm [2, 3]."
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+                                            "content": " with the following subproblem:"
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+                                    "content": "\\min  _ {\\mathcal {B}} \\frac {1}{2} \\| \\mathcal {B} + \\mathcal {R} - \\mathcal {O} \\circ \\tau \\| _ {F} ^ {2} + \\omega \\sum_ {i} \\frac {1}{\\lambda_ {i} ^ {2}} \\| \\mathcal {S} _ {i} \\mathcal {B} \\times_ {3} Q _ {i} - \\mathcal {J} _ {i} \\| _ {F} ^ {2} + \\gamma \\| \\nabla_ {t} \\mathcal {B} \\| _ {1}. \\tag {8}",
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+                                    "content": " norm in Eq. (8), we apply the ADMM [23] to decouple this problem into several"
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+                                    "content": "sub-problems with closed-form solutions. Please refer to the supplementary material for the whole algorithm details."
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+                                    "content": "Discussion. Figure 5 illustrates the comparison results of representative video deraining methods: filter-based methods (median filter[20], SPA[37]), optimization-based (FastDeRain[15]) and learning-based methods (J4R-Net[24]). The first and second rows show the video deraining of the image and rain layer, respectively. RLRTR removes almost all the rain from sky to the ground, including rain streaks and splashing, and preserve the image details well, while other methods more or less have rain streaks residual but also cause noticeable damage to the image. In third row, we randomly choose two 1D section lines of the deraining results. The section line of RLRTR is smoother with less burr than other methods. Moreover, the SPA, FastDeRain and the J4R-Net unexpectedly attenuate the spike signal of the share edge, while the proposed RLRTR has well preserve the spike signal. It is well-known the natural image is isotropic and its gradient distribution along different directions should be close to each other [34]. Compared with other results, in forth row the gradient distributions along the vertical and horizontal directions of RLRTR are most similar to each other, which further indirectly verify the naturalness of the deraining result and produce better paired clean-rainy GT."
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+                                    "content": "It has been proved that the rain such as location [47] serving as an attention would be informative in CNN-based image restoration. In this work, we show the rain attention would also be beneficial in transformer. In Fig. 6, we design a simple two-stream Self- and Cross-attention Deraining Transformer (SCD-Former), in which the two-stream network is designed to restore rain and image layer respectively. On one hand, we utilize the self-attention in each rain/image stream independently; on the other hand, we further exploit the cross-layer attention between the rain and image streams. Thus, the rain collaboratively interactive with the image layer to further improve the discriminative representation."
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+                                    "content": "Self-attention and cross-layer attention. In this work, we exploit self-attention on rain and image layer as Rain layer Self-Attention (RSA) and Image layer Self-Attention (ISA). Given the input feature "
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+                                    "content": ", it will be projected into query "
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+                                    "content": " and value "
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+                                    "content": " by three learnable weight matrices "
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+                                    "type": "text",
+                                    "content": ". Then dot-product, scaling and softmax among "
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+                                    "type": "text",
+                                    "content": " will be conducted. The self-attention function is defined as:"
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+                                    "type": "interline_equation",
+                                    "content": "\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V. \\tag {10}",
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+                                    "content": "We further design a Cross-Layer Attention (CLA) module which bridges the attention relationship between rain and image layer. The CLA conducts attention operation among "
+                                },
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+                                    "type": "text",
+                                    "content": " from rain layer and "
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+                                    "type": "text",
+                                    "content": " from image layer as follow:"
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+                                    "type": "interline_equation",
+                                    "content": "C L A \\left(Q _ {r}, K _ {b}, V _ {b}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {r} K _ {b} {} ^ {T}}{\\sqrt {d _ {k}}}\\right) V _ {b}. \\tag {11}",
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+                                    "content": "The token of rain layer serves as a query token "
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+                                    "content": " to interact with the patch tokens "
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " from the image layer through attention mechanism. By calculating the correlation degree between both layers, the highly attentive location of rain residual can be acquired, which provides an extra prior for enhanced feature representation. Note that, the CLA module has been stacked over the whole network. Compared with previous work, SCD-Former exploits not only the self-attention but also cross-layer attention of the rain and image layer for better restoration."
+                                }
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+                                    "content": "Implementation details. We train the network using the Charbonnier loss[5] supervised by the ground truth of rain and image layer:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\left| \\left| O - B - R \\right| \\right| _ {F} ^ {2} + \\lambda_ {r} \\left| \\left| R - \\hat {R} \\right| \\right| _ {1} + \\lambda_ {b} \\left| \\left| B - \\hat {B} \\right| \\right| _ {1}. \\tag {12}",
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+                                    "type": "text",
+                                    "content": " as 1. The images are randomly cropped into "
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+                                    "type": "text",
+                                    "content": " for training. The learning rate of network is set as 0.0002. The Adam optimizer is adopted for optimization with a batch size of 32."
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+                                    "type": "text",
+                                    "content": "5. Experiments"
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+                                    "type": "text",
+                                    "content": "Datasets. We conduct the experiments on paired datasets SPA-data[37], GT-Rain[1] and LHP-Rain. For the SPA-data, training set is cropped from 29,500 images and 1000 rainy images are used for testing. For the GT-Rain, 89 sequences are used for training and 7 sequences are used for testing. For the LHP-Rain, 2100 sequences are used for training and 300 sequences are used for testing. To evaluate the deraining performance on real scenes, we choose typical real rainy images from Internet-data. For single image deraining methods, we select the representative supervised deraining methods, including the CNN-based SPANet[37],"
+                                }
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+                                            "content": "Figure 8: Evaluation of the diversity of the LHP-Rain. We train SCD-Former on different datasets: Rain100L, SPA-data, GT-Rain and LHP-Rain, and test on other datasets. The model trained on LHP-Rain has achieved better deraining results."
+                                        }
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+                                    "type": "text",
+                                    "content": "PReNet[33], RCDNet[36], JORDER-E[47], MPRNet[27], GT-Rain[1], transformer-based Uformer[39] and IDT[44]. Evaluation metrics. We employ the full-reference PSNR and SSIM to evaluate the single image deraining results. Moreover, mean Average Precision (mAP) and Accuracy (Acc) are employed to evaluate object detection and lane segmentation after restoration by deraining methods."
+                                }
+                            ]
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+                                    "content": "5.1. Quantitative Evaluation"
+                                }
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+                                    "content": "Deraining results on benchmarks. We make comparisons with state-of-the-art deraining methods on three datasets SPA-data (A), GT-Rain (B) and LHP-Rain (C). The quantitative results are reported in Table 2 under the following columns: "
+                                },
+                                {
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+                                    "content": ", "
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": ". It is observed that transformer-based methods perform better than most CNN-based methods except for MPRNet in terms of PSNR and SSIM because of the superior representation of self-attention. Note that SCD-Former outperforms the existing state-of-the-art methods on all benchmarks, which confirms the effectiveness of our method with both self and cross-layer attention."
+                                }
+                            ]
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+                                    "content": "5.2. Qualitative Evaluation"
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+                                    "type": "text",
+                                    "content": "Evaluation on LHP-Rain. To further validate the deraining performance, we compare with the qualitative results of typical methods on LHP-Rain. As shown in Fig. 7, SCD-Former achieves more visual pleasing results without rain residual and artifacts comparing with other methods, which cleans the rain streaks and veiling effect on the trees, highlight occlusion on the red car and the ground splashing water."
+                                }
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+                                    "type": "text",
+                                    "content": "Evaluation on real rainy images. To evaluate the performance on real rainy images, we train SCD-Former on synthetic rain Rain100L[48], real rain SPA-data, GT-Rain and LHP-Rain respectively and test on real rainy images. As shown in Fig. 8, the model trained on Rain100L performs poorly due to the huge domain gap. SPA-data and GT-Rain could remove real rain in the sky partially but they cannot handle the splashing water on the ground. The model trained on LHP-Rain has the best deraining performance which simultaneously removes rain streaks, veiling and ground splashing water without destroying image details."
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+                                            "content": "Figure 9: Ablation study of the robust low-rank tensor recovery model. The first row represents the deraining results, and the second row is corresponding rain. The first column is the original rainy frame and the remaining three columns represent the model without subspace projection, without affine transformation and full RLRTR."
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+                                            "content": "Table 3: Ablation study of cross-layer attention."
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+                                            "html": "<table><tr><td>Cross-layer attention</td><td>PSNR / SSIM</td></tr><tr><td>-</td><td>33.92 0.9384</td></tr><tr><td>✓</td><td>34.33 0.9403</td></tr></table>",
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+                                    "content": "5.3. Ablation Study"
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+                                    "type": "text",
+                                    "content": "Effectiveness of subspace projection. The subspace projection is used to characterize the extreme global low-rank property along the temporal dimension. In Fig. 9, there are obvious rain residual without subspace projection, implying that it is insufficient to characterize the property of the temporal dimension relying on the local prior of the temporal smoothness. Since the temporal low-rank property is neglected, leading to the rain residual in the results."
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+                                    "content": "Effectiveness of affine transformation. The affine transformation is exerted to guarantee the pixel-level alignment of rainy video. As shown in Fig. 9, it can be observed that background residual and distortion obviously exist in the rain layer without affine transformation, because the extreme low-rank property along the temporal dimension is affected by data alignment among each frame in the video."
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+                                    "content": "Effectiveness of cross-layer attention. The design aims to find the correlations between rain layer and image layer. After iterations, the image layer sub-network obtains more attention on the rain features brought by cross-layer attention. In Table 3, We show that the complementary guidance from rain layer promotes the restoration of image layer."
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+                                            "content": "Figure 10: Evaluation of high-level tasks on lane segmentation and object detection. The performance improves significantly after removing rain streak and ground splashing from lanes and bicycles by our proposed SCD-Former."
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+                                            "content": "Table 4: Evaluation of high-level tasks on deraining results."
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+                                            "html": "<table><tr><td>Method</td><td>Det. (mAP)</td><td>Gain (Det.)</td><td>Seg. (Acc)</td><td>Gain (Seg.)</td></tr><tr><td>Rainy</td><td>0.543</td><td>-</td><td>0.237</td><td>-</td></tr><tr><td>SPANet</td><td>0.563</td><td>+0.020</td><td>0.268</td><td>+0.031</td></tr><tr><td>PReNet</td><td>0.560</td><td>+0.022</td><td>0.255</td><td>+0.018</td></tr><tr><td>RCDNet</td><td>0.556</td><td>+0.018</td><td>0.361</td><td>+0.124</td></tr><tr><td>JORDER-E</td><td>0.568</td><td>+0.025</td><td>0.385</td><td>+0.148</td></tr><tr><td>MPRNet</td><td>0.560</td><td>+0.017</td><td>0.350</td><td>+0.113</td></tr><tr><td>Uformer-B</td><td>0.568</td><td>+0.025</td><td>0.306</td><td>+0.069</td></tr><tr><td>IDT</td><td>0.570</td><td>+0.027</td><td>0.365</td><td>+0.128</td></tr><tr><td>SCD-Former</td><td>0.575</td><td>+0.031</td><td>0.449</td><td>+0.212</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Rain diversity of different datasets. The rain diversity of dataset can be validated by the experiment of training models on one dataset and testing on the other unseen datasets among SPA-data (A), GT-Rain (B) and LHP-Rain (C). As shown in Table 2, on one hand, the best results of "
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+                                    "content": " methods positively improve the performance of A, while all "
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+                                    "type": "text",
+                                    "content": " results performing worse than degraded result of C. On the other hand, the best results of "
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+                                    "content": "\\mathrm{C} \\rightarrow \\mathrm{B}"
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+                                    "type": "text",
+                                    "content": " have promotion while "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{B} \\rightarrow \\mathrm{C}"
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+                                    "type": "text",
+                                    "content": " drop severely. Therefore, the outcome proves that our LHP-Rain contains more diverse rain categories than others, because they could not handle extreme challenging cases such as occlusion and ground splashing."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Evaluation on downstream tasks. We further evaluate the image deraining results on high-level tasks. For object detection, we apply the officialYOLOv5 model on deraning results and report the mean average precision (mAP) of different classes in Table 4, where SCD-Former reaches the best average mAP among typical objects. For lane segmentation, we choose the LaneNet[30] to predict the lane on LHP-Rain and SCD-Former has larger promotion on the segmentation accuracy. It is reasonable because SCD-Former performs well on removing ground splashing water and recovering the lane lines. The visualization results in Fig. 10 shows that the lane on the surface of ground and the bicycles could be properly predicted after deraining by SCD-Former."
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+                                    "content": "User study on benchmarks quality. We look for 126 volunteers to anonymously vote for the benchmark with best quality. Among existing benchmarks, we randomly select"
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+                                            "content": "Figure 11: The limitation of RLRTR. The challenging occlusion effect could be removed by RLRTR from the background while the static haze is preserved."
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+                                            "content": "Table 5: User study on benchmarks quality."
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+                                            "type": "table",
+                                            "html": "<table><tr><td></td><td>LHP-Rain</td><td>SPA</td><td>RealRain1K</td><td>GT-Rain</td></tr><tr><td>Rain diversity</td><td>63%</td><td>8%</td><td>13%</td><td>16%</td></tr><tr><td>Image quality</td><td>51%</td><td>14%</td><td>20%</td><td>15%</td></tr><tr><td>GT quality</td><td>55%</td><td>15%</td><td>16%</td><td>14%</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "100 samples and conduct user study including: rain diversity, image quality (resolution, JEPG, blur) and GT quality. The result is listed in Table 5, where LHP-Rain consistently outperforms other benchmarks more than "
+                                },
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "6. Limitation"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Our proposed video deraining method is limited to remove the haze in the heavy rain scenes. RLRTR is adept at separating the static background from the dynamic rain. However, due to the steadiness of mist in the short interval, which is almost motionless in the background, RLRTR cannot decompose the haze from image layer well. Fig. 11 shows examples of rain and mist in our benchmark. Although the challenging rain patterns such as rain streaks are clearly removed, the result still contains haze. We look forward to handling the static haze in the future."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "7. Conclusion"
+                                }
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+                                    "type": "text",
+                                    "content": "In this paper, we propose a large-scale and high-quality paired real rain benchmark. Our proposed LHP-Rain provides diverse rain categories, especially the ground splashing rain issue which is first claimed in deraining community. The model trained on LHP-Rain could generalize well on various real rainy scenes with great rain removal performance. Moreover, the proposed low-rank tensor recovery model could generate high-quality GT and detailed analysis confirms better results than others. In addition, we propose a single deraining baseline which performs well on removing rain from sky to the ground. Extensive experiments verify the superiority of the proposed benchmark and significantly improves segmentation task after removing splashing."
+                                }
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work was supported in part by the National Natural Science Foundation of China under Grant 61971460 and Grant 62101294, in part by JCJQ Program under Grant 2021-JCJQ-JJ-0060 and in part by the Fundamental Research Funds for the Central Universities, HUST: 2022JYCXJJ001."
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+                                        }
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+                                        }
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+                                        }
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+                        },
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+                                        }
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+                                        }
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diff --git a/2023/FrozenRecon_ Pose-free 3D Scene Reconstruction with Frozen Depth Models/db9b9018-f8d0-4575-958b-789f4b1d37cb_content_list.json b/2023/FrozenRecon_ Pose-free 3D Scene Reconstruction with Frozen Depth Models/db9b9018-f8d0-4575-958b-789f4b1d37cb_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..e7a368e6dc2c04176b7df2618b0b5ceebd2edb9d
--- /dev/null
+++ b/2023/FrozenRecon_ Pose-free 3D Scene Reconstruction with Frozen Depth Models/db9b9018-f8d0-4575-958b-789f4b1d37cb_content_list.json	
@@ -0,0 +1,1584 @@
+[
+    {
+        "type": "text",
+        "text": "FrozenRecon: Pose-free 3D Scene Reconstruction with Frozen Depth Models",
+        "text_level": 1,
+        "bbox": [
+            133,
+            162,
+            839,
+            183
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Guangkai  $\\mathrm{Xu}^{1*}$ , Wei Yin $^{2*}$ , Hao Chen $^{3}$ , Chunhua Shen $^{3,4}$ , Kai Cheng $^{1}$ , Feng Zhao $^{1\\dagger}$",
+        "bbox": [
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+            208,
+            828,
+            224
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "<sup>1</sup> University of Science and Technology of China <sup>2</sup> DJI Technology <sup>3</sup> Zhejiang University, China <sup>4</sup> Ant Group",
+        "bbox": [
+            143,
+            231,
+            828,
+            250
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7abfb43abce9143ceefd254fb70a4b3d5046acce3a6f51919a6e9113c34bdc40.jpg",
+        "image_caption": [
+            "Figure 1: Robust 3D scene reconstruction of challenging and diverse scenes. Given a monocular video, our algorithm reconstructs the 3D scene without requiring offline-acquired camera poses. Significantly, our approach only involves dozens of parameters of each frame to optimize online. Here, the red triangulations denote the estimated camera trajectories."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            116,
+            277,
+            859,
+            551
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
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+            330,
+            627
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "3D scene reconstruction is a long-standing vision task. Existing approaches can be categorized into geometry-based and learning-based methods. The former leverages multi-view geometry but may face catastrophic failures due to the reliance on accurate pixel correspondence across views, while the latter mitigates these issues by learning 2D or 3D representation directly. However, without a large-scale video or 3D training data, it can hardly be generalized to diverse real-world scenarios due to the presence of tens of millions or even billions of optimization parameters in the deep network.",
+        "bbox": [
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+            641,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, robust monocular depth estimation models trained with large-scale datasets have been proven to possess weak 3D geometry prior, but they are insufficient for",
+        "bbox": [
+            112,
+            792,
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+            834
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "reconstruction due to the unknown camera parameters, the affine-invariant property, and inter-frame inconsistency. To address these issues, we propose a novel test-time optimization approach that can transfer the robustness of affine-invariant depth models such as LeReS to challenging diverse scenes while ensuring inter-frame consistency, with only dozens of parameters to optimize per video frame. Specifically, our approach involves freezing the pre-trained affine-invariant depth model's depth predictions, rectifying them by optimizing the unknown scale-shift values with a geometric consistency alignment module, and employing the resulting scale-consistent depth maps to robustly obtain camera poses and achieve dense scene reconstruction, even in low-texture regions. Experiments show that our method achieves state-of-the-art cross-dataset reconstruction on five zero-shot testing datasets. Code is available at: https://aim-uofa.github.io/FrozenRecon/",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            138,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            259,
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Both authors contributed equally. † Corresponding author. Email: fzhao956@ustc.edu.cn.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "9310",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Dense 3D reconstruction is a fundamental vision task, which has a wide range of applications in autonomous driving [7], virtual/augmented reality [4, 37], robot navigation, medical-CAD modeling [32], etc. Existing geometry-based methods and learning-based methods have achieved impressive performance. Despite progress, we observe failure cases in certain real-world scenarios, such as incomplete or noisy reconstruction of low-texture scenes, tracking failures for pose estimation, limited generalization to unseen scenes, etc. In this work, we aim to robustly and efficiently reconstruct diverse scenes on monocular videos, with the intrinsic camera parameters and poses jointly optimized at the same time.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Most 3D scene reconstruction algorithms can be categorized into learning-based [20, 30, 35] and geometry-based methods [43, 2, 3, 14, 38, 17, 15, 16]. The first group of methods typically rely on a strong neural network to learn the scene geometry, which often requires large-scale and high-quality data to optimize for millions or billions of learnable parameters. Such an expensive data requirement limits applications to various scenarios. Furthermore, some methods, such as SC-DepthV3 [31], optimize the depth and poses at the same time, for which the optimization can be challenging and may become stuck in trivial solutions, partly due to the large number of optimization parameters.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In contrast, geometry-based methods find feature correspondences across views to achieve dense 3D reconstruction. Thus, fewer/no training data are needed. The drawback is that these methods can easily fail on texture-less or low-texture scenes. Moreover, planar scenes and in-place rotations also lead to degeneration in camera pose optimization. Occlusion, lighting changes, and low-texture regions can make the dense matching intractable and thus lead to incomplete reconstructions. Seeking to mitigate these limitations, we propose to exploit a pre-trained, robust monocular depth model to obtain scene geometry priors, which can largely ease pose optimization and reconstruction.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, foundation models [21, 1] trained with large-scale datasets can generalize to new datasets/tasks with few samples by optimizing for a small portion of parameters (so-called adaptors). Inspired by the success, we use a pretrained monocular depth model of strong performance such as LeReS [41], and optimize for a very sparse set of parameters for quickly rectifying the depth maps on test videos, such that scale-consistent depth maps can be attained.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Models such as LeReS [41], MiDaS [23], and DPT [22] use millions of training images to train a robust monocular depth model, which generalizes well to diverse scenes. Unfortunately, the predicted depth maps of those models are affine-invariant, i.e., up to an unknown scale and shift compared against the ground-truth metric depth. As pointed out in [41], the unknown shift can cause significant distortion.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Naively fusing pre-frame prediction is prone to cause reconstruction distortion and scale misalignment. Furthermore, the unknown intrinsic camera parameters and poses are another obstacle for multi-frame reconstruction. If we have access to accurate camera parameters, we can fine tune the pre-trained model to solve the above issues, as in [17].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Instead, we freeze the monocular depth model, and on the given videos, we optimize for the global scale value, the global shift value, a local scale map and a local shift map to rectify each predicted affine-invariant depth map. Intrinsic camera parameters and camera poses are also optimized at the same time. The number of parameters that need to be optimized online is only around 30 per frame. This is a sharp contrast compared with learning-based approaches, e.g., SC-DepthV3, where tens of millions of parameters are involved in optimization. The shift and scale parameters are optimized by supervising the photometric consistency and geometric consistency between selected keyframes. Due to the sparsity of optimization parameters and the robustness of the monocular depth model, our method works much better in terms of domain gap compared to existing deep learning methods for this task. At the same time, compared with traditional geometry-based 3D scene reconstruction methods, ours can be more robust to low-texture regions.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In order to validate the robustness of our system, we test on 5 unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Experiments show that our pipeline outperforms recent methods and achieves state-of-the-art reconstruction performance. Besides, we also perform extensive ablation studies to explore the effectiveness of components of our reconstruction pipeline. Our main contributions are summarized as follows:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel pipeline for dense 3D scene reconstruction by using a frozen affine-invariant depth model, and jointly optimizing a sparse set of parameters for rectifying depth maps, camera poses, and intrinsic camera parameters. Our method is robust on diverse unseen scenarios.",
+            "- Experiments on diverse datasets show the robustness of our method and verify the usefulness of each component in our method."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            729,
+            629,
+            744
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Learning-based 3D Scene Reconstruction. Learning-based methods [20, 30, 35] rely on a neural network with a large number of learnable parameters to learn the geometry of scenes. Some approaches generate the 3D voxel volume from the 2D image features of the entire sequence [20] or local fragments [30], and estimate an implicit 3D representation from posed images. Besides, some other algorithms [43, 2, 3] attempt to predict poses and depth maps jointly.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "9311",
+        "bbox": [
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+            888,
+            511,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/8f3655f4b5dc8e4f1cabc58901fcbc4c5bc832de587e248c1274ee8b977b1dde.jpg",
+        "image_caption": [
+            "Figure 2: The pipeline of 3D scene reconstruction. Given a monocular video, we use a frozen, robust monocular depth estimation model to obtain the estimated depths of all frames. Then, we propose a geometric consistency alignment module, which optimizes a sparse set of parameters (i.e., scale, shift, and weight factors) to achieve multi-view geometric consistent depths among all frames. The camera's intrinsic parameters and poses are also optimized simultaneously. As a result, we achieve high-quality dense 3D reconstruction with optimized depths and camera parameters."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            123,
+            861,
+            330
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "They employ an ego-motion network and a depth network to predict relative camera poses and depth maps, and supervise the photo-metric consistency [43, 3] and geometric consistency [3].",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Multi-view Geometry Based 3D Scene Reconstruction. Multi-view geometry based methods [43, 2, 3, 14, 38, 6, 13] achieve dense 3D reconstruction by finding feature correspondences across views. Traditional methods [25, 26] extract image features, establish correspondences between frames, and optimize the pose and depth iteratively, typically using bundle adjustment [34]. To achieve robust feature representation, some methods leverage plane sweeping to establish correspondences with assumed depth values. They usually construct a cost volume with the CNN-extracted features between images [13, 38, 14], and employ a ConvNet to predict depth maps after regularization. Compared with those approaches, ours is less likely to suffer from pose catastrophic failures in low-texture regions and can be more robust to diverse scenes.",
+        "bbox": [
+            112,
+            489,
+            473,
+            695
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Besides, visual SLAM systems [18, 19, 5, 9, 10, 11, 24, 33] also estimate the camera motion and construct the map of unknown environments. Methods of [18, 19, 5, 9] rely on the assumption of geometric or photometric consistency to estimate poses and depth through bundle adjustment. Recent works [24, 33] propose to improve the robustness and accuracy by integrating more representative clues and optimization tools from deep learning. These algorithms focus on accurate pose estimation, but may fail to build dense maps with geometry details.",
+        "bbox": [
+            112,
+            696,
+            473,
+            835
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Robust Monocular Depth Estimation. To achieve robust monocular depth estimation, some methods [23, 22, 41, 39]",
+        "bbox": [
+            114,
+            837,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "learn the affine-invariant depth with large-scale datasets, which is more likely to be robust to unseen scenarios but up to an unknown scale and shift. Although they achieve promising robustness, the estimated affine-invariant depth needs to recover scale-shift values by globally aligning [23, 22, 41] with ground-truth depth. Some algorithms [17, 15, 16] propose to employ robust depth prediction and achieve visually consistent video depth estimation. In contrast, this work focuses on leveraging robust monocular depth models and aiming at dense 3D scene reconstruction without extra offline-obtained information.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            500,
+            617,
+            601,
+            631
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Aiming at 3D reconstruction from a monocular video, we propose a lightweight optimization pipeline to jointly optimize depth maps, camera poses, and intrinsic camera parameters in Figure 2. The core components of our method are the geometric consistency alignment module, optimization objectives, camera parameters initialization, and the keyframe sampling strategy.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "With the sampled images  $\\{\\mathbf{I}_i\\}_{i = 1}^P$  , we first use LeReS [41, 40] to obtain affine-invariant depth maps  $\\{\\mathbf{D}_i^a\\}_{i = 1}^P$  To avoid disastrous point cloud duplication and distortion, we leverage a geometric consistency alignment module  $\\mathcal{F}(\\cdot ,\\cdot ,\\cdot ,\\cdot)$  to retrieve unknown scale and shift of affineinvariant depth and compute scale-consistent depth  $\\mathbf{D}_i$  ..",
+        "bbox": [
+            498,
+            734,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {D} _ {i} = \\mathcal {F} \\left(\\mathbf {D} _ {i} ^ {a}; \\alpha_ {i}, \\beta_ {i}, \\boldsymbol {\\omega} _ {i}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            598,
+            827,
+            856,
+            842
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha_{i},\\beta_{i}$  , and  $\\omega_{i}$  are the optimization variables.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "9312",
+        "bbox": [
+            483,
+            888,
+            514,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/e410eb2234a5bd03857e3f64b399409baeb83423f81f3b8bb7aa89e28a2f306d.jpg",
+        "image_caption": [
+            "Figure 3: The geometric consistency alignment module. We propose to first recover the global scale and shift of depth map, then apply the locally weighted linear regression method to compute the scale map and shift map, and finally achieve scale-consistent depth."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            125,
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+            281
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In order to transfer the robustness of the depth model, three optimization objectives are supervised to ensure multi-frame consistency by warping from source frame  $i$  to reference frame  $j$ . With this warping process, we propose to minimize the color and depth difference between warped points and reference points, i.e., photometric and geometric constraints. An additional regularization constraint is also employed to stabilize the optimization process.",
+        "bbox": [
+            112,
+            345,
+            473,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "During optimization, the consistency supervision relies on two conditions: 1) the warped reference image and source images must have overlaps; 2) nicely overlapped frames can be automatically selected as our keyframes. Therefore, the appropriate initialization of camera parameters and the keyframes' sampling strategy are essential.",
+        "bbox": [
+            112,
+            455,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Finally, with the optimized intrinsic camera parameters, camera poses, and scale-consistent depth maps, we can achieve accurate 3D scene reconstruction with a simple TSDF fusion [42].",
+        "bbox": [
+            112,
+            537,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Optimization",
+        "text_level": 1,
+        "bbox": [
+            114,
+            601,
+            243,
+            616
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We assume a simple pinhole camera model, and use homogeneous representation for all image coordinates. By default, the scale factor in homogeneous coordinate is 1.",
+        "bbox": [
+            114,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Geometric Consistency Alignment Module. The details of geometric consistency alignment module  $\\mathcal{F}(\\cdot)$  are shown in Figure 3. The predicted depths  $\\{\\mathbf{D}_i^a\\}_{i = 1}^P$  are affine-invariant. The unknown scale and shift will cause duplications and distortions if they are incorrectly estimated. To retrieve them, we perform a two-stage alignment, i.e., a global scale-shift alignment, and a local scale-shift alignment. In the global alignment [41], we optimize for a global scale  $\\alpha_{i}$  and a global shift  $\\beta_{i}$  to obtain the globally aligned depth map  $\\mathbf{D}_i^g$  as follows:",
+        "bbox": [
+            114,
+            662,
+            473,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {D} _ {i} ^ {g} = \\alpha_ {i} \\mathbf {D} _ {i} ^ {a} + \\beta_ {i}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            235,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the local alignment, we compute a scale map  $\\mathbf{A}_i\\in$ $\\mathbb{R}^{H\\times W}$  and shift map  $\\mathbf{B}_i\\in \\mathbb{R}^{H\\times W}$  for each frame  $i$  to re",
+        "bbox": [
+            114,
+            837,
+            473,
+            864
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "fine the globally aligned depth. Instead of directly optimizing these two maps, we uniformly sample  $M$  sparse global depth  $\\{d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M$  from the globally aligned depth  $\\mathbf{D}_i^g$ :",
+        "bbox": [
+            500,
+            345,
+            857,
+            388
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nd _ {i} ^ {g} (\\mathbf {p} _ {t}) = f _ {\\mathrm {s}} (\\mathbf {D} _ {i} ^ {g}, \\mathbf {p} _ {i, t}), \\quad \\text {f o r} t = 1 \\dots M,\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            557,
+            398,
+            800,
+            414
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $f_{\\mathrm{s}}(\\cdot ,\\cdot)$  retrieves the depth value at a position; e.g.,  $f_{\\mathrm{s}}(\\mathbf{D}_i^g,\\mathbf{p}_{i,t})$  obtains  $d_i^g (\\mathbf{p}_t)$  from  $\\mathbf{D}_i^g$  at the position  $\\mathbf{p}_{i,t}$ . Then, by multiplying sparse global depth  $\\{d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M$  with the weights  $\\{\\omega_{i,t}\\}_{t = 1}^{M}$ , we compute the sparse anchor points  $\\{\\omega_{i,t}\\cdot d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M$  and use the locally weighted linear regression method [36], i.e.,  $f_{\\mathrm{LWL R}}(\\cdot ,\\cdot)$ , to compute the local scale map  $\\mathbf{A}_i\\in \\mathbb{R}^{H\\times W}$  and local shift map  $\\mathbf{B}_i\\in \\mathbb{R}^{H\\times W}$ . We also describe the  $f_{\\mathrm{LWL R}}(\\cdot ,\\cdot)$  module in detail in the supplementary. Such indirect optimization reduces the parameters to ease optimization. The local alignment is as follows.",
+        "bbox": [
+            500,
+            424,
+            857,
+            563
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbf {A} _ {i}, \\mathbf {B} _ {i} = f _ {\\mathrm {L W L R}} \\left(\\mathbf {D} _ {i} ^ {g}, \\left\\{\\omega_ {i, t} \\cdot d _ {i} ^ {g} \\left(\\mathbf {p} _ {t}\\right) \\right\\} _ {t = 1} ^ {M}\\right), \\\\ \\mathbf {D} _ {i} = \\mathbf {A} _ {i} \\odot \\mathbf {D} _ {i} ^ {g} + \\mathbf {B} _ {i}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            550,
+            573,
+            803,
+            606
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\odot$  means element-wise multiplication, and  $M$  is set to 25 in our experiments. Therefore, in this module, we only need to optimize for 27 parameters for each frame, i.e.,  $\\alpha_{i},\\beta_{i},\\omega_{i}$ . With our geometric consistency alignment module, we can achieve scale-consistent depth.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Representation of Camera Positions and Intrinsic Camera Parameters. We propose to optimize for the relative rotation vector  $\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$  (i.e., Euler angles) and relative translation vector  $\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$  between two adjacent frames. They are initialized to 0 and are transformed to  $4\\times 4$  relative pose matrices  $\\{\\mathbf{P}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$  with  $\\mathcal{H}(\\cdot ,\\cdot)$ . The relative pose matrices  $\\{\\mathbf{P}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$  are transformed into camera-to-world poses matrices  $\\{\\mathbf{P}_i\\}_{i = 1}^P$  with the product operation. Such initialization ensures the initial overlap of keyframes. For intrinsic camera parameters, we assume a simple pinhole camera model, initialize the focal length to be  $f_{0} = 1.2\\cdot \\max (H,W)$ , and learn the focal length with a learnable scalar  $\\delta$ . We assume that the optical center is at",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9313",
+        "bbox": [
+            483,
+            888,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the image center. Thus for camera parameters, we need to optimize for  $6(P - 1) + 1$  variables:",
+        "bbox": [
+            114,
+            127,
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+            155
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {P} _ {i \\rightarrow (i + 1)} = \\mathcal {H} (\\mathbf {r} _ {i \\rightarrow (i + 1)}, \\mathbf {t} _ {i \\rightarrow (i + 1)}), \\quad \\mathbf {P} _ {1} = \\mathbf {E} _ {4, 4},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            132,
+            164,
+            437,
+            180
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {P} _ {i} = \\mathbf {P} _ {1} \\prod_ {k = 1} ^ {i - 1} \\mathbf {P} _ {k \\rightarrow (k + 1)}, \\quad \\mathbf {K} = \\left[\\begin{array}{c c c}\\delta f _ {0}&0&W / 2\\\\0&\\delta f _ {0}&H / 2\\\\0&0&1\\end{array}\\right], \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{E}_{4,4}$  is the  $4\\times 4$  elementary matrix.",
+        "bbox": [
+            114,
+            234,
+            374,
+            247
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Optimization Objectives. The image coordinate  $\\mathbf{p}_i$  in frame  $i$  can be wrapped to frame  $j$  as follows.",
+        "bbox": [
+            114,
+            247,
+            472,
+            275
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} f _ {s} \\left(\\mathbf {D} _ {i \\rightarrow j}, \\mathbf {p} _ {i}\\right) \\mathbf {p} _ {i \\rightarrow j} = \\mathbf {K R} _ {j} ^ {\\top} \\left[ \\mathbf {R} _ {i} \\mathbf {K} ^ {- 1} f _ {s} \\left(\\mathbf {D} _ {i}, \\mathbf {p} _ {i}\\right) \\mathbf {p} _ {i} + \\mathbf {t} _ {i} - \\mathbf {t} _ {j} \\right], \\\\ \\mathbf {p} _ {i}, \\mathbf {p} _ {i \\rightarrow j}, \\mathbf {t} _ {i}, \\mathbf {t} _ {j} \\in \\mathbb {R} ^ {3 \\times 1}, \\quad \\mathbf {R} _ {i}, \\mathbf {R} _ {j}, \\mathbf {K} \\in \\mathbb {R} ^ {3 \\times 3}, \\tag {5} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            282,
+            486,
+            330
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{K}$  is the intrinsic camera parameter.  $\\mathbf{R}_i$  and  $\\mathbf{t}_i$  are the camera-to-world rotation and translation matrices, and  $\\mathbf{P}_i = \\begin{bmatrix} \\mathbf{R}_i & \\mathbf{t}_i \\\\ \\mathbf{0} & 1 \\end{bmatrix}$ ,  $\\mathbf{p}_{i\\rightarrow j}$  is the point warped from  $\\mathbf{p}_i$  of frame  $i$  to frame  $j$ , and  $\\mathbf{D}_{i\\rightarrow j}$  is the warped depth map.",
+        "bbox": [
+            114,
+            330,
+            472,
+            398
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To optimize the proposed variables including  $\\{\\alpha_{i}\\}_{i = 1}^{P}$ ,  $\\{\\beta_i\\}_{i = 1}^P$ ,  $\\delta$ ,  $\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$ ,  $\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$ , and  $\\{\\omega_{i}\\}_{i = 1}^{P}$  we propose to use the pixel-wise photometric and geometric constraint [2] together to ensure the consistency of color and depth along the video as follows.",
+        "bbox": [
+            114,
+            397,
+            472,
+            465
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {p c} = \\frac {1}{| V |} \\sum_ {\\substack {\\mathbf {p} \\in V\\\\(i, j) \\in K}} | f _ {\\mathrm {s}} (\\mathbf {I} _ {i}, \\mathbf {p} _ {i}) - f _ {\\mathrm {s}} (\\mathbf {I} _ {j}, \\mathbf {p} _ {i \\rightarrow j}) |, \\tag{6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            140,
+            474,
+            472,
+            513
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {g c} = \\frac {1}{| V |} \\sum_ {\\substack {\\mathbf {p} \\in V\\\\(i, j) \\in K}} \\frac {\\left| f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {j} , \\mathbf {p} _ {i \\rightarrow j}\\right) - f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {i \\rightarrow j} , \\mathbf {p} _ {i}\\right) \\right|}{f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {j} , \\mathbf {p} _ {i \\rightarrow j}\\right) + f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {i \\rightarrow j} , \\mathbf {p} _ {i}\\right)}, \\tag{7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            534,
+            472,
+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $V$  represents all valid points successfully projected from frame  $i$  to frame  $j$ ,  $K$  is the selected keyframe pairs.",
+        "bbox": [
+            114,
+            582,
+            472,
+            609
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we enforce a regularization term on the sampled sparse anchor points:",
+        "bbox": [
+            114,
+            609,
+            472,
+            638
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {r e g u} = \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {M} | 1 - \\omega_ {i, t} |, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            207,
+            646,
+            472,
+            685
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The overall constraints are as follows.",
+        "bbox": [
+            133,
+            691,
+            361,
+            705
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL = \\lambda_ {p c} L _ {p c} + \\lambda_ {g c} L _ {g c} + \\lambda_ {r e g u} L _ {r e g u}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            176,
+            715,
+            472,
+            732
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{pc},\\lambda_{gc}$  , and  $\\lambda_{regu}$  are weights to balance them.",
+        "bbox": [
+            114,
+            739,
+            447,
+            755
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Optimization Details. Before we perform optimization, we first sample  $P$  frames from the video to reduce the time complexity. With these sampled frames, we perform the keyframes sampling and optimization, which consists of two stages, i.e., local keyframes sampling for optimization, and global keyframes sampling for optimization.",
+        "bbox": [
+            114,
+            753,
+            472,
+            835
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Local keyframes sampling and optimization. In optimization, we first sample local keyframes from the  $k$  nearest",
+        "bbox": [
+            114,
+            837,
+            472,
+            864
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Optimization Algorithm",
+        "text_level": 1,
+        "bbox": [
+            501,
+            127,
+            728,
+            140
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Input:  $N$  images  $\\{\\mathbf{I}_i\\}_{i = 1}^N$",
+        "bbox": [
+            501,
+            145,
+            645,
+            159
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Output: scale-consistent depth maps  $\\{\\mathbf{D}_i\\}_{i = 1}^P$  intrinsic camera parameter K, camera-to-world camera poses  $\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}$",
+        "bbox": [
+            501,
+            157,
+            856,
+            184
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Sample  $P$  images  $\\{\\mathbf{I}_i\\}_{i = 1}^P$  from  $\\{\\mathbf{I}_i\\}_{i = 1}^N$",
+            "2: Obtain affine-invariant depth  $\\{\\mathbf{D}_i^q\\}_{i = 1}^P$  from  $\\{\\mathbf{I}_i\\}_{i = 1}^P$",
+            "3: Initialize the global scale  $\\{\\alpha_i\\}_{i = 1}^P$  , global shift  $\\{\\beta_i\\}_{i = 1}^P$  , focal length scalar  $\\delta$  , relative rotation  $\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$  , relative translation  $\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}$  , sparse points weight  $\\{\\omega_{i}\\}_{i = 1}^{P}$"
+        ],
+        "bbox": [
+            508,
+            183,
+            856,
+            247
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4: for stage in [Local, Global] do",
+        "bbox": [
+            508,
+            247,
+            704,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "5: for iter  $= 1$  to iterations do",
+            "6: Compute  $\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}$  and  $\\mathbf{K}$  with Eq. (4)",
+            "7: if stage = Local then",
+            "8: Sample keyframe pairs  $\\{(i_k,j_k)\\}_{k = 1}^K$  with Eq. (10)"
+        ],
+        "bbox": [
+            508,
+            260,
+            846,
+            311
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "9:",
+        "bbox": [
+            508,
+            311,
+            522,
+            320
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "10: Sample keyframe pairs  $\\{(i_k,j_k)\\}_{k = 1}^K$  with Eq. (11)",
+            "11: end if",
+            "12: for keyframe pair  $(i,j)$  in  $\\{(i_k,j_k)\\}_{k = 1}^K$  do",
+            "13: Compute scale-consistent depth  $\\mathbf{D}_i$ ,  $\\mathbf{D}_j$  with Eq. (3);",
+            "14: Warp  $\\mathbf{p}_i$  from frame  $i$  to frame  $j$ , get warped depth  $\\mathbf{D}_{i\\rightarrow j}$  and warped locations  $\\mathbf{p}_{i\\rightarrow j}$  with Eq. (5)",
+            "15: Compute optimization objectives with Eq. (9)",
+            "16: end for",
+            "17: Back-propagate and update  $\\{\\alpha_i\\}_{i=1}^P$ ,  $\\{\\beta_i\\}_{i=1}^P$ ,  $\\delta$ ,  $\\{\\mathbf{r}_{i \\to (i+1)}\\}_{i=1}^{P-1}$ ,  $\\{\\mathbf{t}_{i \\to (i+1)}\\}_{i=1}^{P-1}$ ,  $\\{\\pmb{\\omega}_i\\}_{i=1}^P$",
+            "18: end for",
+            "19: end for",
+            "20: Compute scale-consistent depth maps  $\\{\\mathbf{D}_i\\}_{i = 1}^P$  with Eq. (3), compute camera parameters  $\\mathbf{K}$  and  $\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}$  with Eq. (4)"
+        ],
+        "bbox": [
+            501,
+            321,
+            856,
+            500
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "frames of each reference frame.  $k$  is set to 6 in our experiments. To reduce computation time complexity, we do not use all these local keyframes with the current frame but select them based on probability. The probability for each keyframe is set as follows.",
+        "bbox": [
+            498,
+            526,
+            856,
+            595
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {l} = \\left\\{ \\begin{array}{l} \\frac {1}{k}, \\text {i f k - n e a r e s t n e i g h b o r s ,} \\\\ 0, \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            570,
+            604,
+            854,
+            648
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $p_l$  is the keyframe sample probability.",
+        "bbox": [
+            500,
+            656,
+            767,
+            670
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Global keyframes sampling and optimization. We further perform global keyframes sampling and optimization to improve long-range consistency. For each reference frame, all other frames are regarded as paired keyframes, but they are labeled with different sampling probabilities. We compute the relative pose between each reference frame  $\\mathbf{I}_i$  and any other frame  $\\mathbf{I}_j$ . Based on the relative pose angle  $\\theta_{ij}$ , we set the global sampling probability  $p_g$  as follows.",
+        "bbox": [
+            498,
+            670,
+            856,
+            780
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {g} = \\frac {p _ {l} + p}{2}, p = \\left\\{ \\begin{array}{c} \\frac {\\theta_ {i j}}{\\phi^ {2}}, \\text {i f} 0 <   \\theta_ {i j} \\leq \\phi \\\\ \\frac {2}{\\phi} - \\frac {\\theta_ {i j}}{\\phi^ {2}}, \\text {i f} \\phi <   \\theta_ {i j} <   2 \\phi , \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            517,
+            789,
+            856,
+            868
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "9314",
+        "bbox": [
+            483,
+            888,
+            513,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/be762bba1d9e41b12763bdbf7129e83d21079343fdb2737a24e067ccc97da0f8.jpg",
+        "table_caption": [
+            "Table 1: Quantitative comparison of zero-shot 3D scene reconstruction with state-of-the-art methods. We compare our method with seven categories of reconstruction algorithms on several video sequences of five unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Note that NeuralRecon is trained on ScanNet [8], * denotes ground-truth camera poses are given, and “Rank” means average ranking performance of each column. We evaluate the Chamfer distance  $\\mathrm{C} - {l}_{1}$  and F-score with a threshold of  $5\\mathrm{\\;{cm}}$  . As a result,we achieve state-of-the-art rank on the five zero-shot datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">NYU [28]</td><td colspan=\"2\">ScanNet [8]</td><td colspan=\"2\">7-Scenes [27]</td><td colspan=\"2\">TUM [29]</td><td colspan=\"2\">KITTI [12]</td><td rowspan=\"2\">Rank</td></tr><tr><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>NeuralRecon* [30]</td><td>0.487</td><td>0.185</td><td colspan=\"2\">trained on ScanNet</td><td>0.235</td><td>0.219</td><td>0.435</td><td>0.241</td><td colspan=\"2\">failed on KITTI</td><td>8.125</td></tr><tr><td>DPSNet* [14]</td><td>0.198</td><td>0.391</td><td>0.299</td><td>0.266</td><td>0.574</td><td>0.142</td><td>0.336</td><td>0.263</td><td>0.290</td><td>0.232</td><td>4.800</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.139</td><td>0.481</td><td>0.379</td><td>0.292</td><td>0.235</td><td>0.460</td><td>0.322</td><td>0.439</td><td>2.431</td><td>0.010</td><td>3.600</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.196</td><td>0.458</td><td>0.402</td><td>0.214</td><td>0.252</td><td>0.240</td><td>0.525</td><td>0.244</td><td>4.133</td><td>0.036</td><td>5.500</td></tr><tr><td>CVD [17]</td><td>0.471</td><td>0.302</td><td colspan=\"2\">failed on ScanNet</td><td>0.416</td><td>0.215</td><td>0.378</td><td>0.239</td><td>5.479</td><td>0.029</td><td>7.900</td></tr><tr><td>RCVD [15]</td><td>0.303</td><td>0.346</td><td>0.641</td><td>0.125</td><td>0.497</td><td>0.182</td><td>0.679</td><td>0.218</td><td>58.372</td><td>0.020</td><td>8.300</td></tr><tr><td>GCVD [16]</td><td>0.148</td><td>0.453</td><td>0.631</td><td>0.147</td><td>0.196</td><td>0.326</td><td>0.350</td><td>0.339</td><td>2.127</td><td>0.114</td><td>4.400</td></tr><tr><td>COLMAP [25, 26]</td><td>0.251</td><td>0.343</td><td>0.796</td><td>0.127</td><td>0.513</td><td>0.178</td><td>0.385</td><td>0.249</td><td>107.451</td><td>0.152</td><td>7.300</td></tr><tr><td>DROID-SLAM [33]</td><td>0.224</td><td>0.516</td><td>0.416</td><td>0.384</td><td>0.304</td><td>0.469</td><td>0.285</td><td>0.433</td><td>0.686</td><td>0.155</td><td>3.200</td></tr><tr><td>Ours</td><td>0.099</td><td>0.622</td><td>0.170</td><td>0.410</td><td>0.170</td><td>0.464</td><td>0.211</td><td>0.453</td><td>0.670</td><td>0.151</td><td>1.500</td></tr></table>",
+        "bbox": [
+            114,
+            200,
+            857,
+            351
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/067059cd19850755c30182cfaff9e3c8f69ea7c0971ee9bcdac24a23a31b7462.jpg",
+        "table_caption": [
+            "Table 2: Quantitative comparison of zero-shot depth estimation with state-of-the-art methods. We evaluate the absolute relative error (AbsRel) and percentage of accurate depth pixels  $(\\delta_{1})$  on several videos of five unseen datasets. \"Rank\" means average ranking performance of each column. The gray \"LeReS\" represents performance of affine-invariant depth without any alignment with ground-truth depth. As a result, our algorithm achieves state-of-the-art rank performance."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">NYU [28]</td><td colspan=\"2\">ScanNet [8]</td><td colspan=\"2\">7-Scenes [27]</td><td colspan=\"2\">TUM [29]</td><td colspan=\"2\">KITTI [12]</td><td rowspan=\"2\">Rank</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td></tr><tr><td>DPSNet* [14]</td><td>0.200</td><td>0.662</td><td>0.216</td><td>0.630</td><td>0.201</td><td>0.657</td><td>0.331</td><td>0.457</td><td>0.188</td><td>0.729</td><td>6.4</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.096</td><td>0.921</td><td>0.236</td><td>0.685</td><td>0.145</td><td>0.828</td><td>0.180</td><td>0.742</td><td>0.112</td><td>0.860</td><td>2.7</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.120</td><td>0.858</td><td>0.197</td><td>0.672</td><td>0.188</td><td>0.688</td><td>0.254</td><td>0.569</td><td>0.287</td><td>0.463</td><td>5.2</td></tr><tr><td>CVD [17]</td><td>0.167</td><td>0.837</td><td colspan=\"2\">failed on ScanNet</td><td>0.180</td><td>0.847</td><td>0.148</td><td>0.797</td><td>0.717</td><td>0.215</td><td>5.6</td></tr><tr><td>RCVD [15]</td><td>0.192</td><td>0.700</td><td>0.235</td><td>0.620</td><td>0.241</td><td>0.635</td><td>0.246</td><td>0.612</td><td>0.220</td><td>0.606</td><td>6.6</td></tr><tr><td>GCVD [16]</td><td>0.163</td><td>0.768</td><td>0.316</td><td>0.527</td><td>0.203</td><td>0.650</td><td>0.248</td><td>0.697</td><td>0.240</td><td>0.543</td><td>6.4</td></tr><tr><td>COLMAP [26, 25]</td><td>0.233</td><td>0.722</td><td>0.562</td><td>0.409</td><td>0.268</td><td>0.666</td><td>0.269</td><td>0.665</td><td>0.302</td><td>0.773</td><td>7.2</td></tr><tr><td>DROID-SLAM [33]</td><td>0.143</td><td>0.847</td><td>0.210</td><td>0.773</td><td>0.154</td><td>0.827</td><td>0.210</td><td>0.720</td><td>0.115</td><td>0.914</td><td>3.1</td></tr><tr><td>LeReS [41]</td><td>0.277</td><td>0.508</td><td>0.409</td><td>0.339</td><td>0.414</td><td>0.345</td><td>0.445</td><td>0.320</td><td>0.298</td><td>0.439</td><td>-</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.127</td><td>0.858</td><td>0.135</td><td>0.844</td><td>0.145</td><td>0.799</td><td>0.203</td><td>0.632</td><td>1.8</td></tr></table>",
+        "bbox": [
+            114,
+            425,
+            857,
+            584
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\phi$  is an angle threshold, and  $\\theta_{ij}$  is the relative rotation angle between the source frame  $\\mathbf{I}_i$  and the reference frame  $\\mathbf{I}_j$ .  $p_l$  is the local probability with Eq. (10). The optimization is summarized in Algorithm 1.",
+        "bbox": [
+            114,
+            607,
+            472,
+            662
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            114,
+            674,
+            235,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the 3D reconstruction, scale-consistent depths, optimized camera poses, and optimized intrinsic camera parameters in experiments. More details and analyses including runtime can be found in the supplementary.",
+        "bbox": [
+            112,
+            696,
+            472,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Dense 3D Scene Reconstruction",
+        "text_level": 1,
+        "bbox": [
+            114,
+            760,
+            369,
+            773
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To show the robustness and accuracy of our reconstruction method, we compare it with a learning-based volumetric 3D reconstruction method (NeuralRecon [30]), a multiview depth estimation method (DPSNet [14]), a per-frame scale-shift alignment method (BoostingDepth [36]), an unsupervised video depth estimation method (SC-DepthV3",
+        "bbox": [
+            112,
+            781,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "[31]), some consistent video depth estimation methods (CVD [17], RCVD [15], GCVD [16]), a Structure-from-Motion method COLMAP [26, 25], and a robust deep visual SLAM method (DROID-SLAM [33]) on several video sequences of 5 zero-shot datasets, i.e., NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], KITTI [12]. Note that NeuralRecon is trained on ScanNet, while others are evaluated on unseen scenarios. NeuralRecon and DPSNet require GT poses and camera intrinsic as input, and SC-DepthV3, CVD, and DROID-SLAM require camera intrinsic. For fair comparison, we employ the estimated poses and depths of DROID-SLAM for BoostingDepth (BoostingDepth-DROID) to iteratively align the scale-shift values and filter outliers, as their paper does. Other methods optimize camera parameters on their own.",
+        "bbox": [
+            496,
+            607,
+            857,
+            815
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Quantitative comparisons of zero-shot 3D reconstruction and depth are shown in Table 1 and Table 2 respectively. NeuralRecon [30], DPSNet [14], SC-DepthV3 [31] need",
+        "bbox": [
+            498,
+            821,
+            857,
+            864
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "9315",
+        "bbox": [
+            483,
+            888,
+            513,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/85b5229f03daad98e752a0fd863b5d8d9ccab8bd94b6ef7280648936fd6e2e6b.jpg",
+        "table_caption": [
+            "Table 3: Quantitative comparison of zero-shot pose estimation. \"ATE\", \"RPE-T\", and \"RPE-R\" stand for the absolute trajectory error and the relative pose errors of translation and rotation, respectively. \"%\" represents the percentage of successfully tracked frames. Note that ORB-SLAM3 fails to track the trajectory on some low-texture regions, and can only estimate partial camera poses. Our algorithm achieves comparable performance to ORB-SLAM3 on three unseen datasets and better performance than the video depth estimation algorithms."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">GT Intrinsic</td><td colspan=\"4\">NYU [28]</td><td colspan=\"4\">ScanNet [8]</td><td colspan=\"4\">7-Scenes [27]</td><td colspan=\"4\">TUM [29]</td><td colspan=\"4\">KITTI [12]</td></tr><tr><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td></tr><tr><td>SC-DepthV3 [31]</td><td>✓</td><td>0.241</td><td>0.444</td><td>0.115</td><td>1.000</td><td>0.492</td><td>0.702</td><td>0.327</td><td>1.000</td><td>1.011</td><td>1.644</td><td>0.389</td><td>1.000</td><td>0.528</td><td>0.787</td><td>0.399</td><td>1.000</td><td>1.796</td><td>4.186</td><td>0.077</td><td>1.000</td></tr><tr><td>CVD [17]</td><td>✓</td><td>1.192</td><td>2.049</td><td>0.107</td><td>1.000</td><td>0.734</td><td>1.197</td><td>0.257</td><td>1.000</td><td>0.532</td><td>1.644</td><td>0.378</td><td>1.000</td><td>0.268</td><td>0.844</td><td>0.447</td><td>1.000</td><td>19.32</td><td>24.50</td><td>0.027</td><td>1.000</td></tr><tr><td>RCVD [15]</td><td></td><td>0.460</td><td>1.263</td><td>0.114</td><td>1.000</td><td>1.025</td><td>1.708</td><td>0.615</td><td>1.000</td><td>0.559</td><td>1.545</td><td>0.394</td><td>1.000</td><td>0.626</td><td>1.083</td><td>0.421</td><td>1.000</td><td>134.3</td><td>160.7</td><td>0.463</td><td>1.000</td></tr><tr><td>GCVD [16]</td><td></td><td>0.160</td><td>0.237</td><td>0.083</td><td>1.000</td><td>0.573</td><td>0.979</td><td>0.620</td><td>1.000</td><td>0.259</td><td>0.368</td><td>0.162</td><td>1.000</td><td>0.162</td><td>0.204</td><td>0.113</td><td>1.000</td><td>5.678</td><td>8.733</td><td>0.089</td><td>1.000</td></tr><tr><td>COLMAP [26, 25]</td><td></td><td>0.091</td><td>0.137</td><td>0.055</td><td>1.000</td><td>0.352</td><td>0.426</td><td>0.096</td><td>1.000</td><td>0.062</td><td>0.090</td><td>0.051</td><td>1.000</td><td>0.075</td><td>0.102</td><td>0.064</td><td>1.000</td><td>3.707</td><td>3.454</td><td>0.016</td><td>1.000</td></tr><tr><td>DROID-SLAM [33]</td><td>✓</td><td>0.050</td><td>0.079</td><td>0.032</td><td>1.000</td><td>0.230</td><td>0.230</td><td>0.052</td><td>1.000</td><td>0.050</td><td>0.072</td><td>0.072</td><td>1.000</td><td>0.044</td><td>0.077</td><td>0.079</td><td>1.000</td><td>1.491</td><td>2.302</td><td>0.005</td><td>1.000</td></tr><tr><td>ORB-SLAM3 [5]</td><td>✓</td><td>0.065</td><td>0.097</td><td>0.039</td><td>0.791</td><td>0.208</td><td>0.300</td><td>0.098</td><td>0.426</td><td>0.118</td><td>0.211</td><td>0.121</td><td>0.956</td><td>0.104</td><td>0.144</td><td>0.082</td><td>0.504</td><td>3.124</td><td>3.926</td><td>0.009</td><td>0.971</td></tr><tr><td>Ours</td><td></td><td>0.079</td><td>0.121</td><td>0.046</td><td>1.000</td><td>0.130</td><td>0.184</td><td>0.085</td><td>1.000</td><td>0.141</td><td>0.229</td><td>0.075</td><td>1.000</td><td>0.176</td><td>0.228</td><td>0.151</td><td>1.000</td><td>3.541</td><td>5.663</td><td>0.053</td><td>1.000</td></tr></table>",
+        "bbox": [
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+            205,
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+            306
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/2d084b7b3b792d2363a24ab6bab35f5c970f56211b0f37c840732e39e602c248.jpg",
+        "table_caption": [
+            "Table 4: Quantitative comparison of zero-shot intrinsic camera parameter estimation. \"FOV AbsRel\" represents the absolute relative error of the field of view. Note that only three algorithms can estimate the intrinsic camera parameter from the input video, and our method can achieve accurate and robust performance on four unseen datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td>NYU [28]</td><td>ScanNet [8]</td><td>7-Scenes [27]</td><td>TUM [29]</td><td rowspan=\"2\">Rank</td></tr><tr><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td></tr><tr><td>RCVD [15]</td><td>0.144</td><td>0.148</td><td>0.110</td><td>0.174</td><td>2.75</td></tr><tr><td>GCVD [16]</td><td>0.015</td><td>0.126</td><td>0.143</td><td>0.043</td><td>1.75</td></tr><tr><td>Ours</td><td>0.032</td><td>0.032</td><td>0.085</td><td>0.056</td><td>1.50</td></tr></table>",
+        "bbox": [
+            117,
+            422,
+            470,
+            483
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "to optimize millions of parameters, thus showing less robustness to unseen datasets. Rather than purely per-frame aligning with offline-obtained depth after filtering as BoostingDepth [36] does, we jointly optimize the camera parameters and depth parameters, which ensures consistency between frames and less suffers from outliers of sparse points. CVD [17] fails to reconstruct half of the ScanNet scenarios. Compared with RCVD [15], and GCVD [16], our method employs a global and a local scale-shift recovery strategy, which can rectify the affine-invariant depth to a much more accurate scale-consistent depth. Thus, we can achieve much more accurate reconstructions. The COLMAP [26, 25] struggles to estimate dense depth maps, and thus results in sparse 3D reconstruction. The robust DROID-SLAM [33] focuses on optimizing more robust poses and trajectories with the recurrent module, and spends less effort on dense reconstruction. Thus, their dense reconstruction is more likely to suffer from outliers. In contrast, our optimization is based on dense depth priors and employs a global and local optimization strategy to reduce noise, thus we in general achieve better reconstruction performance.",
+        "bbox": [
+            112,
+            507,
+            473,
+            795
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Quantitative comparisons of zero-shot pose estimation and intrinsic camera parameter estimation are shown in Table 3 and Table 4. Our algorithm achieves comparable performance with the traditional SLAM methods ORBSLAM3 [5] on three datasets. However, the ORB-SLAM3",
+        "bbox": [
+            112,
+            796,
+            473,
+            864
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5dbc8e9eaa44d7abca71bb9cae4e6beb85a27b2e6092d67a041a3ff8e9cf5dc6.jpg",
+        "table_caption": [
+            "Table 5: Runtime analysis on three representative scenes. Our pipeline achieves state-of-the-art reconstruction but only takes around a quarter of an hour to optimize."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>basement_0001a</td><td>bedroom_0015</td><td>chess</td></tr><tr><td>NeuralRecon[30]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DPSNet[14]</td><td>5m 53s</td><td>45s</td><td>12m 20s</td></tr><tr><td>BoostingDepth-DROID[36]</td><td>35s</td><td>10s</td><td>47s</td></tr><tr><td>SC-DepthV3[31]</td><td>1m 47s</td><td>17s</td><td>1m 54s</td></tr><tr><td>CVD[17]</td><td>1h 7m 6s</td><td>12m 30s</td><td>8h 1m 34s</td></tr><tr><td>RCVD[15]</td><td>1h 15m 45s</td><td>10m 6s</td><td>6h 14m 54s</td></tr><tr><td>GCVD[16]</td><td>10m 26s</td><td>2m 37s</td><td>52m 15s</td></tr><tr><td>DROID-SLAM[33]</td><td>35s</td><td>16s</td><td>1m 18s</td></tr><tr><td>COLMAP[25, 26]</td><td>50m 44s</td><td>8m 34s</td><td>9h 40m 49s</td></tr><tr><td>Ours</td><td>14m 55s</td><td>6m 55s</td><td>21m 8s</td></tr></table>",
+        "bbox": [
+            503,
+            381,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "can only estimate the camera poses of partial frames due to the failure of tracking features. In contrast, our algorithm can optimize and interpolate to obtain dense trajectories. Compared to four video depth estimation methods, we can outperform them by a large margin. Note that only ours, RCVD, and GCVD can optimize the intrinsic camera parameters, while others can only employ GT camera intrinsic as input. For intrinsic camera parameter estimation, our algorithm can achieve robust and accurate performance on four unseen datasets.",
+        "bbox": [
+            496,
+            544,
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+            681
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Qualitative comparisons are reported in Figure. 4. NeuralRecon can only reconstruct partial meshes of unseen scenarios. The DPSNet [14] suffers from inaccurate feature correspondences, which cause noisy point clouds. BoostingDepth [36] can only filter out inaccurate points of DROID-SLAM but cannot ensure the temporal consistency, and thus fails to reconstruct consistent mesh. The SC-DepthV3 [31] suffers from the weak supervision of photometric loss and work worse on some low-texture regions. Consistent video depth estimation methods such as GCVD [16] cannot recover the shift of depth maps, which will cause distortions in 3D point clouds. DROID-SLAM [33] concentrates on accurate pose estimation but does not work",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "9316",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/460c41f8206f44978b81beed7426b95a00d7f29102269c04913bc5e04967b497.jpg",
+        "image_caption": [
+            "Figure 4: Qualitative comparison of zero-shot 3D scene reconstruction from a monocular video. We compare our method with five representative algorithms on five unseen datasets. Note that NeuralRecon is trained on ScanNet [8] and can only output uncolored mesh, and * represents the employment of ground-truth camera poses during reconstruction. These methods either suffer from inaccurate pose estimation, or predict noise depth maps (please see the red arrows). As can be seen, our approach can reconstruct better 3D scene shape without any offline-computed camera parameters."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            116,
+            123,
+            859,
+            720
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "well for dense reconstruction, and thus suffering from outliers. In contrast, our method can achieve more robust and",
+        "bbox": [
+            114,
+            823,
+            473,
+            851
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "accurate 3D scene reconstruction, without requiring offline-acquired camera poses and camera intrinsic parameters.",
+        "bbox": [
+            500,
+            823,
+            857,
+            851
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "9317",
+        "bbox": [
+            483,
+            888,
+            513,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/5b330cf71823fca84f8c95305a931a874478c59f49411475daa4aff408286704.jpg",
+        "table_caption": [
+            "Table 6: Comparison of geometric consistency alignment mechanisms on the NYU [28] dataset. \"w/ deform.\" means optimizing the flexible deformation map of RCVD [15] as a replacement for our alignment module. \"Baseline\" means directly optimizing the per-frame pixel-wise depth map without the affine-invariant depth priors. As a result, the employment of our geometric consistency alignment module contributes significantly to the optimization."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr><tr><td>w/ deform. [15]</td><td>0.153</td><td>0.771</td><td>0.145</td><td>0.290</td><td>0.082</td><td>0.160</td><td>0.470</td></tr><tr><td>Baseline</td><td>0.350</td><td>0.466</td><td>0.710</td><td>1.097</td><td>0.215</td><td>0.285</td><td>0.303</td></tr></table>",
+        "bbox": [
+            117,
+            241,
+            470,
+            306
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/89b26cd6ca9d2d464557e349f20d2f733ae7ef168f000601e40996712f4c441c.jpg",
+        "table_caption": [
+            "Table 7: Comparison of optimization objectives on the ScanNet [8] dataset. The photometric constraint supervises the color consistency, the geometric constraint ensures the multi-view geometry consistency, and the regularization constraint stabilizes the convergence of optimization. As a result, the three components of our optimization objectives are all important."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.127</td><td>0.858</td><td>0.271</td><td>0.348</td><td>0.147</td><td>0.170</td><td>0.410</td></tr><tr><td>w/o photo.</td><td>0.219</td><td>0.636</td><td>1.722</td><td>2.331</td><td>1.039</td><td>0.775</td><td>0.169</td></tr><tr><td>w/o geo.</td><td>0.168</td><td>0.750</td><td>0.316</td><td>0.404</td><td>0.179</td><td>0.211</td><td>0.323</td></tr><tr><td>w/o regu.</td><td>0.226</td><td>0.603</td><td>0.245</td><td>0.338</td><td>0.189</td><td>0.220</td><td>0.254</td></tr></table>",
+        "bbox": [
+            117,
+            422,
+            470,
+            507
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "For quantitative efficiency analysis, the runtime comparisons on 40 Intel Xeon Silver 4210 CPUs and an RTX 3090 Ti GPU are presented in Table 5, which includes three representative scenes with 225, 48, and 1000 images, respectively. Our pipeline achieves state-of-the-art reconstruction while only taking about a quarter of an hour to optimize, even for 1000 images. Note that only the time of predicting depth and poses without RGB-D fusion are recorded.",
+        "bbox": [
+            112,
+            531,
+            470,
+            642
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
+            114,
+            650,
+            264,
+            664
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We carry out ablation experiments in terms of essential components of our algorithm to evaluate their effectiveness. Geometric Consistency Alignment Module. Table 6 shows the performance of different geometric consistency alignment modules. Previous consistent video depth methods RCVD and GCVD employ flexible deformation maps (\"w/ deform.\") and aim for more accurate scale-consistent depth. However, they both ignore the shift issues in affine-invariant depth, which is pretty significant in the 3D reconstruction task. By contrast, our method (\"Ours\") proposes a global and local scale shift alignment module for depth rectification. We also compare with a baseline method (\"baseline\"), which directly optimizes all frames' pixel-wise depths without the affine-invariant depth priors. All",
+        "bbox": [
+            112,
+            671,
+            472,
+            864
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/7deb7ca04a014ba926b5d7e11f78bfbd3b7927c9109e33e73b461603a22f16be.jpg",
+        "table_caption": [
+            "Table 8: Effectiveness of our two-stage keyframe sampling and optimization strategy. The \"Local\" stage ensures consistency between the nearest  $k$  keyframes. The \"Global\" stage samples keyframes globally with different sampling probabilities according to the optimized relative poses. As a result, our algorithm achieves better performance with the coarse-to-fine optimization strategy. The experiment is conducted on NYU [28] dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Stage</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Local</td><td>0.111</td><td>0.884</td><td>0.111</td><td>0.179</td><td>0.068</td><td>0.091</td><td>0.593</td></tr><tr><td>Global</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr></table>",
+        "bbox": [
+            503,
+            244,
+            854,
+            306
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "depths are initialized to 1. Our alignment module works much better than previous methods.",
+        "bbox": [
+            496,
+            333,
+            856,
+            359
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Optimization Objectives. To evaluate the effectiveness of each constraint employed in our method, we propose to remove them one by one, and the results are shown in Table 7. We can see that without the photometric constraint or geometric constraint, the performance will degrade a lot. When removing the regularization term, the accuracy of the pose, depth, and reconstruction will also decrease.",
+        "bbox": [
+            496,
+            361,
+            857,
+            455
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of Optimization Stages. Our optimization algorithm is composed of local keyframes optimization (\"Local\") and global keyframes optimization (\"Global\"). The local stage endures the local consistency between the nearest  $k$  keyframes, and can reconstruct roughly accurate 3D scene shapes. The global stage selects long-range keyframes to supervise global consistency. As shown in Table 8, the reconstruction performance improves gradually.",
+        "bbox": [
+            496,
+            458,
+            857,
+            569
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            582,
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+        "type": "text",
+        "text": "In this paper, we have presented an effective pipeline to realize 3D scene reconstruction by leveraging the robustness of affine-invariant depth estimation, freezing the depth model, and jointly optimizing dozens of depth and camera parameters for each frame. Due to the sparsity of parameters, our pipeline can transfer the robustness of seemingly weak depth geometry prior to diverse scenes. Extensive experiments show that our pipeline can achieve robust dense 3D reconstruction on challenging unseen scenes.",
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+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This work was supported by the National Key R&D Program of China (No. 2022ZD0118700), the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            116,
+            126,
+            202,
+            138
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+            "[42] Andy Zeng, Shuran Song, Matthias Nießner, Matthew Fisher, Jianxiong Xiao, and Thomas Funkhouser. 3dmatch: Learning local geometric descriptors from RGB-D recon"
+        ],
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+        "sub_type": "ref_text",
+        "list_items": [
+            "strictions. In IEEE Conf. Comput. Vis. Pattern Recogn., pages 1802-1811, 2017. 4",
+            "[43] Tinghui Zhou, Matthew Brown, Noah Snavely, and David G Lowe. Unsupervised learning of depth and ego-motion from video. In IEEE Conf. Comput. Vis. Pattern Recogn., pages 1851-1858, 2017. 2, 3"
+        ],
+        "bbox": [
+            503,
+            128,
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+]
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diff --git a/2023/FrozenRecon_ Pose-free 3D Scene Reconstruction with Frozen Depth Models/db9b9018-f8d0-4575-958b-789f4b1d37cb_model.json b/2023/FrozenRecon_ Pose-free 3D Scene Reconstruction with Frozen Depth Models/db9b9018-f8d0-4575-958b-789f4b1d37cb_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..c908c63a4340c56e0c26990f4ad1782f0f86fb5c
--- /dev/null
+++ b/2023/FrozenRecon_ Pose-free 3D Scene Reconstruction with Frozen Depth Models/db9b9018-f8d0-4575-958b-789f4b1d37cb_model.json	
@@ -0,0 +1,2279 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.14,
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+                0.209,
+                0.082
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.261,
+                0.044,
+                0.782,
+                0.085
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.135,
+                0.164,
+                0.84,
+                0.184
+            ],
+            "angle": 0,
+            "content": "FrozenRecon: Pose-free 3D Scene Reconstruction with Frozen Depth Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.143,
+                0.209,
+                0.83,
+                0.226
+            ],
+            "angle": 0,
+            "content": "Guangkai \\(\\mathrm{Xu}^{1*}\\), Wei Yin\\(^{2*}\\), Hao Chen\\(^{3}\\), Chunhua Shen\\(^{3,4}\\), Kai Cheng\\(^{1}\\), Feng Zhao\\(^{1\\dagger}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.145,
+                0.232,
+                0.829,
+                0.25
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup> University of Science and Technology of China <sup>2</sup> DJI Technology <sup>3</sup> Zhejiang University, China <sup>4</sup> Ant Group"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.117,
+                0.279,
+                0.861,
+                0.552
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.557,
+                0.86,
+                0.6
+            ],
+            "angle": 0,
+            "content": "Figure 1: Robust 3D scene reconstruction of challenging and diverse scenes. Given a monocular video, our algorithm reconstructs the 3D scene without requiring offline-acquired camera poses. Significantly, our approach only involves dozens of parameters of each frame to optimize online. Here, the red triangulations denote the estimated camera trajectories."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.259,
+                0.613,
+                0.331,
+                0.628
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.642,
+                0.475,
+                0.793
+            ],
+            "angle": 0,
+            "content": "3D scene reconstruction is a long-standing vision task. Existing approaches can be categorized into geometry-based and learning-based methods. The former leverages multi-view geometry but may face catastrophic failures due to the reliance on accurate pixel correspondence across views, while the latter mitigates these issues by learning 2D or 3D representation directly. However, without a large-scale video or 3D training data, it can hardly be generalized to diverse real-world scenarios due to the presence of tens of millions or even billions of optimization parameters in the deep network."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.793,
+                0.474,
+                0.835
+            ],
+            "angle": 0,
+            "content": "Recently, robust monocular depth estimation models trained with large-scale datasets have been proven to possess weak 3D geometry prior, but they are insufficient for"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.615,
+                0.859,
+                0.849
+            ],
+            "angle": 0,
+            "content": "reconstruction due to the unknown camera parameters, the affine-invariant property, and inter-frame inconsistency. To address these issues, we propose a novel test-time optimization approach that can transfer the robustness of affine-invariant depth models such as LeReS to challenging diverse scenes while ensuring inter-frame consistency, with only dozens of parameters to optimize per video frame. Specifically, our approach involves freezing the pre-trained affine-invariant depth model's depth predictions, rectifying them by optimizing the unknown scale-shift values with a geometric consistency alignment module, and employing the resulting scale-consistent depth maps to robustly obtain camera poses and achieve dense scene reconstruction, even in low-texture regions. Experiments show that our method achieves state-of-the-art cross-dataset reconstruction on five zero-shot testing datasets. Code is available at: https://aim-uofa.github.io/FrozenRecon/"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.115,
+                0.841,
+                0.474,
+                0.865
+            ],
+            "angle": 0,
+            "content": "*Both authors contributed equally. † Corresponding author. Email: fzhao956@ustc.edu.cn."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.89,
+                0.516,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9310"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.116,
+                0.127,
+                0.236,
+                0.14
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.15,
+                0.474,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Dense 3D reconstruction is a fundamental vision task, which has a wide range of applications in autonomous driving [7], virtual/augmented reality [4, 37], robot navigation, medical-CAD modeling [32], etc. Existing geometry-based methods and learning-based methods have achieved impressive performance. Despite progress, we observe failure cases in certain real-world scenarios, such as incomplete or noisy reconstruction of low-texture scenes, tracking failures for pose estimation, limited generalization to unseen scenes, etc. In this work, we aim to robustly and efficiently reconstruct diverse scenes on monocular videos, with the intrinsic camera parameters and poses jointly optimized at the same time."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.329,
+                0.474,
+                0.493
+            ],
+            "angle": 0,
+            "content": "Most 3D scene reconstruction algorithms can be categorized into learning-based [20, 30, 35] and geometry-based methods [43, 2, 3, 14, 38, 17, 15, 16]. The first group of methods typically rely on a strong neural network to learn the scene geometry, which often requires large-scale and high-quality data to optimize for millions or billions of learnable parameters. Such an expensive data requirement limits applications to various scenarios. Furthermore, some methods, such as SC-DepthV3 [31], optimize the depth and poses at the same time, for which the optimization can be challenging and may become stuck in trivial solutions, partly due to the large number of optimization parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.494,
+                0.474,
+                0.658
+            ],
+            "angle": 0,
+            "content": "In contrast, geometry-based methods find feature correspondences across views to achieve dense 3D reconstruction. Thus, fewer/no training data are needed. The drawback is that these methods can easily fail on texture-less or low-texture scenes. Moreover, planar scenes and in-place rotations also lead to degeneration in camera pose optimization. Occlusion, lighting changes, and low-texture regions can make the dense matching intractable and thus lead to incomplete reconstructions. Seeking to mitigate these limitations, we propose to exploit a pre-trained, robust monocular depth model to obtain scene geometry priors, which can largely ease pose optimization and reconstruction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.659,
+                0.474,
+                0.768
+            ],
+            "angle": 0,
+            "content": "Recently, foundation models [21, 1] trained with large-scale datasets can generalize to new datasets/tasks with few samples by optimizing for a small portion of parameters (so-called adaptors). Inspired by the success, we use a pretrained monocular depth model of strong performance such as LeReS [41], and optimize for a very sparse set of parameters for quickly rectifying the depth maps on test videos, such that scale-consistent depth maps can be attained."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.769,
+                0.474,
+                0.865
+            ],
+            "angle": 0,
+            "content": "Models such as LeReS [41], MiDaS [23], and DPT [22] use millions of training images to train a robust monocular depth model, which generalizes well to diverse scenes. Unfortunately, the predicted depth maps of those models are affine-invariant, i.e., up to an unknown scale and shift compared against the ground-truth metric depth. As pointed out in [41], the unknown shift can cause significant distortion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.128,
+                0.858,
+                0.21
+            ],
+            "angle": 0,
+            "content": "Naively fusing pre-frame prediction is prone to cause reconstruction distortion and scale misalignment. Furthermore, the unknown intrinsic camera parameters and poses are another obstacle for multi-frame reconstruction. If we have access to accurate camera parameters, we can fine tune the pre-trained model to solve the above issues, as in [17]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.212,
+                0.859,
+                0.459
+            ],
+            "angle": 0,
+            "content": "Instead, we freeze the monocular depth model, and on the given videos, we optimize for the global scale value, the global shift value, a local scale map and a local shift map to rectify each predicted affine-invariant depth map. Intrinsic camera parameters and camera poses are also optimized at the same time. The number of parameters that need to be optimized online is only around 30 per frame. This is a sharp contrast compared with learning-based approaches, e.g., SC-DepthV3, where tens of millions of parameters are involved in optimization. The shift and scale parameters are optimized by supervising the photometric consistency and geometric consistency between selected keyframes. Due to the sparsity of optimization parameters and the robustness of the monocular depth model, our method works much better in terms of domain gap compared to existing deep learning methods for this task. At the same time, compared with traditional geometry-based 3D scene reconstruction methods, ours can be more robust to low-texture regions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.459,
+                0.859,
+                0.568
+            ],
+            "angle": 0,
+            "content": "In order to validate the robustness of our system, we test on 5 unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Experiments show that our pipeline outperforms recent methods and achieves state-of-the-art reconstruction performance. Besides, we also perform extensive ablation studies to explore the effectiveness of components of our reconstruction pipeline. Our main contributions are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.579,
+                0.857,
+                0.661
+            ],
+            "angle": 0,
+            "content": "- We propose a novel pipeline for dense 3D scene reconstruction by using a frozen affine-invariant depth model, and jointly optimizing a sparse set of parameters for rectifying depth maps, camera poses, and intrinsic camera parameters. Our method is robust on diverse unseen scenarios."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.666,
+                0.857,
+                0.707
+            ],
+            "angle": 0,
+            "content": "- Experiments on diverse datasets show the robustness of our method and verify the usefulness of each component in our method."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.518,
+                0.579,
+                0.857,
+                0.707
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+            "bbox": [
+                0.5,
+                0.731,
+                0.63,
+                0.745
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.755,
+                0.859,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Learning-based 3D Scene Reconstruction. Learning-based methods [20, 30, 35] rely on a neural network with a large number of learnable parameters to learn the geometry of scenes. Some approaches generate the 3D voxel volume from the 2D image features of the entire sequence [20] or local fragments [30], and estimate an implicit 3D representation from posed images. Besides, some other algorithms [43, 2, 3] attempt to predict poses and depth maps jointly."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.513,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9311"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.118,
+                0.124,
+                0.862,
+                0.332
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.339,
+                0.862,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Figure 2: The pipeline of 3D scene reconstruction. Given a monocular video, we use a frozen, robust monocular depth estimation model to obtain the estimated depths of all frames. Then, we propose a geometric consistency alignment module, which optimizes a sparse set of parameters (i.e., scale, shift, and weight factors) to achieve multi-view geometric consistent depths among all frames. The camera's intrinsic parameters and poses are also optimized simultaneously. As a result, we achieve high-quality dense 3D reconstruction with optimized depths and camera parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.433,
+                0.474,
+                0.489
+            ],
+            "angle": 0,
+            "content": "They employ an ego-motion network and a depth network to predict relative camera poses and depth maps, and supervise the photo-metric consistency [43, 3] and geometric consistency [3]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.49,
+                0.474,
+                0.696
+            ],
+            "angle": 0,
+            "content": "Multi-view Geometry Based 3D Scene Reconstruction. Multi-view geometry based methods [43, 2, 3, 14, 38, 6, 13] achieve dense 3D reconstruction by finding feature correspondences across views. Traditional methods [25, 26] extract image features, establish correspondences between frames, and optimize the pose and depth iteratively, typically using bundle adjustment [34]. To achieve robust feature representation, some methods leverage plane sweeping to establish correspondences with assumed depth values. They usually construct a cost volume with the CNN-extracted features between images [13, 38, 14], and employ a ConvNet to predict depth maps after regularization. Compared with those approaches, ours is less likely to suffer from pose catastrophic failures in low-texture regions and can be more robust to diverse scenes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.698,
+                0.474,
+                0.836
+            ],
+            "angle": 0,
+            "content": "Besides, visual SLAM systems [18, 19, 5, 9, 10, 11, 24, 33] also estimate the camera motion and construct the map of unknown environments. Methods of [18, 19, 5, 9] rely on the assumption of geometric or photometric consistency to estimate poses and depth through bundle adjustment. Recent works [24, 33] propose to improve the robustness and accuracy by integrating more representative clues and optimization tools from deep learning. These algorithms focus on accurate pose estimation, but may fail to build dense maps with geometry details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.838,
+                0.474,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Robust Monocular Depth Estimation. To achieve robust monocular depth estimation, some methods [23, 22, 41, 39]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.433,
+                0.86,
+                0.584
+            ],
+            "angle": 0,
+            "content": "learn the affine-invariant depth with large-scale datasets, which is more likely to be robust to unseen scenarios but up to an unknown scale and shift. Although they achieve promising robustness, the estimated affine-invariant depth needs to recover scale-shift values by globally aligning [23, 22, 41] with ground-truth depth. Some algorithms [17, 15, 16] propose to employ robust depth prediction and achieve visually consistent video depth estimation. In contrast, this work focuses on leveraging robust monocular depth models and aiming at dense 3D scene reconstruction without extra offline-obtained information."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.596,
+                0.583,
+                0.61
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.618,
+                0.602,
+                0.632
+            ],
+            "angle": 0,
+            "content": "3.1. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.64,
+                0.859,
+                0.736
+            ],
+            "angle": 0,
+            "content": "Aiming at 3D reconstruction from a monocular video, we propose a lightweight optimization pipeline to jointly optimize depth maps, camera poses, and intrinsic camera parameters in Figure 2. The core components of our method are the geometric consistency alignment module, optimization objectives, camera parameters initialization, and the keyframe sampling strategy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.736,
+                0.859,
+                0.82
+            ],
+            "angle": 0,
+            "content": "With the sampled images \\(\\{\\mathbf{I}_i\\}_{i = 1}^P\\) , we first use LeReS [41, 40] to obtain affine-invariant depth maps \\(\\{\\mathbf{D}_i^a\\}_{i = 1}^P\\) To avoid disastrous point cloud duplication and distortion, we leverage a geometric consistency alignment module \\(\\mathcal{F}(\\cdot ,\\cdot ,\\cdot ,\\cdot)\\) to retrieve unknown scale and shift of affineinvariant depth and compute scale-consistent depth \\(\\mathbf{D}_i\\) .."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.599,
+                0.828,
+                0.857,
+                0.843
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {D} _ {i} = \\mathcal {F} \\left(\\mathbf {D} _ {i} ^ {a}; \\alpha_ {i}, \\beta_ {i}, \\boldsymbol {\\omega} _ {i}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.851,
+                0.813,
+                0.865
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha_{i},\\beta_{i}\\) , and \\(\\omega_{i}\\) are the optimization variables."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.515,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9312"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.118,
+                0.125,
+                0.859,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.291,
+                0.86,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Figure 3: The geometric consistency alignment module. We propose to first recover the global scale and shift of depth map, then apply the locally weighted linear regression method to compute the scale map and shift map, and finally achieve scale-consistent depth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.346,
+                0.474,
+                0.456
+            ],
+            "angle": 0,
+            "content": "In order to transfer the robustness of the depth model, three optimization objectives are supervised to ensure multi-frame consistency by warping from source frame \\(i\\) to reference frame \\(j\\). With this warping process, we propose to minimize the color and depth difference between warped points and reference points, i.e., photometric and geometric constraints. An additional regularization constraint is also employed to stabilize the optimization process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.456,
+                0.474,
+                0.539
+            ],
+            "angle": 0,
+            "content": "During optimization, the consistency supervision relies on two conditions: 1) the warped reference image and source images must have overlaps; 2) nicely overlapped frames can be automatically selected as our keyframes. Therefore, the appropriate initialization of camera parameters and the keyframes' sampling strategy are essential."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.539,
+                0.473,
+                0.593
+            ],
+            "angle": 0,
+            "content": "Finally, with the optimized intrinsic camera parameters, camera poses, and scale-consistent depth maps, we can achieve accurate 3D scene reconstruction with a simple TSDF fusion [42]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.116,
+                0.602,
+                0.245,
+                0.617
+            ],
+            "angle": 0,
+            "content": "3.2. Optimization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.623,
+                0.474,
+                0.664
+            ],
+            "angle": 0,
+            "content": "We assume a simple pinhole camera model, and use homogeneous representation for all image coordinates. By default, the scale factor in homogeneous coordinate is 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.664,
+                0.474,
+                0.803
+            ],
+            "angle": 0,
+            "content": "Geometric Consistency Alignment Module. The details of geometric consistency alignment module \\(\\mathcal{F}(\\cdot)\\) are shown in Figure 3. The predicted depths \\(\\{\\mathbf{D}_i^a\\}_{i = 1}^P\\) are affine-invariant. The unknown scale and shift will cause duplications and distortions if they are incorrectly estimated. To retrieve them, we perform a two-stage alignment, i.e., a global scale-shift alignment, and a local scale-shift alignment. In the global alignment [41], we optimize for a global scale \\(\\alpha_{i}\\) and a global shift \\(\\beta_{i}\\) to obtain the globally aligned depth map \\(\\mathbf{D}_i^g\\) as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.236,
+                0.812,
+                0.473,
+                0.828
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {D} _ {i} ^ {g} = \\alpha_ {i} \\mathbf {D} _ {i} ^ {a} + \\beta_ {i}. \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.116,
+                0.838,
+                0.474,
+                0.865
+            ],
+            "angle": 0,
+            "content": "In the local alignment, we compute a scale map \\(\\mathbf{A}_i\\in\\) \\(\\mathbb{R}^{H\\times W}\\) and shift map \\(\\mathbf{B}_i\\in \\mathbb{R}^{H\\times W}\\) for each frame \\(i\\) to re"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.346,
+                0.859,
+                0.389
+            ],
+            "angle": 0,
+            "content": "fine the globally aligned depth. Instead of directly optimizing these two maps, we uniformly sample \\(M\\) sparse global depth \\(\\{d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M\\) from the globally aligned depth \\(\\mathbf{D}_i^g\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.399,
+                0.802,
+                0.415
+            ],
+            "angle": 0,
+            "content": "\\[\nd _ {i} ^ {g} (\\mathbf {p} _ {t}) = f _ {\\mathrm {s}} (\\mathbf {D} _ {i} ^ {g}, \\mathbf {p} _ {i, t}), \\quad \\text {f o r} t = 1 \\dots M,\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.425,
+                0.859,
+                0.564
+            ],
+            "angle": 0,
+            "content": "where \\(f_{\\mathrm{s}}(\\cdot ,\\cdot)\\) retrieves the depth value at a position; e.g., \\(f_{\\mathrm{s}}(\\mathbf{D}_i^g,\\mathbf{p}_{i,t})\\) obtains \\(d_i^g (\\mathbf{p}_t)\\) from \\(\\mathbf{D}_i^g\\) at the position \\(\\mathbf{p}_{i,t}\\). Then, by multiplying sparse global depth \\(\\{d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M\\) with the weights \\(\\{\\omega_{i,t}\\}_{t = 1}^{M}\\), we compute the sparse anchor points \\(\\{\\omega_{i,t}\\cdot d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M\\) and use the locally weighted linear regression method [36], i.e., \\(f_{\\mathrm{LWL R}}(\\cdot ,\\cdot)\\), to compute the local scale map \\(\\mathbf{A}_i\\in \\mathbb{R}^{H\\times W}\\) and local shift map \\(\\mathbf{B}_i\\in \\mathbb{R}^{H\\times W}\\). We also describe the \\(f_{\\mathrm{LWL R}}(\\cdot ,\\cdot)\\) module in detail in the supplementary. Such indirect optimization reduces the parameters to ease optimization. The local alignment is as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.551,
+                0.574,
+                0.805,
+                0.607
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathbf {A} _ {i}, \\mathbf {B} _ {i} = f _ {\\mathrm {L W L R}} \\left(\\mathbf {D} _ {i} ^ {g}, \\left\\{\\omega_ {i, t} \\cdot d _ {i} ^ {g} \\left(\\mathbf {p} _ {t}\\right) \\right\\} _ {t = 1} ^ {M}\\right), \\\\ \\mathbf {D} _ {i} = \\mathbf {A} _ {i} \\odot \\mathbf {D} _ {i} ^ {g} + \\mathbf {B} _ {i}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.613,
+                0.859,
+                0.682
+            ],
+            "angle": 0,
+            "content": "where \\(\\odot\\) means element-wise multiplication, and \\(M\\) is set to 25 in our experiments. Therefore, in this module, we only need to optimize for 27 parameters for each frame, i.e., \\(\\alpha_{i},\\beta_{i},\\omega_{i}\\). With our geometric consistency alignment module, we can achieve scale-consistent depth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.683,
+                0.859,
+                0.865
+            ],
+            "angle": 0,
+            "content": "Representation of Camera Positions and Intrinsic Camera Parameters. We propose to optimize for the relative rotation vector \\(\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\) (i.e., Euler angles) and relative translation vector \\(\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\) between two adjacent frames. They are initialized to 0 and are transformed to \\(4\\times 4\\) relative pose matrices \\(\\{\\mathbf{P}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\) with \\(\\mathcal{H}(\\cdot ,\\cdot)\\). The relative pose matrices \\(\\{\\mathbf{P}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\) are transformed into camera-to-world poses matrices \\(\\{\\mathbf{P}_i\\}_{i = 1}^P\\) with the product operation. Such initialization ensures the initial overlap of keyframes. For intrinsic camera parameters, we assume a simple pinhole camera model, initialize the focal length to be \\(f_{0} = 1.2\\cdot \\max (H,W)\\), and learn the focal length with a learnable scalar \\(\\delta\\). We assume that the optical center is at"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.514,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9313"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.128,
+                0.473,
+                0.156
+            ],
+            "angle": 0,
+            "content": "the image center. Thus for camera parameters, we need to optimize for \\(6(P - 1) + 1\\) variables:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.133,
+                0.165,
+                0.438,
+                0.181
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {P} _ {i \\rightarrow (i + 1)} = \\mathcal {H} (\\mathbf {r} _ {i \\rightarrow (i + 1)}, \\mathbf {t} _ {i \\rightarrow (i + 1)}), \\quad \\mathbf {P} _ {1} = \\mathbf {E} _ {4, 4},\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.125,
+                0.183,
+                0.473,
+                0.228
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {P} _ {i} = \\mathbf {P} _ {1} \\prod_ {k = 1} ^ {i - 1} \\mathbf {P} _ {k \\rightarrow (k + 1)}, \\quad \\mathbf {K} = \\left[\\begin{array}{c c c}\\delta f _ {0}&0&W / 2\\\\0&\\delta f _ {0}&H / 2\\\\0&0&1\\end{array}\\right], \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.235,
+                0.375,
+                0.248
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{E}_{4,4}\\) is the \\(4\\times 4\\) elementary matrix."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.248,
+                0.473,
+                0.276
+            ],
+            "angle": 0,
+            "content": "Optimization Objectives. The image coordinate \\(\\mathbf{p}_i\\) in frame \\(i\\) can be wrapped to frame \\(j\\) as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.115,
+                0.284,
+                0.488,
+                0.332
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} f _ {s} \\left(\\mathbf {D} _ {i \\rightarrow j}, \\mathbf {p} _ {i}\\right) \\mathbf {p} _ {i \\rightarrow j} = \\mathbf {K R} _ {j} ^ {\\top} \\left[ \\mathbf {R} _ {i} \\mathbf {K} ^ {- 1} f _ {s} \\left(\\mathbf {D} _ {i}, \\mathbf {p} _ {i}\\right) \\mathbf {p} _ {i} + \\mathbf {t} _ {i} - \\mathbf {t} _ {j} \\right], \\\\ \\mathbf {p} _ {i}, \\mathbf {p} _ {i \\rightarrow j}, \\mathbf {t} _ {i}, \\mathbf {t} _ {j} \\in \\mathbb {R} ^ {3 \\times 1}, \\quad \\mathbf {R} _ {i}, \\mathbf {R} _ {j}, \\mathbf {K} \\in \\mathbb {R} ^ {3 \\times 3}, \\tag {5} \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.332,
+                0.473,
+                0.399
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{K}\\) is the intrinsic camera parameter. \\(\\mathbf{R}_i\\) and \\(\\mathbf{t}_i\\) are the camera-to-world rotation and translation matrices, and \\(\\mathbf{P}_i = \\begin{bmatrix} \\mathbf{R}_i & \\mathbf{t}_i \\\\ \\mathbf{0} & 1 \\end{bmatrix}\\), \\(\\mathbf{p}_{i\\rightarrow j}\\) is the point warped from \\(\\mathbf{p}_i\\) of frame \\(i\\) to frame \\(j\\), and \\(\\mathbf{D}_{i\\rightarrow j}\\) is the warped depth map."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.398,
+                0.473,
+                0.467
+            ],
+            "angle": 0,
+            "content": "To optimize the proposed variables including \\(\\{\\alpha_{i}\\}_{i = 1}^{P}\\), \\(\\{\\beta_i\\}_{i = 1}^P\\), \\(\\delta\\), \\(\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\), \\(\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\), and \\(\\{\\omega_{i}\\}_{i = 1}^{P}\\) we propose to use the pixel-wise photometric and geometric constraint [2] together to ensure the consistency of color and depth along the video as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.142,
+                0.476,
+                0.473,
+                0.515
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {p c} = \\frac {1}{| V |} \\sum_ {\\substack {\\mathbf {p} \\in V\\\\(i, j) \\in K}} | f _ {\\mathrm {s}} (\\mathbf {I} _ {i}, \\mathbf {p} _ {i}) - f _ {\\mathrm {s}} (\\mathbf {I} _ {j}, \\mathbf {p} _ {i \\rightarrow j}) |, \\tag{6}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.124,
+                0.535,
+                0.473,
+                0.576
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {g c} = \\frac {1}{| V |} \\sum_ {\\substack {\\mathbf {p} \\in V\\\\(i, j) \\in K}} \\frac {\\left| f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {j} , \\mathbf {p} _ {i \\rightarrow j}\\right) - f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {i \\rightarrow j} , \\mathbf {p} _ {i}\\right) \\right|}{f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {j} , \\mathbf {p} _ {i \\rightarrow j}\\right) + f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {i \\rightarrow j} , \\mathbf {p} _ {i}\\right)}, \\tag{7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.583,
+                0.473,
+                0.611
+            ],
+            "angle": 0,
+            "content": "where \\(V\\) represents all valid points successfully projected from frame \\(i\\) to frame \\(j\\), \\(K\\) is the selected keyframe pairs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.611,
+                0.473,
+                0.639
+            ],
+            "angle": 0,
+            "content": "Furthermore, we enforce a regularization term on the sampled sparse anchor points:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.208,
+                0.647,
+                0.473,
+                0.686
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {r e g u} = \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {M} | 1 - \\omega_ {i, t} |, \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.134,
+                0.693,
+                0.362,
+                0.706
+            ],
+            "angle": 0,
+            "content": "The overall constraints are as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.178,
+                0.717,
+                0.473,
+                0.733
+            ],
+            "angle": 0,
+            "content": "\\[\nL = \\lambda_ {p c} L _ {p c} + \\lambda_ {g c} L _ {g c} + \\lambda_ {r e g u} L _ {r e g u}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.741,
+                0.449,
+                0.756
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{pc},\\lambda_{gc}\\) , and \\(\\lambda_{regu}\\) are weights to balance them."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.755,
+                0.473,
+                0.837
+            ],
+            "angle": 0,
+            "content": "Optimization Details. Before we perform optimization, we first sample \\(P\\) frames from the video to reduce the time complexity. With these sampled frames, we perform the keyframes sampling and optimization, which consists of two stages, i.e., local keyframes sampling for optimization, and global keyframes sampling for optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.838,
+                0.473,
+                0.865
+            ],
+            "angle": 0,
+            "content": "Local keyframes sampling and optimization. In optimization, we first sample local keyframes from the \\(k\\) nearest"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.503,
+                0.128,
+                0.73,
+                0.141
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Optimization Algorithm"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.146,
+                0.646,
+                0.16
+            ],
+            "angle": 0,
+            "content": "Input: \\(N\\) images \\(\\{\\mathbf{I}_i\\}_{i = 1}^N\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.159,
+                0.857,
+                0.185
+            ],
+            "angle": 0,
+            "content": "Output: scale-consistent depth maps \\(\\{\\mathbf{D}_i\\}_{i = 1}^P\\) intrinsic camera parameter K, camera-to-world camera poses \\(\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.184,
+                0.743,
+                0.198
+            ],
+            "angle": 0,
+            "content": "1: Sample \\(P\\) images \\(\\{\\mathbf{I}_i\\}_{i = 1}^P\\) from \\(\\{\\mathbf{I}_i\\}_{i = 1}^N\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.197,
+                0.809,
+                0.21
+            ],
+            "angle": 0,
+            "content": "2: Obtain affine-invariant depth \\(\\{\\mathbf{D}_i^q\\}_{i = 1}^P\\) from \\(\\{\\mathbf{I}_i\\}_{i = 1}^P\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.209,
+                0.857,
+                0.248
+            ],
+            "angle": 0,
+            "content": "3: Initialize the global scale \\(\\{\\alpha_i\\}_{i = 1}^P\\) , global shift \\(\\{\\beta_i\\}_{i = 1}^P\\) , focal length scalar \\(\\delta\\) , relative rotation \\(\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\) , relative translation \\(\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}\\) , sparse points weight \\(\\{\\omega_{i}\\}_{i = 1}^{P}\\)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.509,
+                0.184,
+                0.857,
+                0.248
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.248,
+                0.705,
+                0.26
+            ],
+            "angle": 0,
+            "content": "4: for stage in [Local, Global] do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.261,
+                0.703,
+                0.272
+            ],
+            "angle": 0,
+            "content": "5: for iter \\(= 1\\) to iterations do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.272,
+                0.768,
+                0.286
+            ],
+            "angle": 0,
+            "content": "6: Compute \\(\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}\\) and \\(\\mathbf{K}\\) with Eq. (4)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.286,
+                0.678,
+                0.298
+            ],
+            "angle": 0,
+            "content": "7: if stage = Local then"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.298,
+                0.847,
+                0.312
+            ],
+            "angle": 0,
+            "content": "8: Sample keyframe pairs \\(\\{(i_k,j_k)\\}_{k = 1}^K\\) with Eq. (10)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.509,
+                0.261,
+                0.847,
+                0.312
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.312,
+                0.523,
+                0.321
+            ],
+            "angle": 0,
+            "content": "9:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.509,
+                0.322,
+                0.847,
+                0.337
+            ],
+            "angle": 0,
+            "content": "10: Sample keyframe pairs \\(\\{(i_k,j_k)\\}_{k = 1}^K\\) with Eq. (11)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.337,
+                0.591,
+                0.347
+            ],
+            "angle": 0,
+            "content": "11: end if"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.348,
+                0.793,
+                0.362
+            ],
+            "angle": 0,
+            "content": "12: for keyframe pair \\((i,j)\\) in \\(\\{(i_k,j_k)\\}_{k = 1}^K\\) do"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.362,
+                0.857,
+                0.374
+            ],
+            "angle": 0,
+            "content": "13: Compute scale-consistent depth \\(\\mathbf{D}_i\\), \\(\\mathbf{D}_j\\) with Eq. (3);"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.374,
+                0.857,
+                0.399
+            ],
+            "angle": 0,
+            "content": "14: Warp \\(\\mathbf{p}_i\\) from frame \\(i\\) to frame \\(j\\), get warped depth \\(\\mathbf{D}_{i\\rightarrow j}\\) and warped locations \\(\\mathbf{p}_{i\\rightarrow j}\\) with Eq. (5)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.399,
+                0.816,
+                0.412
+            ],
+            "angle": 0,
+            "content": "15: Compute optimization objectives with Eq. (9)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.412,
+                0.598,
+                0.423
+            ],
+            "angle": 0,
+            "content": "16: end for"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.423,
+                0.856,
+                0.451
+            ],
+            "angle": 0,
+            "content": "17: Back-propagate and update \\(\\{\\alpha_i\\}_{i=1}^P\\), \\(\\{\\beta_i\\}_{i=1}^P\\), \\(\\delta\\), \\(\\{\\mathbf{r}_{i \\to (i+1)}\\}_{i=1}^{P-1}\\), \\(\\{\\mathbf{t}_{i \\to (i+1)}\\}_{i=1}^{P-1}\\), \\(\\{\\pmb{\\omega}_i\\}_{i=1}^P\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.451,
+                0.584,
+                0.461
+            ],
+            "angle": 0,
+            "content": "18: end for"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.462,
+                0.569,
+                0.473
+            ],
+            "angle": 0,
+            "content": "19: end for"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.503,
+                0.474,
+                0.856,
+                0.501
+            ],
+            "angle": 0,
+            "content": "20: Compute scale-consistent depth maps \\(\\{\\mathbf{D}_i\\}_{i = 1}^P\\) with Eq. (3), compute camera parameters \\(\\mathbf{K}\\) and \\(\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}\\) with Eq. (4)"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.503,
+                0.322,
+                0.857,
+                0.501
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.527,
+                0.857,
+                0.596
+            ],
+            "angle": 0,
+            "content": "frames of each reference frame. \\( k \\) is set to 6 in our experiments. To reduce computation time complexity, we do not use all these local keyframes with the current frame but select them based on probability. The probability for each keyframe is set as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.571,
+                0.605,
+                0.856,
+                0.649
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {l} = \\left\\{ \\begin{array}{l} \\frac {1}{k}, \\text {i f k - n e a r e s t n e i g h b o r s ,} \\\\ 0, \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.657,
+                0.769,
+                0.671
+            ],
+            "angle": 0,
+            "content": "where \\( p_l \\) is the keyframe sample probability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.671,
+                0.857,
+                0.781
+            ],
+            "angle": 0,
+            "content": "Global keyframes sampling and optimization. We further perform global keyframes sampling and optimization to improve long-range consistency. For each reference frame, all other frames are regarded as paired keyframes, but they are labeled with different sampling probabilities. We compute the relative pose between each reference frame \\(\\mathbf{I}_i\\) and any other frame \\(\\mathbf{I}_j\\). Based on the relative pose angle \\(\\theta_{ij}\\), we set the global sampling probability \\(p_g\\) as follows."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.518,
+                0.79,
+                0.857,
+                0.869
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {g} = \\frac {p _ {l} + p}{2}, p = \\left\\{ \\begin{array}{c} \\frac {\\theta_ {i j}}{\\phi^ {2}}, \\text {i f} 0 <   \\theta_ {i j} \\leq \\phi \\\\ \\frac {2}{\\phi} - \\frac {\\theta_ {i j}}{\\phi^ {2}}, \\text {i f} \\phi <   \\theta_ {i j} <   2 \\phi , \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {11}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.514,
+                0.9
+            ],
+            "angle": 0,
+            "content": "9314"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.126,
+                0.858,
+                0.196
+            ],
+            "angle": 0,
+            "content": "Table 1: Quantitative comparison of zero-shot 3D scene reconstruction with state-of-the-art methods. We compare our method with seven categories of reconstruction algorithms on several video sequences of five unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Note that NeuralRecon is trained on ScanNet [8], * denotes ground-truth camera poses are given, and “Rank” means average ranking performance of each column. We evaluate the Chamfer distance \\( \\mathrm{C} - {l}_{1} \\) and F-score with a threshold of \\( 5\\mathrm{\\;{cm}} \\) . As a result,we achieve state-of-the-art rank on the five zero-shot datasets."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.116,
+                0.202,
+                0.859,
+                0.352
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">NYU [28]</td><td colspan=\"2\">ScanNet [8]</td><td colspan=\"2\">7-Scenes [27]</td><td colspan=\"2\">TUM [29]</td><td colspan=\"2\">KITTI [12]</td><td rowspan=\"2\">Rank</td></tr><tr><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>NeuralRecon* [30]</td><td>0.487</td><td>0.185</td><td colspan=\"2\">trained on ScanNet</td><td>0.235</td><td>0.219</td><td>0.435</td><td>0.241</td><td colspan=\"2\">failed on KITTI</td><td>8.125</td></tr><tr><td>DPSNet* [14]</td><td>0.198</td><td>0.391</td><td>0.299</td><td>0.266</td><td>0.574</td><td>0.142</td><td>0.336</td><td>0.263</td><td>0.290</td><td>0.232</td><td>4.800</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.139</td><td>0.481</td><td>0.379</td><td>0.292</td><td>0.235</td><td>0.460</td><td>0.322</td><td>0.439</td><td>2.431</td><td>0.010</td><td>3.600</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.196</td><td>0.458</td><td>0.402</td><td>0.214</td><td>0.252</td><td>0.240</td><td>0.525</td><td>0.244</td><td>4.133</td><td>0.036</td><td>5.500</td></tr><tr><td>CVD [17]</td><td>0.471</td><td>0.302</td><td colspan=\"2\">failed on ScanNet</td><td>0.416</td><td>0.215</td><td>0.378</td><td>0.239</td><td>5.479</td><td>0.029</td><td>7.900</td></tr><tr><td>RCVD [15]</td><td>0.303</td><td>0.346</td><td>0.641</td><td>0.125</td><td>0.497</td><td>0.182</td><td>0.679</td><td>0.218</td><td>58.372</td><td>0.020</td><td>8.300</td></tr><tr><td>GCVD [16]</td><td>0.148</td><td>0.453</td><td>0.631</td><td>0.147</td><td>0.196</td><td>0.326</td><td>0.350</td><td>0.339</td><td>2.127</td><td>0.114</td><td>4.400</td></tr><tr><td>COLMAP [25, 26]</td><td>0.251</td><td>0.343</td><td>0.796</td><td>0.127</td><td>0.513</td><td>0.178</td><td>0.385</td><td>0.249</td><td>107.451</td><td>0.152</td><td>7.300</td></tr><tr><td>DROID-SLAM [33]</td><td>0.224</td><td>0.516</td><td>0.416</td><td>0.384</td><td>0.304</td><td>0.469</td><td>0.285</td><td>0.433</td><td>0.686</td><td>0.155</td><td>3.200</td></tr><tr><td>Ours</td><td>0.099</td><td>0.622</td><td>0.170</td><td>0.410</td><td>0.170</td><td>0.464</td><td>0.211</td><td>0.453</td><td>0.670</td><td>0.151</td><td>1.500</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.366,
+                0.859,
+                0.422
+            ],
+            "angle": 0,
+            "content": "Table 2: Quantitative comparison of zero-shot depth estimation with state-of-the-art methods. We evaluate the absolute relative error (AbsRel) and percentage of accurate depth pixels \\((\\delta_{1})\\) on several videos of five unseen datasets. \"Rank\" means average ranking performance of each column. The gray \"LeReS\" represents performance of affine-invariant depth without any alignment with ground-truth depth. As a result, our algorithm achieves state-of-the-art rank performance."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.116,
+                0.426,
+                0.859,
+                0.585
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">NYU [28]</td><td colspan=\"2\">ScanNet [8]</td><td colspan=\"2\">7-Scenes [27]</td><td colspan=\"2\">TUM [29]</td><td colspan=\"2\">KITTI [12]</td><td rowspan=\"2\">Rank</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td></tr><tr><td>DPSNet* [14]</td><td>0.200</td><td>0.662</td><td>0.216</td><td>0.630</td><td>0.201</td><td>0.657</td><td>0.331</td><td>0.457</td><td>0.188</td><td>0.729</td><td>6.4</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.096</td><td>0.921</td><td>0.236</td><td>0.685</td><td>0.145</td><td>0.828</td><td>0.180</td><td>0.742</td><td>0.112</td><td>0.860</td><td>2.7</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.120</td><td>0.858</td><td>0.197</td><td>0.672</td><td>0.188</td><td>0.688</td><td>0.254</td><td>0.569</td><td>0.287</td><td>0.463</td><td>5.2</td></tr><tr><td>CVD [17]</td><td>0.167</td><td>0.837</td><td colspan=\"2\">failed on ScanNet</td><td>0.180</td><td>0.847</td><td>0.148</td><td>0.797</td><td>0.717</td><td>0.215</td><td>5.6</td></tr><tr><td>RCVD [15]</td><td>0.192</td><td>0.700</td><td>0.235</td><td>0.620</td><td>0.241</td><td>0.635</td><td>0.246</td><td>0.612</td><td>0.220</td><td>0.606</td><td>6.6</td></tr><tr><td>GCVD [16]</td><td>0.163</td><td>0.768</td><td>0.316</td><td>0.527</td><td>0.203</td><td>0.650</td><td>0.248</td><td>0.697</td><td>0.240</td><td>0.543</td><td>6.4</td></tr><tr><td>COLMAP [26, 25]</td><td>0.233</td><td>0.722</td><td>0.562</td><td>0.409</td><td>0.268</td><td>0.666</td><td>0.269</td><td>0.665</td><td>0.302</td><td>0.773</td><td>7.2</td></tr><tr><td>DROID-SLAM [33]</td><td>0.143</td><td>0.847</td><td>0.210</td><td>0.773</td><td>0.154</td><td>0.827</td><td>0.210</td><td>0.720</td><td>0.115</td><td>0.914</td><td>3.1</td></tr><tr><td>LeReS [41]</td><td>0.277</td><td>0.508</td><td>0.409</td><td>0.339</td><td>0.414</td><td>0.345</td><td>0.445</td><td>0.320</td><td>0.298</td><td>0.439</td><td>-</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.127</td><td>0.858</td><td>0.135</td><td>0.844</td><td>0.145</td><td>0.799</td><td>0.203</td><td>0.632</td><td>1.8</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.608,
+                0.473,
+                0.664
+            ],
+            "angle": 0,
+            "content": "where \\(\\phi\\) is an angle threshold, and \\(\\theta_{ij}\\) is the relative rotation angle between the source frame \\(\\mathbf{I}_i\\) and the reference frame \\(\\mathbf{I}_j\\). \\(p_l\\) is the local probability with Eq. (10). The optimization is summarized in Algorithm 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.675,
+                0.236,
+                0.691
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.698,
+                0.473,
+                0.755
+            ],
+            "angle": 0,
+            "content": "We evaluate the 3D reconstruction, scale-consistent depths, optimized camera poses, and optimized intrinsic camera parameters in experiments. More details and analyses including runtime can be found in the supplementary."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.761,
+                0.37,
+                0.775
+            ],
+            "angle": 0,
+            "content": "4.1. Dense 3D Scene Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.782,
+                0.474,
+                0.866
+            ],
+            "angle": 0,
+            "content": "To show the robustness and accuracy of our reconstruction method, we compare it with a learning-based volumetric 3D reconstruction method (NeuralRecon [30]), a multiview depth estimation method (DPSNet [14]), a per-frame scale-shift alignment method (BoostingDepth [36]), an unsupervised video depth estimation method (SC-DepthV3"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.608,
+                0.859,
+                0.816
+            ],
+            "angle": 0,
+            "content": "[31]), some consistent video depth estimation methods (CVD [17], RCVD [15], GCVD [16]), a Structure-from-Motion method COLMAP [26, 25], and a robust deep visual SLAM method (DROID-SLAM [33]) on several video sequences of 5 zero-shot datasets, i.e., NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], KITTI [12]. Note that NeuralRecon is trained on ScanNet, while others are evaluated on unseen scenarios. NeuralRecon and DPSNet require GT poses and camera intrinsic as input, and SC-DepthV3, CVD, and DROID-SLAM require camera intrinsic. For fair comparison, we employ the estimated poses and depths of DROID-SLAM for BoostingDepth (BoostingDepth-DROID) to iteratively align the scale-shift values and filter outliers, as their paper does. Other methods optimize camera parameters on their own."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.823,
+                0.858,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Quantitative comparisons of zero-shot 3D reconstruction and depth are shown in Table 1 and Table 2 respectively. NeuralRecon [30], DPSNet [14], SC-DepthV3 [31] need"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.514,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9315"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.126,
+                0.861,
+                0.196
+            ],
+            "angle": 0,
+            "content": "Table 3: Quantitative comparison of zero-shot pose estimation. \"ATE\", \"RPE-T\", and \"RPE-R\" stand for the absolute trajectory error and the relative pose errors of translation and rotation, respectively. \"%\" represents the percentage of successfully tracked frames. Note that ORB-SLAM3 fails to track the trajectory on some low-texture regions, and can only estimate partial camera poses. Our algorithm achieves comparable performance to ORB-SLAM3 on three unseen datasets and better performance than the video depth estimation algorithms."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.119,
+                0.206,
+                0.858,
+                0.307
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">GT Intrinsic</td><td colspan=\"4\">NYU [28]</td><td colspan=\"4\">ScanNet [8]</td><td colspan=\"4\">7-Scenes [27]</td><td colspan=\"4\">TUM [29]</td><td colspan=\"4\">KITTI [12]</td></tr><tr><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td></tr><tr><td>SC-DepthV3 [31]</td><td>✓</td><td>0.241</td><td>0.444</td><td>0.115</td><td>1.000</td><td>0.492</td><td>0.702</td><td>0.327</td><td>1.000</td><td>1.011</td><td>1.644</td><td>0.389</td><td>1.000</td><td>0.528</td><td>0.787</td><td>0.399</td><td>1.000</td><td>1.796</td><td>4.186</td><td>0.077</td><td>1.000</td></tr><tr><td>CVD [17]</td><td>✓</td><td>1.192</td><td>2.049</td><td>0.107</td><td>1.000</td><td>0.734</td><td>1.197</td><td>0.257</td><td>1.000</td><td>0.532</td><td>1.644</td><td>0.378</td><td>1.000</td><td>0.268</td><td>0.844</td><td>0.447</td><td>1.000</td><td>19.32</td><td>24.50</td><td>0.027</td><td>1.000</td></tr><tr><td>RCVD [15]</td><td></td><td>0.460</td><td>1.263</td><td>0.114</td><td>1.000</td><td>1.025</td><td>1.708</td><td>0.615</td><td>1.000</td><td>0.559</td><td>1.545</td><td>0.394</td><td>1.000</td><td>0.626</td><td>1.083</td><td>0.421</td><td>1.000</td><td>134.3</td><td>160.7</td><td>0.463</td><td>1.000</td></tr><tr><td>GCVD [16]</td><td></td><td>0.160</td><td>0.237</td><td>0.083</td><td>1.000</td><td>0.573</td><td>0.979</td><td>0.620</td><td>1.000</td><td>0.259</td><td>0.368</td><td>0.162</td><td>1.000</td><td>0.162</td><td>0.204</td><td>0.113</td><td>1.000</td><td>5.678</td><td>8.733</td><td>0.089</td><td>1.000</td></tr><tr><td>COLMAP [26, 25]</td><td></td><td>0.091</td><td>0.137</td><td>0.055</td><td>1.000</td><td>0.352</td><td>0.426</td><td>0.096</td><td>1.000</td><td>0.062</td><td>0.090</td><td>0.051</td><td>1.000</td><td>0.075</td><td>0.102</td><td>0.064</td><td>1.000</td><td>3.707</td><td>3.454</td><td>0.016</td><td>1.000</td></tr><tr><td>DROID-SLAM [33]</td><td>✓</td><td>0.050</td><td>0.079</td><td>0.032</td><td>1.000</td><td>0.230</td><td>0.230</td><td>0.052</td><td>1.000</td><td>0.050</td><td>0.072</td><td>0.072</td><td>1.000</td><td>0.044</td><td>0.077</td><td>0.079</td><td>1.000</td><td>1.491</td><td>2.302</td><td>0.005</td><td>1.000</td></tr><tr><td>ORB-SLAM3 [5]</td><td>✓</td><td>0.065</td><td>0.097</td><td>0.039</td><td>0.791</td><td>0.208</td><td>0.300</td><td>0.098</td><td>0.426</td><td>0.118</td><td>0.211</td><td>0.121</td><td>0.956</td><td>0.104</td><td>0.144</td><td>0.082</td><td>0.504</td><td>3.124</td><td>3.926</td><td>0.009</td><td>0.971</td></tr><tr><td>Ours</td><td></td><td>0.079</td><td>0.121</td><td>0.046</td><td>1.000</td><td>0.130</td><td>0.184</td><td>0.085</td><td>1.000</td><td>0.141</td><td>0.229</td><td>0.075</td><td>1.000</td><td>0.176</td><td>0.228</td><td>0.151</td><td>1.000</td><td>3.541</td><td>5.663</td><td>0.053</td><td>1.000</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.33,
+                0.475,
+                0.414
+            ],
+            "angle": 0,
+            "content": "Table 4: Quantitative comparison of zero-shot intrinsic camera parameter estimation. \"FOV AbsRel\" represents the absolute relative error of the field of view. Note that only three algorithms can estimate the intrinsic camera parameter from the input video, and our method can achieve accurate and robust performance on four unseen datasets."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.119,
+                0.423,
+                0.472,
+                0.484
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td>NYU [28]</td><td>ScanNet [8]</td><td>7-Scenes [27]</td><td>TUM [29]</td><td rowspan=\"2\">Rank</td></tr><tr><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td></tr><tr><td>RCVD [15]</td><td>0.144</td><td>0.148</td><td>0.110</td><td>0.174</td><td>2.75</td></tr><tr><td>GCVD [16]</td><td>0.015</td><td>0.126</td><td>0.143</td><td>0.043</td><td>1.75</td></tr><tr><td>Ours</td><td>0.032</td><td>0.032</td><td>0.085</td><td>0.056</td><td>1.50</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.508,
+                0.474,
+                0.796
+            ],
+            "angle": 0,
+            "content": "to optimize millions of parameters, thus showing less robustness to unseen datasets. Rather than purely per-frame aligning with offline-obtained depth after filtering as BoostingDepth [36] does, we jointly optimize the camera parameters and depth parameters, which ensures consistency between frames and less suffers from outliers of sparse points. CVD [17] fails to reconstruct half of the ScanNet scenarios. Compared with RCVD [15], and GCVD [16], our method employs a global and a local scale-shift recovery strategy, which can rectify the affine-invariant depth to a much more accurate scale-consistent depth. Thus, we can achieve much more accurate reconstructions. The COLMAP [26, 25] struggles to estimate dense depth maps, and thus results in sparse 3D reconstruction. The robust DROID-SLAM [33] focuses on optimizing more robust poses and trajectories with the recurrent module, and spends less effort on dense reconstruction. Thus, their dense reconstruction is more likely to suffer from outliers. In contrast, our optimization is based on dense depth priors and employs a global and local optimization strategy to reduce noise, thus we in general achieve better reconstruction performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.797,
+                0.474,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Quantitative comparisons of zero-shot pose estimation and intrinsic camera parameter estimation are shown in Table 3 and Table 4. Our algorithm achieves comparable performance with the traditional SLAM methods ORBSLAM3 [5] on three datasets. However, the ORB-SLAM3"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.33,
+                0.859,
+                0.373
+            ],
+            "angle": 0,
+            "content": "Table 5: Runtime analysis on three representative scenes. Our pipeline achieves state-of-the-art reconstruction but only takes around a quarter of an hour to optimize."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.382,
+                0.858,
+                0.515
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>basement_0001a</td><td>bedroom_0015</td><td>chess</td></tr><tr><td>NeuralRecon[30]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DPSNet[14]</td><td>5m 53s</td><td>45s</td><td>12m 20s</td></tr><tr><td>BoostingDepth-DROID[36]</td><td>35s</td><td>10s</td><td>47s</td></tr><tr><td>SC-DepthV3[31]</td><td>1m 47s</td><td>17s</td><td>1m 54s</td></tr><tr><td>CVD[17]</td><td>1h 7m 6s</td><td>12m 30s</td><td>8h 1m 34s</td></tr><tr><td>RCVD[15]</td><td>1h 15m 45s</td><td>10m 6s</td><td>6h 14m 54s</td></tr><tr><td>GCVD[16]</td><td>10m 26s</td><td>2m 37s</td><td>52m 15s</td></tr><tr><td>DROID-SLAM[33]</td><td>35s</td><td>16s</td><td>1m 18s</td></tr><tr><td>COLMAP[25, 26]</td><td>50m 44s</td><td>8m 34s</td><td>9h 40m 49s</td></tr><tr><td>Ours</td><td>14m 55s</td><td>6m 55s</td><td>21m 8s</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.545,
+                0.859,
+                0.682
+            ],
+            "angle": 0,
+            "content": "can only estimate the camera poses of partial frames due to the failure of tracking features. In contrast, our algorithm can optimize and interpolate to obtain dense trajectories. Compared to four video depth estimation methods, we can outperform them by a large margin. Note that only ours, RCVD, and GCVD can optimize the intrinsic camera parameters, while others can only employ GT camera intrinsic as input. For intrinsic camera parameter estimation, our algorithm can achieve robust and accurate performance on four unseen datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.687,
+                0.86,
+                0.865
+            ],
+            "angle": 0,
+            "content": "Qualitative comparisons are reported in Figure. 4. NeuralRecon can only reconstruct partial meshes of unseen scenarios. The DPSNet [14] suffers from inaccurate feature correspondences, which cause noisy point clouds. BoostingDepth [36] can only filter out inaccurate points of DROID-SLAM but cannot ensure the temporal consistency, and thus fails to reconstruct consistent mesh. The SC-DepthV3 [31] suffers from the weak supervision of photometric loss and work worse on some low-texture regions. Consistent video depth estimation methods such as GCVD [16] cannot recover the shift of depth maps, which will cause distortions in 3D point clouds. DROID-SLAM [33] concentrates on accurate pose estimation but does not work"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.89,
+                0.516,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9316"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.117,
+                0.124,
+                0.861,
+                0.721
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.731,
+                0.861,
+                0.801
+            ],
+            "angle": 0,
+            "content": "Figure 4: Qualitative comparison of zero-shot 3D scene reconstruction from a monocular video. We compare our method with five representative algorithms on five unseen datasets. Note that NeuralRecon is trained on ScanNet [8] and can only output uncolored mesh, and * represents the employment of ground-truth camera poses during reconstruction. These methods either suffer from inaccurate pose estimation, or predict noise depth maps (please see the red arrows). As can be seen, our approach can reconstruct better 3D scene shape without any offline-computed camera parameters."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.115,
+                0.824,
+                0.474,
+                0.852
+            ],
+            "angle": 0,
+            "content": "well for dense reconstruction, and thus suffering from outliers. In contrast, our method can achieve more robust and"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.501,
+                0.824,
+                0.859,
+                0.852
+            ],
+            "angle": 0,
+            "content": "accurate 3D scene reconstruction, without requiring offline-acquired camera poses and camera intrinsic parameters."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.514,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9317"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.115,
+                0.126,
+                0.472,
+                0.236
+            ],
+            "angle": 0,
+            "content": "Table 6: Comparison of geometric consistency alignment mechanisms on the NYU [28] dataset. \"w/ deform.\" means optimizing the flexible deformation map of RCVD [15] as a replacement for our alignment module. \"Baseline\" means directly optimizing the per-frame pixel-wise depth map without the affine-invariant depth priors. As a result, the employment of our geometric consistency alignment module contributes significantly to the optimization."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.119,
+                0.242,
+                0.472,
+                0.307
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr><tr><td>w/ deform. [15]</td><td>0.153</td><td>0.771</td><td>0.145</td><td>0.290</td><td>0.082</td><td>0.160</td><td>0.470</td></tr><tr><td>Baseline</td><td>0.350</td><td>0.466</td><td>0.710</td><td>1.097</td><td>0.215</td><td>0.285</td><td>0.303</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.114,
+                0.322,
+                0.473,
+                0.418
+            ],
+            "angle": 0,
+            "content": "Table 7: Comparison of optimization objectives on the ScanNet [8] dataset. The photometric constraint supervises the color consistency, the geometric constraint ensures the multi-view geometry consistency, and the regularization constraint stabilizes the convergence of optimization. As a result, the three components of our optimization objectives are all important."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.119,
+                0.423,
+                0.472,
+                0.508
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.127</td><td>0.858</td><td>0.271</td><td>0.348</td><td>0.147</td><td>0.170</td><td>0.410</td></tr><tr><td>w/o photo.</td><td>0.219</td><td>0.636</td><td>1.722</td><td>2.331</td><td>1.039</td><td>0.775</td><td>0.169</td></tr><tr><td>w/o geo.</td><td>0.168</td><td>0.750</td><td>0.316</td><td>0.404</td><td>0.179</td><td>0.211</td><td>0.323</td></tr><tr><td>w/o regu.</td><td>0.226</td><td>0.603</td><td>0.245</td><td>0.338</td><td>0.189</td><td>0.220</td><td>0.254</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.532,
+                0.472,
+                0.643
+            ],
+            "angle": 0,
+            "content": "For quantitative efficiency analysis, the runtime comparisons on 40 Intel Xeon Silver 4210 CPUs and an RTX 3090 Ti GPU are presented in Table 5, which includes three representative scenes with 225, 48, and 1000 images, respectively. Our pipeline achieves state-of-the-art reconstruction while only taking about a quarter of an hour to optimize, even for 1000 images. Note that only the time of predicting depth and poses without RGB-D fusion are recorded."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.115,
+                0.651,
+                0.265,
+                0.665
+            ],
+            "angle": 0,
+            "content": "4.2. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.114,
+                0.672,
+                0.473,
+                0.865
+            ],
+            "angle": 0,
+            "content": "We carry out ablation experiments in terms of essential components of our algorithm to evaluate their effectiveness. Geometric Consistency Alignment Module. Table 6 shows the performance of different geometric consistency alignment modules. Previous consistent video depth methods RCVD and GCVD employ flexible deformation maps (\"w/ deform.\") and aim for more accurate scale-consistent depth. However, they both ignore the shift issues in affine-invariant depth, which is pretty significant in the 3D reconstruction task. By contrast, our method (\"Ours\") proposes a global and local scale shift alignment module for depth rectification. We also compare with a baseline method (\"baseline\"), which directly optimizes all frames' pixel-wise depths without the affine-invariant depth priors. All"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.126,
+                0.858,
+                0.236
+            ],
+            "angle": 0,
+            "content": "Table 8: Effectiveness of our two-stage keyframe sampling and optimization strategy. The \"Local\" stage ensures consistency between the nearest \\( k \\) keyframes. The \"Global\" stage samples keyframes globally with different sampling probabilities according to the optimized relative poses. As a result, our algorithm achieves better performance with the coarse-to-fine optimization strategy. The experiment is conducted on NYU [28] dataset."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.246,
+                0.855,
+                0.308
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Stage</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Local</td><td>0.111</td><td>0.884</td><td>0.111</td><td>0.179</td><td>0.068</td><td>0.091</td><td>0.593</td></tr><tr><td>Global</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.334,
+                0.857,
+                0.361
+            ],
+            "angle": 0,
+            "content": "depths are initialized to 1. Our alignment module works much better than previous methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.362,
+                0.858,
+                0.457
+            ],
+            "angle": 0,
+            "content": "Optimization Objectives. To evaluate the effectiveness of each constraint employed in our method, we propose to remove them one by one, and the results are shown in Table 7. We can see that without the photometric constraint or geometric constraint, the performance will degrade a lot. When removing the regularization term, the accuracy of the pose, depth, and reconstruction will also decrease."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.459,
+                0.858,
+                0.57
+            ],
+            "angle": 0,
+            "content": "Effectiveness of Optimization Stages. Our optimization algorithm is composed of local keyframes optimization (\"Local\") and global keyframes optimization (\"Global\"). The local stage endures the local consistency between the nearest \\(k\\) keyframes, and can reconstruct roughly accurate 3D scene shapes. The global stage selects long-range keyframes to supervise global consistency. As shown in Table 8, the reconstruction performance improves gradually."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.583,
+                0.609,
+                0.598
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.607,
+                0.858,
+                0.731
+            ],
+            "angle": 0,
+            "content": "In this paper, we have presented an effective pipeline to realize 3D scene reconstruction by leveraging the robustness of affine-invariant depth estimation, freezing the depth model, and jointly optimizing dozens of depth and camera parameters for each frame. Due to the sparsity of parameters, our pipeline can transfer the robustness of seemingly weak depth geometry prior to diverse scenes. Extensive experiments show that our pipeline can achieve robust dense 3D reconstruction on challenging unseen scenes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.745,
+                0.645,
+                0.761
+            ],
+            "angle": 0,
+            "content": "Acknowledgments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.768,
+                0.858,
+                0.865
+            ],
+            "angle": 0,
+            "content": "This work was supported by the National Key R&D Program of China (No. 2022ZD0118700), the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.484,
+                0.89,
+                0.514,
+                0.9
+            ],
+            "angle": 0,
+            "content": "9318"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.117,
+                0.127,
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+# FrozenRecon: Pose-free 3D Scene Reconstruction with Frozen Depth Models
+
+Guangkai  $\mathrm{Xu}^{1*}$ , Wei Yin $^{2*}$ , Hao Chen $^{3}$ , Chunhua Shen $^{3,4}$ , Kai Cheng $^{1}$ , Feng Zhao $^{1\dagger}$
+
+<sup>1</sup> University of Science and Technology of China <sup>2</sup> DJI Technology <sup>3</sup> Zhejiang University, China <sup>4</sup> Ant Group
+
+![](images/7abfb43abce9143ceefd254fb70a4b3d5046acce3a6f51919a6e9113c34bdc40.jpg)  
+Figure 1: Robust 3D scene reconstruction of challenging and diverse scenes. Given a monocular video, our algorithm reconstructs the 3D scene without requiring offline-acquired camera poses. Significantly, our approach only involves dozens of parameters of each frame to optimize online. Here, the red triangulations denote the estimated camera trajectories.
+
+# Abstract
+
+3D scene reconstruction is a long-standing vision task. Existing approaches can be categorized into geometry-based and learning-based methods. The former leverages multi-view geometry but may face catastrophic failures due to the reliance on accurate pixel correspondence across views, while the latter mitigates these issues by learning 2D or 3D representation directly. However, without a large-scale video or 3D training data, it can hardly be generalized to diverse real-world scenarios due to the presence of tens of millions or even billions of optimization parameters in the deep network.
+
+Recently, robust monocular depth estimation models trained with large-scale datasets have been proven to possess weak 3D geometry prior, but they are insufficient for
+
+reconstruction due to the unknown camera parameters, the affine-invariant property, and inter-frame inconsistency. To address these issues, we propose a novel test-time optimization approach that can transfer the robustness of affine-invariant depth models such as LeReS to challenging diverse scenes while ensuring inter-frame consistency, with only dozens of parameters to optimize per video frame. Specifically, our approach involves freezing the pre-trained affine-invariant depth model's depth predictions, rectifying them by optimizing the unknown scale-shift values with a geometric consistency alignment module, and employing the resulting scale-consistent depth maps to robustly obtain camera poses and achieve dense scene reconstruction, even in low-texture regions. Experiments show that our method achieves state-of-the-art cross-dataset reconstruction on five zero-shot testing datasets. Code is available at: https://aim-uofa.github.io/FrozenRecon/
+
+# 1. Introduction
+
+Dense 3D reconstruction is a fundamental vision task, which has a wide range of applications in autonomous driving [7], virtual/augmented reality [4, 37], robot navigation, medical-CAD modeling [32], etc. Existing geometry-based methods and learning-based methods have achieved impressive performance. Despite progress, we observe failure cases in certain real-world scenarios, such as incomplete or noisy reconstruction of low-texture scenes, tracking failures for pose estimation, limited generalization to unseen scenes, etc. In this work, we aim to robustly and efficiently reconstruct diverse scenes on monocular videos, with the intrinsic camera parameters and poses jointly optimized at the same time.
+
+Most 3D scene reconstruction algorithms can be categorized into learning-based [20, 30, 35] and geometry-based methods [43, 2, 3, 14, 38, 17, 15, 16]. The first group of methods typically rely on a strong neural network to learn the scene geometry, which often requires large-scale and high-quality data to optimize for millions or billions of learnable parameters. Such an expensive data requirement limits applications to various scenarios. Furthermore, some methods, such as SC-DepthV3 [31], optimize the depth and poses at the same time, for which the optimization can be challenging and may become stuck in trivial solutions, partly due to the large number of optimization parameters.
+
+In contrast, geometry-based methods find feature correspondences across views to achieve dense 3D reconstruction. Thus, fewer/no training data are needed. The drawback is that these methods can easily fail on texture-less or low-texture scenes. Moreover, planar scenes and in-place rotations also lead to degeneration in camera pose optimization. Occlusion, lighting changes, and low-texture regions can make the dense matching intractable and thus lead to incomplete reconstructions. Seeking to mitigate these limitations, we propose to exploit a pre-trained, robust monocular depth model to obtain scene geometry priors, which can largely ease pose optimization and reconstruction.
+
+Recently, foundation models [21, 1] trained with large-scale datasets can generalize to new datasets/tasks with few samples by optimizing for a small portion of parameters (so-called adaptors). Inspired by the success, we use a pretrained monocular depth model of strong performance such as LeReS [41], and optimize for a very sparse set of parameters for quickly rectifying the depth maps on test videos, such that scale-consistent depth maps can be attained.
+
+Models such as LeReS [41], MiDaS [23], and DPT [22] use millions of training images to train a robust monocular depth model, which generalizes well to diverse scenes. Unfortunately, the predicted depth maps of those models are affine-invariant, i.e., up to an unknown scale and shift compared against the ground-truth metric depth. As pointed out in [41], the unknown shift can cause significant distortion.
+
+Naively fusing pre-frame prediction is prone to cause reconstruction distortion and scale misalignment. Furthermore, the unknown intrinsic camera parameters and poses are another obstacle for multi-frame reconstruction. If we have access to accurate camera parameters, we can fine tune the pre-trained model to solve the above issues, as in [17].
+
+Instead, we freeze the monocular depth model, and on the given videos, we optimize for the global scale value, the global shift value, a local scale map and a local shift map to rectify each predicted affine-invariant depth map. Intrinsic camera parameters and camera poses are also optimized at the same time. The number of parameters that need to be optimized online is only around 30 per frame. This is a sharp contrast compared with learning-based approaches, e.g., SC-DepthV3, where tens of millions of parameters are involved in optimization. The shift and scale parameters are optimized by supervising the photometric consistency and geometric consistency between selected keyframes. Due to the sparsity of optimization parameters and the robustness of the monocular depth model, our method works much better in terms of domain gap compared to existing deep learning methods for this task. At the same time, compared with traditional geometry-based 3D scene reconstruction methods, ours can be more robust to low-texture regions.
+
+In order to validate the robustness of our system, we test on 5 unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Experiments show that our pipeline outperforms recent methods and achieves state-of-the-art reconstruction performance. Besides, we also perform extensive ablation studies to explore the effectiveness of components of our reconstruction pipeline. Our main contributions are summarized as follows:
+
+- We propose a novel pipeline for dense 3D scene reconstruction by using a frozen affine-invariant depth model, and jointly optimizing a sparse set of parameters for rectifying depth maps, camera poses, and intrinsic camera parameters. Our method is robust on diverse unseen scenarios.  
+- Experiments on diverse datasets show the robustness of our method and verify the usefulness of each component in our method.
+
+# 2. Related Work
+
+Learning-based 3D Scene Reconstruction. Learning-based methods [20, 30, 35] rely on a neural network with a large number of learnable parameters to learn the geometry of scenes. Some approaches generate the 3D voxel volume from the 2D image features of the entire sequence [20] or local fragments [30], and estimate an implicit 3D representation from posed images. Besides, some other algorithms [43, 2, 3] attempt to predict poses and depth maps jointly.
+
+![](images/8f3655f4b5dc8e4f1cabc58901fcbc4c5bc832de587e248c1274ee8b977b1dde.jpg)  
+Figure 2: The pipeline of 3D scene reconstruction. Given a monocular video, we use a frozen, robust monocular depth estimation model to obtain the estimated depths of all frames. Then, we propose a geometric consistency alignment module, which optimizes a sparse set of parameters (i.e., scale, shift, and weight factors) to achieve multi-view geometric consistent depths among all frames. The camera's intrinsic parameters and poses are also optimized simultaneously. As a result, we achieve high-quality dense 3D reconstruction with optimized depths and camera parameters.
+
+They employ an ego-motion network and a depth network to predict relative camera poses and depth maps, and supervise the photo-metric consistency [43, 3] and geometric consistency [3].
+
+Multi-view Geometry Based 3D Scene Reconstruction. Multi-view geometry based methods [43, 2, 3, 14, 38, 6, 13] achieve dense 3D reconstruction by finding feature correspondences across views. Traditional methods [25, 26] extract image features, establish correspondences between frames, and optimize the pose and depth iteratively, typically using bundle adjustment [34]. To achieve robust feature representation, some methods leverage plane sweeping to establish correspondences with assumed depth values. They usually construct a cost volume with the CNN-extracted features between images [13, 38, 14], and employ a ConvNet to predict depth maps after regularization. Compared with those approaches, ours is less likely to suffer from pose catastrophic failures in low-texture regions and can be more robust to diverse scenes.
+
+Besides, visual SLAM systems [18, 19, 5, 9, 10, 11, 24, 33] also estimate the camera motion and construct the map of unknown environments. Methods of [18, 19, 5, 9] rely on the assumption of geometric or photometric consistency to estimate poses and depth through bundle adjustment. Recent works [24, 33] propose to improve the robustness and accuracy by integrating more representative clues and optimization tools from deep learning. These algorithms focus on accurate pose estimation, but may fail to build dense maps with geometry details.
+
+Robust Monocular Depth Estimation. To achieve robust monocular depth estimation, some methods [23, 22, 41, 39]
+
+learn the affine-invariant depth with large-scale datasets, which is more likely to be robust to unseen scenarios but up to an unknown scale and shift. Although they achieve promising robustness, the estimated affine-invariant depth needs to recover scale-shift values by globally aligning [23, 22, 41] with ground-truth depth. Some algorithms [17, 15, 16] propose to employ robust depth prediction and achieve visually consistent video depth estimation. In contrast, this work focuses on leveraging robust monocular depth models and aiming at dense 3D scene reconstruction without extra offline-obtained information.
+
+# 3. Method
+
+# 3.1. Overview
+
+Aiming at 3D reconstruction from a monocular video, we propose a lightweight optimization pipeline to jointly optimize depth maps, camera poses, and intrinsic camera parameters in Figure 2. The core components of our method are the geometric consistency alignment module, optimization objectives, camera parameters initialization, and the keyframe sampling strategy.
+
+With the sampled images  $\{\mathbf{I}_i\}_{i = 1}^P$  , we first use LeReS [41, 40] to obtain affine-invariant depth maps  $\{\mathbf{D}_i^a\}_{i = 1}^P$  To avoid disastrous point cloud duplication and distortion, we leverage a geometric consistency alignment module  $\mathcal{F}(\cdot ,\cdot ,\cdot ,\cdot)$  to retrieve unknown scale and shift of affineinvariant depth and compute scale-consistent depth  $\mathbf{D}_i$  ..
+
+$$
+\mathbf {D} _ {i} = \mathcal {F} \left(\mathbf {D} _ {i} ^ {a}; \alpha_ {i}, \beta_ {i}, \boldsymbol {\omega} _ {i}\right), \tag {1}
+$$
+
+where  $\alpha_{i},\beta_{i}$  , and  $\omega_{i}$  are the optimization variables.
+
+![](images/e410eb2234a5bd03857e3f64b399409baeb83423f81f3b8bb7aa89e28a2f306d.jpg)  
+Figure 3: The geometric consistency alignment module. We propose to first recover the global scale and shift of depth map, then apply the locally weighted linear regression method to compute the scale map and shift map, and finally achieve scale-consistent depth.
+
+In order to transfer the robustness of the depth model, three optimization objectives are supervised to ensure multi-frame consistency by warping from source frame  $i$  to reference frame  $j$ . With this warping process, we propose to minimize the color and depth difference between warped points and reference points, i.e., photometric and geometric constraints. An additional regularization constraint is also employed to stabilize the optimization process.
+
+During optimization, the consistency supervision relies on two conditions: 1) the warped reference image and source images must have overlaps; 2) nicely overlapped frames can be automatically selected as our keyframes. Therefore, the appropriate initialization of camera parameters and the keyframes' sampling strategy are essential.
+
+Finally, with the optimized intrinsic camera parameters, camera poses, and scale-consistent depth maps, we can achieve accurate 3D scene reconstruction with a simple TSDF fusion [42].
+
+# 3.2. Optimization
+
+We assume a simple pinhole camera model, and use homogeneous representation for all image coordinates. By default, the scale factor in homogeneous coordinate is 1.
+
+Geometric Consistency Alignment Module. The details of geometric consistency alignment module  $\mathcal{F}(\cdot)$  are shown in Figure 3. The predicted depths  $\{\mathbf{D}_i^a\}_{i = 1}^P$  are affine-invariant. The unknown scale and shift will cause duplications and distortions if they are incorrectly estimated. To retrieve them, we perform a two-stage alignment, i.e., a global scale-shift alignment, and a local scale-shift alignment. In the global alignment [41], we optimize for a global scale  $\alpha_{i}$  and a global shift  $\beta_{i}$  to obtain the globally aligned depth map  $\mathbf{D}_i^g$  as follows:
+
+$$
+\mathbf {D} _ {i} ^ {g} = \alpha_ {i} \mathbf {D} _ {i} ^ {a} + \beta_ {i}. \tag {2}
+$$
+
+In the local alignment, we compute a scale map  $\mathbf{A}_i\in$ $\mathbb{R}^{H\times W}$  and shift map  $\mathbf{B}_i\in \mathbb{R}^{H\times W}$  for each frame  $i$  to re
+
+fine the globally aligned depth. Instead of directly optimizing these two maps, we uniformly sample  $M$  sparse global depth  $\{d_i^g (\mathbf{p}_t)\}_{t = 1}^M$  from the globally aligned depth  $\mathbf{D}_i^g$ :
+
+$$
+d _ {i} ^ {g} (\mathbf {p} _ {t}) = f _ {\mathrm {s}} (\mathbf {D} _ {i} ^ {g}, \mathbf {p} _ {i, t}), \quad \text {f o r} t = 1 \dots M,
+$$
+
+where  $f_{\mathrm{s}}(\cdot ,\cdot)$  retrieves the depth value at a position; e.g.,  $f_{\mathrm{s}}(\mathbf{D}_i^g,\mathbf{p}_{i,t})$  obtains  $d_i^g (\mathbf{p}_t)$  from  $\mathbf{D}_i^g$  at the position  $\mathbf{p}_{i,t}$ . Then, by multiplying sparse global depth  $\{d_i^g (\mathbf{p}_t)\}_{t = 1}^M$  with the weights  $\{\omega_{i,t}\}_{t = 1}^{M}$ , we compute the sparse anchor points  $\{\omega_{i,t}\cdot d_i^g (\mathbf{p}_t)\}_{t = 1}^M$  and use the locally weighted linear regression method [36], i.e.,  $f_{\mathrm{LWL R}}(\cdot ,\cdot)$ , to compute the local scale map  $\mathbf{A}_i\in \mathbb{R}^{H\times W}$  and local shift map  $\mathbf{B}_i\in \mathbb{R}^{H\times W}$ . We also describe the  $f_{\mathrm{LWL R}}(\cdot ,\cdot)$  module in detail in the supplementary. Such indirect optimization reduces the parameters to ease optimization. The local alignment is as follows.
+
+$$
+\begin{array}{l} \mathbf {A} _ {i}, \mathbf {B} _ {i} = f _ {\mathrm {L W L R}} \left(\mathbf {D} _ {i} ^ {g}, \left\{\omega_ {i, t} \cdot d _ {i} ^ {g} \left(\mathbf {p} _ {t}\right) \right\} _ {t = 1} ^ {M}\right), \\ \mathbf {D} _ {i} = \mathbf {A} _ {i} \odot \mathbf {D} _ {i} ^ {g} + \mathbf {B} _ {i}, \\ \end{array}
+$$
+
+where  $\odot$  means element-wise multiplication, and  $M$  is set to 25 in our experiments. Therefore, in this module, we only need to optimize for 27 parameters for each frame, i.e.,  $\alpha_{i},\beta_{i},\omega_{i}$ . With our geometric consistency alignment module, we can achieve scale-consistent depth.
+
+Representation of Camera Positions and Intrinsic Camera Parameters. We propose to optimize for the relative rotation vector  $\{\mathbf{r}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$  (i.e., Euler angles) and relative translation vector  $\{\mathbf{t}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$  between two adjacent frames. They are initialized to 0 and are transformed to  $4\times 4$  relative pose matrices  $\{\mathbf{P}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$  with  $\mathcal{H}(\cdot ,\cdot)$ . The relative pose matrices  $\{\mathbf{P}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$  are transformed into camera-to-world poses matrices  $\{\mathbf{P}_i\}_{i = 1}^P$  with the product operation. Such initialization ensures the initial overlap of keyframes. For intrinsic camera parameters, we assume a simple pinhole camera model, initialize the focal length to be  $f_{0} = 1.2\cdot \max (H,W)$ , and learn the focal length with a learnable scalar  $\delta$ . We assume that the optical center is at
+
+the image center. Thus for camera parameters, we need to optimize for  $6(P - 1) + 1$  variables:
+
+$$
+\mathbf {P} _ {i \rightarrow (i + 1)} = \mathcal {H} (\mathbf {r} _ {i \rightarrow (i + 1)}, \mathbf {t} _ {i \rightarrow (i + 1)}), \quad \mathbf {P} _ {1} = \mathbf {E} _ {4, 4},
+$$
+
+$$
+\mathbf {P} _ {i} = \mathbf {P} _ {1} \prod_ {k = 1} ^ {i - 1} \mathbf {P} _ {k \rightarrow (k + 1)}, \quad \mathbf {K} = \left[\begin{array}{c c c}\delta f _ {0}&0&W / 2\\0&\delta f _ {0}&H / 2\\0&0&1\end{array}\right], \tag {4}
+$$
+
+where  $\mathbf{E}_{4,4}$  is the  $4\times 4$  elementary matrix.
+
+Optimization Objectives. The image coordinate  $\mathbf{p}_i$  in frame  $i$  can be wrapped to frame  $j$  as follows.
+
+$$
+\begin{array}{l} f _ {s} \left(\mathbf {D} _ {i \rightarrow j}, \mathbf {p} _ {i}\right) \mathbf {p} _ {i \rightarrow j} = \mathbf {K R} _ {j} ^ {\top} \left[ \mathbf {R} _ {i} \mathbf {K} ^ {- 1} f _ {s} \left(\mathbf {D} _ {i}, \mathbf {p} _ {i}\right) \mathbf {p} _ {i} + \mathbf {t} _ {i} - \mathbf {t} _ {j} \right], \\ \mathbf {p} _ {i}, \mathbf {p} _ {i \rightarrow j}, \mathbf {t} _ {i}, \mathbf {t} _ {j} \in \mathbb {R} ^ {3 \times 1}, \quad \mathbf {R} _ {i}, \mathbf {R} _ {j}, \mathbf {K} \in \mathbb {R} ^ {3 \times 3}, \tag {5} \\ \end{array}
+$$
+
+where  $\mathbf{K}$  is the intrinsic camera parameter.  $\mathbf{R}_i$  and  $\mathbf{t}_i$  are the camera-to-world rotation and translation matrices, and  $\mathbf{P}_i = \begin{bmatrix} \mathbf{R}_i & \mathbf{t}_i \\ \mathbf{0} & 1 \end{bmatrix}$ ,  $\mathbf{p}_{i\rightarrow j}$  is the point warped from  $\mathbf{p}_i$  of frame  $i$  to frame  $j$ , and  $\mathbf{D}_{i\rightarrow j}$  is the warped depth map.
+
+To optimize the proposed variables including  $\{\alpha_{i}\}_{i = 1}^{P}$ ,  $\{\beta_i\}_{i = 1}^P$ ,  $\delta$ ,  $\{\mathbf{r}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$ ,  $\{\mathbf{t}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$ , and  $\{\omega_{i}\}_{i = 1}^{P}$  we propose to use the pixel-wise photometric and geometric constraint [2] together to ensure the consistency of color and depth along the video as follows.
+
+$$
+L _ {p c} = \frac {1}{| V |} \sum_ {\substack {\mathbf {p} \in V\\(i, j) \in K}} | f _ {\mathrm {s}} (\mathbf {I} _ {i}, \mathbf {p} _ {i}) - f _ {\mathrm {s}} (\mathbf {I} _ {j}, \mathbf {p} _ {i \rightarrow j}) |, \tag{6}
+$$
+
+$$
+L _ {g c} = \frac {1}{| V |} \sum_ {\substack {\mathbf {p} \in V\\(i, j) \in K}} \frac {\left| f _ {\mathrm {s}} \left(\mathbf {D} _ {j} , \mathbf {p} _ {i \rightarrow j}\right) - f _ {\mathrm {s}} \left(\mathbf {D} _ {i \rightarrow j} , \mathbf {p} _ {i}\right) \right|}{f _ {\mathrm {s}} \left(\mathbf {D} _ {j} , \mathbf {p} _ {i \rightarrow j}\right) + f _ {\mathrm {s}} \left(\mathbf {D} _ {i \rightarrow j} , \mathbf {p} _ {i}\right)}, \tag{7}
+$$
+
+where  $V$  represents all valid points successfully projected from frame  $i$  to frame  $j$ ,  $K$  is the selected keyframe pairs.
+
+Furthermore, we enforce a regularization term on the sampled sparse anchor points:
+
+$$
+L _ {r e g u} = \sum_ {i = 1} ^ {N} \sum_ {t = 1} ^ {M} | 1 - \omega_ {i, t} |, \tag {8}
+$$
+
+The overall constraints are as follows.
+
+$$
+L = \lambda_ {p c} L _ {p c} + \lambda_ {g c} L _ {g c} + \lambda_ {r e g u} L _ {r e g u}, \tag {9}
+$$
+
+where  $\lambda_{pc},\lambda_{gc}$  , and  $\lambda_{regu}$  are weights to balance them.
+
+Optimization Details. Before we perform optimization, we first sample  $P$  frames from the video to reduce the time complexity. With these sampled frames, we perform the keyframes sampling and optimization, which consists of two stages, i.e., local keyframes sampling for optimization, and global keyframes sampling for optimization.
+
+Local keyframes sampling and optimization. In optimization, we first sample local keyframes from the  $k$  nearest
+
+# Algorithm 1 Optimization Algorithm
+
+Input:  $N$  images  $\{\mathbf{I}_i\}_{i = 1}^N$
+
+Output: scale-consistent depth maps  $\{\mathbf{D}_i\}_{i = 1}^P$  intrinsic camera parameter K, camera-to-world camera poses  $\{\mathbf{P}_i\}_{i = 1}^{P - 1}$
+
+1: Sample  $P$  images  $\{\mathbf{I}_i\}_{i = 1}^P$  from  $\{\mathbf{I}_i\}_{i = 1}^N$  
+2: Obtain affine-invariant depth  $\{\mathbf{D}_i^q\}_{i = 1}^P$  from  $\{\mathbf{I}_i\}_{i = 1}^P$  
+3: Initialize the global scale  $\{\alpha_i\}_{i = 1}^P$  , global shift  $\{\beta_i\}_{i = 1}^P$  , focal length scalar  $\delta$  , relative rotation  $\{\mathbf{r}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$  , relative translation  $\{\mathbf{t}_{i\rightarrow (i + 1)}\}_{i = 1}^{P - 1}$  , sparse points weight  $\{\omega_{i}\}_{i = 1}^{P}$
+
+4: for stage in [Local, Global] do
+
+5: for iter  $= 1$  to iterations do  
+6: Compute  $\{\mathbf{P}_i\}_{i = 1}^{P - 1}$  and  $\mathbf{K}$  with Eq. (4)  
+7: if stage = Local then  
+8: Sample keyframe pairs  $\{(i_k,j_k)\}_{k = 1}^K$  with Eq. (10)
+
+9:
+
+10: Sample keyframe pairs  $\{(i_k,j_k)\}_{k = 1}^K$  with Eq. (11)  
+11: end if  
+12: for keyframe pair  $(i,j)$  in  $\{(i_k,j_k)\}_{k = 1}^K$  do  
+13: Compute scale-consistent depth  $\mathbf{D}_i$ ,  $\mathbf{D}_j$  with Eq. (3);  
+14: Warp  $\mathbf{p}_i$  from frame  $i$  to frame  $j$ , get warped depth  $\mathbf{D}_{i\rightarrow j}$  and warped locations  $\mathbf{p}_{i\rightarrow j}$  with Eq. (5)  
+15: Compute optimization objectives with Eq. (9)  
+16: end for  
+17: Back-propagate and update  $\{\alpha_i\}_{i=1}^P$ ,  $\{\beta_i\}_{i=1}^P$ ,  $\delta$ ,  $\{\mathbf{r}_{i \to (i+1)}\}_{i=1}^{P-1}$ ,  $\{\mathbf{t}_{i \to (i+1)}\}_{i=1}^{P-1}$ ,  $\{\pmb{\omega}_i\}_{i=1}^P$  
+18: end for  
+19: end for  
+20: Compute scale-consistent depth maps  $\{\mathbf{D}_i\}_{i = 1}^P$  with Eq. (3), compute camera parameters  $\mathbf{K}$  and  $\{\mathbf{P}_i\}_{i = 1}^{P - 1}$  with Eq. (4)
+
+frames of each reference frame.  $k$  is set to 6 in our experiments. To reduce computation time complexity, we do not use all these local keyframes with the current frame but select them based on probability. The probability for each keyframe is set as follows.
+
+$$
+p _ {l} = \left\{ \begin{array}{l} \frac {1}{k}, \text {i f k - n e a r e s t n e i g h b o r s ,} \\ 0, \text {o t h e r w i s e ,} \end{array} \right. \tag {10}
+$$
+
+where  $p_l$  is the keyframe sample probability.
+
+Global keyframes sampling and optimization. We further perform global keyframes sampling and optimization to improve long-range consistency. For each reference frame, all other frames are regarded as paired keyframes, but they are labeled with different sampling probabilities. We compute the relative pose between each reference frame  $\mathbf{I}_i$  and any other frame  $\mathbf{I}_j$ . Based on the relative pose angle  $\theta_{ij}$ , we set the global sampling probability  $p_g$  as follows.
+
+$$
+p _ {g} = \frac {p _ {l} + p}{2}, p = \left\{ \begin{array}{c} \frac {\theta_ {i j}}{\phi^ {2}}, \text {i f} 0 <   \theta_ {i j} \leq \phi \\ \frac {2}{\phi} - \frac {\theta_ {i j}}{\phi^ {2}}, \text {i f} \phi <   \theta_ {i j} <   2 \phi , \\ 0, \text {o t h e r w i s e} \end{array} \right. \tag {11}
+$$
+
+Table 1: Quantitative comparison of zero-shot 3D scene reconstruction with state-of-the-art methods. We compare our method with seven categories of reconstruction algorithms on several video sequences of five unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Note that NeuralRecon is trained on ScanNet [8], * denotes ground-truth camera poses are given, and “Rank” means average ranking performance of each column. We evaluate the Chamfer distance  $\mathrm{C} - {l}_{1}$  and F-score with a threshold of  $5\mathrm{\;{cm}}$  . As a result,we achieve state-of-the-art rank on the five zero-shot datasets.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">NYU [28]</td><td colspan="2">ScanNet [8]</td><td colspan="2">7-Scenes [27]</td><td colspan="2">TUM [29]</td><td colspan="2">KITTI [12]</td><td rowspan="2">Rank</td></tr><tr><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>NeuralRecon* [30]</td><td>0.487</td><td>0.185</td><td colspan="2">trained on ScanNet</td><td>0.235</td><td>0.219</td><td>0.435</td><td>0.241</td><td colspan="2">failed on KITTI</td><td>8.125</td></tr><tr><td>DPSNet* [14]</td><td>0.198</td><td>0.391</td><td>0.299</td><td>0.266</td><td>0.574</td><td>0.142</td><td>0.336</td><td>0.263</td><td>0.290</td><td>0.232</td><td>4.800</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.139</td><td>0.481</td><td>0.379</td><td>0.292</td><td>0.235</td><td>0.460</td><td>0.322</td><td>0.439</td><td>2.431</td><td>0.010</td><td>3.600</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.196</td><td>0.458</td><td>0.402</td><td>0.214</td><td>0.252</td><td>0.240</td><td>0.525</td><td>0.244</td><td>4.133</td><td>0.036</td><td>5.500</td></tr><tr><td>CVD [17]</td><td>0.471</td><td>0.302</td><td colspan="2">failed on ScanNet</td><td>0.416</td><td>0.215</td><td>0.378</td><td>0.239</td><td>5.479</td><td>0.029</td><td>7.900</td></tr><tr><td>RCVD [15]</td><td>0.303</td><td>0.346</td><td>0.641</td><td>0.125</td><td>0.497</td><td>0.182</td><td>0.679</td><td>0.218</td><td>58.372</td><td>0.020</td><td>8.300</td></tr><tr><td>GCVD [16]</td><td>0.148</td><td>0.453</td><td>0.631</td><td>0.147</td><td>0.196</td><td>0.326</td><td>0.350</td><td>0.339</td><td>2.127</td><td>0.114</td><td>4.400</td></tr><tr><td>COLMAP [25, 26]</td><td>0.251</td><td>0.343</td><td>0.796</td><td>0.127</td><td>0.513</td><td>0.178</td><td>0.385</td><td>0.249</td><td>107.451</td><td>0.152</td><td>7.300</td></tr><tr><td>DROID-SLAM [33]</td><td>0.224</td><td>0.516</td><td>0.416</td><td>0.384</td><td>0.304</td><td>0.469</td><td>0.285</td><td>0.433</td><td>0.686</td><td>0.155</td><td>3.200</td></tr><tr><td>Ours</td><td>0.099</td><td>0.622</td><td>0.170</td><td>0.410</td><td>0.170</td><td>0.464</td><td>0.211</td><td>0.453</td><td>0.670</td><td>0.151</td><td>1.500</td></tr></table>
+
+Table 2: Quantitative comparison of zero-shot depth estimation with state-of-the-art methods. We evaluate the absolute relative error (AbsRel) and percentage of accurate depth pixels  $(\delta_{1})$  on several videos of five unseen datasets. "Rank" means average ranking performance of each column. The gray "LeReS" represents performance of affine-invariant depth without any alignment with ground-truth depth. As a result, our algorithm achieves state-of-the-art rank performance.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">NYU [28]</td><td colspan="2">ScanNet [8]</td><td colspan="2">7-Scenes [27]</td><td colspan="2">TUM [29]</td><td colspan="2">KITTI [12]</td><td rowspan="2">Rank</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td></tr><tr><td>DPSNet* [14]</td><td>0.200</td><td>0.662</td><td>0.216</td><td>0.630</td><td>0.201</td><td>0.657</td><td>0.331</td><td>0.457</td><td>0.188</td><td>0.729</td><td>6.4</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.096</td><td>0.921</td><td>0.236</td><td>0.685</td><td>0.145</td><td>0.828</td><td>0.180</td><td>0.742</td><td>0.112</td><td>0.860</td><td>2.7</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.120</td><td>0.858</td><td>0.197</td><td>0.672</td><td>0.188</td><td>0.688</td><td>0.254</td><td>0.569</td><td>0.287</td><td>0.463</td><td>5.2</td></tr><tr><td>CVD [17]</td><td>0.167</td><td>0.837</td><td colspan="2">failed on ScanNet</td><td>0.180</td><td>0.847</td><td>0.148</td><td>0.797</td><td>0.717</td><td>0.215</td><td>5.6</td></tr><tr><td>RCVD [15]</td><td>0.192</td><td>0.700</td><td>0.235</td><td>0.620</td><td>0.241</td><td>0.635</td><td>0.246</td><td>0.612</td><td>0.220</td><td>0.606</td><td>6.6</td></tr><tr><td>GCVD [16]</td><td>0.163</td><td>0.768</td><td>0.316</td><td>0.527</td><td>0.203</td><td>0.650</td><td>0.248</td><td>0.697</td><td>0.240</td><td>0.543</td><td>6.4</td></tr><tr><td>COLMAP [26, 25]</td><td>0.233</td><td>0.722</td><td>0.562</td><td>0.409</td><td>0.268</td><td>0.666</td><td>0.269</td><td>0.665</td><td>0.302</td><td>0.773</td><td>7.2</td></tr><tr><td>DROID-SLAM [33]</td><td>0.143</td><td>0.847</td><td>0.210</td><td>0.773</td><td>0.154</td><td>0.827</td><td>0.210</td><td>0.720</td><td>0.115</td><td>0.914</td><td>3.1</td></tr><tr><td>LeReS [41]</td><td>0.277</td><td>0.508</td><td>0.409</td><td>0.339</td><td>0.414</td><td>0.345</td><td>0.445</td><td>0.320</td><td>0.298</td><td>0.439</td><td>-</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.127</td><td>0.858</td><td>0.135</td><td>0.844</td><td>0.145</td><td>0.799</td><td>0.203</td><td>0.632</td><td>1.8</td></tr></table>
+
+where  $\phi$  is an angle threshold, and  $\theta_{ij}$  is the relative rotation angle between the source frame  $\mathbf{I}_i$  and the reference frame  $\mathbf{I}_j$ .  $p_l$  is the local probability with Eq. (10). The optimization is summarized in Algorithm 1.
+
+# 4. Experiments
+
+We evaluate the 3D reconstruction, scale-consistent depths, optimized camera poses, and optimized intrinsic camera parameters in experiments. More details and analyses including runtime can be found in the supplementary.
+
+# 4.1. Dense 3D Scene Reconstruction
+
+To show the robustness and accuracy of our reconstruction method, we compare it with a learning-based volumetric 3D reconstruction method (NeuralRecon [30]), a multiview depth estimation method (DPSNet [14]), a per-frame scale-shift alignment method (BoostingDepth [36]), an unsupervised video depth estimation method (SC-DepthV3
+
+[31]), some consistent video depth estimation methods (CVD [17], RCVD [15], GCVD [16]), a Structure-from-Motion method COLMAP [26, 25], and a robust deep visual SLAM method (DROID-SLAM [33]) on several video sequences of 5 zero-shot datasets, i.e., NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], KITTI [12]. Note that NeuralRecon is trained on ScanNet, while others are evaluated on unseen scenarios. NeuralRecon and DPSNet require GT poses and camera intrinsic as input, and SC-DepthV3, CVD, and DROID-SLAM require camera intrinsic. For fair comparison, we employ the estimated poses and depths of DROID-SLAM for BoostingDepth (BoostingDepth-DROID) to iteratively align the scale-shift values and filter outliers, as their paper does. Other methods optimize camera parameters on their own.
+
+Quantitative comparisons of zero-shot 3D reconstruction and depth are shown in Table 1 and Table 2 respectively. NeuralRecon [30], DPSNet [14], SC-DepthV3 [31] need
+
+Table 3: Quantitative comparison of zero-shot pose estimation. "ATE", "RPE-T", and "RPE-R" stand for the absolute trajectory error and the relative pose errors of translation and rotation, respectively. "%" represents the percentage of successfully tracked frames. Note that ORB-SLAM3 fails to track the trajectory on some low-texture regions, and can only estimate partial camera poses. Our algorithm achieves comparable performance to ORB-SLAM3 on three unseen datasets and better performance than the video depth estimation algorithms.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">GT Intrinsic</td><td colspan="4">NYU [28]</td><td colspan="4">ScanNet [8]</td><td colspan="4">7-Scenes [27]</td><td colspan="4">TUM [29]</td><td colspan="4">KITTI [12]</td></tr><tr><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td></tr><tr><td>SC-DepthV3 [31]</td><td>✓</td><td>0.241</td><td>0.444</td><td>0.115</td><td>1.000</td><td>0.492</td><td>0.702</td><td>0.327</td><td>1.000</td><td>1.011</td><td>1.644</td><td>0.389</td><td>1.000</td><td>0.528</td><td>0.787</td><td>0.399</td><td>1.000</td><td>1.796</td><td>4.186</td><td>0.077</td><td>1.000</td></tr><tr><td>CVD [17]</td><td>✓</td><td>1.192</td><td>2.049</td><td>0.107</td><td>1.000</td><td>0.734</td><td>1.197</td><td>0.257</td><td>1.000</td><td>0.532</td><td>1.644</td><td>0.378</td><td>1.000</td><td>0.268</td><td>0.844</td><td>0.447</td><td>1.000</td><td>19.32</td><td>24.50</td><td>0.027</td><td>1.000</td></tr><tr><td>RCVD [15]</td><td></td><td>0.460</td><td>1.263</td><td>0.114</td><td>1.000</td><td>1.025</td><td>1.708</td><td>0.615</td><td>1.000</td><td>0.559</td><td>1.545</td><td>0.394</td><td>1.000</td><td>0.626</td><td>1.083</td><td>0.421</td><td>1.000</td><td>134.3</td><td>160.7</td><td>0.463</td><td>1.000</td></tr><tr><td>GCVD [16]</td><td></td><td>0.160</td><td>0.237</td><td>0.083</td><td>1.000</td><td>0.573</td><td>0.979</td><td>0.620</td><td>1.000</td><td>0.259</td><td>0.368</td><td>0.162</td><td>1.000</td><td>0.162</td><td>0.204</td><td>0.113</td><td>1.000</td><td>5.678</td><td>8.733</td><td>0.089</td><td>1.000</td></tr><tr><td>COLMAP [26, 25]</td><td></td><td>0.091</td><td>0.137</td><td>0.055</td><td>1.000</td><td>0.352</td><td>0.426</td><td>0.096</td><td>1.000</td><td>0.062</td><td>0.090</td><td>0.051</td><td>1.000</td><td>0.075</td><td>0.102</td><td>0.064</td><td>1.000</td><td>3.707</td><td>3.454</td><td>0.016</td><td>1.000</td></tr><tr><td>DROID-SLAM [33]</td><td>✓</td><td>0.050</td><td>0.079</td><td>0.032</td><td>1.000</td><td>0.230</td><td>0.230</td><td>0.052</td><td>1.000</td><td>0.050</td><td>0.072</td><td>0.072</td><td>1.000</td><td>0.044</td><td>0.077</td><td>0.079</td><td>1.000</td><td>1.491</td><td>2.302</td><td>0.005</td><td>1.000</td></tr><tr><td>ORB-SLAM3 [5]</td><td>✓</td><td>0.065</td><td>0.097</td><td>0.039</td><td>0.791</td><td>0.208</td><td>0.300</td><td>0.098</td><td>0.426</td><td>0.118</td><td>0.211</td><td>0.121</td><td>0.956</td><td>0.104</td><td>0.144</td><td>0.082</td><td>0.504</td><td>3.124</td><td>3.926</td><td>0.009</td><td>0.971</td></tr><tr><td>Ours</td><td></td><td>0.079</td><td>0.121</td><td>0.046</td><td>1.000</td><td>0.130</td><td>0.184</td><td>0.085</td><td>1.000</td><td>0.141</td><td>0.229</td><td>0.075</td><td>1.000</td><td>0.176</td><td>0.228</td><td>0.151</td><td>1.000</td><td>3.541</td><td>5.663</td><td>0.053</td><td>1.000</td></tr></table>
+
+Table 4: Quantitative comparison of zero-shot intrinsic camera parameter estimation. "FOV AbsRel" represents the absolute relative error of the field of view. Note that only three algorithms can estimate the intrinsic camera parameter from the input video, and our method can achieve accurate and robust performance on four unseen datasets.  
+
+<table><tr><td rowspan="2">Method</td><td>NYU [28]</td><td>ScanNet [8]</td><td>7-Scenes [27]</td><td>TUM [29]</td><td rowspan="2">Rank</td></tr><tr><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td></tr><tr><td>RCVD [15]</td><td>0.144</td><td>0.148</td><td>0.110</td><td>0.174</td><td>2.75</td></tr><tr><td>GCVD [16]</td><td>0.015</td><td>0.126</td><td>0.143</td><td>0.043</td><td>1.75</td></tr><tr><td>Ours</td><td>0.032</td><td>0.032</td><td>0.085</td><td>0.056</td><td>1.50</td></tr></table>
+
+to optimize millions of parameters, thus showing less robustness to unseen datasets. Rather than purely per-frame aligning with offline-obtained depth after filtering as BoostingDepth [36] does, we jointly optimize the camera parameters and depth parameters, which ensures consistency between frames and less suffers from outliers of sparse points. CVD [17] fails to reconstruct half of the ScanNet scenarios. Compared with RCVD [15], and GCVD [16], our method employs a global and a local scale-shift recovery strategy, which can rectify the affine-invariant depth to a much more accurate scale-consistent depth. Thus, we can achieve much more accurate reconstructions. The COLMAP [26, 25] struggles to estimate dense depth maps, and thus results in sparse 3D reconstruction. The robust DROID-SLAM [33] focuses on optimizing more robust poses and trajectories with the recurrent module, and spends less effort on dense reconstruction. Thus, their dense reconstruction is more likely to suffer from outliers. In contrast, our optimization is based on dense depth priors and employs a global and local optimization strategy to reduce noise, thus we in general achieve better reconstruction performance.
+
+Quantitative comparisons of zero-shot pose estimation and intrinsic camera parameter estimation are shown in Table 3 and Table 4. Our algorithm achieves comparable performance with the traditional SLAM methods ORBSLAM3 [5] on three datasets. However, the ORB-SLAM3
+
+Table 5: Runtime analysis on three representative scenes. Our pipeline achieves state-of-the-art reconstruction but only takes around a quarter of an hour to optimize.  
+
+<table><tr><td>Method</td><td>basement_0001a</td><td>bedroom_0015</td><td>chess</td></tr><tr><td>NeuralRecon[30]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DPSNet[14]</td><td>5m 53s</td><td>45s</td><td>12m 20s</td></tr><tr><td>BoostingDepth-DROID[36]</td><td>35s</td><td>10s</td><td>47s</td></tr><tr><td>SC-DepthV3[31]</td><td>1m 47s</td><td>17s</td><td>1m 54s</td></tr><tr><td>CVD[17]</td><td>1h 7m 6s</td><td>12m 30s</td><td>8h 1m 34s</td></tr><tr><td>RCVD[15]</td><td>1h 15m 45s</td><td>10m 6s</td><td>6h 14m 54s</td></tr><tr><td>GCVD[16]</td><td>10m 26s</td><td>2m 37s</td><td>52m 15s</td></tr><tr><td>DROID-SLAM[33]</td><td>35s</td><td>16s</td><td>1m 18s</td></tr><tr><td>COLMAP[25, 26]</td><td>50m 44s</td><td>8m 34s</td><td>9h 40m 49s</td></tr><tr><td>Ours</td><td>14m 55s</td><td>6m 55s</td><td>21m 8s</td></tr></table>
+
+can only estimate the camera poses of partial frames due to the failure of tracking features. In contrast, our algorithm can optimize and interpolate to obtain dense trajectories. Compared to four video depth estimation methods, we can outperform them by a large margin. Note that only ours, RCVD, and GCVD can optimize the intrinsic camera parameters, while others can only employ GT camera intrinsic as input. For intrinsic camera parameter estimation, our algorithm can achieve robust and accurate performance on four unseen datasets.
+
+Qualitative comparisons are reported in Figure. 4. NeuralRecon can only reconstruct partial meshes of unseen scenarios. The DPSNet [14] suffers from inaccurate feature correspondences, which cause noisy point clouds. BoostingDepth [36] can only filter out inaccurate points of DROID-SLAM but cannot ensure the temporal consistency, and thus fails to reconstruct consistent mesh. The SC-DepthV3 [31] suffers from the weak supervision of photometric loss and work worse on some low-texture regions. Consistent video depth estimation methods such as GCVD [16] cannot recover the shift of depth maps, which will cause distortions in 3D point clouds. DROID-SLAM [33] concentrates on accurate pose estimation but does not work
+
+![](images/460c41f8206f44978b81beed7426b95a00d7f29102269c04913bc5e04967b497.jpg)  
+Figure 4: Qualitative comparison of zero-shot 3D scene reconstruction from a monocular video. We compare our method with five representative algorithms on five unseen datasets. Note that NeuralRecon is trained on ScanNet [8] and can only output uncolored mesh, and * represents the employment of ground-truth camera poses during reconstruction. These methods either suffer from inaccurate pose estimation, or predict noise depth maps (please see the red arrows). As can be seen, our approach can reconstruct better 3D scene shape without any offline-computed camera parameters.
+
+well for dense reconstruction, and thus suffering from outliers. In contrast, our method can achieve more robust and
+
+accurate 3D scene reconstruction, without requiring offline-acquired camera poses and camera intrinsic parameters.
+
+Table 6: Comparison of geometric consistency alignment mechanisms on the NYU [28] dataset. "w/ deform." means optimizing the flexible deformation map of RCVD [15] as a replacement for our alignment module. "Baseline" means directly optimizing the per-frame pixel-wise depth map without the affine-invariant depth priors. As a result, the employment of our geometric consistency alignment module contributes significantly to the optimization.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Depth</td><td colspan="3">Pose</td><td colspan="2">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr><tr><td>w/ deform. [15]</td><td>0.153</td><td>0.771</td><td>0.145</td><td>0.290</td><td>0.082</td><td>0.160</td><td>0.470</td></tr><tr><td>Baseline</td><td>0.350</td><td>0.466</td><td>0.710</td><td>1.097</td><td>0.215</td><td>0.285</td><td>0.303</td></tr></table>
+
+Table 7: Comparison of optimization objectives on the ScanNet [8] dataset. The photometric constraint supervises the color consistency, the geometric constraint ensures the multi-view geometry consistency, and the regularization constraint stabilizes the convergence of optimization. As a result, the three components of our optimization objectives are all important.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Depth</td><td colspan="3">Pose</td><td colspan="2">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.127</td><td>0.858</td><td>0.271</td><td>0.348</td><td>0.147</td><td>0.170</td><td>0.410</td></tr><tr><td>w/o photo.</td><td>0.219</td><td>0.636</td><td>1.722</td><td>2.331</td><td>1.039</td><td>0.775</td><td>0.169</td></tr><tr><td>w/o geo.</td><td>0.168</td><td>0.750</td><td>0.316</td><td>0.404</td><td>0.179</td><td>0.211</td><td>0.323</td></tr><tr><td>w/o regu.</td><td>0.226</td><td>0.603</td><td>0.245</td><td>0.338</td><td>0.189</td><td>0.220</td><td>0.254</td></tr></table>
+
+For quantitative efficiency analysis, the runtime comparisons on 40 Intel Xeon Silver 4210 CPUs and an RTX 3090 Ti GPU are presented in Table 5, which includes three representative scenes with 225, 48, and 1000 images, respectively. Our pipeline achieves state-of-the-art reconstruction while only taking about a quarter of an hour to optimize, even for 1000 images. Note that only the time of predicting depth and poses without RGB-D fusion are recorded.
+
+# 4.2. Ablation Studies
+
+We carry out ablation experiments in terms of essential components of our algorithm to evaluate their effectiveness. Geometric Consistency Alignment Module. Table 6 shows the performance of different geometric consistency alignment modules. Previous consistent video depth methods RCVD and GCVD employ flexible deformation maps ("w/ deform.") and aim for more accurate scale-consistent depth. However, they both ignore the shift issues in affine-invariant depth, which is pretty significant in the 3D reconstruction task. By contrast, our method ("Ours") proposes a global and local scale shift alignment module for depth rectification. We also compare with a baseline method ("baseline"), which directly optimizes all frames' pixel-wise depths without the affine-invariant depth priors. All
+
+Table 8: Effectiveness of our two-stage keyframe sampling and optimization strategy. The "Local" stage ensures consistency between the nearest  $k$  keyframes. The "Global" stage samples keyframes globally with different sampling probabilities according to the optimized relative poses. As a result, our algorithm achieves better performance with the coarse-to-fine optimization strategy. The experiment is conducted on NYU [28] dataset.  
+
+<table><tr><td rowspan="2">Stage</td><td colspan="2">Depth</td><td colspan="3">Pose</td><td colspan="2">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Local</td><td>0.111</td><td>0.884</td><td>0.111</td><td>0.179</td><td>0.068</td><td>0.091</td><td>0.593</td></tr><tr><td>Global</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr></table>
+
+depths are initialized to 1. Our alignment module works much better than previous methods.
+
+Optimization Objectives. To evaluate the effectiveness of each constraint employed in our method, we propose to remove them one by one, and the results are shown in Table 7. We can see that without the photometric constraint or geometric constraint, the performance will degrade a lot. When removing the regularization term, the accuracy of the pose, depth, and reconstruction will also decrease.
+
+Effectiveness of Optimization Stages. Our optimization algorithm is composed of local keyframes optimization ("Local") and global keyframes optimization ("Global"). The local stage endures the local consistency between the nearest  $k$  keyframes, and can reconstruct roughly accurate 3D scene shapes. The global stage selects long-range keyframes to supervise global consistency. As shown in Table 8, the reconstruction performance improves gradually.
+
+# 5. Conclusion
+
+In this paper, we have presented an effective pipeline to realize 3D scene reconstruction by leveraging the robustness of affine-invariant depth estimation, freezing the depth model, and jointly optimizing dozens of depth and camera parameters for each frame. Due to the sparsity of parameters, our pipeline can transfer the robustness of seemingly weak depth geometry prior to diverse scenes. Extensive experiments show that our pipeline can achieve robust dense 3D reconstruction on challenging unseen scenes.
+
+# Acknowledgments
+
+This work was supported by the National Key R&D Program of China (No. 2022ZD0118700), the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC.
+
+# References
+
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+                                    "content": "Most 3D scene reconstruction algorithms can be categorized into learning-based [20, 30, 35] and geometry-based methods [43, 2, 3, 14, 38, 17, 15, 16]. The first group of methods typically rely on a strong neural network to learn the scene geometry, which often requires large-scale and high-quality data to optimize for millions or billions of learnable parameters. Such an expensive data requirement limits applications to various scenarios. Furthermore, some methods, such as SC-DepthV3 [31], optimize the depth and poses at the same time, for which the optimization can be challenging and may become stuck in trivial solutions, partly due to the large number of optimization parameters."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In contrast, geometry-based methods find feature correspondences across views to achieve dense 3D reconstruction. Thus, fewer/no training data are needed. The drawback is that these methods can easily fail on texture-less or low-texture scenes. Moreover, planar scenes and in-place rotations also lead to degeneration in camera pose optimization. Occlusion, lighting changes, and low-texture regions can make the dense matching intractable and thus lead to incomplete reconstructions. Seeking to mitigate these limitations, we propose to exploit a pre-trained, robust monocular depth model to obtain scene geometry priors, which can largely ease pose optimization and reconstruction."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
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+                                    "type": "text",
+                                    "content": "Recently, foundation models [21, 1] trained with large-scale datasets can generalize to new datasets/tasks with few samples by optimizing for a small portion of parameters (so-called adaptors). Inspired by the success, we use a pretrained monocular depth model of strong performance such as LeReS [41], and optimize for a very sparse set of parameters for quickly rectifying the depth maps on test videos, such that scale-consistent depth maps can be attained."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
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+                                    "content": "Models such as LeReS [41], MiDaS [23], and DPT [22] use millions of training images to train a robust monocular depth model, which generalizes well to diverse scenes. Unfortunately, the predicted depth maps of those models are affine-invariant, i.e., up to an unknown scale and shift compared against the ground-truth metric depth. As pointed out in [41], the unknown shift can cause significant distortion."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Naively fusing pre-frame prediction is prone to cause reconstruction distortion and scale misalignment. Furthermore, the unknown intrinsic camera parameters and poses are another obstacle for multi-frame reconstruction. If we have access to accurate camera parameters, we can fine tune the pre-trained model to solve the above issues, as in [17]."
+                                }
+                            ]
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Instead, we freeze the monocular depth model, and on the given videos, we optimize for the global scale value, the global shift value, a local scale map and a local shift map to rectify each predicted affine-invariant depth map. Intrinsic camera parameters and camera poses are also optimized at the same time. The number of parameters that need to be optimized online is only around 30 per frame. This is a sharp contrast compared with learning-based approaches, e.g., SC-DepthV3, where tens of millions of parameters are involved in optimization. The shift and scale parameters are optimized by supervising the photometric consistency and geometric consistency between selected keyframes. Due to the sparsity of optimization parameters and the robustness of the monocular depth model, our method works much better in terms of domain gap compared to existing deep learning methods for this task. At the same time, compared with traditional geometry-based 3D scene reconstruction methods, ours can be more robust to low-texture regions."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
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+                                    "type": "text",
+                                    "content": "In order to validate the robustness of our system, we test on 5 unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Experiments show that our pipeline outperforms recent methods and achieves state-of-the-art reconstruction performance. Besides, we also perform extensive ablation studies to explore the effectiveness of components of our reconstruction pipeline. Our main contributions are summarized as follows:"
+                                }
+                            ]
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+                                            "type": "text",
+                                            "content": "- We propose a novel pipeline for dense 3D scene reconstruction by using a frozen affine-invariant depth model, and jointly optimizing a sparse set of parameters for rectifying depth maps, camera poses, and intrinsic camera parameters. Our method is robust on diverse unseen scenarios."
+                                        }
+                                    ]
+                                }
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+                                            "content": "- Experiments on diverse datasets show the robustness of our method and verify the usefulness of each component in our method."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 10
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "2. Related Work"
+                                }
+                            ]
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+                    "index": 12
+                },
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+                                    "type": "text",
+                                    "content": "Learning-based 3D Scene Reconstruction. Learning-based methods [20, 30, 35] rely on a neural network with a large number of learnable parameters to learn the geometry of scenes. Some approaches generate the 3D voxel volume from the 2D image features of the entire sequence [20] or local fragments [30], and estimate an implicit 3D representation from posed images. Besides, some other algorithms [43, 2, 3] attempt to predict poses and depth maps jointly."
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 2: The pipeline of 3D scene reconstruction. Given a monocular video, we use a frozen, robust monocular depth estimation model to obtain the estimated depths of all frames. Then, we propose a geometric consistency alignment module, which optimizes a sparse set of parameters (i.e., scale, shift, and weight factors) to achieve multi-view geometric consistent depths among all frames. The camera's intrinsic parameters and poses are also optimized simultaneously. As a result, we achieve high-quality dense 3D reconstruction with optimized depths and camera parameters."
+                                        }
+                                    ]
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+                            ],
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+                                    "type": "text",
+                                    "content": "They employ an ego-motion network and a depth network to predict relative camera poses and depth maps, and supervise the photo-metric consistency [43, 3] and geometric consistency [3]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
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+                                    "type": "text",
+                                    "content": "Multi-view Geometry Based 3D Scene Reconstruction. Multi-view geometry based methods [43, 2, 3, 14, 38, 6, 13] achieve dense 3D reconstruction by finding feature correspondences across views. Traditional methods [25, 26] extract image features, establish correspondences between frames, and optimize the pose and depth iteratively, typically using bundle adjustment [34]. To achieve robust feature representation, some methods leverage plane sweeping to establish correspondences with assumed depth values. They usually construct a cost volume with the CNN-extracted features between images [13, 38, 14], and employ a ConvNet to predict depth maps after regularization. Compared with those approaches, ours is less likely to suffer from pose catastrophic failures in low-texture regions and can be more robust to diverse scenes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Besides, visual SLAM systems [18, 19, 5, 9, 10, 11, 24, 33] also estimate the camera motion and construct the map of unknown environments. Methods of [18, 19, 5, 9] rely on the assumption of geometric or photometric consistency to estimate poses and depth through bundle adjustment. Recent works [24, 33] propose to improve the robustness and accuracy by integrating more representative clues and optimization tools from deep learning. These algorithms focus on accurate pose estimation, but may fail to build dense maps with geometry details."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Robust Monocular Depth Estimation. To achieve robust monocular depth estimation, some methods [23, 22, 41, 39]"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "learn the affine-invariant depth with large-scale datasets, which is more likely to be robust to unseen scenarios but up to an unknown scale and shift. Although they achieve promising robustness, the estimated affine-invariant depth needs to recover scale-shift values by globally aligning [23, 22, 41] with ground-truth depth. Some algorithms [17, 15, 16] propose to employ robust depth prediction and achieve visually consistent video depth estimation. In contrast, this work focuses on leveraging robust monocular depth models and aiming at dense 3D scene reconstruction without extra offline-obtained information."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
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+                                    "content": "3.1. Overview"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "Aiming at 3D reconstruction from a monocular video, we propose a lightweight optimization pipeline to jointly optimize depth maps, camera poses, and intrinsic camera parameters in Figure 2. The core components of our method are the geometric consistency alignment module, optimization objectives, camera parameters initialization, and the keyframe sampling strategy."
+                                }
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+                                    "type": "text",
+                                    "content": "With the sampled images "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{I}_i\\}_{i = 1}^P"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " , we first use LeReS [41, 40] to obtain affine-invariant depth maps "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{D}_i^a\\}_{i = 1}^P"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " To avoid disastrous point cloud duplication and distortion, we leverage a geometric consistency alignment module "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\cdot ,\\cdot ,\\cdot ,\\cdot)"
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+                                {
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+                                    "type": "text",
+                                    "content": " to retrieve unknown scale and shift of affineinvariant depth and compute scale-consistent depth "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_i"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " .."
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {D} _ {i} = \\mathcal {F} \\left(\\mathbf {D} _ {i} ^ {a}; \\alpha_ {i}, \\beta_ {i}, \\boldsymbol {\\omega} _ {i}\\right), \\tag {1}",
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+                                            "type": "text",
+                                            "content": "Figure 3: The geometric consistency alignment module. We propose to first recover the global scale and shift of depth map, then apply the locally weighted linear regression method to compute the scale map and shift map, and finally achieve scale-consistent depth."
+                                        }
+                                    ]
+                                }
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+                                    "type": "text",
+                                    "content": "In order to transfer the robustness of the depth model, three optimization objectives are supervised to ensure multi-frame consistency by warping from source frame "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "content": " to reference frame "
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+                                    "type": "text",
+                                    "content": ". With this warping process, we propose to minimize the color and depth difference between warped points and reference points, i.e., photometric and geometric constraints. An additional regularization constraint is also employed to stabilize the optimization process."
+                                }
+                            ]
+                        }
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+                                    "content": "During optimization, the consistency supervision relies on two conditions: 1) the warped reference image and source images must have overlaps; 2) nicely overlapped frames can be automatically selected as our keyframes. Therefore, the appropriate initialization of camera parameters and the keyframes' sampling strategy are essential."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Finally, with the optimized intrinsic camera parameters, camera poses, and scale-consistent depth maps, we can achieve accurate 3D scene reconstruction with a simple TSDF fusion [42]."
+                                }
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+                                    "type": "text",
+                                    "content": "3.2. Optimization"
+                                }
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+                                    "content": "We assume a simple pinhole camera model, and use homogeneous representation for all image coordinates. By default, the scale factor in homogeneous coordinate is 1."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Geometric Consistency Alignment Module. The details of geometric consistency alignment module "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " are shown in Figure 3. The predicted depths "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{D}_i^a\\}_{i = 1}^P"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are affine-invariant. The unknown scale and shift will cause duplications and distortions if they are incorrectly estimated. To retrieve them, we perform a two-stage alignment, i.e., a global scale-shift alignment, and a local scale-shift alignment. In the global alignment [41], we optimize for a global scale "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and a global shift "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\beta_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " to obtain the globally aligned depth map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_i^g"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as follows:"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {D} _ {i} ^ {g} = \\alpha_ {i} \\mathbf {D} _ {i} ^ {a} + \\beta_ {i}. \\tag {2}",
+                                    "image_path": "e3b441002c13be5aecd59df798e609776f811c070aaa88f969df301141dc966b.jpg"
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+                                    "content": "In the local alignment, we compute a scale map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}_i\\in"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        663,
+                                        290,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbb{R}^{H\\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        663,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and shift map "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{B}_i\\in \\mathbb{R}^{H\\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        663,
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+                                    "type": "text",
+                                    "content": " for each frame "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to re"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        274,
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+                                        308
+                                    ],
+                                    "type": "text",
+                                    "content": "fine the globally aligned depth. Instead of directly optimizing these two maps, we uniformly sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " sparse global depth "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        274,
+                                        525,
+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        274,
+                                        525,
+                                        308
+                                    ],
+                                    "type": "text",
+                                    "content": " from the globally aligned depth "
+                                },
+                                {
+                                    "bbox": [
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+                                        274,
+                                        525,
+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_i^g"
+                                },
+                                {
+                                    "bbox": [
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+                                        308
+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "d _ {i} ^ {g} (\\mathbf {p} _ {t}) = f _ {\\mathrm {s}} (\\mathbf {D} _ {i} ^ {g}, \\mathbf {p} _ {i, t}), \\quad \\text {f o r} t = 1 \\dots M,",
+                                    "image_path": "e787dda4b57d19aedadb1781b9208ca39e742e8f428532fa59735b299e5f8364.jpg"
+                                }
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+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
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+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{s}}(\\cdot ,\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
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+                                    ],
+                                    "type": "text",
+                                    "content": " retrieves the depth value at a position; e.g., "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{s}}(\\mathbf{D}_i^g,\\mathbf{p}_{i,t})"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " obtains "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d_i^g (\\mathbf{p}_t)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " from "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_i^g"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " at the position "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_{i,t}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then, by multiplying sparse global depth "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " with the weights "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\omega_{i,t}\\}_{t = 1}^{M}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ", we compute the sparse anchor points "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\omega_{i,t}\\cdot d_i^g (\\mathbf{p}_t)\\}_{t = 1}^M"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " and use the locally weighted linear regression method [36], i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{LWL R}}(\\cdot ,\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ", to compute the local scale map "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{A}_i\\in \\mathbb{R}^{H\\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " and local shift map "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{B}_i\\in \\mathbb{R}^{H\\times W}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ". We also describe the "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{\\mathrm{LWL R}}(\\cdot ,\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        336,
+                                        525,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " module in detail in the supplementary. Such indirect optimization reduces the parameters to ease optimization. The local alignment is as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        337,
+                        454,
+                        492,
+                        480
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "bbox": [
+                                        337,
+                                        454,
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+                                        480
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathbf {A} _ {i}, \\mathbf {B} _ {i} = f _ {\\mathrm {L W L R}} \\left(\\mathbf {D} _ {i} ^ {g}, \\left\\{\\omega_ {i, t} \\cdot d _ {i} ^ {g} \\left(\\mathbf {p} _ {t}\\right) \\right\\} _ {t = 1} ^ {M}\\right), \\\\ \\mathbf {D} _ {i} = \\mathbf {A} _ {i} \\odot \\mathbf {D} _ {i} ^ {g} + \\mathbf {B} _ {i}, \\\\ \\end{array}",
+                                    "image_path": "7e9b8b53fcfc264d04ab579576db64842f0594471ae261734ba774c73b7dc5ce.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        306,
+                        485,
+                        525,
+                        540
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                306,
+                                485,
+                                525,
+                                540
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\odot"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "text",
+                                    "content": " means element-wise multiplication, and "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "text",
+                                    "content": " is set to 25 in our experiments. Therefore, in this module, we only need to optimize for 27 parameters for each frame, i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha_{i},\\beta_{i},\\omega_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        485,
+                                        525,
+                                        540
+                                    ],
+                                    "type": "text",
+                                    "content": ". With our geometric consistency alignment module, we can achieve scale-consistent depth."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        306,
+                        540,
+                        525,
+                        685
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                525,
+                                685
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": "Representation of Camera Positions and Intrinsic Camera Parameters. We propose to optimize for the relative rotation vector "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " (i.e., Euler angles) and relative translation vector "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " between two adjacent frames. They are initialized to 0 and are transformed to "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "4\\times 4"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " relative pose matrices "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{P}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " with "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{H}(\\cdot ,\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": ". The relative pose matrices "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{P}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " are transformed into camera-to-world poses matrices "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{P}_i\\}_{i = 1}^P"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " with the product operation. Such initialization ensures the initial overlap of keyframes. For intrinsic camera parameters, we assume a simple pinhole camera model, initialize the focal length to be "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f_{0} = 1.2\\cdot \\max (H,W)"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": ", and learn the focal length with a learnable scalar "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        540,
+                                        525,
+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": ". We assume that the optical center is at"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                }
+            ],
+            "discarded_blocks": [
+                {
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+                    ],
+                    "type": "page_number",
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+                                    ],
+                                    "type": "text",
+                                    "content": "9313"
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
+            "page_size": [
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+            ],
+            "page_idx": 3
+        },
+        {
+            "para_blocks": [
+                {
+                    "bbox": [
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+                        123
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
+                                        70,
+                                        101,
+                                        289,
+                                        123
+                                    ],
+                                    "type": "text",
+                                    "content": "the image center. Thus for camera parameters, we need to optimize for "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        101,
+                                        289,
+                                        123
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "6(P - 1) + 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " variables:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                    ],
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+                    "lines": [
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+                                    "bbox": [
+                                        81,
+                                        130,
+                                        268,
+                                        143
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {P} _ {i \\rightarrow (i + 1)} = \\mathcal {H} (\\mathbf {r} _ {i \\rightarrow (i + 1)}, \\mathbf {t} _ {i \\rightarrow (i + 1)}), \\quad \\mathbf {P} _ {1} = \\mathbf {E} _ {4, 4},",
+                                    "image_path": "2431ef5ede2ebc10330132a00e37b6b345bd08e30dfdbea04fddd0157809f911.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
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+                    ],
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+                                    "bbox": [
+                                        76,
+                                        144,
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+                                        180
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {P} _ {i} = \\mathbf {P} _ {1} \\prod_ {k = 1} ^ {i - 1} \\mathbf {P} _ {k \\rightarrow (k + 1)}, \\quad \\mathbf {K} = \\left[\\begin{array}{c c c}\\delta f _ {0}&0&W / 2\\\\0&\\delta f _ {0}&H / 2\\\\0&0&1\\end{array}\\right], \\tag {4}",
+                                    "image_path": "eddf15111db877fca5b0f87ed64812e750432a4b472aa24376445b8a49e3f51a.jpg"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
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+                                        229,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{E}_{4,4}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        186,
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+                                        196
+                                    ],
+                                    "type": "text",
+                                    "content": " is the "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        186,
+                                        229,
+                                        196
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "4\\times 4"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        186,
+                                        229,
+                                        196
+                                    ],
+                                    "type": "text",
+                                    "content": " elementary matrix."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                        196,
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+                        218
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
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+                                        218
+                                    ],
+                                    "type": "text",
+                                    "content": "Optimization Objectives. The image coordinate "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
+                                        289,
+                                        218
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
+                                        289,
+                                        218
+                                    ],
+                                    "type": "text",
+                                    "content": " in frame "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
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+                                        218
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
+                                        289,
+                                        218
+                                    ],
+                                    "type": "text",
+                                    "content": " can be wrapped to frame "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
+                                        289,
+                                        218
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        196,
+                                        289,
+                                        218
+                                    ],
+                                    "type": "text",
+                                    "content": " as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} f _ {s} \\left(\\mathbf {D} _ {i \\rightarrow j}, \\mathbf {p} _ {i}\\right) \\mathbf {p} _ {i \\rightarrow j} = \\mathbf {K R} _ {j} ^ {\\top} \\left[ \\mathbf {R} _ {i} \\mathbf {K} ^ {- 1} f _ {s} \\left(\\mathbf {D} _ {i}, \\mathbf {p} _ {i}\\right) \\mathbf {p} _ {i} + \\mathbf {t} _ {i} - \\mathbf {t} _ {j} \\right], \\\\ \\mathbf {p} _ {i}, \\mathbf {p} _ {i \\rightarrow j}, \\mathbf {t} _ {i}, \\mathbf {t} _ {j} \\in \\mathbb {R} ^ {3 \\times 1}, \\quad \\mathbf {R} _ {i}, \\mathbf {R} _ {j}, \\mathbf {K} \\in \\mathbb {R} ^ {3 \\times 3}, \\tag {5} \\\\ \\end{array}",
+                                    "image_path": "d9e008ef843fb8f2d26cb52d2cd421273b5353004d10a2abb4f661dce3a5268c.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        70,
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+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{K}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " is the intrinsic camera parameter. "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{R}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{t}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " are the camera-to-world rotation and translation matrices, and "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{P}_i = \\begin{bmatrix} \\mathbf{R}_i & \\mathbf{t}_i \\\\ \\mathbf{0} & 1 \\end{bmatrix}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_{i\\rightarrow j}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " is the point warped from "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{p}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
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+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " of frame "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to frame "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
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+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{D}_{i\\rightarrow j}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        262,
+                                        289,
+                                        316
+                                    ],
+                                    "type": "text",
+                                    "content": " is the warped depth map."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        70,
+                        315,
+                        289,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "text",
+                                    "content": "To optimize the proposed variables including "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\alpha_{i}\\}_{i = 1}^{P}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\beta_i\\}_{i = 1}^P"
+                                },
+                                {
+                                    "bbox": [
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+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
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+                                        369
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\delta"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\omega_{i}\\}_{i = 1}^{P}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        315,
+                                        289,
+                                        369
+                                    ],
+                                    "type": "text",
+                                    "content": " we propose to use the pixel-wise photometric and geometric constraint [2] together to ensure the consistency of color and depth along the video as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
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+                            "spans": [
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+                                    "bbox": [
+                                        86,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {p c} = \\frac {1}{| V |} \\sum_ {\\substack {\\mathbf {p} \\in V\\\\(i, j) \\in K}} | f _ {\\mathrm {s}} (\\mathbf {I} _ {i}, \\mathbf {p} _ {i}) - f _ {\\mathrm {s}} (\\mathbf {I} _ {j}, \\mathbf {p} _ {i \\rightarrow j}) |, \\tag{6}",
+                                    "image_path": "65c9e9a247629398703f80091f55e0403cd71bfd8fc4b7d1870f55991bab8621.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                    ],
+                    "type": "interline_equation",
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+                    "lines": [
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+                            "bbox": [
+                                75,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        75,
+                                        423,
+                                        289,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {g c} = \\frac {1}{| V |} \\sum_ {\\substack {\\mathbf {p} \\in V\\\\(i, j) \\in K}} \\frac {\\left| f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {j} , \\mathbf {p} _ {i \\rightarrow j}\\right) - f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {i \\rightarrow j} , \\mathbf {p} _ {i}\\right) \\right|}{f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {j} , \\mathbf {p} _ {i \\rightarrow j}\\right) + f _ {\\mathrm {s}} \\left(\\mathbf {D} _ {i \\rightarrow j} , \\mathbf {p} _ {i}\\right)}, \\tag{7}",
+                                    "image_path": "992732438d5811c14025211455e2992377c6751636ef5677c45f625750b5aab1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        461,
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+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        461,
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+                                    ],
+                                    "type": "text",
+                                    "content": " represents all valid points successfully projected from frame "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to frame "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        461,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "j"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        461,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        461,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the selected keyframe pairs."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        70,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        70,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Furthermore, we enforce a regularization term on the sampled sparse anchor points:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        127,
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+                    ],
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+                    "angle": 0,
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+                                    "bbox": [
+                                        127,
+                                        512,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "L _ {r e g u} = \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {M} | 1 - \\omega_ {i, t} |, \\tag {8}",
+                                    "image_path": "647c5040bfb60df23b70eb5d0bacf25cac955c8b8125f4b140b18abd99b13f05.jpg"
+                                }
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+                        }
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+                    "index": 12
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "type": "text",
+                                    "content": "The overall constraints are as follows."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "interline_equation",
+                                    "content": "L = \\lambda_ {p c} L _ {p c} + \\lambda_ {g c} L _ {g c} + \\lambda_ {r e g u} L _ {r e g u}, \\tag {9}",
+                                    "image_path": "b2d1f335cadf29dddc9dd55db6ba5729ea8b2114dd27ff644416bdab1f4c039c.jpg"
+                                }
+                            ]
+                        }
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+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{pc},\\lambda_{gc}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " , and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{regu}"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        586,
+                                        274,
+                                        598
+                                    ],
+                                    "type": "text",
+                                    "content": " are weights to balance them."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Optimization Details. Before we perform optimization, we first sample "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        597,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P"
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        597,
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+                                    ],
+                                    "type": "text",
+                                    "content": " frames from the video to reduce the time complexity. With these sampled frames, we perform the keyframes sampling and optimization, which consists of two stages, i.e., local keyframes sampling for optimization, and global keyframes sampling for optimization."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                        685
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Local keyframes sampling and optimization. In optimization, we first sample local keyframes from the "
+                                },
+                                {
+                                    "bbox": [
+                                        70,
+                                        663,
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+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " nearest"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
+                    "bbox": [
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+                        111
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                111
+                            ],
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+                                    "bbox": [
+                                        307,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Algorithm 1 Optimization Algorithm"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
+                        307,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                115,
+                                395,
+                                126
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        307,
+                                        115,
+                                        395,
+                                        126
+                                    ],
+                                    "type": "text",
+                                    "content": "Input: "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        115,
+                                        395,
+                                        126
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        115,
+                                        395,
+                                        126
+                                    ],
+                                    "type": "text",
+                                    "content": " images "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        115,
+                                        395,
+                                        126
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{I}_i\\}_{i = 1}^N"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                        125,
+                        524,
+                        146
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                125,
+                                524,
+                                146
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        307,
+                                        125,
+                                        524,
+                                        146
+                                    ],
+                                    "type": "text",
+                                    "content": "Output: scale-consistent depth maps "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        125,
+                                        524,
+                                        146
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{D}_i\\}_{i = 1}^P"
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        125,
+                                        524,
+                                        146
+                                    ],
+                                    "type": "text",
+                                    "content": " intrinsic camera parameter K, camera-to-world camera poses "
+                                },
+                                {
+                                    "bbox": [
+                                        307,
+                                        125,
+                                        524,
+                                        146
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
+                },
+                {
+                    "bbox": [
+                        311,
+                        145,
+                        524,
+                        196
+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 24,
+                    "blocks": [
+                        {
+                            "bbox": [
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+                                145,
+                                454,
+                                156
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                        156
+                                    ],
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+                                        {
+                                            "bbox": [
+                                                311,
+                                                145,
+                                                454,
+                                                156
+                                            ],
+                                            "type": "text",
+                                            "content": "1: Sample "
+                                        },
+                                        {
+                                            "bbox": [
+                                                311,
+                                                145,
+                                                454,
+                                                156
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "P"
+                                        },
+                                        {
+                                            "bbox": [
+                                                311,
+                                                145,
+                                                454,
+                                                156
+                                            ],
+                                            "type": "text",
+                                            "content": " images "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{I}_i\\}_{i = 1}^P"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                454,
+                                                156
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+                                            "type": "text",
+                                            "content": " from "
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+                                        {
+                                            "bbox": [
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+                                                145,
+                                                454,
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+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{I}_i\\}_{i = 1}^N"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 21
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+                        {
+                            "bbox": [
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+                                            "content": "2: Obtain affine-invariant depth "
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+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{D}_i^q\\}_{i = 1}^P"
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+                                        {
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+                                            "type": "text",
+                                            "content": " from "
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+                                                166
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+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{I}_i\\}_{i = 1}^P"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 22
+                        },
+                        {
+                            "bbox": [
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+                                196
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                    "spans": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "3: Initialize the global scale "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\alpha_i\\}_{i = 1}^P"
+                                        },
+                                        {
+                                            "bbox": [
+                                                311,
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+                                            ],
+                                            "type": "text",
+                                            "content": " , global shift "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\beta_i\\}_{i = 1}^P"
+                                        },
+                                        {
+                                            "bbox": [
+                                                311,
+                                                165,
+                                                524,
+                                                196
+                                            ],
+                                            "type": "text",
+                                            "content": " , focal length scalar "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\delta"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                165,
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+                                                196
+                                            ],
+                                            "type": "text",
+                                            "content": " , relative rotation "
+                                        },
+                                        {
+                                            "bbox": [
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+                                                524,
+                                                196
+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{r}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " , relative translation "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{t}_{i\\rightarrow (i + 1)}\\}_{i = 1}^{P - 1}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                165,
+                                                524,
+                                                196
+                                            ],
+                                            "type": "text",
+                                            "content": " , sparse points weight "
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{\\omega_{i}\\}_{i = 1}^{P}"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 23
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4: for stage in [Local, Global] do"
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+                            ]
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+                    ],
+                    "index": 25
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+                    "type": "list",
+                    "angle": 0,
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+                            "lines": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "5: for iter "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "= 1"
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+                                            "type": "text",
+                                            "content": " to iterations do"
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+                                    ]
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+                            ],
+                            "index": 26
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+                            "type": "text",
+                            "angle": 0,
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+                                            "content": "6: Compute "
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+                                        {
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+                                            "type": "inline_equation",
+                                            "content": "\\{\\mathbf{P}_i\\}_{i = 1}^{P - 1}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": " and "
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+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{K}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " with Eq. (4)"
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+                                    ]
+                                }
+                            ],
+                            "index": 27
+                        },
+                        {
+                            "bbox": [
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+                                236
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+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "7: if stage = Local then"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 28
+                        },
+                        {
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+                            "type": "text",
+                            "angle": 0,
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "8: Sample keyframe pairs "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{(i_k,j_k)\\}_{k = 1}^K"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " with Eq. (10)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 29
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "9:"
+                                }
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+                        }
+                    ],
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+                },
+                {
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+                    "type": "list",
+                    "angle": 0,
+                    "index": 43,
+                    "blocks": [
+                        {
+                            "bbox": [
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+                                266
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+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                            "type": "text",
+                                            "content": "10: Sample keyframe pairs "
+                                        },
+                                        {
+                                            "bbox": [
+                                                311,
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{(i_k,j_k)\\}_{k = 1}^K"
+                                        },
+                                        {
+                                            "bbox": [
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+                                                266
+                                            ],
+                                            "type": "text",
+                                            "content": " with Eq. (11)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 32
+                        },
+                        {
+                            "bbox": [
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+                                266,
+                                361,
+                                274
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                            "type": "text",
+                                            "content": "11: end if"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 33
+                        },
+                        {
+                            "bbox": [
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+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "12: for keyframe pair "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "(i,j)"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " in "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\{(i_k,j_k)\\}_{k = 1}^K"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
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+                                                286
+                                            ],
+                                            "type": "text",
+                                            "content": " do"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 34
+                        },
+                        {
+                            "bbox": [
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+                                524,
+                                296
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                    "spans": [
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "13: Compute scale-consistent depth "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{D}_i"
+                                        },
+                                        {
+                                            "bbox": [
+                                                308,
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+                                            ],
+                                            "type": "text",
+                                            "content": ", "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{D}_j"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " with Eq. (3);"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 35
+                        },
+                        {
+                            "bbox": [
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+                                316
+                            ],
+                            "type": "text",
+                            "angle": 0,
+                            "lines": [
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+                                    "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "14: Warp "
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{p}_i"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " from frame "
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+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "i"
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+                                        {
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+                                            "type": "text",
+                                            "content": " to frame "
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+                                            "type": "inline_equation",
+                                            "content": "j"
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+                                        {
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+                                            "type": "text",
+                                            "content": ", get warped depth "
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+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{D}_{i\\rightarrow j}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " and warped locations "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "inline_equation",
+                                            "content": "\\mathbf{p}_{i\\rightarrow j}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " with Eq. (5)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 36
+                        },
+                        {
+                            "bbox": [
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+                                326
+                            ],
+                            "type": "text",
+                            "angle": 0,
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+                                            ],
+                                            "type": "text",
+                                            "content": "15: Compute optimization objectives with Eq. (9)"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 37
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "16: end for"
+                                        }
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+                            ],
+                            "index": 38
+                        },
+                        {
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+                                            "content": "17: Back-propagate and update "
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+                                            "type": "inline_equation",
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+                                        {
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+                                            ],
+                                            "type": "text",
+                                            "content": ", "
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+                                            "content": "18: end for"
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+                                            "content": "20: Compute scale-consistent depth maps "
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+                                            "content": " with Eq. (3), compute camera parameters "
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+                                            "type": "text",
+                                            "content": " with Eq. (4)"
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+                                    "content": " is set to 6 in our experiments. To reduce computation time complexity, we do not use all these local keyframes with the current frame but select them based on probability. The probability for each keyframe is set as follows."
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+                                    "content": "p _ {l} = \\left\\{ \\begin{array}{l} \\frac {1}{k}, \\text {i f k - n e a r e s t n e i g h b o r s ,} \\\\ 0, \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {10}",
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+                                    "content": "Global keyframes sampling and optimization. We further perform global keyframes sampling and optimization to improve long-range consistency. For each reference frame, all other frames are regarded as paired keyframes, but they are labeled with different sampling probabilities. We compute the relative pose between each reference frame "
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+                                    "content": ". Based on the relative pose angle "
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+                                    "content": "p _ {g} = \\frac {p _ {l} + p}{2}, p = \\left\\{ \\begin{array}{c} \\frac {\\theta_ {i j}}{\\phi^ {2}}, \\text {i f} 0 <   \\theta_ {i j} \\leq \\phi \\\\ \\frac {2}{\\phi} - \\frac {\\theta_ {i j}}{\\phi^ {2}}, \\text {i f} \\phi <   \\theta_ {i j} <   2 \\phi , \\\\ 0, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {11}",
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+                                            "content": "Table 1: Quantitative comparison of zero-shot 3D scene reconstruction with state-of-the-art methods. We compare our method with seven categories of reconstruction algorithms on several video sequences of five unseen datasets: NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], and KITTI [12]. Note that NeuralRecon is trained on ScanNet [8], * denotes ground-truth camera poses are given, and “Rank” means average ranking performance of each column. We evaluate the Chamfer distance "
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+                                            "type": "text",
+                                            "content": " and F-score with a threshold of "
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+                                            "type": "text",
+                                            "content": " . As a result,we achieve state-of-the-art rank on the five zero-shot datasets."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">NYU [28]</td><td colspan=\"2\">ScanNet [8]</td><td colspan=\"2\">7-Scenes [27]</td><td colspan=\"2\">TUM [29]</td><td colspan=\"2\">KITTI [12]</td><td rowspan=\"2\">Rank</td></tr><tr><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>NeuralRecon* [30]</td><td>0.487</td><td>0.185</td><td colspan=\"2\">trained on ScanNet</td><td>0.235</td><td>0.219</td><td>0.435</td><td>0.241</td><td colspan=\"2\">failed on KITTI</td><td>8.125</td></tr><tr><td>DPSNet* [14]</td><td>0.198</td><td>0.391</td><td>0.299</td><td>0.266</td><td>0.574</td><td>0.142</td><td>0.336</td><td>0.263</td><td>0.290</td><td>0.232</td><td>4.800</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.139</td><td>0.481</td><td>0.379</td><td>0.292</td><td>0.235</td><td>0.460</td><td>0.322</td><td>0.439</td><td>2.431</td><td>0.010</td><td>3.600</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.196</td><td>0.458</td><td>0.402</td><td>0.214</td><td>0.252</td><td>0.240</td><td>0.525</td><td>0.244</td><td>4.133</td><td>0.036</td><td>5.500</td></tr><tr><td>CVD [17]</td><td>0.471</td><td>0.302</td><td colspan=\"2\">failed on ScanNet</td><td>0.416</td><td>0.215</td><td>0.378</td><td>0.239</td><td>5.479</td><td>0.029</td><td>7.900</td></tr><tr><td>RCVD [15]</td><td>0.303</td><td>0.346</td><td>0.641</td><td>0.125</td><td>0.497</td><td>0.182</td><td>0.679</td><td>0.218</td><td>58.372</td><td>0.020</td><td>8.300</td></tr><tr><td>GCVD [16]</td><td>0.148</td><td>0.453</td><td>0.631</td><td>0.147</td><td>0.196</td><td>0.326</td><td>0.350</td><td>0.339</td><td>2.127</td><td>0.114</td><td>4.400</td></tr><tr><td>COLMAP [25, 26]</td><td>0.251</td><td>0.343</td><td>0.796</td><td>0.127</td><td>0.513</td><td>0.178</td><td>0.385</td><td>0.249</td><td>107.451</td><td>0.152</td><td>7.300</td></tr><tr><td>DROID-SLAM [33]</td><td>0.224</td><td>0.516</td><td>0.416</td><td>0.384</td><td>0.304</td><td>0.469</td><td>0.285</td><td>0.433</td><td>0.686</td><td>0.155</td><td>3.200</td></tr><tr><td>Ours</td><td>0.099</td><td>0.622</td><td>0.170</td><td>0.410</td><td>0.170</td><td>0.464</td><td>0.211</td><td>0.453</td><td>0.670</td><td>0.151</td><td>1.500</td></tr></table>",
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+                                            "content": "Table 2: Quantitative comparison of zero-shot depth estimation with state-of-the-art methods. We evaluate the absolute relative error (AbsRel) and percentage of accurate depth pixels "
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+                                            "content": " on several videos of five unseen datasets. \"Rank\" means average ranking performance of each column. The gray \"LeReS\" represents performance of affine-invariant depth without any alignment with ground-truth depth. As a result, our algorithm achieves state-of-the-art rank performance."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">NYU [28]</td><td colspan=\"2\">ScanNet [8]</td><td colspan=\"2\">7-Scenes [27]</td><td colspan=\"2\">TUM [29]</td><td colspan=\"2\">KITTI [12]</td><td rowspan=\"2\">Rank</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td><td>AbsRel↓</td><td>δ1↑</td></tr><tr><td>DPSNet* [14]</td><td>0.200</td><td>0.662</td><td>0.216</td><td>0.630</td><td>0.201</td><td>0.657</td><td>0.331</td><td>0.457</td><td>0.188</td><td>0.729</td><td>6.4</td></tr><tr><td>BoostingDepth-DROID [36]</td><td>0.096</td><td>0.921</td><td>0.236</td><td>0.685</td><td>0.145</td><td>0.828</td><td>0.180</td><td>0.742</td><td>0.112</td><td>0.860</td><td>2.7</td></tr><tr><td>SC-DepthV3 [31]</td><td>0.120</td><td>0.858</td><td>0.197</td><td>0.672</td><td>0.188</td><td>0.688</td><td>0.254</td><td>0.569</td><td>0.287</td><td>0.463</td><td>5.2</td></tr><tr><td>CVD [17]</td><td>0.167</td><td>0.837</td><td colspan=\"2\">failed on ScanNet</td><td>0.180</td><td>0.847</td><td>0.148</td><td>0.797</td><td>0.717</td><td>0.215</td><td>5.6</td></tr><tr><td>RCVD [15]</td><td>0.192</td><td>0.700</td><td>0.235</td><td>0.620</td><td>0.241</td><td>0.635</td><td>0.246</td><td>0.612</td><td>0.220</td><td>0.606</td><td>6.6</td></tr><tr><td>GCVD [16]</td><td>0.163</td><td>0.768</td><td>0.316</td><td>0.527</td><td>0.203</td><td>0.650</td><td>0.248</td><td>0.697</td><td>0.240</td><td>0.543</td><td>6.4</td></tr><tr><td>COLMAP [26, 25]</td><td>0.233</td><td>0.722</td><td>0.562</td><td>0.409</td><td>0.268</td><td>0.666</td><td>0.269</td><td>0.665</td><td>0.302</td><td>0.773</td><td>7.2</td></tr><tr><td>DROID-SLAM [33]</td><td>0.143</td><td>0.847</td><td>0.210</td><td>0.773</td><td>0.154</td><td>0.827</td><td>0.210</td><td>0.720</td><td>0.115</td><td>0.914</td><td>3.1</td></tr><tr><td>LeReS [41]</td><td>0.277</td><td>0.508</td><td>0.409</td><td>0.339</td><td>0.414</td><td>0.345</td><td>0.445</td><td>0.320</td><td>0.298</td><td>0.439</td><td>-</td></tr><tr><td>Ours</td><td>0.092</td><td>0.923</td><td>0.127</td><td>0.858</td><td>0.135</td><td>0.844</td><td>0.145</td><td>0.799</td><td>0.203</td><td>0.632</td><td>1.8</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is an angle threshold, and "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\theta_{ij}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the relative rotation angle between the source frame "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{I}_i"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the reference frame "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "p_l"
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+                                    "type": "text",
+                                    "content": " is the local probability with Eq. (10). The optimization is summarized in Algorithm 1."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
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+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We evaluate the 3D reconstruction, scale-consistent depths, optimized camera poses, and optimized intrinsic camera parameters in experiments. More details and analyses including runtime can be found in the supplementary."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "4.1. Dense 3D Scene Reconstruction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "To show the robustness and accuracy of our reconstruction method, we compare it with a learning-based volumetric 3D reconstruction method (NeuralRecon [30]), a multiview depth estimation method (DPSNet [14]), a per-frame scale-shift alignment method (BoostingDepth [36]), an unsupervised video depth estimation method (SC-DepthV3"
+                                }
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+                        }
+                    ],
+                    "index": 8
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+                                    "type": "text",
+                                    "content": "[31]), some consistent video depth estimation methods (CVD [17], RCVD [15], GCVD [16]), a Structure-from-Motion method COLMAP [26, 25], and a robust deep visual SLAM method (DROID-SLAM [33]) on several video sequences of 5 zero-shot datasets, i.e., NYU [28], ScanNet [8], 7-Scenes [27], TUM [29], KITTI [12]. Note that NeuralRecon is trained on ScanNet, while others are evaluated on unseen scenarios. NeuralRecon and DPSNet require GT poses and camera intrinsic as input, and SC-DepthV3, CVD, and DROID-SLAM require camera intrinsic. For fair comparison, we employ the estimated poses and depths of DROID-SLAM for BoostingDepth (BoostingDepth-DROID) to iteratively align the scale-shift values and filter outliers, as their paper does. Other methods optimize camera parameters on their own."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "Quantitative comparisons of zero-shot 3D reconstruction and depth are shown in Table 1 and Table 2 respectively. NeuralRecon [30], DPSNet [14], SC-DepthV3 [31] need"
+                                }
+                            ]
+                        }
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+                                            "content": "Table 3: Quantitative comparison of zero-shot pose estimation. \"ATE\", \"RPE-T\", and \"RPE-R\" stand for the absolute trajectory error and the relative pose errors of translation and rotation, respectively. \"%\" represents the percentage of successfully tracked frames. Note that ORB-SLAM3 fails to track the trajectory on some low-texture regions, and can only estimate partial camera poses. Our algorithm achieves comparable performance to ORB-SLAM3 on three unseen datasets and better performance than the video depth estimation algorithms."
+                                        }
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">GT Intrinsic</td><td colspan=\"4\">NYU [28]</td><td colspan=\"4\">ScanNet [8]</td><td colspan=\"4\">7-Scenes [27]</td><td colspan=\"4\">TUM [29]</td><td colspan=\"4\">KITTI [12]</td></tr><tr><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>%↑</td></tr><tr><td>SC-DepthV3 [31]</td><td>✓</td><td>0.241</td><td>0.444</td><td>0.115</td><td>1.000</td><td>0.492</td><td>0.702</td><td>0.327</td><td>1.000</td><td>1.011</td><td>1.644</td><td>0.389</td><td>1.000</td><td>0.528</td><td>0.787</td><td>0.399</td><td>1.000</td><td>1.796</td><td>4.186</td><td>0.077</td><td>1.000</td></tr><tr><td>CVD [17]</td><td>✓</td><td>1.192</td><td>2.049</td><td>0.107</td><td>1.000</td><td>0.734</td><td>1.197</td><td>0.257</td><td>1.000</td><td>0.532</td><td>1.644</td><td>0.378</td><td>1.000</td><td>0.268</td><td>0.844</td><td>0.447</td><td>1.000</td><td>19.32</td><td>24.50</td><td>0.027</td><td>1.000</td></tr><tr><td>RCVD [15]</td><td></td><td>0.460</td><td>1.263</td><td>0.114</td><td>1.000</td><td>1.025</td><td>1.708</td><td>0.615</td><td>1.000</td><td>0.559</td><td>1.545</td><td>0.394</td><td>1.000</td><td>0.626</td><td>1.083</td><td>0.421</td><td>1.000</td><td>134.3</td><td>160.7</td><td>0.463</td><td>1.000</td></tr><tr><td>GCVD [16]</td><td></td><td>0.160</td><td>0.237</td><td>0.083</td><td>1.000</td><td>0.573</td><td>0.979</td><td>0.620</td><td>1.000</td><td>0.259</td><td>0.368</td><td>0.162</td><td>1.000</td><td>0.162</td><td>0.204</td><td>0.113</td><td>1.000</td><td>5.678</td><td>8.733</td><td>0.089</td><td>1.000</td></tr><tr><td>COLMAP [26, 25]</td><td></td><td>0.091</td><td>0.137</td><td>0.055</td><td>1.000</td><td>0.352</td><td>0.426</td><td>0.096</td><td>1.000</td><td>0.062</td><td>0.090</td><td>0.051</td><td>1.000</td><td>0.075</td><td>0.102</td><td>0.064</td><td>1.000</td><td>3.707</td><td>3.454</td><td>0.016</td><td>1.000</td></tr><tr><td>DROID-SLAM [33]</td><td>✓</td><td>0.050</td><td>0.079</td><td>0.032</td><td>1.000</td><td>0.230</td><td>0.230</td><td>0.052</td><td>1.000</td><td>0.050</td><td>0.072</td><td>0.072</td><td>1.000</td><td>0.044</td><td>0.077</td><td>0.079</td><td>1.000</td><td>1.491</td><td>2.302</td><td>0.005</td><td>1.000</td></tr><tr><td>ORB-SLAM3 [5]</td><td>✓</td><td>0.065</td><td>0.097</td><td>0.039</td><td>0.791</td><td>0.208</td><td>0.300</td><td>0.098</td><td>0.426</td><td>0.118</td><td>0.211</td><td>0.121</td><td>0.956</td><td>0.104</td><td>0.144</td><td>0.082</td><td>0.504</td><td>3.124</td><td>3.926</td><td>0.009</td><td>0.971</td></tr><tr><td>Ours</td><td></td><td>0.079</td><td>0.121</td><td>0.046</td><td>1.000</td><td>0.130</td><td>0.184</td><td>0.085</td><td>1.000</td><td>0.141</td><td>0.229</td><td>0.075</td><td>1.000</td><td>0.176</td><td>0.228</td><td>0.151</td><td>1.000</td><td>3.541</td><td>5.663</td><td>0.053</td><td>1.000</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 4: Quantitative comparison of zero-shot intrinsic camera parameter estimation. \"FOV AbsRel\" represents the absolute relative error of the field of view. Note that only three algorithms can estimate the intrinsic camera parameter from the input video, and our method can achieve accurate and robust performance on four unseen datasets."
+                                        }
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td>NYU [28]</td><td>ScanNet [8]</td><td>7-Scenes [27]</td><td>TUM [29]</td><td rowspan=\"2\">Rank</td></tr><tr><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td><td>FOV AbsRel↓</td></tr><tr><td>RCVD [15]</td><td>0.144</td><td>0.148</td><td>0.110</td><td>0.174</td><td>2.75</td></tr><tr><td>GCVD [16]</td><td>0.015</td><td>0.126</td><td>0.143</td><td>0.043</td><td>1.75</td></tr><tr><td>Ours</td><td>0.032</td><td>0.032</td><td>0.085</td><td>0.056</td><td>1.50</td></tr></table>",
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+                                    "content": "to optimize millions of parameters, thus showing less robustness to unseen datasets. Rather than purely per-frame aligning with offline-obtained depth after filtering as BoostingDepth [36] does, we jointly optimize the camera parameters and depth parameters, which ensures consistency between frames and less suffers from outliers of sparse points. CVD [17] fails to reconstruct half of the ScanNet scenarios. Compared with RCVD [15], and GCVD [16], our method employs a global and a local scale-shift recovery strategy, which can rectify the affine-invariant depth to a much more accurate scale-consistent depth. Thus, we can achieve much more accurate reconstructions. The COLMAP [26, 25] struggles to estimate dense depth maps, and thus results in sparse 3D reconstruction. The robust DROID-SLAM [33] focuses on optimizing more robust poses and trajectories with the recurrent module, and spends less effort on dense reconstruction. Thus, their dense reconstruction is more likely to suffer from outliers. In contrast, our optimization is based on dense depth priors and employs a global and local optimization strategy to reduce noise, thus we in general achieve better reconstruction performance."
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+                                    "content": "Quantitative comparisons of zero-shot pose estimation and intrinsic camera parameter estimation are shown in Table 3 and Table 4. Our algorithm achieves comparable performance with the traditional SLAM methods ORBSLAM3 [5] on three datasets. However, the ORB-SLAM3"
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+                                            "content": "Table 5: Runtime analysis on three representative scenes. Our pipeline achieves state-of-the-art reconstruction but only takes around a quarter of an hour to optimize."
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+                                            "html": "<table><tr><td>Method</td><td>basement_0001a</td><td>bedroom_0015</td><td>chess</td></tr><tr><td>NeuralRecon[30]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DPSNet[14]</td><td>5m 53s</td><td>45s</td><td>12m 20s</td></tr><tr><td>BoostingDepth-DROID[36]</td><td>35s</td><td>10s</td><td>47s</td></tr><tr><td>SC-DepthV3[31]</td><td>1m 47s</td><td>17s</td><td>1m 54s</td></tr><tr><td>CVD[17]</td><td>1h 7m 6s</td><td>12m 30s</td><td>8h 1m 34s</td></tr><tr><td>RCVD[15]</td><td>1h 15m 45s</td><td>10m 6s</td><td>6h 14m 54s</td></tr><tr><td>GCVD[16]</td><td>10m 26s</td><td>2m 37s</td><td>52m 15s</td></tr><tr><td>DROID-SLAM[33]</td><td>35s</td><td>16s</td><td>1m 18s</td></tr><tr><td>COLMAP[25, 26]</td><td>50m 44s</td><td>8m 34s</td><td>9h 40m 49s</td></tr><tr><td>Ours</td><td>14m 55s</td><td>6m 55s</td><td>21m 8s</td></tr></table>",
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+                                    "content": "can only estimate the camera poses of partial frames due to the failure of tracking features. In contrast, our algorithm can optimize and interpolate to obtain dense trajectories. Compared to four video depth estimation methods, we can outperform them by a large margin. Note that only ours, RCVD, and GCVD can optimize the intrinsic camera parameters, while others can only employ GT camera intrinsic as input. For intrinsic camera parameter estimation, our algorithm can achieve robust and accurate performance on four unseen datasets."
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+                                    "content": "Qualitative comparisons are reported in Figure. 4. NeuralRecon can only reconstruct partial meshes of unseen scenarios. The DPSNet [14] suffers from inaccurate feature correspondences, which cause noisy point clouds. BoostingDepth [36] can only filter out inaccurate points of DROID-SLAM but cannot ensure the temporal consistency, and thus fails to reconstruct consistent mesh. The SC-DepthV3 [31] suffers from the weak supervision of photometric loss and work worse on some low-texture regions. Consistent video depth estimation methods such as GCVD [16] cannot recover the shift of depth maps, which will cause distortions in 3D point clouds. DROID-SLAM [33] concentrates on accurate pose estimation but does not work"
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+                                            "content": "Figure 4: Qualitative comparison of zero-shot 3D scene reconstruction from a monocular video. We compare our method with five representative algorithms on five unseen datasets. Note that NeuralRecon is trained on ScanNet [8] and can only output uncolored mesh, and * represents the employment of ground-truth camera poses during reconstruction. These methods either suffer from inaccurate pose estimation, or predict noise depth maps (please see the red arrows). As can be seen, our approach can reconstruct better 3D scene shape without any offline-computed camera parameters."
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+                                    "content": "well for dense reconstruction, and thus suffering from outliers. In contrast, our method can achieve more robust and"
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+                                            "content": "Table 6: Comparison of geometric consistency alignment mechanisms on the NYU [28] dataset. \"w/ deform.\" means optimizing the flexible deformation map of RCVD [15] as a replacement for our alignment module. \"Baseline\" means directly optimizing the per-frame pixel-wise depth map without the affine-invariant depth priors. As a result, the employment of our geometric consistency alignment module contributes significantly to the optimization."
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+                                            "content": "Table 7: Comparison of optimization objectives on the ScanNet [8] dataset. The photometric constraint supervises the color consistency, the geometric constraint ensures the multi-view geometry consistency, and the regularization constraint stabilizes the convergence of optimization. As a result, the three components of our optimization objectives are all important."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Ours</td><td>0.127</td><td>0.858</td><td>0.271</td><td>0.348</td><td>0.147</td><td>0.170</td><td>0.410</td></tr><tr><td>w/o photo.</td><td>0.219</td><td>0.636</td><td>1.722</td><td>2.331</td><td>1.039</td><td>0.775</td><td>0.169</td></tr><tr><td>w/o geo.</td><td>0.168</td><td>0.750</td><td>0.316</td><td>0.404</td><td>0.179</td><td>0.211</td><td>0.323</td></tr><tr><td>w/o regu.</td><td>0.226</td><td>0.603</td><td>0.245</td><td>0.338</td><td>0.189</td><td>0.220</td><td>0.254</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "For quantitative efficiency analysis, the runtime comparisons on 40 Intel Xeon Silver 4210 CPUs and an RTX 3090 Ti GPU are presented in Table 5, which includes three representative scenes with 225, 48, and 1000 images, respectively. Our pipeline achieves state-of-the-art reconstruction while only taking about a quarter of an hour to optimize, even for 1000 images. Note that only the time of predicting depth and poses without RGB-D fusion are recorded."
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+                                    "content": "4.2. Ablation Studies"
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+                                    "content": "We carry out ablation experiments in terms of essential components of our algorithm to evaluate their effectiveness. Geometric Consistency Alignment Module. Table 6 shows the performance of different geometric consistency alignment modules. Previous consistent video depth methods RCVD and GCVD employ flexible deformation maps (\"w/ deform.\") and aim for more accurate scale-consistent depth. However, they both ignore the shift issues in affine-invariant depth, which is pretty significant in the 3D reconstruction task. By contrast, our method (\"Ours\") proposes a global and local scale shift alignment module for depth rectification. We also compare with a baseline method (\"baseline\"), which directly optimizes all frames' pixel-wise depths without the affine-invariant depth priors. All"
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+                                            "content": "Table 8: Effectiveness of our two-stage keyframe sampling and optimization strategy. The \"Local\" stage ensures consistency between the nearest "
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+                                            "content": " keyframes. The \"Global\" stage samples keyframes globally with different sampling probabilities according to the optimized relative poses. As a result, our algorithm achieves better performance with the coarse-to-fine optimization strategy. The experiment is conducted on NYU [28] dataset."
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+                                            "html": "<table><tr><td rowspan=\"2\">Stage</td><td colspan=\"2\">Depth</td><td colspan=\"3\">Pose</td><td colspan=\"2\">Reconstruction</td></tr><tr><td>AbsRel↓</td><td>δ1↑</td><td>ATE↓</td><td>RPE-T↓</td><td>RPE-R↓</td><td>C-l1↓</td><td>F-score↑</td></tr><tr><td>Local</td><td>0.111</td><td>0.884</td><td>0.111</td><td>0.179</td><td>0.068</td><td>0.091</td><td>0.593</td></tr><tr><td>Global</td><td>0.092</td><td>0.923</td><td>0.096</td><td>0.144</td><td>0.053</td><td>0.099</td><td>0.622</td></tr></table>",
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+                                    "content": "depths are initialized to 1. Our alignment module works much better than previous methods."
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+                                    "content": "Optimization Objectives. To evaluate the effectiveness of each constraint employed in our method, we propose to remove them one by one, and the results are shown in Table 7. We can see that without the photometric constraint or geometric constraint, the performance will degrade a lot. When removing the regularization term, the accuracy of the pose, depth, and reconstruction will also decrease."
+                                }
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+                                    "type": "text",
+                                    "content": "Effectiveness of Optimization Stages. Our optimization algorithm is composed of local keyframes optimization (\"Local\") and global keyframes optimization (\"Global\"). The local stage endures the local consistency between the nearest "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " keyframes, and can reconstruct roughly accurate 3D scene shapes. The global stage selects long-range keyframes to supervise global consistency. As shown in Table 8, the reconstruction performance improves gradually."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
+                                }
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+                                    "content": "In this paper, we have presented an effective pipeline to realize 3D scene reconstruction by leveraging the robustness of affine-invariant depth estimation, freezing the depth model, and jointly optimizing dozens of depth and camera parameters for each frame. Due to the sparsity of parameters, our pipeline can transfer the robustness of seemingly weak depth geometry prior to diverse scenes. Extensive experiments show that our pipeline can achieve robust dense 3D reconstruction on challenging unseen scenes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Acknowledgments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
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+                                    "content": "This work was supported by the National Key R&D Program of China (No. 2022ZD0118700), the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC."
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+                                            "content": "[41] Wei Yin, Jianming Zhang, Oliver Wang, Simon Niklaus, Long Mai, Simon Chen, and Chunhua Shen. Learning to recover 3d scene shape from a single image. In IEEE Conf. Comput. Vis. Pattern Recogn., pages 204-213, 2021. 2, 3, 4, 6"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
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+                                            "content": "[42] Andy Zeng, Shuran Song, Matthias Nießner, Matthew Fisher, Jianxiong Xiao, and Thomas Funkhouser. 3dmatch: Learning local geometric descriptors from RGB-D recon"
+                                        }
+                                    ]
+                                }
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+                                            "type": "text",
+                                            "content": "strictions. In IEEE Conf. Comput. Vis. Pattern Recogn., pages 1802-1811, 2017. 4"
+                                        }
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+                                            "content": "[43] Tinghui Zhou, Matthew Brown, Noah Snavely, and David G Lowe. Unsupervised learning of depth and ego-motion from video. In IEEE Conf. Comput. Vis. Pattern Recogn., pages 1851-1858, 2017. 2, 3"
+                                        }
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+[
+    {
+        "type": "text",
+        "text": "Full-Body Articulated Human-Object Interaction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Nan Jiang $^{1,2\\star\\dagger}$ , Tengyu Liu $^{2\\star}$ , Zhexuan Cao $^{3\\dagger}$ , Jieming Cui $^{1,2,\\dagger}$ , Zhiyuan Zhang $^{2,3\\dagger}$ , Yixin Chen $^{2}$ , He Wang $^{4}$ , Yixin Zhu $^{5\\boxtimes}$ , Siyuan Huang $^{2\\boxtimes}$",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "https://jnnan.github.io/project/chairs/",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "*Equal contributors † Work done during an internship at BIGAI",
+            "$^{2}$  Beijing Institute of General Artificial Intelligence (BIGAI)",
+            "<sup>4</sup> Center on Frontiers of Computing Studies, Peking University"
+        ],
+        "bbox": [
+            80,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "yixin.zhu@pku.edu.cn, syhuang@bigai.ai",
+        "bbox": [
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+            250,
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+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "<sup>1</sup> School of Intelligence Science and Technology, Peking University",
+            "$^{3}$  Department of Automation, Tsinghua University",
+            "$^{5}$  Institute for Artificial Intelligence, Peking University"
+        ],
+        "bbox": [
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+            311
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/320a280a65e3dd36f7e9c776e9bcfdb3609cc836432ee2f1894e8ecf29a778ba.jpg",
+        "image_caption": [
+            "Figure 1: Examples of the proposed Capturing Human and Articulated-object InterActionS (CHAIRS) dataset. It contains fine-grained interactions between 46 participants and 81 sittable objects with drastically different kinematic structures, providing multi-view RGB-D sequences and ground-truth 3D mesh of humans and articulated objects for over 17.3 hours of recordings."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            589,
+            312,
+            604
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Fine-grained capture of 3D Human-Object Interactions (HOIs) enhances human activity comprehension and supports various downstream visual tasks. However, previous models often assume that humans interact with rigid objects using only a few body parts, constraining their applicability. In this paper, we address the intricate challenge of Full-Body Articulated Human-Object Interaction (f-AHOI), where complete human bodies interact with articulated objects having interconnected movable joints. We introduce CHAIRS, an extensive motion-captured f-AHOI dataset comprising 17.3 hours of diverse interactions involving 46 participants and 81 articulated as well as rigid sittable objects. The CHAIRS provides 3D meshes of both humans and articulated objects throughout the interactive sequences, offering realistic and physically plausible full-body interactions. We demonstrate the utility of CHAIRS through object pose estimation. Leveraging the geometric relationships inherent in HOI, we propose a pioneering model that employs human pose estimation",
+        "bbox": [
+            73,
+            617,
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+            866
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "tion to address articulated object pose and shape estimation within whole-body interactions. Given an image and an estimated human pose, our model reconstructs the object's pose and shape, refining the reconstruction based on a learned interaction prior. Across two evaluation scenarios, our model significantly outperforms baseline methods. Additionally, we showcase the significance of CHAIRS in a downstream task involving human pose generation conditioned on interacting with articulated objects. We anticipate that the availability of CHAIRS will advance the community's understanding of finer-grained interactions.",
+        "bbox": [
+            497,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            500,
+            771,
+            630,
+            786
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In the realm of computer vision and robotics, the fundamental comprehension of Human-Object Interaction (HOI) [30, 31, 64, 62] lies at the core of dissecting intricate human activities. This paper embarks on unraveling the complex challenge of Full-Body Articulated Human-Object",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            129,
+            49,
+            200,
+            85
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            253,
+            48,
+            789,
+            87
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "9365",
+        "bbox": [
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+            889,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "table",
+        "img_path": "images/37e5f25bca16bb7fa7b9e90f02a447fced18ef0c3bcc7a644fb0ae7da7def6ec.jpg",
+        "table_caption": [
+            "Table 1: Comparisons between CHAIRS and other HOI datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td># object</td><td># participants</td><td># instructions</td><td># hours</td><td>fps</td><td># view</td><td>articulated objects</td><td>human</td><td>annotation type</td></tr><tr><td>GRAB [46]</td><td>51</td><td>10</td><td>4</td><td>3.8</td><td>120</td><td>0</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>D3D-HOI [58]</td><td>24</td><td>5</td><td>/</td><td>0.6</td><td>3</td><td>1</td><td>Yes</td><td>Whole-body</td><td>manual</td></tr><tr><td>BEHAVE [2]</td><td>20</td><td>8</td><td>6</td><td>4.2</td><td>30</td><td>4</td><td>No</td><td>Whole-body</td><td>multi-kinect</td></tr><tr><td>ARCTIC [11]</td><td>10</td><td>9</td><td>1</td><td>1.2</td><td>30</td><td>8+1</td><td>Yes</td><td>Two hands</td><td>mocap</td></tr><tr><td>COUCH [67]</td><td>4</td><td>6</td><td>6</td><td>3</td><td>60</td><td>4</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>CHAIRS (Ours)</td><td>81</td><td>46</td><td>32</td><td>17.3</td><td>30</td><td>4</td><td>Yes</td><td>Whole-body</td><td>mocap</td></tr></table>",
+        "bbox": [
+            78,
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+            892,
+            250
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Interaction (f-AHOI). This endeavor mandates tackling two pivotal dimensions: (i) fashioning kinematic-agnostic representations for articulated objects and (ii) delving into the intricate spatial-temporal tapestry interweaving objects with human whole-bodies. Our primary focus resides in addressing the intricate task of object pose estimation within the realm of f-AHOI, considering that reconstructing 3D human poses from frontal viewpoints is comparably uncomplicated.",
+        "bbox": [
+            75,
+            258,
+            470,
+            369
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The crux of object pose estimation within the context of f-AHOI is punctuated by three principal challenges:",
+        "bbox": [
+            75,
+            371,
+            470,
+            399
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The dearth of comprehensive f-AHOI datasets Existing strides in 3D HOI predominantly either assume interactions with rigid objects or confine themselves to involving specific segments of the human anatomy [2, 46, 65, 29, 67, 11, 58, 14]. Regrettably, these assumptions drastically over-simplify genuine human interactions that span diverse body parts engaging with articulated objects embodying moveable elements such as cabinets and office chairs. A more intricate level of interaction necessitates a richer dataset.",
+        "bbox": [
+            75,
+            401,
+            470,
+            524
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The multifaceted landscape of object kinematic structures Objects constituting the realm of f-AHOI exhibit notable disparities in their kinematic frameworks, even when categorized under the same umbrella. Prevailing methodologies often lean towards uniform structures [58, 32, 11, 14], thereby disregarding the diverse tapestry that constitutes real-world scenarios. The endeavor of accurately reconstructing objects manifesting divergent geometries and structures is plagued with its own set of challenges.",
+        "bbox": [
+            75,
+            528,
+            470,
+            652
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The intricacies of complex interactions Engaging with articulated objects entails grappling with intricate spatial and physical relationships, often entailing occlusions and intricate points of contact. The intricacy of these dynamics thrusts conventional pose estimation mechanisms reliant on point cloud template-matching [65, 49, 19, 39, 28] into the realm of insufficiency. The prominence of contacts further compounds the endeavor of precise reconstruction, as slight inaccuracies can swiftly usher implausible interactions into the picture.",
+        "bbox": [
+            75,
+            654,
+            468,
+            792
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The trajectory of this research endeavors to navigate the above three challenges through the prism of three principal solutions, respectively:",
+        "bbox": [
+            75,
+            795,
+            468,
+            836
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To confront the scarcity of f-AHOI datasets, we introduce CHAIRS, a multi-view RGB-D dataset. Illustrated in Fig. 1,",
+        "bbox": [
+            77,
+            838,
+            470,
+            866
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "CHAIRS chronicles a diverse tapestry of interactions, seamlessly intertwining 46 participants with 81 sittable objects (e.g., chairs, sofas, stools, and benches). 28 of these objects are endowed with moveable parts. Each frame encapsulates 3D meshes of both human whole-bodies and objects, casting a spotlight on interactions with sittable objects that encompass a diverse spectrum of structures and distinctive movable elements conducive to multifarious human interactions.",
+        "bbox": [
+            497,
+            258,
+            894,
+            369
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To traverse the labyrinth of kinematic diversity, CHAIRS meticulously selects representative objects characterized by an eclectic array of structures. Unlike traditional datasets and methodologies tethered to uniform kinematics [55, 51, 32], we champion real-world heterogeneity, encompassing the gamut from rigid stools to swivel chairs boasting up to 7 movable components. Each component is linked to its parent through a nexus of revolute, prismatic, or composite joints.",
+        "bbox": [
+            497,
+            372,
+            894,
+            484
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To unravel the enigma of complex interactions, we proffer an innovative approach to articulated object pose estimation, one that harnesses the subtle interplay of fine-grained interaction relationships to reconstruct the object in question. This approach diverges from the conventional recourse of manually labeling contact maps corresponding to human body parts [65, 16, 2]. Instead, our approach melds the intricacies of these relationships with a reconstruction model and an interaction prior, the latter of which is imbued with the essence of a conditional Variational Auto-Encoder (cVAE). This evolution sidesteps the need for predefined knowledge grounded in laborious annotation. Moreover, the significance of these intricate relationships is showcased through our venture into learning human poses within the ambit of articulated objects. By juxtaposing the generative prowess harnessed from CHAIRS with that stemming from a dataset centered on rigid objects [67], we underscore the pivotal role played by the nuanced geometrical relationships encapsulated within CHAIRS in the broader canvas of downstream tasks.",
+        "bbox": [
+            497,
+            488,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions are four-fold: (i) CHAIRS, a sprawling multi-view RGB-D repository infused with diverse 3D meshes. (ii) The seamless extension of articulated object pose estimation to the arduous landscape of f-AHOI. (iii) An object pose estimation approach that transcends the strictures of structure. (iv) An overarching interaction prior that captures the subtleties of fine-grained interactions, acting as a catalyst for the journey of pose estimation.",
+        "bbox": [
+            497,
+            755,
+            894,
+            866
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "9366",
+        "bbox": [
+            468,
+            889,
+            500,
+            899
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/a09a5661244fdebfc04fe6e9952a57b498f938b07aa3431088338978551303e5.jpg",
+        "image_caption": [
+            "(a) sequences of objects articulating over time",
+            "(b) frames of diverse interactions",
+            "Figure 2: Samples from the CHAIRS dataset. CHAIRS encompasses diverse AHOIs captured through precisely calibrated multi-view RGB-D cameras, offering detailed 3D meshes of human participants and articulated objects. The figure showcases (a) RGB frames alongside corresponding ground-truth mesh sequences and (b) an array of varied AHOI instances."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            123,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            77,
+            384,
+            218,
+            397
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3D Human-Object Interaction (HOI) The evolution of HOI research spans from 2D image-based interaction detection [4, 40, 13, 30, 31, 64, 62, 22] to 3D interaction reconstruction [43, 16, 5, 53, 58, 63, 66] and generation [17, 50, 57, 21, 52, 67] within 3D scenes. Notably, PiGraph [43] and D3D-HOI [16, 58] capture daily activities and reconstruct interactions, often relying on visual observations. In contrast, MoCap systems [46, 2, 11, 67] offer fine-grained 3D human-object interactions. GRAB [46] and ARCTIC [11] emphasize interactions with small objects, while BEHAVE [2] and COUCH [67] involve interactions with everyday objects. However, these works often focus on rigid objects or hand-object interactions with articulated objects. In contrast, our CHAIRS dataset captures realistic whole-body interactions with diverse articulated objects.",
+        "bbox": [
+            75,
+            409,
+            470,
+            616
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Articulated Human-Object Interaction Articulated Human-Object Interactions (AHOIs) build on part-level object representations, modeling intricate spatial-temporal interactions between humans and articulated objects [14]. Noteworthy contributions include D3D-HOI [58], ARCTIC [11], and 3DADN [41]. D3D-HOI [58] captures humans interacting with containers, ARCTIC [11] focuses on motion-captured RGB-D hand-object interactions, and 3DADN [41] annotates movable object parts from internet videos. However, these works often emphasize hand-object interactions, whereas our focus extends to AHOIs encompassing diverse articulated objects and multiple body parts.",
+        "bbox": [
+            75,
+            617,
+            468,
+            782
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Contact-Rich HOI The realm of f-AHOI requires a deeper HOI understanding. While 3D HOI literature has expanded, few works address full-body contacts through reconstruction [16] or generation [69, 52, 15, 67]. However, these works often focus on static scenes with limited interactions. In contrast, our CHAIRS dataset encompasses diverse",
+        "bbox": [
+            75,
+            783,
+            470,
+            866
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "articulated objects and interactions.",
+        "bbox": [
+            499,
+            385,
+            734,
+            399
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Articulated Object Pose Estimation The estimation of 6-DOF poses for rigid objects has garnered attention [25, 19, 3, 48, 39, 37, 9]. Template-based methods [20, 60, 49, 26] and regression models [1] are common, with recent strides in articulated object pose estimation [8, 33, 28] leveraging these techniques. Regression and implicit function models [36, 47, 59, 24] are also explored. Despite progress, these methods often assume consistent kinematic structures within object categories. In contrast, our CHAIRS dataset features diverse kinematic structures and models capable of handling various parts and kinematics of 3D objects.",
+        "bbox": [
+            497,
+            400,
+            892,
+            551
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. The CHAIRS Dataset",
+        "text_level": 1,
+        "bbox": [
+            499,
+            564,
+            700,
+            578
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A significant challenge in modeling AHOIs is the lack of accurate 3D annotations. To address this gap, we introduce CHAIRS, a comprehensive AHOI dataset featuring multi-view RGB-D sequences. CHAIRS offers precise 3D meshes of humans and articulated objects during interactions, captured through a hybrid motion capture (MoCap) system that combines inertial and optical tracking techniques. The data collection process prioritizes realism and physical authenticity, resulting in a dataset that significantly advances interaction understanding. A detailed comparison between CHAIRS and previous HOI datasets is outlined in Tab. 1.",
+        "bbox": [
+            497,
+            587,
+            892,
+            739
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Data Collection",
+        "text_level": 1,
+        "bbox": [
+            499,
+            748,
+            655,
+            761
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Overview CHAIRS encompasses a total of 1390 sequences depicting articulated interactions involving humans and sittable objects like chairs, sofas, stools, and benches. Exemplary sequences from CHAIRS and a showcase of the object variety can be seen in Fig. 2. Each object's exploration involves 6 distinct participants, each contributing three interaction sequences, resulting in 18 sequences for each object.",
+        "bbox": [
+            497,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "9367",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/aed7f69d37956bcfb61fd132c12d98eeca96178c0330c09d09530aa2884c54b6.jpg",
+        "image_caption": [
+            "(a) camera setup"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c06416be38a3fa63d999d410c979231a1df41002d66667cba5f55c4ac333d624.jpg",
+        "image_caption": [
+            "(b) mocap on objects",
+            "Figure 3: Setup for data collection in the CHAIRS dataset. Our data collection setup consisted of (a) four front-facing RGB-D cameras supplemented by a network of motion capture cameras surrounding the recording area, (b) hybrid trackers affixed to various movable parts of objects, and (c) a configuration incorporating five hybrid trackers and seventeen IMUs distributed on the participants."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/be508df79c2b3e5517641740bc26feda8f4c346f858bb15f8ae65f61221d3b09.jpg",
+        "image_caption": [
+            "(c) mocap on participants"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In every sequence, participants execute 6 diverse actions drawn randomly from a pool of 32 interactions, such as shifting a stool, reclining on a sofa, or rotating a chair; please refer to the Supplementary Material Appx. C.1 for further details. Participant instructions were kept deliberately high-level to ensure authentic and natural performances.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Object diversity The object gallery in CHAIRS boasts an array of objects, each possessing a range of appearances and kinematic structures. Objects were curated by sourcing them online, with a focus on maximizing stylistic diversity. Notably, 28 objects incorporate at least one articulated joint, contributing to rich interaction scenarios. The 3D meshes of these objects were captured using the Scaniverse app on an iPad Pro (11-inch, 2nd generation) and subsequently refined manually to eliminate any imperfections. The 3D meshes were further segmented using the annotation tool [35] into eight functional parts. Participants received context-specific instructions tailored to the object they were interacting with.",
+        "bbox": [
+            75,
+            406,
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+            572
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Camera and hardware setup As depicted in Fig. 3, all sequences were exclusively captured in a controlled laboratory setup, encompassing a designated area of  $5\\mathrm{m}\\times 4\\mathrm{m}$  ensuring complete visibility of all actions for the cameras. Four Kinect Azure DK cameras, strategically positioned to capture front-facing multi-view perspectives, were employed to record the interactions. These cameras were meticulously calibrated and synchronized. To ensure the precision of ground-truth poses for both humans and objects, a commercial inertial-optical hybrid MoCap system was incorporated alongside the Kinect setup; for further specifics, see the subsequent section.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Motion Capture (MoCap) System",
+        "text_level": 1,
+        "bbox": [
+            77,
+            747,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Hybrid MoCap Our MoCap system is composed of a MoCap suit outfitted with 5 hybrid trackers and 17 wearable Inertial Measurement Units (IMUs), alongside a pair of gloves equipped with 12 IMUs each. The setup further includes supplementary hybrid trackers and a collection of 8 high-speed cameras. A hybrid tracker, which encompasses 4 optical markers and an IMU, is capable of accurately mea",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "suring its own 6D pose even in conditions of substantial occlusion. The arrangement of our data collection setup is illustrated in Fig. 3. For capturing the pose of a human or an object part, either an IMU or a hybrid tracker can be utilized to record the global orientation or 6D pose, respectively.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Capturing articulated object poses The recording process of articulated object poses in the context of interactions unfolds across three phases. First, we position the object into its canonical pose and affix a hybrid tracker to each of its movable components. Subsequently, we calculate the relative transformation between the object part and the trackers. During the recording process, the real-time ground-truth 6D pose of each object part is computed based on the tracker poses. Finally, we match the rigid parts to the kinematic structure of the object to yield high-fidelity object poses.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Capturing human body poses For human poses and shapes, we adopt the SMPL-X [38] representation. Participants are attired in a MoCap suit incorporating 17 IMUs, don a pair of MoCap gloves, and have 5 hybrid trackers affixed to their heads, hands, and feet. It is noteworthy that while hybrid trackers capture 6D poses, IMUs solely measure global orientations. The optimization of human model shape parameters is undertaken to ensure that the reconstructed SMPL-X mesh aligns with the positions of the hybrid trackers. As a result, the MoCap system delivers real-time estimated human poses and shapes during recording.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Post-processing",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Data alignment Due to the disparate 3D coordinates and temporal clocks of Kinect cameras and the MoCap system, alignment becomes crucial. This alignment is achieved by correlating the 3D coordinates of Kinect sequences with MoCap reconstructions through plane-to-plane correspondences [44], a technique that mitigates the influence of outliers, disturbances, and partial overlaps. For the synchronization of temporal sequences from Kinect and MoCap, time-lagged cross-correlation [45] is applied, a common approach for aligning two sequences with relative time shifts.",
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+    {
+        "type": "image",
+        "img_path": "images/b3ae62e9848c04415791ed8580c760d6f6426ca0672a99450026ed6f17395c42.jpg",
+        "image_caption": [
+            "(a) before removal",
+            "Figure 4: Illustration of the penetration removal process. In panels (a) and (d), the small purple points represent human vertices devoid of penetration, while the larger colored points indicate instances of penetration. The red points symbolize the most pronounced penetration, whereas the blue points signify minimal contact. Panels (b) and (c) feature yellow lines that depict the original skeleton configuration, red markers denoting the target joints undergoing optimization, and red lines illustrating the resultant optimized skeleton configuration."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/04f8ee28feac5ebaac3cc9cd56c330d6e813fca1e6e40c8f0a70bc1c7663d1e6.jpg",
+        "image_caption": [
+            "(b) original skeleton"
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/0c07422112ec10ede6c28ebf8159651ba326e8fdc792bff58c26a2ff1558ec21.jpg",
+        "image_caption": [
+            "(c) optimized skeleton"
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/11a22e48700b3407878812e890d72c782019e0032efd186cb1a18c9c586dab5b.jpg",
+        "image_caption": [
+            "(d) after removal"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            815,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9368",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/bc1ef1454888b8a1ee9f9851f33ce0270cca39ba04238284b32e8efbf7144b2f.jpg",
+        "image_caption": [
+            "Figure 5: Model architecture. The reconstruction model leverages the predicted voxelized representation of the human to facilitate the estimation of pose for the interacting object. We undertake root 6D pose regression for the object utilizing the image feature in conjunction with SMPL-X parameters. The predictions along with an interaction prior are harnessed for the refinement of the final estimated pose."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Penetration removal Owing to the limited sensor count and discrepancies in limb lengths, unrealistic contacts and penetrations persist in captured 3D interactions. To address this issue, we rectify these physical anomalies with a carefully devised optimization algorithm, as depicted in Fig. 4. Given a parameterized human body and an articulated object point cloud, we compute penetration depths between the human and object point clouds. Subsequently, we utilize the transpose of the linear-blend-skinning weights of SMPL-X to aggregate the maximum penetration depth and direction to the human skeleton joints. This information is then employed to calculate a target skeleton that mitigates the penetration. Finally, we employ a gradient-based optimization technique to adjust the human model to the new skeleton while maintaining proximity to the MoCap reconstruction. This process reduced the average penetration depth in CHAIRS from 3.5 cm to 2.6 cm, with an average contact value of 0.2 cm.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Ensuring data quality Following data alignment and penetration removal, the Chamfer distances between annotations and observations in CHAIRS are measured at  $2.8\\mathrm{cm}$  for objects and  $1.9\\mathrm{cm}$  for humans. This level of quality is comparable to a recent dataset [2], which reports Chamfer distances of  $2.4\\mathrm{cm}$  and  $1.8\\mathrm{cm}$ , respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Privacy protection To safeguard identities, we apply face blurring [34] to all participant faces. Furthermore, we informed all participants that they retain the right to have their data removed from CHAIRS at any time.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Articulated Object Pose Estimation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "CHAIRS offers extensive potential for various AHOI tasks, including detection, motion generation, physics-based analysis, and even language-guided motion generation with additional annotations. We highlight the value of CHAIRS by focusing on the task of articulated object pose estimation. Despite recent advancements in articulated object pose estimation [58, 11, 14, 68] and HOI reconstruction [5, 46, 69, 54], the challenge of articulated object pose estimation in the context of f-AHOI remains largely unaddressed. This specific context demands accurate object pose estimation in",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "scenarios involving heavy occlusion and dense contact.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Task Definition",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given an observed image  $I$ , the parameterized human model  $H = (\\beta, \\theta_b, \\theta_h, R_b, T_b)$ , and the meshes  $X = \\{X_i, i = 1, \\dots, N\\}$  representing the interacting object with  $N$  parts, our task involves estimating the object pose  $O = \\{(R_i, T_i), i = 0, \\dots, N\\}$ . Here,  $\\beta \\in \\mathbb{R}^{10}$ ,  $\\theta_b \\in \\mathbb{R}^{21 \\times 6}$ ,  $\\theta_h \\in \\mathbb{R}^{30 \\times 6}$ ,  $R_b \\in \\mathbb{R}^6$ , and  $T_b \\in \\mathbb{R}^3$  represent the shape and pose parameters of the SMPL-X [38] model. Specifically,  $(R_0 \\in \\mathbb{R}^6, T_0 \\in \\mathbb{R}^3)$  corresponds to the root pose of the object, while  $\\{(R_i \\in \\mathbb{R}^6, T_i \\in \\mathbb{R}^3)\\}$  denotes the global rotation and translation for each part  $X_i$ . The orthogonal 6D representation [70] is used for representing rotations in both human and object poses.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Model Architecture",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our approach for object pose estimation is rooted in an interaction-aware framework that harnesses the fine-grained geometric relationships present in HOIs, along with learned interaction priors. This approach comprises two key stages. Given an image and estimated SMPL-X [38] parameters, we first estimate object occupancy grids and root poses using a reconstruction model. Subsequently, we fine-tune the reconstructed human-object pair using a learned interaction prior. The overall framework of our model is illustrated in Fig. 5, while Fig. 6 showcases the interaction prior model.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/d9d598602cf4d7f4f1619d266cf34aa666f09abb7cedf13babce7c4cafbb4387.jpg",
+        "image_caption": [
+            "Figure 6: Illustration of the interaction prior model. The interaction prior model, realized as a cVAE, generates object voxels based on conditioning information from human voxels. During optimization, we aim to minimize the norm of the latent code."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "9369",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Object Reconstruction and Pose Initialization",
+        "text_level": 1,
+        "bbox": [
+            77,
+            125,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Given an observation  $I$ , we estimate human pose and shape using an off-the-shelf estimator. These estimated human shapes  $H^{\\prime}$  are then voxelized into four resolutions with Kaolin [23]. To better exploit the geometric relationship between human-object pairs, we guide the estimation of object shape and pose using human pose. Specifically, we begin by extracting ResNet-101 [18] features from the image and subsequently estimate object voxels based on these image features using a 3D decoder. This decoder comprises three 3DConvT layers, along with upsampling layers at distinct resolutions, and two additional 1x1 3DConv layers. Furthermore, we fuse the convolutional feature grids with human voxels at each resolution, amplifying the influence of human pose. The final 3DConv layer generates the estimated object occupancy grid  $\\mathcal{V}_O^{\\prime}$ . Additionally, we concatenate image features extracted from ResNet-101 with SMPL-X parameters, and employ an additional MLP to regress the root pose  $(R_0^{\\prime}, T_0^{\\prime})$  of the object. This root pose also serves as the initialization for the optimization process.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To train the reconstruction model, we first initialize the human shape estimator with pre-trained weights from the PARE model [38], followed by fine-tuning using the CHAIRS. Subsequently, we fix the weights of the PARE model and proceed to train the reconstruction model, utilizing the object pose estimation loss  $\\mathcal{L}^{\\mathcal{O}}$ . This loss is characterized by the L1 loss computed on object voxels.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Interaction Prior",
+        "text_level": 1,
+        "bbox": [
+            77,
+            515,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To capture the nuanced relationship between humans and interacting objects, we introduce an interaction prior model based on a cVAE. This model learns the conditional distribution of object occupancy given the human shape.",
+        "bbox": [
+            75,
+            536,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this context, the cVAE prior model conditions on a multi-resolution voxelized human, with the objective of reconstructing a voxelized object. The architecture employs 3DConvNets as both encoder and decoder components. During training, we feed the voxelized object into the encoder to acquire object features at multiple scales. These object features are then combined with the multi-resolution human voxels corresponding to each layer. An MLP estimates the latent Gaussian distribution  $\\mathcal{N}(\\mu, \\sigma)$ , which is used to parameterize the latent code  $z$  through re-parameterization. This latent code is subsequently decoded using the decoder. The feature grids at each decoder layer are concatenated with the corresponding human voxel condition.",
+        "bbox": [
+            75,
+            593,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training the prior model occurs on CHAIRS and involves four distinct loss components:",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {P}} = \\mathcal {L} _ {\\text {r e c o n}} + \\mathcal {L} _ {\\mathrm {K L}} + \\mathcal {L} _ {\\text {p e n e}} + \\mathcal {L} _ {\\text {c o n t r a}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            137,
+            812,
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+            827
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{\\mathrm{recon}}$  and  $\\mathcal{L}_{\\mathrm{KL}}$  denote the standard reconstruction and KL divergence losses, respectively.  $\\mathcal{L}_{\\mathrm{pene}}$  constitutes a",
+        "bbox": [
+            75,
+            838,
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+            866
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "penetration loss, penalizing voxel grids occupied by both humans and objects.  $\\mathcal{L}_{\\mathrm{contra}}$  serves to maximize the distance of latent variables between original and augmented noisy data. Augmentation of training data involves introducing random noise to a portion of the samples.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.5. Pose Optimization with Interaction Prior",
+        "text_level": 1,
+        "bbox": [
+            497,
+            204,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To reconstruct the intricate human-object relationship and refine the object poses, we employ an optimization stage that builds upon initialized poses, utilizing kinematic insights and the interaction prior. This process involves the object's CAD model, Unified Robot Description Format (URDF), estimated SMPL-X parameters  $H^{\\prime}$ , and object voxels  $\\mathcal{V}_O^\\prime$  from the reconstruction model. We initiate the object model  $\\hat{O}$  using estimated root transformations and random part states. We iteratively update  $\\hat{O}$ 's parameters by minimizing the combined objective  $\\mathcal{J}_{\\mathrm{recon}} + \\mathcal{J}_{\\mathrm{z}}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {J} _ {\\text {r e c o n}} = \\left\\| V (\\hat {O}) - \\mathcal {V} _ {O} ^ {\\prime} \\right\\| _ {2}, \\quad \\mathcal {J} _ {\\mathrm {z}} = \\left\\| \\operatorname {E n c} \\left(H ^ {\\prime}, \\hat {O}\\right) \\right\\|, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            374,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $V(\\cdot)$  is the voxelization function.  $\\mathcal{I}_{\\mathrm{recon}}$  measures the voxelized object model's distance from the estimated object voxels.  $\\mathcal{I}_{\\mathrm{z}}$  enforces a small norm for the latent predicted by the cVAE encoder, regulating proximity to the interaction prior. The process of pose optimization with interaction prior is illustrated in Fig. 7.",
+        "bbox": [
+            497,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/38df2e80767be93985be38da9dacb67983751fb1ae6977d91b004c12a778c42d.jpg",
+        "image_caption": [
+            "Figure 7: An illustration of pose estimation with interaction prior. Starting with the reconstruction output, we optimize the object according to the reconstructed voxel and interaction prior."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            514,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Object pose optimization Optimized parameters include the root 6D pose  $R, T$  of the object and joint parameters  $\\Phi$  (if applicable), controlling part rotation and shift under kinematic constraints. For joints (except the root), we consider revolute, prismatic, or combined revolute-prismatic configurations. The latter, such as the joint linking a chair's base and seat, restricts rotation and shift along the same axis.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "During optimization, we initiate the root pose  $R, T$  using the estimated root 6D pose from the object pose estimation model. All joint parameters  $\\Phi$  are set to zero. Optimization involves minimizing the reconstruction loss  $\\mathcal{I}_{\\mathrm{recon}}$  and interaction prior loss  $\\mathcal{I}_{\\mathrm{z}}$  through gradient descent. Calculating losses necessitates determining object part occupancy postapplication of  $R, T,$  and  $\\Phi$  for each optimization step. As direct voxelization lacks differentiability regarding object",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "9370",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "parameters  $R, T$  and  $\\Phi$ , we employ trilinear interpolation on the affine  $(0,1)$  voxel grid to resample voxel occupancy. This permits gradient flow for root and joint parameter updates. Post-optimization, parameters yield an updated 3D object model and enhanced representation (e.g., mesh) with reduced geometric error.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Contrastive loss We intend our interaction prior to grasp a comprehensive human-object interaction distribution through a conditional Gaussian model. Reasonable and common spatial relationships between human and object latent codes should cluster near the Gaussian mean, in contrast to unreasonable ones. A contrastive loss aids training of the interaction prior model alongside penetration, reconstruction, and KL-divergence losses. Positive examples  $(H,\\mathcal{V}_O)$  involve an observed human  $H$  and object voxel  $\\nu_{O}$ . Corresponding negative examples  $(H,\\mathcal{V}_O^{\\prime})$  are generated by perturbing the object, adding noise to root and articulated poses, and voxelizing  $\\nu_{O}^{\\prime}$ . The contrastive loss  $\\mathcal{L}_{\\mathrm{contra}}$ , defined as  $\\mathcal{L}_{\\mathrm{contra}} = \\max (0,||\\mathrm{Enc}(\\mathcal{V}_O,H)|| - ||\\mathrm{Enc}(\\mathcal{V}_O^{\\prime},H)||)$ , guides latent codes of perturbed human-object pairs away from the distribution centroid. Here, Enc represents the conditional encoder of our proposed cVAE-based prior model.",
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+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Experimental settings We split CHAIRS into training, testing, and validation sets;  $70\\%$  of objects are used for training,  $20\\%$  for testing, and the remaining for validation. We evaluate our model under two settings: with  $(w / opt)$  and without optimization  $(w / o$  opt). In the  $w / opt.$  setting, we report the chamfer distance between objects posed with ground truth and estimated transformation parameters. In the  $w / o$  opt. setting, we do not have the estimated transformation parameters. Thus, we report the chamfer distance between the ground-truth object mesh and the mesh obtained by running the marching cube algorithm on the reconstructed voxels.",
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics We evaluate object pose estimation using mean rotation and translation errors for each object part. Object shape reconstruction is evaluated with chamfer distance and intersection over union (IoU). For reconstructed f-AHOI, we assess penetration depth and contact scores between the human and object. Penetration depth is the maximum depth of the object's surface within the human's body, while contact value is the shortest distance between the human and object. Contact values are clipped to [0,20cm] for distant human-object pairs.",
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+    {
+        "type": "text",
+        "text": "Baseline methods We compare articulated object pose estimation with LASR [59] and ANCSH [28] as baselines, where we use depth maps as input for ANCSH. Both methods are fine-tuned on CHAIRS. Additionally, we compare our model with D3D-HOI [58], PHOSA [65], and CHORE [56] that jointly estimate human and object poses. We adapted D3D-HOI's optimization objectives to better fit CHAIRS's data distribution.",
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+    {
+        "type": "text",
+        "text": "5.1. Results and Analyses",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Quantitative results are presented in Tab. 2. Our model, leveraging geometrical relationships, exhibits substantial improvements in pose estimation and shape reconstruction compared to existing methods. In the w/o opt. setting where the object is unknown, our model surpasses the state-of-the-art LASR method by a significant margin. While D3D-HOI and ANCSH excel, they assume known object structures. Remarkably, our model outperforms all baselines when provided with the object structure in the w/ opt. setting.",
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+    {
+        "type": "table",
+        "img_path": "images/4e49dffb7f41e697f54aa65f6f4205a7a582eeab03cddc3107a9734536286b57.jpg",
+        "table_caption": [
+            "Table 2: Comparisons against existing methods.  $\\ast$  : method requires knowledge of object structure and/or geometry;  $\\dagger$  : method does not rely on object-related knowledge."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Object</td><td colspan=\"2\">HOI</td></tr><tr><td>Rot.↓(°)</td><td>Transl.↓(mm)</td><td>CD↓(mm)</td><td>IoU↑(%)</td><td>Pene.↓(mm)</td><td>Cont.↓(mm)</td></tr><tr><td>LASR†[59]</td><td>/</td><td>/</td><td>205.2</td><td>/</td><td>/</td><td>/</td></tr><tr><td>Ours (w/o opt.)†</td><td>/</td><td>/</td><td>160.2</td><td>11.03</td><td>4.530</td><td>2.720</td></tr><tr><td>ANCSH* [28]</td><td>/</td><td>/</td><td>90.36</td><td>/</td><td>/</td><td>/</td></tr><tr><td>PHOSA* [65]</td><td>29.31</td><td>175.2</td><td>177.9</td><td>7.60</td><td>2.046</td><td>1.689</td></tr><tr><td>D3D-HOI* [58]</td><td>27.31</td><td>119.2</td><td>126.9</td><td>16.60</td><td>7.472</td><td>1.163</td></tr><tr><td>CHORE* [56]</td><td>21.82</td><td>87.58</td><td>95.40</td><td>16.44</td><td>1.050</td><td>1.742</td></tr><tr><td>Ours (w/ opt.)*</td><td>19.35</td><td>66.23</td><td>72.30</td><td>21.57</td><td>1.143</td><td>1.562</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We present qualitative results in Fig. 8, where columns (a)-(h) illustrate the reconstruction outcomes on the test set. In these columns, we display the reconstructed meshes prior to optimization using the marching cubes algorithm. It is evident from the visualizations that our model successfully produces plausible and accurate interaction representations even before the optimization process. Notably, the optimization step enhances the finer interaction details.",
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+    },
+    {
+        "type": "text",
+        "text": "5.2. Ablations",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We conduct three ablation studies to assess the efficacy of our model's design choices. Quantitative results of these ablation studies are presented in Tab. 3.",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/b329d107927814ebd7a9b43254356c69c959b5dcffd8e4b7b1006fb92504ed14.jpg",
+        "table_caption": [
+            "Table 3: Ablation of interaction, prior, and contrastive loss."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Object</td><td colspan=\"2\">HOI</td></tr><tr><td>Rot.↓(°)</td><td>Transl.↓(mm)</td><td>CD↓(mm)</td><td>IoU↑(%)</td><td>Pene.↓(mm)</td><td>Cont.↓(mm)</td></tr><tr><td>Full†</td><td>/</td><td>/</td><td>160.2</td><td>11.03</td><td>4.530</td><td>2.720</td></tr><tr><td>-prior†</td><td>/</td><td>/</td><td>165.3</td><td>10.52</td><td>4.377</td><td>3.295</td></tr><tr><td>Full*</td><td>19.35</td><td>66.23</td><td>72.30</td><td>21.57</td><td>1.143</td><td>1.562</td></tr><tr><td>-prior*</td><td>19.97</td><td>83.39</td><td>87.90</td><td>18.81</td><td>1.749</td><td>2.081</td></tr><tr><td>-contr.*</td><td>21.52</td><td>81.90</td><td>87.28</td><td>18.93</td><td>1.265</td><td>2.393</td></tr><tr><td>-inter.*</td><td>17.88</td><td>69.53</td><td>78.12</td><td>19.50</td><td>1.022</td><td>2.320</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Prior We conduct an experiment where we remove the interaction prior model and solely optimize object poses by minimizing  $\\mathcal{L}_{\\mathrm{recon}}$ . In both * and † settings, we observe a substantial performance drop. This underscores the critical role played by the interaction prior in accurately estimating",
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "9371",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e0c3921a6470b8125cc08482296d5f9e02a1088ed3a0c2e668098388f8c8a26a.jpg",
+        "image_caption": [
+            "Figure 8: Qualitative results. (a)-(h) Test set results. (i)-(p) Wild images results. RGB images, optimized poses, and mesh obtained by running marching cubes on reconstructed voxels are shown. Please refer to Fig. A6 in Supplementary Materials for more qualitative results."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "object poses. It is important to note that both settings involve an optimization step, and the primary distinction is that the * model possesses access to the object's geometry and structure during optimization. When the prior model is omitted in the † setting, we observe a decrease in penetration and a larger increase in contact value. This observation suggests that our interaction prior model exerts influence by pulling the object closer to the human when they are not in contact.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Contrast In this ablation, we exclude the contrastive loss  $\\mathcal{L}_{\\mathrm{contra}}$  from the training of the prior model. The results are analogous to those of the -prior experiment. This outcome underscores the crucial role that the contrastive loss plays in facilitating the learning of a robust interaction prior.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Interaction We proceed to remove the concatenation of human voxels in the 3DConv layers of both the reconstruction model and the interaction prior model. This removal eliminates the interaction awareness in our model. We observe a modest degradation across all object reconstruction metrics, underscoring the importance of interaction aware",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ness in our approach. Interestingly, the removal of interaction awareness leads to increased contact values and decreased penetration, resembling the outcomes of the -prior ablation in the w/o opt. setting. This suggests that interaction awareness also contributes to bringing the human and object into closer proximity. Lastly, we note an unexpected low rotation error, which we attribute to the presence of rotation symmetries in the dataset.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Additionally, we assess our method's performance under varying qualities of human pose estimation in Tab. 4. The results reveal notable improvement in object pose estimation as human poses become more accurate, thus validating our initial hypothesis. Notably, the pose estimation model [27] effectively predicts most challenging poses accurately, leaving the avenue of leveraging interactions to enhance human pose estimation as a potential future research direction.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In summary, our analysis highlights the substantial contributions of all three model components to object pose and shape reconstruction.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "9372",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/1f1b75d1327f37648a87c5750ef3450b9dc27bd195e0a7654902dd2acaaf606c.jpg",
+        "table_caption": [
+            "Table 4: Ablation of human pose estimation quality. GT denotes using ground-truth human poses to optimize the object poses, No prior denotes not considering human-object interaction prior."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Human</td><td colspan=\"2\">Object</td></tr><tr><td>MPJPE↓(mm)</td><td>PA-MPJPE↓(mm)</td><td>CD↓(mm)</td><td>IOU↑(%)</td></tr><tr><td>No prior</td><td>/</td><td>/</td><td>87.90</td><td>18.81</td></tr><tr><td>PARE [27]</td><td>81.09</td><td>47.19</td><td>73.79</td><td>21.66</td></tr><tr><td>PARE(finetune)</td><td>74.50</td><td>43.99</td><td>72.30</td><td>21.57</td></tr><tr><td>GT</td><td>0</td><td>0</td><td>65.50</td><td>23.16</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/91ff32ea7cc9acde770ecc0044ce1b0a7d7f6e4a45b60e27460cb8355826ca22.jpg",
+        "image_caption": [
+            "Figure 9: Failure cases. In situations involving rotation-symmetrical objects, our model encounters challenges with estimating rotation while maintaining a relatively low visual error."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "img_path": "images/04b5233809e556da0989a800ed839cfc4cea5957c8a6e4dd28055914d3c84e8c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/05074b2a2a57ab6d34ac04a4f87aed75bd0cabb7ed5ca8377a7e96f61c69201c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In-the-wild generalization We also assess the model's generalizability on a limited set of internet images. As depicted in Fig. 8 (i-p), the qualitative results illustrate that our model successfully generalizes its capabilities to images captured outside of controlled laboratory settings.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Failure cases Our model encounters challenges in accurately estimating the orientation of object parts when those parts exhibit geometric similarity under specific rotations. Rotation symmetry is commonly observed in spherical and cylindrical object components, such as the base of a stool or a round seat. An illustrative example of this symmetry is presented in Fig. 9. Notably, existing methods [10, 49] address this challenge through (i) accepting multiple equally-valid ground truths and (ii) employing a min-of-N loss to calculate the smallest distance to any of these ground truths. However, implementing such methods necessitates a meticulous classification of symmetry types for each object.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we observe that our model's performance diminishes in scenarios where no f-AHOI is present, such as instances where a human is situated far away from an object like a chair. Under these circumstances, our model is unable to leverage interactions to enhance object pose estimation.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Application: Generating Interacting Humans",
+        "text_level": 1,
+        "bbox": [
+            75,
+            718,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We further investigate the intricate relationships within AHOI by exploring the generation of interacting human poses in the presence of articulated objects. To this end, we employ a 3D conditional diffusion model known as SceneDiffuser [22], trained on our CHAIRS. To evaluate the quality of the generated poses, we compare them with poses generated using the same model trained on COUCH [67], a recent dataset featuring humans seated on rigid chairs. We use the feature extracted from the point cloud of the ob",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/1060fbd5894fb2bbbdcdfb6c51565cc4bef6ba545c8b76be9abe3f69ecd31733.jpg",
+        "image_caption": [
+            "Figure 10: Generated human poses given articulated objects. The models are trained on CHAIRS (a, b) and COUCH [67] (c, d)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ject via Pointnet++ as a conditioning input and flatten the SMPL-X parameters of the human to form tokens for input to a Transformer. The implementation details closely follow those of the human pose generation task described in Huang et al. [22]. Qualitative comparisons of the generated human poses are shown in Fig. 10. Notably, the model trained with CHAIRS captures more nuanced and natural geometrical relationships when interacting with articulated objects. For a more in-depth analysis of this downstream application, we direct readers to the Appx. B in Supplementary Materials.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We advance the study of HOI to encompass fine-grained, articulated interactions with (i) CHAIRS, an extensive dataset, (ii) a challenging object reconstruction problem under f-AHOI, and (iii) a strong baseline. Our CHAIRS captures diverse, natural AHOIs involving various sittable objects. The object reconstruction problem confronts kinematic assumptions, with our model effectively leveraging intricate interactions to resolve ambiguities.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Limitations One limitation of our work lies in the fact that the parametric human model used in CHAIRS does not account for clothing, leading to misalignments between the 3D annotations and the images. Consequently, the usage of pixel-aligned features may be compromised.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment The authors would like to thank four anonymous reviews for constructive feedback and NVIDIA for their generous support of GPUs and hardware. This work is supported in part by the National Key R&D Program of China (2022ZD0114900) and the Beijing Nova Program.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "9373",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            124,
+            171,
+            138
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+            "with semantic control. In European Conference on Computer Vision (ECCV), 2022. 3, 5",
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+            "content": "Fine-grained capture of 3D Human-Object Interactions (HOIs) enhances human activity comprehension and supports various downstream visual tasks. However, previous models often assume that humans interact with rigid objects using only a few body parts, constraining their applicability. In this paper, we address the intricate challenge of Full-Body Articulated Human-Object Interaction (f-AHOI), where complete human bodies interact with articulated objects having interconnected movable joints. We introduce CHAIRS, an extensive motion-captured f-AHOI dataset comprising 17.3 hours of diverse interactions involving 46 participants and 81 articulated as well as rigid sittable objects. The CHAIRS provides 3D meshes of both humans and articulated objects throughout the interactive sequences, offering realistic and physically plausible full-body interactions. We demonstrate the utility of CHAIRS through object pose estimation. Leveraging the geometric relationships inherent in HOI, we propose a pioneering model that employs human pose estimation"
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+            "content": "tion to address articulated object pose and shape estimation within whole-body interactions. Given an image and an estimated human pose, our model reconstructs the object's pose and shape, refining the reconstruction based on a learned interaction prior. Across two evaluation scenarios, our model significantly outperforms baseline methods. Additionally, we showcase the significance of CHAIRS in a downstream task involving human pose generation conditioned on interacting with articulated objects. We anticipate that the availability of CHAIRS will advance the community's understanding of finer-grained interactions."
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+            "content": "In the realm of computer vision and robotics, the fundamental comprehension of Human-Object Interaction (HOI) [30, 31, 64, 62] lies at the core of dissecting intricate human activities. This paper embarks on unraveling the complex challenge of Full-Body Articulated Human-Object"
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+            "content": "<table><tr><td>Dataset</td><td># object</td><td># participants</td><td># instructions</td><td># hours</td><td>fps</td><td># view</td><td>articulated objects</td><td>human</td><td>annotation type</td></tr><tr><td>GRAB [46]</td><td>51</td><td>10</td><td>4</td><td>3.8</td><td>120</td><td>0</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>D3D-HOI [58]</td><td>24</td><td>5</td><td>/</td><td>0.6</td><td>3</td><td>1</td><td>Yes</td><td>Whole-body</td><td>manual</td></tr><tr><td>BEHAVE [2]</td><td>20</td><td>8</td><td>6</td><td>4.2</td><td>30</td><td>4</td><td>No</td><td>Whole-body</td><td>multi-kinect</td></tr><tr><td>ARCTIC [11]</td><td>10</td><td>9</td><td>1</td><td>1.2</td><td>30</td><td>8+1</td><td>Yes</td><td>Two hands</td><td>mocap</td></tr><tr><td>COUCH [67]</td><td>4</td><td>6</td><td>6</td><td>3</td><td>60</td><td>4</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>CHAIRS (Ours)</td><td>81</td><td>46</td><td>32</td><td>17.3</td><td>30</td><td>4</td><td>Yes</td><td>Whole-body</td><td>mocap</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.259,
+                0.471,
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+            ],
+            "angle": 0,
+            "content": "Interaction (f-AHOI). This endeavor mandates tackling two pivotal dimensions: (i) fashioning kinematic-agnostic representations for articulated objects and (ii) delving into the intricate spatial-temporal tapestry interweaving objects with human whole-bodies. Our primary focus resides in addressing the intricate task of object pose estimation within the realm of f-AHOI, considering that reconstructing 3D human poses from frontal viewpoints is comparably uncomplicated."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.372,
+                0.471,
+                0.4
+            ],
+            "angle": 0,
+            "content": "The crux of object pose estimation within the context of f-AHOI is punctuated by three principal challenges:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.402,
+                0.471,
+                0.526
+            ],
+            "angle": 0,
+            "content": "The dearth of comprehensive f-AHOI datasets Existing strides in 3D HOI predominantly either assume interactions with rigid objects or confine themselves to involving specific segments of the human anatomy [2, 46, 65, 29, 67, 11, 58, 14]. Regrettably, these assumptions drastically over-simplify genuine human interactions that span diverse body parts engaging with articulated objects embodying moveable elements such as cabinets and office chairs. A more intricate level of interaction necessitates a richer dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.529,
+                0.471,
+                0.653
+            ],
+            "angle": 0,
+            "content": "The multifaceted landscape of object kinematic structures Objects constituting the realm of f-AHOI exhibit notable disparities in their kinematic frameworks, even when categorized under the same umbrella. Prevailing methodologies often lean towards uniform structures [58, 32, 11, 14], thereby disregarding the diverse tapestry that constitutes real-world scenarios. The endeavor of accurately reconstructing objects manifesting divergent geometries and structures is plagued with its own set of challenges."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.655,
+                0.47,
+                0.793
+            ],
+            "angle": 0,
+            "content": "The intricacies of complex interactions Engaging with articulated objects entails grappling with intricate spatial and physical relationships, often entailing occlusions and intricate points of contact. The intricacy of these dynamics thrusts conventional pose estimation mechanisms reliant on point cloud template-matching [65, 49, 19, 39, 28] into the realm of insufficiency. The prominence of contacts further compounds the endeavor of precise reconstruction, as slight inaccuracies can swiftly usher implausible interactions into the picture."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.796,
+                0.47,
+                0.837
+            ],
+            "angle": 0,
+            "content": "The trajectory of this research endeavors to navigate the above three challenges through the prism of three principal solutions, respectively:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.839,
+                0.471,
+                0.867
+            ],
+            "angle": 0,
+            "content": "To confront the scarcity of f-AHOI datasets, we introduce CHAIRS, a multi-view RGB-D dataset. Illustrated in Fig. 1,"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.259,
+                0.895,
+                0.37
+            ],
+            "angle": 0,
+            "content": "CHAIRS chronicles a diverse tapestry of interactions, seamlessly intertwining 46 participants with 81 sittable objects (e.g., chairs, sofas, stools, and benches). 28 of these objects are endowed with moveable parts. Each frame encapsulates 3D meshes of both human whole-bodies and objects, casting a spotlight on interactions with sittable objects that encompass a diverse spectrum of structures and distinctive movable elements conducive to multifarious human interactions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.374,
+                0.895,
+                0.485
+            ],
+            "angle": 0,
+            "content": "To traverse the labyrinth of kinematic diversity, CHAIRS meticulously selects representative objects characterized by an eclectic array of structures. Unlike traditional datasets and methodologies tethered to uniform kinematics [55, 51, 32], we champion real-world heterogeneity, encompassing the gamut from rigid stools to swivel chairs boasting up to 7 movable components. Each component is linked to its parent through a nexus of revolute, prismatic, or composite joints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.489,
+                0.895,
+                0.751
+            ],
+            "angle": 0,
+            "content": "To unravel the enigma of complex interactions, we proffer an innovative approach to articulated object pose estimation, one that harnesses the subtle interplay of fine-grained interaction relationships to reconstruct the object in question. This approach diverges from the conventional recourse of manually labeling contact maps corresponding to human body parts [65, 16, 2]. Instead, our approach melds the intricacies of these relationships with a reconstruction model and an interaction prior, the latter of which is imbued with the essence of a conditional Variational Auto-Encoder (cVAE). This evolution sidesteps the need for predefined knowledge grounded in laborious annotation. Moreover, the significance of these intricate relationships is showcased through our venture into learning human poses within the ambit of articulated objects. By juxtaposing the generative prowess harnessed from CHAIRS with that stemming from a dataset centered on rigid objects [67], we underscore the pivotal role played by the nuanced geometrical relationships encapsulated within CHAIRS in the broader canvas of downstream tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.756,
+                0.895,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Our contributions are four-fold: (i) CHAIRS, a sprawling multi-view RGB-D repository infused with diverse 3D meshes. (ii) The seamless extension of articulated object pose estimation to the arduous landscape of f-AHOI. (iii) An object pose estimation approach that transcends the strictures of structure. (iv) An overarching interaction prior that captures the subtleties of fine-grained interactions, acting as a catalyst for the journey of pose estimation."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.89,
+                0.502,
+                0.9
+            ],
+            "angle": 0,
+            "content": "9366"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.124,
+                0.891,
+                0.319
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.146,
+                0.32,
+                0.42,
+                0.332
+            ],
+            "angle": 0,
+            "content": "(a) sequences of objects articulating over time"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.588,
+                0.32,
+                0.786,
+                0.332
+            ],
+            "angle": 0,
+            "content": "(b) frames of diverse interactions"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.336,
+                0.893,
+                0.375
+            ],
+            "angle": 0,
+            "content": "Figure 2: Samples from the CHAIRS dataset. CHAIRS encompasses diverse AHOIs captured through precisely calibrated multi-view RGB-D cameras, offering detailed 3D meshes of human participants and articulated objects. The figure showcases (a) RGB frames alongside corresponding ground-truth mesh sequences and (b) an array of varied AHOI instances."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.385,
+                0.219,
+                0.399
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.41,
+                0.471,
+                0.617
+            ],
+            "angle": 0,
+            "content": "3D Human-Object Interaction (HOI) The evolution of HOI research spans from 2D image-based interaction detection [4, 40, 13, 30, 31, 64, 62, 22] to 3D interaction reconstruction [43, 16, 5, 53, 58, 63, 66] and generation [17, 50, 57, 21, 52, 67] within 3D scenes. Notably, PiGraph [43] and D3D-HOI [16, 58] capture daily activities and reconstruct interactions, often relying on visual observations. In contrast, MoCap systems [46, 2, 11, 67] offer fine-grained 3D human-object interactions. GRAB [46] and ARCTIC [11] emphasize interactions with small objects, while BEHAVE [2] and COUCH [67] involve interactions with everyday objects. However, these works often focus on rigid objects or hand-object interactions with articulated objects. In contrast, our CHAIRS dataset captures realistic whole-body interactions with diverse articulated objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.618,
+                0.47,
+                0.783
+            ],
+            "angle": 0,
+            "content": "Articulated Human-Object Interaction Articulated Human-Object Interactions (AHOIs) build on part-level object representations, modeling intricate spatial-temporal interactions between humans and articulated objects [14]. Noteworthy contributions include D3D-HOI [58], ARCTIC [11], and 3DADN [41]. D3D-HOI [58] captures humans interacting with containers, ARCTIC [11] focuses on motion-captured RGB-D hand-object interactions, and 3DADN [41] annotates movable object parts from internet videos. However, these works often emphasize hand-object interactions, whereas our focus extends to AHOIs encompassing diverse articulated objects and multiple body parts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.784,
+                0.471,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Contact-Rich HOI The realm of f-AHOI requires a deeper HOI understanding. While 3D HOI literature has expanded, few works address full-body contacts through reconstruction [16] or generation [69, 52, 15, 67]. However, these works often focus on static scenes with limited interactions. In contrast, our CHAIRS dataset encompasses diverse"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.387,
+                0.736,
+                0.4
+            ],
+            "angle": 0,
+            "content": "articulated objects and interactions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.401,
+                0.893,
+                0.552
+            ],
+            "angle": 0,
+            "content": "Articulated Object Pose Estimation The estimation of 6-DOF poses for rigid objects has garnered attention [25, 19, 3, 48, 39, 37, 9]. Template-based methods [20, 60, 49, 26] and regression models [1] are common, with recent strides in articulated object pose estimation [8, 33, 28] leveraging these techniques. Regression and implicit function models [36, 47, 59, 24] are also explored. Despite progress, these methods often assume consistent kinematic structures within object categories. In contrast, our CHAIRS dataset features diverse kinematic structures and models capable of handling various parts and kinematics of 3D objects."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.565,
+                0.702,
+                0.579
+            ],
+            "angle": 0,
+            "content": "3. The CHAIRS Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.588,
+                0.894,
+                0.74
+            ],
+            "angle": 0,
+            "content": "A significant challenge in modeling AHOIs is the lack of accurate 3D annotations. To address this gap, we introduce CHAIRS, a comprehensive AHOI dataset featuring multi-view RGB-D sequences. CHAIRS offers precise 3D meshes of humans and articulated objects during interactions, captured through a hybrid motion capture (MoCap) system that combines inertial and optical tracking techniques. The data collection process prioritizes realism and physical authenticity, resulting in a dataset that significantly advances interaction understanding. A detailed comparison between CHAIRS and previous HOI datasets is outlined in Tab. 1."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.749,
+                0.657,
+                0.762
+            ],
+            "angle": 0,
+            "content": "3.1. Data Collection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.77,
+                0.894,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Overview CHAIRS encompasses a total of 1390 sequences depicting articulated interactions involving humans and sittable objects like chairs, sofas, stools, and benches. Exemplary sequences from CHAIRS and a showcase of the object variety can be seen in Fig. 2. Each object's exploration involves 6 distinct participants, each contributing three interaction sequences, resulting in 18 sequences for each object."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.89,
+                0.501,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9367"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.124,
+                0.23,
+                0.207
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.107,
+                0.209,
+                0.203,
+                0.22
+            ],
+            "angle": 0,
+            "content": "(a) camera setup"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.246,
+                0.123,
+                0.315,
+                0.208
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.249,
+                0.209,
+                0.31,
+                0.231
+            ],
+            "angle": 0,
+            "content": "(b) mocap on objects"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.325,
+                0.123,
+                0.469,
+                0.208
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.358,
+                0.209,
+                0.433,
+                0.232
+            ],
+            "angle": 0,
+            "content": "(c) mocap on participants"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.235,
+                0.47,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Figure 3: Setup for data collection in the CHAIRS dataset. Our data collection setup consisted of (a) four front-facing RGB-D cameras supplemented by a network of motion capture cameras surrounding the recording area, (b) hybrid trackers affixed to various movable parts of objects, and (c) a configuration incorporating five hybrid trackers and seventeen IMUs distributed on the participants."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.324,
+                0.47,
+                0.406
+            ],
+            "angle": 0,
+            "content": "In every sequence, participants execute 6 diverse actions drawn randomly from a pool of 32 interactions, such as shifting a stool, reclining on a sofa, or rotating a chair; please refer to the Supplementary Material Appx. C.1 for further details. Participant instructions were kept deliberately high-level to ensure authentic and natural performances."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.407,
+                0.47,
+                0.573
+            ],
+            "angle": 0,
+            "content": "Object diversity The object gallery in CHAIRS boasts an array of objects, each possessing a range of appearances and kinematic structures. Objects were curated by sourcing them online, with a focus on maximizing stylistic diversity. Notably, 28 objects incorporate at least one articulated joint, contributing to rich interaction scenarios. The 3D meshes of these objects were captured using the Scaniverse app on an iPad Pro (11-inch, 2nd generation) and subsequently refined manually to eliminate any imperfections. The 3D meshes were further segmented using the annotation tool [35] into eight functional parts. Participants received context-specific instructions tailored to the object they were interacting with."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.573,
+                0.471,
+                0.738
+            ],
+            "angle": 0,
+            "content": "Camera and hardware setup As depicted in Fig. 3, all sequences were exclusively captured in a controlled laboratory setup, encompassing a designated area of \\(5\\mathrm{m}\\times 4\\mathrm{m}\\) ensuring complete visibility of all actions for the cameras. Four Kinect Azure DK cameras, strategically positioned to capture front-facing multi-view perspectives, were employed to record the interactions. These cameras were meticulously calibrated and synchronized. To ensure the precision of ground-truth poses for both humans and objects, a commercial inertial-optical hybrid MoCap system was incorporated alongside the Kinect setup; for further specifics, see the subsequent section."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.748,
+                0.371,
+                0.763
+            ],
+            "angle": 0,
+            "content": "3.2. Motion Capture (MoCap) System"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.77,
+                0.47,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Hybrid MoCap Our MoCap system is composed of a MoCap suit outfitted with 5 hybrid trackers and 17 wearable Inertial Measurement Units (IMUs), alongside a pair of gloves equipped with 12 IMUs each. The setup further includes supplementary hybrid trackers and a collection of 8 high-speed cameras. A hybrid tracker, which encompasses 4 optical markers and an IMU, is capable of accurately mea"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.127,
+                0.892,
+                0.196
+            ],
+            "angle": 0,
+            "content": "suring its own 6D pose even in conditions of substantial occlusion. The arrangement of our data collection setup is illustrated in Fig. 3. For capturing the pose of a human or an object part, either an IMU or a hybrid tracker can be utilized to record the global orientation or 6D pose, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.196,
+                0.893,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Capturing articulated object poses The recording process of articulated object poses in the context of interactions unfolds across three phases. First, we position the object into its canonical pose and affix a hybrid tracker to each of its movable components. Subsequently, we calculate the relative transformation between the object part and the trackers. During the recording process, the real-time ground-truth 6D pose of each object part is computed based on the tracker poses. Finally, we match the rigid parts to the kinematic structure of the object to yield high-fidelity object poses."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.335,
+                0.894,
+                0.486
+            ],
+            "angle": 0,
+            "content": "Capturing human body poses For human poses and shapes, we adopt the SMPL-X [38] representation. Participants are attired in a MoCap suit incorporating 17 IMUs, don a pair of MoCap gloves, and have 5 hybrid trackers affixed to their heads, hands, and feet. It is noteworthy that while hybrid trackers capture 6D poses, IMUs solely measure global orientations. The optimization of human model shape parameters is undertaken to ensure that the reconstructed SMPL-X mesh aligns with the positions of the hybrid trackers. As a result, the MoCap system delivers real-time estimated human poses and shapes during recording."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.497,
+                0.656,
+                0.511
+            ],
+            "angle": 0,
+            "content": "3.3. Post-processing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.519,
+                0.894,
+                0.657
+            ],
+            "angle": 0,
+            "content": "Data alignment Due to the disparate 3D coordinates and temporal clocks of Kinect cameras and the MoCap system, alignment becomes crucial. This alignment is achieved by correlating the 3D coordinates of Kinect sequences with MoCap reconstructions through plane-to-plane correspondences [44], a technique that mitigates the influence of outliers, disturbances, and partial overlaps. For the synchronization of temporal sequences from Kinect and MoCap, time-lagged cross-correlation [45] is applied, a common approach for aligning two sequences with relative time shifts."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.667,
+                0.58,
+                0.736
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.502,
+                0.737,
+                0.579,
+                0.745
+            ],
+            "angle": 0,
+            "content": "(a) before removal"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.612,
+                0.668,
+                0.698,
+                0.736
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.614,
+                0.738,
+                0.697,
+                0.746
+            ],
+            "angle": 0,
+            "content": "(b) original skeleton"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.709,
+                0.668,
+                0.793,
+                0.736
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.706,
+                0.738,
+                0.798,
+                0.745
+            ],
+            "angle": 0,
+            "content": "(c) optimized skeleton"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.816,
+                0.667,
+                0.891,
+                0.735
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.819,
+                0.737,
+                0.888,
+                0.745
+            ],
+            "angle": 0,
+            "content": "(d) after removal"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.749,
+                0.894,
+                0.863
+            ],
+            "angle": 0,
+            "content": "Figure 4: Illustration of the penetration removal process. In panels (a) and (d), the small purple points represent human vertices devoid of penetration, while the larger colored points indicate instances of penetration. The red points symbolize the most pronounced penetration, whereas the blue points signify minimal contact. Panels (b) and (c) feature yellow lines that depict the original skeleton configuration, red markers denoting the target joints undergoing optimization, and red lines illustrating the resultant optimized skeleton configuration."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "9368"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.125,
+                0.894,
+                0.262
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Figure 5: Model architecture. The reconstruction model leverages the predicted voxelized representation of the human to facilitate the estimation of pose for the interacting object. We undertake root 6D pose regression for the object utilizing the image feature in conjunction with SMPL-X parameters. The predictions along with an interaction prior are harnessed for the refinement of the final estimated pose."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.315,
+                0.471,
+                0.549
+            ],
+            "angle": 0,
+            "content": "Penetration removal Owing to the limited sensor count and discrepancies in limb lengths, unrealistic contacts and penetrations persist in captured 3D interactions. To address this issue, we rectify these physical anomalies with a carefully devised optimization algorithm, as depicted in Fig. 4. Given a parameterized human body and an articulated object point cloud, we compute penetration depths between the human and object point clouds. Subsequently, we utilize the transpose of the linear-blend-skinning weights of SMPL-X to aggregate the maximum penetration depth and direction to the human skeleton joints. This information is then employed to calculate a target skeleton that mitigates the penetration. Finally, we employ a gradient-based optimization technique to adjust the human model to the new skeleton while maintaining proximity to the MoCap reconstruction. This process reduced the average penetration depth in CHAIRS from 3.5 cm to 2.6 cm, with an average contact value of 0.2 cm."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.55,
+                0.47,
+                0.633
+            ],
+            "angle": 0,
+            "content": "Ensuring data quality Following data alignment and penetration removal, the Chamfer distances between annotations and observations in CHAIRS are measured at \\(2.8\\mathrm{cm}\\) for objects and \\(1.9\\mathrm{cm}\\) for humans. This level of quality is comparable to a recent dataset [2], which reports Chamfer distances of \\(2.4\\mathrm{cm}\\) and \\(1.8\\mathrm{cm}\\), respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.634,
+                0.47,
+                0.689
+            ],
+            "angle": 0,
+            "content": "Privacy protection To safeguard identities, we apply face blurring [34] to all participant faces. Furthermore, we informed all participants that they retain the right to have their data removed from CHAIRS at any time."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.704,
+                0.398,
+                0.72
+            ],
+            "angle": 0,
+            "content": "4. Articulated Object Pose Estimation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.729,
+                0.471,
+                0.867
+            ],
+            "angle": 0,
+            "content": "CHAIRS offers extensive potential for various AHOI tasks, including detection, motion generation, physics-based analysis, and even language-guided motion generation with additional annotations. We highlight the value of CHAIRS by focusing on the task of articulated object pose estimation. Despite recent advancements in articulated object pose estimation [58, 11, 14, 68] and HOI reconstruction [5, 46, 69, 54], the challenge of articulated object pose estimation in the context of f-AHOI remains largely unaddressed. This specific context demands accurate object pose estimation in"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.315,
+                0.864,
+                0.329
+            ],
+            "angle": 0,
+            "content": "scenarios involving heavy occlusion and dense contact."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.337,
+                0.654,
+                0.351
+            ],
+            "angle": 0,
+            "content": "4.1. Task Definition"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.358,
+                0.894,
+                0.525
+            ],
+            "angle": 0,
+            "content": "Given an observed image \\(I\\), the parameterized human model \\(H = (\\beta, \\theta_b, \\theta_h, R_b, T_b)\\), and the meshes \\(X = \\{X_i, i = 1, \\dots, N\\}\\) representing the interacting object with \\(N\\) parts, our task involves estimating the object pose \\(O = \\{(R_i, T_i), i = 0, \\dots, N\\}\\). Here, \\(\\beta \\in \\mathbb{R}^{10}\\), \\(\\theta_b \\in \\mathbb{R}^{21 \\times 6}\\), \\(\\theta_h \\in \\mathbb{R}^{30 \\times 6}\\), \\(R_b \\in \\mathbb{R}^6\\), and \\(T_b \\in \\mathbb{R}^3\\) represent the shape and pose parameters of the SMPL-X [38] model. Specifically, \\((R_0 \\in \\mathbb{R}^6, T_0 \\in \\mathbb{R}^3)\\) corresponds to the root pose of the object, while \\(\\{(R_i \\in \\mathbb{R}^6, T_i \\in \\mathbb{R}^3)\\}\\) denotes the global rotation and translation for each part \\(X_i\\). The orthogonal 6D representation [70] is used for representing rotations in both human and object poses."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.533,
+                0.688,
+                0.546
+            ],
+            "angle": 0,
+            "content": "4.2. Model Architecture"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.554,
+                0.894,
+                0.693
+            ],
+            "angle": 0,
+            "content": "Our approach for object pose estimation is rooted in an interaction-aware framework that harnesses the fine-grained geometric relationships present in HOIs, along with learned interaction priors. This approach comprises two key stages. Given an image and estimated SMPL-X [38] parameters, we first estimate object occupancy grids and root poses using a reconstruction model. Subsequently, we fine-tune the reconstructed human-object pair using a learned interaction prior. The overall framework of our model is illustrated in Fig. 5, while Fig. 6 showcases the interaction prior model."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.7,
+                0.894,
+                0.811
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.812,
+                0.894,
+                0.863
+            ],
+            "angle": 0,
+            "content": "Figure 6: Illustration of the interaction prior model. The interaction prior model, realized as a cVAE, generates object voxels based on conditioning information from human voxels. During optimization, we aim to minimize the norm of the latent code."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.89,
+                0.502,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9369"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.126,
+                0.463,
+                0.14
+            ],
+            "angle": 0,
+            "content": "4.3. Object Reconstruction and Pose Initialization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.147,
+                0.473,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Given an observation \\(I\\), we estimate human pose and shape using an off-the-shelf estimator. These estimated human shapes \\(H^{\\prime}\\) are then voxelized into four resolutions with Kaolin [23]. To better exploit the geometric relationship between human-object pairs, we guide the estimation of object shape and pose using human pose. Specifically, we begin by extracting ResNet-101 [18] features from the image and subsequently estimate object voxels based on these image features using a 3D decoder. This decoder comprises three 3DConvT layers, along with upsampling layers at distinct resolutions, and two additional 1x1 3DConv layers. Furthermore, we fuse the convolutional feature grids with human voxels at each resolution, amplifying the influence of human pose. The final 3DConv layer generates the estimated object occupancy grid \\(\\mathcal{V}_O^{\\prime}\\). Additionally, we concatenate image features extracted from ResNet-101 with SMPL-X parameters, and employ an additional MLP to regress the root pose \\((R_0^{\\prime}, T_0^{\\prime})\\) of the object. This root pose also serves as the initialization for the optimization process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.41,
+                0.473,
+                0.507
+            ],
+            "angle": 0,
+            "content": "To train the reconstruction model, we first initialize the human shape estimator with pre-trained weights from the PARE model [38], followed by fine-tuning using the CHAIRS. Subsequently, we fix the weights of the PARE model and proceed to train the reconstruction model, utilizing the object pose estimation loss \\(\\mathcal{L}^{\\mathcal{O}}\\). This loss is characterized by the L1 loss computed on object voxels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.516,
+                0.245,
+                0.529
+            ],
+            "angle": 0,
+            "content": "4.4. Interaction Prior"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.538,
+                0.472,
+                0.594
+            ],
+            "angle": 0,
+            "content": "To capture the nuanced relationship between humans and interacting objects, we introduce an interaction prior model based on a cVAE. This model learns the conditional distribution of object occupancy given the human shape."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.594,
+                0.473,
+                0.773
+            ],
+            "angle": 0,
+            "content": "In this context, the cVAE prior model conditions on a multi-resolution voxelized human, with the objective of reconstructing a voxelized object. The architecture employs 3DConvNets as both encoder and decoder components. During training, we feed the voxelized object into the encoder to acquire object features at multiple scales. These object features are then combined with the multi-resolution human voxels corresponding to each layer. An MLP estimates the latent Gaussian distribution \\(\\mathcal{N}(\\mu, \\sigma)\\), which is used to parameterize the latent code \\(z\\) through re-parameterization. This latent code is subsequently decoded using the decoder. The feature grids at each decoder layer are concatenated with the corresponding human voxel condition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.773,
+                0.472,
+                0.802
+            ],
+            "angle": 0,
+            "content": "Training the prior model occurs on CHAIRS and involves four distinct loss components:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.138,
+                0.813,
+                0.47,
+                0.828
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {P}} = \\mathcal {L} _ {\\text {r e c o n}} + \\mathcal {L} _ {\\mathrm {K L}} + \\mathcal {L} _ {\\text {p e n e}} + \\mathcal {L} _ {\\text {c o n t r a}}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.839,
+                0.47,
+                0.868
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}_{\\mathrm{recon}}\\) and \\(\\mathcal{L}_{\\mathrm{KL}}\\) denote the standard reconstruction and KL divergence losses, respectively. \\(\\mathcal{L}_{\\mathrm{pene}}\\) constitutes a"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.127,
+                0.894,
+                0.196
+            ],
+            "angle": 0,
+            "content": "penetration loss, penalizing voxel grids occupied by both humans and objects. \\(\\mathcal{L}_{\\mathrm{contra}}\\) serves to maximize the distance of latent variables between original and augmented noisy data. Augmentation of training data involves introducing random noise to a portion of the samples."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.205,
+                0.851,
+                0.219
+            ],
+            "angle": 0,
+            "content": "4.5. Pose Optimization with Interaction Prior"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.227,
+                0.894,
+                0.366
+            ],
+            "angle": 0,
+            "content": "To reconstruct the intricate human-object relationship and refine the object poses, we employ an optimization stage that builds upon initialized poses, utilizing kinematic insights and the interaction prior. This process involves the object's CAD model, Unified Robot Description Format (URDF), estimated SMPL-X parameters \\(H^{\\prime}\\), and object voxels \\(\\mathcal{V}_O^\\prime\\) from the reconstruction model. We initiate the object model \\(\\hat{O}\\) using estimated root transformations and random part states. We iteratively update \\(\\hat{O}\\)'s parameters by minimizing the combined objective \\(\\mathcal{J}_{\\mathrm{recon}} + \\mathcal{J}_{\\mathrm{z}}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.375,
+                0.893,
+                0.393
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {J} _ {\\text {r e c o n}} = \\left\\| V (\\hat {O}) - \\mathcal {V} _ {O} ^ {\\prime} \\right\\| _ {2}, \\quad \\mathcal {J} _ {\\mathrm {z}} = \\left\\| \\operatorname {E n c} \\left(H ^ {\\prime}, \\hat {O}\\right) \\right\\|, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.403,
+                0.893,
+                0.487
+            ],
+            "angle": 0,
+            "content": "where \\( V(\\cdot) \\) is the voxelization function. \\( \\mathcal{I}_{\\mathrm{recon}} \\) measures the voxelized object model's distance from the estimated object voxels. \\( \\mathcal{I}_{\\mathrm{z}} \\) enforces a small norm for the latent predicted by the cVAE encoder, regulating proximity to the interaction prior. The process of pose optimization with interaction prior is illustrated in Fig. 7."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.515,
+                0.495,
+                0.892,
+                0.606
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.608,
+                0.892,
+                0.647
+            ],
+            "angle": 0,
+            "content": "Figure 7: An illustration of pose estimation with interaction prior. Starting with the reconstruction output, we optimize the object according to the reconstructed voxel and interaction prior."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.894,
+                0.756
+            ],
+            "angle": 0,
+            "content": "Object pose optimization Optimized parameters include the root 6D pose \\(R, T\\) of the object and joint parameters \\(\\Phi\\) (if applicable), controlling part rotation and shift under kinematic constraints. For joints (except the root), we consider revolute, prismatic, or combined revolute-prismatic configurations. The latter, such as the joint linking a chair's base and seat, restricts rotation and shift along the same axis."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.756,
+                0.894,
+                0.868
+            ],
+            "angle": 0,
+            "content": "During optimization, we initiate the root pose \\(R, T\\) using the estimated root 6D pose from the object pose estimation model. All joint parameters \\(\\Phi\\) are set to zero. Optimization involves minimizing the reconstruction loss \\(\\mathcal{I}_{\\mathrm{recon}}\\) and interaction prior loss \\(\\mathcal{I}_{\\mathrm{z}}\\) through gradient descent. Calculating losses necessitates determining object part occupancy postapplication of \\(R, T,\\) and \\(\\Phi\\) for each optimization step. As direct voxelization lacks differentiability regarding object"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.89,
+                0.502,
+                0.9
+            ],
+            "angle": 0,
+            "content": "9370"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.126,
+                0.471,
+                0.209
+            ],
+            "angle": 0,
+            "content": "parameters \\(R, T\\) and \\(\\Phi\\), we employ trilinear interpolation on the affine \\((0,1)\\) voxel grid to resample voxel occupancy. This permits gradient flow for root and joint parameter updates. Post-optimization, parameters yield an updated 3D object model and enhanced representation (e.g., mesh) with reduced geometric error."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.209,
+                0.474,
+                0.431
+            ],
+            "angle": 0,
+            "content": "Contrastive loss We intend our interaction prior to grasp a comprehensive human-object interaction distribution through a conditional Gaussian model. Reasonable and common spatial relationships between human and object latent codes should cluster near the Gaussian mean, in contrast to unreasonable ones. A contrastive loss aids training of the interaction prior model alongside penetration, reconstruction, and KL-divergence losses. Positive examples \\((H,\\mathcal{V}_O)\\) involve an observed human \\(H\\) and object voxel \\(\\nu_{O}\\). Corresponding negative examples \\((H,\\mathcal{V}_O^{\\prime})\\) are generated by perturbing the object, adding noise to root and articulated poses, and voxelizing \\(\\nu_{O}^{\\prime}\\). The contrastive loss \\(\\mathcal{L}_{\\mathrm{contra}}\\), defined as \\(\\mathcal{L}_{\\mathrm{contra}} = \\max (0,||\\mathrm{Enc}(\\mathcal{V}_O,H)|| - ||\\mathrm{Enc}(\\mathcal{V}_O^{\\prime},H)||)\\), guides latent codes of perturbed human-object pairs away from the distribution centroid. Here, Enc represents the conditional encoder of our proposed cVAE-based prior model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.443,
+                0.21,
+                0.458
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.466,
+                0.472,
+                0.619
+            ],
+            "angle": 0,
+            "content": "Experimental settings We split CHAIRS into training, testing, and validation sets; \\(70\\%\\) of objects are used for training, \\(20\\%\\) for testing, and the remaining for validation. We evaluate our model under two settings: with \\((w / opt)\\) and without optimization \\((w / o\\) opt). In the \\(w / opt.\\) setting, we report the chamfer distance between objects posed with ground truth and estimated transformation parameters. In the \\(w / o\\) opt. setting, we do not have the estimated transformation parameters. Thus, we report the chamfer distance between the ground-truth object mesh and the mesh obtained by running the marching cube algorithm on the reconstructed voxels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.619,
+                0.472,
+                0.756
+            ],
+            "angle": 0,
+            "content": "Evaluation metrics We evaluate object pose estimation using mean rotation and translation errors for each object part. Object shape reconstruction is evaluated with chamfer distance and intersection over union (IoU). For reconstructed f-AHOI, we assess penetration depth and contact scores between the human and object. Penetration depth is the maximum depth of the object's surface within the human's body, while contact value is the shortest distance between the human and object. Contact values are clipped to [0,20cm] for distant human-object pairs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.757,
+                0.472,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Baseline methods We compare articulated object pose estimation with LASR [59] and ANCSH [28] as baselines, where we use depth maps as input for ANCSH. Both methods are fine-tuned on CHAIRS. Additionally, we compare our model with D3D-HOI [58], PHOSA [65], and CHORE [56] that jointly estimate human and object poses. We adapted D3D-HOI's optimization objectives to better fit CHAIRS's data distribution."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.126,
+                0.7,
+                0.141
+            ],
+            "angle": 0,
+            "content": "5.1. Results and Analyses"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.147,
+                0.895,
+                0.273
+            ],
+            "angle": 0,
+            "content": "Quantitative results are presented in Tab. 2. Our model, leveraging geometrical relationships, exhibits substantial improvements in pose estimation and shape reconstruction compared to existing methods. In the w/o opt. setting where the object is unknown, our model surpasses the state-of-the-art LASR method by a significant margin. While D3D-HOI and ANCSH excel, they assume known object structures. Remarkably, our model outperforms all baselines when provided with the object structure in the w/ opt. setting."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.28,
+                0.895,
+                0.319
+            ],
+            "angle": 0,
+            "content": "Table 2: Comparisons against existing methods. \\(\\ast\\) : method requires knowledge of object structure and/or geometry; \\(\\dagger\\) : method does not rely on object-related knowledge."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.321,
+                0.892,
+                0.447
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Object</td><td colspan=\"2\">HOI</td></tr><tr><td>Rot.↓(°)</td><td>Transl.↓(mm)</td><td>CD↓(mm)</td><td>IoU↑(%)</td><td>Pene.↓(mm)</td><td>Cont.↓(mm)</td></tr><tr><td>LASR†[59]</td><td>/</td><td>/</td><td>205.2</td><td>/</td><td>/</td><td>/</td></tr><tr><td>Ours (w/o opt.)†</td><td>/</td><td>/</td><td>160.2</td><td>11.03</td><td>4.530</td><td>2.720</td></tr><tr><td>ANCSH* [28]</td><td>/</td><td>/</td><td>90.36</td><td>/</td><td>/</td><td>/</td></tr><tr><td>PHOSA* [65]</td><td>29.31</td><td>175.2</td><td>177.9</td><td>7.60</td><td>2.046</td><td>1.689</td></tr><tr><td>D3D-HOI* [58]</td><td>27.31</td><td>119.2</td><td>126.9</td><td>16.60</td><td>7.472</td><td>1.163</td></tr><tr><td>CHORE* [56]</td><td>21.82</td><td>87.58</td><td>95.40</td><td>16.44</td><td>1.050</td><td>1.742</td></tr><tr><td>Ours (w/ opt.)*</td><td>19.35</td><td>66.23</td><td>72.30</td><td>21.57</td><td>1.143</td><td>1.562</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.457,
+                0.895,
+                0.568
+            ],
+            "angle": 0,
+            "content": "We present qualitative results in Fig. 8, where columns (a)-(h) illustrate the reconstruction outcomes on the test set. In these columns, we display the reconstructed meshes prior to optimization using the marching cubes algorithm. It is evident from the visualizations that our model successfully produces plausible and accurate interaction representations even before the optimization process. Notably, the optimization step enhances the finer interaction details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.575,
+                0.611,
+                0.589
+            ],
+            "angle": 0,
+            "content": "5.2. Ablations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.597,
+                0.892,
+                0.639
+            ],
+            "angle": 0,
+            "content": "We conduct three ablation studies to assess the efficacy of our model's design choices. Quantitative results of these ablation studies are presented in Tab. 3."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.51,
+                0.647,
+                0.881,
+                0.66
+            ],
+            "angle": 0,
+            "content": "Table 3: Ablation of interaction, prior, and contrastive loss."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.663,
+                0.892,
+                0.787
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Object</td><td colspan=\"2\">HOI</td></tr><tr><td>Rot.↓(°)</td><td>Transl.↓(mm)</td><td>CD↓(mm)</td><td>IoU↑(%)</td><td>Pene.↓(mm)</td><td>Cont.↓(mm)</td></tr><tr><td>Full†</td><td>/</td><td>/</td><td>160.2</td><td>11.03</td><td>4.530</td><td>2.720</td></tr><tr><td>-prior†</td><td>/</td><td>/</td><td>165.3</td><td>10.52</td><td>4.377</td><td>3.295</td></tr><tr><td>Full*</td><td>19.35</td><td>66.23</td><td>72.30</td><td>21.57</td><td>1.143</td><td>1.562</td></tr><tr><td>-prior*</td><td>19.97</td><td>83.39</td><td>87.90</td><td>18.81</td><td>1.749</td><td>2.081</td></tr><tr><td>-contr.*</td><td>21.52</td><td>81.90</td><td>87.28</td><td>18.93</td><td>1.265</td><td>2.393</td></tr><tr><td>-inter.*</td><td>17.88</td><td>69.53</td><td>78.12</td><td>19.50</td><td>1.022</td><td>2.320</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.798,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Prior We conduct an experiment where we remove the interaction prior model and solely optimize object poses by minimizing \\(\\mathcal{L}_{\\mathrm{recon}}\\). In both * and † settings, we observe a substantial performance drop. This underscores the critical role played by the interaction prior in accurately estimating"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.468,
+                0.89,
+                0.501,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9371"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.123,
+                0.892,
+                0.562
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.564,
+                0.893,
+                0.591
+            ],
+            "angle": 0,
+            "content": "Figure 8: Qualitative results. (a)-(h) Test set results. (i)-(p) Wild images results. RGB images, optimized poses, and mesh obtained by running marching cubes on reconstructed voxels are shown. Please refer to Fig. A6 in Supplementary Materials for more qualitative results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.602,
+                0.47,
+                0.713
+            ],
+            "angle": 0,
+            "content": "object poses. It is important to note that both settings involve an optimization step, and the primary distinction is that the * model possesses access to the object's geometry and structure during optimization. When the prior model is omitted in the † setting, we observe a decrease in penetration and a larger increase in contact value. This observation suggests that our interaction prior model exerts influence by pulling the object closer to the human when they are not in contact."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.713,
+                0.47,
+                0.784
+            ],
+            "angle": 0,
+            "content": "Contrast In this ablation, we exclude the contrastive loss \\(\\mathcal{L}_{\\mathrm{contra}}\\) from the training of the prior model. The results are analogous to those of the -prior experiment. This outcome underscores the crucial role that the contrastive loss plays in facilitating the learning of a robust interaction prior."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.784,
+                0.471,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Interaction We proceed to remove the concatenation of human voxels in the 3DConv layers of both the reconstruction model and the interaction prior model. This removal eliminates the interaction awareness in our model. We observe a modest degradation across all object reconstruction metrics, underscoring the importance of interaction aware"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.602,
+                0.893,
+                0.713
+            ],
+            "angle": 0,
+            "content": "ness in our approach. Interestingly, the removal of interaction awareness leads to increased contact values and decreased penetration, resembling the outcomes of the -prior ablation in the w/o opt. setting. This suggests that interaction awareness also contributes to bringing the human and object into closer proximity. Lastly, we note an unexpected low rotation error, which we attribute to the presence of rotation symmetries in the dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.713,
+                0.893,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Additionally, we assess our method's performance under varying qualities of human pose estimation in Tab. 4. The results reveal notable improvement in object pose estimation as human poses become more accurate, thus validating our initial hypothesis. Notably, the pose estimation model [27] effectively predicts most challenging poses accurately, leaving the avenue of leveraging interactions to enhance human pose estimation as a potential future research direction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.894,
+                0.868
+            ],
+            "angle": 0,
+            "content": "In summary, our analysis highlights the substantial contributions of all three model components to object pose and shape reconstruction."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.89,
+                0.502,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9372"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.124,
+                0.47,
+                0.163
+            ],
+            "angle": 0,
+            "content": "Table 4: Ablation of human pose estimation quality. GT denotes using ground-truth human poses to optimize the object poses, No prior denotes not considering human-object interaction prior."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.165,
+                0.469,
+                0.236
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Human</td><td colspan=\"2\">Object</td></tr><tr><td>MPJPE↓(mm)</td><td>PA-MPJPE↓(mm)</td><td>CD↓(mm)</td><td>IOU↑(%)</td></tr><tr><td>No prior</td><td>/</td><td>/</td><td>87.90</td><td>18.81</td></tr><tr><td>PARE [27]</td><td>81.09</td><td>47.19</td><td>73.79</td><td>21.66</td></tr><tr><td>PARE(finetune)</td><td>74.50</td><td>43.99</td><td>72.30</td><td>21.57</td></tr><tr><td>GT</td><td>0</td><td>0</td><td>65.50</td><td>23.16</td></tr></table>"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.246,
+                0.227,
+                0.349
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.273,
+                0.254,
+                0.333,
+                0.341
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.365,
+                0.254,
+                0.43,
+                0.341
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.351,
+                0.471,
+                0.39
+            ],
+            "angle": 0,
+            "content": "Figure 9: Failure cases. In situations involving rotation-symmetrical objects, our model encounters challenges with estimating rotation while maintaining a relatively low visual error."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.402,
+                0.471,
+                0.47
+            ],
+            "angle": 0,
+            "content": "In-the-wild generalization We also assess the model's generalizability on a limited set of internet images. As depicted in Fig. 8 (i-p), the qualitative results illustrate that our model successfully generalizes its capabilities to images captured outside of controlled laboratory settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.471,
+                0.471,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Failure cases Our model encounters challenges in accurately estimating the orientation of object parts when those parts exhibit geometric similarity under specific rotations. Rotation symmetry is commonly observed in spherical and cylindrical object components, such as the base of a stool or a round seat. An illustrative example of this symmetry is presented in Fig. 9. Notably, existing methods [10, 49] address this challenge through (i) accepting multiple equally-valid ground truths and (ii) employing a min-of-N loss to calculate the smallest distance to any of these ground truths. However, implementing such methods necessitates a meticulous classification of symmetry types for each object."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.638,
+                0.47,
+                0.707
+            ],
+            "angle": 0,
+            "content": "Furthermore, we observe that our model's performance diminishes in scenarios where no f-AHOI is present, such as instances where a human is situated far away from an object like a chair. Under these circumstances, our model is unable to leverage interactions to enhance object pose estimation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.719,
+                0.47,
+                0.736
+            ],
+            "angle": 0,
+            "content": "6. Application: Generating Interacting Humans"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.742,
+                0.471,
+                0.866
+            ],
+            "angle": 0,
+            "content": "We further investigate the intricate relationships within AHOI by exploring the generation of interacting human poses in the presence of articulated objects. To this end, we employ a 3D conditional diffusion model known as SceneDiffuser [22], trained on our CHAIRS. To evaluate the quality of the generated poses, we compare them with poses generated using the same model trained on COUCH [67], a recent dataset featuring humans seated on rigid chairs. We use the feature extracted from the point cloud of the ob"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.123,
+                0.891,
+                0.401
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.402,
+                0.893,
+                0.428
+            ],
+            "angle": 0,
+            "content": "Figure 10: Generated human poses given articulated objects. The models are trained on CHAIRS (a, b) and COUCH [67] (c, d)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.441,
+                0.893,
+                0.581
+            ],
+            "angle": 0,
+            "content": "ject via Pointnet++ as a conditioning input and flatten the SMPL-X parameters of the human to form tokens for input to a Transformer. The implementation details closely follow those of the human pose generation task described in Huang et al. [22]. Qualitative comparisons of the generated human poses are shown in Fig. 10. Notably, the model trained with CHAIRS captures more nuanced and natural geometrical relationships when interacting with articulated objects. For a more in-depth analysis of this downstream application, we direct readers to the Appx. B in Supplementary Materials."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.501,
+                0.594,
+                0.618,
+                0.608
+            ],
+            "angle": 0,
+            "content": "7. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.617,
+                0.894,
+                0.728
+            ],
+            "angle": 0,
+            "content": "We advance the study of HOI to encompass fine-grained, articulated interactions with (i) CHAIRS, an extensive dataset, (ii) a challenging object reconstruction problem under f-AHOI, and (iii) a strong baseline. Our CHAIRS captures diverse, natural AHOIs involving various sittable objects. The object reconstruction problem confronts kinematic assumptions, with our model effectively leveraging intricate interactions to resolve ambiguities."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.728,
+                0.894,
+                0.798
+            ],
+            "angle": 0,
+            "content": "Limitations One limitation of our work lies in the fact that the parametric human model used in CHAIRS does not account for clothing, leading to misalignments between the 3D annotations and the images. Consequently, the usage of pixel-aligned features may be compromised."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.798,
+                0.894,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Acknowledgment The authors would like to thank four anonymous reviews for constructive feedback and NVIDIA for their generous support of GPUs and hardware. This work is supported in part by the National Key R&D Program of China (2022ZD0114900) and the Beijing Nova Program."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.469,
+                0.89,
+                0.501,
+                0.901
+            ],
+            "angle": 0,
+            "content": "9373"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
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+                0.125,
+                0.173,
+                0.139
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+            "angle": 0,
+            "content": "References"
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+# Full-Body Articulated Human-Object Interaction
+
+Nan Jiang $^{1,2\star\dagger}$ , Tengyu Liu $^{2\star}$ , Zhexuan Cao $^{3\dagger}$ , Jieming Cui $^{1,2,\dagger}$ , Zhiyuan Zhang $^{2,3\dagger}$ , Yixin Chen $^{2}$ , He Wang $^{4}$ , Yixin Zhu $^{5\boxtimes}$ , Siyuan Huang $^{2\boxtimes}$
+
+https://jnnan.github.io/project/chairs/
+
+*Equal contributors † Work done during an internship at BIGAI  
+$^{2}$  Beijing Institute of General Artificial Intelligence (BIGAI)  
+<sup>4</sup> Center on Frontiers of Computing Studies, Peking University
+
+yixin.zhu@pku.edu.cn, syhuang@bigai.ai
+
+<sup>1</sup> School of Intelligence Science and Technology, Peking University  
+$^{3}$  Department of Automation, Tsinghua University  
+$^{5}$  Institute for Artificial Intelligence, Peking University
+
+![](images/320a280a65e3dd36f7e9c776e9bcfdb3609cc836432ee2f1894e8ecf29a778ba.jpg)  
+Figure 1: Examples of the proposed Capturing Human and Articulated-object InterActionS (CHAIRS) dataset. It contains fine-grained interactions between 46 participants and 81 sittable objects with drastically different kinematic structures, providing multi-view RGB-D sequences and ground-truth 3D mesh of humans and articulated objects for over 17.3 hours of recordings.
+
+# Abstract
+
+Fine-grained capture of 3D Human-Object Interactions (HOIs) enhances human activity comprehension and supports various downstream visual tasks. However, previous models often assume that humans interact with rigid objects using only a few body parts, constraining their applicability. In this paper, we address the intricate challenge of Full-Body Articulated Human-Object Interaction (f-AHOI), where complete human bodies interact with articulated objects having interconnected movable joints. We introduce CHAIRS, an extensive motion-captured f-AHOI dataset comprising 17.3 hours of diverse interactions involving 46 participants and 81 articulated as well as rigid sittable objects. The CHAIRS provides 3D meshes of both humans and articulated objects throughout the interactive sequences, offering realistic and physically plausible full-body interactions. We demonstrate the utility of CHAIRS through object pose estimation. Leveraging the geometric relationships inherent in HOI, we propose a pioneering model that employs human pose estimation
+
+tion to address articulated object pose and shape estimation within whole-body interactions. Given an image and an estimated human pose, our model reconstructs the object's pose and shape, refining the reconstruction based on a learned interaction prior. Across two evaluation scenarios, our model significantly outperforms baseline methods. Additionally, we showcase the significance of CHAIRS in a downstream task involving human pose generation conditioned on interacting with articulated objects. We anticipate that the availability of CHAIRS will advance the community's understanding of finer-grained interactions.
+
+# 1. Introduction
+
+In the realm of computer vision and robotics, the fundamental comprehension of Human-Object Interaction (HOI) [30, 31, 64, 62] lies at the core of dissecting intricate human activities. This paper embarks on unraveling the complex challenge of Full-Body Articulated Human-Object
+
+Table 1: Comparisons between CHAIRS and other HOI datasets.  
+
+<table><tr><td>Dataset</td><td># object</td><td># participants</td><td># instructions</td><td># hours</td><td>fps</td><td># view</td><td>articulated objects</td><td>human</td><td>annotation type</td></tr><tr><td>GRAB [46]</td><td>51</td><td>10</td><td>4</td><td>3.8</td><td>120</td><td>0</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>D3D-HOI [58]</td><td>24</td><td>5</td><td>/</td><td>0.6</td><td>3</td><td>1</td><td>Yes</td><td>Whole-body</td><td>manual</td></tr><tr><td>BEHAVE [2]</td><td>20</td><td>8</td><td>6</td><td>4.2</td><td>30</td><td>4</td><td>No</td><td>Whole-body</td><td>multi-kinect</td></tr><tr><td>ARCTIC [11]</td><td>10</td><td>9</td><td>1</td><td>1.2</td><td>30</td><td>8+1</td><td>Yes</td><td>Two hands</td><td>mocap</td></tr><tr><td>COUCH [67]</td><td>4</td><td>6</td><td>6</td><td>3</td><td>60</td><td>4</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>CHAIRS (Ours)</td><td>81</td><td>46</td><td>32</td><td>17.3</td><td>30</td><td>4</td><td>Yes</td><td>Whole-body</td><td>mocap</td></tr></table>
+
+Interaction (f-AHOI). This endeavor mandates tackling two pivotal dimensions: (i) fashioning kinematic-agnostic representations for articulated objects and (ii) delving into the intricate spatial-temporal tapestry interweaving objects with human whole-bodies. Our primary focus resides in addressing the intricate task of object pose estimation within the realm of f-AHOI, considering that reconstructing 3D human poses from frontal viewpoints is comparably uncomplicated.
+
+The crux of object pose estimation within the context of f-AHOI is punctuated by three principal challenges:
+
+The dearth of comprehensive f-AHOI datasets Existing strides in 3D HOI predominantly either assume interactions with rigid objects or confine themselves to involving specific segments of the human anatomy [2, 46, 65, 29, 67, 11, 58, 14]. Regrettably, these assumptions drastically over-simplify genuine human interactions that span diverse body parts engaging with articulated objects embodying moveable elements such as cabinets and office chairs. A more intricate level of interaction necessitates a richer dataset.
+
+The multifaceted landscape of object kinematic structures Objects constituting the realm of f-AHOI exhibit notable disparities in their kinematic frameworks, even when categorized under the same umbrella. Prevailing methodologies often lean towards uniform structures [58, 32, 11, 14], thereby disregarding the diverse tapestry that constitutes real-world scenarios. The endeavor of accurately reconstructing objects manifesting divergent geometries and structures is plagued with its own set of challenges.
+
+The intricacies of complex interactions Engaging with articulated objects entails grappling with intricate spatial and physical relationships, often entailing occlusions and intricate points of contact. The intricacy of these dynamics thrusts conventional pose estimation mechanisms reliant on point cloud template-matching [65, 49, 19, 39, 28] into the realm of insufficiency. The prominence of contacts further compounds the endeavor of precise reconstruction, as slight inaccuracies can swiftly usher implausible interactions into the picture.
+
+The trajectory of this research endeavors to navigate the above three challenges through the prism of three principal solutions, respectively:
+
+To confront the scarcity of f-AHOI datasets, we introduce CHAIRS, a multi-view RGB-D dataset. Illustrated in Fig. 1,
+
+CHAIRS chronicles a diverse tapestry of interactions, seamlessly intertwining 46 participants with 81 sittable objects (e.g., chairs, sofas, stools, and benches). 28 of these objects are endowed with moveable parts. Each frame encapsulates 3D meshes of both human whole-bodies and objects, casting a spotlight on interactions with sittable objects that encompass a diverse spectrum of structures and distinctive movable elements conducive to multifarious human interactions.
+
+To traverse the labyrinth of kinematic diversity, CHAIRS meticulously selects representative objects characterized by an eclectic array of structures. Unlike traditional datasets and methodologies tethered to uniform kinematics [55, 51, 32], we champion real-world heterogeneity, encompassing the gamut from rigid stools to swivel chairs boasting up to 7 movable components. Each component is linked to its parent through a nexus of revolute, prismatic, or composite joints.
+
+To unravel the enigma of complex interactions, we proffer an innovative approach to articulated object pose estimation, one that harnesses the subtle interplay of fine-grained interaction relationships to reconstruct the object in question. This approach diverges from the conventional recourse of manually labeling contact maps corresponding to human body parts [65, 16, 2]. Instead, our approach melds the intricacies of these relationships with a reconstruction model and an interaction prior, the latter of which is imbued with the essence of a conditional Variational Auto-Encoder (cVAE). This evolution sidesteps the need for predefined knowledge grounded in laborious annotation. Moreover, the significance of these intricate relationships is showcased through our venture into learning human poses within the ambit of articulated objects. By juxtaposing the generative prowess harnessed from CHAIRS with that stemming from a dataset centered on rigid objects [67], we underscore the pivotal role played by the nuanced geometrical relationships encapsulated within CHAIRS in the broader canvas of downstream tasks.
+
+Our contributions are four-fold: (i) CHAIRS, a sprawling multi-view RGB-D repository infused with diverse 3D meshes. (ii) The seamless extension of articulated object pose estimation to the arduous landscape of f-AHOI. (iii) An object pose estimation approach that transcends the strictures of structure. (iv) An overarching interaction prior that captures the subtleties of fine-grained interactions, acting as a catalyst for the journey of pose estimation.
+
+![](images/a09a5661244fdebfc04fe6e9952a57b498f938b07aa3431088338978551303e5.jpg)  
+(a) sequences of objects articulating over time  
+(b) frames of diverse interactions  
+Figure 2: Samples from the CHAIRS dataset. CHAIRS encompasses diverse AHOIs captured through precisely calibrated multi-view RGB-D cameras, offering detailed 3D meshes of human participants and articulated objects. The figure showcases (a) RGB frames alongside corresponding ground-truth mesh sequences and (b) an array of varied AHOI instances.
+
+# 2. Related Work
+
+3D Human-Object Interaction (HOI) The evolution of HOI research spans from 2D image-based interaction detection [4, 40, 13, 30, 31, 64, 62, 22] to 3D interaction reconstruction [43, 16, 5, 53, 58, 63, 66] and generation [17, 50, 57, 21, 52, 67] within 3D scenes. Notably, PiGraph [43] and D3D-HOI [16, 58] capture daily activities and reconstruct interactions, often relying on visual observations. In contrast, MoCap systems [46, 2, 11, 67] offer fine-grained 3D human-object interactions. GRAB [46] and ARCTIC [11] emphasize interactions with small objects, while BEHAVE [2] and COUCH [67] involve interactions with everyday objects. However, these works often focus on rigid objects or hand-object interactions with articulated objects. In contrast, our CHAIRS dataset captures realistic whole-body interactions with diverse articulated objects.
+
+Articulated Human-Object Interaction Articulated Human-Object Interactions (AHOIs) build on part-level object representations, modeling intricate spatial-temporal interactions between humans and articulated objects [14]. Noteworthy contributions include D3D-HOI [58], ARCTIC [11], and 3DADN [41]. D3D-HOI [58] captures humans interacting with containers, ARCTIC [11] focuses on motion-captured RGB-D hand-object interactions, and 3DADN [41] annotates movable object parts from internet videos. However, these works often emphasize hand-object interactions, whereas our focus extends to AHOIs encompassing diverse articulated objects and multiple body parts.
+
+Contact-Rich HOI The realm of f-AHOI requires a deeper HOI understanding. While 3D HOI literature has expanded, few works address full-body contacts through reconstruction [16] or generation [69, 52, 15, 67]. However, these works often focus on static scenes with limited interactions. In contrast, our CHAIRS dataset encompasses diverse
+
+articulated objects and interactions.
+
+Articulated Object Pose Estimation The estimation of 6-DOF poses for rigid objects has garnered attention [25, 19, 3, 48, 39, 37, 9]. Template-based methods [20, 60, 49, 26] and regression models [1] are common, with recent strides in articulated object pose estimation [8, 33, 28] leveraging these techniques. Regression and implicit function models [36, 47, 59, 24] are also explored. Despite progress, these methods often assume consistent kinematic structures within object categories. In contrast, our CHAIRS dataset features diverse kinematic structures and models capable of handling various parts and kinematics of 3D objects.
+
+# 3. The CHAIRS Dataset
+
+A significant challenge in modeling AHOIs is the lack of accurate 3D annotations. To address this gap, we introduce CHAIRS, a comprehensive AHOI dataset featuring multi-view RGB-D sequences. CHAIRS offers precise 3D meshes of humans and articulated objects during interactions, captured through a hybrid motion capture (MoCap) system that combines inertial and optical tracking techniques. The data collection process prioritizes realism and physical authenticity, resulting in a dataset that significantly advances interaction understanding. A detailed comparison between CHAIRS and previous HOI datasets is outlined in Tab. 1.
+
+# 3.1. Data Collection
+
+Overview CHAIRS encompasses a total of 1390 sequences depicting articulated interactions involving humans and sittable objects like chairs, sofas, stools, and benches. Exemplary sequences from CHAIRS and a showcase of the object variety can be seen in Fig. 2. Each object's exploration involves 6 distinct participants, each contributing three interaction sequences, resulting in 18 sequences for each object.
+
+![](images/aed7f69d37956bcfb61fd132c12d98eeca96178c0330c09d09530aa2884c54b6.jpg)  
+(a) camera setup
+
+![](images/c06416be38a3fa63d999d410c979231a1df41002d66667cba5f55c4ac333d624.jpg)  
+(b) mocap on objects  
+Figure 3: Setup for data collection in the CHAIRS dataset. Our data collection setup consisted of (a) four front-facing RGB-D cameras supplemented by a network of motion capture cameras surrounding the recording area, (b) hybrid trackers affixed to various movable parts of objects, and (c) a configuration incorporating five hybrid trackers and seventeen IMUs distributed on the participants.
+
+![](images/be508df79c2b3e5517641740bc26feda8f4c346f858bb15f8ae65f61221d3b09.jpg)  
+(c) mocap on participants
+
+In every sequence, participants execute 6 diverse actions drawn randomly from a pool of 32 interactions, such as shifting a stool, reclining on a sofa, or rotating a chair; please refer to the Supplementary Material Appx. C.1 for further details. Participant instructions were kept deliberately high-level to ensure authentic and natural performances.
+
+Object diversity The object gallery in CHAIRS boasts an array of objects, each possessing a range of appearances and kinematic structures. Objects were curated by sourcing them online, with a focus on maximizing stylistic diversity. Notably, 28 objects incorporate at least one articulated joint, contributing to rich interaction scenarios. The 3D meshes of these objects were captured using the Scaniverse app on an iPad Pro (11-inch, 2nd generation) and subsequently refined manually to eliminate any imperfections. The 3D meshes were further segmented using the annotation tool [35] into eight functional parts. Participants received context-specific instructions tailored to the object they were interacting with.
+
+Camera and hardware setup As depicted in Fig. 3, all sequences were exclusively captured in a controlled laboratory setup, encompassing a designated area of  $5\mathrm{m}\times 4\mathrm{m}$  ensuring complete visibility of all actions for the cameras. Four Kinect Azure DK cameras, strategically positioned to capture front-facing multi-view perspectives, were employed to record the interactions. These cameras were meticulously calibrated and synchronized. To ensure the precision of ground-truth poses for both humans and objects, a commercial inertial-optical hybrid MoCap system was incorporated alongside the Kinect setup; for further specifics, see the subsequent section.
+
+# 3.2. Motion Capture (MoCap) System
+
+Hybrid MoCap Our MoCap system is composed of a MoCap suit outfitted with 5 hybrid trackers and 17 wearable Inertial Measurement Units (IMUs), alongside a pair of gloves equipped with 12 IMUs each. The setup further includes supplementary hybrid trackers and a collection of 8 high-speed cameras. A hybrid tracker, which encompasses 4 optical markers and an IMU, is capable of accurately mea
+
+suring its own 6D pose even in conditions of substantial occlusion. The arrangement of our data collection setup is illustrated in Fig. 3. For capturing the pose of a human or an object part, either an IMU or a hybrid tracker can be utilized to record the global orientation or 6D pose, respectively.
+
+Capturing articulated object poses The recording process of articulated object poses in the context of interactions unfolds across three phases. First, we position the object into its canonical pose and affix a hybrid tracker to each of its movable components. Subsequently, we calculate the relative transformation between the object part and the trackers. During the recording process, the real-time ground-truth 6D pose of each object part is computed based on the tracker poses. Finally, we match the rigid parts to the kinematic structure of the object to yield high-fidelity object poses.
+
+Capturing human body poses For human poses and shapes, we adopt the SMPL-X [38] representation. Participants are attired in a MoCap suit incorporating 17 IMUs, don a pair of MoCap gloves, and have 5 hybrid trackers affixed to their heads, hands, and feet. It is noteworthy that while hybrid trackers capture 6D poses, IMUs solely measure global orientations. The optimization of human model shape parameters is undertaken to ensure that the reconstructed SMPL-X mesh aligns with the positions of the hybrid trackers. As a result, the MoCap system delivers real-time estimated human poses and shapes during recording.
+
+# 3.3. Post-processing
+
+Data alignment Due to the disparate 3D coordinates and temporal clocks of Kinect cameras and the MoCap system, alignment becomes crucial. This alignment is achieved by correlating the 3D coordinates of Kinect sequences with MoCap reconstructions through plane-to-plane correspondences [44], a technique that mitigates the influence of outliers, disturbances, and partial overlaps. For the synchronization of temporal sequences from Kinect and MoCap, time-lagged cross-correlation [45] is applied, a common approach for aligning two sequences with relative time shifts.
+
+![](images/b3ae62e9848c04415791ed8580c760d6f6426ca0672a99450026ed6f17395c42.jpg)  
+(a) before removal  
+Figure 4: Illustration of the penetration removal process. In panels (a) and (d), the small purple points represent human vertices devoid of penetration, while the larger colored points indicate instances of penetration. The red points symbolize the most pronounced penetration, whereas the blue points signify minimal contact. Panels (b) and (c) feature yellow lines that depict the original skeleton configuration, red markers denoting the target joints undergoing optimization, and red lines illustrating the resultant optimized skeleton configuration.
+
+![](images/04f8ee28feac5ebaac3cc9cd56c330d6e813fca1e6e40c8f0a70bc1c7663d1e6.jpg)  
+(b) original skeleton
+
+![](images/0c07422112ec10ede6c28ebf8159651ba326e8fdc792bff58c26a2ff1558ec21.jpg)  
+(c) optimized skeleton
+
+![](images/11a22e48700b3407878812e890d72c782019e0032efd186cb1a18c9c586dab5b.jpg)  
+(d) after removal
+
+![](images/bc1ef1454888b8a1ee9f9851f33ce0270cca39ba04238284b32e8efbf7144b2f.jpg)  
+Figure 5: Model architecture. The reconstruction model leverages the predicted voxelized representation of the human to facilitate the estimation of pose for the interacting object. We undertake root 6D pose regression for the object utilizing the image feature in conjunction with SMPL-X parameters. The predictions along with an interaction prior are harnessed for the refinement of the final estimated pose.
+
+Penetration removal Owing to the limited sensor count and discrepancies in limb lengths, unrealistic contacts and penetrations persist in captured 3D interactions. To address this issue, we rectify these physical anomalies with a carefully devised optimization algorithm, as depicted in Fig. 4. Given a parameterized human body and an articulated object point cloud, we compute penetration depths between the human and object point clouds. Subsequently, we utilize the transpose of the linear-blend-skinning weights of SMPL-X to aggregate the maximum penetration depth and direction to the human skeleton joints. This information is then employed to calculate a target skeleton that mitigates the penetration. Finally, we employ a gradient-based optimization technique to adjust the human model to the new skeleton while maintaining proximity to the MoCap reconstruction. This process reduced the average penetration depth in CHAIRS from 3.5 cm to 2.6 cm, with an average contact value of 0.2 cm.
+
+Ensuring data quality Following data alignment and penetration removal, the Chamfer distances between annotations and observations in CHAIRS are measured at  $2.8\mathrm{cm}$  for objects and  $1.9\mathrm{cm}$  for humans. This level of quality is comparable to a recent dataset [2], which reports Chamfer distances of  $2.4\mathrm{cm}$  and  $1.8\mathrm{cm}$ , respectively.
+
+Privacy protection To safeguard identities, we apply face blurring [34] to all participant faces. Furthermore, we informed all participants that they retain the right to have their data removed from CHAIRS at any time.
+
+# 4. Articulated Object Pose Estimation
+
+CHAIRS offers extensive potential for various AHOI tasks, including detection, motion generation, physics-based analysis, and even language-guided motion generation with additional annotations. We highlight the value of CHAIRS by focusing on the task of articulated object pose estimation. Despite recent advancements in articulated object pose estimation [58, 11, 14, 68] and HOI reconstruction [5, 46, 69, 54], the challenge of articulated object pose estimation in the context of f-AHOI remains largely unaddressed. This specific context demands accurate object pose estimation in
+
+scenarios involving heavy occlusion and dense contact.
+
+# 4.1. Task Definition
+
+Given an observed image  $I$ , the parameterized human model  $H = (\beta, \theta_b, \theta_h, R_b, T_b)$ , and the meshes  $X = \{X_i, i = 1, \dots, N\}$  representing the interacting object with  $N$  parts, our task involves estimating the object pose  $O = \{(R_i, T_i), i = 0, \dots, N\}$ . Here,  $\beta \in \mathbb{R}^{10}$ ,  $\theta_b \in \mathbb{R}^{21 \times 6}$ ,  $\theta_h \in \mathbb{R}^{30 \times 6}$ ,  $R_b \in \mathbb{R}^6$ , and  $T_b \in \mathbb{R}^3$  represent the shape and pose parameters of the SMPL-X [38] model. Specifically,  $(R_0 \in \mathbb{R}^6, T_0 \in \mathbb{R}^3)$  corresponds to the root pose of the object, while  $\{(R_i \in \mathbb{R}^6, T_i \in \mathbb{R}^3)\}$  denotes the global rotation and translation for each part  $X_i$ . The orthogonal 6D representation [70] is used for representing rotations in both human and object poses.
+
+# 4.2. Model Architecture
+
+Our approach for object pose estimation is rooted in an interaction-aware framework that harnesses the fine-grained geometric relationships present in HOIs, along with learned interaction priors. This approach comprises two key stages. Given an image and estimated SMPL-X [38] parameters, we first estimate object occupancy grids and root poses using a reconstruction model. Subsequently, we fine-tune the reconstructed human-object pair using a learned interaction prior. The overall framework of our model is illustrated in Fig. 5, while Fig. 6 showcases the interaction prior model.
+
+![](images/d9d598602cf4d7f4f1619d266cf34aa666f09abb7cedf13babce7c4cafbb4387.jpg)  
+Figure 6: Illustration of the interaction prior model. The interaction prior model, realized as a cVAE, generates object voxels based on conditioning information from human voxels. During optimization, we aim to minimize the norm of the latent code.
+
+# 4.3. Object Reconstruction and Pose Initialization
+
+Given an observation  $I$ , we estimate human pose and shape using an off-the-shelf estimator. These estimated human shapes  $H^{\prime}$  are then voxelized into four resolutions with Kaolin [23]. To better exploit the geometric relationship between human-object pairs, we guide the estimation of object shape and pose using human pose. Specifically, we begin by extracting ResNet-101 [18] features from the image and subsequently estimate object voxels based on these image features using a 3D decoder. This decoder comprises three 3DConvT layers, along with upsampling layers at distinct resolutions, and two additional 1x1 3DConv layers. Furthermore, we fuse the convolutional feature grids with human voxels at each resolution, amplifying the influence of human pose. The final 3DConv layer generates the estimated object occupancy grid  $\mathcal{V}_O^{\prime}$ . Additionally, we concatenate image features extracted from ResNet-101 with SMPL-X parameters, and employ an additional MLP to regress the root pose  $(R_0^{\prime}, T_0^{\prime})$  of the object. This root pose also serves as the initialization for the optimization process.
+
+To train the reconstruction model, we first initialize the human shape estimator with pre-trained weights from the PARE model [38], followed by fine-tuning using the CHAIRS. Subsequently, we fix the weights of the PARE model and proceed to train the reconstruction model, utilizing the object pose estimation loss  $\mathcal{L}^{\mathcal{O}}$ . This loss is characterized by the L1 loss computed on object voxels.
+
+# 4.4. Interaction Prior
+
+To capture the nuanced relationship between humans and interacting objects, we introduce an interaction prior model based on a cVAE. This model learns the conditional distribution of object occupancy given the human shape.
+
+In this context, the cVAE prior model conditions on a multi-resolution voxelized human, with the objective of reconstructing a voxelized object. The architecture employs 3DConvNets as both encoder and decoder components. During training, we feed the voxelized object into the encoder to acquire object features at multiple scales. These object features are then combined with the multi-resolution human voxels corresponding to each layer. An MLP estimates the latent Gaussian distribution  $\mathcal{N}(\mu, \sigma)$ , which is used to parameterize the latent code  $z$  through re-parameterization. This latent code is subsequently decoded using the decoder. The feature grids at each decoder layer are concatenated with the corresponding human voxel condition.
+
+Training the prior model occurs on CHAIRS and involves four distinct loss components:
+
+$$
+\mathcal {L} _ {\mathrm {P}} = \mathcal {L} _ {\text {r e c o n}} + \mathcal {L} _ {\mathrm {K L}} + \mathcal {L} _ {\text {p e n e}} + \mathcal {L} _ {\text {c o n t r a}}, \tag {1}
+$$
+
+where  $\mathcal{L}_{\mathrm{recon}}$  and  $\mathcal{L}_{\mathrm{KL}}$  denote the standard reconstruction and KL divergence losses, respectively.  $\mathcal{L}_{\mathrm{pene}}$  constitutes a
+
+penetration loss, penalizing voxel grids occupied by both humans and objects.  $\mathcal{L}_{\mathrm{contra}}$  serves to maximize the distance of latent variables between original and augmented noisy data. Augmentation of training data involves introducing random noise to a portion of the samples.
+
+# 4.5. Pose Optimization with Interaction Prior
+
+To reconstruct the intricate human-object relationship and refine the object poses, we employ an optimization stage that builds upon initialized poses, utilizing kinematic insights and the interaction prior. This process involves the object's CAD model, Unified Robot Description Format (URDF), estimated SMPL-X parameters  $H^{\prime}$ , and object voxels  $\mathcal{V}_O^\prime$  from the reconstruction model. We initiate the object model  $\hat{O}$  using estimated root transformations and random part states. We iteratively update  $\hat{O}$ 's parameters by minimizing the combined objective  $\mathcal{J}_{\mathrm{recon}} + \mathcal{J}_{\mathrm{z}}$ :
+
+$$
+\mathcal {J} _ {\text {r e c o n}} = \left\| V (\hat {O}) - \mathcal {V} _ {O} ^ {\prime} \right\| _ {2}, \quad \mathcal {J} _ {\mathrm {z}} = \left\| \operatorname {E n c} \left(H ^ {\prime}, \hat {O}\right) \right\|, \tag {2}
+$$
+
+where  $V(\cdot)$  is the voxelization function.  $\mathcal{I}_{\mathrm{recon}}$  measures the voxelized object model's distance from the estimated object voxels.  $\mathcal{I}_{\mathrm{z}}$  enforces a small norm for the latent predicted by the cVAE encoder, regulating proximity to the interaction prior. The process of pose optimization with interaction prior is illustrated in Fig. 7.
+
+![](images/38df2e80767be93985be38da9dacb67983751fb1ae6977d91b004c12a778c42d.jpg)  
+Figure 7: An illustration of pose estimation with interaction prior. Starting with the reconstruction output, we optimize the object according to the reconstructed voxel and interaction prior.
+
+Object pose optimization Optimized parameters include the root 6D pose  $R, T$  of the object and joint parameters  $\Phi$  (if applicable), controlling part rotation and shift under kinematic constraints. For joints (except the root), we consider revolute, prismatic, or combined revolute-prismatic configurations. The latter, such as the joint linking a chair's base and seat, restricts rotation and shift along the same axis.
+
+During optimization, we initiate the root pose  $R, T$  using the estimated root 6D pose from the object pose estimation model. All joint parameters  $\Phi$  are set to zero. Optimization involves minimizing the reconstruction loss  $\mathcal{I}_{\mathrm{recon}}$  and interaction prior loss  $\mathcal{I}_{\mathrm{z}}$  through gradient descent. Calculating losses necessitates determining object part occupancy postapplication of  $R, T,$  and  $\Phi$  for each optimization step. As direct voxelization lacks differentiability regarding object
+
+parameters  $R, T$  and  $\Phi$ , we employ trilinear interpolation on the affine  $(0,1)$  voxel grid to resample voxel occupancy. This permits gradient flow for root and joint parameter updates. Post-optimization, parameters yield an updated 3D object model and enhanced representation (e.g., mesh) with reduced geometric error.
+
+Contrastive loss We intend our interaction prior to grasp a comprehensive human-object interaction distribution through a conditional Gaussian model. Reasonable and common spatial relationships between human and object latent codes should cluster near the Gaussian mean, in contrast to unreasonable ones. A contrastive loss aids training of the interaction prior model alongside penetration, reconstruction, and KL-divergence losses. Positive examples  $(H,\mathcal{V}_O)$  involve an observed human  $H$  and object voxel  $\nu_{O}$ . Corresponding negative examples  $(H,\mathcal{V}_O^{\prime})$  are generated by perturbing the object, adding noise to root and articulated poses, and voxelizing  $\nu_{O}^{\prime}$ . The contrastive loss  $\mathcal{L}_{\mathrm{contra}}$ , defined as  $\mathcal{L}_{\mathrm{contra}} = \max (0,||\mathrm{Enc}(\mathcal{V}_O,H)|| - ||\mathrm{Enc}(\mathcal{V}_O^{\prime},H)||)$ , guides latent codes of perturbed human-object pairs away from the distribution centroid. Here, Enc represents the conditional encoder of our proposed cVAE-based prior model.
+
+# 5. Experiments
+
+Experimental settings We split CHAIRS into training, testing, and validation sets;  $70\%$  of objects are used for training,  $20\%$  for testing, and the remaining for validation. We evaluate our model under two settings: with  $(w / opt)$  and without optimization  $(w / o$  opt). In the  $w / opt.$  setting, we report the chamfer distance between objects posed with ground truth and estimated transformation parameters. In the  $w / o$  opt. setting, we do not have the estimated transformation parameters. Thus, we report the chamfer distance between the ground-truth object mesh and the mesh obtained by running the marching cube algorithm on the reconstructed voxels.
+
+Evaluation metrics We evaluate object pose estimation using mean rotation and translation errors for each object part. Object shape reconstruction is evaluated with chamfer distance and intersection over union (IoU). For reconstructed f-AHOI, we assess penetration depth and contact scores between the human and object. Penetration depth is the maximum depth of the object's surface within the human's body, while contact value is the shortest distance between the human and object. Contact values are clipped to [0,20cm] for distant human-object pairs.
+
+Baseline methods We compare articulated object pose estimation with LASR [59] and ANCSH [28] as baselines, where we use depth maps as input for ANCSH. Both methods are fine-tuned on CHAIRS. Additionally, we compare our model with D3D-HOI [58], PHOSA [65], and CHORE [56] that jointly estimate human and object poses. We adapted D3D-HOI's optimization objectives to better fit CHAIRS's data distribution.
+
+# 5.1. Results and Analyses
+
+Quantitative results are presented in Tab. 2. Our model, leveraging geometrical relationships, exhibits substantial improvements in pose estimation and shape reconstruction compared to existing methods. In the w/o opt. setting where the object is unknown, our model surpasses the state-of-the-art LASR method by a significant margin. While D3D-HOI and ANCSH excel, they assume known object structures. Remarkably, our model outperforms all baselines when provided with the object structure in the w/ opt. setting.
+
+Table 2: Comparisons against existing methods.  $\ast$  : method requires knowledge of object structure and/or geometry;  $\dagger$  : method does not rely on object-related knowledge.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Object</td><td colspan="2">HOI</td></tr><tr><td>Rot.↓(°)</td><td>Transl.↓(mm)</td><td>CD↓(mm)</td><td>IoU↑(%)</td><td>Pene.↓(mm)</td><td>Cont.↓(mm)</td></tr><tr><td>LASR†[59]</td><td>/</td><td>/</td><td>205.2</td><td>/</td><td>/</td><td>/</td></tr><tr><td>Ours (w/o opt.)†</td><td>/</td><td>/</td><td>160.2</td><td>11.03</td><td>4.530</td><td>2.720</td></tr><tr><td>ANCSH* [28]</td><td>/</td><td>/</td><td>90.36</td><td>/</td><td>/</td><td>/</td></tr><tr><td>PHOSA* [65]</td><td>29.31</td><td>175.2</td><td>177.9</td><td>7.60</td><td>2.046</td><td>1.689</td></tr><tr><td>D3D-HOI* [58]</td><td>27.31</td><td>119.2</td><td>126.9</td><td>16.60</td><td>7.472</td><td>1.163</td></tr><tr><td>CHORE* [56]</td><td>21.82</td><td>87.58</td><td>95.40</td><td>16.44</td><td>1.050</td><td>1.742</td></tr><tr><td>Ours (w/ opt.)*</td><td>19.35</td><td>66.23</td><td>72.30</td><td>21.57</td><td>1.143</td><td>1.562</td></tr></table>
+
+We present qualitative results in Fig. 8, where columns (a)-(h) illustrate the reconstruction outcomes on the test set. In these columns, we display the reconstructed meshes prior to optimization using the marching cubes algorithm. It is evident from the visualizations that our model successfully produces plausible and accurate interaction representations even before the optimization process. Notably, the optimization step enhances the finer interaction details.
+
+# 5.2. Ablations
+
+We conduct three ablation studies to assess the efficacy of our model's design choices. Quantitative results of these ablation studies are presented in Tab. 3.
+
+Table 3: Ablation of interaction, prior, and contrastive loss.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Object</td><td colspan="2">HOI</td></tr><tr><td>Rot.↓(°)</td><td>Transl.↓(mm)</td><td>CD↓(mm)</td><td>IoU↑(%)</td><td>Pene.↓(mm)</td><td>Cont.↓(mm)</td></tr><tr><td>Full†</td><td>/</td><td>/</td><td>160.2</td><td>11.03</td><td>4.530</td><td>2.720</td></tr><tr><td>-prior†</td><td>/</td><td>/</td><td>165.3</td><td>10.52</td><td>4.377</td><td>3.295</td></tr><tr><td>Full*</td><td>19.35</td><td>66.23</td><td>72.30</td><td>21.57</td><td>1.143</td><td>1.562</td></tr><tr><td>-prior*</td><td>19.97</td><td>83.39</td><td>87.90</td><td>18.81</td><td>1.749</td><td>2.081</td></tr><tr><td>-contr.*</td><td>21.52</td><td>81.90</td><td>87.28</td><td>18.93</td><td>1.265</td><td>2.393</td></tr><tr><td>-inter.*</td><td>17.88</td><td>69.53</td><td>78.12</td><td>19.50</td><td>1.022</td><td>2.320</td></tr></table>
+
+Prior We conduct an experiment where we remove the interaction prior model and solely optimize object poses by minimizing  $\mathcal{L}_{\mathrm{recon}}$ . In both * and † settings, we observe a substantial performance drop. This underscores the critical role played by the interaction prior in accurately estimating
+
+![](images/e0c3921a6470b8125cc08482296d5f9e02a1088ed3a0c2e668098388f8c8a26a.jpg)  
+Figure 8: Qualitative results. (a)-(h) Test set results. (i)-(p) Wild images results. RGB images, optimized poses, and mesh obtained by running marching cubes on reconstructed voxels are shown. Please refer to Fig. A6 in Supplementary Materials for more qualitative results.
+
+object poses. It is important to note that both settings involve an optimization step, and the primary distinction is that the * model possesses access to the object's geometry and structure during optimization. When the prior model is omitted in the † setting, we observe a decrease in penetration and a larger increase in contact value. This observation suggests that our interaction prior model exerts influence by pulling the object closer to the human when they are not in contact.
+
+Contrast In this ablation, we exclude the contrastive loss  $\mathcal{L}_{\mathrm{contra}}$  from the training of the prior model. The results are analogous to those of the -prior experiment. This outcome underscores the crucial role that the contrastive loss plays in facilitating the learning of a robust interaction prior.
+
+Interaction We proceed to remove the concatenation of human voxels in the 3DConv layers of both the reconstruction model and the interaction prior model. This removal eliminates the interaction awareness in our model. We observe a modest degradation across all object reconstruction metrics, underscoring the importance of interaction aware
+
+ness in our approach. Interestingly, the removal of interaction awareness leads to increased contact values and decreased penetration, resembling the outcomes of the -prior ablation in the w/o opt. setting. This suggests that interaction awareness also contributes to bringing the human and object into closer proximity. Lastly, we note an unexpected low rotation error, which we attribute to the presence of rotation symmetries in the dataset.
+
+Additionally, we assess our method's performance under varying qualities of human pose estimation in Tab. 4. The results reveal notable improvement in object pose estimation as human poses become more accurate, thus validating our initial hypothesis. Notably, the pose estimation model [27] effectively predicts most challenging poses accurately, leaving the avenue of leveraging interactions to enhance human pose estimation as a potential future research direction.
+
+In summary, our analysis highlights the substantial contributions of all three model components to object pose and shape reconstruction.
+
+Table 4: Ablation of human pose estimation quality. GT denotes using ground-truth human poses to optimize the object poses, No prior denotes not considering human-object interaction prior.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Human</td><td colspan="2">Object</td></tr><tr><td>MPJPE↓(mm)</td><td>PA-MPJPE↓(mm)</td><td>CD↓(mm)</td><td>IOU↑(%)</td></tr><tr><td>No prior</td><td>/</td><td>/</td><td>87.90</td><td>18.81</td></tr><tr><td>PARE [27]</td><td>81.09</td><td>47.19</td><td>73.79</td><td>21.66</td></tr><tr><td>PARE(finetune)</td><td>74.50</td><td>43.99</td><td>72.30</td><td>21.57</td></tr><tr><td>GT</td><td>0</td><td>0</td><td>65.50</td><td>23.16</td></tr></table>
+
+![](images/91ff32ea7cc9acde770ecc0044ce1b0a7d7f6e4a45b60e27460cb8355826ca22.jpg)  
+Figure 9: Failure cases. In situations involving rotation-symmetrical objects, our model encounters challenges with estimating rotation while maintaining a relatively low visual error.
+
+![](images/04b5233809e556da0989a800ed839cfc4cea5957c8a6e4dd28055914d3c84e8c.jpg)
+
+![](images/05074b2a2a57ab6d34ac04a4f87aed75bd0cabb7ed5ca8377a7e96f61c69201c.jpg)
+
+In-the-wild generalization We also assess the model's generalizability on a limited set of internet images. As depicted in Fig. 8 (i-p), the qualitative results illustrate that our model successfully generalizes its capabilities to images captured outside of controlled laboratory settings.
+
+Failure cases Our model encounters challenges in accurately estimating the orientation of object parts when those parts exhibit geometric similarity under specific rotations. Rotation symmetry is commonly observed in spherical and cylindrical object components, such as the base of a stool or a round seat. An illustrative example of this symmetry is presented in Fig. 9. Notably, existing methods [10, 49] address this challenge through (i) accepting multiple equally-valid ground truths and (ii) employing a min-of-N loss to calculate the smallest distance to any of these ground truths. However, implementing such methods necessitates a meticulous classification of symmetry types for each object.
+
+Furthermore, we observe that our model's performance diminishes in scenarios where no f-AHOI is present, such as instances where a human is situated far away from an object like a chair. Under these circumstances, our model is unable to leverage interactions to enhance object pose estimation.
+
+# 6. Application: Generating Interacting Humans
+
+We further investigate the intricate relationships within AHOI by exploring the generation of interacting human poses in the presence of articulated objects. To this end, we employ a 3D conditional diffusion model known as SceneDiffuser [22], trained on our CHAIRS. To evaluate the quality of the generated poses, we compare them with poses generated using the same model trained on COUCH [67], a recent dataset featuring humans seated on rigid chairs. We use the feature extracted from the point cloud of the ob
+
+![](images/1060fbd5894fb2bbbdcdfb6c51565cc4bef6ba545c8b76be9abe3f69ecd31733.jpg)  
+Figure 10: Generated human poses given articulated objects. The models are trained on CHAIRS (a, b) and COUCH [67] (c, d).
+
+ject via Pointnet++ as a conditioning input and flatten the SMPL-X parameters of the human to form tokens for input to a Transformer. The implementation details closely follow those of the human pose generation task described in Huang et al. [22]. Qualitative comparisons of the generated human poses are shown in Fig. 10. Notably, the model trained with CHAIRS captures more nuanced and natural geometrical relationships when interacting with articulated objects. For a more in-depth analysis of this downstream application, we direct readers to the Appx. B in Supplementary Materials.
+
+# 7. Conclusion
+
+We advance the study of HOI to encompass fine-grained, articulated interactions with (i) CHAIRS, an extensive dataset, (ii) a challenging object reconstruction problem under f-AHOI, and (iii) a strong baseline. Our CHAIRS captures diverse, natural AHOIs involving various sittable objects. The object reconstruction problem confronts kinematic assumptions, with our model effectively leveraging intricate interactions to resolve ambiguities.
+
+Limitations One limitation of our work lies in the fact that the parametric human model used in CHAIRS does not account for clothing, leading to misalignments between the 3D annotations and the images. Consequently, the usage of pixel-aligned features may be compromised.
+
+Acknowledgment The authors would like to thank four anonymous reviews for constructive feedback and NVIDIA for their generous support of GPUs and hardware. This work is supported in part by the National Key R&D Program of China (2022ZD0114900) and the Beijing Nova Program.
+
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+[70] Yi Zhou, Connelly Barnes, Jingwan Lu, Jimei Yang, and Hao Li. On the continuity of rotation representations in neural networks. In Conference on Computer Vision and Pattern Recognition (CVPR), 2019. 5
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+                                            "html": "<table><tr><td>Dataset</td><td># object</td><td># participants</td><td># instructions</td><td># hours</td><td>fps</td><td># view</td><td>articulated objects</td><td>human</td><td>annotation type</td></tr><tr><td>GRAB [46]</td><td>51</td><td>10</td><td>4</td><td>3.8</td><td>120</td><td>0</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>D3D-HOI [58]</td><td>24</td><td>5</td><td>/</td><td>0.6</td><td>3</td><td>1</td><td>Yes</td><td>Whole-body</td><td>manual</td></tr><tr><td>BEHAVE [2]</td><td>20</td><td>8</td><td>6</td><td>4.2</td><td>30</td><td>4</td><td>No</td><td>Whole-body</td><td>multi-kinect</td></tr><tr><td>ARCTIC [11]</td><td>10</td><td>9</td><td>1</td><td>1.2</td><td>30</td><td>8+1</td><td>Yes</td><td>Two hands</td><td>mocap</td></tr><tr><td>COUCH [67]</td><td>4</td><td>6</td><td>6</td><td>3</td><td>60</td><td>4</td><td>No</td><td>Whole-body</td><td>mocap</td></tr><tr><td>CHAIRS (Ours)</td><td>81</td><td>46</td><td>32</td><td>17.3</td><td>30</td><td>4</td><td>Yes</td><td>Whole-body</td><td>mocap</td></tr></table>",
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+                                    "content": "Interaction (f-AHOI). This endeavor mandates tackling two pivotal dimensions: (i) fashioning kinematic-agnostic representations for articulated objects and (ii) delving into the intricate spatial-temporal tapestry interweaving objects with human whole-bodies. Our primary focus resides in addressing the intricate task of object pose estimation within the realm of f-AHOI, considering that reconstructing 3D human poses from frontal viewpoints is comparably uncomplicated."
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+                                    "type": "text",
+                                    "content": "The crux of object pose estimation within the context of f-AHOI is punctuated by three principal challenges:"
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+                                    "content": "The dearth of comprehensive f-AHOI datasets Existing strides in 3D HOI predominantly either assume interactions with rigid objects or confine themselves to involving specific segments of the human anatomy [2, 46, 65, 29, 67, 11, 58, 14]. Regrettably, these assumptions drastically over-simplify genuine human interactions that span diverse body parts engaging with articulated objects embodying moveable elements such as cabinets and office chairs. A more intricate level of interaction necessitates a richer dataset."
+                                }
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+                                    "content": "The multifaceted landscape of object kinematic structures Objects constituting the realm of f-AHOI exhibit notable disparities in their kinematic frameworks, even when categorized under the same umbrella. Prevailing methodologies often lean towards uniform structures [58, 32, 11, 14], thereby disregarding the diverse tapestry that constitutes real-world scenarios. The endeavor of accurately reconstructing objects manifesting divergent geometries and structures is plagued with its own set of challenges."
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+                                    "content": "The intricacies of complex interactions Engaging with articulated objects entails grappling with intricate spatial and physical relationships, often entailing occlusions and intricate points of contact. The intricacy of these dynamics thrusts conventional pose estimation mechanisms reliant on point cloud template-matching [65, 49, 19, 39, 28] into the realm of insufficiency. The prominence of contacts further compounds the endeavor of precise reconstruction, as slight inaccuracies can swiftly usher implausible interactions into the picture."
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+                                    "content": "The trajectory of this research endeavors to navigate the above three challenges through the prism of three principal solutions, respectively:"
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+                                    "content": "To confront the scarcity of f-AHOI datasets, we introduce CHAIRS, a multi-view RGB-D dataset. Illustrated in Fig. 1,"
+                                }
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+                                    "content": "CHAIRS chronicles a diverse tapestry of interactions, seamlessly intertwining 46 participants with 81 sittable objects (e.g., chairs, sofas, stools, and benches). 28 of these objects are endowed with moveable parts. Each frame encapsulates 3D meshes of both human whole-bodies and objects, casting a spotlight on interactions with sittable objects that encompass a diverse spectrum of structures and distinctive movable elements conducive to multifarious human interactions."
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+                                    "content": "To traverse the labyrinth of kinematic diversity, CHAIRS meticulously selects representative objects characterized by an eclectic array of structures. Unlike traditional datasets and methodologies tethered to uniform kinematics [55, 51, 32], we champion real-world heterogeneity, encompassing the gamut from rigid stools to swivel chairs boasting up to 7 movable components. Each component is linked to its parent through a nexus of revolute, prismatic, or composite joints."
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+                                    "type": "text",
+                                    "content": "To unravel the enigma of complex interactions, we proffer an innovative approach to articulated object pose estimation, one that harnesses the subtle interplay of fine-grained interaction relationships to reconstruct the object in question. This approach diverges from the conventional recourse of manually labeling contact maps corresponding to human body parts [65, 16, 2]. Instead, our approach melds the intricacies of these relationships with a reconstruction model and an interaction prior, the latter of which is imbued with the essence of a conditional Variational Auto-Encoder (cVAE). This evolution sidesteps the need for predefined knowledge grounded in laborious annotation. Moreover, the significance of these intricate relationships is showcased through our venture into learning human poses within the ambit of articulated objects. By juxtaposing the generative prowess harnessed from CHAIRS with that stemming from a dataset centered on rigid objects [67], we underscore the pivotal role played by the nuanced geometrical relationships encapsulated within CHAIRS in the broader canvas of downstream tasks."
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+                                    "content": "Our contributions are four-fold: (i) CHAIRS, a sprawling multi-view RGB-D repository infused with diverse 3D meshes. (ii) The seamless extension of articulated object pose estimation to the arduous landscape of f-AHOI. (iii) An object pose estimation approach that transcends the strictures of structure. (iv) An overarching interaction prior that captures the subtleties of fine-grained interactions, acting as a catalyst for the journey of pose estimation."
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+                                            "content": "(a) sequences of objects articulating over time"
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+                                            "content": "(b) frames of diverse interactions"
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+                                            "content": "Figure 2: Samples from the CHAIRS dataset. CHAIRS encompasses diverse AHOIs captured through precisely calibrated multi-view RGB-D cameras, offering detailed 3D meshes of human participants and articulated objects. The figure showcases (a) RGB frames alongside corresponding ground-truth mesh sequences and (b) an array of varied AHOI instances."
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+                                    "content": "2. Related Work"
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+                                    "type": "text",
+                                    "content": "3D Human-Object Interaction (HOI) The evolution of HOI research spans from 2D image-based interaction detection [4, 40, 13, 30, 31, 64, 62, 22] to 3D interaction reconstruction [43, 16, 5, 53, 58, 63, 66] and generation [17, 50, 57, 21, 52, 67] within 3D scenes. Notably, PiGraph [43] and D3D-HOI [16, 58] capture daily activities and reconstruct interactions, often relying on visual observations. In contrast, MoCap systems [46, 2, 11, 67] offer fine-grained 3D human-object interactions. GRAB [46] and ARCTIC [11] emphasize interactions with small objects, while BEHAVE [2] and COUCH [67] involve interactions with everyday objects. However, these works often focus on rigid objects or hand-object interactions with articulated objects. In contrast, our CHAIRS dataset captures realistic whole-body interactions with diverse articulated objects."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Articulated Human-Object Interaction Articulated Human-Object Interactions (AHOIs) build on part-level object representations, modeling intricate spatial-temporal interactions between humans and articulated objects [14]. Noteworthy contributions include D3D-HOI [58], ARCTIC [11], and 3DADN [41]. D3D-HOI [58] captures humans interacting with containers, ARCTIC [11] focuses on motion-captured RGB-D hand-object interactions, and 3DADN [41] annotates movable object parts from internet videos. However, these works often emphasize hand-object interactions, whereas our focus extends to AHOIs encompassing diverse articulated objects and multiple body parts."
+                                }
+                            ]
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+                                    "content": "Contact-Rich HOI The realm of f-AHOI requires a deeper HOI understanding. While 3D HOI literature has expanded, few works address full-body contacts through reconstruction [16] or generation [69, 52, 15, 67]. However, these works often focus on static scenes with limited interactions. In contrast, our CHAIRS dataset encompasses diverse"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "articulated objects and interactions."
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+                                    "type": "text",
+                                    "content": "Articulated Object Pose Estimation The estimation of 6-DOF poses for rigid objects has garnered attention [25, 19, 3, 48, 39, 37, 9]. Template-based methods [20, 60, 49, 26] and regression models [1] are common, with recent strides in articulated object pose estimation [8, 33, 28] leveraging these techniques. Regression and implicit function models [36, 47, 59, 24] are also explored. Despite progress, these methods often assume consistent kinematic structures within object categories. In contrast, our CHAIRS dataset features diverse kinematic structures and models capable of handling various parts and kinematics of 3D objects."
+                                }
+                            ]
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+                                    "content": "3. The CHAIRS Dataset"
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+                                    "content": "A significant challenge in modeling AHOIs is the lack of accurate 3D annotations. To address this gap, we introduce CHAIRS, a comprehensive AHOI dataset featuring multi-view RGB-D sequences. CHAIRS offers precise 3D meshes of humans and articulated objects during interactions, captured through a hybrid motion capture (MoCap) system that combines inertial and optical tracking techniques. The data collection process prioritizes realism and physical authenticity, resulting in a dataset that significantly advances interaction understanding. A detailed comparison between CHAIRS and previous HOI datasets is outlined in Tab. 1."
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+                                    "content": "Overview CHAIRS encompasses a total of 1390 sequences depicting articulated interactions involving humans and sittable objects like chairs, sofas, stools, and benches. Exemplary sequences from CHAIRS and a showcase of the object variety can be seen in Fig. 2. Each object's exploration involves 6 distinct participants, each contributing three interaction sequences, resulting in 18 sequences for each object."
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+                                    "content": "In every sequence, participants execute 6 diverse actions drawn randomly from a pool of 32 interactions, such as shifting a stool, reclining on a sofa, or rotating a chair; please refer to the Supplementary Material Appx. C.1 for further details. Participant instructions were kept deliberately high-level to ensure authentic and natural performances."
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+                                    "content": "Object diversity The object gallery in CHAIRS boasts an array of objects, each possessing a range of appearances and kinematic structures. Objects were curated by sourcing them online, with a focus on maximizing stylistic diversity. Notably, 28 objects incorporate at least one articulated joint, contributing to rich interaction scenarios. The 3D meshes of these objects were captured using the Scaniverse app on an iPad Pro (11-inch, 2nd generation) and subsequently refined manually to eliminate any imperfections. The 3D meshes were further segmented using the annotation tool [35] into eight functional parts. Participants received context-specific instructions tailored to the object they were interacting with."
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+                                    "type": "text",
+                                    "content": "Camera and hardware setup As depicted in Fig. 3, all sequences were exclusively captured in a controlled laboratory setup, encompassing a designated area of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "5\\mathrm{m}\\times 4\\mathrm{m}"
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+                                    "type": "text",
+                                    "content": " ensuring complete visibility of all actions for the cameras. Four Kinect Azure DK cameras, strategically positioned to capture front-facing multi-view perspectives, were employed to record the interactions. These cameras were meticulously calibrated and synchronized. To ensure the precision of ground-truth poses for both humans and objects, a commercial inertial-optical hybrid MoCap system was incorporated alongside the Kinect setup; for further specifics, see the subsequent section."
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+                                    "content": "3.2. Motion Capture (MoCap) System"
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+                                    "content": "Hybrid MoCap Our MoCap system is composed of a MoCap suit outfitted with 5 hybrid trackers and 17 wearable Inertial Measurement Units (IMUs), alongside a pair of gloves equipped with 12 IMUs each. The setup further includes supplementary hybrid trackers and a collection of 8 high-speed cameras. A hybrid tracker, which encompasses 4 optical markers and an IMU, is capable of accurately mea"
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+                                    "content": "suring its own 6D pose even in conditions of substantial occlusion. The arrangement of our data collection setup is illustrated in Fig. 3. For capturing the pose of a human or an object part, either an IMU or a hybrid tracker can be utilized to record the global orientation or 6D pose, respectively."
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+                                    "content": "Capturing articulated object poses The recording process of articulated object poses in the context of interactions unfolds across three phases. First, we position the object into its canonical pose and affix a hybrid tracker to each of its movable components. Subsequently, we calculate the relative transformation between the object part and the trackers. During the recording process, the real-time ground-truth 6D pose of each object part is computed based on the tracker poses. Finally, we match the rigid parts to the kinematic structure of the object to yield high-fidelity object poses."
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+                                    "content": "Capturing human body poses For human poses and shapes, we adopt the SMPL-X [38] representation. Participants are attired in a MoCap suit incorporating 17 IMUs, don a pair of MoCap gloves, and have 5 hybrid trackers affixed to their heads, hands, and feet. It is noteworthy that while hybrid trackers capture 6D poses, IMUs solely measure global orientations. The optimization of human model shape parameters is undertaken to ensure that the reconstructed SMPL-X mesh aligns with the positions of the hybrid trackers. As a result, the MoCap system delivers real-time estimated human poses and shapes during recording."
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+                                    "content": "Data alignment Due to the disparate 3D coordinates and temporal clocks of Kinect cameras and the MoCap system, alignment becomes crucial. This alignment is achieved by correlating the 3D coordinates of Kinect sequences with MoCap reconstructions through plane-to-plane correspondences [44], a technique that mitigates the influence of outliers, disturbances, and partial overlaps. For the synchronization of temporal sequences from Kinect and MoCap, time-lagged cross-correlation [45] is applied, a common approach for aligning two sequences with relative time shifts."
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+                                            "content": "Figure 4: Illustration of the penetration removal process. In panels (a) and (d), the small purple points represent human vertices devoid of penetration, while the larger colored points indicate instances of penetration. The red points symbolize the most pronounced penetration, whereas the blue points signify minimal contact. Panels (b) and (c) feature yellow lines that depict the original skeleton configuration, red markers denoting the target joints undergoing optimization, and red lines illustrating the resultant optimized skeleton configuration."
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+                                            "content": "(b) original skeleton"
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+                                            "type": "text",
+                                            "content": "Figure 5: Model architecture. The reconstruction model leverages the predicted voxelized representation of the human to facilitate the estimation of pose for the interacting object. We undertake root 6D pose regression for the object utilizing the image feature in conjunction with SMPL-X parameters. The predictions along with an interaction prior are harnessed for the refinement of the final estimated pose."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "Penetration removal Owing to the limited sensor count and discrepancies in limb lengths, unrealistic contacts and penetrations persist in captured 3D interactions. To address this issue, we rectify these physical anomalies with a carefully devised optimization algorithm, as depicted in Fig. 4. Given a parameterized human body and an articulated object point cloud, we compute penetration depths between the human and object point clouds. Subsequently, we utilize the transpose of the linear-blend-skinning weights of SMPL-X to aggregate the maximum penetration depth and direction to the human skeleton joints. This information is then employed to calculate a target skeleton that mitigates the penetration. Finally, we employ a gradient-based optimization technique to adjust the human model to the new skeleton while maintaining proximity to the MoCap reconstruction. This process reduced the average penetration depth in CHAIRS from 3.5 cm to 2.6 cm, with an average contact value of 0.2 cm."
+                                }
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+                                    "type": "text",
+                                    "content": "Ensuring data quality Following data alignment and penetration removal, the Chamfer distances between annotations and observations in CHAIRS are measured at "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        463,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2.8\\mathrm{cm}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " for objects and "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                        532
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1.9\\mathrm{cm}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                        532
+                                    ],
+                                    "type": "text",
+                                    "content": " for humans. This level of quality is comparable to a recent dataset [2], which reports Chamfer distances of "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        463,
+                                        279,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "2.4\\mathrm{cm}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        463,
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+                                        532
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "1.8\\mathrm{cm}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                        532
+                                    ],
+                                    "type": "text",
+                                    "content": ", respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                        533,
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+                        580
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Privacy protection To safeguard identities, we apply face blurring [34] to all participant faces. Furthermore, we informed all participants that they retain the right to have their data removed from CHAIRS at any time."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4. Articulated Object Pose Estimation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "type": "text",
+                                    "content": "CHAIRS offers extensive potential for various AHOI tasks, including detection, motion generation, physics-based analysis, and even language-guided motion generation with additional annotations. We highlight the value of CHAIRS by focusing on the task of articulated object pose estimation. Despite recent advancements in articulated object pose estimation [58, 11, 14, 68] and HOI reconstruction [5, 46, 69, 54], the challenge of articulated object pose estimation in the context of f-AHOI remains largely unaddressed. This specific context demands accurate object pose estimation in"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "scenarios involving heavy occlusion and dense contact."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Task Definition"
+                                }
+                            ]
+                        }
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+                },
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+                                    "type": "text",
+                                    "content": "Given an observed image "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "I"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", the parameterized human model "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "H = (\\beta, \\theta_b, \\theta_h, R_b, T_b)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and the meshes "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X = \\{X_i, i = 1, \\dots, N\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
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+                                    ],
+                                    "type": "text",
+                                    "content": " representing the interacting object with "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "N"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": " parts, our task involves estimating the object pose "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "O = \\{(R_i, T_i), i = 0, \\dots, N\\}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Here, "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\beta \\in \\mathbb{R}^{10}"
+                                },
+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta_b \\in \\mathbb{R}^{21 \\times 6}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\theta_h \\in \\mathbb{R}^{30 \\times 6}"
+                                },
+                                {
+                                    "bbox": [
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+                                        301,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R_b \\in \\mathbb{R}^6"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
+                                        531,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
+                                        531,
+                                        442
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "T_b \\in \\mathbb{R}^3"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
+                                        531,
+                                        442
+                                    ],
+                                    "type": "text",
+                                    "content": " represent the shape and pose parameters of the SMPL-X [38] model. Specifically, "
+                                },
+                                {
+                                    "bbox": [
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+                                        301,
+                                        531,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(R_0 \\in \\mathbb{R}^6, T_0 \\in \\mathbb{R}^3)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
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+                                    ],
+                                    "type": "text",
+                                    "content": " corresponds to the root pose of the object, while "
+                                },
+                                {
+                                    "bbox": [
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+                                        301,
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+                                        442
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{(R_i \\in \\mathbb{R}^6, T_i \\in \\mathbb{R}^3)\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
+                                        531,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the global rotation and translation for each part "
+                                },
+                                {
+                                    "bbox": [
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+                                        301,
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+                                        442
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "X_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        301,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". The orthogonal 6D representation [70] is used for representing rotations in both human and object poses."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. Model Architecture"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Our approach for object pose estimation is rooted in an interaction-aware framework that harnesses the fine-grained geometric relationships present in HOIs, along with learned interaction priors. This approach comprises two key stages. Given an image and estimated SMPL-X [38] parameters, we first estimate object occupancy grids and root poses using a reconstruction model. Subsequently, we fine-tune the reconstructed human-object pair using a learned interaction prior. The overall framework of our model is illustrated in Fig. 5, while Fig. 6 showcases the interaction prior model."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                            "type": "text",
+                                            "content": "Figure 6: Illustration of the interaction prior model. The interaction prior model, realized as a cVAE, generates object voxels based on conditioning information from human voxels. During optimization, we aim to minimize the norm of the latent code."
+                                        }
+                                    ]
+                                }
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+                                    "content": "4.3. Object Reconstruction and Pose Initialization"
+                                }
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+                                    "type": "text",
+                                    "content": "Given an observation "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "I"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we estimate human pose and shape using an off-the-shelf estimator. These estimated human shapes "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        123,
+                                        281,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are then voxelized into four resolutions with Kaolin [23]. To better exploit the geometric relationship between human-object pairs, we guide the estimation of object shape and pose using human pose. Specifically, we begin by extracting ResNet-101 [18] features from the image and subsequently estimate object voxels based on these image features using a 3D decoder. This decoder comprises three 3DConvT layers, along with upsampling layers at distinct resolutions, and two additional 1x1 3DConv layers. Furthermore, we fuse the convolutional feature grids with human voxels at each resolution, amplifying the influence of human pose. The final 3DConv layer generates the estimated object occupancy grid "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        123,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}_O^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        123,
+                                        281,
+                                        345
+                                    ],
+                                    "type": "text",
+                                    "content": ". Additionally, we concatenate image features extracted from ResNet-101 with SMPL-X parameters, and employ an additional MLP to regress the root pose "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        123,
+                                        281,
+                                        345
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(R_0^{\\prime}, T_0^{\\prime})"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        123,
+                                        281,
+                                        345
+                                    ],
+                                    "type": "text",
+                                    "content": " of the object. This root pose also serves as the initialization for the optimization process."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
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+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "To train the reconstruction model, we first initialize the human shape estimator with pre-trained weights from the PARE model [38], followed by fine-tuning using the CHAIRS. Subsequently, we fix the weights of the PARE model and proceed to train the reconstruction model, utilizing the object pose estimation loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}^{\\mathcal{O}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". This loss is characterized by the L1 loss computed on object voxels."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "4.4. Interaction Prior"
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+                                    "type": "text",
+                                    "content": "To capture the nuanced relationship between humans and interacting objects, we introduce an interaction prior model based on a cVAE. This model learns the conditional distribution of object occupancy given the human shape."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "In this context, the cVAE prior model conditions on a multi-resolution voxelized human, with the objective of reconstructing a voxelized object. The architecture employs 3DConvNets as both encoder and decoder components. During training, we feed the voxelized object into the encoder to acquire object features at multiple scales. These object features are then combined with the multi-resolution human voxels corresponding to each layer. An MLP estimates the latent Gaussian distribution "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(\\mu, \\sigma)"
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+                                {
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which is used to parameterize the latent code "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "z"
+                                },
+                                {
+                                    "bbox": [
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+                                        500,
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+                                    ],
+                                    "type": "text",
+                                    "content": " through re-parameterization. This latent code is subsequently decoded using the decoder. The feature grids at each decoder layer are concatenated with the corresponding human voxel condition."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "Training the prior model occurs on CHAIRS and involves four distinct loss components:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {P}} = \\mathcal {L} _ {\\text {r e c o n}} + \\mathcal {L} _ {\\mathrm {K L}} + \\mathcal {L} _ {\\text {p e n e}} + \\mathcal {L} _ {\\text {c o n t r a}}, \\tag {1}",
+                                    "image_path": "6bcd8743ed8f57833fa236d356c512d948820aa74149922479ab594742403026.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{recon}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{KL}}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        706,
+                                        279,
+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": " denote the standard reconstruction and KL divergence losses, respectively. "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        706,
+                                        279,
+                                        730
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{pene}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " constitutes a"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "penetration loss, penalizing voxel grids occupied by both humans and objects. "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{contra}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " serves to maximize the distance of latent variables between original and augmented noisy data. Augmentation of training data involves introducing random noise to a portion of the samples."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.5. Pose Optimization with Interaction Prior"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "To reconstruct the intricate human-object relationship and refine the object poses, we employ an optimization stage that builds upon initialized poses, utilizing kinematic insights and the interaction prior. This process involves the object's CAD model, Unified Robot Description Format (URDF), estimated SMPL-X parameters "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", and object voxels "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}_O^\\prime"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": " from the reconstruction model. We initiate the object model "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{O}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": " using estimated root transformations and random part states. We iteratively update "
+                                },
+                                {
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+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{O}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        191,
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+                                    ],
+                                    "type": "text",
+                                    "content": "'s parameters by minimizing the combined objective "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        191,
+                                        531,
+                                        308
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{J}_{\\mathrm{recon}} + \\mathcal{J}_{\\mathrm{z}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ":"
+                                }
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {J} _ {\\text {r e c o n}} = \\left\\| V (\\hat {O}) - \\mathcal {V} _ {O} ^ {\\prime} \\right\\| _ {2}, \\quad \\mathcal {J} _ {\\mathrm {z}} = \\left\\| \\operatorname {E n c} \\left(H ^ {\\prime}, \\hat {O}\\right) \\right\\|, \\tag {2}",
+                                    "image_path": "dd9ca675602505c24261ab5e8e55876835af1da8ff3e2bfd36743b7d5c6ce6fd.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "V(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the voxelization function. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}_{\\mathrm{recon}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " measures the voxelized object model's distance from the estimated object voxels. "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}_{\\mathrm{z}}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        339,
+                                        531,
+                                        410
+                                    ],
+                                    "type": "text",
+                                    "content": " enforces a small norm for the latent predicted by the cVAE encoder, regulating proximity to the interaction prior. The process of pose optimization with interaction prior is illustrated in Fig. 7."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "type": "image",
+                    "bbox": [
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+                                    ]
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+                            ],
+                            "index": 14,
+                            "angle": 0,
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+                        },
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+                                            "type": "text",
+                                            "content": "Figure 7: An illustration of pose estimation with interaction prior. Starting with the reconstruction output, we optimize the object according to the reconstructed voxel and interaction prior."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 15,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Object pose optimization Optimized parameters include the root 6D pose "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        554,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "R, T"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the object and joint parameters "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " (if applicable), controlling part rotation and shift under kinematic constraints. For joints (except the root), we consider revolute, prismatic, or combined revolute-prismatic configurations. The latter, such as the joint linking a chair's base and seat, restricts rotation and shift along the same axis."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
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+                                    "type": "text",
+                                    "content": "During optimization, we initiate the root pose "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " using the estimated root 6D pose from the object pose estimation model. All joint parameters "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\Phi"
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+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": " are set to zero. Optimization involves minimizing the reconstruction loss "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}_{\\mathrm{recon}}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and interaction prior loss "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{I}_{\\mathrm{z}}"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " through gradient descent. Calculating losses necessitates determining object part occupancy postapplication of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "R, T,"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "\\Phi"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " for each optimization step. As direct voxelization lacks differentiability regarding object"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                }
+            ],
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+        {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
+                                        45,
+                                        106,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", we employ trilinear interpolation on the affine "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        106,
+                                        280,
+                                        175
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(0,1)"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " voxel grid to resample voxel occupancy. This permits gradient flow for root and joint parameter updates. Post-optimization, parameters yield an updated 3D object model and enhanced representation (e.g., mesh) with reduced geometric error."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
+                    "bbox": [
+                        45,
+                        175,
+                        282,
+                        362
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Contrastive loss We intend our interaction prior to grasp a comprehensive human-object interaction distribution through a conditional Gaussian model. Reasonable and common spatial relationships between human and object latent codes should cluster near the Gaussian mean, in contrast to unreasonable ones. A contrastive loss aids training of the interaction prior model alongside penetration, reconstruction, and KL-divergence losses. Positive examples "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(H,\\mathcal{V}_O)"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": " involve an observed human "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": " and object voxel "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nu_{O}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": ". Corresponding negative examples "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(H,\\mathcal{V}_O^{\\prime})"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": " are generated by perturbing the object, adding noise to root and articulated poses, and voxelizing "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\nu_{O}^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": ". The contrastive loss "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{contra}}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": ", defined as "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{contra}} = \\max (0,||\\mathrm{Enc}(\\mathcal{V}_O,H)|| - ||\\mathrm{Enc}(\\mathcal{V}_O^{\\prime},H)||)"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        175,
+                                        282,
+                                        362
+                                    ],
+                                    "type": "text",
+                                    "content": ", guides latent codes of perturbed human-object pairs away from the distribution centroid. Here, Enc represents the conditional encoder of our proposed cVAE-based prior model."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
+                    "bbox": [
+                        46,
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+                        124,
+                        385
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "5. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
+                        45,
+                        392,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Experimental settings We split CHAIRS into training, testing, and validation sets; "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "70\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " of objects are used for training, "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "20\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " for testing, and the remaining for validation. We evaluate our model under two settings: with "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(w / opt)"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " and without optimization "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(w / o"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " opt). In the "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w / opt."
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " setting, we report the chamfer distance between objects posed with ground truth and estimated transformation parameters. In the "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "w / o"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        392,
+                                        280,
+                                        521
+                                    ],
+                                    "type": "text",
+                                    "content": " opt. setting, we do not have the estimated transformation parameters. Thus, we report the chamfer distance between the ground-truth object mesh and the mesh obtained by running the marching cube algorithm on the reconstructed voxels."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
+                        45,
+                        521,
+                        280,
+                        636
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                45,
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+                            ],
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+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Evaluation metrics We evaluate object pose estimation using mean rotation and translation errors for each object part. Object shape reconstruction is evaluated with chamfer distance and intersection over union (IoU). For reconstructed f-AHOI, we assess penetration depth and contact scores between the human and object. Penetration depth is the maximum depth of the object's surface within the human's body, while contact value is the shortest distance between the human and object. Contact values are clipped to [0,20cm] for distant human-object pairs."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
+                        45,
+                        637,
+                        280,
+                        729
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                45,
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+                            ],
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+                                {
+                                    "bbox": [
+                                        45,
+                                        637,
+                                        280,
+                                        729
+                                    ],
+                                    "type": "text",
+                                    "content": "Baseline methods We compare articulated object pose estimation with LASR [59] and ANCSH [28] as baselines, where we use depth maps as input for ANCSH. Both methods are fine-tuned on CHAIRS. Additionally, we compare our model with D3D-HOI [58], PHOSA [65], and CHORE [56] that jointly estimate human and object poses. We adapted D3D-HOI's optimization objectives to better fit CHAIRS's data distribution."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        296,
+                        106,
+                        416,
+                        118
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "5.1. Results and Analyses"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
+                        296,
+                        123,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
+                                        296,
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+                                        229
+                                    ],
+                                    "type": "text",
+                                    "content": "Quantitative results are presented in Tab. 2. Our model, leveraging geometrical relationships, exhibits substantial improvements in pose estimation and shape reconstruction compared to existing methods. In the w/o opt. setting where the object is unknown, our model surpasses the state-of-the-art LASR method by a significant margin. While D3D-HOI and ANCSH excel, they assume known object structures. Remarkably, our model outperforms all baselines when provided with the object structure in the w/ opt. setting."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "type": "table",
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+                                            "content": " : method does not rely on object-related knowledge."
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+                                    "content": "We present qualitative results in Fig. 8, where columns (a)-(h) illustrate the reconstruction outcomes on the test set. In these columns, we display the reconstructed meshes prior to optimization using the marching cubes algorithm. It is evident from the visualizations that our model successfully produces plausible and accurate interaction representations even before the optimization process. Notably, the optimization step enhances the finer interaction details."
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+                                    "content": "5.2. Ablations"
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+                                    "content": "We conduct three ablation studies to assess the efficacy of our model's design choices. Quantitative results of these ablation studies are presented in Tab. 3."
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+                                            "content": "Table 3: Ablation of interaction, prior, and contrastive loss."
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+                                    "content": "Prior We conduct an experiment where we remove the interaction prior model and solely optimize object poses by minimizing "
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+                                    "content": ". In both * and † settings, we observe a substantial performance drop. This underscores the critical role played by the interaction prior in accurately estimating"
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+                                            "content": "Figure 8: Qualitative results. (a)-(h) Test set results. (i)-(p) Wild images results. RGB images, optimized poses, and mesh obtained by running marching cubes on reconstructed voxels are shown. Please refer to Fig. A6 in Supplementary Materials for more qualitative results."
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+                                    "content": "object poses. It is important to note that both settings involve an optimization step, and the primary distinction is that the * model possesses access to the object's geometry and structure during optimization. When the prior model is omitted in the † setting, we observe a decrease in penetration and a larger increase in contact value. This observation suggests that our interaction prior model exerts influence by pulling the object closer to the human when they are not in contact."
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+                                    "content": " from the training of the prior model. The results are analogous to those of the -prior experiment. This outcome underscores the crucial role that the contrastive loss plays in facilitating the learning of a robust interaction prior."
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+                                    "content": "Interaction We proceed to remove the concatenation of human voxels in the 3DConv layers of both the reconstruction model and the interaction prior model. This removal eliminates the interaction awareness in our model. We observe a modest degradation across all object reconstruction metrics, underscoring the importance of interaction aware"
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+                                    "content": "ness in our approach. Interestingly, the removal of interaction awareness leads to increased contact values and decreased penetration, resembling the outcomes of the -prior ablation in the w/o opt. setting. This suggests that interaction awareness also contributes to bringing the human and object into closer proximity. Lastly, we note an unexpected low rotation error, which we attribute to the presence of rotation symmetries in the dataset."
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+                                    "content": "Additionally, we assess our method's performance under varying qualities of human pose estimation in Tab. 4. The results reveal notable improvement in object pose estimation as human poses become more accurate, thus validating our initial hypothesis. Notably, the pose estimation model [27] effectively predicts most challenging poses accurately, leaving the avenue of leveraging interactions to enhance human pose estimation as a potential future research direction."
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+                                            "content": "Figure 9: Failure cases. In situations involving rotation-symmetrical objects, our model encounters challenges with estimating rotation while maintaining a relatively low visual error."
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+                                    "type": "text",
+                                    "content": "In-the-wild generalization We also assess the model's generalizability on a limited set of internet images. As depicted in Fig. 8 (i-p), the qualitative results illustrate that our model successfully generalizes its capabilities to images captured outside of controlled laboratory settings."
+                                }
+                            ]
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+                                    "content": "Failure cases Our model encounters challenges in accurately estimating the orientation of object parts when those parts exhibit geometric similarity under specific rotations. Rotation symmetry is commonly observed in spherical and cylindrical object components, such as the base of a stool or a round seat. An illustrative example of this symmetry is presented in Fig. 9. Notably, existing methods [10, 49] address this challenge through (i) accepting multiple equally-valid ground truths and (ii) employing a min-of-N loss to calculate the smallest distance to any of these ground truths. However, implementing such methods necessitates a meticulous classification of symmetry types for each object."
+                                }
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+                                    "type": "text",
+                                    "content": "Furthermore, we observe that our model's performance diminishes in scenarios where no f-AHOI is present, such as instances where a human is situated far away from an object like a chair. Under these circumstances, our model is unable to leverage interactions to enhance object pose estimation."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "6. Application: Generating Interacting Humans"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We further investigate the intricate relationships within AHOI by exploring the generation of interacting human poses in the presence of articulated objects. To this end, we employ a 3D conditional diffusion model known as SceneDiffuser [22], trained on our CHAIRS. To evaluate the quality of the generated poses, we compare them with poses generated using the same model trained on COUCH [67], a recent dataset featuring humans seated on rigid chairs. We use the feature extracted from the point cloud of the ob"
+                                }
+                            ]
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+                                        }
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+                                            "type": "text",
+                                            "content": "Figure 10: Generated human poses given articulated objects. The models are trained on CHAIRS (a, b) and COUCH [67] (c, d)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12,
+                            "angle": 0,
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+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "lines": [
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+                                    "type": "text",
+                                    "content": "ject via Pointnet++ as a conditioning input and flatten the SMPL-X parameters of the human to form tokens for input to a Transformer. The implementation details closely follow those of the human pose generation task described in Huang et al. [22]. Qualitative comparisons of the generated human poses are shown in Fig. 10. Notably, the model trained with CHAIRS captures more nuanced and natural geometrical relationships when interacting with articulated objects. For a more in-depth analysis of this downstream application, we direct readers to the Appx. B in Supplementary Materials."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "7. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We advance the study of HOI to encompass fine-grained, articulated interactions with (i) CHAIRS, an extensive dataset, (ii) a challenging object reconstruction problem under f-AHOI, and (iii) a strong baseline. Our CHAIRS captures diverse, natural AHOIs involving various sittable objects. The object reconstruction problem confronts kinematic assumptions, with our model effectively leveraging intricate interactions to resolve ambiguities."
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "Limitations One limitation of our work lies in the fact that the parametric human model used in CHAIRS does not account for clothing, leading to misalignments between the 3D annotations and the images. Consequently, the usage of pixel-aligned features may be compromised."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Acknowledgment The authors would like to thank four anonymous reviews for constructive feedback and NVIDIA for their generous support of GPUs and hardware. This work is supported in part by the National Key R&D Program of China (2022ZD0114900) and the Beijing Nova Program."
+                                }
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+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                        {
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+                                            "type": "text",
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+                                        }
+                                    ]
+                                }
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+                                            "content": "with semantic control. In European Conference on Computer Vision (ECCV), 2022. 3, 5"
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+                                        }
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diff --git a/2023/Fully Attentional Networks with Self-emerging Token Labeling/caf0e66c-9593-4110-bbb4-fe33ef9d0d27_content_list.json b/2023/Fully Attentional Networks with Self-emerging Token Labeling/caf0e66c-9593-4110-bbb4-fe33ef9d0d27_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..281aa118a8896fcf2bb3e44204176b4e2b5c1ec8
--- /dev/null
+++ b/2023/Fully Attentional Networks with Self-emerging Token Labeling/caf0e66c-9593-4110-bbb4-fe33ef9d0d27_content_list.json	
@@ -0,0 +1,1600 @@
+[
+    {
+        "type": "text",
+        "text": "Fully Attentional Networks with Self-emerging Token Labeling",
+        "text_level": 1,
+        "bbox": [
+            166,
+            130,
+            803,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Bingyin Zhao $^{1,2*}$  Zhiding Yu $^{1\\dagger}$  Shiyi Lan $^{1}$  Yutao Cheng $^{3}$  Anima Anandkumar $^{1,4}$  Yingjie Lao $^{2}$  Jose M. Alvarez $^{1}$ $^{1}$ NVIDIA  $^{2}$ Clemson University  $^{3}$ Fudan University  $^{4}$ Caltech",
+        "bbox": [
+            147,
+            178,
+            790,
+            234
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            268,
+            313,
+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent studies indicate that Vision Transformers (ViTs) are robust against out-of-distribution scenarios. In particular, the Fully Attentional Network (FAN) - a family of ViT backbones, has achieved state-of-the-art robustness. In this paper, we revisit the FAN models and improve their pretraining with a self-emerging token labeling (STL) framework. Our method contains a two-stage training framework. Specifically, we first train a FAN token labeler (FANTL) to generate semantically meaningful patch token labels, followed by a FAN student model training stage that uses both the token labels and the original class label. With the proposed STL framework, our best model based on FAN-L-Hybrid (77.3M parameters) achieves  $84.8\\%$  Top-1 accuracy and  $42.1\\%$  mCE on ImageNet-1K and ImageNet-C, and sets a new state-of-the-art for ImageNet-A  $(46.1\\%)$  and ImageNet-R  $(56.6\\%)$  without using extra data, outperforming the original FAN counterpart by significant margins. The proposed framework also demonstrates significantly enhanced performance on downstream tasks such as semantic segmentation, with up to  $1.7\\%$  improvement in robustness over the counterpart model.",
+        "bbox": [
+            75,
+            300,
+            473,
+            618
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            645,
+            209,
+            660
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Vision Transformers (ViTs) [1] have recently achieved remarkable success in visual recognition tasks. Such success is not only attributed to their self-attention representation but also to the newly developed training recipes. For instance, refinements in training techniques such as strong data augmentation and knowledge distillation [2] greatly alleviate ViT's issue of being data-hungry and make them more accessible for training on ImageNet-1K.",
+        "bbox": [
+            75,
+            670,
+            468,
+            791
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Another important development in the training recipe is token labeling [3], where patch tokens are assigned with labels to ViTs in a dense manner. In some sense, token labeling can also be considered as an alternative form of hard knowledge distillation. However, the dense nature of token",
+        "bbox": [
+            75,
+            791,
+            468,
+            867
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/5c7db0808a168a11f724e603a0d6b293484de2d644d8dd9279340ce971952861.jpg",
+        "image_caption": [
+            "Figure 1. Results of zero-shot robustness against ImageNet-A and ImageNet-R. Models trained on ImageNet-1K with self-emerging token labels from FAN show superior robustness to the out-of-distribution data. Our best model (with only 77.3M parameters) achieves robust accuracy of  $46.1\\%$  and  $56.6\\%$  and sets a new record on ImageNet-A and ImageNet-R."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            268,
+            893,
+            474
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "labeling allows ViTs to leverage more fine-grained information in an image and take different categories and object localization into account. Compared to traditional knowledge distillation methods, token labeling enables ViTs to exploit a wider range of information in the image, leading to more accurate results. The success of token labeling depends on carefully-designed token-level annotators (i.e., token-labelers) that can provide accurate location-specific information (i.e., token labels) to patch tokens. In [3], this is done by a special re-labeling process [4] using convolutional neural networks (CNNs) [5] pre-trained on ImageNet-1K. While Vision Transformers have shown great promise in representation learning, less exploration has been conducted on modeling them as token-labelers. This raises two interesting questions:",
+        "bbox": [
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+            588,
+            890,
+            815
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. Can Transformer-based models self-produce meaningful token labels?",
+            "2. Can one improve the pre-training of ViTs with self-produced knowledge instead of external teachers?"
+        ],
+        "bbox": [
+            511,
+            827,
+            888,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Work done during an internship at NVIDIA.",
+        "bbox": [
+            94,
+            875,
+            336,
+            887
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author.",
+        "bbox": [
+            96,
+            887,
+            222,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "5585",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Our approach: In this paper, we aim to answer the above questions. We propose a self-emerging token labeling (STL) framework that employs the self-produced token labels by ViT token-labelers instead of relying on CNNs. Our work is built on the recently proposed Fully Attentional Network (FAN) [6] for two reasons. First, FAN exhibits excellent self-emerging visual grouping on token features, which can be leveraged to generate high-quality token labels. Second, FAN is a family of ViT backbones with state-of-the-art accuracy and robustness. We aim to further improve this family of powerful backbones through a principled token-labeling design and validate its effectiveness. Our contributions can be summarized as follows:",
+        "bbox": [
+            76,
+            90,
+            472,
+            287
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Our work demonstrates that ViT models can be effective token-labelers. We propose a simple yet effective way to train a FAN token-labeler that can produce semantically meaningful token labels.",
+            "- We perform an in-depth analysis and show critical contributors to the accuracy of token labels. On top of the observations, we design a solution that retains more accurate token labels of the target object for improved model pre-training.",
+            "- Our models trained with STL set a new record on out-of-distribution datasets without using extra data than ImageNet-1K. Our best model achieves robust accuracy of  $46.1\\%$  on ImageNet-A and  $56.6\\%$  on ImageNet-R with only 77M parameters, as shown in Fig. 1.",
+            "- Experiments on downstream tasks demonstrate that the improved performance in backbone models is transferable to semantic segmentation and object detection."
+        ],
+        "bbox": [
+            84,
+            304,
+            468,
+            622
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our STL framework is akin to the teacher-student training strategy introduced in knowledge distillation and consists of two stages:",
+        "bbox": [
+            76,
+            638,
+            468,
+            684
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "First stage: We train a FAN token-labeler (FAN-TL) model to generate token-level annotations. Our task is essentially a \"chicken or the egg\" problem since there is no explicit supervision on how the token labels are generated. We tackle this by assigning supervising both the class token and the global average-pooled token. This produces semantically meaningful token labels as shown in Fig. 2(b).",
+        "bbox": [
+            76,
+            686,
+            467,
+            792
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Second stage: We train a FAN student model using the original class labels and the token labels from FAN-TL. Observing the imperfect quality of token labels, we introduce a token selection approach based on Gumbel-Softmax that adaptively selects tokens with high confidence. Labels of the selected tokens are of better quality and object grounding in general, leading to improved pre-training.",
+        "bbox": [
+            76,
+            795,
+            467,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Vision Transformers",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Vision Transformers [1] are a family of visual recognition models built upon Transformers [7]. ViT splits an input image into a series of small patches, projects each as an embedding (a.k.a patch token) and appends with position embeddings. The resulting patch tokens and an extra learnable class token that aggregates global information for classification are then fed into a sequence of Transformer encoders consisting of multi-head self-attention and FFN blocks. A linear projection layer is appended to the class token to predict the class probabilities.",
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+    },
+    {
+        "type": "text",
+        "text": "2.2. Fully Attentional Networks",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Several concurrent works point out that ViTs exhibit excellent zero-shot robustness against out-of-distribution samples [8-11]. Some works propose to use negative data augmentation [12] and adversarial training [13, 14] to further enhance the robustness. Recently, FAN [15] was introduced as a family of ViT backbones with state-of-the-art accuracy and robustness. FAN inherits the self-attention blocks of plain ViT but additionally introduces a channel attention block that adopts an attention-based design that aggregates the cross-channel information in a more holistic manner, leading to improved representation.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3. Token Labeling",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Token labeling [3] has been proposed to improve ViT pre-training. From the perspective of training strategy, it is similar to knowledge distillation [2, 16] since both adopt a teacher-student mode. It is also related to ReLabel [17], which provides images with multi-label annotations instead of single ones. However, both ReLabel and knowledge distillation depend on image-level labels as global supervision while token labeling assigns labels to each image patch token and supervises the student model in a dense manner. Token labeling is also inherently related to tokenization in BEiT [18], where an offline pre-trained discrete VAE is employed as the tokenizer to encode patches into visual tokens (i.e., code from a visual codebook). Different from token labels, these visual tokens do not possess explicit semantically meanings since they originate from an unsupervisedly trained codebook. Our method differs from prior token labeling and distillation methods where pre-trained convolutional neural networks are widely used as the token-labeler. Instead, our approach to unifies both teacher and student under homogeneous Vision Transformer architectures to generate high-quality token labels.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.4. Emerging Properties of ViTs",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "It was found that the localization of objects emerges in image classification with CNNs. This interesting phe",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "5586",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "nomenon, also known as class activation maps (CAM) [19], lays the foundation for token labeling. Recent studies reveal that ViTs demonstrate excellent capability for object localization without explicit supervision. For instance, DINO [20] shows that self-supervised ViT features generate semantically meaning object segmentation. Methods like GroupViT [21] show that semantic segmentation emerges in ViTs using only text supervision. Similarly, FAN reveals that the robustness of ViT models is correlated to their excellent visual grouping capability. This feature motivates us to develop self-emerging token labeling on top of the FAN models.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As mentioned, we propose a self-emerging token labeling (STL) framework that uses self-produced token labels to improve ViT pre-training. STL consists of two stages: 1) training an effective token-labeler, and 2) training a student model with self-emerging token labels.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In the first stage, we train a FAN token-labeler (FANTL) to generate high-quality token labels. As discussed in Sec. 1 and Sec. 2, FAN demonstrates strong robustness and capability to obtain semantically meaningful visual grouping that can correctly captures the object gestalt. These great features of FAN allow us to obtain high quality token labels without bells and whistles. In the second stage, we then train a FAN student model with image-level labels and self-emerging token labels from FAN-TL. At high level, FAN-TL and FAN student models follow the same architectural design as FAN but slightly modify the structure of patch tokens. We attach a linear layer to each patch token to accommodate token labels, similar to the classification head added to the class token in the original FAN and ViT design. The rest of this section describes the implementation details of the above two-stage pipeline.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Training FAN Token-Labelers",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The original FAN employs the training paradigm that only takes image-level labels as supervision. We denote the input image as  $\\mathbf{I}$ , the sequence of small patches as  $[\\mathbf{I}_{p_1},\\mathbf{I}_{p_2},\\dots,\\mathbf{I}_{p_N}]$ , the output of FAN encoder as  $[\\mathbf{T}_{cls},\\mathbf{T}_{p_1},\\dots,\\mathbf{T}_{p_N}]$ , where  $N$  is the number of patch tokens,  $\\mathbf{T}_{cls}$  represents the class token and  $\\mathbf{T}_{p_1},\\ldots ,\\mathbf{T}_{p_N}$  represent the patch tokens, respectively. The training objective can be mathematically expressed as follows:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {\\text {c l s}}, \\mathbf {Y} _ {\\text {c l s}}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            796,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{H}(\\cdot)$  is the softmax cross entropy loss and  $\\mathbf{Y}_{cls}$  is the image-level label of the corresponding class.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The key to token labeling is the generation of accurate token labels that provide location-specific information. However, following the conventional training paradigm in Eq. 1,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/5acfb3a88d6092486a2439f1fa745c74ccd032688d50993a463e0081a350f250.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of token labels generated by FAN-TL and the token label confidence score distribution. (a). original image (class: \"tench\"), (b). binary color map of token labels (yellow: tokens classified as \"tench\", dark blue: tokens not classified as \"tench\") (c). trinary color map of token labels (cyan: foreground tokens with low confidence, yellow: foreground tokens with high confidence), (d). binary color map of foreground tokens selected by Gumbel-Softmax, (e). token label confidence score distribution of a batch of 16 images."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "token outputs of FAN models are not semantically well-guided since they are not supervised during training. We propose a simple yet effective method to address this issue. Our idea is inspired by the intriguing phenomenon in ViTs training that meaningful object segmentation naturally emerges [20]. Unlike the self-supervised training in DINO, we leverage FAN's strong capability of visual grouping [22] and devise a fully supervised approach that allows FAN to generate accurate and semantically meaningful token labels. We perform global average-pooling on all patch tokens and then simultaneously assign the class label to the class and the average-pooled tokens. The training objective of FANTL can be written as follows:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}\\right) + \\alpha \\cdot \\mathcal {H} \\left(\\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathbf {T} _ {p _ {i}}, \\mathbf {Y} _ {c l s}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            700,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha$  weights the importance of two loss functions. We set  $\\alpha$  to 1 in our experiments. We demonstrate a visualization example of the token labels generated by FAN-TL in Fig. 2(b). The yellow area (i.e., foreground) represents the tokens with the same labels as the image-level label (we term foreground tokens). In contrast, the dark blue area (i.e., background) represents the tokens with different labels from the image-level label (we term background tokens). It can be seen that the self-emerging token labels show a meaningful segmentation of the target object \"tench\".",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "5587",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/fa4d7bb38a6a0c341d102274f8ff604d43adb13f1c820cfafc521fb70b77988f.jpg",
+        "image_caption": [
+            "Generate token labels using FAN-TL"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            103,
+            468,
+            344
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c955b6954053e9af7e7b61ec22320d1560766cb1c2577bfd699d28a711ab7117.jpg",
+        "image_caption": [
+            "Train the student model with self-emerging token labeling",
+            "Figure 3. Illustration of Stage 2: Training student models with self-emerging token labels. In the training, token labels are generated by FAN-TL and assigned to patch tokens of student models. We incorporate the token labels and class labels to train student models jointly. FAN-TL can self-identify the incorrect token labels upon the confidence score. Tokens with high confidence scores offer a more accurate segmentation of objects and are crucial to robustness improvement. By applying spatial-only data augmentation to the inputs and Gumbel-Softmax to the token outputs of FAN-TL, we obtain the most accurate and critical token labels."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Training Student Models with STL",
+        "text_level": 1,
+        "bbox": [
+            75,
+            443,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Training student models is straightforward. As illustrated in Fig. 3, we take the token outputs of FAN-TL and assign them as the labels for patch tokens of student models. We then incorporate token labels with class labels and jointly optimize the loss on the class token and all patch tokens. The training objective is shown as follows:",
+        "bbox": [
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+            467,
+            468,
+            556
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}\\right) + \\beta \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {H} \\left(\\mathbf {T} _ {p _ {i}}, \\mathcal {F} \\left(\\mathbf {I} _ {p _ {i}}\\right)\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            561,
+            468,
+            603
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{F}(\\cdot)$  represents the patch token outputs of FAN-TL and  $\\beta$  is the hyper-parameter to balance two loss functions.  $\\beta$  is set to 1 in our experiments. Note the correctness of token labels (especially the foreground tokens) is critical since wrong labels introduce worthless local information. Thus, we propose several implementation tricks to generate and retain highly accurate token labels based on the following two observations.",
+        "bbox": [
+            75,
+            613,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Observation 1: Data augmentations remarkably affect the accuracy of token labels. Recent studies [2, 23] indicate data augmentations improve the classification accuracy and robustness of ViT models. However, most augmentations undermine the accuracy of token labels. For example, augmentations in RandAug [24], such as posterize and solarize, alter pixel values, CutOut [25] randomly erases a part of images, Mixup [26] and CutMix [27] mix content from two images, which all make it difficult for FAN-TL to assign correct labels to patch tokens. To this end, we disable these data augmentations and keep spatial-",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/46200e18aee196d139b1d4fd36d3979a09107c73bdfbbc2f66b1496ffd789fa5.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1. Detailed settings of data augmentations. We apply spatial-only data augmentations to inputs of FAN-TL in stage 2 to improve the accuracy of token labels."
+        ],
+        "table_body": "<table><tr><td>Model (Stage)</td><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td></tr><tr><td>FAN-TL (Stage1)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Student (Stage2)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FAN-TL (Stage2)</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td></tr></table>",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "only ones (i.e., flip, rotate, shear and translation) for FANTL when generating token labels. Note that we still apply full data augmentations for the student model. The concrete settings of data augmentations are summarized in Table 1. Moreover, the strong data augmentations can be regarded as noises akin to corruptions and perturbations in out-of-distribution datasets. The input data augmentation discrepancy between FANT-LT and the student model enables the self-emerging token labels to provide clean and correct information regardless of the noise, thus improving the model's robustness.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Observation 2: Not all the self-emerging token labels are correct, even with spatial-only data augmentations. For example, as shown in Fig. 2(b), some patches (red squares) that only contain \"human\" and \"lake\" are misclassified as the target object \"tench\" by FAN-TL. It is particularly crucial to ensure the accuracy of foreground token labels as they contain the target object of the image that dominates the prediction result. However, it is challenging to determine which labels are incorrect due to the lack of patch-level ground truth. Interestingly, FAN-TL can",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5588",
+        "bbox": [
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+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "self-identify these misclassified foreground tokens according to the token label confidence score, which may also be attributed to its visual grouping ability. The token label confidence score is defined as the maximal class probability of each token output. We find that tokens with correct labels tend to have higher confidence scores than those with incorrect labels. As shown in Fig. 2(c) and Fig. 2(e), the yellow area indicates the foreground tokens with high confidence scores  $(0.7\\sim 0.9)$ . These tokens yield a highly accurate segmentation of the target object. Contrastly, the cyan area represents the foreground tokens with low confidence scores  $(0\\sim 0.2)$ , which are coincidentally the ones with incorrect labels.",
+        "bbox": [
+            75,
+            90,
+            472,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We attempt to assign highly accurate labels to the target object (i.e., foreground tokens). However, it is intractable to exhaustively examine the confidence score of each patch token for all the images as it significantly increases the training time and requires much more computational resources. Therefore, we propose a lightweight alternative by applying the Gumbel-Softmax [28] on the top of token outputs. Mathematically, it can be expressed as:",
+        "bbox": [
+            75,
+            287,
+            472,
+            409
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {y} _ {i} = \\frac {e ^ {\\left(\\log \\left(\\pi_ {i}\\right) + \\mathcal {G} _ {i}\\right) / \\tau}\\left. \\right)}{\\sum_ {j = 1} ^ {k} e ^ {\\left(\\log \\left(\\pi_ {j}\\right) + \\mathcal {G} _ {j}\\right) / \\tau})} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            174,
+            417,
+            468,
+            457
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{y}$  is the  $k$ -dimension softmax vector,  $\\pi$  are class probabilities,  $\\mathcal{G} \\sim Gumbel(0,1)$  are i.i.d. samples drawn from the standard Gumbel distribution and  $\\tau$  is the softmax temperature. Token labels with high confidence scores remain unchanged after applying Gumbel-Softmax, while labels with low confidence scores are highly likely to change. As shown in Fig. 2(d), we preserve the correct token labels and eliminate the incorrect ones in a simple yet effective way, achieving high accuracy of foreground tokens labels and more precise segmentation of the object. Furthermore, since the training objective of the patch tokens side can be considered a self-training process [29-31], we convert the softmax outputs to \"one-hot\" probability distribution (i.e., hard labels) as [32] shows that the use of hard labels in self-training encourages the model's predictions to be high-confidence via entropy minimization [33]. Following the aforementioned spatial-only data augmentation, we can then rewrite the training objective of the student model:",
+        "bbox": [
+            75,
+            465,
+            472,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {H} (\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}) + \\beta \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {H} (\\mathbf {T} _ {p _ {i}}, \\hat {\\mathcal {F}} (\\hat {\\mathbf {I}} _ {p _ {i}})) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            753,
+            468,
+            796
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\hat{\\mathcal{F}} (\\cdot)$  is the one-hot encoded Gumbel-Softmax outputs of FAN-TL and  $[\\hat{\\mathbf{I}}_{p_1}\\dots \\hat{\\mathbf{I}}_{p_N}]$  are image patches with the spatial-only data augmentation. Meanwhile, we notice that all background tokens (i.e., the dark blue area) also have low confidence scores. This is probably because these tokens neither contain apparent features associated with the",
+        "bbox": [
+            75,
+            806,
+            472,
+            902
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "target object nor clear features related to any other class in the dataset. Nevertheless, we keep all tokens (even those with low confidence scores) in training, following the practice in [3] as involving more tokens for loss computation yields better performance.",
+        "bbox": [
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+            90,
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+            167
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            498,
+            181,
+            633,
+            199
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
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+            207,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our method on the image classification task and its transferability to downstream semantic segmentation and object detection tasks.",
+        "bbox": [
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+            229,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. For image classification, we test model performance and robustness on ImageNet-1K (IN-1K) [34], ImageNet-C (IN-C) [35], ImageNet-A (IN-A) [36] and ImageNet-R (IN-R) [37]. IN-C contains natural corruptions from noise, blur, weather, and digital categories and is widely used to evaluate model's robustness against shifted distribution data. IN-A and IN-R consist of images with different distributions from ImageNet training distribution, such as natural adversarial examples and pictures generated by artistic rendition, thus are widely used to measure the robustness against out-of-distribution data. For semantic segmentation and object detection, we evaluate models on Cityscapes (City) [38], Cityscapes-C (City-C) and COCO [39]. Similar to IN-C, City-C has corruptions from the same four categories.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Metrics. We adopt standard evaluation metrics for image classification: clean accuracy for IN-1K and robust accuracy for IN-C, IN-A and IN-R. We also report mean corruption error (mCE) [35] on IN-C. For semantic segmentation and object detection, we evaluate the model performance using the clean and robust mean Intersection over Union (mIoU) on City and City-C and the mean average precision (mAP) on COCO. Additionally, we use retention rate as the metric to reflect the resilience of the model robustness and fairly compare models with different capacities. The retention rate is defined as  $R = \\frac{\\text{Robust Acc.}}{\\text{Clean Acc.}}$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Experiments are conducted on 8 NVIDIA Tesla V100s and codes are built upon Pytorch [40], timm [41] library and MMSegmentation [42] toolbox. We adopt FAN-Hybrid as the model architecture for FAN-TL and student models. For image classification, we train the models on ImageNet-1K using AdamW optimizer with a learning rate of 4e-3 and batch size of 2048 for 350 epochs. We employ the cosine scheduler with a decay rate of 0.1 to adjust the learning rate every 30 epochs. The loss weight  $\\alpha$  in Eq. 2 and  $\\beta$  in Eq. 5 are set to 1. We apply spatial, RandAug, CutOut, Mixup and CutMix data augmentation in the training and a label smoothing ratio of 0.9 to class and token labels. As discussed in Sec. 3, we apply spatial-only data augmentations",
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+    },
+    {
+        "type": "page_number",
+        "text": "5589",
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+    {
+        "type": "table",
+        "img_path": "images/0ec6c8df2cf8ab0f96aeaa13ec6e76a071ac13494d78d26cbc29018e957bcb89.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 2. Results on image classification. We report clean and robust accuracy on ImageNet-1K and ImageNet-C. Retention rate is defined as Robust Acc. LV-ViTs are vanilla ViTs trained with a CNN token-labeler. Our models trained with STL achieve superior robustness and retention rate in all cases. Meanwhile, our method also improves the clean accuracy of models with a larger capacity (e.g., FAN-B-Hybrid and FAN-L-Hybrid)."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Param./FLOPs</td><td>IN-1K</td><td>IN-C</td><td>Retention</td></tr><tr><td>ResNet18 [45]</td><td>11M/1.8G</td><td>69.9</td><td>32.7</td><td>46.8%</td></tr><tr><td>MBV2 [46]</td><td>4M/0.4G</td><td>73.0</td><td>35.0</td><td>47.9%</td></tr><tr><td>EffiNet-B0 [47]</td><td>5M/0.4G</td><td>77.5</td><td>41.1</td><td>53.0%</td></tr><tr><td>PVTV2-B0 [48]</td><td>3M/0.6G</td><td>70.5</td><td>36.2</td><td>51.3%</td></tr><tr><td>PVTV2-B1 [48]</td><td>13M/2.1G</td><td>78.7</td><td>51.7</td><td>65.7%</td></tr><tr><td>LV-ViT-T [3]</td><td>9M/2.1G</td><td>79.1</td><td>51.6</td><td>65.2%</td></tr><tr><td>FAN-T-Hybrid [15]</td><td>7M/3.5G</td><td>80.1</td><td>57.4</td><td>71.4%</td></tr><tr><td>STL (FAN-T-Hybrid)</td><td>8M/3.6G</td><td>79.9</td><td>58.2</td><td>72.8%</td></tr><tr><td>ResNet50 [45]</td><td>25M/4.1G</td><td>79.0</td><td>50.6</td><td>64.1%</td></tr><tr><td>DeiT-S [2]</td><td>22M/4.6G</td><td>79.9</td><td>58.1</td><td>72.7%</td></tr><tr><td>Swin-T [43]</td><td>28M/4.5G</td><td>81.3</td><td>55.4</td><td>68.1%</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M/4.5G</td><td>82.1</td><td>59.1</td><td>71.9%</td></tr><tr><td>LV-ViT-S [3]</td><td>26M/6.6G</td><td>83.3</td><td>59.7</td><td>71.7%</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M/6.7G</td><td>83.5</td><td>64.7</td><td>77.5%</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>27M/6.8G</td><td>83.4</td><td>65.5</td><td>78.5%</td></tr><tr><td>Swin-S [43]</td><td>50M/8.7G</td><td>83.0</td><td>60.4</td><td>72.8%</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M/8.7G</td><td>83.1</td><td>61.7</td><td>74.2%</td></tr><tr><td>LV-ViT-M [3]</td><td>56M/16.0G</td><td>84.0</td><td>62.0</td><td>73.8%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M/11.3G</td><td>83.9</td><td>66.4</td><td>79.1%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>51M/11.4G</td><td>84.5</td><td>68.2</td><td>80.7%</td></tr><tr><td>DeiT-B [2]</td><td>89M/17.6G</td><td>81.8</td><td>62.7</td><td>76.7%</td></tr><tr><td>Swin-B [43]</td><td>88M/15.4G</td><td>83.5</td><td>60.4</td><td>72.3%</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M/15.4G</td><td>83.8</td><td>63.0</td><td>75.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M/16.9G</td><td>84.3</td><td>68.3</td><td>81.0%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M/17.0G</td><td>84.7</td><td>68.8</td><td>81.2%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "on inputs of FAN-TL and Gumbel-Softmax on patch token outputs to obtain accurate token labels. We employ pretrained image classification models for semantic segmentation as encoders and the SegFormer [11] head as the decoder. We follow the same training recipe as SegFormer and train our models on Cityscapes using AdamW with a learning rate of 6e-5 and a batch size of 8 for 160K iterations. The learning rate scheduler is set to \"poly\" with a default factor of 1.0. Random resizing, flipping, and cropping are applied as data augmentations in training. For object detection, we follow the same practice as Swin Transformer [43] + Cascade Mask R-CNN [44] and employ AdamW (initial learning rate of 1e-4, weight decay of 0.05, and batch size of 16) to train our models on COCO for 36 epochs.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Results on Image Classification",
+        "text_level": 1,
+        "bbox": [
+            76,
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+    },
+    {
+        "type": "text",
+        "text": "We first show the performance of models trained with STL on the image classification task and compare them with other SOTA models in Table 2. To evaluate the zero-shot robustness against the distributional shift, all models are",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e7b76abdb39b07f5692d36e7a52ef84c390743a812a9066ec44fbf167c835d49.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 3. Results on out-of-distribution datasets. We report the mean corruption error (mCE) for ImageNet-C, a lower value indicates better robustness. The improved robustness of models trained with STL is well generalized to out-of-distribution datasets and achieves even better robustness on ImageNet-A and ImageNet-R."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Params (M)</td><td>Clean</td><td>IN-A</td><td>IN-R</td><td>mCE (↓)</td></tr><tr><td>Swin-T [50]</td><td>28.3</td><td>81.2</td><td>21.6</td><td>41.3</td><td>59.6</td></tr><tr><td>ConvNext-T [49]</td><td>28.6</td><td>82.1</td><td>24.2</td><td>47.2</td><td>53.2</td></tr><tr><td>RVT-S [51]</td><td>23.3</td><td>81.9</td><td>25.7</td><td>47.7</td><td>51.4</td></tr><tr><td>XCiT-S12 [52]</td><td>26.3</td><td>81.9</td><td>25.0</td><td>45.5</td><td>51.5</td></tr><tr><td>LV-ViT-S [3]</td><td>26.0</td><td>83.3</td><td>33.9</td><td>45.8</td><td>52.9</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26.3</td><td>83.5</td><td>33.9</td><td>50.7</td><td>47.8</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26.5</td><td>83.4</td><td>38.2</td><td>51.8</td><td>47.3</td></tr><tr><td>Swin-S [50]</td><td>50.0</td><td>83.4</td><td>35.8</td><td>46.6</td><td>52.7</td></tr><tr><td>ConvNext-S [49]</td><td>50.2</td><td>82.1</td><td>31.2</td><td>49.5</td><td>51.2</td></tr><tr><td>XCiT-S24 [52]</td><td>47.7</td><td>82.6</td><td>27.8</td><td>45.5</td><td>49.4</td></tr><tr><td>LV-ViT-M [3]</td><td>56.0</td><td>84.0</td><td>35.2</td><td>47.2</td><td>50.5</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4</td><td>83.9</td><td>39.6</td><td>52.9</td><td>45.2</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9</td><td>84.5</td><td>42.6</td><td>55.3</td><td>43.6</td></tr><tr><td>Swin-B [50]</td><td>87.8</td><td>83.4</td><td>35.8</td><td>46.6</td><td>54.4</td></tr><tr><td>MAE-ViT-B [53]</td><td>86.0</td><td>83.6</td><td>35.9</td><td>48.3</td><td>51.7</td></tr><tr><td>ConvNext-B [49]</td><td>88.6</td><td>83.8</td><td>36.7</td><td>51.3</td><td>46.8</td></tr><tr><td>RVT-B [51]</td><td>91.8</td><td>82.6</td><td>28.5</td><td>48.7</td><td>46.8</td></tr><tr><td>DAT-AugReg-ViT [14]</td><td>86.0</td><td>81.5</td><td>30.2</td><td>47.3</td><td>44.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8</td><td>84.3</td><td>41.8</td><td>53.2</td><td>43.0</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3</td><td>84.7</td><td>46.1</td><td>56.6</td><td>42.5</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "trained on ImageNet-1K data and directly used for inference on ImageNet-C without finetuning. We use the same model type for FAN-TL and the student model. It can be seen that Transformer-based models are more robust than CNN-based models in general. At all size levels, our models show superior robust accuracy and retention rate to other models, including the original FAN models trained solely with the class labels, indicating the effectiveness of STL in improving model robustness. Notably, our models surpass LV-ViTs [3] (i.e., vanilla ViT models trained with a CNN token-labeler) in both clean and robust accuracy by significant margins, which validates the importance of channel attention block in FAN and reveals the potential of self-emerging token labels from Transformer-based models.",
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Robustness against Out-of-distribution Data",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Token labels embed rich local information of image patches. We adopt spatial-only data augmentation and Gumbel-Softmax on FAN-TL to retain highly accurate labels for foreground tokens to ensure that self-emerging token labels always provide correct information for student models. The practice promotes the generalization performance of student models as they can make robust predictions even with different input data distributions. To verify this, we then evaluate model robustness against out-of-distribution data, and results are summarized in Table 3. Similarly, models are not fine-tuned for testing. We find that",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "5590",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 4. Results on semantic segmentation. We use mIoU as the evaluation metric. 'R-' and 'X-' refer to ResNet and Xception, respectively. Models trained with STL demonstrate an impressive transferability to the downstream task and achieve significantly better mIoU than other models on Cityscapes and Cityscapes-C."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Encoder Size</td><td>City</td><td>City-C</td><td>Retention</td></tr><tr><td>DeepLabv3+ (R50) [54]</td><td>25.4M</td><td>76.6</td><td>36.8</td><td>48.0%</td></tr><tr><td>DeepLabv3+ (R101) [54]</td><td>47.9M</td><td>77.1</td><td>39.4</td><td>51.1%</td></tr><tr><td>DeepLabv3+ (X65) [54]</td><td>22.8M</td><td>78.4</td><td>42.7</td><td>54.5%</td></tr><tr><td>DeepLabv3+ (X71) [54]</td><td>-</td><td>78.6</td><td>42.5</td><td>54.1%</td></tr><tr><td>ICNet ([55])</td><td>-</td><td>65.9</td><td>28.0</td><td>42.5%</td></tr><tr><td>FCN8s ([56])</td><td>50.1M</td><td>66.7</td><td>27.4</td><td>41.1%</td></tr><tr><td>DilatedNet ([57])</td><td>-</td><td>68.6</td><td>30.3</td><td>44.2%</td></tr><tr><td>ResNet38 ([58])</td><td>-</td><td>77.5</td><td>32.6</td><td>42.1%</td></tr><tr><td>PSPNet ([59])</td><td>13.7M</td><td>78.8</td><td>34.5</td><td>43.8%</td></tr><tr><td>ConvNeXt-T ([49])</td><td>29.0M</td><td>79.0</td><td>54.4</td><td>68.9%</td></tr><tr><td>SETR ([60])</td><td>22.1M</td><td>76.0</td><td>55.3</td><td>72.8%</td></tr><tr><td>SWIN-T ([43])</td><td>28.4M</td><td>78.1</td><td>47.3</td><td>60.6%</td></tr><tr><td>SegFormer-B0 ([11])</td><td>3.4M</td><td>76.2</td><td>48.8</td><td>64.0%</td></tr><tr><td>SegFormer-B1 ([11])</td><td>13.1M</td><td>78.4</td><td>52.7</td><td>67.2%</td></tr><tr><td>SegFormer-B2 ([11])</td><td>24.2M</td><td>81.0</td><td>59.6</td><td>73.6%</td></tr><tr><td>SegFormer-B5 ([11])</td><td>81.4M</td><td>82.4</td><td>65.8</td><td>79.9%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4M</td><td>82.2</td><td>66.9</td><td>81.5%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9M</td><td>82.5</td><td>68.6</td><td>83.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8M</td><td>82.3</td><td>68.7</td><td>83.5%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3M</td><td>82.8</td><td>69.2</td><td>83.6%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "LV-ViTs and original FAN models generalize well to out-of-distribution data, while other Transformer-based models and the SOTA CNN-based ConvNext models perform weaker. Despite the impressive performance of original FAN models, models trained with STL demonstrate an even better generalization ability and outperform all other models. The performance gains on IN-A and IN-R are more significant than IN-C and set a new state-of-the-art, indicating that the accurate self-emerging token labels are crucial to robustness against out-of-distribution data.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Transferability to Semantic Segmentation",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "[61] shows pre-trained models using different training recipes perform differently in downstream tasks. [3] validates that token labeling with CNN token-labelers benefits semantic segmentation and improves the clean mIoU. We also evaluate the transferability of STL to semantic segmentation. As shown in Table 4, pre-trained models with STL reveal better transferability than original FAN counterparts and other prestigious backbones. Remarkably, our approach achieves superior results on both clean and corrupted datasets. As far as we know, this is the first work to reveal that applying dense supervision in backbone pretraining improves not only the clean performance but also the robustness of the downstream task.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c56641c3e61a9008a7342d2e270a89602b91eac523fdf01032b97e67ead8a2cb.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 5. Results on object detection. Models trained with STL outperform most CNN-based and transformer-based backbones. Even compared with original FAN models, our models achieve at least on par or even better mAP on COCO, indicating our method can also benefit object detection."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Encoder Size</td><td>COCO (mAP)</td></tr><tr><td colspan=\"3\">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50 [45]</td><td>25M</td><td>46.3</td></tr><tr><td>ResNeXt-101-32 [62]</td><td>-</td><td>48.1</td></tr><tr><td>ResNeXt-101-64 [62]</td><td>-</td><td>48.3</td></tr><tr><td>Swin-T [43]</td><td>28M</td><td>50.4</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M</td><td>50.4</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M</td><td>53.3</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26M</td><td>53.4</td></tr><tr><td>Swin-S [43]</td><td>50M</td><td>51.9</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M</td><td>51.9</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M</td><td>53.5</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50M</td><td>53.9</td></tr><tr><td>Swin-B [43]</td><td>88M</td><td>51.9</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M</td><td>52.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M</td><td>54.1</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M</td><td>54.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.6. Transferability to Object Detection",
+        "text_level": 1,
+        "bbox": [
+            500,
+            434,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also validate STL's transferability to the object detection task on COCO and present the results in Table 5. Models trained with STL outperform most CNN-based and Transformer-based backbones. Even compared with original FAN models, STL brings a notable performance gain for FAN-B while achieving comparable mean average precision on FAN-L and FAN-S. We notice the overall improvement in object detection is not as good as in image classification and semantic segmentation, possibly because the semantic segmentation task is more similar to token labeling from the perspective of dense prediction, while object detection involves different techniques such as regression [63, 64] and multi-stage refinement [44, 63].",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1. Impacts of Different Data Augmentation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We apply spatial-only data augmentation on FAN-TL to obtain accurate token labels that provide clean and correct information toward student models, which is vital to model robustness. The strategy is a \"clean teacher noisy student\" design, where the student still uses all the augmentations. Our motivation behind this design is to let the teacher and student spatially aligned, with the teacher being as clean as possible to generate high quality token labels (Strong augmentations make it harder to generate good token labels as shown in Fig. 4). We compare the impacts of different data augmentation imposed on FAN-TL in Table 6. Experiments are conducted on the FAN-S-Hybrid model. The student",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "5591",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/32d9759f0350badc81b86b71551f57be1c5d99c95d5f3e97dc6cc7dc40ebdfa9.jpg",
+        "image_caption": [
+            "Figure 4. Visualization results of token labels generated by FAN-TL with full data augmentations. Strong augmentations significantly affect the quality of token labels."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
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+        "table_footnote": [
+            "Table 6. Ablation on impact to the student model using various data augmentations on FAN-TL. The different data augmentations are only imposed on the token-labeler's inputs, while the student model's inputs are fully augmented. Strong data augmentations on FAN-TL undermine token label accuracy and significantly affect the student model's robust accuracy."
+        ],
+        "table_body": "<table><tr><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td><td>IN-1K</td><td>IN-C</td></tr><tr><td>✓</td><td>✘</td><td>✘</td><td>✘</td><td>✘</td><td>83.4</td><td>65.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✘</td><td>✘</td><td>82.6</td><td>63.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>83.6</td><td>64.9</td></tr></table>",
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+        "type": "text",
+        "text": "model trained with token labels generated by spatial-only data augmentation achieves the best robustness while applying stronger augmentations harms the robust accuracy. Interestingly, applying the consistent full data augmentation on FAN-TL and the student model yields better clean accuracy, which reveals that different combinations of data augmentation may play different roles in improving model robustness and clean performance.",
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+    {
+        "type": "text",
+        "text": "5.2. Impacts of Gumbel-Softmax",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We propose to use Gumbel-Softmax as a lightweight solution to retain correct token labels for foreground tokens and eliminate incorrect ones, which yields a more accurate segmentation of the object. We evaluate the impact of Gumbel-Softmax using the FAN-S-Hybrid model in Table 7. As can be seen, models trained with token labels generated by Softmax and Gumbel-Softmax achieve comparable clean accuracy while Gumbel-Softmax improves robust accuracy. This further validates that accurate foreground token labels are critical to model robustness.",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 7. Comparison of Softmax and Gumbel-Softmax. Both methods achieve comparable clean accuracy while token labels generated by Gumbel-Softmax yield better robustness."
+        ],
+        "table_body": "<table><tr><td>Token Labeling</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>Softmax</td><td>83.4</td><td>65.2</td><td>47.6</td><td>37.2</td><td>51.7</td></tr><tr><td>Gumbel-Softmax</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5.3. Training with Heterogeneous Token-Labelers",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the previous experiments, we train student models with isomorphic FAN token-labelers (e.g., FAN-TL-S-Hybrid for FAN-S-Hybrid). We are interested in the impacts",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 8. Performance comparison of training with different token labelers. The robustness of student models can be further improved by training with a heterogeneous token labeler."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>83.4</td><td>65.5</td><td>47.3</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>83.5</td><td>65.5</td><td>47.4</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.5</td><td>68.2</td><td>43.6</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.3</td><td>68.1</td><td>43.5</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.7</td><td>69.0</td><td>42.4</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.7</td><td>68.8</td><td>42.5</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "of training with a heterogeneous token-labeler and conduct the ablation in Table 8. For each student model, we train with three different FAN token-labelers of model sizes from small to large. Models trained with heterogeneous FAN-TL can achieve at least comparable or even superior performance to ones trained with isomorphic token-labelers. Our large model trained with FAN-TL-B-Hybrid further boosts the clean and robust accuracy to  $84.8\\%$  and  $69.2\\%$  with the mCE of  $42.1\\%$ . This indicates STL is robust to different token-labelers. Such robustness enables us to train a larger student model with a smaller token-labeler, which can reduce the training cost.",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 9. Comparison to the prior SOTA token labeling method. Our proposed method that employs self-emerging token labels always yields better robustness than NFNet-F6, which validates the benefit of encoding local information of image patches via self-attention."
+        ],
+        "table_body": "<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.2</td><td>65.8</td><td>46.9</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.5</td><td>67.4</td><td>44.9</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.9</td><td>68.3</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5.4. Comparison to Prior Token Labeling Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As shown in Sec. 4.3 and Sec. 4.4, models trained with FAN-TL demonstrate superior performance and robustness than LV-ViTs [3] trained with a CNN token-labeler (i.e., NFNet-F6 [5]), which may attribute to the self-emerging token labeling and the channel attention design of FAN models. To better understand the effect of token labeling, we",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "5592",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "train the same FAN models with different methods. Results are summarized in Table 9. It can be seen that STL still significantly outperforms the CNN token-labeler even with the same student model. Note that NFNet-F6 has more than 400M parameters and achieves an  $86.3\\%$  Top-1 accuracy on ImageNet-1K while the largest FAN-TL (i.e., FANTL-L-Hybrid) only has 77.3M parameters and  $84.3\\%$  Top-1 accuracy. However, FAN-TL consistently yields better results than NFNet-F6. The rationale behind this is possibly because self-emerging token labels provide self-consistent information to student models.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.5. Impacts of Loss Weight",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Choosing good loss weights is important when multiple losses are jointly optimized. To study the impact of loss weights and verify STL's robustness against different loss weights when training student models, we vary  $\\beta$  with various values and present the results in Table 10. We find STL not sensitive to  $\\beta$ . Both clean and robust accuracy fluctuates in a small range. We thus set  $\\beta = 1$  to balance the loss with equal weights for simplicity. Similarly, for the training of token-labelers,  $\\alpha$  is also set to 1.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/bd40b347c0c8683f394bbabba070a1149e192793450a4183f0badb7671311616.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 10. Ablation study of loss weight  $\\beta$  ."
+        ],
+        "table_body": "<table><tr><td>β</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>0.5</td><td>83.5</td><td>65.5</td><td>47.3</td><td>38.5</td><td>51.7</td></tr><tr><td>1.0</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr><tr><td>2.0</td><td>83.5</td><td>65.6</td><td>47.2</td><td>37.3</td><td>51.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a self-emerging token labeling (STL) framework built on Transformer-based models instead of CNNs. STL enables FAN token-labelers to self-produce accurate and semantically meaningful token labels for training student models with dense supervision. Through extensive experiments and ablation studies, we demonstrate that models trained with STL significantly surpass the original FAN counterparts trained only with image-level labels and achieve remarkable robustness improvement in various visual recognition tasks. Our study validates that the self-produced knowledge from ViTs can indeed benefit their pre-training. We hope this work sheds light on the potential and understanding of self-emerging token labeling from ViTs and motivates future research.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "type": "list",
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+        ],
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+        "page_idx": 9
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+    {
+        "type": "page_number",
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+        ],
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+    },
+    {
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+        ],
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+            78,
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+        ],
+        "page_idx": 10
+    },
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+        "list_items": [
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+            "[64] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. NeurIPS, 28:91-99, 2015. 7"
+        ],
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diff --git a/2023/Fully Attentional Networks with Self-emerging Token Labeling/caf0e66c-9593-4110-bbb4-fe33ef9d0d27_model.json b/2023/Fully Attentional Networks with Self-emerging Token Labeling/caf0e66c-9593-4110-bbb4-fe33ef9d0d27_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..76731c5be7f0e47fd23399a37d873f1c9b858ff6
--- /dev/null
+++ b/2023/Fully Attentional Networks with Self-emerging Token Labeling/caf0e66c-9593-4110-bbb4-fe33ef9d0d27_model.json	
@@ -0,0 +1,2389 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.167,
+                0.131,
+                0.804,
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+            ],
+            "angle": 0,
+            "content": "Fully Attentional Networks with Self-emerging Token Labeling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.148,
+                0.179,
+                0.792,
+                0.235
+            ],
+            "angle": 0,
+            "content": "Bingyin Zhao\\(^{1,2*}\\) Zhiding Yu\\(^{1\\dagger}\\) Shiyi Lan\\(^{1}\\) Yutao Cheng\\(^{3}\\) Anima Anandkumar\\(^{1,4}\\) Yingjie Lao\\(^{2}\\) Jose M. Alvarez\\(^{1}\\)  \n\\(^{1}\\)NVIDIA \\(^{2}\\)Clemson University \\(^{3}\\)Fudan University \\(^{4}\\)Caltech"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.269,
+                0.314,
+                0.285
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.301,
+                0.474,
+                0.619
+            ],
+            "angle": 0,
+            "content": "Recent studies indicate that Vision Transformers (ViTs) are robust against out-of-distribution scenarios. In particular, the Fully Attentional Network (FAN) - a family of ViT backbones, has achieved state-of-the-art robustness. In this paper, we revisit the FAN models and improve their pretraining with a self-emerging token labeling (STL) framework. Our method contains a two-stage training framework. Specifically, we first train a FAN token labeler (FANTL) to generate semantically meaningful patch token labels, followed by a FAN student model training stage that uses both the token labels and the original class label. With the proposed STL framework, our best model based on FAN-L-Hybrid (77.3M parameters) achieves \\(84.8\\%\\) Top-1 accuracy and \\(42.1\\%\\) mCE on ImageNet-1K and ImageNet-C, and sets a new state-of-the-art for ImageNet-A \\((46.1\\%)\\) and ImageNet-R \\((56.6\\%)\\) without using extra data, outperforming the original FAN counterpart by significant margins. The proposed framework also demonstrates significantly enhanced performance on downstream tasks such as semantic segmentation, with up to \\(1.7\\%\\) improvement in robustness over the counterpart model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.646,
+                0.21,
+                0.661
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.671,
+                0.47,
+                0.792
+            ],
+            "angle": 0,
+            "content": "Vision Transformers (ViTs) [1] have recently achieved remarkable success in visual recognition tasks. Such success is not only attributed to their self-attention representation but also to the newly developed training recipes. For instance, refinements in training techniques such as strong data augmentation and knowledge distillation [2] greatly alleviate ViT's issue of being data-hungry and make them more accessible for training on ImageNet-1K."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.792,
+                0.47,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Another important development in the training recipe is token labeling [3], where patch tokens are assigned with labels to ViTs in a dense manner. In some sense, token labeling can also be considered as an alternative form of hard knowledge distillation. However, the dense nature of token"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.269,
+                0.895,
+                0.476
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.479,
+                0.892,
+                0.563
+            ],
+            "angle": 0,
+            "content": "Figure 1. Results of zero-shot robustness against ImageNet-A and ImageNet-R. Models trained on ImageNet-1K with self-emerging token labels from FAN show superior robustness to the out-of-distribution data. Our best model (with only 77.3M parameters) achieves robust accuracy of \\(46.1\\%\\) and \\(56.6\\%\\) and sets a new record on ImageNet-A and ImageNet-R."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.589,
+                0.892,
+                0.816
+            ],
+            "angle": 0,
+            "content": "labeling allows ViTs to leverage more fine-grained information in an image and take different categories and object localization into account. Compared to traditional knowledge distillation methods, token labeling enables ViTs to exploit a wider range of information in the image, leading to more accurate results. The success of token labeling depends on carefully-designed token-level annotators (i.e., token-labelers) that can provide accurate location-specific information (i.e., token labels) to patch tokens. In [3], this is done by a special re-labeling process [4] using convolutional neural networks (CNNs) [5] pre-trained on ImageNet-1K. While Vision Transformers have shown great promise in representation learning, less exploration has been conducted on modeling them as token-labelers. This raises two interesting questions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.828,
+                0.89,
+                0.856
+            ],
+            "angle": 0,
+            "content": "1. Can Transformer-based models self-produce meaningful token labels?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.871,
+                0.89,
+                0.901
+            ],
+            "angle": 0,
+            "content": "2. Can one improve the pre-training of ViTs with self-produced knowledge instead of external teachers?"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.512,
+                0.828,
+                0.89,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.875,
+                0.337,
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+            ],
+            "angle": 0,
+            "content": "*Work done during an internship at NVIDIA."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.098,
+                0.888,
+                0.223,
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+            ],
+            "angle": 0,
+            "content": "† Corresponding author."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
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+                0.9
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "5585"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "Our approach: In this paper, we aim to answer the above questions. We propose a self-emerging token labeling (STL) framework that employs the self-produced token labels by ViT token-labelers instead of relying on CNNs. Our work is built on the recently proposed Fully Attentional Network (FAN) [6] for two reasons. First, FAN exhibits excellent self-emerging visual grouping on token features, which can be leveraged to generate high-quality token labels. Second, FAN is a family of ViT backbones with state-of-the-art accuracy and robustness. We aim to further improve this family of powerful backbones through a principled token-labeling design and validate its effectiveness. Our contributions can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.085,
+                0.305,
+                0.47,
+                0.368
+            ],
+            "angle": 0,
+            "content": "- Our work demonstrates that ViT models can be effective token-labelers. We propose a simple yet effective way to train a FAN token-labeler that can produce semantically meaningful token labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.085,
+                0.386,
+                0.47,
+                0.463
+            ],
+            "angle": 0,
+            "content": "- We perform an in-depth analysis and show critical contributors to the accuracy of token labels. On top of the observations, we design a solution that retains more accurate token labels of the target object for improved model pre-training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.085,
+                0.481,
+                0.468,
+                0.558
+            ],
+            "angle": 0,
+            "content": "- Our models trained with STL set a new record on out-of-distribution datasets without using extra data than ImageNet-1K. Our best model achieves robust accuracy of \\(46.1\\%\\) on ImageNet-A and \\(56.6\\%\\) on ImageNet-R with only 77M parameters, as shown in Fig. 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.085,
+                0.577,
+                0.468,
+                0.623
+            ],
+            "angle": 0,
+            "content": "- Experiments on downstream tasks demonstrate that the improved performance in backbone models is transferable to semantic segmentation and object detection."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.085,
+                0.305,
+                0.47,
+                0.623
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.64,
+                0.47,
+                0.685
+            ],
+            "angle": 0,
+            "content": "Our STL framework is akin to the teacher-student training strategy introduced in knowledge distillation and consists of two stages:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.687,
+                0.468,
+                0.793
+            ],
+            "angle": 0,
+            "content": "First stage: We train a FAN token-labeler (FAN-TL) model to generate token-level annotations. Our task is essentially a \"chicken or the egg\" problem since there is no explicit supervision on how the token labels are generated. We tackle this by assigning supervising both the class token and the global average-pooled token. This produces semantically meaningful token labels as shown in Fig. 2(b)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.796,
+                0.468,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Second stage: We train a FAN student model using the original class labels and the token labels from FAN-TL. Observing the imperfect quality of token labels, we introduce a token selection approach based on Gumbel-Softmax that adaptively selects tokens with high confidence. Labels of the selected tokens are of better quality and object grounding in general, leading to improved pre-training."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.09,
+                0.642,
+                0.107
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.115,
+                0.695,
+                0.13
+            ],
+            "angle": 0,
+            "content": "2.1. Vision Transformers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.138,
+                0.892,
+                0.29
+            ],
+            "angle": 0,
+            "content": "Vision Transformers [1] are a family of visual recognition models built upon Transformers [7]. ViT splits an input image into a series of small patches, projects each as an embedding (a.k.a patch token) and appends with position embeddings. The resulting patch tokens and an extra learnable class token that aggregates global information for classification are then fed into a sequence of Transformer encoders consisting of multi-head self-attention and FFN blocks. A linear projection layer is appended to the class token to predict the class probabilities."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.299,
+                0.747,
+                0.315
+            ],
+            "angle": 0,
+            "content": "2.2. Fully Attentional Networks"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.322,
+                0.892,
+                0.489
+            ],
+            "angle": 0,
+            "content": "Several concurrent works point out that ViTs exhibit excellent zero-shot robustness against out-of-distribution samples [8-11]. Some works propose to use negative data augmentation [12] and adversarial training [13, 14] to further enhance the robustness. Recently, FAN [15] was introduced as a family of ViT backbones with state-of-the-art accuracy and robustness. FAN inherits the self-attention blocks of plain ViT but additionally introduces a channel attention block that adopts an attention-based design that aggregates the cross-channel information in a more holistic manner, leading to improved representation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.498,
+                0.657,
+                0.514
+            ],
+            "angle": 0,
+            "content": "2.3. Token Labeling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.892,
+                0.839
+            ],
+            "angle": 0,
+            "content": "Token labeling [3] has been proposed to improve ViT pre-training. From the perspective of training strategy, it is similar to knowledge distillation [2, 16] since both adopt a teacher-student mode. It is also related to ReLabel [17], which provides images with multi-label annotations instead of single ones. However, both ReLabel and knowledge distillation depend on image-level labels as global supervision while token labeling assigns labels to each image patch token and supervises the student model in a dense manner. Token labeling is also inherently related to tokenization in BEiT [18], where an offline pre-trained discrete VAE is employed as the tokenizer to encode patches into visual tokens (i.e., code from a visual codebook). Different from token labels, these visual tokens do not possess explicit semantically meanings since they originate from an unsupervisedly trained codebook. Our method differs from prior token labeling and distillation methods where pre-trained convolutional neural networks are widely used as the token-labeler. Instead, our approach to unifies both teacher and student under homogeneous Vision Transformer architectures to generate high-quality token labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.757,
+                0.864
+            ],
+            "angle": 0,
+            "content": "2.4. Emerging Properties of ViTs"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "It was found that the localization of objects emerges in image classification with CNNs. This interesting phe"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5586"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "nomenon, also known as class activation maps (CAM) [19], lays the foundation for token labeling. Recent studies reveal that ViTs demonstrate excellent capability for object localization without explicit supervision. For instance, DINO [20] shows that self-supervised ViT features generate semantically meaning object segmentation. Methods like GroupViT [21] show that semantic segmentation emerges in ViTs using only text supervision. Similarly, FAN reveals that the robustness of ViT models is correlated to their excellent visual grouping capability. This feature motivates us to develop self-emerging token labeling on top of the FAN models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.287,
+                0.17,
+                0.303
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.313,
+                0.47,
+                0.388
+            ],
+            "angle": 0,
+            "content": "As mentioned, we propose a self-emerging token labeling (STL) framework that uses self-produced token labels to improve ViT pre-training. STL consists of two stages: 1) training an effective token-labeler, and 2) training a student model with self-emerging token labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.388,
+                0.471,
+                0.631
+            ],
+            "angle": 0,
+            "content": "In the first stage, we train a FAN token-labeler (FANTL) to generate high-quality token labels. As discussed in Sec. 1 and Sec. 2, FAN demonstrates strong robustness and capability to obtain semantically meaningful visual grouping that can correctly captures the object gestalt. These great features of FAN allow us to obtain high quality token labels without bells and whistles. In the second stage, we then train a FAN student model with image-level labels and self-emerging token labels from FAN-TL. At high level, FAN-TL and FAN student models follow the same architectural design as FAN but slightly modify the structure of patch tokens. We attach a linear layer to each patch token to accommodate token labels, similar to the classification head added to the class token in the original FAN and ViT design. The rest of this section describes the implementation details of the above two-stage pipeline."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.64,
+                0.345,
+                0.655
+            ],
+            "angle": 0,
+            "content": "3.1. Training FAN Token-Labelers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.663,
+                0.47,
+                0.784
+            ],
+            "angle": 0,
+            "content": "The original FAN employs the training paradigm that only takes image-level labels as supervision. We denote the input image as \\(\\mathbf{I}\\), the sequence of small patches as \\([\\mathbf{I}_{p_1},\\mathbf{I}_{p_2},\\dots,\\mathbf{I}_{p_N}]\\), the output of FAN encoder as \\([\\mathbf{T}_{cls},\\mathbf{T}_{p_1},\\dots,\\mathbf{T}_{p_N}]\\), where \\(N\\) is the number of patch tokens, \\(\\mathbf{T}_{cls}\\) represents the class token and \\(\\mathbf{T}_{p_1},\\ldots ,\\mathbf{T}_{p_N}\\) represent the patch tokens, respectively. The training objective can be mathematically expressed as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.204,
+                0.797,
+                0.469,
+                0.814
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {\\text {c l s}}, \\mathbf {Y} _ {\\text {c l s}}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.469,
+                0.856
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{H}(\\cdot)\\) is the softmax cross entropy loss and \\(\\mathbf{Y}_{cls}\\) is the image-level label of the corresponding class."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The key to token labeling is the generation of accurate token labels that provide location-specific information. However, following the conventional training paradigm in Eq. 1,"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.508,
+                0.09,
+                0.892,
+                0.352
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.354,
+                0.895,
+                0.48
+            ],
+            "angle": 0,
+            "content": "Figure 2. Illustration of token labels generated by FAN-TL and the token label confidence score distribution. (a). original image (class: \"tench\"), (b). binary color map of token labels (yellow: tokens classified as \"tench\", dark blue: tokens not classified as \"tench\") (c). trinary color map of token labels (cyan: foreground tokens with low confidence, yellow: foreground tokens with high confidence), (d). binary color map of foreground tokens selected by Gumbel-Softmax, (e). token label confidence score distribution of a batch of 16 images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.503,
+                0.892,
+                0.699
+            ],
+            "angle": 0,
+            "content": "token outputs of FAN models are not semantically well-guided since they are not supervised during training. We propose a simple yet effective method to address this issue. Our idea is inspired by the intriguing phenomenon in ViTs training that meaningful object segmentation naturally emerges [20]. Unlike the self-supervised training in DINO, we leverage FAN's strong capability of visual grouping [22] and devise a fully supervised approach that allows FAN to generate accurate and semantically meaningful token labels. We perform global average-pooling on all patch tokens and then simultaneously assign the class label to the class and the average-pooled tokens. The training objective of FANTL can be written as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.527,
+                0.701,
+                0.892,
+                0.742
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}\\right) + \\alpha \\cdot \\mathcal {H} \\left(\\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathbf {T} _ {p _ {i}}, \\mathbf {Y} _ {c l s}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.895,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) weights the importance of two loss functions. We set \\(\\alpha\\) to 1 in our experiments. We demonstrate a visualization example of the token labels generated by FAN-TL in Fig. 2(b). The yellow area (i.e., foreground) represents the tokens with the same labels as the image-level label (we term foreground tokens). In contrast, the dark blue area (i.e., background) represents the tokens with different labels from the image-level label (we term background tokens). It can be seen that the self-emerging token labels show a meaningful segmentation of the target object \"tench\"."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5587"
+        }
+    ],
+    [
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.154,
+                0.089,
+                0.397,
+                0.103
+            ],
+            "angle": 0,
+            "content": "Generate token labels using FAN-TL"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.104,
+                0.47,
+                0.345
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.089,
+                0.885,
+                0.103
+            ],
+            "angle": 0,
+            "content": "Train the student model with self-emerging token labeling"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.499,
+                0.104,
+                0.888,
+                0.345
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.35,
+                0.892,
+                0.419
+            ],
+            "angle": 0,
+            "content": "Figure 3. Illustration of Stage 2: Training student models with self-emerging token labels. In the training, token labels are generated by FAN-TL and assigned to patch tokens of student models. We incorporate the token labels and class labels to train student models jointly. FAN-TL can self-identify the incorrect token labels upon the confidence score. Tokens with high confidence scores offer a more accurate segmentation of objects and are crucial to robustness improvement. By applying spatial-only data augmentation to the inputs and Gumbel-Softmax to the token outputs of FAN-TL, we obtain the most accurate and critical token labels."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.076,
+                0.444,
+                0.382,
+                0.46
+            ],
+            "angle": 0,
+            "content": "3.2. Training Student Models with STL"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.468,
+                0.47,
+                0.558
+            ],
+            "angle": 0,
+            "content": "Training student models is straightforward. As illustrated in Fig. 3, we take the token outputs of FAN-TL and assign them as the labels for patch tokens of student models. We then incorporate token labels with class labels and jointly optimize the loss on the class token and all patch tokens. The training objective is shown as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.1,
+                0.563,
+                0.469,
+                0.604
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}\\right) + \\beta \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {H} \\left(\\mathbf {T} _ {p _ {i}}, \\mathcal {F} \\left(\\mathbf {I} _ {p _ {i}}\\right)\\right) \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.614,
+                0.469,
+                0.734
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{F}(\\cdot)\\) represents the patch token outputs of FAN-TL and \\(\\beta\\) is the hyper-parameter to balance two loss functions. \\(\\beta\\) is set to 1 in our experiments. Note the correctness of token labels (especially the foreground tokens) is critical since wrong labels introduce worthless local information. Thus, we propose several implementation tricks to generate and retain highly accurate token labels based on the following two observations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.735,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Observation 1: Data augmentations remarkably affect the accuracy of token labels. Recent studies [2, 23] indicate data augmentations improve the classification accuracy and robustness of ViT models. However, most augmentations undermine the accuracy of token labels. For example, augmentations in RandAug [24], such as posterize and solarize, alter pixel values, CutOut [25] randomly erases a part of images, Mixup [26] and CutMix [27] mix content from two images, which all make it difficult for FAN-TL to assign correct labels to patch tokens. To this end, we disable these data augmentations and keep spatial-"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.442,
+                0.889,
+                0.515
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model (Stage)</td><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td></tr><tr><td>FAN-TL (Stage1)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Student (Stage2)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FAN-TL (Stage2)</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.516,
+                0.892,
+                0.557
+            ],
+            "angle": 0,
+            "content": "Table 1. Detailed settings of data augmentations. We apply spatial-only data augmentations to inputs of FAN-TL in stage 2 to improve the accuracy of token labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.748
+            ],
+            "angle": 0,
+            "content": "only ones (i.e., flip, rotate, shear and translation) for FANTL when generating token labels. Note that we still apply full data augmentations for the student model. The concrete settings of data augmentations are summarized in Table 1. Moreover, the strong data augmentations can be regarded as noises akin to corruptions and perturbations in out-of-distribution datasets. The input data augmentation discrepancy between FANT-LT and the student model enables the self-emerging token labels to provide clean and correct information regardless of the noise, thus improving the model's robustness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.893,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Observation 2: Not all the self-emerging token labels are correct, even with spatial-only data augmentations. For example, as shown in Fig. 2(b), some patches (red squares) that only contain \"human\" and \"lake\" are misclassified as the target object \"tench\" by FAN-TL. It is particularly crucial to ensure the accuracy of foreground token labels as they contain the target object of the image that dominates the prediction result. However, it is challenging to determine which labels are incorrect due to the lack of patch-level ground truth. Interestingly, FAN-TL can"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5588"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.287
+            ],
+            "angle": 0,
+            "content": "self-identify these misclassified foreground tokens according to the token label confidence score, which may also be attributed to its visual grouping ability. The token label confidence score is defined as the maximal class probability of each token output. We find that tokens with correct labels tend to have higher confidence scores than those with incorrect labels. As shown in Fig. 2(c) and Fig. 2(e), the yellow area indicates the foreground tokens with high confidence scores \\((0.7\\sim 0.9)\\). These tokens yield a highly accurate segmentation of the target object. Contrastly, the cyan area represents the foreground tokens with low confidence scores \\((0\\sim 0.2)\\), which are coincidentally the ones with incorrect labels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.288,
+                0.473,
+                0.41
+            ],
+            "angle": 0,
+            "content": "We attempt to assign highly accurate labels to the target object (i.e., foreground tokens). However, it is intractable to exhaustively examine the confidence score of each patch token for all the images as it significantly increases the training time and requires much more computational resources. Therefore, we propose a lightweight alternative by applying the Gumbel-Softmax [28] on the top of token outputs. Mathematically, it can be expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.175,
+                0.418,
+                0.47,
+                0.458
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {y} _ {i} = \\frac {e ^ {\\left(\\log \\left(\\pi_ {i}\\right) + \\mathcal {G} _ {i}\\right) / \\tau}\\left. \\right)}{\\sum_ {j = 1} ^ {k} e ^ {\\left(\\log \\left(\\pi_ {j}\\right) + \\mathcal {G} _ {j}\\right) / \\tau})} \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.467,
+                0.473,
+                0.741
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{y}\\) is the \\(k\\)-dimension softmax vector, \\(\\pi\\) are class probabilities, \\(\\mathcal{G} \\sim Gumbel(0,1)\\) are i.i.d. samples drawn from the standard Gumbel distribution and \\(\\tau\\) is the softmax temperature. Token labels with high confidence scores remain unchanged after applying Gumbel-Softmax, while labels with low confidence scores are highly likely to change. As shown in Fig. 2(d), we preserve the correct token labels and eliminate the incorrect ones in a simple yet effective way, achieving high accuracy of foreground tokens labels and more precise segmentation of the object. Furthermore, since the training objective of the patch tokens side can be considered a self-training process [29-31], we convert the softmax outputs to \"one-hot\" probability distribution (i.e., hard labels) as [32] shows that the use of hard labels in self-training encourages the model's predictions to be high-confidence via entropy minimization [33]. Following the aforementioned spatial-only data augmentation, we can then rewrite the training objective of the student model:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.1,
+                0.755,
+                0.47,
+                0.797
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {H} (\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}) + \\beta \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {H} (\\mathbf {T} _ {p _ {i}}, \\hat {\\mathcal {F}} (\\hat {\\mathbf {I}} _ {p _ {i}})) \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.808,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "where \\(\\hat{\\mathcal{F}} (\\cdot)\\) is the one-hot encoded Gumbel-Softmax outputs of FAN-TL and \\([\\hat{\\mathbf{I}}_{p_1}\\dots \\hat{\\mathbf{I}}_{p_N}]\\) are image patches with the spatial-only data augmentation. Meanwhile, we notice that all background tokens (i.e., the dark blue area) also have low confidence scores. This is probably because these tokens neither contain apparent features associated with the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.893,
+                0.168
+            ],
+            "angle": 0,
+            "content": "target object nor clear features related to any other class in the dataset. Nevertheless, we keep all tokens (even those with low confidence scores) in training, following the practice in [3] as involving more tokens for loss computation yields better performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.182,
+                0.634,
+                0.2
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.208,
+                0.787,
+                0.223
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Evaluation Metrics"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.231,
+                0.893,
+                0.276
+            ],
+            "angle": 0,
+            "content": "We evaluate our method on the image classification task and its transferability to downstream semantic segmentation and object detection tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.278,
+                0.895,
+                0.503
+            ],
+            "angle": 0,
+            "content": "Datasets. For image classification, we test model performance and robustness on ImageNet-1K (IN-1K) [34], ImageNet-C (IN-C) [35], ImageNet-A (IN-A) [36] and ImageNet-R (IN-R) [37]. IN-C contains natural corruptions from noise, blur, weather, and digital categories and is widely used to evaluate model's robustness against shifted distribution data. IN-A and IN-R consist of images with different distributions from ImageNet training distribution, such as natural adversarial examples and pictures generated by artistic rendition, thus are widely used to measure the robustness against out-of-distribution data. For semantic segmentation and object detection, we evaluate models on Cityscapes (City) [38], Cityscapes-C (City-C) and COCO [39]. Similar to IN-C, City-C has corruptions from the same four categories."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.505,
+                0.895,
+                0.675
+            ],
+            "angle": 0,
+            "content": "Metrics. We adopt standard evaluation metrics for image classification: clean accuracy for IN-1K and robust accuracy for IN-C, IN-A and IN-R. We also report mean corruption error (mCE) [35] on IN-C. For semantic segmentation and object detection, we evaluate the model performance using the clean and robust mean Intersection over Union (mIoU) on City and City-C and the mean average precision (mAP) on COCO. Additionally, we use retention rate as the metric to reflect the resilience of the model robustness and fairly compare models with different capacities. The retention rate is defined as \\( R = \\frac{\\text{Robust Acc.}}{\\text{Clean Acc.}} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.681,
+                0.719,
+                0.698
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.704,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Experiments are conducted on 8 NVIDIA Tesla V100s and codes are built upon Pytorch [40], timm [41] library and MMSegmentation [42] toolbox. We adopt FAN-Hybrid as the model architecture for FAN-TL and student models. For image classification, we train the models on ImageNet-1K using AdamW optimizer with a learning rate of 4e-3 and batch size of 2048 for 350 epochs. We employ the cosine scheduler with a decay rate of 0.1 to adjust the learning rate every 30 epochs. The loss weight \\(\\alpha\\) in Eq. 2 and \\(\\beta\\) in Eq. 5 are set to 1. We apply spatial, RandAug, CutOut, Mixup and CutMix data augmentation in the training and a label smoothing ratio of 0.9 to class and token labels. As discussed in Sec. 3, we apply spatial-only data augmentations"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5589"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.089,
+                0.468,
+                0.466
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Param./FLOPs</td><td>IN-1K</td><td>IN-C</td><td>Retention</td></tr><tr><td>ResNet18 [45]</td><td>11M/1.8G</td><td>69.9</td><td>32.7</td><td>46.8%</td></tr><tr><td>MBV2 [46]</td><td>4M/0.4G</td><td>73.0</td><td>35.0</td><td>47.9%</td></tr><tr><td>EffiNet-B0 [47]</td><td>5M/0.4G</td><td>77.5</td><td>41.1</td><td>53.0%</td></tr><tr><td>PVTV2-B0 [48]</td><td>3M/0.6G</td><td>70.5</td><td>36.2</td><td>51.3%</td></tr><tr><td>PVTV2-B1 [48]</td><td>13M/2.1G</td><td>78.7</td><td>51.7</td><td>65.7%</td></tr><tr><td>LV-ViT-T [3]</td><td>9M/2.1G</td><td>79.1</td><td>51.6</td><td>65.2%</td></tr><tr><td>FAN-T-Hybrid [15]</td><td>7M/3.5G</td><td>80.1</td><td>57.4</td><td>71.4%</td></tr><tr><td>STL (FAN-T-Hybrid)</td><td>8M/3.6G</td><td>79.9</td><td>58.2</td><td>72.8%</td></tr><tr><td>ResNet50 [45]</td><td>25M/4.1G</td><td>79.0</td><td>50.6</td><td>64.1%</td></tr><tr><td>DeiT-S [2]</td><td>22M/4.6G</td><td>79.9</td><td>58.1</td><td>72.7%</td></tr><tr><td>Swin-T [43]</td><td>28M/4.5G</td><td>81.3</td><td>55.4</td><td>68.1%</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M/4.5G</td><td>82.1</td><td>59.1</td><td>71.9%</td></tr><tr><td>LV-ViT-S [3]</td><td>26M/6.6G</td><td>83.3</td><td>59.7</td><td>71.7%</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M/6.7G</td><td>83.5</td><td>64.7</td><td>77.5%</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>27M/6.8G</td><td>83.4</td><td>65.5</td><td>78.5%</td></tr><tr><td>Swin-S [43]</td><td>50M/8.7G</td><td>83.0</td><td>60.4</td><td>72.8%</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M/8.7G</td><td>83.1</td><td>61.7</td><td>74.2%</td></tr><tr><td>LV-ViT-M [3]</td><td>56M/16.0G</td><td>84.0</td><td>62.0</td><td>73.8%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M/11.3G</td><td>83.9</td><td>66.4</td><td>79.1%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>51M/11.4G</td><td>84.5</td><td>68.2</td><td>80.7%</td></tr><tr><td>DeiT-B [2]</td><td>89M/17.6G</td><td>81.8</td><td>62.7</td><td>76.7%</td></tr><tr><td>Swin-B [43]</td><td>88M/15.4G</td><td>83.5</td><td>60.4</td><td>72.3%</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M/15.4G</td><td>83.8</td><td>63.0</td><td>75.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M/16.9G</td><td>84.3</td><td>68.3</td><td>81.0%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M/17.0G</td><td>84.7</td><td>68.8</td><td>81.2%</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.077,
+                0.467,
+                0.47,
+                0.565
+            ],
+            "angle": 0,
+            "content": "Table 2. Results on image classification. We report clean and robust accuracy on ImageNet-1K and ImageNet-C. Retention rate is defined as Robust Acc. LV-ViTs are vanilla ViTs trained with a CNN token-labeler. Our models trained with STL achieve superior robustness and retention rate in all cases. Meanwhile, our method also improves the clean accuracy of models with a larger capacity (e.g., FAN-B-Hybrid and FAN-L-Hybrid)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.592,
+                0.47,
+                0.803
+            ],
+            "angle": 0,
+            "content": "on inputs of FAN-TL and Gumbel-Softmax on patch token outputs to obtain accurate token labels. We employ pretrained image classification models for semantic segmentation as encoders and the SegFormer [11] head as the decoder. We follow the same training recipe as SegFormer and train our models on Cityscapes using AdamW with a learning rate of 6e-5 and a batch size of 8 for 160K iterations. The learning rate scheduler is set to \"poly\" with a default factor of 1.0. Random resizing, flipping, and cropping are applied as data augmentations in training. For object detection, we follow the same practice as Swin Transformer [43] + Cascade Mask R-CNN [44] and employ AdamW (initial learning rate of 1e-4, weight decay of 0.05, and batch size of 16) to train our models on COCO for 36 epochs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.816,
+                0.353,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.3. Results on Image Classification"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We first show the performance of models trained with STL on the image classification task and compare them with other SOTA models in Table 2. To evaluate the zero-shot robustness against the distributional shift, all models are"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.892,
+                0.383
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Params (M)</td><td>Clean</td><td>IN-A</td><td>IN-R</td><td>mCE (↓)</td></tr><tr><td>Swin-T [50]</td><td>28.3</td><td>81.2</td><td>21.6</td><td>41.3</td><td>59.6</td></tr><tr><td>ConvNext-T [49]</td><td>28.6</td><td>82.1</td><td>24.2</td><td>47.2</td><td>53.2</td></tr><tr><td>RVT-S [51]</td><td>23.3</td><td>81.9</td><td>25.7</td><td>47.7</td><td>51.4</td></tr><tr><td>XCiT-S12 [52]</td><td>26.3</td><td>81.9</td><td>25.0</td><td>45.5</td><td>51.5</td></tr><tr><td>LV-ViT-S [3]</td><td>26.0</td><td>83.3</td><td>33.9</td><td>45.8</td><td>52.9</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26.3</td><td>83.5</td><td>33.9</td><td>50.7</td><td>47.8</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26.5</td><td>83.4</td><td>38.2</td><td>51.8</td><td>47.3</td></tr><tr><td>Swin-S [50]</td><td>50.0</td><td>83.4</td><td>35.8</td><td>46.6</td><td>52.7</td></tr><tr><td>ConvNext-S [49]</td><td>50.2</td><td>82.1</td><td>31.2</td><td>49.5</td><td>51.2</td></tr><tr><td>XCiT-S24 [52]</td><td>47.7</td><td>82.6</td><td>27.8</td><td>45.5</td><td>49.4</td></tr><tr><td>LV-ViT-M [3]</td><td>56.0</td><td>84.0</td><td>35.2</td><td>47.2</td><td>50.5</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4</td><td>83.9</td><td>39.6</td><td>52.9</td><td>45.2</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9</td><td>84.5</td><td>42.6</td><td>55.3</td><td>43.6</td></tr><tr><td>Swin-B [50]</td><td>87.8</td><td>83.4</td><td>35.8</td><td>46.6</td><td>54.4</td></tr><tr><td>MAE-ViT-B [53]</td><td>86.0</td><td>83.6</td><td>35.9</td><td>48.3</td><td>51.7</td></tr><tr><td>ConvNext-B [49]</td><td>88.6</td><td>83.8</td><td>36.7</td><td>51.3</td><td>46.8</td></tr><tr><td>RVT-B [51]</td><td>91.8</td><td>82.6</td><td>28.5</td><td>48.7</td><td>46.8</td></tr><tr><td>DAT-AugReg-ViT [14]</td><td>86.0</td><td>81.5</td><td>30.2</td><td>47.3</td><td>44.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8</td><td>84.3</td><td>41.8</td><td>53.2</td><td>43.0</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3</td><td>84.7</td><td>46.1</td><td>56.6</td><td>42.5</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.499,
+                0.384,
+                0.892,
+                0.467
+            ],
+            "angle": 0,
+            "content": "Table 3. Results on out-of-distribution datasets. We report the mean corruption error (mCE) for ImageNet-C, a lower value indicates better robustness. The improved robustness of models trained with STL is well generalized to out-of-distribution datasets and achieves even better robustness on ImageNet-A and ImageNet-R."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.491,
+                0.892,
+                0.703
+            ],
+            "angle": 0,
+            "content": "trained on ImageNet-1K data and directly used for inference on ImageNet-C without finetuning. We use the same model type for FAN-TL and the student model. It can be seen that Transformer-based models are more robust than CNN-based models in general. At all size levels, our models show superior robust accuracy and retention rate to other models, including the original FAN models trained solely with the class labels, indicating the effectiveness of STL in improving model robustness. Notably, our models surpass LV-ViTs [3] (i.e., vanilla ViT models trained with a CNN token-labeler) in both clean and robust accuracy by significant margins, which validates the importance of channel attention block in FAN and reveals the potential of self-emerging token labels from Transformer-based models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.712,
+                0.875,
+                0.728
+            ],
+            "angle": 0,
+            "content": "4.4. Robustness against Out-of-distribution Data"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Token labels embed rich local information of image patches. We adopt spatial-only data augmentation and Gumbel-Softmax on FAN-TL to retain highly accurate labels for foreground tokens to ensure that self-emerging token labels always provide correct information for student models. The practice promotes the generalization performance of student models as they can make robust predictions even with different input data distributions. To verify this, we then evaluate model robustness against out-of-distribution data, and results are summarized in Table 3. Similarly, models are not fine-tuned for testing. We find that"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5590"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.089,
+                0.47,
+                0.401
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Encoder Size</td><td>City</td><td>City-C</td><td>Retention</td></tr><tr><td>DeepLabv3+ (R50) [54]</td><td>25.4M</td><td>76.6</td><td>36.8</td><td>48.0%</td></tr><tr><td>DeepLabv3+ (R101) [54]</td><td>47.9M</td><td>77.1</td><td>39.4</td><td>51.1%</td></tr><tr><td>DeepLabv3+ (X65) [54]</td><td>22.8M</td><td>78.4</td><td>42.7</td><td>54.5%</td></tr><tr><td>DeepLabv3+ (X71) [54]</td><td>-</td><td>78.6</td><td>42.5</td><td>54.1%</td></tr><tr><td>ICNet ([55])</td><td>-</td><td>65.9</td><td>28.0</td><td>42.5%</td></tr><tr><td>FCN8s ([56])</td><td>50.1M</td><td>66.7</td><td>27.4</td><td>41.1%</td></tr><tr><td>DilatedNet ([57])</td><td>-</td><td>68.6</td><td>30.3</td><td>44.2%</td></tr><tr><td>ResNet38 ([58])</td><td>-</td><td>77.5</td><td>32.6</td><td>42.1%</td></tr><tr><td>PSPNet ([59])</td><td>13.7M</td><td>78.8</td><td>34.5</td><td>43.8%</td></tr><tr><td>ConvNeXt-T ([49])</td><td>29.0M</td><td>79.0</td><td>54.4</td><td>68.9%</td></tr><tr><td>SETR ([60])</td><td>22.1M</td><td>76.0</td><td>55.3</td><td>72.8%</td></tr><tr><td>SWIN-T ([43])</td><td>28.4M</td><td>78.1</td><td>47.3</td><td>60.6%</td></tr><tr><td>SegFormer-B0 ([11])</td><td>3.4M</td><td>76.2</td><td>48.8</td><td>64.0%</td></tr><tr><td>SegFormer-B1 ([11])</td><td>13.1M</td><td>78.4</td><td>52.7</td><td>67.2%</td></tr><tr><td>SegFormer-B2 ([11])</td><td>24.2M</td><td>81.0</td><td>59.6</td><td>73.6%</td></tr><tr><td>SegFormer-B5 ([11])</td><td>81.4M</td><td>82.4</td><td>65.8</td><td>79.9%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4M</td><td>82.2</td><td>66.9</td><td>81.5%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9M</td><td>82.5</td><td>68.6</td><td>83.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8M</td><td>82.3</td><td>68.7</td><td>83.5%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3M</td><td>82.8</td><td>69.2</td><td>83.6%</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.077,
+                0.402,
+                0.47,
+                0.471
+            ],
+            "angle": 0,
+            "content": "Table 4. Results on semantic segmentation. We use mIoU as the evaluation metric. 'R-' and 'X-' refer to ResNet and Xception, respectively. Models trained with STL demonstrate an impressive transferability to the downstream task and achieve significantly better mIoU than other models on Cityscapes and Cityscapes-C."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.498,
+                0.47,
+                0.651
+            ],
+            "angle": 0,
+            "content": "LV-ViTs and original FAN models generalize well to out-of-distribution data, while other Transformer-based models and the SOTA CNN-based ConvNext models perform weaker. Despite the impressive performance of original FAN models, models trained with STL demonstrate an even better generalization ability and outperform all other models. The performance gains on IN-A and IN-R are more significant than IN-C and set a new state-of-the-art, indicating that the accurate self-emerging token labels are crucial to robustness against out-of-distribution data."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.674,
+                0.433,
+                0.691
+            ],
+            "angle": 0,
+            "content": "4.5. Transferability to Semantic Segmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "[61] shows pre-trained models using different training recipes perform differently in downstream tasks. [3] validates that token labeling with CNN token-labelers benefits semantic segmentation and improves the clean mIoU. We also evaluate the transferability of STL to semantic segmentation. As shown in Table 4, pre-trained models with STL reveal better transferability than original FAN counterparts and other prestigious backbones. Remarkably, our approach achieves superior results on both clean and corrupted datasets. As far as we know, this is the first work to reveal that applying dense supervision in backbone pretraining improves not only the clean performance but also the robustness of the downstream task."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.504,
+                0.089,
+                0.892,
+                0.344
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Encoder Size</td><td>COCO (mAP)</td></tr><tr><td colspan=\"3\">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50 [45]</td><td>25M</td><td>46.3</td></tr><tr><td>ResNeXt-101-32 [62]</td><td>-</td><td>48.1</td></tr><tr><td>ResNeXt-101-64 [62]</td><td>-</td><td>48.3</td></tr><tr><td>Swin-T [43]</td><td>28M</td><td>50.4</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M</td><td>50.4</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M</td><td>53.3</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26M</td><td>53.4</td></tr><tr><td>Swin-S [43]</td><td>50M</td><td>51.9</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M</td><td>51.9</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M</td><td>53.5</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50M</td><td>53.9</td></tr><tr><td>Swin-B [43]</td><td>88M</td><td>51.9</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M</td><td>52.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M</td><td>54.1</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M</td><td>54.1</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.499,
+                0.346,
+                0.894,
+                0.415
+            ],
+            "angle": 0,
+            "content": "Table 5. Results on object detection. Models trained with STL outperform most CNN-based and transformer-based backbones. Even compared with original FAN models, our models achieve at least on par or even better mAP on COCO, indicating our method can also benefit object detection."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.435,
+                0.807,
+                0.451
+            ],
+            "angle": 0,
+            "content": "4.6. Transferability to Object Detection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.458,
+                0.892,
+                0.656
+            ],
+            "angle": 0,
+            "content": "We also validate STL's transferability to the object detection task on COCO and present the results in Table 5. Models trained with STL outperform most CNN-based and Transformer-based backbones. Even compared with original FAN models, STL brings a notable performance gain for FAN-B while achieving comparable mean average precision on FAN-L and FAN-S. We notice the overall improvement in object detection is not as good as in image classification and semantic segmentation, possibly because the semantic segmentation task is more similar to token labeling from the perspective of dense prediction, while object detection involves different techniques such as regression [63, 64] and multi-stage refinement [44, 63]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.671,
+                0.652,
+                0.687
+            ],
+            "angle": 0,
+            "content": "5. Ablation Study"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.696,
+                0.847,
+                0.712
+            ],
+            "angle": 0,
+            "content": "5.1. Impacts of Different Data Augmentation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "We apply spatial-only data augmentation on FAN-TL to obtain accurate token labels that provide clean and correct information toward student models, which is vital to model robustness. The strategy is a \"clean teacher noisy student\" design, where the student still uses all the augmentations. Our motivation behind this design is to let the teacher and student spatially aligned, with the teacher being as clean as possible to generate high quality token labels (Strong augmentations make it harder to generate good token labels as shown in Fig. 4). We compare the impacts of different data augmentation imposed on FAN-TL in Table 6. Experiments are conducted on the FAN-S-Hybrid model. The student"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.958
+            ],
+            "angle": 0,
+            "content": "5591"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.157,
+                0.09,
+                0.212,
+                0.176
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.272,
+                0.132
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.277,
+                0.09,
+                0.335,
+                0.132
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.34,
+                0.09,
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+                0.132
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.158,
+                0.134,
+                0.211,
+                0.175
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.219,
+                0.134,
+                0.273,
+                0.175
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.278,
+                0.134,
+                0.336,
+                0.175
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.341,
+                0.134,
+                0.396,
+                0.175
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.179,
+                0.47,
+                0.221
+            ],
+            "angle": 0,
+            "content": "Figure 4. Visualization results of token labels generated by FAN-TL with full data augmentations. Strong augmentations significantly affect the quality of token labels."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.234,
+                0.466,
+                0.306
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td><td>IN-1K</td><td>IN-C</td></tr><tr><td>✓</td><td>✘</td><td>✘</td><td>✘</td><td>✘</td><td>83.4</td><td>65.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✘</td><td>✘</td><td>82.6</td><td>63.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>83.6</td><td>64.9</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.077,
+                0.306,
+                0.469,
+                0.389
+            ],
+            "angle": 0,
+            "content": "Table 6. Ablation on impact to the student model using various data augmentations on FAN-TL. The different data augmentations are only imposed on the token-labeler's inputs, while the student model's inputs are fully augmented. Strong data augmentations on FAN-TL undermine token label accuracy and significantly affect the student model's robust accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.408,
+                0.469,
+                0.528
+            ],
+            "angle": 0,
+            "content": "model trained with token labels generated by spatial-only data augmentation achieves the best robustness while applying stronger augmentations harms the robust accuracy. Interestingly, applying the consistent full data augmentation on FAN-TL and the student model yields better clean accuracy, which reveals that different combinations of data augmentation may play different roles in improving model robustness and clean performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.538,
+                0.332,
+                0.554
+            ],
+            "angle": 0,
+            "content": "5.2. Impacts of Gumbel-Softmax"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.562,
+                0.469,
+                0.711
+            ],
+            "angle": 0,
+            "content": "We propose to use Gumbel-Softmax as a lightweight solution to retain correct token labels for foreground tokens and eliminate incorrect ones, which yields a more accurate segmentation of the object. We evaluate the impact of Gumbel-Softmax using the FAN-S-Hybrid model in Table 7. As can be seen, models trained with token labels generated by Softmax and Gumbel-Softmax achieve comparable clean accuracy while Gumbel-Softmax improves robust accuracy. This further validates that accurate foreground token labels are critical to model robustness."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.722,
+                0.465,
+                0.77
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Token Labeling</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>Softmax</td><td>83.4</td><td>65.2</td><td>47.6</td><td>37.2</td><td>51.7</td></tr><tr><td>Gumbel-Softmax</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.077,
+                0.771,
+                0.468,
+                0.811
+            ],
+            "angle": 0,
+            "content": "Table 7. Comparison of Softmax and Gumbel-Softmax. Both methods achieve comparable clean accuracy while token labels generated by Gumbel-Softmax yield better robustness."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.833,
+                0.462,
+                0.849
+            ],
+            "angle": 0,
+            "content": "5.3. Training with Heterogeneous Token-Labelers"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In the previous experiments, we train student models with isomorphic FAN token-labelers (e.g., FAN-TL-S-Hybrid for FAN-S-Hybrid). We are interested in the impacts"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.889,
+                0.294
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>83.4</td><td>65.5</td><td>47.3</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>83.5</td><td>65.5</td><td>47.4</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.5</td><td>68.2</td><td>43.6</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.3</td><td>68.1</td><td>43.5</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.7</td><td>69.0</td><td>42.4</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.7</td><td>68.8</td><td>42.5</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.295,
+                0.892,
+                0.335
+            ],
+            "angle": 0,
+            "content": "Table 8. Performance comparison of training with different token labelers. The robustness of student models can be further improved by training with a heterogeneous token labeler."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.351,
+                0.892,
+                0.532
+            ],
+            "angle": 0,
+            "content": "of training with a heterogeneous token-labeler and conduct the ablation in Table 8. For each student model, we train with three different FAN token-labelers of model sizes from small to large. Models trained with heterogeneous FAN-TL can achieve at least comparable or even superior performance to ones trained with isomorphic token-labelers. Our large model trained with FAN-TL-B-Hybrid further boosts the clean and robust accuracy to \\(84.8\\%\\) and \\(69.2\\%\\) with the mCE of \\(42.1\\%\\). This indicates STL is robust to different token-labelers. Such robustness enables us to train a larger student model with a smaller token-labeler, which can reduce the training cost."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.543,
+                0.889,
+                0.704
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.2</td><td>65.8</td><td>46.9</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.5</td><td>67.4</td><td>44.9</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.9</td><td>68.3</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.5,
+                0.705,
+                0.892,
+                0.773
+            ],
+            "angle": 0,
+            "content": "Table 9. Comparison to the prior SOTA token labeling method. Our proposed method that employs self-emerging token labels always yields better robustness than NFNet-F6, which validates the benefit of encoding local information of image patches via self-attention."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.787,
+                0.884,
+                0.803
+            ],
+            "angle": 0,
+            "content": "5.4. Comparison to Prior Token Labeling Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "As shown in Sec. 4.3 and Sec. 4.4, models trained with FAN-TL demonstrate superior performance and robustness than LV-ViTs [3] trained with a CNN token-labeler (i.e., NFNet-F6 [5]), which may attribute to the self-emerging token labeling and the channel attention design of FAN models. To better understand the effect of token labeling, we"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5592"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.258
+            ],
+            "angle": 0,
+            "content": "train the same FAN models with different methods. Results are summarized in Table 9. It can be seen that STL still significantly outperforms the CNN token-labeler even with the same student model. Note that NFNet-F6 has more than 400M parameters and achieves an \\(86.3\\%\\) Top-1 accuracy on ImageNet-1K while the largest FAN-TL (i.e., FANTL-L-Hybrid) only has 77.3M parameters and \\(84.3\\%\\) Top-1 accuracy. However, FAN-TL consistently yields better results than NFNet-F6. The rationale behind this is possibly because self-emerging token labels provide self-consistent information to student models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.266,
+                0.295,
+                0.282
+            ],
+            "angle": 0,
+            "content": "5.5. Impacts of Loss Weight"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.289,
+                0.473,
+                0.424
+            ],
+            "angle": 0,
+            "content": "Choosing good loss weights is important when multiple losses are jointly optimized. To study the impact of loss weights and verify STL's robustness against different loss weights when training student models, we vary \\(\\beta\\) with various values and present the results in Table 10. We find STL not sensitive to \\(\\beta\\). Both clean and robust accuracy fluctuates in a small range. We thus set \\(\\beta = 1\\) to balance the loss with equal weights for simplicity. Similarly, for the training of token-labelers, \\(\\alpha\\) is also set to 1."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.434,
+                0.47,
+                0.495
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>β</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>0.5</td><td>83.5</td><td>65.5</td><td>47.3</td><td>38.5</td><td>51.7</td></tr><tr><td>1.0</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr><tr><td>2.0</td><td>83.5</td><td>65.6</td><td>47.2</td><td>37.3</td><td>51.1</td></tr></table>"
+        },
+        {
+            "type": "table_footnote",
+            "bbox": [
+                0.145,
+                0.495,
+                0.403,
+                0.507
+            ],
+            "angle": 0,
+            "content": "Table 10. Ablation study of loss weight \\( \\beta \\) ."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.527,
+                0.196,
+                0.543
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.552,
+                0.473,
+                0.765
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a self-emerging token labeling (STL) framework built on Transformer-based models instead of CNNs. STL enables FAN token-labelers to self-produce accurate and semantically meaningful token labels for training student models with dense supervision. Through extensive experiments and ablation studies, we demonstrate that models trained with STL significantly surpass the original FAN counterparts trained only with image-level labels and achieve remarkable robustness improvement in various visual recognition tasks. Our study validates that the self-produced knowledge from ViTs can indeed benefit their pre-training. We hope this work sheds light on the potential and understanding of self-emerging token labeling from ViTs and motivates future research."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.776,
+                0.174,
+                0.79
+            ],
+            "angle": 0,
+            "content": "References"
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+# Fully Attentional Networks with Self-emerging Token Labeling
+
+Bingyin Zhao $^{1,2*}$  Zhiding Yu $^{1\dagger}$  Shiyi Lan $^{1}$  Yutao Cheng $^{3}$  Anima Anandkumar $^{1,4}$  Yingjie Lao $^{2}$  Jose M. Alvarez $^{1}$ $^{1}$ NVIDIA  $^{2}$ Clemson University  $^{3}$ Fudan University  $^{4}$ Caltech
+
+# Abstract
+
+Recent studies indicate that Vision Transformers (ViTs) are robust against out-of-distribution scenarios. In particular, the Fully Attentional Network (FAN) - a family of ViT backbones, has achieved state-of-the-art robustness. In this paper, we revisit the FAN models and improve their pretraining with a self-emerging token labeling (STL) framework. Our method contains a two-stage training framework. Specifically, we first train a FAN token labeler (FANTL) to generate semantically meaningful patch token labels, followed by a FAN student model training stage that uses both the token labels and the original class label. With the proposed STL framework, our best model based on FAN-L-Hybrid (77.3M parameters) achieves  $84.8\%$  Top-1 accuracy and  $42.1\%$  mCE on ImageNet-1K and ImageNet-C, and sets a new state-of-the-art for ImageNet-A  $(46.1\%)$  and ImageNet-R  $(56.6\%)$  without using extra data, outperforming the original FAN counterpart by significant margins. The proposed framework also demonstrates significantly enhanced performance on downstream tasks such as semantic segmentation, with up to  $1.7\%$  improvement in robustness over the counterpart model.
+
+# 1. Introduction
+
+Vision Transformers (ViTs) [1] have recently achieved remarkable success in visual recognition tasks. Such success is not only attributed to their self-attention representation but also to the newly developed training recipes. For instance, refinements in training techniques such as strong data augmentation and knowledge distillation [2] greatly alleviate ViT's issue of being data-hungry and make them more accessible for training on ImageNet-1K.
+
+Another important development in the training recipe is token labeling [3], where patch tokens are assigned with labels to ViTs in a dense manner. In some sense, token labeling can also be considered as an alternative form of hard knowledge distillation. However, the dense nature of token
+
+![](images/5c7db0808a168a11f724e603a0d6b293484de2d644d8dd9279340ce971952861.jpg)  
+Figure 1. Results of zero-shot robustness against ImageNet-A and ImageNet-R. Models trained on ImageNet-1K with self-emerging token labels from FAN show superior robustness to the out-of-distribution data. Our best model (with only 77.3M parameters) achieves robust accuracy of  $46.1\%$  and  $56.6\%$  and sets a new record on ImageNet-A and ImageNet-R.
+
+labeling allows ViTs to leverage more fine-grained information in an image and take different categories and object localization into account. Compared to traditional knowledge distillation methods, token labeling enables ViTs to exploit a wider range of information in the image, leading to more accurate results. The success of token labeling depends on carefully-designed token-level annotators (i.e., token-labelers) that can provide accurate location-specific information (i.e., token labels) to patch tokens. In [3], this is done by a special re-labeling process [4] using convolutional neural networks (CNNs) [5] pre-trained on ImageNet-1K. While Vision Transformers have shown great promise in representation learning, less exploration has been conducted on modeling them as token-labelers. This raises two interesting questions:
+
+1. Can Transformer-based models self-produce meaningful token labels?  
+2. Can one improve the pre-training of ViTs with self-produced knowledge instead of external teachers?
+
+Our approach: In this paper, we aim to answer the above questions. We propose a self-emerging token labeling (STL) framework that employs the self-produced token labels by ViT token-labelers instead of relying on CNNs. Our work is built on the recently proposed Fully Attentional Network (FAN) [6] for two reasons. First, FAN exhibits excellent self-emerging visual grouping on token features, which can be leveraged to generate high-quality token labels. Second, FAN is a family of ViT backbones with state-of-the-art accuracy and robustness. We aim to further improve this family of powerful backbones through a principled token-labeling design and validate its effectiveness. Our contributions can be summarized as follows:
+
+- Our work demonstrates that ViT models can be effective token-labelers. We propose a simple yet effective way to train a FAN token-labeler that can produce semantically meaningful token labels.  
+- We perform an in-depth analysis and show critical contributors to the accuracy of token labels. On top of the observations, we design a solution that retains more accurate token labels of the target object for improved model pre-training.  
+- Our models trained with STL set a new record on out-of-distribution datasets without using extra data than ImageNet-1K. Our best model achieves robust accuracy of  $46.1\%$  on ImageNet-A and  $56.6\%$  on ImageNet-R with only 77M parameters, as shown in Fig. 1.  
+- Experiments on downstream tasks demonstrate that the improved performance in backbone models is transferable to semantic segmentation and object detection.
+
+Our STL framework is akin to the teacher-student training strategy introduced in knowledge distillation and consists of two stages:
+
+First stage: We train a FAN token-labeler (FAN-TL) model to generate token-level annotations. Our task is essentially a "chicken or the egg" problem since there is no explicit supervision on how the token labels are generated. We tackle this by assigning supervising both the class token and the global average-pooled token. This produces semantically meaningful token labels as shown in Fig. 2(b).
+
+Second stage: We train a FAN student model using the original class labels and the token labels from FAN-TL. Observing the imperfect quality of token labels, we introduce a token selection approach based on Gumbel-Softmax that adaptively selects tokens with high confidence. Labels of the selected tokens are of better quality and object grounding in general, leading to improved pre-training.
+
+# 2. Related Work
+
+# 2.1. Vision Transformers
+
+Vision Transformers [1] are a family of visual recognition models built upon Transformers [7]. ViT splits an input image into a series of small patches, projects each as an embedding (a.k.a patch token) and appends with position embeddings. The resulting patch tokens and an extra learnable class token that aggregates global information for classification are then fed into a sequence of Transformer encoders consisting of multi-head self-attention and FFN blocks. A linear projection layer is appended to the class token to predict the class probabilities.
+
+# 2.2. Fully Attentional Networks
+
+Several concurrent works point out that ViTs exhibit excellent zero-shot robustness against out-of-distribution samples [8-11]. Some works propose to use negative data augmentation [12] and adversarial training [13, 14] to further enhance the robustness. Recently, FAN [15] was introduced as a family of ViT backbones with state-of-the-art accuracy and robustness. FAN inherits the self-attention blocks of plain ViT but additionally introduces a channel attention block that adopts an attention-based design that aggregates the cross-channel information in a more holistic manner, leading to improved representation.
+
+# 2.3. Token Labeling
+
+Token labeling [3] has been proposed to improve ViT pre-training. From the perspective of training strategy, it is similar to knowledge distillation [2, 16] since both adopt a teacher-student mode. It is also related to ReLabel [17], which provides images with multi-label annotations instead of single ones. However, both ReLabel and knowledge distillation depend on image-level labels as global supervision while token labeling assigns labels to each image patch token and supervises the student model in a dense manner. Token labeling is also inherently related to tokenization in BEiT [18], where an offline pre-trained discrete VAE is employed as the tokenizer to encode patches into visual tokens (i.e., code from a visual codebook). Different from token labels, these visual tokens do not possess explicit semantically meanings since they originate from an unsupervisedly trained codebook. Our method differs from prior token labeling and distillation methods where pre-trained convolutional neural networks are widely used as the token-labeler. Instead, our approach to unifies both teacher and student under homogeneous Vision Transformer architectures to generate high-quality token labels.
+
+# 2.4. Emerging Properties of ViTs
+
+It was found that the localization of objects emerges in image classification with CNNs. This interesting phe
+
+nomenon, also known as class activation maps (CAM) [19], lays the foundation for token labeling. Recent studies reveal that ViTs demonstrate excellent capability for object localization without explicit supervision. For instance, DINO [20] shows that self-supervised ViT features generate semantically meaning object segmentation. Methods like GroupViT [21] show that semantic segmentation emerges in ViTs using only text supervision. Similarly, FAN reveals that the robustness of ViT models is correlated to their excellent visual grouping capability. This feature motivates us to develop self-emerging token labeling on top of the FAN models.
+
+# 3. Method
+
+As mentioned, we propose a self-emerging token labeling (STL) framework that uses self-produced token labels to improve ViT pre-training. STL consists of two stages: 1) training an effective token-labeler, and 2) training a student model with self-emerging token labels.
+
+In the first stage, we train a FAN token-labeler (FANTL) to generate high-quality token labels. As discussed in Sec. 1 and Sec. 2, FAN demonstrates strong robustness and capability to obtain semantically meaningful visual grouping that can correctly captures the object gestalt. These great features of FAN allow us to obtain high quality token labels without bells and whistles. In the second stage, we then train a FAN student model with image-level labels and self-emerging token labels from FAN-TL. At high level, FAN-TL and FAN student models follow the same architectural design as FAN but slightly modify the structure of patch tokens. We attach a linear layer to each patch token to accommodate token labels, similar to the classification head added to the class token in the original FAN and ViT design. The rest of this section describes the implementation details of the above two-stage pipeline.
+
+# 3.1. Training FAN Token-Labelers
+
+The original FAN employs the training paradigm that only takes image-level labels as supervision. We denote the input image as  $\mathbf{I}$ , the sequence of small patches as  $[\mathbf{I}_{p_1},\mathbf{I}_{p_2},\dots,\mathbf{I}_{p_N}]$ , the output of FAN encoder as  $[\mathbf{T}_{cls},\mathbf{T}_{p_1},\dots,\mathbf{T}_{p_N}]$ , where  $N$  is the number of patch tokens,  $\mathbf{T}_{cls}$  represents the class token and  $\mathbf{T}_{p_1},\ldots ,\mathbf{T}_{p_N}$  represent the patch tokens, respectively. The training objective can be mathematically expressed as follows:
+
+$$
+\mathcal {L} = \mathcal {H} \left(\mathbf {T} _ {\text {c l s}}, \mathbf {Y} _ {\text {c l s}}\right), \tag {1}
+$$
+
+where  $\mathcal{H}(\cdot)$  is the softmax cross entropy loss and  $\mathbf{Y}_{cls}$  is the image-level label of the corresponding class.
+
+The key to token labeling is the generation of accurate token labels that provide location-specific information. However, following the conventional training paradigm in Eq. 1,
+
+![](images/5acfb3a88d6092486a2439f1fa745c74ccd032688d50993a463e0081a350f250.jpg)  
+Figure 2. Illustration of token labels generated by FAN-TL and the token label confidence score distribution. (a). original image (class: "tench"), (b). binary color map of token labels (yellow: tokens classified as "tench", dark blue: tokens not classified as "tench") (c). trinary color map of token labels (cyan: foreground tokens with low confidence, yellow: foreground tokens with high confidence), (d). binary color map of foreground tokens selected by Gumbel-Softmax, (e). token label confidence score distribution of a batch of 16 images.
+
+token outputs of FAN models are not semantically well-guided since they are not supervised during training. We propose a simple yet effective method to address this issue. Our idea is inspired by the intriguing phenomenon in ViTs training that meaningful object segmentation naturally emerges [20]. Unlike the self-supervised training in DINO, we leverage FAN's strong capability of visual grouping [22] and devise a fully supervised approach that allows FAN to generate accurate and semantically meaningful token labels. We perform global average-pooling on all patch tokens and then simultaneously assign the class label to the class and the average-pooled tokens. The training objective of FANTL can be written as follows:
+
+$$
+\mathcal {L} = \mathcal {H} \left(\mathbf {T} _ {c l s}, \mathbf {Y} _ {c l s}\right) + \alpha \cdot \mathcal {H} \left(\frac {1}{N} \sum_ {i = 1} ^ {N} \mathbf {T} _ {p _ {i}}, \mathbf {Y} _ {c l s}\right), \tag {2}
+$$
+
+where  $\alpha$  weights the importance of two loss functions. We set  $\alpha$  to 1 in our experiments. We demonstrate a visualization example of the token labels generated by FAN-TL in Fig. 2(b). The yellow area (i.e., foreground) represents the tokens with the same labels as the image-level label (we term foreground tokens). In contrast, the dark blue area (i.e., background) represents the tokens with different labels from the image-level label (we term background tokens). It can be seen that the self-emerging token labels show a meaningful segmentation of the target object "tench".
+
+![](images/fa4d7bb38a6a0c341d102274f8ff604d43adb13f1c820cfafc521fb70b77988f.jpg)  
+Generate token labels using FAN-TL
+
+![](images/c955b6954053e9af7e7b61ec22320d1560766cb1c2577bfd699d28a711ab7117.jpg)  
+Train the student model with self-emerging token labeling  
+Figure 3. Illustration of Stage 2: Training student models with self-emerging token labels. In the training, token labels are generated by FAN-TL and assigned to patch tokens of student models. We incorporate the token labels and class labels to train student models jointly. FAN-TL can self-identify the incorrect token labels upon the confidence score. Tokens with high confidence scores offer a more accurate segmentation of objects and are crucial to robustness improvement. By applying spatial-only data augmentation to the inputs and Gumbel-Softmax to the token outputs of FAN-TL, we obtain the most accurate and critical token labels.
+
+# 3.2. Training Student Models with STL
+
+Training student models is straightforward. As illustrated in Fig. 3, we take the token outputs of FAN-TL and assign them as the labels for patch tokens of student models. We then incorporate token labels with class labels and jointly optimize the loss on the class token and all patch tokens. The training objective is shown as follows:
+
+$$
+\mathcal {L} = \mathcal {H} \left(\mathbf {T} _ {c l s}, \mathbf {Y} _ {c l s}\right) + \beta \cdot \frac {1}{N} \sum_ {i = 1} ^ {N} \mathcal {H} \left(\mathbf {T} _ {p _ {i}}, \mathcal {F} \left(\mathbf {I} _ {p _ {i}}\right)\right) \tag {3}
+$$
+
+where  $\mathcal{F}(\cdot)$  represents the patch token outputs of FAN-TL and  $\beta$  is the hyper-parameter to balance two loss functions.  $\beta$  is set to 1 in our experiments. Note the correctness of token labels (especially the foreground tokens) is critical since wrong labels introduce worthless local information. Thus, we propose several implementation tricks to generate and retain highly accurate token labels based on the following two observations.
+
+Observation 1: Data augmentations remarkably affect the accuracy of token labels. Recent studies [2, 23] indicate data augmentations improve the classification accuracy and robustness of ViT models. However, most augmentations undermine the accuracy of token labels. For example, augmentations in RandAug [24], such as posterize and solarize, alter pixel values, CutOut [25] randomly erases a part of images, Mixup [26] and CutMix [27] mix content from two images, which all make it difficult for FAN-TL to assign correct labels to patch tokens. To this end, we disable these data augmentations and keep spatial-
+
+<table><tr><td>Model (Stage)</td><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td></tr><tr><td>FAN-TL (Stage1)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Student (Stage2)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FAN-TL (Stage2)</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td></tr></table>
+
+Table 1. Detailed settings of data augmentations. We apply spatial-only data augmentations to inputs of FAN-TL in stage 2 to improve the accuracy of token labels.
+
+only ones (i.e., flip, rotate, shear and translation) for FANTL when generating token labels. Note that we still apply full data augmentations for the student model. The concrete settings of data augmentations are summarized in Table 1. Moreover, the strong data augmentations can be regarded as noises akin to corruptions and perturbations in out-of-distribution datasets. The input data augmentation discrepancy between FANT-LT and the student model enables the self-emerging token labels to provide clean and correct information regardless of the noise, thus improving the model's robustness.
+
+Observation 2: Not all the self-emerging token labels are correct, even with spatial-only data augmentations. For example, as shown in Fig. 2(b), some patches (red squares) that only contain "human" and "lake" are misclassified as the target object "tench" by FAN-TL. It is particularly crucial to ensure the accuracy of foreground token labels as they contain the target object of the image that dominates the prediction result. However, it is challenging to determine which labels are incorrect due to the lack of patch-level ground truth. Interestingly, FAN-TL can
+
+self-identify these misclassified foreground tokens according to the token label confidence score, which may also be attributed to its visual grouping ability. The token label confidence score is defined as the maximal class probability of each token output. We find that tokens with correct labels tend to have higher confidence scores than those with incorrect labels. As shown in Fig. 2(c) and Fig. 2(e), the yellow area indicates the foreground tokens with high confidence scores  $(0.7\sim 0.9)$ . These tokens yield a highly accurate segmentation of the target object. Contrastly, the cyan area represents the foreground tokens with low confidence scores  $(0\sim 0.2)$ , which are coincidentally the ones with incorrect labels.
+
+We attempt to assign highly accurate labels to the target object (i.e., foreground tokens). However, it is intractable to exhaustively examine the confidence score of each patch token for all the images as it significantly increases the training time and requires much more computational resources. Therefore, we propose a lightweight alternative by applying the Gumbel-Softmax [28] on the top of token outputs. Mathematically, it can be expressed as:
+
+$$
+\mathbf {y} _ {i} = \frac {e ^ {\left(\log \left(\pi_ {i}\right) + \mathcal {G} _ {i}\right) / \tau}\left. \right)}{\sum_ {j = 1} ^ {k} e ^ {\left(\log \left(\pi_ {j}\right) + \mathcal {G} _ {j}\right) / \tau})} \tag {4}
+$$
+
+where  $\mathbf{y}$  is the  $k$ -dimension softmax vector,  $\pi$  are class probabilities,  $\mathcal{G} \sim Gumbel(0,1)$  are i.i.d. samples drawn from the standard Gumbel distribution and  $\tau$  is the softmax temperature. Token labels with high confidence scores remain unchanged after applying Gumbel-Softmax, while labels with low confidence scores are highly likely to change. As shown in Fig. 2(d), we preserve the correct token labels and eliminate the incorrect ones in a simple yet effective way, achieving high accuracy of foreground tokens labels and more precise segmentation of the object. Furthermore, since the training objective of the patch tokens side can be considered a self-training process [29-31], we convert the softmax outputs to "one-hot" probability distribution (i.e., hard labels) as [32] shows that the use of hard labels in self-training encourages the model's predictions to be high-confidence via entropy minimization [33]. Following the aforementioned spatial-only data augmentation, we can then rewrite the training objective of the student model:
+
+$$
+\mathcal {L} = \mathcal {H} (\mathbf {T} _ {c l s}, \mathbf {Y} _ {c l s}) + \beta \cdot \frac {1}{N} \sum_ {i = 1} ^ {N} \mathcal {H} (\mathbf {T} _ {p _ {i}}, \hat {\mathcal {F}} (\hat {\mathbf {I}} _ {p _ {i}})) \tag {5}
+$$
+
+where  $\hat{\mathcal{F}} (\cdot)$  is the one-hot encoded Gumbel-Softmax outputs of FAN-TL and  $[\hat{\mathbf{I}}_{p_1}\dots \hat{\mathbf{I}}_{p_N}]$  are image patches with the spatial-only data augmentation. Meanwhile, we notice that all background tokens (i.e., the dark blue area) also have low confidence scores. This is probably because these tokens neither contain apparent features associated with the
+
+target object nor clear features related to any other class in the dataset. Nevertheless, we keep all tokens (even those with low confidence scores) in training, following the practice in [3] as involving more tokens for loss computation yields better performance.
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation Metrics
+
+We evaluate our method on the image classification task and its transferability to downstream semantic segmentation and object detection tasks.
+
+Datasets. For image classification, we test model performance and robustness on ImageNet-1K (IN-1K) [34], ImageNet-C (IN-C) [35], ImageNet-A (IN-A) [36] and ImageNet-R (IN-R) [37]. IN-C contains natural corruptions from noise, blur, weather, and digital categories and is widely used to evaluate model's robustness against shifted distribution data. IN-A and IN-R consist of images with different distributions from ImageNet training distribution, such as natural adversarial examples and pictures generated by artistic rendition, thus are widely used to measure the robustness against out-of-distribution data. For semantic segmentation and object detection, we evaluate models on Cityscapes (City) [38], Cityscapes-C (City-C) and COCO [39]. Similar to IN-C, City-C has corruptions from the same four categories.
+
+Metrics. We adopt standard evaluation metrics for image classification: clean accuracy for IN-1K and robust accuracy for IN-C, IN-A and IN-R. We also report mean corruption error (mCE) [35] on IN-C. For semantic segmentation and object detection, we evaluate the model performance using the clean and robust mean Intersection over Union (mIoU) on City and City-C and the mean average precision (mAP) on COCO. Additionally, we use retention rate as the metric to reflect the resilience of the model robustness and fairly compare models with different capacities. The retention rate is defined as  $R = \frac{\text{Robust Acc.}}{\text{Clean Acc.}}$ .
+
+# 4.2. Implementation Details
+
+Experiments are conducted on 8 NVIDIA Tesla V100s and codes are built upon Pytorch [40], timm [41] library and MMSegmentation [42] toolbox. We adopt FAN-Hybrid as the model architecture for FAN-TL and student models. For image classification, we train the models on ImageNet-1K using AdamW optimizer with a learning rate of 4e-3 and batch size of 2048 for 350 epochs. We employ the cosine scheduler with a decay rate of 0.1 to adjust the learning rate every 30 epochs. The loss weight  $\alpha$  in Eq. 2 and  $\beta$  in Eq. 5 are set to 1. We apply spatial, RandAug, CutOut, Mixup and CutMix data augmentation in the training and a label smoothing ratio of 0.9 to class and token labels. As discussed in Sec. 3, we apply spatial-only data augmentations
+
+<table><tr><td>Model</td><td>Param./FLOPs</td><td>IN-1K</td><td>IN-C</td><td>Retention</td></tr><tr><td>ResNet18 [45]</td><td>11M/1.8G</td><td>69.9</td><td>32.7</td><td>46.8%</td></tr><tr><td>MBV2 [46]</td><td>4M/0.4G</td><td>73.0</td><td>35.0</td><td>47.9%</td></tr><tr><td>EffiNet-B0 [47]</td><td>5M/0.4G</td><td>77.5</td><td>41.1</td><td>53.0%</td></tr><tr><td>PVTV2-B0 [48]</td><td>3M/0.6G</td><td>70.5</td><td>36.2</td><td>51.3%</td></tr><tr><td>PVTV2-B1 [48]</td><td>13M/2.1G</td><td>78.7</td><td>51.7</td><td>65.7%</td></tr><tr><td>LV-ViT-T [3]</td><td>9M/2.1G</td><td>79.1</td><td>51.6</td><td>65.2%</td></tr><tr><td>FAN-T-Hybrid [15]</td><td>7M/3.5G</td><td>80.1</td><td>57.4</td><td>71.4%</td></tr><tr><td>STL (FAN-T-Hybrid)</td><td>8M/3.6G</td><td>79.9</td><td>58.2</td><td>72.8%</td></tr><tr><td>ResNet50 [45]</td><td>25M/4.1G</td><td>79.0</td><td>50.6</td><td>64.1%</td></tr><tr><td>DeiT-S [2]</td><td>22M/4.6G</td><td>79.9</td><td>58.1</td><td>72.7%</td></tr><tr><td>Swin-T [43]</td><td>28M/4.5G</td><td>81.3</td><td>55.4</td><td>68.1%</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M/4.5G</td><td>82.1</td><td>59.1</td><td>71.9%</td></tr><tr><td>LV-ViT-S [3]</td><td>26M/6.6G</td><td>83.3</td><td>59.7</td><td>71.7%</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M/6.7G</td><td>83.5</td><td>64.7</td><td>77.5%</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>27M/6.8G</td><td>83.4</td><td>65.5</td><td>78.5%</td></tr><tr><td>Swin-S [43]</td><td>50M/8.7G</td><td>83.0</td><td>60.4</td><td>72.8%</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M/8.7G</td><td>83.1</td><td>61.7</td><td>74.2%</td></tr><tr><td>LV-ViT-M [3]</td><td>56M/16.0G</td><td>84.0</td><td>62.0</td><td>73.8%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M/11.3G</td><td>83.9</td><td>66.4</td><td>79.1%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>51M/11.4G</td><td>84.5</td><td>68.2</td><td>80.7%</td></tr><tr><td>DeiT-B [2]</td><td>89M/17.6G</td><td>81.8</td><td>62.7</td><td>76.7%</td></tr><tr><td>Swin-B [43]</td><td>88M/15.4G</td><td>83.5</td><td>60.4</td><td>72.3%</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M/15.4G</td><td>83.8</td><td>63.0</td><td>75.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M/16.9G</td><td>84.3</td><td>68.3</td><td>81.0%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M/17.0G</td><td>84.7</td><td>68.8</td><td>81.2%</td></tr></table>
+
+Table 2. Results on image classification. We report clean and robust accuracy on ImageNet-1K and ImageNet-C. Retention rate is defined as Robust Acc. LV-ViTs are vanilla ViTs trained with a CNN token-labeler. Our models trained with STL achieve superior robustness and retention rate in all cases. Meanwhile, our method also improves the clean accuracy of models with a larger capacity (e.g., FAN-B-Hybrid and FAN-L-Hybrid).
+
+on inputs of FAN-TL and Gumbel-Softmax on patch token outputs to obtain accurate token labels. We employ pretrained image classification models for semantic segmentation as encoders and the SegFormer [11] head as the decoder. We follow the same training recipe as SegFormer and train our models on Cityscapes using AdamW with a learning rate of 6e-5 and a batch size of 8 for 160K iterations. The learning rate scheduler is set to "poly" with a default factor of 1.0. Random resizing, flipping, and cropping are applied as data augmentations in training. For object detection, we follow the same practice as Swin Transformer [43] + Cascade Mask R-CNN [44] and employ AdamW (initial learning rate of 1e-4, weight decay of 0.05, and batch size of 16) to train our models on COCO for 36 epochs.
+
+# 4.3. Results on Image Classification
+
+We first show the performance of models trained with STL on the image classification task and compare them with other SOTA models in Table 2. To evaluate the zero-shot robustness against the distributional shift, all models are
+
+<table><tr><td>Model</td><td>Params (M)</td><td>Clean</td><td>IN-A</td><td>IN-R</td><td>mCE (↓)</td></tr><tr><td>Swin-T [50]</td><td>28.3</td><td>81.2</td><td>21.6</td><td>41.3</td><td>59.6</td></tr><tr><td>ConvNext-T [49]</td><td>28.6</td><td>82.1</td><td>24.2</td><td>47.2</td><td>53.2</td></tr><tr><td>RVT-S [51]</td><td>23.3</td><td>81.9</td><td>25.7</td><td>47.7</td><td>51.4</td></tr><tr><td>XCiT-S12 [52]</td><td>26.3</td><td>81.9</td><td>25.0</td><td>45.5</td><td>51.5</td></tr><tr><td>LV-ViT-S [3]</td><td>26.0</td><td>83.3</td><td>33.9</td><td>45.8</td><td>52.9</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26.3</td><td>83.5</td><td>33.9</td><td>50.7</td><td>47.8</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26.5</td><td>83.4</td><td>38.2</td><td>51.8</td><td>47.3</td></tr><tr><td>Swin-S [50]</td><td>50.0</td><td>83.4</td><td>35.8</td><td>46.6</td><td>52.7</td></tr><tr><td>ConvNext-S [49]</td><td>50.2</td><td>82.1</td><td>31.2</td><td>49.5</td><td>51.2</td></tr><tr><td>XCiT-S24 [52]</td><td>47.7</td><td>82.6</td><td>27.8</td><td>45.5</td><td>49.4</td></tr><tr><td>LV-ViT-M [3]</td><td>56.0</td><td>84.0</td><td>35.2</td><td>47.2</td><td>50.5</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4</td><td>83.9</td><td>39.6</td><td>52.9</td><td>45.2</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9</td><td>84.5</td><td>42.6</td><td>55.3</td><td>43.6</td></tr><tr><td>Swin-B [50]</td><td>87.8</td><td>83.4</td><td>35.8</td><td>46.6</td><td>54.4</td></tr><tr><td>MAE-ViT-B [53]</td><td>86.0</td><td>83.6</td><td>35.9</td><td>48.3</td><td>51.7</td></tr><tr><td>ConvNext-B [49]</td><td>88.6</td><td>83.8</td><td>36.7</td><td>51.3</td><td>46.8</td></tr><tr><td>RVT-B [51]</td><td>91.8</td><td>82.6</td><td>28.5</td><td>48.7</td><td>46.8</td></tr><tr><td>DAT-AugReg-ViT [14]</td><td>86.0</td><td>81.5</td><td>30.2</td><td>47.3</td><td>44.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8</td><td>84.3</td><td>41.8</td><td>53.2</td><td>43.0</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3</td><td>84.7</td><td>46.1</td><td>56.6</td><td>42.5</td></tr></table>
+
+Table 3. Results on out-of-distribution datasets. We report the mean corruption error (mCE) for ImageNet-C, a lower value indicates better robustness. The improved robustness of models trained with STL is well generalized to out-of-distribution datasets and achieves even better robustness on ImageNet-A and ImageNet-R.
+
+trained on ImageNet-1K data and directly used for inference on ImageNet-C without finetuning. We use the same model type for FAN-TL and the student model. It can be seen that Transformer-based models are more robust than CNN-based models in general. At all size levels, our models show superior robust accuracy and retention rate to other models, including the original FAN models trained solely with the class labels, indicating the effectiveness of STL in improving model robustness. Notably, our models surpass LV-ViTs [3] (i.e., vanilla ViT models trained with a CNN token-labeler) in both clean and robust accuracy by significant margins, which validates the importance of channel attention block in FAN and reveals the potential of self-emerging token labels from Transformer-based models.
+
+# 4.4. Robustness against Out-of-distribution Data
+
+Token labels embed rich local information of image patches. We adopt spatial-only data augmentation and Gumbel-Softmax on FAN-TL to retain highly accurate labels for foreground tokens to ensure that self-emerging token labels always provide correct information for student models. The practice promotes the generalization performance of student models as they can make robust predictions even with different input data distributions. To verify this, we then evaluate model robustness against out-of-distribution data, and results are summarized in Table 3. Similarly, models are not fine-tuned for testing. We find that
+
+<table><tr><td>Model</td><td>Encoder Size</td><td>City</td><td>City-C</td><td>Retention</td></tr><tr><td>DeepLabv3+ (R50) [54]</td><td>25.4M</td><td>76.6</td><td>36.8</td><td>48.0%</td></tr><tr><td>DeepLabv3+ (R101) [54]</td><td>47.9M</td><td>77.1</td><td>39.4</td><td>51.1%</td></tr><tr><td>DeepLabv3+ (X65) [54]</td><td>22.8M</td><td>78.4</td><td>42.7</td><td>54.5%</td></tr><tr><td>DeepLabv3+ (X71) [54]</td><td>-</td><td>78.6</td><td>42.5</td><td>54.1%</td></tr><tr><td>ICNet ([55])</td><td>-</td><td>65.9</td><td>28.0</td><td>42.5%</td></tr><tr><td>FCN8s ([56])</td><td>50.1M</td><td>66.7</td><td>27.4</td><td>41.1%</td></tr><tr><td>DilatedNet ([57])</td><td>-</td><td>68.6</td><td>30.3</td><td>44.2%</td></tr><tr><td>ResNet38 ([58])</td><td>-</td><td>77.5</td><td>32.6</td><td>42.1%</td></tr><tr><td>PSPNet ([59])</td><td>13.7M</td><td>78.8</td><td>34.5</td><td>43.8%</td></tr><tr><td>ConvNeXt-T ([49])</td><td>29.0M</td><td>79.0</td><td>54.4</td><td>68.9%</td></tr><tr><td>SETR ([60])</td><td>22.1M</td><td>76.0</td><td>55.3</td><td>72.8%</td></tr><tr><td>SWIN-T ([43])</td><td>28.4M</td><td>78.1</td><td>47.3</td><td>60.6%</td></tr><tr><td>SegFormer-B0 ([11])</td><td>3.4M</td><td>76.2</td><td>48.8</td><td>64.0%</td></tr><tr><td>SegFormer-B1 ([11])</td><td>13.1M</td><td>78.4</td><td>52.7</td><td>67.2%</td></tr><tr><td>SegFormer-B2 ([11])</td><td>24.2M</td><td>81.0</td><td>59.6</td><td>73.6%</td></tr><tr><td>SegFormer-B5 ([11])</td><td>81.4M</td><td>82.4</td><td>65.8</td><td>79.9%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4M</td><td>82.2</td><td>66.9</td><td>81.5%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9M</td><td>82.5</td><td>68.6</td><td>83.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8M</td><td>82.3</td><td>68.7</td><td>83.5%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3M</td><td>82.8</td><td>69.2</td><td>83.6%</td></tr></table>
+
+Table 4. Results on semantic segmentation. We use mIoU as the evaluation metric. 'R-' and 'X-' refer to ResNet and Xception, respectively. Models trained with STL demonstrate an impressive transferability to the downstream task and achieve significantly better mIoU than other models on Cityscapes and Cityscapes-C.
+
+LV-ViTs and original FAN models generalize well to out-of-distribution data, while other Transformer-based models and the SOTA CNN-based ConvNext models perform weaker. Despite the impressive performance of original FAN models, models trained with STL demonstrate an even better generalization ability and outperform all other models. The performance gains on IN-A and IN-R are more significant than IN-C and set a new state-of-the-art, indicating that the accurate self-emerging token labels are crucial to robustness against out-of-distribution data.
+
+# 4.5. Transferability to Semantic Segmentation
+
+[61] shows pre-trained models using different training recipes perform differently in downstream tasks. [3] validates that token labeling with CNN token-labelers benefits semantic segmentation and improves the clean mIoU. We also evaluate the transferability of STL to semantic segmentation. As shown in Table 4, pre-trained models with STL reveal better transferability than original FAN counterparts and other prestigious backbones. Remarkably, our approach achieves superior results on both clean and corrupted datasets. As far as we know, this is the first work to reveal that applying dense supervision in backbone pretraining improves not only the clean performance but also the robustness of the downstream task.
+
+<table><tr><td>Model</td><td>Encoder Size</td><td>COCO (mAP)</td></tr><tr><td colspan="3">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50 [45]</td><td>25M</td><td>46.3</td></tr><tr><td>ResNeXt-101-32 [62]</td><td>-</td><td>48.1</td></tr><tr><td>ResNeXt-101-64 [62]</td><td>-</td><td>48.3</td></tr><tr><td>Swin-T [43]</td><td>28M</td><td>50.4</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M</td><td>50.4</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M</td><td>53.3</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26M</td><td>53.4</td></tr><tr><td>Swin-S [43]</td><td>50M</td><td>51.9</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M</td><td>51.9</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M</td><td>53.5</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50M</td><td>53.9</td></tr><tr><td>Swin-B [43]</td><td>88M</td><td>51.9</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M</td><td>52.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M</td><td>54.1</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M</td><td>54.1</td></tr></table>
+
+Table 5. Results on object detection. Models trained with STL outperform most CNN-based and transformer-based backbones. Even compared with original FAN models, our models achieve at least on par or even better mAP on COCO, indicating our method can also benefit object detection.
+
+# 4.6. Transferability to Object Detection
+
+We also validate STL's transferability to the object detection task on COCO and present the results in Table 5. Models trained with STL outperform most CNN-based and Transformer-based backbones. Even compared with original FAN models, STL brings a notable performance gain for FAN-B while achieving comparable mean average precision on FAN-L and FAN-S. We notice the overall improvement in object detection is not as good as in image classification and semantic segmentation, possibly because the semantic segmentation task is more similar to token labeling from the perspective of dense prediction, while object detection involves different techniques such as regression [63, 64] and multi-stage refinement [44, 63].
+
+# 5. Ablation Study
+
+# 5.1. Impacts of Different Data Augmentation
+
+We apply spatial-only data augmentation on FAN-TL to obtain accurate token labels that provide clean and correct information toward student models, which is vital to model robustness. The strategy is a "clean teacher noisy student" design, where the student still uses all the augmentations. Our motivation behind this design is to let the teacher and student spatially aligned, with the teacher being as clean as possible to generate high quality token labels (Strong augmentations make it harder to generate good token labels as shown in Fig. 4). We compare the impacts of different data augmentation imposed on FAN-TL in Table 6. Experiments are conducted on the FAN-S-Hybrid model. The student
+
+![](images/32d9759f0350badc81b86b71551f57be1c5d99c95d5f3e97dc6cc7dc40ebdfa9.jpg)  
+Figure 4. Visualization results of token labels generated by FAN-TL with full data augmentations. Strong augmentations significantly affect the quality of token labels.
+
+![](images/46a014e4284d84c27a26b65293718196c7203ba5e403c9616bf63ff5f379eebb.jpg)
+
+![](images/6f6eecc16a645f0f4c3268bfb2057fdd0e45242502d8a3233d68486ce7ea385f.jpg)
+
+![](images/ff58b7dfe32cdb901e652340882303ea22831c85bf6fba7cadc3f37f164a1fa0.jpg)
+
+![](images/ee5358fd8bc706f6a0dc5bffeb1d5a77ae19916ba9a1099ab2518e4cc59c8e9c.jpg)
+
+![](images/95285147d2a998d7d43d44238367988d591288441baa0fc94ff95a74207c8bfd.jpg)
+
+![](images/561bc2610ea1713ed503826d163c242feb165177b94aeff9d32d8444f4000d24.jpg)
+
+<table><tr><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td><td>IN-1K</td><td>IN-C</td></tr><tr><td>✓</td><td>✘</td><td>✘</td><td>✘</td><td>✘</td><td>83.4</td><td>65.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✘</td><td>✘</td><td>82.6</td><td>63.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>83.6</td><td>64.9</td></tr></table>
+
+Table 6. Ablation on impact to the student model using various data augmentations on FAN-TL. The different data augmentations are only imposed on the token-labeler's inputs, while the student model's inputs are fully augmented. Strong data augmentations on FAN-TL undermine token label accuracy and significantly affect the student model's robust accuracy.
+
+model trained with token labels generated by spatial-only data augmentation achieves the best robustness while applying stronger augmentations harms the robust accuracy. Interestingly, applying the consistent full data augmentation on FAN-TL and the student model yields better clean accuracy, which reveals that different combinations of data augmentation may play different roles in improving model robustness and clean performance.
+
+# 5.2. Impacts of Gumbel-Softmax
+
+We propose to use Gumbel-Softmax as a lightweight solution to retain correct token labels for foreground tokens and eliminate incorrect ones, which yields a more accurate segmentation of the object. We evaluate the impact of Gumbel-Softmax using the FAN-S-Hybrid model in Table 7. As can be seen, models trained with token labels generated by Softmax and Gumbel-Softmax achieve comparable clean accuracy while Gumbel-Softmax improves robust accuracy. This further validates that accurate foreground token labels are critical to model robustness.
+
+<table><tr><td>Token Labeling</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>Softmax</td><td>83.4</td><td>65.2</td><td>47.6</td><td>37.2</td><td>51.7</td></tr><tr><td>Gumbel-Softmax</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr></table>
+
+Table 7. Comparison of Softmax and Gumbel-Softmax. Both methods achieve comparable clean accuracy while token labels generated by Gumbel-Softmax yield better robustness.
+
+# 5.3. Training with Heterogeneous Token-Labelers
+
+In the previous experiments, we train student models with isomorphic FAN token-labelers (e.g., FAN-TL-S-Hybrid for FAN-S-Hybrid). We are interested in the impacts
+
+<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>83.4</td><td>65.5</td><td>47.3</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>83.5</td><td>65.5</td><td>47.4</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.5</td><td>68.2</td><td>43.6</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.3</td><td>68.1</td><td>43.5</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.7</td><td>69.0</td><td>42.4</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.7</td><td>68.8</td><td>42.5</td></tr></table>
+
+Table 8. Performance comparison of training with different token labelers. The robustness of student models can be further improved by training with a heterogeneous token labeler.
+
+of training with a heterogeneous token-labeler and conduct the ablation in Table 8. For each student model, we train with three different FAN token-labelers of model sizes from small to large. Models trained with heterogeneous FAN-TL can achieve at least comparable or even superior performance to ones trained with isomorphic token-labelers. Our large model trained with FAN-TL-B-Hybrid further boosts the clean and robust accuracy to  $84.8\%$  and  $69.2\%$  with the mCE of  $42.1\%$ . This indicates STL is robust to different token-labelers. Such robustness enables us to train a larger student model with a smaller token-labeler, which can reduce the training cost.
+
+<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.2</td><td>65.8</td><td>46.9</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.5</td><td>67.4</td><td>44.9</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.9</td><td>68.3</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr></table>
+
+Table 9. Comparison to the prior SOTA token labeling method. Our proposed method that employs self-emerging token labels always yields better robustness than NFNet-F6, which validates the benefit of encoding local information of image patches via self-attention.
+
+# 5.4. Comparison to Prior Token Labeling Method
+
+As shown in Sec. 4.3 and Sec. 4.4, models trained with FAN-TL demonstrate superior performance and robustness than LV-ViTs [3] trained with a CNN token-labeler (i.e., NFNet-F6 [5]), which may attribute to the self-emerging token labeling and the channel attention design of FAN models. To better understand the effect of token labeling, we
+
+train the same FAN models with different methods. Results are summarized in Table 9. It can be seen that STL still significantly outperforms the CNN token-labeler even with the same student model. Note that NFNet-F6 has more than 400M parameters and achieves an  $86.3\%$  Top-1 accuracy on ImageNet-1K while the largest FAN-TL (i.e., FANTL-L-Hybrid) only has 77.3M parameters and  $84.3\%$  Top-1 accuracy. However, FAN-TL consistently yields better results than NFNet-F6. The rationale behind this is possibly because self-emerging token labels provide self-consistent information to student models.
+
+# 5.5. Impacts of Loss Weight
+
+Choosing good loss weights is important when multiple losses are jointly optimized. To study the impact of loss weights and verify STL's robustness against different loss weights when training student models, we vary  $\beta$  with various values and present the results in Table 10. We find STL not sensitive to  $\beta$ . Both clean and robust accuracy fluctuates in a small range. We thus set  $\beta = 1$  to balance the loss with equal weights for simplicity. Similarly, for the training of token-labelers,  $\alpha$  is also set to 1.
+
+<table><tr><td>β</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>0.5</td><td>83.5</td><td>65.5</td><td>47.3</td><td>38.5</td><td>51.7</td></tr><tr><td>1.0</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr><tr><td>2.0</td><td>83.5</td><td>65.6</td><td>47.2</td><td>37.3</td><td>51.1</td></tr></table>
+
+Table 10. Ablation study of loss weight  $\beta$  .
+
+# 6. Conclusion
+
+In this paper, we propose a self-emerging token labeling (STL) framework built on Transformer-based models instead of CNNs. STL enables FAN token-labelers to self-produce accurate and semantically meaningful token labels for training student models with dense supervision. Through extensive experiments and ablation studies, we demonstrate that models trained with STL significantly surpass the original FAN counterparts trained only with image-level labels and achieve remarkable robustness improvement in various visual recognition tasks. Our study validates that the self-produced knowledge from ViTs can indeed benefit their pre-training. We hope this work sheds light on the potential and understanding of self-emerging token labeling from ViTs and motivates future research.
+
+# References
+
+[1] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. ICLR, 2020. 1, 2  
+[2] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training
+
+data-efficient image transformers & distillation through attention. In ICML, pages 10347-10357. PMLR, 2021. 1, 2, 4, 6  
+[3] Zi-Hang Jiang, Qibin Hou, Li Yuan, Daquan Zhou, Yujun Shi, Xiaojie Jin, Anran Wang, and Jiashi Feng. All tokens matter: Token labeling for training better vision transformers. NeurIPS, 2021. 1, 2, 5, 6, 7, 8  
+[4] Sangdoo Yun, Seong Joon Oh, Byeongho Heo, Dongyoon Han, Junsuk Choe, and Sanghyuk Chun. Re-labeling image-net: from single to multi-labels, from global to localized labels. arXiv:2101.05022, 2021. 1  
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+                                    "content": " without using extra data, outperforming the original FAN counterpart by significant margins. The proposed framework also demonstrates significantly enhanced performance on downstream tasks such as semantic segmentation, with up to "
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+                                    "content": "Vision Transformers (ViTs) [1] have recently achieved remarkable success in visual recognition tasks. Such success is not only attributed to their self-attention representation but also to the newly developed training recipes. For instance, refinements in training techniques such as strong data augmentation and knowledge distillation [2] greatly alleviate ViT's issue of being data-hungry and make them more accessible for training on ImageNet-1K."
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+                                            "content": "Figure 1. Results of zero-shot robustness against ImageNet-A and ImageNet-R. Models trained on ImageNet-1K with self-emerging token labels from FAN show superior robustness to the out-of-distribution data. Our best model (with only 77.3M parameters) achieves robust accuracy of "
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+                                    "content": "labeling allows ViTs to leverage more fine-grained information in an image and take different categories and object localization into account. Compared to traditional knowledge distillation methods, token labeling enables ViTs to exploit a wider range of information in the image, leading to more accurate results. The success of token labeling depends on carefully-designed token-level annotators (i.e., token-labelers) that can provide accurate location-specific information (i.e., token labels) to patch tokens. In [3], this is done by a special re-labeling process [4] using convolutional neural networks (CNNs) [5] pre-trained on ImageNet-1K. While Vision Transformers have shown great promise in representation learning, less exploration has been conducted on modeling them as token-labelers. This raises two interesting questions:"
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+                                            "content": "1. Can Transformer-based models self-produce meaningful token labels?"
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+                                            "content": "2. Can one improve the pre-training of ViTs with self-produced knowledge instead of external teachers?"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "type": "text",
+                                    "content": "*Work done during an internship at NVIDIA."
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+                                    "type": "text",
+                                    "content": "Our approach: In this paper, we aim to answer the above questions. We propose a self-emerging token labeling (STL) framework that employs the self-produced token labels by ViT token-labelers instead of relying on CNNs. Our work is built on the recently proposed Fully Attentional Network (FAN) [6] for two reasons. First, FAN exhibits excellent self-emerging visual grouping on token features, which can be leveraged to generate high-quality token labels. Second, FAN is a family of ViT backbones with state-of-the-art accuracy and robustness. We aim to further improve this family of powerful backbones through a principled token-labeling design and validate its effectiveness. Our contributions can be summarized as follows:"
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+                                            "content": "- Our work demonstrates that ViT models can be effective token-labelers. We propose a simple yet effective way to train a FAN token-labeler that can produce semantically meaningful token labels."
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+                                            "content": "- We perform an in-depth analysis and show critical contributors to the accuracy of token labels. On top of the observations, we design a solution that retains more accurate token labels of the target object for improved model pre-training."
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+                                            "content": "- Our models trained with STL set a new record on out-of-distribution datasets without using extra data than ImageNet-1K. Our best model achieves robust accuracy of "
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+                                            "content": " on ImageNet-A and "
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+                                            "type": "text",
+                                            "content": " on ImageNet-R with only 77M parameters, as shown in Fig. 1."
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+                                            "content": "- Experiments on downstream tasks demonstrate that the improved performance in backbone models is transferable to semantic segmentation and object detection."
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+                                    "content": "Our STL framework is akin to the teacher-student training strategy introduced in knowledge distillation and consists of two stages:"
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+                                    "content": "First stage: We train a FAN token-labeler (FAN-TL) model to generate token-level annotations. Our task is essentially a \"chicken or the egg\" problem since there is no explicit supervision on how the token labels are generated. We tackle this by assigning supervising both the class token and the global average-pooled token. This produces semantically meaningful token labels as shown in Fig. 2(b)."
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+                                    "content": "Second stage: We train a FAN student model using the original class labels and the token labels from FAN-TL. Observing the imperfect quality of token labels, we introduce a token selection approach based on Gumbel-Softmax that adaptively selects tokens with high confidence. Labels of the selected tokens are of better quality and object grounding in general, leading to improved pre-training."
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+                                    "content": "2. Related Work"
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+                                    "content": "Vision Transformers [1] are a family of visual recognition models built upon Transformers [7]. ViT splits an input image into a series of small patches, projects each as an embedding (a.k.a patch token) and appends with position embeddings. The resulting patch tokens and an extra learnable class token that aggregates global information for classification are then fed into a sequence of Transformer encoders consisting of multi-head self-attention and FFN blocks. A linear projection layer is appended to the class token to predict the class probabilities."
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+                                    "content": "Several concurrent works point out that ViTs exhibit excellent zero-shot robustness against out-of-distribution samples [8-11]. Some works propose to use negative data augmentation [12] and adversarial training [13, 14] to further enhance the robustness. Recently, FAN [15] was introduced as a family of ViT backbones with state-of-the-art accuracy and robustness. FAN inherits the self-attention blocks of plain ViT but additionally introduces a channel attention block that adopts an attention-based design that aggregates the cross-channel information in a more holistic manner, leading to improved representation."
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+                                    "content": "Token labeling [3] has been proposed to improve ViT pre-training. From the perspective of training strategy, it is similar to knowledge distillation [2, 16] since both adopt a teacher-student mode. It is also related to ReLabel [17], which provides images with multi-label annotations instead of single ones. However, both ReLabel and knowledge distillation depend on image-level labels as global supervision while token labeling assigns labels to each image patch token and supervises the student model in a dense manner. Token labeling is also inherently related to tokenization in BEiT [18], where an offline pre-trained discrete VAE is employed as the tokenizer to encode patches into visual tokens (i.e., code from a visual codebook). Different from token labels, these visual tokens do not possess explicit semantically meanings since they originate from an unsupervisedly trained codebook. Our method differs from prior token labeling and distillation methods where pre-trained convolutional neural networks are widely used as the token-labeler. Instead, our approach to unifies both teacher and student under homogeneous Vision Transformer architectures to generate high-quality token labels."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
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+                                    "type": "text",
+                                    "content": "2.4. Emerging Properties of ViTs"
+                                }
+                            ]
+                        }
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+                    "index": 16
+                },
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+                                    "type": "text",
+                                    "content": "It was found that the localization of objects emerges in image classification with CNNs. This interesting phe"
+                                }
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+                                    "type": "text",
+                                    "content": "nomenon, also known as class activation maps (CAM) [19], lays the foundation for token labeling. Recent studies reveal that ViTs demonstrate excellent capability for object localization without explicit supervision. For instance, DINO [20] shows that self-supervised ViT features generate semantically meaning object segmentation. Methods like GroupViT [21] show that semantic segmentation emerges in ViTs using only text supervision. Similarly, FAN reveals that the robustness of ViT models is correlated to their excellent visual grouping capability. This feature motivates us to develop self-emerging token labeling on top of the FAN models."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3. Method"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "As mentioned, we propose a self-emerging token labeling (STL) framework that uses self-produced token labels to improve ViT pre-training. STL consists of two stages: 1) training an effective token-labeler, and 2) training a student model with self-emerging token labels."
+                                }
+                            ]
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+                    ],
+                    "index": 2
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+                                    "type": "text",
+                                    "content": "In the first stage, we train a FAN token-labeler (FANTL) to generate high-quality token labels. As discussed in Sec. 1 and Sec. 2, FAN demonstrates strong robustness and capability to obtain semantically meaningful visual grouping that can correctly captures the object gestalt. These great features of FAN allow us to obtain high quality token labels without bells and whistles. In the second stage, we then train a FAN student model with image-level labels and self-emerging token labels from FAN-TL. At high level, FAN-TL and FAN student models follow the same architectural design as FAN but slightly modify the structure of patch tokens. We attach a linear layer to each patch token to accommodate token labels, similar to the classification head added to the class token in the original FAN and ViT design. The rest of this section describes the implementation details of the above two-stage pipeline."
+                                }
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+                                    "type": "text",
+                                    "content": "3.1. Training FAN Token-Labelers"
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+                                    "content": "The original FAN employs the training paradigm that only takes image-level labels as supervision. We denote the input image as "
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+                                    "content": "\\mathbf{I}"
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+                                    "type": "text",
+                                    "content": ", the sequence of small patches as "
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+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{I}_{p_1},\\mathbf{I}_{p_2},\\dots,\\mathbf{I}_{p_N}]"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", the output of FAN encoder as "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "[\\mathbf{T}_{cls},\\mathbf{T}_{p_1},\\dots,\\mathbf{T}_{p_N}]"
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+                                    "type": "text",
+                                    "content": ", where "
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+                                    "type": "inline_equation",
+                                    "content": "N"
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+                                    "type": "text",
+                                    "content": " is the number of patch tokens, "
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+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{T}_{cls}"
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+                                {
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+                                    "type": "text",
+                                    "content": " represents the class token and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{T}_{p_1},\\ldots ,\\mathbf{T}_{p_N}"
+                                },
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+                                    "type": "text",
+                                    "content": " represent the patch tokens, respectively. The training objective can be mathematically expressed as follows:"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {\\text {c l s}}, \\mathbf {Y} _ {\\text {c l s}}\\right), \\tag {1}",
+                                    "image_path": "c2b21ef1780598d9a012e58c76c47ef346d50c1b480de3374efd0276073326a1.jpg"
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+                                    "type": "text",
+                                    "content": " is the softmax cross entropy loss and "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{Y}_{cls}"
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+                                    "type": "text",
+                                    "content": " is the image-level label of the corresponding class."
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+                                    "type": "text",
+                                    "content": "The key to token labeling is the generation of accurate token labels that provide location-specific information. However, following the conventional training paradigm in Eq. 1,"
+                                }
+                            ]
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+                                            "type": "text",
+                                            "content": "Figure 2. Illustration of token labels generated by FAN-TL and the token label confidence score distribution. (a). original image (class: \"tench\"), (b). binary color map of token labels (yellow: tokens classified as \"tench\", dark blue: tokens not classified as \"tench\") (c). trinary color map of token labels (cyan: foreground tokens with low confidence, yellow: foreground tokens with high confidence), (d). binary color map of foreground tokens selected by Gumbel-Softmax, (e). token label confidence score distribution of a batch of 16 images."
+                                        }
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+                            ],
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+                                    "type": "text",
+                                    "content": "token outputs of FAN models are not semantically well-guided since they are not supervised during training. We propose a simple yet effective method to address this issue. Our idea is inspired by the intriguing phenomenon in ViTs training that meaningful object segmentation naturally emerges [20]. Unlike the self-supervised training in DINO, we leverage FAN's strong capability of visual grouping [22] and devise a fully supervised approach that allows FAN to generate accurate and semantically meaningful token labels. We perform global average-pooling on all patch tokens and then simultaneously assign the class label to the class and the average-pooled tokens. The training objective of FANTL can be written as follows:"
+                                }
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+                                    "content": "\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}\\right) + \\alpha \\cdot \\mathcal {H} \\left(\\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathbf {T} _ {p _ {i}}, \\mathbf {Y} _ {c l s}\\right), \\tag {2}",
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+                                    "type": "text",
+                                    "content": " weights the importance of two loss functions. We set "
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+                                    "type": "text",
+                                    "content": " to 1 in our experiments. We demonstrate a visualization example of the token labels generated by FAN-TL in Fig. 2(b). The yellow area (i.e., foreground) represents the tokens with the same labels as the image-level label (we term foreground tokens). In contrast, the dark blue area (i.e., background) represents the tokens with different labels from the image-level label (we term background tokens). It can be seen that the self-emerging token labels show a meaningful segmentation of the target object \"tench\"."
+                                }
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+                                            "content": "Train the student model with self-emerging token labeling"
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+                                            "type": "text",
+                                            "content": "Figure 3. Illustration of Stage 2: Training student models with self-emerging token labels. In the training, token labels are generated by FAN-TL and assigned to patch tokens of student models. We incorporate the token labels and class labels to train student models jointly. FAN-TL can self-identify the incorrect token labels upon the confidence score. Tokens with high confidence scores offer a more accurate segmentation of objects and are crucial to robustness improvement. By applying spatial-only data augmentation to the inputs and Gumbel-Softmax to the token outputs of FAN-TL, we obtain the most accurate and critical token labels."
+                                        }
+                                    ]
+                                }
+                            ],
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+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.2. Training Student Models with STL"
+                                }
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+                    "index": 5
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+                                    "content": "Training student models is straightforward. As illustrated in Fig. 3, we take the token outputs of FAN-TL and assign them as the labels for patch tokens of student models. We then incorporate token labels with class labels and jointly optimize the loss on the class token and all patch tokens. The training objective is shown as follows:"
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+                                    "content": "\\mathcal {L} = \\mathcal {H} \\left(\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}\\right) + \\beta \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {H} \\left(\\mathbf {T} _ {p _ {i}}, \\mathcal {F} \\left(\\mathbf {I} _ {p _ {i}}\\right)\\right) \\tag {3}",
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+                                    "content": "where "
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+                                    "content": "\\mathcal{F}(\\cdot)"
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+                                    "type": "text",
+                                    "content": " represents the patch token outputs of FAN-TL and "
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+                                    "type": "text",
+                                    "content": " is the hyper-parameter to balance two loss functions. "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " is set to 1 in our experiments. Note the correctness of token labels (especially the foreground tokens) is critical since wrong labels introduce worthless local information. Thus, we propose several implementation tricks to generate and retain highly accurate token labels based on the following two observations."
+                                }
+                            ]
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Observation 1: Data augmentations remarkably affect the accuracy of token labels. Recent studies [2, 23] indicate data augmentations improve the classification accuracy and robustness of ViT models. However, most augmentations undermine the accuracy of token labels. For example, augmentations in RandAug [24], such as posterize and solarize, alter pixel values, CutOut [25] randomly erases a part of images, Mixup [26] and CutMix [27] mix content from two images, which all make it difficult for FAN-TL to assign correct labels to patch tokens. To this end, we disable these data augmentations and keep spatial-"
+                                }
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+                                            "type": "table",
+                                            "html": "<table><tr><td>Model (Stage)</td><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td></tr><tr><td>FAN-TL (Stage1)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Student (Stage2)</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>FAN-TL (Stage2)</td><td>✓</td><td>✗</td><td>✗</td><td>✗</td><td>✗</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 1. Detailed settings of data augmentations. We apply spatial-only data augmentations to inputs of FAN-TL in stage 2 to improve the accuracy of token labels."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
+                            "type": "table_footnote"
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+                                    "type": "text",
+                                    "content": "only ones (i.e., flip, rotate, shear and translation) for FANTL when generating token labels. Note that we still apply full data augmentations for the student model. The concrete settings of data augmentations are summarized in Table 1. Moreover, the strong data augmentations can be regarded as noises akin to corruptions and perturbations in out-of-distribution datasets. The input data augmentation discrepancy between FANT-LT and the student model enables the self-emerging token labels to provide clean and correct information regardless of the noise, thus improving the model's robustness."
+                                }
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+                {
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+                                    "type": "text",
+                                    "content": "Observation 2: Not all the self-emerging token labels are correct, even with spatial-only data augmentations. For example, as shown in Fig. 2(b), some patches (red squares) that only contain \"human\" and \"lake\" are misclassified as the target object \"tench\" by FAN-TL. It is particularly crucial to ensure the accuracy of foreground token labels as they contain the target object of the image that dominates the prediction result. However, it is challenging to determine which labels are incorrect due to the lack of patch-level ground truth. Interestingly, FAN-TL can"
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+                                    "type": "text",
+                                    "content": "self-identify these misclassified foreground tokens according to the token label confidence score, which may also be attributed to its visual grouping ability. The token label confidence score is defined as the maximal class probability of each token output. We find that tokens with correct labels tend to have higher confidence scores than those with incorrect labels. As shown in Fig. 2(c) and Fig. 2(e), the yellow area indicates the foreground tokens with high confidence scores "
+                                },
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+                                    "type": "text",
+                                    "content": ". These tokens yield a highly accurate segmentation of the target object. Contrastly, the cyan area represents the foreground tokens with low confidence scores "
+                                },
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+                                    "type": "text",
+                                    "content": ", which are coincidentally the ones with incorrect labels."
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+                                    "type": "text",
+                                    "content": "We attempt to assign highly accurate labels to the target object (i.e., foreground tokens). However, it is intractable to exhaustively examine the confidence score of each patch token for all the images as it significantly increases the training time and requires much more computational resources. Therefore, we propose a lightweight alternative by applying the Gumbel-Softmax [28] on the top of token outputs. Mathematically, it can be expressed as:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {y} _ {i} = \\frac {e ^ {\\left(\\log \\left(\\pi_ {i}\\right) + \\mathcal {G} _ {i}\\right) / \\tau}\\left. \\right)}{\\sum_ {j = 1} ^ {k} e ^ {\\left(\\log \\left(\\pi_ {j}\\right) + \\mathcal {G} _ {j}\\right) / \\tau})} \\tag {4}",
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+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y}"
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+                                    "type": "text",
+                                    "content": " is the "
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+                                    "type": "inline_equation",
+                                    "content": "k"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "-dimension softmax vector, "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\pi"
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+                                    "type": "text",
+                                    "content": " are class probabilities, "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G} \\sim Gumbel(0,1)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are i.i.d. samples drawn from the standard Gumbel distribution and "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the softmax temperature. Token labels with high confidence scores remain unchanged after applying Gumbel-Softmax, while labels with low confidence scores are highly likely to change. As shown in Fig. 2(d), we preserve the correct token labels and eliminate the incorrect ones in a simple yet effective way, achieving high accuracy of foreground tokens labels and more precise segmentation of the object. Furthermore, since the training objective of the patch tokens side can be considered a self-training process [29-31], we convert the softmax outputs to \"one-hot\" probability distribution (i.e., hard labels) as [32] shows that the use of hard labels in self-training encourages the model's predictions to be high-confidence via entropy minimization [33]. Following the aforementioned spatial-only data augmentation, we can then rewrite the training objective of the student model:"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {H} (\\mathbf {T} _ {c l s}, \\mathbf {Y} _ {c l s}) + \\beta \\cdot \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathcal {H} (\\mathbf {T} _ {p _ {i}}, \\hat {\\mathcal {F}} (\\hat {\\mathbf {I}} _ {p _ {i}})) \\tag {5}",
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{\\mathcal{F}} (\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                        639,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the one-hot encoded Gumbel-Softmax outputs of FAN-TL and "
+                                },
+                                {
+                                    "bbox": [
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+                                        639,
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+                                    "type": "inline_equation",
+                                    "content": "[\\hat{\\mathbf{I}}_{p_1}\\dots \\hat{\\mathbf{I}}_{p_N}]"
+                                },
+                                {
+                                    "bbox": [
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+                                        639,
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+                                    "type": "text",
+                                    "content": " are image patches with the spatial-only data augmentation. Meanwhile, we notice that all background tokens (i.e., the dark blue area) also have low confidence scores. This is probably because these tokens neither contain apparent features associated with the"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "target object nor clear features related to any other class in the dataset. Nevertheless, we keep all tokens (even those with low confidence scores) in training, following the practice in [3] as involving more tokens for loss computation yields better performance."
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
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+                    ],
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+                },
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+                                    "content": "4.1. Datasets and Evaluation Metrics"
+                                }
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+                },
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+                                    "type": "text",
+                                    "content": "We evaluate our method on the image classification task and its transferability to downstream semantic segmentation and object detection tasks."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Datasets. For image classification, we test model performance and robustness on ImageNet-1K (IN-1K) [34], ImageNet-C (IN-C) [35], ImageNet-A (IN-A) [36] and ImageNet-R (IN-R) [37]. IN-C contains natural corruptions from noise, blur, weather, and digital categories and is widely used to evaluate model's robustness against shifted distribution data. IN-A and IN-R consist of images with different distributions from ImageNet training distribution, such as natural adversarial examples and pictures generated by artistic rendition, thus are widely used to measure the robustness against out-of-distribution data. For semantic segmentation and object detection, we evaluate models on Cityscapes (City) [38], Cityscapes-C (City-C) and COCO [39]. Similar to IN-C, City-C has corruptions from the same four categories."
+                                }
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+                                    "type": "text",
+                                    "content": "Metrics. We adopt standard evaluation metrics for image classification: clean accuracy for IN-1K and robust accuracy for IN-C, IN-A and IN-R. We also report mean corruption error (mCE) [35] on IN-C. For semantic segmentation and object detection, we evaluate the model performance using the clean and robust mean Intersection over Union (mIoU) on City and City-C and the mean average precision (mAP) on COCO. Additionally, we use retention rate as the metric to reflect the resilience of the model robustness and fairly compare models with different capacities. The retention rate is defined as "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "R = \\frac{\\text{Robust Acc.}}{\\text{Clean Acc.}}"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
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+                    "index": 11
+                },
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+                                    "type": "text",
+                                    "content": "4.2. Implementation Details"
+                                }
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+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Experiments are conducted on 8 NVIDIA Tesla V100s and codes are built upon Pytorch [40], timm [41] library and MMSegmentation [42] toolbox. We adopt FAN-Hybrid as the model architecture for FAN-TL and student models. For image classification, we train the models on ImageNet-1K using AdamW optimizer with a learning rate of 4e-3 and batch size of 2048 for 350 epochs. We employ the cosine scheduler with a decay rate of 0.1 to adjust the learning rate every 30 epochs. The loss weight "
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " in Eq. 2 and "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " in Eq. 5 are set to 1. We apply spatial, RandAug, CutOut, Mixup and CutMix data augmentation in the training and a label smoothing ratio of 0.9 to class and token labels. As discussed in Sec. 3, we apply spatial-only data augmentations"
+                                }
+                            ]
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+                                            "html": "<table><tr><td>Model</td><td>Param./FLOPs</td><td>IN-1K</td><td>IN-C</td><td>Retention</td></tr><tr><td>ResNet18 [45]</td><td>11M/1.8G</td><td>69.9</td><td>32.7</td><td>46.8%</td></tr><tr><td>MBV2 [46]</td><td>4M/0.4G</td><td>73.0</td><td>35.0</td><td>47.9%</td></tr><tr><td>EffiNet-B0 [47]</td><td>5M/0.4G</td><td>77.5</td><td>41.1</td><td>53.0%</td></tr><tr><td>PVTV2-B0 [48]</td><td>3M/0.6G</td><td>70.5</td><td>36.2</td><td>51.3%</td></tr><tr><td>PVTV2-B1 [48]</td><td>13M/2.1G</td><td>78.7</td><td>51.7</td><td>65.7%</td></tr><tr><td>LV-ViT-T [3]</td><td>9M/2.1G</td><td>79.1</td><td>51.6</td><td>65.2%</td></tr><tr><td>FAN-T-Hybrid [15]</td><td>7M/3.5G</td><td>80.1</td><td>57.4</td><td>71.4%</td></tr><tr><td>STL (FAN-T-Hybrid)</td><td>8M/3.6G</td><td>79.9</td><td>58.2</td><td>72.8%</td></tr><tr><td>ResNet50 [45]</td><td>25M/4.1G</td><td>79.0</td><td>50.6</td><td>64.1%</td></tr><tr><td>DeiT-S [2]</td><td>22M/4.6G</td><td>79.9</td><td>58.1</td><td>72.7%</td></tr><tr><td>Swin-T [43]</td><td>28M/4.5G</td><td>81.3</td><td>55.4</td><td>68.1%</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M/4.5G</td><td>82.1</td><td>59.1</td><td>71.9%</td></tr><tr><td>LV-ViT-S [3]</td><td>26M/6.6G</td><td>83.3</td><td>59.7</td><td>71.7%</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M/6.7G</td><td>83.5</td><td>64.7</td><td>77.5%</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>27M/6.8G</td><td>83.4</td><td>65.5</td><td>78.5%</td></tr><tr><td>Swin-S [43]</td><td>50M/8.7G</td><td>83.0</td><td>60.4</td><td>72.8%</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M/8.7G</td><td>83.1</td><td>61.7</td><td>74.2%</td></tr><tr><td>LV-ViT-M [3]</td><td>56M/16.0G</td><td>84.0</td><td>62.0</td><td>73.8%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M/11.3G</td><td>83.9</td><td>66.4</td><td>79.1%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>51M/11.4G</td><td>84.5</td><td>68.2</td><td>80.7%</td></tr><tr><td>DeiT-B [2]</td><td>89M/17.6G</td><td>81.8</td><td>62.7</td><td>76.7%</td></tr><tr><td>Swin-B [43]</td><td>88M/15.4G</td><td>83.5</td><td>60.4</td><td>72.3%</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M/15.4G</td><td>83.8</td><td>63.0</td><td>75.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M/16.9G</td><td>84.3</td><td>68.3</td><td>81.0%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M/17.0G</td><td>84.7</td><td>68.8</td><td>81.2%</td></tr></table>",
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+                                            "content": "Table 2. Results on image classification. We report clean and robust accuracy on ImageNet-1K and ImageNet-C. Retention rate is defined as Robust Acc. LV-ViTs are vanilla ViTs trained with a CNN token-labeler. Our models trained with STL achieve superior robustness and retention rate in all cases. Meanwhile, our method also improves the clean accuracy of models with a larger capacity (e.g., FAN-B-Hybrid and FAN-L-Hybrid)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
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+                                    "content": "on inputs of FAN-TL and Gumbel-Softmax on patch token outputs to obtain accurate token labels. We employ pretrained image classification models for semantic segmentation as encoders and the SegFormer [11] head as the decoder. We follow the same training recipe as SegFormer and train our models on Cityscapes using AdamW with a learning rate of 6e-5 and a batch size of 8 for 160K iterations. The learning rate scheduler is set to \"poly\" with a default factor of 1.0. Random resizing, flipping, and cropping are applied as data augmentations in training. For object detection, we follow the same practice as Swin Transformer [43] + Cascade Mask R-CNN [44] and employ AdamW (initial learning rate of 1e-4, weight decay of 0.05, and batch size of 16) to train our models on COCO for 36 epochs."
+                                }
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+                                    "content": "4.3. Results on Image Classification"
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+                                    "content": "We first show the performance of models trained with STL on the image classification task and compare them with other SOTA models in Table 2. To evaluate the zero-shot robustness against the distributional shift, all models are"
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+                                            "html": "<table><tr><td>Model</td><td>Params (M)</td><td>Clean</td><td>IN-A</td><td>IN-R</td><td>mCE (↓)</td></tr><tr><td>Swin-T [50]</td><td>28.3</td><td>81.2</td><td>21.6</td><td>41.3</td><td>59.6</td></tr><tr><td>ConvNext-T [49]</td><td>28.6</td><td>82.1</td><td>24.2</td><td>47.2</td><td>53.2</td></tr><tr><td>RVT-S [51]</td><td>23.3</td><td>81.9</td><td>25.7</td><td>47.7</td><td>51.4</td></tr><tr><td>XCiT-S12 [52]</td><td>26.3</td><td>81.9</td><td>25.0</td><td>45.5</td><td>51.5</td></tr><tr><td>LV-ViT-S [3]</td><td>26.0</td><td>83.3</td><td>33.9</td><td>45.8</td><td>52.9</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26.3</td><td>83.5</td><td>33.9</td><td>50.7</td><td>47.8</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26.5</td><td>83.4</td><td>38.2</td><td>51.8</td><td>47.3</td></tr><tr><td>Swin-S [50]</td><td>50.0</td><td>83.4</td><td>35.8</td><td>46.6</td><td>52.7</td></tr><tr><td>ConvNext-S [49]</td><td>50.2</td><td>82.1</td><td>31.2</td><td>49.5</td><td>51.2</td></tr><tr><td>XCiT-S24 [52]</td><td>47.7</td><td>82.6</td><td>27.8</td><td>45.5</td><td>49.4</td></tr><tr><td>LV-ViT-M [3]</td><td>56.0</td><td>84.0</td><td>35.2</td><td>47.2</td><td>50.5</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4</td><td>83.9</td><td>39.6</td><td>52.9</td><td>45.2</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9</td><td>84.5</td><td>42.6</td><td>55.3</td><td>43.6</td></tr><tr><td>Swin-B [50]</td><td>87.8</td><td>83.4</td><td>35.8</td><td>46.6</td><td>54.4</td></tr><tr><td>MAE-ViT-B [53]</td><td>86.0</td><td>83.6</td><td>35.9</td><td>48.3</td><td>51.7</td></tr><tr><td>ConvNext-B [49]</td><td>88.6</td><td>83.8</td><td>36.7</td><td>51.3</td><td>46.8</td></tr><tr><td>RVT-B [51]</td><td>91.8</td><td>82.6</td><td>28.5</td><td>48.7</td><td>46.8</td></tr><tr><td>DAT-AugReg-ViT [14]</td><td>86.0</td><td>81.5</td><td>30.2</td><td>47.3</td><td>44.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8</td><td>84.3</td><td>41.8</td><td>53.2</td><td>43.0</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3</td><td>84.7</td><td>46.1</td><td>56.6</td><td>42.5</td></tr></table>",
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+                                        }
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+                            ],
+                            "index": 5,
+                            "angle": 0,
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+                                            "type": "text",
+                                            "content": "Table 3. Results on out-of-distribution datasets. We report the mean corruption error (mCE) for ImageNet-C, a lower value indicates better robustness. The improved robustness of models trained with STL is well generalized to out-of-distribution datasets and achieves even better robustness on ImageNet-A and ImageNet-R."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6,
+                            "angle": 0,
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+                {
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+                                    "type": "text",
+                                    "content": "trained on ImageNet-1K data and directly used for inference on ImageNet-C without finetuning. We use the same model type for FAN-TL and the student model. It can be seen that Transformer-based models are more robust than CNN-based models in general. At all size levels, our models show superior robust accuracy and retention rate to other models, including the original FAN models trained solely with the class labels, indicating the effectiveness of STL in improving model robustness. Notably, our models surpass LV-ViTs [3] (i.e., vanilla ViT models trained with a CNN token-labeler) in both clean and robust accuracy by significant margins, which validates the importance of channel attention block in FAN and reveals the potential of self-emerging token labels from Transformer-based models."
+                                }
+                            ]
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+                                    "content": "4.4. Robustness against Out-of-distribution Data"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Token labels embed rich local information of image patches. We adopt spatial-only data augmentation and Gumbel-Softmax on FAN-TL to retain highly accurate labels for foreground tokens to ensure that self-emerging token labels always provide correct information for student models. The practice promotes the generalization performance of student models as they can make robust predictions even with different input data distributions. To verify this, we then evaluate model robustness against out-of-distribution data, and results are summarized in Table 3. Similarly, models are not fine-tuned for testing. We find that"
+                                }
+                            ]
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+                                            "html": "<table><tr><td>Model</td><td>Encoder Size</td><td>City</td><td>City-C</td><td>Retention</td></tr><tr><td>DeepLabv3+ (R50) [54]</td><td>25.4M</td><td>76.6</td><td>36.8</td><td>48.0%</td></tr><tr><td>DeepLabv3+ (R101) [54]</td><td>47.9M</td><td>77.1</td><td>39.4</td><td>51.1%</td></tr><tr><td>DeepLabv3+ (X65) [54]</td><td>22.8M</td><td>78.4</td><td>42.7</td><td>54.5%</td></tr><tr><td>DeepLabv3+ (X71) [54]</td><td>-</td><td>78.6</td><td>42.5</td><td>54.1%</td></tr><tr><td>ICNet ([55])</td><td>-</td><td>65.9</td><td>28.0</td><td>42.5%</td></tr><tr><td>FCN8s ([56])</td><td>50.1M</td><td>66.7</td><td>27.4</td><td>41.1%</td></tr><tr><td>DilatedNet ([57])</td><td>-</td><td>68.6</td><td>30.3</td><td>44.2%</td></tr><tr><td>ResNet38 ([58])</td><td>-</td><td>77.5</td><td>32.6</td><td>42.1%</td></tr><tr><td>PSPNet ([59])</td><td>13.7M</td><td>78.8</td><td>34.5</td><td>43.8%</td></tr><tr><td>ConvNeXt-T ([49])</td><td>29.0M</td><td>79.0</td><td>54.4</td><td>68.9%</td></tr><tr><td>SETR ([60])</td><td>22.1M</td><td>76.0</td><td>55.3</td><td>72.8%</td></tr><tr><td>SWIN-T ([43])</td><td>28.4M</td><td>78.1</td><td>47.3</td><td>60.6%</td></tr><tr><td>SegFormer-B0 ([11])</td><td>3.4M</td><td>76.2</td><td>48.8</td><td>64.0%</td></tr><tr><td>SegFormer-B1 ([11])</td><td>13.1M</td><td>78.4</td><td>52.7</td><td>67.2%</td></tr><tr><td>SegFormer-B2 ([11])</td><td>24.2M</td><td>81.0</td><td>59.6</td><td>73.6%</td></tr><tr><td>SegFormer-B5 ([11])</td><td>81.4M</td><td>82.4</td><td>65.8</td><td>79.9%</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50.4M</td><td>82.2</td><td>66.9</td><td>81.5%</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50.9M</td><td>82.5</td><td>68.6</td><td>83.2%</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>76.8M</td><td>82.3</td><td>68.7</td><td>83.5%</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77.3M</td><td>82.8</td><td>69.2</td><td>83.6%</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 4. Results on semantic segmentation. We use mIoU as the evaluation metric. 'R-' and 'X-' refer to ResNet and Xception, respectively. Models trained with STL demonstrate an impressive transferability to the downstream task and achieve significantly better mIoU than other models on Cityscapes and Cityscapes-C."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "table_footnote"
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "LV-ViTs and original FAN models generalize well to out-of-distribution data, while other Transformer-based models and the SOTA CNN-based ConvNext models perform weaker. Despite the impressive performance of original FAN models, models trained with STL demonstrate an even better generalization ability and outperform all other models. The performance gains on IN-A and IN-R are more significant than IN-C and set a new state-of-the-art, indicating that the accurate self-emerging token labels are crucial to robustness against out-of-distribution data."
+                                }
+                            ]
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+                    ],
+                    "index": 2
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+                {
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+                                    "type": "text",
+                                    "content": "4.5. Transferability to Semantic Segmentation"
+                                }
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+                        }
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+                    "index": 3
+                },
+                {
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+                                    "type": "text",
+                                    "content": "[61] shows pre-trained models using different training recipes perform differently in downstream tasks. [3] validates that token labeling with CNN token-labelers benefits semantic segmentation and improves the clean mIoU. We also evaluate the transferability of STL to semantic segmentation. As shown in Table 4, pre-trained models with STL reveal better transferability than original FAN counterparts and other prestigious backbones. Remarkably, our approach achieves superior results on both clean and corrupted datasets. As far as we know, this is the first work to reveal that applying dense supervision in backbone pretraining improves not only the clean performance but also the robustness of the downstream task."
+                                }
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+                                            "html": "<table><tr><td>Model</td><td>Encoder Size</td><td>COCO (mAP)</td></tr><tr><td colspan=\"3\">Cascade Mask-RCNN 3× schedule</td></tr><tr><td>ResNet-50 [45]</td><td>25M</td><td>46.3</td></tr><tr><td>ResNeXt-101-32 [62]</td><td>-</td><td>48.1</td></tr><tr><td>ResNeXt-101-64 [62]</td><td>-</td><td>48.3</td></tr><tr><td>Swin-T [43]</td><td>28M</td><td>50.4</td></tr><tr><td>ConvNeXt-T [49]</td><td>29M</td><td>50.4</td></tr><tr><td>FAN-S-Hybrid [15]</td><td>26M</td><td>53.3</td></tr><tr><td>STL (FAN-S-Hybrid)</td><td>26M</td><td>53.4</td></tr><tr><td>Swin-S [43]</td><td>50M</td><td>51.9</td></tr><tr><td>ConvNeXt-S [49]</td><td>50M</td><td>51.9</td></tr><tr><td>FAN-B-Hybrid [15]</td><td>50M</td><td>53.5</td></tr><tr><td>STL (FAN-B-Hybrid)</td><td>50M</td><td>53.9</td></tr><tr><td>Swin-B [43]</td><td>88M</td><td>51.9</td></tr><tr><td>ConvNeXt-B [49]</td><td>89M</td><td>52.7</td></tr><tr><td>FAN-L-Hybrid [15]</td><td>77M</td><td>54.1</td></tr><tr><td>STL (FAN-L-Hybrid)</td><td>77M</td><td>54.1</td></tr></table>",
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+                            "angle": 0,
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+                                            "content": "Table 5. Results on object detection. Models trained with STL outperform most CNN-based and transformer-based backbones. Even compared with original FAN models, our models achieve at least on par or even better mAP on COCO, indicating our method can also benefit object detection."
+                                        }
+                                    ]
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+                            ],
+                            "index": 6,
+                            "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.6. Transferability to Object Detection"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "type": "text",
+                                    "content": "We also validate STL's transferability to the object detection task on COCO and present the results in Table 5. Models trained with STL outperform most CNN-based and Transformer-based backbones. Even compared with original FAN models, STL brings a notable performance gain for FAN-B while achieving comparable mean average precision on FAN-L and FAN-S. We notice the overall improvement in object detection is not as good as in image classification and semantic segmentation, possibly because the semantic segmentation task is more similar to token labeling from the perspective of dense prediction, while object detection involves different techniques such as regression [63, 64] and multi-stage refinement [44, 63]."
+                                }
+                            ]
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+                    ],
+                    "index": 8
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+                                    "type": "text",
+                                    "content": "5. Ablation Study"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5.1. Impacts of Different Data Augmentation"
+                                }
+                            ]
+                        }
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+                    "index": 10
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+                                    "content": "We apply spatial-only data augmentation on FAN-TL to obtain accurate token labels that provide clean and correct information toward student models, which is vital to model robustness. The strategy is a \"clean teacher noisy student\" design, where the student still uses all the augmentations. Our motivation behind this design is to let the teacher and student spatially aligned, with the teacher being as clean as possible to generate high quality token labels (Strong augmentations make it harder to generate good token labels as shown in Fig. 4). We compare the impacts of different data augmentation imposed on FAN-TL in Table 6. Experiments are conducted on the FAN-S-Hybrid model. The student"
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+                                            "html": "<table><tr><td>Spatial</td><td>RandAug</td><td>CutOut</td><td>MixUp</td><td>CutMix</td><td>IN-1K</td><td>IN-C</td></tr><tr><td>✓</td><td>✘</td><td>✘</td><td>✘</td><td>✘</td><td>83.4</td><td>65.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✘</td><td>✘</td><td>82.6</td><td>63.5</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>83.6</td><td>64.9</td></tr></table>",
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+                                            "content": "Table 6. Ablation on impact to the student model using various data augmentations on FAN-TL. The different data augmentations are only imposed on the token-labeler's inputs, while the student model's inputs are fully augmented. Strong data augmentations on FAN-TL undermine token label accuracy and significantly affect the student model's robust accuracy."
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+                                    "content": "model trained with token labels generated by spatial-only data augmentation achieves the best robustness while applying stronger augmentations harms the robust accuracy. Interestingly, applying the consistent full data augmentation on FAN-TL and the student model yields better clean accuracy, which reveals that different combinations of data augmentation may play different roles in improving model robustness and clean performance."
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+                                    "content": "We propose to use Gumbel-Softmax as a lightweight solution to retain correct token labels for foreground tokens and eliminate incorrect ones, which yields a more accurate segmentation of the object. We evaluate the impact of Gumbel-Softmax using the FAN-S-Hybrid model in Table 7. As can be seen, models trained with token labels generated by Softmax and Gumbel-Softmax achieve comparable clean accuracy while Gumbel-Softmax improves robust accuracy. This further validates that accurate foreground token labels are critical to model robustness."
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+                                            "html": "<table><tr><td>Token Labeling</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>Softmax</td><td>83.4</td><td>65.2</td><td>47.6</td><td>37.2</td><td>51.7</td></tr><tr><td>Gumbel-Softmax</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr></table>",
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+                                            "content": "Table 7. Comparison of Softmax and Gumbel-Softmax. Both methods achieve comparable clean accuracy while token labels generated by Gumbel-Softmax yield better robustness."
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+                                    "content": "In the previous experiments, we train student models with isomorphic FAN token-labelers (e.g., FAN-TL-S-Hybrid for FAN-S-Hybrid). We are interested in the impacts"
+                                }
+                            ]
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+                                            "html": "<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>83.4</td><td>65.5</td><td>47.3</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>83.5</td><td>65.5</td><td>47.4</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.5</td><td>68.2</td><td>43.6</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.3</td><td>68.1</td><td>43.5</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.7</td><td>69.0</td><td>42.4</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-L-Hybrid</td><td>84.7</td><td>68.8</td><td>42.5</td></tr></table>",
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+                                            "content": "Table 8. Performance comparison of training with different token labelers. The robustness of student models can be further improved by training with a heterogeneous token labeler."
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+                                    "type": "text",
+                                    "content": "of training with a heterogeneous token-labeler and conduct the ablation in Table 8. For each student model, we train with three different FAN token-labelers of model sizes from small to large. Models trained with heterogeneous FAN-TL can achieve at least comparable or even superior performance to ones trained with isomorphic token-labelers. Our large model trained with FAN-TL-B-Hybrid further boosts the clean and robust accuracy to "
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+                                    "type": "text",
+                                    "content": " with the mCE of "
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+                                    "type": "text",
+                                    "content": ". This indicates STL is robust to different token-labelers. Such robustness enables us to train a larger student model with a smaller token-labeler, which can reduce the training cost."
+                                }
+                            ]
+                        }
+                    ],
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+                                            "html": "<table><tr><td>Model</td><td>Token-Labeler</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td></tr><tr><td>FAN-S-Hybrid</td><td>-</td><td>83.5</td><td>64.7</td><td>47.8</td></tr><tr><td>FAN-S-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.2</td><td>65.8</td><td>46.9</td></tr><tr><td>FAN-S-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>83.3</td><td>65.8</td><td>46.8</td></tr><tr><td>FAN-B-Hybrid</td><td>-</td><td>83.9</td><td>66.4</td><td>45.2</td></tr><tr><td>FAN-B-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.5</td><td>67.4</td><td>44.9</td></tr><tr><td>FAN-B-Hybrid</td><td>FAN-TL-S-Hybrid</td><td>84.4</td><td>68.5</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>-</td><td>84.3</td><td>68.3</td><td>43.0</td></tr><tr><td>FAN-L-Hybrid</td><td>NFNet-F6 (CNN)</td><td>83.9</td><td>68.3</td><td>43.2</td></tr><tr><td>FAN-L-Hybrid</td><td>FAN-TL-B-Hybrid</td><td>84.8</td><td>69.2</td><td>42.1</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 9. Comparison to the prior SOTA token labeling method. Our proposed method that employs self-emerging token labels always yields better robustness than NFNet-F6, which validates the benefit of encoding local information of image patches via self-attention."
+                                        }
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+                                    "type": "text",
+                                    "content": "5.4. Comparison to Prior Token Labeling Method"
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+                    "index": 23
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+                                    "type": "text",
+                                    "content": "As shown in Sec. 4.3 and Sec. 4.4, models trained with FAN-TL demonstrate superior performance and robustness than LV-ViTs [3] trained with a CNN token-labeler (i.e., NFNet-F6 [5]), which may attribute to the self-emerging token labeling and the channel attention design of FAN models. To better understand the effect of token labeling, we"
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+                                    "type": "text",
+                                    "content": "train the same FAN models with different methods. Results are summarized in Table 9. It can be seen that STL still significantly outperforms the CNN token-labeler even with the same student model. Note that NFNet-F6 has more than 400M parameters and achieves an "
+                                },
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+                                    "content": " Top-1 accuracy on ImageNet-1K while the largest FAN-TL (i.e., FANTL-L-Hybrid) only has 77.3M parameters and "
+                                },
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+                                    "type": "text",
+                                    "content": " Top-1 accuracy. However, FAN-TL consistently yields better results than NFNet-F6. The rationale behind this is possibly because self-emerging token labels provide self-consistent information to student models."
+                                }
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+                        }
+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "5.5. Impacts of Loss Weight"
+                                }
+                            ]
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+                    ],
+                    "index": 1
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+                {
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+                                    "type": "text",
+                                    "content": "Choosing good loss weights is important when multiple losses are jointly optimized. To study the impact of loss weights and verify STL's robustness against different loss weights when training student models, we vary "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " with various values and present the results in Table 10. We find STL not sensitive to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\beta"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Both clean and robust accuracy fluctuates in a small range. We thus set "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\beta = 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to balance the loss with equal weights for simplicity. Similarly, for the training of token-labelers, "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is also set to 1."
+                                }
+                            ]
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+                                            "html": "<table><tr><td>β</td><td>IN-1K</td><td>IN-C</td><td>mCE (↓)</td><td>IN-A</td><td>IN-R</td></tr><tr><td>0.5</td><td>83.5</td><td>65.5</td><td>47.3</td><td>38.5</td><td>51.7</td></tr><tr><td>1.0</td><td>83.4</td><td>65.5</td><td>47.3</td><td>38.2</td><td>51.8</td></tr><tr><td>2.0</td><td>83.5</td><td>65.6</td><td>47.2</td><td>37.3</td><td>51.1</td></tr></table>",
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+                                            "content": "Table 10. Ablation study of loss weight "
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+                                    "type": "text",
+                                    "content": "6. Conclusion"
+                                }
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+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "In this paper, we propose a self-emerging token labeling (STL) framework built on Transformer-based models instead of CNNs. STL enables FAN token-labelers to self-produce accurate and semantically meaningful token labels for training student models with dense supervision. Through extensive experiments and ablation studies, we demonstrate that models trained with STL significantly surpass the original FAN counterparts trained only with image-level labels and achieve remarkable robustness improvement in various visual recognition tasks. Our study validates that the self-produced knowledge from ViTs can indeed benefit their pre-training. We hope this work sheds light on the potential and understanding of self-emerging token labeling from ViTs and motivates future research."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "References"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[1] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. ICLR, 2020. 1, 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                                        288,
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+                                    ],
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+                                        {
+                                            "bbox": [
+                                                52,
+                                                690,
+                                                288,
+                                                714
+                                            ],
+                                            "type": "text",
+                                            "content": "[2] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 9
+                        }
+                    ],
+                    "sub_type": "ref_text"
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "list",
+                    "angle": 0,
+                    "index": 26,
+                    "blocks": [
+                        {
+                            "bbox": [
+                                326,
+                                73,
+                                545,
+                                106
+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
+                            "lines": [
+                                {
+                                    "bbox": [
+                                        326,
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+                                    ],
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+                                        {
+                                            "bbox": [
+                                                326,
+                                                73,
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+                                            ],
+                                            "type": "text",
+                                            "content": "data-efficient image transformers & distillation through attention. In ICML, pages 10347-10357. PMLR, 2021. 1, 2, 4, 6"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11
+                        },
+                        {
+                            "bbox": [
+                                311,
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+                                155
+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[3] Zi-Hang Jiang, Qibin Hou, Li Yuan, Daquan Zhou, Yujun Shi, Xiaojie Jin, Anran Wang, and Jiashi Feng. All tokens matter: Token labeling for training better vision transformers. NeurIPS, 2021. 1, 2, 5, 6, 7, 8"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12
+                        },
+                        {
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diff --git a/2023/FunnyBirds_ A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods/07a936e0-4ced-42c0-9b0c-dba61ee8ef3b_content_list.json b/2023/FunnyBirds_ A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods/07a936e0-4ced-42c0-9b0c-dba61ee8ef3b_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..aaf52afa8123cfaf156d3c596f09272d59d1df7d
--- /dev/null
+++ b/2023/FunnyBirds_ A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods/07a936e0-4ced-42c0-9b0c-dba61ee8ef3b_content_list.json	
@@ -0,0 +1,1452 @@
+[
+    {
+        "type": "text",
+        "text": "FunnyBirds: A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods",
+        "text_level": 1,
+        "bbox": [
+            243,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Robin Hesse<sup>1</sup>",
+        "bbox": [
+            214,
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+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Simone Schaub-Meyer<sup>1,2</sup>",
+        "bbox": [
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+            202,
+            584,
+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Stefan Roth1,2",
+        "bbox": [
+            640,
+            202,
+            754,
+            220
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ Department of Computer Science, TU Darmstadt  $^{2}$ hessian.AI",
+        "bbox": [
+            228,
+            244,
+            740,
+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            297,
+            313,
+            314
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The field of explainable artificial intelligence (XAI) aims to uncover the inner workings of complex deep neural models. While being crucial for safety-critical domains, XAI inherently lacks ground-truth explanations, making its automatic evaluation an unsolved problem. We address this challenge by proposing a novel synthetic vision dataset, named FunnyBirds, and accompanying automatic evaluation protocols. Our dataset allows performing semantically meaningful image interventions, e.g., removing individual object parts, which has three important implications. First, it enables analyzing explanations on a part level, which is closer to human comprehension than existing methods that evaluate on a pixel level. Second, by comparing the model output for inputs with removed parts, we can estimate ground-truth part importances that should be reflected in the explanations. Third, by mapping individual explanations into a common space of part importances, we can analyze a variety of different explanation types in a single common framework. Using our tools, we report results for 24 different combinations of neural models and XAI methods, demonstrating the strengths and weaknesses of the assessed methods in a fully automatic and systematic manner.",
+        "bbox": [
+            75,
+            330,
+            473,
+            664
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            696,
+            209,
+            710
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Even though deep learning models have achieved breakthrough results in computer vision, their inner workings remain largely opaque. As a result, deep networks sometimes receive only limited user trust and cannot be applied blindly in safety-critical domains. To overcome this issue, a growing interest in the field of explainable artificial intelligence (XAI) has emerged, attempting to explain the inner workings of deep neural models in a human-comprehensible way. However, since there are generally no ground-truth explanations, evaluating XAI methods remains an open chal",
+        "bbox": [
+            75,
+            722,
+            468,
+            875
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/2b64e3cc1d04ab83ac9179b59ffe8cdf014e331071576551159c99d8e148e8eb.jpg",
+        "image_caption": [
+            "Figure 1. Schematic illustration of our proposed dataset and analysis framework. For each input image, we render the corresponding part annotation and part interventions (e.g., removed beak). The interventions are used to estimate ground-truth importance scores of each input part, which are then compared to the estimated part importances from the explanation method under inspection (here [44]). We evaluate multiple dimensions of explainability to draw a more conclusive picture. Please refer to Sec. 4.1 for details."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            511,
+            300,
+            879,
+            470
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "lenge. In fact, a third of XAI papers lack sound quantitative evaluation [38], while other work has limited comparability [31] or problematic evaluation protocols [23, 38].",
+        "bbox": [
+            496,
+            609,
+            892,
+            656
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To overcome the issue of missing ground-truth explanations, automatic evaluations are often done via proxy tasks that adhere to the idea of performing image interventions by removing certain input features to then measure the resulting impact on the model output [21, 23, 55]. As image interventions are non-trivial to perform on existing vision datasets, they are usually applied on a pixel level, e.g., masking out single pixels [21, 23, 27, 52, 55]. However, this and related approaches share several downsides. First, performing interventions, as well as evaluating explanations on a pixel level, is disconnected from the downstream task of providing human-understandable explanations since humans perceive images in concepts rather than pixels. Second, existing automatic evaluation protocols are developed for specific explanation types, e.g., pixel-level attribution maps, and thus, cannot be extended to other explanation",
+        "bbox": [
+            496,
+            657,
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+            901
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
+            106,
+            2,
+            181,
+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            238,
+            0,
+            807,
+            46
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "Dataset and code available at github.com/visinf/funnybirds/.",
+        "bbox": [
+            99,
+            887,
+            419,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "3981",
+        "bbox": [
+            482,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "types like prototypes [12]. Third, by performing unrealistic interventions in image space, e.g., masking out pixels, they introduce domain shifts compared to the training distribution [10, 23, 28], which can cause the model to behave unexpectedly, and thus negatively affects the evaluation.",
+        "bbox": [
+            78,
+            90,
+            467,
+            165
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, we address the above and more challenges to contribute an important step toward a more rigorous quantitative evaluation of XAI methods by proposing a thorough, dedicated evaluation/analysis tool. We do so by building a fully controllable, synthetic classification dataset consisting of renderings of artificial bird species. This approach to analyzing XAI methods is analogous to controlled laboratory research, where we have full control over all variables, eliminating the potential influence of irrelevant factors, and therefore, providing clearer evidence of the observed behavior [5]. Our proposed dataset allows us to make the following main contributions: (1) We cover a wide range of dimensions of explainability by considering a collection of different evaluation protocols. (2) We allow to automatically compare various explanation types in a shared framework. (3) We avoid the out-of-domain issue of previous image-space interventions by introducing semantically meaningful interventions at training time. (4) We reduce the gap between the downstream task of human comprehension and XAI evaluation by proposing metrics that operate at a semantically meaningful part level rather than the semantically less meaningful pixel level. (5) We automatically analyze the coherence of explanations. (6) We analyze 24 different combinations of existing XAI methods and neural models, highlighting their strengths and weaknesses as well as identifying new insights that may be of general interest to the XAI community.",
+        "bbox": [
+            80,
+            167,
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+            573
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            80,
+            588,
+            215,
+            603
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "XAI methods. In this work, we focus on image classification explanations for the outcome of one particular input using deep neural networks (DNNs). Perturbation-based explanation methods [1, 11, 33, 44, 47, 63, 68, 69] estimate the impact of pixels/regions by measuring the output change occurring when repeatably perturbing inputs or neurons. Backpropagation-based explanation methods [4, 20, 27, 53, 55, 57, 59] use importance signals, e.g., gradient information, to estimate the importance of each input feature. Both types of methods generate post-hoc explanations for already trained networks. On the other hand, intrinsically explainable models [3, 6, 8, 9, 12, 39] consider explainability already in the design process of the model itself. For example, B-cos networks [9] enforce weight-input alignment to highlight the most important input regions. ProtoPNet [12] computes the feature similarity between test image patches and prototypes to help explain why a decision was made based on this patch looking like that prototype. BagNets [6] use a linear classifier on top",
+        "bbox": [
+            80,
+            613,
+            467,
+            898
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "of each feature extracted from small image patches to highlight task-important regions.  $\\mathcal{X}$  -DNNs [27] remove the bias term in ReLU networks to allow for an efficiently computable closed-form solution of Integrated Gradients [59].",
+        "bbox": [
+            503,
+            90,
+            888,
+            150
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Evaluating XAI methods. A sound evaluation of XAI methods is essential to compare different approaches and unveil their strengths and weaknesses. Nauta et al. [38] argue that explainability is a multi-faceted concept and propose various properties that describe different aspects of explanation quality. Below, we outline existing evaluation protocols for three of these dimensions that have received particularly much attention in related work and that allow for a well-defined automatic evaluation:",
+        "bbox": [
+            503,
+            157,
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+            291
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Correctness denotes the faithfulness of an explanation w.r.t. the model [38]. A common way to measure the correctness of attribution methods is the Incremental Deletion protocol [8, 10, 21, 23, 27, 28, 38, 52, 55, 60], where input pixels are incrementally removed in the order of their relative importance to measure the impact on the output. Similarly, in the Single Deletion protocol [3, 14, 38, 41, 67], individual (input) features are deleted to compute the correlation between feature importance and the actual output change. A drawback of the above protocols is the domain shift occurring when introducing image interventions, which can cause undesirable model behavior influencing the metrics [10, 23, 28]. To reduce this, masked pixels can be inpainted with a generative model [10] or text classification datasets can be augmented with training inputs that have similar alterations as the evaluation protocol [23]. However, none of these approaches achieve an exact alignment of the train and test domain as we do in this work.",
+        "bbox": [
+            503,
+            294,
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+            564
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Completeness measures the degree to which an explanation describes all aspects of the model's decision [38]. In the Preservation/Deletion Check protocols [10, 13, 16, 38, 45], important features are preserved/deleted to test if the output prediction stays the same/changes. However, as above, these protocols introduce unrealistic domain changes. In the Controlled Synthetic Data Check protocol [2, 13, 30, 34, 38, 50], a synthetic dataset is used to evaluate if the explanation of a model with almost perfect accuracy aligns with the dataset generation process. While closely related to our work, existing synthetic datasets for evaluating XAI methods are very small-scale, only evaluate a single dimension of explainability, and do not allow for diverse image-space interventions that are crucial for evaluating correctness.",
+        "bbox": [
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+            566,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Contrastivity measures the degree to which an explanation is discriminative w.r.t. different outputs [38]. It can be measured with the Target Sensitivity protocol [38] that evaluates if the explanations for two different targets are different [45] and sometimes, even more, whether the explanation aligns with the image region of the correct target [8,19,65]. However, these evaluations can require accurate object annotations, which are not given for most classi",
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+        "page_idx": 1
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+        "image_caption": [
+            "(c)",
+            "Figure 2. Generation process of our synthetic dataset. (a) The scene is initialized with a neutral bird body part. (b) Class-specific parts are added. (c) To reflect real-world challenges, random backgrounds, illumination, and viewpoint changes are added/applied."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "fication datasets, or they can also introduce out-of-domain issues when arranging images in a grid as in [8,9,46].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Human studies. Besides above automatic evaluations, there have been efforts to assess the quality of XAI methods with human subjects [15, 40, 51, 54]. Human studies nicely reflect the actual downstream tasks of explanations, i.e., helping humans to understand models, and they can be applied to explanations that go beyond simple heat maps [31]. Downsides of user studies include larger cost and human biases [36]. Further, humans are not capable of directly evaluating if explanations are correct w.r.t. a complex, deep model. With our custom analysis, we aim to reduce the gap between the automatic evaluation and human studies while addressing the described drawbacks of human assessment.",
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+    {
+        "type": "text",
+        "text": "Synthetic datasets. Synthetic datasets have an important and long history in many other disciplines of computer vision [7,18,29,42,48]. Richter et al. [48] utilize a video game to create a large-scale segmentation dataset. The \"Flying Chairs\" dataset [18] and MPI Sintel [7] are popular synthetic datasets used for the training and evaluation of optical flow methods. CLEVR [29] was introduced to test different visual reasoning abilities. All these works advanced their specific sub-fields, showing that synthetic datasets are a valuable tool, even in the absence of full realism.",
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+    },
+    {
+        "type": "text",
+        "text": "3. The FunnyBirds Dataset",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We propose a synthetic vision dataset that is developed to automatically and quantitatively analyze XAI methods. To this end, we made a multitude of carefully considered design choices, which we summarize in the following.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Since XAI methods in computer vision have been developed mainly in the context of classification to date [38], we focus on classification and propose a fine-grained bird species dataset inspired by the CUB-200-2011 dataset [61] commonly used by XAI methods [12, 22, 26, 39, 66]. Our dataset consists of 50500 images (50k train, 500 test) of 50 synthetic bird species. We found 500 test images to be sufficient to produce stable results while allowing efficient evaluations with limited hardware (see supplement).",
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+    {
+        "type": "text",
+        "text": "One particularly important desideratum behind our de",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "sign process is the notion of concepts that we define as mental representations of psychological entities that are crucial to categorization [35, 37, 49, 64]. For instance, humans might categorize a bird as a flamingo when observing the concepts curved beak and pink wings. Similarly, they would communicate their reasoning process in terms of concepts [49]. Hence, we argue that concepts are essential in the context of XAI for humans, and thus, we design our dataset with a particular emphasis on the notion of concepts. To derive a precise level of granularity for the concepts in our dataset, we enforce them to be as granular as possible, while corresponding to an existing individual word, and being attached to the bird's body. This avoids \"unrealistic\" scenarios where the removal of one concept leaves another concept unattached (the body of the bird is never removed) and eliminates overly fine-grained concepts. Following these rules, our FunnyBirds consist of the five human comprehensible concepts beak, wings, feet, eyes, and tail, to which we will refer as parts in the following.",
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+    {
+        "type": "text",
+        "text": "We manually design 4 beaks, 3 eyes, 4 feet, 9 tails, and 6 wings of predefined varied shape and/or color (see supplement). Every FunnyBird class consists of a unique combination of these parts. We randomly sample 50 classes out of the 2592 combinations as our dataset. Using these classes, we follow the data-generation process outlined in Fig. 2 by adding class-specific parts to a neutral body model to obtain an instance of a FunnyBird. To reflect real-world challenges, we randomly add background objects and change the illumination and viewpoint. We also explored more photo-realistic simulations with real background images and textured parts. However, with neural models learning to ignore these \"distractions\", our quantitative analysis was largely unaffected. We thus omit this in pursuit of simplicity. We verified the solvability of our dataset with a human expert who achieved an accuracy of  $97.4\\%$  on the proposed test set. To ensure that removing any part does not result in another valid class, each complete FunnyBird instance contains all five parts. To ensure that images with removed parts are not out-of-distribution, we include images with missing parts in the training set. As these images can no longer be associated with one specific class, we use a multi-label classification training scheme where all classes that contain all of the remaining parts are considered valid (with equal probability).",
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+    {
+        "type": "text",
+        "text": "Our data-generation process has several important implications that make it particularly well suited for evaluating and analyzing XAI methods. First, based on the assumption that humans think in concepts rather than pixels, we argue that a concept-based dataset and the resulting evaluations are better aligned with downstream tasks of human comprehension than pixel-based evaluations. Second, we have pixel-accurate annotations of each object and bird part in the scene, which is required for various automatic evaluation",
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+    {
+        "type": "page_number",
+        "text": "3983",
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+    {
+        "type": "text",
+        "text": "protocols and tailored analyses. Third, having full control over the data-generation process allows applying realistic image-space interventions, such as removing parts, which can be used to estimate ground-truth importance scores.",
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+    {
+        "type": "text",
+        "text": "4. Evaluation Protocols",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We will now outline how our dataset and its functionalities can be used for the quantitative evaluation and analysis of XAI methods. We first propose a general, multi-dimensional analysis framework, named FunnyBirds framework, that allows to evaluate a wide range of existing XAI methods in a common framework. Second, we propose a more tailored way of analysis where our dataset's capabilities are used to gain deeper insights into specific methods similar to what human studies could do.",
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+    },
+    {
+        "type": "text",
+        "text": "4.1. The FunnyBirds framework",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The multi-dimensional FunnyBirds analysis framework for XAI methods entails six evaluation protocols for three explainability dimensions, i.e., completeness, correctness, and contrastivity. They were chosen for their popularity in related work [38], ability to be automatically measurable, and compatibility with our dataset. Most of our protocols are inspired by well-established evaluation practices and follow accepted assumptions. Our dataset generation process ensures that all conducted interventions can be considered in-domain and semantically meaningful, eliminating common downsides [23, 28] of several existing evaluation protocols that rely on image interventions [10,21,23,27,55].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Meaning of ground truth. Our work relies on interventions to estimate \"ground-truth\" importance scores for individual parts. This is motivated by (1) the observation that in XAI we aim to approximate the causal structure of the inspected model, and (2) findings that the causal structure can be estimated via interventions [43]. Since the perfect causal structure (which is too complex to be comprehended) is already given by the model itself, we emphasize that a simplified approximation is needed for XAI, instead. We thus assume such an approximation for estimating the ground-truth scores with interventions. For example, in the single deletion protocol (see Sec. 4.1.3), we assume that a hypothetical simplified model processes each part individually, which generally does not need to hold for the real model. This assumption is implicitly also made in existing single deletion protocols [3, 14, 41, 67]. Further, most existing explanation methods, e.g., attribution maps, communicate the importance of each feature individually, thus evaluating explanations beyond individual concepts is not yet sensible.",
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+    {
+        "type": "text",
+        "text": "Interface functions. The diversity of explanation types presents a major challenge to evaluating XAI methods, which prevents a direct comparison of different methods and created a need for various non-standardized evalua-",
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+    {
+        "type": "text",
+        "text": "tions. We thus propose to build our evaluation framework around so-called interface functions that implement more general properties, such as which object parts are important. They can be derived from a variety of explanation types, and thus, used to evaluate distinct explanations in a common framework. This allows us to not only compare a spectrum of existing methods, but also to potentially include future, novel explanation types. Our evaluation framework currently uses the following interface functions:",
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+    },
+    {
+        "type": "text",
+        "text": "$\\operatorname{PI}(\\cdot)$  - The part importance score for each part. For example, the summed attribution within that part.",
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+    {
+        "type": "text",
+        "text": "$\\mathrm{P}(\\cdot)$  - The parts that are considered to be important, derived from the output of an XAI method. For attribution methods, a part can be considered important if its part importance is at least  $t\\%$  of the total attribution.",
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+    {
+        "type": "text",
+        "text": "Note that different explanation types vary in their suitability for differing downstream tasks, and thus, also in their suitability for above interface functions. Furthermore, just as humans differ in interpreting various explanations, there may not be a single correct way of implementing the interface functions (see supplement). Therefore, comparing different explanation types is not absolutely fair and should be done with caution. Nonetheless, we argue that estimating important image regions and their relative importance are fairly basic challenges in XAI, and thus, appropriate downstream tasks, respectively, interface functions.",
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+    {
+        "type": "text",
+        "text": "**Framework.** For a simple comparison and visualization, we design all metrics to be in the range [0, 1], with higher values indicating better scores. For each dimension (as described below), we report a single score comprised of all included protocols (see Tab. 1). Additionally, we report the average of all our explanation quality dimensions, i.e., completeness, correctness, contrastivity, as a single score that summarizes the overall quality of an XAI method for the inspected model. We let  $\\mathcal{D}$  denote our dataset of size  $N$ , consisting of images  $x_{n}$  with class label  $c_{n}$ ;  $f$  is the inspected model with  $f(x_{n})$  denoting the predicted class or the logit of the target class, and  $e_{f}(x_{n})$  is the explanation of  $f(x_{n})$  w.r.t. the target class  $c_{n}$ .",
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+    {
+        "type": "text",
+        "text": "4.1.1 Accuracy and background independence",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Accuracy (A). An overly simple model may be explainable but not solve the task at hand. To detect such cases, our framework reports the standard classification accuracy.",
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+    },
+    {
+        "type": "text",
+        "text": "Background independence (BI). Similarly, another trivial solution to achieve high explanation scores is a model that is sensitive to the entire image. An explanation would consequently highlight the entire image. To detect this case, we report the background independence as the ratio of background objects that are unimportant, i.e., that, when removed, cause the target logit to drop less than  $5\\%$ .",
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+    },
+    {
+        "type": "page_number",
+        "text": "3984",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/3ba71268a73d2a4cace7db57e38d5bb44140c32141d487eded4e6554aec4539c.jpg",
+        "table_caption": [
+            "Table 1. Overview of our evaluation protocols. \"Interface function\" denotes the required interface function for each protocol."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dimension</td><td>Protocol</td><td>Interface function</td><td>Description</td></tr><tr><td>-</td><td>A</td><td>-</td><td>Percentage of correct predictions over the test dataset</td></tr><tr><td>-</td><td>BI</td><td>-</td><td>The model should not be sensitive to the background objects</td></tr><tr><td>Completeness</td><td>CSDC</td><td>P</td><td>Explanation should highlight all relevant parts</td></tr><tr><td>Completeness</td><td>PC</td><td>P</td><td>Preserving parts identified as important should result in the same prediction</td></tr><tr><td>Completeness</td><td>DC</td><td>P</td><td>Removing parts identified as important should result in a different prediction</td></tr><tr><td>(Over-)Completeness</td><td>D</td><td>P</td><td>Explanation should not highlight irrelevant parts</td></tr><tr><td>Correctness</td><td>SD</td><td>PI</td><td>Estimated importance of each part should be correlated to actual importance</td></tr><tr><td>Contrastivity</td><td>TS</td><td>PI</td><td>Explanations for different classes should highlight class-specific parts</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.1.2 Completeness",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Controlled synthetic data check (CSDC). Our transparent data generation process allows us to know the subsets of parts  $\\{\\mathcal{P}_{c_n,i}'\\mid i = 1,\\ldots \\}$  that are sufficient to correctly categorize an image of class  $c_{n}$  containing parts  $\\mathcal{P}_{c_n}$ . A model that accurately captures the essence of our dataset, i.e., has an accuracy close to 1.0, must thus consider at least one of these sets  $\\mathcal{P}_{c_n,i}'$  [13, 34, 38, 50]. To ensure that this assumption holds and CSDC is faithful w.r.t. the model, we exclude misclassified samples from this protocol. We measure the CSDC completeness of an explanation as the set overlap between the parts that are estimated to be important by the explanation (i.e.,  $\\mathrm{P}(e_f(x_n))$  where  $\\mathrm{P}(\\cdot)$  is the interface function giving the important parts) and the sufficient part set that has the largest overlap with  $\\mathrm{P}(e_f(x_n))$ , normalized by the size of the sufficient part set:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {C S D C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\max  _ {i} \\frac {\\left| \\mathrm {P} \\left(e _ {f} \\left(x _ {n}\\right)\\right) \\cap \\mathcal {P} ^ {\\prime} _ {c _ {n} , i} \\right|}{\\left| \\mathcal {P} ^ {\\prime} _ {c _ {n} , i} \\right|}. \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Preservation check (PC). If an explanation is complete, preserving only the parts of the input that are estimated to be important by the explanation should still result in the same classification output [13,16,38]. To verify this, we first pass the original image through the inspected model to obtain the classification and the corresponding explanation. Afterward, we delete all parts of the image that are estimated to not be important by the explanation, i.e., the inverse of  $\\mathrm{P}(\\cdot)$ , and measure how often the class prediction remains unchanged. We define our PC score as",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {P C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left[ f \\left(x _ {n} ^ {\\prime}\\right) = f \\left(x _ {n}\\right) \\right], \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "with  $[\\cdot]$  denoting the Iverson bracket [32] and  $x_{n}^{\\prime}$  denoting the image arising by removing all bird parts but  $\\mathrm{P}(e_f(x_n))$  from  $x_{n}$ . I.e., the parts estimated to be important remain.",
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+    },
+    {
+        "type": "text",
+        "text": "Deletion check (DC). Similarly, if an explanation is complete, deleting all the parts of the input that are estimated to be important by the explanation should result in a different",
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+    {
+        "type": "text",
+        "text": "classification output [16,38,45]. Thus, the deletion check is the inverse of PC and defined as",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {D C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} [ f (x _ {n} ^ {\\prime \\prime}) \\neq f (x _ {n}) ], \\tag {3}\n$$\n",
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+    },
+    {
+        "type": "text",
+        "text": "with  $x_{n}^{\\prime \\prime}$  denoting the image arising by removing the estimated important parts  $\\mathrm{P}(e_f(x_n))$  from  $x_{n}$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Distractibility (D). As over-complete explanations would achieve high completeness scores, we argue that completeness should be considered together with a metric that counters over-completeness (similar to precision and recall). To this end, we introduce a novel over-completeness score that measures how many actually unimportant input parts are also estimated to be unimportant by the explanation. In detail, we successively remove each background object and bird part from the input and consider it to be unimportant if the logit target output drops less than  $5\\%$  compared to the output for the original image. Next, we measure the overlap between parts  $\\mathrm{P}(e_f(x_n))$  estimated to be important by the explanation and parts  $\\mathcal{P}_{f(x_n)}^{\\prime \\prime}$  that are actually unimportant, normalized by the number of unimportant parts. As the overlap should be small for good evaluations, we subtract the result from 1:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {D} = 1 - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\frac {\\left| \\mathrm {P} \\left(e _ {f} \\left(x _ {n}\\right)\\right) \\cap \\mathcal {P} _ {f \\left(x _ {n}\\right)} ^ {\\prime \\prime} \\right|}{\\left| \\mathcal {P} _ {f \\left(x _ {n}\\right)} ^ {\\prime \\prime} \\right|}. \\tag {4}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The final completeness score (Com.) is computed as the mean of the averaged three completeness metrics (CSDC, PC, and DC), and the over-completeness D. By having complementing metrics, we can also automatically estimate the threshold  $t$  of  $\\mathrm{P}(\\cdot)$ , such that  $t$  optimally trades off the completeness and over-completeness metrics.",
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+    {
+        "type": "text",
+        "text": "4.1.3 Correctness",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Single deletion (SD). In the single deletion protocol, we measure the rank correlation between the explanation's importance score of each part and the actual amount that the model's logit of the target class changes when removing that",
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+    {
+        "type": "page_number",
+        "text": "3985",
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+    {
+        "type": "text",
+        "text": "part [3, 14, 38]. Specifically, we define SD as",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {S D} = \\frac {1}{2} + \\frac {1}{2 N} \\sum_ {n = 1} ^ {N} \\rho \\left(\\mathrm {P I} \\left(e _ {f} \\left(x _ {n}\\right)\\right), f \\left(x _ {n}\\right) - \\left\\{f \\left(x _ {n} ^ {\\prime \\prime \\prime}\\right) \\right\\}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "with  $\\rho$  denoting the Spearman rank-order correlation coefficient,  $\\mathrm{PI}(\\cdot)$  the part importance interface function, and  $\\{f(x_n^{\\prime \\prime \\prime})\\}$  the target scores of the images obtained by removing any individual bird part from  $x_{n}$ .",
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+    {
+        "type": "text",
+        "text": "4.1.4 Contrastivity",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Target sensitivity (TS). If an explanation is sensitive to a target class, it should highlight image regions that are relevant for the respective target [8, 9, 38]. To measure target sensitivity, we take an input sample and select two classes  $\\hat{c}_1$  and  $\\hat{c}_2$  that each have exactly two non-overlapping common parts with the actual class of input sample  $x_n$ . We choose two parts because this is the floor of half the 5 bird parts available in each image. Afterward, we compute the explanations  $e_f(x_n, \\hat{c}_i)$  with respect to  $\\hat{c}_1$  and  $\\hat{c}_2$  and evaluate if they correctly highlight the parts belonging to each respective class:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathrm {T S} = \\frac {1}{2 N} \\sum_ {n = 1} ^ {N} \\left[ \\mathrm {P I} ^ {\\prime} \\left(e _ {f} \\left(x _ {n}, \\hat {c} _ {1}\\right)\\right) > \\mathrm {P I} ^ {\\prime} \\left(e _ {f} \\left(x _ {n}, \\hat {c} _ {2}\\right)\\right) \\right] \\tag {6} \\\\ + \\left[ \\mathrm {P I} ^ {\\prime \\prime} (e _ {f} (x _ {n}, \\hat {c} _ {1})) <   \\mathrm {P I} ^ {\\prime \\prime} (e _ {f} (x _ {n}, \\hat {c} _ {2})) \\right], \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "with  $\\mathrm{PI}'(\\cdot)$  and  $\\mathrm{PI}''(\\cdot)$  denoting the summed part importances of the two parts belonging to class  $\\hat{c}_1$ , respectively  $\\hat{c}_2$ . To ensure that our protocol is faithful w.r.t. the model, we only consider images where removing parts belonging to  $\\hat{c}_1$  causes a larger model output drop for  $\\hat{c}_1$  than removing parts belonging to  $\\hat{c}_2$ , and vice versa.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.2. The FunnyBirds custom analysis",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As it is almost impossible to analyze all aspects of an explanation with a single framework, we also show how full control over our dataset enables more tailored and systematic custom evaluations. Similar to recent human studies [31], we evaluate the coherence of the assessed methods, i.e., how reasonable an explanation is for a human. To the best of our knowledge, this is one of the first methods for evaluating coherence in a fully automatic and systematic manner. We give two illustrative examples for implementing such an evaluation, but other instantiations are possible.",
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+    {
+        "type": "text",
+        "text": "ProtoPNet. ProtoPNet [12] promotes explainability by communicating which patches of the training data, called prototypes, look similar to patches in a test image. However, this only increases interpretability if the detected similarities are compatible with human notions of similarity. To quantitatively verify this in an automatic fashion, we test if relevant part types (e.g., beak or wing) in the detected patch",
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+    {
+        "type": "text",
+        "text": "of the test image are also contained in the corresponding prototype identified by ProtoPNet. This assumes that different part types, i.e., beak and wings, do not look similar to most humans, and therefore, are not helpful similarities for explainability. While debatable for real images, we argue that this is a reasonable assumption for our dataset.",
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+    },
+    {
+        "type": "text",
+        "text": "Counterfactual visual explanations. The objective of counterfactual visual explanations (CVE) [22] is to highlight image regions that discriminate the class  $c$  of a query image from the class  $c'$  of a distractor image. To this end, CVE extracts convolutional neural network (CNN) feature maps from the query and distractor images to then perform feature swaps between the two feature maps that, when fed to the CNN classifier, lead to the strongest class change (from  $c$  to  $c'$ ). The corresponding image locations of the feature swaps are then highlighted to yield the CVE. We argue that this kind of explanation is only meaningful for humans if the swaps are semantically correct, i.e., when a beak is swapped with another beak but not a foot. Using our proposed dataset, we conduct a systematic study and measure the average number of swaps that do not touch the same bird part in both images, and thus, can be considered semantically incorrect. We evaluate four different setups of increasing difficulty where we only use aligned, respectively unaligned, viewpoint pairs with classes that are different in only one, respectively multiple parts.",
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+        "type": "text",
+        "text": "Limitations. As with controlled laboratory research [5], our dataset does not reflect all real-world challenges, and thus, is not fully representative of natural images. However, we argue that, as long as XAI methods are challenged to truthfully explain models trained even on our controlled dataset, our proposed method is a valuable tool to faithfully assess the quality of XAI methods. Nonetheless, for future XAI methods we suggest a two-stream evaluation that utilizes our proposed framework and custom analysis for theoretically grounded assessments of the explanation quality in addition to benchmarks that work on natural image data, e.g., Quantus [25]. Further, while the dimensions of explainability evaluated in our work can be considered relevant for many applications, there are dimensions that we omit here (see supplement). However, our framework can easily be extended with additional protocols if needed.",
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+    {
+        "type": "text",
+        "text": "5. Results and Interpretation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1. FunnyBirds framework",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Results for our multi-dimensional FunnyBirds framework across a broad variety of different XAI methods and three different backbones are given in Fig. 3. For detailed results of each individual evaluation protocol, please refer to the supplement. We plot qualitative explanations for a random image and give the evaluation scores from Sec. 4.1 averaged over the entire test set. From this, we can make",
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+        "type": "page_number",
+        "text": "3986",
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+    {
+        "type": "image",
+        "img_path": "images/c37c580e5a52219cb16254b659eddc9cc259eef283fee92a23fede8b2ac30adc.jpg",
+        "image_caption": [
+            "Figure 3. FunnyBirds evaluation results. Qualitative and quantitative results for our FunnyBirds framework for the XAI methods Input  $\\times$  Gradient (IxG) [56], (absolute) Integrated Gradients (IG (abs.)) [59], Grad-CAM [11,53], RISE [44], LIME [47], Rollout [1], Chefer LRP [11],  $\\mathcal{X}$ -DNN [27], BagNet [6], ProtoPNet [12], and B-cos network [9]. Model-agnostic methods are evaluated on VGG16 [58], ResNet-50 [24], and ViT-B/16 [17]. Other models use a ResNet-50 backbone, if applicable. Quantitative results are averaged over the entire test set; qualitative results are shown for a representative example. Chart colors indicate different explanation types that should only be compared with caution. The center score denotes the mean of the completeness (Com.), correctness (Cor.), and contrastivity (Con.) dimensions. Additionally, we report the accuracy (Acc.) and background independence (B.I.). See Sec. 4.1 for details."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "several interesting findings and derive various hypotheses:",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(1) Overall, BagNet [6] achieves the highest explainability score, which could be due to its internal model structure that is better aligned with the explanatory power of an attribution map, i.e., pixels are processed more independently.",
+            "(2) On average, Integrated Gradients (IG) [59] performs best among model-agnostic methods for different backbones, which is in line with the literature when considering gradient-based approaches [56, 59]. However, LIME [47] and IG achieve similar completeness, with LIME lacking the ability to communicate meaningful importance scores, which impairs practicability for certain downstream tasks. Interestingly, taking the absolute value of IG impairs the mean explanation score slightly, contradicting findings that have been made on pixel-level protocols [62]. Specifically, it slightly increases completeness while reducing contrastivity. We hypothesize that the negative gradient infor"
+        ],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "mation is therefore particularly important in identifying regions that do not belong to the class of interest. Removing the bias term (X-DNN [27] vs. ResNet-50 [24] w/ IG) slightly improves completeness and correctness while reducing contrastivity.",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(3) Explanation scores for model-agnostic XAI methods are consistently better for VGG16 [58] than for ResNet-50 [24], indicating that different backbones vary in their explainability. We also observe that the relative ordering of different XAI methods changes across different backbones (e.g., RISE [44] and IxG [56]), showing the importance of evaluating future XAI methods on different backbones.",
+            "(4) IxG [56] and Grad-CAM [11, 53] seem to work better on CNN-based architectures [24, 58]. Methods developed for vision transformers, i.e., Rollout [1] and Chefer LRP [11], provide strong explanations, with Chefer LRP achieving the second highest explanation score. Rollout"
+        ],
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+        "page_idx": 6
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+    {
+        "type": "page_number",
+        "text": "3987",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e38c18671d0e54d7e71d354584e5a48712d30e4da974888ce4cfc51192f82052.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative results of ProtoPNet [12]. Many of the test image patches (center) highlight the entire bird or just background. Further, prototypes (sides) often do not include important parts."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "cannot compute class-specific explanations, which could be disadvantageous in certain downstream tasks.",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(5) Coarser methods like Grad-CAM [53] and RISE [44] tend to be more incomplete, which could be an artifact of poor localization [46] and our parts being fairly small.",
+            "(6) The B-cos network [9] outperforms competing methods on the same backbone, showing an improved explainability, which is in line with results from [9]. Surprisingly, we see a slight decrease in background independence.",
+            "(7) ProtoPNet [12] has poor correctness and contrastivity, which can be explained by related findings in that ProtoPNet similarities are not semantically reasonable [31] and by its poor localization (see Sec. 5.2 and Fig. 4).",
+            "(8) Especially correctness is a weakness of all examined methods, showing that, while existing approaches tend to accurately identify important areas, they lack the ability to reliably communicate the relative importance of each input area, or that the simple explanation of an attribution map might be too strong of a simplification of the actual model."
+        ],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Finally, since XAI evaluation is multi-faceted and downstream task dependent, we doubt that a single score can be enough to properly compare methods. Hence, our work is less about ranking but more about automatically revealing the strengths and weaknesses of existing and future XAI methods in a systematic and theoretically grounded manner.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.2.Custom evaluations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ProtoPNet. To quantitatively evaluate if prototypes used in [12] promote explainability (see Sec. 4.2), we conduct several sanity checks. First, we measure that out of 1000 examined ProtoPNet patches in the test image, only 510 touch the same part in the corresponding prototype patch, and thus, have a similarity that could be aligned with human notions of similarity. Further, we measure that  $26.3\\%$  of the extracted test image patches do not touch a single bird part, indicating a poor localization of the explanation. Finally,  $18.5\\%$  of the test image patches entail 4 or 5 different bird parts, which shows that the extracted patches are not local but global, and thus, do not promote the interpretability of the examined model. Qualitative results showing the described issues can be seen in Fig. 4. To summarize, many of the communicated prototypes of ProtoPNet [12] trained on our dataset are unlikely to be meaningful for humans. While a similar conclusion was drawn in a recent human",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ffe8454a8cad1bbea0ab1f3342e2f7690df8897ef6dca6fdbcebb649fc913720.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative results of counterfactual visual explanations (CVE) [22]. (left) CVE for an aligned image pair with one part being different. (right) CVE for an unaligned image pair with multiple parts being different. Note how many of the proposed swaps are unrealistic, and therefore, of little quality (e.g., the purple patch around the right eye is swapped with the neck of the other bird)."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "study [31] confirming our findings, our proposed tools allow the same conclusion in a fully automatic manner.",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Counterfactual visual explanations. To quantify if CVE [22] highlights meaningful swaps (see Sec. 4.2), we measure how many of the extracted swaps do not touch the same bird parts in the two images. When considering images that have the same viewpoint and differ only by one part (Fig. 5 - left), CVE with VGG16 [58] produces on average 1.65 swaps that do not touch the same part, and therefore, are semantically meaningless. When changing the viewpoint, CVE produces on average 1.3 swaps that do not touch the same part. When working with aligned viewpoints and birds that differ by multiple parts (4.07 parts on average), 2.75 such swaps are produced and 2.62 when also changing the viewpoint (Fig. 5 - right). Interestingly, the number of different parts has a stronger impact on the absolute number of unreasonable swaps, i.e., swaps that do not touch the same part in both images, than the viewpoint. Further, we observe that even in our controlled environment, CVE produces on average  $\\sim 3$  unreasonable swaps for images with on average only 4 different parts, indicating that many of the proposed swaps are semantically incorrect, and thus, do not promote coherent explanations.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we propose a novel approach to automatically analyzing XAI methods using a synthetic classification dataset that allows for full annotation and part interventions. Using this dataset, we propose an accompanying multi-dimensional analysis framework that faithfully assesses various important aspects of explainability and generalizes to different explanation types by using interface functions. With this easy-to-use tool, we analyzed 24 different setups to uncover various new insights and confirm findings from related work. This shows that, despite the synthetic setting, our findings appear to translate well to real data, and that our proposed tool is a practical and valuable asset for the analysis of future XAI methods. Finally, we showed how to develop tailored analyses to gain a better understanding of two specific XAI methods and discovered their weaknesses in an automatic and quantitative manner.",
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+    {
+        "type": "page_number",
+        "text": "3988",
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+    {
+        "type": "text",
+        "text": "Acknowledgements. We thank Bernt Schiele, Moritz Böhle, and Sukrut Rao for their valuable feedback and helpful discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 866008). The project has also been supported in part by the State of Hesse through the cluster projects \"The Third Wave of Artificial Intelligence (3AI)\" and \"The Adaptive Mind (TAM)\".",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            237,
+            174,
+            253
+        ],
+        "page_idx": 8
+    },
+    {
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+        ],
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+    },
+    {
+        "type": "list",
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+        ],
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+            "tional neural networks. In  $CVPR$  pages 9097-9107, 2019. 2",
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diff --git a/2023/FunnyBirds_ A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods/07a936e0-4ced-42c0-9b0c-dba61ee8ef3b_model.json b/2023/FunnyBirds_ A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods/07a936e0-4ced-42c0-9b0c-dba61ee8ef3b_model.json
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+[
+    [
+        {
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+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "FunnyBirds: A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Robin Hesse<sup>1</sup>"
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Simone Schaub-Meyer<sup>1,2</sup>"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.203,
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+            "angle": 0,
+            "content": "Stefan Roth1,2"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "\\(^{1}\\)Department of Computer Science, TU Darmstadt \\(^{2}\\)hessian.AI"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.299,
+                0.314,
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.332,
+                0.474,
+                0.665
+            ],
+            "angle": 0,
+            "content": "The field of explainable artificial intelligence (XAI) aims to uncover the inner workings of complex deep neural models. While being crucial for safety-critical domains, XAI inherently lacks ground-truth explanations, making its automatic evaluation an unsolved problem. We address this challenge by proposing a novel synthetic vision dataset, named FunnyBirds, and accompanying automatic evaluation protocols. Our dataset allows performing semantically meaningful image interventions, e.g., removing individual object parts, which has three important implications. First, it enables analyzing explanations on a part level, which is closer to human comprehension than existing methods that evaluate on a pixel level. Second, by comparing the model output for inputs with removed parts, we can estimate ground-truth part importances that should be reflected in the explanations. Third, by mapping individual explanations into a common space of part importances, we can analyze a variety of different explanation types in a single common framework. Using our tools, we report results for 24 different combinations of neural models and XAI methods, demonstrating the strengths and weaknesses of the assessed methods in a fully automatic and systematic manner."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.723,
+                0.47,
+                0.875
+            ],
+            "angle": 0,
+            "content": "Even though deep learning models have achieved breakthrough results in computer vision, their inner workings remain largely opaque. As a result, deep networks sometimes receive only limited user trust and cannot be applied blindly in safety-critical domains. To overcome this issue, a growing interest in the field of explainable artificial intelligence (XAI) has emerged, attempting to explain the inner workings of deep neural models in a human-comprehensible way. However, since there are generally no ground-truth explanations, evaluating XAI methods remains an open chal"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
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+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Figure 1. Schematic illustration of our proposed dataset and analysis framework. For each input image, we render the corresponding part annotation and part interventions (e.g., removed beak). The interventions are used to estimate ground-truth importance scores of each input part, which are then compared to the estimated part importances from the explanation method under inspection (here [44]). We evaluate multiple dimensions of explainability to draw a more conclusive picture. Please refer to Sec. 4.1 for details."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "lenge. In fact, a third of XAI papers lack sound quantitative evaluation [38], while other work has limited comparability [31] or problematic evaluation protocols [23, 38]."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "To overcome the issue of missing ground-truth explanations, automatic evaluations are often done via proxy tasks that adhere to the idea of performing image interventions by removing certain input features to then measure the resulting impact on the model output [21, 23, 55]. As image interventions are non-trivial to perform on existing vision datasets, they are usually applied on a pixel level, e.g., masking out single pixels [21, 23, 27, 52, 55]. However, this and related approaches share several downsides. First, performing interventions, as well as evaluating explanations on a pixel level, is disconnected from the downstream task of providing human-understandable explanations since humans perceive images in concepts rather than pixels. Second, existing automatic evaluation protocols are developed for specific explanation types, e.g., pixel-level attribution maps, and thus, cannot be extended to other explanation"
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+            "type": "page_footnote",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Dataset and code available at github.com/visinf/funnybirds/."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "3981"
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+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "types like prototypes [12]. Third, by performing unrealistic interventions in image space, e.g., masking out pixels, they introduce domain shifts compared to the training distribution [10, 23, 28], which can cause the model to behave unexpectedly, and thus negatively affects the evaluation."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "In this work, we address the above and more challenges to contribute an important step toward a more rigorous quantitative evaluation of XAI methods by proposing a thorough, dedicated evaluation/analysis tool. We do so by building a fully controllable, synthetic classification dataset consisting of renderings of artificial bird species. This approach to analyzing XAI methods is analogous to controlled laboratory research, where we have full control over all variables, eliminating the potential influence of irrelevant factors, and therefore, providing clearer evidence of the observed behavior [5]. Our proposed dataset allows us to make the following main contributions: (1) We cover a wide range of dimensions of explainability by considering a collection of different evaluation protocols. (2) We allow to automatically compare various explanation types in a shared framework. (3) We avoid the out-of-domain issue of previous image-space interventions by introducing semantically meaningful interventions at training time. (4) We reduce the gap between the downstream task of human comprehension and XAI evaluation by proposing metrics that operate at a semantically meaningful part level rather than the semantically less meaningful pixel level. (5) We automatically analyze the coherence of explanations. (6) We analyze 24 different combinations of existing XAI methods and neural models, highlighting their strengths and weaknesses as well as identifying new insights that may be of general interest to the XAI community."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "XAI methods. In this work, we focus on image classification explanations for the outcome of one particular input using deep neural networks (DNNs). Perturbation-based explanation methods [1, 11, 33, 44, 47, 63, 68, 69] estimate the impact of pixels/regions by measuring the output change occurring when repeatably perturbing inputs or neurons. Backpropagation-based explanation methods [4, 20, 27, 53, 55, 57, 59] use importance signals, e.g., gradient information, to estimate the importance of each input feature. Both types of methods generate post-hoc explanations for already trained networks. On the other hand, intrinsically explainable models [3, 6, 8, 9, 12, 39] consider explainability already in the design process of the model itself. For example, B-cos networks [9] enforce weight-input alignment to highlight the most important input regions. ProtoPNet [12] computes the feature similarity between test image patches and prototypes to help explain why a decision was made based on this patch looking like that prototype. BagNets [6] use a linear classifier on top"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "of each feature extracted from small image patches to highlight task-important regions. \\(\\mathcal{X}\\) -DNNs [27] remove the bias term in ReLU networks to allow for an efficiently computable closed-form solution of Integrated Gradients [59]."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.158,
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+            "angle": 0,
+            "content": "Evaluating XAI methods. A sound evaluation of XAI methods is essential to compare different approaches and unveil their strengths and weaknesses. Nauta et al. [38] argue that explainability is a multi-faceted concept and propose various properties that describe different aspects of explanation quality. Below, we outline existing evaluation protocols for three of these dimensions that have received particularly much attention in related work and that allow for a well-defined automatic evaluation:"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Correctness denotes the faithfulness of an explanation w.r.t. the model [38]. A common way to measure the correctness of attribution methods is the Incremental Deletion protocol [8, 10, 21, 23, 27, 28, 38, 52, 55, 60], where input pixels are incrementally removed in the order of their relative importance to measure the impact on the output. Similarly, in the Single Deletion protocol [3, 14, 38, 41, 67], individual (input) features are deleted to compute the correlation between feature importance and the actual output change. A drawback of the above protocols is the domain shift occurring when introducing image interventions, which can cause undesirable model behavior influencing the metrics [10, 23, 28]. To reduce this, masked pixels can be inpainted with a generative model [10] or text classification datasets can be augmented with training inputs that have similar alterations as the evaluation protocol [23]. However, none of these approaches achieve an exact alignment of the train and test domain as we do in this work."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Completeness measures the degree to which an explanation describes all aspects of the model's decision [38]. In the Preservation/Deletion Check protocols [10, 13, 16, 38, 45], important features are preserved/deleted to test if the output prediction stays the same/changes. However, as above, these protocols introduce unrealistic domain changes. In the Controlled Synthetic Data Check protocol [2, 13, 30, 34, 38, 50], a synthetic dataset is used to evaluate if the explanation of a model with almost perfect accuracy aligns with the dataset generation process. While closely related to our work, existing synthetic datasets for evaluating XAI methods are very small-scale, only evaluate a single dimension of explainability, and do not allow for diverse image-space interventions that are crucial for evaluating correctness."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Contrastivity measures the degree to which an explanation is discriminative w.r.t. different outputs [38]. It can be measured with the Target Sensitivity protocol [38] that evaluates if the explanations for two different targets are different [45] and sometimes, even more, whether the explanation aligns with the image region of the correct target [8,19,65]. However, these evaluations can require accurate object annotations, which are not given for most classi"
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+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.089,
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+            "angle": 0,
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+            "angle": 0,
+            "content": "(b)"
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+            "content": "(c)"
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+                0.077,
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+            "angle": 0,
+            "content": "Figure 2. Generation process of our synthetic dataset. (a) The scene is initialized with a neutral bird body part. (b) Class-specific parts are added. (c) To reflect real-world challenges, random backgrounds, illumination, and viewpoint changes are added/applied."
+        },
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+            "type": "text",
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+            "angle": 0,
+            "content": "fication datasets, or they can also introduce out-of-domain issues when arranging images in a grid as in [8,9,46]."
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+            ],
+            "angle": 0,
+            "content": "Human studies. Besides above automatic evaluations, there have been efforts to assess the quality of XAI methods with human subjects [15, 40, 51, 54]. Human studies nicely reflect the actual downstream tasks of explanations, i.e., helping humans to understand models, and they can be applied to explanations that go beyond simple heat maps [31]. Downsides of user studies include larger cost and human biases [36]. Further, humans are not capable of directly evaluating if explanations are correct w.r.t. a complex, deep model. With our custom analysis, we aim to reduce the gap between the automatic evaluation and human studies while addressing the described drawbacks of human assessment."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.498,
+                0.469,
+                0.648
+            ],
+            "angle": 0,
+            "content": "Synthetic datasets. Synthetic datasets have an important and long history in many other disciplines of computer vision [7,18,29,42,48]. Richter et al. [48] utilize a video game to create a large-scale segmentation dataset. The \"Flying Chairs\" dataset [18] and MPI Sintel [7] are popular synthetic datasets used for the training and evaluation of optical flow methods. CLEVR [29] was introduced to test different visual reasoning abilities. All these works advanced their specific sub-fields, showing that synthetic datasets are a valuable tool, even in the absence of full realism."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.663,
+                0.308,
+                0.68
+            ],
+            "angle": 0,
+            "content": "3. The FunnyBirds Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.689,
+                0.469,
+                0.749
+            ],
+            "angle": 0,
+            "content": "We propose a synthetic vision dataset that is developed to automatically and quantitatively analyze XAI methods. To this end, we made a multitude of carefully considered design choices, which we summarize in the following."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.469,
+                0.885
+            ],
+            "angle": 0,
+            "content": "Since XAI methods in computer vision have been developed mainly in the context of classification to date [38], we focus on classification and propose a fine-grained bird species dataset inspired by the CUB-200-2011 dataset [61] commonly used by XAI methods [12, 22, 26, 39, 66]. Our dataset consists of 50500 images (50k train, 500 test) of 50 synthetic bird species. We found 500 test images to be sufficient to produce stable results while allowing efficient evaluations with limited hardware (see supplement)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.886,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "One particularly important desideratum behind our de"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.379
+            ],
+            "angle": 0,
+            "content": "sign process is the notion of concepts that we define as mental representations of psychological entities that are crucial to categorization [35, 37, 49, 64]. For instance, humans might categorize a bird as a flamingo when observing the concepts curved beak and pink wings. Similarly, they would communicate their reasoning process in terms of concepts [49]. Hence, we argue that concepts are essential in the context of XAI for humans, and thus, we design our dataset with a particular emphasis on the notion of concepts. To derive a precise level of granularity for the concepts in our dataset, we enforce them to be as granular as possible, while corresponding to an existing individual word, and being attached to the bird's body. This avoids \"unrealistic\" scenarios where the removal of one concept leaves another concept unattached (the body of the bird is never removed) and eliminates overly fine-grained concepts. Following these rules, our FunnyBirds consist of the five human comprehensible concepts beak, wings, feet, eyes, and tail, to which we will refer as parts in the following."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.383,
+                0.893,
+                0.761
+            ],
+            "angle": 0,
+            "content": "We manually design 4 beaks, 3 eyes, 4 feet, 9 tails, and 6 wings of predefined varied shape and/or color (see supplement). Every FunnyBird class consists of a unique combination of these parts. We randomly sample 50 classes out of the 2592 combinations as our dataset. Using these classes, we follow the data-generation process outlined in Fig. 2 by adding class-specific parts to a neutral body model to obtain an instance of a FunnyBird. To reflect real-world challenges, we randomly add background objects and change the illumination and viewpoint. We also explored more photo-realistic simulations with real background images and textured parts. However, with neural models learning to ignore these \"distractions\", our quantitative analysis was largely unaffected. We thus omit this in pursuit of simplicity. We verified the solvability of our dataset with a human expert who achieved an accuracy of \\(97.4\\%\\) on the proposed test set. To ensure that removing any part does not result in another valid class, each complete FunnyBird instance contains all five parts. To ensure that images with removed parts are not out-of-distribution, we include images with missing parts in the training set. As these images can no longer be associated with one specific class, we use a multi-label classification training scheme where all classes that contain all of the remaining parts are considered valid (with equal probability)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our data-generation process has several important implications that make it particularly well suited for evaluating and analyzing XAI methods. First, based on the assumption that humans think in concepts rather than pixels, we argue that a concept-based dataset and the resulting evaluations are better aligned with downstream tasks of human comprehension than pixel-based evaluations. Second, we have pixel-accurate annotations of each object and bird part in the scene, which is required for various automatic evaluation"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3983"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.152
+            ],
+            "angle": 0,
+            "content": "protocols and tailored analyses. Third, having full control over the data-generation process allows applying realistic image-space interventions, such as removing parts, which can be used to estimate ground-truth importance scores."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.167,
+                0.277,
+                0.183
+            ],
+            "angle": 0,
+            "content": "4. Evaluation Protocols"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.193,
+                0.471,
+                0.328
+            ],
+            "angle": 0,
+            "content": "We will now outline how our dataset and its functionalities can be used for the quantitative evaluation and analysis of XAI methods. We first propose a general, multi-dimensional analysis framework, named FunnyBirds framework, that allows to evaluate a wide range of existing XAI methods in a common framework. Second, we propose a more tailored way of analysis where our dataset's capabilities are used to gain deeper insights into specific methods similar to what human studies could do."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.339,
+                0.332,
+                0.355
+            ],
+            "angle": 0,
+            "content": "4.1. The FunnyBirds framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.363,
+                0.47,
+                0.545
+            ],
+            "angle": 0,
+            "content": "The multi-dimensional FunnyBirds analysis framework for XAI methods entails six evaluation protocols for three explainability dimensions, i.e., completeness, correctness, and contrastivity. They were chosen for their popularity in related work [38], ability to be automatically measurable, and compatibility with our dataset. Most of our protocols are inspired by well-established evaluation practices and follow accepted assumptions. Our dataset generation process ensures that all conducted interventions can be considered in-domain and semantically meaningful, eliminating common downsides [23, 28] of several existing evaluation protocols that rely on image interventions [10,21,23,27,55]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.549,
+                0.47,
+                0.837
+            ],
+            "angle": 0,
+            "content": "Meaning of ground truth. Our work relies on interventions to estimate \"ground-truth\" importance scores for individual parts. This is motivated by (1) the observation that in XAI we aim to approximate the causal structure of the inspected model, and (2) findings that the causal structure can be estimated via interventions [43]. Since the perfect causal structure (which is too complex to be comprehended) is already given by the model itself, we emphasize that a simplified approximation is needed for XAI, instead. We thus assume such an approximation for estimating the ground-truth scores with interventions. For example, in the single deletion protocol (see Sec. 4.1.3), we assume that a hypothetical simplified model processes each part individually, which generally does not need to hold for the real model. This assumption is implicitly also made in existing single deletion protocols [3, 14, 41, 67]. Further, most existing explanation methods, e.g., attribution maps, communicate the importance of each feature individually, thus evaluating explanations beyond individual concepts is not yet sensible."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Interface functions. The diversity of explanation types presents a major challenge to evaluating XAI methods, which prevents a direct comparison of different methods and created a need for various non-standardized evalua-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.228
+            ],
+            "angle": 0,
+            "content": "tions. We thus propose to build our evaluation framework around so-called interface functions that implement more general properties, such as which object parts are important. They can be derived from a variety of explanation types, and thus, used to evaluate distinct explanations in a common framework. This allows us to not only compare a spectrum of existing methods, but also to potentially include future, novel explanation types. Our evaluation framework currently uses the following interface functions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.234,
+                0.892,
+                0.265
+            ],
+            "angle": 0,
+            "content": "\\(\\operatorname{PI}(\\cdot)\\) - The part importance score for each part. For example, the summed attribution within that part."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.273,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": "\\(\\mathrm{P}(\\cdot)\\) - The parts that are considered to be important, derived from the output of an XAI method. For attribution methods, a part can be considered important if its part importance is at least \\(t\\%\\) of the total attribution."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.34,
+                0.892,
+                0.506
+            ],
+            "angle": 0,
+            "content": "Note that different explanation types vary in their suitability for differing downstream tasks, and thus, also in their suitability for above interface functions. Furthermore, just as humans differ in interpreting various explanations, there may not be a single correct way of implementing the interface functions (see supplement). Therefore, comparing different explanation types is not absolutely fair and should be done with caution. Nonetheless, we argue that estimating important image regions and their relative importance are fairly basic challenges in XAI, and thus, appropriate downstream tasks, respectively, interface functions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.51,
+                0.892,
+                0.706
+            ],
+            "angle": 0,
+            "content": "**Framework.** For a simple comparison and visualization, we design all metrics to be in the range [0, 1], with higher values indicating better scores. For each dimension (as described below), we report a single score comprised of all included protocols (see Tab. 1). Additionally, we report the average of all our explanation quality dimensions, i.e., completeness, correctness, contrastivity, as a single score that summarizes the overall quality of an XAI method for the inspected model. We let \\(\\mathcal{D}\\) denote our dataset of size \\(N\\), consisting of images \\(x_{n}\\) with class label \\(c_{n}\\); \\(f\\) is the inspected model with \\(f(x_{n})\\) denoting the predicted class or the logit of the target class, and \\(e_{f}(x_{n})\\) is the explanation of \\(f(x_{n})\\) w.r.t. the target class \\(c_{n}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
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+                0.838,
+                0.739
+            ],
+            "angle": 0,
+            "content": "4.1.1 Accuracy and background independence"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.747,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "Accuracy (A). An overly simple model may be explainable but not solve the task at hand. To detect such cases, our framework reports the standard classification accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Background independence (BI). Similarly, another trivial solution to achieve high explanation scores is a model that is sensitive to the entire image. An explanation would consequently highlight the entire image. To detect this case, we report the background independence as the ratio of background objects that are unimportant, i.e., that, when removed, cause the target logit to drop less than \\(5\\%\\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "3984"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.115,
+                0.088,
+                0.852,
+                0.102
+            ],
+            "angle": 0,
+            "content": "Table 1. Overview of our evaluation protocols. \"Interface function\" denotes the required interface function for each protocol."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.078,
+                0.104,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dimension</td><td>Protocol</td><td>Interface function</td><td>Description</td></tr><tr><td>-</td><td>A</td><td>-</td><td>Percentage of correct predictions over the test dataset</td></tr><tr><td>-</td><td>BI</td><td>-</td><td>The model should not be sensitive to the background objects</td></tr><tr><td>Completeness</td><td>CSDC</td><td>P</td><td>Explanation should highlight all relevant parts</td></tr><tr><td>Completeness</td><td>PC</td><td>P</td><td>Preserving parts identified as important should result in the same prediction</td></tr><tr><td>Completeness</td><td>DC</td><td>P</td><td>Removing parts identified as important should result in a different prediction</td></tr><tr><td>(Over-)Completeness</td><td>D</td><td>P</td><td>Explanation should not highlight irrelevant parts</td></tr><tr><td>Correctness</td><td>SD</td><td>PI</td><td>Estimated importance of each part should be correlated to actual importance</td></tr><tr><td>Contrastivity</td><td>TS</td><td>PI</td><td>Explanations for different classes should highlight class-specific parts</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.267,
+                0.228,
+                0.281
+            ],
+            "angle": 0,
+            "content": "4.1.2 Completeness"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.291,
+                0.471,
+                0.518
+            ],
+            "angle": 0,
+            "content": "Controlled synthetic data check (CSDC). Our transparent data generation process allows us to know the subsets of parts \\(\\{\\mathcal{P}_{c_n,i}'\\mid i = 1,\\ldots \\}\\) that are sufficient to correctly categorize an image of class \\(c_{n}\\) containing parts \\(\\mathcal{P}_{c_n}\\). A model that accurately captures the essence of our dataset, i.e., has an accuracy close to 1.0, must thus consider at least one of these sets \\(\\mathcal{P}_{c_n,i}'\\) [13, 34, 38, 50]. To ensure that this assumption holds and CSDC is faithful w.r.t. the model, we exclude misclassified samples from this protocol. We measure the CSDC completeness of an explanation as the set overlap between the parts that are estimated to be important by the explanation (i.e., \\(\\mathrm{P}(e_f(x_n))\\) where \\(\\mathrm{P}(\\cdot)\\) is the interface function giving the important parts) and the sufficient part set that has the largest overlap with \\(\\mathrm{P}(e_f(x_n))\\), normalized by the size of the sufficient part set:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.12,
+                0.53,
+                0.47,
+                0.571
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {C S D C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\max  _ {i} \\frac {\\left| \\mathrm {P} \\left(e _ {f} \\left(x _ {n}\\right)\\right) \\cap \\mathcal {P} ^ {\\prime} _ {c _ {n} , i} \\right|}{\\left| \\mathcal {P} ^ {\\prime} _ {c _ {n} , i} \\right|}. \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.588,
+                0.47,
+                0.74
+            ],
+            "angle": 0,
+            "content": "Preservation check (PC). If an explanation is complete, preserving only the parts of the input that are estimated to be important by the explanation should still result in the same classification output [13,16,38]. To verify this, we first pass the original image through the inspected model to obtain the classification and the corresponding explanation. Afterward, we delete all parts of the image that are estimated to not be important by the explanation, i.e., the inverse of \\(\\mathrm{P}(\\cdot)\\), and measure how often the class prediction remains unchanged. We define our PC score as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.162,
+                0.752,
+                0.469,
+                0.793
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {P C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left[ f \\left(x _ {n} ^ {\\prime}\\right) = f \\left(x _ {n}\\right) \\right], \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.805,
+                0.469,
+                0.852
+            ],
+            "angle": 0,
+            "content": "with \\([\\cdot]\\) denoting the Iverson bracket [32] and \\(x_{n}^{\\prime}\\) denoting the image arising by removing all bird parts but \\(\\mathrm{P}(e_f(x_n))\\) from \\(x_{n}\\). I.e., the parts estimated to be important remain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.856,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Deletion check (DC). Similarly, if an explanation is complete, deleting all the parts of the input that are estimated to be important by the explanation should result in a different"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.267,
+                0.892,
+                0.296
+            ],
+            "angle": 0,
+            "content": "classification output [16,38,45]. Thus, the deletion check is the inverse of PC and defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.583,
+                0.307,
+                0.892,
+                0.348
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {D C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} [ f (x _ {n} ^ {\\prime \\prime}) \\neq f (x _ {n}) ], \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.36,
+                0.892,
+                0.392
+            ],
+            "angle": 0,
+            "content": "with \\( x_{n}^{\\prime \\prime} \\) denoting the image arising by removing the estimated important parts \\( \\mathrm{P}(e_f(x_n)) \\) from \\( x_{n} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.396,
+                0.893,
+                0.637
+            ],
+            "angle": 0,
+            "content": "Distractibility (D). As over-complete explanations would achieve high completeness scores, we argue that completeness should be considered together with a metric that counters over-completeness (similar to precision and recall). To this end, we introduce a novel over-completeness score that measures how many actually unimportant input parts are also estimated to be unimportant by the explanation. In detail, we successively remove each background object and bird part from the input and consider it to be unimportant if the logit target output drops less than \\(5\\%\\) compared to the output for the original image. Next, we measure the overlap between parts \\(\\mathrm{P}(e_f(x_n))\\) estimated to be important by the explanation and parts \\(\\mathcal{P}_{f(x_n)}^{\\prime \\prime}\\) that are actually unimportant, normalized by the number of unimportant parts. As the overlap should be small for good evaluations, we subtract the result from 1:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.559,
+                0.648,
+                0.892,
+                0.69
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {D} = 1 - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\frac {\\left| \\mathrm {P} \\left(e _ {f} \\left(x _ {n}\\right)\\right) \\cap \\mathcal {P} _ {f \\left(x _ {n}\\right)} ^ {\\prime \\prime} \\right|}{\\left| \\mathcal {P} _ {f \\left(x _ {n}\\right)} ^ {\\prime \\prime} \\right|}. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.702,
+                0.892,
+                0.793
+            ],
+            "angle": 0,
+            "content": "The final completeness score (Com.) is computed as the mean of the averaged three completeness metrics (CSDC, PC, and DC), and the over-completeness D. By having complementing metrics, we can also automatically estimate the threshold \\( t \\) of \\( \\mathrm{P}(\\cdot) \\), such that \\( t \\) optimally trades off the completeness and over-completeness metrics."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.816,
+                0.638,
+                0.83
+            ],
+            "angle": 0,
+            "content": "4.1.3 Correctness"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Single deletion (SD). In the single deletion protocol, we measure the rank correlation between the explanation's importance score of each part and the actual amount that the model's logit of the target class changes when removing that"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3985"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.376,
+                0.107
+            ],
+            "angle": 0,
+            "content": "part [3, 14, 38]. Specifically, we define SD as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.117,
+                0.47,
+                0.158
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {S D} = \\frac {1}{2} + \\frac {1}{2 N} \\sum_ {n = 1} ^ {N} \\rho \\left(\\mathrm {P I} \\left(e _ {f} \\left(x _ {n}\\right)\\right), f \\left(x _ {n}\\right) - \\left\\{f \\left(x _ {n} ^ {\\prime \\prime \\prime}\\right) \\right\\}\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.167,
+                0.47,
+                0.229
+            ],
+            "angle": 0,
+            "content": "with \\(\\rho\\) denoting the Spearman rank-order correlation coefficient, \\(\\mathrm{PI}(\\cdot)\\) the part importance interface function, and \\(\\{f(x_n^{\\prime \\prime \\prime})\\}\\) the target scores of the images obtained by removing any individual bird part from \\(x_{n}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.246,
+                0.224,
+                0.26
+            ],
+            "angle": 0,
+            "content": "4.1.4 Contrastivity"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.269,
+                0.471,
+                0.436
+            ],
+            "angle": 0,
+            "content": "Target sensitivity (TS). If an explanation is sensitive to a target class, it should highlight image regions that are relevant for the respective target [8, 9, 38]. To measure target sensitivity, we take an input sample and select two classes \\(\\hat{c}_1\\) and \\(\\hat{c}_2\\) that each have exactly two non-overlapping common parts with the actual class of input sample \\(x_n\\). We choose two parts because this is the floor of half the 5 bird parts available in each image. Afterward, we compute the explanations \\(e_f(x_n, \\hat{c}_i)\\) with respect to \\(\\hat{c}_1\\) and \\(\\hat{c}_2\\) and evaluate if they correctly highlight the parts belonging to each respective class:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.086,
+                0.446,
+                0.469,
+                0.509
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathrm {T S} = \\frac {1}{2 N} \\sum_ {n = 1} ^ {N} \\left[ \\mathrm {P I} ^ {\\prime} \\left(e _ {f} \\left(x _ {n}, \\hat {c} _ {1}\\right)\\right) > \\mathrm {P I} ^ {\\prime} \\left(e _ {f} \\left(x _ {n}, \\hat {c} _ {2}\\right)\\right) \\right] \\tag {6} \\\\ + \\left[ \\mathrm {P I} ^ {\\prime \\prime} (e _ {f} (x _ {n}, \\hat {c} _ {1})) <   \\mathrm {P I} ^ {\\prime \\prime} (e _ {f} (x _ {n}, \\hat {c} _ {2})) \\right], \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.517,
+                0.47,
+                0.61
+            ],
+            "angle": 0,
+            "content": "with \\(\\mathrm{PI}'(\\cdot)\\) and \\(\\mathrm{PI}''(\\cdot)\\) denoting the summed part importances of the two parts belonging to class \\(\\hat{c}_1\\), respectively \\(\\hat{c}_2\\). To ensure that our protocol is faithful w.r.t. the model, we only consider images where removing parts belonging to \\(\\hat{c}_1\\) causes a larger model output drop for \\(\\hat{c}_1\\) than removing parts belonging to \\(\\hat{c}_2\\), and vice versa."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.618,
+                0.367,
+                0.634
+            ],
+            "angle": 0,
+            "content": "4.2. The FunnyBirds custom analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.641,
+                0.469,
+                0.793
+            ],
+            "angle": 0,
+            "content": "As it is almost impossible to analyze all aspects of an explanation with a single framework, we also show how full control over our dataset enables more tailored and systematic custom evaluations. Similar to recent human studies [31], we evaluate the coherence of the assessed methods, i.e., how reasonable an explanation is for a human. To the best of our knowledge, this is one of the first methods for evaluating coherence in a fully automatic and systematic manner. We give two illustrative examples for implementing such an evaluation, but other instantiations are possible."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "ProtoPNet. ProtoPNet [12] promotes explainability by communicating which patches of the training data, called prototypes, look similar to patches in a test image. However, this only increases interpretability if the detected similarities are compatible with human notions of similarity. To quantitatively verify this in an automatic fashion, we test if relevant part types (e.g., beak or wing) in the detected patch"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.183
+            ],
+            "angle": 0,
+            "content": "of the test image are also contained in the corresponding prototype identified by ProtoPNet. This assumes that different part types, i.e., beak and wings, do not look similar to most humans, and therefore, are not helpful similarities for explainability. While debatable for real images, we argue that this is a reasonable assumption for our dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.185,
+                0.893,
+                0.488
+            ],
+            "angle": 0,
+            "content": "Counterfactual visual explanations. The objective of counterfactual visual explanations (CVE) [22] is to highlight image regions that discriminate the class \\( c \\) of a query image from the class \\( c' \\) of a distractor image. To this end, CVE extracts convolutional neural network (CNN) feature maps from the query and distractor images to then perform feature swaps between the two feature maps that, when fed to the CNN classifier, lead to the strongest class change (from \\( c \\) to \\( c' \\)). The corresponding image locations of the feature swaps are then highlighted to yield the CVE. We argue that this kind of explanation is only meaningful for humans if the swaps are semantically correct, i.e., when a beak is swapped with another beak but not a foot. Using our proposed dataset, we conduct a systematic study and measure the average number of swaps that do not touch the same bird part in both images, and thus, can be considered semantically incorrect. We evaluate four different setups of increasing difficulty where we only use aligned, respectively unaligned, viewpoint pairs with classes that are different in only one, respectively multiple parts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.492,
+                0.893,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Limitations. As with controlled laboratory research [5], our dataset does not reflect all real-world challenges, and thus, is not fully representative of natural images. However, we argue that, as long as XAI methods are challenged to truthfully explain models trained even on our controlled dataset, our proposed method is a valuable tool to faithfully assess the quality of XAI methods. Nonetheless, for future XAI methods we suggest a two-stream evaluation that utilizes our proposed framework and custom analysis for theoretically grounded assessments of the explanation quality in addition to benchmarks that work on natural image data, e.g., Quantus [25]. Further, while the dimensions of explainability evaluated in our work can be considered relevant for many applications, there are dimensions that we omit here (see supplement). However, our framework can easily be extended with additional protocols if needed."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.747,
+                0.747,
+                0.764
+            ],
+            "angle": 0,
+            "content": "5. Results and Interpretation"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.772,
+                0.719,
+                0.788
+            ],
+            "angle": 0,
+            "content": "5.1. FunnyBirds framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Results for our multi-dimensional FunnyBirds framework across a broad variety of different XAI methods and three different backbones are given in Fig. 3. For detailed results of each individual evaluation protocol, please refer to the supplement. We plot qualitative explanations for a random image and give the evaluation scores from Sec. 4.1 averaged over the entire test set. From this, we can make"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3986"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.105,
+                0.891,
+                0.515
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.526,
+                0.895,
+                0.624
+            ],
+            "angle": 0,
+            "content": "Figure 3. FunnyBirds evaluation results. Qualitative and quantitative results for our FunnyBirds framework for the XAI methods Input \\(\\times\\) Gradient (IxG) [56], (absolute) Integrated Gradients (IG (abs.)) [59], Grad-CAM [11,53], RISE [44], LIME [47], Rollout [1], Chefer LRP [11], \\(\\mathcal{X}\\)-DNN [27], BagNet [6], ProtoPNet [12], and B-cos network [9]. Model-agnostic methods are evaluated on VGG16 [58], ResNet-50 [24], and ViT-B/16 [17]. Other models use a ResNet-50 backbone, if applicable. Quantitative results are averaged over the entire test set; qualitative results are shown for a representative example. Chart colors indicate different explanation types that should only be compared with caution. The center score denotes the mean of the completeness (Com.), correctness (Cor.), and contrastivity (Con.) dimensions. Additionally, we report the accuracy (Acc.) and background independence (B.I.). See Sec. 4.1 for details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.642,
+                0.462,
+                0.657
+            ],
+            "angle": 0,
+            "content": "several interesting findings and derive various hypotheses:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.658,
+                0.469,
+                0.718
+            ],
+            "angle": 0,
+            "content": "(1) Overall, BagNet [6] achieves the highest explainability score, which could be due to its internal model structure that is better aligned with the explanatory power of an attribution map, i.e., pixels are processed more independently."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.72,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "(2) On average, Integrated Gradients (IG) [59] performs best among model-agnostic methods for different backbones, which is in line with the literature when considering gradient-based approaches [56, 59]. However, LIME [47] and IG achieve similar completeness, with LIME lacking the ability to communicate meaningful importance scores, which impairs practicability for certain downstream tasks. Interestingly, taking the absolute value of IG impairs the mean explanation score slightly, contradicting findings that have been made on pixel-level protocols [62]. Specifically, it slightly increases completeness while reducing contrastivity. We hypothesize that the negative gradient infor"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.076,
+                0.658,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.642,
+                0.892,
+                0.718
+            ],
+            "angle": 0,
+            "content": "mation is therefore particularly important in identifying regions that do not belong to the class of interest. Removing the bias term (X-DNN [27] vs. ResNet-50 [24] w/ IG) slightly improves completeness and correctness while reducing contrastivity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.719,
+                0.892,
+                0.824
+            ],
+            "angle": 0,
+            "content": "(3) Explanation scores for model-agnostic XAI methods are consistently better for VGG16 [58] than for ResNet-50 [24], indicating that different backbones vary in their explainability. We also observe that the relative ordering of different XAI methods changes across different backbones (e.g., RISE [44] and IxG [56]), showing the importance of evaluating future XAI methods on different backbones."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "(4) IxG [56] and Grad-CAM [11, 53] seem to work better on CNN-based architectures [24, 58]. Methods developed for vision transformers, i.e., Rollout [1] and Chefer LRP [11], provide strong explanations, with Chefer LRP achieving the second highest explanation score. Rollout"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.498,
+                0.719,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3987"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.092,
+                0.462,
+                0.174
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.177,
+                0.468,
+                0.22
+            ],
+            "angle": 0,
+            "content": "Figure 4. Qualitative results of ProtoPNet [12]. Many of the test image patches (center) highlight the entire bird or just background. Further, prototypes (sides) often do not include important parts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.234,
+                0.468,
+                0.263
+            ],
+            "angle": 0,
+            "content": "cannot compute class-specific explanations, which could be disadvantageous in certain downstream tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.264,
+                0.469,
+                0.31
+            ],
+            "angle": 0,
+            "content": "(5) Coarser methods like Grad-CAM [53] and RISE [44] tend to be more incomplete, which could be an artifact of poor localization [46] and our parts being fairly small."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.31,
+                0.468,
+                0.37
+            ],
+            "angle": 0,
+            "content": "(6) The B-cos network [9] outperforms competing methods on the same backbone, showing an improved explainability, which is in line with results from [9]. Surprisingly, we see a slight decrease in background independence."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.371,
+                0.469,
+                0.43
+            ],
+            "angle": 0,
+            "content": "(7) ProtoPNet [12] has poor correctness and contrastivity, which can be explained by related findings in that ProtoPNet similarities are not semantically reasonable [31] and by its poor localization (see Sec. 5.2 and Fig. 4)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.431,
+                0.469,
+                0.521
+            ],
+            "angle": 0,
+            "content": "(8) Especially correctness is a weakness of all examined methods, showing that, while existing approaches tend to accurately identify important areas, they lack the ability to reliably communicate the relative importance of each input area, or that the simple explanation of an attribution map might be too strong of a simplification of the actual model."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.077,
+                0.264,
+                0.469,
+                0.521
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.522,
+                0.469,
+                0.612
+            ],
+            "angle": 0,
+            "content": "Finally, since XAI evaluation is multi-faceted and downstream task dependent, we doubt that a single score can be enough to properly compare methods. Hence, our work is less about ranking but more about automatically revealing the strengths and weaknesses of existing and future XAI methods in a systematic and theoretically grounded manner."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.621,
+                0.265,
+                0.636
+            ],
+            "angle": 0,
+            "content": "5.2.Custom evaluations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.644,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "ProtoPNet. To quantitatively evaluate if prototypes used in [12] promote explainability (see Sec. 4.2), we conduct several sanity checks. First, we measure that out of 1000 examined ProtoPNet patches in the test image, only 510 touch the same part in the corresponding prototype patch, and thus, have a similarity that could be aligned with human notions of similarity. Further, we measure that \\(26.3\\%\\) of the extracted test image patches do not touch a single bird part, indicating a poor localization of the explanation. Finally, \\(18.5\\%\\) of the test image patches entail 4 or 5 different bird parts, which shows that the extracted patches are not local but global, and thus, do not promote the interpretability of the examined model. Qualitative results showing the described issues can be seen in Fig. 4. To summarize, many of the communicated prototypes of ProtoPNet [12] trained on our dataset are unlikely to be meaningful for humans. While a similar conclusion was drawn in a recent human"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.089,
+                0.892,
+                0.158
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.16,
+                0.892,
+                0.243
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative results of counterfactual visual explanations (CVE) [22]. (left) CVE for an aligned image pair with one part being different. (right) CVE for an unaligned image pair with multiple parts being different. Note how many of the proposed swaps are unrealistic, and therefore, of little quality (e.g., the purple patch around the right eye is swapped with the neck of the other bird)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.261,
+                0.891,
+                0.291
+            ],
+            "angle": 0,
+            "content": "study [31] confirming our findings, our proposed tools allow the same conclusion in a fully automatic manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.298,
+                0.893,
+                0.614
+            ],
+            "angle": 0,
+            "content": "Counterfactual visual explanations. To quantify if CVE [22] highlights meaningful swaps (see Sec. 4.2), we measure how many of the extracted swaps do not touch the same bird parts in the two images. When considering images that have the same viewpoint and differ only by one part (Fig. 5 - left), CVE with VGG16 [58] produces on average 1.65 swaps that do not touch the same part, and therefore, are semantically meaningless. When changing the viewpoint, CVE produces on average 1.3 swaps that do not touch the same part. When working with aligned viewpoints and birds that differ by multiple parts (4.07 parts on average), 2.75 such swaps are produced and 2.62 when also changing the viewpoint (Fig. 5 - right). Interestingly, the number of different parts has a stronger impact on the absolute number of unreasonable swaps, i.e., swaps that do not touch the same part in both images, than the viewpoint. Further, we observe that even in our controlled environment, CVE produces on average \\(\\sim 3\\) unreasonable swaps for images with on average only 4 different parts, indicating that many of the proposed swaps are semantically incorrect, and thus, do not promote coherent explanations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.633,
+                0.619,
+                0.648
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, we propose a novel approach to automatically analyzing XAI methods using a synthetic classification dataset that allows for full annotation and part interventions. Using this dataset, we propose an accompanying multi-dimensional analysis framework that faithfully assesses various important aspects of explainability and generalizes to different explanation types by using interface functions. With this easy-to-use tool, we analyzed 24 different setups to uncover various new insights and confirm findings from related work. This shows that, despite the synthetic setting, our findings appear to translate well to real data, and that our proposed tool is a practical and valuable asset for the analysis of future XAI methods. Finally, we showed how to develop tailored analyses to gain a better understanding of two specific XAI methods and discovered their weaknesses in an automatic and quantitative manner."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "3988"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.228
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. We thank Bernt Schiele, Moritz Böhle, and Sukrut Rao for their valuable feedback and helpful discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 866008). The project has also been supported in part by the State of Hesse through the cluster projects \"The Third Wave of Artificial Intelligence (3AI)\" and \"The Adaptive Mind (TAM)\"."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.238,
+                0.175,
+                0.255
+            ],
+            "angle": 0,
+            "content": "References"
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
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+            ],
+            "angle": 0,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
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+# FunnyBirds: A Synthetic Vision Dataset for a Part-Based Analysis of Explainable AI Methods
+
+Robin Hesse<sup>1</sup>
+
+Simone Schaub-Meyer<sup>1,2</sup>
+
+Stefan Roth1,2
+
+$^{1}$ Department of Computer Science, TU Darmstadt  $^{2}$ hessian.AI
+
+# Abstract
+
+The field of explainable artificial intelligence (XAI) aims to uncover the inner workings of complex deep neural models. While being crucial for safety-critical domains, XAI inherently lacks ground-truth explanations, making its automatic evaluation an unsolved problem. We address this challenge by proposing a novel synthetic vision dataset, named FunnyBirds, and accompanying automatic evaluation protocols. Our dataset allows performing semantically meaningful image interventions, e.g., removing individual object parts, which has three important implications. First, it enables analyzing explanations on a part level, which is closer to human comprehension than existing methods that evaluate on a pixel level. Second, by comparing the model output for inputs with removed parts, we can estimate ground-truth part importances that should be reflected in the explanations. Third, by mapping individual explanations into a common space of part importances, we can analyze a variety of different explanation types in a single common framework. Using our tools, we report results for 24 different combinations of neural models and XAI methods, demonstrating the strengths and weaknesses of the assessed methods in a fully automatic and systematic manner.
+
+# 1. Introduction
+
+Even though deep learning models have achieved breakthrough results in computer vision, their inner workings remain largely opaque. As a result, deep networks sometimes receive only limited user trust and cannot be applied blindly in safety-critical domains. To overcome this issue, a growing interest in the field of explainable artificial intelligence (XAI) has emerged, attempting to explain the inner workings of deep neural models in a human-comprehensible way. However, since there are generally no ground-truth explanations, evaluating XAI methods remains an open chal
+
+![](images/2b64e3cc1d04ab83ac9179b59ffe8cdf014e331071576551159c99d8e148e8eb.jpg)  
+Figure 1. Schematic illustration of our proposed dataset and analysis framework. For each input image, we render the corresponding part annotation and part interventions (e.g., removed beak). The interventions are used to estimate ground-truth importance scores of each input part, which are then compared to the estimated part importances from the explanation method under inspection (here [44]). We evaluate multiple dimensions of explainability to draw a more conclusive picture. Please refer to Sec. 4.1 for details.
+
+lenge. In fact, a third of XAI papers lack sound quantitative evaluation [38], while other work has limited comparability [31] or problematic evaluation protocols [23, 38].
+
+To overcome the issue of missing ground-truth explanations, automatic evaluations are often done via proxy tasks that adhere to the idea of performing image interventions by removing certain input features to then measure the resulting impact on the model output [21, 23, 55]. As image interventions are non-trivial to perform on existing vision datasets, they are usually applied on a pixel level, e.g., masking out single pixels [21, 23, 27, 52, 55]. However, this and related approaches share several downsides. First, performing interventions, as well as evaluating explanations on a pixel level, is disconnected from the downstream task of providing human-understandable explanations since humans perceive images in concepts rather than pixels. Second, existing automatic evaluation protocols are developed for specific explanation types, e.g., pixel-level attribution maps, and thus, cannot be extended to other explanation
+
+types like prototypes [12]. Third, by performing unrealistic interventions in image space, e.g., masking out pixels, they introduce domain shifts compared to the training distribution [10, 23, 28], which can cause the model to behave unexpectedly, and thus negatively affects the evaluation.
+
+In this work, we address the above and more challenges to contribute an important step toward a more rigorous quantitative evaluation of XAI methods by proposing a thorough, dedicated evaluation/analysis tool. We do so by building a fully controllable, synthetic classification dataset consisting of renderings of artificial bird species. This approach to analyzing XAI methods is analogous to controlled laboratory research, where we have full control over all variables, eliminating the potential influence of irrelevant factors, and therefore, providing clearer evidence of the observed behavior [5]. Our proposed dataset allows us to make the following main contributions: (1) We cover a wide range of dimensions of explainability by considering a collection of different evaluation protocols. (2) We allow to automatically compare various explanation types in a shared framework. (3) We avoid the out-of-domain issue of previous image-space interventions by introducing semantically meaningful interventions at training time. (4) We reduce the gap between the downstream task of human comprehension and XAI evaluation by proposing metrics that operate at a semantically meaningful part level rather than the semantically less meaningful pixel level. (5) We automatically analyze the coherence of explanations. (6) We analyze 24 different combinations of existing XAI methods and neural models, highlighting their strengths and weaknesses as well as identifying new insights that may be of general interest to the XAI community.
+
+# 2. Related Work
+
+XAI methods. In this work, we focus on image classification explanations for the outcome of one particular input using deep neural networks (DNNs). Perturbation-based explanation methods [1, 11, 33, 44, 47, 63, 68, 69] estimate the impact of pixels/regions by measuring the output change occurring when repeatably perturbing inputs or neurons. Backpropagation-based explanation methods [4, 20, 27, 53, 55, 57, 59] use importance signals, e.g., gradient information, to estimate the importance of each input feature. Both types of methods generate post-hoc explanations for already trained networks. On the other hand, intrinsically explainable models [3, 6, 8, 9, 12, 39] consider explainability already in the design process of the model itself. For example, B-cos networks [9] enforce weight-input alignment to highlight the most important input regions. ProtoPNet [12] computes the feature similarity between test image patches and prototypes to help explain why a decision was made based on this patch looking like that prototype. BagNets [6] use a linear classifier on top
+
+of each feature extracted from small image patches to highlight task-important regions.  $\mathcal{X}$  -DNNs [27] remove the bias term in ReLU networks to allow for an efficiently computable closed-form solution of Integrated Gradients [59].
+
+Evaluating XAI methods. A sound evaluation of XAI methods is essential to compare different approaches and unveil their strengths and weaknesses. Nauta et al. [38] argue that explainability is a multi-faceted concept and propose various properties that describe different aspects of explanation quality. Below, we outline existing evaluation protocols for three of these dimensions that have received particularly much attention in related work and that allow for a well-defined automatic evaluation:
+
+Correctness denotes the faithfulness of an explanation w.r.t. the model [38]. A common way to measure the correctness of attribution methods is the Incremental Deletion protocol [8, 10, 21, 23, 27, 28, 38, 52, 55, 60], where input pixels are incrementally removed in the order of their relative importance to measure the impact on the output. Similarly, in the Single Deletion protocol [3, 14, 38, 41, 67], individual (input) features are deleted to compute the correlation between feature importance and the actual output change. A drawback of the above protocols is the domain shift occurring when introducing image interventions, which can cause undesirable model behavior influencing the metrics [10, 23, 28]. To reduce this, masked pixels can be inpainted with a generative model [10] or text classification datasets can be augmented with training inputs that have similar alterations as the evaluation protocol [23]. However, none of these approaches achieve an exact alignment of the train and test domain as we do in this work.
+
+Completeness measures the degree to which an explanation describes all aspects of the model's decision [38]. In the Preservation/Deletion Check protocols [10, 13, 16, 38, 45], important features are preserved/deleted to test if the output prediction stays the same/changes. However, as above, these protocols introduce unrealistic domain changes. In the Controlled Synthetic Data Check protocol [2, 13, 30, 34, 38, 50], a synthetic dataset is used to evaluate if the explanation of a model with almost perfect accuracy aligns with the dataset generation process. While closely related to our work, existing synthetic datasets for evaluating XAI methods are very small-scale, only evaluate a single dimension of explainability, and do not allow for diverse image-space interventions that are crucial for evaluating correctness.
+
+Contrastivity measures the degree to which an explanation is discriminative w.r.t. different outputs [38]. It can be measured with the Target Sensitivity protocol [38] that evaluates if the explanations for two different targets are different [45] and sometimes, even more, whether the explanation aligns with the image region of the correct target [8,19,65]. However, these evaluations can require accurate object annotations, which are not given for most classi
+
+![](images/38d138798e849c51dfc6d3d8611b61af4de36e4d921c29b659aca94b9615e07f.jpg)  
+(a)
+
+![](images/01a9f82185327fabce69f1ac8a54899eedb52cfe0ae8e7d25449b34c76eb363a.jpg)  
+(b)
+
+![](images/477c2555b8330cf3d83bbf18e8ededc1158640debe0ee5bb1a72e10cbcbabf31.jpg)  
+(c)  
+Figure 2. Generation process of our synthetic dataset. (a) The scene is initialized with a neutral bird body part. (b) Class-specific parts are added. (c) To reflect real-world challenges, random backgrounds, illumination, and viewpoint changes are added/applied.
+
+fication datasets, or they can also introduce out-of-domain issues when arranging images in a grid as in [8,9,46].
+
+Human studies. Besides above automatic evaluations, there have been efforts to assess the quality of XAI methods with human subjects [15, 40, 51, 54]. Human studies nicely reflect the actual downstream tasks of explanations, i.e., helping humans to understand models, and they can be applied to explanations that go beyond simple heat maps [31]. Downsides of user studies include larger cost and human biases [36]. Further, humans are not capable of directly evaluating if explanations are correct w.r.t. a complex, deep model. With our custom analysis, we aim to reduce the gap between the automatic evaluation and human studies while addressing the described drawbacks of human assessment.
+
+Synthetic datasets. Synthetic datasets have an important and long history in many other disciplines of computer vision [7,18,29,42,48]. Richter et al. [48] utilize a video game to create a large-scale segmentation dataset. The "Flying Chairs" dataset [18] and MPI Sintel [7] are popular synthetic datasets used for the training and evaluation of optical flow methods. CLEVR [29] was introduced to test different visual reasoning abilities. All these works advanced their specific sub-fields, showing that synthetic datasets are a valuable tool, even in the absence of full realism.
+
+# 3. The FunnyBirds Dataset
+
+We propose a synthetic vision dataset that is developed to automatically and quantitatively analyze XAI methods. To this end, we made a multitude of carefully considered design choices, which we summarize in the following.
+
+Since XAI methods in computer vision have been developed mainly in the context of classification to date [38], we focus on classification and propose a fine-grained bird species dataset inspired by the CUB-200-2011 dataset [61] commonly used by XAI methods [12, 22, 26, 39, 66]. Our dataset consists of 50500 images (50k train, 500 test) of 50 synthetic bird species. We found 500 test images to be sufficient to produce stable results while allowing efficient evaluations with limited hardware (see supplement).
+
+One particularly important desideratum behind our de
+
+sign process is the notion of concepts that we define as mental representations of psychological entities that are crucial to categorization [35, 37, 49, 64]. For instance, humans might categorize a bird as a flamingo when observing the concepts curved beak and pink wings. Similarly, they would communicate their reasoning process in terms of concepts [49]. Hence, we argue that concepts are essential in the context of XAI for humans, and thus, we design our dataset with a particular emphasis on the notion of concepts. To derive a precise level of granularity for the concepts in our dataset, we enforce them to be as granular as possible, while corresponding to an existing individual word, and being attached to the bird's body. This avoids "unrealistic" scenarios where the removal of one concept leaves another concept unattached (the body of the bird is never removed) and eliminates overly fine-grained concepts. Following these rules, our FunnyBirds consist of the five human comprehensible concepts beak, wings, feet, eyes, and tail, to which we will refer as parts in the following.
+
+We manually design 4 beaks, 3 eyes, 4 feet, 9 tails, and 6 wings of predefined varied shape and/or color (see supplement). Every FunnyBird class consists of a unique combination of these parts. We randomly sample 50 classes out of the 2592 combinations as our dataset. Using these classes, we follow the data-generation process outlined in Fig. 2 by adding class-specific parts to a neutral body model to obtain an instance of a FunnyBird. To reflect real-world challenges, we randomly add background objects and change the illumination and viewpoint. We also explored more photo-realistic simulations with real background images and textured parts. However, with neural models learning to ignore these "distractions", our quantitative analysis was largely unaffected. We thus omit this in pursuit of simplicity. We verified the solvability of our dataset with a human expert who achieved an accuracy of  $97.4\%$  on the proposed test set. To ensure that removing any part does not result in another valid class, each complete FunnyBird instance contains all five parts. To ensure that images with removed parts are not out-of-distribution, we include images with missing parts in the training set. As these images can no longer be associated with one specific class, we use a multi-label classification training scheme where all classes that contain all of the remaining parts are considered valid (with equal probability).
+
+Our data-generation process has several important implications that make it particularly well suited for evaluating and analyzing XAI methods. First, based on the assumption that humans think in concepts rather than pixels, we argue that a concept-based dataset and the resulting evaluations are better aligned with downstream tasks of human comprehension than pixel-based evaluations. Second, we have pixel-accurate annotations of each object and bird part in the scene, which is required for various automatic evaluation
+
+protocols and tailored analyses. Third, having full control over the data-generation process allows applying realistic image-space interventions, such as removing parts, which can be used to estimate ground-truth importance scores.
+
+# 4. Evaluation Protocols
+
+We will now outline how our dataset and its functionalities can be used for the quantitative evaluation and analysis of XAI methods. We first propose a general, multi-dimensional analysis framework, named FunnyBirds framework, that allows to evaluate a wide range of existing XAI methods in a common framework. Second, we propose a more tailored way of analysis where our dataset's capabilities are used to gain deeper insights into specific methods similar to what human studies could do.
+
+# 4.1. The FunnyBirds framework
+
+The multi-dimensional FunnyBirds analysis framework for XAI methods entails six evaluation protocols for three explainability dimensions, i.e., completeness, correctness, and contrastivity. They were chosen for their popularity in related work [38], ability to be automatically measurable, and compatibility with our dataset. Most of our protocols are inspired by well-established evaluation practices and follow accepted assumptions. Our dataset generation process ensures that all conducted interventions can be considered in-domain and semantically meaningful, eliminating common downsides [23, 28] of several existing evaluation protocols that rely on image interventions [10,21,23,27,55].
+
+Meaning of ground truth. Our work relies on interventions to estimate "ground-truth" importance scores for individual parts. This is motivated by (1) the observation that in XAI we aim to approximate the causal structure of the inspected model, and (2) findings that the causal structure can be estimated via interventions [43]. Since the perfect causal structure (which is too complex to be comprehended) is already given by the model itself, we emphasize that a simplified approximation is needed for XAI, instead. We thus assume such an approximation for estimating the ground-truth scores with interventions. For example, in the single deletion protocol (see Sec. 4.1.3), we assume that a hypothetical simplified model processes each part individually, which generally does not need to hold for the real model. This assumption is implicitly also made in existing single deletion protocols [3, 14, 41, 67]. Further, most existing explanation methods, e.g., attribution maps, communicate the importance of each feature individually, thus evaluating explanations beyond individual concepts is not yet sensible.
+
+Interface functions. The diversity of explanation types presents a major challenge to evaluating XAI methods, which prevents a direct comparison of different methods and created a need for various non-standardized evalua-
+
+tions. We thus propose to build our evaluation framework around so-called interface functions that implement more general properties, such as which object parts are important. They can be derived from a variety of explanation types, and thus, used to evaluate distinct explanations in a common framework. This allows us to not only compare a spectrum of existing methods, but also to potentially include future, novel explanation types. Our evaluation framework currently uses the following interface functions:
+
+$\operatorname{PI}(\cdot)$  - The part importance score for each part. For example, the summed attribution within that part.
+
+$\mathrm{P}(\cdot)$  - The parts that are considered to be important, derived from the output of an XAI method. For attribution methods, a part can be considered important if its part importance is at least  $t\%$  of the total attribution.
+
+Note that different explanation types vary in their suitability for differing downstream tasks, and thus, also in their suitability for above interface functions. Furthermore, just as humans differ in interpreting various explanations, there may not be a single correct way of implementing the interface functions (see supplement). Therefore, comparing different explanation types is not absolutely fair and should be done with caution. Nonetheless, we argue that estimating important image regions and their relative importance are fairly basic challenges in XAI, and thus, appropriate downstream tasks, respectively, interface functions.
+
+**Framework.** For a simple comparison and visualization, we design all metrics to be in the range [0, 1], with higher values indicating better scores. For each dimension (as described below), we report a single score comprised of all included protocols (see Tab. 1). Additionally, we report the average of all our explanation quality dimensions, i.e., completeness, correctness, contrastivity, as a single score that summarizes the overall quality of an XAI method for the inspected model. We let  $\mathcal{D}$  denote our dataset of size  $N$ , consisting of images  $x_{n}$  with class label  $c_{n}$ ;  $f$  is the inspected model with  $f(x_{n})$  denoting the predicted class or the logit of the target class, and  $e_{f}(x_{n})$  is the explanation of  $f(x_{n})$  w.r.t. the target class  $c_{n}$ .
+
+# 4.1.1 Accuracy and background independence
+
+Accuracy (A). An overly simple model may be explainable but not solve the task at hand. To detect such cases, our framework reports the standard classification accuracy.
+
+Background independence (BI). Similarly, another trivial solution to achieve high explanation scores is a model that is sensitive to the entire image. An explanation would consequently highlight the entire image. To detect this case, we report the background independence as the ratio of background objects that are unimportant, i.e., that, when removed, cause the target logit to drop less than  $5\%$ .
+
+Table 1. Overview of our evaluation protocols. "Interface function" denotes the required interface function for each protocol.  
+
+<table><tr><td>Dimension</td><td>Protocol</td><td>Interface function</td><td>Description</td></tr><tr><td>-</td><td>A</td><td>-</td><td>Percentage of correct predictions over the test dataset</td></tr><tr><td>-</td><td>BI</td><td>-</td><td>The model should not be sensitive to the background objects</td></tr><tr><td>Completeness</td><td>CSDC</td><td>P</td><td>Explanation should highlight all relevant parts</td></tr><tr><td>Completeness</td><td>PC</td><td>P</td><td>Preserving parts identified as important should result in the same prediction</td></tr><tr><td>Completeness</td><td>DC</td><td>P</td><td>Removing parts identified as important should result in a different prediction</td></tr><tr><td>(Over-)Completeness</td><td>D</td><td>P</td><td>Explanation should not highlight irrelevant parts</td></tr><tr><td>Correctness</td><td>SD</td><td>PI</td><td>Estimated importance of each part should be correlated to actual importance</td></tr><tr><td>Contrastivity</td><td>TS</td><td>PI</td><td>Explanations for different classes should highlight class-specific parts</td></tr></table>
+
+# 4.1.2 Completeness
+
+Controlled synthetic data check (CSDC). Our transparent data generation process allows us to know the subsets of parts  $\{\mathcal{P}_{c_n,i}'\mid i = 1,\ldots \}$  that are sufficient to correctly categorize an image of class  $c_{n}$  containing parts  $\mathcal{P}_{c_n}$ . A model that accurately captures the essence of our dataset, i.e., has an accuracy close to 1.0, must thus consider at least one of these sets  $\mathcal{P}_{c_n,i}'$  [13, 34, 38, 50]. To ensure that this assumption holds and CSDC is faithful w.r.t. the model, we exclude misclassified samples from this protocol. We measure the CSDC completeness of an explanation as the set overlap between the parts that are estimated to be important by the explanation (i.e.,  $\mathrm{P}(e_f(x_n))$  where  $\mathrm{P}(\cdot)$  is the interface function giving the important parts) and the sufficient part set that has the largest overlap with  $\mathrm{P}(e_f(x_n))$ , normalized by the size of the sufficient part set:
+
+$$
+\mathrm {C S D C} = \frac {1}{N} \sum_ {n = 1} ^ {N} \max  _ {i} \frac {\left| \mathrm {P} \left(e _ {f} \left(x _ {n}\right)\right) \cap \mathcal {P} ^ {\prime} _ {c _ {n} , i} \right|}{\left| \mathcal {P} ^ {\prime} _ {c _ {n} , i} \right|}. \tag {1}
+$$
+
+Preservation check (PC). If an explanation is complete, preserving only the parts of the input that are estimated to be important by the explanation should still result in the same classification output [13,16,38]. To verify this, we first pass the original image through the inspected model to obtain the classification and the corresponding explanation. Afterward, we delete all parts of the image that are estimated to not be important by the explanation, i.e., the inverse of  $\mathrm{P}(\cdot)$ , and measure how often the class prediction remains unchanged. We define our PC score as
+
+$$
+\mathrm {P C} = \frac {1}{N} \sum_ {n = 1} ^ {N} \left[ f \left(x _ {n} ^ {\prime}\right) = f \left(x _ {n}\right) \right], \tag {2}
+$$
+
+with  $[\cdot]$  denoting the Iverson bracket [32] and  $x_{n}^{\prime}$  denoting the image arising by removing all bird parts but  $\mathrm{P}(e_f(x_n))$  from  $x_{n}$ . I.e., the parts estimated to be important remain.
+
+Deletion check (DC). Similarly, if an explanation is complete, deleting all the parts of the input that are estimated to be important by the explanation should result in a different
+
+classification output [16,38,45]. Thus, the deletion check is the inverse of PC and defined as
+
+$$
+\mathrm {D C} = \frac {1}{N} \sum_ {n = 1} ^ {N} [ f (x _ {n} ^ {\prime \prime}) \neq f (x _ {n}) ], \tag {3}
+$$
+
+with  $x_{n}^{\prime \prime}$  denoting the image arising by removing the estimated important parts  $\mathrm{P}(e_f(x_n))$  from  $x_{n}$ .
+
+Distractibility (D). As over-complete explanations would achieve high completeness scores, we argue that completeness should be considered together with a metric that counters over-completeness (similar to precision and recall). To this end, we introduce a novel over-completeness score that measures how many actually unimportant input parts are also estimated to be unimportant by the explanation. In detail, we successively remove each background object and bird part from the input and consider it to be unimportant if the logit target output drops less than  $5\%$  compared to the output for the original image. Next, we measure the overlap between parts  $\mathrm{P}(e_f(x_n))$  estimated to be important by the explanation and parts  $\mathcal{P}_{f(x_n)}^{\prime \prime}$  that are actually unimportant, normalized by the number of unimportant parts. As the overlap should be small for good evaluations, we subtract the result from 1:
+
+$$
+\mathrm {D} = 1 - \frac {1}{N} \sum_ {n = 1} ^ {N} \frac {\left| \mathrm {P} \left(e _ {f} \left(x _ {n}\right)\right) \cap \mathcal {P} _ {f \left(x _ {n}\right)} ^ {\prime \prime} \right|}{\left| \mathcal {P} _ {f \left(x _ {n}\right)} ^ {\prime \prime} \right|}. \tag {4}
+$$
+
+The final completeness score (Com.) is computed as the mean of the averaged three completeness metrics (CSDC, PC, and DC), and the over-completeness D. By having complementing metrics, we can also automatically estimate the threshold  $t$  of  $\mathrm{P}(\cdot)$ , such that  $t$  optimally trades off the completeness and over-completeness metrics.
+
+# 4.1.3 Correctness
+
+Single deletion (SD). In the single deletion protocol, we measure the rank correlation between the explanation's importance score of each part and the actual amount that the model's logit of the target class changes when removing that
+
+part [3, 14, 38]. Specifically, we define SD as
+
+$$
+\mathrm {S D} = \frac {1}{2} + \frac {1}{2 N} \sum_ {n = 1} ^ {N} \rho \left(\mathrm {P I} \left(e _ {f} \left(x _ {n}\right)\right), f \left(x _ {n}\right) - \left\{f \left(x _ {n} ^ {\prime \prime \prime}\right) \right\}\right), \tag {5}
+$$
+
+with  $\rho$  denoting the Spearman rank-order correlation coefficient,  $\mathrm{PI}(\cdot)$  the part importance interface function, and  $\{f(x_n^{\prime \prime \prime})\}$  the target scores of the images obtained by removing any individual bird part from  $x_{n}$ .
+
+# 4.1.4 Contrastivity
+
+Target sensitivity (TS). If an explanation is sensitive to a target class, it should highlight image regions that are relevant for the respective target [8, 9, 38]. To measure target sensitivity, we take an input sample and select two classes  $\hat{c}_1$  and  $\hat{c}_2$  that each have exactly two non-overlapping common parts with the actual class of input sample  $x_n$ . We choose two parts because this is the floor of half the 5 bird parts available in each image. Afterward, we compute the explanations  $e_f(x_n, \hat{c}_i)$  with respect to  $\hat{c}_1$  and  $\hat{c}_2$  and evaluate if they correctly highlight the parts belonging to each respective class:
+
+$$
+\begin{array}{l} \mathrm {T S} = \frac {1}{2 N} \sum_ {n = 1} ^ {N} \left[ \mathrm {P I} ^ {\prime} \left(e _ {f} \left(x _ {n}, \hat {c} _ {1}\right)\right) > \mathrm {P I} ^ {\prime} \left(e _ {f} \left(x _ {n}, \hat {c} _ {2}\right)\right) \right] \tag {6} \\ + \left[ \mathrm {P I} ^ {\prime \prime} (e _ {f} (x _ {n}, \hat {c} _ {1})) <   \mathrm {P I} ^ {\prime \prime} (e _ {f} (x _ {n}, \hat {c} _ {2})) \right], \\ \end{array}
+$$
+
+with  $\mathrm{PI}'(\cdot)$  and  $\mathrm{PI}''(\cdot)$  denoting the summed part importances of the two parts belonging to class  $\hat{c}_1$ , respectively  $\hat{c}_2$ . To ensure that our protocol is faithful w.r.t. the model, we only consider images where removing parts belonging to  $\hat{c}_1$  causes a larger model output drop for  $\hat{c}_1$  than removing parts belonging to  $\hat{c}_2$ , and vice versa.
+
+# 4.2. The FunnyBirds custom analysis
+
+As it is almost impossible to analyze all aspects of an explanation with a single framework, we also show how full control over our dataset enables more tailored and systematic custom evaluations. Similar to recent human studies [31], we evaluate the coherence of the assessed methods, i.e., how reasonable an explanation is for a human. To the best of our knowledge, this is one of the first methods for evaluating coherence in a fully automatic and systematic manner. We give two illustrative examples for implementing such an evaluation, but other instantiations are possible.
+
+ProtoPNet. ProtoPNet [12] promotes explainability by communicating which patches of the training data, called prototypes, look similar to patches in a test image. However, this only increases interpretability if the detected similarities are compatible with human notions of similarity. To quantitatively verify this in an automatic fashion, we test if relevant part types (e.g., beak or wing) in the detected patch
+
+of the test image are also contained in the corresponding prototype identified by ProtoPNet. This assumes that different part types, i.e., beak and wings, do not look similar to most humans, and therefore, are not helpful similarities for explainability. While debatable for real images, we argue that this is a reasonable assumption for our dataset.
+
+Counterfactual visual explanations. The objective of counterfactual visual explanations (CVE) [22] is to highlight image regions that discriminate the class  $c$  of a query image from the class  $c'$  of a distractor image. To this end, CVE extracts convolutional neural network (CNN) feature maps from the query and distractor images to then perform feature swaps between the two feature maps that, when fed to the CNN classifier, lead to the strongest class change (from  $c$  to  $c'$ ). The corresponding image locations of the feature swaps are then highlighted to yield the CVE. We argue that this kind of explanation is only meaningful for humans if the swaps are semantically correct, i.e., when a beak is swapped with another beak but not a foot. Using our proposed dataset, we conduct a systematic study and measure the average number of swaps that do not touch the same bird part in both images, and thus, can be considered semantically incorrect. We evaluate four different setups of increasing difficulty where we only use aligned, respectively unaligned, viewpoint pairs with classes that are different in only one, respectively multiple parts.
+
+Limitations. As with controlled laboratory research [5], our dataset does not reflect all real-world challenges, and thus, is not fully representative of natural images. However, we argue that, as long as XAI methods are challenged to truthfully explain models trained even on our controlled dataset, our proposed method is a valuable tool to faithfully assess the quality of XAI methods. Nonetheless, for future XAI methods we suggest a two-stream evaluation that utilizes our proposed framework and custom analysis for theoretically grounded assessments of the explanation quality in addition to benchmarks that work on natural image data, e.g., Quantus [25]. Further, while the dimensions of explainability evaluated in our work can be considered relevant for many applications, there are dimensions that we omit here (see supplement). However, our framework can easily be extended with additional protocols if needed.
+
+# 5. Results and Interpretation
+
+# 5.1. FunnyBirds framework
+
+Results for our multi-dimensional FunnyBirds framework across a broad variety of different XAI methods and three different backbones are given in Fig. 3. For detailed results of each individual evaluation protocol, please refer to the supplement. We plot qualitative explanations for a random image and give the evaluation scores from Sec. 4.1 averaged over the entire test set. From this, we can make
+
+![](images/c37c580e5a52219cb16254b659eddc9cc259eef283fee92a23fede8b2ac30adc.jpg)  
+Figure 3. FunnyBirds evaluation results. Qualitative and quantitative results for our FunnyBirds framework for the XAI methods Input  $\times$  Gradient (IxG) [56], (absolute) Integrated Gradients (IG (abs.)) [59], Grad-CAM [11,53], RISE [44], LIME [47], Rollout [1], Chefer LRP [11],  $\mathcal{X}$ -DNN [27], BagNet [6], ProtoPNet [12], and B-cos network [9]. Model-agnostic methods are evaluated on VGG16 [58], ResNet-50 [24], and ViT-B/16 [17]. Other models use a ResNet-50 backbone, if applicable. Quantitative results are averaged over the entire test set; qualitative results are shown for a representative example. Chart colors indicate different explanation types that should only be compared with caution. The center score denotes the mean of the completeness (Com.), correctness (Cor.), and contrastivity (Con.) dimensions. Additionally, we report the accuracy (Acc.) and background independence (B.I.). See Sec. 4.1 for details.
+
+several interesting findings and derive various hypotheses:
+
+(1) Overall, BagNet [6] achieves the highest explainability score, which could be due to its internal model structure that is better aligned with the explanatory power of an attribution map, i.e., pixels are processed more independently.  
+(2) On average, Integrated Gradients (IG) [59] performs best among model-agnostic methods for different backbones, which is in line with the literature when considering gradient-based approaches [56, 59]. However, LIME [47] and IG achieve similar completeness, with LIME lacking the ability to communicate meaningful importance scores, which impairs practicability for certain downstream tasks. Interestingly, taking the absolute value of IG impairs the mean explanation score slightly, contradicting findings that have been made on pixel-level protocols [62]. Specifically, it slightly increases completeness while reducing contrastivity. We hypothesize that the negative gradient infor
+
+mation is therefore particularly important in identifying regions that do not belong to the class of interest. Removing the bias term (X-DNN [27] vs. ResNet-50 [24] w/ IG) slightly improves completeness and correctness while reducing contrastivity.
+
+(3) Explanation scores for model-agnostic XAI methods are consistently better for VGG16 [58] than for ResNet-50 [24], indicating that different backbones vary in their explainability. We also observe that the relative ordering of different XAI methods changes across different backbones (e.g., RISE [44] and IxG [56]), showing the importance of evaluating future XAI methods on different backbones.  
+(4) IxG [56] and Grad-CAM [11, 53] seem to work better on CNN-based architectures [24, 58]. Methods developed for vision transformers, i.e., Rollout [1] and Chefer LRP [11], provide strong explanations, with Chefer LRP achieving the second highest explanation score. Rollout
+
+![](images/e38c18671d0e54d7e71d354584e5a48712d30e4da974888ce4cfc51192f82052.jpg)  
+Figure 4. Qualitative results of ProtoPNet [12]. Many of the test image patches (center) highlight the entire bird or just background. Further, prototypes (sides) often do not include important parts.
+
+cannot compute class-specific explanations, which could be disadvantageous in certain downstream tasks.
+
+(5) Coarser methods like Grad-CAM [53] and RISE [44] tend to be more incomplete, which could be an artifact of poor localization [46] and our parts being fairly small.  
+(6) The B-cos network [9] outperforms competing methods on the same backbone, showing an improved explainability, which is in line with results from [9]. Surprisingly, we see a slight decrease in background independence.  
+(7) ProtoPNet [12] has poor correctness and contrastivity, which can be explained by related findings in that ProtoPNet similarities are not semantically reasonable [31] and by its poor localization (see Sec. 5.2 and Fig. 4).  
+(8) Especially correctness is a weakness of all examined methods, showing that, while existing approaches tend to accurately identify important areas, they lack the ability to reliably communicate the relative importance of each input area, or that the simple explanation of an attribution map might be too strong of a simplification of the actual model.
+
+Finally, since XAI evaluation is multi-faceted and downstream task dependent, we doubt that a single score can be enough to properly compare methods. Hence, our work is less about ranking but more about automatically revealing the strengths and weaknesses of existing and future XAI methods in a systematic and theoretically grounded manner.
+
+# 5.2.Custom evaluations
+
+ProtoPNet. To quantitatively evaluate if prototypes used in [12] promote explainability (see Sec. 4.2), we conduct several sanity checks. First, we measure that out of 1000 examined ProtoPNet patches in the test image, only 510 touch the same part in the corresponding prototype patch, and thus, have a similarity that could be aligned with human notions of similarity. Further, we measure that  $26.3\%$  of the extracted test image patches do not touch a single bird part, indicating a poor localization of the explanation. Finally,  $18.5\%$  of the test image patches entail 4 or 5 different bird parts, which shows that the extracted patches are not local but global, and thus, do not promote the interpretability of the examined model. Qualitative results showing the described issues can be seen in Fig. 4. To summarize, many of the communicated prototypes of ProtoPNet [12] trained on our dataset are unlikely to be meaningful for humans. While a similar conclusion was drawn in a recent human
+
+![](images/ffe8454a8cad1bbea0ab1f3342e2f7690df8897ef6dca6fdbcebb649fc913720.jpg)  
+Figure 5. Qualitative results of counterfactual visual explanations (CVE) [22]. (left) CVE for an aligned image pair with one part being different. (right) CVE for an unaligned image pair with multiple parts being different. Note how many of the proposed swaps are unrealistic, and therefore, of little quality (e.g., the purple patch around the right eye is swapped with the neck of the other bird).
+
+study [31] confirming our findings, our proposed tools allow the same conclusion in a fully automatic manner.
+
+Counterfactual visual explanations. To quantify if CVE [22] highlights meaningful swaps (see Sec. 4.2), we measure how many of the extracted swaps do not touch the same bird parts in the two images. When considering images that have the same viewpoint and differ only by one part (Fig. 5 - left), CVE with VGG16 [58] produces on average 1.65 swaps that do not touch the same part, and therefore, are semantically meaningless. When changing the viewpoint, CVE produces on average 1.3 swaps that do not touch the same part. When working with aligned viewpoints and birds that differ by multiple parts (4.07 parts on average), 2.75 such swaps are produced and 2.62 when also changing the viewpoint (Fig. 5 - right). Interestingly, the number of different parts has a stronger impact on the absolute number of unreasonable swaps, i.e., swaps that do not touch the same part in both images, than the viewpoint. Further, we observe that even in our controlled environment, CVE produces on average  $\sim 3$  unreasonable swaps for images with on average only 4 different parts, indicating that many of the proposed swaps are semantically incorrect, and thus, do not promote coherent explanations.
+
+# 6. Conclusion
+
+In this work, we propose a novel approach to automatically analyzing XAI methods using a synthetic classification dataset that allows for full annotation and part interventions. Using this dataset, we propose an accompanying multi-dimensional analysis framework that faithfully assesses various important aspects of explainability and generalizes to different explanation types by using interface functions. With this easy-to-use tool, we analyzed 24 different setups to uncover various new insights and confirm findings from related work. This shows that, despite the synthetic setting, our findings appear to translate well to real data, and that our proposed tool is a practical and valuable asset for the analysis of future XAI methods. Finally, we showed how to develop tailored analyses to gain a better understanding of two specific XAI methods and discovered their weaknesses in an automatic and quantitative manner.
+
+Acknowledgements. We thank Bernt Schiele, Moritz Böhle, and Sukrut Rao for their valuable feedback and helpful discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 866008). The project has also been supported in part by the State of Hesse through the cluster projects "The Third Wave of Artificial Intelligence (3AI)" and "The Adaptive Mind (TAM)".
+
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+                                    "content": "The field of explainable artificial intelligence (XAI) aims to uncover the inner workings of complex deep neural models. While being crucial for safety-critical domains, XAI inherently lacks ground-truth explanations, making its automatic evaluation an unsolved problem. We address this challenge by proposing a novel synthetic vision dataset, named FunnyBirds, and accompanying automatic evaluation protocols. Our dataset allows performing semantically meaningful image interventions, e.g., removing individual object parts, which has three important implications. First, it enables analyzing explanations on a part level, which is closer to human comprehension than existing methods that evaluate on a pixel level. Second, by comparing the model output for inputs with removed parts, we can estimate ground-truth part importances that should be reflected in the explanations. Third, by mapping individual explanations into a common space of part importances, we can analyze a variety of different explanation types in a single common framework. Using our tools, we report results for 24 different combinations of neural models and XAI methods, demonstrating the strengths and weaknesses of the assessed methods in a fully automatic and systematic manner."
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+                                    "content": "1. Introduction"
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+                                    "content": "Even though deep learning models have achieved breakthrough results in computer vision, their inner workings remain largely opaque. As a result, deep networks sometimes receive only limited user trust and cannot be applied blindly in safety-critical domains. To overcome this issue, a growing interest in the field of explainable artificial intelligence (XAI) has emerged, attempting to explain the inner workings of deep neural models in a human-comprehensible way. However, since there are generally no ground-truth explanations, evaluating XAI methods remains an open chal"
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+                                            "type": "text",
+                                            "content": "Figure 1. Schematic illustration of our proposed dataset and analysis framework. For each input image, we render the corresponding part annotation and part interventions (e.g., removed beak). The interventions are used to estimate ground-truth importance scores of each input part, which are then compared to the estimated part importances from the explanation method under inspection (here [44]). We evaluate multiple dimensions of explainability to draw a more conclusive picture. Please refer to Sec. 4.1 for details."
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+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "lenge. In fact, a third of XAI papers lack sound quantitative evaluation [38], while other work has limited comparability [31] or problematic evaluation protocols [23, 38]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "To overcome the issue of missing ground-truth explanations, automatic evaluations are often done via proxy tasks that adhere to the idea of performing image interventions by removing certain input features to then measure the resulting impact on the model output [21, 23, 55]. As image interventions are non-trivial to perform on existing vision datasets, they are usually applied on a pixel level, e.g., masking out single pixels [21, 23, 27, 52, 55]. However, this and related approaches share several downsides. First, performing interventions, as well as evaluating explanations on a pixel level, is disconnected from the downstream task of providing human-understandable explanations since humans perceive images in concepts rather than pixels. Second, existing automatic evaluation protocols are developed for specific explanation types, e.g., pixel-level attribution maps, and thus, cannot be extended to other explanation"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "Dataset and code available at github.com/visinf/funnybirds/."
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+                                    "content": "types like prototypes [12]. Third, by performing unrealistic interventions in image space, e.g., masking out pixels, they introduce domain shifts compared to the training distribution [10, 23, 28], which can cause the model to behave unexpectedly, and thus negatively affects the evaluation."
+                                }
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+                                    "type": "text",
+                                    "content": "In this work, we address the above and more challenges to contribute an important step toward a more rigorous quantitative evaluation of XAI methods by proposing a thorough, dedicated evaluation/analysis tool. We do so by building a fully controllable, synthetic classification dataset consisting of renderings of artificial bird species. This approach to analyzing XAI methods is analogous to controlled laboratory research, where we have full control over all variables, eliminating the potential influence of irrelevant factors, and therefore, providing clearer evidence of the observed behavior [5]. Our proposed dataset allows us to make the following main contributions: (1) We cover a wide range of dimensions of explainability by considering a collection of different evaluation protocols. (2) We allow to automatically compare various explanation types in a shared framework. (3) We avoid the out-of-domain issue of previous image-space interventions by introducing semantically meaningful interventions at training time. (4) We reduce the gap between the downstream task of human comprehension and XAI evaluation by proposing metrics that operate at a semantically meaningful part level rather than the semantically less meaningful pixel level. (5) We automatically analyze the coherence of explanations. (6) We analyze 24 different combinations of existing XAI methods and neural models, highlighting their strengths and weaknesses as well as identifying new insights that may be of general interest to the XAI community."
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+                                    "content": "2. Related Work"
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+                                    "content": "XAI methods. In this work, we focus on image classification explanations for the outcome of one particular input using deep neural networks (DNNs). Perturbation-based explanation methods [1, 11, 33, 44, 47, 63, 68, 69] estimate the impact of pixels/regions by measuring the output change occurring when repeatably perturbing inputs or neurons. Backpropagation-based explanation methods [4, 20, 27, 53, 55, 57, 59] use importance signals, e.g., gradient information, to estimate the importance of each input feature. Both types of methods generate post-hoc explanations for already trained networks. On the other hand, intrinsically explainable models [3, 6, 8, 9, 12, 39] consider explainability already in the design process of the model itself. For example, B-cos networks [9] enforce weight-input alignment to highlight the most important input regions. ProtoPNet [12] computes the feature similarity between test image patches and prototypes to help explain why a decision was made based on this patch looking like that prototype. BagNets [6] use a linear classifier on top"
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+                                    "type": "text",
+                                    "content": "of each feature extracted from small image patches to highlight task-important regions. "
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+                                    "content": " -DNNs [27] remove the bias term in ReLU networks to allow for an efficiently computable closed-form solution of Integrated Gradients [59]."
+                                }
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+                                    "content": "Evaluating XAI methods. A sound evaluation of XAI methods is essential to compare different approaches and unveil their strengths and weaknesses. Nauta et al. [38] argue that explainability is a multi-faceted concept and propose various properties that describe different aspects of explanation quality. Below, we outline existing evaluation protocols for three of these dimensions that have received particularly much attention in related work and that allow for a well-defined automatic evaluation:"
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+                                    "content": "Correctness denotes the faithfulness of an explanation w.r.t. the model [38]. A common way to measure the correctness of attribution methods is the Incremental Deletion protocol [8, 10, 21, 23, 27, 28, 38, 52, 55, 60], where input pixels are incrementally removed in the order of their relative importance to measure the impact on the output. Similarly, in the Single Deletion protocol [3, 14, 38, 41, 67], individual (input) features are deleted to compute the correlation between feature importance and the actual output change. A drawback of the above protocols is the domain shift occurring when introducing image interventions, which can cause undesirable model behavior influencing the metrics [10, 23, 28]. To reduce this, masked pixels can be inpainted with a generative model [10] or text classification datasets can be augmented with training inputs that have similar alterations as the evaluation protocol [23]. However, none of these approaches achieve an exact alignment of the train and test domain as we do in this work."
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+                                    "type": "text",
+                                    "content": "Completeness measures the degree to which an explanation describes all aspects of the model's decision [38]. In the Preservation/Deletion Check protocols [10, 13, 16, 38, 45], important features are preserved/deleted to test if the output prediction stays the same/changes. However, as above, these protocols introduce unrealistic domain changes. In the Controlled Synthetic Data Check protocol [2, 13, 30, 34, 38, 50], a synthetic dataset is used to evaluate if the explanation of a model with almost perfect accuracy aligns with the dataset generation process. While closely related to our work, existing synthetic datasets for evaluating XAI methods are very small-scale, only evaluate a single dimension of explainability, and do not allow for diverse image-space interventions that are crucial for evaluating correctness."
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+                                            "content": "Figure 2. Generation process of our synthetic dataset. (a) The scene is initialized with a neutral bird body part. (b) Class-specific parts are added. (c) To reflect real-world challenges, random backgrounds, illumination, and viewpoint changes are added/applied."
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+                                    "type": "text",
+                                    "content": "fication datasets, or they can also introduce out-of-domain issues when arranging images in a grid as in [8,9,46]."
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+                                    "content": "Human studies. Besides above automatic evaluations, there have been efforts to assess the quality of XAI methods with human subjects [15, 40, 51, 54]. Human studies nicely reflect the actual downstream tasks of explanations, i.e., helping humans to understand models, and they can be applied to explanations that go beyond simple heat maps [31]. Downsides of user studies include larger cost and human biases [36]. Further, humans are not capable of directly evaluating if explanations are correct w.r.t. a complex, deep model. With our custom analysis, we aim to reduce the gap between the automatic evaluation and human studies while addressing the described drawbacks of human assessment."
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+                                    "content": "Synthetic datasets. Synthetic datasets have an important and long history in many other disciplines of computer vision [7,18,29,42,48]. Richter et al. [48] utilize a video game to create a large-scale segmentation dataset. The \"Flying Chairs\" dataset [18] and MPI Sintel [7] are popular synthetic datasets used for the training and evaluation of optical flow methods. CLEVR [29] was introduced to test different visual reasoning abilities. All these works advanced their specific sub-fields, showing that synthetic datasets are a valuable tool, even in the absence of full realism."
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+                                    "content": "3. The FunnyBirds Dataset"
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+                                    "content": "We propose a synthetic vision dataset that is developed to automatically and quantitatively analyze XAI methods. To this end, we made a multitude of carefully considered design choices, which we summarize in the following."
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+                                    "content": "Since XAI methods in computer vision have been developed mainly in the context of classification to date [38], we focus on classification and propose a fine-grained bird species dataset inspired by the CUB-200-2011 dataset [61] commonly used by XAI methods [12, 22, 26, 39, 66]. Our dataset consists of 50500 images (50k train, 500 test) of 50 synthetic bird species. We found 500 test images to be sufficient to produce stable results while allowing efficient evaluations with limited hardware (see supplement)."
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+                                    "content": "One particularly important desideratum behind our de"
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+                                    "content": "sign process is the notion of concepts that we define as mental representations of psychological entities that are crucial to categorization [35, 37, 49, 64]. For instance, humans might categorize a bird as a flamingo when observing the concepts curved beak and pink wings. Similarly, they would communicate their reasoning process in terms of concepts [49]. Hence, we argue that concepts are essential in the context of XAI for humans, and thus, we design our dataset with a particular emphasis on the notion of concepts. To derive a precise level of granularity for the concepts in our dataset, we enforce them to be as granular as possible, while corresponding to an existing individual word, and being attached to the bird's body. This avoids \"unrealistic\" scenarios where the removal of one concept leaves another concept unattached (the body of the bird is never removed) and eliminates overly fine-grained concepts. Following these rules, our FunnyBirds consist of the five human comprehensible concepts beak, wings, feet, eyes, and tail, to which we will refer as parts in the following."
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+                                    "content": "We manually design 4 beaks, 3 eyes, 4 feet, 9 tails, and 6 wings of predefined varied shape and/or color (see supplement). Every FunnyBird class consists of a unique combination of these parts. We randomly sample 50 classes out of the 2592 combinations as our dataset. Using these classes, we follow the data-generation process outlined in Fig. 2 by adding class-specific parts to a neutral body model to obtain an instance of a FunnyBird. To reflect real-world challenges, we randomly add background objects and change the illumination and viewpoint. We also explored more photo-realistic simulations with real background images and textured parts. However, with neural models learning to ignore these \"distractions\", our quantitative analysis was largely unaffected. We thus omit this in pursuit of simplicity. We verified the solvability of our dataset with a human expert who achieved an accuracy of "
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+                                    "content": " on the proposed test set. To ensure that removing any part does not result in another valid class, each complete FunnyBird instance contains all five parts. To ensure that images with removed parts are not out-of-distribution, we include images with missing parts in the training set. As these images can no longer be associated with one specific class, we use a multi-label classification training scheme where all classes that contain all of the remaining parts are considered valid (with equal probability)."
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+                                    "content": "Our data-generation process has several important implications that make it particularly well suited for evaluating and analyzing XAI methods. First, based on the assumption that humans think in concepts rather than pixels, we argue that a concept-based dataset and the resulting evaluations are better aligned with downstream tasks of human comprehension than pixel-based evaluations. Second, we have pixel-accurate annotations of each object and bird part in the scene, which is required for various automatic evaluation"
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+                                    "content": "protocols and tailored analyses. Third, having full control over the data-generation process allows applying realistic image-space interventions, such as removing parts, which can be used to estimate ground-truth importance scores."
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+                                    "content": "We will now outline how our dataset and its functionalities can be used for the quantitative evaluation and analysis of XAI methods. We first propose a general, multi-dimensional analysis framework, named FunnyBirds framework, that allows to evaluate a wide range of existing XAI methods in a common framework. Second, we propose a more tailored way of analysis where our dataset's capabilities are used to gain deeper insights into specific methods similar to what human studies could do."
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+                                    "content": "The multi-dimensional FunnyBirds analysis framework for XAI methods entails six evaluation protocols for three explainability dimensions, i.e., completeness, correctness, and contrastivity. They were chosen for their popularity in related work [38], ability to be automatically measurable, and compatibility with our dataset. Most of our protocols are inspired by well-established evaluation practices and follow accepted assumptions. Our dataset generation process ensures that all conducted interventions can be considered in-domain and semantically meaningful, eliminating common downsides [23, 28] of several existing evaluation protocols that rely on image interventions [10,21,23,27,55]."
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+                                    "type": "text",
+                                    "content": "Meaning of ground truth. Our work relies on interventions to estimate \"ground-truth\" importance scores for individual parts. This is motivated by (1) the observation that in XAI we aim to approximate the causal structure of the inspected model, and (2) findings that the causal structure can be estimated via interventions [43]. Since the perfect causal structure (which is too complex to be comprehended) is already given by the model itself, we emphasize that a simplified approximation is needed for XAI, instead. We thus assume such an approximation for estimating the ground-truth scores with interventions. For example, in the single deletion protocol (see Sec. 4.1.3), we assume that a hypothetical simplified model processes each part individually, which generally does not need to hold for the real model. This assumption is implicitly also made in existing single deletion protocols [3, 14, 41, 67]. Further, most existing explanation methods, e.g., attribution maps, communicate the importance of each feature individually, thus evaluating explanations beyond individual concepts is not yet sensible."
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+                                    "content": "Interface functions. The diversity of explanation types presents a major challenge to evaluating XAI methods, which prevents a direct comparison of different methods and created a need for various non-standardized evalua-"
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+                                    "content": "tions. We thus propose to build our evaluation framework around so-called interface functions that implement more general properties, such as which object parts are important. They can be derived from a variety of explanation types, and thus, used to evaluate distinct explanations in a common framework. This allows us to not only compare a spectrum of existing methods, but also to potentially include future, novel explanation types. Our evaluation framework currently uses the following interface functions:"
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+                                    "content": " - The part importance score for each part. For example, the summed attribution within that part."
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+                                    "content": " - The parts that are considered to be important, derived from the output of an XAI method. For attribution methods, a part can be considered important if its part importance is at least "
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+                                    "type": "text",
+                                    "content": " of the total attribution."
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+                                    "content": "Note that different explanation types vary in their suitability for differing downstream tasks, and thus, also in their suitability for above interface functions. Furthermore, just as humans differ in interpreting various explanations, there may not be a single correct way of implementing the interface functions (see supplement). Therefore, comparing different explanation types is not absolutely fair and should be done with caution. Nonetheless, we argue that estimating important image regions and their relative importance are fairly basic challenges in XAI, and thus, appropriate downstream tasks, respectively, interface functions."
+                                }
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+                                    "content": "**Framework.** For a simple comparison and visualization, we design all metrics to be in the range [0, 1], with higher values indicating better scores. For each dimension (as described below), we report a single score comprised of all included protocols (see Tab. 1). Additionally, we report the average of all our explanation quality dimensions, i.e., completeness, correctness, contrastivity, as a single score that summarizes the overall quality of an XAI method for the inspected model. We let "
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+                                    "type": "text",
+                                    "content": " denote our dataset of size "
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+                                    "content": ", consisting of images "
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+                                    "content": " with class label "
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+                                    "content": " is the inspected model with "
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+                                    "type": "text",
+                                    "content": " denoting the predicted class or the logit of the target class, and "
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+                                    "type": "text",
+                                    "content": " is the explanation of "
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+                                    "type": "text",
+                                    "content": " w.r.t. the target class "
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+                                    "type": "text",
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+                                    "content": "4.1.1 Accuracy and background independence"
+                                }
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+                                    "content": "Accuracy (A). An overly simple model may be explainable but not solve the task at hand. To detect such cases, our framework reports the standard classification accuracy."
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+                                    "type": "text",
+                                    "content": "Background independence (BI). Similarly, another trivial solution to achieve high explanation scores is a model that is sensitive to the entire image. An explanation would consequently highlight the entire image. To detect this case, we report the background independence as the ratio of background objects that are unimportant, i.e., that, when removed, cause the target logit to drop less than "
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+                                            "type": "text",
+                                            "content": "Table 1. Overview of our evaluation protocols. \"Interface function\" denotes the required interface function for each protocol."
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+                                            "html": "<table><tr><td>Dimension</td><td>Protocol</td><td>Interface function</td><td>Description</td></tr><tr><td>-</td><td>A</td><td>-</td><td>Percentage of correct predictions over the test dataset</td></tr><tr><td>-</td><td>BI</td><td>-</td><td>The model should not be sensitive to the background objects</td></tr><tr><td>Completeness</td><td>CSDC</td><td>P</td><td>Explanation should highlight all relevant parts</td></tr><tr><td>Completeness</td><td>PC</td><td>P</td><td>Preserving parts identified as important should result in the same prediction</td></tr><tr><td>Completeness</td><td>DC</td><td>P</td><td>Removing parts identified as important should result in a different prediction</td></tr><tr><td>(Over-)Completeness</td><td>D</td><td>P</td><td>Explanation should not highlight irrelevant parts</td></tr><tr><td>Correctness</td><td>SD</td><td>PI</td><td>Estimated importance of each part should be correlated to actual importance</td></tr><tr><td>Contrastivity</td><td>TS</td><td>PI</td><td>Explanations for different classes should highlight class-specific parts</td></tr></table>",
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+                                    "content": "4.1.2 Completeness"
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+                                    "content": "Controlled synthetic data check (CSDC). Our transparent data generation process allows us to know the subsets of parts "
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+                                    "content": "\\{\\mathcal{P}_{c_n,i}'\\mid i = 1,\\ldots \\}"
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+                                    "type": "text",
+                                    "content": " that are sufficient to correctly categorize an image of class "
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+                                    "content": " containing parts "
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+                                    "type": "text",
+                                    "content": ". A model that accurately captures the essence of our dataset, i.e., has an accuracy close to 1.0, must thus consider at least one of these sets "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{c_n,i}'"
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+                                    "type": "text",
+                                    "content": " [13, 34, 38, 50]. To ensure that this assumption holds and CSDC is faithful w.r.t. the model, we exclude misclassified samples from this protocol. We measure the CSDC completeness of an explanation as the set overlap between the parts that are estimated to be important by the explanation (i.e., "
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+                                    "type": "text",
+                                    "content": " where "
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+                                    "content": " is the interface function giving the important parts) and the sufficient part set that has the largest overlap with "
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+                                    "content": ", normalized by the size of the sufficient part set:"
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+                                    "content": "\\mathrm {C S D C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\max  _ {i} \\frac {\\left| \\mathrm {P} \\left(e _ {f} \\left(x _ {n}\\right)\\right) \\cap \\mathcal {P} ^ {\\prime} _ {c _ {n} , i} \\right|}{\\left| \\mathcal {P} ^ {\\prime} _ {c _ {n} , i} \\right|}. \\tag {1}",
+                                    "image_path": "e43885ef4448656eb9ca1c9cf5546215f7849345a1e5f5b2384ae7e0c5e91bc9.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Preservation check (PC). If an explanation is complete, preserving only the parts of the input that are estimated to be important by the explanation should still result in the same classification output [13,16,38]. To verify this, we first pass the original image through the inspected model to obtain the classification and the corresponding explanation. Afterward, we delete all parts of the image that are estimated to not be important by the explanation, i.e., the inverse of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{P}(\\cdot)"
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and measure how often the class prediction remains unchanged. We define our PC score as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {P C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left[ f \\left(x _ {n} ^ {\\prime}\\right) = f \\left(x _ {n}\\right) \\right], \\tag {2}",
+                                    "image_path": "733c26bc9cd9fa873104da0213192052b6b8dfd0d97ec664960f61ce7c55fd77.jpg"
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+                                    "type": "text",
+                                    "content": "with "
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+                                    "type": "inline_equation",
+                                    "content": "[\\cdot]"
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denoting the Iverson bracket [32] and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{n}^{\\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " denoting the image arising by removing all bird parts but "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{P}(e_f(x_n))"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " from "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". I.e., the parts estimated to be important remain."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Deletion check (DC). Similarly, if an explanation is complete, deleting all the parts of the input that are estimated to be important by the explanation should result in a different"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
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+                                    "type": "text",
+                                    "content": "classification output [16,38,45]. Thus, the deletion check is the inverse of PC and defined as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {D C} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} [ f (x _ {n} ^ {\\prime \\prime}) \\neq f (x _ {n}) ], \\tag {3}",
+                                    "image_path": "b2bba886d7141626960ce90170cc0c04e21bde3404418dd7f9818fc0c265e47f.jpg"
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+                                    "type": "text",
+                                    "content": "with "
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+                                    "type": "inline_equation",
+                                    "content": "x_{n}^{\\prime \\prime}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denoting the image arising by removing the estimated important parts "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " from "
+                                },
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+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Distractibility (D). As over-complete explanations would achieve high completeness scores, we argue that completeness should be considered together with a metric that counters over-completeness (similar to precision and recall). To this end, we introduce a novel over-completeness score that measures how many actually unimportant input parts are also estimated to be unimportant by the explanation. In detail, we successively remove each background object and bird part from the input and consider it to be unimportant if the logit target output drops less than "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "5\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
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+                                    ],
+                                    "type": "text",
+                                    "content": " compared to the output for the original image. Next, we measure the overlap between parts "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        546,
+                                        504
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{P}(e_f(x_n))"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        546,
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+                                    ],
+                                    "type": "text",
+                                    "content": " estimated to be important by the explanation and parts "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
+                                        546,
+                                        504
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{P}_{f(x_n)}^{\\prime \\prime}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        313,
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+                                    ],
+                                    "type": "text",
+                                    "content": " that are actually unimportant, normalized by the number of unimportant parts. As the overlap should be small for good evaluations, we subtract the result from 1:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {D} = 1 - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\frac {\\left| \\mathrm {P} \\left(e _ {f} \\left(x _ {n}\\right)\\right) \\cap \\mathcal {P} _ {f \\left(x _ {n}\\right)} ^ {\\prime \\prime} \\right|}{\\left| \\mathcal {P} _ {f \\left(x _ {n}\\right)} ^ {\\prime \\prime} \\right|}. \\tag {4}",
+                                    "image_path": "7cd12344c88477b4796a9b6de8e8535b43a24e4ac7d963762928eb6bc60c427c.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "The final completeness score (Com.) is computed as the mean of the averaged three completeness metrics (CSDC, PC, and DC), and the over-completeness D. By having complementing metrics, we can also automatically estimate the threshold "
+                                },
+                                {
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+                                    "content": "t"
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+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{P}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", such that "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " optimally trades off the completeness and over-completeness metrics."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "4.1.3 Correctness"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Single deletion (SD). In the single deletion protocol, we measure the rank correlation between the explanation's importance score of each part and the actual amount that the model's logit of the target class changes when removing that"
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+                                    "type": "text",
+                                    "content": "part [3, 14, 38]. Specifically, we define SD as"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathrm {S D} = \\frac {1}{2} + \\frac {1}{2 N} \\sum_ {n = 1} ^ {N} \\rho \\left(\\mathrm {P I} \\left(e _ {f} \\left(x _ {n}\\right)\\right), f \\left(x _ {n}\\right) - \\left\\{f \\left(x _ {n} ^ {\\prime \\prime \\prime}\\right) \\right\\}\\right), \\tag {5}",
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denoting the Spearman rank-order correlation coefficient, "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{PI}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " the part importance interface function, and "
+                                },
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+                                    "type": "inline_equation",
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+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " the target scores of the images obtained by removing any individual bird part from "
+                                },
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+                                    "type": "text",
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+                                    "type": "text",
+                                    "content": "4.1.4 Contrastivity"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
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+                                    "type": "text",
+                                    "content": "Target sensitivity (TS). If an explanation is sensitive to a target class, it should highlight image regions that are relevant for the respective target [8, 9, 38]. To measure target sensitivity, we take an input sample and select two classes "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{c}_2"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " that each have exactly two non-overlapping common parts with the actual class of input sample "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x_n"
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We choose two parts because this is the floor of half the 5 bird parts available in each image. Afterward, we compute the explanations "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "e_f(x_n, \\hat{c}_i)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with respect to "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and "
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+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and evaluate if they correctly highlight the parts belonging to each respective class:"
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathrm {T S} = \\frac {1}{2 N} \\sum_ {n = 1} ^ {N} \\left[ \\mathrm {P I} ^ {\\prime} \\left(e _ {f} \\left(x _ {n}, \\hat {c} _ {1}\\right)\\right) > \\mathrm {P I} ^ {\\prime} \\left(e _ {f} \\left(x _ {n}, \\hat {c} _ {2}\\right)\\right) \\right] \\tag {6} \\\\ + \\left[ \\mathrm {P I} ^ {\\prime \\prime} (e _ {f} (x _ {n}, \\hat {c} _ {1})) <   \\mathrm {P I} ^ {\\prime \\prime} (e _ {f} (x _ {n}, \\hat {c} _ {2})) \\right], \\\\ \\end{array}",
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+                                    "type": "text",
+                                    "content": " denoting the summed part importances of the two parts belonging to class "
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+                                    "type": "text",
+                                    "content": ", respectively "
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". To ensure that our protocol is faithful w.r.t. the model, we only consider images where removing parts belonging to "
+                                },
+                                {
+                                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " causes a larger model output drop for "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\hat{c}_1"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " than removing parts belonging to "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{c}_2"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and vice versa."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "4.2. The FunnyBirds custom analysis"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "As it is almost impossible to analyze all aspects of an explanation with a single framework, we also show how full control over our dataset enables more tailored and systematic custom evaluations. Similar to recent human studies [31], we evaluate the coherence of the assessed methods, i.e., how reasonable an explanation is for a human. To the best of our knowledge, this is one of the first methods for evaluating coherence in a fully automatic and systematic manner. We give two illustrative examples for implementing such an evaluation, but other instantiations are possible."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "ProtoPNet. ProtoPNet [12] promotes explainability by communicating which patches of the training data, called prototypes, look similar to patches in a test image. However, this only increases interpretability if the detected similarities are compatible with human notions of similarity. To quantitatively verify this in an automatic fashion, we test if relevant part types (e.g., beak or wing) in the detected patch"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "of the test image are also contained in the corresponding prototype identified by ProtoPNet. This assumes that different part types, i.e., beak and wings, do not look similar to most humans, and therefore, are not helpful similarities for explainability. While debatable for real images, we argue that this is a reasonable assumption for our dataset."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Counterfactual visual explanations. The objective of counterfactual visual explanations (CVE) [22] is to highlight image regions that discriminate the class "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        146,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " of a query image from the class "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c'"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " of a distractor image. To this end, CVE extracts convolutional neural network (CNN) feature maps from the query and distractor images to then perform feature swaps between the two feature maps that, when fed to the CNN classifier, lead to the strongest class change (from "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to "
+                                },
+                                {
+                                    "bbox": [
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+                                        146,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "c'"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        146,
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+                                    ],
+                                    "type": "text",
+                                    "content": "). The corresponding image locations of the feature swaps are then highlighted to yield the CVE. We argue that this kind of explanation is only meaningful for humans if the swaps are semantically correct, i.e., when a beak is swapped with another beak but not a foot. Using our proposed dataset, we conduct a systematic study and measure the average number of swaps that do not touch the same bird part in both images, and thus, can be considered semantically incorrect. We evaluate four different setups of increasing difficulty where we only use aligned, respectively unaligned, viewpoint pairs with classes that are different in only one, respectively multiple parts."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Limitations. As with controlled laboratory research [5], our dataset does not reflect all real-world challenges, and thus, is not fully representative of natural images. However, we argue that, as long as XAI methods are challenged to truthfully explain models trained even on our controlled dataset, our proposed method is a valuable tool to faithfully assess the quality of XAI methods. Nonetheless, for future XAI methods we suggest a two-stream evaluation that utilizes our proposed framework and custom analysis for theoretically grounded assessments of the explanation quality in addition to benchmarks that work on natural image data, e.g., Quantus [25]. Further, while the dimensions of explainability evaluated in our work can be considered relevant for many applications, there are dimensions that we omit here (see supplement). However, our framework can easily be extended with additional protocols if needed."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "5. Results and Interpretation"
+                                }
+                            ]
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+                                    "content": "5.1. FunnyBirds framework"
+                                }
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+                    ],
+                    "index": 14
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+                                    "type": "text",
+                                    "content": "Results for our multi-dimensional FunnyBirds framework across a broad variety of different XAI methods and three different backbones are given in Fig. 3. For detailed results of each individual evaluation protocol, please refer to the supplement. We plot qualitative explanations for a random image and give the evaluation scores from Sec. 4.1 averaged over the entire test set. From this, we can make"
+                                }
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+                                            "content": "Figure 3. FunnyBirds evaluation results. Qualitative and quantitative results for our FunnyBirds framework for the XAI methods Input "
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+                                            "type": "text",
+                                            "content": "-DNN [27], BagNet [6], ProtoPNet [12], and B-cos network [9]. Model-agnostic methods are evaluated on VGG16 [58], ResNet-50 [24], and ViT-B/16 [17]. Other models use a ResNet-50 backbone, if applicable. Quantitative results are averaged over the entire test set; qualitative results are shown for a representative example. Chart colors indicate different explanation types that should only be compared with caution. The center score denotes the mean of the completeness (Com.), correctness (Cor.), and contrastivity (Con.) dimensions. Additionally, we report the accuracy (Acc.) and background independence (B.I.). See Sec. 4.1 for details."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "several interesting findings and derive various hypotheses:"
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "(1) Overall, BagNet [6] achieves the highest explainability score, which could be due to its internal model structure that is better aligned with the explanatory power of an attribution map, i.e., pixels are processed more independently."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
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+                        {
+                            "bbox": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "(2) On average, Integrated Gradients (IG) [59] performs best among model-agnostic methods for different backbones, which is in line with the literature when considering gradient-based approaches [56, 59]. However, LIME [47] and IG achieve similar completeness, with LIME lacking the ability to communicate meaningful importance scores, which impairs practicability for certain downstream tasks. Interestingly, taking the absolute value of IG impairs the mean explanation score slightly, contradicting findings that have been made on pixel-level protocols [62]. Specifically, it slightly increases completeness while reducing contrastivity. We hypothesize that the negative gradient infor"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        }
+                    ],
+                    "sub_type": "text"
+                },
+                {
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+                                    "type": "text",
+                                    "content": "mation is therefore particularly important in identifying regions that do not belong to the class of interest. Removing the bias term (X-DNN [27] vs. ResNet-50 [24] w/ IG) slightly improves completeness and correctness while reducing contrastivity."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
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+                                            "type": "text",
+                                            "content": "(3) Explanation scores for model-agnostic XAI methods are consistently better for VGG16 [58] than for ResNet-50 [24], indicating that different backbones vary in their explainability. We also observe that the relative ordering of different XAI methods changes across different backbones (e.g., RISE [44] and IxG [56]), showing the importance of evaluating future XAI methods on different backbones."
+                                        }
+                                    ]
+                                }
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+                                            "content": "(4) IxG [56] and Grad-CAM [11, 53] seem to work better on CNN-based architectures [24, 58]. Methods developed for vision transformers, i.e., Rollout [1] and Chefer LRP [11], provide strong explanations, with Chefer LRP achieving the second highest explanation score. Rollout"
+                                        }
+                                    ]
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 4. Qualitative results of ProtoPNet [12]. Many of the test image patches (center) highlight the entire bird or just background. Further, prototypes (sides) often do not include important parts."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "content": "cannot compute class-specific explanations, which could be disadvantageous in certain downstream tasks."
+                                }
+                            ]
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+                    ],
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+                                            "type": "text",
+                                            "content": "(5) Coarser methods like Grad-CAM [53] and RISE [44] tend to be more incomplete, which could be an artifact of poor localization [46] and our parts being fairly small."
+                                        }
+                                    ]
+                                }
+                            ],
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+                        {
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+                                            "type": "text",
+                                            "content": "(6) The B-cos network [9] outperforms competing methods on the same backbone, showing an improved explainability, which is in line with results from [9]. Surprisingly, we see a slight decrease in background independence."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
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+                        {
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+                                            "type": "text",
+                                            "content": "(7) ProtoPNet [12] has poor correctness and contrastivity, which can be explained by related findings in that ProtoPNet similarities are not semantically reasonable [31] and by its poor localization (see Sec. 5.2 and Fig. 4)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
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+                            "type": "text",
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+                            "lines": [
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "(8) Especially correctness is a weakness of all examined methods, showing that, while existing approaches tend to accurately identify important areas, they lack the ability to reliably communicate the relative importance of each input area, or that the simple explanation of an attribution map might be too strong of a simplification of the actual model."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        }
+                    ],
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+                },
+                {
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "Finally, since XAI evaluation is multi-faceted and downstream task dependent, we doubt that a single score can be enough to properly compare methods. Hence, our work is less about ranking but more about automatically revealing the strengths and weaknesses of existing and future XAI methods in a systematic and theoretically grounded manner."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "5.2.Custom evaluations"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "ProtoPNet. To quantitatively evaluate if prototypes used in [12] promote explainability (see Sec. 4.2), we conduct several sanity checks. First, we measure that out of 1000 examined ProtoPNet patches in the test image, only 510 touch the same part in the corresponding prototype patch, and thus, have a similarity that could be aligned with human notions of similarity. Further, we measure that "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "26.3\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the extracted test image patches do not touch a single bird part, indicating a poor localization of the explanation. Finally, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        510,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "18.5\\%"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of the test image patches entail 4 or 5 different bird parts, which shows that the extracted patches are not local but global, and thus, do not promote the interpretability of the examined model. Qualitative results showing the described issues can be seen in Fig. 4. To summarize, many of the communicated prototypes of ProtoPNet [12] trained on our dataset are unlikely to be meaningful for humans. While a similar conclusion was drawn in a recent human"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 11,
+                            "angle": 0,
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+                        },
+                        {
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+                                            "type": "text",
+                                            "content": "Figure 5. Qualitative results of counterfactual visual explanations (CVE) [22]. (left) CVE for an aligned image pair with one part being different. (right) CVE for an unaligned image pair with multiple parts being different. Note how many of the proposed swaps are unrealistic, and therefore, of little quality (e.g., the purple patch around the right eye is swapped with the neck of the other bird)."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 12,
+                            "angle": 0,
+                            "type": "image_caption"
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "type": "text",
+                                    "content": "study [31] confirming our findings, our proposed tools allow the same conclusion in a fully automatic manner."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    "type": "text",
+                                    "content": "Counterfactual visual explanations. To quantify if CVE [22] highlights meaningful swaps (see Sec. 4.2), we measure how many of the extracted swaps do not touch the same bird parts in the two images. When considering images that have the same viewpoint and differ only by one part (Fig. 5 - left), CVE with VGG16 [58] produces on average 1.65 swaps that do not touch the same part, and therefore, are semantically meaningless. When changing the viewpoint, CVE produces on average 1.3 swaps that do not touch the same part. When working with aligned viewpoints and birds that differ by multiple parts (4.07 parts on average), 2.75 such swaps are produced and 2.62 when also changing the viewpoint (Fig. 5 - right). Interestingly, the number of different parts has a stronger impact on the absolute number of unreasonable swaps, i.e., swaps that do not touch the same part in both images, than the viewpoint. Further, we observe that even in our controlled environment, CVE produces on average "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        236,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sim 3"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " unreasonable swaps for images with on average only 4 different parts, indicating that many of the proposed swaps are semantically incorrect, and thus, do not promote coherent explanations."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
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+                                    "type": "text",
+                                    "content": "6. Conclusion"
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "content": "In this work, we propose a novel approach to automatically analyzing XAI methods using a synthetic classification dataset that allows for full annotation and part interventions. Using this dataset, we propose an accompanying multi-dimensional analysis framework that faithfully assesses various important aspects of explainability and generalizes to different explanation types by using interface functions. With this easy-to-use tool, we analyzed 24 different setups to uncover various new insights and confirm findings from related work. This shows that, despite the synthetic setting, our findings appear to translate well to real data, and that our proposed tool is a practical and valuable asset for the analysis of future XAI methods. Finally, we showed how to develop tailored analyses to gain a better understanding of two specific XAI methods and discovered their weaknesses in an automatic and quantitative manner."
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+                                    "content": "Acknowledgements. We thank Bernt Schiele, Moritz Böhle, and Sukrut Rao for their valuable feedback and helpful discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 866008). The project has also been supported in part by the State of Hesse through the cluster projects \"The Third Wave of Artificial Intelligence (3AI)\" and \"The Adaptive Mind (TAM)\"."
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new file mode 100644
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+        "text": "$^{1}$ School of Electronic and Computer Engineering, Peking University",
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+    {
+        "type": "text",
+        "text": "$^{2}$ International Digital Economy Academy (IDEA)",
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+    {
+        "type": "text",
+        "text": "{lihongxiang,chengxx,zhihongzhu,ywl}@stu.pku.edu.cn; {mengcao,zouyx}@pku.edu.cn",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The recent video grounding works attempt to introduce vanilla contrastive learning into video grounding. However, we claim that this naive solution is suboptimal. Contrastive learning requires two key properties: (1) alignment of features of similar samples, and (2) uniformity of the induced distribution of the normalized features on the hypersphere. Due to two annoying issues in video grounding: (1) the coexistence of some visual entities in both ground truth and other moments, i.e. semantic overlapping; (2) only a few moments in the video are annotated, i.e. sparse annotation dilemma, vanilla contrastive learning is unable to model the correlations between temporally distant moments and learned inconsistent video representations. Both characteristics lead to vanilla contrastive learning being unsuitable for video grounding. In this paper, we introduce Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework via geodesic and game theory. We quantify the correlations among moments leveraging the geodesic distance that guides the model to learn the correct cross-modal representations. Furthermore, from the novel perspective of game theory, we propose semantic Shapley interaction based on geodesic distance sampling to learn fine-grained semantic alignment in similar moments. Experiments on three benchmarks demonstrate the effectiveness of our method.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Video grounding [18, 59, 36, 45, 17, 75, 8, 69, 72, 67, 6, 25] aims to identify the timestamps semantically corresponding to a given query within an untrimmed video, which is a challenging multimedia retrieval task due to flexibility and complexity of the query and video content. The video grounding model needs well to model the complex cross-modal correlations and semantic information.",
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+    {
+        "type": "text",
+        "text": "Query  $\\boxed{q}$  : The person sharpens the blade on the second belt.",
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+        "type": "image",
+        "img_path": "images/683dbfe8345cd9b7cfd7dd4cb174128e00a5c090db8cf8b41aa392fae0f877c0.jpg",
+        "image_caption": [
+            "(a)"
+        ],
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+    {
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+        "img_path": "images/87b109d938ba991f278cdb12f28431919a653b190b70b37927dae2a604fc661c.jpg",
+        "image_caption": [
+            "(b)",
+            "Figure 1. (a) Illustration of video grounding. 'GT' indicates the ground truth. A comparison of (b) existing contrastive learning-based methods and (c) our proposed G2L method. G2L makes semantically similar video moments closer in representation space while exploring nuances among similar moments."
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+        "img_path": "images/610f8cbb120c89915c4b720008353a18bb90473ec957ccad17131ae7cf59b3d4.jpg",
+        "image_caption": [
+            "(c)"
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+        "type": "text",
+        "text": "Contrastive learning [10, 23, 43] is proposed to learn representations by contrasting positive pairs against negative pairs. With the popularity of contrastive learning in vision-language tasks [34, 13, 46, 7, 5, 64, 62], several works also apply it to video grounding. Nan et al. [45] propose a dual contrast learning to learn more informative feature representations by maximizing the mutual information between the query and the corresponding video clips. This naive solution, however, achieves sub-optimum performance.",
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+    {
+        "type": "text",
+        "text": "Generally, contrastive learning requires two key properties [58]: alignment and uniformity. Alignment favors encoders that assign similar features to similar samples. Uniformity prefers a feature distribution that preserves maximal information, i.e., the uniform distribution on the unit hypersphere. We argue that these two issues are not satisfied in current video grounding works with contrastive learning.",
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+        "type": "text",
+        "text": "Firstly, the semantic overlapping issue is widespread,",
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+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "12032",
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+    {
+        "type": "text",
+        "text": "i.e., the co-existence of some visual entities in both ground truth and other moments. As shown in Figure 1(a), the entity of 'person', 'blade' and 'belt' appear in both ground-truth moment  $m_4$  and others. Since there exist no classification labels in video grounding, previous methods distinguish positive and negative samples only based on the annotated moments. This strict scheme, however, ignores the semantic overlapping among video moments, which leads to the contradiction in feature representations. As shown in Figure 1(a)(b), the moment  $m_1$  of \"sharpen the blade on the first belt\" only differs from target moment  $m_4$  in the 'second' order. They share similar semantic meanings but are forced to be pushed away in feature space. It is not consistent with the alignment principle of the ideal contrastive learning.",
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+    {
+        "type": "text",
+        "text": "Another issue lies in the sparse annotation dilemma [67, 31]. Due to the costly labeling process, only a few moments are annotated regardless of the thousands of frames contained. Such severe data imbalance leads to significant learning bias for vanilla contrastive learning, i.e., unannotated moments are pushed away by different queries, regardless of the semantic relationships. Consequently, their representations are close, although they don't necessarily have strong semantic similarities. This undermines the uniformity requirement of contrastive learning. For example in Figure 1(b), wrong results always exist when encountering these unannotated moments (e.g.,  $m_1$ ).",
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+    {
+        "type": "text",
+        "text": "To address the issues mentioned above, we propose a novel Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework as shown in Figure 1(c). We propose to measure the similarity according to the geodesic distance [29] between two video moments along the manifold. In Figure 1(c), the geodesic distance between  $m_4$  to  $m_6$  is the length of the shortest path as the moment graph, i.e.  $m_4 \\rightarrow m_2 \\rightarrow m_3 \\rightarrow m_5 \\rightarrow m_6$ . In contrast to previous methods, we construct positive and negative pairs based on the geodesic distance rather than the temporal moment to relax the strict positional principle. The geodesics from the target moment to other moments are used to guide the maximizing mutual information. In this manner, the distance between video moments correctly reflects semantic relevance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unfortunately, the relaxed contrastive objective with geodesic leads to one side-effect, i.e., the model may confuse similar video moments. As shown in Figure 1(c), the model may falsely map  $m_{1}$  to be as close to the query  $q$  since  $m_{1}$  shares a similar appearance with the ground truth  $m_{4}$ . To further prevent the model from confusing similar video moments, we formulate video moments and queries as multiple players into a cooperative game and quantify their game-theoretic interactions (i.e., Shapley interactions [49, 20]). Through this, we evaluate the marginal contributions of each fine-grained component, which leads",
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+    {
+        "type": "text",
+        "text": "to a more accurate division. However, computing the exact Shapley interaction for all players is an NP-hard problem [41] and is difficult to achieve solutions in the video grounding setting. Therefore, we further propose a semantic Shapley interaction module, which samples similar intravideo moments by geodesic distance with a focus on their nuances.",
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+    {
+        "type": "text",
+        "text": "In sum, our contributions are summarized as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We present G2L which introduces geodesic and game theory to learn the semantic alignment and uniformity between video and query for video grounding.",
+            "- We propose a novel geodesic-guided contrastive learning scheme that considers the correct semantics of all moments in the video.",
+            "- We introduce an effective semantic Shapley interaction strategy based on geodesic distance.",
+            "- Extensive experiments on three public datasets demonstrate the effectiveness of our G2L."
+        ],
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Video Grounding. Video grounding proposed by [18, 1], which aims to predict the start and end boundaries of the activity described by a given language query within a video. Early approaches focus on carefully designed complex video-text interaction modules. Yuan et al. [66] propose an approach which can directly predict the coordinates of the queried video clip using attention mechanism. Zeng et al. [67] propose a pyramid neural network to consider multi-scale information. Liu et al. [39] advise a memory attention to emphasize the visual features and simultaneously utilize the context information. Xu et al. [61] introduce a multi-level model to integrate visual and textual features earlier and further re-generate queries as an auxiliary task. To improve the representation of the model, several methods introduce contrastive learning or cross-modal discrimination. Ding et al. [17] propose to combine discriminative contrastive objective and generative caption objective to optimize dual-encoder. Nan et al. [45] introduce introducing causal intervention and dual contrastive learning to improve representation. In this paper, we propose to model semantic alignment and uniformity by approximate geodesics and game-theoretic interactions.",
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+    {
+        "type": "text",
+        "text": "Contrastive Learning. Contrastive learning (CL) often serves as an unsupervised objective to learn representations by contrasting positive pairs against negative pairs [10, 23, 43, 35, 12, 11]. Some prior works consider maximizing the mutual information (MI) between latent representations [24]. MI quantifies the \"amount of information\" gained about one random variable by observing another random variable [2]. Contrastive learning has been applied to vision-language tasks to learn the joint representations of visual and textual modalities [42, 51]. Sun et al. [71] pro",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "12033",
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+    {
+        "type": "text",
+        "text": "pose a retrieval and localization network with contrastive learning for video corpus moment retrieval.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Shapley Value. The Shapley value [49, 26] originates from cooperative game theory. It has been theoretically proven to be the unique metric to fairly estimate the contribution of each player in a cooperative game such that satisfying certain desirable axioms [60] and is widely used in deep learning. Li et al. [32] propose a semantically aligned vision-language pre-training based on Shapley value to model fine-grained semantics. Ren et al. [48] propose to explain adversarial attacks by Shapley value. Li et al. [33] propose to explicit credit assignment for multi-agent reinforcement learning using Shapley value.",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3. Geodesic and Game Localization (G2L)",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation and Model Overview",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Let  $Q_{i}$  and  $V_{i}$  be a given textual query and untrimmed video respectively. The purpose of video grounding is to locate the most relevant video interval  $A_{i} = (t_{i}^{s}, t_{i}^{e})$ , where  $t_{i}^{s}$  and  $t_{i}^{e}$  are starting and ending times respectively. The key to video grounding is to learn semantics between video and query. To this end, previous methods [45, 17] incorporate vanilla contrastive learning into existing cross-modal interaction architectures. Typically, at the training stage, they employ two loss functions: video grounding loss  $\\mathcal{L}_{\\mathrm{VG}}$  and vanilla contrastive loss  $\\mathcal{L}_{\\mathrm{VCL}}$ .  $\\mathcal{L}_{\\mathrm{VG}}$  computes the cross entry between the target timestamp and the prediction timestamp to optimize the model.  $\\mathcal{L}_{\\mathrm{VCL}}$  discriminates between positive samples and negative samples based on the temporal moment and adopts noise-contrastive estimation (NCE) [21] to obtain MI of videos and queries.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, vanilla contrastive learning is not appropriate for video grounding due to the semantic overlapping and sparse annotation dilemma. To learn correct semantics and improve representations, as illustrated in Figure 2, we propose Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework that germinates from geodesic and cooperative game theory. Our G2L learns semantic alignment and uniformity from two components. With geodesic-guided contrastive learning (GCL), complete semantic alignment and uniformly distributed video features are learned. By semantic Shapley interaction(SSI), we learn the fine-grained semantic alignment between similar moments and target queries. Combined with the two novel proposed training objectives, the full training objective of semantically aligned and uniform video grounding can be formulated as:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {V G}} + \\mathcal {L} _ {\\mathrm {G C L}} + \\mathcal {L} _ {\\mathrm {S S I}} \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "During inference, it can be directly removed, rendering a semantics-sensitive dual encoder.",
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+    {
+        "type": "text",
+        "text": "3.2. Feature Encoder",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Video Encoder. For an input video  $V_{i}$ , we first segment it into small video clips and perform a fixed-interval sampling over these clips. Then the video clips are fed into a pretrained 3D CNN model (e.g. C3D) to extract the video features  $F_{i}^{V}$ . Referring to the previous works [75], we employ sparse sampling and a proposal network to construct the feature map  $F_{i}^{M} = \\{m_{i}\\}_{i=1}^{N_{m}}$  of moment candidates based on  $F_{i}^{V}$ , where  $N_{m}$  is the number of proposals in the video.",
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+    },
+    {
+        "type": "text",
+        "text": "Query Encoder. For a textual query  $Q_{i}$ , we generate the tokens of words by the tokenizer and add a class embedding token '[CLS]' in the beginning. Then the tokens are fed into pre-trained BERT [27], and we perform average pooling of its last two hidden states to obtain the sentence feature  $q_{i}$ .",
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+    {
+        "type": "text",
+        "text": "3.3. Geodesic Distance Computation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Video content is intricate and flexible, and for video clips, temporal proximity does not always equate to semantic similarity. Conversely, two video clips can have strong correlations even though they are temporally distant. We propose to measure correlations of video representations using the geodesic distance. Formally, we define a mini-batch of video-query pairs as  $\\{V_i, Q_i\\}_{i=1}^B$ , where  $B$  is the size of the mini-batch. After fed into the video and query encoders, we obtain textual representation  $L = \\{q_i\\}_{i=1}^B$  and moment representations  $M = \\{m_i\\}_{i=1}^{B \\times N_m}$ .",
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+    },
+    {
+        "type": "text",
+        "text": "The video moments representations may lie in a high-dimensional manifold, and our purpose is to measure the geodesic distance between two points along the manifold. However, computing the exact geodesic distance [29] is difficult without explicit knowledge of the manifold structure. To obtain the geodesic distance, we first employ the K-NN graph [15] to approximate the manifold structure [52, 14]. In this graph, each moment  $m_{i}$  forms a node, and each node connects to at most  $n$  other nodes. A directed edge exists from node  $m_{i}$  to node  $m_{j}$  if node  $m_{j}$  is among the  $n$  nearest neighbors of  $m_{i}$ . The edge weight  $d(m_{i},m_{j})$  is defined using cosine similarity:  $d(m_{i},m_{j}) = 1 - m_{i}m_{j}^{\\top}$ . Finally, we utilize the shortest path algorithm, i.e., Dijkstra [16], to compute the length of the shortest path between two moments along the obtained weighted directed graph as the geodesic distance  $\\mathcal{G}(m_i,m_j)$ .",
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+    {
+        "type": "text",
+        "text": "3.4. Geodesic-guided Contrastive Learning",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Previous Contrastive Scheme. In video grounding, a query usually corresponds to multiple clips. An intuitive method [17] to learn representations is to set the clips in ground truth intervals as positive samples, while others are negatives. Another scheme [59] is to calculate the intersection over union (IoU) between the ground truth and other moments, where those with higher IoU are considered as positive samples and the lower ones are regarded as negative samples. Then they learn the joint representation by",
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+    {
+        "type": "page_number",
+        "text": "12034",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a58681c68be132cd2127c73d26c98c5974f2ad6cb42e0f70148266c5083cfa06.jpg",
+        "image_caption": [
+            "Figure 2. Overview of Geodesic and Game Localization (G2L). Our framework encourages the model to learn semantically aligned and uniform joint representations. In the inference stage, we directly fuse the video features and query features to compute the predicted moments. In the training stage, the grounding loss  $\\mathcal{L}_{\\mathrm{VG}}$  is obtained by calculating the cross-entropy between the predicted moment and the target moment. Then, we approximate the high-dimensional manifold structure of the video representations through a moment graph and calculate the geodesic distance from the target moment to other moments. Finally, we leverage geodesic distance for cross-modal discrimination and semantic Sharpley interaction modeling."
+        ],
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "pulling the query features and ground truth moment features together, and pushing the query features and non-ground truth moment features apart. The previous contrastive loss  $\\mathcal{L}_{\\mathrm{VCL}}$  can be formulated as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V C L}} = - \\sum_ {i = 1} ^ {B} \\left(\\log \\frac {\\exp \\left(q _ {i} m _ {i} ^ {\\top} / \\tau\\right)}{\\sum_ {m _ {j} \\in M} \\exp \\left(q _ {i} m _ {j} ^ {\\top} / \\tau\\right)}\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau$  is the temperature hyper-parameter.",
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+    },
+    {
+        "type": "text",
+        "text": "While intuitive, such a manner fails to capture semantic alignment and uniformity between queries and video content. To learn complete semantic alignment and uniformity for video grounding, we propose geodesic-guided contrastive learning.",
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+    {
+        "type": "text",
+        "text": "Semantic Alignment. In vanilla supervised contrastive learning [56, 28], all classes play the same role: pulling is done within every class and pushing between every pair of different classes. Such uniform contrastive learning works well for symmetric and equal cross-modal learning. In fact, due to semantic overlapping, the semantics of the video and text are asymmetric and unequal in video grounding. Temporally distant moments may have similar semantics. To model semantic alignment, we discriminate positive pairs based on the geodesic distance instead of the temporal moment. For a query feature  $q_{i}$ , we define the  $k$  moments with the closest geodesic distance from the target moment  $\\hat{m}_i \\in M$  as its semantic positive samples  $P_{i}$ :",
+        "bbox": [
+            75,
+            656,
+            470,
+            836
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {i} = \\left\\{p _ {i} ^ {k} \\right\\} = \\underset {k} {\\arg \\operatorname {t o p k}} \\mathcal {G} (\\hat {m} _ {i}, m _ {k}) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            154,
+            844,
+            468,
+            870
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$P_{i}$  contains  $m_{i}$  and moments adjacent to  $m_{i}$  geodesic which is used to construct positive pairs with  $q_{i}$  to relax the previous strict positional principle.",
+        "bbox": [
+            497,
+            448,
+            890,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Semantic Uniformity. Due to the sparse annotation dilemma [67, 31], most of the moments are only marked as negative while pushed away by different queries. Notably, this push operation is undifferentiated, i.e., the model is encouraged to learn to push all unannotated moments from the annotated ones. This clearly undermines the model to learn correct semantics. To learn semantic uniformity, we introduce the geodesic distance to differentially push negative samples away from the query based on semantic relationships. The similarity between query and moment  $s(q_i, m_j)$  is defined as:",
+        "bbox": [
+            497,
+            489,
+            892,
+            641
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ns \\left(q _ {i}, m _ {j}\\right) = \\exp \\left(q _ {i} m _ {j} ^ {\\top} \\left(\\hat {m} _ {i} m _ {j} ^ {\\top} \\log \\frac {1}{\\exp \\left(\\mathcal {G} \\left(\\hat {m} _ {i} , m _ {j}\\right) + 1\\right)}\\right)\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            499,
+            657,
+            890,
+            700
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We assign corresponding weights according to the geodesic distance  $\\mathcal{G}(\\hat{m}_i, m_j)$  between the target moment  $\\hat{m}_i$  and all moments  $m_j$ .  $s(q_i, m_j)$  considers the relationships between negative samples while maximizing mutual information.",
+        "bbox": [
+            497,
+            701,
+            890,
+            756
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Finally, our geodesic-guided contrastive loss can be formulated as:",
+        "bbox": [
+            497,
+            756,
+            890,
+            782
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {G C L}} = - \\sum_ {i = 1} ^ {B} \\left(\\log \\frac {\\sum_ {p _ {i} ^ {k} \\in P _ {i}} \\exp \\left(q _ {i} p _ {i} ^ {k} ^ {\\top} / \\tau\\right)}{\\sum_ {m _ {j} \\in M} s \\left(q _ {i} , m _ {j}\\right) / \\tau}\\right) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            546,
+            786,
+            890,
+            847
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In contrast to Equation 2,  $\\mathcal{L}_{\\mathrm{GCL}}$  is designed for representa",
+        "bbox": [
+            499,
+            852,
+            890,
+            866
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "12035",
+        "bbox": [
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+            887,
+            504,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tion learning rather than directly learning localization.",
+        "bbox": [
+            77,
+            125,
+            433,
+            140
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Semantic Shapley Interaction Modeling",
+        "text_level": 1,
+        "bbox": [
+            77,
+            148,
+            416,
+            163
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To prevent the model from confusing similar video moments due to the relaxed contrastive objective in Equation 3, we propose semantic Shapley interaction to model fine-grained semantic alignment.",
+        "bbox": [
+            77,
+            169,
+            468,
+            225
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5.1 Preliminaries",
+        "text_level": 1,
+        "bbox": [
+            77,
+            231,
+            225,
+            244
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Shapley Value. The Shapley value [49] is a classical game theory solution for the unbiased estimation of the contribution of each player in a cooperation game. Assume a game consists of  $\\mathcal{N}$  players,  $\\mathcal{U} \\subseteq \\mathcal{N}$  represents a potential subset of players. A game function  $f(\\cdot)$  maps each subset  $\\mathcal{U}$  of players to a score, estimating the cooperated contribution of a set of players. For a player  $i$ , its Shapley value  $\\phi(i|\\mathcal{N})$  is computed as the average marginal contribution of player  $i$  to all possible coalitions  $\\mathcal{U}$  without  $i$ :",
+        "bbox": [
+            75,
+            252,
+            470,
+            377
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\phi (i \\mid \\mathcal {N}) = \\sum_ {\\mathcal {U} \\subseteq \\mathcal {N} \\backslash \\{i \\}} p (\\mathcal {U}) [ f (\\mathcal {U} \\cup \\{i \\}) - f (\\mathcal {U}) ] (6) \\\\ p (\\mathcal {U}) = \\frac {| \\mathcal {U} | ! (| \\mathcal {N} | - | \\mathcal {U} | - 1) !}{| \\mathcal {N} | !} (7) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            117,
+            388,
+            468,
+            451
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $p(\\mathcal{U})$  is the likelihood of  $\\mathcal{U}$  being sampled. The Shapley value has been proved to be the unique metric that satisfies the following axioms: Linearity, Symmetry, Dummy, and Efficiency. We summarize these axioms in the supplementary material.",
+        "bbox": [
+            75,
+            461,
+            468,
+            530
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Shapley Interaction. In game theory, some players tend to form a small cooperative coalition and always participate in the game together. This cooperation provides additional contributions to the game. The Shapley interaction [20] measures the additional contributions made by the coalition compared to players working individually. We define  $[\\mathcal{U}]$  as a single hypothetical player, which is the union of the players in  $\\mathcal{U}$ . A reduced game is formed by removing the individual players in  $\\mathcal{U}$  from the game and adding  $[\\mathcal{U}]$  to the game. Finally, according to Equation 6, the Shapley interaction for coalition  $\\mathcal{U}$  is formulated as:",
+        "bbox": [
+            75,
+            530,
+            468,
+            681
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Im ([ \\mathcal {U} ]) = \\phi ([ \\mathcal {U} ] \\mid \\mathcal {N} \\backslash \\mathcal {U} \\cup \\{[ \\mathcal {U} ] \\}) - \\sum_ {i \\in \\mathcal {U}} \\phi (i \\mid \\mathcal {N} \\backslash \\mathcal {U} \\cup \\{i \\}) \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            691,
+            468,
+            720
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Im ([\\mathcal{U}])$  reflects the interactions inside  $\\mathcal{U}$ . The higher value of  $\\Im ([\\mathcal{U}])$  indicates that players in  $\\mathcal{U}$  cooperate closely with each other.",
+        "bbox": [
+            75,
+            730,
+            468,
+            771
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5.2 Fine-Grained Semantic Alignment via Shapley",
+        "text_level": 1,
+        "bbox": [
+            77,
+            789,
+            453,
+            804
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "According to Equation 6 and Equation 8, it can be known that the computational complexity of the Shapley interaction grows factorially as the number of players increases. To reduce the computational cost, we propose semantic",
+        "bbox": [
+            75,
+            811,
+            468,
+            866
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Shapley interaction based on geodesic distance sampling. Specifically, as in Equation 3, we sample semantic similar moments based on geodesic distances to investigate their nuances. Then, we consider queries and semantic similar moments from the same video as players in the same cooperative game.",
+        "bbox": [
+            497,
+            125,
+            890,
+            209
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To avoid confusion with the previous symbols, we define  $\\mathcal{H}_i^V = \\{\\mathbf{h}_{ix}^V\\}_{x=1}^{N_i^v}$  and  $\\mathcal{H}_i^Q = \\{\\mathbf{h}_{iy}^Q\\}_{y=1}^{N_i^q}$  are a set of semantic positive samples and queries from the video  $V_i$  respectively, where  $N_i^v = KN_i^q$  and  $N_i^q$  indicate the number of similar moments and queries in video  $V_i$  respectively.  $K$  is the number of moments sampled for each query  $\\mathbf{h}_{iy}^Q$ . We investigate the effect of  $K$  on computational cost and performance in the supplementary material.",
+        "bbox": [
+            497,
+            212,
+            890,
+            325
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "If a query and a video moment have strong semantic correspondence, then they tend to cooperate with each other and contribute to the coalition. Thus, we can take  $\\mathcal{H}^i = \\mathcal{H}_i^V \\cup \\mathcal{H}_i^Q$  as the players in the same game inspired by [32]. We define the alignment matrix as:  $\\mathcal{A}_i = [a_{xy}^i]$ , where  $a_{xy}^i = h_{ix}^{V^\\top}h_{iy}^Q$  represents the alignment score between  $x$ -th moment and  $y$ -th query in video  $V_i$ . Next,  $\\tilde{\\mathcal{A}}_i$  is obtained by applying softmax-normalization over each row of  $\\mathcal{A}_i$ . Then we average the maximum alignment score  $\\max_y \\tilde{a}_{xy}^i$  as the fine-grained moment-to-query similarity  $\\psi_1$ . Similarly, we can obtain the fine-grained query-to-moment similarity  $\\psi_2$ . The total fine-grained similarity score can be defined:  $\\psi = (\\psi_1 + \\psi_2) / 2$ , which be considered as the game score  $f(\\cdot)$  in our game.",
+        "bbox": [
+            497,
+            328,
+            890,
+            529
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "According to Equation 8, the semantic Shapley interaction of them can be formulated as:",
+        "bbox": [
+            497,
+            532,
+            890,
+            559
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\Im \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right]\\right) = \\phi \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right] \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\{\\left[ \\mathcal {H} _ {x y} ^ {i} \\right] \\}\\right) \\\\ - \\phi \\left(\\mathbf {h} _ {i x} ^ {V} \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\left\\{\\mathbf {h} _ {i x} ^ {V} \\right\\}\\right) \\\\ - \\phi \\left(\\mathbf {h} _ {i y} ^ {Q} \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\left\\{\\mathbf {h} _ {i y} ^ {Q} \\right\\}\\right) (9) \\\\ = \\mathbb {E} _ {\\mathcal {C}} \\left\\{\\underset {| \\mathcal {U} | = \\mathcal {C}} {\\mathcal {U} \\subseteq \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i}} \\mathbb {E} \\left[ f \\left(\\mathcal {U} \\cup \\mathcal {H} _ {x y} ^ {i}\\right) - f \\left(\\mathcal {U} \\cup \\left\\{\\mathbf {h} _ {i x} ^ {V} \\right\\}\\right) \\right. \\right. \\\\ \\left. - f \\left(\\mathcal {U} \\cup \\left\\{\\mathbf {h} _ {i y} ^ {Q} \\right\\}\\right) + f (\\mathcal {U}) \\right] \\rbrace (10) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            576,
+            890,
+            680
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Im \\left(\\left[\\mathcal{H}_{xy}^{i}\\right]\\right)$  represents the single player formed by the coalition of  $x$ -th moment and  $y$ -th query in video  $V_{i}, \\mathcal{C}$  represents the coalition size. We take normalized  $\\Im'\\left(\\left[\\mathcal{H}_{xy}^{i}\\right]\\right)$  as soft labels, the fine-grained semantic alignment loss can be defined as:",
+        "bbox": [
+            497,
+            695,
+            890,
+            764
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S S I}} = - \\sum_ {i = 1} ^ {T} \\frac {1}{N _ {i} ^ {v} N _ {i} ^ {q}} \\sum_ {x = 1} ^ {N _ {i} ^ {v}} \\sum_ {y = 1} ^ {N _ {i} ^ {q}} \\Im^ {\\prime} \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right]\\right) \\log \\left(\\tilde {a} _ {x y} ^ {i}\\right) \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            510,
+            781,
+            890,
+            821
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $T$  is the total number of unique videos in a minibatch, i.e.  $T \\leq B$ .",
+        "bbox": [
+            497,
+            838,
+            890,
+            866
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "12036",
+        "bbox": [
+            465,
+            887,
+            504,
+            897
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/3eb81a72e98cfeac88b4b54d49cc00211177d8864bf08bba8143dc312f49771e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>CTRL [18]</td><td>29.01</td><td>10.34</td><td>59.17</td><td>37.54</td></tr><tr><td>ACRN [39]</td><td>31.67</td><td>11.25</td><td>60.34</td><td>38.57</td></tr><tr><td>TripNet [22]</td><td>32.19</td><td>13.93</td><td>-</td><td>-</td></tr><tr><td>SCDM [65]</td><td>36.75</td><td>19.86</td><td>64.99</td><td>41.53</td></tr><tr><td>LGI [44]</td><td>41.51</td><td>23.07</td><td></td><td></td></tr><tr><td>VSLNet [73]</td><td>43.22</td><td>26.16</td><td>-</td><td>-</td></tr><tr><td>2D-TAN [75]</td><td>44.51</td><td>26.54</td><td>77.13</td><td>61.96</td></tr><tr><td>DRN [67]</td><td>45.45</td><td>24.39</td><td>77.97</td><td>50.30</td></tr><tr><td>DPIN [54]</td><td>47.27</td><td>28.31</td><td>77.45</td><td>60.03</td></tr><tr><td>CBLN [37]</td><td>48.12</td><td>27.60</td><td>79.32</td><td>63.41</td></tr><tr><td>SMIN [55]</td><td>48.46</td><td>30.34</td><td>81.16</td><td>62.11</td></tr><tr><td>MATN [74]</td><td>48.02</td><td>31.78</td><td>78.02</td><td>63.18</td></tr><tr><td>GTR [4]</td><td>50.57</td><td>29.11</td><td>80.43</td><td>65.14</td></tr><tr><td>CMAS [63]</td><td>46.23</td><td>29.48</td><td>77.04</td><td>60.25</td></tr><tr><td>MMN [59]</td><td>48.59</td><td>29.26</td><td>79.50</td><td>64.76</td></tr><tr><td>CL-based:</td><td></td><td></td><td></td><td></td></tr><tr><td>IVG-DCL [45]</td><td>43.84</td><td>27.10</td><td>-</td><td>-</td></tr><tr><td>SSCS [17]</td><td>46.67</td><td>27.56</td><td>78.37</td><td>63.78</td></tr><tr><td>G2L (ours)</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr></table>",
+        "bbox": [
+            80,
+            122,
+            463,
+            448
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            75,
+            495,
+            206,
+            510
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Evaluation",
+        "text_level": 1,
+        "bbox": [
+            75,
+            519,
+            299,
+            534
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ActivityNet-Captions. ActivityNet-Captions [30] contains 20,000 untrimmed videos and 100,000 descriptions [3], covering a wide range of complex human behavior. The video clips with annotations have much larger variations. Following the public split [75], we use 37417, 17505 and 17031 sentence-video pairs for training, validation and testing, respectively.",
+        "bbox": [
+            75,
+            542,
+            467,
+            638
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Charades-STA. The Charades dataset [50] is collected for video action recognition and video captioning. Gao et al. [18] adapt the Charades dataset to the video grounding task by collecting the query annotations. The Charades-STA dataset contains 6672 videos and involves 16128 video-query pairs, where 12408 pairs are used for training and 3720 for testing. We follow the same split of the dataset as in Gao et al. [18] for fair comparisons.",
+        "bbox": [
+            75,
+            641,
+            467,
+            751
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "TACoS. TACoS [47] contains 127 videos from the cooking scenarios. We follow the standard split [18], which has 10146, 4589 and 4083 video query pairs for training, validation and testing, respectively.",
+        "bbox": [
+            75,
+            752,
+            467,
+            809
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation. Following previous work [18, 75], we adopt \"R@n, IoU=m\" as the evaluation metric. It calculates the percentage of IoU greater than \"m\" between at least one of the top \"n\" video moments retrieved and the ground truth.",
+        "bbox": [
+            75,
+            809,
+            467,
+            866
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/305811baa596b5909170b1f4731989b9bfa459307543ebf3a2838a660eb3eb7c.jpg",
+        "table_caption": [
+            "Table 1. Performance comparisons on ActivityNet-Captions using C3D features."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>MCN [1]</td><td>17.46</td><td>8.01</td><td>48.22</td><td>26.73</td></tr><tr><td>SAP [9]</td><td>27.42</td><td>13.36</td><td>66.37</td><td>38.15</td></tr><tr><td>TripNet [22]</td><td>36.61</td><td>14.50 -</td><td>-</td><td></td></tr><tr><td>MAN [70]</td><td>41.21</td><td>20.54</td><td>83.21</td><td>51.85</td></tr><tr><td>2D-TAN [75]</td><td>39.70</td><td>23.31</td><td>80.32</td><td>51.26</td></tr><tr><td>DRN [67]</td><td>42.90</td><td>23.68</td><td>87.80</td><td>54.87</td></tr><tr><td>FVMR [19]</td><td>42.36</td><td>24.14</td><td>83.97</td><td>50.15</td></tr><tr><td>CBLN [37]</td><td>43.67</td><td>24.44</td><td>88.39</td><td>56.49</td></tr><tr><td>MMRG [68]</td><td>44.25</td><td>-</td><td>60.22</td><td>-</td></tr><tr><td>MMN [59]</td><td>47.31</td><td>27.28</td><td>83.74</td><td>58.41</td></tr><tr><td>CL-based:SSCS [17]</td><td>43.15</td><td>25.54</td><td>84.26</td><td>54.17</td></tr><tr><td>G2L(Ours)</td><td>47.91</td><td>28.42</td><td>84.80</td><td>59.33</td></tr></table>",
+        "bbox": [
+            510,
+            123,
+            882,
+            357
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Performance comparisons on Charades-STA using VGG features.",
+        "bbox": [
+            499,
+            366,
+            890,
+            391
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For a fair comparison, we extracted video features from a pre-trained 3D CNN (C3D for ActivityNet-Captions and TACoS, VGG for Charades-STA) following previous works [59, 17, 45]. We uniformly sampled (256, 32, 256) clips as the input video sequence and set the length of 2D feature map [75] (64, 16, 128) for ActivityNet-Captions, Charades-STA, and TACoS, respectively. For the language query, the pre-trained BERT[27] was employed for each word of the query. The average pooling outputs of the first and last layers were used to obtain the embedding of the whole sentence. We employed the AdamW optimizer [40] to train our model and set the temperature weight  $\\tau$  to 0.1. The learning rates were set to  $(8\\times 10^{-4},8\\times 10^{-4},1\\times 10^{-4})$  for ActivityNet-Captions, Charades-STA, and TACoS, respectively. We conducted experiments on 8 A100 GPUs with batch size 48 for ActivityNet-Captions and Charades-STA, and on 4 A100 GPUs with batch size 8 for TACoS.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Comparisons with State-of-the-art Methods",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison on ActivityNet-Captions. In Table 1, we report our performance in comparison with other state-of-the-art methods on ActivityNet-Captions. Compared with IVG-DCL [45] and SSCS [17], which are also based on contrastive learning, our method achieves significant improvements. Notably, ActivityNet-Captions is currently the dataset with the most severe semantic overlapping and sparse annotation dilemma. We observe that our model showed even more significant improvements on ActivityNet-Captions, achieving absolute improvements of up to  $7.8\\%$  and  $5.7\\%$  compared to IVG-DCL [45] and SSCS [17], respectively. They encourage the model to focus on cross-modal alignment in favor of grounding while ig-",
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+    },
+    {
+        "type": "page_number",
+        "text": "12037",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/9b6351342c9d6748eeb7064c78b040de263e1c7a43cbf37fe235f1b3504fe6e5.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>R@1 IoU0.3</td><td>R@1 IoU0.5</td><td>R@5 IoU0.3</td><td>R@5 IoU0.5</td></tr><tr><td>CTRL [18]</td><td>18.32</td><td>13.30</td><td>36.69</td><td>25.42</td></tr><tr><td>CBP [57]</td><td>27.31</td><td>24.79</td><td>43.64</td><td>37.40</td></tr><tr><td>SCDM [65]</td><td>26.11</td><td>21.17</td><td>40.16</td><td>32.18</td></tr><tr><td>2D-TAN [75]</td><td>37.29</td><td>25.32</td><td>57.81</td><td>45.04</td></tr><tr><td>DRN [67]</td><td>-</td><td>23.17</td><td>-</td><td>33.36</td></tr><tr><td>CMIN [76]</td><td>24.64</td><td>18.05</td><td>-</td><td>-</td></tr><tr><td>CSMGAN [38]</td><td>33.90</td><td>27.09</td><td>53.98</td><td>41.22</td></tr><tr><td>CBLN [37]</td><td>38.98</td><td>27.65</td><td>59.96</td><td>46.24</td></tr><tr><td>MMN [59]</td><td>39.24</td><td>26.17</td><td>62.03</td><td>47.39</td></tr><tr><td>GTR [4]</td><td>40.39</td><td>30.22</td><td>61.94</td><td>47.73</td></tr><tr><td>FVMR [19]</td><td>41.48</td><td>29.12</td><td>64.53</td><td>50.00</td></tr><tr><td>CL-based:</td><td></td><td></td><td></td><td></td></tr><tr><td>IVG-DCL [45]</td><td>38.84</td><td>29.07</td><td>-</td><td>-</td></tr><tr><td>SSCS [17]</td><td>41.33</td><td>29.56</td><td>60.65</td><td>48.01</td></tr><tr><td>G2L(Ours)</td><td>42.74</td><td>30.95</td><td>65.83</td><td>49.86</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "noring the semantics among full moments, especially unannotated moments. In contrast, our method conducts cross-modal discrimination guided by the geodesic distance such that overcoming data bias.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Comparison on Charades-STA. Table 2 reports the result comparison between state-of-the-art methods on Charades-STA. Compared with SSCS [17], our method achieves a performance improvement of up to  $5.1\\%$ . On more stringent evaluation metrics, such as “R@1 IoU=0.7”, our method achieves a performance improvement of  $1.1\\%$  compared to the cutting-edge method MMN [59], which indicates that exploring fine-grained semantic alignment information between similar video moments can improve grounding quality. Notably, MMN [59] and SSCS [17] have similar loss functions, and MMN [59] from a perspective on temporal grounding as a metric-learning problem proposes a mutual matching network to enhance joint representation learning by mining more negative samples achieving better performances. However, it also constructs cross-modal pairs based on the temporal moment, which results in a large number of constructed negative pairs containing potential weak semantic positive pairs, thus hindering learning.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison on TACoS. Table 3 summarizes the comparisons on the TACoS. We observe that our model achieves state-of-the-art results in most settings. However, the performance gain on this dataset is smaller than the previous three datasets. The reason is that the sparse annotation dilemma and semantic overlapping are insignificant on TACoS. It contains only 127 videos but has about 20,000 queries and focuses on cooking activities with more uniform objects, roles, and actions. Nevertheless, our method still outperforms previous contrastive learning-based methods in various metrics.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/28e813f8e5f60936d7a33a15980daad0cada21fee7973f327afd96c514691f50.jpg",
+        "table_caption": [
+            "Table 3. Performance comparisons on TACoS using C3D features."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>Full Model</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr><tr><td>w/o SA</td><td>50.85</td><td>30.73</td><td>79.22</td><td>65.47</td></tr><tr><td>w/o SU</td><td>49.10</td><td>31.14</td><td>79.48</td><td>65.46</td></tr><tr><td>w/o GCL</td><td>48.74</td><td>28.62</td><td>78.89</td><td>64.44</td></tr><tr><td>w/o SSI</td><td>50.65</td><td>30.01</td><td>79.54</td><td>66.76</td></tr><tr><td>w/o GCL+SSI</td><td>45.74</td><td>26.74</td><td>77.26</td><td>61.64</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7f3e13214741bf10753f0d0c301cb41f05babd8380c5622ac4a99804452197bc.jpg",
+        "table_caption": [
+            "Table 4. Ablation studies of main components on ActivityNetCaptions. \"SA\" and \"SU\" denote the Semantic Alignment and the Semantic Uniformity in GCL, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>Euclidean</td><td>47.83</td><td>28.44</td><td>79.42</td><td>65.46</td></tr><tr><td>Timestamp</td><td>49.85</td><td>29.73</td><td>78.15</td><td>65.47</td></tr><tr><td>Cosine</td><td>50.94</td><td>30.09</td><td>79.57</td><td>65.84</td></tr><tr><td>Geodesic</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 5. Comparison of different distance metrics on ActivityNet-Captions.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of Individual Components. In Table 4, we conduct a thorough ablation study on the proposed components to verify their effectiveness. As shown in Table 4, removing the entire GCL will result in up to  $4.5\\%$  of performance degradation, demonstrating the contribution of GCL by learning semantic alignment and unification. We also observe that removing either SA or SU results in about 2 points of performance drop on average, indicating that our method enables the vanilla contrastive learning to be more suitable for video grounding setting. Removing SSI leads to a  $3.3\\%$  drop in performance on the more stringent metric (i.e., \"R@1 IoU=0.7\"), which highlights the importance of fine-grained semantic alignment for high-quality moment retrieval. The last row shows our baseline, and our method achieves up to 6 points of performance improvement without modifying the architecture compared to the baseline, confirming the superiority of our model.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of Geodesic Distance. To demonstrate the effectiveness of the geodesic, we substitute it with different distance metrics in the model, including euclidean distance, timestamp distance, and cosine distance, and compare their performances as shown in Table 5. It can be observed that when using euclidean distance, the performances drop by up to  $5\\%$ . This is due to the fact that video representations often lie in a high dimensional manifold and euclidean distance cannot accurately quantify the correlations among video moments. When using timestamp distance, the performances decrease by  $2\\%$  on average, indicating that the temporal adjacency does not necessarily",
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "12038",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/e9973cb053574b6aa17329ae474862beff0cce59ba1f0e66b8ec4fbbd7fd350d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Inference Time</td><td>Inference Time</td></tr><tr><td>2D-TAN [75]</td><td>0.13s</td><td>32s</td></tr><tr><td>MMN [59]</td><td>0.32s</td><td>37s</td></tr><tr><td>Base Model</td><td>0.39s</td><td>40s</td></tr><tr><td>G2L(Ours)</td><td>0.84s</td><td>43s</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6. Time consumption on ActivityNet-Captions.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/16426f8df1310933afd5e9c14e649c42a076169790f2eac0e1dadc50397e4670.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            85,
+            232,
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+            328
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/f98ff92db4edb8a6f20528f0a83afc2bc213ae8763554728d6ccd146b7e166ef.jpg",
+        "image_caption": [
+            "(b)",
+            "Figure 3. Projected video moment features (a): learned representations of the previous method with vanilla contrastive learning; (b): learned representations of our method."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "correspond to semantic similarity due to the flexibility and complexity of video content. Using cosine distance results in performances dropping by up to  $3\\%$ . Due to the insufficient representation capacity of the model in the early training stage to accurately calculate similarity. We approximate the manifold structure of video features using the moment graph, where the reachability and the shortest path in the graph can facilitate similarity measurement.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The efficiency of our method. In Table 6, we compute the average training time per iteration and total inference time. Due to the K-NN graph and Shapley interaction, G2L requires more training costs. During inference, GCL and SSI can be removed thus our G2L only needs additional 3s compared to the base model.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Qualitative Analysis",
+        "text_level": 1,
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We visualize a sample video from the ActivityNetCaptions into the 2D images using t-SNE [53]. In Figure 3(a), we observe that there is a clear \"island\" in the learned representations of the previous method. We argue that it is formed by a few moments which are temporally adjacent to the ground truth. The reason is that the previous method divides positive and negative samples based on the strict temporal moment while pushing negative samples away by different queries, regardless of the semantic relationships. In contrast, our method relaxes the previous strict contrastive objective using geodesic distance, mitigating semantic overlapping and sparse annotation dilemma. Furthermore, the semantic Shapley interaction enables our model to capture discriminative features between similar moments. Our method learns aligned and uniform representations thus eliminating the \"island\" in Figure 4(b),",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We present two qualitative results from ActivityNet-",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Query: The old woman is on the chair knitting again.",
+        "bbox": [
+            514,
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+            737,
+            133
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/6e00f76a6053631d14538ee591689d935f13025efe5c8794a0da7234b521a9d9.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            131,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Query: The person sharpens the blade on the second belt.",
+        "bbox": [
+            514,
+            212,
+            756,
+            220
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/d95b64d011b941fce4c09c71f171aef4f1a53dad980ad439abaef769e49c49cf.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative results of our method on the ActivityNet-Captions."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            510,
+            220,
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+            299
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Captions in Figure 4. We observe that our approach can successfully model the relationships of temporally distant moments. For instance, \"knitting again\" in Figure 4(a) and \"the second belt\" in Figure 4(b) are far away from their first appearances. Our method can capture the information of \"first knitting\" and \"the first belt\" and infer precisely the location of the target moment. Previous contrastive learning-based methods fail to capture this semantic association due to tending to perform cross-modal contrast by the strict positional principle. These models only focus on the contextual content related to the target moment. Our method demonstrates that these large volumes of unannotated moments contain rich information and modeling their relationships can improve representation learning.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion and Future Work",
+        "text_level": 1,
+        "bbox": [
+            499,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This paper introduces a novel semantically aligned and uniform video grounding method, Geodesic and Game Localization (G2L), which explores more semantic information by measuring the correlation between video moments through the geodesic and models the nuances of similar moments using game-theoretic interactions. By contrasting the video features and query features in the shared space, the learned bi-modal features become similar when their semantics match, and the similarity between video moments is modeled by the geodesic-guided pushing operation. Extensive experiments demonstrate that our novel training objective significantly improves the performance of existing contrastive learning-based methods in video grounding. This paper provides a novel perspective for cross-modal contrastive learning. In the future, we intend to apply this idea to multi-modal pre-training.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment. This paper was partially supported by NSFC (No: 62176008) and Shenzhen Science & Technology Research Program (No: GXWD20201231165807007-20200814115301001).",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "12039",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
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+        "sub_type": "ref_text",
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+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
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+            "content": "G2L: Semantically Aligned and Uniform Video Grounding via Geodesic and Game Theory"
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+            "content": "Hongxiang Li\\(^{1}\\), Meng Cao\\(^{2,1}\\), Xuxin Cheng\\(^{1}\\), Yaowei Li\\(^{1}\\), Zhihong Zhu\\(^{1}\\), Yuexian Zou\\(^{1\\dagger}\\)"
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+            "content": "{lihongxiang,chengxx,zhihongzhu,ywl}@stu.pku.edu.cn; {mengcao,zouyx}@pku.edu.cn"
+        },
+        {
+            "type": "title",
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+            "content": "The recent video grounding works attempt to introduce vanilla contrastive learning into video grounding. However, we claim that this naive solution is suboptimal. Contrastive learning requires two key properties: (1) alignment of features of similar samples, and (2) uniformity of the induced distribution of the normalized features on the hypersphere. Due to two annoying issues in video grounding: (1) the coexistence of some visual entities in both ground truth and other moments, i.e. semantic overlapping; (2) only a few moments in the video are annotated, i.e. sparse annotation dilemma, vanilla contrastive learning is unable to model the correlations between temporally distant moments and learned inconsistent video representations. Both characteristics lead to vanilla contrastive learning being unsuitable for video grounding. In this paper, we introduce Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework via geodesic and game theory. We quantify the correlations among moments leveraging the geodesic distance that guides the model to learn the correct cross-modal representations. Furthermore, from the novel perspective of game theory, we propose semantic Shapley interaction based on geodesic distance sampling to learn fine-grained semantic alignment in similar moments. Experiments on three benchmarks demonstrate the effectiveness of our method."
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+            "content": "Query \\(\\boxed{q}\\) : The person sharpens the blade on the second belt."
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+            "content": "Figure 1. (a) Illustration of video grounding. 'GT' indicates the ground truth. A comparison of (b) existing contrastive learning-based methods and (c) our proposed G2L method. G2L makes semantically similar video moments closer in representation space while exploring nuances among similar moments."
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+            "content": "Contrastive learning [10, 23, 43] is proposed to learn representations by contrasting positive pairs against negative pairs. With the popularity of contrastive learning in vision-language tasks [34, 13, 46, 7, 5, 64, 62], several works also apply it to video grounding. Nan et al. [45] propose a dual contrast learning to learn more informative feature representations by maximizing the mutual information between the query and the corresponding video clips. This naive solution, however, achieves sub-optimum performance."
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+            "content": "Generally, contrastive learning requires two key properties [58]: alignment and uniformity. Alignment favors encoders that assign similar features to similar samples. Uniformity prefers a feature distribution that preserves maximal information, i.e., the uniform distribution on the unit hypersphere. We argue that these two issues are not satisfied in current video grounding works with contrastive learning."
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+            "content": "† Corresponding author."
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+            ],
+            "angle": 0,
+            "content": "i.e., the co-existence of some visual entities in both ground truth and other moments. As shown in Figure 1(a), the entity of 'person', 'blade' and 'belt' appear in both ground-truth moment \\( m_4 \\) and others. Since there exist no classification labels in video grounding, previous methods distinguish positive and negative samples only based on the annotated moments. This strict scheme, however, ignores the semantic overlapping among video moments, which leads to the contradiction in feature representations. As shown in Figure 1(a)(b), the moment \\( m_1 \\) of \"sharpen the blade on the first belt\" only differs from target moment \\( m_4 \\) in the 'second' order. They share similar semantic meanings but are forced to be pushed away in feature space. It is not consistent with the alignment principle of the ideal contrastive learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.336,
+                0.473,
+                0.502
+            ],
+            "angle": 0,
+            "content": "Another issue lies in the sparse annotation dilemma [67, 31]. Due to the costly labeling process, only a few moments are annotated regardless of the thousands of frames contained. Such severe data imbalance leads to significant learning bias for vanilla contrastive learning, i.e., unannotated moments are pushed away by different queries, regardless of the semantic relationships. Consequently, their representations are close, although they don't necessarily have strong semantic similarities. This undermines the uniformity requirement of contrastive learning. For example in Figure 1(b), wrong results always exist when encountering these unannotated moments (e.g., \\( m_1 \\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.505,
+                0.473,
+                0.713
+            ],
+            "angle": 0,
+            "content": "To address the issues mentioned above, we propose a novel Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework as shown in Figure 1(c). We propose to measure the similarity according to the geodesic distance [29] between two video moments along the manifold. In Figure 1(c), the geodesic distance between \\( m_4 \\) to \\( m_6 \\) is the length of the shortest path as the moment graph, i.e. \\( m_4 \\rightarrow m_2 \\rightarrow m_3 \\rightarrow m_5 \\rightarrow m_6 \\). In contrast to previous methods, we construct positive and negative pairs based on the geodesic distance rather than the temporal moment to relax the strict positional principle. The geodesics from the target moment to other moments are used to guide the maximizing mutual information. In this manner, the distance between video moments correctly reflects semantic relevance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.714,
+                0.473,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Unfortunately, the relaxed contrastive objective with geodesic leads to one side-effect, i.e., the model may confuse similar video moments. As shown in Figure 1(c), the model may falsely map \\( m_{1} \\) to be as close to the query \\( q \\) since \\( m_{1} \\) shares a similar appearance with the ground truth \\( m_{4} \\). To further prevent the model from confusing similar video moments, we formulate video moments and queries as multiple players into a cooperative game and quantify their game-theoretic interactions (i.e., Shapley interactions [49, 20]). Through this, we evaluate the marginal contributions of each fine-grained component, which leads"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.127,
+                0.895,
+                0.222
+            ],
+            "angle": 0,
+            "content": "to a more accurate division. However, computing the exact Shapley interaction for all players is an NP-hard problem [41] and is difficult to achieve solutions in the video grounding setting. Therefore, we further propose a semantic Shapley interaction module, which samples similar intravideo moments by geodesic distance with a focus on their nuances."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.518,
+                0.224,
+                0.872,
+                0.236
+            ],
+            "angle": 0,
+            "content": "In sum, our contributions are summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.239,
+                0.891,
+                0.28
+            ],
+            "angle": 0,
+            "content": "- We present G2L which introduces geodesic and game theory to learn the semantic alignment and uniformity between video and query for video grounding."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.283,
+                0.892,
+                0.323
+            ],
+            "angle": 0,
+            "content": "- We propose a novel geodesic-guided contrastive learning scheme that considers the correct semantics of all moments in the video."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.328,
+                0.891,
+                0.355
+            ],
+            "angle": 0,
+            "content": "- We introduce an effective semantic Shapley interaction strategy based on geodesic distance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.359,
+                0.891,
+                0.385
+            ],
+            "angle": 0,
+            "content": "- Extensive experiments on three public datasets demonstrate the effectiveness of our G2L."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.507,
+                0.239,
+                0.892,
+                0.385
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.4,
+                0.642,
+                0.415
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.424,
+                0.895,
+                0.728
+            ],
+            "angle": 0,
+            "content": "Video Grounding. Video grounding proposed by [18, 1], which aims to predict the start and end boundaries of the activity described by a given language query within a video. Early approaches focus on carefully designed complex video-text interaction modules. Yuan et al. [66] propose an approach which can directly predict the coordinates of the queried video clip using attention mechanism. Zeng et al. [67] propose a pyramid neural network to consider multi-scale information. Liu et al. [39] advise a memory attention to emphasize the visual features and simultaneously utilize the context information. Xu et al. [61] introduce a multi-level model to integrate visual and textual features earlier and further re-generate queries as an auxiliary task. To improve the representation of the model, several methods introduce contrastive learning or cross-modal discrimination. Ding et al. [17] propose to combine discriminative contrastive objective and generative caption objective to optimize dual-encoder. Nan et al. [45] introduce introducing causal intervention and dual contrastive learning to improve representation. In this paper, we propose to model semantic alignment and uniformity by approximate geodesics and game-theoretic interactions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.729,
+                0.895,
+                0.868
+            ],
+            "angle": 0,
+            "content": "Contrastive Learning. Contrastive learning (CL) often serves as an unsupervised objective to learn representations by contrasting positive pairs against negative pairs [10, 23, 43, 35, 12, 11]. Some prior works consider maximizing the mutual information (MI) between latent representations [24]. MI quantifies the \"amount of information\" gained about one random variable by observing another random variable [2]. Contrastive learning has been applied to vision-language tasks to learn the joint representations of visual and textual modalities [42, 51]. Sun et al. [71] pro"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.888,
+                0.506,
+                0.899
+            ],
+            "angle": 0,
+            "content": "12033"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.127,
+                0.468,
+                0.154
+            ],
+            "angle": 0,
+            "content": "pose a retrieval and localization network with contrastive learning for video corpus moment retrieval."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.155,
+                0.468,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Shapley Value. The Shapley value [49, 26] originates from cooperative game theory. It has been theoretically proven to be the unique metric to fairly estimate the contribution of each player in a cooperative game such that satisfying certain desirable axioms [60] and is widely used in deep learning. Li et al. [32] propose a semantically aligned vision-language pre-training based on Shapley value to model fine-grained semantics. Ren et al. [48] propose to explain adversarial attacks by Shapley value. Li et al. [33] propose to explicit credit assignment for multi-agent reinforcement learning using Shapley value."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.323,
+                0.433,
+                0.338
+            ],
+            "angle": 0,
+            "content": "3. Geodesic and Game Localization (G2L)"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.346,
+                0.444,
+                0.361
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Formulation and Model Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.369,
+                0.468,
+                0.576
+            ],
+            "angle": 0,
+            "content": "Let \\( Q_{i} \\) and \\( V_{i} \\) be a given textual query and untrimmed video respectively. The purpose of video grounding is to locate the most relevant video interval \\( A_{i} = (t_{i}^{s}, t_{i}^{e}) \\), where \\( t_{i}^{s} \\) and \\( t_{i}^{e} \\) are starting and ending times respectively. The key to video grounding is to learn semantics between video and query. To this end, previous methods [45, 17] incorporate vanilla contrastive learning into existing cross-modal interaction architectures. Typically, at the training stage, they employ two loss functions: video grounding loss \\( \\mathcal{L}_{\\mathrm{VG}} \\) and vanilla contrastive loss \\( \\mathcal{L}_{\\mathrm{VCL}} \\). \\( \\mathcal{L}_{\\mathrm{VG}} \\) computes the cross entry between the target timestamp and the prediction timestamp to optimize the model. \\( \\mathcal{L}_{\\mathrm{VCL}} \\) discriminates between positive samples and negative samples based on the temporal moment and adopts noise-contrastive estimation (NCE) [21] to obtain MI of videos and queries."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.578,
+                0.468,
+                0.797
+            ],
+            "angle": 0,
+            "content": "However, vanilla contrastive learning is not appropriate for video grounding due to the semantic overlapping and sparse annotation dilemma. To learn correct semantics and improve representations, as illustrated in Figure 2, we propose Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework that germinates from geodesic and cooperative game theory. Our G2L learns semantic alignment and uniformity from two components. With geodesic-guided contrastive learning (GCL), complete semantic alignment and uniformly distributed video features are learned. By semantic Shapley interaction(SSI), we learn the fine-grained semantic alignment between similar moments and target queries. Combined with the two novel proposed training objectives, the full training objective of semantically aligned and uniform video grounding can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.183,
+                0.811,
+                0.468,
+                0.827
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {V G}} + \\mathcal {L} _ {\\mathrm {G C L}} + \\mathcal {L} _ {\\mathrm {S S I}} \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.839,
+                0.468,
+                0.866
+            ],
+            "angle": 0,
+            "content": "During inference, it can be directly removed, rendering a semantics-sensitive dual encoder."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.126,
+                0.665,
+                0.139
+            ],
+            "angle": 0,
+            "content": "3.2. Feature Encoder"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.147,
+                0.892,
+                0.258
+            ],
+            "angle": 0,
+            "content": "Video Encoder. For an input video \\( V_{i} \\), we first segment it into small video clips and perform a fixed-interval sampling over these clips. Then the video clips are fed into a pretrained 3D CNN model (e.g. C3D) to extract the video features \\( F_{i}^{V} \\). Referring to the previous works [75], we employ sparse sampling and a proposal network to construct the feature map \\( F_{i}^{M} = \\{m_{i}\\}_{i=1}^{N_{m}} \\) of moment candidates based on \\( F_{i}^{V} \\), where \\( N_{m} \\) is the number of proposals in the video."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.258,
+                0.892,
+                0.327
+            ],
+            "angle": 0,
+            "content": "Query Encoder. For a textual query \\( Q_{i} \\), we generate the tokens of words by the tokenizer and add a class embedding token '[CLS]' in the beginning. Then the tokens are fed into pre-trained BERT [27], and we perform average pooling of its last two hidden states to obtain the sentence feature \\( q_{i} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.334,
+                0.782,
+                0.348
+            ],
+            "angle": 0,
+            "content": "3.3. Geodesic Distance Computation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.355,
+                0.892,
+                0.493
+            ],
+            "angle": 0,
+            "content": "Video content is intricate and flexible, and for video clips, temporal proximity does not always equate to semantic similarity. Conversely, two video clips can have strong correlations even though they are temporally distant. We propose to measure correlations of video representations using the geodesic distance. Formally, we define a mini-batch of video-query pairs as \\(\\{V_i, Q_i\\}_{i=1}^B\\), where \\(B\\) is the size of the mini-batch. After fed into the video and query encoders, we obtain textual representation \\(L = \\{q_i\\}_{i=1}^B\\) and moment representations \\(M = \\{m_i\\}_{i=1}^{B \\times N_m}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.494,
+                0.892,
+                0.716
+            ],
+            "angle": 0,
+            "content": "The video moments representations may lie in a high-dimensional manifold, and our purpose is to measure the geodesic distance between two points along the manifold. However, computing the exact geodesic distance [29] is difficult without explicit knowledge of the manifold structure. To obtain the geodesic distance, we first employ the K-NN graph [15] to approximate the manifold structure [52, 14]. In this graph, each moment \\( m_{i} \\) forms a node, and each node connects to at most \\( n \\) other nodes. A directed edge exists from node \\( m_{i} \\) to node \\( m_{j} \\) if node \\( m_{j} \\) is among the \\( n \\) nearest neighbors of \\( m_{i} \\). The edge weight \\( d(m_{i},m_{j}) \\) is defined using cosine similarity: \\( d(m_{i},m_{j}) = 1 - m_{i}m_{j}^{\\top} \\). Finally, we utilize the shortest path algorithm, i.e., Dijkstra [16], to compute the length of the shortest path between two moments along the obtained weighted directed graph as the geodesic distance \\( \\mathcal{G}(m_i,m_j) \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.721,
+                0.833,
+                0.736
+            ],
+            "angle": 0,
+            "content": "3.4. Geodesic-guided Contrastive Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.742,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Previous Contrastive Scheme. In video grounding, a query usually corresponds to multiple clips. An intuitive method [17] to learn representations is to set the clips in ground truth intervals as positive samples, while others are negatives. Another scheme [59] is to calculate the intersection over union (IoU) between the ground truth and other moments, where those with higher IoU are considered as positive samples and the lower ones are regarded as negative samples. Then they learn the joint representation by"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.888,
+                0.505,
+                0.899
+            ],
+            "angle": 0,
+            "content": "12034"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.123,
+                0.87,
+                0.341
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.349,
+                0.895,
+                0.427
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overview of Geodesic and Game Localization (G2L). Our framework encourages the model to learn semantically aligned and uniform joint representations. In the inference stage, we directly fuse the video features and query features to compute the predicted moments. In the training stage, the grounding loss \\(\\mathcal{L}_{\\mathrm{VG}}\\) is obtained by calculating the cross-entropy between the predicted moment and the target moment. Then, we approximate the high-dimensional manifold structure of the video representations through a moment graph and calculate the geodesic distance from the target moment to other moments. Finally, we leverage geodesic distance for cross-modal discrimination and semantic Sharpley interaction modeling."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.449,
+                0.471,
+                0.505
+            ],
+            "angle": 0,
+            "content": "pulling the query features and ground truth moment features together, and pushing the query features and non-ground truth moment features apart. The previous contrastive loss \\(\\mathcal{L}_{\\mathrm{VCL}}\\) can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.124,
+                0.513,
+                0.47,
+                0.565
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {V C L}} = - \\sum_ {i = 1} ^ {B} \\left(\\log \\frac {\\exp \\left(q _ {i} m _ {i} ^ {\\top} / \\tau\\right)}{\\sum_ {m _ {j} \\in M} \\exp \\left(q _ {i} m _ {j} ^ {\\top} / \\tau\\right)}\\right) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.574,
+                0.373,
+                0.587
+            ],
+            "angle": 0,
+            "content": "where \\(\\tau\\) is the temperature hyper-parameter."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.587,
+                0.47,
+                0.656
+            ],
+            "angle": 0,
+            "content": "While intuitive, such a manner fails to capture semantic alignment and uniformity between queries and video content. To learn complete semantic alignment and uniformity for video grounding, we propose geodesic-guided contrastive learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.657,
+                0.471,
+                0.837
+            ],
+            "angle": 0,
+            "content": "Semantic Alignment. In vanilla supervised contrastive learning [56, 28], all classes play the same role: pulling is done within every class and pushing between every pair of different classes. Such uniform contrastive learning works well for symmetric and equal cross-modal learning. In fact, due to semantic overlapping, the semantics of the video and text are asymmetric and unequal in video grounding. Temporally distant moments may have similar semantics. To model semantic alignment, we discriminate positive pairs based on the geodesic distance instead of the temporal moment. For a query feature \\( q_{i} \\), we define the \\( k \\) moments with the closest geodesic distance from the target moment \\( \\hat{m}_i \\in M \\) as its semantic positive samples \\( P_{i} \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.155,
+                0.845,
+                0.47,
+                0.871
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {i} = \\left\\{p _ {i} ^ {k} \\right\\} = \\underset {k} {\\arg \\operatorname {t o p k}} \\mathcal {G} (\\hat {m} _ {i}, m _ {k}) \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.449,
+                0.892,
+                0.49
+            ],
+            "angle": 0,
+            "content": "\\(P_{i}\\) contains \\(m_{i}\\) and moments adjacent to \\(m_{i}\\) geodesic which is used to construct positive pairs with \\(q_{i}\\) to relax the previous strict positional principle."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.49,
+                0.893,
+                0.642
+            ],
+            "angle": 0,
+            "content": "Semantic Uniformity. Due to the sparse annotation dilemma [67, 31], most of the moments are only marked as negative while pushed away by different queries. Notably, this push operation is undifferentiated, i.e., the model is encouraged to learn to push all unannotated moments from the annotated ones. This clearly undermines the model to learn correct semantics. To learn semantic uniformity, we introduce the geodesic distance to differentially push negative samples away from the query based on semantic relationships. The similarity between query and moment \\( s(q_i, m_j) \\) is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.5,
+                0.659,
+                0.892,
+                0.701
+            ],
+            "angle": 0,
+            "content": "\\[\ns \\left(q _ {i}, m _ {j}\\right) = \\exp \\left(q _ {i} m _ {j} ^ {\\top} \\left(\\hat {m} _ {i} m _ {j} ^ {\\top} \\log \\frac {1}{\\exp \\left(\\mathcal {G} \\left(\\hat {m} _ {i} , m _ {j}\\right) + 1\\right)}\\right)\\right) \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.702,
+                0.892,
+                0.757
+            ],
+            "angle": 0,
+            "content": "We assign corresponding weights according to the geodesic distance \\(\\mathcal{G}(\\hat{m}_i, m_j)\\) between the target moment \\(\\hat{m}_i\\) and all moments \\(m_j\\). \\(s(q_i, m_j)\\) considers the relationships between negative samples while maximizing mutual information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.757,
+                0.892,
+                0.783
+            ],
+            "angle": 0,
+            "content": "Finally, our geodesic-guided contrastive loss can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.547,
+                0.787,
+                0.892,
+                0.849
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {G C L}} = - \\sum_ {i = 1} ^ {B} \\left(\\log \\frac {\\sum_ {p _ {i} ^ {k} \\in P _ {i}} \\exp \\left(q _ {i} p _ {i} ^ {k} ^ {\\top} / \\tau\\right)}{\\sum_ {m _ {j} \\in M} s \\left(q _ {i} , m _ {j}\\right) / \\tau}\\right) \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.853,
+                0.892,
+                0.868
+            ],
+            "angle": 0,
+            "content": "In contrast to Equation 2, \\(\\mathcal{L}_{\\mathrm{GCL}}\\) is designed for representa"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.888,
+                0.505,
+                0.899
+            ],
+            "angle": 0,
+            "content": "12035"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.127,
+                0.435,
+                0.141
+            ],
+            "angle": 0,
+            "content": "tion learning rather than directly learning localization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.149,
+                0.418,
+                0.164
+            ],
+            "angle": 0,
+            "content": "3.5. Semantic Shapley Interaction Modeling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.17,
+                0.47,
+                0.226
+            ],
+            "angle": 0,
+            "content": "To prevent the model from confusing similar video moments due to the relaxed contrastive objective in Equation 3, we propose semantic Shapley interaction to model fine-grained semantic alignment."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.232,
+                0.226,
+                0.245
+            ],
+            "angle": 0,
+            "content": "3.5.1 Preliminaries"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.254,
+                0.471,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Shapley Value. The Shapley value [49] is a classical game theory solution for the unbiased estimation of the contribution of each player in a cooperation game. Assume a game consists of \\(\\mathcal{N}\\) players, \\(\\mathcal{U} \\subseteq \\mathcal{N}\\) represents a potential subset of players. A game function \\(f(\\cdot)\\) maps each subset \\(\\mathcal{U}\\) of players to a score, estimating the cooperated contribution of a set of players. For a player \\(i\\), its Shapley value \\(\\phi(i|\\mathcal{N})\\) is computed as the average marginal contribution of player \\(i\\) to all possible coalitions \\(\\mathcal{U}\\) without \\(i\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.119,
+                0.389,
+                0.47,
+                0.452
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\phi (i \\mid \\mathcal {N}) = \\sum_ {\\mathcal {U} \\subseteq \\mathcal {N} \\backslash \\{i \\}} p (\\mathcal {U}) [ f (\\mathcal {U} \\cup \\{i \\}) - f (\\mathcal {U}) ] (6) \\\\ p (\\mathcal {U}) = \\frac {| \\mathcal {U} | ! (| \\mathcal {N} | - | \\mathcal {U} | - 1) !}{| \\mathcal {N} | !} (7) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.462,
+                0.469,
+                0.531
+            ],
+            "angle": 0,
+            "content": "where \\( p(\\mathcal{U}) \\) is the likelihood of \\( \\mathcal{U} \\) being sampled. The Shapley value has been proved to be the unique metric that satisfies the following axioms: Linearity, Symmetry, Dummy, and Efficiency. We summarize these axioms in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.532,
+                0.469,
+                0.682
+            ],
+            "angle": 0,
+            "content": "Shapley Interaction. In game theory, some players tend to form a small cooperative coalition and always participate in the game together. This cooperation provides additional contributions to the game. The Shapley interaction [20] measures the additional contributions made by the coalition compared to players working individually. We define \\([\\mathcal{U}]\\) as a single hypothetical player, which is the union of the players in \\(\\mathcal{U}\\). A reduced game is formed by removing the individual players in \\(\\mathcal{U}\\) from the game and adding \\([\\mathcal{U}]\\) to the game. Finally, according to Equation 6, the Shapley interaction for coalition \\(\\mathcal{U}\\) is formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.085,
+                0.692,
+                0.469,
+                0.721
+            ],
+            "angle": 0,
+            "content": "\\[\n\\Im ([ \\mathcal {U} ]) = \\phi ([ \\mathcal {U} ] \\mid \\mathcal {N} \\backslash \\mathcal {U} \\cup \\{[ \\mathcal {U} ] \\}) - \\sum_ {i \\in \\mathcal {U}} \\phi (i \\mid \\mathcal {N} \\backslash \\mathcal {U} \\cup \\{i \\}) \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.731,
+                0.469,
+                0.772
+            ],
+            "angle": 0,
+            "content": "where \\(\\Im ([\\mathcal{U}])\\) reflects the interactions inside \\(\\mathcal{U}\\). The higher value of \\(\\Im ([\\mathcal{U}])\\) indicates that players in \\(\\mathcal{U}\\) cooperate closely with each other."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.79,
+                0.455,
+                0.805
+            ],
+            "angle": 0,
+            "content": "3.5.2 Fine-Grained Semantic Alignment via Shapley"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.812,
+                0.469,
+                0.867
+            ],
+            "angle": 0,
+            "content": "According to Equation 6 and Equation 8, it can be known that the computational complexity of the Shapley interaction grows factorially as the number of players increases. To reduce the computational cost, we propose semantic"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.127,
+                0.892,
+                0.21
+            ],
+            "angle": 0,
+            "content": "Shapley interaction based on geodesic distance sampling. Specifically, as in Equation 3, we sample semantic similar moments based on geodesic distances to investigate their nuances. Then, we consider queries and semantic similar moments from the same video as players in the same cooperative game."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.213,
+                0.892,
+                0.326
+            ],
+            "angle": 0,
+            "content": "To avoid confusion with the previous symbols, we define \\(\\mathcal{H}_i^V = \\{\\mathbf{h}_{ix}^V\\}_{x=1}^{N_i^v}\\) and \\(\\mathcal{H}_i^Q = \\{\\mathbf{h}_{iy}^Q\\}_{y=1}^{N_i^q}\\) are a set of semantic positive samples and queries from the video \\(V_i\\) respectively, where \\(N_i^v = KN_i^q\\) and \\(N_i^q\\) indicate the number of similar moments and queries in video \\(V_i\\) respectively. \\(K\\) is the number of moments sampled for each query \\(\\mathbf{h}_{iy}^Q\\). We investigate the effect of \\(K\\) on computational cost and performance in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.329,
+                0.892,
+                0.53
+            ],
+            "angle": 0,
+            "content": "If a query and a video moment have strong semantic correspondence, then they tend to cooperate with each other and contribute to the coalition. Thus, we can take \\(\\mathcal{H}^i = \\mathcal{H}_i^V \\cup \\mathcal{H}_i^Q\\) as the players in the same game inspired by [32]. We define the alignment matrix as: \\(\\mathcal{A}_i = [a_{xy}^i]\\), where \\(a_{xy}^i = h_{ix}^{V^\\top}h_{iy}^Q\\) represents the alignment score between \\(x\\)-th moment and \\(y\\)-th query in video \\(V_i\\). Next, \\(\\tilde{\\mathcal{A}}_i\\) is obtained by applying softmax-normalization over each row of \\(\\mathcal{A}_i\\). Then we average the maximum alignment score \\(\\max_y \\tilde{a}_{xy}^i\\) as the fine-grained moment-to-query similarity \\(\\psi_1\\). Similarly, we can obtain the fine-grained query-to-moment similarity \\(\\psi_2\\). The total fine-grained similarity score can be defined: \\(\\psi = (\\psi_1 + \\psi_2) / 2\\), which be considered as the game score \\(f(\\cdot)\\) in our game."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.533,
+                0.892,
+                0.56
+            ],
+            "angle": 0,
+            "content": "According to Equation 8, the semantic Shapley interaction of them can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.501,
+                0.577,
+                0.891,
+                0.681
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\Im \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right]\\right) = \\phi \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right] \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\{\\left[ \\mathcal {H} _ {x y} ^ {i} \\right] \\}\\right) \\\\ - \\phi \\left(\\mathbf {h} _ {i x} ^ {V} \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\left\\{\\mathbf {h} _ {i x} ^ {V} \\right\\}\\right) \\\\ - \\phi \\left(\\mathbf {h} _ {i y} ^ {Q} \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\left\\{\\mathbf {h} _ {i y} ^ {Q} \\right\\}\\right) (9) \\\\ = \\mathbb {E} _ {\\mathcal {C}} \\left\\{\\underset {| \\mathcal {U} | = \\mathcal {C}} {\\mathcal {U} \\subseteq \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i}} \\mathbb {E} \\left[ f \\left(\\mathcal {U} \\cup \\mathcal {H} _ {x y} ^ {i}\\right) - f \\left(\\mathcal {U} \\cup \\left\\{\\mathbf {h} _ {i x} ^ {V} \\right\\}\\right) \\right. \\right. \\\\ \\left. - f \\left(\\mathcal {U} \\cup \\left\\{\\mathbf {h} _ {i y} ^ {Q} \\right\\}\\right) + f (\\mathcal {U}) \\right] \\rbrace (10) \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.697,
+                0.892,
+                0.766
+            ],
+            "angle": 0,
+            "content": "where \\(\\Im \\left(\\left[\\mathcal{H}_{xy}^{i}\\right]\\right)\\) represents the single player formed by the coalition of \\(x\\)-th moment and \\(y\\)-th query in video \\(V_{i}, \\mathcal{C}\\) represents the coalition size. We take normalized \\(\\Im'\\left(\\left[\\mathcal{H}_{xy}^{i}\\right]\\right)\\) as soft labels, the fine-grained semantic alignment loss can be defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.512,
+                0.782,
+                0.891,
+                0.822
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {S S I}} = - \\sum_ {i = 1} ^ {T} \\frac {1}{N _ {i} ^ {v} N _ {i} ^ {q}} \\sum_ {x = 1} ^ {N _ {i} ^ {v}} \\sum_ {y = 1} ^ {N _ {i} ^ {q}} \\Im^ {\\prime} \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right]\\right) \\log \\left(\\tilde {a} _ {x y} ^ {i}\\right) \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.839,
+                0.891,
+                0.867
+            ],
+            "angle": 0,
+            "content": "where \\(T\\) is the total number of unique videos in a minibatch, i.e. \\(T \\leq B\\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.888,
+                0.505,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12036"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.123,
+                0.465,
+                0.449
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>CTRL [18]</td><td>29.01</td><td>10.34</td><td>59.17</td><td>37.54</td></tr><tr><td>ACRN [39]</td><td>31.67</td><td>11.25</td><td>60.34</td><td>38.57</td></tr><tr><td>TripNet [22]</td><td>32.19</td><td>13.93</td><td>-</td><td>-</td></tr><tr><td>SCDM [65]</td><td>36.75</td><td>19.86</td><td>64.99</td><td>41.53</td></tr><tr><td>LGI [44]</td><td>41.51</td><td>23.07</td><td></td><td></td></tr><tr><td>VSLNet [73]</td><td>43.22</td><td>26.16</td><td>-</td><td>-</td></tr><tr><td>2D-TAN [75]</td><td>44.51</td><td>26.54</td><td>77.13</td><td>61.96</td></tr><tr><td>DRN [67]</td><td>45.45</td><td>24.39</td><td>77.97</td><td>50.30</td></tr><tr><td>DPIN [54]</td><td>47.27</td><td>28.31</td><td>77.45</td><td>60.03</td></tr><tr><td>CBLN [37]</td><td>48.12</td><td>27.60</td><td>79.32</td><td>63.41</td></tr><tr><td>SMIN [55]</td><td>48.46</td><td>30.34</td><td>81.16</td><td>62.11</td></tr><tr><td>MATN [74]</td><td>48.02</td><td>31.78</td><td>78.02</td><td>63.18</td></tr><tr><td>GTR [4]</td><td>50.57</td><td>29.11</td><td>80.43</td><td>65.14</td></tr><tr><td>CMAS [63]</td><td>46.23</td><td>29.48</td><td>77.04</td><td>60.25</td></tr><tr><td>MMN [59]</td><td>48.59</td><td>29.26</td><td>79.50</td><td>64.76</td></tr><tr><td>CL-based:</td><td></td><td></td><td></td><td></td></tr><tr><td>IVG-DCL [45]</td><td>43.84</td><td>27.10</td><td>-</td><td>-</td></tr><tr><td>SSCS [17]</td><td>46.67</td><td>27.56</td><td>78.37</td><td>63.78</td></tr><tr><td>G2L (ours)</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.459,
+                0.468,
+                0.484
+            ],
+            "angle": 0,
+            "content": "Table 1. Performance comparisons on ActivityNet-Captions using C3D features."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.496,
+                0.208,
+                0.511
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.52,
+                0.3,
+                0.535
+            ],
+            "angle": 0,
+            "content": "4.1. Datasets and Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.543,
+                0.468,
+                0.64
+            ],
+            "angle": 0,
+            "content": "ActivityNet-Captions. ActivityNet-Captions [30] contains 20,000 untrimmed videos and 100,000 descriptions [3], covering a wide range of complex human behavior. The video clips with annotations have much larger variations. Following the public split [75], we use 37417, 17505 and 17031 sentence-video pairs for training, validation and testing, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.642,
+                0.468,
+                0.752
+            ],
+            "angle": 0,
+            "content": "Charades-STA. The Charades dataset [50] is collected for video action recognition and video captioning. Gao et al. [18] adapt the Charades dataset to the video grounding task by collecting the query annotations. The Charades-STA dataset contains 6672 videos and involves 16128 video-query pairs, where 12408 pairs are used for training and 3720 for testing. We follow the same split of the dataset as in Gao et al. [18] for fair comparisons."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.754,
+                0.468,
+                0.81
+            ],
+            "angle": 0,
+            "content": "TACoS. TACoS [47] contains 127 videos from the cooking scenarios. We follow the standard split [18], which has 10146, 4589 and 4083 video query pairs for training, validation and testing, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.811,
+                0.468,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Evaluation. Following previous work [18, 75], we adopt \"R@n, IoU=m\" as the evaluation metric. It calculates the percentage of IoU greater than \"m\" between at least one of the top \"n\" video moments retrieved and the ground truth."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.511,
+                0.124,
+                0.883,
+                0.358
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>MCN [1]</td><td>17.46</td><td>8.01</td><td>48.22</td><td>26.73</td></tr><tr><td>SAP [9]</td><td>27.42</td><td>13.36</td><td>66.37</td><td>38.15</td></tr><tr><td>TripNet [22]</td><td>36.61</td><td>14.50 -</td><td>-</td><td></td></tr><tr><td>MAN [70]</td><td>41.21</td><td>20.54</td><td>83.21</td><td>51.85</td></tr><tr><td>2D-TAN [75]</td><td>39.70</td><td>23.31</td><td>80.32</td><td>51.26</td></tr><tr><td>DRN [67]</td><td>42.90</td><td>23.68</td><td>87.80</td><td>54.87</td></tr><tr><td>FVMR [19]</td><td>42.36</td><td>24.14</td><td>83.97</td><td>50.15</td></tr><tr><td>CBLN [37]</td><td>43.67</td><td>24.44</td><td>88.39</td><td>56.49</td></tr><tr><td>MMRG [68]</td><td>44.25</td><td>-</td><td>60.22</td><td>-</td></tr><tr><td>MMN [59]</td><td>47.31</td><td>27.28</td><td>83.74</td><td>58.41</td></tr><tr><td>CL-based:SSCS [17]</td><td>43.15</td><td>25.54</td><td>84.26</td><td>54.17</td></tr><tr><td>G2L(Ours)</td><td>47.91</td><td>28.42</td><td>84.80</td><td>59.33</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.367,
+                0.892,
+                0.392
+            ],
+            "angle": 0,
+            "content": "Table 2. Performance comparisons on Charades-STA using VGG features."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.401,
+                0.716,
+                0.416
+            ],
+            "angle": 0,
+            "content": "4.2. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.422,
+                0.892,
+                0.657
+            ],
+            "angle": 0,
+            "content": "For a fair comparison, we extracted video features from a pre-trained 3D CNN (C3D for ActivityNet-Captions and TACoS, VGG for Charades-STA) following previous works [59, 17, 45]. We uniformly sampled (256, 32, 256) clips as the input video sequence and set the length of 2D feature map [75] (64, 16, 128) for ActivityNet-Captions, Charades-STA, and TACoS, respectively. For the language query, the pre-trained BERT[27] was employed for each word of the query. The average pooling outputs of the first and last layers were used to obtain the embedding of the whole sentence. We employed the AdamW optimizer [40] to train our model and set the temperature weight \\(\\tau\\) to 0.1. The learning rates were set to \\((8\\times 10^{-4},8\\times 10^{-4},1\\times 10^{-4})\\) for ActivityNet-Captions, Charades-STA, and TACoS, respectively. We conducted experiments on 8 A100 GPUs with batch size 48 for ActivityNet-Captions and Charades-STA, and on 4 A100 GPUs with batch size 8 for TACoS."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.666,
+                0.871,
+                0.68
+            ],
+            "angle": 0,
+            "content": "4.3. Comparisons with State-of-the-art Methods"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.687,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Comparison on ActivityNet-Captions. In Table 1, we report our performance in comparison with other state-of-the-art methods on ActivityNet-Captions. Compared with IVG-DCL [45] and SSCS [17], which are also based on contrastive learning, our method achieves significant improvements. Notably, ActivityNet-Captions is currently the dataset with the most severe semantic overlapping and sparse annotation dilemma. We observe that our model showed even more significant improvements on ActivityNet-Captions, achieving absolute improvements of up to \\(7.8\\%\\) and \\(5.7\\%\\) compared to IVG-DCL [45] and SSCS [17], respectively. They encourage the model to focus on cross-modal alignment in favor of grounding while ig-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.888,
+                0.505,
+                0.899
+            ],
+            "angle": 0,
+            "content": "12037"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.082,
+                0.123,
+                0.467,
+                0.365
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>R@1 IoU0.3</td><td>R@1 IoU0.5</td><td>R@5 IoU0.3</td><td>R@5 IoU0.5</td></tr><tr><td>CTRL [18]</td><td>18.32</td><td>13.30</td><td>36.69</td><td>25.42</td></tr><tr><td>CBP [57]</td><td>27.31</td><td>24.79</td><td>43.64</td><td>37.40</td></tr><tr><td>SCDM [65]</td><td>26.11</td><td>21.17</td><td>40.16</td><td>32.18</td></tr><tr><td>2D-TAN [75]</td><td>37.29</td><td>25.32</td><td>57.81</td><td>45.04</td></tr><tr><td>DRN [67]</td><td>-</td><td>23.17</td><td>-</td><td>33.36</td></tr><tr><td>CMIN [76]</td><td>24.64</td><td>18.05</td><td>-</td><td>-</td></tr><tr><td>CSMGAN [38]</td><td>33.90</td><td>27.09</td><td>53.98</td><td>41.22</td></tr><tr><td>CBLN [37]</td><td>38.98</td><td>27.65</td><td>59.96</td><td>46.24</td></tr><tr><td>MMN [59]</td><td>39.24</td><td>26.17</td><td>62.03</td><td>47.39</td></tr><tr><td>GTR [4]</td><td>40.39</td><td>30.22</td><td>61.94</td><td>47.73</td></tr><tr><td>FVMR [19]</td><td>41.48</td><td>29.12</td><td>64.53</td><td>50.00</td></tr><tr><td>CL-based:</td><td></td><td></td><td></td><td></td></tr><tr><td>IVG-DCL [45]</td><td>38.84</td><td>29.07</td><td>-</td><td>-</td></tr><tr><td>SSCS [17]</td><td>41.33</td><td>29.56</td><td>60.65</td><td>48.01</td></tr><tr><td>G2L(Ours)</td><td>42.74</td><td>30.95</td><td>65.83</td><td>49.86</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.081,
+                0.376,
+                0.467,
+                0.387
+            ],
+            "angle": 0,
+            "content": "Table 3. Performance comparisons on TACoS using C3D features."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.406,
+                0.467,
+                0.46
+            ],
+            "angle": 0,
+            "content": "noring the semantics among full moments, especially unannotated moments. In contrast, our method conducts cross-modal discrimination guided by the geodesic distance such that overcoming data bias."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.464,
+                0.468,
+                0.712
+            ],
+            "angle": 0,
+            "content": "Comparison on Charades-STA. Table 2 reports the result comparison between state-of-the-art methods on Charades-STA. Compared with SSCS [17], our method achieves a performance improvement of up to \\(5.1\\%\\). On more stringent evaluation metrics, such as “R@1 IoU=0.7”, our method achieves a performance improvement of \\(1.1\\%\\) compared to the cutting-edge method MMN [59], which indicates that exploring fine-grained semantic alignment information between similar video moments can improve grounding quality. Notably, MMN [59] and SSCS [17] have similar loss functions, and MMN [59] from a perspective on temporal grounding as a metric-learning problem proposes a mutual matching network to enhance joint representation learning by mining more negative samples achieving better performances. However, it also constructs cross-modal pairs based on the temporal moment, which results in a large number of constructed negative pairs containing potential weak semantic positive pairs, thus hindering learning."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.715,
+                0.468,
+                0.865
+            ],
+            "angle": 0,
+            "content": "Comparison on TACoS. Table 3 summarizes the comparisons on the TACoS. We observe that our model achieves state-of-the-art results in most settings. However, the performance gain on this dataset is smaller than the previous three datasets. The reason is that the sparse annotation dilemma and semantic overlapping are insignificant on TACoS. It contains only 127 videos but has about 20,000 queries and focuses on cooking activities with more uniform objects, roles, and actions. Nevertheless, our method still outperforms previous contrastive learning-based methods in various metrics."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.123,
+                0.885,
+                0.251
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>Full Model</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr><tr><td>w/o SA</td><td>50.85</td><td>30.73</td><td>79.22</td><td>65.47</td></tr><tr><td>w/o SU</td><td>49.10</td><td>31.14</td><td>79.48</td><td>65.46</td></tr><tr><td>w/o GCL</td><td>48.74</td><td>28.62</td><td>78.89</td><td>64.44</td></tr><tr><td>w/o SSI</td><td>50.65</td><td>30.01</td><td>79.54</td><td>66.76</td></tr><tr><td>w/o GCL+SSI</td><td>45.74</td><td>26.74</td><td>77.26</td><td>61.64</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.503,
+                0.261,
+                0.891,
+                0.299
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation studies of main components on ActivityNetCaptions. \"SA\" and \"SU\" denote the Semantic Alignment and the Semantic Uniformity in GCL, respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.31,
+                0.875,
+                0.398
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Metric</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>Euclidean</td><td>47.83</td><td>28.44</td><td>79.42</td><td>65.46</td></tr><tr><td>Timestamp</td><td>49.85</td><td>29.73</td><td>78.15</td><td>65.47</td></tr><tr><td>Cosine</td><td>50.94</td><td>30.09</td><td>79.57</td><td>65.84</td></tr><tr><td>Geodesic</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.503,
+                0.407,
+                0.89,
+                0.432
+            ],
+            "angle": 0,
+            "content": "Table 5. Comparison of different distance metrics on ActivityNet-Captions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.443,
+                0.649,
+                0.458
+            ],
+            "angle": 0,
+            "content": "5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.466,
+                0.89,
+                0.7
+            ],
+            "angle": 0,
+            "content": "Effectiveness of Individual Components. In Table 4, we conduct a thorough ablation study on the proposed components to verify their effectiveness. As shown in Table 4, removing the entire GCL will result in up to \\(4.5\\%\\) of performance degradation, demonstrating the contribution of GCL by learning semantic alignment and unification. We also observe that removing either SA or SU results in about 2 points of performance drop on average, indicating that our method enables the vanilla contrastive learning to be more suitable for video grounding setting. Removing SSI leads to a \\(3.3\\%\\) drop in performance on the more stringent metric (i.e., \"R@1 IoU=0.7\"), which highlights the importance of fine-grained semantic alignment for high-quality moment retrieval. The last row shows our baseline, and our method achieves up to 6 points of performance improvement without modifying the architecture compared to the baseline, confirming the superiority of our model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.701,
+                0.89,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Effectiveness of Geodesic Distance. To demonstrate the effectiveness of the geodesic, we substitute it with different distance metrics in the model, including euclidean distance, timestamp distance, and cosine distance, and compare their performances as shown in Table 5. It can be observed that when using euclidean distance, the performances drop by up to \\(5\\%\\). This is due to the fact that video representations often lie in a high dimensional manifold and euclidean distance cannot accurately quantify the correlations among video moments. When using timestamp distance, the performances decrease by \\(2\\%\\) on average, indicating that the temporal adjacency does not necessarily"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.468,
+                0.888,
+                0.504,
+                0.898
+            ],
+            "angle": 0,
+            "content": "12038"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.1,
+                0.123,
+                0.449,
+                0.198
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Inference Time</td><td>Inference Time</td></tr><tr><td>2D-TAN [75]</td><td>0.13s</td><td>32s</td></tr><tr><td>MMN [59]</td><td>0.32s</td><td>37s</td></tr><tr><td>Base Model</td><td>0.39s</td><td>40s</td></tr><tr><td>G2L(Ours)</td><td>0.84s</td><td>43s</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.115,
+                0.206,
+                0.432,
+                0.22
+            ],
+            "angle": 0,
+            "content": "Table 6. Time consumption on ActivityNet-Captions."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.233,
+                0.273,
+                0.329
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.171,
+                0.333,
+                0.187,
+                0.342
+            ],
+            "angle": 0,
+            "content": "(a)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.276,
+                0.233,
+                0.464,
+                0.331
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.362,
+                0.333,
+                0.378,
+                0.342
+            ],
+            "angle": 0,
+            "content": "(b)"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.077,
+                0.349,
+                0.47,
+                0.388
+            ],
+            "angle": 0,
+            "content": "Figure 3. Projected video moment features (a): learned representations of the previous method with vanilla contrastive learning; (b): learned representations of our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.402,
+                0.469,
+                0.514
+            ],
+            "angle": 0,
+            "content": "correspond to semantic similarity due to the flexibility and complexity of video content. Using cosine distance results in performances dropping by up to \\(3\\%\\). Due to the insufficient representation capacity of the model in the early training stage to accurately calculate similarity. We approximate the manifold structure of video features using the moment graph, where the reachability and the shortest path in the graph can facilitate similarity measurement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.513,
+                0.469,
+                0.596
+            ],
+            "angle": 0,
+            "content": "The efficiency of our method. In Table 6, we compute the average training time per iteration and total inference time. Due to the K-NN graph and Shapley interaction, G2L requires more training costs. During inference, GCL and SSI can be removed thus our G2L only needs additional 3s compared to the base model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.608,
+                0.273,
+                0.625
+            ],
+            "angle": 0,
+            "content": "6. Qualitative Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.632,
+                0.469,
+                0.852
+            ],
+            "angle": 0,
+            "content": "We visualize a sample video from the ActivityNetCaptions into the 2D images using t-SNE [53]. In Figure 3(a), we observe that there is a clear \"island\" in the learned representations of the previous method. We argue that it is formed by a few moments which are temporally adjacent to the ground truth. The reason is that the previous method divides positive and negative samples based on the strict temporal moment while pushing negative samples away by different queries, regardless of the semantic relationships. In contrast, our method relaxes the previous strict contrastive objective using geodesic distance, mitigating semantic overlapping and sparse annotation dilemma. Furthermore, the semantic Shapley interaction enables our model to capture discriminative features between similar moments. Our method learns aligned and uniform representations thus eliminating the \"island\" in Figure 4(b),"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.853,
+                0.469,
+                0.867
+            ],
+            "angle": 0,
+            "content": "We present two qualitative results from ActivityNet-"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.515,
+                0.124,
+                0.738,
+                0.134
+            ],
+            "angle": 0,
+            "content": "Query: The old woman is on the chair knitting again."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.513,
+                0.133,
+                0.882,
+                0.209
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.515,
+                0.213,
+                0.757,
+                0.222
+            ],
+            "angle": 0,
+            "content": "Query: The person sharpens the blade on the second belt."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.512,
+                0.222,
+                0.881,
+                0.3
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.304,
+                0.892,
+                0.331
+            ],
+            "angle": 0,
+            "content": "Figure 4. Qualitative results of our method on the ActivityNet-Captions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.345,
+                0.892,
+                0.553
+            ],
+            "angle": 0,
+            "content": "Captions in Figure 4. We observe that our approach can successfully model the relationships of temporally distant moments. For instance, \"knitting again\" in Figure 4(a) and \"the second belt\" in Figure 4(b) are far away from their first appearances. Our method can capture the information of \"first knitting\" and \"the first belt\" and infer precisely the location of the target moment. Previous contrastive learning-based methods fail to capture this semantic association due to tending to perform cross-modal contrast by the strict positional principle. These models only focus on the contextual content related to the target moment. Our method demonstrates that these large volumes of unannotated moments contain rich information and modeling their relationships can improve representation learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.566,
+                0.771,
+                0.581
+            ],
+            "angle": 0,
+            "content": "7. Conclusion and Future Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.59,
+                0.892,
+                0.811
+            ],
+            "angle": 0,
+            "content": "This paper introduces a novel semantically aligned and uniform video grounding method, Geodesic and Game Localization (G2L), which explores more semantic information by measuring the correlation between video moments through the geodesic and models the nuances of similar moments using game-theoretic interactions. By contrasting the video features and query features in the shared space, the learned bi-modal features become similar when their semantics match, and the similarity between video moments is modeled by the geodesic-guided pushing operation. Extensive experiments demonstrate that our novel training objective significantly improves the performance of existing contrastive learning-based methods in video grounding. This paper provides a novel perspective for cross-modal contrastive learning. In the future, we intend to apply this idea to multi-modal pre-training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Acknowledgment. This paper was partially supported by NSFC (No: 62176008) and Shenzhen Science & Technology Research Program (No: GXWD20201231165807007-20200814115301001)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.466,
+                0.888,
+                0.506,
+                0.899
+            ],
+            "angle": 0,
+            "content": "12039"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.125,
+                0.174,
+                0.14
+            ],
+            "angle": 0,
+            "content": "References"
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+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.503,
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+            ],
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+        },
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+        },
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+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.503,
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+                0.893,
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+            ],
+            "angle": 0,
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+        },
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+]
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+# G2L: Semantically Aligned and Uniform Video Grounding via Geodesic and Game Theory
+
+Hongxiang Li $^{1}$ , Meng Cao $^{2,1}$ , Xuxin Cheng $^{1}$ , Yaowei Li $^{1}$ , Zhihong Zhu $^{1}$ , Yuexian Zou $^{1\dagger}$
+
+$^{1}$ School of Electronic and Computer Engineering, Peking University
+
+$^{2}$ International Digital Economy Academy (IDEA)
+
+{lihongxiang,chengxx,zhihongzhu,ywl}@stu.pku.edu.cn; {mengcao,zouyx}@pku.edu.cn
+
+# Abstract
+
+The recent video grounding works attempt to introduce vanilla contrastive learning into video grounding. However, we claim that this naive solution is suboptimal. Contrastive learning requires two key properties: (1) alignment of features of similar samples, and (2) uniformity of the induced distribution of the normalized features on the hypersphere. Due to two annoying issues in video grounding: (1) the coexistence of some visual entities in both ground truth and other moments, i.e. semantic overlapping; (2) only a few moments in the video are annotated, i.e. sparse annotation dilemma, vanilla contrastive learning is unable to model the correlations between temporally distant moments and learned inconsistent video representations. Both characteristics lead to vanilla contrastive learning being unsuitable for video grounding. In this paper, we introduce Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework via geodesic and game theory. We quantify the correlations among moments leveraging the geodesic distance that guides the model to learn the correct cross-modal representations. Furthermore, from the novel perspective of game theory, we propose semantic Shapley interaction based on geodesic distance sampling to learn fine-grained semantic alignment in similar moments. Experiments on three benchmarks demonstrate the effectiveness of our method.
+
+# 1. Introduction
+
+Video grounding [18, 59, 36, 45, 17, 75, 8, 69, 72, 67, 6, 25] aims to identify the timestamps semantically corresponding to a given query within an untrimmed video, which is a challenging multimedia retrieval task due to flexibility and complexity of the query and video content. The video grounding model needs well to model the complex cross-modal correlations and semantic information.
+
+Query  $\boxed{q}$  : The person sharpens the blade on the second belt.
+
+![](images/683dbfe8345cd9b7cfd7dd4cb174128e00a5c090db8cf8b41aa392fae0f877c0.jpg)  
+(a)
+
+![](images/87b109d938ba991f278cdb12f28431919a653b190b70b37927dae2a604fc661c.jpg)  
+(b)  
+Figure 1. (a) Illustration of video grounding. 'GT' indicates the ground truth. A comparison of (b) existing contrastive learning-based methods and (c) our proposed G2L method. G2L makes semantically similar video moments closer in representation space while exploring nuances among similar moments.
+
+![](images/610f8cbb120c89915c4b720008353a18bb90473ec957ccad17131ae7cf59b3d4.jpg)  
+(c)
+
+Contrastive learning [10, 23, 43] is proposed to learn representations by contrasting positive pairs against negative pairs. With the popularity of contrastive learning in vision-language tasks [34, 13, 46, 7, 5, 64, 62], several works also apply it to video grounding. Nan et al. [45] propose a dual contrast learning to learn more informative feature representations by maximizing the mutual information between the query and the corresponding video clips. This naive solution, however, achieves sub-optimum performance.
+
+Generally, contrastive learning requires two key properties [58]: alignment and uniformity. Alignment favors encoders that assign similar features to similar samples. Uniformity prefers a feature distribution that preserves maximal information, i.e., the uniform distribution on the unit hypersphere. We argue that these two issues are not satisfied in current video grounding works with contrastive learning.
+
+Firstly, the semantic overlapping issue is widespread,
+
+i.e., the co-existence of some visual entities in both ground truth and other moments. As shown in Figure 1(a), the entity of 'person', 'blade' and 'belt' appear in both ground-truth moment  $m_4$  and others. Since there exist no classification labels in video grounding, previous methods distinguish positive and negative samples only based on the annotated moments. This strict scheme, however, ignores the semantic overlapping among video moments, which leads to the contradiction in feature representations. As shown in Figure 1(a)(b), the moment  $m_1$  of "sharpen the blade on the first belt" only differs from target moment  $m_4$  in the 'second' order. They share similar semantic meanings but are forced to be pushed away in feature space. It is not consistent with the alignment principle of the ideal contrastive learning.
+
+Another issue lies in the sparse annotation dilemma [67, 31]. Due to the costly labeling process, only a few moments are annotated regardless of the thousands of frames contained. Such severe data imbalance leads to significant learning bias for vanilla contrastive learning, i.e., unannotated moments are pushed away by different queries, regardless of the semantic relationships. Consequently, their representations are close, although they don't necessarily have strong semantic similarities. This undermines the uniformity requirement of contrastive learning. For example in Figure 1(b), wrong results always exist when encountering these unannotated moments (e.g.,  $m_1$ ).
+
+To address the issues mentioned above, we propose a novel Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework as shown in Figure 1(c). We propose to measure the similarity according to the geodesic distance [29] between two video moments along the manifold. In Figure 1(c), the geodesic distance between  $m_4$  to  $m_6$  is the length of the shortest path as the moment graph, i.e.  $m_4 \rightarrow m_2 \rightarrow m_3 \rightarrow m_5 \rightarrow m_6$ . In contrast to previous methods, we construct positive and negative pairs based on the geodesic distance rather than the temporal moment to relax the strict positional principle. The geodesics from the target moment to other moments are used to guide the maximizing mutual information. In this manner, the distance between video moments correctly reflects semantic relevance.
+
+Unfortunately, the relaxed contrastive objective with geodesic leads to one side-effect, i.e., the model may confuse similar video moments. As shown in Figure 1(c), the model may falsely map  $m_{1}$  to be as close to the query  $q$  since  $m_{1}$  shares a similar appearance with the ground truth  $m_{4}$ . To further prevent the model from confusing similar video moments, we formulate video moments and queries as multiple players into a cooperative game and quantify their game-theoretic interactions (i.e., Shapley interactions [49, 20]). Through this, we evaluate the marginal contributions of each fine-grained component, which leads
+
+to a more accurate division. However, computing the exact Shapley interaction for all players is an NP-hard problem [41] and is difficult to achieve solutions in the video grounding setting. Therefore, we further propose a semantic Shapley interaction module, which samples similar intravideo moments by geodesic distance with a focus on their nuances.
+
+In sum, our contributions are summarized as follows:
+
+- We present G2L which introduces geodesic and game theory to learn the semantic alignment and uniformity between video and query for video grounding.  
+- We propose a novel geodesic-guided contrastive learning scheme that considers the correct semantics of all moments in the video.  
+- We introduce an effective semantic Shapley interaction strategy based on geodesic distance.  
+- Extensive experiments on three public datasets demonstrate the effectiveness of our G2L.
+
+# 2. Related Work
+
+Video Grounding. Video grounding proposed by [18, 1], which aims to predict the start and end boundaries of the activity described by a given language query within a video. Early approaches focus on carefully designed complex video-text interaction modules. Yuan et al. [66] propose an approach which can directly predict the coordinates of the queried video clip using attention mechanism. Zeng et al. [67] propose a pyramid neural network to consider multi-scale information. Liu et al. [39] advise a memory attention to emphasize the visual features and simultaneously utilize the context information. Xu et al. [61] introduce a multi-level model to integrate visual and textual features earlier and further re-generate queries as an auxiliary task. To improve the representation of the model, several methods introduce contrastive learning or cross-modal discrimination. Ding et al. [17] propose to combine discriminative contrastive objective and generative caption objective to optimize dual-encoder. Nan et al. [45] introduce introducing causal intervention and dual contrastive learning to improve representation. In this paper, we propose to model semantic alignment and uniformity by approximate geodesics and game-theoretic interactions.
+
+Contrastive Learning. Contrastive learning (CL) often serves as an unsupervised objective to learn representations by contrasting positive pairs against negative pairs [10, 23, 43, 35, 12, 11]. Some prior works consider maximizing the mutual information (MI) between latent representations [24]. MI quantifies the "amount of information" gained about one random variable by observing another random variable [2]. Contrastive learning has been applied to vision-language tasks to learn the joint representations of visual and textual modalities [42, 51]. Sun et al. [71] pro
+
+pose a retrieval and localization network with contrastive learning for video corpus moment retrieval.
+
+Shapley Value. The Shapley value [49, 26] originates from cooperative game theory. It has been theoretically proven to be the unique metric to fairly estimate the contribution of each player in a cooperative game such that satisfying certain desirable axioms [60] and is widely used in deep learning. Li et al. [32] propose a semantically aligned vision-language pre-training based on Shapley value to model fine-grained semantics. Ren et al. [48] propose to explain adversarial attacks by Shapley value. Li et al. [33] propose to explicit credit assignment for multi-agent reinforcement learning using Shapley value.
+
+# 3. Geodesic and Game Localization (G2L)
+
+# 3.1. Problem Formulation and Model Overview
+
+Let  $Q_{i}$  and  $V_{i}$  be a given textual query and untrimmed video respectively. The purpose of video grounding is to locate the most relevant video interval  $A_{i} = (t_{i}^{s}, t_{i}^{e})$ , where  $t_{i}^{s}$  and  $t_{i}^{e}$  are starting and ending times respectively. The key to video grounding is to learn semantics between video and query. To this end, previous methods [45, 17] incorporate vanilla contrastive learning into existing cross-modal interaction architectures. Typically, at the training stage, they employ two loss functions: video grounding loss  $\mathcal{L}_{\mathrm{VG}}$  and vanilla contrastive loss  $\mathcal{L}_{\mathrm{VCL}}$ .  $\mathcal{L}_{\mathrm{VG}}$  computes the cross entry between the target timestamp and the prediction timestamp to optimize the model.  $\mathcal{L}_{\mathrm{VCL}}$  discriminates between positive samples and negative samples based on the temporal moment and adopts noise-contrastive estimation (NCE) [21] to obtain MI of videos and queries.
+
+However, vanilla contrastive learning is not appropriate for video grounding due to the semantic overlapping and sparse annotation dilemma. To learn correct semantics and improve representations, as illustrated in Figure 2, we propose Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework that germinates from geodesic and cooperative game theory. Our G2L learns semantic alignment and uniformity from two components. With geodesic-guided contrastive learning (GCL), complete semantic alignment and uniformly distributed video features are learned. By semantic Shapley interaction(SSI), we learn the fine-grained semantic alignment between similar moments and target queries. Combined with the two novel proposed training objectives, the full training objective of semantically aligned and uniform video grounding can be formulated as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {V G}} + \mathcal {L} _ {\mathrm {G C L}} + \mathcal {L} _ {\mathrm {S S I}} \tag {1}
+$$
+
+During inference, it can be directly removed, rendering a semantics-sensitive dual encoder.
+
+# 3.2. Feature Encoder
+
+Video Encoder. For an input video  $V_{i}$ , we first segment it into small video clips and perform a fixed-interval sampling over these clips. Then the video clips are fed into a pretrained 3D CNN model (e.g. C3D) to extract the video features  $F_{i}^{V}$ . Referring to the previous works [75], we employ sparse sampling and a proposal network to construct the feature map  $F_{i}^{M} = \{m_{i}\}_{i=1}^{N_{m}}$  of moment candidates based on  $F_{i}^{V}$ , where  $N_{m}$  is the number of proposals in the video.
+
+Query Encoder. For a textual query  $Q_{i}$ , we generate the tokens of words by the tokenizer and add a class embedding token '[CLS]' in the beginning. Then the tokens are fed into pre-trained BERT [27], and we perform average pooling of its last two hidden states to obtain the sentence feature  $q_{i}$ .
+
+# 3.3. Geodesic Distance Computation
+
+Video content is intricate and flexible, and for video clips, temporal proximity does not always equate to semantic similarity. Conversely, two video clips can have strong correlations even though they are temporally distant. We propose to measure correlations of video representations using the geodesic distance. Formally, we define a mini-batch of video-query pairs as  $\{V_i, Q_i\}_{i=1}^B$ , where  $B$  is the size of the mini-batch. After fed into the video and query encoders, we obtain textual representation  $L = \{q_i\}_{i=1}^B$  and moment representations  $M = \{m_i\}_{i=1}^{B \times N_m}$ .
+
+The video moments representations may lie in a high-dimensional manifold, and our purpose is to measure the geodesic distance between two points along the manifold. However, computing the exact geodesic distance [29] is difficult without explicit knowledge of the manifold structure. To obtain the geodesic distance, we first employ the K-NN graph [15] to approximate the manifold structure [52, 14]. In this graph, each moment  $m_{i}$  forms a node, and each node connects to at most  $n$  other nodes. A directed edge exists from node  $m_{i}$  to node  $m_{j}$  if node  $m_{j}$  is among the  $n$  nearest neighbors of  $m_{i}$ . The edge weight  $d(m_{i},m_{j})$  is defined using cosine similarity:  $d(m_{i},m_{j}) = 1 - m_{i}m_{j}^{\top}$ . Finally, we utilize the shortest path algorithm, i.e., Dijkstra [16], to compute the length of the shortest path between two moments along the obtained weighted directed graph as the geodesic distance  $\mathcal{G}(m_i,m_j)$ .
+
+# 3.4. Geodesic-guided Contrastive Learning
+
+Previous Contrastive Scheme. In video grounding, a query usually corresponds to multiple clips. An intuitive method [17] to learn representations is to set the clips in ground truth intervals as positive samples, while others are negatives. Another scheme [59] is to calculate the intersection over union (IoU) between the ground truth and other moments, where those with higher IoU are considered as positive samples and the lower ones are regarded as negative samples. Then they learn the joint representation by
+
+![](images/a58681c68be132cd2127c73d26c98c5974f2ad6cb42e0f70148266c5083cfa06.jpg)  
+Figure 2. Overview of Geodesic and Game Localization (G2L). Our framework encourages the model to learn semantically aligned and uniform joint representations. In the inference stage, we directly fuse the video features and query features to compute the predicted moments. In the training stage, the grounding loss  $\mathcal{L}_{\mathrm{VG}}$  is obtained by calculating the cross-entropy between the predicted moment and the target moment. Then, we approximate the high-dimensional manifold structure of the video representations through a moment graph and calculate the geodesic distance from the target moment to other moments. Finally, we leverage geodesic distance for cross-modal discrimination and semantic Sharpley interaction modeling.
+
+pulling the query features and ground truth moment features together, and pushing the query features and non-ground truth moment features apart. The previous contrastive loss  $\mathcal{L}_{\mathrm{VCL}}$  can be formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {V C L}} = - \sum_ {i = 1} ^ {B} \left(\log \frac {\exp \left(q _ {i} m _ {i} ^ {\top} / \tau\right)}{\sum_ {m _ {j} \in M} \exp \left(q _ {i} m _ {j} ^ {\top} / \tau\right)}\right) \tag {2}
+$$
+
+where  $\tau$  is the temperature hyper-parameter.
+
+While intuitive, such a manner fails to capture semantic alignment and uniformity between queries and video content. To learn complete semantic alignment and uniformity for video grounding, we propose geodesic-guided contrastive learning.
+
+Semantic Alignment. In vanilla supervised contrastive learning [56, 28], all classes play the same role: pulling is done within every class and pushing between every pair of different classes. Such uniform contrastive learning works well for symmetric and equal cross-modal learning. In fact, due to semantic overlapping, the semantics of the video and text are asymmetric and unequal in video grounding. Temporally distant moments may have similar semantics. To model semantic alignment, we discriminate positive pairs based on the geodesic distance instead of the temporal moment. For a query feature  $q_{i}$ , we define the  $k$  moments with the closest geodesic distance from the target moment  $\hat{m}_i \in M$  as its semantic positive samples  $P_{i}$ :
+
+$$
+P _ {i} = \left\{p _ {i} ^ {k} \right\} = \underset {k} {\arg \operatorname {t o p k}} \mathcal {G} (\hat {m} _ {i}, m _ {k}) \tag {3}
+$$
+
+$P_{i}$  contains  $m_{i}$  and moments adjacent to  $m_{i}$  geodesic which is used to construct positive pairs with  $q_{i}$  to relax the previous strict positional principle.
+
+Semantic Uniformity. Due to the sparse annotation dilemma [67, 31], most of the moments are only marked as negative while pushed away by different queries. Notably, this push operation is undifferentiated, i.e., the model is encouraged to learn to push all unannotated moments from the annotated ones. This clearly undermines the model to learn correct semantics. To learn semantic uniformity, we introduce the geodesic distance to differentially push negative samples away from the query based on semantic relationships. The similarity between query and moment  $s(q_i, m_j)$  is defined as:
+
+$$
+s \left(q _ {i}, m _ {j}\right) = \exp \left(q _ {i} m _ {j} ^ {\top} \left(\hat {m} _ {i} m _ {j} ^ {\top} \log \frac {1}{\exp \left(\mathcal {G} \left(\hat {m} _ {i} , m _ {j}\right) + 1\right)}\right)\right) \tag {4}
+$$
+
+We assign corresponding weights according to the geodesic distance  $\mathcal{G}(\hat{m}_i, m_j)$  between the target moment  $\hat{m}_i$  and all moments  $m_j$ .  $s(q_i, m_j)$  considers the relationships between negative samples while maximizing mutual information.
+
+Finally, our geodesic-guided contrastive loss can be formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {G C L}} = - \sum_ {i = 1} ^ {B} \left(\log \frac {\sum_ {p _ {i} ^ {k} \in P _ {i}} \exp \left(q _ {i} p _ {i} ^ {k} ^ {\top} / \tau\right)}{\sum_ {m _ {j} \in M} s \left(q _ {i} , m _ {j}\right) / \tau}\right) \tag {5}
+$$
+
+In contrast to Equation 2,  $\mathcal{L}_{\mathrm{GCL}}$  is designed for representa
+
+tion learning rather than directly learning localization.
+
+# 3.5. Semantic Shapley Interaction Modeling
+
+To prevent the model from confusing similar video moments due to the relaxed contrastive objective in Equation 3, we propose semantic Shapley interaction to model fine-grained semantic alignment.
+
+# 3.5.1 Preliminaries
+
+Shapley Value. The Shapley value [49] is a classical game theory solution for the unbiased estimation of the contribution of each player in a cooperation game. Assume a game consists of  $\mathcal{N}$  players,  $\mathcal{U} \subseteq \mathcal{N}$  represents a potential subset of players. A game function  $f(\cdot)$  maps each subset  $\mathcal{U}$  of players to a score, estimating the cooperated contribution of a set of players. For a player  $i$ , its Shapley value  $\phi(i|\mathcal{N})$  is computed as the average marginal contribution of player  $i$  to all possible coalitions  $\mathcal{U}$  without  $i$ :
+
+$$
+\begin{array}{l} \phi (i \mid \mathcal {N}) = \sum_ {\mathcal {U} \subseteq \mathcal {N} \backslash \{i \}} p (\mathcal {U}) [ f (\mathcal {U} \cup \{i \}) - f (\mathcal {U}) ] (6) \\ p (\mathcal {U}) = \frac {| \mathcal {U} | ! (| \mathcal {N} | - | \mathcal {U} | - 1) !}{| \mathcal {N} | !} (7) \\ \end{array}
+$$
+
+where  $p(\mathcal{U})$  is the likelihood of  $\mathcal{U}$  being sampled. The Shapley value has been proved to be the unique metric that satisfies the following axioms: Linearity, Symmetry, Dummy, and Efficiency. We summarize these axioms in the supplementary material.
+
+Shapley Interaction. In game theory, some players tend to form a small cooperative coalition and always participate in the game together. This cooperation provides additional contributions to the game. The Shapley interaction [20] measures the additional contributions made by the coalition compared to players working individually. We define  $[\mathcal{U}]$  as a single hypothetical player, which is the union of the players in  $\mathcal{U}$ . A reduced game is formed by removing the individual players in  $\mathcal{U}$  from the game and adding  $[\mathcal{U}]$  to the game. Finally, according to Equation 6, the Shapley interaction for coalition  $\mathcal{U}$  is formulated as:
+
+$$
+\Im ([ \mathcal {U} ]) = \phi ([ \mathcal {U} ] \mid \mathcal {N} \backslash \mathcal {U} \cup \{[ \mathcal {U} ] \}) - \sum_ {i \in \mathcal {U}} \phi (i \mid \mathcal {N} \backslash \mathcal {U} \cup \{i \}) \tag {8}
+$$
+
+where  $\Im ([\mathcal{U}])$  reflects the interactions inside  $\mathcal{U}$ . The higher value of  $\Im ([\mathcal{U}])$  indicates that players in  $\mathcal{U}$  cooperate closely with each other.
+
+# 3.5.2 Fine-Grained Semantic Alignment via Shapley
+
+According to Equation 6 and Equation 8, it can be known that the computational complexity of the Shapley interaction grows factorially as the number of players increases. To reduce the computational cost, we propose semantic
+
+Shapley interaction based on geodesic distance sampling. Specifically, as in Equation 3, we sample semantic similar moments based on geodesic distances to investigate their nuances. Then, we consider queries and semantic similar moments from the same video as players in the same cooperative game.
+
+To avoid confusion with the previous symbols, we define  $\mathcal{H}_i^V = \{\mathbf{h}_{ix}^V\}_{x=1}^{N_i^v}$  and  $\mathcal{H}_i^Q = \{\mathbf{h}_{iy}^Q\}_{y=1}^{N_i^q}$  are a set of semantic positive samples and queries from the video  $V_i$  respectively, where  $N_i^v = KN_i^q$  and  $N_i^q$  indicate the number of similar moments and queries in video  $V_i$  respectively.  $K$  is the number of moments sampled for each query  $\mathbf{h}_{iy}^Q$ . We investigate the effect of  $K$  on computational cost and performance in the supplementary material.
+
+If a query and a video moment have strong semantic correspondence, then they tend to cooperate with each other and contribute to the coalition. Thus, we can take  $\mathcal{H}^i = \mathcal{H}_i^V \cup \mathcal{H}_i^Q$  as the players in the same game inspired by [32]. We define the alignment matrix as:  $\mathcal{A}_i = [a_{xy}^i]$ , where  $a_{xy}^i = h_{ix}^{V^\top}h_{iy}^Q$  represents the alignment score between  $x$ -th moment and  $y$ -th query in video  $V_i$ . Next,  $\tilde{\mathcal{A}}_i$  is obtained by applying softmax-normalization over each row of  $\mathcal{A}_i$ . Then we average the maximum alignment score  $\max_y \tilde{a}_{xy}^i$  as the fine-grained moment-to-query similarity  $\psi_1$ . Similarly, we can obtain the fine-grained query-to-moment similarity  $\psi_2$ . The total fine-grained similarity score can be defined:  $\psi = (\psi_1 + \psi_2) / 2$ , which be considered as the game score  $f(\cdot)$  in our game.
+
+According to Equation 8, the semantic Shapley interaction of them can be formulated as:
+
+$$
+\begin{array}{l} \Im \left(\left[ \mathcal {H} _ {x y} ^ {i} \right]\right) = \phi \left(\left[ \mathcal {H} _ {x y} ^ {i} \right] \mid \mathcal {H} ^ {i} \backslash \mathcal {H} _ {x y} ^ {i} \cup \{\left[ \mathcal {H} _ {x y} ^ {i} \right] \}\right) \\ - \phi \left(\mathbf {h} _ {i x} ^ {V} \mid \mathcal {H} ^ {i} \backslash \mathcal {H} _ {x y} ^ {i} \cup \left\{\mathbf {h} _ {i x} ^ {V} \right\}\right) \\ - \phi \left(\mathbf {h} _ {i y} ^ {Q} \mid \mathcal {H} ^ {i} \backslash \mathcal {H} _ {x y} ^ {i} \cup \left\{\mathbf {h} _ {i y} ^ {Q} \right\}\right) (9) \\ = \mathbb {E} _ {\mathcal {C}} \left\{\underset {| \mathcal {U} | = \mathcal {C}} {\mathcal {U} \subseteq \mathcal {H} ^ {i} \backslash \mathcal {H} _ {x y} ^ {i}} \mathbb {E} \left[ f \left(\mathcal {U} \cup \mathcal {H} _ {x y} ^ {i}\right) - f \left(\mathcal {U} \cup \left\{\mathbf {h} _ {i x} ^ {V} \right\}\right) \right. \right. \\ \left. - f \left(\mathcal {U} \cup \left\{\mathbf {h} _ {i y} ^ {Q} \right\}\right) + f (\mathcal {U}) \right] \rbrace (10) \\ \end{array}
+$$
+
+where  $\Im \left(\left[\mathcal{H}_{xy}^{i}\right]\right)$  represents the single player formed by the coalition of  $x$ -th moment and  $y$ -th query in video  $V_{i}, \mathcal{C}$  represents the coalition size. We take normalized  $\Im'\left(\left[\mathcal{H}_{xy}^{i}\right]\right)$  as soft labels, the fine-grained semantic alignment loss can be defined as:
+
+$$
+\mathcal {L} _ {\mathrm {S S I}} = - \sum_ {i = 1} ^ {T} \frac {1}{N _ {i} ^ {v} N _ {i} ^ {q}} \sum_ {x = 1} ^ {N _ {i} ^ {v}} \sum_ {y = 1} ^ {N _ {i} ^ {q}} \Im^ {\prime} \left(\left[ \mathcal {H} _ {x y} ^ {i} \right]\right) \log \left(\tilde {a} _ {x y} ^ {i}\right) \tag {11}
+$$
+
+where  $T$  is the total number of unique videos in a minibatch, i.e.  $T \leq B$ .
+
+<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>CTRL [18]</td><td>29.01</td><td>10.34</td><td>59.17</td><td>37.54</td></tr><tr><td>ACRN [39]</td><td>31.67</td><td>11.25</td><td>60.34</td><td>38.57</td></tr><tr><td>TripNet [22]</td><td>32.19</td><td>13.93</td><td>-</td><td>-</td></tr><tr><td>SCDM [65]</td><td>36.75</td><td>19.86</td><td>64.99</td><td>41.53</td></tr><tr><td>LGI [44]</td><td>41.51</td><td>23.07</td><td></td><td></td></tr><tr><td>VSLNet [73]</td><td>43.22</td><td>26.16</td><td>-</td><td>-</td></tr><tr><td>2D-TAN [75]</td><td>44.51</td><td>26.54</td><td>77.13</td><td>61.96</td></tr><tr><td>DRN [67]</td><td>45.45</td><td>24.39</td><td>77.97</td><td>50.30</td></tr><tr><td>DPIN [54]</td><td>47.27</td><td>28.31</td><td>77.45</td><td>60.03</td></tr><tr><td>CBLN [37]</td><td>48.12</td><td>27.60</td><td>79.32</td><td>63.41</td></tr><tr><td>SMIN [55]</td><td>48.46</td><td>30.34</td><td>81.16</td><td>62.11</td></tr><tr><td>MATN [74]</td><td>48.02</td><td>31.78</td><td>78.02</td><td>63.18</td></tr><tr><td>GTR [4]</td><td>50.57</td><td>29.11</td><td>80.43</td><td>65.14</td></tr><tr><td>CMAS [63]</td><td>46.23</td><td>29.48</td><td>77.04</td><td>60.25</td></tr><tr><td>MMN [59]</td><td>48.59</td><td>29.26</td><td>79.50</td><td>64.76</td></tr><tr><td>CL-based:</td><td></td><td></td><td></td><td></td></tr><tr><td>IVG-DCL [45]</td><td>43.84</td><td>27.10</td><td>-</td><td>-</td></tr><tr><td>SSCS [17]</td><td>46.67</td><td>27.56</td><td>78.37</td><td>63.78</td></tr><tr><td>G2L (ours)</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr></table>
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation
+
+ActivityNet-Captions. ActivityNet-Captions [30] contains 20,000 untrimmed videos and 100,000 descriptions [3], covering a wide range of complex human behavior. The video clips with annotations have much larger variations. Following the public split [75], we use 37417, 17505 and 17031 sentence-video pairs for training, validation and testing, respectively.
+
+Charades-STA. The Charades dataset [50] is collected for video action recognition and video captioning. Gao et al. [18] adapt the Charades dataset to the video grounding task by collecting the query annotations. The Charades-STA dataset contains 6672 videos and involves 16128 video-query pairs, where 12408 pairs are used for training and 3720 for testing. We follow the same split of the dataset as in Gao et al. [18] for fair comparisons.
+
+TACoS. TACoS [47] contains 127 videos from the cooking scenarios. We follow the standard split [18], which has 10146, 4589 and 4083 video query pairs for training, validation and testing, respectively.
+
+Evaluation. Following previous work [18, 75], we adopt "R@n, IoU=m" as the evaluation metric. It calculates the percentage of IoU greater than "m" between at least one of the top "n" video moments retrieved and the ground truth.
+
+Table 1. Performance comparisons on ActivityNet-Captions using C3D features.  
+
+<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>MCN [1]</td><td>17.46</td><td>8.01</td><td>48.22</td><td>26.73</td></tr><tr><td>SAP [9]</td><td>27.42</td><td>13.36</td><td>66.37</td><td>38.15</td></tr><tr><td>TripNet [22]</td><td>36.61</td><td>14.50 -</td><td>-</td><td></td></tr><tr><td>MAN [70]</td><td>41.21</td><td>20.54</td><td>83.21</td><td>51.85</td></tr><tr><td>2D-TAN [75]</td><td>39.70</td><td>23.31</td><td>80.32</td><td>51.26</td></tr><tr><td>DRN [67]</td><td>42.90</td><td>23.68</td><td>87.80</td><td>54.87</td></tr><tr><td>FVMR [19]</td><td>42.36</td><td>24.14</td><td>83.97</td><td>50.15</td></tr><tr><td>CBLN [37]</td><td>43.67</td><td>24.44</td><td>88.39</td><td>56.49</td></tr><tr><td>MMRG [68]</td><td>44.25</td><td>-</td><td>60.22</td><td>-</td></tr><tr><td>MMN [59]</td><td>47.31</td><td>27.28</td><td>83.74</td><td>58.41</td></tr><tr><td>CL-based:SSCS [17]</td><td>43.15</td><td>25.54</td><td>84.26</td><td>54.17</td></tr><tr><td>G2L(Ours)</td><td>47.91</td><td>28.42</td><td>84.80</td><td>59.33</td></tr></table>
+
+Table 2. Performance comparisons on Charades-STA using VGG features.
+
+# 4.2. Implementation Details
+
+For a fair comparison, we extracted video features from a pre-trained 3D CNN (C3D for ActivityNet-Captions and TACoS, VGG for Charades-STA) following previous works [59, 17, 45]. We uniformly sampled (256, 32, 256) clips as the input video sequence and set the length of 2D feature map [75] (64, 16, 128) for ActivityNet-Captions, Charades-STA, and TACoS, respectively. For the language query, the pre-trained BERT[27] was employed for each word of the query. The average pooling outputs of the first and last layers were used to obtain the embedding of the whole sentence. We employed the AdamW optimizer [40] to train our model and set the temperature weight  $\tau$  to 0.1. The learning rates were set to  $(8\times 10^{-4},8\times 10^{-4},1\times 10^{-4})$  for ActivityNet-Captions, Charades-STA, and TACoS, respectively. We conducted experiments on 8 A100 GPUs with batch size 48 for ActivityNet-Captions and Charades-STA, and on 4 A100 GPUs with batch size 8 for TACoS.
+
+# 4.3. Comparisons with State-of-the-art Methods
+
+Comparison on ActivityNet-Captions. In Table 1, we report our performance in comparison with other state-of-the-art methods on ActivityNet-Captions. Compared with IVG-DCL [45] and SSCS [17], which are also based on contrastive learning, our method achieves significant improvements. Notably, ActivityNet-Captions is currently the dataset with the most severe semantic overlapping and sparse annotation dilemma. We observe that our model showed even more significant improvements on ActivityNet-Captions, achieving absolute improvements of up to  $7.8\%$  and  $5.7\%$  compared to IVG-DCL [45] and SSCS [17], respectively. They encourage the model to focus on cross-modal alignment in favor of grounding while ig-
+
+<table><tr><td>Model</td><td>R@1 IoU0.3</td><td>R@1 IoU0.5</td><td>R@5 IoU0.3</td><td>R@5 IoU0.5</td></tr><tr><td>CTRL [18]</td><td>18.32</td><td>13.30</td><td>36.69</td><td>25.42</td></tr><tr><td>CBP [57]</td><td>27.31</td><td>24.79</td><td>43.64</td><td>37.40</td></tr><tr><td>SCDM [65]</td><td>26.11</td><td>21.17</td><td>40.16</td><td>32.18</td></tr><tr><td>2D-TAN [75]</td><td>37.29</td><td>25.32</td><td>57.81</td><td>45.04</td></tr><tr><td>DRN [67]</td><td>-</td><td>23.17</td><td>-</td><td>33.36</td></tr><tr><td>CMIN [76]</td><td>24.64</td><td>18.05</td><td>-</td><td>-</td></tr><tr><td>CSMGAN [38]</td><td>33.90</td><td>27.09</td><td>53.98</td><td>41.22</td></tr><tr><td>CBLN [37]</td><td>38.98</td><td>27.65</td><td>59.96</td><td>46.24</td></tr><tr><td>MMN [59]</td><td>39.24</td><td>26.17</td><td>62.03</td><td>47.39</td></tr><tr><td>GTR [4]</td><td>40.39</td><td>30.22</td><td>61.94</td><td>47.73</td></tr><tr><td>FVMR [19]</td><td>41.48</td><td>29.12</td><td>64.53</td><td>50.00</td></tr><tr><td>CL-based:</td><td></td><td></td><td></td><td></td></tr><tr><td>IVG-DCL [45]</td><td>38.84</td><td>29.07</td><td>-</td><td>-</td></tr><tr><td>SSCS [17]</td><td>41.33</td><td>29.56</td><td>60.65</td><td>48.01</td></tr><tr><td>G2L(Ours)</td><td>42.74</td><td>30.95</td><td>65.83</td><td>49.86</td></tr></table>
+
+noring the semantics among full moments, especially unannotated moments. In contrast, our method conducts cross-modal discrimination guided by the geodesic distance such that overcoming data bias.
+
+Comparison on Charades-STA. Table 2 reports the result comparison between state-of-the-art methods on Charades-STA. Compared with SSCS [17], our method achieves a performance improvement of up to  $5.1\%$ . On more stringent evaluation metrics, such as “R@1 IoU=0.7”, our method achieves a performance improvement of  $1.1\%$  compared to the cutting-edge method MMN [59], which indicates that exploring fine-grained semantic alignment information between similar video moments can improve grounding quality. Notably, MMN [59] and SSCS [17] have similar loss functions, and MMN [59] from a perspective on temporal grounding as a metric-learning problem proposes a mutual matching network to enhance joint representation learning by mining more negative samples achieving better performances. However, it also constructs cross-modal pairs based on the temporal moment, which results in a large number of constructed negative pairs containing potential weak semantic positive pairs, thus hindering learning.
+
+Comparison on TACoS. Table 3 summarizes the comparisons on the TACoS. We observe that our model achieves state-of-the-art results in most settings. However, the performance gain on this dataset is smaller than the previous three datasets. The reason is that the sparse annotation dilemma and semantic overlapping are insignificant on TACoS. It contains only 127 videos but has about 20,000 queries and focuses on cooking activities with more uniform objects, roles, and actions. Nevertheless, our method still outperforms previous contrastive learning-based methods in various metrics.
+
+Table 3. Performance comparisons on TACoS using C3D features.  
+
+<table><tr><td>Model</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>Full Model</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr><tr><td>w/o SA</td><td>50.85</td><td>30.73</td><td>79.22</td><td>65.47</td></tr><tr><td>w/o SU</td><td>49.10</td><td>31.14</td><td>79.48</td><td>65.46</td></tr><tr><td>w/o GCL</td><td>48.74</td><td>28.62</td><td>78.89</td><td>64.44</td></tr><tr><td>w/o SSI</td><td>50.65</td><td>30.01</td><td>79.54</td><td>66.76</td></tr><tr><td>w/o GCL+SSI</td><td>45.74</td><td>26.74</td><td>77.26</td><td>61.64</td></tr></table>
+
+Table 4. Ablation studies of main components on ActivityNetCaptions. "SA" and "SU" denote the Semantic Alignment and the Semantic Uniformity in GCL, respectively.  
+
+<table><tr><td>Metric</td><td>R@1 IoU0.5</td><td>R@1 IoU0.7</td><td>R@5 IoU0.5</td><td>R@5 IoU0.7</td></tr><tr><td>Euclidean</td><td>47.83</td><td>28.44</td><td>79.42</td><td>65.46</td></tr><tr><td>Timestamp</td><td>49.85</td><td>29.73</td><td>78.15</td><td>65.47</td></tr><tr><td>Cosine</td><td>50.94</td><td>30.09</td><td>79.57</td><td>65.84</td></tr><tr><td>Geodesic</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr></table>
+
+Table 5. Comparison of different distance metrics on ActivityNet-Captions.
+
+# 5. Ablation Study
+
+Effectiveness of Individual Components. In Table 4, we conduct a thorough ablation study on the proposed components to verify their effectiveness. As shown in Table 4, removing the entire GCL will result in up to  $4.5\%$  of performance degradation, demonstrating the contribution of GCL by learning semantic alignment and unification. We also observe that removing either SA or SU results in about 2 points of performance drop on average, indicating that our method enables the vanilla contrastive learning to be more suitable for video grounding setting. Removing SSI leads to a  $3.3\%$  drop in performance on the more stringent metric (i.e., "R@1 IoU=0.7"), which highlights the importance of fine-grained semantic alignment for high-quality moment retrieval. The last row shows our baseline, and our method achieves up to 6 points of performance improvement without modifying the architecture compared to the baseline, confirming the superiority of our model.
+
+Effectiveness of Geodesic Distance. To demonstrate the effectiveness of the geodesic, we substitute it with different distance metrics in the model, including euclidean distance, timestamp distance, and cosine distance, and compare their performances as shown in Table 5. It can be observed that when using euclidean distance, the performances drop by up to  $5\%$ . This is due to the fact that video representations often lie in a high dimensional manifold and euclidean distance cannot accurately quantify the correlations among video moments. When using timestamp distance, the performances decrease by  $2\%$  on average, indicating that the temporal adjacency does not necessarily
+
+<table><tr><td>Model</td><td>Inference Time</td><td>Inference Time</td></tr><tr><td>2D-TAN [75]</td><td>0.13s</td><td>32s</td></tr><tr><td>MMN [59]</td><td>0.32s</td><td>37s</td></tr><tr><td>Base Model</td><td>0.39s</td><td>40s</td></tr><tr><td>G2L(Ours)</td><td>0.84s</td><td>43s</td></tr></table>
+
+Table 6. Time consumption on ActivityNet-Captions.
+
+![](images/16426f8df1310933afd5e9c14e649c42a076169790f2eac0e1dadc50397e4670.jpg)  
+(a)
+
+![](images/f98ff92db4edb8a6f20528f0a83afc2bc213ae8763554728d6ccd146b7e166ef.jpg)  
+(b)  
+Figure 3. Projected video moment features (a): learned representations of the previous method with vanilla contrastive learning; (b): learned representations of our method.
+
+correspond to semantic similarity due to the flexibility and complexity of video content. Using cosine distance results in performances dropping by up to  $3\%$ . Due to the insufficient representation capacity of the model in the early training stage to accurately calculate similarity. We approximate the manifold structure of video features using the moment graph, where the reachability and the shortest path in the graph can facilitate similarity measurement.
+
+The efficiency of our method. In Table 6, we compute the average training time per iteration and total inference time. Due to the K-NN graph and Shapley interaction, G2L requires more training costs. During inference, GCL and SSI can be removed thus our G2L only needs additional 3s compared to the base model.
+
+# 6. Qualitative Analysis
+
+We visualize a sample video from the ActivityNetCaptions into the 2D images using t-SNE [53]. In Figure 3(a), we observe that there is a clear "island" in the learned representations of the previous method. We argue that it is formed by a few moments which are temporally adjacent to the ground truth. The reason is that the previous method divides positive and negative samples based on the strict temporal moment while pushing negative samples away by different queries, regardless of the semantic relationships. In contrast, our method relaxes the previous strict contrastive objective using geodesic distance, mitigating semantic overlapping and sparse annotation dilemma. Furthermore, the semantic Shapley interaction enables our model to capture discriminative features between similar moments. Our method learns aligned and uniform representations thus eliminating the "island" in Figure 4(b),
+
+We present two qualitative results from ActivityNet-
+
+Query: The old woman is on the chair knitting again.
+
+![](images/6e00f76a6053631d14538ee591689d935f13025efe5c8794a0da7234b521a9d9.jpg)
+
+Query: The person sharpens the blade on the second belt.
+
+![](images/d95b64d011b941fce4c09c71f171aef4f1a53dad980ad439abaef769e49c49cf.jpg)  
+Figure 4. Qualitative results of our method on the ActivityNet-Captions.
+
+Captions in Figure 4. We observe that our approach can successfully model the relationships of temporally distant moments. For instance, "knitting again" in Figure 4(a) and "the second belt" in Figure 4(b) are far away from their first appearances. Our method can capture the information of "first knitting" and "the first belt" and infer precisely the location of the target moment. Previous contrastive learning-based methods fail to capture this semantic association due to tending to perform cross-modal contrast by the strict positional principle. These models only focus on the contextual content related to the target moment. Our method demonstrates that these large volumes of unannotated moments contain rich information and modeling their relationships can improve representation learning.
+
+# 7. Conclusion and Future Work
+
+This paper introduces a novel semantically aligned and uniform video grounding method, Geodesic and Game Localization (G2L), which explores more semantic information by measuring the correlation between video moments through the geodesic and models the nuances of similar moments using game-theoretic interactions. By contrasting the video features and query features in the shared space, the learned bi-modal features become similar when their semantics match, and the similarity between video moments is modeled by the geodesic-guided pushing operation. Extensive experiments demonstrate that our novel training objective significantly improves the performance of existing contrastive learning-based methods in video grounding. This paper provides a novel perspective for cross-modal contrastive learning. In the future, we intend to apply this idea to multi-modal pre-training.
+
+Acknowledgment. This paper was partially supported by NSFC (No: 62176008) and Shenzhen Science & Technology Research Program (No: GXWD20201231165807007-20200814115301001).
+
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+                                            "content": "Figure 1. (a) Illustration of video grounding. 'GT' indicates the ground truth. A comparison of (b) existing contrastive learning-based methods and (c) our proposed G2L method. G2L makes semantically similar video moments closer in representation space while exploring nuances among similar moments."
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+                                            "content": "(c)"
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+                                    "content": "Contrastive learning [10, 23, 43] is proposed to learn representations by contrasting positive pairs against negative pairs. With the popularity of contrastive learning in vision-language tasks [34, 13, 46, 7, 5, 64, 62], several works also apply it to video grounding. Nan et al. [45] propose a dual contrast learning to learn more informative feature representations by maximizing the mutual information between the query and the corresponding video clips. This naive solution, however, achieves sub-optimum performance."
+                                }
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+                                    "content": "Generally, contrastive learning requires two key properties [58]: alignment and uniformity. Alignment favors encoders that assign similar features to similar samples. Uniformity prefers a feature distribution that preserves maximal information, i.e., the uniform distribution on the unit hypersphere. We argue that these two issues are not satisfied in current video grounding works with contrastive learning."
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+                                    "content": "Firstly, the semantic overlapping issue is widespread,"
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+                                    "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+                                    "content": "† Corresponding author."
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+                                    "type": "text",
+                                    "content": "i.e., the co-existence of some visual entities in both ground truth and other moments. As shown in Figure 1(a), the entity of 'person', 'blade' and 'belt' appear in both ground-truth moment "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " and others. Since there exist no classification labels in video grounding, previous methods distinguish positive and negative samples only based on the annotated moments. This strict scheme, however, ignores the semantic overlapping among video moments, which leads to the contradiction in feature representations. As shown in Figure 1(a)(b), the moment "
+                                },
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+                                    "type": "text",
+                                    "content": " of \"sharpen the blade on the first belt\" only differs from target moment "
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " in the 'second' order. They share similar semantic meanings but are forced to be pushed away in feature space. It is not consistent with the alignment principle of the ideal contrastive learning."
+                                }
+                            ]
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+                    ],
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+                                    "content": "Another issue lies in the sparse annotation dilemma [67, 31]. Due to the costly labeling process, only a few moments are annotated regardless of the thousands of frames contained. Such severe data imbalance leads to significant learning bias for vanilla contrastive learning, i.e., unannotated moments are pushed away by different queries, regardless of the semantic relationships. Consequently, their representations are close, although they don't necessarily have strong semantic similarities. This undermines the uniformity requirement of contrastive learning. For example in Figure 1(b), wrong results always exist when encountering these unannotated moments (e.g., "
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+                                    "content": ")."
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+                                    "type": "text",
+                                    "content": "To address the issues mentioned above, we propose a novel Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework as shown in Figure 1(c). We propose to measure the similarity according to the geodesic distance [29] between two video moments along the manifold. In Figure 1(c), the geodesic distance between "
+                                },
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+                                    "content": " to "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " is the length of the shortest path as the moment graph, i.e. "
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+                                {
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+                                    "type": "inline_equation",
+                                    "content": "m_4 \\rightarrow m_2 \\rightarrow m_3 \\rightarrow m_5 \\rightarrow m_6"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". In contrast to previous methods, we construct positive and negative pairs based on the geodesic distance rather than the temporal moment to relax the strict positional principle. The geodesics from the target moment to other moments are used to guide the maximizing mutual information. In this manner, the distance between video moments correctly reflects semantic relevance."
+                                }
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+                                    "type": "text",
+                                    "content": "Unfortunately, the relaxed contrastive objective with geodesic leads to one side-effect, i.e., the model may confuse similar video moments. As shown in Figure 1(c), the model may falsely map "
+                                },
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+                                    "content": " to be as close to the query "
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+                                    "type": "text",
+                                    "content": " since "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " shares a similar appearance with the ground truth "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". To further prevent the model from confusing similar video moments, we formulate video moments and queries as multiple players into a cooperative game and quantify their game-theoretic interactions (i.e., Shapley interactions [49, 20]). Through this, we evaluate the marginal contributions of each fine-grained component, which leads"
+                                }
+                            ]
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+                    ],
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+                                    "type": "text",
+                                    "content": "to a more accurate division. However, computing the exact Shapley interaction for all players is an NP-hard problem [41] and is difficult to achieve solutions in the video grounding setting. Therefore, we further propose a semantic Shapley interaction module, which samples similar intravideo moments by geodesic distance with a focus on their nuances."
+                                }
+                            ]
+                        }
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+                                    "content": "In sum, our contributions are summarized as follows:"
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+                                            "content": "- We present G2L which introduces geodesic and game theory to learn the semantic alignment and uniformity between video and query for video grounding."
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+                                            "content": "- We propose a novel geodesic-guided contrastive learning scheme that considers the correct semantics of all moments in the video."
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+                                            "content": "- We introduce an effective semantic Shapley interaction strategy based on geodesic distance."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 8
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+                        {
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+                                            "content": "- Extensive experiments on three public datasets demonstrate the effectiveness of our G2L."
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+                                    "type": "text",
+                                    "content": "2. Related Work"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "content": "Video Grounding. Video grounding proposed by [18, 1], which aims to predict the start and end boundaries of the activity described by a given language query within a video. Early approaches focus on carefully designed complex video-text interaction modules. Yuan et al. [66] propose an approach which can directly predict the coordinates of the queried video clip using attention mechanism. Zeng et al. [67] propose a pyramid neural network to consider multi-scale information. Liu et al. [39] advise a memory attention to emphasize the visual features and simultaneously utilize the context information. Xu et al. [61] introduce a multi-level model to integrate visual and textual features earlier and further re-generate queries as an auxiliary task. To improve the representation of the model, several methods introduce contrastive learning or cross-modal discrimination. Ding et al. [17] propose to combine discriminative contrastive objective and generative caption objective to optimize dual-encoder. Nan et al. [45] introduce introducing causal intervention and dual contrastive learning to improve representation. In this paper, we propose to model semantic alignment and uniformity by approximate geodesics and game-theoretic interactions."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "Contrastive Learning. Contrastive learning (CL) often serves as an unsupervised objective to learn representations by contrasting positive pairs against negative pairs [10, 23, 43, 35, 12, 11]. Some prior works consider maximizing the mutual information (MI) between latent representations [24]. MI quantifies the \"amount of information\" gained about one random variable by observing another random variable [2]. Contrastive learning has been applied to vision-language tasks to learn the joint representations of visual and textual modalities [42, 51]. Sun et al. [71] pro"
+                                }
+                            ]
+                        }
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+                                    "type": "text",
+                                    "content": "pose a retrieval and localization network with contrastive learning for video corpus moment retrieval."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
+                {
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+                                    "content": "Shapley Value. The Shapley value [49, 26] originates from cooperative game theory. It has been theoretically proven to be the unique metric to fairly estimate the contribution of each player in a cooperative game such that satisfying certain desirable axioms [60] and is widely used in deep learning. Li et al. [32] propose a semantically aligned vision-language pre-training based on Shapley value to model fine-grained semantics. Ren et al. [48] propose to explain adversarial attacks by Shapley value. Li et al. [33] propose to explicit credit assignment for multi-agent reinforcement learning using Shapley value."
+                                }
+                            ]
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+                    ],
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+                                    "content": "3. Geodesic and Game Localization (G2L)"
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+                                    "content": "3.1. Problem Formulation and Model Overview"
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+                                    "type": "text",
+                                    "content": "Let "
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+                                    "type": "inline_equation",
+                                    "content": "Q_{i}"
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+                                    "type": "text",
+                                    "content": " and "
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+                                    "type": "inline_equation",
+                                    "content": "V_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " be a given textual query and untrimmed video respectively. The purpose of video grounding is to locate the most relevant video interval "
+                                },
+                                {
+                                    "bbox": [
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+                                        310,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "A_{i} = (t_{i}^{s}, t_{i}^{e})"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        310,
+                                        278,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                        484
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_{i}^{s}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "t_{i}^{e}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " are starting and ending times respectively. The key to video grounding is to learn semantics between video and query. To this end, previous methods [45, 17] incorporate vanilla contrastive learning into existing cross-modal interaction architectures. Typically, at the training stage, they employ two loss functions: video grounding loss "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        310,
+                                        278,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{VG}}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        310,
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+                                        484
+                                    ],
+                                    "type": "text",
+                                    "content": " and vanilla contrastive loss "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{VCL}}"
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+                                {
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+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{VG}}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        310,
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+                                        484
+                                    ],
+                                    "type": "text",
+                                    "content": " computes the cross entry between the target timestamp and the prediction timestamp to optimize the model. "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        310,
+                                        278,
+                                        484
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{VCL}}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " discriminates between positive samples and negative samples based on the temporal moment and adopts noise-contrastive estimation (NCE) [21] to obtain MI of videos and queries."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "type": "text",
+                                    "content": "However, vanilla contrastive learning is not appropriate for video grounding due to the semantic overlapping and sparse annotation dilemma. To learn correct semantics and improve representations, as illustrated in Figure 2, we propose Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework that germinates from geodesic and cooperative game theory. Our G2L learns semantic alignment and uniformity from two components. With geodesic-guided contrastive learning (GCL), complete semantic alignment and uniformly distributed video features are learned. By semantic Shapley interaction(SSI), we learn the fine-grained semantic alignment between similar moments and target queries. Combined with the two novel proposed training objectives, the full training objective of semantically aligned and uniform video grounding can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {V G}} + \\mathcal {L} _ {\\mathrm {G C L}} + \\mathcal {L} _ {\\mathrm {S S I}} \\tag {1}",
+                                    "image_path": "0970978427126ebdc4953b83de9f1197b7ccd6811a07b4d76ec7fe028cde1f3f.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "During inference, it can be directly removed, rendering a semantics-sensitive dual encoder."
+                                }
+                            ]
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+                    ],
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+                                    "content": "3.2. Feature Encoder"
+                                }
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+                                    "type": "text",
+                                    "content": "Video Encoder. For an input video "
+                                },
+                                {
+                                    "bbox": [
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+                                        123,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we first segment it into small video clips and perform a fixed-interval sampling over these clips. Then the video clips are fed into a pretrained 3D CNN model (e.g. C3D) to extract the video features "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "F_{i}^{V}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Referring to the previous works [75], we employ sparse sampling and a proposal network to construct the feature map "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        123,
+                                        530,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F_{i}^{M} = \\{m_{i}\\}_{i=1}^{N_{m}}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        123,
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+                                    "type": "text",
+                                    "content": " of moment candidates based on "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "F_{i}^{V}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "N_{m}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the number of proposals in the video."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Query Encoder. For a textual query "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        217,
+                                        530,
+                                        275
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "Q_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        217,
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+                                        275
+                                    ],
+                                    "type": "text",
+                                    "content": ", we generate the tokens of words by the tokenizer and add a class embedding token '[CLS]' in the beginning. Then the tokens are fed into pre-trained BERT [27], and we perform average pooling of its last two hidden states to obtain the sentence feature "
+                                },
+                                {
+                                    "bbox": [
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+                                        217,
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+                                    "type": "inline_equation",
+                                    "content": "q_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.3. Geodesic Distance Computation"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Video content is intricate and flexible, and for video clips, temporal proximity does not always equate to semantic similarity. Conversely, two video clips can have strong correlations even though they are temporally distant. We propose to measure correlations of video representations using the geodesic distance. Formally, we define a mini-batch of video-query pairs as "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{V_i, Q_i\\}_{i=1}^B"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "B"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " is the size of the mini-batch. After fed into the video and query encoders, we obtain textual representation "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L = \\{q_i\\}_{i=1}^B"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " and moment representations "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "M = \\{m_i\\}_{i=1}^{B \\times N_m}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        298,
+                                        530,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "The video moments representations may lie in a high-dimensional manifold, and our purpose is to measure the geodesic distance between two points along the manifold. However, computing the exact geodesic distance [29] is difficult without explicit knowledge of the manifold structure. To obtain the geodesic distance, we first employ the K-NN graph [15] to approximate the manifold structure [52, 14]. In this graph, each moment "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " forms a node, and each node connects to at most "
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " other nodes. A directed edge exists from node "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                    "bbox": [
+                                        296,
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+                                    "type": "text",
+                                    "content": " to node "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_{j}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": " if node "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                        602
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+                                    "type": "inline_equation",
+                                    "content": "m_{j}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is among the "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "n"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        415,
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+                                        602
+                                    ],
+                                    "type": "text",
+                                    "content": " nearest neighbors of "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        415,
+                                        530,
+                                        602
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_{i}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        415,
+                                        530,
+                                        602
+                                    ],
+                                    "type": "text",
+                                    "content": ". The edge weight "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        415,
+                                        530,
+                                        602
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d(m_{i},m_{j})"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        415,
+                                        530,
+                                        602
+                                    ],
+                                    "type": "text",
+                                    "content": " is defined using cosine similarity: "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        415,
+                                        530,
+                                        602
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d(m_{i},m_{j}) = 1 - m_{i}m_{j}^{\\top}"
+                                },
+                                {
+                                    "bbox": [
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+                                        415,
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+                                        602
+                                    ],
+                                    "type": "text",
+                                    "content": ". Finally, we utilize the shortest path algorithm, i.e., Dijkstra [16], to compute the length of the shortest path between two moments along the obtained weighted directed graph as the geodesic distance "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}(m_i,m_j)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "type": "text",
+                                    "content": "3.4. Geodesic-guided Contrastive Learning"
+                                }
+                            ]
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+                    ],
+                    "index": 14
+                },
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+                                    "type": "text",
+                                    "content": "Previous Contrastive Scheme. In video grounding, a query usually corresponds to multiple clips. An intuitive method [17] to learn representations is to set the clips in ground truth intervals as positive samples, while others are negatives. Another scheme [59] is to calculate the intersection over union (IoU) between the ground truth and other moments, where those with higher IoU are considered as positive samples and the lower ones are regarded as negative samples. Then they learn the joint representation by"
+                                }
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+                                            "type": "text",
+                                            "content": "Figure 2. Overview of Geodesic and Game Localization (G2L). Our framework encourages the model to learn semantically aligned and uniform joint representations. In the inference stage, we directly fuse the video features and query features to compute the predicted moments. In the training stage, the grounding loss "
+                                        },
+                                        {
+                                            "bbox": [
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+                                            "type": "inline_equation",
+                                            "content": "\\mathcal{L}_{\\mathrm{VG}}"
+                                        },
+                                        {
+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": " is obtained by calculating the cross-entropy between the predicted moment and the target moment. Then, we approximate the high-dimensional manifold structure of the video representations through a moment graph and calculate the geodesic distance from the target moment to other moments. Finally, we leverage geodesic distance for cross-modal discrimination and semantic Sharpley interaction modeling."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1,
+                            "angle": 0,
+                            "type": "image_caption"
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+                                    "type": "text",
+                                    "content": "pulling the query features and ground truth moment features together, and pushing the query features and non-ground truth moment features apart. The previous contrastive loss "
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+                                    "type": "text",
+                                    "content": " can be formulated as:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {V C L}} = - \\sum_ {i = 1} ^ {B} \\left(\\log \\frac {\\exp \\left(q _ {i} m _ {i} ^ {\\top} / \\tau\\right)}{\\sum_ {m _ {j} \\in M} \\exp \\left(q _ {i} m _ {j} ^ {\\top} / \\tau\\right)}\\right) \\tag {2}",
+                                    "image_path": "e290ff949f61a304383a8629bd5a0722112c2803c5d0621cf684152d95b2b199.jpg"
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+                                    "content": "where "
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+                                    "content": "\\tau"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the temperature hyper-parameter."
+                                }
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+                    ],
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+                {
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+                    "lines": [
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+                                    "type": "text",
+                                    "content": "While intuitive, such a manner fails to capture semantic alignment and uniformity between queries and video content. To learn complete semantic alignment and uniformity for video grounding, we propose geodesic-guided contrastive learning."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
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+                {
+                    "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Semantic Alignment. In vanilla supervised contrastive learning [56, 28], all classes play the same role: pulling is done within every class and pushing between every pair of different classes. Such uniform contrastive learning works well for symmetric and equal cross-modal learning. In fact, due to semantic overlapping, the semantics of the video and text are asymmetric and unequal in video grounding. Temporally distant moments may have similar semantics. To model semantic alignment, we discriminate positive pairs based on the geodesic distance instead of the temporal moment. For a query feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": ", we define the "
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+                                    "type": "inline_equation",
+                                    "content": "k"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " moments with the closest geodesic distance from the target moment "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{m}_i \\in M"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " as its semantic positive samples "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "P_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ":"
+                                }
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+                                    "type": "interline_equation",
+                                    "content": "P _ {i} = \\left\\{p _ {i} ^ {k} \\right\\} = \\underset {k} {\\arg \\operatorname {t o p k}} \\mathcal {G} (\\hat {m} _ {i}, m _ {k}) \\tag {3}",
+                                    "image_path": "cba02909c16e7261bf5b6b40c47ed8a7f18e5afa90ee33d364e64a2d3c0d0021.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": " contains "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and moments adjacent to "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_{i}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " geodesic which is used to construct positive pairs with "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
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+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to relax the previous strict positional principle."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Semantic Uniformity. Due to the sparse annotation dilemma [67, 31], most of the moments are only marked as negative while pushed away by different queries. Notably, this push operation is undifferentiated, i.e., the model is encouraged to learn to push all unannotated moments from the annotated ones. This clearly undermines the model to learn correct semantics. To learn semantic uniformity, we introduce the geodesic distance to differentially push negative samples away from the query based on semantic relationships. The similarity between query and moment "
+                                },
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "s(q_i, m_j)"
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+                                    ],
+                                    "type": "text",
+                                    "content": " is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "s \\left(q _ {i}, m _ {j}\\right) = \\exp \\left(q _ {i} m _ {j} ^ {\\top} \\left(\\hat {m} _ {i} m _ {j} ^ {\\top} \\log \\frac {1}{\\exp \\left(\\mathcal {G} \\left(\\hat {m} _ {i} , m _ {j}\\right) + 1\\right)}\\right)\\right) \\tag {4}",
+                                    "image_path": "2ade1a2ffed461ebc629888f6869e4c19a24135387c3f11d671ffde1f1936bb2.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "We assign corresponding weights according to the geodesic distance "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}(\\hat{m}_i, m_j)"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " between the target moment "
+                                },
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{m}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and all moments "
+                                },
+                                {
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "m_j"
+                                },
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+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s(q_i, m_j)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " considers the relationships between negative samples while maximizing mutual information."
+                                }
+                            ]
+                        }
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+                    "index": 11
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+                                    "type": "text",
+                                    "content": "Finally, our geodesic-guided contrastive loss can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} _ {\\mathrm {G C L}} = - \\sum_ {i = 1} ^ {B} \\left(\\log \\frac {\\sum_ {p _ {i} ^ {k} \\in P _ {i}} \\exp \\left(q _ {i} p _ {i} ^ {k} ^ {\\top} / \\tau\\right)}{\\sum_ {m _ {j} \\in M} s \\left(q _ {i} , m _ {j}\\right) / \\tau}\\right) \\tag {5}",
+                                    "image_path": "20aa180a61d4538c5d21e6560e517f4659042dbded7a69b711f62fa95e083ccd.jpg"
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+                                    "type": "text",
+                                    "content": "In contrast to Equation 2, "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{GCL}}"
+                                },
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+                                    "type": "text",
+                                    "content": " is designed for representa"
+                                }
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+                                    "type": "text",
+                                    "content": "tion learning rather than directly learning localization."
+                                }
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+                                    "type": "text",
+                                    "content": "3.5. Semantic Shapley Interaction Modeling"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "type": "text",
+                                    "content": "To prevent the model from confusing similar video moments due to the relaxed contrastive objective in Equation 3, we propose semantic Shapley interaction to model fine-grained semantic alignment."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.5.1 Preliminaries"
+                                }
+                            ]
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+                    "index": 3
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+                                    "type": "text",
+                                    "content": "Shapley Value. The Shapley value [49] is a classical game theory solution for the unbiased estimation of the contribution of each player in a cooperation game. Assume a game consists of "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " players, "
+                                },
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U} \\subseteq \\mathcal{N}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        213,
+                                        280,
+                                        318
+                                    ],
+                                    "type": "text",
+                                    "content": " represents a potential subset of players. A game function "
+                                },
+                                {
+                                    "bbox": [
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+                                        213,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " maps each subset "
+                                },
+                                {
+                                    "bbox": [
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+                                        318
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": " of players to a score, estimating the cooperated contribution of a set of players. For a player "
+                                },
+                                {
+                                    "bbox": [
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+                                        213,
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+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", its Shapley value "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        213,
+                                        280,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\phi(i|\\mathcal{N})"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        213,
+                                        280,
+                                        318
+                                    ],
+                                    "type": "text",
+                                    "content": " is computed as the average marginal contribution of player "
+                                },
+                                {
+                                    "bbox": [
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+                                        213,
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+                                        318
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        213,
+                                        280,
+                                        318
+                                    ],
+                                    "type": "text",
+                                    "content": " to all possible coalitions "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " without "
+                                },
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ":"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\phi (i \\mid \\mathcal {N}) = \\sum_ {\\mathcal {U} \\subseteq \\mathcal {N} \\backslash \\{i \\}} p (\\mathcal {U}) [ f (\\mathcal {U} \\cup \\{i \\}) - f (\\mathcal {U}) ] (6) \\\\ p (\\mathcal {U}) = \\frac {| \\mathcal {U} | ! (| \\mathcal {N} | - | \\mathcal {U} | - 1) !}{| \\mathcal {N} | !} (7) \\\\ \\end{array}",
+                                    "image_path": "e44748b547f4baa06c2cf05b253684c8291543c869fb4e2552cdc195a1747a23.jpg"
+                                }
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+                {
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+                    "lines": [
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+                                {
+                                    "bbox": [
+                                        45,
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        389,
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+                                        447
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p(\\mathcal{U})"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        389,
+                                        279,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is the likelihood of "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        389,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        389,
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+                                    ],
+                                    "type": "text",
+                                    "content": " being sampled. The Shapley value has been proved to be the unique metric that satisfies the following axioms: Linearity, Symmetry, Dummy, and Efficiency. We summarize these axioms in the supplementary material."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                        {
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Shapley Interaction. In game theory, some players tend to form a small cooperative coalition and always participate in the game together. This cooperation provides additional contributions to the game. The Shapley interaction [20] measures the additional contributions made by the coalition compared to players working individually. We define "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathcal{U}]"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as a single hypothetical player, which is the union of the players in "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ". A reduced game is formed by removing the individual players in "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " from the game and adding "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "[\\mathcal{U}]"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " to the game. Finally, according to Equation 6, the Shapley interaction for coalition "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        447,
+                                        279,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
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+                                        279,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        50,
+                                        582,
+                                        279,
+                                        607
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\Im ([ \\mathcal {U} ]) = \\phi ([ \\mathcal {U} ] \\mid \\mathcal {N} \\backslash \\mathcal {U} \\cup \\{[ \\mathcal {U} ] \\}) - \\sum_ {i \\in \\mathcal {U}} \\phi (i \\mid \\mathcal {N} \\backslash \\mathcal {U} \\cup \\{i \\}) \\tag {8}",
+                                    "image_path": "914deb1da0e7a36f40a6ae5f26288b94cfc188d05c497dc0938e3baa900f7349.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        45,
+                        615,
+                        279,
+                        650
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                45,
+                                615,
+                                279,
+                                650
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Im ([\\mathcal{U}])"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "text",
+                                    "content": " reflects the interactions inside "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "text",
+                                    "content": ". The higher value of "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Im ([\\mathcal{U}])"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "text",
+                                    "content": " indicates that players in "
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{U}"
+                                },
+                                {
+                                    "bbox": [
+                                        45,
+                                        615,
+                                        279,
+                                        650
+                                    ],
+                                    "type": "text",
+                                    "content": " cooperate closely with each other."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        46,
+                        665,
+                        270,
+                        677
+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                665,
+                                270,
+                                677
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        665,
+                                        270,
+                                        677
+                                    ],
+                                    "type": "text",
+                                    "content": "3.5.2 Fine-Grained Semantic Alignment via Shapley"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        45,
+                        683,
+                        279,
+                        730
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                45,
+                                683,
+                                279,
+                                730
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        45,
+                                        683,
+                                        279,
+                                        730
+                                    ],
+                                    "type": "text",
+                                    "content": "According to Equation 6 and Equation 8, it can be known that the computational complexity of the Shapley interaction grows factorially as the number of players increases. To reduce the computational cost, we propose semantic"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
+                        296,
+                        106,
+                        530,
+                        176
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                296,
+                                106,
+                                530,
+                                176
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
+                                        106,
+                                        530,
+                                        176
+                                    ],
+                                    "type": "text",
+                                    "content": "Shapley interaction based on geodesic distance sampling. Specifically, as in Equation 3, we sample semantic similar moments based on geodesic distances to investigate their nuances. Then, we consider queries and semantic similar moments from the same video as players in the same cooperative game."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
+                        296,
+                        179,
+                        530,
+                        274
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                296,
+                                179,
+                                530,
+                                274
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": "To avoid confusion with the previous symbols, we define "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{H}_i^V = \\{\\mathbf{h}_{ix}^V\\}_{x=1}^{N_i^v}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{H}_i^Q = \\{\\mathbf{h}_{iy}^Q\\}_{y=1}^{N_i^q}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " are a set of semantic positive samples and queries from the video "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " respectively, where "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_i^v = KN_i^q"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N_i^q"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " indicate the number of similar moments and queries in video "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " respectively. "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " is the number of moments sampled for each query "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{h}_{iy}^Q"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": ". We investigate the effect of "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        179,
+                                        530,
+                                        274
+                                    ],
+                                    "type": "text",
+                                    "content": " on computational cost and performance in the supplementary material."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
+                    "bbox": [
+                        296,
+                        277,
+                        530,
+                        446
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                296,
+                                277,
+                                530,
+                                446
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": "If a query and a video moment have strong semantic correspondence, then they tend to cooperate with each other and contribute to the coalition. Thus, we can take "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{H}^i = \\mathcal{H}_i^V \\cup \\mathcal{H}_i^Q"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " as the players in the same game inspired by [32]. We define the alignment matrix as: "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}_i = [a_{xy}^i]"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{xy}^i = h_{ix}^{V^\\top}h_{iy}^Q"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the alignment score between "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": "-th moment and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": "-th query in video "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ". Next, "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{\\mathcal{A}}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " is obtained by applying softmax-normalization over each row of "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we average the maximum alignment score "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\max_y \\tilde{a}_{xy}^i"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " as the fine-grained moment-to-query similarity "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\psi_1"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ". Similarly, we can obtain the fine-grained query-to-moment similarity "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\psi_2"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ". The total fine-grained similarity score can be defined: "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\psi = (\\psi_1 + \\psi_2) / 2"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": ", which be considered as the game score "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "f(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        277,
+                                        530,
+                                        446
+                                    ],
+                                    "type": "text",
+                                    "content": " in our game."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 14
+                },
+                {
+                    "bbox": [
+                        296,
+                        448,
+                        530,
+                        471
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                296,
+                                448,
+                                530,
+                                471
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
+                                        448,
+                                        530,
+                                        471
+                                    ],
+                                    "type": "text",
+                                    "content": "According to Equation 8, the semantic Shapley interaction of them can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
+                        298,
+                        485,
+                        530,
+                        573
+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                298,
+                                485,
+                                530,
+                                573
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        298,
+                                        485,
+                                        530,
+                                        573
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\Im \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right]\\right) = \\phi \\left(\\left[ \\mathcal {H} _ {x y} ^ {i} \\right] \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\{\\left[ \\mathcal {H} _ {x y} ^ {i} \\right] \\}\\right) \\\\ - \\phi \\left(\\mathbf {h} _ {i x} ^ {V} \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\left\\{\\mathbf {h} _ {i x} ^ {V} \\right\\}\\right) \\\\ - \\phi \\left(\\mathbf {h} _ {i y} ^ {Q} \\mid \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i} \\cup \\left\\{\\mathbf {h} _ {i y} ^ {Q} \\right\\}\\right) (9) \\\\ = \\mathbb {E} _ {\\mathcal {C}} \\left\\{\\underset {| \\mathcal {U} | = \\mathcal {C}} {\\mathcal {U} \\subseteq \\mathcal {H} ^ {i} \\backslash \\mathcal {H} _ {x y} ^ {i}} \\mathbb {E} \\left[ f \\left(\\mathcal {U} \\cup \\mathcal {H} _ {x y} ^ {i}\\right) - f \\left(\\mathcal {U} \\cup \\left\\{\\mathbf {h} _ {i x} ^ {V} \\right\\}\\right) \\right. \\right. \\\\ \\left. - f \\left(\\mathcal {U} \\cup \\left\\{\\mathbf {h} _ {i y} ^ {Q} \\right\\}\\right) + f (\\mathcal {U}) \\right] \\rbrace (10) \\\\ \\end{array}",
+                                    "image_path": "56436c50a3ad80062241ff10d7c61dd59c2dd162c7526f3af590ce0d27877c5b.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
+                        296,
+                        586,
+                        530,
+                        644
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                296,
+                                586,
+                                530,
+                                644
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Im \\left(\\left[\\mathcal{H}_{xy}^{i}\\right]\\right)"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the single player formed by the coalition of "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "text",
+                                    "content": "-th moment and "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "text",
+                                    "content": "-th query in video "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "V_{i}, \\mathcal{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "text",
+                                    "content": " represents the coalition size. We take normalized "
+                                },
+                                {
+                                    "bbox": [
+                                        296,
+                                        586,
+                                        530,
+                                        644
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Im'\\left(\\left[\\mathcal{H}_{xy}^{i}\\right]\\right)"
+                                },
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+                                    "content": "ActivityNet-Captions. ActivityNet-Captions [30] contains 20,000 untrimmed videos and 100,000 descriptions [3], covering a wide range of complex human behavior. The video clips with annotations have much larger variations. Following the public split [75], we use 37417, 17505 and 17031 sentence-video pairs for training, validation and testing, respectively."
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+                                    "content": "Charades-STA. The Charades dataset [50] is collected for video action recognition and video captioning. Gao et al. [18] adapt the Charades dataset to the video grounding task by collecting the query annotations. The Charades-STA dataset contains 6672 videos and involves 16128 video-query pairs, where 12408 pairs are used for training and 3720 for testing. We follow the same split of the dataset as in Gao et al. [18] for fair comparisons."
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+                                    "content": "Evaluation. Following previous work [18, 75], we adopt \"R@n, IoU=m\" as the evaluation metric. It calculates the percentage of IoU greater than \"m\" between at least one of the top \"n\" video moments retrieved and the ground truth."
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+                                            "content": "Table 1. Performance comparisons on ActivityNet-Captions using C3D features."
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+                                    "content": "4.2. Implementation Details"
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+                                    "content": "For a fair comparison, we extracted video features from a pre-trained 3D CNN (C3D for ActivityNet-Captions and TACoS, VGG for Charades-STA) following previous works [59, 17, 45]. We uniformly sampled (256, 32, 256) clips as the input video sequence and set the length of 2D feature map [75] (64, 16, 128) for ActivityNet-Captions, Charades-STA, and TACoS, respectively. For the language query, the pre-trained BERT[27] was employed for each word of the query. The average pooling outputs of the first and last layers were used to obtain the embedding of the whole sentence. We employed the AdamW optimizer [40] to train our model and set the temperature weight "
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+                                    "content": " to 0.1. The learning rates were set to "
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+                                    "content": " for ActivityNet-Captions, Charades-STA, and TACoS, respectively. We conducted experiments on 8 A100 GPUs with batch size 48 for ActivityNet-Captions and Charades-STA, and on 4 A100 GPUs with batch size 8 for TACoS."
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+                                    "content": "Comparison on ActivityNet-Captions. In Table 1, we report our performance in comparison with other state-of-the-art methods on ActivityNet-Captions. Compared with IVG-DCL [45] and SSCS [17], which are also based on contrastive learning, our method achieves significant improvements. Notably, ActivityNet-Captions is currently the dataset with the most severe semantic overlapping and sparse annotation dilemma. We observe that our model showed even more significant improvements on ActivityNet-Captions, achieving absolute improvements of up to "
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+                                    "content": " compared to IVG-DCL [45] and SSCS [17], respectively. They encourage the model to focus on cross-modal alignment in favor of grounding while ig-"
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+                                    "content": "noring the semantics among full moments, especially unannotated moments. In contrast, our method conducts cross-modal discrimination guided by the geodesic distance such that overcoming data bias."
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+                                    "content": "Comparison on Charades-STA. Table 2 reports the result comparison between state-of-the-art methods on Charades-STA. Compared with SSCS [17], our method achieves a performance improvement of up to "
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+                                    "content": ". On more stringent evaluation metrics, such as “R@1 IoU=0.7”, our method achieves a performance improvement of "
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+                                    "content": " compared to the cutting-edge method MMN [59], which indicates that exploring fine-grained semantic alignment information between similar video moments can improve grounding quality. Notably, MMN [59] and SSCS [17] have similar loss functions, and MMN [59] from a perspective on temporal grounding as a metric-learning problem proposes a mutual matching network to enhance joint representation learning by mining more negative samples achieving better performances. However, it also constructs cross-modal pairs based on the temporal moment, which results in a large number of constructed negative pairs containing potential weak semantic positive pairs, thus hindering learning."
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+                                    "content": "Comparison on TACoS. Table 3 summarizes the comparisons on the TACoS. We observe that our model achieves state-of-the-art results in most settings. However, the performance gain on this dataset is smaller than the previous three datasets. The reason is that the sparse annotation dilemma and semantic overlapping are insignificant on TACoS. It contains only 127 videos but has about 20,000 queries and focuses on cooking activities with more uniform objects, roles, and actions. Nevertheless, our method still outperforms previous contrastive learning-based methods in various metrics."
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+                                            "content": "Table 3. Performance comparisons on TACoS using C3D features."
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+                                            "content": "Table 4. Ablation studies of main components on ActivityNetCaptions. \"SA\" and \"SU\" denote the Semantic Alignment and the Semantic Uniformity in GCL, respectively."
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+                                    "content": "Table 5. Comparison of different distance metrics on ActivityNet-Captions."
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+                                    "content": "5. Ablation Study"
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+                                    "content": "Effectiveness of Individual Components. In Table 4, we conduct a thorough ablation study on the proposed components to verify their effectiveness. As shown in Table 4, removing the entire GCL will result in up to "
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+                                    "type": "text",
+                                    "content": " of performance degradation, demonstrating the contribution of GCL by learning semantic alignment and unification. We also observe that removing either SA or SU results in about 2 points of performance drop on average, indicating that our method enables the vanilla contrastive learning to be more suitable for video grounding setting. Removing SSI leads to a "
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+                                    "type": "text",
+                                    "content": " drop in performance on the more stringent metric (i.e., \"R@1 IoU=0.7\"), which highlights the importance of fine-grained semantic alignment for high-quality moment retrieval. The last row shows our baseline, and our method achieves up to 6 points of performance improvement without modifying the architecture compared to the baseline, confirming the superiority of our model."
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+                                    "content": "Effectiveness of Geodesic Distance. To demonstrate the effectiveness of the geodesic, we substitute it with different distance metrics in the model, including euclidean distance, timestamp distance, and cosine distance, and compare their performances as shown in Table 5. It can be observed that when using euclidean distance, the performances drop by up to "
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+                                    "content": ". This is due to the fact that video representations often lie in a high dimensional manifold and euclidean distance cannot accurately quantify the correlations among video moments. When using timestamp distance, the performances decrease by "
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+                                    "content": " on average, indicating that the temporal adjacency does not necessarily"
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+                                            "content": "Figure 3. Projected video moment features (a): learned representations of the previous method with vanilla contrastive learning; (b): learned representations of our method."
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+                                    "type": "text",
+                                    "content": "correspond to semantic similarity due to the flexibility and complexity of video content. Using cosine distance results in performances dropping by up to "
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+                                    "content": ". Due to the insufficient representation capacity of the model in the early training stage to accurately calculate similarity. We approximate the manifold structure of video features using the moment graph, where the reachability and the shortest path in the graph can facilitate similarity measurement."
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+                                    "content": "The efficiency of our method. In Table 6, we compute the average training time per iteration and total inference time. Due to the K-NN graph and Shapley interaction, G2L requires more training costs. During inference, GCL and SSI can be removed thus our G2L only needs additional 3s compared to the base model."
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+                                    "content": "6. Qualitative Analysis"
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+                                    "content": "We visualize a sample video from the ActivityNetCaptions into the 2D images using t-SNE [53]. In Figure 3(a), we observe that there is a clear \"island\" in the learned representations of the previous method. We argue that it is formed by a few moments which are temporally adjacent to the ground truth. The reason is that the previous method divides positive and negative samples based on the strict temporal moment while pushing negative samples away by different queries, regardless of the semantic relationships. In contrast, our method relaxes the previous strict contrastive objective using geodesic distance, mitigating semantic overlapping and sparse annotation dilemma. Furthermore, the semantic Shapley interaction enables our model to capture discriminative features between similar moments. Our method learns aligned and uniform representations thus eliminating the \"island\" in Figure 4(b),"
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+                                    "type": "text",
+                                    "content": "We present two qualitative results from ActivityNet-"
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+                                    "type": "text",
+                                    "content": "Query: The old woman is on the chair knitting again."
+                                }
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+                                    "content": "Query: The person sharpens the blade on the second belt."
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+                                            "content": "Figure 4. Qualitative results of our method on the ActivityNet-Captions."
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+                                    "content": "Captions in Figure 4. We observe that our approach can successfully model the relationships of temporally distant moments. For instance, \"knitting again\" in Figure 4(a) and \"the second belt\" in Figure 4(b) are far away from their first appearances. Our method can capture the information of \"first knitting\" and \"the first belt\" and infer precisely the location of the target moment. Previous contrastive learning-based methods fail to capture this semantic association due to tending to perform cross-modal contrast by the strict positional principle. These models only focus on the contextual content related to the target moment. Our method demonstrates that these large volumes of unannotated moments contain rich information and modeling their relationships can improve representation learning."
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+                                    "content": "This paper introduces a novel semantically aligned and uniform video grounding method, Geodesic and Game Localization (G2L), which explores more semantic information by measuring the correlation between video moments through the geodesic and models the nuances of similar moments using game-theoretic interactions. By contrasting the video features and query features in the shared space, the learned bi-modal features become similar when their semantics match, and the similarity between video moments is modeled by the geodesic-guided pushing operation. Extensive experiments demonstrate that our novel training objective significantly improves the performance of existing contrastive learning-based methods in video grounding. This paper provides a novel perspective for cross-modal contrastive learning. In the future, we intend to apply this idea to multi-modal pre-training."
+                                }
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+                                    "type": "text",
+                                    "content": "Acknowledgment. This paper was partially supported by NSFC (No: 62176008) and Shenzhen Science & Technology Research Program (No: GXWD20201231165807007-20200814115301001)."
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+                                }
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+                    ],
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+                                            "bbox": [
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+                                            "type": "text",
+                                            "content": "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In Proceedings of the IEEE international conference on computer vision, pages 5803-5812, 2017. 2, 6"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 1
+                        },
+                        {
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+                                51,
+                                182,
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+                                        {
+                                            "bbox": [
+                                                51,
+                                                182,
+                                                279,
+                                                214
+                                            ],
+                                            "type": "text",
+                                            "content": "[2] Anthony J Bell and Terrence J Sejnowski. An information-maximization approach to blind separation and blind deconvolution. Neural computation, 7(6):1129-1159, 1995. 2"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 2
+                        },
+                        {
+                            "bbox": [
+                                51,
+                                216,
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+                                            "bbox": [
+                                                51,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[3] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 961-970, 2015. 6"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 3
+                        },
+                        {
+                            "bbox": [
+                                51,
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+                            ],
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+                                            "bbox": [
+                                                51,
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+                                            ],
+                                            "type": "text",
+                                            "content": "[4] Meng Cao, Long Chen, Mike Zheng Shou, Can Zhang, and Yuexian Zou. On pursuit of designing multi-modal transformer for video grounding. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 9810-9823, 2021. 6, 7"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 4
+                        },
+                        {
+                            "bbox": [
+                                51,
+                                328,
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+                            ],
+                            "type": "ref_text",
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+                                            "bbox": [
+                                                51,
+                                                328,
+                                                279,
+                                                370
+                                            ],
+                                            "type": "text",
+                                            "content": "[5] Meng Cao, Ji Jiang, Long Chen, and Yuexian Zou. Correspondence matters for video referring expression comprehension. In Proceedings of the 30th ACM International Conference on Multimedia, pages 4967-4976, 2022. 1"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
+                            "bbox": [
+                                51,
+                                373,
+                                279,
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+                            ],
+                            "type": "ref_text",
+                            "angle": 0,
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+                                        {
+                                            "bbox": [
+                                                51,
+                                                373,
+                                                279,
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+                                            "type": "text",
+                                            "content": "[6] Meng Cao, Fangyun Wei, Can Xu, Xiubo Geng, Long Chen, Can Zhang, Yuexian Zou, Tao Shen, and Daxin Jiang. Iterative proposal refinement for weakly-supervised video grounding. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6524-6534, 2023. 1"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 6
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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+                                            "bbox": [
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+                                            ],
+                                            "type": "text",
+                                            "content": "[7] Meng Cao, Tianyu Yang, Junwu Weng, Can Zhang, Jue Wang, and Yuexian Zou. Locvtp: Video-text pre-training for temporal localization. In European Conference on Computer Vision, pages 38-56. Springer, 2022. 1"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 7
+                        },
+                        {
+                            "bbox": [
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+                            "type": "ref_text",
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diff --git a/2023/GACE_ Geometry Aware Confidence Enhancement for Black-Box 3D Object Detectors on LiDAR-Data/4d4269c1-ea16-4959-9423-14c51ea10997_content_list.json b/2023/GACE_ Geometry Aware Confidence Enhancement for Black-Box 3D Object Detectors on LiDAR-Data/4d4269c1-ea16-4959-9423-14c51ea10997_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..69be208a1d1e2069d48e9574bbc25496c66dc706
--- /dev/null
+++ b/2023/GACE_ Geometry Aware Confidence Enhancement for Black-Box 3D Object Detectors on LiDAR-Data/4d4269c1-ea16-4959-9423-14c51ea10997_content_list.json	
@@ -0,0 +1,1423 @@
+[
+    {
+        "type": "text",
+        "text": "GACE: Geometry Aware Confidence Enhancement for Black-box 3D Object Detectors on LiDAR-Data",
+        "text_level": 1,
+        "bbox": [
+            207,
+            130,
+            759,
+            174
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "David Schinagl<sup>1,2</sup> Georg Krispel<sup>1</sup> Christian Fruhwirth-Reisinger<sup>1,2</sup> Horst Possegger<sup>1</sup> Horst Bischof<sup>1,2</sup>",
+        "bbox": [
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+            202,
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+            222
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "{david.schinagl,georg.krispel,reisinger,possegger,bischof}@icg.tugraz.at",
+        "bbox": [
+            166,
+            223,
+            802,
+            238
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$  Graz University of Technology  $^{2}$  Christian Doppler Laboratory for Embedded Machine Learning",
+        "bbox": [
+            94,
+            238,
+            874,
+            257
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            291,
+            313,
+            306
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Widely-used LiDAR-based 3D object detectors often neglect fundamental geometric information readily available from the object proposals in their confidence estimation. This is mostly due to architectural design choices, which were often adopted from the 2D image domain, where geometric context is rarely available. In 3D, however, considering the object properties and its surroundings in a holistic way is important to distinguish between true and false positive detections, e.g. occluded pedestrians in a group. To address this, we present GACE, an intuitive and highly efficient method to improve the confidence estimation of a given black-box 3D object detector. We aggregate geometric cues of detections and their spatial relationships, which enables us to properly assess their plausibility and consequently, improve the confidence estimation. This leads to consistent performance gains over a variety of state-of-the-art detectors. Across all evaluated detectors, GACE proves to be especially beneficial for the vulnerable road user classes, i.e. pedestrians and cyclists.",
+        "bbox": [
+            75,
+            324,
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+            612
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            645,
+            209,
+            660
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Three-dimensional perception of surrounding objects is a critical component for autonomous vehicles and robots. Many modern perception systems use point cloud data from LiDAR (Light Detection and Ranging) sensors for this task, since they can provide accurate 3D information even over long distances. The popularity of these sensors can be seen in the increased research interest in LiDAR-based 3D object detection approaches, e.g. [10,29,38,40,45,47] and the large number of recently published autonomous driving datasets that include LiDAR data, e.g. [1,6,20,33].",
+        "bbox": [
+            75,
+            672,
+            468,
+            823
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "However, the characteristics of LiDAR data impose significant challenges for object detection. Unlike pixels in an image, which are aligned in a regular grid, point clouds represent 3D data as a collection of individual points in space, each with its own set of coordinates. In addition to the un",
+        "bbox": [
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+            824,
+            468,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/5265d3d98b486110eac37ada6f65e0f93fa999e2f324a65deb45154152d3621c.jpg",
+        "image_caption": [],
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+        "image_caption": [
+            "Figure 1. Context matters: a baseline detector struggles at detecting true positive objects confidently if the sampling pattern is atypical, e.g. the occluded pedestrian in the orange bounding box (close-up top-left). GACE exploits the geometric properties of the detection and its surrounding objects to significantly increase the score for this detection, which is intuitively correct for a human observer considering this scene."
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+        "text": "structured nature of the data, the highly variable point density poses a major challenge. Due to the angular offset of the LiDAR beams, the density is highly dependent on the distance to the object and can be altered by occlusions in the foreground. This often requires detecting objects based on very few data points, which is especially true for classes with smaller spatial dimensions, such as pedestrians and cyclists. For example, in the Waymo Open Dataset [33], one of the most widely used and challenging datasets to date, about 30 percent of all annotated pedestrians consist of less than merely 20 points. Detecting these sparsely sensed objects naturally leads to a large number of false positive detections at test time. For this reason, determining a meaningful confidence value for the detections is critical to find a trade-off between precision and recall that adequately dis",
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+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_number",
+        "text": "6566",
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+    {
+        "type": "text",
+        "text": "tinguishes true positives from false positives. The potential that could be exploited by improving the confidence score is considerable: Suppose we have an oracle that could correctly classify the detections of a SECOND [38] model on the Waymo dataset into true and false positives. This would increase the LEVEL_1 average precision for vehicles by  $+3.96\\mathrm{AP}$  and, more importantly, for pedestrians and cyclists by as much as  $+10.71\\mathrm{AP}$  and  $+13.74\\mathrm{AP}$ , respectively.",
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+        "type": "text",
+        "text": "Existing 3D object recognition pipelines, including confidence estimation approaches, were largely inspired by 2D image-based object recognition models and then gradually adapted to point cloud processing. However, the conventional backbone - neck - head architecture of the 2D detection model was largely retained, e.g. in [8, 10, 15, 27, 38, 45]. After extracting features (point-based, voxel-based, or region-based) over multiple levels in the backbone, they are fused in the neck module and then passed to the detection head, where bounding box regression and confidence estimation are performed on a dense feature representation. Typically, separate branches are used within the head for bounding box regression and confidence estimation, each consisting of one or more fully connected layers on top of the common feature representation.",
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+        "type": "text",
+        "text": "Unlike image-based object detection, there are several highly relevant geometric properties inherent to objects in 3D point clouds that have been largely unexploited in assessing the confidence of a detection. In the image case, it is usually not possible to easily derive geometric properties for the objects, such as height or orientation, unless a static and fully calibrated camera and a known or constant scene are given. In contrast, in 3D object detection, many geometric features are directly available in the object properties and associated 3D data points to better assess the presence of a real object. On the one hand, these are instance-specific properties, such as the dimension of the object, the heading direction, the position, or the point distribution within the bounding box. For example, as shown in Figure 2, the precision of a SECOND [38] model for detecting a vehicle is highly dependent on the size of the object and from which side it is detected by the LiDAR. It can be seen that vehicle categories between passenger cars and heavy duty vehicles (i.e. vehicles with a length of 6 to  $13\\mathrm{m}$ ) are harder to detect, potentially because they are underrepresented in the dataset, and that vehicles are easier to detect from behind (i.e. viewing angle between  $\\pm 45$  degrees), presumably because of the highly reflective license plates, as shown in [25]. On the other hand, contextual properties, i.e. geometric relationships to neighboring objects, can contribute to a more reliable estimation of the confidence. For example, as shown in Figure 1, a pedestrian that appears atypical due to occlusions can be assessed more reliably by additionally taking neighboring vehicles and pedestrians into consideration.",
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+        "type": "image",
+        "img_path": "images/d43d792d566597fdd64b3566ecc7d6b662aea91997f90cc4dec1bfc62233b66f.jpg",
+        "image_caption": [],
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+        "img_path": "images/d86719ac89cf3ca1ec802290accc6699089b58527ce30848f53141709098fee8.jpg",
+        "image_caption": [
+            "Figure 2. Precision of a SECOND [38] model for the Waymo [33] vehicle class as a function of the object length (top) and of the viewing angle (bottom), indicating from which side the vehicle is seen by the LiDAR, where 0 degrees corresponds to the rear view. These examples illustrate the strong dependence of the precision on simple geometric object properties."
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+        "type": "text",
+        "text": "Nevertheless, these simple but highly informative metric properties are neglected when estimating the confidence score in current detector architectures for the following reasons: First, in grid-based models, information such as the exact point distribution within the bounding box or the number of points is already partially discarded by the discretization (voxelization) in the preprocessing phase. Second, the bounding box properties (object dimensions & rotation) are determined in the parallel and separate box regression head and are therefore not accessible to the confidence estimation head. Finally, confidence estimation is usually performed using only features within a small area around the object (depending on the receptive field and detector), and no explicit information about neighboring objects and their geometric properties or confidence values is used, preventing a holistic estimation.",
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+        "type": "text",
+        "text": "Inspired by these observations, we present GACE, an intuitive and highly effective method to improve the confidence estimation of any black-box detector using geometric information. Given a set of detections from the base detector, we explicitly use these neglected features to enhance the expressiveness of the confidence values with the help of these additional cues. Our model-agnostic approach is intentionally applied after the actual detector training process to perform an auxiliary geometric assessment independent of the initial features. In a detailed evaluation on the Waymo dataset, we show that GACE consistently improves the performance of several state-of-the-art detection pipelines. Furthermore, we demonstrate the generalizability and transferability of our method by applying it to other datasets and even other detectors. Without retraining them, we achieve highly compelling performance gains.",
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+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "LiDAR-based 3D Object Detection: Depending on how existing methods for 3D object detection in single frame LiDAR data deal with the unstructured nature of point clouds, they can be broadly categorized into point-based, grid-based, and hybrid approaches.",
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+        "type": "text",
+        "text": "Point-based methods extract information directly from the individual raw 3D points [23,24,30,32,40,44]. The pioneering works, PointNet [23] and PointNet++ [24], used shared multilayer perceptrons in combination with global pooling functions to directly extract features from the irregular point cloud data. In Point-RCNN [30] features extracted in this manner are used to segment foreground points and generate proposals based on them. The advantages of point-based 3D object detectors are that there is no loss of point information due to discretization and the large receptive field, but at the cost of high computational demands.",
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+        "type": "text",
+        "text": "Instead of processing the points directly, grid-based methods [4, 15, 21, 27, 34, 38, 39, 43, 46] discretize the non-uniform 3D points into regular grids that can then be processed with 2D/3D convolutions. Voxelnet [46], a pioneering method, divides the point cloud into uniformly spaced 3D voxels, aggregates information from the points within them and generates predictions using 3D convolutions. To better handle the large number of empty voxels, SECOND [38] introduced sparse 3D convolutions. To reduce complexity, PointPillars [15] and PillarNet [27] use a 2D grid on the ground plane to create a column representation, a single pillar-shaped voxel per location, that can be processed using 2D convolutions. As an alternative to such anchor-based methods, Centerpoint [43] predicts a bird's-eye view heat map and detects the object center using a keypoint detector. Recently, transformer-based backbones have also been used to enable long-range relationships between voxels [5, 21, 34, 47]. Object relations within a frame and across multiple frames are mapped by Ret3D [37] using a graph and a transformer. The advantage of grid-based methods is that they can process data faster due to the regular format, but are limited by the loss of point information during the initial discretization phase.",
+        "bbox": [
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+        "type": "text",
+        "text": "In order to obtain both, multi-scale features and fine-grained information, hybrid methods process voxel and point information jointly [22, 26, 28, 29, 31, 41, 42]. PV-RCNN [28], uses a set abstraction module that combines surrounding point and voxel features at keypoints to improve the detections. Part-A² [31] predicts the position of parts within an object based on point features to improve the accuracy, while LiDAR R-CNN [17] uses features of a PointNet [23] model that processes points within and around box proposals. Pyramid R-CNN [19] creates point features using a pyramid grid structure to acquire fine-grained and long-range contextual information.",
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+    {
+        "type": "text",
+        "text": "Confidence Estimation: In the usual backbone - neck - head detector architecture, after the feature extraction and aggregation, the box regression and confidence estimation are performed. This is usually done in two separate branches based on a common dense feature representation [15, 38, 40, 46]. This has the disadvantage that the accuracy of the localization is hardly included in the confidence score. Inspired by 2D object detection methods [11,12,36], IoU guided supervision is frequently used to obtain a better correlation between the classification result and the localization accuracy [9, 10, 16, 27, 28, 31, 41, 45]. Thereby, the IoU between the predicted box and the ground truth is learned in a third branch during training and then incorporated into the final confidence score at test time. Hu et al. [9] leverage the inherent relationship between object distance and point density to better assess a detection. Inspired by the 2D approach [3], a spatial transformation on the feature maps is done by He et al. [8] to better align the confidence prediction and bounding box regression. Related to confidence estimation are also calibration methods [7, 14] where the score should represent a true probability, i.e. how likely a detection is. Detection pipelines, however, aim at the best separation of true and false positives as optimization goal for the confidence prediction.",
+        "bbox": [
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+        "type": "text",
+        "text": "In our confidence estimation method we also pursue this optimization objective, but in contrast to existing approaches, we present a method for refining the confidence values for a given set of detections by exploiting the rich geometric information contained directly in the detections as well as in the underlying 3D points. While these useful cues for assessing the plausibility of a detection have been largely untapped due to the architecture of common detection pipelines, they allow us to increase the expressiveness of the confidence values.",
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+    {
+        "type": "text",
+        "text": "3. Geometry-Aware Confidence Enhancement",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our goal is to optimize the confidence scores for a given set of detections from a base detector in order to better separate true positives from false positives, thus increasing the overall detection performance. We use the detector in a pure black box manner, i.e. we do not assume any knowledge about the architecture of the base model, nor access to its internals like parameters, features or gradients. This black-box optimization, taking only the point cloud and the set of objects detected in it as input, enables universal applicability and easy transferability of our enhancement module to any base 3D object detection pipeline. The basic idea is to revalidate the detections by exploiting as much as possible the geometric information they inherently contain.",
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+        "image_caption": [
+            "Figure 3. Schematic of GACE: To re-evaluate the confidence score of a detection (orange), we aggregate geometric properties of the detection itself and the points it contains into a feature vector (top). To capture the context of the detection, geometric relationships to neighboring detections are aggregated using a shared MLP and subsequent pooling function (bottom). By merging both features (right), we obtain a new confidence score that takes into account the underlying geometric properties of the detection."
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+    {
+        "type": "text",
+        "text": "In our proposed approach called GACE (Geometry Aware Confidence Enhancement) we exploit two types of geometric information, as shown in Figure 3:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- Instance-specific Geometric Properties (Section 3.1): Attributes of the bounding box itself, combined with the point data inside. For example, how well is the size of the object or the heading angle supported by the point distribution?",
+            "- Contextual Geometric Properties (Section 3.2): Relationships to surrounding objects can provide useful information to better validate an uncertain detection, e.g., a partially occluded vehicle moving in the same lane and same direction as the surrounding vehicles."
+        ],
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+    {
+        "type": "text",
+        "text": "These useful cues to estimate the plausibility of an object are usually not used for the confidence estimation in common detection pipelines. The reasons are that information is often already discarded during preprocessing (discretization), essential properties such as the estimated size of the object are not available (separate box regression in a parallel branch), or the objects are only evaluated individually and not more holistically. Therefore, we explicitly use these easily accessible and rich sources of information as input to our enhancement module. After merging the instance-specific and contextual features, we determine the new confidence value of each proposed object via an auxiliary task (Section 3.3).",
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+    {
+        "type": "text",
+        "text": "To generate the training data for our enhancement module, we use the black-box base model in a single inference run on the training set. The resulting set of all",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "detections from the base model represents the training data to learn our improved confidence estimator. Formally, this can be described as follows.",
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+    {
+        "type": "text",
+        "text": "Definitions & Notations: Let  $\\widetilde{\\mathcal{X}} = \\{\\widetilde{\\mathbf{x}}_k\\}_{k=1\\dots K}$  be a LiDAR point cloud, where each of the  $K$  unordered points  $\\widetilde{\\mathbf{x}}_k \\in \\mathbb{R}^5$  consists of the 3D coordinates, intensity/reflectance and the elongation value. Furthermore, let  $\\widetilde{\\mathcal{Y}} = \\{\\widetilde{\\mathbf{y}}_i\\}_{j=1\\dots M}$  be the set of corresponding ground truth objects. Each object annotation  $\\widetilde{\\mathbf{y}} = [\\widetilde{\\mathbf{b}}, \\widetilde{\\mathbf{y}}]$  includes the bounding box parameters  $\\widetilde{\\mathbf{b}} = [\\widetilde{c}_x, \\widetilde{c}_y, \\widetilde{c}_z, \\widetilde{d}_x, \\widetilde{d}_y, \\widetilde{d}_z, \\widetilde{\\Theta}]$  and the corresponding class label  $\\widetilde{y}$ . For a given black-box 3D object detector  $F$ , let  $F(\\widetilde{\\mathcal{X}}) = \\mathcal{Y} = \\{\\mathbf{y}_{i=1\\dots N}\\}$  be the set of proposed detections for this input point cloud, where  $\\mathbf{y} = [\\mathbf{b}, y, s]$ . In addition to the box properties  $\\mathbf{b}$  and the corresponding class label  $y$ , the detector predicts a confidence value  $s$  that should ideally indicate the prevalence of a true positive example.",
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+        "type": "text",
+        "text": "Confidence Optimization: Based on the known ground truth objects, a category label  $\\{u_i\\in \\{0,1\\} \\}_{i = 1\\dots N}$  can be assigned to each detection, indicating whether it is a true positive or false positive detection. Moreover, we know the IoU with a possible ground truth bounding box for each object which we define as  $\\{v_{i}\\}_{i = 1\\dots N}$ . We aim to improve the confidence estimate of the original detector by focusing exclusively on the binary classification of detections into true positive and false positive examples. We determine the revised confidence score  $\\{\\widehat{s}_i\\} = H(\\mathcal{V},\\mathcal{X})$  using our module  $H$ , where only the set of detections  $\\mathcal{V}$  and the points they include  $\\mathcal{X}\\subset \\widetilde{\\mathcal{X}}$  are used as input.",
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+    {
+        "type": "page_number",
+        "text": "6569",
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+    {
+        "type": "text",
+        "text": "3.1. Instance-specific Geometric Properties",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "In common 2D and 3D object detection architectures, the bounding box regression and the confidence estimation are performed completely separated in different branches. This is well suited for 2D where it is desired to detect objects in the image regardless of their scale. For 3D, however, important cues for plausibility estimation remain largely unused. Let us consider the available context directly provided by an object proposal: The position of the possible object in combination with the dimensions indicates, for example, which point density is to be expected. Furthermore, the direction angle provides an indication of the expected point distribution within the box. This information can even be further refined by knowing the class of the object. This directly available geometrical knowledge about an object allows for a more profound estimation of the confidence score.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We extract these basic properties and transform them into a compact representation using a multilayer perceptron (MLP)  $H_{I}$ . As input parameters, we first use the object parameters, i.e. the position  $(c_x, c_y, c_z)$ , the size  $(d_x, d_y, d_z)$ , and the heading angle  $\\Theta$  of the bounding box, as well as the initial confidence value  $s_i$  of the detection estimated by the base detector. Additionally, we use the distance  $\\| \\mathbf{c} \\|$  from the LiDAR sensor to the object center, and the angle  $\\alpha$  between the line of sight to the object and the heading angle of the object:",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha = \\Theta - \\operatorname {a t a n 2} \\left(c _ {y}, c _ {x}\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This angle describes from which side an object is seen from the LiDAR center, independent of the position of the object relative to the LiDAR, e.g. a vehicle driving directly towards the LiDAR always has the same angle  $\\alpha$ , no matter from which direction the vehicle approaches. We complement these cues with information about the points  $\\mathcal{X}_{\\mathrm{b}} \\subset \\mathcal{X}$  inside the bounding box  $\\mathbf{b}$ . Besides the overall number of points  $|\\mathcal{X}_{\\mathrm{b}}|$ , we extract elementary low-level statistics. Therefore, we scale the box and the associated points to a uniform size and then align them w.r.t. their center and yaw angle. In this canonical representation we compute the mean, standard deviation, minimum and maximum of  $\\mathcal{X}_{\\mathrm{b}}$  for all axes, denoted as  $\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{mean}}$ ,  $\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{std}}$ ,  $\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{min}}$ ,  $\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{max}}$ . We then aggregate these attributes into one feature vector representing the instance-specific plausibility per object as",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {f} ^ {I} = H _ {I} \\left(\\left[ \\mathbf {b}, \\alpha , \\| \\mathbf {c} \\|, | \\mathcal {X} _ {\\mathbf {b}} |, \\mathcal {X} _ {\\mathbf {b}} ^ {\\text {m e a n}}, \\mathcal {X} _ {\\mathbf {b}} ^ {\\text {s t d}}, \\mathcal {X} _ {\\mathbf {b}} ^ {\\min }, \\mathcal {X} _ {\\mathbf {b}} ^ {\\max } \\right] ^ {\\top}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where we pass all angles as direction vectors  $(\\cos(\\cdot), \\sin(\\cdot))$  and normalize all metric properties to unit length using the corresponding maximum value range.",
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+    {
+        "type": "text",
+        "text": "3.2. Contextual Geometric Properties",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Especially in the case of uncertain detections, e.g. detections that are far away and therefore consist of only a few 3D points, or detections that are partially occluded and therefore appear atypical, geometric contextual information can be very useful in assessing a confidence score. Examples include a vehicle that is heavily occluded but in a convoy with other vehicles, or cyclists moving in a group. However, this information is usually not available for the confidence estimation, since the object proposals are evaluated individually within the receptive field but without explicit knowledge of the objects detected in its vicinity and their properties. In order to assess the plausibility of a detection  $\\mathbf{y}$  in a more holistic way, we use the geometric relations to surrounding objects in the scene. We thereby consider all neighbors that are within a certain radius  $r$  around the object to be evaluated.",
+        "bbox": [
+            496,
+            119,
+            893,
+            362
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We therefore create a representation per object, which captures the relationships to its neighboring objects. In order to be independent of the number of neighboring objects, we first create a feature vector for each neighbor, which we then combine into a unified representation using a symmetric pooling function. As input parameters per neighbor we use the distance to the object to be evaluated  $\\| \\mathbf{c} - \\mathbf{c}_n\\|$ , the direction vector  $\\mathbf{c} - \\mathbf{c}_n$ , the difference between the two heading angles  $\\Theta - \\Theta_n$ , and the neighbor's class label  $y_{n}$ . To incorporate the validity of the neighbor, we leverage  $\\mathbf{f}_n^I$ , which represents the instance-specific properties of the neighbor. This information is encoded via the shared weight MLP  $H_{C}$  to form the feature vector  $\\mathbf{f}_n^C$  for each individual neighbor,",
+        "bbox": [
+            496,
+            383,
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+            582
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {f} _ {n} ^ {C} = H _ {C} \\left(\\left[ \\| \\mathbf {c} - \\mathbf {c} _ {n} \\|, \\mathbf {c} - \\mathbf {c} _ {n}, \\Theta - \\Theta_ {n}, y _ {n}, \\mathbf {f} _ {n} ^ {I} \\right] ^ {\\top}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            604,
+            890,
+            631
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the angle  $\\Theta -\\Theta_{n}$  is provided as direction vector and the metric features are normalized to unit length.",
+        "bbox": [
+            498,
+            652,
+            893,
+            683
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, we aggregate the information from the individual neighbors into a unified representation for later processing, as shown in Figure 3. This requires accumulating features of an unknown (and varying) number of neighbors. To impose no constraint on the number of features, we take inspiration from the pooling step of point-based detectors, e.g. [23], and employ a symmetric max pooling function to form a plausibility signature  $\\mathbf{f}^C$  over the feature vectors of all neighbors. Thus, in this representation the geometric relations to the surrounding objects are accumulated for the subsequent confidence estimation, taking into account the respective local properties of the neighbors.",
+        "bbox": [
+            496,
+            704,
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+            887
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "6570",
+        "bbox": [
+            482,
+            944,
+            514,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Data Fusion & Confidence Prediction",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            401,
+            104
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To estimate the new confidence value for a detection, we merge the instance-specific and contextual geometric features. The instance-specific information encoded in  $\\mathbf{f}^I$ , as well as the contextual information in  $\\mathbf{f}^C$  are concatenated and processed using  $H_{F}$ , a MLP with sigmoid output function, to estimate the new confidence score",
+        "bbox": [
+            76,
+            113,
+            468,
+            203
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widehat {s} = H _ {F} \\left(\\left[ \\mathbf {f} ^ {I}, \\mathbf {f} ^ {C} \\right] ^ {\\top}\\right). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            213,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We train the whole module including the two feature encoding networks  $H_{I}$  and  $H_{C}$  using an end-to-end training strategy. As loss function  $\\mathcal{L}_{\\mathrm{conf}}(\\widehat{s},u)$  for this task we use the focal loss [18] to focus learning on hard examples. The goal is to divide the set of detections as good as possible into true or false positive examples using the binary category label  $u\\in \\{0,1\\}$  as target. As auxiliary task during training we estimate the IoU with the ground truth bounding box in a further output  $\\widehat{v}$  of  $H_{F}$ . Therefore, we add an IoU-guidance [16, 41, 45] L1-loss term  $\\mathcal{L}_{\\mathrm{IoU}}(\\widehat{v},v)$ . This increases the importance of the point distribution statistics within the features, as they provide evidence of the bounding box accuracy from which the confidence estimate also benefits. The overall loss function is therefore",
+        "bbox": [
+            75,
+            250,
+            468,
+            459
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {c o n f}} (\\widehat {s}, u) + \\lambda_ {\\mathrm {I o U}} \\mathcal {L} _ {\\mathrm {I o U}} (\\widehat {v}, v), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            470,
+            468,
+            488
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{\\mathrm{IoU}}$  is a hyper-parameter to adjust the influence of the auxiliary task.",
+        "bbox": [
+            76,
+            500,
+            468,
+            529
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            542,
+            209,
+            559
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the benefits of GACE, we evaluate our black-box confidence optimization method on several well-known state-of-the-art 3D object detection pipelines. In particular, we apply it to the pillar-based PointPillars [15], the voxel-based SECOND [38] and Centerpoint [43], as well as the hybrid methods Part-A² [31], PV-RCNN [28] and PV-RCNN++ [29].",
+        "bbox": [
+            75,
+            568,
+            468,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets: For the evaluation of our approach we use the Waymo Open Dataset [33] as well as the KITTI Dataset [6]. The Waymo dataset is one of the largest and most challenging public datasets for autonomous driving research. It provides 798 training scenes and 202 validation scenes, where each scene consists of about 200 LiDAR samples covering the full  $360^{\\circ}$  field-of-view. In total, the dataset consists of over 8.9M annotated objects classified into vehicles, pedestrians and cyclists. We follow the common evaluation protocol using the standard metrics average precision (AP), as well as average precision with heading (APH), where true positives are weighted by their heading accuracy. In addition, we use the KITTI dataset, one of the most popular datasets for 3D object detection.",
+        "bbox": [
+            75,
+            689,
+            468,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We thereby use the standard split [2] into a training set (3712 samples) and validation set (3769 samples). We also follow the common evaluation practice using average precision with 40 recall points. For both datasets, the 3D IoU threshold for a true positive sample is 0.7 for vehicles and 0.5 for pedestrians and cyclists.",
+        "bbox": [
+            496,
+            90,
+            890,
+            181
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details: Our experimental setup is based on the open-source toolbox OpenPCDet [35]. To ensure the reproducibility of our results, all base models used in the experiments have been trained on the training set using the default configuration and default training policies of OpenPCDet. This includes augmenting the data by randomly rotating, scaling and flipping the point cloud, as well as ground truth sampling [38], i.e. the placement of objects from other training examples in the current frame. To create the training data for our module, we use the base model as a black-box detection pipeline. In a single inference run on the training set, we collect the output of the base model, i.e. the set of all detections, which represents our training data. The actual training process of our module is therefore entirely decoupled from the base model.",
+        "bbox": [
+            496,
+            196,
+            890,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our sub-networks for feature transformation, i.e.  $H_{I}$  and the shared network  $H_{C}$ , as well as the confidence prediction network  $H_{F}$  are two-layer MLP's with 256 feature dimensions. The feature vector  $\\mathbf{f}^{I}$  in which the instance-specific information is encoded is 128-dimensional and  $\\mathbf{f}^{C}$  for the contextual information is 64-dimensional. When determining the contextual geometric properties, we accumulate the neighboring objects that are within a radius of  $r = 40m$ .",
+        "bbox": [
+            496,
+            426,
+            890,
+            546
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We train our model end to end with the Adam [13] optimizer and a learning rate of 0.001. The weighting of the auxiliary loss term during training is set to  $\\lambda_{\\mathrm{IoU}} = 0.5$ . In all experiments we use the same architecture as well as hyperparameters, regardless of the underlying black-box base model. We train our module over 5 epochs on a single NVIDIA® GeForce® RTX 3090 GPU, which takes less than 10 minutes due to our favorable lightweight model size and low feature dimensions.",
+        "bbox": [
+            496,
+            547,
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+            681
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Main Results",
+        "text_level": 1,
+        "bbox": [
+            500,
+            696,
+            637,
+            710
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1 summarizes the results of our confidence optimization on the Waymo dataset for different baseline detection pipelines. For each detector architecture, we report the performance of the base detector as well as the results after applying our GACE module. Please note that for better traceability, the results of the base detectors correspond to the respective OpenPCDet implementations (see OpenPCDet model zoo). Some reported baseline scores are even higher than in their original papers due to augmentation techniques used in OpenPCDet.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "1https://github.com/dschinagl/gace",
+        "bbox": [
+            517,
+            887,
+            785,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6571",
+        "bbox": [
+            482,
+            945,
+            513,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/bb08e02d370209c88f348ce86ca5459aade720f50534ce15d457a50605cae056.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">Overall</td><td colspan=\"4\">Vehicles (IoU=0.7)</td><td colspan=\"4\">Pedestrians (IoU=0.5)</td><td colspan=\"4\">Cyclists (IoU=0.5)</td></tr><tr><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td></tr><tr><td>mAP</td><td>mAPH</td><td>mAP</td><td>mAPH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td></tr><tr><td>PointPillars [15]</td><td>64.72</td><td>57.07</td><td>58.57</td><td>51.73</td><td>70.99</td><td>70.35</td><td>62.79</td><td>62.20</td><td>66.36</td><td>47.15</td><td>58.27</td><td>41.32</td><td>56.81</td><td>53.71</td><td>54.66</td><td>51.67</td></tr><tr><td>+ GACE (Ours)</td><td>69.25</td><td>61.24</td><td>62.98</td><td>55.73</td><td>71.92</td><td>71.28</td><td>63.63</td><td>63.04</td><td>72.18</td><td>51.97</td><td>64.06</td><td>45.96</td><td>63.64</td><td>60.47</td><td>61.25</td><td>58.20</td></tr><tr><td>Improvement</td><td>+4.53</td><td>+4.17</td><td>+4.41</td><td>+4.00</td><td>+0.93</td><td>+0.93</td><td>+0.84</td><td>+0.84</td><td>+5.82</td><td>+4.82</td><td>+5.79</td><td>+4.64</td><td>+6.83</td><td>+6.76</td><td>+6.59</td><td>+6.53</td></tr><tr><td>SECOND [38]</td><td>65.13</td><td>60.81</td><td>59.01</td><td>55.12</td><td>70.93</td><td>70.30</td><td>62.65</td><td>62.07</td><td>65.67</td><td>54.96</td><td>57.78</td><td>48.25</td><td>58.78</td><td>57.18</td><td>56.59</td><td>55.05</td></tr><tr><td>+ GACE (Ours)</td><td>70.17</td><td>66.13</td><td>63.74</td><td>60.06</td><td>71.56</td><td>70.92</td><td>63.22</td><td>62.63</td><td>71.71</td><td>61.87</td><td>63.27</td><td>54.37</td><td>67.22</td><td>65.59</td><td>64.73</td><td>63.16</td></tr><tr><td>Improvement</td><td>+5.04</td><td>+5.32</td><td>+4.73</td><td>+4.94</td><td>+0.63</td><td>+0.62</td><td>+0.57</td><td>+0.56</td><td>+6.04</td><td>+6.91</td><td>+5.49</td><td>+6.12</td><td>+8.44</td><td>+8.41</td><td>+8.14</td><td>+8.11</td></tr><tr><td>Part-A2[31]</td><td>70.30</td><td>66.66</td><td>63.53</td><td>60.27</td><td>73.35</td><td>72.81</td><td>64.73</td><td>64.24</td><td>70.02</td><td>61.01</td><td>60.83</td><td>52.85</td><td>67.53</td><td>66.18</td><td>65.03</td><td>63.73</td></tr><tr><td>+ GACE (Ours)</td><td>73.07</td><td>69.21</td><td>66.24</td><td>62.77</td><td>73.99</td><td>73.43</td><td>65.38</td><td>64.87</td><td>72.36</td><td>62.93</td><td>63.21</td><td>54.81</td><td>72.84</td><td>71.28</td><td>70.13</td><td>68.63</td></tr><tr><td>Improvement</td><td>+2.77</td><td>+2.55</td><td>+2.71</td><td>+2.50</td><td>+0.64</td><td>+0.62</td><td>+0.65</td><td>+0.63</td><td>+2.34</td><td>+1.92</td><td>+2.38</td><td>+1.96</td><td>+5.31</td><td>+5.10</td><td>+5.10</td><td>+4.90</td></tr><tr><td>Centerpoint [43]</td><td>73.01</td><td>70.35</td><td>66.79</td><td>64.33</td><td>72.87</td><td>72.33</td><td>64.76</td><td>64.27</td><td>74.48</td><td>68.22</td><td>66.55</td><td>60.81</td><td>71.69</td><td>70.50</td><td>69.06</td><td>67.92</td></tr><tr><td>+ GACE (Ours)</td><td>75.58</td><td>72.98</td><td>69.19</td><td>66.76</td><td>74.49</td><td>73.99</td><td>66.19</td><td>65.73</td><td>78.62</td><td>72.48</td><td>70.44</td><td>64.73</td><td>73.64</td><td>72.48</td><td>70.94</td><td>69.83</td></tr><tr><td>Improvement</td><td>+2.57</td><td>+2.63</td><td>+2.40</td><td>+2.43</td><td>+1.62</td><td>+1.66</td><td>+1.43</td><td>+1.46</td><td>+4.14</td><td>+4.26</td><td>+3.89</td><td>+3.92</td><td>+1.95</td><td>+1.98</td><td>+1.88</td><td>+1.91</td></tr><tr><td>PV-RCNN [28]</td><td>71.11</td><td>66.78</td><td>64.40</td><td>60.50</td><td>74.79</td><td>74.17</td><td>66.17</td><td>65.61</td><td>72.06</td><td>61.46</td><td>63.00</td><td>53.56</td><td>66.48</td><td>64.72</td><td>64.03</td><td>62.34</td></tr><tr><td>+ GACE (Ours)</td><td>73.38</td><td>68.89</td><td>66.65</td><td>62.57</td><td>75.20</td><td>74.55</td><td>66.57</td><td>65.97</td><td>73.84</td><td>62.97</td><td>64.88</td><td>55.14</td><td>71.12</td><td>69.16</td><td>68.50</td><td>66.60</td></tr><tr><td>Improvement</td><td>+2.27</td><td>+2.11</td><td>+2.25</td><td>+2.07</td><td>+0.41</td><td>+0.38</td><td>+0.40</td><td>+0.36</td><td>+1.78</td><td>+1.51</td><td>+1.88</td><td>+1.58</td><td>+4.64</td><td>+4.44</td><td>+4.47</td><td>+4.26</td></tr><tr><td>PV-RCNN++ [29]</td><td>75.72</td><td>73.05</td><td>69.22</td><td>66.73</td><td>77.30</td><td>76.81</td><td>68.92</td><td>68.47</td><td>78.91</td><td>72.42</td><td>70.43</td><td>64.41</td><td>70.95</td><td>69.90</td><td>68.31</td><td>67.31</td></tr><tr><td>+ GACE (Ours)</td><td>76.76</td><td>74.02</td><td>70.31</td><td>67.75</td><td>77.42</td><td>76.93</td><td>69.05</td><td>68.59</td><td>79.59</td><td>72.97</td><td>71.34</td><td>65.18</td><td>73.26</td><td>72.16</td><td>70.54</td><td>69.48</td></tr><tr><td>Improvement</td><td>+1.04</td><td>+0.97</td><td>+1.09</td><td>+1.02</td><td>+0.12</td><td>+0.12</td><td>+0.13</td><td>+0.12</td><td>+0.68</td><td>+0.55</td><td>+0.91</td><td>+0.77</td><td>+2.31</td><td>+2.26</td><td>+2.23</td><td>+2.17</td></tr></table>",
+        "bbox": [
+            106,
+            84,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Performance comparison on the Waymo Open Dataset [33] validation set for different baseline methods with and without our confidence enhancement module GACE.",
+        "bbox": [
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+            353,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For all baseline detectors and all classes, adjusting the confidence level with our approach leads to an increase in performance without exception. The overall performance gains range from  $+1.02\\mathrm{mAPH}$  (LEVEL_2) for PV-RCNN++ to  $+4.94\\mathrm{mAPH}$  (LEVEL_2) for SECOND, demonstrating the significance of this geometric information in estimating a confidence score for a detection.",
+        "bbox": [
+            75,
+            404,
+            470,
+            510
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Object Classes: The performance improvements are significantly higher for the classes of pedestrians and cyclists. Intuitively, objects of these vulnerable road users contain significantly fewer 3D points due to their smaller spatial extent compared to vehicles. This effect is even aggravated by possible occlusions. Furthermore, the class of cyclists in particular is underrepresented in the training data. These properties make objects of these classes more difficult to detect, which leads to a higher number of false positives, but also makes confidence estimation more complex. Especially in these cases, our confidence enhancement method benefits from the additional geometric information when separating false positives from true positives, resulting in a higher impact of GACE.",
+        "bbox": [
+            75,
+            531,
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+            743
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Base Detectors: The overall performance gain is highest when applying GACE on pillar-based (PointPillars [15]) and voxel-based methods (SECOND [38] and Centerpoint [43]). These methods lose valuable point information already in their preprocessing stage, i.e. by voxelization. Thus, the optimization potential for these methods is higher than for the hybrid methods, which explicitly incorporate point-level information at detection locations. However, by explicitly exploiting both instance-specific and contextual geometric properties of the detections, GACE also leads to",
+        "bbox": [
+            75,
+            750,
+            470,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "a significant performance improvement for these methods, i.e. Part- $\\mathrm{A}^2$  [31], PV-RCNN [28] and PV-RCNN++ [29], most notably for the classes of pedestrians and cyclists.",
+        "bbox": [
+            498,
+            404,
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+            450
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Precision/Recall Plots: To better illustrate the impact of our method, Figure 4 shows the precision/recall plots before and after applying GACE with a SECOND [38] model as the base detector (See the supplemental material for the other base detectors). Since recall remains unaffected, the significant performance gains of GACE are entirely due to an increase in precision. The better separation of true and false positives is mainly seen in the more challenging classes of pedestrians and cyclists, where the number of false detections is significantly higher and confidence estimation is more difficult. Furthermore, we see that the precision gains are higher in regions of higher recall, i.e. for detections with a lower confidence score. Especially these initially underrated detections of objects of the vulnerable classes represent a safety risk that can be reduced by GACE.",
+        "bbox": [
+            496,
+            470,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Range-based Evaluation: Table 2 summarizes our evaluation across the different distance ranges of Waymo. This also shows that GACE can consistently improve the performance of all baseline detectors and in all sub-ranges, especially in the far range. Detections at long distances are more challenging due to the lower point density, making it harder to distinguish true positives from false positives. Therefore, the geometric information is even more valuable in these cases, e.g. from  $+2.93\\mathrm{mAPH}$  (LEVEL_2) for PV-RCNN++ up to  $+4.97\\mathrm{mAPH}$  (LEVEL_2) for PointPillars. The detailed evaluation results for all subclasses can be found in the supplemental material.",
+        "bbox": [
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+        "text": "6572",
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+    {
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+        "img_path": "images/ecc7cbb4923b0bfbdb21b9abdeb9ef12261c90cfce7ed8b4cd3e9b14ceb58276.jpg",
+        "image_caption": [
+            "Figure 4. Precision-recall plots for a SECOND [38] model as base detector with and without our confidence enhancement module on the Waymo Open Dataset [33] validation set for LEVEL_2 APH. Especially at higher recall levels, GACE's better separation of true and false positives leads to higher precision."
+        ],
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+    {
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+        "img_path": "images/0474b9602bcd25ed377f5165e43123c58e249d489e692d5d169def866b49f096.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/eef7a1074d3ebdea335310f9a6bc9126f091115a5056a52f25fdfc332b4a34cc.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"3\">Overall (LEVEL_2)</td></tr><tr><td>0-30m</td><td>30-50m</td><td>50m-Inf</td></tr><tr><td>mAP / mAPH</td><td>mAP / mAPH</td><td>mAP / mAPH</td></tr><tr><td>PointPillars [15]</td><td>75.10 / 67.59</td><td>55.31 / 48.53</td><td>37.18 / 31.00</td></tr><tr><td>+ GACE (Ours)</td><td>78.32 / 70.68</td><td>60.17 / 53.01</td><td>42.88 / 35.97</td></tr><tr><td>Improvement</td><td>+3.22 / +3.09</td><td>+4.86 / +4.48</td><td>+5.70 / +4.97</td></tr><tr><td>SECOND [38]</td><td>75.55 / 71.87</td><td>56.55 / 52.42</td><td>37.73 / 33.39</td></tr><tr><td>+ GACE (Ours)</td><td>78.64 / 75.39</td><td>60.10 / 56.13</td><td>41.69 / 37.39</td></tr><tr><td>Improvement</td><td>+3.09 / +3.52</td><td>+3.55 / +3.71</td><td>+3.96 / +4.00</td></tr><tr><td>Part-A² [31]</td><td>79.93 / 76.93</td><td>61.77 / 58.01</td><td>40.13 / 36.44</td></tr><tr><td>+ GACE (Ours)</td><td>81.62 / 78.52</td><td>64.63 / 60.59</td><td>45.06 / 40.94</td></tr><tr><td>Improvement</td><td>+1.69 / +1.59</td><td>+2.86 / +2.58</td><td>+4.93 / +4.50</td></tr><tr><td>Centerpoint [43]</td><td>81.29 / 79.12</td><td>65.45 / 62.66</td><td>46.45 / 43.27</td></tr><tr><td>+ GACE (Ours)</td><td>82.94 / 80.90</td><td>67.56 / 64.76</td><td>50.20 / 46.80</td></tr><tr><td>Improvement</td><td>+1.65 / +1.78</td><td>+2.11 / +2.10</td><td>+3.75 / +3.53</td></tr><tr><td>PV-RCNN [28]</td><td>79.77 / 76.24</td><td>62.57 / 58.10</td><td>42.51 / 37.77</td></tr><tr><td>+ GACE (Ours)</td><td>81.25 / 77.66</td><td>64.76 / 60.11</td><td>47.01 / 41.90</td></tr><tr><td>Improvement</td><td>+1.48 / +1.42</td><td>+2.19 / +2.01</td><td>+4.50 / +4.13</td></tr><tr><td>PV-RCNN++ [29]</td><td>83.08 / 80.98</td><td>67.86 / 65.04</td><td>48.69 / 45.26</td></tr><tr><td>+ GACE (Ours)</td><td>83.59 / 81.43</td><td>68.69 / 65.83</td><td>51.81 / 48.19</td></tr><tr><td>Improvement</td><td>+0.51 / +0.45</td><td>+0.83 / +0.79</td><td>+3.12 / +2.93</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.2. Ablation Studies",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Main Components: We evaluate the contribution of our proposed instance-specific and contextual properties as well as the influence of the auxiliary IoU loss for a SECOND [38] model as baseline in Table 3. Incorporating the instance-specific geometric properties already leads to a significant performance increase of  $+3.65\\mathrm{AP} / + 3.32\\mathrm{APH}$ . Including also the contextual information, i.e. incorporating the relationships to the neighboring detection hypotheses further increases the performance by another  $+0.71\\mathrm{AP} / + 1.14\\mathrm{APH}$ . Compared to the contributions of these two components, there is only a minor impact of incorporating the IoU guidance, leading to additional  $+0.37\\mathrm{AP} / + 0.48\\mathrm{APH}$ . Note that the degradation when adding  $\\mathcal{L}_{\\mathrm{IoU}}$  to only contextual features is caused by the lack of point information, which does not allow a reasonable estimation of the IoU. Overall, the instance-specific geometric information contributes stronger than the contextual geometric information.",
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+    {
+        "type": "table",
+        "img_path": "images/9d9a0119a8dd7db776cc9148db286b64bcd3522da11dd4204276ac60d07e8730.jpg",
+        "table_caption": [
+            "Table 2. Consistent performance gains on the Waymo Open Dataset [33] validation set across distance ranges for different baseline methods for LEVEL_2 over all classes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Baseline</td><td>Instance Specific</td><td>Contextual</td><td>Aux-Loss LIoU</td><td>LEVEL_2 mAP</td><td>LEVEL_2 mAPH</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>59.01</td><td>55.12</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>62.66</td><td>58.44</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>60.33</td><td>56.90</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>63.37</td><td>59.58</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>62.94</td><td>58.78</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>60.19</td><td>56.77</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>63.74</td><td>60.06</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/d27e9d5875bfd676f3a4a69b7c143181cb1a8dadcbcb9db884f8899639347bec.jpg",
+        "table_caption": [
+            "Table 3. Ablation experiments for a SECOND [38] model as base detector over all classes on the Waymo Open Dataset [33] validation set. We show the impact of each GACE component."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Box Properties</td><td># Points</td><td>Viewing Angle</td><td>Point Stat.</td></tr><tr><td>56.98+1.86</td><td>55.96+0.84</td><td>55.86+0.74</td><td>58.15+3.03</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4. Impact of the different instance-specific feature groups when used exclusively for a SECOND model as base detector on the Waymo Open Dataset [33] over all classes (LEVEL_2 mAPH).",
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+    {
+        "type": "text",
+        "text": "Instance-Specific Properties: We analyze the contribution of each feature group within the instance-specific properties, namely box properties  $(\\mathbf{b},\\| \\mathbf{c}\\|)$ , number of points  $(|\\mathcal{X}_{\\mathbf{b}}|)$ , viewing angle  $(\\alpha)$ , and point statistics  $(\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{mean}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{std}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{min}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{max}})$ . Table 4 shows the impact of each group on the overall performance when used exclusively, indicating a high contribution of box properties and point statistics. A complete list of the combinations can be found in the supplemental material.",
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+    {
+        "type": "text",
+        "text": "Contextual Properties Radius: The dependence of the performance on the chosen context radius  $r$  is shown in Figure 5. It can be seen that the performance increases significantly up to  $\\sim 15m$ , followed by a slight degradation starting at  $\\sim 40m$ , which illustrates the importance of neighboring objects in the near and middle ranges.",
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+        "text": "6573",
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+    },
+    {
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+        "img_path": "images/5aee07c939caf967a0871ba90c4c7a19b4c2e0af3cfdb4662c570ec3d1178d32.jpg",
+        "image_caption": [
+            "Figure 5. Performance of purely context-based GACE for different radius  $r$  (SECOND base model / Waymo overall)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2d46f9155154e7b3748d9b7e31ce19c6ea34e77239547074e8291d6b0dcfbb98.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Car</td><td>Pedestrian</td><td>Cyclist</td></tr><tr><td>SECOND (KITTI)</td><td>81.61</td><td>51.14</td><td>66.74</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.04+0.43</td><td>57.11+5.97</td><td>70.99+4.25</td></tr><tr><td>PointPillars (KITTI)</td><td>78.39</td><td>51.41</td><td>62.94</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>78.51+0.12</td><td>55.30+3.89</td><td>67.94+5.00</td></tr><tr><td>Part-A2 (KITTI)</td><td>82.92</td><td>59.73</td><td>70.10</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.94+0.02</td><td>64.21+4.48</td><td>72.16+2.06</td></tr><tr><td>PV-RCNN (KITTI)</td><td>82.86</td><td>53.64</td><td>70.42</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.84-0.02</td><td>61.06+7.42</td><td>72.70+2.28</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Generalization and Transferability",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Since we use only the detection attributes and corresponding properties of the underlying point cloud as input, a GACE module trained on base detector A can be directly applied to another base detector B. Furthermore, since all metric features are normalized to their maximum possible value and the statistical parameters (point distribution) are computed from a normalized unit-length box, GACE can be applied not only to a different detector, but also directly to a different detector on a different dataset. Therefore, to demonstrate the general applicability of GACE, we freeze a GACE module trained on detections from a SECOND detector on Waymo, and apply it directly to detections of a SECOND detector on the KITTI dataset [6]. As shown in Table 5, first row, this also leads to considerable performance improvements despite the distribution shift to a different dataset (different LiDAR sensor, different country). Even more remarkably, significant performance gains are also obtained when the same GACE module is applied even to a different base detector, e.g. +7.42AP for PV-RCNN on pedestrians while achieving the same performance for cars. The results demonstrate the excellent generalization capability of GACE and the general validity of the geometric information regardless of the dataset.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.4. Runtime Analysis",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Table 6 we show the runtime analysis of GACE for a  $360^{\\circ}$  field-of-view Waymo point cloud using a single NVIDIA® GeForce® RTX 3090 GPU. The computationally most intensive part is the feature extraction, especially ex",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/98a2c73ca694917b361c77e22ce1be0fd171e69b8ec0e5fd6fc156a61afe172a.jpg",
+        "table_caption": [
+            "Table 5. Model Transfer: Applying a GACE module trained on SECOND detections on Waymo (without LiDAR elongation, which is not available on KITTI) to different detectors on the KITTI dataset (moderate difficulty / @R40)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Feature Extraction</td><td>Points in Boxes Query</td><td>0.56 ms</td></tr><tr><td>Geometric &amp; Statistical Features</td><td>0.98 ms</td></tr><tr><td>Neighboring Object ID&#x27;s Query</td><td>0.07 ms</td></tr><tr><td rowspan=\"3\">Network Inference</td><td>HI (Instance-specific)</td><td>0.14 ms</td></tr><tr><td>HC (Contextual)</td><td>0.17 ms</td></tr><tr><td>HF (Confidence Estimation)</td><td>0.12 ms</td></tr><tr><td colspan=\"2\">Overall</td><td>2.04 ms</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 6. GACE runtime analysis per  $360^{\\circ}$  field-of-view Waymo point cloud on a single NVIDIA® GeForce® RTX 3090 GPU.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "tracting the statistical features for all detections. However, this can be solved efficiently via PyTorch einsum. During inference, we first compute the instance-specific plausibility  $\\mathbf{f}^I$  for each detection via  $H_{I}$ , which is then used as input to  $H_{C}$  for the corresponding neighbors. Overall, GACE is capable of processing  $\\sim 490$  Waymo point clouds per second with  $\\sim 100$  detections each.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5. Limitations",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "While our method has proven effective in improving object detection performance for vulnerable classes such as pedestrians and cyclists, it is worth noting that it may not offer such significant benefits for simpler classes such as vehicles. This is because all detectors typically have few false positives for these easier-to-detect objects. Therefore, there is less room for improvement for this class. However, it is important to consider the context in which our method is applied. Even if the performance improvement is not as large for simpler classes, the overall impact of our method on safety should not be underestimated. In many real-world scenarios, pedestrians and cyclists are particularly vulnerable, and any improvement in their detection can make a significant contribution to safety.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We proposed GACE, a method to better evaluate object hypotheses from black-box LiDAR-based 3D object detectors by explicitly assessing numerous geometric properties inherent in the detections. This enables a better separation between true and false positive detections and thus significantly improves the performance. In a comprehensive analysis, we were able to show the performance of our method for several state-of-the-art detectors and also demonstrate the generalisation capabilities of GACE. This underlines the importance and general validity of the geometric information inherent in 3D detections, which has been largely neglected in the past.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements This work was partially funded by the Austrian FFG project iLIDS4SAM (878713) and by the Christian Doppler Laboratory for Embedded Machine Learning.",
+        "bbox": [
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+        "type": "page_number",
+        "text": "6574",
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            173,
+            104
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+            "[20] Jiageng Mao, Minzhe Niu, Chenhan Jiang, Xiaodan Liang, Yamin Li, Chaoqiang Ye, Wei Zhang, Zhenguo Li, Jie Yu, Chunjing Xu, et al. One Million Scenes for Autonomous Driving: ONCE Dataset. 2021. 1",
+            "[21] Jiageng Mao, Yujing Xue, Minzhe Niu, Haoyue Bai, Jiashi Feng, Xiaodan Liang, Hang Xu, and Chunjing Xu. Voxel Transformer for 3D Object Detection. In Proc. ICCV, 2021. 3",
+            "[22] Jongyoun Noh, Sanghoon Lee, and Bumsub Ham. HVPR: Hybrid Voxel-Point Representation for Single-stage 3D Object Detection. In Proc. CVPR, 2021. 3",
+            "[23] Charles Ruizhongtai Qi, Hao Su, Kaichun Mo, and Leonidas J. Guibas. PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. In Proc. CVPR, 2017. 3, 5",
+            "[24] Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J. Guibas. PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space. In NeurIPS, 2017. 3",
+            "[25] David Schinagl, Georg Krispel, Horst Possegger, Peter M Roth, and Horst Bischof. OccAM's Laser: Occlusion-Based Attribution Maps for 3D Object Detectors on LiDAR Data. In Proc. CVPR, 2022. 2",
+            "[26] Hualian Sheng, Sijia Cai, Yuan Liu, Bing Deng, Jianqiang Huang, Xian-Sheng Hua, and Min-Jian Zhao. Improving 3D Object Detection with Channel-wise Transformer. In Proc. ICCV, 2021. 3",
+            "[27] Guangsheng Shi, Ruifeng Li, and Chao Ma. PillarNet: High-Performance Pillar-based 3D Object Detection. In Proc. ECCV, 2022. 2, 3",
+            "[28] Shaoshuai Shi, Chaoxu Guo, Li Jiang, Zhe Wang, Jianping Shi, Xiaogang Wang, and Hongsheng Li. PV-RCNN: Point-Voxel Feature Set Abstraction for 3D Object Detection. In Proc. CVPR, 2020. 3, 6, 7, 8",
+            "[29] Shaoshuai Shi, Li Jiang, Jiajun Deng, Zhe Wang, Chaoxu Guo, Jianping Shi, Xiaogang Wang, and Hongsheng Li. PV-RCNN++: Point-Voxel Feature Set Abstraction With Local Vector Representation for 3D Object Detection. IJCV, pages 1–21, 2022. 1, 3, 6, 7, 8",
+            "[30] Shaoshuai Shi, Xiaogang Wang, and Hongsheng Li. PointR-CNN: 3D Object Proposal Generation and Detection from Point Cloud. In Proc. CVPR, 2019. 3",
+            "[31] Shaoshuai Shi, Zhe Wang, Jianping Shi, Xiaogang Wang, and Hongsheng Li. From Points to Parts: 3D Object Detection from Point Cloud with Part-aware and Part-aggregation Network. PAMI, pages 2647-2664, 2021. 3, 6, 7, 8",
+            "[32] Weijing Shi and Ragunathan Rajkumar. Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud. In Proc. CVPR, 2020. 3"
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            898
+        ],
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+    },
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[33] Pei Sun, Henrik Kretzschmar, Xerxes Dotiwalla, Aurelien Chouard, Vijaysai Patnaik, Paul Tsui, James Guo, Yin Zhou, Yuning Chai, Benjamin Caine, et al. Scalability in Perception for Autonomous Driving: Waymo Open Dataset. In Proc. CVPR, 2020. 1, 2, 6, 7, 8",
+            "[34] Pei Sun, Mingxing Tan, Weiyue Wang, Chenxi Liu, Fei Xia, Zhaoqi Leng, and Dragomir Anguelov. SWFormer: Sparse Window Transformer for 3D Object Detection in Point Clouds. In Proc. ECCV, 2022. 3",
+            "[35] OpenPCDet Development Team. OpenPCDet: An opensource toolbox for 3D object detection from point clouds. https://github.com/open-mmlab/OpenPCDet, 2020.6",
+            "[36] Lachlan Tychsen-Smith and Lars Petersson. Improving Object Localization with Fitness NMS and Bounded IoU Loss. In Proc. CVPR, 2018. 3",
+            "[37] Yu-Huan Wu, Da Zhang, Le Zhang, Xin Zhan, Dengxin Dai, Yun Liu, and Ming-Ming Cheng. Ret3D: Rethinking Object Relations for Efficient 3D Object Detection in Driving Scenes. arXiv:2208.08621, 2022. 3",
+            "[38] Yan Yan, Yuxing Mao, and Bo Li. SECOND: Sparsely Embedded Convolutional Detection. Sensors, 18(10):3337, 2018. 1, 2, 3, 6, 7, 8",
+            "[39] Bin Yang, Wenjie Luo, and Raquel Urtasun. **PIXOR: Real-time 3D Object Detection from Point Clouds.** In Proc. CVPR, 2018. 3",
+            "[40] Zetong Yang, Yanan Sun, Shu Liu, and Jiaya Jia. 3DSSD: Point-based 3D Single Stage Object Detector. In Proc. CVPR, 2020. 1, 3",
+            "[41] Zetong Yang, Yanan Sun, Shu Liu, Xiaoyong Shen, and Jiaya Jia. STD: Sparse-to-Dense 3D Object Detector for Point Cloud. In Proc. ICCV, 2019. 3, 6",
+            "[42] Maosheng Ye, Shuangjie Xu, and Tongyi Cao. HVNet: Hybrid Voxel Network for LiDAR Based 3D Object Detection. In Proc. CVPR, 2020. 3",
+            "[43] Tianwei Yin, Xingyi Zhou, and Philipp Kähenbuhl. Center-based 3D Object Detection and Tracking. In Proc. CVPR, 2021. 3, 6, 7, 8",
+            "[44] Yifan Zhang, Qingyong Hu, Guoquan Xu, Yanxin Ma, Jianwei Wan, and Yulan Guo. Not all points are equal: Learning highly efficient point-based detectors for 3d lidar point clouds. In Proc. CVPR, 2022. 3",
+            "[45] Wu Zheng, Weiliang Tang, Sijin Chen, Li Jiang, and ChiWing Fu. CIA-SSD: Confident IoU-Aware Single-Stage Object Detector From Point Cloud. In Proc. AAAI, 2021. 1, 2, 3, 6",
+            "[46] Yin Zhou and Oncel Tuzel. VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection. In Proc. CVPR, 2018. 3",
+            "[47] Zixiang Zhou, Xiangchen Zhao, Yu Wang, Panqu Wang, and Hassan Foroosh. Centerformer: Center-based transformer for 3d object detection. In Proc. ECCV, 2022. 1, 3"
+        ],
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diff --git a/2023/GACE_ Geometry Aware Confidence Enhancement for Black-Box 3D Object Detectors on LiDAR-Data/4d4269c1-ea16-4959-9423-14c51ea10997_model.json b/2023/GACE_ Geometry Aware Confidence Enhancement for Black-Box 3D Object Detectors on LiDAR-Data/4d4269c1-ea16-4959-9423-14c51ea10997_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..fcea59f13a57c10c72e050e15d17bb67698120df
--- /dev/null
+++ b/2023/GACE_ Geometry Aware Confidence Enhancement for Black-Box 3D Object Detectors on LiDAR-Data/4d4269c1-ea16-4959-9423-14c51ea10997_model.json	
@@ -0,0 +1,1938 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
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+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.209,
+                0.131,
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+            ],
+            "angle": 0,
+            "content": "GACE: Geometry Aware Confidence Enhancement for Black-box 3D Object Detectors on LiDAR-Data"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.088,
+                0.203,
+                0.882,
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+            ],
+            "angle": 0,
+            "content": "David Schinagl<sup>1,2</sup> Georg Krispel<sup>1</sup> Christian Fruhwirth-Reisinger<sup>1,2</sup> Horst Possegger<sup>1</sup> Horst Bischof<sup>1,2</sup>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.167,
+                0.224,
+                0.803,
+                0.239
+            ],
+            "angle": 0,
+            "content": "{david.schinagl,georg.krispel,reisinger,possegger,bischof}@icg.tugraz.at"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{1}\\) Graz University of Technology \\(^{2}\\) Christian Doppler Laboratory for Embedded Machine Learning"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.292,
+                0.314,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.325,
+                0.474,
+                0.613
+            ],
+            "angle": 0,
+            "content": "Widely-used LiDAR-based 3D object detectors often neglect fundamental geometric information readily available from the object proposals in their confidence estimation. This is mostly due to architectural design choices, which were often adopted from the 2D image domain, where geometric context is rarely available. In 3D, however, considering the object properties and its surroundings in a holistic way is important to distinguish between true and false positive detections, e.g. occluded pedestrians in a group. To address this, we present GACE, an intuitive and highly efficient method to improve the confidence estimation of a given black-box 3D object detector. We aggregate geometric cues of detections and their spatial relationships, which enables us to properly assess their plausibility and consequently, improve the confidence estimation. This leads to consistent performance gains over a variety of state-of-the-art detectors. Across all evaluated detectors, GACE proves to be especially beneficial for the vulnerable road user classes, i.e. pedestrians and cyclists."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.646,
+                0.21,
+                0.661
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.673,
+                0.47,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Three-dimensional perception of surrounding objects is a critical component for autonomous vehicles and robots. Many modern perception systems use point cloud data from LiDAR (Light Detection and Ranging) sensors for this task, since they can provide accurate 3D information even over long distances. The popularity of these sensors can be seen in the increased research interest in LiDAR-based 3D object detection approaches, e.g. [10,29,38,40,45,47] and the large number of recently published autonomous driving datasets that include LiDAR data, e.g. [1,6,20,33]."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.825,
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+            ],
+            "angle": 0,
+            "content": "However, the characteristics of LiDAR data impose significant challenges for object detection. Unlike pixels in an image, which are aligned in a regular grid, point clouds represent 3D data as a collection of individual points in space, each with its own set of coordinates. In addition to the un"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.288,
+                0.891,
+                0.416
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.42,
+                0.889,
+                0.548
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.551,
+                0.894,
+                0.648
+            ],
+            "angle": 0,
+            "content": "Figure 1. Context matters: a baseline detector struggles at detecting true positive objects confidently if the sampling pattern is atypical, e.g. the occluded pedestrian in the orange bounding box (close-up top-left). GACE exploits the geometric properties of the detection and its surrounding objects to significantly increase the score for this detection, which is intuitively correct for a human observer considering this scene."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.675,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "structured nature of the data, the highly variable point density poses a major challenge. Due to the angular offset of the LiDAR beams, the density is highly dependent on the distance to the object and can be altered by occlusions in the foreground. This often requires detecting objects based on very few data points, which is especially true for classes with smaller spatial dimensions, such as pedestrians and cyclists. For example, in the Waymo Open Dataset [33], one of the most widely used and challenging datasets to date, about 30 percent of all annotated pedestrians consist of less than merely 20 points. Detecting these sparsely sensed objects naturally leads to a large number of false positive detections at test time. For this reason, determining a meaningful confidence value for the detections is critical to find a trade-off between precision and recall that adequately dis"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
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+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6566"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.471,
+                0.213
+            ],
+            "angle": 0,
+            "content": "tinguishes true positives from false positives. The potential that could be exploited by improving the confidence score is considerable: Suppose we have an oracle that could correctly classify the detections of a SECOND [38] model on the Waymo dataset into true and false positives. This would increase the LEVEL_1 average precision for vehicles by \\(+3.96\\mathrm{AP}\\) and, more importantly, for pedestrians and cyclists by as much as \\(+10.71\\mathrm{AP}\\) and \\(+13.74\\mathrm{AP}\\), respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.217,
+                0.471,
+                0.445
+            ],
+            "angle": 0,
+            "content": "Existing 3D object recognition pipelines, including confidence estimation approaches, were largely inspired by 2D image-based object recognition models and then gradually adapted to point cloud processing. However, the conventional backbone - neck - head architecture of the 2D detection model was largely retained, e.g. in [8, 10, 15, 27, 38, 45]. After extracting features (point-based, voxel-based, or region-based) over multiple levels in the backbone, they are fused in the neck module and then passed to the detection head, where bounding box regression and confidence estimation are performed on a dense feature representation. Typically, separate branches are used within the head for bounding box regression and confidence estimation, each consisting of one or more fully connected layers on top of the common feature representation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.448,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Unlike image-based object detection, there are several highly relevant geometric properties inherent to objects in 3D point clouds that have been largely unexploited in assessing the confidence of a detection. In the image case, it is usually not possible to easily derive geometric properties for the objects, such as height or orientation, unless a static and fully calibrated camera and a known or constant scene are given. In contrast, in 3D object detection, many geometric features are directly available in the object properties and associated 3D data points to better assess the presence of a real object. On the one hand, these are instance-specific properties, such as the dimension of the object, the heading direction, the position, or the point distribution within the bounding box. For example, as shown in Figure 2, the precision of a SECOND [38] model for detecting a vehicle is highly dependent on the size of the object and from which side it is detected by the LiDAR. It can be seen that vehicle categories between passenger cars and heavy duty vehicles (i.e. vehicles with a length of 6 to \\(13\\mathrm{m}\\)) are harder to detect, potentially because they are underrepresented in the dataset, and that vehicles are easier to detect from behind (i.e. viewing angle between \\(\\pm 45\\) degrees), presumably because of the highly reflective license plates, as shown in [25]. On the other hand, contextual properties, i.e. geometric relationships to neighboring objects, can contribute to a more reliable estimation of the confidence. For example, as shown in Figure 1, a pedestrian that appears atypical due to occlusions can be assessed more reliably by additionally taking neighboring vehicles and pedestrians into consideration."
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.874,
+                0.19
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.193,
+                0.874,
+                0.292
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.294,
+                0.892,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Figure 2. Precision of a SECOND [38] model for the Waymo [33] vehicle class as a function of the object length (top) and of the viewing angle (bottom), indicating from which side the vehicle is seen by the LiDAR, where 0 degrees corresponds to the rear view. These examples illustrate the strong dependence of the precision on simple geometric object properties."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.418,
+                0.892,
+                0.658
+            ],
+            "angle": 0,
+            "content": "Nevertheless, these simple but highly informative metric properties are neglected when estimating the confidence score in current detector architectures for the following reasons: First, in grid-based models, information such as the exact point distribution within the bounding box or the number of points is already partially discarded by the discretization (voxelization) in the preprocessing phase. Second, the bounding box properties (object dimensions & rotation) are determined in the parallel and separate box regression head and are therefore not accessible to the confidence estimation head. Finally, confidence estimation is usually performed using only features within a small area around the object (depending on the receptive field and detector), and no explicit information about neighboring objects and their geometric properties or confidence values is used, preventing a holistic estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Inspired by these observations, we present GACE, an intuitive and highly effective method to improve the confidence estimation of any black-box detector using geometric information. Given a set of detections from the base detector, we explicitly use these neglected features to enhance the expressiveness of the confidence values with the help of these additional cues. Our model-agnostic approach is intentionally applied after the actual detector training process to perform an auxiliary geometric assessment independent of the initial features. In a detailed evaluation on the Waymo dataset, we show that GACE consistently improves the performance of several state-of-the-art detection pipelines. Furthermore, we demonstrate the generalizability and transferability of our method by applying it to other datasets and even other detectors. Without retraining them, we achieve highly compelling performance gains."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.516,
+                0.956
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+            "angle": 0,
+            "content": "6567"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.09,
+                0.22,
+                0.107
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.115,
+                0.468,
+                0.191
+            ],
+            "angle": 0,
+            "content": "LiDAR-based 3D Object Detection: Depending on how existing methods for 3D object detection in single frame LiDAR data deal with the unstructured nature of point clouds, they can be broadly categorized into point-based, grid-based, and hybrid approaches."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.191,
+                0.468,
+                0.356
+            ],
+            "angle": 0,
+            "content": "Point-based methods extract information directly from the individual raw 3D points [23,24,30,32,40,44]. The pioneering works, PointNet [23] and PointNet++ [24], used shared multilayer perceptrons in combination with global pooling functions to directly extract features from the irregular point cloud data. In Point-RCNN [30] features extracted in this manner are used to segment foreground points and generate proposals based on them. The advantages of point-based 3D object detectors are that there is no loss of point information due to discretization and the large receptive field, but at the cost of high computational demands."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.357,
+                0.468,
+                0.705
+            ],
+            "angle": 0,
+            "content": "Instead of processing the points directly, grid-based methods [4, 15, 21, 27, 34, 38, 39, 43, 46] discretize the non-uniform 3D points into regular grids that can then be processed with 2D/3D convolutions. Voxelnet [46], a pioneering method, divides the point cloud into uniformly spaced 3D voxels, aggregates information from the points within them and generates predictions using 3D convolutions. To better handle the large number of empty voxels, SECOND [38] introduced sparse 3D convolutions. To reduce complexity, PointPillars [15] and PillarNet [27] use a 2D grid on the ground plane to create a column representation, a single pillar-shaped voxel per location, that can be processed using 2D convolutions. As an alternative to such anchor-based methods, Centerpoint [43] predicts a bird's-eye view heat map and detects the object center using a keypoint detector. Recently, transformer-based backbones have also been used to enable long-range relationships between voxels [5, 21, 34, 47]. Object relations within a frame and across multiple frames are mapped by Ret3D [37] using a graph and a transformer. The advantage of grid-based methods is that they can process data faster due to the regular format, but are limited by the loss of point information during the initial discretization phase."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.468,
+                0.886
+            ],
+            "angle": 0,
+            "content": "In order to obtain both, multi-scale features and fine-grained information, hybrid methods process voxel and point information jointly [22, 26, 28, 29, 31, 41, 42]. PV-RCNN [28], uses a set abstraction module that combines surrounding point and voxel features at keypoints to improve the detections. Part-A² [31] predicts the position of parts within an object based on point features to improve the accuracy, while LiDAR R-CNN [17] uses features of a PointNet [23] model that processes points within and around box proposals. Pyramid R-CNN [19] creates point features using a pyramid grid structure to acquire fine-grained and long-range contextual information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.469
+            ],
+            "angle": 0,
+            "content": "Confidence Estimation: In the usual backbone - neck - head detector architecture, after the feature extraction and aggregation, the box regression and confidence estimation are performed. This is usually done in two separate branches based on a common dense feature representation [15, 38, 40, 46]. This has the disadvantage that the accuracy of the localization is hardly included in the confidence score. Inspired by 2D object detection methods [11,12,36], IoU guided supervision is frequently used to obtain a better correlation between the classification result and the localization accuracy [9, 10, 16, 27, 28, 31, 41, 45]. Thereby, the IoU between the predicted box and the ground truth is learned in a third branch during training and then incorporated into the final confidence score at test time. Hu et al. [9] leverage the inherent relationship between object distance and point density to better assess a detection. Inspired by the 2D approach [3], a spatial transformation on the feature maps is done by He et al. [8] to better align the confidence prediction and bounding box regression. Related to confidence estimation are also calibration methods [7, 14] where the score should represent a true probability, i.e. how likely a detection is. Detection pipelines, however, aim at the best separation of true and false positives as optimization goal for the confidence prediction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.484,
+                0.892,
+                0.634
+            ],
+            "angle": 0,
+            "content": "In our confidence estimation method we also pursue this optimization objective, but in contrast to existing approaches, we present a method for refining the confidence values for a given set of detections by exploiting the rich geometric information contained directly in the detections as well as in the underlying 3D points. While these useful cues for assessing the plausibility of a detection have been largely untapped due to the architecture of common detection pipelines, they allow us to increase the expressiveness of the confidence values."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.649,
+                0.886,
+                0.666
+            ],
+            "angle": 0,
+            "content": "3. Geometry-Aware Confidence Enhancement"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Our goal is to optimize the confidence scores for a given set of detections from a base detector in order to better separate true positives from false positives, thus increasing the overall detection performance. We use the detector in a pure black box manner, i.e. we do not assume any knowledge about the architecture of the base model, nor access to its internals like parameters, features or gradients. This black-box optimization, taking only the point cloud and the set of objects detected in it as input, enables universal applicability and easy transferability of our enhancement module to any base 3D object detection pipeline. The basic idea is to revalidate the detections by exploiting as much as possible the geometric information they inherently contain."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "6568"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.088,
+                0.245,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.252,
+                0.089,
+                0.777,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.778,
+                0.089,
+                0.892,
+                0.358
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.361,
+                0.893,
+                0.417
+            ],
+            "angle": 0,
+            "content": "Figure 3. Schematic of GACE: To re-evaluate the confidence score of a detection (orange), we aggregate geometric properties of the detection itself and the points it contains into a feature vector (top). To capture the context of the detection, geometric relationships to neighboring detections are aggregated using a shared MLP and subsequent pooling function (bottom). By merging both features (right), we obtain a new confidence score that takes into account the underlying geometric properties of the detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.428,
+                0.471,
+                0.473
+            ],
+            "angle": 0,
+            "content": "In our proposed approach called GACE (Geometry Aware Confidence Enhancement) we exploit two types of geometric information, as shown in Figure 3:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.484,
+                0.47,
+                0.561
+            ],
+            "angle": 0,
+            "content": "- Instance-specific Geometric Properties (Section 3.1): Attributes of the bounding box itself, combined with the point data inside. For example, how well is the size of the object or the heading angle supported by the point distribution?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.572,
+                0.469,
+                0.648
+            ],
+            "angle": 0,
+            "content": "- Contextual Geometric Properties (Section 3.2): Relationships to surrounding objects can provide useful information to better validate an uncertain detection, e.g., a partially occluded vehicle moving in the same lane and same direction as the surrounding vehicles."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.484,
+                0.47,
+                0.648
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.659,
+                0.47,
+                0.853
+            ],
+            "angle": 0,
+            "content": "These useful cues to estimate the plausibility of an object are usually not used for the confidence estimation in common detection pipelines. The reasons are that information is often already discarded during preprocessing (discretization), essential properties such as the estimated size of the object are not available (separate box regression in a parallel branch), or the objects are only evaluated individually and not more holistically. Therefore, we explicitly use these easily accessible and rich sources of information as input to our enhancement module. After merging the instance-specific and contextual features, we determine the new confidence value of each proposed object via an auxiliary task (Section 3.3)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To generate the training data for our enhancement module, we use the black-box base model in a single inference run on the training set. The resulting set of all"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.428,
+                0.892,
+                0.472
+            ],
+            "angle": 0,
+            "content": "detections from the base model represents the training data to learn our improved confidence estimator. Formally, this can be described as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.487,
+                0.893,
+                0.705
+            ],
+            "angle": 0,
+            "content": "Definitions & Notations: Let \\(\\widetilde{\\mathcal{X}} = \\{\\widetilde{\\mathbf{x}}_k\\}_{k=1\\dots K}\\) be a LiDAR point cloud, where each of the \\(K\\) unordered points \\(\\widetilde{\\mathbf{x}}_k \\in \\mathbb{R}^5\\) consists of the 3D coordinates, intensity/reflectance and the elongation value. Furthermore, let \\(\\widetilde{\\mathcal{Y}} = \\{\\widetilde{\\mathbf{y}}_i\\}_{j=1\\dots M}\\) be the set of corresponding ground truth objects. Each object annotation \\(\\widetilde{\\mathbf{y}} = [\\widetilde{\\mathbf{b}}, \\widetilde{\\mathbf{y}}]\\) includes the bounding box parameters \\(\\widetilde{\\mathbf{b}} = [\\widetilde{c}_x, \\widetilde{c}_y, \\widetilde{c}_z, \\widetilde{d}_x, \\widetilde{d}_y, \\widetilde{d}_z, \\widetilde{\\Theta}]\\) and the corresponding class label \\(\\widetilde{y}\\). For a given black-box 3D object detector \\(F\\), let \\(F(\\widetilde{\\mathcal{X}}) = \\mathcal{Y} = \\{\\mathbf{y}_{i=1\\dots N}\\}\\) be the set of proposed detections for this input point cloud, where \\(\\mathbf{y} = [\\mathbf{b}, y, s]\\). In addition to the box properties \\(\\mathbf{b}\\) and the corresponding class label \\(y\\), the detector predicts a confidence value \\(s\\) that should ideally indicate the prevalence of a true positive example."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Confidence Optimization: Based on the known ground truth objects, a category label \\(\\{u_i\\in \\{0,1\\} \\}_{i = 1\\dots N}\\) can be assigned to each detection, indicating whether it is a true positive or false positive detection. Moreover, we know the IoU with a possible ground truth bounding box for each object which we define as \\(\\{v_{i}\\}_{i = 1\\dots N}\\). We aim to improve the confidence estimate of the original detector by focusing exclusively on the binary classification of detections into true positive and false positive examples. We determine the revised confidence score \\(\\{\\widehat{s}_i\\} = H(\\mathcal{V},\\mathcal{X})\\) using our module \\(H\\), where only the set of detections \\(\\mathcal{V}\\) and the points they include \\(\\mathcal{X}\\subset \\widetilde{\\mathcal{X}}\\) are used as input."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6569"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.411,
+                0.108
+            ],
+            "angle": 0,
+            "content": "3.1. Instance-specific Geometric Properties"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.114,
+                0.473,
+                0.356
+            ],
+            "angle": 0,
+            "content": "In common 2D and 3D object detection architectures, the bounding box regression and the confidence estimation are performed completely separated in different branches. This is well suited for 2D where it is desired to detect objects in the image regardless of their scale. For 3D, however, important cues for plausibility estimation remain largely unused. Let us consider the available context directly provided by an object proposal: The position of the possible object in combination with the dimensions indicates, for example, which point density is to be expected. Furthermore, the direction angle provides an indication of the expected point distribution within the box. This information can even be further refined by knowing the class of the object. This directly available geometrical knowledge about an object allows for a more profound estimation of the confidence score."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.372,
+                0.473,
+                0.524
+            ],
+            "angle": 0,
+            "content": "We extract these basic properties and transform them into a compact representation using a multilayer perceptron (MLP) \\( H_{I} \\). As input parameters, we first use the object parameters, i.e. the position \\( (c_x, c_y, c_z) \\), the size \\( (d_x, d_y, d_z) \\), and the heading angle \\( \\Theta \\) of the bounding box, as well as the initial confidence value \\( s_i \\) of the detection estimated by the base detector. Additionally, we use the distance \\( \\| \\mathbf{c} \\| \\) from the LiDAR sensor to the object center, and the angle \\( \\alpha \\) between the line of sight to the object and the heading angle of the object:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.192,
+                0.536,
+                0.47,
+                0.553
+            ],
+            "angle": 0,
+            "content": "\\[\n\\alpha = \\Theta - \\operatorname {a t a n 2} \\left(c _ {y}, c _ {x}\\right). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.565,
+                0.473,
+                0.793
+            ],
+            "angle": 0,
+            "content": "This angle describes from which side an object is seen from the LiDAR center, independent of the position of the object relative to the LiDAR, e.g. a vehicle driving directly towards the LiDAR always has the same angle \\(\\alpha\\), no matter from which direction the vehicle approaches. We complement these cues with information about the points \\(\\mathcal{X}_{\\mathrm{b}} \\subset \\mathcal{X}\\) inside the bounding box \\(\\mathbf{b}\\). Besides the overall number of points \\(|\\mathcal{X}_{\\mathrm{b}}|\\), we extract elementary low-level statistics. Therefore, we scale the box and the associated points to a uniform size and then align them w.r.t. their center and yaw angle. In this canonical representation we compute the mean, standard deviation, minimum and maximum of \\(\\mathcal{X}_{\\mathrm{b}}\\) for all axes, denoted as \\(\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{mean}}\\), \\(\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{std}}\\), \\(\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{min}}\\), \\(\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{max}}\\). We then aggregate these attributes into one feature vector representing the instance-specific plausibility per object as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.082,
+                0.802,
+                0.468,
+                0.841
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {f} ^ {I} = H _ {I} \\left(\\left[ \\mathbf {b}, \\alpha , \\| \\mathbf {c} \\|, | \\mathcal {X} _ {\\mathbf {b}} |, \\mathcal {X} _ {\\mathbf {b}} ^ {\\text {m e a n}}, \\mathcal {X} _ {\\mathbf {b}} ^ {\\text {s t d}}, \\mathcal {X} _ {\\mathbf {b}} ^ {\\min }, \\mathcal {X} _ {\\mathbf {b}} ^ {\\max } \\right] ^ {\\top}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.468,
+                0.887
+            ],
+            "angle": 0,
+            "content": "where we pass all angles as direction vectors \\((\\cos(\\cdot), \\sin(\\cdot))\\) and normalize all metric properties to unit length using the corresponding maximum value range."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.091,
+                0.791,
+                0.108
+            ],
+            "angle": 0,
+            "content": "3.2. Contextual Geometric Properties"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.121,
+                0.895,
+                0.363
+            ],
+            "angle": 0,
+            "content": "Especially in the case of uncertain detections, e.g. detections that are far away and therefore consist of only a few 3D points, or detections that are partially occluded and therefore appear atypical, geometric contextual information can be very useful in assessing a confidence score. Examples include a vehicle that is heavily occluded but in a convoy with other vehicles, or cyclists moving in a group. However, this information is usually not available for the confidence estimation, since the object proposals are evaluated individually within the receptive field but without explicit knowledge of the objects detected in its vicinity and their properties. In order to assess the plausibility of a detection \\(\\mathbf{y}\\) in a more holistic way, we use the geometric relations to surrounding objects in the scene. We thereby consider all neighbors that are within a certain radius \\(r\\) around the object to be evaluated."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.384,
+                0.895,
+                0.583
+            ],
+            "angle": 0,
+            "content": "We therefore create a representation per object, which captures the relationships to its neighboring objects. In order to be independent of the number of neighboring objects, we first create a feature vector for each neighbor, which we then combine into a unified representation using a symmetric pooling function. As input parameters per neighbor we use the distance to the object to be evaluated \\(\\| \\mathbf{c} - \\mathbf{c}_n\\|\\), the direction vector \\(\\mathbf{c} - \\mathbf{c}_n\\), the difference between the two heading angles \\(\\Theta - \\Theta_n\\), and the neighbor's class label \\(y_{n}\\). To incorporate the validity of the neighbor, we leverage \\(\\mathbf{f}_n^I\\), which represents the instance-specific properties of the neighbor. This information is encoded via the shared weight MLP \\(H_{C}\\) to form the feature vector \\(\\mathbf{f}_n^C\\) for each individual neighbor,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.513,
+                0.605,
+                0.892,
+                0.632
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {f} _ {n} ^ {C} = H _ {C} \\left(\\left[ \\| \\mathbf {c} - \\mathbf {c} _ {n} \\|, \\mathbf {c} - \\mathbf {c} _ {n}, \\Theta - \\Theta_ {n}, y _ {n}, \\mathbf {f} _ {n} ^ {I} \\right] ^ {\\top}\\right), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.653,
+                0.894,
+                0.684
+            ],
+            "angle": 0,
+            "content": "where the angle \\(\\Theta -\\Theta_{n}\\) is provided as direction vector and the metric features are normalized to unit length."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.895,
+                0.888
+            ],
+            "angle": 0,
+            "content": "Finally, we aggregate the information from the individual neighbors into a unified representation for later processing, as shown in Figure 3. This requires accumulating features of an unknown (and varying) number of neighbors. To impose no constraint on the number of features, we take inspiration from the pooling step of point-based detectors, e.g. [23], and employ a symmetric max pooling function to form a plausibility signature \\(\\mathbf{f}^C\\) over the feature vectors of all neighbors. Thus, in this representation the geometric relations to the surrounding objects are accumulated for the subsequent confidence estimation, taking into account the respective local properties of the neighbors."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6570"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.402,
+                0.106
+            ],
+            "angle": 0,
+            "content": "3.3. Data Fusion & Confidence Prediction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.114,
+                0.47,
+                0.204
+            ],
+            "angle": 0,
+            "content": "To estimate the new confidence value for a detection, we merge the instance-specific and contextual geometric features. The instance-specific information encoded in \\(\\mathbf{f}^I\\), as well as the contextual information in \\(\\mathbf{f}^C\\) are concatenated and processed using \\(H_{F}\\), a MLP with sigmoid output function, to estimate the new confidence score"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.195,
+                0.214,
+                0.469,
+                0.241
+            ],
+            "angle": 0,
+            "content": "\\[\n\\widehat {s} = H _ {F} \\left(\\left[ \\mathbf {f} ^ {I}, \\mathbf {f} ^ {C} \\right] ^ {\\top}\\right). \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.25,
+                0.47,
+                0.46
+            ],
+            "angle": 0,
+            "content": "We train the whole module including the two feature encoding networks \\( H_{I} \\) and \\( H_{C} \\) using an end-to-end training strategy. As loss function \\( \\mathcal{L}_{\\mathrm{conf}}(\\widehat{s},u) \\) for this task we use the focal loss [18] to focus learning on hard examples. The goal is to divide the set of detections as good as possible into true or false positive examples using the binary category label \\( u\\in \\{0,1\\} \\) as target. As auxiliary task during training we estimate the IoU with the ground truth bounding box in a further output \\( \\widehat{v} \\) of \\( H_{F} \\). Therefore, we add an IoU-guidance [16, 41, 45] L1-loss term \\( \\mathcal{L}_{\\mathrm{IoU}}(\\widehat{v},v) \\). This increases the importance of the point distribution statistics within the features, as they provide evidence of the bounding box accuracy from which the confidence estimate also benefits. The overall loss function is therefore"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.152,
+                0.472,
+                0.469,
+                0.489
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {c o n f}} (\\widehat {s}, u) + \\lambda_ {\\mathrm {I o U}} \\mathcal {L} _ {\\mathrm {I o U}} (\\widehat {v}, v), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.5,
+                0.47,
+                0.53
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{\\mathrm{IoU}}\\) is a hyper-parameter to adjust the influence of the auxiliary task."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.544,
+                0.21,
+                0.56
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.569,
+                0.469,
+                0.675
+            ],
+            "angle": 0,
+            "content": "To demonstrate the benefits of GACE, we evaluate our black-box confidence optimization method on several well-known state-of-the-art 3D object detection pipelines. In particular, we apply it to the pillar-based PointPillars [15], the voxel-based SECOND [38] and Centerpoint [43], as well as the hybrid methods Part-A² [31], PV-RCNN [28] and PV-RCNN++ [29]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.69,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets: For the evaluation of our approach we use the Waymo Open Dataset [33] as well as the KITTI Dataset [6]. The Waymo dataset is one of the largest and most challenging public datasets for autonomous driving research. It provides 798 training scenes and 202 validation scenes, where each scene consists of about 200 LiDAR samples covering the full \\(360^{\\circ}\\) field-of-view. In total, the dataset consists of over 8.9M annotated objects classified into vehicles, pedestrians and cyclists. We follow the common evaluation protocol using the standard metrics average precision (AP), as well as average precision with heading (APH), where true positives are weighted by their heading accuracy. In addition, we use the KITTI dataset, one of the most popular datasets for 3D object detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "We thereby use the standard split [2] into a training set (3712 samples) and validation set (3769 samples). We also follow the common evaluation practice using average precision with 40 recall points. For both datasets, the 3D IoU threshold for a true positive sample is 0.7 for vehicles and 0.5 for pedestrians and cyclists."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.198,
+                0.892,
+                0.424
+            ],
+            "angle": 0,
+            "content": "Implementation Details: Our experimental setup is based on the open-source toolbox OpenPCDet [35]. To ensure the reproducibility of our results, all base models used in the experiments have been trained on the training set using the default configuration and default training policies of OpenPCDet. This includes augmenting the data by randomly rotating, scaling and flipping the point cloud, as well as ground truth sampling [38], i.e. the placement of objects from other training examples in the current frame. To create the training data for our module, we use the base model as a black-box detection pipeline. In a single inference run on the training set, we collect the output of the base model, i.e. the set of all detections, which represents our training data. The actual training process of our module is therefore entirely decoupled from the base model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.427,
+                0.892,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Our sub-networks for feature transformation, i.e. \\( H_{I} \\) and the shared network \\( H_{C} \\), as well as the confidence prediction network \\( H_{F} \\) are two-layer MLP's with 256 feature dimensions. The feature vector \\( \\mathbf{f}^{I} \\) in which the instance-specific information is encoded is 128-dimensional and \\( \\mathbf{f}^{C} \\) for the contextual information is 64-dimensional. When determining the contextual geometric properties, we accumulate the neighboring objects that are within a radius of \\( r = 40m \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.548,
+                0.892,
+                0.683
+            ],
+            "angle": 0,
+            "content": "We train our model end to end with the Adam [13] optimizer and a learning rate of 0.001. The weighting of the auxiliary loss term during training is set to \\(\\lambda_{\\mathrm{IoU}} = 0.5\\). In all experiments we use the same architecture as well as hyperparameters, regardless of the underlying black-box base model. We train our module over 5 epochs on a single NVIDIA® GeForce® RTX 3090 GPU, which takes less than 10 minutes due to our favorable lightweight model size and low feature dimensions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.698,
+                0.638,
+                0.712
+            ],
+            "angle": 0,
+            "content": "4.1. Main Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.722,
+                0.892,
+                0.873
+            ],
+            "angle": 0,
+            "content": "Table 1 summarizes the results of our confidence optimization on the Waymo dataset for different baseline detection pipelines. For each detector architecture, we report the performance of the base detector as well as the results after applying our GACE module. Please note that for better traceability, the results of the base detectors correspond to the respective OpenPCDet implementations (see OpenPCDet model zoo). Some reported baseline scores are even higher than in their original papers due to augmentation techniques used in OpenPCDet."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.518,
+                0.888,
+                0.787,
+                0.9
+            ],
+            "angle": 0,
+            "content": "1https://github.com/dschinagl/gace"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6571"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.107,
+                0.085,
+                0.864,
+                0.344
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">Overall</td><td colspan=\"4\">Vehicles (IoU=0.7)</td><td colspan=\"4\">Pedestrians (IoU=0.5)</td><td colspan=\"4\">Cyclists (IoU=0.5)</td></tr><tr><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td></tr><tr><td>mAP</td><td>mAPH</td><td>mAP</td><td>mAPH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td></tr><tr><td>PointPillars [15]</td><td>64.72</td><td>57.07</td><td>58.57</td><td>51.73</td><td>70.99</td><td>70.35</td><td>62.79</td><td>62.20</td><td>66.36</td><td>47.15</td><td>58.27</td><td>41.32</td><td>56.81</td><td>53.71</td><td>54.66</td><td>51.67</td></tr><tr><td>+ GACE (Ours)</td><td>69.25</td><td>61.24</td><td>62.98</td><td>55.73</td><td>71.92</td><td>71.28</td><td>63.63</td><td>63.04</td><td>72.18</td><td>51.97</td><td>64.06</td><td>45.96</td><td>63.64</td><td>60.47</td><td>61.25</td><td>58.20</td></tr><tr><td>Improvement</td><td>+4.53</td><td>+4.17</td><td>+4.41</td><td>+4.00</td><td>+0.93</td><td>+0.93</td><td>+0.84</td><td>+0.84</td><td>+5.82</td><td>+4.82</td><td>+5.79</td><td>+4.64</td><td>+6.83</td><td>+6.76</td><td>+6.59</td><td>+6.53</td></tr><tr><td>SECOND [38]</td><td>65.13</td><td>60.81</td><td>59.01</td><td>55.12</td><td>70.93</td><td>70.30</td><td>62.65</td><td>62.07</td><td>65.67</td><td>54.96</td><td>57.78</td><td>48.25</td><td>58.78</td><td>57.18</td><td>56.59</td><td>55.05</td></tr><tr><td>+ GACE (Ours)</td><td>70.17</td><td>66.13</td><td>63.74</td><td>60.06</td><td>71.56</td><td>70.92</td><td>63.22</td><td>62.63</td><td>71.71</td><td>61.87</td><td>63.27</td><td>54.37</td><td>67.22</td><td>65.59</td><td>64.73</td><td>63.16</td></tr><tr><td>Improvement</td><td>+5.04</td><td>+5.32</td><td>+4.73</td><td>+4.94</td><td>+0.63</td><td>+0.62</td><td>+0.57</td><td>+0.56</td><td>+6.04</td><td>+6.91</td><td>+5.49</td><td>+6.12</td><td>+8.44</td><td>+8.41</td><td>+8.14</td><td>+8.11</td></tr><tr><td>Part-A2[31]</td><td>70.30</td><td>66.66</td><td>63.53</td><td>60.27</td><td>73.35</td><td>72.81</td><td>64.73</td><td>64.24</td><td>70.02</td><td>61.01</td><td>60.83</td><td>52.85</td><td>67.53</td><td>66.18</td><td>65.03</td><td>63.73</td></tr><tr><td>+ GACE (Ours)</td><td>73.07</td><td>69.21</td><td>66.24</td><td>62.77</td><td>73.99</td><td>73.43</td><td>65.38</td><td>64.87</td><td>72.36</td><td>62.93</td><td>63.21</td><td>54.81</td><td>72.84</td><td>71.28</td><td>70.13</td><td>68.63</td></tr><tr><td>Improvement</td><td>+2.77</td><td>+2.55</td><td>+2.71</td><td>+2.50</td><td>+0.64</td><td>+0.62</td><td>+0.65</td><td>+0.63</td><td>+2.34</td><td>+1.92</td><td>+2.38</td><td>+1.96</td><td>+5.31</td><td>+5.10</td><td>+5.10</td><td>+4.90</td></tr><tr><td>Centerpoint [43]</td><td>73.01</td><td>70.35</td><td>66.79</td><td>64.33</td><td>72.87</td><td>72.33</td><td>64.76</td><td>64.27</td><td>74.48</td><td>68.22</td><td>66.55</td><td>60.81</td><td>71.69</td><td>70.50</td><td>69.06</td><td>67.92</td></tr><tr><td>+ GACE (Ours)</td><td>75.58</td><td>72.98</td><td>69.19</td><td>66.76</td><td>74.49</td><td>73.99</td><td>66.19</td><td>65.73</td><td>78.62</td><td>72.48</td><td>70.44</td><td>64.73</td><td>73.64</td><td>72.48</td><td>70.94</td><td>69.83</td></tr><tr><td>Improvement</td><td>+2.57</td><td>+2.63</td><td>+2.40</td><td>+2.43</td><td>+1.62</td><td>+1.66</td><td>+1.43</td><td>+1.46</td><td>+4.14</td><td>+4.26</td><td>+3.89</td><td>+3.92</td><td>+1.95</td><td>+1.98</td><td>+1.88</td><td>+1.91</td></tr><tr><td>PV-RCNN [28]</td><td>71.11</td><td>66.78</td><td>64.40</td><td>60.50</td><td>74.79</td><td>74.17</td><td>66.17</td><td>65.61</td><td>72.06</td><td>61.46</td><td>63.00</td><td>53.56</td><td>66.48</td><td>64.72</td><td>64.03</td><td>62.34</td></tr><tr><td>+ GACE (Ours)</td><td>73.38</td><td>68.89</td><td>66.65</td><td>62.57</td><td>75.20</td><td>74.55</td><td>66.57</td><td>65.97</td><td>73.84</td><td>62.97</td><td>64.88</td><td>55.14</td><td>71.12</td><td>69.16</td><td>68.50</td><td>66.60</td></tr><tr><td>Improvement</td><td>+2.27</td><td>+2.11</td><td>+2.25</td><td>+2.07</td><td>+0.41</td><td>+0.38</td><td>+0.40</td><td>+0.36</td><td>+1.78</td><td>+1.51</td><td>+1.88</td><td>+1.58</td><td>+4.64</td><td>+4.44</td><td>+4.47</td><td>+4.26</td></tr><tr><td>PV-RCNN++ [29]</td><td>75.72</td><td>73.05</td><td>69.22</td><td>66.73</td><td>77.30</td><td>76.81</td><td>68.92</td><td>68.47</td><td>78.91</td><td>72.42</td><td>70.43</td><td>64.41</td><td>70.95</td><td>69.90</td><td>68.31</td><td>67.31</td></tr><tr><td>+ GACE (Ours)</td><td>76.76</td><td>74.02</td><td>70.31</td><td>67.75</td><td>77.42</td><td>76.93</td><td>69.05</td><td>68.59</td><td>79.59</td><td>72.97</td><td>71.34</td><td>65.18</td><td>73.26</td><td>72.16</td><td>70.54</td><td>69.48</td></tr><tr><td>Improvement</td><td>+1.04</td><td>+0.97</td><td>+1.09</td><td>+1.02</td><td>+0.12</td><td>+0.12</td><td>+0.13</td><td>+0.12</td><td>+0.68</td><td>+0.55</td><td>+0.91</td><td>+0.77</td><td>+2.31</td><td>+2.26</td><td>+2.23</td><td>+2.17</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.354,
+                0.895,
+                0.384
+            ],
+            "angle": 0,
+            "content": "Table 1. Performance comparison on the Waymo Open Dataset [33] validation set for different baseline methods with and without our confidence enhancement module GACE."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.405,
+                0.471,
+                0.511
+            ],
+            "angle": 0,
+            "content": "For all baseline detectors and all classes, adjusting the confidence level with our approach leads to an increase in performance without exception. The overall performance gains range from \\(+1.02\\mathrm{mAPH}\\) (LEVEL_2) for PV-RCNN++ to \\(+4.94\\mathrm{mAPH}\\) (LEVEL_2) for SECOND, demonstrating the significance of this geometric information in estimating a confidence score for a detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.532,
+                0.47,
+                0.744
+            ],
+            "angle": 0,
+            "content": "Object Classes: The performance improvements are significantly higher for the classes of pedestrians and cyclists. Intuitively, objects of these vulnerable road users contain significantly fewer 3D points due to their smaller spatial extent compared to vehicles. This effect is even aggravated by possible occlusions. Furthermore, the class of cyclists in particular is underrepresented in the training data. These properties make objects of these classes more difficult to detect, which leads to a higher number of false positives, but also makes confidence estimation more complex. Especially in these cases, our confidence enhancement method benefits from the additional geometric information when separating false positives from true positives, resulting in a higher impact of GACE."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Base Detectors: The overall performance gain is highest when applying GACE on pillar-based (PointPillars [15]) and voxel-based methods (SECOND [38] and Centerpoint [43]). These methods lose valuable point information already in their preprocessing stage, i.e. by voxelization. Thus, the optimization potential for these methods is higher than for the hybrid methods, which explicitly incorporate point-level information at detection locations. However, by explicitly exploiting both instance-specific and contextual geometric properties of the detections, GACE also leads to"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.405,
+                0.895,
+                0.452
+            ],
+            "angle": 0,
+            "content": "a significant performance improvement for these methods, i.e. Part-\\(\\mathrm{A}^2\\) [31], PV-RCNN [28] and PV-RCNN++ [29], most notably for the classes of pedestrians and cyclists."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.471,
+                0.895,
+                0.7
+            ],
+            "angle": 0,
+            "content": "Precision/Recall Plots: To better illustrate the impact of our method, Figure 4 shows the precision/recall plots before and after applying GACE with a SECOND [38] model as the base detector (See the supplemental material for the other base detectors). Since recall remains unaffected, the significant performance gains of GACE are entirely due to an increase in precision. The better separation of true and false positives is mainly seen in the more challenging classes of pedestrians and cyclists, where the number of false detections is significantly higher and confidence estimation is more difficult. Furthermore, we see that the precision gains are higher in regions of higher recall, i.e. for detections with a lower confidence score. Especially these initially underrated detections of objects of the vulnerable classes represent a safety risk that can be reduced by GACE."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.72,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Range-based Evaluation: Table 2 summarizes our evaluation across the different distance ranges of Waymo. This also shows that GACE can consistently improve the performance of all baseline detectors and in all sub-ranges, especially in the far range. Detections at long distances are more challenging due to the lower point density, making it harder to distinguish true positives from false positives. Therefore, the geometric information is even more valuable in these cases, e.g. from \\(+2.93\\mathrm{mAPH}\\) (LEVEL_2) for PV-RCNN++ up to \\(+4.97\\mathrm{mAPH}\\) (LEVEL_2) for PointPillars. The detailed evaluation results for all subclasses can be found in the supplemental material."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.958
+            ],
+            "angle": 0,
+            "content": "6572"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.091,
+                0.348,
+                0.21
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.359,
+                0.09,
+                0.621,
+                0.21
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.632,
+                0.091,
+                0.891,
+                0.21
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.215,
+                0.894,
+                0.258
+            ],
+            "angle": 0,
+            "content": "Figure 4. Precision-recall plots for a SECOND [38] model as base detector with and without our confidence enhancement module on the Waymo Open Dataset [33] validation set for LEVEL_2 APH. Especially at higher recall levels, GACE's better separation of true and false positives leads to higher precision."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.094,
+                0.274,
+                0.456,
+                0.535
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"3\">Overall (LEVEL_2)</td></tr><tr><td>0-30m</td><td>30-50m</td><td>50m-Inf</td></tr><tr><td>mAP / mAPH</td><td>mAP / mAPH</td><td>mAP / mAPH</td></tr><tr><td>PointPillars [15]</td><td>75.10 / 67.59</td><td>55.31 / 48.53</td><td>37.18 / 31.00</td></tr><tr><td>+ GACE (Ours)</td><td>78.32 / 70.68</td><td>60.17 / 53.01</td><td>42.88 / 35.97</td></tr><tr><td>Improvement</td><td>+3.22 / +3.09</td><td>+4.86 / +4.48</td><td>+5.70 / +4.97</td></tr><tr><td>SECOND [38]</td><td>75.55 / 71.87</td><td>56.55 / 52.42</td><td>37.73 / 33.39</td></tr><tr><td>+ GACE (Ours)</td><td>78.64 / 75.39</td><td>60.10 / 56.13</td><td>41.69 / 37.39</td></tr><tr><td>Improvement</td><td>+3.09 / +3.52</td><td>+3.55 / +3.71</td><td>+3.96 / +4.00</td></tr><tr><td>Part-A² [31]</td><td>79.93 / 76.93</td><td>61.77 / 58.01</td><td>40.13 / 36.44</td></tr><tr><td>+ GACE (Ours)</td><td>81.62 / 78.52</td><td>64.63 / 60.59</td><td>45.06 / 40.94</td></tr><tr><td>Improvement</td><td>+1.69 / +1.59</td><td>+2.86 / +2.58</td><td>+4.93 / +4.50</td></tr><tr><td>Centerpoint [43]</td><td>81.29 / 79.12</td><td>65.45 / 62.66</td><td>46.45 / 43.27</td></tr><tr><td>+ GACE (Ours)</td><td>82.94 / 80.90</td><td>67.56 / 64.76</td><td>50.20 / 46.80</td></tr><tr><td>Improvement</td><td>+1.65 / +1.78</td><td>+2.11 / +2.10</td><td>+3.75 / +3.53</td></tr><tr><td>PV-RCNN [28]</td><td>79.77 / 76.24</td><td>62.57 / 58.10</td><td>42.51 / 37.77</td></tr><tr><td>+ GACE (Ours)</td><td>81.25 / 77.66</td><td>64.76 / 60.11</td><td>47.01 / 41.90</td></tr><tr><td>Improvement</td><td>+1.48 / +1.42</td><td>+2.19 / +2.01</td><td>+4.50 / +4.13</td></tr><tr><td>PV-RCNN++ [29]</td><td>83.08 / 80.98</td><td>67.86 / 65.04</td><td>48.69 / 45.26</td></tr><tr><td>+ GACE (Ours)</td><td>83.59 / 81.43</td><td>68.69 / 65.83</td><td>51.81 / 48.19</td></tr><tr><td>Improvement</td><td>+0.51 / +0.45</td><td>+0.83 / +0.79</td><td>+3.12 / +2.93</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.545,
+                0.47,
+                0.586
+            ],
+            "angle": 0,
+            "content": "Table 2. Consistent performance gains on the Waymo Open Dataset [33] validation set across distance ranges for different baseline methods for LEVEL_2 over all classes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.617,
+                0.241,
+                0.632
+            ],
+            "angle": 0,
+            "content": "4.2. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.644,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Main Components: We evaluate the contribution of our proposed instance-specific and contextual properties as well as the influence of the auxiliary IoU loss for a SECOND [38] model as baseline in Table 3. Incorporating the instance-specific geometric properties already leads to a significant performance increase of \\(+3.65\\mathrm{AP} / + 3.32\\mathrm{APH}\\). Including also the contextual information, i.e. incorporating the relationships to the neighboring detection hypotheses further increases the performance by another \\(+0.71\\mathrm{AP} / + 1.14\\mathrm{APH}\\). Compared to the contributions of these two components, there is only a minor impact of incorporating the IoU guidance, leading to additional \\(+0.37\\mathrm{AP} / + 0.48\\mathrm{APH}\\). Note that the degradation when adding \\(\\mathcal{L}_{\\mathrm{IoU}}\\) to only contextual features is caused by the lack of point information, which does not allow a reasonable estimation of the IoU. Overall, the instance-specific geometric information contributes stronger than the contextual geometric information."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.28,
+                0.891,
+                0.422
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Baseline</td><td>Instance Specific</td><td>Contextual</td><td>Aux-Loss LIoU</td><td>LEVEL_2 mAP</td><td>LEVEL_2 mAPH</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>59.01</td><td>55.12</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>62.66</td><td>58.44</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>60.33</td><td>56.90</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>63.37</td><td>59.58</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>62.94</td><td>58.78</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>60.19</td><td>56.77</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>63.74</td><td>60.06</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.431,
+                0.893,
+                0.474
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation experiments for a SECOND [38] model as base detector over all classes on the Waymo Open Dataset [33] validation set. We show the impact of each GACE component."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.508,
+                0.887,
+                0.536
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Box Properties</td><td># Points</td><td>Viewing Angle</td><td>Point Stat.</td></tr><tr><td>56.98+1.86</td><td>55.96+0.84</td><td>55.86+0.74</td><td>58.15+3.03</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.54,
+                0.893,
+                0.582
+            ],
+            "angle": 0,
+            "content": "Table 4. Impact of the different instance-specific feature groups when used exclusively for a SECOND model as base detector on the Waymo Open Dataset [33] over all classes (LEVEL_2 mAPH)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.639,
+                0.895,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Instance-Specific Properties: We analyze the contribution of each feature group within the instance-specific properties, namely box properties \\((\\mathbf{b},\\| \\mathbf{c}\\|)\\), number of points \\((|\\mathcal{X}_{\\mathbf{b}}|)\\), viewing angle \\((\\alpha)\\), and point statistics \\((\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{mean}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{std}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{min}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{max}})\\). Table 4 shows the impact of each group on the overall performance when used exclusively, indicating a high contribution of box properties and point statistics. A complete list of the combinations can be found in the supplemental material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.795,
+                0.894,
+                0.887
+            ],
+            "angle": 0,
+            "content": "Contextual Properties Radius: The dependence of the performance on the chosen context radius \\( r \\) is shown in Figure 5. It can be seen that the performance increases significantly up to \\( \\sim 15m \\), followed by a slight degradation starting at \\( \\sim 40m \\), which illustrates the importance of neighboring objects in the near and middle ranges."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "6573"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.085,
+                0.092,
+                0.46,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.195,
+                0.47,
+                0.223
+            ],
+            "angle": 0,
+            "content": "Figure 5. Performance of purely context-based GACE for different radius \\( r \\) (SECOND base model / Waymo overall)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.09,
+                0.232,
+                0.455,
+                0.351
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Car</td><td>Pedestrian</td><td>Cyclist</td></tr><tr><td>SECOND (KITTI)</td><td>81.61</td><td>51.14</td><td>66.74</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.04+0.43</td><td>57.11+5.97</td><td>70.99+4.25</td></tr><tr><td>PointPillars (KITTI)</td><td>78.39</td><td>51.41</td><td>62.94</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>78.51+0.12</td><td>55.30+3.89</td><td>67.94+5.00</td></tr><tr><td>Part-A2 (KITTI)</td><td>82.92</td><td>59.73</td><td>70.10</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.94+0.02</td><td>64.21+4.48</td><td>72.16+2.06</td></tr><tr><td>PV-RCNN (KITTI)</td><td>82.86</td><td>53.64</td><td>70.42</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.84-0.02</td><td>61.06+7.42</td><td>72.70+2.28</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.356,
+                0.47,
+                0.412
+            ],
+            "angle": 0,
+            "content": "Table 5. Model Transfer: Applying a GACE module trained on SECOND detections on Waymo (without LiDAR elongation, which is not available on KITTI) to different detectors on the KITTI dataset (moderate difficulty / @R40)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.436,
+                0.381,
+                0.453
+            ],
+            "angle": 0,
+            "content": "4.3. Generalization and Transferability"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.46,
+                0.471,
+                0.807
+            ],
+            "angle": 0,
+            "content": "Since we use only the detection attributes and corresponding properties of the underlying point cloud as input, a GACE module trained on base detector A can be directly applied to another base detector B. Furthermore, since all metric features are normalized to their maximum possible value and the statistical parameters (point distribution) are computed from a normalized unit-length box, GACE can be applied not only to a different detector, but also directly to a different detector on a different dataset. Therefore, to demonstrate the general applicability of GACE, we freeze a GACE module trained on detections from a SECOND detector on Waymo, and apply it directly to detections of a SECOND detector on the KITTI dataset [6]. As shown in Table 5, first row, this also leads to considerable performance improvements despite the distribution shift to a different dataset (different LiDAR sensor, different country). Even more remarkably, significant performance gains are also obtained when the same GACE module is applied even to a different base detector, e.g. +7.42AP for PV-RCNN on pedestrians while achieving the same performance for cars. The results demonstrate the excellent generalization capability of GACE and the general validity of the geometric information regardless of the dataset."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.817,
+                0.251,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.4. Runtime Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In Table 6 we show the runtime analysis of GACE for a \\(360^{\\circ}\\) field-of-view Waymo point cloud using a single NVIDIA® GeForce® RTX 3090 GPU. The computationally most intensive part is the feature extraction, especially ex"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.52,
+                0.084,
+                0.875,
+                0.172
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"3\">Feature Extraction</td><td>Points in Boxes Query</td><td>0.56 ms</td></tr><tr><td>Geometric &amp; Statistical Features</td><td>0.98 ms</td></tr><tr><td>Neighboring Object ID&#x27;s Query</td><td>0.07 ms</td></tr><tr><td rowspan=\"3\">Network Inference</td><td>HI (Instance-specific)</td><td>0.14 ms</td></tr><tr><td>HC (Contextual)</td><td>0.17 ms</td></tr><tr><td>HF (Confidence Estimation)</td><td>0.12 ms</td></tr><tr><td colspan=\"2\">Overall</td><td>2.04 ms</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.178,
+                0.892,
+                0.207
+            ],
+            "angle": 0,
+            "content": "Table 6. GACE runtime analysis per \\(360^{\\circ}\\) field-of-view Waymo point cloud on a single NVIDIA® GeForce® RTX 3090 GPU."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.238,
+                0.892,
+                0.343
+            ],
+            "angle": 0,
+            "content": "tracting the statistical features for all detections. However, this can be solved efficiently via PyTorch einsum. During inference, we first compute the instance-specific plausibility \\(\\mathbf{f}^I\\) for each detection via \\(H_{I}\\), which is then used as input to \\(H_{C}\\) for the corresponding neighbors. Overall, GACE is capable of processing \\(\\sim 490\\) Waymo point clouds per second with \\(\\sim 100\\) detections each."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.366,
+                0.623,
+                0.381
+            ],
+            "angle": 0,
+            "content": "5. Limitations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.394,
+                0.892,
+                0.606
+            ],
+            "angle": 0,
+            "content": "While our method has proven effective in improving object detection performance for vulnerable classes such as pedestrians and cyclists, it is worth noting that it may not offer such significant benefits for simpler classes such as vehicles. This is because all detectors typically have few false positives for these easier-to-detect objects. Therefore, there is less room for improvement for this class. However, it is important to consider the context in which our method is applied. Even if the performance improvement is not as large for simpler classes, the overall impact of our method on safety should not be underestimated. In many real-world scenarios, pedestrians and cyclists are particularly vulnerable, and any improvement in their detection can make a significant contribution to safety."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.628,
+                0.619,
+                0.644
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.656,
+                0.892,
+                0.839
+            ],
+            "angle": 0,
+            "content": "We proposed GACE, a method to better evaluate object hypotheses from black-box LiDAR-based 3D object detectors by explicitly assessing numerous geometric properties inherent in the detections. This enables a better separation between true and false positive detections and thus significantly improves the performance. In a comprehensive analysis, we were able to show the performance of our method for several state-of-the-art detectors and also demonstrate the generalisation capabilities of GACE. This underlines the importance and general validity of the geometric information inherent in 3D detections, which has been largely neglected in the past."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.857,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Acknowledgements This work was partially funded by the Austrian FFG project iLIDS4SAM (878713) and by the Christian Doppler Laboratory for Embedded Machine Learning."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "6574"
+        }
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+                0.469,
+                0.374
+            ],
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+        },
+        {
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+            ],
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+            ],
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+        },
+        {
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+            ],
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+        },
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+            ],
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+        },
+        {
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+            ],
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+        },
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+            ],
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+        },
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+            ],
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+        },
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+            ],
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+        {
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+# GACE: Geometry Aware Confidence Enhancement for Black-box 3D Object Detectors on LiDAR-Data
+
+David Schinagl<sup>1,2</sup> Georg Krispel<sup>1</sup> Christian Fruhwirth-Reisinger<sup>1,2</sup> Horst Possegger<sup>1</sup> Horst Bischof<sup>1,2</sup>
+
+{david.schinagl,georg.krispel,reisinger,possegger,bischof}@icg.tugraz.at
+
+$^{1}$  Graz University of Technology  $^{2}$  Christian Doppler Laboratory for Embedded Machine Learning
+
+# Abstract
+
+Widely-used LiDAR-based 3D object detectors often neglect fundamental geometric information readily available from the object proposals in their confidence estimation. This is mostly due to architectural design choices, which were often adopted from the 2D image domain, where geometric context is rarely available. In 3D, however, considering the object properties and its surroundings in a holistic way is important to distinguish between true and false positive detections, e.g. occluded pedestrians in a group. To address this, we present GACE, an intuitive and highly efficient method to improve the confidence estimation of a given black-box 3D object detector. We aggregate geometric cues of detections and their spatial relationships, which enables us to properly assess their plausibility and consequently, improve the confidence estimation. This leads to consistent performance gains over a variety of state-of-the-art detectors. Across all evaluated detectors, GACE proves to be especially beneficial for the vulnerable road user classes, i.e. pedestrians and cyclists.
+
+# 1. Introduction
+
+Three-dimensional perception of surrounding objects is a critical component for autonomous vehicles and robots. Many modern perception systems use point cloud data from LiDAR (Light Detection and Ranging) sensors for this task, since they can provide accurate 3D information even over long distances. The popularity of these sensors can be seen in the increased research interest in LiDAR-based 3D object detection approaches, e.g. [10,29,38,40,45,47] and the large number of recently published autonomous driving datasets that include LiDAR data, e.g. [1,6,20,33].
+
+However, the characteristics of LiDAR data impose significant challenges for object detection. Unlike pixels in an image, which are aligned in a regular grid, point clouds represent 3D data as a collection of individual points in space, each with its own set of coordinates. In addition to the un
+
+![](images/5265d3d98b486110eac37ada6f65e0f93fa999e2f324a65deb45154152d3621c.jpg)
+
+![](images/eb7def388558088b946fe24106729ada1e4a2992dbfcc471de4e28def97c9a69.jpg)  
+Figure 1. Context matters: a baseline detector struggles at detecting true positive objects confidently if the sampling pattern is atypical, e.g. the occluded pedestrian in the orange bounding box (close-up top-left). GACE exploits the geometric properties of the detection and its surrounding objects to significantly increase the score for this detection, which is intuitively correct for a human observer considering this scene.
+
+structured nature of the data, the highly variable point density poses a major challenge. Due to the angular offset of the LiDAR beams, the density is highly dependent on the distance to the object and can be altered by occlusions in the foreground. This often requires detecting objects based on very few data points, which is especially true for classes with smaller spatial dimensions, such as pedestrians and cyclists. For example, in the Waymo Open Dataset [33], one of the most widely used and challenging datasets to date, about 30 percent of all annotated pedestrians consist of less than merely 20 points. Detecting these sparsely sensed objects naturally leads to a large number of false positive detections at test time. For this reason, determining a meaningful confidence value for the detections is critical to find a trade-off between precision and recall that adequately dis
+
+tinguishes true positives from false positives. The potential that could be exploited by improving the confidence score is considerable: Suppose we have an oracle that could correctly classify the detections of a SECOND [38] model on the Waymo dataset into true and false positives. This would increase the LEVEL_1 average precision for vehicles by  $+3.96\mathrm{AP}$  and, more importantly, for pedestrians and cyclists by as much as  $+10.71\mathrm{AP}$  and  $+13.74\mathrm{AP}$ , respectively.
+
+Existing 3D object recognition pipelines, including confidence estimation approaches, were largely inspired by 2D image-based object recognition models and then gradually adapted to point cloud processing. However, the conventional backbone - neck - head architecture of the 2D detection model was largely retained, e.g. in [8, 10, 15, 27, 38, 45]. After extracting features (point-based, voxel-based, or region-based) over multiple levels in the backbone, they are fused in the neck module and then passed to the detection head, where bounding box regression and confidence estimation are performed on a dense feature representation. Typically, separate branches are used within the head for bounding box regression and confidence estimation, each consisting of one or more fully connected layers on top of the common feature representation.
+
+Unlike image-based object detection, there are several highly relevant geometric properties inherent to objects in 3D point clouds that have been largely unexploited in assessing the confidence of a detection. In the image case, it is usually not possible to easily derive geometric properties for the objects, such as height or orientation, unless a static and fully calibrated camera and a known or constant scene are given. In contrast, in 3D object detection, many geometric features are directly available in the object properties and associated 3D data points to better assess the presence of a real object. On the one hand, these are instance-specific properties, such as the dimension of the object, the heading direction, the position, or the point distribution within the bounding box. For example, as shown in Figure 2, the precision of a SECOND [38] model for detecting a vehicle is highly dependent on the size of the object and from which side it is detected by the LiDAR. It can be seen that vehicle categories between passenger cars and heavy duty vehicles (i.e. vehicles with a length of 6 to  $13\mathrm{m}$ ) are harder to detect, potentially because they are underrepresented in the dataset, and that vehicles are easier to detect from behind (i.e. viewing angle between  $\pm 45$  degrees), presumably because of the highly reflective license plates, as shown in [25]. On the other hand, contextual properties, i.e. geometric relationships to neighboring objects, can contribute to a more reliable estimation of the confidence. For example, as shown in Figure 1, a pedestrian that appears atypical due to occlusions can be assessed more reliably by additionally taking neighboring vehicles and pedestrians into consideration.
+
+![](images/d43d792d566597fdd64b3566ecc7d6b662aea91997f90cc4dec1bfc62233b66f.jpg)
+
+![](images/d86719ac89cf3ca1ec802290accc6699089b58527ce30848f53141709098fee8.jpg)  
+Figure 2. Precision of a SECOND [38] model for the Waymo [33] vehicle class as a function of the object length (top) and of the viewing angle (bottom), indicating from which side the vehicle is seen by the LiDAR, where 0 degrees corresponds to the rear view. These examples illustrate the strong dependence of the precision on simple geometric object properties.
+
+Nevertheless, these simple but highly informative metric properties are neglected when estimating the confidence score in current detector architectures for the following reasons: First, in grid-based models, information such as the exact point distribution within the bounding box or the number of points is already partially discarded by the discretization (voxelization) in the preprocessing phase. Second, the bounding box properties (object dimensions & rotation) are determined in the parallel and separate box regression head and are therefore not accessible to the confidence estimation head. Finally, confidence estimation is usually performed using only features within a small area around the object (depending on the receptive field and detector), and no explicit information about neighboring objects and their geometric properties or confidence values is used, preventing a holistic estimation.
+
+Inspired by these observations, we present GACE, an intuitive and highly effective method to improve the confidence estimation of any black-box detector using geometric information. Given a set of detections from the base detector, we explicitly use these neglected features to enhance the expressiveness of the confidence values with the help of these additional cues. Our model-agnostic approach is intentionally applied after the actual detector training process to perform an auxiliary geometric assessment independent of the initial features. In a detailed evaluation on the Waymo dataset, we show that GACE consistently improves the performance of several state-of-the-art detection pipelines. Furthermore, we demonstrate the generalizability and transferability of our method by applying it to other datasets and even other detectors. Without retraining them, we achieve highly compelling performance gains.
+
+# 2. Related Work
+
+LiDAR-based 3D Object Detection: Depending on how existing methods for 3D object detection in single frame LiDAR data deal with the unstructured nature of point clouds, they can be broadly categorized into point-based, grid-based, and hybrid approaches.
+
+Point-based methods extract information directly from the individual raw 3D points [23,24,30,32,40,44]. The pioneering works, PointNet [23] and PointNet++ [24], used shared multilayer perceptrons in combination with global pooling functions to directly extract features from the irregular point cloud data. In Point-RCNN [30] features extracted in this manner are used to segment foreground points and generate proposals based on them. The advantages of point-based 3D object detectors are that there is no loss of point information due to discretization and the large receptive field, but at the cost of high computational demands.
+
+Instead of processing the points directly, grid-based methods [4, 15, 21, 27, 34, 38, 39, 43, 46] discretize the non-uniform 3D points into regular grids that can then be processed with 2D/3D convolutions. Voxelnet [46], a pioneering method, divides the point cloud into uniformly spaced 3D voxels, aggregates information from the points within them and generates predictions using 3D convolutions. To better handle the large number of empty voxels, SECOND [38] introduced sparse 3D convolutions. To reduce complexity, PointPillars [15] and PillarNet [27] use a 2D grid on the ground plane to create a column representation, a single pillar-shaped voxel per location, that can be processed using 2D convolutions. As an alternative to such anchor-based methods, Centerpoint [43] predicts a bird's-eye view heat map and detects the object center using a keypoint detector. Recently, transformer-based backbones have also been used to enable long-range relationships between voxels [5, 21, 34, 47]. Object relations within a frame and across multiple frames are mapped by Ret3D [37] using a graph and a transformer. The advantage of grid-based methods is that they can process data faster due to the regular format, but are limited by the loss of point information during the initial discretization phase.
+
+In order to obtain both, multi-scale features and fine-grained information, hybrid methods process voxel and point information jointly [22, 26, 28, 29, 31, 41, 42]. PV-RCNN [28], uses a set abstraction module that combines surrounding point and voxel features at keypoints to improve the detections. Part-A² [31] predicts the position of parts within an object based on point features to improve the accuracy, while LiDAR R-CNN [17] uses features of a PointNet [23] model that processes points within and around box proposals. Pyramid R-CNN [19] creates point features using a pyramid grid structure to acquire fine-grained and long-range contextual information.
+
+Confidence Estimation: In the usual backbone - neck - head detector architecture, after the feature extraction and aggregation, the box regression and confidence estimation are performed. This is usually done in two separate branches based on a common dense feature representation [15, 38, 40, 46]. This has the disadvantage that the accuracy of the localization is hardly included in the confidence score. Inspired by 2D object detection methods [11,12,36], IoU guided supervision is frequently used to obtain a better correlation between the classification result and the localization accuracy [9, 10, 16, 27, 28, 31, 41, 45]. Thereby, the IoU between the predicted box and the ground truth is learned in a third branch during training and then incorporated into the final confidence score at test time. Hu et al. [9] leverage the inherent relationship between object distance and point density to better assess a detection. Inspired by the 2D approach [3], a spatial transformation on the feature maps is done by He et al. [8] to better align the confidence prediction and bounding box regression. Related to confidence estimation are also calibration methods [7, 14] where the score should represent a true probability, i.e. how likely a detection is. Detection pipelines, however, aim at the best separation of true and false positives as optimization goal for the confidence prediction.
+
+In our confidence estimation method we also pursue this optimization objective, but in contrast to existing approaches, we present a method for refining the confidence values for a given set of detections by exploiting the rich geometric information contained directly in the detections as well as in the underlying 3D points. While these useful cues for assessing the plausibility of a detection have been largely untapped due to the architecture of common detection pipelines, they allow us to increase the expressiveness of the confidence values.
+
+# 3. Geometry-Aware Confidence Enhancement
+
+Our goal is to optimize the confidence scores for a given set of detections from a base detector in order to better separate true positives from false positives, thus increasing the overall detection performance. We use the detector in a pure black box manner, i.e. we do not assume any knowledge about the architecture of the base model, nor access to its internals like parameters, features or gradients. This black-box optimization, taking only the point cloud and the set of objects detected in it as input, enables universal applicability and easy transferability of our enhancement module to any base 3D object detection pipeline. The basic idea is to revalidate the detections by exploiting as much as possible the geometric information they inherently contain.
+
+![](images/52c4db5fdc5a397587c5bcd23a96b137c30da9c2f55e5352ffbc13795ce96305.jpg)  
+Figure 3. Schematic of GACE: To re-evaluate the confidence score of a detection (orange), we aggregate geometric properties of the detection itself and the points it contains into a feature vector (top). To capture the context of the detection, geometric relationships to neighboring detections are aggregated using a shared MLP and subsequent pooling function (bottom). By merging both features (right), we obtain a new confidence score that takes into account the underlying geometric properties of the detection.
+
+![](images/e2f057ba5df389936a7d67e4d5e7584db6e03069f36e6efa9cbc06561fd9bb9d.jpg)
+
+![](images/23b07f6642cc31a0a44856686d48363adf60249d5dd81d474ef7572669ebd4bf.jpg)
+
+In our proposed approach called GACE (Geometry Aware Confidence Enhancement) we exploit two types of geometric information, as shown in Figure 3:
+
+- Instance-specific Geometric Properties (Section 3.1): Attributes of the bounding box itself, combined with the point data inside. For example, how well is the size of the object or the heading angle supported by the point distribution?  
+- Contextual Geometric Properties (Section 3.2): Relationships to surrounding objects can provide useful information to better validate an uncertain detection, e.g., a partially occluded vehicle moving in the same lane and same direction as the surrounding vehicles.
+
+These useful cues to estimate the plausibility of an object are usually not used for the confidence estimation in common detection pipelines. The reasons are that information is often already discarded during preprocessing (discretization), essential properties such as the estimated size of the object are not available (separate box regression in a parallel branch), or the objects are only evaluated individually and not more holistically. Therefore, we explicitly use these easily accessible and rich sources of information as input to our enhancement module. After merging the instance-specific and contextual features, we determine the new confidence value of each proposed object via an auxiliary task (Section 3.3).
+
+To generate the training data for our enhancement module, we use the black-box base model in a single inference run on the training set. The resulting set of all
+
+detections from the base model represents the training data to learn our improved confidence estimator. Formally, this can be described as follows.
+
+Definitions & Notations: Let  $\widetilde{\mathcal{X}} = \{\widetilde{\mathbf{x}}_k\}_{k=1\dots K}$  be a LiDAR point cloud, where each of the  $K$  unordered points  $\widetilde{\mathbf{x}}_k \in \mathbb{R}^5$  consists of the 3D coordinates, intensity/reflectance and the elongation value. Furthermore, let  $\widetilde{\mathcal{Y}} = \{\widetilde{\mathbf{y}}_i\}_{j=1\dots M}$  be the set of corresponding ground truth objects. Each object annotation  $\widetilde{\mathbf{y}} = [\widetilde{\mathbf{b}}, \widetilde{\mathbf{y}}]$  includes the bounding box parameters  $\widetilde{\mathbf{b}} = [\widetilde{c}_x, \widetilde{c}_y, \widetilde{c}_z, \widetilde{d}_x, \widetilde{d}_y, \widetilde{d}_z, \widetilde{\Theta}]$  and the corresponding class label  $\widetilde{y}$ . For a given black-box 3D object detector  $F$ , let  $F(\widetilde{\mathcal{X}}) = \mathcal{Y} = \{\mathbf{y}_{i=1\dots N}\}$  be the set of proposed detections for this input point cloud, where  $\mathbf{y} = [\mathbf{b}, y, s]$ . In addition to the box properties  $\mathbf{b}$  and the corresponding class label  $y$ , the detector predicts a confidence value  $s$  that should ideally indicate the prevalence of a true positive example.
+
+Confidence Optimization: Based on the known ground truth objects, a category label  $\{u_i\in \{0,1\} \}_{i = 1\dots N}$  can be assigned to each detection, indicating whether it is a true positive or false positive detection. Moreover, we know the IoU with a possible ground truth bounding box for each object which we define as  $\{v_{i}\}_{i = 1\dots N}$ . We aim to improve the confidence estimate of the original detector by focusing exclusively on the binary classification of detections into true positive and false positive examples. We determine the revised confidence score  $\{\widehat{s}_i\} = H(\mathcal{V},\mathcal{X})$  using our module  $H$ , where only the set of detections  $\mathcal{V}$  and the points they include  $\mathcal{X}\subset \widetilde{\mathcal{X}}$  are used as input.
+
+# 3.1. Instance-specific Geometric Properties
+
+In common 2D and 3D object detection architectures, the bounding box regression and the confidence estimation are performed completely separated in different branches. This is well suited for 2D where it is desired to detect objects in the image regardless of their scale. For 3D, however, important cues for plausibility estimation remain largely unused. Let us consider the available context directly provided by an object proposal: The position of the possible object in combination with the dimensions indicates, for example, which point density is to be expected. Furthermore, the direction angle provides an indication of the expected point distribution within the box. This information can even be further refined by knowing the class of the object. This directly available geometrical knowledge about an object allows for a more profound estimation of the confidence score.
+
+We extract these basic properties and transform them into a compact representation using a multilayer perceptron (MLP)  $H_{I}$ . As input parameters, we first use the object parameters, i.e. the position  $(c_x, c_y, c_z)$ , the size  $(d_x, d_y, d_z)$ , and the heading angle  $\Theta$  of the bounding box, as well as the initial confidence value  $s_i$  of the detection estimated by the base detector. Additionally, we use the distance  $\| \mathbf{c} \|$  from the LiDAR sensor to the object center, and the angle  $\alpha$  between the line of sight to the object and the heading angle of the object:
+
+$$
+\alpha = \Theta - \operatorname {a t a n 2} \left(c _ {y}, c _ {x}\right). \tag {1}
+$$
+
+This angle describes from which side an object is seen from the LiDAR center, independent of the position of the object relative to the LiDAR, e.g. a vehicle driving directly towards the LiDAR always has the same angle  $\alpha$ , no matter from which direction the vehicle approaches. We complement these cues with information about the points  $\mathcal{X}_{\mathrm{b}} \subset \mathcal{X}$  inside the bounding box  $\mathbf{b}$ . Besides the overall number of points  $|\mathcal{X}_{\mathrm{b}}|$ , we extract elementary low-level statistics. Therefore, we scale the box and the associated points to a uniform size and then align them w.r.t. their center and yaw angle. In this canonical representation we compute the mean, standard deviation, minimum and maximum of  $\mathcal{X}_{\mathrm{b}}$  for all axes, denoted as  $\mathcal{X}_{\mathrm{b}}^{\mathrm{mean}}$ ,  $\mathcal{X}_{\mathrm{b}}^{\mathrm{std}}$ ,  $\mathcal{X}_{\mathrm{b}}^{\mathrm{min}}$ ,  $\mathcal{X}_{\mathrm{b}}^{\mathrm{max}}$ . We then aggregate these attributes into one feature vector representing the instance-specific plausibility per object as
+
+$$
+\mathbf {f} ^ {I} = H _ {I} \left(\left[ \mathbf {b}, \alpha , \| \mathbf {c} \|, | \mathcal {X} _ {\mathbf {b}} |, \mathcal {X} _ {\mathbf {b}} ^ {\text {m e a n}}, \mathcal {X} _ {\mathbf {b}} ^ {\text {s t d}}, \mathcal {X} _ {\mathbf {b}} ^ {\min }, \mathcal {X} _ {\mathbf {b}} ^ {\max } \right] ^ {\top}\right), \tag {2}
+$$
+
+where we pass all angles as direction vectors  $(\cos(\cdot), \sin(\cdot))$  and normalize all metric properties to unit length using the corresponding maximum value range.
+
+# 3.2. Contextual Geometric Properties
+
+Especially in the case of uncertain detections, e.g. detections that are far away and therefore consist of only a few 3D points, or detections that are partially occluded and therefore appear atypical, geometric contextual information can be very useful in assessing a confidence score. Examples include a vehicle that is heavily occluded but in a convoy with other vehicles, or cyclists moving in a group. However, this information is usually not available for the confidence estimation, since the object proposals are evaluated individually within the receptive field but without explicit knowledge of the objects detected in its vicinity and their properties. In order to assess the plausibility of a detection  $\mathbf{y}$  in a more holistic way, we use the geometric relations to surrounding objects in the scene. We thereby consider all neighbors that are within a certain radius  $r$  around the object to be evaluated.
+
+We therefore create a representation per object, which captures the relationships to its neighboring objects. In order to be independent of the number of neighboring objects, we first create a feature vector for each neighbor, which we then combine into a unified representation using a symmetric pooling function. As input parameters per neighbor we use the distance to the object to be evaluated  $\| \mathbf{c} - \mathbf{c}_n\|$ , the direction vector  $\mathbf{c} - \mathbf{c}_n$ , the difference between the two heading angles  $\Theta - \Theta_n$ , and the neighbor's class label  $y_{n}$ . To incorporate the validity of the neighbor, we leverage  $\mathbf{f}_n^I$ , which represents the instance-specific properties of the neighbor. This information is encoded via the shared weight MLP  $H_{C}$  to form the feature vector  $\mathbf{f}_n^C$  for each individual neighbor,
+
+$$
+\mathbf {f} _ {n} ^ {C} = H _ {C} \left(\left[ \| \mathbf {c} - \mathbf {c} _ {n} \|, \mathbf {c} - \mathbf {c} _ {n}, \Theta - \Theta_ {n}, y _ {n}, \mathbf {f} _ {n} ^ {I} \right] ^ {\top}\right), \tag {3}
+$$
+
+where the angle  $\Theta -\Theta_{n}$  is provided as direction vector and the metric features are normalized to unit length.
+
+Finally, we aggregate the information from the individual neighbors into a unified representation for later processing, as shown in Figure 3. This requires accumulating features of an unknown (and varying) number of neighbors. To impose no constraint on the number of features, we take inspiration from the pooling step of point-based detectors, e.g. [23], and employ a symmetric max pooling function to form a plausibility signature  $\mathbf{f}^C$  over the feature vectors of all neighbors. Thus, in this representation the geometric relations to the surrounding objects are accumulated for the subsequent confidence estimation, taking into account the respective local properties of the neighbors.
+
+# 3.3. Data Fusion & Confidence Prediction
+
+To estimate the new confidence value for a detection, we merge the instance-specific and contextual geometric features. The instance-specific information encoded in  $\mathbf{f}^I$ , as well as the contextual information in  $\mathbf{f}^C$  are concatenated and processed using  $H_{F}$ , a MLP with sigmoid output function, to estimate the new confidence score
+
+$$
+\widehat {s} = H _ {F} \left(\left[ \mathbf {f} ^ {I}, \mathbf {f} ^ {C} \right] ^ {\top}\right). \tag {4}
+$$
+
+We train the whole module including the two feature encoding networks  $H_{I}$  and  $H_{C}$  using an end-to-end training strategy. As loss function  $\mathcal{L}_{\mathrm{conf}}(\widehat{s},u)$  for this task we use the focal loss [18] to focus learning on hard examples. The goal is to divide the set of detections as good as possible into true or false positive examples using the binary category label  $u\in \{0,1\}$  as target. As auxiliary task during training we estimate the IoU with the ground truth bounding box in a further output  $\widehat{v}$  of  $H_{F}$ . Therefore, we add an IoU-guidance [16, 41, 45] L1-loss term  $\mathcal{L}_{\mathrm{IoU}}(\widehat{v},v)$ . This increases the importance of the point distribution statistics within the features, as they provide evidence of the bounding box accuracy from which the confidence estimate also benefits. The overall loss function is therefore
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {c o n f}} (\widehat {s}, u) + \lambda_ {\mathrm {I o U}} \mathcal {L} _ {\mathrm {I o U}} (\widehat {v}, v), \tag {5}
+$$
+
+where  $\lambda_{\mathrm{IoU}}$  is a hyper-parameter to adjust the influence of the auxiliary task.
+
+# 4. Experiments
+
+To demonstrate the benefits of GACE, we evaluate our black-box confidence optimization method on several well-known state-of-the-art 3D object detection pipelines. In particular, we apply it to the pillar-based PointPillars [15], the voxel-based SECOND [38] and Centerpoint [43], as well as the hybrid methods Part-A² [31], PV-RCNN [28] and PV-RCNN++ [29].
+
+Datasets: For the evaluation of our approach we use the Waymo Open Dataset [33] as well as the KITTI Dataset [6]. The Waymo dataset is one of the largest and most challenging public datasets for autonomous driving research. It provides 798 training scenes and 202 validation scenes, where each scene consists of about 200 LiDAR samples covering the full  $360^{\circ}$  field-of-view. In total, the dataset consists of over 8.9M annotated objects classified into vehicles, pedestrians and cyclists. We follow the common evaluation protocol using the standard metrics average precision (AP), as well as average precision with heading (APH), where true positives are weighted by their heading accuracy. In addition, we use the KITTI dataset, one of the most popular datasets for 3D object detection.
+
+We thereby use the standard split [2] into a training set (3712 samples) and validation set (3769 samples). We also follow the common evaluation practice using average precision with 40 recall points. For both datasets, the 3D IoU threshold for a true positive sample is 0.7 for vehicles and 0.5 for pedestrians and cyclists.
+
+Implementation Details: Our experimental setup is based on the open-source toolbox OpenPCDet [35]. To ensure the reproducibility of our results, all base models used in the experiments have been trained on the training set using the default configuration and default training policies of OpenPCDet. This includes augmenting the data by randomly rotating, scaling and flipping the point cloud, as well as ground truth sampling [38], i.e. the placement of objects from other training examples in the current frame. To create the training data for our module, we use the base model as a black-box detection pipeline. In a single inference run on the training set, we collect the output of the base model, i.e. the set of all detections, which represents our training data. The actual training process of our module is therefore entirely decoupled from the base model.
+
+Our sub-networks for feature transformation, i.e.  $H_{I}$  and the shared network  $H_{C}$ , as well as the confidence prediction network  $H_{F}$  are two-layer MLP's with 256 feature dimensions. The feature vector  $\mathbf{f}^{I}$  in which the instance-specific information is encoded is 128-dimensional and  $\mathbf{f}^{C}$  for the contextual information is 64-dimensional. When determining the contextual geometric properties, we accumulate the neighboring objects that are within a radius of  $r = 40m$ .
+
+We train our model end to end with the Adam [13] optimizer and a learning rate of 0.001. The weighting of the auxiliary loss term during training is set to  $\lambda_{\mathrm{IoU}} = 0.5$ . In all experiments we use the same architecture as well as hyperparameters, regardless of the underlying black-box base model. We train our module over 5 epochs on a single NVIDIA® GeForce® RTX 3090 GPU, which takes less than 10 minutes due to our favorable lightweight model size and low feature dimensions.
+
+# 4.1. Main Results
+
+Table 1 summarizes the results of our confidence optimization on the Waymo dataset for different baseline detection pipelines. For each detector architecture, we report the performance of the base detector as well as the results after applying our GACE module. Please note that for better traceability, the results of the base detectors correspond to the respective OpenPCDet implementations (see OpenPCDet model zoo). Some reported baseline scores are even higher than in their original papers due to augmentation techniques used in OpenPCDet.
+
+<table><tr><td rowspan="3">Method</td><td colspan="4">Overall</td><td colspan="4">Vehicles (IoU=0.7)</td><td colspan="4">Pedestrians (IoU=0.5)</td><td colspan="4">Cyclists (IoU=0.5)</td></tr><tr><td colspan="2">LEVEL_1</td><td colspan="2">LEVEL_2</td><td colspan="2">LEVEL_1</td><td colspan="2">LEVEL_2</td><td colspan="2">LEVEL_1</td><td colspan="2">LEVEL_2</td><td colspan="2">LEVEL_1</td><td colspan="2">LEVEL_2</td></tr><tr><td>mAP</td><td>mAPH</td><td>mAP</td><td>mAPH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td></tr><tr><td>PointPillars [15]</td><td>64.72</td><td>57.07</td><td>58.57</td><td>51.73</td><td>70.99</td><td>70.35</td><td>62.79</td><td>62.20</td><td>66.36</td><td>47.15</td><td>58.27</td><td>41.32</td><td>56.81</td><td>53.71</td><td>54.66</td><td>51.67</td></tr><tr><td>+ GACE (Ours)</td><td>69.25</td><td>61.24</td><td>62.98</td><td>55.73</td><td>71.92</td><td>71.28</td><td>63.63</td><td>63.04</td><td>72.18</td><td>51.97</td><td>64.06</td><td>45.96</td><td>63.64</td><td>60.47</td><td>61.25</td><td>58.20</td></tr><tr><td>Improvement</td><td>+4.53</td><td>+4.17</td><td>+4.41</td><td>+4.00</td><td>+0.93</td><td>+0.93</td><td>+0.84</td><td>+0.84</td><td>+5.82</td><td>+4.82</td><td>+5.79</td><td>+4.64</td><td>+6.83</td><td>+6.76</td><td>+6.59</td><td>+6.53</td></tr><tr><td>SECOND [38]</td><td>65.13</td><td>60.81</td><td>59.01</td><td>55.12</td><td>70.93</td><td>70.30</td><td>62.65</td><td>62.07</td><td>65.67</td><td>54.96</td><td>57.78</td><td>48.25</td><td>58.78</td><td>57.18</td><td>56.59</td><td>55.05</td></tr><tr><td>+ GACE (Ours)</td><td>70.17</td><td>66.13</td><td>63.74</td><td>60.06</td><td>71.56</td><td>70.92</td><td>63.22</td><td>62.63</td><td>71.71</td><td>61.87</td><td>63.27</td><td>54.37</td><td>67.22</td><td>65.59</td><td>64.73</td><td>63.16</td></tr><tr><td>Improvement</td><td>+5.04</td><td>+5.32</td><td>+4.73</td><td>+4.94</td><td>+0.63</td><td>+0.62</td><td>+0.57</td><td>+0.56</td><td>+6.04</td><td>+6.91</td><td>+5.49</td><td>+6.12</td><td>+8.44</td><td>+8.41</td><td>+8.14</td><td>+8.11</td></tr><tr><td>Part-A2[31]</td><td>70.30</td><td>66.66</td><td>63.53</td><td>60.27</td><td>73.35</td><td>72.81</td><td>64.73</td><td>64.24</td><td>70.02</td><td>61.01</td><td>60.83</td><td>52.85</td><td>67.53</td><td>66.18</td><td>65.03</td><td>63.73</td></tr><tr><td>+ GACE (Ours)</td><td>73.07</td><td>69.21</td><td>66.24</td><td>62.77</td><td>73.99</td><td>73.43</td><td>65.38</td><td>64.87</td><td>72.36</td><td>62.93</td><td>63.21</td><td>54.81</td><td>72.84</td><td>71.28</td><td>70.13</td><td>68.63</td></tr><tr><td>Improvement</td><td>+2.77</td><td>+2.55</td><td>+2.71</td><td>+2.50</td><td>+0.64</td><td>+0.62</td><td>+0.65</td><td>+0.63</td><td>+2.34</td><td>+1.92</td><td>+2.38</td><td>+1.96</td><td>+5.31</td><td>+5.10</td><td>+5.10</td><td>+4.90</td></tr><tr><td>Centerpoint [43]</td><td>73.01</td><td>70.35</td><td>66.79</td><td>64.33</td><td>72.87</td><td>72.33</td><td>64.76</td><td>64.27</td><td>74.48</td><td>68.22</td><td>66.55</td><td>60.81</td><td>71.69</td><td>70.50</td><td>69.06</td><td>67.92</td></tr><tr><td>+ GACE (Ours)</td><td>75.58</td><td>72.98</td><td>69.19</td><td>66.76</td><td>74.49</td><td>73.99</td><td>66.19</td><td>65.73</td><td>78.62</td><td>72.48</td><td>70.44</td><td>64.73</td><td>73.64</td><td>72.48</td><td>70.94</td><td>69.83</td></tr><tr><td>Improvement</td><td>+2.57</td><td>+2.63</td><td>+2.40</td><td>+2.43</td><td>+1.62</td><td>+1.66</td><td>+1.43</td><td>+1.46</td><td>+4.14</td><td>+4.26</td><td>+3.89</td><td>+3.92</td><td>+1.95</td><td>+1.98</td><td>+1.88</td><td>+1.91</td></tr><tr><td>PV-RCNN [28]</td><td>71.11</td><td>66.78</td><td>64.40</td><td>60.50</td><td>74.79</td><td>74.17</td><td>66.17</td><td>65.61</td><td>72.06</td><td>61.46</td><td>63.00</td><td>53.56</td><td>66.48</td><td>64.72</td><td>64.03</td><td>62.34</td></tr><tr><td>+ GACE (Ours)</td><td>73.38</td><td>68.89</td><td>66.65</td><td>62.57</td><td>75.20</td><td>74.55</td><td>66.57</td><td>65.97</td><td>73.84</td><td>62.97</td><td>64.88</td><td>55.14</td><td>71.12</td><td>69.16</td><td>68.50</td><td>66.60</td></tr><tr><td>Improvement</td><td>+2.27</td><td>+2.11</td><td>+2.25</td><td>+2.07</td><td>+0.41</td><td>+0.38</td><td>+0.40</td><td>+0.36</td><td>+1.78</td><td>+1.51</td><td>+1.88</td><td>+1.58</td><td>+4.64</td><td>+4.44</td><td>+4.47</td><td>+4.26</td></tr><tr><td>PV-RCNN++ [29]</td><td>75.72</td><td>73.05</td><td>69.22</td><td>66.73</td><td>77.30</td><td>76.81</td><td>68.92</td><td>68.47</td><td>78.91</td><td>72.42</td><td>70.43</td><td>64.41</td><td>70.95</td><td>69.90</td><td>68.31</td><td>67.31</td></tr><tr><td>+ GACE (Ours)</td><td>76.76</td><td>74.02</td><td>70.31</td><td>67.75</td><td>77.42</td><td>76.93</td><td>69.05</td><td>68.59</td><td>79.59</td><td>72.97</td><td>71.34</td><td>65.18</td><td>73.26</td><td>72.16</td><td>70.54</td><td>69.48</td></tr><tr><td>Improvement</td><td>+1.04</td><td>+0.97</td><td>+1.09</td><td>+1.02</td><td>+0.12</td><td>+0.12</td><td>+0.13</td><td>+0.12</td><td>+0.68</td><td>+0.55</td><td>+0.91</td><td>+0.77</td><td>+2.31</td><td>+2.26</td><td>+2.23</td><td>+2.17</td></tr></table>
+
+Table 1. Performance comparison on the Waymo Open Dataset [33] validation set for different baseline methods with and without our confidence enhancement module GACE.
+
+For all baseline detectors and all classes, adjusting the confidence level with our approach leads to an increase in performance without exception. The overall performance gains range from  $+1.02\mathrm{mAPH}$  (LEVEL_2) for PV-RCNN++ to  $+4.94\mathrm{mAPH}$  (LEVEL_2) for SECOND, demonstrating the significance of this geometric information in estimating a confidence score for a detection.
+
+Object Classes: The performance improvements are significantly higher for the classes of pedestrians and cyclists. Intuitively, objects of these vulnerable road users contain significantly fewer 3D points due to their smaller spatial extent compared to vehicles. This effect is even aggravated by possible occlusions. Furthermore, the class of cyclists in particular is underrepresented in the training data. These properties make objects of these classes more difficult to detect, which leads to a higher number of false positives, but also makes confidence estimation more complex. Especially in these cases, our confidence enhancement method benefits from the additional geometric information when separating false positives from true positives, resulting in a higher impact of GACE.
+
+Base Detectors: The overall performance gain is highest when applying GACE on pillar-based (PointPillars [15]) and voxel-based methods (SECOND [38] and Centerpoint [43]). These methods lose valuable point information already in their preprocessing stage, i.e. by voxelization. Thus, the optimization potential for these methods is higher than for the hybrid methods, which explicitly incorporate point-level information at detection locations. However, by explicitly exploiting both instance-specific and contextual geometric properties of the detections, GACE also leads to
+
+a significant performance improvement for these methods, i.e. Part- $\mathrm{A}^2$  [31], PV-RCNN [28] and PV-RCNN++ [29], most notably for the classes of pedestrians and cyclists.
+
+Precision/Recall Plots: To better illustrate the impact of our method, Figure 4 shows the precision/recall plots before and after applying GACE with a SECOND [38] model as the base detector (See the supplemental material for the other base detectors). Since recall remains unaffected, the significant performance gains of GACE are entirely due to an increase in precision. The better separation of true and false positives is mainly seen in the more challenging classes of pedestrians and cyclists, where the number of false detections is significantly higher and confidence estimation is more difficult. Furthermore, we see that the precision gains are higher in regions of higher recall, i.e. for detections with a lower confidence score. Especially these initially underrated detections of objects of the vulnerable classes represent a safety risk that can be reduced by GACE.
+
+Range-based Evaluation: Table 2 summarizes our evaluation across the different distance ranges of Waymo. This also shows that GACE can consistently improve the performance of all baseline detectors and in all sub-ranges, especially in the far range. Detections at long distances are more challenging due to the lower point density, making it harder to distinguish true positives from false positives. Therefore, the geometric information is even more valuable in these cases, e.g. from  $+2.93\mathrm{mAPH}$  (LEVEL_2) for PV-RCNN++ up to  $+4.97\mathrm{mAPH}$  (LEVEL_2) for PointPillars. The detailed evaluation results for all subclasses can be found in the supplemental material.
+
+![](images/ecc7cbb4923b0bfbdb21b9abdeb9ef12261c90cfce7ed8b4cd3e9b14ceb58276.jpg)  
+Figure 4. Precision-recall plots for a SECOND [38] model as base detector with and without our confidence enhancement module on the Waymo Open Dataset [33] validation set for LEVEL_2 APH. Especially at higher recall levels, GACE's better separation of true and false positives leads to higher precision.
+
+![](images/be290b934fd98d9a327a6719d87844424845c8c21d824fc298d2be04c3ed5626.jpg)
+
+![](images/0474b9602bcd25ed377f5165e43123c58e249d489e692d5d169def866b49f096.jpg)
+
+<table><tr><td rowspan="3">Method</td><td colspan="3">Overall (LEVEL_2)</td></tr><tr><td>0-30m</td><td>30-50m</td><td>50m-Inf</td></tr><tr><td>mAP / mAPH</td><td>mAP / mAPH</td><td>mAP / mAPH</td></tr><tr><td>PointPillars [15]</td><td>75.10 / 67.59</td><td>55.31 / 48.53</td><td>37.18 / 31.00</td></tr><tr><td>+ GACE (Ours)</td><td>78.32 / 70.68</td><td>60.17 / 53.01</td><td>42.88 / 35.97</td></tr><tr><td>Improvement</td><td>+3.22 / +3.09</td><td>+4.86 / +4.48</td><td>+5.70 / +4.97</td></tr><tr><td>SECOND [38]</td><td>75.55 / 71.87</td><td>56.55 / 52.42</td><td>37.73 / 33.39</td></tr><tr><td>+ GACE (Ours)</td><td>78.64 / 75.39</td><td>60.10 / 56.13</td><td>41.69 / 37.39</td></tr><tr><td>Improvement</td><td>+3.09 / +3.52</td><td>+3.55 / +3.71</td><td>+3.96 / +4.00</td></tr><tr><td>Part-A² [31]</td><td>79.93 / 76.93</td><td>61.77 / 58.01</td><td>40.13 / 36.44</td></tr><tr><td>+ GACE (Ours)</td><td>81.62 / 78.52</td><td>64.63 / 60.59</td><td>45.06 / 40.94</td></tr><tr><td>Improvement</td><td>+1.69 / +1.59</td><td>+2.86 / +2.58</td><td>+4.93 / +4.50</td></tr><tr><td>Centerpoint [43]</td><td>81.29 / 79.12</td><td>65.45 / 62.66</td><td>46.45 / 43.27</td></tr><tr><td>+ GACE (Ours)</td><td>82.94 / 80.90</td><td>67.56 / 64.76</td><td>50.20 / 46.80</td></tr><tr><td>Improvement</td><td>+1.65 / +1.78</td><td>+2.11 / +2.10</td><td>+3.75 / +3.53</td></tr><tr><td>PV-RCNN [28]</td><td>79.77 / 76.24</td><td>62.57 / 58.10</td><td>42.51 / 37.77</td></tr><tr><td>+ GACE (Ours)</td><td>81.25 / 77.66</td><td>64.76 / 60.11</td><td>47.01 / 41.90</td></tr><tr><td>Improvement</td><td>+1.48 / +1.42</td><td>+2.19 / +2.01</td><td>+4.50 / +4.13</td></tr><tr><td>PV-RCNN++ [29]</td><td>83.08 / 80.98</td><td>67.86 / 65.04</td><td>48.69 / 45.26</td></tr><tr><td>+ GACE (Ours)</td><td>83.59 / 81.43</td><td>68.69 / 65.83</td><td>51.81 / 48.19</td></tr><tr><td>Improvement</td><td>+0.51 / +0.45</td><td>+0.83 / +0.79</td><td>+3.12 / +2.93</td></tr></table>
+
+# 4.2. Ablation Studies
+
+Main Components: We evaluate the contribution of our proposed instance-specific and contextual properties as well as the influence of the auxiliary IoU loss for a SECOND [38] model as baseline in Table 3. Incorporating the instance-specific geometric properties already leads to a significant performance increase of  $+3.65\mathrm{AP} / + 3.32\mathrm{APH}$ . Including also the contextual information, i.e. incorporating the relationships to the neighboring detection hypotheses further increases the performance by another  $+0.71\mathrm{AP} / + 1.14\mathrm{APH}$ . Compared to the contributions of these two components, there is only a minor impact of incorporating the IoU guidance, leading to additional  $+0.37\mathrm{AP} / + 0.48\mathrm{APH}$ . Note that the degradation when adding  $\mathcal{L}_{\mathrm{IoU}}$  to only contextual features is caused by the lack of point information, which does not allow a reasonable estimation of the IoU. Overall, the instance-specific geometric information contributes stronger than the contextual geometric information.
+
+Table 2. Consistent performance gains on the Waymo Open Dataset [33] validation set across distance ranges for different baseline methods for LEVEL_2 over all classes.  
+
+<table><tr><td>Baseline</td><td>Instance Specific</td><td>Contextual</td><td>Aux-Loss LIoU</td><td>LEVEL_2 mAP</td><td>LEVEL_2 mAPH</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>59.01</td><td>55.12</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>62.66</td><td>58.44</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>60.33</td><td>56.90</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>63.37</td><td>59.58</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>62.94</td><td>58.78</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>60.19</td><td>56.77</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>63.74</td><td>60.06</td></tr></table>
+
+Table 3. Ablation experiments for a SECOND [38] model as base detector over all classes on the Waymo Open Dataset [33] validation set. We show the impact of each GACE component.  
+
+<table><tr><td>Box Properties</td><td># Points</td><td>Viewing Angle</td><td>Point Stat.</td></tr><tr><td>56.98+1.86</td><td>55.96+0.84</td><td>55.86+0.74</td><td>58.15+3.03</td></tr></table>
+
+Table 4. Impact of the different instance-specific feature groups when used exclusively for a SECOND model as base detector on the Waymo Open Dataset [33] over all classes (LEVEL_2 mAPH).
+
+Instance-Specific Properties: We analyze the contribution of each feature group within the instance-specific properties, namely box properties  $(\mathbf{b},\| \mathbf{c}\|)$ , number of points  $(|\mathcal{X}_{\mathbf{b}}|)$ , viewing angle  $(\alpha)$ , and point statistics  $(\mathcal{X}_{\mathbf{b}}^{\mathrm{mean}},\mathcal{X}_{\mathbf{b}}^{\mathrm{std}},\mathcal{X}_{\mathbf{b}}^{\mathrm{min}},\mathcal{X}_{\mathbf{b}}^{\mathrm{max}})$ . Table 4 shows the impact of each group on the overall performance when used exclusively, indicating a high contribution of box properties and point statistics. A complete list of the combinations can be found in the supplemental material.
+
+Contextual Properties Radius: The dependence of the performance on the chosen context radius  $r$  is shown in Figure 5. It can be seen that the performance increases significantly up to  $\sim 15m$ , followed by a slight degradation starting at  $\sim 40m$ , which illustrates the importance of neighboring objects in the near and middle ranges.
+
+![](images/5aee07c939caf967a0871ba90c4c7a19b4c2e0af3cfdb4662c570ec3d1178d32.jpg)  
+Figure 5. Performance of purely context-based GACE for different radius  $r$  (SECOND base model / Waymo overall).
+
+<table><tr><td>Method</td><td>Car</td><td>Pedestrian</td><td>Cyclist</td></tr><tr><td>SECOND (KITTI)</td><td>81.61</td><td>51.14</td><td>66.74</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.04+0.43</td><td>57.11+5.97</td><td>70.99+4.25</td></tr><tr><td>PointPillars (KITTI)</td><td>78.39</td><td>51.41</td><td>62.94</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>78.51+0.12</td><td>55.30+3.89</td><td>67.94+5.00</td></tr><tr><td>Part-A2 (KITTI)</td><td>82.92</td><td>59.73</td><td>70.10</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.94+0.02</td><td>64.21+4.48</td><td>72.16+2.06</td></tr><tr><td>PV-RCNN (KITTI)</td><td>82.86</td><td>53.64</td><td>70.42</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.84-0.02</td><td>61.06+7.42</td><td>72.70+2.28</td></tr></table>
+
+# 4.3. Generalization and Transferability
+
+Since we use only the detection attributes and corresponding properties of the underlying point cloud as input, a GACE module trained on base detector A can be directly applied to another base detector B. Furthermore, since all metric features are normalized to their maximum possible value and the statistical parameters (point distribution) are computed from a normalized unit-length box, GACE can be applied not only to a different detector, but also directly to a different detector on a different dataset. Therefore, to demonstrate the general applicability of GACE, we freeze a GACE module trained on detections from a SECOND detector on Waymo, and apply it directly to detections of a SECOND detector on the KITTI dataset [6]. As shown in Table 5, first row, this also leads to considerable performance improvements despite the distribution shift to a different dataset (different LiDAR sensor, different country). Even more remarkably, significant performance gains are also obtained when the same GACE module is applied even to a different base detector, e.g. +7.42AP for PV-RCNN on pedestrians while achieving the same performance for cars. The results demonstrate the excellent generalization capability of GACE and the general validity of the geometric information regardless of the dataset.
+
+# 4.4. Runtime Analysis
+
+In Table 6 we show the runtime analysis of GACE for a  $360^{\circ}$  field-of-view Waymo point cloud using a single NVIDIA® GeForce® RTX 3090 GPU. The computationally most intensive part is the feature extraction, especially ex
+
+Table 5. Model Transfer: Applying a GACE module trained on SECOND detections on Waymo (without LiDAR elongation, which is not available on KITTI) to different detectors on the KITTI dataset (moderate difficulty / @R40).  
+
+<table><tr><td rowspan="3">Feature Extraction</td><td>Points in Boxes Query</td><td>0.56 ms</td></tr><tr><td>Geometric &amp; Statistical Features</td><td>0.98 ms</td></tr><tr><td>Neighboring Object ID&#x27;s Query</td><td>0.07 ms</td></tr><tr><td rowspan="3">Network Inference</td><td>HI (Instance-specific)</td><td>0.14 ms</td></tr><tr><td>HC (Contextual)</td><td>0.17 ms</td></tr><tr><td>HF (Confidence Estimation)</td><td>0.12 ms</td></tr><tr><td colspan="2">Overall</td><td>2.04 ms</td></tr></table>
+
+Table 6. GACE runtime analysis per  $360^{\circ}$  field-of-view Waymo point cloud on a single NVIDIA® GeForce® RTX 3090 GPU.
+
+tracting the statistical features for all detections. However, this can be solved efficiently via PyTorch einsum. During inference, we first compute the instance-specific plausibility  $\mathbf{f}^I$  for each detection via  $H_{I}$ , which is then used as input to  $H_{C}$  for the corresponding neighbors. Overall, GACE is capable of processing  $\sim 490$  Waymo point clouds per second with  $\sim 100$  detections each.
+
+# 5. Limitations
+
+While our method has proven effective in improving object detection performance for vulnerable classes such as pedestrians and cyclists, it is worth noting that it may not offer such significant benefits for simpler classes such as vehicles. This is because all detectors typically have few false positives for these easier-to-detect objects. Therefore, there is less room for improvement for this class. However, it is important to consider the context in which our method is applied. Even if the performance improvement is not as large for simpler classes, the overall impact of our method on safety should not be underestimated. In many real-world scenarios, pedestrians and cyclists are particularly vulnerable, and any improvement in their detection can make a significant contribution to safety.
+
+# 6. Conclusion
+
+We proposed GACE, a method to better evaluate object hypotheses from black-box LiDAR-based 3D object detectors by explicitly assessing numerous geometric properties inherent in the detections. This enables a better separation between true and false positive detections and thus significantly improves the performance. In a comprehensive analysis, we were able to show the performance of our method for several state-of-the-art detectors and also demonstrate the generalisation capabilities of GACE. This underlines the importance and general validity of the geometric information inherent in 3D detections, which has been largely neglected in the past.
+
+Acknowledgements This work was partially funded by the Austrian FFG project iLIDS4SAM (878713) and by the Christian Doppler Laboratory for Embedded Machine Learning.
+
+# References
+
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+
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\ No newline at end of file
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+                                            "content": "Figure 1. Context matters: a baseline detector struggles at detecting true positive objects confidently if the sampling pattern is atypical, e.g. the occluded pedestrian in the orange bounding box (close-up top-left). GACE exploits the geometric properties of the detection and its surrounding objects to significantly increase the score for this detection, which is intuitively correct for a human observer considering this scene."
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+                                    "content": "structured nature of the data, the highly variable point density poses a major challenge. Due to the angular offset of the LiDAR beams, the density is highly dependent on the distance to the object and can be altered by occlusions in the foreground. This often requires detecting objects based on very few data points, which is especially true for classes with smaller spatial dimensions, such as pedestrians and cyclists. For example, in the Waymo Open Dataset [33], one of the most widely used and challenging datasets to date, about 30 percent of all annotated pedestrians consist of less than merely 20 points. Detecting these sparsely sensed objects naturally leads to a large number of false positive detections at test time. For this reason, determining a meaningful confidence value for the detections is critical to find a trade-off between precision and recall that adequately dis"
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+                                    "content": "tinguishes true positives from false positives. The potential that could be exploited by improving the confidence score is considerable: Suppose we have an oracle that could correctly classify the detections of a SECOND [38] model on the Waymo dataset into true and false positives. This would increase the LEVEL_1 average precision for vehicles by "
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+                                    "type": "text",
+                                    "content": ", respectively."
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+                                    "content": "Existing 3D object recognition pipelines, including confidence estimation approaches, were largely inspired by 2D image-based object recognition models and then gradually adapted to point cloud processing. However, the conventional backbone - neck - head architecture of the 2D detection model was largely retained, e.g. in [8, 10, 15, 27, 38, 45]. After extracting features (point-based, voxel-based, or region-based) over multiple levels in the backbone, they are fused in the neck module and then passed to the detection head, where bounding box regression and confidence estimation are performed on a dense feature representation. Typically, separate branches are used within the head for bounding box regression and confidence estimation, each consisting of one or more fully connected layers on top of the common feature representation."
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+                                    "content": "Unlike image-based object detection, there are several highly relevant geometric properties inherent to objects in 3D point clouds that have been largely unexploited in assessing the confidence of a detection. In the image case, it is usually not possible to easily derive geometric properties for the objects, such as height or orientation, unless a static and fully calibrated camera and a known or constant scene are given. In contrast, in 3D object detection, many geometric features are directly available in the object properties and associated 3D data points to better assess the presence of a real object. On the one hand, these are instance-specific properties, such as the dimension of the object, the heading direction, the position, or the point distribution within the bounding box. For example, as shown in Figure 2, the precision of a SECOND [38] model for detecting a vehicle is highly dependent on the size of the object and from which side it is detected by the LiDAR. It can be seen that vehicle categories between passenger cars and heavy duty vehicles (i.e. vehicles with a length of 6 to "
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+                                    "type": "text",
+                                    "content": ") are harder to detect, potentially because they are underrepresented in the dataset, and that vehicles are easier to detect from behind (i.e. viewing angle between "
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+                                    "type": "text",
+                                    "content": " degrees), presumably because of the highly reflective license plates, as shown in [25]. On the other hand, contextual properties, i.e. geometric relationships to neighboring objects, can contribute to a more reliable estimation of the confidence. For example, as shown in Figure 1, a pedestrian that appears atypical due to occlusions can be assessed more reliably by additionally taking neighboring vehicles and pedestrians into consideration."
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+                                            "content": "Figure 2. Precision of a SECOND [38] model for the Waymo [33] vehicle class as a function of the object length (top) and of the viewing angle (bottom), indicating from which side the vehicle is seen by the LiDAR, where 0 degrees corresponds to the rear view. These examples illustrate the strong dependence of the precision on simple geometric object properties."
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+                                    "content": "Nevertheless, these simple but highly informative metric properties are neglected when estimating the confidence score in current detector architectures for the following reasons: First, in grid-based models, information such as the exact point distribution within the bounding box or the number of points is already partially discarded by the discretization (voxelization) in the preprocessing phase. Second, the bounding box properties (object dimensions & rotation) are determined in the parallel and separate box regression head and are therefore not accessible to the confidence estimation head. Finally, confidence estimation is usually performed using only features within a small area around the object (depending on the receptive field and detector), and no explicit information about neighboring objects and their geometric properties or confidence values is used, preventing a holistic estimation."
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+                                    "content": "Inspired by these observations, we present GACE, an intuitive and highly effective method to improve the confidence estimation of any black-box detector using geometric information. Given a set of detections from the base detector, we explicitly use these neglected features to enhance the expressiveness of the confidence values with the help of these additional cues. Our model-agnostic approach is intentionally applied after the actual detector training process to perform an auxiliary geometric assessment independent of the initial features. In a detailed evaluation on the Waymo dataset, we show that GACE consistently improves the performance of several state-of-the-art detection pipelines. Furthermore, we demonstrate the generalizability and transferability of our method by applying it to other datasets and even other detectors. Without retraining them, we achieve highly compelling performance gains."
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+                                    "content": "LiDAR-based 3D Object Detection: Depending on how existing methods for 3D object detection in single frame LiDAR data deal with the unstructured nature of point clouds, they can be broadly categorized into point-based, grid-based, and hybrid approaches."
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+                                    "content": "Point-based methods extract information directly from the individual raw 3D points [23,24,30,32,40,44]. The pioneering works, PointNet [23] and PointNet++ [24], used shared multilayer perceptrons in combination with global pooling functions to directly extract features from the irregular point cloud data. In Point-RCNN [30] features extracted in this manner are used to segment foreground points and generate proposals based on them. The advantages of point-based 3D object detectors are that there is no loss of point information due to discretization and the large receptive field, but at the cost of high computational demands."
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+                                    "content": "Instead of processing the points directly, grid-based methods [4, 15, 21, 27, 34, 38, 39, 43, 46] discretize the non-uniform 3D points into regular grids that can then be processed with 2D/3D convolutions. Voxelnet [46], a pioneering method, divides the point cloud into uniformly spaced 3D voxels, aggregates information from the points within them and generates predictions using 3D convolutions. To better handle the large number of empty voxels, SECOND [38] introduced sparse 3D convolutions. To reduce complexity, PointPillars [15] and PillarNet [27] use a 2D grid on the ground plane to create a column representation, a single pillar-shaped voxel per location, that can be processed using 2D convolutions. As an alternative to such anchor-based methods, Centerpoint [43] predicts a bird's-eye view heat map and detects the object center using a keypoint detector. Recently, transformer-based backbones have also been used to enable long-range relationships between voxels [5, 21, 34, 47]. Object relations within a frame and across multiple frames are mapped by Ret3D [37] using a graph and a transformer. The advantage of grid-based methods is that they can process data faster due to the regular format, but are limited by the loss of point information during the initial discretization phase."
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+                                    "content": "In order to obtain both, multi-scale features and fine-grained information, hybrid methods process voxel and point information jointly [22, 26, 28, 29, 31, 41, 42]. PV-RCNN [28], uses a set abstraction module that combines surrounding point and voxel features at keypoints to improve the detections. Part-A² [31] predicts the position of parts within an object based on point features to improve the accuracy, while LiDAR R-CNN [17] uses features of a PointNet [23] model that processes points within and around box proposals. Pyramid R-CNN [19] creates point features using a pyramid grid structure to acquire fine-grained and long-range contextual information."
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+                                    "content": "Confidence Estimation: In the usual backbone - neck - head detector architecture, after the feature extraction and aggregation, the box regression and confidence estimation are performed. This is usually done in two separate branches based on a common dense feature representation [15, 38, 40, 46]. This has the disadvantage that the accuracy of the localization is hardly included in the confidence score. Inspired by 2D object detection methods [11,12,36], IoU guided supervision is frequently used to obtain a better correlation between the classification result and the localization accuracy [9, 10, 16, 27, 28, 31, 41, 45]. Thereby, the IoU between the predicted box and the ground truth is learned in a third branch during training and then incorporated into the final confidence score at test time. Hu et al. [9] leverage the inherent relationship between object distance and point density to better assess a detection. Inspired by the 2D approach [3], a spatial transformation on the feature maps is done by He et al. [8] to better align the confidence prediction and bounding box regression. Related to confidence estimation are also calibration methods [7, 14] where the score should represent a true probability, i.e. how likely a detection is. Detection pipelines, however, aim at the best separation of true and false positives as optimization goal for the confidence prediction."
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+                                    "content": "In our confidence estimation method we also pursue this optimization objective, but in contrast to existing approaches, we present a method for refining the confidence values for a given set of detections by exploiting the rich geometric information contained directly in the detections as well as in the underlying 3D points. While these useful cues for assessing the plausibility of a detection have been largely untapped due to the architecture of common detection pipelines, they allow us to increase the expressiveness of the confidence values."
+                                }
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+                                    "content": "3. Geometry-Aware Confidence Enhancement"
+                                }
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+                                    "content": "Our goal is to optimize the confidence scores for a given set of detections from a base detector in order to better separate true positives from false positives, thus increasing the overall detection performance. We use the detector in a pure black box manner, i.e. we do not assume any knowledge about the architecture of the base model, nor access to its internals like parameters, features or gradients. This black-box optimization, taking only the point cloud and the set of objects detected in it as input, enables universal applicability and easy transferability of our enhancement module to any base 3D object detection pipeline. The basic idea is to revalidate the detections by exploiting as much as possible the geometric information they inherently contain."
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+                                            "content": "Figure 3. Schematic of GACE: To re-evaluate the confidence score of a detection (orange), we aggregate geometric properties of the detection itself and the points it contains into a feature vector (top). To capture the context of the detection, geometric relationships to neighboring detections are aggregated using a shared MLP and subsequent pooling function (bottom). By merging both features (right), we obtain a new confidence score that takes into account the underlying geometric properties of the detection."
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+                                    "type": "text",
+                                    "content": "In our proposed approach called GACE (Geometry Aware Confidence Enhancement) we exploit two types of geometric information, as shown in Figure 3:"
+                                }
+                            ]
+                        }
+                    ],
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+                                            "type": "text",
+                                            "content": "- Instance-specific Geometric Properties (Section 3.1): Attributes of the bounding box itself, combined with the point data inside. For example, how well is the size of the object or the heading angle supported by the point distribution?"
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 5
+                        },
+                        {
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+                                            "type": "text",
+                                            "content": "- Contextual Geometric Properties (Section 3.2): Relationships to surrounding objects can provide useful information to better validate an uncertain detection, e.g., a partially occluded vehicle moving in the same lane and same direction as the surrounding vehicles."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                    "type": "text",
+                                    "content": "These useful cues to estimate the plausibility of an object are usually not used for the confidence estimation in common detection pipelines. The reasons are that information is often already discarded during preprocessing (discretization), essential properties such as the estimated size of the object are not available (separate box regression in a parallel branch), or the objects are only evaluated individually and not more holistically. Therefore, we explicitly use these easily accessible and rich sources of information as input to our enhancement module. After merging the instance-specific and contextual features, we determine the new confidence value of each proposed object via an auxiliary task (Section 3.3)."
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "To generate the training data for our enhancement module, we use the black-box base model in a single inference run on the training set. The resulting set of all"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
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+                                    "type": "text",
+                                    "content": "detections from the base model represents the training data to learn our improved confidence estimator. Formally, this can be described as follows."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Definitions & Notations: Let "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathcal{X}} = \\{\\widetilde{\\mathbf{x}}_k\\}_{k=1\\dots K}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                    ],
+                                    "type": "text",
+                                    "content": " be a LiDAR point cloud, where each of the "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "K"
+                                },
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+                                    "type": "text",
+                                    "content": " unordered points "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{x}}_k \\in \\mathbb{R}^5"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": " consists of the 3D coordinates, intensity/reflectance and the elongation value. Furthermore, let "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathcal{Y}} = \\{\\widetilde{\\mathbf{y}}_i\\}_{j=1\\dots M}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
+                                        546,
+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": " be the set of corresponding ground truth objects. Each object annotation "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{y}} = [\\widetilde{\\mathbf{b}}, \\widetilde{\\mathbf{y}}]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
+                                        546,
+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": " includes the bounding box parameters "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{\\mathbf{b}} = [\\widetilde{c}_x, \\widetilde{c}_y, \\widetilde{c}_z, \\widetilde{d}_x, \\widetilde{d}_y, \\widetilde{d}_z, \\widetilde{\\Theta}]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the corresponding class label "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widetilde{y}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
+                                        546,
+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": ". For a given black-box 3D object detector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", let "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "F(\\widetilde{\\mathcal{X}}) = \\mathcal{Y} = \\{\\mathbf{y}_{i=1\\dots N}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
+                                        546,
+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": " be the set of proposed detections for this input point cloud, where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
+                                        546,
+                                        558
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y} = [\\mathbf{b}, y, s]"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". In addition to the box properties "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
+                                        546,
+                                        558
+                                    ],
+                                    "type": "text",
+                                    "content": " and the corresponding class label "
+                                },
+                                {
+                                    "bbox": [
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+                                        385,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        385,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", the detector predicts a confidence value "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " that should ideally indicate the prevalence of a true positive example."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Confidence Optimization: Based on the known ground truth objects, a category label "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{u_i\\in \\{0,1\\} \\}_{i = 1\\dots N}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be assigned to each detection, indicating whether it is a true positive or false positive detection. Moreover, we know the IoU with a possible ground truth bounding box for each object which we define as "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{v_{i}\\}_{i = 1\\dots N}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". We aim to improve the confidence estimate of the original detector by focusing exclusively on the binary classification of detections into true positive and false positive examples. We determine the revised confidence score "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\widehat{s}_i\\} = H(\\mathcal{V},\\mathcal{X})"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " using our module "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", where only the set of detections "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{V}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the points they include "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}\\subset \\widetilde{\\mathcal{X}}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        570,
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+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " are used as input."
+                                }
+                            ]
+                        }
+                    ],
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+                }
+            ],
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+                                    "type": "text",
+                                    "content": "3.1. Instance-specific Geometric Properties"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    "type": "text",
+                                    "content": "In common 2D and 3D object detection architectures, the bounding box regression and the confidence estimation are performed completely separated in different branches. This is well suited for 2D where it is desired to detect objects in the image regardless of their scale. For 3D, however, important cues for plausibility estimation remain largely unused. Let us consider the available context directly provided by an object proposal: The position of the possible object in combination with the dimensions indicates, for example, which point density is to be expected. Furthermore, the direction angle provides an indication of the expected point distribution within the box. This information can even be further refined by knowing the class of the object. This directly available geometrical knowledge about an object allows for a more profound estimation of the confidence score."
+                                }
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "We extract these basic properties and transform them into a compact representation using a multilayer perceptron (MLP) "
+                                },
+                                {
+                                    "bbox": [
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+                                        294,
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+                                    "type": "inline_equation",
+                                    "content": "H_{I}"
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+                                    "type": "text",
+                                    "content": ". As input parameters, we first use the object parameters, i.e. the position "
+                                },
+                                {
+                                    "bbox": [
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+                                        415
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+                                    "type": "inline_equation",
+                                    "content": "(c_x, c_y, c_z)"
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+                                    "type": "text",
+                                    "content": ", the size "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(d_x, d_y, d_z)"
+                                },
+                                {
+                                    "bbox": [
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+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the heading angle "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
+                                        289,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " of the bounding box, as well as the initial confidence value "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
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+                                        415
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "s_i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
+                                        289,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " of the detection estimated by the base detector. Additionally, we use the distance "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
+                                        289,
+                                        415
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{c} \\|"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
+                                        289,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " from the LiDAR sensor to the object center, and the angle "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
+                                        289,
+                                        415
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        294,
+                                        289,
+                                        415
+                                    ],
+                                    "type": "text",
+                                    "content": " between the line of sight to the object and the heading angle of the object:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
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+                                    "bbox": [
+                                        117,
+                                        424,
+                                        287,
+                                        437
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\alpha = \\Theta - \\operatorname {a t a n 2} \\left(c _ {y}, c _ {x}\\right). \\tag {1}",
+                                    "image_path": "2ce739d38a14bdc94b0637e041c4f4a4167363d2017b811845ee57ea2a4727f1.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "This angle describes from which side an object is seen from the LiDAR center, independent of the position of the object relative to the LiDAR, e.g. a vehicle driving directly towards the LiDAR always has the same angle "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "\\alpha"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", no matter from which direction the vehicle approaches. We complement these cues with information about the points "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_{\\mathrm{b}} \\subset \\mathcal{X}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": " inside the bounding box "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{b}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": ". Besides the overall number of points "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "|\\mathcal{X}_{\\mathrm{b}}|"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": ", we extract elementary low-level statistics. Therefore, we scale the box and the associated points to a uniform size and then align them w.r.t. their center and yaw angle. In this canonical representation we compute the mean, standard deviation, minimum and maximum of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_{\\mathrm{b}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": " for all axes, denoted as "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{mean}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{std}}"
+                                },
+                                {
+                                    "bbox": [
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+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{min}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": ", "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{X}_{\\mathrm{b}}^{\\mathrm{max}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        447,
+                                        289,
+                                        628
+                                    ],
+                                    "type": "text",
+                                    "content": ". We then aggregate these attributes into one feature vector representing the instance-specific plausibility per object as"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                                    "bbox": [
+                                        50,
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+                                        666
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {f} ^ {I} = H _ {I} \\left(\\left[ \\mathbf {b}, \\alpha , \\| \\mathbf {c} \\|, | \\mathcal {X} _ {\\mathbf {b}} |, \\mathcal {X} _ {\\mathbf {b}} ^ {\\text {m e a n}}, \\mathcal {X} _ {\\mathbf {b}} ^ {\\text {s t d}}, \\mathcal {X} _ {\\mathbf {b}} ^ {\\min }, \\mathcal {X} _ {\\mathbf {b}} ^ {\\max } \\right] ^ {\\top}\\right), \\tag {2}",
+                                    "image_path": "042d2fe026d541351d88ea061be533b6fedbf6c823070f3e121c4b103bae7fb0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                46,
+                                665,
+                                286,
+                                702
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        665,
+                                        286,
+                                        702
+                                    ],
+                                    "type": "text",
+                                    "content": "where we pass all angles as direction vectors "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        665,
+                                        286,
+                                        702
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\cos(\\cdot), \\sin(\\cdot))"
+                                },
+                                {
+                                    "bbox": [
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+                                        665,
+                                        286,
+                                        702
+                                    ],
+                                    "type": "text",
+                                    "content": " and normalize all metric properties to unit length using the corresponding maximum value range."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                {
+                                    "bbox": [
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+                                        85
+                                    ],
+                                    "type": "text",
+                                    "content": "3.2. Contextual Geometric Properties"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        304,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        95,
+                                        547,
+                                        287
+                                    ],
+                                    "type": "text",
+                                    "content": "Especially in the case of uncertain detections, e.g. detections that are far away and therefore consist of only a few 3D points, or detections that are partially occluded and therefore appear atypical, geometric contextual information can be very useful in assessing a confidence score. Examples include a vehicle that is heavily occluded but in a convoy with other vehicles, or cyclists moving in a group. However, this information is usually not available for the confidence estimation, since the object proposals are evaluated individually within the receptive field but without explicit knowledge of the objects detected in its vicinity and their properties. In order to assess the plausibility of a detection "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        95,
+                                        547,
+                                        287
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{y}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        95,
+                                        547,
+                                        287
+                                    ],
+                                    "type": "text",
+                                    "content": " in a more holistic way, we use the geometric relations to surrounding objects in the scene. We thereby consider all neighbors that are within a certain radius "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        95,
+                                        547,
+                                        287
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        95,
+                                        547,
+                                        287
+                                    ],
+                                    "type": "text",
+                                    "content": " around the object to be evaluated."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
+                        304,
+                        547,
+                        461
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                461
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": "We therefore create a representation per object, which captures the relationships to its neighboring objects. In order to be independent of the number of neighboring objects, we first create a feature vector for each neighbor, which we then combine into a unified representation using a symmetric pooling function. As input parameters per neighbor we use the distance to the object to be evaluated "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\| \\mathbf{c} - \\mathbf{c}_n\\|"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": ", the direction vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{c} - \\mathbf{c}_n"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": ", the difference between the two heading angles "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta - \\Theta_n"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the neighbor's class label "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "y_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": ". To incorporate the validity of the neighbor, we leverage "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_n^I"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": ", which represents the instance-specific properties of the neighbor. This information is encoded via the shared weight MLP "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
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+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": " to form the feature vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_n^C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        304,
+                                        547,
+                                        461
+                                    ],
+                                    "type": "text",
+                                    "content": " for each individual neighbor,"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
+                                        313,
+                                        479,
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+                                        500
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathbf {f} _ {n} ^ {C} = H _ {C} \\left(\\left[ \\| \\mathbf {c} - \\mathbf {c} _ {n} \\|, \\mathbf {c} - \\mathbf {c} _ {n}, \\Theta - \\Theta_ {n}, y _ {n}, \\mathbf {f} _ {n} ^ {I} \\right] ^ {\\top}\\right), \\tag {3}",
+                                    "image_path": "72c50b2dc9e0da9fc6b73fd839ba0cd73ad44e0ad829c79bddc1ded4835eab9e.jpg"
+                                }
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+                    ],
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+                                {
+                                    "bbox": [
+                                        305,
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+                                    "type": "text",
+                                    "content": "where the angle "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        517,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\Theta -\\Theta_{n}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        517,
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+                                    "type": "text",
+                                    "content": " is provided as direction vector and the metric features are normalized to unit length."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Finally, we aggregate the information from the individual neighbors into a unified representation for later processing, as shown in Figure 3. This requires accumulating features of an unknown (and varying) number of neighbors. To impose no constraint on the number of features, we take inspiration from the pooling step of point-based detectors, e.g. [23], and employ a symmetric max pooling function to form a plausibility signature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}^C"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        558,
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+                                    ],
+                                    "type": "text",
+                                    "content": " over the feature vectors of all neighbors. Thus, in this representation the geometric relations to the surrounding objects are accumulated for the subsequent confidence estimation, taking into account the respective local properties of the neighbors."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                }
+            ],
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+                                    "type": "text",
+                                    "content": "3.3. Data Fusion & Confidence Prediction"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    "type": "text",
+                                    "content": "To estimate the new confidence value for a detection, we merge the instance-specific and contextual geometric features. The instance-specific information encoded in "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        90,
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}^I"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", as well as the contextual information in "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                        287,
+                                        161
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}^C"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        90,
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+                                        161
+                                    ],
+                                    "type": "text",
+                                    "content": " are concatenated and processed using "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        90,
+                                        287,
+                                        161
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", a MLP with sigmoid output function, to estimate the new confidence score"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                    "angle": 0,
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+                                    "bbox": [
+                                        119,
+                                        169,
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+                                        190
+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\widehat {s} = H _ {F} \\left(\\left[ \\mathbf {f} ^ {I}, \\mathbf {f} ^ {C} \\right] ^ {\\top}\\right). \\tag {4}",
+                                    "image_path": "76fe1b4cf9d1cbf2f77a5d637dffe53a7b2fca6624a926f9f2da0c1a836d71f0.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 2
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "We train the whole module including the two feature encoding networks "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{I}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "text",
+                                    "content": " using an end-to-end training strategy. As loss function "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{conf}}(\\widehat{s},u)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "text",
+                                    "content": " for this task we use the focal loss [18] to focus learning on hard examples. The goal is to divide the set of detections as good as possible into true or false positive examples using the binary category label "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "u\\in \\{0,1\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "text",
+                                    "content": " as target. As auxiliary task during training we estimate the IoU with the ground truth bounding box in a further output "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\widehat{v}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "text",
+                                    "content": " of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "text",
+                                    "content": ". Therefore, we add an IoU-guidance [16, 41, 45] L1-loss term "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{IoU}}(\\widehat{v},v)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        198,
+                                        287,
+                                        364
+                                    ],
+                                    "type": "text",
+                                    "content": ". This increases the importance of the point distribution statistics within the features, as they provide evidence of the bounding box accuracy from which the confidence estimate also benefits. The overall loss function is therefore"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
+                                        93,
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {c o n f}} (\\widehat {s}, u) + \\lambda_ {\\mathrm {I o U}} \\mathcal {L} _ {\\mathrm {I o U}} (\\widehat {v}, v), \\tag {5}",
+                                    "image_path": "6058ff460594de0b9aa58b35e10dfa5cacfec5ca7eda548fd433382aa4dc32f3.jpg"
+                                }
+                            ]
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+                    ],
+                    "index": 4
+                },
+                {
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{\\mathrm{IoU}}"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a hyper-parameter to adjust the influence of the auxiliary task."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4. Experiments"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "To demonstrate the benefits of GACE, we evaluate our black-box confidence optimization method on several well-known state-of-the-art 3D object detection pipelines. In particular, we apply it to the pillar-based PointPillars [15], the voxel-based SECOND [38] and Centerpoint [43], as well as the hybrid methods Part-A² [31], PV-RCNN [28] and PV-RCNN++ [29]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
+                    "bbox": [
+                        46,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": "Datasets: For the evaluation of our approach we use the Waymo Open Dataset [33] as well as the KITTI Dataset [6]. The Waymo dataset is one of the largest and most challenging public datasets for autonomous driving research. It provides 798 training scenes and 202 validation scenes, where each scene consists of about 200 LiDAR samples covering the full "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        546,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "360^{\\circ}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        546,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " field-of-view. In total, the dataset consists of over 8.9M annotated objects classified into vehicles, pedestrians and cyclists. We follow the common evaluation protocol using the standard metrics average precision (AP), as well as average precision with heading (APH), where true positives are weighted by their heading accuracy. In addition, we use the KITTI dataset, one of the most popular datasets for 3D object detection."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
+                        304,
+                        72,
+                        545,
+                        144
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
+                                304,
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
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+                                        144
+                                    ],
+                                    "type": "text",
+                                    "content": "We thereby use the standard split [2] into a training set (3712 samples) and validation set (3769 samples). We also follow the common evaluation practice using average precision with 40 recall points. For both datasets, the 3D IoU threshold for a true positive sample is 0.7 for vehicles and 0.5 for pedestrians and cyclists."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
+                        304,
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+                        545,
+                        335
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                        335
+                                    ],
+                                    "type": "text",
+                                    "content": "Implementation Details: Our experimental setup is based on the open-source toolbox OpenPCDet [35]. To ensure the reproducibility of our results, all base models used in the experiments have been trained on the training set using the default configuration and default training policies of OpenPCDet. This includes augmenting the data by randomly rotating, scaling and flipping the point cloud, as well as ground truth sampling [38], i.e. the placement of objects from other training examples in the current frame. To create the training data for our module, we use the base model as a black-box detection pipeline. In a single inference run on the training set, we collect the output of the base model, i.e. the set of all detections, which represents our training data. The actual training process of our module is therefore entirely decoupled from the base model."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
+                    "bbox": [
+                        304,
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+                        545,
+                        433
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                433
+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Our sub-networks for feature transformation, i.e. "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        338,
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+                                        433
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{I}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the shared network "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{C}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        338,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", as well as the confidence prediction network "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        338,
+                                        545,
+                                        433
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "H_{F}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        338,
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+                                        433
+                                    ],
+                                    "type": "text",
+                                    "content": " are two-layer MLP's with 256 feature dimensions. The feature vector "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}^{I}"
+                                },
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+                                    "type": "text",
+                                    "content": " in which the instance-specific information is encoded is 128-dimensional and "
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+                                    "content": "\\mathbf{f}^{C}"
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+                                    "type": "text",
+                                    "content": " for the contextual information is 64-dimensional. When determining the contextual geometric properties, we accumulate the neighboring objects that are within a radius of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "r = 40m"
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "We train our model end to end with the Adam [13] optimizer and a learning rate of 0.001. The weighting of the auxiliary loss term during training is set to "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\lambda_{\\mathrm{IoU}} = 0.5"
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+                                    "type": "text",
+                                    "content": ". In all experiments we use the same architecture as well as hyperparameters, regardless of the underlying black-box base model. We train our module over 5 epochs on a single NVIDIA® GeForce® RTX 3090 GPU, which takes less than 10 minutes due to our favorable lightweight model size and low feature dimensions."
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+                                    "type": "text",
+                                    "content": "4.1. Main Results"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
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+                                    "type": "text",
+                                    "content": "Table 1 summarizes the results of our confidence optimization on the Waymo dataset for different baseline detection pipelines. For each detector architecture, we report the performance of the base detector as well as the results after applying our GACE module. Please note that for better traceability, the results of the base detectors correspond to the respective OpenPCDet implementations (see OpenPCDet model zoo). Some reported baseline scores are even higher than in their original papers due to augmentation techniques used in OpenPCDet."
+                                }
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+                                    "type": "text",
+                                    "content": "1https://github.com/dschinagl/gace"
+                                }
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">Overall</td><td colspan=\"4\">Vehicles (IoU=0.7)</td><td colspan=\"4\">Pedestrians (IoU=0.5)</td><td colspan=\"4\">Cyclists (IoU=0.5)</td></tr><tr><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td><td colspan=\"2\">LEVEL_1</td><td colspan=\"2\">LEVEL_2</td></tr><tr><td>mAP</td><td>mAPH</td><td>mAP</td><td>mAPH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td><td>AP</td><td>APH</td></tr><tr><td>PointPillars [15]</td><td>64.72</td><td>57.07</td><td>58.57</td><td>51.73</td><td>70.99</td><td>70.35</td><td>62.79</td><td>62.20</td><td>66.36</td><td>47.15</td><td>58.27</td><td>41.32</td><td>56.81</td><td>53.71</td><td>54.66</td><td>51.67</td></tr><tr><td>+ GACE (Ours)</td><td>69.25</td><td>61.24</td><td>62.98</td><td>55.73</td><td>71.92</td><td>71.28</td><td>63.63</td><td>63.04</td><td>72.18</td><td>51.97</td><td>64.06</td><td>45.96</td><td>63.64</td><td>60.47</td><td>61.25</td><td>58.20</td></tr><tr><td>Improvement</td><td>+4.53</td><td>+4.17</td><td>+4.41</td><td>+4.00</td><td>+0.93</td><td>+0.93</td><td>+0.84</td><td>+0.84</td><td>+5.82</td><td>+4.82</td><td>+5.79</td><td>+4.64</td><td>+6.83</td><td>+6.76</td><td>+6.59</td><td>+6.53</td></tr><tr><td>SECOND [38]</td><td>65.13</td><td>60.81</td><td>59.01</td><td>55.12</td><td>70.93</td><td>70.30</td><td>62.65</td><td>62.07</td><td>65.67</td><td>54.96</td><td>57.78</td><td>48.25</td><td>58.78</td><td>57.18</td><td>56.59</td><td>55.05</td></tr><tr><td>+ GACE (Ours)</td><td>70.17</td><td>66.13</td><td>63.74</td><td>60.06</td><td>71.56</td><td>70.92</td><td>63.22</td><td>62.63</td><td>71.71</td><td>61.87</td><td>63.27</td><td>54.37</td><td>67.22</td><td>65.59</td><td>64.73</td><td>63.16</td></tr><tr><td>Improvement</td><td>+5.04</td><td>+5.32</td><td>+4.73</td><td>+4.94</td><td>+0.63</td><td>+0.62</td><td>+0.57</td><td>+0.56</td><td>+6.04</td><td>+6.91</td><td>+5.49</td><td>+6.12</td><td>+8.44</td><td>+8.41</td><td>+8.14</td><td>+8.11</td></tr><tr><td>Part-A2[31]</td><td>70.30</td><td>66.66</td><td>63.53</td><td>60.27</td><td>73.35</td><td>72.81</td><td>64.73</td><td>64.24</td><td>70.02</td><td>61.01</td><td>60.83</td><td>52.85</td><td>67.53</td><td>66.18</td><td>65.03</td><td>63.73</td></tr><tr><td>+ GACE (Ours)</td><td>73.07</td><td>69.21</td><td>66.24</td><td>62.77</td><td>73.99</td><td>73.43</td><td>65.38</td><td>64.87</td><td>72.36</td><td>62.93</td><td>63.21</td><td>54.81</td><td>72.84</td><td>71.28</td><td>70.13</td><td>68.63</td></tr><tr><td>Improvement</td><td>+2.77</td><td>+2.55</td><td>+2.71</td><td>+2.50</td><td>+0.64</td><td>+0.62</td><td>+0.65</td><td>+0.63</td><td>+2.34</td><td>+1.92</td><td>+2.38</td><td>+1.96</td><td>+5.31</td><td>+5.10</td><td>+5.10</td><td>+4.90</td></tr><tr><td>Centerpoint [43]</td><td>73.01</td><td>70.35</td><td>66.79</td><td>64.33</td><td>72.87</td><td>72.33</td><td>64.76</td><td>64.27</td><td>74.48</td><td>68.22</td><td>66.55</td><td>60.81</td><td>71.69</td><td>70.50</td><td>69.06</td><td>67.92</td></tr><tr><td>+ GACE (Ours)</td><td>75.58</td><td>72.98</td><td>69.19</td><td>66.76</td><td>74.49</td><td>73.99</td><td>66.19</td><td>65.73</td><td>78.62</td><td>72.48</td><td>70.44</td><td>64.73</td><td>73.64</td><td>72.48</td><td>70.94</td><td>69.83</td></tr><tr><td>Improvement</td><td>+2.57</td><td>+2.63</td><td>+2.40</td><td>+2.43</td><td>+1.62</td><td>+1.66</td><td>+1.43</td><td>+1.46</td><td>+4.14</td><td>+4.26</td><td>+3.89</td><td>+3.92</td><td>+1.95</td><td>+1.98</td><td>+1.88</td><td>+1.91</td></tr><tr><td>PV-RCNN [28]</td><td>71.11</td><td>66.78</td><td>64.40</td><td>60.50</td><td>74.79</td><td>74.17</td><td>66.17</td><td>65.61</td><td>72.06</td><td>61.46</td><td>63.00</td><td>53.56</td><td>66.48</td><td>64.72</td><td>64.03</td><td>62.34</td></tr><tr><td>+ GACE (Ours)</td><td>73.38</td><td>68.89</td><td>66.65</td><td>62.57</td><td>75.20</td><td>74.55</td><td>66.57</td><td>65.97</td><td>73.84</td><td>62.97</td><td>64.88</td><td>55.14</td><td>71.12</td><td>69.16</td><td>68.50</td><td>66.60</td></tr><tr><td>Improvement</td><td>+2.27</td><td>+2.11</td><td>+2.25</td><td>+2.07</td><td>+0.41</td><td>+0.38</td><td>+0.40</td><td>+0.36</td><td>+1.78</td><td>+1.51</td><td>+1.88</td><td>+1.58</td><td>+4.64</td><td>+4.44</td><td>+4.47</td><td>+4.26</td></tr><tr><td>PV-RCNN++ [29]</td><td>75.72</td><td>73.05</td><td>69.22</td><td>66.73</td><td>77.30</td><td>76.81</td><td>68.92</td><td>68.47</td><td>78.91</td><td>72.42</td><td>70.43</td><td>64.41</td><td>70.95</td><td>69.90</td><td>68.31</td><td>67.31</td></tr><tr><td>+ GACE (Ours)</td><td>76.76</td><td>74.02</td><td>70.31</td><td>67.75</td><td>77.42</td><td>76.93</td><td>69.05</td><td>68.59</td><td>79.59</td><td>72.97</td><td>71.34</td><td>65.18</td><td>73.26</td><td>72.16</td><td>70.54</td><td>69.48</td></tr><tr><td>Improvement</td><td>+1.04</td><td>+0.97</td><td>+1.09</td><td>+1.02</td><td>+0.12</td><td>+0.12</td><td>+0.13</td><td>+0.12</td><td>+0.68</td><td>+0.55</td><td>+0.91</td><td>+0.77</td><td>+2.31</td><td>+2.26</td><td>+2.23</td><td>+2.17</td></tr></table>",
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+                                    "content": "Table 1. Performance comparison on the Waymo Open Dataset [33] validation set for different baseline methods with and without our confidence enhancement module GACE."
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+                                    "content": "For all baseline detectors and all classes, adjusting the confidence level with our approach leads to an increase in performance without exception. The overall performance gains range from "
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+                                    "type": "text",
+                                    "content": " (LEVEL_2) for SECOND, demonstrating the significance of this geometric information in estimating a confidence score for a detection."
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+                                    "content": "Object Classes: The performance improvements are significantly higher for the classes of pedestrians and cyclists. Intuitively, objects of these vulnerable road users contain significantly fewer 3D points due to their smaller spatial extent compared to vehicles. This effect is even aggravated by possible occlusions. Furthermore, the class of cyclists in particular is underrepresented in the training data. These properties make objects of these classes more difficult to detect, which leads to a higher number of false positives, but also makes confidence estimation more complex. Especially in these cases, our confidence enhancement method benefits from the additional geometric information when separating false positives from true positives, resulting in a higher impact of GACE."
+                                }
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+                                    "content": "Base Detectors: The overall performance gain is highest when applying GACE on pillar-based (PointPillars [15]) and voxel-based methods (SECOND [38] and Centerpoint [43]). These methods lose valuable point information already in their preprocessing stage, i.e. by voxelization. Thus, the optimization potential for these methods is higher than for the hybrid methods, which explicitly incorporate point-level information at detection locations. However, by explicitly exploiting both instance-specific and contextual geometric properties of the detections, GACE also leads to"
+                                }
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+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "a significant performance improvement for these methods, i.e. Part-"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{A}^2"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": " [31], PV-RCNN [28] and PV-RCNN++ [29], most notably for the classes of pedestrians and cyclists."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Precision/Recall Plots: To better illustrate the impact of our method, Figure 4 shows the precision/recall plots before and after applying GACE with a SECOND [38] model as the base detector (See the supplemental material for the other base detectors). Since recall remains unaffected, the significant performance gains of GACE are entirely due to an increase in precision. The better separation of true and false positives is mainly seen in the more challenging classes of pedestrians and cyclists, where the number of false detections is significantly higher and confidence estimation is more difficult. Furthermore, we see that the precision gains are higher in regions of higher recall, i.e. for detections with a lower confidence score. Especially these initially underrated detections of objects of the vulnerable classes represent a safety risk that can be reduced by GACE."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Range-based Evaluation: Table 2 summarizes our evaluation across the different distance ranges of Waymo. This also shows that GACE can consistently improve the performance of all baseline detectors and in all sub-ranges, especially in the far range. Detections at long distances are more challenging due to the lower point density, making it harder to distinguish true positives from false positives. Therefore, the geometric information is even more valuable in these cases, e.g. from "
+                                },
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+                                    "type": "text",
+                                    "content": " (LEVEL_2) for PV-RCNN++ up to "
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+                                    "type": "text",
+                                    "content": " (LEVEL_2) for PointPillars. The detailed evaluation results for all subclasses can be found in the supplemental material."
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+                                            "content": "Figure 4. Precision-recall plots for a SECOND [38] model as base detector with and without our confidence enhancement module on the Waymo Open Dataset [33] validation set for LEVEL_2 APH. Especially at higher recall levels, GACE's better separation of true and false positives leads to higher precision."
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+                                            "type": "table",
+                                            "html": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"3\">Overall (LEVEL_2)</td></tr><tr><td>0-30m</td><td>30-50m</td><td>50m-Inf</td></tr><tr><td>mAP / mAPH</td><td>mAP / mAPH</td><td>mAP / mAPH</td></tr><tr><td>PointPillars [15]</td><td>75.10 / 67.59</td><td>55.31 / 48.53</td><td>37.18 / 31.00</td></tr><tr><td>+ GACE (Ours)</td><td>78.32 / 70.68</td><td>60.17 / 53.01</td><td>42.88 / 35.97</td></tr><tr><td>Improvement</td><td>+3.22 / +3.09</td><td>+4.86 / +4.48</td><td>+5.70 / +4.97</td></tr><tr><td>SECOND [38]</td><td>75.55 / 71.87</td><td>56.55 / 52.42</td><td>37.73 / 33.39</td></tr><tr><td>+ GACE (Ours)</td><td>78.64 / 75.39</td><td>60.10 / 56.13</td><td>41.69 / 37.39</td></tr><tr><td>Improvement</td><td>+3.09 / +3.52</td><td>+3.55 / +3.71</td><td>+3.96 / +4.00</td></tr><tr><td>Part-A² [31]</td><td>79.93 / 76.93</td><td>61.77 / 58.01</td><td>40.13 / 36.44</td></tr><tr><td>+ GACE (Ours)</td><td>81.62 / 78.52</td><td>64.63 / 60.59</td><td>45.06 / 40.94</td></tr><tr><td>Improvement</td><td>+1.69 / +1.59</td><td>+2.86 / +2.58</td><td>+4.93 / +4.50</td></tr><tr><td>Centerpoint [43]</td><td>81.29 / 79.12</td><td>65.45 / 62.66</td><td>46.45 / 43.27</td></tr><tr><td>+ GACE (Ours)</td><td>82.94 / 80.90</td><td>67.56 / 64.76</td><td>50.20 / 46.80</td></tr><tr><td>Improvement</td><td>+1.65 / +1.78</td><td>+2.11 / +2.10</td><td>+3.75 / +3.53</td></tr><tr><td>PV-RCNN [28]</td><td>79.77 / 76.24</td><td>62.57 / 58.10</td><td>42.51 / 37.77</td></tr><tr><td>+ GACE (Ours)</td><td>81.25 / 77.66</td><td>64.76 / 60.11</td><td>47.01 / 41.90</td></tr><tr><td>Improvement</td><td>+1.48 / +1.42</td><td>+2.19 / +2.01</td><td>+4.50 / +4.13</td></tr><tr><td>PV-RCNN++ [29]</td><td>83.08 / 80.98</td><td>67.86 / 65.04</td><td>48.69 / 45.26</td></tr><tr><td>+ GACE (Ours)</td><td>83.59 / 81.43</td><td>68.69 / 65.83</td><td>51.81 / 48.19</td></tr><tr><td>Improvement</td><td>+0.51 / +0.45</td><td>+0.83 / +0.79</td><td>+3.12 / +2.93</td></tr></table>",
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+                                    "content": "4.2. Ablation Studies"
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+                                    "type": "text",
+                                    "content": "Main Components: We evaluate the contribution of our proposed instance-specific and contextual properties as well as the influence of the auxiliary IoU loss for a SECOND [38] model as baseline in Table 3. Incorporating the instance-specific geometric properties already leads to a significant performance increase of "
+                                },
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+                                    "content": "+3.65\\mathrm{AP} / + 3.32\\mathrm{APH}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Including also the contextual information, i.e. incorporating the relationships to the neighboring detection hypotheses further increases the performance by another "
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+                                    "content": "+0.71\\mathrm{AP} / + 1.14\\mathrm{APH}"
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+                                    "type": "text",
+                                    "content": ". Compared to the contributions of these two components, there is only a minor impact of incorporating the IoU guidance, leading to additional "
+                                },
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+                                    "content": "+0.37\\mathrm{AP} / + 0.48\\mathrm{APH}"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". Note that the degradation when adding "
+                                },
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{L}_{\\mathrm{IoU}}"
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+                                    "type": "text",
+                                    "content": " to only contextual features is caused by the lack of point information, which does not allow a reasonable estimation of the IoU. Overall, the instance-specific geometric information contributes stronger than the contextual geometric information."
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+                                            "type": "text",
+                                            "content": "Table 2. Consistent performance gains on the Waymo Open Dataset [33] validation set across distance ranges for different baseline methods for LEVEL_2 over all classes."
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+                                            "html": "<table><tr><td>Baseline</td><td>Instance Specific</td><td>Contextual</td><td>Aux-Loss LIoU</td><td>LEVEL_2 mAP</td><td>LEVEL_2 mAPH</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>59.01</td><td>55.12</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>62.66</td><td>58.44</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td>60.33</td><td>56.90</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>63.37</td><td>59.58</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td>62.94</td><td>58.78</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td>60.19</td><td>56.77</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>63.74</td><td>60.06</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 3. Ablation experiments for a SECOND [38] model as base detector over all classes on the Waymo Open Dataset [33] validation set. We show the impact of each GACE component."
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+                                            "html": "<table><tr><td>Box Properties</td><td># Points</td><td>Viewing Angle</td><td>Point Stat.</td></tr><tr><td>56.98+1.86</td><td>55.96+0.84</td><td>55.86+0.74</td><td>58.15+3.03</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 4. Impact of the different instance-specific feature groups when used exclusively for a SECOND model as base detector on the Waymo Open Dataset [33] over all classes (LEVEL_2 mAPH)."
+                                }
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+                                    "type": "text",
+                                    "content": "Instance-Specific Properties: We analyze the contribution of each feature group within the instance-specific properties, namely box properties "
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+                                    "type": "inline_equation",
+                                    "content": "(\\mathbf{b},\\| \\mathbf{c}\\|)"
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+                                    "type": "text",
+                                    "content": ", number of points "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", viewing angle "
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+                                    "type": "inline_equation",
+                                    "content": "(\\alpha)"
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+                                    "type": "text",
+                                    "content": ", and point statistics "
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{mean}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{std}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{min}},\\mathcal{X}_{\\mathbf{b}}^{\\mathrm{max}})"
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+                                    "type": "text",
+                                    "content": ". Table 4 shows the impact of each group on the overall performance when used exclusively, indicating a high contribution of box properties and point statistics. A complete list of the combinations can be found in the supplemental material."
+                                }
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+                                    "content": "Contextual Properties Radius: The dependence of the performance on the chosen context radius "
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+                                    "content": " is shown in Figure 5. It can be seen that the performance increases significantly up to "
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+                                            "content": " (SECOND base model / Waymo overall)."
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+                                            "html": "<table><tr><td>Method</td><td>Car</td><td>Pedestrian</td><td>Cyclist</td></tr><tr><td>SECOND (KITTI)</td><td>81.61</td><td>51.14</td><td>66.74</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.04+0.43</td><td>57.11+5.97</td><td>70.99+4.25</td></tr><tr><td>PointPillars (KITTI)</td><td>78.39</td><td>51.41</td><td>62.94</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>78.51+0.12</td><td>55.30+3.89</td><td>67.94+5.00</td></tr><tr><td>Part-A2 (KITTI)</td><td>82.92</td><td>59.73</td><td>70.10</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.94+0.02</td><td>64.21+4.48</td><td>72.16+2.06</td></tr><tr><td>PV-RCNN (KITTI)</td><td>82.86</td><td>53.64</td><td>70.42</td></tr><tr><td>+GACE (SECOND Waymo)</td><td>82.84-0.02</td><td>61.06+7.42</td><td>72.70+2.28</td></tr></table>",
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+                                    "content": "4.3. Generalization and Transferability"
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+                                    "content": "Since we use only the detection attributes and corresponding properties of the underlying point cloud as input, a GACE module trained on base detector A can be directly applied to another base detector B. Furthermore, since all metric features are normalized to their maximum possible value and the statistical parameters (point distribution) are computed from a normalized unit-length box, GACE can be applied not only to a different detector, but also directly to a different detector on a different dataset. Therefore, to demonstrate the general applicability of GACE, we freeze a GACE module trained on detections from a SECOND detector on Waymo, and apply it directly to detections of a SECOND detector on the KITTI dataset [6]. As shown in Table 5, first row, this also leads to considerable performance improvements despite the distribution shift to a different dataset (different LiDAR sensor, different country). Even more remarkably, significant performance gains are also obtained when the same GACE module is applied even to a different base detector, e.g. +7.42AP for PV-RCNN on pedestrians while achieving the same performance for cars. The results demonstrate the excellent generalization capability of GACE and the general validity of the geometric information regardless of the dataset."
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+                                    "content": "In Table 6 we show the runtime analysis of GACE for a "
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+                                    "content": " field-of-view Waymo point cloud using a single NVIDIA® GeForce® RTX 3090 GPU. The computationally most intensive part is the feature extraction, especially ex"
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+                                            "content": "Table 5. Model Transfer: Applying a GACE module trained on SECOND detections on Waymo (without LiDAR elongation, which is not available on KITTI) to different detectors on the KITTI dataset (moderate difficulty / @R40)."
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+                                            "html": "<table><tr><td rowspan=\"3\">Feature Extraction</td><td>Points in Boxes Query</td><td>0.56 ms</td></tr><tr><td>Geometric &amp; Statistical Features</td><td>0.98 ms</td></tr><tr><td>Neighboring Object ID&#x27;s Query</td><td>0.07 ms</td></tr><tr><td rowspan=\"3\">Network Inference</td><td>HI (Instance-specific)</td><td>0.14 ms</td></tr><tr><td>HC (Contextual)</td><td>0.17 ms</td></tr><tr><td>HF (Confidence Estimation)</td><td>0.12 ms</td></tr><tr><td colspan=\"2\">Overall</td><td>2.04 ms</td></tr></table>",
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+                                    "content": "Table 6. GACE runtime analysis per "
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+                                    "content": " field-of-view Waymo point cloud on a single NVIDIA® GeForce® RTX 3090 GPU."
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+                                    "type": "text",
+                                    "content": "tracting the statistical features for all detections. However, this can be solved efficiently via PyTorch einsum. During inference, we first compute the instance-specific plausibility "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " for each detection via "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", which is then used as input to "
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+                                    "type": "text",
+                                    "content": " for the corresponding neighbors. Overall, GACE is capable of processing "
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+                                    "type": "inline_equation",
+                                    "content": "\\sim 490"
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+                                    "type": "text",
+                                    "content": " Waymo point clouds per second with "
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+                                    "type": "text",
+                                    "content": " detections each."
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+                                    "content": "5. Limitations"
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+                                    "content": "While our method has proven effective in improving object detection performance for vulnerable classes such as pedestrians and cyclists, it is worth noting that it may not offer such significant benefits for simpler classes such as vehicles. This is because all detectors typically have few false positives for these easier-to-detect objects. Therefore, there is less room for improvement for this class. However, it is important to consider the context in which our method is applied. Even if the performance improvement is not as large for simpler classes, the overall impact of our method on safety should not be underestimated. In many real-world scenarios, pedestrians and cyclists are particularly vulnerable, and any improvement in their detection can make a significant contribution to safety."
+                                }
+                            ]
+                        }
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+                                    "content": "6. Conclusion"
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+                                    "type": "text",
+                                    "content": "We proposed GACE, a method to better evaluate object hypotheses from black-box LiDAR-based 3D object detectors by explicitly assessing numerous geometric properties inherent in the detections. This enables a better separation between true and false positive detections and thus significantly improves the performance. In a comprehensive analysis, we were able to show the performance of our method for several state-of-the-art detectors and also demonstrate the generalisation capabilities of GACE. This underlines the importance and general validity of the geometric information inherent in 3D detections, which has been largely neglected in the past."
+                                }
+                            ]
+                        }
+                    ],
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+                },
+                {
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+                                    "type": "text",
+                                    "content": "Acknowledgements This work was partially funded by the Austrian FFG project iLIDS4SAM (878713) and by the Christian Doppler Laboratory for Embedded Machine Learning."
+                                }
+                            ]
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+                                    "content": "References"
+                                }
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+                                        }
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+                                        }
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diff --git a/2023/GAFlow_ Incorporating Gaussian Attention into Optical Flow/b25f2d39-f04e-4319-bbbf-98d2b295ade7_content_list.json b/2023/GAFlow_ Incorporating Gaussian Attention into Optical Flow/b25f2d39-f04e-4319-bbbf-98d2b295ade7_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..0c9bc34e2cfa0d2ef85ac78739c5650a6b35b88d
--- /dev/null
+++ b/2023/GAFlow_ Incorporating Gaussian Attention into Optical Flow/b25f2d39-f04e-4319-bbbf-98d2b295ade7_content_list.json	
@@ -0,0 +1,1639 @@
+[
+    {
+        "type": "text",
+        "text": "GAFlow: Incorporating Gaussian Attention into Optical Flow",
+        "text_level": 1,
+        "bbox": [
+            171,
+            130,
+            797,
+            152
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ao Luo $^{1}$ , Fan Yang $^{2}$ , Xin Li $^{2}$ , Lang Nie $^{3}$ , Chunyu Lin $^{3}$ , Haoqiang Fan $^{1}$ , and Shuaicheng Liu $^{4,1*}$ $^{1}$ Megvii Technology Group 42 Beijing Jiaotong University  \n $^{4}$ University of Electronic Science and Technology of China",
+        "bbox": [
+            112,
+            179,
+            864,
+            234
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
+            233,
+            268,
+            313,
+            284
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Optical flow, or the estimation of motion fields from image sequences, is one of the fundamental problems in computer vision. Unlike most pixel-wise tasks that aim at achieving consistent representations of the same category, optical flow raises extra demands for obtaining local discrimination and smoothness, which yet is not fully explored by existing approaches. In this paper, we push Gaussian Attention (GA) into the optical flow models to accentuate local properties during representation learning and enforce the motion affinity during matching. Specifically, we introduce a novel Gaussian-Constrained Layer (GCL) which can be easily plugged into existing Transformer blocks to highlight the local neighborhood that contains fine-grained structural information. Moreover, for reliable motion analysis, we provide a new Gaussian-Guided Attention Module (GGAM) which not only inherits properties from Gaussian distribution to instinctively revolve around the neighbor fields of each point but also is empowered to put the emphasis on contextually related regions during matching. Our fully-equipped model, namely Gaussian Attention Flow network (GAFlow), naturally incorporates a series of novel Gaussian-based modules into the conventional optical flow framework for reliable motion analysis. Extensive experiments on standard optical flow datasets consistently demonstrate the exceptional performance of the proposed approach in terms of both generalization ability evaluation and online benchmark testing. Code is available at https://github.com/LA30/GAFlow.",
+        "bbox": [
+            76,
+            301,
+            473,
+            724
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+            756,
+            209,
+            771
+        ],
+        "page_idx": 0
+    },
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+        "text": "Optical flow aims to establish pixel-wise correspondences across images, playing a crucial role in video understanding. It unifies representation learning and feature matching as a problem of pixel-wise motion inference. Modern optical flow models typically focus on either improving representation learning techniques (e.g., alternative",
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+        "image_caption": [
+            "Figure 1: Visualization of feature discrimination (left) and smoothness constraint (right). For a random point  $P$  in frame  $t$ , our GCL enhances feature discrimination by emphasizing fine-grained structural details. Concurrently, our GGAM effectively captures smoothness constraints, centering on pertinent local regions."
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+        "text": "learning [40, 20, 54] and reinforcement learning [1]) or refining feature similarity measurement methodologies (e.g., 4D correlation volumes [42] or 4D Transformer [16]). Despite these significant advancements, a glaring limitation persists: these models largely neglect the exploration of local structural information. This oversight hinders their performance, particularly in challenging scenarios involving large motions, occlusions, blurring effects, and shifts in appearance. Such situations demand an elevated focus on local discrimination and flow consistency. This brings us to an intriguing inquiry: Is it feasible to architect optical flow models that intrinsically focus on local structural information during both representation learning and feature matching?",
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+        "text": "In response to the aforementioned challenge, we present the Gaussian Attention Flow network (GAFlow), a pioneering framework that leverages Gaussian Attention (GA) to inform both the feature encoder and the matching mod",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "9642",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ule. Central to our approach is a novel attention mechanism equipped with a learnable Gaussian kernel. This mechanism naturally prioritizes the local surroundings of each point, thereby accentuating the importance of local structural information. For the representation learning component, we introduce a novel Gaussian-Constrained Layer (GCL) embedded within the canonical feature encoder. This layer, fortified with a learnable Gaussian kernel, naturally prioritizes the local surroundings of each point, thus accentuating the significance of local structural data. It's worth noting that while the GCL builds upon the pixel-wise modeling typical of the Vision Transformer block, it possesses a sharper focus on local connections, which effectively enhances the feature discrimination for cross-frame matching, as depicted in Fig. 1. Moreover, our GCL is dynamic, comprising learnable parameters that can be finetuned in concert with the encoder.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In optical flow prediction, traditional techniques prioritize the matching function, viewing it as indispensable when paired with distinctive features. These methods incorporate feature-similarity measures and smoothness constraints to optimize results [15, 5, 6]. With the advent of deep learning, the spotlight has largely shifted to feature-similarity [16, 42], often sidelining the crucial smoothness constraint. When considering it, the implicit smoothness loss is primarily employed [51, 26], presuming uniform flow fields — a simplification that overlooks intricate object deformations. While some approaches employ Graph techniques [30] or Transformers [22] to capture global motion, they tend to neglect the inherent locality of motion, potentially introducing inaccuracies. The challenge of leveraging neural networks to model motion relationships remains somewhat uncharted.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "An ideal neural module for motion modeling should have three key properties: i) Neighbourhood priority. The motion of object(s) appears locally in visual scenes, and thus the module should instinctively focus more on the nearest neighbor fields for each pixel. ii) Matching-prior awareness. Previous work [4] shows that matching prior helps in large displacements and avoids over-smoothing; iii) High-order relation centered. Mining high-order relations [30, 22, 29] is essential for dealing with occlusions and lighting changes, as low-level similarities (like color) are often fragile. It would also be advantageous if this module's parameters could be trained in a data-driven manner.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Targeting the above goals, we introduce a novel Gaussian-Guided Attention Module (GGAM) to explicitly model the motion affinities for optical flow. To meet the neighborhood priority requirement, our GGAM is formulated as Gaussian-guided attention that naturally emphasizes the neighboring fields of each point. Second, unlike conventional Non-Local operation [44], our GGAM is built across the context feature map and embedded correlation",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "(cost) volume for more comprehensive relation modeling. Specifically, for capturing the matching-prior knowledge, the 4D correlation volumes [42] are mapped to be the amplitudes and offsets. The amplitude for each position is set to the Gaussian attention for scaling its amplitude value and the offsets are encoded by the Gaussian attention via the warping operation. It enables free-form deformation of the Gaussian attention and adaptive attention for handling the large displacement of objects. For the last requirement, we draw inspiration from self-attention operations, and map the context feature to the query and key features for modeling the appearance self-similarities. All these operations are fully differentiable in our GGAM.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our fully-equipped model, called Gaussian Attention Flow network (GAFlow), unites GCL and GGAM to conduct motion analysis by considering both feature similarities and motion affinities. It achieves the top performance on both Sintel and KITTI benchmarks with limited extra computational cost. Overall, the main contributions of this paper are: 1) We introduce a novel approach to enhance the local properties of underlying representations. Our proposed Gaussian-Constrained Layer (GCL) can work complementarily with the standard feature encoder to build more discriminative features for optical flow. 2) We analyze three important properties for motion affinity modeling, leading to a novel Gaussian-Guided Attention Module (GGAM). For the first time, we show that it is feasible to capture the local relations by learning the Gaussian attention and refining the motion fields for a more reliable optical flow estimation. 3) We unite our GCL and GGAM into the contemporary optical flow architecture, making the model stronger at highlighting local structural information. Our Gaussian Attention Flow networks set new records on a variety of benchmarks, e.g., Sintel (clean and final) and KITTI datasets, and outperform existing optical flow models by a relatively large margin.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Optical Flow. In the epoch of deep learning, early optical flow models, such as [2, 46], viewed flow field prediction as a mapping challenge, translating two input frames into corresponding flow fields, predominantly harnessing the potency of data. Subsequent models significantly elevated flow estimation accuracy either by adopting more robust representation learning paradigms [40, 20, 54] or by implementing explicit feature-similarity measurement techniques [50, 43]. With the integration of advanced feature learning and cost-volume filtering modules, unsupervised methods have also witnessed remarkable advancements [31, 27, 25]. A notable development is RAFT [42], which employs a 4D correlation volume and a recurrent strategy for optical flow estimation. Building on its recurrent feature-matching paradigm, a slew of contempor",
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+    {
+        "type": "page_number",
+        "text": "9643",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/ed65cd02f149664235355d72240dcf92ec2474350708d34f3209836bebf3fef4.jpg",
+        "image_caption": [
+            "Figure 2: An overview of the proposed Gaussian Attention Flow network (GAFlow), architecled with recurrent learning at its core. During the decoding process, the residual flows are iteratively refined and accumulated to derive the final flow field. “ $\\times$ ” denotes multiplication. Best viewed in color."
+        ],
+        "image_footnote": [],
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+        "page_idx": 2
+    },
+    {
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+        "img_path": "images/7c036716e95d5a09ab0b055a28bf4359bd3842d488ff6ea96fe3f9a2c949b814.jpg",
+        "image_caption": [
+            "Figure 3: A simple illustration of the Gaussian constraint. \"Q\" represents the query point. The blue circle represents contextual affinity, mirroring the analogous patterns observed in the ground truth flow. Through the Gaussian constraint, we can effectively filter out deceptive relations, as highlighted within the red circle."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "rary models [3, 13, 32, 21, 8] have substantially bolstered the dependability of optical flow predictions. To navigate challenges like occlusions and blur effects, innovative tactics—including joint representation learning [53], feature-driven flow regularization [19], iterative refinement [20, 18], and comprehensive motion analysis [22, 30]—have been employed. Addressing the smoothness constraint, [22]",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "proposed a global motion refinement strategy anchored on attention mechanisms. Meanwhile, [30] captures motion affinities using graph techniques and [29] introduced kernel patch attention (KPA) for the same purpose, though KPA's static kernel window size could potentially curb its efficacy in managing variations in scale and shape.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Self-Attention. Self-attention operations have become instrumental in computer vision for discerning global contexts in images and videos [44, 45, 57]. Notably, non-local attention, exemplified by [57] and [17], is pivotal in visual Transformers [10, 12]. Recent advancements, such as Swin [28] and NAT [14], harness the inductive bias to enhance Transformers by applying attention within local windows. Inspired by these, our paper presents two Gaussian-based attention modules for optical flow.",
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+    {
+        "type": "text",
+        "text": "3. Our Approach",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Motivation. Fig. 3 visually elucidates the core motivation driving our research. It can be observed that the ground truth optical flow field reveals the intricate nature of motion affinities. These affinities are not only deeply intertwined with contextual relationships but also exhibit pronounced local characteristics. Conventional methods often fall short in aligning with the inherent dynamics of the optical flow field. This observation has propelled us to integrate Gaussian attention into the optical flow model, aiming for a marked enhancement in its precision.",
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+    {
+        "type": "text",
+        "text": "3.2. Overview",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our GAFlow encompasses two pivotal sub-modules: representation learning module  $(\\mathbb{R}_{\\beta})$  and feature matching module  $(\\mathbb{F}_{\\gamma})$ , as visualized in Fig. 2. Specifically,  $\\mathbb{R}_{\\beta}$  represents the functions of acquiring the feature maps  $(\\mathbf{f}_1,\\mathbf{f}_2,\\mathbf{f}_c)$ ,",
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+    {
+        "type": "page_number",
+        "text": "9644",
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+    {
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+        "img_path": "images/d6b6f053f7311a2dc7f0760cb881c0e4939ef3106b6af311851563df0b96972c.jpg",
+        "image_caption": [
+            "(a) Non-local Attention"
+        ],
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+    {
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+        "img_path": "images/faff0e6af18e467d7aa151e8e5e349c02edcd112465222a134dd6151732db464.jpg",
+        "image_caption": [
+            "(b) Gaussian Constrained Attention"
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+    },
+    {
+        "type": "image",
+        "img_path": "images/60e8c876a6c800f27e9a9702c815f016918a333320755e416a847a04c5f8825e.jpg",
+        "image_caption": [
+            "(c) Gaussian Guided Attention",
+            "Figure 4: Architecture comparisons. (a) Standard Non-local Attention, (b) Our Gaussian-Constrained Attention tailored for representation enhancement, and (c) Our Gaussian-Guided Attention, designed to model motion affinities using learnable Gaussian attention. Here,  $\\mathbf{X}$  represents the basic/context feature, while  $\\mathbf{Y}$  signifies the motion feature."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "corresponding to the feature encoders combined with the proposed Gaussian-Constrained Layer (GCL).  $\\mathbb{F}_{\\gamma}$  pertains to the recurrent flow decoder, fortified with our bespoke Gaussian-Guided Attention Module (GGAM).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "At their core, these Gaussian-centric modules can be seamlessly integrated into flow models. Their inclusion accentuates local attributes during both the phases of representation learning and feature matching. Subsequent sections further unpack the mechanics of our GCL and GGAM.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3. Gaussian-Constrained Layer",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The pixel-wise matching is susceptible to feature quality; Yet, the appearance changes caused by the motion blur and the illumination variations lower the feature discrimination. To avoid ambiguities, we propose Gaussian-Constrained Layer (GCL) to obtain the fine-grained structural information and locally discriminative representations for feature matching. Our GCL is designed based upon the standard Transformer [10, 28] block (see Fig. 4 (b)). Specifically, given the base feature  $\\mathbf{x}$ , it is formulated as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {x}} = \\operatorname {G C A} (\\mathrm {L N} (\\mathbf {x})) + \\mathbf {x}, \\tag {1} \\\\ \\mathbf {y} = \\operatorname {F F N} (\\operatorname {L N} (\\hat {\\mathbf {x}})) + \\hat {\\mathbf {x}}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{LN}(\\cdot)$  and  $\\mathrm{FFN}(\\cdot)$  denote the general layer normalization and feed-forward network respectively in Transformer block.  $\\mathrm{GCA}(\\cdot)$  indicates Gaussian Constrained Attention, which is the core component in our GCL.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here, we formulate GCA as a task-specific local operation, which not only avoids global misleading context but also reduces the complexity of attention computation. Therefore, it can be formulated as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathrm {Q} _ {i} = L _ {i} ^ {Q} (\\mathbf {x} ^ {\\prime}), \\mathrm {K} _ {i} = L _ {i} ^ {K} (\\mathbf {x} ^ {\\prime}), \\mathrm {V} _ {i} = L _ {i} ^ {V} (\\mathbf {x} ^ {\\prime}), \\\\ h _ {i} = \\mathcal {G} _ {\\mathrm {A}} \\left(\\mathrm {Q} _ {i}, \\bar {\\mathrm {K}} _ {i}, \\bar {\\mathrm {V}} _ {i}\\right), \\tag {2} \\\\ \\mathrm {H} = \\operatorname {C o n c a t} \\left(h _ {1}, h _ {2}, \\dots , h _ {n}\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{x}' = \\mathrm{LN}(\\mathbf{x})$ .  $L_{i}^{Q}(\\cdot), L_{i}^{K}(\\cdot)$ , and  $L_{i}^{V}(\\cdot)$  denote linear",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "projections for the  $i$ -th head.  $\\mathcal{G}_{\\mathrm{A}}(\\cdot)$  is Gaussian attention function, which takes the query feature  $\\mathrm{Q}_i$ , and the regional features of key  $\\bar{\\mathrm{K}}_i$  and value  $\\bar{\\mathrm{V}}_i$  as inputs:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {G} _ {\\mathrm {A}} (\\mathrm {Q}, \\bar {\\mathrm {K}}, \\bar {\\mathrm {V}}) = \\operatorname {S o f t m a x} \\left(\\mathrm {G} _ {l r} \\cdot \\left(\\mathrm {Q} \\bar {\\mathrm {K}} ^ {\\top}\\right) / \\sqrt {d}\\right) \\cdot \\bar {\\mathrm {V}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{G}_{lr}$  means a learnable Gaussian kernel with the shape of  $k\\times k$ . It is initialized as a standard Gaussian distribution and can be updated by adding a learnable amplitude matrix  $\\mathcal{A}$  during model training. In the inference process,  $\\mathrm{G}_{lr}$  works as a constraint mask to reorganize the weights of attentive feature aggregation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Let the neighborhood of a pixel at the point  $p$  be  $\\mathcal{N}(p)$ ; thus the attention on a single pixel can be defined as:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh _ {(p)} = \\operatorname {S o f t m a x} \\left(\\mathrm {G} _ {l r} \\cdot \\left(\\mathrm {Q} _ {(p)} \\bar {\\mathrm {K}}\\right) _ {\\mathcal {N} (p)} ^ {\\intercal} / \\sqrt {d}\\right) \\cdot \\bar {\\mathrm {V}} _ {\\mathcal {N} (p)}. \\tag {4}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Note that the operating range is scalable with the varying region of  $\\mathcal{N}(p)$ . For instance, it can be extended to all pixels (i.e.,  $\\mathcal{N}(p)$  is equivalent to the image size), leading to a global self-attention in a Gaussian-constrained manner.",
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+    {
+        "type": "text",
+        "text": "3.4. Gaussian-Guided Attention Module",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our Idea/Formulation. In image processing, the Gaussian filter is a widely-used operator that provides a linear scale space for smoothing, where the input image is smoothed at a constant rate in all directions [47]. Here, our idea is to apply the spatially variant Gaussian to smooth the motion feature  $\\mathbf{f}_m$ . Formally, it can be given as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\mathrm {F} * \\mathcal {G}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} \\left(p _ {i} - p\\right) \\mathbf {f} _ {m} ^ {i}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            578,
+            779,
+            890,
+            814
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{N}_p$  denotes a square neighborhood, centered at the pixel  $p$ , with the pre-defined kernel size  $k\\times k$ , and  $p_i$  indicates the position  $i$  in 2D grid space within  $\\mathcal{N}_p$ .  $\\mathbf{f}_m^i$  refers to the feature at position  $i$  within  $\\mathbf{f}_m$ , utilized in the calculation.  $\\mathcal{G}(\\cdot)$  is a 2D Gaussian function, which is defined as:",
+        "bbox": [
+            496,
+            824,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9645",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/6fc3f1f91ded73269c752a9df8830c608142c3d6752fa580ec9c5915b03a019c.jpg",
+        "image_caption": [
+            "Reference"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            93,
+            246,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/eb96313ca206fda03bdc3640a3c609c6bde033fd006347d246b2995444d68bcc.jpg",
+        "image_caption": [
+            "GT"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            251,
+            93,
+            405,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/44c77683b503028e4aa22f466fbc74a19d08b0040e232d5fa9fc6cfdf627eecf.jpg",
+        "image_caption": [
+            "RAFT",
+            "Figure 5: Qualitative comparisons with RAFT [42] and GMFlow [49] on some challenging samples, including large motion, occlusion and motion blur, of Sintel test set. The quantitative results are provided by the official website."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            406,
+            93,
+            563,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8df7b2a54ca541dcdc2e143be4ef30c3b91c020d424d6b5d076020ecc0d14847.jpg",
+        "image_caption": [
+            "GMFlow"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            563,
+            93,
+            720,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/786d5c2e0b8f75d5753931cddec8d130f6af427bf50018fd117e9d6864b2a06f.jpg",
+        "image_caption": [
+            "Ours"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            723,
+            93,
+            880,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {G} (x, y) = A \\exp \\left(- \\left(\\frac {(x - x _ {0}) ^ {2}}{2 \\sigma_ {x} ^ {2}} + \\frac {(y - y _ {0}) ^ {2}}{2 \\sigma_ {y} ^ {2}}\\right)\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            114,
+            351,
+            468,
+            388
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $A$  denotes the static amplitude ( $A = 1$  as the default setting) and  $p_0 = (x_0, y_0)$  means the center point.  $(\\sigma_x; \\sigma_y)$  indicate the variances which are set to  $\\sigma_x = \\sigma_y = \\sigma$ , determining the operating range of smoothness. However, directly applying the Gaussian smoothing is sub-optimal for capturing the local properties, as the kernel is rigid (or fixed) and the clutters could be inevitably involved in providing false guidance. Next, we show how to make the Gaussian attention more adaptive and also end-to-end trainable.",
+        "bbox": [
+            75,
+            390,
+            468,
+            526
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Gaussian-Guided Attention with Context (GGAC). To begin with, we incorporate the contextual information, which preserves the fine-grained structural information, into the Gaussian Attention. Specifically, given the context feature  $\\mathbf{f}_c\\in \\mathbb{R}^{c\\times h\\times w}$  and motion feature  $\\mathbf{f}_m\\in \\mathbb{R}^{c\\times h\\times w}$ , we rewrite Eq. (5) as:",
+        "bbox": [
+            75,
+            526,
+            468,
+            617
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\mathrm {F} * \\mathcal {G} _ {\\mathbb {C}}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} _ {\\mathbb {C} (p _ {i} - p)} \\left(\\mathbf {f} _ {c}\\right) \\rho \\left(\\mathbf {f} _ {m}\\right) ^ {i}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            135,
+            625,
+            468,
+            660
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}_{\\mathbb{C}(p_i - p)}(\\cdot)$  is an adaptive kernel function taking the context features in  $\\mathcal{N}_p$  as inputs to obtain the context-preserving kernel.  $\\rho (\\cdot)$  is a linear operation for producing the embedded motion feature. We formulate the context-preserving kernel function as:",
+        "bbox": [
+            75,
+            667,
+            468,
+            744
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {G} _ {\\mathrm {C} \\left(p _ {i} - p\\right)} \\left(\\mathbf {f} _ {c}\\right) = \\mathcal {G} ^ {\\prime} \\left(p _ {i} - p\\right) \\mathcal {F} \\left(\\mathbf {f} _ {c}\\right), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            161,
+            753,
+            468,
+            771
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{k \\times k \\times h \\times w}$  denotes the expanded Gaussian kernel in the spatial dimension, which is prepared for generating the data-dependent kernel matrices with the shape of  $k \\times k$  based on the corresponding weights on each position in  $h \\times w$ , and  $\\mathcal{F}(\\cdot)$  is the dynamic weight function for mining the guidance prior on the context feature  $\\mathbf{f}_c$ .",
+        "bbox": [
+            75,
+            777,
+            468,
+            869
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Rather than simply utilizing a learnable matrix as in convolution kernels, we follow [22] to apply the embedded",
+        "bbox": [
+            76,
+            869,
+            468,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Gaussian with normalization [44] on the context feature  $\\mathbf{f}_c$  to produce the attention map. To match the dimension of the pre-defined Gaussian kernel  $\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{K \\times N}$ , where  $N = h \\times w$ , and  $K = k \\times k$  denoting the spatial dimension of kernel size, a naive solution is to discard the redundant information in  $\\mathcal{F}(\\mathbf{f}_c)$ . Here, we present a kernel-based context-preserving attention operation, which takes the asymmetric query and key feature maps in the spatial dimension as inputs. In detail, given the embedded context features  $\\theta(\\mathbf{f}_c) \\in \\mathbb{R}^{c \\times h \\times w}$ , we employ an unfolding operator (e.g., torch.nn.Unfold) to get  $\\mathrm{U}(\\theta(\\mathbf{f}_c))$ , thus the dimension is transformed from  $c \\times N$  to  $c \\times N \\times K$ . Then we measure the similarities between all pairs within the kernel region as:",
+        "bbox": [
+            496,
+            340,
+            890,
+            539
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} \\left(\\mathbf {f} _ {c}\\right) = \\frac {\\exp \\left(\\mathrm {U} \\left(\\theta \\left(\\mathbf {f} _ {c}\\right)\\right) _ {l} ^ {T} \\phi \\left(\\mathbf {f} _ {c}\\right) _ {j} / \\sqrt {c}\\right)}{\\sum_ {\\forall j} \\exp \\left(\\mathrm {U} \\left(\\theta \\left(\\mathbf {f} _ {c}\\right)\\right) _ {l} ^ {T} \\phi \\left(\\mathbf {f} _ {c}\\right) _ {j} / \\sqrt {c}\\right)}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            549,
+            551,
+            890,
+            592
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $l \\in K$  and  $j \\in c$ , and the size of  $\\mathcal{F}(\\mathbf{f}_c)$  is  $K \\times N$ .  $\\theta(\\cdot)$  and  $\\phi(\\cdot)$  indicates linear projections for channel-wise feature aggregation [22].",
+        "bbox": [
+            498,
+            599,
+            890,
+            645
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Gaussian-Guided Attention with Deformation (GGAD). While Gaussian attention with context effectively addresses the problem of flow field over-smoothing caused by the data-agnostic Gaussian kernel, it still faces a limitation due to the rigid operating region of the Gaussian kernel. This constraint hinders the smoothness performance for motion feature refinement. To mitigate this issue, we take a further step to optimize the operating region of the Gaussian kernel by learning the deformable kernels in a data-driven manner, as shown in Fig. 4 (c). To avoid the static amplitude  $A$  of the Gaussian function, we design a dynamic amplitude operator based on the cross-frame matching features. In practice, similar to Eq. (7), our Gaussian-guided attention can be further formulated as:",
+        "bbox": [
+            496,
+            646,
+            890,
+            856
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(\\mathrm {F} * \\mathcal {G} _ {\\mathbb {D}}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} _ {\\mathbb {D} \\left(p _ {i} - p\\right)} \\left(\\mathbf {f} _ {c}, \\mathbf {f} _ {m}\\right) \\rho \\left(\\mathbf {f} _ {m}\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            534,
+            867,
+            890,
+            904
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "9646",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/7bd2de6459f571e7659fb48f96f2bfe1de5966ab5734a0cba6691d6dab83686a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Training</td><td rowspan=\"2\">Method</td><td rowspan=\"2\">Reference</td><td colspan=\"2\">Sintel (Val)</td><td colspan=\"2\">KITTI-15 (Val)</td><td colspan=\"2\">Sintel (Test)</td><td>KITTI-15 (Test)</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td><td>Clean</td><td>Final</td><td>F1-all</td></tr><tr><td rowspan=\"14\">Val: C + T / Test: +S+K+H</td><td>RAFT [42]</td><td>ECCV-20</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>1.61</td><td>2.86</td><td>5.10</td></tr><tr><td>SCV [23]</td><td>CVPR-21</td><td>1.29</td><td>2.95</td><td>6.80</td><td>19.3</td><td>1.77</td><td>3.88</td><td>6.17</td></tr><tr><td>GMA [22]</td><td>ICCV-21</td><td>1.30</td><td>2.74</td><td>4.69</td><td>17.1</td><td>1.39</td><td>2.47</td><td>5.15</td></tr><tr><td>SeparableFlow[52]</td><td>ICCV-21</td><td>1.30</td><td>2.59</td><td>4.60</td><td>15.9</td><td>1.50</td><td>2.67</td><td>4.64</td></tr><tr><td>Flow1D [48]</td><td>ICCV-21</td><td>1.98</td><td>3.27</td><td>6.69</td><td>23.0</td><td>2.24</td><td>3.81</td><td>6.27</td></tr><tr><td>AGFlow [30]</td><td>AAAI-22</td><td>1.31</td><td>2.69</td><td>4.82</td><td>17.0</td><td>1.43</td><td>2.47</td><td>4.89</td></tr><tr><td>GMFlowNet [55]</td><td>CVPR-22</td><td>1.14</td><td>2.71</td><td>4.24</td><td>15.4</td><td>1.39</td><td>2.65</td><td>4.79</td></tr><tr><td>GMFlow [49]</td><td>CVPR-22</td><td>1.08</td><td>2.48</td><td>7.77</td><td>23.4</td><td>1.74</td><td>2.90</td><td>9.32</td></tr><tr><td>CRAFT [37]</td><td>CVPR-22</td><td>1.27</td><td>2.79</td><td>4.88</td><td>17.5</td><td>1.45</td><td>2.42</td><td>4.79</td></tr><tr><td>DIP [56]</td><td>CVPR-22</td><td>1.30</td><td>2.82</td><td>4.29</td><td>13.7</td><td>1.44</td><td>2.83</td><td>4.21</td></tr><tr><td>KPA-Flow [30]</td><td>CVPR-22</td><td>1.28</td><td>2.68</td><td>4.46</td><td>15.9</td><td>1.35</td><td>2.36</td><td>4.60</td></tr><tr><td>OCTC [21]</td><td>CVPR-22</td><td>1.31</td><td>2.67</td><td>4.72</td><td>16.3</td><td>1.41</td><td>2.57</td><td>4.33</td></tr><tr><td>SKFlow [41]</td><td>NeurIPS-22</td><td>1.22</td><td>2.46</td><td>4.27</td><td>15.5</td><td>1.28</td><td>2.27</td><td>4.84</td></tr><tr><td>GAFlow (ours)</td><td></td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>1.21</td><td>2.24</td><td>4.52</td></tr><tr><td rowspan=\"2\">A / +TSKHV</td><td>RAFT-A [39]</td><td>CVPR-21</td><td>1.95</td><td>2.57</td><td>4.23</td><td>-</td><td>2.01</td><td>3.14</td><td>4.78</td></tr><tr><td>RAFT-it [38]</td><td>ECCV-22</td><td>1.74</td><td>2.41</td><td>4.18</td><td>13.4</td><td>1.55</td><td>2.90</td><td>4.31</td></tr><tr><td rowspan=\"2\">I+CT / +SKH</td><td>FlowFormer [16]</td><td>ECCV-22</td><td>1.01</td><td>2.40</td><td>4.09</td><td>14.7</td><td>1.16</td><td>2.09</td><td>4.68</td></tr><tr><td>GAFlow-FF (ours)</td><td></td><td>0.95</td><td>2.34</td><td>3.92</td><td>13.9</td><td>1.15</td><td>2.05</td><td>4.42</td></tr></table>",
+        "bbox": [
+            84,
+            88,
+            885,
+            383
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Quantitative comparison with state-of-the-art models on standard benchmarks for cross-dataset evaluation and online testing. “C+T” indicates the models trained on FlyingChairs and FlyingThings for generalization ability evaluation. “+S+K+H” denotes more training data involved from Sintel, KITTI-2015, and HD1K. “A” indicates the models are trained on AutoFlow [39] dataset for Val set evaluation. “V” denotes VIPER [36] dataset. “T” means the encoders are pre-trained on ImageNet [9]. The best and second-best results are marked in bold and underline, respectively.",
+        "bbox": [
+            75,
+            393,
+            890,
+            470
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}_{\\mathbb{D}(p_i - p)}(\\cdot)$  is the deformable Gaussian kernel function that is used to produce the more flexible Gaussian attention for adaptively capturing the relevant information and avoiding rigid kernel boundary in a data-dependent manner. Specifically, the deformable Gaussian kernel is given by:",
+        "bbox": [
+            75,
+            496,
+            468,
+            571
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {G} _ {\\mathbb {D} (p _ {i} - p)} \\left(\\mathbf {f} _ {c}, \\mathbf {f} _ {m}\\right) = \\mathcal {A} \\left(\\mathbf {f} _ {m}\\right) \\mathcal {D} _ {(p _ {i} - p)} \\left(\\mathbf {f} _ {m}\\right) \\mathcal {F} \\left(\\mathbf {f} _ {c}\\right), \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            106,
+            580,
+            467,
+            599
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{A}(\\cdot)$  indicates the amplitude operator taking the motion feature  $\\mathbf{f}_{\\mathbf{m}}$  to produce adaptive amplitudes,  $\\mathcal{F}(\\mathbf{f}_c)$  is the kernel-based context-preserving attention matrix as in Eq. (9), and  $\\mathcal{D}_{(p_i - p)}(\\cdot)$  denotes the deformable Gaussian operator, which can be formulated as:",
+        "bbox": [
+            75,
+            604,
+            468,
+            679
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {(p _ {i} - p)} \\left(\\mathbf {f} _ {m}\\right) = \\mathcal {W} \\left(\\mathcal {G} ^ {\\prime} (p _ {i} - p), \\mathcal {O} \\left(\\mathbf {f} _ {m}\\right)\\right), \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            688,
+            468,
+            705
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{k \\times k \\times h \\times w}$  indicates the spatially expanded Gaussian kernel as in Eq. (8), and  $\\mathcal{O}(\\mathbf{f}_m)$  denotes the offset maps predicted from the motion feature.  $\\mathcal{W}(\\cdot)$  is the warp function taking the obtained offsets as inputs and operating on the Gaussian kernel.",
+        "bbox": [
+            75,
+            712,
+            468,
+            787
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Another important component in the deformable Gaussian kernel (Eq. (11)) is the amplitude operator  $\\mathcal{A}(\\cdot)$ , which is given by:",
+        "bbox": [
+            75,
+            789,
+            468,
+            833
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {A} \\left(\\mathbf {f} _ {m}\\right) = 1 + \\vartheta \\left(\\mathbf {f} _ {m}\\right) \\lambda , \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            834,
+            467,
+            851
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  indicates a learnable parameter to constrain the fluctuation of the generated amplitude, and  $\\vartheta(\\cdot)$  is a linear function. Finally, similar to the expanding strategy in",
+        "bbox": [
+            75,
+            854,
+            468,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the deformable Gaussian operator, the learned amplitude  $\\mathcal{A}(\\mathbf{f}_m)$  can be easily transformed to operate on the Gaussian kernel  $\\mathcal{G}'(p_i - p)$  for generating a more flexible one.",
+        "bbox": [
+            498,
+            496,
+            890,
+            544
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experimental Results",
+        "text_level": 1,
+        "bbox": [
+            498,
+            560,
+            705,
+            578
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            500,
+            587,
+            715,
+            603
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For fair comparison with existing methods [22, 37, 29], we first plug 1 GCL and 1 GGAM into RAFT [42] to build a small model, i.e., GAFlow-S. Specifically, Gaussian-Constrained Layer (GCL) is appended to the motion encoder with  $\\sigma = 9$ . Gaussian-Guided Attention Module (GGAM) performs feature smoothing on context and motion features, where we set sigma to 20 and 15 for Sintel and KITTI, respectively. Besides, to further explore the potential of our approach, we also employ a stronger baseline with POLA [55] modules and SKBlocks [41], which is regarded as the default model of GAFlow. Furthermore, we enhance the model's capabilities by integrating the proposed module into FlowFormer [16], resulting in a robust and advanced model termed GAFlow-FF.",
+        "bbox": [
+            496,
+            611,
+            890,
+            821
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "All experiments are conducted based on PyTorch toolbox. During training our GAFlow model, we follow RAFT to set the batch sizes to 6 and adopt AdamW optimizer with one-cycle learning rate policy [42]. Similar to previous works [42, 22, 30], the synthetic datasets are also involved",
+        "bbox": [
+            496,
+            824,
+            890,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "9647",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/be22d090b1f9a65da7586b8ca8f2df4a7ec2610281d85b29ea7ee79ed5767900.jpg",
+        "image_caption": [
+            "(a) Reference"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
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+        "img_path": "images/aa01ee786dddc31a82bbdef9c2ded12d73dbaced06dc769de504653c9115757e.jpg",
+        "image_caption": [
+            "(c) Flow of GGAD (ours)"
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+        "image_caption": [
+            "(e) Flow of GMA"
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+        "img_path": "images/ab48a96144bd9b989ff8382fbdd9a4851ac1ae16f0ef3be9986b535c2aa990ab.jpg",
+        "image_caption": [
+            "(b) GGAC (ours)"
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+    },
+    {
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+        "img_path": "images/d46930a9c231877111598407569039b1914df62d99f95e7370748280d78b3d7a.jpg",
+        "image_caption": [
+            "(d) GGAD (ours)",
+            "Figure 6: A challenging sample from the Sintel final pass. The second row provides attention maps of our GGAC, GGAD and GMA [22], respectively. “P” indicates the query point to obtain attention maps."
+        ],
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+        "img_path": "images/a386f0ba9caf6aacba9a9955f84a314b4a92747d860ae2effb33324579a3233d.jpg",
+        "image_caption": [
+            "(f) GMA"
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+    {
+        "type": "text",
+        "text": "in model pre-training. The pre-training iterations on FlyingChairs [11] and FlyingThings [33] are set to 120k and 160k, respectively. Then the fine-tuning for Sintel online evaluation is conducted on the combined training data of Sintel [7], KITTI-2015 [34], and HD1K [24] for 160k iterations. Finally, the trained model requires another 50k iterations of finetuning on data of KITTI-2015 [34] before KITTI testing. We use only a single GPU and set the batch size to 1 for evaluation and online testing.",
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+    {
+        "type": "text",
+        "text": "4.2. Comparison with State-of-the-Arts",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Results on Sintel. We first compare the proposed approach with state-of-the-art methods for generalization evaluation on Sintel. As shown in Val sets of Tab. 1, our approach consistently achieves the best performance on all metrics. Specifically, GAFlow achieves the best EPE scores at 1.02 and 2.45 on the \"C + T\" setting. Besides, GAFlow-FF improves the SOTA performance to 0.95 and 2.34 in EPE on Sintel clean and final passes, respectively. For online testing, we follow prior works [22, 29, 37] to utilize the warm-start strategy [42]. GAFlow achieves the best EPE scores at 1.21 and 2.24 on the standard training setting. Moreover, GAFlow-FF sets a new record at 1.15 and 2.05 in EPE, outperforming recent works by a relatively large margin.",
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+    {
+        "type": "text",
+        "text": "We compare the proposed GAFlow with the well-known methods RAFT [42] and GMFlow [49] on Sintel test set, and some qualitative comparisons are illustrated in Fig. 5. The results demonstrate that the proposed approach can effectively leverage the local structural information and high-order relations to resolve the ambiguities in motion learning, leading to a more robust and flexible model for handling the challenges in optical flow estimation.",
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+    {
+        "type": "text",
+        "text": "Results on KITTI. As shown in Tab. 1, GFlow achieves 3.98 in EPE and  $15.0\\%$  in F1-all on the KITTI Val set, which is comparable with the SOTA model FlowFormer yet with less computational overhead. Moreover, GFlow-FF further boosts the scores to 3.92 and  $13.9\\%$ . For online testing, our models achieve the top-ranked performances at  $4.52\\%$  and  $4.42\\%$  in F1-score.",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/58dbeb61f2778db702ca1b9d54002f1548a7bb85d15815fe8af8d94e61a99346.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Sintel</td><td>Type</td><td>RAFT[42] (EPE)</td><td>GMA[22] (EPE)</td><td>KPA[29] (EPE)</td><td>GAFlow-S (EPE)</td></tr><tr><td rowspan=\"4\">Clean (train)</td><td>s0-10</td><td>0.32</td><td>0.27</td><td>0.26</td><td>0.24</td></tr><tr><td>s10-40</td><td>1.55</td><td>1.35</td><td>1.38</td><td>1.29</td></tr><tr><td>s40+</td><td>8.83</td><td>8.55</td><td>8.43</td><td>7.92</td></tr><tr><td>All</td><td>1.41</td><td>1.31</td><td>1.28</td><td>1.21</td></tr><tr><td rowspan=\"4\">Final (train)</td><td>s0-10</td><td>0.52</td><td>0.54</td><td>0.54</td><td>0.51</td></tr><tr><td>s10-40</td><td>3.00</td><td>3.07</td><td>3.02</td><td>2.83</td></tr><tr><td>s40+</td><td>17.45</td><td>17.57</td><td>17.34</td><td>17.02</td></tr><tr><td>All</td><td>2.69</td><td>2.74</td><td>2.68</td><td>2.56</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Quantitative results on different displacements. All methods are trained on “C+T” and evaluated on Sintel for fair comparison. s0-10, s10-40 and s40+ denote the ground truth flow value belonging to 0-10, 10-40 and 40+ pixels [7], respectively.",
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+    {
+        "type": "text",
+        "text": "4.3. Ablation Analysis",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Comparison with GMA. GMA [22] presents a global strategy for handling occlusion in flow estimation. As shown in Tab. 2, our GAflow-S achieves better performance on all metrics. This is because the global attention on context features involves too much misleading information for motion guidance, which contains long-range similarities in appearance but is improper for motion refinement (see Fig. 6 (f)). In contrast, our approach effectively takes the local property of regional context affinities into consideration, and leverages the extracted high-order relations with the flexible operating range to better infer the flow fields.",
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+    {
+        "type": "text",
+        "text": "Comparison with KPA. The recent work KPA-Flow [29] shares a similar insight with our approach, leveraging local attention to avoid global misleading information. However, its intrinsic defects in formulation inevitably hinder the effect of motion refinement. First, the zero padding patches (out of the image) lead to obvious deviation for similarity measurement. Second, the neighboring pixels could be partitioned into distinct pre-defined (fixed) patch and kernel windows, leading to abrupt shifts in operating regions. In contrast, our approach enables a flexible constraint and freeform operating regions in a learnable manner, ensuring the proper and stable guidance pattern. Moreover, we provide quantitative comparisons in Tab. 2, where our approach achieves better performance on all metrics.",
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+    {
+        "type": "text",
+        "text": "Ablation for Feature Enhancement. In Tab. 3 (# 1), we first compare the proposed GCL with the widely recognized Transformer blocks [28, 55, 35], which have been extensively demonstrated to be effective for feature extraction. Swin Transformer [28] requires at least two blocks to perform the window shifting strategy, consuming more computation overhead. For other methods, only one block is applied for fair comparison. POLA [55] has been shown to be an effective local attention-based approach for fea",
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+    {
+        "type": "page_number",
+        "text": "9648",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/b7bec3970716e086bd3772345fbabee60584ca3cf5d7cc1a0bc94a502f2971bd.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Sintel (Val)</td><td colspan=\"2\">KITTI-15 (Val)</td><td rowspan=\"2\">Param.</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td></tr><tr><td>RAFT [42]</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>5.3M</td></tr><tr><td colspan=\"6\"># 1: Feature Enhancement</td></tr><tr><td>Swin Trans. [28]</td><td>1.45</td><td>2.75</td><td>5.16</td><td>17.3</td><td>7.3M</td></tr><tr><td>POLA×1 [55]</td><td>1.42</td><td>2.68</td><td>4.91</td><td>16.9</td><td>6.5M</td></tr><tr><td>cosFormer [35]</td><td>1.29</td><td>2.82</td><td>4.95</td><td>17.3</td><td>6.7M</td></tr><tr><td>L.Kernel</td><td>1.42</td><td>2.76</td><td>4.69</td><td>16.6</td><td>6.5M</td></tr><tr><td>GCL</td><td>1.33</td><td>2.67</td><td>4.61</td><td>16.5</td><td>6.5M</td></tr><tr><td colspan=\"6\"># 2: Stronger Encoder</td></tr><tr><td>POLAs [55]</td><td>1.18</td><td>2.63</td><td>4.52</td><td>16.6</td><td>10.0M</td></tr><tr><td>No</td><td>1.33</td><td>2.67</td><td>4.61</td><td>16.5</td><td>6.5M</td></tr><tr><td colspan=\"6\"># 3: Smoothing Pattern</td></tr><tr><td>+ GGAC</td><td>1.13</td><td>2.62</td><td>4.33</td><td>15.8</td><td>10.1M</td></tr><tr><td>+ GGAD</td><td>1.08</td><td>2.56</td><td>4.26</td><td>15.6</td><td>10.1M</td></tr><tr><td colspan=\"6\"># 4: Compatibility with SOTA modules</td></tr><tr><td>Refine.Sp4 [49]</td><td>1.03</td><td>2.45</td><td>4.10</td><td>14.6</td><td>12.5M</td></tr><tr><td>SKBlocks [41]</td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>10.4M</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ture extraction with 6 or 12 stacked blocks (requiring extra  $4.35 / 8.7\\mathrm{M}$  parameters). As shown in the table, using one block  $(\\mathrm{POLA}_{\\times 1})$  significantly weaken the power. The advanced linear Transformer cosFormer [35] exhibits a lower EPE score on Sintel Clean, whereas our GCL performs better on other metrics. Besides, we conduct an extra ablation for using a learnable kernel without Gaussian (L.Kernel). As can be seen, our GCL outperforms L.Kernel across all metrics. Particularly on the challenging Sintel, without a Gaussian constraint, performance declines significantly due to the uncontrolled misleading similarities at the kernel border. All experiments illustrate that, requiring similar computational overhead, the proposed GCL surpasses other methods by a relatively large margin.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Ablation for Stronger Encoder. The smoothness constraint for flow estimation can be naturally regarded as a complementary component to the feature matching process, and benefits from stronger encoders for feature extraction. Thus, to further explore the potential of our approach, we follow prior work [55] to employ a stronger motion encoder with the standard POLA blocks, which largely boosts the performance on Sintel clean pass, as in Tab. 3 (# 2). Inspired by GMFlowNet [55], we build two types of encoding modules for separately handling Sintel and KITTI datasets.",
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+    },
+    {
+        "type": "text",
+        "text": "Ablation for Smoothing Pattern. The proposed GGAC is capable of producing flexible weight matrices for motion feature smoothing, which effectively tackles the issue of flow field over-smoothing caused by the data-agnostic Gaussian kernel. However, the issues of rigid operating re",
+        "bbox": [
+            75,
+            824,
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/88fe3ffd89ee47da8c3ad01f2e72e792885261da02c97fbf86995e02fa5dac8b.jpg",
+        "table_caption": [
+            "Table 3: Ablation experiments. L.Kernel indicates the learnable kernel without Gaussian. Settings as default are underlined. Refer to Sec. 4.3 for detailed comparisons."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">KITTI-15 (Val)</td><td rowspan=\"2\">Param.</td><td rowspan=\"2\">Time (s)</td></tr><tr><td>EPE</td><td>F1-all</td></tr><tr><td>GMFlowNet [55]</td><td>4.24</td><td>15.4</td><td>9.3M</td><td>0.32</td></tr><tr><td>FlowFormer [16]</td><td>4.09</td><td>14.7</td><td>18.2M</td><td>1.77</td></tr><tr><td>GAFlow (ours)</td><td>3.98</td><td>15.0</td><td>10.4M</td><td>0.48</td></tr><tr><td>GAFlow-FF (ours)</td><td>3.92</td><td>13.9</td><td>18.2M</td><td>1.85</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Quantitative comparisons for computational complexity. The input size is  $376 \\times 1248$  as in KITTI dataset.",
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+    {
+        "type": "text",
+        "text": "gion and static amplitude still affect the motion refinement (see Fig. 6 (b) and Tab. 3 (# 3)). Thus we further improve the approach with the spatially deformable kernel with the dynamic amplitude in a data-driven manner, i.e., GGAD, which boosts the performance by around  $3\\%$ .",
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+    {
+        "type": "text",
+        "text": "Ablation for Compatibility with SOTA modules. In Tab. 3 (# 4), similar to prior work [49], we further perform flow refinement with the flow decoder on 1/4 features, termed Refine.Sp4, which helps to boost the performance on both Sintel and KITTI datasets. Moreover, we follow SKFlow [41] to employ SKBlocks in the motion encoding and state updating modules of the flow decoder. The ablation indicates that the GGAD module is compatible with SKBlocks, and the integration of the decoder leads to improved performance across all metrics, while introducing minimal additional parameters  $(10.1\\rightarrow 10.4\\mathrm{M})$",
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+    },
+    {
+        "type": "text",
+        "text": "Runtime Comparison. The comparisons of KITTI evaluation results, parameters and runtime are presented in Tab. 4. Although FlowFormer [16] uses ImageNet for encoder pretraining, our GAFlow achieves a competitive performance (even better in online testing, see Tab. 1) while consuming fewer parameters by  $7.8\\mathrm{M}$  and reducing the inference time by  $72.9\\%$ . Moreover, built on the previous SOTA model FlowFormer, our GAFlow-FF largely reduces the error by  $4.8\\%$  with negligible computational complexity.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we introduce a novel Gaussian Attention Flow network (GAFlow) to explicitly highlight local properties during representation learning and enforce the motion affinity during matching. We deliver two Gaussian-based modules, i.e. Gaussian-Constrained Layer (GCL) and Gaussian-Guided Attention Module (GGAM), which works well with existing flow architectures and can greatly enhance the reliability of optical flow estimation. Extensive quantitative and qualitative comparisons performed on commonly-used datasets demonstrate that our method significantly outperforms the current alternatives.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work is supported by Sichuan Science and Technology Program of China under grant No.2023NSFSC0462.",
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+    {
+        "type": "page_number",
+        "text": "9649",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
+            80,
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+            104
+        ],
+        "page_idx": 8
+    },
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+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            900
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9650",
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+            482,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "Zhong. cosformer: Rethinking softmax in attention. In ICLR, 2022.",
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+            "[50] Gengshan Yang and D. Ramanan. Volumetric correspondence networks for optical flow. In NeurIPS, 2019.",
+            "[51] Jason J Yu, Adam W Harley, and Konstantinos G Derpanis. Back to basics: Unsupervised learning of optical flow via brightness constancy and motion smoothness. In ECCV, 2016.",
+            "[52] Feihu Zhang, Oliver J Woodford, Victor Adrian Prisacariu, and Philip HS Torr. Separable flow: Learning motion cost volumes for optical flow estimation. In ICCV, 2021.",
+            "[53] Chengqian Zhao, Cheng Feng, Dengwang Li, and Shuo Li. Of-msrn: optical flow-auxiliary multi-task regression network for direct quantitative measurement, segmentation and motion estimation. In AAAI, 2020."
+        ],
+        "bbox": [
+            78,
+            90,
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+        ],
+        "page_idx": 9
+    },
+    {
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+        "list_items": [
+            "[54] Shengyu Zhao, Yilun Sheng, Yue Dong, E. Chang, and Yan Xu. Maskflownet: Asymmetric feature matching with learnable occlusion mask. In CVPR, 2020.",
+            "[55] Shiyu Zhao, Long Zhao, Zhixing Zhang, Enyu Zhou, and Dimitris Metaxas. Global matching with overlapping attention for optical flow estimation. In CVPR, 2022.",
+            "[56] Zihua Zheng, Ni Nie, Zhi Ling, Pengfei Xiong, Jiangyu Liu, Hao Wang, and Jiankun Li. Dip: Deep inverse patchmatch for high-resolution optical flow. In CVPR, 2022.",
+            "[57] Zhen Zhu, Mengde Xu, Song Bai, Tengteng Huang, and Xiang Bai. Asymmetric non-local neural networks for semantic segmentation. In CVPR, 2019."
+        ],
+        "bbox": [
+            501,
+            92,
+            890,
+            261
+        ],
+        "page_idx": 9
+    },
+    {
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+    }
+]
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diff --git a/2023/GAFlow_ Incorporating Gaussian Attention into Optical Flow/b25f2d39-f04e-4319-bbbf-98d2b295ade7_model.json b/2023/GAFlow_ Incorporating Gaussian Attention into Optical Flow/b25f2d39-f04e-4319-bbbf-98d2b295ade7_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ed6fcfe38b9b99bde6d14b4a1c75d67f6b4717c
--- /dev/null
+++ b/2023/GAFlow_ Incorporating Gaussian Attention into Optical Flow/b25f2d39-f04e-4319-bbbf-98d2b295ade7_model.json	
@@ -0,0 +1,2343 @@
+[
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.107,
+                0.003,
+                0.182,
+                0.043
+            ],
+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.239,
+                0.001,
+                0.808,
+                0.047
+            ],
+            "angle": 0,
+            "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.172,
+                0.131,
+                0.798,
+                0.154
+            ],
+            "angle": 0,
+            "content": "GAFlow: Incorporating Gaussian Attention into Optical Flow"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.113,
+                0.18,
+                0.865,
+                0.236
+            ],
+            "angle": 0,
+            "content": "Ao Luo\\(^{1}\\), Fan Yang\\(^{2}\\), Xin Li\\(^{2}\\), Lang Nie\\(^{3}\\), Chunyu Lin\\(^{3}\\), Haoqiang Fan\\(^{1}\\), and Shuaicheng Liu\\(^{4,1*}\\)  \n\\(^{1}\\)Megvii Technology Group 42 Beijing Jiaotong University  \n\\(^{4}\\)University of Electronic Science and Technology of China"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.269,
+                0.314,
+                0.285
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.302,
+                0.474,
+                0.725
+            ],
+            "angle": 0,
+            "content": "Optical flow, or the estimation of motion fields from image sequences, is one of the fundamental problems in computer vision. Unlike most pixel-wise tasks that aim at achieving consistent representations of the same category, optical flow raises extra demands for obtaining local discrimination and smoothness, which yet is not fully explored by existing approaches. In this paper, we push Gaussian Attention (GA) into the optical flow models to accentuate local properties during representation learning and enforce the motion affinity during matching. Specifically, we introduce a novel Gaussian-Constrained Layer (GCL) which can be easily plugged into existing Transformer blocks to highlight the local neighborhood that contains fine-grained structural information. Moreover, for reliable motion analysis, we provide a new Gaussian-Guided Attention Module (GGAM) which not only inherits properties from Gaussian distribution to instinctively revolve around the neighbor fields of each point but also is empowered to put the emphasis on contextually related regions during matching. Our fully-equipped model, namely Gaussian Attention Flow network (GAFlow), naturally incorporates a series of novel Gaussian-based modules into the conventional optical flow framework for reliable motion analysis. Extensive experiments on standard optical flow datasets consistently demonstrate the exceptional performance of the proposed approach in terms of both generalization ability evaluation and online benchmark testing. Code is available at https://github.com/LA30/GAFlow."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.757,
+                0.21,
+                0.772
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.783,
+                0.47,
+                0.875
+            ],
+            "angle": 0,
+            "content": "Optical flow aims to establish pixel-wise correspondences across images, playing a crucial role in video understanding. It unifies representation learning and feature matching as a problem of pixel-wise motion inference. Modern optical flow models typically focus on either improving representation learning techniques (e.g., alternative"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.511,
+                0.271,
+                0.695,
+                0.334
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.271,
+                0.884,
+                0.334
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.695,
+                0.472
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
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+                0.884,
+                0.472
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.497,
+                0.895,
+                0.59
+            ],
+            "angle": 0,
+            "content": "Figure 1: Visualization of feature discrimination (left) and smoothness constraint (right). For a random point \\( P \\) in frame \\( t \\), our GCL enhances feature discrimination by emphasizing fine-grained structural details. Concurrently, our GGAM effectively captures smoothness constraints, centering on pertinent local regions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.624,
+                0.895,
+                0.837
+            ],
+            "angle": 0,
+            "content": "learning [40, 20, 54] and reinforcement learning [1]) or refining feature similarity measurement methodologies (e.g., 4D correlation volumes [42] or 4D Transformer [16]). Despite these significant advancements, a glaring limitation persists: these models largely neglect the exploration of local structural information. This oversight hinders their performance, particularly in challenging scenarios involving large motions, occlusions, blurring effects, and shifts in appearance. Such situations demand an elevated focus on local discrimination and flow consistency. This brings us to an intriguing inquiry: Is it feasible to architect optical flow models that intrinsically focus on local structural information during both representation learning and feature matching?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In response to the aforementioned challenge, we present the Gaussian Attention Flow network (GAFlow), a pioneering framework that leverages Gaussian Attention (GA) to inform both the feature encoder and the matching mod"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.221,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*Corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9642"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.092,
+                0.468,
+                0.346
+            ],
+            "angle": 0,
+            "content": "ule. Central to our approach is a novel attention mechanism equipped with a learnable Gaussian kernel. This mechanism naturally prioritizes the local surroundings of each point, thereby accentuating the importance of local structural information. For the representation learning component, we introduce a novel Gaussian-Constrained Layer (GCL) embedded within the canonical feature encoder. This layer, fortified with a learnable Gaussian kernel, naturally prioritizes the local surroundings of each point, thus accentuating the significance of local structural data. It's worth noting that while the GCL builds upon the pixel-wise modeling typical of the Vision Transformer block, it possesses a sharper focus on local connections, which effectively enhances the feature discrimination for cross-frame matching, as depicted in Fig. 1. Moreover, our GCL is dynamic, comprising learnable parameters that can be finetuned in concert with the encoder."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.352,
+                0.468,
+                0.591
+            ],
+            "angle": 0,
+            "content": "In optical flow prediction, traditional techniques prioritize the matching function, viewing it as indispensable when paired with distinctive features. These methods incorporate feature-similarity measures and smoothness constraints to optimize results [15, 5, 6]. With the advent of deep learning, the spotlight has largely shifted to feature-similarity [16, 42], often sidelining the crucial smoothness constraint. When considering it, the implicit smoothness loss is primarily employed [51, 26], presuming uniform flow fields — a simplification that overlooks intricate object deformations. While some approaches employ Graph techniques [30] or Transformers [22] to capture global motion, they tend to neglect the inherent locality of motion, potentially introducing inaccuracies. The challenge of leveraging neural networks to model motion relationships remains somewhat uncharted."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.596,
+                0.468,
+                0.776
+            ],
+            "angle": 0,
+            "content": "An ideal neural module for motion modeling should have three key properties: i) Neighbourhood priority. The motion of object(s) appears locally in visual scenes, and thus the module should instinctively focus more on the nearest neighbor fields for each pixel. ii) Matching-prior awareness. Previous work [4] shows that matching prior helps in large displacements and avoids over-smoothing; iii) High-order relation centered. Mining high-order relations [30, 22, 29] is essential for dealing with occlusions and lighting changes, as low-level similarities (like color) are often fragile. It would also be advantageous if this module's parameters could be trained in a data-driven manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.081,
+                0.78,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Targeting the above goals, we introduce a novel Gaussian-Guided Attention Module (GGAM) to explicitly model the motion affinities for optical flow. To meet the neighborhood priority requirement, our GGAM is formulated as Gaussian-guided attention that naturally emphasizes the neighboring fields of each point. Second, unlike conventional Non-Local operation [44], our GGAM is built across the context feature map and embedded correlation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.092,
+                0.89,
+                0.286
+            ],
+            "angle": 0,
+            "content": "(cost) volume for more comprehensive relation modeling. Specifically, for capturing the matching-prior knowledge, the 4D correlation volumes [42] are mapped to be the amplitudes and offsets. The amplitude for each position is set to the Gaussian attention for scaling its amplitude value and the offsets are encoded by the Gaussian attention via the warping operation. It enables free-form deformation of the Gaussian attention and adaptive attention for handling the large displacement of objects. For the last requirement, we draw inspiration from self-attention operations, and map the context feature to the query and key features for modeling the appearance self-similarities. All these operations are fully differentiable in our GGAM."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.289,
+                0.89,
+                0.634
+            ],
+            "angle": 0,
+            "content": "Our fully-equipped model, called Gaussian Attention Flow network (GAFlow), unites GCL and GGAM to conduct motion analysis by considering both feature similarities and motion affinities. It achieves the top performance on both Sintel and KITTI benchmarks with limited extra computational cost. Overall, the main contributions of this paper are: 1) We introduce a novel approach to enhance the local properties of underlying representations. Our proposed Gaussian-Constrained Layer (GCL) can work complementarily with the standard feature encoder to build more discriminative features for optical flow. 2) We analyze three important properties for motion affinity modeling, leading to a novel Gaussian-Guided Attention Module (GGAM). For the first time, we show that it is feasible to capture the local relations by learning the Gaussian attention and refining the motion fields for a more reliable optical flow estimation. 3) We unite our GCL and GGAM into the contemporary optical flow architecture, making the model stronger at highlighting local structural information. Our Gaussian Attention Flow networks set new records on a variety of benchmarks, e.g., Sintel (clean and final) and KITTI datasets, and outperform existing optical flow models by a relatively large margin."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.504,
+                0.649,
+                0.64,
+                0.665
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.504,
+                0.675,
+                0.89,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Optical Flow. In the epoch of deep learning, early optical flow models, such as [2, 46], viewed flow field prediction as a mapping challenge, translating two input frames into corresponding flow fields, predominantly harnessing the potency of data. Subsequent models significantly elevated flow estimation accuracy either by adopting more robust representation learning paradigms [40, 20, 54] or by implementing explicit feature-similarity measurement techniques [50, 43]. With the integration of advanced feature learning and cost-volume filtering modules, unsupervised methods have also witnessed remarkable advancements [31, 27, 25]. A notable development is RAFT [42], which employs a 4D correlation volume and a recurrent strategy for optical flow estimation. Building on its recurrent feature-matching paradigm, a slew of contempor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.485,
+                0.947,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9643"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.093,
+                0.885,
+                0.278
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.301,
+                0.895,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Figure 2: An overview of the proposed Gaussian Attention Flow network (GAFlow), architecled with recurrent learning at its core. During the decoding process, the residual flows are iteratively refined and accumulated to derive the final flow field. “\\(\\times\\)” denotes multiplication. Best viewed in color."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.375,
+                0.458,
+                0.641
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.663,
+                0.473,
+                0.754
+            ],
+            "angle": 0,
+            "content": "Figure 3: A simple illustration of the Gaussian constraint. \"Q\" represents the query point. The blue circle represents contextual affinity, mirroring the analogous patterns observed in the ground truth flow. Through the Gaussian constraint, we can effectively filter out deceptive relations, as highlighted within the red circle."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.795,
+                0.473,
+                0.904
+            ],
+            "angle": 0,
+            "content": "rary models [3, 13, 32, 21, 8] have substantially bolstered the dependability of optical flow predictions. To navigate challenges like occlusions and blur effects, innovative tactics—including joint representation learning [53], feature-driven flow regularization [19], iterative refinement [20, 18], and comprehensive motion analysis [22, 30]—have been employed. Addressing the smoothness constraint, [22]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.374,
+                0.892,
+                0.464
+            ],
+            "angle": 0,
+            "content": "proposed a global motion refinement strategy anchored on attention mechanisms. Meanwhile, [30] captures motion affinities using graph techniques and [29] introduced kernel patch attention (KPA) for the same purpose, though KPA's static kernel window size could potentially curb its efficacy in managing variations in scale and shape."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.464,
+                0.893,
+                0.601
+            ],
+            "angle": 0,
+            "content": "Self-Attention. Self-attention operations have become instrumental in computer vision for discerning global contexts in images and videos [44, 45, 57]. Notably, non-local attention, exemplified by [57] and [17], is pivotal in visual Transformers [10, 12]. Recent advancements, such as Swin [28] and NAT [14], harness the inductive bias to enhance Transformers by applying attention within local windows. Inspired by these, our paper presents two Gaussian-based attention modules for optical flow."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.611,
+                0.649,
+                0.629
+            ],
+            "angle": 0,
+            "content": "3. Our Approach"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.636,
+                0.642,
+                0.651
+            ],
+            "angle": 0,
+            "content": "3.1. Preliminaries"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.892,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Motivation. Fig. 3 visually elucidates the core motivation driving our research. It can be observed that the ground truth optical flow field reveals the intricate nature of motion affinities. These affinities are not only deeply intertwined with contextual relationships but also exhibit pronounced local characteristics. Conventional methods often fall short in aligning with the inherent dynamics of the optical flow field. This observation has propelled us to integrate Gaussian attention into the optical flow model, aiming for a marked enhancement in its precision."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.818,
+                0.611,
+                0.832
+            ],
+            "angle": 0,
+            "content": "3.2. Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Our GAFlow encompasses two pivotal sub-modules: representation learning module \\((\\mathbb{R}_{\\beta})\\) and feature matching module \\((\\mathbb{F}_{\\gamma})\\), as visualized in Fig. 2. Specifically, \\(\\mathbb{R}_{\\beta}\\) represents the functions of acquiring the feature maps \\((\\mathbf{f}_1,\\mathbf{f}_2,\\mathbf{f}_c)\\),"
+        },
+        {
+            "type": "page_number",
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+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.116,
+                0.236,
+                0.258,
+                0.25
+            ],
+            "angle": 0,
+            "content": "(a) Non-local Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.329,
+                0.092,
+                0.579,
+                0.231
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.347,
+                0.236,
+                0.559,
+                0.25
+            ],
+            "angle": 0,
+            "content": "(b) Gaussian Constrained Attention"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.612,
+                0.088,
+                0.895,
+                0.232
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.661,
+                0.236,
+                0.844,
+                0.25
+            ],
+            "angle": 0,
+            "content": "(c) Gaussian Guided Attention"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.262,
+                0.895,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Figure 4: Architecture comparisons. (a) Standard Non-local Attention, (b) Our Gaussian-Constrained Attention tailored for representation enhancement, and (c) Our Gaussian-Guided Attention, designed to model motion affinities using learnable Gaussian attention. Here, \\(\\mathbf{X}\\) represents the basic/context feature, while \\(\\mathbf{Y}\\) signifies the motion feature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.335,
+                0.469,
+                0.394
+            ],
+            "angle": 0,
+            "content": "corresponding to the feature encoders combined with the proposed Gaussian-Constrained Layer (GCL). \\(\\mathbb{F}_{\\gamma}\\) pertains to the recurrent flow decoder, fortified with our bespoke Gaussian-Guided Attention Module (GGAM)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.396,
+                0.47,
+                0.471
+            ],
+            "angle": 0,
+            "content": "At their core, these Gaussian-centric modules can be seamlessly integrated into flow models. Their inclusion accentuates local attributes during both the phases of representation learning and feature matching. Subsequent sections further unpack the mechanics of our GCL and GGAM."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.479,
+                0.336,
+                0.495
+            ],
+            "angle": 0,
+            "content": "3.3. Gaussian-Constrained Layer"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.502,
+                0.47,
+                0.638
+            ],
+            "angle": 0,
+            "content": "The pixel-wise matching is susceptible to feature quality; Yet, the appearance changes caused by the motion blur and the illumination variations lower the feature discrimination. To avoid ambiguities, we propose Gaussian-Constrained Layer (GCL) to obtain the fine-grained structural information and locally discriminative representations for feature matching. Our GCL is designed based upon the standard Transformer [10, 28] block (see Fig. 4 (b)). Specifically, given the base feature \\(\\mathbf{x}\\), it is formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.189,
+                0.647,
+                0.469,
+                0.682
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {x}} = \\operatorname {G C A} (\\mathrm {L N} (\\mathbf {x})) + \\mathbf {x}, \\tag {1} \\\\ \\mathbf {y} = \\operatorname {F F N} (\\operatorname {L N} (\\hat {\\mathbf {x}})) + \\hat {\\mathbf {x}}, \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.69,
+                0.469,
+                0.75
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathrm{LN}(\\cdot)\\) and \\(\\mathrm{FFN}(\\cdot)\\) denote the general layer normalization and feed-forward network respectively in Transformer block. \\(\\mathrm{GCA}(\\cdot)\\) indicates Gaussian Constrained Attention, which is the core component in our GCL."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.751,
+                0.469,
+                0.811
+            ],
+            "angle": 0,
+            "content": "Here, we formulate GCA as a task-specific local operation, which not only avoids global misleading context but also reduces the complexity of attention computation. Therefore, it can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.126,
+                0.818,
+                0.469,
+                0.874
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\mathrm {Q} _ {i} = L _ {i} ^ {Q} (\\mathbf {x} ^ {\\prime}), \\mathrm {K} _ {i} = L _ {i} ^ {K} (\\mathbf {x} ^ {\\prime}), \\mathrm {V} _ {i} = L _ {i} ^ {V} (\\mathbf {x} ^ {\\prime}), \\\\ h _ {i} = \\mathcal {G} _ {\\mathrm {A}} \\left(\\mathrm {Q} _ {i}, \\bar {\\mathrm {K}} _ {i}, \\bar {\\mathrm {V}} _ {i}\\right), \\tag {2} \\\\ \\mathrm {H} = \\operatorname {C o n c a t} \\left(h _ {1}, h _ {2}, \\dots , h _ {n}\\right), \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.884,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{x}' = \\mathrm{LN}(\\mathbf{x})\\). \\(L_{i}^{Q}(\\cdot), L_{i}^{K}(\\cdot)\\), and \\(L_{i}^{V}(\\cdot)\\) denote linear"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.335,
+                0.892,
+                0.381
+            ],
+            "angle": 0,
+            "content": "projections for the \\(i\\)-th head. \\(\\mathcal{G}_{\\mathrm{A}}(\\cdot)\\) is Gaussian attention function, which takes the query feature \\(\\mathrm{Q}_i\\), and the regional features of key \\(\\bar{\\mathrm{K}}_i\\) and value \\(\\bar{\\mathrm{V}}_i\\) as inputs:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.523,
+                0.391,
+                0.892,
+                0.41
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {G} _ {\\mathrm {A}} (\\mathrm {Q}, \\bar {\\mathrm {K}}, \\bar {\\mathrm {V}}) = \\operatorname {S o f t m a x} \\left(\\mathrm {G} _ {l r} \\cdot \\left(\\mathrm {Q} \\bar {\\mathrm {K}} ^ {\\top}\\right) / \\sqrt {d}\\right) \\cdot \\bar {\\mathrm {V}}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.421,
+                0.892,
+                0.512
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathrm{G}_{lr}\\) means a learnable Gaussian kernel with the shape of \\(k\\times k\\). It is initialized as a standard Gaussian distribution and can be updated by adding a learnable amplitude matrix \\(\\mathcal{A}\\) during model training. In the inference process, \\(\\mathrm{G}_{lr}\\) works as a constraint mask to reorganize the weights of attentive feature aggregation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.512,
+                0.892,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Let the neighborhood of a pixel at the point \\( p \\) be \\( \\mathcal{N}(p) \\); thus the attention on a single pixel can be defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.517,
+                0.553,
+                0.892,
+                0.574
+            ],
+            "angle": 0,
+            "content": "\\[\nh _ {(p)} = \\operatorname {S o f t m a x} \\left(\\mathrm {G} _ {l r} \\cdot \\left(\\mathrm {Q} _ {(p)} \\bar {\\mathrm {K}}\\right) _ {\\mathcal {N} (p)} ^ {\\intercal} / \\sqrt {d}\\right) \\cdot \\bar {\\mathrm {V}} _ {\\mathcal {N} (p)}. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.583,
+                0.892,
+                0.644
+            ],
+            "angle": 0,
+            "content": "Note that the operating range is scalable with the varying region of \\(\\mathcal{N}(p)\\). For instance, it can be extended to all pixels (i.e., \\(\\mathcal{N}(p)\\) is equivalent to the image size), leading to a global self-attention in a Gaussian-constrained manner."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.654,
+                0.81,
+                0.669
+            ],
+            "angle": 0,
+            "content": "3.4. Gaussian-Guided Attention Module"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.677,
+                0.892,
+                0.768
+            ],
+            "angle": 0,
+            "content": "Our Idea/Formulation. In image processing, the Gaussian filter is a widely-used operator that provides a linear scale space for smoothing, where the input image is smoothed at a constant rate in all directions [47]. Here, our idea is to apply the spatially variant Gaussian to smooth the motion feature \\(\\mathbf{f}_m\\). Formally, it can be given as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.58,
+                0.78,
+                0.892,
+                0.815
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(\\mathrm {F} * \\mathcal {G}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} \\left(p _ {i} - p\\right) \\mathbf {f} _ {m} ^ {i}, \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{N}_p\\) denotes a square neighborhood, centered at the pixel \\(p\\), with the pre-defined kernel size \\(k\\times k\\), and \\(p_i\\) indicates the position \\(i\\) in 2D grid space within \\(\\mathcal{N}_p\\). \\(\\mathbf{f}_m^i\\) refers to the feature at position \\(i\\) within \\(\\mathbf{f}_m\\), utilized in the calculation. \\(\\mathcal{G}(\\cdot)\\) is a 2D Gaussian function, which is defined as:"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9645"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.088,
+                0.094,
+                0.248,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.136,
+                0.262,
+                0.203,
+                0.274
+            ],
+            "angle": 0,
+            "content": "Reference"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.252,
+                0.094,
+                0.406,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.324,
+                0.262,
+                0.344,
+                0.273
+            ],
+            "angle": 0,
+            "content": "GT"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.408,
+                0.094,
+                0.564,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.465,
+                0.262,
+                0.502,
+                0.273
+            ],
+            "angle": 0,
+            "content": "RAFT"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.565,
+                0.094,
+                0.722,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.621,
+                0.262,
+                0.674,
+                0.273
+            ],
+            "angle": 0,
+            "content": "GMFlow"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.725,
+                0.094,
+                0.882,
+                0.259
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.794,
+                0.262,
+                0.825,
+                0.273
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.285,
+                0.893,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Figure 5: Qualitative comparisons with RAFT [42] and GMFlow [49] on some challenging samples, including large motion, occlusion and motion blur, of Sintel test set. The quantitative results are provided by the official website."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.115,
+                0.352,
+                0.469,
+                0.389
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {G} (x, y) = A \\exp \\left(- \\left(\\frac {(x - x _ {0}) ^ {2}}{2 \\sigma_ {x} ^ {2}} + \\frac {(y - y _ {0}) ^ {2}}{2 \\sigma_ {y} ^ {2}}\\right)\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.391,
+                0.469,
+                0.527
+            ],
+            "angle": 0,
+            "content": "where \\( A \\) denotes the static amplitude (\\( A = 1 \\) as the default setting) and \\( p_0 = (x_0, y_0) \\) means the center point. \\( (\\sigma_x; \\sigma_y) \\) indicate the variances which are set to \\( \\sigma_x = \\sigma_y = \\sigma \\), determining the operating range of smoothness. However, directly applying the Gaussian smoothing is sub-optimal for capturing the local properties, as the kernel is rigid (or fixed) and the clutters could be inevitably involved in providing false guidance. Next, we show how to make the Gaussian attention more adaptive and also end-to-end trainable."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.527,
+                0.469,
+                0.618
+            ],
+            "angle": 0,
+            "content": "Gaussian-Guided Attention with Context (GGAC). To begin with, we incorporate the contextual information, which preserves the fine-grained structural information, into the Gaussian Attention. Specifically, given the context feature \\(\\mathbf{f}_c\\in \\mathbb{R}^{c\\times h\\times w}\\) and motion feature \\(\\mathbf{f}_m\\in \\mathbb{R}^{c\\times h\\times w}\\), we rewrite Eq. (5) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.136,
+                0.626,
+                0.469,
+                0.661
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(\\mathrm {F} * \\mathcal {G} _ {\\mathbb {C}}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} _ {\\mathbb {C} (p _ {i} - p)} \\left(\\mathbf {f} _ {c}\\right) \\rho \\left(\\mathbf {f} _ {m}\\right) ^ {i}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.669,
+                0.469,
+                0.745
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{G}_{\\mathbb{C}(p_i - p)}(\\cdot)\\) is an adaptive kernel function taking the context features in \\(\\mathcal{N}_p\\) as inputs to obtain the context-preserving kernel. \\(\\rho (\\cdot)\\) is a linear operation for producing the embedded motion feature. We formulate the context-preserving kernel function as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.162,
+                0.754,
+                0.469,
+                0.772
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {G} _ {\\mathrm {C} \\left(p _ {i} - p\\right)} \\left(\\mathbf {f} _ {c}\\right) = \\mathcal {G} ^ {\\prime} \\left(p _ {i} - p\\right) \\mathcal {F} \\left(\\mathbf {f} _ {c}\\right), \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.779,
+                0.469,
+                0.871
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{k \\times k \\times h \\times w}\\) denotes the expanded Gaussian kernel in the spatial dimension, which is prepared for generating the data-dependent kernel matrices with the shape of \\(k \\times k\\) based on the corresponding weights on each position in \\(h \\times w\\), and \\(\\mathcal{F}(\\cdot)\\) is the dynamic weight function for mining the guidance prior on the context feature \\(\\mathbf{f}_c\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Rather than simply utilizing a learnable matrix as in convolution kernels, we follow [22] to apply the embedded"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.342,
+                0.892,
+                0.54
+            ],
+            "angle": 0,
+            "content": "Gaussian with normalization [44] on the context feature \\(\\mathbf{f}_c\\) to produce the attention map. To match the dimension of the pre-defined Gaussian kernel \\(\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{K \\times N}\\), where \\(N = h \\times w\\), and \\(K = k \\times k\\) denoting the spatial dimension of kernel size, a naive solution is to discard the redundant information in \\(\\mathcal{F}(\\mathbf{f}_c)\\). Here, we present a kernel-based context-preserving attention operation, which takes the asymmetric query and key feature maps in the spatial dimension as inputs. In detail, given the embedded context features \\(\\theta(\\mathbf{f}_c) \\in \\mathbb{R}^{c \\times h \\times w}\\), we employ an unfolding operator (e.g., torch.nn.Unfold) to get \\(\\mathrm{U}(\\theta(\\mathbf{f}_c))\\), thus the dimension is transformed from \\(c \\times N\\) to \\(c \\times N \\times K\\). Then we measure the similarities between all pairs within the kernel region as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.55,
+                0.552,
+                0.892,
+                0.593
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {F} \\left(\\mathbf {f} _ {c}\\right) = \\frac {\\exp \\left(\\mathrm {U} \\left(\\theta \\left(\\mathbf {f} _ {c}\\right)\\right) _ {l} ^ {T} \\phi \\left(\\mathbf {f} _ {c}\\right) _ {j} / \\sqrt {c}\\right)}{\\sum_ {\\forall j} \\exp \\left(\\mathrm {U} \\left(\\theta \\left(\\mathbf {f} _ {c}\\right)\\right) _ {l} ^ {T} \\phi \\left(\\mathbf {f} _ {c}\\right) _ {j} / \\sqrt {c}\\right)}, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.6,
+                0.891,
+                0.646
+            ],
+            "angle": 0,
+            "content": "where \\(l \\in K\\) and \\(j \\in c\\), and the size of \\(\\mathcal{F}(\\mathbf{f}_c)\\) is \\(K \\times N\\). \\(\\theta(\\cdot)\\) and \\(\\phi(\\cdot)\\) indicates linear projections for channel-wise feature aggregation [22]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.647,
+                0.892,
+                0.857
+            ],
+            "angle": 0,
+            "content": "Gaussian-Guided Attention with Deformation (GGAD). While Gaussian attention with context effectively addresses the problem of flow field over-smoothing caused by the data-agnostic Gaussian kernel, it still faces a limitation due to the rigid operating region of the Gaussian kernel. This constraint hinders the smoothness performance for motion feature refinement. To mitigate this issue, we take a further step to optimize the operating region of the Gaussian kernel by learning the deformable kernels in a data-driven manner, as shown in Fig. 4 (c). To avoid the static amplitude \\( A \\) of the Gaussian function, we design a dynamic amplitude operator based on the cross-frame matching features. In practice, similar to Eq. (7), our Gaussian-guided attention can be further formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.535,
+                0.868,
+                0.892,
+                0.905
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left(\\mathrm {F} * \\mathcal {G} _ {\\mathbb {D}}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} _ {\\mathbb {D} \\left(p _ {i} - p\\right)} \\left(\\mathbf {f} _ {c}, \\mathbf {f} _ {m}\\right) \\rho \\left(\\mathbf {f} _ {m}\\right), \\tag {10}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "9646"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.086,
+                0.089,
+                0.887,
+                0.384
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Training</td><td rowspan=\"2\">Method</td><td rowspan=\"2\">Reference</td><td colspan=\"2\">Sintel (Val)</td><td colspan=\"2\">KITTI-15 (Val)</td><td colspan=\"2\">Sintel (Test)</td><td>KITTI-15 (Test)</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td><td>Clean</td><td>Final</td><td>F1-all</td></tr><tr><td rowspan=\"14\">Val: C + T / Test: +S+K+H</td><td>RAFT [42]</td><td>ECCV-20</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>1.61</td><td>2.86</td><td>5.10</td></tr><tr><td>SCV [23]</td><td>CVPR-21</td><td>1.29</td><td>2.95</td><td>6.80</td><td>19.3</td><td>1.77</td><td>3.88</td><td>6.17</td></tr><tr><td>GMA [22]</td><td>ICCV-21</td><td>1.30</td><td>2.74</td><td>4.69</td><td>17.1</td><td>1.39</td><td>2.47</td><td>5.15</td></tr><tr><td>SeparableFlow[52]</td><td>ICCV-21</td><td>1.30</td><td>2.59</td><td>4.60</td><td>15.9</td><td>1.50</td><td>2.67</td><td>4.64</td></tr><tr><td>Flow1D [48]</td><td>ICCV-21</td><td>1.98</td><td>3.27</td><td>6.69</td><td>23.0</td><td>2.24</td><td>3.81</td><td>6.27</td></tr><tr><td>AGFlow [30]</td><td>AAAI-22</td><td>1.31</td><td>2.69</td><td>4.82</td><td>17.0</td><td>1.43</td><td>2.47</td><td>4.89</td></tr><tr><td>GMFlowNet [55]</td><td>CVPR-22</td><td>1.14</td><td>2.71</td><td>4.24</td><td>15.4</td><td>1.39</td><td>2.65</td><td>4.79</td></tr><tr><td>GMFlow [49]</td><td>CVPR-22</td><td>1.08</td><td>2.48</td><td>7.77</td><td>23.4</td><td>1.74</td><td>2.90</td><td>9.32</td></tr><tr><td>CRAFT [37]</td><td>CVPR-22</td><td>1.27</td><td>2.79</td><td>4.88</td><td>17.5</td><td>1.45</td><td>2.42</td><td>4.79</td></tr><tr><td>DIP [56]</td><td>CVPR-22</td><td>1.30</td><td>2.82</td><td>4.29</td><td>13.7</td><td>1.44</td><td>2.83</td><td>4.21</td></tr><tr><td>KPA-Flow [30]</td><td>CVPR-22</td><td>1.28</td><td>2.68</td><td>4.46</td><td>15.9</td><td>1.35</td><td>2.36</td><td>4.60</td></tr><tr><td>OCTC [21]</td><td>CVPR-22</td><td>1.31</td><td>2.67</td><td>4.72</td><td>16.3</td><td>1.41</td><td>2.57</td><td>4.33</td></tr><tr><td>SKFlow [41]</td><td>NeurIPS-22</td><td>1.22</td><td>2.46</td><td>4.27</td><td>15.5</td><td>1.28</td><td>2.27</td><td>4.84</td></tr><tr><td>GAFlow (ours)</td><td></td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>1.21</td><td>2.24</td><td>4.52</td></tr><tr><td rowspan=\"2\">A / +TSKHV</td><td>RAFT-A [39]</td><td>CVPR-21</td><td>1.95</td><td>2.57</td><td>4.23</td><td>-</td><td>2.01</td><td>3.14</td><td>4.78</td></tr><tr><td>RAFT-it [38]</td><td>ECCV-22</td><td>1.74</td><td>2.41</td><td>4.18</td><td>13.4</td><td>1.55</td><td>2.90</td><td>4.31</td></tr><tr><td rowspan=\"2\">I+CT / +SKH</td><td>FlowFormer [16]</td><td>ECCV-22</td><td>1.01</td><td>2.40</td><td>4.09</td><td>14.7</td><td>1.16</td><td>2.09</td><td>4.68</td></tr><tr><td>GAFlow-FF (ours)</td><td></td><td>0.95</td><td>2.34</td><td>3.92</td><td>13.9</td><td>1.15</td><td>2.05</td><td>4.42</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.395,
+                0.892,
+                0.472
+            ],
+            "angle": 0,
+            "content": "Table 1: Quantitative comparison with state-of-the-art models on standard benchmarks for cross-dataset evaluation and online testing. “C+T” indicates the models trained on FlyingChairs and FlyingThings for generalization ability evaluation. “+S+K+H” denotes more training data involved from Sintel, KITTI-2015, and HD1K. “A” indicates the models are trained on AutoFlow [39] dataset for Val set evaluation. “V” denotes VIPER [36] dataset. “T” means the encoders are pre-trained on ImageNet [9]. The best and second-best results are marked in bold and underline, respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.497,
+                0.47,
+                0.573
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{G}_{\\mathbb{D}(p_i - p)}(\\cdot)\\) is the deformable Gaussian kernel function that is used to produce the more flexible Gaussian attention for adaptively capturing the relevant information and avoiding rigid kernel boundary in a data-dependent manner. Specifically, the deformable Gaussian kernel is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.107,
+                0.581,
+                0.468,
+                0.6
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {G} _ {\\mathbb {D} (p _ {i} - p)} \\left(\\mathbf {f} _ {c}, \\mathbf {f} _ {m}\\right) = \\mathcal {A} \\left(\\mathbf {f} _ {m}\\right) \\mathcal {D} _ {(p _ {i} - p)} \\left(\\mathbf {f} _ {m}\\right) \\mathcal {F} \\left(\\mathbf {f} _ {c}\\right), \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.606,
+                0.469,
+                0.68
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{A}(\\cdot)\\) indicates the amplitude operator taking the motion feature \\(\\mathbf{f}_{\\mathbf{m}}\\) to produce adaptive amplitudes, \\(\\mathcal{F}(\\mathbf{f}_c)\\) is the kernel-based context-preserving attention matrix as in Eq. (9), and \\(\\mathcal{D}_{(p_i - p)}(\\cdot)\\) denotes the deformable Gaussian operator, which can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.689,
+                0.469,
+                0.707
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {D} _ {(p _ {i} - p)} \\left(\\mathbf {f} _ {m}\\right) = \\mathcal {W} \\left(\\mathcal {G} ^ {\\prime} (p _ {i} - p), \\mathcal {O} \\left(\\mathbf {f} _ {m}\\right)\\right), \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.713,
+                0.469,
+                0.789
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{k \\times k \\times h \\times w}\\) indicates the spatially expanded Gaussian kernel as in Eq. (8), and \\(\\mathcal{O}(\\mathbf{f}_m)\\) denotes the offset maps predicted from the motion feature. \\(\\mathcal{W}(\\cdot)\\) is the warp function taking the obtained offsets as inputs and operating on the Gaussian kernel."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.79,
+                0.469,
+                0.834
+            ],
+            "angle": 0,
+            "content": "Another important component in the deformable Gaussian kernel (Eq. (11)) is the amplitude operator \\(\\mathcal{A}(\\cdot)\\), which is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.196,
+                0.835,
+                0.468,
+                0.852
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {A} \\left(\\mathbf {f} _ {m}\\right) = 1 + \\vartheta \\left(\\mathbf {f} _ {m}\\right) \\lambda , \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) indicates a learnable parameter to constrain the fluctuation of the generated amplitude, and \\(\\vartheta(\\cdot)\\) is a linear function. Finally, similar to the expanding strategy in"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.497,
+                0.892,
+                0.545
+            ],
+            "angle": 0,
+            "content": "the deformable Gaussian operator, the learned amplitude \\(\\mathcal{A}(\\mathbf{f}_m)\\) can be easily transformed to operate on the Gaussian kernel \\(\\mathcal{G}'(p_i - p)\\) for generating a more flexible one."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.561,
+                0.707,
+                0.579
+            ],
+            "angle": 0,
+            "content": "4. Experimental Results"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.588,
+                0.717,
+                0.604
+            ],
+            "angle": 0,
+            "content": "4.1. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.612,
+                0.892,
+                0.822
+            ],
+            "angle": 0,
+            "content": "For fair comparison with existing methods [22, 37, 29], we first plug 1 GCL and 1 GGAM into RAFT [42] to build a small model, i.e., GAFlow-S. Specifically, Gaussian-Constrained Layer (GCL) is appended to the motion encoder with \\(\\sigma = 9\\). Gaussian-Guided Attention Module (GGAM) performs feature smoothing on context and motion features, where we set sigma to 20 and 15 for Sintel and KITTI, respectively. Besides, to further explore the potential of our approach, we also employ a stronger baseline with POLA [55] modules and SKBlocks [41], which is regarded as the default model of GAFlow. Furthermore, we enhance the model's capabilities by integrating the proposed module into FlowFormer [16], resulting in a robust and advanced model termed GAFlow-FF."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "All experiments are conducted based on PyTorch toolbox. During training our GAFlow model, we follow RAFT to set the batch sizes to 6 and adopt AdamW optimizer with one-cycle learning rate policy [42]. Similar to previous works [42, 22, 30], the synthetic datasets are also involved"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9647"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.092,
+                0.209,
+                0.134
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.114,
+                0.135,
+                0.176,
+                0.144
+            ],
+            "angle": 0,
+            "content": "(a) Reference"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.212,
+                0.092,
+                0.335,
+                0.135
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.217,
+                0.135,
+                0.332,
+                0.144
+            ],
+            "angle": 0,
+            "content": "(c) Flow of GGAD (ours)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.338,
+                0.092,
+                0.463,
+                0.135
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.365,
+                0.135,
+                0.445,
+                0.144
+            ],
+            "angle": 0,
+            "content": "(e) Flow of GMA"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.147,
+                0.209,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.11,
+                0.19,
+                0.188,
+                0.201
+            ],
+            "angle": 0,
+            "content": "(b) GGAC (ours)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.212,
+                0.147,
+                0.336,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.24,
+                0.19,
+                0.319,
+                0.2
+            ],
+            "angle": 0,
+            "content": "(d) GGAD (ours)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.338,
+                0.147,
+                0.462,
+                0.189
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.382,
+                0.19,
+                0.423,
+                0.2
+            ],
+            "angle": 0,
+            "content": "(f) GMA"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.219,
+                0.468,
+                0.28
+            ],
+            "angle": 0,
+            "content": "Figure 6: A challenging sample from the Sintel final pass. The second row provides attention maps of our GGAC, GGAD and GMA [22], respectively. “P” indicates the query point to obtain attention maps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.307,
+                0.468,
+                0.442
+            ],
+            "angle": 0,
+            "content": "in model pre-training. The pre-training iterations on FlyingChairs [11] and FlyingThings [33] are set to 120k and 160k, respectively. Then the fine-tuning for Sintel online evaluation is conducted on the combined training data of Sintel [7], KITTI-2015 [34], and HD1K [24] for 160k iterations. Finally, the trained model requires another 50k iterations of finetuning on data of KITTI-2015 [34] before KITTI testing. We use only a single GPU and set the batch size to 1 for evaluation and online testing."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.454,
+                0.382,
+                0.47
+            ],
+            "angle": 0,
+            "content": "4.2. Comparison with State-of-the-Arts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.478,
+                0.468,
+                0.674
+            ],
+            "angle": 0,
+            "content": "Results on Sintel. We first compare the proposed approach with state-of-the-art methods for generalization evaluation on Sintel. As shown in Val sets of Tab. 1, our approach consistently achieves the best performance on all metrics. Specifically, GAFlow achieves the best EPE scores at 1.02 and 2.45 on the \"C + T\" setting. Besides, GAFlow-FF improves the SOTA performance to 0.95 and 2.34 in EPE on Sintel clean and final passes, respectively. For online testing, we follow prior works [22, 29, 37] to utilize the warm-start strategy [42]. GAFlow achieves the best EPE scores at 1.21 and 2.24 on the standard training setting. Moreover, GAFlow-FF sets a new record at 1.15 and 2.05 in EPE, outperforming recent works by a relatively large margin."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.675,
+                0.468,
+                0.795
+            ],
+            "angle": 0,
+            "content": "We compare the proposed GAFlow with the well-known methods RAFT [42] and GMFlow [49] on Sintel test set, and some qualitative comparisons are illustrated in Fig. 5. The results demonstrate that the proposed approach can effectively leverage the local structural information and high-order relations to resolve the ambiguities in motion learning, leading to a more robust and flexible model for handling the challenges in optical flow estimation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.468,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Results on KITTI. As shown in Tab. 1, GFlow achieves 3.98 in EPE and \\(15.0\\%\\) in F1-all on the KITTI Val set, which is comparable with the SOTA model FlowFormer yet with less computational overhead. Moreover, GFlow-FF further boosts the scores to 3.92 and \\(13.9\\%\\). For online testing, our models achieve the top-ranked performances at \\(4.52\\%\\) and \\(4.42\\%\\) in F1-score."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.517,
+                0.089,
+                0.878,
+                0.248
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Sintel</td><td>Type</td><td>RAFT[42] (EPE)</td><td>GMA[22] (EPE)</td><td>KPA[29] (EPE)</td><td>GAFlow-S (EPE)</td></tr><tr><td rowspan=\"4\">Clean (train)</td><td>s0-10</td><td>0.32</td><td>0.27</td><td>0.26</td><td>0.24</td></tr><tr><td>s10-40</td><td>1.55</td><td>1.35</td><td>1.38</td><td>1.29</td></tr><tr><td>s40+</td><td>8.83</td><td>8.55</td><td>8.43</td><td>7.92</td></tr><tr><td>All</td><td>1.41</td><td>1.31</td><td>1.28</td><td>1.21</td></tr><tr><td rowspan=\"4\">Final (train)</td><td>s0-10</td><td>0.52</td><td>0.54</td><td>0.54</td><td>0.51</td></tr><tr><td>s10-40</td><td>3.00</td><td>3.07</td><td>3.02</td><td>2.83</td></tr><tr><td>s40+</td><td>17.45</td><td>17.57</td><td>17.34</td><td>17.02</td></tr><tr><td>All</td><td>2.69</td><td>2.74</td><td>2.68</td><td>2.56</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.258,
+                0.892,
+                0.335
+            ],
+            "angle": 0,
+            "content": "Table 2: Quantitative results on different displacements. All methods are trained on “C+T” and evaluated on Sintel for fair comparison. s0-10, s10-40 and s40+ denote the ground truth flow value belonging to 0-10, 10-40 and 40+ pixels [7], respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.362,
+                0.673,
+                0.379
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.386,
+                0.892,
+                0.552
+            ],
+            "angle": 0,
+            "content": "Comparison with GMA. GMA [22] presents a global strategy for handling occlusion in flow estimation. As shown in Tab. 2, our GAflow-S achieves better performance on all metrics. This is because the global attention on context features involves too much misleading information for motion guidance, which contains long-range similarities in appearance but is improper for motion refinement (see Fig. 6 (f)). In contrast, our approach effectively takes the local property of regional context affinities into consideration, and leverages the extracted high-order relations with the flexible operating range to better infer the flow fields."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.553,
+                0.892,
+                0.764
+            ],
+            "angle": 0,
+            "content": "Comparison with KPA. The recent work KPA-Flow [29] shares a similar insight with our approach, leveraging local attention to avoid global misleading information. However, its intrinsic defects in formulation inevitably hinder the effect of motion refinement. First, the zero padding patches (out of the image) lead to obvious deviation for similarity measurement. Second, the neighboring pixels could be partitioned into distinct pre-defined (fixed) patch and kernel windows, leading to abrupt shifts in operating regions. In contrast, our approach enables a flexible constraint and freeform operating regions in a learnable manner, ensuring the proper and stable guidance pattern. Moreover, we provide quantitative comparisons in Tab. 2, where our approach achieves better performance on all metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Ablation for Feature Enhancement. In Tab. 3 (# 1), we first compare the proposed GCL with the widely recognized Transformer blocks [28, 55, 35], which have been extensively demonstrated to be effective for feature extraction. Swin Transformer [28] requires at least two blocks to perform the window shifting strategy, consuming more computation overhead. For other methods, only one block is applied for fair comparison. POLA [55] has been shown to be an effective local attention-based approach for fea"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "9648"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.084,
+                0.088,
+                0.462,
+                0.375
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Sintel (Val)</td><td colspan=\"2\">KITTI-15 (Val)</td><td rowspan=\"2\">Param.</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td></tr><tr><td>RAFT [42]</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>5.3M</td></tr><tr><td colspan=\"6\"># 1: Feature Enhancement</td></tr><tr><td>Swin Trans. [28]</td><td>1.45</td><td>2.75</td><td>5.16</td><td>17.3</td><td>7.3M</td></tr><tr><td>POLA×1 [55]</td><td>1.42</td><td>2.68</td><td>4.91</td><td>16.9</td><td>6.5M</td></tr><tr><td>cosFormer [35]</td><td>1.29</td><td>2.82</td><td>4.95</td><td>17.3</td><td>6.7M</td></tr><tr><td>L.Kernel</td><td>1.42</td><td>2.76</td><td>4.69</td><td>16.6</td><td>6.5M</td></tr><tr><td>GCL</td><td>1.33</td><td>2.67</td><td>4.61</td><td>16.5</td><td>6.5M</td></tr><tr><td colspan=\"6\"># 2: Stronger Encoder</td></tr><tr><td>POLAs [55]</td><td>1.18</td><td>2.63</td><td>4.52</td><td>16.6</td><td>10.0M</td></tr><tr><td>No</td><td>1.33</td><td>2.67</td><td>4.61</td><td>16.5</td><td>6.5M</td></tr><tr><td colspan=\"6\"># 3: Smoothing Pattern</td></tr><tr><td>+ GGAC</td><td>1.13</td><td>2.62</td><td>4.33</td><td>15.8</td><td>10.1M</td></tr><tr><td>+ GGAD</td><td>1.08</td><td>2.56</td><td>4.26</td><td>15.6</td><td>10.1M</td></tr><tr><td colspan=\"6\"># 4: Compatibility with SOTA modules</td></tr><tr><td>Refine.Sp4 [49]</td><td>1.03</td><td>2.45</td><td>4.10</td><td>14.6</td><td>12.5M</td></tr><tr><td>SKBlocks [41]</td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>10.4M</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.385,
+                0.472,
+                0.432
+            ],
+            "angle": 0,
+            "content": "Table 3: Ablation experiments. L.Kernel indicates the learnable kernel without Gaussian. Settings as default are underlined. Refer to Sec. 4.3 for detailed comparisons."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.461,
+                0.47,
+                0.672
+            ],
+            "angle": 0,
+            "content": "ture extraction with 6 or 12 stacked blocks (requiring extra \\(4.35 / 8.7\\mathrm{M}\\) parameters). As shown in the table, using one block \\((\\mathrm{POLA}_{\\times 1})\\) significantly weaken the power. The advanced linear Transformer cosFormer [35] exhibits a lower EPE score on Sintel Clean, whereas our GCL performs better on other metrics. Besides, we conduct an extra ablation for using a learnable kernel without Gaussian (L.Kernel). As can be seen, our GCL outperforms L.Kernel across all metrics. Particularly on the challenging Sintel, without a Gaussian constraint, performance declines significantly due to the uncontrolled misleading similarities at the kernel border. All experiments illustrate that, requiring similar computational overhead, the proposed GCL surpasses other methods by a relatively large margin."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.673,
+                0.47,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Ablation for Stronger Encoder. The smoothness constraint for flow estimation can be naturally regarded as a complementary component to the feature matching process, and benefits from stronger encoders for feature extraction. Thus, to further explore the potential of our approach, we follow prior work [55] to employ a stronger motion encoder with the standard POLA blocks, which largely boosts the performance on Sintel clean pass, as in Tab. 3 (# 2). Inspired by GMFlowNet [55], we build two types of encoding modules for separately handling Sintel and KITTI datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.825,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Ablation for Smoothing Pattern. The proposed GGAC is capable of producing flexible weight matrices for motion feature smoothing, which effectively tackles the issue of flow field over-smoothing caused by the data-agnostic Gaussian kernel. However, the issues of rigid operating re"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.508,
+                0.089,
+                0.885,
+                0.187
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">KITTI-15 (Val)</td><td rowspan=\"2\">Param.</td><td rowspan=\"2\">Time (s)</td></tr><tr><td>EPE</td><td>F1-all</td></tr><tr><td>GMFlowNet [55]</td><td>4.24</td><td>15.4</td><td>9.3M</td><td>0.32</td></tr><tr><td>FlowFormer [16]</td><td>4.09</td><td>14.7</td><td>18.2M</td><td>1.77</td></tr><tr><td>GAFlow (ours)</td><td>3.98</td><td>15.0</td><td>10.4M</td><td>0.48</td></tr><tr><td>GAFlow-FF (ours)</td><td>3.92</td><td>13.9</td><td>18.2M</td><td>1.85</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.198,
+                0.892,
+                0.229
+            ],
+            "angle": 0,
+            "content": "Table 4: Quantitative comparisons for computational complexity. The input size is \\(376 \\times 1248\\) as in KITTI dataset."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.259,
+                0.892,
+                0.334
+            ],
+            "angle": 0,
+            "content": "gion and static amplitude still affect the motion refinement (see Fig. 6 (b) and Tab. 3 (# 3)). Thus we further improve the approach with the spatially deformable kernel with the dynamic amplitude in a data-driven manner, i.e., GGAD, which boosts the performance by around \\(3\\%\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.337,
+                0.892,
+                0.503
+            ],
+            "angle": 0,
+            "content": "Ablation for Compatibility with SOTA modules. In Tab. 3 (# 4), similar to prior work [49], we further perform flow refinement with the flow decoder on 1/4 features, termed Refine.Sp4, which helps to boost the performance on both Sintel and KITTI datasets. Moreover, we follow SKFlow [41] to employ SKBlocks in the motion encoding and state updating modules of the flow decoder. The ablation indicates that the GGAD module is compatible with SKBlocks, and the integration of the decoder leads to improved performance across all metrics, while introducing minimal additional parameters \\((10.1\\rightarrow 10.4\\mathrm{M})\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.505,
+                0.892,
+                0.641
+            ],
+            "angle": 0,
+            "content": "Runtime Comparison. The comparisons of KITTI evaluation results, parameters and runtime are presented in Tab. 4. Although FlowFormer [16] uses ImageNet for encoder pretraining, our GAFlow achieves a competitive performance (even better in online testing, see Tab. 1) while consuming fewer parameters by \\(7.8\\mathrm{M}\\) and reducing the inference time by \\(72.9\\%\\). Moreover, built on the previous SOTA model FlowFormer, our GAFlow-FF largely reduces the error by \\(4.8\\%\\) with negligible computational complexity."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.66,
+                0.62,
+                0.675
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.688,
+                0.892,
+                0.853
+            ],
+            "angle": 0,
+            "content": "In this work, we introduce a novel Gaussian Attention Flow network (GAFlow) to explicitly highlight local properties during representation learning and enforce the motion affinity during matching. We deliver two Gaussian-based modules, i.e. Gaussian-Constrained Layer (GCL) and Gaussian-Guided Attention Module (GGAM), which works well with existing flow architectures and can greatly enhance the reliability of optical flow estimation. Extensive quantitative and qualitative comparisons performed on commonly-used datasets demonstrate that our method significantly outperforms the current alternatives."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.856,
+                0.892,
+                0.9
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This work is supported by Sichuan Science and Technology Program of China under grant No.2023NSFSC0462."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
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+                0.516,
+                0.956
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+            "angle": 0,
+            "content": "9649"
+        }
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+# GAFlow: Incorporating Gaussian Attention into Optical Flow
+
+Ao Luo $^{1}$ , Fan Yang $^{2}$ , Xin Li $^{2}$ , Lang Nie $^{3}$ , Chunyu Lin $^{3}$ , Haoqiang Fan $^{1}$ , and Shuaicheng Liu $^{4,1*}$ $^{1}$ Megvii Technology Group 42 Beijing Jiaotong University  
+ $^{4}$ University of Electronic Science and Technology of China
+
+# Abstract
+
+Optical flow, or the estimation of motion fields from image sequences, is one of the fundamental problems in computer vision. Unlike most pixel-wise tasks that aim at achieving consistent representations of the same category, optical flow raises extra demands for obtaining local discrimination and smoothness, which yet is not fully explored by existing approaches. In this paper, we push Gaussian Attention (GA) into the optical flow models to accentuate local properties during representation learning and enforce the motion affinity during matching. Specifically, we introduce a novel Gaussian-Constrained Layer (GCL) which can be easily plugged into existing Transformer blocks to highlight the local neighborhood that contains fine-grained structural information. Moreover, for reliable motion analysis, we provide a new Gaussian-Guided Attention Module (GGAM) which not only inherits properties from Gaussian distribution to instinctively revolve around the neighbor fields of each point but also is empowered to put the emphasis on contextually related regions during matching. Our fully-equipped model, namely Gaussian Attention Flow network (GAFlow), naturally incorporates a series of novel Gaussian-based modules into the conventional optical flow framework for reliable motion analysis. Extensive experiments on standard optical flow datasets consistently demonstrate the exceptional performance of the proposed approach in terms of both generalization ability evaluation and online benchmark testing. Code is available at https://github.com/LA30/GAFlow.
+
+# 1. Introduction
+
+Optical flow aims to establish pixel-wise correspondences across images, playing a crucial role in video understanding. It unifies representation learning and feature matching as a problem of pixel-wise motion inference. Modern optical flow models typically focus on either improving representation learning techniques (e.g., alternative
+
+![](images/62a0ad9ed43f74abeab283b1786d81a1cbed99448d5250e71e31af775abf2d9b.jpg)
+
+![](images/2b2ac604611ac8195380d247ace3d6d62ae4839992517dd430e3394c4a8e679e.jpg)
+
+![](images/a7cb2849ef7889f02d48d1921a6c6a742b39f20efe1af5e4bb3be61f9857451a.jpg)  
+Figure 1: Visualization of feature discrimination (left) and smoothness constraint (right). For a random point  $P$  in frame  $t$ , our GCL enhances feature discrimination by emphasizing fine-grained structural details. Concurrently, our GGAM effectively captures smoothness constraints, centering on pertinent local regions.
+
+![](images/e7cb062cf3a737ebd9af618249b112a90595d306a30c84010b9857a15192146c.jpg)
+
+learning [40, 20, 54] and reinforcement learning [1]) or refining feature similarity measurement methodologies (e.g., 4D correlation volumes [42] or 4D Transformer [16]). Despite these significant advancements, a glaring limitation persists: these models largely neglect the exploration of local structural information. This oversight hinders their performance, particularly in challenging scenarios involving large motions, occlusions, blurring effects, and shifts in appearance. Such situations demand an elevated focus on local discrimination and flow consistency. This brings us to an intriguing inquiry: Is it feasible to architect optical flow models that intrinsically focus on local structural information during both representation learning and feature matching?
+
+In response to the aforementioned challenge, we present the Gaussian Attention Flow network (GAFlow), a pioneering framework that leverages Gaussian Attention (GA) to inform both the feature encoder and the matching mod
+
+ule. Central to our approach is a novel attention mechanism equipped with a learnable Gaussian kernel. This mechanism naturally prioritizes the local surroundings of each point, thereby accentuating the importance of local structural information. For the representation learning component, we introduce a novel Gaussian-Constrained Layer (GCL) embedded within the canonical feature encoder. This layer, fortified with a learnable Gaussian kernel, naturally prioritizes the local surroundings of each point, thus accentuating the significance of local structural data. It's worth noting that while the GCL builds upon the pixel-wise modeling typical of the Vision Transformer block, it possesses a sharper focus on local connections, which effectively enhances the feature discrimination for cross-frame matching, as depicted in Fig. 1. Moreover, our GCL is dynamic, comprising learnable parameters that can be finetuned in concert with the encoder.
+
+In optical flow prediction, traditional techniques prioritize the matching function, viewing it as indispensable when paired with distinctive features. These methods incorporate feature-similarity measures and smoothness constraints to optimize results [15, 5, 6]. With the advent of deep learning, the spotlight has largely shifted to feature-similarity [16, 42], often sidelining the crucial smoothness constraint. When considering it, the implicit smoothness loss is primarily employed [51, 26], presuming uniform flow fields — a simplification that overlooks intricate object deformations. While some approaches employ Graph techniques [30] or Transformers [22] to capture global motion, they tend to neglect the inherent locality of motion, potentially introducing inaccuracies. The challenge of leveraging neural networks to model motion relationships remains somewhat uncharted.
+
+An ideal neural module for motion modeling should have three key properties: i) Neighbourhood priority. The motion of object(s) appears locally in visual scenes, and thus the module should instinctively focus more on the nearest neighbor fields for each pixel. ii) Matching-prior awareness. Previous work [4] shows that matching prior helps in large displacements and avoids over-smoothing; iii) High-order relation centered. Mining high-order relations [30, 22, 29] is essential for dealing with occlusions and lighting changes, as low-level similarities (like color) are often fragile. It would also be advantageous if this module's parameters could be trained in a data-driven manner.
+
+Targeting the above goals, we introduce a novel Gaussian-Guided Attention Module (GGAM) to explicitly model the motion affinities for optical flow. To meet the neighborhood priority requirement, our GGAM is formulated as Gaussian-guided attention that naturally emphasizes the neighboring fields of each point. Second, unlike conventional Non-Local operation [44], our GGAM is built across the context feature map and embedded correlation
+
+(cost) volume for more comprehensive relation modeling. Specifically, for capturing the matching-prior knowledge, the 4D correlation volumes [42] are mapped to be the amplitudes and offsets. The amplitude for each position is set to the Gaussian attention for scaling its amplitude value and the offsets are encoded by the Gaussian attention via the warping operation. It enables free-form deformation of the Gaussian attention and adaptive attention for handling the large displacement of objects. For the last requirement, we draw inspiration from self-attention operations, and map the context feature to the query and key features for modeling the appearance self-similarities. All these operations are fully differentiable in our GGAM.
+
+Our fully-equipped model, called Gaussian Attention Flow network (GAFlow), unites GCL and GGAM to conduct motion analysis by considering both feature similarities and motion affinities. It achieves the top performance on both Sintel and KITTI benchmarks with limited extra computational cost. Overall, the main contributions of this paper are: 1) We introduce a novel approach to enhance the local properties of underlying representations. Our proposed Gaussian-Constrained Layer (GCL) can work complementarily with the standard feature encoder to build more discriminative features for optical flow. 2) We analyze three important properties for motion affinity modeling, leading to a novel Gaussian-Guided Attention Module (GGAM). For the first time, we show that it is feasible to capture the local relations by learning the Gaussian attention and refining the motion fields for a more reliable optical flow estimation. 3) We unite our GCL and GGAM into the contemporary optical flow architecture, making the model stronger at highlighting local structural information. Our Gaussian Attention Flow networks set new records on a variety of benchmarks, e.g., Sintel (clean and final) and KITTI datasets, and outperform existing optical flow models by a relatively large margin.
+
+# 2. Related Work
+
+Optical Flow. In the epoch of deep learning, early optical flow models, such as [2, 46], viewed flow field prediction as a mapping challenge, translating two input frames into corresponding flow fields, predominantly harnessing the potency of data. Subsequent models significantly elevated flow estimation accuracy either by adopting more robust representation learning paradigms [40, 20, 54] or by implementing explicit feature-similarity measurement techniques [50, 43]. With the integration of advanced feature learning and cost-volume filtering modules, unsupervised methods have also witnessed remarkable advancements [31, 27, 25]. A notable development is RAFT [42], which employs a 4D correlation volume and a recurrent strategy for optical flow estimation. Building on its recurrent feature-matching paradigm, a slew of contempor
+
+![](images/ed65cd02f149664235355d72240dcf92ec2474350708d34f3209836bebf3fef4.jpg)  
+Figure 2: An overview of the proposed Gaussian Attention Flow network (GAFlow), architecled with recurrent learning at its core. During the decoding process, the residual flows are iteratively refined and accumulated to derive the final flow field. “ $\times$ ” denotes multiplication. Best viewed in color.
+
+![](images/7c036716e95d5a09ab0b055a28bf4359bd3842d488ff6ea96fe3f9a2c949b814.jpg)  
+Figure 3: A simple illustration of the Gaussian constraint. "Q" represents the query point. The blue circle represents contextual affinity, mirroring the analogous patterns observed in the ground truth flow. Through the Gaussian constraint, we can effectively filter out deceptive relations, as highlighted within the red circle.
+
+rary models [3, 13, 32, 21, 8] have substantially bolstered the dependability of optical flow predictions. To navigate challenges like occlusions and blur effects, innovative tactics—including joint representation learning [53], feature-driven flow regularization [19], iterative refinement [20, 18], and comprehensive motion analysis [22, 30]—have been employed. Addressing the smoothness constraint, [22]
+
+proposed a global motion refinement strategy anchored on attention mechanisms. Meanwhile, [30] captures motion affinities using graph techniques and [29] introduced kernel patch attention (KPA) for the same purpose, though KPA's static kernel window size could potentially curb its efficacy in managing variations in scale and shape.
+
+Self-Attention. Self-attention operations have become instrumental in computer vision for discerning global contexts in images and videos [44, 45, 57]. Notably, non-local attention, exemplified by [57] and [17], is pivotal in visual Transformers [10, 12]. Recent advancements, such as Swin [28] and NAT [14], harness the inductive bias to enhance Transformers by applying attention within local windows. Inspired by these, our paper presents two Gaussian-based attention modules for optical flow.
+
+# 3. Our Approach
+
+# 3.1. Preliminaries
+
+Motivation. Fig. 3 visually elucidates the core motivation driving our research. It can be observed that the ground truth optical flow field reveals the intricate nature of motion affinities. These affinities are not only deeply intertwined with contextual relationships but also exhibit pronounced local characteristics. Conventional methods often fall short in aligning with the inherent dynamics of the optical flow field. This observation has propelled us to integrate Gaussian attention into the optical flow model, aiming for a marked enhancement in its precision.
+
+# 3.2. Overview
+
+Our GAFlow encompasses two pivotal sub-modules: representation learning module  $(\mathbb{R}_{\beta})$  and feature matching module  $(\mathbb{F}_{\gamma})$ , as visualized in Fig. 2. Specifically,  $\mathbb{R}_{\beta}$  represents the functions of acquiring the feature maps  $(\mathbf{f}_1,\mathbf{f}_2,\mathbf{f}_c)$ ,
+
+![](images/d6b6f053f7311a2dc7f0760cb881c0e4939ef3106b6af311851563df0b96972c.jpg)  
+(a) Non-local Attention
+
+![](images/faff0e6af18e467d7aa151e8e5e349c02edcd112465222a134dd6151732db464.jpg)  
+(b) Gaussian Constrained Attention
+
+![](images/60e8c876a6c800f27e9a9702c815f016918a333320755e416a847a04c5f8825e.jpg)  
+(c) Gaussian Guided Attention  
+Figure 4: Architecture comparisons. (a) Standard Non-local Attention, (b) Our Gaussian-Constrained Attention tailored for representation enhancement, and (c) Our Gaussian-Guided Attention, designed to model motion affinities using learnable Gaussian attention. Here,  $\mathbf{X}$  represents the basic/context feature, while  $\mathbf{Y}$  signifies the motion feature.
+
+corresponding to the feature encoders combined with the proposed Gaussian-Constrained Layer (GCL).  $\mathbb{F}_{\gamma}$  pertains to the recurrent flow decoder, fortified with our bespoke Gaussian-Guided Attention Module (GGAM).
+
+At their core, these Gaussian-centric modules can be seamlessly integrated into flow models. Their inclusion accentuates local attributes during both the phases of representation learning and feature matching. Subsequent sections further unpack the mechanics of our GCL and GGAM.
+
+# 3.3. Gaussian-Constrained Layer
+
+The pixel-wise matching is susceptible to feature quality; Yet, the appearance changes caused by the motion blur and the illumination variations lower the feature discrimination. To avoid ambiguities, we propose Gaussian-Constrained Layer (GCL) to obtain the fine-grained structural information and locally discriminative representations for feature matching. Our GCL is designed based upon the standard Transformer [10, 28] block (see Fig. 4 (b)). Specifically, given the base feature  $\mathbf{x}$ , it is formulated as:
+
+$$
+\begin{array}{l} \hat {\mathbf {x}} = \operatorname {G C A} (\mathrm {L N} (\mathbf {x})) + \mathbf {x}, \tag {1} \\ \mathbf {y} = \operatorname {F F N} (\operatorname {L N} (\hat {\mathbf {x}})) + \hat {\mathbf {x}}, \\ \end{array}
+$$
+
+where  $\mathrm{LN}(\cdot)$  and  $\mathrm{FFN}(\cdot)$  denote the general layer normalization and feed-forward network respectively in Transformer block.  $\mathrm{GCA}(\cdot)$  indicates Gaussian Constrained Attention, which is the core component in our GCL.
+
+Here, we formulate GCA as a task-specific local operation, which not only avoids global misleading context but also reduces the complexity of attention computation. Therefore, it can be formulated as:
+
+$$
+\begin{array}{l} \mathrm {Q} _ {i} = L _ {i} ^ {Q} (\mathbf {x} ^ {\prime}), \mathrm {K} _ {i} = L _ {i} ^ {K} (\mathbf {x} ^ {\prime}), \mathrm {V} _ {i} = L _ {i} ^ {V} (\mathbf {x} ^ {\prime}), \\ h _ {i} = \mathcal {G} _ {\mathrm {A}} \left(\mathrm {Q} _ {i}, \bar {\mathrm {K}} _ {i}, \bar {\mathrm {V}} _ {i}\right), \tag {2} \\ \mathrm {H} = \operatorname {C o n c a t} \left(h _ {1}, h _ {2}, \dots , h _ {n}\right), \\ \end{array}
+$$
+
+where  $\mathbf{x}' = \mathrm{LN}(\mathbf{x})$ .  $L_{i}^{Q}(\cdot), L_{i}^{K}(\cdot)$ , and  $L_{i}^{V}(\cdot)$  denote linear
+
+projections for the  $i$ -th head.  $\mathcal{G}_{\mathrm{A}}(\cdot)$  is Gaussian attention function, which takes the query feature  $\mathrm{Q}_i$ , and the regional features of key  $\bar{\mathrm{K}}_i$  and value  $\bar{\mathrm{V}}_i$  as inputs:
+
+$$
+\mathcal {G} _ {\mathrm {A}} (\mathrm {Q}, \bar {\mathrm {K}}, \bar {\mathrm {V}}) = \operatorname {S o f t m a x} \left(\mathrm {G} _ {l r} \cdot \left(\mathrm {Q} \bar {\mathrm {K}} ^ {\top}\right) / \sqrt {d}\right) \cdot \bar {\mathrm {V}}, \tag {3}
+$$
+
+where  $\mathrm{G}_{lr}$  means a learnable Gaussian kernel with the shape of  $k\times k$ . It is initialized as a standard Gaussian distribution and can be updated by adding a learnable amplitude matrix  $\mathcal{A}$  during model training. In the inference process,  $\mathrm{G}_{lr}$  works as a constraint mask to reorganize the weights of attentive feature aggregation.
+
+Let the neighborhood of a pixel at the point  $p$  be  $\mathcal{N}(p)$ ; thus the attention on a single pixel can be defined as:
+
+$$
+h _ {(p)} = \operatorname {S o f t m a x} \left(\mathrm {G} _ {l r} \cdot \left(\mathrm {Q} _ {(p)} \bar {\mathrm {K}}\right) _ {\mathcal {N} (p)} ^ {\intercal} / \sqrt {d}\right) \cdot \bar {\mathrm {V}} _ {\mathcal {N} (p)}. \tag {4}
+$$
+
+Note that the operating range is scalable with the varying region of  $\mathcal{N}(p)$ . For instance, it can be extended to all pixels (i.e.,  $\mathcal{N}(p)$  is equivalent to the image size), leading to a global self-attention in a Gaussian-constrained manner.
+
+# 3.4. Gaussian-Guided Attention Module
+
+Our Idea/Formulation. In image processing, the Gaussian filter is a widely-used operator that provides a linear scale space for smoothing, where the input image is smoothed at a constant rate in all directions [47]. Here, our idea is to apply the spatially variant Gaussian to smooth the motion feature  $\mathbf{f}_m$ . Formally, it can be given as:
+
+$$
+\left(\mathrm {F} * \mathcal {G}\right) (p) = \sum_ {p _ {i} \in \mathcal {N} _ {p}} \mathcal {G} \left(p _ {i} - p\right) \mathbf {f} _ {m} ^ {i}, \tag {5}
+$$
+
+where  $\mathcal{N}_p$  denotes a square neighborhood, centered at the pixel  $p$ , with the pre-defined kernel size  $k\times k$ , and  $p_i$  indicates the position  $i$  in 2D grid space within  $\mathcal{N}_p$ .  $\mathbf{f}_m^i$  refers to the feature at position  $i$  within  $\mathbf{f}_m$ , utilized in the calculation.  $\mathcal{G}(\cdot)$  is a 2D Gaussian function, which is defined as:
+
+![](images/6fc3f1f91ded73269c752a9df8830c608142c3d6752fa580ec9c5915b03a019c.jpg)  
+Reference
+
+![](images/eb96313ca206fda03bdc3640a3c609c6bde033fd006347d246b2995444d68bcc.jpg)  
+GT
+
+![](images/44c77683b503028e4aa22f466fbc74a19d08b0040e232d5fa9fc6cfdf627eecf.jpg)  
+RAFT  
+Figure 5: Qualitative comparisons with RAFT [42] and GMFlow [49] on some challenging samples, including large motion, occlusion and motion blur, of Sintel test set. The quantitative results are provided by the official website.
+
+![](images/8df7b2a54ca541dcdc2e143be4ef30c3b91c020d424d6b5d076020ecc0d14847.jpg)  
+GMFlow
+
+![](images/786d5c2e0b8f75d5753931cddec8d130f6af427bf50018fd117e9d6864b2a06f.jpg)  
+Ours
+
+$$
+\mathcal {G} (x, y) = A \exp \left(- \left(\frac {(x - x _ {0}) ^ {2}}{2 \sigma_ {x} ^ {2}} + \frac {(y - y _ {0}) ^ {2}}{2 \sigma_ {y} ^ {2}}\right)\right), \tag {6}
+$$
+
+where  $A$  denotes the static amplitude ( $A = 1$  as the default setting) and  $p_0 = (x_0, y_0)$  means the center point.  $(\sigma_x; \sigma_y)$  indicate the variances which are set to  $\sigma_x = \sigma_y = \sigma$ , determining the operating range of smoothness. However, directly applying the Gaussian smoothing is sub-optimal for capturing the local properties, as the kernel is rigid (or fixed) and the clutters could be inevitably involved in providing false guidance. Next, we show how to make the Gaussian attention more adaptive and also end-to-end trainable.
+
+Gaussian-Guided Attention with Context (GGAC). To begin with, we incorporate the contextual information, which preserves the fine-grained structural information, into the Gaussian Attention. Specifically, given the context feature  $\mathbf{f}_c\in \mathbb{R}^{c\times h\times w}$  and motion feature  $\mathbf{f}_m\in \mathbb{R}^{c\times h\times w}$ , we rewrite Eq. (5) as:
+
+$$
+\left(\mathrm {F} * \mathcal {G} _ {\mathbb {C}}\right) (p) = \sum_ {p _ {i} \in \mathcal {N} _ {p}} \mathcal {G} _ {\mathbb {C} (p _ {i} - p)} \left(\mathbf {f} _ {c}\right) \rho \left(\mathbf {f} _ {m}\right) ^ {i}, \tag {7}
+$$
+
+where  $\mathcal{G}_{\mathbb{C}(p_i - p)}(\cdot)$  is an adaptive kernel function taking the context features in  $\mathcal{N}_p$  as inputs to obtain the context-preserving kernel.  $\rho (\cdot)$  is a linear operation for producing the embedded motion feature. We formulate the context-preserving kernel function as:
+
+$$
+\mathcal {G} _ {\mathrm {C} \left(p _ {i} - p\right)} \left(\mathbf {f} _ {c}\right) = \mathcal {G} ^ {\prime} \left(p _ {i} - p\right) \mathcal {F} \left(\mathbf {f} _ {c}\right), \tag {8}
+$$
+
+where  $\mathcal{G}'(p_i - p) \in \mathbb{R}^{k \times k \times h \times w}$  denotes the expanded Gaussian kernel in the spatial dimension, which is prepared for generating the data-dependent kernel matrices with the shape of  $k \times k$  based on the corresponding weights on each position in  $h \times w$ , and  $\mathcal{F}(\cdot)$  is the dynamic weight function for mining the guidance prior on the context feature  $\mathbf{f}_c$ .
+
+Rather than simply utilizing a learnable matrix as in convolution kernels, we follow [22] to apply the embedded
+
+Gaussian with normalization [44] on the context feature  $\mathbf{f}_c$  to produce the attention map. To match the dimension of the pre-defined Gaussian kernel  $\mathcal{G}'(p_i - p) \in \mathbb{R}^{K \times N}$ , where  $N = h \times w$ , and  $K = k \times k$  denoting the spatial dimension of kernel size, a naive solution is to discard the redundant information in  $\mathcal{F}(\mathbf{f}_c)$ . Here, we present a kernel-based context-preserving attention operation, which takes the asymmetric query and key feature maps in the spatial dimension as inputs. In detail, given the embedded context features  $\theta(\mathbf{f}_c) \in \mathbb{R}^{c \times h \times w}$ , we employ an unfolding operator (e.g., torch.nn.Unfold) to get  $\mathrm{U}(\theta(\mathbf{f}_c))$ , thus the dimension is transformed from  $c \times N$  to  $c \times N \times K$ . Then we measure the similarities between all pairs within the kernel region as:
+
+$$
+\mathcal {F} \left(\mathbf {f} _ {c}\right) = \frac {\exp \left(\mathrm {U} \left(\theta \left(\mathbf {f} _ {c}\right)\right) _ {l} ^ {T} \phi \left(\mathbf {f} _ {c}\right) _ {j} / \sqrt {c}\right)}{\sum_ {\forall j} \exp \left(\mathrm {U} \left(\theta \left(\mathbf {f} _ {c}\right)\right) _ {l} ^ {T} \phi \left(\mathbf {f} _ {c}\right) _ {j} / \sqrt {c}\right)}, \tag {9}
+$$
+
+where  $l \in K$  and  $j \in c$ , and the size of  $\mathcal{F}(\mathbf{f}_c)$  is  $K \times N$ .  $\theta(\cdot)$  and  $\phi(\cdot)$  indicates linear projections for channel-wise feature aggregation [22].
+
+Gaussian-Guided Attention with Deformation (GGAD). While Gaussian attention with context effectively addresses the problem of flow field over-smoothing caused by the data-agnostic Gaussian kernel, it still faces a limitation due to the rigid operating region of the Gaussian kernel. This constraint hinders the smoothness performance for motion feature refinement. To mitigate this issue, we take a further step to optimize the operating region of the Gaussian kernel by learning the deformable kernels in a data-driven manner, as shown in Fig. 4 (c). To avoid the static amplitude  $A$  of the Gaussian function, we design a dynamic amplitude operator based on the cross-frame matching features. In practice, similar to Eq. (7), our Gaussian-guided attention can be further formulated as:
+
+$$
+\left(\mathrm {F} * \mathcal {G} _ {\mathbb {D}}\right) (p) = \sum_ {p _ {i} \in \mathcal {N} _ {p}} \mathcal {G} _ {\mathbb {D} \left(p _ {i} - p\right)} \left(\mathbf {f} _ {c}, \mathbf {f} _ {m}\right) \rho \left(\mathbf {f} _ {m}\right), \tag {10}
+$$
+
+<table><tr><td rowspan="2">Training</td><td rowspan="2">Method</td><td rowspan="2">Reference</td><td colspan="2">Sintel (Val)</td><td colspan="2">KITTI-15 (Val)</td><td colspan="2">Sintel (Test)</td><td>KITTI-15 (Test)</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td><td>Clean</td><td>Final</td><td>F1-all</td></tr><tr><td rowspan="14">Val: C + T / Test: +S+K+H</td><td>RAFT [42]</td><td>ECCV-20</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>1.61</td><td>2.86</td><td>5.10</td></tr><tr><td>SCV [23]</td><td>CVPR-21</td><td>1.29</td><td>2.95</td><td>6.80</td><td>19.3</td><td>1.77</td><td>3.88</td><td>6.17</td></tr><tr><td>GMA [22]</td><td>ICCV-21</td><td>1.30</td><td>2.74</td><td>4.69</td><td>17.1</td><td>1.39</td><td>2.47</td><td>5.15</td></tr><tr><td>SeparableFlow[52]</td><td>ICCV-21</td><td>1.30</td><td>2.59</td><td>4.60</td><td>15.9</td><td>1.50</td><td>2.67</td><td>4.64</td></tr><tr><td>Flow1D [48]</td><td>ICCV-21</td><td>1.98</td><td>3.27</td><td>6.69</td><td>23.0</td><td>2.24</td><td>3.81</td><td>6.27</td></tr><tr><td>AGFlow [30]</td><td>AAAI-22</td><td>1.31</td><td>2.69</td><td>4.82</td><td>17.0</td><td>1.43</td><td>2.47</td><td>4.89</td></tr><tr><td>GMFlowNet [55]</td><td>CVPR-22</td><td>1.14</td><td>2.71</td><td>4.24</td><td>15.4</td><td>1.39</td><td>2.65</td><td>4.79</td></tr><tr><td>GMFlow [49]</td><td>CVPR-22</td><td>1.08</td><td>2.48</td><td>7.77</td><td>23.4</td><td>1.74</td><td>2.90</td><td>9.32</td></tr><tr><td>CRAFT [37]</td><td>CVPR-22</td><td>1.27</td><td>2.79</td><td>4.88</td><td>17.5</td><td>1.45</td><td>2.42</td><td>4.79</td></tr><tr><td>DIP [56]</td><td>CVPR-22</td><td>1.30</td><td>2.82</td><td>4.29</td><td>13.7</td><td>1.44</td><td>2.83</td><td>4.21</td></tr><tr><td>KPA-Flow [30]</td><td>CVPR-22</td><td>1.28</td><td>2.68</td><td>4.46</td><td>15.9</td><td>1.35</td><td>2.36</td><td>4.60</td></tr><tr><td>OCTC [21]</td><td>CVPR-22</td><td>1.31</td><td>2.67</td><td>4.72</td><td>16.3</td><td>1.41</td><td>2.57</td><td>4.33</td></tr><tr><td>SKFlow [41]</td><td>NeurIPS-22</td><td>1.22</td><td>2.46</td><td>4.27</td><td>15.5</td><td>1.28</td><td>2.27</td><td>4.84</td></tr><tr><td>GAFlow (ours)</td><td></td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>1.21</td><td>2.24</td><td>4.52</td></tr><tr><td rowspan="2">A / +TSKHV</td><td>RAFT-A [39]</td><td>CVPR-21</td><td>1.95</td><td>2.57</td><td>4.23</td><td>-</td><td>2.01</td><td>3.14</td><td>4.78</td></tr><tr><td>RAFT-it [38]</td><td>ECCV-22</td><td>1.74</td><td>2.41</td><td>4.18</td><td>13.4</td><td>1.55</td><td>2.90</td><td>4.31</td></tr><tr><td rowspan="2">I+CT / +SKH</td><td>FlowFormer [16]</td><td>ECCV-22</td><td>1.01</td><td>2.40</td><td>4.09</td><td>14.7</td><td>1.16</td><td>2.09</td><td>4.68</td></tr><tr><td>GAFlow-FF (ours)</td><td></td><td>0.95</td><td>2.34</td><td>3.92</td><td>13.9</td><td>1.15</td><td>2.05</td><td>4.42</td></tr></table>
+
+Table 1: Quantitative comparison with state-of-the-art models on standard benchmarks for cross-dataset evaluation and online testing. “C+T” indicates the models trained on FlyingChairs and FlyingThings for generalization ability evaluation. “+S+K+H” denotes more training data involved from Sintel, KITTI-2015, and HD1K. “A” indicates the models are trained on AutoFlow [39] dataset for Val set evaluation. “V” denotes VIPER [36] dataset. “T” means the encoders are pre-trained on ImageNet [9]. The best and second-best results are marked in bold and underline, respectively.
+
+where  $\mathcal{G}_{\mathbb{D}(p_i - p)}(\cdot)$  is the deformable Gaussian kernel function that is used to produce the more flexible Gaussian attention for adaptively capturing the relevant information and avoiding rigid kernel boundary in a data-dependent manner. Specifically, the deformable Gaussian kernel is given by:
+
+$$
+\mathcal {G} _ {\mathbb {D} (p _ {i} - p)} \left(\mathbf {f} _ {c}, \mathbf {f} _ {m}\right) = \mathcal {A} \left(\mathbf {f} _ {m}\right) \mathcal {D} _ {(p _ {i} - p)} \left(\mathbf {f} _ {m}\right) \mathcal {F} \left(\mathbf {f} _ {c}\right), \tag {11}
+$$
+
+where  $\mathcal{A}(\cdot)$  indicates the amplitude operator taking the motion feature  $\mathbf{f}_{\mathbf{m}}$  to produce adaptive amplitudes,  $\mathcal{F}(\mathbf{f}_c)$  is the kernel-based context-preserving attention matrix as in Eq. (9), and  $\mathcal{D}_{(p_i - p)}(\cdot)$  denotes the deformable Gaussian operator, which can be formulated as:
+
+$$
+\mathcal {D} _ {(p _ {i} - p)} \left(\mathbf {f} _ {m}\right) = \mathcal {W} \left(\mathcal {G} ^ {\prime} (p _ {i} - p), \mathcal {O} \left(\mathbf {f} _ {m}\right)\right), \tag {12}
+$$
+
+where  $\mathcal{G}'(p_i - p) \in \mathbb{R}^{k \times k \times h \times w}$  indicates the spatially expanded Gaussian kernel as in Eq. (8), and  $\mathcal{O}(\mathbf{f}_m)$  denotes the offset maps predicted from the motion feature.  $\mathcal{W}(\cdot)$  is the warp function taking the obtained offsets as inputs and operating on the Gaussian kernel.
+
+Another important component in the deformable Gaussian kernel (Eq. (11)) is the amplitude operator  $\mathcal{A}(\cdot)$ , which is given by:
+
+$$
+\mathcal {A} \left(\mathbf {f} _ {m}\right) = 1 + \vartheta \left(\mathbf {f} _ {m}\right) \lambda , \tag {13}
+$$
+
+where  $\lambda$  indicates a learnable parameter to constrain the fluctuation of the generated amplitude, and  $\vartheta(\cdot)$  is a linear function. Finally, similar to the expanding strategy in
+
+the deformable Gaussian operator, the learned amplitude  $\mathcal{A}(\mathbf{f}_m)$  can be easily transformed to operate on the Gaussian kernel  $\mathcal{G}'(p_i - p)$  for generating a more flexible one.
+
+# 4. Experimental Results
+
+# 4.1. Implementation Details
+
+For fair comparison with existing methods [22, 37, 29], we first plug 1 GCL and 1 GGAM into RAFT [42] to build a small model, i.e., GAFlow-S. Specifically, Gaussian-Constrained Layer (GCL) is appended to the motion encoder with  $\sigma = 9$ . Gaussian-Guided Attention Module (GGAM) performs feature smoothing on context and motion features, where we set sigma to 20 and 15 for Sintel and KITTI, respectively. Besides, to further explore the potential of our approach, we also employ a stronger baseline with POLA [55] modules and SKBlocks [41], which is regarded as the default model of GAFlow. Furthermore, we enhance the model's capabilities by integrating the proposed module into FlowFormer [16], resulting in a robust and advanced model termed GAFlow-FF.
+
+All experiments are conducted based on PyTorch toolbox. During training our GAFlow model, we follow RAFT to set the batch sizes to 6 and adopt AdamW optimizer with one-cycle learning rate policy [42]. Similar to previous works [42, 22, 30], the synthetic datasets are also involved
+
+![](images/be22d090b1f9a65da7586b8ca8f2df4a7ec2610281d85b29ea7ee79ed5767900.jpg)  
+(a) Reference
+
+![](images/aa01ee786dddc31a82bbdef9c2ded12d73dbaced06dc769de504653c9115757e.jpg)  
+(c) Flow of GGAD (ours)
+
+![](images/9dca02923b61327c9709f0f91b50cb776f8f4bcb2c25a60e289e1cfe5d8cebf8.jpg)  
+(e) Flow of GMA
+
+![](images/ab48a96144bd9b989ff8382fbdd9a4851ac1ae16f0ef3be9986b535c2aa990ab.jpg)  
+(b) GGAC (ours)
+
+![](images/d46930a9c231877111598407569039b1914df62d99f95e7370748280d78b3d7a.jpg)  
+(d) GGAD (ours)  
+Figure 6: A challenging sample from the Sintel final pass. The second row provides attention maps of our GGAC, GGAD and GMA [22], respectively. “P” indicates the query point to obtain attention maps.
+
+![](images/a386f0ba9caf6aacba9a9955f84a314b4a92747d860ae2effb33324579a3233d.jpg)  
+(f) GMA
+
+in model pre-training. The pre-training iterations on FlyingChairs [11] and FlyingThings [33] are set to 120k and 160k, respectively. Then the fine-tuning for Sintel online evaluation is conducted on the combined training data of Sintel [7], KITTI-2015 [34], and HD1K [24] for 160k iterations. Finally, the trained model requires another 50k iterations of finetuning on data of KITTI-2015 [34] before KITTI testing. We use only a single GPU and set the batch size to 1 for evaluation and online testing.
+
+# 4.2. Comparison with State-of-the-Arts
+
+Results on Sintel. We first compare the proposed approach with state-of-the-art methods for generalization evaluation on Sintel. As shown in Val sets of Tab. 1, our approach consistently achieves the best performance on all metrics. Specifically, GAFlow achieves the best EPE scores at 1.02 and 2.45 on the "C + T" setting. Besides, GAFlow-FF improves the SOTA performance to 0.95 and 2.34 in EPE on Sintel clean and final passes, respectively. For online testing, we follow prior works [22, 29, 37] to utilize the warm-start strategy [42]. GAFlow achieves the best EPE scores at 1.21 and 2.24 on the standard training setting. Moreover, GAFlow-FF sets a new record at 1.15 and 2.05 in EPE, outperforming recent works by a relatively large margin.
+
+We compare the proposed GAFlow with the well-known methods RAFT [42] and GMFlow [49] on Sintel test set, and some qualitative comparisons are illustrated in Fig. 5. The results demonstrate that the proposed approach can effectively leverage the local structural information and high-order relations to resolve the ambiguities in motion learning, leading to a more robust and flexible model for handling the challenges in optical flow estimation.
+
+Results on KITTI. As shown in Tab. 1, GFlow achieves 3.98 in EPE and  $15.0\%$  in F1-all on the KITTI Val set, which is comparable with the SOTA model FlowFormer yet with less computational overhead. Moreover, GFlow-FF further boosts the scores to 3.92 and  $13.9\%$ . For online testing, our models achieve the top-ranked performances at  $4.52\%$  and  $4.42\%$  in F1-score.
+
+<table><tr><td>Sintel</td><td>Type</td><td>RAFT[42] (EPE)</td><td>GMA[22] (EPE)</td><td>KPA[29] (EPE)</td><td>GAFlow-S (EPE)</td></tr><tr><td rowspan="4">Clean (train)</td><td>s0-10</td><td>0.32</td><td>0.27</td><td>0.26</td><td>0.24</td></tr><tr><td>s10-40</td><td>1.55</td><td>1.35</td><td>1.38</td><td>1.29</td></tr><tr><td>s40+</td><td>8.83</td><td>8.55</td><td>8.43</td><td>7.92</td></tr><tr><td>All</td><td>1.41</td><td>1.31</td><td>1.28</td><td>1.21</td></tr><tr><td rowspan="4">Final (train)</td><td>s0-10</td><td>0.52</td><td>0.54</td><td>0.54</td><td>0.51</td></tr><tr><td>s10-40</td><td>3.00</td><td>3.07</td><td>3.02</td><td>2.83</td></tr><tr><td>s40+</td><td>17.45</td><td>17.57</td><td>17.34</td><td>17.02</td></tr><tr><td>All</td><td>2.69</td><td>2.74</td><td>2.68</td><td>2.56</td></tr></table>
+
+Table 2: Quantitative results on different displacements. All methods are trained on “C+T” and evaluated on Sintel for fair comparison. s0-10, s10-40 and s40+ denote the ground truth flow value belonging to 0-10, 10-40 and 40+ pixels [7], respectively.
+
+# 4.3. Ablation Analysis
+
+Comparison with GMA. GMA [22] presents a global strategy for handling occlusion in flow estimation. As shown in Tab. 2, our GAflow-S achieves better performance on all metrics. This is because the global attention on context features involves too much misleading information for motion guidance, which contains long-range similarities in appearance but is improper for motion refinement (see Fig. 6 (f)). In contrast, our approach effectively takes the local property of regional context affinities into consideration, and leverages the extracted high-order relations with the flexible operating range to better infer the flow fields.
+
+Comparison with KPA. The recent work KPA-Flow [29] shares a similar insight with our approach, leveraging local attention to avoid global misleading information. However, its intrinsic defects in formulation inevitably hinder the effect of motion refinement. First, the zero padding patches (out of the image) lead to obvious deviation for similarity measurement. Second, the neighboring pixels could be partitioned into distinct pre-defined (fixed) patch and kernel windows, leading to abrupt shifts in operating regions. In contrast, our approach enables a flexible constraint and freeform operating regions in a learnable manner, ensuring the proper and stable guidance pattern. Moreover, we provide quantitative comparisons in Tab. 2, where our approach achieves better performance on all metrics.
+
+Ablation for Feature Enhancement. In Tab. 3 (# 1), we first compare the proposed GCL with the widely recognized Transformer blocks [28, 55, 35], which have been extensively demonstrated to be effective for feature extraction. Swin Transformer [28] requires at least two blocks to perform the window shifting strategy, consuming more computation overhead. For other methods, only one block is applied for fair comparison. POLA [55] has been shown to be an effective local attention-based approach for fea
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Sintel (Val)</td><td colspan="2">KITTI-15 (Val)</td><td rowspan="2">Param.</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td></tr><tr><td>RAFT [42]</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>5.3M</td></tr><tr><td colspan="6"># 1: Feature Enhancement</td></tr><tr><td>Swin Trans. [28]</td><td>1.45</td><td>2.75</td><td>5.16</td><td>17.3</td><td>7.3M</td></tr><tr><td>POLA×1 [55]</td><td>1.42</td><td>2.68</td><td>4.91</td><td>16.9</td><td>6.5M</td></tr><tr><td>cosFormer [35]</td><td>1.29</td><td>2.82</td><td>4.95</td><td>17.3</td><td>6.7M</td></tr><tr><td>L.Kernel</td><td>1.42</td><td>2.76</td><td>4.69</td><td>16.6</td><td>6.5M</td></tr><tr><td>GCL</td><td>1.33</td><td>2.67</td><td>4.61</td><td>16.5</td><td>6.5M</td></tr><tr><td colspan="6"># 2: Stronger Encoder</td></tr><tr><td>POLAs [55]</td><td>1.18</td><td>2.63</td><td>4.52</td><td>16.6</td><td>10.0M</td></tr><tr><td>No</td><td>1.33</td><td>2.67</td><td>4.61</td><td>16.5</td><td>6.5M</td></tr><tr><td colspan="6"># 3: Smoothing Pattern</td></tr><tr><td>+ GGAC</td><td>1.13</td><td>2.62</td><td>4.33</td><td>15.8</td><td>10.1M</td></tr><tr><td>+ GGAD</td><td>1.08</td><td>2.56</td><td>4.26</td><td>15.6</td><td>10.1M</td></tr><tr><td colspan="6"># 4: Compatibility with SOTA modules</td></tr><tr><td>Refine.Sp4 [49]</td><td>1.03</td><td>2.45</td><td>4.10</td><td>14.6</td><td>12.5M</td></tr><tr><td>SKBlocks [41]</td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>10.4M</td></tr></table>
+
+ture extraction with 6 or 12 stacked blocks (requiring extra  $4.35 / 8.7\mathrm{M}$  parameters). As shown in the table, using one block  $(\mathrm{POLA}_{\times 1})$  significantly weaken the power. The advanced linear Transformer cosFormer [35] exhibits a lower EPE score on Sintel Clean, whereas our GCL performs better on other metrics. Besides, we conduct an extra ablation for using a learnable kernel without Gaussian (L.Kernel). As can be seen, our GCL outperforms L.Kernel across all metrics. Particularly on the challenging Sintel, without a Gaussian constraint, performance declines significantly due to the uncontrolled misleading similarities at the kernel border. All experiments illustrate that, requiring similar computational overhead, the proposed GCL surpasses other methods by a relatively large margin.
+
+Ablation for Stronger Encoder. The smoothness constraint for flow estimation can be naturally regarded as a complementary component to the feature matching process, and benefits from stronger encoders for feature extraction. Thus, to further explore the potential of our approach, we follow prior work [55] to employ a stronger motion encoder with the standard POLA blocks, which largely boosts the performance on Sintel clean pass, as in Tab. 3 (# 2). Inspired by GMFlowNet [55], we build two types of encoding modules for separately handling Sintel and KITTI datasets.
+
+Ablation for Smoothing Pattern. The proposed GGAC is capable of producing flexible weight matrices for motion feature smoothing, which effectively tackles the issue of flow field over-smoothing caused by the data-agnostic Gaussian kernel. However, the issues of rigid operating re
+
+Table 3: Ablation experiments. L.Kernel indicates the learnable kernel without Gaussian. Settings as default are underlined. Refer to Sec. 4.3 for detailed comparisons.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">KITTI-15 (Val)</td><td rowspan="2">Param.</td><td rowspan="2">Time (s)</td></tr><tr><td>EPE</td><td>F1-all</td></tr><tr><td>GMFlowNet [55]</td><td>4.24</td><td>15.4</td><td>9.3M</td><td>0.32</td></tr><tr><td>FlowFormer [16]</td><td>4.09</td><td>14.7</td><td>18.2M</td><td>1.77</td></tr><tr><td>GAFlow (ours)</td><td>3.98</td><td>15.0</td><td>10.4M</td><td>0.48</td></tr><tr><td>GAFlow-FF (ours)</td><td>3.92</td><td>13.9</td><td>18.2M</td><td>1.85</td></tr></table>
+
+Table 4: Quantitative comparisons for computational complexity. The input size is  $376 \times 1248$  as in KITTI dataset.
+
+gion and static amplitude still affect the motion refinement (see Fig. 6 (b) and Tab. 3 (# 3)). Thus we further improve the approach with the spatially deformable kernel with the dynamic amplitude in a data-driven manner, i.e., GGAD, which boosts the performance by around  $3\%$ .
+
+Ablation for Compatibility with SOTA modules. In Tab. 3 (# 4), similar to prior work [49], we further perform flow refinement with the flow decoder on 1/4 features, termed Refine.Sp4, which helps to boost the performance on both Sintel and KITTI datasets. Moreover, we follow SKFlow [41] to employ SKBlocks in the motion encoding and state updating modules of the flow decoder. The ablation indicates that the GGAD module is compatible with SKBlocks, and the integration of the decoder leads to improved performance across all metrics, while introducing minimal additional parameters  $(10.1\rightarrow 10.4\mathrm{M})$
+
+Runtime Comparison. The comparisons of KITTI evaluation results, parameters and runtime are presented in Tab. 4. Although FlowFormer [16] uses ImageNet for encoder pretraining, our GAFlow achieves a competitive performance (even better in online testing, see Tab. 1) while consuming fewer parameters by  $7.8\mathrm{M}$  and reducing the inference time by  $72.9\%$ . Moreover, built on the previous SOTA model FlowFormer, our GAFlow-FF largely reduces the error by  $4.8\%$  with negligible computational complexity.
+
+# 5. Conclusion
+
+In this work, we introduce a novel Gaussian Attention Flow network (GAFlow) to explicitly highlight local properties during representation learning and enforce the motion affinity during matching. We deliver two Gaussian-based modules, i.e. Gaussian-Constrained Layer (GCL) and Gaussian-Guided Attention Module (GGAM), which works well with existing flow architectures and can greatly enhance the reliability of optical flow estimation. Extensive quantitative and qualitative comparisons performed on commonly-used datasets demonstrate that our method significantly outperforms the current alternatives.
+
+Acknowledgements. This work is supported by Sichuan Science and Technology Program of China under grant No.2023NSFSC0462.
+
+# References
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\ No newline at end of file
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+                                    "content": "learning [40, 20, 54] and reinforcement learning [1]) or refining feature similarity measurement methodologies (e.g., 4D correlation volumes [42] or 4D Transformer [16]). Despite these significant advancements, a glaring limitation persists: these models largely neglect the exploration of local structural information. This oversight hinders their performance, particularly in challenging scenarios involving large motions, occlusions, blurring effects, and shifts in appearance. Such situations demand an elevated focus on local discrimination and flow consistency. This brings us to an intriguing inquiry: Is it feasible to architect optical flow models that intrinsically focus on local structural information during both representation learning and feature matching?"
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+                                    "content": "ule. Central to our approach is a novel attention mechanism equipped with a learnable Gaussian kernel. This mechanism naturally prioritizes the local surroundings of each point, thereby accentuating the importance of local structural information. For the representation learning component, we introduce a novel Gaussian-Constrained Layer (GCL) embedded within the canonical feature encoder. This layer, fortified with a learnable Gaussian kernel, naturally prioritizes the local surroundings of each point, thus accentuating the significance of local structural data. It's worth noting that while the GCL builds upon the pixel-wise modeling typical of the Vision Transformer block, it possesses a sharper focus on local connections, which effectively enhances the feature discrimination for cross-frame matching, as depicted in Fig. 1. Moreover, our GCL is dynamic, comprising learnable parameters that can be finetuned in concert with the encoder."
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+                                    "content": "In optical flow prediction, traditional techniques prioritize the matching function, viewing it as indispensable when paired with distinctive features. These methods incorporate feature-similarity measures and smoothness constraints to optimize results [15, 5, 6]. With the advent of deep learning, the spotlight has largely shifted to feature-similarity [16, 42], often sidelining the crucial smoothness constraint. When considering it, the implicit smoothness loss is primarily employed [51, 26], presuming uniform flow fields — a simplification that overlooks intricate object deformations. While some approaches employ Graph techniques [30] or Transformers [22] to capture global motion, they tend to neglect the inherent locality of motion, potentially introducing inaccuracies. The challenge of leveraging neural networks to model motion relationships remains somewhat uncharted."
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+                                    "content": "Targeting the above goals, we introduce a novel Gaussian-Guided Attention Module (GGAM) to explicitly model the motion affinities for optical flow. To meet the neighborhood priority requirement, our GGAM is formulated as Gaussian-guided attention that naturally emphasizes the neighboring fields of each point. Second, unlike conventional Non-Local operation [44], our GGAM is built across the context feature map and embedded correlation"
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+                                    "content": "(cost) volume for more comprehensive relation modeling. Specifically, for capturing the matching-prior knowledge, the 4D correlation volumes [42] are mapped to be the amplitudes and offsets. The amplitude for each position is set to the Gaussian attention for scaling its amplitude value and the offsets are encoded by the Gaussian attention via the warping operation. It enables free-form deformation of the Gaussian attention and adaptive attention for handling the large displacement of objects. For the last requirement, we draw inspiration from self-attention operations, and map the context feature to the query and key features for modeling the appearance self-similarities. All these operations are fully differentiable in our GGAM."
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+                                    "content": "Optical Flow. In the epoch of deep learning, early optical flow models, such as [2, 46], viewed flow field prediction as a mapping challenge, translating two input frames into corresponding flow fields, predominantly harnessing the potency of data. Subsequent models significantly elevated flow estimation accuracy either by adopting more robust representation learning paradigms [40, 20, 54] or by implementing explicit feature-similarity measurement techniques [50, 43]. With the integration of advanced feature learning and cost-volume filtering modules, unsupervised methods have also witnessed remarkable advancements [31, 27, 25]. A notable development is RAFT [42], which employs a 4D correlation volume and a recurrent strategy for optical flow estimation. Building on its recurrent feature-matching paradigm, a slew of contempor"
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+                                            "content": "Figure 3: A simple illustration of the Gaussian constraint. \"Q\" represents the query point. The blue circle represents contextual affinity, mirroring the analogous patterns observed in the ground truth flow. Through the Gaussian constraint, we can effectively filter out deceptive relations, as highlighted within the red circle."
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+                                    "content": "rary models [3, 13, 32, 21, 8] have substantially bolstered the dependability of optical flow predictions. To navigate challenges like occlusions and blur effects, innovative tactics—including joint representation learning [53], feature-driven flow regularization [19], iterative refinement [20, 18], and comprehensive motion analysis [22, 30]—have been employed. Addressing the smoothness constraint, [22]"
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+                                    "content": "proposed a global motion refinement strategy anchored on attention mechanisms. Meanwhile, [30] captures motion affinities using graph techniques and [29] introduced kernel patch attention (KPA) for the same purpose, though KPA's static kernel window size could potentially curb its efficacy in managing variations in scale and shape."
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+                                    "content": "Self-Attention. Self-attention operations have become instrumental in computer vision for discerning global contexts in images and videos [44, 45, 57]. Notably, non-local attention, exemplified by [57] and [17], is pivotal in visual Transformers [10, 12]. Recent advancements, such as Swin [28] and NAT [14], harness the inductive bias to enhance Transformers by applying attention within local windows. Inspired by these, our paper presents two Gaussian-based attention modules for optical flow."
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+                                    "content": "Motivation. Fig. 3 visually elucidates the core motivation driving our research. It can be observed that the ground truth optical flow field reveals the intricate nature of motion affinities. These affinities are not only deeply intertwined with contextual relationships but also exhibit pronounced local characteristics. Conventional methods often fall short in aligning with the inherent dynamics of the optical flow field. This observation has propelled us to integrate Gaussian attention into the optical flow model, aiming for a marked enhancement in its precision."
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+                                    "content": "corresponding to the feature encoders combined with the proposed Gaussian-Constrained Layer (GCL). "
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+                                    "content": "The pixel-wise matching is susceptible to feature quality; Yet, the appearance changes caused by the motion blur and the illumination variations lower the feature discrimination. To avoid ambiguities, we propose Gaussian-Constrained Layer (GCL) to obtain the fine-grained structural information and locally discriminative representations for feature matching. Our GCL is designed based upon the standard Transformer [10, 28] block (see Fig. 4 (b)). Specifically, given the base feature "
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+                                    "content": ", it is formulated as:"
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+                                    "content": "\\begin{array}{l} \\hat {\\mathbf {x}} = \\operatorname {G C A} (\\mathrm {L N} (\\mathbf {x})) + \\mathbf {x}, \\tag {1} \\\\ \\mathbf {y} = \\operatorname {F F N} (\\operatorname {L N} (\\hat {\\mathbf {x}})) + \\hat {\\mathbf {x}}, \\\\ \\end{array}",
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\begin{array}{l} \\mathrm {Q} _ {i} = L _ {i} ^ {Q} (\\mathbf {x} ^ {\\prime}), \\mathrm {K} _ {i} = L _ {i} ^ {K} (\\mathbf {x} ^ {\\prime}), \\mathrm {V} _ {i} = L _ {i} ^ {V} (\\mathbf {x} ^ {\\prime}), \\\\ h _ {i} = \\mathcal {G} _ {\\mathrm {A}} \\left(\\mathrm {Q} _ {i}, \\bar {\\mathrm {K}} _ {i}, \\bar {\\mathrm {V}} _ {i}\\right), \\tag {2} \\\\ \\mathrm {H} = \\operatorname {C o n c a t} \\left(h _ {1}, h _ {2}, \\dots , h _ {n}\\right), \\\\ \\end{array}",
+                                    "image_path": "2e71efb79e13422e7ba7ad431816877f800f443dfdf04b5ca802ce63e980528a.jpg"
+                                }
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{x}' = \\mathrm{LN}(\\mathbf{x})"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". "
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+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{i}^{Q}(\\cdot), L_{i}^{K}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        700,
+                                        287,
+                                        714
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+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        700,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "L_{i}^{V}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        47,
+                                        700,
+                                        287,
+                                        714
+                                    ],
+                                    "type": "text",
+                                    "content": " denote linear"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                        265,
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+                        301
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                301
+                            ],
+                            "spans": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "projections for the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "-th head. "
+                                },
+                                {
+                                    "bbox": [
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+                                        265,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}_{\\mathrm{A}}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        265,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": " is Gaussian attention function, which takes the query feature "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        265,
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+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{Q}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": ", and the regional features of key "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        265,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathrm{K}}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        265,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": " and value "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        265,
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+                                        301
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{\\mathrm{V}}_i"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        265,
+                                        545,
+                                        301
+                                    ],
+                                    "type": "text",
+                                    "content": " as inputs:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {G} _ {\\mathrm {A}} (\\mathrm {Q}, \\bar {\\mathrm {K}}, \\bar {\\mathrm {V}}) = \\operatorname {S o f t m a x} \\left(\\mathrm {G} _ {l r} \\cdot \\left(\\mathrm {Q} \\bar {\\mathrm {K}} ^ {\\top}\\right) / \\sqrt {d}\\right) \\cdot \\bar {\\mathrm {V}}, \\tag {3}",
+                                    "image_path": "15c2dfb45d562cd445d8eccad07cf10fbf9446525d7445f1bc65755727639ccc.jpg"
+                                }
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+                    ],
+                    "index": 17
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+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            ],
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        405
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{G}_{lr}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": " means a learnable Gaussian kernel with the shape of "
+                                },
+                                {
+                                    "bbox": [
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+                                        333,
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+                                        405
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k\\times k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        333,
+                                        545,
+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": ". It is initialized as a standard Gaussian distribution and can be updated by adding a learnable amplitude matrix "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        333,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " during model training. In the inference process, "
+                                },
+                                {
+                                    "bbox": [
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+                                        333,
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+                                        405
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{G}_{lr}"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        333,
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+                                        405
+                                    ],
+                                    "type": "text",
+                                    "content": " works as a constraint mask to reorganize the weights of attentive feature aggregation."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Let the neighborhood of a pixel at the point "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " be "
+                                },
+                                {
+                                    "bbox": [
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+                                        405,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(p)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": "; thus the attention on a single pixel can be defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "h _ {(p)} = \\operatorname {S o f t m a x} \\left(\\mathrm {G} _ {l r} \\cdot \\left(\\mathrm {Q} _ {(p)} \\bar {\\mathrm {K}}\\right) _ {\\mathcal {N} (p)} ^ {\\intercal} / \\sqrt {d}\\right) \\cdot \\bar {\\mathrm {V}} _ {\\mathcal {N} (p)}. \\tag {4}",
+                                    "image_path": "3853750a6aa48a3d338ca26cefeb3b7957901f5a98b8791da884b08aefbb695a.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 20
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+                {
+                    "bbox": [
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+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
+                                        545,
+                                        510
+                                    ],
+                                    "type": "text",
+                                    "content": "Note that the operating range is scalable with the varying region of "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
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+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(p)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". For instance, it can be extended to all pixels (i.e., "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        510
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}(p)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        461,
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+                                        510
+                                    ],
+                                    "type": "text",
+                                    "content": " is equivalent to the image size), leading to a global self-attention in a Gaussian-constrained manner."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 21
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.4. Gaussian-Guided Attention Module"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 22
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Our Idea/Formulation. In image processing, the Gaussian filter is a widely-used operator that provides a linear scale space for smoothing, where the input image is smoothed at a constant rate in all directions [47]. Here, our idea is to apply the spatially variant Gaussian to smooth the motion feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_m"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        536,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Formally, it can be given as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 23
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\left(\\mathrm {F} * \\mathcal {G}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} \\left(p _ {i} - p\\right) \\mathbf {f} _ {m} ^ {i}, \\tag {5}",
+                                    "image_path": "7ff4bb3534bc707d590293dfae6878f597c2862ddf675f33434f0d53a1146808.jpg"
+                                }
+                            ]
+                        }
+                    ],
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+                {
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+                    "angle": 0,
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+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}_p"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " denotes a square neighborhood, centered at the pixel "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", with the pre-defined kernel size "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k\\times k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        653,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " indicates the position "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": " in 2D grid space within "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}_p"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        653,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        653,
+                                        545,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_m^i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " refers to the feature at position "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " within "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        653,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_m"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", utilized in the calculation. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a 2D Gaussian function, which is defined as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 25
+                }
+            ],
+            "discarded_blocks": [
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+                                        }
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+                                            "type": "text",
+                                            "content": "Ours"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {G} (x, y) = A \\exp \\left(- \\left(\\frac {(x - x _ {0}) ^ {2}}{2 \\sigma_ {x} ^ {2}} + \\frac {(y - y _ {0}) ^ {2}}{2 \\sigma_ {y} ^ {2}}\\right)\\right), \\tag {6}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "A"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " denotes the static amplitude ("
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "A = 1"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " as the default setting) and "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "p_0 = (x_0, y_0)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " means the center point. "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "(\\sigma_x; \\sigma_y)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        309,
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+                                        417
+                                    ],
+                                    "type": "text",
+                                    "content": " indicate the variances which are set to "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\sigma_x = \\sigma_y = \\sigma"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        309,
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+                                        417
+                                    ],
+                                    "type": "text",
+                                    "content": ", determining the operating range of smoothness. However, directly applying the Gaussian smoothing is sub-optimal for capturing the local properties, as the kernel is rigid (or fixed) and the clutters could be inevitably involved in providing false guidance. Next, we show how to make the Gaussian attention more adaptive and also end-to-end trainable."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Gaussian-Guided Attention with Context (GGAC). To begin with, we incorporate the contextual information, which preserves the fine-grained structural information, into the Gaussian Attention. Specifically, given the context feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_c\\in \\mathbb{R}^{c\\times h\\times w}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and motion feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        417,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_m\\in \\mathbb{R}^{c\\times h\\times w}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        417,
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+                                        489
+                                    ],
+                                    "type": "text",
+                                    "content": ", we rewrite Eq. (5) as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\left(\\mathrm {F} * \\mathcal {G} _ {\\mathbb {C}}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} _ {\\mathbb {C} (p _ {i} - p)} \\left(\\mathbf {f} _ {c}\\right) \\rho \\left(\\mathbf {f} _ {m}\\right) ^ {i}, \\tag {7}",
+                                    "image_path": "839325d7ab404c45c843d5161149053db4045022b3ac1d9f93892dc77450c00f.jpg"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                        590
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}_{\\mathbb{C}(p_i - p)}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        529,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is an adaptive kernel function taking the context features in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        529,
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+                                        590
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{N}_p"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        529,
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+                                    ],
+                                    "type": "text",
+                                    "content": " as inputs to obtain the context-preserving kernel. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        529,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\rho (\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        529,
+                                        287,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is a linear operation for producing the embedded motion feature. We formulate the context-preserving kernel function as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 15
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
+                    "lines": [
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+                            "bbox": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {G} _ {\\mathrm {C} \\left(p _ {i} - p\\right)} \\left(\\mathbf {f} _ {c}\\right) = \\mathcal {G} ^ {\\prime} \\left(p _ {i} - p\\right) \\mathcal {F} \\left(\\mathbf {f} _ {c}\\right), \\tag {8}",
+                                    "image_path": "a10efae4371462670639bacba7516c0d97bee6063218587f97ef799659f1b2cf.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 16
+                },
+                {
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+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            "spans": [
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
+                                        287,
+                                        689
+                                    ],
+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
+                                        287,
+                                        689
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{k \\times k \\times h \\times w}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
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+                                        689
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the expanded Gaussian kernel in the spatial dimension, which is prepared for generating the data-dependent kernel matrices with the shape of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "k \\times k"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
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+                                    ],
+                                    "type": "text",
+                                    "content": " based on the corresponding weights on each position in "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
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+                                        689
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "h \\times w"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        616,
+                                        287,
+                                        689
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        689
+                                    ],
+                                    "type": "text",
+                                    "content": " is the dynamic weight function for mining the guidance prior on the context feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_c"
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+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 17
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Rather than simply utilizing a learnable matrix as in convolution kernels, we follow [22] to apply the embedded"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 18
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Gaussian with normalization [44] on the context feature "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_c"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " to produce the attention map. To match the dimension of the pre-defined Gaussian kernel "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{K \\times N}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", where "
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+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "N = h \\times w"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", and "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        270,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K = k \\times k"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        270,
+                                        545,
+                                        427
+                                    ],
+                                    "type": "text",
+                                    "content": " denoting the spatial dimension of kernel size, a naive solution is to discard the redundant information in "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        270,
+                                        545,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\mathbf{f}_c)"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Here, we present a kernel-based context-preserving attention operation, which takes the asymmetric query and key feature maps in the spatial dimension as inputs. In detail, given the embedded context features "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "\\theta(\\mathbf{f}_c) \\in \\mathbb{R}^{c \\times h \\times w}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", we employ an unfolding operator (e.g., torch.nn.Unfold) to get "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathrm{U}(\\theta(\\mathbf{f}_c))"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", thus the dimension is transformed from "
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+                                {
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+                                    "type": "inline_equation",
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+                                    "type": "text",
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "c \\times N \\times K"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        270,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Then we measure the similarities between all pairs within the kernel region as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 19
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+                                    "content": "\\mathcal {F} \\left(\\mathbf {f} _ {c}\\right) = \\frac {\\exp \\left(\\mathrm {U} \\left(\\theta \\left(\\mathbf {f} _ {c}\\right)\\right) _ {l} ^ {T} \\phi \\left(\\mathbf {f} _ {c}\\right) _ {j} / \\sqrt {c}\\right)}{\\sum_ {\\forall j} \\exp \\left(\\mathrm {U} \\left(\\theta \\left(\\mathbf {f} _ {c}\\right)\\right) _ {l} ^ {T} \\phi \\left(\\mathbf {f} _ {c}\\right) _ {j} / \\sqrt {c}\\right)}, \\tag {9}",
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "text",
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ", and the size of "
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "K \\times N"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". "
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+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\theta(\\cdot)"
+                                },
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and "
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+                                {
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+                                {
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+                                    "type": "text",
+                                    "content": " indicates linear projections for channel-wise feature aggregation [22]."
+                                }
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+                                    "type": "text",
+                                    "content": "Gaussian-Guided Attention with Deformation (GGAD). While Gaussian attention with context effectively addresses the problem of flow field over-smoothing caused by the data-agnostic Gaussian kernel, it still faces a limitation due to the rigid operating region of the Gaussian kernel. This constraint hinders the smoothness performance for motion feature refinement. To mitigate this issue, we take a further step to optimize the operating region of the Gaussian kernel by learning the deformable kernels in a data-driven manner, as shown in Fig. 4 (c). To avoid the static amplitude "
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+                                    "type": "text",
+                                    "content": " of the Gaussian function, we design a dynamic amplitude operator based on the cross-frame matching features. In practice, similar to Eq. (7), our Gaussian-guided attention can be further formulated as:"
+                                }
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+                                    "content": "\\left(\\mathrm {F} * \\mathcal {G} _ {\\mathbb {D}}\\right) (p) = \\sum_ {p _ {i} \\in \\mathcal {N} _ {p}} \\mathcal {G} _ {\\mathbb {D} \\left(p _ {i} - p\\right)} \\left(\\mathbf {f} _ {c}, \\mathbf {f} _ {m}\\right) \\rho \\left(\\mathbf {f} _ {m}\\right), \\tag {10}",
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+                                            "html": "<table><tr><td rowspan=\"2\">Training</td><td rowspan=\"2\">Method</td><td rowspan=\"2\">Reference</td><td colspan=\"2\">Sintel (Val)</td><td colspan=\"2\">KITTI-15 (Val)</td><td colspan=\"2\">Sintel (Test)</td><td>KITTI-15 (Test)</td></tr><tr><td>Clean</td><td>Final</td><td>EPE</td><td>F1-all</td><td>Clean</td><td>Final</td><td>F1-all</td></tr><tr><td rowspan=\"14\">Val: C + T / Test: +S+K+H</td><td>RAFT [42]</td><td>ECCV-20</td><td>1.43</td><td>2.71</td><td>5.04</td><td>17.4</td><td>1.61</td><td>2.86</td><td>5.10</td></tr><tr><td>SCV [23]</td><td>CVPR-21</td><td>1.29</td><td>2.95</td><td>6.80</td><td>19.3</td><td>1.77</td><td>3.88</td><td>6.17</td></tr><tr><td>GMA [22]</td><td>ICCV-21</td><td>1.30</td><td>2.74</td><td>4.69</td><td>17.1</td><td>1.39</td><td>2.47</td><td>5.15</td></tr><tr><td>SeparableFlow[52]</td><td>ICCV-21</td><td>1.30</td><td>2.59</td><td>4.60</td><td>15.9</td><td>1.50</td><td>2.67</td><td>4.64</td></tr><tr><td>Flow1D [48]</td><td>ICCV-21</td><td>1.98</td><td>3.27</td><td>6.69</td><td>23.0</td><td>2.24</td><td>3.81</td><td>6.27</td></tr><tr><td>AGFlow [30]</td><td>AAAI-22</td><td>1.31</td><td>2.69</td><td>4.82</td><td>17.0</td><td>1.43</td><td>2.47</td><td>4.89</td></tr><tr><td>GMFlowNet [55]</td><td>CVPR-22</td><td>1.14</td><td>2.71</td><td>4.24</td><td>15.4</td><td>1.39</td><td>2.65</td><td>4.79</td></tr><tr><td>GMFlow [49]</td><td>CVPR-22</td><td>1.08</td><td>2.48</td><td>7.77</td><td>23.4</td><td>1.74</td><td>2.90</td><td>9.32</td></tr><tr><td>CRAFT [37]</td><td>CVPR-22</td><td>1.27</td><td>2.79</td><td>4.88</td><td>17.5</td><td>1.45</td><td>2.42</td><td>4.79</td></tr><tr><td>DIP [56]</td><td>CVPR-22</td><td>1.30</td><td>2.82</td><td>4.29</td><td>13.7</td><td>1.44</td><td>2.83</td><td>4.21</td></tr><tr><td>KPA-Flow [30]</td><td>CVPR-22</td><td>1.28</td><td>2.68</td><td>4.46</td><td>15.9</td><td>1.35</td><td>2.36</td><td>4.60</td></tr><tr><td>OCTC [21]</td><td>CVPR-22</td><td>1.31</td><td>2.67</td><td>4.72</td><td>16.3</td><td>1.41</td><td>2.57</td><td>4.33</td></tr><tr><td>SKFlow [41]</td><td>NeurIPS-22</td><td>1.22</td><td>2.46</td><td>4.27</td><td>15.5</td><td>1.28</td><td>2.27</td><td>4.84</td></tr><tr><td>GAFlow (ours)</td><td></td><td>1.02</td><td>2.45</td><td>3.98</td><td>15.0</td><td>1.21</td><td>2.24</td><td>4.52</td></tr><tr><td rowspan=\"2\">A / +TSKHV</td><td>RAFT-A [39]</td><td>CVPR-21</td><td>1.95</td><td>2.57</td><td>4.23</td><td>-</td><td>2.01</td><td>3.14</td><td>4.78</td></tr><tr><td>RAFT-it [38]</td><td>ECCV-22</td><td>1.74</td><td>2.41</td><td>4.18</td><td>13.4</td><td>1.55</td><td>2.90</td><td>4.31</td></tr><tr><td rowspan=\"2\">I+CT / +SKH</td><td>FlowFormer [16]</td><td>ECCV-22</td><td>1.01</td><td>2.40</td><td>4.09</td><td>14.7</td><td>1.16</td><td>2.09</td><td>4.68</td></tr><tr><td>GAFlow-FF (ours)</td><td></td><td>0.95</td><td>2.34</td><td>3.92</td><td>13.9</td><td>1.15</td><td>2.05</td><td>4.42</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 1: Quantitative comparison with state-of-the-art models on standard benchmarks for cross-dataset evaluation and online testing. “C+T” indicates the models trained on FlyingChairs and FlyingThings for generalization ability evaluation. “+S+K+H” denotes more training data involved from Sintel, KITTI-2015, and HD1K. “A” indicates the models are trained on AutoFlow [39] dataset for Val set evaluation. “V” denotes VIPER [36] dataset. “T” means the encoders are pre-trained on ImageNet [9]. The best and second-best results are marked in bold and underline, respectively."
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}_{\\mathbb{D}(p_i - p)}(\\cdot)"
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " is the deformable Gaussian kernel function that is used to produce the more flexible Gaussian attention for adaptively capturing the relevant information and avoiding rigid kernel boundary in a data-dependent manner. Specifically, the deformable Gaussian kernel is given by:"
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {G} _ {\\mathbb {D} (p _ {i} - p)} \\left(\\mathbf {f} _ {c}, \\mathbf {f} _ {m}\\right) = \\mathcal {A} \\left(\\mathbf {f} _ {m}\\right) \\mathcal {D} _ {(p _ {i} - p)} \\left(\\mathbf {f} _ {m}\\right) \\mathcal {F} \\left(\\mathbf {f} _ {c}\\right), \\tag {11}",
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                        287,
+                                        538
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates the amplitude operator taking the motion feature "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
+                                        287,
+                                        538
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathbf{f}_{\\mathbf{m}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
+                                        287,
+                                        538
+                                    ],
+                                    "type": "text",
+                                    "content": " to produce adaptive amplitudes, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
+                                        287,
+                                        538
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{F}(\\mathbf{f}_c)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
+                                        287,
+                                        538
+                                    ],
+                                    "type": "text",
+                                    "content": " is the kernel-based context-preserving attention matrix as in Eq. (9), and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
+                                        287,
+                                        538
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{D}_{(p_i - p)}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        479,
+                                        287,
+                                        538
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the deformable Gaussian operator, which can be formulated as:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
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+                                    "bbox": [
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {D} _ {(p _ {i} - p)} \\left(\\mathbf {f} _ {m}\\right) = \\mathcal {W} \\left(\\mathcal {G} ^ {\\prime} (p _ {i} - p), \\mathcal {O} \\left(\\mathbf {f} _ {m}\\right)\\right), \\tag {12}",
+                                    "image_path": "0e9d780feaed992437474beb3fccf15c1525b4ba8f24b8f217c9f42d3fb178e9.jpg"
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}'(p_i - p) \\in \\mathbb{R}^{k \\times k \\times h \\times w}"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " indicates the spatially expanded Gaussian kernel as in Eq. (8), and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        564,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{O}(\\mathbf{f}_m)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        564,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " denotes the offset maps predicted from the motion feature. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        564,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{W}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        564,
+                                        287,
+                                        624
+                                    ],
+                                    "type": "text",
+                                    "content": " is the warp function taking the obtained offsets as inputs and operating on the Gaussian kernel."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Another important component in the deformable Gaussian kernel (Eq. (11)) is the amplitude operator "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": ", which is given by:"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "interline_equation",
+                                    "content": "\\mathcal {A} \\left(\\mathbf {f} _ {m}\\right) = 1 + \\vartheta \\left(\\mathbf {f} _ {m}\\right) \\lambda , \\tag {13}",
+                                    "image_path": "665b97afbe97923a79fe2e6eb87f32aedc3e4afb9acc0500a09e990691a987c1.jpg"
+                                }
+                            ]
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+                {
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
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+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\lambda"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " indicates a learnable parameter to constrain the fluctuation of the generated amplitude, and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\vartheta(\\cdot)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        677,
+                                        287,
+                                        713
+                                    ],
+                                    "type": "text",
+                                    "content": " is a linear function. Finally, similar to the expanding strategy in"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    "angle": 0,
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "the deformable Gaussian operator, the learned amplitude "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        393,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{A}(\\mathbf{f}_m)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " can be easily transformed to operate on the Gaussian kernel "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\mathcal{G}'(p_i - p)"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                        431
+                                    ],
+                                    "type": "text",
+                                    "content": " for generating a more flexible one."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                    "type": "title",
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+                                    "type": "text",
+                                    "content": "4. Experimental Results"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
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+                                    "type": "text",
+                                    "content": "4.1. Implementation Details"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "For fair comparison with existing methods [22, 37, 29], we first plug 1 GCL and 1 GGAM into RAFT [42] to build a small model, i.e., GAFlow-S. Specifically, Gaussian-Constrained Layer (GCL) is appended to the motion encoder with "
+                                },
+                                {
+                                    "bbox": [
+                                        304,
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+                                    "type": "inline_equation",
+                                    "content": "\\sigma = 9"
+                                },
+                                {
+                                    "bbox": [
+                                        304,
+                                        484,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". Gaussian-Guided Attention Module (GGAM) performs feature smoothing on context and motion features, where we set sigma to 20 and 15 for Sintel and KITTI, respectively. Besides, to further explore the potential of our approach, we also employ a stronger baseline with POLA [55] modules and SKBlocks [41], which is regarded as the default model of GAFlow. Furthermore, we enhance the model's capabilities by integrating the proposed module into FlowFormer [16], resulting in a robust and advanced model termed GAFlow-FF."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "All experiments are conducted based on PyTorch toolbox. During training our GAFlow model, we follow RAFT to set the batch sizes to 6 and adopt AdamW optimizer with one-cycle learning rate policy [42]. Similar to previous works [42, 22, 30], the synthetic datasets are also involved"
+                                }
+                            ]
+                        }
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+                                            "type": "text",
+                                            "content": "(a) Reference"
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+                                            "content": "(c) Flow of GGAD (ours)"
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+                                            "type": "text",
+                                            "content": "(e) Flow of GMA"
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+                                            "content": "Figure 6: A challenging sample from the Sintel final pass. The second row provides attention maps of our GGAC, GGAD and GMA [22], respectively. “P” indicates the query point to obtain attention maps."
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+                                            "content": "(f) GMA"
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+                                    "type": "text",
+                                    "content": "in model pre-training. The pre-training iterations on FlyingChairs [11] and FlyingThings [33] are set to 120k and 160k, respectively. Then the fine-tuning for Sintel online evaluation is conducted on the combined training data of Sintel [7], KITTI-2015 [34], and HD1K [24] for 160k iterations. Finally, the trained model requires another 50k iterations of finetuning on data of KITTI-2015 [34] before KITTI testing. We use only a single GPU and set the batch size to 1 for evaluation and online testing."
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+                                    "content": "4.2. Comparison with State-of-the-Arts"
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+                                    "content": "Results on Sintel. We first compare the proposed approach with state-of-the-art methods for generalization evaluation on Sintel. As shown in Val sets of Tab. 1, our approach consistently achieves the best performance on all metrics. Specifically, GAFlow achieves the best EPE scores at 1.02 and 2.45 on the \"C + T\" setting. Besides, GAFlow-FF improves the SOTA performance to 0.95 and 2.34 in EPE on Sintel clean and final passes, respectively. For online testing, we follow prior works [22, 29, 37] to utilize the warm-start strategy [42]. GAFlow achieves the best EPE scores at 1.21 and 2.24 on the standard training setting. Moreover, GAFlow-FF sets a new record at 1.15 and 2.05 in EPE, outperforming recent works by a relatively large margin."
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+                                    "content": "We compare the proposed GAFlow with the well-known methods RAFT [42] and GMFlow [49] on Sintel test set, and some qualitative comparisons are illustrated in Fig. 5. The results demonstrate that the proposed approach can effectively leverage the local structural information and high-order relations to resolve the ambiguities in motion learning, leading to a more robust and flexible model for handling the challenges in optical flow estimation."
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+                                    "content": "Results on KITTI. As shown in Tab. 1, GFlow achieves 3.98 in EPE and "
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+                                    "content": " in F1-all on the KITTI Val set, which is comparable with the SOTA model FlowFormer yet with less computational overhead. Moreover, GFlow-FF further boosts the scores to 3.92 and "
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+                                    "content": " in F1-score."
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+                                            "html": "<table><tr><td>Sintel</td><td>Type</td><td>RAFT[42] (EPE)</td><td>GMA[22] (EPE)</td><td>KPA[29] (EPE)</td><td>GAFlow-S (EPE)</td></tr><tr><td rowspan=\"4\">Clean (train)</td><td>s0-10</td><td>0.32</td><td>0.27</td><td>0.26</td><td>0.24</td></tr><tr><td>s10-40</td><td>1.55</td><td>1.35</td><td>1.38</td><td>1.29</td></tr><tr><td>s40+</td><td>8.83</td><td>8.55</td><td>8.43</td><td>7.92</td></tr><tr><td>All</td><td>1.41</td><td>1.31</td><td>1.28</td><td>1.21</td></tr><tr><td rowspan=\"4\">Final (train)</td><td>s0-10</td><td>0.52</td><td>0.54</td><td>0.54</td><td>0.51</td></tr><tr><td>s10-40</td><td>3.00</td><td>3.07</td><td>3.02</td><td>2.83</td></tr><tr><td>s40+</td><td>17.45</td><td>17.57</td><td>17.34</td><td>17.02</td></tr><tr><td>All</td><td>2.69</td><td>2.74</td><td>2.68</td><td>2.56</td></tr></table>",
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+                                    "content": "Table 2: Quantitative results on different displacements. All methods are trained on “C+T” and evaluated on Sintel for fair comparison. s0-10, s10-40 and s40+ denote the ground truth flow value belonging to 0-10, 10-40 and 40+ pixels [7], respectively."
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+                                    "content": "Comparison with GMA. GMA [22] presents a global strategy for handling occlusion in flow estimation. As shown in Tab. 2, our GAflow-S achieves better performance on all metrics. This is because the global attention on context features involves too much misleading information for motion guidance, which contains long-range similarities in appearance but is improper for motion refinement (see Fig. 6 (f)). In contrast, our approach effectively takes the local property of regional context affinities into consideration, and leverages the extracted high-order relations with the flexible operating range to better infer the flow fields."
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+                                    "content": "Comparison with KPA. The recent work KPA-Flow [29] shares a similar insight with our approach, leveraging local attention to avoid global misleading information. However, its intrinsic defects in formulation inevitably hinder the effect of motion refinement. First, the zero padding patches (out of the image) lead to obvious deviation for similarity measurement. Second, the neighboring pixels could be partitioned into distinct pre-defined (fixed) patch and kernel windows, leading to abrupt shifts in operating regions. In contrast, our approach enables a flexible constraint and freeform operating regions in a learnable manner, ensuring the proper and stable guidance pattern. Moreover, we provide quantitative comparisons in Tab. 2, where our approach achieves better performance on all metrics."
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+                                    "content": "Ablation for Feature Enhancement. In Tab. 3 (# 1), we first compare the proposed GCL with the widely recognized Transformer blocks [28, 55, 35], which have been extensively demonstrated to be effective for feature extraction. Swin Transformer [28] requires at least two blocks to perform the window shifting strategy, consuming more computation overhead. For other methods, only one block is applied for fair comparison. POLA [55] has been shown to be an effective local attention-based approach for fea"
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+                                    "content": " parameters). As shown in the table, using one block "
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+                                    "content": " significantly weaken the power. The advanced linear Transformer cosFormer [35] exhibits a lower EPE score on Sintel Clean, whereas our GCL performs better on other metrics. Besides, we conduct an extra ablation for using a learnable kernel without Gaussian (L.Kernel). As can be seen, our GCL outperforms L.Kernel across all metrics. Particularly on the challenging Sintel, without a Gaussian constraint, performance declines significantly due to the uncontrolled misleading similarities at the kernel border. All experiments illustrate that, requiring similar computational overhead, the proposed GCL surpasses other methods by a relatively large margin."
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+                                    "content": "Ablation for Stronger Encoder. The smoothness constraint for flow estimation can be naturally regarded as a complementary component to the feature matching process, and benefits from stronger encoders for feature extraction. Thus, to further explore the potential of our approach, we follow prior work [55] to employ a stronger motion encoder with the standard POLA blocks, which largely boosts the performance on Sintel clean pass, as in Tab. 3 (# 2). Inspired by GMFlowNet [55], we build two types of encoding modules for separately handling Sintel and KITTI datasets."
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+                                    "content": "Ablation for Smoothing Pattern. The proposed GGAC is capable of producing flexible weight matrices for motion feature smoothing, which effectively tackles the issue of flow field over-smoothing caused by the data-agnostic Gaussian kernel. However, the issues of rigid operating re"
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+                                            "content": "Table 3: Ablation experiments. L.Kernel indicates the learnable kernel without Gaussian. Settings as default are underlined. Refer to Sec. 4.3 for detailed comparisons."
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+                                            "html": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">KITTI-15 (Val)</td><td rowspan=\"2\">Param.</td><td rowspan=\"2\">Time (s)</td></tr><tr><td>EPE</td><td>F1-all</td></tr><tr><td>GMFlowNet [55]</td><td>4.24</td><td>15.4</td><td>9.3M</td><td>0.32</td></tr><tr><td>FlowFormer [16]</td><td>4.09</td><td>14.7</td><td>18.2M</td><td>1.77</td></tr><tr><td>GAFlow (ours)</td><td>3.98</td><td>15.0</td><td>10.4M</td><td>0.48</td></tr><tr><td>GAFlow-FF (ours)</td><td>3.92</td><td>13.9</td><td>18.2M</td><td>1.85</td></tr></table>",
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+                                    "content": "Table 4: Quantitative comparisons for computational complexity. The input size is "
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+                                    "content": " as in KITTI dataset."
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+                                    "type": "text",
+                                    "content": "gion and static amplitude still affect the motion refinement (see Fig. 6 (b) and Tab. 3 (# 3)). Thus we further improve the approach with the spatially deformable kernel with the dynamic amplitude in a data-driven manner, i.e., GGAD, which boosts the performance by around "
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+                                    "type": "text",
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+                                    "content": "Ablation for Compatibility with SOTA modules. In Tab. 3 (# 4), similar to prior work [49], we further perform flow refinement with the flow decoder on 1/4 features, termed Refine.Sp4, which helps to boost the performance on both Sintel and KITTI datasets. Moreover, we follow SKFlow [41] to employ SKBlocks in the motion encoding and state updating modules of the flow decoder. The ablation indicates that the GGAD module is compatible with SKBlocks, and the integration of the decoder leads to improved performance across all metrics, while introducing minimal additional parameters "
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+                                    "content": "(10.1\\rightarrow 10.4\\mathrm{M})"
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+                                    "type": "text",
+                                    "content": "Runtime Comparison. The comparisons of KITTI evaluation results, parameters and runtime are presented in Tab. 4. Although FlowFormer [16] uses ImageNet for encoder pretraining, our GAFlow achieves a competitive performance (even better in online testing, see Tab. 1) while consuming fewer parameters by "
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+                                    "content": "7.8\\mathrm{M}"
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+                                    "type": "text",
+                                    "content": " and reducing the inference time by "
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+                                    "content": "72.9\\%"
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+                                    "type": "text",
+                                    "content": ". Moreover, built on the previous SOTA model FlowFormer, our GAFlow-FF largely reduces the error by "
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+                                    "content": " with negligible computational complexity."
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+                                    "type": "text",
+                                    "content": "5. Conclusion"
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+                                    "type": "text",
+                                    "content": "In this work, we introduce a novel Gaussian Attention Flow network (GAFlow) to explicitly highlight local properties during representation learning and enforce the motion affinity during matching. We deliver two Gaussian-based modules, i.e. Gaussian-Constrained Layer (GCL) and Gaussian-Guided Attention Module (GGAM), which works well with existing flow architectures and can greatly enhance the reliability of optical flow estimation. Extensive quantitative and qualitative comparisons performed on commonly-used datasets demonstrate that our method significantly outperforms the current alternatives."
+                                }
+                            ]
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+                    ],
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+                {
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+                                    "type": "text",
+                                    "content": "Acknowledgements. This work is supported by Sichuan Science and Technology Program of China under grant No.2023NSFSC0462."
+                                }
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+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                        }
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diff --git a/2023/GAIT_ Generating Aesthetic Indoor Tours with Deep Reinforcement Learning/04ba10a4-1e2a-4899-bb30-52b2658d3ca3_content_list.json b/2023/GAIT_ Generating Aesthetic Indoor Tours with Deep Reinforcement Learning/04ba10a4-1e2a-4899-bb30-52b2658d3ca3_content_list.json
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+        "type": "text",
+        "text": "Arie E. Kaufman<sup>1</sup>",
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+        "text": "Stony Brook University",
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+        "type": "text",
+        "text": "2Adobe Research",
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Placing and orienting a camera to compose aesthetically meaningful shots of a scene is not only a key objective in real-world photography and cinematography but also for virtual content creation. The framing of a camera often significantly contributes to the story telling in movies, games, and mixed reality applications. Generating single camera poses or even contiguous trajectories either requires a significant amount of manual labor or requires solving high-dimensional optimization problems, which can be computationally demanding and error-prone. In this paper, we introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) agent, that learns to automatically control a camera to generate a sequence of aesthetically meaningful views for synthetic 3D indoor scenes. To generate sequences of frames with high aesthetic value, GAIT relies on a neural aesthetics estimator, which is trained on a crowd-sourced dataset. Additionally, we introduce regularization techniques for diversity and smoothness to generate visually interesting trajectories for a 3D environment, and to constrain agent acceleration in the reward function to generate a smooth sequence of camera frames. We validated our method by comparing it to baseline algorithms, based on a perceptual user study, and through ablation studies. Code and visual results are available on the project website: https://desaixie.github.io/gait-rl",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Composing a shot by framing a scene with a camera plays an integral part in photography and cinematography. A carefully composed frame does not only provide the information of a scene, but also serves to define the visual style, to instill a desired emotion in the viewer, and to carry forward the story the artist wants to convey [39]. Photographers and movie directors commonly spend a significant amount of time to perfect the camera framing, which – consequently – often leads to extensive cost footprints. While framing scenes in virtual setups, such as games or mixed reality applications, is arguably less involved, defining aes",
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+        "img_path": "images/52c9b521338145e606db0cd6575476c8976543d6985a9c49ce9fb345866e0381.jpg",
+        "image_caption": [
+            "Figure 1: Our novel DRL agent, GAIT, automatically generates camera poses so as to obtain aesthetic views of 3D indoor scenes. Left: Views of three camera poses from a generated sequence. Right: the 3D indoor environment with three highlighted camera poses. Red, yellow, orange corresponds to the three frames on the left respectively, where the red dot is the initial pose. GAIT maintains high aesthetic views throughout the sequence, while satisfying the initial pose, diversity, smoothness, and boundary constraints."
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+        "type": "text",
+        "text": "thetically valuable camera poses and trajectories still requires a considerable amount of manual work. An artist has to position key frames in space, define the orientation of the camera, and specify the temporal profile for the interpolation between keyframes. While this provides a high degree of control, for many applications, it would be desirable to frame a scene automatically by computing camera poses.",
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+        "text": "Existing methods for automatically computing single camera poses or camera trajectories either rely on handcrafted methods with heuristics, which commonly do not generalize [40], are limited to specific applications, such as a trip between two cities [19], or specifically focus on moving targets [36]. Recently, it has been recognized that neural aesthetics estimators can serve as more generic solution for generating camera poses for the purpose of obtaining aesthetically meaningful camera frames [32] - a 2D image is mapped to a score that quantifies the aesthetics. An aesthetics estimator can be used to compare any two images with different contents or styles, which makes them applicable for finding views in lower dimensional spaces such as im",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "7409",
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+    {
+        "type": "text",
+        "text": "ages and videos [49], or in constrained robotics settings [1]. In a 3D environment, finding a desired camera pose requires searching in a continuous  $R^6$  space (i.e., position  $R^3$  and orientation in  $R^3$ ) while also considering obstacles or even dynamically moving objects. Computing camera paths in a flexible and versatile manner therefore is a challenging and open problem.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel method for automatically generating trajectories to aesthetically frame synthetic 3D indoor scenes. We introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) network that learns to move the camera so as to generate trajectories that show the most aesthetic views while also satisfying smoothness constraints. Our method is able to robustly generate diverse trajectories with varying start and end camera poses. Camera poses are optimized with a neural aesthetic metric [49] without any pre-determined targets in the view.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "GAIT computes camera transformations – the translation in 3D Euclidean space and the rotation (defined as yaw and pitch) – in a continuous 5D space for each step of the sequence. We define diversity regularization to provide control for either generating diverse sets of trajectories with varying start and end poses or to generate more uniform trajectories that always converge to the same final pose. To constrain the agent from taking actions that would create discontinuities in camera pose, we define smoothness regularization. Smooth trajectories tend to be more pleasing visually, which is important when the generated trajectories are used for video tours. To obtain a GAIT agent, we introduce a flexible framework to leverage existing RL methods for policy training, such as DrQ-v2 [50] and CURL [27].",
+        "bbox": [
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+        "text": "Based on a number of experiments we show that our method is able to generate trajectories of camera poses that frame scenes in an aesthetically meaningful manner. We show that our method is able to generate camera trajectories for a variety of complex 3D indoor scenes, which can be used to automatically create aesthetic video tours. Moreover, we show that the learned policies are robust against random initial camera poses - independent of the starting pose of the agent, it can converge to the same target pose.",
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+        "text": "In summary, our contributions are: (1) We propose GAIT, the first DRL-based framework for generating sequences of camera poses with constrained globally optimal aesthetics in 3D synthetic indoor scenes; (2) We allow for user control based on diversity regularization and use smoothness regularization to constrain the agent to generate smooth and visually pleasing camera poses; (3) We show that employing image augmentation techniques facilitates learning representation of 3D scene aesthetics from a high-dimensional pixel-space, which is commonly considered challenging for DRL algorithms; (4) We implemented our algorithm to efficiently utilizes multiple GPUs: on a 8-GPU compute node, it can finish training in 3.5 hours; (5) We",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "show that the generated camera poses can be interpolated to generate high-quality video tours of a scene; (6) Finally, we perform an extensive set of experiments and carefully validate our method based on quantitative and qualitative visual evaluations, via comparison with baseline method in a user study, and ablation studies to validate our algorithm design.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "Automatically generating views based on optimized camera control has received a considerable amount of research attention in the past decades. Existing approaches range from scientific visualization [5], surveillance [41, 6, 9] and robot photography [25] to 3D reconstruction [54, 31], virtual cinematography [23] - even focusing on characters [23, 22] - and tracking dynamics objects [14]. The breadths of these approaches is a testament for the importance of automatically generating camera poses, which remains challenging as finding solutions commonly requires solving highly complex solution spaces. Finding optimal views can be accomplished by defining metrics for information measurement [5], heuristics and rules of photography [8], or data-driven aesthetics assessment [9, 49].",
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+        "type": "text",
+        "text": "Deep aesthetic assessment: Methods for deep aesthetic assessment enable to categorize images based on aesthetic quality [35, 32]. To this end, Lu et al. [32] employ learned style attributes, while the approach of Kao et al. [24] relies on multi-task convolutional neural networks (CNN). Deng et al. [10] provide a survey of different techniques for aesthetic scoring and report that deep aesthetic assessment methods provide superior performance compared to handcrafted methods. Liu et al. [30] evaluate aesthetic quality based on graphs, where nodes represent local information of the different parts of an image. Finally, it has been recognized that defining uniform rules to assess aesthetics of motion is challenging [40]. Our method employs the deep aesthetics model developed by Wei et al. [49] because of its robustness and lightweight inference cost. They built a large photo pair dataset including more than 1M comparisons between different views from the same image that enables robust training for estimating aesthetic quality.",
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+    {
+        "type": "text",
+        "text": "Aesthetic view finding: A number of methods address the problem of automatically generating aesthetics and finding views. View finding techniques can be categorized based on various metrics, such as information metrics [5, 44, 12, 41, 19, 42, 23] or aesthetic metrics [7, 8, 47, 53, 49]. Chang and Chen [7] present a method for finding views in a panoramic image, while Cheng et al. [8] and Wei et al. [49] aim to select cropped views in a larger input image to compute 2D image compositions. Aesthetics models are also used for view recommendation that can even be computed in real time [47]. Yeh et al. [53] incorporate both image and motion aesthetic attributes into their video aesthetic assessment and Ma et al. [33] developed an instant photo tool",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "7410",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "based on the view proposal network of Wei et al. [49]. Hong et al. [18] introduce key composition maps to encode rules for composition-aware image cropping.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For finding viewpoints in 3D space, Zhu et al. [55] trained a robot as a reinforcement learning agent to search a given target view in a room. Fang et al. [11] extended this framework to not only support reinforcement but also imitation learning. Gschwindt et al. [15] control drone movement with DRL and Bonatti et al. [4] define an aesthetic metric of short video clips based on crowd sourcing data. In AutoPhoto [1], the authors train a reinforcement learning agent for a ground robot mounted camera to find views according to the aesthetics model from [49]. In their work, however, the agent is only tasked to find aesthetic views in the vicinity of its initial location. Unlike these methods, GAIT generates a sequence of camera poses in a 3D synthetic scene and moves the camera in a 5D continuous space. The aesthetics of all frames are optimized globally, while satisfying the diversity and smoothness constraints.",
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+    {
+        "type": "text",
+        "text": "Reinforcement learning: Learning directly on image observations is commonly considered challenging for standard RL algorithms. In this setting, the underlying state information has to be extracted from the high-dimensional space of image observations. The RL loss does not provide sufficient signal for the implicit representation learning in addition to the regular policy learning [51], which often leads to sample inefficiency or learning stagnation. In Data Regularized Q (DrQ) [51], Yarats et al. employ regularization on task invariant image augmentation to facilitate the representation learning in RL [51]. Contrastive Unsupervised Representations for Reinforcement Learning (CURL) [27] further extends this augmentation strategy by also adopting contrastive learning on the augmented images.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Actor-critic RL methods tend to perform well in continuous action space domains where the policy needs to be explicitly expressed, which differs from the  $\\epsilon$ -greedy policy in DQN [34]. The actor and the critic models represent the agent's policy  $\\pi(a_t|s_t)$  and the state-action value function  $Q(s_t, a_t)$  respectively. In Deep Deterministic Policy Gradient (DDPG) [29], the actor and the critic are represented as neural networks. The critic is updated according to Q-learning [34], and the actor is updated using its action value from the critic and the chain rule, following DPG [45]. DDPG also integrates techniques including experience replay, target networks, and exploration noise, which make it one of the most widely adopted algorithms for the continuous action domain. Soft Actor Critic (SAC) differs from DDPG in that it has a policy entropy term in addition to the RL objective for a better exploration and multi-modal behavior. In this work, we employ two Visual DRL algorithms, DrQ-v2 [50] and CURL [27] that use DDPG [29] and SAC [16] as their base actor-critic RL algorithms.",
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+    {
+        "type": "text",
+        "text": "3. GAIT Agent",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To generate aesthetic indoor tours, we introduce GAIT, a framework for training a DRL agent based on existing policy training approaches. Specifically, we show that a GAIT agent can be trained with DrQ-v2 [50], which is an efficient visual RL method that leverages task invariant image augmentation to help representation learning from pixels, as well as with CURL [27], which uses contrastive learning with on top of data augmentation. To predict camera pose trajectories, we unify both approaches into a single framework and extend by introducing diversity and smoothness regularization terms in the reward function. Furthermore, we evaluate aesthetics based on images instead of parametric models or heuristics.",
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+        "type": "text",
+        "text": "In the following sections we describe our framework. The formulation of our aesthetic camera RL framework is discussed in Section 3.1; the design of our reward function based on a neural aesthetics score, the out-of-bound penalty, and constrains for diversity and smoothness, is described in Section 3.2; and finally, in Section 3.3 we describe the two DRL algorithms we implement with our framework, DrQv2 and CURL. An overview of the agent in the multi-GPU setting is shown in Figure 2.",
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+    {
+        "type": "text",
+        "text": "3.1. Formulation",
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+        "type": "text",
+        "text": "Markov Decision Process (MDP): We consider the standard Reinforcement learning (RL) setting, formulated by the Markov Decision Processes (MDP) [3]. In MDP, an agent interacts with the environment in discrete time steps. At step  $t$ , given state  $s_t$ , the agent selects an action  $a_t$  according to its policy  $\\pi(a_t | s_t)$ , and receives a scalar reward  $r_t$  along with the next state  $s_{t+1}$  from the environment. This process repeats until a terminal state  $s_T$  is reached.",
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+        "text": "Objective: We aim at generating view sequences with superior aesthetic quality, smoothness and controlled diversity. Given an arbitrary initial camera pose  $x_0^P$  and the corresponding view  $x_0^I$  in a 3D indoor scene, we move the camera for  $T = 15$  time steps consecutively to produce an aesthetic sequence of 16 images. Start at time step  $t = 1$ , our agent transforms the camera pose to optimize the expected return of the following steps",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} [ R _ {1} ] = \\mathbb {E} [ \\sum_ {t = 1} ^ {\\tau} \\gamma^ {t - 1} r _ {t} ], \\tag {1}\n$$\n",
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+        "type": "text",
+        "text": "which is the sum of discounted reward. The reward  $r_t$  for time step  $t$  will be detailed in Section 3.2.",
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+        "type": "text",
+        "text": "Observation: At time step  $t$ , the observation of the agent includes the time step  $x_{t}^{T}$ , camera pose  $x_{t}^{P}$ , view image  $x_{t}^{I}$ , diversity regularization observations  $x_{t}^{D}$  and temporal smoothness regularization observations  $x_{t}^{S}$ . The time step number  $x_{t}^{T}$  is normalized to [0, 1]. A camera pose is represented as a 5D vector, i.e. the position  $\\{x, y, z\\}$ , and the",
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+        "text": "7411",
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+    {
+        "type": "image",
+        "img_path": "images/0c386a1abdba4868d2392f8852a5af4f97f6b53eac1d8e6c282ed8dc3c30a8c4.jpg",
+        "image_caption": [
+            "Figure 2: Overview of the GAIT framework in the multi-GPU setting: we describe the shared components for the two actor-critic algorithms, DrQ-v2 and CURL. In the Data loop, the actor interacts with the environment repeatedly and saves each transition in the Replay Buffer. The Update worker samples a batch of transitions from the Replay Buffer and updates the actor and the critic networks based on the RL loss functions of DrQ-v2 and CURL. The Data and Update workers communicate their steps through the shared Storage, to maintain a data-update step ratio of  $2:1$ , as well as the updated weights of the actor network."
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+    {
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+        "img_path": "images/63d714c1fcbd5874a4c0d1747c8e0b0be11500e6a49222ff7dec806f6eeefd29.jpg",
+        "image_caption": [
+            "Figure 3: Actor-critic network architecture: while the network architecture for our actor and critic networks are similar, they do not share layers except for the encoder."
+        ],
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+    {
+        "type": "text",
+        "text": "rotation of yaw  $\\psi$  and pitch  $\\theta$ . The camera pose is limited in an axis-aligned bounding box, within which its position  $\\{x,y,z\\}$  is normalized to  $[-1,1]$ . The angle of yaw  $\\theta$  is limited in  $[- \\pi, \\pi]$  and the angle of pitch  $\\psi$  is limited in  $[- \\pi/2, \\pi/2]$ , both of them are also normalized to  $[-1,1]$ . A view image is rendered with the camera pose in a resolution of  $84 \\times 84$  with 3 color channels. The evaluations of diversity and smoothness will be detailed in Section 3.2.",
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+    {
+        "type": "text",
+        "text": "Action: An action taken by our agent is also a 5D vector in the same space of camera pose. For each time step, the camera pose is transformed by adding the action vector,",
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+    {
+        "type": "equation",
+        "text": "\n$$\nx _ {t + 1} ^ {P} = x _ {t} ^ {P} \\oplus a _ {t}, \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\oplus$  means the result of the addition is normalized to  $[-1, 1]$ .",
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+    {
+        "type": "text",
+        "text": "Actor-critic RL: For our GAIT framework, we employ two state-of-the-art visual actor-critic DRL algorithms DrQ-v2 [50] and CURL [27]. For both, the actor network represents the policy  $\\pi (a_t|x_t)$ , while the critic network represents the state-action value function  $Q(s_{t},a_{t})$ . The critic network is optimized to approximate the expected return given state-action pairs,",
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+        "type": "equation",
+        "text": "\n$$\nQ ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {a _ {i > t} \\sim \\pi} \\left[ R _ {t} \\mid s _ {t}, a _ {t} \\right], \\tag {3}\n$$\n",
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+    {
+        "type": "text",
+        "text": "where the actions are selected by the actor network. The actor network is optimized on the expected return over all possible initial states in the environment:",
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+        "type": "equation",
+        "text": "\n$$\n\\pi^ {*} = \\underset {\\pi} {\\operatorname {a r g m a x}} \\mathbb {E} _ {a _ {i} \\sim \\pi} [ R _ {1} ]. \\tag {4}\n$$\n",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For DrQv2, we employ Q-learning to update the critic as described in DDPG [29]. We use the action value from the critic and the chain rule following DPG [45], to update the actor. For CURL, the actor and the critic update targets also include the entropy of policy as introduced in SAC [16].",
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+    {
+        "type": "text",
+        "text": "3.2. Reward Function",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The reward function consists of several components: first, we introduce an out-of-boundary penalty to prevent the camera being placed outside the indoor scene. For each scene, we set an axis-aligned bounding-box as the domain of the camera position. The position within the domain is normalized as  $[-1, 1]^3$ . If the camera is placed out-of-boundary, the reward is a negative constant  $r^{\\mathcal{B}}$ :",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr _ {t} = \\left\\{ \\begin{array}{l l} r _ {t} ^ {\\mathcal {A}} r _ {t} ^ {\\mathcal {S}} r _ {t} ^ {\\mathcal {D}}, & \\text {i f i n s i d e b o u n d a r y}, \\\\ r ^ {\\mathcal {B}}, & \\text {o t h e r w i s e}. \\end{array} \\right. \\tag {5}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "$r^{\\mathcal{B}}$  is set to be  $-10$  for all experiments in this paper. When the camera is placed inside the boundary, the reward is the product of the evaluations of view aesthetics  $r_t^A$ , temporal smoothness  $r_t^S$  and diversity regularization  $r_t^D$ .",
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+    },
+    {
+        "type": "text",
+        "text": "View Aesthetics: We employ the neural aesthetic model [49] to evaluate the aesthetics of a view. The model performs generic aesthetics assessment based on crowd sourcing data, which also works well 3D indoor scenes. Instead of using the view image  $x_{t}^{I}$  in the observation with the resolution of  $84 \\times 84$ , we render an image with higher resolution of  $240 \\times 240$  to evaluate the aesthetics  $r_{t}^{\\mathcal{A}}$  – the higher resolution is required by the neural aesthetic model.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Temporal Smoothness: Obtaining aesthetics assessment for temporal sequences of frames is an open research",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "7412",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "problem. Therefore, we rely on an aesthetic model [49] for single frames to assess aesthetics. However, if we would only use single frames instead of an entire sequence to quantify the aesthetics, the agent would diverge, which would then lead to degenerated results. Therefore, we introduce the temporal smoothness term  $r_t^S$  in the reward function (Equation 5) to penalize the agent when it takes an action which is too different from the its preceding time steps.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adding the smoothness term generates smoother camera trajectories and it forces the camera poses of a sequence to be moderately different from each other. Consequently, the GAIT agent will generate a sequence of aesthetic views instead of converging to a single view with high aesthetic value. On the contrary, without the smoothness term, our agent tends to take abrupt actions and also stays at the same aesthetic view until an episode terminates (Section 4.5).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in Section 3.1, the 5D vector of action is composed of two parts, including a 3D translation and 2D rotation  $a_{t} = \\{\\tilde{a}_{t},\\hat{a}_{t}\\}$ . The temporal smoothness term compares the current action  $a_{t}$  with the actions at the last three time steps  $\\{a_{t - 3},a_{t - 2},a_{t - 1}\\}$ ,",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr _ {t} ^ {\\mathcal {S}} = \\frac {1}{2} \\left(\\min  _ {i = 1} ^ {3} r _ {t, i} ^ {\\mathcal {S}} + \\frac {1}{3} \\sum_ {i = 1} ^ {3} r _ {t, i} ^ {\\mathcal {S}}\\right), r _ {t, i} ^ {\\mathcal {S}} = \\tilde {r} ^ {\\mathcal {S}} _ {t, i} + \\hat {r} ^ {\\mathcal {S}} _ {t, i}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $r_{t,i}^{S}$  is evaluated with  $a_{t}$  and the action taken  $i$  time steps earlier  $a_{t - i}$ . It consists of two parts,  $\\tilde{r^S}_{t,i}$  and  $\\tilde{r^S}_{t,i}$ , for translation and rotation respectively.  $\\tilde{r^S}_{t,i}$  is a 1D Gaussian function with the amplitude of 1, the mean of  $\\tilde{a}_{t - i}$  and the standard deviation of  $\\max \\left(\\frac{1}{2} |\\tilde{a}_{t - i}|,0.1\\right)$ .  $\\hat{r^S}_{t,i}$  is evaluated similarly except the standard deviation is  $\\max \\left(|\\hat{a}_{t - i}|,0.1\\right)$ . Therefore,  $S_{t}$  will penalize the agent when  $a_{t}$  is close to zero or  $a_{t}$  is very different from  $\\{a_{t - i}\\}$ . Translation is more penalized than rotation. The Smoothness observation contains the recent actions  $x_{t}^{S} = \\{a_{t - i}\\}$ , while the Critic additionally observes the distance between its current action and recent actions  $\\{\\| a_t - a_{t - i}\\|^2\\}$ , where  $i = 1,2,3$ . See Supplementary Material for a visualization of the Gaussian smoothness function for Temporal Smoothness.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Diversity Regularization: Without Diversity Regularization, GAIT generates sequences in a robust manner - varying initial camera poses lead to trajectories toward the globally most aesthetic target pose. While this may be wanted in many situations, GAIT also allows for generating diverse aesthetic trajectories. We enable this by specifying a diversity regularization term  $r_t^{\\mathcal{D}}$  in the reward function (Equation 5). Specifically, we define up to 4 camera poses and the corresponding distances,  $\\{\\bar{x}_j^P,d_j\\}_{0\\leq j < 4}$  that",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "we refer to as exclusion poses. The diversity regularization term penalizes the agent if the distance between its pose and any exclusion poses  $\\bar{x}_j^P$  is less than the corresponding distance  $d_j$ ,",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr _ {t} ^ {\\mathcal {D}} = \\min  _ {j = 0} ^ {4} \\left(\\min  \\left(\\frac {\\left\\| x _ {t} ^ {P} - \\bar {x} _ {j} ^ {P} \\right\\| ^ {2}}{d _ {j}}, 1\\right)\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The Diversity observation includes the exclusion poses and agent's current distances to the exclusion poses,  $x_{t}^{D} = \\{\\bar{x}_{j}^{P},d_{j},\\left\\| x_{t}^{P} - \\bar{x}_{j}^{P}\\right\\|^{2}\\}_{0\\leq j < 4}$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To train the GAIT agent with exclusion poses, the naive strategy is to to randomly sample them in the 5D space. However, as most random camera poses in the scene only have low aesthetics scores (e.g. the camera is placed inside an object or the view may be occluded), selecting exclusion poses randomly would actually lead to inefficient training. Therefore, we follow another strategy: for each episode, we set the exclusion poses to be the ending camera poses of the last 4 episodes with a random excluding distance in [0.3, 1.3]. Because our GAIT agent tends to end at camera poses with high aesthetics scores to maximize the reward, selecting the end poses as the exclusion poses converges faster compared to selecting the exclusion poses randomly.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Once trained, a user can define the exclusion camera poses  $\\{\\bar{x}_j^P,d_j\\}$  at runtime, which then produces trajectories of camera poses that avoid the provided exclusion poses. This way, our agent can produce sets of diverse, yet aesthetically meaningful, trajectories with diversity regularization, while without diversity regularization it is possible to generate aesthetic trajectories from various different initial conditions that all converge to the same globally most aesthetic camera pose. Diversity Regularization can be disabled by defining out-of-boundary excluding poses.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Visual Deep Reinforcement Learning",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Sample inefficiency or learning stagnation are known to occur in the Visual DRL setting. This is because the supervision from the RL loss is not sufficient to support both policy learning and representation learning [51]. For the Aesthetic Tour problem, learning the complex representation of 3D scene appearance and aesthetics calls for a Visual DRL algorithm. Model-free Visual RL algorithms addresses the representation learning challenge mainly in three ways: image augmentation as task-invariant perturbation, image augmentation for contrastive learning, or self-supervised learning [28]. We adopt DrQ-v2 and CURL in GAIT, which belongs to the first and the second category respectively.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The DrQ-v2 image augmentation strategy includes randomly shifting the original observation image  $x_{t}^{I}$  by 4 pixels as well as bilinearly interpolating the shifted image [50]. Both operations act as a task-invariant perturbation to regularize the  $Q$  function, which is first introduced in DrQ [51].",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>The temporal smoothness term makes the reward function non-Markovian, since it considers prior time steps.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "7413",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1f4c51359d08ec2e4a8bf885a22721c04d60e18f7b06ec8d00a1dd481db799c6.jpg",
+        "image_caption": [
+            "Figure 4: Camera trajectories generated with three different initial camera poses. Left: selected view images including the initial and ending camera poses. Right: visualization of the trajectories whose initial camera poses are located at large dots. All sequences start showing aesthetically pleasing views since time step 3 and ending with similar views."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            88,
+            630,
+            300
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f98b5a7543e3ed4194861650aeea62bb9cb637c61231f432d362992897082ca6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            645,
+            92,
+            898,
+            300
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "CURL relies on the random crop augmentation for contrastive learning, cropping from original image of resolution  $100 \\times 100$  to  $x_{t}^{I}$  with resolution  $84 \\times 84$ . The anchor and the positive images are generated from two different random crops of the same image while the negatives are obtained by cropping other images [27]. Anchors, postives, and negatives are then used to compute the additional InfoNCE loss [38] to train the encoder.",
+        "bbox": [
+            75,
+            363,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Other than representation learning, DrQ-v2 and CURL share common components. Both methods are actor-critic, use a replay buffer for off-policy learning, rely on the network architecture introduced in SAC-AE [52], and use clipped double  $Q$  learning introduced in TD3 [13]. We modify the shared network architecture by adding inputs as detailed in Section 3.1. DrQ-v2 additionally integrates a linear exploration noise decay schedule, n-step TD, introduced in D4PG [2], and fast implementations of the replay buffer and the image augmentation module. We further enables higher training throughput for CURL by adopting DrQ-v2's fast replay buffer and image augmentation.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We conducted the training and testing experiments in the Habitat-Sim simulation framework [43, 48] that provides support for rendering and the realistic indoor dataset Replica [46]. We use the Adam [26] adaptive gradient descent as our network optimizer. The discount factor  $\\gamma$  is set to 0.99. It is very close to 1 as our objective is the aesthetics of the whole sequence instead of the last view.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our multiple-GPU implementation boosts the training performance significantly. As shown in Figure 2, on a 8-GPU compute node, we run 7 Data Workers and 1 Update Worker, with each worker running on one GPU. 8-GPU implementation brings us much more speedup compared with 1-GPU, as shown in Figure 8.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our view sequences can contribute to the indoor tour video generation. To generate tour videos for evaluation, 9 intermediate camera poses are interpolated based on the spherical interpolation between the adjacent two frames in each view sequence, producing a 5-second video clip in 30 FPS play mode from the original 16-frame sequence. We refer to the supplementary material for additional implementation details.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experimental Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We have conducted an extensive set of quantitative and qualitative experiments to validate GAIT. In Section 4.1, we show that GAIT stably converges to the same global-near-optimal ending pose from different initial poses. In Section 4.3, we compare results of GAIT trained with or without Temporal Smoothness. In Section 4.2, we compare results of GAIT training with or without Diversity Regularization. In Section 4.4, we compare GAIT implementations, GAIT-DrQ-v2 and GAIT-CURL, with baseline algorithms, CMA-ES and MPC. In Section 4.5, we identify important components of DrQ-v2 and CURL that significantly contribute to convergence rate. The experiments in this section are conducted with three scenes, Room, Apartment and Office. Figures 1, 4, 5, 6 are rendered in Room. More comprehensive experimental results are in the supplementary material.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Aesthetic Camera Sequence Generation",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "A camera sequence of 16 frames is generated with an arbitrary initial camera pose. Because the initial camera pose is set randomly, its view image is usually with a low aesthetics score. GAIT agent transforms the camera pose effectively that the view aesthetics has been substantially improved at the time step 2 or 3, and the rest frames are all with good aesthetics. The statistics of aesthetic scores in",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "7414",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/3997d39669669d7f40002ecef9eee6e625577321e295988dfa2591500c2b7dda.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>Maximum</td><td>6.12</td><td>6.67</td><td>5.20</td></tr><tr><td>Mean ± std</td><td>-0.38 ± 1.33</td><td>0.01 ± 1.35</td><td>-0.47 ± 1.26</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a618df61bdbf78bb33734f0a611773e3058be5d53ed5d33ba62b107a3d638d3f.jpg",
+        "image_caption": [
+            "(a) GAIT-DrQ-v2",
+            "Figure 5: The comparisons of training with and without the regularization. The reward is lower with diversity regularization and temporal smoothness regularization because the corresponding terms of  $\\mathcal{D}_t$  and  $S_{t}$  is introduced into the reward function in Equation 5. But they converge with similar time steps. This is tested with the scene of Room with one random seed. Results with 3 seeds can be found in the supplementary material."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            250
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/46b0a98aff5e135eee92ca008fb89acdb0d70fca0f096d26f135e952b039a231.jpg",
+        "image_caption": [
+            "(b) GAIT-CURL"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            169,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Room, Apartment, and Office are shown in Table 1.",
+        "bbox": [
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+            421
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "GAIT is robust in that the camera trajectory generation is not sensitive to the initial camera pose, as shown in Figure 4. Similar initial camera poses introduce similar trajectories. The global optimal views are always explored even with very different initial camera poses. The ending camera poses are similar if diversity regularization is not applied.",
+        "bbox": [
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+            422,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2. Diversity Regularization",
+        "text_level": 1,
+        "bbox": [
+            76,
+            531,
+            302,
+            547
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Although GAIT is robust to explore global optimal views, users would like to have more control of the generation for different trajectories. The diversity regularization module helps explore the areas with sub-optimal but still plausible aesthetics scores. As shown in Figure 6, the camera poses are effectively moved out of the exclusion regions. The training with diversity regularization is stable and converges with similar time steps, as shown in Figure 5. Although the reward is slightly declined as expected, the quality of sequences are still plausible with the camera exploring nice views outside the exclusions.",
+        "bbox": [
+            75,
+            556,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Temporal Smoothness Regularization",
+        "text_level": 1,
+        "bbox": [
+            76,
+            738,
+            401,
+            755
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Temporal smoothness regularization is critical to produce aesthetic camera sequence because the neural aesthetics model [49] is for individual images. Without the temporal smoothness regularization, the accumulated aesthetics of all images is still good but the camera trajectory is trivial, such as the sequence 1 shown in Figure 7, where the camera transforms little after the time step 6. The temporal smoothness regularization reduces the reward of training, as shown in Figure 5, which prevents being stuck in optimal poses.",
+        "bbox": [
+            75,
+            763,
+            468,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/e9a631e9fe3187a46d12b9e2cec84f2432733cf0c54ca506e9e9af7eab2fb6a8.jpg",
+        "table_caption": [
+            "Table 1: The statistics of aesthetic scores in Room, Apartment, and Office."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td>time (hours) ↓</td><td>training steps</td><td>throughput (FPS) ↑</td></tr><tr><td rowspan=\"2\">GAIT-DrQ-v2</td><td>1 GPU</td><td>16.33</td><td>1.5M</td><td>25.52</td></tr><tr><td>8 GPUs</td><td>3.38</td><td>3M</td><td>246</td></tr><tr><td rowspan=\"2\">GAIT-CURL</td><td>1 GPU</td><td>36.27</td><td>1.5M</td><td>11.49</td></tr><tr><td>8 GPUs</td><td>23.03</td><td>1.5M</td><td>17.63</td></tr></table>",
+        "bbox": [
+            504,
+            88,
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+            143
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3baa3ada5c1b765ef795925ea8a5f7636dd39d3163dbdc25875f26640c7c6169.jpg",
+        "table_caption": [
+            "Table 2: The statistics of training. Note that GAIT-CURL only need  $1.5\\mathrm{M}$  steps to converge on 8-GPU."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>GAIT-DrQ-v2</td><td>38.34</td><td>20.10</td><td>42.10</td></tr><tr><td>GAIT-CURL</td><td>33.95</td><td>32.40</td><td>32.67</td></tr><tr><td>CMA-ES</td><td>32.06</td><td>32.29</td><td>31.78</td></tr><tr><td>MPC</td><td>6.32</td><td>/</td><td>/</td></tr></table>",
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+        "type": "text",
+        "text": "Table 3: The comparison of the averaged reward over 9 sequences. The 9 sequences start with 3 different initial positions and generated with 0, 1 and 2 exclusion regions.",
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+        "type": "text",
+        "text": "4.4. Comparisons",
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+        "type": "text",
+        "text": "We use Evaluation Episode Reward over the training process to compare the performance of DrQ-v2 [50], CURL [27], CMA-ES [17] and MPC [37]. It is defined as the average sum of rewards per episode under the Evaluation mode. For every 300 training episodes, a Evaluation of 10 episodes are run with random initial poses  $x_0^P$ , random excluding distances  $d_j$ , and ending poses of up to 4 previous Evaluation episodes as excluding poses. During Evaluation, the GAIT agent acts deterministically, i.e. the exploration noises used for training are turned off. The training processes shown in Figure 8 illustrate similar pattern across different scenes. GAIT-DrQ-v2 and GAIT-CURL take similar time steps to converge, but the latter is 2-8 times slower depending on the number of GPUs. Our implementation of CMA-ES and MPC are detailed in the supplementary material.",
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+        "type": "text",
+        "text": "We compare the average reward of 9 camera sequences in Table 3 with one seed. Results with 3 seeds can be found in the supplementary material. GAIT-DrQ-v2 and GAIT-CURL performs generally better than CMA-ES, except the reward with CMA-ES is better than GAIT-DrQ-v2 in the scene of Apartment. Still, both GAIT-DrQ-v2 and GAIT-CURL are better in the user study, which is shown in Section 4.6 and supplementary material. MPC performs significantly worse than others, though only tested in Room. The view sequences are generated instantly with GAIT-DrQ-v2 and GAIT-CURL. Both CMA-ES and MPC take more than 1 hour to generate a sequence, which is not scalable nor applicable to interactive scenarios.",
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+        "text": "4.5. Ablation Study",
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+        "text": "GAIT can be trained with DrQ-v2 [50] or CURL [27]. DrQ-v2 is improved upon DDPG [29], the linear decayed exploration noise and image augmentation are critical for the learning. As shown in Figure 9 (a), the episode reward will be significantly lower in training without image augmentation or linear decayed exploration noise. CURL is",
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+        "image_caption": [
+            "Figure 6: Camera trajectories generated with different diversity regularization. Three trajectories from the same initial camera pose diverge according to the exclusion regions and ending with very different views.",
+            "Figure 7: Comparison of temporal smoothness regularization. Without the smoothness, the camera is transformed to the aesthetically optimal pose in a few time steps and stuck there until the end."
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+            "(a) Room"
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+            "(c) Office"
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+    {
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+        "img_path": "images/ebb606d40864e55865bdf35290ac03c18cb05231c9c67d901e25deef2bf988db.jpg",
+        "image_caption": [
+            "Figure 8: The comparisons between the training our method and CMA-ES. Our method is trained with DrQ-v2 and CURL. CMA-ES does not need to train. The dashed line is only for reference. It is achieved by averaging the reward of 9 trajectories it generates with up to 2 exclusion regions.",
+            "(a) GAIT-DrQ-v2",
+            "Figure 9: The ablation experiments of the training algorithms. The image augmentation is critical for both GAIT-DrQ-v2 and GAIT-CURL. The linear decayed exploration noise significantly helps the training with GAIT-DrQ-v2. This is tested with the scene of Room."
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/bf6b289c4f453c2d821300a1ef4ae2a854c87cded45b2eefb062c774c7f5ddfa.jpg",
+        "image_caption": [
+            "(b) GAIT-CURL"
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+    {
+        "type": "text",
+        "text": "based on SAC [16] and use image augmentation for contrastive learning. As shown in Figure 9 (b), GAIT-CURL can hardly converge without image augmentation.",
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+    {
+        "type": "text",
+        "text": "4.6. User Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To further evaluate the aesthetics in the generated tours, we conduct a user study. We recruited 10 participants (2 females and 8 males, with the age range of 25-35) to rate the video smoothness, video aesthetics, and subjective general preference, of the tours generated using three methods (i.e., CMA-ES, GAIT-DrQ-v2 and GAIT-CURL). Specifically, we prepared the video clips in three indoor scenes using the video generation described in Section 3.4.",
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+    {
+        "type": "text",
+        "text": "We asked for participants' feedback via 2-alternative forced choice. For each initial pose with the same exclusion level, every participant watch two video pairs,  $\\{GAIT-DrQ-v2 vs. CMA-ES\\}$ , and  $\\{GAIT-DrQ-v2 vs. GAIT-CURL\\}$ . In each pair, participants chose the preferred video clip based on (1) video smoothness and (2) video content aesthetics. After comparing the video clips rooted from the same initial pose, participants are also asked to rate \"which method provides higher video content diversity\" and \"which method is the overall preferred aesthetic video generation method\".",
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+    {
+        "type": "text",
+        "text": "When asked about \"overall which method provides bet",
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+    {
+        "type": "page_number",
+        "text": "7416",
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+    {
+        "type": "text",
+        "text": "ter aesthetic videos\" in  $\\{GAIT-DrQ-v2 vs. CMA-ES\\}$  in the three scenes,  $93.3\\%$ ,  $96.7\\%$ , and  $66.7\\%$  users favor  $GAIT-DrQ-v2$ . With the same question in  $\\{GAIT-DrQ-v2 vs. GAIT-CURL\\}$ ,  $60.0\\%$ ,  $53.3\\%$ , and  $43.3\\%$  users favor  $GAIT-DrQ-v2$ . We have learned from the users' feedback that majority participants favor the video clips generated in  $GAIT-DrQ-v2$  over CMA-ES but  $GAIT-DrQ-v2$  and  $GAIT-CURL$  generate the view sequences with different capabilities.  $GAIT-DrQ-v2$  is better at video aesthetics while  $GAIT-CURL$  performs better in video smoothness. Please refer to our supplementary materials for the collected data and the comprehensive data analysis.",
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+    {
+        "type": "text",
+        "text": "5. Conclusions",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose GAIT, a novel DRL agent to generate aesthetically meaningful sequences of camera poses in 3D indoor scenes. Starting with an arbitrary initial camera pose without any pre-determined targets, a view sequence is transformed sequentially by the GAIT agent according to the neural aesthetics model. While the diversity regularization term is user-controlled to generate diverse, yet aesthetically meaningful trajectories, temporal smoothness regularization is introduced to avoid discontinuities camera poses for more visually pleasing trajectories. Our framework enables training GAIT agents with existing RL methods, including DrQ-v2 and CURL. We evaluate our method extensively. The conducted user study indicates GAIT is robust for high quality view sequences and it is easy to control for diverse outputs.",
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+    {
+        "type": "text",
+        "text": "Discussion: Manually defining trajectories of camera poses in 3D spaces is a challenging task, that even takes professional users a couple of hours. In 2D motion graphics, which is a similar domain, the authoring of a video requires a designer 3-4 hours of manual work [21, 20]. GAIT training requires 3.38 hours of computing time for a single scene. However, once trained GAIT can generate multiple tours for the same scene, while an artist has to manually define every single trajectory. As GAIT only makes minimal assumptions about the environment, it can also be used to generate aesthetically valuable view sequences for real-world scenes that are represented as radiance fields. This can be achieved by using the view synthesis function of a NeRF-based approach to replace the rendering of a 3D scene simulator. This allows users to avoid the tedious manual selection of viewpoints for these scenes.",
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+    {
+        "type": "text",
+        "text": "Limitations and Future Work: GAIT-DrQ-v2 and GAIT-CURL can generalize to arbitrary initial and excluding poses within the trained scene, but they generalize poorly to unseen, new scenes. Making GAIT agents generalize across scenes is our key objective for future work, as this would make GAIT a more generic framework for view sequence generation. However, this would require a substantial increase in compute resources, the availability of a",
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+    },
+    {
+        "type": "text",
+        "text": "larger scene dataset, and a scalable DRL algorithm, which are outside the scope of this work.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While our method is able to reliably generate aesthetic camera tours for indoor scenes, it also has a few limitations that are interesting avenues for future research. First, we only tested our GAIT agent for indoor scenes and it is not clear whether it would work similarly well for outdoor scenes. Second, the scenes we used for our experiments where only single room layouts and it is not clear whether GAIT could also generate trajectories for more complex room layouts or whether it could take care of transitioning from one level of a building to another. Third, we did not test GAIT on scenes with dynamically moving objects. To this end it would be interesting to train and test a GAIT agent to generate aesthetically valuable tours under consideration of different types of scene dynamics. Finally, the neural aesthetics estimator only considers the per-frame aesthetics, while the inter-frame smoothness term is heuristic. A neural temporal aesthetics model is needed for this task. However, to the best of our knowledge, such a model is unavailable. Therefore, our goal is to work on a neural temporal aesthetics model in the future.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This project was supported in part by NSF grants OAC1919752, ICER1940302, and IIS2107224, and by IBM, SUNY and Adobe.",
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+            "[39] Des O'Rawe. Towards a poetics of the cinematographic frame. Journal of Aesthetics & Culture, 3(1):5378, 2011. 1",
+            "[40] Madhura V Phatak, Manasi S Patwardhan, and Meenakshi S Arya. Deep learning for motion based video aesthetics. In 2019 IEEE Bombay Section Signature Conference (IBSSC), pages 1-6, 2019. 1, 2",
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+            "[43] Manolis Savva, Abhishek Kadian, Oleksandr Maksymets, Yili Zhao, Erik Wijmans, Bhavana Jain, Julian Straub, Jia Liu, Vladlen Koltun, Jitendra Malik, Devi Parikh, and Dhruv Batra. Habitat: A Platform for Embodied AI Research. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019. 6",
+            "[44] Adrian Secord, Jingwan Lu, Adam Finkelstein, Manish Singh, and Andrew Nealen. Perceptual models of viewpoint preference. ACM Transactions on Graphics (TOG), 30(5):1-12, 2011. 2",
+            "[45] David Silver, Guy Lever, Nicolas Heess, Thomas Degris, Daan Wierstra, and Martin Riedmiller. Deterministic policy gradient algorithms. In International conference on machine learning, pages 387-395. Pmlr, 2014. 3, 4",
+            "[46] Julian Straub, Thomas Whelan, Lingni Ma, Yufan Chen, Erik Wijmans, Simon Green, Jakob J. Engel, Raul Mur-Artal, Carl Ren, Shobhit Verma, Anton Clarkson, Mingfei Yan, Brian Budge, Yajie Yan, Xiaqing Pan, June Yon, Yuyang Zou, Kimberly Leon, Nigel Carter, Jesus Briales, Tyler Gillingham, Elias Mueggler, Luis Pesqueira, Manolis Savva, Dhruv Batra, Hauke M. Strasdat, Renzo De Nardi, Michael Goesele, Steven Lovegrove, and Richard Newcombe. The Replica dataset: A digital replica of indoor spaces. arXiv preprint arXiv:1906.05797, 2019. 6"
+        ],
+        "bbox": [
+            78,
+            90,
+            468,
+            900
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[47] Hsiao-Hang Su, Tse-Wei Chen, Chieh-Chi Kao, Winston H Hsu, and Shao-Yi Chien. Preference-aware view recommendation system for scenic photos based on bag-of-aesthetics-preserving features. IEEE Transactions on Multimedia, 14(3):833-843, 2012. 2",
+            "[48] Andrew Szot, Alex Clegg, Eric Undersander, Erik Wijmans, Yili Zhao, John Turner, Noah Maestre, Mustafa Mukadam, Devendra Chaplot, Oleksandr Maksymets, Aaron Gokaslan, Vladimir Vondrus, Sameer Dharur, Franziska Meier, Wojciech Galuba, Angel Chang, Zsolt Kira, Vladlen Koltun, Jitendra Malik, Manolis Savva, and Dhruv Batra. Habitat 2.0: Training home assistants to rearrange their habitat. In Advances in Neural Information Processing Systems (NeurIPS), 2021. 6",
+            "[49] Zijun Wei, Jianming Zhang, Xiaohui Shen, Zhe Lin, Radomir Mech, Minh Hoai, and Dimitris Samaras. Good view hunting: Learning photo composition from dense view pairs. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5437-5446, 2018. 2, 3, 4, 5, 7",
+            "[50] Denis Yarats, Rob Fergus, Alessandro Lazaric, and Lerel Pinto. Mastering visual continuous control: Improved data-augmented reinforcement learning. arXiv preprint arXiv:2107.09645, 2021. 2, 3, 4, 5, 7",
+            "[51] Denis Yarats, Ilya Kostrikov, and Rob Fergus. Image augmentation is all you need: Regularizing deep reinforcement learning from pixels. In International Conference on Learning Representations, 2020. 3, 5",
+            "[52] Denis Yarats, Amy Zhang, Ilya Kostrikov, Brandon Amos, Joelle Pineau, and Rob Fergus. Improving sample efficiency in model-free reinforcement learning from images, 2019. 6",
+            "[53] Hsin-Ho Yeh, Chun-Yu Yang, Ming-Sui Lee, and Chu-Song Chen. Video aesthetic quality assessment by temporal integration of photo-and motion-based features. IEEE transactions on multimedia, 15(8):1944-1957, 2013. 2",
+            "[54] Han Zhang, Yuong Yao, Ke Xie, Chi-Wing Fu, Hao Zhang, and Hui Huang. Continuous aerial path planning for 3d urban scene reconstruction. ACM Transactions on Graphics (TOG), 40(6):1-15, 2021. 2",
+            "[55] Yuke Zhu, Roozbeh Mottaghi, Eric Kolve, Joseph J Lim, Abhinav Gupta, Li Fei-Fei, and Ali Farhadi. Target-driven visual navigation in indoor scenes using deep reinforcement learning. In IEEE International Conference on Robotics and Automation (ICRA), pages 3357–3364, 2017. 3"
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new file mode 100644
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+++ b/2023/GAIT_ Generating Aesthetic Indoor Tours with Deep Reinforcement Learning/04ba10a4-1e2a-4899-bb30-52b2658d3ca3_model.json	
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+            "content": "GAIT: Generating Aesthetic Indoor Tours with Deep Reinforcement Learning"
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+            "content": "2Adobe Research"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
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+            "bbox": [
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+            "content": "Placing and orienting a camera to compose aesthetically meaningful shots of a scene is not only a key objective in real-world photography and cinematography but also for virtual content creation. The framing of a camera often significantly contributes to the story telling in movies, games, and mixed reality applications. Generating single camera poses or even contiguous trajectories either requires a significant amount of manual labor or requires solving high-dimensional optimization problems, which can be computationally demanding and error-prone. In this paper, we introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) agent, that learns to automatically control a camera to generate a sequence of aesthetically meaningful views for synthetic 3D indoor scenes. To generate sequences of frames with high aesthetic value, GAIT relies on a neural aesthetics estimator, which is trained on a crowd-sourced dataset. Additionally, we introduce regularization techniques for diversity and smoothness to generate visually interesting trajectories for a 3D environment, and to constrain agent acceleration in the reward function to generate a smooth sequence of camera frames. We validated our method by comparing it to baseline algorithms, based on a perceptual user study, and through ablation studies. Code and visual results are available on the project website: https://desaixie.github.io/gait-rl"
+        },
+        {
+            "type": "title",
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+            "content": "1. Introduction"
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+            "content": "Composing a shot by framing a scene with a camera plays an integral part in photography and cinematography. A carefully composed frame does not only provide the information of a scene, but also serves to define the visual style, to instill a desired emotion in the viewer, and to carry forward the story the artist wants to convey [39]. Photographers and movie directors commonly spend a significant amount of time to perfect the camera framing, which – consequently – often leads to extensive cost footprints. While framing scenes in virtual setups, such as games or mixed reality applications, is arguably less involved, defining aes"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "Figure 1: Our novel DRL agent, GAIT, automatically generates camera poses so as to obtain aesthetic views of 3D indoor scenes. Left: Views of three camera poses from a generated sequence. Right: the 3D indoor environment with three highlighted camera poses. Red, yellow, orange corresponds to the three frames on the left respectively, where the red dot is the initial pose. GAIT maintains high aesthetic views throughout the sequence, while satisfying the initial pose, diversity, smoothness, and boundary constraints."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "thetically valuable camera poses and trajectories still requires a considerable amount of manual work. An artist has to position key frames in space, define the orientation of the camera, and specify the temporal profile for the interpolation between keyframes. While this provides a high degree of control, for many applications, it would be desirable to frame a scene automatically by computing camera poses."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Existing methods for automatically computing single camera poses or camera trajectories either rely on handcrafted methods with heuristics, which commonly do not generalize [40], are limited to specific applications, such as a trip between two cities [19], or specifically focus on moving targets [36]. Recently, it has been recognized that neural aesthetics estimators can serve as more generic solution for generating camera poses for the purpose of obtaining aesthetically meaningful camera frames [32] - a 2D image is mapped to a score that quantifies the aesthetics. An aesthetics estimator can be used to compare any two images with different contents or styles, which makes them applicable for finding views in lower dimensional spaces such as im"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+    [
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "ages and videos [49], or in constrained robotics settings [1]. In a 3D environment, finding a desired camera pose requires searching in a continuous \\( R^6 \\) space (i.e., position \\( R^3 \\) and orientation in \\( R^3 \\)) while also considering obstacles or even dynamically moving objects. Computing camera paths in a flexible and versatile manner therefore is a challenging and open problem."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.2,
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+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a novel method for automatically generating trajectories to aesthetically frame synthetic 3D indoor scenes. We introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) network that learns to move the camera so as to generate trajectories that show the most aesthetic views while also satisfying smoothness constraints. Our method is able to robustly generate diverse trajectories with varying start and end camera poses. Camera poses are optimized with a neural aesthetic metric [49] without any pre-determined targets in the view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.353,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "GAIT computes camera transformations – the translation in 3D Euclidean space and the rotation (defined as yaw and pitch) – in a continuous 5D space for each step of the sequence. We define diversity regularization to provide control for either generating diverse sets of trajectories with varying start and end poses or to generate more uniform trajectories that always converge to the same final pose. To constrain the agent from taking actions that would create discontinuities in camera pose, we define smoothness regularization. Smooth trajectories tend to be more pleasing visually, which is important when the generated trajectories are used for video tours. To obtain a GAIT agent, we introduce a flexible framework to leverage existing RL methods for policy training, such as DrQ-v2 [50] and CURL [27]."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Based on a number of experiments we show that our method is able to generate trajectories of camera poses that frame scenes in an aesthetically meaningful manner. We show that our method is able to generate camera trajectories for a variety of complex 3D indoor scenes, which can be used to automatically create aesthetic video tours. Moreover, we show that the learned policies are robust against random initial camera poses - independent of the starting pose of the agent, it can converge to the same target pose."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.705,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "In summary, our contributions are: (1) We propose GAIT, the first DRL-based framework for generating sequences of camera poses with constrained globally optimal aesthetics in 3D synthetic indoor scenes; (2) We allow for user control based on diversity regularization and use smoothness regularization to constrain the agent to generate smooth and visually pleasing camera poses; (3) We show that employing image augmentation techniques facilitates learning representation of 3D scene aesthetics from a high-dimensional pixel-space, which is commonly considered challenging for DRL algorithms; (4) We implemented our algorithm to efficiently utilizes multiple GPUs: on a 8-GPU compute node, it can finish training in 3.5 hours; (5) We"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.184
+            ],
+            "angle": 0,
+            "content": "show that the generated camera poses can be interpolated to generate high-quality video tours of a scene; (6) Finally, we perform an extensive set of experiments and carefully validate our method based on quantitative and qualitative visual evaluations, via comparison with baseline method in a user study, and ablation studies to validate our algorithm design."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.222,
+                0.892,
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+            "angle": 0,
+            "content": "Automatically generating views based on optimized camera control has received a considerable amount of research attention in the past decades. Existing approaches range from scientific visualization [5], surveillance [41, 6, 9] and robot photography [25] to 3D reconstruction [54, 31], virtual cinematography [23] - even focusing on characters [23, 22] - and tracking dynamics objects [14]. The breadths of these approaches is a testament for the importance of automatically generating camera poses, which remains challenging as finding solutions commonly requires solving highly complex solution spaces. Finding optimal views can be accomplished by defining metrics for information measurement [5], heuristics and rules of photography [8], or data-driven aesthetics assessment [9, 49]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.434,
+                0.892,
+                0.705
+            ],
+            "angle": 0,
+            "content": "Deep aesthetic assessment: Methods for deep aesthetic assessment enable to categorize images based on aesthetic quality [35, 32]. To this end, Lu et al. [32] employ learned style attributes, while the approach of Kao et al. [24] relies on multi-task convolutional neural networks (CNN). Deng et al. [10] provide a survey of different techniques for aesthetic scoring and report that deep aesthetic assessment methods provide superior performance compared to handcrafted methods. Liu et al. [30] evaluate aesthetic quality based on graphs, where nodes represent local information of the different parts of an image. Finally, it has been recognized that defining uniform rules to assess aesthetics of motion is challenging [40]. Our method employs the deep aesthetics model developed by Wei et al. [49] because of its robustness and lightweight inference cost. They built a large photo pair dataset including more than 1M comparisons between different views from the same image that enables robust training for estimating aesthetic quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.705,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Aesthetic view finding: A number of methods address the problem of automatically generating aesthetics and finding views. View finding techniques can be categorized based on various metrics, such as information metrics [5, 44, 12, 41, 19, 42, 23] or aesthetic metrics [7, 8, 47, 53, 49]. Chang and Chen [7] present a method for finding views in a panoramic image, while Cheng et al. [8] and Wei et al. [49] aim to select cropped views in a larger input image to compute 2D image compositions. Aesthetics models are also used for view recommendation that can even be computed in real time [47]. Yeh et al. [53] incorporate both image and motion aesthetic attributes into their video aesthetic assessment and Ma et al. [33] developed an instant photo tool"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.957
+            ],
+            "angle": 0,
+            "content": "7410"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.091,
+                0.47,
+                0.137
+            ],
+            "angle": 0,
+            "content": "based on the view proposal network of Wei et al. [49]. Hong et al. [18] introduce key composition maps to encode rules for composition-aware image cropping."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.14,
+                0.471,
+                0.382
+            ],
+            "angle": 0,
+            "content": "For finding viewpoints in 3D space, Zhu et al. [55] trained a robot as a reinforcement learning agent to search a given target view in a room. Fang et al. [11] extended this framework to not only support reinforcement but also imitation learning. Gschwindt et al. [15] control drone movement with DRL and Bonatti et al. [4] define an aesthetic metric of short video clips based on crowd sourcing data. In AutoPhoto [1], the authors train a reinforcement learning agent for a ground robot mounted camera to find views according to the aesthetics model from [49]. In their work, however, the agent is only tasked to find aesthetic views in the vicinity of its initial location. Unlike these methods, GAIT generates a sequence of camera poses in a 3D synthetic scene and moves the camera in a 5D continuous space. The aesthetics of all frames are optimized globally, while satisfying the diversity and smoothness constraints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.385,
+                0.47,
+                0.612
+            ],
+            "angle": 0,
+            "content": "Reinforcement learning: Learning directly on image observations is commonly considered challenging for standard RL algorithms. In this setting, the underlying state information has to be extracted from the high-dimensional space of image observations. The RL loss does not provide sufficient signal for the implicit representation learning in addition to the regular policy learning [51], which often leads to sample inefficiency or learning stagnation. In Data Regularized Q (DrQ) [51], Yarats et al. employ regularization on task invariant image augmentation to facilitate the representation learning in RL [51]. Contrastive Unsupervised Representations for Reinforcement Learning (CURL) [27] further extends this augmentation strategy by also adopting contrastive learning on the augmented images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.614,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Actor-critic RL methods tend to perform well in continuous action space domains where the policy needs to be explicitly expressed, which differs from the \\(\\epsilon\\)-greedy policy in DQN [34]. The actor and the critic models represent the agent's policy \\(\\pi(a_t|s_t)\\) and the state-action value function \\(Q(s_t, a_t)\\) respectively. In Deep Deterministic Policy Gradient (DDPG) [29], the actor and the critic are represented as neural networks. The critic is updated according to Q-learning [34], and the actor is updated using its action value from the critic and the chain rule, following DPG [45]. DDPG also integrates techniques including experience replay, target networks, and exploration noise, which make it one of the most widely adopted algorithms for the continuous action domain. Soft Actor Critic (SAC) differs from DDPG in that it has a policy entropy term in addition to the RL objective for a better exploration and multi-modal behavior. In this work, we employ two Visual DRL algorithms, DrQ-v2 [50] and CURL [27] that use DDPG [29] and SAC [16] as their base actor-critic RL algorithms."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
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+            "angle": 0,
+            "content": "3. GAIT Agent"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.115,
+                0.892,
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+            ],
+            "angle": 0,
+            "content": "To generate aesthetic indoor tours, we introduce GAIT, a framework for training a DRL agent based on existing policy training approaches. Specifically, we show that a GAIT agent can be trained with DrQ-v2 [50], which is an efficient visual RL method that leverages task invariant image augmentation to help representation learning from pixels, as well as with CURL [27], which uses contrastive learning with on top of data augmentation. To predict camera pose trajectories, we unify both approaches into a single framework and extend by introducing diversity and smoothness regularization terms in the reward function. Furthermore, we evaluate aesthetics based on images instead of parametric models or heuristics."
+        },
+        {
+            "type": "text",
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+            ],
+            "angle": 0,
+            "content": "In the following sections we describe our framework. The formulation of our aesthetic camera RL framework is discussed in Section 3.1; the design of our reward function based on a neural aesthetics score, the out-of-bound penalty, and constrains for diversity and smoothness, is described in Section 3.2; and finally, in Section 3.3 we describe the two DRL algorithms we implement with our framework, DrQv2 and CURL. An overview of the agent in the multi-GPU setting is shown in Figure 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.456,
+                0.634,
+                0.47
+            ],
+            "angle": 0,
+            "content": "3.1. Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.479,
+                0.892,
+                0.6
+            ],
+            "angle": 0,
+            "content": "Markov Decision Process (MDP): We consider the standard Reinforcement learning (RL) setting, formulated by the Markov Decision Processes (MDP) [3]. In MDP, an agent interacts with the environment in discrete time steps. At step \\( t \\), given state \\( s_t \\), the agent selects an action \\( a_t \\) according to its policy \\( \\pi(a_t | s_t) \\), and receives a scalar reward \\( r_t \\) along with the next state \\( s_{t+1} \\) from the environment. This process repeats until a terminal state \\( s_T \\) is reached."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.601,
+                0.892,
+                0.722
+            ],
+            "angle": 0,
+            "content": "Objective: We aim at generating view sequences with superior aesthetic quality, smoothness and controlled diversity. Given an arbitrary initial camera pose \\( x_0^P \\) and the corresponding view \\( x_0^I \\) in a 3D indoor scene, we move the camera for \\( T = 15 \\) time steps consecutively to produce an aesthetic sequence of 16 images. Start at time step \\( t = 1 \\), our agent transforms the camera pose to optimize the expected return of the following steps"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.614,
+                0.73,
+                0.892,
+                0.772
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbb {E} [ R _ {1} ] = \\mathbb {E} [ \\sum_ {t = 1} ^ {\\tau} \\gamma^ {t - 1} r _ {t} ], \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.891,
+                0.81
+            ],
+            "angle": 0,
+            "content": "which is the sum of discounted reward. The reward \\( r_t \\) for time step \\( t \\) will be detailed in Section 3.2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Observation: At time step \\( t \\), the observation of the agent includes the time step \\( x_{t}^{T} \\), camera pose \\( x_{t}^{P} \\), view image \\( x_{t}^{I} \\), diversity regularization observations \\( x_{t}^{D} \\) and temporal smoothness regularization observations \\( x_{t}^{S} \\). The time step number \\( x_{t}^{T} \\) is normalized to [0, 1]. A camera pose is represented as a 5D vector, i.e. the position \\( \\{x, y, z\\} \\), and the"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "7411"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.086,
+                0.092,
+                0.885,
+                0.219
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.227,
+                0.895,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Figure 2: Overview of the GAIT framework in the multi-GPU setting: we describe the shared components for the two actor-critic algorithms, DrQ-v2 and CURL. In the Data loop, the actor interacts with the environment repeatedly and saves each transition in the Replay Buffer. The Update worker samples a batch of transitions from the Replay Buffer and updates the actor and the critic networks based on the RL loss functions of DrQ-v2 and CURL. The Data and Update workers communicate their steps through the shared Storage, to maintain a data-update step ratio of \\(2:1\\), as well as the updated weights of the actor network."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.331,
+                0.468,
+                0.463
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.469,
+                0.47,
+                0.515
+            ],
+            "angle": 0,
+            "content": "Figure 3: Actor-critic network architecture: while the network architecture for our actor and critic networks are similar, they do not share layers except for the encoder."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.527,
+                0.47,
+                0.648
+            ],
+            "angle": 0,
+            "content": "rotation of yaw \\(\\psi\\) and pitch \\(\\theta\\). The camera pose is limited in an axis-aligned bounding box, within which its position \\(\\{x,y,z\\}\\) is normalized to \\([-1,1]\\). The angle of yaw \\(\\theta\\) is limited in \\([- \\pi, \\pi]\\) and the angle of pitch \\(\\psi\\) is limited in \\([- \\pi/2, \\pi/2]\\), both of them are also normalized to \\([-1,1]\\). A view image is rendered with the camera pose in a resolution of \\(84 \\times 84\\) with 3 color channels. The evaluations of diversity and smoothness will be detailed in Section 3.2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.648,
+                0.47,
+                0.693
+            ],
+            "angle": 0,
+            "content": "Action: An action taken by our agent is also a 5D vector in the same space of camera pose. For each time step, the camera pose is transformed by adding the action vector,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.214,
+                0.703,
+                0.469,
+                0.722
+            ],
+            "angle": 0,
+            "content": "\\[\nx _ {t + 1} ^ {P} = x _ {t} ^ {P} \\oplus a _ {t}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.733,
+                0.47,
+                0.763
+            ],
+            "angle": 0,
+            "content": "where \\(\\oplus\\) means the result of the addition is normalized to \\([-1, 1]\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.763,
+                0.469,
+                0.869
+            ],
+            "angle": 0,
+            "content": "Actor-critic RL: For our GAIT framework, we employ two state-of-the-art visual actor-critic DRL algorithms DrQ-v2 [50] and CURL [27]. For both, the actor network represents the policy \\(\\pi (a_t|x_t)\\), while the critic network represents the state-action value function \\(Q(s_{t},a_{t})\\). The critic network is optimized to approximate the expected return given state-action pairs,"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.161,
+                0.88,
+                0.47,
+                0.898
+            ],
+            "angle": 0,
+            "content": "\\[\nQ ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {a _ {i > t} \\sim \\pi} \\left[ R _ {t} \\mid s _ {t}, a _ {t} \\right], \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.331,
+                0.893,
+                0.376
+            ],
+            "angle": 0,
+            "content": "where the actions are selected by the actor network. The actor network is optimized on the expected return over all possible initial states in the environment:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.608,
+                0.386,
+                0.893,
+                0.41
+            ],
+            "angle": 0,
+            "content": "\\[\n\\pi^ {*} = \\underset {\\pi} {\\operatorname {a r g m a x}} \\mathbb {E} _ {a _ {i} \\sim \\pi} [ R _ {1} ]. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.418,
+                0.893,
+                0.495
+            ],
+            "angle": 0,
+            "content": "For DrQv2, we employ Q-learning to update the critic as described in DDPG [29]. We use the action value from the critic and the chain rule following DPG [45], to update the actor. For CURL, the actor and the critic update targets also include the entropy of policy as introduced in SAC [16]."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.502,
+                0.671,
+                0.516
+            ],
+            "angle": 0,
+            "content": "3.2. Reward Function"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.525,
+                0.892,
+                0.631
+            ],
+            "angle": 0,
+            "content": "The reward function consists of several components: first, we introduce an out-of-boundary penalty to prevent the camera being placed outside the indoor scene. For each scene, we set an axis-aligned bounding-box as the domain of the camera position. The position within the domain is normalized as \\([-1, 1]^3\\). If the camera is placed out-of-boundary, the reward is a negative constant \\(r^{\\mathcal{B}}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.565,
+                0.64,
+                0.892,
+                0.68
+            ],
+            "angle": 0,
+            "content": "\\[\nr _ {t} = \\left\\{ \\begin{array}{l l} r _ {t} ^ {\\mathcal {A}} r _ {t} ^ {\\mathcal {S}} r _ {t} ^ {\\mathcal {D}}, & \\text {i f i n s i d e b o u n d a r y}, \\\\ r ^ {\\mathcal {B}}, & \\text {o t h e r w i s e}. \\end{array} \\right. \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.689,
+                0.892,
+                0.75
+            ],
+            "angle": 0,
+            "content": "\\(r^{\\mathcal{B}}\\) is set to be \\(-10\\) for all experiments in this paper. When the camera is placed inside the boundary, the reward is the product of the evaluations of view aesthetics \\(r_t^A\\), temporal smoothness \\(r_t^S\\) and diversity regularization \\(r_t^D\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.75,
+                0.893,
+                0.871
+            ],
+            "angle": 0,
+            "content": "View Aesthetics: We employ the neural aesthetic model [49] to evaluate the aesthetics of a view. The model performs generic aesthetics assessment based on crowd sourcing data, which also works well 3D indoor scenes. Instead of using the view image \\( x_{t}^{I} \\) in the observation with the resolution of \\( 84 \\times 84 \\), we render an image with higher resolution of \\( 240 \\times 240 \\) to evaluate the aesthetics \\( r_{t}^{\\mathcal{A}} \\) – the higher resolution is required by the neural aesthetic model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Temporal Smoothness: Obtaining aesthetics assessment for temporal sequences of frames is an open research"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "7412"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.468,
+                0.212
+            ],
+            "angle": 0,
+            "content": "problem. Therefore, we rely on an aesthetic model [49] for single frames to assess aesthetics. However, if we would only use single frames instead of an entire sequence to quantify the aesthetics, the agent would diverge, which would then lead to degenerated results. Therefore, we introduce the temporal smoothness term \\( r_t^S \\) in the reward function (Equation 5) to penalize the agent when it takes an action which is too different from the its preceding time steps."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.213,
+                0.468,
+                0.333
+            ],
+            "angle": 0,
+            "content": "Adding the smoothness term generates smoother camera trajectories and it forces the camera poses of a sequence to be moderately different from each other. Consequently, the GAIT agent will generate a sequence of aesthetic views instead of converging to a single view with high aesthetic value. On the contrary, without the smoothness term, our agent tends to take abrupt actions and also stays at the same aesthetic view until an episode terminates (Section 4.5)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.334,
+                0.468,
+                0.41
+            ],
+            "angle": 0,
+            "content": "As mentioned in Section 3.1, the 5D vector of action is composed of two parts, including a 3D translation and 2D rotation \\(a_{t} = \\{\\tilde{a}_{t},\\hat{a}_{t}\\}\\). The temporal smoothness term compares the current action \\(a_{t}\\) with the actions at the last three time steps \\(\\{a_{t - 3},a_{t - 2},a_{t - 1}\\}\\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.092,
+                0.421,
+                0.468,
+                0.477
+            ],
+            "angle": 0,
+            "content": "\\[\nr _ {t} ^ {\\mathcal {S}} = \\frac {1}{2} \\left(\\min  _ {i = 1} ^ {3} r _ {t, i} ^ {\\mathcal {S}} + \\frac {1}{3} \\sum_ {i = 1} ^ {3} r _ {t, i} ^ {\\mathcal {S}}\\right), r _ {t, i} ^ {\\mathcal {S}} = \\tilde {r} ^ {\\mathcal {S}} _ {t, i} + \\hat {r} ^ {\\mathcal {S}} _ {t, i}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.49,
+                0.468,
+                0.726
+            ],
+            "angle": 0,
+            "content": "where \\(r_{t,i}^{S}\\) is evaluated with \\(a_{t}\\) and the action taken \\(i\\) time steps earlier \\(a_{t - i}\\). It consists of two parts, \\(\\tilde{r^S}_{t,i}\\) and \\(\\tilde{r^S}_{t,i}\\), for translation and rotation respectively. \\(\\tilde{r^S}_{t,i}\\) is a 1D Gaussian function with the amplitude of 1, the mean of \\(\\tilde{a}_{t - i}\\) and the standard deviation of \\(\\max \\left(\\frac{1}{2} |\\tilde{a}_{t - i}|,0.1\\right)\\). \\(\\hat{r^S}_{t,i}\\) is evaluated similarly except the standard deviation is \\(\\max \\left(|\\hat{a}_{t - i}|,0.1\\right)\\). Therefore, \\(S_{t}\\) will penalize the agent when \\(a_{t}\\) is close to zero or \\(a_{t}\\) is very different from \\(\\{a_{t - i}\\}\\). Translation is more penalized than rotation. The Smoothness observation contains the recent actions \\(x_{t}^{S} = \\{a_{t - i}\\}\\), while the Critic additionally observes the distance between its current action and recent actions \\(\\{\\| a_t - a_{t - i}\\|^2\\}\\), where \\(i = 1,2,3\\). See Supplementary Material for a visualization of the Gaussian smoothness function for Temporal Smoothness."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.728,
+                0.468,
+                0.866
+            ],
+            "angle": 0,
+            "content": "Diversity Regularization: Without Diversity Regularization, GAIT generates sequences in a robust manner - varying initial camera poses lead to trajectories toward the globally most aesthetic target pose. While this may be wanted in many situations, GAIT also allows for generating diverse aesthetic trajectories. We enable this by specifying a diversity regularization term \\( r_t^{\\mathcal{D}} \\) in the reward function (Equation 5). Specifically, we define up to 4 camera poses and the corresponding distances, \\( \\{\\bar{x}_j^P,d_j\\}_{0\\leq j < 4} \\) that"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.092,
+                0.892,
+                0.153
+            ],
+            "angle": 0,
+            "content": "we refer to as exclusion poses. The diversity regularization term penalizes the agent if the distance between its pose and any exclusion poses \\(\\bar{x}_j^P\\) is less than the corresponding distance \\(d_j\\),"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.561,
+                0.164,
+                0.892,
+                0.207
+            ],
+            "angle": 0,
+            "content": "\\[\nr _ {t} ^ {\\mathcal {D}} = \\min  _ {j = 0} ^ {4} \\left(\\min  \\left(\\frac {\\left\\| x _ {t} ^ {P} - \\bar {x} _ {j} ^ {P} \\right\\| ^ {2}}{d _ {j}}, 1\\right)\\right). \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.216,
+                0.892,
+                0.265
+            ],
+            "angle": 0,
+            "content": "The Diversity observation includes the exclusion poses and agent's current distances to the exclusion poses, \\( x_{t}^{D} = \\{\\bar{x}_{j}^{P},d_{j},\\left\\| x_{t}^{P} - \\bar{x}_{j}^{P}\\right\\|^{2}\\}_{0\\leq j < 4} \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.265,
+                0.892,
+                0.46
+            ],
+            "angle": 0,
+            "content": "To train the GAIT agent with exclusion poses, the naive strategy is to to randomly sample them in the 5D space. However, as most random camera poses in the scene only have low aesthetics scores (e.g. the camera is placed inside an object or the view may be occluded), selecting exclusion poses randomly would actually lead to inefficient training. Therefore, we follow another strategy: for each episode, we set the exclusion poses to be the ending camera poses of the last 4 episodes with a random excluding distance in [0.3, 1.3]. Because our GAIT agent tends to end at camera poses with high aesthetics scores to maximize the reward, selecting the end poses as the exclusion poses converges faster compared to selecting the exclusion poses randomly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.461,
+                0.892,
+                0.611
+            ],
+            "angle": 0,
+            "content": "Once trained, a user can define the exclusion camera poses \\(\\{\\bar{x}_j^P,d_j\\}\\) at runtime, which then produces trajectories of camera poses that avoid the provided exclusion poses. This way, our agent can produce sets of diverse, yet aesthetically meaningful, trajectories with diversity regularization, while without diversity regularization it is possible to generate aesthetic trajectories from various different initial conditions that all converge to the same globally most aesthetic camera pose. Diversity Regularization can be disabled by defining out-of-boundary excluding poses."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.621,
+                0.821,
+                0.637
+            ],
+            "angle": 0,
+            "content": "3.3. Visual Deep Reinforcement Learning"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.644,
+                0.892,
+                0.825
+            ],
+            "angle": 0,
+            "content": "Sample inefficiency or learning stagnation are known to occur in the Visual DRL setting. This is because the supervision from the RL loss is not sufficient to support both policy learning and representation learning [51]. For the Aesthetic Tour problem, learning the complex representation of 3D scene appearance and aesthetics calls for a Visual DRL algorithm. Model-free Visual RL algorithms addresses the representation learning challenge mainly in three ways: image augmentation as task-invariant perturbation, image augmentation for contrastive learning, or self-supervised learning [28]. We adopt DrQ-v2 and CURL in GAIT, which belongs to the first and the second category respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.826,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The DrQ-v2 image augmentation strategy includes randomly shifting the original observation image \\( x_{t}^{I} \\) by 4 pixels as well as bilinearly interpolating the shifted image [50]. Both operations act as a task-invariant perturbation to regularize the \\( Q \\) function, which is first introduced in DrQ [51]."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.077,
+                0.875,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>The temporal smoothness term makes the reward function non-Markovian, since it considers prior time steps."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "7413"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.631,
+                0.301
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.647,
+                0.093,
+                0.9,
+                0.301
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.306,
+                0.892,
+                0.352
+            ],
+            "angle": 0,
+            "content": "Figure 4: Camera trajectories generated with three different initial camera poses. Left: selected view images including the initial and ending camera poses. Right: visualization of the trajectories whose initial camera poses are located at large dots. All sequences start showing aesthetically pleasing views since time step 3 and ending with similar views."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.364,
+                0.468,
+                0.484
+            ],
+            "angle": 0,
+            "content": "CURL relies on the random crop augmentation for contrastive learning, cropping from original image of resolution \\(100 \\times 100\\) to \\(x_{t}^{I}\\) with resolution \\(84 \\times 84\\). The anchor and the positive images are generated from two different random crops of the same image while the negatives are obtained by cropping other images [27]. Anchors, postives, and negatives are then used to compute the additional InfoNCE loss [38] to train the encoder."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.486,
+                0.468,
+                0.668
+            ],
+            "angle": 0,
+            "content": "Other than representation learning, DrQ-v2 and CURL share common components. Both methods are actor-critic, use a replay buffer for off-policy learning, rely on the network architecture introduced in SAC-AE [52], and use clipped double \\( Q \\) learning introduced in TD3 [13]. We modify the shared network architecture by adding inputs as detailed in Section 3.1. DrQ-v2 additionally integrates a linear exploration noise decay schedule, n-step TD, introduced in D4PG [2], and fast implementations of the replay buffer and the image augmentation module. We further enables higher training throughput for CURL by adopting DrQ-v2's fast replay buffer and image augmentation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.68,
+                0.295,
+                0.696
+            ],
+            "angle": 0,
+            "content": "3.4. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.704,
+                0.468,
+                0.809
+            ],
+            "angle": 0,
+            "content": "We conducted the training and testing experiments in the Habitat-Sim simulation framework [43, 48] that provides support for rendering and the realistic indoor dataset Replica [46]. We use the Adam [26] adaptive gradient descent as our network optimizer. The discount factor \\(\\gamma\\) is set to 0.99. It is very close to 1 as our objective is the aesthetics of the whole sequence instead of the last view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our multiple-GPU implementation boosts the training performance significantly. As shown in Figure 2, on a 8-GPU compute node, we run 7 Data Workers and 1 Update Worker, with each worker running on one GPU. 8-GPU implementation brings us much more speedup compared with 1-GPU, as shown in Figure 8."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.364,
+                0.892,
+                0.484
+            ],
+            "angle": 0,
+            "content": "Our view sequences can contribute to the indoor tour video generation. To generate tour videos for evaluation, 9 intermediate camera poses are interpolated based on the spherical interpolation between the adjacent two frames in each view sequence, producing a 5-second video clip in 30 FPS play mode from the original 16-frame sequence. We refer to the supplementary material for additional implementation details."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.497,
+                0.706,
+                0.515
+            ],
+            "angle": 0,
+            "content": "4. Experimental Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.522,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "We have conducted an extensive set of quantitative and qualitative experiments to validate GAIT. In Section 4.1, we show that GAIT stably converges to the same global-near-optimal ending pose from different initial poses. In Section 4.3, we compare results of GAIT trained with or without Temporal Smoothness. In Section 4.2, we compare results of GAIT training with or without Diversity Regularization. In Section 4.4, we compare GAIT implementations, GAIT-DrQ-v2 and GAIT-CURL, with baseline algorithms, CMA-ES and MPC. In Section 4.5, we identify important components of DrQ-v2 and CURL that significantly contribute to convergence rate. The experiments in this section are conducted with three scenes, Room, Apartment and Office. Figures 1, 4, 5, 6 are rendered in Room. More comprehensive experimental results are in the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.772,
+                0.842,
+                0.789
+            ],
+            "angle": 0,
+            "content": "4.1. Aesthetic Camera Sequence Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "A camera sequence of 16 frames is generated with an arbitrary initial camera pose. Because the initial camera pose is set randomly, its view image is usually with a low aesthetics score. GAIT agent transforms the camera pose effectively that the view aesthetics has been substantially improved at the time step 2 or 3, and the rest frames are all with good aesthetics. The statistics of aesthetic scores in"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "7414"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.107,
+                0.089,
+                0.442,
+                0.127
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>Maximum</td><td>6.12</td><td>6.67</td><td>5.20</td></tr><tr><td>Mean ± std</td><td>-0.38 ± 1.33</td><td>0.01 ± 1.35</td><td>-0.47 ± 1.26</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.128,
+                0.468,
+                0.157
+            ],
+            "angle": 0,
+            "content": "Table 1: The statistics of aesthetic scores in Room, Apartment, and Office."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.093,
+                0.17,
+                0.262,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.123,
+                0.251,
+                0.237,
+                0.264
+            ],
+            "angle": 0,
+            "content": "(a) GAIT-DrQ-v2"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.286,
+                0.17,
+                0.455,
+                0.25
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.323,
+                0.251,
+                0.43,
+                0.263
+            ],
+            "angle": 0,
+            "content": "(b) GAIT-CURL"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.269,
+                0.47,
+                0.39
+            ],
+            "angle": 0,
+            "content": "Figure 5: The comparisons of training with and without the regularization. The reward is lower with diversity regularization and temporal smoothness regularization because the corresponding terms of \\(\\mathcal{D}_t\\) and \\(S_{t}\\) is introduced into the reward function in Equation 5. But they converge with similar time steps. This is tested with the scene of Room with one random seed. Results with 3 seeds can be found in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.407,
+                0.42,
+                0.422
+            ],
+            "angle": 0,
+            "content": "Room, Apartment, and Office are shown in Table 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.424,
+                0.469,
+                0.515
+            ],
+            "angle": 0,
+            "content": "GAIT is robust in that the camera trajectory generation is not sensitive to the initial camera pose, as shown in Figure 4. Similar initial camera poses introduce similar trajectories. The global optimal views are always explored even with very different initial camera poses. The ending camera poses are similar if diversity regularization is not applied."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.532,
+                0.303,
+                0.548
+            ],
+            "angle": 0,
+            "content": "4.2. Diversity Regularization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.557,
+                0.47,
+                0.723
+            ],
+            "angle": 0,
+            "content": "Although GAIT is robust to explore global optimal views, users would like to have more control of the generation for different trajectories. The diversity regularization module helps explore the areas with sub-optimal but still plausible aesthetics scores. As shown in Figure 6, the camera poses are effectively moved out of the exclusion regions. The training with diversity regularization is stable and converges with similar time steps, as shown in Figure 5. Although the reward is slightly declined as expected, the quality of sequences are still plausible with the camera exploring nice views outside the exclusions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.739,
+                0.402,
+                0.756
+            ],
+            "angle": 0,
+            "content": "4.3. Temporal Smoothness Regularization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Temporal smoothness regularization is critical to produce aesthetic camera sequence because the neural aesthetics model [49] is for individual images. Without the temporal smoothness regularization, the accumulated aesthetics of all images is still good but the camera trajectory is trivial, such as the sequence 1 shown in Figure 7, where the camera transforms little after the time step 6. The temporal smoothness regularization reduces the reward of training, as shown in Figure 5, which prevents being stuck in optimal poses."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.505,
+                0.089,
+                0.892,
+                0.145
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"2\"></td><td>time (hours) ↓</td><td>training steps</td><td>throughput (FPS) ↑</td></tr><tr><td rowspan=\"2\">GAIT-DrQ-v2</td><td>1 GPU</td><td>16.33</td><td>1.5M</td><td>25.52</td></tr><tr><td>8 GPUs</td><td>3.38</td><td>3M</td><td>246</td></tr><tr><td rowspan=\"2\">GAIT-CURL</td><td>1 GPU</td><td>36.27</td><td>1.5M</td><td>11.49</td></tr><tr><td>8 GPUs</td><td>23.03</td><td>1.5M</td><td>17.63</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.5,
+                0.146,
+                0.892,
+                0.175
+            ],
+            "angle": 0,
+            "content": "Table 2: The statistics of training. Note that GAIT-CURL only need \\(1.5\\mathrm{M}\\) steps to converge on 8-GPU."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.568,
+                0.19,
+                0.826,
+                0.252
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>GAIT-DrQ-v2</td><td>38.34</td><td>20.10</td><td>42.10</td></tr><tr><td>GAIT-CURL</td><td>33.95</td><td>32.40</td><td>32.67</td></tr><tr><td>CMA-ES</td><td>32.06</td><td>32.29</td><td>31.78</td></tr><tr><td>MPC</td><td>6.32</td><td>/</td><td>/</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.253,
+                0.892,
+                0.299
+            ],
+            "angle": 0,
+            "content": "Table 3: The comparison of the averaged reward over 9 sequences. The 9 sequences start with 3 different initial positions and generated with 0, 1 and 2 exclusion regions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.31,
+                0.64,
+                0.327
+            ],
+            "angle": 0,
+            "content": "4.4. Comparisons"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.334,
+                0.892,
+                0.575
+            ],
+            "angle": 0,
+            "content": "We use Evaluation Episode Reward over the training process to compare the performance of DrQ-v2 [50], CURL [27], CMA-ES [17] and MPC [37]. It is defined as the average sum of rewards per episode under the Evaluation mode. For every 300 training episodes, a Evaluation of 10 episodes are run with random initial poses \\( x_0^P \\), random excluding distances \\( d_j \\), and ending poses of up to 4 previous Evaluation episodes as excluding poses. During Evaluation, the GAIT agent acts deterministically, i.e. the exploration noises used for training are turned off. The training processes shown in Figure 8 illustrate similar pattern across different scenes. GAIT-DrQ-v2 and GAIT-CURL take similar time steps to converge, but the latter is 2-8 times slower depending on the number of GPUs. Our implementation of CMA-ES and MPC are detailed in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.578,
+                0.892,
+                0.773
+            ],
+            "angle": 0,
+            "content": "We compare the average reward of 9 camera sequences in Table 3 with one seed. Results with 3 seeds can be found in the supplementary material. GAIT-DrQ-v2 and GAIT-CURL performs generally better than CMA-ES, except the reward with CMA-ES is better than GAIT-DrQ-v2 in the scene of Apartment. Still, both GAIT-DrQ-v2 and GAIT-CURL are better in the user study, which is shown in Section 4.6 and supplementary material. MPC performs significantly worse than others, though only tested in Room. The view sequences are generated instantly with GAIT-DrQ-v2 and GAIT-CURL. Both CMA-ES and MPC take more than 1 hour to generate a sequence, which is not scalable nor applicable to interactive scenarios."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.786,
+                0.655,
+                0.803
+            ],
+            "angle": 0,
+            "content": "4.5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "GAIT can be trained with DrQ-v2 [50] or CURL [27]. DrQ-v2 is improved upon DDPG [29], the linear decayed exploration noise and image augmentation are critical for the learning. As shown in Figure 9 (a), the episode reward will be significantly lower in training without image augmentation or linear decayed exploration noise. CURL is"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "7415"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.63,
+                0.302
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.647,
+                0.093,
+                0.9,
+                0.301
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.306,
+                0.892,
+                0.336
+            ],
+            "angle": 0,
+            "content": "Figure 6: Camera trajectories generated with different diversity regularization. Three trajectories from the same initial camera pose diverge according to the exclusion regions and ending with very different views."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.337,
+                0.831,
+                0.482
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.486,
+                0.89,
+                0.516
+            ],
+            "angle": 0,
+            "content": "Figure 7: Comparison of temporal smoothness regularization. Without the smoothness, the camera is transformed to the aesthetically optimal pose in a few time steps and stuck there until the end."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.535,
+                0.2,
+                0.614
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.115,
+                0.615,
+                0.179,
+                0.628
+            ],
+            "angle": 0,
+            "content": "(a) Room"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.214,
+                0.536,
+                0.331,
+                0.614
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.23,
+                0.615,
+                0.325,
+                0.628
+            ],
+            "angle": 0,
+            "content": "(b) Apartment"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.344,
+                0.535,
+                0.461,
+                0.614
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.376,
+                0.615,
+                0.44,
+                0.628
+            ],
+            "angle": 0,
+            "content": "(c) Office"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.634,
+                0.47,
+                0.709
+            ],
+            "angle": 0,
+            "content": "Figure 8: The comparisons between the training our method and CMA-ES. Our method is trained with DrQ-v2 and CURL. CMA-ES does not need to train. The dashed line is only for reference. It is achieved by averaging the reward of 9 trajectories it generates with up to 2 exclusion regions."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.717,
+                0.26,
+                0.796
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.122,
+                0.797,
+                0.237,
+                0.81
+            ],
+            "angle": 0,
+            "content": "(a) GAIT-DrQ-v2"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.286,
+                0.717,
+                0.455,
+                0.796
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.323,
+                0.797,
+                0.429,
+                0.81
+            ],
+            "angle": 0,
+            "content": "(b) GAIT-CURL"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.816,
+                0.468,
+                0.89
+            ],
+            "angle": 0,
+            "content": "Figure 9: The ablation experiments of the training algorithms. The image augmentation is critical for both GAIT-DrQ-v2 and GAIT-CURL. The linear decayed exploration noise significantly helps the training with GAIT-DrQ-v2. This is tested with the scene of Room."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.529,
+                0.892,
+                0.574
+            ],
+            "angle": 0,
+            "content": "based on SAC [16] and use image augmentation for contrastive learning. As shown in Figure 9 (b), GAIT-CURL can hardly converge without image augmentation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.587,
+                0.621,
+                0.603
+            ],
+            "angle": 0,
+            "content": "4.6. User Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.612,
+                0.892,
+                0.732
+            ],
+            "angle": 0,
+            "content": "To further evaluate the aesthetics in the generated tours, we conduct a user study. We recruited 10 participants (2 females and 8 males, with the age range of 25-35) to rate the video smoothness, video aesthetics, and subjective general preference, of the tours generated using three methods (i.e., CMA-ES, GAIT-DrQ-v2 and GAIT-CURL). Specifically, we prepared the video clips in three indoor scenes using the video generation described in Section 3.4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.733,
+                0.892,
+                0.884
+            ],
+            "angle": 0,
+            "content": "We asked for participants' feedback via 2-alternative forced choice. For each initial pose with the same exclusion level, every participant watch two video pairs, \\(\\{GAIT-DrQ-v2 vs. CMA-ES\\}\\), and \\(\\{GAIT-DrQ-v2 vs. GAIT-CURL\\}\\). In each pair, participants chose the preferred video clip based on (1) video smoothness and (2) video content aesthetics. After comparing the video clips rooted from the same initial pose, participants are also asked to rate \"which method provides higher video content diversity\" and \"which method is the overall preferred aesthetic video generation method\"."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.886,
+                0.891,
+                0.901
+            ],
+            "angle": 0,
+            "content": "When asked about \"overall which method provides bet"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "7416"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.473,
+                0.273
+            ],
+            "angle": 0,
+            "content": "ter aesthetic videos\" in \\(\\{GAIT-DrQ-v2 vs. CMA-ES\\}\\) in the three scenes, \\(93.3\\%\\), \\(96.7\\%\\), and \\(66.7\\%\\) users favor \\(GAIT-DrQ-v2\\). With the same question in \\(\\{GAIT-DrQ-v2 vs. GAIT-CURL\\}\\), \\(60.0\\%\\), \\(53.3\\%\\), and \\(43.3\\%\\) users favor \\(GAIT-DrQ-v2\\). We have learned from the users' feedback that majority participants favor the video clips generated in \\(GAIT-DrQ-v2\\) over CMA-ES but \\(GAIT-DrQ-v2\\) and \\(GAIT-CURL\\) generate the view sequences with different capabilities. \\(GAIT-DrQ-v2\\) is better at video aesthetics while \\(GAIT-CURL\\) performs better in video smoothness. Please refer to our supplementary materials for the collected data and the comprehensive data analysis."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.287,
+                0.206,
+                0.303
+            ],
+            "angle": 0,
+            "content": "5. Conclusions"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.312,
+                0.473,
+                0.538
+            ],
+            "angle": 0,
+            "content": "We propose GAIT, a novel DRL agent to generate aesthetically meaningful sequences of camera poses in 3D indoor scenes. Starting with an arbitrary initial camera pose without any pre-determined targets, a view sequence is transformed sequentially by the GAIT agent according to the neural aesthetics model. While the diversity regularization term is user-controlled to generate diverse, yet aesthetically meaningful trajectories, temporal smoothness regularization is introduced to avoid discontinuities camera poses for more visually pleasing trajectories. Our framework enables training GAIT agents with existing RL methods, including DrQ-v2 and CURL. We evaluate our method extensively. The conducted user study indicates GAIT is robust for high quality view sequences and it is easy to control for diverse outputs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.539,
+                0.473,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Discussion: Manually defining trajectories of camera poses in 3D spaces is a challenging task, that even takes professional users a couple of hours. In 2D motion graphics, which is a similar domain, the authoring of a video requires a designer 3-4 hours of manual work [21, 20]. GAIT training requires 3.38 hours of computing time for a single scene. However, once trained GAIT can generate multiple tours for the same scene, while an artist has to manually define every single trajectory. As GAIT only makes minimal assumptions about the environment, it can also be used to generate aesthetically valuable view sequences for real-world scenes that are represented as radiance fields. This can be achieved by using the view synthesis function of a NeRF-based approach to replace the rendering of a 3D scene simulator. This allows users to avoid the tedious manual selection of viewpoints for these scenes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.781,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Limitations and Future Work: GAIT-DrQ-v2 and GAIT-CURL can generalize to arbitrary initial and excluding poses within the trained scene, but they generalize poorly to unseen, new scenes. Making GAIT agents generalize across scenes is our key objective for future work, as this would make GAIT a more generic framework for view sequence generation. However, this would require a substantial increase in compute resources, the availability of a"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.121
+            ],
+            "angle": 0,
+            "content": "larger scene dataset, and a scalable DRL algorithm, which are outside the scope of this work."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.121,
+                0.893,
+                0.424
+            ],
+            "angle": 0,
+            "content": "While our method is able to reliably generate aesthetic camera tours for indoor scenes, it also has a few limitations that are interesting avenues for future research. First, we only tested our GAIT agent for indoor scenes and it is not clear whether it would work similarly well for outdoor scenes. Second, the scenes we used for our experiments where only single room layouts and it is not clear whether GAIT could also generate trajectories for more complex room layouts or whether it could take care of transitioning from one level of a building to another. Third, we did not test GAIT on scenes with dynamically moving objects. To this end it would be interesting to train and test a GAIT agent to generate aesthetically valuable tours under consideration of different types of scene dynamics. Finally, the neural aesthetics estimator only considers the per-frame aesthetics, while the inter-frame smoothness term is heuristic. A neural temporal aesthetics model is needed for this task. However, to the best of our knowledge, such a model is unavailable. Therefore, our goal is to work on a neural temporal aesthetics model in the future."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.438,
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+            "angle": 0,
+            "content": "Acknowledgements"
+        },
+        {
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+            "bbox": [
+                0.498,
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+            ],
+            "angle": 0,
+            "content": "This project was supported in part by NSF grants OAC1919752, ICER1940302, and IIS2107224, and by IBM, SUNY and Adobe."
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+# GAIT: Generating Aesthetic Indoor Tours with Deep Reinforcement Learning
+
+Desai Xie
+
+Ping Hu<sup>1</sup>
+
+Xin Sun
+
+Soren Pirk2
+
+Jianming Zhang
+
+Radomír
+
+Arie E. Kaufman<sup>1</sup>
+
+Stony Brook University
+
+2Adobe Research
+
+# Abstract
+
+Placing and orienting a camera to compose aesthetically meaningful shots of a scene is not only a key objective in real-world photography and cinematography but also for virtual content creation. The framing of a camera often significantly contributes to the story telling in movies, games, and mixed reality applications. Generating single camera poses or even contiguous trajectories either requires a significant amount of manual labor or requires solving high-dimensional optimization problems, which can be computationally demanding and error-prone. In this paper, we introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) agent, that learns to automatically control a camera to generate a sequence of aesthetically meaningful views for synthetic 3D indoor scenes. To generate sequences of frames with high aesthetic value, GAIT relies on a neural aesthetics estimator, which is trained on a crowd-sourced dataset. Additionally, we introduce regularization techniques for diversity and smoothness to generate visually interesting trajectories for a 3D environment, and to constrain agent acceleration in the reward function to generate a smooth sequence of camera frames. We validated our method by comparing it to baseline algorithms, based on a perceptual user study, and through ablation studies. Code and visual results are available on the project website: https://desaixie.github.io/gait-rl
+
+# 1. Introduction
+
+Composing a shot by framing a scene with a camera plays an integral part in photography and cinematography. A carefully composed frame does not only provide the information of a scene, but also serves to define the visual style, to instill a desired emotion in the viewer, and to carry forward the story the artist wants to convey [39]. Photographers and movie directors commonly spend a significant amount of time to perfect the camera framing, which – consequently – often leads to extensive cost footprints. While framing scenes in virtual setups, such as games or mixed reality applications, is arguably less involved, defining aes
+
+![](images/52c9b521338145e606db0cd6575476c8976543d6985a9c49ce9fb345866e0381.jpg)  
+Figure 1: Our novel DRL agent, GAIT, automatically generates camera poses so as to obtain aesthetic views of 3D indoor scenes. Left: Views of three camera poses from a generated sequence. Right: the 3D indoor environment with three highlighted camera poses. Red, yellow, orange corresponds to the three frames on the left respectively, where the red dot is the initial pose. GAIT maintains high aesthetic views throughout the sequence, while satisfying the initial pose, diversity, smoothness, and boundary constraints.
+
+![](images/33c421caf430adabdb4752e2a0ae73d6c0bdc7184e8f9ccf9f578d430f1c8a35.jpg)
+
+thetically valuable camera poses and trajectories still requires a considerable amount of manual work. An artist has to position key frames in space, define the orientation of the camera, and specify the temporal profile for the interpolation between keyframes. While this provides a high degree of control, for many applications, it would be desirable to frame a scene automatically by computing camera poses.
+
+Existing methods for automatically computing single camera poses or camera trajectories either rely on handcrafted methods with heuristics, which commonly do not generalize [40], are limited to specific applications, such as a trip between two cities [19], or specifically focus on moving targets [36]. Recently, it has been recognized that neural aesthetics estimators can serve as more generic solution for generating camera poses for the purpose of obtaining aesthetically meaningful camera frames [32] - a 2D image is mapped to a score that quantifies the aesthetics. An aesthetics estimator can be used to compare any two images with different contents or styles, which makes them applicable for finding views in lower dimensional spaces such as im
+
+ages and videos [49], or in constrained robotics settings [1]. In a 3D environment, finding a desired camera pose requires searching in a continuous  $R^6$  space (i.e., position  $R^3$  and orientation in  $R^3$ ) while also considering obstacles or even dynamically moving objects. Computing camera paths in a flexible and versatile manner therefore is a challenging and open problem.
+
+In this paper, we propose a novel method for automatically generating trajectories to aesthetically frame synthetic 3D indoor scenes. We introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) network that learns to move the camera so as to generate trajectories that show the most aesthetic views while also satisfying smoothness constraints. Our method is able to robustly generate diverse trajectories with varying start and end camera poses. Camera poses are optimized with a neural aesthetic metric [49] without any pre-determined targets in the view.
+
+GAIT computes camera transformations – the translation in 3D Euclidean space and the rotation (defined as yaw and pitch) – in a continuous 5D space for each step of the sequence. We define diversity regularization to provide control for either generating diverse sets of trajectories with varying start and end poses or to generate more uniform trajectories that always converge to the same final pose. To constrain the agent from taking actions that would create discontinuities in camera pose, we define smoothness regularization. Smooth trajectories tend to be more pleasing visually, which is important when the generated trajectories are used for video tours. To obtain a GAIT agent, we introduce a flexible framework to leverage existing RL methods for policy training, such as DrQ-v2 [50] and CURL [27].
+
+Based on a number of experiments we show that our method is able to generate trajectories of camera poses that frame scenes in an aesthetically meaningful manner. We show that our method is able to generate camera trajectories for a variety of complex 3D indoor scenes, which can be used to automatically create aesthetic video tours. Moreover, we show that the learned policies are robust against random initial camera poses - independent of the starting pose of the agent, it can converge to the same target pose.
+
+In summary, our contributions are: (1) We propose GAIT, the first DRL-based framework for generating sequences of camera poses with constrained globally optimal aesthetics in 3D synthetic indoor scenes; (2) We allow for user control based on diversity regularization and use smoothness regularization to constrain the agent to generate smooth and visually pleasing camera poses; (3) We show that employing image augmentation techniques facilitates learning representation of 3D scene aesthetics from a high-dimensional pixel-space, which is commonly considered challenging for DRL algorithms; (4) We implemented our algorithm to efficiently utilizes multiple GPUs: on a 8-GPU compute node, it can finish training in 3.5 hours; (5) We
+
+show that the generated camera poses can be interpolated to generate high-quality video tours of a scene; (6) Finally, we perform an extensive set of experiments and carefully validate our method based on quantitative and qualitative visual evaluations, via comparison with baseline method in a user study, and ablation studies to validate our algorithm design.
+
+# 2. Related Work
+
+Automatically generating views based on optimized camera control has received a considerable amount of research attention in the past decades. Existing approaches range from scientific visualization [5], surveillance [41, 6, 9] and robot photography [25] to 3D reconstruction [54, 31], virtual cinematography [23] - even focusing on characters [23, 22] - and tracking dynamics objects [14]. The breadths of these approaches is a testament for the importance of automatically generating camera poses, which remains challenging as finding solutions commonly requires solving highly complex solution spaces. Finding optimal views can be accomplished by defining metrics for information measurement [5], heuristics and rules of photography [8], or data-driven aesthetics assessment [9, 49].
+
+Deep aesthetic assessment: Methods for deep aesthetic assessment enable to categorize images based on aesthetic quality [35, 32]. To this end, Lu et al. [32] employ learned style attributes, while the approach of Kao et al. [24] relies on multi-task convolutional neural networks (CNN). Deng et al. [10] provide a survey of different techniques for aesthetic scoring and report that deep aesthetic assessment methods provide superior performance compared to handcrafted methods. Liu et al. [30] evaluate aesthetic quality based on graphs, where nodes represent local information of the different parts of an image. Finally, it has been recognized that defining uniform rules to assess aesthetics of motion is challenging [40]. Our method employs the deep aesthetics model developed by Wei et al. [49] because of its robustness and lightweight inference cost. They built a large photo pair dataset including more than 1M comparisons between different views from the same image that enables robust training for estimating aesthetic quality.
+
+Aesthetic view finding: A number of methods address the problem of automatically generating aesthetics and finding views. View finding techniques can be categorized based on various metrics, such as information metrics [5, 44, 12, 41, 19, 42, 23] or aesthetic metrics [7, 8, 47, 53, 49]. Chang and Chen [7] present a method for finding views in a panoramic image, while Cheng et al. [8] and Wei et al. [49] aim to select cropped views in a larger input image to compute 2D image compositions. Aesthetics models are also used for view recommendation that can even be computed in real time [47]. Yeh et al. [53] incorporate both image and motion aesthetic attributes into their video aesthetic assessment and Ma et al. [33] developed an instant photo tool
+
+based on the view proposal network of Wei et al. [49]. Hong et al. [18] introduce key composition maps to encode rules for composition-aware image cropping.
+
+For finding viewpoints in 3D space, Zhu et al. [55] trained a robot as a reinforcement learning agent to search a given target view in a room. Fang et al. [11] extended this framework to not only support reinforcement but also imitation learning. Gschwindt et al. [15] control drone movement with DRL and Bonatti et al. [4] define an aesthetic metric of short video clips based on crowd sourcing data. In AutoPhoto [1], the authors train a reinforcement learning agent for a ground robot mounted camera to find views according to the aesthetics model from [49]. In their work, however, the agent is only tasked to find aesthetic views in the vicinity of its initial location. Unlike these methods, GAIT generates a sequence of camera poses in a 3D synthetic scene and moves the camera in a 5D continuous space. The aesthetics of all frames are optimized globally, while satisfying the diversity and smoothness constraints.
+
+Reinforcement learning: Learning directly on image observations is commonly considered challenging for standard RL algorithms. In this setting, the underlying state information has to be extracted from the high-dimensional space of image observations. The RL loss does not provide sufficient signal for the implicit representation learning in addition to the regular policy learning [51], which often leads to sample inefficiency or learning stagnation. In Data Regularized Q (DrQ) [51], Yarats et al. employ regularization on task invariant image augmentation to facilitate the representation learning in RL [51]. Contrastive Unsupervised Representations for Reinforcement Learning (CURL) [27] further extends this augmentation strategy by also adopting contrastive learning on the augmented images.
+
+Actor-critic RL methods tend to perform well in continuous action space domains where the policy needs to be explicitly expressed, which differs from the  $\epsilon$ -greedy policy in DQN [34]. The actor and the critic models represent the agent's policy  $\pi(a_t|s_t)$  and the state-action value function  $Q(s_t, a_t)$  respectively. In Deep Deterministic Policy Gradient (DDPG) [29], the actor and the critic are represented as neural networks. The critic is updated according to Q-learning [34], and the actor is updated using its action value from the critic and the chain rule, following DPG [45]. DDPG also integrates techniques including experience replay, target networks, and exploration noise, which make it one of the most widely adopted algorithms for the continuous action domain. Soft Actor Critic (SAC) differs from DDPG in that it has a policy entropy term in addition to the RL objective for a better exploration and multi-modal behavior. In this work, we employ two Visual DRL algorithms, DrQ-v2 [50] and CURL [27] that use DDPG [29] and SAC [16] as their base actor-critic RL algorithms.
+
+# 3. GAIT Agent
+
+To generate aesthetic indoor tours, we introduce GAIT, a framework for training a DRL agent based on existing policy training approaches. Specifically, we show that a GAIT agent can be trained with DrQ-v2 [50], which is an efficient visual RL method that leverages task invariant image augmentation to help representation learning from pixels, as well as with CURL [27], which uses contrastive learning with on top of data augmentation. To predict camera pose trajectories, we unify both approaches into a single framework and extend by introducing diversity and smoothness regularization terms in the reward function. Furthermore, we evaluate aesthetics based on images instead of parametric models or heuristics.
+
+In the following sections we describe our framework. The formulation of our aesthetic camera RL framework is discussed in Section 3.1; the design of our reward function based on a neural aesthetics score, the out-of-bound penalty, and constrains for diversity and smoothness, is described in Section 3.2; and finally, in Section 3.3 we describe the two DRL algorithms we implement with our framework, DrQv2 and CURL. An overview of the agent in the multi-GPU setting is shown in Figure 2.
+
+# 3.1. Formulation
+
+Markov Decision Process (MDP): We consider the standard Reinforcement learning (RL) setting, formulated by the Markov Decision Processes (MDP) [3]. In MDP, an agent interacts with the environment in discrete time steps. At step  $t$ , given state  $s_t$ , the agent selects an action  $a_t$  according to its policy  $\pi(a_t | s_t)$ , and receives a scalar reward  $r_t$  along with the next state  $s_{t+1}$  from the environment. This process repeats until a terminal state  $s_T$  is reached.
+
+Objective: We aim at generating view sequences with superior aesthetic quality, smoothness and controlled diversity. Given an arbitrary initial camera pose  $x_0^P$  and the corresponding view  $x_0^I$  in a 3D indoor scene, we move the camera for  $T = 15$  time steps consecutively to produce an aesthetic sequence of 16 images. Start at time step  $t = 1$ , our agent transforms the camera pose to optimize the expected return of the following steps
+
+$$
+\mathbb {E} [ R _ {1} ] = \mathbb {E} [ \sum_ {t = 1} ^ {\tau} \gamma^ {t - 1} r _ {t} ], \tag {1}
+$$
+
+which is the sum of discounted reward. The reward  $r_t$  for time step  $t$  will be detailed in Section 3.2.
+
+Observation: At time step  $t$ , the observation of the agent includes the time step  $x_{t}^{T}$ , camera pose  $x_{t}^{P}$ , view image  $x_{t}^{I}$ , diversity regularization observations  $x_{t}^{D}$  and temporal smoothness regularization observations  $x_{t}^{S}$ . The time step number  $x_{t}^{T}$  is normalized to [0, 1]. A camera pose is represented as a 5D vector, i.e. the position  $\{x, y, z\}$ , and the
+
+![](images/0c386a1abdba4868d2392f8852a5af4f97f6b53eac1d8e6c282ed8dc3c30a8c4.jpg)  
+Figure 2: Overview of the GAIT framework in the multi-GPU setting: we describe the shared components for the two actor-critic algorithms, DrQ-v2 and CURL. In the Data loop, the actor interacts with the environment repeatedly and saves each transition in the Replay Buffer. The Update worker samples a batch of transitions from the Replay Buffer and updates the actor and the critic networks based on the RL loss functions of DrQ-v2 and CURL. The Data and Update workers communicate their steps through the shared Storage, to maintain a data-update step ratio of  $2:1$ , as well as the updated weights of the actor network.
+
+![](images/63d714c1fcbd5874a4c0d1747c8e0b0be11500e6a49222ff7dec806f6eeefd29.jpg)  
+Figure 3: Actor-critic network architecture: while the network architecture for our actor and critic networks are similar, they do not share layers except for the encoder.
+
+rotation of yaw  $\psi$  and pitch  $\theta$ . The camera pose is limited in an axis-aligned bounding box, within which its position  $\{x,y,z\}$  is normalized to  $[-1,1]$ . The angle of yaw  $\theta$  is limited in  $[- \pi, \pi]$  and the angle of pitch  $\psi$  is limited in  $[- \pi/2, \pi/2]$ , both of them are also normalized to  $[-1,1]$ . A view image is rendered with the camera pose in a resolution of  $84 \times 84$  with 3 color channels. The evaluations of diversity and smoothness will be detailed in Section 3.2.
+
+Action: An action taken by our agent is also a 5D vector in the same space of camera pose. For each time step, the camera pose is transformed by adding the action vector,
+
+$$
+x _ {t + 1} ^ {P} = x _ {t} ^ {P} \oplus a _ {t}, \tag {2}
+$$
+
+where  $\oplus$  means the result of the addition is normalized to  $[-1, 1]$ .
+
+Actor-critic RL: For our GAIT framework, we employ two state-of-the-art visual actor-critic DRL algorithms DrQ-v2 [50] and CURL [27]. For both, the actor network represents the policy  $\pi (a_t|x_t)$ , while the critic network represents the state-action value function  $Q(s_{t},a_{t})$ . The critic network is optimized to approximate the expected return given state-action pairs,
+
+$$
+Q ^ {\pi} \left(s _ {t}, a _ {t}\right) = \mathbb {E} _ {a _ {i > t} \sim \pi} \left[ R _ {t} \mid s _ {t}, a _ {t} \right], \tag {3}
+$$
+
+where the actions are selected by the actor network. The actor network is optimized on the expected return over all possible initial states in the environment:
+
+$$
+\pi^ {*} = \underset {\pi} {\operatorname {a r g m a x}} \mathbb {E} _ {a _ {i} \sim \pi} [ R _ {1} ]. \tag {4}
+$$
+
+For DrQv2, we employ Q-learning to update the critic as described in DDPG [29]. We use the action value from the critic and the chain rule following DPG [45], to update the actor. For CURL, the actor and the critic update targets also include the entropy of policy as introduced in SAC [16].
+
+# 3.2. Reward Function
+
+The reward function consists of several components: first, we introduce an out-of-boundary penalty to prevent the camera being placed outside the indoor scene. For each scene, we set an axis-aligned bounding-box as the domain of the camera position. The position within the domain is normalized as  $[-1, 1]^3$ . If the camera is placed out-of-boundary, the reward is a negative constant  $r^{\mathcal{B}}$ :
+
+$$
+r _ {t} = \left\{ \begin{array}{l l} r _ {t} ^ {\mathcal {A}} r _ {t} ^ {\mathcal {S}} r _ {t} ^ {\mathcal {D}}, & \text {i f i n s i d e b o u n d a r y}, \\ r ^ {\mathcal {B}}, & \text {o t h e r w i s e}. \end{array} \right. \tag {5}
+$$
+
+$r^{\mathcal{B}}$  is set to be  $-10$  for all experiments in this paper. When the camera is placed inside the boundary, the reward is the product of the evaluations of view aesthetics  $r_t^A$ , temporal smoothness  $r_t^S$  and diversity regularization  $r_t^D$ .
+
+View Aesthetics: We employ the neural aesthetic model [49] to evaluate the aesthetics of a view. The model performs generic aesthetics assessment based on crowd sourcing data, which also works well 3D indoor scenes. Instead of using the view image  $x_{t}^{I}$  in the observation with the resolution of  $84 \times 84$ , we render an image with higher resolution of  $240 \times 240$  to evaluate the aesthetics  $r_{t}^{\mathcal{A}}$  – the higher resolution is required by the neural aesthetic model.
+
+Temporal Smoothness: Obtaining aesthetics assessment for temporal sequences of frames is an open research
+
+problem. Therefore, we rely on an aesthetic model [49] for single frames to assess aesthetics. However, if we would only use single frames instead of an entire sequence to quantify the aesthetics, the agent would diverge, which would then lead to degenerated results. Therefore, we introduce the temporal smoothness term  $r_t^S$  in the reward function (Equation 5) to penalize the agent when it takes an action which is too different from the its preceding time steps.
+
+Adding the smoothness term generates smoother camera trajectories and it forces the camera poses of a sequence to be moderately different from each other. Consequently, the GAIT agent will generate a sequence of aesthetic views instead of converging to a single view with high aesthetic value. On the contrary, without the smoothness term, our agent tends to take abrupt actions and also stays at the same aesthetic view until an episode terminates (Section 4.5).
+
+As mentioned in Section 3.1, the 5D vector of action is composed of two parts, including a 3D translation and 2D rotation  $a_{t} = \{\tilde{a}_{t},\hat{a}_{t}\}$ . The temporal smoothness term compares the current action  $a_{t}$  with the actions at the last three time steps  $\{a_{t - 3},a_{t - 2},a_{t - 1}\}$ ,
+
+$$
+r _ {t} ^ {\mathcal {S}} = \frac {1}{2} \left(\min  _ {i = 1} ^ {3} r _ {t, i} ^ {\mathcal {S}} + \frac {1}{3} \sum_ {i = 1} ^ {3} r _ {t, i} ^ {\mathcal {S}}\right), r _ {t, i} ^ {\mathcal {S}} = \tilde {r} ^ {\mathcal {S}} _ {t, i} + \hat {r} ^ {\mathcal {S}} _ {t, i}, \tag {6}
+$$
+
+where  $r_{t,i}^{S}$  is evaluated with  $a_{t}$  and the action taken  $i$  time steps earlier  $a_{t - i}$ . It consists of two parts,  $\tilde{r^S}_{t,i}$  and  $\tilde{r^S}_{t,i}$ , for translation and rotation respectively.  $\tilde{r^S}_{t,i}$  is a 1D Gaussian function with the amplitude of 1, the mean of  $\tilde{a}_{t - i}$  and the standard deviation of  $\max \left(\frac{1}{2} |\tilde{a}_{t - i}|,0.1\right)$ .  $\hat{r^S}_{t,i}$  is evaluated similarly except the standard deviation is  $\max \left(|\hat{a}_{t - i}|,0.1\right)$ . Therefore,  $S_{t}$  will penalize the agent when  $a_{t}$  is close to zero or  $a_{t}$  is very different from  $\{a_{t - i}\}$ . Translation is more penalized than rotation. The Smoothness observation contains the recent actions  $x_{t}^{S} = \{a_{t - i}\}$ , while the Critic additionally observes the distance between its current action and recent actions  $\{\| a_t - a_{t - i}\|^2\}$ , where  $i = 1,2,3$ . See Supplementary Material for a visualization of the Gaussian smoothness function for Temporal Smoothness.
+
+Diversity Regularization: Without Diversity Regularization, GAIT generates sequences in a robust manner - varying initial camera poses lead to trajectories toward the globally most aesthetic target pose. While this may be wanted in many situations, GAIT also allows for generating diverse aesthetic trajectories. We enable this by specifying a diversity regularization term  $r_t^{\mathcal{D}}$  in the reward function (Equation 5). Specifically, we define up to 4 camera poses and the corresponding distances,  $\{\bar{x}_j^P,d_j\}_{0\leq j < 4}$  that
+
+we refer to as exclusion poses. The diversity regularization term penalizes the agent if the distance between its pose and any exclusion poses  $\bar{x}_j^P$  is less than the corresponding distance  $d_j$ ,
+
+$$
+r _ {t} ^ {\mathcal {D}} = \min  _ {j = 0} ^ {4} \left(\min  \left(\frac {\left\| x _ {t} ^ {P} - \bar {x} _ {j} ^ {P} \right\| ^ {2}}{d _ {j}}, 1\right)\right). \tag {7}
+$$
+
+The Diversity observation includes the exclusion poses and agent's current distances to the exclusion poses,  $x_{t}^{D} = \{\bar{x}_{j}^{P},d_{j},\left\| x_{t}^{P} - \bar{x}_{j}^{P}\right\|^{2}\}_{0\leq j < 4}$ .
+
+To train the GAIT agent with exclusion poses, the naive strategy is to to randomly sample them in the 5D space. However, as most random camera poses in the scene only have low aesthetics scores (e.g. the camera is placed inside an object or the view may be occluded), selecting exclusion poses randomly would actually lead to inefficient training. Therefore, we follow another strategy: for each episode, we set the exclusion poses to be the ending camera poses of the last 4 episodes with a random excluding distance in [0.3, 1.3]. Because our GAIT agent tends to end at camera poses with high aesthetics scores to maximize the reward, selecting the end poses as the exclusion poses converges faster compared to selecting the exclusion poses randomly.
+
+Once trained, a user can define the exclusion camera poses  $\{\bar{x}_j^P,d_j\}$  at runtime, which then produces trajectories of camera poses that avoid the provided exclusion poses. This way, our agent can produce sets of diverse, yet aesthetically meaningful, trajectories with diversity regularization, while without diversity regularization it is possible to generate aesthetic trajectories from various different initial conditions that all converge to the same globally most aesthetic camera pose. Diversity Regularization can be disabled by defining out-of-boundary excluding poses.
+
+# 3.3. Visual Deep Reinforcement Learning
+
+Sample inefficiency or learning stagnation are known to occur in the Visual DRL setting. This is because the supervision from the RL loss is not sufficient to support both policy learning and representation learning [51]. For the Aesthetic Tour problem, learning the complex representation of 3D scene appearance and aesthetics calls for a Visual DRL algorithm. Model-free Visual RL algorithms addresses the representation learning challenge mainly in three ways: image augmentation as task-invariant perturbation, image augmentation for contrastive learning, or self-supervised learning [28]. We adopt DrQ-v2 and CURL in GAIT, which belongs to the first and the second category respectively.
+
+The DrQ-v2 image augmentation strategy includes randomly shifting the original observation image  $x_{t}^{I}$  by 4 pixels as well as bilinearly interpolating the shifted image [50]. Both operations act as a task-invariant perturbation to regularize the  $Q$  function, which is first introduced in DrQ [51].
+
+![](images/1f4c51359d08ec2e4a8bf885a22721c04d60e18f7b06ec8d00a1dd481db799c6.jpg)  
+Figure 4: Camera trajectories generated with three different initial camera poses. Left: selected view images including the initial and ending camera poses. Right: visualization of the trajectories whose initial camera poses are located at large dots. All sequences start showing aesthetically pleasing views since time step 3 and ending with similar views.
+
+![](images/f98b5a7543e3ed4194861650aeea62bb9cb637c61231f432d362992897082ca6.jpg)
+
+CURL relies on the random crop augmentation for contrastive learning, cropping from original image of resolution  $100 \times 100$  to  $x_{t}^{I}$  with resolution  $84 \times 84$ . The anchor and the positive images are generated from two different random crops of the same image while the negatives are obtained by cropping other images [27]. Anchors, postives, and negatives are then used to compute the additional InfoNCE loss [38] to train the encoder.
+
+Other than representation learning, DrQ-v2 and CURL share common components. Both methods are actor-critic, use a replay buffer for off-policy learning, rely on the network architecture introduced in SAC-AE [52], and use clipped double  $Q$  learning introduced in TD3 [13]. We modify the shared network architecture by adding inputs as detailed in Section 3.1. DrQ-v2 additionally integrates a linear exploration noise decay schedule, n-step TD, introduced in D4PG [2], and fast implementations of the replay buffer and the image augmentation module. We further enables higher training throughput for CURL by adopting DrQ-v2's fast replay buffer and image augmentation.
+
+# 3.4. Implementation Details
+
+We conducted the training and testing experiments in the Habitat-Sim simulation framework [43, 48] that provides support for rendering and the realistic indoor dataset Replica [46]. We use the Adam [26] adaptive gradient descent as our network optimizer. The discount factor  $\gamma$  is set to 0.99. It is very close to 1 as our objective is the aesthetics of the whole sequence instead of the last view.
+
+Our multiple-GPU implementation boosts the training performance significantly. As shown in Figure 2, on a 8-GPU compute node, we run 7 Data Workers and 1 Update Worker, with each worker running on one GPU. 8-GPU implementation brings us much more speedup compared with 1-GPU, as shown in Figure 8.
+
+Our view sequences can contribute to the indoor tour video generation. To generate tour videos for evaluation, 9 intermediate camera poses are interpolated based on the spherical interpolation between the adjacent two frames in each view sequence, producing a 5-second video clip in 30 FPS play mode from the original 16-frame sequence. We refer to the supplementary material for additional implementation details.
+
+# 4. Experimental Results
+
+We have conducted an extensive set of quantitative and qualitative experiments to validate GAIT. In Section 4.1, we show that GAIT stably converges to the same global-near-optimal ending pose from different initial poses. In Section 4.3, we compare results of GAIT trained with or without Temporal Smoothness. In Section 4.2, we compare results of GAIT training with or without Diversity Regularization. In Section 4.4, we compare GAIT implementations, GAIT-DrQ-v2 and GAIT-CURL, with baseline algorithms, CMA-ES and MPC. In Section 4.5, we identify important components of DrQ-v2 and CURL that significantly contribute to convergence rate. The experiments in this section are conducted with three scenes, Room, Apartment and Office. Figures 1, 4, 5, 6 are rendered in Room. More comprehensive experimental results are in the supplementary material.
+
+# 4.1. Aesthetic Camera Sequence Generation
+
+A camera sequence of 16 frames is generated with an arbitrary initial camera pose. Because the initial camera pose is set randomly, its view image is usually with a low aesthetics score. GAIT agent transforms the camera pose effectively that the view aesthetics has been substantially improved at the time step 2 or 3, and the rest frames are all with good aesthetics. The statistics of aesthetic scores in
+
+<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>Maximum</td><td>6.12</td><td>6.67</td><td>5.20</td></tr><tr><td>Mean ± std</td><td>-0.38 ± 1.33</td><td>0.01 ± 1.35</td><td>-0.47 ± 1.26</td></tr></table>
+
+![](images/a618df61bdbf78bb33734f0a611773e3058be5d53ed5d33ba62b107a3d638d3f.jpg)  
+(a) GAIT-DrQ-v2  
+Figure 5: The comparisons of training with and without the regularization. The reward is lower with diversity regularization and temporal smoothness regularization because the corresponding terms of  $\mathcal{D}_t$  and  $S_{t}$  is introduced into the reward function in Equation 5. But they converge with similar time steps. This is tested with the scene of Room with one random seed. Results with 3 seeds can be found in the supplementary material.
+
+![](images/46b0a98aff5e135eee92ca008fb89acdb0d70fca0f096d26f135e952b039a231.jpg)  
+(b) GAIT-CURL
+
+Room, Apartment, and Office are shown in Table 1.
+
+GAIT is robust in that the camera trajectory generation is not sensitive to the initial camera pose, as shown in Figure 4. Similar initial camera poses introduce similar trajectories. The global optimal views are always explored even with very different initial camera poses. The ending camera poses are similar if diversity regularization is not applied.
+
+# 4.2. Diversity Regularization
+
+Although GAIT is robust to explore global optimal views, users would like to have more control of the generation for different trajectories. The diversity regularization module helps explore the areas with sub-optimal but still plausible aesthetics scores. As shown in Figure 6, the camera poses are effectively moved out of the exclusion regions. The training with diversity regularization is stable and converges with similar time steps, as shown in Figure 5. Although the reward is slightly declined as expected, the quality of sequences are still plausible with the camera exploring nice views outside the exclusions.
+
+# 4.3. Temporal Smoothness Regularization
+
+Temporal smoothness regularization is critical to produce aesthetic camera sequence because the neural aesthetics model [49] is for individual images. Without the temporal smoothness regularization, the accumulated aesthetics of all images is still good but the camera trajectory is trivial, such as the sequence 1 shown in Figure 7, where the camera transforms little after the time step 6. The temporal smoothness regularization reduces the reward of training, as shown in Figure 5, which prevents being stuck in optimal poses.
+
+Table 1: The statistics of aesthetic scores in Room, Apartment, and Office.  
+
+<table><tr><td colspan="2"></td><td>time (hours) ↓</td><td>training steps</td><td>throughput (FPS) ↑</td></tr><tr><td rowspan="2">GAIT-DrQ-v2</td><td>1 GPU</td><td>16.33</td><td>1.5M</td><td>25.52</td></tr><tr><td>8 GPUs</td><td>3.38</td><td>3M</td><td>246</td></tr><tr><td rowspan="2">GAIT-CURL</td><td>1 GPU</td><td>36.27</td><td>1.5M</td><td>11.49</td></tr><tr><td>8 GPUs</td><td>23.03</td><td>1.5M</td><td>17.63</td></tr></table>
+
+Table 2: The statistics of training. Note that GAIT-CURL only need  $1.5\mathrm{M}$  steps to converge on 8-GPU.  
+
+<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>GAIT-DrQ-v2</td><td>38.34</td><td>20.10</td><td>42.10</td></tr><tr><td>GAIT-CURL</td><td>33.95</td><td>32.40</td><td>32.67</td></tr><tr><td>CMA-ES</td><td>32.06</td><td>32.29</td><td>31.78</td></tr><tr><td>MPC</td><td>6.32</td><td>/</td><td>/</td></tr></table>
+
+Table 3: The comparison of the averaged reward over 9 sequences. The 9 sequences start with 3 different initial positions and generated with 0, 1 and 2 exclusion regions.
+
+# 4.4. Comparisons
+
+We use Evaluation Episode Reward over the training process to compare the performance of DrQ-v2 [50], CURL [27], CMA-ES [17] and MPC [37]. It is defined as the average sum of rewards per episode under the Evaluation mode. For every 300 training episodes, a Evaluation of 10 episodes are run with random initial poses  $x_0^P$ , random excluding distances  $d_j$ , and ending poses of up to 4 previous Evaluation episodes as excluding poses. During Evaluation, the GAIT agent acts deterministically, i.e. the exploration noises used for training are turned off. The training processes shown in Figure 8 illustrate similar pattern across different scenes. GAIT-DrQ-v2 and GAIT-CURL take similar time steps to converge, but the latter is 2-8 times slower depending on the number of GPUs. Our implementation of CMA-ES and MPC are detailed in the supplementary material.
+
+We compare the average reward of 9 camera sequences in Table 3 with one seed. Results with 3 seeds can be found in the supplementary material. GAIT-DrQ-v2 and GAIT-CURL performs generally better than CMA-ES, except the reward with CMA-ES is better than GAIT-DrQ-v2 in the scene of Apartment. Still, both GAIT-DrQ-v2 and GAIT-CURL are better in the user study, which is shown in Section 4.6 and supplementary material. MPC performs significantly worse than others, though only tested in Room. The view sequences are generated instantly with GAIT-DrQ-v2 and GAIT-CURL. Both CMA-ES and MPC take more than 1 hour to generate a sequence, which is not scalable nor applicable to interactive scenarios.
+
+# 4.5. Ablation Study
+
+GAIT can be trained with DrQ-v2 [50] or CURL [27]. DrQ-v2 is improved upon DDPG [29], the linear decayed exploration noise and image augmentation are critical for the learning. As shown in Figure 9 (a), the episode reward will be significantly lower in training without image augmentation or linear decayed exploration noise. CURL is
+
+![](images/e34d0fe0e46d6cff92b5a21d6e902618029cfcd45e55617195d3ffaa3a19653f.jpg)
+
+![](images/ab07ff73ad2069a6a58f0d045fd2dde8b4e5f8a8a913e8be9d113dce8c482064.jpg)
+
+![](images/476ea941680fc7968527901a2aacf5e3df3476cb4935124dba468a322cf72120.jpg)  
+Figure 6: Camera trajectories generated with different diversity regularization. Three trajectories from the same initial camera pose diverge according to the exclusion regions and ending with very different views.  
+Figure 7: Comparison of temporal smoothness regularization. Without the smoothness, the camera is transformed to the aesthetically optimal pose in a few time steps and stuck there until the end.
+
+![](images/d08c9d905b54da2408c717d19663bddeb033e33450418d654dbd4269a0cf2763.jpg)  
+(a) Room
+
+![](images/a77798fb757c653f2bfb404bf66ba36bcad70a143562945052c8ea14b6965801.jpg)  
+(b) Apartment
+
+![](images/83588d400b02b55fd519c9cae41de55ecd58710d01f649e42f7cfa47f16b7170.jpg)  
+(c) Office
+
+![](images/ebb606d40864e55865bdf35290ac03c18cb05231c9c67d901e25deef2bf988db.jpg)  
+Figure 8: The comparisons between the training our method and CMA-ES. Our method is trained with DrQ-v2 and CURL. CMA-ES does not need to train. The dashed line is only for reference. It is achieved by averaging the reward of 9 trajectories it generates with up to 2 exclusion regions.  
+(a) GAIT-DrQ-v2  
+Figure 9: The ablation experiments of the training algorithms. The image augmentation is critical for both GAIT-DrQ-v2 and GAIT-CURL. The linear decayed exploration noise significantly helps the training with GAIT-DrQ-v2. This is tested with the scene of Room.
+
+![](images/bf6b289c4f453c2d821300a1ef4ae2a854c87cded45b2eefb062c774c7f5ddfa.jpg)  
+(b) GAIT-CURL
+
+based on SAC [16] and use image augmentation for contrastive learning. As shown in Figure 9 (b), GAIT-CURL can hardly converge without image augmentation.
+
+# 4.6. User Study
+
+To further evaluate the aesthetics in the generated tours, we conduct a user study. We recruited 10 participants (2 females and 8 males, with the age range of 25-35) to rate the video smoothness, video aesthetics, and subjective general preference, of the tours generated using three methods (i.e., CMA-ES, GAIT-DrQ-v2 and GAIT-CURL). Specifically, we prepared the video clips in three indoor scenes using the video generation described in Section 3.4.
+
+We asked for participants' feedback via 2-alternative forced choice. For each initial pose with the same exclusion level, every participant watch two video pairs,  $\{GAIT-DrQ-v2 vs. CMA-ES\}$ , and  $\{GAIT-DrQ-v2 vs. GAIT-CURL\}$ . In each pair, participants chose the preferred video clip based on (1) video smoothness and (2) video content aesthetics. After comparing the video clips rooted from the same initial pose, participants are also asked to rate "which method provides higher video content diversity" and "which method is the overall preferred aesthetic video generation method".
+
+When asked about "overall which method provides bet
+
+ter aesthetic videos" in  $\{GAIT-DrQ-v2 vs. CMA-ES\}$  in the three scenes,  $93.3\%$ ,  $96.7\%$ , and  $66.7\%$  users favor  $GAIT-DrQ-v2$ . With the same question in  $\{GAIT-DrQ-v2 vs. GAIT-CURL\}$ ,  $60.0\%$ ,  $53.3\%$ , and  $43.3\%$  users favor  $GAIT-DrQ-v2$ . We have learned from the users' feedback that majority participants favor the video clips generated in  $GAIT-DrQ-v2$  over CMA-ES but  $GAIT-DrQ-v2$  and  $GAIT-CURL$  generate the view sequences with different capabilities.  $GAIT-DrQ-v2$  is better at video aesthetics while  $GAIT-CURL$  performs better in video smoothness. Please refer to our supplementary materials for the collected data and the comprehensive data analysis.
+
+# 5. Conclusions
+
+We propose GAIT, a novel DRL agent to generate aesthetically meaningful sequences of camera poses in 3D indoor scenes. Starting with an arbitrary initial camera pose without any pre-determined targets, a view sequence is transformed sequentially by the GAIT agent according to the neural aesthetics model. While the diversity regularization term is user-controlled to generate diverse, yet aesthetically meaningful trajectories, temporal smoothness regularization is introduced to avoid discontinuities camera poses for more visually pleasing trajectories. Our framework enables training GAIT agents with existing RL methods, including DrQ-v2 and CURL. We evaluate our method extensively. The conducted user study indicates GAIT is robust for high quality view sequences and it is easy to control for diverse outputs.
+
+Discussion: Manually defining trajectories of camera poses in 3D spaces is a challenging task, that even takes professional users a couple of hours. In 2D motion graphics, which is a similar domain, the authoring of a video requires a designer 3-4 hours of manual work [21, 20]. GAIT training requires 3.38 hours of computing time for a single scene. However, once trained GAIT can generate multiple tours for the same scene, while an artist has to manually define every single trajectory. As GAIT only makes minimal assumptions about the environment, it can also be used to generate aesthetically valuable view sequences for real-world scenes that are represented as radiance fields. This can be achieved by using the view synthesis function of a NeRF-based approach to replace the rendering of a 3D scene simulator. This allows users to avoid the tedious manual selection of viewpoints for these scenes.
+
+Limitations and Future Work: GAIT-DrQ-v2 and GAIT-CURL can generalize to arbitrary initial and excluding poses within the trained scene, but they generalize poorly to unseen, new scenes. Making GAIT agents generalize across scenes is our key objective for future work, as this would make GAIT a more generic framework for view sequence generation. However, this would require a substantial increase in compute resources, the availability of a
+
+larger scene dataset, and a scalable DRL algorithm, which are outside the scope of this work.
+
+While our method is able to reliably generate aesthetic camera tours for indoor scenes, it also has a few limitations that are interesting avenues for future research. First, we only tested our GAIT agent for indoor scenes and it is not clear whether it would work similarly well for outdoor scenes. Second, the scenes we used for our experiments where only single room layouts and it is not clear whether GAIT could also generate trajectories for more complex room layouts or whether it could take care of transitioning from one level of a building to another. Third, we did not test GAIT on scenes with dynamically moving objects. To this end it would be interesting to train and test a GAIT agent to generate aesthetically valuable tours under consideration of different types of scene dynamics. Finally, the neural aesthetics estimator only considers the per-frame aesthetics, while the inter-frame smoothness term is heuristic. A neural temporal aesthetics model is needed for this task. However, to the best of our knowledge, such a model is unavailable. Therefore, our goal is to work on a neural temporal aesthetics model in the future.
+
+# Acknowledgements
+
+This project was supported in part by NSF grants OAC1919752, ICER1940302, and IIS2107224, and by IBM, SUNY and Adobe.
+
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+[49] Zijun Wei, Jianming Zhang, Xiaohui Shen, Zhe Lin, Radomir Mech, Minh Hoai, and Dimitris Samaras. Good view hunting: Learning photo composition from dense view pairs. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5437-5446, 2018. 2, 3, 4, 5, 7  
+[50] Denis Yarats, Rob Fergus, Alessandro Lazaric, and Lerel Pinto. Mastering visual continuous control: Improved data-augmented reinforcement learning. arXiv preprint arXiv:2107.09645, 2021. 2, 3, 4, 5, 7  
+[51] Denis Yarats, Ilya Kostrikov, and Rob Fergus. Image augmentation is all you need: Regularizing deep reinforcement learning from pixels. In International Conference on Learning Representations, 2020. 3, 5  
+[52] Denis Yarats, Amy Zhang, Ilya Kostrikov, Brandon Amos, Joelle Pineau, and Rob Fergus. Improving sample efficiency in model-free reinforcement learning from images, 2019. 6  
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+[55] Yuke Zhu, Roozbeh Mottaghi, Eric Kolve, Joseph J Lim, Abhinav Gupta, Li Fei-Fei, and Ali Farhadi. Target-driven visual navigation in indoor scenes using deep reinforcement learning. In IEEE International Conference on Robotics and Automation (ICRA), pages 3357–3364, 2017. 3
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+                                    "type": "text",
+                                    "content": " and orientation in "
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+                                    "type": "text",
+                                    "content": ") while also considering obstacles or even dynamically moving objects. Computing camera paths in a flexible and versatile manner therefore is a challenging and open problem."
+                                }
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+                                    "content": "In this paper, we propose a novel method for automatically generating trajectories to aesthetically frame synthetic 3D indoor scenes. We introduce GAIT, a framework for training a Deep Reinforcement Learning (DRL) network that learns to move the camera so as to generate trajectories that show the most aesthetic views while also satisfying smoothness constraints. Our method is able to robustly generate diverse trajectories with varying start and end camera poses. Camera poses are optimized with a neural aesthetic metric [49] without any pre-determined targets in the view."
+                                }
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+                                    "content": "GAIT computes camera transformations – the translation in 3D Euclidean space and the rotation (defined as yaw and pitch) – in a continuous 5D space for each step of the sequence. We define diversity regularization to provide control for either generating diverse sets of trajectories with varying start and end poses or to generate more uniform trajectories that always converge to the same final pose. To constrain the agent from taking actions that would create discontinuities in camera pose, we define smoothness regularization. Smooth trajectories tend to be more pleasing visually, which is important when the generated trajectories are used for video tours. To obtain a GAIT agent, we introduce a flexible framework to leverage existing RL methods for policy training, such as DrQ-v2 [50] and CURL [27]."
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+                                    "content": "Based on a number of experiments we show that our method is able to generate trajectories of camera poses that frame scenes in an aesthetically meaningful manner. We show that our method is able to generate camera trajectories for a variety of complex 3D indoor scenes, which can be used to automatically create aesthetic video tours. Moreover, we show that the learned policies are robust against random initial camera poses - independent of the starting pose of the agent, it can converge to the same target pose."
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+                                    "content": "In summary, our contributions are: (1) We propose GAIT, the first DRL-based framework for generating sequences of camera poses with constrained globally optimal aesthetics in 3D synthetic indoor scenes; (2) We allow for user control based on diversity regularization and use smoothness regularization to constrain the agent to generate smooth and visually pleasing camera poses; (3) We show that employing image augmentation techniques facilitates learning representation of 3D scene aesthetics from a high-dimensional pixel-space, which is commonly considered challenging for DRL algorithms; (4) We implemented our algorithm to efficiently utilizes multiple GPUs: on a 8-GPU compute node, it can finish training in 3.5 hours; (5) We"
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+                                    "content": "show that the generated camera poses can be interpolated to generate high-quality video tours of a scene; (6) Finally, we perform an extensive set of experiments and carefully validate our method based on quantitative and qualitative visual evaluations, via comparison with baseline method in a user study, and ablation studies to validate our algorithm design."
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+                                    "content": "2. Related Work"
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+                                    "content": "Automatically generating views based on optimized camera control has received a considerable amount of research attention in the past decades. Existing approaches range from scientific visualization [5], surveillance [41, 6, 9] and robot photography [25] to 3D reconstruction [54, 31], virtual cinematography [23] - even focusing on characters [23, 22] - and tracking dynamics objects [14]. The breadths of these approaches is a testament for the importance of automatically generating camera poses, which remains challenging as finding solutions commonly requires solving highly complex solution spaces. Finding optimal views can be accomplished by defining metrics for information measurement [5], heuristics and rules of photography [8], or data-driven aesthetics assessment [9, 49]."
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+                                    "content": "Deep aesthetic assessment: Methods for deep aesthetic assessment enable to categorize images based on aesthetic quality [35, 32]. To this end, Lu et al. [32] employ learned style attributes, while the approach of Kao et al. [24] relies on multi-task convolutional neural networks (CNN). Deng et al. [10] provide a survey of different techniques for aesthetic scoring and report that deep aesthetic assessment methods provide superior performance compared to handcrafted methods. Liu et al. [30] evaluate aesthetic quality based on graphs, where nodes represent local information of the different parts of an image. Finally, it has been recognized that defining uniform rules to assess aesthetics of motion is challenging [40]. Our method employs the deep aesthetics model developed by Wei et al. [49] because of its robustness and lightweight inference cost. They built a large photo pair dataset including more than 1M comparisons between different views from the same image that enables robust training for estimating aesthetic quality."
+                                }
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+                                    "content": "Aesthetic view finding: A number of methods address the problem of automatically generating aesthetics and finding views. View finding techniques can be categorized based on various metrics, such as information metrics [5, 44, 12, 41, 19, 42, 23] or aesthetic metrics [7, 8, 47, 53, 49]. Chang and Chen [7] present a method for finding views in a panoramic image, while Cheng et al. [8] and Wei et al. [49] aim to select cropped views in a larger input image to compute 2D image compositions. Aesthetics models are also used for view recommendation that can even be computed in real time [47]. Yeh et al. [53] incorporate both image and motion aesthetic attributes into their video aesthetic assessment and Ma et al. [33] developed an instant photo tool"
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+                                    "content": "based on the view proposal network of Wei et al. [49]. Hong et al. [18] introduce key composition maps to encode rules for composition-aware image cropping."
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+                                    "content": "For finding viewpoints in 3D space, Zhu et al. [55] trained a robot as a reinforcement learning agent to search a given target view in a room. Fang et al. [11] extended this framework to not only support reinforcement but also imitation learning. Gschwindt et al. [15] control drone movement with DRL and Bonatti et al. [4] define an aesthetic metric of short video clips based on crowd sourcing data. In AutoPhoto [1], the authors train a reinforcement learning agent for a ground robot mounted camera to find views according to the aesthetics model from [49]. In their work, however, the agent is only tasked to find aesthetic views in the vicinity of its initial location. Unlike these methods, GAIT generates a sequence of camera poses in a 3D synthetic scene and moves the camera in a 5D continuous space. The aesthetics of all frames are optimized globally, while satisfying the diversity and smoothness constraints."
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+                                    "content": "Reinforcement learning: Learning directly on image observations is commonly considered challenging for standard RL algorithms. In this setting, the underlying state information has to be extracted from the high-dimensional space of image observations. The RL loss does not provide sufficient signal for the implicit representation learning in addition to the regular policy learning [51], which often leads to sample inefficiency or learning stagnation. In Data Regularized Q (DrQ) [51], Yarats et al. employ regularization on task invariant image augmentation to facilitate the representation learning in RL [51]. Contrastive Unsupervised Representations for Reinforcement Learning (CURL) [27] further extends this augmentation strategy by also adopting contrastive learning on the augmented images."
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+                                    "content": "-greedy policy in DQN [34]. The actor and the critic models represent the agent's policy "
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+                                    "content": " and the state-action value function "
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+                                    "content": " respectively. In Deep Deterministic Policy Gradient (DDPG) [29], the actor and the critic are represented as neural networks. The critic is updated according to Q-learning [34], and the actor is updated using its action value from the critic and the chain rule, following DPG [45]. DDPG also integrates techniques including experience replay, target networks, and exploration noise, which make it one of the most widely adopted algorithms for the continuous action domain. Soft Actor Critic (SAC) differs from DDPG in that it has a policy entropy term in addition to the RL objective for a better exploration and multi-modal behavior. In this work, we employ two Visual DRL algorithms, DrQ-v2 [50] and CURL [27] that use DDPG [29] and SAC [16] as their base actor-critic RL algorithms."
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+                                    "content": "To generate aesthetic indoor tours, we introduce GAIT, a framework for training a DRL agent based on existing policy training approaches. Specifically, we show that a GAIT agent can be trained with DrQ-v2 [50], which is an efficient visual RL method that leverages task invariant image augmentation to help representation learning from pixels, as well as with CURL [27], which uses contrastive learning with on top of data augmentation. To predict camera pose trajectories, we unify both approaches into a single framework and extend by introducing diversity and smoothness regularization terms in the reward function. Furthermore, we evaluate aesthetics based on images instead of parametric models or heuristics."
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+                                    "content": "In the following sections we describe our framework. The formulation of our aesthetic camera RL framework is discussed in Section 3.1; the design of our reward function based on a neural aesthetics score, the out-of-bound penalty, and constrains for diversity and smoothness, is described in Section 3.2; and finally, in Section 3.3 we describe the two DRL algorithms we implement with our framework, DrQv2 and CURL. An overview of the agent in the multi-GPU setting is shown in Figure 2."
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+                                    "content": "3.1. Formulation"
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+                                    "content": "Markov Decision Process (MDP): We consider the standard Reinforcement learning (RL) setting, formulated by the Markov Decision Processes (MDP) [3]. In MDP, an agent interacts with the environment in discrete time steps. At step "
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+                                    "type": "text",
+                                    "content": " from the environment. This process repeats until a terminal state "
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+                                    "type": "text",
+                                    "content": " is reached."
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+                                    "type": "text",
+                                    "content": "Objective: We aim at generating view sequences with superior aesthetic quality, smoothness and controlled diversity. Given an arbitrary initial camera pose "
+                                },
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+                                    "type": "text",
+                                    "content": " in a 3D indoor scene, we move the camera for "
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+                                    "type": "inline_equation",
+                                    "content": "T = 15"
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+                                    "type": "text",
+                                    "content": " time steps consecutively to produce an aesthetic sequence of 16 images. Start at time step "
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+                                    "type": "text",
+                                    "content": ", our agent transforms the camera pose to optimize the expected return of the following steps"
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+                                    "content": "\\mathbb {E} [ R _ {1} ] = \\mathbb {E} [ \\sum_ {t = 1} ^ {\\tau} \\gamma^ {t - 1} r _ {t} ], \\tag {1}",
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+                                    "type": "text",
+                                    "content": ", the observation of the agent includes the time step "
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+                                    "type": "text",
+                                    "content": ", camera pose "
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+                                    "content": ", diversity regularization observations "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". The time step number "
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+                                    "type": "text",
+                                    "content": " is normalized to [0, 1]. A camera pose is represented as a 5D vector, i.e. the position "
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+                                            "content": "Figure 2: Overview of the GAIT framework in the multi-GPU setting: we describe the shared components for the two actor-critic algorithms, DrQ-v2 and CURL. In the Data loop, the actor interacts with the environment repeatedly and saves each transition in the Replay Buffer. The Update worker samples a batch of transitions from the Replay Buffer and updates the actor and the critic networks based on the RL loss functions of DrQ-v2 and CURL. The Data and Update workers communicate their steps through the shared Storage, to maintain a data-update step ratio of "
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+                                            "type": "text",
+                                            "content": ", as well as the updated weights of the actor network."
+                                        }
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+                                            "content": "Figure 3: Actor-critic network architecture: while the network architecture for our actor and critic networks are similar, they do not share layers except for the encoder."
+                                        }
+                                    ]
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": ". The angle of yaw "
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+                                    "type": "inline_equation",
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+                                    "content": " is limited in "
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+                                    "type": "inline_equation",
+                                    "content": "[- \\pi, \\pi]"
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+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " and the angle of pitch "
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+                                    "type": "text",
+                                    "content": " is limited in "
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+                                    "type": "inline_equation",
+                                    "content": "[- \\pi/2, \\pi/2]"
+                                },
+                                {
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+                                    "type": "text",
+                                    "content": ", both of them are also normalized to "
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+                                    "type": "inline_equation",
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ". A view image is rendered with the camera pose in a resolution of "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "84 \\times 84"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": " with 3 color channels. The evaluations of diversity and smoothness will be detailed in Section 3.2."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "Action: An action taken by our agent is also a 5D vector in the same space of camera pose. For each time step, the camera pose is transformed by adding the action vector,"
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "where "
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+                                    "type": "inline_equation",
+                                    "content": "\\oplus"
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+                                    "type": "text",
+                                    "content": " means the result of the addition is normalized to "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "."
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+                        }
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+                                    "type": "text",
+                                    "content": "Actor-critic RL: For our GAIT framework, we employ two state-of-the-art visual actor-critic DRL algorithms DrQ-v2 [50] and CURL [27]. For both, the actor network represents the policy "
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+                                    "content": ", while the critic network represents the state-action value function "
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+                                    "content": "Q(s_{t},a_{t})"
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+                                    "type": "text",
+                                    "content": ". The critic network is optimized to approximate the expected return given state-action pairs,"
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+                            ]
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+                                    "content": "Q ^ {\\pi} \\left(s _ {t}, a _ {t}\\right) = \\mathbb {E} _ {a _ {i > t} \\sim \\pi} \\left[ R _ {t} \\mid s _ {t}, a _ {t} \\right], \\tag {3}",
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+                                    "type": "text",
+                                    "content": "where the actions are selected by the actor network. The actor network is optimized on the expected return over all possible initial states in the environment:"
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+                                    "content": "\\pi^ {*} = \\underset {\\pi} {\\operatorname {a r g m a x}} \\mathbb {E} _ {a _ {i} \\sim \\pi} [ R _ {1} ]. \\tag {4}",
+                                    "image_path": "ab842b4da12b449e2b9b817b7fae04234b0e380eca3efa062da9471fe715bc2c.jpg"
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+                                    "content": "For DrQv2, we employ Q-learning to update the critic as described in DDPG [29]. We use the action value from the critic and the chain rule following DPG [45], to update the actor. For CURL, the actor and the critic update targets also include the entropy of policy as introduced in SAC [16]."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "3.2. Reward Function"
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+                                    "type": "text",
+                                    "content": "The reward function consists of several components: first, we introduce an out-of-boundary penalty to prevent the camera being placed outside the indoor scene. For each scene, we set an axis-aligned bounding-box as the domain of the camera position. The position within the domain is normalized as "
+                                },
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+                                    "type": "text",
+                                    "content": ". If the camera is placed out-of-boundary, the reward is a negative constant "
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+                                    "content": "r^{\\mathcal{B}}"
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+                                    "type": "interline_equation",
+                                    "content": "r _ {t} = \\left\\{ \\begin{array}{l l} r _ {t} ^ {\\mathcal {A}} r _ {t} ^ {\\mathcal {S}} r _ {t} ^ {\\mathcal {D}}, & \\text {i f i n s i d e b o u n d a r y}, \\\\ r ^ {\\mathcal {B}}, & \\text {o t h e r w i s e}. \\end{array} \\right. \\tag {5}",
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+                                    "content": " is set to be "
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+                                    "type": "text",
+                                    "content": " for all experiments in this paper. When the camera is placed inside the boundary, the reward is the product of the evaluations of view aesthetics "
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+                                {
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+                                    "type": "text",
+                                    "content": ", temporal smoothness "
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " and diversity regularization "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": "."
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+                                    "type": "text",
+                                    "content": "View Aesthetics: We employ the neural aesthetic model [49] to evaluate the aesthetics of a view. The model performs generic aesthetics assessment based on crowd sourcing data, which also works well 3D indoor scenes. Instead of using the view image "
+                                },
+                                {
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+                                    "content": "x_{t}^{I}"
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+                                    "type": "text",
+                                    "content": " in the observation with the resolution of "
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+                                    "type": "inline_equation",
+                                    "content": "84 \\times 84"
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+                                    "type": "text",
+                                    "content": ", we render an image with higher resolution of "
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+                                    "type": "inline_equation",
+                                    "content": "240 \\times 240"
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+                                    "type": "text",
+                                    "content": " to evaluate the aesthetics "
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+                                    "type": "inline_equation",
+                                    "content": "r_{t}^{\\mathcal{A}}"
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+                                    "type": "text",
+                                    "content": " – the higher resolution is required by the neural aesthetic model."
+                                }
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+                                    "type": "text",
+                                    "content": "Temporal Smoothness: Obtaining aesthetics assessment for temporal sequences of frames is an open research"
+                                }
+                            ]
+                        }
+                    ],
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+            ],
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+                                    "type": "text",
+                                    "content": "problem. Therefore, we rely on an aesthetic model [49] for single frames to assess aesthetics. However, if we would only use single frames instead of an entire sequence to quantify the aesthetics, the agent would diverge, which would then lead to degenerated results. Therefore, we introduce the temporal smoothness term "
+                                },
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+                                    "type": "text",
+                                    "content": " in the reward function (Equation 5) to penalize the agent when it takes an action which is too different from the its preceding time steps."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 0
+                },
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+                                    "type": "text",
+                                    "content": "Adding the smoothness term generates smoother camera trajectories and it forces the camera poses of a sequence to be moderately different from each other. Consequently, the GAIT agent will generate a sequence of aesthetic views instead of converging to a single view with high aesthetic value. On the contrary, without the smoothness term, our agent tends to take abrupt actions and also stays at the same aesthetic view until an episode terminates (Section 4.5)."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 1
+                },
+                {
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "As mentioned in Section 3.1, the 5D vector of action is composed of two parts, including a 3D translation and 2D rotation "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "a_{t} = \\{\\tilde{a}_{t},\\hat{a}_{t}\\}"
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+                                    "type": "text",
+                                    "content": ". The temporal smoothness term compares the current action "
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+                                    "type": "text",
+                                    "content": " with the actions at the last three time steps "
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+                                    "content": "\\{a_{t - 3},a_{t - 2},a_{t - 1}\\}"
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+                                    "content": "r _ {t} ^ {\\mathcal {S}} = \\frac {1}{2} \\left(\\min  _ {i = 1} ^ {3} r _ {t, i} ^ {\\mathcal {S}} + \\frac {1}{3} \\sum_ {i = 1} ^ {3} r _ {t, i} ^ {\\mathcal {S}}\\right), r _ {t, i} ^ {\\mathcal {S}} = \\tilde {r} ^ {\\mathcal {S}} _ {t, i} + \\hat {r} ^ {\\mathcal {S}} _ {t, i}, \\tag {6}",
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+                            "spans": [
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "where "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r_{t,i}^{S}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is evaluated with "
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "text",
+                                    "content": " and the action taken "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
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+                                    ],
+                                    "type": "text",
+                                    "content": " time steps earlier "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{t - i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
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+                                    ],
+                                    "type": "text",
+                                    "content": ". It consists of two parts, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{r^S}_{t,i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " and "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{r^S}_{t,i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ", for translation and rotation respectively. "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{r^S}_{t,i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " is a 1D Gaussian function with the amplitude of 1, the mean of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\tilde{a}_{t - i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " and the standard deviation of "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\max \\left(\\frac{1}{2} |\\tilde{a}_{t - i}|,0.1\\right)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ". "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\hat{r^S}_{t,i}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " is evaluated similarly except the standard deviation is "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\max \\left(|\\hat{a}_{t - i}|,0.1\\right)"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ". Therefore, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "S_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " will penalize the agent when "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": " is close to zero or "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "a_{t}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
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+                                    ],
+                                    "type": "text",
+                                    "content": " is very different from "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{a_{t - i}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ". Translation is more penalized than rotation. The Smoothness observation contains the recent actions "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{t}^{S} = \\{a_{t - i}\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ", while the Critic additionally observes the distance between its current action and recent actions "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\| a_t - a_{t - i}\\|^2\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ", where "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "i = 1,2,3"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        388,
+                                        286,
+                                        574
+                                    ],
+                                    "type": "text",
+                                    "content": ". See Supplementary Material for a visualization of the Gaussian smoothness function for Temporal Smoothness."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 4
+                },
+                {
+                    "bbox": [
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+                        685
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Diversity Regularization: Without Diversity Regularization, GAIT generates sequences in a robust manner - varying initial camera poses lead to trajectories toward the globally most aesthetic target pose. While this may be wanted in many situations, GAIT also allows for generating diverse aesthetic trajectories. We enable this by specifying a diversity regularization term "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
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+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "r_t^{\\mathcal{D}}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        576,
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+                                        685
+                                    ],
+                                    "type": "text",
+                                    "content": " in the reward function (Equation 5). Specifically, we define up to 4 camera poses and the corresponding distances, "
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        576,
+                                        286,
+                                        685
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\bar{x}_j^P,d_j\\}_{0\\leq j < 4}"
+                                },
+                                {
+                                    "bbox": [
+                                        46,
+                                        576,
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+                                    ],
+                                    "type": "text",
+                                    "content": " that"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
+                    "bbox": [
+                        306,
+                        72,
+                        545,
+                        121
+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                            ],
+                            "spans": [
+                                {
+                                    "bbox": [
+                                        306,
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+                                    ],
+                                    "type": "text",
+                                    "content": "we refer to as exclusion poses. The diversity regularization term penalizes the agent if the distance between its pose and any exclusion poses "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
+                                        545,
+                                        121
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\bar{x}_j^P"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
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+                                        121
+                                    ],
+                                    "type": "text",
+                                    "content": " is less than the corresponding distance "
+                                },
+                                {
+                                    "bbox": [
+                                        306,
+                                        72,
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+                                        121
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "d_j"
+                                },
+                                {
+                                    "bbox": [
+                                        306,
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+                                    ],
+                                    "type": "text",
+                                    "content": ","
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "interline_equation",
+                    "angle": 0,
+                    "lines": [
+                        {
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+                                    ],
+                                    "type": "interline_equation",
+                                    "content": "r _ {t} ^ {\\mathcal {D}} = \\min  _ {j = 0} ^ {4} \\left(\\min  \\left(\\frac {\\left\\| x _ {t} ^ {P} - \\bar {x} _ {j} ^ {P} \\right\\| ^ {2}}{d _ {j}}, 1\\right)\\right). \\tag {7}",
+                                    "image_path": "d653e5ed0d84a43448d7b471cf3992a0a7af9da7f508d02136279a6cf66eac03.jpg"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
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+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "The Diversity observation includes the exclusion poses and agent's current distances to the exclusion poses, "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        171,
+                                        545,
+                                        209
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "x_{t}^{D} = \\{\\bar{x}_{j}^{P},d_{j},\\left\\| x_{t}^{P} - \\bar{x}_{j}^{P}\\right\\|^{2}\\}_{0\\leq j < 4}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 8
+                },
+                {
+                    "bbox": [
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+                        209,
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                    "type": "text",
+                                    "content": "To train the GAIT agent with exclusion poses, the naive strategy is to to randomly sample them in the 5D space. However, as most random camera poses in the scene only have low aesthetics scores (e.g. the camera is placed inside an object or the view may be occluded), selecting exclusion poses randomly would actually lead to inefficient training. Therefore, we follow another strategy: for each episode, we set the exclusion poses to be the ending camera poses of the last 4 episodes with a random excluding distance in [0.3, 1.3]. Because our GAIT agent tends to end at camera poses with high aesthetics scores to maximize the reward, selecting the end poses as the exclusion poses converges faster compared to selecting the exclusion poses randomly."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 9
+                },
+                {
+                    "bbox": [
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+                    ],
+                    "type": "text",
+                    "angle": 0,
+                    "lines": [
+                        {
+                            "bbox": [
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+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": "Once trained, a user can define the exclusion camera poses "
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        365,
+                                        545,
+                                        483
+                                    ],
+                                    "type": "inline_equation",
+                                    "content": "\\{\\bar{x}_j^P,d_j\\}"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
+                                        365,
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+                                    ],
+                                    "type": "text",
+                                    "content": " at runtime, which then produces trajectories of camera poses that avoid the provided exclusion poses. This way, our agent can produce sets of diverse, yet aesthetically meaningful, trajectories with diversity regularization, while without diversity regularization it is possible to generate aesthetic trajectories from various different initial conditions that all converge to the same globally most aesthetic camera pose. Diversity Regularization can be disabled by defining out-of-boundary excluding poses."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 10
+                },
+                {
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+                    "type": "title",
+                    "angle": 0,
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+                                    "type": "text",
+                                    "content": "3.3. Visual Deep Reinforcement Learning"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 11
+                },
+                {
+                    "bbox": [
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+                                    "type": "text",
+                                    "content": "Sample inefficiency or learning stagnation are known to occur in the Visual DRL setting. This is because the supervision from the RL loss is not sufficient to support both policy learning and representation learning [51]. For the Aesthetic Tour problem, learning the complex representation of 3D scene appearance and aesthetics calls for a Visual DRL algorithm. Model-free Visual RL algorithms addresses the representation learning challenge mainly in three ways: image augmentation as task-invariant perturbation, image augmentation for contrastive learning, or self-supervised learning [28]. We adopt DrQ-v2 and CURL in GAIT, which belongs to the first and the second category respectively."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 12
+                },
+                {
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+                                    "type": "text",
+                                    "content": "The DrQ-v2 image augmentation strategy includes randomly shifting the original observation image "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "x_{t}^{I}"
+                                },
+                                {
+                                    "bbox": [
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+                                    ],
+                                    "type": "text",
+                                    "content": " by 4 pixels as well as bilinearly interpolating the shifted image [50]. Both operations act as a task-invariant perturbation to regularize the "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "Q"
+                                },
+                                {
+                                    "bbox": [
+                                        305,
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+                                    ],
+                                    "type": "text",
+                                    "content": " function, which is first introduced in DrQ [51]."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 13
+                }
+            ],
+            "discarded_blocks": [
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+                                    "type": "text",
+                                    "content": "<sup>1</sup>The temporal smoothness term makes the reward function non-Markovian, since it considers prior time steps."
+                                }
+                            ]
+                        }
+                    ],
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+                                            "content": "Figure 4: Camera trajectories generated with three different initial camera poses. Left: selected view images including the initial and ending camera poses. Right: visualization of the trajectories whose initial camera poses are located at large dots. All sequences start showing aesthetically pleasing views since time step 3 and ending with similar views."
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+                                    "content": "CURL relies on the random crop augmentation for contrastive learning, cropping from original image of resolution "
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+                                    "type": "text",
+                                    "content": " with resolution "
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+                                    "content": ". The anchor and the positive images are generated from two different random crops of the same image while the negatives are obtained by cropping other images [27]. Anchors, postives, and negatives are then used to compute the additional InfoNCE loss [38] to train the encoder."
+                                }
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+                                    "content": "Other than representation learning, DrQ-v2 and CURL share common components. Both methods are actor-critic, use a replay buffer for off-policy learning, rely on the network architecture introduced in SAC-AE [52], and use clipped double "
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+                                    "content": " learning introduced in TD3 [13]. We modify the shared network architecture by adding inputs as detailed in Section 3.1. DrQ-v2 additionally integrates a linear exploration noise decay schedule, n-step TD, introduced in D4PG [2], and fast implementations of the replay buffer and the image augmentation module. We further enables higher training throughput for CURL by adopting DrQ-v2's fast replay buffer and image augmentation."
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+                                    "content": "3.4. Implementation Details"
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+                                    "content": "We conducted the training and testing experiments in the Habitat-Sim simulation framework [43, 48] that provides support for rendering and the realistic indoor dataset Replica [46]. We use the Adam [26] adaptive gradient descent as our network optimizer. The discount factor "
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+                                    "content": " is set to 0.99. It is very close to 1 as our objective is the aesthetics of the whole sequence instead of the last view."
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+                                    "content": "Our multiple-GPU implementation boosts the training performance significantly. As shown in Figure 2, on a 8-GPU compute node, we run 7 Data Workers and 1 Update Worker, with each worker running on one GPU. 8-GPU implementation brings us much more speedup compared with 1-GPU, as shown in Figure 8."
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+                                    "content": "Our view sequences can contribute to the indoor tour video generation. To generate tour videos for evaluation, 9 intermediate camera poses are interpolated based on the spherical interpolation between the adjacent two frames in each view sequence, producing a 5-second video clip in 30 FPS play mode from the original 16-frame sequence. We refer to the supplementary material for additional implementation details."
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+                                    "content": "We have conducted an extensive set of quantitative and qualitative experiments to validate GAIT. In Section 4.1, we show that GAIT stably converges to the same global-near-optimal ending pose from different initial poses. In Section 4.3, we compare results of GAIT trained with or without Temporal Smoothness. In Section 4.2, we compare results of GAIT training with or without Diversity Regularization. In Section 4.4, we compare GAIT implementations, GAIT-DrQ-v2 and GAIT-CURL, with baseline algorithms, CMA-ES and MPC. In Section 4.5, we identify important components of DrQ-v2 and CURL that significantly contribute to convergence rate. The experiments in this section are conducted with three scenes, Room, Apartment and Office. Figures 1, 4, 5, 6 are rendered in Room. More comprehensive experimental results are in the supplementary material."
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+                                    "content": "A camera sequence of 16 frames is generated with an arbitrary initial camera pose. Because the initial camera pose is set randomly, its view image is usually with a low aesthetics score. GAIT agent transforms the camera pose effectively that the view aesthetics has been substantially improved at the time step 2 or 3, and the rest frames are all with good aesthetics. The statistics of aesthetic scores in"
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+                                            "content": "Figure 5: The comparisons of training with and without the regularization. The reward is lower with diversity regularization and temporal smoothness regularization because the corresponding terms of "
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+                                            "content": " is introduced into the reward function in Equation 5. But they converge with similar time steps. This is tested with the scene of Room with one random seed. Results with 3 seeds can be found in the supplementary material."
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+                                    "content": "Room, Apartment, and Office are shown in Table 1."
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+                                    "content": "GAIT is robust in that the camera trajectory generation is not sensitive to the initial camera pose, as shown in Figure 4. Similar initial camera poses introduce similar trajectories. The global optimal views are always explored even with very different initial camera poses. The ending camera poses are similar if diversity regularization is not applied."
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+                                    "content": "Although GAIT is robust to explore global optimal views, users would like to have more control of the generation for different trajectories. The diversity regularization module helps explore the areas with sub-optimal but still plausible aesthetics scores. As shown in Figure 6, the camera poses are effectively moved out of the exclusion regions. The training with diversity regularization is stable and converges with similar time steps, as shown in Figure 5. Although the reward is slightly declined as expected, the quality of sequences are still plausible with the camera exploring nice views outside the exclusions."
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+                                    "content": "4.3. Temporal Smoothness Regularization"
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+                                    "content": "Temporal smoothness regularization is critical to produce aesthetic camera sequence because the neural aesthetics model [49] is for individual images. Without the temporal smoothness regularization, the accumulated aesthetics of all images is still good but the camera trajectory is trivial, such as the sequence 1 shown in Figure 7, where the camera transforms little after the time step 6. The temporal smoothness regularization reduces the reward of training, as shown in Figure 5, which prevents being stuck in optimal poses."
+                                }
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+                                            "type": "text",
+                                            "content": "Table 1: The statistics of aesthetic scores in Room, Apartment, and Office."
+                                        }
+                                    ]
+                                }
+                            ],
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+                                            "html": "<table><tr><td colspan=\"2\"></td><td>time (hours) ↓</td><td>training steps</td><td>throughput (FPS) ↑</td></tr><tr><td rowspan=\"2\">GAIT-DrQ-v2</td><td>1 GPU</td><td>16.33</td><td>1.5M</td><td>25.52</td></tr><tr><td>8 GPUs</td><td>3.38</td><td>3M</td><td>246</td></tr><tr><td rowspan=\"2\">GAIT-CURL</td><td>1 GPU</td><td>36.27</td><td>1.5M</td><td>11.49</td></tr><tr><td>8 GPUs</td><td>23.03</td><td>1.5M</td><td>17.63</td></tr></table>",
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+                                            "type": "text",
+                                            "content": "Table 2: The statistics of training. Note that GAIT-CURL only need "
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+                                            "content": "1.5\\mathrm{M}"
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+                                            "type": "text",
+                                            "content": " steps to converge on 8-GPU."
+                                        }
+                                    ]
+                                }
+                            ],
+                            "index": 14,
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+                                            "html": "<table><tr><td>scene</td><td>Room</td><td>Apartment</td><td>Office</td></tr><tr><td>GAIT-DrQ-v2</td><td>38.34</td><td>20.10</td><td>42.10</td></tr><tr><td>GAIT-CURL</td><td>33.95</td><td>32.40</td><td>32.67</td></tr><tr><td>CMA-ES</td><td>32.06</td><td>32.29</td><td>31.78</td></tr><tr><td>MPC</td><td>6.32</td><td>/</td><td>/</td></tr></table>",
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+                                    "type": "text",
+                                    "content": "Table 3: The comparison of the averaged reward over 9 sequences. The 9 sequences start with 3 different initial positions and generated with 0, 1 and 2 exclusion regions."
+                                }
+                            ]
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+                                    "content": "4.4. Comparisons"
+                                }
+                            ]
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+                },
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+                                    "type": "text",
+                                    "content": "We use Evaluation Episode Reward over the training process to compare the performance of DrQ-v2 [50], CURL [27], CMA-ES [17] and MPC [37]. It is defined as the average sum of rewards per episode under the Evaluation mode. For every 300 training episodes, a Evaluation of 10 episodes are run with random initial poses "
+                                },
+                                {
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+                                    "type": "inline_equation",
+                                    "content": "x_0^P"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", random excluding distances "
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "inline_equation",
+                                    "content": "d_j"
+                                },
+                                {
+                                    "bbox": [
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+                                    "type": "text",
+                                    "content": ", and ending poses of up to 4 previous Evaluation episodes as excluding poses. During Evaluation, the GAIT agent acts deterministically, i.e. the exploration noises used for training are turned off. The training processes shown in Figure 8 illustrate similar pattern across different scenes. GAIT-DrQ-v2 and GAIT-CURL take similar time steps to converge, but the latter is 2-8 times slower depending on the number of GPUs. Our implementation of CMA-ES and MPC are detailed in the supplementary material."
+                                }
+                            ]
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+                                    "type": "text",
+                                    "content": "We compare the average reward of 9 camera sequences in Table 3 with one seed. Results with 3 seeds can be found in the supplementary material. GAIT-DrQ-v2 and GAIT-CURL performs generally better than CMA-ES, except the reward with CMA-ES is better than GAIT-DrQ-v2 in the scene of Apartment. Still, both GAIT-DrQ-v2 and GAIT-CURL are better in the user study, which is shown in Section 4.6 and supplementary material. MPC performs significantly worse than others, though only tested in Room. The view sequences are generated instantly with GAIT-DrQ-v2 and GAIT-CURL. Both CMA-ES and MPC take more than 1 hour to generate a sequence, which is not scalable nor applicable to interactive scenarios."
+                                }
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+                                    "content": "4.5. Ablation Study"
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+                                    "content": "GAIT can be trained with DrQ-v2 [50] or CURL [27]. DrQ-v2 is improved upon DDPG [29], the linear decayed exploration noise and image augmentation are critical for the learning. As shown in Figure 9 (a), the episode reward will be significantly lower in training without image augmentation or linear decayed exploration noise. CURL is"
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+                                            "content": "(a) GAIT-DrQ-v2"
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+                                            "content": "Figure 9: The ablation experiments of the training algorithms. The image augmentation is critical for both GAIT-DrQ-v2 and GAIT-CURL. The linear decayed exploration noise significantly helps the training with GAIT-DrQ-v2. This is tested with the scene of Room."
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+                                    "content": "based on SAC [16] and use image augmentation for contrastive learning. As shown in Figure 9 (b), GAIT-CURL can hardly converge without image augmentation."
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+                                    "content": "4.6. User Study"
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+                                    "content": "To further evaluate the aesthetics in the generated tours, we conduct a user study. We recruited 10 participants (2 females and 8 males, with the age range of 25-35) to rate the video smoothness, video aesthetics, and subjective general preference, of the tours generated using three methods (i.e., CMA-ES, GAIT-DrQ-v2 and GAIT-CURL). Specifically, we prepared the video clips in three indoor scenes using the video generation described in Section 3.4."
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+                                    "type": "text",
+                                    "content": "We asked for participants' feedback via 2-alternative forced choice. For each initial pose with the same exclusion level, every participant watch two video pairs, "
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+                                    "type": "text",
+                                    "content": ". In each pair, participants chose the preferred video clip based on (1) video smoothness and (2) video content aesthetics. After comparing the video clips rooted from the same initial pose, participants are also asked to rate \"which method provides higher video content diversity\" and \"which method is the overall preferred aesthetic video generation method\"."
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+                                    "content": ". We have learned from the users' feedback that majority participants favor the video clips generated in "
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+                                    "type": "text",
+                                    "content": " generate the view sequences with different capabilities. "
+                                },
+                                {
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+                                    "type": "inline_equation",
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+                                {
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+                                    "type": "text",
+                                    "content": " is better at video aesthetics while "
+                                },
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+                                    "type": "inline_equation",
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+                                    "type": "text",
+                                    "content": " performs better in video smoothness. Please refer to our supplementary materials for the collected data and the comprehensive data analysis."
+                                }
+                            ]
+                        }
+                    ],
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+                                    "type": "text",
+                                    "content": "5. Conclusions"
+                                }
+                            ]
+                        }
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+                    "index": 1
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+                                    "type": "text",
+                                    "content": "We propose GAIT, a novel DRL agent to generate aesthetically meaningful sequences of camera poses in 3D indoor scenes. Starting with an arbitrary initial camera pose without any pre-determined targets, a view sequence is transformed sequentially by the GAIT agent according to the neural aesthetics model. While the diversity regularization term is user-controlled to generate diverse, yet aesthetically meaningful trajectories, temporal smoothness regularization is introduced to avoid discontinuities camera poses for more visually pleasing trajectories. Our framework enables training GAIT agents with existing RL methods, including DrQ-v2 and CURL. We evaluate our method extensively. The conducted user study indicates GAIT is robust for high quality view sequences and it is easy to control for diverse outputs."
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+                                    "content": "Discussion: Manually defining trajectories of camera poses in 3D spaces is a challenging task, that even takes professional users a couple of hours. In 2D motion graphics, which is a similar domain, the authoring of a video requires a designer 3-4 hours of manual work [21, 20]. GAIT training requires 3.38 hours of computing time for a single scene. However, once trained GAIT can generate multiple tours for the same scene, while an artist has to manually define every single trajectory. As GAIT only makes minimal assumptions about the environment, it can also be used to generate aesthetically valuable view sequences for real-world scenes that are represented as radiance fields. This can be achieved by using the view synthesis function of a NeRF-based approach to replace the rendering of a 3D scene simulator. This allows users to avoid the tedious manual selection of viewpoints for these scenes."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 3
+                },
+                {
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+                                    "content": "Limitations and Future Work: GAIT-DrQ-v2 and GAIT-CURL can generalize to arbitrary initial and excluding poses within the trained scene, but they generalize poorly to unseen, new scenes. Making GAIT agents generalize across scenes is our key objective for future work, as this would make GAIT a more generic framework for view sequence generation. However, this would require a substantial increase in compute resources, the availability of a"
+                                }
+                            ]
+                        }
+                    ],
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+                },
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+                                    "type": "text",
+                                    "content": "larger scene dataset, and a scalable DRL algorithm, which are outside the scope of this work."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 5
+                },
+                {
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+                                    "type": "text",
+                                    "content": "While our method is able to reliably generate aesthetic camera tours for indoor scenes, it also has a few limitations that are interesting avenues for future research. First, we only tested our GAIT agent for indoor scenes and it is not clear whether it would work similarly well for outdoor scenes. Second, the scenes we used for our experiments where only single room layouts and it is not clear whether GAIT could also generate trajectories for more complex room layouts or whether it could take care of transitioning from one level of a building to another. Third, we did not test GAIT on scenes with dynamically moving objects. To this end it would be interesting to train and test a GAIT agent to generate aesthetically valuable tours under consideration of different types of scene dynamics. Finally, the neural aesthetics estimator only considers the per-frame aesthetics, while the inter-frame smoothness term is heuristic. A neural temporal aesthetics model is needed for this task. However, to the best of our knowledge, such a model is unavailable. Therefore, our goal is to work on a neural temporal aesthetics model in the future."
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 6
+                },
+                {
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+                                    "type": "text",
+                                    "content": "Acknowledgements"
+                                }
+                            ]
+                        }
+                    ],
+                    "index": 7
+                },
+                {
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+                                    "content": "This project was supported in part by NSF grants OAC1919752, ICER1940302, and IIS2107224, and by IBM, SUNY and Adobe."
+                                }
+                            ]
+                        }
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+                                    "type": "text",
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